Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.3 | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.j.557.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30986 | + | 0.533177i | −0.926208 | + | 0.377013i | ||||
\(3\) | 0.667305 | − | 1.59834i | 0.385268 | − | 0.922805i | ||||
\(4\) | 1.43144 | − | 1.39677i | 0.715722 | − | 0.698385i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0218716 | + | 2.44939i | −0.00892904 | + | 0.999960i | ||||
\(7\) | −0.582772 | + | 0.582772i | −0.220267 | + | 0.220267i | −0.808611 | − | 0.588344i | \(-0.799780\pi\) |
0.588344 | + | 0.808611i | \(0.299780\pi\) | |||||||
\(8\) | −1.13026 | + | 2.59278i | −0.399606 | + | 0.916687i | ||||
\(9\) | −2.10941 | − | 2.13317i | −0.703136 | − | 0.711055i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.68607 | −1.11139 | −0.555695 | − | 0.831386i | \(-0.687548\pi\) | ||||
−0.555695 | + | 0.831386i | \(0.687548\pi\) | |||||||
\(12\) | −1.27731 | − | 3.22001i | −0.368728 | − | 0.929537i | ||||
\(13\) | −3.88771 | + | 3.88771i | −1.07826 | + | 1.07826i | −0.0815911 | + | 0.996666i | \(0.526000\pi\) |
−0.996666 | + | 0.0815911i | \(0.974000\pi\) | |||||||
\(14\) | 0.452626 | − | 1.07407i | 0.120969 | − | 0.287057i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0980619 | − | 3.99880i | 0.0245155 | − | 0.999699i | ||||
\(17\) | −0.880105 | − | 0.880105i | −0.213457 | − | 0.213457i | 0.592277 | − | 0.805734i | \(-0.298229\pi\) |
−0.805734 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(18\) | 3.90038 | + | 1.66945i | 0.919328 | + | 0.393493i | ||||
\(19\) | −6.32919 | −1.45201 | −0.726007 | − | 0.687687i | \(-0.758626\pi\) | ||||
−0.726007 | + | 0.687687i | \(0.758626\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.542584 | + | 1.32036i | 0.118402 | + | 0.288125i | ||||
\(22\) | 4.82821 | − | 1.96533i | 1.02938 | − | 0.419009i | ||||
\(23\) | 2.06626 | − | 2.06626i | 0.430844 | − | 0.430844i | −0.458071 | − | 0.888916i | \(-0.651460\pi\) |
0.888916 | + | 0.458071i | \(0.151460\pi\) | |||||||
\(24\) | 3.38993 | + | 3.53672i | 0.691967 | + | 0.721929i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.01950 | − | 7.16518i | 0.592173 | − | 1.40521i | ||||
\(27\) | −4.81715 | + | 1.94809i | −0.927061 | + | 0.374910i | ||||
\(28\) | −0.0202063 | + | 1.64820i | −0.00381863 | + | 0.311481i | ||||
\(29\) | 1.37122i | 0.254630i | 0.991862 | + | 0.127315i | \(0.0406359\pi\) | ||||
−0.991862 | + | 0.127315i | \(0.959364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32075 | 0.596425 | 0.298212 | − | 0.954500i | \(-0.403610\pi\) | ||||
0.298212 | + | 0.954500i | \(0.403610\pi\) | |||||||
\(32\) | 2.00362 | + | 5.29013i | 0.354194 | + | 0.935172i | ||||
\(33\) | −2.45973 | + | 5.89160i | −0.428184 | + | 1.02560i | ||||
\(34\) | 1.62206 | + | 0.683558i | 0.278181 | + | 0.117229i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.99904 | − | 0.107144i | −0.999841 | − | 0.0178574i | ||||
\(37\) | −2.44147 | − | 2.44147i | −0.401376 | − | 0.401376i | 0.477342 | − | 0.878718i | \(-0.341600\pi\) |
−0.878718 | + | 0.477342i | \(0.841600\pi\) | |||||||
\(38\) | 8.29032 | − | 3.37458i | 1.34487 | − | 0.547429i | ||||
\(39\) | 3.61961 | + | 8.80819i | 0.579602 | + | 1.41044i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.648104i | − | 0.101217i | −0.998719 | − | 0.0506084i | \(-0.983884\pi\) | ||
0.998719 | − | 0.0506084i | \(-0.0161160\pi\) | |||||||
\(42\) | −1.41469 | − | 1.44018i | −0.218292 | − | 0.222225i | ||||
\(43\) | −0.819412 | + | 0.819412i | −0.124959 | + | 0.124959i | −0.766821 | − | 0.641861i | \(-0.778162\pi\) |
0.641861 | + | 0.766821i | \(0.278162\pi\) | |||||||
\(44\) | −5.27640 | + | 5.14859i | −0.795447 | + | 0.776179i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.60482 | + | 3.80818i | −0.236617 | + | 0.561485i | ||||
\(47\) | −6.28508 | − | 6.28508i | −0.916772 | − | 0.916772i | 0.0800208 | − | 0.996793i | \(-0.474501\pi\) |
−0.996793 | + | 0.0800208i | \(0.974501\pi\) | |||||||
\(48\) | −6.32602 | − | 2.82515i | −0.913082 | − | 0.407776i | ||||
\(49\) | 6.32075i | 0.902965i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.99401 | + | 0.819412i | −0.279217 | + | 0.114741i | ||||
\(52\) | −0.134798 | + | 10.9953i | −0.0186931 | + | 1.52477i | ||||
\(53\) | 5.60782 | + | 5.60782i | 0.770293 | + | 0.770293i | 0.978158 | − | 0.207864i | \(-0.0666512\pi\) |
−0.207864 | + | 0.978158i | \(0.566651\pi\) | |||||||
\(54\) | 5.27109 | − | 5.12011i | 0.717305 | − | 0.696759i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.852318 | − | 2.16968i | −0.113896 | − | 0.289936i | ||||
\(57\) | −4.22349 | + | 10.1162i | −0.559415 | + | 1.33993i | ||||
\(58\) | −0.731106 | − | 1.79611i | −0.0959989 | − | 0.235840i | ||||
\(59\) | − | 6.12026i | − | 0.796790i | −0.917214 | − | 0.398395i | \(-0.869567\pi\) | ||
0.917214 | − | 0.398395i | \(-0.130433\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.13471i | 0.657432i | 0.944429 | + | 0.328716i | \(0.106616\pi\) | ||||
−0.944429 | + | 0.328716i | \(0.893384\pi\) | |||||||
\(62\) | −4.34971 | + | 1.77055i | −0.552413 | + | 0.224860i | ||||
\(63\) | 2.47245 | + | 0.0138443i | 0.311500 | + | 0.00174421i | ||||
\(64\) | −5.44503 | − | 5.86102i | −0.680629 | − | 0.732628i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0806201 | − | 9.02862i | 0.00992365 | − | 1.11135i | ||||
\(67\) | −4.90636 | − | 4.90636i | −0.599408 | − | 0.599408i | 0.340747 | − | 0.940155i | \(-0.389320\pi\) |
−0.940155 | + | 0.340747i | \(0.889320\pi\) | |||||||
\(68\) | −2.48912 | − | 0.0305156i | −0.301851 | − | 0.00370056i | ||||
\(69\) | −1.92377 | − | 4.68141i | −0.231594 | − | 0.563576i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.13251i | − | 0.490439i | −0.969468 | − | 0.245220i | \(-0.921140\pi\) | ||
0.969468 | − | 0.245220i | \(-0.0788601\pi\) | |||||||
\(72\) | 7.91501 | − | 3.05821i | 0.932793 | − | 0.360414i | ||||
\(73\) | −4.69820 | − | 4.69820i | −0.549883 | − | 0.549883i | 0.376524 | − | 0.926407i | \(-0.377119\pi\) |
−0.926407 | + | 0.376524i | \(0.877119\pi\) | |||||||
\(74\) | 4.49972 | + | 1.89624i | 0.523082 | + | 0.220433i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.05987 | + | 8.84042i | −1.03924 | + | 1.01407i | ||||
\(77\) | 2.14814 | − | 2.14814i | 0.244803 | − | 0.244803i | ||||
\(78\) | −9.43750 | − | 9.60756i | −1.06859 | − | 1.08784i | ||||
\(79\) | − | 1.10079i | − | 0.123848i | −0.998081 | − | 0.0619241i | \(-0.980276\pi\) | ||
0.998081 | − | 0.0619241i | \(-0.0197237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.100786 | + | 8.99944i | −0.0111985 | + | 0.999937i | ||||
\(82\) | 0.345554 | + | 0.848922i | 0.0381601 | + | 0.0937478i | ||||
\(83\) | −6.27439 | − | 6.27439i | −0.688703 | − | 0.688703i | 0.273242 | − | 0.961945i | \(-0.411904\pi\) |
−0.961945 | + | 0.273242i | \(0.911904\pi\) | |||||||
\(84\) | 2.62091 | + | 1.13215i | 0.285965 | + | 0.123528i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.636420 | − | 1.51020i | 0.0686269 | − | 0.162849i | ||||
\(87\) | 2.19169 | + | 0.915024i | 0.234974 | + | 0.0981009i | ||||
\(88\) | 4.16621 | − | 9.55717i | 0.444119 | − | 1.01880i | ||||
\(89\) | −15.3562 | −1.62775 | −0.813875 | − | 0.581040i | \(-0.802646\pi\) | ||||
−0.813875 | + | 0.581040i | \(0.802646\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4.53130i | − | 0.475009i | ||||||
\(92\) | 0.0716428 | − | 5.84382i | 0.00746928 | − | 0.609260i | ||||
\(93\) | 2.21595 | − | 5.30771i | 0.229784 | − | 0.550384i | ||||
\(94\) | 11.5836 | + | 4.88148i | 1.19476 | + | 0.503486i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79248 | + | 0.327652i | 0.999441 | + | 0.0334409i | ||||
\(97\) | 5.42154 | − | 5.42154i | 0.550474 | − | 0.550474i | −0.376104 | − | 0.926578i | \(-0.622736\pi\) |
0.926578 | + | 0.376104i | \(0.122736\pi\) | |||||||
\(98\) | −3.37008 | − | 8.27927i | −0.340430 | − | 0.836333i | ||||
\(99\) | 7.77542 | + | 7.86299i | 0.781459 | + | 0.790260i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.84442 | 0.979556 | 0.489778 | − | 0.871847i | \(-0.337078\pi\) | ||||
0.489778 | + | 0.871847i | \(0.337078\pi\) | |||||||
\(102\) | 2.17497 | − | 2.13647i | 0.215354 | − | 0.211542i | ||||
\(103\) | 8.28098 | + | 8.28098i | 0.815949 | + | 0.815949i | 0.985518 | − | 0.169569i | \(-0.0542377\pi\) |
−0.169569 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(104\) | −5.68587 | − | 14.4741i | −0.557545 | − | 1.41930i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.3354 | − | 4.35547i | −1.00386 | − | 0.423041i | ||||
\(107\) | 5.84678 | − | 5.84678i | 0.565230 | − | 0.565230i | −0.365559 | − | 0.930788i | \(-0.619122\pi\) |
0.930788 | + | 0.365559i | \(0.119122\pi\) | |||||||
\(108\) | −4.17444 | + | 9.51704i | −0.401686 | + | 0.915777i | ||||
\(109\) | −11.7033 | −1.12097 | −0.560487 | − | 0.828163i | \(-0.689386\pi\) | ||||
−0.560487 | + | 0.828163i | \(0.689386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.53152 | + | 2.27311i | −0.525029 | + | 0.215754i | ||||
\(112\) | 2.27324 | + | 2.38754i | 0.214801 | + | 0.225601i | ||||
\(113\) | −8.58333 | + | 8.58333i | −0.807452 | + | 0.807452i | −0.984248 | − | 0.176796i | \(-0.943427\pi\) |
0.176796 | + | 0.984248i | \(0.443427\pi\) | |||||||
\(114\) | 0.138429 | − | 15.5027i | 0.0129651 | − | 1.45196i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.91529 | + | 1.96283i | 0.177830 | + | 0.182244i | ||||
\(117\) | 16.4939 | + | 0.0923560i | 1.52486 | + | 0.00853832i | ||||
\(118\) | 3.26318 | + | 8.01666i | 0.300400 | + | 0.737993i | ||||
