Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1519,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.g (of order \(2\), degree \(1\), 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32x^{14} + 380x^{12} - 1752x^{10} + 1904x^{8} + 7824x^{6} + 7352x^{4} + 2992x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.5 | ||
Root | \(-0.213388 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1519 |
Dual form | 1520.2.g.f.1519.11 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.80775i | − | 1.04370i | −0.853036 | − | 0.521852i | \(-0.825241\pi\) | ||
0.853036 | − | 0.521852i | \(-0.174759\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.73205 | − | 1.41421i | 0.774597 | − | 0.632456i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.12976 | −0.804975 | −0.402488 | − | 0.915425i | \(-0.631854\pi\) | ||||
−0.402488 | + | 0.915425i | \(0.631854\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.267949 | −0.0893164 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.11439i | 1.24054i | 0.784390 | + | 0.620268i | \(0.212976\pi\) | ||||
−0.784390 | + | 0.620268i | \(0.787024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.72241 | −0.755062 | −0.377531 | − | 0.925997i | \(-0.623227\pi\) | ||||
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.55654 | − | 3.13111i | −0.660096 | − | 0.808449i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.79315i | − | 0.434903i | −0.976071 | − | 0.217451i | \(-0.930226\pi\) | ||
0.976071 | − | 0.217451i | \(-0.0697744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.49230 | − | 2.60842i | −0.801188 | − | 0.598412i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.85008i | 0.840155i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.68886 | −0.769181 | −0.384590 | − | 0.923087i | \(-0.625657\pi\) | ||||
−0.384590 | + | 0.923087i | \(0.625657\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 4.89898i | 0.200000 | − | 0.979796i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.93886i | − | 0.950483i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 10.5186i | − | 1.95326i | −0.214938 | − | 0.976628i | \(-0.568955\pi\) | ||
0.214938 | − | 0.976628i | \(-0.431045\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.42806 | −0.795303 | −0.397651 | − | 0.917537i | \(-0.630175\pi\) | ||||
−0.397651 | + | 0.917537i | \(0.630175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.43778 | 1.29475 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.68886 | + | 3.01194i | −0.623531 | + | 0.509111i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1602 | −1.67033 | −0.835163 | − | 0.550003i | \(-0.814626\pi\) | ||||
−0.835163 | + | 0.550003i | \(0.814626\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.92144i | 0.788061i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.85008i | − | 0.601281i | −0.953738 | − | 0.300640i | \(-0.902800\pi\) | ||
0.953738 | − | 0.300640i | \(-0.0972004\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.94839 | −1.21212 | −0.606059 | − | 0.795420i | \(-0.707251\pi\) | ||||
−0.606059 | + | 0.795420i | \(0.707251\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.464102 | + | 0.378937i | −0.0691842 | + | 0.0564886i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.38929 | 0.931974 | 0.465987 | − | 0.884791i | \(-0.345699\pi\) | ||||
0.465987 | + | 0.884791i | \(0.345699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.46410 | −0.352015 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.24156 | −0.453910 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.71536 | 0.647705 | 0.323852 | − | 0.946108i | \(-0.395022\pi\) | ||||
0.323852 | + | 0.946108i | \(0.395022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.81863 | + | 7.12633i | 0.784583 | + | 0.960914i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.71536 | + | 6.31319i | −0.624565 | + | 0.836203i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.42806 | 0.576484 | 0.288242 | − | 0.957558i | \(-0.406929\pi\) | ||||
0.288242 | + | 0.957558i | \(0.406929\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.19615 | 1.04941 | 0.524705 | − | 0.851284i | \(-0.324176\pi\) | ||||
0.524705 | + | 0.851284i | \(0.324176\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.570669 | 0.0718975 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.71536 | + | 3.85008i | −0.584869 | + | 0.477543i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.13111i | − | 0.382526i | −0.981539 | − | 0.191263i | \(-0.938742\pi\) | ||
0.981539 | − | 0.191263i | \(-0.0612583\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.66853i | 0.802796i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.5257 | −1.96124 | −0.980622 | − | 0.195909i | \(-0.937234\pi\) | ||||
−0.980622 | + | 0.195909i | \(0.937234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.3843i | 1.56651i | 0.621701 | + | 0.783255i | \(0.286442\pi\) | ||||
−0.621701 | + | 0.783255i | \(0.713558\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.85612 | − | 1.80775i | −1.02262 | − | 0.208741i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.76268i | − | 0.998600i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.29958 | 0.708758 | 0.354379 | − | 0.935102i | \(-0.384692\pi\) | ||||
0.354379 | + | 0.935102i | \(0.384692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.73205 | −1.08134 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7670 | 1.51113 | 0.755563 | − | 0.655076i | \(-0.227363\pi\) | ||||
0.755563 | + | 0.655076i | \(0.227363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.53590 | − | 3.10583i | −0.275057 | − | 0.336874i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.0150 | −2.03862 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5186i | 1.11497i | 0.830187 | + | 0.557485i | \(0.188234\pi\) | ||||
−0.830187 | + | 0.557485i | \(0.811766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.79810 | 0.607806 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00481i | 0.830060i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.73770 | + | 0.420943i | −0.999067 | + | 0.0431879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1602 | 1.03161 | 0.515806 | − | 0.856706i | \(-0.327493\pi\) | ||||
0.515806 | + | 0.856706i | \(0.327493\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.10245i | − | 0.110800i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.19615 | −0.218525 | −0.109263 | − | 0.994013i | \(-0.534849\pi\) | ||||
−0.109263 | + | 0.994013i | \(0.534849\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.39333i | − | 0.925552i | −0.886475 | − | 0.462776i | \(-0.846853\pi\) | ||
0.886475 | − | 0.462776i | \(-0.153147\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.44483 | + | 6.66853i | 0.531361 | + | 0.650782i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.484384i | 0.0468272i | 0.999726 | + | 0.0234136i | \(0.00745346\pi\) | ||||
−0.999726 | + | 0.0234136i | \(0.992547\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.66853i | − | 0.638729i | −0.947632 | − | 0.319365i | \(-0.896531\pi\) | ||
