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: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
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 | ||||||||
\(3\) | −2.20855 | −1.27510 | −0.637552 | − | 0.770407i | \(-0.720053\pi\) | ||||
−0.637552 | + | 0.770407i | \(0.720053\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.60744 | 0.718869 | 0.359435 | − | 0.933170i | \(-0.382970\pi\) | ||||
0.359435 | + | 0.933170i | \(0.382970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.65561 | 1.00373 | 0.501864 | − | 0.864947i | \(-0.332648\pi\) | ||||
0.501864 | + | 0.864947i | \(0.332648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.87768 | 0.625892 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.47814 | 1.35021 | 0.675105 | − | 0.737721i | \(-0.264098\pi\) | ||||
0.675105 | + | 0.737721i | \(0.264098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.08744 | 0.301601 | 0.150800 | − | 0.988564i | \(-0.451815\pi\) | ||||
0.150800 | + | 0.988564i | \(0.451815\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.55011 | −0.916634 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.02699 | 0.734154 | 0.367077 | − | 0.930191i | \(-0.380359\pi\) | ||||
0.367077 | + | 0.930191i | \(0.380359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.18417 | −1.18933 | −0.594665 | − | 0.803973i | \(-0.702715\pi\) | ||||
−0.594665 | + | 0.803973i | \(0.702715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.86504 | −1.27986 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.23537 | 1.09165 | 0.545825 | − | 0.837899i | \(-0.316216\pi\) | ||||
0.545825 | + | 0.837899i | \(0.316216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.41613 | −0.483227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.47870 | 0.477026 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.98529 | 0.554354 | 0.277177 | − | 0.960819i | \(-0.410601\pi\) | ||||
0.277177 | + | 0.960819i | \(0.410601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.02345 | 0.722633 | 0.361317 | − | 0.932443i | \(-0.382327\pi\) | ||||
0.361317 | + | 0.932443i | \(0.382327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.89019 | −1.72166 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.26874 | 0.721549 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.78179 | 0.621722 | 0.310861 | − | 0.950455i | \(-0.399383\pi\) | ||||
0.310861 | + | 0.950455i | \(0.399383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.40166 | −0.384573 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92897 | 1.08212 | 0.541061 | − | 0.840983i | \(-0.318023\pi\) | ||||
0.541061 | + | 0.840983i | \(0.318023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.848422 | −0.129383 | −0.0646916 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646916 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.01826 | 0.449935 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.09493 | 1.03490 | 0.517451 | − | 0.855713i | \(-0.326881\pi\) | ||||
0.517451 | + | 0.855713i | \(0.326881\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0522760 | 0.00746799 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.68525 | −0.936123 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4675 | −1.43783 | −0.718914 | − | 0.695099i | \(-0.755360\pi\) | ||||
−0.718914 | + | 0.695099i | \(0.755360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.19835 | 0.970625 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.4495 | 1.51652 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0083 | 1.43315 | 0.716576 | − | 0.697509i | \(-0.245708\pi\) | ||||
0.716576 | + | 0.697509i | \(0.245708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.16946 | 0.917955 | 0.458978 | − | 0.888448i | \(-0.348216\pi\) | ||||
0.458978 | + | 0.888448i | \(0.348216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.98638 | 0.628225 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.74799 | 0.216812 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.97542 | −1.09652 | −0.548261 | − | 0.836307i | \(-0.684710\pi\) | ||||
−0.548261 | + | 0.836307i | \(0.684710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.5626 | −1.39197 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.41486 | 0.761303 | 0.380652 | − | 0.924718i | \(-0.375700\pi\) | ||||
0.380652 | + | 0.924718i | \(0.375700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.477645 | −0.0559041 | −0.0279520 | − | 0.999609i | \(-0.508899\pi\) | ||||
−0.0279520 | + | 0.999609i | \(0.508899\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.33614 | 0.616165 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.8922 | 1.35524 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.29507 | 0.933268 | 0.466634 | − | 0.884450i | \(-0.345466\pi\) | ||||
0.466634 | + | 0.884450i | \(0.345466\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1074 | −1.23415 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.54030 | −0.827655 | −0.413828 | − | 0.910355i | \(-0.635808\pi\) | ||||
−0.413828 | + | 0.910355i | \(0.635808\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.86571 | 0.527761 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.59315 | −0.706859 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.6302 | −1.65680 | −0.828398 | − | 0.560139i | \(-0.810748\pi\) | ||||
−0.828398 | + | 0.560139i | \(0.810748\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.88781 | 0.302725 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.88598 | −0.921433 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.33325 | −0.854973 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.09371 | −0.517188 | −0.258594 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258594 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.40851 | 0.845087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.33734 | 0.133070 | 0.0665351 | − | 0.997784i | \(-0.478806\pi\) | ||||
0.0665351 | + | 0.997784i | \(0.478806\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.79026 | −0.274932 | −0.137466 | − | 0.990506i | \(-0.543896\pi\) | ||||
−0.137466 | + | 0.990506i | \(0.543896\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.42771 | −0.920050 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5180 | 1.79020 | 0.895102 | − | 0.445861i | \(-0.147102\pi\) | ||||
