Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,2,Mod(8,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("57.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.f (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: | \(0.455147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.4 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 57.8 |
Dual form | 57.2.f.a.50.4 |
$q$-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 \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.965926 | − | 1.67303i | 0.683013 | − | 1.18301i | −0.291044 | − | 0.956710i | \(-0.594003\pi\) |
0.974057 | − | 0.226303i | \(-0.0726640\pi\) | |||||||
\(3\) | 0.158919 | + | 1.72474i | 0.0917517 | + | 0.995782i | ||||
\(4\) | −0.866025 | − | 1.50000i | −0.433013 | − | 0.750000i | ||||
\(5\) | −1.22474 | − | 0.707107i | −0.547723 | − | 0.316228i | 0.200480 | − | 0.979698i | \(-0.435750\pi\) |
−0.748203 | + | 0.663470i | \(0.769083\pi\) | |||||||
\(6\) | 3.03906 | + | 1.40010i | 1.24069 | + | 0.571588i | ||||
\(7\) | −3.73205 | −1.41058 | −0.705291 | − | 0.708918i | \(-0.749184\pi\) | ||||
−0.705291 | + | 0.708918i | \(0.749184\pi\) | |||||||
\(8\) | 0.517638 | 0.183013 | ||||||||
\(9\) | −2.94949 | + | 0.548188i | −0.983163 | + | 0.182729i | ||||
\(10\) | −2.36603 | + | 1.36603i | −0.748203 | + | 0.431975i | ||||
\(11\) | 0.378937i | 0.114254i | 0.998367 | + | 0.0571270i | \(0.0181940\pi\) | ||||
−0.998367 | + | 0.0571270i | \(0.981806\pi\) | |||||||
\(12\) | 2.44949 | − | 1.73205i | 0.707107 | − | 0.500000i | ||||
\(13\) | 3.23205 | − | 1.86603i | 0.896410 | − | 0.517542i | 0.0203760 | − | 0.999792i | \(-0.493514\pi\) |
0.876034 | + | 0.482250i | \(0.160180\pi\) | |||||||
\(14\) | −3.60488 | + | 6.24384i | −0.963446 | + | 1.66874i | ||||
\(15\) | 1.02494 | − | 2.22474i | 0.264639 | − | 0.574427i | ||||
\(16\) | 2.23205 | − | 3.86603i | 0.558013 | − | 0.966506i | ||||
\(17\) | 4.24264 | + | 2.44949i | 1.02899 | + | 0.594089i | 0.916696 | − | 0.399586i | \(-0.130846\pi\) |
0.112296 | + | 0.993675i | \(0.464180\pi\) | |||||||
\(18\) | −1.93185 | + | 5.46410i | −0.455342 | + | 1.28790i | ||||
\(19\) | −1.73205 | + | 4.00000i | −0.397360 | + | 0.917663i | ||||
\(20\) | 2.44949i | 0.547723i | ||||||||
\(21\) | −0.593092 | − | 6.43684i | −0.129423 | − | 1.40463i | ||||
\(22\) | 0.633975 | + | 0.366025i | 0.135164 | + | 0.0780369i | ||||
\(23\) | 0.328169 | − | 0.189469i | 0.0684280 | − | 0.0395070i | −0.465396 | − | 0.885103i | \(-0.654088\pi\) |
0.533824 | + | 0.845596i | \(0.320755\pi\) | |||||||
\(24\) | 0.0822623 | + | 0.892794i | 0.0167917 | + | 0.182241i | ||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | − | 7.20977i | − | 1.41395i | ||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | 3.23205 | + | 5.59808i | 0.610800 | + | 1.05794i | ||||
\(29\) | −3.86370 | − | 6.69213i | −0.717472 | − | 1.24270i | −0.961998 | − | 0.273055i | \(-0.911966\pi\) |
0.244527 | − | 0.969643i | \(-0.421367\pi\) | |||||||
\(30\) | −2.73205 | − | 3.86370i | −0.498802 | − | 0.705412i | ||||
\(31\) | 4.46410i | 0.801776i | 0.916127 | + | 0.400888i | \(0.131298\pi\) | ||||
−0.916127 | + | 0.400888i | \(0.868702\pi\) | |||||||
\(32\) | −3.79435 | − | 6.57201i | −0.670753 | − | 1.16178i | ||||
\(33\) | −0.653570 | + | 0.0602202i | −0.113772 | + | 0.0104830i | ||||
\(34\) | 8.19615 | − | 4.73205i | 1.40563 | − | 0.811540i | ||||
\(35\) | 4.57081 | + | 2.63896i | 0.772608 | + | 0.446065i | ||||
\(36\) | 3.37662 | + | 3.94949i | 0.562769 | + | 0.658248i | ||||
\(37\) | 4.26795i | 0.701647i | 0.936442 | + | 0.350823i | \(0.114098\pi\) | ||||
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 5.01910 | + | 6.76148i | 0.814205 | + | 1.09686i | ||||
\(39\) | 3.73205 | + | 5.27792i | 0.597606 | + | 0.845143i | ||||
\(40\) | −0.633975 | − | 0.366025i | −0.100240 | − | 0.0578737i | ||||
\(41\) | −2.82843 | + | 4.89898i | −0.441726 | + | 0.765092i | −0.997818 | − | 0.0660290i | \(-0.978967\pi\) |
0.556092 | + | 0.831121i | \(0.312300\pi\) | |||||||
\(42\) | −11.3419 | − | 5.22524i | −1.75010 | − | 0.806272i | ||||
\(43\) | −1.13397 | + | 1.96410i | −0.172930 | + | 0.299523i | −0.939443 | − | 0.342706i | \(-0.888657\pi\) |
0.766513 | + | 0.642228i | \(0.221990\pi\) | |||||||
\(44\) | 0.568406 | − | 0.328169i | 0.0856904 | − | 0.0494734i | ||||
\(45\) | 4.00000 | + | 1.41421i | 0.596285 | + | 0.210819i | ||||
\(46\) | − | 0.732051i | − | 0.107935i | ||||||
\(47\) | 9.14162 | − | 5.27792i | 1.33344 | − | 0.769863i | 0.347617 | − | 0.937637i | \(-0.386991\pi\) |
0.985826 | + | 0.167773i | \(0.0536577\pi\) | |||||||
\(48\) | 7.02262 | + | 3.23533i | 1.01363 | + | 0.466980i | ||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | −5.79555 | −0.819615 | ||||||||
\(51\) | −3.55051 | + | 7.70674i | −0.497171 | + | 1.07916i | ||||
\(52\) | −5.59808 | − | 3.23205i | −0.776313 | − | 0.448205i | ||||
\(53\) | −3.01790 | − | 5.22715i | −0.414540 | − | 0.718004i | 0.580840 | − | 0.814018i | \(-0.302724\pi\) |
−0.995380 | + | 0.0960135i | \(0.969391\pi\) | |||||||
\(54\) | −9.73119 | − | 2.46360i | −1.32425 | − | 0.335254i | ||||
\(55\) | 0.267949 | − | 0.464102i | 0.0361303 | − | 0.0625794i | ||||
\(56\) | −1.93185 | −0.258155 | ||||||||
\(57\) | −7.17423 | − | 2.35167i | −0.950251 | − | 0.311486i | ||||
\(58\) | −14.9282 | −1.96017 | ||||||||
\(59\) | −4.19187 | + | 7.26054i | −0.545735 | + | 0.945241i | 0.452825 | + | 0.891599i | \(0.350416\pi\) |
−0.998560 | + | 0.0536419i | \(0.982917\pi\) | |||||||
\(60\) | −4.22474 | + | 0.389270i | −0.545412 | + | 0.0502545i | ||||
\(61\) | 1.76795 | + | 3.06218i | 0.226363 | + | 0.392072i | 0.956727 | − | 0.290986i | \(-0.0939832\pi\) |
−0.730365 | + | 0.683057i | \(0.760650\pi\) | |||||||
\(62\) | 7.46859 | + | 4.31199i | 0.948512 | + | 0.547623i | ||||
\(63\) | 11.0076 | − | 2.04587i | 1.38683 | − | 0.257755i | ||||
\(64\) | −5.73205 | −0.716506 | ||||||||
\(65\) | −5.27792 | −0.654645 | ||||||||
\(66\) | −0.530550 | + | 1.15161i | −0.0653062 | + | 0.141754i | ||||
\(67\) | 0.866025 | − | 0.500000i | 0.105802 | − | 0.0610847i | −0.446165 | − | 0.894951i | \(-0.647211\pi\) |
0.551967 | + | 0.833866i | \(0.313877\pi\) | |||||||
\(68\) | − | 8.48528i | − | 1.02899i | ||||||
\(69\) | 0.378937 | + | 0.535898i | 0.0456187 | + | 0.0645146i | ||||
\(70\) | 8.83013 | − | 5.09808i | 1.05540 | − | 0.609337i | ||||
\(71\) | −1.79315 | + | 3.10583i | −0.212808 | + | 0.368594i | −0.952592 | − | 0.304250i | \(-0.901594\pi\) |
0.739784 | + | 0.672844i | \(0.234928\pi\) | |||||||
\(72\) | −1.52677 | + | 0.283763i | −0.179931 | + | 0.0334418i | ||||
\(73\) | 1.50000 | − | 2.59808i | 0.175562 | − | 0.304082i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | 7.14042 | + | 4.12252i | 0.830057 | + | 0.479233i | ||||
\(75\) | 4.24264 | − | 3.00000i | 0.489898 | − | 0.346410i | ||||
\(76\) | 7.50000 | − | 0.866025i | 0.860309 | − | 0.0993399i | ||||
\(77\) | − | 1.41421i | − | 0.161165i | ||||||
\(78\) | 12.4350 | − | 1.14577i | 1.40799 | − | 0.129733i | ||||
\(79\) | −3.06218 | − | 1.76795i | −0.344522 | − | 0.198910i | 0.317748 | − | 0.948175i | \(-0.397073\pi\) |
−0.662270 | + | 0.749265i | \(0.730407\pi\) | |||||||
\(80\) | −5.46739 | + | 3.15660i | −0.611272 | + | 0.352918i | ||||
\(81\) | 8.39898 | − | 3.23375i | 0.933220 | − | 0.359306i | ||||
\(82\) | 5.46410 | + | 9.46410i | 0.603409 | + | 1.04514i | ||||
\(83\) | 7.72741i | 0.848193i | 0.905617 | + | 0.424097i | \(0.139408\pi\) | ||||
−0.905617 | + | 0.424097i | \(0.860592\pi\) | |||||||
\(84\) | −9.14162 | + | 6.46410i | −0.997433 | + | 0.705291i | ||||
\(85\) | −3.46410 | − | 6.00000i | −0.375735 | − | 0.650791i | ||||
\(86\) | 2.19067 | + | 3.79435i | 0.236226 | + | 0.409156i | ||||
\(87\) | 10.9282 | − | 7.72741i | 1.17163 | − | 0.828465i | ||||
\(88\) | 0.196152i | 0.0209099i | ||||||||
\(89\) | −3.67423 | − | 6.36396i | −0.389468 | − | 0.674579i | 0.602910 | − | 0.797809i | \(-0.294008\pi\) |
−0.992378 | + | 0.123231i | \(0.960674\pi\) | |||||||
\(90\) | 6.22973 | − | 5.32611i | 0.656671 | − | 0.561421i | ||||
\(91\) | −12.0622 | + | 6.96410i | −1.26446 | + | 0.730036i | ||||
\(92\) | −0.568406 | − | 0.328169i | −0.0592604 | − | 0.0342140i | ||||
\(93\) | −7.69944 | + | 0.709429i | −0.798394 | + | 0.0735643i | ||||
\(94\) | − | 20.3923i | − | 2.10331i | ||||||
\(95\) | 4.94975 | − | 3.67423i | 0.507833 | − | 0.376969i | ||||
\(96\) | 10.7321 | − | 7.58871i | 1.09534 | − | 0.774519i | ||||
\(97\) | 6.46410 | + | 3.73205i | 0.656330 | + | 0.378932i | 0.790877 | − | 0.611975i | \(-0.209625\pi\) |
−0.134547 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(98\) | 6.69213 | − | 11.5911i | 0.676007 | − | 1.17088i | ||||
\(99\) | −0.207729 | − | 1.11767i | −0.0208775 | − | 0.112330i | ||||
\(100\) | −2.59808 | + | 4.50000i | −0.259808 | + | 0.450000i | ||||
\(101\) | −6.69213 | + | 3.86370i | −0.665892 | + | 0.384453i | −0.794518 | − | 0.607240i | \(-0.792277\pi\) |
0.128626 | + | 0.991693i | \(0.458943\pi\) | |||||||
\(102\) | 9.46410 | + | 13.3843i | 0.937086 | + | 1.32524i | ||||
\(103\) | − | 10.4641i | − | 1.03106i | −0.856872 | − | 0.515529i | \(-0.827595\pi\) | ||
0.856872 | − | 0.515529i | \(-0.172405\pi\) | |||||||
\(104\) | 1.67303 | − | 0.965926i | 0.164054 | − | 0.0947168i | ||||
\(105\) | −3.82514 | + | 8.30286i | −0.373296 | + | 0.810276i | ||||
\(106\) | −11.6603 | −1.13254 | ||||||||
\(107\) | −4.89898 | −0.473602 | −0.236801 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236801 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(108\) | −6.27526 | + | 6.45145i | −0.603837 | + | 0.620791i | ||||
\(109\) | −12.4641 | − | 7.19615i | −1.19384 | − | 0.689266i | −0.234668 | − | 0.972076i | \(-0.575400\pi\) |
−0.959176 | + | 0.282809i | \(0.908734\pi\) | |||||||
\(110\) | −0.517638 | − | 0.896575i | −0.0493549 | − | 0.0854851i | ||||
\(111\) | −7.36112 | + | 0.678257i | −0.698687 | + | 0.0643773i | ||||
\(112\) | −8.33013 | + | 14.4282i | −0.787123 | + | 1.36334i | ||||
\(113\) | 18.6622 | 1.75559 | 0.877795 | − | 0.479036i | \(-0.159014\pi\) | ||||
0.877795 | + | 0.479036i | \(0.159014\pi\) | |||||||