\(119\) | 1.02580 | 0.0940350 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.58708 | 0.235189 | ||||||||
\(122\) | −2.73771 | − | 6.72573i | −0.247861 | − | 0.608919i | ||||
\(123\) | −1.03589 | − | 0.432483i | −0.0934033 | − | 0.0389956i | ||||
\(124\) | 4.75347 | − | 4.63833i | 0.426874 | − | 0.416535i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.24594 | + | 1.30012i | −0.289171 | + | 0.115824i | ||||
\(127\) | 0.0146460 | − | 0.0146460i | 0.00129962 | − | 0.00129962i | −0.706457 | − | 0.707756i | \(-0.749707\pi\) |
0.707756 | + | 0.706457i | \(0.249707\pi\) | |||||||
\(128\) | 10.2572 | + | 4.77393i | 0.906615 | + | 0.421959i | ||||
\(129\) | 0.762905 | + | 1.85650i | 0.0671701 | + | 0.163456i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.23989 | 0.457811 | 0.228906 | − | 0.973449i | \(-0.426485\pi\) | ||||
0.228906 | + | 0.973449i | \(0.426485\pi\) | |||||||
\(132\) | 4.70826 | + | 11.8692i | 0.409801 | + | 1.03308i | ||||
\(133\) | 3.68847 | − | 3.68847i | 0.319831 | − | 0.319831i | ||||
\(134\) | 9.04259 | + | 3.81066i | 0.781161 | + | 0.329191i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.27666 | − | 1.28717i | 0.280972 | − | 0.110374i | ||||
\(137\) | 14.0984 | + | 14.0984i | 1.20450 | + | 1.20450i | 0.972782 | + | 0.231722i | \(0.0744360\pi\) |
0.231722 | + | 0.972782i | \(0.425564\pi\) | |||||||
\(138\) | 5.01588 | + | 5.10627i | 0.426980 | + | 0.434674i | ||||
\(139\) | 9.22166 | 0.782171 | 0.391085 | − | 0.920354i | \(-0.372100\pi\) | ||||
0.391085 | + | 0.920354i | \(0.372100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −14.2398 | + | 5.85165i | −1.19921 | + | 0.492798i | ||||
\(142\) | 2.20336 | + | 5.41300i | 0.184902 | + | 0.454249i | ||||
\(143\) | 14.3304 | − | 14.3304i | 1.19836 | − | 1.19836i | ||||
\(144\) | −8.73695 | + | 8.22592i | −0.728079 | + | 0.685493i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.65895 | + | 3.64899i | 0.716619 | + | 0.301993i | ||||
\(147\) | 10.1027 | + | 4.21787i | 0.833260 | + | 0.347884i | ||||
\(148\) | −6.90501 | − | 0.0846526i | −0.567589 | − | 0.00695840i | ||||
\(149\) | 14.0054i | 1.14737i | 0.819076 | + | 0.573685i | \(0.194487\pi\) | ||||
−0.819076 | + | 0.573685i | \(0.805513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.1301 | 1.06851 | 0.534255 | − | 0.845323i | \(-0.320592\pi\) | ||||
0.534255 | + | 0.845323i | \(0.320592\pi\) | |||||||
\(152\) | 7.15361 | − | 16.4102i | 0.580234 | − | 1.33104i | ||||
\(153\) | −0.0209077 | + | 3.73391i | −0.00169028 | + | 0.301869i | ||||
\(154\) | −1.66841 | + | 3.95909i | −0.134444 | + | 0.319032i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 17.4843 | + | 7.55265i | 1.39986 | + | 0.604696i | ||||
\(157\) | −6.36936 | − | 6.36936i | −0.508330 | − | 0.508330i | 0.405683 | − | 0.914014i | \(-0.367034\pi\) |
−0.914014 | + | 0.405683i | \(0.867034\pi\) | |||||||
\(158\) | 0.586914 | + | 1.44187i | 0.0466924 | + | 0.114709i | ||||
\(159\) | 12.7054 | − | 5.22110i | 1.00760 | − | 0.414060i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.40831i | 0.189802i | ||||||||
\(162\) | −4.66628 | − | 11.8417i | −0.366618 | − | 0.930372i | ||||
\(163\) | −3.46013 | + | 3.46013i | −0.271018 | + | 0.271018i | −0.829510 | − | 0.558492i | \(-0.811380\pi\) |
0.558492 | + | 0.829510i | \(0.311380\pi\) | |||||||
\(164\) | −0.905253 | − | 0.927724i | −0.0706884 | − | 0.0724431i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.5639 | + | 4.87318i | 0.897533 | + | 0.378232i | ||||
\(167\) | −0.954151 | − | 0.954151i | −0.0738345 | − | 0.0738345i | 0.669225 | − | 0.743060i | \(-0.266626\pi\) |
−0.743060 | + | 0.669225i | \(0.766626\pi\) | |||||||
\(168\) | −4.03666 | − | 0.0855420i | −0.311435 | − | 0.00659971i | ||||
\(169\) | − | 17.2286i | − | 1.32528i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.3508 | + | 13.5012i | 1.02096 | + | 1.03246i | ||||
\(172\) | −0.0284113 | + | 2.31747i | −0.00216634 | + | 0.176706i | ||||
\(173\) | −1.80240 | − | 1.80240i | −0.137034 | − | 0.137034i | 0.635262 | − | 0.772296i | \(-0.280892\pi\) |
−0.772296 | + | 0.635262i | \(0.780892\pi\) | |||||||
\(174\) | −3.35867 | − | 0.0299909i | −0.254620 | − | 0.00227360i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.361463 | + | 14.7398i | −0.0272463 | + | 1.11106i | ||||
\(177\) | −9.78228 | − | 4.08408i | −0.735281 | − | 0.306978i | ||||
\(178\) | 20.1144 | − | 8.18756i | 1.50763 | − | 0.613683i | ||||
\(179\) | − | 24.0166i | − | 1.79508i | −0.440930 | − | 0.897541i | \(-0.645351\pi\) | ||
0.440930 | − | 0.897541i | \(-0.354649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.7210i | − | 1.61451i | −0.590205 | − | 0.807253i | \(-0.700953\pi\) | ||
0.590205 | − | 0.807253i | \(-0.299047\pi\) | |||||||
\(182\) | 2.41599 | + | 5.93535i | 0.179085 | + | 0.439957i | ||||
\(183\) | 8.20703 | + | 3.42641i | 0.606681 | + | 0.253288i | ||||
\(184\) | 3.02195 | + | 7.69276i | 0.222781 | + | 0.567117i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0726302 | + | 8.13383i | −0.00532550 | + | 0.596401i | ||||
\(187\) | 3.24412 | + | 3.24412i | 0.237234 | + | 0.237234i | ||||
\(188\) | −17.7755 | − | 0.217921i | −1.29641 | − | 0.0158935i | ||||
\(189\) | 1.67201 | − | 3.94259i | 0.121621 | − | 0.286781i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.9839i | − | 0.939479i | −0.882805 | − | 0.469739i | \(-0.844348\pi\) | ||
0.882805 | − | 0.469739i | \(-0.155652\pi\) | |||||||
\(192\) | −13.0014 | + | 4.79195i | −0.938297 | + | 0.345829i | ||||
\(193\) | −9.48630 | − | 9.48630i | −0.682839 | − | 0.682839i | 0.277800 | − | 0.960639i | \(-0.410395\pi\) |
−0.960639 | + | 0.277800i | \(0.910395\pi\) | |||||||
\(194\) | −4.21079 | + | 9.99208i | −0.302317 | + | 0.717389i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.82864 | + | 9.04780i | 0.630617 | + | 0.646272i | ||||
\(197\) | −12.8606 | + | 12.8606i | −0.916280 | + | 0.916280i | −0.996757 | − | 0.0804765i | \(-0.974356\pi\) |
0.0804765 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(198\) | −14.3770 | − | 6.15370i | −1.02173 | − | 0.437324i | ||||
\(199\) | 0.0463625i | 0.00328655i | 0.999999 | + | 0.00164328i | \(0.000523071\pi\) | ||||
−0.999999 | + | 0.00164328i | \(0.999477\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.1161 | + | 4.56802i | −0.784069 | + | 0.322203i | ||||
\(202\) | −12.8948 | + | 5.24882i | −0.907273 | + | 0.369306i | ||||
\(203\) | −0.799111 | − | 0.799111i | −0.0560866 | − | 0.0560866i | ||||
\(204\) | −1.70978 | + | 3.95812i | −0.119708 | + | 0.277123i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −15.2621 | − | 6.43165i | −1.06336 | − | 0.448115i | ||||
\(207\) | −8.76625 | − | 0.0490858i | −0.609296 | − | 0.00341170i | ||||
\(208\) | 15.1649 | + | 15.9274i | 1.05150 | + | 1.10437i | ||||
\(209\) | 23.3298 | 1.61376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.591066i | − | 0.0406907i | −0.999793 | − | 0.0203453i | \(-0.993523\pi\) | ||
0.999793 | − | 0.0203453i | \(-0.00647657\pi\) | |||||||
\(212\) | 15.8601 | + | 0.194439i | 1.08928 | + | 0.0133541i | ||||
\(213\) | −6.60518 | − | 2.75765i | −0.452579 | − | 0.188951i | ||||
\(214\) | −4.54107 | + | 10.7758i | −0.310421 | + | 0.736619i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.393647 | − | 14.6917i | 0.0267843 | − | 0.999641i | ||||
\(217\) | −1.93524 | + | 1.93524i | −0.131373 | + | 0.131373i | ||||
\(218\) | 15.3296 | − | 6.23994i | 1.03825 | − | 0.422622i | ||||
\(219\) | −10.6445 | + | 4.37421i | −0.719287 | + | 0.295582i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.84318 | 0.460322 | ||||||||
\(222\) | 6.03353 | − | 5.92673i | 0.404944 | − | 0.397776i | ||||
\(223\) | −16.8577 | − | 16.8577i | −1.12888 | − | 1.12888i | −0.990360 | − | 0.138517i | \(-0.955767\pi\) |
−0.138517 | − | 0.990360i | \(-0.544233\pi\) | |||||||
\(224\) | −4.25060 | − | 1.91529i | −0.284005 | − | 0.127970i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.66649 | − | 15.8194i | 0.443448 | − | 1.05229i | ||||
\(227\) | −7.23390 | + | 7.23390i | −0.480131 | + | 0.480131i | −0.905173 | − | 0.425043i | \(-0.860259\pi\) |
0.425043 | + | 0.905173i | \(0.360259\pi\) | |||||||
\(228\) | 8.08434 | + | 20.3800i | 0.535399 | + | 1.34970i | ||||
\(229\) | 23.0081 | 1.52042 | 0.760210 | − | 0.649677i | \(-0.225096\pi\) | ||||
0.760210 | + | 0.649677i | \(0.225096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | − | 4.86692i | −0.131590 | − | 0.320220i | ||||
\(232\) | −3.55529 | − | 1.54984i | −0.233416 | − | 0.101752i | ||||
\(233\) | 4.45082 | − | 4.45082i | 0.291583 | − | 0.291583i | −0.546122 | − | 0.837705i | \(-0.683897\pi\) |
0.837705 | + | 0.546122i | \(0.183897\pi\) | |||||||
\(234\) | −21.6539 | + | 8.67320i | −1.41556 | + | 0.566985i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.54860 | − | 8.76081i | −0.556466 | − | 0.570280i | ||||
\(237\) | −1.75944 | − | 0.734560i | −0.114288 | − | 0.0477148i | ||||
\(238\) | −1.34365 | + | 0.546934i | −0.0870959 | + | 0.0354524i | ||||
\(239\) | 4.03472 | 0.260984 | 0.130492 | − | 0.991449i | \(-0.458344\pi\) | ||||
0.130492 | + | 0.991449i | \(0.458344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4612 | −0.738279 | −0.369139 | − | 0.929374i | \(-0.620347\pi\) | ||||
−0.369139 | + | 0.929374i | \(0.620347\pi\) | |||||||
\(242\) | −3.38871 | + | 1.37937i | −0.217834 | + | 0.0886696i | ||||
\(243\) | 14.3169 | + | 6.16646i | 0.918432 | + | 0.395578i | ||||
\(244\) | 7.17201 | + | 7.35005i | 0.459141 | + | 0.470538i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.58746 | + | 0.0141751i | 0.101213 | + | 0.000903769i | ||||
