Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.3829849.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 6x^{4} + 15x^{3} - 5x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.63651\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.297484 | −0.210353 | −0.105176 | − | 0.994454i | \(-0.533541\pi\) | ||||
−0.105176 | + | 0.994454i | \(0.533541\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.91150 | −0.955752 | ||||||||
\(5\) | 3.06404 | 1.37028 | 0.685141 | − | 0.728411i | \(-0.259741\pi\) | ||||
0.685141 | + | 0.728411i | \(0.259741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.16361 | 0.411398 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.911503 | −0.288243 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.38835 | 1.49446 | 0.747230 | − | 0.664565i | \(-0.231383\pi\) | ||||
0.747230 | + | 0.664565i | \(0.231383\pi\) | |||||||
\(14\) | −0.297484 | −0.0795059 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.47685 | 0.869213 | ||||||||
\(17\) | −6.72305 | −1.63058 | −0.815290 | − | 0.579053i | \(-0.803422\pi\) | ||||
−0.815290 | + | 0.579053i | \(0.803422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.434652 | −0.0997160 | −0.0498580 | − | 0.998756i | \(-0.515877\pi\) | ||||
−0.0498580 | + | 0.998756i | \(0.515877\pi\) | |||||||
\(20\) | −5.85693 | −1.30965 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.92219 | −0.609318 | −0.304659 | − | 0.952461i | \(-0.598543\pi\) | ||||
−0.304659 | + | 0.952461i | \(0.598543\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.38835 | 0.877671 | ||||||||
\(26\) | −1.60295 | −0.314364 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.91150 | −0.361240 | ||||||||
\(29\) | 6.86491 | 1.27478 | 0.637391 | − | 0.770541i | \(-0.280014\pi\) | ||||
0.637391 | + | 0.770541i | \(0.280014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.95370 | 0.889711 | 0.444856 | − | 0.895602i | \(-0.353255\pi\) | ||||
0.444856 | + | 0.895602i | \(0.353255\pi\) | |||||||
\(32\) | −3.36153 | −0.594239 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 3.06404 | 0.517918 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.38835 | −0.557042 | −0.278521 | − | 0.960430i | \(-0.589844\pi\) | ||||
−0.278521 | + | 0.960430i | \(0.589844\pi\) | |||||||
\(38\) | 0.129302 | 0.0209755 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.56535 | 0.563731 | ||||||||
\(41\) | 9.92895 | 1.55064 | 0.775321 | − | 0.631568i | \(-0.217588\pi\) | ||||
0.775321 | + | 0.631568i | \(0.217588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82301 | −0.278006 | −0.139003 | − | 0.990292i | \(-0.544390\pi\) | ||||
−0.139003 | + | 0.990292i | \(0.544390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.869304 | 0.128172 | ||||||||
\(47\) | −7.45988 | −1.08813 | −0.544067 | − | 0.839042i | \(-0.683116\pi\) | ||||
−0.544067 | + | 0.839042i | \(0.683116\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.30547 | −0.184621 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.2999 | −1.42833 | ||||||||
\(53\) | 9.33398 | 1.28212 | 0.641061 | − | 0.767490i | \(-0.278495\pi\) | ||||
0.641061 | + | 0.767490i | \(0.278495\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.16361 | 0.155494 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.04220 | −0.268154 | ||||||||
\(59\) | 7.17616 | 0.934257 | 0.467129 | − | 0.884189i | \(-0.345289\pi\) | ||||
0.467129 | + | 0.884189i | \(0.345289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.77671 | −0.867669 | −0.433834 | − | 0.900993i | \(-0.642840\pi\) | ||||
−0.433834 | + | 0.900993i | \(0.642840\pi\) | |||||||
\(62\) | −1.47365 | −0.187153 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.95370 | −0.744213 | ||||||||
\(65\) | 16.5101 | 2.04783 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.56535 | 0.435577 | 0.217788 | − | 0.975996i | \(-0.430116\pi\) | ||||
0.217788 | + | 0.975996i | \(0.430116\pi\) | |||||||
\(68\) | 12.8511 | 1.55843 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.911503 | −0.108945 | ||||||||
\(71\) | −8.50796 | −1.00971 | −0.504854 | − | 0.863205i | \(-0.668454\pi\) | ||||
−0.504854 | + | 0.863205i | \(0.668454\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.61165 | 0.305670 | 0.152835 | − | 0.988252i | \(-0.451160\pi\) | ||||
0.152835 | + | 0.988252i | \(0.451160\pi\) | |||||||
\(74\) | 1.00798 | 0.117175 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.830838 | 0.0953037 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.6460 | 1.31028 | 0.655139 | − | 0.755508i | \(-0.272610\pi\) | ||||
0.655139 | + | 0.755508i | \(0.272610\pi\) | |||||||
\(80\) | 10.6532 | 1.19107 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.95370 | −0.326182 | ||||||||
\(83\) | −1.73225 | −0.190139 | −0.0950696 | − | 0.995471i | \(-0.530307\pi\) | ||||
−0.0950696 | + | 0.995471i | \(0.530307\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.5997 | −2.23435 | ||||||||
\(86\) | 0.542315 | 0.0584793 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.31802 | −0.775709 | −0.387854 | − | 0.921721i | \(-0.626784\pi\) | ||||
−0.387854 | + | 0.921721i | \(0.626784\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.38835 | 0.564853 | ||||||||
\(92\) | 5.58577 | 0.582357 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.21919 | 0.228892 | ||||||||
\(95\) | −1.33179 | −0.136639 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.95370 | −0.706042 | −0.353021 | − | 0.935615i | \(-0.614846\pi\) | ||||
−0.353021 | + | 0.935615i | \(0.614846\pi\) | |||||||
\(98\) | −0.297484 | −0.0300504 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.38835 | −0.838835 | ||||||||
\(101\) | 7.91299 | 0.787372 | 0.393686 | − | 0.919245i | \(-0.371200\pi\) | ||||
0.393686 | + | 0.919245i | \(0.371200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4227 | 1.81524 | 0.907622 | − | 0.419788i | \(-0.137895\pi\) | ||||
0.907622 | + | 0.419788i | \(0.137895\pi\) | |||||||
\(104\) | 6.26994 | 0.614818 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.77671 | −0.269698 | ||||||||
\(107\) | 13.3042 | 1.28617 | 0.643085 | − | 0.765795i | \(-0.277654\pi\) | ||||
0.643085 | + | 0.765795i | \(0.277654\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.953703 | −0.0913482 | −0.0456741 | − | 0.998956i | \(-0.514544\pi\) | ||||