\(114\) | −10.8642 | + | 9.73119i | −1.01753 | + | 0.911409i | ||||
\(115\) | −0.535898 | −0.0499728 | ||||||||
\(116\) | −6.69213 | + | 11.5911i | −0.621349 | + | 1.07621i | ||||
\(117\) | −8.50997 | + | 7.27559i | −0.786747 | + | 0.672629i | ||||
\(118\) | 8.09808 | + | 14.0263i | 0.745488 | + | 1.29122i | ||||
\(119\) | −15.8338 | − | 9.14162i | −1.45148 | − | 0.838011i | ||||
\(120\) | 0.530550 | − | 1.15161i | 0.0484324 | − | 0.105127i | ||||
\(121\) | 10.8564 | 0.986946 | ||||||||
\(122\) | 6.83083 | 0.618434 | ||||||||
\(123\) | −8.89898 | − | 4.09978i | −0.802394 | − | 0.369664i | ||||
\(124\) | 6.69615 | − | 3.86603i | 0.601332 | − | 0.347179i | ||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 7.20977 | − | 20.3923i | 0.642297 | − | 1.81669i | ||||
\(127\) | 6.80385 | − | 3.92820i | 0.603744 | − | 0.348572i | −0.166769 | − | 0.985996i | \(-0.553333\pi\) |
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(128\) | 2.05197 | − | 3.55412i | 0.181370 | − | 0.314142i | ||||
\(129\) | −3.56778 | − | 1.64368i | −0.314126 | − | 0.144718i | ||||
\(130\) | −5.09808 | + | 8.83013i | −0.447131 | + | 0.774453i | ||||
\(131\) | −6.03579 | − | 3.48477i | −0.527350 | − | 0.304465i | 0.212587 | − | 0.977142i | \(-0.431811\pi\) |
−0.739936 | + | 0.672677i | \(0.765144\pi\) | |||||||
\(132\) | 0.656339 | + | 0.928203i | 0.0571270 | + | 0.0807897i | ||||
\(133\) | 6.46410 | − | 14.9282i | 0.560509 | − | 1.29444i | ||||
\(134\) | − | 1.93185i | − | 0.166887i | ||||||
\(135\) | −1.80348 | + | 7.12372i | −0.155219 | + | 0.613113i | ||||
\(136\) | 2.19615 | + | 1.26795i | 0.188319 | + | 0.108726i | ||||
\(137\) | −0.656339 | + | 0.378937i | −0.0560748 | + | 0.0323748i | −0.527775 | − | 0.849384i | \(-0.676974\pi\) |
0.471700 | + | 0.881759i | \(0.343640\pi\) | |||||||
\(138\) | 1.26260 | − | 0.116337i | 0.107480 | − | 0.00990322i | ||||
\(139\) | −6.59808 | − | 11.4282i | −0.559642 | − | 0.969328i | −0.997526 | − | 0.0702964i | \(-0.977605\pi\) |
0.437885 | − | 0.899031i | \(-0.355728\pi\) | |||||||
\(140\) | − | 9.14162i | − | 0.772608i | ||||||
\(141\) | 10.5558 | + | 14.9282i | 0.888962 | + | 1.25718i | ||||
\(142\) | 3.46410 | + | 6.00000i | 0.290701 | + | 0.503509i | ||||
\(143\) | 0.707107 | + | 1.22474i | 0.0591312 | + | 0.102418i | ||||
\(144\) | −4.46410 | + | 12.6264i | −0.372008 | + | 1.05220i | ||||
\(145\) | 10.9282i | 0.907538i | ||||||||
\(146\) | −2.89778 | − | 5.01910i | −0.239822 | − | 0.415383i | ||||
\(147\) | 1.10102 | + | 11.9494i | 0.0908106 | + | 0.985568i | ||||
\(148\) | 6.40192 | − | 3.69615i | 0.526235 | − | 0.303822i | ||||
\(149\) | 14.6090 | + | 8.43451i | 1.19682 | + | 0.690982i | 0.959844 | − | 0.280534i | \(-0.0905116\pi\) |
0.236972 | + | 0.971516i | \(0.423845\pi\) | |||||||
\(150\) | −0.921022 | − | 9.99585i | −0.0752011 | − | 0.816158i | ||||
\(151\) | 2.00000i | 0.162758i | 0.996683 | + | 0.0813788i | \(0.0259324\pi\) | ||||
−0.996683 | + | 0.0813788i | \(0.974068\pi\) | |||||||
\(152\) | −0.896575 | + | 2.07055i | −0.0727219 | + | 0.167944i | ||||
\(153\) | −13.8564 | − | 4.89898i | −1.12022 | − | 0.396059i | ||||
\(154\) | −2.36603 | − | 1.36603i | −0.190660 | − | 0.110077i | ||||
\(155\) | 3.15660 | − | 5.46739i | 0.253544 | − | 0.439151i | ||||
\(156\) | 4.68482 | − | 10.1689i | 0.375086 | − | 0.814162i | ||||
\(157\) | −1.76795 | + | 3.06218i | −0.141098 | + | 0.244388i | −0.927910 | − | 0.372804i | \(-0.878397\pi\) |
0.786813 | + | 0.617192i | \(0.211730\pi\) | |||||||
\(158\) | −5.91567 | + | 3.41542i | −0.470626 | + | 0.271716i | ||||
\(159\) | 8.53590 | − | 6.03579i | 0.676941 | − | 0.478669i | ||||
\(160\) | 10.7321i | 0.848443i | ||||||||
\(161\) | −1.22474 | + | 0.707107i | −0.0965234 | + | 0.0557278i | ||||
\(162\) | 2.70262 | − | 17.1753i | 0.212338 | − | 1.34942i | ||||
\(163\) | 5.19615 | 0.406994 | 0.203497 | − | 0.979076i | \(-0.434769\pi\) | ||||
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | 9.79796 | 0.765092 | ||||||||
\(165\) | 0.843039 | + | 0.388390i | 0.0656305 | + | 0.0302361i | ||||
\(166\) | 12.9282 | + | 7.46410i | 1.00342 | + | 0.579327i | ||||
\(167\) | −3.81294 | − | 6.60420i | −0.295054 | − | 0.511048i | 0.679944 | − | 0.733264i | \(-0.262004\pi\) |
−0.974997 | + | 0.222216i | \(0.928671\pi\) | |||||||
\(168\) | −0.307007 | − | 3.33195i | −0.0236861 | − | 0.257066i | ||||
\(169\) | 0.464102 | − | 0.803848i | 0.0357001 | − | 0.0618344i | ||||
\(170\) | −13.3843 | −1.02653 | ||||||||
\(171\) | 2.91591 | − | 12.7474i | 0.222985 | − | 0.974822i | ||||
\(172\) | 3.92820 | 0.299523 | ||||||||
\(173\) | 5.93426 | − | 10.2784i | 0.451173 | − | 0.781455i | −0.547286 | − | 0.836946i | \(-0.684339\pi\) |
0.998459 | + | 0.0554909i | \(0.0176724\pi\) | |||||||
\(174\) | −2.37237 | − | 25.7473i | −0.179849 | − | 1.95190i | ||||
\(175\) | 5.59808 | + | 9.69615i | 0.423175 | + | 0.732960i | ||||
\(176\) | 1.46498 | + | 0.845807i | 0.110427 | + | 0.0637551i | ||||
\(177\) | −13.1887 | − | 6.07608i | −0.991326 | − | 0.456706i | ||||
\(178\) | −14.1962 | −1.06405 | ||||||||
\(179\) | 1.41421 | 0.105703 | 0.0528516 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528516 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(180\) | −1.34278 | − | 7.22474i | −0.100085 | − | 0.538501i | ||||
\(181\) | −3.00000 | + | 1.73205i | −0.222988 | + | 0.128742i | −0.607333 | − | 0.794447i | \(-0.707761\pi\) |
0.384345 | + | 0.923190i | \(0.374427\pi\) | |||||||
\(182\) | 26.9072i | 1.99450i | ||||||||
\(183\) | −5.00052 | + | 3.53590i | −0.369649 | + | 0.261381i | ||||
\(184\) | 0.169873 | − | 0.0980762i | 0.0125232 | − | 0.00723027i | ||||
\(185\) | 3.01790 | − | 5.22715i | 0.221880 | − | 0.384308i | ||||
\(186\) | −6.25019 | + | 13.5667i | −0.458286 | + | 0.994756i | ||||
\(187\) | −0.928203 | + | 1.60770i | −0.0678769 | + | 0.117566i | ||||
\(188\) | −15.8338 | − | 9.14162i | −1.15479 | − | 0.666721i | ||||
\(189\) | 5.27792 | + | 18.6603i | 0.383912 | + | 1.35733i | ||||
\(190\) | −1.36603 | − | 11.8301i | −0.0991019 | − | 0.858248i | ||||
\(191\) | − | 1.69161i | − | 0.122401i | −0.998125 | − | 0.0612005i | \(-0.980507\pi\) | ||
0.998125 | − | 0.0612005i | \(-0.0194929\pi\) | |||||||
\(192\) | −0.910930 | − | 9.88633i | −0.0657407 | − | 0.713484i | ||||
\(193\) | 11.4282 | + | 6.59808i | 0.822620 | + | 0.474940i | 0.851319 | − | 0.524648i | \(-0.175803\pi\) |
−0.0286991 | + | 0.999588i | \(0.509136\pi\) | |||||||
\(194\) | 12.4877 | − | 7.20977i | 0.896564 | − | 0.517631i | ||||
\(195\) | −0.838759 | − | 9.10306i | −0.0600648 | − | 0.651884i | ||||
\(196\) | −6.00000 | − | 10.3923i | −0.428571 | − | 0.742307i | ||||
\(197\) | 9.14162i | 0.651313i | 0.945488 | + | 0.325657i | \(0.105585\pi\) | ||||
−0.945488 | + | 0.325657i | \(0.894415\pi\) | |||||||
\(198\) | −2.07055 | − | 0.732051i | −0.147148 | − | 0.0520246i | ||||
\(199\) | 6.40192 | + | 11.0885i | 0.453820 | + | 0.786040i | 0.998620 | − | 0.0525267i | \(-0.0167275\pi\) |
−0.544799 | + | 0.838567i | \(0.683394\pi\) | |||||||
\(200\) | −0.776457 | − | 1.34486i | −0.0549038 | − | 0.0950962i | ||||
\(201\) | 1.00000 | + | 1.41421i | 0.0705346 | + | 0.0997509i | ||||
\(202\) | 14.9282i | 1.05034i | ||||||||
\(203\) | 14.4195 | + | 24.9754i | 1.01205 | + | 1.75293i | ||||
\(204\) | 14.6349 | − | 1.34847i | 1.02465 | − | 0.0944117i | ||||
\(205\) | 6.92820 | − | 4.00000i | 0.483887 | − | 0.279372i | ||||
\(206\) | −17.5068 | − | 10.1075i | −1.21976 | − | 0.704226i | ||||
\(207\) | −0.864068 | + | 0.738735i | −0.0600569 | + | 0.0513456i | ||||
\(208\) | − | 16.6603i | − | 1.15518i | ||||||
\(209\) | −1.51575 | − | 0.656339i | −0.104847 | − | 0.0453999i | ||||
\(210\) | 10.1962 | + | 14.4195i | 0.703601 | + | 0.995043i | ||||
\(211\) | −9.52628 | − | 5.50000i | −0.655816 | − | 0.378636i | 0.134865 | − | 0.990864i | \(-0.456940\pi\) |
−0.790681 | + | 0.612228i | \(0.790273\pi\) | |||||||
\(212\) | −5.22715 | + | 9.05369i | −0.359002 | + | 0.621810i | ||||
\(213\) | −5.64173 | − | 2.59915i | −0.386565 | − | 0.178091i | ||||
\(214\) | −4.73205 | + | 8.19615i | −0.323476 | + | 0.560277i | ||||
\(215\) | 2.77766 | − | 1.60368i | 0.189435 | − | 0.109370i | ||||
\(216\) | −0.732051 | − | 2.58819i | −0.0498097 | − | 0.176104i | ||||
\(217\) | − | 16.6603i | − | 1.13097i | ||||||
\(218\) | −24.0788 | + | 13.9019i | −1.63082 | + | 0.941555i | ||||
\(219\) | 4.71940 | + | 2.17423i | 0.318907 | + | 0.146921i | ||||
\(220\) | −0.928203 | −0.0625794 | ||||||||
\(221\) | 18.2832 | 1.22986 | ||||||||
\(222\) | −5.97555 | + | 12.9705i | −0.401053 | + | 0.870526i | ||||
\(223\) | −8.13397 | − | 4.69615i | −0.544691 | − | 0.314478i | 0.202287 | − | 0.979326i | \(-0.435163\pi\) |
−0.746978 | + | 0.664849i | \(0.768496\pi\) | |||||||
\(224\) | 14.1607 | + | 24.5271i | 0.946153 | + | 1.63878i | ||||
\(225\) | 5.84847 | + | 6.84072i | 0.389898 | + | 0.456048i | ||||
\(226\) | 18.0263 | − | 31.2224i | 1.19909 | − | 2.07689i | ||||
\(227\) | −24.5964 | −1.63252 | −0.816261 | − | 0.577683i | \(-0.803957\pi\) | ||||
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(228\) | 2.68556 | + | 12.7980i | 0.177856 | + | 0.847566i | ||||
\(229\) | 9.39230 | 0.620661 | 0.310330 | − | 0.950629i | \(-0.399560\pi\) | ||||
0.310330 | + | 0.950629i | \(0.399560\pi\) | |||||||
\(230\) | −0.517638 | + | 0.896575i | −0.0341320 | + | 0.0591184i | ||||
\(231\) | 2.43916 | − | 0.224745i | 0.160485 | − | 0.0147871i | ||||
\(232\) | −2.00000 | − | 3.46410i | −0.131306 | − | 0.227429i | ||||
\(233\) | 3.10583 | + | 1.79315i | 0.203470 | + | 0.117473i | 0.598273 | − | 0.801292i | \(-0.295854\pi\) |
−0.394803 | + | 0.918766i | \(0.629187\pi\) | |||||||
\(234\) | 3.95231 | + | 21.2651i | 0.258371 | + | 1.39015i | ||||
\(235\) | −14.9282 | −0.973809 | ||||||||
\(236\) | 14.5211 | 0.945241 | ||||||||
\(237\) | 2.56262 | − | 5.56244i | 0.166460 | − | 0.361319i | ||||
\(238\) | −30.5885 | + | 17.6603i | −1.98276 | + | 1.14474i | ||||
\(239\) | − | 29.9759i | − | 1.93898i | −0.245133 | − | 0.969489i | \(-0.578832\pi\) | ||
0.245133 | − | 0.969489i | \(-0.421168\pi\) | |||||||
