Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(113,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("912.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.f (of order \(2\), degree \(1\), not 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.20322144469993472.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(1.39399 - 1.02801i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.113 |
Dual form | 912.2.f.h.113.3 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.39399 | + | 1.02801i | −0.804818 | + | 0.593522i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.12291i | 0.502180i | 0.967964 | + | 0.251090i | \(0.0807890\pi\) | ||||
−0.967964 | + | 0.251090i | \(0.919211\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.21832 | −1.21641 | −0.608206 | − | 0.793779i | \(-0.708111\pi\) | ||||
−0.608206 | + | 0.793779i | \(0.708111\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.886389 | − | 2.86606i | 0.295463 | − | 0.955354i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.06841i | − | 0.925162i | −0.886577 | − | 0.462581i | \(-0.846924\pi\) | ||
0.886577 | − | 0.462581i | \(-0.153076\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.110515i | 0.0306514i | 0.999883 | + | 0.0153257i | \(0.00487852\pi\) | ||||
−0.999883 | + | 0.0153257i | \(0.995121\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.15436 | − | 1.56532i | −0.298055 | − | 0.404163i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.89721i | − | 0.460141i | −0.973174 | − | 0.230071i | \(-0.926104\pi\) | ||
0.973174 | − | 0.230071i | \(-0.0738957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.66196 | + | 3.45166i | 0.610695 | + | 0.791866i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.48630 | − | 3.30847i | 0.978990 | − | 0.721968i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.89866i | − | 1.64698i | −0.567327 | − | 0.823492i | \(-0.692023\pi\) | ||
0.567327 | − | 0.823492i | \(-0.307977\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.73908 | 0.747815 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.71073 | + | 4.90647i | 0.329230 | + | 0.944250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.77278 | 0.329197 | 0.164598 | − | 0.986361i | \(-0.447367\pi\) | ||||
0.164598 | + | 0.986361i | \(0.447367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.07614i | 0.911702i | 0.890056 | + | 0.455851i | \(0.150665\pi\) | ||||
−0.890056 | + | 0.455851i | \(0.849335\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.15436 | + | 4.27732i | 0.549104 | + | 0.744586i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.61388i | − | 0.610858i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.59682i | − | 0.591314i | −0.955294 | − | 0.295657i | \(-0.904461\pi\) | ||
0.955294 | − | 0.295657i | \(-0.0955386\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.113611 | − | 0.154057i | −0.0181923 | − | 0.0246688i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.01519 | −0.158546 | −0.0792732 | − | 0.996853i | \(-0.525260\pi\) | ||||
−0.0792732 | + | 0.996853i | \(0.525260\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.31502 | 1.26803 | 0.634014 | − | 0.773321i | \(-0.281406\pi\) | ||||
0.634014 | + | 0.773321i | \(0.281406\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.21832 | + | 0.995334i | 0.479760 | + | 0.148376i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.68383i | 0.829072i | 0.910033 | + | 0.414536i | \(0.136056\pi\) | ||||
−0.910033 | + | 0.414536i | \(0.863944\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.35762 | 0.479659 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.95035 | + | 2.64468i | 0.273104 | + | 0.370330i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.535944 | −0.0736176 | −0.0368088 | − | 0.999322i | \(-0.511719\pi\) | ||||
−0.0368088 | + | 0.999322i | \(0.511719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.44555 | 0.464597 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.25908 | − | 2.07505i | −0.961488 | − | 0.274847i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.5182 | 1.62972 | 0.814862 | − | 0.579655i | \(-0.196813\pi\) | ||||
0.814862 | + | 0.579655i | \(0.196813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.02149 | 0.899009 | 0.449505 | − | 0.893278i | \(-0.351601\pi\) | ||||
0.449505 | + | 0.893278i | \(0.351601\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.85269 | + | 9.22392i | −0.359405 | + | 1.16210i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.124099 | −0.0153925 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.5389i | − | 1.53187i | −0.642920 | − | 0.765933i | \(-0.722277\pi\) | ||
0.642920 | − | 0.765933i | \(-0.277723\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.11991 | + | 11.0106i | 0.977522 | + | 1.32552i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.76317 | 0.327927 | 0.163964 | − | 0.986466i | \(-0.447572\pi\) | ||||
0.163964 | + | 0.986466i | \(0.447572\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.47035 | −0.640256 | −0.320128 | − | 0.947374i | \(-0.603726\pi\) | ||||
−0.320128 | + | 0.947374i | \(0.603726\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.21222 | + | 3.84381i | −0.601855 | + | 0.443845i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.87515i | 1.12538i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 17.5218i | − | 1.97136i | −0.168638 | − | 0.985678i | \(-0.553937\pi\) | ||
0.168638 | − | 0.985678i | \(-0.446063\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.42863 | − | 5.08089i | −0.825403 | − | 0.564544i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.67296i | − | 0.951981i | −0.879450 | − | 0.475991i | \(-0.842090\pi\) | ||
0.879450 | − | 0.475991i | \(-0.157910\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.13039 | 0.231074 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.47123 | + | 1.82243i | −0.264943 | + | 0.195385i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.12793 | 0.225560 | 0.112780 | − | 0.993620i | \(-0.464024\pi\) | ||||
0.112780 | + | 0.993620i | \(0.464024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 0.355674i | − | 0.0372848i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.21832 | − | 7.07606i | −0.541115 | − | 0.733754i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.87590 | + | 2.98913i | −0.397659 | + | 0.306679i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.8252i | − | 1.30221i | −0.758989 | − | 0.651103i | \(-0.774306\pi\) | ||
0.758989 | − | 0.651103i | \(-0.225694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.79427 | − | 2.71981i | −0.883857 | − | 0.273351i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.75789i | − | 0.771939i | −0.922511 | − | 0.385970i | \(-0.873867\pi\) | ||
0.922511 | − | 0.385970i | \(-0.126133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13610i | 0.111943i | 0.998432 | + | 0.0559717i | \(0.0178257\pi\) | ||||
−0.998432 | + | 0.0559717i | \(0.982174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.71511 | + | 5.03770i | 0.362558 | + | 0.491629i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.2398 | 1.56996 | 0.784981 | − | 0.619520i | \(-0.212673\pi\) | ||||
0.784981 | + | 0.619520i | \(0.212673\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.2633i | 1.36618i | 0.730334 | + | 0.683090i | \(0.239364\pi\) | ||||
