Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8044,2,Mod(1,8044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8044 = 2^{2} \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8044.a (trivial) |
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: | yes |
Analytic conductor: | \(64.2316633859\) |
Analytic rank: | \(1\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8044.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −2.88063 | −1.66313 | −0.831565 | − | 0.555428i | \(-0.812555\pi\) | ||||
−0.831565 | + | 0.555428i | \(0.812555\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.02746 | 1.80114 | 0.900568 | − | 0.434715i | \(-0.143151\pi\) | ||||
0.900568 | + | 0.434715i | \(0.143151\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.18923 | 0.827450 | 0.413725 | − | 0.910402i | \(-0.364228\pi\) | ||||
0.413725 | + | 0.910402i | \(0.364228\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.29800 | 1.76600 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.81439 | −0.848570 | −0.424285 | − | 0.905529i | \(-0.639474\pi\) | ||||
−0.424285 | + | 0.905529i | \(0.639474\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.88746 | 0.800836 | 0.400418 | − | 0.916333i | \(-0.368865\pi\) | ||||
0.400418 | + | 0.916333i | \(0.368865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.6016 | −2.99552 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.25726 | 0.790003 | 0.395001 | − | 0.918681i | \(-0.370744\pi\) | ||||
0.395001 | + | 0.918681i | \(0.370744\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.41551 | −1.01299 | −0.506494 | − | 0.862243i | \(-0.669059\pi\) | ||||
−0.506494 | + | 0.862243i | \(0.669059\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.30634 | −1.37616 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.689969 | 0.143868 | 0.0719342 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719342 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.2205 | 2.24409 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.61968 | −1.27396 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.82147 | −0.709629 | −0.354814 | − | 0.934937i | \(-0.615456\pi\) | ||||
−0.354814 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.66502 | −0.658256 | −0.329128 | − | 0.944285i | \(-0.606755\pi\) | ||||
−0.329128 | + | 0.944285i | \(0.606755\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.10719 | 1.41128 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.81703 | 1.49035 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.9330 | −1.79737 | −0.898683 | − | 0.438598i | \(-0.855475\pi\) | ||||
−0.898683 | + | 0.438598i | \(0.855475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.31768 | −1.33189 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.86122 | −0.446847 | −0.223423 | − | 0.974721i | \(-0.571723\pi\) | ||||
−0.223423 | + | 0.974721i | \(0.571723\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.80191 | −0.427287 | −0.213644 | − | 0.976912i | \(-0.568533\pi\) | ||||
−0.213644 | + | 0.976912i | \(0.568533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21.3375 | 3.18081 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.38720 | −1.36926 | −0.684632 | − | 0.728889i | \(-0.740037\pi\) | ||||
−0.684632 | + | 0.728889i | \(0.740037\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.20729 | −0.315327 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.38296 | −1.31388 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.15319 | −0.707845 | −0.353922 | − | 0.935275i | \(-0.615152\pi\) | ||||
−0.353922 | + | 0.935275i | \(0.615152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.3348 | −1.52839 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.7194 | 1.68473 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.9848 | 1.95085 | 0.975427 | − | 0.220322i | \(-0.0707107\pi\) | ||||
0.975427 | + | 0.220322i | \(0.0707107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.99398 | 0.639413 | 0.319706 | − | 0.947517i | \(-0.396416\pi\) | ||||
0.319706 | + | 0.947517i | \(0.396416\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.5985 | 1.46128 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.6291 | 1.44242 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.4932 | −1.52629 | −0.763143 | − | 0.646230i | \(-0.776345\pi\) | ||||
−0.763143 | + | 0.646230i | \(0.776345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.98754 | −0.239272 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.1409 | −1.67822 | −0.839111 | − | 0.543961i | \(-0.816924\pi\) | ||||
−0.839111 | + | 0.543961i | \(0.816924\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.97005 | −1.16691 | −0.583453 | − | 0.812147i | \(-0.698299\pi\) | ||||
−0.583453 | + | 0.812147i | \(0.698299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32.3219 | −3.73222 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.16133 | −0.702148 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6789 | −1.31397 | −0.656987 | − | 0.753902i | \(-0.728169\pi\) | ||||
−0.656987 | + | 0.753902i | \(0.728169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.17482 | 0.352758 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.38123 | −0.590667 | −0.295334 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295334 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.1185 | 1.42290 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.0082 | 1.18020 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.97089 | −0.632913 | −0.316457 | − | 0.948607i | \(-0.602493\pi\) | ||||
−0.316457 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.32129 | 0.662652 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.5575 | 1.09477 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.7833 | −1.82453 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.78569 | −0.384379 | −0.192189 | − | 0.981358i | \(-0.561559\pi\) | ||||
−0.192189 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.9106 | −1.49857 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.742353 | −0.0738669 | −0.0369334 | − | 0.999318i | \(-0.511759\pi\) | ||||
−0.0369334 | + | 0.999318i | \(0.511759\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.33922 | −0.920221 | −0.460110 | − | 0.887862i | \(-0.652190\pi\) | ||||
−0.460110 | + | 0.887862i | \(0.652190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −25.3985 | −2.47864 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.22599 | −0.215195 | −0.107597 | − | 0.994195i | \(-0.534316\pi\) | ||||