\(240\) | −6.31319 | − | 8.92820i | −0.407515 | − | 0.576313i | ||||
\(241\) | −24.8205 | + | 14.3301i | −1.59883 | + | 0.923085i | −0.607116 | + | 0.794613i | \(0.707674\pi\) |
−0.991713 | + | 0.128472i | \(0.958993\pi\) | |||||||
\(242\) | 10.4865 | − | 18.1631i | 0.674097 | − | 1.16757i | ||||
\(243\) | 6.91215 | + | 13.9722i | 0.443415 | + | 0.896317i | ||||
\(244\) | 3.06218 | − | 5.30385i | 0.196036 | − | 0.339544i | ||||
\(245\) | −8.48528 | − | 4.89898i | −0.542105 | − | 0.312984i | ||||
\(246\) | −15.4548 | + | 10.9282i | −0.985363 | + | 0.696757i | ||||
\(247\) | 1.86603 | + | 16.1603i | 0.118732 | + | 1.02825i | ||||
\(248\) | 2.31079i | 0.146735i | ||||||||
\(249\) | −13.3278 | + | 1.22803i | −0.844615 | + | 0.0778232i | ||||
\(250\) | 18.9282 | + | 10.9282i | 1.19712 | + | 0.691160i | ||||
\(251\) | 12.7279 | − | 7.34847i | 0.803379 | − | 0.463831i | −0.0412721 | − | 0.999148i | \(-0.513141\pi\) |
0.844651 | + | 0.535317i | \(0.179808\pi\) | |||||||
\(252\) | −12.6017 | − | 14.7397i | −0.793832 | − | 0.928514i | ||||
\(253\) | 0.0717968 | + | 0.124356i | 0.00451382 | + | 0.00781817i | ||||
\(254\) | − | 15.1774i | − | 0.952316i | ||||||
\(255\) | 9.79796 | − | 6.92820i | 0.613572 | − | 0.433861i | ||||
\(256\) | −9.69615 | − | 16.7942i | −0.606010 | − | 1.04964i | ||||
\(257\) | −1.60368 | − | 2.77766i | −0.100035 | − | 0.173266i | 0.811664 | − | 0.584125i | \(-0.198562\pi\) |
−0.911699 | + | 0.410859i | \(0.865229\pi\) | |||||||
\(258\) | −6.19615 | + | 4.38134i | −0.385756 | + | 0.272770i | ||||
\(259\) | − | 15.9282i | − | 0.989730i | ||||||
\(260\) | 4.57081 | + | 7.91688i | 0.283470 | + | 0.490984i | ||||
\(261\) | 15.0645 | + | 17.6203i | 0.932469 | + | 1.09067i | ||||
\(262\) | −11.6603 | + | 6.73205i | −0.720373 | + | 0.415907i | ||||
\(263\) | 0.480473 | + | 0.277401i | 0.0296273 | + | 0.0171053i | 0.514740 | − | 0.857346i | \(-0.327888\pi\) |
−0.485113 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(264\) | −0.338313 | + | 0.0311723i | −0.0208217 | + | 0.00191852i | ||||
\(265\) | 8.53590i | 0.524356i | ||||||||
\(266\) | −18.7315 | − | 25.2342i | −1.14850 | − | 1.54721i | ||||
\(267\) | 10.3923 | − | 7.34847i | 0.635999 | − | 0.449719i | ||||
\(268\) | −1.50000 | − | 0.866025i | −0.0916271 | − | 0.0529009i | ||||
\(269\) | −3.01790 | + | 5.22715i | −0.184004 | + | 0.318705i | −0.943241 | − | 0.332110i | \(-0.892239\pi\) |
0.759236 | + | 0.650815i | \(0.225573\pi\) | |||||||
\(270\) | 10.1762 | + | 9.89828i | 0.619303 | + | 0.602390i | ||||
\(271\) | 3.46410 | − | 6.00000i | 0.210429 | − | 0.364474i | −0.741420 | − | 0.671042i | \(-0.765847\pi\) |
0.951849 | + | 0.306568i | \(0.0991805\pi\) | |||||||
\(272\) | 18.9396 | − | 10.9348i | 1.14838 | − | 0.663018i | ||||
\(273\) | −13.9282 | − | 19.6975i | −0.842973 | − | 1.19214i | ||||
\(274\) | 1.46410i | 0.0884496i | ||||||||
\(275\) | 0.984508 | − | 0.568406i | 0.0593681 | − | 0.0342762i | ||||
\(276\) | 0.475678 | − | 1.03251i | 0.0286325 | − | 0.0621497i | ||||
\(277\) | −9.85641 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595689\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595689\pi\) | |||||||
\(278\) | −25.4930 | −1.52897 | ||||||||
\(279\) | −2.44717 | − | 13.1668i | −0.146508 | − | 0.788277i | ||||
\(280\) | 2.36603 | + | 1.36603i | 0.141397 | + | 0.0816356i | ||||
\(281\) | 7.53794 | + | 13.0561i | 0.449676 | + | 0.778861i | 0.998365 | − | 0.0571654i | \(-0.0182062\pi\) |
−0.548689 | + | 0.836027i | \(0.684873\pi\) | |||||||
\(282\) | 35.1715 | − | 3.24072i | 2.09443 | − | 0.192982i | ||||
\(283\) | 10.9282 | − | 18.9282i | 0.649614 | − | 1.12516i | −0.333601 | − | 0.942714i | \(-0.608264\pi\) |
0.983215 | − | 0.182450i | \(-0.0584029\pi\) | |||||||
\(284\) | 6.21166 | 0.368594 | ||||||||
\(285\) | 7.12372 | + | 7.95315i | 0.421973 | + | 0.471104i | ||||
\(286\) | 2.73205 | 0.161550 | ||||||||
\(287\) | 10.5558 | − | 18.2832i | 0.623091 | − | 1.07923i | ||||
\(288\) | 14.7941 | + | 17.3041i | 0.871751 | + | 1.01965i | ||||
\(289\) | 3.50000 | + | 6.06218i | 0.205882 | + | 0.356599i | ||||
\(290\) | 18.2832 | + | 10.5558i | 1.07363 | + | 0.619860i | ||||
\(291\) | −5.40957 | + | 11.7420i | −0.317115 | + | 0.688329i | ||||
\(292\) | −5.19615 | −0.304082 | ||||||||
\(293\) | −25.2528 | −1.47528 | −0.737641 | − | 0.675193i | \(-0.764060\pi\) | ||||
−0.737641 | + | 0.675193i | \(0.764060\pi\) | |||||||
\(294\) | 21.0552 | + | 9.70017i | 1.22796 | + | 0.565726i | ||||
\(295\) | 10.2679 | − | 5.92820i | 0.597823 | − | 0.345153i | ||||
\(296\) | 2.20925i | 0.128410i | ||||||||
\(297\) | 1.89469 | − | 0.535898i | 0.109941 | − | 0.0310960i | ||||
\(298\) | 28.2224 | − | 16.2942i | 1.63488 | − | 0.943899i | ||||
\(299\) | 0.707107 | − | 1.22474i | 0.0408930 | − | 0.0708288i | ||||
\(300\) | −8.17423 | − | 3.76588i | −0.471940 | − | 0.217423i | ||||
\(301\) | 4.23205 | − | 7.33013i | 0.243931 | − | 0.422501i | ||||
\(302\) | 3.34607 | + | 1.93185i | 0.192544 | + | 0.111166i | ||||
\(303\) | −7.72741 | − | 10.9282i | −0.443928 | − | 0.627809i | ||||
\(304\) | 11.5981 | + | 15.6244i | 0.665195 | + | 0.896118i | ||||
\(305\) | − | 5.00052i | − | 0.286329i | ||||||
\(306\) | −21.5804 | + | 18.4502i | −1.23367 | + | 1.05473i | ||||
\(307\) | −12.0000 | − | 6.92820i | −0.684876 | − | 0.395413i | 0.116814 | − | 0.993154i | \(-0.462732\pi\) |
−0.801690 | + | 0.597740i | \(0.796065\pi\) | |||||||
\(308\) | −2.12132 | + | 1.22474i | −0.120873 | + | 0.0697863i | ||||
\(309\) | 18.0479 | − | 1.66294i | 1.02671 | − | 0.0946014i | ||||
\(310\) | −6.09808 | − | 10.5622i | −0.346347 | − | 0.599891i | ||||
\(311\) | 27.1475i | 1.53939i | 0.638411 | + | 0.769696i | \(0.279592\pi\) | ||||
−0.638411 | + | 0.769696i | \(0.720408\pi\) | |||||||
\(312\) | 1.93185 | + | 2.73205i | 0.109370 | + | 0.154672i | ||||
\(313\) | 12.3923 | + | 21.4641i | 0.700454 | + | 1.21322i | 0.968307 | + | 0.249763i | \(0.0803527\pi\) |
−0.267853 | + | 0.963460i | \(0.586314\pi\) | |||||||
\(314\) | 3.41542 | + | 5.91567i | 0.192743 | + | 0.333841i | ||||
\(315\) | −14.9282 | − | 5.27792i | −0.841109 | − | 0.297377i | ||||
\(316\) | 6.12436i | 0.344522i | ||||||||
\(317\) | 6.88160 | + | 11.9193i | 0.386509 | + | 0.669453i | 0.991977 | − | 0.126416i | \(-0.0403474\pi\) |
−0.605468 | + | 0.795870i | \(0.707014\pi\) | |||||||
\(318\) | −1.85303 | − | 20.1110i | −0.103913 | − | 1.12777i | ||||
\(319\) | 2.53590 | − | 1.46410i | 0.141983 | − | 0.0819740i | ||||
\(320\) | 7.02030 | + | 4.05317i | 0.392447 | + | 0.226579i | ||||
\(321\) | −0.778539 | − | 8.44949i | −0.0434538 | − | 0.471605i | ||||
\(322\) | 2.73205i | 0.152251i | ||||||||
\(323\) | −17.1464 | + | 12.7279i | −0.954053 | + | 0.708201i | ||||
\(324\) | −12.1244 | − | 9.79796i | −0.673575 | − | 0.544331i | ||||
\(325\) | −9.69615 | − | 5.59808i | −0.537846 | − | 0.310525i | ||||
\(326\) | 5.01910 | − | 8.69333i | 0.277982 | − | 0.481479i | ||||
\(327\) | 10.4307 | − | 22.6410i | 0.576822 | − | 1.25205i | ||||
\(328\) | −1.46410 | + | 2.53590i | −0.0808415 | + | 0.140022i | ||||
\(329\) | −34.1170 | + | 19.6975i | −1.88093 | + | 1.08596i | ||||
\(330\) | 1.46410 | − | 1.03528i | 0.0805961 | − | 0.0569901i | ||||
\(331\) | 31.9282i | 1.75493i | 0.479638 | + | 0.877466i | \(0.340768\pi\) | ||||
−0.479638 | + | 0.877466i | \(0.659232\pi\) | |||||||
\(332\) | 11.5911 | − | 6.69213i | 0.636145 | − | 0.367278i | ||||
\(333\) | −2.33964 | − | 12.5883i | −0.128211 | − | 0.689833i | ||||
\(334\) | −14.7321 | −0.806102 | ||||||||
\(335\) | −1.41421 | −0.0772667 | ||||||||
\(336\) | −26.2088 | − | 12.0744i | −1.42981 | − | 0.658714i | ||||
\(337\) | 6.35641 | + | 3.66987i | 0.346256 | + | 0.199911i | 0.663035 | − | 0.748589i | \(-0.269268\pi\) |
−0.316779 | + | 0.948499i | \(0.602601\pi\) | |||||||
\(338\) | −0.896575 | − | 1.55291i | −0.0487673 | − | 0.0844674i | ||||
\(339\) | 2.96577 | + | 32.1875i | 0.161078 | + | 1.74818i | ||||
\(340\) | −6.00000 | + | 10.3923i | −0.325396 | + | 0.563602i | ||||
\(341\) | −1.69161 | −0.0916061 | ||||||||
\(342\) | −18.5103 | − | 17.1915i | −1.00092 | − | 0.929610i | ||||
\(343\) | 0.267949 | 0.0144679 | ||||||||
\(344\) | −0.586988 | + | 1.01669i | −0.0316483 | + | 0.0548165i | ||||
\(345\) | −0.0851642 | − | 0.924288i | −0.00458509 | − | 0.0497620i | ||||
\(346\) | −11.4641 | − | 19.8564i | −0.616314 | − | 1.06749i | ||||
\(347\) | −21.5414 | − | 12.4369i | −1.15640 | − | 0.667649i | −0.205963 | − | 0.978560i | \(-0.566032\pi\) |
−0.950439 | + | 0.310911i | \(0.899366\pi\) | |||||||
\(348\) | −21.0552 | − | 9.70017i | −1.12868 | − | 0.519984i | ||||
\(349\) | −11.3923 | −0.609816 | −0.304908 | − | 0.952382i | \(-0.598626\pi\) | ||||
−0.304908 | + | 0.952382i | \(0.598626\pi\) | |||||||
\(350\) | 21.6293 | 1.15614 | ||||||||
\(351\) | −13.9009 | − | 13.5213i | −0.741977 | − | 0.721713i | ||||
\(352\) | 2.49038 | − | 1.43782i | 0.132738 | − | 0.0766362i | ||||
\(353\) | − | 11.9700i | − | 0.637101i | −0.947906 | − | 0.318551i | \(-0.896804\pi\) | ||
0.947906 | − | 0.318551i | \(-0.103196\pi\) | |||||||
\(354\) | −22.9048 | + | 16.1962i | −1.21738 | + | 0.860816i | ||||
\(355\) | 4.39230 | − | 2.53590i | 0.233119 | − | 0.134592i | ||||
\(356\) | −6.36396 | + | 11.0227i | −0.337289 | + | 0.584202i | ||||
\(357\) | 13.2507 | − | 28.7620i | 0.701301 | − | 1.52224i | ||||
\(358\) | 1.36603 | − | 2.36603i | 0.0721967 | − | 0.125048i | ||||
\(359\) | 23.1822 | + | 13.3843i | 1.22351 | + | 0.706394i | 0.965665 | − | 0.259792i | \(-0.0836539\pi\) |
0.257846 | + | 0.966186i | \(0.416987\pi\) | |||||||
\(360\) | 2.07055 | + | 0.732051i | 0.109128 | + | 0.0385825i | ||||
\(361\) | −13.0000 | − | 13.8564i | −0.684211 | − | 0.729285i | ||||
\(362\) | 6.69213i | 0.351731i | ||||||||
\(363\) | 1.72529 | + | 18.7245i | 0.0905540 | + | 0.982783i | ||||
\(364\) | 20.8923 | + | 12.0622i | 1.09505 | + | 0.632230i | ||||
\(365\) | −3.67423 | + | 2.12132i | −0.192318 | + | 0.111035i | ||||
\(366\) | 1.08555 | + | 11.7814i | 0.0567424 | + | 0.615826i | ||||
\(367\) | 8.52628 | + | 14.7679i | 0.445068 | + | 0.770881i | 0.998057 | − | 0.0623080i | \(-0.0198461\pi\) |
