Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, 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("1386.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.40405\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.09174 | 0.488243 | 0.244121 | − | 0.969745i | \(-0.421500\pi\) | ||||
0.244121 | + | 0.969745i | \(0.421500\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.09174 | 0.345240 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.80809 | 1.88823 | 0.944113 | − | 0.329623i | \(-0.106922\pi\) | ||||
0.944113 | + | 0.329623i | \(0.106922\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.09174 | 0.264787 | 0.132393 | − | 0.991197i | \(-0.457734\pi\) | ||||
0.132393 | + | 0.991197i | \(0.457734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.89984 | −0.894684 | −0.447342 | − | 0.894363i | \(-0.647629\pi\) | ||||
−0.447342 | + | 0.894363i | \(0.647629\pi\) | |||||||
\(20\) | 1.09174 | 0.244121 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −6.99158 | −1.45785 | −0.728923 | − | 0.684596i | \(-0.759979\pi\) | ||||
−0.728923 | + | 0.684596i | \(0.759979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.80809 | −0.761619 | ||||||||
\(26\) | 6.80809 | 1.33518 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.80809 | 0.892841 | 0.446420 | − | 0.894823i | \(-0.352699\pi\) | ||||
0.446420 | + | 0.894823i | \(0.352699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27523 | −0.229039 | −0.114519 | − | 0.993421i | \(-0.536533\pi\) | ||||
−0.114519 | + | 0.993421i | \(0.536533\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.09174 | 0.187233 | ||||||||
\(35\) | 1.09174 | 0.184538 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.18349 | 0.687761 | 0.343881 | − | 0.939013i | \(-0.388258\pi\) | ||||
0.343881 | + | 0.939013i | \(0.388258\pi\) | |||||||
\(38\) | −3.89984 | −0.632637 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.09174 | 0.172620 | ||||||||
\(41\) | −1.09174 | −0.170502 | −0.0852509 | − | 0.996360i | \(-0.527169\pi\) | ||||
−0.0852509 | + | 0.996360i | \(0.527169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6246 | 1.62024 | 0.810119 | − | 0.586266i | \(-0.199403\pi\) | ||||
0.810119 | + | 0.586266i | \(0.199403\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.99158 | −1.03085 | ||||||||
\(47\) | −9.71635 | −1.41728 | −0.708638 | − | 0.705573i | \(-0.750690\pi\) | ||||
−0.708638 | + | 0.705573i | \(0.750690\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.80809 | −0.538546 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.80809 | 0.944113 | ||||||||
\(53\) | 3.81651 | 0.524238 | 0.262119 | − | 0.965036i | \(-0.415579\pi\) | ||||
0.262119 | + | 0.965036i | \(0.415579\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.09174 | 0.147211 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.80809 | 0.631334 | ||||||||
\(59\) | 11.7997 | 1.53619 | 0.768094 | − | 0.640338i | \(-0.221206\pi\) | ||||
0.768094 | + | 0.640338i | \(0.221206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1751 | 1.43082 | 0.715411 | − | 0.698704i | \(-0.246240\pi\) | ||||
0.715411 | + | 0.698704i | \(0.246240\pi\) | |||||||
\(62\) | −1.27523 | −0.161955 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.43270 | 0.921913 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.99158 | 1.09850 | 0.549248 | − | 0.835659i | \(-0.314914\pi\) | ||||
0.549248 | + | 0.835659i | \(0.314914\pi\) | |||||||
\(68\) | 1.09174 | 0.132393 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.09174 | 0.130488 | ||||||||
\(71\) | −9.17507 | −1.08888 | −0.544440 | − | 0.838800i | \(-0.683258\pi\) | ||||
−0.544440 | + | 0.838800i | \(0.683258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.09174 | −0.595944 | −0.297972 | − | 0.954575i | \(-0.596310\pi\) | ||||
−0.297972 | + | 0.954575i | \(0.596310\pi\) | |||||||
\(74\) | 4.18349 | 0.486321 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.89984 | −0.447342 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.99158 | −0.561597 | −0.280798 | − | 0.959767i | \(-0.590599\pi\) | ||||
−0.280798 | + | 0.959767i | \(0.590599\pi\) | |||||||
\(80\) | 1.09174 | 0.122061 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.09174 | −0.120563 | ||||||||
\(83\) | −7.09174 | −0.778420 | −0.389210 | − | 0.921149i | \(-0.627252\pi\) | ||||
−0.389210 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.19191 | 0.129280 | ||||||||
\(86\) | 10.6246 | 1.14568 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −12.9916 | −1.37711 | −0.688553 | − | 0.725186i | \(-0.741754\pi\) | ||||
−0.688553 | + | 0.725186i | \(0.741754\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.80809 | 0.713682 | ||||||||
\(92\) | −6.99158 | −0.728923 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.71635 | −1.00216 | ||||||||
\(95\) | −4.25763 | −0.436823 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.61619 | −0.773307 | −0.386653 | − | 0.922225i | \(-0.626369\pi\) | ||||
−0.386653 | + | 0.922225i | \(0.626369\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.80809 | −0.380809 | ||||||||
\(101\) | −15.6162 | −1.55387 | −0.776934 | − | 0.629582i | \(-0.783226\pi\) | ||||
−0.776934 | + | 0.629582i | \(0.783226\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.09174 | 0.304639 | 0.152319 | − | 0.988331i | \(-0.451326\pi\) | ||||
0.152319 | + | 0.988331i | \(0.451326\pi\) | |||||||
\(104\) | 6.80809 | 0.667589 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.81651 | 0.370692 | ||||||||
\(107\) | −2.18349 | −0.211086 | −0.105543 | − | 0.994415i | \(-0.533658\pi\) | ||||
−0.105543 | + | 0.994415i | \(0.533658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 1.09174 | 0.104094 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 3.17507 | 0.298686 | 0.149343 | − | 0.988785i | \(-0.452284\pi\) | ||||
0.149343 | + | 0.988785i | \(0.452284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.63302 | −0.711783 | ||||||||
\(116\) | 4.80809 | 0.446420 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7997 | 1.08625 | ||||||||
\(119\) | 1.09174 | 0.100080 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 11.1751 | 1.01174 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.27523 | −0.114519 | ||||||||
\(125\) | −9.61619 | −0.860098 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.99158 | −0.442931 | −0.221466 | − | 0.975168i | \(-0.571084\pi\) | ||||
