Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2013) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.66112\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66112 | −1.17459 | −0.587294 | − | 0.809374i | \(-0.699807\pi\) | ||||
−0.587294 | + | 0.809374i | \(0.699807\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.759316 | 0.379658 | ||||||||
\(5\) | 1.47319 | 0.658832 | 0.329416 | − | 0.944185i | \(-0.393148\pi\) | ||||
0.329416 | + | 0.944185i | \(0.393148\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.81455 | −1.06380 | −0.531900 | − | 0.846807i | \(-0.678522\pi\) | ||||
−0.531900 | + | 0.846807i | \(0.678522\pi\) | |||||||
\(8\) | 2.06092 | 0.728647 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.44715 | −0.773857 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.11864 | 1.14231 | 0.571153 | − | 0.820844i | \(-0.306496\pi\) | ||||
0.571153 | + | 0.820844i | \(0.306496\pi\) | |||||||
\(14\) | 4.67530 | 1.24953 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.94207 | −1.23552 | ||||||||
\(17\) | 4.46728 | 1.08347 | 0.541737 | − | 0.840548i | \(-0.317767\pi\) | ||||
0.541737 | + | 0.840548i | \(0.317767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.28705 | 0.524685 | 0.262343 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262343 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(20\) | 1.11862 | 0.250131 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.66112 | 0.354152 | ||||||||
\(23\) | 7.49465 | 1.56274 | 0.781372 | − | 0.624066i | \(-0.214520\pi\) | ||||
0.781372 | + | 0.624066i | \(0.214520\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.82970 | −0.565940 | ||||||||
\(26\) | −6.84155 | −1.34174 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.13713 | −0.403880 | ||||||||
\(29\) | 10.0128 | 1.85933 | 0.929664 | − | 0.368407i | \(-0.120097\pi\) | ||||
0.929664 | + | 0.368407i | \(0.120097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.99425 | 0.896995 | 0.448497 | − | 0.893784i | \(-0.351959\pi\) | ||||
0.448497 | + | 0.893784i | \(0.351959\pi\) | |||||||
\(32\) | 4.08752 | 0.722578 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.42068 | −1.27264 | ||||||||
\(35\) | −4.14637 | −0.700865 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.685924 | −0.112765 | −0.0563826 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563826 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(38\) | −3.79906 | −0.616289 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.03614 | 0.480056 | ||||||||
\(41\) | 9.33901 | 1.45851 | 0.729254 | − | 0.684243i | \(-0.239867\pi\) | ||||
0.729254 | + | 0.684243i | \(0.239867\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.98858 | −1.06575 | −0.532874 | − | 0.846194i | \(-0.678888\pi\) | ||||
−0.532874 | + | 0.846194i | \(0.678888\pi\) | |||||||
\(44\) | −0.759316 | −0.114471 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.4495 | −1.83558 | ||||||||
\(47\) | −1.45467 | −0.212186 | −0.106093 | − | 0.994356i | \(-0.533834\pi\) | ||||
−0.106093 | + | 0.994356i | \(0.533834\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.921685 | 0.131669 | ||||||||
\(50\) | 4.70047 | 0.664747 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.12735 | 0.433686 | ||||||||
\(53\) | 4.15316 | 0.570480 | 0.285240 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285240 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.47319 | −0.198645 | ||||||||
\(56\) | −5.80057 | −0.775134 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −16.6324 | −2.18395 | ||||||||
\(59\) | −13.8976 | −1.80932 | −0.904659 | − | 0.426136i | \(-0.859875\pi\) | ||||
−0.904659 | + | 0.426136i | \(0.859875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | −8.29605 | −1.05360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.09428 | 0.386786 | ||||||||
\(65\) | 6.06756 | 0.752588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.34866 | −0.286934 | −0.143467 | − | 0.989655i | \(-0.545825\pi\) | ||||
−0.143467 | + | 0.989655i | \(0.545825\pi\) | |||||||
\(68\) | 3.39208 | 0.411350 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.88762 | 0.823228 | ||||||||
\(71\) | −1.88712 | −0.223960 | −0.111980 | − | 0.993710i | \(-0.535719\pi\) | ||||
−0.111980 | + | 0.993710i | \(0.535719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5870 | 1.35615 | 0.678075 | − | 0.734992i | \(-0.262814\pi\) | ||||
0.678075 | + | 0.734992i | \(0.262814\pi\) | |||||||
\(74\) | 1.13940 | 0.132453 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.73659 | 0.199201 | ||||||||
\(77\) | 2.81455 | 0.320748 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0173 | −1.23954 | −0.619771 | − | 0.784783i | \(-0.712774\pi\) | ||||
−0.619771 | + | 0.784783i | \(0.712774\pi\) | |||||||
\(80\) | −7.28063 | −0.813999 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −15.5132 | −1.71315 | ||||||||
\(83\) | −1.63500 | −0.179464 | −0.0897322 | − | 0.995966i | \(-0.528601\pi\) | ||||
−0.0897322 | + | 0.995966i | \(0.528601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.58117 | 0.713828 | ||||||||
\(86\) | 11.6089 | 1.25182 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.06092 | −0.219695 | ||||||||
\(89\) | 11.4605 | 1.21481 | 0.607404 | − | 0.794393i | \(-0.292211\pi\) | ||||
0.607404 | + | 0.794393i | \(0.292211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.5921 | −1.21518 | ||||||||
\(92\) | 5.69081 | 0.593308 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.41639 | 0.249231 | ||||||||
\(95\) | 3.36927 | 0.345680 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.9390 | −1.21222 | −0.606109 | − | 0.795382i | \(-0.707270\pi\) | ||||
−0.606109 | + | 0.795382i | \(0.707270\pi\) | |||||||
\(98\) | −1.53103 | −0.154657 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.14864 | −0.214864 | ||||||||
\(101\) | −13.8985 | −1.38295 | −0.691477 | − | 0.722398i | \(-0.743040\pi\) | ||||
−0.691477 | + | 0.722398i | \(0.743040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.8872 | 1.76248 | 0.881240 | − | 0.472668i | \(-0.156709\pi\) | ||||
0.881240 | + | 0.472668i | \(0.156709\pi\) | |||||||
\(104\) | 8.48821 | 0.832337 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.89889 | −0.670080 | ||||||||
\(107\) | −5.91853 | −0.572166 | −0.286083 | − | 0.958205i | \(-0.592353\pi\) | ||||
−0.286083 | + | 0.958205i | \(0.592353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.2248 | 1.17092 | 0.585459 | − | 0.810702i | \(-0.300914\pi\) | ||||
0.585459 | + | 0.810702i | \(0.300914\pi\) | |||||||
\(110\) | 2.44715 | 0.233327 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.9097 | 1.31434 | ||||||||