−0.730334 | + | 0.683090i | \(0.760636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.69757 | + | 5.01392i | 0.350958 | + | 0.475900i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.7428 | −1.48096 | −0.740478 | − | 0.672081i | \(-0.765401\pi\) | ||||
−0.740478 | + | 0.672081i | \(0.765401\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.86947 | 0.827082 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.316744 | + | 0.0979596i | 0.0292830 | + | 0.00905637i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.10584i | 0.559722i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58484 | 0.144076 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.41516 | − | 1.04363i | 0.127601 | − | 0.0941008i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.81318i | 0.877718i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.71514i | 0.329666i | 0.986322 | + | 0.164833i | \(0.0527084\pi\) | ||||
−0.986322 | + | 0.164833i | \(0.947292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.5910 | + | 8.54793i | −1.02053 | + | 0.752603i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 0.822597i | − | 0.0718707i | −0.999354 | − | 0.0359353i | \(-0.988559\pi\) | ||
0.999354 | − | 0.0359353i | \(-0.0114410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.56704 | − | 11.1086i | −0.742857 | − | 0.963236i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.50951 | + | 1.92099i | −0.474183 | + | 0.165333i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.34296i | − | 0.114736i | −0.998353 | − | 0.0573682i | \(-0.981729\pi\) | ||
0.998353 | − | 0.0573682i | \(-0.0182709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.1430 | 1.53887 | 0.769434 | − | 0.638726i | \(-0.220538\pi\) | ||||
0.769434 | + | 0.638726i | \(0.220538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.84304 | − | 7.92318i | −0.492072 | − | 0.667252i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.339107 | 0.0283575 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99067i | 0.165316i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.68047 | + | 3.45166i | −0.386038 | + | 0.284688i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 20.8112i | − | 1.70492i | −0.522790 | − | 0.852462i | \(-0.675109\pi\) | ||
0.522790 | − | 0.852462i | \(-0.324891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.63958i | − | 0.621700i | −0.950459 | − | 0.310850i | \(-0.899386\pi\) | ||
0.950459 | − | 0.310850i | \(-0.100614\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.43753 | − | 1.68167i | −0.439598 | − | 0.135955i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.70004 | −0.457838 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.71523 | −0.535934 | −0.267967 | − | 0.963428i | \(-0.586352\pi\) | ||||
−0.267967 | + | 0.963428i | \(0.586352\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.747098 | − | 0.550956i | 0.0592488 | − | 0.0436937i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.4205i | 2.00341i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.5885 | −1.06434 | −0.532168 | − | 0.846639i | \(-0.678623\pi\) | ||||
−0.532168 | + | 0.846639i | \(0.678623\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.80304 | + | 3.54206i | −0.373916 | + | 0.275749i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.4907 | −1.97253 | −0.986267 | − | 0.165161i | \(-0.947185\pi\) | ||||
−0.986267 | + | 0.165161i | \(0.947185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9878 | 0.999060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.2522 | − | 4.56982i | 0.936950 | − | 0.349463i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.36476 | −0.559932 | −0.279966 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279966 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0336 | −0.909652 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.4501 | + | 12.8688i | −1.31163 | + | 0.967277i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.71906 | −0.352719 | −0.176360 | − | 0.984326i | \(-0.556432\pi\) | ||||
−0.176360 | + | 0.984326i | \(0.556432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.17885i | 0.384941i | 0.981303 | + | 0.192471i | \(0.0616500\pi\) | ||||
−0.981303 | + | 0.192471i | \(0.938350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.78785 | + | 7.21816i | −0.723539 | + | 0.533582i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.03890 | 0.296946 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.82143 | −0.425705 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.50568 | − | 15.7906i | −0.400479 | − | 1.14860i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.6896i | 1.71412i | 0.515217 | + | 0.857060i | \(0.327711\pi\) | ||||
−0.515217 | + | 0.857060i | \(0.672289\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 12.9367i | − | 0.931207i | −0.884993 | − | 0.465604i | \(-0.845837\pi\) | ||
0.884993 | − | 0.465604i | \(-0.154163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.172992 | − | 0.127575i | 0.0123882 | − | 0.00913581i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.76723i | 0.410898i | 0.978668 | + | 0.205449i | \(0.0658655\pi\) | ||||
−0.978668 | + | 0.205449i | \(0.934135\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.8246 | −1.05089 | −0.525446 | − | 0.850827i | \(-0.676101\pi\) | ||||
−0.525446 | + | 0.850827i | \(0.676101\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8901 | + | 17.4790i | 0.909196 | + | 1.23287i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.70538 | −0.400439 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.13997i | − | 0.0796188i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.6381 | − | 7.00129i | −1.57345 | − | 0.486623i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.5911 | − | 8.16799i | 0.732604 | − | 0.564991i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5203i | 0.930774i | 0.885107 | + | 0.465387i | \(0.154085\pi\) | ||||
−0.885107 | + | 0.465387i | \(0.845915\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.85181 | + | 2.84056i | −0.263922 | + | 0.194632i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.33700i | 0.636778i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.3367i | − | 1.10901i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.62559 | − | 5.62358i | 0.515289 | − | 0.380006i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.209671 | 0.0141040 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.3249i | − | 1.29409i | −0.762453 | − | 0.647044i | \(-0.776005\pi\) | ||
0.762453 | − | 0.647044i | \(-0.223995\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.31428 | − | 10.7164i | 0.220952 | − | 0.714429i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.4358 | −1.42274 | −0.711372 | − | 0.702816i | \(-0.751926\pi\) | ||||
−0.711372 | + | 0.702816i | \(0.751926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.96072 | 0.195650 | 0.0978249 | − | 0.995204i | \(-0.468811\pi\) | ||||
0.0978249 | + | 0.995204i | \(0.468811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.1518 | − | 13.7658i | −0.667937 | − | 0.905724i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.63499i | − | 0.434672i | −0.976097 | − | 0.217336i | \(-0.930263\pi\) | ||
