Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(529,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.ba (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 529.8 | ||
Character | \(\chi\) | \(=\) | 1110.529 |
Dual form | 1110.2.ba.b.619.8 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.653296 | + | 2.13851i | 0.292163 | + | 0.956369i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 3.20005 | + | 1.84755i | 1.20951 | + | 0.698309i | 0.962652 | − | 0.270743i | \(-0.0872694\pi\) |
0.246855 | + | 0.969052i | \(0.420603\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | −1.52535 | + | 1.63502i | −0.482359 | + | 0.517040i | ||||
\(11\) | 4.44239 | 1.33943 | 0.669716 | − | 0.742617i | \(-0.266416\pi\) | ||||
0.669716 | + | 0.742617i | \(0.266416\pi\) | |||||||
\(12\) | 0.866025 | − | 0.500000i | 0.250000 | − | 0.144338i | ||||
\(13\) | 3.09657 | − | 5.36341i | 0.858833 | − | 1.48754i | −0.0142091 | − | 0.999899i | \(-0.504523\pi\) |
0.873043 | − | 0.487644i | \(-0.162144\pi\) | |||||||
\(14\) | 3.69510i | 0.987558i | ||||||||
\(15\) | 0.503482 | − | 2.17865i | 0.129998 | − | 0.562524i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.67263 | − | 2.89708i | −0.405673 | − | 0.702646i | 0.588727 | − | 0.808332i | \(-0.299629\pi\) |
−0.994400 | + | 0.105686i | \(0.966296\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 4.88936 | + | 2.82287i | 1.12170 | + | 0.647611i | 0.941833 | − | 0.336081i | \(-0.109101\pi\) |
0.179862 | + | 0.983692i | \(0.442435\pi\) | |||||||
\(20\) | −2.17865 | − | 0.503482i | −0.487160 | − | 0.112582i | ||||
\(21\) | −1.84755 | − | 3.20005i | −0.403169 | − | 0.698309i | ||||
\(22\) | 2.22120 | + | 3.84723i | 0.473561 | + | 0.820231i | ||||
\(23\) | −3.31793 | −0.691837 | −0.345918 | − | 0.938265i | \(-0.612433\pi\) | ||||
−0.345918 | + | 0.938265i | \(0.612433\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | −4.14641 | + | 2.79415i | −0.829282 | + | 0.558831i | ||||
\(26\) | 6.19314 | 1.21457 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.20005 | + | 1.84755i | −0.604753 | + | 0.349155i | ||||
\(29\) | − | 0.108323i | − | 0.0201151i | −0.999949 | − | 0.0100575i | \(-0.996799\pi\) | ||
0.999949 | − | 0.0100575i | \(-0.00320147\pi\) | |||||||
\(30\) | 2.13851 | − | 0.653296i | 0.390436 | − | 0.119275i | ||||
\(31\) | − | 3.58380i | − | 0.643670i | −0.946796 | − | 0.321835i | \(-0.895700\pi\) | ||
0.946796 | − | 0.321835i | \(-0.104300\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −3.84723 | − | 2.22120i | −0.669716 | − | 0.386661i | ||||
\(34\) | 1.67263 | − | 2.89708i | 0.286854 | − | 0.496846i | ||||
\(35\) | −1.86042 | + | 8.05033i | −0.314468 | + | 1.36075i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 1.62326 | + | 5.86217i | 0.266863 | + | 0.963734i | ||||
\(38\) | 5.64574i | 0.915861i | ||||||||
\(39\) | −5.36341 | + | 3.09657i | −0.858833 | + | 0.495848i | ||||
\(40\) | −0.653296 | − | 2.13851i | −0.103295 | − | 0.338127i | ||||
\(41\) | 0.667426 | − | 1.15602i | 0.104234 | − | 0.180539i | −0.809191 | − | 0.587546i | \(-0.800094\pi\) |
0.913425 | + | 0.407007i | \(0.133427\pi\) | |||||||
\(42\) | 1.84755 | − | 3.20005i | 0.285084 | − | 0.493779i | ||||
\(43\) | 1.49655 | 0.228221 | 0.114111 | − | 0.993468i | \(-0.463598\pi\) | ||||
0.114111 | + | 0.993468i | \(0.463598\pi\) | |||||||
\(44\) | −2.22120 | + | 3.84723i | −0.334858 | + | 0.579991i | ||||
\(45\) | −1.52535 | + | 1.63502i | −0.227386 | + | 0.243735i | ||||
\(46\) | −1.65897 | − | 2.87341i | −0.244601 | − | 0.423662i | ||||
\(47\) | 1.22763i | 0.179069i | 0.995984 | + | 0.0895343i | \(0.0285379\pi\) | ||||
−0.995984 | + | 0.0895343i | \(0.971462\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 3.32690 | + | 5.76236i | 0.475271 | + | 0.823194i | ||||
\(50\) | −4.49301 | − | 2.19382i | −0.635408 | − | 0.310253i | ||||
\(51\) | 3.34526i | 0.468431i | ||||||||
\(52\) | 3.09657 | + | 5.36341i | 0.429417 | + | 0.743772i | ||||
\(53\) | −7.70341 | + | 4.44757i | −1.05814 | + | 0.610920i | −0.924919 | − | 0.380165i | \(-0.875867\pi\) |
−0.133226 | + | 0.991086i | \(0.542534\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 2.90220 | + | 9.50008i | 0.391332 | + | 1.28099i | ||||
\(56\) | −3.20005 | − | 1.84755i | −0.427625 | − | 0.246890i | ||||
\(57\) | −2.82287 | − | 4.88936i | −0.373899 | − | 0.647611i | ||||
\(58\) | 0.0938106 | − | 0.0541616i | 0.0123179 | − | 0.00711176i | ||||
\(59\) | −0.292750 | + | 0.169019i | −0.0381128 | + | 0.0220044i | −0.518935 | − | 0.854814i | \(-0.673671\pi\) |
0.480823 | + | 0.876818i | \(0.340338\pi\) | |||||||
\(60\) | 1.63502 | + | 1.52535i | 0.211081 | + | 0.196922i | ||||
\(61\) | 11.4397 | + | 6.60469i | 1.46470 | + | 0.845644i | 0.999223 | − | 0.0394160i | \(-0.0125497\pi\) |
0.465476 | + | 0.885060i | \(0.345883\pi\) | |||||||
\(62\) | 3.10366 | − | 1.79190i | 0.394166 | − | 0.227572i | ||||
\(63\) | 3.69510i | 0.465539i | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.4927 | + | 3.11813i | 1.67356 | + | 0.386756i | ||||
\(66\) | − | 4.44239i | − | 0.546821i | ||||||
\(67\) | −12.7735 | − | 7.37478i | −1.56053 | − | 0.900972i | −0.997203 | − | 0.0747384i | \(-0.976188\pi\) |
−0.563327 | − | 0.826234i | \(-0.690479\pi\) | |||||||
\(68\) | 3.34526 | 0.405673 | ||||||||
\(69\) | 2.87341 | + | 1.65897i | 0.345918 | + | 0.199716i | ||||
\(70\) | −7.90200 | + | 2.41400i | −0.944470 | + | 0.288528i | ||||
\(71\) | 2.66182 | − | 4.61040i | 0.315899 | − | 0.547154i | −0.663729 | − | 0.747973i | \(-0.731027\pi\) |
0.979628 | + | 0.200819i | \(0.0643605\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 2.67315i | 0.312868i | 0.987688 | + | 0.156434i | \(0.0499999\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(74\) | −4.26515 | + | 4.33687i | −0.495814 | + | 0.504151i | ||||
\(75\) | 4.98797 | − | 0.346604i | 0.575961 | − | 0.0400224i | ||||
\(76\) | −4.88936 | + | 2.82287i | −0.560848 | + | 0.323806i | ||||
\(77\) | 14.2159 | + | 8.20755i | 1.62005 | + | 0.935338i | ||||
\(78\) | −5.36341 | − | 3.09657i | −0.607287 | − | 0.350617i | ||||
\(79\) | −4.87431 | − | 2.81418i | −0.548403 | − | 0.316620i | 0.200075 | − | 0.979781i | \(-0.435881\pi\) |
−0.748478 | + | 0.663160i | \(0.769215\pi\) | |||||||
\(80\) | 1.52535 | − | 1.63502i | 0.170540 | − | 0.182801i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.33485 | 0.147410 | ||||||||
\(83\) | 5.20372 | − | 3.00437i | 0.571182 | − | 0.329772i | −0.186439 | − | 0.982466i | \(-0.559695\pi\) |
0.757621 | + | 0.652694i | \(0.226361\pi\) | |||||||
\(84\) | 3.69510 | 0.403169 | ||||||||
\(85\) | 5.10271 | − | 5.46959i | 0.553466 | − | 0.593260i | ||||
\(86\) | 0.748273 | + | 1.29605i | 0.0806884 | + | 0.139756i | ||||
\(87\) | −0.0541616 | + | 0.0938106i | −0.00580673 | + | 0.0100575i | ||||
\(88\) | −4.44239 | −0.473561 | ||||||||
\(89\) | −13.9095 | + | 8.03066i | −1.47440 | + | 0.851248i | −0.999584 | − | 0.0288348i | \(-0.990820\pi\) |
−0.474820 | + | 0.880083i | \(0.657487\pi\) | |||||||
\(90\) | −2.17865 | − | 0.503482i | −0.229650 | − | 0.0530716i | ||||
\(91\) | 19.8184 | − | 11.4421i | 2.07753 | − | 1.19946i | ||||
\(92\) | 1.65897 | − | 2.87341i | 0.172959 | − | 0.299574i | ||||
\(93\) | −1.79190 | + | 3.10366i | −0.185811 | + | 0.321835i | ||||
\(94\) | −1.06316 | + | 0.613817i | −0.109657 | + | 0.0633103i | ||||
\(95\) | −2.84253 | + | 12.3001i | −0.291637 | + | 1.26196i | ||||
\(96\) | −0.866025 | + | 0.500000i | −0.0883883 | + | 0.0510310i | ||||
\(97\) | 12.8116 | 1.30082 | 0.650410 | − | 0.759583i | \(-0.274597\pi\) | ||||
0.650410 | + | 0.759583i | \(0.274597\pi\) | |||||||
\(98\) | −3.32690 | + | 5.76236i | −0.336068 | + | 0.582086i | ||||
\(99\) | 2.22120 | + | 3.84723i | 0.223239 | + | 0.386661i | ||||
\(100\) | −0.346604 | − | 4.98797i | −0.0346604 | − | 0.498797i | ||||
\(101\) | −10.2462 | −1.01953 | −0.509766 | − | 0.860313i | \(-0.670268\pi\) | ||||
−0.509766 | + | 0.860313i | \(0.670268\pi\) | |||||||
\(102\) | −2.89708 | + | 1.67263i | −0.286854 | + | 0.165615i | ||||
\(103\) | −5.94305 | −0.585586 | −0.292793 | − | 0.956176i | \(-0.594585\pi\) | ||||
−0.292793 | + | 0.956176i | \(0.594585\pi\) | |||||||
\(104\) | −3.09657 | + | 5.36341i | −0.303643 | + | 0.525926i | ||||
\(105\) | 5.63633 | − | 6.04158i | 0.550050 | − | 0.589598i | ||||
\(106\) | −7.70341 | − | 4.44757i | −0.748221 | − | 0.431986i | ||||
\(107\) | −9.10060 | − | 5.25423i | −0.879788 | − | 0.507946i | −0.00919937 | − | 0.999958i | \(-0.502928\pi\) |
−0.870588 | + | 0.492012i | \(0.836262\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | −1.27969 | + | 0.738832i | −0.122573 | + | 0.0707673i | −0.560033 | − | 0.828471i | \(-0.689211\pi\) |
0.437460 | + | 0.899238i | \(0.355878\pi\) | |||||||
\(110\) | −6.77621 | + | 7.26342i | −0.646087 | + | 0.692540i | ||||
\(111\) | 1.52530 | − | 5.88842i | 0.144775 | − | 0.558904i | ||||
\(112\) | − | 3.69510i | − | 0.349155i | ||||||
\(113\) | 3.19271 | + | 5.52994i | 0.300345 | + | 0.520213i | 0.976214 | − | 0.216809i | \(-0.0695647\pi\) |
−0.675869 | + | 0.737022i | \(0.736231\pi\) | |||||||
\(114\) | 2.82287 | − | 4.88936i | 0.264386 | − | 0.457930i | ||||
\(115\) | −2.16759 | − | 7.09542i | −0.202129 | − | 0.661651i | ||||
\(116\) | 0.0938106 | + | 0.0541616i | 0.00871009 | + | 0.00502877i | ||||
\(117\) | 6.19314 | 0.572556 | ||||||||
\(118\) | −0.292750 | − | 0.169019i | −0.0269498 | − | 0.0155595i | ||||
\(119\) | − | 12.3611i | − | 1.13314i | ||||||
\(120\) | −0.503482 | + | 2.17865i | −0.0459614 | + | 0.198882i | ||||
\(121\) | 8.73486 | 0.794078 | ||||||||
\(122\) | 13.2094i | 1.19592i | ||||||||
\(123\) | −1.15602 | + | 0.667426i | −0.104234 | + | 0.0601797i | ||||
