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: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.325374 | 0.187855 | 0.0939273 | − | 0.995579i | \(-0.470058\pi\) | ||||
0.0939273 | + | 0.995579i | \(0.470058\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.38648 | −1.51448 | −0.757239 | − | 0.653138i | \(-0.773452\pi\) | ||||
−0.757239 | + | 0.653138i | \(0.773452\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.980947 | 0.370763 | 0.185382 | − | 0.982667i | \(-0.440648\pi\) | ||||
0.185382 | + | 0.982667i | \(0.440648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.89413 | −0.964711 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93018 | −0.883482 | −0.441741 | − | 0.897143i | \(-0.645639\pi\) | ||||
−0.441741 | + | 0.897143i | \(0.645639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83935 | 1.34219 | 0.671097 | − | 0.741370i | \(-0.265824\pi\) | ||||
0.671097 | + | 0.741370i | \(0.265824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.10187 | −0.284502 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.26129 | 1.76112 | 0.880561 | − | 0.473933i | \(-0.157166\pi\) | ||||
0.880561 | + | 0.473933i | \(0.157166\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.24836 | −0.745225 | −0.372613 | − | 0.927987i | \(-0.621538\pi\) | ||||
−0.372613 | + | 0.927987i | \(0.621538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.319174 | 0.0696496 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.67797 | −0.975424 | −0.487712 | − | 0.873004i | \(-0.662168\pi\) | ||||
−0.487712 | + | 0.873004i | \(0.662168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.46823 | 1.29365 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.91780 | −0.369080 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.705257 | 0.130963 | 0.0654814 | − | 0.997854i | \(-0.479142\pi\) | ||||
0.0654814 | + | 0.997854i | \(0.479142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.40928 | −0.432720 | −0.216360 | − | 0.976314i | \(-0.569418\pi\) | ||||
−0.216360 | + | 0.976314i | \(0.569418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.953404 | −0.165966 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.32196 | −0.561513 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.15042 | 0.517926 | 0.258963 | − | 0.965887i | \(-0.416619\pi\) | ||||
0.258963 | + | 0.965887i | \(0.416619\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.57460 | 0.252137 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.63708 | −1.19271 | −0.596356 | − | 0.802720i | \(-0.703385\pi\) | ||||
−0.596356 | + | 0.802720i | \(0.703385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.860565 | 0.131235 | 0.0656175 | − | 0.997845i | \(-0.479098\pi\) | ||||
0.0656175 | + | 0.997845i | \(0.479098\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.80091 | 1.46103 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.21523 | −1.05245 | −0.526225 | − | 0.850346i | \(-0.676393\pi\) | ||||
−0.526225 | + | 0.850346i | \(0.676393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.03774 | −0.862535 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.36263 | 0.330835 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24924 | −0.583678 | −0.291839 | − | 0.956468i | \(-0.594267\pi\) | ||||
−0.291839 | + | 0.956468i | \(0.594267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.92299 | 1.33802 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.05693 | −0.139994 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.60491 | −1.12026 | −0.560132 | − | 0.828403i | \(-0.689250\pi\) | ||||
−0.560132 | + | 0.828403i | \(0.689250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.47883 | 0.445418 | 0.222709 | − | 0.974885i | \(-0.428510\pi\) | ||||
0.222709 | + | 0.974885i | \(0.428510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.83899 | −0.357679 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.3883 | −2.03272 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7506 | 1.55773 | 0.778866 | − | 0.627190i | \(-0.215795\pi\) | ||||
0.778866 | + | 0.627190i | \(0.215795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.52209 | −0.183238 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.381676 | −0.0452966 | −0.0226483 | − | 0.999743i | \(-0.507210\pi\) | ||||
−0.0226483 | + | 0.999743i | \(0.507210\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.63372 | 0.191213 | 0.0956065 | − | 0.995419i | \(-0.469521\pi\) | ||||
0.0956065 | + | 0.995419i | \(0.469521\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.10459 | 0.243017 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.87435 | −0.327563 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.41258 | −0.383945 | −0.191973 | − | 0.981400i | \(-0.561489\pi\) | ||||
−0.191973 | + | 0.981400i | \(0.561489\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.05840 | 0.895377 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.72394 | 0.738049 | 0.369024 | − | 0.929420i | \(-0.379692\pi\) | ||||
0.369024 | + | 0.929420i | \(0.379692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.5902 | −2.66718 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.229472 | 0.0246020 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.86150 | 0.303318 | 0.151659 | − | 0.988433i | \(-0.451538\pi\) | ||||
0.151659 | + | 0.988433i | \(0.451538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.74714 | 0.497636 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.783917 | −0.0812884 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0005 | 1.12863 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6477 | 1.48725 | 0.743626 | − | 0.668596i | \(-0.233105\pi\) | ||||
0.743626 | + | 0.668596i | \(0.233105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.48033 | 0.852305 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7322 | −1.26691 | −0.633453 | − | 0.773781i | \(-0.718363\pi\) | ||||
−0.633453 | + | 0.773781i | \(0.718363\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.94224 | 0.881105 | 0.440552 | − | 0.897727i | \(-0.354783\pi\) | ||||
0.440552 | + | 0.897727i | \(0.354783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.08088 | −0.105483 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.67961 | −0.935764 | −0.467882 | − | 0.883791i | \(-0.654983\pi\) | ||||