0.976097 | − | 0.217336i | \(-0.0697368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.38242 | −0.416343 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.0126 | + | 24.4251i | 1.17004 | + | 1.58658i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.04461i | − | 0.0675703i | −0.999429 | − | 0.0337851i | \(-0.989244\pi\) | ||
0.999429 | − | 0.0337851i | \(-0.0107562\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 2.51441i | − | 0.161967i | −0.996715 | − | 0.0809836i | \(-0.974194\pi\) | ||
0.996715 | − | 0.0809836i | \(-0.0258061\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5786 | − | 0.554018i | 0.999368 | − | 0.0355403i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.77029i | 0.240875i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.381462 | + | 0.294187i | −0.0242718 | + | 0.0187187i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.91590 | + | 12.0900i | 0.565022 | + | 0.766172i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.74389i | − | 0.615029i | −0.951543 | − | 0.307514i | \(-0.900503\pi\) | ||
0.951543 | − | 0.307514i | \(-0.0994973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.2364 | −1.52373 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.96974 | + | 2.19007i | −0.185972 | + | 0.137147i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9086 | 1.30424 | 0.652122 | − | 0.758114i | \(-0.273879\pi\) | ||||
0.652122 | + | 0.758114i | \(0.273879\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5757i | 0.719282i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.57137 | − | 5.08089i | 0.0972654 | − | 0.314499i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.87701i | 0.362392i | 0.983447 | + | 0.181196i | \(0.0579968\pi\) | ||||
−0.983447 | + | 0.181196i | \(0.942003\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.601816i | − | 0.0369693i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.96630 | + | 2.18753i | −0.181535 | + | 0.133875i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8973 | −1.09121 | −0.545607 | − | 0.838041i | \(-0.683701\pi\) | ||||
−0.545607 | + | 0.838041i | \(0.683701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.33760 | 0.263490 | 0.131745 | − | 0.991284i | \(-0.457942\pi\) | ||||
0.131745 | + | 0.991284i | \(0.457942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.365637 | + | 0.495805i | 0.0221293 | + | 0.0300075i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 11.4730i | − | 0.691850i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.7189 | 1.54530 | 0.772650 | − | 0.634832i | \(-0.218931\pi\) | ||||
0.772650 | + | 0.634832i | \(0.218931\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5485 | + | 4.49944i | 0.870998 | + | 0.269374i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.74797 | 0.581515 | 0.290758 | − | 0.956797i | \(-0.406093\pi\) | ||||
0.290758 | + | 0.956797i | \(0.406093\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.99110 | 0.415578 | 0.207789 | − | 0.978174i | \(-0.433373\pi\) | ||||
0.207789 | + | 0.978174i | \(0.433373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.33009 | − | 8.15127i | 0.138023 | − | 0.482840i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.26722 | 0.192858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.4006 | 0.788270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.1845 | + | 17.8782i | 0.772888 | + | 1.04804i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.3072 | −0.718995 | −0.359498 | − | 0.933146i | \(-0.617052\pi\) | ||||
−0.359498 | + | 0.933146i | \(0.617052\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.0567i | 0.818415i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0551 | − | 5.24922i | 0.873584 | − | 0.304591i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.872923 | 0.0504824 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.7604 | −1.54245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.97520 | + | 10.8144i | 0.458163 | + | 0.621270i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.88449i | 0.451464i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1837i | 0.923654i | 0.886970 | + | 0.461827i | \(0.152806\pi\) | ||||
−0.886970 | + | 0.461827i | \(0.847194\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.16792 | − | 1.58371i | −0.0664408 | − | 0.0900940i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9076i | 0.902037i | 0.892515 | + | 0.451018i | \(0.148939\pi\) | ||||
−0.892515 | + | 0.451018i | \(0.851061\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6852 | 1.16920 | 0.584599 | − | 0.811322i | \(-0.301252\pi\) | ||||
0.584599 | + | 0.811322i | \(0.301252\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.3576 | − | 3.20331i | −0.583586 | − | 0.180486i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.2638 | 1.19429 | 0.597146 | − | 0.802133i | \(-0.296301\pi\) | ||||
0.597146 | + | 0.802133i | \(0.296301\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5.43962i | − | 0.304560i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.6381 | + | 16.6947i | −1.26353 | + | 0.931807i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.54853 | − | 5.05029i | 0.364370 | − | 0.281006i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.413225i | 0.0229216i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.6629 | − | 19.8829i | −0.810858 | − | 1.09953i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 18.2924i | − | 1.00849i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.9164i | − | 1.20463i | −0.798258 | − | 0.602316i | \(-0.794245\pi\) | ||
0.798258 | − | 0.602316i | \(-0.205755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.3087 | − | 3.18819i | −0.564915 | − | 0.174711i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0800 | 0.769272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 32.9088i | − | 1.79266i | −0.443392 | − | 0.896328i | \(-0.646225\pi\) | ||
0.443392 | − | 0.896328i | \(-0.353775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.9452 | − | 16.1837i | 1.19190 | − | 0.878980i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.5757 | 0.843471 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.7224 | 0.632949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.3639 | + | 9.11791i | −0.665651 | + | 0.490892i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.3356i | 1.57482i | 0.616430 | + | 0.787410i | \(0.288578\pi\) | ||||
−0.616430 | + | 0.787410i | \(0.711422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.7429 | −0.682112 | −0.341056 | − | 0.940043i | \(-0.610785\pi\) | ||||
−0.341056 | + | 0.940043i | \(0.610785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.542240 | + | 0.189062i | −0.0289426 | + | 0.0100914i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.79475i | 0.0955248i | 0.998859 | + | 0.0477624i | \(0.0152090\pi\) | ||||
−0.998859 | + | 0.0477624i | \(0.984791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.10278i | 0.164679i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.27687 | − | 8.51145i | −0.332207 | − | 0.450474i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 22.2796i | − | 1.17587i | −0.808908 | − | 0.587936i | \(-0.799941\pi\) | ||
