Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.0368230 | −0.0212598 | −0.0106299 | − | 0.999944i | \(-0.503384\pi\) | ||||
−0.0106299 | + | 0.999944i | \(0.503384\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.59158 | −1.60620 | −0.803102 | − | 0.595842i | \(-0.796819\pi\) | ||||
−0.803102 | + | 0.595842i | \(0.796819\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.547211 | −0.206826 | −0.103413 | − | 0.994638i | \(-0.532976\pi\) | ||||
−0.103413 | + | 0.994638i | \(0.532976\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99864 | −0.999548 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30756 | 0.394243 | 0.197122 | − | 0.980379i | \(-0.436841\pi\) | ||||
0.197122 | + | 0.980379i | \(0.436841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.987833 | 0.273976 | 0.136988 | − | 0.990573i | \(-0.456258\pi\) | ||||
0.136988 | + | 0.990573i | \(0.456258\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.132253 | 0.0341476 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.11658 | 0.270809 | 0.135405 | − | 0.990790i | \(-0.456767\pi\) | ||||
0.135405 | + | 0.990790i | \(0.456767\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.02241 | 1.15222 | 0.576110 | − | 0.817373i | \(-0.304570\pi\) | ||||
0.576110 | + | 0.817373i | \(0.304570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0201500 | 0.00439708 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.20016 | −0.458765 | −0.229383 | − | 0.973336i | \(-0.573671\pi\) | ||||
−0.229383 | + | 0.973336i | \(0.573671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.89946 | 1.57989 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.220888 | 0.0425100 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0479181 | 0.00889817 | 0.00444909 | − | 0.999990i | \(-0.498584\pi\) | ||||
0.00444909 | + | 0.999990i | \(0.498584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.20026 | 0.574784 | 0.287392 | − | 0.957813i | \(-0.407212\pi\) | ||||
0.287392 | + | 0.957813i | \(0.407212\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0481482 | −0.00838153 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.96535 | 0.332205 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.60748 | −1.08626 | −0.543131 | − | 0.839648i | \(-0.682761\pi\) | ||||
−0.543131 | + | 0.839648i | \(0.682761\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0363750 | −0.00582467 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.410505 | −0.0641101 | −0.0320551 | − | 0.999486i | \(-0.510205\pi\) | ||||
−0.0320551 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.81229 | −1.19136 | −0.595682 | − | 0.803221i | \(-0.703118\pi\) | ||||
−0.595682 | + | 0.803221i | \(0.703118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.7699 | 1.60548 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.58834 | 1.39860 | 0.699302 | − | 0.714827i | \(-0.253494\pi\) | ||||
0.699302 | + | 0.714827i | \(0.253494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.70056 | −0.957223 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0411157 | −0.00575735 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.16958 | −0.160655 | −0.0803274 | − | 0.996769i | \(-0.525597\pi\) | ||||
−0.0803274 | + | 0.996769i | \(0.525597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.69620 | −0.633235 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.184940 | −0.0244959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.75541 | 1.00967 | 0.504834 | − | 0.863216i | \(-0.331554\pi\) | ||||
0.504834 | + | 0.863216i | \(0.331554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.47931 | 1.08566 | 0.542832 | − | 0.839841i | \(-0.317352\pi\) | ||||
0.542832 | + | 0.839841i | \(0.317352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.64089 | 0.206733 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.54788 | −0.440061 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.28110 | 0.645189 | 0.322594 | − | 0.946537i | \(-0.395445\pi\) | ||||
0.322594 | + | 0.946537i | \(0.395445\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0810166 | 0.00975325 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7035 | 1.74498 | 0.872491 | − | 0.488631i | \(-0.162504\pi\) | ||||
0.872491 | + | 0.488631i | \(0.162504\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4830 | −1.22694 | −0.613469 | − | 0.789719i | \(-0.710227\pi\) | ||||
−0.613469 | + | 0.789719i | \(0.710227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.290882 | −0.0335882 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.715509 | −0.0815399 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.56063 | 0.625620 | 0.312810 | − | 0.949816i | \(-0.398730\pi\) | ||||
0.312810 | + | 0.949816i | \(0.398730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.98780 | 0.998644 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.439874 | −0.0482824 | −0.0241412 | − | 0.999709i | \(-0.507685\pi\) | ||||
−0.0241412 | + | 0.999709i | \(0.507685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.01027 | −0.434975 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.00176449 | −0.000189173 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3734 | 1.20558 | 0.602791 | − | 0.797899i | \(-0.294055\pi\) | ||||
0.602791 | + | 0.797899i | \(0.294055\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.540553 | −0.0566654 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.117843 | −0.0122198 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.0384 | −1.85070 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.5419 | −1.78111 | −0.890553 | − | 0.454880i | \(-0.849682\pi\) | ||||
−0.890553 | + | 0.454880i | \(0.849682\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.92090 | −0.394065 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.46866 | 0.245641 | 0.122821 | − | 0.992429i | \(-0.460806\pi\) | ||||
0.122821 | + | 0.992429i | \(0.460806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0932 | 1.68424 | 0.842119 | − | 0.539291i | \(-0.181308\pi\) | ||||
0.842119 | + | 0.539291i | \(0.181308\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0723702 | −0.00706261 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5655 | −1.31143 | −0.655714 | − | 0.755009i | \(-0.727632\pi\) | ||||
−0.655714 | + | 0.755009i | \(0.727632\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.90938 | 0.566016 | 0.283008 | − | 0.959118i | \(-0.408668\pi\) | ||||