\(247\) | 24.6060 | − | 24.6060i | 1.56564 | − | 1.56564i | ||||
\(248\) | −3.75331 | + | 8.60999i | −0.238335 | + | 0.546735i | ||||
\(249\) | −14.2156 | + | 5.84170i | −0.900874 | + | 0.370203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4804 | −1.10335 | −0.551677 | − | 0.834058i | \(-0.686012\pi\) | ||||
−0.551677 | + | 0.834058i | \(0.686012\pi\) | |||||||
\(252\) | 3.55851 | − | 3.43363i | 0.224165 | − | 0.216299i | ||||
\(253\) | −7.61636 | + | 7.61636i | −0.478836 | + | 0.478836i | ||||
\(254\) | −0.0113752 | + | 0.0269930i | −0.000713745 | + | 0.00169369i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9808 | − | 0.784260i | −0.998798 | − | 0.0490162i | ||||
\(257\) | −6.77283 | − | 6.77283i | −0.422477 | − | 0.422477i | 0.463578 | − | 0.886056i | \(-0.346565\pi\) |
−0.886056 | + | 0.463578i | \(0.846565\pi\) | |||||||
\(258\) | −1.98914 | − | 2.02498i | −0.123838 | − | 0.126070i | ||||
\(259\) | 2.84565 | 0.176820 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.92505 | − | 2.89247i | 0.181056 | − | 0.179040i | ||||
\(262\) | −6.86350 | + | 2.79379i | −0.424028 | + | 0.172601i | ||||
\(263\) | −15.3708 | + | 15.3708i | −0.947805 | + | 0.947805i | −0.998704 | − | 0.0508987i | \(-0.983791\pi\) |
0.0508987 | + | 0.998704i | \(0.483791\pi\) | |||||||
\(264\) | −12.4955 | − | 13.0366i | −0.769046 | − | 0.802345i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.86476 | + | 6.79798i | −0.175649 | + | 0.416811i | ||||
\(267\) | −10.2472 | + | 24.5444i | −0.627121 | + | 1.50209i | ||||
\(268\) | −13.8762 | − | 0.170117i | −0.847627 | − | 0.0103916i | ||||
\(269\) | 9.58859i | 0.584627i | 0.956323 | + | 0.292313i | \(0.0944250\pi\) | ||||
−0.956323 | + | 0.292313i | \(0.905575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.9078 | −1.27006 | −0.635030 | − | 0.772487i | \(-0.719012\pi\) | ||||
−0.635030 | + | 0.772487i | \(0.719012\pi\) | |||||||
\(272\) | −3.60567 | + | 3.43306i | −0.218626 | + | 0.208160i | ||||
\(273\) | −7.24257 | − | 3.02376i | −0.438341 | − | 0.183006i | ||||
\(274\) | −25.9837 | − | 10.9499i | −1.56974 | − | 0.661507i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.29263 | − | 4.01412i | −0.559350 | − | 0.241621i | ||||
\(277\) | 8.86336 | + | 8.86336i | 0.532547 | + | 0.532547i | 0.921330 | − | 0.388782i | \(-0.127104\pi\) |
−0.388782 | + | 0.921330i | \(0.627104\pi\) | |||||||
\(278\) | −12.0790 | + | 4.91678i | −0.724453 | + | 0.294889i | ||||
\(279\) | −7.00483 | − | 7.08372i | −0.419368 | − | 0.424091i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 12.1925i | − | 0.727341i | −0.931528 | − | 0.363670i | \(-0.881523\pi\) | ||
0.931528 | − | 0.363670i | \(-0.118477\pi\) | |||||||
\(282\) | 15.5321 | − | 15.2571i | 0.924922 | − | 0.908550i | ||||
\(283\) | 11.6799 | − | 11.6799i | 0.694298 | − | 0.694298i | −0.268877 | − | 0.963175i | \(-0.586652\pi\) |
0.963175 | + | 0.268877i | \(0.0866525\pi\) | |||||||
\(284\) | −5.77217 | − | 5.91546i | −0.342516 | − | 0.351018i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.1301 | + | 26.4113i | −0.658135 | + | 1.56173i | ||||
\(287\) | 0.377697 | + | 0.377697i | 0.0222947 | + | 0.0222947i | ||||
\(288\) | 7.05827 | − | 15.4331i | 0.415912 | − | 0.909405i | ||||
\(289\) | − | 15.4508i | − | 0.908872i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.04767 | − | 12.2833i | −0.295900 | − | 0.720060i | ||||
\(292\) | −13.2875 | − | 0.162900i | −0.777594 | − | 0.00953298i | ||||
\(293\) | 5.16432 | + | 5.16432i | 0.301703 | + | 0.301703i | 0.841680 | − | 0.539977i | \(-0.181567\pi\) |
−0.539977 | + | 0.841680i | \(0.681567\pi\) | |||||||
\(294\) | −15.4820 | − | 0.138245i | −0.902929 | − | 0.00806261i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.08971 | − | 3.57071i | 0.528328 | − | 0.207544i | ||||
\(297\) | 17.7563 | − | 7.18079i | 1.03033 | − | 0.416672i | ||||
\(298\) | −7.46739 | − | 18.3451i | −0.432574 | − | 1.06270i | ||||
\(299\) | 16.0660i | 0.929122i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 0.955061i | − | 0.0550488i | ||||||
\(302\) | −17.1985 | + | 7.00066i | −0.989663 | + | 0.402843i | ||||
\(303\) | 6.56923 | − | 15.7348i | 0.377392 | − | 0.903939i | ||||
\(304\) | −0.620652 | + | 25.3091i | −0.0355968 | + | 1.45158i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.96345 | − | 4.90203i | −0.112243 | − | 0.280230i | ||||
\(307\) | −9.19824 | − | 9.19824i | −0.524972 | − | 0.524972i | 0.394097 | − | 0.919069i | \(-0.371057\pi\) |
−0.919069 | + | 0.394097i | \(0.871057\pi\) | |||||||
\(308\) | 0.0744818 | − | 6.07539i | 0.00424399 | − | 0.346177i | ||||
\(309\) | 18.7618 | − | 7.70992i | 1.06732 | − | 0.438602i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5690i | 1.73341i | 0.498821 | + | 0.866705i | \(0.333767\pi\) | ||||
−0.498821 | + | 0.866705i | \(0.666233\pi\) | |||||||
\(312\) | −26.9288 | − | 0.570656i | −1.52454 | − | 0.0323071i | ||||
\(313\) | 16.4612 | + | 16.4612i | 0.930440 | + | 0.930440i | 0.997733 | − | 0.0672931i | \(-0.0214363\pi\) |
−0.0672931 | + | 0.997733i | \(0.521436\pi\) | |||||||
\(314\) | 11.7389 | + | 4.94694i | 0.662467 | + | 0.279172i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.53755 | − | 1.57571i | −0.0864937 | − | 0.0886408i | ||||
\(317\) | 0.000616701 | 0 | 0.000616701i | 3.46374e−5 | 0 | 3.46374e-5i | −0.707089 | − | 0.707124i | \(-0.749992\pi\) |
0.707124 | + | 0.707089i | \(0.249992\pi\) | |||||||
\(318\) | −13.8584 | + | 13.6131i | −0.777141 | + | 0.763385i | ||||
\(319\) | − | 5.05442i | − | 0.282993i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.44358 | − | 13.2468i | −0.303831 | − | 0.739362i | ||||
\(322\) | −1.28406 | − | 3.15454i | −0.0715578 | − | 0.175796i | ||||
\(323\) | 5.57034 | + | 5.57034i | 0.309942 | + | 0.309942i | ||||
\(324\) | 12.4259 | + | 13.0230i | 0.690327 | + | 0.723498i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.68740 | − | 6.37713i | 0.148842 | − | 0.353196i | ||||
\(327\) | −7.80967 | + | 18.7059i | −0.431876 | + | 1.03444i | ||||
\(328\) | 1.68039 | + | 0.732524i | 0.0927841 | + | 0.0404469i | ||||
\(329\) | 7.32553 | 0.403870 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 8.28613i | − | 0.455447i | −0.973726 | − | 0.227724i | \(-0.926872\pi\) | ||
0.973726 | − | 0.227724i | \(-0.0731283\pi\) | |||||||
\(332\) | −17.7453 | − | 0.217550i | −0.973901 | − | 0.0119396i | ||||
\(333\) | −0.0579994 | + | 10.3581i | −0.00317835 | + | 0.567622i | ||||
\(334\) | 1.75853 | + | 0.741069i | 0.0962226 | + | 0.0405495i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.33305 | − | 2.04021i | 0.290942 | − | 0.111302i | ||||
\(337\) | −2.27666 | + | 2.27666i | −0.124018 | + | 0.124018i | −0.766392 | − | 0.642374i | \(-0.777950\pi\) |
0.642374 | + | 0.766392i | \(0.277950\pi\) | |||||||
\(338\) | 9.18590 | + | 22.5670i | 0.499647 | + | 1.22748i | ||||
\(339\) | 7.99142 | + | 19.4468i | 0.434035 | + | 1.05621i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.2405 | −0.662861 | ||||||||
\(342\) | −24.6862 | − | 10.5663i | −1.33488 | − | 0.571357i | ||||
\(343\) | −7.76296 | − | 7.76296i | −0.419161 | − | 0.419161i | ||||
\(344\) | −1.19841 | − | 3.05070i | −0.0646139 | − | 0.164483i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.32189 | + | 1.39989i | 0.178586 | + | 0.0752584i | ||||
\(347\) | 18.6384 | − | 18.6384i | 1.00056 | − | 1.00056i | 0.000564305 | − | 1.00000i | \(-0.499820\pi\) |
1.00000 | 0.000564305i | \(-0.000179624\pi\) | ||||||||
\(348\) | 4.41536 | − | 1.75148i | 0.236688 | − | 0.0938892i | ||||
\(349\) | −17.7267 | −0.948889 | −0.474445 | − | 0.880285i | \(-0.657351\pi\) | ||||
−0.474445 | + | 0.880285i | \(0.657351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.1541 | − | 26.3013i | 0.595360 | − | 1.40386i | ||||
\(352\) | −7.38548 | − | 19.4998i | −0.393648 | − | 1.03934i | ||||
\(353\) | 10.5779 | − | 10.5779i | 0.563007 | − | 0.563007i | −0.367153 | − | 0.930160i | \(-0.619668\pi\) |
0.930160 | + | 0.367153i | \(0.119668\pi\) | |||||||
\(354\) | 14.9909 | + | 0.133860i | 0.796758 | + | 0.00711457i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −21.9815 | + | 21.4490i | −1.16502 | + | 1.13680i | ||||
\(357\) | 0.684521 | − | 1.63958i | 0.0362287 | − | 0.0867759i | ||||
\(358\) | 12.8051 | + | 31.4582i | 0.676770 | + | 1.66262i | ||||
\(359\) | −24.7266 | −1.30502 | −0.652510 | − | 0.757780i | \(-0.726284\pi\) | ||||
−0.652510 | + | 0.757780i | \(0.726284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.0586 | 1.10835 | ||||||||
\(362\) | 11.5811 | + | 28.4513i | 0.608691 | + | 1.49537i | ||||
\(363\) | 1.72637 | − | 4.13505i | 0.0906111 | − | 0.217034i | ||||
\(364\) | −6.32919 | − | 6.48630i | −0.331739 | − | 0.339974i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.5769 | − | 0.112304i | −0.657406 | − | 0.00587024i | ||||
\(367\) | −9.33767 | + | 9.33767i | −0.487423 | + | 0.487423i | −0.907492 | − | 0.420069i | \(-0.862006\pi\) |
0.420069 | + | 0.907492i | \(0.362006\pi\) | |||||||
\(368\) | −8.05992 | − | 8.46516i | −0.420152 | − | 0.441277i | ||||
\(369\) | −1.38251 | + | 1.36712i | −0.0719707 | + | 0.0711692i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.53616 | −0.339341 | ||||||||
\(372\) | −4.24164 | − | 10.6929i | −0.219919 | − | 0.554399i | ||||
\(373\) | 11.9025 | − | 11.9025i | 0.616291 | − | 0.616291i | −0.328287 | − | 0.944578i | \(-0.606471\pi\) |
0.944578 | + | 0.328287i | \(0.106471\pi\) | |||||||
