Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3381,2,Mod(1,3381)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3381, 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("3381.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3381 = 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3381.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: | \(26.9974209234\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 100x^{3} - 17x^{2} - 28x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.54861\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3381.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.54861 | 1.09503 | 0.547516 | − | 0.836795i | \(-0.315573\pi\) | ||||
0.547516 | + | 0.836795i | \(0.315573\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.398191 | 0.199096 | ||||||||
\(5\) | −1.02582 | −0.458760 | −0.229380 | − | 0.973337i | \(-0.573670\pi\) | ||||
−0.229380 | + | 0.973337i | \(0.573670\pi\) | |||||||
\(6\) | −1.54861 | −0.632217 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.48058 | −0.877016 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.58859 | −0.502356 | ||||||||
\(11\) | −6.58109 | −1.98427 | −0.992137 | − | 0.125157i | \(-0.960057\pi\) | ||||
−0.992137 | + | 0.125157i | \(0.960057\pi\) | |||||||
\(12\) | −0.398191 | −0.114948 | ||||||||
\(13\) | −0.0967108 | −0.0268228 | −0.0134114 | − | 0.999910i | \(-0.504269\pi\) | ||||
−0.0134114 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.02582 | 0.264865 | ||||||||
\(16\) | −4.63783 | −1.15946 | ||||||||
\(17\) | −2.79145 | −0.677025 | −0.338513 | − | 0.940962i | \(-0.609924\pi\) | ||||
−0.338513 | + | 0.940962i | \(0.609924\pi\) | |||||||
\(18\) | 1.54861 | 0.365011 | ||||||||
\(19\) | 5.99168 | 1.37459 | 0.687293 | − | 0.726381i | \(-0.258799\pi\) | ||||
0.687293 | + | 0.726381i | \(0.258799\pi\) | |||||||
\(20\) | −0.408472 | −0.0913370 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.1915 | −2.17284 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.48058 | 0.506345 | ||||||||
\(25\) | −3.94770 | −0.789540 | ||||||||
\(26\) | −0.149767 | −0.0293718 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.41057 | 0.447632 | 0.223816 | − | 0.974631i | \(-0.428149\pi\) | ||||
0.223816 | + | 0.974631i | \(0.428149\pi\) | |||||||
\(30\) | 1.58859 | 0.290036 | ||||||||
\(31\) | 10.1033 | 1.81460 | 0.907301 | − | 0.420481i | \(-0.138139\pi\) | ||||
0.907301 | + | 0.420481i | \(0.138139\pi\) | |||||||
\(32\) | −2.22103 | −0.392626 | ||||||||
\(33\) | 6.58109 | 1.14562 | ||||||||
\(34\) | −4.32286 | −0.741364 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.398191 | 0.0663652 | ||||||||
\(37\) | 0.972553 | 0.159887 | 0.0799434 | − | 0.996799i | \(-0.474526\pi\) | ||||
0.0799434 | + | 0.996799i | \(0.474526\pi\) | |||||||
\(38\) | 9.27877 | 1.50522 | ||||||||
\(39\) | 0.0967108 | 0.0154861 | ||||||||
\(40\) | 2.54462 | 0.402339 | ||||||||
\(41\) | 7.47823 | 1.16790 | 0.583952 | − | 0.811788i | \(-0.301506\pi\) | ||||
0.583952 | + | 0.811788i | \(0.301506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.72262 | 1.02519 | 0.512595 | − | 0.858630i | \(-0.328684\pi\) | ||||
0.512595 | + | 0.858630i | \(0.328684\pi\) | |||||||
\(44\) | −2.62053 | −0.395060 | ||||||||
\(45\) | −1.02582 | −0.152920 | ||||||||
\(46\) | 1.54861 | 0.228330 | ||||||||
\(47\) | −5.72919 | −0.835689 | −0.417844 | − | 0.908519i | \(-0.637214\pi\) | ||||
−0.417844 | + | 0.908519i | \(0.637214\pi\) | |||||||
\(48\) | 4.63783 | 0.669413 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.11344 | −0.864571 | ||||||||
\(51\) | 2.79145 | 0.390881 | ||||||||
\(52\) | −0.0385094 | −0.00534029 | ||||||||
\(53\) | −4.91819 | −0.675566 | −0.337783 | − | 0.941224i | \(-0.609677\pi\) | ||||
−0.337783 | + | 0.941224i | \(0.609677\pi\) | |||||||
\(54\) | −1.54861 | −0.210739 | ||||||||
\(55\) | 6.75100 | 0.910305 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.99168 | −0.793617 | ||||||||
\(58\) | 3.73303 | 0.490171 | ||||||||
\(59\) | 4.38060 | 0.570305 | 0.285153 | − | 0.958482i | \(-0.407956\pi\) | ||||
0.285153 | + | 0.958482i | \(0.407956\pi\) | |||||||
\(60\) | 0.408472 | 0.0527335 | ||||||||
\(61\) | 14.4067 | 1.84459 | 0.922294 | − | 0.386490i | \(-0.126313\pi\) | ||||
0.922294 | + | 0.386490i | \(0.126313\pi\) | |||||||
\(62\) | 15.6460 | 1.98705 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.83615 | 0.729518 | ||||||||
\(65\) | 0.0992076 | 0.0123052 | ||||||||
\(66\) | 10.1915 | 1.25449 | ||||||||
\(67\) | −4.09150 | −0.499856 | −0.249928 | − | 0.968264i | \(-0.580407\pi\) | ||||
−0.249928 | + | 0.968264i | \(0.580407\pi\) | |||||||
\(68\) | −1.11153 | −0.134793 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.63827 | 0.194427 | 0.0972134 | − | 0.995264i | \(-0.469007\pi\) | ||||
0.0972134 | + | 0.995264i | \(0.469007\pi\) | |||||||
\(72\) | −2.48058 | −0.292339 | ||||||||
\(73\) | −7.70434 | −0.901725 | −0.450862 | − | 0.892594i | \(-0.648883\pi\) | ||||
−0.450862 | + | 0.892594i | \(0.648883\pi\) | |||||||
\(74\) | 1.50610 | 0.175081 | ||||||||
\(75\) | 3.94770 | 0.455841 | ||||||||
\(76\) | 2.38583 | 0.273674 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.149767 | 0.0169578 | ||||||||
\(79\) | 7.79626 | 0.877148 | 0.438574 | − | 0.898695i | \(-0.355484\pi\) | ||||
0.438574 | + | 0.898695i | \(0.355484\pi\) | |||||||
\(80\) | 4.75756 | 0.531912 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5809 | 1.27889 | ||||||||
\(83\) | −12.4798 | −1.36983 | −0.684916 | − | 0.728622i | \(-0.740161\pi\) | ||||
−0.684916 | + | 0.728622i | \(0.740161\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.86351 | 0.310592 | ||||||||
\(86\) | 10.4107 | 1.12262 | ||||||||
\(87\) | −2.41057 | −0.258440 | ||||||||
\(88\) | 16.3249 | 1.74024 | ||||||||
\(89\) | −2.59708 | −0.275290 | −0.137645 | − | 0.990482i | \(-0.543953\pi\) | ||||
−0.137645 | + | 0.990482i | \(0.543953\pi\) | |||||||
\(90\) | −1.58859 | −0.167452 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.398191 | 0.0415143 | ||||||||
\(93\) | −10.1033 | −1.04766 | ||||||||
\(94\) | −8.87228 | −0.915106 | ||||||||
\(95\) | −6.14637 | −0.630604 | ||||||||
\(96\) | 2.22103 | 0.226683 | ||||||||
\(97\) | −0.921222 | −0.0935359 | −0.0467679 | − | 0.998906i | \(-0.514892\pi\) | ||||
−0.0467679 | + | 0.998906i | \(0.514892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.58109 | −0.661425 | ||||||||
\(100\) | −1.57194 | −0.157194 | ||||||||
\(101\) | 16.4828 | 1.64010 | 0.820052 | − | 0.572289i | \(-0.193944\pi\) | ||||
0.820052 | + | 0.572289i | \(0.193944\pi\) | |||||||
\(102\) | 4.32286 | 0.428027 | ||||||||
\(103\) | 2.02573 | 0.199602 | 0.0998008 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998008 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(104\) | 0.239899 | 0.0235240 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.61636 | −0.739766 | ||||||||
\(107\) | −16.9125 | −1.63500 | −0.817499 | − | 0.575930i | \(-0.804640\pi\) | ||||
−0.817499 | + | 0.575930i | \(0.804640\pi\) | |||||||