0.895102 | + | 0.445861i | \(0.147102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.24626 | −0.694066 | −0.347033 | − | 0.937853i | \(-0.612811\pi\) | ||||
−0.347033 | + | 0.937853i | \(0.612811\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.35225 | −0.792761 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.63779 | −0.718503 | −0.359251 | − | 0.933241i | \(-0.616968\pi\) | ||||
−0.359251 | + | 0.933241i | \(0.616968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.41555 | 0.784754 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.04186 | 0.188770 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.03852 | 0.736890 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05376 | 0.823069 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.3029 | −1.37982 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9210 | −1.06625 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.542716 | −0.0481583 | −0.0240791 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240791 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.87378 | 0.164977 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.11006 | 0.184357 | 0.0921783 | − | 0.995743i | \(-0.470617\pi\) | ||||
0.0921783 | + | 0.995743i | \(0.470617\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.7671 | −1.19376 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.98437 | 0.342920 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.8806 | 0.929595 | 0.464797 | − | 0.885417i | \(-0.346127\pi\) | ||||
0.464797 | + | 0.885417i | \(0.346127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.9272 | −1.43575 | −0.717874 | − | 0.696173i | \(-0.754885\pi\) | ||||
−0.717874 | + | 0.696173i | \(0.754885\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.6695 | −1.31961 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.86970 | 0.407225 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.79867 | 0.398508 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.115454 | −0.00952248 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.63520 | 0.297807 | 0.148903 | − | 0.988852i | \(-0.452426\pi\) | ||||
0.148903 | + | 0.988852i | \(0.452426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.15497 | −0.0939898 | −0.0469949 | − | 0.998895i | \(-0.514964\pi\) | ||||
−0.0469949 | + | 0.998895i | \(0.514964\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.68372 | 0.459501 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.46746 | 0.519479 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6115 | −1.08631 | −0.543157 | − | 0.839631i | \(-0.682771\pi\) | ||||
−0.543157 | + | 0.839631i | \(0.682771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.1181 | 1.83338 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.9031 | 1.09572 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.2232 | −0.957394 | −0.478697 | − | 0.877980i | \(-0.658891\pi\) | ||||
−0.478697 | + | 0.877980i | \(0.658891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.8979 | −1.23765 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.1049 | 1.47838 | 0.739192 | − | 0.673494i | \(-0.235207\pi\) | ||||
0.739192 | + | 0.673494i | \(0.235207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8175 | −0.909037 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.73420 | −0.744393 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.6005 | 1.11006 | 0.555029 | − | 0.831831i | \(-0.312707\pi\) | ||||
0.555029 | + | 0.831831i | \(0.312707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.41632 | −0.485028 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.3122 | −1.82742 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.3446 | −1.52062 | −0.760312 | − | 0.649558i | \(-0.774954\pi\) | ||||
−0.760312 | + | 0.649558i | \(0.774954\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8148 | −0.952517 | −0.476259 | − | 0.879305i | \(-0.658007\pi\) | ||||
−0.476259 | + | 0.879305i | \(0.658007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.8341 | −1.17049 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.07900 | 0.446937 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5553 | 0.991262 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.58247 | 0.478804 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.797137 | 0.0576788 | 0.0288394 | − | 0.999584i | \(-0.490819\pi\) | ||||
0.0288394 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.71354 | −0.195325 | −0.0976623 | − | 0.995220i | \(-0.531137\pi\) | ||||
−0.0976623 | + | 0.995220i | \(0.531137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.86052 | −0.276458 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.43993 | 0.458826 | 0.229413 | − | 0.973329i | \(-0.426319\pi\) | ||||
0.229413 | + | 0.973329i | \(0.426319\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.5434 | −1.38540 | −0.692699 | − | 0.721227i | \(-0.743579\pi\) | ||||
−0.692699 | + | 0.721227i | \(0.743579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.8226 | 1.39818 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.92776 | 0.556420 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1379 | 0.777905 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.83034 | 0.683256 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −23.2155 | −1.60585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.9163 | 1.57762 | 0.788812 | − | 0.614635i | \(-0.210697\pi\) | ||||
0.788812 | + | 0.614635i | \(0.210697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.1675 | −0.970742 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.36379 | −0.0930096 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6847 | 0.725327 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.05490 | 0.0712836 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.29167 | 0.221421 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.5578 | 0.707000 | 0.353500 | − | 0.935434i | \(-0.384991\pi\) | ||||
0.353500 | + | 0.935434i | \(0.384991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.53672 | −0.302448 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2185 | −0.744601 | −0.372301 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372301 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.718830 | −0.0475016 | −0.0237508 | − | 0.999718i | \(-0.507561\pi\) | ||||
