Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8012,2,Mod(1,8012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8012 = 2^{2} \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8012.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: | \(63.9761420994\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.80739 | −1.62085 | −0.810423 | − | 0.585845i | \(-0.800763\pi\) | ||||
−0.810423 | + | 0.585845i | \(0.800763\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.13337 | 0.954073 | 0.477036 | − | 0.878884i | \(-0.341711\pi\) | ||||
0.477036 | + | 0.878884i | \(0.341711\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.30534 | −0.493370 | −0.246685 | − | 0.969096i | \(-0.579341\pi\) | ||||
−0.246685 | + | 0.969096i | \(0.579341\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.88143 | 1.62714 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64263 | 0.796783 | 0.398392 | − | 0.917215i | \(-0.369569\pi\) | ||||
0.398392 | + | 0.917215i | \(0.369569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.23341 | −0.342087 | −0.171044 | − | 0.985263i | \(-0.554714\pi\) | ||||
−0.171044 | + | 0.985263i | \(0.554714\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.98920 | −1.54641 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.89582 | −0.459804 | −0.229902 | − | 0.973214i | \(-0.573841\pi\) | ||||
−0.229902 | + | 0.973214i | \(0.573841\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.77330 | 1.09507 | 0.547535 | − | 0.836783i | \(-0.315566\pi\) | ||||
0.547535 | + | 0.836783i | \(0.315566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.66458 | 0.799678 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.45037 | 0.719452 | 0.359726 | − | 0.933058i | \(-0.382870\pi\) | ||||
0.359726 | + | 0.933058i | \(0.382870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.448727 | −0.0897454 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.28191 | −1.01650 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.68254 | 0.498134 | 0.249067 | − | 0.968486i | \(-0.419876\pi\) | ||||
0.249067 | + | 0.968486i | \(0.419876\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2146 | −1.83460 | −0.917301 | − | 0.398194i | \(-0.869637\pi\) | ||||
−0.917301 | + | 0.398194i | \(0.869637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.41889 | −1.29146 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.78477 | −0.470711 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.381771 | −0.0627627 | −0.0313814 | − | 0.999507i | \(-0.509991\pi\) | ||||
−0.0313814 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.46267 | 0.554471 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.80784 | 0.438511 | 0.219255 | − | 0.975668i | \(-0.429637\pi\) | ||||
0.219255 | + | 0.975668i | \(0.429637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5225 | 1.60467 | 0.802337 | − | 0.596872i | \(-0.203590\pi\) | ||||
0.802337 | + | 0.596872i | \(0.203590\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4139 | 1.55241 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0749 | 1.61545 | 0.807723 | − | 0.589563i | \(-0.200700\pi\) | ||||
0.807723 | + | 0.589563i | \(0.200700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.29610 | −0.756586 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32230 | 0.745272 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.75066 | −0.652554 | −0.326277 | − | 0.945274i | \(-0.605794\pi\) | ||||
−0.326277 | + | 0.945274i | \(0.605794\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.63771 | 0.760189 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.4005 | −1.77494 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.4162 | 1.87683 | 0.938413 | − | 0.345515i | \(-0.112296\pi\) | ||||
0.938413 | + | 0.345515i | \(0.112296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.262609 | 0.0336236 | 0.0168118 | − | 0.999859i | \(-0.494648\pi\) | ||||
0.0168118 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.37190 | −0.802785 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.63133 | −0.326376 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.07270 | 0.253220 | 0.126610 | − | 0.991953i | \(-0.459590\pi\) | ||||
0.126610 | + | 0.991953i | \(0.459590\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.68653 | −1.16612 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.11912 | 0.370172 | 0.185086 | − | 0.982722i | \(-0.440744\pi\) | ||||
0.185086 | + | 0.982722i | \(0.440744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.33681 | −1.09279 | −0.546396 | − | 0.837527i | \(-0.684000\pi\) | ||||
−0.546396 | + | 0.837527i | \(0.684000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.25975 | 0.145464 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.44952 | −0.393109 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.5084 | −1.74483 | −0.872416 | − | 0.488764i | \(-0.837448\pi\) | ||||
−0.872416 | + | 0.488764i | \(0.837448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.184073 | 0.0204526 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7805 | 1.51260 | 0.756302 | − | 0.654223i | \(-0.227004\pi\) | ||||