−0.221466 | + | 0.975168i | \(0.571084\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.43270 | 0.651891 | ||||||||
\(131\) | −16.9083 | −1.47728 | −0.738641 | − | 0.674099i | \(-0.764532\pi\) | ||||
−0.738641 | + | 0.674099i | \(0.764532\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.89984 | −0.338159 | ||||||||
\(134\) | 8.99158 | 0.776754 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.09174 | 0.0936163 | ||||||||
\(137\) | 15.1751 | 1.29649 | 0.648247 | − | 0.761430i | \(-0.275502\pi\) | ||||
0.648247 | + | 0.761430i | \(0.275502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.26682 | −0.701182 | −0.350591 | − | 0.936529i | \(-0.614019\pi\) | ||||
−0.350591 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(140\) | 1.09174 | 0.0922692 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.17507 | −0.769955 | ||||||||
\(143\) | 6.80809 | 0.569321 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.24921 | 0.435923 | ||||||||
\(146\) | −5.09174 | −0.421396 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.18349 | 0.343881 | ||||||||
\(149\) | −15.6162 | −1.27933 | −0.639664 | − | 0.768655i | \(-0.720926\pi\) | ||||
−0.639664 | + | 0.768655i | \(0.720926\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.9832 | 1.78896 | 0.894482 | − | 0.447103i | \(-0.147544\pi\) | ||||
0.894482 | + | 0.447103i | \(0.147544\pi\) | |||||||
\(152\) | −3.89984 | −0.316319 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −1.39223 | −0.111827 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9083 | −1.18981 | −0.594904 | − | 0.803797i | \(-0.702810\pi\) | ||||
−0.594904 | + | 0.803797i | \(0.702810\pi\) | |||||||
\(158\) | −4.99158 | −0.397109 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.09174 | 0.0863100 | ||||||||
\(161\) | −6.99158 | −0.551014 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.98317 | 0.781942 | 0.390971 | − | 0.920403i | \(-0.372139\pi\) | ||||
0.390971 | + | 0.920403i | \(0.372139\pi\) | |||||||
\(164\) | −1.09174 | −0.0852509 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.09174 | −0.550426 | ||||||||
\(167\) | 7.43270 | 0.575160 | 0.287580 | − | 0.957757i | \(-0.407149\pi\) | ||||
0.287580 | + | 0.957757i | \(0.407149\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.3501 | 2.56540 | ||||||||
\(170\) | 1.19191 | 0.0914150 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.6246 | 0.810119 | ||||||||
\(173\) | 5.79968 | 0.440941 | 0.220471 | − | 0.975394i | \(-0.429241\pi\) | ||||
0.220471 | + | 0.975394i | \(0.429241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.80809 | −0.287865 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9916 | −0.973760 | ||||||||
\(179\) | 4.25763 | 0.318230 | 0.159115 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159115 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.09174 | −0.378466 | −0.189233 | − | 0.981932i | \(-0.560600\pi\) | ||||
−0.189233 | + | 0.981932i | \(0.560600\pi\) | |||||||
\(182\) | 6.80809 | 0.504650 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.99158 | −0.515426 | ||||||||
\(185\) | 4.56730 | 0.335795 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.09174 | 0.0798363 | ||||||||
\(188\) | −9.71635 | −0.708638 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.25763 | −0.308881 | ||||||||
\(191\) | −24.2408 | −1.75400 | −0.877001 | − | 0.480488i | \(-0.840459\pi\) | ||||
−0.877001 | + | 0.480488i | \(0.840459\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.63302 | −0.405474 | −0.202737 | − | 0.979233i | \(-0.564984\pi\) | ||||
−0.202737 | + | 0.979233i | \(0.564984\pi\) | |||||||
\(194\) | −7.61619 | −0.546810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −26.4243 | −1.88265 | −0.941326 | − | 0.337498i | \(-0.890419\pi\) | ||||
−0.941326 | + | 0.337498i | \(0.890419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0917 | −0.786273 | −0.393136 | − | 0.919480i | \(-0.628610\pi\) | ||||
−0.393136 | + | 0.919480i | \(0.628610\pi\) | |||||||
\(200\) | −3.80809 | −0.269273 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.6162 | −1.09875 | ||||||||
\(203\) | 4.80809 | 0.337462 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.19191 | −0.0832463 | ||||||||
\(206\) | 3.09174 | 0.215412 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.80809 | 0.472056 | ||||||||
\(209\) | −3.89984 | −0.269757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.6078 | −1.41870 | −0.709349 | − | 0.704858i | \(-0.751011\pi\) | ||||
−0.709349 | + | 0.704858i | \(0.751011\pi\) | |||||||
\(212\) | 3.81651 | 0.262119 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.18349 | −0.149260 | ||||||||
\(215\) | 11.5994 | 0.791069 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.27523 | −0.0865685 | ||||||||
\(218\) | 8.00000 | 0.541828 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.09174 | 0.0736054 | ||||||||
\(221\) | 7.43270 | 0.499977 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.64221 | −0.377830 | −0.188915 | − | 0.981993i | \(-0.560497\pi\) | ||||
−0.188915 | + | 0.981993i | \(0.560497\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.17507 | 0.211203 | ||||||||
\(227\) | −11.4587 | −0.760542 | −0.380271 | − | 0.924875i | \(-0.624169\pi\) | ||||
−0.380271 | + | 0.924875i | \(0.624169\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5244 | −0.827639 | −0.413819 | − | 0.910359i | \(-0.635805\pi\) | ||||
−0.413819 | + | 0.910359i | \(0.635805\pi\) | |||||||
\(230\) | −7.63302 | −0.503307 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.80809 | 0.315667 | ||||||||
\(233\) | 25.2324 | 1.65303 | 0.826514 | − | 0.562916i | \(-0.190321\pi\) | ||||
0.826514 | + | 0.562916i | \(0.190321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6078 | −0.691975 | ||||||||
\(236\) | 11.7997 | 0.768094 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09174 | 0.0707673 | ||||||||
\(239\) | −13.9832 | −0.904496 | −0.452248 | − | 0.891892i | \(-0.649378\pi\) | ||||
−0.452248 | + | 0.891892i | \(0.649378\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.27523 | −0.468639 | −0.234319 | − | 0.972160i | \(-0.575286\pi\) | ||||
−0.234319 | + | 0.972160i | \(0.575286\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.1751 | 0.715411 | ||||||||
\(245\) | 1.09174 | 0.0697490 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.5505 | −1.68937 | ||||||||
\(248\) | −1.27523 | −0.0809774 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.61619 | −0.608181 | ||||||||
