Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (of order \(6\), degree \(2\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Character | \(\chi\) | \(=\) | 224.17 |
Dual form | 224.3.n.a.145.4 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −1.70138 | + | 2.94687i | −0.567126 | + | 0.982291i | 0.429722 | + | 0.902961i | \(0.358612\pi\) |
−0.996848 | + | 0.0793303i | \(0.974722\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.15858 | − | 3.73877i | −0.431716 | − | 0.747754i | 0.565305 | − | 0.824882i | \(-0.308758\pi\) |
−0.997021 | + | 0.0771275i | \(0.975425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.43197 | + | 6.85197i | 0.204567 | + | 0.978853i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.28938 | − | 2.23327i | −0.143264 | − | 0.248141i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.4899 | − | 8.94308i | −1.40817 | − | 0.813007i | −0.412958 | − | 0.910750i | \(-0.635504\pi\) |
−0.995212 | + | 0.0977432i | \(0.968838\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.25607 | −0.250467 | −0.125233 | − | 0.992127i | \(-0.539968\pi\) | ||||
−0.125233 | + | 0.992127i | \(0.539968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 14.6903 | 0.979350 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.6263 | − | 7.86717i | −0.801550 | − | 0.462775i | 0.0424631 | − | 0.999098i | \(-0.486479\pi\) |
−0.844013 | + | 0.536323i | \(0.819813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.778522 | + | 1.34844i | 0.0409748 | + | 0.0709705i | 0.885786 | − | 0.464095i | \(-0.153620\pi\) |
−0.844811 | + | 0.535065i | \(0.820287\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −22.6282 | − | 7.43796i | −1.07753 | − | 0.354188i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −20.7069 | − | 35.8655i | −0.900301 | − | 1.55937i | −0.827103 | − | 0.562050i | \(-0.810013\pi\) |
−0.0731984 | − | 0.997317i | \(-0.523321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.18105 | − | 5.50975i | 0.127242 | − | 0.220390i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −21.8499 | −0.809257 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.74374i | 0.129095i | 0.997915 | + | 0.0645473i | \(0.0205603\pi\) | ||||
−0.997915 | + | 0.0645473i | \(0.979440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0145172 | + | 0.00838150i | 0.000468296 | + | 0.000270371i | 0.500234 | − | 0.865890i | \(-0.333247\pi\) |
−0.499766 | + | 0.866161i | \(0.666581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52.7082 | − | 30.4311i | 1.59722 | − | 0.922155i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.5269 | − | 20.1443i | 0.643626 | − | 0.575553i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.16774 | − | 0.674194i | 0.0315605 | − | 0.0182215i | −0.484137 | − | 0.874992i | \(-0.660866\pi\) |
0.515697 | + | 0.856771i | \(0.327533\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.53981 | − | 9.59523i | 0.142046 | − | 0.246031i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.3018i | 1.71468i | 0.514753 | + | 0.857339i | \(0.327884\pi\) | ||||
−0.514753 | + | 0.857339i | \(0.672116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0380i | 0.303210i | 0.988441 | + | 0.151605i | \(0.0484442\pi\) | ||||
−0.988441 | + | 0.151605i | \(0.951556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.56646 | + | 9.64139i | −0.123699 | + | 0.214253i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −30.9797 | + | 17.8862i | −0.659144 | + | 0.380557i | −0.791951 | − | 0.610585i | \(-0.790934\pi\) |
0.132807 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.8989 | + | 19.6236i | −0.916305 | + | 0.400482i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 46.3671 | − | 26.7701i | 0.909160 | − | 0.524904i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −39.7989 | − | 22.9779i | −0.750923 | − | 0.433546i | 0.0751042 | − | 0.997176i | \(-0.476071\pi\) |
−0.826027 | + | 0.563630i | \(0.809404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 77.2174i | 1.40395i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.29824 | −0.0929516 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.3509 | + | 59.4974i | −0.582218 | + | 1.00843i | 0.412998 | + | 0.910732i | \(0.364482\pi\) |
−0.995216 | + | 0.0976993i | \(0.968852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 48.0386 | + | 83.2052i | 0.787517 | + | 1.36402i | 0.927484 | + | 0.373864i | \(0.121967\pi\) |
−0.139966 | + | 0.990156i | \(0.544699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.4559 | − | 12.0328i | 0.213586 | − | 0.190996i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.02849 | + | 12.1737i | 0.108131 | + | 0.187288i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0808 | + | 6.97484i | 0.180310 | + | 0.104102i | 0.587438 | − | 0.809269i | \(-0.300136\pi\) |
−0.407128 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 140.921 | 2.04234 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 75.7095 | 1.06633 | 0.533166 | − | 0.846011i | \(-0.321002\pi\) | ||||
0.533166 | + | 0.846011i | \(0.321002\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −46.0282 | − | 26.5744i | −0.630523 | − | 0.364033i | 0.150432 | − | 0.988620i | \(-0.451934\pi\) |
−0.780955 | + | 0.624588i | \(0.785267\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.8244 | + | 18.7483i | 0.144325 | + | 0.249978i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 39.0967 | − | 118.942i | 0.507749 | − | 1.54470i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6744 | − | 20.2206i | −0.147777 | − | 0.255957i | 0.782628 | − | 0.622489i | \(-0.213878\pi\) |
−0.930406 | + | 0.366532i | \(0.880545\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 48.7794 | − | 84.4884i | 0.602215 | − | 1.04307i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 102.487 | 1.23479 | 0.617393 | − | 0.786655i | \(-0.288189\pi\) | ||||
0.617393 | + | 0.786655i | \(0.288189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 67.9277i | 0.799150i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.0323 | − | 6.36952i | −0.126808 | − | 0.0732129i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −76.6985 | + | 44.2819i | −0.861781 | + | 0.497549i | −0.864608 | − | 0.502447i | \(-0.832433\pi\) |
0.00282755 | + | 0.999996i | \(0.499100\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.66259 | − | 22.3105i | −0.0512373 | − | 0.245170i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0493984 | + | 0.0285202i | −0.000531166 | + | 0.000306669i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.36100 | − | 5.82143i | 0.0353790 | − | 0.0612782i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 140.869i | − | 1.45226i | −0.687558 | − | 0.726130i | \(-0.741317\pi\) | ||
0.687558 | − | 0.726130i | \(-0.258683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 46.1241i | 0.465900i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.6988 | + | 30.6553i | −0.175236 | + | 0.303518i | −0.940243 | − | 0.340504i | \(-0.889402\pi\) |
0.765007 | + | 0.644022i | \(0.222735\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −87.1651 | + | 50.3248i | −0.846263 | + | 0.488590i | −0.859388 | − | 0.511324i | \(-0.829155\pi\) |
0.0131250 | + | 0.999914i | \(0.495822\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.0360 | + | 100.657i | 0.200343 | + | 0.958640i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 92.6215 | − | 53.4751i | 0.865622 | − | 0.499767i | −0.000269099 | − | 1.00000i | \(-0.500086\pi\) |
0.865891 | + | 0.500233i | \(0.166752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −45.5799 | − | 26.3156i | −0.418165 | − | 0.241427i | 0.276127 | − | 0.961121i | \(-0.410949\pi\) |
−0.694292 | + | 0.719694i | \(0.744282\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.58824i | 0.0413355i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 45.4346 | 0.402076 | 0.201038 | − | 0.979583i | \(-0.435568\pi\) | ||||