−0.467882 | + | 0.883791i | \(0.654983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.27681 | 0.696992 | 0.348496 | − | 0.937310i | \(-0.386693\pi\) | ||||
0.348496 | + | 0.937310i | \(0.386693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.02506 | 0.0972948 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.975504 | 0.0917677 | 0.0458838 | − | 0.998947i | \(-0.485390\pi\) | ||||
0.0458838 | + | 0.998947i | \(0.485390\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.8418 | 1.47726 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.0057 | −1.29483 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.12295 | 0.652959 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.41405 | −0.219459 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.48490 | −0.224056 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.97212 | −0.444720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6668 | −1.65641 | −0.828205 | − | 0.560426i | \(-0.810637\pi\) | ||||
−0.828205 | + | 0.560426i | \(0.810637\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.280005 | 0.0246531 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.6390 | 1.62850 | 0.814249 | − | 0.580516i | \(-0.197149\pi\) | ||||
0.814249 | + | 0.580516i | \(0.197149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.18647 | −0.276302 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.49457 | 0.558964 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.8063 | 1.00868 | 0.504342 | − | 0.863504i | \(-0.331735\pi\) | ||||
0.504342 | + | 0.863504i | \(0.331735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.6784 | 1.49946 | 0.749729 | − | 0.661745i | \(-0.230184\pi\) | ||||
0.749729 | + | 0.661745i | \(0.230184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.34765 | −0.197707 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.1802 | −1.18580 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.38834 | −0.198341 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.96452 | −0.162031 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.8028 | 1.78615 | 0.893076 | − | 0.449906i | \(-0.148543\pi\) | ||||
0.893076 | + | 0.449906i | \(0.148543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2206 | 1.40139 | 0.700696 | − | 0.713460i | \(-0.252873\pi\) | ||||
0.700696 | + | 0.713460i | \(0.252873\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.0151 | −1.69897 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.15897 | 0.655345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2403 | 1.13650 | 0.568250 | − | 0.822856i | \(-0.307621\pi\) | ||||
0.568250 | + | 0.822856i | \(0.307621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.38259 | −0.109647 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.58884 | −0.361651 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7027 | −0.994949 | −0.497474 | − | 0.867479i | \(-0.665739\pi\) | ||||
−0.497474 | + | 0.867479i | \(0.665739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.22868 | 0.251352 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.9001 | 1.07562 | 0.537812 | − | 0.843065i | \(-0.319251\pi\) | ||||
0.537812 | + | 0.843065i | \(0.319251\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4193 | 0.801482 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.40119 | 0.718927 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.63995 | 0.200711 | 0.100356 | − | 0.994952i | \(-0.468002\pi\) | ||||
0.100356 | + | 0.994952i | \(0.468002\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.34499 | 0.479636 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.79981 | −0.210447 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.5349 | 1.46011 | 0.730054 | − | 0.683389i | \(-0.239495\pi\) | ||||
0.730054 | + | 0.683389i | \(0.239495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.2303 | 1.28072 | 0.640358 | − | 0.768077i | \(-0.278786\pi\) | ||||
0.640358 | + | 0.768077i | \(0.278786\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.13192 | 0.0836739 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.6688 | −0.784388 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.2769 | −1.55592 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.88126 | −0.136841 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5169 | 0.833337 | 0.416669 | − | 0.909058i | \(-0.363198\pi\) | ||||
0.416669 | + | 0.909058i | \(0.363198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.32103 | −0.383016 | −0.191508 | − | 0.981491i | \(-0.561338\pi\) | ||||
−0.191508 | + | 0.981491i | \(0.561338\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.33233 | −0.381856 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9254 | 0.778406 | 0.389203 | − | 0.921152i | \(-0.372750\pi\) | ||||
0.389203 | + | 0.921152i | \(0.372750\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6818 | 0.898991 | 0.449496 | − | 0.893283i | \(-0.351604\pi\) | ||||
0.449496 | + | 0.893283i | \(0.351604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.14871 | 0.292627 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.691820 | 0.0485562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.8628 | 1.80634 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.5387 | 0.941002 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.51828 | 0.658393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.47480 | 0.445744 | 0.222872 | − | 0.974848i | \(-0.428457\pi\) | ||||
0.222872 | + | 0.974848i | \(0.428457\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.124187 | −0.00850918 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.91429 | −0.198753 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.36338 | −0.160436 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.531571 | 0.0359202 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.1399 | 2.36377 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.4768 | −1.17033 | −0.585166 | − | 0.810913i | \(-0.698971\pi\) | ||||
−0.585166 | + | 0.810913i | \(0.698971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.7199 | −1.24799 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.45740 | −0.494965 | −0.247483 | − | 0.968892i | \(-0.579603\pi\) | ||||
−0.247483 | + | 0.968892i | \(0.579603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.28630 | 0.349329 | 0.174664 | − | 0.984628i | \(-0.444116\pi\) | ||||
