Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.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: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | −0.254882 | −0.147156 | −0.0735780 | − | 0.997289i | \(-0.523442\pi\) | ||||
−0.0735780 | + | 0.997289i | \(0.523442\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.76559 | 1.68403 | 0.842013 | − | 0.539458i | \(-0.181371\pi\) | ||||
0.842013 | + | 0.539458i | \(0.181371\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.29648 | −0.867988 | −0.433994 | − | 0.900916i | \(-0.642896\pi\) | ||||
−0.433994 | + | 0.900916i | \(0.642896\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.93504 | −0.978345 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.49668 | −0.752777 | −0.376388 | − | 0.926462i | \(-0.622834\pi\) | ||||
−0.376388 | + | 0.926462i | \(0.622834\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.47840 | 1.79679 | 0.898393 | − | 0.439193i | \(-0.144736\pi\) | ||||
0.898393 | + | 0.439193i | \(0.144736\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.959781 | −0.247814 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.17796 | 1.25584 | 0.627920 | − | 0.778278i | \(-0.283907\pi\) | ||||
0.627920 | + | 0.778278i | \(0.283907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78611 | 0.409762 | 0.204881 | − | 0.978787i | \(-0.434319\pi\) | ||||
0.204881 | + | 0.978787i | \(0.434319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.585331 | 0.127730 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.62486 | −0.338807 | −0.169403 | − | 0.985547i | \(-0.554184\pi\) | ||||
−0.169403 | + | 0.985547i | \(0.554184\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.17970 | 1.83594 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.51273 | 0.291125 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.13341 | 0.581859 | 0.290930 | − | 0.956744i | \(-0.406035\pi\) | ||||
0.290930 | + | 0.956744i | \(0.406035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76790 | −0.497130 | −0.248565 | − | 0.968615i | \(-0.579959\pi\) | ||||
−0.248565 | + | 0.968615i | \(0.579959\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.636357 | 0.110776 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.64762 | −1.46171 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.433471 | −0.0712622 | −0.0356311 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356311 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.65123 | −0.264408 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.69738 | −0.577434 | −0.288717 | − | 0.957415i | \(-0.593229\pi\) | ||||
−0.288717 | + | 0.957415i | \(0.593229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.958002 | 0.146094 | 0.0730470 | − | 0.997328i | \(-0.476728\pi\) | ||||
0.0730470 | + | 0.997328i | \(0.476728\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.0522 | −1.64756 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.36228 | 0.198709 | 0.0993546 | − | 0.995052i | \(-0.468322\pi\) | ||||
0.0993546 | + | 0.995052i | \(0.468322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.72618 | −0.246596 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.31977 | −0.184804 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.03300 | 1.24078 | 0.620389 | − | 0.784294i | \(-0.286975\pi\) | ||||
0.620389 | + | 0.784294i | \(0.286975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.40148 | −1.26769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.455247 | −0.0602990 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.59760 | −0.989123 | −0.494562 | − | 0.869143i | \(-0.664671\pi\) | ||||
−0.494562 | + | 0.869143i | \(0.664671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.79810 | −0.998445 | −0.499222 | − | 0.866474i | \(-0.666381\pi\) | ||||
−0.499222 | + | 0.866474i | \(0.666381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.74025 | 0.849192 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 24.3950 | 3.02583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.83170 | 0.590286 | 0.295143 | − | 0.955453i | \(-0.404633\pi\) | ||||
0.295143 | + | 0.955453i | \(0.404633\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.414147 | 0.0498574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.52115 | 0.299205 | 0.149603 | − | 0.988746i | \(-0.452201\pi\) | ||||
0.149603 | + | 0.988746i | \(0.452201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.72787 | −0.553356 | −0.276678 | − | 0.960963i | \(-0.589233\pi\) | ||||
−0.276678 | + | 0.960963i | \(0.589233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.33974 | −0.270170 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.73357 | 0.653401 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.4664 | 1.62760 | 0.813798 | − | 0.581148i | \(-0.197396\pi\) | ||||
0.813798 | + | 0.581148i | \(0.197396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.41954 | 0.935504 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.5950 | 1.71177 | 0.855885 | − | 0.517165i | \(-0.173013\pi\) | ||||
0.855885 | + | 0.517165i | \(0.173013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.4981 | 2.11487 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.798648 | −0.0856241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.46665 | 0.261465 | 0.130732 | − | 0.991418i | \(-0.458267\pi\) | ||||
0.130732 | + | 0.991418i | \(0.458267\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.8775 | −1.55959 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.705487 | 0.0731556 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.72578 | 0.690050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.53018 | 0.358435 | 0.179218 | − | 0.983809i | \(-0.442643\pi\) | ||||
0.179218 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.32784 | 0.736475 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2339 | −1.21732 | −0.608661 | − | 0.793430i | \(-0.708293\pi\) | ||||
−0.608661 | + | 0.793430i | \(0.708293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9722 | 1.77085 | 0.885425 | − | 0.464783i | \(-0.153868\pi\) | ||||
0.885425 | + | 0.464783i | \(0.153868\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.20412 | 0.215100 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.94819 | −0.188338 | −0.0941691 | − | 0.995556i | \(-0.530019\pi\) | ||||