\(251\) | 28.1667 | 1.77786 | 0.888932 | − | 0.458040i | \(-0.151448\pi\) | ||||
0.888932 | + | 0.458040i | \(0.151448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.99158 | −0.439557 | ||||||||
\(254\) | −4.99158 | −0.313200 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.62461 | 0.537988 | 0.268994 | − | 0.963142i | \(-0.413309\pi\) | ||||
0.268994 | + | 0.963142i | \(0.413309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.18349 | 0.259949 | ||||||||
\(260\) | 7.43270 | 0.460956 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.9083 | −1.04460 | ||||||||
\(263\) | −22.6078 | −1.39405 | −0.697027 | − | 0.717044i | \(-0.745494\pi\) | ||||
−0.697027 | + | 0.717044i | \(0.745494\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.16665 | 0.255956 | ||||||||
\(266\) | −3.89984 | −0.239114 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.99158 | 0.549248 | ||||||||
\(269\) | 22.9083 | 1.39674 | 0.698370 | − | 0.715736i | \(-0.253909\pi\) | ||||
0.698370 | + | 0.715736i | \(0.253909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8165 | −0.839293 | −0.419647 | − | 0.907688i | \(-0.637846\pi\) | ||||
−0.419647 | + | 0.907688i | \(0.637846\pi\) | |||||||
\(272\) | 1.09174 | 0.0661967 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.1751 | 0.916760 | ||||||||
\(275\) | −3.80809 | −0.229637 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.6162 | 1.05845 | 0.529227 | − | 0.848480i | \(-0.322482\pi\) | ||||
0.529227 | + | 0.848480i | \(0.322482\pi\) | |||||||
\(278\) | −8.26682 | −0.495811 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.09174 | 0.0652442 | ||||||||
\(281\) | −19.9832 | −1.19210 | −0.596048 | − | 0.802949i | \(-0.703263\pi\) | ||||
−0.596048 | + | 0.802949i | \(0.703263\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5329 | −1.39888 | −0.699442 | − | 0.714690i | \(-0.746568\pi\) | ||||
−0.699442 | + | 0.714690i | \(0.746568\pi\) | |||||||
\(284\) | −9.17507 | −0.544440 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.80809 | 0.402571 | ||||||||
\(287\) | −1.09174 | −0.0644436 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8081 | −0.929888 | ||||||||
\(290\) | 5.24921 | 0.308244 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.09174 | −0.297972 | ||||||||
\(293\) | 3.81651 | 0.222963 | 0.111481 | − | 0.993767i | \(-0.464440\pi\) | ||||
0.111481 | + | 0.993767i | \(0.464440\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8822 | 0.750033 | ||||||||
\(296\) | 4.18349 | 0.243160 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.6162 | −0.904621 | ||||||||
\(299\) | −47.5994 | −2.75274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.6246 | 0.612392 | ||||||||
\(302\) | 21.9832 | 1.26499 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.89984 | −0.223671 | ||||||||
\(305\) | 12.2003 | 0.698588 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.5160 | 1.68457 | 0.842284 | − | 0.539034i | \(-0.181210\pi\) | ||||
0.842284 | + | 0.539034i | \(0.181210\pi\) | |||||||
\(308\) | 1.00000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.39223 | −0.0790733 | ||||||||
\(311\) | −9.71635 | −0.550964 | −0.275482 | − | 0.961306i | \(-0.588837\pi\) | ||||
−0.275482 | + | 0.961306i | \(0.588837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.7997 | −1.23219 | −0.616095 | − | 0.787672i | \(-0.711286\pi\) | ||||
−0.616095 | + | 0.787672i | \(0.711286\pi\) | |||||||
\(314\) | −14.9083 | −0.841322 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.99158 | −0.280798 | ||||||||
\(317\) | 29.7997 | 1.67372 | 0.836858 | − | 0.547420i | \(-0.184390\pi\) | ||||
0.836858 | + | 0.547420i | \(0.184390\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.80809 | 0.269202 | ||||||||
\(320\) | 1.09174 | 0.0610304 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.99158 | −0.389626 | ||||||||
\(323\) | −4.25763 | −0.236901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.9259 | −1.43811 | ||||||||
\(326\) | 9.98317 | 0.552916 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.09174 | −0.0602815 | ||||||||
\(329\) | −9.71635 | −0.535680 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.6246 | −0.693911 | −0.346956 | − | 0.937882i | \(-0.612785\pi\) | ||||
−0.346956 | + | 0.937882i | \(0.612785\pi\) | |||||||
\(332\) | −7.09174 | −0.389210 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.43270 | 0.406699 | ||||||||
\(335\) | 9.81651 | 0.536333 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.56730 | −0.139850 | −0.0699249 | − | 0.997552i | \(-0.522276\pi\) | ||||
−0.0699249 | + | 0.997552i | \(0.522276\pi\) | |||||||
\(338\) | 33.3501 | 1.81401 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.19191 | 0.0646402 | ||||||||
\(341\) | −1.27523 | −0.0690578 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 10.6246 | 0.572840 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.79968 | 0.311793 | ||||||||
\(347\) | −2.18349 | −0.117216 | −0.0586079 | − | 0.998281i | \(-0.518666\pi\) | ||||
−0.0586079 | + | 0.998281i | \(0.518666\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00842 | 0.375152 | 0.187576 | − | 0.982250i | \(-0.439937\pi\) | ||||
0.187576 | + | 0.982250i | \(0.439937\pi\) | |||||||
\(350\) | −3.80809 | −0.203551 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 8.62461 | 0.459041 | 0.229521 | − | 0.973304i | \(-0.426284\pi\) | ||||
0.229521 | + | 0.973304i | \(0.426284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0168 | −0.531638 | ||||||||
\(356\) | −12.9916 | −0.688553 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.25763 | 0.225023 | ||||||||
\(359\) | 26.9747 | 1.42367 | 0.711836 | − | 0.702345i | \(-0.247864\pi\) | ||||
0.711836 | + | 0.702345i | \(0.247864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.79126 | −0.199540 | ||||||||
\(362\) | −5.09174 | −0.267616 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.80809 | 0.356841 | ||||||||
\(365\) | −5.55888 | −0.290965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.72477 | −0.351030 | −0.175515 | − | 0.984477i | \(-0.556159\pi\) | ||||
−0.175515 | + | 0.984477i | \(0.556159\pi\) | |||||||
\(368\) | −6.99158 | −0.364461 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.56730 | 0.237443 | ||||||||
\(371\) | 3.81651 | 0.198143 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.4411 | −0.540620 | −0.270310 | − | 0.962773i | \(-0.587126\pi\) | ||||