−0.0237508 | + | 0.999718i | \(0.507561\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.2645 | −1.72808 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.584824 | −0.0383131 | −0.0191566 | − | 0.999816i | \(-0.506098\pi\) | ||||
−0.0191566 | + | 0.999816i | \(0.506098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4047 | 0.743960 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18.3200 | −1.19001 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.9018 | 1.48140 | 0.740698 | − | 0.671838i | \(-0.234495\pi\) | ||||
0.740698 | + | 0.671838i | \(0.234495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.7423 | 0.820806 | 0.410403 | − | 0.911904i | \(-0.365388\pi\) | ||||
0.410403 | + | 0.911904i | \(0.365388\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.0950 | 1.09665 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.0840305 | 0.00536851 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.63746 | −0.358703 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.6531 | 1.05535 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.80846 | −0.177269 | −0.0886343 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886343 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.4447 | 1.47396 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.7461 | −0.672950 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4565 | −1.52556 | −0.762778 | − | 0.646660i | \(-0.776165\pi\) | ||||
−0.762778 | + | 0.646660i | \(0.776165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0430 | 0.624039 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.60541 | 0.346966 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.3538 | 1.56338 | 0.781691 | − | 0.623665i | \(-0.214357\pi\) | ||||
0.781691 | + | 0.623665i | \(0.214357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.8260 | −1.03361 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.5200 | 2.11259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.93401 | 0.239861 | 0.119930 | − | 0.992782i | \(-0.461733\pi\) | ||||
0.119930 | + | 0.992782i | \(0.461733\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8838 | −0.964870 | −0.482435 | − | 0.875932i | \(-0.660248\pi\) | ||||
−0.482435 | + | 0.875932i | \(0.660248\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.37787 | −0.386006 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.8198 | −0.652458 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.5110 | 1.29247 | 0.646235 | − | 0.763139i | \(-0.276343\pi\) | ||||
0.646235 | + | 0.763139i | \(0.276343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.55475 | 0.452291 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6096 | 1.70670 | 0.853352 | − | 0.521336i | \(-0.174566\pi\) | ||||
0.853352 | + | 0.521336i | \(0.174566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.41164 | 0.559464 | 0.279732 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279732 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.4044 | 1.09018 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.4006 | 1.08616 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.83731 | −0.461019 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.2497 | 0.659469 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.1645 | −0.593819 | −0.296910 | − | 0.954906i | \(-0.595956\pi\) | ||||
−0.296910 | + | 0.954906i | \(0.595956\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.6951 | 1.03025 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.1000 | 0.644086 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.69314 | 0.329243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.25308 | −0.129865 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.95358 | −0.169679 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.5245 | 0.659890 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0429 | 0.858546 | 0.429273 | − | 0.903175i | \(-0.358770\pi\) | ||||
0.429273 | + | 0.903175i | \(0.358770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.16242 | 0.350568 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3959 | 0.646204 | 0.323102 | − | 0.946364i | \(-0.395274\pi\) | ||||
0.323102 | + | 0.946364i | \(0.395274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.93769 | 0.279095 | 0.139547 | − | 0.990215i | \(-0.455435\pi\) | ||||
0.139547 | + | 0.990215i | \(0.455435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.01531 | 0.451612 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.4712 | −1.43060 | −0.715302 | − | 0.698816i | \(-0.753711\pi\) | ||||
−0.715302 | + | 0.698816i | \(0.753711\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3685 | 0.748495 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −40.8979 | −2.28270 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6924 | −0.873151 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.62740 | −0.145742 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.0037 | 0.885006 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.8414 | 1.03876 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.7684 | 1.47132 | 0.735662 | − | 0.677349i | \(-0.236871\pi\) | ||||
0.735662 | + | 0.677349i | \(0.236871\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.10098 | 0.389131 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.4275 | −0.788256 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4559 | 0.678517 | 0.339258 | − | 0.940693i | \(-0.389824\pi\) | ||||
0.339258 | + | 0.940693i | \(0.389824\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.8684 | 0.916166 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.0176 | 0.975707 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4505 | −0.996231 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.5861 | −1.00064 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6481 | −0.625300 | −0.312650 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312650 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.85226 | 0.473851 | 0.236925 | − | 0.971528i | \(-0.423860\pi\) | ||||
0.236925 | + | 0.971528i | \(0.423860\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.69543 | 0.143872 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.3446 | −1.34896 | −0.674478 | − | 0.738295i | \(-0.735631\pi\) | ||||