0.756302 | + | 0.654223i | \(0.227004\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.04449 | −0.438686 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.53092 | −0.807399 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.3267 | −1.73063 | −0.865314 | − | 0.501230i | \(-0.832881\pi\) | ||||
−0.865314 | + | 0.501230i | \(0.832881\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61002 | 0.168776 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 28.6764 | 2.97361 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.1832 | 1.04478 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.59892 | 0.466949 | 0.233475 | − | 0.972363i | \(-0.424990\pi\) | ||||
0.233475 | + | 0.972363i | \(0.424990\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.8998 | 1.29648 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.95495 | 0.891051 | 0.445525 | − | 0.895269i | \(-0.353017\pi\) | ||||
0.445525 | + | 0.895269i | \(0.353017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.197783 | −0.0194882 | −0.00974408 | − | 0.999953i | \(-0.503102\pi\) | ||||
−0.00974408 | + | 0.999953i | \(0.503102\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.81792 | 0.762951 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.32578 | 0.804883 | 0.402442 | − | 0.915446i | \(-0.368162\pi\) | ||||
0.402442 | + | 0.915446i | \(0.368162\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.67112 | −0.351630 | −0.175815 | − | 0.984423i | \(-0.556256\pi\) | ||||
−0.175815 | + | 0.984423i | \(0.556256\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.07178 | 0.101729 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.86361 | 0.645674 | 0.322837 | − | 0.946455i | \(-0.395363\pi\) | ||||
0.322837 | + | 0.946455i | \(0.395363\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.36092 | 0.686409 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.02082 | −0.556625 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.47468 | 0.226854 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.01650 | −0.365137 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.88269 | −0.710758 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.6242 | −1.03970 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1033 | 1.16273 | 0.581364 | − | 0.813643i | \(-0.302519\pi\) | ||||
0.581364 | + | 0.813643i | \(0.302519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −29.5409 | −2.60093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.30900 | −0.725960 | −0.362980 | − | 0.931797i | \(-0.618241\pi\) | ||||
−0.362980 | + | 0.931797i | \(0.618241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.23075 | −0.540275 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.2683 | −0.969818 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.4619 | 1.66274 | 0.831371 | − | 0.555717i | \(-0.187556\pi\) | ||||
0.831371 | + | 0.555717i | \(0.187556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.90790 | 0.161826 | 0.0809131 | − | 0.996721i | \(-0.474216\pi\) | ||||
0.0809131 | + | 0.996721i | \(0.474216\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −31.0916 | −2.61839 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.25946 | −0.272569 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.72284 | 0.475256 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.8682 | 1.22631 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.48829 | −0.613464 | −0.306732 | − | 0.951796i | \(-0.599236\pi\) | ||||
−0.306732 | + | 0.951796i | \(0.599236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.72876 | −0.222064 | −0.111032 | − | 0.993817i | \(-0.535416\pi\) | ||||
−0.111032 | + | 0.993817i | \(0.535416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.25432 | −0.748167 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.7916 | −1.75034 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.526050 | 0.0419834 | 0.0209917 | − | 0.999780i | \(-0.493318\pi\) | ||||
0.0209917 | + | 0.999780i | \(0.493318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.3370 | 1.05769 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.50389 | −0.354956 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.98689 | 0.468929 | 0.234465 | − | 0.972125i | \(-0.424666\pi\) | ||||
0.234465 | + | 0.972125i | \(0.424666\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.8272 | −1.23215 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.09559 | 0.703838 | 0.351919 | − | 0.936030i | \(-0.385529\pi\) | ||||
0.351919 | + | 0.936030i | \(0.385529\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.4787 | −0.882976 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.3005 | 1.78183 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.303013 | 0.0230377 | 0.0115188 | − | 0.999934i | \(-0.496333\pi\) | ||||
0.0115188 | + | 0.999934i | \(0.496333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.585739 | 0.0442777 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −40.4718 | −3.04205 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2797 | −1.21680 | −0.608402 | − | 0.793629i | \(-0.708189\pi\) | ||||
−0.608402 | + | 0.793629i | \(0.708189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5830 | −1.00961 | −0.504807 | − | 0.863232i | \(-0.668436\pi\) | ||||