−0.0941691 | + | 0.995556i | \(0.530019\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.61401 | 0.154594 | 0.0772969 | − | 0.997008i | \(-0.475371\pi\) | ||||
0.0772969 | + | 0.997008i | \(0.475371\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.110484 | 0.0104867 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.16562 | 0.674085 | 0.337043 | − | 0.941489i | \(-0.390573\pi\) | ||||
0.337043 | + | 0.941489i | \(0.390573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.11856 | −0.570559 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.0143 | −1.75788 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.8911 | −1.09005 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.76660 | −0.433327 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.942394 | 0.0849728 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15.7391 | 1.40774 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.54603 | 0.669602 | 0.334801 | − | 0.942289i | \(-0.391331\pi\) | ||||
0.334801 | + | 0.942289i | \(0.391331\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.244177 | −0.0214986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.2282 | 1.33049 | 0.665246 | − | 0.746624i | \(-0.268326\pi\) | ||||
0.665246 | + | 0.746624i | \(0.268326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.10177 | −0.355669 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.69633 | 0.490262 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.6590 | 1.67958 | 0.839790 | − | 0.542912i | \(-0.182678\pi\) | ||||
0.839790 | + | 0.542912i | \(0.182678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.206999 | −0.0175574 | −0.00877872 | − | 0.999961i | \(-0.502794\pi\) | ||||
−0.00877872 | + | 0.999961i | \(0.502794\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.347221 | −0.0292413 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.1745 | −1.35258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7991 | 0.979866 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.439970 | 0.0362882 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.86694 | −0.480639 | −0.240319 | − | 0.970694i | \(-0.577252\pi\) | ||||
−0.240319 | + | 0.970694i | \(0.577252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8060 | −1.28628 | −0.643138 | − | 0.765751i | \(-0.722368\pi\) | ||||
−0.643138 | + | 0.765751i | \(0.722368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.1975 | −1.22864 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.4228 | −0.837179 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6152 | 1.32604 | 0.663018 | − | 0.748603i | \(-0.269275\pi\) | ||||
0.663018 | + | 0.748603i | \(0.269275\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.30235 | −0.182588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.73146 | 0.294080 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.08622 | −0.320058 | −0.160029 | − | 0.987112i | \(-0.551159\pi\) | ||||
−0.160029 | + | 0.987112i | \(0.551159\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.39626 | 0.186549 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.4703 | 1.66142 | 0.830709 | − | 0.556707i | \(-0.187935\pi\) | ||||
0.830709 | + | 0.556707i | \(0.187935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.9697 | 2.22844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.24231 | −0.400889 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1278 | −1.15015 | −0.575073 | − | 0.818102i | \(-0.695026\pi\) | ||||
−0.575073 | + | 0.818102i | \(0.695026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.0810 | −1.59357 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.93649 | 0.145555 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.10224 | 0.605590 | 0.302795 | − | 0.953056i | \(-0.402080\pi\) | ||||
0.302795 | + | 0.953056i | \(0.402080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.7758 | −1.54425 | −0.772127 | − | 0.635468i | \(-0.780807\pi\) | ||||
−0.772127 | + | 0.635468i | \(0.780807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.98759 | 0.146927 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.63228 | −0.120007 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9277 | −0.945367 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.47396 | −0.252693 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.04226 | −0.581917 | −0.290959 | − | 0.956736i | \(-0.593974\pi\) | ||||
−0.290959 | + | 0.956736i | \(0.593974\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5805 | 1.04953 | 0.524764 | − | 0.851248i | \(-0.324154\pi\) | ||||
0.524764 | + | 0.851248i | \(0.324154\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.21785 | −0.445269 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.351844 | −0.0250678 | −0.0125339 | − | 0.999921i | \(-0.503990\pi\) | ||||
−0.0125339 | + | 0.999921i | \(0.503990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.10629 | −0.291087 | −0.145544 | − | 0.989352i | \(-0.546493\pi\) | ||||
−0.145544 | + | 0.989352i | \(0.546493\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.23151 | −0.0868641 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.19581 | −0.505047 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9228 | −0.972413 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.76902 | 0.331470 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.45935 | −0.308460 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3899 | 1.33486 | 0.667428 | − | 0.744675i | \(-0.267395\pi\) | ||||
0.667428 | + | 0.744675i | \(0.267395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.642594 | −0.0440298 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.60745 | 0.246026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.35643 | 0.431503 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.20505 | 0.0814296 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.5449 | 2.25647 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.39184 | 0.160170 | 0.0800848 | − | 0.996788i | \(-0.474481\pi\) | ||||
0.0800848 | + | 0.996788i | \(0.474481\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −26.9427 | −1.79618 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.87067 | −0.323278 | −0.161639 | − | 0.986850i | \(-0.551678\pi\) | ||||