−0.270310 | + | 0.962773i | \(0.587126\pi\) | |||||||
\(374\) | 1.09174 | 0.0564528 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.71635 | −0.501082 | ||||||||
\(377\) | 32.7340 | 1.68588 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3501 | 0.737117 | 0.368559 | − | 0.929604i | \(-0.379851\pi\) | ||||
0.368559 | + | 0.929604i | \(0.379851\pi\) | |||||||
\(380\) | −4.25763 | −0.218412 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.2408 | −1.24027 | ||||||||
\(383\) | 9.91667 | 0.506718 | 0.253359 | − | 0.967372i | \(-0.418465\pi\) | ||||
0.253359 | + | 0.967372i | \(0.418465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.09174 | 0.0556405 | ||||||||
\(386\) | −5.63302 | −0.286713 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.61619 | −0.386653 | ||||||||
\(389\) | 33.9663 | 1.72216 | 0.861081 | − | 0.508468i | \(-0.169788\pi\) | ||||
0.861081 | + | 0.508468i | \(0.169788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.63302 | −0.386019 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −26.4243 | −1.33124 | ||||||||
\(395\) | −5.44953 | −0.274196 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7079 | −1.34043 | −0.670216 | − | 0.742166i | \(-0.733799\pi\) | ||||
−0.670216 | + | 0.742166i | \(0.733799\pi\) | |||||||
\(398\) | −11.0917 | −0.555979 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.80809 | −0.190405 | ||||||||
\(401\) | 15.1751 | 0.757807 | 0.378903 | − | 0.925436i | \(-0.376301\pi\) | ||||
0.378903 | + | 0.925436i | \(0.376301\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.68191 | −0.432477 | ||||||||
\(404\) | −15.6162 | −0.776934 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.80809 | 0.238622 | ||||||||
\(407\) | 4.18349 | 0.207368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.7248 | −0.629199 | −0.314600 | − | 0.949224i | \(-0.601870\pi\) | ||||
−0.314600 | + | 0.949224i | \(0.601870\pi\) | |||||||
\(410\) | −1.19191 | −0.0588640 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.09174 | 0.152319 | ||||||||
\(413\) | 11.7997 | 0.580624 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.74237 | −0.380058 | ||||||||
\(416\) | 6.80809 | 0.333794 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.89984 | −0.190747 | ||||||||
\(419\) | −31.2324 | −1.52580 | −0.762901 | − | 0.646516i | \(-0.776225\pi\) | ||||
−0.762901 | + | 0.646516i | \(0.776225\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3670 | 0.895152 | 0.447576 | − | 0.894246i | \(-0.352287\pi\) | ||||
0.447576 | + | 0.894246i | \(0.352287\pi\) | |||||||
\(422\) | −20.6078 | −1.00317 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.81651 | 0.185346 | ||||||||
\(425\) | −4.15747 | −0.201667 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.1751 | 0.540800 | ||||||||
\(428\) | −2.18349 | −0.105543 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.5994 | 0.559371 | ||||||||
\(431\) | 3.37539 | 0.162587 | 0.0812935 | − | 0.996690i | \(-0.474095\pi\) | ||||
0.0812935 | + | 0.996690i | \(0.474095\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.26604 | 0.253070 | 0.126535 | − | 0.991962i | \(-0.459614\pi\) | ||||
0.126535 | + | 0.991962i | \(0.459614\pi\) | |||||||
\(434\) | −1.27523 | −0.0612132 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 27.2660 | 1.30431 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.79968 | −0.181349 | −0.0906743 | − | 0.995881i | \(-0.528902\pi\) | ||||
−0.0906743 | + | 0.995881i | \(0.528902\pi\) | |||||||
\(440\) | 1.09174 | 0.0520469 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.43270 | 0.353537 | ||||||||
\(443\) | −20.6246 | −0.979905 | −0.489952 | − | 0.871749i | \(-0.662986\pi\) | ||||
−0.489952 | + | 0.871749i | \(0.662986\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.1835 | −0.672362 | ||||||||
\(446\) | −5.64221 | −0.267166 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 27.1751 | 1.28247 | 0.641235 | − | 0.767344i | \(-0.278422\pi\) | ||||
0.641235 | + | 0.767344i | \(0.278422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.09174 | −0.0514082 | ||||||||
\(452\) | 3.17507 | 0.149343 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.4587 | −0.537784 | ||||||||
\(455\) | 7.43270 | 0.348450 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.2492 | −0.713328 | −0.356664 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356664 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(458\) | −12.5244 | −0.585229 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.63302 | −0.355891 | ||||||||
\(461\) | 13.2324 | 0.616293 | 0.308147 | − | 0.951339i | \(-0.400291\pi\) | ||||
0.308147 | + | 0.951339i | \(0.400291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.63302 | 0.168841 | 0.0844204 | − | 0.996430i | \(-0.473096\pi\) | ||||
0.0844204 | + | 0.996430i | \(0.473096\pi\) | |||||||
\(464\) | 4.80809 | 0.223210 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.2324 | 1.16887 | ||||||||
\(467\) | −13.9832 | −0.647064 | −0.323532 | − | 0.946217i | \(-0.604870\pi\) | ||||
−0.323532 | + | 0.946217i | \(0.604870\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.99158 | 0.415193 | ||||||||
\(470\) | −10.6078 | −0.489300 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.7997 | 0.543124 | ||||||||
\(473\) | 10.6246 | 0.488520 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.8510 | 0.681408 | ||||||||
\(476\) | 1.09174 | 0.0500400 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.9832 | −0.639575 | ||||||||
\(479\) | −16.3670 | −0.747826 | −0.373913 | − | 0.927464i | \(-0.621984\pi\) | ||||
−0.373913 | + | 0.927464i | \(0.621984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.4816 | 1.29865 | ||||||||
\(482\) | −7.27523 | −0.331378 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −8.31493 | −0.377562 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.1667 | 1.09510 | 0.547548 | − | 0.836774i | \(-0.315561\pi\) | ||||
0.547548 | + | 0.836774i | \(0.315561\pi\) | |||||||
\(488\) | 11.1751 | 0.505872 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.09174 | 0.0493200 | ||||||||
\(491\) | −7.63302 | −0.344473 | −0.172237 | − | 0.985056i | \(-0.555099\pi\) | ||||
−0.172237 | + | 0.985056i | \(0.555099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.24921 | 0.236413 | ||||||||
\(494\) | −26.5505 | −1.19456 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.27523 | −0.0572597 | ||||||||