−0.674478 | + | 0.738295i | \(0.735631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3115 | 0.547278 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.7534 | −0.939612 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.44745 | 0.287506 | 0.143753 | − | 0.989614i | \(-0.454083\pi\) | ||||
0.143753 | + | 0.989614i | \(0.454083\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.87563 | 0.414507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.9957 | −1.04950 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.767785 | −0.0401877 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.5424 | 1.90750 | 0.953749 | − | 0.300605i | \(-0.0971886\pi\) | ||||
0.953749 | + | 0.300605i | \(0.0971886\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.0104 | 0.677292 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.7977 | −1.44319 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.2974 | 0.740290 | 0.370145 | − | 0.928974i | \(-0.379308\pi\) | ||||
0.370145 | + | 0.928974i | \(0.379308\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26.3281 | 1.35958 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.24631 | 0.167194 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.8729 | 0.969438 | 0.484719 | − | 0.874670i | \(-0.338922\pi\) | ||||
0.484719 | + | 0.874670i | \(0.338922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.19861 | 0.0614069 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.8179 | 0.910450 | 0.455225 | − | 0.890376i | \(-0.349559\pi\) | ||||
0.455225 | + | 0.890376i | \(0.349559\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.1160 | 0.974243 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.59306 | −0.0809799 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.54769 | −0.179875 | −0.0899375 | − | 0.995947i | \(-0.528667\pi\) | ||||
−0.0899375 | + | 0.995947i | \(0.528667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8474 | 0.801439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.66016 | −0.235074 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.3338 | 0.670898 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.3852 | −0.972917 | −0.486458 | − | 0.873704i | \(-0.661711\pi\) | ||||
−0.486458 | + | 0.873704i | \(0.661711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.4054 | 1.52217 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.71381 | −0.385209 | −0.192605 | − | 0.981276i | \(-0.561693\pi\) | ||||
−0.192605 | + | 0.981276i | \(0.561693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.37525 | 0.217947 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −17.8544 | −0.887193 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9354 | 0.839456 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.06419 | 0.299855 | 0.149927 | − | 0.988697i | \(-0.452096\pi\) | ||||
0.149927 | + | 0.988697i | \(0.452096\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −24.0304 | −1.18533 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.2337 | 1.43849 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.1206 | −0.594976 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.3845 | 1.83073 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.0131139 | 0.000640656 0 | 0.000320328 | − | 1.00000i | \(-0.499898\pi\) | ||||
0.000320328 | 1.00000i | \(0.499898\pi\) | ||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.58321 | −0.467057 | −0.233529 | − | 0.972350i | \(-0.575027\pi\) | ||||
−0.233529 | + | 0.972350i | \(0.575027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.3220 | 0.647738 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.31362 | −0.354763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.0393 | 0.921377 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.7550 | −0.519254 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.7659 | 0.952090 | 0.476045 | − | 0.879421i | \(-0.342070\pi\) | ||||
0.476045 | + | 0.879421i | \(0.342070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0026 | 1.10544 | 0.552718 | − | 0.833368i | \(-0.313591\pi\) | ||||
0.552718 | + | 0.833368i | \(0.313591\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.5981 | −0.508140 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.1411 | −1.29833 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.2747 | 1.20630 | 0.603148 | − | 0.797629i | \(-0.293913\pi\) | ||||
0.603148 | + | 0.797629i | \(0.293913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0981574 | 0.00467416 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85051 | 0.135432 | 0.0677159 | − | 0.997705i | \(-0.478429\pi\) | ||||
0.0677159 | + | 0.997705i | \(0.478429\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.1246 | −1.19102 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.02850 | −0.379735 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5114 | −0.873605 | −0.436802 | − | 0.899557i | \(-0.643889\pi\) | ||||
−0.436802 | + | 0.899557i | \(0.643889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.0289 | 1.46109 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.55080 | 0.119847 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.64199 | 0.217620 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.1170 | −1.45559 | −0.727796 | − | 0.685793i | \(-0.759455\pi\) | ||||
−0.727796 | + | 0.685793i | \(0.759455\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50301 | 0.350211 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8861 | 1.06591 | 0.532955 | − | 0.846143i | \(-0.321081\pi\) | ||||
0.532955 | + | 0.846143i | \(0.321081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8132 | −1.06022 | −0.530110 | − | 0.847929i | \(-0.677850\pi\) | ||||
−0.530110 | + | 0.847929i | \(0.677850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.2837 | −0.662390 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.2916 | −1.67937 | −0.839687 | − | 0.543071i | \(-0.817261\pi\) | ||||
−0.839687 | + | 0.543071i | \(0.817261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.8352 | −1.10061 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0615 | 1.38516 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.79935 | −0.174694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.5257 | 0.574716 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −19.6547 | −0.899925 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.2731 | 0.880612 | 0.440306 | − | 0.897848i | \(-0.354870\pi\) | ||||
