Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2850) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.267949 | −0.0807897 | −0.0403949 | − | 0.999184i | \(-0.512862\pi\) | ||||
−0.0403949 | + | 0.999184i | \(0.512862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.732051 | 0.203034 | 0.101517 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101517 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(14\) | −2.73205 | −0.730171 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.19615 | −1.01772 | −0.508858 | − | 0.860850i | \(-0.669932\pi\) | ||||
−0.508858 | + | 0.860850i | \(0.669932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.267949 | −0.0571270 | ||||||||
\(23\) | 7.92820 | 1.65314 | 0.826572 | − | 0.562831i | \(-0.190288\pi\) | ||||
0.826572 | + | 0.562831i | \(0.190288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.732051 | 0.143567 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.73205 | −0.516309 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.46410 | 0.801776 | 0.400888 | − | 0.916127i | \(-0.368702\pi\) | ||||
0.400888 | + | 0.916127i | \(0.368702\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.19615 | −0.719634 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.9282 | −1.70670 | −0.853349 | − | 0.521340i | \(-0.825432\pi\) | ||||
−0.853349 | + | 0.521340i | \(0.825432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.19615 | 0.334910 | 0.167455 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167455 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(44\) | −0.267949 | −0.0403949 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.92820 | 1.16895 | ||||||||
\(47\) | 3.46410 | 0.505291 | 0.252646 | − | 0.967559i | \(-0.418699\pi\) | ||||
0.252646 | + | 0.967559i | \(0.418699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.732051 | 0.101517 | ||||||||
\(53\) | −1.73205 | −0.237915 | −0.118958 | − | 0.992899i | \(-0.537955\pi\) | ||||
−0.118958 | + | 0.992899i | \(0.537955\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.73205 | −0.365086 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.73205 | −0.227429 | ||||||||
\(59\) | −2.19615 | −0.285915 | −0.142957 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142957 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.66025 | −0.852758 | −0.426379 | − | 0.904545i | \(-0.640211\pi\) | ||||
−0.426379 | + | 0.904545i | \(0.640211\pi\) | |||||||
\(62\) | 4.46410 | 0.566941 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.73205 | −0.455943 | −0.227971 | − | 0.973668i | \(-0.573209\pi\) | ||||
−0.227971 | + | 0.973668i | \(0.573209\pi\) | |||||||
\(68\) | −4.19615 | −0.508858 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.80385 | −0.214077 | −0.107039 | − | 0.994255i | \(-0.534137\pi\) | ||||
−0.107039 | + | 0.994255i | \(0.534137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.46410 | 0.522484 | 0.261242 | − | 0.965273i | \(-0.415868\pi\) | ||||
0.261242 | + | 0.965273i | \(0.415868\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0.732051 | 0.0834249 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4641 | −1.40232 | −0.701160 | − | 0.713003i | \(-0.747334\pi\) | ||||
−0.701160 | + | 0.713003i | \(0.747334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.9282 | −1.20682 | ||||||||
\(83\) | −0.267949 | −0.0294112 | −0.0147056 | − | 0.999892i | \(-0.504681\pi\) | ||||
−0.0147056 | + | 0.999892i | \(0.504681\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.19615 | 0.236817 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.267949 | −0.0285635 | ||||||||
\(89\) | 16.8564 | 1.78678 | 0.893388 | − | 0.449286i | \(-0.148322\pi\) | ||||
0.893388 | + | 0.449286i | \(0.148322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 7.92820 | 0.826572 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.46410 | 0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.12436 | 0.926438 | 0.463219 | − | 0.886244i | \(-0.346694\pi\) | ||||
0.463219 | + | 0.886244i | \(0.346694\pi\) | |||||||
\(98\) | 0.464102 | 0.0468813 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7321 | −1.26689 | −0.633443 | − | 0.773789i | \(-0.718359\pi\) | ||||
−0.633443 | + | 0.773789i | \(0.718359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4641 | −1.03106 | −0.515529 | − | 0.856872i | \(-0.672405\pi\) | ||||
−0.515529 | + | 0.856872i | \(0.672405\pi\) | |||||||
\(104\) | 0.732051 | 0.0717835 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.73205 | −0.168232 | ||||||||
\(107\) | 8.19615 | 0.792352 | 0.396176 | − | 0.918175i | \(-0.370337\pi\) | ||||
0.396176 | + | 0.918175i | \(0.370337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3923 | −1.76166 | −0.880832 | − | 0.473430i | \(-0.843016\pi\) | ||||
−0.880832 | + | 0.473430i | \(0.843016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.73205 | −0.258155 | ||||||||
\(113\) | −7.39230 | −0.695410 | −0.347705 | − | 0.937604i | \(-0.613039\pi\) | ||||
−0.347705 | + | 0.937604i | \(0.613039\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.19615 | −0.202172 | ||||||||
\(119\) | 11.4641 | 1.05091 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9282 | −0.993473 | ||||||||
\(122\) | −6.66025 | −0.602991 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.46410 | 0.400888 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7321 | −1.19977 | −0.599887 | − | 0.800084i | \(-0.704788\pi\) | ||||
−0.599887 | + | 0.800084i | \(0.704788\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73205 | 0.236899 | ||||||||