−0.107597 | + | 0.994195i | \(0.534316\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4969 | −1.00542 | −0.502709 | − | 0.864456i | \(-0.667663\pi\) | ||||
−0.502709 | + | 0.864456i | \(0.667663\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 31.4937 | 2.98925 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.93364 | −0.934478 | −0.467239 | − | 0.884131i | \(-0.654751\pi\) | ||||
−0.467239 | + | 0.884131i | \(0.654751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.77883 | 0.259127 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.2977 | 1.41428 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.13089 | 0.653687 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.07923 | −0.279930 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.24209 | 0.743164 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 25.0527 | 2.24078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6331 | −0.943533 | −0.471767 | − | 0.881723i | \(-0.656384\pi\) | ||||
−0.471767 | + | 0.881723i | \(0.656384\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.07125 | 0.710634 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.21504 | 0.193529 | 0.0967643 | − | 0.995307i | \(-0.469151\pi\) | ||||
0.0967643 | + | 0.995307i | \(0.469151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.66656 | −0.838197 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −26.6605 | −2.29457 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.53067 | −0.387082 | −0.193541 | − | 0.981092i | \(-0.561997\pi\) | ||||
−0.193541 | + | 0.981092i | \(0.561997\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.4565 | 1.14137 | 0.570683 | − | 0.821170i | \(-0.306678\pi\) | ||||
0.570683 | + | 0.821170i | \(0.306678\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.0410 | 2.27726 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.12642 | −0.679565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.3908 | −1.27814 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.35838 | 0.524430 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.90700 | 0.320074 | 0.160037 | − | 0.987111i | \(-0.448839\pi\) | ||||
0.160037 | + | 0.987111i | \(0.448839\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.7696 | 1.20193 | 0.600965 | − | 0.799275i | \(-0.294783\pi\) | ||||
0.600965 | + | 0.799275i | \(0.294783\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.2570 | 1.39515 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.7607 | −1.18561 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.89008 | 0.310462 | 0.155231 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155231 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 14.8444 | 1.17724 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.51050 | 0.119044 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.37660 | 0.342802 | 0.171401 | − | 0.985201i | \(-0.445171\pi\) | ||||
0.171401 | + | 0.985201i | \(0.445171\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 32.6514 | 2.54191 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.2986 | 1.33860 | 0.669301 | − | 0.742991i | \(-0.266594\pi\) | ||||
0.669301 | + | 0.742991i | \(0.266594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.66260 | −0.358661 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.3934 | −1.78894 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.01438 | 0.533293 | 0.266647 | − | 0.963794i | \(-0.414084\pi\) | ||||
0.266647 | + | 0.963794i | \(0.414084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.5641 | 1.85687 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −43.1656 | −3.24452 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.8965 | −1.63662 | −0.818311 | − | 0.574776i | \(-0.805089\pi\) | ||||
−0.818311 | + | 0.574776i | \(0.805089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7968 | 1.02551 | 0.512753 | − | 0.858536i | \(-0.328626\pi\) | ||||
0.512753 | + | 0.858536i | \(0.328626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.3858 | −1.06343 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −44.0321 | −3.23730 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.16720 | −0.670372 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.4920 | −1.05414 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.5104 | −0.832861 | −0.416430 | − | 0.909168i | \(-0.636719\pi\) | ||||
−0.416430 | + | 0.909168i | \(0.636719\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.84065 | 0.708346 | 0.354173 | − | 0.935180i | \(-0.384762\pi\) | ||||
0.354173 | + | 0.935180i | \(0.384762\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.4991 | −2.39892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5789 | 1.03871 | 0.519353 | − | 0.854560i | \(-0.326173\pi\) | ||||
0.519353 | + | 0.854560i | \(0.326173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4151 | 0.880081 | 0.440041 | − | 0.897978i | \(-0.354964\pi\) | ||||
0.440041 | + | 0.897978i | \(0.354964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.9882 | 2.53841 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.36605 | −0.587182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.5234 | −0.804832 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.65546 | 0.254072 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.4270 | 0.859591 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.63380 | 0.525532 | 0.262766 | − | 0.964860i | \(-0.415365\pi\) | ||||
0.262766 | + | 0.964860i | \(0.415365\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.7348 | 2.79110 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.2846 | −0.769602 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.02355 | −0.544674 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 28.7200 | 1.94072 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.40521 | 0.632663 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.9379 | −1.46907 | −0.734535 | − | 0.678571i | \(-0.762600\pi\) | ||||
−0.734535 | + | 0.678571i | \(0.762600\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 59.4460 | 3.96307 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.5318 | 1.89372 | 0.946860 | − | 0.321647i | \(-0.104237\pi\) | ||||
0.946860 | + | 0.321647i | \(0.104237\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.8590 | 1.04799 | 0.523996 | − | 0.851721i | \(-0.324441\pi\) | ||||
