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: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 171.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.171 |
Dual form | 280.2.bj.c.131.2 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.866025 | + | 0.500000i | ||||
\(3\) | −0.275255 | − | 0.158919i | −0.158919 | − | 0.0917517i | 0.418432 | − | 0.908248i | \(-0.362580\pi\) |
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 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 | ||||
\(10\) | 1.41421i | 0.447214i | ||||||||
\(11\) | −2.44949 | + | 4.24264i | −0.738549 | + | 1.27920i | 0.214600 | + | 0.976702i | \(0.431155\pi\) |
−0.953149 | + | 0.302502i | \(0.902178\pi\) | |||||||
\(12\) | − | 0.635674i | − | 0.183503i | ||||||
\(13\) | 4.44949 | 1.23407 | 0.617033 | − | 0.786937i | \(-0.288334\pi\) | ||||
0.617033 | + | 0.786937i | \(0.288334\pi\) | |||||||
\(14\) | 3.67423 | + | 0.707107i | 0.981981 | + | 0.188982i | ||||
\(15\) | − | 0.317837i | − | 0.0820652i | ||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −4.22474 | − | 2.43916i | −1.02465 | − | 0.591583i | −0.109203 | − | 0.994019i | \(-0.534830\pi\) |
−0.915448 | + | 0.402437i | \(0.868163\pi\) | |||||||
\(18\) | − | 4.09978i | − | 0.966326i | ||||||
\(19\) | 3.67423 | − | 2.12132i | 0.842927 | − | 0.486664i | −0.0153309 | − | 0.999882i | \(-0.504880\pi\) |
0.858258 | + | 0.513218i | \(0.171547\pi\) | |||||||
\(20\) | −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 | \(-0.824386\pi\) |
0.0281052 | + | 0.999605i | \(0.491053\pi\) | |||||||
\(24\) | 0.449490 | − | 0.778539i | 0.0917517 | − | 0.158919i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 5.44949 | + | 3.14626i | 1.06873 | + | 0.617033i | ||||
\(27\) | 1.87492i | 0.360828i | ||||||||
\(28\) | 4.00000 | + | 3.46410i | 0.755929 | + | 0.654654i | ||||
\(29\) | − | 7.24604i | − | 1.34556i | −0.739844 | − | 0.672778i | \(-0.765101\pi\) | ||
0.739844 | − | 0.672778i | \(-0.234899\pi\) | |||||||
\(30\) | 0.224745 | − | 0.389270i | 0.0410326 | − | 0.0710706i | ||||
\(31\) | 0.775255 | − | 1.34278i | 0.139240 | − | 0.241171i | −0.787969 | − | 0.615715i | \(-0.788867\pi\) |
0.927209 | + | 0.374544i | \(0.122201\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.866025 | + | 0.500000i | ||||
\(33\) | 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 | \(-0.574757\pi\) |
0.725900 | + | 0.687800i | \(0.241424\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | −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 | \(-0.784440\pi\) | ||
0.779329 | − | 0.626614i | \(-0.215560\pi\) | |||||||
\(42\) | −0.898979 | − | 0.778539i | −0.138716 | − | 0.120131i | ||||
\(43\) | −9.44949 | −1.44103 | −0.720517 | − | 0.693437i | \(-0.756095\pi\) | ||||
−0.720517 | + | 0.693437i | \(0.756095\pi\) | |||||||
\(44\) | −9.79796 | −1.47710 | ||||||||
\(45\) | 1.44949 | − | 2.51059i | 0.216077 | − | 0.374257i | ||||
\(46\) | −6.44949 | −0.950925 | ||||||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | 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 | ||||
\(52\) | 4.44949 | + | 7.70674i | 0.617033 | + | 1.06873i | ||||
\(53\) | 1.77526 | + | 1.02494i | 0.243850 | + | 0.140787i | 0.616945 | − | 0.787006i | \(-0.288370\pi\) |
−0.373095 | + | 0.927793i | \(0.621703\pi\) | |||||||
\(54\) | −1.32577 | + | 2.29629i | −0.180414 | + | 0.312486i | ||||
\(55\) | −4.89898 | −0.660578 | ||||||||
\(56\) | 2.44949 | + | 7.07107i | 0.327327 | + | 0.944911i | ||||
\(57\) | −1.34847 | −0.178609 | ||||||||
\(58\) | 5.12372 | − | 8.87455i | 0.672778 | − | 1.16529i | ||||
\(59\) | 3.12372 | + | 1.80348i | 0.406674 | + | 0.234794i | 0.689360 | − | 0.724419i | \(-0.257892\pi\) |
−0.282686 | + | 0.959213i | \(0.591225\pi\) | |||||||
\(60\) | 0.550510 | − | 0.317837i | 0.0710706 | − | 0.0410326i | ||||
\(61\) | −0.174235 | − | 0.301783i | −0.0223085 | − | 0.0386394i | 0.854656 | − | 0.519195i | \(-0.173768\pi\) |
−0.876964 | + | 0.480556i | \(0.840435\pi\) | |||||||
\(62\) | 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 | ||||
\(66\) | 2.20204 | 0.271053 | ||||||||
\(67\) | −6.17423 | + | 10.6941i | −0.754303 | + | 1.30649i | 0.191417 | + | 0.981509i | \(0.438692\pi\) |
−0.945720 | + | 0.324982i | \(0.894642\pi\) | |||||||
\(68\) | − | 9.75663i | − | 1.18317i | ||||||
\(69\) | 1.44949 | 0.174498 | ||||||||
\(70\) | 1.22474 | + | 3.53553i | 0.146385 | + | 0.422577i | ||||
\(71\) | 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 | −0.187775 | − | 0.982212i | \(-0.560128\pi\) |
−0.944508 | + | 0.328488i | \(0.893461\pi\) | |||||||
\(74\) | 4.89898 | 0.569495 | ||||||||
\(75\) | 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 | \(-0.523932\pi\) |
0.826023 | + | 0.563637i | \(0.190598\pi\) | |||||||
\(80\) | −4.00000 | −0.447214 | ||||||||
\(81\) | −4.05051 | + | 7.01569i | −0.450057 | + | 0.779521i | ||||
\(82\) | 5.67423 | − | 9.82806i | 0.626614 | − | 1.08533i | ||||
\(83\) | − | 1.87492i | − | 0.205799i | −0.994692 | − | 0.102899i | \(-0.967188\pi\) | ||
0.994692 | − | 0.102899i | \(-0.0328120\pi\) | |||||||
\(84\) | −0.550510 | − | 1.58919i | −0.0600656 | − | 0.173394i | ||||
\(85\) | − | 4.87832i | − | 0.529128i | ||||||
\(86\) | −11.5732 | − | 6.68180i | −1.24797 | − | 0.720517i | ||||
\(87\) | −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 | 0.0891414 | − | 0.996019i | \(-0.471588\pi\) |
0.907148 | + | 0.420811i | \(0.138254\pi\) | |||||||
\(90\) | 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 | ||||
\(94\) | − | 8.48528i | − | 0.875190i | ||||||
\(95\) | 3.67423 | + | 2.12132i | 0.376969 | + | 0.217643i | ||||
\(96\) | 1.79796 | 0.183503 | ||||||||
\(97\) | 11.9494i | 1.21328i | 0.794978 | + | 0.606638i | \(0.207482\pi\) | ||||
−0.794978 | + | 0.606638i | \(0.792518\pi\) | |||||||
\(98\) | 9.79796 | − | 1.41421i | 0.989743 | − | 0.142857i | ||||
\(99\) | 14.2020 | 1.42736 | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | −7.62372 | + | 13.2047i | −0.758589 | + | 1.31391i | 0.184981 | + | 0.982742i | \(0.440778\pi\) |
−0.943570 | + | 0.331173i | \(0.892556\pi\) | |||||||
\(102\) | 2.19275i | 0.217115i | ||||||||
\(103\) | 8.39898 | + | 14.5475i | 0.827576 | + | 1.43340i | 0.899935 | + | 0.436025i | \(0.143614\pi\) |
−0.0723585 | + | 0.997379i | \(0.523053\pi\) | |||||||
\(104\) | 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 | 0.967146 | − | 0.254221i | \(-0.0818191\pi\) |
−0.703735 | + | 0.710462i | \(0.748486\pi\) | |||||||
\(108\) | −3.24745 | + | 1.87492i | −0.312486 | + | 0.180414i | ||||
\(109\) | 6.82577 | + | 3.94086i | 0.653790 | + | 0.377466i | 0.789907 | − | 0.613227i | \(-0.210129\pi\) |
−0.136117 | + | 0.990693i | \(0.543462\pi\) | |||||||
\(110\) | −6.00000 | − | 3.46410i | −0.572078 | − | 0.330289i | ||||
\(111\) | −1.10102 | −0.104504 | ||||||||
\(112\) | −2.00000 | + | 10.3923i | −0.188982 | + | 0.981981i | ||||
\(113\) | 8.44949 | 0.794861 | 0.397431 | − | 0.917632i | \(-0.369902\pi\) | ||||
0.397431 | + | 0.917632i | \(0.369902\pi\) | |||||||
\(114\) | −1.65153 | − | 0.953512i | −0.154680 | − | 0.0893046i | ||||
