Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(24,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 16]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.u (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 24.3 | ||
Character | \(\chi\) | \(=\) | 475.24 |
Dual form | 475.2.u.b.99.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{8}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.105338 | − | 0.289414i | −0.0744854 | − | 0.204647i | 0.896862 | − | 0.442310i | \(-0.145841\pi\) |
−0.971348 | + | 0.237663i | \(0.923619\pi\) | |||||||
\(3\) | −1.61894 | − | 0.285463i | −0.934697 | − | 0.164812i | −0.314499 | − | 0.949258i | \(-0.601837\pi\) |
−0.620198 | + | 0.784445i | \(0.712948\pi\) | |||||||
\(4\) | 1.45942 | − | 1.22460i | 0.729712 | − | 0.612301i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0879194 | + | 0.498616i | 0.0358929 | + | 0.203559i | ||||
\(7\) | −0.0772459 | + | 0.0445979i | −0.0291962 | + | 0.0168564i | −0.514527 | − | 0.857474i | \(-0.672032\pi\) |
0.485331 | + | 0.874331i | \(0.338699\pi\) | |||||||
\(8\) | −1.04160 | − | 0.601369i | −0.368262 | − | 0.212616i | ||||
\(9\) | −0.279590 | − | 0.101762i | −0.0931966 | − | 0.0339208i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.68341 | − | 2.91575i | 0.507567 | − | 0.879133i | −0.492394 | − | 0.870372i | \(-0.663878\pi\) |
0.999962 | − | 0.00876033i | \(-0.00278854\pi\) | |||||||
\(12\) | −2.71230 | + | 1.56595i | −0.782975 | + | 0.452051i | ||||
\(13\) | −0.209636 | + | 0.0369645i | −0.0581426 | + | 0.0102521i | −0.202644 | − | 0.979253i | \(-0.564953\pi\) |
0.144501 | + | 0.989505i | \(0.453842\pi\) | |||||||
\(14\) | 0.0210442 | + | 0.0176582i | 0.00562431 | + | 0.00471935i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.597325 | − | 3.38760i | 0.149331 | − | 0.846899i | ||||
\(17\) | −0.859918 | − | 2.36261i | −0.208561 | − | 0.573016i | 0.790670 | − | 0.612243i | \(-0.209733\pi\) |
−0.999230 | + | 0.0392271i | \(0.987510\pi\) | |||||||
\(18\) | 0.0916368i | 0.0215990i | ||||||||
\(19\) | −0.949628 | + | 4.25420i | −0.217860 | + | 0.975980i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.137788 | − | 0.0501507i | 0.0300678 | − | 0.0109438i | ||||
\(22\) | −1.02119 | − | 0.180063i | −0.217718 | − | 0.0383896i | ||||
\(23\) | −3.83550 | − | 4.57098i | −0.799758 | − | 0.953114i | 0.199885 | − | 0.979819i | \(-0.435943\pi\) |
−0.999643 | + | 0.0267049i | \(0.991499\pi\) | |||||||
\(24\) | 1.51463 | + | 1.27092i | 0.309172 | + | 0.259426i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.0327807 | + | 0.0567779i | 0.00642883 | + | 0.0111351i | ||||
\(27\) | 4.69462 | + | 2.71044i | 0.903479 | + | 0.521624i | ||||
\(28\) | −0.0581198 | + | 0.159683i | −0.0109836 | + | 0.0301772i | ||||
\(29\) | −4.51826 | − | 1.64451i | −0.839019 | − | 0.305378i | −0.113464 | − | 0.993542i | \(-0.536195\pi\) |
−0.725555 | + | 0.688164i | \(0.758417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.03407 | − | 6.98722i | −0.724541 | − | 1.25494i | −0.959163 | − | 0.282855i | \(-0.908718\pi\) |
0.234621 | − | 0.972087i | \(-0.424615\pi\) | |||||||
\(32\) | −3.41227 | + | 0.601676i | −0.603210 | + | 0.106362i | ||||
\(33\) | −3.55769 | + | 4.23989i | −0.619314 | + | 0.738070i | ||||
\(34\) | −0.593190 | + | 0.497745i | −0.101731 | + | 0.0853626i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.532659 | + | 0.193872i | −0.0887765 | + | 0.0323120i | ||||
\(37\) | − | 1.84372i | − | 0.303106i | −0.988449 | − | 0.151553i | \(-0.951573\pi\) | ||
0.988449 | − | 0.151553i | \(-0.0484274\pi\) | |||||||
\(38\) | 1.33126 | − | 0.173294i | 0.215959 | − | 0.0281119i | ||||
\(39\) | 0.349941 | 0.0560354 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.523087 | + | 2.96657i | −0.0816925 | + | 0.463301i | 0.916329 | + | 0.400426i | \(0.131138\pi\) |
−0.998021 | + | 0.0628748i | \(0.979973\pi\) | |||||||
\(42\) | −0.0290286 | − | 0.0345950i | −0.00447922 | − | 0.00533812i | ||||
\(43\) | 1.57346 | − | 1.87518i | 0.239951 | − | 0.285962i | −0.632607 | − | 0.774473i | \(-0.718015\pi\) |
0.872558 | + | 0.488511i | \(0.162460\pi\) | |||||||
\(44\) | −1.11383 | − | 6.31683i | −0.167916 | − | 0.952298i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.918881 | + | 1.59155i | −0.135482 | + | 0.234661i | ||||
\(47\) | 2.60562 | − | 7.15887i | 0.380068 | − | 1.04423i | −0.591259 | − | 0.806482i | \(-0.701369\pi\) |
0.971327 | − | 0.237747i | \(-0.0764090\pi\) | |||||||
\(48\) | −1.93407 | + | 5.31381i | −0.279159 | + | 0.766983i | ||||
\(49\) | −3.49602 | + | 6.05529i | −0.499432 | + | 0.865041i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.717721 | + | 4.07040i | 0.100501 | + | 0.569970i | ||||
\(52\) | −0.260681 | + | 0.310668i | −0.0361500 | + | 0.0430818i | ||||
\(53\) | −5.39920 | − | 6.43452i | −0.741637 | − | 0.883849i | 0.254902 | − | 0.966967i | \(-0.417957\pi\) |
−0.996540 | + | 0.0831178i | \(0.973512\pi\) | |||||||
\(54\) | 0.289917 | − | 1.64420i | 0.0394527 | − | 0.223747i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.107279 | 0.0143358 | ||||||||
\(57\) | 2.75181 | − | 6.61622i | 0.364486 | − | 0.876340i | ||||
\(58\) | 1.48088i | 0.194449i | ||||||||
\(59\) | 9.80610 | − | 3.56913i | 1.27665 | − | 0.464661i | 0.387324 | − | 0.921944i | \(-0.373400\pi\) |
0.889321 | + | 0.457283i | \(0.151177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.757296 | + | 0.635447i | −0.0969618 | + | 0.0813606i | −0.689980 | − | 0.723828i | \(-0.742381\pi\) |
0.593018 | + | 0.805189i | \(0.297936\pi\) | |||||||
\(62\) | −1.59726 | + | 1.90354i | −0.202852 | + | 0.241750i | ||||
\(63\) | 0.0261356 | − | 0.00460841i | 0.00329277 | − | 0.000580605i | ||||
\(64\) | −2.90628 | − | 5.03383i | −0.363285 | − | 0.629228i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.60184 | + | 0.583024i | 0.197173 | + | 0.0717653i | ||||
\(67\) | −3.41324 | + | 9.37780i | −0.416994 | + | 1.14568i | 0.536403 | + | 0.843962i | \(0.319783\pi\) |
−0.953397 | + | 0.301719i | \(0.902440\pi\) | |||||||
\(68\) | −4.14824 | − | 2.39499i | −0.503048 | − | 0.290435i | ||||
\(69\) | 4.90462 | + | 8.49505i | 0.590447 | + | 1.02268i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.73200 | + | 3.97062i | 0.561585 | + | 0.471226i | 0.878841 | − | 0.477114i | \(-0.158317\pi\) |
−0.317256 | + | 0.948340i | \(0.602762\pi\) | |||||||
\(72\) | 0.230025 | + | 0.274133i | 0.0271087 | + | 0.0323068i | ||||
\(73\) | 15.5058 | + | 2.73409i | 1.81482 | + | 0.320001i | 0.974888 | − | 0.222695i | \(-0.0714855\pi\) |
0.839929 | + | 0.542696i | \(0.182597\pi\) | |||||||
\(74\) | −0.533599 | + | 0.194214i | −0.0620296 | + | 0.0225769i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.82379 | + | 7.37160i | 0.438619 | + | 0.845580i | ||||
\(77\) | 0.300307i | 0.0342231i | ||||||||
\(78\) | −0.0368621 | − | 0.101278i | −0.00417381 | − | 0.0114675i | ||||
\(79\) | 0.178596 | − | 1.01287i | 0.0200936 | − | 0.113957i | −0.973111 | − | 0.230336i | \(-0.926018\pi\) |
0.993205 | + | 0.116379i | \(0.0371287\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.14281 | − | 5.15443i | −0.682535 | − | 0.572715i | ||||
\(82\) | 0.913670 | − | 0.161105i | 0.100898 | − | 0.0177910i | ||||
\(83\) | 15.5354 | − | 8.96939i | 1.70524 | − | 0.984518i | 0.764976 | − | 0.644059i | \(-0.222751\pi\) |
0.940259 | − | 0.340459i | \(-0.110582\pi\) | |||||||
\(84\) | 0.139676 | − | 0.241926i | 0.0152399 | − | 0.0263963i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.708449 | − | 0.257854i | −0.0763940 | − | 0.0278052i | ||||
\(87\) | 6.84536 | + | 3.95217i | 0.733899 | + | 0.423717i | ||||
\(88\) | −3.50689 | + | 2.02470i | −0.373836 | + | 0.215834i | ||||
\(89\) | −0.113975 | − | 0.646383i | −0.0120813 | − | 0.0685164i | 0.978171 | − | 0.207801i | \(-0.0666307\pi\) |
−0.990252 | + | 0.139285i | \(0.955520\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0145450 | − | 0.0122047i | 0.00152473 | − | 0.00127940i | ||||
\(92\) | −11.1953 | − | 1.97403i | −1.16719 | − | 0.205806i | ||||
\(93\) | 4.53634 | + | 12.4635i | 0.470397 | + | 1.29240i | ||||
\(94\) | −2.34635 | −0.242008 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.69603 | 0.581349 | ||||||||
\(97\) | 5.75040 | + | 15.7991i | 0.583865 | + | 1.60416i | 0.781518 | + | 0.623883i | \(0.214446\pi\) |
−0.197653 | + | 0.980272i | \(0.563332\pi\) | |||||||
\(98\) | 2.12075 | + | 0.373946i | 0.214228 | + | 0.0377742i | ||||
\(99\) | −0.767379 | + | 0.643907i | −0.0771245 | + | 0.0647151i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.638978 | + | 3.62382i | 0.0635806 | + | 0.360584i | 0.999954 | + | 0.00957849i | \(0.00304897\pi\) |
−0.936373 | + | 0.351005i | \(0.885840\pi\) | |||||||
\(102\) | 1.10243 | − | 0.636488i | 0.109157 | − | 0.0630217i | ||||
\(103\) | 3.06071 | + | 1.76710i | 0.301580 | + | 0.174118i | 0.643153 | − | 0.765738i | \(-0.277626\pi\) |
−0.341572 | + | 0.939856i | \(0.610959\pi\) | |||||||
\(104\) | 0.240587 | + | 0.0875664i | 0.0235915 | + | 0.00858659i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.29350 | + | 2.24041i | −0.125636 | + | 0.217608i | ||||
\(107\) | 1.63384 | − | 0.943300i | 0.157950 | − | 0.0911923i | −0.418942 | − | 0.908013i | \(-0.637599\pi\) |
0.576891 | + | 0.816821i | \(0.304266\pi\) | |||||||
\(108\) | 10.1706 | − | 1.79336i | 0.978671 | − | 0.172566i | ||||
\(109\) | 10.0810 | + | 8.45901i | 0.965589 | + | 0.810226i | 0.981853 | − | 0.189642i | \(-0.0607327\pi\) |
−0.0162639 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.526315 | + | 2.98488i | −0.0499556 | + | 0.283312i | ||||
\(112\) | 0.104939 | + | 0.288318i | 0.00991580 | + | 0.0272434i | ||||
\(113\) | 12.3456i | 1.16138i | 0.814125 | + | 0.580689i | \(0.197217\pi\) | ||||
