Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(131,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.131");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 131.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.131 |
Dual form | 280.2.bj.b.171.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 1.00000i | ||||||
\(3\) | −0.275255 | + | 0.158919i | −0.158919 | + | 0.0917517i | −0.577350 | − | 0.816497i | \(-0.695913\pi\) |
0.418432 | + | 0.908248i | \(0.362580\pi\) | |||||||
\(4\) | −2.00000 | −1.00000 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.224745 | + | 0.389270i | 0.0917517 | + | 0.158919i | ||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | −1.44949 | + | 2.51059i | −0.483163 | + | 0.836863i | ||||
\(10\) | 1.22474 | + | 0.707107i | 0.387298 | + | 0.223607i | ||||
\(11\) | −2.44949 | − | 4.24264i | −0.738549 | − | 1.27920i | −0.953149 | − | 0.302502i | \(-0.902178\pi\) |
0.214600 | − | 0.976702i | \(-0.431155\pi\) | |||||||
\(12\) | 0.550510 | − | 0.317837i | 0.158919 | − | 0.0917517i | ||||
\(13\) | −4.44949 | −1.23407 | −0.617033 | − | 0.786937i | \(-0.711666\pi\) | ||||
−0.617033 | + | 0.786937i | \(0.711666\pi\) | |||||||
\(14\) | −1.22474 | + | 3.53553i | −0.327327 | + | 0.944911i | ||||
\(15\) | − | 0.317837i | − | 0.0820652i | ||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −4.22474 | + | 2.43916i | −1.02465 | + | 0.591583i | −0.915448 | − | 0.402437i | \(-0.868163\pi\) |
−0.109203 | + | 0.994019i | \(0.534830\pi\) | |||||||
\(18\) | 3.55051 | + | 2.04989i | 0.836863 | + | 0.483163i | ||||
\(19\) | 3.67423 | + | 2.12132i | 0.842927 | + | 0.486664i | 0.858258 | − | 0.513218i | \(-0.171547\pi\) |
−0.0153309 | + | 0.999882i | \(0.504880\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 0.825765 | − | 0.158919i | 0.180197 | − | 0.0346789i | ||||
\(22\) | −6.00000 | + | 3.46410i | −1.27920 | + | 0.738549i | ||||
\(23\) | 3.94949 | + | 2.28024i | 0.823526 | + | 0.475463i | 0.851631 | − | 0.524142i | \(-0.175614\pi\) |
−0.0281052 | + | 0.999605i | \(0.508947\pi\) | |||||||
\(24\) | −0.449490 | − | 0.778539i | −0.0917517 | − | 0.158919i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 6.29253i | 1.23407i | ||||||||
\(27\) | − | 1.87492i | − | 0.360828i | ||||||
\(28\) | 5.00000 | + | 1.73205i | 0.944911 | + | 0.327327i | ||||
\(29\) | − | 7.24604i | − | 1.34556i | −0.739844 | − | 0.672778i | \(-0.765101\pi\) | ||
0.739844 | − | 0.672778i | \(-0.234899\pi\) | |||||||
\(30\) | −0.449490 | −0.0820652 | ||||||||
\(31\) | −0.775255 | − | 1.34278i | −0.139240 | − | 0.241171i | 0.787969 | − | 0.615715i | \(-0.211133\pi\) |
−0.927209 | + | 0.374544i | \(0.877799\pi\) | |||||||
\(32\) | − | 5.65685i | − | 1.00000i | ||||||
\(33\) | 1.34847 | + | 0.778539i | 0.234738 | + | 0.135526i | ||||
\(34\) | 3.44949 | + | 5.97469i | 0.591583 | + | 1.02465i | ||||
\(35\) | 2.00000 | − | 1.73205i | 0.338062 | − | 0.292770i | ||||
\(36\) | 2.89898 | − | 5.02118i | 0.483163 | − | 0.836863i | ||||
\(37\) | −3.00000 | − | 1.73205i | −0.493197 | − | 0.284747i | 0.232703 | − | 0.972548i | \(-0.425243\pi\) |
−0.725900 | + | 0.687800i | \(0.758576\pi\) | |||||||
\(38\) | 3.00000 | − | 5.19615i | 0.486664 | − | 0.842927i | ||||
\(39\) | 1.22474 | − | 0.707107i | 0.196116 | − | 0.113228i | ||||
\(40\) | −2.44949 | − | 1.41421i | −0.387298 | − | 0.223607i | ||||
\(41\) | 8.02458i | 1.25323i | 0.779329 | + | 0.626614i | \(0.215560\pi\) | ||||
−0.779329 | + | 0.626614i | \(0.784440\pi\) | |||||||
\(42\) | −0.224745 | − | 1.16781i | −0.0346789 | − | 0.180197i | ||||
\(43\) | −9.44949 | −1.44103 | −0.720517 | − | 0.693437i | \(-0.756095\pi\) | ||||
−0.720517 | + | 0.693437i | \(0.756095\pi\) | |||||||
\(44\) | 4.89898 | + | 8.48528i | 0.738549 | + | 1.27920i | ||||
\(45\) | −1.44949 | − | 2.51059i | −0.216077 | − | 0.374257i | ||||
\(46\) | 3.22474 | − | 5.58542i | 0.475463 | − | 0.823526i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | −1.10102 | + | 0.635674i | −0.158919 | + | 0.0917517i | ||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | −1.22474 | + | 0.707107i | −0.173205 | + | 0.100000i | ||||
\(51\) | 0.775255 | − | 1.34278i | 0.108557 | − | 0.188027i | ||||
\(52\) | 8.89898 | 1.23407 | ||||||||
\(53\) | −1.77526 | + | 1.02494i | −0.243850 | + | 0.140787i | −0.616945 | − | 0.787006i | \(-0.711630\pi\) |
0.373095 | + | 0.927793i | \(0.378297\pi\) | |||||||
\(54\) | −2.65153 | −0.360828 | ||||||||
\(55\) | 4.89898 | 0.660578 | ||||||||
\(56\) | 2.44949 | − | 7.07107i | 0.327327 | − | 0.944911i | ||||
\(57\) | −1.34847 | −0.178609 | ||||||||
\(58\) | −10.2474 | −1.34556 | ||||||||
\(59\) | 3.12372 | − | 1.80348i | 0.406674 | − | 0.234794i | −0.282686 | − | 0.959213i | \(-0.591225\pi\) |
0.689360 | + | 0.724419i | \(0.257892\pi\) | |||||||
\(60\) | 0.635674i | 0.0820652i | ||||||||
\(61\) | 0.174235 | − | 0.301783i | 0.0223085 | − | 0.0386394i | −0.854656 | − | 0.519195i | \(-0.826232\pi\) |
0.876964 | + | 0.480556i | \(0.159565\pi\) | |||||||
\(62\) | −1.89898 | + | 1.09638i | −0.241171 | + | 0.139240i | ||||
\(63\) | 5.79796 | − | 5.02118i | 0.730474 | − | 0.632609i | ||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 2.22474 | − | 3.85337i | 0.275946 | − | 0.477952i | ||||
\(66\) | 1.10102 | − | 1.90702i | 0.135526 | − | 0.234738i | ||||
\(67\) | −6.17423 | − | 10.6941i | −0.754303 | − | 1.30649i | −0.945720 | − | 0.324982i | \(-0.894642\pi\) |
0.191417 | − | 0.981509i | \(-0.438692\pi\) | |||||||
\(68\) | 8.44949 | − | 4.87832i | 1.02465 | − | 0.591583i | ||||
\(69\) | −1.44949 | −0.174498 | ||||||||
\(70\) | −2.44949 | − | 2.82843i | −0.292770 | − | 0.338062i | ||||
\(71\) | 1.41421i | 0.167836i | 0.996473 | + | 0.0839181i | \(0.0267434\pi\) | ||||
−0.996473 | + | 0.0839181i | \(0.973257\pi\) | |||||||
\(72\) | −7.10102 | − | 4.09978i | −0.836863 | − | 0.483163i | ||||
\(73\) | −9.67423 | + | 5.58542i | −1.13228 | + | 0.653724i | −0.944508 | − | 0.328488i | \(-0.893461\pi\) |
−0.187775 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(74\) | −2.44949 | + | 4.24264i | −0.284747 | + | 0.493197i | ||||
\(75\) | 0.275255 | + | 0.158919i | 0.0317837 | + | 0.0183503i | ||||
\(76\) | −7.34847 | − | 4.24264i | −0.842927 | − | 0.486664i | ||||
\(77\) | 2.44949 | + | 12.7279i | 0.279145 | + | 1.45048i | ||||
\(78\) | −1.00000 | − | 1.73205i | −0.113228 | − | 0.196116i | ||||
\(79\) | −6.67423 | − | 3.85337i | −0.750910 | − | 0.433538i | 0.0751126 | − | 0.997175i | \(-0.476068\pi\) |
−0.826023 | + | 0.563637i | \(0.809402\pi\) | |||||||
\(80\) | −2.00000 | + | 3.46410i | −0.223607 | + | 0.387298i | ||||
\(81\) | −4.05051 | − | 7.01569i | −0.450057 | − | 0.779521i | ||||
\(82\) | 11.3485 | 1.25323 | ||||||||
\(83\) | 1.87492i | 0.205799i | 0.994692 | + | 0.102899i | \(0.0328120\pi\) | ||||
−0.994692 | + | 0.102899i | \(0.967188\pi\) | |||||||
\(84\) | −1.65153 | + | 0.317837i | −0.180197 | + | 0.0346789i | ||||
\(85\) | − | 4.87832i | − | 0.529128i | ||||||
\(86\) | 13.3636i | 1.44103i | ||||||||
\(87\) | 1.15153 | + | 1.99451i | 0.123457 | + | 0.213834i | ||||
\(88\) | 12.0000 | − | 6.92820i | 1.27920 | − | 0.738549i | ||||
\(89\) | 9.39898 | + | 5.42650i | 0.996290 | + | 0.575208i | 0.907148 | − | 0.420811i | \(-0.138254\pi\) |
0.0891414 | + | 0.996019i | \(0.471588\pi\) | |||||||
\(90\) | −3.55051 | + | 2.04989i | −0.374257 | + | 0.216077i | ||||
\(91\) | 11.1237 | + | 3.85337i | 1.16608 | + | 0.403943i | ||||
\(92\) | −7.89898 | − | 4.56048i | −0.823526 | − | 0.475463i | ||||
\(93\) | 0.426786 | + | 0.246405i | 0.0442556 | + | 0.0255510i | ||||
\(94\) | −7.34847 | − | 4.24264i | −0.757937 | − | 0.437595i | ||||
\(95\) | −3.67423 | + | 2.12132i | −0.376969 | + | 0.217643i | ||||
\(96\) | 0.898979 | + | 1.55708i | 0.0917517 | + | 0.158919i | ||||
\(97\) | − | 11.9494i | − | 1.21328i | −0.794978 | − | 0.606638i | \(-0.792518\pi\) | ||
0.794978 | − | 0.606638i | \(-0.207482\pi\) | |||||||
\(98\) | 6.12372 | − | 7.77817i | 0.618590 | − | 0.785714i | ||||
\(99\) | 14.2020 | 1.42736 | ||||||||
\(100\) | 1.00000 | + | 1.73205i | 0.100000 | + | 0.173205i | ||||
\(101\) | 7.62372 | + | 13.2047i | 0.758589 | + | 1.31391i | 0.943570 | + | 0.331173i | \(0.107444\pi\) |
−0.184981 | + | 0.982742i | \(0.559222\pi\) | |||||||
\(102\) | −1.89898 | − | 1.09638i | −0.188027 | − | 0.108557i | ||||
\(103\) | −8.39898 | + | 14.5475i | −0.827576 | + | 1.43340i | 0.0723585 | + | 0.997379i | \(0.476947\pi\) |
−0.899935 | + | 0.436025i | \(0.856386\pi\) | |||||||
\(104\) | − | 12.5851i | − | 1.23407i | ||||||
\(105\) | −0.275255 | + | 0.794593i | −0.0268622 | + | 0.0775443i | ||||
\(106\) | 1.44949 | + | 2.51059i | 0.140787 | + | 0.243850i | ||||
\(107\) | 2.72474 | − | 4.71940i | 0.263411 | − | 0.456241i | −0.703735 | − | 0.710462i | \(-0.748486\pi\) |
0.967146 | + | 0.254221i | \(0.0818191\pi\) | |||||||
\(108\) | 3.74983i | 0.360828i | ||||||||
\(109\) | −6.82577 | + | 3.94086i | −0.653790 | + | 0.377466i | −0.789907 | − | 0.613227i | \(-0.789871\pi\) |
0.136117 | + | 0.990693i | \(0.456538\pi\) | |||||||
\(110\) | − | 6.92820i | − | 0.660578i | ||||||
\(111\) | 1.10102 | 0.104504 | ||||||||
\(112\) | −10.0000 | − | 3.46410i | −0.944911 | − | 0.327327i | ||||
\(113\) | 8.44949 | 0.794861 | 0.397431 | − | 0.917632i | \(-0.369902\pi\) | ||||
0.397431 | + | 0.917632i | \(0.369902\pi\) | |||||||
\(114\) | 1.90702i | 0.178609i | ||||||||
\(115\) | −3.94949 | + | 2.28024i | −0.368292 | + | 0.212633i | ||||
\(116\) | 14.4921i | 1.34556i | ||||||||
\(117\) | 6.44949 | − | 11.1708i | 0.596256 | − | 1.03274i | ||||
\(118\) | −2.55051 | − | 4.41761i | −0.234794 | − | 0.406674i | ||||
\(119\) | 12.6742 | − | 2.43916i | 1.16185 | − | 0.223597i | ||||
\(120\) | 0.898979 | 0.0820652 | ||||||||