\(115\) | −3.94949 | − | 2.28024i | −0.368292 | − | 0.212633i | ||||
\(116\) | 12.5505 | − | 7.24604i | 1.16529 | − | 0.672778i | ||||
\(117\) | −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 | ||||
\(122\) | − | 0.492810i | − | 0.0446169i | ||||||
\(123\) | −1.27526 | + | 2.20881i | −0.114986 | + | 0.199161i | ||||
\(124\) | 3.10102 | 0.278480 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.55051 | − | 10.2494i | −0.316305 | − | 0.913093i | ||||
\(127\) | 6.92820i | 0.614779i | 0.951584 | + | 0.307389i | \(0.0994554\pi\) | ||||
−0.951584 | + | 0.307389i | \(0.900545\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.866025 | − | 0.500000i | ||||
\(129\) | 2.60102 | + | 1.50170i | 0.229007 | + | 0.132217i | ||||
\(130\) | 6.29253i | 0.551891i | ||||||||
\(131\) | −9.79796 | + | 5.65685i | −0.856052 | + | 0.494242i | −0.862688 | − | 0.505736i | \(-0.831221\pi\) |
0.00663646 | + | 0.999978i | \(0.497888\pi\) | |||||||
\(132\) | 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 | −0.577246 | − | 0.816571i | \(-0.695872\pi\) |
0.995794 | + | 0.0916241i | \(0.0292058\pi\) | |||||||
\(138\) | 1.77526 | + | 1.02494i | 0.151120 | + | 0.0872490i | ||||
\(139\) | − | 6.92820i | − | 0.587643i | −0.955860 | − | 0.293821i | \(-0.905073\pi\) | ||
0.955860 | − | 0.293821i | \(-0.0949270\pi\) | |||||||
\(140\) | −1.00000 | + | 5.19615i | −0.0845154 | + | 0.439155i | ||||
\(141\) | 1.90702i | 0.160600i | ||||||||
\(142\) | −1.00000 | + | 1.73205i | −0.0839181 | + | 0.145350i | ||||
\(143\) | −10.8990 | + | 18.8776i | −0.911418 | + | 1.57862i | ||||
\(144\) | 11.5959 | 0.966326 | ||||||||
\(145\) | 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 | \(-0.954660\pi\) |
−0.371996 | + | 0.928234i | \(0.621327\pi\) | |||||||
\(150\) | 0.449490 | 0.0367007 | ||||||||
\(151\) | 6.67423 | + | 3.85337i | 0.543142 | + | 0.313583i | 0.746351 | − | 0.665552i | \(-0.231804\pi\) |
−0.203210 | + | 0.979135i | \(0.565137\pi\) | |||||||
\(152\) | 6.00000 | + | 10.3923i | 0.486664 | + | 0.842927i | ||||
\(153\) | 14.1421i | 1.14332i | ||||||||
\(154\) | −12.0000 | + | 13.8564i | −0.966988 | + | 1.11658i | ||||
\(155\) | 1.55051 | 0.124540 | ||||||||
\(156\) | − | 2.82843i | − | 0.226455i | ||||||
\(157\) | −5.34847 | + | 9.26382i | −0.426854 | + | 0.739333i | −0.996592 | − | 0.0824935i | \(-0.973712\pi\) |
0.569737 | + | 0.821827i | \(0.307045\pi\) | |||||||
\(158\) | 10.8990 | 0.867076 | ||||||||
\(159\) | −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 | 0.729872 | − | 0.683584i | \(-0.239580\pi\) |
−0.956937 | + | 0.290295i | \(0.906247\pi\) | |||||||
\(164\) | 13.8990 | − | 8.02458i | 1.08533 | − | 0.626614i | ||||
\(165\) | 1.34847 | + | 0.778539i | 0.104978 | + | 0.0606092i | ||||
\(166\) | 1.32577 | − | 2.29629i | 0.102899 | − | 0.178227i | ||||
\(167\) | 3.00000 | 0.232147 | 0.116073 | − | 0.993241i | \(-0.462969\pi\) | ||||
0.116073 | + | 0.993241i | \(0.462969\pi\) | |||||||
\(168\) | 0.449490 | − | 2.33562i | 0.0346789 | − | 0.180197i | ||||
\(169\) | 6.79796 | 0.522920 | ||||||||
\(170\) | 3.44949 | − | 5.97469i | 0.264564 | − | 0.458238i | ||||
\(171\) | −10.6515 | − | 6.14966i | −0.814543 | − | 0.470277i | ||||
\(172\) | −9.44949 | − | 16.3670i | −0.720517 | − | 1.24797i | ||||
\(173\) | 5.44949 | + | 9.43879i | 0.414317 | + | 0.717618i | 0.995356 | − | 0.0962572i | \(-0.0306871\pi\) |
−0.581039 | + | 0.813875i | \(0.697354\pi\) | |||||||
\(174\) | −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 | ||||
\(178\) | 15.3485 | 1.15042 | ||||||||
\(179\) | −4.77526 | + | 8.27098i | −0.356919 | + | 0.618202i | −0.987444 | − | 0.157966i | \(-0.949506\pi\) |
0.630525 | + | 0.776169i | \(0.282840\pi\) | |||||||
\(180\) | 5.79796 | 0.432154 | ||||||||
\(181\) | 12.3485 | 0.917854 | 0.458927 | − | 0.888474i | \(-0.348234\pi\) | ||||
0.458927 | + | 0.888474i | \(0.348234\pi\) | |||||||
\(182\) | 16.3485 | + | 3.14626i | 1.21183 | + | 0.233217i | ||||
\(183\) | 0.110756i | 0.00818736i | ||||||||
\(184\) | −6.44949 | − | 11.1708i | −0.475463 | − | 0.823526i | ||||
\(185\) | 3.00000 | + | 1.73205i | 0.220564 | + | 0.127343i | ||||
\(186\) | −0.696938 | −0.0511020 | ||||||||
\(187\) | 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 | 0.682784 | − | 0.730620i | \(-0.260769\pi\) |
0.974128 | − | 0.225999i | \(-0.0725645\pi\) | |||||||
\(192\) | 2.20204 | + | 1.27135i | 0.158919 | + | 0.0917517i | ||||
\(193\) | −11.3485 | + | 19.6561i | −0.816881 | + | 1.41488i | 0.0910889 | + | 0.995843i | \(0.470965\pi\) |
−0.907970 | + | 0.419036i | \(0.862368\pi\) | |||||||
\(194\) | −8.44949 | + | 14.6349i | −0.606638 | + | 1.05073i | ||||
\(195\) | − | 1.41421i | − | 0.101274i | ||||||
\(196\) | 13.0000 | + | 5.19615i | 0.928571 | + | 0.371154i | ||||
\(197\) | − | 0.921404i | − | 0.0656473i | −0.999461 | − | 0.0328236i | \(-0.989550\pi\) | ||
0.999461 | − | 0.0328236i | \(-0.0104500\pi\) | |||||||
\(198\) | 17.3939 | + | 10.0424i | 1.23613 | + | 0.713679i | ||||
\(199\) | 12.3485 | − | 21.3882i | 0.875360 | − | 1.51617i | 0.0189808 | − | 0.999820i | \(-0.493958\pi\) |
0.856379 | − | 0.516348i | \(-0.172709\pi\) | |||||||
\(200\) | −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 | ||||
\(206\) | 23.7559i | 1.65515i | ||||||||
\(207\) | 11.4495 | + | 6.61037i | 0.795795 | + | 0.459452i | ||||
\(208\) | −8.89898 | + | 15.4135i | −0.617033 | + | 1.06873i | ||||
\(209\) | 20.7846i | 1.43770i | ||||||||
\(210\) | 0.224745 | − | 1.16781i | 0.0155089 | − | 0.0805865i | ||||
\(211\) | 8.24745 | 0.567778 | 0.283889 | − | 0.958857i | \(-0.408375\pi\) | ||||
0.283889 | + | 0.958857i | \(0.408375\pi\) | |||||||
\(212\) | 4.09978i | 0.281574i | ||||||||
\(213\) | 0.224745 | − | 0.389270i | 0.0153993 | − | 0.0266723i | ||||
\(214\) | 7.70674i | 0.526822i | ||||||||
\(215\) | −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 | ||||
\(220\) | −4.89898 | − | 8.48528i | −0.330289 | − | 0.572078i | ||||
\(221\) | −18.7980 | − | 10.8530i | −1.26449 | − | 0.730052i | ||||
\(222\) | −1.34847 | − | 0.778539i | −0.0905033 | − | 0.0522521i | ||||
\(223\) | −24.6969 | −1.65383 | −0.826915 | − | 0.562327i | \(-0.809906\pi\) | ||||
−0.826915 | + | 0.562327i | \(0.809906\pi\) | |||||||
\(224\) | −9.79796 | + | 11.3137i | −0.654654 | + | 0.755929i | ||||
\(225\) | 2.89898 | 0.193265 | ||||||||
\(226\) | 10.3485 | + | 5.97469i | 0.688370 | + | 0.397431i | ||||
\(227\) | −9.24745 | − | 5.33902i | −0.613775 | − | 0.354363i | 0.160667 | − | 0.987009i | \(-0.448636\pi\) |
−0.774441 | + | 0.632646i | \(0.781969\pi\) | |||||||
\(228\) | −1.34847 | − | 2.33562i | −0.0893046 | − | 0.154680i | ||||
\(229\) | −8.34847 | − | 14.4600i | −0.551682 | − | 0.955542i | −0.998153 | − | 0.0607438i | \(-0.980653\pi\) |
0.446471 | − | 0.894798i | \(-0.352681\pi\) | |||||||
\(230\) | −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 | 0.870050 | − | 0.492964i | \(-0.164087\pi\) |
−0.861944 | + | 0.507003i | \(0.830753\pi\) | |||||||
\(234\) | − | 18.2419i | − | 1.19251i | ||||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | 7.21393i | 0.469587i | ||||||||
\(237\) | −2.44949 | −0.159111 | ||||||||