0.808908 | − | 0.587936i | \(-0.200059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.82797 | + | 18.3764i | −0.254103 | + | 0.967177i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.20924 | + | 1.62923i | −0.115955 | + | 0.0855124i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.14270i | − | 0.321524i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7819 | 1.45020 | 0.725102 | − | 0.688641i | \(-0.241793\pi\) | ||||
0.725102 | + | 0.688641i | \(0.241793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.899855 | + | 2.90960i | −0.0468446 | + | 0.151468i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.72484 | 0.0895494 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 37.1660i | 1.92438i | 0.272379 | + | 0.962190i | \(0.412190\pi\) | ||||
−0.272379 | + | 0.962190i | \(0.587810\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.0881 | − | 13.6794i | −0.520945 | − | 0.706403i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.195919i | 0.0100903i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.1179i | − | 0.776555i | −0.921543 | − | 0.388277i | \(-0.873070\pi\) | ||
0.921543 | − | 0.388277i | \(-0.126930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.81920 | − | 5.17885i | −0.195664 | − | 0.265321i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −32.3643 | −1.65374 | −0.826869 | − | 0.562395i | \(-0.809880\pi\) | ||||
−0.826869 | + | 0.562395i | \(0.809880\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.0889 | −0.565142 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.37034 | − | 23.8314i | 0.374655 | − | 1.21142i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10.5965i | − | 0.537263i | −0.963243 | − | 0.268632i | \(-0.913429\pi\) | ||
0.963243 | − | 0.268632i | \(-0.0865715\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9854 | −0.757846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.845639 | + | 1.14669i | 0.0426568 | + | 0.0578428i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 19.6754 | 0.989975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8103 | 0.542554 | 0.271277 | − | 0.962501i | \(-0.412554\pi\) | ||||
0.271277 | + | 0.962501i | \(0.412554\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.3621 | + | 6.67818i | 1.16957 | + | 0.334327i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.786462 | 0.0392740 | 0.0196370 | − | 0.999807i | \(-0.493749\pi\) | ||||
0.0196370 | + | 0.999807i | \(0.493749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.560991 | −0.0279450 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.70538 | − | 8.34167i | 0.283502 | − | 0.414501i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.0365 | −0.547061 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.5912i | 1.26540i | 0.774396 | + | 0.632701i | \(0.218054\pi\) | ||||
−0.774396 | + | 0.632701i | \(0.781946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.38057 | + | 1.87206i | 0.0680986 | + | 0.0923419i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.2875 | −1.98242 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.73894 | 0.478066 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.2911 | + | 18.6512i | −1.23851 | + | 0.913352i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.6591i | 1.44894i | 0.689305 | + | 0.724472i | \(0.257916\pi\) | ||||
−0.689305 | + | 0.724472i | \(0.742084\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.61195i | 0.468458i | 0.972181 | + | 0.234229i | \(0.0752565\pi\) | ||||
−0.972181 | + | 0.234229i | \(0.924743\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.2902 | + | 5.03809i | 0.792057 | + | 0.244960i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 7.09382i | − | 0.344101i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.5974 | −1.09357 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.472710 | + | 0.348605i | −0.0228226 | + | 0.0168308i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.5325 | 1.27803 | 0.639013 | − | 0.769196i | \(-0.279343\pi\) | ||||
0.639013 | + | 0.769196i | \(0.279343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.9367i | − | 0.621700i | −0.950459 | − | 0.310850i | \(-0.899386\pi\) | ||
0.950459 | − | 0.310850i | \(-0.100614\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.04643 | − | 2.77496i | −0.0981186 | − | 0.133049i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.2635 | − | 21.0259i | 1.30419 | − | 1.00581i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.57572i | − | 0.313842i | −0.987611 | − | 0.156921i | \(-0.949843\pi\) | ||
0.987611 | − | 0.156921i | \(-0.0501568\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.97615 | − | 9.62314i | 0.141722 | − | 0.458245i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.7194i | 1.36450i | 0.731119 | + | 0.682250i | \(0.238998\pi\) | ||||
−0.731119 | + | 0.682250i | \(0.761002\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.38947i | 0.113272i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.3942 | + | 29.0106i | 1.01191 | + | 1.37215i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0178 | −0.567155 | −0.283577 | − | 0.958949i | \(-0.591521\pi\) | ||||
−0.283577 | + | 0.958949i | \(0.591521\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.11503i | 0.146681i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.85356 | + | 10.6495i | 0.368993 | + | 0.500355i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.399389 | 0.0187237 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.96247 | 0.232135 | 0.116067 | − | 0.993241i | \(-0.462971\pi\) | ||||
0.116067 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.30860 | − | 3.24561i | 0.434488 | − | 0.151492i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.4495i | − | 0.905856i | −0.891547 | − | 0.452928i | \(-0.850380\pi\) | ||
0.891547 | − | 0.452928i | \(-0.149620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.9667 | −0.881456 | −0.440728 | − | 0.897641i | \(-0.645280\pi\) | ||||
−0.440728 | + | 0.897641i | \(0.645280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.94577 | − | 5.85970i | 0.368476 | − | 0.271737i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 42.2099i | − | 1.95324i | −0.214969 | − | 0.976621i | \(-0.568965\pi\) | ||
0.214969 | − | 0.976621i | \(-0.431035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.3541i | 1.86338i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.36093 | − | 6.90333i | 0.431329 | − | 0.318089i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 25.5139i | − | 1.17313i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.95326 | + | 12.9060i | 0.456687 | + | 0.592170i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.475055 | + | 1.53605i | −0.0217513 | + | 0.0703309i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 38.2201i | − | 1.74632i | −0.487433 | − | 0.873160i | \(-0.662067\pi\) | ||
0.487433 | − | 0.873160i | \(-0.337933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.397504 | 0.0181246 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.1325 | − | 35.4357i | −1.18907 | − | 1.61238i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.4016 | 0.653942 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.549890i | − | 0.0249179i | −0.999922 | − | 0.0124589i | \(-0.996034\pi\) | ||