\(124\) | 3.10366 | + | 1.79190i | 0.278717 | + | 0.160917i | ||||
\(125\) | −8.68414 | − | 7.04171i | −0.776734 | − | 0.629829i | ||||
\(126\) | −3.20005 | + | 1.84755i | −0.285084 | + | 0.164593i | ||||
\(127\) | −15.2469 | + | 8.80279i | −1.35294 | + | 0.781122i | −0.988661 | − | 0.150167i | \(-0.952019\pi\) |
−0.364282 | + | 0.931289i | \(0.618685\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.29605 | − | 0.748273i | −0.114111 | − | 0.0658818i | ||||
\(130\) | 4.04595 | + | 13.2441i | 0.354853 | + | 1.16158i | ||||
\(131\) | −18.6551 | + | 10.7705i | −1.62990 | + | 0.941025i | −0.645783 | + | 0.763521i | \(0.723469\pi\) |
−0.984120 | + | 0.177504i | \(0.943198\pi\) | |||||||
\(132\) | 3.84723 | − | 2.22120i | 0.334858 | − | 0.193330i | ||||
\(133\) | 10.4308 | + | 18.0667i | 0.904466 | + | 1.56658i | ||||
\(134\) | − | 14.7496i | − | 1.27417i | ||||||
\(135\) | 2.13851 | − | 0.653296i | 0.184053 | − | 0.0562268i | ||||
\(136\) | 1.67263 | + | 2.89708i | 0.143427 | + | 0.248423i | ||||
\(137\) | − | 10.1403i | − | 0.866343i | −0.901312 | − | 0.433171i | \(-0.857394\pi\) | ||
0.901312 | − | 0.433171i | \(-0.142606\pi\) | |||||||
\(138\) | 3.31793i | 0.282441i | ||||||||
\(139\) | −3.23928 | − | 5.61060i | −0.274752 | − | 0.475885i | 0.695320 | − | 0.718700i | \(-0.255263\pi\) |
−0.970073 | + | 0.242815i | \(0.921929\pi\) | |||||||
\(140\) | −6.04158 | − | 5.63633i | −0.510607 | − | 0.476357i | ||||
\(141\) | 0.613817 | − | 1.06316i | 0.0516927 | − | 0.0895343i | ||||
\(142\) | 5.32363 | 0.446749 | ||||||||
\(143\) | 13.7562 | − | 23.8264i | 1.15035 | − | 1.99246i | ||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0.231650 | − | 0.0707671i | 0.0192374 | − | 0.00587689i | ||||
\(146\) | −2.31501 | + | 1.33657i | −0.191592 | + | 0.110616i | ||||
\(147\) | − | 6.65380i | − | 0.548796i | ||||||
\(148\) | −5.88842 | − | 1.52530i | −0.484025 | − | 0.125378i | ||||
\(149\) | 1.79951 | 0.147421 | 0.0737107 | − | 0.997280i | \(-0.476516\pi\) | ||||
0.0737107 | + | 0.997280i | \(0.476516\pi\) | |||||||
\(150\) | 2.79415 | + | 4.14641i | 0.228142 | + | 0.338553i | ||||
\(151\) | 5.78284 | − | 10.0162i | 0.470601 | − | 0.815104i | −0.528834 | − | 0.848725i | \(-0.677371\pi\) |
0.999435 | + | 0.0336210i | \(0.0107039\pi\) | |||||||
\(152\) | −4.88936 | − | 2.82287i | −0.396579 | − | 0.228965i | ||||
\(153\) | 1.67263 | − | 2.89708i | 0.135224 | − | 0.234215i | ||||
\(154\) | 16.4151i | 1.32277i | ||||||||
\(155\) | 7.66398 | − | 2.34128i | 0.615586 | − | 0.188056i | ||||
\(156\) | − | 6.19314i | − | 0.495848i | ||||||
\(157\) | 17.0546 | − | 9.84650i | 1.36111 | − | 0.785836i | 0.371337 | − | 0.928498i | \(-0.378899\pi\) |
0.989771 | + | 0.142662i | \(0.0455661\pi\) | |||||||
\(158\) | − | 5.62837i | − | 0.447769i | ||||||
\(159\) | 8.89513 | 0.705430 | ||||||||
\(160\) | 2.17865 | + | 0.503482i | 0.172237 | + | 0.0398037i | ||||
\(161\) | −10.6176 | − | 6.13005i | −0.836781 | − | 0.483116i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.25810 | − | 14.3034i | −0.646824 | − | 1.12033i | −0.983877 | − | 0.178847i | \(-0.942763\pi\) |
0.337053 | − | 0.941486i | \(-0.390570\pi\) | |||||||
\(164\) | 0.667426 | + | 1.15602i | 0.0521172 | + | 0.0902696i | ||||
\(165\) | 2.23666 | − | 9.67841i | 0.174124 | − | 0.753463i | ||||
\(166\) | 5.20372 | + | 3.00437i | 0.403887 | + | 0.233184i | ||||
\(167\) | −5.60293 | + | 9.70456i | −0.433568 | + | 0.750961i | −0.997178 | − | 0.0750799i | \(-0.976079\pi\) |
0.563610 | + | 0.826041i | \(0.309412\pi\) | |||||||
\(168\) | 1.84755 | + | 3.20005i | 0.142542 | + | 0.246890i | ||||
\(169\) | −12.6775 | − | 21.9580i | −0.975190 | − | 1.68908i | ||||
\(170\) | 7.28815 | + | 1.68428i | 0.558976 | + | 0.129178i | ||||
\(171\) | 5.64574i | 0.431741i | ||||||||
\(172\) | −0.748273 | + | 1.29605i | −0.0570553 | + | 0.0988227i | ||||
\(173\) | −12.4041 | + | 7.16151i | −0.943066 | + | 0.544480i | −0.890920 | − | 0.454160i | \(-0.849940\pi\) |
−0.0521462 | + | 0.998639i | \(0.516606\pi\) | |||||||
\(174\) | −0.108323 | −0.00821195 | ||||||||
\(175\) | −18.4311 | + | 1.28074i | −1.39326 | + | 0.0968147i | ||||
\(176\) | −2.22120 | − | 3.84723i | −0.167429 | − | 0.289996i | ||||
\(177\) | 0.338038 | 0.0254085 | ||||||||
\(178\) | −13.9095 | − | 8.03066i | −1.04256 | − | 0.601923i | ||||
\(179\) | 6.16211i | 0.460578i | 0.973122 | + | 0.230289i | \(0.0739671\pi\) | ||||
−0.973122 | + | 0.230289i | \(0.926033\pi\) | |||||||
\(180\) | −0.653296 | − | 2.13851i | −0.0486938 | − | 0.159395i | ||||
\(181\) | −1.83239 | + | 3.17379i | −0.136200 | + | 0.235906i | −0.926055 | − | 0.377388i | \(-0.876822\pi\) |
0.789855 | + | 0.613294i | \(0.210156\pi\) | |||||||
\(182\) | 19.8184 | + | 11.4421i | 1.46904 | + | 0.848148i | ||||
\(183\) | −6.60469 | − | 11.4397i | −0.488233 | − | 0.845644i | ||||
\(184\) | 3.31793 | 0.244601 | ||||||||
\(185\) | −11.4758 | + | 7.30109i | −0.843718 | + | 0.536787i | ||||
\(186\) | −3.58380 | −0.262777 | ||||||||
\(187\) | −7.43049 | − | 12.8700i | −0.543371 | − | 0.941147i | ||||
\(188\) | −1.06316 | − | 0.613817i | −0.0775390 | − | 0.0447672i | ||||
\(189\) | 1.84755 | − | 3.20005i | 0.134390 | − | 0.232770i | ||||
\(190\) | −12.0735 | + | 3.68834i | −0.875900 | + | 0.267580i | ||||
\(191\) | − | 17.0867i | − | 1.23635i | −0.786040 | − | 0.618176i | \(-0.787872\pi\) | ||
0.786040 | − | 0.618176i | \(-0.212128\pi\) | |||||||
\(192\) | −0.866025 | − | 0.500000i | −0.0625000 | − | 0.0360844i | ||||
\(193\) | 24.1866 | 1.74099 | 0.870495 | − | 0.492177i | \(-0.163799\pi\) | ||||
0.870495 | + | 0.492177i | \(0.163799\pi\) | |||||||
\(194\) | 6.40580 | + | 11.0952i | 0.459910 | + | 0.796587i | ||||
\(195\) | −10.1259 | − | 9.44671i | −0.725132 | − | 0.676493i | ||||
\(196\) | −6.65380 | −0.475271 | ||||||||
\(197\) | 8.50118 | − | 4.90816i | 0.605684 | − | 0.349692i | −0.165591 | − | 0.986195i | \(-0.552953\pi\) |
0.771274 | + | 0.636503i | \(0.219620\pi\) | |||||||
\(198\) | −2.22120 | + | 3.84723i | −0.157854 | + | 0.273410i | ||||
\(199\) | − | 22.0251i | − | 1.56132i | −0.624958 | − | 0.780659i | \(-0.714884\pi\) | ||
0.624958 | − | 0.780659i | \(-0.285116\pi\) | |||||||
\(200\) | 4.14641 | − | 2.79415i | 0.293195 | − | 0.197577i | ||||
\(201\) | 7.37478 | + | 12.7735i | 0.520177 | + | 0.900972i | ||||
\(202\) | −5.12308 | − | 8.87344i | −0.360459 | − | 0.624333i | ||||
\(203\) | 0.200133 | − | 0.346640i | 0.0140466 | − | 0.0243294i | ||||
\(204\) | −2.89708 | − | 1.67263i | −0.202836 | − | 0.117108i | ||||
\(205\) | 2.90817 | + | 0.672073i | 0.203115 | + | 0.0469396i | ||||
\(206\) | −2.97152 | − | 5.14683i | −0.207036 | − | 0.358597i | ||||
\(207\) | −1.65897 | − | 2.87341i | −0.115306 | − | 0.199716i | ||||
\(208\) | −6.19314 | −0.429417 | ||||||||
\(209\) | 21.7205 | + | 12.5403i | 1.50244 | + | 0.867431i | ||||
\(210\) | 8.05033 | + | 1.86042i | 0.555526 | + | 0.128381i | ||||
\(211\) | −7.17457 | −0.493918 | −0.246959 | − | 0.969026i | \(-0.579431\pi\) | ||||
−0.246959 | + | 0.969026i | \(0.579431\pi\) | |||||||
\(212\) | − | 8.89513i | − | 0.610920i | ||||||
\(213\) | −4.61040 | + | 2.66182i | −0.315899 | + | 0.182385i | ||||
\(214\) | − | 10.5085i | − | 0.718344i | ||||||
\(215\) | 0.977688 | + | 3.20037i | 0.0666777 | + | 0.218264i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 6.62126 | − | 11.4684i | 0.449481 | − | 0.778523i | ||||
\(218\) | −1.27969 | − | 0.738832i | −0.0866719 | − | 0.0500400i | ||||
\(219\) | 1.33657 | − | 2.31501i | 0.0903173 | − | 0.156434i | ||||
\(220\) | −9.67841 | − | 2.23666i | −0.652518 | − | 0.150796i | ||||
\(221\) | −20.7177 | −1.39362 | ||||||||
\(222\) | 5.86217 | − | 1.62326i | 0.393443 | − | 0.108946i | ||||
\(223\) | 0.219842i | 0.0147217i | 0.999973 | + | 0.00736087i | \(0.00234306\pi\) | ||||
−0.999973 | + | 0.00736087i | \(0.997657\pi\) | |||||||
\(224\) | 3.20005 | − | 1.84755i | 0.213813 | − | 0.123445i | ||||
\(225\) | −4.49301 | − | 2.19382i | −0.299534 | − | 0.146255i | ||||
\(226\) | −3.19271 | + | 5.52994i | −0.212376 | + | 0.367846i | ||||
\(227\) | 12.3956 | − | 21.4699i | 0.822728 | − | 1.42501i | −0.0809161 | − | 0.996721i | \(-0.525785\pi\) |
0.903644 | − | 0.428285i | \(-0.140882\pi\) | |||||||
\(228\) | 5.64574 | 0.373899 | ||||||||
\(229\) | −5.65301 | + | 9.79129i | −0.373561 | + | 0.647027i | −0.990111 | − | 0.140289i | \(-0.955197\pi\) |
0.616549 | + | 0.787316i | \(0.288530\pi\) | |||||||
\(230\) | 5.06101 | − | 5.42490i | 0.333713 | − | 0.357707i | ||||
\(231\) | −8.20755 | − | 14.2159i | −0.540017 | − | 0.935338i | ||||
\(232\) | 0.108323i | 0.00711176i | ||||||||
\(233\) | 14.3078i | 0.937337i | 0.883374 | + | 0.468669i | \(0.155266\pi\) | ||||
−0.883374 | + | 0.468669i | \(0.844734\pi\) | |||||||
\(234\) | 3.09657 | + | 5.36341i | 0.202429 | + | 0.350617i | ||||
\(235\) | −2.62530 | + | 0.802008i | −0.171256 | + | 0.0523172i | ||||
\(236\) | − | 0.338038i | − | 0.0220044i | ||||||
\(237\) | 2.81418 | + | 4.87431i | 0.182801 | + | 0.316620i | ||||
\(238\) | 10.7050 | − | 6.18055i | 0.693904 | − | 0.400626i | ||||
\(239\) | 5.88745 | − | 3.39912i | 0.380828 | − | 0.219871i | −0.297351 | − | 0.954768i | \(-0.596103\pi\) |
0.678178 | + | 0.734897i | \(0.262770\pi\) | |||||||
\(240\) | −2.13851 | + | 0.653296i | −0.138040 | + | 0.0421701i | ||||
\(241\) | −4.79812 | − | 2.77020i | −0.309074 | − | 0.178444i | 0.337438 | − | 0.941348i | \(-0.390440\pi\) |
−0.646512 | + | 0.762904i | \(0.723773\pi\) | |||||||
\(242\) | 4.36743 | + | 7.56461i | 0.280749 | + | 0.486272i | ||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −11.4397 | + | 6.60469i | −0.732350 | + | 0.422822i | ||||
\(245\) | −10.1494 | + | 10.8791i | −0.648420 | + | 0.695041i | ||||
