Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(123,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.123");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(58\) |
Relative dimension: | \(29\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 123.16 | ||
Character | \(\chi\) | \(=\) | 349.123 |
Dual form | 349.2.e.a.227.16 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.228167 | − | 0.131732i | 0.161338 | − | 0.0931487i | −0.417157 | − | 0.908834i | \(-0.636973\pi\) |
0.578495 | + | 0.815686i | \(0.303640\pi\) | |||||||
\(3\) | 0.150552 | − | 0.260763i | 0.0869211 | − | 0.150552i | −0.819287 | − | 0.573383i | \(-0.805631\pi\) |
0.906208 | + | 0.422832i | \(0.138964\pi\) | |||||||
\(4\) | −0.965293 | + | 1.67194i | −0.482647 | + | 0.835969i | ||||
\(5\) | 0.807178 | − | 1.39807i | 0.360981 | − | 0.625237i | −0.627142 | − | 0.778905i | \(-0.715775\pi\) |
0.988123 | + | 0.153668i | \(0.0491087\pi\) | |||||||
\(6\) | − | 0.0793300i | − | 0.0323863i | ||||||
\(7\) | 1.23534 | − | 0.713223i | 0.466914 | − | 0.269573i | −0.248033 | − | 0.968752i | \(-0.579784\pi\) |
0.714947 | + | 0.699179i | \(0.246451\pi\) | |||||||
\(8\) | 1.03557i | 0.366129i | ||||||||
\(9\) | 1.45467 | + | 2.51956i | 0.484889 | + | 0.839853i | ||||
\(10\) | − | 0.425325i | − | 0.134499i | ||||||
\(11\) | 2.29478i | 0.691903i | 0.938252 | + | 0.345951i | \(0.112444\pi\) | ||||
−0.938252 | + | 0.345951i | \(0.887556\pi\) | |||||||
\(12\) | 0.290653 | + | 0.503426i | 0.0839043 | + | 0.145327i | ||||
\(13\) | 0.932614 | − | 0.538445i | 0.258661 | − | 0.149338i | −0.365063 | − | 0.930983i | \(-0.618953\pi\) |
0.623723 | + | 0.781645i | \(0.285619\pi\) | |||||||
\(14\) | 0.187909 | − | 0.325468i | 0.0502207 | − | 0.0869849i | ||||
\(15\) | −0.243044 | − | 0.420964i | −0.0627537 | − | 0.108693i | ||||
\(16\) | −1.79417 | − | 3.10759i | −0.448542 | − | 0.776898i | ||||
\(17\) | 6.95728 | 1.68739 | 0.843694 | − | 0.536824i | \(-0.180376\pi\) | ||||
0.843694 | + | 0.536824i | \(0.180376\pi\) | |||||||
\(18\) | 0.663814 | + | 0.383253i | 0.156462 | + | 0.0903336i | ||||
\(19\) | 0.461520 | − | 0.799377i | 0.105880 | − | 0.183390i | −0.808217 | − | 0.588884i | \(-0.799567\pi\) |
0.914097 | + | 0.405495i | \(0.132901\pi\) | |||||||
\(20\) | 1.55833 | + | 2.69910i | 0.348452 | + | 0.603537i | ||||
\(21\) | − | 0.429508i | − | 0.0937263i | ||||||
\(22\) | 0.302296 | + | 0.523593i | 0.0644498 | + | 0.111630i | ||||
\(23\) | −2.46875 | − | 4.27600i | −0.514769 | − | 0.891607i | −0.999853 | − | 0.0171390i | \(-0.994544\pi\) |
0.485084 | − | 0.874468i | \(-0.338789\pi\) | |||||||
\(24\) | 0.270038 | + | 0.155907i | 0.0551213 | + | 0.0318243i | ||||
\(25\) | 1.19693 | + | 2.07314i | 0.239386 | + | 0.414628i | ||||
\(26\) | 0.141861 | − | 0.245710i | 0.0278212 | − | 0.0481878i | ||||
\(27\) | 1.77932 | 0.342431 | ||||||||
\(28\) | 2.75388i | 0.520434i | ||||||||
\(29\) | −4.87947 | + | 8.45149i | −0.906095 | + | 1.56940i | −0.0866541 | + | 0.996238i | \(0.527618\pi\) |
−0.819441 | + | 0.573164i | \(0.805716\pi\) | |||||||
\(30\) | −0.110909 | − | 0.0640334i | −0.0202491 | − | 0.0116908i | ||||
\(31\) | 10.1669 | 1.82603 | 0.913016 | − | 0.407924i | \(-0.133747\pi\) | ||||
0.913016 | + | 0.407924i | \(0.133747\pi\) | |||||||
\(32\) | −2.61240 | − | 1.50827i | −0.461811 | − | 0.266627i | ||||
\(33\) | 0.598395 | + | 0.345483i | 0.104167 | + | 0.0601409i | ||||
\(34\) | 1.58742 | − | 0.916497i | 0.272240 | − | 0.157178i | ||||
\(35\) | − | 2.30279i | − | 0.389243i | ||||||
\(36\) | −5.61673 | −0.936121 | ||||||||
\(37\) | −0.988427 | −0.162496 | −0.0812482 | − | 0.996694i | \(-0.525891\pi\) | ||||
−0.0812482 | + | 0.996694i | \(0.525891\pi\) | |||||||
\(38\) | − | 0.243188i | − | 0.0394503i | ||||||
\(39\) | − | 0.324255i | − | 0.0519224i | ||||||
\(40\) | 1.44780 | + | 0.835888i | 0.228917 | + | 0.132165i | ||||
\(41\) | −9.20028 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(42\) | −0.0565800 | − | 0.0979994i | −0.00873048 | − | 0.0151216i | ||||
\(43\) | −3.45983 | − | 1.99754i | −0.527620 | − | 0.304621i | 0.212427 | − | 0.977177i | \(-0.431863\pi\) |
−0.740047 | + | 0.672556i | \(0.765197\pi\) | |||||||
\(44\) | −3.83673 | − | 2.21514i | −0.578409 | − | 0.333945i | ||||
\(45\) | 4.69670 | 0.700143 | ||||||||
\(46\) | −1.12657 | − | 0.650427i | −0.166104 | − | 0.0959002i | ||||
\(47\) | − | 7.91493i | − | 1.15451i | −0.816563 | − | 0.577256i | \(-0.804124\pi\) | ||
0.816563 | − | 0.577256i | \(-0.195876\pi\) | |||||||
\(48\) | −1.08046 | −0.155951 | ||||||||
\(49\) | −2.48262 | + | 4.30003i | −0.354661 | + | 0.614290i | ||||
\(50\) | 0.546199 | + | 0.315348i | 0.0772441 | + | 0.0445969i | ||||
\(51\) | 1.04743 | − | 1.81420i | 0.146670 | − | 0.254039i | ||||
\(52\) | 2.07903i | 0.288309i | ||||||||
\(53\) | − | 11.3001i | − | 1.55218i | −0.630620 | − | 0.776092i | \(-0.717199\pi\) | ||
0.630620 | − | 0.776092i | \(-0.282801\pi\) | |||||||
\(54\) | 0.405982 | − | 0.234394i | 0.0552471 | − | 0.0318969i | ||||
\(55\) | 3.20827 | + | 1.85230i | 0.432603 | + | 0.249764i | ||||
\(56\) | 0.738592 | + | 1.27928i | 0.0986985 | + | 0.170951i | ||||
\(57\) | −0.138965 | − | 0.240695i | −0.0184064 | − | 0.0318808i | ||||
\(58\) | 2.57113i | 0.337606i | ||||||||
\(59\) | −7.66776 | − | 4.42698i | −0.998258 | − | 0.576344i | −0.0905253 | − | 0.995894i | \(-0.528855\pi\) |
−0.907732 | + | 0.419550i | \(0.862188\pi\) | |||||||
\(60\) | 0.938434 | 0.121151 | ||||||||
\(61\) | − | 7.83978i | − | 1.00378i | −0.864931 | − | 0.501890i | \(-0.832638\pi\) | ||
0.864931 | − | 0.501890i | \(-0.167362\pi\) | |||||||
\(62\) | 2.31975 | − | 1.33931i | 0.294609 | − | 0.170092i | ||||
\(63\) | 3.59402 | + | 2.07501i | 0.452804 | + | 0.261426i | ||||
\(64\) | 6.38193 | 0.797741 | ||||||||
\(65\) | − | 1.73848i | − | 0.215632i | ||||||
\(66\) | 0.182045 | 0.0224082 | ||||||||
\(67\) | −15.4898 | −1.89238 | −0.946192 | − | 0.323607i | \(-0.895105\pi\) | ||||
−0.946192 | + | 0.323607i | \(0.895105\pi\) | |||||||
\(68\) | −6.71582 | + | 11.6321i | −0.814413 | + | 1.41060i | ||||
\(69\) | −1.48670 | −0.178977 | ||||||||
\(70\) | −0.303352 | − | 0.525420i | −0.0362574 | − | 0.0627997i | ||||
\(71\) | −0.457735 | + | 0.264273i | −0.0543231 | + | 0.0313635i | −0.526916 | − | 0.849918i | \(-0.676652\pi\) |
0.472592 | + | 0.881281i | \(0.343318\pi\) | |||||||
\(72\) | −2.60918 | + | 1.50641i | −0.307494 | + | 0.177532i | ||||
\(73\) | −0.909516 | + | 1.57533i | −0.106451 | + | 0.184378i | −0.914330 | − | 0.404970i | \(-0.867282\pi\) |
0.807879 | + | 0.589348i | \(0.200615\pi\) | |||||||
\(74\) | −0.225526 | + | 0.130208i | −0.0262169 | + | 0.0151363i | ||||
\(75\) | 0.720799 | 0.0832306 | ||||||||
\(76\) | 0.891005 | + | 1.54327i | 0.102205 | + | 0.177025i | ||||
\(77\) | 1.63669 | + | 2.83483i | 0.186518 | + | 0.323059i | ||||
\(78\) | −0.0427148 | − | 0.0739842i | −0.00483650 | − | 0.00837706i | ||||
\(79\) | 0.588986i | 0.0662661i | 0.999451 | + | 0.0331330i | \(0.0105485\pi\) | ||||
−0.999451 | + | 0.0331330i | \(0.989451\pi\) | |||||||
\(80\) | −5.79285 | −0.647661 | ||||||||
\(81\) | −4.09613 | + | 7.09470i | −0.455125 | + | 0.788300i | ||||
\(82\) | −2.09920 | + | 1.21197i | −0.231818 | + | 0.133840i | ||||
\(83\) | 3.82294 | + | 6.62153i | 0.419622 | + | 0.726807i | 0.995901 | − | 0.0904459i | \(-0.0288292\pi\) |
−0.576279 | + | 0.817253i | \(0.695496\pi\) | |||||||
\(84\) | 0.718110 | + | 0.414601i | 0.0783522 | + | 0.0452367i | ||||
\(85\) | 5.61576 | − | 9.72678i | 0.609115 | − | 1.05502i | ||||
\(86\) | −1.05256 | −0.113500 | ||||||||
\(87\) | 1.46922 | + | 2.54477i | 0.157517 | + | 0.272828i | ||||
\(88\) | −2.37640 | −0.253326 | ||||||||
\(89\) | −14.4224 | − | 8.32678i | −1.52877 | − | 0.882637i | −0.999414 | − | 0.0342383i | \(-0.989099\pi\) |
−0.529358 | − | 0.848398i | \(-0.677567\pi\) | |||||||
\(90\) | 1.07163 | − | 0.618706i | 0.112960 | − | 0.0652174i | ||||
\(91\) | 0.768063 | − | 1.33032i | 0.0805149 | − | 0.139456i | ||||
\(92\) | 9.53226 | 0.993807 | ||||||||
\(93\) | 1.53065 | − | 2.65116i | 0.158721 | − | 0.274912i | ||||
\(94\) | −1.04265 | − | 1.80592i | −0.107541 | − | 0.186267i | ||||
\(95\) | −0.745058 | − | 1.29048i | −0.0764413 | − | 0.132400i | ||||
\(96\) | −0.786601 | + | 0.454145i | −0.0802822 | + | 0.0463509i | ||||
\(97\) | 10.7513 | − | 6.20729i | 1.09163 | − | 0.630255i | 0.157623 | − | 0.987499i | \(-0.449617\pi\) |
0.934011 | + | 0.357245i | \(0.116284\pi\) | |||||||
\(98\) | 1.30817i | 0.132145i | ||||||||
\(99\) | −5.78184 | + | 3.33815i | −0.581097 | + | 0.335496i | ||||
\(100\) | −4.62155 | −0.462155 | ||||||||
\(101\) | 12.6666i | 1.26037i | 0.776445 | + | 0.630185i | \(0.217021\pi\) | ||||
−0.776445 | + | 0.630185i | \(0.782979\pi\) | |||||||
\(102\) | − | 0.551921i | − | 0.0546483i | ||||||
\(103\) | 9.75770i | 0.961455i | 0.876870 | + | 0.480727i | \(0.159627\pi\) | ||||
−0.876870 | + | 0.480727i | \(0.840373\pi\) | |||||||
\(104\) | 0.557597 | + | 0.965786i | 0.0546769 | + | 0.0947031i | ||||
\(105\) | −0.600483 | − | 0.346689i | −0.0586012 | − | 0.0338334i | ||||
\(106\) | −1.48858 | − | 2.57830i | −0.144584 | − | 0.250427i | ||||
\(107\) | 4.95963 | − | 2.86344i | 0.479465 | − | 0.276819i | −0.240728 | − | 0.970593i | \(-0.577386\pi\) |
0.720194 | + | 0.693773i | \(0.244053\pi\) | |||||||
\(108\) | −1.71757 | + | 2.97491i | −0.165273 | + | 0.286261i | ||||
\(109\) | −3.74145 | + | 6.48038i | −0.358366 | + | 0.620708i | −0.987688 | − | 0.156437i | \(-0.949999\pi\) |
0.629322 | + | 0.777145i | \(0.283333\pi\) | |||||||
\(110\) | 0.976028 | 0.0930606 | ||||||||
\(111\) | −0.148809 | + | 0.257745i | −0.0141244 | + | 0.0244641i | ||||
\(112\) | −4.43281 | − | 2.55929i | −0.418862 | − | 0.241830i | ||||