0.201038 | + | 0.979583i | \(0.435568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −89.3952 | + | 154.837i | −0.777350 | + | 1.34641i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.19831 | + | 7.27168i | 0.0358830 | + | 0.0621511i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.3931 | − | 104.633i | 0.289018 | − | 0.879267i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 99.4572 | + | 172.265i | 0.821961 | + | 1.42368i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −207.171 | − | 119.610i | −1.68431 | − | 0.972439i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −135.395 | −1.08316 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −125.695 | −0.989723 | −0.494861 | − | 0.868972i | \(-0.664781\pi\) | ||||
−0.494861 | + | 0.868972i | \(0.664781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −38.4215 | − | 22.1827i | −0.297841 | − | 0.171959i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −56.6504 | − | 98.1214i | −0.432446 | − | 0.749018i | 0.564638 | − | 0.825339i | \(-0.309016\pi\) |
−0.997083 | + | 0.0763210i | \(0.975683\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.12464 | + | 7.26533i | −0.0610875 | + | 0.0546265i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 47.1648 | + | 81.6919i | 0.349369 | + | 0.605125i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −39.1679 | + | 67.8408i | −0.285897 | + | 0.495188i | −0.972826 | − | 0.231536i | \(-0.925625\pi\) |
0.686929 | + | 0.726724i | \(0.258958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 149.038 | 1.07222 | 0.536109 | − | 0.844149i | \(-0.319894\pi\) | ||||
0.536109 | + | 0.844149i | \(0.319894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 121.725i | − | 0.863295i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 50.4361 | + | 29.1193i | 0.352700 | + | 0.203631i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.9970 | − | 8.08117i | 0.0965310 | − | 0.0557322i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.5617 | − | 165.699i | 0.126270 | − | 1.12720i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −73.8369 | + | 42.6298i | −0.495550 | + | 0.286106i | −0.726874 | − | 0.686771i | \(-0.759028\pi\) |
0.231324 | + | 0.972877i | \(0.425694\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 65.9012 | − | 114.144i | 0.436432 | − | 0.755922i | −0.560979 | − | 0.827830i | \(-0.689575\pi\) |
0.997411 | + | 0.0719076i | \(0.0229087\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.5751i | 0.265197i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.0723686i | − | 0.000466894i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −122.552 | + | 212.267i | −0.780589 | + | 1.35202i | 0.151010 | + | 0.988532i | \(0.451747\pi\) |
−0.931599 | + | 0.363487i | \(0.881586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 135.426 | − | 78.1883i | 0.851737 | − | 0.491750i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 216.097 | − | 193.241i | 1.34222 | − | 1.20026i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −208.089 | + | 120.140i | −1.27662 | + | 0.737057i | −0.976225 | − | 0.216758i | \(-0.930452\pi\) |
−0.300395 | + | 0.953815i | \(0.597118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −227.550 | − | 131.376i | −1.37909 | − | 0.796219i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 73.1965i | − | 0.438302i | −0.975691 | − | 0.219151i | \(-0.929671\pi\) | ||
0.975691 | − | 0.219151i | \(-0.0703288\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −158.398 | −0.937266 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00762 | − | 3.47730i | 0.0117405 | − | 0.0203351i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.5246 | + | 32.0855i | 0.107078 | + | 0.185465i | 0.914585 | − | 0.404393i | \(-0.132517\pi\) |
−0.807507 | + | 0.589858i | \(0.799184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 42.3078 | + | 13.9067i | 0.241759 | + | 0.0794668i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −116.888 | − | 202.455i | −0.660382 | − | 1.14382i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −205.982 | − | 118.924i | −1.15074 | − | 0.664379i | −0.201672 | − | 0.979453i | \(-0.564637\pi\) |
−0.949067 | + | 0.315074i | \(0.897971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 292.553 | 1.61631 | 0.808157 | − | 0.588966i | \(-0.200465\pi\) | ||||
0.808157 | + | 0.588966i | \(0.200465\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −326.927 | −1.78649 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.04132 | − | 2.91061i | −0.0272504 | − | 0.0157330i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 140.713 | + | 243.723i | 0.752478 | + | 1.30333i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −31.2884 | − | 149.715i | −0.165547 | − | 0.792143i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 70.6135 | + | 122.306i | 0.369704 | + | 0.640346i | 0.989519 | − | 0.144402i | \(-0.0461257\pi\) |
−0.619815 | + | 0.784748i | \(0.712792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 32.9799 | − | 57.1229i | 0.170880 | − | 0.295973i | −0.767848 | − | 0.640633i | \(-0.778672\pi\) |
0.938728 | + | 0.344659i | \(0.112006\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −47.8325 | −0.245295 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 199.421i | − | 1.01229i | −0.862448 | − | 0.506145i | \(-0.831070\pi\) | ||
0.862448 | − | 0.506145i | \(-0.168930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −58.6230 | − | 33.8460i | −0.294588 | − | 0.170080i | 0.345421 | − | 0.938448i | \(-0.387736\pi\) |
−0.640009 | + | 0.768367i | \(0.721069\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −41.1079 | + | 23.7337i | −0.204517 | + | 0.118078i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.6520 | + | 5.36092i | −0.126365 | + | 0.0264085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 262.842 | − | 151.752i | 1.28216 | − | 0.740254i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −53.3982 | + | 92.4884i | −0.257962 | + | 0.446804i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 27.8495i | − | 0.133251i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 62.1464i | 0.294533i | 0.989097 | + | 0.147266i | \(0.0470475\pi\) | ||||
−0.989097 | + | 0.147266i | \(0.952953\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −128.811 | + | 223.106i | −0.604744 | + | 1.04745i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 48.7463 | − | 28.1437i | 0.226727 | − | 0.130901i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0366416 | + | 0.111473i | −0.000168855 | + | 0.000513702i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 156.623 | − | 90.4261i | 0.715172 | − | 0.412905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 44.3683 | + | 25.6161i | 0.200762 | + | 0.115910i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 115.525i | − | 0.518050i | −0.965871 | − | 0.259025i | \(-0.916599\pi\) | ||
0.965871 | − | 0.259025i | \(-0.0834012\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.4063 | −0.0729171 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.2532 | − | 48.9360i | 0.124463 | − | 0.215577i | −0.797060 | − | 0.603901i | \(-0.793612\pi\) |
0.921523 | + | 0.388324i | \(0.126946\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −59.1696 | − | 102.485i | −0.258383 | − | 0.447532i | 0.707426 | − | 0.706787i | \(-0.249856\pi\) |
−0.965809 | + | 0.259255i | \(0.916523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 283.990 | + | 317.579i | 1.22939 | + | 1.37480i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3403 | + | 21.3740i | 0.0529625 | + | 0.0917337i | 0.891291 | − | 0.453431i | \(-0.149800\pi\) |
−0.838329 | + | 0.545165i | \(0.816467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 133.745 | + | 77.2175i | 0.569126 | + | 0.328585i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 79.4503 | 0.335233 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 251.189 | 1.05100 | 0.525499 | − | 0.850794i | \(-0.323879\pi\) | ||||
0.525499 | + | 0.850794i | \(0.323879\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 97.3782 | + | 56.2213i | 0.404059 | + | 0.233283i | 0.688234 | − | 0.725489i | \(-0.258386\pi\) |