\(497\) | −9.17507 | −0.411558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.2576 | 0.548727 | 0.274363 | − | 0.961626i | \(-0.411533\pi\) | ||||
0.274363 | + | 0.961626i | \(0.411533\pi\) | |||||||
\(500\) | −9.61619 | −0.430049 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.1667 | 1.25714 | ||||||||
\(503\) | 31.4327 | 1.40151 | 0.700757 | − | 0.713400i | \(-0.252846\pi\) | ||||
0.700757 | + | 0.713400i | \(0.252846\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0489 | −0.758666 | ||||||||
\(506\) | −6.99158 | −0.310814 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.99158 | −0.221466 | ||||||||
\(509\) | 37.7737 | 1.67429 | 0.837144 | − | 0.546983i | \(-0.184224\pi\) | ||||
0.837144 | + | 0.546983i | \(0.184224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.09174 | −0.225246 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.62461 | 0.380415 | ||||||||
\(515\) | 3.37539 | 0.148738 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.71635 | −0.427325 | ||||||||
\(518\) | 4.18349 | 0.183812 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.43270 | 0.325945 | ||||||||
\(521\) | 4.25763 | 0.186530 | 0.0932650 | − | 0.995641i | \(-0.470270\pi\) | ||||
0.0932650 | + | 0.995641i | \(0.470270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.83412 | 0.211381 | 0.105691 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105691 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(524\) | −16.9083 | −0.738641 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.6078 | −0.985746 | ||||||||
\(527\) | −1.39223 | −0.0606465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.8822 | 1.12531 | ||||||||
\(530\) | 4.16665 | 0.180988 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.89984 | −0.169079 | ||||||||
\(533\) | −7.43270 | −0.321946 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.38381 | −0.103061 | ||||||||
\(536\) | 8.99158 | 0.388377 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.9083 | 0.987645 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.0573 | −0.862331 | −0.431165 | − | 0.902273i | \(-0.641897\pi\) | ||||
−0.431165 | + | 0.902273i | \(0.641897\pi\) | |||||||
\(542\) | −13.8165 | −0.593470 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.09174 | 0.0468082 | ||||||||
\(545\) | 8.73396 | 0.374122 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9090 | 1.10779 | 0.553895 | − | 0.832587i | \(-0.313141\pi\) | ||||
0.553895 | + | 0.832587i | \(0.313141\pi\) | |||||||
\(548\) | 15.1751 | 0.648247 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.80809 | −0.162378 | ||||||||
\(551\) | −18.7508 | −0.798811 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.99158 | −0.212264 | ||||||||
\(554\) | 17.6162 | 0.748440 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.26682 | −0.350591 | ||||||||
\(557\) | −1.54205 | −0.0653387 | −0.0326694 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326694 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 72.3333 | 3.05937 | ||||||||
\(560\) | 1.09174 | 0.0461346 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.9832 | −0.842939 | ||||||||
\(563\) | −31.0917 | −1.31036 | −0.655180 | − | 0.755472i | \(-0.727407\pi\) | ||||
−0.655180 | + | 0.755472i | \(0.727407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.46637 | 0.145831 | ||||||||
\(566\) | −23.5329 | −0.989160 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.17507 | −0.384977 | ||||||||
\(569\) | 16.0168 | 0.671461 | 0.335730 | − | 0.941958i | \(-0.391017\pi\) | ||||
0.335730 | + | 0.941958i | \(0.391017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8081 | 0.536002 | 0.268001 | − | 0.963419i | \(-0.413637\pi\) | ||||
0.268001 | + | 0.963419i | \(0.413637\pi\) | |||||||
\(572\) | 6.80809 | 0.284661 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.09174 | −0.0455685 | ||||||||
\(575\) | 26.6246 | 1.11032 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7997 | −0.907532 | −0.453766 | − | 0.891121i | \(-0.649920\pi\) | ||||
−0.453766 | + | 0.891121i | \(0.649920\pi\) | |||||||
\(578\) | −15.8081 | −0.657530 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.24921 | 0.217962 | ||||||||
\(581\) | −7.09174 | −0.294215 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.81651 | 0.158064 | ||||||||
\(584\) | −5.09174 | −0.210698 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.81651 | 0.157659 | ||||||||
\(587\) | 9.81651 | 0.405171 | 0.202585 | − | 0.979265i | \(-0.435066\pi\) | ||||
0.202585 | + | 0.979265i | \(0.435066\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.97320 | 0.204917 | ||||||||
\(590\) | 12.8822 | 0.530353 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.18349 | 0.171940 | ||||||||
\(593\) | −9.82570 | −0.403493 | −0.201747 | − | 0.979438i | \(-0.564662\pi\) | ||||
−0.201747 | + | 0.979438i | \(0.564662\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.19191 | 0.0488634 | ||||||||
\(596\) | −15.6162 | −0.639664 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −47.5994 | −1.94648 | ||||||||
\(599\) | 2.82493 | 0.115423 | 0.0577117 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577117 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.2416 | 1.60070 | 0.800348 | − | 0.599535i | \(-0.204648\pi\) | ||||
0.800348 | + | 0.599535i | \(0.204648\pi\) | |||||||
\(602\) | 10.6246 | 0.433027 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.9832 | 0.894482 | ||||||||
\(605\) | 1.09174 | 0.0443857 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.8822 | −0.685229 | −0.342614 | − | 0.939476i | \(-0.611312\pi\) | ||||
−0.342614 | + | 0.939476i | \(0.611312\pi\) | |||||||
\(608\) | −3.89984 | −0.158159 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.2003 | 0.493977 | ||||||||
\(611\) | −66.1498 | −2.67614 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.7913 | 1.80910 | 0.904551 | − | 0.426365i | \(-0.140206\pi\) | ||||
0.904551 | + | 0.426365i | \(0.140206\pi\) | |||||||
\(614\) | 29.5160 | 1.19117 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −37.9832 | −1.52914 | −0.764572 | − | 0.644538i | \(-0.777050\pi\) | ||||
−0.764572 | + | 0.644538i | \(0.777050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.98317 | 0.401257 | 0.200629 | − | 0.979667i | \(-0.435702\pi\) | ||||
0.200629 | + | 0.979667i | \(0.435702\pi\) | |||||||
\(620\) | −1.39223 | −0.0559133 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.71635 | −0.389590 | ||||||||