\(121\) | −6.50000 | + | 11.2583i | −0.590909 | + | 1.02348i | ||||
\(122\) | −0.426786 | − | 0.246405i | −0.0386394 | − | 0.0223085i | ||||
\(123\) | −1.27526 | − | 2.20881i | −0.114986 | − | 0.199161i | ||||
\(124\) | 1.55051 | + | 2.68556i | 0.139240 | + | 0.241171i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −7.10102 | − | 8.19955i | −0.632609 | − | 0.730474i | ||||
\(127\) | 6.92820i | 0.614779i | 0.951584 | + | 0.307389i | \(0.0994554\pi\) | ||||
−0.951584 | + | 0.307389i | \(0.900545\pi\) | |||||||
\(128\) | 11.3137i | 1.00000i | ||||||||
\(129\) | 2.60102 | − | 1.50170i | 0.229007 | − | 0.132217i | ||||
\(130\) | −5.44949 | − | 3.14626i | −0.477952 | − | 0.275946i | ||||
\(131\) | −9.79796 | − | 5.65685i | −0.856052 | − | 0.494242i | 0.00663646 | − | 0.999978i | \(-0.497888\pi\) |
−0.862688 | + | 0.505736i | \(0.831221\pi\) | |||||||
\(132\) | −2.69694 | − | 1.55708i | −0.234738 | − | 0.135526i | ||||
\(133\) | −7.34847 | − | 8.48528i | −0.637193 | − | 0.735767i | ||||
\(134\) | −15.1237 | + | 8.73169i | −1.30649 | + | 0.754303i | ||||
\(135\) | 1.62372 | + | 0.937458i | 0.139748 | + | 0.0806835i | ||||
\(136\) | −6.89898 | − | 11.9494i | −0.591583 | − | 1.02465i | ||||
\(137\) | 4.89898 | + | 8.48528i | 0.418548 | + | 0.724947i | 0.995794 | − | 0.0916241i | \(-0.0292058\pi\) |
−0.577246 | + | 0.816571i | \(0.695872\pi\) | |||||||
\(138\) | 2.04989i | 0.174498i | ||||||||
\(139\) | 6.92820i | 0.587643i | 0.955860 | + | 0.293821i | \(0.0949270\pi\) | ||||
−0.955860 | + | 0.293821i | \(0.905073\pi\) | |||||||
\(140\) | −4.00000 | + | 3.46410i | −0.338062 | + | 0.292770i | ||||
\(141\) | 1.90702i | 0.160600i | ||||||||
\(142\) | 2.00000 | 0.167836 | ||||||||
\(143\) | 10.8990 | + | 18.8776i | 0.911418 | + | 1.57862i | ||||
\(144\) | −5.79796 | + | 10.0424i | −0.483163 | + | 0.836863i | ||||
\(145\) | 6.27526 | + | 3.62302i | 0.521132 | + | 0.300875i | ||||
\(146\) | 7.89898 | + | 13.6814i | 0.653724 | + | 1.13228i | ||||
\(147\) | −2.20204 | − | 0.317837i | −0.181621 | − | 0.0262148i | ||||
\(148\) | 6.00000 | + | 3.46410i | 0.493197 | + | 0.284747i | ||||
\(149\) | 16.6237 | + | 9.59771i | 1.36187 | + | 0.786275i | 0.989873 | − | 0.141959i | \(-0.0453402\pi\) |
0.371996 | + | 0.928234i | \(0.378673\pi\) | |||||||
\(150\) | 0.224745 | − | 0.389270i | 0.0183503 | − | 0.0317837i | ||||
\(151\) | −6.67423 | + | 3.85337i | −0.543142 | + | 0.313583i | −0.746351 | − | 0.665552i | \(-0.768196\pi\) |
0.203210 | + | 0.979135i | \(0.434863\pi\) | |||||||
\(152\) | −6.00000 | + | 10.3923i | −0.486664 | + | 0.842927i | ||||
\(153\) | − | 14.1421i | − | 1.14332i | ||||||
\(154\) | 18.0000 | − | 3.46410i | 1.45048 | − | 0.279145i | ||||
\(155\) | 1.55051 | 0.124540 | ||||||||
\(156\) | −2.44949 | + | 1.41421i | −0.196116 | + | 0.113228i | ||||
\(157\) | 5.34847 | + | 9.26382i | 0.426854 | + | 0.739333i | 0.996592 | − | 0.0824935i | \(-0.0262884\pi\) |
−0.569737 | + | 0.821827i | \(0.692955\pi\) | |||||||
\(158\) | −5.44949 | + | 9.43879i | −0.433538 | + | 0.750910i | ||||
\(159\) | 0.325765 | − | 0.564242i | 0.0258349 | − | 0.0447473i | ||||
\(160\) | 4.89898 | + | 2.82843i | 0.387298 | + | 0.223607i | ||||
\(161\) | −7.89898 | − | 9.12096i | −0.622527 | − | 0.718832i | ||||
\(162\) | −9.92168 | + | 5.72829i | −0.779521 | + | 0.450057i | ||||
\(163\) | −2.89898 | + | 5.02118i | −0.227066 | + | 0.393289i | −0.956937 | − | 0.290295i | \(-0.906247\pi\) |
0.729872 | + | 0.683584i | \(0.239580\pi\) | |||||||
\(164\) | − | 16.0492i | − | 1.25323i | ||||||
\(165\) | −1.34847 | + | 0.778539i | −0.104978 | + | 0.0606092i | ||||
\(166\) | 2.65153 | 0.205799 | ||||||||
\(167\) | −3.00000 | −0.232147 | −0.116073 | − | 0.993241i | \(-0.537031\pi\) | ||||
−0.116073 | + | 0.993241i | \(0.537031\pi\) | |||||||
\(168\) | 0.449490 | + | 2.33562i | 0.0346789 | + | 0.180197i | ||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | −6.89898 | −0.529128 | ||||||||
\(171\) | −10.6515 | + | 6.14966i | −0.814543 | + | 0.470277i | ||||
\(172\) | 18.8990 | 1.44103 | ||||||||
\(173\) | −5.44949 | + | 9.43879i | −0.414317 | + | 0.717618i | −0.995356 | − | 0.0962572i | \(-0.969313\pi\) |
0.581039 | + | 0.813875i | \(0.302646\pi\) | |||||||
\(174\) | 2.82066 | − | 1.62851i | 0.213834 | − | 0.123457i | ||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | −9.79796 | − | 16.9706i | −0.738549 | − | 1.27920i | ||||
\(177\) | −0.573214 | + | 0.992836i | −0.0430854 | + | 0.0746261i | ||||
\(178\) | 7.67423 | − | 13.2922i | 0.575208 | − | 0.996290i | ||||
\(179\) | −4.77526 | − | 8.27098i | −0.356919 | − | 0.618202i | 0.630525 | − | 0.776169i | \(-0.282840\pi\) |
−0.987444 | + | 0.157966i | \(0.949506\pi\) | |||||||
\(180\) | 2.89898 | + | 5.02118i | 0.216077 | + | 0.374257i | ||||
\(181\) | −12.3485 | −0.917854 | −0.458927 | − | 0.888474i | \(-0.651766\pi\) | ||||
−0.458927 | + | 0.888474i | \(0.651766\pi\) | |||||||
\(182\) | 5.44949 | − | 15.7313i | 0.403943 | − | 1.16608i | ||||
\(183\) | 0.110756i | 0.00818736i | ||||||||
\(184\) | −6.44949 | + | 11.1708i | −0.475463 | + | 0.823526i | ||||
\(185\) | 3.00000 | − | 1.73205i | 0.220564 | − | 0.127343i | ||||
\(186\) | 0.348469 | − | 0.603566i | 0.0255510 | − | 0.0442556i | ||||
\(187\) | 20.6969 | + | 11.9494i | 1.51351 | + | 0.873825i | ||||
\(188\) | −6.00000 | + | 10.3923i | −0.437595 | + | 0.757937i | ||||
\(189\) | −1.62372 | + | 4.68729i | −0.118109 | + | 0.340950i | ||||
\(190\) | 3.00000 | + | 5.19615i | 0.217643 | + | 0.376969i | ||||
\(191\) | −22.8990 | − | 13.2207i | −1.65691 | − | 0.956619i | −0.974128 | − | 0.225999i | \(-0.927435\pi\) |
−0.682784 | − | 0.730620i | \(-0.739231\pi\) | |||||||
\(192\) | 2.20204 | − | 1.27135i | 0.158919 | − | 0.0917517i | ||||
\(193\) | −11.3485 | − | 19.6561i | −0.816881 | − | 1.41488i | −0.907970 | − | 0.419036i | \(-0.862368\pi\) |
0.0910889 | − | 0.995843i | \(-0.470965\pi\) | |||||||
\(194\) | −16.8990 | −1.21328 | ||||||||
\(195\) | 1.41421i | 0.101274i | ||||||||
\(196\) | −11.0000 | − | 8.66025i | −0.785714 | − | 0.618590i | ||||
\(197\) | − | 0.921404i | − | 0.0656473i | −0.999461 | − | 0.0328236i | \(-0.989550\pi\) | ||
0.999461 | − | 0.0328236i | \(-0.0104500\pi\) | |||||||
\(198\) | − | 20.0847i | − | 1.42736i | ||||||
\(199\) | −12.3485 | − | 21.3882i | −0.875360 | − | 1.51617i | −0.856379 | − | 0.516348i | \(-0.827291\pi\) |
−0.0189808 | − | 0.999820i | \(-0.506042\pi\) | |||||||
\(200\) | 2.44949 | − | 1.41421i | 0.173205 | − | 0.100000i | ||||
\(201\) | 3.39898 | + | 1.96240i | 0.239746 | + | 0.138417i | ||||
\(202\) | 18.6742 | − | 10.7816i | 1.31391 | − | 0.758589i | ||||
\(203\) | −6.27526 | + | 18.1151i | −0.440437 | + | 1.27143i | ||||
\(204\) | −1.55051 | + | 2.68556i | −0.108557 | + | 0.188027i | ||||
\(205\) | −6.94949 | − | 4.01229i | −0.485373 | − | 0.280230i | ||||
\(206\) | 20.5732 | + | 11.8780i | 1.43340 | + | 0.827576i | ||||
\(207\) | −11.4495 | + | 6.61037i | −0.795795 | + | 0.459452i | ||||
\(208\) | −17.7980 | −1.23407 | ||||||||
\(209\) | − | 20.7846i | − | 1.43770i | ||||||
\(210\) | 1.12372 | + | 0.389270i | 0.0775443 | + | 0.0268622i | ||||
\(211\) | 8.24745 | 0.567778 | 0.283889 | − | 0.958857i | \(-0.408375\pi\) | ||||
0.283889 | + | 0.958857i | \(0.408375\pi\) | |||||||
\(212\) | 3.55051 | − | 2.04989i | 0.243850 | − | 0.140787i | ||||
\(213\) | −0.224745 | − | 0.389270i | −0.0153993 | − | 0.0266723i | ||||
\(214\) | −6.67423 | − | 3.85337i | −0.456241 | − | 0.263411i | ||||
\(215\) | 4.72474 | − | 8.18350i | 0.322225 | − | 0.558110i | ||||
\(216\) | 5.30306 | 0.360828 | ||||||||
\(217\) | 0.775255 | + | 4.02834i | 0.0526277 | + | 0.273462i | ||||
\(218\) | 5.57321 | + | 9.65309i | 0.377466 | + | 0.653790i | ||||
\(219\) | 1.77526 | − | 3.07483i | 0.119961 | − | 0.207778i | ||||
\(220\) | −9.79796 | −0.660578 | ||||||||
\(221\) | 18.7980 | − | 10.8530i | 1.26449 | − | 0.730052i | ||||
\(222\) | − | 1.55708i | − | 0.104504i | ||||||
\(223\) | 24.6969 | 1.65383 | 0.826915 | − | 0.562327i | \(-0.190094\pi\) | ||||
0.826915 | + | 0.562327i | \(0.190094\pi\) | |||||||
\(224\) | −4.89898 | + | 14.1421i | −0.327327 | + | 0.944911i | ||||
\(225\) | 2.89898 | 0.193265 | ||||||||
\(226\) | − | 11.9494i | − | 0.794861i | ||||||
\(227\) | −9.24745 | + | 5.33902i | −0.613775 | + | 0.354363i | −0.774441 | − | 0.632646i | \(-0.781969\pi\) |
0.160667 | + | 0.987009i | \(0.448636\pi\) | |||||||
\(228\) | 2.69694 | 0.178609 | ||||||||
\(229\) | 8.34847 | − | 14.4600i | 0.551682 | − | 0.955542i | −0.446471 | − | 0.894798i | \(-0.647319\pi\) |
0.998153 | − | 0.0607438i | \(-0.0193473\pi\) | |||||||
\(230\) | 3.22474 | + | 5.58542i | 0.212633 | + | 0.368292i | ||||
\(231\) | −2.69694 | − | 3.11416i | −0.177446 | − | 0.204896i | ||||
\(232\) | 20.4949 | 1.34556 | ||||||||
\(233\) | 0.123724 | − | 0.214297i | 0.00810545 | − | 0.0140391i | −0.861944 | − | 0.507003i | \(-0.830753\pi\) |
0.870050 | + | 0.492964i | \(0.164087\pi\) | |||||||
\(234\) | −15.7980 | − | 9.12096i | −1.03274 | − | 0.596256i | ||||
\(235\) | 3.00000 | + | 5.19615i | 0.195698 | + | 0.338960i | ||||
\(236\) | −6.24745 | + | 3.60697i | −0.406674 | + | 0.234794i | ||||
\(237\) | 2.44949 | 0.159111 | ||||||||
\(238\) | −3.44949 | − | 17.9241i | −0.223597 | − | 1.16185i | ||||
\(239\) | 3.32124i | 0.214833i | 0.994214 | + | 0.107416i | \(0.0342578\pi\) | ||||
−0.994214 | + | 0.107416i | \(0.965742\pi\) | |||||||
\(240\) | − | 1.27135i | − | 0.0820652i | ||||||
\(241\) | −17.6969 | + | 10.2173i | −1.13996 | + | 0.658156i | −0.946421 | − | 0.322936i | \(-0.895330\pi\) |
−0.193539 | + | 0.981093i | \(0.561997\pi\) | |||||||
\(242\) | 15.9217 | + | 9.19239i | 1.02348 | + | 0.590909i | ||||
\(243\) | 7.10102 | + | 4.09978i | 0.455531 | + | 0.263001i | ||||