0.174664 | + | 0.984628i | \(0.444116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.935238 | −0.0615342 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.11458 | −0.138531 | −0.0692655 | − | 0.997598i | \(-0.522066\pi\) | ||||
−0.0692655 | + | 0.997598i | \(0.522066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.4342 | 1.59391 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.11036 | −0.0721259 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.46049 | 0.288525 | 0.144262 | − | 0.989539i | \(-0.453919\pi\) | ||||
0.144262 | + | 0.989539i | \(0.453919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.2174 | −1.04465 | −0.522327 | − | 0.852745i | \(-0.674936\pi\) | ||||
−0.522327 | + | 0.852745i | \(0.674936\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.37538 | 0.537281 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.4467 | 1.30629 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.7199 | −1.00024 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.18780 | 0.138646 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.3620 | −0.717161 | −0.358581 | − | 0.933499i | \(-0.616739\pi\) | ||||
−0.358581 | + | 0.933499i | \(0.616739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7073 | 0.861770 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00101 | −0.501042 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1107 | −1.37923 | −0.689614 | − | 0.724177i | \(-0.742220\pi\) | ||||
−0.689614 | + | 0.724177i | \(0.742220\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.09040 | 0.192028 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.04111 | −0.126341 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3247 | −0.821637 | −0.410819 | − | 0.911717i | \(-0.634757\pi\) | ||||
−0.410819 | + | 0.911717i | \(0.634757\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.3899 | 0.883967 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.931056 | 0.0569797 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.35083 | 0.143333 | 0.0716663 | − | 0.997429i | \(-0.477168\pi\) | ||||
0.0716663 | + | 0.997429i | \(0.477168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.879378 | 0.0534184 | 0.0267092 | − | 0.999643i | \(-0.491497\pi\) | ||||
0.0267092 | + | 0.999643i | \(0.491497\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.54460 | 0.0934832 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.9531 | −1.14291 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.43286 | −0.146176 | −0.0730882 | − | 0.997325i | \(-0.523285\pi\) | ||||
−0.0730882 | + | 0.997325i | \(0.523285\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.97278 | 0.417449 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.7384 | 0.998532 | 0.499266 | − | 0.866449i | \(-0.333603\pi\) | ||||
0.499266 | + | 0.866449i | \(0.333603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.69773 | 0.338695 | 0.169347 | − | 0.985556i | \(-0.445834\pi\) | ||||
0.169347 | + | 0.985556i | \(0.445834\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.57928 | 0.212018 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.49157 | −0.442213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.7264 | 2.10155 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.76599 | 0.279387 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 32.2603 | 1.88467 | 0.942333 | − | 0.334677i | \(-0.108627\pi\) | ||||
0.942333 | + | 0.334677i | \(0.108627\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.1403 | 1.69662 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.61949 | 0.326076 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −22.6383 | −1.30921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.844169 | 0.0486571 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.14274 | −0.237994 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7810 | −0.674576 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.928452 | −0.0529895 | −0.0264948 | − | 0.999649i | \(-0.508435\pi\) | ||||
−0.0264948 | + | 0.999649i | \(0.508435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.90957 | 0.165520 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.09507 | 0.345619 | 0.172810 | − | 0.984955i | \(-0.444715\pi\) | ||||
0.172810 | + | 0.984955i | \(0.444715\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.4959 | −1.61068 | −0.805341 | − | 0.592812i | \(-0.798018\pi\) | ||||
−0.805341 | + | 0.592812i | \(0.798018\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.61418 | 0.541697 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.47666 | 0.139103 | 0.0695516 | − | 0.997578i | \(-0.477843\pi\) | ||||
0.0695516 | + | 0.997578i | \(0.477843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.06653 | −0.115703 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.14949 | −0.175788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5873 | −1.31243 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.3020 | 1.73632 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.36768 | 0.130933 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.07776 | −0.390209 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.3182 | −0.567141 | −0.283571 | − | 0.958951i | \(-0.591519\pi\) | ||||
−0.283571 | + | 0.958951i | \(0.591519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.11773 | −0.499649 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43.1796 | −2.35915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5304 | 0.682572 | 0.341286 | − | 0.939960i | \(-0.389138\pi\) | ||||
0.341286 | + | 0.939960i | \(0.389138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.317403 | 0.0172390 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.05963 | 0.382300 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.7893 | −0.690559 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.15452 | 0.277510 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2613 | 0.550857 | 0.275429 | − | 0.961322i | \(-0.411180\pi\) | ||||
0.275429 | + | 0.961322i | \(0.411180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.5683 | −0.726296 | −0.363148 | − | 0.931731i | \(-0.618298\pi\) | ||||
−0.363148 | + | 0.931731i | \(0.618298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.28088 | −0.495377 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9948 | 0.957766 | 0.478883 | − | 0.877879i | \(-0.341042\pi\) | ||||