−0.284175 | + | 0.958772i | \(0.591720\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 67.6598 | + | 117.190i | 0.278436 | + | 0.482265i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 170.286 | + | 125.508i | 0.695046 | + | 0.512276i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.53492 | − | 4.39061i | −0.0102628 | − | 0.0177758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −174.370 | + | 302.017i | −0.700280 | + | 1.21292i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 121.248 | 0.483059 | 0.241529 | − | 0.970394i | \(-0.422351\pi\) | ||||
0.241529 | + | 0.970394i | \(0.422351\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 740.735i | 2.92781i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −200.174 | − | 115.571i | −0.784998 | − | 0.453219i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −90.7377 | + | 52.3874i | −0.353065 | + | 0.203842i | −0.666034 | − | 0.745921i | \(-0.732010\pi\) |
0.312969 | + | 0.949763i | \(0.398676\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.29172 | + | 7.03588i | 0.0242924 | + | 0.0271656i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.36079 | − | 4.82710i | 0.0320337 | − | 0.0184946i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −52.3392 | + | 90.6542i | −0.199008 | + | 0.344693i | −0.948207 | − | 0.317653i | \(-0.897105\pi\) |
0.749199 | + | 0.662345i | \(0.230439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 198.399i | 0.748675i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 301.361i | − | 1.12869i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 152.466 | − | 264.079i | 0.566789 | − | 0.981707i | −0.430092 | − | 0.902785i | \(-0.641519\pi\) |
0.996881 | − | 0.0789222i | \(-0.0251479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −88.8942 | + | 51.3231i | −0.328023 | + | 0.189384i | −0.654963 | − | 0.755661i | \(-0.727316\pi\) |
0.326940 | + | 0.945045i | \(0.393982\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.6790 | + | 24.2185i | 0.269886 | + | 0.0887125i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −98.5482 | + | 56.8968i | −0.358357 | + | 0.206898i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4235 | − | 8.32739i | −0.0520703 | − | 0.0300628i | 0.473739 | − | 0.880665i | \(-0.342904\pi\) |
−0.525809 | + | 0.850603i | \(0.676237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.0432277i | − | 0.000154938i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 75.8291 | 0.269855 | 0.134927 | − | 0.990856i | \(-0.456920\pi\) | ||||
0.134927 | + | 0.990856i | \(0.456920\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 43.6656 | − | 75.6311i | 0.154296 | − | 0.267248i | −0.778507 | − | 0.627636i | \(-0.784023\pi\) |
0.932802 | + | 0.360389i | \(0.117356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.4367 | + | 19.8089i | 0.0401287 | + | 0.0695050i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −481.706 | + | 100.670i | −1.67842 | + | 0.350767i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.7152 | − | 35.8798i | −0.0716789 | − | 0.124151i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 415.124 | + | 239.672i | 1.42654 | + | 0.823614i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.5057 | −0.0938760 | −0.0469380 | − | 0.998898i | \(-0.514946\pi\) | ||||
−0.0469380 | + | 0.998898i | \(0.514946\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 296.597 | 1.00541 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 338.452 | + | 195.406i | 1.13957 | + | 0.657931i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 67.4232 | + | 116.780i | 0.225496 | + | 0.390570i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −89.3363 | + | 18.6701i | −0.296798 | + | 0.0620269i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −60.2248 | − | 104.312i | −0.198762 | − | 0.344266i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 207.390 | − | 359.211i | 0.679968 | − | 1.17774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 247.996 | 0.807805 | 0.403902 | − | 0.914802i | \(-0.367654\pi\) | ||||
0.403902 | + | 0.914802i | \(0.367654\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 342.486i | − | 1.10837i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −378.484 | − | 218.518i | −1.21699 | − | 0.702630i | −0.252717 | − | 0.967540i | \(-0.581324\pi\) |
−0.964273 | + | 0.264910i | \(0.914658\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −71.7330 | + | 41.4151i | −0.229179 | + | 0.132317i | −0.610193 | − | 0.792253i | \(-0.708908\pi\) |
0.381014 | + | 0.924569i | \(0.375575\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −74.0335 | − | 24.3350i | −0.235027 | − | 0.0772540i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 211.775 | − | 122.268i | 0.668059 | − | 0.385704i | −0.127282 | − | 0.991867i | \(-0.540625\pi\) |
0.795341 | + | 0.606162i | \(0.207292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.4806 | − | 57.9900i | 0.104955 | − | 0.181787i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 363.925i | 1.13372i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 24.4991i | − | 0.0758485i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.3577 | + | 17.9401i | −0.0318699 | + | 0.0552004i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 155.097 | − | 89.5456i | 0.474304 | − | 0.273840i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −166.917 | − | 186.660i | −0.507348 | − | 0.567355i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −66.2919 | + | 38.2736i | −0.200278 | + | 0.115630i | −0.596785 | − | 0.802401i | \(-0.703555\pi\) |
0.396507 | + | 0.918032i | \(0.370222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.01132 | − | 1.73858i | −0.00904299 | − | 0.00522097i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 60.2230i | − | 0.179770i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −38.2520 | −0.113507 | −0.0567537 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567537 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −77.3015 | + | 133.890i | −0.228028 | + | 0.394956i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.149913 | − | 0.259656i | −0.000439627 | − | 0.000761456i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −198.754 | − | 279.546i | −0.579459 | − | 0.815002i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −304.190 | − | 526.873i | −0.881711 | − | 1.52717i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −208.395 | − | 120.317i | −0.600561 | − | 0.346734i | 0.168701 | − | 0.985667i | \(-0.446043\pi\) |
−0.769262 | + | 0.638933i | \(0.779376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −430.367 | −1.23314 | −0.616572 | − | 0.787298i | \(-0.711479\pi\) | ||||
−0.616572 | + | 0.787298i | \(0.711479\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 71.1449 | 0.202692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −265.950 | − | 153.546i | −0.753399 | − | 0.434975i | 0.0735214 | − | 0.997294i | \(-0.476576\pi\) |
−0.826921 | + | 0.562318i | \(0.809910\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −163.425 | − | 283.061i | −0.460353 | − | 0.797354i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 249.824 | + | 279.372i | 0.699787 | + | 0.782555i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 230.880 | + | 399.896i | 0.643120 | + | 1.11392i | 0.984732 | + | 0.174075i | \(0.0556935\pi\) |
−0.341613 | + | 0.939841i | \(0.610973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 179.288 | − | 310.536i | 0.496642 | − | 0.860209i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −676.858 | −1.86462 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 229.452i | 0.628635i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 542.949 | + | 313.471i | 1.47942 | + | 0.854146i | 0.999729 | − | 0.0232895i | \(-0.00741394\pi\) |
0.479695 | + | 0.877435i | \(0.340747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 157.003 | − | 90.6457i | 0.425482 | − | 0.245652i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 100.453 | − | 305.605i | 0.270763 | − | 0.823732i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −357.317 | + | 206.297i | −0.957953 | + | 0.553075i | −0.895543 | − | 0.444976i | \(-0.853212\pi\) |