\(246\) | −1.15602 | − | 0.667426i | −0.0737048 | − | 0.0425535i | ||||
\(247\) | 30.2805 | − | 17.4824i | 1.92670 | − | 1.11238i | ||||
\(248\) | 3.58380i | 0.227572i | ||||||||
\(249\) | −6.00873 | −0.380788 | ||||||||
\(250\) | 1.75622 | − | 11.0415i | 0.111073 | − | 0.698329i | ||||
\(251\) | 30.0814i | 1.89872i | 0.314193 | + | 0.949359i | \(0.398266\pi\) | ||||
−0.314193 | + | 0.949359i | \(0.601734\pi\) | |||||||
\(252\) | −3.20005 | − | 1.84755i | −0.201584 | − | 0.116385i | ||||
\(253\) | −14.7396 | −0.926668 | ||||||||
\(254\) | −15.2469 | − | 8.80279i | −0.956675 | − | 0.552336i | ||||
\(255\) | −7.15387 | + | 2.18545i | −0.447992 | + | 0.136858i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.7565 | + | 20.3629i | 0.733350 | + | 1.27020i | 0.955443 | + | 0.295174i | \(0.0953777\pi\) |
−0.222093 | + | 0.975025i | \(0.571289\pi\) | |||||||
\(258\) | − | 1.49655i | − | 0.0931709i | ||||||
\(259\) | −5.63613 | + | 21.7583i | −0.350212 | + | 1.35200i | ||||
\(260\) | −9.44671 | + | 10.1259i | −0.585860 | + | 0.627983i | ||||
\(261\) | 0.0938106 | − | 0.0541616i | 0.00580673 | − | 0.00335252i | ||||
\(262\) | −18.6551 | − | 10.7705i | −1.15252 | − | 0.665405i | ||||
\(263\) | 23.8858 | + | 13.7905i | 1.47286 | + | 0.850357i | 0.999534 | − | 0.0305303i | \(-0.00971960\pi\) |
0.473327 | + | 0.880887i | \(0.343053\pi\) | |||||||
\(264\) | 3.84723 | + | 2.22120i | 0.236780 | + | 0.136705i | ||||
\(265\) | −14.5438 | − | 13.5682i | −0.893416 | − | 0.833488i | ||||
\(266\) | −10.4308 | + | 18.0667i | −0.639554 | + | 1.10774i | ||||
\(267\) | 16.0613 | 0.982936 | ||||||||
\(268\) | 12.7735 | − | 7.37478i | 0.780265 | − | 0.450486i | ||||
\(269\) | −13.5863 | −0.828370 | −0.414185 | − | 0.910193i | \(-0.635933\pi\) | ||||
−0.414185 | + | 0.910193i | \(0.635933\pi\) | |||||||
\(270\) | 1.63502 | + | 1.52535i | 0.0995044 | + | 0.0928300i | ||||
\(271\) | 4.97694 | + | 8.62031i | 0.302327 | + | 0.523646i | 0.976663 | − | 0.214779i | \(-0.0689031\pi\) |
−0.674335 | + | 0.738425i | \(0.735570\pi\) | |||||||
\(272\) | −1.67263 | + | 2.89708i | −0.101418 | + | 0.175662i | ||||
\(273\) | −22.8843 | −1.38502 | ||||||||
\(274\) | 8.78174 | − | 5.07014i | 0.530525 | − | 0.306299i | ||||
\(275\) | −18.4200 | + | 12.4127i | −1.11077 | + | 0.748516i | ||||
\(276\) | −2.87341 | + | 1.65897i | −0.172959 | + | 0.0998580i | ||||
\(277\) | 13.3467 | − | 23.1172i | 0.801926 | − | 1.38898i | −0.116421 | − | 0.993200i | \(-0.537142\pi\) |
0.918347 | − | 0.395777i | \(-0.129525\pi\) | |||||||
\(278\) | 3.23928 | − | 5.61060i | 0.194279 | − | 0.336502i | ||||
\(279\) | 3.10366 | − | 1.79190i | 0.185811 | − | 0.107278i | ||||
\(280\) | 1.86042 | − | 8.05033i | 0.111181 | − | 0.481099i | ||||
\(281\) | −0.674004 | + | 0.389137i | −0.0402077 | + | 0.0232139i | −0.519969 | − | 0.854185i | \(-0.674057\pi\) |
0.479761 | + | 0.877399i | \(0.340723\pi\) | |||||||
\(282\) | 1.22763 | 0.0731045 | ||||||||
\(283\) | −5.81231 | + | 10.0672i | −0.345506 | + | 0.598434i | −0.985446 | − | 0.169991i | \(-0.945626\pi\) |
0.639940 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(284\) | 2.66182 | + | 4.61040i | 0.157950 | + | 0.273577i | ||||
\(285\) | 8.61175 | − | 9.23092i | 0.510116 | − | 0.546793i | ||||
\(286\) | 27.5123 | 1.62684 | ||||||||
\(287\) | 4.27160 | − | 2.46621i | 0.252144 | − | 0.145576i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 2.90460 | − | 5.03092i | 0.170859 | − | 0.295936i | ||||
\(290\) | 0.177111 | + | 0.165231i | 0.0104003 | + | 0.00970269i | ||||
\(291\) | −11.0952 | − | 6.40580i | −0.650410 | − | 0.375515i | ||||
\(292\) | −2.31501 | − | 1.33657i | −0.135476 | − | 0.0782170i | ||||
\(293\) | −9.00934 | − | 5.20154i | −0.526331 | − | 0.303877i | 0.213190 | − | 0.977011i | \(-0.431615\pi\) |
−0.739521 | + | 0.673133i | \(0.764948\pi\) | |||||||
\(294\) | 5.76236 | − | 3.32690i | 0.336068 | − | 0.194029i | ||||
\(295\) | −0.552700 | − | 0.515627i | −0.0321795 | − | 0.0300210i | ||||
\(296\) | −1.62326 | − | 5.86217i | −0.0943504 | − | 0.340732i | ||||
\(297\) | − | 4.44239i | − | 0.257774i | ||||||
\(298\) | 0.899754 | + | 1.55842i | 0.0521213 | + | 0.0902768i | ||||
\(299\) | −10.2742 | + | 17.7954i | −0.594173 | + | 1.02914i | ||||
\(300\) | −2.19382 | + | 4.49301i | −0.126660 | + | 0.259404i | ||||
\(301\) | 4.78903 | + | 2.76495i | 0.276035 | + | 0.159369i | ||||
\(302\) | 11.5657 | 0.665530 | ||||||||
\(303\) | 8.87344 | + | 5.12308i | 0.509766 | + | 0.294313i | ||||
\(304\) | − | 5.64574i | − | 0.323806i | ||||||
\(305\) | −6.65068 | + | 28.7786i | −0.380817 | + | 1.64786i | ||||
\(306\) | 3.34526 | 0.191236 | ||||||||
\(307\) | − | 18.4064i | − | 1.05051i | −0.850945 | − | 0.525254i | \(-0.823970\pi\) | ||
0.850945 | − | 0.525254i | \(-0.176030\pi\) | |||||||
\(308\) | −14.2159 | + | 8.20755i | −0.810026 | + | 0.467669i | ||||
\(309\) | 5.14683 | + | 2.97152i | 0.292793 | + | 0.169044i | ||||
\(310\) | 5.85960 | + | 5.46656i | 0.332803 | + | 0.310480i | ||||
\(311\) | 16.0430 | − | 9.26245i | 0.909717 | − | 0.525225i | 0.0293771 | − | 0.999568i | \(-0.490648\pi\) |
0.880340 | + | 0.474343i | \(0.157314\pi\) | |||||||
\(312\) | 5.36341 | − | 3.09657i | 0.303643 | − | 0.175309i | ||||
\(313\) | 10.9094 | + | 18.8956i | 0.616634 | + | 1.06804i | 0.990095 | + | 0.140396i | \(0.0448376\pi\) |
−0.373461 | + | 0.927646i | \(0.621829\pi\) | |||||||
\(314\) | 17.0546 | + | 9.84650i | 0.962449 | + | 0.555670i | ||||
\(315\) | −7.90200 | + | 2.41400i | −0.445227 | + | 0.136013i | ||||
\(316\) | 4.87431 | − | 2.81418i | 0.274201 | − | 0.158310i | ||||
\(317\) | 24.1836 | − | 13.9624i | 1.35829 | − | 0.784207i | 0.368894 | − | 0.929472i | \(-0.379737\pi\) |
0.989393 | + | 0.145264i | \(0.0464033\pi\) | |||||||
\(318\) | 4.44757 | + | 7.70341i | 0.249407 | + | 0.431986i | ||||
\(319\) | − | 0.481214i | − | 0.0269428i | ||||||
\(320\) | 0.653296 | + | 2.13851i | 0.0365204 | + | 0.119546i | ||||
\(321\) | 5.25423 | + | 9.10060i | 0.293263 | + | 0.507946i | ||||
\(322\) | − | 12.2601i | − | 0.683229i | ||||||
\(323\) | − | 18.8865i | − | 1.05087i | ||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.14656 | + | 30.8912i | 0.119070 | + | 1.71353i | ||||
\(326\) | 8.25810 | − | 14.3034i | 0.457374 | − | 0.792195i | ||||
\(327\) | 1.47766 | 0.0817150 | ||||||||
\(328\) | −0.667426 | + | 1.15602i | −0.0368524 | + | 0.0638303i | ||||
\(329\) | −2.26812 | + | 3.92849i | −0.125045 | + | 0.216585i | ||||
\(330\) | 9.50008 | − | 2.90220i | 0.522962 | − | 0.159761i | ||||
\(331\) | 28.7591 | − | 16.6041i | 1.58074 | − | 0.912642i | 0.585991 | − | 0.810318i | \(-0.300706\pi\) |
0.994751 | − | 0.102324i | \(-0.0326278\pi\) | |||||||
\(332\) | 6.00873i | 0.329772i | ||||||||
\(333\) | −4.26515 | + | 4.33687i | −0.233729 | + | 0.237659i | ||||
\(334\) | −11.2059 | −0.613157 | ||||||||
\(335\) | 7.42613 | − | 32.1341i | 0.405733 | − | 1.75567i | ||||
\(336\) | −1.84755 | + | 3.20005i | −0.100792 | + | 0.174577i | ||||
\(337\) | −5.47768 | − | 3.16254i | −0.298388 | − | 0.172275i | 0.343330 | − | 0.939215i | \(-0.388445\pi\) |
−0.641719 | + | 0.766940i | \(0.721778\pi\) | |||||||
\(338\) | 12.6775 | − | 21.9580i | 0.689563 | − | 1.19436i | ||||
\(339\) | − | 6.38543i | − | 0.346809i | ||||||
\(340\) | 2.18545 | + | 7.15387i | 0.118523 | + | 0.387973i | ||||
\(341\) | − | 15.9207i | − | 0.862152i | ||||||
\(342\) | −4.88936 | + | 2.82287i | −0.264386 | + | 0.152643i | ||||
\(343\) | − | 1.27925i | − | 0.0690733i | ||||||
\(344\) | −1.49655 | −0.0806884 | ||||||||
\(345\) | −1.67052 | + | 7.22861i | −0.0899377 | + | 0.389175i | ||||
\(346\) | −12.4041 | − | 7.16151i | −0.666849 | − | 0.385005i | ||||
\(347\) | −26.7305 | −1.43497 | −0.717483 | − | 0.696576i | \(-0.754706\pi\) | ||||
−0.717483 | + | 0.696576i | \(0.754706\pi\) | |||||||
\(348\) | −0.0541616 | − | 0.0938106i | −0.00290336 | − | 0.00502877i | ||||
\(349\) | −9.72032 | − | 16.8361i | −0.520317 | − | 0.901215i | −0.999721 | − | 0.0236209i | \(-0.992481\pi\) |
0.479404 | − | 0.877594i | \(-0.340853\pi\) | |||||||
\(350\) | −10.3247 | − | 15.3214i | −0.551878 | − | 0.818964i | ||||
\(351\) | −5.36341 | − | 3.09657i | −0.286278 | − | 0.165283i | ||||
\(352\) | 2.22120 | − | 3.84723i | 0.118390 | − | 0.205058i | ||||
\(353\) | −2.02075 | − | 3.50004i | −0.107554 | − | 0.186288i | 0.807225 | − | 0.590244i | \(-0.200968\pi\) |
−0.914779 | + | 0.403955i | \(0.867635\pi\) | |||||||
\(354\) | 0.169019 | + | 0.292750i | 0.00898326 | + | 0.0155595i | ||||
\(355\) | 11.5983 | + | 2.68035i | 0.615575 | + | 0.142258i | ||||
\(356\) | − | 16.0613i | − | 0.851248i | ||||||
\(357\) | −6.18055 | + | 10.7050i | −0.327109 | + | 0.566570i | ||||
\(358\) | −5.33654 | + | 3.08106i | −0.282045 | + | 0.162839i | ||||
\(359\) | −0.449208 | −0.0237083 | −0.0118542 | − | 0.999930i | \(-0.503773\pi\) | ||||
−0.0118542 | + | 0.999930i | \(0.503773\pi\) | |||||||
\(360\) | 1.52535 | − | 1.63502i | 0.0803931 | − | 0.0861733i | ||||
\(361\) | 6.43721 | + | 11.1496i | 0.338801 | + | 0.586820i | ||||
\(362\) | −3.66478 | −0.192617 | ||||||||
\(363\) | −7.56461 | − | 4.36743i | −0.397039 | − | 0.229231i | ||||
\(364\) | 22.8843i | 1.19946i | ||||||||
\(365\) | −5.71654 | + | 1.74636i | −0.299217 | + | 0.0914085i | ||||
\(366\) | 6.60469 | − | 11.4397i | 0.345233 | − | 0.597961i | ||||
\(367\) | 28.8599 | + | 16.6623i | 1.50647 | + | 0.869763i | 0.999972 | + | 0.00752386i | \(0.00239494\pi\) |
0.506502 | + | 0.862239i | \(0.330938\pi\) | |||||||
\(368\) | 1.65897 | + | 2.87341i | 0.0864796 | + | 0.149787i | ||||
\(369\) | 1.33485 | 0.0694896 | ||||||||
\(370\) | −12.0608 | − | 6.28779i | −0.627013 | − | 0.326887i | ||||
\(371\) | −32.8684 | −1.70644 | ||||||||