0.999922 | − | 0.0124589i | \(-0.00396591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9422 | − | 13.9692i | 0.856596 | − | 0.631707i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.5830i | − | 0.883767i | −0.897073 | − | 0.441883i | \(-0.854311\pi\) | ||
0.897073 | − | 0.441883i | \(-0.145689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.36333i | − | 0.151477i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.05410 | − | 9.87515i | 0.137271 | − | 0.443855i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.89277 | −0.398895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8013 | 0.662596 | 0.331298 | − | 0.943526i | \(-0.392513\pi\) | ||||
0.331298 | + | 0.943526i | \(0.392513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.5337 | − | 26.2048i | 1.58753 | − | 1.17074i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.38174i | 0.0616089i | 0.999525 | + | 0.0308045i | \(0.00980691\pi\) | ||||
−0.999525 | + | 0.0308045i | \(0.990193\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.71140 | 0.387652 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.1048 | + | 13.3516i | −0.804062 | + | 0.592964i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.6491 | 1.66877 | 0.834383 | − | 0.551186i | \(-0.185824\pi\) | ||||
0.834383 | + | 0.551186i | \(0.185824\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.6054 | 0.778816 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3816 | + | 18.9657i | −0.546660 | + | 0.837355i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.27574 | −0.0562157 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.4403 | 0.767025 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.2664 | − | 7.57105i | 0.450644 | − | 0.332332i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.7627 | −1.56679 | −0.783396 | − | 0.621523i | \(-0.786514\pi\) | ||||
−0.783396 | + | 0.621523i | \(0.786514\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.9246i | 1.26478i | 0.774649 | + | 0.632391i | \(0.217927\pi\) | ||||
−0.774649 | + | 0.632391i | \(0.782073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.7746 | − | 12.3706i | 0.732104 | − | 0.539899i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.63051 | 0.419512 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −39.3888 | −1.71256 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0960 | − | 35.8778i | 0.481523 | − | 1.55696i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.112194i | − | 0.00485967i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.2358i | 0.788403i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.57830 | − | 4.85124i | 0.283875 | − | 0.209347i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.3026i | − | 0.443762i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.9541 | −1.07286 | −0.536430 | − | 0.843945i | \(-0.680227\pi\) | ||||
−0.536430 | + | 0.843945i | \(0.680227\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.32391 | − | 7.21924i | −0.228471 | − | 0.309807i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.0164 | −0.686068 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3342i | 0.783912i | 0.919984 | + | 0.391956i | \(0.128201\pi\) | ||||
−0.919984 | + | 0.391956i | \(0.871799\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.22377 | − | 20.1240i | 0.265624 | − | 0.858872i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.71906 | + | 6.11903i | 0.201039 | + | 0.260680i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 56.3908i | 2.39798i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.63017 | + | 4.15203i | −0.238987 | + | 0.176244i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.8056i | 0.923933i | 0.886897 | + | 0.461966i | \(0.152856\pi\) | ||||
−0.886897 | + | 0.461966i | \(0.847144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.918937i | 0.0388669i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.11498 | − | 5.98449i | 0.342615 | − | 0.252665i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.1632 | 0.765489 | 0.382745 | − | 0.923854i | \(-0.374979\pi\) | ||||
0.382745 | + | 0.923854i | \(0.374979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.6777i | − | 0.743706i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.9077 | + | 16.3520i | 1.00403 | + | 0.686718i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.8909 | 1.12732 | 0.563662 | − | 0.826006i | \(-0.309392\pi\) | ||||
0.563662 | + | 0.826006i | \(0.309392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.32391 | −0.222799 | −0.111399 | − | 0.993776i | \(-0.535533\pi\) | ||||
−0.111399 | + | 0.993776i | \(0.535533\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.3532 | − | 33.0230i | −1.01737 | − | 1.37955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 29.5337i | − | 1.23164i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1457 | 1.21335 | 0.606676 | − | 0.794949i | \(-0.292503\pi\) | ||||
0.606676 | + | 0.794949i | \(0.292503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.2991 | + | 18.0336i | 0.552692 | + | 0.749452i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.9124i | 1.15800i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.64450i | 0.0681082i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.110000 | + | 0.355674i | −0.00454792 | + | 0.0147053i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.7041i | 1.14347i | 0.820438 | + | 0.571735i | \(0.193729\pi\) | ||||
−0.820438 | + | 0.571735i | \(0.806271\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5211 | + | 13.5125i | −0.721946 | + | 0.556772i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.92877 | − | 8.03943i | −0.243877 | − | 0.330698i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.1676i | 1.15670i | 0.815788 | + | 0.578352i | \(0.196304\pi\) | ||||
−0.815788 | + | 0.578352i | \(0.803696\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.85630 | −0.281081 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.6653 | − | 15.2399i | 0.845776 | − | 0.623727i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.0200 | 1.71689 | 0.858445 | − | 0.512906i | \(-0.171431\pi\) | ||||
0.858445 | + | 0.512906i | \(0.171431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.5141i | − | 1.61181i | −0.592044 | − | 0.805906i | \(-0.701679\pi\) | ||
0.592044 | − | 0.805906i | \(-0.298321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.9372 | − | 11.1143i | −1.46347 | − | 0.452610i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.77963i | 0.0723521i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3596i | 0.907548i | 0.891117 | + | 0.453774i | \(0.149923\pi\) | ||||
−0.891117 | + | 0.453774i | \(0.850077\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.95321 | − | 5.86519i | 0.322280 | − | 0.237669i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.628150 | −0.0254122 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.7108 | −1.15962 | −0.579810 | − | 0.814752i | \(-0.696873\pi\) | ||||
−0.579810 | + | 0.814752i | \(0.696873\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.17190 | + | 1.58910i | 0.0472555 | + | 0.0640786i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.09571i | 0.124629i | 0.998057 | + | 0.0623144i | \(0.0198481\pi\) | ||||
−0.998057 | + | 0.0623144i | \(0.980152\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.06313 | 0.364278 | 0.182139 | − | 0.983273i | \(-0.441698\pi\) | ||||