−0.0624108 | + | 0.998051i | \(0.519879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 230.359 | − | 398.993i | 0.614290 | − | 1.06398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 12.1899i | − | 0.0323339i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 327.118i | 0.863107i | 0.902087 | + | 0.431554i | \(0.142034\pi\) | ||||
−0.902087 | + | 0.431554i | \(0.857966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 213.854 | − | 370.407i | 0.561298 | − | 0.972196i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 215.523 | − | 124.432i | 0.562724 | − | 0.324889i | −0.191514 | − | 0.981490i | \(-0.561340\pi\) |
0.754238 | + | 0.656601i | \(0.228006\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −529.091 | + | 110.573i | −1.37426 | + | 0.287203i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.1175 | − | 16.8110i | 0.0752390 | − | 0.0434392i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 326.728 | + | 188.637i | 0.839918 | + | 0.484927i | 0.857236 | − | 0.514923i | \(-0.172179\pi\) |
−0.0173181 | + | 0.999850i | \(0.505513\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 651.620i | 1.66655i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 385.535 | 0.981005 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −50.4003 | + | 87.2958i | −0.127596 | + | 0.221002i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −335.874 | − | 581.752i | −0.846031 | − | 1.46537i | −0.884723 | − | 0.466118i | \(-0.845652\pi\) |
0.0386913 | − | 0.999251i | \(-0.487681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.58692 | − | 36.3034i | −0.0190148 | − | 0.0909859i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 235.200 | + | 407.378i | 0.586534 | + | 1.01591i | 0.994682 | + | 0.102991i | \(0.0328411\pi\) |
−0.408149 | + | 0.912915i | \(0.633826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0472689 | − | 0.0272907i | −0.000117293 | − | 6.77189e-5i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −421.177 | −1.03994 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.1175 | −0.0592567 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −57.7400 | − | 33.3362i | −0.141174 | − | 0.0815067i | 0.427750 | − | 0.903897i | \(-0.359307\pi\) |
−0.568923 | + | 0.822391i | \(0.692640\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −133.279 | − | 230.846i | −0.324279 | − | 0.561669i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −456.864 | − | 150.172i | −1.10621 | − | 0.363614i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −221.227 | − | 383.177i | −0.533077 | − | 0.923317i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −253.571 | + | 439.197i | −0.608083 | + | 1.05323i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −437.380 | −1.04387 | −0.521933 | − | 0.852986i | \(-0.674789\pi\) | ||||
−0.521933 | + | 0.852986i | \(0.674789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 703.800i | − | 1.67173i | −0.548933 | − | 0.835867i | \(-0.684966\pi\) | ||
0.548933 | − | 0.835867i | \(-0.315034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 79.8893 | + | 46.1241i | 0.188864 | + | 0.109040i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −86.6923 | + | 50.0518i | −0.203982 | + | 0.117769i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −501.330 | + | 448.306i | −1.17407 | + | 1.04990i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −171.622 | + | 99.0858i | −0.400051 | + | 0.230969i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −274.869 | + | 476.087i | −0.637747 | + | 1.10461i | 0.348178 | + | 0.937428i | \(0.386800\pi\) |
−0.985926 | + | 0.167183i | \(0.946533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 355.012i | − | 0.819890i | −0.912110 | − | 0.409945i | \(-0.865548\pi\) | ||
0.912110 | − | 0.409945i | \(-0.134452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 54.9965i | 0.126429i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.2416 | − | 55.8441i | 0.0737794 | − | 0.127790i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −477.032 | + | 275.415i | −1.08663 | + | 0.627369i | −0.932678 | − | 0.360709i | \(-0.882535\pi\) |
−0.153956 | + | 0.988078i | \(0.549201\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 101.717 | + | 74.9692i | 0.230650 | + | 0.169998i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −234.027 | + | 135.116i | −0.528278 | + | 0.305001i | −0.740315 | − | 0.672260i | \(-0.765324\pi\) |
0.212037 | + | 0.977262i | \(0.431990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 331.120 | + | 191.172i | 0.744089 | + | 0.429600i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 290.117i | − | 0.649032i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 455.397 | 1.01425 | 0.507124 | − | 0.861873i | \(-0.330709\pi\) | ||||
0.507124 | + | 0.861873i | \(0.330709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 628.714 | − | 1088.96i | 1.39404 | − | 2.41456i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 224.246 | + | 388.405i | 0.495024 | + | 0.857406i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −73.3492 | + | 65.5914i | −0.161207 | + | 0.144157i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 84.3172 | + | 146.042i | 0.184501 | + | 0.319566i | 0.943408 | − | 0.331633i | \(-0.107600\pi\) |
−0.758907 | + | 0.651199i | \(0.774266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 297.735 | + | 171.897i | 0.648659 | + | 0.374504i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −265.062 | −0.574971 | −0.287485 | − | 0.957785i | \(-0.592819\pi\) | ||||
−0.287485 | + | 0.957785i | \(0.592819\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −97.4735 | −0.210526 | −0.105263 | − | 0.994444i | \(-0.533568\pi\) | ||||
−0.105263 | + | 0.994444i | \(0.533568\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.213261 | + | 0.123126i | 0.000458626 | + | 0.000264788i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.0997 | − | 64.2586i | −0.0794427 | − | 0.137599i | 0.823567 | − | 0.567219i | \(-0.191981\pi\) |
−0.903010 | + | 0.429620i | \(0.858647\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.4921 | + | 92.7648i | −0.0650150 | + | 0.197793i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −417.016 | − | 722.293i | −0.885385 | − | 1.53353i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 116.600 | − | 201.958i | 0.246512 | − | 0.426972i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.90608 | 0.0208549 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 118.509i | 0.248447i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 475.220 | + | 274.368i | 0.992108 | + | 0.572794i | 0.905904 | − | 0.423484i | \(-0.139193\pi\) |
0.0862043 | + | 0.996277i | \(0.472526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.80224 | + | 2.19522i | −0.00790486 | + | 0.00456387i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 201.795 | + | 965.588i | 0.417795 | + | 1.99915i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −526.678 | + | 304.078i | −1.08593 | + | 0.626964i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 283.938 | − | 491.795i | 0.583034 | − | 1.00985i | −0.412083 | − | 0.911146i | \(-0.635199\pi\) |
0.995117 | − | 0.0986990i | \(-0.0314681\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 817.617i | − | 1.67202i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 78.8005i | − | 0.160490i | −0.996775 | − | 0.0802449i | \(-0.974430\pi\) | ||
0.996775 | − | 0.0802449i | \(-0.0255702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.4527 | − | 51.0135i | 0.0597417 | − | 0.103476i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 172.447 | − | 99.5626i | 0.348379 | − | 0.201136i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 108.414 | + | 518.759i | 0.218136 | + | 1.04378i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 290.932 | − | 167.970i | 0.583030 | − | 0.336612i | −0.179307 | − | 0.983793i | \(-0.557385\pi\) |