\(134\) | −3.73205 | −0.322400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.19615 | −0.359817 | ||||||||
\(137\) | −8.39230 | −0.717003 | −0.358501 | − | 0.933529i | \(-0.616712\pi\) | ||||
−0.358501 | + | 0.933529i | \(0.616712\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.12436 | 0.265004 | 0.132502 | − | 0.991183i | \(-0.457699\pi\) | ||||
0.132502 | + | 0.991183i | \(0.457699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.80385 | −0.151376 | ||||||||
\(143\) | −0.196152 | −0.0164031 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.46410 | 0.369452 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −5.85641 | −0.479776 | −0.239888 | − | 0.970801i | \(-0.577111\pi\) | ||||
−0.239888 | + | 0.970801i | \(0.577111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.53590 | −0.369126 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.732051 | 0.0589903 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8564 | −1.10586 | −0.552931 | − | 0.833227i | \(-0.686491\pi\) | ||||
−0.552931 | + | 0.833227i | \(0.686491\pi\) | |||||||
\(158\) | −12.4641 | −0.991591 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.6603 | −1.70707 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | −0.156652 | −0.0783260 | − | 0.996928i | \(-0.524958\pi\) | ||||
−0.0783260 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(164\) | −10.9282 | −0.853349 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.267949 | −0.0207969 | ||||||||
\(167\) | −4.92820 | −0.381356 | −0.190678 | − | 0.981653i | \(-0.561069\pi\) | ||||
−0.190678 | + | 0.981653i | \(0.561069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4641 | −0.958777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.19615 | 0.167455 | ||||||||
\(173\) | 17.5885 | 1.33723 | 0.668613 | − | 0.743611i | \(-0.266888\pi\) | ||||
0.668613 | + | 0.743611i | \(0.266888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.267949 | −0.0201974 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.8564 | 1.26344 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5885 | 1.08435 | 0.542176 | − | 0.840265i | \(-0.317601\pi\) | ||||
0.542176 | + | 0.840265i | \(0.317601\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.92820 | 0.584475 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12436 | 0.0822210 | ||||||||
\(188\) | 3.46410 | 0.252646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0526 | −1.15549 | −0.577744 | − | 0.816218i | \(-0.696067\pi\) | ||||
−0.577744 | + | 0.816218i | \(0.696067\pi\) | |||||||
\(194\) | 9.12436 | 0.655091 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.464102 | 0.0331501 | ||||||||
\(197\) | 6.58846 | 0.469408 | 0.234704 | − | 0.972067i | \(-0.424588\pi\) | ||||
0.234704 | + | 0.972067i | \(0.424588\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.7321 | −0.895824 | ||||||||
\(203\) | 4.73205 | 0.332125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.4641 | −0.729069 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.732051 | 0.0507586 | ||||||||
\(209\) | 0.267949 | 0.0185344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7321 | −0.945353 | −0.472677 | − | 0.881236i | \(-0.656712\pi\) | ||||
−0.472677 | + | 0.881236i | \(0.656712\pi\) | |||||||
\(212\) | −1.73205 | −0.118958 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.19615 | 0.560277 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.1962 | −0.827929 | ||||||||
\(218\) | −18.3923 | −1.24568 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.07180 | −0.206631 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4641 | −0.700728 | −0.350364 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350364 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(224\) | −2.73205 | −0.182543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.39230 | −0.491729 | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.73205 | −0.643112 | −0.321556 | − | 0.946891i | \(-0.604206\pi\) | ||||
−0.321556 | + | 0.946891i | \(0.604206\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.73205 | −0.113715 | ||||||||
\(233\) | −3.12436 | −0.204683 | −0.102342 | − | 0.994749i | \(-0.532634\pi\) | ||||
−0.102342 | + | 0.994749i | \(0.532634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.19615 | −0.142957 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.4641 | 0.743107 | ||||||||
\(239\) | 14.0000 | 0.905585 | 0.452792 | − | 0.891616i | \(-0.350428\pi\) | ||||
0.452792 | + | 0.891616i | \(0.350428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.8038 | −1.27568 | −0.637839 | − | 0.770170i | \(-0.720171\pi\) | ||||
−0.637839 | + | 0.770170i | \(0.720171\pi\) | |||||||
\(242\) | −10.9282 | −0.702492 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.66025 | −0.426379 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.732051 | −0.0465793 | ||||||||
\(248\) | 4.46410 | 0.283471 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.53590 | −0.286303 | −0.143152 | − | 0.989701i | \(-0.545724\pi\) | ||||
−0.143152 | + | 0.989701i | \(0.545724\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.12436 | −0.133557 | ||||||||
\(254\) | −5.00000 | −0.313728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.00000 | −0.561405 | −0.280702 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280702 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.46410 | 0.339523 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.7321 | −0.848369 | ||||||||
\(263\) | −15.0000 | −0.924940 | −0.462470 | − | 0.886635i | \(-0.653037\pi\) | ||||
