Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(64,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.z (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 484.2 | ||
Character | \(\chi\) | \(=\) | 525.484 |
Dual form | 525.2.z.b.64.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36398 | + | 1.87736i | −0.964481 | + | 1.32749i | −0.0196950 | + | 0.999806i | \(0.506270\pi\) |
−0.944786 | + | 0.327688i | \(0.893730\pi\) | |||||||
\(3\) | −0.951057 | + | 0.309017i | −0.549093 | + | 0.178411i | ||||
\(4\) | −1.04600 | − | 3.21926i | −0.523000 | − | 1.60963i | ||||
\(5\) | −1.94902 | − | 1.09605i | −0.871628 | − | 0.490168i | ||||
\(6\) | 0.717088 | − | 2.20697i | 0.292750 | − | 0.900991i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 3.05649 | + | 0.993115i | 1.08063 | + | 0.351119i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 4.71611 | − | 2.16402i | 1.49136 | − | 0.684323i | ||||
\(11\) | −4.18719 | − | 3.04217i | −1.26249 | − | 0.917250i | −0.263609 | − | 0.964630i | \(-0.584913\pi\) |
−0.998877 | + | 0.0473799i | \(0.984913\pi\) | |||||||
\(12\) | 1.98961 | + | 2.73846i | 0.574351 | + | 0.790527i | ||||
\(13\) | 2.62561 | + | 3.61385i | 0.728215 | + | 1.00230i | 0.999211 | + | 0.0397209i | \(0.0126469\pi\) |
−0.270996 | + | 0.962580i | \(0.587353\pi\) | |||||||
\(14\) | 1.87736 | + | 1.36398i | 0.501746 | + | 0.364540i | ||||
\(15\) | 2.19233 | + | 0.440125i | 0.566056 | + | 0.113640i | ||||
\(16\) | −0.556510 | + | 0.404328i | −0.139127 | + | 0.101082i | ||||
\(17\) | 2.52913 | + | 0.821764i | 0.613404 | + | 0.199307i | 0.599209 | − | 0.800592i | \(-0.295482\pi\) |
0.0141942 | + | 0.999899i | \(0.495482\pi\) | |||||||
\(18\) | 2.32054i | 0.546958i | ||||||||
\(19\) | −0.867165 | + | 2.66886i | −0.198941 | + | 0.612278i | 0.800967 | + | 0.598709i | \(0.204319\pi\) |
−0.999908 | + | 0.0135692i | \(0.995681\pi\) | |||||||
\(20\) | −1.48979 | + | 7.42086i | −0.333127 | + | 1.65936i | ||||
\(21\) | 0.309017 | + | 0.951057i | 0.0674330 | + | 0.207538i | ||||
\(22\) | 11.4225 | − | 3.71140i | 2.43529 | − | 0.791273i | ||||
\(23\) | −0.553499 | + | 0.761825i | −0.115412 | + | 0.158852i | −0.862815 | − | 0.505520i | \(-0.831301\pi\) |
0.747402 | + | 0.664372i | \(0.231301\pi\) | |||||||
\(24\) | −3.21379 | −0.656012 | ||||||||
\(25\) | 2.59735 | + | 4.27244i | 0.519471 | + | 0.854488i | ||||
\(26\) | −10.3658 | −2.03290 | ||||||||
\(27\) | −0.587785 | + | 0.809017i | −0.113119 | + | 0.155695i | ||||
\(28\) | −3.21926 | + | 1.04600i | −0.608383 | + | 0.197675i | ||||
\(29\) | 1.57767 | + | 4.85556i | 0.292966 | + | 0.901655i | 0.983897 | + | 0.178735i | \(0.0572005\pi\) |
−0.690932 | + | 0.722920i | \(0.742799\pi\) | |||||||
\(30\) | −3.81656 | + | 3.51546i | −0.696806 | + | 0.641833i | ||||
\(31\) | 1.74288 | − | 5.36403i | 0.313030 | − | 0.963408i | −0.663528 | − | 0.748152i | \(-0.730941\pi\) |
0.976558 | − | 0.215256i | \(-0.0690585\pi\) | |||||||
\(32\) | 4.83131i | 0.854063i | ||||||||
\(33\) | 4.92234 | + | 1.59937i | 0.856869 | + | 0.278414i | ||||
\(34\) | −4.99243 | + | 3.62721i | −0.856195 | + | 0.622062i | ||||
\(35\) | −1.09605 | + | 1.94902i | −0.185266 | + | 0.329444i | ||||
\(36\) | −2.73846 | − | 1.98961i | −0.456411 | − | 0.331602i | ||||
\(37\) | 4.39962 | + | 6.05555i | 0.723293 | + | 0.995527i | 0.999408 | + | 0.0344023i | \(0.0109528\pi\) |
−0.276116 | + | 0.961124i | \(0.589047\pi\) | |||||||
\(38\) | −3.82761 | − | 5.26825i | −0.620921 | − | 0.854624i | ||||
\(39\) | −3.61385 | − | 2.62561i | −0.578679 | − | 0.420435i | ||||
\(40\) | −4.86866 | − | 5.28567i | −0.769803 | − | 0.835738i | ||||
\(41\) | −1.27791 | + | 0.928456i | −0.199576 | + | 0.145000i | −0.683085 | − | 0.730339i | \(-0.739362\pi\) |
0.483509 | + | 0.875339i | \(0.339362\pi\) | |||||||
\(42\) | −2.20697 | − | 0.717088i | −0.340543 | − | 0.110649i | ||||
\(43\) | 0 | 0.000338608i | 0 | 5.16372e-5i | 1.00000 | 2.58186e-5i | \(8.21831e-6\pi\) | |||
−1.00000 | 2.58186e-5i | \(0.999992\pi\) | ||||||||
\(44\) | −5.41374 | + | 16.6618i | −0.816151 | + | 2.51186i | ||||
\(45\) | −2.22103 | + | 0.258882i | −0.331092 | + | 0.0385919i | ||||
\(46\) | −0.675259 | − | 2.07823i | −0.0995615 | − | 0.306419i | ||||
\(47\) | 8.04788 | − | 2.61492i | 1.17390 | − | 0.381425i | 0.343806 | − | 0.939041i | \(-0.388284\pi\) |
0.830099 | + | 0.557616i | \(0.188284\pi\) | |||||||
\(48\) | 0.404328 | − | 0.556510i | 0.0583597 | − | 0.0803253i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −11.5637 | − | 0.951368i | −1.63535 | − | 0.134544i | ||||
\(51\) | −2.65928 | −0.372374 | ||||||||
\(52\) | 8.88752 | − | 12.2326i | 1.23248 | − | 1.69636i | ||||
\(53\) | −5.52958 | + | 1.79667i | −0.759546 | + | 0.246791i | −0.663084 | − | 0.748545i | \(-0.730753\pi\) |
−0.0964621 | + | 0.995337i | \(0.530753\pi\) | |||||||
\(54\) | −0.717088 | − | 2.20697i | −0.0975833 | − | 0.300330i | ||||
\(55\) | 4.82655 | + | 10.5186i | 0.650811 | + | 1.41833i | ||||
\(56\) | 0.993115 | − | 3.05649i | 0.132711 | − | 0.408441i | ||||
\(57\) | − | 2.80620i | − | 0.371691i | ||||||
\(58\) | −11.2676 | − | 3.66105i | −1.47950 | − | 0.480719i | ||||
\(59\) | 9.94650 | − | 7.22656i | 1.29492 | − | 0.940817i | 0.295032 | − | 0.955487i | \(-0.404670\pi\) |
0.999892 | + | 0.0146702i | \(0.00466982\pi\) | |||||||
\(60\) | −0.876298 | − | 7.51803i | −0.113130 | − | 0.970574i | ||||
\(61\) | −7.69704 | − | 5.59223i | −0.985505 | − | 0.716012i | −0.0265731 | − | 0.999647i | \(-0.508459\pi\) |
−0.958932 | + | 0.283635i | \(0.908459\pi\) | |||||||
\(62\) | 7.69296 | + | 10.5884i | 0.977006 | + | 1.34473i | ||||
\(63\) | −0.587785 | − | 0.809017i | −0.0740540 | − | 0.101927i | ||||
\(64\) | −10.1831 | − | 7.39848i | −1.27289 | − | 0.924810i | ||||
\(65\) | −1.15642 | − | 9.92126i | −0.143436 | − | 1.23058i | ||||
\(66\) | −9.71657 | + | 7.05950i | −1.19603 | + | 0.868964i | ||||
\(67\) | −1.64256 | − | 0.533701i | −0.200671 | − | 0.0652019i | 0.206957 | − | 0.978350i | \(-0.433644\pi\) |
−0.407628 | + | 0.913148i | \(0.633644\pi\) | |||||||
\(68\) | − | 9.00148i | − | 1.09159i | ||||||
\(69\) | 0.290991 | − | 0.895580i | 0.0350313 | − | 0.107815i | ||||
\(70\) | −2.16402 | − | 4.71611i | −0.258650 | − | 0.563683i | ||||
\(71\) | 4.05432 | + | 12.4779i | 0.481160 | + | 1.48086i | 0.837467 | + | 0.546488i | \(0.184036\pi\) |
−0.356307 | + | 0.934369i | \(0.615964\pi\) | |||||||
\(72\) | 3.05649 | − | 0.993115i | 0.360211 | − | 0.117040i | ||||
\(73\) | −1.76480 | + | 2.42904i | −0.206554 | + | 0.284298i | −0.899708 | − | 0.436492i | \(-0.856221\pi\) |
0.693154 | + | 0.720790i | \(0.256221\pi\) | |||||||
\(74\) | −17.3695 | −2.01916 | ||||||||
\(75\) | −3.79049 | − | 3.26071i | −0.437688 | − | 0.376514i | ||||
\(76\) | 9.49880 | 1.08959 | ||||||||
\(77\) | −3.04217 | + | 4.18719i | −0.346688 | + | 0.477175i | ||||
\(78\) | 9.85845 | − | 3.20320i | 1.11625 | − | 0.362691i | ||||
\(79\) | 1.83100 | + | 5.63523i | 0.206003 | + | 0.634013i | 0.999671 | + | 0.0256611i | \(0.00816908\pi\) |
−0.793667 | + | 0.608352i | \(0.791831\pi\) | |||||||
\(80\) | 1.52781 | − | 0.178081i | 0.170815 | − | 0.0199101i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | − | 3.66549i | − | 0.404786i | ||||||
\(83\) | 8.07227 | + | 2.62284i | 0.886047 | + | 0.287894i | 0.716466 | − | 0.697622i | \(-0.245759\pi\) |
0.169581 | + | 0.985516i | \(0.445759\pi\) | |||||||
\(84\) | 2.73846 | − | 1.98961i | 0.298791 | − | 0.217084i | ||||
\(85\) | −4.02863 | − | 4.37368i | −0.436966 | − | 0.474392i | ||||
\(86\) | −0.000635689 | 0 | 0.000461855i | −6.85481e−5 | 0 | 4.98031e-5i | ||||
\(87\) | −3.00090 | − | 4.13039i | −0.321731 | − | 0.442824i | ||||
\(88\) | −9.77690 | − | 13.4568i | −1.04222 | − | 1.43449i | ||||
\(89\) | 14.8266 | + | 10.7722i | 1.57162 | + | 1.14185i | 0.925587 | + | 0.378536i | \(0.123572\pi\) |
0.646031 | + | 0.763311i | \(0.276428\pi\) | |||||||
\(90\) | 2.54343 | − | 4.52279i | 0.268101 | − | 0.476744i | ||||
\(91\) | 3.61385 | − | 2.62561i | 0.378834 | − | 0.275239i | ||||
\(92\) | 3.03147 | + | 0.984985i | 0.316053 | + | 0.102692i | ||||
\(93\) | 5.64007i | 0.584848i | ||||||||
\(94\) | −6.06803 | + | 18.6755i | −0.625869 | + | 1.92623i | ||||
\(95\) | 4.61532 | − | 4.25120i | 0.473522 | − | 0.436164i | ||||
\(96\) | −1.49296 | − | 4.59485i | −0.152374 | − | 0.468960i | ||||
\(97\) | 8.70890 | − | 2.82969i | 0.884255 | − | 0.287312i | 0.168532 | − | 0.985696i | \(-0.446097\pi\) |
0.715723 | + | 0.698384i | \(0.246097\pi\) | |||||||
\(98\) | 1.36398 | − | 1.87736i | 0.137783 | − | 0.189642i | ||||
\(99\) | −5.17565 | −0.520173 | ||||||||
\(100\) | 11.0373 | − | 12.8305i | 1.10373 | − | 1.28305i | ||||
\(101\) | −5.44108 | −0.541407 | −0.270704 | − | 0.962663i | \(-0.587256\pi\) | ||||
−0.270704 | + | 0.962663i | \(0.587256\pi\) | |||||||
\(102\) | 3.62721 | − | 4.99243i | 0.359148 | − | 0.494324i | ||||
\(103\) | 10.6207 | − | 3.45087i | 1.04649 | − | 0.340024i | 0.265197 | − | 0.964194i | \(-0.414563\pi\) |
0.781288 | + | 0.624170i | \(0.214563\pi\) | |||||||
\(104\) | 4.43621 | + | 13.6532i | 0.435006 | + | 1.33881i | ||||
\(105\) | 0.440125 | − | 2.19233i | 0.0429518 | − | 0.213949i | ||||
\(106\) | 4.16925 | − | 12.8316i | 0.404953 | − | 1.24632i | ||||
\(107\) | 19.0588i | 1.84249i | 0.388985 | + | 0.921244i | \(0.372826\pi\) | ||||
−0.388985 | + | 0.921244i | \(0.627174\pi\) | |||||||
\(108\) | 3.21926 | + | 1.04600i | 0.309773 | + | 0.100651i | ||||
\(109\) | 4.76672 | − | 3.46323i | 0.456569 | − | 0.331717i | −0.335615 | − | 0.941999i | \(-0.608944\pi\) |
0.792184 | + | 0.610282i | \(0.208944\pi\) | |||||||
\(110\) | −26.3306 | − | 5.28604i | −2.51052 | − | 0.504005i | ||||
\(111\) | −6.05555 | − | 4.39962i | −0.574768 | − | 0.417593i | ||||
\(112\) | 0.404328 | + | 0.556510i | 0.0382054 | + | 0.0525852i | ||||
\(113\) | 7.84198 | + | 10.7936i | 0.737711 | + | 1.01537i | 0.998747 | + | 0.0500432i | \(0.0159359\pi\) |
−0.261036 | + | 0.965329i | \(0.584064\pi\) | |||||||
\(114\) | 5.26825 | + | 3.82761i | 0.493417 | + | 0.358489i | ||||
\(115\) | 1.91378 | − | 0.878151i | 0.178461 | − | 0.0818880i | ||||