\(113\) | 5.48746 | − | 3.16819i | 0.516217 | − | 0.298038i | −0.219168 | − | 0.975687i | \(-0.570334\pi\) |
0.735386 | + | 0.677649i | \(0.237001\pi\) | |||||||
\(114\) | −0.0634145 | − | 0.0366124i | −0.00593931 | − | 0.00342906i | ||||
\(115\) | −7.97087 | −0.743287 | ||||||||
\(116\) | −9.42024 | − | 16.3163i | −0.874647 | − | 1.51493i | ||||
\(117\) | 2.71329 | + | 1.56652i | 0.250844 | + | 0.144825i | ||||
\(118\) | −2.33270 | −0.214743 | ||||||||
\(119\) | 8.59460 | − | 4.96210i | 0.787866 | − | 0.454875i | ||||
\(120\) | 0.435938 | − | 0.251689i | 0.0397955 | − | 0.0229759i | ||||
\(121\) | 5.73397 | 0.521270 | ||||||||
\(122\) | −1.03275 | − | 1.78878i | −0.0935008 | − | 0.161948i | ||||
\(123\) | −1.38512 | + | 2.39909i | −0.124892 | + | 0.216319i | ||||
\(124\) | −9.81405 | + | 16.9984i | −0.881328 | + | 1.52650i | ||||
\(125\) | 11.9363 | 1.06762 | ||||||||
\(126\) | 1.09338 | 0.0974060 | ||||||||
\(127\) | − | 21.7667i | − | 1.93148i | −0.259504 | − | 0.965742i | \(-0.583559\pi\) | ||
0.259504 | − | 0.965742i | \(-0.416441\pi\) | |||||||
\(128\) | 6.68094 | − | 3.85724i | 0.590517 | − | 0.340935i | ||||
\(129\) | −1.04177 | + | 0.601465i | −0.0917225 | + | 0.0529560i | ||||
\(130\) | −0.229014 | − | 0.396664i | −0.0200859 | − | 0.0347897i | ||||
\(131\) | − | 18.3057i | − | 1.59938i | −0.600416 | − | 0.799688i | \(-0.704998\pi\) | ||
0.600416 | − | 0.799688i | \(-0.295002\pi\) | |||||||
\(132\) | −1.15525 | + | 0.666985i | −0.100552 | + | 0.0580536i | ||||
\(133\) | − | 1.31667i | − | 0.114170i | ||||||
\(134\) | −3.53426 | + | 2.04051i | −0.305314 | + | 0.176273i | ||||
\(135\) | 1.43623 | − | 2.48762i | 0.123611 | − | 0.214100i | ||||
\(136\) | 7.20474i | 0.617802i | ||||||||
\(137\) | −0.994485 | − | 0.574166i | −0.0849646 | − | 0.0490543i | 0.456916 | − | 0.889510i | \(-0.348954\pi\) |
−0.541880 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(138\) | −0.339215 | + | 0.195846i | −0.0288759 | + | 0.0166715i | ||||
\(139\) | 3.10135 | 0.263053 | 0.131526 | − | 0.991313i | \(-0.458012\pi\) | ||||
0.131526 | + | 0.991313i | \(0.458012\pi\) | |||||||
\(140\) | 3.85012 | + | 2.22287i | 0.325395 | + | 0.187867i | ||||
\(141\) | −2.06392 | − | 1.19161i | −0.173814 | − | 0.100351i | ||||
\(142\) | −0.0696266 | + | 0.120597i | −0.00584293 | + | 0.0101203i | ||||
\(143\) | 1.23561 | + | 2.14015i | 0.103327 | + | 0.178968i | ||||
\(144\) | 5.21984 | − | 9.04103i | 0.434987 | − | 0.753419i | ||||
\(145\) | 7.87720 | + | 13.6437i | 0.654166 | + | 1.13305i | ||||
\(146\) | 0.479250i | 0.0396630i | ||||||||
\(147\) | 0.747527 | + | 1.29475i | 0.0616550 | + | 0.106790i | ||||
\(148\) | 0.954122 | − | 1.65259i | 0.0784283 | − | 0.135842i | ||||
\(149\) | 2.08586 | − | 1.20427i | 0.170880 | − | 0.0986576i | −0.412121 | − | 0.911129i | \(-0.635212\pi\) |
0.583001 | + | 0.812472i | \(0.301878\pi\) | |||||||
\(150\) | 0.164462 | − | 0.0949523i | 0.0134283 | − | 0.00775282i | ||||
\(151\) | −1.38393 | + | 2.39704i | −0.112623 | + | 0.195068i | −0.916827 | − | 0.399285i | \(-0.869258\pi\) |
0.804204 | + | 0.594353i | \(0.202592\pi\) | |||||||
\(152\) | 0.827810 | + | 0.477936i | 0.0671442 | + | 0.0387657i | ||||
\(153\) | 10.1205 | + | 17.5293i | 0.818197 | + | 1.41716i | ||||
\(154\) | 0.746877 | + | 0.431210i | 0.0601851 | + | 0.0347479i | ||||
\(155\) | 8.20650 | − | 14.2141i | 0.659162 | − | 1.14170i | ||||
\(156\) | 0.542134 | + | 0.313001i | 0.0434055 | + | 0.0250602i | ||||
\(157\) | −7.99617 | + | 13.8498i | −0.638164 | + | 1.10533i | 0.347671 | + | 0.937617i | \(0.386973\pi\) |
−0.985835 | + | 0.167716i | \(0.946361\pi\) | |||||||
\(158\) | 0.0775883 | + | 0.134387i | 0.00617259 | + | 0.0106912i | ||||
\(159\) | −2.94664 | − | 1.70124i | −0.233684 | − | 0.134917i | ||||
\(160\) | −4.21734 | + | 2.43488i | −0.333410 | + | 0.192494i | ||||
\(161\) | −6.09948 | − | 3.52154i | −0.480706 | − | 0.277536i | ||||
\(162\) | 2.15836i | 0.169577i | ||||||||
\(163\) | 16.5453i | 1.29593i | 0.761671 | + | 0.647965i | \(0.224380\pi\) | ||||
−0.761671 | + | 0.647965i | \(0.775620\pi\) | |||||||
\(164\) | 8.88097 | − | 15.3823i | 0.693487 | − | 1.20115i | ||||
\(165\) | 0.966021 | − | 0.557733i | 0.0752047 | − | 0.0434194i | ||||
\(166\) | 1.74454 | + | 1.00721i | 0.135402 | + | 0.0781745i | ||||
\(167\) | − | 21.7742i | − | 1.68493i | −0.538747 | − | 0.842467i | \(-0.681102\pi\) | ||
0.538747 | − | 0.842467i | \(-0.318898\pi\) | |||||||
\(168\) | 0.444785 | 0.0343159 | ||||||||
\(169\) | −5.92015 | + | 10.2540i | −0.455396 | + | 0.788770i | ||||
\(170\) | − | 2.95910i | − | 0.226953i | ||||||
\(171\) | 2.68544 | 0.205360 | ||||||||
\(172\) | 6.67951 | − | 3.85642i | 0.509308 | − | 0.294049i | ||||
\(173\) | −13.3729 | + | 7.72082i | −1.01672 | + | 0.587003i | −0.913152 | − | 0.407619i | \(-0.866359\pi\) |
−0.103567 | + | 0.994622i | \(0.533026\pi\) | |||||||
\(174\) | 0.670456 | + | 0.387088i | 0.0508272 | + | 0.0293451i | ||||
\(175\) | 2.95723 | + | 1.70736i | 0.223545 | + | 0.129064i | ||||
\(176\) | 7.13125 | − | 4.11723i | 0.537538 | − | 0.310348i | ||||
\(177\) | −2.30879 | + | 1.33298i | −0.173539 | + | 0.100193i | ||||
\(178\) | −4.38762 | −0.328866 | ||||||||
\(179\) | 15.3849i | 1.14992i | 0.818181 | + | 0.574961i | \(0.194983\pi\) | ||||
−0.818181 | + | 0.574961i | \(0.805017\pi\) | |||||||
\(180\) | −4.53370 | + | 7.85259i | −0.337922 | + | 0.585298i | ||||
\(181\) | 16.8627 | 1.25340 | 0.626699 | − | 0.779262i | \(-0.284406\pi\) | ||||
0.626699 | + | 0.779262i | \(0.284406\pi\) | |||||||
\(182\) | − | 0.404714i | − | 0.0299994i | ||||||
\(183\) | −2.04432 | − | 1.18029i | −0.151121 | − | 0.0872497i | ||||
\(184\) | 4.42809 | − | 2.55656i | 0.326443 | − | 0.188472i | ||||
\(185\) | −0.797836 | + | 1.38189i | −0.0586581 | + | 0.101599i | ||||
\(186\) | − | 0.806541i | − | 0.0591384i | ||||||
\(187\) | 15.9654i | 1.16751i | ||||||||
\(188\) | 13.2333 | + | 7.64023i | 0.965135 | + | 0.557221i | ||||
\(189\) | 2.19806 | − | 1.26905i | 0.159886 | − | 0.0923101i | ||||
\(190\) | −0.339995 | − | 0.196296i | −0.0246658 | − | 0.0142408i | ||||
\(191\) | −6.88001 | − | 11.9165i | −0.497820 | − | 0.862250i | 0.502176 | − | 0.864765i | \(-0.332533\pi\) |
−0.999997 | + | 0.00251495i | \(0.999199\pi\) | |||||||
\(192\) | 0.960810 | − | 1.66417i | 0.0693405 | − | 0.120101i | ||||
\(193\) | 18.4964 | + | 10.6789i | 1.33140 | + | 0.768684i | 0.985514 | − | 0.169593i | \(-0.0542453\pi\) |
0.345885 | + | 0.938277i | \(0.387579\pi\) | |||||||
\(194\) | 1.63540 | − | 2.83259i | 0.117415 | − | 0.203368i | ||||
\(195\) | −0.453332 | − | 0.261731i | −0.0324638 | − | 0.0187430i | ||||
\(196\) | −4.79292 | − | 8.30158i | −0.342352 | − | 0.592970i | ||||
\(197\) | −2.28052 | − | 1.31666i | −0.162480 | − | 0.0938079i | 0.416555 | − | 0.909110i | \(-0.363237\pi\) |
−0.579035 | + | 0.815303i | \(0.696571\pi\) | |||||||
\(198\) | −0.879482 | + | 1.52331i | −0.0625021 | + | 0.108257i | ||||
\(199\) | 19.5884 | − | 11.3094i | 1.38859 | − | 0.801700i | 0.395429 | − | 0.918496i | \(-0.370596\pi\) |
0.993156 | + | 0.116796i | \(0.0372624\pi\) | |||||||
\(200\) | −2.14688 | + | 1.23950i | −0.151807 | + | 0.0876460i | ||||
\(201\) | −2.33202 | + | 4.03918i | −0.164488 | + | 0.284901i | ||||
\(202\) | 1.66859 | + | 2.89009i | 0.117402 | + | 0.203346i | ||||
\(203\) | 13.9206i | 0.977035i | ||||||||
\(204\) | 2.02216 | + | 3.50248i | 0.141579 | + | 0.245222i | ||||
\(205\) | −7.42626 | + | 12.8627i | −0.518672 | + | 0.898367i | ||||
\(206\) | 1.28540 | + | 2.22638i | 0.0895582 | + | 0.155119i | ||||
\(207\) | 7.18242 | − | 12.4403i | 0.499213 | − | 0.864661i | ||||
\(208\) | −3.34653 | − | 1.93212i | −0.232040 | − | 0.133969i | ||||
\(209\) | 1.83440 | + | 1.05909i | 0.126888 | + | 0.0732587i | ||||
\(210\) | −0.182680 | −0.0126061 | ||||||||
\(211\) | 1.31819 | − | 0.761056i | 0.0907477 | − | 0.0523932i | −0.453939 | − | 0.891033i | \(-0.649982\pi\) |
0.544687 | + | 0.838639i | \(0.316648\pi\) | |||||||
\(212\) | 18.8930 | + | 10.9079i | 1.29758 | + | 0.749156i | ||||
\(213\) | 0.159147i | 0.0109046i | ||||||||
\(214\) | 0.754414 | − | 1.30668i | 0.0515707 | − | 0.0893231i | ||||
\(215\) | −5.58540 | + | 3.22473i | −0.380921 | + | 0.219925i | ||||
\(216\) | 1.84261i | 0.125374i | ||||||||
\(217\) | 12.5596 | − | 7.25128i | 0.852600 | − | 0.492249i | ||||
\(218\) | 1.97148i | 0.133525i | ||||||||
\(219\) | 0.273858 | + | 0.474337i | 0.0185056 | + | 0.0320527i | ||||
\(220\) | −6.19385 | + | 3.57602i | −0.417589 | + | 0.241095i | ||||
\(221\) | 6.48846 | − | 3.74611i | 0.436461 | − | 0.251991i | ||||
\(222\) | 0.0784119i | 0.00526266i | ||||||||
\(223\) | −15.1017 | −1.01128 | −0.505642 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505642 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(224\) | −4.30293 | −0.287501 | ||||||||
\(225\) | −3.48227 | + | 6.03147i | −0.232151 | + | 0.402098i | ||||
\(226\) | 0.834704 | − | 1.44575i | 0.0555237 | − | 0.0961699i | ||||
\(227\) | −4.68430 | − | 8.11345i | −0.310908 | − | 0.538509i | 0.667651 | − | 0.744474i | \(-0.267300\pi\) |
−0.978559 | + | 0.205966i | \(0.933966\pi\) | |||||||
\(228\) | 0.536569 | 0.0355352 | ||||||||
\(229\) | −11.0112 | + | 6.35729i | −0.727638 | + | 0.420102i | −0.817557 | − | 0.575847i | \(-0.804672\pi\) |
0.0899196 | + | 0.995949i | \(0.471339\pi\) | |||||||
\(230\) | −1.81869 | + | 1.05002i | −0.119921 | + | 0.0692362i | ||||
\(231\) | 0.985627 | 0.0648495 | ||||||||
\(232\) | −8.75210 | − | 5.05303i | −0.574604 | − | 0.331747i | ||||
\(233\) | −11.9504 | − | 20.6987i | −0.782896 | − | 1.35602i | −0.930248 | − | 0.366931i | \(-0.880408\pi\) |
0.147352 | − | 0.989084i | \(-0.452925\pi\) | |||||||