−0.161639 | + | 0.986850i | \(0.551678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.11633 | −0.338097 | −0.169048 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169048 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.46138 | −0.0961519 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.04425 | −0.0684111 | −0.0342056 | − | 0.999415i | \(-0.510890\pi\) | ||||
−0.0342056 | + | 0.999415i | \(0.510890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.12980 | 0.334631 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.68722 | −0.239511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.2524 | −1.50407 | −0.752035 | − | 0.659123i | \(-0.770928\pi\) | ||||
−0.752035 | + | 0.659123i | \(0.770928\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7651 | 0.886686 | 0.443343 | − | 0.896352i | \(-0.353792\pi\) | ||||
0.443343 | + | 0.896352i | \(0.353792\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.68418 | −0.428790 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.50008 | −0.415275 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5712 | 0.736255 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.97487 | −0.251897 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6552 | 0.988150 | 0.494075 | − | 0.869419i | \(-0.335507\pi\) | ||||
0.494075 | + | 0.869419i | \(0.335507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.05675 | 0.255046 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.96971 | −0.311215 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.61866 | −0.163348 | −0.0816739 | − | 0.996659i | \(-0.526027\pi\) | ||||
−0.0816739 | + | 0.996659i | \(0.526027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.995458 | 0.0618548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.19666 | −0.569259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.9242 | −1.04359 | −0.521794 | − | 0.853072i | \(-0.674737\pi\) | ||||
−0.521794 | + | 0.853072i | \(0.674737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.0146 | 2.08950 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.628705 | −0.0384761 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.53746 | −0.459567 | −0.229784 | − | 0.973242i | \(-0.573802\pi\) | ||||
−0.229784 | + | 0.973242i | \(0.573802\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8582 | 1.26705 | 0.633523 | − | 0.773724i | \(-0.281608\pi\) | ||||
0.633523 | + | 0.773724i | \(0.281608\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.79201 | 0.229503 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.9188 | −1.38205 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.5550 | −1.35520 | −0.677600 | − | 0.735430i | \(-0.736980\pi\) | ||||
−0.677600 | + | 0.735430i | \(0.736980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.12388 | 0.486364 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.34033 | −0.258923 | −0.129461 | − | 0.991584i | \(-0.541325\pi\) | ||||
−0.129461 | + | 0.991584i | \(0.541325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6361 | 1.10780 | 0.553902 | − | 0.832582i | \(-0.313138\pi\) | ||||
0.553902 | + | 0.832582i | \(0.313138\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.71428 | −0.101545 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.49096 | 0.501206 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.81127 | 0.577133 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.899777 | −0.0527459 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.4643 | −0.669752 | −0.334876 | − | 0.942262i | \(-0.608694\pi\) | ||||
−0.334876 | + | 0.942262i | \(0.608694\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.6095 | −1.66571 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.77680 | −0.219152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5265 | −0.608763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.20003 | −0.126808 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.11821 | 0.179136 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29.3645 | −1.68141 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.47828 | −0.483881 | −0.241940 | − | 0.970291i | \(-0.577784\pi\) | ||||
−0.241940 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.58077 | −0.260591 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2474 | 0.864602 | 0.432301 | − | 0.901729i | \(-0.357702\pi\) | ||||
0.432301 | + | 0.901729i | \(0.357702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.6356 | 1.16639 | 0.583196 | − | 0.812331i | \(-0.301802\pi\) | ||||
0.583196 | + | 0.812331i | \(0.301802\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.3811 | 1.43006 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.37620 | −0.526620 | −0.263310 | − | 0.964711i | \(-0.584814\pi\) | ||||
−0.263310 | + | 0.964711i | \(0.584814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.82311 | −0.438010 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.496557 | 0.0277151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.24842 | 0.514596 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 59.4698 | 3.29879 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.411381 | −0.0227494 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.12846 | −0.172477 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8337 | −0.980226 | −0.490113 | − | 0.871659i | \(-0.663045\pi\) | ||||
−0.490113 | + | 0.871659i | \(0.663045\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.27225 | 0.0697191 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.1942 | 0.994056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.315403 | −0.0171811 | −0.00859054 | − | 0.999963i | \(-0.502734\pi\) | ||||
−0.00859054 | + | 0.999963i | \(0.502734\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.82639 | −0.0991957 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.91056 | 0.374228 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0395 | 1.08203 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.55951 | 0.0839612 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.17570 | −0.331529 | −0.165765 | − | 0.986165i | \(-0.553009\pi\) | ||||
−0.165765 | + | 0.986165i | \(0.553009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.5980 | 0.567300 | 0.283650 | − | 0.958928i | \(-0.408455\pi\) | ||||
0.283650 | + | 0.958928i | \(0.408455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.80008 | 0.523090 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2080 | −1.18201 | −0.591007 | − | 0.806666i | \(-0.701269\pi\) | ||||