\(374\) | −5.97903 | − | 2.51964i | −0.309168 | − | 0.130288i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 23.3996 | − | 9.19207i | 1.20674 | − | 0.474045i | ||||
\(377\) | −5.33092 | − | 5.33092i | −0.274557 | − | 0.274557i | ||||
\(378\) | −0.0879865 | + | 6.05570i | −0.00452554 | + | 0.311472i | ||||
\(379\) | −2.73341 | −0.140406 | −0.0702029 | − | 0.997533i | \(-0.522365\pi\) | ||||
−0.0702029 | + | 0.997533i | \(0.522365\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0136360 | − | 0.0331827i | −0.000698593 | − | 0.00170000i | ||||
\(382\) | 6.92270 | + | 17.0070i | 0.354196 | + | 0.870153i | ||||
\(383\) | −17.6065 | + | 17.6065i | −0.899651 | + | 0.899651i | −0.995405 | − | 0.0957539i | \(-0.969474\pi\) |
0.0957539 | + | 0.995405i | \(0.469474\pi\) | |||||||
\(384\) | 14.4750 | − | 13.2088i | 0.738676 | − | 0.674060i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.4836 | + | 7.36780i | 0.889890 | + | 0.375011i | ||||
\(387\) | 3.47642 | + | 0.0194659i | 0.176716 | + | 0.000989506i | ||||
\(388\) | 0.187980 | − | 15.3333i | 0.00954322 | − | 0.778429i | ||||
\(389\) | 25.1335i | 1.27432i | 0.770731 | + | 0.637160i | \(0.219891\pi\) | ||||
−0.770731 | + | 0.637160i | \(0.780109\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.63704 | −0.183933 | ||||||||
\(392\) | −16.3883 | − | 7.14408i | −0.827736 | − | 0.360831i | ||||
\(393\) | 3.49660 | − | 8.37515i | 0.176380 | − | 0.422470i | ||||
\(394\) | 9.98855 | − | 23.7025i | 0.503216 | − | 1.19412i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 22.1129 | + | 0.394941i | 1.11121 | + | 0.0198465i | ||||
\(397\) | −5.42664 | − | 5.42664i | −0.272355 | − | 0.272355i | 0.557692 | − | 0.830048i | \(-0.311687\pi\) |
−0.830048 | + | 0.557692i | \(0.811687\pi\) | |||||||
\(398\) | −0.0247195 | − | 0.0607282i | −0.00123907 | − | 0.00304403i | ||||
\(399\) | −3.43411 | − | 8.35678i | −0.171921 | − | 0.418362i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.15831i | 0.257594i | 0.991671 | + | 0.128797i | \(0.0411115\pi\) | ||||
−0.991671 | + | 0.128797i | \(0.958888\pi\) | |||||||
\(402\) | 12.1249 | − | 11.9103i | 0.604736 | − | 0.594032i | ||||
\(403\) | −12.9101 | + | 12.9101i | −0.643099 | + | 0.643099i | ||||
\(404\) | 14.0917 | − | 13.7504i | 0.701090 | − | 0.684108i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.47279 | + | 0.620652i | 0.0730933 | + | 0.0308025i | ||||
\(407\) | 8.99944 | + | 8.99944i | 0.446085 | + | 0.446085i | ||||
\(408\) | 0.129186 | − | 6.09617i | 0.00639565 | − | 0.301806i | ||||
\(409\) | 14.1638i | 0.700356i | 0.936683 | + | 0.350178i | \(0.113879\pi\) | ||||
−0.936683 | + | 0.350178i | \(0.886121\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.9419 | − | 13.1261i | 1.57558 | − | 0.647464i | ||||
\(412\) | 23.4204 | + | 0.287124i | 1.15384 | + | 0.0141456i | ||||
\(413\) | 3.56672 | + | 3.56672i | 0.175507 | + | 0.175507i | ||||
\(414\) | 11.5087 | − | 4.60967i | 0.565621 | − | 0.226553i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −28.3560 | − | 12.7770i | −1.39027 | − | 0.626444i | ||||
\(417\) | 6.15365 | − | 14.7394i | 0.301346 | − | 0.721791i | ||||
\(418\) | −30.5587 | + | 12.4389i | −1.49467 | + | 0.608407i | ||||
\(419\) | 4.80514i | 0.234746i | 0.993088 | + | 0.117373i | \(0.0374474\pi\) | ||||
−0.993088 | + | 0.117373i | \(0.962553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.2187i | 0.741716i | 0.928690 | + | 0.370858i | \(0.120936\pi\) | ||||
−0.928690 | + | 0.370858i | \(0.879064\pi\) | |||||||
\(422\) | 0.315143 | + | 0.774212i | 0.0153409 | + | 0.0376880i | ||||
\(423\) | −0.149308 | + | 26.6649i | −0.00725958 | + | 1.29649i | ||||
\(424\) | −20.8781 | + | 8.20157i | −1.01393 | + | 0.398304i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.1221 | + | 0.0903846i | 0.490420 | + | 0.00437915i | ||||
\(427\) | −2.99236 | − | 2.99236i | −0.144811 | − | 0.144811i | ||||
\(428\) | 0.202724 | − | 16.5359i | 0.00979903 | − | 0.799295i | ||||
\(429\) | −13.3421 | − | 32.4676i | −0.644164 | − | 1.56755i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.8760i | 1.34274i | 0.741122 | + | 0.671370i | \(0.234294\pi\) | ||||
−0.741122 | + | 0.671370i | \(0.765706\pi\) | |||||||
\(432\) | 7.31764 | + | 19.4538i | 0.352070 | + | 0.935974i | ||||
\(433\) | 2.78003 | + | 2.78003i | 0.133600 | + | 0.133600i | 0.770744 | − | 0.637145i | \(-0.219885\pi\) |
−0.637145 | + | 0.770744i | \(0.719885\pi\) | |||||||
\(434\) | 1.50306 | − | 3.56672i | 0.0721492 | − | 0.171208i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.7526 | + | 16.3468i | −0.802305 | + | 0.782872i | ||||
\(437\) | −13.0777 | + | 13.0777i | −0.625592 | + | 0.625592i | ||||
\(438\) | 11.6105 | − | 11.4050i | 0.554771 | − | 0.544951i | ||||
\(439\) | 10.8174i | 0.516286i | 0.966107 | + | 0.258143i | \(0.0831105\pi\) | ||||
−0.966107 | + | 0.258143i | \(0.916889\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.4832 | − | 13.3331i | 0.642058 | − | 0.634907i | ||||
\(442\) | −8.96358 | + | 3.64863i | −0.426354 | + | 0.173548i | ||||
\(443\) | −5.74963 | − | 5.74963i | −0.273173 | − | 0.273173i | 0.557203 | − | 0.830376i | \(-0.311874\pi\) |
−0.830376 | + | 0.557203i | \(0.811874\pi\) | |||||||
\(444\) | −4.74305 | + | 10.9801i | −0.225095 | + | 0.521092i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 31.0693 | + | 13.0930i | 1.47118 | + | 0.619973i | ||||
\(447\) | 22.3855 | + | 9.34590i | 1.05880 | + | 0.442046i | ||||
\(448\) | 6.58885 | + | 0.242427i | 0.311294 | + | 0.0114536i | ||||
\(449\) | 6.91183 | 0.326189 | 0.163095 | − | 0.986610i | \(-0.447852\pi\) | ||||
0.163095 | + | 0.986610i | \(0.447852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38895i | 0.112491i | ||||||||
\(452\) | −0.297608 | + | 24.2755i | −0.0139983 | + | 1.14182i | ||||
\(453\) | 8.76176 | − | 20.9864i | 0.411663 | − | 0.986026i | ||||
\(454\) | 5.61841 | − | 13.3323i | 0.263685 | − | 0.625716i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.4555 | − | 22.3845i | −1.00475 | − | 1.04825i | ||||
\(457\) | 5.15748 | − | 5.15748i | 0.241257 | − | 0.241257i | −0.576113 | − | 0.817370i | \(-0.695431\pi\) |
0.817370 | + | 0.576113i | \(0.195431\pi\) | |||||||
\(458\) | −30.1373 | + | 12.2674i | −1.40823 | + | 0.573219i | ||||
\(459\) | 5.95412 | + | 2.52507i | 0.277915 | + | 0.117860i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4555 | 0.859558 | 0.429779 | − | 0.902934i | \(-0.358592\pi\) | ||||
0.429779 | + | 0.902934i | \(0.358592\pi\) | |||||||
\(462\) | 5.21464 | + | 5.30861i | 0.242607 | + | 0.246979i | ||||
\(463\) | 19.6899 | + | 19.6899i | 0.915068 | + | 0.915068i | 0.996665 | − | 0.0815977i | \(-0.0260023\pi\) |
−0.0815977 | + | 0.996665i | \(0.526002\pi\) | |||||||
\(464\) | 5.48325 | + | 0.134465i | 0.254553 | + | 0.00624238i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.45685 | + | 8.20301i | −0.160136 | + | 0.379997i | ||||
\(467\) | −2.07946 | + | 2.07946i | −0.0962257 | + | 0.0962257i | −0.753581 | − | 0.657355i | \(-0.771675\pi\) |
0.657355 | + | 0.753581i | \(0.271675\pi\) | |||||||
\(468\) | 23.7391 | − | 22.9060i | 1.09734 | − | 1.05883i | ||||
\(469\) | 5.71858 | 0.264060 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.4307 | + | 5.93013i | −0.664933 | + | 0.273246i | ||||
\(472\) | 15.8685 | + | 6.91747i | 0.730407 | + | 0.318402i | ||||
\(473\) | 3.02041 | − | 3.02041i | 0.138879 | − | 0.138879i | ||||
\(474\) | 2.69626 | + | 0.0240759i | 0.123843 | + | 0.00110584i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.46838 | − | 1.43281i | 0.0673029 | − | 0.0656727i | ||||
\(477\) | 0.133219 | − | 23.7916i | 0.00609967 | − | 1.08934i | ||||
\(478\) | −5.28490 | + | 2.15122i | −0.241725 | + | 0.0983945i | ||||
\(479\) | 19.7088 | 0.900517 | 0.450259 | − | 0.892898i | \(-0.351332\pi\) | ||||
0.450259 | + | 0.892898i | \(0.351332\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9835 | 0.865573 | ||||||||
\(482\) | 15.0125 | − | 6.11083i | 0.683799 | − | 0.278341i | ||||
\(483\) | 3.84931 | + | 1.60708i | 0.175150 | + | 0.0731246i | ||||
\(484\) | 3.70326 | − | 3.61356i | 0.168330 | − | 0.164253i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0409 | − | 0.443697i | −0.999797 | − | 0.0201265i | ||||
\(487\) | −4.21395 | + | 4.21395i | −0.190952 | + | 0.190952i | −0.796107 | − | 0.605155i | \(-0.793111\pi\) |
0.605155 | + | 0.796107i | \(0.293111\pi\) | |||||||
\(488\) | −13.3132 | − | 5.80354i | −0.602659 | − | 0.262714i | ||||
\(489\) | 3.22151 | + | 7.83943i | 0.145682 | + | 0.354511i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.7215 | −1.25105 | −0.625527 | − | 0.780203i | \(-0.715116\pi\) | ||||
−0.625527 | + | 0.780203i | \(0.715116\pi\) | |||||||
\(492\) | −2.08690 | + | 0.827831i | −0.0940848 | + | 0.0373215i | ||||
\(493\) | 1.20682 | − | 1.20682i | 0.0543525 | − | 0.0543525i | ||||
\(494\) | −19.1110 | + | 45.3497i | −0.859843 | + | 2.04038i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.325640 | − | 13.2790i | 0.0146216 | − | 0.596246i | ||||
\(497\) | 2.40831 | + | 2.40831i | 0.108028 | + | 0.108028i | ||||
\(498\) | 15.5057 | − | 15.2312i | 0.694825 | − | 0.682527i | ||||
\(499\) | −5.14705 | −0.230414 | −0.115207 | − | 0.993342i | \(-0.536753\pi\) | ||||
−0.115207 | + | 0.993342i | \(0.536753\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.16177 | + | 0.888353i | −0.0965809 | + | 0.0396887i | ||||
\(502\) | 22.8968 | − | 9.32016i | 1.02193 | − | 0.415979i | ||||
\(503\) | −12.2281 | + | 12.2281i | −0.545224 | + | 0.545224i | −0.925056 | − | 0.379832i | \(-0.875982\pi\) |
