Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 2012) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | 2.41348 | 1.39342 | 0.696711 | − | 0.717352i | \(-0.254646\pi\) | ||||
0.696711 | + | 0.717352i | \(0.254646\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.469286 | −0.209871 | −0.104936 | − | 0.994479i | \(-0.533464\pi\) | ||||
−0.104936 | + | 0.994479i | \(0.533464\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19654 | 0.452249 | 0.226125 | − | 0.974098i | \(-0.427394\pi\) | ||||
0.226125 | + | 0.974098i | \(0.427394\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82487 | 0.941624 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.91448 | −1.48177 | −0.740886 | − | 0.671631i | \(-0.765594\pi\) | ||||
−0.740886 | + | 0.671631i | \(0.765594\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.71686 | −1.03087 | −0.515436 | − | 0.856928i | \(-0.672370\pi\) | ||||
−0.515436 | + | 0.856928i | \(0.672370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13261 | −0.292439 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.40011 | 0.339578 | 0.169789 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169789 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.52014 | 1.95465 | 0.977327 | − | 0.211736i | \(-0.0679115\pi\) | ||||
0.977327 | + | 0.211736i | \(0.0679115\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.88782 | 0.630174 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.20246 | −1.50182 | −0.750908 | − | 0.660407i | \(-0.770384\pi\) | ||||
−0.750908 | + | 0.660407i | \(0.770384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77977 | −0.955954 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.422667 | −0.0813424 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.58126 | 0.479327 | 0.239664 | − | 0.970856i | \(-0.422963\pi\) | ||||
0.239664 | + | 0.970856i | \(0.422963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.69726 | 1.20286 | 0.601432 | − | 0.798924i | \(-0.294597\pi\) | ||||
0.601432 | + | 0.798924i | \(0.294597\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.8610 | −2.06473 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.561519 | −0.0949140 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.35249 | −0.715545 | −0.357773 | − | 0.933809i | \(-0.616464\pi\) | ||||
−0.357773 | + | 0.933809i | \(0.616464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.97056 | −1.43644 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.56215 | −0.868661 | −0.434331 | − | 0.900753i | \(-0.643015\pi\) | ||||
−0.434331 | + | 0.900753i | \(0.643015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.72159 | −1.33003 | −0.665015 | − | 0.746830i | \(-0.731575\pi\) | ||||
−0.665015 | + | 0.746830i | \(0.731575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.32567 | −0.197620 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.39690 | 0.495488 | 0.247744 | − | 0.968825i | \(-0.420311\pi\) | ||||
0.247744 | + | 0.968825i | \(0.420311\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.56830 | −0.795471 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.37914 | 0.473175 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.71607 | 1.05988 | 0.529942 | − | 0.848034i | \(-0.322214\pi\) | ||||
0.529942 | + | 0.848034i | \(0.322214\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.30630 | 0.310981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20.5632 | 2.72366 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.21327 | −1.19947 | −0.599733 | − | 0.800200i | \(-0.704727\pi\) | ||||
−0.599733 | + | 0.800200i | \(0.704727\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.50326 | −0.192473 | −0.0962365 | − | 0.995358i | \(-0.530681\pi\) | ||||
−0.0962365 | + | 0.995358i | \(0.530681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.38007 | 0.425849 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.74427 | 0.216350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.93819 | −0.969804 | −0.484902 | − | 0.874569i | \(-0.661145\pi\) | ||||
−0.484902 | + | 0.874569i | \(0.661145\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17.3830 | −2.09266 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.98538 | −0.235621 | −0.117811 | − | 0.993036i | \(-0.537588\pi\) | ||||
−0.117811 | + | 0.993036i | \(0.537588\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.131679 | 0.0154119 | 0.00770594 | − | 0.999970i | \(-0.497547\pi\) | ||||
0.00770594 | + | 0.999970i | \(0.497547\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.5359 | −1.33205 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.88036 | −0.670130 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.67451 | −0.525923 | −0.262962 | − | 0.964806i | \(-0.584699\pi\) | ||||
−0.262962 | + | 0.964806i | \(0.584699\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.49471 | −1.05497 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.94828 | −0.652909 | −0.326455 | − | 0.945213i | \(-0.605854\pi\) | ||||
−0.326455 | + | 0.945213i | \(0.605854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.657054 | −0.0712675 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.22980 | 0.667905 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.4631 | 1.10908 | 0.554542 | − | 0.832156i | \(-0.312894\pi\) | ||||
0.554542 | + | 0.832156i | \(0.312894\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44737 | −0.466211 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.1637 | 1.67610 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.99838 | −0.410225 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.97655 | −0.911430 | −0.455715 | − | 0.890126i | \(-0.650616\pi\) | ||||
−0.455715 | + | 0.890126i | \(0.650616\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8828 | −1.39527 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2532 | 1.11973 | 0.559867 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559867 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.95816 | −0.587075 | −0.293538 | − | 0.955948i | \(-0.594833\pi\) | ||||
−0.293538 | + | 0.955948i | \(0.594833\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.35521 | −0.132255 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.78724 | 0.269452 | 0.134726 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134726 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4059 | 0.996708 | 0.498354 | − | 0.866974i | \(-0.333938\pi\) | ||||