\(113\) | 12.9974 | 1.22270 | 0.611348 | − | 0.791362i | \(-0.290628\pi\) | ||||
0.611348 | + | 0.791362i | \(0.290628\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0411 | 1.02959 | ||||||||
\(116\) | 7.60287 | 0.705909 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.0856 | 2.12520 | ||||||||
\(119\) | −12.5734 | −1.15260 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.66112 | 0.150391 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.79222 | 0.340551 | ||||||||
\(125\) | −11.5347 | −1.03169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1093 | −1.51821 | −0.759104 | − | 0.650969i | \(-0.774363\pi\) | ||||
−0.759104 | + | 0.650969i | \(0.774363\pi\) | |||||||
\(128\) | −13.3150 | −1.17689 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.0789 | −0.883981 | ||||||||
\(131\) | −0.913423 | −0.0798061 | −0.0399031 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399031 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.43701 | −0.558160 | ||||||||
\(134\) | 3.90140 | 0.337029 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.20672 | 0.789470 | ||||||||
\(137\) | 0.476568 | 0.0407159 | 0.0203580 | − | 0.999793i | \(-0.493519\pi\) | ||||
0.0203580 | + | 0.999793i | \(0.493519\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.4643 | −1.73576 | −0.867881 | − | 0.496772i | \(-0.834519\pi\) | ||||
−0.867881 | + | 0.496772i | \(0.834519\pi\) | |||||||
\(140\) | −3.14841 | −0.266089 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.13474 | 0.263061 | ||||||||
\(143\) | −4.11864 | −0.344418 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.7508 | 1.22499 | ||||||||
\(146\) | −19.2473 | −1.59292 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.520833 | −0.0428122 | ||||||||
\(149\) | −9.95783 | −0.815777 | −0.407888 | − | 0.913032i | \(-0.633735\pi\) | ||||
−0.407888 | + | 0.913032i | \(0.633735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.7514 | 1.60735 | 0.803673 | − | 0.595071i | \(-0.202876\pi\) | ||||
0.803673 | + | 0.595071i | \(0.202876\pi\) | |||||||
\(152\) | 4.71344 | 0.382310 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.67530 | −0.376746 | ||||||||
\(155\) | 7.35750 | 0.590969 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9385 | 1.59127 | 0.795633 | − | 0.605779i | \(-0.207139\pi\) | ||||
0.795633 | + | 0.605779i | \(0.207139\pi\) | |||||||
\(158\) | 18.3010 | 1.45595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.02171 | 0.476058 | ||||||||
\(161\) | −21.0941 | −1.66245 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.22975 | 0.722930 | 0.361465 | − | 0.932386i | \(-0.382277\pi\) | ||||
0.361465 | + | 0.932386i | \(0.382277\pi\) | |||||||
\(164\) | 7.09126 | 0.553734 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.71593 | 0.210797 | ||||||||
\(167\) | −2.23571 | −0.173004 | −0.0865022 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865022 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.96321 | 0.304862 | ||||||||
\(170\) | −10.9321 | −0.838454 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.30654 | −0.404620 | ||||||||
\(173\) | 1.61105 | 0.122486 | 0.0612431 | − | 0.998123i | \(-0.480494\pi\) | ||||
0.0612431 | + | 0.998123i | \(0.480494\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.96433 | 0.602047 | ||||||||
\(176\) | 4.94207 | 0.372523 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.0372 | −1.42690 | ||||||||
\(179\) | 11.9794 | 0.895385 | 0.447692 | − | 0.894188i | \(-0.352246\pi\) | ||||
0.447692 | + | 0.894188i | \(0.352246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4236 | 1.07210 | 0.536050 | − | 0.844187i | \(-0.319916\pi\) | ||||
0.536050 | + | 0.844187i | \(0.319916\pi\) | |||||||
\(182\) | 19.2559 | 1.42734 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.4459 | 1.13869 | ||||||||
\(185\) | −1.01050 | −0.0742933 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.46728 | −0.326680 | ||||||||
\(188\) | −1.10456 | −0.0805581 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.59675 | −0.406031 | ||||||||
\(191\) | 3.99785 | 0.289274 | 0.144637 | − | 0.989485i | \(-0.453799\pi\) | ||||
0.144637 | + | 0.989485i | \(0.453799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.35056 | 0.241178 | 0.120589 | − | 0.992702i | \(-0.461522\pi\) | ||||
0.120589 | + | 0.992702i | \(0.461522\pi\) | |||||||
\(194\) | 19.8320 | 1.42386 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.699850 | 0.0499893 | ||||||||
\(197\) | −18.5321 | −1.32036 | −0.660178 | − | 0.751109i | \(-0.729519\pi\) | ||||
−0.660178 | + | 0.751109i | \(0.729519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.45817 | −0.386920 | −0.193460 | − | 0.981108i | \(-0.561971\pi\) | ||||
−0.193460 | + | 0.981108i | \(0.561971\pi\) | |||||||
\(200\) | −5.83180 | −0.412370 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 23.0871 | 1.62440 | ||||||||
\(203\) | −28.1815 | −1.97795 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.7582 | 0.960912 | ||||||||
\(206\) | −29.7128 | −2.07019 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −20.3546 | −1.41134 | ||||||||
\(209\) | −2.28705 | −0.158199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.49774 | −0.240794 | −0.120397 | − | 0.992726i | \(-0.538417\pi\) | ||||
−0.120397 | + | 0.992726i | \(0.538417\pi\) | |||||||
\(212\) | 3.15356 | 0.216587 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.83139 | 0.672060 | ||||||||
\(215\) | −10.2955 | −0.702149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.0566 | −0.954222 | ||||||||
\(218\) | −20.3068 | −1.37535 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.11862 | −0.0754173 | ||||||||
\(221\) | 18.3991 | 1.23766 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.888363 | −0.0594892 | −0.0297446 | − | 0.999558i | \(-0.509469\pi\) | ||||
−0.0297446 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(224\) | −11.5045 | −0.768679 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.5903 | −1.43616 | ||||||||
\(227\) | 23.7868 | 1.57878 | 0.789392 | − | 0.613890i | \(-0.210396\pi\) | ||||
0.789392 | + | 0.613890i | \(0.210396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.175995 | 0.0116301 | 0.00581505 | − | 0.999983i | \(-0.498149\pi\) | ||||
0.00581505 | + | 0.999983i | \(0.498149\pi\) | |||||||
\(230\) | −18.3405 | −1.20934 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.6356 | 1.35479 | ||||||||
\(233\) | 17.5376 | 1.14892 | 0.574462 | − | 0.818531i | \(-0.305211\pi\) | ||||
0.574462 | + | 0.818531i | \(0.305211\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.14302 | −0.139795 | ||||||||