−0.552989 | + | 0.833189i | \(0.686513\pi\) | |||||||
\(368\) | − | 1.69161i | − | 0.0881815i | ||||||
\(369\) | 5.65685 | − | 16.0000i | 0.294484 | − | 0.832927i | ||||
\(370\) | −5.83013 | − | 10.0981i | −0.303094 | − | 0.524974i | ||||
\(371\) | 11.2629 | + | 19.5080i | 0.584743 | + | 1.01280i | ||||
\(372\) | 7.73205 | + | 10.9348i | 0.400888 | + | 0.566941i | ||||
\(373\) | 12.5359i | 0.649084i | 0.945871 | + | 0.324542i | \(0.105210\pi\) | ||||
−0.945871 | + | 0.324542i | \(0.894790\pi\) | |||||||
\(374\) | 1.79315 | + | 3.10583i | 0.0927216 | + | 0.160599i | ||||
\(375\) | −19.5133 | + | 1.79796i | −1.00766 | + | 0.0928462i | ||||
\(376\) | 4.73205 | − | 2.73205i | 0.244037 | − | 0.140895i | ||||
\(377\) | −24.9754 | − | 14.4195i | −1.28630 | − | 0.742644i | ||||
\(378\) | 36.3173 | + | 9.19429i | 1.86796 | + | 0.472903i | ||||
\(379\) | 17.7846i | 0.913534i | 0.889586 | + | 0.456767i | \(0.150993\pi\) | ||||
−0.889586 | + | 0.456767i | \(0.849007\pi\) | |||||||
\(380\) | −9.79796 | − | 4.24264i | −0.502625 | − | 0.217643i | ||||
\(381\) | 7.85641 | + | 11.1106i | 0.402496 | + | 0.569215i | ||||
\(382\) | −2.83013 | − | 1.63397i | −0.144802 | − | 0.0836014i | ||||
\(383\) | −13.3335 | + | 23.0943i | −0.681310 | + | 1.18006i | 0.293272 | + | 0.956029i | \(0.405256\pi\) |
−0.974581 | + | 0.224034i | \(0.928077\pi\) | |||||||
\(384\) | 6.45604 | + | 2.97431i | 0.329458 | + | 0.151782i | ||||
\(385\) | −1.00000 | + | 1.73205i | −0.0509647 | + | 0.0882735i | ||||
\(386\) | 22.0776 | − | 12.7465i | 1.12372 | − | 0.648780i | ||||
\(387\) | 2.26795 | − | 6.41473i | 0.115286 | − | 0.326079i | ||||
\(388\) | − | 12.9282i | − | 0.656330i | ||||||
\(389\) | −4.33057 | + | 2.50026i | −0.219569 | + | 0.126768i | −0.605751 | − | 0.795655i | \(-0.707127\pi\) |
0.386182 | + | 0.922423i | \(0.373794\pi\) | |||||||
\(390\) | −16.0399 | − | 7.38961i | −0.812212 | − | 0.374187i | ||||
\(391\) | 1.85641 | 0.0938825 | ||||||||
\(392\) | 3.58630 | 0.181136 | ||||||||
\(393\) | 5.05113 | − | 10.9640i | 0.254796 | − | 0.553060i | ||||
\(394\) | 15.2942 | + | 8.83013i | 0.770512 | + | 0.444855i | ||||
\(395\) | 2.50026 | + | 4.33057i | 0.125802 | + | 0.217895i | ||||
\(396\) | −1.49661 | + | 1.27953i | −0.0752074 | + | 0.0642986i | ||||
\(397\) | −4.16025 | + | 7.20577i | −0.208797 | + | 0.361647i | −0.951336 | − | 0.308156i | \(-0.900288\pi\) |
0.742539 | + | 0.669803i | \(0.233622\pi\) | |||||||
\(398\) | 24.7351 | 1.23986 | ||||||||
\(399\) | 26.7746 | + | 8.77656i | 1.34041 | + | 0.439377i | ||||
\(400\) | −13.3923 | −0.669615 | ||||||||
\(401\) | 5.74479 | − | 9.95026i | 0.286881 | − | 0.496892i | −0.686183 | − | 0.727429i | \(-0.740715\pi\) |
0.973064 | + | 0.230537i | \(0.0740482\pi\) | |||||||
\(402\) | 3.33195 | − | 0.307007i | 0.166183 | − | 0.0153121i | ||||
\(403\) | 8.33013 | + | 14.4282i | 0.414953 | + | 0.718720i | ||||
\(404\) | 11.5911 | + | 6.69213i | 0.576679 | + | 0.332946i | ||||
\(405\) | −12.5732 | − | 1.97846i | −0.624768 | − | 0.0983103i | ||||
\(406\) | 55.7128 | 2.76498 | ||||||||
\(407\) | −1.61729 | −0.0801659 | ||||||||
\(408\) | −1.83788 | + | 3.98930i | −0.0909886 | + | 0.197500i | ||||
\(409\) | 24.4641 | − | 14.1244i | 1.20967 | − | 0.698404i | 0.246984 | − | 0.969019i | \(-0.420560\pi\) |
0.962688 | + | 0.270615i | \(0.0872270\pi\) | |||||||
\(410\) | − | 15.4548i | − | 0.763259i | ||||||
\(411\) | −0.757875 | − | 1.07180i | −0.0373832 | − | 0.0528678i | ||||
\(412\) | −15.6962 | + | 9.06218i | −0.773294 | + | 0.446461i | ||||
\(413\) | 15.6443 | − | 27.0967i | 0.769805 | − | 1.33334i | ||||
\(414\) | 0.401302 | + | 2.15918i | 0.0197229 | + | 0.106118i | ||||
\(415\) | 5.46410 | − | 9.46410i | 0.268222 | − | 0.464574i | ||||
\(416\) | −24.5271 | − | 14.1607i | −1.20254 | − | 0.694286i | ||||
\(417\) | 18.6622 | − | 13.1962i | 0.913891 | − | 0.646218i | ||||
\(418\) | −2.56218 | + | 1.90192i | −0.125320 | + | 0.0930261i | ||||
\(419\) | − | 32.0464i | − | 1.56557i | −0.622292 | − | 0.782785i | \(-0.713798\pi\) | ||
0.622292 | − | 0.782785i | \(-0.286202\pi\) | |||||||
\(420\) | 15.7670 | − | 1.45277i | 0.769349 | − | 0.0708881i | ||||
\(421\) | −30.7128 | − | 17.7321i | −1.49685 | − | 0.864207i | −0.496857 | − | 0.867832i | \(-0.665513\pi\) |
−0.999993 | + | 0.00362487i | \(0.998846\pi\) | |||||||
\(422\) | −18.4034 | + | 10.6252i | −0.895861 | + | 0.517226i | ||||
\(423\) | −24.0698 | + | 20.5785i | −1.17031 | + | 1.00056i | ||||
\(424\) | −1.56218 | − | 2.70577i | −0.0758661 | − | 0.131404i | ||||
\(425\) | − | 14.6969i | − | 0.712906i | ||||||
\(426\) | −9.79796 | + | 6.92820i | −0.474713 | + | 0.335673i | ||||
\(427\) | −6.59808 | − | 11.4282i | −0.319303 | − | 0.553050i | ||||
\(428\) | 4.24264 | + | 7.34847i | 0.205076 | + | 0.355202i | ||||
\(429\) | −2.00000 | + | 1.41421i | −0.0965609 | + | 0.0682789i | ||||
\(430\) | − | 6.19615i | − | 0.298805i | ||||||
\(431\) | −12.7279 | − | 22.0454i | −0.613082 | − | 1.06189i | −0.990718 | − | 0.135935i | \(-0.956596\pi\) |
0.377635 | − | 0.925954i | \(-0.376737\pi\) | |||||||
\(432\) | −22.4867 | − | 5.69287i | −1.08189 | − | 0.273898i | ||||
\(433\) | 2.89230 | − | 1.66987i | 0.138995 | − | 0.0802490i | −0.428890 | − | 0.903357i | \(-0.641095\pi\) |
0.567885 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(434\) | −27.8731 | − | 16.0926i | −1.33795 | − | 0.772468i | ||||
\(435\) | −18.8484 | + | 1.73670i | −0.903710 | + | 0.0832682i | ||||
\(436\) | 24.9282i | 1.19384i | ||||||||
\(437\) | 0.189469 | + | 1.64085i | 0.00906352 | + | 0.0784924i | ||||
\(438\) | 8.19615 | − | 5.79555i | 0.391627 | − | 0.276922i | ||||
\(439\) | 19.4545 | + | 11.2321i | 0.928512 | + | 0.536077i | 0.886341 | − | 0.463034i | \(-0.153239\pi\) |
0.0421712 | + | 0.999110i | \(0.486573\pi\) | |||||||
\(440\) | 0.138701 | − | 0.240237i | 0.00661230 | − | 0.0114528i | ||||
\(441\) | −20.4347 | + | 3.79796i | −0.973079 | + | 0.180855i | ||||
\(442\) | 17.6603 | − | 30.5885i | 0.840013 | − | 1.45494i | ||||
\(443\) | 33.4607 | − | 19.3185i | 1.58976 | − | 0.917850i | 0.596419 | − | 0.802674i | \(-0.296590\pi\) |
0.993345 | − | 0.115177i | \(-0.0367435\pi\) | |||||||
\(444\) | 7.39230 | + | 10.4543i | 0.350823 | + | 0.496139i | ||||
\(445\) | 10.3923i | 0.492642i | ||||||||
\(446\) | −15.7136 | + | 9.07227i | −0.744062 | + | 0.429584i | ||||
\(447\) | −12.2257 | + | 26.5372i | −0.578258 | + | 1.25517i | ||||
\(448\) | 21.3923 | 1.01069 | ||||||||
\(449\) | 34.4959 | 1.62796 | 0.813982 | − | 0.580890i | \(-0.197296\pi\) | ||||
0.813982 | + | 0.580890i | \(0.197296\pi\) | |||||||
\(450\) | 17.0939 | − | 3.17705i | 0.805816 | − | 0.149768i | ||||
\(451\) | −1.85641 | − | 1.07180i | −0.0874148 | − | 0.0504689i | ||||
\(452\) | −16.1619 | − | 27.9933i | −0.760193 | − | 1.31669i | ||||
\(453\) | −3.44949 | + | 0.317837i | −0.162071 | + | 0.0149333i | ||||
\(454\) | −23.7583 | + | 41.1506i | −1.11503 | + | 1.93129i | ||||
\(455\) | 19.6975 | 0.923431 | ||||||||
\(456\) | −3.71366 | − | 1.21731i | −0.173908 | − | 0.0570060i | ||||
\(457\) | −20.7128 | −0.968905 | −0.484452 | − | 0.874818i | \(-0.660981\pi\) | ||||
−0.484452 | + | 0.874818i | \(0.660981\pi\) | |||||||
\(458\) | 9.07227 | − | 15.7136i | 0.423919 | − | 0.734250i | ||||
\(459\) | 6.24745 | − | 24.6773i | 0.291606 | − | 1.15184i | ||||
\(460\) | 0.464102 | + | 0.803848i | 0.0216388 | + | 0.0374796i | ||||
\(461\) | 28.4737 | + | 16.4393i | 1.32615 | + | 0.765656i | 0.984703 | − | 0.174244i | \(-0.0557481\pi\) |
0.341452 | + | 0.939899i | \(0.389081\pi\) | |||||||
\(462\) | 1.98004 | − | 4.29788i | 0.0921198 | − | 0.199955i | ||||
\(463\) | −29.5885 | −1.37509 | −0.687546 | − | 0.726141i | \(-0.741312\pi\) | ||||
−0.687546 | + | 0.726141i | \(0.741312\pi\) | |||||||
\(464\) | −34.4959 | −1.60143 | ||||||||
\(465\) | 9.93149 | + | 4.57545i | 0.460562 | + | 0.212182i | ||||
\(466\) | 6.00000 | − | 3.46410i | 0.277945 | − | 0.160471i | ||||
\(467\) | 22.6274i | 1.04707i | 0.852004 | + | 0.523536i | \(0.175387\pi\) | ||||
−0.852004 | + | 0.523536i | \(0.824613\pi\) | |||||||
\(468\) | 18.2832 | + | 6.46410i | 0.845143 | + | 0.298803i | ||||
\(469\) | −3.23205 | + | 1.86603i | −0.149242 | + | 0.0861650i | ||||
\(470\) | −14.4195 | + | 24.9754i | −0.665124 | + | 1.15203i | ||||
\(471\) | −5.56244 | − | 2.56262i | −0.256304 | − | 0.118079i | ||||
\(472\) | −2.16987 | + | 3.75833i | −0.0998765 | + | 0.172991i | ||||
\(473\) | −0.744272 | − | 0.429705i | −0.0342216 | − | 0.0197579i | ||||
\(474\) | −6.83083 | − | 9.66025i | −0.313750 | − | 0.443710i | ||||
\(475\) | 12.9904 | − | 1.50000i | 0.596040 | − | 0.0688247i | ||||
\(476\) | 31.6675i | 1.45148i | ||||||||
\(477\) | 11.7667 | + | 13.7630i | 0.538761 | + | 0.630167i | ||||
\(478\) | −50.1506 | − | 28.9545i | −2.29384 | − | 1.32435i | ||||
\(479\) | −10.2784 | + | 5.93426i | −0.469634 | + | 0.271143i | −0.716086 | − | 0.698012i | \(-0.754068\pi\) |
0.246453 | + | 0.969155i | \(0.420735\pi\) | |||||||
\(480\) | −18.5100 | + | 1.70552i | −0.844864 | + | 0.0778461i | ||||
\(481\) | 7.96410 | + | 13.7942i | 0.363132 | + | 0.628963i | ||||
\(482\) | 55.3674i | 2.52191i | ||||||||
\(483\) | −1.41421 | − | 2.00000i | −0.0643489 | − | 0.0910032i | ||||
\(484\) | −9.40192 | − | 16.2846i | −0.427360 | − | 0.740210i | ||||
\(485\) | −5.27792 | − | 9.14162i | −0.239658 | − | 0.415100i | ||||
\(486\) | 30.0526 | + | 1.93185i | 1.36321 | + | 0.0876306i | ||||
\(487\) | − | 24.9282i | − | 1.12960i | −0.825226 | − | 0.564802i | \(-0.808952\pi\) | ||
0.825226 | − | 0.564802i | \(-0.191048\pi\) | |||||||
\(488\) | 0.915158 | + | 1.58510i | 0.0414272 | + | 0.0717541i | ||||
\(489\) | 0.825765 | + | 8.96204i | 0.0373424 | + | 0.405277i | ||||
\(490\) | −16.3923 | + | 9.46410i | −0.740529 | + | 0.427545i | ||||
\(491\) | 8.66115 | + | 5.00052i | 0.390872 | + | 0.225670i | 0.682538 | − | 0.730850i | \(-0.260876\pi\) |
−0.291666 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(492\) | 1.55708 | + | 16.8990i | 0.0701985 | + | 0.761865i | ||||
\(493\) | − | 37.8564i | − | 1.70497i | ||||||