\(116\) | 13.9811 | − | 10.1578i | 1.29811 | − | 0.943132i | ||||
\(117\) | 4.24833 | + | 1.38037i | 0.392759 | + | 0.127615i | ||||
\(118\) | 28.5301i | 2.62640i | ||||||||
\(119\) | 0.821764 | − | 2.52913i | 0.0753309 | − | 0.231845i | ||||
\(120\) | 6.26374 | + | 3.52247i | 0.571798 | + | 0.321556i | ||||
\(121\) | 4.87857 | + | 15.0147i | 0.443507 | + | 1.36497i | ||||
\(122\) | 20.9973 | − | 6.82242i | 1.90100 | − | 0.617673i | ||||
\(123\) | 0.928456 | − | 1.27791i | 0.0837160 | − | 0.115225i | ||||
\(124\) | −19.0912 | −1.71444 | ||||||||
\(125\) | −0.379484 | − | 11.1739i | −0.0339421 | − | 0.999424i | ||||
\(126\) | 2.32054 | 0.206731 | ||||||||
\(127\) | −4.91633 | + | 6.76675i | −0.436254 | + | 0.600452i | −0.969374 | − | 0.245587i | \(-0.921019\pi\) |
0.533121 | + | 0.846039i | \(0.321019\pi\) | |||||||
\(128\) | 18.5895 | − | 6.04010i | 1.64310 | − | 0.533875i | ||||
\(129\) | −0.000104636 | 0 | 0.000322035i | −9.21265e−6 | 0 | 2.83536e-5i | ||||
\(130\) | 20.2031 | + | 11.3614i | 1.77193 | + | 0.996462i | ||||
\(131\) | 6.17484 | − | 19.0042i | 0.539498 | − | 1.66040i | −0.194226 | − | 0.980957i | \(-0.562220\pi\) |
0.733724 | − | 0.679447i | \(-0.237780\pi\) | |||||||
\(132\) | − | 17.5192i | − | 1.52485i | ||||||
\(133\) | 2.66886 | + | 0.867165i | 0.231419 | + | 0.0751927i | ||||
\(134\) | 3.24237 | − | 2.35572i | 0.280098 | − | 0.203503i | ||||
\(135\) | 2.03233 | − | 0.932548i | 0.174915 | − | 0.0802610i | ||||
\(136\) | 6.91416 | + | 5.02343i | 0.592884 | + | 0.430756i | ||||
\(137\) | −7.85983 | − | 10.8181i | −0.671511 | − | 0.924255i | 0.328283 | − | 0.944579i | \(-0.393530\pi\) |
−0.999793 | + | 0.0203245i | \(0.993530\pi\) | |||||||
\(138\) | 1.28442 | + | 1.76785i | 0.109337 | + | 0.150489i | ||||
\(139\) | −1.76113 | − | 1.27953i | −0.149377 | − | 0.108529i | 0.510587 | − | 0.859826i | \(-0.329428\pi\) |
−0.659963 | + | 0.751298i | \(0.729428\pi\) | |||||||
\(140\) | 7.42086 | + | 1.48979i | 0.627178 | + | 0.125910i | ||||
\(141\) | −6.84594 | + | 4.97387i | −0.576532 | + | 0.418875i | ||||
\(142\) | −28.9556 | − | 9.40824i | −2.42990 | − | 0.789522i | ||||
\(143\) | − | 23.1195i | − | 1.93335i | ||||||
\(144\) | −0.212568 | + | 0.654216i | −0.0177140 | + | 0.0545180i | ||||
\(145\) | 2.24703 | − | 11.1928i | 0.186606 | − | 0.929510i | ||||
\(146\) | −2.15303 | − | 6.62633i | −0.178186 | − | 0.548399i | ||||
\(147\) | 0.951057 | − | 0.309017i | 0.0784418 | − | 0.0254873i | ||||
\(148\) | 14.8924 | − | 20.4976i | 1.22415 | − | 1.68489i | ||||
\(149\) | 14.1901 | 1.16250 | 0.581249 | − | 0.813726i | \(-0.302564\pi\) | ||||
0.581249 | + | 0.813726i | \(0.302564\pi\) | |||||||
\(150\) | 11.2917 | − | 2.66856i | 0.921962 | − | 0.217887i | ||||
\(151\) | 1.90118 | 0.154716 | 0.0773580 | − | 0.997003i | \(-0.475352\pi\) | ||||
0.0773580 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(152\) | −5.30097 | + | 7.29616i | −0.429965 | + | 0.591796i | ||||
\(153\) | 2.52913 | − | 0.821764i | 0.204468 | − | 0.0664356i | ||||
\(154\) | −3.71140 | − | 11.4225i | −0.299073 | − | 0.920452i | ||||
\(155\) | −9.27614 | + | 8.54431i | −0.745077 | + | 0.686296i | ||||
\(156\) | −4.67244 | + | 14.3803i | −0.374095 | + | 1.15135i | ||||
\(157\) | 18.5547i | 1.48082i | 0.672153 | + | 0.740412i | \(0.265370\pi\) | ||||
−0.672153 | + | 0.740412i | \(0.734630\pi\) | |||||||
\(158\) | −13.0768 | − | 4.24891i | −1.04033 | − | 0.338025i | ||||
\(159\) | 4.70374 | − | 3.41747i | 0.373031 | − | 0.271023i | ||||
\(160\) | 5.29536 | − | 9.41632i | 0.418635 | − | 0.744425i | ||||
\(161\) | 0.761825 | + | 0.553499i | 0.0600403 | + | 0.0436218i | ||||
\(162\) | 1.36398 | + | 1.87736i | 0.107165 | + | 0.147499i | ||||
\(163\) | −5.45357 | − | 7.50620i | −0.427157 | − | 0.587931i | 0.540141 | − | 0.841575i | \(-0.318371\pi\) |
−0.967298 | + | 0.253644i | \(0.918371\pi\) | |||||||
\(164\) | 4.32563 | + | 3.14276i | 0.337775 | + | 0.245408i | ||||
\(165\) | −7.84075 | − | 8.51232i | −0.610402 | − | 0.662683i | ||||
\(166\) | −15.9345 | + | 11.5771i | −1.23675 | + | 0.898554i | ||||
\(167\) | −15.8223 | − | 5.14098i | −1.22437 | − | 0.397821i | −0.375696 | − | 0.926743i | \(-0.622596\pi\) |
−0.848670 | + | 0.528922i | \(0.822596\pi\) | |||||||
\(168\) | 3.21379i | 0.247949i | ||||||||
\(169\) | −2.14883 | + | 6.61341i | −0.165294 | + | 0.508724i | ||||
\(170\) | 13.7059 | − | 1.59756i | 1.05120 | − | 0.122527i | ||||
\(171\) | 0.867165 | + | 2.66886i | 0.0663137 | + | 0.204093i | ||||
\(172\) | 0.00109007 | 0.000354184i | 8.31167e−5 | 2.70063e-5i | ||||||
\(173\) | −1.07522 | + | 1.47992i | −0.0817477 | + | 0.112516i | −0.847932 | − | 0.530104i | \(-0.822153\pi\) |
0.766185 | + | 0.642620i | \(0.222153\pi\) | |||||||
\(174\) | 11.8474 | 0.898149 | ||||||||
\(175\) | 4.27244 | − | 2.59735i | 0.322966 | − | 0.196341i | ||||
\(176\) | 3.56025 | 0.268364 | ||||||||
\(177\) | −7.22656 | + | 9.94650i | −0.543181 | + | 0.747625i | ||||
\(178\) | −40.4465 | + | 13.1419i | −3.03159 | + | 0.985024i | ||||
\(179\) | 4.96964 | + | 15.2950i | 0.371449 | + | 1.14320i | 0.945844 | + | 0.324623i | \(0.105237\pi\) |
−0.574395 | + | 0.818578i | \(0.694763\pi\) | |||||||
\(180\) | 3.15661 | + | 6.87928i | 0.235280 | + | 0.512751i | ||||
\(181\) | −1.57723 | + | 4.85421i | −0.117235 | + | 0.360811i | −0.992407 | − | 0.123001i | \(-0.960748\pi\) |
0.875172 | + | 0.483812i | \(0.160748\pi\) | |||||||
\(182\) | 10.3658i | 0.768363i | ||||||||
\(183\) | 9.04842 | + | 2.94001i | 0.668878 | + | 0.217332i | ||||
\(184\) | −2.44835 | + | 1.77883i | −0.180494 | + | 0.131137i | ||||
\(185\) | −1.93775 | − | 16.6246i | −0.142467 | − | 1.22226i | ||||
\(186\) | −10.5884 | − | 7.69296i | −0.776383 | − | 0.564075i | ||||
\(187\) | −8.09000 | − | 11.1349i | −0.591599 | − | 0.814266i | ||||
\(188\) | −16.8362 | − | 23.1730i | −1.22790 | − | 1.69007i | ||||
\(189\) | 0.809017 | + | 0.587785i | 0.0588473 | + | 0.0427551i | ||||
\(190\) | 1.68582 | + | 14.4632i | 0.122302 | + | 1.04927i | ||||
\(191\) | 21.4682 | − | 15.5976i | 1.55339 | − | 1.12860i | 0.612206 | − | 0.790698i | \(-0.290282\pi\) |
0.941181 | − | 0.337904i | \(-0.109718\pi\) | |||||||
\(192\) | 11.9710 | + | 3.88961i | 0.863932 | + | 0.280708i | ||||
\(193\) | − | 5.11772i | − | 0.368382i | −0.982891 | − | 0.184191i | \(-0.941034\pi\) | ||
0.982891 | − | 0.184191i | \(-0.0589664\pi\) | |||||||
\(194\) | −6.56643 | + | 20.2094i | −0.471442 | + | 1.45095i | ||||
\(195\) | 4.16566 | + | 9.07833i | 0.298309 | + | 0.650113i | ||||
\(196\) | 1.04600 | + | 3.21926i | 0.0747143 | + | 0.229947i | ||||
\(197\) | −20.4420 | + | 6.64200i | −1.45643 | + | 0.473223i | −0.926978 | − | 0.375116i | \(-0.877603\pi\) |
−0.529453 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(198\) | 7.05950 | − | 9.71657i | 0.501697 | − | 0.690526i | ||||
\(199\) | 13.5664 | 0.961693 | 0.480847 | − | 0.876805i | \(-0.340329\pi\) | ||||
0.480847 | + | 0.876805i | \(0.340329\pi\) | |||||||
\(200\) | 3.69577 | + | 15.6382i | 0.261330 | + | 1.10579i | ||||
\(201\) | 1.72709 | 0.121820 | ||||||||
\(202\) | 7.42153 | − | 10.2149i | 0.522177 | − | 0.718715i | ||||
\(203\) | 4.85556 | − | 1.57767i | 0.340794 | − | 0.110731i | ||||
\(204\) | 2.78161 | + | 8.56092i | 0.194752 | + | 0.599384i | ||||
\(205\) | 3.50830 | − | 0.408926i | 0.245031 | − | 0.0285607i | ||||
\(206\) | −8.00789 | + | 24.6457i | −0.557936 | + | 1.71715i | ||||
\(207\) | 0.941668i | 0.0654505i | ||||||||
\(208\) | −2.92236 | − | 0.949532i | −0.202629 | − | 0.0658382i | ||||
\(209\) | 11.7501 | − | 8.53696i | 0.812772 | − | 0.590514i | ||||
\(210\) | 3.51546 | + | 3.81656i | 0.242590 | + | 0.263368i | ||||
\(211\) | 2.48123 | + | 1.80272i | 0.170815 | + | 0.124104i | 0.669908 | − | 0.742444i | \(-0.266333\pi\) |
−0.499093 | + | 0.866548i | \(0.666333\pi\) | |||||||
\(212\) | 11.5679 | + | 15.9218i | 0.794485 | + | 1.09352i | ||||
\(213\) | −7.71178 | − | 10.6144i | −0.528403 | − | 0.727284i | ||||
\(214\) | −35.7803 | − | 25.9959i | −2.44589 | − | 1.77705i | ||||
\(215\) | 0.000371131 | 0 | 0.000659953i | 2.53109e−5 | 0 | 4.50084e-5i | ||||
\(216\) | −2.60001 | + | 1.88902i | −0.176908 | + | 0.128531i | ||||
\(217\) | −5.36403 | − | 1.74288i | −0.364134 | − | 0.118314i | ||||
\(218\) | 13.6726i | 0.926028i | ||||||||
\(219\) | 0.927811 | − | 2.85551i | 0.0626956 | − | 0.192957i | ||||
\(220\) | 28.8136 | − | 26.5404i | 1.94261 | − | 1.78935i | ||||
\(221\) | 3.67079 | + | 11.2975i | 0.246924 | + | 0.759953i | ||||
\(222\) | 16.5193 | − | 5.36746i | 1.10870 | − | 0.360240i | ||||
\(223\) | 3.40625 | − | 4.68830i | 0.228100 | − | 0.313952i | −0.679592 | − | 0.733590i | \(-0.737843\pi\) |
0.907691 | + | 0.419638i | \(0.137843\pi\) | |||||||
\(224\) | 4.83131 | 0.322806 | ||||||||
\(225\) | 4.61258 | + | 1.92979i | 0.307505 | + | 0.128653i | ||||
\(226\) | −30.9597 | −2.05941 | ||||||||
\(227\) | −6.77250 | + | 9.32154i | −0.449506 | + | 0.618692i | −0.972291 | − | 0.233772i | \(-0.924893\pi\) |
0.522785 | + | 0.852465i | \(0.324893\pi\) | |||||||
\(228\) | −9.03389 | + | 2.93529i | −0.598284 | + | 0.194394i | ||||
\(229\) | 2.56148 | + | 7.88344i | 0.169268 | + | 0.520952i | 0.999325 | − | 0.0367252i | \(-0.0116926\pi\) |
−0.830058 | + | 0.557677i | \(0.811693\pi\) | |||||||
\(230\) | −0.961753 | + | 4.79063i | −0.0634161 | + | 0.315885i | ||||
\(231\) | 1.59937 | − | 4.92234i | 0.105230 | − | 0.323866i | ||||
\(232\) | 16.4078i | 1.07723i | ||||||||
\(233\) | −26.3766 | − | 8.57027i | −1.72799 | − | 0.561457i | −0.734832 | − | 0.678249i | \(-0.762739\pi\) |
−0.993156 | + | 0.116792i | \(0.962739\pi\) | |||||||
\(234\) | −8.38610 | + | 6.09286i | −0.548216 | + | 0.398303i | ||||
\(235\) | −18.5516 | − | 3.72435i | −1.21017 | − | 0.242950i | ||||
\(236\) | −33.6682 | − | 24.4614i | −2.19161 | − | 1.59230i | ||||
\(237\) | −3.48276 | − | 4.79361i | −0.226230 | − | 0.311379i | ||||
\(238\) | 3.62721 | + | 4.99243i | 0.235117 | + | 0.323611i | ||||
\(239\) | −12.4374 | − | 9.03629i | −0.804507 | − | 0.584509i | 0.107726 | − | 0.994181i | \(-0.465643\pi\) |
−0.912233 | + | 0.409672i | \(0.865643\pi\) | |||||||