−0.504807 | + | 0.863232i | \(0.668436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.737246 | −0.0544988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.814459 | −0.0598802 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00995 | −0.366364 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.89466 | 0.501513 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7009 | −0.991361 | −0.495681 | − | 0.868505i | \(-0.665081\pi\) | ||||
−0.495681 | + | 0.868505i | \(0.665081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.9353 | −1.65092 | −0.825458 | − | 0.564463i | \(-0.809083\pi\) | ||||
−0.825458 | + | 0.564463i | \(0.809083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.38716 | 0.529006 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.35603 | −0.0966128 | −0.0483064 | − | 0.998833i | \(-0.515382\pi\) | ||||
−0.0483064 | + | 0.998833i | \(0.515382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.8043 | 1.82922 | 0.914608 | − | 0.404341i | \(-0.132499\pi\) | ||||
0.914608 | + | 0.404341i | \(0.132499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.81887 | −0.410431 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.50161 | −0.245765 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.99016 | 0.418371 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.8427 | 1.17065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.6141 | 0.872533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.96593 | −0.341869 | −0.170934 | − | 0.985282i | \(-0.554679\pi\) | ||||
−0.170934 | + | 0.985282i | \(0.554679\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.75660 | −0.599992 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.4485 | 1.53097 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.3335 | 0.905139 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.2121 | 1.77125 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.33833 | 0.157293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6187 | −1.38073 | −0.690365 | − | 0.723461i | \(-0.742550\pi\) | ||||
−0.690365 | + | 0.723461i | \(0.742550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.19043 | −0.146029 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.2988 | −1.14816 | −0.574081 | − | 0.818798i | \(-0.694641\pi\) | ||||
−0.574081 | + | 0.818798i | \(0.694641\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8279 | 0.979856 | 0.489928 | − | 0.871763i | \(-0.337023\pi\) | ||||
0.489928 | + | 0.871763i | \(0.337023\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.68414 | 0.637170 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6404 | 1.22117 | 0.610587 | − | 0.791950i | \(-0.290934\pi\) | ||||
0.610587 | + | 0.791950i | \(0.290934\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.6269 | 1.54125 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 43.5381 | 2.82810 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.5288 | −1.32789 | −0.663947 | − | 0.747779i | \(-0.731120\pi\) | ||||
−0.663947 | + | 0.747779i | \(0.731120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1279 | 1.42538 | 0.712690 | − | 0.701479i | \(-0.247477\pi\) | ||||
0.712690 | + | 0.701479i | \(0.247477\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.3290 | 0.983353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2985 | −0.721838 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.88745 | −0.374609 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −38.6871 | −2.45170 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.20213 | 0.328356 | 0.164178 | − | 0.986431i | \(-0.447503\pi\) | ||||
0.164178 | + | 0.986431i | \(0.447503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.11805 | 0.573247 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.3545 | 0.711043 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5121 | 1.59140 | 0.795702 | − | 0.605688i | \(-0.207102\pi\) | ||||
0.795702 | + | 0.605688i | \(0.207102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.498339 | 0.0309653 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.0946 | 0.810536 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.1137 | −0.623639 | −0.311819 | − | 0.950141i | \(-0.600938\pi\) | ||||
−0.311819 | + | 0.950141i | \(0.600938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.1349 | −0.622584 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 45.8354 | 2.80508 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.1915 | 1.59692 | 0.798462 | − | 0.602045i | \(-0.205647\pi\) | ||||
0.798462 | + | 0.602045i | \(0.205647\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6976 | −0.649831 | −0.324916 | − | 0.945743i | \(-0.605336\pi\) | ||||
−0.324916 | + | 0.945743i | \(0.605336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.51995 | −0.273560 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.18582 | −0.0715076 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.3522 | 1.16276 | 0.581380 | − | 0.813632i | \(-0.302513\pi\) | ||||
0.581380 | + | 0.813632i | \(0.302513\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −49.8620 | −2.98516 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.9173 | 1.84437 | 0.922186 | − | 0.386748i | \(-0.126402\pi\) | ||||