0.947632 | − | 0.319365i | \(-0.103469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.3671i | 1.74332i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5980 | 1.65548 | 0.827739 | − | 0.561114i | \(-0.189627\pi\) | ||||
0.827739 | + | 0.561114i | \(0.189627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.38929 | + | 5.21684i | −0.595805 | + | 0.486473i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.729469 | 0.0674394 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.81899i | 0.350086i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.92820 | −0.538928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.95996 | −0.627559 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.19615 | − | 9.89949i | −0.464758 | − | 0.885438i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.838978i | 0.0744473i | 0.999307 | + | 0.0372236i | \(0.0118514\pi\) | ||||
−0.999307 | + | 0.0372236i | \(0.988149\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.3687i | 1.26509i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.20489i | − | 0.192643i | −0.995350 | − | 0.0963213i | \(-0.969292\pi\) | ||
0.995350 | − | 0.0963213i | \(-0.0307076\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.43778 | + | 5.55532i | 0.644937 | + | 0.481707i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.98460 | − | 8.55435i | −0.601138 | − | 0.736241i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.4195i | 1.23194i | 0.787768 | + | 0.615972i | \(0.211237\pi\) | ||||
−0.787768 | + | 0.615972i | \(0.788763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.1622i | − | 1.37086i | −0.728140 | − | 0.685428i | \(-0.759615\pi\) | ||
0.728140 | − | 0.685428i | \(-0.240385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 11.5502i | − | 0.972705i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.2011i | − | 0.936681i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.8756 | − | 18.2188i | −1.23535 | − | 1.51299i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.45447i | 0.367399i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.66025 | 0.463706 | 0.231853 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231853 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.24156 | −0.263795 | −0.131897 | − | 0.991263i | \(-0.542107\pi\) | ||||
−0.131897 | + | 0.991263i | \(0.542107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.480473i | 0.0388440i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.66962 | + | 6.26222i | −0.616039 | + | 0.502994i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.69213i | − | 0.534090i | −0.963684 | − | 0.267045i | \(-0.913953\pi\) | ||
0.963684 | − | 0.267045i | \(-0.0860473\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 8.52418i | − | 0.676011i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.85641 | 0.619172 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.570669 | 0.0446982 | 0.0223491 | − | 0.999750i | \(-0.492885\pi\) | ||||
0.0223491 | + | 0.999750i | \(0.492885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.8826 | − | 10.5186i | 1.00291 | − | 0.818872i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.9477i | − | 1.38883i | −0.719573 | − | 0.694417i | \(-0.755663\pi\) | ||
0.719573 | − | 0.694417i | \(-0.244337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.58846 | −0.429881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.935759 | + | 0.698924i | 0.0715593 | + | 0.0534480i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.16724 | −0.620944 | −0.310472 | − | 0.950583i | \(-0.600487\pi\) | ||||
−0.310472 | + | 0.950583i | \(0.600487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.12976 | + | 10.4337i | −0.160995 | + | 0.788712i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.00481i | − | 0.601678i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.7673 | 1.47748 | 0.738739 | − | 0.673992i | \(-0.235422\pi\) | ||||
0.738739 | + | 0.673992i | \(0.235422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.2188i | 1.35419i | 0.735896 | + | 0.677095i | \(0.236761\pi\) | ||||
−0.735896 | + | 0.677095i | \(0.763239\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.8166i | − | 1.09527i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.5980 | + | 14.3687i | −1.29383 | + | 1.05641i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.37772 | 0.539512 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.5186i | 0.765116i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.2407i | 0.813350i | 0.913573 | + | 0.406675i | \(0.133312\pi\) | ||||
−0.913573 | + | 0.406675i | \(0.866688\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.6050 | −1.12327 | −0.561637 | − | 0.827384i | \(-0.689828\pi\) | ||||
−0.561637 | + | 0.827384i | \(0.689828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.95996 | + | 8.52418i | 0.498413 | + | 0.610429i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 6.69213i | − | 0.476795i | −0.971168 | − | 0.238397i | \(-0.923378\pi\) | ||
0.971168 | − | 0.238397i | \(-0.0766220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.4695i | − | 1.38016i | −0.723735 | − | 0.690078i | \(-0.757576\pi\) | ||
0.723735 | − | 0.690078i | \(-0.242424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.66025 | −0.399244 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.4022i | 1.57232i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.44483 | − | 6.66853i | −0.380283 | − | 0.465750i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.988427 | 0.0687004 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.7321 | − | 14.3687i | 0.742351 | − | 0.993902i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98460 | 0.480840 | 0.240420 | − | 0.970669i | \(-0.422715\pi\) | ||||
0.240420 | + | 0.970669i | \(0.422715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.8744i | 2.04696i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.7670 | + | 11.2407i | −0.938903 | + | 0.766611i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.43072 | 0.640199 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.1954 | 1.63497 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.88170i | 0.328379i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.2099i | 1.62121i | 0.585590 | + | 0.810607i | \(0.300863\pi\) | ||||
−0.585590 | + | 0.810607i | \(0.699137\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.267949 | + | 1.31268i | −0.0178633 | + | 0.0875118i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9776i | 0.927725i | 0.885907 | + | 0.463863i | \(0.153537\pi\) | ||||
−0.885907 | + | 0.463863i | \(0.846463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.12436 | 0.602954 | 0.301477 | − | 0.953473i | \(-0.402520\pi\) | ||||
0.301477 | + | 0.953473i | \(0.402520\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.8407 | −1.04224 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.93426i | − | 0.388766i | −0.980926 | − | 0.194383i | \(-0.937730\pi\) | ||