\(238\) | −13.7980 | − | 11.9494i | −0.894389 | − | 0.774563i | ||||
\(239\) | 3.32124i | 0.214833i | 0.994214 | + | 0.107416i | \(0.0342578\pi\) | ||||
−0.994214 | + | 0.107416i | \(0.965742\pi\) | |||||||
\(240\) | 1.10102 | + | 0.635674i | 0.0710706 | + | 0.0410326i | ||||
\(241\) | −17.6969 | − | 10.2173i | −1.13996 | − | 0.658156i | −0.193539 | − | 0.981093i | \(-0.561997\pi\) |
−0.946421 | + | 0.322936i | \(0.895330\pi\) | |||||||
\(242\) | − | 18.3848i | − | 1.18182i | ||||||
\(243\) | 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 | ||||
\(250\) | −1.22474 | − | 0.707107i | −0.0774597 | − | 0.0447214i | ||||
\(251\) | 13.7135i | 0.865591i | 0.901492 | + | 0.432796i | \(0.142473\pi\) | ||||
−0.901492 | + | 0.432796i | \(0.857527\pi\) | |||||||
\(252\) | 2.89898 | − | 15.0635i | 0.182619 | − | 0.948914i | ||||
\(253\) | − | 22.3417i | − | 1.40461i | ||||||
\(254\) | −4.89898 | + | 8.48528i | −0.307389 | + | 0.532414i | ||||
\(255\) | −0.775255 | + | 1.34278i | −0.0485484 | + | 0.0840882i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −11.4495 | + | 6.61037i | −0.714200 | + | 0.412343i | −0.812614 | − | 0.582802i | \(-0.801956\pi\) |
0.0984145 | + | 0.995146i | \(0.468623\pi\) | |||||||
\(258\) | 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 | ||||
\(262\) | −16.0000 | −0.988483 | ||||||||
\(263\) | −4.74745 | − | 2.74094i | −0.292740 | − | 0.169014i | 0.346437 | − | 0.938073i | \(-0.387392\pi\) |
−0.639177 | + | 0.769060i | \(0.720725\pi\) | |||||||
\(264\) | 2.20204 | + | 3.81405i | 0.135526 | + | 0.234738i | ||||
\(265\) | 2.04989i | 0.125924i | ||||||||
\(266\) | 15.0000 | − | 5.19615i | 0.919709 | − | 0.318597i | ||||
\(267\) | −3.44949 | −0.211105 | ||||||||
\(268\) | −24.6969 | −1.50861 | ||||||||
\(269\) | 8.17423 | − | 14.1582i | 0.498392 | − | 0.863240i | −0.501606 | − | 0.865096i | \(-0.667257\pi\) |
0.999998 | + | 0.00185590i | \(0.000590752\pi\) | |||||||
\(270\) | −2.65153 | −0.161367 | ||||||||
\(271\) | −1.67423 | − | 2.89986i | −0.101703 | − | 0.176154i | 0.810684 | − | 0.585484i | \(-0.199096\pi\) |
−0.912386 | + | 0.409330i | \(0.865762\pi\) | |||||||
\(272\) | 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 | ||||
\(276\) | 1.44949 | + | 2.51059i | 0.0872490 | + | 0.151120i | ||||
\(277\) | −5.02270 | − | 2.89986i | −0.301785 | − | 0.174236i | 0.341459 | − | 0.939896i | \(-0.389079\pi\) |
−0.643245 | + | 0.765661i | \(0.722412\pi\) | |||||||
\(278\) | 4.89898 | − | 8.48528i | 0.293821 | − | 0.508913i | ||||
\(279\) | −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 | \(0.331841\pi\) | |||||||
\(282\) | −1.34847 | + | 2.33562i | −0.0803002 | + | 0.139084i | ||||
\(283\) | −7.34847 | − | 4.24264i | −0.436821 | − | 0.252199i | 0.265427 | − | 0.964131i | \(-0.414487\pi\) |
−0.702248 | + | 0.711932i | \(0.747820\pi\) | |||||||
\(284\) | −2.44949 | + | 1.41421i | −0.145350 | + | 0.0839181i | ||||
\(285\) | −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 | ||||
\(290\) | 10.2474 | 0.601751 | ||||||||
\(291\) | 1.89898 | − | 3.28913i | 0.111320 | − | 0.192812i | ||||
\(292\) | − | 22.3417i | − | 1.30745i | ||||||
\(293\) | 24.4949 | 1.43101 | 0.715504 | − | 0.698609i | \(-0.246197\pi\) | ||||
0.715504 | + | 0.698609i | \(0.246197\pi\) | |||||||
\(294\) | −2.92168 | − | 1.16781i | −0.170396 | − | 0.0681080i | ||||
\(295\) | 3.60697i | 0.210006i | ||||||||
\(296\) | 4.89898 | + | 8.48528i | 0.284747 | + | 0.493197i | ||||
\(297\) | −7.95459 | − | 4.59259i | −0.461572 | − | 0.266489i | ||||
\(298\) | −27.1464 | −1.57255 | ||||||||
\(299\) | −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 | ||||
\(304\) | 16.9706i | 0.973329i | ||||||||
\(305\) | 0.174235 | − | 0.301783i | 0.00997664 | − | 0.0172801i | ||||
\(306\) | −10.0000 | + | 17.3205i | −0.571662 | + | 0.990148i | ||||
\(307\) | − | 27.9664i | − | 1.59613i | −0.602572 | − | 0.798064i | \(-0.705857\pi\) | ||
0.602572 | − | 0.798064i | \(-0.294143\pi\) | |||||||
\(308\) | −24.4949 | + | 8.48528i | −1.39573 | + | 0.483494i | ||||
\(309\) | − | 5.33902i | − | 0.303726i | ||||||
\(310\) | 1.89898 | + | 1.09638i | 0.107855 | + | 0.0622700i | ||||
\(311\) | 5.57321 | − | 9.65309i | 0.316028 | − | 0.547377i | −0.663628 | − | 0.748063i | \(-0.730984\pi\) |
0.979655 | + | 0.200687i | \(0.0643173\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | −5.69694 | + | 3.28913i | −0.322010 | + | 0.185913i | −0.652288 | − | 0.757971i | \(-0.726191\pi\) |
0.330278 | + | 0.943884i | \(0.392857\pi\) | |||||||
\(314\) | −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 | \(-0.671072\pi\) |
0.487967 | + | 0.872862i | \(0.337739\pi\) | |||||||
\(318\) | − | 0.921404i | − | 0.0516698i | ||||||
\(319\) | 30.7423 | + | 17.7491i | 1.72124 | + | 0.993759i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.223607 | − | 0.387298i | ||||
\(321\) | − | 1.73205i | − | 0.0966736i | ||||||
\(322\) | −16.1237 | + | 5.58542i | −0.898540 | + | 0.311263i | ||||
\(323\) | −20.6969 | −1.15161 | ||||||||
\(324\) | −16.2020 | −0.900113 | ||||||||
\(325\) | −2.22474 | + | 3.85337i | −0.123407 | + | 0.213747i | ||||
\(326\) | − | 8.19955i | − | 0.454131i | ||||||
\(327\) | −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 | 0.906017 | − | 0.423240i | \(-0.139107\pi\) |
−0.819546 | + | 0.573014i | \(0.805774\pi\) | |||||||
\(332\) | 3.24745 | − | 1.87492i | 0.178227 | − | 0.102899i | ||||
\(333\) | −8.69694 | − | 5.02118i | −0.476589 | − | 0.275159i | ||||
\(334\) | 3.67423 | + | 2.12132i | 0.201045 | + | 0.116073i | ||||
\(335\) | −12.3485 | −0.674669 | ||||||||
\(336\) | 2.20204 | − | 2.54270i | 0.120131 | − | 0.138716i | ||||
\(337\) | 20.2474 | 1.10295 | 0.551474 | − | 0.834192i | \(-0.314065\pi\) | ||||
0.551474 | + | 0.834192i | \(0.314065\pi\) | |||||||
\(338\) | 8.32577 | + | 4.80688i | 0.452862 | + | 0.261460i | ||||
\(339\) | −2.32577 | − | 1.34278i | −0.126318 | − | 0.0729299i | ||||
\(340\) | 8.44949 | − | 4.87832i | 0.458238 | − | 0.264564i | ||||
\(341\) | 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 | ||||
\(346\) | 15.4135i | 0.828634i | ||||||||
\(347\) | 3.82577 | − | 6.62642i | 0.205378 | − | 0.355725i | −0.744875 | − | 0.667204i | \(-0.767491\pi\) |
0.950253 | + | 0.311479i | \(0.100824\pi\) | |||||||
\(348\) | −4.60612 | −0.246914 | ||||||||
\(349\) | −7.24745 | −0.387947 | −0.193974 | − | 0.981007i | \(-0.562138\pi\) | ||||
−0.193974 | + | 0.981007i | \(0.562138\pi\) | |||||||
\(350\) | −2.44949 | + | 2.82843i | −0.130931 | + | 0.151186i | ||||
\(351\) | 8.34242i | 0.445285i | ||||||||
\(352\) | − | 27.7128i | − | 1.47710i | ||||||
\(353\) | 29.8207 | + | 17.2170i | 1.58719 | + | 0.916367i | 0.993767 | + | 0.111479i | \(0.0355587\pi\) |
0.593427 | + | 0.804888i | \(0.297775\pi\) | |||||||
\(354\) | − | 1.62129i | − | 0.0861708i | ||||||
\(355\) | −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 | \(-0.872527\pi\) |
−0.122820 | + | 0.992429i | \(0.539194\pi\) | |||||||
\(360\) | 7.10102 | + | 4.09978i | 0.374257 | + | 0.216077i | ||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | 15.1237 | + | 8.73169i | 0.794885 | + | 0.458927i | ||||