\(244\) | −0.348469 | + | 0.603566i | −0.0223085 | + | 0.0386394i | ||||
\(245\) | −6.50000 | + | 2.59808i | −0.415270 | + | 0.165985i | ||||
\(246\) | −3.12372 | + | 1.80348i | −0.199161 | + | 0.114986i | ||||
\(247\) | −16.3485 | − | 9.43879i | −1.04023 | − | 0.600576i | ||||
\(248\) | 3.79796 | − | 2.19275i | 0.241171 | − | 0.139240i | ||||
\(249\) | −0.297959 | − | 0.516080i | −0.0188824 | − | 0.0327052i | ||||
\(250\) | − | 1.41421i | − | 0.0894427i | ||||||
\(251\) | − | 13.7135i | − | 0.865591i | −0.901492 | − | 0.432796i | \(-0.857527\pi\) | ||
0.901492 | − | 0.432796i | \(-0.142473\pi\) | |||||||
\(252\) | −11.5959 | + | 10.0424i | −0.730474 | + | 0.632609i | ||||
\(253\) | − | 22.3417i | − | 1.40461i | ||||||
\(254\) | 9.79796 | 0.614779 | ||||||||
\(255\) | 0.775255 | + | 1.34278i | 0.0485484 | + | 0.0840882i | ||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −11.4495 | − | 6.61037i | −0.714200 | − | 0.412343i | 0.0984145 | − | 0.995146i | \(-0.468623\pi\) |
−0.812614 | + | 0.582802i | \(0.801956\pi\) | |||||||
\(258\) | −2.12372 | − | 3.67840i | −0.132217 | − | 0.229007i | ||||
\(259\) | 6.00000 | + | 6.92820i | 0.372822 | + | 0.430498i | ||||
\(260\) | −4.44949 | + | 7.70674i | −0.275946 | + | 0.477952i | ||||
\(261\) | 18.1918 | + | 10.5031i | 1.12605 | + | 0.650123i | ||||
\(262\) | −8.00000 | + | 13.8564i | −0.494242 | + | 0.856052i | ||||
\(263\) | 4.74745 | − | 2.74094i | 0.292740 | − | 0.169014i | −0.346437 | − | 0.938073i | \(-0.612608\pi\) |
0.639177 | + | 0.769060i | \(0.279275\pi\) | |||||||
\(264\) | −2.20204 | + | 3.81405i | −0.135526 | + | 0.234738i | ||||
\(265\) | − | 2.04989i | − | 0.125924i | ||||||
\(266\) | −12.0000 | + | 10.3923i | −0.735767 | + | 0.637193i | ||||
\(267\) | −3.44949 | −0.211105 | ||||||||
\(268\) | 12.3485 | + | 21.3882i | 0.754303 | + | 1.30649i | ||||
\(269\) | −8.17423 | − | 14.1582i | −0.498392 | − | 0.863240i | 0.501606 | − | 0.865096i | \(-0.332743\pi\) |
−0.999998 | + | 0.00185590i | \(0.999409\pi\) | |||||||
\(270\) | 1.32577 | − | 2.29629i | 0.0806835 | − | 0.139748i | ||||
\(271\) | 1.67423 | − | 2.89986i | 0.101703 | − | 0.176154i | −0.810684 | − | 0.585484i | \(-0.800904\pi\) |
0.912386 | + | 0.409330i | \(0.134238\pi\) | |||||||
\(272\) | −16.8990 | + | 9.75663i | −1.02465 | + | 0.591583i | ||||
\(273\) | −3.67423 | + | 0.707107i | −0.222375 | + | 0.0427960i | ||||
\(274\) | 12.0000 | − | 6.92820i | 0.724947 | − | 0.418548i | ||||
\(275\) | −2.44949 | + | 4.24264i | −0.147710 | + | 0.255841i | ||||
\(276\) | 2.89898 | 0.174498 | ||||||||
\(277\) | 5.02270 | − | 2.89986i | 0.301785 | − | 0.174236i | −0.341459 | − | 0.939896i | \(-0.610921\pi\) |
0.643245 | + | 0.765661i | \(0.277588\pi\) | |||||||
\(278\) | 9.79796 | 0.587643 | ||||||||
\(279\) | 4.49490 | 0.269102 | ||||||||
\(280\) | 4.89898 | + | 5.65685i | 0.292770 | + | 0.338062i | ||||
\(281\) | 16.8990 | 1.00811 | 0.504054 | − | 0.863672i | \(-0.331841\pi\) | ||||
0.504054 | + | 0.863672i | \(0.331841\pi\) | |||||||
\(282\) | 2.69694 | 0.160600 | ||||||||
\(283\) | −7.34847 | + | 4.24264i | −0.436821 | + | 0.252199i | −0.702248 | − | 0.711932i | \(-0.747820\pi\) |
0.265427 | + | 0.964131i | \(0.414487\pi\) | |||||||
\(284\) | − | 2.82843i | − | 0.167836i | ||||||
\(285\) | 0.674235 | − | 1.16781i | 0.0399382 | − | 0.0691750i | ||||
\(286\) | 26.6969 | − | 15.4135i | 1.57862 | − | 0.911418i | ||||
\(287\) | 6.94949 | − | 20.0614i | 0.410215 | − | 1.18419i | ||||
\(288\) | 14.2020 | + | 8.19955i | 0.836863 | + | 0.483163i | ||||
\(289\) | 3.39898 | − | 5.88721i | 0.199940 | − | 0.346306i | ||||
\(290\) | 5.12372 | − | 8.87455i | 0.300875 | − | 0.521132i | ||||
\(291\) | 1.89898 | + | 3.28913i | 0.111320 | + | 0.192812i | ||||
\(292\) | 19.3485 | − | 11.1708i | 1.13228 | − | 0.653724i | ||||
\(293\) | −24.4949 | −1.43101 | −0.715504 | − | 0.698609i | \(-0.753803\pi\) | ||||
−0.715504 | + | 0.698609i | \(0.753803\pi\) | |||||||
\(294\) | −0.449490 | + | 3.11416i | −0.0262148 | + | 0.181621i | ||||
\(295\) | 3.60697i | 0.210006i | ||||||||
\(296\) | 4.89898 | − | 8.48528i | 0.284747 | − | 0.493197i | ||||
\(297\) | −7.95459 | + | 4.59259i | −0.461572 | + | 0.266489i | ||||
\(298\) | 13.5732 | − | 23.5095i | 0.786275 | − | 1.36187i | ||||
\(299\) | −17.5732 | − | 10.1459i | −1.01629 | − | 0.586753i | ||||
\(300\) | −0.550510 | − | 0.317837i | −0.0317837 | − | 0.0183503i | ||||
\(301\) | 23.6237 | + | 8.18350i | 1.36165 | + | 0.471689i | ||||
\(302\) | 5.44949 | + | 9.43879i | 0.313583 | + | 0.543142i | ||||
\(303\) | −4.19694 | − | 2.42310i | −0.241108 | − | 0.139204i | ||||
\(304\) | 14.6969 | + | 8.48528i | 0.842927 | + | 0.486664i | ||||
\(305\) | 0.174235 | + | 0.301783i | 0.00997664 | + | 0.0172801i | ||||
\(306\) | −20.0000 | −1.14332 | ||||||||
\(307\) | 27.9664i | 1.59613i | 0.602572 | + | 0.798064i | \(0.294143\pi\) | ||||
−0.602572 | + | 0.798064i | \(0.705857\pi\) | |||||||
\(308\) | −4.89898 | − | 25.4558i | −0.279145 | − | 1.45048i | ||||
\(309\) | − | 5.33902i | − | 0.303726i | ||||||
\(310\) | − | 2.19275i | − | 0.124540i | ||||||
\(311\) | −5.57321 | − | 9.65309i | −0.316028 | − | 0.547377i | 0.663628 | − | 0.748063i | \(-0.269016\pi\) |
−0.979655 | + | 0.200687i | \(0.935683\pi\) | |||||||
\(312\) | 2.00000 | + | 3.46410i | 0.113228 | + | 0.196116i | ||||
\(313\) | −5.69694 | − | 3.28913i | −0.322010 | − | 0.185913i | 0.330278 | − | 0.943884i | \(-0.392857\pi\) |
−0.652288 | + | 0.757971i | \(0.726191\pi\) | |||||||
\(314\) | 13.1010 | − | 7.56388i | 0.739333 | − | 0.426854i | ||||
\(315\) | 1.44949 | + | 7.53177i | 0.0816695 | + | 0.424367i | ||||
\(316\) | 13.3485 | + | 7.70674i | 0.750910 | + | 0.433538i | ||||
\(317\) | 0.426786 | + | 0.246405i | 0.0239707 | + | 0.0138395i | 0.511937 | − | 0.859023i | \(-0.328928\pi\) |
−0.487967 | + | 0.872862i | \(0.662261\pi\) | |||||||
\(318\) | −0.797959 | − | 0.460702i | −0.0447473 | − | 0.0258349i | ||||
\(319\) | −30.7423 | + | 17.7491i | −1.72124 | + | 0.993759i | ||||
\(320\) | 4.00000 | − | 6.92820i | 0.223607 | − | 0.387298i | ||||
\(321\) | 1.73205i | 0.0966736i | ||||||||
\(322\) | −12.8990 | + | 11.1708i | −0.718832 | + | 0.622527i | ||||
\(323\) | −20.6969 | −1.15161 | ||||||||
\(324\) | 8.10102 | + | 14.0314i | 0.450057 | + | 0.779521i | ||||
\(325\) | 2.22474 | + | 3.85337i | 0.123407 | + | 0.213747i | ||||
\(326\) | 7.10102 | + | 4.09978i | 0.393289 | + | 0.227066i | ||||
\(327\) | 1.25255 | − | 2.16948i | 0.0692662 | − | 0.119973i | ||||
\(328\) | −22.6969 | −1.25323 | ||||||||
\(329\) | −12.0000 | + | 10.3923i | −0.661581 | + | 0.572946i | ||||
\(330\) | 1.10102 | + | 1.90702i | 0.0606092 | + | 0.104978i | ||||
\(331\) | 1.57321 | − | 2.72489i | 0.0864717 | − | 0.149773i | −0.819546 | − | 0.573014i | \(-0.805774\pi\) |
0.906017 | + | 0.423240i | \(0.139107\pi\) | |||||||
\(332\) | − | 3.74983i | − | 0.205799i | ||||||
\(333\) | 8.69694 | − | 5.02118i | 0.476589 | − | 0.275159i | ||||
\(334\) | 4.24264i | 0.232147i | ||||||||
\(335\) | 12.3485 | 0.674669 | ||||||||
\(336\) | 3.30306 | − | 0.635674i | 0.180197 | − | 0.0346789i | ||||
\(337\) | 20.2474 | 1.10295 | 0.551474 | − | 0.834192i | \(-0.314065\pi\) | ||||
0.551474 | + | 0.834192i | \(0.314065\pi\) | |||||||
\(338\) | − | 9.61377i | − | 0.522920i | ||||||
\(339\) | −2.32577 | + | 1.34278i | −0.126318 | + | 0.0729299i | ||||
\(340\) | 9.75663i | 0.529128i | ||||||||
\(341\) | −3.79796 | + | 6.57826i | −0.205671 | + | 0.356233i | ||||
\(342\) | 8.69694 | + | 15.0635i | 0.470277 | + | 0.814543i | ||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | − | 26.7272i | − | 1.44103i | ||||||
\(345\) | 0.724745 | − | 1.25529i | 0.0390190 | − | 0.0675828i | ||||
\(346\) | 13.3485 | + | 7.70674i | 0.717618 | + | 0.414317i | ||||
\(347\) | 3.82577 | + | 6.62642i | 0.205378 | + | 0.355725i | 0.950253 | − | 0.311479i | \(-0.100824\pi\) |
−0.744875 | + | 0.667204i | \(0.767491\pi\) | |||||||
\(348\) | −2.30306 | − | 3.98902i | −0.123457 | − | 0.213834i | ||||
\(349\) | 7.24745 | 0.387947 | 0.193974 | − | 0.981007i | \(-0.437862\pi\) | ||||
0.193974 | + | 0.981007i | \(0.437862\pi\) | |||||||
\(350\) | 3.67423 | − | 0.707107i | 0.196396 | − | 0.0377964i | ||||
\(351\) | 8.34242i | 0.445285i | ||||||||
\(352\) | −24.0000 | + | 13.8564i | −1.27920 | + | 0.738549i | ||||
\(353\) | 29.8207 | − | 17.2170i | 1.58719 | − | 0.916367i | 0.593427 | − | 0.804888i | \(-0.297775\pi\) |
0.993767 | − | 0.111479i | \(-0.0355587\pi\) | |||||||
\(354\) | 1.40408 | + | 0.810647i | 0.0746261 | + | 0.0430854i | ||||
\(355\) | −1.22474 | − | 0.707107i | −0.0650027 | − | 0.0375293i | ||||
\(356\) | −18.7980 | − | 10.8530i | −0.996290 | − | 0.575208i | ||||
\(357\) | −3.10102 | + | 2.68556i | −0.164123 | + | 0.142135i | ||||
\(358\) | −11.6969 | + | 6.75323i | −0.618202 | + | 0.356919i | ||||
\(359\) | 19.7753 | + | 11.4172i | 1.04370 | + | 0.602579i | 0.920879 | − | 0.389850i | \(-0.127473\pi\) |
0.122820 | + | 0.992429i | \(0.460806\pi\) | |||||||
\(360\) | 7.10102 | − | 4.09978i | 0.374257 | − | 0.216077i | ||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | 17.4634i | 0.917854i | ||||||||
\(363\) | − | 4.13188i | − | 0.216868i | ||||||
\(364\) | −22.2474 | − | 7.70674i | −1.16608 | − | 0.403943i | ||||
\(365\) | − | 11.1708i | − | 0.584709i | ||||||
\(366\) | 0.156633 | 0.00818736 | ||||||||
\(367\) | −4.05051 | − | 7.01569i | −0.211435 | − | 0.366216i | 0.740729 | − | 0.671804i | \(-0.234480\pi\) |
−0.952164 | + | 0.305588i | \(0.901147\pi\) | |||||||
\(368\) | 15.7980 | + | 9.12096i | 0.823526 | + | 0.475463i | ||||
\(369\) | −20.1464 | − | 11.6315i | −1.04878 | − | 0.605514i | ||||
\(370\) | −2.44949 | − | 4.24264i | −0.127343 | − | 0.220564i | ||||