−0.0456741 | + | 0.998956i | \(0.514544\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.47685 | 0.328532 | ||||||||
\(113\) | 14.9198 | 1.40353 | 0.701766 | − | 0.712407i | \(-0.252395\pi\) | ||||
0.701766 | + | 0.712407i | \(0.252395\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.95370 | −0.834937 | ||||||||
\(116\) | −13.1223 | −1.21837 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.13479 | −0.196524 | ||||||||
\(119\) | −6.72305 | −0.616301 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.01596 | 0.182517 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.46902 | −0.850343 | ||||||||
\(125\) | −1.87411 | −0.167625 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.7304 | 1.75079 | 0.875396 | − | 0.483407i | \(-0.160601\pi\) | ||||
0.875396 | + | 0.483407i | \(0.160601\pi\) | |||||||
\(128\) | 8.49418 | 0.750787 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.91150 | −0.430767 | ||||||||
\(131\) | −7.31802 | −0.639378 | −0.319689 | − | 0.947522i | \(-0.603578\pi\) | ||||
−0.319689 | + | 0.947522i | \(0.603578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.434652 | −0.0376891 | ||||||||
\(134\) | −1.06063 | −0.0916248 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.82301 | −0.670817 | ||||||||
\(137\) | −17.5582 | −1.50010 | −0.750050 | − | 0.661381i | \(-0.769971\pi\) | ||||
−0.750050 | + | 0.661381i | \(0.769971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.6460 | 1.66635 | 0.833177 | − | 0.553007i | \(-0.186520\pi\) | ||||
0.833177 | + | 0.553007i | \(0.186520\pi\) | |||||||
\(140\) | −5.85693 | −0.495001 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.53098 | 0.212395 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.0344 | 1.74681 | ||||||||
\(146\) | −0.776922 | −0.0642986 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.47685 | 0.532394 | ||||||||
\(149\) | 11.5193 | 0.943702 | 0.471851 | − | 0.881678i | \(-0.343586\pi\) | ||||
0.471851 | + | 0.881678i | \(0.343586\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.5997 | −1.67638 | −0.838191 | − | 0.545377i | \(-0.816386\pi\) | ||||
−0.838191 | + | 0.545377i | \(0.816386\pi\) | |||||||
\(152\) | −0.505765 | −0.0410229 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.1784 | 1.21915 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.13070 | −0.409474 | −0.204737 | − | 0.978817i | \(-0.565634\pi\) | ||||
−0.204737 | + | 0.978817i | \(0.565634\pi\) | |||||||
\(158\) | −3.46450 | −0.275621 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.2999 | −0.814275 | ||||||||
\(161\) | −2.92219 | −0.230301 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.56535 | 0.279260 | 0.139630 | − | 0.990204i | \(-0.455409\pi\) | ||||
0.139630 | + | 0.990204i | \(0.455409\pi\) | |||||||
\(164\) | −18.9792 | −1.48203 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.515317 | 0.0399963 | ||||||||
\(167\) | −21.0227 | −1.62679 | −0.813394 | − | 0.581713i | \(-0.802383\pi\) | ||||
−0.813394 | + | 0.581713i | \(0.802383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.0344 | 1.23341 | ||||||||
\(170\) | 6.12808 | 0.470003 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.48468 | 0.265705 | ||||||||
\(173\) | −3.80087 | −0.288974 | −0.144487 | − | 0.989507i | \(-0.546153\pi\) | ||||
−0.144487 | + | 0.989507i | \(0.546153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.38835 | 0.331728 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.17699 | 0.163173 | ||||||||
\(179\) | −24.5123 | −1.83214 | −0.916069 | − | 0.401021i | \(-0.868656\pi\) | ||||
−0.916069 | + | 0.401021i | \(0.868656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.04630 | −0.375088 | −0.187544 | − | 0.982256i | \(-0.560053\pi\) | ||||
−0.187544 | + | 0.982256i | \(0.560053\pi\) | |||||||
\(182\) | −1.60295 | −0.118818 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.40028 | −0.250672 | ||||||||
\(185\) | −10.3821 | −0.763304 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 14.2596 | 1.03999 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.396187 | 0.0287424 | ||||||||
\(191\) | −0.826027 | −0.0597692 | −0.0298846 | − | 0.999553i | \(-0.509514\pi\) | ||||
−0.0298846 | + | 0.999553i | \(0.509514\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.04630 | 0.507204 | 0.253602 | − | 0.967309i | \(-0.418385\pi\) | ||||
0.253602 | + | 0.967309i | \(0.418385\pi\) | |||||||
\(194\) | 2.06861 | 0.148518 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.91150 | −0.136536 | ||||||||
\(197\) | 14.5834 | 1.03902 | 0.519512 | − | 0.854463i | \(-0.326114\pi\) | ||||
0.519512 | + | 0.854463i | \(0.326114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7304 | −1.11510 | −0.557550 | − | 0.830144i | \(-0.688258\pi\) | ||||
−0.557550 | + | 0.830144i | \(0.688258\pi\) | |||||||
\(200\) | 5.10633 | 0.361072 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.35399 | −0.165626 | ||||||||
\(203\) | 6.86491 | 0.481822 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.4227 | 2.12482 | ||||||||
\(206\) | −5.48046 | −0.381842 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.7345 | 1.29900 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.5534 | −0.933056 | −0.466528 | − | 0.884506i | \(-0.654495\pi\) | ||||
−0.466528 | + | 0.884506i | \(0.654495\pi\) | |||||||
\(212\) | −17.8419 | −1.22539 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.95780 | −0.270550 | ||||||||
\(215\) | −5.58577 | −0.380946 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.95370 | 0.336279 | ||||||||
\(218\) | 0.283711 | 0.0192154 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −36.2262 | −2.43684 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.6460 | −1.04773 | −0.523867 | − | 0.851800i | \(-0.675511\pi\) | ||||
−0.523867 | + | 0.851800i | \(0.675511\pi\) | |||||||
\(224\) | −3.36153 | −0.224601 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.43839 | −0.295237 | ||||||||
\(227\) | 0.906224 | 0.0601482 | 0.0300741 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300741 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4690 | 1.02222 | 0.511111 | − | 0.859515i | \(-0.329234\pi\) | ||||
0.511111 | + | 0.859515i | \(0.329234\pi\) | |||||||
\(230\) | 2.66358 | 0.175631 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.98807 | 0.524443 | ||||||||
\(233\) | −17.5307 | −1.14847 | −0.574237 | − | 0.818689i | \(-0.694701\pi\) | ||||