\(363\) | 4.13188i | 0.216868i | ||||||||
\(364\) | 17.7980 | + | 15.4135i | 0.932867 | + | 0.807886i | ||||
\(365\) | − | 11.1708i | − | 0.584709i | ||||||
\(366\) | −0.0783167 | + | 0.135648i | −0.00409368 | + | 0.00709046i | ||||
\(367\) | 4.05051 | − | 7.01569i | 0.211435 | − | 0.366216i | −0.740729 | − | 0.671804i | \(-0.765520\pi\) |
0.952164 | + | 0.305588i | \(0.0988530\pi\) | |||||||
\(368\) | − | 18.2419i | − | 0.950925i | ||||||
\(369\) | −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 | \(-0.518657\pi\) |
0.835249 | + | 0.549872i | \(0.185323\pi\) | |||||||
\(374\) | 33.7980 | 1.74765 | ||||||||
\(375\) | 0.275255 | + | 0.158919i | 0.0142141 | + | 0.00820652i | ||||
\(376\) | 14.6969 | − | 8.48528i | 0.757937 | − | 0.437595i | ||||
\(377\) | − | 32.2412i | − | 1.66051i | ||||||
\(378\) | −1.32577 | + | 6.88888i | −0.0681900 | + | 0.354326i | ||||
\(379\) | −17.3485 | −0.891131 | −0.445566 | − | 0.895249i | \(-0.646997\pi\) | ||||
−0.445566 | + | 0.895249i | \(0.646997\pi\) | |||||||
\(380\) | 8.48528i | 0.435286i | ||||||||
\(381\) | 1.10102 | − | 1.90702i | 0.0564070 | − | 0.0976998i | ||||
\(382\) | 37.3939 | 1.91324 | ||||||||
\(383\) | 2.60102 | + | 4.50510i | 0.132906 | + | 0.230200i | 0.924796 | − | 0.380464i | \(-0.124236\pi\) |
−0.791890 | + | 0.610664i | \(0.790903\pi\) | |||||||
\(384\) | 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 | ||||
\(388\) | −20.6969 | + | 11.9494i | −1.05073 | + | 0.606638i | ||||
\(389\) | 9.79796 | + | 5.65685i | 0.496776 | + | 0.286814i | 0.727381 | − | 0.686234i | \(-0.240737\pi\) |
−0.230605 | + | 0.973047i | \(0.574071\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | 22.2474 | 1.12510 | ||||||||
\(392\) | 12.2474 | + | 15.5563i | 0.618590 | + | 0.785714i | ||||
\(393\) | 3.59592 | 0.181390 | ||||||||
\(394\) | 0.651531 | − | 1.12848i | 0.0328236 | − | 0.0568522i | ||||
\(395\) | 6.67423 | + | 3.85337i | 0.335817 | + | 0.193884i | ||||
\(396\) | 14.2020 | + | 24.5987i | 0.713679 | + | 1.23613i | ||||
\(397\) | 0.348469 | + | 0.603566i | 0.0174892 | + | 0.0302921i | 0.874638 | − | 0.484777i | \(-0.161099\pi\) |
−0.857148 | + | 0.515070i | \(0.827766\pi\) | |||||||
\(398\) | 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 | 0.938112 | + | 0.346332i | \(0.112573\pi\) |
−0.169124 | + | 0.985595i | \(0.554094\pi\) | |||||||
\(402\) | 5.55051 | 0.276834 | ||||||||
\(403\) | 3.44949 | − | 5.97469i | 0.171831 | − | 0.297621i | ||||
\(404\) | −30.4949 | −1.51718 | ||||||||
\(405\) | −8.10102 | −0.402543 | ||||||||
\(406\) | 5.12372 | − | 26.6237i | 0.254286 | − | 1.32131i | ||||
\(407\) | 16.9706i | 0.841200i | ||||||||
\(408\) | −3.79796 | + | 2.19275i | −0.188027 | + | 0.108557i | ||||
\(409\) | −10.1969 | − | 5.88721i | −0.504206 | − | 0.291104i | 0.226243 | − | 0.974071i | \(-0.427356\pi\) |
−0.730449 | + | 0.682967i | \(0.760689\pi\) | |||||||
\(410\) | 11.3485 | 0.560461 | ||||||||
\(411\) | −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 | ||||
\(416\) | −21.7980 | + | 12.5851i | −1.06873 | + | 0.617033i | ||||
\(417\) | −1.10102 | + | 1.90702i | −0.0539172 | + | 0.0933873i | ||||
\(418\) | −14.6969 | + | 25.4558i | −0.718851 | + | 1.24509i | ||||
\(419\) | − | 16.6848i | − | 0.815107i | −0.913181 | − | 0.407554i | \(-0.866382\pi\) | ||
0.913181 | − | 0.407554i | \(-0.133618\pi\) | |||||||
\(420\) | 1.10102 | − | 1.27135i | 0.0537243 | − | 0.0620355i | ||||
\(421\) | 4.06767i | 0.198246i | 0.995075 | + | 0.0991230i | \(0.0316037\pi\) | ||||
−0.995075 | + | 0.0991230i | \(0.968396\pi\) | |||||||
\(422\) | 10.1010 | + | 5.83183i | 0.491710 | + | 0.283889i | ||||
\(423\) | −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 | ||||
\(430\) | − | 13.3636i | − | 0.644450i | ||||||
\(431\) | −8.20204 | − | 4.73545i | −0.395078 | − | 0.228099i | 0.289280 | − | 0.957245i | \(-0.406584\pi\) |
−0.684358 | + | 0.729146i | \(0.739918\pi\) | |||||||
\(432\) | −6.49490 | − | 3.74983i | −0.312486 | − | 0.180414i | ||||
\(433\) | 7.70674i | 0.370362i | 0.982704 | + | 0.185181i | \(0.0592872\pi\) | ||||
−0.982704 | + | 0.185181i | \(0.940713\pi\) | |||||||
\(434\) | 3.79796 | − | 4.38551i | 0.182308 | − | 0.210511i | ||||
\(435\) | −2.30306 | −0.110423 | ||||||||
\(436\) | 15.7634i | 0.754931i | ||||||||
\(437\) | −9.67423 | + | 16.7563i | −0.462781 | + | 0.801561i | ||||
\(438\) | 5.02118i | 0.239921i | ||||||||
\(439\) | 5.55051 | + | 9.61377i | 0.264911 | + | 0.458840i | 0.967540 | − | 0.252716i | \(-0.0813240\pi\) |
−0.702629 | + | 0.711556i | \(0.747991\pi\) | |||||||
\(440\) | − | 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 | 0.992230 | − | 0.124414i | \(-0.0397051\pi\) |
−0.603861 | + | 0.797090i | \(0.706372\pi\) | |||||||
\(444\) | −1.10102 | − | 1.90702i | −0.0522521 | − | 0.0905033i | ||||
\(445\) | 9.39898 | + | 5.42650i | 0.445554 | + | 0.257241i | ||||
\(446\) | −30.2474 | − | 17.4634i | −1.43226 | − | 0.826915i | ||||
\(447\) | 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 | \(0.510548\pi\) | |||||||
\(450\) | 3.55051 | + | 2.04989i | 0.167373 | + | 0.0966326i | ||||
\(451\) | 34.0454 | + | 19.6561i | 1.60314 | + | 0.925571i | ||||
\(452\) | 8.44949 | + | 14.6349i | 0.397431 | + | 0.688370i | ||||
\(453\) | −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 | 0.731712 | − | 0.681614i | \(-0.238722\pi\) |
−0.956151 | + | 0.292874i | \(0.905388\pi\) | |||||||
\(458\) | − | 23.6130i | − | 1.10336i | ||||||
\(459\) | 4.57321 | − | 7.92104i | 0.213459 | − | 0.369722i | ||||
\(460\) | − | 9.12096i | − | 0.425267i | ||||||
\(461\) | 38.6969 | 1.80230 | 0.901148 | − | 0.433511i | \(-0.142726\pi\) | ||||
0.901148 | + | 0.433511i | \(0.142726\pi\) | |||||||
\(462\) | 5.50510 | − | 1.90702i | 0.256121 | − | 0.0887228i | ||||
\(463\) | 12.1244i | 0.563467i | 0.959493 | + | 0.281733i | \(0.0909093\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(464\) | 25.1010 | + | 14.4921i | 1.16529 | + | 0.672778i | ||||
\(465\) | −0.426786 | − | 0.246405i | −0.0197917 | − | 0.0114268i | ||||
\(466\) | 0.349945i | 0.0162109i | ||||||||
\(467\) | −19.6237 | + | 11.3298i | −0.908078 | + | 0.524279i | −0.879812 | − | 0.475322i | \(-0.842332\pi\) |
−0.0282655 | + | 0.999600i | \(0.508998\pi\) | |||||||
\(468\) | 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 | ||||
\(474\) | −3.00000 | − | 1.73205i | −0.137795 | − | 0.0795557i | ||||
\(475\) | 4.24264i | 0.194666i | ||||||||
\(476\) | −8.44949 | − | 24.3916i | −0.387282 | − | 1.11799i | ||||
\(477\) | − | 5.94258i | − | 0.272092i | ||||||
\(478\) | −2.34847 | + | 4.06767i | −0.107416 | + | 0.186051i | ||||
\(479\) | 4.22474 | − | 7.31747i | 0.193034 | − | 0.334344i | −0.753221 | − | 0.657768i | \(-0.771501\pi\) |
0.946254 | + | 0.323424i | \(0.104834\pi\) | |||||||
\(480\) | 0.898979 | + | 1.55708i | 0.0410326 | + | 0.0710706i | ||||
\(481\) | 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 | ||||
\(486\) | 11.5959 | 0.526002 | ||||||||
\(487\) | −26.3939 | − | 15.2385i | −1.19602 | − | 0.690523i | −0.236355 | − | 0.971667i | \(-0.575953\pi\) |