\(371\) | 5.32577 | − | 1.02494i | 0.276500 | − | 0.0532124i | ||||
\(372\) | −0.853572 | − | 0.492810i | −0.0442556 | − | 0.0255510i | ||||
\(373\) | −15.0000 | − | 8.66025i | −0.776671 | − | 0.448411i | 0.0585785 | − | 0.998283i | \(-0.481343\pi\) |
−0.835249 | + | 0.549872i | \(0.814677\pi\) | |||||||
\(374\) | 16.8990 | − | 29.2699i | 0.873825 | − | 1.51351i | ||||
\(375\) | −0.275255 | + | 0.158919i | −0.0142141 | + | 0.00820652i | ||||
\(376\) | 14.6969 | + | 8.48528i | 0.757937 | + | 0.437595i | ||||
\(377\) | 32.2412i | 1.66051i | ||||||||
\(378\) | 6.62883 | + | 2.29629i | 0.340950 | + | 0.118109i | ||||
\(379\) | −17.3485 | −0.891131 | −0.445566 | − | 0.895249i | \(-0.646997\pi\) | ||||
−0.445566 | + | 0.895249i | \(0.646997\pi\) | |||||||
\(380\) | 7.34847 | − | 4.24264i | 0.376969 | − | 0.217643i | ||||
\(381\) | −1.10102 | − | 1.90702i | −0.0564070 | − | 0.0976998i | ||||
\(382\) | −18.6969 | + | 32.3840i | −0.956619 | + | 1.65691i | ||||
\(383\) | −2.60102 | + | 4.50510i | −0.132906 | + | 0.230200i | −0.924796 | − | 0.380464i | \(-0.875764\pi\) |
0.791890 | + | 0.610664i | \(0.209097\pi\) | |||||||
\(384\) | −1.79796 | − | 3.11416i | −0.0917517 | − | 0.158919i | ||||
\(385\) | −12.2474 | − | 4.24264i | −0.624188 | − | 0.216225i | ||||
\(386\) | −27.7980 | + | 16.0492i | −1.41488 | + | 0.816881i | ||||
\(387\) | 13.6969 | − | 23.7238i | 0.696255 | − | 1.20595i | ||||
\(388\) | 23.8988i | 1.21328i | ||||||||
\(389\) | −9.79796 | + | 5.65685i | −0.496776 | + | 0.286814i | −0.727381 | − | 0.686234i | \(-0.759263\pi\) |
0.230605 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(390\) | 2.00000 | 0.101274 | ||||||||
\(391\) | −22.2474 | −1.12510 | ||||||||
\(392\) | −12.2474 | + | 15.5563i | −0.618590 | + | 0.785714i | ||||
\(393\) | 3.59592 | 0.181390 | ||||||||
\(394\) | −1.30306 | −0.0656473 | ||||||||
\(395\) | 6.67423 | − | 3.85337i | 0.335817 | − | 0.193884i | ||||
\(396\) | −28.4041 | −1.42736 | ||||||||
\(397\) | −0.348469 | + | 0.603566i | −0.0174892 | + | 0.0302921i | −0.874638 | − | 0.484777i | \(-0.838901\pi\) |
0.857148 | + | 0.515070i | \(0.172234\pi\) | |||||||
\(398\) | −30.2474 | + | 17.4634i | −1.51617 | + | 0.875360i | ||||
\(399\) | 3.37117 | + | 1.16781i | 0.168770 | + | 0.0584636i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | 15.3990 | − | 26.6718i | 0.768988 | − | 1.33193i | −0.169124 | − | 0.985595i | \(-0.554094\pi\) |
0.938112 | − | 0.346332i | \(-0.112573\pi\) | |||||||
\(402\) | 2.77526 | − | 4.80688i | 0.138417 | − | 0.239746i | ||||
\(403\) | 3.44949 | + | 5.97469i | 0.171831 | + | 0.297621i | ||||
\(404\) | −15.2474 | − | 26.4094i | −0.758589 | − | 1.31391i | ||||
\(405\) | 8.10102 | 0.402543 | ||||||||
\(406\) | 25.6186 | + | 8.87455i | 1.27143 | + | 0.440437i | ||||
\(407\) | 16.9706i | 0.841200i | ||||||||
\(408\) | 3.79796 | + | 2.19275i | 0.188027 | + | 0.108557i | ||||
\(409\) | −10.1969 | + | 5.88721i | −0.504206 | + | 0.291104i | −0.730449 | − | 0.682967i | \(-0.760689\pi\) |
0.226243 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(410\) | −5.67423 | + | 9.82806i | −0.280230 | + | 0.485373i | ||||
\(411\) | −2.69694 | − | 1.55708i | −0.133030 | − | 0.0768050i | ||||
\(412\) | 16.7980 | − | 29.0949i | 0.827576 | − | 1.43340i | ||||
\(413\) | −9.37117 | + | 1.80348i | −0.461125 | + | 0.0887436i | ||||
\(414\) | 9.34847 | + | 16.1920i | 0.459452 | + | 0.795795i | ||||
\(415\) | −1.62372 | − | 0.937458i | −0.0797055 | − | 0.0460180i | ||||
\(416\) | 25.1701i | 1.23407i | ||||||||
\(417\) | −1.10102 | − | 1.90702i | −0.0539172 | − | 0.0933873i | ||||
\(418\) | −29.3939 | −1.43770 | ||||||||
\(419\) | 16.6848i | 0.815107i | 0.913181 | + | 0.407554i | \(0.133618\pi\) | ||||
−0.913181 | + | 0.407554i | \(0.866382\pi\) | |||||||
\(420\) | 0.550510 | − | 1.58919i | 0.0268622 | − | 0.0775443i | ||||
\(421\) | 4.06767i | 0.198246i | 0.995075 | + | 0.0991230i | \(0.0316037\pi\) | ||||
−0.995075 | + | 0.0991230i | \(0.968396\pi\) | |||||||
\(422\) | − | 11.6637i | − | 0.567778i | ||||||
\(423\) | 8.69694 | + | 15.0635i | 0.422860 | + | 0.732414i | ||||
\(424\) | −2.89898 | − | 5.02118i | −0.140787 | − | 0.243850i | ||||
\(425\) | 4.22474 | + | 2.43916i | 0.204930 | + | 0.118317i | ||||
\(426\) | −0.550510 | + | 0.317837i | −0.0266723 | + | 0.0153993i | ||||
\(427\) | −0.696938 | + | 0.603566i | −0.0337272 | + | 0.0292086i | ||||
\(428\) | −5.44949 | + | 9.43879i | −0.263411 | + | 0.456241i | ||||
\(429\) | −6.00000 | − | 3.46410i | −0.289683 | − | 0.167248i | ||||
\(430\) | −11.5732 | − | 6.68180i | −0.558110 | − | 0.322225i | ||||
\(431\) | 8.20204 | − | 4.73545i | 0.395078 | − | 0.228099i | −0.289280 | − | 0.957245i | \(-0.593416\pi\) |
0.684358 | + | 0.729146i | \(0.260082\pi\) | |||||||
\(432\) | − | 7.49966i | − | 0.360828i | ||||||
\(433\) | − | 7.70674i | − | 0.370362i | −0.982704 | − | 0.185181i | \(-0.940713\pi\) | ||
0.982704 | − | 0.185181i | \(-0.0592872\pi\) | |||||||
\(434\) | 5.69694 | − | 1.09638i | 0.273462 | − | 0.0526277i | ||||
\(435\) | −2.30306 | −0.110423 | ||||||||
\(436\) | 13.6515 | − | 7.88171i | 0.653790 | − | 0.377466i | ||||
\(437\) | 9.67423 | + | 16.7563i | 0.462781 | + | 0.801561i | ||||
\(438\) | −4.34847 | − | 2.51059i | −0.207778 | − | 0.119961i | ||||
\(439\) | −5.55051 | + | 9.61377i | −0.264911 | + | 0.458840i | −0.967540 | − | 0.252716i | \(-0.918676\pi\) |
0.702629 | + | 0.711556i | \(0.252009\pi\) | |||||||
\(440\) | 13.8564i | 0.660578i | ||||||||
\(441\) | −18.8434 | + | 7.53177i | −0.897303 | + | 0.358656i | ||||
\(442\) | −15.3485 | − | 26.5843i | −0.730052 | − | 1.26449i | ||||
\(443\) | 8.17423 | − | 14.1582i | 0.388370 | − | 0.672676i | −0.603861 | − | 0.797090i | \(-0.706372\pi\) |
0.992230 | + | 0.124414i | \(0.0397051\pi\) | |||||||
\(444\) | −2.20204 | −0.104504 | ||||||||
\(445\) | −9.39898 | + | 5.42650i | −0.445554 | + | 0.257241i | ||||
\(446\) | − | 34.9267i | − | 1.65383i | ||||||
\(447\) | −6.10102 | −0.288568 | ||||||||
\(448\) | 20.0000 | + | 6.92820i | 0.944911 | + | 0.327327i | ||||
\(449\) | −1.40408 | −0.0662627 | −0.0331314 | − | 0.999451i | \(-0.510548\pi\) | ||||
−0.0331314 | + | 0.999451i | \(0.510548\pi\) | |||||||
\(450\) | − | 4.09978i | − | 0.193265i | ||||||
\(451\) | 34.0454 | − | 19.6561i | 1.60314 | − | 0.925571i | ||||
\(452\) | −16.8990 | −0.794861 | ||||||||
\(453\) | 1.22474 | − | 2.12132i | 0.0575435 | − | 0.0996683i | ||||
\(454\) | 7.55051 | + | 13.0779i | 0.354363 | + | 0.613775i | ||||
\(455\) | −8.89898 | + | 7.70674i | −0.417191 | + | 0.361298i | ||||
\(456\) | − | 3.81405i | − | 0.178609i | ||||||
\(457\) | −4.79796 | + | 8.31031i | −0.224439 | + | 0.388740i | −0.956151 | − | 0.292874i | \(-0.905388\pi\) |
0.731712 | + | 0.681614i | \(0.238722\pi\) | |||||||
\(458\) | −20.4495 | − | 11.8065i | −0.955542 | − | 0.551682i | ||||
\(459\) | 4.57321 | + | 7.92104i | 0.213459 | + | 0.369722i | ||||
\(460\) | 7.89898 | − | 4.56048i | 0.368292 | − | 0.212633i | ||||
\(461\) | −38.6969 | −1.80230 | −0.901148 | − | 0.433511i | \(-0.857274\pi\) | ||||
−0.901148 | + | 0.433511i | \(0.857274\pi\) | |||||||
\(462\) | −4.40408 | + | 3.81405i | −0.204896 | + | 0.177446i | ||||
\(463\) | 12.1244i | 0.563467i | 0.959493 | + | 0.281733i | \(0.0909093\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(464\) | − | 28.9842i | − | 1.34556i | ||||||
\(465\) | −0.426786 | + | 0.246405i | −0.0197917 | + | 0.0114268i | ||||
\(466\) | −0.303062 | − | 0.174973i | −0.0140391 | − | 0.00810545i | ||||
\(467\) | −19.6237 | − | 11.3298i | −0.908078 | − | 0.524279i | −0.0282655 | − | 0.999600i | \(-0.508998\pi\) |
−0.879812 | + | 0.475322i | \(0.842332\pi\) | |||||||
\(468\) | −12.8990 | + | 22.3417i | −0.596256 | + | 1.03274i | ||||
\(469\) | 6.17423 | + | 32.0823i | 0.285100 | + | 1.48142i | ||||
\(470\) | 7.34847 | − | 4.24264i | 0.338960 | − | 0.195698i | ||||
\(471\) | −2.94439 | − | 1.69994i | −0.135670 | − | 0.0783292i | ||||
\(472\) | 5.10102 | + | 8.83523i | 0.234794 | + | 0.406674i | ||||
\(473\) | 23.1464 | + | 40.0908i | 1.06427 | + | 1.84338i | ||||
\(474\) | − | 3.46410i | − | 0.159111i | ||||||
\(475\) | − | 4.24264i | − | 0.194666i | ||||||
\(476\) | −25.3485 | + | 4.87832i | −1.16185 | + | 0.223597i | ||||
\(477\) | − | 5.94258i | − | 0.272092i | ||||||
\(478\) | 4.69694 | 0.214833 | ||||||||
\(479\) | −4.22474 | − | 7.31747i | −0.193034 | − | 0.334344i | 0.753221 | − | 0.657768i | \(-0.228499\pi\) |
−0.946254 | + | 0.323424i | \(0.895166\pi\) | |||||||
\(480\) | −1.79796 | −0.0820652 | ||||||||
\(481\) | 13.3485 | + | 7.70674i | 0.608638 | + | 0.351397i | ||||
\(482\) | 14.4495 | + | 25.0273i | 0.658156 | + | 1.13996i | ||||
\(483\) | 3.62372 | + | 1.25529i | 0.164885 | + | 0.0571179i | ||||
\(484\) | 13.0000 | − | 22.5167i | 0.590909 | − | 1.02348i | ||||
\(485\) | 10.3485 | + | 5.97469i | 0.469900 | + | 0.271297i | ||||
\(486\) | 5.79796 | − | 10.0424i | 0.263001 | − | 0.455531i | ||||
\(487\) | 26.3939 | − | 15.2385i | 1.19602 | − | 0.690523i | 0.236355 | − | 0.971667i | \(-0.424047\pi\) |
0.959666 | + | 0.281144i | \(0.0907138\pi\) | |||||||
\(488\) | 0.853572 | + | 0.492810i | 0.0386394 | + | 0.0223085i | ||||
\(489\) | − | 1.84281i | − | 0.0833346i | ||||||
\(490\) | 3.67423 | + | 9.19239i | 0.165985 | + | 0.415270i | ||||
\(491\) | 0.853572 | 0.0385212 | 0.0192606 | − | 0.999814i | \(-0.493869\pi\) | ||||
0.0192606 | + | 0.999814i | \(0.493869\pi\) | |||||||
\(492\) | 2.55051 | + | 4.41761i | 0.114986 | + | 0.199161i | ||||
\(493\) | 17.6742 | + | 30.6127i | 0.796007 | + | 1.37873i | ||||
\(494\) | −13.3485 | + | 23.1202i | −0.600576 | + | 1.04023i | ||||
\(495\) | −7.10102 | + | 12.2993i | −0.319167 | + | 0.552814i | ||||
\(496\) | −3.10102 | − | 5.37113i | −0.139240 | − | 0.241171i | ||||