0.980926 | − | 0.194383i | \(-0.0622705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0666 | − | 9.03583i | 0.721904 | − | 0.589432i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 11.3880i | − | 0.739733i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 16.4576i | − | 1.06455i | −0.846571 | − | 0.532276i | \(-0.821337\pi\) | ||
0.846571 | − | 0.532276i | \(-0.178663\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.66853i | − | 0.429558i | −0.976663 | − | 0.214779i | \(-0.931097\pi\) | ||
0.976663 | − | 0.214779i | \(-0.0689031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.77652i | 0.178114i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.26795 | + | 3.48477i | −0.272669 | + | 0.222634i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.50749 | + | 7.10120i | 0.604947 | + | 0.451838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 24.8873i | − | 1.57717i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 25.4934i | − | 1.60913i | −0.593866 | − | 0.804564i | \(-0.702399\pi\) | ||
0.593866 | − | 0.804564i | \(-0.297601\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.1774i | − | 0.954196i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.61455 | + | 4.58426i | −0.351597 | + | 0.287078i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.0499 | −1.31305 | −0.656527 | − | 0.754303i | \(-0.727975\pi\) | ||||
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6388 | 1.34457 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.81845i | 0.174458i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4675 | −1.01543 | −0.507713 | − | 0.861526i | \(-0.669509\pi\) | ||||
−0.507713 | + | 0.861526i | \(0.669509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.16724 | − | 6.66853i | 0.501710 | − | 0.409644i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.0150 | 1.16370 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.85008i | 0.234743i | 0.993088 | + | 0.117372i | \(0.0374469\pi\) | ||||
−0.993088 | + | 0.117372i | \(0.962553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.1622i | − | 0.981781i | −0.871221 | − | 0.490891i | \(-0.836671\pi\) | ||
0.871221 | − | 0.490891i | \(-0.163329\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 10.4815i | − | 0.634369i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.1563 | + | 4.11439i | 1.21547 | + | 0.248107i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 23.6627i | − | 1.42175i | −0.703317 | − | 0.710877i | \(-0.748298\pi\) | ||
0.703317 | − | 0.710877i | \(-0.251702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.18649 | 0.0710336 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.3687i | − | 0.857164i | −0.903503 | − | 0.428582i | \(-0.859013\pi\) | ||
0.903503 | − | 0.428582i | \(-0.140987\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.4043 | 1.51013 | 0.755063 | − | 0.655652i | \(-0.227606\pi\) | ||||
0.755063 | + | 0.655652i | \(0.227606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.760959 | + | 17.6033i | 0.0450753 | + | 1.04273i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.19976i | 0.484016i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7846 | 0.810859 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 18.3671i | − | 1.07670i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.71536 | −0.275474 | −0.137737 | − | 0.990469i | \(-0.543983\pi\) | ||||
−0.137737 | + | 0.990469i | \(0.543983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.66962 | − | 6.26222i | 0.446543 | − | 0.364601i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 20.3204 | 1.17911 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.0426 | 0.580779 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.9282 | 0.975725 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.97009i | 0.228076i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.1962 | − | 11.5911i | 0.812869 | − | 0.663705i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.7642i | 1.86995i | 0.354708 | + | 0.934977i | \(0.384580\pi\) | ||||
−0.354708 | + | 0.934977i | \(0.615420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.9808 | −0.966002 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.0056i | 1.75817i | 0.476667 | + | 0.879084i | \(0.341845\pi\) | ||||
−0.476667 | + | 0.879084i | \(0.658155\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.4901i | − | 0.932075i | −0.884765 | − | 0.466037i | \(-0.845681\pi\) | ||
0.884765 | − | 0.466037i | \(-0.154319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.988427 | − | 0.807048i | 0.0556916 | − | 0.0454720i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.16724 | −0.458718 | −0.229359 | − | 0.973342i | \(-0.573663\pi\) | ||||
−0.229359 | + | 0.973342i | \(0.573663\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.2776 | 2.42308 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.875644 | 0.0488737 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.67729 | + | 6.26222i | −0.260251 | + | 0.348439i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.72241 | + | 13.3371i | −0.151012 | + | 0.739807i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.0550 | −0.666644 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6077 | −0.750217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.1954 | 1.32990 | 0.664949 | − | 0.746889i | \(-0.268453\pi\) | ||||
0.664949 | + | 0.746889i | \(0.268453\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.72241 | 0.149187 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.42806 | − | 5.42324i | −0.241931 | − | 0.296303i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1531 | 0.662024 | 0.331012 | − | 0.943627i | \(-0.392610\pi\) | ||||
0.331012 | + | 0.943627i | \(0.392610\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 31.8127i | − | 1.72783i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 18.2188i | − | 0.986601i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1563 | 1.08834 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.43072 | + | 11.5502i | 0.507733 | + | 0.621843i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.68886 | 0.198028 | 0.0990142 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990142 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.4456i | 0.717674i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.1459i | − | 0.646462i | −0.946320 | − | 0.323231i | \(-0.895231\pi\) | ||
0.946320 | − | 0.323231i | \(-0.104769\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.6234 | + | 23.3709i | −1.51917 | + | 1.24040i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.90377 | 0.365386 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.31928i | − | 0.333519i | −0.985998 | − | 0.166760i | \(-0.946670\pi\) | ||
0.985998 | − | 0.166760i | \(-0.0533304\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.39230 | + | 18.2188i | 0.283806 | + | 0.958882i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.7167i | 0.562480i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.9282 | + | 23.1822i | 0.990747 | + | 1.21341i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.80705 | 0.355325 | 0.177663 | − | 0.984091i | \(-0.443146\pi\) | ||||