0.182139 | + | 0.983273i | \(0.441698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.7545 | − | 13.5125i | 1.55516 | − | 0.542237i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.84836 | −0.274374 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.67609 | 0.307043 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.36711 | + | 22.2738i | −0.254278 | + | 0.889532i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.82393 | −0.272088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.1845 | −1.16182 | −0.580908 | − | 0.813969i | \(-0.697302\pi\) | ||||
−0.580908 | + | 0.813969i | \(0.697302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.8990 | − | 18.8471i | −0.552435 | − | 0.749103i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.17176 | −0.165551 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.371068i | 0.0147022i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.44924 | − | 7.91941i | 0.0968905 | − | 0.313287i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.7454 | −1.37236 | −0.686180 | − | 0.727432i | \(-0.740714\pi\) | ||||
−0.686180 | + | 0.727432i | \(0.740714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.6626 | −1.52471 | −0.762353 | − | 0.647162i | \(-0.775956\pi\) | ||||
−0.762353 | + | 0.647162i | \(0.775956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.59853 | − | 13.0156i | −0.377942 | − | 0.512490i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 37.4963i | − | 1.47413i | −0.675822 | − | 0.737065i | \(-0.736211\pi\) | ||
0.675822 | − | 0.737065i | \(-0.263789\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 38.4109i | − | 1.50776i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.7943 | + | 22.7731i | 0.658219 | + | 0.892547i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.8643i | 1.56001i | 0.625772 | + | 0.780006i | \(0.284784\pi\) | ||||
−0.625772 | + | 0.780006i | \(0.715216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.923701 | 0.0360920 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.84886 | + | 15.6784i | −0.189172 | + | 0.611671i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.67263 | 0.104111 | 0.0520555 | − | 0.998644i | \(-0.483423\pi\) | ||||
0.0520555 | + | 0.998644i | \(0.483423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9290i | 0.619567i | 0.950807 | + | 0.309783i | \(0.100257\pi\) | ||||
−0.950807 | + | 0.309783i | \(0.899743\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.292278 | + | 0.215544i | −0.0113511 | + | 0.00837103i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.4739 | − | 9.62000i | 0.483717 | − | 0.373048i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.0026i | − | 0.542182i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.8662 | + | 26.9386i | 0.768070 | + | 1.04151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.5448i | − | 0.831729i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.62485i | − | 0.332464i | −0.986087 | − | 0.166232i | \(-0.946840\pi\) | ||
0.986087 | − | 0.166232i | \(-0.0531600\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.39655 | + | 18.3457i | 0.246203 | + | 0.706125i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.8459 | 1.22394 | 0.611968 | − | 0.790882i | \(-0.290378\pi\) | ||||
0.611968 | + | 0.790882i | \(0.290378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.2758i | 1.58402i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.8812 | − | 22.0362i | 1.14505 | − | 0.844430i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.6721 | −1.74759 | −0.873797 | − | 0.486290i | \(-0.838350\pi\) | ||||
−0.873797 | + | 0.486290i | \(0.838350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.50802 | 0.0576183 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.12720 | + | 3.04365i | −0.157462 | + | 0.116122i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 0.0592301i | − | 0.00225649i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.7339 | −1.39742 | −0.698711 | − | 0.715404i | \(-0.746243\pi\) | ||||
−0.698711 | + | 0.715404i | \(0.746243\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.3028 | + | 8.75323i | 1.07513 | + | 0.332508i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.3729i | 0.772788i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.92603i | 0.0729537i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.82083 | + | 9.24907i | 0.257988 | + | 0.349832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.3805i | 1.26077i | 0.776284 | + | 0.630383i | \(0.217102\pi\) | ||||
−0.776284 | + | 0.630383i | \(0.782898\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.4150 | − | 9.57459i | 0.468242 | − | 0.361113i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.89700 | − | 6.56119i | 0.335080 | − | 0.247109i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9674i | 0.938997i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.93260 | 0.147692 | 0.0738459 | − | 0.997270i | \(-0.476473\pi\) | ||||
0.0738459 | + | 0.997270i | \(0.476473\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −50.2186 | − | 15.5311i | −1.88334 | − | 0.582463i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40.0947 | 1.50156 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.380786i | 0.0142406i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.07387 | + | 1.45617i | 0.0401045 | + | 0.0543818i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.3129i | 0.944013i | 0.881595 | + | 0.472007i | \(0.156470\pi\) | ||||
−0.881595 | + | 0.472007i | \(0.843530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.65634i | − | 0.136169i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.58484 | + | 3.50505i | 0.0961311 | + | 0.130354i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.62855 | 0.246178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.67940 | −0.358989 | −0.179495 | − | 0.983759i | \(-0.557446\pi\) | ||||
−0.179495 | + | 0.983759i | \(0.557446\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.1468 | + | 16.7873i | −0.783215 | + | 0.621751i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 15.7753i | − | 0.583472i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.1166 | 0.558343 | 0.279172 | − | 0.960241i | \(-0.409940\pi\) | ||||
0.279172 | + | 0.960241i | \(0.409940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.87590 | − | 5.25573i | −0.142965 | − | 0.193861i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.4744 | −1.41722 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2840 | 0.415088 | 0.207544 | − | 0.978226i | \(-0.433453\pi\) | ||||
0.207544 | + | 0.978226i | \(0.433453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.229325 | − | 0.802239i | 0.00842445 | − | 0.0294710i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.2922 | −0.634388 | −0.317194 | − | 0.948361i | \(-0.602741\pi\) | ||||
−0.317194 | + | 0.948361i | \(0.602741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.3691 | 0.856178 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.8573 | − | 7.68762i | −0.909479 | − | 0.281275i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52.2650 | −1.90972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.2993i | 1.25160i | 0.779983 | + | 0.625800i | \(0.215227\pi\) | ||||