0.498354 | + | 0.866974i | \(0.333938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5046 | −0.997056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7264 | 1.19720 | 0.598602 | − | 0.801047i | \(-0.295723\pi\) | ||||
0.598602 | + | 0.801047i | \(0.295723\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.38001 | 0.315188 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.4997 | −0.970694 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.67529 | 0.153574 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.1521 | 1.19565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.4241 | −1.21041 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.58951 | 0.410498 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.9016 | −1.32230 | −0.661152 | − | 0.750252i | \(-0.729932\pi\) | ||||
−0.661152 | + | 0.750252i | \(0.729932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.0494 | −1.85329 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.38001 | −0.120572 | −0.0602858 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602858 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.1947 | 0.883990 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.198352 | 0.0170714 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.76427 | −0.407039 | −0.203519 | − | 0.979071i | \(-0.565238\pi\) | ||||
−0.203519 | + | 0.979071i | \(0.565238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.3225 | −1.04519 | −0.522593 | − | 0.852583i | \(-0.675035\pi\) | ||||
−0.522593 | + | 0.852583i | \(0.675035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.19833 | 0.690424 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.2664 | 1.52752 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.21135 | −0.100597 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.4390 | −1.10843 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.14290 | −0.339400 | −0.169700 | − | 0.985496i | \(-0.554280\pi\) | ||||
−0.169700 | + | 0.985496i | \(0.554280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5882 | −1.10579 | −0.552895 | − | 0.833251i | \(-0.686477\pi\) | ||||
−0.552895 | + | 0.833251i | \(0.686477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.95514 | 0.319754 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.14293 | −0.252446 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.32518 | −0.265378 | −0.132689 | − | 0.991158i | \(-0.542361\pi\) | ||||
−0.132689 | + | 0.991158i | \(0.542361\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 18.6226 | 1.47686 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.61802 | −0.679195 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.5563 | −1.14014 | −0.570069 | − | 0.821597i | \(-0.693084\pi\) | ||||
−0.570069 | + | 0.821597i | \(0.693084\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.56620 | 0.433328 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.1284 | −1.55758 | −0.778790 | − | 0.627284i | \(-0.784166\pi\) | ||||
−0.778790 | + | 0.627284i | \(0.784166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.815066 | 0.0626974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.0683 | 1.84055 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.2292 | 1.00580 | 0.502898 | − | 0.864346i | \(-0.332267\pi\) | ||||
0.502898 | + | 0.864346i | \(0.332267\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.71918 | −0.432329 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.2360 | −1.67136 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.9923 | 1.64378 | 0.821889 | − | 0.569647i | \(-0.192920\pi\) | ||||
0.821889 | + | 0.569647i | \(0.192920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.06078 | −0.599153 | −0.299576 | − | 0.954072i | \(-0.596845\pi\) | ||||
−0.299576 | + | 0.954072i | \(0.596845\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.62809 | −0.268196 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.04256 | 0.150172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.88083 | −0.503176 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.505738 | −0.0367870 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.580381 | 0.0419949 | 0.0209975 | − | 0.999780i | \(-0.493316\pi\) | ||||
0.0209975 | + | 0.999780i | \(0.493316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.32214 | −0.239133 | −0.119567 | − | 0.992826i | \(-0.538151\pi\) | ||||
−0.119567 | + | 0.992826i | \(0.538151\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.20976 | 0.301467 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.2811 | −1.30247 | −0.651236 | − | 0.758875i | \(-0.725749\pi\) | ||||
−0.651236 | + | 0.758875i | \(0.725749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.22831 | 0.654178 | 0.327089 | − | 0.944994i | \(-0.393932\pi\) | ||||
0.327089 | + | 0.944994i | \(0.393932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.1586 | −1.35135 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.08857 | 0.216775 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.61024 | 0.182307 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.3460 | −1.41415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −41.8721 | −2.89635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.5409 | −1.68947 | −0.844734 | − | 0.535187i | \(-0.820241\pi\) | ||||
−0.844734 | + | 0.535187i | \(0.820241\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.79167 | −0.328320 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.09292 | 0.279135 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.01353 | 0.543994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.317805 | 0.0214752 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.20403 | −0.350061 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6366 | −1.38193 | −0.690964 | − | 0.722889i | \(-0.742814\pi\) | ||||
−0.690964 | + | 0.722889i | \(0.742814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.5022 | −0.900149 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.66140 | −0.442132 | −0.221066 | − | 0.975259i | \(-0.570954\pi\) | ||||
−0.221066 | + | 0.975259i | \(0.570954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.59570 | 0.501938 | 0.250969 | − | 0.967995i | \(-0.419251\pi\) | ||||