\(623\) | −12.9916 | −0.520497 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.54205 | 0.341682 | ||||||||
\(626\) | −21.7997 | −0.871290 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.9083 | −0.594904 | ||||||||
\(629\) | 4.56730 | 0.182110 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.41586 | −0.0563647 | −0.0281823 | − | 0.999603i | \(-0.508972\pi\) | ||||
−0.0281823 | + | 0.999603i | \(0.508972\pi\) | |||||||
\(632\) | −4.99158 | −0.198555 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.7997 | 1.18350 | ||||||||
\(635\) | −5.44953 | −0.216258 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.80809 | 0.269747 | ||||||||
\(638\) | 4.80809 | 0.190354 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.09174 | 0.0431550 | ||||||||
\(641\) | −33.2155 | −1.31194 | −0.655968 | − | 0.754789i | \(-0.727739\pi\) | ||||
−0.655968 | + | 0.754789i | \(0.727739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.7997 | −1.09631 | −0.548156 | − | 0.836376i | \(-0.684670\pi\) | ||||
−0.548156 | + | 0.836376i | \(0.684670\pi\) | |||||||
\(644\) | −6.99158 | −0.275507 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.25763 | −0.167514 | ||||||||
\(647\) | 14.2837 | 0.561548 | 0.280774 | − | 0.959774i | \(-0.409409\pi\) | ||||
0.280774 | + | 0.959774i | \(0.409409\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.7997 | 0.463178 | ||||||||
\(650\) | −25.9259 | −1.01690 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.98317 | 0.390971 | ||||||||
\(653\) | −37.2324 | −1.45702 | −0.728508 | − | 0.685038i | \(-0.759786\pi\) | ||||
−0.728508 | + | 0.685038i | \(0.759786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.4595 | −0.721272 | ||||||||
\(656\) | −1.09174 | −0.0426255 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −9.71635 | −0.378783 | ||||||||
\(659\) | 23.3990 | 0.911497 | 0.455748 | − | 0.890109i | \(-0.349372\pi\) | ||||
0.455748 | + | 0.890109i | \(0.349372\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.1238 | −1.40505 | −0.702526 | − | 0.711658i | \(-0.747945\pi\) | ||||
−0.702526 | + | 0.711658i | \(0.747945\pi\) | |||||||
\(662\) | −12.6246 | −0.490669 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.09174 | −0.275213 | ||||||||
\(665\) | −4.25763 | −0.165104 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.6162 | −1.30162 | ||||||||
\(668\) | 7.43270 | 0.287580 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 9.81651 | 0.379245 | ||||||||
\(671\) | 11.1751 | 0.431409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.1667 | 1.16284 | 0.581420 | − | 0.813604i | \(-0.302498\pi\) | ||||
0.581420 | + | 0.813604i | \(0.302498\pi\) | |||||||
\(674\) | −2.56730 | −0.0988887 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.3501 | 1.28270 | ||||||||
\(677\) | 2.93428 | 0.112773 | 0.0563867 | − | 0.998409i | \(-0.482042\pi\) | ||||
0.0563867 | + | 0.998409i | \(0.482042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.61619 | −0.292282 | ||||||||
\(680\) | 1.19191 | 0.0457075 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.27523 | −0.0488312 | ||||||||
\(683\) | −17.3586 | −0.664207 | −0.332103 | − | 0.943243i | \(-0.607758\pi\) | ||||
−0.332103 | + | 0.943243i | \(0.607758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5673 | 0.633004 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10.6246 | 0.405059 | ||||||||
\(689\) | 25.9832 | 0.989880 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 50.1498 | 1.90779 | 0.953895 | − | 0.300142i | \(-0.0970341\pi\) | ||||
0.953895 | + | 0.300142i | \(0.0970341\pi\) | |||||||
\(692\) | 5.79968 | 0.220471 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.18349 | −0.0828841 | ||||||||
\(695\) | −9.02525 | −0.342347 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.19191 | −0.0451467 | ||||||||
\(698\) | 7.00842 | 0.265272 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.80809 | −0.143932 | ||||||||
\(701\) | 43.5825 | 1.64609 | 0.823045 | − | 0.567977i | \(-0.192274\pi\) | ||||
0.823045 | + | 0.567977i | \(0.192274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3149 | −0.615329 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.62461 | 0.324591 | ||||||||
\(707\) | −15.6162 | −0.587307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7660 | 1.56856 | 0.784278 | − | 0.620410i | \(-0.213034\pi\) | ||||
0.784278 | + | 0.620410i | \(0.213034\pi\) | |||||||
\(710\) | −10.0168 | −0.375925 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.9916 | −0.486880 | ||||||||
\(713\) | 8.91590 | 0.333903 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.43270 | 0.277967 | ||||||||
\(716\) | 4.25763 | 0.159115 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.9747 | 1.00669 | ||||||||
\(719\) | 28.2668 | 1.05417 | 0.527087 | − | 0.849811i | \(-0.323284\pi\) | ||||
0.527087 | + | 0.849811i | \(0.323284\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.09174 | 0.115143 | ||||||||
\(722\) | −3.79126 | −0.141096 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.09174 | −0.189233 | ||||||||
\(725\) | −18.3097 | −0.680004 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.2416 | −1.08451 | −0.542255 | − | 0.840214i | \(-0.682429\pi\) | ||||
−0.542255 | + | 0.840214i | \(0.682429\pi\) | |||||||
\(728\) | 6.80809 | 0.252325 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.55888 | −0.205744 | ||||||||
\(731\) | 11.5994 | 0.429018 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.4243 | −1.34536 | −0.672681 | − | 0.739933i | \(-0.734857\pi\) | ||||
−0.672681 | + | 0.739933i | \(0.734857\pi\) | |||||||
\(734\) | −6.72477 | −0.248216 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.99158 | −0.257713 | ||||||||
\(737\) | 8.99158 | 0.331209 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.4243 | 1.70774 | 0.853872 | − | 0.520482i | \(-0.174248\pi\) | ||||
0.853872 | + | 0.520482i | \(0.174248\pi\) | |||||||
\(740\) | 4.56730 | 0.167897 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.81651 | 0.140109 | ||||||||
\(743\) | 4.36698 | 0.160209 | 0.0801044 | − | 0.996786i | \(-0.474475\pi\) | ||||
0.0801044 | + | 0.996786i | \(0.474475\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.0489 | −0.624623 | ||||||||
\(746\) | −10.4411 | −0.382276 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.09174 | 0.0399181 | ||||||||