−0.779983 | + | 0.625800i | \(0.784773\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.0168 | + | 13.5828i | 0.365033 | + | 0.494986i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.57854 | 0.312205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.2944 | 0.701266 | 0.350633 | − | 0.936513i | \(-0.385966\pi\) | ||||
0.350633 | + | 0.936513i | \(0.385966\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.7851 | − | 24.9152i | 1.22632 | − | 0.904366i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1046i | 0.692540i | 0.938135 | + | 0.346270i | \(0.112552\pi\) | ||||
−0.938135 | + | 0.346270i | \(0.887448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 45.9041i | − | 1.66184i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.88836 | − | 6.10584i | 0.0682737 | − | 0.220757i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.38345i | 0.0499534i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.5296 | −0.523953 | −0.261976 | − | 0.965074i | \(-0.584374\pi\) | ||||
−0.261976 | + | 0.965074i | \(0.584374\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −29.1463 | + | 21.4943i | −1.04968 | + | 0.774097i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.31337 | 0.191109 | 0.0955544 | − | 0.995424i | \(-0.469538\pi\) | ||||
0.0955544 | + | 0.995424i | \(0.469538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.9801i | 0.681785i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.9000 | − | 16.1364i | −0.426910 | − | 0.578891i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.70240 | − | 3.50410i | −0.0968235 | − | 0.125547i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 8.47854i | − | 0.303386i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.03274 | + | 8.69808i | 0.108381 | + | 0.310844i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.54059i | − | 0.269135i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 30.6337i | − | 1.09197i | −0.837794 | − | 0.545987i | \(-0.816155\pi\) | ||
0.837794 | − | 0.545987i | \(-0.183845\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.04163 | − | 8.19246i | −0.215088 | − | 0.291659i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.6654 | 1.80145 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.775982i | 0.0275559i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.618673 | + | 0.838923i | 0.0219421 | + | 0.0297535i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.97137 | 0.353204 | 0.176602 | − | 0.984282i | \(-0.443489\pi\) | ||||
0.176602 | + | 0.984282i | \(0.443489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7834 | 0.381490 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.88617 | − | 6.09877i | 0.0666446 | − | 0.215490i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.7853i | 0.592340i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.5448 | −1.00607 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.9485 | − | 18.3986i | 0.878229 | − | 0.647660i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 22.4569i | − | 0.789543i | −0.918779 | − | 0.394772i | \(-0.870824\pi\) | ||
0.918779 | − | 0.394772i | \(-0.129176\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.60463i | 0.126576i | 0.997995 | + | 0.0632878i | \(0.0201586\pi\) | ||||
−0.997995 | + | 0.0632878i | \(0.979841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.04655 | + | 4.45910i | −0.212062 | + | 0.156387i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.2587i | − | 0.534488i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.1342 | + | 28.7006i | 0.774378 | + | 1.00411i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.01938 | − | 0.315266i | −0.0356202 | − | 0.0110163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.90493i | − | 0.310784i | −0.987853 | − | 0.155392i | \(-0.950336\pi\) | ||
0.987853 | − | 0.155392i | \(-0.0496641\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.08397 | −0.281789 | −0.140895 | − | 0.990025i | \(-0.544998\pi\) | ||||
−0.140895 | + | 0.990025i | \(0.544998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.7944 | + | 15.9932i | 0.410628 | + | 0.556813i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.6610 | −1.30960 | −0.654801 | − | 0.755801i | \(-0.727248\pi\) | ||||
−0.654801 | + | 0.755801i | \(0.727248\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.3065i | 0.878931i | 0.898259 | + | 0.439466i | \(0.144832\pi\) | ||||
−0.898259 | + | 0.439466i | \(0.855168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.8518 | + | 26.4393i | −1.24369 | + | 0.917170i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.37011i | − | 0.220711i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 28.6238i | − | 0.990566i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.9059 | + | 8.68390i | −0.860874 | + | 0.300159i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.6367 | −0.608887 | −0.304443 | − | 0.952530i | \(-0.598470\pi\) | ||||
−0.304443 | + | 0.952530i | \(0.598470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.8573 | −0.891630 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.5885 | + | 10.0210i | −0.468014 | + | 0.345142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5841i | 0.501708i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.10052 | −0.175256 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.74549 | + | 7.18693i | −0.334464 | + | 0.246655i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.4101 | −0.973886 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.26845 | −0.214627 | −0.107314 | − | 0.994225i | \(-0.534225\pi\) | ||||
−0.107314 | + | 0.994225i | \(0.534225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.13149 | + | 13.7581i | 0.175493 | + | 0.470517i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7290 | 0.810569 | 0.405284 | − | 0.914191i | \(-0.367172\pi\) | ||||
0.405284 | + | 0.914191i | \(0.367172\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.13279 | −0.0727699 | −0.0363850 | − | 0.999338i | \(-0.511584\pi\) | ||||
−0.0363850 | + | 0.999338i | \(0.511584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.55445 | + | 3.35873i | −0.155215 | + | 0.114465i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.1020 | 0.582160 | 0.291080 | − | 0.956699i | \(-0.405985\pi\) | ||||
0.291080 | + | 0.956699i | \(0.405985\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 8.26995i | − | 0.281187i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.6802 | + | 13.7759i | −0.634414 | + | 0.467856i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.7641 | −1.82382 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.38574 | 0.0469539 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −36.7580 | − | 11.3682i | −1.24407 | − | 0.384754i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 31.5820i | − | 1.06767i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 36.5776i | − | 1.23514i | −0.786517 | − | 0.617569i | \(-0.788118\pi\) | ||
0.786517 | − | 0.617569i | \(-0.211882\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.1561 | − | 12.6519i | 0.578660 | − | 0.426739i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.9469i | 0.840483i | 0.907412 | + | 0.420241i | \(0.138055\pi\) | ||||