\(234\) | 0.825442 | 0.0539609 | ||||||||
\(235\) | −11.0656 | − | 6.38875i | −0.721843 | − | 0.416756i | ||||
\(236\) | 14.8033 | − | 8.54668i | 0.963611 | − | 0.556341i | ||||
\(237\) | 0.153586 | + | 0.0886728i | 0.00997647 | + | 0.00575992i | ||||
\(238\) | 1.30733 | − | 2.26437i | 0.0847419 | − | 0.146777i | ||||
\(239\) | 6.62978 | 0.428845 | 0.214422 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214422 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(240\) | −0.872124 | + | 1.51056i | −0.0562953 | + | 0.0975064i | ||||
\(241\) | −0.372777 | + | 0.645668i | −0.0240127 | + | 0.0415911i | −0.877782 | − | 0.479060i | \(-0.840978\pi\) |
0.853769 | + | 0.520651i | \(0.174311\pi\) | |||||||
\(242\) | 1.30830 | − | 0.755348i | 0.0841008 | − | 0.0485556i | ||||
\(243\) | 3.90234 | + | 6.75905i | 0.250335 | + | 0.433593i | ||||
\(244\) | 13.1076 | + | 7.56768i | 0.839129 | + | 0.484471i | ||||
\(245\) | 4.00784 | + | 6.94178i | 0.256051 | + | 0.443494i | ||||
\(246\) | 0.729858i | 0.0465340i | ||||||||
\(247\) | − | 0.994013i | − | 0.0632475i | ||||||
\(248\) | 10.5285i | 0.668563i | ||||||||
\(249\) | 2.30220 | 0.145896 | ||||||||
\(250\) | 2.72347 | − | 1.57240i | 0.172247 | − | 0.0994470i | ||||
\(251\) | − | 9.84495i | − | 0.621408i | −0.950507 | − | 0.310704i | \(-0.899435\pi\) | ||
0.950507 | − | 0.310704i | \(-0.100565\pi\) | |||||||
\(252\) | −6.93856 | + | 4.00598i | −0.437088 | + | 0.252353i | ||||
\(253\) | 9.81248 | − | 5.66524i | 0.616905 | − | 0.356170i | ||||
\(254\) | −2.86738 | − | 4.96644i | −0.179915 | − | 0.311622i | ||||
\(255\) | −1.69092 | − | 2.92877i | −0.105890 | − | 0.183407i | ||||
\(256\) | −5.36568 | + | 9.29363i | −0.335355 | + | 0.580852i | ||||
\(257\) | 9.77861 | 0.609973 | 0.304986 | − | 0.952357i | \(-0.401348\pi\) | ||||
0.304986 | + | 0.952357i | \(0.401348\pi\) | |||||||
\(258\) | −0.158464 | + | 0.274468i | −0.00986557 | + | 0.0170877i | ||||
\(259\) | −1.22104 | + | 0.704969i | −0.0758719 | + | 0.0438047i | ||||
\(260\) | 2.90663 | + | 1.67815i | 0.180262 | + | 0.104074i | ||||
\(261\) | −28.3920 | −1.75742 | ||||||||
\(262\) | −2.41145 | − | 4.17675i | −0.148980 | − | 0.258040i | ||||
\(263\) | −11.9681 | −0.737986 | −0.368993 | − | 0.929432i | \(-0.620297\pi\) | ||||
−0.368993 | + | 0.929432i | \(0.620297\pi\) | |||||||
\(264\) | −0.357772 | + | 0.619679i | −0.0220193 | + | 0.0381386i | ||||
\(265\) | −15.7983 | − | 9.12116i | −0.970483 | − | 0.560308i | ||||
\(266\) | −0.173448 | − | 0.300420i | −0.0106347 | − | 0.0184199i | ||||
\(267\) | −4.34263 | + | 2.50722i | −0.265765 | + | 0.153439i | ||||
\(268\) | 14.9522 | − | 25.8980i | 0.913352 | − | 1.58197i | ||||
\(269\) | 4.76791 | 0.290705 | 0.145352 | − | 0.989380i | \(-0.453568\pi\) | ||||
0.145352 | + | 0.989380i | \(0.453568\pi\) | |||||||
\(270\) | − | 0.756789i | − | 0.0460567i | ||||||
\(271\) | −10.7221 | − | 18.5713i | −0.651324 | − | 1.12813i | −0.982802 | − | 0.184663i | \(-0.940881\pi\) |
0.331478 | − | 0.943463i | \(-0.392453\pi\) | |||||||
\(272\) | −12.4825 | − | 21.6204i | −0.756865 | − | 1.31093i | ||||
\(273\) | −0.231266 | − | 0.400565i | −0.0139969 | − | 0.0242433i | ||||
\(274\) | −0.302545 | −0.0182774 | ||||||||
\(275\) | −4.75741 | + | 2.74669i | −0.286883 | + | 0.165632i | ||||
\(276\) | 1.43510 | − | 2.48566i | 0.0863827 | − | 0.149619i | ||||
\(277\) | −11.7762 | + | 6.79900i | −0.707564 | + | 0.408512i | −0.810158 | − | 0.586211i | \(-0.800619\pi\) |
0.102595 | + | 0.994723i | \(0.467286\pi\) | |||||||
\(278\) | 0.707624 | − | 0.408547i | 0.0424405 | − | 0.0245030i | ||||
\(279\) | 14.7895 | + | 25.6161i | 0.885423 | + | 1.53360i | ||||
\(280\) | 2.38470 | 0.142513 | ||||||||
\(281\) | −3.25545 | + | 5.63860i | −0.194204 | + | 0.336371i | −0.946639 | − | 0.322295i | \(-0.895546\pi\) |
0.752435 | + | 0.658666i | \(0.228879\pi\) | |||||||
\(282\) | −0.627891 | −0.0373904 | ||||||||
\(283\) | 16.5940 | 0.986409 | 0.493205 | − | 0.869913i | \(-0.335825\pi\) | ||||
0.493205 | + | 0.869913i | \(0.335825\pi\) | |||||||
\(284\) | − | 1.02041i | − | 0.0605499i | ||||||
\(285\) | −0.448679 | −0.0265774 | ||||||||
\(286\) | 0.563852 | + | 0.325540i | 0.0333413 | + | 0.0192496i | ||||
\(287\) | −11.3655 | + | 6.56185i | −0.670882 | + | 0.387334i | ||||
\(288\) | − | 8.77612i | − | 0.517138i | ||||||
\(289\) | 31.4038 | 1.84728 | ||||||||
\(290\) | 3.59463 | + | 2.07536i | 0.211084 | + | 0.121869i | ||||
\(291\) | − | 3.73807i | − | 0.219130i | ||||||
\(292\) | −1.75590 | − | 3.04131i | −0.102756 | − | 0.177979i | ||||
\(293\) | −2.72794 | − | 4.72494i | −0.159368 | − | 0.276034i | 0.775273 | − | 0.631627i | \(-0.217612\pi\) |
−0.934641 | + | 0.355593i | \(0.884279\pi\) | |||||||
\(294\) | 0.341121 | + | 0.196947i | 0.0198946 | + | 0.0114862i | ||||
\(295\) | −12.3785 | + | 7.14673i | −0.720704 | + | 0.416098i | ||||
\(296\) | − | 1.02358i | − | 0.0594946i | ||||||
\(297\) | 4.08315i | 0.236929i | ||||||||
\(298\) | 0.317282 | − | 0.549549i | 0.0183797 | − | 0.0318345i | ||||
\(299\) | −4.60478 | − | 2.65857i | −0.266301 | − | 0.153749i | ||||
\(300\) | −0.695782 | + | 1.20513i | −0.0401710 | + | 0.0695782i | ||||
\(301\) | −5.69876 | −0.328471 | ||||||||
\(302\) | 0.729232i | 0.0419626i | ||||||||
\(303\) | 3.30297 | + | 1.90697i | 0.189751 | + | 0.109553i | ||||
\(304\) | −3.31218 | −0.189967 | ||||||||
\(305\) | −10.9606 | − | 6.32809i | −0.627601 | − | 0.362345i | ||||
\(306\) | 4.61834 | + | 2.66640i | 0.264013 | + | 0.152428i | ||||
\(307\) | −1.40390 | − | 2.43162i | −0.0801246 | − | 0.138780i | 0.823179 | − | 0.567782i | \(-0.192198\pi\) |
−0.903303 | + | 0.429002i | \(0.858865\pi\) | |||||||
\(308\) | −6.31955 | −0.360090 | ||||||||
\(309\) | 2.54445 | + | 1.46904i | 0.144749 | + | 0.0835706i | ||||
\(310\) | − | 4.32424i | − | 0.245600i | ||||||
\(311\) | 13.6304i | 0.772909i | 0.922309 | + | 0.386454i | \(0.126300\pi\) | ||||
−0.922309 | + | 0.386454i | \(0.873700\pi\) | |||||||
\(312\) | 0.335788 | 0.0190103 | ||||||||
\(313\) | −17.7039 | −1.00068 | −0.500341 | − | 0.865829i | \(-0.666792\pi\) | ||||
−0.500341 | + | 0.865829i | \(0.666792\pi\) | |||||||
\(314\) | 4.21341i | 0.237777i | ||||||||
\(315\) | 5.80202 | − | 3.34980i | 0.326907 | − | 0.188740i | ||||
\(316\) | −0.984747 | − | 0.568544i | −0.0553963 | − | 0.0319831i | ||||
\(317\) | −5.14241 | − | 2.96897i | −0.288826 | − | 0.166754i | 0.348586 | − | 0.937277i | \(-0.386662\pi\) |
−0.637412 | + | 0.770523i | \(0.719995\pi\) | |||||||
\(318\) | −0.896434 | −0.0502695 | ||||||||
\(319\) | −19.3943 | − | 11.1973i | −1.08587 | − | 0.626930i | ||||
\(320\) | 5.15135 | − | 8.92240i | 0.287969 | − | 0.498777i | ||||
\(321\) | − | 1.72438i | − | 0.0962457i | ||||||
\(322\) | −1.85560 | −0.103408 | ||||||||
\(323\) | 3.21093 | − | 5.56149i | 0.178661 | − | 0.309450i | ||||
\(324\) | −7.90792 | − | 13.6969i | −0.439329 | − | 0.760940i | ||||
\(325\) | 2.23254 | + | 1.28896i | 0.123839 | + | 0.0714987i | ||||
\(326\) | 2.17955 | + | 3.77509i | 0.120714 | + | 0.209083i | ||||
\(327\) | 1.12656 | + | 1.95126i | 0.0622991 | + | 0.107905i | ||||
\(328\) | − | 9.52752i | − | 0.526069i | ||||||
\(329\) | −5.64511 | − | 9.77762i | −0.311225 | − | 0.539058i | ||||
\(330\) | 0.146943 | − | 0.254512i | 0.00808892 | − | 0.0140104i | ||||
\(331\) | −17.4079 | − | 10.0504i | −0.956824 | − | 0.552422i | −0.0616297 | − | 0.998099i | \(-0.519630\pi\) |
−0.895194 | + | 0.445677i | \(0.852963\pi\) | |||||||
\(332\) | −14.7610 | −0.810117 | ||||||||
\(333\) | −1.43783 | − | 2.49040i | −0.0787928 | − | 0.136473i | ||||
\(334\) | −2.86835 | − | 4.96814i | −0.156949 | − | 0.271844i | ||||
\(335\) | −12.5030 | + | 21.6559i | −0.683114 | + | 1.18319i | ||||
\(336\) | −1.33474 | + | 0.770610i | −0.0728158 | + | 0.0420402i | ||||
\(337\) | 12.8702 | + | 22.2918i | 0.701082 | + | 1.21431i | 0.968087 | + | 0.250615i | \(0.0806327\pi\) |
−0.267005 | + | 0.963695i | \(0.586034\pi\) | |||||||
\(338\) | 3.11950i | 0.169678i | ||||||||
\(339\) | − | 1.90790i | − | 0.103623i | ||||||
\(340\) | 10.8417 | + | 18.7784i | 0.587975 | + | 1.01840i | ||||
\(341\) | 23.3309i | 1.26344i | ||||||||
\(342\) | 0.612727 | − | 0.353758i | 0.0331325 | − | 0.0191291i | ||||
\(343\) | 17.0678i | 0.921574i | ||||||||
\(344\) | 2.06859 | − | 3.58290i | 0.111531 | − | 0.193177i | ||||
\(345\) | −1.20003 | + | 2.07851i | −0.0646073 | + | 0.111903i | ||||
\(346\) | −2.03416 | + | 3.52327i | −0.109357 | + | 0.189412i | ||||
\(347\) | −23.9913 | + | 13.8514i | −1.28792 | + | 0.743582i | −0.978283 | − | 0.207272i | \(-0.933542\pi\) |
−0.309639 | + | 0.950854i | \(0.600208\pi\) | |||||||
\(348\) | −5.67293 | −0.304101 | ||||||||
\(349\) | 2.39700 | − | 18.5271i | 0.128309 | − | 0.991734i | ||||
\(350\) | 0.899654 | 0.0480885 | ||||||||
\(351\) | 1.65942 | − | 0.958066i | 0.0885733 | − | 0.0511378i | ||||
\(352\) | 3.46115 | − | 5.99488i | 0.184480 | − | 0.319528i | ||||
\(353\) | −5.73692 | + | 9.93664i | −0.305346 | + | 0.528874i | −0.977338 | − | 0.211684i | \(-0.932105\pi\) |
0.671993 | + | 0.740558i | \(0.265439\pi\) | |||||||
\(354\) | −0.351192 | + | 0.608283i | −0.0186657 | + | 0.0323299i | ||||
\(355\) | 0.853262i | 0.0452865i | ||||||||
\(356\) | 27.8437 | − | 16.0756i | 1.47571 | − | 0.852003i | ||||
\(357\) | − | 2.98821i | − | 0.158153i | ||||||
\(358\) | 2.02669 | + | 3.51032i | 0.107114 | + | 0.185526i | ||||
\(359\) | 12.4405i | 0.656585i | 0.944576 | + | 0.328292i | \(0.106473\pi\) | ||||
−0.944576 | + | 0.328292i | \(0.893527\pi\) | |||||||
\(360\) | 4.86376i | 0.256343i | ||||||||
\(361\) | 9.07400 | + | 15.7166i | 0.477579 | + | 0.827191i | ||||
\(362\) | 3.84751 | − | 2.22136i | 0.202221 | − | 0.116752i | ||||