\(240\) | −1.39800 | + | 0.641485i | −0.0902408 | + | 0.0414077i | ||||
\(241\) | −16.2048 | + | 11.7735i | −1.04384 | + | 0.758395i | −0.971032 | − | 0.238951i | \(-0.923197\pi\) |
−0.0728098 | + | 0.997346i | \(0.523197\pi\) | |||||||
\(242\) | −34.8423 | − | 11.3209i | −2.23975 | − | 0.727738i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −9.95172 | + | 30.6282i | −0.637094 | + | 1.96077i | ||||
\(245\) | 1.94902 | + | 1.09605i | 0.124518 | + | 0.0700240i | ||||
\(246\) | 1.13270 | + | 3.48609i | 0.0722183 | + | 0.222265i | ||||
\(247\) | −11.9217 | + | 3.87359i | −0.758559 | + | 0.246471i | ||||
\(248\) | 10.6542 | − | 14.6642i | 0.676542 | − | 0.931180i | ||||
\(249\) | −8.48769 | −0.537886 | ||||||||
\(250\) | 21.4950 | + | 14.5286i | 1.35947 | + | 0.918867i | ||||
\(251\) | 0.298988 | 0.0188719 | 0.00943597 | − | 0.999955i | \(-0.496996\pi\) | ||||
0.00943597 | + | 0.999955i | \(0.496996\pi\) | |||||||
\(252\) | −1.98961 | + | 2.73846i | −0.125334 | + | 0.172507i | ||||
\(253\) | 4.63521 | − | 1.50607i | 0.291413 | − | 0.0946859i | ||||
\(254\) | −5.99784 | − | 18.4594i | −0.376338 | − | 1.15825i | ||||
\(255\) | 5.18299 | + | 2.91470i | 0.324572 | + | 0.182526i | ||||
\(256\) | −6.23710 | + | 19.1958i | −0.389819 | + | 1.19974i | ||||
\(257\) | − | 13.8078i | − | 0.861310i | −0.902517 | − | 0.430655i | \(-0.858283\pi\) | ||
0.902517 | − | 0.430655i | \(-0.141717\pi\) | |||||||
\(258\) | 0.000747297 | 0 | 0.000242811i | 4.65247e−5 | 0 | 1.51168e-5i | ||||
\(259\) | 6.05555 | − | 4.39962i | 0.376274 | − | 0.273379i | ||||
\(260\) | −30.7295 | + | 14.1005i | −1.90576 | + | 0.874473i | ||||
\(261\) | 4.13039 | + | 3.00090i | 0.255665 | + | 0.185751i | ||||
\(262\) | 27.2554 | + | 37.5138i | 1.68384 | + | 2.31761i | ||||
\(263\) | 1.82712 | + | 2.51481i | 0.112665 | + | 0.155070i | 0.861625 | − | 0.507545i | \(-0.169447\pi\) |
−0.748961 | + | 0.662614i | \(0.769447\pi\) | |||||||
\(264\) | 13.4568 | + | 9.77690i | 0.828206 | + | 0.601727i | ||||
\(265\) | 12.7465 | + | 2.55895i | 0.783011 | + | 0.157195i | ||||
\(266\) | −5.26825 | + | 3.82761i | −0.323017 | + | 0.234686i | ||||
\(267\) | −17.4297 | − | 5.66326i | −1.06668 | − | 0.346586i | ||||
\(268\) | 5.84608i | 0.357106i | ||||||||
\(269\) | −4.80841 | + | 14.7988i | −0.293174 | + | 0.902297i | 0.690655 | + | 0.723185i | \(0.257323\pi\) |
−0.983829 | + | 0.179112i | \(0.942677\pi\) | |||||||
\(270\) | −1.02133 | + | 5.08739i | −0.0621561 | + | 0.309609i | ||||
\(271\) | −4.79752 | − | 14.7652i | −0.291429 | − | 0.896925i | −0.984398 | − | 0.175958i | \(-0.943698\pi\) |
0.692969 | − | 0.720967i | \(-0.256302\pi\) | |||||||
\(272\) | −1.73975 | + | 0.565278i | −0.105488 | + | 0.0342750i | ||||
\(273\) | −2.62561 | + | 3.61385i | −0.158909 | + | 0.218720i | ||||
\(274\) | 31.0302 | 1.87460 | ||||||||
\(275\) | 2.12189 | − | 25.7911i | 0.127955 | − | 1.55526i | ||||
\(276\) | −3.18748 | −0.191864 | ||||||||
\(277\) | −14.5003 | + | 19.9579i | −0.871237 | + | 1.19915i | 0.107535 | + | 0.994201i | \(0.465704\pi\) |
−0.978772 | + | 0.204954i | \(0.934296\pi\) | |||||||
\(278\) | 4.80429 | − | 1.56101i | 0.288142 | − | 0.0936230i | ||||
\(279\) | −1.74288 | − | 5.36403i | −0.104343 | − | 0.321136i | ||||
\(280\) | −5.28567 | + | 4.86866i | −0.315879 | + | 0.290958i | ||||
\(281\) | 5.61246 | − | 17.2734i | 0.334812 | − | 1.03044i | −0.632003 | − | 0.774966i | \(-0.717767\pi\) |
0.966815 | − | 0.255478i | \(-0.0822329\pi\) | |||||||
\(282\) | − | 19.6366i | − | 1.16934i | ||||||
\(283\) | −25.2398 | − | 8.20092i | −1.50035 | − | 0.487494i | −0.560231 | − | 0.828336i | \(-0.689288\pi\) |
−0.940120 | + | 0.340842i | \(0.889288\pi\) | |||||||
\(284\) | 35.9288 | − | 26.1038i | 2.13198 | − | 1.54898i | ||||
\(285\) | −3.07574 | + | 5.46934i | −0.182191 | + | 0.323976i | ||||
\(286\) | 43.4035 | + | 31.5345i | 2.56651 | + | 1.86468i | ||||
\(287\) | 0.928456 | + | 1.27791i | 0.0548050 | + | 0.0754326i | ||||
\(288\) | 2.83977 | + | 3.90861i | 0.167335 | + | 0.230317i | ||||
\(289\) | −8.03210 | − | 5.83566i | −0.472476 | − | 0.343274i | ||||
\(290\) | 17.9480 | + | 19.4852i | 1.05394 | + | 1.14421i | ||||
\(291\) | −7.40823 | + | 5.38240i | −0.434278 | + | 0.315522i | ||||
\(292\) | 9.66569 | + | 3.14057i | 0.565642 | + | 0.183788i | ||||
\(293\) | − | 17.1749i | − | 1.00337i | −0.865051 | − | 0.501684i | \(-0.832714\pi\) | ||
0.865051 | − | 0.501684i | \(-0.167286\pi\) | |||||||
\(294\) | −0.717088 | + | 2.20697i | −0.0418214 | + | 0.128713i | ||||
\(295\) | −27.3066 | + | 3.18284i | −1.58985 | + | 0.185312i | ||||
\(296\) | 7.43354 | + | 22.8781i | 0.432066 | + | 1.32976i | ||||
\(297\) | 4.92234 | − | 1.59937i | 0.285623 | − | 0.0928046i | ||||
\(298\) | −19.3550 | + | 26.6399i | −1.12121 | + | 1.54321i | ||||
\(299\) | −4.20640 | −0.243262 | ||||||||
\(300\) | −6.53221 | + | 15.6133i | −0.377137 | + | 0.901432i | ||||
\(301\) | 0.000338608 | 0 | 1.95170e−5 | 0 | ||||||
\(302\) | −2.59318 | + | 3.56920i | −0.149221 | + | 0.205385i | ||||
\(303\) | 5.17477 | − | 1.68138i | 0.297283 | − | 0.0965930i | ||||
\(304\) | −0.596508 | − | 1.83586i | −0.0342121 | − | 0.105294i | ||||
\(305\) | 8.87233 | + | 19.3357i | 0.508028 | + | 1.10716i | ||||
\(306\) | −1.90694 | + | 5.86895i | −0.109012 | + | 0.335506i | ||||
\(307\) | 1.04893i | 0.0598658i | 0.999552 | + | 0.0299329i | \(0.00952936\pi\) | ||||
−0.999552 | + | 0.0299329i | \(0.990471\pi\) | |||||||
\(308\) | 16.6618 | + | 5.41374i | 0.949392 | + | 0.308476i | ||||
\(309\) | −9.03448 | + | 6.56394i | −0.513954 | + | 0.373409i | ||||
\(310\) | −3.38826 | − | 29.0689i | −0.192440 | − | 1.65101i | ||||
\(311\) | 4.12322 | + | 2.99570i | 0.233806 | + | 0.169870i | 0.698520 | − | 0.715591i | \(-0.253843\pi\) |
−0.464713 | + | 0.885461i | \(0.653843\pi\) | |||||||
\(312\) | −8.43817 | − | 11.6141i | −0.477717 | − | 0.657522i | ||||
\(313\) | 14.7072 | + | 20.2427i | 0.831299 | + | 1.14418i | 0.987680 | + | 0.156488i | \(0.0500173\pi\) |
−0.156381 | + | 0.987697i | \(0.549983\pi\) | |||||||
\(314\) | −34.8338 | − | 25.3082i | −1.96579 | − | 1.42823i | ||||
\(315\) | 0.258882 | + | 2.22103i | 0.0145864 | + | 0.125141i | ||||
\(316\) | 16.2260 | − | 11.7889i | 0.912786 | − | 0.663178i | ||||
\(317\) | 30.1417 | + | 9.79362i | 1.69292 | + | 0.550064i | 0.987348 | − | 0.158569i | \(-0.0506881\pi\) |
0.705576 | + | 0.708634i | \(0.250688\pi\) | |||||||
\(318\) | 13.4920i | 0.756592i | ||||||||
\(319\) | 8.16546 | − | 25.1307i | 0.457178 | − | 1.40705i | ||||
\(320\) | 11.7380 | + | 25.5810i | 0.656176 | + | 1.43002i | ||||
\(321\) | −5.88951 | − | 18.1260i | −0.328720 | − | 1.01170i | ||||
\(322\) | −2.07823 | + | 0.675259i | −0.115815 | + | 0.0376307i | ||||
\(323\) | −4.38634 | + | 6.03728i | −0.244063 | + | 0.335923i | ||||
\(324\) | −3.38493 | −0.188052 | ||||||||
\(325\) | −8.62031 | + | 20.6042i | −0.478169 | + | 1.14292i | ||||
\(326\) | 21.5304 | 1.19246 | ||||||||
\(327\) | −3.46323 | + | 4.76672i | −0.191517 | + | 0.263600i | ||||
\(328\) | −4.82799 | + | 1.56871i | −0.266581 | + | 0.0866174i | ||||
\(329\) | −2.61492 | − | 8.04788i | −0.144165 | − | 0.443694i | ||||
\(330\) | 26.6753 | − | 3.10927i | 1.46843 | − | 0.171159i | ||||
\(331\) | −8.04458 | + | 24.7587i | −0.442170 | + | 1.36086i | 0.443387 | + | 0.896330i | \(0.353777\pi\) |
−0.885557 | + | 0.464530i | \(0.846223\pi\) | |||||||
\(332\) | − | 28.7302i | − | 1.57678i | ||||||
\(333\) | 7.11873 | + | 2.31302i | 0.390104 | + | 0.126752i | ||||
\(334\) | 31.2328 | − | 22.6920i | 1.70898 | − | 1.24165i | ||||
\(335\) | 2.61642 | + | 2.84052i | 0.142950 | + | 0.155194i | ||||
\(336\) | −0.556510 | − | 0.404328i | −0.0303601 | − | 0.0220579i | ||||
\(337\) | 13.0626 | + | 17.9791i | 0.711566 | + | 0.979387i | 0.999762 | + | 0.0218151i | \(0.00694451\pi\) |
−0.288196 | + | 0.957571i | \(0.593055\pi\) | |||||||
\(338\) | −9.48480 | − | 13.0547i | −0.515905 | − | 0.710082i | ||||
\(339\) | −10.7936 | − | 7.84198i | −0.586225 | − | 0.425918i | ||||
\(340\) | −9.86607 | + | 17.5441i | −0.535063 | + | 0.951460i | ||||
\(341\) | −23.6161 | + | 17.1581i | −1.27888 | + | 0.929162i | ||||
\(342\) | −6.19321 | − | 2.01229i | −0.334890 | − | 0.108812i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −0.000336276 | 0.00103495i | −1.81308e−5 | 5.58009e-5i | ||||||
\(345\) | −1.54875 | + | 1.42656i | −0.0833817 | + | 0.0768035i | ||||
\(346\) | −1.31175 | − | 4.03716i | −0.0705203 | − | 0.217039i | ||||
\(347\) | −6.85580 | + | 2.22758i | −0.368039 | + | 0.119583i | −0.487197 | − | 0.873292i | \(-0.661980\pi\) |
0.119158 | + | 0.992875i | \(0.461980\pi\) | |||||||
\(348\) | −10.1578 | + | 13.9811i | −0.544517 | + | 0.749464i | ||||
\(349\) | 14.7927 | 0.791835 | 0.395917 | − | 0.918286i | \(-0.370427\pi\) | ||||
0.395917 | + | 0.918286i | \(0.370427\pi\) | |||||||
\(350\) | −0.951368 | + | 11.5637i | −0.0508527 | + | 0.618103i | ||||
\(351\) | −4.46696 | −0.238429 | ||||||||
\(352\) | 14.6977 | − | 20.2296i | 0.783389 | − | 1.07824i | ||||
\(353\) | 0.953456 | − | 0.309797i | 0.0507473 | − | 0.0164888i | −0.283533 | − | 0.958962i | \(-0.591507\pi\) |
0.334281 | + | 0.942474i | \(0.391507\pi\) | |||||||
\(354\) | −8.81627 | − | 27.1337i | −0.468580 | − | 1.44214i | ||||
\(355\) | 5.77446 | − | 28.7635i | 0.306477 | − | 1.52661i | ||||
\(356\) | 19.1697 | − | 58.9984i | 1.01599 | − | 3.12691i | ||||
\(357\) | 2.65928i | 0.140744i | ||||||||
\(358\) | −35.4927 | − | 11.5323i | −1.87585 | − | 0.609500i | ||||
\(359\) | 15.6940 | − | 11.4023i | 0.828297 | − | 0.601793i | −0.0907803 | − | 0.995871i | \(-0.528936\pi\) |
0.919077 | + | 0.394078i | \(0.128936\pi\) | |||||||
\(360\) | −7.04567 | − | 1.41447i | −0.371339 | − | 0.0745490i | ||||
\(361\) | 9.00049 | + | 6.53924i | 0.473710 | + | 0.344171i | ||||
\(362\) | −6.96180 | − | 9.58209i | −0.365904 | − | 0.503623i | ||||
\(363\) | −9.27960 | − | 12.7723i | −0.487053 | − | 0.670370i | ||||
\(364\) | −12.2326 | − | 8.88752i | −0.641163 | − | 0.465833i | ||||
\(365\) | 6.10198 | − | 2.79994i | 0.319392 | − | 0.146555i | ||||