0.478883 | + | 0.877879i | \(0.341042\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.29254 | 0.0686008 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.31762 | 0.122661 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.9258 | −0.576643 | −0.288322 | − | 0.957534i | \(-0.593097\pi\) | ||||
−0.288322 | + | 0.957534i | \(0.593097\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.44814 | −0.444639 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.785468 | −0.0412264 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.53257 | −0.289588 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7073 | 1.28971 | 0.644855 | − | 0.764305i | \(-0.276918\pi\) | ||||
0.644855 | + | 0.764305i | \(0.276918\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.1027 | 1.15062 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.16828 | −0.216406 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.8403 | 1.28618 | 0.643092 | − | 0.765789i | \(-0.277651\pi\) | ||||
0.643092 | + | 0.765789i | \(0.277651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.61780 | −0.0835427 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.41298 | 0.175778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.66407 | −0.136844 | −0.0684222 | − | 0.997656i | \(-0.521796\pi\) | ||||
−0.0684222 | + | 0.997656i | \(0.521796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.07368 | −0.311164 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.22225 | −0.317942 | −0.158971 | − | 0.987283i | \(-0.550818\pi\) | ||||
−0.158971 | + | 0.987283i | \(0.550818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.73392 | 0.496087 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.49059 | −0.126604 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.40510 | −0.426155 | −0.213078 | − | 0.977035i | \(-0.568349\pi\) | ||||
−0.213078 | + | 0.977035i | \(0.568349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.9681 | −1.71784 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.06464 | 0.305921 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.5566 | 0.581477 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.187258 | 0.00939823 | 0.00469912 | − | 0.999989i | \(-0.498504\pi\) | ||||
0.00469912 | + | 0.999989i | \(0.498504\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.03679 | −0.0519046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3224 | 0.515475 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.6593 | −0.580793 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.2896 | −1.35603 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.23129 | −0.457578 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.98644 | −0.246564 | −0.123282 | − | 0.992372i | \(-0.539342\pi\) | ||||
−0.123282 | + | 0.992372i | \(0.539342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.84147 | 0.189486 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.44096 | −0.415353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.7705 | −1.11776 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.75207 | 0.281680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.1370 | −1.56999 | −0.784997 | − | 0.619500i | \(-0.787335\pi\) | ||||
−0.784997 | + | 0.619500i | \(0.787335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.8353 | 0.869241 | 0.434620 | − | 0.900614i | \(-0.356883\pi\) | ||||
0.434620 | + | 0.900614i | \(0.356883\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.8818 | 1.01531 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 46.9677 | 2.27827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.41255 | 0.165145 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.61385 | −0.222759 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.24739 | −0.397263 | −0.198631 | − | 0.980074i | \(-0.563650\pi\) | ||||
−0.198631 | + | 0.980074i | \(0.563650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.05087 | 0.242729 | 0.121365 | − | 0.992608i | \(-0.461273\pi\) | ||||
0.121365 | + | 0.992608i | \(0.461273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.777102 | −0.0372592 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.1957 | 0.726911 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.4052 | −1.11707 | −0.558535 | − | 0.829481i | \(-0.688636\pi\) | ||||
−0.558535 | + | 0.829481i | \(0.688636\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.4740 | 0.832096 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.09062 | 0.241863 | 0.120931 | − | 0.992661i | \(-0.461412\pi\) | ||||
0.120931 | + | 0.992661i | \(0.461412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.69039 | −0.459369 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.09405 | 0.335537 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.6395 | 1.21000 | 0.605001 | − | 0.796225i | \(-0.293173\pi\) | ||||
0.605001 | + | 0.796225i | \(0.293173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3780 | 1.05374 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.60313 | 0.263258 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.0761 | −0.753659 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9163 | −1.21231 | −0.606156 | − | 0.795345i | \(-0.707289\pi\) | ||||
−0.606156 | + | 0.795345i | \(0.707289\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.9257 | −0.649995 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.85042 | −0.225906 | −0.112953 | − | 0.993600i | \(-0.536031\pi\) | ||||
−0.112953 | + | 0.993600i | \(0.536031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8229 | 1.20009 | 0.600046 | − | 0.799965i | \(-0.295149\pi\) | ||||
0.600046 | + | 0.799965i | \(0.295149\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.65472 | 0.123110 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.530213 | −0.0245353 | −0.0122677 | − | 0.999925i | \(-0.503905\pi\) | ||||
−0.0122677 | + | 0.999925i | \(0.503905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5077 | 0.577550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.63342 | 0.213497 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.52161 | −0.115944 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.0111 | −0.964057 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2979 | 0.563080 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.50480 | 0.160138 | 0.0800691 | − | 0.996789i | \(-0.474486\pi\) | ||||