−0.462470 | + | 0.886635i | \(0.653037\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.73205 | 0.167513 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.73205 | −0.227971 | ||||||||
\(269\) | 27.4641 | 1.67452 | 0.837258 | − | 0.546808i | \(-0.184157\pi\) | ||||
0.837258 | + | 0.546808i | \(0.184157\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.1962 | −1.59130 | −0.795651 | − | 0.605755i | \(-0.792871\pi\) | ||||
−0.795651 | + | 0.605755i | \(0.792871\pi\) | |||||||
\(272\) | −4.19615 | −0.254429 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.39230 | −0.506998 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.803848 | 0.0482985 | 0.0241493 | − | 0.999708i | \(-0.492312\pi\) | ||||
0.0241493 | + | 0.999708i | \(0.492312\pi\) | |||||||
\(278\) | 3.12436 | 0.187386 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7846 | 1.41887 | 0.709435 | − | 0.704770i | \(-0.248950\pi\) | ||||
0.709435 | + | 0.704770i | \(0.248950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | 0.237775 | 0.118888 | − | 0.992908i | \(-0.462067\pi\) | ||||
0.118888 | + | 0.992908i | \(0.462067\pi\) | |||||||
\(284\) | −1.80385 | −0.107039 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.196152 | −0.0115987 | ||||||||
\(287\) | 29.8564 | 1.76237 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.607695 | 0.0357468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.46410 | 0.261242 | ||||||||
\(293\) | 24.2679 | 1.41775 | 0.708874 | − | 0.705335i | \(-0.249203\pi\) | ||||
0.708874 | + | 0.705335i | \(0.249203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.85641 | −0.339253 | ||||||||
\(299\) | 5.80385 | 0.335645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | −4.53590 | −0.261012 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.7321 | −1.35446 | −0.677230 | − | 0.735772i | \(-0.736820\pi\) | ||||
−0.677230 | + | 0.735772i | \(0.736820\pi\) | |||||||
\(308\) | 0.732051 | 0.0417125 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.32051 | −0.301698 | −0.150849 | − | 0.988557i | \(-0.548201\pi\) | ||||
−0.150849 | + | 0.988557i | \(0.548201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.92820 | 0.561175 | 0.280588 | − | 0.959828i | \(-0.409471\pi\) | ||||
0.280588 | + | 0.959828i | \(0.409471\pi\) | |||||||
\(314\) | −13.8564 | −0.781962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.4641 | −0.701160 | ||||||||
\(317\) | −1.73205 | −0.0972817 | −0.0486408 | − | 0.998816i | \(-0.515489\pi\) | ||||
−0.0486408 | + | 0.998816i | \(0.515489\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.464102 | 0.0259847 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.6603 | −1.20708 | ||||||||
\(323\) | 4.19615 | 0.233480 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.9282 | −0.603409 | ||||||||
\(329\) | −9.46410 | −0.521773 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.7321 | −1.41436 | −0.707181 | − | 0.707033i | \(-0.750033\pi\) | ||||
−0.707181 | + | 0.707033i | \(0.750033\pi\) | |||||||
\(332\) | −0.267949 | −0.0147056 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.92820 | −0.269659 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4641 | 0.951330 | 0.475665 | − | 0.879626i | \(-0.342207\pi\) | ||||
0.475665 | + | 0.879626i | \(0.342207\pi\) | |||||||
\(338\) | −12.4641 | −0.677958 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.19615 | −0.0647753 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 2.19615 | 0.118409 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.5885 | 0.945561 | ||||||||
\(347\) | −20.7846 | −1.11578 | −0.557888 | − | 0.829916i | \(-0.688388\pi\) | ||||
−0.557888 | + | 0.829916i | \(0.688388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.0526 | 1.12692 | 0.563459 | − | 0.826144i | \(-0.309470\pi\) | ||||
0.563459 | + | 0.826144i | \(0.309470\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.267949 | −0.0142817 | ||||||||
\(353\) | 22.0526 | 1.17374 | 0.586870 | − | 0.809681i | \(-0.300360\pi\) | ||||
0.586870 | + | 0.809681i | \(0.300360\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.8564 | 0.893388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.0000 | 0.634220 | ||||||||
\(359\) | 3.07180 | 0.162123 | 0.0810616 | − | 0.996709i | \(-0.474169\pi\) | ||||
0.0810616 | + | 0.996709i | \(0.474169\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 14.5885 | 0.766752 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.7321 | −0.873406 | −0.436703 | − | 0.899606i | \(-0.643854\pi\) | ||||
−0.436703 | + | 0.899606i | \(0.643854\pi\) | |||||||
\(368\) | 7.92820 | 0.413286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.73205 | 0.245676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5167 | 0.699866 | 0.349933 | − | 0.936775i | \(-0.386204\pi\) | ||||
0.349933 | + | 0.936775i | \(0.386204\pi\) | |||||||
\(374\) | 1.12436 | 0.0581390 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.46410 | 0.178647 | ||||||||
\(377\) | −1.26795 | −0.0653027 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.3923 | 1.04748 | 0.523741 | − | 0.851877i | \(-0.324536\pi\) | ||||
0.523741 | + | 0.851877i | \(0.324536\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | −0.153493 | ||||||||
\(383\) | −25.5167 | −1.30384 | −0.651920 | − | 0.758288i | \(-0.726036\pi\) | ||||
−0.651920 | + | 0.758288i | \(0.726036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.0526 | −0.817054 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.12436 | 0.463219 | ||||||||
\(389\) | 33.7128 | 1.70931 | 0.854654 | − | 0.519198i | \(-0.173769\pi\) | ||||