\(363\) | 0.863259 | − | 1.49521i | 0.0453094 | − | 0.0784781i | ||||
\(364\) | 1.48281 | + | 2.56831i | 0.0777205 | + | 0.134616i | ||||
\(365\) | 1.46828 | + | 2.54314i | 0.0768534 | + | 0.133114i | ||||
\(366\) | −0.621929 | −0.0325088 | ||||||||
\(367\) | 1.12969 | + | 0.652228i | 0.0589695 | + | 0.0340460i | 0.529195 | − | 0.848500i | \(-0.322494\pi\) |
−0.470225 | + | 0.882546i | \(0.655827\pi\) | |||||||
\(368\) | −8.85870 | + | 15.3437i | −0.461792 | + | 0.799847i | ||||
\(369\) | −13.3834 | − | 23.1807i | −0.696710 | − | 1.20674i | ||||
\(370\) | 0.420402i | 0.0218557i | ||||||||
\(371\) | −8.05947 | − | 13.9594i | −0.418427 | − | 0.724737i | ||||
\(372\) | 2.95504 | + | 5.11829i | 0.153212 | + | 0.265371i | ||||
\(373\) | 31.8980 | + | 18.4163i | 1.65161 | + | 0.953560i | 0.976409 | + | 0.215931i | \(0.0692785\pi\) |
0.675206 | + | 0.737629i | \(0.264055\pi\) | |||||||
\(374\) | 2.10316 | + | 3.64278i | 0.108752 | + | 0.188364i | ||||
\(375\) | 1.79703 | − | 3.11255i | 0.0927983 | − | 0.160731i | ||||
\(376\) | 8.19646 | 0.422700 | ||||||||
\(377\) | 10.5093i | 0.541257i | ||||||||
\(378\) | 0.334350 | − | 0.579111i | 0.0171971 | − | 0.0297863i | ||||
\(379\) | −14.8281 | − | 8.56103i | −0.761670 | − | 0.439750i | 0.0682250 | − | 0.997670i | \(-0.478266\pi\) |
−0.829895 | + | 0.557920i | \(0.811600\pi\) | |||||||
\(380\) | 2.87680 | 0.147577 | ||||||||
\(381\) | −5.67596 | − | 3.27702i | −0.290788 | − | 0.167887i | ||||
\(382\) | −3.13958 | − | 1.81264i | −0.160635 | − | 0.0927426i | ||||
\(383\) | −14.5715 | + | 8.41285i | −0.744568 | + | 0.429876i | −0.823728 | − | 0.566986i | \(-0.808110\pi\) |
0.0791601 | + | 0.996862i | \(0.474776\pi\) | |||||||
\(384\) | − | 2.32286i | − | 0.118538i | ||||||
\(385\) | 5.28441 | 0.269318 | ||||||||
\(386\) | 5.62701 | 0.286407 | ||||||||
\(387\) | − | 11.6230i | − | 0.590831i | ||||||
\(388\) | 23.9674i | 1.21676i | ||||||||
\(389\) | 7.64661 | + | 4.41477i | 0.387698 | + | 0.223838i | 0.681162 | − | 0.732132i | \(-0.261475\pi\) |
−0.293464 | + | 0.955970i | \(0.594808\pi\) | |||||||
\(390\) | −0.137914 | −0.00698353 | ||||||||
\(391\) | −17.1758 | − | 29.7493i | −0.868616 | − | 1.50449i | ||||
\(392\) | −4.45298 | − | 2.57093i | −0.224909 | − | 0.129852i | ||||
\(393\) | −4.77345 | − | 2.75595i | −0.240789 | − | 0.139019i | ||||
\(394\) | −0.693784 | −0.0349523 | ||||||||
\(395\) | 0.823445 | + | 0.475416i | 0.0414320 | + | 0.0239208i | ||||
\(396\) | − | 12.8892i | − | 0.647705i | ||||||
\(397\) | −8.74650 | −0.438974 | −0.219487 | − | 0.975615i | \(-0.570438\pi\) | ||||
−0.219487 | + | 0.975615i | \(0.570438\pi\) | |||||||
\(398\) | 2.97961 | − | 5.16084i | 0.149355 | − | 0.258690i | ||||
\(399\) | −0.343339 | − | 0.198227i | −0.0171884 | − | 0.00992375i | ||||
\(400\) | 4.29498 | − | 7.43913i | 0.214749 | − | 0.371957i | ||||
\(401\) | − | 14.0713i | − | 0.702688i | −0.936246 | − | 0.351344i | \(-0.885725\pi\) | ||
0.936246 | − | 0.351344i | \(-0.114275\pi\) | |||||||
\(402\) | 1.22881i | 0.0612873i | ||||||||
\(403\) | 9.48180 | − | 5.47432i | 0.472322 | − | 0.272695i | ||||
\(404\) | −21.1777 | − | 12.2269i | −1.05363 | − | 0.608313i | ||||
\(405\) | 6.61260 | + | 11.4534i | 0.328583 | + | 0.569122i | ||||
\(406\) | 1.83379 | + | 3.17622i | 0.0910095 | + | 0.157633i | ||||
\(407\) | − | 2.26822i | − | 0.112432i | ||||||
\(408\) | 1.87873 | + | 1.08469i | 0.0930111 | + | 0.0537000i | ||||
\(409\) | −14.1651 | −0.700419 | −0.350209 | − | 0.936671i | \(-0.613890\pi\) | ||||
−0.350209 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(410\) | 3.91311i | 0.193255i | ||||||||
\(411\) | −0.299443 | + | 0.172883i | −0.0147704 | + | 0.00852771i | ||||
\(412\) | −16.3143 | − | 9.41904i | −0.803746 | − | 0.464043i | ||||
\(413\) | −12.6297 | −0.621468 | ||||||||
\(414\) | − | 3.78462i | − | 0.186004i | ||||||
\(415\) | 12.3432 | 0.605902 | ||||||||
\(416\) | −3.24848 | −0.159270 | ||||||||
\(417\) | 0.466913 | − | 0.808717i | 0.0228648 | − | 0.0396030i | ||||
\(418\) | 0.558064 | 0.0272958 | ||||||||
\(419\) | −14.8950 | − | 25.7990i | −0.727670 | − | 1.26036i | −0.957866 | − | 0.287217i | \(-0.907270\pi\) |
0.230196 | − | 0.973144i | \(-0.426063\pi\) | |||||||
\(420\) | 1.15928 | − | 0.669313i | 0.0565673 | − | 0.0326592i | ||||
\(421\) | 19.7861 | − | 11.4235i | 0.964315 | − | 0.556748i | 0.0668167 | − | 0.997765i | \(-0.478716\pi\) |
0.897498 | + | 0.441018i | \(0.145382\pi\) | |||||||
\(422\) | 0.200511 | − | 0.347295i | 0.00976072 | − | 0.0169061i | ||||
\(423\) | 19.9421 | − | 11.5136i | 0.969620 | − | 0.559810i | ||||
\(424\) | 11.7020 | 0.568299 | ||||||||
\(425\) | 8.32737 | + | 14.4234i | 0.403937 | + | 0.699639i | ||||
\(426\) | 0.0209648 | + | 0.0363121i | 0.00101575 | + | 0.00175933i | ||||
\(427\) | −5.59151 | − | 9.68478i | −0.270592 | − | 0.468679i | ||||
\(428\) | 11.0562i | 0.534424i | ||||||||
\(429\) | 0.744095 | 0.0359252 | ||||||||
\(430\) | −0.849602 | + | 1.47155i | −0.0409714 | + | 0.0709646i | ||||
\(431\) | −1.46490 | + | 0.845761i | −0.0705618 | + | 0.0407389i | −0.534866 | − | 0.844937i | \(-0.679638\pi\) |
0.464304 | + | 0.885676i | \(0.346305\pi\) | |||||||
\(432\) | −3.19240 | − | 5.52940i | −0.153595 | − | 0.266034i | ||||
\(433\) | 5.38392 | + | 3.10841i | 0.258735 | + | 0.149381i | 0.623757 | − | 0.781618i | \(-0.285605\pi\) |
−0.365023 | + | 0.930999i | \(0.618939\pi\) | |||||||
\(434\) | 1.91045 | − | 3.30900i | 0.0917047 | − | 0.158837i | ||||
\(435\) | 4.74370 | 0.227443 | ||||||||
\(436\) | −7.22319 | − | 12.5109i | −0.345928 | − | 0.599165i | ||||
\(437\) | −4.55751 | −0.218015 | ||||||||
\(438\) | 0.124971 | + | 0.0721519i | 0.00597133 | + | 0.00344755i | ||||
\(439\) | 25.4833 | − | 14.7128i | 1.21625 | − | 0.702203i | 0.252137 | − | 0.967692i | \(-0.418867\pi\) |
0.964114 | + | 0.265489i | \(0.0855334\pi\) | |||||||
\(440\) | −1.91818 | + | 3.32239i | −0.0914457 | + | 0.158389i | ||||
\(441\) | −14.4456 | −0.687885 | ||||||||
\(442\) | 0.986967 | − | 1.70948i | 0.0469452 | − | 0.0813115i | ||||
\(443\) | 1.79917 | + | 3.11626i | 0.0854812 | + | 0.148058i | 0.905596 | − | 0.424141i | \(-0.139424\pi\) |
−0.820115 | + | 0.572199i | \(0.806091\pi\) | |||||||
\(444\) | −0.287289 | − | 0.497600i | −0.0136341 | − | 0.0236150i | ||||
\(445\) | −23.2829 | + | 13.4424i | −1.10371 | + | 0.637230i | ||||
\(446\) | −3.44570 | + | 1.98938i | −0.163159 | + | 0.0941997i | ||||
\(447\) | − | 0.725219i | − | 0.0343017i | ||||||
\(448\) | 7.88384 | − | 4.55174i | 0.372477 | − | 0.215049i | ||||
\(449\) | −6.85482 | −0.323499 | −0.161750 | − | 0.986832i | \(-0.551714\pi\) | ||||
−0.161750 | + | 0.986832i | \(0.551714\pi\) | |||||||
\(450\) | 1.83491i | 0.0864983i | ||||||||
\(451\) | − | 21.1126i | − | 0.994155i | ||||||
\(452\) | 12.2329i | 0.575388i | ||||||||
\(453\) | 0.416706 | + | 0.721756i | 0.0195785 | + | 0.0339110i | ||||
\(454\) | −2.13760 | − | 1.23415i | −0.100323 | − | 0.0579213i | ||||
\(455\) | −1.23993 | − | 2.14762i | −0.0581286 | − | 0.100682i | ||||
\(456\) | 0.249256 | − | 0.143908i | 0.0116725 | − | 0.00673912i | ||||
\(457\) | 10.1856 | − | 17.6420i | 0.476464 | − | 0.825260i | −0.523173 | − | 0.852227i | \(-0.675252\pi\) |
0.999636 | + | 0.0269673i | \(0.00858499\pi\) | |||||||
\(458\) | −1.67492 | + | 2.90105i | −0.0782638 | + | 0.135557i | ||||
\(459\) | 12.3792 | 0.577813 | ||||||||
\(460\) | 7.69423 | − | 13.3268i | 0.358745 | − | 0.621365i | ||||
\(461\) | 16.3078 | + | 9.41533i | 0.759532 | + | 0.438516i | 0.829128 | − | 0.559060i | \(-0.188838\pi\) |
−0.0695960 | + | 0.997575i | \(0.522171\pi\) | |||||||
\(462\) | 0.224887 | − | 0.129839i | 0.0104627 | − | 0.00604064i | ||||
\(463\) | 22.0626 | + | 12.7379i | 1.02534 | + | 0.591978i | 0.915645 | − | 0.401988i | \(-0.131680\pi\) |
0.109691 | + | 0.993966i | \(0.465014\pi\) | |||||||
\(464\) | 35.0184 | 1.62569 | ||||||||
\(465\) | −2.47101 | − | 4.27991i | −0.114590 | − | 0.198476i | ||||
\(466\) | −5.45336 | − | 3.14850i | −0.252622 | − | 0.145851i | ||||
\(467\) | 1.95622 | 0.0905229 | 0.0452614 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452614 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(468\) | −5.23824 | + | 3.02430i | −0.242138 | + | 0.139798i | ||||
\(469\) | −19.1352 | + | 11.0477i | −0.883581 | + | 0.510136i | ||||
\(470\) | −3.36642 | −0.155281 | ||||||||
\(471\) | 2.40767 | + | 4.17022i | 0.110940 | + | 0.192153i | ||||
\(472\) | 4.58445 | − | 7.94050i | 0.211016 | − | 0.365491i | ||||
\(473\) | 4.58391 | − | 7.93957i | 0.210768 | − | 0.365062i | ||||
\(474\) | 0.0467242 | 0.00214611 | ||||||||
\(475\) | 2.20963 | 0.101385 | ||||||||
\(476\) | 19.1595i | 0.878175i | ||||||||
\(477\) | 28.4712 | − | 16.4379i | 1.30361 | − | 0.752637i | ||||
\(478\) | 1.51269 | − | 0.873355i | 0.0691890 | − | 0.0399463i | ||||
\(479\) | 6.34681 | + | 10.9930i | 0.289993 | + | 0.502282i | 0.973808 | − | 0.227373i | \(-0.0730137\pi\) |
−0.683815 | + | 0.729656i | \(0.739680\pi\) | |||||||
\(480\) | 1.46630i | 0.0669272i | ||||||||
\(481\) | −0.921821 | + | 0.532213i | −0.0420314 | + | 0.0242668i | ||||
\(482\) | 0.196427i | 0.00894699i | ||||||||
\(483\) | −1.83657 | + | 1.06035i | −0.0835670 | + | 0.0482474i | ||||
\(484\) | −5.53497 | + | 9.58684i | −0.251589 | + | 0.435766i | ||||
\(485\) | − | 20.0415i | − | 0.910040i | ||||||
\(486\) | 1.78077 | + | 1.02813i | 0.0807772 | + | 0.0466368i | ||||
\(487\) | −12.2172 | + | 7.05357i | −0.553612 | + | 0.319628i | −0.750578 | − | 0.660782i | \(-0.770225\pi\) |
0.196966 | + | 0.980410i | \(0.436891\pi\) | |||||||
\(488\) | 8.11863 | 0.367513 | ||||||||
\(489\) | 4.31441 | + | 2.49092i | 0.195104 | + | 0.112644i | ||||