\(372\) | −1.79190 | − | 3.10366i | −0.0929057 | − | 0.160917i | ||||
\(373\) | 0.921169 | + | 0.531837i | 0.0476963 | + | 0.0275375i | 0.523659 | − | 0.851928i | \(-0.324567\pi\) |
−0.475962 | + | 0.879466i | \(0.657900\pi\) | |||||||
\(374\) | 7.43049 | − | 12.8700i | 0.384222 | − | 0.665491i | ||||
\(375\) | 3.99984 | + | 10.4404i | 0.206551 | + | 0.539138i | ||||
\(376\) | − | 1.22763i | − | 0.0633103i | ||||||
\(377\) | −0.580982 | − | 0.335430i | −0.0299221 | − | 0.0172755i | ||||
\(378\) | 3.69510 | 0.190056 | ||||||||
\(379\) | −11.9117 | − | 20.6317i | −0.611863 | − | 1.05978i | −0.990926 | − | 0.134407i | \(-0.957087\pi\) |
0.379063 | − | 0.925371i | \(-0.376246\pi\) | |||||||
\(380\) | −9.23092 | − | 8.61175i | −0.473536 | − | 0.441773i | ||||
\(381\) | 17.6056 | 0.901962 | ||||||||
\(382\) | 14.7975 | − | 8.54336i | 0.757107 | − | 0.437116i | ||||
\(383\) | 12.3247 | − | 21.3470i | 0.629762 | − | 1.09078i | −0.357838 | − | 0.933784i | \(-0.616486\pi\) |
0.987599 | − | 0.156995i | \(-0.0501807\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −8.26471 | + | 35.7627i | −0.421208 | + | 1.82264i | ||||
\(386\) | 12.0933 | + | 20.9462i | 0.615533 | + | 1.06613i | ||||
\(387\) | 0.748273 | + | 1.29605i | 0.0380369 | + | 0.0658818i | ||||
\(388\) | −6.40580 | + | 11.0952i | −0.325205 | + | 0.563272i | ||||
\(389\) | 3.99858 | + | 2.30858i | 0.202736 | + | 0.117050i | 0.597931 | − | 0.801548i | \(-0.295990\pi\) |
−0.395195 | + | 0.918597i | \(0.629323\pi\) | |||||||
\(390\) | 3.11813 | − | 13.4927i | 0.157893 | − | 0.683228i | ||||
\(391\) | 5.54968 | + | 9.61233i | 0.280659 | + | 0.486116i | ||||
\(392\) | −3.32690 | − | 5.76236i | −0.168034 | − | 0.291043i | ||||
\(393\) | 21.5410 | 1.08660 | ||||||||
\(394\) | 8.50118 | + | 4.90816i | 0.428283 | + | 0.247269i | ||||
\(395\) | 2.83378 | − | 12.2622i | 0.142583 | − | 0.616980i | ||||
\(396\) | −4.44239 | −0.223239 | ||||||||
\(397\) | 11.6194i | 0.583162i | 0.956546 | + | 0.291581i | \(0.0941813\pi\) | ||||
−0.956546 | + | 0.291581i | \(0.905819\pi\) | |||||||
\(398\) | 19.0743 | − | 11.0125i | 0.956108 | − | 0.552009i | ||||
\(399\) | − | 20.8616i | − | 1.04439i | ||||||
\(400\) | 4.49301 | + | 2.19382i | 0.224651 | + | 0.109691i | ||||
\(401\) | 6.31885i | 0.315548i | 0.987475 | + | 0.157774i | \(0.0504318\pi\) | ||||
−0.987475 | + | 0.157774i | \(0.949568\pi\) | |||||||
\(402\) | −7.37478 | + | 12.7735i | −0.367820 | + | 0.637084i | ||||
\(403\) | −19.2214 | − | 11.0975i | −0.957487 | − | 0.552805i | ||||
\(404\) | 5.12308 | − | 8.87344i | 0.254883 | − | 0.441470i | ||||
\(405\) | −2.17865 | − | 0.503482i | −0.108258 | − | 0.0250182i | ||||
\(406\) | 0.400265 | 0.0198648 | ||||||||
\(407\) | 7.21118 | + | 26.0421i | 0.357445 | + | 1.29086i | ||||
\(408\) | − | 3.34526i | − | 0.165615i | ||||||
\(409\) | −12.2422 | + | 7.06806i | −0.605340 | + | 0.349493i | −0.771139 | − | 0.636666i | \(-0.780313\pi\) |
0.165799 | + | 0.986159i | \(0.446980\pi\) | |||||||
\(410\) | 0.872053 | + | 2.85459i | 0.0430676 | + | 0.140978i | ||||
\(411\) | −5.07014 | + | 8.78174i | −0.250092 | + | 0.433171i | ||||
\(412\) | 2.97152 | − | 5.14683i | 0.146396 | − | 0.253566i | ||||
\(413\) | −1.24909 | −0.0614635 | ||||||||
\(414\) | 1.65897 | − | 2.87341i | 0.0815337 | − | 0.141221i | ||||
\(415\) | 9.82442 | + | 9.16543i | 0.482262 | + | 0.449913i | ||||
\(416\) | −3.09657 | − | 5.36341i | −0.151822 | − | 0.262963i | ||||
\(417\) | 6.47856i | 0.317257i | ||||||||
\(418\) | 25.0806i | 1.22673i | ||||||||
\(419\) | −19.8015 | − | 34.2972i | −0.967366 | − | 1.67553i | −0.703119 | − | 0.711073i | \(-0.748210\pi\) |
−0.264248 | − | 0.964455i | \(-0.585124\pi\) | |||||||
\(420\) | 2.41400 | + | 7.90200i | 0.117791 | + | 0.385578i | ||||
\(421\) | − | 7.95090i | − | 0.387503i | −0.981051 | − | 0.193752i | \(-0.937934\pi\) | ||
0.981051 | − | 0.193752i | \(-0.0620656\pi\) | |||||||
\(422\) | −3.58728 | − | 6.21336i | −0.174626 | − | 0.302462i | ||||
\(423\) | −1.06316 | + | 0.613817i | −0.0516927 | + | 0.0298448i | ||||
\(424\) | 7.70341 | − | 4.44757i | 0.374111 | − | 0.215993i | ||||
\(425\) | 15.0303 | + | 7.33890i | 0.729077 | + | 0.355989i | ||||
\(426\) | −4.61040 | − | 2.66182i | −0.223375 | − | 0.128965i | ||||
\(427\) | 24.4050 | + | 42.2708i | 1.18104 | + | 2.04563i | ||||
\(428\) | 9.10060 | − | 5.25423i | 0.439894 | − | 0.253973i | ||||
\(429\) | −23.8264 | + | 13.7562i | −1.15035 | + | 0.664154i | ||||
\(430\) | −2.28276 | + | 2.44689i | −0.110084 | + | 0.117999i | ||||
\(431\) | 9.99522 | + | 5.77074i | 0.481453 | + | 0.277967i | 0.721022 | − | 0.692912i | \(-0.243673\pi\) |
−0.239569 | + | 0.970879i | \(0.577006\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 14.0193i | 0.673725i | 0.941554 | + | 0.336862i | \(0.109366\pi\) | ||||
−0.941554 | + | 0.336862i | \(0.890634\pi\) | |||||||
\(434\) | 13.2425 | 0.635661 | ||||||||
\(435\) | −0.235998 | − | 0.0545387i | −0.0113152 | − | 0.00261493i | ||||
\(436\) | − | 1.47766i | − | 0.0707673i | ||||||
\(437\) | −16.2226 | − | 9.36610i | −0.776030 | − | 0.448041i | ||||
\(438\) | 2.67315 | 0.127728 | ||||||||
\(439\) | −20.7334 | − | 11.9704i | −0.989551 | − | 0.571317i | −0.0844108 | − | 0.996431i | \(-0.526901\pi\) |
−0.905140 | + | 0.425114i | \(0.860234\pi\) | |||||||
\(440\) | −2.90220 | − | 9.50008i | −0.138357 | − | 0.452899i | ||||
\(441\) | −3.32690 | + | 5.76236i | −0.158424 | + | 0.274398i | ||||
\(442\) | −10.3588 | − | 17.9420i | −0.492720 | − | 0.853416i | ||||
\(443\) | 26.2329i | 1.24636i | 0.782077 | + | 0.623182i | \(0.214160\pi\) | ||||
−0.782077 | + | 0.623182i | \(0.785840\pi\) | |||||||
\(444\) | 4.33687 | + | 4.26515i | 0.205819 | + | 0.202415i | ||||
\(445\) | −26.2606 | − | 24.4992i | −1.24487 | − | 1.16137i | ||||
\(446\) | −0.190389 | + | 0.109921i | −0.00901519 | + | 0.00520492i | ||||
\(447\) | −1.55842 | − | 0.899754i | −0.0737107 | − | 0.0425569i | ||||
\(448\) | 3.20005 | + | 1.84755i | 0.151188 | + | 0.0872886i | ||||
\(449\) | 16.5697 | + | 9.56655i | 0.781974 | + | 0.451473i | 0.837130 | − | 0.547005i | \(-0.184232\pi\) |
−0.0551551 | + | 0.998478i | \(0.517565\pi\) | |||||||
\(450\) | −0.346604 | − | 4.98797i | −0.0163391 | − | 0.235135i | ||||
\(451\) | 2.96497 | − | 5.13547i | 0.139615 | − | 0.241820i | ||||
\(452\) | −6.38543 | −0.300345 | ||||||||
\(453\) | −10.0162 | + | 5.78284i | −0.470601 | + | 0.271701i | ||||
\(454\) | 24.7913 | 1.16351 | ||||||||
\(455\) | 37.4163 | + | 34.9066i | 1.75411 | + | 1.63645i | ||||
\(456\) | 2.82287 | + | 4.88936i | 0.132193 | + | 0.228965i | ||||
\(457\) | −20.5198 | + | 35.5413i | −0.959875 | + | 1.66255i | −0.237081 | + | 0.971490i | \(0.576191\pi\) |
−0.722794 | + | 0.691063i | \(0.757143\pi\) | |||||||
\(458\) | −11.3060 | −0.528295 | ||||||||
\(459\) | −2.89708 | + | 1.67263i | −0.135224 | + | 0.0780718i | ||||
\(460\) | 7.22861 | + | 1.67052i | 0.337036 | + | 0.0778883i | ||||
\(461\) | −9.56724 | + | 5.52365i | −0.445591 | + | 0.257262i | −0.705966 | − | 0.708245i | \(-0.749487\pi\) |
0.260375 | + | 0.965507i | \(0.416154\pi\) | |||||||
\(462\) | 8.20755 | − | 14.2159i | 0.381850 | − | 0.661384i | ||||
\(463\) | −4.02668 | + | 6.97442i | −0.187136 | + | 0.324129i | −0.944294 | − | 0.329103i | \(-0.893254\pi\) |
0.757158 | + | 0.653231i | \(0.226587\pi\) | |||||||
\(464\) | −0.0938106 | + | 0.0541616i | −0.00435505 | + | 0.00251439i | ||||
\(465\) | −7.80784 | − | 1.80438i | −0.362080 | − | 0.0836761i | ||||
\(466\) | −12.3909 | + | 7.15391i | −0.573999 | + | 0.331399i | ||||
\(467\) | −9.63792 | −0.445990 | −0.222995 | − | 0.974820i | \(-0.571583\pi\) | ||||
−0.222995 | + | 0.974820i | \(0.571583\pi\) | |||||||
\(468\) | −3.09657 | + | 5.36341i | −0.143139 | + | 0.247924i | ||||
\(469\) | −27.2506 | − | 47.1994i | −1.25831 | − | 2.17946i | ||||
\(470\) | −2.00721 | − | 1.87257i | −0.0925856 | − | 0.0863753i | ||||
\(471\) | −19.6930 | −0.907406 | ||||||||
\(472\) | 0.292750 | − | 0.169019i | 0.0134749 | − | 0.00777973i | ||||
\(473\) | 6.64825 | 0.305687 | ||||||||
\(474\) | −2.81418 | + | 4.87431i | −0.129260 | + | 0.223884i | ||||
\(475\) | −28.1608 | + | 1.95684i | −1.29211 | + | 0.0897858i | ||||
\(476\) | 10.7050 | + | 6.18055i | 0.490664 | + | 0.283285i | ||||
\(477\) | −7.70341 | − | 4.44757i | −0.352715 | − | 0.203640i | ||||
\(478\) | 5.88745 | + | 3.39912i | 0.269286 | + | 0.155472i | ||||
\(479\) | −27.4842 | + | 15.8680i | −1.25578 | + | 0.725027i | −0.972252 | − | 0.233936i | \(-0.924840\pi\) |
−0.283532 | + | 0.958963i | \(0.591506\pi\) | |||||||
\(480\) | −1.63502 | − | 1.52535i | −0.0746283 | − | 0.0696225i | ||||
\(481\) | 36.4678 | + | 9.44636i | 1.66279 | + | 0.430717i | ||||
\(482\) | − | 5.54039i | − | 0.252358i | ||||||
\(483\) | 6.13005 | + | 10.6176i | 0.278927 | + | 0.483116i | ||||
\(484\) | −4.36743 | + | 7.56461i | −0.198520 | + | 0.343846i | ||||
\(485\) | 8.36977 | + | 27.3977i | 0.380052 | + | 1.24406i | ||||
\(486\) | 0.866025 | + | 0.500000i | 0.0392837 | + | 0.0226805i | ||||
\(487\) | −4.48336 | −0.203161 | −0.101580 | − | 0.994827i | \(-0.532390\pi\) | ||||
−0.101580 | + | 0.994827i | \(0.532390\pi\) | |||||||
\(488\) | −11.4397 | − | 6.60469i | −0.517849 | − | 0.298980i | ||||
\(489\) | 16.5162i | 0.746888i | ||||||||
\(490\) | −14.4963 | − | 3.35006i | −0.654875 | − | 0.151341i | ||||
\(491\) | −8.90853 | −0.402037 | −0.201018 | − | 0.979587i | \(-0.564425\pi\) | ||||
−0.201018 | + | 0.979587i | \(0.564425\pi\) | |||||||
\(492\) | − | 1.33485i | − | 0.0601797i | ||||||
\(493\) | −0.313821 | + | 0.181185i | −0.0141338 | + | 0.00816015i | ||||
\(494\) | 30.2805 | + | 17.4824i | 1.36238 | + | 0.786572i | ||||
\(495\) | −6.77621 | + | 7.26342i | −0.304568 | + | 0.326466i | ||||