0.0800691 | + | 0.996789i | \(0.474486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2460 | 0.695156 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.49309 | −0.0679379 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −49.6042 | −2.25241 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.8777 | 1.21795 | 0.608973 | − | 0.793191i | \(-0.291582\pi\) | ||||
0.608973 | + | 0.793191i | \(0.291582\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.13311 | −0.186906 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.8720 | −1.03220 | −0.516099 | − | 0.856529i | \(-0.672616\pi\) | ||||
−0.516099 | + | 0.856529i | \(0.672616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.12108 | 0.230642 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −28.7184 | −1.29080 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.374404 | −0.0167943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.0977 | 1.48166 | 0.740829 | − | 0.671693i | \(-0.234433\pi\) | ||||
0.740829 | + | 0.671693i | \(0.234433\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.52273 | 0.202061 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.8957 | −1.42216 | −0.711080 | − | 0.703111i | \(-0.751794\pi\) | ||||
−0.711080 | + | 0.703111i | \(0.751794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.1174 | 1.91870 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.39016 | 0.150562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.7795 | −0.788064 | −0.394032 | − | 0.919097i | \(-0.628920\pi\) | ||||
−0.394032 | + | 0.919097i | \(0.628920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.60260 | 0.0708947 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.22970 | 0.275048 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −30.2827 | −1.33441 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.1419 | 0.929820 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.858969 | 0.0377046 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.4500 | −0.720688 | −0.360344 | − | 0.932820i | \(-0.617341\pi\) | ||||
−0.360344 | + | 0.932820i | \(0.617341\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −41.5433 | −1.81656 | −0.908282 | − | 0.418359i | \(-0.862605\pi\) | ||||
−0.908282 | + | 0.418359i | \(0.862605\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.06449 | 0.0901019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.4945 | −0.762072 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.11659 | −0.0485473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 24.9037 | 1.08073 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.9585 | −1.60085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.7798 | 1.41719 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.35615 | 0.274288 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.6917 | 0.762034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.2181 | 1.72911 | 0.864556 | − | 0.502537i | \(-0.167600\pi\) | ||||
0.864556 | + | 0.502537i | \(0.167600\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.60627 | 0.240588 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.6427 | −1.05558 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.75359 | 0.0749780 | 0.0374890 | − | 0.999297i | \(-0.488064\pi\) | ||||
0.0374890 | + | 0.999297i | \(0.488064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0682 | −0.429700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.29093 | −0.0975969 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.34756 | −0.142353 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.47136 | −0.147351 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.5762 | 0.871842 | 0.435921 | − | 0.899985i | \(-0.356423\pi\) | ||||
0.435921 | + | 0.899985i | \(0.356423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.16457 | 0.176143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.92294 | −0.292287 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.34244 | 0.183012 | 0.0915060 | − | 0.995805i | \(-0.470832\pi\) | ||||
0.0915060 | + | 0.995805i | \(0.470832\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.30352 | −0.138980 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.90486 | 0.331973 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.32669 | −0.223306 | −0.111653 | − | 0.993747i | \(-0.535615\pi\) | ||||
−0.111653 | + | 0.993747i | \(0.535615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.48575 | 0.396966 | 0.198483 | − | 0.980104i | \(-0.436398\pi\) | ||||
0.198483 | + | 0.980104i | \(0.436398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.74731 | 0.156546 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.2582 | −1.26185 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.16813 | −0.340044 | −0.170022 | − | 0.985440i | \(-0.554384\pi\) | ||||
−0.170022 | + | 0.985440i | \(0.554384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.73132 | −0.0719513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.59583 | 0.273641 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.4510 | 0.515669 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 47.4300 | 1.96099 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.9722 | −0.783068 | −0.391534 | − | 0.920164i | \(-0.628055\pi\) | ||||
−0.391534 | + | 0.920164i | \(0.628055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.82622 | 0.322474 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.55485 | 0.146227 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.94720 | 0.203157 | 0.101579 | − | 0.994828i | \(-0.467611\pi\) | ||||
0.101579 | + | 0.994828i | \(0.467611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.1217 | −0.988893 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.12634 | 0.168880 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0329 | 1.34969 | 0.674843 | − | 0.737961i | \(-0.264211\pi\) | ||||
0.674843 | + | 0.737961i | \(0.264211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.3306 | −0.829303 | −0.414652 | − | 0.909980i | \(-0.636097\pi\) | ||||
−0.414652 | + | 0.909980i | \(0.636097\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.9019 | −1.50276 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.17512 | 0.332366 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.35601 | −0.0550386 | −0.0275193 | − | 0.999621i | \(-0.508761\pi\) | ||||