\(490\) | 1.82891 | + | 1.05592i | 0.0826217 | + | 0.0477017i | ||||
\(491\) | −12.2865 | + | 21.2809i | −0.554483 | + | 0.960392i | 0.443461 | + | 0.896294i | \(0.353750\pi\) |
−0.997944 | + | 0.0640984i | \(0.979583\pi\) | |||||||
\(492\) | −2.67409 | − | 4.63166i | −0.120557 | − | 0.208811i | ||||
\(493\) | −33.9478 | + | 58.7994i | −1.52893 | + | 2.64819i | ||||
\(494\) | −0.130943 | − | 0.226801i | −0.00589142 | − | 0.0102042i | ||||
\(495\) | 10.7779i | 0.484431i | ||||||||
\(496\) | −18.2412 | − | 31.5946i | −0.819052 | − | 1.41864i | ||||
\(497\) | −0.376972 | + | 0.652935i | −0.0169095 | + | 0.0292881i | ||||
\(498\) | 0.525285 | − | 0.303274i | 0.0235386 | − | 0.0135900i | ||||
\(499\) | −20.6915 | + | 11.9463i | −0.926280 | + | 0.534788i | −0.885633 | − | 0.464386i | \(-0.846275\pi\) |
−0.0406467 | + | 0.999174i | \(0.512942\pi\) | |||||||
\(500\) | −11.5220 | + | 19.9568i | −0.515281 | + | 0.892494i | ||||
\(501\) | −5.67790 | − | 3.27814i | −0.253670 | − | 0.146456i | ||||
\(502\) | −1.29690 | − | 2.24629i | −0.0578833 | − | 0.100257i | ||||
\(503\) | 28.7114 | + | 16.5765i | 1.28018 | + | 0.739110i | 0.976880 | − | 0.213786i | \(-0.0685796\pi\) |
0.303296 | + | 0.952896i | \(0.401913\pi\) | |||||||
\(504\) | −2.14881 | + | 3.72185i | −0.0957157 | + | 0.165784i | ||||
\(505\) | 17.7088 | + | 10.2242i | 0.788030 | + | 0.454969i | ||||
\(506\) | 1.49259 | − | 2.58524i | 0.0663536 | − | 0.114928i | ||||
\(507\) | 1.78258 | + | 3.08752i | 0.0791671 | + | 0.137121i | ||||
\(508\) | 36.3926 | + | 21.0113i | 1.61466 | + | 0.932224i | ||||
\(509\) | −13.6609 | + | 7.88715i | −0.605510 | + | 0.349592i | −0.771206 | − | 0.636585i | \(-0.780346\pi\) |
0.165696 | + | 0.986177i | \(0.447013\pi\) | |||||||
\(510\) | −0.771625 | − | 0.445498i | −0.0341681 | − | 0.0197270i | ||||
\(511\) | 2.59475i | 0.114785i | ||||||||
\(512\) | 18.2563i | 0.806822i | ||||||||
\(513\) | 0.821193 | − | 1.42235i | 0.0362566 | − | 0.0627982i | ||||
\(514\) | 2.23115 | − | 1.28816i | 0.0984119 | − | 0.0568181i | ||||
\(515\) | 13.6420 | + | 7.87619i | 0.601137 | + | 0.347067i | ||||
\(516\) | − | 2.32236i | − | 0.102236i | ||||||
\(517\) | 18.1630 | 0.798810 | ||||||||
\(518\) | −0.185734 | + | 0.321701i | −0.00816069 | + | 0.0141347i | ||||
\(519\) | 4.64953i | 0.204092i | ||||||||
\(520\) | 1.80032 | 0.0789492 | ||||||||
\(521\) | 5.70170 | − | 3.29188i | 0.249796 | − | 0.144220i | −0.369875 | − | 0.929082i | \(-0.620599\pi\) |
0.619671 | + | 0.784862i | \(0.287266\pi\) | |||||||
\(522\) | −6.47812 | + | 3.74014i | −0.283540 | + | 0.163702i | ||||
\(523\) | 4.25033 | + | 2.45393i | 0.185854 | + | 0.107303i | 0.590040 | − | 0.807374i | \(-0.299112\pi\) |
−0.404186 | + | 0.914677i | \(0.632445\pi\) | |||||||
\(524\) | 30.6060 | + | 17.6704i | 1.33703 | + | 0.771933i | ||||
\(525\) | 0.890431 | − | 0.514090i | 0.0388616 | − | 0.0224367i | ||||
\(526\) | −2.73073 | + | 1.57658i | −0.119065 | + | 0.0687424i | ||||
\(527\) | 70.7341 | 3.08123 | ||||||||
\(528\) | − | 2.47942i | − | 0.107903i | ||||||
\(529\) | −0.689427 | + | 1.19412i | −0.0299751 | + | 0.0519183i | ||||
\(530\) | −4.80620 | −0.208768 | ||||||||
\(531\) | − | 25.7592i | − | 1.11785i | ||||||
\(532\) | 2.20139 | + | 1.27097i | 0.0954422 | + | 0.0551036i | ||||
\(533\) | −8.58031 | + | 4.95384i | −0.371654 | + | 0.214575i | ||||
\(534\) | −0.660563 | + | 1.14413i | −0.0285854 | + | 0.0495113i | ||||
\(535\) | − | 9.24522i | − | 0.399706i | ||||||
\(536\) | − | 16.0408i | − | 0.692856i | ||||||
\(537\) | 4.01182 | + | 2.31622i | 0.173123 | + | 0.0999524i | ||||
\(538\) | 1.08788 | − | 0.628087i | 0.0469017 | − | 0.0270787i | ||||
\(539\) | −9.86764 | − | 5.69708i | −0.425029 | − | 0.245391i | ||||
\(540\) | 2.77276 | + | 4.80257i | 0.119321 | + | 0.206670i | ||||
\(541\) | 10.0677 | − | 17.4377i | 0.432843 | − | 0.749706i | −0.564274 | − | 0.825587i | \(-0.690844\pi\) |
0.997117 | + | 0.0758820i | \(0.0241772\pi\) | |||||||
\(542\) | −4.89287 | − | 2.82490i | −0.210167 | − | 0.121340i | ||||
\(543\) | 2.53871 | − | 4.39718i | 0.108947 | − | 0.188701i | ||||
\(544\) | −18.1752 | − | 10.4934i | −0.779254 | − | 0.449903i | ||||
\(545\) | 6.04003 | + | 10.4616i | 0.258726 | + | 0.448127i | ||||
\(546\) | −0.105535 | − | 0.0609304i | −0.00451646 | − | 0.00260758i | ||||
\(547\) | −6.43133 | + | 11.1394i | −0.274984 | + | 0.476286i | −0.970131 | − | 0.242581i | \(-0.922006\pi\) |
0.695147 | + | 0.718867i | \(0.255339\pi\) | |||||||
\(548\) | 1.91994 | − | 1.10848i | 0.0820158 | − | 0.0473518i | ||||
\(549\) | 19.7528 | − | 11.4043i | 0.843028 | − | 0.486723i | ||||
\(550\) | −0.723655 | + | 1.25341i | −0.0308567 | + | 0.0534454i | ||||
\(551\) | 4.50395 | + | 7.80107i | 0.191875 | + | 0.332337i | ||||
\(552\) | − | 1.53958i | − | 0.0655287i | ||||||
\(553\) | 0.420078 | + | 0.727597i | 0.0178635 | + | 0.0309406i | ||||
\(554\) | −1.79129 | + | 3.10261i | −0.0761047 | + | 0.131817i | ||||
\(555\) | 0.240231 | + | 0.416093i | 0.0101972 | + | 0.0176621i | ||||
\(556\) | −2.99371 | + | 5.18526i | −0.126962 | + | 0.219904i | ||||
\(557\) | 16.1028 | + | 9.29695i | 0.682297 | + | 0.393924i | 0.800720 | − | 0.599039i | \(-0.204451\pi\) |
−0.118423 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(558\) | 6.74894 | + | 3.89650i | 0.285705 | + | 0.164952i | ||||
\(559\) | −4.30225 | −0.181966 | ||||||||
\(560\) | −7.15614 | + | 4.13160i | −0.302402 | + | 0.174592i | ||||
\(561\) | 4.16320 | + | 2.40362i | 0.175770 | + | 0.101481i | ||||
\(562\) | 1.71539i | 0.0723593i | ||||||||
\(563\) | 7.07944 | − | 12.2620i | 0.298363 | − | 0.516780i | −0.677399 | − | 0.735616i | \(-0.736893\pi\) |
0.975762 | + | 0.218836i | \(0.0702261\pi\) | |||||||
\(564\) | 3.98458 | − | 2.30050i | 0.167781 | − | 0.0968685i | ||||
\(565\) | − | 10.2292i | − | 0.430344i | ||||||
\(566\) | 3.78619 | − | 2.18596i | 0.159146 | − | 0.0918827i | ||||
\(567\) | 11.6858i | 0.490758i | ||||||||
\(568\) | −0.273673 | − | 0.474016i | −0.0114831 | − | 0.0198893i | ||||
\(569\) | 15.2521 | − | 8.80581i | 0.639402 | − | 0.369159i | −0.144982 | − | 0.989434i | \(-0.546313\pi\) |
0.784384 | + | 0.620275i | \(0.212979\pi\) | |||||||
\(570\) | −0.102374 | + | 0.0591054i | −0.00428796 | + | 0.00247565i | ||||
\(571\) | 18.5509i | 0.776332i | 0.921590 | + | 0.388166i | \(0.126891\pi\) | ||||
−0.921590 | + | 0.388166i | \(0.873109\pi\) | |||||||
\(572\) | −4.77092 | −0.199482 | ||||||||
\(573\) | −4.14319 | −0.173084 | ||||||||
\(574\) | −1.72881 | + | 2.99439i | −0.0721593 | + | 0.124984i | ||||
\(575\) | 5.90983 | − | 10.2361i | 0.246457 | − | 0.426876i | ||||
\(576\) | 9.28359 | + | 16.0796i | 0.386816 | + | 0.669985i | ||||
\(577\) | −12.8099 | −0.533283 | −0.266642 | − | 0.963796i | \(-0.585914\pi\) | ||||
−0.266642 | + | 0.963796i | \(0.585914\pi\) | |||||||
\(578\) | 7.16529 | − | 4.13688i | 0.298037 | − | 0.172072i | ||||
\(579\) | 5.56933 | − | 3.21545i | 0.231453 | − | 0.133630i | ||||
\(580\) | −30.4152 | −1.26292 | ||||||||
\(581\) | 9.44526 | + | 5.45322i | 0.391855 | + | 0.226238i | ||||
\(582\) | −0.492424 | − | 0.852904i | −0.0204116 | − | 0.0353540i | ||||
\(583\) | 25.9312 | 1.07396 | ||||||||
\(584\) | −1.63136 | − | 0.941867i | −0.0675062 | − | 0.0389747i | ||||
\(585\) | 4.38021 | − | 2.52892i | 0.181099 | − | 0.104558i | ||||
\(586\) | −1.24485 | − | 0.718716i | −0.0514244 | − | 0.0296899i | ||||
\(587\) | −16.5620 | + | 28.6863i | −0.683589 | + | 1.18401i | 0.290290 | + | 0.956939i | \(0.406248\pi\) |
−0.973878 | + | 0.227071i | \(0.927085\pi\) | |||||||
\(588\) | −2.88633 | −0.119030 | ||||||||
\(589\) | 4.69224 | − | 8.12720i | 0.193340 | − | 0.334875i | ||||
\(590\) | −1.88291 | + | 3.26129i | −0.0775180 | + | 0.134265i | ||||
\(591\) | −0.686671 | + | 0.396450i | −0.0282459 | + | 0.0163078i | ||||
\(592\) | 1.77341 | + | 3.07163i | 0.0728865 | + | 0.126243i | ||||
\(593\) | −4.07226 | − | 2.35112i | −0.167228 | − | 0.0965489i | 0.414050 | − | 0.910254i | \(-0.364114\pi\) |
−0.581278 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(594\) | 0.537882 | + | 0.931640i | 0.0220696 | + | 0.0382256i | ||||
\(595\) | − | 16.0212i | − | 0.656804i | ||||||
\(596\) | 4.64989i | 0.190467i | ||||||||
\(597\) | − | 6.81058i | − | 0.278738i | ||||||
\(598\) | −1.40088 | −0.0572860 | ||||||||
\(599\) | −6.82546 | + | 3.94068i | −0.278881 | + | 0.161012i | −0.632917 | − | 0.774220i | \(-0.718142\pi\) |
0.354036 | + | 0.935232i | \(0.384809\pi\) | |||||||
\(600\) | 0.746436i | 0.0304731i | ||||||||
\(601\) | −6.88820 | + | 3.97690i | −0.280975 | + | 0.162221i | −0.633865 | − | 0.773444i | \(-0.718532\pi\) |
0.352889 | + | 0.935665i | \(0.385199\pi\) | |||||||
\(602\) | −1.30027 | + | 0.750709i | −0.0529949 | + | 0.0305966i | ||||
\(603\) | −22.5326 | − | 39.0275i | −0.917597 | − | 1.58932i | ||||
\(604\) | −2.67180 | − | 4.62769i | −0.108714 | − | 0.188298i | ||||
\(605\) | 4.62834 | − | 8.01651i | 0.188169 | − | 0.325918i | ||||
\(606\) | 1.00484 | 0.0408187 | ||||||||
\(607\) | −10.2194 | + | 17.7005i | −0.414793 | + | 0.718443i | −0.995407 | − | 0.0957364i | \(-0.969479\pi\) |
0.580613 | + | 0.814179i | \(0.302813\pi\) | |||||||
\(608\) | −2.41135 | + | 1.39219i | −0.0977931 | + | 0.0564609i | ||||
\(609\) | 3.62998 | + | 2.09577i | 0.147094 | + | 0.0849249i | ||||
\(610\) | −3.33445 | −0.135008 | ||||||||
\(611\) | −4.26175 | − | 7.38157i | −0.172412 | − | 0.298627i | ||||
\(612\) | −39.0772 | −1.57960 | ||||||||
\(613\) | 8.65475 | − | 14.9905i | 0.349562 | − | 0.605459i | −0.636610 | − | 0.771186i | \(-0.719664\pi\) |
0.986172 | + | 0.165727i | \(0.0529970\pi\) | |||||||
\(614\) | −0.640645 | − | 0.369876i | −0.0258543 | − | 0.0149270i | ||||
\(615\) | 2.23607 | + | 3.87299i | 0.0901671 | + | 0.156174i | ||||