\(496\) | −3.10366 | + | 1.79190i | −0.139359 | + | 0.0804587i | ||||
\(497\) | 17.0359 | − | 9.83569i | 0.764165 | − | 0.441191i | ||||
\(498\) | −3.00437 | − | 5.20372i | −0.134629 | − | 0.233184i | ||||
\(499\) | 31.6688 | + | 18.2840i | 1.41769 | + | 0.818503i | 0.996096 | − | 0.0882814i | \(-0.0281375\pi\) |
0.421594 | + | 0.906785i | \(0.361471\pi\) | |||||||
\(500\) | 10.4404 | − | 3.99984i | 0.466908 | − | 0.178878i | ||||
\(501\) | 9.70456 | − | 5.60293i | 0.433568 | − | 0.250320i | ||||
\(502\) | −26.0512 | + | 15.0407i | −1.16272 | + | 0.671298i | ||||
\(503\) | −4.13426 | − | 7.16075i | −0.184338 | − | 0.319282i | 0.759016 | − | 0.651073i | \(-0.225681\pi\) |
−0.943353 | + | 0.331790i | \(0.892347\pi\) | |||||||
\(504\) | − | 3.69510i | − | 0.164593i | ||||||
\(505\) | −6.69378 | − | 21.9115i | −0.297869 | − | 0.975048i | ||||
\(506\) | −7.36978 | − | 12.7648i | −0.327627 | − | 0.567466i | ||||
\(507\) | 25.3549i | 1.12605i | ||||||||
\(508\) | − | 17.6056i | − | 0.781122i | ||||||
\(509\) | −18.6383 | − | 32.2825i | −0.826129 | − | 1.43090i | −0.901053 | − | 0.433709i | \(-0.857205\pi\) |
0.0749237 | − | 0.997189i | \(-0.476129\pi\) | |||||||
\(510\) | −5.46959 | − | 5.10271i | −0.242197 | − | 0.225952i | ||||
\(511\) | −4.93878 | + | 8.55421i | −0.218479 | + | 0.378416i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.82287 | − | 4.88936i | 0.124633 | − | 0.215870i | ||||
\(514\) | −11.7565 | + | 20.3629i | −0.518557 | + | 0.898167i | ||||
\(515\) | −3.88257 | − | 12.7092i | −0.171086 | − | 0.560036i | ||||
\(516\) | 1.29605 | − | 0.748273i | 0.0570553 | − | 0.0329409i | ||||
\(517\) | 5.45363i | 0.239850i | ||||||||
\(518\) | −21.6613 | + | 5.99813i | −0.951744 | + | 0.263543i | ||||
\(519\) | 14.3230 | 0.628711 | ||||||||
\(520\) | −13.4927 | − | 3.11813i | −0.591692 | − | 0.136739i | ||||
\(521\) | −2.11581 | + | 3.66469i | −0.0926953 | + | 0.160553i | −0.908644 | − | 0.417571i | \(-0.862882\pi\) |
0.815949 | + | 0.578124i | \(0.196215\pi\) | |||||||
\(522\) | 0.0938106 | + | 0.0541616i | 0.00410598 | + | 0.00237059i | ||||
\(523\) | 6.66483 | − | 11.5438i | 0.291433 | − | 0.504776i | −0.682716 | − | 0.730684i | \(-0.739201\pi\) |
0.974149 | + | 0.225908i | \(0.0725348\pi\) | |||||||
\(524\) | − | 21.5410i | − | 0.941025i | ||||||
\(525\) | 16.6022 | + | 8.10639i | 0.724577 | + | 0.353792i | ||||
\(526\) | 27.5809i | 1.20259i | ||||||||
\(527\) | −10.3826 | + | 5.99438i | −0.452272 | + | 0.261119i | ||||
\(528\) | 4.44239i | 0.193330i | ||||||||
\(529\) | −11.9913 | −0.521362 | ||||||||
\(530\) | 4.47854 | − | 19.3794i | 0.194535 | − | 0.841786i | ||||
\(531\) | −0.292750 | − | 0.169019i | −0.0127043 | − | 0.00733480i | ||||
\(532\) | −20.8616 | −0.904466 | ||||||||
\(533\) | −4.13346 | − | 7.15936i | −0.179040 | − | 0.310106i | ||||
\(534\) | 8.03066 | + | 13.9095i | 0.347521 | + | 0.601923i | ||||
\(535\) | 5.29082 | − | 22.8942i | 0.228742 | − | 0.989804i | ||||
\(536\) | 12.7735 | + | 7.37478i | 0.551731 | + | 0.318542i | ||||
\(537\) | 3.08106 | − | 5.33654i | 0.132957 | − | 0.230289i | ||||
\(538\) | −6.79314 | − | 11.7661i | −0.292873 | − | 0.507271i | ||||
\(539\) | 14.7794 | + | 25.5987i | 0.636594 | + | 1.10261i | ||||
\(540\) | −0.503482 | + | 2.17865i | −0.0216664 | + | 0.0937541i | ||||
\(541\) | 8.60984i | 0.370166i | 0.982723 | + | 0.185083i | \(0.0592554\pi\) | ||||
−0.982723 | + | 0.185083i | \(0.940745\pi\) | |||||||
\(542\) | −4.97694 | + | 8.62031i | −0.213778 | + | 0.370274i | ||||
\(543\) | 3.17379 | − | 1.83239i | 0.136200 | − | 0.0786354i | ||||
\(544\) | −3.34526 | −0.143427 | ||||||||
\(545\) | −2.41602 | − | 2.25396i | −0.103491 | − | 0.0965489i | ||||
\(546\) | −11.4421 | − | 19.8184i | −0.489678 | − | 0.848148i | ||||
\(547\) | −16.9211 | −0.723496 | −0.361748 | − | 0.932276i | \(-0.617820\pi\) | ||||
−0.361748 | + | 0.932276i | \(0.617820\pi\) | |||||||
\(548\) | 8.78174 | + | 5.07014i | 0.375138 | + | 0.216586i | ||||
\(549\) | 13.2094i | 0.563763i | ||||||||
\(550\) | −19.9597 | − | 9.74580i | −0.851086 | − | 0.415563i | ||||
\(551\) | 0.305782 | − | 0.529631i | 0.0130268 | − | 0.0225630i | ||||
\(552\) | −2.87341 | − | 1.65897i | −0.122301 | − | 0.0706103i | ||||
\(553\) | −10.3987 | − | 18.0111i | −0.442198 | − | 0.765909i | ||||
\(554\) | 26.6934 | 1.13409 | ||||||||
\(555\) | 13.5889 | − | 0.585029i | 0.576816 | − | 0.0248331i | ||||
\(556\) | 6.47856 | 0.274752 | ||||||||
\(557\) | −17.5570 | − | 30.4096i | −0.743914 | − | 1.28850i | −0.950701 | − | 0.310110i | \(-0.899634\pi\) |
0.206787 | − | 0.978386i | \(-0.433699\pi\) | |||||||
\(558\) | 3.10366 | + | 1.79190i | 0.131389 | + | 0.0758572i | ||||
\(559\) | 4.63416 | − | 8.02659i | 0.196004 | − | 0.339489i | ||||
\(560\) | 7.90200 | − | 2.41400i | 0.333920 | − | 0.102010i | ||||
\(561\) | 14.8610i | 0.627431i | ||||||||
\(562\) | −0.674004 | − | 0.389137i | −0.0284312 | − | 0.0164147i | ||||
\(563\) | 13.6442 | 0.575035 | 0.287518 | − | 0.957775i | \(-0.407170\pi\) | ||||
0.287518 | + | 0.957775i | \(0.407170\pi\) | |||||||
\(564\) | 0.613817 | + | 1.06316i | 0.0258463 | + | 0.0447672i | ||||
\(565\) | −9.74003 | + | 10.4403i | −0.409766 | + | 0.439228i | ||||
\(566\) | −11.6246 | −0.488619 | ||||||||
\(567\) | −3.20005 | + | 1.84755i | −0.134390 | + | 0.0775899i | ||||
\(568\) | −2.66182 | + | 4.61040i | −0.111687 | + | 0.193448i | ||||
\(569\) | − | 32.8741i | − | 1.37815i | −0.724689 | − | 0.689076i | \(-0.758016\pi\) | ||
0.724689 | − | 0.689076i | \(-0.241984\pi\) | |||||||
\(570\) | 12.3001 | + | 2.84253i | 0.515194 | + | 0.119060i | ||||
\(571\) | 15.5801 | + | 26.9856i | 0.652008 | + | 1.12931i | 0.982635 | + | 0.185550i | \(0.0594066\pi\) |
−0.330627 | + | 0.943762i | \(0.607260\pi\) | |||||||
\(572\) | 13.7562 | + | 23.8264i | 0.575175 | + | 0.996232i | ||||
\(573\) | −8.54336 | + | 14.7975i | −0.356904 | + | 0.618176i | ||||
\(574\) | 4.27160 | + | 2.46621i | 0.178293 | + | 0.102938i | ||||
\(575\) | 13.7575 | − | 9.27081i | 0.573728 | − | 0.386620i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 5.44050 | + | 9.42322i | 0.226491 | + | 0.392294i | 0.956766 | − | 0.290860i | \(-0.0939413\pi\) |
−0.730275 | + | 0.683154i | \(0.760608\pi\) | |||||||
\(578\) | 5.80920 | 0.241631 | ||||||||
\(579\) | −20.9462 | − | 12.0933i | −0.870495 | − | 0.502581i | ||||
\(580\) | −0.0545387 | + | 0.235998i | −0.00226460 | + | 0.00979928i | ||||
\(581\) | 22.2029 | 0.921131 | ||||||||
\(582\) | − | 12.8116i | − | 0.531058i | ||||||
\(583\) | −34.2216 | + | 19.7578i | −1.41731 | + | 0.818286i | ||||
\(584\) | − | 2.67315i | − | 0.110616i | ||||||
\(585\) | 4.04595 | + | 13.2441i | 0.167279 | + | 0.547574i | ||||
\(586\) | − | 10.4031i | − | 0.429748i | ||||||
\(587\) | −12.4630 | + | 21.5865i | −0.514403 | + | 0.890971i | 0.485458 | + | 0.874260i | \(0.338653\pi\) |
−0.999860 | + | 0.0167112i | \(0.994680\pi\) | |||||||
\(588\) | 5.76236 | + | 3.32690i | 0.237636 | + | 0.137199i | ||||
\(589\) | 10.1166 | − | 17.5225i | 0.416848 | − | 0.722002i | ||||
\(590\) | 0.170196 | − | 0.736466i | 0.00700686 | − | 0.0303198i | ||||
\(591\) | −9.81631 | −0.403789 | ||||||||
\(592\) | 4.26515 | − | 4.33687i | 0.175297 | − | 0.178244i | ||||
\(593\) | 14.2693i | 0.585969i | 0.956117 | + | 0.292984i | \(0.0946484\pi\) | ||||
−0.956117 | + | 0.292984i | \(0.905352\pi\) | |||||||
\(594\) | 3.84723 | − | 2.22120i | 0.157854 | − | 0.0911368i | ||||
\(595\) | 26.4343 | − | 8.07546i | 1.08370 | − | 0.331062i | ||||
\(596\) | −0.899754 | + | 1.55842i | −0.0368554 | + | 0.0638354i | ||||
\(597\) | −11.0125 | + | 19.0743i | −0.450714 | + | 0.780659i | ||||
\(598\) | −20.5484 | −0.840287 | ||||||||
\(599\) | 10.1315 | − | 17.5483i | 0.413962 | − | 0.717003i | −0.581357 | − | 0.813648i | \(-0.697478\pi\) |
0.995319 | + | 0.0966459i | \(0.0308114\pi\) | |||||||
\(600\) | −4.98797 | + | 0.346604i | −0.203633 | + | 0.0141500i | ||||
\(601\) | −6.63186 | − | 11.4867i | −0.270519 | − | 0.468553i | 0.698476 | − | 0.715634i | \(-0.253862\pi\) |
−0.968995 | + | 0.247081i | \(0.920529\pi\) | |||||||
\(602\) | 5.52989i | 0.225382i | ||||||||
\(603\) | − | 14.7496i | − | 0.600648i | ||||||
\(604\) | 5.78284 | + | 10.0162i | 0.235300 | + | 0.407552i | ||||
\(605\) | 5.70645 | + | 18.6795i | 0.232000 | + | 0.759432i | ||||
\(606\) | 10.2462i | 0.416222i | ||||||||
\(607\) | 1.63728 | + | 2.83585i | 0.0664552 | + | 0.115104i | 0.897339 | − | 0.441343i | \(-0.145498\pi\) |
−0.830883 | + | 0.556447i | \(0.812164\pi\) | |||||||
\(608\) | 4.88936 | − | 2.82287i | 0.198290 | − | 0.114483i | ||||
\(609\) | −0.346640 | + | 0.200133i | −0.0140466 | + | 0.00810978i | ||||
\(610\) | −28.2483 | + | 8.62964i | −1.14374 | + | 0.349404i | ||||
\(611\) | 6.58430 | + | 3.80145i | 0.266372 | + | 0.153790i | ||||
\(612\) | 1.67263 | + | 2.89708i | 0.0676122 | + | 0.117108i | ||||
\(613\) | −26.8039 | + | 15.4752i | −1.08260 | + | 0.625039i | −0.931597 | − | 0.363494i | \(-0.881584\pi\) |
−0.151003 | + | 0.988533i | \(0.548250\pi\) | |||||||
\(614\) | 15.9404 | − | 9.20320i | 0.643302 | − | 0.371411i | ||||
\(615\) | −2.18251 | − | 2.03612i | −0.0880074 | − | 0.0821042i | ||||
\(616\) | −14.2159 | − | 8.20755i | −0.572775 | − | 0.330692i | ||||
\(617\) | 0.416548 | − | 0.240494i | 0.0167696 | − | 0.00968194i | −0.491592 | − | 0.870826i | \(-0.663585\pi\) |
0.508361 | + | 0.861144i | \(0.330251\pi\) | |||||||
\(618\) | 5.94305i | 0.239064i | ||||||||
\(619\) | −0.362624 | −0.0145751 | −0.00728754 | − | 0.999973i | \(-0.502320\pi\) | ||||
−0.00728754 | + | 0.999973i | \(0.502320\pi\) | |||||||
\(620\) | −1.80438 | + | 7.80784i | −0.0724656 | + | 0.313571i | ||||
\(621\) | 3.31793i | 0.133144i | ||||||||