\(497\) | 1.22474 | − | 3.53553i | 0.0549373 | − | 0.158590i | ||||
\(498\) | −0.729847 | + | 0.421378i | −0.0327052 | + | 0.0188824i | ||||
\(499\) | 13.6969 | − | 23.7238i | 0.613159 | − | 1.06202i | −0.377545 | − | 0.925991i | \(-0.623232\pi\) |
0.990704 | − | 0.136032i | \(-0.0434349\pi\) | |||||||
\(500\) | −2.00000 | −0.0894427 | ||||||||
\(501\) | 0.825765 | − | 0.476756i | 0.0368925 | − | 0.0212999i | ||||
\(502\) | −19.3939 | −0.865591 | ||||||||
\(503\) | 23.6969 | 1.05659 | 0.528297 | − | 0.849060i | \(-0.322831\pi\) | ||||
0.528297 | + | 0.849060i | \(0.322831\pi\) | |||||||
\(504\) | 14.2020 | + | 16.3991i | 0.632609 | + | 0.730474i | ||||
\(505\) | −15.2474 | −0.678503 | ||||||||
\(506\) | −31.5959 | −1.40461 | ||||||||
\(507\) | −1.87117 | + | 1.08032i | −0.0831017 | + | 0.0479788i | ||||
\(508\) | − | 13.8564i | − | 0.614779i | ||||||
\(509\) | −8.72474 | + | 15.1117i | −0.386718 | + | 0.669814i | −0.992006 | − | 0.126192i | \(-0.959724\pi\) |
0.605288 | + | 0.796006i | \(0.293058\pi\) | |||||||
\(510\) | 1.89898 | − | 1.09638i | 0.0840882 | − | 0.0485484i | ||||
\(511\) | 29.0227 | − | 5.58542i | 1.28389 | − | 0.247085i | ||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 3.97730 | − | 6.88888i | 0.175602 | − | 0.304151i | ||||
\(514\) | −9.34847 | + | 16.1920i | −0.412343 | + | 0.714200i | ||||
\(515\) | −8.39898 | − | 14.5475i | −0.370103 | − | 0.641038i | ||||
\(516\) | −5.20204 | + | 3.00340i | −0.229007 | + | 0.132217i | ||||
\(517\) | −29.3939 | −1.29274 | ||||||||
\(518\) | 9.79796 | − | 8.48528i | 0.430498 | − | 0.372822i | ||||
\(519\) | − | 3.46410i | − | 0.152057i | ||||||
\(520\) | 10.8990 | + | 6.29253i | 0.477952 | + | 0.275946i | ||||
\(521\) | −9.24745 | + | 5.33902i | −0.405138 | + | 0.233907i | −0.688699 | − | 0.725048i | \(-0.741818\pi\) |
0.283560 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(522\) | 14.8536 | − | 25.7271i | 0.650123 | − | 1.12605i | ||||
\(523\) | −10.3485 | − | 5.97469i | −0.452507 | − | 0.261255i | 0.256381 | − | 0.966576i | \(-0.417470\pi\) |
−0.708888 | + | 0.705321i | \(0.750803\pi\) | |||||||
\(524\) | 19.5959 | + | 11.3137i | 0.856052 | + | 0.494242i | ||||
\(525\) | −0.550510 | − | 0.635674i | −0.0240262 | − | 0.0277431i | ||||
\(526\) | −3.87628 | − | 6.71391i | −0.169014 | − | 0.292740i | ||||
\(527\) | 6.55051 | + | 3.78194i | 0.285345 | + | 0.164744i | ||||
\(528\) | 5.39388 | + | 3.11416i | 0.234738 | + | 0.135526i | ||||
\(529\) | −1.10102 | − | 1.90702i | −0.0478705 | − | 0.0829141i | ||||
\(530\) | −2.89898 | −0.125924 | ||||||||
\(531\) | 10.4565i | 0.453774i | ||||||||
\(532\) | 14.6969 | + | 16.9706i | 0.637193 | + | 0.735767i | ||||
\(533\) | − | 35.7053i | − | 1.54657i | ||||||
\(534\) | 4.87832i | 0.211105i | ||||||||
\(535\) | 2.72474 | + | 4.71940i | 0.117801 | + | 0.204037i | ||||
\(536\) | 30.2474 | − | 17.4634i | 1.30649 | − | 0.754303i | ||||
\(537\) | 2.62883 | + | 1.51775i | 0.113442 | + | 0.0654959i | ||||
\(538\) | −20.0227 | + | 11.5601i | −0.863240 | + | 0.498392i | ||||
\(539\) | 4.89898 | − | 33.9411i | 0.211014 | − | 1.46195i | ||||
\(540\) | −3.24745 | − | 1.87492i | −0.139748 | − | 0.0806835i | ||||
\(541\) | 24.5227 | + | 14.1582i | 1.05431 | + | 0.608708i | 0.923854 | − | 0.382746i | \(-0.125021\pi\) |
0.130460 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(542\) | −4.10102 | − | 2.36773i | −0.176154 | − | 0.101703i | ||||
\(543\) | 3.39898 | − | 1.96240i | 0.145864 | − | 0.0842147i | ||||
\(544\) | 13.7980 | + | 23.8988i | 0.591583 | + | 1.02465i | ||||
\(545\) | − | 7.88171i | − | 0.337616i | ||||||
\(546\) | 1.00000 | + | 5.19615i | 0.0427960 | + | 0.222375i | ||||
\(547\) | 9.04541 | 0.386754 | 0.193377 | − | 0.981125i | \(-0.438056\pi\) | ||||
0.193377 | + | 0.981125i | \(0.438056\pi\) | |||||||
\(548\) | −9.79796 | − | 16.9706i | −0.418548 | − | 0.724947i | ||||
\(549\) | 0.505103 | + | 0.874863i | 0.0215573 | + | 0.0373383i | ||||
\(550\) | 6.00000 | + | 3.46410i | 0.255841 | + | 0.147710i | ||||
\(551\) | 15.3712 | − | 26.6237i | 0.654834 | − | 1.13421i | ||||
\(552\) | − | 4.09978i | − | 0.174498i | ||||||
\(553\) | 13.3485 | + | 15.4135i | 0.567635 | + | 0.655448i | ||||
\(554\) | −4.10102 | − | 7.10318i | −0.174236 | − | 0.301785i | ||||
\(555\) | −0.550510 | + | 0.953512i | −0.0233679 | + | 0.0404743i | ||||
\(556\) | − | 13.8564i | − | 0.587643i | ||||||
\(557\) | 13.8990 | − | 8.02458i | 0.588919 | − | 0.340012i | −0.175751 | − | 0.984435i | \(-0.556235\pi\) |
0.764670 | + | 0.644422i | \(0.222902\pi\) | |||||||
\(558\) | − | 6.35674i | − | 0.269102i | ||||||
\(559\) | 42.0454 | 1.77833 | ||||||||
\(560\) | 8.00000 | − | 6.92820i | 0.338062 | − | 0.292770i | ||||
\(561\) | −7.59592 | −0.320700 | ||||||||
\(562\) | − | 23.8988i | − | 1.00811i | ||||||
\(563\) | 16.6237 | − | 9.59771i | 0.700606 | − | 0.404495i | −0.106967 | − | 0.994263i | \(-0.534114\pi\) |
0.807573 | + | 0.589767i | \(0.200781\pi\) | |||||||
\(564\) | − | 3.81405i | − | 0.160600i | ||||||
\(565\) | −4.22474 | + | 7.31747i | −0.177736 | + | 0.307848i | ||||
\(566\) | 6.00000 | + | 10.3923i | 0.252199 | + | 0.436821i | ||||
\(567\) | 4.05051 | + | 21.0471i | 0.170105 | + | 0.883894i | ||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −20.6969 | + | 35.8481i | −0.867661 | + | 1.50283i | −0.00328010 | + | 0.999995i | \(0.501044\pi\) |
−0.864381 | + | 0.502838i | \(0.832289\pi\) | |||||||
\(570\) | −1.65153 | − | 0.953512i | −0.0691750 | − | 0.0399382i | ||||
\(571\) | −5.22474 | − | 9.04952i | −0.218649 | − | 0.378711i | 0.735746 | − | 0.677257i | \(-0.236832\pi\) |
−0.954395 | + | 0.298546i | \(0.903498\pi\) | |||||||
\(572\) | −21.7980 | − | 37.7552i | −0.911418 | − | 1.57862i | ||||
\(573\) | 8.40408 | 0.351086 | ||||||||
\(574\) | −28.3712 | − | 9.82806i | −1.18419 | − | 0.410215i | ||||
\(575\) | − | 4.56048i | − | 0.190185i | ||||||
\(576\) | 11.5959 | − | 20.0847i | 0.483163 | − | 0.836863i | ||||
\(577\) | 25.3485 | − | 14.6349i | 1.05527 | − | 0.609261i | 0.131150 | − | 0.991362i | \(-0.458133\pi\) |
0.924120 | + | 0.382102i | \(0.124800\pi\) | |||||||
\(578\) | −8.32577 | − | 4.80688i | −0.346306 | − | 0.199940i | ||||
\(579\) | 6.24745 | + | 3.60697i | 0.259635 | + | 0.149900i | ||||
\(580\) | −12.5505 | − | 7.24604i | −0.521132 | − | 0.300875i | ||||
\(581\) | 1.62372 | − | 4.68729i | 0.0673634 | − | 0.194461i | ||||
\(582\) | 4.65153 | − | 2.68556i | 0.192812 | − | 0.111320i | ||||
\(583\) | 8.69694 | + | 5.02118i | 0.360190 | + | 0.207956i | ||||
\(584\) | −15.7980 | − | 27.3629i | −0.653724 | − | 1.13228i | ||||
\(585\) | 6.44949 | + | 11.1708i | 0.266654 | + | 0.461858i | ||||
\(586\) | 34.6410i | 1.43101i | ||||||||
\(587\) | − | 5.30691i | − | 0.219040i | −0.993985 | − | 0.109520i | \(-0.965069\pi\) | ||
0.993985 | − | 0.109520i | \(-0.0349313\pi\) | |||||||
\(588\) | 4.40408 | + | 0.635674i | 0.181621 | + | 0.0262148i | ||||
\(589\) | − | 6.57826i | − | 0.271052i | ||||||
\(590\) | 5.10102 | 0.210006 | ||||||||
\(591\) | 0.146428 | + | 0.253621i | 0.00602325 | + | 0.0104326i | ||||
\(592\) | −12.0000 | − | 6.92820i | −0.493197 | − | 0.284747i | ||||
\(593\) | 8.57321 | + | 4.94975i | 0.352060 | + | 0.203262i | 0.665592 | − | 0.746316i | \(-0.268179\pi\) |
−0.313532 | + | 0.949578i | \(0.601512\pi\) | |||||||
\(594\) | 6.49490 | + | 11.2495i | 0.266489 | + | 0.461572i | ||||
\(595\) | −4.22474 | + | 12.1958i | −0.173198 | + | 0.499979i | ||||
\(596\) | −33.2474 | − | 19.1954i | −1.36187 | − | 0.786275i | ||||
\(597\) | 6.79796 | + | 3.92480i | 0.278222 | + | 0.160632i | ||||
\(598\) | −14.3485 | + | 24.8523i | −0.586753 | + | 1.01629i | ||||
\(599\) | −11.1464 | + | 6.43539i | −0.455431 | + | 0.262943i | −0.710121 | − | 0.704080i | \(-0.751360\pi\) |
0.254690 | + | 0.967023i | \(0.418026\pi\) | |||||||
\(600\) | −0.449490 | + | 0.778539i | −0.0183503 | + | 0.0317837i | ||||
\(601\) | 25.8058i | 1.05264i | 0.850287 | + | 0.526320i | \(0.176429\pi\) | ||||
−0.850287 | + | 0.526320i | \(0.823571\pi\) | |||||||
\(602\) | 11.5732 | − | 33.4090i | 0.471689 | − | 1.36165i | ||||
\(603\) | 35.7980 | 1.45781 | ||||||||
\(604\) | 13.3485 | − | 7.70674i | 0.543142 | − | 0.313583i | ||||
\(605\) | −6.50000 | − | 11.2583i | −0.264263 | − | 0.457716i | ||||
\(606\) | −3.42679 | + | 5.93537i | −0.139204 | + | 0.241108i | ||||
\(607\) | −10.8485 | + | 18.7901i | −0.440326 | + | 0.762667i | −0.997713 | − | 0.0675857i | \(-0.978470\pi\) |
0.557388 | + | 0.830252i | \(0.311804\pi\) | |||||||
\(608\) | 12.0000 | − | 20.7846i | 0.486664 | − | 0.842927i | ||||
\(609\) | −1.15153 | − | 5.98353i | −0.0466624 | − | 0.242465i | ||||
\(610\) | 0.426786 | − | 0.246405i | 0.0172801 | − | 0.00997664i | ||||
\(611\) | −13.3485 | + | 23.1202i | −0.540021 | + | 0.935344i | ||||
\(612\) | 28.2843i | 1.14332i | ||||||||
\(613\) | 0.674235 | − | 0.389270i | 0.0272321 | − | 0.0157224i | −0.486322 | − | 0.873780i | \(-0.661662\pi\) |
0.513554 | + | 0.858057i | \(0.328329\pi\) | |||||||
\(614\) | 39.5505 | 1.59613 | ||||||||
\(615\) | 2.55051 | 0.102846 | ||||||||
\(616\) | −36.0000 | + | 6.92820i | −1.45048 | + | 0.279145i | ||||
\(617\) | 3.30306 | 0.132976 | 0.0664881 | − | 0.997787i | \(-0.478821\pi\) | ||||
0.0664881 | + | 0.997787i | \(0.478821\pi\) | |||||||
\(618\) | −7.55051 | −0.303726 | ||||||||
\(619\) | −13.3485 | + | 7.70674i | −0.536520 | + | 0.309760i | −0.743668 | − | 0.668550i | \(-0.766915\pi\) |
0.207147 | + | 0.978310i | \(0.433582\pi\) | |||||||
\(620\) | −3.10102 | −0.124540 | ||||||||
\(621\) | 4.27526 | − | 7.40496i | 0.171560 | − | 0.297151i | ||||
\(622\) | −13.6515 | + | 7.88171i | −0.547377 | + | 0.316028i | ||||
\(623\) | −18.7980 | − | 21.7060i | −0.753124 | − | 0.869633i | ||||