−0.814125 | + | 0.580689i | \(0.802783\pi\) | |||||||
\(114\) | −2.20470 | − | 0.0994730i | −0.206489 | − | 0.00931650i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.60793 | + | 3.13303i | −0.799226 | + | 0.290895i | ||||
\(117\) | 0.0623737 | + | 0.0109982i | 0.00576645 | + | 0.00101678i | ||||
\(118\) | −2.06591 | − | 2.46206i | −0.190183 | − | 0.226651i | ||||
\(119\) | 0.171793 | + | 0.144151i | 0.0157482 | + | 0.0132143i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.167744 | − | 0.290542i | −0.0152495 | − | 0.0264129i | ||||
\(122\) | 0.263680 | + | 0.152235i | 0.0238724 | + | 0.0137827i | ||||
\(123\) | 1.69370 | − | 4.65339i | 0.152716 | − | 0.419582i | ||||
\(124\) | −14.4440 | − | 5.25718i | −1.29711 | − | 0.472109i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.00408681 | − | 0.00707857i | −0.000364082 | − | 0.000630609i | ||||
\(127\) | 20.8898 | − | 3.68344i | 1.85367 | − | 0.326852i | 0.868137 | − | 0.496325i | \(-0.165318\pi\) |
0.985535 | + | 0.169473i | \(0.0542066\pi\) | |||||||
\(128\) | −5.60512 | + | 6.67993i | −0.495428 | + | 0.590428i | ||||
\(129\) | −3.08264 | + | 2.58664i | −0.271411 | + | 0.227741i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.53156 | + | 2.37729i | −0.570665 | + | 0.207705i | −0.611204 | − | 0.791473i | \(-0.709315\pi\) |
0.0405392 | + | 0.999178i | \(0.487092\pi\) | |||||||
\(132\) | 10.5445i | 0.917785i | ||||||||
\(133\) | −0.116374 | − | 0.370971i | −0.0100909 | − | 0.0321673i | ||||
\(134\) | 3.07361 | 0.265520 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.525106 | + | 2.97802i | −0.0450275 | + | 0.255363i | ||||
\(137\) | −13.5029 | − | 16.0922i | −1.15363 | − | 1.37485i | −0.914860 | − | 0.403772i | \(-0.867699\pi\) |
−0.238774 | − | 0.971075i | \(-0.576746\pi\) | |||||||
\(138\) | 1.94194 | − | 2.31432i | 0.165309 | − | 0.197008i | ||||
\(139\) | −2.72999 | − | 15.4826i | −0.231555 | − | 1.31321i | −0.849749 | − | 0.527188i | \(-0.823246\pi\) |
0.618194 | − | 0.786026i | \(-0.287865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.26194 | + | 10.8460i | −0.527351 | + | 0.913398i | ||||
\(142\) | 0.650694 | − | 1.78777i | 0.0546050 | − | 0.150026i | ||||
\(143\) | −0.245124 | + | 0.673473i | −0.0204983 | + | 0.0563187i | ||||
\(144\) | −0.511736 | + | 0.886353i | −0.0426447 | + | 0.0738627i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.842068 | − | 4.77561i | −0.0696901 | − | 0.395232i | ||||
\(147\) | 7.38842 | − | 8.80518i | 0.609387 | − | 0.726239i | ||||
\(148\) | −2.25782 | − | 2.69077i | −0.185592 | − | 0.221180i | ||||
\(149\) | 3.38951 | − | 19.2229i | 0.277679 | − | 1.57480i | −0.452641 | − | 0.891693i | \(-0.649518\pi\) |
0.730320 | − | 0.683105i | \(-0.239371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2284 | 0.913758 | 0.456879 | − | 0.889529i | \(-0.348967\pi\) | ||||
0.456879 | + | 0.889529i | \(0.348967\pi\) | |||||||
\(152\) | 3.54748 | − | 3.86010i | 0.287739 | − | 0.313096i | ||||
\(153\) | 0.748068i | 0.0604777i | ||||||||
\(154\) | 0.0869131 | − | 0.0316338i | 0.00700365 | − | 0.00254912i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.510712 | − | 0.428538i | 0.0408897 | − | 0.0343105i | ||||
\(157\) | 2.96506 | − | 3.53362i | 0.236637 | − | 0.282014i | −0.634636 | − | 0.772811i | \(-0.718850\pi\) |
0.871274 | + | 0.490797i | \(0.163295\pi\) | |||||||
\(158\) | −0.311951 | + | 0.0550055i | −0.0248175 | + | 0.00437600i | ||||
\(159\) | 6.90418 | + | 11.9584i | 0.547537 | + | 0.948362i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.500133 | + | 0.182034i | 0.0394160 | + | 0.0143463i | ||||
\(162\) | −0.844694 | + | 2.32078i | −0.0663654 | + | 0.182337i | ||||
\(163\) | 0.497735 | + | 0.287367i | 0.0389856 | + | 0.0225084i | 0.519366 | − | 0.854552i | \(-0.326168\pi\) |
−0.480381 | + | 0.877060i | \(0.659501\pi\) | |||||||
\(164\) | 2.86947 | + | 4.97007i | 0.224068 | + | 0.388097i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.23234 | − | 3.55136i | −0.328494 | − | 0.275639i | ||||
\(167\) | −2.64958 | − | 3.15765i | −0.205031 | − | 0.244346i | 0.653724 | − | 0.756733i | \(-0.273206\pi\) |
−0.858755 | + | 0.512387i | \(0.828761\pi\) | |||||||
\(168\) | −0.173679 | − | 0.0306243i | −0.0133996 | − | 0.00236272i | ||||
\(169\) | −12.1734 | + | 4.43076i | −0.936417 | + | 0.340828i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.698424 | − | 1.09279i | 0.0534098 | − | 0.0835681i | ||||
\(172\) | − | 4.66355i | − | 0.355592i | ||||||
\(173\) | 2.20075 | + | 6.04652i | 0.167320 | + | 0.459709i | 0.994807 | − | 0.101776i | \(-0.0324525\pi\) |
−0.827487 | + | 0.561485i | \(0.810230\pi\) | |||||||
\(174\) | 0.422737 | − | 2.39746i | 0.0320476 | − | 0.181751i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.87186 | − | 7.44437i | −0.668741 | − | 0.561141i | ||||
\(177\) | −16.8944 | + | 2.97893i | −1.26986 | + | 0.223910i | ||||
\(178\) | −0.175066 | + | 0.101075i | −0.0131218 | + | 0.00757587i | ||||
\(179\) | 1.91516 | − | 3.31715i | 0.143146 | − | 0.247936i | −0.785534 | − | 0.618819i | \(-0.787612\pi\) |
0.928680 | + | 0.370883i | \(0.120945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.6814 | − | 5.70755i | −1.16559 | − | 0.424239i | −0.314496 | − | 0.949259i | \(-0.601836\pi\) |
−0.851090 | + | 0.525020i | \(0.824058\pi\) | |||||||
\(182\) | −0.00506435 | − | 0.00292391i | −0.000375395 | − | 0.000216734i | ||||
\(183\) | 1.40742 | − | 0.812572i | 0.104039 | − | 0.0600670i | ||||
\(184\) | 1.24622 | + | 7.06769i | 0.0918729 | + | 0.521037i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.12926 | − | 2.62576i | 0.229449 | − | 0.192530i | ||||
\(187\) | −8.33637 | − | 1.46993i | −0.609616 | − | 0.107492i | ||||
\(188\) | −4.96407 | − | 13.6387i | −0.362042 | − | 0.994703i | ||||
\(189\) | −0.483520 | −0.0351709 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.92694 | 0.573573 | 0.286787 | − | 0.957994i | \(-0.407413\pi\) | ||||
0.286787 | + | 0.957994i | \(0.407413\pi\) | |||||||
\(192\) | 3.26813 | + | 8.97912i | 0.235857 | + | 0.648012i | ||||
\(193\) | −20.9438 | − | 3.69296i | −1.50757 | − | 0.265825i | −0.642034 | − | 0.766676i | \(-0.721909\pi\) |
−0.865533 | + | 0.500851i | \(0.833020\pi\) | |||||||
\(194\) | 3.96675 | − | 3.32850i | 0.284796 | − | 0.238972i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.31314 | + | 13.1185i | 0.165224 | + | 0.937034i | ||||
\(197\) | −2.50058 | + | 1.44371i | −0.178159 | + | 0.102860i | −0.586427 | − | 0.810002i | \(-0.699466\pi\) |
0.408268 | + | 0.912862i | \(0.366133\pi\) | |||||||
\(198\) | 0.267190 | + | 0.154262i | 0.0189884 | + | 0.0109629i | ||||
\(199\) | 10.9144 | + | 3.97251i | 0.773701 | + | 0.281604i | 0.698544 | − | 0.715568i | \(-0.253832\pi\) |
0.0751574 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.20286 | − | 14.2078i | 0.578585 | − | 1.00214i | ||||
\(202\) | 0.981477 | − | 0.566656i | 0.0690565 | − | 0.0398698i | ||||
\(203\) | 0.422359 | − | 0.0744732i | 0.0296438 | − | 0.00522700i | ||||
\(204\) | 6.03208 | + | 5.06152i | 0.422330 | + | 0.354377i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.189015 | − | 1.07196i | 0.0131693 | − | 0.0746867i | ||||
\(207\) | 0.607215 | + | 1.66831i | 0.0422043 | + | 0.115955i | ||||
\(208\) | 0.732242i | 0.0507719i | ||||||||
\(209\) | 10.8056 | + | 9.93045i | 0.747437 | + | 0.686903i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.2708 | − | 8.10590i | 1.53318 | − | 0.558033i | 0.568784 | − | 0.822487i | \(-0.307414\pi\) |
0.964398 | + | 0.264454i | \(0.0851916\pi\) | |||||||
\(212\) | −15.7595 | − | 2.77882i | −1.08236 | − | 0.190850i | ||||
\(213\) | −6.52737 | − | 7.77902i | −0.447248 | − | 0.533010i | ||||
\(214\) | −0.445111 | − | 0.373492i | −0.0304272 | − | 0.0255314i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.25995 | − | 5.64639i | −0.221811 | − | 0.384188i | ||||
\(217\) | 0.623232 | + | 0.359823i | 0.0423077 | + | 0.0244264i | ||||
\(218\) | 1.38624 | − | 3.80866i | 0.0938879 | − | 0.257955i | ||||
\(219\) | −24.3225 | − | 8.85268i | −1.64356 | − | 0.598209i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.267602 | + | 0.463501i | 0.0180009 | + | 0.0311784i | ||||
\(222\) | 0.919308 | − | 0.162099i | 0.0616999 | − | 0.0108794i | ||||
\(223\) | 5.66673 | − | 6.75335i | 0.379472 | − | 0.452237i | −0.542175 | − | 0.840265i | \(-0.682399\pi\) |
0.921648 | + | 0.388028i | \(0.126844\pi\) | |||||||
\(224\) | 0.236751 | − | 0.198657i | 0.0158186 | − | 0.0132734i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.57300 | − | 1.30047i | 0.237672 | − | 0.0865057i | ||||
\(227\) | 1.04512i | 0.0693671i | 0.999398 | + | 0.0346835i | \(0.0110423\pi\) | ||||
−0.999398 | + | 0.0346835i | \(0.988958\pi\) | |||||||
\(228\) | −4.08618 | − | 13.0258i | −0.270614 | − | 0.862651i | ||||
\(229\) | 13.4837 | 0.891031 | 0.445515 | − | 0.895274i | \(-0.353020\pi\) | ||||
0.445515 | + | 0.895274i | \(0.353020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0857266 | − | 0.486179i | 0.00564039 | − | 0.0319883i | ||||
\(232\) | 3.71727 | + | 4.43007i | 0.244051 | + | 0.290848i | ||||
\(233\) | −7.21068 | + | 8.59336i | −0.472388 | + | 0.562970i | −0.948648 | − | 0.316335i | \(-0.897548\pi\) |
0.476260 | + | 0.879305i | \(0.341992\pi\) | |||||||
\(234\) | −0.00338731 | − | 0.0192104i | −0.000221435 | − | 0.00125582i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.94050 | − | 17.2174i | 0.647071 | − | 1.12076i | ||||
\(237\) | −0.578273 | + | 1.58879i | −0.0375629 | + | 0.103203i | ||||
\(238\) | 0.0236231 | − | 0.0649038i | 0.00153126 | − | 0.00420709i | ||||
\(239\) | −10.1645 | + | 17.6054i | −0.657487 | + | 1.13880i | 0.323777 | + | 0.946133i | \(0.395047\pi\) |