0.250969 | + | 0.967995i | \(0.419251\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.1921 | −0.933773 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.08213 | 0.332942 | 0.166471 | − | 0.986046i | \(-0.446763\pi\) | ||||
0.166471 | + | 0.986046i | \(0.446763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.59412 | −0.103989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.2818 | −0.732833 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.2123 | 1.17805 | 0.589026 | − | 0.808114i | \(-0.299511\pi\) | ||||
0.589026 | + | 0.808114i | \(0.299511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.9353 | −1.54181 | −0.770904 | − | 0.636951i | \(-0.780195\pi\) | ||||
−0.770904 | + | 0.636951i | \(0.780195\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6473 | −1.38867 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.61312 | 0.166946 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.6682 | −2.01500 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.3560 | −0.909778 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.886610 | −0.0559623 | −0.0279812 | − | 0.999608i | \(-0.508908\pi\) | ||||
−0.0279812 | + | 0.999608i | \(0.508908\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.3963 | 2.22535 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.58579 | −0.0993057 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.39773 | 0.523836 | 0.261918 | − | 0.965090i | \(-0.415645\pi\) | ||||
0.261918 | + | 0.965090i | \(0.415645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.20792 | −0.323605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.29172 | 0.451346 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.45866 | −0.398258 | −0.199129 | − | 0.979973i | \(-0.563811\pi\) | ||||
−0.199129 | + | 0.979973i | \(0.563811\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.62104 | −0.222439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.2524 | 1.54542 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.7114 | 1.68960 | 0.844798 | − | 0.535085i | \(-0.179721\pi\) | ||||
0.844798 | + | 0.535085i | \(0.179721\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.26899 | 0.502305 | 0.251153 | − | 0.967947i | \(-0.419190\pi\) | ||||
0.251153 | + | 0.967947i | \(0.419190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.7336 | −0.649628 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.4901 | 1.41651 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0883 | 1.02673 | 0.513367 | − | 0.858169i | \(-0.328398\pi\) | ||||
0.513367 | + | 0.858169i | \(0.328398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 18.9189 | 1.13265 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.50366 | −0.328321 | −0.164160 | − | 0.986434i | \(-0.552491\pi\) | ||||
−0.164160 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1214 | 0.720541 | 0.360270 | − | 0.932848i | \(-0.382684\pi\) | ||||
0.360270 | + | 0.932848i | \(0.382684\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.65001 | −0.571617 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.65532 | −0.392851 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0397 | −0.884687 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.6647 | −1.27001 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.1420 | 1.87775 | 0.938877 | − | 0.344252i | \(-0.111868\pi\) | ||||
0.938877 | + | 0.344252i | \(0.111868\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.32366 | 0.251733 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.07719 | 0.120531 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.7705 | 1.54818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.4357 | −0.601505 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.1593 | 1.56026 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.705460 | 0.0403945 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.8336 | 0.960746 | 0.480373 | − | 0.877064i | \(-0.340501\pi\) | ||||
0.480373 | + | 0.877064i | \(0.340501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.3799 | −0.818044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.1838 | 1.25793 | 0.628963 | − | 0.777435i | \(-0.283480\pi\) | ||||
0.628963 | + | 0.777435i | \(0.283480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2574 | −1.20154 | −0.600769 | − | 0.799423i | \(-0.705139\pi\) | ||||
−0.600769 | + | 0.799423i | \(0.705139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.58622 | −0.0893733 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.77219 | −0.155702 | −0.0778509 | − | 0.996965i | \(-0.524806\pi\) | ||||
−0.0778509 | + | 0.996965i | \(0.524806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.6855 | −0.710253 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.72694 | 0.375461 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.9292 | 0.663757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.7657 | 0.985466 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.1145 | 1.38883 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.06452 | 0.224084 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6587 | 0.750750 | 0.375375 | − | 0.926873i | \(-0.377514\pi\) | ||||
0.375375 | + | 0.926873i | \(0.377514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.2952 | −0.673775 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.72528 | 0.203534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.3896 | −0.947274 | −0.473637 | − | 0.880720i | \(-0.657059\pi\) | ||||
−0.473637 | + | 0.880720i | \(0.657059\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 30.7150 | 1.66821 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.9136 | −1.78237 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0384 | −0.812000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.15758 | 0.439189 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.1589 | −1.40428 | −0.702141 | − | 0.712038i | \(-0.747772\pi\) | ||||
−0.702141 | + | 0.712038i | \(0.747772\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.9003 | 1.06524 | 0.532619 | − | 0.846355i | \(-0.321208\pi\) | ||||
0.532619 | + | 0.846355i | \(0.321208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57100 | 0.0838536 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.8376 | 1.80099 | 0.900496 | − | 0.434864i | \(-0.143204\pi\) | ||||