0.177663 | + | 0.984091i | \(0.443146\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.03162i | 0.0537042i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0426 | −0.521386 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1602 | 0.526075 | 0.263037 | − | 0.964786i | \(-0.415276\pi\) | ||||
0.263037 | + | 0.964786i | \(0.415276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.8958 | + | 9.39333i | −0.924134 | + | 0.485069i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 28.6360i | 1.47483i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.9538 | 1.07632 | 0.538162 | − | 0.842841i | \(-0.319119\pi\) | ||||
0.538162 | + | 0.842841i | \(0.319119\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.51666 | 0.0777009 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 0.484384i | − | 0.0247509i | −0.999923 | − | 0.0123754i | \(-0.996061\pi\) | ||
0.999923 | − | 0.0123754i | \(-0.00393933\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.3923 | − | 15.1774i | −0.631570 | − | 0.773513i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.12976 | 0.108262 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.5359 | 0.736999 | 0.368500 | − | 0.929628i | \(-0.379872\pi\) | ||||
0.368500 | + | 0.929628i | \(0.379872\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.61468i | 0.334519i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.98589 | −0.201062 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.9112 | − | 8.90894i | 0.549001 | − | 0.448258i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2832i | 0.917610i | 0.888537 | + | 0.458805i | \(0.151722\pi\) | ||||
−0.888537 | + | 0.458805i | \(0.848278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.0426 | − | 13.4456i | 0.502759 | − | 0.673123i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0372i | 1.05055i | 0.850933 | + | 0.525274i | \(0.176037\pi\) | ||||
−0.850933 | + | 0.525274i | \(0.823963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0550 | 0.600503 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.8564 | + | 13.7632i | −0.837602 | + | 0.683899i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 41.8030i | − | 2.07210i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11.5502i | − | 0.571122i | −0.958361 | − | 0.285561i | \(-0.907820\pi\) | ||
0.958361 | − | 0.285561i | \(-0.0921799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.0669 | 1.28578 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.43072 | −0.464055 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.8452 | − | 19.4695i | 1.17051 | − | 0.955720i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.2171 | −1.43077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 18.6625i | − | 0.911721i | −0.890051 | − | 0.455860i | \(-0.849332\pi\) | ||
0.890051 | − | 0.455860i | \(-0.150668\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.5502i | − | 0.562924i | −0.959572 | − | 0.281462i | \(-0.909181\pi\) | ||
0.959572 | − | 0.281462i | \(-0.0908193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.71201 | −0.0832406 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.78461 | − | 1.79315i | −0.426116 | − | 0.0869806i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4559 | −0.844749 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.2487 | −0.977617 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.8099 | −1.43589 | −0.717946 | − | 0.696098i | \(-0.754918\pi\) | ||||
−0.717946 | + | 0.696098i | \(0.754918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1531 | −0.584042 | −0.292021 | − | 0.956412i | \(-0.594328\pi\) | ||||
−0.292021 | + | 0.956412i | \(0.594328\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −32.9349 | + | 26.8912i | −1.57911 | + | 1.28934i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.8826 | + | 9.62209i | 0.616259 | + | 0.460287i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.03967 | 0.431440 | 0.215720 | − | 0.976455i | \(-0.430790\pi\) | ||||
0.215720 | + | 0.976455i | \(0.430790\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.660254 | 0.0314407 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.68886 | −0.175263 | −0.0876315 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876315 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8756 | + | 18.2188i | 0.705169 | + | 0.863652i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 10.2323i | − | 0.483972i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3687i | 0.678100i | 0.940768 | + | 0.339050i | \(0.110106\pi\) | ||||
−0.940768 | + | 0.339050i | \(0.889894\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8407 | 0.745910 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.85993i | 0.275323i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.0426 | − | 8.19976i | 0.470805 | − | 0.384411i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.4558i | 1.19077i | 0.803439 | + | 0.595387i | \(0.203001\pi\) | ||||
−0.803439 | + | 0.595387i | \(0.796999\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.85612 | −0.413368 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.2487 | −1.12938 | −0.564688 | − | 0.825305i | \(-0.691003\pi\) | ||||
−0.564688 | + | 0.825305i | \(0.691003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.1047 | −1.30614 | −0.653068 | − | 0.757299i | \(-0.726518\pi\) | ||||
−0.653068 | + | 0.757299i | \(0.726518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.3205 | + | 13.8647i | 0.524976 | + | 0.642962i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.0666 | 0.512100 | 0.256050 | − | 0.966663i | \(-0.417579\pi\) | ||||
0.256050 | + | 0.966663i | \(0.417579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.66853i | 0.307924i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0977 | −0.557432 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 32.7028i | − | 1.50368i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.2709 | + | 14.5003i | −0.746560 | + | 0.665319i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.26348 | −0.0578506 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4.11439i | − | 0.187991i | −0.995573 | − | 0.0939956i | \(-0.970036\pi\) | ||
0.995573 | − | 0.0939956i | \(-0.0299640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.6603 | 1.26120 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 14.2024i | − | 0.646231i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.5980 | − | 14.3687i | 0.799082 | − | 0.652448i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8241i | 1.12489i | 0.826836 | + | 0.562443i | \(0.190138\pi\) | ||||
−0.826836 | + | 0.562443i | \(0.809862\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.03162i | − | 0.0466517i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8554i | 0.805803i | 0.915243 | + | 0.402902i | \(0.131998\pi\) | ||||