0.762337 | + | 0.647181i | \(0.224052\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 215.701 | + | 124.535i | 0.430541 | + | 0.248573i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 274.052i | − | 0.544836i | −0.962179 | − | 0.272418i | \(-0.912177\pi\) | ||
0.962179 | − | 0.272418i | \(-0.0878233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 152.817 | 0.302609 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 269.495 | − | 466.779i | 0.531548 | − | 0.920669i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 168.009 | + | 291.000i | 0.330076 | + | 0.571709i | 0.982526 | − | 0.186123i | \(-0.0595923\pi\) |
−0.652450 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 116.176 | − | 353.437i | 0.227350 | − | 0.691658i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −17.0106 | − | 29.4633i | −0.0331591 | − | 0.0574333i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 376.306 | + | 217.260i | 0.730691 | + | 0.421865i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 639.829 | 1.23758 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −126.069 | −0.242908 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −547.572 | − | 316.141i | −1.05100 | − | 0.606796i | −0.128072 | − | 0.991765i | \(-0.540879\pi\) |
−0.922930 | + | 0.384969i | \(0.874212\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −389.623 | − | 674.847i | −0.744977 | − | 1.29034i | −0.950206 | − | 0.311624i | \(-0.899127\pi\) |
0.205229 | − | 0.978714i | \(-0.434206\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −112.963 | + | 101.015i | −0.215167 | + | 0.192410i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.131877 | − | 0.228418i | −0.000250242 | − | 0.000433431i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −593.054 | + | 1027.20i | −1.12109 | + | 1.94178i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 177.165 | 0.333644 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 228.907i | − | 0.429470i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −399.862 | − | 230.861i | −0.747406 | − | 0.431515i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 700.908 | − | 404.669i | 1.30523 | − | 0.753574i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 870.974 | + | 97.5673i | 1.61591 | + | 0.181015i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 583.617 | − | 336.952i | 1.07878 | − | 0.622831i | 0.148209 | − | 0.988956i | \(-0.452649\pi\) |
0.930566 | + | 0.366125i | \(0.119316\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −497.743 | + | 862.117i | −0.916655 | + | 1.58769i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 227.217i | 0.416913i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 52.5329i | 0.0960382i | 0.998846 | + | 0.0480191i | \(0.0152908\pi\) | ||||
−0.998846 | + | 0.0480191i | \(0.984709\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 123.880 | − | 214.566i | 0.225646 | − | 0.390831i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.04821 | + | 2.91458i | −0.00916190 | + | 0.00528963i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 121.834 | − | 108.948i | 0.220314 | − | 0.197012i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17.1544 | − | 9.90409i | 0.0309088 | − | 0.0178452i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 678.123 | + | 391.515i | 1.21746 | + | 0.702899i | 0.964373 | − | 0.264546i | \(-0.0852220\pi\) |
0.253083 | + | 0.967445i | \(0.418555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 42.4528i | − | 0.0759441i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −957.628 | −1.70700 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −446.202 | + | 772.844i | −0.792543 | + | 1.37272i | 0.131845 | + | 0.991270i | \(0.457910\pi\) |
−0.924388 | + | 0.381454i | \(0.875423\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −98.0743 | − | 169.870i | −0.173583 | − | 0.300654i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 648.763 | + | 213.250i | 1.14420 | + | 0.376102i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 148.722 | + | 257.593i | 0.261373 | + | 0.452712i | 0.966607 | − | 0.256263i | \(-0.0824912\pi\) |
−0.705234 | + | 0.708975i | \(0.749158\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 218.885 | + | 126.373i | 0.383335 | + | 0.221319i | 0.679268 | − | 0.733890i | \(-0.262297\pi\) |
−0.295933 | + | 0.955209i | \(0.595631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −480.561 | −0.838676 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −263.479 | −0.458225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 764.454 | + | 441.358i | 1.32488 | + | 0.764918i | 0.984502 | − | 0.175371i | \(-0.0561126\pi\) |
0.340375 | + | 0.940290i | \(0.389446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 112.223 | + | 194.375i | 0.193821 | + | 0.335709i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 146.759 | + | 702.239i | 0.252597 | + | 1.20867i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 410.987 | + | 711.850i | 0.704951 | + | 1.22101i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.1248 | − | 31.3930i | 0.0309825 | − | 0.0536633i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 66.7814 | 0.113767 | 0.0568836 | − | 0.998381i | \(-0.481884\pi\) | ||||
0.0568836 | + | 0.998381i | \(0.481884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0261007i | 4.43136e-5i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 587.670 | + | 339.291i | 0.994365 | + | 0.574097i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −311.911 | + | 180.082i | −0.525989 | + | 0.303680i | −0.739381 | − | 0.673287i | \(-0.764882\pi\) |
0.213393 | + | 0.976967i | \(0.431549\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −465.439 | + | 97.2704i | −0.782250 | + | 0.163480i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 199.480 | − | 115.170i | 0.334137 | − | 0.192914i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −99.0219 | + | 171.511i | −0.165312 | + | 0.286329i | −0.936766 | − | 0.349956i | \(-0.886196\pi\) |
0.771454 | + | 0.636285i | \(0.219530\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 373.907i | − | 0.622141i | −0.950387 | − | 0.311071i | \(-0.899312\pi\) | ||
0.950387 | − | 0.311071i | \(-0.100688\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 35.9728i | − | 0.0596565i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 429.373 | − | 743.696i | 0.709708 | − | 1.22925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −200.164 | + | 115.565i | −0.329760 | + | 0.190387i | −0.655735 | − | 0.754992i | \(-0.727641\pi\) |
0.325975 | + | 0.945379i | \(0.394308\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.8458 | − | 84.7142i | 0.0457238 | − | 0.139104i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 100.872 | − | 58.2386i | 0.165094 | − | 0.0953168i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −444.718 | − | 256.758i | −0.725479 | − | 0.418855i | 0.0912873 | − | 0.995825i | \(-0.470902\pi\) |
−0.816766 | + | 0.576969i | \(0.804235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1032.75i | 1.67927i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1119.01 | −1.81363 | −0.906815 | − | 0.421529i | \(-0.861493\pi\) | ||||
−0.906815 | + | 0.421529i | \(0.861493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −64.1019 | + | 111.028i | −0.103557 | + | 0.179366i | −0.913148 | − | 0.407629i | \(-0.866356\pi\) |
0.809591 | + | 0.586995i | \(0.199689\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 452.445 | + | 783.658i | 0.728575 | + | 1.26193i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −413.248 | − | 462.125i | −0.663319 | − | 0.741774i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 212.735 | + | 368.469i | 0.340377 | + | 0.589550i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 82.0690 | + | 47.3826i | 0.130892 | + | 0.0755703i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2160 | −0.0337297 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −313.995 | −0.497615 | −0.248808 | − | 0.968553i | \(-0.580039\pi\) | ||||