−0.591007 | + | 0.806666i | \(0.701269\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.49362 | 0.503869 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.03082 | 0.160408 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.4903 | −1.13422 | −0.567108 | − | 0.823643i | \(-0.691938\pi\) | ||||
−0.567108 | + | 0.823643i | \(0.691938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8098 | −0.832095 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.21492 | 0.0637667 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.8032 | −0.931865 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.59560 | −0.187689 | −0.0938445 | − | 0.995587i | \(-0.529916\pi\) | ||||
−0.0938445 | + | 0.995587i | \(0.529916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.8519 | 0.564929 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.7441 | −1.07698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.38095 | 0.433949 | 0.216975 | − | 0.976177i | \(-0.430381\pi\) | ||||
0.216975 | + | 0.976177i | \(0.430381\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.01160 | −0.207158 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.2995 | 1.04548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.3157 | −0.529884 | −0.264942 | − | 0.964264i | \(-0.585353\pi\) | ||||
−0.264942 | + | 0.964264i | \(0.585353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.92334 | −0.0985359 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.93463 | 0.507636 | 0.253818 | − | 0.967252i | \(-0.418314\pi\) | ||||
0.253818 | + | 0.967252i | \(0.418314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.5903 | 1.10034 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.81177 | −0.142930 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4919 | 0.684065 | 0.342033 | − | 0.939688i | \(-0.388885\pi\) | ||||
0.342033 | + | 0.939688i | \(0.388885\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.41346 | −0.425487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.88139 | −0.195790 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 54.4746 | 2.74091 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.92914 | −0.498329 | −0.249165 | − | 0.968461i | \(-0.580156\pi\) | ||||
−0.249165 | + | 0.968461i | \(0.580156\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.04547 | 0.0523388 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4777 | 1.02261 | 0.511304 | − | 0.859400i | \(-0.329163\pi\) | ||||
0.511304 | + | 0.859400i | \(0.329163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.9316 | −0.893235 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 31.7046 | 1.57541 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.08224 | 0.0536446 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.70617 | 0.282152 | 0.141076 | − | 0.989999i | \(-0.454944\pi\) | ||||
0.141076 | + | 0.989999i | \(0.454944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.01071 | −0.247160 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.4477 | 0.858547 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 58.7244 | 2.88267 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0527603 | 0.00258368 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.94903 | −0.388335 | −0.194168 | − | 0.980968i | \(-0.562201\pi\) | ||||
−0.194168 | + | 0.980968i | \(0.562201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.37442 | 0.310670 | 0.155335 | − | 0.987862i | \(-0.450354\pi\) | ||||
0.155335 | + | 0.987862i | \(0.450354\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.99835 | −0.194406 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 47.5321 | 2.30565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.9082 | 0.866638 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.12258 | 0.199040 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.9371 | −0.815829 | −0.407915 | − | 0.913020i | \(-0.633744\pi\) | ||||
−0.407915 | + | 0.913020i | \(0.633744\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4676 | −1.27195 | −0.635977 | − | 0.771708i | \(-0.719403\pi\) | ||||
−0.635977 | + | 0.771708i | \(0.719403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00739 | −0.144193 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.90218 | −0.138830 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2998 | 1.25522 | 0.627611 | − | 0.778527i | \(-0.284033\pi\) | ||||
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.06639 | 0.241256 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3165 | 0.490151 | 0.245075 | − | 0.969504i | \(-0.421187\pi\) | ||||
0.245075 | + | 0.969504i | \(0.421187\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.28842 | 0.440313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.49538 | 0.0707288 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.7813 | 1.54704 | 0.773522 | − | 0.633769i | \(-0.218493\pi\) | ||||
0.773522 | + | 0.633769i | \(0.218493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.23117 | 0.434679 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.02866 | 0.189283 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −56.0227 | −2.62639 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00367 | 0.374396 | 0.187198 | − | 0.982322i | \(-0.440059\pi\) | ||||
0.187198 | + | 0.982322i | \(0.440059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.83286 | 0.365607 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.1178 | −1.03013 | −0.515065 | − | 0.857151i | \(-0.672232\pi\) | ||||
−0.515065 | + | 0.857151i | \(0.672232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1882 | −0.612907 | −0.306454 | − | 0.951886i | \(-0.599142\pi\) | ||||
−0.306454 | + | 0.951886i | \(0.599142\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.65658 | 0.123196 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.2615 | 1.12269 | 0.561344 | − | 0.827583i | \(-0.310285\pi\) | ||||
0.561344 | + | 0.827583i | \(0.310285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0959 | −0.512361 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.23491 | −0.195134 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.39182 | −0.109976 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.3960 | 0.752299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.5122 | −1.21391 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.4445 | −0.979824 | −0.489912 | − | 0.871772i | \(-0.662971\pi\) | ||||