−0.0275193 | + | 0.999621i | \(0.508761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.225100 | 0.00912151 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.9170 | −1.41259 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.7337 | 1.52405 | 0.762025 | − | 0.647548i | \(-0.224205\pi\) | ||||
0.762025 | + | 0.647548i | \(0.224205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.41507 | 0.339329 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.5979 | −0.507174 | −0.253587 | − | 0.967313i | \(-0.581610\pi\) | ||||
−0.253587 | + | 0.967313i | \(0.581610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.48413 | 0.180232 | 0.0901161 | − | 0.995931i | \(-0.471276\pi\) | ||||
0.0901161 | + | 0.995931i | \(0.471276\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.97139 | 0.360010 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.80698 | 0.112459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5032 | −0.620127 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.09700 | 0.123682 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.8761 | 0.912131 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3761 | 1.16945 | 0.584723 | − | 0.811233i | \(-0.301203\pi\) | ||||
0.584723 | + | 0.811233i | \(0.301203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.10673 | 0.0837350 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 63.2146 | 2.50860 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.2187 | −1.15769 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.10462 | 0.0436982 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.57893 | 0.378345 | 0.189172 | − | 0.981944i | \(-0.439419\pi\) | ||||
0.189172 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.1231 | −0.438653 | −0.219327 | − | 0.975651i | \(-0.570386\pi\) | ||||
−0.219327 | + | 0.975651i | \(0.570386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.948232 | −0.0373366 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.6967 | 0.813673 | 0.406837 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406837 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.2139 | 0.989733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.768981 | −0.0301387 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.78120 | 0.108837 | 0.0544183 | − | 0.998518i | \(-0.482670\pi\) | ||||
0.0544183 | + | 0.998518i | \(0.482670\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −63.1206 | −2.46632 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.72821 | −0.184465 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.82839 | −0.188087 | −0.0940436 | − | 0.995568i | \(-0.529979\pi\) | ||||
−0.0940436 | + | 0.995568i | \(0.529979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7121 | 0.883399 | 0.441699 | − | 0.897163i | \(-0.354376\pi\) | ||||
0.441699 | + | 0.897163i | \(0.354376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.4336 | 0.444044 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.7909 | 0.418454 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.29917 | −0.127744 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.68649 | −0.219852 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.1936 | −0.393519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.4100 | 0.478370 | 0.239185 | − | 0.970974i | \(-0.423120\pi\) | ||||
0.239185 | + | 0.970974i | \(0.423120\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.4047 | −0.477459 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.5670 | −0.482990 | −0.241495 | − | 0.970402i | \(-0.577638\pi\) | ||||
−0.241495 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.3686 | 0.551418 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.42644 | −0.0929815 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.76729 | 0.105888 | 0.0529438 | − | 0.998597i | \(-0.483140\pi\) | ||||
0.0529438 | + | 0.998597i | \(0.483140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −39.9819 | −1.52763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.72002 | 0.0656230 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20.5635 | −0.783408 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2383 | 1.07424 | 0.537118 | − | 0.843507i | \(-0.319513\pi\) | ||||
0.537118 | + | 0.843507i | \(0.319513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.31875 | 0.316003 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −59.8673 | −2.27090 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.4551 | −2.10051 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.688030 | −0.0260237 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0454 | −0.492716 | −0.246358 | − | 0.969179i | \(-0.579234\pi\) | ||||
−0.246358 | + | 0.969179i | \(0.579234\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.2337 | −0.385971 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.95025 | 0.299424 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.4897 | −0.469722 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3975 | −0.465597 | −0.232799 | − | 0.972525i | \(-0.574788\pi\) | ||||
−0.232799 | + | 0.972525i | \(0.574788\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.87646 | 0.370396 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.2705 | 0.422085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 48.0208 | 1.79587 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.45133 | 0.0542007 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.0452 | 0.710266 | 0.355133 | − | 0.934816i | \(-0.384436\pi\) | ||||
0.355133 | + | 0.934816i | \(0.384436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.77186 | 0.326681 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.27672 | −0.196243 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.56176 | 0.169420 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.34849 | 0.309628 | 0.154814 | − | 0.987944i | \(-0.450522\pi\) | ||||
0.154814 | + | 0.987944i | \(0.450522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.4501 | −0.794447 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24882 | 0.231121 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.2981 | 1.52538 | 0.762691 | − | 0.646763i | \(-0.223878\pi\) | ||||
0.762691 | + | 0.646763i | \(0.223878\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.65281 | 0.245393 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.3615 | −1.37623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.6059 | −0.905144 | −0.452572 | − | 0.891728i | \(-0.649494\pi\) | ||||