−0.959666 | + | 0.281144i | \(0.909286\pi\) | |||||||
\(488\) | 0.853572 | − | 0.492810i | 0.0386394 | − | 0.0223085i | ||||
\(489\) | 1.84281i | 0.0833346i | ||||||||
\(490\) | 6.12372 | + | 7.77817i | 0.276642 | + | 0.351382i | ||||
\(491\) | 0.853572 | 0.0385212 | 0.0192606 | − | 0.999814i | \(-0.493869\pi\) | ||||
0.0192606 | + | 0.999814i | \(0.493869\pi\) | |||||||
\(492\) | −5.10102 | −0.229972 | ||||||||
\(493\) | −17.6742 | + | 30.6127i | −0.796007 | + | 1.37873i | ||||
\(494\) | 26.6969 | 1.20115 | ||||||||
\(495\) | 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 | 0.990704 | + | 0.136032i | \(0.0434349\pi\) |
−0.377545 | + | 0.925991i | \(0.623232\pi\) | |||||||
\(500\) | −1.00000 | − | 1.73205i | −0.0447214 | − | 0.0774597i | ||||
\(501\) | −0.825765 | − | 0.476756i | −0.0368925 | − | 0.0212999i | ||||
\(502\) | −9.69694 | + | 16.7956i | −0.432796 | + | 0.749624i | ||||
\(503\) | −23.6969 | −1.05659 | −0.528297 | − | 0.849060i | \(-0.677169\pi\) | ||||
−0.528297 | + | 0.849060i | \(0.677169\pi\) | |||||||
\(504\) | 14.2020 | − | 16.3991i | 0.632609 | − | 0.730474i | ||||
\(505\) | −15.2474 | −0.678503 | ||||||||
\(506\) | 15.7980 | − | 27.3629i | 0.702305 | − | 1.21643i | ||||
\(507\) | −1.87117 | − | 1.08032i | −0.0831017 | − | 0.0479788i | ||||
\(508\) | −12.0000 | + | 6.92820i | −0.532414 | + | 0.307389i | ||||
\(509\) | 8.72474 | + | 15.1117i | 0.386718 | + | 0.669814i | 0.992006 | − | 0.126192i | \(-0.0402755\pi\) |
−0.605288 | + | 0.796006i | \(0.706942\pi\) | |||||||
\(510\) | −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 | ||||
\(514\) | −18.6969 | −0.824687 | ||||||||
\(515\) | −8.39898 | + | 14.5475i | −0.370103 | + | 0.641038i | ||||
\(516\) | 6.00680i | 0.264435i | ||||||||
\(517\) | 29.3939 | 1.29274 | ||||||||
\(518\) | 12.2474 | − | 4.24264i | 0.538122 | − | 0.186411i | ||||
\(519\) | − | 3.46410i | − | 0.152057i | ||||||
\(520\) | −10.8990 | + | 6.29253i | −0.477952 | + | 0.275946i | ||||
\(521\) | −9.24745 | − | 5.33902i | −0.405138 | − | 0.233907i | 0.283560 | − | 0.958954i | \(-0.408484\pi\) |
−0.688699 | + | 0.725048i | \(0.741818\pi\) | |||||||
\(522\) | −29.7071 | −1.30025 | ||||||||
\(523\) | −10.3485 | + | 5.97469i | −0.452507 | + | 0.261255i | −0.708888 | − | 0.705321i | \(-0.750803\pi\) |
0.256381 | + | 0.966576i | \(0.417470\pi\) | |||||||
\(524\) | −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 | ||||
\(528\) | 6.22831i | 0.271053i | ||||||||
\(529\) | −1.10102 | + | 1.90702i | −0.0478705 | + | 0.0829141i | ||||
\(530\) | −1.44949 | + | 2.51059i | −0.0629618 | + | 0.109053i | ||||
\(531\) | − | 10.4565i | − | 0.453774i | ||||||
\(532\) | 22.0454 | + | 4.24264i | 0.955790 | + | 0.183942i | ||||
\(533\) | − | 35.7053i | − | 1.54657i | ||||||
\(534\) | −4.22474 | − | 2.43916i | −0.182823 | − | 0.105553i | ||||
\(535\) | −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 | \(-0.874979\pi\) |
−0.130460 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(542\) | − | 4.73545i | − | 0.203405i | ||||||
\(543\) | −3.39898 | − | 1.96240i | −0.145864 | − | 0.0842147i | ||||
\(544\) | 27.5959 | 1.18317 | ||||||||
\(545\) | 7.88171i | 0.337616i | ||||||||
\(546\) | −4.00000 | − | 3.46410i | −0.171184 | − | 0.148250i | ||||
\(547\) | 9.04541 | 0.386754 | 0.193377 | − | 0.981125i | \(-0.438056\pi\) | ||||
0.193377 | + | 0.981125i | \(0.438056\pi\) | |||||||
\(548\) | 19.5959 | 0.837096 | ||||||||
\(549\) | −0.505103 | + | 0.874863i | −0.0215573 | + | 0.0373383i | ||||
\(550\) | − | 6.92820i | − | 0.295420i | ||||||
\(551\) | −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 | ||||
\(556\) | 12.0000 | − | 6.92820i | 0.508913 | − | 0.293821i | ||||
\(557\) | −13.8990 | − | 8.02458i | −0.588919 | − | 0.340012i | 0.175751 | − | 0.984435i | \(-0.443765\pi\) |
−0.764670 | + | 0.644422i | \(0.777098\pi\) | |||||||
\(558\) | −5.50510 | − | 3.17837i | −0.233050 | − | 0.134551i | ||||
\(559\) | −42.0454 | −1.77833 | ||||||||
\(560\) | −10.0000 | + | 3.46410i | −0.422577 | + | 0.146385i | ||||
\(561\) | −7.59592 | −0.320700 | ||||||||
\(562\) | 20.6969 | + | 11.9494i | 0.873048 | + | 0.504054i | ||||
\(563\) | 16.6237 | + | 9.59771i | 0.700606 | + | 0.404495i | 0.807573 | − | 0.589767i | \(-0.200781\pi\) |
−0.106967 | + | 0.994263i | \(0.534114\pi\) | |||||||
\(564\) | −3.30306 | + | 1.90702i | −0.139084 | + | 0.0803002i | ||||
\(565\) | 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 | −0.864381 | − | 0.502838i | \(-0.832289\pi\) |
−0.00328010 | − | 0.999995i | \(-0.501044\pi\) | |||||||
\(570\) | − | 1.90702i | − | 0.0798764i | ||||||
\(571\) | −5.22474 | + | 9.04952i | −0.218649 | + | 0.378711i | −0.954395 | − | 0.298546i | \(-0.903498\pi\) |
0.735746 | + | 0.677257i | \(0.236832\pi\) | |||||||
\(572\) | −43.5959 | −1.82284 | ||||||||
\(573\) | −8.40408 | −0.351086 | ||||||||
\(574\) | 5.67423 | − | 29.4842i | 0.236838 | − | 1.23065i | ||||
\(575\) | − | 4.56048i | − | 0.190185i | ||||||
\(576\) | 11.5959 | + | 20.0847i | 0.483163 | + | 0.836863i | ||||
\(577\) | 25.3485 | + | 14.6349i | 1.05527 | + | 0.609261i | 0.924120 | − | 0.382102i | \(-0.124800\pi\) |
0.131150 | + | 0.991362i | \(0.458133\pi\) | |||||||
\(578\) | 9.61377i | 0.399880i | ||||||||
\(579\) | 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 | ||||
\(586\) | 30.0000 | + | 17.3205i | 1.23929 | + | 0.715504i | ||||
\(587\) | 5.30691i | 0.219040i | 0.993985 | + | 0.109520i | \(0.0349313\pi\) | ||||
−0.993985 | + | 0.109520i | \(0.965069\pi\) | |||||||
\(588\) | −2.75255 | − | 3.49621i | −0.113513 | − | 0.144181i | ||||
\(589\) | − | 6.57826i | − | 0.271052i | ||||||
\(590\) | −2.55051 | + | 4.41761i | −0.105003 | + | 0.181870i | ||||
\(591\) | −0.146428 | + | 0.253621i | −0.00602325 | + | 0.0104326i | ||||
\(592\) | 13.8564i | 0.569495i | ||||||||
\(593\) | 8.57321 | − | 4.94975i | 0.352060 | − | 0.203262i | −0.313532 | − | 0.949578i | \(-0.601512\pi\) |
0.665592 | + | 0.746316i | \(0.268179\pi\) | |||||||
\(594\) | −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 | ||||
\(598\) | −28.6969 | −1.17351 | ||||||||
\(599\) | 11.1464 | + | 6.43539i | 0.455431 | + | 0.262943i | 0.710121 | − | 0.704080i | \(-0.248640\pi\) |
−0.254690 | + | 0.967023i | \(0.581974\pi\) | |||||||
\(600\) | 0.449490 | + | 0.778539i | 0.0183503 | + | 0.0317837i | ||||
\(601\) | − | 25.8058i | − | 1.05264i | −0.850287 | − | 0.526320i | \(-0.823571\pi\) | ||
0.850287 | − | 0.526320i | \(-0.176429\pi\) | |||||||
\(602\) | −34.7196 | − | 6.68180i | −1.41507 | − | 0.272330i | ||||
\(603\) | 35.7980 | 1.45781 | ||||||||
\(604\) | 15.4135i | 0.627166i | ||||||||
\(605\) | 6.50000 | − | 11.2583i | 0.264263 | − | 0.457716i | ||||
\(606\) | 6.85357 | 0.278407 | ||||||||
\(607\) | 10.8485 | + | 18.7901i | 0.440326 | + | 0.762667i | 0.997713 | − | 0.0675857i | \(-0.0215296\pi\) |
−0.557388 | + | 0.830252i | \(0.688196\pi\) | |||||||
\(608\) | −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 | ||||
\(612\) | −24.4949 | + | 14.1421i | −0.990148 | + | 0.571662i | ||||
\(613\) | −0.674235 | − | 0.389270i | −0.0272321 | − | 0.0157224i | 0.486322 | − | 0.873780i | \(-0.338338\pi\) |