−0.248808 | + | 0.968553i | \(0.580039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −183.138 | − | 105.735i | −0.289317 | − | 0.167037i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 271.322 | + | 469.944i | 0.427279 | + | 0.740070i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 146.194 | − | 63.8959i | 0.229504 | − | 0.100307i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −97.6183 | − | 169.080i | −0.152767 | − | 0.264601i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 115.594 | − | 200.215i | 0.180334 | − | 0.312348i | −0.761660 | − | 0.647977i | \(-0.775615\pi\) |
0.941994 | + | 0.335629i | \(0.108949\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −637.869 | −0.992020 | −0.496010 | − | 0.868317i | \(-0.665202\pi\) | ||||
−0.496010 | + | 0.868317i | \(0.665202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 191.532i | 0.296949i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 586.461 | + | 338.594i | 0.906432 | + | 0.523329i | 0.879281 | − | 0.476303i | \(-0.158023\pi\) |
0.0271505 | + | 0.999631i | \(0.491357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1064.18 | − | 614.405i | 1.63972 | − | 0.946695i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.266157 | − | 0.297636i | −0.000408843 | − | 0.000457199i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −916.022 | + | 528.865i | −1.40279 | + | 0.809901i | −0.994678 | − | 0.103031i | \(-0.967146\pi\) |
−0.408112 | + | 0.912932i | \(0.633813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −244.569 | + | 423.606i | −0.373388 | + | 0.646726i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 137.058i | 0.208612i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 644.502i | − | 0.978000i | −0.872284 | − | 0.489000i | \(-0.837362\pi\) | ||
0.872284 | − | 0.489000i | \(-0.162638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 560.069 | − | 970.068i | 0.847306 | − | 1.46758i | −0.0362979 | − | 0.999341i | \(-0.511557\pi\) |
0.883604 | − | 0.468236i | \(-0.155110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −150.975 | + | 87.1652i | −0.227714 | + | 0.131471i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.7011 | + | 14.6934i | 0.0672197 | + | 0.0220953i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 134.271 | − | 77.5214i | 0.201306 | − | 0.116224i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 340.438 | + | 196.552i | 0.508876 | + | 0.293800i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1718.45i | − | 2.56103i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −307.811 | −0.457371 | −0.228686 | − | 0.973500i | \(-0.573443\pi\) | ||||
−0.228686 | + | 0.973500i | \(0.573443\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −69.5058 | + | 120.388i | −0.102972 | + | 0.178352i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −507.773 | − | 879.488i | −0.750033 | − | 1.29910i | −0.947806 | − | 0.318848i | \(-0.896704\pi\) |
0.197773 | − | 0.980248i | \(-0.436629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 965.231 | − | 201.720i | 1.42155 | − | 0.297084i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 96.1388 | + | 166.517i | 0.141173 | + | 0.244519i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 840.220 | + | 485.102i | 1.23019 | + | 0.710251i | 0.967070 | − | 0.254512i | \(-0.0819147\pi\) |
0.263121 | + | 0.964763i | \(0.415248\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 338.188 | 0.493706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 402.680 | 0.586143 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 129.588 | + | 74.8177i | 0.188081 | + | 0.108589i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −274.581 | − | 475.588i | −0.397367 | − | 0.688260i | 0.596033 | − | 0.802960i | \(-0.296743\pi\) |
−0.993400 | + | 0.114700i | \(0.963409\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −316.041 | + | 66.0483i | −0.456047 | + | 0.0953078i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −321.711 | − | 557.221i | −0.462894 | − | 0.801756i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 553.076 | − | 957.956i | 0.793510 | − | 1.37440i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −83.9818 | −0.120146 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 452.665i | − | 0.645742i | −0.946443 | − | 0.322871i | \(-0.895352\pi\) | ||
0.946443 | − | 0.322871i | \(-0.104648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.81822 | + | 1.04975i | 0.00258637 | + | 0.00149324i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −455.100 | + | 262.752i | −0.645533 | + | 0.372698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −235.393 | − | 77.3744i | −0.332946 | − | 0.109440i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −609.174 | + | 351.707i | −0.859202 | + | 0.496060i | −0.863745 | − | 0.503929i | \(-0.831887\pi\) |
0.00454321 | + | 0.999990i | \(0.498554\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.1054 | + | 52.1442i | −0.0423424 | + | 0.0733392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.694220i | − | 0.000973661i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 251.425i | − | 0.351644i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −427.367 | + | 740.221i | −0.596049 | + | 1.03239i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −54.1160 | + | 31.2439i | −0.0752656 | + | 0.0434546i | −0.537161 | − | 0.843480i | \(-0.680503\pi\) |
0.461895 | + | 0.886935i | \(0.347170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −469.642 | − | 525.189i | −0.651376 | − | 0.728417i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −331.354 | + | 191.307i | −0.458305 | + | 0.264602i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.6271 | + | 11.9090i | 0.0284511 | + | 0.0164263i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 889.995i | − | 1.22420i | −0.790779 | − | 0.612101i | \(-0.790324\pi\) | ||
0.790779 | − | 0.612101i | \(-0.209676\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 417.569 | 0.572797 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 102.573 | − | 177.661i | 0.140318 | − | 0.243038i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −456.127 | − | 790.035i | −0.622274 | − | 1.07781i | −0.989061 | − | 0.147505i | \(-0.952876\pi\) |
0.366787 | − | 0.930305i | \(-0.380458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −659.577 | + | 288.276i | −0.897383 | + | 0.392212i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −124.753 | − | 216.079i | −0.169271 | − | 0.293187i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1081.52 | − | 624.415i | −1.46349 | − | 0.844946i | −0.464319 | − | 0.885668i | \(-0.653701\pi\) |
−0.999171 | + | 0.0407224i | \(0.987034\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.2514 | 0.0232813 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 305.880 | 0.411682 | 0.205841 | − | 0.978585i | \(-0.434007\pi\) | ||||
0.205841 | + | 0.978585i | \(0.434007\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 318.766 | + | 184.040i | 0.427874 | + | 0.247033i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −132.145 | − | 228.882i | −0.176901 | − | 0.306401i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 499.041 | + | 558.065i | 0.666276 | + | 0.745080i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 258.895 | + | 448.420i | 0.344734 | + | 0.597097i | 0.985305 | − | 0.170802i | \(-0.0546358\pi\) |
−0.640571 | + | 0.767899i | \(0.721302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −206.288 | + | 357.302i | −0.273955 | + | 0.474504i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −569.012 | −0.753659 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 939.898i | 1.24161i | 0.783965 | + | 0.620804i | \(0.213194\pi\) | ||||
−0.783965 | + | 0.620804i | \(0.786806\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2182.85 | − | 1260.27i | −2.87596 | − | 1.66044i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −976.757 | + | 563.931i | −1.28352 | + | 0.741039i | −0.977490 | − | 0.210983i | \(-0.932334\pi\) |