−0.489912 | + | 0.871772i | \(0.662971\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.80820 | −0.128043 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.951081 | −0.0432757 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.2932 | 0.603614 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.0633 | 1.63418 | 0.817092 | − | 0.576508i | \(-0.195585\pi\) | ||||
0.817092 | + | 0.576508i | \(0.195585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04150 | 0.0470984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.1007 | −1.13278 | −0.566389 | − | 0.824138i | \(-0.691660\pi\) | ||||
−0.566389 | + | 0.824138i | \(0.691660\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.2247 | 0.730722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.5937 | 1.24024 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.78977 | −0.259707 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.7534 | −1.24241 | −0.621207 | − | 0.783647i | \(-0.713357\pi\) | ||||
−0.621207 | + | 0.783647i | \(0.713357\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.47237 | −0.244488 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.0680 | −2.05000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.38384 | −0.327928 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7904 | 1.14314 | 0.571569 | − | 0.820554i | \(-0.306335\pi\) | ||||
0.571569 | + | 0.820554i | \(0.306335\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8575 | 0.480306 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.70191 | 0.119292 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 67.6759 | 2.98215 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.40118 | −0.149584 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.85580 | 0.169251 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.9650 | −0.743251 | −0.371625 | − | 0.928383i | \(-0.621199\pi\) | ||||
−0.371625 | + | 0.928383i | \(0.621199\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.31401 | −0.232366 | −0.116183 | − | 0.993228i | \(-0.537066\pi\) | ||||
−0.116183 | + | 0.993228i | \(0.537066\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.37316 | 0.234504 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.3321 | −0.624315 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.3598 | −0.885210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.2992 | 0.967704 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.9531 | −1.03752 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.33608 | −0.317166 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.06511 | −0.0891161 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.30970 | 0.185632 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.28080 | −0.313026 | −0.156513 | − | 0.987676i | \(-0.550025\pi\) | ||||
−0.156513 | + | 0.987676i | \(0.550025\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.29538 | 0.227246 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.07770 | 0.260340 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5475 | 0.835791 | 0.417896 | − | 0.908495i | \(-0.362768\pi\) | ||||
0.417896 | + | 0.908495i | \(0.362768\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.8877 | 0.976823 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.59662 | 0.238424 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.2218 | −1.41273 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.416037 | 0.0176598 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.3433 | 1.37043 | 0.685215 | − | 0.728341i | \(-0.259708\pi\) | ||||
0.685215 | + | 0.728341i | \(0.259708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.20632 | 0.262500 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.29503 | 0.139116 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.8155 | −1.59373 | −0.796867 | − | 0.604155i | \(-0.793511\pi\) | ||||
−0.796867 | + | 0.604155i | \(0.793511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.9828 | 1.13518 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.3353 | −0.812007 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.04535 | −0.379201 | −0.189600 | − | 0.981861i | \(-0.560719\pi\) | ||||
−0.189600 | + | 0.981861i | \(0.560719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.5230 | −1.94693 | −0.973464 | − | 0.228842i | \(-0.926506\pi\) | ||||
−0.973464 | + | 0.228842i | \(0.926506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.04982 | 0.0856326 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.9157 | −0.622029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.5655 | −1.10593 | −0.552967 | − | 0.833203i | \(-0.686505\pi\) | ||||
−0.552967 | + | 0.833203i | \(0.686505\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.71630 | −0.154444 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.8136 | −1.48580 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.5525 | −0.934029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −71.6003 | −2.96031 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 46.8735 | 1.93467 | 0.967337 | − | 0.253492i | \(-0.0815793\pi\) | ||||
0.967337 | + | 0.253492i | \(0.0815793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.94378 | −0.203705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0896786 | 0.00368888 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.6191 | −1.79122 | −0.895612 | − | 0.444836i | \(-0.853262\pi\) | ||||
−0.895612 | + | 0.444836i | \(0.853262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −44.7770 | −1.83568 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.04662 | 0.0428353 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.7730 | 1.13477 | 0.567386 | − | 0.823452i | \(-0.307955\pi\) | ||||
0.567386 | + | 0.823452i | \(0.307955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.8823 | −0.443900 | −0.221950 | − | 0.975058i | \(-0.571242\pi\) | ||||
−0.221950 | + | 0.975058i | \(0.571242\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.1812 | −0.577503 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.9491 | −0.729734 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.6998 | −0.799588 | −0.399794 | − | 0.916605i | \(-0.630918\pi\) | ||||