−0.981264 | + | 0.192667i | \(0.938286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.667594 | − | 3.78611i | −0.0430035 | − | 0.243885i | 0.955727 | − | 0.294254i | \(-0.0950713\pi\) |
−0.998731 | + | 0.0503694i | \(0.983960\pi\) | |||||||
\(242\) | −0.0664171 | + | 0.0791528i | −0.00426945 | + | 0.00508814i | ||||
\(243\) | −1.97995 | − | 2.35961i | −0.127014 | − | 0.151369i | ||||
\(244\) | −0.327046 | + | 1.85477i | −0.0209370 | + | 0.118740i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.52517 | −0.0972413 | ||||||||
\(247\) | 0.0418221 | − | 0.926936i | 0.00266107 | − | 0.0589795i | ||||
\(248\) | 9.70387i | 0.616197i | ||||||||
\(249\) | −27.7114 | + | 10.0861i | −1.75614 | + | 0.639183i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.08068 | + | 5.10229i | −0.383809 | + | 0.322054i | −0.814196 | − | 0.580591i | \(-0.802822\pi\) |
0.430387 | + | 0.902645i | \(0.358377\pi\) | |||||||
\(252\) | 0.0324994 | − | 0.0387313i | 0.00204727 | − | 0.00243984i | ||||
\(253\) | −19.7846 | + | 3.48855i | −1.24385 | + | 0.219323i | ||||
\(254\) | −3.26654 | − | 5.65781i | −0.204961 | − | 0.355002i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.40034 | − | 3.05747i | −0.525021 | − | 0.191092i | ||||
\(257\) | −8.28638 | + | 22.7666i | −0.516890 | + | 1.42014i | 0.357038 | + | 0.934090i | \(0.383787\pi\) |
−0.873929 | + | 0.486054i | \(0.838436\pi\) | |||||||
\(258\) | 1.07333 | + | 0.619688i | 0.0668227 | + | 0.0385801i | ||||
\(259\) | 0.0822262 | + | 0.142420i | 0.00510928 | + | 0.00884954i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.09591 | + | 0.919578i | 0.0678351 | + | 0.0569204i | ||||
\(262\) | 1.37605 | + | 1.63991i | 0.0850124 | + | 0.101314i | ||||
\(263\) | −12.1892 | − | 2.14928i | −0.751617 | − | 0.132530i | −0.215301 | − | 0.976548i | \(-0.569073\pi\) |
−0.536316 | + | 0.844017i | \(0.680184\pi\) | |||||||
\(264\) | 6.25543 | − | 2.27679i | 0.384995 | − | 0.140127i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.0951057 | + | 0.0727576i | −0.00583131 | + | 0.00446105i | ||||
\(267\) | 1.07899i | 0.0660333i | ||||||||
\(268\) | 6.50271 | + | 17.8660i | 0.397216 | + | 1.09134i | ||||
\(269\) | 4.23334 | − | 24.0085i | 0.258111 | − | 1.46382i | −0.529846 | − | 0.848094i | \(-0.677750\pi\) |
0.787958 | − | 0.615729i | \(-0.211138\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3432 | + | 11.1963i | 0.810540 | + | 0.680124i | 0.950737 | − | 0.310000i | \(-0.100329\pi\) |
−0.140196 | + | 0.990124i | \(0.544773\pi\) | |||||||
\(272\) | −8.51721 | + | 1.50181i | −0.516432 | + | 0.0910608i | ||||
\(273\) | −0.0270315 | + | 0.0156066i | −0.00163602 | + | 0.000944557i | ||||
\(274\) | −3.23493 | + | 5.60306i | −0.195429 | + | 0.338494i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 17.5610 | + | 6.39167i | 1.05705 | + | 0.384733i | ||||
\(277\) | 17.9994 | + | 10.3920i | 1.08148 | + | 0.624393i | 0.931295 | − | 0.364265i | \(-0.118680\pi\) |
0.150185 | + | 0.988658i | \(0.452013\pi\) | |||||||
\(278\) | −4.19330 | + | 2.42100i | −0.251498 | + | 0.145202i | ||||
\(279\) | 0.416850 | + | 2.36407i | 0.0249562 | + | 0.141533i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.60383 | + | 3.86307i | −0.274641 | + | 0.230452i | −0.769696 | − | 0.638410i | \(-0.779592\pi\) |
0.495055 | + | 0.868862i | \(0.335148\pi\) | |||||||
\(282\) | 3.79861 | + | 0.669797i | 0.226204 | + | 0.0398859i | ||||
\(283\) | −3.95849 | − | 10.8759i | −0.235308 | − | 0.646502i | −0.999998 | − | 0.00210419i | \(-0.999330\pi\) |
0.764690 | − | 0.644398i | \(-0.222892\pi\) | |||||||
\(284\) | 11.7684 | 0.698327 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.220734 | 0.0130523 | ||||||||
\(287\) | −0.0918968 | − | 0.252484i | −0.00542450 | − | 0.0149037i | ||||
\(288\) | 1.01526 | + | 0.179019i | 0.0598251 | + | 0.0105488i | ||||
\(289\) | 8.18031 | − | 6.86409i | 0.481195 | − | 0.403770i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.79951 | − | 27.2194i | −0.281352 | − | 1.59563i | ||||
\(292\) | 25.9777 | − | 14.9982i | 1.52023 | − | 0.877706i | ||||
\(293\) | −15.1289 | − | 8.73466i | −0.883838 | − | 0.510284i | −0.0119163 | − | 0.999929i | \(-0.503793\pi\) |
−0.871922 | + | 0.489645i | \(0.837126\pi\) | |||||||
\(294\) | −3.32663 | − | 1.21079i | −0.194013 | − | 0.0706149i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.10876 | + | 1.92042i | −0.0644452 | + | 0.111622i | ||||
\(297\) | 15.8059 | − | 9.12556i | 0.917153 | − | 0.529519i | ||||
\(298\) | −5.92042 | + | 1.04393i | −0.342961 | + | 0.0604732i | ||||
\(299\) | 0.973024 | + | 0.816464i | 0.0562714 | + | 0.0472173i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0379144 | + | 0.215023i | −0.00218535 | + | 0.0123937i | ||||
\(302\) | −1.18278 | − | 3.24967i | −0.0680616 | − | 0.186998i | ||||
\(303\) | − | 6.04917i | − | 0.347516i | ||||||
\(304\) | 13.8443 | + | 5.75810i | 0.794024 | + | 0.330250i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.216502 | − | 0.0788002i | 0.0123766 | − | 0.00450470i | ||||
\(307\) | −29.2028 | − | 5.14924i | −1.66669 | − | 0.293883i | −0.740815 | − | 0.671709i | \(-0.765560\pi\) |
−0.925876 | + | 0.377827i | \(0.876672\pi\) | |||||||
\(308\) | 0.367756 | + | 0.438275i | 0.0209549 | + | 0.0249730i | ||||
\(309\) | −4.45067 | − | 3.73455i | −0.253190 | − | 0.212451i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.81119 | + | 10.0653i | 0.329522 | + | 0.570749i | 0.982417 | − | 0.186699i | \(-0.0597790\pi\) |
−0.652895 | + | 0.757449i | \(0.726446\pi\) | |||||||
\(312\) | −0.364499 | − | 0.210444i | −0.0206357 | − | 0.0119140i | ||||
\(313\) | −0.162413 | + | 0.446226i | −0.00918012 | + | 0.0252222i | −0.944198 | − | 0.329378i | \(-0.893161\pi\) |
0.935018 | + | 0.354600i | \(0.115383\pi\) | |||||||
\(314\) | −1.33501 | − | 0.485905i | −0.0753392 | − | 0.0274212i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.979713 | − | 1.69691i | −0.0551132 | − | 0.0954588i | ||||
\(317\) | −19.9209 | + | 3.51260i | −1.11887 | + | 0.197287i | −0.702345 | − | 0.711836i | \(-0.747864\pi\) |
−0.416526 | + | 0.909124i | \(0.636753\pi\) | |||||||
\(318\) | 2.73366 | − | 3.25784i | 0.153296 | − | 0.182691i | ||||
\(319\) | −12.4011 | + | 10.4057i | −0.694327 | + | 0.582609i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.91438 | + | 1.06075i | −0.162665 | + | 0.0592051i | ||||
\(322\) | − | 0.163921i | − | 0.00913495i | ||||||
\(323\) | 10.8676 | − | 1.41467i | 0.604689 | − | 0.0787141i | ||||
\(324\) | −15.2771 | −0.848728 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.0307377 | − | 0.174322i | 0.00170241 | − | 0.00965483i | ||||
\(327\) | −13.9059 | − | 16.5724i | −0.768999 | − | 0.916457i | ||||
\(328\) | 2.32886 | − | 2.77542i | 0.128590 | − | 0.153247i | ||||
\(329\) | 0.117998 | + | 0.669199i | 0.00650543 | + | 0.0368941i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.00653 | − | 5.20746i | 0.165254 | − | 0.286228i | −0.771492 | − | 0.636240i | \(-0.780489\pi\) |
0.936745 | + | 0.350012i | \(0.113822\pi\) | |||||||
\(332\) | 11.6889 | − | 32.1149i | 0.641509 | − | 1.76253i | ||||
\(333\) | −0.187621 | + | 0.515486i | −0.0102816 | + | 0.0282484i | ||||
\(334\) | −0.634767 | + | 1.09945i | −0.0347329 | + | 0.0601591i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.0875862 | − | 0.496726i | −0.00477822 | − | 0.0270986i | ||||
\(337\) | −5.69981 | + | 6.79277i | −0.310488 | + | 0.370026i | −0.898611 | − | 0.438746i | \(-0.855423\pi\) |
0.588123 | + | 0.808772i | \(0.299867\pi\) | |||||||
\(338\) | 2.56465 | + | 3.05643i | 0.139499 | + | 0.166248i | ||||
\(339\) | 3.52422 | − | 19.9869i | 0.191409 | − | 1.08554i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.1640 | −1.47101 | ||||||||
\(342\) | −0.389841 | − | 0.0870209i | −0.0210802 | − | 0.00470555i | ||||
\(343\) | − | 1.24803i | − | 0.0673874i | ||||||
\(344\) | −2.76660 | + | 1.00696i | −0.149165 | + | 0.0542916i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.51813 | − | 1.27386i | 0.0816150 | − | 0.0684831i | ||||
\(347\) | 12.8372 | − | 15.2988i | 0.689139 | − | 0.821284i | −0.302112 | − | 0.953272i | \(-0.597692\pi\) |
0.991251 | + | 0.131989i | \(0.0421362\pi\) | |||||||
\(348\) | 14.8301 | − | 2.61495i | 0.794977 | − | 0.140176i | ||||
\(349\) | −0.405107 | − | 0.701666i | −0.0216849 | − | 0.0375593i | 0.854979 | − | 0.518662i | \(-0.173570\pi\) |
−0.876664 | + | 0.481103i | \(0.840236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.08435 | − | 0.394671i | −0.0578783 | − | 0.0210660i | ||||
\(352\) | −3.98992 | + | 10.9622i | −0.212663 | + | 0.584288i | ||||
\(353\) | 18.1435 | + | 10.4751i | 0.965681 | + | 0.557536i | 0.897917 | − | 0.440165i | \(-0.145080\pi\) |
0.0677639 | + | 0.997701i | \(0.478414\pi\) | |||||||
\(354\) | 2.64177 | + | 4.57568i | 0.140408 | + | 0.243195i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.957899 | − | 0.803773i | −0.0507686 | − | 0.0425999i | ||||
\(357\) | −0.236973 | − | 0.282413i | −0.0125419 | − | 0.0149469i | ||||
\(358\) | −1.16177 | − | 0.204851i | −0.0614015 | − | 0.0108267i | ||||
\(359\) | 24.1518 | − | 8.79055i | 1.27469 | − | 0.463948i | 0.386015 | − | 0.922493i | \(-0.373851\pi\) |
0.888671 | + | 0.458545i | \(0.151629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1964 | − | 8.07982i | −0.905074 | − | 0.425253i | ||||
\(362\) | 5.13963i | 0.270133i | ||||||||
\(363\) | 0.188630 | + | 0.518256i | 0.00990049 | + | 0.0272014i | ||||
\(364\) | 0.00628141 | − | 0.0356236i | 0.000329235 | − | 0.00186719i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.383425 | − | 0.321731i | −0.0200419 | − | 0.0168172i | ||||
\(367\) | −23.9170 | + | 4.21721i | −1.24846 | + | 0.220137i | −0.758537 | − | 0.651630i | \(-0.774085\pi\) |