\(108\) | −0.398191 | −0.0383160 | ||||||||
\(109\) | 11.3564 | 1.08775 | 0.543875 | − | 0.839167i | \(-0.316957\pi\) | ||||
0.543875 | + | 0.839167i | \(0.316957\pi\) | |||||||
\(110\) | 10.4547 | 0.996813 | ||||||||
\(111\) | −0.972553 | −0.0923106 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0458 | −1.22724 | −0.613620 | − | 0.789601i | \(-0.710288\pi\) | ||||
−0.613620 | + | 0.789601i | \(0.710288\pi\) | |||||||
\(114\) | −9.27877 | −0.869036 | ||||||||
\(115\) | −1.02582 | −0.0956580 | ||||||||
\(116\) | 0.959869 | 0.0891216 | ||||||||
\(117\) | −0.0967108 | −0.00894092 | ||||||||
\(118\) | 6.78384 | 0.624503 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.54462 | −0.232291 | ||||||||
\(121\) | 32.3108 | 2.93734 | ||||||||
\(122\) | 22.3103 | 2.01988 | ||||||||
\(123\) | −7.47823 | −0.674290 | ||||||||
\(124\) | 4.02304 | 0.361280 | ||||||||
\(125\) | 9.17871 | 0.820968 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0382 | −1.24569 | −0.622846 | − | 0.782344i | \(-0.714024\pi\) | ||||
−0.622846 | + | 0.782344i | \(0.714024\pi\) | |||||||
\(128\) | 13.4800 | 1.19147 | ||||||||
\(129\) | −6.72262 | −0.591894 | ||||||||
\(130\) | 0.153634 | 0.0134746 | ||||||||
\(131\) | 2.72724 | 0.238280 | 0.119140 | − | 0.992877i | \(-0.461986\pi\) | ||||
0.119140 | + | 0.992877i | \(0.461986\pi\) | |||||||
\(132\) | 2.62053 | 0.228088 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.33614 | −0.547359 | ||||||||
\(135\) | 1.02582 | 0.0882883 | ||||||||
\(136\) | 6.92439 | 0.593762 | ||||||||
\(137\) | 14.5708 | 1.24487 | 0.622435 | − | 0.782672i | \(-0.286144\pi\) | ||||
0.622435 | + | 0.782672i | \(0.286144\pi\) | |||||||
\(138\) | −1.54861 | −0.131826 | ||||||||
\(139\) | 3.91027 | 0.331665 | 0.165832 | − | 0.986154i | \(-0.446969\pi\) | ||||
0.165832 | + | 0.986154i | \(0.446969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.72919 | 0.482485 | ||||||||
\(142\) | 2.53704 | 0.212904 | ||||||||
\(143\) | 0.636463 | 0.0532237 | ||||||||
\(144\) | −4.63783 | −0.386486 | ||||||||
\(145\) | −2.47281 | −0.205355 | ||||||||
\(146\) | −11.9310 | −0.987417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.387262 | 0.0318327 | ||||||||
\(149\) | 20.7291 | 1.69819 | 0.849097 | − | 0.528237i | \(-0.177147\pi\) | ||||
0.849097 | + | 0.528237i | \(0.177147\pi\) | |||||||
\(150\) | 6.11344 | 0.499161 | ||||||||
\(151\) | 4.02391 | 0.327461 | 0.163730 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163730 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(152\) | −14.8628 | −1.20553 | ||||||||
\(153\) | −2.79145 | −0.225675 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3641 | −0.832466 | ||||||||
\(156\) | 0.0385094 | 0.00308322 | ||||||||
\(157\) | 5.63781 | 0.449947 | 0.224973 | − | 0.974365i | \(-0.427771\pi\) | ||||
0.224973 | + | 0.974365i | \(0.427771\pi\) | |||||||
\(158\) | 12.0734 | 0.960505 | ||||||||
\(159\) | 4.91819 | 0.390038 | ||||||||
\(160\) | 2.27837 | 0.180121 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.54861 | 0.121670 | ||||||||
\(163\) | 18.0803 | 1.41616 | 0.708079 | − | 0.706133i | \(-0.249562\pi\) | ||||
0.708079 | + | 0.706133i | \(0.249562\pi\) | |||||||
\(164\) | 2.97777 | 0.232525 | ||||||||
\(165\) | −6.75100 | −0.525565 | ||||||||
\(166\) | −19.3263 | −1.50001 | ||||||||
\(167\) | 16.9232 | 1.30955 | 0.654776 | − | 0.755823i | \(-0.272763\pi\) | ||||
0.654776 | + | 0.755823i | \(0.272763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9906 | −0.999281 | ||||||||
\(170\) | 4.43447 | 0.340108 | ||||||||
\(171\) | 5.99168 | 0.458195 | ||||||||
\(172\) | 2.67689 | 0.204111 | ||||||||
\(173\) | −5.89586 | −0.448254 | −0.224127 | − | 0.974560i | \(-0.571953\pi\) | ||||
−0.224127 | + | 0.974560i | \(0.571953\pi\) | |||||||
\(174\) | −3.73303 | −0.283001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 30.5220 | 2.30068 | ||||||||
\(177\) | −4.38060 | −0.329266 | ||||||||
\(178\) | −4.02186 | −0.301451 | ||||||||
\(179\) | −18.2272 | −1.36237 | −0.681183 | − | 0.732113i | \(-0.738534\pi\) | ||||
−0.681183 | + | 0.732113i | \(0.738534\pi\) | |||||||
\(180\) | −0.408472 | −0.0304457 | ||||||||
\(181\) | −24.5989 | −1.82842 | −0.914210 | − | 0.405242i | \(-0.867187\pi\) | ||||
−0.914210 | + | 0.405242i | \(0.867187\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.4067 | −1.06497 | ||||||||
\(184\) | −2.48058 | −0.182870 | ||||||||
\(185\) | −0.997662 | −0.0733495 | ||||||||
\(186\) | −15.6460 | −1.14722 | ||||||||
\(187\) | 18.3708 | 1.34340 | ||||||||
\(188\) | −2.28132 | −0.166382 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.51832 | −0.690532 | ||||||||
\(191\) | 19.6107 | 1.41898 | 0.709490 | − | 0.704716i | \(-0.248925\pi\) | ||||
0.709490 | + | 0.704716i | \(0.248925\pi\) | |||||||
\(192\) | −5.83615 | −0.421188 | ||||||||
\(193\) | −10.5101 | −0.756533 | −0.378267 | − | 0.925697i | \(-0.623480\pi\) | ||||
−0.378267 | + | 0.925697i | \(0.623480\pi\) | |||||||
\(194\) | −1.42661 | −0.102425 | ||||||||
\(195\) | −0.0992076 | −0.00710441 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.33222 | 0.522399 | 0.261199 | − | 0.965285i | \(-0.415882\pi\) | ||||
0.261199 | + | 0.965285i | \(0.415882\pi\) | |||||||
\(198\) | −10.1915 | −0.724281 | ||||||||
\(199\) | 7.36088 | 0.521799 | 0.260899 | − | 0.965366i | \(-0.415981\pi\) | ||||
0.260899 | + | 0.965366i | \(0.415981\pi\) | |||||||
\(200\) | 9.79257 | 0.692439 | ||||||||
\(201\) | 4.09150 | 0.288592 | ||||||||
\(202\) | 25.5255 | 1.79597 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.11153 | 0.0778226 | ||||||||
\(205\) | −7.67130 | −0.535787 | ||||||||
\(206\) | 3.13707 | 0.218570 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0.448528 | 0.0310998 | ||||||||
\(209\) | −39.4318 | −2.72755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.515133 | −0.0354632 | −0.0177316 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177316 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(212\) | −1.95838 | −0.134502 | ||||||||
\(213\) | −1.63827 | −0.112252 | ||||||||
\(214\) | −26.1909 | −1.79038 | ||||||||
\(215\) | −6.89619 | −0.470316 | ||||||||
\(216\) | 2.48058 | 0.168782 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.5867 | 1.19112 | ||||||||
\(219\) | 7.70434 | 0.520611 | ||||||||
\(220\) | 2.68819 | 0.181238 | ||||||||
\(221\) | 0.269963 | 0.0181597 | ||||||||
\(222\) | −1.50610 | −0.101083 | ||||||||
\(223\) | 16.5692 | 1.10956 | 0.554778 | − | 0.831998i | \(-0.312803\pi\) | ||||
0.554778 | + | 0.831998i | \(0.312803\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.94770 | −0.263180 | ||||||||
\(226\) | −20.2028 | −1.34387 | ||||||||
\(227\) | 2.13077 | 0.141424 | 0.0707120 | − | 0.997497i | \(-0.477473\pi\) | ||||
0.0707120 | + | 0.997497i | \(0.477473\pi\) | |||||||
\(228\) | −2.38583 | −0.158006 | ||||||||
\(229\) | −14.4259 | −0.953290 | −0.476645 | − | 0.879096i | \(-0.658147\pi\) | ||||
−0.476645 | + | 0.879096i | \(0.658147\pi\) | |||||||