0.854654 | + | 0.519198i | \(0.173769\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.2679 | −1.68243 | ||||||||
\(392\) | 0.464102 | 0.0234407 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.58846 | 0.331922 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.26795 | 0.414956 | 0.207478 | − | 0.978240i | \(-0.433474\pi\) | ||||
0.207478 | + | 0.978240i | \(0.433474\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.8564 | 0.542143 | 0.271072 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271072 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.26795 | 0.162788 | ||||||||
\(404\) | −12.7321 | −0.633443 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.73205 | 0.234848 | ||||||||
\(407\) | 0.535898 | 0.0265635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.3923 | 1.10723 | 0.553614 | − | 0.832773i | \(-0.313248\pi\) | ||||
0.553614 | + | 0.832773i | \(0.313248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.4641 | −0.515529 | ||||||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.732051 | 0.0358917 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.267949 | 0.0131058 | ||||||||
\(419\) | 13.8564 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.7846 | −1.69530 | −0.847649 | − | 0.530557i | \(-0.821983\pi\) | ||||
−0.847649 | + | 0.530557i | \(0.821983\pi\) | |||||||
\(422\) | −13.7321 | −0.668466 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.73205 | −0.0841158 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.1962 | 0.880574 | ||||||||
\(428\) | 8.19615 | 0.396176 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.32051 | −0.256280 | −0.128140 | − | 0.991756i | \(-0.540901\pi\) | ||||
−0.128140 | + | 0.991756i | \(0.540901\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.8038 | 0.663371 | 0.331685 | − | 0.943390i | \(-0.392383\pi\) | ||||
0.331685 | + | 0.943390i | \(0.392383\pi\) | |||||||
\(434\) | −12.1962 | −0.585434 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.3923 | −0.880832 | ||||||||
\(437\) | −7.92820 | −0.379257 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7846 | −0.753358 | −0.376679 | − | 0.926344i | \(-0.622934\pi\) | ||||
−0.376679 | + | 0.926344i | \(0.622934\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.07180 | −0.146110 | ||||||||
\(443\) | −20.6603 | −0.981598 | −0.490799 | − | 0.871273i | \(-0.663295\pi\) | ||||
−0.490799 | + | 0.871273i | \(0.663295\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.4641 | −0.495490 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.73205 | −0.129077 | ||||||||
\(449\) | −17.5359 | −0.827570 | −0.413785 | − | 0.910375i | \(-0.635794\pi\) | ||||
−0.413785 | + | 0.910375i | \(0.635794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92820 | 0.137884 | ||||||||
\(452\) | −7.39230 | −0.347705 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9282 | 0.885424 | 0.442712 | − | 0.896664i | \(-0.354016\pi\) | ||||
0.442712 | + | 0.896664i | \(0.354016\pi\) | |||||||
\(458\) | −9.73205 | −0.454749 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.85641 | −0.459059 | −0.229529 | − | 0.973302i | \(-0.573719\pi\) | ||||
−0.229529 | + | 0.973302i | \(0.573719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.679492 | 0.0315787 | 0.0157893 | − | 0.999875i | \(-0.494974\pi\) | ||||
0.0157893 | + | 0.999875i | \(0.494974\pi\) | |||||||
\(464\) | −1.73205 | −0.0804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.12436 | −0.144733 | ||||||||
\(467\) | −3.19615 | −0.147900 | −0.0739501 | − | 0.997262i | \(-0.523561\pi\) | ||||
−0.0739501 | + | 0.997262i | \(0.523561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1962 | 0.470815 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.19615 | −0.101086 | ||||||||
\(473\) | −0.588457 | −0.0270573 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.4641 | 0.525456 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.0000 | 0.640345 | ||||||||
\(479\) | −30.8564 | −1.40987 | −0.704933 | − | 0.709274i | \(-0.749023\pi\) | ||||
−0.704933 | + | 0.709274i | \(0.749023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.46410 | −0.0667573 | ||||||||
\(482\) | −19.8038 | −0.902041 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9282 | −0.496737 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.8564 | −1.35292 | −0.676461 | − | 0.736478i | \(-0.736487\pi\) | ||||
−0.676461 | + | 0.736478i | \(0.736487\pi\) | |||||||
\(488\) | −6.66025 | −0.301496 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.9282 | −0.493183 | −0.246591 | − | 0.969120i | \(-0.579311\pi\) | ||||
−0.246591 | + | 0.969120i | \(0.579311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.26795 | 0.327332 | ||||||||
\(494\) | −0.732051 | −0.0329365 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.46410 | 0.200444 | ||||||||
\(497\) | 4.92820 | 0.221060 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.3731 | −1.40445 | −0.702226 | − | 0.711954i | \(-0.747810\pi\) | ||||
−0.702226 | + | 0.711954i | \(0.747810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.53590 | −0.202447 | ||||||||
\(503\) | 9.85641 | 0.439475 | 0.219738 | − | 0.975559i | \(-0.429480\pi\) | ||||
0.219738 | + | 0.975559i | \(0.429480\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.12436 | −0.0944391 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.00000 | −0.221839 | ||||||||
\(509\) | −38.1244 | −1.68983 | −0.844916 | − | 0.534899i | \(-0.820350\pi\) | ||||