\(749\) | −2.18349 | −0.0797830 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.1498 | −1.24614 | −0.623072 | − | 0.782164i | \(-0.714116\pi\) | ||||
−0.623072 | + | 0.782164i | \(0.714116\pi\) | |||||||
\(752\) | −9.71635 | −0.354319 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.7340 | 1.19210 | ||||||||
\(755\) | 24.0000 | 0.873449 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.93428 | −0.252031 | −0.126015 | − | 0.992028i | \(-0.540219\pi\) | ||||
−0.126015 | + | 0.992028i | \(0.540219\pi\) | |||||||
\(758\) | 14.3501 | 0.521221 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.25763 | −0.154440 | ||||||||
\(761\) | −40.1575 | −1.45571 | −0.727853 | − | 0.685733i | \(-0.759482\pi\) | ||||
−0.727853 | + | 0.685733i | \(0.759482\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | −24.2408 | −0.877001 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.91667 | 0.358304 | ||||||||
\(767\) | 80.3333 | 2.90067 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.1406 | −0.365681 | −0.182840 | − | 0.983143i | \(-0.558529\pi\) | ||||
−0.182840 | + | 0.983143i | \(0.558529\pi\) | |||||||
\(770\) | 1.09174 | 0.0393437 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.63302 | −0.202737 | ||||||||
\(773\) | −2.17430 | −0.0782041 | −0.0391021 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391021 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.85621 | 0.174440 | ||||||||
\(776\) | −7.61619 | −0.273405 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.9663 | 1.21775 | ||||||||
\(779\) | 4.25763 | 0.152545 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.17507 | −0.328310 | ||||||||
\(782\) | −7.63302 | −0.272956 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −16.2760 | −0.580916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.66746 | −0.308962 | −0.154481 | − | 0.987996i | \(-0.549370\pi\) | ||||
−0.154481 | + | 0.987996i | \(0.549370\pi\) | |||||||
\(788\) | −26.4243 | −0.941326 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.44953 | −0.193886 | ||||||||
\(791\) | 3.17507 | 0.112893 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 76.0809 | 2.70171 | ||||||||
\(794\) | −26.7079 | −0.947829 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.0917 | −0.393136 | ||||||||
\(797\) | 3.47556 | 0.123111 | 0.0615553 | − | 0.998104i | \(-0.480394\pi\) | ||||
0.0615553 | + | 0.998104i | \(0.480394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6078 | −0.375276 | ||||||||
\(800\) | −3.80809 | −0.134636 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.1751 | 0.535850 | ||||||||
\(803\) | −5.09174 | −0.179684 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.63302 | −0.269029 | ||||||||
\(806\) | −8.68191 | −0.305807 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.6162 | −0.549376 | ||||||||
\(809\) | 10.1667 | 0.357441 | 0.178720 | − | 0.983900i | \(-0.442804\pi\) | ||||
0.178720 | + | 0.983900i | \(0.442804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.8493 | −1.60999 | −0.804994 | − | 0.593283i | \(-0.797832\pi\) | ||||
−0.804994 | + | 0.593283i | \(0.797832\pi\) | |||||||
\(812\) | 4.80809 | 0.168731 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.18349 | 0.146631 | ||||||||
\(815\) | 10.8991 | 0.381778 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.4342 | −1.44960 | ||||||||
\(818\) | −12.7248 | −0.444911 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.19191 | −0.0416232 | ||||||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.41586 | −0.0493539 | −0.0246770 | − | 0.999695i | \(-0.507856\pi\) | ||||
−0.0246770 | + | 0.999695i | \(0.507856\pi\) | |||||||
\(824\) | 3.09174 | 0.107706 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7997 | 0.410563 | ||||||||
\(827\) | −16.3670 | −0.569136 | −0.284568 | − | 0.958656i | \(-0.591850\pi\) | ||||
−0.284568 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.1238 | 1.81033 | 0.905167 | − | 0.425056i | \(-0.139746\pi\) | ||||
0.905167 | + | 0.425056i | \(0.139746\pi\) | |||||||
\(830\) | −7.74237 | −0.268742 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.80809 | 0.236028 | ||||||||
\(833\) | 1.09174 | 0.0378267 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.11461 | 0.280818 | ||||||||
\(836\) | −3.89984 | −0.134879 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −31.2324 | −1.07890 | ||||||||
\(839\) | 28.2668 | 0.975879 | 0.487939 | − | 0.872877i | \(-0.337749\pi\) | ||||
0.487939 | + | 0.872877i | \(0.337749\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.88223 | −0.202836 | ||||||||
\(842\) | 18.3670 | 0.632968 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.6078 | −0.709349 | ||||||||
\(845\) | 36.4098 | 1.25254 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 3.81651 | 0.131060 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.15747 | −0.142600 | ||||||||
\(851\) | −29.2492 | −1.00265 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5252 | 0.600052 | 0.300026 | − | 0.953931i | \(-0.403005\pi\) | ||||
0.300026 | + | 0.953931i | \(0.403005\pi\) | |||||||
\(854\) | 11.1751 | 0.382403 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.18349 | −0.0746301 | ||||||||
\(857\) | −3.95714 | −0.135173 | −0.0675867 | − | 0.997713i | \(-0.521530\pi\) | ||||
−0.0675867 | + | 0.997713i | \(0.521530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.4159 | 1.82253 | 0.911263 | − | 0.411825i | \(-0.135109\pi\) | ||||
0.911263 | + | 0.411825i | \(0.135109\pi\) | |||||||
\(860\) | 11.5994 | 0.395535 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.37539 | 0.114966 | ||||||||
\(863\) | −6.10935 | −0.207965 | −0.103982 | − | 0.994579i | \(-0.533159\pi\) | ||||
−0.103982 | + | 0.994579i | \(0.533159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.33177 | 0.215286 | ||||||||
\(866\) | 5.26604 | 0.178947 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.27523 | −0.0432842 | ||||||||
\(869\) | −4.99158 | −0.169328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.2155 | 2.07421 | ||||||||
\(872\) | 8.00000 | 0.270914 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 27.2660 | 0.922288 | ||||||||
\(875\) | −9.61619 | −0.325086 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.366978 | 0.0123920 | 0.00619598 | − | 0.999981i | \(-0.498028\pi\) | ||||
0.00619598 | + | 0.999981i | \(0.498028\pi\) | |||||||
\(878\) | −3.79968 | −0.128233 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.09174 | 0.0368027 | ||||||||