\(230\) | −1.58859 | −0.104749 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.97961 | −0.392580 | ||||||||
\(233\) | −2.22006 | −0.145441 | −0.0727206 | − | 0.997352i | \(-0.523168\pi\) | ||||
−0.0727206 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(234\) | −0.149767 | −0.00979059 | ||||||||
\(235\) | 5.87711 | 0.383380 | ||||||||
\(236\) | 1.74432 | 0.113545 | ||||||||
\(237\) | −7.79626 | −0.506422 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.4611 | 0.935412 | 0.467706 | − | 0.883884i | \(-0.345081\pi\) | ||||
0.467706 | + | 0.883884i | \(0.345081\pi\) | |||||||
\(240\) | −4.75756 | −0.307099 | ||||||||
\(241\) | −17.8066 | −1.14703 | −0.573513 | − | 0.819196i | \(-0.694420\pi\) | ||||
−0.573513 | + | 0.819196i | \(0.694420\pi\) | |||||||
\(242\) | 50.0368 | 3.21649 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.73662 | 0.367249 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.5809 | −0.738369 | ||||||||
\(247\) | −0.579460 | −0.0368702 | ||||||||
\(248\) | −25.0620 | −1.59144 | ||||||||
\(249\) | 12.4798 | 0.790873 | ||||||||
\(250\) | 14.2142 | 0.898987 | ||||||||
\(251\) | 27.5761 | 1.74059 | 0.870293 | − | 0.492535i | \(-0.163930\pi\) | ||||
0.870293 | + | 0.492535i | \(0.163930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.58109 | −0.413750 | ||||||||
\(254\) | −21.7397 | −1.36407 | ||||||||
\(255\) | −2.86351 | −0.179320 | ||||||||
\(256\) | 9.20292 | 0.575182 | ||||||||
\(257\) | −17.0021 | −1.06056 | −0.530280 | − | 0.847822i | \(-0.677913\pi\) | ||||
−0.530280 | + | 0.847822i | \(0.677913\pi\) | |||||||
\(258\) | −10.4107 | −0.648143 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.0395036 | 0.00244991 | ||||||||
\(261\) | 2.41057 | 0.149211 | ||||||||
\(262\) | 4.22344 | 0.260925 | ||||||||
\(263\) | −20.0349 | −1.23540 | −0.617702 | − | 0.786412i | \(-0.711936\pi\) | ||||
−0.617702 | + | 0.786412i | \(0.711936\pi\) | |||||||
\(264\) | −16.3249 | −1.00473 | ||||||||
\(265\) | 5.04517 | 0.309922 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.59708 | 0.158939 | ||||||||
\(268\) | −1.62920 | −0.0995192 | ||||||||
\(269\) | 18.1520 | 1.10675 | 0.553373 | − | 0.832934i | \(-0.313340\pi\) | ||||
0.553373 | + | 0.832934i | \(0.313340\pi\) | |||||||
\(270\) | 1.58859 | 0.0966785 | ||||||||
\(271\) | 7.58594 | 0.460813 | 0.230406 | − | 0.973094i | \(-0.425994\pi\) | ||||
0.230406 | + | 0.973094i | \(0.425994\pi\) | |||||||
\(272\) | 12.9462 | 0.784981 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.5645 | 1.36317 | ||||||||
\(275\) | 25.9802 | 1.56666 | ||||||||
\(276\) | −0.398191 | −0.0239683 | ||||||||
\(277\) | 19.5130 | 1.17242 | 0.586212 | − | 0.810158i | \(-0.300619\pi\) | ||||
0.586212 | + | 0.810158i | \(0.300619\pi\) | |||||||
\(278\) | 6.05548 | 0.363184 | ||||||||
\(279\) | 10.1033 | 0.604868 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.47664 | 0.0880892 | 0.0440446 | − | 0.999030i | \(-0.485976\pi\) | ||||
0.0440446 | + | 0.999030i | \(0.485976\pi\) | |||||||
\(282\) | 8.87228 | 0.528337 | ||||||||
\(283\) | −1.23515 | −0.0734218 | −0.0367109 | − | 0.999326i | \(-0.511688\pi\) | ||||
−0.0367109 | + | 0.999326i | \(0.511688\pi\) | |||||||
\(284\) | 0.652345 | 0.0387095 | ||||||||
\(285\) | 6.14637 | 0.364079 | ||||||||
\(286\) | 0.985632 | 0.0582817 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.22103 | −0.130875 | ||||||||
\(289\) | −9.20783 | −0.541637 | ||||||||
\(290\) | −3.82941 | −0.224871 | ||||||||
\(291\) | 0.921222 | 0.0540030 | ||||||||
\(292\) | −3.06780 | −0.179529 | ||||||||
\(293\) | 9.74857 | 0.569517 | 0.284759 | − | 0.958599i | \(-0.408087\pi\) | ||||
0.284759 | + | 0.958599i | \(0.408087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.49369 | −0.261633 | ||||||||
\(296\) | −2.41249 | −0.140223 | ||||||||
\(297\) | 6.58109 | 0.381874 | ||||||||
\(298\) | 32.1013 | 1.85958 | ||||||||
\(299\) | −0.0967108 | −0.00559293 | ||||||||
\(300\) | 1.57194 | 0.0907560 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.23146 | 0.358580 | ||||||||
\(303\) | −16.4828 | −0.946915 | ||||||||
\(304\) | −27.7884 | −1.59377 | ||||||||
\(305\) | −14.7786 | −0.846222 | ||||||||
\(306\) | −4.32286 | −0.247121 | ||||||||
\(307\) | 27.7926 | 1.58621 | 0.793105 | − | 0.609085i | \(-0.208463\pi\) | ||||
0.793105 | + | 0.609085i | \(0.208463\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.02573 | −0.115240 | ||||||||
\(310\) | −16.0500 | −0.911577 | ||||||||
\(311\) | −3.96040 | −0.224574 | −0.112287 | − | 0.993676i | \(-0.535818\pi\) | ||||
−0.112287 | + | 0.993676i | \(0.535818\pi\) | |||||||
\(312\) | −0.239899 | −0.0135816 | ||||||||
\(313\) | −4.81964 | −0.272422 | −0.136211 | − | 0.990680i | \(-0.543492\pi\) | ||||
−0.136211 | + | 0.990680i | \(0.543492\pi\) | |||||||
\(314\) | 8.73077 | 0.492706 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.10440 | 0.174636 | ||||||||
\(317\) | −16.8489 | −0.946326 | −0.473163 | − | 0.880975i | \(-0.656888\pi\) | ||||
−0.473163 | + | 0.880975i | \(0.656888\pi\) | |||||||
\(318\) | 7.61636 | 0.427104 | ||||||||
\(319\) | −15.8642 | −0.888225 | ||||||||
\(320\) | −5.98682 | −0.334673 | ||||||||
\(321\) | 16.9125 | 0.943966 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.7254 | −0.930629 | ||||||||
\(324\) | 0.398191 | 0.0221217 | ||||||||
\(325\) | 0.381785 | 0.0211776 | ||||||||
\(326\) | 27.9993 | 1.55074 | ||||||||
\(327\) | −11.3564 | −0.628012 | ||||||||
\(328\) | −18.5503 | −1.02427 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.4547 | −0.575510 | ||||||||
\(331\) | 10.0553 | 0.552689 | 0.276344 | − | 0.961059i | \(-0.410877\pi\) | ||||
0.276344 | + | 0.961059i | \(0.410877\pi\) | |||||||
\(332\) | −4.96933 | −0.272728 | ||||||||
\(333\) | 0.972553 | 0.0532956 | ||||||||
\(334\) | 26.2074 | 1.43400 | ||||||||
\(335\) | 4.19713 | 0.229314 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.6099 | −1.55848 | −0.779240 | − | 0.626725i | \(-0.784395\pi\) | ||||
−0.779240 | + | 0.626725i | \(0.784395\pi\) | |||||||
\(338\) | −20.1174 | −1.09424 | ||||||||
\(339\) | 13.0458 | 0.708548 | ||||||||
\(340\) | 1.14023 | 0.0618375 | ||||||||
\(341\) | −66.4906 | −3.60067 | ||||||||
\(342\) | 9.27877 | 0.501738 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −16.6760 | −0.899109 | ||||||||
\(345\) | 1.02582 | 0.0552282 | ||||||||
\(346\) | −9.13039 | −0.490853 | ||||||||
\(347\) | 19.4460 | 1.04392 | 0.521958 | − | 0.852971i | \(-0.325202\pi\) | ||||
0.521958 | + | 0.852971i | \(0.325202\pi\) | |||||||
\(348\) | −0.959869 | −0.0514544 | ||||||||
\(349\) | −11.4642 | −0.613663 | −0.306832 | − | 0.951764i | \(-0.599269\pi\) | ||||
−0.306832 | + | 0.951764i | \(0.599269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.0967108 | 0.00516204 | ||||||||
\(352\) | 14.6168 | 0.779078 | ||||||||
\(353\) | 31.1454 | 1.65770 | 0.828850 | − | 0.559471i | \(-0.188996\pi\) | ||||
0.828850 | + | 0.559471i | \(0.188996\pi\) | |||||||
\(354\) | −6.78384 | −0.360557 | ||||||||
\(355\) | −1.68057 | −0.0891952 | ||||||||