0.922186 | + | 0.386748i | \(0.126402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8357 | 0.822445 | 0.411222 | − | 0.911535i | \(-0.365102\pi\) | ||||
0.411222 | + | 0.911535i | \(0.365102\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.5882 | −1.69342 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.66517 | −0.216348 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.4059 | −0.788580 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9110 | −0.756853 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.06755 | −0.179208 | −0.0896042 | − | 0.995977i | \(-0.528560\pi\) | ||||
−0.0896042 | + | 0.995977i | \(0.528560\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.7551 | 1.79063 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.9581 | −0.809933 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.25573 | −0.246115 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.7355 | −0.791698 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.1400 | −1.44426 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.560243 | 0.0320794 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.5692 | −1.91590 | −0.957949 | − | 0.286940i | \(-0.907362\pi\) | ||||
−0.957949 | + | 0.286940i | \(0.907362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.555255 | 0.0315873 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.493489 | 0.0279832 | 0.0139916 | − | 0.999902i | \(-0.495546\pi\) | ||||
0.0139916 | + | 0.999902i | \(0.495546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.2159 | 1.76443 | 0.882215 | − | 0.470847i | \(-0.156052\pi\) | ||||
0.882215 | + | 0.470847i | \(0.156052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.5936 | −0.765915 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.75608 | 0.379459 | 0.189730 | − | 0.981836i | \(-0.439239\pi\) | ||||
0.189730 | + | 0.981836i | \(0.439239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.08895 | 0.396905 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.3737 | −1.30459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.04931 | −0.503517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.553466 | 0.0307008 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3063 | 0.569938 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.4565 | −0.797013 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0730 | −1.21324 | −0.606620 | − | 0.794992i | \(-0.707475\pi\) | ||||
−0.606620 | + | 0.794992i | \(0.707475\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.86359 | −0.102124 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.42184 | 0.241591 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.308315 | 0.0167950 | 0.00839749 | − | 0.999965i | \(-0.497327\pi\) | ||||
0.00839749 | + | 0.999965i | \(0.497327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.2688 | −1.04654 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.9935 | −1.46178 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.0505 | 0.866647 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.6650 | −1.11256 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.33516 | 0.501138 | 0.250569 | − | 0.968099i | \(-0.419382\pi\) | ||||
0.250569 | + | 0.968099i | \(0.419382\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.0277 | −1.60735 | −0.803673 | − | 0.595072i | \(-0.797124\pi\) | ||||
−0.803673 | + | 0.595072i | \(0.797124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.51478 | 0.347733 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.8659 | 1.32348 | 0.661739 | − | 0.749734i | \(-0.269819\pi\) | ||||
0.661739 | + | 0.749734i | \(0.269819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.65425 | 0.353171 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.94739 | −0.367695 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2427 | 1.70170 | 0.850852 | − | 0.525406i | \(-0.176087\pi\) | ||||
0.850852 | + | 0.525406i | \(0.176087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.78435 | 0.199177 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2759 | 0.591830 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.9189 | −1.04260 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.3223 | −1.47841 | −0.739206 | − | 0.673479i | \(-0.764799\pi\) | ||||
−0.739206 | + | 0.673479i | \(0.764799\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.7063 | 0.713520 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.20121 | 0.321951 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0391 | −0.623360 | −0.311680 | − | 0.950187i | \(-0.600892\pi\) | ||||
−0.311680 | + | 0.950187i | \(0.600892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 32.6335 | 1.68519 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.30868 | −0.170405 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.6192 | 1.41870 | 0.709352 | − | 0.704854i | \(-0.248988\pi\) | ||||
0.709352 | + | 0.704854i | \(0.248988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.7860 | −1.88461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.9082 | 0.659576 | 0.329788 | − | 0.944055i | \(-0.393023\pi\) | ||||