−0.844916 | + | 0.534899i | \(0.820350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1962 | −0.539526 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.00000 | −0.396973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.928203 | −0.0408223 | ||||||||
\(518\) | 5.46410 | 0.240079 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.1769 | 1.67256 | 0.836280 | − | 0.548302i | \(-0.184726\pi\) | ||||
0.836280 | + | 0.548302i | \(0.184726\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | −13.7321 | −0.599887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0000 | −0.654031 | ||||||||
\(527\) | −18.7321 | −0.815981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.8564 | 1.73289 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.73205 | 0.118449 | ||||||||
\(533\) | −8.00000 | −0.346518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.73205 | −0.161200 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.4641 | 1.18406 | ||||||||
\(539\) | −0.124356 | −0.00535638 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.80385 | 0.292520 | 0.146260 | − | 0.989246i | \(-0.453276\pi\) | ||||
0.146260 | + | 0.989246i | \(0.453276\pi\) | |||||||
\(542\) | −26.1962 | −1.12522 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.19615 | −0.179909 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.4449 | −0.660375 | −0.330187 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330187 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(548\) | −8.39230 | −0.358501 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.73205 | 0.0737878 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.0526 | 1.44806 | ||||||||
\(554\) | 0.803848 | 0.0341522 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.12436 | 0.132502 | ||||||||
\(557\) | −14.1962 | −0.601510 | −0.300755 | − | 0.953701i | \(-0.597239\pi\) | ||||
−0.300755 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.60770 | 0.0679983 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.7846 | 1.00329 | ||||||||
\(563\) | 9.66025 | 0.407131 | 0.203566 | − | 0.979061i | \(-0.434747\pi\) | ||||
0.203566 | + | 0.979061i | \(0.434747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | 0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.80385 | −0.0756878 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.19615 | 0.175604 | 0.0878018 | − | 0.996138i | \(-0.472016\pi\) | ||||
0.0878018 | + | 0.996138i | \(0.472016\pi\) | |||||||
\(572\) | −0.196152 | −0.00820154 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 29.8564 | 1.24618 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.2487 | 1.30090 | 0.650450 | − | 0.759549i | \(-0.274580\pi\) | ||||
0.650450 | + | 0.759549i | \(0.274580\pi\) | |||||||
\(578\) | 0.607695 | 0.0252768 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.732051 | 0.0303706 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.464102 | 0.0192211 | ||||||||
\(584\) | 4.46410 | 0.184726 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 24.2679 | 1.00250 | ||||||||
\(587\) | 15.7321 | 0.649331 | 0.324666 | − | 0.945829i | \(-0.394748\pi\) | ||||
0.324666 | + | 0.945829i | \(0.394748\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.46410 | −0.183940 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.00000 | −0.0821995 | ||||||||
\(593\) | 48.3923 | 1.98723 | 0.993617 | − | 0.112807i | \(-0.0359843\pi\) | ||||
0.993617 | + | 0.112807i | \(0.0359843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.85641 | −0.239888 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.80385 | 0.237337 | ||||||||
\(599\) | −13.6603 | −0.558143 | −0.279071 | − | 0.960270i | \(-0.590027\pi\) | ||||
−0.279071 | + | 0.960270i | \(0.590027\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0526 | 1.14429 | 0.572144 | − | 0.820153i | \(-0.306112\pi\) | ||||
0.572144 | + | 0.820153i | \(0.306112\pi\) | |||||||
\(602\) | −6.00000 | −0.244542 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.53590 | −0.184563 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.7846 | 1.20892 | 0.604460 | − | 0.796635i | \(-0.293389\pi\) | ||||
0.604460 | + | 0.796635i | \(0.293389\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.53590 | 0.102591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.78461 | −0.112469 | −0.0562347 | − | 0.998418i | \(-0.517909\pi\) | ||||
−0.0562347 | + | 0.998418i | \(0.517909\pi\) | |||||||
\(614\) | −23.7321 | −0.957748 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.732051 | 0.0294952 | ||||||||
\(617\) | −25.6077 | −1.03093 | −0.515463 | − | 0.856912i | \(-0.672380\pi\) | ||||
−0.515463 | + | 0.856912i | \(0.672380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1962 | 0.409818 | 0.204909 | − | 0.978781i | \(-0.434310\pi\) | ||||
0.204909 | + | 0.978781i | \(0.434310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.32051 | −0.213333 | ||||||||
\(623\) | −46.0526 | −1.84506 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.92820 | 0.396811 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.8564 | −0.552931 | ||||||||
\(629\) | 8.39230 | 0.334623 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.9282 | −0.435045 | −0.217522 | − | 0.976055i | \(-0.569798\pi\) | ||||
−0.217522 | + | 0.976055i | \(0.569798\pi\) | |||||||
\(632\) | −12.4641 | −0.495795 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.73205 | −0.0687885 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.339746 | 0.0134612 | ||||||||
\(638\) | 0.464102 | 0.0183740 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.4641 | −0.689791 | −0.344895 | − | 0.938641i | \(-0.612086\pi\) | ||||