−0.574237 | + | 0.818689i | \(0.694701\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.8574 | −1.49105 | ||||||||
\(236\) | −13.7173 | −0.892918 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | 0.129641 | ||||||||
\(239\) | −2.23802 | −0.144765 | −0.0723826 | − | 0.997377i | \(-0.523060\pi\) | ||||
−0.0723826 | + | 0.997377i | \(0.523060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.0344 | 1.09728 | 0.548640 | − | 0.836059i | \(-0.315146\pi\) | ||||
0.548640 | + | 0.836059i | \(0.315146\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.9537 | 0.829276 | ||||||||
\(245\) | 3.06404 | 0.195754 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.34206 | −0.149022 | ||||||||
\(248\) | 5.76418 | 0.366025 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.557517 | 0.0352604 | ||||||||
\(251\) | −19.4323 | −1.22656 | −0.613279 | − | 0.789866i | \(-0.710150\pi\) | ||||
−0.613279 | + | 0.789866i | \(0.710150\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.86948 | −0.368284 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.38052 | 0.586283 | ||||||||
\(257\) | −0.400459 | −0.0249800 | −0.0124900 | − | 0.999922i | \(-0.503976\pi\) | ||||
−0.0124900 | + | 0.999922i | \(0.503976\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.38835 | −0.210542 | ||||||||
\(260\) | −31.5592 | −1.95722 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.17699 | 0.134495 | ||||||||
\(263\) | −5.98623 | −0.369127 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.5997 | 1.75687 | ||||||||
\(266\) | 0.129302 | 0.00792801 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.81517 | −0.416303 | ||||||||
\(269\) | 11.3499 | 0.692018 | 0.346009 | − | 0.938231i | \(-0.387537\pi\) | ||||
0.346009 | + | 0.938231i | \(0.387537\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.5653 | 1.43149 | 0.715746 | − | 0.698360i | \(-0.246087\pi\) | ||||
0.715746 | + | 0.698360i | \(0.246087\pi\) | |||||||
\(272\) | −23.3751 | −1.41732 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.22329 | 0.315551 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1307 | 0.909115 | 0.454558 | − | 0.890717i | \(-0.349797\pi\) | ||||
0.454558 | + | 0.890717i | \(0.349797\pi\) | |||||||
\(278\) | −5.84437 | −0.350522 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.56535 | 0.213070 | ||||||||
\(281\) | 26.1554 | 1.56030 | 0.780150 | − | 0.625593i | \(-0.215143\pi\) | ||||
0.780150 | + | 0.625593i | \(0.215143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0807 | −1.19367 | −0.596836 | − | 0.802363i | \(-0.703576\pi\) | ||||
−0.596836 | + | 0.802363i | \(0.703576\pi\) | |||||||
\(284\) | 16.2630 | 0.965031 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.92895 | 0.586087 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.1994 | 1.65879 | ||||||||
\(290\) | −6.25739 | −0.367446 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.99217 | −0.292145 | ||||||||
\(293\) | 19.5215 | 1.14046 | 0.570230 | − | 0.821485i | \(-0.306854\pi\) | ||||
0.570230 | + | 0.821485i | \(0.306854\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.9881 | 1.28020 | ||||||||
\(296\) | −3.94272 | −0.229166 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.42682 | −0.198510 | ||||||||
\(299\) | −15.7458 | −0.910602 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.82301 | −0.105076 | ||||||||
\(302\) | 6.12808 | 0.352632 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.51122 | −0.0866744 | ||||||||
\(305\) | −20.7641 | −1.18895 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2920 | 1.32935 | 0.664673 | − | 0.747134i | \(-0.268571\pi\) | ||||
0.664673 | + | 0.747134i | \(0.268571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.51532 | −0.256453 | ||||||||
\(311\) | 8.79167 | 0.498530 | 0.249265 | − | 0.968435i | \(-0.419811\pi\) | ||||
0.249265 | + | 0.968435i | \(0.419811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.3764 | 1.43436 | 0.717180 | − | 0.696888i | \(-0.245432\pi\) | ||||
0.717180 | + | 0.696888i | \(0.245432\pi\) | |||||||
\(314\) | 1.52630 | 0.0861341 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.2614 | −1.25230 | ||||||||
\(317\) | −0.258604 | −0.0145246 | −0.00726232 | − | 0.999974i | \(-0.502312\pi\) | ||||
−0.00726232 | + | 0.999974i | \(0.502312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −18.2424 | −1.01978 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.869304 | 0.0484444 | ||||||||
\(323\) | 2.92219 | 0.162595 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.6460 | 1.31164 | ||||||||
\(326\) | −1.06063 | −0.0587431 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.5534 | 0.637931 | ||||||||
\(329\) | −7.45988 | −0.411276 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.2920 | −1.50011 | −0.750053 | − | 0.661378i | \(-0.769972\pi\) | ||||
−0.750053 | + | 0.661378i | \(0.769972\pi\) | |||||||
\(332\) | 3.31120 | 0.181726 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.25392 | 0.342199 | ||||||||
\(335\) | 10.9244 | 0.596863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.3383 | 1.21685 | 0.608423 | − | 0.793613i | \(-0.291802\pi\) | ||||
0.608423 | + | 0.793613i | \(0.291802\pi\) | |||||||
\(338\) | −4.76997 | −0.259452 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 39.3764 | 2.13549 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.12127 | −0.114371 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.13070 | 0.0607866 | ||||||||
\(347\) | 35.6839 | 1.91561 | 0.957805 | − | 0.287417i | \(-0.0927967\pi\) | ||||
0.957805 | + | 0.287417i | \(0.0927967\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.03437 | 0.483599 | 0.241799 | − | 0.970326i | \(-0.422262\pi\) | ||||
0.241799 | + | 0.970326i | \(0.422262\pi\) | |||||||
\(350\) | −1.30547 | −0.0697800 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 36.0843 | 1.92058 | 0.960288 | − | 0.279012i | \(-0.0900068\pi\) | ||||
0.960288 | + | 0.279012i | \(0.0900068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.0687 | −1.38358 | ||||||||
\(356\) | 13.9884 | 0.741385 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.29203 | 0.385396 | ||||||||
\(359\) | −23.3224 | −1.23091 | −0.615455 | − | 0.788172i | \(-0.711028\pi\) | ||||
−0.615455 | + | 0.788172i | \(0.711028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8111 | −0.990057 | ||||||||