0.900496 | + | 0.434864i | \(0.143204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.931711 | 0.0494501 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.04328 | 0.213993 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.84125 | −0.361067 | −0.180534 | − | 0.983569i | \(-0.557782\pi\) | ||||
−0.180534 | + | 0.983569i | \(0.557782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 53.5928 | 2.82067 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 31.7423 | 1.66604 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.0617952 | −0.00323451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.87311 | 0.202174 | 0.101087 | − | 0.994878i | \(-0.467768\pi\) | ||||
0.101087 | + | 0.994878i | \(0.467768\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.7124 | −0.817952 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.23257 | 0.479331 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.75357 | 0.142575 | 0.0712873 | − | 0.997456i | \(-0.477289\pi\) | ||||
0.0712873 | + | 0.997456i | \(0.477289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0767 | 0.571997 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.59417 | −0.494125 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.57451 | 0.286344 | 0.143172 | − | 0.989698i | \(-0.454270\pi\) | ||||
0.143172 | + | 0.989698i | \(0.454270\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.9647 | −1.84253 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −29.2495 | −1.49458 | −0.747291 | − | 0.664497i | \(-0.768646\pi\) | ||||
−0.747291 | + | 0.664497i | \(0.768646\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.75957 | 0.140641 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.6374 | −1.25239 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.17508 | 0.465195 | 0.232598 | − | 0.972573i | \(-0.425277\pi\) | ||||
0.232598 | + | 0.972573i | \(0.425277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0843 | −0.509983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.33061 | −0.168007 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.19368 | 0.110376 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.2492 | −1.66873 | −0.834365 | − | 0.551212i | \(-0.814166\pi\) | ||||
−0.834365 | + | 0.551212i | \(0.814166\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 24.6046 | 1.23177 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.6476 | −1.43059 | −0.715297 | − | 0.698820i | \(-0.753709\pi\) | ||||
−0.715297 | + | 0.698820i | \(0.753709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.8928 | −1.24000 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.45574 | 0.221407 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.3902 | 1.06027 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5040 | 0.519389 | 0.259695 | − | 0.965691i | \(-0.416378\pi\) | ||||
0.259695 | + | 0.965691i | \(0.416378\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4985 | −0.567177 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.0240 | −0.542457 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.79145 | 0.137027 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.7402 | −1.45638 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.6684 | 0.716597 | 0.358299 | − | 0.933607i | \(-0.383357\pi\) | ||||
0.358299 | + | 0.933607i | \(0.383357\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.4857 | −1.29083 | −0.645416 | − | 0.763831i | \(-0.723316\pi\) | ||||
−0.645416 | + | 0.763831i | \(0.723316\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.59580 | 0.466564 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.69223 | −0.324621 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.79871 | −0.0870457 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44.0857 | 2.12848 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.8093 | 1.29136 | 0.645679 | − | 0.763609i | \(-0.276575\pi\) | ||||
0.645679 | + | 0.763609i | \(0.276575\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.2785 | −0.782296 | −0.391148 | − | 0.920328i | \(-0.627922\pi\) | ||||
−0.391148 | + | 0.920328i | \(0.627922\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.92356 | −0.140174 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −61.3659 | −2.93553 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.15846 | 0.0552904 | 0.0276452 | − | 0.999618i | \(-0.491199\pi\) | ||||
0.0276452 | + | 0.999618i | \(0.491199\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.7297 | −0.749034 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2823 | −0.536038 | −0.268019 | − | 0.963414i | \(-0.586369\pi\) | ||||
−0.268019 | + | 0.963414i | \(0.586369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.91017 | −0.232765 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.99880 | −0.472927 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.72243 | 0.270058 | 0.135029 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135029 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3351 | 1.28716 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.7947 | −1.54083 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.08709 | 0.0978442 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.47866 | −0.303059 | −0.151529 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151529 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.591783 | −0.0276221 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.28966 | 0.432662 | 0.216331 | − | 0.976320i | \(-0.430591\pi\) | ||||
0.216331 | + | 0.976320i | \(0.430591\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.4220 | 1.04204 | 0.521019 | − | 0.853545i | \(-0.325552\pi\) | ||||
0.521019 | + | 0.853545i | \(0.325552\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.58539 | −0.351764 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.00761 | 0.231724 | 0.115862 | − | 0.993265i | \(-0.463037\pi\) | ||||
0.115862 | + | 0.993265i | \(0.463037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.49835 | −0.438593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.02525 | −0.369784 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 42.8621 | 1.97080 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.7243 | −1.86856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.7969 | 0.998012 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.9556 | −0.911793 | −0.455896 | − | 0.890033i | \(-0.650681\pi\) | ||||