\(366\) | −17.8613 | + | 12.9770i | −0.933627 | + | 0.678320i | ||||
\(367\) | −7.43395 | − | 2.41544i | −0.388049 | − | 0.126085i | 0.108493 | − | 0.994097i | \(-0.465397\pi\) |
−0.496543 | + | 0.868012i | \(0.665397\pi\) | |||||||
\(368\) | − | 0.647758i | − | 0.0337667i | ||||||
\(369\) | −0.488118 | + | 1.50227i | −0.0254104 | + | 0.0782052i | ||||
\(370\) | 33.8534 | + | 19.0378i | 1.75995 | + | 0.989727i | ||||
\(371\) | 1.79667 | + | 5.52958i | 0.0932784 | + | 0.287081i | ||||
\(372\) | 18.1568 | − | 5.89952i | 0.941389 | − | 0.305876i | ||||
\(373\) | 7.31748 | − | 10.0716i | 0.378885 | − | 0.521490i | −0.576404 | − | 0.817165i | \(-0.695544\pi\) |
0.955289 | + | 0.295675i | \(0.0955445\pi\) | |||||||
\(374\) | 31.9389 | 1.65152 | ||||||||
\(375\) | 3.81384 | + | 10.5097i | 0.196946 | + | 0.542721i | ||||
\(376\) | 27.1952 | 1.40249 | ||||||||
\(377\) | −13.4049 | + | 18.4503i | −0.690388 | + | 0.950238i | ||||
\(378\) | −2.20697 | + | 0.717088i | −0.113514 | + | 0.0368830i | ||||
\(379\) | −10.7804 | − | 33.1785i | −0.553750 | − | 1.70427i | −0.699223 | − | 0.714904i | \(-0.746470\pi\) |
0.145473 | − | 0.989362i | \(-0.453530\pi\) | |||||||
\(380\) | −18.5133 | − | 10.4111i | −0.949714 | − | 0.534081i | ||||
\(381\) | 2.58467 | − | 7.95479i | 0.132417 | − | 0.407536i | ||||
\(382\) | 61.5784i | 3.15063i | ||||||||
\(383\) | −10.0040 | − | 3.25051i | −0.511183 | − | 0.166093i | 0.0420573 | − | 0.999115i | \(-0.486609\pi\) |
−0.553240 | + | 0.833022i | \(0.686609\pi\) | |||||||
\(384\) | −15.8132 | + | 11.4890i | −0.806963 | + | 0.586293i | ||||
\(385\) | 10.5186 | − | 4.82655i | 0.536079 | − | 0.245984i | ||||
\(386\) | 9.60781 | + | 6.98048i | 0.489024 | + | 0.355297i | ||||
\(387\) | 0.000199029 | 0 | 0.000273939i | 1.01172e−5 | 0 | 1.39251e-5i | ||||
\(388\) | −18.2190 | − | 25.0763i | −0.924931 | − | 1.27306i | ||||
\(389\) | 20.9037 | + | 15.1875i | 1.05986 | + | 0.770035i | 0.974063 | − | 0.226278i | \(-0.0726556\pi\) |
0.0857993 | + | 0.996312i | \(0.472656\pi\) | |||||||
\(390\) | −22.7252 | − | 4.56224i | −1.15073 | − | 0.231018i | ||||
\(391\) | −2.02591 | + | 1.47191i | −0.102455 | + | 0.0744376i | ||||
\(392\) | −3.05649 | − | 0.993115i | −0.154376 | − | 0.0501599i | ||||
\(393\) | 19.9822i | 1.00797i | ||||||||
\(394\) | 15.4131 | − | 47.4365i | 0.776499 | − | 2.38982i | ||||
\(395\) | 2.60784 | − | 12.9900i | 0.131215 | − | 0.653600i | ||||
\(396\) | 5.41374 | + | 16.6618i | 0.272050 | + | 0.837285i | ||||
\(397\) | 30.8636 | − | 10.0282i | 1.54900 | − | 0.503301i | 0.595158 | − | 0.803609i | \(-0.297089\pi\) |
0.953842 | + | 0.300308i | \(0.0970894\pi\) | |||||||
\(398\) | −18.5043 | + | 25.4689i | −0.927535 | + | 1.27664i | ||||
\(399\) | −2.80620 | −0.140486 | ||||||||
\(400\) | −3.17292 | − | 1.32747i | −0.158646 | − | 0.0663737i | ||||
\(401\) | −20.1859 | −1.00804 | −0.504018 | − | 0.863693i | \(-0.668145\pi\) | ||||
−0.504018 | + | 0.863693i | \(0.668145\pi\) | |||||||
\(402\) | −2.35572 | + | 3.24237i | −0.117493 | + | 0.161715i | ||||
\(403\) | 23.9609 | − | 7.78537i | 1.19358 | − | 0.387817i | ||||
\(404\) | 5.69137 | + | 17.5162i | 0.283156 | + | 0.871465i | ||||
\(405\) | −1.64468 | + | 1.51493i | −0.0817250 | + | 0.0752775i | ||||
\(406\) | −3.66105 | + | 11.2676i | −0.181695 | + | 0.559199i | ||||
\(407\) | − | 38.7402i | − | 1.92028i | ||||||
\(408\) | −8.12808 | − | 2.64097i | −0.402400 | − | 0.130748i | ||||
\(409\) | 2.97174 | − | 2.15910i | 0.146943 | − | 0.106760i | −0.511885 | − | 0.859054i | \(-0.671053\pi\) |
0.658828 | + | 0.752294i | \(0.271053\pi\) | |||||||
\(410\) | −4.01756 | + | 7.14412i | −0.198413 | + | 0.352823i | ||||
\(411\) | 10.8181 | + | 7.85983i | 0.533619 | + | 0.387697i | ||||
\(412\) | −22.2185 | − | 30.5811i | −1.09462 | − | 1.50662i | ||||
\(413\) | −7.22656 | − | 9.94650i | −0.355596 | − | 0.489435i | ||||
\(414\) | −1.76785 | − | 1.28442i | −0.0868851 | − | 0.0631257i | ||||
\(415\) | −12.8583 | − | 13.9596i | −0.631187 | − | 0.685249i | ||||
\(416\) | −17.4596 | + | 12.6852i | −0.856029 | + | 0.621941i | ||||
\(417\) | 2.07033 | + | 0.672690i | 0.101384 | + | 0.0329418i | ||||
\(418\) | 33.7035i | 1.64849i | ||||||||
\(419\) | −8.44992 | + | 26.0062i | −0.412805 | + | 1.27048i | 0.501394 | + | 0.865219i | \(0.332821\pi\) |
−0.914199 | + | 0.405265i | \(0.867179\pi\) | |||||||
\(420\) | −7.51803 | + | 0.876298i | −0.366842 | + | 0.0427590i | ||||
\(421\) | −8.21384 | − | 25.2796i | −0.400318 | − | 1.23205i | −0.924742 | − | 0.380595i | \(-0.875719\pi\) |
0.524424 | − | 0.851457i | \(-0.324281\pi\) | |||||||
\(422\) | −6.76871 | + | 2.19929i | −0.329496 | + | 0.107060i | ||||
\(423\) | 4.97387 | − | 6.84594i | 0.241838 | − | 0.332861i | ||||
\(424\) | −18.6854 | −0.907444 | ||||||||
\(425\) | 3.05810 | + | 12.9400i | 0.148340 | + | 0.627680i | ||||
\(426\) | 30.4457 | 1.47510 | ||||||||
\(427\) | −5.59223 | + | 7.69704i | −0.270627 | + | 0.372486i | ||||
\(428\) | 61.3554 | − | 19.9356i | 2.96572 | − | 0.963622i | ||||
\(429\) | 7.14430 | + | 21.9879i | 0.344930 | + | 1.06159i | ||||
\(430\) | 0.000732754 | 0.00159691i | 3.53365e−5 | 7.70098e-5i | ||||||
\(431\) | 3.04293 | − | 9.36517i | 0.146573 | − | 0.451104i | −0.850637 | − | 0.525753i | \(-0.823784\pi\) |
0.997210 | + | 0.0746487i | \(0.0237836\pi\) | |||||||
\(432\) | − | 0.687884i | − | 0.0330958i | ||||||
\(433\) | 33.9462 | + | 11.0298i | 1.63135 | + | 0.530057i | 0.974581 | − | 0.224036i | \(-0.0719233\pi\) |
0.656767 | + | 0.754093i | \(0.271923\pi\) | |||||||
\(434\) | 10.5884 | − | 7.69296i | 0.508262 | − | 0.369274i | ||||
\(435\) | 1.32171 | + | 11.3393i | 0.0633711 | + | 0.543680i | ||||
\(436\) | −16.1350 | − | 11.7228i | −0.772727 | − | 0.561419i | ||||
\(437\) | −1.55323 | − | 2.13784i | −0.0743011 | − | 0.102267i | ||||
\(438\) | 4.09530 | + | 5.63670i | 0.195681 | + | 0.269332i | ||||
\(439\) | −16.8325 | − | 12.2296i | −0.803374 | − | 0.583685i | 0.108528 | − | 0.994093i | \(-0.465386\pi\) |
−0.911902 | + | 0.410408i | \(0.865386\pi\) | |||||||
\(440\) | 4.30611 | + | 36.9434i | 0.205286 | + | 1.76121i | ||||
\(441\) | −0.809017 | + | 0.587785i | −0.0385246 | + | 0.0279898i | ||||
\(442\) | −26.2164 | − | 8.51823i | −1.24699 | − | 0.405171i | ||||
\(443\) | 20.6984i | 0.983409i | 0.870762 | + | 0.491705i | \(0.163626\pi\) | ||||
−0.870762 | + | 0.491705i | \(0.836374\pi\) | |||||||
\(444\) | −7.82939 | + | 24.0964i | −0.371566 | + | 1.14356i | ||||
\(445\) | −17.0905 | − | 37.2459i | −0.810169 | − | 1.76562i | ||||
\(446\) | 4.15557 | + | 12.7895i | 0.196772 | + | 0.605602i | ||||
\(447\) | −13.4956 | + | 4.38498i | −0.638319 | + | 0.207402i | ||||
\(448\) | −7.39848 | + | 10.1831i | −0.349545 | + | 0.481108i | ||||
\(449\) | 20.1811 | 0.952403 | 0.476202 | − | 0.879336i | \(-0.342013\pi\) | ||||
0.476202 | + | 0.879336i | \(0.342013\pi\) | |||||||
\(450\) | −9.91439 | + | 6.02727i | −0.467369 | + | 0.284128i | ||||
\(451\) | 8.17538 | 0.384963 | ||||||||
\(452\) | 26.5445 | − | 36.5354i | 1.24855 | − | 1.71848i | ||||
\(453\) | −1.80813 | + | 0.587497i | −0.0849534 | + | 0.0276030i | ||||
\(454\) | −8.26233 | − | 25.4288i | −0.387770 | − | 1.19343i | ||||
\(455\) | −9.92126 | + | 1.15642i | −0.465116 | + | 0.0542137i | ||||
\(456\) | 2.78688 | − | 8.57715i | 0.130508 | − | 0.401662i | ||||
\(457\) | − | 2.77398i | − | 0.129761i | −0.997893 | − | 0.0648806i | \(-0.979333\pi\) | ||
0.997893 | − | 0.0648806i | \(-0.0206666\pi\) | |||||||
\(458\) | −18.2939 | − | 5.94404i | −0.854816 | − | 0.277747i | ||||
\(459\) | −2.15140 | + | 1.56309i | −0.100419 | + | 0.0729587i | ||||
\(460\) | −4.82881 | − | 5.24240i | −0.225144 | − | 0.244428i | ||||
\(461\) | 5.87667 | + | 4.26965i | 0.273704 | + | 0.198858i | 0.716167 | − | 0.697929i | \(-0.245895\pi\) |
−0.442463 | + | 0.896787i | \(0.645895\pi\) | |||||||
\(462\) | 7.05950 | + | 9.71657i | 0.328438 | + | 0.452056i | ||||
\(463\) | 11.0040 | + | 15.1457i | 0.511398 | + | 0.703879i | 0.984154 | − | 0.177314i | \(-0.0567409\pi\) |
−0.472756 | + | 0.881193i | \(0.656741\pi\) | |||||||
\(464\) | −2.84123 | − | 2.06427i | −0.131901 | − | 0.0958314i | ||||
\(465\) | 6.18180 | − | 10.9926i | 0.286674 | − | 0.509770i | ||||
\(466\) | 52.0667 | − | 37.8287i | 2.41194 | − | 1.75238i | ||||
\(467\) | 22.5250 | + | 7.31883i | 1.04233 | + | 0.338675i | 0.779656 | − | 0.626208i | \(-0.215394\pi\) |
0.262679 | + | 0.964883i | \(0.415394\pi\) | |||||||
\(468\) | − | 15.1203i | − | 0.698938i | ||||||
\(469\) | −0.533701 | + | 1.64256i | −0.0246440 | + | 0.0758464i | ||||
\(470\) | 32.2959 | − | 29.7480i | 1.48970 | − | 1.37217i | ||||
\(471\) | −5.73371 | − | 17.6465i | −0.264195 | − | 0.813110i | ||||
\(472\) | 37.5782 | − | 12.2099i | 1.72968 | − | 0.562006i | ||||
\(473\) | 0.00103010 | − | 0.00141782i | 4.73642e−5 | − | 6.51912e-5i | ||||
\(474\) | 13.7498 | 0.631548 | ||||||||
\(475\) | −13.6549 | + | 3.22706i | −0.626529 | + | 0.148067i | ||||
\(476\) | −9.00148 | −0.412582 | ||||||||
\(477\) | −3.41747 | + | 4.70374i | −0.156475 | + | 0.215369i | ||||
\(478\) | 33.9287 | − | 11.0241i | 1.55186 | − | 0.504231i | ||||
\(479\) | 10.8092 | + | 33.2674i | 0.493887 | + | 1.52003i | 0.818685 | + | 0.574243i | \(0.194704\pi\) |
−0.324798 | + | 0.945783i | \(0.605296\pi\) | |||||||
\(480\) | −2.12638 | + | 10.5918i | −0.0970555 | + | 0.483448i | ||||
\(481\) | −10.3322 | + | 31.7991i | −0.471106 | + | 1.44991i | ||||
\(482\) | − | 46.4810i | − | 2.11715i | ||||||
\(483\) | −0.895580 | − | 0.290991i | −0.0407503 | − | 0.0132406i | ||||
\(484\) | 43.2332 | − | 31.4108i | 1.96515 | − | 1.42776i | ||||
\(485\) | −20.0753 | − | 4.03026i | −0.911572 | − | 0.183004i | ||||
\(486\) | −1.87736 | − | 1.36398i | −0.0851588 | − | 0.0618715i | ||||
\(487\) | 1.09813 | + | 1.51144i | 0.0497609 | + | 0.0684899i | 0.833172 | − | 0.553013i | \(-0.186522\pi\) |
−0.783411 | + | 0.621503i | \(0.786522\pi\) | |||||||
\(488\) | −17.9722 | − | 24.7367i | −0.813565 | − | 1.11978i | ||||
\(489\) | 7.50620 | + | 5.45357i | 0.339442 | + | 0.246619i | ||||
\(490\) | −4.71611 | + | 2.16402i | −0.213052 | + | 0.0977605i | ||||