0.283008 | + | 0.959118i | \(0.408668\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.243307 | 0.0230937 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81842 | −0.829567 | −0.414784 | − | 0.909920i | \(-0.636143\pi\) | ||||
−0.414784 | + | 0.909920i | \(0.636143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.90205 | 0.736870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.96216 | −0.273852 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.611002 | −0.0560105 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.29029 | −0.844572 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0151160 | 0.00136297 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4136 | −0.931424 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1932 | −1.43691 | −0.718457 | − | 0.695571i | \(-0.755151\pi\) | ||||
−0.718457 | + | 0.695571i | \(0.755151\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.287672 | 0.0253281 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.30546 | 0.376170 | 0.188085 | − | 0.982153i | \(-0.439772\pi\) | ||||
0.188085 | + | 0.982153i | \(0.439772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.74831 | −0.238309 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.793338 | −0.0682797 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.2477 | −1.55901 | −0.779503 | − | 0.626399i | \(-0.784528\pi\) | ||||
−0.779503 | + | 0.626399i | \(0.784528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.2483 | −1.29334 | −0.646672 | − | 0.762768i | \(-0.723840\pi\) | ||||
−0.646672 | + | 0.762768i | \(0.723840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.353072 | −0.0297340 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.29165 | 0.108013 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.172102 | −0.0142923 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.246735 | 0.0203504 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5489 | 0.864199 | 0.432099 | − | 0.901826i | \(-0.357773\pi\) | ||||
0.432099 | + | 0.901826i | \(0.357773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.6271 | 0.864823 | 0.432411 | − | 0.901676i | \(-0.357663\pi\) | ||||
0.432411 | + | 0.901676i | \(0.357663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.34821 | −0.270687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4940 | −0.923220 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.9067 | −1.42911 | −0.714556 | − | 0.699578i | \(-0.753371\pi\) | ||||
−0.714556 | + | 0.699578i | \(0.753371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0430677 | 0.00341549 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.20395 | 0.0948846 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0276 | −0.785421 | −0.392710 | − | 0.919662i | \(-0.628463\pi\) | ||||
−0.392710 | + | 0.919662i | \(0.628463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.172928 | 0.0134625 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.6913 | −1.36899 | −0.684497 | − | 0.729016i | \(-0.739978\pi\) | ||||
−0.684497 | + | 0.729016i | \(0.739978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0242 | −0.924937 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.0604 | −1.15170 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3232 | 0.784857 | 0.392428 | − | 0.919783i | \(-0.371635\pi\) | ||||
0.392428 | + | 0.919783i | \(0.371635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.32267 | −0.326763 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.285578 | −0.0214653 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.442138 | −0.0330469 | −0.0165235 | − | 0.999863i | \(-0.505260\pi\) | ||||
−0.0165235 | + | 0.999863i | \(0.505260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.333021 | 0.0247533 | 0.0123766 | − | 0.999923i | \(-0.496060\pi\) | ||||
0.0123766 | + | 0.999923i | \(0.496060\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.312234 | −0.0230810 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.7313 | 1.74476 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.45999 | 0.106765 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.120872 | −0.00879218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5590 | −1.05345 | −0.526726 | − | 0.850035i | \(-0.676581\pi\) | ||||
−0.526726 | + | 0.850035i | \(0.676581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.1033 | −1.66301 | −0.831504 | − | 0.555518i | \(-0.812520\pi\) | ||||
−0.831504 | + | 0.555518i | \(0.812520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.130644 | 0.00935560 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.1008 | 1.21838 | 0.609192 | − | 0.793023i | \(-0.291494\pi\) | ||||
0.609192 | + | 0.793023i | \(0.291494\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.75739 | −0.691683 | −0.345842 | − | 0.938293i | \(-0.612407\pi\) | ||||
−0.345842 | + | 0.938293i | \(0.612407\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.194466 | −0.0137166 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0262213 | −0.00184038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.47436 | 0.102974 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.59750 | 0.458558 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.56708 | 0.454255 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.30499 | −0.640582 | −0.320291 | − | 0.947319i | \(-0.603781\pi\) | ||||
−0.320291 | + | 0.947319i | \(0.603781\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.541427 | −0.0370979 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28.0585 | 1.91357 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.75122 | −0.118880 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.386015 | 0.0260845 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.10299 | 0.0741952 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9472 | −1.06790 | −0.533951 | − | 0.845516i | \(-0.679293\pi\) | ||||
−0.533951 | + | 0.845516i | \(0.679293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.6877 | −1.57918 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.8186 | −1.51453 | −0.757263 | − | 0.653110i | \(-0.773464\pi\) | ||||
−0.757263 | + | 0.653110i | \(0.773464\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.3410 | −0.881597 | −0.440798 | − | 0.897606i | \(-0.645305\pi\) | ||||