−0.489921 | + | 0.871767i | \(0.662974\pi\) | |||||||
\(368\) | −17.7757 | + | 10.2628i | −0.926621 | + | 0.534985i | ||||
\(369\) | 0.448136 | − | 0.776194i | 0.0233290 | − | 0.0404070i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.704033 | + | 0.256247i | 0.0365515 | + | 0.0133037i | ||||
\(372\) | 21.8833 | + | 12.6343i | 1.13460 | + | 0.655059i | ||||
\(373\) | 9.42310 | − | 5.44043i | 0.487910 | − | 0.281695i | −0.235797 | − | 0.971802i | \(-0.575770\pi\) |
0.723707 | + | 0.690107i | \(0.242437\pi\) | |||||||
\(374\) | 0.452720 | + | 2.56750i | 0.0234096 | + | 0.132763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.01914 | + | 5.88976i | −0.361985 | + | 0.303741i | ||||
\(377\) | 1.00798 | + | 0.177734i | 0.0519135 | + | 0.00915375i | ||||
\(378\) | 0.0509331 | + | 0.139938i | 0.00261972 | + | 0.00719761i | ||||
\(379\) | −19.3318 | −0.993008 | −0.496504 | − | 0.868034i | \(-0.665383\pi\) | ||||
−0.496504 | + | 0.868034i | \(0.665383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.8709 | −1.78649 | ||||||||
\(382\) | −0.835009 | − | 2.29417i | −0.0427228 | − | 0.117380i | ||||
\(383\) | −1.02720 | − | 0.181124i | −0.0524876 | − | 0.00925498i | 0.147343 | − | 0.989086i | \(-0.452928\pi\) |
−0.199830 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(384\) | 10.9813 | − | 9.21437i | 0.560385 | − | 0.470219i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.13739 | + | 6.45045i | 0.0578915 | + | 0.328319i | ||||
\(387\) | −0.630747 | + | 0.364162i | −0.0320627 | + | 0.0185114i | ||||
\(388\) | 27.7399 | + | 16.0156i | 1.40828 | + | 0.813070i | ||||
\(389\) | 24.9988 | + | 9.09880i | 1.26749 | + | 0.461328i | 0.886275 | − | 0.463160i | \(-0.153284\pi\) |
0.381213 | + | 0.924487i | \(0.375507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.50120 | + | 12.9925i | −0.379352 | + | 0.657056i | ||||
\(392\) | 7.28293 | − | 4.20480i | 0.367843 | − | 0.212374i | ||||
\(393\) | 11.2529 | − | 1.98418i | 0.567632 | − | 0.100089i | ||||
\(394\) | 0.681238 | + | 0.571627i | 0.0343203 | + | 0.0287981i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.331401 | + | 1.87947i | −0.0166535 | + | 0.0944468i | ||||
\(397\) | −1.26464 | − | 3.47457i | −0.0634705 | − | 0.174384i | 0.903903 | − | 0.427737i | \(-0.140689\pi\) |
−0.967374 | + | 0.253353i | \(0.918467\pi\) | |||||||
\(398\) | − | 3.57724i | − | 0.179311i | ||||||
\(399\) | 0.0825037 | + | 0.633801i | 0.00413035 | + | 0.0317298i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0147 | − | 6.92080i | 0.949551 | − | 0.345608i | 0.179620 | − | 0.983736i | \(-0.442513\pi\) |
0.769930 | + | 0.638128i | \(0.220291\pi\) | |||||||
\(402\) | −4.97601 | − | 0.877404i | −0.248181 | − | 0.0437609i | ||||
\(403\) | 1.10397 | + | 1.31566i | 0.0549925 | + | 0.0655375i | ||||
\(404\) | 5.37028 | + | 4.50620i | 0.267181 | + | 0.224192i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0660441 | − | 0.114392i | −0.00327772 | − | 0.00567717i | ||||
\(407\) | −5.37583 | − | 3.10374i | −0.266470 | − | 0.153847i | ||||
\(408\) | 1.70023 | − | 4.67135i | 0.0841741 | − | 0.231266i | ||||
\(409\) | 11.7244 | + | 4.26733i | 0.579733 | + | 0.211006i | 0.615208 | − | 0.788365i | \(-0.289072\pi\) |
−0.0354746 | + | 0.999371i | \(0.511294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.2668 | + | 29.9069i | 0.851707 | + | 1.47520i | ||||
\(412\) | 6.63087 | − | 1.16920i | 0.326679 | − | 0.0576024i | ||||
\(413\) | −0.598305 | + | 0.713032i | −0.0294407 | + | 0.0350860i | ||||
\(414\) | 0.418870 | − | 0.351473i | 0.0205863 | − | 0.0172740i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.693095 | − | 0.252266i | 0.0339818 | − | 0.0123683i | ||||
\(417\) | 25.8447i | 1.26562i | ||||||||
\(418\) | 1.73577 | − | 4.17334i | 0.0848994 | − | 0.204125i | ||||
\(419\) | −28.9962 | −1.41656 | −0.708279 | − | 0.705933i | \(-0.750528\pi\) | ||||
−0.708279 | + | 0.705933i | \(0.750528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.53458 | − | 14.3743i | 0.123528 | − | 0.700561i | −0.858644 | − | 0.512573i | \(-0.828692\pi\) |
0.982171 | − | 0.187988i | \(-0.0601965\pi\) | |||||||
\(422\) | −4.69193 | − | 5.59162i | −0.228399 | − | 0.272196i | ||||
\(423\) | −1.45701 | + | 1.73639i | −0.0708422 | + | 0.0844264i | ||||
\(424\) | 1.75430 | + | 9.94912i | 0.0851963 | + | 0.483172i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.56378 | + | 2.70854i | −0.0757653 | + | 0.131229i | ||||
\(427\) | 0.0301584 | − | 0.0828595i | 0.00145947 | − | 0.00400985i | ||||
\(428\) | 1.22930 | − | 3.37749i | 0.0594207 | − | 0.163257i | ||||
\(429\) | 0.589094 | − | 1.02034i | 0.0284417 | − | 0.0492625i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.34566 | + | 13.3029i | 0.112986 | + | 0.640778i | 0.987727 | + | 0.156187i | \(0.0499204\pi\) |
−0.874741 | + | 0.484591i | \(0.838969\pi\) | |||||||
\(432\) | 11.9861 | − | 14.2845i | 0.576681 | − | 0.687261i | ||||
\(433\) | 24.4391 | + | 29.1254i | 1.17447 | + | 1.39968i | 0.898761 | + | 0.438438i | \(0.144468\pi\) |
0.275709 | + | 0.961241i | \(0.411087\pi\) | |||||||
\(434\) | 0.0384878 | − | 0.218275i | 0.00184747 | − | 0.0104775i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 25.0714 | 1.20070 | ||||||||
\(437\) | 23.0881 | − | 11.9763i | 1.10446 | − | 0.572903i | ||||
\(438\) | 7.97181i | 0.380908i | ||||||||
\(439\) | −22.3525 | + | 8.13563i | −1.06682 | + | 0.388292i | −0.814988 | − | 0.579478i | \(-0.803257\pi\) |
−0.251836 | + | 0.967770i | \(0.581034\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.59365 | − | 1.33723i | 0.0758882 | − | 0.0636778i | ||||
\(442\) | 0.105955 | − | 0.126272i | 0.00503977 | − | 0.00600616i | ||||
\(443\) | 19.0059 | − | 3.35126i | 0.902999 | − | 0.159223i | 0.297176 | − | 0.954823i | \(-0.403955\pi\) |
0.605823 | + | 0.795600i | \(0.292844\pi\) | |||||||
\(444\) | 2.88717 | + | 5.00073i | 0.137019 | + | 0.237324i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.55144 | − | 0.928648i | −0.120814 | − | 0.0439727i | ||||
\(447\) | −10.9748 | + | 30.1531i | −0.519092 | + | 1.42619i | ||||
\(448\) | 0.448997 | + | 0.259228i | 0.0212131 | + | 0.0122474i | ||||
\(449\) | −13.2068 | − | 22.8749i | −0.623268 | − | 1.07953i | −0.988873 | − | 0.148761i | \(-0.952471\pi\) |
0.365605 | − | 0.930770i | \(-0.380862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.76923 | + | 6.51916i | 0.365839 | + | 0.306975i | ||||
\(452\) | 15.1185 | + | 18.0175i | 0.711113 | + | 0.847472i | ||||
\(453\) | −18.1782 | − | 3.20531i | −0.854087 | − | 0.150599i | ||||
\(454\) | 0.302473 | − | 0.110091i | 0.0141958 | − | 0.00516683i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.84509 | + | 5.23661i | −0.320551 | + | 0.245227i | ||||
\(457\) | 38.4641i | 1.79927i | 0.436638 | + | 0.899637i | \(0.356169\pi\) | ||||
−0.436638 | + | 0.899637i | \(0.643831\pi\) | |||||||
\(458\) | −1.42035 | − | 3.90239i | −0.0663687 | − | 0.182347i | ||||
\(459\) | 2.36671 | − | 13.4223i | 0.110469 | − | 0.626498i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.0330 | + | 21.8442i | 1.21248 | + | 1.01739i | 0.999184 | + | 0.0403991i | \(0.0128629\pi\) |
0.213292 | + | 0.976989i | \(0.431582\pi\) | |||||||
\(462\) | −0.149738 | + | 0.0264028i | −0.00696642 | + | 0.00122837i | ||||
\(463\) | −4.67174 | + | 2.69723i | −0.217114 | + | 0.125351i | −0.604613 | − | 0.796519i | \(-0.706672\pi\) |
0.387499 | + | 0.921870i | \(0.373339\pi\) | |||||||
\(464\) | −8.26981 | + | 14.3237i | −0.383916 | + | 0.664963i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.24660 | + | 1.18167i | 0.150396 | + | 0.0547396i | ||||
\(467\) | 19.4240 | + | 11.2144i | 0.898834 | + | 0.518942i | 0.876822 | − | 0.480815i | \(-0.159659\pi\) |
0.0220125 | + | 0.999758i | \(0.492993\pi\) | |||||||
\(468\) | 0.104498 | − | 0.0603320i | 0.00483043 | − | 0.00278885i | ||||
\(469\) | −0.154572 | − | 0.876620i | −0.00713746 | − | 0.0404786i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.80898 | + | 4.87431i | −0.267664 | + | 0.224597i | ||||
\(472\) | −12.3604 | − | 2.17947i | −0.568934 | − | 0.100318i | ||||
\(473\) | −2.81878 | − | 7.74452i | −0.129607 | − | 0.356093i | ||||
\(474\) | 0.520734 | 0.0239181 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.427246 | 0.0195828 | ||||||||
\(477\) | 0.854770 | + | 2.34846i | 0.0391372 | + | 0.107529i | ||||
\(478\) | 6.16597 | + | 1.08723i | 0.282025 | + | 0.0497286i | ||||
\(479\) | 22.0166 | − | 18.4741i | 1.00596 | − | 0.844104i | 0.0181649 | − | 0.999835i | \(-0.494218\pi\) |
0.987800 | + | 0.155731i | \(0.0497732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0681522 | + | 0.386510i | 0.00310747 | + | 0.0176233i | ||||
\(482\) | −1.02543 | + | 0.592033i | −0.0467071 | + | 0.0269664i | ||||
\(483\) | −0.757723 | − | 0.437472i | −0.0344776 | − | 0.0199057i | ||||
\(484\) | −0.600609 | − | 0.218604i | −0.0273004 | − | 0.00993653i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.474341 | + | 0.821582i | −0.0215165 | + | 0.0372677i | ||||
\(487\) | 29.8295 | − | 17.2221i | 1.35170 | − | 0.780406i | 0.363215 | − | 0.931705i | \(-0.381679\pi\) |
0.988488 | + | 0.151299i | \(0.0483456\pi\) | |||||||
\(488\) | 1.17094 | − | 0.206468i | 0.0530059 | − | 0.00934637i | ||||
\(489\) | −0.723772 | − | 0.607317i | −0.0327301 | − | 0.0274638i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.36638 | + | 19.0917i | −0.151923 | + | 0.861596i | 0.809623 | + | 0.586950i | \(0.199672\pi\) |
−0.961546 | + | 0.274645i | \(0.911440\pi\) | |||||||
\(492\) | −3.22674 | − | 8.86538i | −0.145472 | − | 0.399682i | ||||
\(493\) | 12.0890i | 0.544462i | ||||||||
\(494\) | −0.272674 | + | 0.0855378i | −0.0122682 | + | 0.00384853i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −26.0796 | + | 9.49218i | −1.17101 | + | 0.426212i | ||||