−0.455896 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.1776 | 0.737636 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −20.7994 | −0.946405 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.21257 | 0.191283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.3497 | 1.55653 | 0.778267 | − | 0.627934i | \(-0.216099\pi\) | ||||
0.778267 | + | 0.627934i | \(0.216099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.1313 | −1.58869 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5459 | −0.566187 | −0.283094 | − | 0.959092i | \(-0.591361\pi\) | ||||
−0.283094 | + | 0.959092i | \(0.591361\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.61405 | 0.162769 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.51499 | 0.292827 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.37558 | −0.106559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.00374 | 0.403063 | 0.201531 | − | 0.979482i | \(-0.435408\pi\) | ||||
0.201531 | + | 0.979482i | \(0.435408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −48.5794 | −2.17037 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.28097 | −0.235000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.96714 | 0.0873639 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.3723 | 1.34623 | 0.673114 | − | 0.739539i | \(-0.264957\pi\) | ||||
0.673114 | + | 0.739539i | \(0.264957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.157559 | 0.00697001 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.60119 | −0.158996 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.79608 | 0.123210 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6940 | −0.734201 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.9284 | 1.40150 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.2835 | 1.41437 | 0.707183 | − | 0.707030i | \(-0.249966\pi\) | ||||
0.707183 | + | 0.707030i | \(0.249966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.59901 | −0.288554 | −0.144277 | − | 0.989537i | \(-0.546086\pi\) | ||||
−0.144277 | + | 0.989537i | \(0.546086\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.8031 | −0.602417 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.37693 | 0.408466 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.8754 | 1.25545 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0263 | −1.12945 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.6737 | 0.895479 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.30801 | −0.0565503 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 53.0778 | 2.29048 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.3653 | 1.17871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.7942 | −1.19497 | −0.597483 | − | 0.801882i | \(-0.703832\pi\) | ||||
−0.597483 | + | 0.801882i | \(0.703832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −19.4545 | −0.834872 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.88336 | −0.209180 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1074 | −1.15903 | −0.579515 | − | 0.814961i | \(-0.696758\pi\) | ||||
−0.579515 | + | 0.814961i | \(0.696758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.24652 | −0.181237 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.9927 | 0.936919 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.59323 | −0.237848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.92968 | 0.209253 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.6307 | −0.789408 | −0.394704 | − | 0.918808i | \(-0.629153\pi\) | ||||
−0.394704 | + | 0.918808i | \(0.629153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.4169 | 1.37109 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.6067 | −0.701137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.4672 | −0.904734 | −0.452367 | − | 0.891832i | \(-0.649420\pi\) | ||||
−0.452367 | + | 0.891832i | \(0.649420\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.97234 | −0.251258 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.3608 | −0.477108 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.05449 | 0.379584 | 0.189792 | − | 0.981824i | \(-0.439219\pi\) | ||||
0.189792 | + | 0.981824i | \(0.439219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.2430 | 1.76781 | 0.883907 | − | 0.467663i | \(-0.154904\pi\) | ||||
0.883907 | + | 0.467663i | \(0.154904\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.40074 | 0.0585166 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 34.4261 | 1.43567 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.2208 | 1.34137 | 0.670686 | − | 0.741742i | \(-0.266000\pi\) | ||||
0.670686 | + | 0.741742i | \(0.266000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.01792 | −0.333213 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.11735 | −0.295277 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.9205 | −1.57051 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.92734 | 0.203721 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.8527 | 1.72745 | 0.863723 | − | 0.503967i | \(-0.168127\pi\) | ||||
0.863723 | + | 0.503967i | \(0.168127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.0616 | 2.35118 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.1209 | −1.81489 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.7022 | 1.17866 | 0.589329 | − | 0.807893i | \(-0.299392\pi\) | ||||
0.589329 | + | 0.807893i | \(0.299392\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.786191 | −0.0322307 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.2723 | 0.911546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.109129 | −0.00445889 | −0.00222944 | − | 0.999998i | \(-0.500710\pi\) | ||||
−0.00222944 | + | 0.999998i | \(0.500710\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4723 | −0.549546 | −0.274773 | − | 0.961509i | \(-0.588603\pi\) | ||||
−0.274773 | + | 0.961509i | \(0.588603\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.4244 | −0.913191 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.17210 | −0.250932 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.37863 | −0.299489 | −0.149745 | − | 0.988725i | \(-0.547845\pi\) | ||||
−0.149745 | + | 0.988725i | \(0.547845\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.45420 | 0.302059 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.6258 | −0.510785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.2749 | −1.14201 | −0.571007 | − | 0.820946i | \(-0.693447\pi\) | ||||