−0.440798 | + | 0.897606i | \(0.645305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0263472 | 0.00173352 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.87184 | 0.384677 | 0.192339 | − | 0.981329i | \(-0.438393\pi\) | ||||
0.192339 | + | 0.981329i | \(0.438393\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −34.4373 | −2.24644 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.204759 | −0.0133006 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.1257 | −0.719662 | −0.359831 | − | 0.933018i | \(-0.617166\pi\) | ||||
−0.359831 | + | 0.933018i | \(0.617166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6564 | −1.52384 | −0.761921 | − | 0.647670i | \(-0.775744\pi\) | ||||
−0.761921 | + | 0.647670i | \(0.775744\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.993623 | −0.0637409 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.0656 | 1.53750 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.96130 | 0.315680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0161975 | 0.00102647 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.674814 | 0.0425939 | 0.0212969 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212969 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.87684 | −0.180865 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.147670 | 0.00924749 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.1791 | 1.75776 | 0.878881 | − | 0.477042i | \(-0.158291\pi\) | ||||
0.878881 | + | 0.477042i | \(0.158291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.61568 | 0.224668 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.143689 | −0.00889415 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.1677 | 1.55190 | 0.775952 | − | 0.630792i | \(-0.217270\pi\) | ||||
0.775952 | + | 0.630792i | \(0.217270\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.20066 | 0.258044 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.418805 | −0.0256304 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.5178 | −1.55585 | −0.777923 | − | 0.628359i | \(-0.783727\pi\) | ||||
−0.777923 | + | 0.628359i | \(0.783727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0696 | −0.733177 | −0.366589 | − | 0.930383i | \(-0.619474\pi\) | ||||
−0.366589 | + | 0.930383i | \(0.619474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0199048 | 0.00120469 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3290 | 0.622862 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.71005 | −0.343084 | −0.171542 | − | 0.985177i | \(-0.554875\pi\) | ||||
−0.171542 | + | 0.985177i | \(0.554875\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.59644 | −0.574524 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.212448 | −0.0126736 | −0.00633680 | − | 0.999980i | \(-0.502017\pi\) | ||||
−0.00633680 | + | 0.999980i | \(0.502017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3052 | −0.909802 | −0.454901 | − | 0.890542i | \(-0.650325\pi\) | ||||
−0.454901 | + | 0.890542i | \(0.650325\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.664228 | 0.0393455 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.224633 | 0.0132597 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7533 | −0.926662 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.645944 | 0.0378659 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.9617 | 1.39986 | 0.699929 | − | 0.714212i | \(-0.253215\pi\) | ||||
0.699929 | + | 0.714212i | \(0.253215\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −27.8542 | −1.62173 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.288824 | 0.0167593 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.17339 | −0.125690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.27497 | 0.246405 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.0909037 | −0.00522228 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.4541 | −1.74380 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.9475 | 1.76627 | 0.883133 | − | 0.469123i | \(-0.155430\pi\) | ||||
0.883133 | + | 0.469123i | \(0.155430\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.629422 | −0.0358066 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.8105 | −1.57699 | −0.788495 | − | 0.615041i | \(-0.789140\pi\) | ||||
−0.788495 | + | 0.615041i | \(0.789140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.2987 | 1.82563 | 0.912814 | − | 0.408375i | \(-0.133904\pi\) | ||||
0.912814 | + | 0.408375i | \(0.133904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.89339 | −0.332055 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.6102 | −1.83157 | −0.915787 | − | 0.401665i | \(-0.868432\pi\) | ||||
−0.915787 | + | 0.401665i | \(0.868432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0626557 | 0.00350805 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.499524 | 0.0278807 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.60790 | 0.312032 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.80335 | 0.432852 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.217601 | −0.0120334 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.24684 | −0.289268 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4948 | −0.906636 | −0.453318 | − | 0.891349i | \(-0.649760\pi\) | ||||
−0.453318 | + | 0.891349i | \(0.649760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.8135 | 1.08577 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −18.9675 | −1.03630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.05633 | −0.112015 | −0.0560077 | − | 0.998430i | \(-0.517837\pi\) | ||||
−0.0560077 | + | 0.998430i | \(0.517837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.324721 | 0.0176364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.18453 | 0.226605 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.49709 | 0.404805 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.290978 | −0.0156657 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.7232 | −0.629334 | −0.314667 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314667 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.49831 | 0.508433 | 0.254217 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254217 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.218201 | 0.0116467 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6099 | 1.52275 | 0.761377 | − | 0.648310i | \(-0.224524\pi\) | ||||