0.329788 | + | 0.944055i | \(0.393023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.35911 | −0.375055 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 51.3651 | 2.61103 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.2037 | 1.73420 | 0.867098 | − | 0.498138i | \(-0.165983\pi\) | ||||
0.867098 | + | 0.498138i | \(0.165983\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.54128 | −0.330807 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.3266 | 1.17667 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −33.0852 | −1.66470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2872 | 0.566486 | 0.283243 | − | 0.959048i | \(-0.408590\pi\) | ||||
0.283243 | + | 0.959048i | \(0.408590\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 17.4921 | 0.875703 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.9681 | 0.647594 | 0.323797 | − | 0.946127i | \(-0.395041\pi\) | ||||
0.323797 | + | 0.946127i | \(0.395041\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5989 | 0.627594 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.392697 | 0.0195133 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00888 | −0.0500083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.07234 | 0.448598 | 0.224299 | − | 0.974520i | \(-0.427991\pi\) | ||||
0.224299 | + | 0.974520i | \(0.427991\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.6371 | −2.69505 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.8179 | −0.925971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3989 | 1.44313 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.35623 | −0.262296 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.3301 | 0.993188 | 0.496594 | − | 0.867983i | \(-0.334584\pi\) | ||||
0.496594 | + | 0.867983i | \(0.334584\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.08127 | −0.198909 | −0.0994544 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994544 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 54.0615 | 2.62856 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.850706 | 0.0412653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.342793 | −0.0165889 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.15056 | 0.441793 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.5483 | −1.51963 | −0.759815 | − | 0.650139i | \(-0.774711\pi\) | ||||
−0.759815 | + | 0.650139i | \(0.774711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.606781 | 0.0291600 | 0.0145800 | − | 0.999894i | \(-0.495359\pi\) | ||||
0.0145800 | + | 0.999894i | \(0.495359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.0662 | −0.770318 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.4696 | 0.787849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.57029 | −0.361310 | −0.180655 | − | 0.983547i | \(-0.557822\pi\) | ||||
−0.180655 | + | 0.983547i | \(0.557822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −25.8525 | −1.23107 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.3363 | 0.538602 | 0.269301 | − | 0.963056i | \(-0.413207\pi\) | ||||
0.269301 | + | 0.963056i | \(0.413207\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.8309 | −1.65114 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.0225 | 0.994332 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6132 | −1.35034 | −0.675171 | − | 0.737662i | \(-0.735930\pi\) | ||||
−0.675171 | + | 0.737662i | \(0.735930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.42008 | 0.349398 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.66070 | 0.359931 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.43477 | 0.161024 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.22205 | −0.431389 | −0.215695 | − | 0.976461i | \(-0.569202\pi\) | ||||
−0.215695 | + | 0.976461i | \(0.569202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0135 | 0.467392 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.8277 | 1.01662 | 0.508309 | − | 0.861175i | \(-0.330271\pi\) | ||||
0.508309 | + | 0.861175i | \(0.330271\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.383705 | 0.0178323 | 0.00891614 | − | 0.999960i | \(-0.497162\pi\) | ||||
0.00891614 | + | 0.999960i | \(0.497162\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 61.1775 | 2.83704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1149 | 1.53237 | 0.766186 | − | 0.642618i | \(-0.222152\pi\) | ||||
0.766186 | + | 0.642618i | \(0.222152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.70557 | −0.124931 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.47683 | −0.0680486 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.8072 | 1.27858 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.14191 | −0.0982775 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.1900 | −1.06180 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.7935 | 1.13284 | 0.566422 | − | 0.824116i | \(-0.308327\pi\) | ||||
0.566422 | + | 0.824116i | \(0.308327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.470881 | 0.0214703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.6442 | 0.575330 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.81120 | 0.445504 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.8922 | 0.765458 | 0.382729 | − | 0.923861i | \(-0.374984\pi\) | ||||