\(624\) | 4.89898 | − | 2.82843i | 0.196116 | − | 0.113228i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.65153 | + | 8.05669i | −0.185913 | + | 0.322010i | ||||
\(627\) | 3.30306 | + | 5.72107i | 0.131912 | + | 0.228478i | ||||
\(628\) | −10.6969 | − | 18.5276i | −0.426854 | − | 0.739333i | ||||
\(629\) | 16.8990 | 0.673806 | ||||||||
\(630\) | 10.6515 | − | 2.04989i | 0.424367 | − | 0.0816695i | ||||
\(631\) | 39.3123i | 1.56500i | 0.622653 | + | 0.782498i | \(0.286055\pi\) | ||||
−0.622653 | + | 0.782498i | \(0.713945\pi\) | |||||||
\(632\) | 10.8990 | − | 18.8776i | 0.433538 | − | 0.750910i | ||||
\(633\) | −2.27015 | + | 1.31067i | −0.0902305 | + | 0.0520946i | ||||
\(634\) | 0.348469 | − | 0.603566i | 0.0138395 | − | 0.0239707i | ||||
\(635\) | −6.00000 | − | 3.46410i | −0.238103 | − | 0.137469i | ||||
\(636\) | −0.651531 | + | 1.12848i | −0.0258349 | + | 0.0447473i | ||||
\(637\) | −24.4722 | − | 19.2669i | −0.969624 | − | 0.763381i | ||||
\(638\) | 25.1010 | + | 43.4762i | 0.993759 | + | 1.72124i | ||||
\(639\) | −3.55051 | − | 2.04989i | −0.140456 | − | 0.0810923i | ||||
\(640\) | −9.79796 | − | 5.65685i | −0.387298 | − | 0.223607i | ||||
\(641\) | 21.6464 | + | 37.4927i | 0.854983 | + | 1.48087i | 0.876661 | + | 0.481108i | \(0.159766\pi\) |
−0.0216787 | + | 0.999765i | \(0.506901\pi\) | |||||||
\(642\) | 2.44949 | 0.0966736 | ||||||||
\(643\) | − | 6.57826i | − | 0.259421i | −0.991552 | − | 0.129711i | \(-0.958595\pi\) | ||
0.991552 | − | 0.129711i | \(-0.0414048\pi\) | |||||||
\(644\) | 15.7980 | + | 18.2419i | 0.622527 | + | 0.718832i | ||||
\(645\) | 3.00340i | 0.118259i | ||||||||
\(646\) | 29.2699i | 1.15161i | ||||||||
\(647\) | −5.29796 | − | 9.17633i | −0.208284 | − | 0.360759i | 0.742890 | − | 0.669414i | \(-0.233455\pi\) |
−0.951174 | + | 0.308655i | \(0.900121\pi\) | |||||||
\(648\) | 19.8434 | − | 11.4566i | 0.779521 | − | 0.450057i | ||||
\(649\) | −15.3031 | − | 8.83523i | −0.600698 | − | 0.346813i | ||||
\(650\) | 5.44949 | − | 3.14626i | 0.213747 | − | 0.123407i | ||||
\(651\) | −0.853572 | − | 0.985620i | −0.0334541 | − | 0.0386295i | ||||
\(652\) | 5.79796 | − | 10.0424i | 0.227066 | − | 0.393289i | ||||
\(653\) | 16.7753 | + | 9.68520i | 0.656466 | + | 0.379011i | 0.790929 | − | 0.611908i | \(-0.209598\pi\) |
−0.134463 | + | 0.990919i | \(0.542931\pi\) | |||||||
\(654\) | −3.06811 | − | 1.77138i | −0.119973 | − | 0.0692662i | ||||
\(655\) | 9.79796 | − | 5.65685i | 0.382838 | − | 0.221032i | ||||
\(656\) | 32.0983i | 1.25323i | ||||||||
\(657\) | − | 32.3840i | − | 1.26342i | ||||||
\(658\) | 14.6969 | + | 16.9706i | 0.572946 | + | 0.661581i | ||||
\(659\) | −36.7423 | −1.43128 | −0.715639 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715639 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(660\) | 2.69694 | − | 1.55708i | 0.104978 | − | 0.0606092i | ||||
\(661\) | −24.8712 | − | 43.0781i | −0.967377 | − | 1.67555i | −0.703090 | − | 0.711101i | \(-0.748197\pi\) |
−0.264287 | − | 0.964444i | \(-0.585137\pi\) | |||||||
\(662\) | −3.85357 | − | 2.22486i | −0.149773 | − | 0.0864717i | ||||
\(663\) | −3.44949 | + | 5.97469i | −0.133967 | + | 0.232038i | ||||
\(664\) | −5.30306 | −0.205799 | ||||||||
\(665\) | 11.0227 | − | 2.12132i | 0.427442 | − | 0.0822613i | ||||
\(666\) | −7.10102 | − | 12.2993i | −0.275159 | − | 0.476589i | ||||
\(667\) | 16.5227 | − | 28.6182i | 0.639762 | − | 1.10810i | ||||
\(668\) | 6.00000 | 0.232147 | ||||||||
\(669\) | −6.79796 | + | 3.92480i | −0.262824 | + | 0.151742i | ||||
\(670\) | − | 17.4634i | − | 0.674669i | ||||||
\(671\) | −1.70714 | −0.0659035 | ||||||||
\(672\) | −0.898979 | − | 4.67123i | −0.0346789 | − | 0.180197i | ||||
\(673\) | −26.8990 | −1.03688 | −0.518440 | − | 0.855114i | \(-0.673487\pi\) | ||||
−0.518440 | + | 0.855114i | \(0.673487\pi\) | |||||||
\(674\) | − | 28.6342i | − | 1.10295i | ||||||
\(675\) | −1.62372 | + | 0.937458i | −0.0624972 | + | 0.0360828i | ||||
\(676\) | −13.5959 | −0.522920 | ||||||||
\(677\) | 15.6742 | − | 27.1486i | 0.602410 | − | 1.04340i | −0.390045 | − | 0.920796i | \(-0.627541\pi\) |
0.992455 | − | 0.122609i | \(-0.0391260\pi\) | |||||||
\(678\) | 1.89898 | + | 3.28913i | 0.0729299 | + | 0.126318i | ||||
\(679\) | −10.3485 | + | 29.8735i | −0.397138 | + | 1.14644i | ||||
\(680\) | 13.7980 | 0.529128 | ||||||||
\(681\) | 1.69694 | − | 2.93918i | 0.0650268 | − | 0.112630i | ||||
\(682\) | 9.30306 | + | 5.37113i | 0.356233 | + | 0.205671i | ||||
\(683\) | 5.72474 | + | 9.91555i | 0.219051 | + | 0.379408i | 0.954518 | − | 0.298153i | \(-0.0963705\pi\) |
−0.735467 | + | 0.677561i | \(0.763037\pi\) | |||||||
\(684\) | 21.3031 | − | 12.2993i | 0.814543 | − | 0.470277i | ||||
\(685\) | −9.79796 | −0.374361 | ||||||||
\(686\) | −22.0454 | + | 14.1421i | −0.841698 | + | 0.539949i | ||||
\(687\) | 5.30691i | 0.202471i | ||||||||
\(688\) | −37.7980 | −1.44103 | ||||||||
\(689\) | 7.89898 | − | 4.56048i | 0.300927 | − | 0.173740i | ||||
\(690\) | −1.77526 | − | 1.02494i | −0.0675828 | − | 0.0390190i | ||||
\(691\) | −27.0000 | − | 15.5885i | −1.02713 | − | 0.593013i | −0.110968 | − | 0.993824i | \(-0.535395\pi\) |
−0.916161 | + | 0.400811i | \(0.868728\pi\) | |||||||
\(692\) | 10.8990 | − | 18.8776i | 0.414317 | − | 0.717618i | ||||
\(693\) | −35.5051 | − | 12.2993i | −1.34873 | − | 0.467213i | ||||
\(694\) | 9.37117 | − | 5.41045i | 0.355725 | − | 0.205378i | ||||
\(695\) | −6.00000 | − | 3.46410i | −0.227593 | − | 0.131401i | ||||
\(696\) | −5.64133 | + | 3.25702i | −0.213834 | + | 0.123457i | ||||
\(697\) | −19.5732 | − | 33.9018i | −0.741388 | − | 1.28412i | ||||
\(698\) | − | 10.2494i | − | 0.387947i | ||||||
\(699\) | 0.0786484i | 0.00297476i | ||||||||
\(700\) | −1.00000 | − | 5.19615i | −0.0377964 | − | 0.196396i | ||||
\(701\) | 23.5809i | 0.890639i | 0.895372 | + | 0.445320i | \(0.146910\pi\) | ||||
−0.895372 | + | 0.445320i | \(0.853090\pi\) | |||||||
\(702\) | 11.7980 | 0.445285 | ||||||||
\(703\) | −7.34847 | − | 12.7279i | −0.277153 | − | 0.480043i | ||||
\(704\) | 19.5959 | + | 33.9411i | 0.738549 | + | 1.27920i | ||||
\(705\) | −1.65153 | − | 0.953512i | −0.0622002 | − | 0.0359113i | ||||
\(706\) | −24.3485 | − | 42.1728i | −0.916367 | − | 1.58719i | ||||
\(707\) | −7.62372 | − | 39.6140i | −0.286720 | − | 1.48984i | ||||
\(708\) | 1.14643 | − | 1.98567i | 0.0430854 | − | 0.0746261i | ||||
\(709\) | 9.21964 | + | 5.32296i | 0.346251 | + | 0.199908i | 0.663033 | − | 0.748590i | \(-0.269269\pi\) |
−0.316782 | + | 0.948498i | \(0.602602\pi\) | |||||||
\(710\) | −1.00000 | + | 1.73205i | −0.0375293 | + | 0.0650027i | ||||
\(711\) | 19.3485 | − | 11.1708i | 0.725624 | − | 0.418939i | ||||
\(712\) | −15.3485 | + | 26.5843i | −0.575208 | + | 0.996290i | ||||
\(713\) | − | 7.07107i | − | 0.264814i | ||||||
\(714\) | 3.79796 | + | 4.38551i | 0.142135 | + | 0.164123i | ||||
\(715\) | −21.7980 | −0.815197 | ||||||||
\(716\) | 9.55051 | + | 16.5420i | 0.356919 | + | 0.618202i | ||||
\(717\) | −0.527806 | − | 0.914188i | −0.0197113 | − | 0.0341410i | ||||
\(718\) | 16.1464 | − | 27.9664i | 0.602579 | − | 1.04370i | ||||
\(719\) | 19.5959 | − | 33.9411i | 0.730804 | − | 1.26579i | −0.225735 | − | 0.974189i | \(-0.572478\pi\) |
0.956540 | − | 0.291602i | \(-0.0941882\pi\) | |||||||
\(720\) | −5.79796 | − | 10.0424i | −0.216077 | − | 0.374257i | ||||
\(721\) | 33.5959 | − | 29.0949i | 1.25118 | − | 1.08355i | ||||
\(722\) | −1.22474 | + | 0.707107i | −0.0455803 | + | 0.0263158i | ||||
\(723\) | 3.24745 | − | 5.62475i | 0.120774 | − | 0.209187i | ||||
\(724\) | 24.6969 | 0.917854 | ||||||||
\(725\) | −6.27526 | + | 3.62302i | −0.233057 | + | 0.134556i | ||||
\(726\) | −5.84337 | −0.216868 | ||||||||
\(727\) | 14.5959 | 0.541333 | 0.270666 | − | 0.962673i | \(-0.412756\pi\) | ||||
0.270666 | + | 0.962673i | \(0.412756\pi\) | |||||||
\(728\) | −10.8990 | + | 31.4626i | −0.403943 | + | 1.16608i | ||||
\(729\) | 21.6969 | 0.803590 | ||||||||
\(730\) | −15.7980 | −0.584709 | ||||||||
\(731\) | 39.9217 | − | 23.0488i | 1.47656 | − | 0.852490i | ||||
\(732\) | − | 0.221513i | − | 0.00818736i | ||||||
\(733\) | −8.55051 | + | 14.8099i | −0.315820 | + | 0.547017i | −0.979612 | − | 0.200901i | \(-0.935613\pi\) |
0.663791 | + | 0.747918i | \(0.268946\pi\) | |||||||
\(734\) | −9.92168 | + | 5.72829i | −0.366216 | + | 0.211435i | ||||
\(735\) | 1.37628 | − | 1.74810i | 0.0507647 | − | 0.0644798i | ||||
\(736\) | 12.8990 | − | 22.3417i | 0.475463 | − | 0.823526i | ||||
\(737\) | −30.2474 | + | 52.3901i | −1.11418 | + | 1.92981i | ||||
\(738\) | −16.4495 | + | 28.4914i | −0.605514 | + | 1.04878i | ||||
\(739\) | 0.348469 | + | 0.603566i | 0.0128186 | + | 0.0222025i | 0.872364 | − | 0.488858i | \(-0.162586\pi\) |
−0.859545 | + | 0.511060i | \(0.829253\pi\) | |||||||
\(740\) | −6.00000 | + | 3.46410i | −0.220564 | + | 0.127343i | ||||
\(741\) | 6.00000 | 0.220416 | ||||||||
\(742\) | −1.44949 | − | 7.53177i | −0.0532124 | − | 0.276500i | ||||
\(743\) | − | 51.1509i | − | 1.87654i | −0.345899 | − | 0.938272i | \(-0.612426\pi\) | ||
0.345899 | − | 0.938272i | \(-0.387574\pi\) | |||||||
\(744\) | −0.696938 | + | 1.20713i | −0.0255510 | + | 0.0442556i | ||||
\(745\) | −16.6237 | + | 9.59771i | −0.609046 | + | 0.351633i | ||||
\(746\) | −12.2474 | + | 21.2132i | −0.448411 | + | 0.776671i | ||||
\(747\) | −4.70714 | − | 2.71767i | −0.172225 | − | 0.0994344i | ||||
\(748\) | −41.3939 | − | 23.8988i | −1.51351 | − | 0.873825i | ||||
\(749\) | −10.8990 | + | 9.43879i | −0.398240 | + | 0.344886i | ||||
\(750\) | 0.224745 | + | 0.389270i | 0.00820652 | + | 0.0142141i | ||||
\(751\) | −43.0454 | − | 24.8523i | −1.57075 | − | 0.906872i | −0.996077 | − | 0.0884887i | \(-0.971796\pi\) |