0.761377 | + | 0.648310i | \(0.224524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −52.8087 | −2.80280 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0224990 | 0.00119077 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.76360 | 0.515303 | 0.257651 | − | 0.966238i | \(-0.417051\pi\) | ||||
0.257651 | + | 0.966238i | \(0.417051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.22456 | 0.327609 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.342097 | 0.0179554 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.6504 | 1.97071 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7863 | −0.667437 | −0.333719 | − | 0.942673i | \(-0.608304\pi\) | ||||
−0.333719 | + | 0.942673i | \(0.608304\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.23096 | 0.0640812 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.640009 | 0.0332276 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.6501 | 1.27633 | 0.638166 | − | 0.769899i | \(-0.279693\pi\) | ||||
0.638166 | + | 0.769899i | \(0.279693\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.383462 | 0.0198019 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0473351 | 0.00243788 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.3795 | 0.738626 | 0.369313 | − | 0.929305i | \(-0.379593\pi\) | ||||
0.369313 | + | 0.929305i | \(0.379593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.596283 | 0.0305485 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.9455 | −1.32575 | −0.662877 | − | 0.748728i | \(-0.730665\pi\) | ||||
−0.662877 | + | 0.748728i | \(0.730665\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.56981 | 0.130970 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 23.4263 | 1.19082 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0273 | −1.57314 | −0.786572 | − | 0.617498i | \(-0.788146\pi\) | ||||
−0.786572 | + | 0.617498i | \(0.788146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.45665 | −0.124238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.158540 | −0.00799730 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.9715 | −1.00487 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.06988 | 0.455204 | 0.227602 | − | 0.973754i | \(-0.426911\pi\) | ||||
0.227602 | + | 0.973754i | \(0.426911\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.101201 | 0.00506640 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.2787 | −1.51204 | −0.756022 | − | 0.654546i | \(-0.772860\pi\) | ||||
−0.756022 | + | 0.654546i | \(0.772860\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.16133 | 0.157477 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −32.2804 | −1.60403 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.63966 | −0.428252 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.15860 | −0.156183 | −0.0780913 | − | 0.996946i | \(-0.524883\pi\) | ||||
−0.0780913 | + | 0.996946i | \(0.524883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.671935 | 0.0331441 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.24384 | −0.208826 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.57984 | 0.0775514 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.561489 | 0.0274962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.9861 | −0.732117 | −0.366058 | − | 0.930592i | \(-0.619293\pi\) | ||||
−0.366058 | + | 0.930592i | \(0.619293\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3764 | 1.09056 | 0.545279 | − | 0.838255i | \(-0.316424\pi\) | ||||
0.545279 | + | 0.838255i | \(0.316424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.7520 | −1.39797 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.82035 | 0.427850 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.63997 | −0.224544 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0475624 | −0.00229634 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3150 | 1.12304 | 0.561522 | − | 0.827462i | \(-0.310216\pi\) | ||||
0.561522 | + | 0.827462i | \(0.310216\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.8072 | 1.52856 | 0.764278 | − | 0.644887i | \(-0.223096\pi\) | ||||
0.764278 | + | 0.644887i | \(0.223096\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.00633731 | 0.000303851 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.0501 | −0.528598 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.9005 | 1.23616 | 0.618081 | − | 0.786115i | \(-0.287911\pi\) | ||||
0.618081 | + | 0.786115i | \(0.287911\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.0926 | 0.956790 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0153 | −0.665887 | −0.332943 | − | 0.942947i | \(-0.608042\pi\) | ||||
−0.332943 | + | 0.942947i | \(0.608042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.8486 | −1.93641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.388442 | −0.0183727 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.2077 | 1.66155 | 0.830776 | − | 0.556607i | \(-0.187897\pi\) | ||||
0.830776 | + | 0.556607i | \(0.187897\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.536759 | −0.0252750 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.391323 | −0.0183860 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.94144 | 0.0910161 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.5389 | −0.492991 | −0.246495 | − | 0.969144i | \(-0.579279\pi\) | ||||
−0.246495 | + | 0.969144i | \(0.579279\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.246639 | 0.0115121 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.3500 | 0.575199 | 0.287599 | − | 0.957751i | \(-0.407143\pi\) | ||||
0.287599 | + | 0.957751i | \(0.407143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1695 | −1.16972 | −0.584862 | − | 0.811133i | \(-0.698851\pi\) | ||||
−0.584862 | + | 0.811133i | \(0.698851\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.423244 | 0.0196275 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.6410 | 0.492407 | 0.246203 | − | 0.969218i | \(-0.420817\pi\) | ||||
0.246203 | + | 0.969218i | \(0.420817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.88987 | −0.133442 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.659380 | 0.0303826 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2150 | −0.469687 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39.6743 | 1.82038 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.50717 | 0.160582 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.1910 | 1.24239 | 0.621193 | − | 0.783657i | \(-0.286648\pi\) | ||||