0.523996 | + | 0.851721i | \(0.324441\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.7485 | 1.16776 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3382 | 1.33240 | 0.666200 | − | 0.745773i | \(-0.267920\pi\) | ||||
0.666200 | + | 0.745773i | \(0.267920\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.8066 | −2.46623 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.6424 | 2.18531 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.88479 | 0.510024 | 0.255012 | − | 0.966938i | \(-0.417921\pi\) | ||||
0.255012 | + | 0.966938i | \(0.417921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.19444 | −0.0769409 | −0.0384704 | − | 0.999260i | \(-0.512249\pi\) | ||||
−0.0384704 | + | 0.999260i | \(0.512249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7136 | 0.687277 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.88978 | −0.567947 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.7496 | −0.811238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.5013 | 0.982356 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.49534 | 0.346862 | 0.173431 | − | 0.984846i | \(-0.444515\pi\) | ||||
0.173431 | + | 0.984846i | \(0.444515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.94184 | −0.122082 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −37.7895 | −2.36647 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.7025 | −1.10425 | −0.552125 | − | 0.833761i | \(-0.686183\pi\) | ||||
−0.552125 | + | 0.833761i | \(0.686183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9347 | −1.48723 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.2461 | −1.25320 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.6126 | −1.51768 | −0.758838 | − | 0.651280i | \(-0.774232\pi\) | ||||
−0.758838 | + | 0.651280i | \(0.774232\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.7543 | −1.27492 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1999 | 1.05262 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.6349 | −0.831335 | −0.415668 | − | 0.909517i | \(-0.636452\pi\) | ||||
−0.415668 | + | 0.909517i | \(0.636452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.1052 | 0.978320 | 0.489160 | − | 0.872194i | \(-0.337303\pi\) | ||||
0.489160 | + | 0.872194i | \(0.337303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.2093 | −1.10208 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −31.5787 | −1.90427 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3838 | 1.16466 | 0.582329 | − | 0.812954i | \(-0.302142\pi\) | ||||
0.582329 | + | 0.812954i | \(0.302142\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −19.4173 | −1.16248 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.93293 | −0.353929 | −0.176965 | − | 0.984217i | \(-0.556628\pi\) | ||||
−0.176965 | + | 0.984217i | \(0.556628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.4726 | 1.45474 | 0.727372 | − | 0.686243i | \(-0.240741\pi\) | ||||
0.727372 | + | 0.686243i | \(0.240741\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 51.2271 | 3.03443 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.26385 | −0.369743 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.39023 | −0.375896 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.9052 | 0.639272 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.27294 | 0.191207 | 0.0956036 | − | 0.995419i | \(-0.469522\pi\) | ||||
0.0956036 | + | 0.995419i | \(0.469522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 60.3507 | 3.51376 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.6303 | 1.08104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.99226 | 0.115215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.13401 | −0.353558 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.13844 | 0.122850 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.1131 | 1.15167 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.01264 | −0.514379 | −0.257189 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257189 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.9028 | 1.53045 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8784 | 1.01379 | 0.506896 | − | 0.862007i | \(-0.330793\pi\) | ||||
0.506896 | + | 0.862007i | \(0.330793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.1676 | −0.574709 | −0.287355 | − | 0.957824i | \(-0.592776\pi\) | ||||
−0.287355 | + | 0.957824i | \(0.592776\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 46.7126 | 2.63196 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.7938 | 1.33639 | 0.668196 | − | 0.743985i | \(-0.267067\pi\) | ||||
0.668196 | + | 0.743985i | \(0.267067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.7551 | 0.602169 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.41225 | 0.357897 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.3825 | −0.800263 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 32.3986 | 1.79715 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.2375 | 1.67214 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.5507 | −1.13300 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9231 | 1.53479 | 0.767395 | − | 0.641174i | \(-0.221552\pi\) | ||||
0.767395 | + | 0.641174i | \(0.221552\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −57.9228 | −3.17415 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −50.3158 | −2.74905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.1817 | 0.718055 | 0.359028 | − | 0.933327i | \(-0.383108\pi\) | ||||
0.359028 | + | 0.933327i | \(0.383108\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.6151 | 1.55416 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3148 | 0.558576 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1568 | −1.08837 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.00475 | −0.430961 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.2251 | 0.871007 | 0.435503 | − | 0.900187i | \(-0.356570\pi\) | ||||
0.435503 | + | 0.900187i | \(0.356570\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2122 | 0.600176 | 0.300088 | − | 0.953912i | \(-0.402984\pi\) | ||||
0.300088 | + | 0.953912i | \(0.402984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.1140 | −1.02023 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.1704 | −1.39291 | −0.696456 | − | 0.717600i | \(-0.745241\pi\) | ||||