\(356\) | −1.03413 | −0.0548090 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.2268 | −1.49183 | ||||||||
\(359\) | −15.8708 | −0.837628 | −0.418814 | − | 0.908072i | \(-0.637554\pi\) | ||||
−0.418814 | + | 0.908072i | \(0.637554\pi\) | |||||||
\(360\) | 2.54462 | 0.134113 | ||||||||
\(361\) | 16.9002 | 0.889485 | ||||||||
\(362\) | −38.0940 | −2.00218 | ||||||||
\(363\) | −32.3108 | −1.69588 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.90324 | 0.413675 | ||||||||
\(366\) | −22.3103 | −1.16618 | ||||||||
\(367\) | 0.586635 | 0.0306221 | 0.0153111 | − | 0.999883i | \(-0.495126\pi\) | ||||
0.0153111 | + | 0.999883i | \(0.495126\pi\) | |||||||
\(368\) | −4.63783 | −0.241763 | ||||||||
\(369\) | 7.47823 | 0.389301 | ||||||||
\(370\) | −1.54499 | −0.0803201 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.02304 | −0.208585 | ||||||||
\(373\) | −10.9030 | −0.564537 | −0.282268 | − | 0.959335i | \(-0.591087\pi\) | ||||
−0.282268 | + | 0.959335i | \(0.591087\pi\) | |||||||
\(374\) | 28.4491 | 1.47107 | ||||||||
\(375\) | −9.17871 | −0.473986 | ||||||||
\(376\) | 14.2117 | 0.732913 | ||||||||
\(377\) | −0.233128 | −0.0120067 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2093 | 1.14081 | 0.570407 | − | 0.821362i | \(-0.306786\pi\) | ||||
0.570407 | + | 0.821362i | \(0.306786\pi\) | |||||||
\(380\) | −2.44743 | −0.125551 | ||||||||
\(381\) | 14.0382 | 0.719201 | ||||||||
\(382\) | 30.3693 | 1.55383 | ||||||||
\(383\) | 16.1733 | 0.826417 | 0.413209 | − | 0.910636i | \(-0.364408\pi\) | ||||
0.413209 | + | 0.910636i | \(0.364408\pi\) | |||||||
\(384\) | −13.4800 | −0.687897 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.2760 | −0.828429 | ||||||||
\(387\) | 6.72262 | 0.341730 | ||||||||
\(388\) | −0.366822 | −0.0186226 | ||||||||
\(389\) | −8.60710 | −0.436397 | −0.218199 | − | 0.975904i | \(-0.570018\pi\) | ||||
−0.218199 | + | 0.975904i | \(0.570018\pi\) | |||||||
\(390\) | −0.153634 | −0.00777955 | ||||||||
\(391\) | −2.79145 | −0.141170 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.72724 | −0.137571 | ||||||||
\(394\) | 11.3547 | 0.572044 | ||||||||
\(395\) | −7.99754 | −0.402400 | ||||||||
\(396\) | −2.62053 | −0.131687 | ||||||||
\(397\) | 5.16626 | 0.259287 | 0.129644 | − | 0.991561i | \(-0.458617\pi\) | ||||
0.129644 | + | 0.991561i | \(0.458617\pi\) | |||||||
\(398\) | 11.3991 | 0.571386 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.3087 | 0.915437 | ||||||||
\(401\) | 25.6945 | 1.28312 | 0.641561 | − | 0.767072i | \(-0.278287\pi\) | ||||
0.641561 | + | 0.767072i | \(0.278287\pi\) | |||||||
\(402\) | 6.33614 | 0.316018 | ||||||||
\(403\) | −0.977096 | −0.0486726 | ||||||||
\(404\) | 6.56333 | 0.326538 | ||||||||
\(405\) | −1.02582 | −0.0509733 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.40046 | −0.317259 | ||||||||
\(408\) | −6.92439 | −0.342809 | ||||||||
\(409\) | −14.7987 | −0.731749 | −0.365874 | − | 0.930664i | \(-0.619230\pi\) | ||||
−0.365874 | + | 0.930664i | \(0.619230\pi\) | |||||||
\(410\) | −11.8799 | −0.586704 | ||||||||
\(411\) | −14.5708 | −0.718726 | ||||||||
\(412\) | 0.806630 | 0.0397398 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.54861 | 0.0761100 | ||||||||
\(415\) | 12.8020 | 0.628424 | ||||||||
\(416\) | 0.214798 | 0.0105313 | ||||||||
\(417\) | −3.91027 | −0.191487 | ||||||||
\(418\) | −61.0644 | −2.98676 | ||||||||
\(419\) | −6.43007 | −0.314130 | −0.157065 | − | 0.987588i | \(-0.550203\pi\) | ||||
−0.157065 | + | 0.987588i | \(0.550203\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.1314 | −0.883670 | −0.441835 | − | 0.897096i | \(-0.645672\pi\) | ||||
−0.441835 | + | 0.897096i | \(0.645672\pi\) | |||||||
\(422\) | −0.797740 | −0.0388334 | ||||||||
\(423\) | −5.72919 | −0.278563 | ||||||||
\(424\) | 12.2000 | 0.592482 | ||||||||
\(425\) | 11.0198 | 0.534538 | ||||||||
\(426\) | −2.53704 | −0.122920 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.73443 | −0.325521 | ||||||||
\(429\) | −0.636463 | −0.0307287 | ||||||||
\(430\) | −10.6795 | −0.515011 | ||||||||
\(431\) | −15.6712 | −0.754856 | −0.377428 | − | 0.926039i | \(-0.623191\pi\) | ||||
−0.377428 | + | 0.926039i | \(0.623191\pi\) | |||||||
\(432\) | 4.63783 | 0.223138 | ||||||||
\(433\) | −23.4459 | −1.12674 | −0.563368 | − | 0.826206i | \(-0.690495\pi\) | ||||
−0.563368 | + | 0.826206i | \(0.690495\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.47281 | 0.118562 | ||||||||
\(436\) | 4.52203 | 0.216566 | ||||||||
\(437\) | 5.99168 | 0.286621 | ||||||||
\(438\) | 11.9310 | 0.570086 | ||||||||
\(439\) | 6.77828 | 0.323510 | 0.161755 | − | 0.986831i | \(-0.448285\pi\) | ||||
0.161755 | + | 0.986831i | \(0.448285\pi\) | |||||||
\(440\) | −16.7464 | −0.798352 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.418067 | 0.0198854 | ||||||||
\(443\) | −29.1655 | −1.38569 | −0.692847 | − | 0.721085i | \(-0.743644\pi\) | ||||
−0.692847 | + | 0.721085i | \(0.743644\pi\) | |||||||
\(444\) | −0.387262 | −0.0183786 | ||||||||
\(445\) | 2.66413 | 0.126292 | ||||||||
\(446\) | 25.6592 | 1.21500 | ||||||||
\(447\) | −20.7291 | −0.980453 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.9760 | 1.74501 | 0.872503 | − | 0.488609i | \(-0.162496\pi\) | ||||
0.872503 | + | 0.488609i | \(0.162496\pi\) | |||||||
\(450\) | −6.11344 | −0.288190 | ||||||||
\(451\) | −49.2150 | −2.31744 | ||||||||
\(452\) | −5.19470 | −0.244338 | ||||||||
\(453\) | −4.02391 | −0.189060 | ||||||||
\(454\) | 3.29973 | 0.154864 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.8628 | 0.696015 | ||||||||
\(457\) | 27.7671 | 1.29889 | 0.649445 | − | 0.760409i | \(-0.275001\pi\) | ||||
0.649445 | + | 0.760409i | \(0.275001\pi\) | |||||||
\(458\) | −22.3401 | −1.04388 | ||||||||
\(459\) | 2.79145 | 0.130294 | ||||||||
\(460\) | −0.408472 | −0.0190451 | ||||||||
\(461\) | 26.9409 | 1.25476 | 0.627380 | − | 0.778713i | \(-0.284127\pi\) | ||||
0.627380 | + | 0.778713i | \(0.284127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.8087 | 1.24591 | 0.622954 | − | 0.782258i | \(-0.285932\pi\) | ||||
0.622954 | + | 0.782258i | \(0.285932\pi\) | |||||||
\(464\) | −11.1798 | −0.519010 | ||||||||
\(465\) | 10.3641 | 0.480625 | ||||||||
\(466\) | −3.43801 | −0.159263 | ||||||||
\(467\) | 16.0527 | 0.742833 | 0.371416 | − | 0.928466i | \(-0.378872\pi\) | ||||
0.371416 | + | 0.928466i | \(0.378872\pi\) | |||||||
\(468\) | −0.0385094 | −0.00178010 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.10134 | 0.419814 | ||||||||
\(471\) | −5.63781 | −0.259777 | ||||||||
\(472\) | −10.8664 | −0.500167 | ||||||||
\(473\) | −44.2422 | −2.03426 | ||||||||
\(474\) | −12.0734 | −0.554548 | ||||||||
\(475\) | −23.6533 | −1.08529 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.91819 | −0.225189 | ||||||||
\(478\) | 22.3946 | 1.02431 | ||||||||
\(479\) | −8.08384 | −0.369360 | −0.184680 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184680 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(480\) | −2.27837 | −0.103993 | ||||||||
\(481\) | −0.0940564 | −0.00428860 | ||||||||