0.382729 | + | 0.923861i | \(0.374984\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.8075 | −0.760062 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.5978 | −0.749048 | −0.374524 | − | 0.927217i | \(-0.622194\pi\) | ||||
−0.374524 | + | 0.927217i | \(0.622194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.08560 | −0.229044 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.5201 | 1.23694 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.07150 | −0.182632 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8499 | −1.20196 | −0.600982 | − | 0.799262i | \(-0.705224\pi\) | ||||
−0.600982 | + | 0.799262i | \(0.705224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.5349 | −1.14081 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.1035 | 1.83272 | 0.916358 | − | 0.400359i | \(-0.131115\pi\) | ||||
0.916358 | + | 0.400359i | \(0.131115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1042 | 0.850127 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.2251 | 1.43117 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.6386 | −0.515870 | −0.257935 | − | 0.966162i | \(-0.583042\pi\) | ||||
−0.257935 | + | 0.966162i | \(0.583042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1877 | 0.539151 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −25.2121 | −1.11314 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.421945 | −0.0185931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.2670 | 1.28716 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.850676 | −0.0373405 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.4871 | 0.459448 | 0.229724 | − | 0.973256i | \(-0.426218\pi\) | ||||
0.229724 | + | 0.973256i | \(0.426218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.6885 | 1.60427 | 0.802137 | − | 0.597139i | \(-0.203696\pi\) | ||||
0.802137 | + | 0.597139i | \(0.203696\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.64440 | −0.0717674 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.3651 | 0.843558 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0950 | −0.482389 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 70.3716 | 3.05387 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.46323 | −0.150009 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.7620 | 0.767917 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.7036 | 1.97225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.9956 | −0.602835 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.6895 | 1.06148 | 0.530742 | − | 0.847534i | \(-0.321913\pi\) | ||||
0.530742 | + | 0.847534i | \(0.321913\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.1327 | 1.63643 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.83186 | −0.335480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.1350 | 0.561612 | 0.280806 | − | 0.959765i | \(-0.409398\pi\) | ||||
0.280806 | + | 0.959765i | \(0.409398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.28191 | 0.0547105 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.8045 | 0.545492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.2437 | 0.860848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.28650 | 0.0970566 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1909 | 0.474175 | 0.237088 | − | 0.971488i | \(-0.423807\pi\) | ||||
0.237088 | + | 0.971488i | \(0.423807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.9787 | −0.548938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.0649 | 0.593820 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.66122 | −0.0700123 | −0.0350061 | − | 0.999387i | \(-0.511145\pi\) | ||||
−0.0350061 | + | 0.999387i | \(0.511145\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6426 | 0.616020 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.240278 | −0.0100907 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 27.7642 | 1.16394 | 0.581969 | − | 0.813211i | \(-0.302283\pi\) | ||||
0.581969 | + | 0.813211i | \(0.302283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.321419 | 0.0134510 | 0.00672548 | − | 0.999977i | \(-0.497859\pi\) | ||||
0.00672548 | + | 0.999977i | \(0.497859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 38.4637 | 1.60684 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.54827 | −0.0645675 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.0897 | 1.08613 | 0.543065 | − | 0.839691i | \(-0.317264\pi\) | ||||
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 64.3882 | 2.67588 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.9881 | −0.746274 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.5542 | −0.519944 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.8446 | −0.531061 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.9747 | 1.23719 | 0.618594 | − | 0.785711i | \(-0.287703\pi\) | ||||
0.618594 | + | 0.785711i | \(0.287703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.7575 | −2.00902 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.80689 | 0.156595 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.89995 | 0.160152 | 0.0800759 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800759 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.27941 | 0.216435 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −72.4426 | −2.96488 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5532 | 0.758062 | 0.379031 | − | 0.925384i | \(-0.376257\pi\) | ||||