−0.915243 | + | 0.402902i | \(0.868002\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.8614 | −0.849477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.55910 | − | 1.90949i | −0.0700762 | − | 0.0858254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 35.1959 | 1.57875 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.1622i | − | 0.723518i | −0.932272 | − | 0.361759i | \(-0.882176\pi\) | ||
0.932272 | − | 0.361759i | \(-0.117824\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.4449 | −1.44953 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4675 | −0.734247 | −0.367124 | − | 0.930172i | \(-0.619657\pi\) | ||||
−0.367124 | + | 0.930172i | \(0.619657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.80385 | + | 3.10583i | −0.169269 | + | 0.138208i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1025i | 0.448669i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 15.4003i | − | 0.682606i | −0.939953 | − | 0.341303i | \(-0.889132\pi\) | ||
0.939953 | − | 0.341303i | \(-0.110868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 28.5053i | − | 1.26100i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.8826 | + | 17.2480i | −0.568781 | + | 0.761516i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2842 | − | 16.2697i | −0.585371 | − | 0.716930i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.2880i | 1.15615i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7643i | 0.648081i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.5186i | 0.460828i | 0.973093 | + | 0.230414i | \(0.0740081\pi\) | ||||
−0.973093 | + | 0.230414i | \(0.925992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.838978i | − | 0.0366860i | −0.999832 | − | 0.0183430i | \(-0.994161\pi\) | ||
0.999832 | − | 0.0183430i | \(-0.00583908\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.8614 | + | 3.85008i | 0.823181 | + | 0.168031i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.94018i | 0.345879i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.39230 | −0.408361 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.18649 | −0.0514895 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.4815i | 0.454004i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.685023 | + | 0.838978i | 0.0296161 | + | 0.0362722i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 35.7343i | − | 1.54205i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.1383i | − | 0.436686i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.80385 | 0.0775535 | 0.0387767 | − | 0.999248i | \(-0.487654\pi\) | ||||
0.0387767 | + | 0.999248i | \(0.487654\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.9349 | 1.41337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.43072 | − | 11.5502i | −0.403968 | − | 0.494757i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.0564i | − | 1.49890i | −0.662059 | − | 0.749451i | \(-0.730317\pi\) | ||
0.662059 | − | 0.749451i | \(-0.269683\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.19615 | −0.0937295 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.4369 | + | 36.7341i | −1.16885 | + | 1.56493i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4166 | −0.570532 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.9749 | + | 31.8127i | 1.10257 | + | 1.35037i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 11.0363i | − | 0.467623i | −0.972282 | − | 0.233812i | \(-0.924880\pi\) | ||
0.972282 | − | 0.233812i | \(-0.0751199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.6388 | 0.915224 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 13.3371i | − | 0.563091i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17.9477i | − | 0.756405i | −0.925723 | − | 0.378202i | \(-0.876542\pi\) | ||
0.925723 | − | 0.378202i | \(-0.123458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.4806 | − | 24.8873i | 1.28233 | − | 1.04702i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.7270 | 0.870451 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.03162i | 0.0432480i | 0.999766 | + | 0.0216240i | \(0.00688366\pi\) | ||||
−0.999766 | + | 0.0216240i | \(0.993116\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 30.4148i | − | 1.27282i | −0.771351 | − | 0.636410i | \(-0.780419\pi\) | ||
0.771351 | − | 0.636410i | \(-0.219581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.3204 | 0.848896 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.68886 | + | 18.0717i | −0.153836 | + | 0.753640i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.00481i | 0.333245i | 0.986021 | + | 0.166622i | \(0.0532860\pi\) | ||||
−0.986021 | + | 0.166622i | \(0.946714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 28.2099i | 1.17236i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.3205 | −1.21642 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4008i | 0.803500i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.26348 | − | 1.03162i | 0.0522384 | − | 0.0426524i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.36615 | −0.345308 | −0.172654 | − | 0.984983i | \(-0.555234\pi\) | ||||
−0.172654 | + | 0.984983i | \(0.555234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.4641 | + | 11.5502i | 0.637187 | + | 0.475919i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.0977 | −0.497632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11.8685i | − | 0.487381i | −0.969853 | − | 0.243691i | \(-0.921642\pi\) | ||
0.969853 | − | 0.243691i | \(-0.0783582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.40087 | + | 6.61468i | 0.221414 | + | 0.271176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.1959 | −1.44047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.5257 | 0.675223 | 0.337612 | − | 0.941285i | \(-0.390381\pi\) | ||||
0.337612 | + | 0.941285i | \(0.390381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.66853i | 0.272015i | 0.990708 | + | 0.136007i | \(0.0434271\pi\) | ||||
−0.990708 | + | 0.136007i | \(0.956573\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.838978i | 0.0341658i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.2679 | + | 8.38375i | −0.417451 | + | 0.340848i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.0863i | 1.26175i | 0.775883 | + | 0.630877i | \(0.217305\pi\) | ||||
−0.775883 | + | 0.630877i | \(0.782695\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.4974 | 1.64104 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.3943 | −0.703698 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 29.0421i | − | 1.17300i | −0.809949 | − | 0.586501i | \(-0.800505\pi\) | ||
0.809949 | − | 0.586501i | \(-0.199495\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0550 | + | 9.84287i | −0.486105 | + | 0.396903i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.8792i | 1.52496i | 0.647013 | + | 0.762479i | \(0.276018\pi\) | ||||
−0.647013 | + | 0.762479i | \(0.723982\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 22.7768i | − | 0.915479i | −0.889086 | − | 0.457739i | \(-0.848659\pi\) | ||