\(482\) | −27.5755 | −1.25603 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.8659 | 0.584812 | ||||||||
\(485\) | 0.945005 | 0.0429105 | ||||||||
\(486\) | −1.54861 | −0.0702464 | ||||||||
\(487\) | −22.2419 | −1.00787 | −0.503937 | − | 0.863740i | \(-0.668116\pi\) | ||||
−0.503937 | + | 0.863740i | \(0.668116\pi\) | |||||||
\(488\) | −35.7369 | −1.61773 | ||||||||
\(489\) | −18.0803 | −0.817619 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.0527 | −1.13061 | −0.565307 | − | 0.824881i | \(-0.691242\pi\) | ||||
−0.565307 | + | 0.824881i | \(0.691242\pi\) | |||||||
\(492\) | −2.97777 | −0.134248 | ||||||||
\(493\) | −6.72898 | −0.303058 | ||||||||
\(494\) | −0.897357 | −0.0403740 | ||||||||
\(495\) | 6.75100 | 0.303435 | ||||||||
\(496\) | −46.8573 | −2.10395 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 19.3263 | 0.866031 | ||||||||
\(499\) | 22.4671 | 1.00576 | 0.502882 | − | 0.864355i | \(-0.332273\pi\) | ||||
0.502882 | + | 0.864355i | \(0.332273\pi\) | |||||||
\(500\) | 3.65488 | 0.163451 | ||||||||
\(501\) | −16.9232 | −0.756071 | ||||||||
\(502\) | 42.7045 | 1.90600 | ||||||||
\(503\) | 14.3313 | 0.638999 | 0.319500 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319500 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.9084 | −0.752413 | ||||||||
\(506\) | −10.1915 | −0.453069 | ||||||||
\(507\) | 12.9906 | 0.576935 | ||||||||
\(508\) | −5.58990 | −0.248012 | ||||||||
\(509\) | −20.5708 | −0.911786 | −0.455893 | − | 0.890035i | \(-0.650680\pi\) | ||||
−0.455893 | + | 0.890035i | \(0.650680\pi\) | |||||||
\(510\) | −4.43447 | −0.196361 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12.7082 | −0.561629 | ||||||||
\(513\) | −5.99168 | −0.264539 | ||||||||
\(514\) | −26.3296 | −1.16135 | ||||||||
\(515\) | −2.07803 | −0.0915691 | ||||||||
\(516\) | −2.67689 | −0.117844 | ||||||||
\(517\) | 37.7044 | 1.65824 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.89586 | 0.258800 | ||||||||
\(520\) | −0.246092 | −0.0107919 | ||||||||
\(521\) | −30.8216 | −1.35032 | −0.675160 | − | 0.737672i | \(-0.735925\pi\) | ||||
−0.675160 | + | 0.737672i | \(0.735925\pi\) | |||||||
\(522\) | 3.73303 | 0.163390 | ||||||||
\(523\) | 3.49880 | 0.152992 | 0.0764958 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764958 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(524\) | 1.08597 | 0.0474406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.0262 | −1.35281 | ||||||||
\(527\) | −28.2028 | −1.22853 | ||||||||
\(528\) | −30.5220 | −1.32830 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 7.81299 | 0.339375 | ||||||||
\(531\) | 4.38060 | 0.190102 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.723226 | −0.0313264 | ||||||||
\(534\) | 4.02186 | 0.174043 | ||||||||
\(535\) | 17.3492 | 0.750071 | ||||||||
\(536\) | 10.1493 | 0.438382 | ||||||||
\(537\) | 18.2272 | 0.786563 | ||||||||
\(538\) | 28.1103 | 1.21192 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.408472 | 0.0175778 | ||||||||
\(541\) | −35.7811 | −1.53835 | −0.769175 | − | 0.639038i | \(-0.779333\pi\) | ||||
−0.769175 | + | 0.639038i | \(0.779333\pi\) | |||||||
\(542\) | 11.7477 | 0.504605 | ||||||||
\(543\) | 24.5989 | 1.05564 | ||||||||
\(544\) | 6.19988 | 0.265818 | ||||||||
\(545\) | −11.6496 | −0.499015 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2676 | 1.20864 | 0.604318 | − | 0.796743i | \(-0.293446\pi\) | ||||
0.604318 | + | 0.796743i | \(0.293446\pi\) | |||||||
\(548\) | 5.80198 | 0.247848 | ||||||||
\(549\) | 14.4067 | 0.614862 | ||||||||
\(550\) | 40.2331 | 1.71555 | ||||||||
\(551\) | 14.4434 | 0.615308 | ||||||||
\(552\) | 2.48058 | 0.105580 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 30.2180 | 1.28384 | ||||||||
\(555\) | 0.997662 | 0.0423484 | ||||||||
\(556\) | 1.55704 | 0.0660330 | ||||||||
\(557\) | 13.3099 | 0.563960 | 0.281980 | − | 0.959420i | \(-0.409009\pi\) | ||||
0.281980 | + | 0.959420i | \(0.409009\pi\) | |||||||
\(558\) | 15.6460 | 0.662350 | ||||||||
\(559\) | −0.650151 | −0.0274984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.3708 | −0.775614 | ||||||||
\(562\) | 2.28674 | 0.0964605 | ||||||||
\(563\) | −20.4179 | −0.860513 | −0.430257 | − | 0.902707i | \(-0.641577\pi\) | ||||
−0.430257 | + | 0.902707i | \(0.641577\pi\) | |||||||
\(564\) | 2.28132 | 0.0960607 | ||||||||
\(565\) | 13.3826 | 0.563008 | ||||||||
\(566\) | −1.91276 | −0.0803992 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.06385 | −0.170515 | ||||||||
\(569\) | −7.25109 | −0.303982 | −0.151991 | − | 0.988382i | \(-0.548568\pi\) | ||||
−0.151991 | + | 0.988382i | \(0.548568\pi\) | |||||||
\(570\) | 9.51832 | 0.398679 | ||||||||
\(571\) | 20.9061 | 0.874893 | 0.437446 | − | 0.899244i | \(-0.355883\pi\) | ||||
0.437446 | + | 0.899244i | \(0.355883\pi\) | |||||||
\(572\) | 0.253434 | 0.0105966 | ||||||||
\(573\) | −19.6107 | −0.819248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.94770 | −0.164630 | ||||||||
\(576\) | 5.83615 | 0.243173 | ||||||||
\(577\) | −28.3400 | −1.17981 | −0.589905 | − | 0.807473i | \(-0.700835\pi\) | ||||
−0.589905 | + | 0.807473i | \(0.700835\pi\) | |||||||
\(578\) | −14.2593 | −0.593110 | ||||||||
\(579\) | 10.5101 | 0.436785 | ||||||||
\(580\) | −0.984650 | −0.0408854 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.42661 | 0.0591350 | ||||||||
\(583\) | 32.3671 | 1.34051 | ||||||||
\(584\) | 19.1112 | 0.790827 | ||||||||
\(585\) | 0.0992076 | 0.00410173 | ||||||||
\(586\) | 15.0967 | 0.623640 | ||||||||
\(587\) | 23.3149 | 0.962310 | 0.481155 | − | 0.876635i | \(-0.340217\pi\) | ||||
0.481155 | + | 0.876635i | \(0.340217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.5356 | 2.49433 | ||||||||
\(590\) | −6.95898 | −0.286497 | ||||||||
\(591\) | −7.33222 | −0.301607 | ||||||||
\(592\) | −4.51053 | −0.185382 | ||||||||
\(593\) | −8.07712 | −0.331687 | −0.165844 | − | 0.986152i | \(-0.553035\pi\) | ||||
−0.165844 | + | 0.986152i | \(0.553035\pi\) | |||||||
\(594\) | 10.1915 | 0.418164 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.25415 | 0.338103 | ||||||||
\(597\) | −7.36088 | −0.301261 | ||||||||
\(598\) | −0.149767 | −0.00612444 | ||||||||
\(599\) | 22.2393 | 0.908673 | 0.454337 | − | 0.890830i | \(-0.349876\pi\) | ||||
0.454337 | + | 0.890830i | \(0.349876\pi\) | |||||||
\(600\) | −9.79257 | −0.399780 | ||||||||
\(601\) | −34.9803 | −1.42688 | −0.713438 | − | 0.700719i | \(-0.752863\pi\) | ||||
−0.713438 | + | 0.700719i | \(0.752863\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.09150 | −0.166619 | ||||||||
\(604\) | 1.60228 | 0.0651960 | ||||||||
\(605\) | −33.1450 | −1.34753 | ||||||||
\(606\) | −25.5255 | −1.03690 | ||||||||
\(607\) | −14.3826 | −0.583771 | −0.291886 | − | 0.956453i | \(-0.594283\pi\) | ||||
−0.291886 | + | 0.956453i | \(0.594283\pi\) | |||||||
\(608\) | −13.3077 | −0.539698 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.8863 | −0.926640 | ||||||||
\(611\) | 0.554075 | 0.0224155 | ||||||||
\(612\) | −1.11153 | −0.0449309 | ||||||||