−0.513554 | + | 0.858057i | \(0.671671\pi\) | |||||||
\(614\) | 19.7753 | − | 34.2517i | 0.798064 | − | 1.38229i | ||||
\(615\) | −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 | \(0.478821\pi\) | |||||||
\(618\) | 3.77526 | − | 6.53893i | 0.151863 | − | 0.263034i | ||||
\(619\) | −13.3485 | − | 7.70674i | −0.536520 | − | 0.309760i | 0.207147 | − | 0.978310i | \(-0.433582\pi\) |
−0.743668 | + | 0.668550i | \(0.766915\pi\) | |||||||
\(620\) | 1.55051 | + | 2.68556i | 0.0622700 | + | 0.107855i | ||||
\(621\) | −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 | ||||
\(626\) | −9.30306 | −0.371825 | ||||||||
\(627\) | 3.30306 | − | 5.72107i | 0.131912 | − | 0.228478i | ||||
\(628\) | −21.3939 | −0.853709 | ||||||||
\(629\) | −16.8990 | −0.673806 | ||||||||
\(630\) | 7.10102 | − | 8.19955i | 0.282911 | − | 0.326678i | ||||
\(631\) | 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 | ||||
\(634\) | −0.696938 | −0.0276790 | ||||||||
\(635\) | −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 | ||||
\(640\) | − | 11.3137i | − | 0.447214i | ||||||
\(641\) | 21.6464 | − | 37.4927i | 0.854983 | − | 1.48087i | −0.0216787 | − | 0.999765i | \(-0.506901\pi\) |
0.876661 | − | 0.481108i | \(-0.159766\pi\) | |||||||
\(642\) | 1.22474 | − | 2.12132i | 0.0483368 | − | 0.0837218i | ||||
\(643\) | 6.57826i | 0.259421i | 0.991552 | + | 0.129711i | \(0.0414048\pi\) | ||||
−0.991552 | + | 0.129711i | \(0.958595\pi\) | |||||||
\(644\) | −23.6969 | − | 4.56048i | −0.933790 | − | 0.179708i | ||||
\(645\) | 3.00340i | 0.118259i | ||||||||
\(646\) | −25.3485 | − | 14.6349i | −0.997322 | − | 0.575804i | ||||
\(647\) | 5.29796 | − | 9.17633i | 0.208284 | − | 0.360759i | −0.742890 | − | 0.669414i | \(-0.766545\pi\) |
0.951174 | + | 0.308655i | \(0.0998788\pi\) | |||||||
\(648\) | −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 | \(-0.790402\pi\) |
0.134463 | + | 0.990919i | \(0.457069\pi\) | |||||||
\(654\) | − | 3.54275i | − | 0.138532i | ||||||
\(655\) | −9.79796 | − | 5.65685i | −0.382838 | − | 0.221032i | ||||
\(656\) | 27.7980 | + | 16.0492i | 1.08533 | + | 0.626614i | ||||
\(657\) | 32.3840i | 1.26342i | ||||||||
\(658\) | −7.34847 | − | 21.2132i | −0.286473 | − | 0.826977i | ||||
\(659\) | −36.7423 | −1.43128 | −0.715639 | − | 0.698470i | \(-0.753865\pi\) | ||||
−0.715639 | + | 0.698470i | \(0.753865\pi\) | |||||||
\(660\) | 3.11416i | 0.121218i | ||||||||
\(661\) | 24.8712 | − | 43.0781i | 0.967377 | − | 1.67555i | 0.264287 | − | 0.964444i | \(-0.414863\pi\) |
0.703090 | − | 0.711101i | \(-0.251803\pi\) | |||||||
\(662\) | 4.44972i | 0.172943i | ||||||||
\(663\) | 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 | ||||
\(668\) | 3.00000 | + | 5.19615i | 0.116073 | + | 0.201045i | ||||
\(669\) | 6.79796 | + | 3.92480i | 0.262824 | + | 0.151742i | ||||
\(670\) | −15.1237 | − | 8.73169i | −0.584280 | − | 0.337334i | ||||
\(671\) | 1.70714 | 0.0659035 | ||||||||
\(672\) | 4.49490 | − | 1.55708i | 0.173394 | − | 0.0600656i | ||||
\(673\) | −26.8990 | −1.03688 | −0.518440 | − | 0.855114i | \(-0.673487\pi\) | ||||
−0.518440 | + | 0.855114i | \(0.673487\pi\) | |||||||
\(674\) | 24.7980 | + | 14.3171i | 0.955182 | + | 0.551474i | ||||
\(675\) | −1.62372 | − | 0.937458i | −0.0624972 | − | 0.0360828i | ||||
\(676\) | 6.79796 | + | 11.7744i | 0.261460 | + | 0.452862i | ||||
\(677\) | −15.6742 | − | 27.1486i | −0.602410 | − | 1.04340i | −0.992455 | − | 0.122609i | \(-0.960874\pi\) |
0.390045 | − | 0.920796i | \(-0.372459\pi\) | |||||||
\(678\) | −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 | ||||
\(682\) | 10.7423i | 0.411342i | ||||||||
\(683\) | 5.72474 | − | 9.91555i | 0.219051 | − | 0.379408i | −0.735467 | − | 0.677561i | \(-0.763037\pi\) |
0.954518 | + | 0.298153i | \(0.0963705\pi\) | |||||||
\(684\) | − | 24.5987i | − | 0.940553i | ||||||
\(685\) | 9.79796 | 0.374361 | ||||||||
\(686\) | 23.2702 | − | 12.0208i | 0.888459 | − | 0.458957i | ||||
\(687\) | 5.30691i | 0.202471i | ||||||||
\(688\) | 18.8990 | − | 32.7340i | 0.720517 | − | 1.24797i | ||||
\(689\) | 7.89898 | + | 4.56048i | 0.300927 | + | 0.173740i | ||||
\(690\) | 2.04989i | 0.0780379i | ||||||||
\(691\) | −27.0000 | + | 15.5885i | −1.02713 | + | 0.593013i | −0.916161 | − | 0.400811i | \(-0.868728\pi\) |
−0.110968 | + | 0.993824i | \(0.535395\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | −8.87628 | − | 5.12472i | −0.335972 | − | 0.193974i | ||||
\(699\) | − | 0.0786484i | − | 0.00297476i | ||||||
\(700\) | −5.00000 | + | 1.73205i | −0.188982 | + | 0.0654654i | ||||
\(701\) | 23.5809i | 0.890639i | 0.895372 | + | 0.445320i | \(0.146910\pi\) | ||||
−0.895372 | + | 0.445320i | \(0.853090\pi\) | |||||||
\(702\) | −5.89898 | + | 10.2173i | −0.222643 | + | 0.385628i | ||||
\(703\) | 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 | \(-0.730731\pi\) |
0.316782 | + | 0.948498i | \(0.397398\pi\) | |||||||
\(710\) | −2.00000 | −0.0750587 | ||||||||
\(711\) | −19.3485 | − | 11.1708i | −0.725624 | − | 0.418939i | ||||
\(712\) | 15.3485 | + | 26.5843i | 0.575208 | + | 0.996290i | ||||
\(713\) | 7.07107i | 0.264814i | ||||||||
\(714\) | 1.89898 | + | 5.48188i | 0.0710675 | + | 0.205154i | ||||
\(715\) | −21.7980 | −0.815197 | ||||||||
\(716\) | −19.1010 | −0.713839 | ||||||||
\(717\) | 0.527806 | − | 0.914188i | 0.0197113 | − | 0.0341410i | ||||
\(718\) | −32.2929 | −1.20516 | ||||||||
\(719\) | −19.5959 | − | 33.9411i | −0.730804 | − | 1.26579i | −0.956540 | − | 0.291602i | \(-0.905812\pi\) |
0.225735 | − | 0.974189i | \(-0.427522\pi\) | |||||||
\(720\) | 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 | ||||
\(724\) | 12.3485 | + | 21.3882i | 0.458927 | + | 0.794885i | ||||
\(725\) | 6.27526 | + | 3.62302i | 0.233057 | + | 0.134556i | ||||
\(726\) | −2.92168 | + | 5.06050i | −0.108434 | + | 0.187813i | ||||
\(727\) | −14.5959 | −0.541333 | −0.270666 | − | 0.962673i | \(-0.587244\pi\) | ||||
−0.270666 | + | 0.962673i | \(0.587244\pi\) | |||||||
\(728\) | 10.8990 | + | 31.4626i | 0.403943 | + | 1.16608i | ||||
\(729\) | 21.6969 | 0.803590 | ||||||||
\(730\) | 7.89898 | − | 13.6814i | 0.292354 | − | 0.506373i | ||||
\(731\) | 39.9217 | + | 23.0488i | 1.47656 | + | 0.852490i | ||||
\(732\) | −0.191836 | + | 0.110756i | −0.00709046 | + | 0.00409368i | ||||
\(733\) | 8.55051 | + | 14.8099i | 0.315820 | + | 0.547017i | 0.979612 | − | 0.200901i | \(-0.0643870\pi\) |
−0.663791 | + | 0.747918i | \(0.731054\pi\) | |||||||
\(734\) | 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 | ||||
\(738\) | −32.8990 | −1.21103 | ||||||||
\(739\) | 0.348469 | − | 0.603566i | 0.0128186 | − | 0.0222025i | −0.859545 | − | 0.511060i | \(-0.829253\pi\) |
0.872364 | + | 0.488858i | \(0.162586\pi\) | |||||||
\(740\) | 6.92820i | 0.254686i | ||||||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | 5.79796 | + | 5.02118i | 0.212850 | + | 0.184333i | ||||
\(743\) | − | 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 | ||||
\(746\) | 24.4949 | 0.896822 | ||||||||