\(881\) | 36.3906 | 1.22603 | 0.613015 | − | 0.790071i | \(-0.289956\pi\) | ||||
0.613015 | + | 0.790071i | \(0.289956\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0841 | 0.776842 | 0.388421 | − | 0.921482i | \(-0.373021\pi\) | ||||
0.388421 | + | 0.921482i | \(0.373021\pi\) | |||||||
\(884\) | 7.43270 | 0.249989 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.6246 | −0.692897 | ||||||||
\(887\) | 29.2492 | 0.982092 | 0.491046 | − | 0.871134i | \(-0.336615\pi\) | ||||
0.491046 | + | 0.871134i | \(0.336615\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.99158 | −0.167412 | ||||||||
\(890\) | −14.1835 | −0.475432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.64221 | −0.188915 | ||||||||
\(893\) | 37.8922 | 1.26801 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.64824 | 0.155374 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.1751 | 0.906844 | ||||||||
\(899\) | −6.13144 | −0.204495 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.16665 | 0.138811 | ||||||||
\(902\) | −1.09174 | −0.0363511 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.17507 | 0.105601 | ||||||||
\(905\) | −5.55888 | −0.184784 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.6246 | −0.817647 | −0.408823 | − | 0.912614i | \(-0.634061\pi\) | ||||
−0.408823 | + | 0.912614i | \(0.634061\pi\) | |||||||
\(908\) | −11.4587 | −0.380271 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.43270 | 0.246392 | ||||||||
\(911\) | 17.8906 | 0.592744 | 0.296372 | − | 0.955073i | \(-0.404223\pi\) | ||||
0.296372 | + | 0.955073i | \(0.404223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.09174 | −0.234702 | ||||||||
\(914\) | −15.2492 | −0.504399 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.5244 | −0.413819 | ||||||||
\(917\) | −16.9083 | −0.558360 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.61619 | −0.0533131 | −0.0266566 | − | 0.999645i | \(-0.508486\pi\) | ||||
−0.0266566 | + | 0.999645i | \(0.508486\pi\) | |||||||
\(920\) | −7.63302 | −0.251653 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.2324 | 0.435785 | ||||||||
\(923\) | −62.4648 | −2.05605 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.9311 | −0.523812 | ||||||||
\(926\) | 3.63302 | 0.119389 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.80809 | 0.157833 | ||||||||
\(929\) | 38.9747 | 1.27872 | 0.639360 | − | 0.768908i | \(-0.279199\pi\) | ||||
0.639360 | + | 0.768908i | \(0.279199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.89984 | −0.127812 | ||||||||
\(932\) | 25.2324 | 0.826514 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.9832 | −0.457543 | ||||||||
\(935\) | 1.19191 | 0.0389795 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.92509 | 0.160896 | 0.0804478 | − | 0.996759i | \(-0.474365\pi\) | ||||
0.0804478 | + | 0.996759i | \(0.474365\pi\) | |||||||
\(938\) | 8.99158 | 0.293586 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.6078 | −0.345987 | ||||||||
\(941\) | 45.7660 | 1.49193 | 0.745965 | − | 0.665986i | \(-0.231989\pi\) | ||||
0.745965 | + | 0.665986i | \(0.231989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.63302 | 0.248565 | ||||||||
\(944\) | 11.7997 | 0.384047 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.6246 | 0.345436 | ||||||||
\(947\) | 25.5825 | 0.831320 | 0.415660 | − | 0.909520i | \(-0.363551\pi\) | ||||
0.415660 | + | 0.909520i | \(0.363551\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.6651 | −1.12528 | ||||||||
\(950\) | 14.8510 | 0.481828 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.09174 | 0.0353836 | ||||||||
\(953\) | 32.1835 | 1.04253 | 0.521263 | − | 0.853396i | \(-0.325461\pi\) | ||||
0.521263 | + | 0.853396i | \(0.325461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26.4648 | −0.856379 | ||||||||
\(956\) | −13.9832 | −0.452248 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.3670 | −0.528793 | ||||||||
\(959\) | 15.1751 | 0.490029 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3738 | −0.947541 | ||||||||
\(962\) | 28.4816 | 0.918283 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.27523 | −0.234319 | ||||||||
\(965\) | −6.14982 | −0.197970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.35014 | 0.0755755 | 0.0377878 | − | 0.999286i | \(-0.487969\pi\) | ||||
0.0377878 | + | 0.999286i | \(0.487969\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.31493 | −0.266976 | ||||||||
\(971\) | −1.98317 | −0.0636428 | −0.0318214 | − | 0.999494i | \(-0.510131\pi\) | ||||
−0.0318214 | + | 0.999494i | \(0.510131\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.26682 | −0.265022 | ||||||||
\(974\) | 24.1667 | 0.774350 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.1751 | 0.357705 | ||||||||
\(977\) | 1.98317 | 0.0634471 | 0.0317235 | − | 0.999497i | \(-0.489900\pi\) | ||||
0.0317235 | + | 0.999497i | \(0.489900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.9916 | −0.415213 | ||||||||
\(980\) | 1.09174 | 0.0348745 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.63302 | −0.243580 | ||||||||
\(983\) | −48.5817 | −1.54952 | −0.774759 | − | 0.632257i | \(-0.782129\pi\) | ||||
−0.774759 | + | 0.632257i | \(0.782129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.8486 | −0.919192 | ||||||||
\(986\) | 5.24921 | 0.167169 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −26.5505 | −0.844683 | ||||||||
\(989\) | −74.2828 | −2.36206 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.3501 | 0.455847 | 0.227924 | − | 0.973679i | \(-0.426806\pi\) | ||||
0.227924 | + | 0.973679i | \(0.426806\pi\) | |||||||
\(992\) | −1.27523 | −0.0404887 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.17507 | −0.291016 | ||||||||
\(995\) | −12.1094 | −0.383892 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.6246 | −1.15991 | −0.579956 | − | 0.814647i | \(-0.696930\pi\) | ||||
−0.579956 | + | 0.814647i | \(0.696930\pi\) | |||||||
\(998\) | 12.2576 | 0.388008 | ||||||||
\(999\) | 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 | 1386.2.a.r.1.2 | yes | 3 | |
3.2 | odd | 2 | 1386.2.a.q.1.2 | ✓ | 3 | ||
7.6 | odd | 2 | 9702.2.a.dy.1.2 | 3 | |||
21.20 | even | 2 | 9702.2.a.dx.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.a.q.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1386.2.a.r.1.2 | yes | 3 | 1.1 | even | 1 | trivial | |
9702.2.a.dx.1.2 | 3 | 21.20 | even | 2 | |||
9702.2.a.dy.1.2 | 3 | 7.6 | odd | 2 |