0.379832 | + | 0.925056i | \(0.375982\pi\) | |||||||
\(504\) | −2.83040 | + | 6.39488i | −0.126076 | + | 0.284851i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.91546 | − | 14.0372i | 0.262974 | − | 0.624030i | ||||
\(507\) | −27.5372 | − | 11.4967i | −1.22297 | − | 0.510587i | ||||
\(508\) | 0.000507817 | − | 0.0414220i | 2.25307e−5 | − | 0.00183780i | ||||
\(509\) | − | 35.8361i | − | 1.58841i | −0.607651 | − | 0.794204i | \(-0.707888\pi\) | ||
0.607651 | − | 0.794204i | \(-0.292112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.47596 | 0.242242 | ||||||||
\(512\) | 21.3506 | − | 7.49332i | 0.943574 | − | 0.331161i | ||||
\(513\) | 30.4886 | − | 12.3298i | 1.34611 | − | 0.544375i | ||||
\(514\) | 12.4825 | + | 5.26031i | 0.550581 | + | 0.232022i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.68516 | + | 1.59187i | 0.162230 | + | 0.0700783i | ||||
\(517\) | 23.1672 | + | 23.1672i | 1.01889 | + | 1.01889i | ||||
\(518\) | −3.72738 | + | 1.51723i | −0.163772 | + | 0.0666634i | ||||
\(519\) | −4.08361 | + | 1.67811i | −0.179251 | + | 0.0736608i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1715i | 0.796107i | 0.917362 | + | 0.398054i | \(0.130314\pi\) | ||||
−0.917362 | + | 0.398054i | \(0.869686\pi\) | |||||||
\(522\) | −2.28919 | + | 5.34829i | −0.100195 | + | 0.234088i | ||||
\(523\) | −21.7444 | + | 21.7444i | −0.950815 | + | 0.950815i | −0.998846 | − | 0.0480305i | \(-0.984706\pi\) |
0.0480305 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(524\) | 7.50061 | − | 7.31893i | 0.327666 | − | 0.319729i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.9382 | − | 28.3289i | 0.520529 | − | 1.23520i | ||||
\(527\) | −2.92261 | − | 2.92261i | −0.127311 | − | 0.127311i | ||||
\(528\) | 23.3181 | + | 10.4137i | 1.01479 | + | 0.453198i | ||||
\(529\) | 14.4612i | 0.628746i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.0555 | + | 12.9101i | −0.566561 | + | 0.560252i | ||||
\(532\) | 0.127889 | − | 10.4318i | 0.00554471 | − | 0.452275i | ||||
\(533\) | 2.51964 | + | 2.51964i | 0.109138 | + | 0.109138i | ||||
\(534\) | 0.335864 | − | 37.6133i | 0.0145342 | − | 1.62768i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.2666 | − | 7.17567i | 0.788996 | − | 0.309942i | ||||
\(537\) | −38.3867 | − | 16.0264i | −1.65651 | − | 0.691589i | ||||
\(538\) | −5.11242 | − | 12.5597i | −0.220412 | − | 0.541486i | ||||
\(539\) | − | 23.2987i | − | 1.00355i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.6843i | 1.14725i | 0.819119 | + | 0.573623i | \(0.194463\pi\) | ||||
−0.819119 | + | 0.573623i | \(0.805537\pi\) | |||||||
\(542\) | 27.3862 | − | 11.1476i | 1.17634 | − | 0.478830i | ||||
\(543\) | −34.7176 | − | 14.4945i | −1.48987 | − | 0.622019i | ||||
\(544\) | 2.89247 | − | 6.41927i | 0.124014 | − | 0.275224i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.0989 | + | 0.0991067i | 0.474990 | + | 0.00424138i | ||||
\(547\) | 22.2551 | + | 22.2551i | 0.951559 | + | 0.951559i | 0.998880 | − | 0.0473207i | \(-0.0150683\pi\) |
−0.0473207 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(548\) | 39.8732 | + | 0.488829i | 1.70330 | + | 0.0208817i | ||||
\(549\) | 10.9532 | − | 10.8312i | 0.467470 | − | 0.462264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.67873i | − | 0.369726i | ||||||
\(552\) | 14.3122 | + | 0.303295i | 0.609169 | + | 0.0129091i | ||||
\(553\) | 0.641507 | + | 0.641507i | 0.0272797 | + | 0.0272797i | ||||
\(554\) | −16.3355 | − | 6.88398i | −0.694027 | − | 0.292472i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.2003 | − | 12.8805i | 0.559817 | − | 0.546257i | ||||
\(557\) | 7.30615 | − | 7.30615i | 0.309572 | − | 0.309572i | −0.535172 | − | 0.844743i | \(-0.679753\pi\) |
0.844743 | + | 0.535172i | \(0.179753\pi\) | |||||||
\(558\) | 12.9522 | + | 5.54383i | 0.548310 | + | 0.234689i | ||||
\(559\) | − | 6.37128i | − | 0.269476i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.35005 | − | 3.02041i | 0.310319 | − | 0.127522i | ||||
\(562\) | 6.50074 | + | 15.9704i | 0.274217 | + | 0.673669i | ||||
\(563\) | −21.3458 | − | 21.3458i | −0.899616 | − | 0.899616i | 0.0957856 | − | 0.995402i | \(-0.469464\pi\) |
−0.995402 | + | 0.0957856i | \(0.969464\pi\) | |||||||
\(564\) | −12.2100 | + | 28.2660i | −0.514134 | + | 1.19021i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.07152 | + | 21.5264i | −0.381304 | + | 0.904823i | ||||
\(567\) | −5.18588 | − | 5.30335i | −0.217787 | − | 0.222720i | ||||
\(568\) | 10.7147 | + | 4.67081i | 0.449579 | + | 0.195983i | ||||
\(569\) | 35.6410 | 1.49415 | 0.747075 | − | 0.664740i | \(-0.231458\pi\) | ||||
0.747075 | + | 0.664740i | \(0.231458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.49296i | 0.397268i | 0.980074 | + | 0.198634i | \(0.0636505\pi\) | ||||
−0.980074 | + | 0.198634i | \(0.936350\pi\) | |||||||
\(572\) | 0.496873 | − | 40.5293i | 0.0207753 | − | 1.69462i | ||||
\(573\) | −20.7527 | − | 8.66419i | −0.866955 | − | 0.361952i | ||||
\(574\) | −0.696108 | − | 0.293349i | −0.0290550 | − | 0.0122441i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.01673 | + | 23.9785i | −0.0423636 | + | 0.999102i | ||||
\(577\) | −10.6312 | + | 10.6312i | −0.442582 | + | 0.442582i | −0.892879 | − | 0.450297i | \(-0.851318\pi\) |
0.450297 | + | 0.892879i | \(0.351318\pi\) | |||||||
\(578\) | 8.23803 | + | 20.2384i | 0.342657 | + | 0.841805i | ||||
\(579\) | −21.4926 | + | 8.83212i | −0.893203 | + | 0.367050i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.31307 | 0.303397 | ||||||||
\(582\) | 13.1609 | + | 13.3981i | 0.545537 | + | 0.555367i | ||||
\(583\) | −20.6708 | − | 20.6708i | −0.856097 | − | 0.856097i | ||||
\(584\) | 17.4916 | − | 6.87124i | 0.723808 | − | 0.284334i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.51801 | − | 4.01102i | −0.393186 | − | 0.165694i | ||||
\(587\) | 17.1910 | − | 17.1910i | 0.709550 | − | 0.709550i | −0.256891 | − | 0.966441i | \(-0.582698\pi\) |
0.966441 | + | 0.256891i | \(0.0826980\pi\) | |||||||
\(588\) | 20.3529 | − | 8.07357i | 0.839339 | − | 0.332949i | ||||
\(589\) | −21.0177 | −0.866018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9737 | + | 29.1376i | 0.492534 | + | 1.19856i | ||||
\(592\) | −10.0024 | + | 9.52355i | −0.411095 | + | 0.391415i | ||||
\(593\) | 9.69544 | − | 9.69544i | 0.398144 | − | 0.398144i | −0.479434 | − | 0.877578i | \(-0.659158\pi\) |
0.877578 | + | 0.479434i | \(0.159158\pi\) | |||||||
\(594\) | −19.4296 | + | 18.8731i | −0.797206 | + | 0.774372i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.5624 | + | 20.0480i | 0.801307 | + | 0.821198i | ||||
\(597\) | 0.0741033 | + | 0.0309379i | 0.00303285 | + | 0.00126621i | ||||
\(598\) | −8.56604 | − | 21.0442i | −0.350291 | − | 0.860560i | ||||
\(599\) | −26.8502 | −1.09707 | −0.548535 | − | 0.836128i | \(-0.684814\pi\) | ||||
−0.548535 | + | 0.836128i | \(0.684814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.9566 | −1.75224 | −0.876119 | − | 0.482095i | \(-0.839876\pi\) | ||||
−0.876119 | + | 0.482095i | \(0.839876\pi\) | |||||||
\(602\) | 0.509217 | + | 1.25099i | 0.0207541 | + | 0.0509866i | ||||
\(603\) | −0.116555 | + | 20.8156i | −0.00474649 | + | 0.847677i | ||||
\(604\) | 18.7950 | − | 18.3397i | 0.764756 | − | 0.746232i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.215313 | + | 24.1128i | −0.00874650 | + | 0.979517i | ||||
\(607\) | −32.0417 | + | 32.0417i | −1.30053 | + | 1.30053i | −0.372498 | + | 0.928033i | \(0.621499\pi\) |
−0.928033 | + | 0.372498i | \(0.878501\pi\) | |||||||
\(608\) | −12.6813 | − | 33.4822i | −0.514294 | − | 1.35788i | ||||
\(609\) | −1.81051 | + | 0.744004i | −0.0733654 | + | 0.0301486i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.8691 | 1.97703 | ||||||||
\(612\) | 5.18549 | + | 5.37408i | 0.209611 | + | 0.217234i | ||||
\(613\) | −20.1419 | + | 20.1419i | −0.813522 | + | 0.813522i | −0.985160 | − | 0.171638i | \(-0.945094\pi\) |
0.171638 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(614\) | 16.9527 | + | 7.14408i | 0.684154 | + | 0.288311i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.14170 | + | 7.99760i | 0.126583 | + | 0.322232i | ||||
\(617\) | −7.33463 | − | 7.33463i | −0.295281 | − | 0.295281i | 0.543881 | − | 0.839162i | \(-0.316954\pi\) |
−0.839162 | + | 0.543881i | \(0.816954\pi\) | |||||||
\(618\) | −20.4645 | + | 20.1022i | −0.823202 | + | 0.808631i | ||||
\(619\) | −11.9287 | −0.479456 | −0.239728 | − | 0.970840i | \(-0.577058\pi\) | ||||
−0.239728 | + | 0.970840i | \(0.577058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.92821 | + | 13.9787i | −0.237891 | + | 0.560947i | ||||
\(622\) | −16.2987 | − | 40.0410i | −0.653519 | − | 1.60550i | ||||
\(623\) | 8.94914 | − | 8.94914i | 0.358540 | − | 0.358540i | ||||
\(624\) | 35.5771 | − | 13.6104i | 1.42422 | − | 0.544850i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.3385 | − | 12.7850i | −1.21257 | − | 0.510993i | ||||
\(627\) | 15.5681 | − | 37.2890i | 0.621729 | − | 1.48918i | ||||
\(628\) | −18.0139 | − | 0.220843i | −0.718834 | − | 0.00881260i | ||||
\(629\) | 4.29751i | 0.171353i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.13985 | 0.284233 | 0.142116 | − | 0.989850i | \(-0.454609\pi\) | ||||
0.142116 | + | 0.989850i | \(0.454609\pi\) | |||||||
\(632\) | 2.85410 | + | 1.24417i | 0.113530 | + | 0.0494905i | ||||
\(633\) | −0.944728 | − | 0.394421i | −0.0375496 | − | 0.0156768i | ||||
\(634\) | −0.000478978 | 0.00113660i | −1.90227e−5 | 4.51402e-5i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.8943 | − | 25.2202i | 0.431988 | − | 1.00005i | ||||