\(362\) | 1.50119 | 0.0789009 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.2999 | −0.539859 | ||||||||
\(365\) | 8.00219 | 0.418854 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.1994 | −1.10660 | −0.553301 | − | 0.832982i | \(-0.686632\pi\) | ||||
−0.553301 | + | 0.832982i | \(0.686632\pi\) | |||||||
\(368\) | −10.1600 | −0.529627 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.08850 | 0.160563 | ||||||||
\(371\) | 9.33398 | 0.484596 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.82301 | 0.508616 | 0.254308 | − | 0.967123i | \(-0.418152\pi\) | ||||
0.254308 | + | 0.967123i | \(0.418152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.68038 | −0.447656 | ||||||||
\(377\) | 36.9906 | 1.90511 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0807 | 1.23694 | 0.618470 | − | 0.785808i | \(-0.287753\pi\) | ||||
0.618470 | + | 0.785808i | \(0.287753\pi\) | |||||||
\(380\) | 2.54572 | 0.130593 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.245730 | 0.0125726 | ||||||||
\(383\) | 32.7366 | 1.67276 | 0.836381 | − | 0.548149i | \(-0.184667\pi\) | ||||
0.836381 | + | 0.548149i | \(0.184667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.09616 | −0.106692 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.2920 | 0.674800 | ||||||||
\(389\) | −6.69551 | −0.339476 | −0.169738 | − | 0.985489i | \(-0.554292\pi\) | ||||
−0.169738 | + | 0.985489i | \(0.554292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.6460 | 0.993542 | ||||||||
\(392\) | 1.16361 | 0.0587711 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.33832 | −0.218562 | ||||||||
\(395\) | 35.6839 | 1.79545 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.0224 | 1.45659 | 0.728297 | − | 0.685261i | \(-0.240312\pi\) | ||||
0.728297 | + | 0.685261i | \(0.240312\pi\) | |||||||
\(398\) | 4.67954 | 0.234564 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.2577 | 0.762883 | ||||||||
\(401\) | −32.4780 | −1.62187 | −0.810936 | − | 0.585134i | \(-0.801042\pi\) | ||||
−0.810936 | + | 0.585134i | \(0.801042\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.6923 | 1.32964 | ||||||||
\(404\) | −15.1257 | −0.752532 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.04220 | −0.101353 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.4227 | −0.515370 | −0.257685 | − | 0.966229i | \(-0.582960\pi\) | ||||
−0.257685 | + | 0.966229i | \(0.582960\pi\) | |||||||
\(410\) | −9.05027 | −0.446961 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −35.2151 | −1.73492 | ||||||||
\(413\) | 7.17616 | 0.353116 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.30769 | −0.260544 | ||||||||
\(416\) | −18.1131 | −0.888068 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.5077 | 1.39269 | 0.696346 | − | 0.717706i | \(-0.254808\pi\) | ||||
0.696346 | + | 0.717706i | \(0.254808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.16506 | −0.300467 | −0.150233 | − | 0.988651i | \(-0.548003\pi\) | ||||
−0.150233 | + | 0.988651i | \(0.548003\pi\) | |||||||
\(422\) | 4.03192 | 0.196271 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.8611 | 0.527462 | ||||||||
\(425\) | −29.5031 | −1.43111 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.77671 | −0.327948 | ||||||||
\(428\) | −25.4311 | −1.22926 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.66168 | 0.0801332 | ||||||||
\(431\) | −26.4666 | −1.27485 | −0.637427 | − | 0.770511i | \(-0.720001\pi\) | ||||
−0.637427 | + | 0.770511i | \(0.720001\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.8693 | −0.906801 | −0.453400 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453400 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(434\) | −1.47365 | −0.0707373 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.82301 | 0.0873062 | ||||||||
\(437\) | 1.27013 | 0.0607587 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.8574 | 0.709104 | 0.354552 | − | 0.935036i | \(-0.384633\pi\) | ||||
0.354552 | + | 0.935036i | \(0.384633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.7767 | 0.512596 | ||||||||
\(443\) | 20.7641 | 0.986533 | 0.493267 | − | 0.869878i | \(-0.335803\pi\) | ||||
0.493267 | + | 0.869878i | \(0.335803\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.4227 | −1.06294 | ||||||||
\(446\) | 4.65444 | 0.220394 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.95370 | −0.281286 | ||||||||
\(449\) | −33.5877 | −1.58510 | −0.792551 | − | 0.609805i | \(-0.791248\pi\) | ||||
−0.792551 | + | 0.609805i | \(0.791248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −28.5192 | −1.34143 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.269587 | −0.0126524 | ||||||||
\(455\) | 16.5101 | 0.774008 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5071 | 1.42706 | 0.713532 | − | 0.700623i | \(-0.247095\pi\) | ||||
0.713532 | + | 0.700623i | \(0.247095\pi\) | |||||||
\(458\) | −4.60178 | −0.215027 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.1150 | 0.797993 | ||||||||
\(461\) | −10.5515 | −0.491431 | −0.245715 | − | 0.969342i | \(-0.579023\pi\) | ||||
−0.245715 | + | 0.969342i | \(0.579023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6960 | −0.682983 | −0.341492 | − | 0.939885i | \(-0.610932\pi\) | ||||
−0.341492 | + | 0.939885i | \(0.610932\pi\) | |||||||
\(464\) | 23.8683 | 1.10806 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.21510 | 0.241585 | ||||||||
\(467\) | −9.83975 | −0.455329 | −0.227665 | − | 0.973740i | \(-0.573109\pi\) | ||||
−0.227665 | + | 0.973740i | \(0.573109\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.56535 | 0.164632 | ||||||||
\(470\) | 6.79970 | 0.313647 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.35025 | 0.384352 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.90741 | −0.0875178 | ||||||||
\(476\) | 12.8511 | 0.589031 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.665774 | 0.0304518 | ||||||||
\(479\) | −13.8100 | −0.630996 | −0.315498 | − | 0.948926i | \(-0.602171\pi\) | ||||
−0.315498 | + | 0.948926i | \(0.602171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2577 | −0.832478 | ||||||||
\(482\) | −5.06745 | −0.230816 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.3064 | −0.967476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.26139 | −0.283731 | −0.141865 | − | 0.989886i | \(-0.545310\pi\) | ||||