0.379031 | + | 0.925384i | \(0.376257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.5534 | 1.08313 | 0.541567 | − | 0.840658i | \(-0.317831\pi\) | ||||
0.541567 | + | 0.840658i | \(0.317831\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.1177 | 0.412026 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.56869 | −0.348367 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.2820 | 1.22911 | 0.614555 | − | 0.788874i | \(-0.289336\pi\) | ||||
0.614555 | + | 0.788874i | \(0.289336\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.83038 | 0.398347 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.6600 | −0.552623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.62975 | −0.267773 | −0.133887 | − | 0.990997i | \(-0.542746\pi\) | ||||
−0.133887 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.8167 | −0.678115 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.4413 | 1.26578 | 0.632889 | − | 0.774243i | \(-0.281869\pi\) | ||||
0.632889 | + | 0.774243i | \(0.281869\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.71192 | 0.390355 | 0.195178 | − | 0.980768i | \(-0.437472\pi\) | ||||
0.195178 | + | 0.980768i | \(0.437472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.2245 | −0.731325 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.3118 | 0.853841 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.5550 | −0.902200 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −35.4126 | −1.41424 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.723769 | 0.0288585 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.9579 | −1.55089 | −0.775445 | − | 0.631415i | \(-0.782474\pi\) | ||||
−0.775445 | + | 0.631415i | \(0.782474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.9413 | 0.554117 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 27.9542 | 1.10933 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.53228 | 0.258818 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.2258 | 0.602323 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.08952 | 0.240522 | 0.120261 | − | 0.992742i | \(-0.461627\pi\) | ||||
0.120261 | + | 0.992742i | \(0.461627\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.3951 | 0.488814 | 0.244407 | − | 0.969673i | \(-0.421407\pi\) | ||||
0.244407 | + | 0.969673i | \(0.421407\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −63.0217 | −2.48148 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.4905 | 0.412425 | 0.206212 | − | 0.978507i | \(-0.433886\pi\) | ||||
0.206212 | + | 0.978507i | \(0.433886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.0966 | 1.49542 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.4324 | −1.46709 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.4212 | 0.564344 | 0.282172 | − | 0.959364i | \(-0.408945\pi\) | ||||
0.282172 | + | 0.959364i | \(0.408945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.7262 | −0.692619 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −45.5770 | −1.77813 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.2443 | 1.45083 | 0.725416 | − | 0.688311i | \(-0.241647\pi\) | ||||
0.725416 | + | 0.688311i | \(0.241647\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.2991 | −0.906228 | −0.453114 | − | 0.891453i | \(-0.649687\pi\) | ||||
−0.453114 | + | 0.891453i | \(0.649687\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.56460 | −0.254948 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.2925 | −0.515461 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.25574 | 0.358384 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 57.8847 | 2.23795 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.693979 | 0.0267908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.3854 | 1.47965 | 0.739825 | − | 0.672799i | \(-0.234908\pi\) | ||||
0.739825 | + | 0.672799i | \(0.234908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.37014 | 0.0912265 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.0194 | −1.73023 | −0.865117 | − | 0.501570i | \(-0.832756\pi\) | ||||
−0.865117 | + | 0.501570i | \(0.832756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.00313 | −0.230379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.5645 | 1.86100 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.840213 | −0.0321498 | −0.0160749 | − | 0.999871i | \(-0.505117\pi\) | ||||
−0.0160749 | + | 0.999871i | \(0.505117\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.5195 | 1.58638 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.6277 | −1.58820 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.85953 | 0.223230 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.9672 | 1.25413 | 0.627065 | − | 0.778967i | \(-0.284256\pi\) | ||||
0.627065 | + | 0.778967i | \(0.284256\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.8386 | −0.639645 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.07027 | 0.154394 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.32316 | −0.201629 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −52.3308 | −1.97933 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.9407 | −1.39523 | −0.697616 | − | 0.716472i | \(-0.745756\pi\) | ||||