\(613\) | −30.0109 | −1.21213 | −0.606065 | − | 0.795415i | \(-0.707253\pi\) | ||||
−0.606065 | + | 0.795415i | \(0.707253\pi\) | |||||||
\(614\) | 43.0400 | 1.73695 | ||||||||
\(615\) | 7.67130 | 0.309337 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.0763 | −0.566690 | −0.283345 | − | 0.959018i | \(-0.591444\pi\) | ||||
−0.283345 | + | 0.959018i | \(0.591444\pi\) | |||||||
\(618\) | −3.13707 | −0.126192 | ||||||||
\(619\) | 27.4497 | 1.10330 | 0.551648 | − | 0.834077i | \(-0.313999\pi\) | ||||
0.551648 | + | 0.834077i | \(0.313999\pi\) | |||||||
\(620\) | −4.12690 | −0.165740 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −6.13311 | −0.245916 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.448528 | −0.0179555 | ||||||||
\(625\) | 10.3228 | 0.412913 | ||||||||
\(626\) | −7.46373 | −0.298311 | ||||||||
\(627\) | 39.4318 | 1.57475 | ||||||||
\(628\) | 2.24493 | 0.0895824 | ||||||||
\(629\) | −2.71483 | −0.108247 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.9335 | 0.912970 | 0.456485 | − | 0.889731i | \(-0.349108\pi\) | ||||
0.456485 | + | 0.889731i | \(0.349108\pi\) | |||||||
\(632\) | −19.3392 | −0.769273 | ||||||||
\(633\) | 0.515133 | 0.0204747 | ||||||||
\(634\) | −26.0923 | −1.03626 | ||||||||
\(635\) | 14.4007 | 0.571473 | ||||||||
\(636\) | 1.95838 | 0.0776549 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.5674 | −0.972635 | ||||||||
\(639\) | 1.63827 | 0.0648089 | ||||||||
\(640\) | −13.8280 | −0.546599 | ||||||||
\(641\) | −4.93467 | −0.194908 | −0.0974539 | − | 0.995240i | \(-0.531070\pi\) | ||||
−0.0974539 | + | 0.995240i | \(0.531070\pi\) | |||||||
\(642\) | 26.1909 | 1.03367 | ||||||||
\(643\) | 2.11089 | 0.0832453 | 0.0416226 | − | 0.999133i | \(-0.486747\pi\) | ||||
0.0416226 | + | 0.999133i | \(0.486747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.89619 | 0.271537 | ||||||||
\(646\) | −25.9012 | −1.01907 | ||||||||
\(647\) | 29.9015 | 1.17555 | 0.587774 | − | 0.809025i | \(-0.300004\pi\) | ||||
0.587774 | + | 0.809025i | \(0.300004\pi\) | |||||||
\(648\) | −2.48058 | −0.0974462 | ||||||||
\(649\) | −28.8291 | −1.13164 | ||||||||
\(650\) | 0.591236 | 0.0231902 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.19941 | 0.281951 | ||||||||
\(653\) | −31.7412 | −1.24213 | −0.621065 | − | 0.783759i | \(-0.713300\pi\) | ||||
−0.621065 | + | 0.783759i | \(0.713300\pi\) | |||||||
\(654\) | −17.5867 | −0.687694 | ||||||||
\(655\) | −2.79766 | −0.109313 | ||||||||
\(656\) | −34.6828 | −1.35413 | ||||||||
\(657\) | −7.70434 | −0.300575 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.60404 | 0.101439 | 0.0507195 | − | 0.998713i | \(-0.483849\pi\) | ||||
0.0507195 | + | 0.998713i | \(0.483849\pi\) | |||||||
\(660\) | −2.68819 | −0.104638 | ||||||||
\(661\) | 38.2421 | 1.48744 | 0.743722 | − | 0.668489i | \(-0.233059\pi\) | ||||
0.743722 | + | 0.668489i | \(0.233059\pi\) | |||||||
\(662\) | 15.5717 | 0.605212 | ||||||||
\(663\) | −0.269963 | −0.0104845 | ||||||||
\(664\) | 30.9570 | 1.20136 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.50610 | 0.0583604 | ||||||||
\(667\) | 2.41057 | 0.0933377 | ||||||||
\(668\) | 6.73865 | 0.260726 | ||||||||
\(669\) | −16.5692 | −0.640603 | ||||||||
\(670\) | 6.49972 | 0.251106 | ||||||||
\(671\) | −94.8117 | −3.66017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.2699 | 1.20536 | 0.602682 | − | 0.797981i | \(-0.294099\pi\) | ||||
0.602682 | + | 0.797981i | \(0.294099\pi\) | |||||||
\(674\) | −44.3056 | −1.70659 | ||||||||
\(675\) | 3.94770 | 0.151947 | ||||||||
\(676\) | −5.17276 | −0.198952 | ||||||||
\(677\) | 10.1973 | 0.391915 | 0.195958 | − | 0.980612i | \(-0.437219\pi\) | ||||
0.195958 | + | 0.980612i | \(0.437219\pi\) | |||||||
\(678\) | 20.2028 | 0.775883 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −7.10317 | −0.272394 | ||||||||
\(681\) | −2.13077 | −0.0816512 | ||||||||
\(682\) | −102.968 | −3.94285 | ||||||||
\(683\) | −12.6603 | −0.484432 | −0.242216 | − | 0.970222i | \(-0.577874\pi\) | ||||
−0.242216 | + | 0.970222i | \(0.577874\pi\) | |||||||
\(684\) | 2.38583 | 0.0912246 | ||||||||
\(685\) | −14.9470 | −0.571096 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.4259 | 0.550382 | ||||||||
\(688\) | −31.1784 | −1.18866 | ||||||||
\(689\) | 0.475642 | 0.0181205 | ||||||||
\(690\) | 1.58859 | 0.0604766 | ||||||||
\(691\) | −6.74340 | −0.256531 | −0.128266 | − | 0.991740i | \(-0.540941\pi\) | ||||
−0.128266 | + | 0.991740i | \(0.540941\pi\) | |||||||
\(692\) | −2.34768 | −0.0892454 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.1143 | 1.14312 | ||||||||
\(695\) | −4.01122 | −0.152154 | ||||||||
\(696\) | 5.97961 | 0.226656 | ||||||||
\(697\) | −20.8751 | −0.790700 | ||||||||
\(698\) | −17.7535 | −0.671981 | ||||||||
\(699\) | 2.22006 | 0.0839705 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1107 | 0.721803 | 0.360901 | − | 0.932604i | \(-0.382469\pi\) | ||||
0.360901 | + | 0.932604i | \(0.382469\pi\) | |||||||
\(702\) | 0.149767 | 0.00565260 | ||||||||
\(703\) | 5.82722 | 0.219778 | ||||||||
\(704\) | −38.4082 | −1.44756 | ||||||||
\(705\) | −5.87711 | −0.221345 | ||||||||
\(706\) | 48.2320 | 1.81524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.74432 | −0.0655554 | ||||||||
\(709\) | 10.9432 | 0.410980 | 0.205490 | − | 0.978659i | \(-0.434121\pi\) | ||||
0.205490 | + | 0.978659i | \(0.434121\pi\) | |||||||
\(710\) | −2.60254 | −0.0976716 | ||||||||
\(711\) | 7.79626 | 0.292383 | ||||||||
\(712\) | 6.44225 | 0.241434 | ||||||||
\(713\) | 10.1033 | 0.378371 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.652895 | −0.0244169 | ||||||||
\(716\) | −7.25792 | −0.271241 | ||||||||
\(717\) | −14.4611 | −0.540060 | ||||||||
\(718\) | −24.5776 | −0.917230 | ||||||||
\(719\) | 45.3780 | 1.69232 | 0.846158 | − | 0.532932i | \(-0.178910\pi\) | ||||
0.846158 | + | 0.532932i | \(0.178910\pi\) | |||||||
\(720\) | 4.75756 | 0.177304 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.1718 | 0.974014 | ||||||||
\(723\) | 17.8066 | 0.662236 | ||||||||
\(724\) | −9.79505 | −0.364030 | ||||||||
\(725\) | −9.51621 | −0.353423 | ||||||||
\(726\) | −50.0368 | −1.85704 | ||||||||
\(727\) | 19.4657 | 0.721942 | 0.360971 | − | 0.932577i | \(-0.382445\pi\) | ||||
0.360971 | + | 0.932577i | \(0.382445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.2390 | 0.452987 | ||||||||
\(731\) | −18.7658 | −0.694080 | ||||||||
\(732\) | −5.73662 | −0.212032 | ||||||||
\(733\) | 10.3542 | 0.382442 | 0.191221 | − | 0.981547i | \(-0.438755\pi\) | ||||
0.191221 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(734\) | 0.908469 | 0.0335322 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.22103 | −0.0818682 | ||||||||
\(737\) | 26.9265 | 0.991852 | ||||||||
\(738\) | 11.5809 | 0.426298 | ||||||||
\(739\) | −35.4220 | −1.30302 | −0.651510 | − | 0.758640i | \(-0.725864\pi\) | ||||
−0.651510 | + | 0.758640i | \(0.725864\pi\) | |||||||
\(740\) | −0.397260 | −0.0146036 | ||||||||
\(741\) | 0.579460 | 0.0212870 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.5211 | 1.55995 | 0.779974 | − | 0.625812i | \(-0.215232\pi\) | ||||