\(491\) | −21.5149 | + | 15.6315i | −0.970952 | + | 0.705438i | −0.955668 | − | 0.294445i | \(-0.904865\pi\) |
−0.0152839 | + | 0.999883i | \(0.504865\pi\) | |||||||
\(492\) | −5.08509 | − | 1.65224i | −0.229253 | − | 0.0744890i | ||||
\(493\) | 13.5768i | 0.611469i | ||||||||
\(494\) | 8.98884 | − | 27.6648i | 0.404427 | − | 1.24470i | ||||
\(495\) | 10.0874 | + | 5.67277i | 0.453397 | + | 0.254972i | ||||
\(496\) | 1.19890 | + | 3.68983i | 0.0538321 | + | 0.165678i | ||||
\(497\) | 12.4779 | − | 4.05432i | 0.559711 | − | 0.181861i | ||||
\(498\) | 11.5771 | − | 15.9345i | 0.518780 | − | 0.714040i | ||||
\(499\) | −29.5129 | −1.32118 | −0.660590 | − | 0.750747i | \(-0.729694\pi\) | ||||
−0.660590 | + | 0.750747i | \(0.729694\pi\) | |||||||
\(500\) | −35.5747 | + | 12.9096i | −1.59095 | + | 0.577333i | ||||
\(501\) | 16.6366 | 0.743267 | ||||||||
\(502\) | −0.407814 | + | 0.561308i | −0.0182016 | + | 0.0250524i | ||||
\(503\) | 24.6477 | − | 8.00852i | 1.09899 | − | 0.357082i | 0.297274 | − | 0.954792i | \(-0.403923\pi\) |
0.801713 | + | 0.597710i | \(0.203923\pi\) | |||||||
\(504\) | −0.993115 | − | 3.05649i | −0.0442369 | − | 0.136147i | ||||
\(505\) | 10.6048 | + | 5.96369i | 0.471906 | + | 0.265381i | ||||
\(506\) | −3.49491 | + | 10.7562i | −0.155367 | + | 0.478172i | ||||
\(507\) | − | 6.95375i | − | 0.308827i | ||||||
\(508\) | 26.9264 | + | 8.74892i | 1.19467 | + | 0.388170i | ||||
\(509\) | 2.74657 | − | 1.99550i | 0.121740 | − | 0.0884491i | −0.525249 | − | 0.850948i | \(-0.676028\pi\) |
0.646989 | + | 0.762499i | \(0.276028\pi\) | |||||||
\(510\) | −12.5415 | + | 5.75474i | −0.555345 | + | 0.254824i | ||||
\(511\) | 2.42904 | + | 1.76480i | 0.107454 | + | 0.0780702i | ||||
\(512\) | −4.55228 | − | 6.26568i | −0.201184 | − | 0.276907i | ||||
\(513\) | −1.64945 | − | 2.27027i | −0.0728248 | − | 0.100235i | ||||
\(514\) | 25.9223 | + | 18.8336i | 1.14338 | + | 0.830717i | ||||
\(515\) | −24.4822 | − | 4.91497i | −1.07882 | − | 0.216580i | ||||
\(516\) | −0.000927265 | 0 | 0.000673698i | −4.08206e−5 | 0 | 2.96579e-5i | ||||
\(517\) | −41.6531 | − | 13.5339i | −1.83190 | − | 0.595220i | ||||
\(518\) | 17.3695i | 0.763170i | ||||||||
\(519\) | 0.565278 | − | 1.73975i | 0.0248129 | − | 0.0763664i | ||||
\(520\) | 6.31837 | − | 31.4727i | 0.277079 | − | 1.38017i | ||||
\(521\) | 8.24271 | + | 25.3684i | 0.361119 | + | 1.11141i | 0.952376 | + | 0.304928i | \(0.0986323\pi\) |
−0.591256 | + | 0.806484i | \(0.701368\pi\) | |||||||
\(522\) | −11.2676 | + | 3.66105i | −0.493167 | + | 0.160240i | ||||
\(523\) | −21.2217 | + | 29.2092i | −0.927961 | + | 1.27723i | 0.0326887 | + | 0.999466i | \(0.489593\pi\) |
−0.960650 | + | 0.277763i | \(0.910407\pi\) | |||||||
\(524\) | −67.6383 | −2.95479 | ||||||||
\(525\) | −3.26071 | + | 3.79049i | −0.142309 | + | 0.165430i | ||||
\(526\) | −7.21335 | −0.314517 | ||||||||
\(527\) | 8.81592 | − | 12.1341i | 0.384028 | − | 0.528569i | ||||
\(528\) | −3.38600 | + | 1.10018i | −0.147357 | + | 0.0478791i | ||||
\(529\) | 6.83337 | + | 21.0310i | 0.297103 | + | 0.914390i | ||||
\(530\) | −22.1900 | + | 20.4394i | −0.963874 | + | 0.887831i | ||||
\(531\) | 3.79922 | − | 11.6928i | 0.164872 | − | 0.507425i | ||||
\(532\) | − | 9.49880i | − | 0.411825i | ||||||
\(533\) | −6.71060 | − | 2.18041i | −0.290668 | − | 0.0944438i | ||||
\(534\) | 34.4058 | − | 24.9973i | 1.48889 | − | 1.08174i | ||||
\(535\) | 20.8894 | − | 37.1461i | 0.903129 | − | 1.60596i | ||||
\(536\) | −4.49045 | − | 3.26251i | −0.193958 | − | 0.140919i | ||||
\(537\) | −9.45282 | − | 13.0107i | −0.407919 | − | 0.561453i | ||||
\(538\) | −21.2240 | − | 29.2124i | −0.915033 | − | 1.25944i | ||||
\(539\) | 4.18719 | + | 3.04217i | 0.180355 | + | 0.131036i | ||||
\(540\) | −5.12793 | − | 5.56714i | −0.220671 | − | 0.239572i | ||||
\(541\) | 6.30383 | − | 4.58000i | 0.271023 | − | 0.196910i | −0.443969 | − | 0.896042i | \(-0.646430\pi\) |
0.714992 | + | 0.699132i | \(0.246430\pi\) | |||||||
\(542\) | 34.2634 | + | 11.1329i | 1.47174 | + | 0.478197i | ||||
\(543\) | − | 5.10402i | − | 0.219035i | ||||||
\(544\) | −3.97020 | + | 12.2190i | −0.170221 | + | 0.523886i | ||||
\(545\) | −13.0863 | + | 1.52533i | −0.560556 | + | 0.0653381i | ||||
\(546\) | −3.20320 | − | 9.85845i | −0.137084 | − | 0.421903i | ||||
\(547\) | −24.1224 | + | 7.83784i | −1.03140 | + | 0.335122i | −0.775343 | − | 0.631540i | \(-0.782423\pi\) |
−0.256055 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(548\) | −26.6050 | + | 36.6186i | −1.13651 | + | 1.56427i | ||||
\(549\) | −9.51407 | −0.406051 | ||||||||
\(550\) | 45.5250 | + | 39.1622i | 1.94119 | + | 1.66988i | ||||
\(551\) | −14.3269 | −0.610347 | ||||||||
\(552\) | 1.77883 | − | 2.44835i | 0.0757119 | − | 0.104209i | ||||
\(553\) | 5.63523 | − | 1.83100i | 0.239634 | − | 0.0778619i | ||||
\(554\) | −17.6901 | − | 54.4445i | −0.751580 | − | 2.31312i | ||||
\(555\) | 6.98019 | + | 15.2121i | 0.296293 | + | 0.645719i | ||||
\(556\) | −2.27701 | + | 7.00791i | −0.0965666 | + | 0.297202i | ||||
\(557\) | − | 23.7938i | − | 1.00818i | −0.863652 | − | 0.504088i | \(-0.831829\pi\) | ||
0.863652 | − | 0.504088i | \(-0.168171\pi\) | |||||||
\(558\) | 12.4475 | + | 4.04443i | 0.526943 | + | 0.171214i | ||||
\(559\) | −0.00122368 | 0.000889053i | −5.17560e−5 | 3.76030e-5i | ||||||
\(560\) | −0.178081 | − | 1.52781i | −0.00752530 | − | 0.0645618i | ||||
\(561\) | 11.1349 | + | 8.09000i | 0.470117 | + | 0.341560i | ||||
\(562\) | 24.7731 | + | 34.0972i | 1.04499 | + | 1.43830i | ||||
\(563\) | 6.13365 | + | 8.44224i | 0.258502 | + | 0.355798i | 0.918466 | − | 0.395499i | \(-0.129428\pi\) |
−0.659964 | + | 0.751297i | \(0.729428\pi\) | |||||||
\(564\) | 23.1730 | + | 16.8362i | 0.975760 | + | 0.708931i | ||||
\(565\) | −3.45390 | − | 29.6320i | −0.145307 | − | 1.24663i | ||||
\(566\) | 49.8227 | − | 36.1983i | 2.09421 | − | 1.52153i | ||||
\(567\) | −0.951057 | − | 0.309017i | −0.0399406 | − | 0.0129775i | ||||
\(568\) | 42.1651i | 1.76921i | ||||||||
\(569\) | −11.3054 | + | 34.7944i | −0.473947 | + | 1.45866i | 0.373426 | + | 0.927660i | \(0.378183\pi\) |
−0.847373 | + | 0.530998i | \(0.821817\pi\) | |||||||
\(570\) | −6.07268 | − | 13.2344i | −0.254357 | − | 0.554326i | ||||
\(571\) | −8.14400 | − | 25.0647i | −0.340816 | − | 1.04892i | −0.963786 | − | 0.266678i | \(-0.914074\pi\) |
0.622970 | − | 0.782246i | \(-0.285926\pi\) | |||||||
\(572\) | −74.4275 | + | 24.1830i | −3.11197 | + | 1.01114i | ||||
\(573\) | −15.5976 | + | 21.4682i | −0.651599 | + | 0.896848i | ||||
\(574\) | −3.66549 | −0.152995 | ||||||||
\(575\) | −4.69249 | − | 0.386061i | −0.195690 | − | 0.0160999i | ||||
\(576\) | −12.5870 | −0.524460 | ||||||||
\(577\) | −23.1382 | + | 31.8470i | −0.963254 | + | 1.32581i | −0.0178728 | + | 0.999840i | \(0.505689\pi\) |
−0.945382 | + | 0.325966i | \(0.894311\pi\) | |||||||
\(578\) | 21.9113 | − | 7.11940i | 0.911389 | − | 0.296128i | ||||
\(579\) | 1.58146 | + | 4.86724i | 0.0657233 | + | 0.202276i | ||||
\(580\) | −38.3829 | + | 4.47389i | −1.59376 | + | 0.185768i | ||||
\(581\) | 2.62284 | − | 8.07227i | 0.108814 | − | 0.334894i | ||||
\(582\) | − | 21.2494i | − | 0.880816i | ||||||
\(583\) | 28.6192 | + | 9.29893i | 1.18529 | + | 0.385122i | ||||
\(584\) | −7.80642 | + | 5.67170i | −0.323032 | + | 0.234696i | ||||
\(585\) | −6.76713 | − | 7.34675i | −0.279787 | − | 0.303751i | ||||
\(586\) | 32.2435 | + | 23.4262i | 1.33196 | + | 0.967729i | ||||
\(587\) | 11.9192 | + | 16.4053i | 0.491956 | + | 0.677120i | 0.980747 | − | 0.195281i | \(-0.0625619\pi\) |
−0.488791 | + | 0.872401i | \(0.662562\pi\) | |||||||
\(588\) | −1.98961 | − | 2.73846i | −0.0820502 | − | 0.112932i | ||||
\(589\) | 12.8045 | + | 9.30299i | 0.527599 | + | 0.383323i | ||||
\(590\) | 31.2703 | − | 55.6056i | 1.28738 | − | 2.28925i | ||||
\(591\) | 17.3890 | − | 12.6338i | 0.715287 | − | 0.519687i | ||||
\(592\) | −4.89686 | − | 1.59109i | −0.201260 | − | 0.0653932i | ||||
\(593\) | − | 19.2384i | − | 0.790026i | −0.918676 | − | 0.395013i | \(-0.870740\pi\) | ||
0.918676 | − | 0.395013i | \(-0.129260\pi\) | |||||||
\(594\) | −3.71140 | + | 11.4225i | −0.152281 | + | 0.468671i | ||||
\(595\) | −4.37368 | + | 4.02863i | −0.179303 | + | 0.165158i | ||||
\(596\) | −14.8428 | − | 45.6816i | −0.607986 | − | 1.87119i | ||||
\(597\) | −12.9024 | + | 4.19223i | −0.528059 | + | 0.171577i | ||||
\(598\) | 5.73745 | − | 7.89692i | 0.234622 | − | 0.322929i | ||||
\(599\) | −19.3811 | −0.791891 | −0.395945 | − | 0.918274i | \(-0.629583\pi\) | ||||
−0.395945 | + | 0.918274i | \(0.629583\pi\) | |||||||
\(600\) | −8.34734 | − | 13.7307i | −0.340779 | − | 0.560555i | ||||
\(601\) | −7.35381 | −0.299968 | −0.149984 | − | 0.988688i | \(-0.547922\pi\) | ||||
−0.149984 | + | 0.988688i | \(0.547922\pi\) | |||||||
\(602\) | −0.000461855 | 0 | 0.000635689i | −1.88238e−5 | 0 | 2.59087e-5i | ||||
\(603\) | −1.64256 | + | 0.533701i | −0.0668903 | + | 0.0217340i | ||||
\(604\) | −1.98864 | − | 6.12040i | −0.0809165 | − | 0.249035i | ||||
\(605\) | 6.94842 | − | 34.6111i | 0.282493 | − | 1.40714i | ||||
\(606\) | −3.90173 | + | 12.0083i | −0.158497 | + | 0.487803i | ||||
\(607\) | 16.9661i | 0.688633i | 0.938854 | + | 0.344317i | \(0.111889\pi\) | ||||
−0.938854 | + | 0.344317i | \(0.888111\pi\) | |||||||
\(608\) | −12.8941 | − | 4.18954i | −0.522924 | − | 0.169908i | ||||
\(609\) | −4.13039 | + | 3.00090i | −0.167372 | + | 0.121603i | ||||
\(610\) | −48.4018 | − | 9.71699i | −1.95973 | − | 0.393430i | ||||
\(611\) | 30.5806 | + | 22.2181i | 1.23716 | + | 0.898847i | ||||
\(612\) | −5.29094 | − | 7.28235i | −0.213873 | − | 0.294372i | ||||
\(613\) | −4.93803 | − | 6.79661i | −0.199445 | − | 0.274513i | 0.697566 | − | 0.716520i | \(-0.254266\pi\) |
−0.897011 | + | 0.442008i | \(0.854266\pi\) | |||||||
\(614\) | −1.96923 | − | 1.43073i | −0.0794715 | − | 0.0577394i | ||||
\(615\) | −3.21023 | + | 1.47304i | −0.129449 | + | 0.0593986i | ||||
\(616\) | −13.4568 | + | 9.77690i | −0.542188 | + | 0.393923i | ||||
\(617\) | −7.23935 | − | 2.35221i | −0.291445 | − | 0.0946963i | 0.159645 | − | 0.987174i | \(-0.448965\pi\) |