\(494\) | 28.8391 | + | 12.4877i | 1.29753 | + | 0.561848i | ||||
\(495\) | −0.535898 | + | 1.51575i | −0.0240868 | + | 0.0681279i | ||||
\(496\) | 17.2583 | + | 9.96410i | 0.774922 | + | 0.447401i | ||||
\(497\) | 6.69213 | − | 11.5911i | 0.300183 | − | 0.519932i | ||||
\(498\) | −10.8191 | + | 23.4840i | −0.484817 | + | 1.05234i | ||||
\(499\) | 8.06218 | − | 13.9641i | 0.360913 | − | 0.625119i | −0.627199 | − | 0.778859i | \(-0.715799\pi\) |
0.988111 | + | 0.153740i | \(0.0491319\pi\) | |||||||
\(500\) | 16.9706 | − | 9.79796i | 0.758947 | − | 0.438178i | ||||
\(501\) | 10.7846 | − | 7.62587i | 0.481821 | − | 0.340699i | ||||
\(502\) | − | 28.3923i | − | 1.26721i | ||||||
\(503\) | −15.8338 | + | 9.14162i | −0.705992 | + | 0.407605i | −0.809575 | − | 0.587016i | \(-0.800303\pi\) |
0.103583 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(504\) | 5.69798 | − | 1.05902i | 0.253808 | − | 0.0471724i | ||||
\(505\) | 10.9282 | 0.486299 | ||||||||
\(506\) | 0.277401 | 0.0123320 | ||||||||
\(507\) | 1.46019 | + | 0.672711i | 0.0648492 | + | 0.0298761i | ||||
\(508\) | −11.7846 | − | 6.80385i | −0.522858 | − | 0.301872i | ||||
\(509\) | −6.79367 | − | 11.7670i | −0.301124 | − | 0.521562i | 0.675267 | − | 0.737574i | \(-0.264028\pi\) |
−0.976391 | + | 0.216011i | \(0.930695\pi\) | |||||||
\(510\) | −2.12701 | − | 23.0844i | −0.0941855 | − | 1.02220i | ||||
\(511\) | −5.59808 | + | 9.69615i | −0.247644 | + | 0.428933i | ||||
\(512\) | −29.2552 | −1.29291 | ||||||||
\(513\) | 22.4495 | + | 3.00340i | 0.991169 | + | 0.132603i | ||||
\(514\) | −6.19615 | −0.273301 | ||||||||
\(515\) | −7.39924 | + | 12.8159i | −0.326049 | + | 0.564734i | ||||
\(516\) | 0.624265 | + | 6.77515i | 0.0274817 | + | 0.298259i | ||||
\(517\) | 2.00000 | + | 3.46410i | 0.0879599 | + | 0.152351i | ||||
\(518\) | −26.6484 | − | 15.3855i | −1.17086 | − | 0.675998i | ||||
\(519\) | 18.6707 | + | 8.60164i | 0.819554 | + | 0.377570i | ||||
\(520\) | −2.73205 | −0.119808 | ||||||||
\(521\) | −4.52004 | −0.198027 | −0.0990133 | − | 0.995086i | \(-0.531569\pi\) | ||||
−0.0990133 | + | 0.995086i | \(0.531569\pi\) | |||||||
\(522\) | 44.0306 | − | 8.18346i | 1.92717 | − | 0.358180i | ||||
\(523\) | −14.5981 | + | 8.42820i | −0.638329 | + | 0.368540i | −0.783971 | − | 0.620798i | \(-0.786809\pi\) |
0.145641 | + | 0.989337i | \(0.453475\pi\) | |||||||
\(524\) | 12.0716i | 0.527350i | ||||||||
\(525\) | −15.8338 | + | 11.1962i | −0.691042 | + | 0.488640i | ||||
\(526\) | 0.928203 | − | 0.535898i | 0.0404716 | − | 0.0233663i | ||||
\(527\) | −10.9348 | + | 18.9396i | −0.476326 | + | 0.825021i | ||||
\(528\) | −1.22599 | + | 2.66113i | −0.0533543 | + | 0.115811i | ||||
\(529\) | −11.4282 | + | 19.7942i | −0.496878 | + | 0.860619i | ||||
\(530\) | 14.2808 | + | 8.24504i | 0.620320 | + | 0.358142i | ||||
\(531\) | 8.38375 | − | 23.7128i | 0.363824 | − | 1.02905i | ||||
\(532\) | −27.9904 | + | 3.23205i | −1.21354 | + | 0.140127i | ||||
\(533\) | 21.1117i | 0.914448i | ||||||||
\(534\) | −2.25603 | − | 24.4847i | −0.0976281 | − | 1.05956i | ||||
\(535\) | 6.00000 | + | 3.46410i | 0.259403 | + | 0.149766i | ||||
\(536\) | 0.448288 | − | 0.258819i | 0.0193631 | − | 0.0111793i | ||||
\(537\) | 0.224745 | + | 2.43916i | 0.00969846 | + | 0.105257i | ||||
\(538\) | 5.83013 | + | 10.0981i | 0.251355 | + | 0.435359i | ||||
\(539\) | 2.62536i | 0.113082i | ||||||||
\(540\) | 12.2474 | − | 3.46410i | 0.527046 | − | 0.149071i | ||||
\(541\) | 8.76795 | + | 15.1865i | 0.376964 | + | 0.652920i | 0.990619 | − | 0.136654i | \(-0.0436349\pi\) |
−0.613655 | + | 0.789574i | \(0.710302\pi\) | |||||||
\(542\) | −6.69213 | − | 11.5911i | −0.287452 | − | 0.497881i | ||||
\(543\) | −3.46410 | − | 4.89898i | −0.148659 | − | 0.210235i | ||||
\(544\) | − | 37.1769i | − | 1.59395i | ||||||
\(545\) | 10.1769 | + | 17.6269i | 0.435930 | + | 0.755054i | ||||
\(546\) | −46.4081 | + | 4.27606i | −1.98608 | + | 0.182998i | ||||
\(547\) | −11.1340 | + | 6.42820i | −0.476054 | + | 0.274850i | −0.718771 | − | 0.695247i | \(-0.755295\pi\) |
0.242716 | + | 0.970097i | \(0.421962\pi\) | |||||||
\(548\) | 1.13681 | + | 0.656339i | 0.0485622 | + | 0.0280374i | ||||
\(549\) | −6.89320 | − | 8.06269i | −0.294195 | − | 0.344107i | ||||
\(550\) | − | 2.19615i | − | 0.0936443i | ||||||
\(551\) | 33.4607 | − | 3.86370i | 1.42547 | − | 0.164599i | ||||
\(552\) | 0.196152 | + | 0.277401i | 0.00834880 | + | 0.0118070i | ||||
\(553\) | 11.4282 | + | 6.59808i | 0.485977 | + | 0.280579i | ||||
\(554\) | −9.52056 | + | 16.4901i | −0.404490 | + | 0.700597i | ||||
\(555\) | 9.49510 | + | 4.37441i | 0.403044 | + | 0.185683i | ||||
\(556\) | −11.4282 | + | 19.7942i | −0.484664 | + | 0.839462i | ||||
\(557\) | −2.92996 | + | 1.69161i | −0.124147 | + | 0.0716760i | −0.560787 | − | 0.827960i | \(-0.689501\pi\) |
0.436641 | + | 0.899636i | \(0.356168\pi\) | |||||||
\(558\) | −24.3923 | − | 8.62398i | −1.03261 | − | 0.365082i | ||||
\(559\) | 8.46410i | 0.357993i | ||||||||
\(560\) | 20.4046 | − | 11.7806i | 0.862250 | − | 0.497820i | ||||
\(561\) | −2.92037 | − | 1.34542i | −0.123298 | − | 0.0568037i | ||||
\(562\) | 29.1244 | 1.22854 | ||||||||
\(563\) | 3.38323 | 0.142586 | 0.0712931 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712931 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(564\) | 13.2507 | − | 28.7620i | 0.557954 | − | 1.21110i | ||||
\(565\) | −22.8564 | − | 13.1962i | −0.961576 | − | 0.555166i | ||||
\(566\) | −21.1117 | − | 36.5665i | −0.887390 | − | 1.53700i | ||||
\(567\) | −31.3454 | + | 12.0685i | −1.31638 | + | 0.506830i | ||||
\(568\) | −0.928203 | + | 1.60770i | −0.0389465 | + | 0.0674574i | ||||
\(569\) | −13.9391 | −0.584356 | −0.292178 | − | 0.956364i | \(-0.594380\pi\) | ||||
−0.292178 | + | 0.956364i | \(0.594380\pi\) | |||||||
\(570\) | 20.1869 | − | 4.23607i | 0.845535 | − | 0.177430i | ||||
\(571\) | 25.1962 | 1.05443 | 0.527213 | − | 0.849733i | \(-0.323237\pi\) | ||||
0.527213 | + | 0.849733i | \(0.323237\pi\) | |||||||
\(572\) | 1.22474 | − | 2.12132i | 0.0512092 | − | 0.0886969i | ||||
\(573\) | 2.91760 | − | 0.268829i | 0.121885 | − | 0.0112305i | ||||
\(574\) | −20.3923 | − | 35.3205i | −0.851158 | − | 1.47425i | ||||
\(575\) | −0.984508 | − | 0.568406i | −0.0410568 | − | 0.0237042i | ||||
\(576\) | 16.9066 | − | 3.14224i | 0.704443 | − | 0.130927i | ||||
\(577\) | 42.9282 | 1.78712 | 0.893562 | − | 0.448939i | \(-0.148198\pi\) | ||||
0.893562 | + | 0.448939i | \(0.148198\pi\) | |||||||
\(578\) | 13.5230 | 0.562481 | ||||||||
\(579\) | −9.56384 | + | 20.7593i | −0.397460 | + | 0.862727i | ||||
\(580\) | 16.3923 | − | 9.46410i | 0.680653 | − | 0.392975i | ||||
\(581\) | − | 28.8391i | − | 1.19645i | ||||||
\(582\) | 14.4195 | + | 20.3923i | 0.597709 | + | 0.845288i | ||||
\(583\) | 1.98076 | − | 1.14359i | 0.0820348 | − | 0.0473628i | ||||
\(584\) | 0.776457 | − | 1.34486i | 0.0321300 | − | 0.0556508i | ||||
\(585\) | 15.5672 | − | 2.89329i | 0.643623 | − | 0.119623i | ||||
\(586\) | −24.3923 | + | 42.2487i | −1.00764 | + | 1.74528i | ||||
\(587\) | 9.29392 | + | 5.36585i | 0.383601 | + | 0.221472i | 0.679384 | − | 0.733783i | \(-0.262247\pi\) |
−0.295783 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(588\) | 16.9706 | − | 12.0000i | 0.699854 | − | 0.494872i | ||||
\(589\) | −17.8564 | − | 7.73205i | −0.735760 | − | 0.318594i | ||||
\(590\) | − | 22.9048i | − | 0.942976i | ||||||
\(591\) | −15.7670 | + | 1.45277i | −0.648566 | + | 0.0597591i | ||||
\(592\) | 16.5000 | + | 9.52628i | 0.678146 | + | 0.391528i | ||||
\(593\) | −21.7816 | + | 12.5756i | −0.894463 | + | 0.516419i | −0.875400 | − | 0.483400i | \(-0.839402\pi\) |
−0.0190636 | + | 0.999818i | \(0.506069\pi\) | |||||||
\(594\) | 0.933552 | − | 3.68751i | 0.0383041 | − | 0.151300i | ||||
\(595\) | 12.9282 | + | 22.3923i | 0.530005 | + | 0.917995i | ||||
\(596\) | − | 29.2180i | − | 1.19682i | ||||||
\(597\) | −18.1074 | + | 12.8038i | −0.741086 | + | 0.524027i | ||||
\(598\) | −1.36603 | − | 2.36603i | −0.0558609 | − | 0.0967540i | ||||
\(599\) | −8.43451 | − | 14.6090i | −0.344625 | − | 0.596908i | 0.640661 | − | 0.767824i | \(-0.278661\pi\) |
−0.985286 | + | 0.170916i | \(0.945327\pi\) | |||||||
\(600\) | 2.19615 | − | 1.55291i | 0.0896575 | − | 0.0633975i | ||||
\(601\) | − | 44.3731i | − | 1.81002i | −0.425395 | − | 0.905008i | \(-0.639865\pi\) | ||
0.425395 | − | 0.905008i | \(-0.360135\pi\) | |||||||
\(602\) | −8.17569 | − | 14.1607i | −0.333216 | − | 0.577148i | ||||
\(603\) | −2.28024 | + | 1.94949i | −0.0928585 | + | 0.0793894i | ||||
\(604\) | 3.00000 | − | 1.73205i | 0.122068 | − | 0.0704761i | ||||
\(605\) | −13.2963 | − | 7.67664i | −0.540573 | − | 0.312100i | ||||
\(606\) | −25.7473 | + | 2.37237i | −1.04591 | + | 0.0963709i | ||||
\(607\) | 13.2487i | 0.537749i | 0.963175 | + | 0.268874i | \(0.0866516\pi\) | ||||
−0.963175 | + | 0.268874i | \(0.913348\pi\) | |||||||
\(608\) | 32.8601 | − | 3.79435i | 1.33265 | − | 0.153881i | ||||
\(609\) | −40.7846 | + | 28.8391i | −1.65268 | + | 1.16862i | ||||
\(610\) | −8.36603 | − | 4.83013i | −0.338730 | − | 0.195566i | ||||
\(611\) | 19.6975 | − | 34.1170i | 0.796874 | − | 1.38023i | ||||
\(612\) | 4.65153 | + | 25.0273i | 0.188027 | + | 1.01167i | ||||
\(613\) | −11.3205 | + | 19.6077i | −0.457231 | + | 0.791947i | −0.998813 | − | 0.0487003i | \(-0.984492\pi\) |
0.541582 | + | 0.840648i | \(0.317825\pi\) | |||||||
\(614\) | −23.1822 | + | 13.3843i | −0.935558 | + | 0.540145i | ||||
\(615\) | 8.00000 | + | 11.3137i | 0.322591 | + | 0.456213i | ||||
\(616\) | − | 0.732051i | − | 0.0294952i | ||||||
\(617\) | 22.4379 | − | 12.9546i | 0.903318 | − | 0.521531i | 0.0250427 | − | 0.999686i | \(-0.492028\pi\) |
0.878275 | + | 0.478156i | \(0.158695\pi\) | |||||||
\(618\) | 14.6508 | − | 31.8010i | 0.589341 | − | 1.27922i | ||||
\(619\) | 2.80385 | 0.112696 | 0.0563481 | − | 0.998411i | \(-0.482054\pi\) | ||||
0.0563481 | + | 0.998411i | \(0.482054\pi\) | |||||||
\(620\) | −10.9348 | −0.439151 | ||||||||
\(621\) | −1.41145 | − | 1.37290i | −0.0566393 | − | 0.0550925i | ||||