\(236\) | −10.5527 | −0.686922 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.8859 | 1.35383 | ||||||||
\(239\) | 7.95670 | 0.514676 | 0.257338 | − | 0.966321i | \(-0.417155\pi\) | ||||
0.257338 | + | 0.966321i | \(0.417155\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8700 | −0.700200 | −0.350100 | − | 0.936712i | \(-0.613852\pi\) | ||||
−0.350100 | + | 0.936712i | \(0.613852\pi\) | |||||||
\(242\) | −1.66112 | −0.106781 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.759316 | −0.0486102 | ||||||||
\(245\) | 1.35782 | 0.0867480 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.41954 | 0.599351 | ||||||||
\(248\) | 10.2928 | 0.653592 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.1604 | 1.21181 | ||||||||
\(251\) | −4.89538 | −0.308994 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.49465 | −0.471185 | ||||||||
\(254\) | 28.4207 | 1.78327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9293 | 0.995579 | ||||||||
\(257\) | −0.151447 | −0.00944702 | −0.00472351 | − | 0.999989i | \(-0.501504\pi\) | ||||
−0.00472351 | + | 0.999989i | \(0.501504\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.93057 | 0.119960 | ||||||||
\(260\) | 4.60719 | 0.285726 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.51730 | 0.0937394 | ||||||||
\(263\) | 25.8581 | 1.59448 | 0.797240 | − | 0.603663i | \(-0.206293\pi\) | ||||
0.797240 | + | 0.603663i | \(0.206293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.11841 | 0.375851 | ||||||||
\(266\) | 10.6926 | 0.655608 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.78337 | −0.108937 | ||||||||
\(269\) | 8.79991 | 0.536540 | 0.268270 | − | 0.963344i | \(-0.413548\pi\) | ||||
0.268270 | + | 0.963344i | \(0.413548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.84554 | −0.294346 | −0.147173 | − | 0.989111i | \(-0.547017\pi\) | ||||
−0.147173 | + | 0.989111i | \(0.547017\pi\) | |||||||
\(272\) | −22.0776 | −1.33865 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.791636 | −0.0478245 | ||||||||
\(275\) | 2.82970 | 0.170637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.29485 | −0.258053 | −0.129026 | − | 0.991641i | \(-0.541185\pi\) | ||||
−0.129026 | + | 0.991641i | \(0.541185\pi\) | |||||||
\(278\) | 33.9937 | 2.03881 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.54536 | −0.510683 | ||||||||
\(281\) | −19.1622 | −1.14312 | −0.571561 | − | 0.820560i | \(-0.693662\pi\) | ||||
−0.571561 | + | 0.820560i | \(0.693662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.4385 | −1.15550 | −0.577751 | − | 0.816213i | \(-0.696069\pi\) | ||||
−0.577751 | + | 0.816213i | \(0.696069\pi\) | |||||||
\(284\) | −1.43292 | −0.0850283 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.84155 | 0.404550 | ||||||||
\(287\) | −26.2851 | −1.55156 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.95658 | 0.173917 | ||||||||
\(290\) | −24.5028 | −1.43885 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.79816 | 0.514873 | ||||||||
\(293\) | −17.2668 | −1.00874 | −0.504369 | − | 0.863488i | \(-0.668275\pi\) | ||||
−0.504369 | + | 0.863488i | \(0.668275\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.4739 | −1.19204 | ||||||||
\(296\) | −1.41364 | −0.0821660 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.5411 | 0.958202 | ||||||||
\(299\) | 30.8678 | 1.78513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.6697 | 1.13374 | ||||||||
\(302\) | −32.8094 | −1.88797 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.3028 | −0.648258 | ||||||||
\(305\) | −1.47319 | −0.0843548 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.2925 | −1.78596 | −0.892979 | − | 0.450099i | \(-0.851389\pi\) | ||||
−0.892979 | + | 0.450099i | \(0.851389\pi\) | |||||||
\(308\) | 2.13713 | 0.121774 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.2217 | −0.694145 | ||||||||
\(311\) | 31.4841 | 1.78530 | 0.892650 | − | 0.450750i | \(-0.148843\pi\) | ||||
0.892650 | + | 0.450750i | \(0.148843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.86327 | 0.500982 | 0.250491 | − | 0.968119i | \(-0.419408\pi\) | ||||
0.250491 | + | 0.968119i | \(0.419408\pi\) | |||||||
\(314\) | −33.1202 | −1.86908 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.36560 | −0.470602 | ||||||||
\(317\) | −28.8880 | −1.62251 | −0.811255 | − | 0.584693i | \(-0.801215\pi\) | ||||
−0.811255 | + | 0.584693i | \(0.801215\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0128 | −0.560609 | ||||||||
\(320\) | 4.55848 | 0.254827 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 35.0398 | 1.95269 | ||||||||
\(323\) | 10.2169 | 0.568483 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.6545 | −0.646477 | ||||||||
\(326\) | −15.3317 | −0.849145 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.2470 | 1.06274 | ||||||||
\(329\) | 4.09425 | 0.225723 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1372 | 0.722086 | 0.361043 | − | 0.932549i | \(-0.382421\pi\) | ||||
0.361043 | + | 0.932549i | \(0.382421\pi\) | |||||||
\(332\) | −1.24148 | −0.0681351 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.71378 | 0.203209 | ||||||||
\(335\) | −3.46002 | −0.189041 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.2216 | −1.37391 | −0.686953 | − | 0.726702i | \(-0.741052\pi\) | ||||
−0.686953 | + | 0.726702i | \(0.741052\pi\) | |||||||
\(338\) | −6.58337 | −0.358088 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.99718 | 0.271010 | ||||||||
\(341\) | −4.99425 | −0.270454 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1077 | 0.923730 | ||||||||
\(344\) | −14.4029 | −0.776554 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.67615 | −0.143871 | ||||||||
\(347\) | −3.68914 | −0.198043 | −0.0990217 | − | 0.995085i | \(-0.531571\pi\) | ||||
−0.0990217 | + | 0.995085i | \(0.531571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.2145 | 1.29617 | 0.648087 | − | 0.761567i | \(-0.275569\pi\) | ||||
0.648087 | + | 0.761567i | \(0.275569\pi\) | |||||||
\(350\) | −13.2297 | −0.707157 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.08752 | −0.217866 | ||||||||
\(353\) | 35.5517 | 1.89222 | 0.946112 | − | 0.323839i | \(-0.104974\pi\) | ||||
0.946112 | + | 0.323839i | \(0.104974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.78010 | −0.147552 | ||||||||
\(356\) | 8.70212 | 0.461211 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.8993 | −1.05171 | ||||||||
\(359\) | 8.51892 | 0.449611 | 0.224806 | − | 0.974404i | \(-0.427825\pi\) | ||||
0.224806 | + | 0.974404i | \(0.427825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7694 | −0.724705 | ||||||||