\(497\) | −0.542609 | − | 0.0956766i | −0.0243393 | − | 0.00429168i | ||||
\(498\) | 5.83814 | + | 6.95763i | 0.261613 | + | 0.311779i | ||||
\(499\) | −8.63214 | − | 7.24323i | −0.386428 | − | 0.324251i | 0.428792 | − | 0.903403i | \(-0.358939\pi\) |
−0.815220 | + | 0.579152i | \(0.803384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.38813 | + | 5.86842i | 0.151371 | + | 0.262181i | ||||
\(502\) | 2.11720 | + | 1.22237i | 0.0944955 | + | 0.0545570i | ||||
\(503\) | 3.62262 | − | 9.95307i | 0.161525 | − | 0.443785i | −0.832356 | − | 0.554241i | \(-0.813009\pi\) |
0.993881 | + | 0.110455i | \(0.0352309\pi\) | |||||||
\(504\) | −0.0299942 | − | 0.0109170i | −0.00133605 | − | 0.000486282i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.09371 | + | 5.35846i | 0.137532 | + | 0.238213i | ||||
\(507\) | 20.9729 | − | 3.69809i | 0.931439 | − | 0.164238i | ||||
\(508\) | 25.9764 | − | 30.9574i | 1.15251 | − | 1.37351i | ||||
\(509\) | 1.66949 | − | 1.40087i | 0.0739990 | − | 0.0620925i | −0.605038 | − | 0.796197i | \(-0.706842\pi\) |
0.679037 | + | 0.734104i | \(0.262398\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.31969 | + | 0.480330i | −0.0583799 | + | 0.0212485i | ||||
\(512\) | 20.1933i | 0.892426i | ||||||||
\(513\) | −15.9889 | + | 17.3979i | −0.705926 | + | 0.768137i | ||||
\(514\) | 7.46186 | 0.329129 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.33127 | + | 7.55002i | −0.0586060 | + | 0.332371i | ||||
\(517\) | −16.4872 | − | 19.6487i | −0.725106 | − | 0.864147i | ||||
\(518\) | 0.0325568 | − | 0.0387997i | 0.00143046 | − | 0.00170476i | ||||
\(519\) | −1.83684 | − | 10.4172i | −0.0806282 | − | 0.457265i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.72367 | − | 9.91369i | 0.250759 | − | 0.434327i | −0.712976 | − | 0.701188i | \(-0.752653\pi\) |
0.963735 | + | 0.266862i | \(0.0859866\pi\) | |||||||
\(522\) | 0.150698 | − | 0.414039i | 0.00659586 | − | 0.0181220i | ||||
\(523\) | −3.33548 | + | 9.16414i | −0.145850 | + | 0.400720i | −0.991009 | − | 0.133795i | \(-0.957284\pi\) |
0.845159 | + | 0.534515i | \(0.179506\pi\) | |||||||
\(524\) | −6.62108 | + | 11.4680i | −0.289243 | + | 0.500984i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.661953 | + | 3.75412i | 0.0288625 | + | 0.163688i | ||||
\(527\) | −13.0391 | + | 15.5394i | −0.567991 | + | 0.676906i | ||||
\(528\) | 12.2379 | + | 14.5846i | 0.532588 | + | 0.634713i | ||||
\(529\) | −2.18882 | + | 12.4134i | −0.0951661 | + | 0.539714i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.10489 | −0.134741 | ||||||||
\(532\) | −0.624130 | − | 0.398893i | −0.0270595 | − | 0.0172942i | ||||
\(533\) | − | 0.641237i | − | 0.0277750i | ||||||
\(534\) | 0.312276 | − | 0.113659i | 0.0135135 | − | 0.00491851i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.19476 | − | 7.71532i | 0.397153 | − | 0.333251i | ||||
\(537\) | −4.04746 | + | 4.82357i | −0.174661 | + | 0.208153i | ||||
\(538\) | −7.39433 | + | 1.30382i | −0.318792 | + | 0.0562117i | ||||
\(539\) | 11.7705 | + | 20.3871i | 0.506991 | + | 0.878133i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.4401 | − | 7.80354i | −0.921780 | − | 0.335501i | −0.162834 | − | 0.986654i | \(-0.552063\pi\) |
−0.758947 | + | 0.651153i | \(0.774286\pi\) | |||||||
\(542\) | 1.83481 | − | 5.04110i | 0.0788118 | − | 0.216534i | ||||
\(543\) | 23.7579 | + | 13.7166i | 1.01955 | + | 0.588638i | ||||
\(544\) | 4.35580 | + | 7.54446i | 0.186753 | + | 0.323466i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.00736423 | + | 0.00617933i | 0.000315160 | + | 0.000264451i | ||||
\(547\) | −19.8732 | − | 23.6840i | −0.849716 | − | 1.01265i | −0.999713 | − | 0.0239661i | \(-0.992371\pi\) |
0.149996 | − | 0.988687i | \(-0.452074\pi\) | |||||||
\(548\) | −39.4130 | − | 6.94958i | −1.68364 | − | 0.296871i | ||||
\(549\) | 0.276397 | − | 0.100600i | 0.0117963 | − | 0.00429351i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.2867 | − | 17.6599i | 0.480831 | − | 0.752337i | ||||
\(552\) | − | 11.7979i | − | 0.502154i | ||||||
\(553\) | 0.0313760 | + | 0.0862049i | 0.00133424 | + | 0.00366581i | ||||
\(554\) | 1.11156 | − | 6.30396i | 0.0472256 | − | 0.267830i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.9442 | − | 19.2525i | −0.973051 | − | 0.816486i | ||||
\(557\) | −9.67955 | + | 1.70677i | −0.410136 | + | 0.0723180i | −0.374910 | − | 0.927061i | \(-0.622326\pi\) |
−0.0352261 | + | 0.999379i | \(0.511215\pi\) | |||||||
\(558\) | 0.640287 | − | 0.369670i | 0.0271055 | − | 0.0156494i | ||||
\(559\) | −0.260539 | + | 0.451267i | −0.0110196 | + | 0.0190866i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0765 | + | 4.75946i | 0.552090 | + | 0.200944i | ||||
\(562\) | 1.60299 | + | 0.925485i | 0.0676179 | + | 0.0390392i | ||||
\(563\) | 28.9420 | − | 16.7096i | 1.21976 | − | 0.704228i | 0.254892 | − | 0.966970i | \(-0.417960\pi\) |
0.964866 | + | 0.262742i | \(0.0846268\pi\) | |||||||
\(564\) | 4.14321 | + | 23.4973i | 0.174461 | + | 0.989415i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.73065 | + | 2.29129i | −0.114778 | + | 0.0963099i | ||||
\(567\) | 0.704384 | + | 0.124202i | 0.0295814 | + | 0.00521599i | ||||
\(568\) | −2.54105 | − | 6.98148i | −0.106620 | − | 0.292936i | ||||
\(569\) | −37.6326 | −1.57764 | −0.788820 | − | 0.614624i | \(-0.789308\pi\) | ||||
−0.788820 | + | 0.614624i | \(0.789308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.75232 | −0.115181 | −0.0575904 | − | 0.998340i | \(-0.518342\pi\) | ||||
−0.0575904 | + | 0.998340i | \(0.518342\pi\) | |||||||
\(572\) | 0.466997 | + | 1.28306i | 0.0195261 | + | 0.0536476i | ||||
\(573\) | −12.8333 | − | 2.26285i | −0.536117 | − | 0.0945319i | ||||
\(574\) | −0.0633924 | + | 0.0531925i | −0.00264595 | + | 0.00222021i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.300313 | + | 1.70316i | 0.0125130 | + | 0.0709649i | ||||
\(577\) | −0.0321295 | + | 0.0185500i | −0.00133757 | + | 0.000772245i | −0.500669 | − | 0.865639i | \(-0.666912\pi\) |
0.499331 | + | 0.866411i | \(0.333579\pi\) | |||||||
\(578\) | −2.84827 | − | 1.64445i | −0.118472 | − | 0.0684000i | ||||
\(579\) | 32.8526 | + | 11.9574i | 1.36531 | + | 0.496932i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.800032 | + | 1.38570i | −0.0331909 | + | 0.0574884i | ||||
\(582\) | −7.37210 | + | 4.25629i | −0.305584 | + | 0.176429i | ||||
\(583\) | −27.8505 | + | 4.91080i | −1.15345 | + | 0.203385i | ||||
\(584\) | −14.5067 | − | 12.1725i | −0.600291 | − | 0.503704i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.934287 | + | 5.29861i | −0.0385951 | + | 0.218883i | ||||
\(587\) | −1.23359 | − | 3.38927i | −0.0509158 | − | 0.139890i | 0.911628 | − | 0.411016i | \(-0.134826\pi\) |
−0.962544 | + | 0.271126i | \(0.912604\pi\) | |||||||
\(588\) | − | 21.8984i | − | 0.903074i | ||||||
\(589\) | 33.5559 | − | 10.5265i | 1.38265 | − | 0.433736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.46043 | − | 1.62346i | 0.183478 | − | 0.0667804i | ||||
\(592\) | −6.24578 | − | 1.10130i | −0.256700 | − | 0.0452632i | ||||
\(593\) | 11.4696 | + | 13.6689i | 0.470998 | + | 0.561314i | 0.948279 | − | 0.317437i | \(-0.102822\pi\) |
−0.477281 | + | 0.878751i | \(0.658378\pi\) | |||||||
\(594\) | −4.30604 | − | 3.61319i | −0.176679 | − | 0.148251i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.5936 | − | 32.2051i | −0.761625 | − | 1.31917i | ||||
\(597\) | −16.5358 | − | 9.54694i | −0.676764 | − | 0.390730i | ||||
\(598\) | 0.133800 | − | 0.367612i | 0.00547148 | − | 0.0150328i | ||||
\(599\) | −20.6214 | − | 7.50558i | −0.842568 | − | 0.306670i | −0.115561 | − | 0.993300i | \(-0.536867\pi\) |
−0.727006 | + | 0.686631i | \(0.759089\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.14039 | − | 8.90342i | −0.209681 | − | 0.363178i | 0.741933 | − | 0.670474i | \(-0.233909\pi\) |
−0.951614 | + | 0.307296i | \(0.900576\pi\) | |||||||
\(602\) | 0.0662246 | − | 0.0116772i | 0.00269911 | − | 0.000475926i | ||||
\(603\) | 1.90861 | − | 2.27460i | 0.0777248 | − | 0.0926288i | ||||
\(604\) | 16.3871 | − | 13.7504i | 0.666780 | − | 0.559495i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.75072 | + | 0.637208i | −0.0711180 | + | 0.0258848i | ||||
\(607\) | − | 32.2616i | − | 1.30946i | −0.755864 | − | 0.654729i | \(-0.772783\pi\) | ||
0.755864 | − | 0.654729i | \(-0.227217\pi\) | |||||||
\(608\) | 0.680743 | − | 15.0879i | 0.0276078 | − | 0.611893i | ||||
\(609\) | −0.705034 | −0.0285694 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.281607 | + | 1.59707i | −0.0113926 | + | 0.0646107i | ||||
\(612\) | 0.916086 | + | 1.09175i | 0.0370306 | + | 0.0441313i | ||||
\(613\) | 10.5389 | − | 12.5598i | 0.425664 | − | 0.507286i | −0.510002 | − | 0.860173i | \(-0.670355\pi\) |
0.935666 | + | 0.352887i | \(0.114800\pi\) | |||||||
\(614\) | 1.58591 | + | 8.99412i | 0.0640019 | + | 0.362973i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.180595 | − | 0.312800i | 0.00727639 | − | 0.0126031i | ||||
\(617\) | 4.36994 | − | 12.0063i | 0.175927 | − | 0.483356i | −0.820119 | − | 0.572193i | \(-0.806093\pi\) |
0.996046 | + | 0.0888371i | \(0.0283151\pi\) | |||||||
\(618\) | −0.612008 | + | 1.68148i | −0.0246186 | + | 0.0676390i | ||||
\(619\) | 2.14103 | − | 3.70838i | 0.0860555 | − | 0.149052i | −0.819785 | − | 0.572671i | \(-0.805907\pi\) |
0.905840 | + | 0.423619i | \(0.139240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.61687 | − | 31.8549i | −0.225397 | − | 1.27829i | ||||
\(622\) | 2.30089 | − | 2.74210i | 0.0922575 | − | 0.109948i | ||||
\(623\) | 0.0376314 | + | 0.0448474i | 0.00150767 | + | 0.00179677i | ||||