\(622\) | 45.4186 | + | 26.2224i | 1.82112 | + | 1.05142i | ||||
\(623\) | 13.7124 | + | 23.7506i | 0.549377 | + | 0.951549i | ||||
\(624\) | 28.7347 | − | 2.64762i | 1.15031 | − | 0.105990i | ||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 47.8802 | 1.91368 | ||||||||
\(627\) | 0.891136 | − | 2.71859i | 0.0355885 | − | 0.108570i | ||||
\(628\) | 6.12436 | 0.244388 | ||||||||
\(629\) | −10.4543 | + | 18.1074i | −0.416840 | + | 0.721988i | ||||
\(630\) | −23.2497 | + | 19.8773i | −0.926289 | + | 0.791930i | ||||
\(631\) | −24.5263 | − | 42.4808i | −0.976376 | − | 1.69113i | −0.675318 | − | 0.737526i | \(-0.735994\pi\) |
−0.301058 | − | 0.953606i | \(-0.597340\pi\) | |||||||
\(632\) | −1.58510 | − | 0.915158i | −0.0630519 | − | 0.0364030i | ||||
\(633\) | 7.97219 | − | 17.3045i | 0.316866 | − | 0.687790i | ||||
\(634\) | 26.5885 | 1.05596 | ||||||||
\(635\) | −11.1106 | −0.440912 | ||||||||
\(636\) | −16.4460 | − | 7.57670i | −0.652126 | − | 0.300436i | ||||
\(637\) | 22.3923 | − | 12.9282i | 0.887215 | − | 0.512234i | ||||
\(638\) | − | 5.65685i | − | 0.223957i | ||||||
\(639\) | 3.58630 | − | 10.1436i | 0.141872 | − | 0.401274i | ||||
\(640\) | −5.02628 | + | 2.90192i | −0.198681 | + | 0.114709i | ||||
\(641\) | −6.41473 | + | 11.1106i | −0.253367 | + | 0.438844i | −0.964451 | − | 0.264263i | \(-0.914871\pi\) |
0.711084 | + | 0.703107i | \(0.248205\pi\) | |||||||
\(642\) | −14.8883 | − | 6.85906i | −0.587594 | − | 0.270705i | ||||
\(643\) | 21.7942 | − | 37.7487i | 0.859480 | − | 1.48866i | −0.0129447 | − | 0.999916i | \(-0.504121\pi\) |
0.872425 | − | 0.488748i | \(-0.162546\pi\) | |||||||
\(644\) | 2.12132 | + | 1.22474i | 0.0835917 | + | 0.0482617i | ||||
\(645\) | 3.20736 | + | 4.53590i | 0.126290 | + | 0.178601i | ||||
\(646\) | 4.73205 | + | 40.9808i | 0.186180 | + | 1.61237i | ||||
\(647\) | 20.5569i | 0.808174i | 0.914721 | + | 0.404087i | \(0.132411\pi\) | ||||
−0.914721 | + | 0.404087i | \(0.867589\pi\) | |||||||
\(648\) | 4.34763 | − | 1.67391i | 0.170791 | − | 0.0657575i | ||||
\(649\) | −2.75129 | − | 1.58846i | −0.107998 | − | 0.0623524i | ||||
\(650\) | −18.7315 | + | 10.8147i | −0.734711 | + | 0.424186i | ||||
\(651\) | 28.7347 | − | 2.64762i | 1.12620 | − | 0.103769i | ||||
\(652\) | −4.50000 | − | 7.79423i | −0.176234 | − | 0.305246i | ||||
\(653\) | − | 47.1223i | − | 1.84404i | −0.387144 | − | 0.922019i | \(-0.626538\pi\) | ||
0.387144 | − | 0.922019i | \(-0.373462\pi\) | |||||||
\(654\) | −27.8038 | − | 39.3205i | −1.08721 | − | 1.53755i | ||||
\(655\) | 4.92820 | + | 8.53590i | 0.192561 | + | 0.333525i | ||||
\(656\) | 12.6264 | + | 21.8695i | 0.492978 | + | 0.853862i | ||||
\(657\) | −3.00000 | + | 8.48528i | −0.117041 | + | 0.331042i | ||||
\(658\) | 76.1051i | 2.96689i | ||||||||
\(659\) | −16.5409 | − | 28.6496i | −0.644340 | − | 1.11603i | −0.984453 | − | 0.175646i | \(-0.943799\pi\) |
0.340113 | − | 0.940385i | \(-0.389535\pi\) | |||||||
\(660\) | −0.147509 | − | 1.60091i | −0.00574177 | − | 0.0623155i | ||||
\(661\) | 5.32051 | − | 3.07180i | 0.206944 | − | 0.119479i | −0.392946 | − | 0.919561i | \(-0.628544\pi\) |
0.599890 | + | 0.800082i | \(0.295211\pi\) | |||||||
\(662\) | 53.4169 | + | 30.8403i | 2.07611 | + | 1.19864i | ||||
\(663\) | 2.90555 | + | 31.5339i | 0.112842 | + | 1.22468i | ||||
\(664\) | 4.00000i | 0.155230i | ||||||||
\(665\) | −18.4727 | + | 13.7124i | −0.716341 | + | 0.531745i | ||||
\(666\) | −23.3205 | − | 8.24504i | −0.903651 | − | 0.319489i | ||||
\(667\) | −2.53590 | − | 1.46410i | −0.0981904 | − | 0.0566902i | ||||
\(668\) | −6.60420 | + | 11.4388i | −0.255524 | + | 0.442581i | ||||
\(669\) | 6.80702 | − | 14.7753i | 0.263175 | − | 0.571248i | ||||
\(670\) | −1.36603 | + | 2.36603i | −0.0527742 | + | 0.0914075i | ||||
\(671\) | −1.16037 | + | 0.669942i | −0.0447957 | + | 0.0258628i | ||||
\(672\) | −40.0526 | + | 28.3214i | −1.54506 | + | 1.09252i | ||||
\(673\) | 21.9808i | 0.847296i | 0.905827 | + | 0.423648i | \(0.139251\pi\) | ||||
−0.905827 | + | 0.423648i | \(0.860749\pi\) | |||||||
\(674\) | 12.2796 | − | 7.08965i | 0.472994 | − | 0.273083i | ||||
\(675\) | −10.8691 | + | 11.1742i | −0.418350 | + | 0.430096i | ||||
\(676\) | −1.60770 | −0.0618344 | ||||||||
\(677\) | −18.8380 | −0.724005 | −0.362002 | − | 0.932177i | \(-0.617907\pi\) | ||||
−0.362002 | + | 0.932177i | \(0.617907\pi\) | |||||||
\(678\) | 56.7154 | + | 26.1289i | 2.17814 | + | 1.00347i | ||||
\(679\) | −24.1244 | − | 13.9282i | −0.925808 | − | 0.534515i | ||||
\(680\) | −1.79315 | − | 3.10583i | −0.0687642 | − | 0.119103i | ||||
\(681\) | −3.90883 | − | 42.4226i | −0.149787 | − | 1.62564i | ||||
\(682\) | −1.63397 | + | 2.83013i | −0.0625681 | + | 0.108371i | ||||
\(683\) | −16.3142 | −0.624246 | −0.312123 | − | 0.950042i | \(-0.601040\pi\) | ||||
−0.312123 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(684\) | −21.6464 | + | 6.66574i | −0.827672 | + | 0.254871i | ||||
\(685\) | 1.07180 | 0.0409512 | ||||||||
\(686\) | 0.258819 | − | 0.448288i | 0.00988176 | − | 0.0171157i | ||||
\(687\) | 1.49261 | + | 16.1993i | 0.0569467 | + | 0.618043i | ||||
\(688\) | 5.06218 | + | 8.76795i | 0.192994 | + | 0.334275i | ||||
\(689\) | −19.5080 | − | 11.2629i | −0.743195 | − | 0.429084i | ||||
\(690\) | −1.62863 | − | 0.750311i | −0.0620007 | − | 0.0285639i | ||||
\(691\) | 9.85641 | 0.374955 | 0.187478 | − | 0.982269i | \(-0.439969\pi\) | ||||
0.187478 | + | 0.982269i | \(0.439969\pi\) | |||||||
\(692\) | −20.5569 | −0.781455 | ||||||||
\(693\) | 0.775255 | + | 4.17121i | 0.0294495 | + | 0.158451i | ||||
\(694\) | −41.6147 | + | 24.0263i | −1.57967 | + | 0.912025i | ||||
\(695\) | 18.6622i | 0.707897i | ||||||||
\(696\) | 5.65685 | − | 4.00000i | 0.214423 | − | 0.151620i | ||||
\(697\) | −24.0000 | + | 13.8564i | −0.909065 | + | 0.524849i | ||||
\(698\) | −11.0041 | + | 19.0597i | −0.416512 | + | 0.721420i | ||||
\(699\) | −2.59915 | + | 5.64173i | −0.0983090 | + | 0.213390i | ||||
\(700\) | 9.69615 | − | 16.7942i | 0.366480 | − | 0.634762i | ||||
\(701\) | 17.2344 | + | 9.95026i | 0.650933 | + | 0.375816i | 0.788814 | − | 0.614633i | \(-0.210696\pi\) |
−0.137881 | + | 0.990449i | \(0.544029\pi\) | |||||||
\(702\) | −36.0488 | + | 10.1962i | −1.36058 | + | 0.384829i | ||||
\(703\) | −17.0718 | − | 7.39230i | −0.643875 | − | 0.278806i | ||||
\(704\) | − | 2.17209i | − | 0.0818637i | ||||||
\(705\) | −2.37237 | − | 25.7473i | −0.0893486 | − | 0.969701i | ||||
\(706\) | −20.0263 | − | 11.5622i | −0.753699 | − | 0.435148i | ||||
\(707\) | 24.9754 | − | 14.4195i | 0.939295 | − | 0.542303i | ||||
\(708\) | 2.30767 | + | 25.0451i | 0.0867275 | + | 0.941254i | ||||
\(709\) | −21.1603 | − | 36.6506i | −0.794690 | − | 1.37644i | −0.923036 | − | 0.384714i | \(-0.874300\pi\) |
0.128346 | − | 0.991729i | \(-0.459033\pi\) | |||||||
\(710\) | − | 9.79796i | − | 0.367711i | ||||||
\(711\) | 10.0010 | + | 3.53590i | 0.375068 | + | 0.132607i | ||||
\(712\) | −1.90192 | − | 3.29423i | −0.0712776 | − | 0.123456i | ||||
\(713\) | 0.845807 | + | 1.46498i | 0.0316757 | + | 0.0548640i | ||||
\(714\) | −35.3205 | − | 49.9507i | −1.32184 | − | 1.86936i | ||||
\(715\) | − | 2.00000i | − | 0.0747958i | ||||||
\(716\) | −1.22474 | − | 2.12132i | −0.0457709 | − | 0.0792775i | ||||
\(717\) | 51.7008 | − | 4.76373i | 1.93080 | − | 0.177905i | ||||
\(718\) | 44.7846 | − | 25.8564i | 1.67135 | − | 0.964953i | ||||
\(719\) | −5.22715 | − | 3.01790i | −0.194940 | − | 0.112549i | 0.399353 | − | 0.916797i | \(-0.369235\pi\) |
−0.594293 | + | 0.804249i | \(0.702568\pi\) | |||||||
\(720\) | 14.3956 | − | 12.3075i | 0.536492 | − | 0.458674i | ||||
\(721\) | 39.0526i | 1.45439i | ||||||||
\(722\) | −35.7393 | + | 8.36516i | −1.33008 | + | 0.311319i | ||||
\(723\) | −28.6603 | − | 40.5317i | −1.06589 | − | 1.50739i | ||||
\(724\) | 5.19615 | + | 3.00000i | 0.193113 | + | 0.111494i | ||||
\(725\) | −11.5911 | + | 20.0764i | −0.430483 | + | 0.745618i | ||||
\(726\) | 32.9932 | + | 15.2001i | 1.22449 | + | 0.564127i | ||||
\(727\) | 6.79423 | − | 11.7679i | 0.251984 | − | 0.436449i | −0.712088 | − | 0.702090i | \(-0.752250\pi\) |
0.964072 | + | 0.265641i | \(0.0855836\pi\) | |||||||
\(728\) | −6.24384 | + | 3.60488i | −0.231412 | + | 0.133606i | ||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 8.19615i | 0.303353i | ||||||||
\(731\) | −9.62209 | + | 5.55532i | −0.355886 | + | 0.205471i | ||||
\(732\) | 9.63442 | + | 4.43860i | 0.356098 | + | 0.164055i | ||||
\(733\) | −35.7128 | −1.31908 | −0.659541 | − | 0.751668i | \(-0.729249\pi\) | ||||
−0.659541 | + | 0.751668i | \(0.729249\pi\) | |||||||
\(734\) | 32.9430 | 1.21595 | ||||||||
\(735\) | 7.10102 | − | 15.4135i | 0.261925 | − | 0.568535i | ||||
\(736\) | −2.49038 | − | 1.43782i | −0.0917967 | − | 0.0529988i | ||||
\(737\) | 0.189469 | + | 0.328169i | 0.00697917 | + | 0.0120883i | ||||
\(738\) | −21.3044 | − | 24.9189i | −0.784227 | − | 0.917278i | ||||
\(739\) | 17.4019 | − | 30.1410i | 0.640140 | − | 1.10876i | −0.345261 | − | 0.938507i | \(-0.612210\pi\) |
0.985401 | − | 0.170249i | \(-0.0544570\pi\) | |||||||
\(740\) | −10.4543 | −0.384308 | ||||||||
\(741\) | −27.5758 | + | 5.78658i | −1.01302 | + | 0.212575i | ||||
\(742\) | 43.5167 | 1.59755 | ||||||||
\(743\) | 3.53553 | − | 6.12372i | 0.129706 | − | 0.224658i | −0.793857 | − | 0.608105i | \(-0.791930\pi\) |
0.923563 | + | 0.383447i | \(0.125263\pi\) | |||||||
\(744\) | −3.98552 | + | 0.367227i | −0.146116 | + | 0.0134632i | ||||
\(745\) | −11.9282 | − | 20.6603i | −0.437016 | − | 0.756933i | ||||
\(746\) | 20.9730 | + | 12.1087i | 0.767875 | + | 0.443333i | ||||
\(747\) | −4.23607 | − | 22.7919i | −0.154990 | − | 0.833912i | ||||
\(748\) | 3.21539 | 0.117566 | ||||||||
\(749\) | 18.2832 | 0.668055 | ||||||||
\(750\) | −15.8403 | + | 34.3830i | −0.578407 | + | 1.25549i | ||||
\(751\) | −7.45448 | + | 4.30385i | −0.272018 | + | 0.157050i | −0.629804 | − | 0.776754i | \(-0.716865\pi\) |
0.357786 | + | 0.933803i | \(0.383532\pi\) | |||||||
\(752\) | − | 47.1223i | − | 1.71837i | ||||||
\(753\) | 14.6969 | + | 20.7846i | 0.535586 | + | 0.757433i | ||||