\(362\) | −23.9593 | −1.25928 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.80208 | −0.461354 | ||||||||
\(365\) | 17.0698 | 0.893475 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.27453 | 0.118729 | 0.0593646 | − | 0.998236i | \(-0.481093\pi\) | ||||
0.0593646 | + | 0.998236i | \(0.481093\pi\) | |||||||
\(368\) | −37.0391 | −1.93080 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.67856 | 0.0872641 | ||||||||
\(371\) | −11.6893 | −0.606877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.0163 | −0.984629 | −0.492314 | − | 0.870418i | \(-0.663849\pi\) | ||||
−0.492314 | + | 0.870418i | \(0.663849\pi\) | |||||||
\(374\) | 7.42068 | 0.383714 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.99797 | −0.154609 | ||||||||
\(377\) | 41.2391 | 2.12392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.07661 | 0.106668 | 0.0533341 | − | 0.998577i | \(-0.483015\pi\) | ||||
0.0533341 | + | 0.998577i | \(0.483015\pi\) | |||||||
\(380\) | 2.55834 | 0.131240 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.64090 | −0.339778 | ||||||||
\(383\) | 18.3744 | 0.938889 | 0.469445 | − | 0.882962i | \(-0.344454\pi\) | ||||
0.469445 | + | 0.882962i | \(0.344454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.14637 | 0.211319 | ||||||||
\(386\) | −5.56567 | −0.283285 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.06544 | −0.460228 | ||||||||
\(389\) | 0.191275 | 0.00969801 | 0.00484901 | − | 0.999988i | \(-0.498457\pi\) | ||||
0.00484901 | + | 0.999988i | \(0.498457\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.4807 | 1.69319 | ||||||||
\(392\) | 1.89952 | 0.0959404 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 30.7840 | 1.55087 | ||||||||
\(395\) | −16.2306 | −0.816649 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.4396 | −0.975646 | −0.487823 | − | 0.872942i | \(-0.662209\pi\) | ||||
−0.487823 | + | 0.872942i | \(0.662209\pi\) | |||||||
\(398\) | 9.06667 | 0.454471 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.9846 | 0.699229 | ||||||||
\(401\) | 8.50930 | 0.424934 | 0.212467 | − | 0.977168i | \(-0.431850\pi\) | ||||
0.212467 | + | 0.977168i | \(0.431850\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.5695 | 1.02464 | ||||||||
\(404\) | −10.5534 | −0.525050 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 46.8128 | 2.32328 | ||||||||
\(407\) | 0.685924 | 0.0340000 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.98566 | 0.493759 | 0.246880 | − | 0.969046i | \(-0.420595\pi\) | ||||
0.246880 | + | 0.969046i | \(0.420595\pi\) | |||||||
\(410\) | −22.8539 | −1.12868 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.5821 | 0.669140 | ||||||||
\(413\) | 39.1156 | 1.92475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.40867 | −0.118237 | ||||||||
\(416\) | 16.8350 | 0.825406 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.79906 | 0.185818 | ||||||||
\(419\) | −38.1216 | −1.86236 | −0.931181 | − | 0.364557i | \(-0.881220\pi\) | ||||
−0.931181 | + | 0.364557i | \(0.881220\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.7144 | −1.10703 | −0.553516 | − | 0.832839i | \(-0.686714\pi\) | ||||
−0.553516 | + | 0.832839i | \(0.686714\pi\) | |||||||
\(422\) | 5.81017 | 0.282834 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.55935 | 0.415679 | ||||||||
\(425\) | −12.6411 | −0.613182 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.81455 | 0.136206 | ||||||||
\(428\) | −4.49404 | −0.217228 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.1021 | 0.824737 | ||||||||
\(431\) | 19.4262 | 0.935727 | 0.467863 | − | 0.883801i | \(-0.345024\pi\) | ||||
0.467863 | + | 0.883801i | \(0.345024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0574 | 1.15612 | 0.578062 | − | 0.815993i | \(-0.303809\pi\) | ||||
0.578062 | + | 0.815993i | \(0.303809\pi\) | |||||||
\(434\) | 23.3496 | 1.12082 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.28245 | 0.444549 | ||||||||
\(437\) | 17.1407 | 0.819949 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.3119 | −0.778523 | −0.389262 | − | 0.921127i | \(-0.627270\pi\) | ||||
−0.389262 | + | 0.921127i | \(0.627270\pi\) | |||||||
\(440\) | −3.03614 | −0.144742 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −30.5631 | −1.45374 | ||||||||
\(443\) | −11.8617 | −0.563567 | −0.281783 | − | 0.959478i | \(-0.590926\pi\) | ||||
−0.281783 | + | 0.959478i | \(0.590926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.8835 | 0.800354 | ||||||||
\(446\) | 1.47568 | 0.0698753 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.70901 | −0.411462 | ||||||||
\(449\) | 14.9882 | 0.707335 | 0.353668 | − | 0.935371i | \(-0.384934\pi\) | ||||
0.353668 | + | 0.935371i | \(0.384934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.33901 | −0.439757 | ||||||||
\(452\) | 9.86916 | 0.464206 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −39.5127 | −1.85442 | ||||||||
\(455\) | −17.0774 | −0.800602 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.3763 | −1.04672 | −0.523358 | − | 0.852113i | \(-0.675321\pi\) | ||||
−0.523358 | + | 0.852113i | \(0.675321\pi\) | |||||||
\(458\) | −0.292349 | −0.0136606 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.38367 | 0.390890 | ||||||||
\(461\) | −19.8786 | −0.925837 | −0.462919 | − | 0.886401i | \(-0.653198\pi\) | ||||
−0.462919 | + | 0.886401i | \(0.653198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.0105 | 1.34823 | 0.674116 | − | 0.738626i | \(-0.264525\pi\) | ||||
0.674116 | + | 0.738626i | \(0.264525\pi\) | |||||||
\(464\) | −49.4839 | −2.29723 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.1320 | −1.34951 | ||||||||
\(467\) | 36.6315 | 1.69510 | 0.847552 | − | 0.530712i | \(-0.178076\pi\) | ||||
0.847552 | + | 0.530712i | \(0.178076\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.61041 | 0.305240 | ||||||||
\(470\) | 3.55980 | 0.164201 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −28.6420 | −1.31835 | ||||||||
\(473\) | 6.98858 | 0.321335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.47167 | −0.296941 | ||||||||
\(476\) | −9.54717 | −0.437594 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.2170 | −0.604533 | ||||||||
\(479\) | 37.5446 | 1.71546 | 0.857729 | − | 0.514101i | \(-0.171875\pi\) | ||||
0.857729 | + | 0.514101i | \(0.171875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82508 | −0.128812 | ||||||||
\(482\) | 18.0564 | 0.822447 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.759316 | 0.0345144 | ||||||||
\(485\) | −17.5884 | −0.798647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4607 | 0.655275 | 0.327638 | − | 0.944803i | \(-0.393747\pi\) | ||||