−0.907412 | + | 0.420241i | \(0.861945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6173 | −1.19862 | −0.599309 | − | 0.800518i | \(-0.704558\pi\) | ||||
−0.599309 | + | 0.800518i | \(0.704558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.4505 | − | 19.5949i | −0.485747 | − | 0.658675i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.8871 | 1.13782 | 0.568909 | − | 0.822400i | \(-0.307366\pi\) | ||||
0.568909 | + | 0.822400i | \(0.307366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 11.9565i | − | 0.401009i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.5903 | + | 22.7941i | −0.522294 | + | 0.763631i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19.6187 | + | 15.1301i | −0.656514 | + | 0.506310i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 5.29907i | − | 0.177128i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.21684 | + | 0.897374i | −0.0406292 | + | 0.0299624i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.99887i | 0.300129i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01680i | 0.0338745i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.3036 | − | 27.5100i | 1.24139 | − | 0.915475i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.81538 | −0.193310 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 20.7685i | − | 0.689607i | −0.938675 | − | 0.344804i | \(-0.887945\pi\) | ||
0.938675 | − | 0.344804i | \(-0.112055\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.2346 | − | 6.87651i | −0.737475 | − | 0.228080i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.4137 | −1.80280 | −0.901402 | − | 0.432982i | \(-0.857461\pi\) | ||||
−0.901402 | + | 0.432982i | \(0.857461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.6122 | −0.880737 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.10533 | − | 10.9909i | −0.267954 | − | 0.363346i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.64739i | 0.0874244i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.5253 | 1.73265 | 0.866325 | − | 0.499481i | \(-0.166476\pi\) | ||||
0.866325 | + | 0.499481i | \(0.166476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.6370 | − | 22.5599i | −0.548209 | − | 0.743373i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.305372i | 0.0100514i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 13.4488i | − | 0.442194i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.25614 | + | 1.00703i | 0.106946 | + | 0.0330751i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.4235i | 0.768501i | 0.923229 | + | 0.384250i | \(0.125540\pi\) | ||||
−0.923229 | + | 0.384250i | \(0.874460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.93783 | + | 11.5894i | 0.292926 | + | 0.379826i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.3532 | − | 22.1749i | −0.535379 | − | 0.725975i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.53693i | − | 0.213780i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.73733 | −0.220099 | −0.110049 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110049 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.8349 | + | 21.2646i | −0.940991 | + | 0.693945i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.9061 | −1.43130 | −0.715650 | − | 0.698459i | \(-0.753869\pi\) | ||||
−0.715650 | + | 0.698459i | \(0.753869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.01866i | 0.261123i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.7314 | − | 6.18237i | 0.576802 | − | 0.201113i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.1163i | 1.30360i | 0.758389 | + | 0.651802i | \(0.225987\pi\) | ||||
−0.758389 | + | 0.651802i | \(0.774013\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 0.604558i | − | 0.0196248i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.6414 | + | 21.8594i | −0.961187 | + | 0.708839i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.3795 | −1.08127 | −0.540634 | − | 0.841258i | \(-0.681815\pi\) | ||||
−0.540634 | + | 0.841258i | \(0.681815\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.6013 | −0.860796 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.59198 | + | 7.58275i | 0.180763 | + | 0.245115i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.32207i | 0.139567i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.23280 | 0.168800 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.3948 | − | 46.5443i | 0.463866 | − | 1.49987i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.5268 | 0.467634 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.50334 | −0.176975 | −0.0884877 | − | 0.996077i | \(-0.528203\pi\) | ||||
−0.0884877 | + | 0.996077i | \(0.528203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.93680 | + | 13.7720i | −0.126468 | + | 0.442420i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.4580 | 0.720712 | 0.360356 | − | 0.932815i | \(-0.382655\pi\) | ||||
0.360356 | + | 0.932815i | \(0.382655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −58.3900 | −1.87190 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.424800 | − | 0.576030i | −0.0136045 | − | 0.0184477i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36.5252 | −1.16854 | −0.584272 | − | 0.811558i | \(-0.698620\pi\) | ||||
−0.584272 | + | 0.811558i | \(0.698620\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6.52936i | − | 0.208679i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 40.8796 | + | 12.6429i | 1.30519 | + | 0.403656i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.3826 | 0.618207 | 0.309104 | − | 0.951028i | \(-0.399971\pi\) | ||||
0.309104 | + | 0.951028i | \(0.399971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.47607 | −0.206345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.8048 | + | 25.4994i | 0.598563 | + | 0.811653i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 65.6775i | − | 2.08842i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 42.9880i | − | 1.36556i | −0.730624 | − | 0.682780i | \(-0.760771\pi\) | ||
0.730624 | − | 0.682780i | \(-0.239229\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.5302 | + | 30.5511i | 0.714976 | + | 0.969509i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 16.6467i | − | 0.527736i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.8836 | −0.883083 | −0.441542 | − | 0.897241i | \(-0.645568\pi\) | ||||
−0.441542 | + | 0.897241i | \(0.645568\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.6477 | − | 6.15319i | 0.558348 | − | 0.194678i |
(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 | 912.2.f.h.113.4 | 10 | ||
3.2 | odd | 2 | 912.2.f.i.113.8 | 10 | |||
4.3 | odd | 2 | 456.2.f.b.113.7 | yes | 10 | ||
12.11 | even | 2 | 456.2.f.a.113.3 | ✓ | 10 | ||
19.18 | odd | 2 | 912.2.f.i.113.7 | 10 | |||
57.56 | even | 2 | inner | 912.2.f.h.113.3 | 10 | ||
76.75 | even | 2 | 456.2.f.a.113.4 | yes | 10 | ||
228.227 | odd | 2 | 456.2.f.b.113.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.f.a.113.3 | ✓ | 10 | 12.11 | even | 2 | ||
456.2.f.a.113.4 | yes | 10 | 76.75 | even | 2 | ||
456.2.f.b.113.7 | yes | 10 | 4.3 | odd | 2 | ||
456.2.f.b.113.8 | yes | 10 | 228.227 | odd | 2 | ||
912.2.f.h.113.3 | 10 | 57.56 | even | 2 | inner | ||
912.2.f.h.113.4 | 10 | 1.1 | even | 1 | trivial | ||
912.2.f.i.113.7 | 10 | 19.18 | odd | 2 | |||
912.2.f.i.113.8 | 10 | 3.2 | odd | 2 |