−0.571007 | + | 0.820946i | \(0.693447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.29975 | 0.254030 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.9131 | −1.00296 | −0.501481 | − | 0.865168i | \(-0.667211\pi\) | ||||
−0.501481 | + | 0.865168i | \(0.667211\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.2744 | −1.85992 | −0.929962 | − | 0.367655i | \(-0.880161\pi\) | ||||
−0.929962 | + | 0.367655i | \(0.880161\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.04424 | 0.122161 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.5195 | 0.501582 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7451 | 0.869802 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −101.057 | −4.03584 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.09399 | −0.242983 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.8627 | 1.30825 | 0.654123 | − | 0.756389i | \(-0.273038\pi\) | ||||
0.654123 | + | 0.756389i | \(0.273038\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.2290 | −2.35414 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.99311 | 0.277513 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.6966 | 0.820029 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.60844 | −0.221867 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.8874 | 0.864501 | 0.432250 | − | 0.901754i | \(-0.357720\pi\) | ||||
0.432250 | + | 0.901754i | \(0.357720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.3591 | −0.842322 | −0.421161 | − | 0.906986i | \(-0.638377\pi\) | ||||
−0.421161 | + | 0.906986i | \(0.638377\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.87817 | 0.388952 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.8909 | −1.52896 | −0.764480 | − | 0.644648i | \(-0.777004\pi\) | ||||
−0.764480 | + | 0.644648i | \(0.777004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 45.2785 | 1.77733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.3405 | 0.758013 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.851542 | −0.0333234 | −0.0166617 | − | 0.999861i | \(-0.505304\pi\) | ||||
−0.0166617 | + | 0.999861i | \(0.505304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.647617 | 0.0253045 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.371977 | 0.0145122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.5657 | 0.917991 | 0.458996 | − | 0.888439i | \(-0.348209\pi\) | ||||
0.458996 | + | 0.888439i | \(0.348209\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6262 | 1.69686 | 0.848431 | − | 0.529306i | \(-0.177548\pi\) | ||||
0.848431 | + | 0.529306i | \(0.177548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.5598 | −0.487783 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.78422 | −0.185524 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.5914 | −0.719861 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.8060 | −1.92561 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.38775 | 0.285201 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.0843 | −0.504364 | −0.252182 | − | 0.967680i | \(-0.581148\pi\) | ||||
−0.252182 | + | 0.967680i | \(0.581148\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.02025 | 0.0777596 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.40790 | −0.361575 | −0.180788 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180788 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7408 | −0.412194 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.0771 | −0.616077 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.6814 | −1.48010 | −0.740051 | − | 0.672550i | \(-0.765199\pi\) | ||||
−0.740051 | + | 0.672550i | \(0.765199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.23581 | 0.0854257 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.3320 | 0.699411 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.6796 | −1.09260 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.87534 | 0.261550 | 0.130775 | − | 0.991412i | \(-0.458253\pi\) | ||||
0.130775 | + | 0.991412i | \(0.458253\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.6113 | −0.631010 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.78280 | 0.219354 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.78764 | −0.294978 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.2656 | 0.463928 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7236 | 1.61365 | 0.806825 | − | 0.590791i | \(-0.201184\pi\) | ||||
0.806825 | + | 0.590791i | \(0.201184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.0838 | −1.39864 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.84736 | −0.144900 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.4649 | 0.506399 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.2041 | 1.02167 | 0.510836 | − | 0.859678i | \(-0.329336\pi\) | ||||
0.510836 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2049 | −0.495222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.2367 | −1.80648 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.57219 | −0.320582 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.9549 | 1.64152 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.5483 | −1.40031 | −0.700157 | − | 0.713989i | \(-0.746887\pi\) | ||||
−0.700157 | + | 0.713989i | \(0.746887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.12917 | −0.265504 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −57.7673 | −2.14839 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.3378 | −0.458215 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.60879 | −0.356370 | −0.178185 | − | 0.983997i | \(-0.557023\pi\) | ||||
−0.178185 | + | 0.983997i | \(0.557023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.7611 | −0.880039 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.2112 | −0.451648 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2399 | 0.415156 | 0.207578 | − | 0.978218i | \(-0.433442\pi\) | ||||
0.207578 | + | 0.978218i | \(0.433442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.30671 | 0.232627 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.0121 | 1.43703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3498 | 1.37393 | 0.686967 | − | 0.726688i | \(-0.258942\pi\) | ||||
0.686967 | + | 0.726688i | \(0.258942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −76.4304 | −2.80774 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.14462 | 0.335483 | 0.167742 | − | 0.985831i | \(-0.446353\pi\) | ||||