−0.451091 | + | 0.892478i | \(0.648965\pi\) | |||||||
\(618\) | − | 25.9141i | − | 1.04242i | ||||||
\(619\) | 2.02277 | − | 6.22546i | 0.0813022 | − | 0.250222i | −0.902140 | − | 0.431443i | \(-0.858005\pi\) |
0.983443 | + | 0.181220i | \(0.0580047\pi\) | |||||||
\(620\) | 37.2092 | + | 20.9249i | 1.49436 | + | 0.840366i | ||||
\(621\) | −0.290991 | − | 0.895580i | −0.0116771 | − | 0.0359384i | ||||
\(622\) | −11.2480 | + | 3.65470i | −0.451004 | + | 0.146540i | ||||
\(623\) | 10.7722 | − | 14.8266i | 0.431578 | − | 0.594016i | ||||
\(624\) | 3.07275 | 0.123008 | ||||||||
\(625\) | −11.5075 | + | 22.1941i | −0.460301 | + | 0.887763i | ||||
\(626\) | −58.0632 | −2.32067 | ||||||||
\(627\) | −8.53696 | + | 11.7501i | −0.340933 | + | 0.469254i | ||||
\(628\) | 59.7323 | − | 19.4082i | 2.38358 | − | 0.774472i | ||||
\(629\) | 6.15096 | + | 18.9307i | 0.245255 | + | 0.754817i | ||||
\(630\) | −4.52279 | − | 2.54343i | −0.180192 | − | 0.101333i | ||||
\(631\) | 3.76901 | − | 11.5998i | 0.150042 | − | 0.461782i | −0.847583 | − | 0.530663i | \(-0.821943\pi\) |
0.997625 | + | 0.0688813i | \(0.0219430\pi\) | |||||||
\(632\) | 19.0424i | 0.757468i | ||||||||
\(633\) | −2.91686 | − | 0.947746i | −0.115935 | − | 0.0376695i | ||||
\(634\) | −59.4988 | + | 43.2284i | −2.36300 | + | 1.71682i | ||||
\(635\) | 16.9987 | − | 7.79998i | 0.674573 | − | 0.309533i | ||||
\(636\) | −15.9218 | − | 11.5679i | −0.631341 | − | 0.458696i | ||||
\(637\) | −2.62561 | − | 3.61385i | −0.104031 | − | 0.143186i | ||||
\(638\) | 36.0419 | + | 49.6074i | 1.42691 | + | 1.96397i | ||||
\(639\) | 10.6144 | + | 7.71178i | 0.419898 | + | 0.305073i | ||||
\(640\) | −42.8516 | − | 8.60275i | −1.69386 | − | 0.340054i | ||||
\(641\) | 28.1749 | − | 20.4703i | 1.11284 | − | 0.808528i | 0.129734 | − | 0.991549i | \(-0.458588\pi\) |
0.983109 | + | 0.183021i | \(0.0585876\pi\) | |||||||
\(642\) | 42.0623 | + | 13.6669i | 1.66007 | + | 0.539388i | ||||
\(643\) | − | 35.4073i | − | 1.39633i | −0.715937 | − | 0.698165i | \(-0.754000\pi\) | ||
0.715937 | − | 0.698165i | \(-0.246000\pi\) | |||||||
\(644\) | 0.984985 | − | 3.03147i | 0.0388139 | − | 0.119457i | ||||
\(645\) | −0.000149030 | 0 | 0.000742338i | −5.86803e−6 | 0 | 2.92295e-5i | ||||
\(646\) | −5.35126 | − | 16.4695i | −0.210542 | − | 0.647983i | ||||
\(647\) | 7.56790 | − | 2.45896i | 0.297525 | − | 0.0966717i | −0.156451 | − | 0.987686i | \(-0.550005\pi\) |
0.453976 | + | 0.891014i | \(0.350005\pi\) | |||||||
\(648\) | 1.88902 | − | 2.60001i | 0.0742076 | − | 0.102138i | ||||
\(649\) | −63.6323 | −2.49779 | ||||||||
\(650\) | −26.9236 | − | 44.2872i | −1.05603 | − | 1.73709i | ||||
\(651\) | 5.64007 | 0.221052 | ||||||||
\(652\) | −18.4599 | + | 25.4079i | −0.722947 | + | 0.995052i | ||||
\(653\) | −22.3450 | + | 7.26033i | −0.874427 | + | 0.284119i | −0.711642 | − | 0.702543i | \(-0.752048\pi\) |
−0.162786 | + | 0.986661i | \(0.552048\pi\) | |||||||
\(654\) | −4.22508 | − | 13.0034i | −0.165214 | − | 0.508475i | ||||
\(655\) | −32.8644 | + | 30.2716i | −1.28412 | + | 1.18281i | ||||
\(656\) | 0.335769 | − | 1.03339i | 0.0131096 | − | 0.0403471i | ||||
\(657\) | 3.00246i | 0.117137i | ||||||||
\(658\) | 18.6755 | + | 6.06803i | 0.728046 | + | 0.236556i | ||||
\(659\) | −31.7548 | + | 23.0712i | −1.23699 | + | 0.898726i | −0.997394 | − | 0.0721462i | \(-0.977015\pi\) |
−0.239597 | + | 0.970873i | \(0.577015\pi\) | |||||||
\(660\) | −19.2019 | + | 34.1453i | −0.747434 | + | 1.32910i | ||||
\(661\) | 7.41041 | + | 5.38398i | 0.288231 | + | 0.209412i | 0.722500 | − | 0.691371i | \(-0.242993\pi\) |
−0.434268 | + | 0.900784i | \(0.642993\pi\) | |||||||
\(662\) | −35.5083 | − | 48.8730i | −1.38007 | − | 1.89950i | ||||
\(663\) | −6.98225 | − | 9.61024i | −0.271168 | − | 0.373231i | ||||
\(664\) | 22.0681 | + | 16.0334i | 0.856407 | + | 0.622216i | ||||
\(665\) | −4.25120 | − | 4.61532i | −0.164855 | − | 0.178974i | ||||
\(666\) | −14.0522 | + | 10.2095i | −0.544511 | + | 0.395610i | ||||
\(667\) | −4.57233 | − | 1.48564i | −0.177041 | − | 0.0575242i | ||||
\(668\) | 56.3136i | 2.17884i | ||||||||
\(669\) | −1.79077 | + | 5.51143i | −0.0692353 | + | 0.213084i | ||||
\(670\) | −8.90143 | + | 1.03755i | −0.343892 | + | 0.0400839i | ||||
\(671\) | 15.2165 | + | 46.8315i | 0.587425 | + | 1.80791i | ||||
\(672\) | −4.59485 | + | 1.49296i | −0.177250 | + | 0.0575921i | ||||
\(673\) | 12.0813 | − | 16.6284i | 0.465698 | − | 0.640979i | −0.509980 | − | 0.860186i | \(-0.670347\pi\) |
0.975678 | + | 0.219207i | \(0.0703471\pi\) | |||||||
\(674\) | −51.5705 | −1.98642 | ||||||||
\(675\) | −4.98316 | − | 0.409976i | −0.191802 | − | 0.0157800i | ||||
\(676\) | 23.5380 | 0.905306 | ||||||||
\(677\) | 13.0856 | − | 18.0108i | 0.502921 | − | 0.692212i | −0.479784 | − | 0.877386i | \(-0.659285\pi\) |
0.982706 | + | 0.185175i | \(0.0592851\pi\) | |||||||
\(678\) | 29.4444 | − | 9.56708i | 1.13081 | − | 0.367421i | ||||
\(679\) | −2.82969 | − | 8.70890i | −0.108594 | − | 0.334217i | ||||
\(680\) | −7.96990 | − | 17.3690i | −0.305632 | − | 0.666072i | ||||
\(681\) | 3.56051 | − | 10.9581i | 0.136439 | − | 0.419916i | ||||
\(682\) | − | 67.7392i | − | 2.59387i | ||||||
\(683\) | −17.0845 | − | 5.55108i | −0.653718 | − | 0.212406i | −0.0366655 | − | 0.999328i | \(-0.511674\pi\) |
−0.617053 | + | 0.786922i | \(0.711674\pi\) | |||||||
\(684\) | 7.68469 | − | 5.58325i | 0.293831 | − | 0.213481i | ||||
\(685\) | 3.46176 | + | 29.6995i | 0.132267 | + | 1.13476i | ||||
\(686\) | −1.87736 | − | 1.36398i | −0.0716779 | − | 0.0520771i | ||||
\(687\) | −4.87223 | − | 6.70605i | −0.185887 | − | 0.255852i | ||||
\(688\) | −0.000136909 | 0 | 0.000188438i | −5.21959e−6 | 0 | 7.18415e-6i | ||||
\(689\) | −21.0114 | − | 15.2657i | −0.800472 | − | 0.581577i | ||||
\(690\) | −0.565705 | − | 4.85336i | −0.0215360 | − | 0.184764i | ||||
\(691\) | 13.5245 | − | 9.82614i | 0.514497 | − | 0.373804i | −0.300030 | − | 0.953930i | \(-0.596997\pi\) |
0.814527 | + | 0.580126i | \(0.196997\pi\) | |||||||
\(692\) | 5.88892 | + | 1.91343i | 0.223863 | + | 0.0727375i | ||||
\(693\) | 5.17565i | 0.196607i | ||||||||
\(694\) | 5.16921 | − | 15.9092i | 0.196220 | − | 0.603904i | ||||
\(695\) | 2.03004 | + | 4.42411i | 0.0770037 | + | 0.167816i | ||||
\(696\) | −5.07029 | − | 15.6048i | −0.192189 | − | 0.591497i | ||||
\(697\) | −3.99497 | + | 1.29804i | −0.151320 | + | 0.0491669i | ||||
\(698\) | −20.1770 | + | 27.7712i | −0.763710 | + | 1.05116i | ||||
\(699\) | 27.7340 | 1.04900 | ||||||||
\(700\) | −12.8305 | − | 11.0373i | −0.484948 | − | 0.417169i | ||||
\(701\) | 6.05281 | 0.228611 | 0.114306 | − | 0.993446i | \(-0.463536\pi\) | ||||
0.114306 | + | 0.993446i | \(0.463536\pi\) | |||||||
\(702\) | 6.09286 | − | 8.38610i | 0.229960 | − | 0.316513i | ||||
\(703\) | −19.9766 | + | 6.49079i | −0.753432 | + | 0.244805i | ||||
\(704\) | 20.1313 | + | 61.9577i | 0.758726 | + | 2.33512i | ||||
\(705\) | 18.7945 | − | 2.19067i | 0.707841 | − | 0.0825056i | ||||
\(706\) | −0.718897 | + | 2.21254i | −0.0270560 | + | 0.0832699i | ||||
\(707\) | 5.44108i | 0.204633i | ||||||||
\(708\) | 39.5793 | + | 12.8601i | 1.48748 | + | 0.483312i | ||||
\(709\) | −1.82096 | + | 1.32300i | −0.0683875 | + | 0.0496864i | −0.621454 | − | 0.783451i | \(-0.713458\pi\) |
0.553066 | + | 0.833137i | \(0.313458\pi\) | |||||||
\(710\) | 46.1231 | + | 50.0736i | 1.73097 | + | 1.87923i | ||||
\(711\) | 4.79361 | + | 3.48276i | 0.179775 | + | 0.130614i | ||||
\(712\) | 34.6195 | + | 47.6496i | 1.29742 | + | 1.78574i | ||||
\(713\) | 3.12177 | + | 4.29675i | 0.116911 | + | 0.160915i | ||||
\(714\) | −4.99243 | − | 3.62721i | −0.186837 | − | 0.135745i | ||||
\(715\) | −25.3401 | + | 45.0603i | −0.947664 | + | 1.68516i | ||||
\(716\) | 44.0403 | − | 31.9971i | 1.64586 | − | 1.19579i | ||||
\(717\) | 14.6210 | + | 4.75066i | 0.546032 | + | 0.177417i | ||||
\(718\) | 45.0158i | 1.67998i | ||||||||
\(719\) | 12.4551 | − | 38.3330i | 0.464499 | − | 1.42958i | −0.395114 | − | 0.918632i | \(-0.629295\pi\) |
0.859612 | − | 0.510947i | \(-0.170705\pi\) | |||||||
\(720\) | 1.13135 | − | 1.04210i | 0.0421630 | − | 0.0388366i | ||||
\(721\) | −3.45087 | − | 10.6207i | −0.128517 | − | 0.395534i | ||||
\(722\) | −24.5530 | + | 7.97776i | −0.913769 | + | 0.296902i | ||||
\(723\) | 11.7735 | − | 16.2048i | 0.437860 | − | 0.602662i | ||||
\(724\) | 17.2768 | 0.642085 | ||||||||
\(725\) | −16.6473 | + | 19.3521i | −0.618267 | + | 0.718719i | ||||
\(726\) | 36.6354 | 1.35967 | ||||||||
\(727\) | 15.6801 | − | 21.5818i | 0.581544 | − | 0.800426i | −0.412320 | − | 0.911039i | \(-0.635281\pi\) |
0.993864 | + | 0.110613i | \(0.0352813\pi\) | |||||||
\(728\) | 13.6532 | − | 4.43621i | 0.506023 | − | 0.164417i | ||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | −3.06650 | + | 15.2747i | −0.113496 | + | 0.565341i | ||||
\(731\) | −0.000278255 | 0 | 0.000856382i | −1.02916e−5 | 0 | 3.16744e-5i | ||||
\(732\) | − | 32.2044i | − | 1.19031i | ||||||
\(733\) | 4.83856 | + | 1.57214i | 0.178716 | + | 0.0580684i | 0.397008 | − | 0.917815i | \(-0.370048\pi\) |
−0.218292 | + | 0.975884i | \(0.570048\pi\) | |||||||
\(734\) | 14.6744 | − | 10.6616i | 0.541643 | − | 0.393527i | ||||
\(735\) | −2.19233 | − | 0.440125i | −0.0808651 | − | 0.0162342i | ||||
\(736\) | −3.68062 | − | 2.67412i | −0.135669 | − | 0.0985695i | ||||
\(737\) | 5.25411 | + | 7.23166i | 0.193538 | + | 0.266382i | ||||
\(738\) | −2.15452 | − | 2.96545i | −0.0793091 | − | 0.109160i | ||||
\(739\) | 13.5298 | + | 9.82996i | 0.497701 | + | 0.361601i | 0.808138 | − | 0.588993i | \(-0.200475\pi\) |
−0.310437 | + | 0.950594i | \(0.600475\pi\) | |||||||
\(740\) | −51.4919 | + | 23.6275i | −1.89288 | + | 0.868563i | ||||
\(741\) | 10.1412 | − | 7.36801i | 0.372546 | − | 0.270671i | ||||
\(742\) | −12.8316 | − | 4.16925i | −0.471064 | − | 0.153058i | ||||
\(743\) | 40.3290i | 1.47953i | 0.672867 | + | 0.739764i | \(0.265063\pi\) | ||||
−0.672867 | + | 0.739764i | \(0.734937\pi\) | |||||||
\(744\) | −5.60124 | + | 17.2388i | −0.205351 | + | 0.632007i | ||||
\(745\) | −27.6568 | − | 15.5530i | −1.01327 | − | 0.569819i | ||||