0.621193 | + | 0.783657i | \(0.286648\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.52709 | −0.297610 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0443331 | −0.00201723 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 63.0030 | 2.86082 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.2201 | −0.599061 | −0.299531 | − | 0.954087i | \(-0.596830\pi\) | ||||
−0.299531 | + | 0.954087i | \(0.596830\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.369246 | 0.0166979 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 41.1468 | 1.85693 | 0.928464 | − | 0.371422i | \(-0.121130\pi\) | ||||
0.928464 | + | 0.371422i | \(0.121130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0535042 | 0.00240971 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.0822 | 0.632949 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.04590 | −0.360908 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7054 | 1.50886 | 0.754430 | − | 0.656380i | \(-0.227913\pi\) | ||||
0.754430 | + | 0.656380i | \(0.227913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.651447 | 0.0291045 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −43.2694 | −1.92929 | −0.964645 | − | 0.263554i | \(-0.915105\pi\) | ||||
−0.964645 | + | 0.263554i | \(0.915105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.86641 | −0.394550 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.442767 | 0.0196640 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3195 | 0.590375 | 0.295188 | − | 0.955439i | \(-0.404618\pi\) | ||||
0.295188 | + | 0.955439i | \(0.404618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.73639 | 0.253763 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.10939 | 0.0489808 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −61.3915 | −2.70523 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.5373 | 0.551390 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.380131 | −0.0166859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.5245 | 0.461087 | 0.230544 | − | 0.973062i | \(-0.425950\pi\) | ||||
0.230544 | + | 0.973062i | \(0.425950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.6580 | −1.86531 | −0.932653 | − | 0.360775i | \(-0.882512\pi\) | ||||
−0.932653 | + | 0.360775i | \(0.882512\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.159174 | 0.00694691 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.57334 | 0.155657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1593 | −0.789535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.2557 | −1.00921 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.405511 | −0.0175646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.7217 | 2.10642 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0162809 | 0.000702571 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.76137 | −0.377379 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.8753 | −1.06947 | −0.534737 | − | 0.845018i | \(-0.679589\pi\) | ||||
−0.534737 | + | 0.845018i | \(0.679589\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.0122629 | −0.000526250 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.2240 | −0.909137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.4320 | 1.64323 | 0.821616 | − | 0.570041i | \(-0.193073\pi\) | ||||
0.821616 | + | 0.570041i | \(0.193073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.4264 | −1.08517 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.240664 | 0.0102526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.04284 | −0.129395 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.873859 | −0.0370932 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.34246 | 0.268739 | 0.134369 | − | 0.990931i | \(-0.457099\pi\) | ||||
0.134369 | + | 0.990931i | \(0.457099\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.71724 | −0.326405 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0537612 | −0.00226980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.2363 | 0.684280 | 0.342140 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342140 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.6721 | 1.33245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.91822 | −0.206546 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.88953 | −0.288824 | −0.144412 | − | 0.989518i | \(-0.546129\pi\) | ||||
−0.144412 | + | 0.989518i | \(0.546129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.1366 | 0.591597 | 0.295798 | − | 0.955250i | \(-0.404414\pi\) | ||||
0.295798 | + | 0.955250i | \(0.404414\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.536106 | 0.0223962 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.3801 | −0.724799 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.91701 | 0.287959 | 0.143979 | − | 0.989581i | \(-0.454010\pi\) | ||||
0.143979 | + | 0.989581i | \(0.454010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.850732 | 0.0353552 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.240704 | 0.00998607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.52930 | −0.0633371 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.6388 | 0.439862 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.4326 | 1.21481 | 0.607407 | − | 0.794391i | \(-0.292210\pi\) | ||||
0.607407 | + | 0.794391i | \(0.292210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0730 | 0.662277 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.629705 | −0.0259026 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.5283 | −1.00725 | −0.503627 | − | 0.863921i | \(-0.668002\pi\) | ||||
−0.503627 | + | 0.863921i | \(0.668002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.19446 | 0.0899643 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.359297 | 0.0147050 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5940 | −1.33176 | −0.665878 | − | 0.746061i | \(-0.731943\pi\) | ||||
−0.665878 | + | 0.746061i | \(0.731943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3281 | 0.747618 | 0.373809 | − | 0.927506i | \(-0.378052\pi\) | ||||
0.373809 | + | 0.927506i | \(0.378052\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.8361 | −0.644897 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.3668 | 1.35656 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.6995 | −1.48959 | −0.744794 | − | 0.667294i | \(-0.767452\pi\) | ||||