−0.344895 | + | 0.938641i | \(0.612086\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.9282 | 1.61405 | 0.807025 | − | 0.590517i | \(-0.201076\pi\) | ||||
0.807025 | + | 0.590517i | \(0.201076\pi\) | |||||||
\(644\) | −21.6603 | −0.853534 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.19615 | 0.165095 | ||||||||
\(647\) | 11.3923 | 0.447878 | 0.223939 | − | 0.974603i | \(-0.428108\pi\) | ||||
0.223939 | + | 0.974603i | \(0.428108\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.588457 | 0.0230990 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | −0.0783260 | ||||||||
\(653\) | 10.5359 | 0.412302 | 0.206151 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206151 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.9282 | −0.426675 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.46410 | −0.368949 | ||||||||
\(659\) | −38.5885 | −1.50319 | −0.751596 | − | 0.659623i | \(-0.770716\pi\) | ||||
−0.751596 | + | 0.659623i | \(0.770716\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.6410 | 1.81413 | 0.907063 | − | 0.420996i | \(-0.138319\pi\) | ||||
0.907063 | + | 0.420996i | \(0.138319\pi\) | |||||||
\(662\) | −25.7321 | −1.00010 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.267949 | −0.0103984 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.7321 | −0.531707 | ||||||||
\(668\) | −4.92820 | −0.190678 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.78461 | 0.0688941 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.9808 | −1.73388 | −0.866940 | − | 0.498412i | \(-0.833917\pi\) | ||||
−0.866940 | + | 0.498412i | \(0.833917\pi\) | |||||||
\(674\) | 17.4641 | 0.672692 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.4641 | −0.479389 | ||||||||
\(677\) | −8.66025 | −0.332841 | −0.166420 | − | 0.986055i | \(-0.553221\pi\) | ||||
−0.166420 | + | 0.986055i | \(0.553221\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9282 | −0.956657 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.19615 | −0.0458030 | ||||||||
\(683\) | 4.98076 | 0.190584 | 0.0952918 | − | 0.995449i | \(-0.469622\pi\) | ||||
0.0952918 | + | 0.995449i | \(0.469622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.8564 | 0.681761 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.19615 | 0.0837275 | ||||||||
\(689\) | −1.26795 | −0.0483050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8038 | −0.449040 | −0.224520 | − | 0.974470i | \(-0.572081\pi\) | ||||
−0.224520 | + | 0.974470i | \(0.572081\pi\) | |||||||
\(692\) | 17.5885 | 0.668613 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.7846 | −0.788973 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.8564 | 1.73694 | ||||||||
\(698\) | 21.0526 | 0.796851 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.3923 | −0.921285 | −0.460642 | − | 0.887586i | \(-0.652381\pi\) | ||||
−0.460642 | + | 0.887586i | \(0.652381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.00000 | 0.0754314 | ||||||||
\(704\) | −0.267949 | −0.0100987 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0526 | 0.829959 | ||||||||
\(707\) | 34.7846 | 1.30821 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.3013 | −1.47599 | −0.737995 | − | 0.674806i | \(-0.764227\pi\) | ||||
−0.737995 | + | 0.674806i | \(0.764227\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.8564 | 0.631721 | ||||||||
\(713\) | 35.3923 | 1.32545 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.07180 | 0.114638 | ||||||||
\(719\) | 50.1769 | 1.87128 | 0.935642 | − | 0.352952i | \(-0.114822\pi\) | ||||
0.935642 | + | 0.352952i | \(0.114822\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.5885 | 1.06469 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.5885 | 0.542176 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1051 | 1.41324 | 0.706620 | − | 0.707593i | \(-0.250219\pi\) | ||||
0.706620 | + | 0.707593i | \(0.250219\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.21539 | −0.340844 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5167 | 0.905544 | 0.452772 | − | 0.891626i | \(-0.350435\pi\) | ||||
0.452772 | + | 0.891626i | \(0.350435\pi\) | |||||||
\(734\) | −16.7321 | −0.617591 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.92820 | 0.292237 | ||||||||
\(737\) | 1.00000 | 0.0368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.17691 | 0.337578 | 0.168789 | − | 0.985652i | \(-0.446014\pi\) | ||||
0.168789 | + | 0.985652i | \(0.446014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.73205 | 0.173719 | ||||||||
\(743\) | 18.9282 | 0.694408 | 0.347204 | − | 0.937790i | \(-0.387131\pi\) | ||||
0.347204 | + | 0.937790i | \(0.387131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.5167 | 0.494880 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.12436 | 0.0411105 | ||||||||
\(749\) | −22.3923 | −0.818197 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.535898 | 0.0195552 | 0.00977760 | − | 0.999952i | \(-0.496888\pi\) | ||||
0.00977760 | + | 0.999952i | \(0.496888\pi\) | |||||||
\(752\) | 3.46410 | 0.126323 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.26795 | −0.0461760 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.5885 | 0.639263 | 0.319632 | − | 0.947542i | \(-0.396441\pi\) | ||||
0.319632 | + | 0.947542i | \(0.396441\pi\) | |||||||
\(758\) | 20.3923 | 0.740682 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.73205 | −0.171537 | −0.0857684 | − | 0.996315i | \(-0.527334\pi\) | ||||
−0.0857684 | + | 0.996315i | \(0.527334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 50.2487 | 1.81913 | ||||||||