0.327638 | + | 0.944803i | \(0.393747\pi\) | |||||||
\(488\) | −2.06092 | −0.0932936 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.25550 | −0.101893 | ||||||||
\(491\) | −23.7449 | −1.07159 | −0.535797 | − | 0.844347i | \(-0.679989\pi\) | ||||
−0.535797 | + | 0.844347i | \(0.679989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.7299 | 2.01454 | ||||||||
\(494\) | −15.6470 | −0.703991 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.6820 | −1.10825 | ||||||||
\(497\) | 5.31140 | 0.238249 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.8268 | 0.708504 | 0.354252 | − | 0.935150i | \(-0.384736\pi\) | ||||
0.354252 | + | 0.935150i | \(0.384736\pi\) | |||||||
\(500\) | −8.75846 | −0.391690 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.13180 | 0.362940 | ||||||||
\(503\) | 29.6249 | 1.32091 | 0.660455 | − | 0.750865i | \(-0.270363\pi\) | ||||
0.660455 | + | 0.750865i | \(0.270363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.4752 | −0.911135 | ||||||||
\(506\) | 12.4495 | 0.553448 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.9914 | −0.576400 | ||||||||
\(509\) | −20.3765 | −0.903171 | −0.451585 | − | 0.892228i | \(-0.649141\pi\) | ||||
−0.451585 | + | 0.892228i | \(0.649141\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.6121 | −1.44267 | ||||||||
\(512\) | 0.169642 | 0.00749719 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.251572 | 0.0110964 | ||||||||
\(515\) | 26.3513 | 1.16118 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.45467 | 0.0639765 | ||||||||
\(518\) | −3.20690 | −0.140903 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.5048 | 0.548370 | ||||||||
\(521\) | −6.10030 | −0.267259 | −0.133630 | − | 0.991031i | \(-0.542663\pi\) | ||||
−0.133630 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.29661 | −0.231605 | −0.115802 | − | 0.993272i | \(-0.536944\pi\) | ||||
−0.115802 | + | 0.993272i | \(0.536944\pi\) | |||||||
\(524\) | −0.693577 | −0.0302990 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −42.9534 | −1.87286 | ||||||||
\(527\) | 22.3107 | 0.971871 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.1699 | 1.44217 | ||||||||
\(530\) | −10.1634 | −0.441470 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.88773 | −0.211910 | ||||||||
\(533\) | 38.4640 | 1.66606 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.71914 | −0.376961 | ||||||||
\(536\) | −4.84040 | −0.209073 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.6177 | −0.630214 | ||||||||
\(539\) | −0.921685 | −0.0396998 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.7253 | 1.06303 | 0.531513 | − | 0.847050i | \(-0.321624\pi\) | ||||
0.531513 | + | 0.847050i | \(0.321624\pi\) | |||||||
\(542\) | 8.04902 | 0.345735 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.2601 | 0.782895 | ||||||||
\(545\) | 18.0094 | 0.771439 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.4147 | 0.488057 | 0.244028 | − | 0.969768i | \(-0.421531\pi\) | ||||
0.244028 | + | 0.969768i | \(0.421531\pi\) | |||||||
\(548\) | 0.361865 | 0.0154581 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.70047 | −0.200429 | ||||||||
\(551\) | 22.8998 | 0.975563 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.0087 | 1.31862 | ||||||||
\(554\) | 7.13426 | 0.303106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.5389 | −0.658996 | ||||||||
\(557\) | 42.5738 | 1.80391 | 0.901954 | − | 0.431831i | \(-0.142132\pi\) | ||||
0.901954 | + | 0.431831i | \(0.142132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.7835 | −1.21741 | ||||||||
\(560\) | 20.4917 | 0.865931 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.8307 | 1.34270 | ||||||||
\(563\) | −24.4660 | −1.03112 | −0.515560 | − | 0.856854i | \(-0.672416\pi\) | ||||
−0.515560 | + | 0.856854i | \(0.672416\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.1477 | 0.805551 | ||||||||
\(566\) | 32.2897 | 1.35724 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.88922 | −0.163188 | ||||||||
\(569\) | 4.26207 | 0.178675 | 0.0893376 | − | 0.996001i | \(-0.471525\pi\) | ||||
0.0893376 | + | 0.996001i | \(0.471525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3495 | −0.474962 | −0.237481 | − | 0.971392i | \(-0.576322\pi\) | ||||
−0.237481 | + | 0.971392i | \(0.576322\pi\) | |||||||
\(572\) | −3.12735 | −0.130761 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 43.6627 | 1.82244 | ||||||||
\(575\) | −21.2076 | −0.884420 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.5215 | −1.22900 | −0.614498 | − | 0.788918i | \(-0.710642\pi\) | ||||
−0.614498 | + | 0.788918i | \(0.710642\pi\) | |||||||
\(578\) | −4.91124 | −0.204280 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 11.2005 | 0.465076 | ||||||||
\(581\) | 4.60179 | 0.190914 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.15316 | −0.172006 | ||||||||
\(584\) | 23.8798 | 0.988154 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.6822 | 1.18485 | ||||||||
\(587\) | 18.6594 | 0.770156 | 0.385078 | − | 0.922884i | \(-0.374175\pi\) | ||||
0.385078 | + | 0.922884i | \(0.374175\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4221 | 0.470640 | ||||||||
\(590\) | 34.0096 | 1.40015 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.38989 | 0.139323 | ||||||||
\(593\) | −26.6484 | −1.09432 | −0.547159 | − | 0.837028i | \(-0.684291\pi\) | ||||
−0.547159 | + | 0.837028i | \(0.684291\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.5230 | −0.759369 | ||||||||
\(596\) | −7.56114 | −0.309716 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −51.2751 | −2.09679 | ||||||||
\(599\) | −1.09807 | −0.0448660 | −0.0224330 | − | 0.999748i | \(-0.507141\pi\) | ||||
−0.0224330 | + | 0.999748i | \(0.507141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.6922 | 1.65987 | 0.829934 | − | 0.557862i | \(-0.188378\pi\) | ||||
0.829934 | + | 0.557862i | \(0.188378\pi\) | |||||||
\(602\) | −32.6737 | −1.33168 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.9976 | 0.610242 | ||||||||
\(605\) | 1.47319 | 0.0598938 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.3651 | 1.11071 | 0.555357 | − | 0.831612i | \(-0.312582\pi\) | ||||
0.555357 | + | 0.831612i | \(0.312582\pi\) | |||||||
\(608\) | 9.34837 | 0.379126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.44715 | 0.0990822 | ||||||||
\(611\) | −5.99128 | −0.242381 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.10876 | −0.0851720 | −0.0425860 | − | 0.999093i | \(-0.513560\pi\) | ||||
−0.0425860 | + | 0.999093i | \(0.513560\pi\) | |||||||