0.889086 | − | 0.457739i | \(-0.151341\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.2188i | 0.731093i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 22.4022i | − | 0.897523i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | − | 9.79796i | −0.920000 | − | 0.391918i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.9749 | − | 19.4008i | −1.03734 | − | 0.774795i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.2188i | 0.726429i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 8.52418i | − | 0.339342i | −0.985501 | − | 0.169671i | \(-0.945729\pi\) | ||
0.985501 | − | 0.169671i | \(-0.0542705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 12.6264i | − | 0.501854i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.18649 | + | 1.45315i | 0.0470846 | + | 0.0576666i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.70831 | 0.265793 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.42806 | 0.175171 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 27.7057i | − | 1.09431i | −0.837031 | − | 0.547155i | \(-0.815711\pi\) | ||
0.837031 | − | 0.547155i | \(-0.184289\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.80705 | 0.268444 | 0.134222 | − | 0.990951i | \(-0.457146\pi\) | ||||
0.134222 | + | 0.990951i | \(0.457146\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 20.3204 | + | 24.8873i | 0.800114 | + | 0.979936i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.7019 | −1.83604 | −0.918021 | − | 0.396532i | \(-0.870214\pi\) | ||||
−0.918021 | + | 0.396532i | \(0.870214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.2188i | 0.715149i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 17.0484i | − | 0.668178i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 45.0518i | − | 1.76301i | −0.472173 | − | 0.881506i | \(-0.656530\pi\) | ||
0.472173 | − | 0.881506i | \(-0.343470\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.11819 | − | 3.81899i | −0.121838 | − | 0.149220i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 3.58630i | − | 0.139915i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.0089 | −0.896298 | −0.448149 | − | 0.893959i | \(-0.647917\pi\) | ||||
−0.448149 | + | 0.893959i | \(0.647917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8873i | 0.968003i | 0.875067 | + | 0.484002i | \(0.160817\pi\) | ||||
−0.875067 | + | 0.484002i | \(0.839183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.82488 | 0.342730 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.7390 | − | 0.896510i | 0.804224 | − | 0.0347652i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.8017i | 1.50241i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.7654 | 1.69207 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.7222i | 1.30183i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1531 | 0.468469 | 0.234234 | − | 0.972180i | \(-0.424742\pi\) | ||||
0.234234 | + | 0.972180i | \(0.424742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.1954 | − | 4.93886i | −0.931280 | − | 0.190097i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.4806 | −1.17146 | −0.585732 | − | 0.810505i | \(-0.699193\pi\) | ||||
−0.585732 | + | 0.810505i | \(0.699193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.6388 | −0.830422 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.2679 | 0.968270 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 25.1787i | − | 0.963435i | −0.876327 | − | 0.481717i | \(-0.840013\pi\) | ||
0.876327 | − | 0.481717i | \(-0.159987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3923 | + | 24.9754i | 0.779150 | + | 0.954260i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16.4945i | − | 0.629305i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.8372 | −0.489057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9811i | 0.760119i | 0.924962 | + | 0.380059i | \(0.124096\pi\) | ||||
−0.924962 | + | 0.380059i | \(0.875904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.34795i | 0.0891914i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8567 | − | 27.9937i | −0.867006 | − | 1.06186i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.90377 | −0.261499 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.7276 | −0.405756 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.51666 | 0.283900 | 0.141950 | − | 0.989874i | \(-0.454663\pi\) | ||||
0.141950 | + | 0.989874i | \(0.454663\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.4824 | + | 26.5020i | 1.33824 | + | 0.999543i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.3345 | − | 20.0056i | −0.615192 | − | 0.753454i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.67729 | 0.175908 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.60770 | −0.285713 | −0.142856 | − | 0.989743i | \(-0.545629\pi\) | ||||
−0.142856 | + | 0.989743i | \(0.545629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.68797 | −0.0633037 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3345 | 0.611731 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.8407 | − | 19.4008i | −0.592409 | − | 0.725550i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.7511 | −1.11108 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.52359i | 0.131408i | 0.997839 | + | 0.0657039i | \(0.0209293\pi\) | ||||
−0.997839 | + | 0.0657039i | \(0.979071\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0056i | 0.745047i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.0550 | −0.448331 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −51.5304 | − | 10.5186i | −1.91379 | − | 0.390651i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.2610 | 1.78990 | 0.894951 | − | 0.446165i | \(-0.147210\pi\) | ||||
0.894951 | + | 0.446165i | \(0.147210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.1769 | −0.895441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.2527i | 0.527154i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20.0764i | − | 0.741538i | −0.928725 | − | 0.370769i | \(-0.879094\pi\) | ||
0.928725 | − | 0.370769i | \(-0.120906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.29958 | + | 7.71537i | 0.232363 | + | 0.284586i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.8826 | 0.474537 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.7222i | 1.24049i | 0.784408 | + | 0.620245i | \(0.212967\pi\) | ||||
−0.784408 | + | 0.620245i | \(0.787033\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.8372 | − | 17.1871i | 0.471585 | − | 0.631385i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 44.9341i | − | 1.64847i | −0.566246 | − | 0.824236i | \(-0.691605\pi\) | ||
0.566246 | − | 0.824236i | \(-0.308395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.80385 | − | 8.00481i | 0.359185 | − | 0.293273i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.68886 | −0.134968 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.03162i | − | 0.0376947i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.4369 | 1.00119 | 0.500594 | − | 0.865682i | \(-0.333115\pi\) | ||||