\(747\) | −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 | 0.574672 | − | 0.818384i | \(-0.305130\pi\) |
0.996077 | − | 0.0884887i | \(-0.0282037\pi\) | |||||||
\(752\) | 24.0000 | 0.875190 | ||||||||
\(753\) | 2.17934 | − | 3.77472i | 0.0794195 | − | 0.137559i | ||||
\(754\) | 22.7980 | − | 39.4872i | 0.830253 | − | 1.43804i | ||||
\(755\) | 7.70674i | 0.280477i | ||||||||
\(756\) | −6.49490 | + | 7.49966i | −0.236217 | + | 0.272760i | ||||
\(757\) | 33.5125i | 1.21803i | 0.793157 | + | 0.609017i | \(0.208436\pi\) | ||||
−0.793157 | + | 0.609017i | \(0.791564\pi\) | |||||||
\(758\) | −21.2474 | − | 12.2672i | −0.771742 | − | 0.445566i | ||||
\(759\) | −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 | −0.295500 | − | 0.955343i | \(-0.595486\pi\) |
0.679601 | + | 0.733582i | \(0.262153\pi\) | |||||||
\(762\) | 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 | ||||
\(766\) | 7.35680i | 0.265812i | ||||||||
\(767\) | 13.8990 | + | 8.02458i | 0.501863 | + | 0.289751i | ||||
\(768\) | 5.08540i | 0.183503i | ||||||||
\(769\) | − | 46.5904i | − | 1.68009i | −0.542515 | − | 0.840046i | \(-0.682528\pi\) | ||
0.542515 | − | 0.840046i | \(-0.317472\pi\) | |||||||
\(770\) | −18.0000 | − | 3.46410i | −0.648675 | − | 0.124838i | ||||
\(771\) | 4.20204 | 0.151333 | ||||||||
\(772\) | −45.3939 | −1.63376 | ||||||||
\(773\) | 5.87628 | − | 10.1780i | 0.211355 | − | 0.366078i | −0.740784 | − | 0.671743i | \(-0.765546\pi\) |
0.952139 | + | 0.305666i | \(0.0988791\pi\) | |||||||
\(774\) | 38.7408i | 1.39251i | ||||||||
\(775\) | 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 | ||||
\(780\) | 2.44949 | − | 1.41421i | 0.0877058 | − | 0.0506370i | ||||
\(781\) | −6.00000 | − | 3.46410i | −0.214697 | − | 0.123955i | ||||
\(782\) | 27.2474 | + | 15.7313i | 0.974367 | + | 0.562551i | ||||
\(783\) | 13.5857 | 0.485514 | ||||||||
\(784\) | 4.00000 | + | 27.7128i | 0.142857 | + | 0.989743i | ||||
\(785\) | −10.6969 | −0.381790 | ||||||||
\(786\) | 4.40408 | + | 2.54270i | 0.157088 | + | 0.0906950i | ||||
\(787\) | −7.87117 | − | 4.54442i | −0.280577 | − | 0.161991i | 0.353108 | − | 0.935583i | \(-0.385125\pi\) |
−0.633685 | + | 0.773592i | \(0.718458\pi\) | |||||||
\(788\) | 1.59592 | − | 0.921404i | 0.0568522 | − | 0.0328236i | ||||
\(789\) | 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 | ||||
\(794\) | 0.985620i | 0.0349783i | ||||||||
\(795\) | 0.325765 | − | 0.564242i | 0.0115537 | − | 0.0200116i | ||||
\(796\) | 49.3939 | 1.75072 | ||||||||
\(797\) | 3.30306 | 0.117000 | 0.0585002 | − | 0.998287i | \(-0.481368\pi\) | ||||
0.0585002 | + | 0.998287i | \(0.481368\pi\) | |||||||
\(798\) | −4.95459 | − | 0.953512i | −0.175391 | − | 0.0337539i | ||||
\(799\) | 29.2699i | 1.03549i | ||||||||
\(800\) | − | 5.65685i | − | 0.200000i | ||||||
\(801\) | −27.2474 | − | 15.7313i | −0.962741 | − | 0.555839i | ||||
\(802\) | 43.5549i | 1.53798i | ||||||||
\(803\) | 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 | −0.731336 | − | 0.682017i | \(-0.761103\pi\) |
0.956312 | + | 0.292347i | \(0.0944363\pi\) | |||||||
\(810\) | −9.92168 | − | 5.72829i | −0.348612 | − | 0.201271i | ||||
\(811\) | − | 47.3689i | − | 1.66335i | −0.555264 | − | 0.831674i | \(-0.687383\pi\) | ||
0.555264 | − | 0.831674i | \(-0.312617\pi\) | |||||||
\(812\) | 25.1010 | − | 28.9842i | 0.880873 | − | 1.01714i | ||||
\(813\) | 1.06427i | 0.0373255i | ||||||||
\(814\) | −12.0000 | + | 20.7846i | −0.420600 | + | 0.728500i | ||||
\(815\) | 2.89898 | − | 5.02118i | 0.101547 | − | 0.175884i | ||||
\(816\) | −6.20204 | −0.217115 | ||||||||
\(817\) | −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 | 0.511013 | − | 0.859573i | \(-0.329271\pi\) |
0.999919 | − | 0.0127632i | \(-0.00406277\pi\) | |||||||
\(822\) | −4.40408 | −0.153610 | ||||||||
\(823\) | −9.15153 | − | 5.28364i | −0.319002 | − | 0.184176i | 0.331945 | − | 0.943299i | \(-0.392295\pi\) |
−0.650948 | + | 0.759123i | \(0.725628\pi\) | |||||||
\(824\) | −41.1464 | + | 23.7559i | −1.43340 | + | 0.827576i | ||||
\(825\) | 1.55708i | 0.0542105i | ||||||||
\(826\) | 10.2020 | + | 8.83523i | 0.354974 | + | 0.307417i | ||||
\(827\) | −13.0454 | −0.453633 | −0.226817 | − | 0.973937i | \(-0.572832\pi\) | ||||
−0.226817 | + | 0.973937i | \(0.572832\pi\) | |||||||
\(828\) | 26.4415i | 0.918904i | ||||||||
\(829\) | 12.6515 | − | 21.9131i | 0.439406 | − | 0.761073i | −0.558238 | − | 0.829681i | \(-0.688522\pi\) |
0.997644 | + | 0.0686077i | \(0.0218557\pi\) | |||||||
\(830\) | 2.65153 | 0.0920360 | ||||||||
\(831\) | 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 | ||||
\(836\) | −36.0000 | + | 20.7846i | −1.24509 | + | 0.718851i | ||||
\(837\) | 2.51760 | + | 1.45354i | 0.0870210 | + | 0.0502416i | ||||
\(838\) | 11.7980 | − | 20.4347i | 0.407554 | − | 0.705904i | ||||
\(839\) | 30.4949 | 1.05280 | 0.526400 | − | 0.850237i | \(-0.323541\pi\) | ||||
0.526400 | + | 0.850237i | \(0.323541\pi\) | |||||||
\(840\) | 2.24745 | − | 0.778539i | 0.0775443 | − | 0.0268622i | ||||
\(841\) | −23.5051 | −0.810521 | ||||||||
\(842\) | −2.87628 | + | 4.98186i | −0.0991230 | + | 0.171686i | ||||
\(843\) | −4.65153 | − | 2.68556i | −0.160207 | − | 0.0924957i | ||||
\(844\) | 8.24745 | + | 14.2850i | 0.283889 | + | 0.491710i | ||||
\(845\) | 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 | ||||
\(850\) | 6.89898 | 0.236633 | ||||||||
\(851\) | −7.89898 | + | 13.6814i | −0.270774 | + | 0.468994i | ||||
\(852\) | 0.898979 | 0.0307985 | ||||||||
\(853\) | −48.4495 | −1.65888 | −0.829439 | − | 0.558597i | \(-0.811340\pi\) | ||||
−0.829439 | + | 0.558597i | \(0.811340\pi\) | |||||||
\(854\) | −0.426786 | − | 1.23202i | −0.0146043 | − | 0.0421590i | ||||
\(855\) | − | 12.2993i | − | 0.420628i | ||||||
\(856\) | −13.3485 | + | 7.70674i | −0.456241 | + | 0.263411i | ||||
\(857\) | 48.1918 | + | 27.8236i | 1.64620 | + | 0.950435i | 0.978562 | + | 0.205950i | \(0.0660285\pi\) |
0.667639 | + | 0.744485i | \(0.267305\pi\) | |||||||
\(858\) | 9.79796 | 0.334497 | ||||||||
\(859\) | 21.0000 | − | 12.1244i | 0.716511 | − | 0.413678i | −0.0969563 | − | 0.995289i | \(-0.530911\pi\) |
0.813467 | + | 0.581611i | \(0.197577\pi\) | |||||||
\(860\) | 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 | \(-0.653836\pi\) |
0.534494 | + | 0.845172i | \(0.320502\pi\) | |||||||
\(864\) | −5.30306 | − | 9.18517i | −0.180414 | − | 0.312486i | ||||
\(865\) | −5.44949 | + | 9.43879i | −0.185288 | + | 0.320929i | ||||
\(866\) | −5.44949 | + | 9.43879i | −0.185181 | + | 0.320743i | ||||
\(867\) | − | 2.16064i | − | 0.0733793i | ||||||
\(868\) | 7.75255 | − | 2.68556i | 0.263139 | − | 0.0911539i | ||||
\(869\) | 37.7552i | 1.28076i | ||||||||
\(870\) | −2.82066 | − | 1.62851i | −0.0956294 | − | 0.0552117i | ||||
\(871\) | −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 | \(-0.655993\pi\) |
0.528753 | + | 0.848776i | \(0.322660\pi\) | |||||||
\(878\) | 15.6992i | 0.529823i | ||||||||
\(879\) | −6.74235 | − | 3.89270i | −0.227414 | − | 0.131297i | ||||
\(880\) | 9.79796 | − | 16.9706i | 0.330289 | − | 0.572078i | ||||
\(881\) | 36.6588i | 1.23507i | 0.786545 | + | 0.617533i | \(0.211868\pi\) | ||||