−0.399794 | + | 0.916605i | \(0.630918\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.83408 | 0.0743207 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.82541 | 0.357038 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7591 | −0.474945 | −0.237473 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237473 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.54867 | 0.143096 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7062 | 0.793341 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.6273 | −1.19082 | −0.595412 | − | 0.803421i | \(-0.703011\pi\) | ||||
−0.595412 | + | 0.803421i | \(0.703011\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.45798 | −0.0986352 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.66463 | −0.226948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3684 | 0.534736 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.13661 | 0.0453917 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.24450 | −0.0894939 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.5798 | −1.65526 | −0.827632 | − | 0.561271i | \(-0.810312\pi\) | ||||
−0.827632 | + | 0.561271i | \(0.810312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.94213 | −0.196432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.4153 | 1.12763 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.1829 | −0.443081 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.39966 | −0.292726 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.84120 | 0.0727229 | 0.0363614 | − | 0.999339i | \(-0.488423\pi\) | ||||
0.0363614 | + | 0.999339i | \(0.488423\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.0244 | 0.513632 | 0.256816 | − | 0.966460i | \(-0.417327\pi\) | ||||
0.256816 | + | 0.966460i | \(0.417327\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.919472 | −0.0362042 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.1412 | −1.53880 | −0.769400 | − | 0.638768i | \(-0.779444\pi\) | ||||
−0.769400 | + | 0.638768i | \(0.779444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.9688 | 0.744589 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.62014 | −0.0634982 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.681012 | −0.0266500 | −0.0133250 | − | 0.999911i | \(-0.504242\pi\) | ||||
−0.0133250 | + | 0.999911i | \(0.504242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.3432 | 2.24058 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.8765 | 0.541373 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −51.0887 | −1.99013 | −0.995067 | − | 0.0992042i | \(-0.968370\pi\) | ||||
−0.995067 | + | 0.0992042i | \(0.968370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9346 | 1.39769 | 0.698846 | − | 0.715272i | \(-0.253697\pi\) | ||||
0.698846 | + | 0.715272i | \(0.253697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.54998 | −0.332054 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.4456 | −0.598955 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.09135 | −0.197138 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.609637 | −0.0235699 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.4693 | 0.751606 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3616 | −0.939071 | −0.469536 | − | 0.882914i | \(-0.655579\pi\) | ||||
−0.469536 | + | 0.882914i | \(0.655579\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.8864 | 0.534489 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.63011 | 0.254816 | 0.127408 | − | 0.991850i | \(-0.459334\pi\) | ||||
0.127408 | + | 0.991850i | \(0.459334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.10698 | −0.311117 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.24145 | 0.0475723 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7217 | −1.55817 | −0.779086 | − | 0.626917i | \(-0.784317\pi\) | ||||
−0.779086 | + | 0.626917i | \(0.784317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 74.0277 | 2.82845 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.30406 | 0.0497529 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 58.5194 | 2.22941 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2262 | −1.53028 | −0.765139 | − | 0.643865i | \(-0.777330\pi\) | ||||
−0.765139 | + | 0.643865i | \(0.777330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8282 | −0.639252 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.779475 | −0.0295672 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.1449 | −0.725164 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.266160 | 0.0100671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.9940 | −0.415238 | −0.207619 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207619 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.774229 | −0.0292006 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.30749 | −0.0492430 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0950 | 1.05662 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.57925 | 0.0593100 | 0.0296550 | − | 0.999560i | \(-0.490559\pi\) | ||||
0.0296550 | + | 0.999560i | \(0.490559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.4594 | −1.59235 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.49745 | 0.168431 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −60.9065 | −2.27778 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.92660 | 0.221333 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.6811 | −1.14421 | −0.572107 | − | 0.820179i | \(-0.693874\pi\) | ||||
−0.572107 | + | 0.820179i | \(0.693874\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −41.2727 | −1.53708 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.50847 | −0.130481 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.7638 | 1.06826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.2511 | −0.380192 | −0.190096 | − | 0.981766i | \(-0.560880\pi\) | ||||
−0.190096 | + | 0.981766i | \(0.560880\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.5549 | −0.872405 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.96050 | 0.183471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.81655 | 0.325647 | 0.162823 | − | 0.986655i | \(-0.447940\pi\) | ||||
0.162823 | + | 0.986655i | \(0.447940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.65675 | 0.0611102 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0632 | −0.444353 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.6509 | −1.38501 | −0.692505 | − | 0.721413i | \(-0.743493\pi\) | ||||
−0.692505 | + | 0.721413i | \(0.743493\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.94928 | −0.108344 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.6691 | 0.464785 | 0.232392 | − | 0.972622i | \(-0.425345\pi\) | ||||