0.500594 | + | 0.865682i | \(0.333115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.0856 | −1.67945 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.61455 | + | 4.58426i | −0.204334 | + | 0.166838i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 24.0144i | − | 0.872819i | −0.899748 | − | 0.436410i | \(-0.856250\pi\) | ||
0.899748 | − | 0.436410i | \(-0.143750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −27.4369 | −0.995897 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.4449 | 1.17613 | 0.588063 | − | 0.808815i | \(-0.299891\pi\) | ||||
0.588063 | + | 0.808815i | \(0.299891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.2024i | 0.514161i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.679492 | + | 0.832204i | 0.0245671 | + | 0.0300884i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.0550 | −0.435281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8038 | 0.497779 | 0.248890 | − | 0.968532i | \(-0.419934\pi\) | ||||
0.248890 | + | 0.968532i | \(0.419934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 38.0528i | 1.37044i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.5980 | 0.632955 | 0.316477 | − | 0.948600i | \(-0.397500\pi\) | ||||
0.316477 | + | 0.948600i | \(0.397500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.42806 | + | 21.6930i | −0.159061 | + | 0.779234i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 39.1175i | − | 1.40333i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.0426 | + | 13.4456i | −0.359814 | + | 0.481739i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 67.9933i | − | 2.43299i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −51.9499 | −1.85654 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.46410 | − | 11.5911i | −0.337788 | − | 0.413704i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 44.2249i | − | 1.57645i | −0.615389 | − | 0.788224i | \(-0.711001\pi\) | ||
0.615389 | − | 0.788224i | \(-0.288999\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.7690i | 1.05980i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −37.4795 | −1.33262 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.3133 | −0.792369 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.0550 | − | 14.7643i | −0.427547 | − | 0.523636i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.3420 | 1.74778 | 0.873892 | − | 0.486120i | \(-0.161588\pi\) | ||||
0.873892 | + | 0.486120i | \(0.161588\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.4570i | − | 0.405318i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.81845i | − | 0.0995851i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −55.0681 | −1.94331 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6077 | − | 11.1106i | 0.479608 | − | 0.391598i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.95996 | 0.245002 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.46410 | −0.332740 | −0.166370 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166370 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.92953 | 0.173099 | 0.0865496 | − | 0.996248i | \(-0.472416\pi\) | ||||
0.0865496 | + | 0.996248i | \(0.472416\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.2171 | −1.02469 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.988427 | − | 0.807048i | 0.0346231 | − | 0.0282696i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.7582 | + | 20.7327i | 0.971135 | + | 0.725346i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.55360 | −0.0542871 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.3205 | 1.23269 | 0.616347 | − | 0.787475i | \(-0.288612\pi\) | ||||
0.616347 | + | 0.787475i | \(0.288612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.570669 | −0.0198923 | −0.00994613 | − | 0.999951i | \(-0.503166\pi\) | ||||
−0.00994613 | + | 0.999951i | \(0.503166\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.43778 | − | 36.4375i | 0.258950 | − | 1.26859i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.6855i | − | 0.406343i | −0.979143 | − | 0.203172i | \(-0.934875\pi\) | ||
0.979143 | − | 0.203172i | \(-0.0651249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 43.1060i | − | 1.49713i | −0.663059 | − | 0.748567i | \(-0.730742\pi\) | ||
0.663059 | − | 0.748567i | \(-0.269258\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.7762 | −1.48389 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.41851i | 0.153092i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.3819 | − | 31.0863i | −0.878375 | − | 1.07579i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.8695i | 0.755922i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.42806 | 0.152874 | 0.0764368 | − | 0.997074i | \(-0.475646\pi\) | ||||
0.0764368 | + | 0.997074i | \(0.475646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −81.6410 | −2.81521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −25.9749 | −0.894624 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.67949 | + | 7.90327i | −0.332985 | + | 0.271881i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.6257 | 0.433823 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 45.9245i | − | 1.57612i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 37.4795 | 1.28478 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.79796i | 0.335476i | 0.985832 | + | 0.167738i | \(0.0536462\pi\) | ||||
−0.985832 | + | 0.167738i | \(0.946354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.60921 | − | 0.112791i | 0.0892331 | − | 0.00385738i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.71536 | 0.161074 | 0.0805368 | − | 0.996752i | \(-0.474337\pi\) | ||||
0.0805368 | + | 0.996752i | \(0.474337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.5053i | 0.972589i | 0.873795 | + | 0.486295i | \(0.161652\pi\) | ||||
−0.873795 | + | 0.486295i | \(0.838348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.8231 | 0.505169 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.3010i | 0.520851i | 0.965494 | + | 0.260425i | \(0.0838628\pi\) | ||||
−0.965494 | + | 0.260425i | \(0.916137\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.1461 | + | 11.5502i | −0.480981 | + | 0.392720i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 24.9191i | − | 0.846297i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.9189i | 0.879239i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.52418i | 0.288831i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.72241 | −0.0921398 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.0666 | + | 21.0836i | 0.374119 | + | 0.712756i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.5909 | −0.661538 | −0.330769 | − | 0.943712i | \(-0.607308\pi\) | ||||
−0.330769 | + | 0.943712i | \(0.607308\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.52418i | 0.287513i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.3013 | −1.76207 | −0.881037 | − | 0.473047i | \(-0.843154\pi\) | ||||
−0.881037 | + | 0.473047i | \(0.843154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.2861 | −0.749986 | −0.374993 | − | 0.927028i | \(-0.622355\pi\) | ||||