\(614\) | 51.9806 | 2.09777 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.80057 | 0.233712 | ||||||||
\(617\) | 4.11409 | 0.165627 | 0.0828136 | − | 0.996565i | \(-0.473609\pi\) | ||||
0.0828136 | + | 0.996565i | \(0.473609\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.1725 | 1.41370 | 0.706850 | − | 0.707363i | \(-0.250115\pi\) | ||||
0.706850 | + | 0.707363i | \(0.250115\pi\) | |||||||
\(620\) | 5.58667 | 0.224366 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −52.2989 | −2.09699 | ||||||||
\(623\) | −32.2560 | −1.29231 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.84428 | −0.113771 | ||||||||
\(626\) | −14.7230 | −0.588448 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.1396 | 0.604137 | ||||||||
\(629\) | −3.06421 | −0.122178 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.37797 | 0.214093 | 0.107047 | − | 0.994254i | \(-0.465861\pi\) | ||||
0.107047 | + | 0.994254i | \(0.465861\pi\) | |||||||
\(632\) | −22.7058 | −0.903187 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 47.9863 | 1.90578 | ||||||||
\(635\) | −25.2054 | −1.00024 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.79609 | 0.150407 | ||||||||
\(638\) | 16.6324 | 0.658485 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −19.6156 | −0.775374 | ||||||||
\(641\) | 18.7103 | 0.739013 | 0.369506 | − | 0.929228i | \(-0.379527\pi\) | ||||
0.369506 | + | 0.929228i | \(0.379527\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.4398 | −0.608885 | −0.304442 | − | 0.952531i | \(-0.598470\pi\) | ||||
−0.304442 | + | 0.952531i | \(0.598470\pi\) | |||||||
\(644\) | −16.0171 | −0.631161 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.9715 | −0.667734 | ||||||||
\(647\) | 17.3725 | 0.682984 | 0.341492 | − | 0.939885i | \(-0.389068\pi\) | ||||
0.341492 | + | 0.939885i | \(0.389068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.8976 | 0.545530 | ||||||||
\(650\) | 19.3596 | 0.759344 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.00830 | 0.274466 | ||||||||
\(653\) | 25.2136 | 0.986683 | 0.493341 | − | 0.869836i | \(-0.335775\pi\) | ||||
0.493341 | + | 0.869836i | \(0.335775\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.34565 | −0.0525788 | ||||||||
\(656\) | −46.1540 | −1.80201 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.80104 | −0.265132 | ||||||||
\(659\) | −18.5187 | −0.721387 | −0.360694 | − | 0.932684i | \(-0.617460\pi\) | ||||
−0.360694 | + | 0.932684i | \(0.617460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9891 | 0.505219 | 0.252609 | − | 0.967568i | \(-0.418711\pi\) | ||||
0.252609 | + | 0.967568i | \(0.418711\pi\) | |||||||
\(662\) | −21.8225 | −0.848154 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.36961 | −0.130766 | ||||||||
\(665\) | −9.48297 | −0.367734 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 75.0424 | 2.90565 | ||||||||
\(668\) | −1.69761 | −0.0656825 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.74751 | 0.222046 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.7463 | −0.529881 | −0.264941 | − | 0.964265i | \(-0.585352\pi\) | ||||
−0.264941 | + | 0.964265i | \(0.585352\pi\) | |||||||
\(674\) | 41.8960 | 1.61377 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00933 | 0.115743 | ||||||||
\(677\) | 1.82406 | 0.0701044 | 0.0350522 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350522 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.6028 | 1.28956 | ||||||||
\(680\) | 13.5633 | 0.520128 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.29605 | 0.317672 | ||||||||
\(683\) | −32.9064 | −1.25913 | −0.629565 | − | 0.776948i | \(-0.716767\pi\) | ||||
−0.629565 | + | 0.776948i | \(0.716767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.702076 | 0.0268250 | ||||||||
\(686\) | −28.4179 | −1.08500 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 34.5381 | 1.31675 | ||||||||
\(689\) | 17.1054 | 0.651663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5172 | −0.932677 | −0.466338 | − | 0.884606i | \(-0.654427\pi\) | ||||
−0.466338 | + | 0.884606i | \(0.654427\pi\) | |||||||
\(692\) | 1.22330 | 0.0465029 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.12810 | 0.232620 | ||||||||
\(695\) | −30.1479 | −1.14358 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.7199 | 1.58026 | ||||||||
\(698\) | −40.2232 | −1.52247 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.04745 | 0.228572 | ||||||||
\(701\) | 31.3871 | 1.18548 | 0.592738 | − | 0.805395i | \(-0.298047\pi\) | ||||
0.592738 | + | 0.805395i | \(0.298047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.56874 | −0.0591663 | ||||||||
\(704\) | −3.09428 | −0.116620 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −59.0556 | −2.22259 | ||||||||
\(707\) | 39.1181 | 1.47119 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.3497 | 1.36514 | 0.682570 | − | 0.730820i | \(-0.260862\pi\) | ||||
0.682570 | + | 0.730820i | \(0.260862\pi\) | |||||||
\(710\) | 4.61807 | 0.173313 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 23.6191 | 0.885165 | ||||||||
\(713\) | 37.4302 | 1.40177 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.06756 | −0.226914 | ||||||||
\(716\) | 9.09618 | 0.339940 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.1509 | −0.528108 | ||||||||
\(719\) | 44.5308 | 1.66072 | 0.830358 | − | 0.557230i | \(-0.188136\pi\) | ||||
0.830358 | + | 0.557230i | \(0.188136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.3445 | −1.87493 | ||||||||
\(722\) | 22.8726 | 0.851230 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.9521 | 0.407031 | ||||||||
\(725\) | −28.3332 | −1.05227 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.6665 | −1.54532 | −0.772662 | − | 0.634818i | \(-0.781075\pi\) | ||||
−0.772662 | + | 0.634818i | \(0.781075\pi\) | |||||||
\(728\) | −23.8905 | −0.885440 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.3550 | −1.04947 | ||||||||
\(731\) | −31.2199 | −1.15471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5219 | 1.42284 | 0.711420 | − | 0.702767i | \(-0.248052\pi\) | ||||
0.711420 | + | 0.702767i | \(0.248052\pi\) | |||||||
\(734\) | −3.77826 | −0.139458 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.6346 | 1.12920 | ||||||||
\(737\) | 2.34866 | 0.0865139 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.61423 | 0.169737 | 0.0848686 | − | 0.996392i | \(-0.472953\pi\) | ||||
0.0848686 | + | 0.996392i | \(0.472953\pi\) | |||||||
\(740\) | −0.767288 | −0.0282061 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.4173 | 0.712830 | ||||||||
\(743\) | 50.4021 | 1.84907 | 0.924537 | − | 0.381093i | \(-0.124452\pi\) | ||||