−0.452572 | + | 0.891728i | \(0.649494\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.11486 | −0.187899 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.6199 | −0.976591 | −0.488295 | − | 0.872678i | \(-0.662381\pi\) | ||||
−0.488295 | + | 0.872678i | \(0.662381\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −73.8345 | −2.70509 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.4600 | −0.712004 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.49519 | −0.346947 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.69689 | −0.134722 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −58.3172 | −2.12238 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3819 | 0.995212 | 0.497606 | − | 0.867403i | \(-0.334213\pi\) | ||||
0.497606 | + | 0.867403i | \(0.334213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.45999 | 0.161888 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.8639 | −1.48132 | −0.740658 | − | 0.671882i | \(-0.765486\pi\) | ||||
−0.740658 | + | 0.671882i | \(0.765486\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.13817 | 0.258419 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 71.1673 | 2.57306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −41.6421 | −1.50361 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.6250 | 0.779817 | 0.389908 | − | 0.920854i | \(-0.372507\pi\) | ||||
0.389908 | + | 0.920854i | \(0.372507\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.19424 | −0.259094 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 40.3624 | 1.45174 | 0.725868 | − | 0.687834i | \(-0.241438\pi\) | ||||
0.725868 | + | 0.687834i | \(0.241438\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.5838 | −0.559786 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00553 | 0.0360733 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.8080 | 0.888839 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.11838 | 0.0400188 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.35254 | −0.0483358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −48.2245 | −1.72121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.4325 | 1.19174 | 0.595870 | − | 0.803081i | \(-0.296808\pi\) | ||||
0.595870 | + | 0.803081i | \(0.296808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.33551 | −0.154348 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.956918 | 0.0340241 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8353 | 0.597837 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.68211 | 0.166057 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.6478 | 0.908492 | 0.454246 | − | 0.890876i | \(-0.349909\pi\) | ||||
0.454246 | + | 0.890876i | \(0.349909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.3919 | −1.85349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.28155 | −0.292614 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.78710 | −0.168933 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.5400 | 0.547713 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.764898 | 0.0269257 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.0703 | 1.12753 | 0.563766 | − | 0.825935i | \(-0.309352\pi\) | ||||
0.563766 | + | 0.825935i | \(0.309352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7578 | 0.904479 | 0.452240 | − | 0.891896i | \(-0.350625\pi\) | ||||
0.452240 | + | 0.891896i | \(0.350625\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.286126 | 0.0100349 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.0172 | 1.50683 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.79543 | −0.0977997 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.7389 | −0.480075 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.80881 | 0.0631281 | 0.0315640 | − | 0.999502i | \(-0.489951\pi\) | ||||
0.0315640 | + | 0.999502i | \(0.489951\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.42577 | −0.189130 | −0.0945652 | − | 0.995519i | \(-0.530146\pi\) | ||||
−0.0945652 | + | 0.995519i | \(0.530146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.16683 | −0.214701 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.890182 | 0.0309547 | 0.0154773 | − | 0.999880i | \(-0.495073\pi\) | ||||
0.0154773 | + | 0.999880i | \(0.495073\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.56934 | −0.262894 | −0.131447 | − | 0.991323i | \(-0.541962\pi\) | ||||
−0.131447 | + | 0.991323i | \(0.541962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.791589 | −0.0274599 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.8418 | −1.51903 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.0724 | −1.62901 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.62051 | 0.159708 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.64242 | 0.0912266 | 0.0456133 | − | 0.998959i | \(-0.485476\pi\) | ||||
0.0456133 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5026 | −0.982849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.44625 | 0.187579 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −35.2846 | −1.21383 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.36805 | −0.0813673 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.85389 | 0.0636254 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7376 | −0.505197 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.9393 | −1.33326 | −0.666629 | − | 0.745390i | \(-0.732263\pi\) | ||||
−0.666629 | + | 0.745390i | \(0.732263\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.8369 | −1.08880 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.6786 | 0.979644 | 0.489822 | − | 0.871823i | \(-0.337062\pi\) | ||||
0.489822 | + | 0.871823i | \(0.337062\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.5112 | 1.85990 | 0.929948 | − | 0.367690i | \(-0.119851\pi\) | ||||
0.929948 | + | 0.367690i | \(0.119851\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.43756 | −0.0830718 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.5516 | −1.27827 | −0.639136 | − | 0.769094i | \(-0.720708\pi\) | ||||