\(624\) | 0.209028 | − | 1.18546i | 0.00836783 | − | 0.0474563i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.146252 | 0.00584542 | ||||||||
\(627\) | −14.6588 | − | 19.1614i | −0.585418 | − | 0.765234i | ||||
\(628\) | − | 8.78807i | − | 0.350682i | ||||||
\(629\) | −4.35599 | + | 1.58545i | −0.173685 | + | 0.0632160i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.4565 | + | 14.6477i | −0.694933 | + | 0.583118i | −0.920327 | − | 0.391150i | \(-0.872077\pi\) |
0.225394 | + | 0.974268i | \(0.427633\pi\) | |||||||
\(632\) | −0.795133 | + | 0.947603i | −0.0316287 | + | 0.0376936i | ||||
\(633\) | −38.3690 | + | 6.76550i | −1.52503 | + | 0.268904i | ||||
\(634\) | 3.11503 | + | 5.39540i | 0.123714 | + | 0.214279i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 24.7204 | + | 8.99749i | 0.980228 | + | 0.356774i | ||||
\(637\) | 0.509061 | − | 1.39863i | 0.0201698 | − | 0.0554159i | ||||
\(638\) | 4.31788 | + | 2.49293i | 0.170946 | + | 0.0986959i | ||||
\(639\) | −0.918959 | − | 1.59168i | −0.0363535 | − | 0.0629661i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.0251 | − | 20.1595i | −0.948935 | − | 0.796251i | 0.0301829 | − | 0.999544i | \(-0.490391\pi\) |
−0.979118 | + | 0.203293i | \(0.934835\pi\) | |||||||
\(642\) | 0.613991 | + | 0.731726i | 0.0242323 | + | 0.0288789i | ||||
\(643\) | −10.9796 | − | 1.93601i | −0.432995 | − | 0.0763487i | −0.0470972 | − | 0.998890i | \(-0.514997\pi\) |
−0.385898 | + | 0.922542i | \(0.626108\pi\) | |||||||
\(644\) | 0.952825 | − | 0.346800i | 0.0375466 | − | 0.0136658i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.55420 | − | 2.99622i | −0.0611491 | − | 0.117885i | ||||
\(647\) | 17.5536i | 0.690102i | 0.938584 | + | 0.345051i | \(0.112138\pi\) | ||||
−0.938584 | + | 0.345051i | \(0.887862\pi\) | |||||||
\(648\) | 3.29865 | + | 9.06297i | 0.129583 | + | 0.356027i | ||||
\(649\) | 6.10100 | − | 34.6005i | 0.239485 | − | 1.35819i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.906260 | − | 0.760443i | −0.0355191 | − | 0.0298041i | ||||
\(652\) | 1.07832 | − | 0.190136i | 0.0422302 | − | 0.00744632i | ||||
\(653\) | −1.81461 | + | 1.04766i | −0.0710111 | + | 0.0409983i | −0.535085 | − | 0.844798i | \(-0.679720\pi\) |
0.464074 | + | 0.885796i | \(0.346387\pi\) | |||||||
\(654\) | −3.33147 | + | 5.77028i | −0.130271 | + | 0.225636i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.73711 | + | 3.54402i | 0.380170 | + | 0.138371i | ||||
\(657\) | −4.05704 | − | 2.34233i | −0.158280 | − | 0.0913831i | ||||
\(658\) | 0.181246 | − | 0.104642i | 0.00706571 | − | 0.00407939i | ||||
\(659\) | 2.25744 | + | 12.8026i | 0.0879373 | + | 0.498717i | 0.996684 | + | 0.0813691i | \(0.0259292\pi\) |
−0.908747 | + | 0.417348i | \(0.862960\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.1833 | − | 24.4877i | 1.13510 | − | 0.952462i | 0.135833 | − | 0.990732i | \(-0.456629\pi\) |
0.999267 | + | 0.0382694i | \(0.0121845\pi\) | |||||||
\(662\) | −1.82382 | − | 0.321588i | −0.0708846 | − | 0.0124989i | ||||
\(663\) | −0.300920 | − | 0.826772i | −0.0116868 | − | 0.0321092i | ||||
\(664\) | −21.5756 | −0.837298 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.168953 | 0.00654678 | ||||||||
\(667\) | 9.81278 | + | 26.9604i | 0.379952 | + | 1.04391i | ||||
\(668\) | −7.73373 | − | 1.36367i | −0.299227 | − | 0.0527618i | ||||
\(669\) | −11.1019 | + | 9.31564i | −0.429226 | + | 0.360163i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.577966 | + | 3.27781i | 0.0223121 | + | 0.126538i | ||||
\(672\) | −0.439995 | + | 0.254031i | −0.0169732 | + | 0.00979947i | ||||
\(673\) | −29.4013 | − | 16.9749i | −1.13334 | − | 0.654333i | −0.188566 | − | 0.982061i | \(-0.560384\pi\) |
−0.944772 | + | 0.327728i | \(0.893717\pi\) | |||||||
\(674\) | 2.56633 | + | 0.934069i | 0.0988514 | + | 0.0359790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3403 | + | 21.3740i | −0.474626 | + | 0.822076i | ||||
\(677\) | 14.3381 | − | 8.27810i | 0.551058 | − | 0.318153i | −0.198491 | − | 0.980103i | \(-0.563604\pi\) |
0.749549 | + | 0.661949i | \(0.230271\pi\) | |||||||
\(678\) | −6.15572 | + | 1.08542i | −0.236409 | + | 0.0416853i | ||||
\(679\) | −1.14880 | − | 0.963959i | −0.0440870 | − | 0.0369934i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.298344 | − | 1.69199i | 0.0114326 | − | 0.0648372i | ||||
\(682\) | 2.86141 | + | 7.86166i | 0.109569 | + | 0.301038i | ||||
\(683\) | 5.33328i | 0.204072i | 0.994781 | + | 0.102036i | \(0.0325357\pi\) | ||||
−0.994781 | + | 0.102036i | \(0.967464\pi\) | |||||||
\(684\) | −0.318942 | − | 2.45014i | −0.0121950 | − | 0.0936835i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.361199 | + | 0.131466i | −0.0137906 | + | 0.00501938i | ||||
\(687\) | −21.8294 | − | 3.84911i | −0.832844 | − | 0.146853i | ||||
\(688\) | −5.41248 | − | 6.45035i | −0.206349 | − | 0.245917i | ||||
\(689\) | 1.36972 | + | 1.14933i | 0.0521820 | + | 0.0437859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.06510 | + | 12.2371i | 0.268769 | + | 0.465522i | 0.968544 | − | 0.248842i | \(-0.0800498\pi\) |
−0.699775 | + | 0.714363i | \(0.746717\pi\) | |||||||
\(692\) | 10.6164 | + | 6.12940i | 0.403576 | + | 0.233005i | ||||
\(693\) | 0.0305599 | − | 0.0839627i | 0.00116088 | − | 0.00318948i | ||||
\(694\) | −5.77995 | − | 2.10373i | −0.219404 | − | 0.0798565i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.75342 | − | 8.23317i | −0.180178 | − | 0.312078i | ||||
\(697\) | 7.45866 | − | 1.31516i | 0.282517 | − | 0.0498153i | ||||
\(698\) | −0.160399 | + | 0.191156i | −0.00607119 | + | 0.00723536i | ||||
\(699\) | 14.1268 | − | 11.8538i | 0.534324 | − | 0.448351i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.8607 | − | 13.0522i | 1.35444 | − | 0.492976i | 0.440110 | − | 0.897944i | \(-0.354939\pi\) |
0.914331 | + | 0.404967i | \(0.132717\pi\) | |||||||
\(702\) | 0.355400i | 0.0134137i | ||||||||
\(703\) | 7.84355 | + | 1.75085i | 0.295825 | + | 0.0660345i | ||||
\(704\) | −19.5699 | −0.737567 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.12046 | − | 6.35442i | 0.0421689 | − | 0.239152i | ||||
\(707\) | −0.210973 | − | 0.251428i | −0.00793447 | − | 0.00945594i | ||||
\(708\) | −21.0080 | + | 25.0364i | −0.789531 | + | 0.940926i | ||||
\(709\) | −5.75948 | − | 32.6636i | −0.216302 | − | 1.22671i | −0.878633 | − | 0.477497i | \(-0.841544\pi\) |
0.662331 | − | 0.749211i | \(-0.269567\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.153005 | + | 0.265013i | −0.00573815 | + | 0.00993878i | ||||
\(712\) | −0.269998 | + | 0.741814i | −0.0101186 | + | 0.0278007i | ||||
\(713\) | −16.4657 | + | 45.2392i | −0.616646 | + | 1.69422i | ||||
\(714\) | −0.0567721 | + | 0.0983321i | −0.00212464 | + | 0.00367999i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.26716 | − | 7.18644i | −0.0473561 | − | 0.268570i | ||||
\(717\) | 21.4814 | − | 25.6006i | 0.802239 | − | 0.956072i | ||||
\(718\) | −5.08822 | − | 6.06391i | −0.189891 | − | 0.226303i | ||||
\(719\) | −7.35244 | + | 41.6978i | −0.274200 | + | 1.55506i | 0.467292 | + | 0.884103i | \(0.345230\pi\) |
−0.741492 | + | 0.670962i | \(0.765881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.315236 | −0.0117400 | ||||||||
\(722\) | −0.526975 | + | 5.82800i | −0.0196120 | + | 0.216896i | ||||
\(723\) | 6.32007i | 0.235046i | ||||||||
\(724\) | −29.8752 | + | 10.8737i | −1.11030 | + | 0.404118i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.130121 | − | 0.109184i | 0.00482923 | − | 0.00405221i | ||||
\(727\) | −2.70075 | + | 3.21863i | −0.100165 | + | 0.119372i | −0.813798 | − | 0.581147i | \(-0.802604\pi\) |
0.713633 | + | 0.700520i | \(0.247048\pi\) | |||||||
\(728\) | −0.0224896 | + | 0.00396552i | −0.000833520 | + | 0.000146972i | ||||
\(729\) | 14.5602 | + | 25.2189i | 0.539265 | + | 0.934034i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.78336 | − | 2.10497i | −0.213905 | − | 0.0778551i | ||||
\(732\) | 1.05894 | − | 2.90941i | 0.0391395 | − | 0.107535i | ||||
\(733\) | −14.6668 | − | 8.46787i | −0.541730 | − | 0.312768i | 0.204050 | − | 0.978960i | \(-0.434590\pi\) |
−0.745780 | + | 0.666193i | \(0.767923\pi\) | |||||||
\(734\) | 3.73990 | + | 6.47769i | 0.138042 | + | 0.239096i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.8380 | + | 13.2897i | 0.583798 | + | 0.489864i | ||||
\(737\) | 21.5975 | + | 25.7388i | 0.795553 | + | 0.948103i | ||||
\(738\) | −0.271847 | − | 0.0479340i | −0.0100068 | − | 0.00176448i | ||||
\(739\) | 19.5893 | − | 7.12993i | 0.720605 | − | 0.262279i | 0.0444223 | − | 0.999013i | \(-0.485855\pi\) |
0.676183 | + | 0.736734i | \(0.263633\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.332314 | + | 1.48872i | −0.0122079 | + | 0.0546894i | ||||
\(742\) | − | 0.230750i | − | 0.00847109i | ||||||
\(743\) | −15.5106 | − | 42.6150i | −0.569028 | − | 1.56339i | −0.806025 | − | 0.591881i | \(-0.798385\pi\) |
0.236997 | − | 0.971510i | \(-0.423837\pi\) | |||||||
\(744\) | 2.77010 | − | 15.7100i | 0.101557 | − | 0.575957i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.56715 | − | 2.15410i | −0.0939901 | − | 0.0788671i | ||||
\(747\) | −5.25630 | + | 0.926827i | −0.192318 | + | 0.0339108i | ||||
\(748\) | −13.9664 | + | 8.06349i | −0.510661 | + | 0.294831i | ||||
\(749\) | −0.0841385 | + | 0.145732i | −0.00307435 | + | 0.00532494i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.15355 | + | 2.96765i | 0.297527 | + | 0.108291i | 0.486471 | − | 0.873697i | \(-0.338284\pi\) |
−0.188943 | + | 0.981988i | \(0.560506\pi\) | |||||||
\(752\) | −22.6950 | − | 13.1030i | −0.827601 | − | 0.477816i | ||||
\(753\) | 11.3008 | − | 6.52451i | 0.411824 | − | 0.237767i | ||||