\(637\) | −24.5733 | − | 24.5733i | −0.973628 | − | 0.973628i | ||||
\(638\) | 2.69490 | + | 6.62057i | 0.106692 | + | 0.262111i | ||||
\(639\) | −8.81533 | + | 8.71716i | −0.348729 | + | 0.344846i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 30.0187i | − | 1.18567i | −0.805325 | − | 0.592834i | \(-0.798009\pi\) | ||
0.805325 | − | 0.592834i | \(-0.201991\pi\) | |||||||
\(642\) | 14.1932 | + | 14.4489i | 0.560160 | + | 0.570254i | ||||
\(643\) | 32.7048 | − | 32.7048i | 1.28975 | − | 1.28975i | 0.354812 | − | 0.934938i | \(-0.384545\pi\) |
0.934938 | − | 0.354812i | \(-0.115455\pi\) | |||||||
\(644\) | 3.36386 | + | 3.44736i | 0.132555 | + | 0.135845i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.2663 | − | 4.32637i | −0.403923 | − | 0.170219i | ||||
\(647\) | 2.53026 | + | 2.53026i | 0.0994747 | + | 0.0994747i | 0.755093 | − | 0.655618i | \(-0.227592\pi\) |
−0.655618 | + | 0.755093i | \(0.727592\pi\) | |||||||
\(648\) | −23.2197 | − | 10.4330i | −0.912154 | − | 0.409847i | ||||
\(649\) | 22.5597i | 0.885545i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80179 | + | 4.38458i | 0.0706176 | + | 0.171845i | ||||
\(652\) | −0.119972 | + | 9.78598i | −0.00469847 | + | 0.383248i | ||||
\(653\) | −23.8061 | − | 23.8061i | −0.931604 | − | 0.931604i | 0.0662023 | − | 0.997806i | \(-0.478912\pi\) |
−0.997806 | + | 0.0662023i | \(0.978912\pi\) | |||||||
\(654\) | 0.255970 | − | 28.6660i | 0.0100092 | − | 1.12093i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.59164 | − | 0.0635543i | −0.101186 | − | 0.00248138i | ||||
\(657\) | −0.111610 | + | 19.9325i | −0.00435432 | + | 0.777640i | ||||
\(658\) | −9.59539 | + | 3.90581i | −0.374067 | + | 0.152264i | ||||
\(659\) | − | 15.7130i | − | 0.612093i | −0.952017 | − | 0.306047i | \(-0.900994\pi\) | ||
0.952017 | − | 0.306047i | \(-0.0990063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 25.2637i | − | 0.982643i | −0.870978 | − | 0.491322i | \(-0.836514\pi\) | ||
0.870978 | − | 0.491322i | \(-0.163486\pi\) | |||||||
\(662\) | 4.41798 | + | 10.8536i | 0.171710 | + | 0.421839i | ||||
\(663\) | 4.56649 | − | 10.9378i | 0.177348 | − | 0.424788i | ||||
\(664\) | 23.3598 | − | 9.17644i | 0.906536 | − | 0.356115i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.44675 | − | 13.5986i | −0.211057 | − | 0.526935i | ||||
\(667\) | 2.83330 | + | 2.83330i | 0.109706 | + | 0.109706i | ||||
\(668\) | −2.69854 | − | 0.0330830i | −0.104410 | − | 0.00128002i | ||||
\(669\) | −38.1937 | + | 15.6952i | −1.47665 | + | 0.606812i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.9269i | − | 0.730664i | ||||||
\(672\) | −5.89773 | + | 5.51584i | −0.227510 | + | 0.212778i | ||||
\(673\) | 15.4486 | + | 15.4486i | 0.595498 | + | 0.595498i | 0.939111 | − | 0.343613i | \(-0.111651\pi\) |
−0.343613 | + | 0.939111i | \(0.611651\pi\) | |||||||
\(674\) | 1.76824 | − | 4.19597i | 0.0681099 | − | 0.161623i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.0644 | − | 24.6618i | −0.925554 | − | 0.948529i | ||||
\(677\) | −3.86002 | + | 3.86002i | −0.148353 | + | 0.148353i | −0.777382 | − | 0.629029i | \(-0.783453\pi\) |
0.629029 | + | 0.777382i | \(0.283453\pi\) | |||||||
\(678\) | −20.8362 | − | 21.2117i | −0.800210 | − | 0.814630i | ||||
\(679\) | 6.31904i | 0.242503i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.73505 | + | 16.3895i | 0.258088 | + | 0.628046i | ||||
\(682\) | 16.0333 | − | 6.52637i | 0.613947 | − | 0.249908i | ||||
\(683\) | 20.9584 | + | 20.9584i | 0.801949 | + | 0.801949i | 0.983400 | − | 0.181451i | \(-0.0580793\pi\) |
−0.181451 | + | 0.983400i | \(0.558079\pi\) | |||||||
\(684\) | 37.9691 | + | 0.678136i | 1.45178 | + | 0.0259292i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.3074 | + | 6.02932i | 0.546259 | + | 0.230201i | ||||
\(687\) | 15.3534 | − | 36.7749i | 0.585770 | − | 1.40305i | ||||
\(688\) | 3.19631 | + | 3.35702i | 0.121858 | + | 0.127985i | ||||
\(689\) | −43.6032 | −1.66115 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8902i | 1.02295i | 0.859298 | + | 0.511475i | \(0.170901\pi\) | ||||
−0.859298 | + | 0.511475i | \(0.829099\pi\) | |||||||
\(692\) | −5.09759 | − | 0.0624943i | −0.193781 | − | 0.00237568i | ||||
\(693\) | −9.11363 | − | 0.0510309i | −0.346198 | − | 0.00193850i | ||||
\(694\) | −14.4761 | + | 34.3513i | −0.549504 | + | 1.30396i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.84963 | + | 4.64836i | −0.183825 | + | 0.176196i | ||||
\(697\) | −0.570399 | + | 0.570399i | −0.0216054 | + | 0.0216054i | ||||
\(698\) | 23.2194 | − | 9.45148i | 0.878869 | − | 0.357744i | ||||
\(699\) | −4.14389 | − | 10.0840i | −0.156736 | − | 0.381412i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.7956 | −1.35198 | −0.675990 | − | 0.736911i | \(-0.736284\pi\) | ||||
−0.675990 | + | 0.736911i | \(0.736284\pi\) | |||||||
\(702\) | −0.586964 | + | 40.3980i | −0.0221535 | + | 1.52472i | ||||
\(703\) | 15.4525 | + | 15.4525i | 0.582804 | + | 0.582804i | ||||
\(704\) | 20.0708 | + | 21.6041i | 0.756445 | + | 0.814236i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.21566 | + | 19.4955i | −0.309200 | + | 0.733723i | ||||
\(707\) | −5.73705 | + | 5.73705i | −0.215764 | + | 0.215764i | ||||
\(708\) | −19.7073 | + | 7.81748i | −0.740646 | + | 0.293799i | ||||
\(709\) | 31.6856 | 1.18998 | 0.594988 | − | 0.803735i | \(-0.297157\pi\) | ||||
0.594988 | + | 0.803735i | \(0.297157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34816 | + | 2.32201i | −0.0880628 | + | 0.0870821i | ||||
\(712\) | 17.3564 | − | 39.8152i | 0.650459 | − | 1.49214i | ||||
\(713\) | 6.86153 | − | 6.86153i | 0.256966 | − | 0.256966i | ||||
\(714\) | −0.0224359 | + | 2.51259i | −0.000839642 | + | 0.0940312i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.5456 | − | 34.3784i | −1.25366 | − | 1.28478i | ||||
\(717\) | 2.69238 | − | 6.44887i | 0.100549 | − | 0.240837i | ||||
\(718\) | 32.3883 | − | 13.1837i | 1.20872 | − | 0.492010i | ||||
\(719\) | −47.9558 | −1.78845 | −0.894225 | − | 0.447618i | \(-0.852272\pi\) | ||||
−0.894225 | + | 0.447618i | \(0.852272\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.65184 | −0.359453 | ||||||||
\(722\) | −27.5837 | + | 11.2280i | −1.02656 | + | 0.417861i | ||||
\(723\) | −7.64809 | + | 18.3189i | −0.284435 | + | 0.681287i | ||||
\(724\) | −30.3392 | − | 31.0923i | −1.12755 | − | 1.15554i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.0565836 | + | 6.33678i | −0.00210002 | + | 0.235180i | ||||
\(727\) | −20.8052 | + | 20.8052i | −0.771622 | + | 0.771622i | −0.978390 | − | 0.206768i | \(-0.933705\pi\) |
0.206768 | + | 0.978390i | \(0.433705\pi\) | |||||||
\(728\) | 11.7487 | + | 5.12153i | 0.435435 | + | 0.189817i | ||||
\(729\) | 19.4099 | − | 18.7685i | 0.718884 | − | 0.695130i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.44234 | 0.0533468 | ||||||||
\(732\) | 16.5338 | − | 6.55862i | 0.611108 | − | 0.242414i | ||||
\(733\) | 11.3990 | − | 11.3990i | 0.421033 | − | 0.421033i | −0.464526 | − | 0.885559i | \(-0.653775\pi\) |
0.885559 | + | 0.464526i | \(0.153775\pi\) | |||||||
\(734\) | 7.25237 | − | 17.2096i | 0.267690 | − | 0.635219i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.0708 | + | 6.79077i | 0.555516 | + | 0.250311i | ||||
\(737\) | 18.0852 | + | 18.0852i | 0.666176 | + | 0.666176i | ||||
\(738\) | 1.08198 | − | 2.52785i | 0.0398281 | − | 0.0930514i | ||||
\(739\) | −9.60683 | −0.353393 | −0.176697 | − | 0.984265i | \(-0.556541\pi\) | ||||
−0.176697 | + | 0.984265i | \(0.556541\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −22.9092 | − | 55.7487i | −0.841591 | − | 2.04798i | ||||
\(742\) | 8.56143 | − | 3.48493i | 0.314300 | − | 0.127936i | ||||
\(743\) | −2.71436 | + | 2.71436i | −0.0995802 | + | 0.0995802i | −0.755142 | − | 0.655562i | \(-0.772432\pi\) |
0.655562 | + | 0.755142i | \(0.272432\pi\) | |||||||
\(744\) | 11.2571 | + | 11.7446i | 0.412706 | + | 0.430577i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.24445 | + | 21.9368i | −0.338463 | + | 0.803163i | ||||
\(747\) | −0.149054 | + | 26.6196i | −0.00545359 | + | 0.973958i | ||||
\(748\) | 9.17508 | + | 0.112483i | 0.335474 | + | 0.00411277i | ||||
\(749\) | 6.81468i | 0.249003i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9690 | −0.692189 | −0.346094 | − | 0.938200i | \(-0.612492\pi\) | ||||
−0.346094 | + | 0.938200i | \(0.612492\pi\) | |||||||
\(752\) | −25.7491 | + | 24.5164i | −0.938972 | + | 0.894022i | ||||
\(753\) | −11.6648 | + | 27.9397i | −0.425087 | + | 1.01818i | ||||
\(754\) | 9.82507 | + | 4.14041i | 0.357808 | + | 0.150785i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.11352 | − | 7.97901i | −0.113237 | − | 0.290194i | ||||
\(757\) | 0.279592 | + | 0.279592i | 0.0101620 | + | 0.0101620i | 0.712170 | − | 0.702008i | \(-0.247713\pi\) |
−0.702008 | + | 0.712170i | \(0.747713\pi\) | |||||||
\(758\) | 3.58037 | − | 1.45739i | 0.130045 | − | 0.0529349i | ||||
\(759\) | 7.09113 | + | 17.2560i | 0.257392 | + | 0.626353i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 20.3237i | − | 0.736733i | −0.929681 | − | 0.368366i | \(-0.879917\pi\) | ||
0.929681 | − | 0.368366i | \(-0.120083\pi\) | |||||||
\(762\) | 0.0355534 | + | 0.0361941i | 0.00128797 | + | 0.00131117i | ||||
\(763\) | 6.82036 | − | 6.82036i | 0.246914 | − | 0.246914i | ||||
\(764\) | −18.1355 | − | 18.5857i | −0.656118 | − | 0.672406i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.6746 | − | 32.4494i | 0.494083 | − | 1.17244i | ||||
\(767\) | 23.7938 | + | 23.7938i | 0.859144 | + | 0.859144i | ||||