−0.696456 | + | 0.717600i | \(0.745241\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −56.9521 | −3.02270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.5414 | −1.08717 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.09697 | 0.321786 | 0.160893 | − | 0.986972i | \(-0.448563\pi\) | ||||
0.160893 | + | 0.986972i | \(0.448563\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.496758 | 0.0261452 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.87010 | 0.465559 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −40.1540 | −2.10176 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.41993 | 0.0741196 | 0.0370598 | − | 0.999313i | \(-0.488201\pi\) | ||||
0.0370598 | + | 0.999313i | \(0.488201\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.1587 | −0.789132 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.2815 | −0.585706 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.02630 | 0.104918 | 0.0524590 | − | 0.998623i | \(-0.483294\pi\) | ||||
0.0524590 | + | 0.998623i | \(0.483294\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −72.1674 | −3.72671 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.0343 | −0.568296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0338 | −1.44000 | −0.719999 | − | 0.693975i | \(-0.755858\pi\) | ||||
−0.719999 | + | 0.693975i | \(0.755858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.6299 | 1.56922 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.45631 | 0.432097 | 0.216049 | − | 0.976383i | \(-0.430683\pi\) | ||||
0.216049 | + | 0.976383i | \(0.430683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.8145 | −1.26467 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.8445 | −0.754589 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.97459 | −0.505732 | −0.252866 | − | 0.967501i | \(-0.581373\pi\) | ||||
−0.252866 | + | 0.967501i | \(0.581373\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.24741 | 0.113656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.38069 | −0.321863 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −47.0362 | −2.36665 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.6900 | −1.49010 | −0.745050 | − | 0.667009i | \(-0.767574\pi\) | ||||
−0.745050 | + | 0.667009i | \(0.767574\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 27.8457 | 1.39403 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.99761 | 0.299507 | 0.149753 | − | 0.988723i | \(-0.452152\pi\) | ||||
0.149753 | + | 0.988723i | \(0.452152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.5826 | −0.527155 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7865 | 0.635364 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.7696 | 1.52519 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.76904 | 0.0874734 | 0.0437367 | − | 0.999043i | \(-0.486074\pi\) | ||||
0.0437367 | + | 0.999043i | \(0.486074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.0512 | 0.643767 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 32.8051 | 1.61423 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21.6727 | −1.06387 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.7632 | −1.89824 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −23.5304 | −1.14954 | −0.574768 | − | 0.818317i | \(-0.694908\pi\) | ||||
−0.574768 | + | 0.818317i | \(0.694908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8726 | −0.822322 | −0.411161 | − | 0.911563i | \(-0.634877\pi\) | ||||
−0.411161 | + | 0.911563i | \(0.634877\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −49.7334 | −2.41812 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 36.5480 | 1.77284 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.9329 | 0.529082 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.4092 | 1.13021 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.7006 | −1.43063 | −0.715314 | − | 0.698803i | \(-0.753716\pi\) | ||||
−0.715314 | + | 0.698803i | \(0.753716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.97169 | 0.0947536 | 0.0473768 | − | 0.998877i | \(-0.484914\pi\) | ||||
0.0473768 | + | 0.998877i | \(0.484914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 44.3352 | 2.12571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.04657 | −0.145737 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.8492 | 1.42462 | 0.712311 | − | 0.701864i | \(-0.247648\pi\) | ||||
0.712311 | + | 0.701864i | \(0.247648\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.6942 | −0.556868 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.0344 | 0.904350 | 0.452175 | − | 0.891929i | \(-0.350648\pi\) | ||||
0.452175 | + | 0.891929i | \(0.350648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0475 | −1.13996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.2546 | −0.532325 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.8222 | −1.31301 | −0.656504 | − | 0.754322i | \(-0.727966\pi\) | ||||
−0.656504 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.05257 | 0.379181 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −42.5456 | −1.99897 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.4588 | 1.19353 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.03433 | −0.0483839 | −0.0241919 | − | 0.999707i | \(-0.507701\pi\) | ||||
−0.0241919 | + | 0.999707i | \(0.507701\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.5621 | −1.00643 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.01510 | −0.0938528 | −0.0469264 | − | 0.998898i | \(-0.514943\pi\) | ||||
−0.0469264 | + | 0.998898i | \(0.514943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4114 | 1.27392 | 0.636958 | − | 0.770899i | \(-0.280193\pi\) | ||||
0.636958 | + | 0.770899i | \(0.280193\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.5201 | 1.97182 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −40.5519 | −1.87652 | −0.938259 | − | 0.345934i | \(-0.887562\pi\) | ||||
−0.938259 | + | 0.345934i | \(0.887562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.3504 | −1.26292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2059 | −0.516339 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.88566 | 0.362583 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −49.5441 | −2.27324 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −27.3016 | −1.25005 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6003 | −1.30678 | −0.653390 | − | 0.757022i | \(-0.726654\pi\) | ||||