\(754\) | −0.0547399 | − | 0.310445i | −0.00199351 | − | 0.0113058i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.705661 | + | 0.592119i | −0.0256646 | + | 0.0215352i | ||||
\(757\) | −9.92320 | − | 1.74973i | −0.360665 | − | 0.0635950i | −0.00962040 | − | 0.999954i | \(-0.503062\pi\) |
−0.351045 | + | 0.936359i | \(0.614173\pi\) | |||||||
\(758\) | 2.03638 | + | 5.59490i | 0.0739645 | + | 0.203216i | ||||
\(759\) | 33.0259 | 1.19877 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.52014 | 0.163855 | 0.0819275 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819275 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(762\) | 3.67324 | + | 10.0921i | 0.133067 | + | 0.365600i | ||||
\(763\) | −1.15597 | − | 0.203829i | −0.0418491 | − | 0.00737912i | ||||
\(764\) | 11.5688 | − | 9.70735i | 0.418543 | − | 0.351200i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.0557839 | + | 0.316366i | 0.00201556 | + | 0.0114308i | ||||
\(767\) | −1.92378 | + | 1.11070i | −0.0694637 | + | 0.0401049i | ||||
\(768\) | 12.7269 | + | 7.34787i | 0.459242 | + | 0.265143i | ||||
\(769\) | −37.1897 | − | 13.5360i | −1.34110 | − | 0.488119i | −0.430939 | − | 0.902381i | \(-0.641818\pi\) |
−0.910158 | + | 0.414262i | \(0.864040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9142 | − | 34.4924i | 0.717193 | − | 1.24221i | ||||
\(772\) | −35.0883 | + | 20.2582i | −1.26286 | + | 0.729110i | ||||
\(773\) | 23.1416 | − | 4.08049i | 0.832347 | − | 0.146765i | 0.258793 | − | 0.965933i | \(-0.416675\pi\) |
0.573554 | + | 0.819168i | \(0.305564\pi\) | |||||||
\(774\) | 0.171835 | + | 0.144187i | 0.00617649 | + | 0.00518269i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.51146 | − | 19.9145i | 0.126054 | − | 0.714888i | ||||
\(777\) | −0.0924638 | − | 0.254042i | −0.00331712 | − | 0.00911372i | ||||
\(778\) | − | 8.19345i | − | 0.293749i | ||||||
\(779\) | −12.1237 | − | 5.04246i | −0.434375 | − | 0.180665i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5432 | − | 7.11316i | 0.699312 | − | 0.254529i | ||||
\(782\) | 4.55036 | + | 0.802352i | 0.162721 | + | 0.0286920i | ||||
\(783\) | −16.7541 | − | 19.9668i | −0.598744 | − | 0.713555i | ||||
\(784\) | 18.4246 | + | 15.4601i | 0.658022 | + | 0.552146i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.75961 | − | 3.04773i | −0.0627631 | − | 0.108709i | ||||
\(787\) | 6.51669 | + | 3.76242i | 0.232295 | + | 0.134116i | 0.611630 | − | 0.791144i | \(-0.290514\pi\) |
−0.379335 | + | 0.925259i | \(0.623847\pi\) | |||||||
\(788\) | −1.88144 | + | 5.16921i | −0.0670235 | + | 0.184145i | ||||
\(789\) | 19.1200 | + | 6.95913i | 0.680692 | + | 0.247751i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.550589 | − | 0.953649i | −0.0195767 | − | 0.0339078i | ||||
\(792\) | 1.18653 | − | 0.209217i | 0.0421615 | − | 0.00743421i | ||||
\(793\) | 0.135268 | − | 0.161206i | 0.00480349 | − | 0.00572458i | ||||
\(794\) | −0.872376 | + | 0.732010i | −0.0309595 | + | 0.0259781i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.7935 | − | 7.56821i | 0.737006 | − | 0.268248i | ||||
\(797\) | 18.7858i | 0.665426i | 0.943028 | + | 0.332713i | \(0.107964\pi\) | ||||
−0.943028 | + | 0.332713i | \(0.892036\pi\) | |||||||
\(798\) | 0.174740 | − | 0.0906412i | 0.00618574 | − | 0.00320866i | ||||
\(799\) | −19.1542 | −0.677627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0339113 | + | 0.192320i | −0.00119820 | + | 0.00679531i | ||||
\(802\) | −4.00596 | − | 4.77411i | −0.141455 | − | 0.168580i | ||||
\(803\) | 34.0746 | − | 40.6085i | 1.20247 | − | 1.43304i | ||||
\(804\) | −5.42742 | − | 30.7804i | −0.191410 | − | 1.08554i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.264480 | − | 0.458092i | 0.00931590 | − | 0.0161356i | ||||
\(807\) | −13.7071 | + | 37.6599i | −0.482512 | + | 1.32569i | ||||
\(808\) | 1.51369 | − | 4.15884i | 0.0532516 | − | 0.146308i | ||||
\(809\) | −9.74651 | + | 16.8815i | −0.342669 | + | 0.593520i | −0.984927 | − | 0.172968i | \(-0.944664\pi\) |
0.642258 | + | 0.766488i | \(0.277998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.64049 | + | 14.9750i | 0.0927201 | + | 0.525842i | 0.995422 | + | 0.0955756i | \(0.0304692\pi\) |
−0.902702 | + | 0.430266i | \(0.858420\pi\) | |||||||
\(812\) | 0.525201 | − | 0.625910i | 0.0184309 | − | 0.0219651i | ||||
\(813\) | −18.4057 | − | 21.9351i | −0.645517 | − | 0.769297i | ||||
\(814\) | −0.331986 | + | 1.88279i | −0.0116361 | + | 0.0659916i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.2176 | 0.497715 | ||||||||
\(817\) | 6.48318 | + | 8.47454i | 0.226818 | + | 0.296487i | ||||
\(818\) | − | 3.84272i | − | 0.134357i | ||||||
\(819\) | −0.00530861 | + | 0.00193218i | −0.000185498 | + | 6.75157e-5i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.5043 | + | 17.2051i | −0.715604 | + | 0.600463i | −0.926165 | − | 0.377118i | \(-0.876915\pi\) |
0.210562 | + | 0.977581i | \(0.432471\pi\) | |||||||
\(822\) | 6.83664 | − | 8.14759i | 0.238455 | − | 0.284180i | ||||
\(823\) | −27.2284 | + | 4.80109i | −0.949121 | + | 0.167356i | −0.626717 | − | 0.779247i | \(-0.715602\pi\) |
−0.322404 | + | 0.946602i | \(0.604491\pi\) | |||||||
\(824\) | −2.12536 | − | 3.68123i | −0.0740404 | − | 0.128242i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.269386 | + | 0.0980486i | 0.00937314 | + | 0.00341155i | ||||
\(827\) | −4.38543 | + | 12.0489i | −0.152496 | + | 0.418980i | −0.992292 | − | 0.123923i | \(-0.960453\pi\) |
0.839796 | + | 0.542903i | \(0.182675\pi\) | |||||||
\(828\) | 2.92920 | + | 1.69117i | 0.101797 | + | 0.0587724i | ||||
\(829\) | 22.7266 | + | 39.3636i | 0.789326 | + | 1.36715i | 0.926380 | + | 0.376590i | \(0.122903\pi\) |
−0.137054 | + | 0.990564i | \(0.543763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.1735 | − | 21.9622i | −0.907949 | − | 0.761860i | ||||
\(832\) | 0.795334 | + | 0.947842i | 0.0275732 | + | 0.0328605i | ||||
\(833\) | 17.3126 | + | 3.05267i | 0.599844 | + | 0.105769i | ||||
\(834\) | 7.47983 | − | 2.72243i | 0.259005 | − | 0.0942702i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 27.9308 | + | 1.26020i | 0.966006 | + | 0.0435849i | ||||
\(837\) | − | 43.7364i | − | 1.51175i | ||||||
\(838\) | 3.05441 | + | 8.39192i | 0.105513 | + | 0.289894i | ||||
\(839\) | −4.04829 | + | 22.9590i | −0.139762 | + | 0.792632i | 0.831662 | + | 0.555282i | \(0.187390\pi\) |
−0.971424 | + | 0.237350i | \(0.923721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50505 | − | 3.78019i | −0.155347 | − | 0.130351i | ||||
\(842\) | −4.42712 | + | 0.780620i | −0.152569 | + | 0.0269019i | ||||
\(843\) | 8.55610 | − | 4.93987i | 0.294688 | − | 0.170138i | ||||
\(844\) | 22.5760 | − | 39.1028i | 0.777098 | − | 1.34597i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.656016 | + | 0.238770i | 0.0225543 | + | 0.00820909i | ||||
\(847\) | 0.0259151 | + | 0.0149621i | 0.000890455 | + | 0.000514104i | ||||
\(848\) | −25.0226 | + | 14.4468i | −0.859281 | + | 0.496106i | ||||
\(849\) | 3.30391 | + | 18.7374i | 0.113390 | + | 0.643066i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.42760 | + | 7.07160i | −0.288894 | + | 0.242411i | ||||
\(852\) | −19.0524 | − | 3.35945i | −0.652725 | − | 0.115093i | ||||
\(853\) | 15.6588 | + | 43.0221i | 0.536146 | + | 1.47305i | 0.851643 | + | 0.524122i | \(0.175607\pi\) |
−0.315497 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(854\) | −0.0271576 | −0.000929312 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.26909 | −0.0775558 | ||||||||
\(857\) | 2.20568 | + | 6.06004i | 0.0753444 | + | 0.207007i | 0.971647 | − | 0.236436i | \(-0.0759792\pi\) |
−0.896303 | + | 0.443443i | \(0.853757\pi\) | |||||||
\(858\) | −0.357355 | − | 0.0630114i | −0.0121999 | − | 0.00215117i | ||||
\(859\) | 11.1359 | − | 9.34415i | 0.379953 | − | 0.318818i | −0.432731 | − | 0.901523i | \(-0.642450\pi\) |
0.812684 | + | 0.582705i | \(0.198006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0767007 | + | 0.434991i | 0.00261395 | + | 0.0148245i | ||||
\(862\) | 3.60296 | − | 2.08017i | 0.122717 | − | 0.0708509i | ||||
\(863\) | 3.95891 | + | 2.28568i | 0.134763 | + | 0.0778054i | 0.565866 | − | 0.824497i | \(-0.308542\pi\) |
−0.431103 | + | 0.902303i | \(0.641875\pi\) | |||||||
\(864\) | −17.6501 | − | 6.42412i | −0.600469 | − | 0.218553i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.85494 | − | 10.1411i | 0.198959 | − | 0.344607i | ||||
\(867\) | −15.2029 | + | 8.77740i | −0.516318 | + | 0.298096i | ||||
\(868\) | 1.35020 | − | 0.238077i | 0.0458288 | − | 0.00808085i | ||||
\(869\) | −2.65262 | − | 2.22581i | −0.0899841 | − | 0.0755056i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.368892 | − | 2.09209i | 0.0124994 | − | 0.0708879i | ||||
\(872\) | −5.41346 | − | 14.8733i | −0.183323 | − | 0.503675i | ||||
\(873\) | − | 5.00244i | − | 0.169307i | ||||||
\(874\) | −5.89817 | − | 5.42048i | −0.199508 | − | 0.183351i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −46.3379 | + | 16.8656i | −1.56561 | + | 0.569836i | ||||
\(877\) | −32.4562 | − | 5.72291i | −1.09597 | − | 0.193249i | −0.403702 | − | 0.914890i | \(-0.632277\pi\) |
−0.692267 | + | 0.721641i | \(0.743388\pi\) | |||||||
\(878\) | 4.70913 | + | 5.61213i | 0.158926 | + | 0.189400i | ||||
\(879\) | 21.9994 | + | 18.4597i | 0.742020 | + | 0.622629i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.12066 | + | 14.0654i | 0.273592 | + | 0.473875i | 0.969779 | − | 0.243985i | \(-0.0784549\pi\) |
−0.696187 | + | 0.717860i | \(0.745122\pi\) | |||||||
\(882\) | −0.554887 | − | 0.320364i | −0.0186840 | − | 0.0107872i | ||||
\(883\) | −9.75238 | + | 26.7945i | −0.328194 | + | 0.901705i | 0.660375 | + | 0.750936i | \(0.270397\pi\) |
−0.988569 | + | 0.150769i | \(0.951825\pi\) | |||||||