−0.744794 | + | 0.667294i | \(0.767452\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.000965548 0 | 3.91260e−5 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.47168 | 0.383183 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.1587 | 1.25849 | 0.629245 | − | 0.777207i | \(-0.283364\pi\) | ||||
0.629245 | + | 0.777207i | \(0.283364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0542905 | −0.00218920 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.30996 | 0.374805 | 0.187402 | − | 0.982283i | \(-0.439993\pi\) | ||||
0.187402 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.72625 | −0.270351 | −0.135175 | − | 0.990822i | \(-0.543160\pi\) | ||||
−0.135175 | + | 0.990822i | \(0.543160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.485990 | −0.0195021 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.22367 | −0.249346 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.09586 | −0.0838346 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.241820 | −0.00965736 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.37775 | −0.294170 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.1334 | 0.403405 | 0.201702 | − | 0.979447i | \(-0.435353\pi\) | ||||
0.201702 | + | 0.979447i | \(0.435353\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.342638 | 0.0136186 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 58.1592 | 2.30798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.61904 | −0.262256 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −44.0905 | −1.74419 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.01212 | −0.276962 | −0.138481 | − | 0.990365i | \(-0.544222\pi\) | ||||
−0.138481 | + | 0.990365i | \(0.544222\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.7876 | −1.41133 | −0.705663 | − | 0.708547i | \(-0.749351\pi\) | ||||
−0.705663 | + | 0.708547i | \(0.749351\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.03320 | −0.0406821 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.566397 | 0.0222674 | 0.0111337 | − | 0.999938i | \(-0.496456\pi\) | ||||
0.0111337 | + | 0.999938i | \(0.496456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1406 | 0.398055 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0644851 | 0.00252737 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.1741 | −1.14167 | −0.570836 | − | 0.821064i | \(-0.693381\pi\) | ||||
−0.570836 | + | 0.821064i | \(0.693381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.4634 | −0.604206 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 31.4347 | 1.22638 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.5997 | −1.38677 | −0.693383 | − | 0.720569i | \(-0.743881\pi\) | ||||
−0.693383 | + | 0.720569i | \(0.743881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7417 | −0.690071 | −0.345035 | − | 0.938590i | \(-0.612133\pi\) | ||||
−0.345035 | + | 0.938590i | \(0.612133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0406155 | −0.00157738 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.87079 | 0.382773 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.105428 | −0.00408217 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.587223 | 0.0227034 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0872 | 0.428016 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9294 | 0.614034 | 0.307017 | − | 0.951704i | \(-0.400669\pi\) | ||||
0.307017 | + | 0.951704i | \(0.400669\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.74490 | 0.0671611 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.3273 | 0.704377 | 0.352188 | − | 0.935929i | \(-0.385438\pi\) | ||||
0.352188 | + | 0.935929i | \(0.385438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.59909 | 0.368379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.840252 | 0.0321985 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.9610 | 0.534205 | 0.267102 | − | 0.963668i | \(-0.413934\pi\) | ||||
0.267102 | + | 0.963668i | \(0.413934\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 65.5381 | 2.50408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.491255 | 0.0187426 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.15535 | −0.0440155 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.3418 | 0.469504 | 0.234752 | − | 0.972055i | \(-0.424572\pi\) | ||||
0.234752 | + | 0.972055i | \(0.424572\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.14556 | 0.0815030 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 54.7655 | 2.07737 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.458360 | −0.0173616 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.216219 | −0.00817816 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.7980 | 1.57869 | 0.789345 | − | 0.613950i | \(-0.210420\pi\) | ||||
0.789345 | + | 0.613950i | \(0.210420\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.1854 | −1.25161 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.26809 | 0.0477589 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.35088 | −0.0508051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.58664 | 0.209811 | 0.104905 | − | 0.994482i | \(-0.466546\pi\) | ||||
0.104905 | + | 0.994482i | \(0.466546\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.6744 | −0.625338 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.04109 | −0.263691 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.63906 | −0.173491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.409682 | 0.0152999 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.2923 | −1.20430 | −0.602150 | − | 0.798383i | \(-0.705689\pi\) | ||||
−0.602150 | + | 0.798383i | \(0.705689\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.35356 | −0.348345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.871100 | 0.0323966 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.378527 | 0.0140581 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.9665 | −0.851779 | −0.425890 | − | 0.904775i | \(-0.640039\pi\) | ||||
−0.425890 | + | 0.904775i | \(0.640039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9268 | −0.997289 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.72302 | −0.322632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.3379 | −1.67460 | −0.837298 | − | 0.546747i | \(-0.815866\pi\) | ||||
−0.837298 | + | 0.546747i | \(0.815866\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.886169 | −0.0326868 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.90534 | 0.254361 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5760 | −0.572974 | −0.286487 | − | 0.958084i | \(-0.592487\pi\) | ||||