−0.653390 | + | 0.757022i | \(0.726654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.5684 | −1.43940 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.35118 | −0.197985 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.2467 | −0.692319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.75337 | 0.124767 | 0.0623836 | − | 0.998052i | \(-0.480130\pi\) | ||||
0.0623836 | + | 0.998052i | \(0.480130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.6074 | −0.570124 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 43.3598 | 1.95680 | 0.978400 | − | 0.206720i | \(-0.0662789\pi\) | ||||
0.978400 | + | 0.206720i | \(0.0662789\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.4475 | −0.560609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60.0520 | −2.69914 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.9577 | −1.38864 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.8056 | 1.87148 | 0.935738 | − | 0.352695i | \(-0.114735\pi\) | ||||
0.935738 | + | 0.352695i | \(0.114735\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.8306 | −2.22627 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.51368 | 0.0674916 | 0.0337458 | − | 0.999430i | \(-0.489256\pi\) | ||||
0.0337458 | + | 0.999430i | \(0.489256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.98980 | −0.133044 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.4312 | 0.596500 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.94261 | 0.0861047 | 0.0430523 | − | 0.999073i | \(-0.486292\pi\) | ||||
0.0430523 | + | 0.999073i | \(0.486292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.8267 | −0.965556 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 29.2293 | 1.29050 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.6134 | −1.65744 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.4192 | 1.16192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.2058 | −0.886936 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.4113 | 0.806614 | 0.403307 | − | 0.915065i | \(-0.367861\pi\) | ||||
0.403307 | + | 0.915065i | \(0.367861\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.3274 | 0.582768 | 0.291384 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291384 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −70.7600 | −3.08822 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.9379 | −0.520024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5239 | −0.979302 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 79.3895 | 3.44521 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.26163 | −0.357851 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.96511 | −0.387595 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 63.0756 | 2.72191 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.21217 | 0.267577 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.6613 | −1.27524 | −0.637619 | − | 0.770352i | \(-0.720081\pi\) | ||||
−0.637619 | + | 0.770352i | \(0.720081\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.7433 | −1.70555 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −42.2757 | −1.81089 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.2208 | −0.736308 | −0.368154 | − | 0.929765i | \(-0.620010\pi\) | ||||
−0.368154 | + | 0.929765i | \(0.620010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 26.4581 | 1.12920 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.8737 | 0.718846 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.5677 | −1.08725 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 126.840 | 5.38405 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.2886 | 1.19863 | 0.599314 | − | 0.800514i | \(-0.295440\pi\) | ||||
0.599314 | + | 0.800514i | \(0.295440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.09039 | −0.342187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.4073 | 1.11492 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −27.8785 | −1.17494 | −0.587469 | − | 0.809247i | \(-0.699875\pi\) | ||||
−0.587469 | + | 0.809247i | \(0.699875\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −40.0074 | −1.68312 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.95039 | 0.291889 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.7995 | 0.704270 | 0.352135 | − | 0.935949i | \(-0.385456\pi\) | ||||
0.352135 | + | 0.935949i | \(0.385456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.8780 | −0.999263 | −0.499632 | − | 0.866238i | \(-0.666531\pi\) | ||||
−0.499632 | + | 0.866238i | \(0.666531\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.1571 | 1.38516 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.74177 | 0.322854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.91836 | −0.0798622 | −0.0399311 | − | 0.999202i | \(-0.512714\pi\) | ||||
−0.0399311 | + | 0.999202i | \(0.512714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.3472 | −1.17807 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.7807 | −0.488747 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5031 | 0.600655 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 61.6111 | 2.54731 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.7367 | 1.22736 | 0.613682 | − | 0.789553i | \(-0.289688\pi\) | ||||
0.613682 | + | 0.789553i | \(0.289688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.1829 | 0.666806 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.9965 | −1.72750 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.05925 | 0.0845634 | 0.0422817 | − | 0.999106i | \(-0.486537\pi\) | ||||
0.0422817 | + | 0.999106i | \(0.486537\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.7194 | 1.17738 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.7632 | −1.46369 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.3144 | −1.11604 | −0.558019 | − | 0.829828i | \(-0.688438\pi\) | ||||
−0.558019 | + | 0.829828i | \(0.688438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.5811 | 0.513192 | 0.256596 | − | 0.966519i | \(-0.417399\pi\) | ||||
0.256596 | + | 0.966519i | \(0.417399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.1889 | −2.69542 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.4015 | −0.504192 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3640 | 0.583018 | 0.291509 | − | 0.956568i | \(-0.405843\pi\) | ||||
0.291509 | + | 0.956568i | \(0.405843\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0995 | 0.976560 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.1051 | −1.09656 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.1018 | −1.66008 | −0.830042 | − | 0.557700i | \(-0.811684\pi\) | ||||