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(488\) | −7.88544 | −0.356957 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.911503 | −0.0411775 | ||||||||
\(491\) | 13.8717 | 0.626020 | 0.313010 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313010 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.1531 | −2.07863 | ||||||||
\(494\) | 0.696725 | 0.0313471 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17.2233 | 0.773349 | ||||||||
\(497\) | −8.50796 | −0.381634 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6960 | 0.836950 | 0.418475 | − | 0.908228i | \(-0.362565\pi\) | ||||
0.418475 | + | 0.908228i | \(0.362565\pi\) | |||||||
\(500\) | 3.58236 | 0.160208 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.78081 | 0.258010 | ||||||||
\(503\) | −11.4301 | −0.509645 | −0.254822 | − | 0.966988i | \(-0.582017\pi\) | ||||
−0.254822 | + | 0.966988i | \(0.582017\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.2457 | 1.07892 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −37.7147 | −1.67332 | ||||||||
\(509\) | −14.8144 | −0.656639 | −0.328319 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328319 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.61165 | 0.115532 | ||||||||
\(512\) | −19.7789 | −0.874113 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.119130 | 0.00525461 | ||||||||
\(515\) | 56.4480 | 2.48740 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.00798 | 0.0442881 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.2114 | 0.842474 | ||||||||
\(521\) | 19.3521 | 0.847832 | 0.423916 | − | 0.905701i | \(-0.360655\pi\) | ||||
0.423916 | + | 0.905701i | \(0.360655\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.7267 | 1.03750 | 0.518748 | − | 0.854927i | \(-0.326398\pi\) | ||||
0.518748 | + | 0.854927i | \(0.326398\pi\) | |||||||
\(524\) | 13.9884 | 0.611087 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.78081 | 0.0776469 | ||||||||
\(527\) | −33.3040 | −1.45075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.4608 | −0.628732 | ||||||||
\(530\) | −8.50796 | −0.369562 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.830838 | 0.0360214 | ||||||||
\(533\) | 53.5007 | 2.31737 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.7648 | 1.76242 | ||||||||
\(536\) | 4.14867 | 0.179195 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.37643 | −0.145568 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5153 | 0.882022 | 0.441011 | − | 0.897502i | \(-0.354620\pi\) | ||||
0.441011 | + | 0.897502i | \(0.354620\pi\) | |||||||
\(542\) | −7.01031 | −0.301119 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.5997 | 0.968955 | ||||||||
\(545\) | −2.92219 | −0.125173 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.6841 | 1.22644 | 0.613222 | − | 0.789911i | \(-0.289873\pi\) | ||||
0.613222 | + | 0.789911i | \(0.289873\pi\) | |||||||
\(548\) | 33.5626 | 1.43372 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.98384 | −0.127116 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.6460 | 0.495239 | ||||||||
\(554\) | −4.50114 | −0.191235 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.5534 | −1.59262 | ||||||||
\(557\) | 26.7228 | 1.13228 | 0.566141 | − | 0.824309i | \(-0.308436\pi\) | ||||
0.566141 | + | 0.824309i | \(0.308436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.82301 | −0.415469 | ||||||||
\(560\) | 10.6532 | 0.450181 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.78081 | −0.328214 | ||||||||
\(563\) | −20.6839 | −0.871724 | −0.435862 | − | 0.900014i | \(-0.643556\pi\) | ||||
−0.435862 | + | 0.900014i | \(0.643556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 45.7147 | 1.92323 | ||||||||
\(566\) | 5.97368 | 0.251092 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.89994 | −0.415392 | ||||||||
\(569\) | −7.54908 | −0.316474 | −0.158237 | − | 0.987401i | \(-0.550581\pi\) | ||||
−0.158237 | + | 0.987401i | \(0.550581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.7767 | −1.12057 | −0.560285 | − | 0.828300i | \(-0.689308\pi\) | ||||
−0.560285 | + | 0.828300i | \(0.689308\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.95370 | −0.123285 | ||||||||
\(575\) | −12.8236 | −0.534781 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.5616 | −0.564577 | −0.282289 | − | 0.959330i | \(-0.591094\pi\) | ||||
−0.282289 | + | 0.959330i | \(0.591094\pi\) | |||||||
\(578\) | −8.38888 | −0.348931 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −40.2073 | −1.66952 | ||||||||
\(581\) | −1.73225 | −0.0718659 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.03893 | 0.125752 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.80734 | −0.239899 | ||||||||
\(587\) | 16.2515 | 0.670773 | 0.335386 | − | 0.942081i | \(-0.391133\pi\) | ||||
0.335386 | + | 0.942081i | \(0.391133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.15314 | −0.0887184 | ||||||||
\(590\) | −6.54110 | −0.269293 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.7808 | −0.484188 | ||||||||
\(593\) | 25.6496 | 1.05330 | 0.526652 | − | 0.850081i | \(-0.323447\pi\) | ||||
0.526652 | + | 0.850081i | \(0.323447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.5997 | −0.844506 | ||||||||
\(596\) | −22.0193 | −0.901944 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.68412 | 0.191548 | ||||||||
\(599\) | −6.41180 | −0.261979 | −0.130989 | − | 0.991384i | \(-0.541815\pi\) | ||||
−0.130989 | + | 0.991384i | \(0.541815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.5191 | 0.836990 | 0.418495 | − | 0.908219i | \(-0.362558\pi\) | ||||
0.418495 | + | 0.908219i | \(0.362558\pi\) | |||||||
\(602\) | 0.542315 | 0.0221031 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39.3764 | 1.60220 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.1733 | −0.412920 | −0.206460 | − | 0.978455i | \(-0.566194\pi\) | ||||
−0.206460 | + | 0.978455i | \(0.566194\pi\) | |||||||
\(608\) | 1.46109 | 0.0592552 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.17699 | 0.250099 | ||||||||
\(611\) | −40.1965 | −1.62617 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.46902 | −0.220892 | −0.110446 | − | 0.993882i | \(-0.535228\pi\) | ||||
−0.110446 | + | 0.993882i | \(0.535228\pi\) | |||||||
\(614\) | −6.92900 | −0.279632 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.46450 | −0.139476 | −0.0697378 | − | 0.997565i | \(-0.522216\pi\) | ||||