\(616\) | −2.93567 | + | 1.69491i | −0.118281 | + | 0.0682898i | ||||
\(617\) | −16.7959 | + | 29.0913i | −0.676175 | + | 1.17117i | 0.299948 | + | 0.953955i | \(0.403031\pi\) |
−0.976124 | + | 0.217215i | \(0.930303\pi\) | |||||||
\(618\) | 0.774078 | 0.0311380 | ||||||||
\(619\) | − | 17.3770i | − | 0.698442i | −0.937040 | − | 0.349221i | \(-0.886446\pi\) | ||
0.937040 | − | 0.349221i | \(-0.113554\pi\) | |||||||
\(620\) | 15.8434 | + | 27.4415i | 0.636285 | + | 1.10208i | ||||
\(621\) | −4.39269 | − | 7.60837i | −0.176273 | − | 0.305313i | ||||
\(622\) | 1.79556 | + | 3.11000i | 0.0719954 | + | 0.124700i | ||||
\(623\) | −23.7554 | −0.951741 | ||||||||
\(624\) | −1.00765 | + | 0.581768i | −0.0403384 | + | 0.0232894i | ||||
\(625\) | 3.65008 | − | 6.32212i | 0.146003 | − | 0.252885i | ||||
\(626\) | −4.03943 | + | 2.33217i | −0.161448 | + | 0.0932121i | ||||
\(627\) | 0.552343 | − | 0.318895i | 0.0220584 | − | 0.0127354i | ||||
\(628\) | −15.4373 | − | 26.7382i | −0.616016 | − | 1.06697i | ||||
\(629\) | −6.87677 | −0.274195 | ||||||||
\(630\) | 0.882552 | − | 1.52862i | 0.0351617 | − | 0.0609019i | ||||
\(631\) | 49.3236 | 1.96354 | 0.981770 | − | 0.190070i | \(-0.0608716\pi\) | ||||
0.981770 | + | 0.190070i | \(0.0608716\pi\) | |||||||
\(632\) | −0.609935 | −0.0242619 | ||||||||
\(633\) | − | 0.458313i | − | 0.0182163i | ||||||
\(634\) | −1.56443 | −0.0621316 | ||||||||
\(635\) | −30.4315 | − | 17.5696i | −1.20764 | − | 0.697229i | ||||
\(636\) | 5.68875 | − | 3.28440i | 0.225573 | − | 0.130235i | ||||
\(637\) | 5.34703i | 0.211857i | ||||||||
\(638\) | −5.90019 | −0.233591 | ||||||||
\(639\) | −1.33171 | − | 0.768860i | −0.0526814 | − | 0.0304156i | ||||
\(640\) | − | 12.4539i | − | 0.492284i | ||||||
\(641\) | −24.8742 | − | 43.0833i | −0.982471 | − | 1.70169i | −0.652676 | − | 0.757637i | \(-0.726354\pi\) |
−0.329795 | − | 0.944053i | \(-0.606980\pi\) | |||||||
\(642\) | −0.227157 | − | 0.393447i | −0.00896516 | − | 0.0155281i | ||||
\(643\) | 2.35775 | + | 1.36125i | 0.0929806 | + | 0.0536824i | 0.545769 | − | 0.837935i | \(-0.316237\pi\) |
−0.452789 | + | 0.891618i | \(0.649571\pi\) | |||||||
\(644\) | 11.7756 | − | 6.79863i | 0.464023 | − | 0.267904i | ||||
\(645\) | 1.94196i | 0.0764644i | ||||||||
\(646\) | − | 1.69193i | − | 0.0665681i | ||||||
\(647\) | 13.9952 | − | 24.2404i | 0.550207 | − | 0.952987i | −0.448052 | − | 0.894008i | \(-0.647882\pi\) |
0.998259 | − | 0.0589796i | \(-0.0187847\pi\) | |||||||
\(648\) | −7.34705 | − | 4.24182i | −0.288619 | − | 0.166634i | ||||
\(649\) | 10.1590 | − | 17.5958i | 0.398774 | − | 0.690697i | ||||
\(650\) | 0.679190 | 0.0266400 | ||||||||
\(651\) | − | 4.36677i | − | 0.171147i | ||||||
\(652\) | −27.6627 | − | 15.9711i | −1.08336 | − | 0.625476i | ||||
\(653\) | −4.23861 | −0.165870 | −0.0829348 | − | 0.996555i | \(-0.526429\pi\) | ||||
−0.0829348 | + | 0.996555i | \(0.526429\pi\) | |||||||
\(654\) | 0.514088 | + | 0.296809i | 0.0201024 | + | 0.0116062i | ||||
\(655\) | −25.5927 | − | 14.7759i | −0.999989 | − | 0.577344i | ||||
\(656\) | 16.5069 | + | 28.5907i | 0.644484 | + | 1.11628i | ||||
\(657\) | −5.29218 | −0.206468 | ||||||||
\(658\) | −2.57605 | − | 1.48729i | −0.100425 | − | 0.0579804i | ||||
\(659\) | 6.43426i | 0.250643i | 0.992116 | + | 0.125322i | \(0.0399963\pi\) | ||||
−0.992116 | + | 0.125322i | \(0.960004\pi\) | |||||||
\(660\) | 2.15350i | 0.0838250i | ||||||||
\(661\) | −3.71144 | −0.144358 | −0.0721792 | − | 0.997392i | \(-0.522995\pi\) | ||||
−0.0721792 | + | 0.997392i | \(0.522995\pi\) | |||||||
\(662\) | −5.29586 | −0.205830 | ||||||||
\(663\) | − | 2.25593i | − | 0.0876132i | ||||||
\(664\) | −6.85705 | + | 3.95892i | −0.266105 | + | 0.153636i | ||||
\(665\) | −1.84080 | − | 1.06279i | −0.0713831 | − | 0.0412130i | ||||
\(666\) | −0.656131 | − | 0.378818i | −0.0254246 | − | 0.0146789i | ||||
\(667\) | 48.1847 | 1.86572 | ||||||||
\(668\) | 36.4050 | + | 21.0184i | 1.40855 | + | 0.813228i | ||||
\(669\) | −2.27358 | + | 3.93796i | −0.0879018 | + | 0.152250i | ||||
\(670\) | 6.58821i | 0.254525i | ||||||||
\(671\) | 17.9906 | 0.694519 | ||||||||
\(672\) | −0.647813 | + | 1.12205i | −0.0249899 | + | 0.0432838i | ||||
\(673\) | 10.9305 | + | 18.9321i | 0.421338 | + | 0.729779i | 0.996071 | − | 0.0885620i | \(-0.0282271\pi\) |
−0.574732 | + | 0.818341i | \(0.694894\pi\) | |||||||
\(674\) | 5.87308 | + | 3.39082i | 0.226223 | + | 0.130610i | ||||
\(675\) | 2.12972 | + | 3.68878i | 0.0819730 | + | 0.141981i | ||||
\(676\) | −11.4294 | − | 19.7963i | −0.439591 | − | 0.761394i | ||||
\(677\) | 30.3095i | 1.16489i | 0.812871 | + | 0.582444i | \(0.197903\pi\) | ||||
−0.812871 | + | 0.582444i | \(0.802097\pi\) | |||||||
\(678\) | −0.251332 | − | 0.435320i | −0.00965236 | − | 0.0167184i | ||||
\(679\) | 8.85437 | − | 15.3362i | 0.339800 | − | 0.588550i | ||||
\(680\) | 10.0728 | + | 5.81551i | 0.386273 | + | 0.223015i | ||||
\(681\) | −2.82092 | −0.108098 | ||||||||
\(682\) | 3.07342 | + | 5.32332i | 0.117687 | + | 0.203841i | ||||
\(683\) | −6.11410 | − | 10.5899i | −0.233949 | − | 0.405212i | 0.725017 | − | 0.688731i | \(-0.241832\pi\) |
−0.958967 | + | 0.283518i | \(0.908498\pi\) | |||||||
\(684\) | −2.59223 | + | 4.48988i | −0.0991165 | + | 0.171675i | ||||
\(685\) | −1.60545 | + | 0.926908i | −0.0613412 | + | 0.0354154i | ||||
\(686\) | 2.24838 | + | 3.89430i | 0.0858434 | + | 0.148685i | ||||
\(687\) | 3.82841i | 0.146063i | ||||||||
\(688\) | 14.3357i | 0.546542i | ||||||||
\(689\) | −6.08446 | − | 10.5386i | −0.231800 | − | 0.401489i | ||||
\(690\) | 0.632329i | 0.0240723i | ||||||||
\(691\) | −1.58963 | + | 0.917771i | −0.0604722 | + | 0.0349136i | −0.529931 | − | 0.848041i | \(-0.677782\pi\) |
0.469459 | + | 0.882954i | \(0.344449\pi\) | |||||||
\(692\) | − | 29.8114i | − | 1.13326i | ||||||
\(693\) | −4.76169 | + | 8.24749i | −0.180882 | + | 0.313296i | ||||
\(694\) | −3.64935 | + | 6.32086i | −0.138527 | + | 0.239936i | ||||
\(695\) | 2.50334 | − | 4.33591i | 0.0949570 | − | 0.164470i | ||||
\(696\) | −2.63529 | + | 1.52148i | −0.0998903 | + | 0.0576717i | ||||
\(697\) | −64.0089 | −2.42451 | ||||||||
\(698\) | −1.89370 | − | 4.54304i | −0.0716776 | − | 0.171956i | ||||
\(699\) | −7.19660 | −0.272201 | ||||||||
\(700\) | −5.70918 | + | 3.29620i | −0.215787 | + | 0.124585i | ||||
\(701\) | 19.0609 | − | 33.0144i | 0.719919 | − | 1.24694i | −0.241112 | − | 0.970497i | \(-0.577512\pi\) |
0.961031 | − | 0.276440i | \(-0.0891546\pi\) | |||||||
\(702\) | 0.252416 | − | 0.437198i | 0.00952683 | − | 0.0165010i | ||||
\(703\) | −0.456179 | + | 0.790126i | −0.0172051 | + | 0.0298002i | ||||
\(704\) | 14.6451i | 0.551959i | ||||||||
\(705\) | −3.33190 | + | 1.92368i | −0.125487 | + | 0.0724498i | ||||
\(706\) | 3.02295i | 0.113770i | ||||||||
\(707\) | 9.03409 | + | 15.6475i | 0.339762 | + | 0.588485i | ||||
\(708\) | − | 5.14687i | − | 0.193431i | ||||||
\(709\) | 17.0720i | 0.641153i | 0.947223 | + | 0.320576i | \(0.103877\pi\) | ||||
−0.947223 | + | 0.320576i | \(0.896123\pi\) | |||||||
\(710\) | 0.112402 | + | 0.194686i | 0.00421837 | + | 0.00730644i | ||||
\(711\) | −1.48398 | + | 0.856779i | −0.0556538 | + | 0.0321317i | ||||
\(712\) | 8.62295 | − | 14.9354i | 0.323159 | − | 0.559727i | ||||
\(713\) | −25.0995 | − | 43.4737i | −0.939985 | − | 1.62810i | ||||
\(714\) | −0.393643 | − | 0.681809i | −0.0147317 | − | 0.0255161i | ||||
\(715\) | 3.98944 | 0.149197 | ||||||||
\(716\) | −25.7226 | − | 14.8509i | −0.961298 | − | 0.555006i | ||||
\(717\) | 0.998124 | − | 1.72880i | 0.0372756 | − | 0.0645633i | ||||
\(718\) | 1.63881 | + | 2.83851i | 0.0611600 | + | 0.105932i | ||||
\(719\) | 30.1437i | 1.12417i | 0.827079 | + | 0.562086i | \(0.190001\pi\) | ||||
−0.827079 | + | 0.562086i | \(0.809999\pi\) | |||||||
\(720\) | −8.42668 | − | 14.5954i | −0.314044 | − | 0.543940i | ||||
\(721\) | 6.95942 | + | 12.0541i | 0.259182 | + | 0.448917i | ||||
\(722\) | 4.14077 | + | 2.39067i | 0.154103 | + | 0.0889717i | ||||
\(723\) | 0.112244 | + | 0.194413i | 0.00417441 | + | 0.00723029i | ||||
\(724\) | −16.2775 | + | 28.1934i | −0.604948 | + | 1.04780i | ||||
\(725\) | −23.3615 | −0.867625 | ||||||||
\(726\) | − | 0.454876i | − | 0.0168820i | ||||||
\(727\) | 10.6416 | − | 18.4318i | 0.394675 | − | 0.683597i | −0.598385 | − | 0.801209i | \(-0.704191\pi\) |
0.993060 | + | 0.117612i | \(0.0375240\pi\) | |||||||
\(728\) | 1.37764 | + | 0.795382i | 0.0510588 | + | 0.0294788i | ||||
\(729\) | −22.2267 | −0.823213 | ||||||||
\(730\) | 0.670026 | + | 0.386840i | 0.0247988 | + | 0.0143176i | ||||
\(731\) | −24.0710 | − | 13.8974i | −0.890300 | − | 0.514015i | ||||
\(732\) | 3.94675 | − | 2.27865i | 0.145876 | − | 0.0842215i | ||||
\(733\) | 10.3040i | 0.380588i | 0.981727 | + | 0.190294i | \(0.0609441\pi\) | ||||
−0.981727 | + | 0.190294i | \(0.939056\pi\) | |||||||
\(734\) | 0.343677 | 0.0126854 | ||||||||
\(735\) | 2.41355 | 0.0890250 | ||||||||
\(736\) | 14.8941i | 0.549005i | ||||||||
\(737\) | − | 35.5458i | − | 1.30935i | ||||||
\(738\) | −6.10727 | − | 3.52603i | −0.224812 | − | 0.129795i | ||||
\(739\) | 30.1693 | 1.10980 | 0.554898 | − | 0.831919i | \(-0.312757\pi\) | ||||
0.554898 | + | 0.831919i | \(0.312757\pi\) | |||||||
\(740\) | −1.54029 | − | 2.66786i | −0.0566222 | − | 0.0980726i | ||||
\(741\) | −0.259202 | − | 0.149650i | −0.00952202 | − | 0.00549754i | ||||
\(742\) | −3.67781 | − | 2.12338i | −0.135017 | − | 0.0779518i | ||||
\(743\) | −29.1395 | −1.06902 | −0.534512 | − | 0.845161i | \(-0.679505\pi\) | ||||
−0.534512 | + | 0.845161i | \(0.679505\pi\) | |||||||
\(744\) | 2.74545 | + | 1.58509i | 0.100653 | + | 0.0581122i | ||||
\(745\) | − | 3.88824i | − | 0.142454i | ||||||