−0.306028 | + | 0.952022i | \(0.599000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 115.044 | − | 349.995i | 0.150779 | − | 0.458710i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 151.701 | − | 87.5846i | 0.198302 | − | 0.114490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 111.849 | − | 193.728i | 0.145826 | − | 0.252579i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 300.115i | 0.390267i | 0.980777 | + | 0.195133i | \(0.0625139\pi\) | ||||
−0.980777 | + | 0.195133i | \(0.937486\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 356.524i | − | 0.462417i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −375.120 | + | 649.727i | −0.485278 | + | 0.840527i | −0.999857 | − | 0.0169165i | \(-0.994615\pi\) |
0.514579 | + | 0.857443i | \(0.327948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0923598 | − | 0.0533240i | 0.000119174 | − | 6.88051e-5i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.4385 | + | 6.57022i | −0.0404613 | + | 0.00845588i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −94.7977 | + | 54.7315i | −0.121691 | + | 0.0702586i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1172.73 | − | 677.076i | −1.50158 | − | 0.866935i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 81.8005i | − | 0.104471i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1058.16 | 1.34797 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 144.776 | − | 250.760i | 0.183960 | − | 0.318627i | −0.759266 | − | 0.650781i | \(-0.774442\pi\) |
0.943225 | + | 0.332153i | \(0.107775\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −178.098 | − | 308.474i | −0.225726 | − | 0.390969i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 65.0610 | + | 311.316i | 0.0822516 | + | 0.393573i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −156.417 | − | 270.922i | −0.197247 | − | 0.341642i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −584.657 | − | 337.552i | −0.735417 | − | 0.424593i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1086.57 | −1.36332 | −0.681659 | − | 0.731670i | \(-0.738741\pi\) | ||||
−0.681659 | + | 0.731670i | \(0.738741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 562.854 | 0.704448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 197.787 | + | 114.192i | 0.246925 | + | 0.142562i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 475.313 | + | 823.267i | 0.591922 | + | 1.02524i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1188.95 | − | 390.811i | −1.47696 | − | 0.485480i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 518.806 | + | 898.598i | 0.642882 | + | 1.11350i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −90.9745 | + | 157.572i | −0.112453 | + | 0.194774i | −0.916759 | − | 0.399441i | \(-0.869204\pi\) |
0.804306 | + | 0.594216i | \(0.202537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1005.31 | 1.23960 | 0.619799 | − | 0.784760i | \(-0.287214\pi\) | ||||
0.619799 | + | 0.784760i | \(0.287214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 349.280i | − | 0.429619i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 898.355 | + | 518.665i | 1.10228 | + | 0.636399i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.5810 | + | 10.1504i | −0.0215190 | + | 0.0124240i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −43.8135 | + | 39.1795i | −0.0534963 | + | 0.0478382i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 851.009 | − | 491.330i | 1.03655 | − | 0.598453i | 0.117697 | − | 0.993050i | \(-0.462449\pi\) |
0.918855 | + | 0.394596i | \(0.129115\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 742.505 | − | 1286.06i | 0.902194 | − | 1.56265i | 0.0775532 | − | 0.996988i | \(-0.475289\pi\) |
0.824641 | − | 0.565657i | \(-0.191377\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 387.212i | − | 0.469348i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 708.113i | 0.856243i | 0.903721 | + | 0.428121i | \(0.140824\pi\) | ||||
−0.903721 | + | 0.428121i | \(0.859176\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −75.0164 | + | 129.932i | −0.0904902 | + | 0.156734i | −0.907718 | − | 0.419582i | \(-0.862177\pi\) |
0.817227 | + | 0.576316i | \(0.195510\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.0796 | − | 28.3361i | 0.0590609 | − | 0.0340988i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 766.191 | + | 85.8294i | 0.919797 | + | 0.103037i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −273.665 | + | 158.001i | −0.327743 | + | 0.189222i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.317199 | − | 0.183135i | −0.000378972 | − | 0.000218799i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1106.41i | 1.31873i | 0.751824 | + | 0.659364i | \(0.229174\pi\) | ||||
−0.751824 | + | 0.659364i | \(0.770826\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 826.984 | 0.983335 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −129.014 | + | 223.459i | −0.153042 | + | 0.265076i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 341.915 | + | 592.214i | 0.404633 | + | 0.700845i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1037.93 | + | 928.156i | −1.22542 | + | 1.09582i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 148.584 | + | 257.354i | 0.175010 | + | 0.303126i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −48.3606 | − | 27.9210i | −0.0568279 | − | 0.0328096i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1243.82 | 1.45817 | 0.729086 | − | 0.684423i | \(-0.239946\pi\) | ||||
0.729086 | + | 0.684423i | \(0.239946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.3344 | −0.0202742 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 245.650 | + | 141.826i | 0.286639 | + | 0.165491i | 0.636425 | − | 0.771339i | \(-0.280412\pi\) |
−0.349786 | + | 0.936830i | \(0.613746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −455.900 | − | 789.641i | −0.530733 | − | 0.919256i | −0.999357 | − | 0.0358586i | \(-0.988583\pi\) |
0.468624 | − | 0.883398i | \(-0.344750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 522.902 | − | 1590.80i | 0.607319 | − | 1.84762i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −436.908 | − | 756.747i | −0.506266 | − | 0.876879i | −0.999974 | − | 0.00725099i | \(-0.997692\pi\) |
0.493707 | − | 0.869628i | \(-0.335641\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 79.9735 | − | 138.518i | 0.0924550 | − | 0.160137i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 140.978 | 0.162604 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 417.620i | 0.480575i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.3358 | − | 22.7105i | −0.0451617 | − | 0.0260741i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −314.599 | + | 181.634i | −0.360365 | + | 0.208057i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −193.882 | − | 927.724i | −0.221579 | − | 1.06026i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 549.476 | − | 317.240i | 0.626540 | − | 0.361733i | −0.152871 | − | 0.988246i | \(-0.548852\pi\) |
0.779411 | + | 0.626513i | \(0.215518\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 46.7975 | − | 81.0557i | 0.0532395 | − | 0.0922136i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 670.044i | 0.760549i | 0.924874 | + | 0.380274i | \(0.124170\pi\) | ||||
−0.924874 | + | 0.380274i | \(0.875830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 875.514i | 0.991522i | 0.868459 | + | 0.495761i | \(0.165111\pi\) | ||||
−0.868459 | + | 0.495761i | \(0.834889\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −504.623 | + | 874.033i | −0.570196 | + | 0.987608i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −854.152 | + | 493.145i | −0.962967 | + | 0.555969i | −0.897085 | − | 0.441858i | \(-0.854319\pi\) |