−0.0697378 | + | 0.997565i | \(0.522216\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.08440 | 0.324939 | 0.162470 | − | 0.986714i | \(-0.448054\pi\) | ||||
0.162470 | + | 0.986714i | \(0.448054\pi\) | |||||||
\(620\) | −29.0135 | −1.16521 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.61538 | −0.104867 | ||||||||
\(623\) | −7.31802 | −0.293190 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.6841 | −1.10736 | ||||||||
\(626\) | −7.54908 | −0.301722 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.80734 | 0.391356 | ||||||||
\(629\) | 22.7801 | 0.908302 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2920 | 0.927241 | 0.463620 | − | 0.886034i | \(-0.346550\pi\) | ||||
0.463620 | + | 0.886034i | \(0.346550\pi\) | |||||||
\(632\) | 13.5514 | 0.539046 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0769305 | 0.00305530 | ||||||||
\(635\) | 60.4548 | 2.39908 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.38835 | 0.213494 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.0265 | 1.02879 | ||||||||
\(641\) | −36.2262 | −1.43085 | −0.715424 | − | 0.698690i | \(-0.753767\pi\) | ||||
−0.715424 | + | 0.698690i | \(0.753767\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.5616 | −1.08692 | −0.543462 | − | 0.839434i | \(-0.682887\pi\) | ||||
−0.543462 | + | 0.839434i | \(0.682887\pi\) | |||||||
\(644\) | 5.58577 | 0.220110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.869304 | −0.0342023 | ||||||||
\(647\) | −29.3086 | −1.15224 | −0.576121 | − | 0.817365i | \(-0.695434\pi\) | ||||
−0.576121 | + | 0.817365i | \(0.695434\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.03431 | −0.275908 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.81517 | −0.266903 | ||||||||
\(653\) | −39.1484 | −1.53199 | −0.765997 | − | 0.642844i | \(-0.777754\pi\) | ||||
−0.765997 | + | 0.642844i | \(0.777754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.4227 | −0.876128 | ||||||||
\(656\) | 34.5215 | 1.34784 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.21919 | 0.0865132 | ||||||||
\(659\) | −1.33179 | −0.0518792 | −0.0259396 | − | 0.999664i | \(-0.508258\pi\) | ||||
−0.0259396 | + | 0.999664i | \(0.508258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.6378 | 1.23057 | 0.615284 | − | 0.788305i | \(-0.289041\pi\) | ||||
0.615284 | + | 0.788305i | \(0.289041\pi\) | |||||||
\(662\) | 8.11894 | 0.315552 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.01566 | −0.0782229 | ||||||||
\(665\) | −1.33179 | −0.0516447 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.0605 | −0.776747 | ||||||||
\(668\) | 40.1850 | 1.55480 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.24983 | −0.125552 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.0844 | 1.23676 | 0.618381 | − | 0.785878i | \(-0.287789\pi\) | ||||
0.618381 | + | 0.785878i | \(0.287789\pi\) | |||||||
\(674\) | −6.64529 | −0.255967 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.6497 | −1.17884 | ||||||||
\(677\) | 15.1508 | 0.582293 | 0.291146 | − | 0.956678i | \(-0.405963\pi\) | ||||
0.291146 | + | 0.956678i | \(0.405963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.95370 | −0.266859 | ||||||||
\(680\) | −23.9700 | −0.919208 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −30.0981 | −1.15167 | −0.575836 | − | 0.817565i | \(-0.695323\pi\) | ||||
−0.575836 | + | 0.817565i | \(0.695323\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −53.7991 | −2.05556 | ||||||||
\(686\) | −0.297484 | −0.0113580 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.33832 | −0.241646 | ||||||||
\(689\) | 50.2948 | 1.91608 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1994 | 0.958632 | 0.479316 | − | 0.877643i | \(-0.340885\pi\) | ||||
0.479316 | + | 0.877643i | \(0.340885\pi\) | |||||||
\(692\) | 7.26537 | 0.276188 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.6154 | −0.402954 | ||||||||
\(695\) | 60.1962 | 2.28337 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −66.7529 | −2.52844 | ||||||||
\(698\) | −2.68758 | −0.101726 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.38835 | −0.317050 | ||||||||
\(701\) | −39.8235 | −1.50411 | −0.752057 | − | 0.659098i | \(-0.770938\pi\) | ||||
−0.752057 | + | 0.659098i | \(0.770938\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.47275 | 0.0555460 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.7345 | −0.403999 | ||||||||
\(707\) | 7.91299 | 0.297599 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.9418 | 1.53760 | 0.768800 | − | 0.639489i | \(-0.220854\pi\) | ||||
0.768800 | + | 0.639489i | \(0.220854\pi\) | |||||||
\(710\) | 7.75503 | 0.291041 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.51532 | −0.319125 | ||||||||
\(713\) | −14.4756 | −0.542117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 46.8554 | 1.75107 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.93804 | 0.258925 | ||||||||
\(719\) | −3.14424 | −0.117260 | −0.0586302 | − | 0.998280i | \(-0.518673\pi\) | ||||
−0.0586302 | + | 0.998280i | \(0.518673\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.4227 | 0.686098 | ||||||||
\(722\) | 5.59599 | 0.208261 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.64601 | 0.358491 | ||||||||
\(725\) | 30.1257 | 1.11884 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.9843 | 1.70546 | 0.852732 | − | 0.522348i | \(-0.174944\pi\) | ||||
0.852732 | + | 0.522348i | \(0.174944\pi\) | |||||||
\(728\) | 6.26994 | 0.232379 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.38052 | −0.0881071 | ||||||||
\(731\) | 12.2562 | 0.453311 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7767 | −0.545790 | −0.272895 | − | 0.962044i | \(-0.587981\pi\) | ||||
−0.272895 | + | 0.962044i | \(0.587981\pi\) | |||||||
\(734\) | 6.30649 | 0.232777 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.82301 | 0.362081 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.3526 | 1.88903 | 0.944517 | − | 0.328461i | \(-0.106530\pi\) | ||||
0.944517 | + | 0.328461i | \(0.106530\pi\) | |||||||
\(740\) | 19.8453 | 0.729529 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.77671 | −0.101936 | ||||||||
\(743\) | −16.4299 | −0.602756 | −0.301378 | − | 0.953505i | \(-0.597447\pi\) | ||||
−0.301378 | + | 0.953505i | \(0.597447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.2958 | 1.29314 | ||||||||