\(622\) | 16.0430 | + | 9.26245i | 0.643267 | + | 0.371391i | ||||
\(623\) | −59.3482 | −2.37774 | ||||||||
\(624\) | 5.36341 | + | 3.09657i | 0.214708 | + | 0.123962i | ||||
\(625\) | 9.38541 | − | 23.1714i | 0.375416 | − | 0.926856i | ||||
\(626\) | −10.9094 | + | 18.8956i | −0.436026 | + | 0.755220i | ||||
\(627\) | −12.5403 | − | 21.7205i | −0.500812 | − | 0.867431i | ||||
\(628\) | 19.6930i | 0.785836i | ||||||||
\(629\) | 14.2681 | − | 14.5080i | 0.568905 | − | 0.578471i | ||||
\(630\) | −6.04158 | − | 5.63633i | −0.240702 | − | 0.224557i | ||||
\(631\) | −16.6855 | + | 9.63338i | −0.664239 | + | 0.383499i | −0.793890 | − | 0.608061i | \(-0.791948\pi\) |
0.129651 | + | 0.991560i | \(0.458614\pi\) | |||||||
\(632\) | 4.87431 | + | 2.81418i | 0.193890 | + | 0.111942i | ||||
\(633\) | 6.21336 | + | 3.58728i | 0.246959 | + | 0.142582i | ||||
\(634\) | 24.1836 | + | 13.9624i | 0.960454 | + | 0.554518i | ||||
\(635\) | −28.7856 | − | 26.8547i | −1.14232 | − | 1.06570i | ||||
\(636\) | −4.44757 | + | 7.70341i | −0.176357 | + | 0.305460i | ||||
\(637\) | 41.2079 | 1.63272 | ||||||||
\(638\) | 0.416744 | − | 0.240607i | 0.0164990 | − | 0.00952572i | ||||
\(639\) | 5.32363 | 0.210600 | ||||||||
\(640\) | −1.52535 | + | 1.63502i | −0.0602948 | + | 0.0646300i | ||||
\(641\) | −6.93767 | − | 12.0164i | −0.274021 | − | 0.474619i | 0.695866 | − | 0.718171i | \(-0.255021\pi\) |
−0.969888 | + | 0.243552i | \(0.921687\pi\) | |||||||
\(642\) | −5.25423 | + | 9.10060i | −0.207368 | + | 0.359172i | ||||
\(643\) | −32.7410 | −1.29118 | −0.645589 | − | 0.763685i | \(-0.723388\pi\) | ||||
−0.645589 | + | 0.763685i | \(0.723388\pi\) | |||||||
\(644\) | 10.6176 | − | 6.13005i | 0.418391 | − | 0.241558i | ||||
\(645\) | 0.753483 | − | 3.26045i | 0.0296684 | − | 0.128380i | ||||
\(646\) | 16.3562 | − | 9.44325i | 0.643526 | − | 0.371540i | ||||
\(647\) | 10.0075 | − | 17.3335i | 0.393435 | − | 0.681449i | −0.599465 | − | 0.800401i | \(-0.704620\pi\) |
0.992900 | + | 0.118952i | \(0.0379533\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | −1.30051 | + | 0.750849i | −0.0510495 | + | 0.0294734i | ||||
\(650\) | −25.6793 | + | 17.3046i | −1.00722 | + | 0.678741i | ||||
\(651\) | −11.4684 | + | 6.62126i | −0.449481 | + | 0.259508i | ||||
\(652\) | 16.5162 | 0.646824 | ||||||||
\(653\) | 12.6958 | − | 21.9898i | 0.496825 | − | 0.860526i | −0.503168 | − | 0.864188i | \(-0.667832\pi\) |
0.999993 | + | 0.00366254i | \(0.00116582\pi\) | |||||||
\(654\) | 0.738832 | + | 1.27969i | 0.0288906 | + | 0.0500400i | ||||
\(655\) | −35.2201 | − | 32.8577i | −1.37616 | − | 1.28386i | ||||
\(656\) | −1.33485 | −0.0521172 | ||||||||
\(657\) | −2.31501 | + | 1.33657i | −0.0903173 | + | 0.0521447i | ||||
\(658\) | −4.53623 | −0.176841 | ||||||||
\(659\) | 10.2268 | − | 17.7134i | 0.398381 | − | 0.690016i | −0.595145 | − | 0.803618i | \(-0.702906\pi\) |
0.993526 | + | 0.113602i | \(0.0362388\pi\) | |||||||
\(660\) | 7.26342 | + | 6.77621i | 0.282728 | + | 0.263764i | ||||
\(661\) | 0.419280 | + | 0.242071i | 0.0163081 | + | 0.00941548i | 0.508132 | − | 0.861279i | \(-0.330336\pi\) |
−0.491824 | + | 0.870695i | \(0.663670\pi\) | |||||||
\(662\) | 28.7591 | + | 16.6041i | 1.11775 | + | 0.645335i | ||||
\(663\) | 17.9420 | + | 10.3588i | 0.696811 | + | 0.402304i | ||||
\(664\) | −5.20372 | + | 3.00437i | −0.201943 | + | 0.116592i | ||||
\(665\) | −31.8213 | + | 34.1092i | −1.23398 | + | 1.32270i | ||||
\(666\) | −5.88842 | − | 1.52530i | −0.228172 | − | 0.0591040i | ||||
\(667\) | 0.359409i | 0.0139164i | ||||||||
\(668\) | −5.60293 | − | 9.70456i | −0.216784 | − | 0.375481i | ||||
\(669\) | 0.109921 | − | 0.190389i | 0.00424980 | − | 0.00736087i | ||||
\(670\) | 31.5420 | − | 9.63583i | 1.21857 | − | 0.372264i | ||||
\(671\) | 50.8195 | + | 29.3407i | 1.96187 | + | 1.13268i | ||||
\(672\) | −3.69510 | −0.142542 | ||||||||
\(673\) | −35.6479 | − | 20.5813i | −1.37413 | − | 0.793352i | −0.382681 | − | 0.923880i | \(-0.624999\pi\) |
−0.991445 | + | 0.130529i | \(0.958333\pi\) | |||||||
\(674\) | − | 6.32508i | − | 0.243633i | ||||||
\(675\) | 2.79415 | + | 4.14641i | 0.107547 | + | 0.159595i | ||||
\(676\) | 25.3549 | 0.975190 | ||||||||
\(677\) | − | 15.4030i | − | 0.591984i | −0.955190 | − | 0.295992i | \(-0.904350\pi\) | ||
0.955190 | − | 0.295992i | \(-0.0956501\pi\) | |||||||
\(678\) | 5.52994 | − | 3.19271i | 0.212376 | − | 0.122615i | ||||
\(679\) | 40.9978 | + | 23.6701i | 1.57335 | + | 0.908375i | ||||
\(680\) | −5.10271 | + | 5.46959i | −0.195680 | + | 0.209749i | ||||
\(681\) | −21.4699 | + | 12.3956i | −0.822728 | + | 0.475002i | ||||
\(682\) | 13.7877 | − | 7.96033i | 0.527958 | − | 0.304817i | ||||
\(683\) | 7.89432 | + | 13.6734i | 0.302068 | + | 0.523197i | 0.976604 | − | 0.215045i | \(-0.0689897\pi\) |
−0.674536 | + | 0.738242i | \(0.735656\pi\) | |||||||
\(684\) | −4.88936 | − | 2.82287i | −0.186949 | − | 0.107935i | ||||
\(685\) | 21.6851 | − | 6.62461i | 0.828543 | − | 0.253113i | ||||
\(686\) | 1.10787 | − | 0.639627i | 0.0422986 | − | 0.0244211i | ||||
\(687\) | 9.79129 | − | 5.65301i | 0.373561 | − | 0.215676i | ||||
\(688\) | −0.748273 | − | 1.29605i | −0.0285276 | − | 0.0494113i | ||||
\(689\) | 55.0888i | 2.09871i | ||||||||
\(690\) | −7.09542 | + | 2.16759i | −0.270118 | + | 0.0825188i | ||||
\(691\) | 13.8305 | + | 23.9551i | 0.526137 | + | 0.911297i | 0.999536 | + | 0.0304486i | \(0.00969358\pi\) |
−0.473399 | + | 0.880848i | \(0.656973\pi\) | |||||||
\(692\) | − | 14.3230i | − | 0.544480i | ||||||
\(693\) | 16.4151i | 0.623558i | ||||||||
\(694\) | −13.3652 | − | 23.1493i | −0.507337 | − | 0.878734i | ||||
\(695\) | 9.88209 | − | 10.5926i | 0.374849 | − | 0.401800i | ||||
\(696\) | 0.0541616 | − | 0.0938106i | 0.00205299 | − | 0.00355588i | ||||
\(697\) | −4.46543 | −0.169140 | ||||||||
\(698\) | 9.72032 | − | 16.8361i | 0.367920 | − | 0.637255i | ||||
\(699\) | 7.15391 | − | 12.3909i | 0.270586 | − | 0.468669i | ||||
\(700\) | 8.10639 | − | 16.6022i | 0.306393 | − | 0.627502i | ||||
\(701\) | −10.6850 | + | 6.16897i | −0.403566 | + | 0.232999i | −0.688021 | − | 0.725690i | \(-0.741521\pi\) |
0.284456 | + | 0.958689i | \(0.408187\pi\) | |||||||
\(702\) | − | 6.19314i | − | 0.233745i | ||||||
\(703\) | −8.61143 | + | 33.2445i | −0.324786 | + | 1.25384i | ||||
\(704\) | 4.44239 | 0.167429 | ||||||||
\(705\) | 2.67458 | + | 0.618091i | 0.100731 | + | 0.0232786i | ||||
\(706\) | 2.02075 | − | 3.50004i | 0.0760519 | − | 0.131726i | ||||
\(707\) | −32.7883 | − | 18.9303i | −1.23313 | − | 0.711948i | ||||
\(708\) | −0.169019 | + | 0.292750i | −0.00635213 | + | 0.0110022i | ||||
\(709\) | 40.5310i | 1.52217i | 0.648651 | + | 0.761086i | \(0.275334\pi\) | ||||
−0.648651 | + | 0.761086i | \(0.724666\pi\) | |||||||
\(710\) | 3.47791 | + | 11.3846i | 0.130524 | + | 0.427257i | ||||
\(711\) | − | 5.62837i | − | 0.211080i | ||||||
\(712\) | 13.9095 | − | 8.03066i | 0.521281 | − | 0.300962i | ||||
\(713\) | 11.8908i | 0.445314i | ||||||||
\(714\) | −12.3611 | −0.462603 | ||||||||
\(715\) | 59.9397 | + | 13.8520i | 2.24162 | + | 0.518034i | ||||
\(716\) | −5.33654 | − | 3.08106i | −0.199436 | − | 0.115144i | ||||
\(717\) | −6.79825 | −0.253885 | ||||||||
\(718\) | −0.224604 | − | 0.389026i | −0.00838216 | − | 0.0145183i | ||||
\(719\) | −2.47337 | − | 4.28400i | −0.0922412 | − | 0.159766i | 0.816213 | − | 0.577752i | \(-0.196070\pi\) |
−0.908454 | + | 0.417985i | \(0.862736\pi\) | |||||||
\(720\) | 2.17865 | + | 0.503482i | 0.0811934 | + | 0.0187637i | ||||
\(721\) | −19.0181 | − | 10.9801i | −0.708270 | − | 0.408920i | ||||
\(722\) | −6.43721 | + | 11.1496i | −0.239568 | + | 0.414944i | ||||
\(723\) | 2.77020 | + | 4.79812i | 0.103025 | + | 0.178444i | ||||
\(724\) | −1.83239 | − | 3.17379i | −0.0681002 | − | 0.117953i | ||||
\(725\) | 0.302671 | + | 0.449152i | 0.0112409 | + | 0.0166811i | ||||
\(726\) | − | 8.73486i | − | 0.324181i | ||||||
\(727\) | −17.2930 | + | 29.9524i | −0.641363 | + | 1.11087i | 0.343766 | + | 0.939055i | \(0.388297\pi\) |
−0.985129 | + | 0.171817i | \(0.945036\pi\) | |||||||
\(728\) | −19.8184 | + | 11.4421i | −0.734518 | + | 0.424074i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.37066 | − | 4.07749i | −0.161765 | − | 0.150915i | ||||
\(731\) | −2.50317 | − | 4.33562i | −0.0925831 | − | 0.160359i | ||||
\(732\) | 13.2094 | 0.488233 | ||||||||
\(733\) | 34.9113 | + | 20.1561i | 1.28948 | + | 0.744481i | 0.978561 | − | 0.205956i | \(-0.0660304\pi\) |
0.310917 | + | 0.950437i | \(0.399364\pi\) | |||||||
\(734\) | 33.3245i | 1.23003i | ||||||||
\(735\) | 14.2292 | − | 4.34690i | 0.524851 | − | 0.160338i | ||||
\(736\) | −1.65897 | + | 2.87341i | −0.0611503 | + | 0.105915i | ||||
\(737\) | −56.7449 | − | 32.7617i | −2.09022 | − | 1.20679i | ||||
\(738\) | 0.667426 | + | 1.15602i | 0.0245683 | + | 0.0425535i | ||||
\(739\) | −15.1392 | −0.556904 | −0.278452 | − | 0.960450i | \(-0.589821\pi\) | ||||
−0.278452 | + | 0.960450i | \(0.589821\pi\) | |||||||
\(740\) | −0.585029 | − | 13.5889i | −0.0215061 | − | 0.499537i | ||||
\(741\) | −34.9649 | −1.28447 | ||||||||
\(742\) | −16.4342 | − | 28.4649i | −0.603319 | − | 1.04498i | ||||
\(743\) | 13.4411 | + | 7.76020i | 0.493105 | + | 0.284694i | 0.725862 | − | 0.687841i | \(-0.241441\pi\) |
−0.232757 | + | 0.972535i | \(0.574775\pi\) | |||||||
\(744\) | 1.79190 | − | 3.10366i | 0.0656943 | − | 0.113786i | ||||
\(745\) | 1.17561 | + | 3.84826i | 0.0430711 | + | 0.140989i | ||||
\(746\) | 1.06367i | 0.0389439i | ||||||||
\(747\) | 5.20372 | + | 3.00437i | 0.190394 | + | 0.109924i | ||||
\(748\) | 14.8610 | 0.543371 | ||||||||
\(749\) | −19.4149 | − | 33.6277i | −0.709406 | − | 1.22873i | ||||
\(750\) | −7.04171 | + | 8.68414i | −0.257127 | + | 0.317100i | ||||