\(746\) | 8.92720 | + | 27.4751i | 0.326848 | + | 1.00593i | ||||
\(747\) | 8.07227 | − | 2.62284i | 0.295349 | − | 0.0959647i | ||||
\(748\) | −27.3841 | + | 37.6909i | −1.00126 | + | 1.37812i | ||||
\(749\) | 19.0588 | 0.696395 | ||||||||
\(750\) | −24.9326 | − | 7.17516i | −0.910409 | − | 0.262000i | ||||
\(751\) | −18.9864 | −0.692822 | −0.346411 | − | 0.938083i | \(-0.612600\pi\) | ||||
−0.346411 | + | 0.938083i | \(0.612600\pi\) | |||||||
\(752\) | −3.42144 | + | 4.70921i | −0.124767 | + | 0.171727i | ||||
\(753\) | −0.284354 | + | 0.0923923i | −0.0103624 | + | 0.00336696i | ||||
\(754\) | −16.3538 | − | 50.3317i | −0.595569 | − | 1.83297i | ||||
\(755\) | −3.70544 | − | 2.08379i | −0.134855 | − | 0.0758368i | ||||
\(756\) | 1.04600 | − | 3.21926i | 0.0380427 | − | 0.117083i | ||||
\(757\) | 25.6342i | 0.931690i | 0.884866 | + | 0.465845i | \(0.154250\pi\) | ||||
−0.884866 | + | 0.465845i | \(0.845750\pi\) | |||||||
\(758\) | 76.9923 | + | 25.0163i | 2.79648 | + | 0.908633i | ||||
\(759\) | −3.94295 | + | 2.86472i | −0.143120 | + | 0.103983i | ||||
\(760\) | 18.3286 | − | 8.41023i | 0.664849 | − | 0.305071i | ||||
\(761\) | 2.57348 | + | 1.86974i | 0.0932886 | + | 0.0677782i | 0.633452 | − | 0.773782i | \(-0.281637\pi\) |
−0.540163 | + | 0.841560i | \(0.681637\pi\) | |||||||
\(762\) | 11.4086 | + | 15.7025i | 0.413289 | + | 0.568843i | ||||
\(763\) | −3.46323 | − | 4.76672i | −0.125377 | − | 0.172567i | ||||
\(764\) | −72.6684 | − | 52.7967i | −2.62905 | − | 1.91012i | ||||
\(765\) | −5.83001 | − | 1.17042i | −0.210785 | − | 0.0423165i | ||||
\(766\) | 19.7477 | − | 14.3476i | 0.713514 | − | 0.518398i | ||||
\(767\) | 52.2314 | + | 16.9710i | 1.88596 | + | 0.612787i | ||||
\(768\) | − | 20.1837i | − | 0.728316i | ||||||
\(769\) | −13.3440 | + | 41.0687i | −0.481198 | + | 1.48098i | 0.356215 | + | 0.934404i | \(0.384067\pi\) |
−0.837413 | + | 0.546571i | \(0.815933\pi\) | |||||||
\(770\) | −5.28604 | + | 26.3306i | −0.190496 | + | 0.948888i | ||||
\(771\) | 4.26686 | + | 13.1320i | 0.153667 | + | 0.472939i | ||||
\(772\) | −16.4753 | + | 5.35314i | −0.592958 | + | 0.192664i | ||||
\(773\) | 5.40026 | − | 7.43283i | 0.194234 | − | 0.267340i | −0.700781 | − | 0.713377i | \(-0.747165\pi\) |
0.895015 | + | 0.446037i | \(0.147165\pi\) | |||||||
\(774\) | −0.000785754 | 0 | −2.82434e−5 | 0 | ||||||
\(775\) | 27.4444 | − | 6.48592i | 0.985831 | − | 0.232981i | ||||
\(776\) | 29.4289 | 1.05644 | ||||||||
\(777\) | −4.39962 | + | 6.05555i | −0.157835 | + | 0.217242i | ||||
\(778\) | −57.0247 | + | 18.5284i | −2.04443 | + | 0.664277i | ||||
\(779\) | −1.36976 | − | 4.21568i | −0.0490767 | − | 0.151043i | ||||
\(780\) | 24.8682 | − | 22.9063i | 0.890425 | − | 0.820176i | ||||
\(781\) | 20.9838 | − | 64.5814i | 0.750859 | − | 2.31091i | ||||
\(782\) | − | 5.81102i | − | 0.207802i | ||||||
\(783\) | −4.85556 | − | 1.57767i | −0.173524 | − | 0.0563813i | ||||
\(784\) | 0.556510 | − | 0.404328i | 0.0198753 | − | 0.0144403i | ||||
\(785\) | 20.3368 | − | 36.1634i | 0.725853 | − | 1.29073i | ||||
\(786\) | −37.5138 | − | 27.2554i | −1.33807 | − | 0.972166i | ||||
\(787\) | 4.70018 | + | 6.46925i | 0.167543 | + | 0.230604i | 0.884530 | − | 0.466483i | \(-0.154479\pi\) |
−0.716987 | + | 0.697087i | \(0.754479\pi\) | |||||||
\(788\) | 42.7646 | + | 58.8605i | 1.52343 | + | 2.09682i | ||||
\(789\) | −2.51481 | − | 1.82712i | −0.0895295 | − | 0.0650470i | ||||
\(790\) | 20.8299 | + | 22.6140i | 0.741096 | + | 0.804571i | ||||
\(791\) | 10.7936 | − | 7.84198i | 0.383775 | − | 0.278829i | ||||
\(792\) | −15.8194 | − | 5.14002i | −0.562116 | − | 0.182643i | ||||
\(793\) | − | 42.4990i | − | 1.50918i | ||||||
\(794\) | −23.2709 | + | 71.6204i | −0.825853 | + | 2.54171i | ||||
\(795\) | −12.9134 | + | 1.50518i | −0.457991 | + | 0.0533832i | ||||
\(796\) | −14.1904 | − | 43.6736i | −0.502966 | − | 1.54797i | ||||
\(797\) | 40.1674 | − | 13.0512i | 1.42280 | − | 0.462297i | 0.506311 | − | 0.862351i | \(-0.331009\pi\) |
0.916491 | + | 0.400054i | \(0.131009\pi\) | |||||||
\(798\) | 3.82761 | − | 5.26825i | 0.135496 | − | 0.186494i | ||||
\(799\) | 22.5030 | 0.796098 | ||||||||
\(800\) | −20.6415 | + | 12.5486i | −0.729787 | + | 0.443661i | ||||
\(801\) | 18.3267 | 0.647542 | ||||||||
\(802\) | 27.5332 | − | 37.8962i | 0.972232 | − | 1.33816i | ||||
\(803\) | 14.7791 | − | 4.80203i | 0.521544 | − | 0.169460i | ||||
\(804\) | −1.80654 | − | 5.55995i | −0.0637117 | − | 0.196084i | ||||
\(805\) | −0.878151 | − | 1.91378i | −0.0309508 | − | 0.0674518i | ||||
\(806\) | −18.0663 | + | 55.6024i | −0.636358 | + | 1.95851i | ||||
\(807\) | − | 15.5604i | − | 0.547750i | ||||||
\(808\) | −16.6306 | − | 5.40362i | −0.585063 | − | 0.190099i | ||||
\(809\) | 2.89419 | − | 2.10275i | 0.101754 | − | 0.0739287i | −0.535745 | − | 0.844380i | \(-0.679969\pi\) |
0.637499 | + | 0.770451i | \(0.279969\pi\) | |||||||
\(810\) | −0.600748 | − | 5.15400i | −0.0211081 | − | 0.181093i | ||||
\(811\) | 45.7545 | + | 33.2426i | 1.60666 | + | 1.16731i | 0.872908 | + | 0.487885i | \(0.162231\pi\) |
0.733750 | + | 0.679420i | \(0.237769\pi\) | |||||||
\(812\) | −10.1578 | − | 13.9811i | −0.356470 | − | 0.490639i | ||||
\(813\) | 9.12542 | + | 12.5601i | 0.320043 | + | 0.440501i | ||||
\(814\) | 72.7292 | + | 52.8409i | 2.54916 | + | 1.85207i | ||||
\(815\) | 2.40195 | + | 20.6071i | 0.0841368 | + | 0.721835i | ||||
\(816\) | 1.47992 | − | 1.07522i | 0.0518074 | − | 0.0376403i | ||||
\(817\) | −0.000903696 | 0 | 0.000293629i | −3.16163e−5 | 0 | 1.02728e-5i | ||||
\(818\) | 8.52400i | 0.298035i | ||||||||
\(819\) | 1.38037 | − | 4.24833i | 0.0482339 | − | 0.148449i | ||||
\(820\) | −4.98613 | − | 10.8664i | −0.174123 | − | 0.379471i | ||||
\(821\) | −3.72071 | − | 11.4512i | −0.129854 | − | 0.399649i | 0.864900 | − | 0.501944i | \(-0.167381\pi\) |
−0.994754 | + | 0.102295i | \(0.967381\pi\) | |||||||
\(822\) | −29.5115 | + | 9.58886i | −1.02933 | + | 0.334450i | ||||
\(823\) | 13.1583 | − | 18.1108i | 0.458668 | − | 0.631302i | −0.515564 | − | 0.856851i | \(-0.672417\pi\) |
0.974232 | + | 0.225549i | \(0.0724175\pi\) | |||||||
\(824\) | 35.8891 | 1.25026 | ||||||||
\(825\) | 5.95186 | + | 25.1845i | 0.207217 | + | 0.876813i | ||||
\(826\) | 28.5301 | 0.992688 | ||||||||
\(827\) | −9.39440 | + | 12.9303i | −0.326675 | + | 0.449630i | −0.940491 | − | 0.339820i | \(-0.889634\pi\) |
0.613815 | + | 0.789450i | \(0.289634\pi\) | |||||||
\(828\) | 3.03147 | − | 0.984985i | 0.105351 | − | 0.0342306i | ||||
\(829\) | 0.0162211 | + | 0.0499233i | 0.000563381 | + | 0.00173391i | 0.951338 | − | 0.308150i | \(-0.0997098\pi\) |
−0.950774 | + | 0.309884i | \(0.899710\pi\) | |||||||
\(830\) | 43.7456 | − | 5.09897i | 1.51843 | − | 0.176988i | ||||
\(831\) | 7.62325 | − | 23.4619i | 0.264447 | − | 0.813886i | ||||
\(832\) | − | 56.2259i | − | 1.94928i | ||||||
\(833\) | −2.52913 | − | 0.821764i | −0.0876291 | − | 0.0284724i | ||||
\(834\) | −4.08677 | + | 2.96921i | −0.141513 | + | 0.102815i | ||||
\(835\) | 25.2032 | + | 27.3619i | 0.872193 | + | 0.946897i | ||||
\(836\) | −39.7733 | − | 28.8970i | −1.37559 | − | 0.999423i | ||||
\(837\) | 3.31515 | + | 4.56291i | 0.114588 | + | 0.157717i | ||||
\(838\) | −37.2974 | − | 51.3355i | −1.28842 | − | 1.77335i | ||||
\(839\) | −1.41909 | − | 1.03103i | −0.0489925 | − | 0.0355951i | 0.563019 | − | 0.826444i | \(-0.309640\pi\) |
−0.612012 | + | 0.790848i | \(0.709640\pi\) | |||||||
\(840\) | 3.52247 | − | 6.26374i | 0.121537 | − | 0.216119i | ||||
\(841\) | 2.37404 | − | 1.72484i | 0.0818635 | − | 0.0594773i | ||||
\(842\) | 58.6624 | + | 19.0606i | 2.02164 | + | 0.656871i | ||||
\(843\) | 18.1623i | 0.625543i | ||||||||
\(844\) | 3.20805 | − | 9.87337i | 0.110426 | − | 0.339855i | ||||
\(845\) | 11.4367 | − | 10.5344i | 0.393436 | − | 0.362396i | ||||
\(846\) | 6.06803 | + | 18.6755i | 0.208623 | + | 0.642076i | ||||
\(847\) | 15.0147 | − | 4.87857i | 0.515911 | − | 0.167630i | ||||
\(848\) | 2.35082 | − | 3.23563i | 0.0807275 | − | 0.111112i | ||||
\(849\) | 26.5387 | 0.910807 | ||||||||
\(850\) | −28.4642 | − | 11.9087i | −0.976313 | − | 0.408466i | ||||
\(851\) | −7.04846 | −0.241618 | ||||||||
\(852\) | −26.1038 | + | 35.9288i | −0.894303 | + | 1.23090i | ||||
\(853\) | −34.0995 | + | 11.0796i | −1.16754 | + | 0.379358i | −0.827726 | − | 0.561133i | \(-0.810366\pi\) |
−0.339819 | + | 0.940491i | \(0.610366\pi\) | |||||||
\(854\) | −6.82242 | − | 20.9973i | −0.233458 | − | 0.718511i | ||||
\(855\) | 1.23508 | − | 6.15211i | 0.0422388 | − | 0.210398i | ||||
\(856\) | −18.9276 | + | 58.2533i | −0.646933 | + | 1.99106i | ||||
\(857\) | − | 38.5172i | − | 1.31572i | −0.753140 | − | 0.657861i | \(-0.771462\pi\) | ||
0.753140 | − | 0.657861i | \(-0.228538\pi\) | |||||||
\(858\) | −51.0239 | − | 16.5787i | −1.74193 | − | 0.565987i | ||||
\(859\) | −16.3219 | + | 11.8585i | −0.556895 | + | 0.404608i | −0.830321 | − | 0.557285i | \(-0.811843\pi\) |
0.273426 | + | 0.961893i | \(0.411843\pi\) | |||||||
\(860\) | −0.00251276 | 0.000504454i | −8.56845e−5 | 1.72018e-5i | ||||||
\(861\) | −1.27791 | − | 0.928456i | −0.0435510 | − | 0.0316417i | ||||
\(862\) | 13.4313 | + | 18.4866i | 0.457472 | + | 0.629656i | ||||
\(863\) | 14.2071 | + | 19.5544i | 0.483614 | + | 0.665638i | 0.979194 | − | 0.202924i | \(-0.0650445\pi\) |
−0.495580 | + | 0.868562i | \(0.665045\pi\) | |||||||
\(864\) | −3.90861 | − | 2.83977i | −0.132974 | − | 0.0966111i | ||||
\(865\) | 3.71769 | − | 1.70589i | 0.126405 | − | 0.0580020i | ||||
\(866\) | −67.0088 | + | 48.6848i | −2.27705 | + | 1.65438i | ||||
\(867\) | 9.44229 | + | 3.06799i | 0.320677 | + | 0.104194i | ||||
\(868\) | 19.0912i | 0.647999i | ||||||||
\(869\) | 9.47661 | − | 29.1660i | 0.321472 | − | 0.989389i | ||||
\(870\) | −23.0908 | − | 12.9853i | −0.782852 | − | 0.440244i | ||||
\(871\) | −2.38402 | − | 7.33726i | −0.0807795 | − | 0.248614i | ||||
\(872\) | 18.0088 | − | 5.85143i | 0.609856 | − | 0.198154i | ||||
\(873\) | 5.38240 | − | 7.40823i | 0.182167 | − | 0.250731i | ||||
\(874\) | 6.13207 | 0.207420 | ||||||||