−0.574672 | − | 0.818384i | \(-0.694870\pi\) | |||||||
\(752\) | 12.0000 | − | 20.7846i | 0.437595 | − | 0.757937i | ||||
\(753\) | 2.17934 | + | 3.77472i | 0.0794195 | + | 0.137559i | ||||
\(754\) | 45.5959 | 1.66051 | ||||||||
\(755\) | − | 7.70674i | − | 0.280477i | ||||||
\(756\) | 3.24745 | − | 9.37458i | 0.118109 | − | 0.340950i | ||||
\(757\) | 33.5125i | 1.21803i | 0.793157 | + | 0.609017i | \(0.208436\pi\) | ||||
−0.793157 | + | 0.609017i | \(0.791564\pi\) | |||||||
\(758\) | 24.5344i | 0.891131i | ||||||||
\(759\) | 3.55051 | + | 6.14966i | 0.128875 | + | 0.223219i | ||||
\(760\) | −6.00000 | − | 10.3923i | −0.217643 | − | 0.376969i | ||||
\(761\) | 10.5959 | + | 6.11756i | 0.384102 | + | 0.221761i | 0.679601 | − | 0.733582i | \(-0.262153\pi\) |
−0.295500 | + | 0.955343i | \(0.595486\pi\) | |||||||
\(762\) | −2.69694 | + | 1.55708i | −0.0976998 | + | 0.0564070i | ||||
\(763\) | 20.4773 | − | 3.94086i | 0.741328 | − | 0.142669i | ||||
\(764\) | 45.7980 | + | 26.4415i | 1.65691 | + | 0.956619i | ||||
\(765\) | 12.2474 | + | 7.07107i | 0.442807 | + | 0.255655i | ||||
\(766\) | 6.37117 | + | 3.67840i | 0.230200 | + | 0.132906i | ||||
\(767\) | −13.8990 | + | 8.02458i | −0.501863 | + | 0.289751i | ||||
\(768\) | −4.40408 | + | 2.54270i | −0.158919 | + | 0.0917517i | ||||
\(769\) | 46.5904i | 1.68009i | 0.542515 | + | 0.840046i | \(0.317472\pi\) | ||||
−0.542515 | + | 0.840046i | \(0.682528\pi\) | |||||||
\(770\) | −6.00000 | + | 17.3205i | −0.216225 | + | 0.624188i | ||||
\(771\) | 4.20204 | 0.151333 | ||||||||
\(772\) | 22.6969 | + | 39.3123i | 0.816881 | + | 1.41488i | ||||
\(773\) | −5.87628 | − | 10.1780i | −0.211355 | − | 0.366078i | 0.740784 | − | 0.671743i | \(-0.234454\pi\) |
−0.952139 | + | 0.305666i | \(0.901121\pi\) | |||||||
\(774\) | −33.5505 | − | 19.3704i | −1.20595 | − | 0.696255i | ||||
\(775\) | −0.775255 | + | 1.34278i | −0.0278480 | + | 0.0482341i | ||||
\(776\) | 33.7980 | 1.21328 | ||||||||
\(777\) | −2.75255 | − | 0.953512i | −0.0987472 | − | 0.0342070i | ||||
\(778\) | 8.00000 | + | 13.8564i | 0.286814 | + | 0.496776i | ||||
\(779\) | −17.0227 | + | 29.4842i | −0.609902 | + | 1.05638i | ||||
\(780\) | − | 2.82843i | − | 0.101274i | ||||||
\(781\) | 6.00000 | − | 3.46410i | 0.214697 | − | 0.123955i | ||||
\(782\) | 31.4626i | 1.12510i | ||||||||
\(783\) | −13.5857 | −0.485514 | ||||||||
\(784\) | 22.0000 | + | 17.3205i | 0.785714 | + | 0.618590i | ||||
\(785\) | −10.6969 | −0.381790 | ||||||||
\(786\) | − | 5.08540i | − | 0.181390i | ||||||
\(787\) | −7.87117 | + | 4.54442i | −0.280577 | + | 0.161991i | −0.633685 | − | 0.773592i | \(-0.718458\pi\) |
0.353108 | + | 0.935583i | \(0.385125\pi\) | |||||||
\(788\) | 1.84281i | 0.0656473i | ||||||||
\(789\) | −0.871173 | + | 1.50892i | −0.0310146 | + | 0.0537188i | ||||
\(790\) | −5.44949 | − | 9.43879i | −0.193884 | − | 0.335817i | ||||
\(791\) | −21.1237 | − | 7.31747i | −0.751073 | − | 0.260179i | ||||
\(792\) | 40.1694i | 1.42736i | ||||||||
\(793\) | −0.775255 | + | 1.34278i | −0.0275301 | + | 0.0476836i | ||||
\(794\) | 0.853572 | + | 0.492810i | 0.0302921 | + | 0.0174892i | ||||
\(795\) | 0.325765 | + | 0.564242i | 0.0115537 | + | 0.0200116i | ||||
\(796\) | 24.6969 | + | 42.7764i | 0.875360 | + | 1.51617i | ||||
\(797\) | −3.30306 | −0.117000 | −0.0585002 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0585002 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(798\) | 1.65153 | − | 4.76756i | 0.0584636 | − | 0.168770i | ||||
\(799\) | 29.2699i | 1.03549i | ||||||||
\(800\) | −4.89898 | + | 2.82843i | −0.173205 | + | 0.100000i | ||||
\(801\) | −27.2474 | + | 15.7313i | −0.962741 | + | 0.555839i | ||||
\(802\) | −37.7196 | − | 21.7774i | −1.33193 | − | 0.768988i | ||||
\(803\) | 47.3939 | + | 27.3629i | 1.67249 | + | 0.965615i | ||||
\(804\) | −6.79796 | − | 3.92480i | −0.239746 | − | 0.138417i | ||||
\(805\) | 11.8485 | − | 2.28024i | 0.417604 | − | 0.0803679i | ||||
\(806\) | 8.44949 | − | 4.87832i | 0.297621 | − | 0.171831i | ||||
\(807\) | 4.50000 | + | 2.59808i | 0.158408 | + | 0.0914566i | ||||
\(808\) | −37.3485 | + | 21.5631i | −1.31391 | + | 0.758589i | ||||
\(809\) | 6.39898 | + | 11.0834i | 0.224976 | + | 0.389670i | 0.956312 | − | 0.292347i | \(-0.0944363\pi\) |
−0.731336 | + | 0.682017i | \(0.761103\pi\) | |||||||
\(810\) | − | 11.4566i | − | 0.402543i | ||||||
\(811\) | 47.3689i | 1.66335i | 0.555264 | + | 0.831674i | \(0.312617\pi\) | ||||
−0.555264 | + | 0.831674i | \(0.687383\pi\) | |||||||
\(812\) | 12.5505 | − | 36.2302i | 0.440437 | − | 1.27143i | ||||
\(813\) | 1.06427i | 0.0373255i | ||||||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | −2.89898 | − | 5.02118i | −0.101547 | − | 0.175884i | ||||
\(816\) | 3.10102 | − | 5.37113i | 0.108557 | − | 0.188027i | ||||
\(817\) | −34.7196 | − | 20.0454i | −1.21469 | − | 0.701300i | ||||
\(818\) | 8.32577 | + | 14.4206i | 0.291104 | + | 0.504206i | ||||
\(819\) | −25.7980 | + | 22.3417i | −0.901454 | + | 0.780682i | ||||
\(820\) | 13.8990 | + | 8.02458i | 0.485373 | + | 0.280230i | ||||
\(821\) | −43.2929 | − | 24.9951i | −1.51093 | − | 0.872336i | −0.999919 | − | 0.0127632i | \(-0.995937\pi\) |
−0.511013 | − | 0.859573i | \(-0.670729\pi\) | |||||||
\(822\) | −2.20204 | + | 3.81405i | −0.0768050 | + | 0.133030i | ||||
\(823\) | 9.15153 | − | 5.28364i | 0.319002 | − | 0.184176i | −0.331945 | − | 0.943299i | \(-0.607705\pi\) |
0.650948 | + | 0.759123i | \(0.274372\pi\) | |||||||
\(824\) | −41.1464 | − | 23.7559i | −1.43340 | − | 0.827576i | ||||
\(825\) | − | 1.55708i | − | 0.0542105i | ||||||
\(826\) | 2.55051 | + | 13.2528i | 0.0887436 | + | 0.461125i | ||||
\(827\) | −13.0454 | −0.453633 | −0.226817 | − | 0.973937i | \(-0.572832\pi\) | ||||
−0.226817 | + | 0.973937i | \(0.572832\pi\) | |||||||
\(828\) | 22.8990 | − | 13.2207i | 0.795795 | − | 0.459452i | ||||
\(829\) | −12.6515 | − | 21.9131i | −0.439406 | − | 0.761073i | 0.558238 | − | 0.829681i | \(-0.311478\pi\) |
−0.997644 | + | 0.0686077i | \(0.978144\pi\) | |||||||
\(830\) | −1.32577 | + | 2.29629i | −0.0460180 | + | 0.0797055i | ||||
\(831\) | −0.921683 | + | 1.59640i | −0.0319728 | + | 0.0553786i | ||||
\(832\) | 35.5959 | 1.23407 | ||||||||
\(833\) | −33.7980 | − | 4.87832i | −1.17103 | − | 0.169024i | ||||
\(834\) | −2.69694 | + | 1.55708i | −0.0933873 | + | 0.0539172i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 41.5692i | 1.43770i | ||||||||
\(837\) | −2.51760 | + | 1.45354i | −0.0870210 | + | 0.0502416i | ||||
\(838\) | 23.5959 | 0.815107 | ||||||||
\(839\) | −30.4949 | −1.05280 | −0.526400 | − | 0.850237i | \(-0.676459\pi\) | ||||
−0.526400 | + | 0.850237i | \(0.676459\pi\) | |||||||
\(840\) | −2.24745 | − | 0.778539i | −0.0775443 | − | 0.0268622i | ||||
\(841\) | −23.5051 | −0.810521 | ||||||||
\(842\) | 5.75255 | 0.198246 | ||||||||
\(843\) | −4.65153 | + | 2.68556i | −0.160207 | + | 0.0924957i | ||||
\(844\) | −16.4949 | −0.567778 | ||||||||
\(845\) | −3.39898 | + | 5.88721i | −0.116928 | + | 0.202526i | ||||
\(846\) | 21.3031 | − | 12.2993i | 0.732414 | − | 0.422860i | ||||
\(847\) | 26.0000 | − | 22.5167i | 0.893371 | − | 0.773682i | ||||
\(848\) | −7.10102 | + | 4.09978i | −0.243850 | + | 0.140787i | ||||
\(849\) | 1.34847 | − | 2.33562i | 0.0462793 | − | 0.0801582i | ||||
\(850\) | 3.44949 | − | 5.97469i | 0.118317 | − | 0.204930i | ||||
\(851\) | −7.89898 | − | 13.6814i | −0.270774 | − | 0.468994i | ||||
\(852\) | 0.449490 | + | 0.778539i | 0.0153993 | + | 0.0266723i | ||||
\(853\) | 48.4495 | 1.65888 | 0.829439 | − | 0.558597i | \(-0.188660\pi\) | ||||
0.829439 | + | 0.558597i | \(0.188660\pi\) | |||||||
\(854\) | 0.853572 | + | 0.985620i | 0.0292086 | + | 0.0337272i | ||||
\(855\) | − | 12.2993i | − | 0.420628i | ||||||
\(856\) | 13.3485 | + | 7.70674i | 0.456241 | + | 0.263411i | ||||
\(857\) | 48.1918 | − | 27.8236i | 1.64620 | − | 0.950435i | 0.667639 | − | 0.744485i | \(-0.267305\pi\) |
0.978562 | − | 0.205950i | \(-0.0660285\pi\) | |||||||
\(858\) | −4.89898 | + | 8.48528i | −0.167248 | + | 0.289683i | ||||
\(859\) | 21.0000 | + | 12.1244i | 0.716511 | + | 0.413678i | 0.813467 | − | 0.581611i | \(-0.197577\pi\) |
−0.0969563 | + | 0.995289i | \(0.530911\pi\) | |||||||
\(860\) | −9.44949 | + | 16.3670i | −0.322225 | + | 0.558110i | ||||
\(861\) | 1.27526 | + | 6.62642i | 0.0434606 | + | 0.225828i | ||||
\(862\) | −6.69694 | − | 11.5994i | −0.228099 | − | 0.395078i | ||||
\(863\) | −2.05051 | − | 1.18386i | −0.0698002 | − | 0.0402992i | 0.464694 | − | 0.885471i | \(-0.346164\pi\) |
−0.534494 | + | 0.845172i | \(0.679498\pi\) | |||||||
\(864\) | −10.6061 | −0.360828 | ||||||||
\(865\) | −5.44949 | − | 9.43879i | −0.185288 | − | 0.320929i | ||||
\(866\) | −10.8990 | −0.370362 | ||||||||
\(867\) | 2.16064i | 0.0733793i | ||||||||
\(868\) | −1.55051 | − | 8.05669i | −0.0526277 | − | 0.273462i | ||||
\(869\) | 37.7552i | 1.28076i | ||||||||
\(870\) | 3.25702i | 0.110423i | ||||||||
\(871\) | 27.4722 | + | 47.5832i | 0.930860 | + | 1.61230i | ||||
\(872\) | −11.1464 | − | 19.3062i | −0.377466 | − | 0.653790i | ||||
\(873\) | 30.0000 | + | 17.3205i | 1.01535 | + | 0.586210i | ||||
\(874\) | 23.6969 | − | 13.6814i | 0.801561 | − | 0.462781i | ||||
\(875\) | −2.50000 | − | 0.866025i | −0.0845154 | − | 0.0292770i | ||||
\(876\) | −3.55051 | + | 6.14966i | −0.119961 | + | 0.207778i | ||||
\(877\) | −1.71964 | − | 0.992836i | −0.0580682 | − | 0.0335257i | 0.470685 | − | 0.882301i | \(-0.344007\pi\) |
−0.528753 | + | 0.848776i | \(0.677340\pi\) | |||||||
\(878\) | 13.5959 | + | 7.84961i | 0.458840 | + | 0.264911i | ||||
\(879\) | 6.74235 | − | 3.89270i | 0.227414 | − | 0.131297i | ||||
\(880\) | 19.5959 | 0.660578 | ||||||||
\(881\) | − | 36.6588i | − | 1.23507i | −0.786545 | − | 0.617533i | \(-0.788132\pi\) | ||