\(751\) | 17.8620 | 0.651793 | 0.325896 | − | 0.945406i | \(-0.394334\pi\) | ||||
0.325896 | + | 0.945406i | \(0.394334\pi\) | |||||||
\(752\) | 1.06316 | − | 0.613817i | 0.0387695 | − | 0.0223836i | ||||
\(753\) | 15.0407 | − | 26.0512i | 0.548113 | − | 0.949359i | ||||
\(754\) | − | 0.670860i | − | 0.0244313i | ||||||
\(755\) | 25.1975 | + | 5.82311i | 0.917032 | + | 0.211925i | ||||
\(756\) | 1.84755 | + | 3.20005i | 0.0671948 | + | 0.116385i | ||||
\(757\) | 5.03804 | + | 8.72614i | 0.183111 | + | 0.317157i | 0.942938 | − | 0.332968i | \(-0.108050\pi\) |
−0.759828 | + | 0.650125i | \(0.774717\pi\) | |||||||
\(758\) | 11.9117 | − | 20.6317i | 0.432652 | − | 0.749376i | ||||
\(759\) | 12.7648 | + | 7.36978i | 0.463334 | + | 0.267506i | ||||
\(760\) | 2.84253 | − | 12.3001i | 0.103109 | − | 0.446171i | ||||
\(761\) | 14.5679 | + | 25.2324i | 0.528086 | + | 0.914672i | 0.999464 | + | 0.0327408i | \(0.0104236\pi\) |
−0.471378 | + | 0.881931i | \(0.656243\pi\) | |||||||
\(762\) | 8.80279 | + | 15.2469i | 0.318892 | + | 0.552336i | ||||
\(763\) | −5.46012 | −0.197670 | ||||||||
\(764\) | 14.7975 | + | 8.54336i | 0.535356 | + | 0.309088i | ||||
\(765\) | 7.28815 | + | 1.68428i | 0.263504 | + | 0.0608952i | ||||
\(766\) | 24.6494 | 0.890617 | ||||||||
\(767\) | 2.09352i | 0.0755925i | ||||||||
\(768\) | 0.866025 | − | 0.500000i | 0.0312500 | − | 0.0180422i | ||||
\(769\) | 48.5732i | 1.75160i | 0.482678 | + | 0.875798i | \(0.339664\pi\) | ||||
−0.482678 | + | 0.875798i | \(0.660336\pi\) | |||||||
\(770\) | −35.1038 | + | 10.7239i | −1.26505 | + | 0.386463i | ||||
\(771\) | − | 23.5130i | − | 0.846800i | ||||||
\(772\) | −12.0933 | + | 20.9462i | −0.435248 | + | 0.753871i | ||||
\(773\) | −24.3124 | − | 14.0368i | −0.874458 | − | 0.504868i | −0.00563072 | − | 0.999984i | \(-0.501792\pi\) |
−0.868827 | + | 0.495116i | \(0.835126\pi\) | |||||||
\(774\) | −0.748273 | + | 1.29605i | −0.0268961 | + | 0.0465854i | ||||
\(775\) | 10.0137 | + | 14.8599i | 0.359703 | + | 0.533784i | ||||
\(776\) | −12.8116 | −0.459910 | ||||||||
\(777\) | 15.7602 | − | 16.0252i | 0.565394 | − | 0.574901i | ||||
\(778\) | 4.61716i | 0.165533i | ||||||||
\(779\) | 6.52657 | − | 3.76811i | 0.233838 | − | 0.135007i | ||||
\(780\) | 13.2441 | − | 4.04595i | 0.474213 | − | 0.144868i | ||||
\(781\) | 11.8248 | − | 20.4812i | 0.423126 | − | 0.732875i | ||||
\(782\) | −5.54968 | + | 9.61233i | −0.198456 | + | 0.343736i | ||||
\(783\) | −0.108323 | −0.00387115 | ||||||||
\(784\) | 3.32690 | − | 5.76236i | 0.118818 | − | 0.205798i | ||||
\(785\) | 32.1985 | + | 30.0388i | 1.14921 | + | 1.07213i | ||||
\(786\) | 10.7705 | + | 18.6551i | 0.384172 | + | 0.665405i | ||||
\(787\) | 18.8436i | 0.671702i | 0.941915 | + | 0.335851i | \(0.109024\pi\) | ||||
−0.941915 | + | 0.335851i | \(0.890976\pi\) | |||||||
\(788\) | 9.81631i | 0.349692i | ||||||||
\(789\) | −13.7905 | − | 23.8858i | −0.490954 | − | 0.850357i | ||||
\(790\) | 12.0363 | − | 3.67699i | 0.428232 | − | 0.130821i | ||||
\(791\) | 23.5948i | 0.838936i | ||||||||
\(792\) | −2.22120 | − | 3.84723i | −0.0789268 | − | 0.136705i | ||||
\(793\) | 70.8474 | − | 40.9038i | 2.51587 | − | 1.45254i | ||||
\(794\) | −10.0627 | + | 5.80971i | −0.357113 | + | 0.206179i | ||||
\(795\) | 5.81115 | + | 19.0223i | 0.206100 | + | 0.674651i | ||||
\(796\) | 19.0743 | + | 11.0125i | 0.676070 | + | 0.390329i | ||||
\(797\) | 14.8187 | + | 25.6667i | 0.524905 | + | 0.909163i | 0.999579 | + | 0.0290012i | \(0.00923265\pi\) |
−0.474674 | + | 0.880162i | \(0.657434\pi\) | |||||||
\(798\) | 18.0667 | − | 10.4308i | 0.639554 | − | 0.369247i | ||||
\(799\) | 3.55656 | − | 2.05338i | 0.125822 | − | 0.0726433i | ||||
\(800\) | 0.346604 | + | 4.98797i | 0.0122543 | + | 0.176351i | ||||
\(801\) | −13.9095 | − | 8.03066i | −0.491468 | − | 0.283749i | ||||
\(802\) | −5.47228 | + | 3.15942i | −0.193233 | + | 0.111563i | ||||
\(803\) | 11.8752i | 0.419066i | ||||||||
\(804\) | −14.7496 | −0.520177 | ||||||||
\(805\) | 6.17274 | − | 26.7105i | 0.217560 | − | 0.941420i | ||||
\(806\) | − | 22.1950i | − | 0.781785i | ||||||
\(807\) | 11.7661 | + | 6.79314i | 0.414185 | + | 0.239130i | ||||
\(808\) | 10.2462 | 0.360459 | ||||||||
\(809\) | 32.2806 | + | 18.6372i | 1.13493 | + | 0.655251i | 0.945169 | − | 0.326580i | \(-0.105896\pi\) |
0.189758 | + | 0.981831i | \(0.439230\pi\) | |||||||
\(810\) | −0.653296 | − | 2.13851i | −0.0229545 | − | 0.0751394i | ||||
\(811\) | 8.33056 | − | 14.4289i | 0.292525 | − | 0.506669i | −0.681881 | − | 0.731463i | \(-0.738838\pi\) |
0.974406 | + | 0.224794i | \(0.0721711\pi\) | |||||||
\(812\) | 0.200133 | + | 0.346640i | 0.00702328 | + | 0.0121647i | ||||
\(813\) | − | 9.95387i | − | 0.349098i | ||||||
\(814\) | −18.9475 | + | 19.2661i | −0.664109 | + | 0.675276i | ||||
\(815\) | 25.1930 | − | 27.0044i | 0.882473 | − | 0.945922i | ||||
\(816\) | 2.89708 | − | 1.67263i | 0.101418 | − | 0.0585538i | ||||
\(817\) | 7.31715 | + | 4.22456i | 0.255995 | + | 0.147799i | ||||
\(818\) | −12.2422 | − | 7.06806i | −0.428040 | − | 0.247129i | ||||
\(819\) | 19.8184 | + | 11.4421i | 0.692510 | + | 0.399821i | ||||
\(820\) | −2.03612 | + | 2.18251i | −0.0711043 | + | 0.0762167i | ||||
\(821\) | −10.5880 | + | 18.3390i | −0.369525 | + | 0.640037i | −0.989491 | − | 0.144592i | \(-0.953813\pi\) |
0.619966 | + | 0.784629i | \(0.287146\pi\) | |||||||
\(822\) | −10.1403 | −0.353683 | ||||||||
\(823\) | 17.6753 | − | 10.2048i | 0.616121 | − | 0.355717i | −0.159236 | − | 0.987240i | \(-0.550903\pi\) |
0.775357 | + | 0.631523i | \(0.217570\pi\) | |||||||
\(824\) | 5.94305 | 0.207036 | ||||||||
\(825\) | 22.1585 | − | 1.53975i | 0.771461 | − | 0.0536072i | ||||
\(826\) | −0.624543 | − | 1.08174i | −0.0217306 | − | 0.0376386i | ||||
\(827\) | 9.94714 | − | 17.2290i | 0.345896 | − | 0.599110i | −0.639620 | − | 0.768691i | \(-0.720908\pi\) |
0.985516 | + | 0.169582i | \(0.0542416\pi\) | |||||||
\(828\) | 3.31793 | 0.115306 | ||||||||
\(829\) | −33.0369 | + | 19.0739i | −1.14742 | + | 0.662463i | −0.948257 | − | 0.317503i | \(-0.897156\pi\) |
−0.199163 | + | 0.979966i | \(0.563822\pi\) | |||||||
\(830\) | −3.02529 | + | 13.0909i | −0.105009 | + | 0.454392i | ||||
\(831\) | −23.1172 | + | 13.3467i | −0.801926 | + | 0.462992i | ||||
\(832\) | 3.09657 | − | 5.36341i | 0.107354 | − | 0.185943i | ||||
\(833\) | 11.1294 | − | 19.2766i | 0.385609 | − | 0.667895i | ||||
\(834\) | −5.61060 | + | 3.23928i | −0.194279 | + | 0.112167i | ||||
\(835\) | −24.4136 | − | 5.64194i | −0.844868 | − | 0.195247i | ||||
\(836\) | −21.7205 | + | 12.5403i | −0.751218 | + | 0.433716i | ||||
\(837\) | −3.58380 | −0.123874 | ||||||||
\(838\) | 19.8015 | − | 34.2972i | 0.684031 | − | 1.18478i | ||||
\(839\) | −24.9103 | − | 43.1458i | −0.859998 | − | 1.48956i | −0.871930 | − | 0.489631i | \(-0.837132\pi\) |
0.0119323 | − | 0.999929i | \(-0.496202\pi\) | |||||||
\(840\) | −5.63633 | + | 6.04158i | −0.194472 | + | 0.208454i | ||||
\(841\) | 28.9883 | 0.999595 | ||||||||
\(842\) | 6.88568 | − | 3.97545i | 0.237296 | − | 0.137003i | ||||
\(843\) | 0.778273 | 0.0268051 | ||||||||
\(844\) | 3.58728 | − | 6.21336i | 0.123479 | − | 0.213873i | ||||
\(845\) | 38.6752 | − | 41.4559i | 1.33047 | − | 1.42613i | ||||
\(846\) | −1.06316 | − | 0.613817i | −0.0365522 | − | 0.0211034i | ||||
\(847\) | 27.9520 | + | 16.1381i | 0.960443 | + | 0.554512i | ||||
\(848\) | 7.70341 | + | 4.44757i | 0.264536 | + | 0.152730i | ||||
\(849\) | 10.0672 | − | 5.81231i | 0.345506 | − | 0.199478i | ||||
\(850\) | 1.15948 | + | 16.6861i | 0.0397699 | + | 0.572328i | ||||
\(851\) | −5.38588 | − | 19.4503i | −0.184626 | − | 0.666747i | ||||
\(852\) | − | 5.32363i | − | 0.182385i | ||||||
\(853\) | 15.7852 | + | 27.3408i | 0.540475 | + | 0.936130i | 0.998877 | + | 0.0473848i | \(0.0150887\pi\) |
−0.458402 | + | 0.888745i | \(0.651578\pi\) | |||||||
\(854\) | −24.4050 | + | 42.2708i | −0.835123 | + | 1.44648i | ||||
\(855\) | −12.0735 | + | 3.68834i | −0.412903 | + | 0.126139i | ||||
\(856\) | 9.10060 | + | 5.25423i | 0.311052 | + | 0.179586i | ||||
\(857\) | 51.4712 | 1.75822 | 0.879112 | − | 0.476615i | \(-0.158137\pi\) | ||||
0.879112 | + | 0.476615i | \(0.158137\pi\) | |||||||
\(858\) | −23.8264 | − | 13.7562i | −0.813420 | − | 0.469628i | ||||
\(859\) | − | 8.76509i | − | 0.299061i | −0.988757 | − | 0.149531i | \(-0.952224\pi\) | ||
0.988757 | − | 0.149531i | \(-0.0477762\pi\) | |||||||
\(860\) | −3.26045 | − | 0.753483i | −0.111180 | − | 0.0256936i | ||||
\(861\) | −4.93242 | −0.168096 | ||||||||
\(862\) | 11.5415i | 0.393104i | ||||||||
\(863\) | 42.3921 | − | 24.4751i | 1.44305 | − | 0.833143i | 0.444993 | − | 0.895534i | \(-0.353206\pi\) |
0.998052 | + | 0.0623913i | \(0.0198727\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | −23.4185 | − | 21.8476i | −0.796252 | − | 0.742842i | ||||
\(866\) | −12.1411 | + | 7.00965i | −0.412571 | + | 0.238198i | ||||
\(867\) | −5.03092 | + | 2.90460i | −0.170859 | + | 0.0986455i | ||||
\(868\) | 6.62126 | + | 11.4684i | 0.224740 | + | 0.389262i | ||||
\(869\) | −21.6536 | − | 12.5017i | −0.734548 | − | 0.424092i | ||||
\(870\) | −0.0707671 | − | 0.231650i | −0.00239923 | − | 0.00785366i | ||||
\(871\) | −79.1080 | + | 45.6730i | −2.68047 | + | 1.54757i | ||||
\(872\) | 1.27969 | − | 0.738832i | 0.0433359 | − | 0.0250200i | ||||
\(873\) | 6.40580 | + | 11.0952i | 0.216803 | + | 0.375515i | ||||
\(874\) | − | 18.7322i | − | 0.633626i | ||||||
\(875\) | −14.7798 | − | 38.5783i | −0.499649 | − | 1.30418i | ||||
\(876\) | 1.33657 | + | 2.31501i | 0.0451586 | + | 0.0782170i | ||||
\(877\) | − | 36.6528i | − | 1.23768i | −0.785518 | − | 0.618839i | \(-0.787603\pi\) | ||
0.785518 | − | 0.618839i | \(-0.212397\pi\) | |||||||