\(875\) | −11.1739 | + | 0.379484i | −0.377747 | + | 0.0128289i | ||||
\(876\) | −10.1631 | −0.343380 | ||||||||
\(877\) | −5.42670 | + | 7.46921i | −0.183247 | + | 0.252217i | −0.890751 | − | 0.454492i | \(-0.849821\pi\) |
0.707504 | + | 0.706709i | \(0.249821\pi\) | |||||||
\(878\) | 45.9186 | − | 14.9199i | 1.54968 | − | 0.503521i | ||||
\(879\) | 5.30733 | + | 16.3343i | 0.179012 | + | 0.550942i | ||||
\(880\) | −6.93899 | − | 3.90221i | −0.233913 | − | 0.131543i | ||||
\(881\) | −8.22581 | + | 25.3164i | −0.277134 | + | 0.852932i | 0.711512 | + | 0.702674i | \(0.248011\pi\) |
−0.988647 | + | 0.150258i | \(0.951989\pi\) | |||||||
\(882\) | − | 2.32054i | − | 0.0781368i | ||||||
\(883\) | −30.8191 | − | 10.0137i | −1.03714 | − | 0.336988i | −0.259533 | − | 0.965734i | \(-0.583569\pi\) |
−0.777611 | + | 0.628746i | \(0.783569\pi\) | |||||||
\(884\) | 32.5300 | − | 23.6344i | 1.09410 | − | 0.794912i | ||||
\(885\) | 24.9865 | − | 11.4653i | 0.839914 | − | 0.385401i | ||||
\(886\) | −38.8583 | − | 28.2322i | −1.30547 | − | 0.948480i | ||||
\(887\) | −15.5231 | − | 21.3658i | −0.521216 | − | 0.717392i | 0.464544 | − | 0.885550i | \(-0.346218\pi\) |
−0.985760 | + | 0.168158i | \(0.946218\pi\) | |||||||
\(888\) | −14.1394 | − | 19.4613i | −0.474489 | − | 0.653077i | ||||
\(889\) | 6.76675 | + | 4.91633i | 0.226949 | + | 0.164888i | ||||
\(890\) | 93.2351 | + | 18.7176i | 3.12525 | + | 0.627415i | ||||
\(891\) | −4.18719 | + | 3.04217i | −0.140276 | + | 0.101917i | ||||
\(892\) | −18.6558 | − | 6.06164i | −0.624643 | − | 0.202959i | ||||
\(893\) | 23.7462i | 0.794637i | ||||||||
\(894\) | 10.1755 | − | 31.3171i | 0.340321 | − | 1.04740i | ||||
\(895\) | 7.07813 | − | 35.2572i | 0.236596 | − | 1.17852i | ||||
\(896\) | −6.04010 | − | 18.5895i | −0.201786 | − | 0.621032i | ||||
\(897\) | 4.00052 | − | 1.29985i | 0.133573 | − | 0.0434007i | ||||
\(898\) | −27.5266 | + | 37.8871i | −0.918575 | + | 1.26431i | ||||
\(899\) | 28.7950 | 0.960369 | ||||||||
\(900\) | 1.38774 | − | 16.8677i | 0.0462580 | − | 0.562255i | ||||
\(901\) | −15.4614 | −0.515095 | ||||||||
\(902\) | −11.1511 | + | 15.3481i | −0.371290 | + | 0.511037i | ||||
\(903\) | −0.000322035 | 0 | 0.000104636i | −1.07167e−5 | 0 | 3.48205e-6i | ||||
\(904\) | 13.2497 | + | 40.7784i | 0.440679 | + | 1.35627i | ||||
\(905\) | 8.39451 | − | 7.73224i | 0.279043 | − | 0.257028i | ||||
\(906\) | 1.36331 | − | 4.19585i | 0.0452931 | − | 0.139398i | ||||
\(907\) | − | 0.471242i | − | 0.0156473i | −0.999969 | − | 0.00782367i | \(-0.997510\pi\) | ||
0.999969 | − | 0.00782367i | \(-0.00249038\pi\) | |||||||
\(908\) | 37.0925 | + | 12.0521i | 1.23096 | + | 0.399962i | ||||
\(909\) | −4.40192 | + | 3.19818i | −0.146003 | + | 0.106077i | ||||
\(910\) | 11.3614 | − | 20.2031i | 0.376627 | − | 0.669727i | ||||
\(911\) | −23.1612 | − | 16.8276i | −0.767365 | − | 0.557523i | 0.133796 | − | 0.991009i | \(-0.457283\pi\) |
−0.901160 | + | 0.433486i | \(0.857283\pi\) | |||||||
\(912\) | 1.13463 | + | 1.56168i | 0.0375712 | + | 0.0517124i | ||||
\(913\) | −25.8210 | − | 35.5396i | −0.854551 | − | 1.17619i | ||||
\(914\) | 5.20775 | + | 3.78365i | 0.172257 | + | 0.125152i | ||||
\(915\) | −14.4131 | − | 15.6476i | −0.476484 | − | 0.517295i | ||||
\(916\) | 22.6995 | − | 16.4922i | 0.750013 | − | 0.544916i | ||||
\(917\) | −19.0042 | − | 6.17484i | −0.627574 | − | 0.203911i | ||||
\(918\) | − | 6.17098i | − | 0.203673i | ||||||
\(919\) | −15.4330 | + | 47.4979i | −0.509088 | + | 1.56681i | 0.284700 | + | 0.958617i | \(0.408106\pi\) |
−0.793788 | + | 0.608195i | \(0.791894\pi\) | |||||||
\(920\) | 6.72156 | − | 0.783462i | 0.221603 | − | 0.0258300i | ||||
\(921\) | −0.324138 | − | 0.997595i | −0.0106807 | − | 0.0328719i | ||||
\(922\) | −16.0314 | + | 5.20890i | −0.527965 | + | 0.171546i | ||||
\(923\) | −34.4482 | + | 47.4139i | −1.13388 | + | 1.56065i | ||||
\(924\) | −17.5192 | −0.576340 | ||||||||
\(925\) | −14.4446 | + | 34.5255i | −0.474937 | + | 1.13519i | ||||
\(926\) | −43.4431 | −1.42763 | ||||||||
\(927\) | 6.56394 | − | 9.03448i | 0.215588 | − | 0.296731i | ||||
\(928\) | −23.4587 | + | 7.62221i | −0.770071 | + | 0.250211i | ||||
\(929\) | −10.7065 | − | 32.9512i | −0.351268 | − | 1.08109i | −0.958142 | − | 0.286294i | \(-0.907577\pi\) |
0.606874 | − | 0.794798i | \(-0.292423\pi\) | |||||||
\(930\) | 12.2052 | + | 26.5992i | 0.400225 | + | 0.872221i | ||||
\(931\) | 0.867165 | − | 2.66886i | 0.0284202 | − | 0.0874683i | ||||
\(932\) | 93.8776i | 3.07506i | ||||||||
\(933\) | −4.84714 | − | 1.57493i | −0.158688 | − | 0.0515609i | ||||
\(934\) | −44.4638 | + | 32.3049i | −1.45490 | + | 1.05705i | ||||
\(935\) | 3.56314 | + | 30.5692i | 0.116527 | + | 0.999720i | ||||
\(936\) | 11.6141 | + | 8.43817i | 0.379620 | + | 0.275810i | ||||
\(937\) | −1.24560 | − | 1.71442i | −0.0406919 | − | 0.0560076i | 0.788186 | − | 0.615437i | \(-0.211020\pi\) |
−0.828878 | + | 0.559429i | \(0.811020\pi\) | |||||||
\(938\) | −2.35572 | − | 3.24237i | −0.0769170 | − | 0.105867i | ||||
\(939\) | −20.2427 | − | 14.7072i | −0.660595 | − | 0.479951i | ||||
\(940\) | 7.41528 | + | 63.6179i | 0.241860 | + | 2.07499i | ||||
\(941\) | −5.94898 | + | 4.32219i | −0.193931 | + | 0.140899i | −0.680514 | − | 0.732735i | \(-0.738243\pi\) |
0.486582 | + | 0.873635i | \(0.338243\pi\) | |||||||
\(942\) | 40.9496 | + | 13.3053i | 1.33421 | + | 0.433511i | ||||
\(943\) | − | 1.48744i | − | 0.0484378i | ||||||
\(944\) | −2.61343 | + | 8.04330i | −0.0850597 | + | 0.261787i | ||||
\(945\) | −0.932548 | − | 2.03233i | −0.0303358 | − | 0.0661116i | ||||
\(946\) | 0.00125671 | + | 0.00386775i | 4.08591e−5 | + | 0.000125751i | ||||
\(947\) | 12.8267 | − | 4.16766i | 0.416813 | − | 0.135431i | −0.0931000 | − | 0.995657i | \(-0.529678\pi\) |
0.509913 | + | 0.860226i | \(0.329678\pi\) | |||||||
\(948\) | −11.7889 | + | 16.2260i | −0.382886 | + | 0.526997i | ||||
\(949\) | −13.4119 | −0.435368 | ||||||||
\(950\) | 12.5667 | − | 30.0368i | 0.407716 | − | 0.974521i | ||||
\(951\) | −31.6928 | −1.02771 | ||||||||
\(952\) | 5.02343 | − | 6.91416i | 0.162810 | − | 0.224089i | ||||
\(953\) | −32.3471 | + | 10.5102i | −1.04783 | + | 0.340459i | −0.781815 | − | 0.623511i | \(-0.785706\pi\) |
−0.266011 | + | 0.963970i | \(0.585706\pi\) | |||||||
\(954\) | −4.16925 | − | 12.8316i | −0.134984 | − | 0.415439i | ||||
\(955\) | −58.9377 | + | 6.86976i | −1.90718 | + | 0.222300i | ||||
\(956\) | −16.0806 | + | 49.4911i | −0.520085 | + | 1.60066i | ||||
\(957\) | 26.4240i | 0.854166i | ||||||||
\(958\) | −77.1985 | − | 25.0833i | −2.49417 | − | 0.810405i | ||||
\(959\) | −10.8181 | + | 7.85983i | −0.349336 | + | 0.253807i | ||||
\(960\) | −19.0685 | − | 20.7017i | −0.615433 | − | 0.668145i | ||||
\(961\) | −0.655631 | − | 0.476344i | −0.0211494 | − | 0.0153659i | ||||
\(962\) | −45.6055 | − | 62.7706i | −1.47038 | − | 2.02380i | ||||
\(963\) | 11.2025 | + | 15.4189i | 0.360996 | + | 0.496868i | ||||
\(964\) | 54.8520 | + | 39.8523i | 1.76666 | + | 1.28356i | ||||
\(965\) | −5.60927 | + | 9.97454i | −0.180569 | + | 0.321092i | ||||
\(966\) | 1.76785 | − | 1.28442i | 0.0568796 | − | 0.0413255i | ||||
\(967\) | 11.9868 | + | 3.89474i | 0.385468 | + | 0.125246i | 0.495339 | − | 0.868700i | \(-0.335044\pi\) |
−0.109871 | + | 0.993946i | \(0.535044\pi\) | |||||||
\(968\) | 50.7373i | 1.63076i | ||||||||
\(969\) | 2.30604 | − | 7.09725i | 0.0740805 | − | 0.227996i | ||||
\(970\) | 34.9486 | − | 32.1914i | 1.12213 | − | 1.03360i | ||||
\(971\) | 10.9966 | + | 33.8439i | 0.352896 | + | 1.08610i | 0.957219 | + | 0.289364i | \(0.0934437\pi\) |
−0.604323 | + | 0.796739i | \(0.706556\pi\) | |||||||
\(972\) | 3.21926 | − | 1.04600i | 0.103258 | − | 0.0335505i | ||||
\(973\) | −1.27953 | + | 1.76113i | −0.0410199 | + | 0.0564591i | ||||
\(974\) | −4.33534 | −0.138913 | ||||||||
\(975\) | 1.83135 | − | 22.2596i | 0.0586501 | − | 0.712878i | ||||
\(976\) | 6.54457 | 0.209487 | ||||||||
\(977\) | −1.64254 | + | 2.26076i | −0.0525495 | + | 0.0723282i | −0.834483 | − | 0.551034i | \(-0.814234\pi\) |
0.781934 | + | 0.623362i | \(0.214234\pi\) | |||||||
\(978\) | −20.4766 | + | 6.65326i | −0.654771 | + | 0.212748i | ||||
\(979\) | −29.3111 | − | 90.2102i | −0.936786 | − | 2.88313i | ||||
\(980\) | 1.48979 | − | 7.42086i | 0.0475896 | − | 0.237051i | ||||
\(981\) | 1.82073 | − | 5.60362i | 0.0581313 | − | 0.178910i | ||||
\(982\) | − | 61.7122i | − | 1.96932i | ||||||
\(983\) | −30.0303 | − | 9.75743i | −0.957818 | − | 0.311214i | −0.211929 | − | 0.977285i | \(-0.567975\pi\) |
−0.745888 | + | 0.666071i | \(0.767975\pi\) | |||||||
\(984\) | 4.10693 | − | 2.98386i | 0.130924 | − | 0.0951220i | ||||
\(985\) | 47.1218 | + | 9.46002i | 1.50142 | + | 0.301421i | ||||
\(986\) | −25.4886 | − | 18.5185i | −0.811721 | − | 0.589750i | ||||
\(987\) | 4.97387 | + | 6.84594i | 0.158320 | + | 0.217909i | ||||
\(988\) | 24.9402 | + | 34.3272i | 0.793453 | + | 1.09209i | ||||
\(989\) | −0.000257960 | 0 | 0.000187419i | −8.20265e−6 | 0 | 5.95957e-6i | ||||
\(990\) | −24.4089 | + | 11.2002i | −0.775767 | + | 0.355966i | ||||
\(991\) | −1.33266 | + | 0.968235i | −0.0423334 | + | 0.0307570i | −0.608751 | − | 0.793362i | \(-0.708329\pi\) |
0.566417 | + | 0.824119i | \(0.308329\pi\) | |||||||
\(992\) | 25.9153 | + | 8.42039i | 0.822811 | + | 0.267348i | ||||
\(993\) | − | 26.0328i | − | 0.826127i | ||||||
\(994\) | −9.40824 | + | 28.9556i | −0.298411 | + | 0.918415i | ||||
\(995\) | −26.4411 | − | 14.8694i | −0.838239 | − | 0.471391i | ||||
\(996\) | 8.87813 | + | 27.3241i | 0.281314 | + | 0.865796i | ||||
\(997\) | 43.0771 | − | 13.9966i | 1.36427 | − | 0.443277i | 0.466801 | − | 0.884362i | \(-0.345406\pi\) |
0.897465 | + | 0.441086i | \(0.145406\pi\) | |||||||
\(998\) | 40.2551 | − | 55.4064i | 1.27425 | − | 1.75386i | ||||
\(999\) | −7.48508 | −0.236817 |
(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 | 525.2.z.b.484.2 | yes | 72 | |
25.14 | even | 10 | inner | 525.2.z.b.64.2 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.z.b.64.2 | ✓ | 72 | 25.14 | even | 10 | inner | |
525.2.z.b.484.2 | yes | 72 | 1.1 | even | 1 | trivial |