0.440306 | + | 0.897848i | \(0.354870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.11246 | 0.187512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.7057 | −1.39716 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.18784 | −0.371791 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.66094 | 0.211208 | 0.105604 | − | 0.994408i | \(-0.466322\pi\) | ||||
0.105604 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.9955 | 1.22078 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.3204 | −1.41347 | −0.706735 | − | 0.707478i | \(-0.749833\pi\) | ||||
−0.706735 | + | 0.707478i | \(0.749833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.03644 | 0.406981 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.5162 | 0.607507 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.0354 | 0.764141 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6492 | −1.05868 | −0.529342 | − | 0.848409i | \(-0.677561\pi\) | ||||
−0.529342 | + | 0.848409i | \(0.677561\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.1942 | −1.88510 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.5488 | 1.45128 | 0.725639 | − | 0.688076i | \(-0.241544\pi\) | ||||
0.725639 | + | 0.688076i | \(0.241544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.14969 | 0.0956602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.0995 | 1.15912 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.74314 | −0.298884 | −0.149442 | − | 0.988770i | \(-0.547748\pi\) | ||||
−0.149442 | + | 0.988770i | \(0.547748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.26844 | −0.0561124 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.8500 | −0.567342 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.48518 | −0.197640 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.7721 | 1.39734 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.2460 | −1.41544 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.4860 | 1.33562 | 0.667808 | − | 0.744334i | \(-0.267233\pi\) | ||||
0.667808 | + | 0.744334i | \(0.267233\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3799 | −1.54705 | −0.773527 | − | 0.633764i | \(-0.781509\pi\) | ||||
−0.773527 | + | 0.633764i | \(0.781509\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.1707 | 0.618461 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.1790 | 0.530524 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.40911 | 0.191701 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.6700 | 0.896999 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.53482 | 0.326369 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.7666 | 1.28692 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.9319 | 1.93895 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.234099 | 0.0100834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.92707 | 0.0828512 | 0.0414256 | − | 0.999142i | \(-0.486810\pi\) | ||||
0.0414256 | + | 0.999142i | \(0.486810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 28.3021 | 1.21456 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.6479 | −0.498943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.8308 | −1.83131 | −0.915656 | − | 0.401963i | \(-0.868328\pi\) | ||||
−0.915656 | + | 0.401963i | \(0.868328\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.4619 | 0.574541 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.4762 | −0.659310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.0285 | 0.936747 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.4258 | −0.569891 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.70629 | −0.284155 | −0.142077 | − | 0.989856i | \(-0.545378\pi\) | ||||
−0.142077 | + | 0.989856i | \(0.545378\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.922606 | −0.0390221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.9375 | −1.26396 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.5296 | 1.45525 | 0.727624 | − | 0.685976i | \(-0.240624\pi\) | ||||
0.727624 | + | 0.685976i | \(0.240624\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.2773 | −0.516510 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.4968 | −1.23875 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.7919 | 1.03933 | 0.519665 | − | 0.854370i | \(-0.326057\pi\) | ||||
0.519665 | + | 0.854370i | \(0.326057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.782690 | 0.0327545 | 0.0163773 | − | 0.999866i | \(-0.494787\pi\) | ||||
0.0163773 | + | 0.999866i | \(0.494787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.76051 | −0.0735466 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.6494 | −0.527515 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1602 | 1.75515 | 0.877576 | − | 0.479437i | \(-0.159159\pi\) | ||||
0.877576 | + | 0.479437i | \(0.159159\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.99297 | 0.249059 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.0241 | −0.830740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.8752 | −1.94137 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.28216 | 0.135701 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.15934 | −0.336772 | −0.168386 | − | 0.985721i | \(-0.553855\pi\) | ||||
−0.168386 | + | 0.985721i | \(0.553855\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.8583 | −0.859450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.2229 | −0.585051 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.2316 | 1.20040 | 0.600199 | − | 0.799851i | \(-0.295088\pi\) | ||||
0.600199 | + | 0.799851i | \(0.295088\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9214 | 0.529728 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 43.1626 | 1.76653 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.45872 | −0.345614 | −0.172807 | − | 0.984956i | \(-0.555284\pi\) | ||||
−0.172807 | + | 0.984956i | \(0.555284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7306 | −0.478499 | −0.239250 | − | 0.970958i | \(-0.576901\pi\) | ||||
−0.239250 | + | 0.970958i | \(0.576901\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.8529 | −0.686305 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.5534 | 0.591679 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.54902 | 0.144050 | 0.0720252 | − | 0.997403i | \(-0.477054\pi\) | ||||
0.0720252 | + | 0.997403i | \(0.477054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.5088 | −0.709494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.71530 | 0.312128 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.42995 | 0.340483 | 0.170241 | − | 0.985402i | \(-0.445545\pi\) | ||||