\(878\) | − | 23.9409i | − | 0.807965i | ||||||
\(879\) | 5.20154 | + | 9.00934i | 0.175444 | + | 0.303877i | ||||
\(880\) | 6.77621 | − | 7.26342i | 0.228426 | − | 0.244850i | ||||
\(881\) | 13.2691 | − | 22.9828i | 0.447048 | − | 0.774310i | −0.551144 | − | 0.834410i | \(-0.685809\pi\) |
0.998192 | + | 0.0600998i | \(0.0191419\pi\) | |||||||
\(882\) | −6.65380 | −0.224045 | ||||||||
\(883\) | −19.8327 | + | 34.3512i | −0.667422 | + | 1.15601i | 0.311201 | + | 0.950344i | \(0.399269\pi\) |
−0.978623 | + | 0.205665i | \(0.934064\pi\) | |||||||
\(884\) | 10.3588 | − | 17.9420i | 0.348405 | − | 0.603456i | ||||
\(885\) | 0.220839 | + | 0.722896i | 0.00742342 | + | 0.0242999i | ||||
\(886\) | −22.7184 | + | 13.1165i | −0.763239 | + | 0.440656i | ||||
\(887\) | − | 0.635075i | − | 0.0213237i | −0.999943 | − | 0.0106619i | \(-0.996606\pi\) | ||
0.999943 | − | 0.0106619i | \(-0.00339384\pi\) | |||||||
\(888\) | −1.52530 | + | 5.88842i | −0.0511856 | + | 0.197602i | ||||
\(889\) | −65.0545 | −2.18186 | ||||||||
\(890\) | 8.08658 | − | 34.9919i | 0.271063 | − | 1.17293i | ||||
\(891\) | −2.22120 | + | 3.84723i | −0.0744129 | + | 0.128887i | ||||
\(892\) | −0.190389 | − | 0.109921i | −0.00637470 | − | 0.00368044i | ||||
\(893\) | −3.46545 | + | 6.00234i | −0.115967 | + | 0.200861i | ||||
\(894\) | − | 1.79951i | − | 0.0601845i | ||||||
\(895\) | −13.1777 | + | 4.02568i | −0.440482 | + | 0.134564i | ||||
\(896\) | 3.69510i | 0.123445i | ||||||||
\(897\) | 17.7954 | − | 10.2742i | 0.594173 | − | 0.343046i | ||||
\(898\) | 19.1331i | 0.638479i | ||||||||
\(899\) | −0.388209 | −0.0129475 | ||||||||
\(900\) | 4.14641 | − | 2.79415i | 0.138214 | − | 0.0931385i | ||||
\(901\) | 25.7699 | + | 14.8783i | 0.858521 | + | 0.495668i | ||||
\(902\) | 5.92994 | 0.197445 | ||||||||
\(903\) | −2.76495 | − | 4.78903i | −0.0920117 | − | 0.159369i | ||||
\(904\) | −3.19271 | − | 5.52994i | −0.106188 | − | 0.183923i | ||||
\(905\) | −7.98426 | − | 1.84515i | −0.265406 | − | 0.0613348i | ||||
\(906\) | −10.0162 | − | 5.78284i | −0.332765 | − | 0.192122i | ||||
\(907\) | −6.74363 | + | 11.6803i | −0.223919 | + | 0.387838i | −0.955994 | − | 0.293385i | \(-0.905218\pi\) |
0.732076 | + | 0.681223i | \(0.238552\pi\) | |||||||
\(908\) | 12.3956 | + | 21.4699i | 0.411364 | + | 0.712503i | ||||
\(909\) | −5.12308 | − | 8.87344i | −0.169922 | − | 0.294313i | ||||
\(910\) | −11.5218 | + | 49.8568i | −0.381945 | + | 1.65274i | ||||
\(911\) | − | 1.13010i | − | 0.0374418i | −0.999825 | − | 0.0187209i | \(-0.994041\pi\) | ||
0.999825 | − | 0.0187209i | \(-0.00595939\pi\) | |||||||
\(912\) | −2.82287 | + | 4.88936i | −0.0934746 | + | 0.161903i | ||||
\(913\) | 23.1170 | − | 13.3466i | 0.765059 | − | 0.441707i | ||||
\(914\) | −41.0396 | −1.35747 | ||||||||
\(915\) | 20.1490 | − | 21.5977i | 0.666104 | − | 0.713997i | ||||
\(916\) | −5.65301 | − | 9.79129i | −0.186781 | − | 0.323513i | ||||
\(917\) | −79.5964 | −2.62851 | ||||||||
\(918\) | −2.89708 | − | 1.67263i | −0.0956180 | − | 0.0552051i | ||||
\(919\) | − | 32.5408i | − | 1.07342i | −0.843766 | − | 0.536712i | \(-0.819666\pi\) | ||
0.843766 | − | 0.536712i | \(-0.180334\pi\) | |||||||
\(920\) | 2.16759 | + | 7.09542i | 0.0714634 | + | 0.233929i | ||||
\(921\) | −9.20320 | + | 15.9404i | −0.303256 | + | 0.525254i | ||||
\(922\) | −9.56724 | − | 5.52365i | −0.315080 | − | 0.181912i | ||||
\(923\) | −16.4850 | − | 28.5528i | −0.542610 | − | 0.939828i | ||||
\(924\) | 16.4151 | 0.540017 | ||||||||
\(925\) | −23.1105 | − | 19.7713i | −0.759869 | − | 0.650076i | ||||
\(926\) | −8.05337 | −0.264650 | ||||||||
\(927\) | −2.97152 | − | 5.14683i | −0.0975976 | − | 0.169044i | ||||
\(928\) | −0.0938106 | − | 0.0541616i | −0.00307948 | − | 0.00177794i | ||||
\(929\) | 0.825374 | − | 1.42959i | 0.0270797 | − | 0.0469033i | −0.852168 | − | 0.523268i | \(-0.824713\pi\) |
0.879248 | + | 0.476365i | \(0.158046\pi\) | |||||||
\(930\) | −2.34128 | − | 7.66398i | −0.0767737 | − | 0.251312i | ||||
\(931\) | 37.5656i | 1.23116i | ||||||||
\(932\) | −12.3909 | − | 7.15391i | −0.405879 | − | 0.234334i | ||||
\(933\) | −18.5249 | −0.606478 | ||||||||
\(934\) | −4.81896 | − | 8.34668i | −0.157681 | − | 0.273112i | ||||
\(935\) | 22.6682 | − | 24.2981i | 0.741330 | − | 0.794631i | ||||
\(936\) | −6.19314 | −0.202429 | ||||||||
\(937\) | −47.2940 | + | 27.3052i | −1.54503 | + | 0.892022i | −0.546517 | + | 0.837448i | \(0.684047\pi\) |
−0.998510 | + | 0.0545738i | \(0.982620\pi\) | |||||||
\(938\) | 27.2506 | − | 47.1994i | 0.889763 | − | 1.54111i | ||||
\(939\) | − | 21.8188i | − | 0.712028i | ||||||
\(940\) | 0.618091 | − | 2.67458i | 0.0201599 | − | 0.0872352i | ||||
\(941\) | 5.39829 | + | 9.35012i | 0.175979 | + | 0.304805i | 0.940500 | − | 0.339794i | \(-0.110357\pi\) |
−0.764520 | + | 0.644599i | \(0.777024\pi\) | |||||||
\(942\) | −9.84650 | − | 17.0546i | −0.320816 | − | 0.555670i | ||||
\(943\) | −2.21447 | + | 3.83558i | −0.0721132 | + | 0.124904i | ||||
\(944\) | 0.292750 | + | 0.169019i | 0.00952819 | + | 0.00550110i | ||||
\(945\) | 8.05033 | + | 1.86042i | 0.261877 | + | 0.0605194i | ||||
\(946\) | 3.32412 | + | 5.75755i | 0.108077 | + | 0.187194i | ||||
\(947\) | −26.1293 | − | 45.2573i | −0.849089 | − | 1.47067i | −0.882022 | − | 0.471208i | \(-0.843818\pi\) |
0.0329334 | − | 0.999458i | \(-0.489515\pi\) | |||||||
\(948\) | −5.62837 | −0.182801 | ||||||||
\(949\) | 14.3372 | + | 8.27758i | 0.465405 | + | 0.268702i | ||||
\(950\) | −15.7751 | − | 23.4096i | −0.511811 | − | 0.759506i | ||||
\(951\) | −27.9248 | −0.905524 | ||||||||
\(952\) | 12.3611i | 0.400626i | ||||||||
\(953\) | 44.8260 | − | 25.8803i | 1.45206 | − | 0.838345i | 0.453457 | − | 0.891278i | \(-0.350190\pi\) |
0.998598 | + | 0.0529333i | \(0.0168571\pi\) | |||||||
\(954\) | − | 8.89513i | − | 0.287991i | ||||||
\(955\) | 36.5400 | − | 11.1627i | 1.18241 | − | 0.361216i | ||||
\(956\) | 6.79825i | 0.219871i | ||||||||
\(957\) | −0.240607 | + | 0.416744i | −0.00777772 | + | 0.0134714i | ||||
\(958\) | −27.4842 | − | 15.8680i | −0.887973 | − | 0.512672i | ||||
\(959\) | 18.7347 | − | 32.4495i | 0.604975 | − | 1.04785i | ||||
\(960\) | 0.503482 | − | 2.17865i | 0.0162498 | − | 0.0703156i | ||||
\(961\) | 18.1564 | 0.585689 | ||||||||
\(962\) | 10.0531 | + | 36.3052i | 0.324125 | + | 1.17053i | ||||
\(963\) | − | 10.5085i | − | 0.338630i | ||||||
\(964\) | 4.79812 | − | 2.77020i | 0.154537 | − | 0.0892220i | ||||
\(965\) | 15.8010 | + | 51.7232i | 0.508653 | + | 1.66503i | ||||
\(966\) | −6.13005 | + | 10.6176i | −0.197231 | + | 0.341615i | ||||
\(967\) | −6.57419 | + | 11.3868i | −0.211412 | + | 0.366176i | −0.952157 | − | 0.305611i | \(-0.901139\pi\) |
0.740745 | + | 0.671787i | \(0.234473\pi\) | |||||||
\(968\) | −8.73486 | −0.280749 | ||||||||
\(969\) | −9.44325 | + | 16.3562i | −0.303361 | + | 0.525437i | ||||
\(970\) | −19.5422 | + | 20.9473i | −0.627462 | + | 0.672576i | ||||
\(971\) | −15.3443 | − | 26.5771i | −0.492423 | − | 0.852901i | 0.507539 | − | 0.861629i | \(-0.330555\pi\) |
−0.999962 | + | 0.00872744i | \(0.997222\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 23.9390i | − | 0.767448i | ||||||
\(974\) | −2.24168 | − | 3.88271i | −0.0718281 | − | 0.124410i | ||||
\(975\) | 13.5866 | − | 27.8258i | 0.435120 | − | 0.891140i | ||||
\(976\) | − | 13.2094i | − | 0.422822i | ||||||
\(977\) | 2.65295 | + | 4.59505i | 0.0848755 | + | 0.147009i | 0.905338 | − | 0.424691i | \(-0.139617\pi\) |
−0.820463 | + | 0.571700i | \(0.806284\pi\) | |||||||
\(978\) | −14.3034 | + | 8.25810i | −0.457374 | + | 0.264065i | ||||
\(979\) | −61.7915 | + | 35.6753i | −1.97486 | + | 1.14019i | ||||
\(980\) | −4.34690 | − | 14.2292i | −0.138857 | − | 0.454534i | ||||
\(981\) | −1.27969 | − | 0.738832i | −0.0408575 | − | 0.0235891i | ||||
\(982\) | −4.45427 | − | 7.71502i | −0.142141 | − | 0.246196i | ||||
\(983\) | 6.62158 | − | 3.82297i | 0.211196 | − | 0.121934i | −0.390671 | − | 0.920530i | \(-0.627757\pi\) |
0.601867 | + | 0.798596i | \(0.294424\pi\) | |||||||
\(984\) | 1.15602 | − | 0.667426i | 0.0368524 | − | 0.0212768i | ||||
\(985\) | 16.0499 | + | 14.9733i | 0.511392 | + | 0.477090i | ||||
\(986\) | −0.313821 | − | 0.181185i | −0.00999410 | − | 0.00577010i | ||||
\(987\) | 3.92849 | − | 2.26812i | 0.125045 | − | 0.0721949i | ||||
\(988\) | 34.9649i | 1.11238i | ||||||||
\(989\) | −4.96544 | −0.157892 | ||||||||
\(990\) | −9.67841 | − | 2.23666i | −0.307600 | − | 0.0710858i | ||||
\(991\) | − | 5.76561i | − | 0.183151i | −0.995798 | − | 0.0915753i | \(-0.970810\pi\) | ||
0.995798 | − | 0.0915753i | \(-0.0291902\pi\) | |||||||
\(992\) | −3.10366 | − | 1.79190i | −0.0985414 | − | 0.0568929i | ||||
\(993\) | −33.2081 | −1.05383 | ||||||||
\(994\) | 17.0359 | + | 9.83569i | 0.540346 | + | 0.311969i | ||||
\(995\) | 47.1008 | − | 14.3889i | 1.49319 | − | 0.456159i | ||||
\(996\) | 3.00437 | − | 5.20372i | 0.0951970 | − | 0.164886i | ||||
\(997\) | −8.96717 | − | 15.5316i | −0.283993 | − | 0.491891i | 0.688371 | − | 0.725358i | \(-0.258326\pi\) |
−0.972365 | + | 0.233468i | \(0.924993\pi\) | |||||||
\(998\) | 36.5680i | 1.15754i | ||||||||
\(999\) | 5.86217 | − | 1.62326i | 0.185471 | − | 0.0513578i |
(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 | 1110.2.ba.b.529.8 | yes | 36 | |
5.4 | even | 2 | 1110.2.ba.a.529.11 | ✓ | 36 | ||
37.27 | even | 6 | 1110.2.ba.a.619.11 | yes | 36 | ||
185.64 | even | 6 | inner | 1110.2.ba.b.619.8 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.ba.a.529.11 | ✓ | 36 | 5.4 | even | 2 | ||
1110.2.ba.a.619.11 | yes | 36 | 37.27 | even | 6 | ||
1110.2.ba.b.529.8 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.ba.b.619.8 | yes | 36 | 185.64 | even | 6 | inner |