\(746\) | −2.92219 | −0.106989 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.3042 | 0.486127 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.9500 | 1.05640 | 0.528200 | − | 0.849120i | \(-0.322867\pi\) | ||||
0.528200 | + | 0.849120i | \(0.322867\pi\) | |||||||
\(752\) | −25.9369 | −0.945821 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.0041 | −0.400746 | ||||||||
\(755\) | −63.1184 | −2.29711 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0725 | 1.31108 | 0.655538 | − | 0.755162i | \(-0.272442\pi\) | ||||
0.655538 | + | 0.755162i | \(0.272442\pi\) | |||||||
\(758\) | −7.16361 | −0.260194 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.54968 | −0.0562130 | ||||||||
\(761\) | 34.8303 | 1.26260 | 0.631299 | − | 0.775540i | \(-0.282522\pi\) | ||||
0.631299 | + | 0.775540i | \(0.282522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.953703 | −0.0345264 | ||||||||
\(764\) | 1.57895 | 0.0571245 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.73861 | −0.351870 | ||||||||
\(767\) | 38.6677 | 1.39621 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.35025 | −0.156874 | −0.0784371 | − | 0.996919i | \(-0.524993\pi\) | ||||
−0.0784371 | + | 0.996919i | \(0.524993\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.4690 | −0.484761 | ||||||||
\(773\) | 1.41199 | 0.0507857 | 0.0253929 | − | 0.999678i | \(-0.491916\pi\) | ||||
0.0253929 | + | 0.999678i | \(0.491916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.7386 | 0.780874 | ||||||||
\(776\) | −8.09139 | −0.290464 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.99181 | 0.0714097 | ||||||||
\(779\) | −4.31564 | −0.154624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.84437 | −0.208994 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.47685 | 0.124173 | ||||||||
\(785\) | −15.7207 | −0.561095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7886 | 0.455866 | 0.227933 | − | 0.973677i | \(-0.426803\pi\) | ||||
0.227933 | + | 0.973677i | \(0.426803\pi\) | |||||||
\(788\) | −27.8762 | −0.993048 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.6154 | −0.377678 | ||||||||
\(791\) | 14.9198 | 0.530485 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.5153 | −1.29670 | ||||||||
\(794\) | −8.63371 | −0.306399 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30.0687 | 1.06576 | ||||||||
\(797\) | −8.90842 | −0.315552 | −0.157776 | − | 0.987475i | \(-0.550432\pi\) | ||||
−0.157776 | + | 0.987475i | \(0.550432\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.1531 | 1.77429 | ||||||||
\(800\) | −14.7516 | −0.521547 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.66168 | 0.341166 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.95370 | −0.315577 | ||||||||
\(806\) | −7.94053 | −0.279693 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.20763 | 0.323923 | ||||||||
\(809\) | −54.9834 | −1.93311 | −0.966556 | − | 0.256456i | \(-0.917445\pi\) | ||||
−0.966556 | + | 0.256456i | \(0.917445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.21136 | −0.112766 | −0.0563831 | − | 0.998409i | \(-0.517957\pi\) | ||||
−0.0563831 | + | 0.998409i | \(0.517957\pi\) | |||||||
\(812\) | −13.1223 | −0.460502 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.9244 | 0.382664 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.792373 | 0.0277216 | ||||||||
\(818\) | 3.10059 | 0.108410 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −58.1531 | −2.03080 | ||||||||
\(821\) | 25.2492 | 0.881202 | 0.440601 | − | 0.897703i | \(-0.354765\pi\) | ||||
0.440601 | + | 0.897703i | \(0.354765\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.82674 | 0.203107 | 0.101554 | − | 0.994830i | \(-0.467619\pi\) | ||||
0.101554 | + | 0.994830i | \(0.467619\pi\) | |||||||
\(824\) | 21.4369 | 0.746788 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.13479 | −0.0742790 | ||||||||
\(827\) | 19.7160 | 0.685594 | 0.342797 | − | 0.939409i | \(-0.388626\pi\) | ||||
0.342797 | + | 0.939409i | \(0.388626\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.03810 | 0.244443 | 0.122222 | − | 0.992503i | \(-0.460998\pi\) | ||||
0.122222 | + | 0.992503i | \(0.460998\pi\) | |||||||
\(830\) | 1.57895 | 0.0548062 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32.0807 | −1.11220 | ||||||||
\(833\) | −6.72305 | −0.232940 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −64.4145 | −2.22916 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.48059 | −0.292957 | ||||||||
\(839\) | 22.9471 | 0.792220 | 0.396110 | − | 0.918203i | \(-0.370360\pi\) | ||||
0.396110 | + | 0.918203i | \(0.370360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.1270 | 0.625068 | ||||||||
\(842\) | 1.83401 | 0.0632041 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.9074 | 0.891770 | ||||||||
\(845\) | 49.1300 | 1.69012 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 32.4529 | 1.11444 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.77671 | 0.301039 | ||||||||
\(851\) | 9.90141 | 0.339416 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.5915 | 1.45831 | 0.729153 | − | 0.684351i | \(-0.239914\pi\) | ||||
0.729153 | + | 0.684351i | \(0.239914\pi\) | |||||||
\(854\) | 2.01596 | 0.0689848 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.4809 | 0.529128 | ||||||||
\(857\) | 4.42338 | 0.151100 | 0.0755499 | − | 0.997142i | \(-0.475929\pi\) | ||||
0.0755499 | + | 0.997142i | \(0.475929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.4466 | −0.356433 | −0.178216 | − | 0.983991i | \(-0.557033\pi\) | ||||
−0.178216 | + | 0.983991i | \(0.557033\pi\) | |||||||
\(860\) | 10.6772 | 0.364090 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.87340 | 0.268169 | ||||||||
\(863\) | −0.258604 | −0.00880298 | −0.00440149 | − | 0.999990i | \(-0.501401\pi\) | ||||
−0.00440149 | + | 0.999990i | \(0.501401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6460 | −0.395976 | ||||||||
\(866\) | 5.61331 | 0.190748 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9.46902 | −0.321399 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.2114 | 0.650952 | ||||||||
\(872\) | −1.10974 | −0.0375805 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.377844 | −0.0127808 | ||||||||
\(875\) | −1.87411 | −0.0633564 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7529 | −1.30859 | −0.654295 | − | 0.756239i | \(-0.727035\pi\) | ||||