0.170241 | + | 0.985402i | \(0.445545\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.5986 | −0.991910 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.6871 | −1.15490 | −0.577449 | − | 0.816427i | \(-0.695952\pi\) | ||||
−0.577449 | + | 0.816427i | \(0.695952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2215 | −1.01374 | −0.506868 | − | 0.862024i | \(-0.669197\pi\) | ||||
−0.506868 | + | 0.862024i | \(0.669197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9769 | 0.520746 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −41.5077 | −1.66297 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.08162 | −0.283265 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 51.2724 | 2.04762 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.4474 | 0.456439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6730 | 1.22107 | 0.610536 | − | 0.791989i | \(-0.290954\pi\) | ||||
0.610536 | + | 0.791989i | \(0.290954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.6117 | −2.01164 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.872384 | −0.0346195 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0568469 | 0.00225235 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.0450 | 0.476494 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.3878 | −1.31874 | −0.659370 | − | 0.751819i | \(-0.729177\pi\) | ||||
−0.659370 | + | 0.751819i | \(0.729177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.72479 | −0.265200 | −0.132600 | − | 0.991170i | \(-0.542333\pi\) | ||||
−0.132600 | + | 0.991170i | \(0.542333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.01199 | 0.118597 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2355 | −0.402399 | −0.201200 | − | 0.979550i | \(-0.564484\pi\) | ||||
−0.201200 | + | 0.979550i | \(0.564484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.2965 | 1.93506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.5977 | −0.924868 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.4659 | 0.879158 | 0.439579 | − | 0.898204i | \(-0.355128\pi\) | ||||
0.439579 | + | 0.898204i | \(0.355128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.39179 | 0.132528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.896862 | −0.0349899 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.6052 | −0.413120 | −0.206560 | − | 0.978434i | \(-0.566227\pi\) | ||||
−0.206560 | + | 0.978434i | \(0.566227\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.705434 | 0.0274382 | 0.0137191 | − | 0.999906i | \(-0.495633\pi\) | ||||
0.0137191 | + | 0.999906i | \(0.495633\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.26980 | −0.282336 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.1299 | −0.858160 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6291 | 0.605161 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.3173 | −0.901499 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.1059 | 1.23943 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8397 | 1.22733 | 0.613665 | − | 0.789567i | \(-0.289695\pi\) | ||||
0.613665 | + | 0.789567i | \(0.289695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.98888 | −0.230512 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0631 | 1.57818 | 0.789091 | − | 0.614277i | \(-0.210552\pi\) | ||||
0.789091 | + | 0.614277i | \(0.210552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.5269 | −0.519116 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.7767 | 0.949444 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.7471 | −0.908657 | −0.454328 | − | 0.890834i | \(-0.650121\pi\) | ||||
−0.454328 | + | 0.890834i | \(0.650121\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.4900 | 0.668257 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.58757 | 0.0605696 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3828 | −0.433650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.5998 | 1.73470 | 0.867349 | − | 0.497700i | \(-0.165822\pi\) | ||||
0.867349 | + | 0.497700i | \(0.165822\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22.3297 | 0.848236 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.2095 | −1.03211 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.9739 | 0.794444 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.29161 | 0.0488532 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.9376 | −0.601956 | −0.300978 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300978 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.6054 | −0.739433 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.1878 | −0.948627 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.55146 | 0.133566 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.0498 | 1.27877 | 0.639384 | − | 0.768888i | \(-0.279190\pi\) | ||||
0.639384 | + | 0.768888i | \(0.279190\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.5755 | 0.584126 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.0643 | 0.788863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.82776 | 0.292742 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −50.5798 | −1.88894 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.0650 | −0.785591 | −0.392795 | − | 0.919626i | \(-0.628492\pi\) | ||||
−0.392795 | + | 0.919626i | \(0.628492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.40984 | −0.275957 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.1420 | −1.04661 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.21285 | −0.267879 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.8528 | 1.58932 | 0.794661 | − | 0.607053i | \(-0.207649\pi\) | ||||
0.794661 | + | 0.607053i | \(0.207649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.43305 | −0.164187 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.56817 | −0.0949871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0540 | 1.03620 | 0.518098 | − | 0.855321i | \(-0.326640\pi\) | ||||
0.518098 | + | 0.855321i | \(0.326640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.185585 | −0.00684542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.1932 | −1.48054 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0444 | −0.921275 | −0.460637 | − | 0.887588i | \(-0.652379\pi\) | ||||