−0.0658820 | + | 0.997827i | \(0.520986\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −179.991 | − | 861.257i | −0.202465 | − | 0.968793i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1511.17 | + | 872.476i | −1.69604 | + | 0.979210i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −48.2368 | − | 27.8495i | −0.0540166 | − | 0.0311865i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1026.83i | 1.14729i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −458.850 | −0.511538 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.0313782 | + | 0.0543486i | −3.49034e−5 | + | 6.04545e-5i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 361.543 | + | 626.210i | 0.401268 | + | 0.695017i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 96.9764 | − | 295.028i | 0.107394 | − | 0.326719i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −631.499 | − | 1093.79i | −0.697789 | − | 1.20861i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 750.592 | + | 433.355i | 0.827555 | + | 0.477789i | 0.853015 | − | 0.521887i | \(-0.174772\pi\) |
−0.0254599 | + | 0.999676i | \(0.508105\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 91.2820 | 0.100420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 128.713 | 0.141288 | 0.0706438 | − | 0.997502i | \(-0.477495\pi\) | ||||
0.0706438 | + | 0.997502i | \(0.477495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1587.51 | − | 916.552i | −1.73879 | − | 1.00389i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 705.699 | + | 1222.31i | 0.771256 | + | 1.33585i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 591.203 | − | 528.673i | 0.644714 | − | 0.576525i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 430.087 | + | 744.933i | 0.467995 | + | 0.810591i | 0.999331 | − | 0.0365701i | \(-0.0116432\pi\) |
−0.531336 | + | 0.847161i | \(0.678310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −421.935 | + | 730.813i | −0.458127 | + | 0.793500i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −246.515 | −0.267081 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 8.57859i | − | 0.00927415i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 224.778 | + | 129.776i | 0.242479 | + | 0.139995i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 202.025 | − | 116.639i | 0.217465 | − | 0.125554i | −0.387311 | − | 0.921949i | \(-0.626596\pi\) |
0.604776 | + | 0.796396i | \(0.293263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61.4160 | − | 45.2661i | −0.0659678 | − | 0.0486209i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1287.89 | − | 743.563i | 1.38037 | − | 0.796960i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 607.483 | − | 1052.19i | 0.649714 | − | 1.12534i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1426.29i | 1.52219i | 0.648641 | + | 0.761095i | \(0.275338\pi\) | ||||
−0.648641 | + | 0.761095i | \(0.724662\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 281.851i | − | 0.300161i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −635.425 | + | 1100.59i | −0.675265 | + | 1.16959i | 0.301126 | + | 0.953584i | \(0.402638\pi\) |
−0.976391 | + | 0.216010i | \(0.930696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2521.41 | − | 1455.73i | 2.67381 | − | 1.54373i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −492.212 | + | 440.152i | −0.520859 | + | 0.465770i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1413.50 | − | 816.086i | 1.49261 | − | 0.861759i | 0.492646 | − | 0.870230i | \(-0.336030\pi\) |
0.999964 | + | 0.00847064i | \(0.00269632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 149.871 | + | 86.5280i | 0.157925 | + | 0.0911781i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 832.098i | 0.874972i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 95.9158 | 0.100646 | 0.0503231 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503231 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 304.850 | − | 528.015i | 0.319215 | − | 0.552896i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 113.926 | + | 197.326i | 0.119045 | + | 0.206192i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −520.930 | − | 171.231i | −0.543201 | − | 0.178552i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −480.500 | − | 832.250i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −238.849 | − | 137.899i | −0.248025 | − | 0.143198i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −284.759 | −0.295087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1419.97 | −1.46843 | −0.734216 | − | 0.678916i | \(-0.762450\pi\) | ||||
−0.734216 | + | 0.678916i | \(0.762450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.1956 | + | 41.6822i | 0.0745053 | + | 0.0430157i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 329.817 | + | 571.261i | 0.339668 | + | 0.588322i | 0.984370 | − | 0.176112i | \(-0.0563520\pi\) |
−0.644702 | + | 0.764434i | \(0.723019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 213.418 | + | 1021.21i | 0.219341 | + | 1.04954i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.2448 | − | 61.0459i | −0.0361486 | − | 0.0626111i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 957.151 | − | 1657.83i | 0.979683 | − | 1.69686i | 0.316160 | − | 0.948706i | \(-0.397606\pi\) |
0.663523 | − | 0.748156i | \(-0.269060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1584.07 | 1.61804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 135.723i | 0.138352i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −193.655 | − | 111.806i | −0.197004 | − | 0.113740i | 0.398253 | − | 0.917275i | \(-0.369616\pi\) |
−0.595257 | + | 0.803535i | \(0.702950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −745.591 | + | 430.467i | −0.756945 | + | 0.437022i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 834.053 | − | 174.306i | 0.845038 | − | 0.176602i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 467.616 | − | 269.978i | 0.472816 | − | 0.272981i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −736.371 | + | 1275.43i | −0.743058 | + | 1.28701i | 0.208038 | + | 0.978121i | \(0.433292\pi\) |
−0.951096 | + | 0.308894i | \(0.900041\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 260.472i | − | 0.262308i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 292.237i | 0.293706i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.4480 | + | 92.5746i | −0.0536088 | + | 0.0928532i | −0.891584 | − | 0.452854i | \(-0.850406\pi\) |
0.837976 | + | 0.545708i | \(0.183739\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.5150 | + | 14.7311i | −0.0255405 | + | 0.0147458i |
(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 | 224.3.n.a.17.4 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.45.5 | yes | 28 | ||
7.3 | odd | 6 | 1568.3.h.a.881.8 | 28 | |||
7.4 | even | 3 | 1568.3.h.a.881.22 | 28 | |||
7.5 | odd | 6 | inner | 224.3.n.a.145.11 | 28 | ||
8.3 | odd | 2 | 56.3.j.a.45.14 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.17.11 | 28 | ||
28.3 | even | 6 | 392.3.h.a.293.10 | 28 | |||
28.11 | odd | 6 | 392.3.h.a.293.9 | 28 | |||
28.19 | even | 6 | 56.3.j.a.5.14 | yes | 28 | ||
28.23 | odd | 6 | 392.3.j.e.117.14 | 28 | |||
28.27 | even | 2 | 392.3.j.e.325.5 | 28 | |||
56.3 | even | 6 | 392.3.h.a.293.11 | 28 | |||
56.5 | odd | 6 | inner | 224.3.n.a.145.4 | 28 | ||
56.11 | odd | 6 | 392.3.h.a.293.12 | 28 | |||
56.19 | even | 6 | 56.3.j.a.5.5 | ✓ | 28 | ||
56.27 | even | 2 | 392.3.j.e.325.14 | 28 | |||
56.45 | odd | 6 | 1568.3.h.a.881.21 | 28 | |||
56.51 | odd | 6 | 392.3.j.e.117.5 | 28 | |||
56.53 | even | 6 | 1568.3.h.a.881.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.5 | ✓ | 28 | 56.19 | even | 6 | ||
56.3.j.a.5.14 | yes | 28 | 28.19 | even | 6 | ||
56.3.j.a.45.5 | yes | 28 | 4.3 | odd | 2 | ||
56.3.j.a.45.14 | yes | 28 | 8.3 | odd | 2 | ||
224.3.n.a.17.4 | 28 | 1.1 | even | 1 | trivial | ||
224.3.n.a.17.11 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.4 | 28 | 56.5 | odd | 6 | inner | ||
224.3.n.a.145.11 | 28 | 7.5 | odd | 6 | inner | ||
392.3.h.a.293.9 | 28 | 28.11 | odd | 6 | |||
392.3.h.a.293.10 | 28 | 28.3 | even | 6 | |||
392.3.h.a.293.11 | 28 | 56.3 | even | 6 | |||
392.3.h.a.293.12 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.117.5 | 28 | 56.51 | odd | 6 | |||
392.3.j.e.117.14 | 28 | 28.23 | odd | 6 | |||
392.3.j.e.325.5 | 28 | 28.27 | even | 2 | |||
392.3.j.e.325.14 | 28 | 56.27 | even | 2 | |||
1568.3.h.a.881.7 | 28 | 56.53 | even | 6 | |||
1568.3.h.a.881.8 | 28 | 7.3 | odd | 6 | |||
1568.3.h.a.881.21 | 28 | 56.45 | odd | 6 | |||
1568.3.h.a.881.22 | 28 | 7.4 | even | 3 |