\(746\) | 9.70407 | 0.355291 | ||||||||
\(747\) | −11.1222 | + | 19.2643i | −0.406941 | + | 0.704842i | ||||
\(748\) | −26.6932 | − | 15.4113i | −0.976001 | − | 0.563494i | ||||
\(749\) | 4.08455 | − | 7.07464i | 0.149246 | − | 0.258502i | ||||
\(750\) | − | 0.946907i | − | 0.0345762i | ||||||
\(751\) | 13.9733i | 0.509892i | 0.966955 | + | 0.254946i | \(0.0820577\pi\) | ||||
−0.966955 | + | 0.254946i | \(0.917942\pi\) | |||||||
\(752\) | −24.5964 | + | 14.2007i | −0.896937 | + | 0.517847i | ||||
\(753\) | −2.56720 | − | 1.48217i | −0.0935539 | − | 0.0540134i | ||||
\(754\) | 1.38441 | + | 2.39787i | 0.0504173 | + | 0.0873254i | ||||
\(755\) | 2.23415 | + | 3.86967i | 0.0813092 | + | 0.140832i | ||||
\(756\) | 4.90004i | 0.178213i | ||||||||
\(757\) | 5.39746 | + | 3.11623i | 0.196174 | + | 0.113261i | 0.594870 | − | 0.803822i | \(-0.297204\pi\) |
−0.398696 | + | 0.917083i | \(0.630537\pi\) | |||||||
\(758\) | −4.51105 | −0.163849 | ||||||||
\(759\) | − | 3.41164i | − | 0.123835i | ||||||
\(760\) | 1.33638 | − | 0.771559i | 0.0484756 | − | 0.0279874i | ||||
\(761\) | 36.0638 | + | 20.8214i | 1.30731 | + | 0.754776i | 0.981647 | − | 0.190710i | \(-0.0610789\pi\) |
0.325664 | + | 0.945486i | \(0.394412\pi\) | |||||||
\(762\) | −1.72675 | −0.0625537 | ||||||||
\(763\) | 10.6740i | 0.386423i | ||||||||
\(764\) | 26.5649 | 0.961085 | ||||||||
\(765\) | 32.6763 | 1.18141 | ||||||||
\(766\) | −2.21648 | + | 3.83906i | −0.0800848 | + | 0.138711i | ||||
\(767\) | −9.53475 | −0.344280 | ||||||||
\(768\) | 1.61562 | + | 2.79834i | 0.0582988 | + | 0.100977i | ||||
\(769\) | −20.2038 | + | 11.6647i | −0.728567 | + | 0.420638i | −0.817898 | − | 0.575364i | \(-0.804860\pi\) |
0.0893309 | + | 0.996002i | \(0.471527\pi\) | |||||||
\(770\) | 1.20573 | − | 0.696126i | 0.0434513 | − | 0.0250866i | ||||
\(771\) | 1.47219 | − | 2.54990i | 0.0530195 | − | 0.0918324i | ||||
\(772\) | −35.7089 | + | 20.6165i | −1.28519 | + | 0.742005i | ||||
\(773\) | −11.5799 | −0.416499 | −0.208249 | − | 0.978076i | \(-0.566777\pi\) | ||||
−0.208249 | + | 0.978076i | \(0.566777\pi\) | |||||||
\(774\) | −1.53112 | − | 2.65198i | −0.0550351 | − | 0.0953236i | ||||
\(775\) | 12.1691 | + | 21.0775i | 0.437126 | + | 0.757124i | ||||
\(776\) | 6.42808 | + | 11.1338i | 0.230755 | + | 0.399679i | ||||
\(777\) | 0.424537i | 0.0152302i | ||||||||
\(778\) | 2.32627 | 0.0834007 | ||||||||
\(779\) | −4.24612 | + | 7.35449i | −0.152133 | + | 0.263502i | ||||
\(780\) | 0.875197 | − | 0.505295i | 0.0313371 | − | 0.0180925i | ||||
\(781\) | −0.606450 | − | 1.05040i | −0.0217005 | − | 0.0375863i | ||||
\(782\) | −7.83788 | − | 4.52520i | −0.280282 | − | 0.161821i | ||||
\(783\) | −8.68214 | + | 15.0379i | −0.310275 | + | 0.537411i | ||||
\(784\) | 17.8170 | 0.636321 | ||||||||
\(785\) | 12.9087 | + | 22.3585i | 0.460730 | + | 0.798008i | ||||
\(786\) | −1.45219 | −0.0517979 | ||||||||
\(787\) | −23.6846 | − | 13.6743i | −0.844266 | − | 0.487437i | 0.0144458 | − | 0.999896i | \(-0.495402\pi\) |
−0.858712 | + | 0.512458i | \(0.828735\pi\) | |||||||
\(788\) | 4.40274 | − | 2.54192i | 0.156841 | − | 0.0905522i | ||||
\(789\) | −1.80182 | + | 3.12084i | −0.0641465 | + | 0.111105i | ||||
\(790\) | 0.250510 | 0.00891275 | ||||||||
\(791\) | 4.51925 | − | 7.82757i | 0.160686 | − | 0.278316i | ||||
\(792\) | −3.45688 | − | 5.98749i | −0.122835 | − | 0.212756i | ||||
\(793\) | −4.22129 | − | 7.31148i | −0.149902 | − | 0.259638i | ||||
\(794\) | −1.99566 | + | 1.15219i | −0.0708233 | + | 0.0408899i | ||||
\(795\) | −4.75693 | + | 2.74641i | −0.168711 | + | 0.0974052i | ||||
\(796\) | 43.6674i | 1.54775i | ||||||||
\(797\) | 20.5438 | − | 11.8610i | 0.727699 | − | 0.420137i | −0.0898807 | − | 0.995953i | \(-0.528649\pi\) |
0.817580 | + | 0.575815i | \(0.195315\pi\) | |||||||
\(798\) | −0.104451 | −0.00369753 | ||||||||
\(799\) | − | 55.0664i | − | 1.94811i | ||||||
\(800\) | − | 7.22116i | − | 0.255306i | ||||||
\(801\) | − | 48.4508i | − | 1.71193i | ||||||
\(802\) | −1.85364 | − | 3.21061i | −0.0654545 | − | 0.113370i | ||||
\(803\) | −3.61504 | − | 2.08714i | −0.127572 | − | 0.0736536i | ||||
\(804\) | −4.50216 | − | 7.79798i | −0.158779 | − | 0.275013i | ||||
\(805\) | −9.84673 | + | 5.68501i | −0.347052 | + | 0.200370i | ||||
\(806\) | 1.44229 | − | 2.49812i | 0.0508024 | − | 0.0879924i | ||||
\(807\) | 0.717817 | − | 1.24329i | 0.0252683 | − | 0.0437661i | ||||
\(808\) | −13.1171 | −0.461458 | ||||||||
\(809\) | −7.81992 | + | 13.5445i | −0.274934 | + | 0.476199i | −0.970118 | − | 0.242632i | \(-0.921989\pi\) |
0.695185 | + | 0.718831i | \(0.255323\pi\) | |||||||
\(810\) | 3.01755 | + | 1.74218i | 0.106026 | + | 0.0612141i | ||||
\(811\) | −30.7378 | + | 17.7465i | −1.07935 | + | 0.623162i | −0.930721 | − | 0.365731i | \(-0.880819\pi\) |
−0.148628 | + | 0.988893i | \(0.547486\pi\) | |||||||
\(812\) | −23.2744 | − | 13.4375i | −0.816771 | − | 0.471563i | ||||
\(813\) | −6.45694 | −0.226455 | ||||||||
\(814\) | −0.298798 | − | 0.517533i | −0.0104729 | − | 0.0181395i | ||||
\(815\) | 23.1315 | + | 13.3550i | 0.810263 | + | 0.467805i | ||||
\(816\) | −7.51707 | −0.263150 | ||||||||
\(817\) | −3.19357 | + | 1.84381i | −0.111729 | + | 0.0645067i | ||||
\(818\) | −3.23200 | + | 1.86600i | −0.113004 | + | 0.0652431i | ||||
\(819\) | 4.46911 | 0.156163 | ||||||||
\(820\) | −14.3370 | − | 24.8325i | −0.500671 | − | 0.867188i | ||||
\(821\) | 3.56750 | − | 6.17910i | 0.124507 | − | 0.215652i | −0.797033 | − | 0.603935i | \(-0.793598\pi\) |
0.921540 | + | 0.388283i | \(0.126932\pi\) | |||||||
\(822\) | −0.0455486 | + | 0.0788925i | −0.00158869 | + | 0.00275169i | ||||
\(823\) | 21.2447 | 0.740542 | 0.370271 | − | 0.928924i | \(-0.379265\pi\) | ||||
0.370271 | + | 0.928924i | \(0.379265\pi\) | |||||||
\(824\) | −10.1048 | −0.352016 | ||||||||
\(825\) | 1.65408i | 0.0575875i | ||||||||
\(826\) | −2.88168 | + | 1.66374i | −0.100266 | + | 0.0578889i | ||||
\(827\) | 39.7586 | − | 22.9546i | 1.38254 | − | 0.798210i | 0.390081 | − | 0.920781i | \(-0.372447\pi\) |
0.992460 | + | 0.122571i | \(0.0391138\pi\) | |||||||
\(828\) | 13.8663 | + | 24.0171i | 0.481887 | + | 0.834652i | ||||
\(829\) | − | 14.2142i | − | 0.493678i | −0.969057 | − | 0.246839i | \(-0.920608\pi\) | ||
0.969057 | − | 0.246839i | \(-0.0793919\pi\) | |||||||
\(830\) | 2.81630 | − | 1.62599i | 0.0977552 | − | 0.0564390i | ||||
\(831\) | 4.09440i | 0.142033i | ||||||||
\(832\) | 5.95187 | − | 3.43632i | 0.206344 | − | 0.119133i | ||||
\(833\) | −17.2723 | + | 29.9165i | −0.598450 | + | 1.03655i | ||||
\(834\) | − | 0.246030i | − | 0.00851931i | ||||||
\(835\) | −30.4418 | − | 17.5756i | −1.05348 | − | 0.608229i | ||||
\(836\) | −3.54146 | + | 2.04466i | −0.122484 | + | 0.0707161i | ||||
\(837\) | 18.0902 | 0.625289 | ||||||||
\(838\) | −6.79710 | − | 3.92431i | −0.234802 | − | 0.135563i | ||||
\(839\) | −19.5216 | − | 11.2708i | −0.673961 | − | 0.389112i | 0.123615 | − | 0.992330i | \(-0.460551\pi\) |
−0.797576 | + | 0.603219i | \(0.793885\pi\) | |||||||
\(840\) | 0.359020 | − | 0.621842i | 0.0123874 | − | 0.0214556i | ||||
\(841\) | −33.1185 | − | 57.3629i | −1.14202 | − | 1.97803i | ||||
\(842\) | 3.00968 | − | 5.21293i | 0.103721 | − | 0.179649i | ||||
\(843\) | 0.980227 | + | 1.69780i | 0.0337608 | + | 0.0584754i | ||||
\(844\) | 2.93857i | 0.101150i | ||||||||
\(845\) | 9.55723 | + | 16.5536i | 0.328779 | + | 0.569462i | ||||
\(846\) | 3.03342 | − | 5.25404i | 0.104291 | − | 0.180638i | ||||
\(847\) | 7.08340 | − | 4.08960i | 0.243389 | − | 0.140520i | ||||
\(848\) | −35.1160 | + | 20.2742i | −1.20589 | + | 0.696220i | ||||
\(849\) | 2.49825 | − | 4.32710i | 0.0857397 | − | 0.148506i | ||||
\(850\) | 3.80006 | + | 2.19396i | 0.130341 | + | 0.0752523i | ||||
\(851\) | 2.44018 | + | 4.22651i | 0.0836482 | + | 0.144883i | ||||
\(852\) | −0.266084 | − | 0.153624i | −0.00911589 | − | 0.00526306i | ||||
\(853\) | 4.66536 | − | 8.08064i | 0.159739 | − | 0.276676i | −0.775036 | − | 0.631918i | \(-0.782268\pi\) |
0.934774 | + | 0.355242i | \(0.115601\pi\) | |||||||
\(854\) | −2.55159 | − | 1.47316i | −0.0873137 | − | 0.0504106i | ||||
\(855\) | 2.16762 | − | 3.75444i | 0.0741312 | − | 0.128399i | ||||
\(856\) | 2.96529 | + | 5.13604i | 0.101352 | + | 0.175546i | ||||
\(857\) | 37.1371 | + | 21.4411i | 1.26858 | + | 0.732415i | 0.974719 | − | 0.223433i | \(-0.0717264\pi\) |
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(858\) | 0.169778 | − | 0.0980212i | 0.00579611 | − | 0.00334639i | ||||
\(859\) | 34.8643 | + | 20.1289i | 1.18955 | + | 0.686789i | 0.958205 | − | 0.286082i | \(-0.0923530\pi\) |
0.231348 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(860\) | − | 12.4513i | − | 0.424584i | ||||||
\(861\) | 3.95159i | 0.134670i | ||||||||
\(862\) | −0.222828 | + | 0.385949i | −0.00758954 | + | 0.0131455i | ||||
\(863\) | −6.96178 | + | 4.01938i | −0.236982 | + | 0.136821i | −0.613789 | − | 0.789470i | \(-0.710355\pi\) |
0.376807 | + | 0.926292i | \(0.377022\pi\) | |||||||
\(864\) | −4.64829 | − | 2.68369i | −0.158138 | − | 0.0913011i | ||||
\(865\) | 24.9283i | 0.847587i | ||||||||
\(866\) | 1.63791 | 0.0556584 | ||||||||
\(867\) | 4.72789 | − | 8.18895i | 0.160568 | − | 0.278111i | ||||
\(868\) | 27.9985i | 0.950329i | ||||||||
\(869\) | −1.35159 | −0.0458497 | ||||||||
\(870\) | 1.08235 | − | 0.624898i | 0.0366953 | − | 0.0211860i | ||||
\(871\) | −14.4460 | + | 8.34042i | −0.489485 | + | 0.282604i | ||||
\(872\) | −6.71088 | − | 3.87453i | −0.227259 | − | 0.131208i | ||||
\(873\) | 31.2793 | + | 18.0591i | 1.05864 | + | 0.611208i | ||||
\(874\) | −1.03987 | + | 0.600370i | −0.0351742 | + | 0.0203078i | ||||
\(875\) | 14.7454 | − | 8.51326i | 0.498485 | − | 0.287801i | ||||