0.232392 | + | 0.972622i | \(0.425345\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.0925 | −0.809407 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −45.7718 | −1.67470 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.47397 | 0.163475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.5008 | 1.00352 | 0.501760 | − | 0.865007i | \(-0.332686\pi\) | ||||
0.501760 | + | 0.865007i | \(0.332686\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.99023 | −0.145412 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −59.5190 | −2.16612 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0830 | 1.20242 | 0.601210 | − | 0.799091i | \(-0.294685\pi\) | ||||
0.601210 | + | 0.799091i | \(0.294685\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.03399 | −0.0375315 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.6329 | −1.00169 | −0.500845 | − | 0.865537i | \(-0.666977\pi\) | ||||
−0.500845 | + | 0.865537i | \(0.666977\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.70654 | −0.134186 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −57.2276 | −2.06907 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −49.2203 | −1.77724 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.70938 | −0.205885 | −0.102943 | − | 0.994687i | \(-0.532826\pi\) | ||||
−0.102943 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.667449 | 0.0240376 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.3190 | 0.946630 | 0.473315 | − | 0.880893i | \(-0.343057\pi\) | ||||
0.473315 | + | 0.880893i | \(0.343057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.4085 | −0.912700 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.253724 | −0.00910230 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.60394 | −0.236611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.29449 | −0.225235 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.74001 | 0.169394 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 62.5661 | 2.23308 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0879 | 0.894285 | 0.447143 | − | 0.894463i | \(-0.352442\pi\) | ||||
0.447143 | + | 0.894463i | \(0.352442\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.31366 | 0.153570 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4557 | −0.585098 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.5192 | −1.79399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.66970 | −0.307483 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0432 | −0.816232 | −0.408116 | − | 0.912930i | \(-0.633814\pi\) | ||||
−0.408116 | + | 0.912930i | \(0.633814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.05384 | 0.249547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.23972 | −0.255803 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.8040 | 0.416553 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.0512 | 0.495239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.92116 | 0.0676281 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.8340 | −1.36533 | −0.682666 | − | 0.730731i | \(-0.739179\pi\) | ||||
−0.682666 | + | 0.730731i | \(0.739179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.7626 | 0.377927 | 0.188963 | − | 0.981984i | \(-0.439487\pi\) | ||||
0.188963 | + | 0.981984i | \(0.439487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.31638 | −0.186454 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.3871 | −0.538985 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.71110 | 0.0598638 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43.6661 | 1.52582 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.7704 | 1.59740 | 0.798698 | − | 0.601732i | \(-0.205522\pi\) | ||||
0.798698 | + | 0.601732i | \(0.205522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.4088 | −0.641690 | −0.320845 | − | 0.947132i | \(-0.603967\pi\) | ||||
−0.320845 | + | 0.947132i | \(0.603967\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.84157 | 0.203377 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.1709 | −0.597092 | −0.298546 | − | 0.954395i | \(-0.596502\pi\) | ||||
−0.298546 | + | 0.954395i | \(0.596502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.60351 | 0.264081 | 0.132040 | − | 0.991244i | \(-0.457847\pi\) | ||||
0.132040 | + | 0.991244i | \(0.457847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.74886 | 0.199426 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.93807 | −0.309686 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 80.8483 | 2.79787 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.18709 | −0.144727 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.3593 | 0.910022 | 0.455011 | − | 0.890486i | \(-0.349635\pi\) | ||||
0.455011 | + | 0.890486i | \(0.349635\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.1818 | −0.661440 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.10627 | 0.0381020 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 109.088 | 3.75274 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9464 | 0.376123 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.75001 | −0.163020 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.704330 | 0.0241441 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0149 | 1.06193 | 0.530964 | − | 0.847394i | \(-0.321830\pi\) | ||||
0.530964 | + | 0.847394i | \(0.321830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.7404 | −0.675107 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.68851 | −0.262634 | −0.131317 | − | 0.991340i | \(-0.541921\pi\) | ||||
−0.131317 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.9513 | −1.19252 | −0.596262 | − | 0.802790i | \(-0.703348\pi\) | ||||
−0.596262 | + | 0.802790i | \(0.703348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.16419 | −0.0737554 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1875 | −0.789310 | −0.394655 | − | 0.918829i | \(-0.629136\pi\) | ||||
−0.394655 | + | 0.918829i | \(0.629136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.9652 | −1.93688 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.50071 | −0.0849286 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.1179 | −1.22522 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.3017 | 1.06062 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.3612 | −0.350673 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −36.1445 | −1.22191 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.6000 | 0.931987 | 0.465993 | − | 0.884788i | \(-0.345697\pi\) | ||||