\(768\) | −11.9176 | + | 25.0194i | −0.430038 | + | 0.902811i | ||||
\(769\) | 25.1716i | 0.907711i | 0.891075 | + | 0.453855i | \(0.149952\pi\) | ||||
−0.891075 | + | 0.453855i | \(0.850048\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.3448 | + | 6.30577i | −0.552631 | + | 0.227097i | ||||
\(772\) | −26.8293 | − | 0.328916i | −0.965607 | − | 0.0118379i | ||||
\(773\) | −24.0474 | − | 24.0474i | −0.864925 | − | 0.864925i | 0.126980 | − | 0.991905i | \(-0.459472\pi\) |
−0.991905 | + | 0.126980i | \(0.959472\pi\) | |||||||
\(774\) | −4.56398 | + | 1.82805i | −0.164049 | + | 0.0657079i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.92913 | + | 20.1846i | 0.284639 | + | 0.724585i | ||||
\(777\) | 1.89891 | − | 4.54832i | 0.0681231 | − | 0.163170i | ||||
\(778\) | −13.4006 | − | 32.9213i | −0.480436 | − | 1.18029i | ||||
\(779\) | 4.10197i | 0.146968i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2327i | 0.545070i | ||||||||
\(782\) | 4.76400 | − | 1.93919i | 0.170360 | − | 0.0693453i | ||||
\(783\) | −2.67127 | − | 6.60539i | −0.0954634 | − | 0.236058i | ||||
\(784\) | 25.2754 | + | 0.619825i | 0.902693 | + | 0.0221366i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.114605 | + | 12.8345i | −0.00408782 | + | 0.457793i | ||||
\(787\) | 6.79695 | + | 6.79695i | 0.242285 | + | 0.242285i | 0.817795 | − | 0.575510i | \(-0.195196\pi\) |
−0.575510 | + | 0.817795i | \(0.695196\pi\) | |||||||
\(788\) | −0.445912 | + | 36.3725i | −0.0158850 | + | 1.29572i | ||||
\(789\) | 14.3108 | + | 34.8249i | 0.509479 | + | 1.23980i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.0043i | − | 0.355710i | ||||||
\(792\) | −29.1752 | + | 11.2728i | −1.03670 | + | 0.400560i | ||||
\(793\) | −19.9623 | − | 19.9623i | −0.708881 | − | 0.708881i | ||||
\(794\) | 10.0015 | + | 4.21476i | 0.354939 | + | 0.149576i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.0647578 | + | 0.0663654i | 0.00229528 | + | 0.00235226i | ||||
\(797\) | −6.72322 | + | 6.72322i | −0.238149 | + | 0.238149i | −0.816083 | − | 0.577935i | \(-0.803859\pi\) |
0.577935 | + | 0.816083i | \(0.303859\pi\) | |||||||
\(798\) | 8.95384 | + | 9.11519i | 0.316963 | + | 0.322674i | ||||
\(799\) | 11.0630i | 0.391382i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.3924 | + | 32.7572i | 1.14453 | + | 1.15742i | ||||
\(802\) | −2.75030 | − | 6.75665i | −0.0971164 | − | 0.238585i | ||||
\(803\) | 17.3179 | + | 17.3179i | 0.611135 | + | 0.611135i | ||||
\(804\) | −9.53159 | + | 22.0655i | −0.336153 | + | 0.778190i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0270 | − | 23.7938i | 0.353187 | − | 0.838101i | ||||
\(807\) | 15.3259 | + | 6.39851i | 0.539496 | + | 0.225238i | ||||
\(808\) | −11.1267 | + | 25.5244i | −0.391437 | + | 0.897946i | ||||
\(809\) | 35.3381 | 1.24242 | 0.621212 | − | 0.783643i | \(-0.286641\pi\) | ||||
0.621212 | + | 0.783643i | \(0.286641\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.1596i | 1.30485i | 0.757854 | + | 0.652425i | \(0.226248\pi\) | ||||
−0.757854 | + | 0.652425i | \(0.773752\pi\) | |||||||
\(812\) | −2.26006 | − | 0.0277074i | −0.0793125 | − | 0.000972338i | ||||
\(813\) | −13.9519 | + | 33.4179i | −0.489314 | + | 1.17202i | ||||
\(814\) | −16.5863 | − | 6.98967i | −0.581348 | − | 0.244988i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.08113 | + | 8.05399i | 0.107861 | + | 0.281946i | ||||
\(817\) | 5.18621 | − | 5.18621i | 0.181443 | − | 0.181443i | ||||
\(818\) | −7.55184 | − | 18.5526i | −0.264044 | − | 0.648676i | ||||
\(819\) | −9.66601 | + | 9.55836i | −0.337758 | + | 0.333996i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.5674 | 0.997010 | 0.498505 | − | 0.866887i | \(-0.333882\pi\) | ||||
0.498505 | + | 0.866887i | \(0.333882\pi\) | |||||||
\(822\) | −34.8408 | + | 34.2241i | −1.21521 | + | 1.19370i | ||||
\(823\) | 28.5682 | + | 28.5682i | 0.995823 | + | 0.995823i | 0.999991 | − | 0.00416817i | \(-0.00132677\pi\) |
−0.00416817 | + | 0.999991i | \(0.501327\pi\) | |||||||
\(824\) | −30.8304 | + | 12.1111i | −1.07403 | + | 0.421911i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.57357 | − | 2.77019i | −0.228724 | − | 0.0963872i | ||||
\(827\) | 5.31276 | − | 5.31276i | 0.184743 | − | 0.184743i | −0.608676 | − | 0.793419i | \(-0.708299\pi\) |
0.793419 | + | 0.608676i | \(0.208299\pi\) | |||||||
\(828\) | −12.6170 | + | 12.1742i | −0.438469 | + | 0.423082i | ||||
\(829\) | −4.51176 | −0.156700 | −0.0783500 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783500 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.0813 | − | 8.25214i | 0.696611 | − | 0.286263i | ||||
\(832\) | 43.9547 | + | 1.61725i | 1.52385 | + | 0.0560679i | ||||
\(833\) | 5.56292 | − | 5.56292i | 0.192744 | − | 0.192744i | ||||
\(834\) | −0.201692 | + | 22.5875i | −0.00698403 | + | 0.782140i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 33.3953 | − | 32.5864i | 1.15500 | − | 1.12702i | ||||
\(837\) | −15.9966 | + | 6.46913i | −0.552922 | + | 0.223606i | ||||
\(838\) | −2.56199 | − | 6.29404i | −0.0885025 | − | 0.217424i | ||||
\(839\) | 42.7255 | 1.47505 | 0.737523 | − | 0.675322i | \(-0.235995\pi\) | ||||
0.737523 | + | 0.675322i | \(0.235995\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.1197 | 0.935164 | ||||||||
\(842\) | −8.11428 | − | 19.9343i | −0.279637 | − | 0.686983i | ||||
\(843\) | −19.4877 | − | 8.13608i | −0.671193 | − | 0.280221i | ||||
\(844\) | −0.825584 | − | 0.846078i | −0.0284178 | − | 0.0291232i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.0215 | − | 35.0068i | −0.482071 | − | 1.20356i | ||||
\(847\) | −1.50768 | + | 1.50768i | −0.0518045 | + | 0.0518045i | ||||
\(848\) | 22.9745 | − | 21.8746i | 0.788946 | − | 0.751178i | ||||
\(849\) | −10.8744 | − | 26.4625i | −0.373210 | − | 0.908192i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0894 | −0.345861 | ||||||||
\(852\) | −13.3067 | + | 5.27851i | −0.455881 | + | 0.180839i | ||||
\(853\) | 28.1027 | − | 28.1027i | 0.962217 | − | 0.962217i | −0.0370946 | − | 0.999312i | \(-0.511810\pi\) |
0.999312 | + | 0.0370946i | \(0.0118103\pi\) | |||||||
\(854\) | 5.51503 | + | 2.32410i | 0.188720 | + | 0.0795292i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.55106 | + | 21.7678i | 0.292269 | + | 0.744008i | ||||
\(857\) | −35.8406 | − | 35.8406i | −1.22429 | − | 1.22429i | −0.966092 | − | 0.258198i | \(-0.916871\pi\) |
−0.258198 | − | 0.966092i | \(-0.583129\pi\) | |||||||
\(858\) | 34.7872 | + | 35.4141i | 1.18762 | + | 1.20902i | ||||
\(859\) | −1.55128 | −0.0529289 | −0.0264645 | − | 0.999650i | \(-0.508425\pi\) | ||||
−0.0264645 | + | 0.999650i | \(0.508425\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.855728 | − | 0.351651i | 0.0291631 | − | 0.0119842i | ||||
\(862\) | −14.8629 | − | 36.5136i | −0.506231 | − | 1.24366i | ||||
\(863\) | −22.7893 | + | 22.7893i | −0.775758 | + | 0.775758i | −0.979107 | − | 0.203348i | \(-0.934818\pi\) |
0.203348 | + | 0.979107i | \(0.434818\pi\) | |||||||
\(864\) | −19.9574 | − | 21.5801i | −0.678965 | − | 0.734171i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.12369 | − | 2.15919i | −0.174110 | − | 0.0733723i | ||||
\(867\) | −24.6957 | − | 10.3104i | −0.838712 | − | 0.350160i | ||||
\(868\) | −0.0671001 | + | 5.47328i | −0.00227753 | + | 0.185775i | ||||
\(869\) | 4.05757i | 0.137644i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.1490 | 1.29263 | ||||||||
\(872\) | 13.2278 | − | 30.3441i | 0.447948 | − | 1.02758i | ||||
\(873\) | −23.0013 | − | 0.128793i | −0.778476 | − | 0.00435900i | ||||
\(874\) | 10.1572 | − | 24.1027i | 0.343572 | − | 0.815285i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.12720 | + | 21.1293i | −0.308379 | + | 0.713894i | ||||
\(877\) | −22.8089 | − | 22.8089i | −0.770202 | − | 0.770202i | 0.207940 | − | 0.978142i | \(-0.433324\pi\) |
−0.978142 | + | 0.207940i | \(0.933324\pi\) | |||||||
\(878\) | −5.76759 | − | 14.1692i | −0.194647 | − | 0.478188i | ||||
\(879\) | 11.7005 | − | 4.80819i | 0.394649 | − | 0.162176i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.47551i | − | 0.0497114i | −0.999691 | − | 0.0248557i | \(-0.992087\pi\) | ||
0.999691 | − | 0.0248557i | \(-0.00791262\pi\) | |||||||
\(882\) | −10.5522 | + | 24.6533i | −0.355310 | + | 0.830121i | ||||
\(883\) | 3.02812 | − | 3.02812i | 0.101904 | − | 0.101904i | −0.654316 | − | 0.756221i | \(-0.727044\pi\) |
0.756221 | + | 0.654316i | \(0.227044\pi\) | |||||||
\(884\) | 9.79563 | − | 9.55836i | 0.329463 | − | 0.321482i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5968 | + | 4.46561i | 0.356005 | + | 0.150025i | ||||
\(887\) | −19.9170 | − | 19.9170i | −0.668749 | − | 0.668749i | 0.288678 | − | 0.957426i | \(-0.406784\pi\) |
−0.957426 | + | 0.288678i | \(0.906784\pi\) | |||||||
\(888\) | 0.358371 | − | 16.9112i | 0.0120261 | − | 0.567504i | ||||
\(889\) | 0.0170705i | 0.000572528i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.371504 | − | 33.1725i | 0.0124459 | − | 1.11132i | ||||
\(892\) | −47.6773 | − | 0.584504i | −1.59635 | − | 0.0195706i | ||||
\(893\) | 39.7794 | + | 39.7794i | 1.33117 | + | 1.33117i | ||||
\(894\) | −34.3048 | − | 0.306321i | −1.14733 | − | 0.0102449i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.75970 | + | 3.19548i | −0.292641 | + | 0.106754i | ||||
\(897\) | 25.6790 | + | 10.7209i | 0.857398 | + | 0.357961i | ||||
\(898\) | −9.05349 | + | 3.68523i | −0.302119 | + | 0.122978i | ||||
\(899\) | 4.55350i | 0.151868i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.87094i | − | 0.328849i | ||||||