0.167742 | + | 0.985831i | \(0.446353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.94421 | 0.0712302 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.8031 | −0.614795 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.33504 | 0.121860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5312 | −0.749195 | −0.374598 | − | 0.927187i | \(-0.622219\pi\) | ||||
−0.374598 | + | 0.927187i | \(0.622219\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.13981 | −0.0779791 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.37674 | 0.232073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.1360 | 1.60415 | 0.802075 | − | 0.597223i | \(-0.203729\pi\) | ||||
0.802075 | + | 0.597223i | \(0.203729\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 85.4282 | 3.10085 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.4882 | −1.32270 | −0.661348 | − | 0.750079i | \(-0.730015\pi\) | ||||
−0.661348 | + | 0.750079i | \(0.730015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.4511 | 0.450760 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.85609 | −0.0671072 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.2445 | 1.23650 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.0855 | −1.08491 | −0.542456 | − | 0.840084i | \(-0.682505\pi\) | ||||
−0.542456 | + | 0.840084i | \(0.682505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.2677 | 0.729925 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.0194 | −1.36746 | −0.683732 | − | 0.729734i | \(-0.739644\pi\) | ||||
−0.683732 | + | 0.729734i | \(0.739644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0114 | −1.14988 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.5692 | −0.450918 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.3903 | −1.69793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.75711 | 0.349137 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.09101 | −0.0389896 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.56046 | 0.0556953 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.8636 | −0.387247 | −0.193624 | − | 0.981076i | \(-0.562024\pi\) | ||||
−0.193624 | + | 0.981076i | \(0.562024\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.5878 | −0.554941 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2277 | 0.541434 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.58742 | 0.198415 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.73931 | −0.309951 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.2809 | 1.32056 | 0.660279 | − | 0.751020i | \(-0.270438\pi\) | ||||
0.660279 | + | 0.751020i | \(0.270438\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.75604 | 0.168257 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.5568 | 1.04434 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.647134 | −0.0228369 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.04431 | 0.142543 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 66.8809 | 2.35432 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.187390 | 0.00658828 | 0.00329414 | − | 0.999995i | \(-0.498951\pi\) | ||||
0.00329414 | + | 0.999995i | \(0.498951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.9796 | 0.842036 | 0.421018 | − | 0.907052i | \(-0.361673\pi\) | ||||
0.421018 | + | 0.907052i | \(0.361673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.9570 | 0.699923 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.83107 | 0.239282 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −74.3091 | −2.59975 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.5632 | −0.438995 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.9517 | −1.35942 | −0.679711 | − | 0.733480i | \(-0.737895\pi\) | ||||
−0.679711 | + | 0.733480i | \(0.737895\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6913 | 1.03497 | 0.517486 | − | 0.855691i | \(-0.326868\pi\) | ||||
0.517486 | + | 0.855691i | \(0.326868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 56.6928 | 1.97379 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.3192 | −1.68022 | −0.840111 | − | 0.542414i | \(-0.817510\pi\) | ||||
−0.840111 | + | 0.542414i | \(0.817510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.5168 | 1.05989 | 0.529946 | − | 0.848032i | \(-0.322212\pi\) | ||||
0.529946 | + | 0.848032i | \(0.322212\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 41.2421 | 1.43067 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.79625 | −0.270124 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.44597 | 0.326891 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.83071 | −0.0978438 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.5394 | −0.571004 | −0.285502 | − | 0.958378i | \(-0.592160\pi\) | ||||
−0.285502 | + | 0.958378i | \(0.592160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3371 | −0.770245 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.2829 | −0.457489 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.382499 | −0.0131584 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.7370 | 0.540730 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.2546 | 1.00402 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 31.3486 | 1.07462 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.1321 | 0.757788 | 0.378894 | − | 0.925440i | \(-0.376305\pi\) | ||||
0.378894 | + | 0.925440i | \(0.376305\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11.2949 | −0.386278 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.2714 | 0.999892 | 0.499946 | − | 0.866057i | \(-0.333353\pi\) | ||||
0.499946 | + | 0.866057i | \(0.333353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.2672 | −0.623270 | −0.311635 | − | 0.950202i | \(-0.600877\pi\) | ||||
−0.311635 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0625 | −0.547408 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.1450 | 0.481501 | 0.240751 | − | 0.970587i | \(-0.422606\pi\) | ||||
0.240751 | + | 0.970587i | \(0.422606\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.20828 | −0.211088 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.2979 | −1.23274 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.9728 | 0.779298 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.5051 | 0.999744 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −25.3576 | −0.858225 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.49153 | 0.185647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.2115 | 0.851333 | 0.425666 | − | 0.904880i | \(-0.360040\pi\) | ||||