−0.460637 | + | 0.887588i | \(0.652379\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.4506 | 0.457384 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.425752 | −0.0156193 | −0.00780966 | − | 0.999970i | \(-0.502486\pi\) | ||||
−0.00780966 | + | 0.999970i | \(0.502486\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.84336 | 0.214084 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1583 | −0.518023 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.1767 | 1.79688 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.20262 | 0.226036 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.85654 | −0.0675664 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.3086 | 1.10159 | 0.550793 | − | 0.834642i | \(-0.314325\pi\) | ||||
0.550793 | + | 0.834642i | \(0.314325\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −51.7788 | −1.87945 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.338351 | 0.0122652 | 0.00613260 | − | 0.999981i | \(-0.498048\pi\) | ||||
0.00613260 | + | 0.999981i | \(0.498048\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.2433 | −0.696652 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.13624 | 0.330321 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.9708 | 0.432240 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2516 | −1.30727 | −0.653633 | − | 0.756812i | \(-0.726756\pi\) | ||||
−0.653633 | + | 0.756812i | \(0.726756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 54.0134 | 1.94524 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.6655 | 0.743288 | 0.371644 | − | 0.928375i | \(-0.378794\pi\) | ||||
0.371644 | + | 0.928375i | \(0.378794\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.72120 | −0.349196 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22.1803 | −0.795715 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.9209 | −1.28700 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7266 | 1.02792 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.39964 | 0.264441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.8796 | −0.780917 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.2909 | 0.509415 | 0.254707 | − | 0.967018i | \(-0.418021\pi\) | ||||
0.254707 | + | 0.967018i | \(0.418021\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −55.9951 | −1.99348 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.2830 | −0.721181 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.79634 | 0.276856 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 37.1609 | 1.31796 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.90991 | 0.0676523 | 0.0338262 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338262 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.4763 | 0.759777 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.3485 | −1.03698 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.13896 | −0.0754823 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.3484 | 0.787679 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.68844 | −0.305848 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.0175 | −0.422511 | −0.211256 | − | 0.977431i | \(-0.567755\pi\) | ||||
−0.211256 | + | 0.977431i | \(0.567755\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.607304 | 0.0213253 | 0.0106627 | − | 0.999943i | \(-0.496606\pi\) | ||||
0.0106627 | + | 0.999943i | \(0.496606\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.0800 | 1.23031 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.6480 | −0.688241 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.39836 | 0.153879 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.42238 | 0.189473 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.1372 | 1.54040 | 0.770200 | − | 0.637802i | \(-0.220156\pi\) | ||||
0.770200 | + | 0.637802i | \(0.220156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.9532 | 1.60183 | 0.800913 | − | 0.598780i | \(-0.204348\pi\) | ||||
0.800913 | + | 0.598780i | \(0.204348\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.8960 | 0.831953 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.6020 | −1.55096 | −0.775482 | − | 0.631370i | \(-0.782493\pi\) | ||||
−0.775482 | + | 0.631370i | \(0.782493\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.83199 | −0.341479 | −0.170739 | − | 0.985316i | \(-0.554616\pi\) | ||||
−0.170739 | + | 0.985316i | \(0.554616\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −47.5080 | −1.64803 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.158239 | 0.00548266 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.7101 | 1.06277 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.97294 | 0.344715 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.6718 | 0.920814 | 0.460407 | − | 0.887708i | \(-0.347704\pi\) | ||||
0.460407 | + | 0.887708i | \(0.347704\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0881 | −0.692692 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −63.1856 | −2.17623 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.9959 | −0.653479 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.0433 | 0.826137 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.7861 | −0.713376 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7991 | 0.678703 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.61905 | −0.0896745 | −0.0448373 | − | 0.998994i | \(-0.514277\pi\) | ||||
−0.0448373 | + | 0.998994i | \(0.514277\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.6472 | −0.535121 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.6206 | −0.396952 | −0.198476 | − | 0.980106i | \(-0.563599\pi\) | ||||
−0.198476 | + | 0.980106i | \(0.563599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.3272 | −1.13711 | −0.568554 | − | 0.822646i | \(-0.692497\pi\) | ||||
−0.568554 | + | 0.822646i | \(0.692497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −40.6387 | −1.38496 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −53.1382 | −1.80885 | −0.904423 | − | 0.426636i | \(-0.859698\pi\) | ||||
−0.904423 | + | 0.426636i | \(0.859698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.4695 | 0.797987 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3091 | 0.587847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.1465 | 1.26011 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.76021 | −0.330712 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.56435 | −0.323704 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.6575 | −1.07022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.1446 | −0.578931 | −0.289466 | − | 0.957188i | \(-0.593478\pi\) | ||||