−0.786545 | + | 0.617533i | \(0.788132\pi\) | |||||||
\(882\) | −17.7526 | − | 22.5488i | −0.597759 | − | 0.759257i | ||||
\(883\) | −40.4949 | −1.36276 | −0.681381 | − | 0.731929i | \(-0.738620\pi\) | ||||
−0.681381 | + | 0.731929i | \(0.738620\pi\) | |||||||
\(884\) | − | 43.4120i | − | 1.46010i | ||||||
\(885\) | 0.573214 | − | 0.992836i | 0.0192684 | − | 0.0333738i | ||||
\(886\) | 23.1202i | 0.776739i | ||||||||
\(887\) | 13.5000 | + | 23.3827i | 0.453286 | + | 0.785114i | 0.998588 | − | 0.0531258i | \(-0.0169184\pi\) |
−0.545302 | + | 0.838240i | \(0.683585\pi\) | |||||||
\(888\) | − | 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 | ||||
\(892\) | −24.6969 | − | 42.7764i | −0.826915 | − | 1.43226i | ||||
\(893\) | −22.0454 | − | 12.7279i | −0.737721 | − | 0.425924i | ||||
\(894\) | 7.47219 | + | 4.31407i | 0.249908 | + | 0.144284i | ||||
\(895\) | −9.55051 | −0.319238 | ||||||||
\(896\) | −29.3939 | − | 5.65685i | −0.981981 | − | 0.188982i | ||||
\(897\) | 6.44949 | 0.215342 | ||||||||
\(898\) | −1.71964 | − | 0.992836i | −0.0573852 | − | 0.0331314i | ||||
\(899\) | −9.72985 | − | 5.61753i | −0.324509 | − | 0.187355i | ||||
\(900\) | 2.89898 | + | 5.02118i | 0.0966326 | + | 0.167373i | ||||
\(901\) | −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 | ||||
\(906\) | − | 3.46410i | − | 0.115087i | ||||||
\(907\) | 4.17423 | − | 7.22999i | 0.138603 | − | 0.240068i | −0.788365 | − | 0.615208i | \(-0.789072\pi\) |
0.926968 | + | 0.375140i | \(0.122405\pi\) | |||||||
\(908\) | − | 21.3561i | − | 0.708726i | ||||||
\(909\) | 44.2020 | 1.46609 | ||||||||
\(910\) | 5.44949 | + | 15.7313i | 0.180649 | + | 0.521488i | ||||
\(911\) | 41.5050i | 1.37512i | 0.726127 | + | 0.687561i | \(0.241319\pi\) | ||||
−0.726127 | + | 0.687561i | \(0.758681\pi\) | |||||||
\(912\) | 2.69694 | − | 4.67123i | 0.0893046 | − | 0.154680i | ||||
\(913\) | 7.95459 | + | 4.59259i | 0.263259 | + | 0.151992i | ||||
\(914\) | − | 13.5707i | − | 0.448878i | ||||||
\(915\) | −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 | \(-0.590958\pi\) |
0.689968 | + | 0.723840i | \(0.257625\pi\) | |||||||
\(920\) | 6.44949 | − | 11.1708i | 0.212633 | − | 0.368292i | ||||
\(921\) | −4.44439 | + | 7.69790i | −0.146448 | + | 0.253655i | ||||
\(922\) | 47.3939 | + | 27.3629i | 1.56083 | + | 0.901148i | ||||
\(923\) | 6.29253i | 0.207121i | ||||||||
\(924\) | 8.09082 | + | 1.55708i | 0.266168 | + | 0.0512241i | ||||
\(925\) | 3.46410i | 0.113899i | ||||||||
\(926\) | −8.57321 | + | 14.8492i | −0.281733 | + | 0.487976i | ||||
\(927\) | 24.3485 | − | 42.1728i | 0.799709 | − | 1.38514i | ||||
\(928\) | 20.4949 | + | 35.4982i | 0.672778 | + | 1.16529i | ||||
\(929\) | −5.29796 | + | 3.05878i | −0.173820 | + | 0.100355i | −0.584386 | − | 0.811476i | \(-0.698665\pi\) |
0.410566 | + | 0.911831i | \(0.365331\pi\) | |||||||
\(930\) | −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 | ||||
\(934\) | −32.0454 | −1.04856 | ||||||||
\(935\) | 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 | \(0.0524509\pi\) | ||||
−0.986455 | + | 0.164035i | \(0.947549\pi\) | |||||||
\(938\) | −30.2474 | + | 34.9267i | −0.987614 | + | 1.14040i | ||||
\(939\) | 2.09082 | 0.0682312 | ||||||||
\(940\) | 12.0000 | 0.391397 | ||||||||
\(941\) | 7.89898 | − | 13.6814i | 0.257499 | − | 0.446002i | −0.708072 | − | 0.706140i | \(-0.750435\pi\) |
0.965571 | + | 0.260138i | \(0.0837681\pi\) | |||||||
\(942\) | 4.80816 | 0.156658 | ||||||||
\(943\) | 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 | −0.937042 | − | 0.349215i | \(-0.886448\pi\) |
0.166092 | − | 0.986110i | \(-0.446885\pi\) | |||||||
\(948\) | −2.44949 | − | 4.24264i | −0.0795557 | − | 0.137795i | ||||
\(949\) | −43.0454 | − | 24.8523i | −1.39731 | − | 0.806739i | ||||
\(950\) | −3.00000 | + | 5.19615i | −0.0973329 | + | 0.168585i | ||||
\(951\) | 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 | \(0.556486\pi\) | |||||||
\(954\) | 4.20204 | − | 7.27815i | 0.136046 | − | 0.235639i | ||||
\(955\) | 22.8990 | + | 13.2207i | 0.740994 | + | 0.427813i | ||||
\(956\) | −5.75255 | + | 3.32124i | −0.186051 | + | 0.107416i | ||||
\(957\) | −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 | ||||
\(962\) | 21.7980 | 0.702794 | ||||||||
\(963\) | 7.89898 | − | 13.6814i | 0.254541 | − | 0.440878i | ||||
\(964\) | − | 40.8693i | − | 1.31631i | ||||||
\(965\) | −22.6969 | −0.730640 | ||||||||
\(966\) | 5.32577 | + | 1.02494i | 0.171354 | + | 0.0329770i | ||||
\(967\) | − | 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 | ||||
\(970\) | −16.8990 | −0.542594 | ||||||||
\(971\) | −26.1464 | + | 15.0956i | −0.839079 | + | 0.484442i | −0.856951 | − | 0.515398i | \(-0.827644\pi\) |
0.0178722 | + | 0.999840i | \(0.494311\pi\) | |||||||
\(972\) | 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 | ||||
\(976\) | 1.39388 | 0.0446169 | ||||||||
\(977\) | 14.6969 | − | 25.4558i | 0.470197 | − | 0.814405i | −0.529222 | − | 0.848483i | \(-0.677516\pi\) |
0.999419 | + | 0.0340785i | \(0.0108496\pi\) | |||||||
\(978\) | −1.30306 | + | 2.25697i | −0.0416673 | + | 0.0721699i | ||||
\(979\) | 53.1687i | 1.69928i | ||||||||
\(980\) | 2.00000 | + | 13.8564i | 0.0638877 | + | 0.442627i | ||||
\(981\) | − | 22.8489i | − | 0.729510i | ||||||
\(982\) | 1.04541 | + | 0.603566i | 0.0333603 | + | 0.0192606i | ||||
\(983\) | 7.50000 | − | 12.9904i | 0.239213 | − | 0.414329i | −0.721276 | − | 0.692648i | \(-0.756444\pi\) |
0.960489 | + | 0.278319i | \(0.0897773\pi\) | |||||||
\(984\) | −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 | ||||
\(990\) | 20.0847i | 0.638334i | ||||||||
\(991\) | −25.7196 | − | 14.8492i | −0.817011 | − | 0.471702i | 0.0323734 | − | 0.999476i | \(-0.489693\pi\) |
−0.849385 | + | 0.527774i | \(0.823027\pi\) | |||||||
\(992\) | 8.77101i | 0.278480i | ||||||||
\(993\) | − | 1.00005i | − | 0.0317357i | ||||||
\(994\) | −1.00000 | + | 5.19615i | −0.0317181 | + | 0.164812i | ||||
\(995\) | 24.6969 | 0.782946 | ||||||||
\(996\) | −1.19184 | −0.0377648 | ||||||||
\(997\) | 13.3258 | − | 23.0809i | 0.422031 | − | 0.730980i | −0.574107 | − | 0.818780i | \(-0.694651\pi\) |
0.996138 | + | 0.0878009i | \(0.0279839\pi\) | |||||||
\(998\) | 38.7408i | 1.22632i | ||||||||
\(999\) | 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.c.171.2 | yes | 4 | |
4.3 | odd | 2 | 1120.2.bz.c.591.1 | 4 | |||
7.5 | odd | 6 | 280.2.bj.b.131.1 | ✓ | 4 | ||
8.3 | odd | 2 | 280.2.bj.b.171.2 | yes | 4 | ||
8.5 | even | 2 | 1120.2.bz.b.591.1 | 4 | |||
28.19 | even | 6 | 1120.2.bz.b.271.1 | 4 | |||
56.5 | odd | 6 | 1120.2.bz.c.271.1 | 4 | |||
56.19 | even | 6 | inner | 280.2.bj.c.131.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.bj.b.131.1 | ✓ | 4 | 7.5 | odd | 6 | ||
280.2.bj.b.171.2 | yes | 4 | 8.3 | odd | 2 | ||
280.2.bj.c.131.2 | yes | 4 | 56.19 | even | 6 | inner | |
280.2.bj.c.171.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1120.2.bz.b.271.1 | 4 | 28.19 | even | 6 | |||
1120.2.bz.b.591.1 | 4 | 8.5 | even | 2 | |||
1120.2.bz.c.271.1 | 4 | 56.5 | odd | 6 | |||
1120.2.bz.c.591.1 | 4 | 4.3 | odd | 2 |