\(902\) | −1.27374 | − | 3.12918i | −0.0424108 | − | 0.104190i | ||||
\(903\) | −1.52652 | − | 0.637317i | −0.0507993 | − | 0.0212086i | ||||
\(904\) | −12.5533 | − | 31.9561i | −0.417518 | − | 1.06284i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.287176 | + | 32.1607i | −0.00954077 | + | 1.06847i | ||||
\(907\) | −6.11318 | − | 6.11318i | −0.202985 | − | 0.202985i | 0.598293 | − | 0.801278i | \(-0.295846\pi\) |
−0.801278 | + | 0.598293i | \(0.795846\pi\) | |||||||
\(908\) | −0.250819 | + | 20.4590i | −0.00832372 | + | 0.678956i | ||||
\(909\) | −20.7659 | − | 20.9998i | −0.688762 | − | 0.696518i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.1492i | 0.932625i | 0.884620 | + | 0.466313i | \(0.154418\pi\) | ||||
−0.884620 | + | 0.466313i | \(0.845582\pi\) | |||||||
\(912\) | 40.0385 | + | 17.8809i | 1.32581 | + | 0.592096i | ||||
\(913\) | 23.1278 | + | 23.1278i | 0.765419 | + | 0.765419i | ||||
\(914\) | −4.00570 | + | 9.50541i | −0.132497 | + | 0.314411i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32.9349 | − | 32.1371i | 1.08820 | − | 1.06184i | ||||
\(917\) | −3.05366 | + | 3.05366i | −0.100841 | + | 0.100841i | ||||
\(918\) | −9.14535 | − | 0.132878i | −0.301842 | − | 0.00438561i | ||||
\(919\) | − | 49.4285i | − | 1.63049i | −0.579113 | − | 0.815247i | \(-0.696601\pi\) | ||
0.579113 | − | 0.815247i | \(-0.303399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.8400 | + | 8.56393i | −0.686701 | + | 0.282191i | ||||
\(922\) | −24.1740 | + | 9.84005i | −0.796129 | + | 0.324065i | ||||
\(923\) | 16.0660 | + | 16.0660i | 0.528819 | + | 0.528819i | ||||
\(924\) | −9.66086 | − | 4.17318i | −0.317819 | − | 0.137288i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −36.2892 | − | 15.2927i | −1.19254 | − | 0.502550i | ||||
\(927\) | 0.196722 | − | 35.1327i | 0.00646120 | − | 1.15391i | ||||
\(928\) | −7.25396 | + | 2.74741i | −0.238123 | + | 0.0901883i | ||||
\(929\) | −38.9204 | −1.27694 | −0.638468 | − | 0.769649i | \(-0.720431\pi\) | ||||
−0.638468 | + | 0.769649i | \(0.720431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 40.0052i | − | 1.31112i | ||||||
\(932\) | 0.154322 | − | 12.5879i | 0.00505499 | − | 0.412329i | ||||
\(933\) | 48.8598 | + | 20.3988i | 1.59960 | + | 0.667828i | ||||
\(934\) | 1.61507 | − | 3.83251i | 0.0528466 | − | 0.125403i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.8818 | + | 42.6607i | −0.617172 | + | 1.39441i | ||||
\(937\) | 4.49303 | − | 4.49303i | 0.146781 | − | 0.146781i | −0.629897 | − | 0.776678i | \(-0.716903\pi\) |
0.776678 | + | 0.629897i | \(0.216903\pi\) | |||||||
\(938\) | −7.49052 | + | 3.04902i | −0.244574 | + | 0.0995540i | ||||
\(939\) | 37.2952 | − | 15.3260i | 1.21708 | − | 0.500145i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2736 | −0.758696 | −0.379348 | − | 0.925254i | \(-0.623852\pi\) | ||||
−0.379348 | + | 0.925254i | \(0.623852\pi\) | |||||||
\(942\) | 15.7404 | − | 15.4618i | 0.512849 | − | 0.503771i | ||||
\(943\) | −1.33915 | − | 1.33915i | −0.0436087 | − | 0.0436087i | ||||
\(944\) | −24.4737 | − | 0.600164i | −0.796550 | − | 0.0195337i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.34589 | + | 5.56671i | −0.0762713 | + | 0.180989i | ||||
\(947\) | −28.1797 | + | 28.1797i | −0.915717 | + | 0.915717i | −0.996714 | − | 0.0809978i | \(-0.974189\pi\) |
0.0809978 | + | 0.996714i | \(0.474189\pi\) | |||||||
\(948\) | −3.54454 | + | 1.40605i | −0.115121 | + | 0.0456663i | ||||
\(949\) | 36.5305 | 1.18583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.000574173 | − | 0.00139723i | −1.86188e−5 | − | 4.53082e-5i | ||||
\(952\) | −1.15942 | + | 2.65968i | −0.0375770 | + | 0.0862006i | ||||
\(953\) | −28.5653 | + | 28.5653i | −0.925321 | + | 0.925321i | −0.997399 | − | 0.0720776i | \(-0.977037\pi\) |
0.0720776 | + | 0.997399i | \(0.477037\pi\) | |||||||
\(954\) | 12.5106 | + | 31.2346i | 0.405047 | + | 1.01126i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.77547 | − | 5.63557i | 0.186792 | − | 0.182267i | ||||
\(957\) | −8.07871 | − | 3.37284i | −0.261148 | − | 0.109028i | ||||
\(958\) | −25.8157 | + | 10.5083i | −0.834066 | + | 0.339507i | ||||
\(959\) | −16.4323 | −0.530625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.9726 | −0.644277 | ||||||||
\(962\) | −24.8656 | + | 10.1216i | −0.801700 | + | 0.326332i | ||||
\(963\) | −24.8054 | − | 0.138895i | −0.799343 | − | 0.00447584i | ||||
\(964\) | −16.4060 | + | 16.0086i | −0.528402 | + | 0.515603i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.89890 | − | 0.0526736i | −0.189794 | − | 0.00169475i | ||||
\(967\) | 37.0606 | − | 37.0606i | 1.19179 | − | 1.19179i | 0.215225 | − | 0.976565i | \(-0.430952\pi\) |
0.976565 | − | 0.215225i | \(-0.0690484\pi\) | |||||||
\(968\) | −2.92407 | + | 6.70774i | −0.0939832 | + | 0.215595i | ||||
\(969\) | 12.6204 | − | 5.18621i | 0.405427 | − | 0.166605i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.8114 | 0.379044 | 0.189522 | − | 0.981876i | \(-0.439306\pi\) | ||||
0.189522 | + | 0.981876i | \(0.439306\pi\) | |||||||
\(972\) | 29.1070 | − | 11.1706i | 0.933608 | − | 0.358296i | ||||
\(973\) | −5.37412 | + | 5.37412i | −0.172287 | + | 0.172287i | ||||
\(974\) | 3.27288 | − | 7.76644i | 0.104870 | − | 0.248853i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.5327 | + | 0.503519i | 0.657234 | + | 0.0161173i | ||||
\(977\) | 5.34002 | + | 5.34002i | 0.170842 | + | 0.170842i | 0.787349 | − | 0.616507i | \(-0.211453\pi\) |
−0.616507 | + | 0.787349i | \(0.711453\pi\) | |||||||
\(978\) | −8.39953 | − | 8.55088i | −0.268587 | − | 0.273427i | ||||
\(979\) | 56.6038 | 1.80907 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.6871 | + | 24.9651i | 0.788197 | + | 0.797074i | ||||
\(982\) | 36.3111 | − | 14.7805i | 1.15874 | − | 0.471664i | ||||
\(983\) | 42.6490 | − | 42.6490i | 1.36029 | − | 1.36029i | 0.486753 | − | 0.873540i | \(-0.338181\pi\) |
0.873540 | − | 0.486753i | \(-0.161819\pi\) | |||||||
\(984\) | 2.29216 | − | 2.19703i | 0.0730714 | − | 0.0700387i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.937311 | + | 2.22421i | −0.0298501 | + | 0.0708333i | ||||
\(987\) | 4.88836 | − | 11.7087i | 0.155598 | − | 0.372693i | ||||
\(988\) | 0.853159 | − | 69.5912i | 0.0271426 | − | 2.21399i | ||||
\(989\) | 3.38623i | 0.107676i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.5197 | −1.00126 | −0.500629 | − | 0.865662i | \(-0.666898\pi\) | ||||
−0.500629 | + | 0.865662i | \(0.666898\pi\) | |||||||
\(992\) | 6.65353 | + | 17.5672i | 0.211250 | + | 0.557760i | ||||
\(993\) | −13.2441 | − | 5.52938i | −0.420289 | − | 0.175469i | ||||
\(994\) | −4.43860 | − | 1.87048i | −0.140784 | − | 0.0593282i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.1892 | + | 28.2179i | −0.386231 | + | 0.894120i | ||||
\(997\) | 38.3474 | + | 38.3474i | 1.21447 | + | 1.21447i | 0.969540 | + | 0.244935i | \(0.0787666\pi\) |
0.244935 | + | 0.969540i | \(0.421233\pi\) | |||||||
\(998\) | 6.74190 | − | 2.74429i | 0.213411 | − | 0.0868690i | ||||
\(999\) | 16.5172 | + | 7.00473i | 0.522580 | + | 0.221620i |
(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 | 600.2.w.j.293.3 | 32 | ||
3.2 | odd | 2 | inner | 600.2.w.j.293.14 | 32 | ||
5.2 | odd | 4 | inner | 600.2.w.j.557.6 | 32 | ||
5.3 | odd | 4 | 120.2.w.c.77.11 | yes | 32 | ||
5.4 | even | 2 | 120.2.w.c.53.14 | yes | 32 | ||
8.5 | even | 2 | inner | 600.2.w.j.293.11 | 32 | ||
15.2 | even | 4 | inner | 600.2.w.j.557.11 | 32 | ||
15.8 | even | 4 | 120.2.w.c.77.6 | yes | 32 | ||
15.14 | odd | 2 | 120.2.w.c.53.3 | ✓ | 32 | ||
20.3 | even | 4 | 480.2.bi.c.17.3 | 32 | |||
20.19 | odd | 2 | 480.2.bi.c.113.11 | 32 | |||
24.5 | odd | 2 | inner | 600.2.w.j.293.6 | 32 | ||
40.3 | even | 4 | 480.2.bi.c.17.14 | 32 | |||
40.13 | odd | 4 | 120.2.w.c.77.3 | yes | 32 | ||
40.19 | odd | 2 | 480.2.bi.c.113.6 | 32 | |||
40.29 | even | 2 | 120.2.w.c.53.6 | yes | 32 | ||
40.37 | odd | 4 | inner | 600.2.w.j.557.14 | 32 | ||
60.23 | odd | 4 | 480.2.bi.c.17.6 | 32 | |||
60.59 | even | 2 | 480.2.bi.c.113.14 | 32 | |||
120.29 | odd | 2 | 120.2.w.c.53.11 | yes | 32 | ||
120.53 | even | 4 | 120.2.w.c.77.14 | yes | 32 | ||
120.59 | even | 2 | 480.2.bi.c.113.3 | 32 | |||
120.77 | even | 4 | inner | 600.2.w.j.557.3 | 32 | ||
120.83 | odd | 4 | 480.2.bi.c.17.11 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.w.c.53.3 | ✓ | 32 | 15.14 | odd | 2 | ||
120.2.w.c.53.6 | yes | 32 | 40.29 | even | 2 | ||
120.2.w.c.53.11 | yes | 32 | 120.29 | odd | 2 | ||
120.2.w.c.53.14 | yes | 32 | 5.4 | even | 2 | ||
120.2.w.c.77.3 | yes | 32 | 40.13 | odd | 4 | ||
120.2.w.c.77.6 | yes | 32 | 15.8 | even | 4 | ||
120.2.w.c.77.11 | yes | 32 | 5.3 | odd | 4 | ||
120.2.w.c.77.14 | yes | 32 | 120.53 | even | 4 | ||
480.2.bi.c.17.3 | 32 | 20.3 | even | 4 | |||
480.2.bi.c.17.6 | 32 | 60.23 | odd | 4 | |||
480.2.bi.c.17.11 | 32 | 120.83 | odd | 4 | |||
480.2.bi.c.17.14 | 32 | 40.3 | even | 4 | |||
480.2.bi.c.113.3 | 32 | 120.59 | even | 2 | |||
480.2.bi.c.113.6 | 32 | 40.19 | odd | 2 | |||
480.2.bi.c.113.11 | 32 | 20.19 | odd | 2 | |||
480.2.bi.c.113.14 | 32 | 60.59 | even | 2 | |||
600.2.w.j.293.3 | 32 | 1.1 | even | 1 | trivial | ||
600.2.w.j.293.6 | 32 | 24.5 | odd | 2 | inner | ||
600.2.w.j.293.11 | 32 | 8.5 | even | 2 | inner | ||
600.2.w.j.293.14 | 32 | 3.2 | odd | 2 | inner | ||
600.2.w.j.557.3 | 32 | 120.77 | even | 4 | inner | ||
600.2.w.j.557.6 | 32 | 5.2 | odd | 4 | inner | ||
600.2.w.j.557.11 | 32 | 15.2 | even | 4 | inner | ||
600.2.w.j.557.14 | 32 | 40.37 | odd | 4 | inner |