\(764\) | −3.00000 | −0.108536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.5167 | −0.921954 | ||||||||
\(767\) | −1.60770 | −0.0580505 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.7128 | 0.746923 | 0.373462 | − | 0.927646i | \(-0.378171\pi\) | ||||
0.373462 | + | 0.927646i | \(0.378171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0526 | −0.577744 | ||||||||
\(773\) | 10.6795 | 0.384115 | 0.192057 | − | 0.981384i | \(-0.438484\pi\) | ||||
0.192057 | + | 0.981384i | \(0.438484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.12436 | 0.327545 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.7128 | 1.20866 | ||||||||
\(779\) | 10.9282 | 0.391544 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.483340 | 0.0172952 | ||||||||
\(782\) | −33.2679 | −1.18966 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.464102 | 0.0165751 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.1244 | −0.788648 | −0.394324 | − | 0.918971i | \(-0.629021\pi\) | ||||
−0.394324 | + | 0.918971i | \(0.629021\pi\) | |||||||
\(788\) | 6.58846 | 0.234704 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.1962 | 0.718093 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.87564 | −0.173139 | ||||||||
\(794\) | 8.26795 | 0.293419 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | −20.0000 | −0.708436 | −0.354218 | − | 0.935163i | \(-0.615253\pi\) | ||||
−0.354218 | + | 0.935163i | \(0.615253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.5359 | −0.514243 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.8564 | 0.383353 | ||||||||
\(803\) | −1.19615 | −0.0422113 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.26795 | 0.115109 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.7321 | −0.447912 | ||||||||
\(809\) | 7.51666 | 0.264272 | 0.132136 | − | 0.991232i | \(-0.457816\pi\) | ||||
0.132136 | + | 0.991232i | \(0.457816\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.3731 | −1.90930 | −0.954648 | − | 0.297736i | \(-0.903769\pi\) | ||||
−0.954648 | + | 0.297736i | \(0.903769\pi\) | |||||||
\(812\) | 4.73205 | 0.166062 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.535898 | 0.0187832 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.19615 | −0.0768336 | ||||||||
\(818\) | 22.3923 | 0.782929 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.5167 | −1.65834 | −0.829171 | − | 0.558994i | \(-0.811187\pi\) | ||||
−0.829171 | + | 0.558994i | \(0.811187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.7846 | 1.21252 | 0.606258 | − | 0.795268i | \(-0.292670\pi\) | ||||
0.606258 | + | 0.795268i | \(0.292670\pi\) | |||||||
\(824\) | −10.4641 | −0.364534 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | −3.26795 | −0.113638 | −0.0568189 | − | 0.998385i | \(-0.518096\pi\) | ||||
−0.0568189 | + | 0.998385i | \(0.518096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.19615 | −0.145738 | −0.0728692 | − | 0.997342i | \(-0.523216\pi\) | ||||
−0.0728692 | + | 0.997342i | \(0.523216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.732051 | 0.0253793 | ||||||||
\(833\) | −1.94744 | −0.0674748 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.267949 | 0.00926722 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.8564 | 0.478662 | ||||||||
\(839\) | 15.4115 | 0.532066 | 0.266033 | − | 0.963964i | \(-0.414287\pi\) | ||||
0.266033 | + | 0.963964i | \(0.414287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | −34.7846 | −1.19876 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.7321 | −0.472677 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.8564 | 1.02588 | ||||||||
\(848\) | −1.73205 | −0.0594789 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8564 | −0.543551 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4641 | −0.392523 | −0.196262 | − | 0.980552i | \(-0.562880\pi\) | ||||
−0.196262 | + | 0.980552i | \(0.562880\pi\) | |||||||
\(854\) | 18.1962 | 0.622660 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.19615 | 0.280139 | ||||||||
\(857\) | 29.0718 | 0.993074 | 0.496537 | − | 0.868016i | \(-0.334605\pi\) | ||||
0.496537 | + | 0.868016i | \(0.334605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.0718 | 1.46959 | 0.734795 | − | 0.678289i | \(-0.237278\pi\) | ||||
0.734795 | + | 0.678289i | \(0.237278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.32051 | −0.181217 | ||||||||
\(863\) | 20.6795 | 0.703938 | 0.351969 | − | 0.936012i | \(-0.385512\pi\) | ||||
0.351969 | + | 0.936012i | \(0.385512\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 13.8038 | 0.469074 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.1962 | −0.413964 | ||||||||
\(869\) | 3.33975 | 0.113293 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.73205 | −0.0925720 | ||||||||
\(872\) | −18.3923 | −0.622842 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.92820 | −0.268175 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.1769 | −1.05277 | −0.526385 | − | 0.850246i | \(-0.676453\pi\) | ||||
−0.526385 | + | 0.850246i | \(0.676453\pi\) | |||||||
\(878\) | −15.7846 | −0.532705 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.4641 | 1.12743 | 0.563717 | − | 0.825968i | \(-0.309371\pi\) | ||||
0.563717 | + | 0.825968i | \(0.309371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.7321 | 1.03422 | 0.517108 | − | 0.855920i | \(-0.327009\pi\) | ||||
0.517108 | + | 0.855920i | \(0.327009\pi\) | |||||||
\(884\) | −3.07180 | −0.103316 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.6603 | −0.694095 | ||||||||
\(887\) | 28.3923 | 0.953320 | 0.476660 | − | 0.879088i | \(-0.341847\pi\) | ||||