\(884\) | 0.958150 | + | 0.348738i | 0.0322261 | + | 0.0117293i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.97195 | − | 5.14757i | −0.0998447 | − | 0.172936i | ||||
\(887\) | 38.0483 | − | 6.70894i | 1.27754 | − | 0.225264i | 0.506602 | − | 0.862180i | \(-0.330901\pi\) |
0.770933 | + | 0.636916i | \(0.219790\pi\) | |||||||
\(888\) | 2.34322 | − | 2.79255i | 0.0786335 | − | 0.0937117i | ||||
\(889\) | −1.44938 | + | 1.21617i | −0.0486106 | + | 0.0407891i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.3699 | + | 9.23390i | −0.849925 | + | 0.309347i | ||||
\(892\) | − | 16.7955i | − | 0.562355i | ||||||
\(893\) | 27.9809 | + | 17.8831i | 0.936345 | + | 0.598435i | ||||
\(894\) | 9.88282 | 0.330531 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.135062 | − | 0.765974i | 0.00451210 | − | 0.0255894i | ||||
\(897\) | −1.34220 | − | 1.59957i | −0.0448147 | − | 0.0534081i | ||||
\(898\) | −5.22913 | + | 6.23184i | −0.174498 | + | 0.207959i | ||||
\(899\) | 6.73642 | + | 38.2042i | 0.224672 | + | 1.27418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.5594 | + | 18.2893i | −0.351783 | + | 0.609306i | ||||
\(902\) | 1.06834 | − | 2.93524i | 0.0355719 | − | 0.0977329i | ||||
\(903\) | 0.122762 | − | 0.337287i | 0.00408528 | − | 0.0112242i | ||||
\(904\) | 7.42428 | − | 12.8592i | 0.246928 | − | 0.427691i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.987198 | + | 5.59868i | 0.0327975 | + | 0.186004i | ||||
\(907\) | 18.4200 | − | 21.9521i | 0.611627 | − | 0.728908i | −0.367980 | − | 0.929834i | \(-0.619951\pi\) |
0.979606 | + | 0.200926i | \(0.0643950\pi\) | |||||||
\(908\) | 1.27986 | + | 1.52527i | 0.0424735 | + | 0.0506180i | ||||
\(909\) | 0.190117 | − | 1.07821i | 0.00630579 | − | 0.0357619i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.5952 | −1.57690 | −0.788450 | − | 0.615099i | \(-0.789116\pi\) | ||||
−0.788450 | + | 0.615099i | \(0.789116\pi\) | |||||||
\(912\) | −20.7694 | − | 13.2741i | −0.687743 | − | 0.439548i | ||||
\(913\) | − | 60.3966i | − | 1.99884i | ||||||
\(914\) | 11.1321 | − | 4.05174i | 0.368216 | − | 0.134020i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.6785 | − | 16.5122i | 0.650196 | − | 0.545579i | ||||
\(917\) | 0.398514 | − | 0.474930i | 0.0131601 | − | 0.0156836i | ||||
\(918\) | −4.13391 | + | 0.728919i | −0.136439 | + | 0.0240579i | ||||
\(919\) | −13.6098 | − | 23.5728i | −0.448945 | − | 0.777596i | 0.549372 | − | 0.835578i | \(-0.314867\pi\) |
−0.998318 | + | 0.0579814i | \(0.981534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.8077 | + | 16.6727i | 1.50942 | + | 0.549383i | ||||
\(922\) | 3.57977 | − | 9.83534i | 0.117894 | − | 0.323910i | ||||
\(923\) | −1.13877 | − | 0.657469i | −0.0374830 | − | 0.0216408i | ||||
\(924\) | −0.470265 | − | 0.814523i | −0.0154706 | − | 0.0267958i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.27273 | + | 1.06795i | 0.0418245 | + | 0.0350949i | ||||
\(927\) | −0.675919 | − | 0.805528i | −0.0222001 | − | 0.0264570i | ||||
\(928\) | 16.4070 | + | 2.89300i | 0.538586 | + | 0.0949672i | ||||
\(929\) | −30.2956 | + | 11.0267i | −0.993967 | + | 0.361774i | −0.787255 | − | 0.616627i | \(-0.788499\pi\) |
−0.206712 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.4405 | − | 20.6230i | −0.735457 | − | 0.675893i | ||||
\(932\) | 21.3716i | 0.700049i | ||||||||
\(933\) | −6.53472 | − | 17.9540i | −0.213937 | − | 0.587787i | ||||
\(934\) | 1.19953 | − | 6.80288i | 0.0392499 | − | 0.222597i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.0583546 | − | 0.0489653i | −0.00190738 | − | 0.00160048i | ||||
\(937\) | 17.8964 | − | 3.15561i | 0.584649 | − | 0.103089i | 0.126503 | − | 0.991966i | \(-0.459625\pi\) |
0.458146 | + | 0.888877i | \(0.348514\pi\) | |||||||
\(938\) | −0.237424 | + | 0.137077i | −0.00775217 | + | 0.00447572i | ||||
\(939\) | 0.390318 | − | 0.676051i | 0.0127376 | − | 0.0220621i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.1364 | − | 8.05700i | −0.721627 | − | 0.262651i | −0.0450107 | − | 0.998987i | \(-0.514332\pi\) |
−0.676616 | + | 0.736336i | \(0.736554\pi\) | |||||||
\(942\) | 2.02260 | + | 1.16775i | 0.0659000 | + | 0.0380474i | ||||
\(943\) | 15.5664 | − | 8.98729i | 0.506913 | − | 0.292666i | ||||
\(944\) | −6.23334 | − | 35.3510i | −0.202878 | − | 1.15058i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.94445 | + | 1.63159i | −0.0632195 | + | 0.0530475i | ||||
\(947\) | 8.30348 | + | 1.46413i | 0.269827 | + | 0.0475777i | 0.306924 | − | 0.951734i | \(-0.400700\pi\) |
−0.0370976 | + | 0.999312i | \(0.511811\pi\) | |||||||
\(948\) | 1.10169 | + | 3.02688i | 0.0357813 | + | 0.0983084i | ||||
\(949\) | −3.35164 | −0.108799 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.2536 | 1.07832 | ||||||||
\(952\) | −0.0922515 | − | 0.253459i | −0.00298989 | − | 0.00821465i | ||||
\(953\) | 49.3134 | + | 8.69527i | 1.59742 | + | 0.281668i | 0.900293 | − | 0.435284i | \(-0.143352\pi\) |
0.697123 | + | 0.716952i | \(0.254463\pi\) | |||||||
\(954\) | 0.589639 | − | 0.494766i | 0.0190903 | − | 0.0160186i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.72533 | + | 38.1413i | 0.217513 | + | 1.23358i | ||||
\(957\) | 23.0471 | − | 13.3062i | 0.745007 | − | 0.430130i | ||||
\(958\) | −7.66587 | − | 4.42589i | −0.247673 | − | 0.142994i | ||||
\(959\) | 1.76072 | + | 0.640851i | 0.0568568 | + | 0.0206942i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0475 | + | 29.5272i | −0.549920 | + | 0.952489i | ||||
\(962\) | 0.104683 | − | 0.0604385i | 0.00337510 | − | 0.00194862i | ||||
\(963\) | −0.552799 | + | 0.0974734i | −0.0178137 | + | 0.00314104i | ||||
\(964\) | −5.61078 | − | 4.70801i | −0.180711 | − | 0.151635i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.0467934 | + | 0.265378i | −0.00150555 | + | 0.00853841i | ||||
\(967\) | −2.05501 | − | 5.64610i | −0.0660847 | − | 0.181566i | 0.902255 | − | 0.431203i | \(-0.141911\pi\) |
−0.968339 | + | 0.249637i | \(0.919689\pi\) | |||||||
\(968\) | 0.403505i | 0.0129692i | ||||||||
\(969\) | −17.9979 | − | 0.812039i | −0.578175 | − | 0.0260864i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.8031 | + | 12.3033i | −1.08479 | + | 0.394832i | −0.821689 | − | 0.569936i | \(-0.806968\pi\) |
−0.263103 | + | 0.964768i | \(0.584746\pi\) | |||||||
\(972\) | −5.77917 | − | 1.01902i | −0.185367 | − | 0.0326852i | ||||
\(973\) | 0.901371 | + | 1.07421i | 0.0288966 | + | 0.0344377i | ||||
\(974\) | −8.12650 | − | 6.81894i | −0.260390 | − | 0.218493i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.70029 | + | 2.94498i | 0.0544248 | + | 0.0942666i | ||||
\(977\) | 29.1285 | + | 16.8174i | 0.931905 | + | 0.538035i | 0.887413 | − | 0.460974i | \(-0.152500\pi\) |
0.0444913 | + | 0.999010i | \(0.485833\pi\) | |||||||
\(978\) | −0.0995253 | + | 0.273444i | −0.00318247 | + | 0.00874376i | ||||
\(979\) | −2.07656 | − | 0.755805i | −0.0663671 | − | 0.0241556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.95775 | − | 3.39092i | −0.0625062 | − | 0.108264i | ||||
\(982\) | 5.88002 | − | 1.03681i | 0.187639 | − | 0.0330858i | ||||
\(983\) | −28.9508 | + | 34.5023i | −0.923388 | + | 1.10045i | 0.0712938 | + | 0.997455i | \(0.477287\pi\) |
−0.994682 | + | 0.102996i | \(0.967157\pi\) | |||||||
\(984\) | −4.56257 | + | 3.82845i | −0.145449 | + | 0.122046i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.49873 | − | 1.27343i | 0.111422 | − | 0.0405544i | ||||
\(987\) | − | 1.11708i | − | 0.0355570i | ||||||
\(988\) | −1.07409 | − | 1.40401i | −0.0341714 | − | 0.0446674i | ||||
\(989\) | −14.6064 | −0.464457 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.06445 | + | 6.03681i | −0.0338134 | + | 0.191765i | −0.997036 | − | 0.0769404i | \(-0.975485\pi\) |
0.963222 | + | 0.268706i | \(0.0865960\pi\) | |||||||
\(992\) | 17.9694 | + | 21.4151i | 0.570529 | + | 0.679930i | ||||
\(993\) | −6.35394 | + | 7.57233i | −0.201636 | + | 0.240301i | ||||
\(994\) | 0.0294673 | + | 0.167117i | 0.000934645 | + | 0.00530064i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −28.0912 | + | 48.6554i | −0.890104 | + | 1.54171i | ||||
\(997\) | 15.3626 | − | 42.2085i | 0.486539 | − | 1.33676i | −0.417255 | − | 0.908789i | \(-0.637008\pi\) |
0.903795 | − | 0.427967i | \(-0.140770\pi\) | |||||||
\(998\) | −1.18700 | + | 3.26125i | −0.0375738 | + | 0.103233i | ||||
\(999\) | 4.99729 | − | 8.65556i | 0.158107 | − | 0.273850i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 475.2.u.b.24.3 | 36 | ||
5.2 | odd | 4 | 95.2.k.a.81.3 | yes | 18 | ||
5.3 | odd | 4 | 475.2.l.c.176.1 | 18 | |||
5.4 | even | 2 | inner | 475.2.u.b.24.4 | 36 | ||
15.2 | even | 4 | 855.2.bs.c.271.1 | 18 | |||
19.4 | even | 9 | inner | 475.2.u.b.99.4 | 36 | ||
95.2 | even | 36 | 1805.2.a.s.1.7 | 9 | |||
95.4 | even | 18 | inner | 475.2.u.b.99.3 | 36 | ||
95.17 | odd | 36 | 1805.2.a.v.1.3 | 9 | |||
95.23 | odd | 36 | 475.2.l.c.251.1 | 18 | |||
95.42 | odd | 36 | 95.2.k.a.61.3 | ✓ | 18 | ||
95.78 | even | 36 | 9025.2.a.cf.1.3 | 9 | |||
95.93 | odd | 36 | 9025.2.a.cc.1.7 | 9 | |||
285.137 | even | 36 | 855.2.bs.c.631.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.a.61.3 | ✓ | 18 | 95.42 | odd | 36 | ||
95.2.k.a.81.3 | yes | 18 | 5.2 | odd | 4 | ||
475.2.l.c.176.1 | 18 | 5.3 | odd | 4 | |||
475.2.l.c.251.1 | 18 | 95.23 | odd | 36 | |||
475.2.u.b.24.3 | 36 | 1.1 | even | 1 | trivial | ||
475.2.u.b.24.4 | 36 | 5.4 | even | 2 | inner | ||
475.2.u.b.99.3 | 36 | 95.4 | even | 18 | inner | ||
475.2.u.b.99.4 | 36 | 19.4 | even | 9 | inner | ||
855.2.bs.c.271.1 | 18 | 15.2 | even | 4 | |||
855.2.bs.c.631.1 | 18 | 285.137 | even | 36 | |||
1805.2.a.s.1.7 | 9 | 95.2 | even | 36 | |||
1805.2.a.v.1.3 | 9 | 95.17 | odd | 36 | |||
9025.2.a.cc.1.7 | 9 | 95.93 | odd | 36 | |||
9025.2.a.cf.1.3 | 9 | 95.78 | even | 36 |