0.924537 | + | 0.381093i | \(0.124452\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.6698 | −0.537460 | ||||||||
\(746\) | 31.5884 | 1.15653 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.39208 | −0.124027 | ||||||||
\(749\) | 16.6580 | 0.608670 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.2161 | 0.956639 | 0.478319 | − | 0.878186i | \(-0.341246\pi\) | ||||
0.478319 | + | 0.878186i | \(0.341246\pi\) | |||||||
\(752\) | 7.18910 | 0.262160 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −68.5031 | −2.49473 | ||||||||
\(755\) | 29.0976 | 1.05897 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1801 | 0.588075 | 0.294037 | − | 0.955794i | \(-0.405001\pi\) | ||||
0.294037 | + | 0.955794i | \(0.405001\pi\) | |||||||
\(758\) | −3.44949 | −0.125291 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.94380 | 0.251878 | ||||||||
\(761\) | 23.9432 | 0.867941 | 0.433970 | − | 0.900927i | \(-0.357112\pi\) | ||||
0.433970 | + | 0.900927i | \(0.357112\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.4072 | −1.24562 | ||||||||
\(764\) | 3.03563 | 0.109825 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.5221 | −1.10281 | ||||||||
\(767\) | −57.2394 | −2.06679 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.4165 | −0.411690 | −0.205845 | − | 0.978585i | \(-0.565994\pi\) | ||||
−0.205845 | + | 0.978585i | \(0.565994\pi\) | |||||||
\(770\) | −6.88762 | −0.248213 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.54413 | 0.0915653 | ||||||||
\(773\) | −10.0161 | −0.360253 | −0.180126 | − | 0.983643i | \(-0.557651\pi\) | ||||
−0.180126 | + | 0.983643i | \(0.557651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.1323 | −0.507645 | ||||||||
\(776\) | −24.6053 | −0.883278 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.317730 | −0.0113912 | ||||||||
\(779\) | 21.3588 | 0.765258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.88712 | 0.0675266 | ||||||||
\(782\) | −55.6154 | −1.98880 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.55503 | −0.162680 | ||||||||
\(785\) | 29.3733 | 1.04838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.994185 | −0.0354389 | −0.0177194 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177194 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(788\) | −14.0717 | −0.501284 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 26.9609 | 0.959227 | ||||||||
\(791\) | −36.5819 | −1.30070 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.11864 | −0.146257 | ||||||||
\(794\) | 32.2915 | 1.14598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.14448 | −0.146897 | ||||||||
\(797\) | 14.5631 | 0.515850 | 0.257925 | − | 0.966165i | \(-0.416961\pi\) | ||||
0.257925 | + | 0.966165i | \(0.416961\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.49843 | −0.229898 | ||||||||
\(800\) | −11.5665 | −0.408936 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1350 | −0.499123 | ||||||||
\(803\) | −11.5870 | −0.408895 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.0756 | −1.09527 | ||||||||
\(806\) | −34.1685 | −1.20353 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.6438 | −1.00768 | ||||||||
\(809\) | 19.4621 | 0.684251 | 0.342125 | − | 0.939654i | \(-0.388853\pi\) | ||||
0.342125 | + | 0.939654i | \(0.388853\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.09086 | 0.108535 | 0.0542674 | − | 0.998526i | \(-0.482718\pi\) | ||||
0.0542674 | + | 0.998526i | \(0.482718\pi\) | |||||||
\(812\) | −21.3987 | −0.750946 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.13940 | −0.0399360 | ||||||||
\(815\) | 13.5972 | 0.476290 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.9832 | −0.559183 | ||||||||
\(818\) | −16.5874 | −0.579964 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.4468 | 0.364818 | ||||||||
\(821\) | −45.1084 | −1.57429 | −0.787147 | − | 0.616766i | \(-0.788443\pi\) | ||||
−0.787147 | + | 0.616766i | \(0.788443\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.9386 | −1.63618 | −0.818088 | − | 0.575093i | \(-0.804966\pi\) | ||||
−0.818088 | + | 0.575093i | \(0.804966\pi\) | |||||||
\(824\) | 36.8642 | 1.28423 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −64.9756 | −2.26079 | ||||||||
\(827\) | −11.4404 | −0.397820 | −0.198910 | − | 0.980018i | \(-0.563740\pi\) | ||||
−0.198910 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.5722 | 1.44386 | 0.721931 | − | 0.691965i | \(-0.243255\pi\) | ||||
0.721931 | + | 0.691965i | \(0.243255\pi\) | |||||||
\(830\) | 4.00109 | 0.138880 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.7442 | 0.441827 | ||||||||
\(833\) | 4.11742 | 0.142660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.29363 | −0.113981 | ||||||||
\(836\) | −1.73659 | −0.0600614 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 63.3245 | 2.18751 | ||||||||
\(839\) | 18.1912 | 0.628029 | 0.314015 | − | 0.949418i | \(-0.398326\pi\) | ||||
0.314015 | + | 0.949418i | \(0.398326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 71.2560 | 2.45710 | ||||||||
\(842\) | 37.7313 | 1.30031 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.65589 | −0.0914196 | ||||||||
\(845\) | 5.83858 | 0.200853 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.81455 | −0.0967090 | ||||||||
\(848\) | −20.5252 | −0.704839 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.9983 | 0.720236 | ||||||||
\(851\) | −5.14076 | −0.176223 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.3960 | 1.38313 | 0.691567 | − | 0.722313i | \(-0.256921\pi\) | ||||
0.691567 | + | 0.722313i | \(0.256921\pi\) | |||||||
\(854\) | −4.67530 | −0.159985 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.1976 | −0.416907 | ||||||||
\(857\) | 43.5580 | 1.48791 | 0.743957 | − | 0.668228i | \(-0.232947\pi\) | ||||
0.743957 | + | 0.668228i | \(0.232947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.7316 | −1.04855 | −0.524275 | − | 0.851549i | \(-0.675664\pi\) | ||||
−0.524275 | + | 0.851549i | \(0.675664\pi\) | |||||||
\(860\) | −7.81756 | −0.266577 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.2692 | −1.09909 | ||||||||
\(863\) | −53.2458 | −1.81251 | −0.906255 | − | 0.422732i | \(-0.861071\pi\) | ||||
−0.906255 | + | 0.422732i | \(0.861071\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.37339 | 0.0806978 | ||||||||
\(866\) | −39.9622 | −1.35797 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.6734 | −0.362278 | ||||||||
\(869\) | 11.0173 | 0.373736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.67327 | −0.327766 | ||||||||
\(872\) | 25.1943 | 0.853186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −28.4727 | −0.963102 | ||||||||