0.786545 | − | 0.617533i | \(-0.211868\pi\) | |||||||
\(882\) | 10.6515 | + | 26.6485i | 0.358656 | + | 0.897303i | ||||
\(883\) | −40.4949 | −1.36276 | −0.681381 | − | 0.731929i | \(-0.738620\pi\) | ||||
−0.681381 | + | 0.731929i | \(0.738620\pi\) | |||||||
\(884\) | −37.5959 | + | 21.7060i | −1.26449 | + | 0.730052i | ||||
\(885\) | −0.573214 | − | 0.992836i | −0.0192684 | − | 0.0333738i | ||||
\(886\) | −20.0227 | − | 11.5601i | −0.672676 | − | 0.388370i | ||||
\(887\) | −13.5000 | + | 23.3827i | −0.453286 | + | 0.785114i | −0.998588 | − | 0.0531258i | \(-0.983082\pi\) |
0.545302 | + | 0.838240i | \(0.316415\pi\) | |||||||
\(888\) | 3.11416i | 0.104504i | ||||||||
\(889\) | 6.00000 | − | 17.3205i | 0.201234 | − | 0.580911i | ||||
\(890\) | 7.67423 | + | 13.2922i | 0.257241 | + | 0.445554i | ||||
\(891\) | −19.8434 | + | 34.3697i | −0.664778 | + | 1.15143i | ||||
\(892\) | −49.3939 | −1.65383 | ||||||||
\(893\) | 22.0454 | − | 12.7279i | 0.737721 | − | 0.425924i | ||||
\(894\) | 8.62815i | 0.288568i | ||||||||
\(895\) | 9.55051 | 0.319238 | ||||||||
\(896\) | 9.79796 | − | 28.2843i | 0.327327 | − | 0.944911i | ||||
\(897\) | 6.44949 | 0.215342 | ||||||||
\(898\) | 1.98567i | 0.0662627i | ||||||||
\(899\) | −9.72985 | + | 5.61753i | −0.324509 | + | 0.187355i | ||||
\(900\) | −5.79796 | −0.193265 | ||||||||
\(901\) | 5.00000 | − | 8.66025i | 0.166574 | − | 0.288515i | ||||
\(902\) | −27.7980 | − | 48.1475i | −0.925571 | − | 1.60314i | ||||
\(903\) | −7.80306 | + | 1.50170i | −0.259670 | + | 0.0499734i | ||||
\(904\) | 23.8988i | 0.794861i | ||||||||
\(905\) | 6.17423 | − | 10.6941i | 0.205239 | − | 0.355484i | ||||
\(906\) | −3.00000 | − | 1.73205i | −0.0996683 | − | 0.0575435i | ||||
\(907\) | 4.17423 | + | 7.22999i | 0.138603 | + | 0.240068i | 0.926968 | − | 0.375140i | \(-0.122405\pi\) |
−0.788365 | + | 0.615208i | \(0.789072\pi\) | |||||||
\(908\) | 18.4949 | − | 10.6780i | 0.613775 | − | 0.354363i | ||||
\(909\) | −44.2020 | −1.46609 | ||||||||
\(910\) | 10.8990 | + | 12.5851i | 0.361298 | + | 0.417191i | ||||
\(911\) | 41.5050i | 1.37512i | 0.726127 | + | 0.687561i | \(0.241319\pi\) | ||||
−0.726127 | + | 0.687561i | \(0.758681\pi\) | |||||||
\(912\) | −5.39388 | −0.178609 | ||||||||
\(913\) | 7.95459 | − | 4.59259i | 0.263259 | − | 0.151992i | ||||
\(914\) | 11.7526 | + | 6.78534i | 0.388740 | + | 0.224439i | ||||
\(915\) | −0.0959179 | − | 0.0553782i | −0.00317095 | − | 0.00183075i | ||||
\(916\) | −16.6969 | + | 28.9199i | −0.551682 | + | 0.955542i | ||||
\(917\) | 19.5959 | + | 22.6274i | 0.647114 | + | 0.747223i | ||||
\(918\) | 11.2020 | − | 6.46750i | 0.369722 | − | 0.213459i | ||||
\(919\) | −12.3712 | − | 7.14250i | −0.408087 | − | 0.235609i | 0.281880 | − | 0.959450i | \(-0.409042\pi\) |
−0.689968 | + | 0.723840i | \(0.742375\pi\) | |||||||
\(920\) | −6.44949 | − | 11.1708i | −0.212633 | − | 0.368292i | ||||
\(921\) | −4.44439 | − | 7.69790i | −0.146448 | − | 0.253655i | ||||
\(922\) | 54.7257i | 1.80230i | ||||||||
\(923\) | − | 6.29253i | − | 0.207121i | ||||||
\(924\) | 5.39388 | + | 6.22831i | 0.177446 | + | 0.204896i | ||||
\(925\) | 3.46410i | 0.113899i | ||||||||
\(926\) | 17.1464 | 0.563467 | ||||||||
\(927\) | −24.3485 | − | 42.1728i | −0.799709 | − | 1.38514i | ||||
\(928\) | −40.9898 | −1.34556 | ||||||||
\(929\) | −5.29796 | − | 3.05878i | −0.173820 | − | 0.100355i | 0.410566 | − | 0.911831i | \(-0.365331\pi\) |
−0.584386 | + | 0.811476i | \(0.698665\pi\) | |||||||
\(930\) | 0.348469 | + | 0.603566i | 0.0114268 | + | 0.0197917i | ||||
\(931\) | 11.0227 | + | 27.5772i | 0.361255 | + | 0.903805i | ||||
\(932\) | −0.247449 | + | 0.428594i | −0.00810545 | + | 0.0140391i | ||||
\(933\) | 3.06811 | + | 1.77138i | 0.100445 | + | 0.0579922i | ||||
\(934\) | −16.0227 | + | 27.7521i | −0.524279 | + | 0.908078i | ||||
\(935\) | −20.6969 | + | 11.9494i | −0.676862 | + | 0.390787i | ||||
\(936\) | 31.5959 | + | 18.2419i | 1.03274 | + | 0.596256i | ||||
\(937\) | − | 10.0424i | − | 0.328070i | −0.986455 | − | 0.164035i | \(-0.947549\pi\) | ||
0.986455 | − | 0.164035i | \(-0.0524509\pi\) | |||||||
\(938\) | 45.3712 | − | 8.73169i | 1.48142 | − | 0.285100i | ||||
\(939\) | 2.09082 | 0.0682312 | ||||||||
\(940\) | −6.00000 | − | 10.3923i | −0.195698 | − | 0.338960i | ||||
\(941\) | −7.89898 | − | 13.6814i | −0.257499 | − | 0.446002i | 0.708072 | − | 0.706140i | \(-0.249565\pi\) |
−0.965571 | + | 0.260138i | \(0.916232\pi\) | |||||||
\(942\) | −2.40408 | + | 4.16399i | −0.0783292 | + | 0.135670i | ||||
\(943\) | −18.2980 | + | 31.6930i | −0.595864 | + | 1.03207i | ||||
\(944\) | 12.4949 | − | 7.21393i | 0.406674 | − | 0.234794i | ||||
\(945\) | −3.24745 | − | 3.74983i | −0.105640 | − | 0.121982i | ||||
\(946\) | 56.6969 | − | 32.7340i | 1.84338 | − | 1.06427i | ||||
\(947\) | −23.7247 | + | 41.0925i | −0.770951 | + | 1.33533i | 0.166092 | + | 0.986110i | \(0.446885\pi\) |
−0.937042 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(948\) | −4.89898 | −0.159111 | ||||||||
\(949\) | 43.0454 | − | 24.8523i | 1.39731 | − | 0.806739i | ||||
\(950\) | −6.00000 | −0.194666 | ||||||||
\(951\) | −0.156633 | −0.00507918 | ||||||||
\(952\) | 6.89898 | + | 35.8481i | 0.223597 | + | 1.16185i | ||||
\(953\) | −10.8990 | −0.353053 | −0.176526 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176526 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(954\) | −8.40408 | −0.272092 | ||||||||
\(955\) | 22.8990 | − | 13.2207i | 0.740994 | − | 0.427813i | ||||
\(956\) | − | 6.64247i | − | 0.214833i | ||||||
\(957\) | 5.64133 | − | 9.77106i | 0.182358 | − | 0.315854i | ||||
\(958\) | −10.3485 | + | 5.97469i | −0.334344 | + | 0.193034i | ||||
\(959\) | −4.89898 | − | 25.4558i | −0.158196 | − | 0.822012i | ||||
\(960\) | 2.54270i | 0.0820652i | ||||||||
\(961\) | 14.2980 | − | 24.7648i | 0.461224 | − | 0.798864i | ||||
\(962\) | 10.8990 | − | 18.8776i | 0.351397 | − | 0.608638i | ||||
\(963\) | 7.89898 | + | 13.6814i | 0.254541 | + | 0.440878i | ||||
\(964\) | 35.3939 | − | 20.4347i | 1.13996 | − | 0.658156i | ||||
\(965\) | 22.6969 | 0.730640 | ||||||||
\(966\) | 1.77526 | − | 5.12472i | 0.0571179 | − | 0.164885i | ||||
\(967\) | − | 52.6437i | − | 1.69291i | −0.532461 | − | 0.846454i | \(-0.678733\pi\) | ||
0.532461 | − | 0.846454i | \(-0.321267\pi\) | |||||||
\(968\) | −31.8434 | − | 18.3848i | −1.02348 | − | 0.590909i | ||||
\(969\) | 5.69694 | − | 3.28913i | 0.183012 | − | 0.105662i | ||||
\(970\) | 8.44949 | − | 14.6349i | 0.271297 | − | 0.469900i | ||||
\(971\) | −26.1464 | − | 15.0956i | −0.839079 | − | 0.484442i | 0.0178722 | − | 0.999840i | \(-0.494311\pi\) |
−0.856951 | + | 0.515398i | \(0.827644\pi\) | |||||||
\(972\) | −14.2020 | − | 8.19955i | −0.455531 | − | 0.263001i | ||||
\(973\) | 6.00000 | − | 17.3205i | 0.192351 | − | 0.555270i | ||||
\(974\) | −21.5505 | − | 37.3266i | −0.690523 | − | 1.19602i | ||||
\(975\) | −1.22474 | − | 0.707107i | −0.0392232 | − | 0.0226455i | ||||
\(976\) | 0.696938 | − | 1.20713i | 0.0223085 | − | 0.0386394i | ||||
\(977\) | 14.6969 | + | 25.4558i | 0.470197 | + | 0.814405i | 0.999419 | − | 0.0340785i | \(-0.0108496\pi\) |
−0.529222 | + | 0.848483i | \(0.677516\pi\) | |||||||
\(978\) | −2.60612 | −0.0833346 | ||||||||
\(979\) | − | 53.1687i | − | 1.69928i | ||||||
\(980\) | 13.0000 | − | 5.19615i | 0.415270 | − | 0.165985i | ||||
\(981\) | − | 22.8489i | − | 0.729510i | ||||||
\(982\) | − | 1.20713i | − | 0.0385212i | ||||||
\(983\) | −7.50000 | − | 12.9904i | −0.239213 | − | 0.414329i | 0.721276 | − | 0.692648i | \(-0.243556\pi\) |
−0.960489 | + | 0.278319i | \(0.910223\pi\) | |||||||
\(984\) | 6.24745 | − | 3.60697i | 0.199161 | − | 0.114986i | ||||
\(985\) | 0.797959 | + | 0.460702i | 0.0254251 | + | 0.0146792i | ||||
\(986\) | 43.2929 | − | 24.9951i | 1.37873 | − | 0.796007i | ||||
\(987\) | 1.65153 | − | 4.76756i | 0.0525688 | − | 0.151753i | ||||
\(988\) | 32.6969 | + | 18.8776i | 1.04023 | + | 0.600576i | ||||
\(989\) | −37.3207 | − | 21.5471i | −1.18673 | − | 0.685158i | ||||
\(990\) | 17.3939 | + | 10.0424i | 0.552814 | + | 0.319167i | ||||
\(991\) | 25.7196 | − | 14.8492i | 0.817011 | − | 0.471702i | −0.0323734 | − | 0.999476i | \(-0.510307\pi\) |
0.849385 | + | 0.527774i | \(0.176973\pi\) | |||||||
\(992\) | −7.59592 | + | 4.38551i | −0.241171 | + | 0.139240i | ||||
\(993\) | 1.00005i | 0.0317357i | ||||||||
\(994\) | −5.00000 | − | 1.73205i | −0.158590 | − | 0.0549373i | ||||
\(995\) | 24.6969 | 0.782946 | ||||||||
\(996\) | 0.595918 | + | 1.03216i | 0.0188824 | + | 0.0327052i | ||||
\(997\) | −13.3258 | − | 23.0809i | −0.422031 | − | 0.730980i | 0.574107 | − | 0.818780i | \(-0.305349\pi\) |
−0.996138 | + | 0.0878009i | \(0.972016\pi\) | |||||||
\(998\) | −33.5505 | − | 19.3704i | −1.06202 | − | 0.613159i | ||||
\(999\) | −3.24745 | + | 5.62475i | −0.102745 | + | 0.177959i |
(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 | 280.2.bj.b.131.1 | ✓ | 4 | |
4.3 | odd | 2 | 1120.2.bz.b.271.1 | 4 | |||
7.3 | odd | 6 | 280.2.bj.c.171.2 | yes | 4 | ||
8.3 | odd | 2 | 280.2.bj.c.131.2 | yes | 4 | ||
8.5 | even | 2 | 1120.2.bz.c.271.1 | 4 | |||
28.3 | even | 6 | 1120.2.bz.c.591.1 | 4 | |||
56.3 | even | 6 | inner | 280.2.bj.b.171.2 | yes | 4 | |
56.45 | odd | 6 | 1120.2.bz.b.591.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.b.131.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
280.2.bj.b.171.2 | yes | 4 | 56.3 | even | 6 | inner | |
280.2.bj.c.131.2 | yes | 4 | 8.3 | odd | 2 | ||
280.2.bj.c.171.2 | yes | 4 | 7.3 | odd | 6 | ||
1120.2.bz.b.271.1 | 4 | 4.3 | odd | 2 | |||
1120.2.bz.b.591.1 | 4 | 56.45 | odd | 6 | |||
1120.2.bz.c.271.1 | 4 | 8.5 | even | 2 | |||
1120.2.bz.c.591.1 | 4 | 28.3 | even | 6 |