−0.830042 | + | 0.557700i | \(0.811684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 33.1947 | 1.33854 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.6348 | 1.39434 | 0.697172 | − | 0.716904i | \(-0.254441\pi\) | ||||
0.697172 | + | 0.716904i | \(0.254441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.4686 | −1.18444 | −0.592221 | − | 0.805776i | \(-0.701749\pi\) | ||||
−0.592221 | + | 0.805776i | \(0.701749\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.56738 | −0.183282 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.0716 | −0.523704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.7965 | 1.79186 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.7974 | −1.42961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −35.6115 | −1.41992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.4432 | 0.973067 | 0.486533 | − | 0.873662i | \(-0.338261\pi\) | ||||
0.486533 | + | 0.873662i | \(0.338261\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.9901 | −0.874028 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −42.8243 | −1.69943 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.37346 | −0.252525 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −74.9187 | −2.96374 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.30973 | −0.328214 | −0.164107 | − | 0.986443i | \(-0.552474\pi\) | ||||
−0.164107 | + | 0.986443i | \(0.552474\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.8173 | 1.80686 | 0.903429 | − | 0.428738i | \(-0.141042\pi\) | ||||
0.903429 | + | 0.428738i | \(0.141042\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.5067 | 1.27995 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8809 | −1.21405 | −0.607027 | − | 0.794681i | \(-0.707638\pi\) | ||||
−0.607027 | + | 0.794681i | \(0.707638\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.1730 | −1.65544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.1128 | 0.905863 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.0073 | −1.21341 | −0.606705 | − | 0.794927i | \(-0.707509\pi\) | ||||
−0.606705 | + | 0.794927i | \(0.707509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.92097 | 0.348571 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −52.8214 | −2.06076 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.4937 | 0.603549 | 0.301774 | − | 0.953379i | \(-0.402421\pi\) | ||||
0.301774 | + | 0.953379i | \(0.402421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.28068 | 0.244290 | 0.122145 | − | 0.992512i | \(-0.461023\pi\) | ||||
0.122145 | + | 0.992512i | \(0.461023\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.0929 | −1.05220 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −38.9317 | −1.50971 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.63669 | −0.102093 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 63.1949 | 2.44325 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0550 | −0.542586 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.7391 | −0.452509 | −0.226255 | − | 0.974068i | \(-0.572648\pi\) | ||||
−0.226255 | + | 0.974068i | \(0.572648\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −74.2759 | −2.85888 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.2012 | 1.04543 | 0.522713 | − | 0.852509i | \(-0.324920\pi\) | ||||
0.522713 | + | 0.852509i | \(0.324920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.28774 | −0.318054 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −82.1893 | −3.14950 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.7803 | −0.909927 | −0.454963 | − | 0.890510i | \(-0.650348\pi\) | ||||
−0.454963 | + | 0.890510i | \(0.650348\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2471 | −0.697187 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −45.6838 | −1.74295 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.8796 | −0.566868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5877 | −0.440815 | −0.220408 | − | 0.975408i | \(-0.570739\pi\) | ||||
−0.220408 | + | 0.975408i | \(0.570739\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.6427 | −1.23999 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 54.1956 | 2.05576 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.31973 | −0.353010 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −58.5867 | −2.21595 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0421 | 0.870288 | 0.435144 | − | 0.900361i | \(-0.356697\pi\) | ||||
0.435144 | + | 0.900361i | \(0.356697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.2746 | 1.82071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 108.907 | 4.10166 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.62518 | −0.0611211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.87677 | 0.370930 | 0.185465 | − | 0.982651i | \(-0.440621\pi\) | ||||
0.185465 | + | 0.982651i | \(0.440621\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −61.8746 | −2.32048 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.52875 | −0.0947023 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.7289 | −1.22399 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.7131 | −0.848237 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.9798 | 0.707826 | 0.353913 | − | 0.935278i | \(-0.384851\pi\) | ||||
0.353913 | + | 0.935278i | \(0.384851\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.4457 | −0.761436 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.44074 | 0.127963 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.8786 | −1.59247 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.7037 | −0.990385 | −0.495193 | − | 0.868783i | \(-0.664903\pi\) | ||||
−0.495193 | + | 0.868783i | \(0.664903\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.3863 | −1.49579 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.12656 | −0.337558 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.0068 | 1.84704 | 0.923521 | − | 0.383548i | \(-0.125298\pi\) | ||||
0.923521 | + | 0.383548i | \(0.125298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 25.6081 | 0.944570 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.1606 | 1.29516 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.6690 | −1.09139 | −0.545696 | − | 0.837983i | \(-0.683735\pi\) | ||||