−0.286487 | + | 0.958084i | \(0.592487\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.182690 | −0.00671129 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.24312 | −0.155665 | −0.0778326 | − | 0.996966i | \(-0.524800\pi\) | ||||
−0.0778326 | + | 0.996966i | \(0.524800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8872 | −1.38808 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.31902 | 0.0482606 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.42320 | 0.271238 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0248487 | −0.000905537 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.1682 | −1.38908 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.9764 | 1.59835 | 0.799174 | − | 0.601099i | \(-0.205270\pi\) | ||||
0.799174 | + | 0.601099i | \(0.205270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.105934 | 0.00384515 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.95905 | 0.324765 | 0.162383 | − | 0.986728i | \(-0.448082\pi\) | ||||
0.162383 | + | 0.986728i | \(0.448082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.23367 | −0.117067 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.0254 | 0.434779 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.66106 | 0.276625 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.5452 | −1.46210 | −0.731049 | − | 0.682325i | \(-0.760969\pi\) | ||||
−0.731049 | + | 0.682325i | \(0.760969\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.03764 | −0.0373696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.1455 | 0.688615 | 0.344307 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344307 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2803 | 0.908096 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.133140 | −0.00477639 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.06172 | −0.0738689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2256 | 0.687947 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0105846 | 0.000378261 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 64.3135 | 2.29545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6116 | 0.984247 | 0.492124 | − | 0.870525i | \(-0.336221\pi\) | ||||
0.492124 | + | 0.870525i | \(0.336221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.926750 | −0.0329932 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.82554 | 0.171576 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.37614 | 0.297446 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.154681 | −0.00548597 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.2018 | 1.45944 | 0.729721 | − | 0.683745i | \(-0.239650\pi\) | ||||
0.729721 | + | 0.683745i | \(0.239650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7061 | 0.378755 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.1049 | −1.20504 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.7071 | −0.483712 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.32409 | −0.152404 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.939642 | 0.0330770 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.1610 | −1.76357 | −0.881783 | − | 0.471655i | \(-0.843657\pi\) | ||||
−0.881783 | + | 0.471655i | \(0.843657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6046 | 0.688411 | 0.344206 | − | 0.938894i | \(-0.388148\pi\) | ||||
0.344206 | + | 0.938894i | \(0.388148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.444440 | 0.0155872 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.0149 | 1.26155 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.2365 | −1.37271 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.62093 | 0.0566397 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5097 | 0.436593 | 0.218297 | − | 0.975882i | \(-0.429950\pi\) | ||||
0.218297 | + | 0.975882i | \(0.429950\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4157 | 0.781363 | 0.390682 | − | 0.920526i | \(-0.372239\pi\) | ||||
0.390682 | + | 0.920526i | \(0.372239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.380345 | −0.0132419 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.43398 | −0.223731 | −0.111866 | − | 0.993723i | \(-0.535683\pi\) | ||||
−0.111866 | + | 0.993723i | \(0.535683\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.2022 | 1.53520 | 0.767602 | − | 0.640927i | \(-0.221450\pi\) | ||||
0.767602 | + | 0.640927i | \(0.221450\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.210262 | 0.00729389 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.48169 | −0.259225 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.5397 | 2.19888 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.706900 | 0.0244340 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.3849 | 1.08353 | 0.541763 | − | 0.840531i | \(-0.317757\pi\) | ||||
0.541763 | + | 0.840531i | \(0.317757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9977 | −0.999921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.00782299 | 0.000269438 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.1858 | 1.48564 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.08375 | 0.174680 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.563585 | 0.0193422 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5375 | 0.498339 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.7815 | −0.677305 | −0.338653 | − | 0.940911i | \(-0.609971\pi\) | ||||
−0.338653 | + | 0.940911i | \(0.609971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 54.0907 | 1.84986 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.0193 | −0.957122 | −0.478561 | − | 0.878054i | \(-0.658842\pi\) | ||||
−0.478561 | + | 0.878054i | \(0.658842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4600 | 0.561606 | 0.280803 | − | 0.959765i | \(-0.409399\pi\) | ||||
0.280803 | + | 0.959765i | \(0.409399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.00827166 | −0.000281897 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.60626 | −0.156799 | −0.0783995 | − | 0.996922i | \(-0.524981\pi\) | ||||
−0.0783995 | + | 0.996922i | \(0.524981\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.0765 | −1.26064 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.580083 | 0.0197006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.27085 | 0.246647 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.21684 | 0.176766 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 52.6018 | 1.78030 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.69845 | 0.192643 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.1424 | 1.55812 | 0.779059 | − | 0.626951i | \(-0.215697\pi\) | ||||