−0.374993 | + | 0.927028i | \(0.622355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.3205 | − | 13.8647i | −0.380535 | − | 0.466058i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 51.8105i | − | 1.73963i | −0.493382 | − | 0.869813i | \(-0.664239\pi\) | ||
0.493382 | − | 0.869813i | \(-0.335761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.78683i | − | 0.0599282i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 40.0415i | − | 1.34144i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.3133 | − | 16.6660i | −0.746687 | − | 0.557705i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.2380 | − | 27.9552i | 1.14445 | − | 0.934439i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 18.1545i | − | 0.606161i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 46.5770i | 1.55343i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.45535i | − | 0.281689i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 30.6019i | − | 1.01837i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.7652 | + | 31.5558i | 0.856465 | + | 1.04895i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.39333i | − | 0.311900i | −0.987765 | − | 0.155950i | \(-0.950156\pi\) | ||
0.987765 | − | 0.155950i | \(-0.0498439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.588457 | 0.0195179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.8099 | −0.987646 | −0.493823 | − | 0.869562i | \(-0.664401\pi\) | ||||
−0.493823 | + | 0.869562i | \(0.664401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.6429i | 1.87461i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.9538 | − | 25.6631i | −0.692711 | − | 0.848394i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.69591i | 0.155073i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.0717i | − | 0.596129i | −0.954546 | − | 0.298064i | \(-0.903659\pi\) | ||
0.954546 | − | 0.298064i | \(-0.0963410\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.2295 | 1.95168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.9899 | 1.48086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1602 | + | 49.7746i | −0.334065 | + | 1.63658i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.51693i | 0.0826670i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.2487 | −1.18928 | −0.594641 | − | 0.803991i | \(-0.702706\pi\) | ||||
−0.594641 | + | 0.803991i | \(0.702706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.60538 | + | 6.42741i | 0.282030 | + | 0.210650i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 56.0503 | 1.83501 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.7786 | − | 10.4337i | 0.417905 | − | 0.341218i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.0127i | 1.50317i | 0.659636 | + | 0.751585i | \(0.270710\pi\) | ||||
−0.659636 | + | 0.751585i | \(0.729290\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.8099 | −0.972810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.63690i | 0.183758i | 0.995770 | + | 0.0918789i | \(0.0292873\pi\) | ||||
−0.995770 | + | 0.0918789i | \(0.970713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2024i | 0.462494i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.8756 | + | 18.2188i | 0.483902 | + | 0.592656i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.1997 | −1.07885 | −0.539423 | − | 0.842035i | \(-0.681358\pi\) | ||||
−0.539423 | + | 0.842035i | \(0.681358\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 36.4375i | − | 1.18281i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.7643i | 0.478766i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.71536 | −0.152746 | −0.0763728 | − | 0.997079i | \(-0.524334\pi\) | ||||
−0.0763728 | + | 0.997079i | \(0.524334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.8968 | + | 19.4695i | 0.514408 | + | 0.630018i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 78.2350i | − | 2.52898i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 30.7102i | − | 0.991685i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3923 | −0.367494 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 0.129790i | − | 0.00418244i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.0287 | + | 22.0688i | −0.870084 | + | 0.710421i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.8433 | −1.53854 | −0.769268 | − | 0.638927i | \(-0.779379\pi\) | ||||
−0.769268 | + | 0.638927i | \(0.779379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3205 | + | 8.45535i | 0.363667 | + | 0.271625i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.3819 | −0.814542 | −0.407271 | − | 0.913307i | \(-0.633520\pi\) | ||||
−0.407271 | + | 0.913307i | \(0.633520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.4216i | 1.10351i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.1100 | + | 4.92144i | 0.772139 | + | 0.157612i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.16724 | 0.261293 | 0.130647 | − | 0.991429i | \(-0.458295\pi\) | ||||
0.130647 | + | 0.991429i | \(0.458295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.2776 | −1.38316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78683i | 0.0570490i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.71537i | 0.246082i | 0.992402 | + | 0.123041i | \(0.0392647\pi\) | ||||
−0.992402 | + | 0.123041i | \(0.960735\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.46410 | − | 11.5911i | −0.301551 | − | 0.369323i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.5993i | 0.783003i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.3205 | 0.932338 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.9230 | 1.10937 | 0.554683 | − | 0.832062i | \(-0.312840\pi\) | ||||
0.554683 | + | 0.832062i | \(0.312840\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 43.7391i | − | 1.38802i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.5340 | − | 33.7222i | −0.872888 | − | 1.06906i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8028i | 0.563819i | 0.959441 | + | 0.281910i | \(0.0909678\pi\) | ||||
−0.959441 | + | 0.281910i | \(0.909032\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50.1797i | 1.58762i |
(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 | 1520.2.g.f.1519.5 | ✓ | 16 | |
4.3 | odd | 2 | inner | 1520.2.g.f.1519.10 | yes | 16 | |
5.4 | even | 2 | inner | 1520.2.g.f.1519.12 | yes | 16 | |
19.18 | odd | 2 | inner | 1520.2.g.f.1519.9 | yes | 16 | |
20.19 | odd | 2 | inner | 1520.2.g.f.1519.7 | yes | 16 | |
76.75 | even | 2 | inner | 1520.2.g.f.1519.6 | yes | 16 | |
95.94 | odd | 2 | inner | 1520.2.g.f.1519.8 | yes | 16 | |
380.379 | even | 2 | inner | 1520.2.g.f.1519.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1520.2.g.f.1519.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1520.2.g.f.1519.6 | yes | 16 | 76.75 | even | 2 | inner | |
1520.2.g.f.1519.7 | yes | 16 | 20.19 | odd | 2 | inner | |
1520.2.g.f.1519.8 | yes | 16 | 95.94 | odd | 2 | inner | |
1520.2.g.f.1519.9 | yes | 16 | 19.18 | odd | 2 | inner | |
1520.2.g.f.1519.10 | yes | 16 | 4.3 | odd | 2 | inner | |
1520.2.g.f.1519.11 | yes | 16 | 380.379 | even | 2 | inner | |
1520.2.g.f.1519.12 | yes | 16 | 5.4 | even | 2 | inner |