\(754\) | −48.2487 | + | 27.8564i | −1.75711 | + | 1.01447i | ||||
\(755\) | 1.41421 | − | 2.44949i | 0.0514685 | − | 0.0891461i | ||||
\(756\) | 23.4196 | − | 24.0771i | 0.851762 | − | 0.875677i | ||||
\(757\) | −2.30385 | + | 3.99038i | −0.0837348 | + | 0.145033i | −0.904851 | − | 0.425728i | \(-0.860018\pi\) |
0.821117 | + | 0.570760i | \(0.193352\pi\) | |||||||
\(758\) | 29.7542 | + | 17.1786i | 1.08072 | + | 0.623955i | ||||
\(759\) | −0.203072 | + | 0.143594i | −0.00737104 | + | 0.00521212i | ||||
\(760\) | 2.56218 | − | 1.90192i | 0.0929400 | − | 0.0689900i | ||||
\(761\) | 46.2629i | 1.67703i | 0.544879 | + | 0.838514i | \(0.316575\pi\) | ||||
−0.544879 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(762\) | 26.1772 | − | 2.41197i | 0.948299 | − | 0.0873766i | ||||
\(763\) | 46.5167 | + | 26.8564i | 1.68402 | + | 0.972267i | ||||
\(764\) | −2.53742 | + | 1.46498i | −0.0918007 | + | 0.0530012i | ||||
\(765\) | 13.5065 | + | 15.7980i | 0.488327 | + | 0.571176i | ||||
\(766\) | 25.7583 | + | 44.6147i | 0.930686 | + | 1.61200i | ||||
\(767\) | 31.2886i | 1.12976i | ||||||||
\(768\) | 27.4249 | − | 19.3923i | 0.989609 | − | 0.699760i | ||||
\(769\) | 0.428203 | + | 0.741670i | 0.0154414 | + | 0.0267453i | 0.873643 | − | 0.486568i | \(-0.161751\pi\) |
−0.858201 | + | 0.513313i | \(0.828418\pi\) | |||||||
\(770\) | 1.93185 | + | 3.34607i | 0.0696191 | + | 0.120584i | ||||
\(771\) | 4.53590 | − | 3.20736i | 0.163356 | − | 0.115510i | ||||
\(772\) | − | 22.8564i | − | 0.822620i | ||||||
\(773\) | −9.04008 | − | 15.6579i | −0.325149 | − | 0.563175i | 0.656393 | − | 0.754419i | \(-0.272081\pi\) |
−0.981543 | + | 0.191244i | \(0.938748\pi\) | |||||||
\(774\) | −8.54138 | − | 9.99051i | −0.307014 | − | 0.359101i | ||||
\(775\) | 11.5981 | − | 6.69615i | 0.416615 | − | 0.240533i | ||||
\(776\) | 3.34607 | + | 1.93185i | 0.120117 | + | 0.0693494i | ||||
\(777\) | 27.4721 | − | 2.53129i | 0.985556 | − | 0.0908095i | ||||
\(778\) | 9.66025i | 0.346337i | ||||||||
\(779\) | −14.6969 | − | 19.7990i | −0.526572 | − | 0.709372i | ||||
\(780\) | −12.9282 | + | 9.14162i | −0.462904 | + | 0.327323i | ||||
\(781\) | −1.17691 | − | 0.679492i | −0.0421133 | − | 0.0243141i | ||||
\(782\) | 1.79315 | − | 3.10583i | 0.0641229 | − | 0.111064i | ||||
\(783\) | −27.9966 | + | 28.7826i | −1.00052 | + | 1.02861i | ||||
\(784\) | 15.4641 | − | 26.7846i | 0.552289 | − | 0.956593i | ||||
\(785\) | 4.33057 | − | 2.50026i | 0.154565 | − | 0.0892380i | ||||
\(786\) | −13.4641 | − | 19.0411i | −0.480249 | − | 0.679174i | ||||
\(787\) | − | 24.0718i | − | 0.858067i | −0.903289 | − | 0.429033i | \(-0.858854\pi\) | ||
0.903289 | − | 0.429033i | \(-0.141146\pi\) | |||||||
\(788\) | 13.7124 | − | 7.91688i | 0.488485 | − | 0.282027i | ||||
\(789\) | −0.402091 | + | 0.872778i | −0.0143148 | + | 0.0310717i | ||||
\(790\) | 9.66025 | 0.343696 | ||||||||
\(791\) | −69.6482 | −2.47640 | ||||||||
\(792\) | −0.107528 | − | 0.578550i | −0.00382086 | − | 0.0205579i | ||||
\(793\) | 11.4282 | + | 6.59808i | 0.405827 | + | 0.234305i | ||||
\(794\) | 8.03699 | + | 13.9205i | 0.285222 | + | 0.494019i | ||||
\(795\) | −14.7222 | + | 1.35651i | −0.522144 | + | 0.0481106i | ||||
\(796\) | 11.0885 | − | 19.2058i | 0.393020 | − | 0.680731i | ||||
\(797\) | 14.4939 | 0.513399 | 0.256700 | − | 0.966491i | \(-0.417365\pi\) | ||||
0.256700 | + | 0.966491i | \(0.417365\pi\) | |||||||
\(798\) | 40.5458 | − | 36.3173i | 1.43530 | − | 1.28562i | ||||
\(799\) | 51.7128 | 1.82947 | ||||||||
\(800\) | −11.3831 | + | 19.7160i | −0.402452 | + | 0.697067i | ||||
\(801\) | 14.3258 | + | 16.7563i | 0.506176 | + | 0.592054i | ||||
\(802\) | −11.0981 | − | 19.2224i | −0.391887 | − | 0.678768i | ||||
\(803\) | 0.984508 | + | 0.568406i | 0.0347425 | + | 0.0200586i | ||||
\(804\) | 1.25529 | − | 2.72474i | 0.0442708 | − | 0.0960943i | ||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 32.1851 | 1.13367 | ||||||||
\(807\) | −9.49510 | − | 4.37441i | −0.334243 | − | 0.153986i | ||||
\(808\) | −3.46410 | + | 2.00000i | −0.121867 | + | 0.0703598i | ||||
\(809\) | 51.1619i | 1.79876i | 0.437172 | + | 0.899378i | \(0.355980\pi\) | ||||
−0.437172 | + | 0.899378i | \(0.644020\pi\) | |||||||
\(810\) | −15.4548 | + | 19.1244i | −0.543027 | + | 0.671961i | ||||
\(811\) | 18.8038 | − | 10.8564i | 0.660292 | − | 0.381220i | −0.132096 | − | 0.991237i | \(-0.542171\pi\) |
0.792388 | + | 0.610017i | \(0.208837\pi\) | |||||||
\(812\) | 24.9754 | − | 43.2586i | 0.876464 | − | 1.51808i | ||||
\(813\) | 10.8990 | + | 5.02118i | 0.382244 | + | 0.176100i | ||||
\(814\) | −1.56218 | + | 2.70577i | −0.0547543 | + | 0.0948372i | ||||
\(815\) | −6.36396 | − | 3.67423i | −0.222920 | − | 0.128703i | ||||
\(816\) | 21.8695 | + | 30.9282i | 0.765587 | + | 1.08270i | ||||
\(817\) | −5.89230 | − | 7.93782i | −0.206146 | − | 0.277709i | ||||
\(818\) | − | 54.5723i | − | 1.90808i | ||||||
\(819\) | 31.7596 | − | 27.1529i | 1.10977 | − | 0.948799i | ||||
\(820\) | −12.0000 | − | 6.92820i | −0.419058 | − | 0.241943i | ||||
\(821\) | 29.8744 | − | 17.2480i | 1.04262 | − | 0.601958i | 0.122047 | − | 0.992524i | \(-0.461054\pi\) |
0.920575 | + | 0.390566i | \(0.127721\pi\) | |||||||
\(822\) | −2.52520 | + | 0.232673i | −0.0880765 | + | 0.00811540i | ||||
\(823\) | 4.00000 | + | 6.92820i | 0.139431 | + | 0.241502i | 0.927281 | − | 0.374365i | \(-0.122139\pi\) |
−0.787850 | + | 0.615867i | \(0.788806\pi\) | |||||||
\(824\) | − | 5.41662i | − | 0.188697i | ||||||
\(825\) | 1.13681 | + | 1.60770i | 0.0395787 | + | 0.0559728i | ||||
\(826\) | −30.2224 | − | 52.3468i | −1.05157 | − | 1.82138i | ||||
\(827\) | −12.2474 | − | 21.2132i | −0.425886 | − | 0.737655i | 0.570617 | − | 0.821216i | \(-0.306704\pi\) |
−0.996503 | + | 0.0835608i | \(0.973371\pi\) | |||||||
\(828\) | 1.85641 | + | 0.656339i | 0.0645146 | + | 0.0228093i | ||||
\(829\) | 38.6603i | 1.34273i | 0.741129 | + | 0.671363i | \(0.234291\pi\) | ||||
−0.741129 | + | 0.671363i | \(0.765709\pi\) | |||||||
\(830\) | −10.5558 | − | 18.2832i | −0.366398 | − | 0.634621i | ||||
\(831\) | −1.56637 | − | 16.9998i | −0.0543367 | − | 0.589716i | ||||
\(832\) | −18.5263 | + | 10.6962i | −0.642283 | + | 0.370822i | ||||
\(833\) | 29.3939 | + | 16.9706i | 1.01844 | + | 0.587995i | ||||
\(834\) | −4.05131 | − | 43.9689i | −0.140286 | − | 1.52252i | ||||
\(835\) | 10.7846i | 0.373217i | ||||||||
\(836\) | 0.328169 | + | 2.84203i | 0.0113500 | + | 0.0982937i | ||||
\(837\) | 22.3205 | − | 6.31319i | 0.771510 | − | 0.218216i | ||||
\(838\) | −53.6147 | − | 30.9545i | −1.85209 | − | 1.06930i | ||||
\(839\) | 2.87920 | − | 4.98691i | 0.0994009 | − | 0.172167i | −0.812036 | − | 0.583607i | \(-0.801641\pi\) |
0.911437 | + | 0.411440i | \(0.134974\pi\) | |||||||
\(840\) | −1.98004 | + | 4.29788i | −0.0683179 | + | 0.148291i | ||||
\(841\) | −15.3564 | + | 26.5981i | −0.529531 | + | 0.917175i | ||||
\(842\) | −59.3326 | + | 34.2557i | −2.04474 | + | 1.18053i | ||||
\(843\) | −21.3205 | + | 15.0759i | −0.734317 | + | 0.519241i | ||||
\(844\) | 19.0526i | 0.655816i | ||||||||
\(845\) | −1.13681 | + | 0.656339i | −0.0391075 | + | 0.0225787i | ||||
\(846\) | 11.1788 | + | 60.1469i | 0.384336 | + | 2.06789i | ||||
\(847\) | −40.5167 | −1.39217 | ||||||||
\(848\) | −26.9444 | −0.925274 | ||||||||
\(849\) | 34.3830 | + | 15.8403i | 1.18002 | + | 0.543638i | ||||
\(850\) | −24.5885 | − | 14.1962i | −0.843377 | − | 0.486924i | ||||
\(851\) | 0.808643 | + | 1.40061i | 0.0277199 | + | 0.0480123i | ||||
\(852\) | 0.987148 | + | 10.7135i | 0.0338191 | + | 0.367039i | ||||
\(853\) | −9.83975 | + | 17.0429i | −0.336906 | + | 0.583539i | −0.983849 | − | 0.178999i | \(-0.942714\pi\) |
0.646943 | + | 0.762539i | \(0.276047\pi\) | |||||||
\(854\) | −25.4930 | −0.872353 | ||||||||
\(855\) | −12.5851 | + | 13.5505i | −0.430400 | + | 0.463418i | ||||
\(856\) | −2.53590 | −0.0866752 | ||||||||
\(857\) | 1.51575 | − | 2.62536i | 0.0517770 | − | 0.0896804i | −0.838975 | − | 0.544170i | \(-0.816845\pi\) |
0.890752 | + | 0.454489i | \(0.150178\pi\) | |||||||
\(858\) | 0.434174 | + | 4.71209i | 0.0148224 | + | 0.160868i | ||||
\(859\) | 2.33013 | + | 4.03590i | 0.0795029 | + | 0.137703i | 0.903036 | − | 0.429566i | \(-0.141333\pi\) |
−0.823533 | + | 0.567269i | \(0.808000\pi\) | |||||||
\(860\) | −4.81105 | − | 2.77766i | −0.164055 | − | 0.0947174i | ||||
\(861\) | 33.2114 | + | 15.3006i | 1.13184 | + | 0.521442i | ||||
\(862\) | −49.1769 | −1.67497 | ||||||||
\(863\) | 18.2832 | 0.622369 | 0.311184 | − | 0.950350i | \(-0.399274\pi\) | ||||
0.311184 | + | 0.950350i | \(0.399274\pi\) | |||||||
\(864\) | −27.4940 | + | 28.2660i | −0.935366 | + | 0.961629i | ||||
\(865\) | −14.5359 | + | 8.39230i | −0.494235 | + | 0.285347i | ||||
\(866\) | − | 6.45189i | − | 0.219244i | ||||||
\(867\) | −9.89949 | + | 7.00000i | −0.336204 | + | 0.237732i | ||||
\(868\) | −24.9904 | + | 14.4282i | −0.848229 | + | 0.489725i | ||||
\(869\) | 0.669942 | − | 1.16037i | 0.0227262 | − | 0.0393630i | ||||
\(870\) | −15.3006 | + | 33.2114i | −0.518738 | + | 1.12597i | ||||
\(871\) | 1.86603 | − | 3.23205i | 0.0632279 | − | 0.109514i | ||||
\(872\) | −6.45189 | − | 3.72500i | −0.218489 | − | 0.126145i | ||||
\(873\) | −21.1117 | − | 7.46410i | −0.714522 | − | 0.252622i | ||||
\(874\) | 2.92820 | + | 1.26795i | 0.0990480 | + | 0.0428890i | ||||
\(875\) | − | 42.2233i | − | 1.42741i | ||||||
\(876\) | −0.825765 | − | 8.96204i | −0.0279000 | − | 0.302799i | ||||
\(877\) | −3.23205 | − | 1.86603i | −0.109139 | − | 0.0630112i | 0.444437 | − | 0.895810i | \(-0.353404\pi\) |
−0.553576 | + | 0.832799i | \(0.686737\pi\) | |||||||
\(878\) | 37.5832 | − | 21.6987i | 1.26837 | − | 0.732294i | ||||
\(879\) | −4.01314 | − | 43.5546i | −0.135360 | − | 1.46906i | ||||
\(880\) | −1.19615 | − | 2.07180i | −0.0403223 | − | 0.0698403i | ||||
\(881\) | − | 39.8482i | − | 1.34252i | −0.741222 | − | 0.671260i | \(-0.765754\pi\) | ||
0.741222 | − | 0.671260i | \(-0.234246\pi\) | |||||||
\(882\) | −13.3843 | + | 37.8564i | −0.450672 | + | 1.27469i | ||||
\(883\) | 11.1340 | + | 19.2846i | 0.374688 | + | 0.648979i | 0.990280 | − | 0.139086i | \(-0.0444165\pi\) |