0.779059 | + | 0.626951i | \(0.215697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.882343 | −0.0297607 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.07723 | 0.171056 | 0.0855280 | − | 0.996336i | \(-0.472742\pi\) | ||||
0.0855280 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −54.4257 | −1.83157 | −0.915786 | − | 0.401668i | \(-0.868431\pi\) | ||||
−0.915786 | + | 0.401668i | \(0.868431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.02568 | 0.0344777 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.9554 | −0.703613 | −0.351806 | − | 0.936073i | \(-0.614432\pi\) | ||||
−0.351806 | + | 0.936073i | \(0.614432\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.86109 | 0.297191 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.7521 | 0.393709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.1565 | 1.61150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.58797 | 0.0530801 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0800309 | 0.00267215 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.153351 | 0.00511453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.30593 | −0.0435068 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.157417 | −0.00523852 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.19607 | −0.0397588 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46.8048 | −1.55413 | −0.777063 | − | 0.629422i | \(-0.783292\pi\) | ||||
−0.777063 | + | 0.629422i | \(0.783292\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.40265 | −0.245530 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.9833 | −1.19218 | −0.596090 | − | 0.802917i | \(-0.703280\pi\) | ||||
−0.596090 | + | 0.802917i | \(0.703280\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.575160 | −0.0190350 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.12141 | 0.0370728 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.35600 | −0.0778018 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.3043 | −1.69237 | −0.846186 | − | 0.532888i | \(-0.821107\pi\) | ||||
−0.846186 | + | 0.532888i | \(0.821107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13958 | −0.0375504 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5246 | 0.478082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −52.1955 | −1.71618 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.2563 | −1.68348 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.2441 | 1.25475 | 0.627374 | − | 0.778718i | \(-0.284130\pi\) | ||||
0.627374 | + | 0.778718i | \(0.284130\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.6529 | −1.10293 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.02407 | 0.0335265 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.24366 | −0.171486 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.3953 | −1.80969 | −0.904843 | − | 0.425746i | \(-0.860012\pi\) | ||||
−0.904843 | + | 0.425746i | \(0.860012\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.18934 | −0.0388125 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.61479 | −0.0526406 | −0.0263203 | − | 0.999654i | \(-0.508379\pi\) | ||||
−0.0263203 | + | 0.999654i | \(0.508379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.903177 | 0.0294115 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.434123 | 0.0141220 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.3784 | −0.889677 | −0.444839 | − | 0.895611i | \(-0.646739\pi\) | ||||
−0.444839 | + | 0.895611i | \(0.646739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.3554 | −0.336151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.20081 | 0.0389389 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.3160 | −1.40314 | −0.701572 | − | 0.712599i | \(-0.747518\pi\) | ||||
−0.701572 | + | 0.712599i | \(0.747518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.2898 | 1.69206 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.00230717 | −7.45803e−5 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.98533 | 0.322443 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7583 | −0.669624 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.6782 | 1.31084 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 82.9772 | 2.67113 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.91608 | −0.125933 | −0.0629664 | − | 0.998016i | \(-0.520056\pi\) | ||||
−0.0629664 | + | 0.998016i | \(0.520056\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.206500 | −0.00663373 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.4920 | 0.882260 | 0.441130 | − | 0.897443i | \(-0.354578\pi\) | ||||
0.441130 | + | 0.897443i | \(0.354578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.34403 | 0.267497 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.287343 | −0.00920234 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.7942 | −0.665265 | −0.332632 | − | 0.943057i | \(-0.607937\pi\) | ||||
−0.332632 | + | 0.943057i | \(0.607937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.8714 | 0.475293 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.7201 | −0.565760 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.2392 | −0.358474 | −0.179237 | − | 0.983806i | \(-0.557363\pi\) | ||||
−0.179237 | + | 0.983806i | \(0.557363\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61.4190 | −1.95697 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.193205 | 0.00614977 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.1883 | 0.546556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.4475 | 1.63428 | 0.817142 | − | 0.576436i | \(-0.195557\pi\) | ||||
0.817142 | + | 0.576436i | \(0.195557\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.607388 | 0.0192749 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.0445 | 1.11098 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.3824 | −1.56396 | −0.781979 | − | 0.623305i | \(-0.785789\pi\) | ||||
−0.781979 | + | 0.623305i | \(0.785789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.45952 | −0.0461770 |
(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 | 6008.2.a.b.1.26 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.26 | ✓ | 44 | 1.1 | even | 1 | trivial |