−0.654295 | + | 0.756239i | \(0.727035\pi\) | |||||||
\(878\) | −4.41983 | −0.149162 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.3888 | 0.990135 | 0.495067 | − | 0.868855i | \(-0.335143\pi\) | ||||
0.495067 | + | 0.868855i | \(0.335143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.788639 | 0.0265398 | 0.0132699 | − | 0.999912i | \(-0.495776\pi\) | ||||
0.0132699 | + | 0.999912i | \(0.495776\pi\) | |||||||
\(884\) | 69.2465 | 2.32901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.17699 | −0.207520 | ||||||||
\(887\) | 18.4094 | 0.618126 | 0.309063 | − | 0.951042i | \(-0.399985\pi\) | ||||
0.309063 | + | 0.951042i | \(0.399985\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.7304 | 0.661737 | ||||||||
\(890\) | 6.67040 | 0.223592 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.9074 | 1.00137 | ||||||||
\(893\) | 3.24245 | 0.108504 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −75.1068 | −2.51054 | ||||||||
\(896\) | 8.49418 | 0.283771 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.99181 | 0.333431 | ||||||||
\(899\) | 34.0067 | 1.13419 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −62.7529 | −2.09060 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.3608 | 0.577410 | ||||||||
\(905\) | −15.4621 | −0.513976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.3846 | −0.842882 | −0.421441 | − | 0.906856i | \(-0.638476\pi\) | ||||
−0.421441 | + | 0.906856i | \(0.638476\pi\) | |||||||
\(908\) | −1.73225 | −0.0574868 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.91150 | −0.162815 | ||||||||
\(911\) | 31.9357 | 1.05808 | 0.529038 | − | 0.848598i | \(-0.322553\pi\) | ||||
0.529038 | + | 0.848598i | \(0.322553\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −9.07538 | −0.300187 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29.5691 | −0.976990 | ||||||||
\(917\) | −7.31802 | −0.241662 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.7991 | −0.982983 | −0.491492 | − | 0.870882i | \(-0.663548\pi\) | ||||
−0.491492 | + | 0.870882i | \(0.663548\pi\) | |||||||
\(920\) | −10.4186 | −0.343491 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.13889 | 0.103374 | ||||||||
\(923\) | −45.8439 | −1.50897 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.8693 | −0.488900 | ||||||||
\(926\) | 4.37184 | 0.143667 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.0766 | −0.757525 | ||||||||
\(929\) | −30.5237 | −1.00145 | −0.500725 | − | 0.865607i | \(-0.666933\pi\) | ||||
−0.500725 | + | 0.865607i | \(0.666933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.434652 | −0.0142451 | ||||||||
\(932\) | 33.5100 | 1.09766 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.92717 | 0.0957798 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2995 | −0.369138 | −0.184569 | − | 0.982820i | \(-0.559089\pi\) | ||||
−0.184569 | + | 0.982820i | \(0.559089\pi\) | |||||||
\(938\) | −1.06063 | −0.0346309 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 43.6919 | 1.42507 | ||||||||
\(941\) | −7.99319 | −0.260570 | −0.130285 | − | 0.991477i | \(-0.541589\pi\) | ||||
−0.130285 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.0142 | −0.944834 | ||||||||
\(944\) | 24.9505 | 0.812068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.5921 | −1.61153 | −0.805763 | − | 0.592238i | \(-0.798245\pi\) | ||||
−0.805763 | + | 0.592238i | \(0.798245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.0725 | 0.456812 | ||||||||
\(950\) | 0.567423 | 0.0184096 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.82301 | −0.253545 | ||||||||
\(953\) | 13.7939 | 0.446829 | 0.223414 | − | 0.974724i | \(-0.428280\pi\) | ||||
0.223414 | + | 0.974724i | \(0.428280\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.53098 | −0.0819006 | ||||||||
\(956\) | 4.27797 | 0.138360 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.10826 | 0.132732 | ||||||||
\(959\) | −17.5582 | −0.566985 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.46083 | −0.208414 | ||||||||
\(962\) | 5.43136 | 0.175114 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −32.5613 | −1.04873 | ||||||||
\(965\) | 21.5902 | 0.695012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.1613 | −1.03424 | −0.517119 | − | 0.855913i | \(-0.672996\pi\) | ||||
−0.517119 | + | 0.855913i | \(0.672996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.33832 | 0.203511 | ||||||||
\(971\) | −2.41642 | −0.0775467 | −0.0387733 | − | 0.999248i | \(-0.512345\pi\) | ||||
−0.0387733 | + | 0.999248i | \(0.512345\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6460 | 0.629822 | ||||||||
\(974\) | 1.86266 | 0.0596836 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.5616 | −0.754189 | ||||||||
\(977\) | 5.30206 | 0.169628 | 0.0848139 | − | 0.996397i | \(-0.472970\pi\) | ||||
0.0848139 | + | 0.996397i | \(0.472970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −5.85693 | −0.187093 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.12660 | −0.131685 | ||||||||
\(983\) | −4.03192 | −0.128598 | −0.0642992 | − | 0.997931i | \(-0.520481\pi\) | ||||
−0.0642992 | + | 0.997931i | \(0.520481\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.6841 | 1.42375 | ||||||||
\(986\) | 13.7298 | 0.437246 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.47685 | 0.142428 | ||||||||
\(989\) | 5.32717 | 0.169394 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.1188 | 0.924988 | 0.462494 | − | 0.886622i | \(-0.346955\pi\) | ||||
0.462494 | + | 0.886622i | \(0.346955\pi\) | |||||||
\(992\) | −16.6520 | −0.528702 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.53098 | 0.0802778 | ||||||||
\(995\) | −48.1986 | −1.52800 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.1307 | −0.352513 | −0.176256 | − | 0.984344i | \(-0.556399\pi\) | ||||
−0.176256 | + | 0.984344i | \(0.556399\pi\) | |||||||
\(998\) | −5.56177 | −0.176055 | ||||||||
\(999\) | 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 | 7623.2.a.cr.1.3 | yes | 6 | |
3.2 | odd | 2 | inner | 7623.2.a.cr.1.4 | yes | 6 | |
11.10 | odd | 2 | 7623.2.a.cq.1.4 | yes | 6 | ||
33.32 | even | 2 | 7623.2.a.cq.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7623.2.a.cq.1.3 | ✓ | 6 | 33.32 | even | 2 | ||
7623.2.a.cq.1.4 | yes | 6 | 11.10 | odd | 2 | ||
7623.2.a.cr.1.3 | yes | 6 | 1.1 | even | 1 | trivial | |
7623.2.a.cr.1.4 | yes | 6 | 3.2 | odd | 2 | inner |