0.779974 | + | 0.625812i | \(0.215232\pi\) | |||||||
\(744\) | 25.0620 | 0.918816 | ||||||||
\(745\) | −21.2643 | −0.779063 | ||||||||
\(746\) | −16.8845 | −0.618186 | ||||||||
\(747\) | −12.4798 | −0.456611 | ||||||||
\(748\) | 7.31508 | 0.267466 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −14.2142 | −0.519030 | ||||||||
\(751\) | −37.4114 | −1.36516 | −0.682581 | − | 0.730810i | \(-0.739142\pi\) | ||||
−0.682581 | + | 0.730810i | \(0.739142\pi\) | |||||||
\(752\) | 26.5710 | 0.968945 | ||||||||
\(753\) | −27.5761 | −1.00493 | ||||||||
\(754\) | −0.361025 | −0.0131477 | ||||||||
\(755\) | −4.12779 | −0.150226 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.8670 | 1.95783 | 0.978914 | − | 0.204271i | \(-0.0654822\pi\) | ||||
0.978914 | + | 0.204271i | \(0.0654822\pi\) | |||||||
\(758\) | 34.3935 | 1.24923 | ||||||||
\(759\) | 6.58109 | 0.238879 | ||||||||
\(760\) | 15.2465 | 0.553050 | ||||||||
\(761\) | 19.9697 | 0.723900 | 0.361950 | − | 0.932197i | \(-0.382111\pi\) | ||||
0.361950 | + | 0.932197i | \(0.382111\pi\) | |||||||
\(762\) | 21.7397 | 0.787548 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.80881 | 0.282513 | ||||||||
\(765\) | 2.86351 | 0.103531 | ||||||||
\(766\) | 25.0461 | 0.904953 | ||||||||
\(767\) | −0.423651 | −0.0152972 | ||||||||
\(768\) | −9.20292 | −0.332082 | ||||||||
\(769\) | −46.6660 | −1.68282 | −0.841409 | − | 0.540399i | \(-0.818273\pi\) | ||||
−0.841409 | + | 0.540399i | \(0.818273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.0021 | 0.612315 | ||||||||
\(772\) | −4.18503 | −0.150623 | ||||||||
\(773\) | 16.8883 | 0.607429 | 0.303714 | − | 0.952763i | \(-0.401773\pi\) | ||||
0.303714 | + | 0.952763i | \(0.401773\pi\) | |||||||
\(774\) | 10.4107 | 0.374206 | ||||||||
\(775\) | −39.8847 | −1.43270 | ||||||||
\(776\) | 2.28516 | 0.0820325 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.3290 | −0.477869 | ||||||||
\(779\) | 44.8072 | 1.60538 | ||||||||
\(780\) | −0.0395036 | −0.00141446 | ||||||||
\(781\) | −10.7816 | −0.385796 | ||||||||
\(782\) | −4.32286 | −0.154585 | ||||||||
\(783\) | −2.41057 | −0.0861468 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.78337 | −0.206417 | ||||||||
\(786\) | −4.22344 | −0.150645 | ||||||||
\(787\) | −32.9203 | −1.17348 | −0.586741 | − | 0.809774i | \(-0.699590\pi\) | ||||
−0.586741 | + | 0.809774i | \(0.699590\pi\) | |||||||
\(788\) | 2.91963 | 0.104007 | ||||||||
\(789\) | 20.0349 | 0.713261 | ||||||||
\(790\) | −12.3851 | −0.440641 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 16.3249 | 0.580080 | ||||||||
\(793\) | −1.39328 | −0.0494769 | ||||||||
\(794\) | 8.00052 | 0.283928 | ||||||||
\(795\) | −5.04517 | −0.178934 | ||||||||
\(796\) | 2.93104 | 0.103888 | ||||||||
\(797\) | −21.6726 | −0.767684 | −0.383842 | − | 0.923399i | \(-0.625399\pi\) | ||||
−0.383842 | + | 0.923399i | \(0.625399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9927 | 0.565782 | ||||||||
\(800\) | 8.76796 | 0.309994 | ||||||||
\(801\) | −2.59708 | −0.0917632 | ||||||||
\(802\) | 39.7908 | 1.40506 | ||||||||
\(803\) | 50.7030 | 1.78927 | ||||||||
\(804\) | 1.62920 | 0.0574575 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.51314 | −0.0532981 | ||||||||
\(807\) | −18.1520 | −0.638980 | ||||||||
\(808\) | −40.8869 | −1.43840 | ||||||||
\(809\) | −53.1040 | −1.86704 | −0.933519 | − | 0.358529i | \(-0.883278\pi\) | ||||
−0.933519 | + | 0.358529i | \(0.883278\pi\) | |||||||
\(810\) | −1.58859 | −0.0558174 | ||||||||
\(811\) | 29.7443 | 1.04446 | 0.522232 | − | 0.852804i | \(-0.325100\pi\) | ||||
0.522232 | + | 0.852804i | \(0.325100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.58594 | −0.266050 | ||||||||
\(814\) | −9.91181 | −0.347409 | ||||||||
\(815\) | −18.5471 | −0.649676 | ||||||||
\(816\) | −12.9462 | −0.453209 | ||||||||
\(817\) | 40.2798 | 1.40921 | ||||||||
\(818\) | −22.9174 | −0.801288 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.05465 | −0.106673 | ||||||||
\(821\) | 26.3798 | 0.920663 | 0.460331 | − | 0.887747i | \(-0.347731\pi\) | ||||
0.460331 | + | 0.887747i | \(0.347731\pi\) | |||||||
\(822\) | −22.5645 | −0.787028 | ||||||||
\(823\) | −5.25436 | −0.183155 | −0.0915777 | − | 0.995798i | \(-0.529191\pi\) | ||||
−0.0915777 | + | 0.995798i | \(0.529191\pi\) | |||||||
\(824\) | −5.02499 | −0.175054 | ||||||||
\(825\) | −25.9802 | −0.904513 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.44455 | 0.0502318 | 0.0251159 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251159 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(828\) | 0.398191 | 0.0138381 | ||||||||
\(829\) | 30.9757 | 1.07583 | 0.537915 | − | 0.842999i | \(-0.319212\pi\) | ||||
0.537915 | + | 0.842999i | \(0.319212\pi\) | |||||||
\(830\) | 19.8252 | 0.688144 | ||||||||
\(831\) | −19.5130 | −0.676899 | ||||||||
\(832\) | −0.564418 | −0.0195677 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.05548 | −0.209684 | ||||||||
\(835\) | −17.3601 | −0.600770 | ||||||||
\(836\) | −15.7014 | −0.543044 | ||||||||
\(837\) | −10.1033 | −0.349220 | ||||||||
\(838\) | −9.95767 | −0.343982 | ||||||||
\(839\) | 27.1001 | 0.935598 | 0.467799 | − | 0.883835i | \(-0.345047\pi\) | ||||
0.467799 | + | 0.883835i | \(0.345047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1891 | −0.799626 | ||||||||
\(842\) | −28.0784 | −0.967647 | ||||||||
\(843\) | −1.47664 | −0.0508583 | ||||||||
\(844\) | −0.205121 | −0.00706057 | ||||||||
\(845\) | 13.3260 | 0.458429 | ||||||||
\(846\) | −8.87228 | −0.305035 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 22.8097 | 0.783289 | ||||||||
\(849\) | 1.23515 | 0.0423901 | ||||||||
\(850\) | 17.0653 | 0.585337 | ||||||||
\(851\) | 0.972553 | 0.0333387 | ||||||||
\(852\) | −0.652345 | −0.0223490 | ||||||||
\(853\) | 44.5874 | 1.52664 | 0.763322 | − | 0.646019i | \(-0.223567\pi\) | ||||
0.763322 | + | 0.646019i | \(0.223567\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.14637 | −0.210201 | ||||||||
\(856\) | 41.9529 | 1.43392 | ||||||||
\(857\) | 10.7743 | 0.368045 | 0.184022 | − | 0.982922i | \(-0.441088\pi\) | ||||
0.184022 | + | 0.982922i | \(0.441088\pi\) | |||||||
\(858\) | −0.985632 | −0.0336489 | ||||||||
\(859\) | 22.9846 | 0.784224 | 0.392112 | − | 0.919917i | \(-0.371745\pi\) | ||||
0.392112 | + | 0.919917i | \(0.371745\pi\) | |||||||
\(860\) | −2.74600 | −0.0936379 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.2686 | −0.826591 | ||||||||
\(863\) | −23.9034 | −0.813682 | −0.406841 | − | 0.913499i | \(-0.633370\pi\) | ||||
−0.406841 | + | 0.913499i | \(0.633370\pi\) | |||||||
\(864\) | 2.22103 | 0.0755610 | ||||||||
\(865\) | 6.04808 | 0.205641 | ||||||||
\(866\) | −36.3085 | −1.23381 | ||||||||
\(867\) | 9.20783 | 0.312714 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.3079 | −1.74050 | ||||||||
\(870\) | 3.82941 | 0.129829 | ||||||||
\(871\) | 0.395692 | 0.0134075 | ||||||||
\(872\) | −28.1705 | −0.953973 | ||||||||
\(873\) | −0.921222 | −0.0311786 | ||||||||