−0.615592 | + | 0.788065i | \(0.711083\pi\) | |||||||
\(884\) | −15.8338 | − | 27.4249i | −0.532547 | − | 0.922398i | ||||
\(885\) | 11.8564 | + | 16.7675i | 0.398549 | + | 0.563633i | ||||
\(886\) | − | 74.6410i | − | 2.50761i | ||||||
\(887\) | −5.98502 | − | 10.3664i | −0.200957 | − | 0.348068i | 0.747880 | − | 0.663834i | \(-0.231072\pi\) |
−0.948837 | + | 0.315766i | \(0.897739\pi\) | |||||||
\(888\) | −3.81040 | + | 0.351091i | −0.127869 | + | 0.0117819i | ||||
\(889\) | −25.3923 | + | 14.6603i | −0.851631 | + | 0.491689i | ||||
\(890\) | 17.3867 | + | 10.0382i | 0.582802 | + | 0.336481i | ||||
\(891\) | 1.22539 | + | 3.18269i | 0.0410521 | + | 0.106624i | ||||
\(892\) | 16.2679i | 0.544691i | ||||||||
\(893\) | 5.27792 | + | 45.7081i | 0.176619 | + | 1.52956i | ||||
\(894\) | 32.5885 | + | 46.0870i | 1.08992 | + | 1.54138i | ||||
\(895\) | −1.73205 | − | 1.00000i | −0.0578961 | − | 0.0334263i | ||||
\(896\) | −7.65806 | + | 13.2641i | −0.255838 | + | 0.443124i | ||||
\(897\) | 2.22474 | + | 1.02494i | 0.0742821 | + | 0.0342219i | ||||
\(898\) | 33.3205 | − | 57.7128i | 1.11192 | − | 1.92590i | ||||
\(899\) | 29.8744 | − | 17.2480i | 0.996365 | − | 0.575252i | ||||
\(900\) | 5.19615 | − | 14.6969i | 0.173205 | − | 0.489898i | ||||
\(901\) | − | 29.5692i | − | 0.985094i | ||||||
\(902\) | −3.58630 | + | 2.07055i | −0.119411 | + | 0.0689419i | ||||
\(903\) | 13.3152 | + | 6.13431i | 0.443100 | + | 0.204137i | ||||
\(904\) | 9.66025 | 0.321295 | ||||||||
\(905\) | 4.89898 | 0.162848 | ||||||||
\(906\) | −2.80020 | + | 6.07812i | −0.0930304 | + | 0.201932i | ||||
\(907\) | 35.4449 | + | 20.4641i | 1.17693 | + | 0.679499i | 0.955302 | − | 0.295632i | \(-0.0955304\pi\) |
0.221626 | + | 0.975132i | \(0.428864\pi\) | |||||||
\(908\) | 21.3011 | + | 36.8947i | 0.706903 | + | 1.22439i | ||||
\(909\) | 17.6203 | − | 15.0645i | 0.584430 | − | 0.499658i | ||||
\(910\) | 19.0263 | − | 32.9545i | 0.630715 | − | 1.09243i | ||||
\(911\) | −40.9107 | −1.35543 | −0.677715 | − | 0.735324i | \(-0.737030\pi\) | ||||
−0.677715 | + | 0.735324i | \(0.737030\pi\) | |||||||
\(912\) | −25.1049 | + | 22.4867i | −0.831306 | + | 0.744610i | ||||
\(913\) | −2.92820 | −0.0969094 | ||||||||
\(914\) | −20.0070 | + | 34.6532i | −0.661774 | + | 1.14623i | ||||
\(915\) | 8.62461 | − | 0.794675i | 0.285121 | − | 0.0262711i | ||||
\(916\) | −8.13397 | − | 14.0885i | −0.268754 | − | 0.465496i | ||||
\(917\) | 22.5259 | + | 13.0053i | 0.743870 | + | 0.429474i | ||||
\(918\) | −35.2514 | − | 34.2886i | −1.16347 | − | 1.13169i | ||||
\(919\) | −31.9808 | −1.05495 | −0.527474 | − | 0.849571i | \(-0.676861\pi\) | ||||
−0.527474 | + | 0.849571i | \(0.676861\pi\) | |||||||
\(920\) | −0.277401 | −0.00914565 | ||||||||
\(921\) | 10.0424 | − | 21.7980i | 0.330907 | − | 0.718267i | ||||
\(922\) | 55.0070 | − | 31.7583i | 1.81156 | − | 1.04590i | ||||
\(923\) | 13.3843i | 0.440548i | ||||||||
\(924\) | −2.44949 | − | 3.46410i | −0.0805823 | − | 0.113961i | ||||
\(925\) | 11.0885 | − | 6.40192i | 0.364586 | − | 0.210494i | ||||
\(926\) | −28.5803 | + | 49.5025i | −0.939205 | + | 1.62675i | ||||
\(927\) | 5.73630 | + | 30.8638i | 0.188405 | + | 1.01370i | ||||
\(928\) | −29.3205 | + | 50.7846i | −0.962493 | + | 1.66709i | ||||
\(929\) | 17.7148 | + | 10.2277i | 0.581205 | + | 0.335559i | 0.761612 | − | 0.648033i | \(-0.224408\pi\) |
−0.180407 | + | 0.983592i | \(0.557742\pi\) | |||||||
\(930\) | 17.2480 | − | 12.1962i | 0.565583 | − | 0.399928i | ||||
\(931\) | −12.0000 | + | 27.7128i | −0.393284 | + | 0.908251i | ||||
\(932\) | − | 6.21166i | − | 0.203470i | ||||||
\(933\) | −46.8224 | + | 4.31424i | −1.53290 | + | 0.141242i | ||||
\(934\) | 37.8564 | + | 21.8564i | 1.23870 | + | 0.715163i | ||||
\(935\) | 2.27362 | − | 1.31268i | 0.0743555 | − | 0.0429291i | ||||
\(936\) | −4.40508 | + | 3.76612i | −0.143985 | + | 0.123100i | ||||
\(937\) | −2.89230 | − | 5.00962i | −0.0944875 | − | 0.163657i | 0.814907 | − | 0.579592i | \(-0.196788\pi\) |
−0.909395 | + | 0.415934i | \(0.863455\pi\) | |||||||
\(938\) | 7.20977i | 0.235407i | ||||||||
\(939\) | −35.0507 | + | 24.7846i | −1.14384 | + | 0.808815i | ||||
\(940\) | 12.9282 | + | 22.3923i | 0.421671 | + | 0.730356i | ||||
\(941\) | −6.96953 | − | 12.0716i | −0.227200 | − | 0.393522i | 0.729777 | − | 0.683685i | \(-0.239624\pi\) |
−0.956977 | + | 0.290163i | \(0.906291\pi\) | |||||||
\(942\) | −9.66025 | + | 6.83083i | −0.314748 | + | 0.222561i | ||||
\(943\) | 2.14359i | 0.0698050i | ||||||||
\(944\) | 18.7129 | + | 32.4118i | 0.609055 | + | 1.05491i | ||||
\(945\) | 6.73069 | − | 26.5861i | 0.218949 | − | 0.864846i | ||||
\(946\) | −1.43782 | + | 0.830127i | −0.0467476 | + | 0.0269898i | ||||
\(947\) | 38.3596 | + | 22.1469i | 1.24652 | + | 0.719679i | 0.970414 | − | 0.241448i | \(-0.0776223\pi\) |
0.276107 | + | 0.961127i | \(0.410956\pi\) | |||||||
\(948\) | −10.5630 | + | 0.973274i | −0.343069 | + | 0.0316105i | ||||
\(949\) | − | 11.1962i | − | 0.363442i | ||||||
\(950\) | 10.0382 | − | 23.1822i | 0.325682 | − | 0.752131i | ||||
\(951\) | −19.4641 | + | 13.7632i | −0.631167 | + | 0.446302i | ||||
\(952\) | −8.19615 | − | 4.73205i | −0.265639 | − | 0.153367i | ||||
\(953\) | 21.3011 | − | 36.8947i | 0.690011 | − | 1.19513i | −0.281822 | − | 0.959467i | \(-0.590939\pi\) |
0.971834 | − | 0.235668i | \(-0.0757279\pi\) | |||||||
\(954\) | 34.3918 | − | 6.39201i | 1.11348 | − | 0.206949i | ||||
\(955\) | −1.19615 | + | 2.07180i | −0.0387066 | + | 0.0670418i | ||||
\(956\) | −44.9638 | + | 25.9599i | −1.45423 | + | 0.839602i | ||||
\(957\) | 2.92820 | + | 4.14110i | 0.0946554 | + | 0.133863i | ||||
\(958\) | 22.9282i | 0.740777i | ||||||||
\(959\) | 2.44949 | − | 1.41421i | 0.0790981 | − | 0.0456673i | ||||
\(960\) | −5.87503 | + | 12.7524i | −0.189616 | + | 0.411580i | ||||
\(961\) | 11.0718 | 0.357155 | ||||||||
\(962\) | 30.7709 | 0.992094 | ||||||||
\(963\) | 14.4495 | − | 2.68556i | 0.465628 | − | 0.0865410i | ||||
\(964\) | 42.9904 | + | 24.8205i | 1.38463 | + | 0.799415i | ||||
\(965\) | −9.33109 | − | 16.1619i | −0.300378 | − | 0.520271i | ||||
\(966\) | −4.71209 | + | 0.434174i | −0.151609 | + | 0.0139693i | ||||
\(967\) | 4.40192 | − | 7.62436i | 0.141556 | − | 0.245183i | −0.786527 | − | 0.617556i | \(-0.788123\pi\) |
0.928083 | + | 0.372374i | \(0.121456\pi\) | |||||||
\(968\) | 5.61969 | 0.180624 | ||||||||
\(969\) | −24.6773 | − | 27.5505i | −0.792749 | − | 0.885050i | ||||
\(970\) | −20.3923 | −0.654757 | ||||||||
\(971\) | −7.17260 | + | 12.4233i | −0.230180 | + | 0.398683i | −0.957861 | − | 0.287232i | \(-0.907265\pi\) |
0.727681 | + | 0.685916i | \(0.240598\pi\) | |||||||
\(972\) | 14.9722 | − | 22.4685i | 0.480233 | − | 0.720677i | ||||
\(973\) | 24.6244 | + | 42.6506i | 0.789421 | + | 1.36732i | ||||
\(974\) | −41.7057 | − | 24.0788i | −1.33634 | − | 0.771534i | ||||
\(975\) | 8.11435 | − | 17.6130i | 0.259867 | − | 0.564068i | ||||
\(976\) | 15.7846 | 0.505253 | ||||||||
\(977\) | 20.3538 | 0.651176 | 0.325588 | − | 0.945512i | \(-0.394438\pi\) | ||||
0.325588 | + | 0.945512i | \(0.394438\pi\) | |||||||
\(978\) | 15.7914 | + | 7.27513i | 0.504954 | + | 0.232633i | ||||
\(979\) | 2.41154 | − | 1.39230i | 0.0770732 | − | 0.0444983i | ||||
\(980\) | 16.9706i | 0.542105i | ||||||||
\(981\) | 40.7076 | + | 14.3923i | 1.29969 | + | 0.459511i | ||||
\(982\) | 16.7321 | − | 9.66025i | 0.533941 | − | 0.308271i | ||||
\(983\) | 16.2635 | − | 28.1691i | 0.518724 | − | 0.898456i | −0.481040 | − | 0.876699i | \(-0.659741\pi\) |
0.999763 | − | 0.0217569i | \(-0.00692599\pi\) | |||||||
\(984\) | −4.60645 | − | 2.12220i | −0.146848 | − | 0.0676533i | ||||
\(985\) | 6.46410 | − | 11.1962i | 0.205963 | − | 0.356739i | ||||
\(986\) | −63.3350 | − | 36.5665i | −2.01700 | − | 1.16451i | ||||
\(987\) | −39.3949 | − | 55.7128i | −1.25395 | − | 1.77336i | ||||
\(988\) | 22.6244 | − | 16.7942i | 0.719777 | − | 0.534296i | ||||
\(989\) | 0.859411i | 0.0273277i | ||||||||
\(990\) | 2.01826 | + | 2.36068i | 0.0641445 | + | 0.0750272i | ||||
\(991\) | −3.61731 | − | 2.08846i | −0.114908 | − | 0.0663420i | 0.441445 | − | 0.897289i | \(-0.354466\pi\) |
−0.556352 | + | 0.830946i | \(0.687800\pi\) | |||||||
\(992\) | 29.3381 | − | 16.9384i | 0.931487 | − | 0.537794i | ||||
\(993\) | −55.0680 | + | 5.07399i | −1.74753 | + | 0.161018i | ||||
\(994\) | −12.9282 | − | 22.3923i | −0.410058 | − | 0.710241i | ||||
\(995\) | − | 18.1074i | − | 0.574042i | ||||||
\(996\) | 13.3843 | + | 18.9282i | 0.424097 | + | 0.599763i | ||||
\(997\) | −25.0885 | − | 43.4545i | −0.794559 | − | 1.37622i | −0.923119 | − | 0.384515i | \(-0.874369\pi\) |
0.128559 | − | 0.991702i | \(-0.458965\pi\) | |||||||
\(998\) | −15.5749 | − | 26.9766i | −0.493016 | − | 0.853928i | ||||
\(999\) | 21.3397 | − | 6.03579i | 0.675160 | − | 0.190964i |
(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 | 57.2.f.a.8.4 | yes | 8 | |
3.2 | odd | 2 | inner | 57.2.f.a.8.1 | ✓ | 8 | |
4.3 | odd | 2 | 912.2.bn.m.65.2 | 8 | |||
12.11 | even | 2 | 912.2.bn.m.65.1 | 8 | |||
19.8 | odd | 6 | 1083.2.d.b.1082.8 | 8 | |||
19.11 | even | 3 | 1083.2.d.b.1082.1 | 8 | |||
19.12 | odd | 6 | inner | 57.2.f.a.50.1 | yes | 8 | |
57.8 | even | 6 | 1083.2.d.b.1082.2 | 8 | |||
57.11 | odd | 6 | 1083.2.d.b.1082.7 | 8 | |||
57.50 | even | 6 | inner | 57.2.f.a.50.4 | yes | 8 | |
76.31 | even | 6 | 912.2.bn.m.449.1 | 8 | |||
228.107 | odd | 6 | 912.2.bn.m.449.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.f.a.8.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
57.2.f.a.8.4 | yes | 8 | 1.1 | even | 1 | trivial | |
57.2.f.a.50.1 | yes | 8 | 19.12 | odd | 6 | inner | |
57.2.f.a.50.4 | yes | 8 | 57.50 | even | 6 | inner | |
912.2.bn.m.65.1 | 8 | 12.11 | even | 2 | |||
912.2.bn.m.65.2 | 8 | 4.3 | odd | 2 | |||
912.2.bn.m.449.1 | 8 | 76.31 | even | 6 | |||
912.2.bn.m.449.2 | 8 | 228.107 | odd | 6 | |||
1083.2.d.b.1082.1 | 8 | 19.11 | even | 3 | |||
1083.2.d.b.1082.2 | 8 | 57.8 | even | 6 | |||
1083.2.d.b.1082.7 | 8 | 57.11 | odd | 6 | |||
1083.2.d.b.1082.8 | 8 | 19.8 | odd | 6 |