0.476660 | + | 0.879088i | \(0.341847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6603 | 0.458150 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.4641 | −0.350364 | ||||||||
\(893\) | −3.46410 | −0.115922 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.73205 | −0.0912714 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.5359 | −0.585181 | ||||||||
\(899\) | −7.73205 | −0.257878 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.26795 | 0.242130 | ||||||||
\(902\) | 2.92820 | 0.0974985 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.39230 | −0.245864 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.6795 | 0.487425 | 0.243712 | − | 0.969848i | \(-0.421635\pi\) | ||||
0.243712 | + | 0.969848i | \(0.421635\pi\) | |||||||
\(908\) | 6.00000 | 0.199117 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.1051 | 1.39500 | 0.697502 | − | 0.716582i | \(-0.254295\pi\) | ||||
0.697502 | + | 0.716582i | \(0.254295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0717968 | 0.00237613 | ||||||||
\(914\) | 18.9282 | 0.626089 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.73205 | −0.321556 | ||||||||
\(917\) | 37.5167 | 1.23891 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.5167 | −1.63340 | −0.816702 | − | 0.577060i | \(-0.804200\pi\) | ||||
−0.816702 | + | 0.577060i | \(0.804200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.85641 | −0.324603 | ||||||||
\(923\) | −1.32051 | −0.0434651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.679492 | 0.0223295 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.73205 | −0.0568574 | ||||||||
\(929\) | −29.0718 | −0.953815 | −0.476907 | − | 0.878954i | \(-0.658242\pi\) | ||||
−0.476907 | + | 0.878954i | \(0.658242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.464102 | −0.0152103 | ||||||||
\(932\) | −3.12436 | −0.102342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.19615 | −0.104581 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.7846 | −1.78974 | −0.894868 | − | 0.446332i | \(-0.852730\pi\) | ||||
−0.894868 | + | 0.446332i | \(0.852730\pi\) | |||||||
\(938\) | 10.1962 | 0.332916 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.7321 | 0.512850 | 0.256425 | − | 0.966564i | \(-0.417455\pi\) | ||||
0.256425 | + | 0.966564i | \(0.417455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −86.6410 | −2.82142 | ||||||||
\(944\) | −2.19615 | −0.0714787 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.588457 | −0.0191324 | ||||||||
\(947\) | 21.8564 | 0.710238 | 0.355119 | − | 0.934821i | \(-0.384440\pi\) | ||||
0.355119 | + | 0.934821i | \(0.384440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.26795 | 0.106082 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.4641 | 0.371554 | ||||||||
\(953\) | 43.2487 | 1.40096 | 0.700482 | − | 0.713670i | \(-0.252969\pi\) | ||||
0.700482 | + | 0.713670i | \(0.252969\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.0000 | 0.452792 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.8564 | −0.996925 | ||||||||
\(959\) | 22.9282 | 0.740390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0718 | −0.357155 | ||||||||
\(962\) | −1.46410 | −0.0472045 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −19.8038 | −0.637839 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58.1051 | 1.86853 | 0.934267 | − | 0.356573i | \(-0.116055\pi\) | ||||
0.934267 | + | 0.356573i | \(0.116055\pi\) | |||||||
\(968\) | −10.9282 | −0.351246 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55.7654 | −1.78960 | −0.894798 | − | 0.446471i | \(-0.852681\pi\) | ||||
−0.894798 | + | 0.446471i | \(0.852681\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.53590 | −0.273648 | ||||||||
\(974\) | −29.8564 | −0.956661 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.66025 | −0.213190 | ||||||||
\(977\) | 5.46410 | 0.174812 | 0.0874060 | − | 0.996173i | \(-0.472142\pi\) | ||||
0.0874060 | + | 0.996173i | \(0.472142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.51666 | −0.144353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.9282 | −0.348733 | ||||||||
\(983\) | −47.6603 | −1.52013 | −0.760063 | − | 0.649849i | \(-0.774832\pi\) | ||||
−0.760063 | + | 0.649849i | \(0.774832\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.26795 | 0.231459 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.732051 | −0.0232896 | ||||||||
\(989\) | 17.4115 | 0.553655 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.67949 | −0.180415 | −0.0902075 | − | 0.995923i | \(-0.528753\pi\) | ||||
−0.0902075 | + | 0.995923i | \(0.528753\pi\) | |||||||
\(992\) | 4.46410 | 0.141735 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.92820 | 0.156313 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.9474 | 0.790093 | 0.395047 | − | 0.918661i | \(-0.370728\pi\) | ||||
0.395047 | + | 0.918661i | \(0.370728\pi\) | |||||||
\(998\) | −31.3731 | −0.993097 | ||||||||
\(999\) | 0 | 0 |
(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 | 8550.2.a.by.1.1 | 2 | ||
3.2 | odd | 2 | 2850.2.a.bd.1.1 | ✓ | 2 | ||
5.4 | even | 2 | 8550.2.a.bs.1.2 | 2 | |||
15.2 | even | 4 | 2850.2.d.x.799.1 | 4 | |||
15.8 | even | 4 | 2850.2.d.x.799.4 | 4 | |||
15.14 | odd | 2 | 2850.2.a.bi.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bd.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
2850.2.a.bi.1.2 | yes | 2 | 15.14 | odd | 2 | ||
2850.2.d.x.799.1 | 4 | 15.2 | even | 4 | |||
2850.2.d.x.799.4 | 4 | 15.8 | even | 4 | |||
8550.2.a.bs.1.2 | 2 | 5.4 | even | 2 | |||
8550.2.a.by.1.1 | 2 | 1.1 | even | 1 | trivial |