−0.545696 | + | 0.837983i | \(0.683735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.7268 | 1.34919 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.0775 | 1.91054 | 0.955269 | − | 0.295739i | \(-0.0955659\pi\) | ||||
0.955269 | + | 0.295739i | \(0.0955659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.7353 | 0.576497 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −28.5098 | −1.04312 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.87320 | −0.178063 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.3957 | −0.452327 | −0.226164 | − | 0.974089i | \(-0.572618\pi\) | ||||
−0.226164 | + | 0.974089i | \(0.572618\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.8300 | −0.576877 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 59.4839 | 2.16484 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7010 | −1.33392 | −0.666961 | − | 0.745093i | \(-0.732405\pi\) | ||||
−0.666961 | + | 0.745093i | \(0.732405\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.59371 | 0.203039 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.3328 | −1.38956 | −0.694781 | − | 0.719222i | \(-0.744499\pi\) | ||||
−0.694781 | + | 0.719222i | \(0.744499\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.9800 | −0.831932 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 69.5019 | 2.51285 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 43.2679 | 1.56231 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.5522 | 1.10174 | 0.550871 | − | 0.834590i | \(-0.314296\pi\) | ||||
0.550871 | + | 0.834590i | \(0.314296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.9942 | 1.83651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.3474 | −0.516040 | −0.258020 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258020 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.1232 | −1.47719 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 68.9469 | 2.47346 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.6337 | 0.452651 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.7981 | 1.42409 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 25.2969 | 0.904037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.6672 | 0.559185 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.1073 | −1.35838 | −0.679189 | − | 0.733964i | \(-0.737668\pi\) | ||||
−0.679189 | + | 0.733964i | \(0.737668\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 70.8995 | 2.52409 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.7470 | −0.773233 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.4199 | 0.512065 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 59.7853 | 2.12037 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.5254 | 0.691625 | 0.345813 | − | 0.938304i | \(-0.387603\pi\) | ||||
0.345813 | + | 0.938304i | \(0.387603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.5766 | −1.08172 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.6338 | −1.11773 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.0596 | 0.990201 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.08348 | 0.214414 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.2771 | 1.38262 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.6321 | −0.619910 | −0.309955 | − | 0.950751i | \(-0.600314\pi\) | ||||
−0.309955 | + | 0.950751i | \(0.600314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.35861 | 0.153052 | 0.0765258 | − | 0.997068i | \(-0.475617\pi\) | ||||
0.0765258 | + | 0.997068i | \(0.475617\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.3930 | −1.62707 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.6266 | 0.617433 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3719 | 0.432837 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 33.4902 | 1.17024 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.14538 | −0.179575 | −0.0897875 | − | 0.995961i | \(-0.528619\pi\) | ||||
−0.0897875 | + | 0.995961i | \(0.528619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.6339 | 1.93928 | 0.969638 | − | 0.244544i | \(-0.0786382\pi\) | ||||
0.969638 | + | 0.244544i | \(0.0786382\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 90.9665 | 3.16705 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8159 | 1.10635 | 0.553173 | − | 0.833066i | \(-0.313417\pi\) | ||||
0.553173 | + | 0.833066i | \(0.313417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.8243 | 1.52208 | 0.761041 | − | 0.648704i | \(-0.224689\pi\) | ||||
0.761041 | + | 0.648704i | \(0.224689\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −55.8373 | −1.93698 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.18973 | −0.249109 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 69.6693 | 2.41100 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.2612 | 0.838591 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.8342 | 0.650230 | 0.325115 | − | 0.945675i | \(-0.394597\pi\) | ||||
0.325115 | + | 0.945675i | \(0.394597\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3964 | −0.496427 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.0906 | 0.588630 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.7784 | −0.645998 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.74112 | −0.231628 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70.4964 | −2.41943 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.54340 | −0.258584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.32013 | 0.0794397 | 0.0397199 | − | 0.999211i | \(-0.487353\pi\) | ||||
0.0397199 | + | 0.999211i | \(0.487353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −94.2161 | −3.22212 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1104 | −0.550320 | −0.275160 | − | 0.961398i | \(-0.588731\pi\) | ||||
−0.275160 | + | 0.961398i | \(0.588731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.3512 | 1.44500 | 0.722502 | − | 0.691369i | \(-0.242992\pi\) | ||||
0.722502 | + | 0.691369i | \(0.242992\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0438 | 0.614931 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.2014 | 0.347259 | 0.173629 | − | 0.984811i | \(-0.444451\pi\) | ||||