−0.289466 | + | 0.957188i | \(0.593478\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.4489 | 0.757182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.7788 | −1.84554 | −0.922772 | − | 0.385347i | \(-0.874082\pi\) | ||||
−0.922772 | + | 0.385347i | \(0.874082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.7119 | −1.20180 | −0.600900 | − | 0.799324i | \(-0.705191\pi\) | ||||
−0.600900 | + | 0.799324i | \(0.705191\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −39.0805 | −1.31368 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5614 | 1.22761 | 0.613805 | − | 0.789457i | \(-0.289638\pi\) | ||||
0.613805 | + | 0.789457i | \(0.289638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.44124 | −0.0483378 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −49.7403 | −1.66636 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −36.7814 | −1.23084 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.7027 | −1.09313 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.5736 | −0.419819 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0112 | 0.400595 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.6852 | −1.05559 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.97603 | 0.165592 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5990 | −0.684735 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4497 | −1.07747 | −0.538737 | − | 0.842474i | \(-0.681098\pi\) | ||||
−0.538737 | + | 0.842474i | \(0.681098\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.51109 | 0.0832877 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.6143 | 0.417929 | 0.208964 | − | 0.977923i | \(-0.432991\pi\) | ||||
0.208964 | + | 0.977923i | \(0.432991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.7665 | −1.11751 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.4524 | −0.841429 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.60349 | 0.185044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5072 | 0.379588 | 0.189794 | − | 0.981824i | \(-0.439218\pi\) | ||||
0.189794 | + | 0.981824i | \(0.439218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.2230 | −1.09474 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.97576 | 0.229610 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.13731 | −0.300433 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.23921 | −0.172078 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.9189 | 0.489473 | 0.244737 | − | 0.969590i | \(-0.421299\pi\) | ||||
0.244737 | + | 0.969590i | \(0.421299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.271008 | −0.00888191 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25.1684 | −0.823978 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.7894 | 0.712588 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3883 | −0.666058 | −0.333029 | − | 0.942917i | \(-0.608071\pi\) | ||||
−0.333029 | + | 0.942917i | \(0.608071\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.9051 | −0.355875 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.0180 | −1.95653 | −0.978265 | − | 0.207359i | \(-0.933513\pi\) | ||||
−0.978265 | + | 0.207359i | \(0.933513\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.2757 | 1.18130 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.5809 | 0.344198 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.7314 | −1.48607 | −0.743036 | − | 0.669252i | \(-0.766615\pi\) | ||||
−0.743036 | + | 0.669252i | \(0.766615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.519409 | −0.0168607 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.2542 | 1.82417 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.0813 | 1.52511 | 0.762556 | − | 0.646922i | \(-0.223944\pi\) | ||||
0.762556 | + | 0.646922i | \(0.223944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.28135 | 0.0414635 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.5250 | −0.954409 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.8947 | 0.933059 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.8118 | −0.477801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 34.7709 | 1.12048 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.36185 | −0.140413 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.7960 | −0.540124 | −0.270062 | − | 0.962843i | \(-0.587044\pi\) | ||||
−0.270062 | + | 0.962843i | \(0.587044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 34.6575 | 1.11336 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.9338 | −0.960621 | −0.480310 | − | 0.877099i | \(-0.659476\pi\) | ||||
−0.480310 | + | 0.877099i | \(0.659476\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.9521 | −1.44110 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.80273 | 0.185836 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38.6717 | 1.23722 | 0.618608 | − | 0.785700i | \(-0.287697\pi\) | ||||
0.618608 | + | 0.785700i | \(0.287697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −69.9942 | −2.23703 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6061 | −0.434410 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.61706 | 0.242946 | 0.121473 | − | 0.992595i | \(-0.461238\pi\) | ||||
0.121473 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.3518 | 0.329836 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.6121 | −1.32453 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.44180 | −0.141241 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.5352 | −0.938218 | −0.469109 | − | 0.883140i | \(-0.655425\pi\) | ||||
−0.469109 | + | 0.883140i | \(0.655425\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.1192 | −1.87609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.4149 | −0.995920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.4567 | −1.05958 | −0.529792 | − | 0.848127i | \(-0.677730\pi\) | ||||
−0.529792 | + | 0.848127i | \(0.677730\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.37392 | 0.296578 |
(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.d.1.8 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.8 | ✓ | 49 | 1.1 | even | 1 | trivial |