0.425666 | + | 0.904880i | \(0.360040\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 77.5739 | 2.61650 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.8475 | 0.837133 | 0.418567 | − | 0.908186i | \(-0.362533\pi\) | ||||
0.418567 | + | 0.908186i | \(0.362533\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.9797 | 1.74926 | 0.874629 | − | 0.484793i | \(-0.161105\pi\) | ||||
0.874629 | + | 0.484793i | \(0.161105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.4351 | 0.350771 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.94768 | 0.266857 | 0.133428 | − | 0.991058i | \(-0.457401\pi\) | ||||
0.133428 | + | 0.991058i | \(0.457401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.8303 | −0.598010 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 46.6616 | 1.56322 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.9420 | 0.968508 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3207 | −0.344982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 64.6101 | 2.15727 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.2873 | 0.576565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8034 | 0.359913 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25.1864 | −0.838150 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.78281 | 0.125745 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.7947 | −1.25495 | −0.627476 | − | 0.778636i | \(-0.715912\pi\) | ||||
−0.627476 | + | 0.778636i | \(0.715912\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.7888 | 1.05437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.62265 | −0.285681 | −0.142841 | − | 0.989746i | \(-0.545624\pi\) | ||||
−0.142841 | + | 0.989746i | \(0.545624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.2327 | 0.967462 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.70261 | 0.0562866 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.65123 | −0.0545284 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6950 | 0.451756 | 0.225878 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225878 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.6276 | 1.33872 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.37938 | 0.242895 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.8039 | 0.684028 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.8311 | −0.552804 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.6443 | −1.03822 | −0.519108 | − | 0.854709i | \(-0.673736\pi\) | ||||
−0.519108 | + | 0.854709i | \(0.673736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −47.4427 | −1.55487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.5400 | 1.75282 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.22908 | 0.105602 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.0094 | −0.751684 | −0.375842 | − | 0.926684i | \(-0.622646\pi\) | ||||
−0.375842 | + | 0.926684i | \(0.622646\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −51.3042 | −1.67425 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.9570 | 1.04177 | 0.520884 | − | 0.853628i | \(-0.325602\pi\) | ||||
0.520884 | + | 0.853628i | \(0.325602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0611 | 1.30457 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.237336 | 0.00772053 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.64024 | 0.248274 | 0.124137 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124137 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.489433 | −0.0158877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.69062 | −0.216958 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.845695 | −0.0273947 | −0.0136974 | − | 0.999906i | \(-0.504360\pi\) | ||||
−0.0136974 | + | 0.999906i | \(0.504360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.272365 | −0.00881352 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.6162 | −0.989682 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.70063 | −0.184083 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8533 | 0.446881 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.87359 | 0.253723 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.55904 | 0.0501872 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56.5661 | 1.81904 | 0.909521 | − | 0.415657i | \(-0.136448\pi\) | ||||
0.909521 | + | 0.415657i | \(0.136448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.7908 | 0.924893 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.3347 | −0.909304 | −0.454652 | − | 0.890669i | \(-0.650236\pi\) | ||||
−0.454652 | + | 0.890669i | \(0.650236\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.7444 | −0.472684 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42.8772 | 1.37317 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.15495 | 0.0689429 | 0.0344715 | − | 0.999406i | \(-0.489025\pi\) | ||||
0.0344715 | + | 0.999406i | \(0.489025\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.4205 | −1.64341 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.3954 | 0.938524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.7182 | −0.884074 | −0.442037 | − | 0.896997i | \(-0.645744\pi\) | ||||
−0.442037 | + | 0.896997i | \(0.645744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.57905 | 0.273351 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.80962 | 0.312244 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 62.8168 | 1.99746 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.5255 | −1.16027 | −0.580135 | − | 0.814520i | \(-0.697000\pi\) | ||||
−0.580135 | + | 0.814520i | \(0.697000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.9650 | 1.04611 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.33072 | −0.137293 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0526 | −0.920105 | −0.460052 | − | 0.887892i | \(-0.652169\pi\) | ||||
−0.460052 | + | 0.887892i | \(0.652169\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.83966 | 0.0582042 |
(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 | 8048.2.a.s.1.20 | 21 | ||
4.3 | odd | 2 | 2012.2.a.b.1.2 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2012.2.a.b.1.2 | ✓ | 21 | 4.3 | odd | 2 | ||
8048.2.a.s.1.20 | 21 | 1.1 | even | 1 | trivial |