0.465993 | + | 0.884788i | \(0.345697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.92204 | 0.0985580 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.22776 | −0.176128 | −0.0880638 | − | 0.996115i | \(-0.528068\pi\) | ||||
−0.0880638 | + | 0.996115i | \(0.528068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3174 | 0.717389 | 0.358695 | − | 0.933455i | \(-0.383222\pi\) | ||||
0.358695 | + | 0.933455i | \(0.383222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.29203 | 0.245119 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.36692 | 0.247357 | 0.123678 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123678 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3293 | −0.581207 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.0209 | −0.704226 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.43319 | 0.0814236 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.5097 | 1.01983 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.68301 | 0.0895831 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.67296 | −0.289259 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.7725 | 1.55822 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.560748 | 0.0186605 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −78.2333 | −2.60056 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.1488 | −1.56555 | −0.782775 | − | 0.622305i | \(-0.786196\pi\) | ||||
−0.782775 | + | 0.622305i | \(0.786196\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 35.9070 | 1.19096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.1113 | −0.533790 | −0.266895 | − | 0.963726i | \(-0.585998\pi\) | ||||
−0.266895 | + | 0.963726i | \(0.585998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.9356 | −1.28858 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.48447 | 0.247429 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.9712 | −1.15485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.3023 | −0.768673 | −0.384336 | − | 0.923193i | \(-0.625570\pi\) | ||||
−0.384336 | + | 0.923193i | \(0.625570\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.16096 | 0.0712060 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.3330 | 0.537607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.97914 | −0.130833 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.7489 | −1.73250 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0596 | 0.428470 | 0.214235 | − | 0.976782i | \(-0.431274\pi\) | ||||
0.214235 | + | 0.976782i | \(0.431274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.08314 | −0.101046 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.88629 | −0.127231 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48.6805 | −1.59202 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.6979 | 1.75423 | 0.877117 | − | 0.480277i | \(-0.159464\pi\) | ||||
0.877117 | + | 0.480277i | \(0.159464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.25964 | −0.171642 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.4900 | 1.09174 | 0.545871 | − | 0.837869i | \(-0.316199\pi\) | ||||
0.545871 | + | 0.837869i | \(0.316199\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00772 | 0.195638 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0815 | −0.425542 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21.3996 | 0.695394 | 0.347697 | − | 0.937607i | \(-0.386964\pi\) | ||||
0.347697 | + | 0.937607i | \(0.386964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.6291 | −0.994261 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.38982 | 0.0774952 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.2342 | −1.07656 | −0.538281 | − | 0.842765i | \(-0.680926\pi\) | ||||
−0.538281 | + | 0.842765i | \(0.680926\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.2839 | −0.979963 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.99397 | 0.0644558 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.1465 | −1.45786 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3387 | −0.752862 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.71799 | 0.184260 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54.9042 | 1.76743 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.816852 | 0.0262682 | 0.0131341 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131341 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.35725 | −0.0757259 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.2870 | −0.843591 | −0.421796 | − | 0.906691i | \(-0.638600\pi\) | ||||
−0.421796 | + | 0.906691i | \(0.638600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.475369 | 0.0152396 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.1578 | −0.485437 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.6146 | 1.26738 | 0.633691 | − | 0.773586i | \(-0.281539\pi\) | ||||
0.633691 | + | 0.773586i | \(0.281539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.15844 | −0.196825 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.73717 | −0.151246 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.3907 | 0.873626 | 0.436813 | − | 0.899552i | \(-0.356107\pi\) | ||||
0.436813 | + | 0.899552i | \(0.356107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.32490 | −0.0422149 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.797386 | 0.0253811 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55662 | −0.0494976 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.6080 | −1.35349 | −0.676743 | − | 0.736219i | \(-0.736609\pi\) | ||||
−0.676743 | + | 0.736219i | \(0.736609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.54547 | 0.144246 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.4626 | −0.490199 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.4457 | −0.774204 | −0.387102 | − | 0.922037i | \(-0.626524\pi\) | ||||
−0.387102 | + | 0.922037i | \(0.626524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.655726 | −0.0207462 |
(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 | 4024.2.a.f.1.15 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.19 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.15 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.19 | 33 | 4.3 | odd | 2 |