\(875\) | 32.4649 | 1.09751 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5194 | −1.03057 | −0.515283 | − | 0.857020i | \(-0.672313\pi\) | ||||
−0.515283 | + | 0.857020i | \(0.672313\pi\) | |||||||
\(878\) | 27.0960 | 0.914444 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.28063 | 0.245430 | ||||||||
\(881\) | −38.7833 | −1.30664 | −0.653320 | − | 0.757081i | \(-0.726625\pi\) | ||||
−0.653320 | + | 0.757081i | \(0.726625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0742 | 0.339025 | 0.169513 | − | 0.985528i | \(-0.445781\pi\) | ||||
0.169513 | + | 0.985528i | \(0.445781\pi\) | |||||||
\(884\) | 13.9708 | 0.469887 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.7037 | 0.661959 | ||||||||
\(887\) | −20.8428 | −0.699834 | −0.349917 | − | 0.936781i | \(-0.613790\pi\) | ||||
−0.349917 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.1551 | 1.61507 | ||||||||
\(890\) | −28.0455 | −0.940086 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.674549 | −0.0225856 | ||||||||
\(893\) | −3.32691 | −0.111331 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6480 | 0.589908 | ||||||||
\(896\) | 37.4758 | 1.25198 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.8971 | −0.830828 | ||||||||
\(899\) | 50.0064 | 1.66781 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.5533 | 0.618101 | ||||||||
\(902\) | 15.5132 | 0.516533 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.7867 | 0.890913 | ||||||||
\(905\) | 21.2488 | 0.706333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.8755 | 1.19122 | 0.595612 | − | 0.803272i | \(-0.296909\pi\) | ||||
0.595612 | + | 0.803272i | \(0.296909\pi\) | |||||||
\(908\) | 18.0617 | 0.599398 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 28.3676 | 0.940378 | ||||||||
\(911\) | −5.46997 | −0.181228 | −0.0906140 | − | 0.995886i | \(-0.528883\pi\) | ||||
−0.0906140 | + | 0.995886i | \(0.528883\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.63500 | 0.0541106 | ||||||||
\(914\) | 37.1696 | 1.22946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.133636 | 0.00441546 | ||||||||
\(917\) | 2.57087 | 0.0848977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.8018 | −0.818137 | −0.409069 | − | 0.912504i | \(-0.634146\pi\) | ||||
−0.409069 | + | 0.912504i | \(0.634146\pi\) | |||||||
\(920\) | 22.7548 | 0.750204 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 33.0207 | 1.08748 | ||||||||
\(923\) | −7.77238 | −0.255831 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.94096 | 0.0638184 | ||||||||
\(926\) | −48.1899 | −1.58362 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 40.9275 | 1.34351 | ||||||||
\(929\) | −22.3547 | −0.733434 | −0.366717 | − | 0.930332i | \(-0.619518\pi\) | ||||
−0.366717 | + | 0.930332i | \(0.619518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.10794 | 0.0690849 | ||||||||
\(932\) | 13.3166 | 0.436198 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −60.8493 | −1.99105 | ||||||||
\(935\) | −6.58117 | −0.215227 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.9976 | −1.73136 | −0.865678 | − | 0.500601i | \(-0.833112\pi\) | ||||
−0.865678 | + | 0.500601i | \(0.833112\pi\) | |||||||
\(938\) | −10.9807 | −0.358532 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.62723 | −0.0530743 | ||||||||
\(941\) | 19.0962 | 0.622517 | 0.311259 | − | 0.950325i | \(-0.399249\pi\) | ||||
0.311259 | + | 0.950325i | \(0.399249\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69.9926 | 2.27927 | ||||||||
\(944\) | 68.6831 | 2.23544 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.6089 | −0.377437 | ||||||||
\(947\) | 3.98469 | 0.129485 | 0.0647425 | − | 0.997902i | \(-0.479377\pi\) | ||||
0.0647425 | + | 0.997902i | \(0.479377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 47.7225 | 1.54914 | ||||||||
\(950\) | 10.7502 | 0.348783 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.9128 | −0.839838 | ||||||||
\(953\) | −53.9687 | −1.74822 | −0.874109 | − | 0.485730i | \(-0.838554\pi\) | ||||
−0.874109 | + | 0.485730i | \(0.838554\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.88960 | 0.190583 | ||||||||
\(956\) | 6.04165 | 0.195401 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −62.3661 | −2.01496 | ||||||||
\(959\) | −1.34132 | −0.0433136 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.05742 | −0.195401 | ||||||||
\(962\) | 4.69279 | 0.151302 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.25378 | −0.265836 | ||||||||
\(965\) | 4.93602 | 0.158896 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.4105 | −1.42815 | −0.714073 | − | 0.700071i | \(-0.753152\pi\) | ||||
−0.714073 | + | 0.700071i | \(0.753152\pi\) | |||||||
\(968\) | 2.06092 | 0.0662406 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29.2164 | 0.938082 | ||||||||
\(971\) | −36.8254 | −1.18178 | −0.590891 | − | 0.806751i | \(-0.701224\pi\) | ||||
−0.590891 | + | 0.806751i | \(0.701224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 57.5979 | 1.84650 | ||||||||
\(974\) | −24.0209 | −0.769679 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.94207 | 0.158192 | ||||||||
\(977\) | −16.0019 | −0.511947 | −0.255974 | − | 0.966684i | \(-0.582396\pi\) | ||||
−0.255974 | + | 0.966684i | \(0.582396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4605 | −0.366278 | ||||||||
\(980\) | 1.03101 | 0.0329346 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39.4431 | 1.25868 | ||||||||
\(983\) | −10.0083 | −0.319216 | −0.159608 | − | 0.987180i | \(-0.551023\pi\) | ||||
−0.159608 | + | 0.987180i | \(0.551023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.3013 | −0.869893 | ||||||||
\(986\) | −74.3017 | −2.36625 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.15241 | 0.227548 | ||||||||
\(989\) | −52.3770 | −1.66549 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3552 | 0.328944 | 0.164472 | − | 0.986382i | \(-0.447408\pi\) | ||||
0.164472 | + | 0.986382i | \(0.447408\pi\) | |||||||
\(992\) | 20.4141 | 0.648149 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.82287 | −0.279844 | ||||||||
\(995\) | −8.04094 | −0.254915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.3712 | −0.898525 | −0.449263 | − | 0.893400i | \(-0.648313\pi\) | ||||
−0.449263 | + | 0.893400i | \(0.648313\pi\) | |||||||
\(998\) | −26.2901 | −0.832200 | ||||||||
\(999\) | 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 | 6039.2.a.f.1.2 | 12 | ||
3.2 | odd | 2 | 2013.2.a.c.1.11 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.2.a.c.1.11 | ✓ | 12 | 3.2 | odd | 2 | ||
6039.2.a.f.1.2 | 12 | 1.1 | even | 1 | trivial |