\(874\) | 9.27877 | 0.313859 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.06780 | 0.103651 | ||||||||
\(877\) | 20.0265 | 0.676247 | 0.338123 | − | 0.941102i | \(-0.390208\pi\) | ||||
0.338123 | + | 0.941102i | \(0.390208\pi\) | |||||||
\(878\) | 10.4969 | 0.354253 | ||||||||
\(879\) | −9.74857 | −0.328811 | ||||||||
\(880\) | −31.3100 | −1.05546 | ||||||||
\(881\) | −8.33251 | −0.280730 | −0.140365 | − | 0.990100i | \(-0.544828\pi\) | ||||
−0.140365 | + | 0.990100i | \(0.544828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.0846 | 1.65183 | 0.825915 | − | 0.563795i | \(-0.190659\pi\) | ||||
0.825915 | + | 0.563795i | \(0.190659\pi\) | |||||||
\(884\) | 0.107497 | 0.00361551 | ||||||||
\(885\) | 4.49369 | 0.151054 | ||||||||
\(886\) | −45.1659 | −1.51738 | ||||||||
\(887\) | 3.74487 | 0.125740 | 0.0628701 | − | 0.998022i | \(-0.479975\pi\) | ||||
0.0628701 | + | 0.998022i | \(0.479975\pi\) | |||||||
\(888\) | 2.41249 | 0.0809579 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.12569 | 0.138294 | ||||||||
\(891\) | −6.58109 | −0.220475 | ||||||||
\(892\) | 6.59772 | 0.220908 | ||||||||
\(893\) | −34.3275 | −1.14873 | ||||||||
\(894\) | −32.1013 | −1.07363 | ||||||||
\(895\) | 18.6978 | 0.624998 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0967108 | 0.00322908 | ||||||||
\(898\) | 57.2614 | 1.91084 | ||||||||
\(899\) | 24.3547 | 0.812274 | ||||||||
\(900\) | −1.57194 | −0.0523980 | ||||||||
\(901\) | 13.7289 | 0.457375 | ||||||||
\(902\) | −76.2147 | −2.53767 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.3610 | 1.07631 | ||||||||
\(905\) | 25.2339 | 0.838805 | ||||||||
\(906\) | −6.23146 | −0.207026 | ||||||||
\(907\) | 10.0339 | 0.333170 | 0.166585 | − | 0.986027i | \(-0.446726\pi\) | ||||
0.166585 | + | 0.986027i | \(0.446726\pi\) | |||||||
\(908\) | 0.848453 | 0.0281569 | ||||||||
\(909\) | 16.4828 | 0.546701 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63188 | −0.219724 | −0.109862 | − | 0.993947i | \(-0.535041\pi\) | ||||
−0.109862 | + | 0.993947i | \(0.535041\pi\) | |||||||
\(912\) | 27.7884 | 0.920165 | ||||||||
\(913\) | 82.1305 | 2.71812 | ||||||||
\(914\) | 43.0004 | 1.42233 | ||||||||
\(915\) | 14.7786 | 0.488567 | ||||||||
\(916\) | −5.74427 | −0.189796 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.32286 | 0.142676 | ||||||||
\(919\) | 6.24684 | 0.206064 | 0.103032 | − | 0.994678i | \(-0.467146\pi\) | ||||
0.103032 | + | 0.994678i | \(0.467146\pi\) | |||||||
\(920\) | 2.54462 | 0.0838936 | ||||||||
\(921\) | −27.7926 | −0.915799 | ||||||||
\(922\) | 41.7209 | 1.37400 | ||||||||
\(923\) | −0.158438 | −0.00521506 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.83935 | −0.126237 | ||||||||
\(926\) | 41.5163 | 1.36431 | ||||||||
\(927\) | 2.02573 | 0.0665339 | ||||||||
\(928\) | −5.35395 | −0.175752 | ||||||||
\(929\) | 1.74181 | 0.0571471 | 0.0285735 | − | 0.999592i | \(-0.490904\pi\) | ||||
0.0285735 | + | 0.999592i | \(0.490904\pi\) | |||||||
\(930\) | 16.0500 | 0.526299 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.884010 | −0.0289567 | ||||||||
\(933\) | 3.96040 | 0.129658 | ||||||||
\(934\) | 24.8594 | 0.813426 | ||||||||
\(935\) | −18.8451 | −0.616299 | ||||||||
\(936\) | 0.239899 | 0.00784133 | ||||||||
\(937\) | 1.99662 | 0.0652267 | 0.0326134 | − | 0.999468i | \(-0.489617\pi\) | ||||
0.0326134 | + | 0.999468i | \(0.489617\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.81964 | 0.157283 | ||||||||
\(940\) | 2.34021 | 0.0763293 | ||||||||
\(941\) | −33.7616 | −1.10060 | −0.550298 | − | 0.834968i | \(-0.685486\pi\) | ||||
−0.550298 | + | 0.834968i | \(0.685486\pi\) | |||||||
\(942\) | −8.73077 | −0.284464 | ||||||||
\(943\) | 7.47823 | 0.243525 | ||||||||
\(944\) | −20.3165 | −0.661244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −68.5139 | −2.22758 | ||||||||
\(947\) | −4.41249 | −0.143387 | −0.0716933 | − | 0.997427i | \(-0.522840\pi\) | ||||
−0.0716933 | + | 0.997427i | \(0.522840\pi\) | |||||||
\(948\) | −3.10440 | −0.100826 | ||||||||
\(949\) | 0.745093 | 0.0241867 | ||||||||
\(950\) | −36.6298 | −1.18843 | ||||||||
\(951\) | 16.8489 | 0.546361 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.9581 | 0.873258 | 0.436629 | − | 0.899642i | \(-0.356172\pi\) | ||||
0.436629 | + | 0.899642i | \(0.356172\pi\) | |||||||
\(954\) | −7.61636 | −0.246589 | ||||||||
\(955\) | −20.1170 | −0.650970 | ||||||||
\(956\) | 5.75829 | 0.186236 | ||||||||
\(957\) | 15.8642 | 0.512817 | ||||||||
\(958\) | −12.5187 | −0.404461 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.98682 | 0.193224 | ||||||||
\(961\) | 71.0763 | 2.29278 | ||||||||
\(962\) | −0.145657 | −0.00469616 | ||||||||
\(963\) | −16.9125 | −0.544999 | ||||||||
\(964\) | −7.09045 | −0.228368 | ||||||||
\(965\) | 10.7814 | 0.347067 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8724 | −0.832001 | −0.416000 | − | 0.909364i | \(-0.636568\pi\) | ||||
−0.416000 | + | 0.909364i | \(0.636568\pi\) | |||||||
\(968\) | −80.1493 | −2.57610 | ||||||||
\(969\) | 16.7254 | 0.537299 | ||||||||
\(970\) | 1.46344 | 0.0469884 | ||||||||
\(971\) | 16.1998 | 0.519877 | 0.259938 | − | 0.965625i | \(-0.416298\pi\) | ||||
0.259938 | + | 0.965625i | \(0.416298\pi\) | |||||||
\(972\) | −0.398191 | −0.0127720 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −34.4439 | −1.10366 | ||||||||
\(975\) | −0.381785 | −0.0122269 | ||||||||
\(976\) | −66.8157 | −2.13872 | ||||||||
\(977\) | −19.2228 | −0.614992 | −0.307496 | − | 0.951549i | \(-0.599491\pi\) | ||||
−0.307496 | + | 0.951549i | \(0.599491\pi\) | |||||||
\(978\) | −27.9993 | −0.895319 | ||||||||
\(979\) | 17.0916 | 0.546250 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3564 | 0.362583 | ||||||||
\(982\) | −38.7969 | −1.23806 | ||||||||
\(983\) | −53.9905 | −1.72203 | −0.861014 | − | 0.508581i | \(-0.830170\pi\) | ||||
−0.861014 | + | 0.508581i | \(0.830170\pi\) | |||||||
\(984\) | 18.5503 | 0.591363 | ||||||||
\(985\) | −7.52152 | −0.239655 | ||||||||
\(986\) | −10.4206 | −0.331858 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.230736 | −0.00734069 | ||||||||
\(989\) | 6.72262 | 0.213767 | ||||||||
\(990\) | 10.4547 | 0.332271 | ||||||||
\(991\) | 19.5181 | 0.620011 | 0.310006 | − | 0.950735i | \(-0.399669\pi\) | ||||
0.310006 | + | 0.950735i | \(0.399669\pi\) | |||||||
\(992\) | −22.4397 | −0.712461 | ||||||||
\(993\) | −10.0553 | −0.319095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.55092 | −0.239380 | ||||||||
\(996\) | 4.96933 | 0.157459 | ||||||||
\(997\) | 47.2150 | 1.49531 | 0.747657 | − | 0.664085i | \(-0.231179\pi\) | ||||
0.747657 | + | 0.664085i | \(0.231179\pi\) | |||||||
\(998\) | 34.7927 | 1.10134 | ||||||||
\(999\) | −0.972553 | −0.0307702 |
(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 | 3381.2.a.bg.1.9 | ✓ | 10 | |
7.6 | odd | 2 | 3381.2.a.bh.1.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3381.2.a.bg.1.9 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3381.2.a.bh.1.9 | yes | 10 | 7.6 | odd | 2 |