\(876\) | −1.05741 | −0.0357267 | ||||||||
\(877\) | − | 42.4971i | − | 1.43502i | −0.696546 | − | 0.717512i | \(-0.745281\pi\) | ||
0.696546 | − | 0.717512i | \(-0.254719\pi\) | |||||||
\(878\) | 3.87629 | − | 6.71393i | 0.130818 | − | 0.226584i | ||||
\(879\) | −1.64279 | −0.0554098 | ||||||||
\(880\) | − | 13.2933i | − | 0.448118i | ||||||
\(881\) | 32.1268 | + | 18.5484i | 1.08238 | + | 0.624911i | 0.931537 | − | 0.363647i | \(-0.118468\pi\) |
0.150841 | + | 0.988558i | \(0.451802\pi\) | |||||||
\(882\) | −3.29600 | + | 1.90295i | −0.110982 | + | 0.0640756i | ||||
\(883\) | 25.2766 | − | 43.7803i | 0.850625 | − | 1.47333i | −0.0300202 | − | 0.999549i | \(-0.509557\pi\) |
0.880645 | − | 0.473776i | \(-0.157109\pi\) | |||||||
\(884\) | 14.4644i | 0.486490i | ||||||||
\(885\) | 4.30381i | 0.144671i | ||||||||
\(886\) | 0.821022 | + | 0.474017i | 0.0275828 | + | 0.0159249i | ||||
\(887\) | −3.95535 | + | 2.28362i | −0.132808 | + | 0.0766766i | −0.564932 | − | 0.825138i | \(-0.691098\pi\) |
0.432124 | + | 0.901814i | \(0.357764\pi\) | |||||||
\(888\) | −0.266913 | − | 0.154102i | −0.00895702 | − | 0.00517134i | ||||
\(889\) | −15.5245 | − | 26.8893i | −0.520676 | − | 0.901838i | ||||
\(890\) | −3.54159 | + | 6.13421i | −0.118714 | + | 0.205619i | ||||
\(891\) | −16.2808 | − | 9.39972i | −0.545427 | − | 0.314902i | ||||
\(892\) | 14.5775 | − | 25.2491i | 0.488092 | − | 0.845401i | ||||
\(893\) | −6.32701 | − | 3.65290i | −0.211725 | − | 0.122240i | ||||
\(894\) | −0.0955347 | − | 0.165471i | −0.00319516 | − | 0.00553418i | ||||
\(895\) | 21.5092 | + | 12.4183i | 0.718974 | + | 0.415100i | ||||
\(896\) | 5.50215 | − | 9.53000i | 0.183814 | − | 0.318375i | ||||
\(897\) | −1.38651 | + | 0.800504i | −0.0462943 | + | 0.0267280i | ||||
\(898\) | −1.56404 | + | 0.903000i | −0.0521928 | + | 0.0301335i | ||||
\(899\) | −49.6092 | + | 85.9256i | −1.65456 | + | 2.86578i | ||||
\(900\) | −6.72282 | − | 11.6443i | −0.224094 | − | 0.388142i | ||||
\(901\) | − | 78.6178i | − | 2.61914i | ||||||
\(902\) | −2.78121 | − | 4.81720i | −0.0926042 | − | 0.160395i | ||||
\(903\) | −0.857958 | + | 1.48603i | −0.0285510 | + | 0.0494519i | ||||
\(904\) | 3.28088 | + | 5.68265i | 0.109120 | + | 0.189002i | ||||
\(905\) | 13.6112 | − | 23.5753i | 0.452452 | − | 0.783670i | ||||
\(906\) | 0.190157 | + | 0.109787i | 0.00631754 | + | 0.00364743i | ||||
\(907\) | 10.2991 | + | 5.94621i | 0.341977 | + | 0.197441i | 0.661146 | − | 0.750257i | \(-0.270070\pi\) |
−0.319169 | + | 0.947698i | \(0.603404\pi\) | |||||||
\(908\) | 18.0869 | 0.600235 | ||||||||
\(909\) | −31.9142 | + | 18.4256i | −1.05853 | + | 0.611140i | ||||
\(910\) | −0.565820 | − | 0.326676i | −0.0187567 | − | 0.0108292i | ||||
\(911\) | 40.9427i | 1.35649i | 0.734834 | + | 0.678247i | \(0.237260\pi\) | ||||
−0.734834 | + | 0.678247i | \(0.762740\pi\) | |||||||
\(912\) | −0.498655 | + | 0.863695i | −0.0165121 | + | 0.0285998i | ||||
\(913\) | −15.1950 | + | 8.77282i | −0.502880 | + | 0.290338i | ||||
\(914\) | − | 5.36710i | − | 0.177528i | ||||||
\(915\) | −3.30027 | + | 1.90541i | −0.109103 | + | 0.0629909i | ||||
\(916\) | − | 24.5466i | − | 0.811043i | ||||||
\(917\) | −13.0560 | − | 22.6137i | −0.431149 | − | 0.746771i | ||||
\(918\) | 2.82453 | − | 1.63074i | 0.0932234 | − | 0.0538225i | ||||
\(919\) | −1.61802 | + | 0.934167i | −0.0533737 | + | 0.0308153i | −0.526449 | − | 0.850206i | \(-0.676477\pi\) |
0.473076 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(920\) | − | 8.25438i | − | 0.272139i | ||||||
\(921\) | −0.845436 | −0.0278581 | ||||||||
\(922\) | 4.96121 | 0.163389 | ||||||||
\(923\) | −0.284593 | + | 0.492930i | −0.00936750 | + | 0.0162250i | ||||
\(924\) | −0.951419 | + | 1.64791i | −0.0312994 | + | 0.0542121i | ||||
\(925\) | −1.18308 | − | 2.04915i | −0.0388993 | − | 0.0673756i | ||||
\(926\) | 6.71194 | 0.220568 | ||||||||
\(927\) | −24.5851 | + | 14.1942i | −0.807481 | + | 0.466199i | ||||
\(928\) | 25.4942 | − | 14.7191i | 0.836889 | − | 0.483178i | ||||
\(929\) | 7.35532 | 0.241320 | 0.120660 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120660 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(930\) | −1.12760 | − | 0.651022i | −0.0369755 | − | 0.0213478i | ||||
\(931\) | 2.29156 | + | 3.96911i | 0.0751030 | + | 0.130082i | ||||
\(932\) | 46.1425 | 1.51145 | ||||||||
\(933\) | 3.55430 | + | 2.05208i | 0.116363 | + | 0.0671820i | ||||
\(934\) | 0.446343 | − | 0.257696i | 0.0146048 | − | 0.00843209i | ||||
\(935\) | 22.3209 | + | 12.8870i | 0.729970 | + | 0.421448i | ||||
\(936\) | −1.62224 | + | 2.80980i | −0.0530245 | + | 0.0918411i | ||||
\(937\) | 16.9665 | 0.554271 | 0.277136 | − | 0.960831i | \(-0.410615\pi\) | ||||
0.277136 | + | 0.960831i | \(0.410615\pi\) | |||||||
\(938\) | −2.91067 | + | 5.04144i | −0.0950369 | + | 0.164609i | ||||
\(939\) | −2.66535 | + | 4.61651i | −0.0869803 | + | 0.150654i | ||||
\(940\) | 21.3632 | − | 12.3340i | 0.696790 | − | 0.402292i | ||||
\(941\) | 5.44623 | + | 9.43315i | 0.177542 | + | 0.307512i | 0.941038 | − | 0.338301i | \(-0.109852\pi\) |
−0.763496 | + | 0.645813i | \(0.776519\pi\) | |||||||
\(942\) | 1.09870 | + | 0.634336i | 0.0357977 | + | 0.0206678i | ||||
\(943\) | 22.7132 | + | 39.3404i | 0.739642 | + | 1.28110i | ||||
\(944\) | 31.7710i | 1.03406i | ||||||||
\(945\) | − | 4.09741i | − | 0.133289i | ||||||
\(946\) | − | 2.41539i | − | 0.0785312i | ||||||
\(947\) | −37.6411 | −1.22317 | −0.611586 | − | 0.791178i | \(-0.709468\pi\) | ||||
−0.611586 | + | 0.791178i | \(0.709468\pi\) | |||||||
\(948\) | −0.296511 | + | 0.171190i | −0.00963022 | + | 0.00556001i | ||||
\(949\) | 1.95890i | 0.0635885i | ||||||||
\(950\) | 0.504164 | − | 0.291079i | 0.0163572 | − | 0.00944385i | ||||
\(951\) | −1.54840 | + | 0.893967i | −0.0502102 | + | 0.0289889i | ||||
\(952\) | 5.13859 | + | 8.90030i | 0.166543 | + | 0.288460i | ||||
\(953\) | 7.69558 | + | 13.3291i | 0.249284 | + | 0.431773i | 0.963327 | − | 0.268329i | \(-0.0864714\pi\) |
−0.714043 | + | 0.700102i | \(0.753138\pi\) | |||||||
\(954\) | 4.33079 | − | 7.50114i | 0.140214 | − | 0.242858i | ||||
\(955\) | −22.2136 | −0.718814 | ||||||||
\(956\) | −6.39968 | + | 11.0846i | −0.206980 | + | 0.358501i | ||||
\(957\) | −5.83970 | + | 3.37155i | −0.188771 | + | 0.108987i | ||||
\(958\) | 2.89626 | + | 1.67216i | 0.0935739 | + | 0.0540249i | ||||
\(959\) | −1.63804 | −0.0528949 | ||||||||
\(960\) | −1.55109 | − | 2.68656i | −0.0500612 | − | 0.0867085i | ||||
\(961\) | 72.3661 | 2.33439 | ||||||||
\(962\) | −0.140219 | + | 0.242867i | −0.00452085 | + | 0.00783034i | ||||
\(963\) | 14.4292 | + | 8.33072i | 0.464975 | + | 0.268454i | ||||
\(964\) | −0.719678 | − | 1.24652i | −0.0231793 | − | 0.0401476i | ||||
\(965\) | 29.8597 | − | 17.2395i | 0.961219 | − | 0.554960i | ||||
\(966\) | −0.279363 | + | 0.483871i | −0.00898837 | + | 0.0155683i | ||||
\(967\) | 5.64108 | 0.181405 | 0.0907024 | − | 0.995878i | \(-0.471089\pi\) | ||||
0.0907024 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(968\) | 5.93793i | 0.190852i | ||||||||
\(969\) | −0.966821 | − | 1.67458i | −0.0310588 | − | 0.0537954i | ||||
\(970\) | −2.64011 | − | 4.57281i | −0.0847690 | − | 0.146824i | ||||
\(971\) | −4.47390 | − | 7.74903i | −0.143574 | − | 0.248678i | 0.785266 | − | 0.619159i | \(-0.212526\pi\) |
−0.928840 | + | 0.370481i | \(0.879193\pi\) | |||||||
\(972\) | −15.0676 | −0.483294 | ||||||||
\(973\) | 3.83122 | − | 2.21195i | 0.122823 | − | 0.0709120i | ||||
\(974\) | −1.85836 | + | 3.21878i | −0.0595458 | + | 0.103136i | ||||
\(975\) | 0.672227 | − | 0.388110i | 0.0215285 | − | 0.0124295i | ||||
\(976\) | −24.3628 | + | 14.0659i | −0.779835 | + | 0.450238i | ||||
\(977\) | 9.76481 | + | 16.9131i | 0.312404 | + | 0.541100i | 0.978882 | − | 0.204425i | \(-0.0655324\pi\) |
−0.666478 | + | 0.745524i | \(0.732199\pi\) | |||||||
\(978\) | 1.31254 | 0.0419704 | ||||||||
\(979\) | 19.1081 | − | 33.0963i | 0.610699 | − | 1.05776i | ||||
\(980\) | −15.4750 | −0.494329 | ||||||||
\(981\) | −21.7703 | −0.695071 | ||||||||
\(982\) | 6.47411i | 0.206597i | ||||||||
\(983\) | −38.9600 | −1.24263 | −0.621315 | − | 0.783561i | \(-0.713401\pi\) | ||||
−0.621315 | + | 0.783561i | \(0.713401\pi\) | |||||||
\(984\) | −2.48443 | − | 1.43438i | −0.0792006 | − | 0.0457265i | ||||
\(985\) | −3.68156 | + | 2.12555i | −0.117304 | + | 0.0677257i | ||||
\(986\) | 17.8881i | 0.569673i | ||||||||
\(987\) | −3.39953 | −0.108208 | ||||||||
\(988\) | 1.66193 | + | 0.959514i | 0.0528730 | + | 0.0305262i | ||||
\(989\) | 19.7256i | 0.627239i | ||||||||
\(990\) | 1.41980 | + | 2.45916i | 0.0451241 | + | 0.0781572i | ||||
\(991\) | 14.3881 | + | 24.9210i | 0.457054 | + | 0.791641i | 0.998804 | − | 0.0488992i | \(-0.0155713\pi\) |
−0.541750 | + | 0.840540i | \(0.682238\pi\) | |||||||
\(992\) | −26.5600 | − | 15.3344i | −0.843281 | − | 0.486869i | ||||
\(993\) | −5.24157 | + | 3.02622i | −0.166336 | + | 0.0960343i | ||||
\(994\) | 0.198637i | 0.00630039i | ||||||||
\(995\) | − | 36.5147i | − | 1.15759i | ||||||
\(996\) | −2.22230 | + | 3.84913i | −0.0704162 | + | 0.121964i | ||||
\(997\) | 30.4397 | + | 17.5744i | 0.964035 | + | 0.556586i | 0.897412 | − | 0.441193i | \(-0.145444\pi\) |
0.0666222 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(998\) | −3.14741 | + | 5.45147i | −0.0996295 | + | 0.172563i | ||||
\(999\) | −1.75873 | −0.0556437 |
(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 | 349.2.e.a.123.16 | ✓ | 58 | |
349.227 | even | 6 | inner | 349.2.e.a.227.16 | yes | 58 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.e.a.123.16 | ✓ | 58 | 1.1 | even | 1 | trivial | |
349.2.e.a.227.16 | yes | 58 | 349.227 | even | 6 | inner |