0.173629 | + | 0.984811i | \(0.444451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2501 | 0.960534 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.4079 | 0.625163 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.8688 | 1.11500 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0735 | −1.22230 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.0566 | −0.678813 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 54.8460 | 1.85413 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.3354 | −1.02435 | −0.512177 | − | 0.858880i | \(-0.671161\pi\) | ||||
−0.512177 | + | 0.858880i | \(0.671161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.42811 | −0.318002 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.4805 | 1.16168 | 0.580839 | − | 0.814018i | \(-0.302724\pi\) | ||||
0.580839 | + | 0.814018i | \(0.302724\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.2115 | −0.713824 | −0.356912 | − | 0.934138i | \(-0.616170\pi\) | ||||
−0.356912 | + | 0.934138i | \(0.616170\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −173.848 | −5.84383 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.0321 | 1.41130 | 0.705650 | − | 0.708560i | \(-0.250655\pi\) | ||||
0.705650 | + | 0.708560i | \(0.250655\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23.2782 | −0.780726 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.93517 | −0.299339 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.4493 | 1.38705 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −88.1874 | −2.94778 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.73894 | −0.191618 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.0057 | 0.467118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.7853 | −0.559199 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.6698 | 0.588014 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.5660 | 1.84708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.9833 | −0.563922 | −0.281961 | − | 0.959426i | \(-0.590985\pi\) | ||||
−0.281961 | + | 0.959426i | \(0.590985\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.93299 | −0.130449 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0992 | −0.699048 | −0.349524 | − | 0.936927i | \(-0.613657\pi\) | ||||
−0.349524 | + | 0.936927i | \(0.613657\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.1449 | 0.501222 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −57.9382 | −1.91538 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.84921 | 0.160135 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.8808 | 0.622819 | 0.311409 | − | 0.950276i | \(-0.399199\pi\) | ||||
0.311409 | + | 0.950276i | \(0.399199\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.9620 | 0.855478 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −40.8313 | −1.34398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −122.673 | −4.03346 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.4792 | −1.62511 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.1420 | 0.332749 | 0.166375 | − | 0.986063i | \(-0.446794\pi\) | ||||
0.166375 | + | 0.986063i | \(0.446794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.74632 | 0.319423 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −51.5010 | −1.68607 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.9206 | −1.20743 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.5444 | 1.74922 | 0.874610 | − | 0.484828i | \(-0.161118\pi\) | ||||
0.874610 | + | 0.484828i | \(0.161118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.2892 | 0.955816 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.6888 | −1.26122 | −0.630610 | − | 0.776100i | \(-0.717195\pi\) | ||||
−0.630610 | + | 0.776100i | \(0.717195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.97415 | −0.0642872 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −58.3659 | −1.89864 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.4543 | 0.534694 | 0.267347 | − | 0.963600i | \(-0.413853\pi\) | ||||
0.267347 | + | 0.963600i | \(0.413853\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.7881 | −0.934501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −68.5410 | −2.22259 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.87484 | 0.190305 | 0.0951523 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951523 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.3576 | −1.50010 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.9814 | −1.00149 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.91867 | −0.320291 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.5677 | −0.566699 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.7933 | −0.380034 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.6329 | 1.27583 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.31660 | 0.138812 | 0.0694062 | − | 0.997588i | \(-0.477890\pi\) | ||||
0.0694062 | + | 0.997588i | \(0.477890\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.4306 | 1.33094 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.7700 | 0.570266 | 0.285133 | − | 0.958488i | \(-0.407962\pi\) | ||||
0.285133 | + | 0.958488i | \(0.407962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.4594 | 0.944424 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −93.3282 | −2.98889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.3810 | 1.61183 | 0.805916 | − | 0.592030i | \(-0.201673\pi\) | ||||
0.805916 | + | 0.592030i | \(0.201673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.8044 | 0.537071 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55.6124 | −1.77557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.7248 | −1.26702 | −0.633512 | − | 0.773733i | \(-0.718387\pi\) | ||||
−0.633512 | + | 0.773733i | \(0.718387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58.7161 | 1.87085 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 59.1988 | 1.88432 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.93323 | −0.0614731 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.4204 | −0.775740 | −0.387870 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387870 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −80.4359 | −2.55256 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.0013 | 1.58515 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.3298 | 1.18225 | 0.591123 | − | 0.806582i | \(-0.298685\pi\) | ||||
0.591123 | + | 0.806582i | \(0.298685\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 72.3727 | 2.28977 |
(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 | 8044.2.a.a.1.7 | ✓ | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8044.2.a.a.1.7 | ✓ | 80 | 1.1 | even | 1 | trivial |