−0.639136 | + | 0.769094i | \(0.720708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.94012 | −0.303973 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.6244 | 0.394786 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.99948 | 0.339209 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.7045 | 2.09078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −42.3924 | −1.43477 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.87739 | −0.164886 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.0598 | −1.01505 | −0.507523 | − | 0.861638i | \(-0.669439\pi\) | ||||
−0.507523 | + | 0.861638i | \(0.669439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4966 | 0.354043 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.3371 | −0.381958 | −0.190979 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190979 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.23356 | 0.176123 | 0.0880617 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880617 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.48150 | 0.318717 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.1560 | 0.609618 | 0.304809 | − | 0.952413i | \(-0.401407\pi\) | ||||
0.304809 | + | 0.952413i | \(0.401407\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.3111 | −0.614136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.6125 | −0.791050 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.4377 | 0.784312 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −66.1546 | −2.21130 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.36592 | −0.245941 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.69916 | −0.0566702 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.8550 | −1.02793 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.274671 | 0.00914046 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −58.3499 | −1.93962 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −58.5778 | −1.94504 | −0.972522 | − | 0.232812i | \(-0.925207\pi\) | ||||
−0.972522 | + | 0.232812i | \(0.925207\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.8488 | 1.22220 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.5561 | −0.912975 | −0.456488 | − | 0.889730i | \(-0.650893\pi\) | ||||
−0.456488 | + | 0.889730i | \(0.650893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.7024 | −0.652053 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.83322 | −0.126722 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.2839 | 0.603787 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1780 | 1.25938 | 0.629688 | − | 0.776848i | \(-0.283183\pi\) | ||||
0.629688 | + | 0.776848i | \(0.283183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.302094 | −0.00995433 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.84706 | −0.0607968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.3776 | 0.670012 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −25.8800 | −0.850011 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.4504 | 0.638148 | 0.319074 | − | 0.947730i | \(-0.396628\pi\) | ||||
0.319074 | + | 0.947730i | \(0.396628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.6128 | 0.642783 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.98317 | 0.0649262 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 72.0537 | 2.35641 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.0860 | −1.50556 | −0.752782 | − | 0.658270i | \(-0.771288\pi\) | ||||
−0.752782 | + | 0.658270i | \(0.771288\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.27181 | −0.302574 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.3167 | 1.05349 | 0.526747 | − | 0.850022i | \(-0.323411\pi\) | ||||
0.526747 | + | 0.850022i | \(0.323411\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.7260 | 1.16340 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.37083 | 0.207243 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.9224 | −0.809870 | −0.404935 | − | 0.914345i | \(-0.632706\pi\) | ||||
−0.404935 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.90616 | 0.256645 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.805841 | 0.0261312 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.6130 | 1.76909 | 0.884544 | − | 0.466456i | \(-0.154469\pi\) | ||||
0.884544 | + | 0.466456i | \(0.154469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.0019 | −1.26207 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.672394 | −0.0217354 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.5814 | 0.373983 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.1954 | −0.812754 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.0141 | 0.902741 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.0195 | 0.580069 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.0859 | 1.19260 | 0.596301 | − | 0.802761i | \(-0.296637\pi\) | ||||
0.596301 | + | 0.802761i | \(0.296637\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.67469 | −0.246547 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.6621 | −1.52955 | −0.764776 | − | 0.644297i | \(-0.777150\pi\) | ||||
−0.764776 | + | 0.644297i | \(0.777150\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.3415 | 0.555944 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.1848 | 0.326176 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.9441 | −1.30992 | −0.654960 | − | 0.755664i | \(-0.727314\pi\) | ||||
−0.654960 | + | 0.755664i | \(0.727314\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.38470 | −0.267976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.0600 | −0.672396 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.1264 | 0.514352 | 0.257176 | − | 0.966365i | \(-0.417208\pi\) | ||||
0.257176 | + | 0.966365i | \(0.417208\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.9988 | −1.17888 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.30292 | −0.0733026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.02570 | −0.128010 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.7527 | 1.54868 | 0.774340 | − | 0.632770i | \(-0.218082\pi\) | ||||
0.774340 | + | 0.632770i | \(0.218082\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.35728 | −0.106540 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −42.9467 | −1.36150 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8374 | 0.564917 | 0.282459 | − | 0.959279i | \(-0.408850\pi\) | ||||
0.282459 | + | 0.959279i | \(0.408850\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.04186 | −0.191156 |
(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.e.1.26 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.26 | ✓ | 50 | 1.1 | even | 1 | trivial |