−0.697616 | + | 0.716472i | \(0.745756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.82230 | −0.0687295 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −66.3300 | −2.49813 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11.6892 | −0.439618 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.32612 | 0.162471 | 0.0812353 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812353 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −75.7032 | −2.83909 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −35.2443 | −1.31991 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.95363 | −0.260051 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 57.6322 | 2.15231 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.7216 | 1.07113 | 0.535567 | − | 0.844493i | \(-0.320098\pi\) | ||||
0.535567 | + | 0.844493i | \(0.320098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.258174 | 0.00961489 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −62.1215 | −2.31032 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.20373 | −0.0447053 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5287 | −0.761367 | −0.380684 | − | 0.924705i | \(-0.624311\pi\) | ||||
−0.380684 | + | 0.924705i | \(0.624311\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.5866 | −1.61432 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.9489 | −0.737835 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.3244 | −0.935378 | −0.467689 | − | 0.883893i | \(-0.654913\pi\) | ||||
−0.467689 | + | 0.883893i | \(0.654913\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.7194 | 1.16999 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.47738 | 0.201762 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.9084 | 1.50484 | 0.752421 | − | 0.658683i | \(-0.228886\pi\) | ||||
0.752421 | + | 0.658683i | \(0.228886\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.5284 | 0.607184 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.4513 | −0.456796 | −0.228398 | − | 0.973568i | \(-0.573349\pi\) | ||||
−0.228398 | + | 0.973568i | \(0.573349\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9753 | −0.585290 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 67.2684 | 2.46122 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8679 | −0.397106 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.904509 | −0.0330060 | −0.0165030 | − | 0.999864i | \(-0.505253\pi\) | ||||
−0.0165030 | + | 0.999864i | \(0.505253\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6044 | −0.532214 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.82147 | −0.211865 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.4117 | −0.923605 | −0.461802 | − | 0.886983i | \(-0.652797\pi\) | ||||
−0.461802 | + | 0.886983i | \(0.652797\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.5979 | −0.929145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.6769 | −0.967037 | −0.483518 | − | 0.875334i | \(-0.660641\pi\) | ||||
−0.483518 | + | 0.875334i | \(0.660641\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.79204 | 0.173484 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.7429 | −0.713806 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.7811 | −0.642039 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.7904 | −1.39882 | −0.699409 | − | 0.714721i | \(-0.746554\pi\) | ||||
−0.699409 | + | 0.714721i | \(0.746554\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −71.6225 | −2.57942 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.8460 | 0.677844 | 0.338922 | − | 0.940814i | \(-0.389938\pi\) | ||||
0.338922 | + | 0.940814i | \(0.389938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.58358 | 0.164647 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.39903 | −0.0501899 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.4026 | 0.480199 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.24270 | 0.294947 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14.1689 | −0.506355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.12226 | 0.0400552 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1304 | 0.681924 | 0.340962 | − | 0.940077i | \(-0.389247\pi\) | ||||
0.340962 | + | 0.940077i | \(0.389247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.3931 | 1.01082 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.95931 | −0.318556 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.323906 | −0.0115022 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 28.4527 | 1.00911 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6477 | −0.837644 | −0.418822 | − | 0.908068i | \(-0.637557\pi\) | ||||
−0.418822 | + | 0.908068i | \(0.637557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.9961 | −0.742788 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −79.6977 | −2.81598 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.6737 | −0.870717 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.60847 | −0.338654 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −73.5298 | −2.58837 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.2406 | 1.76637 | 0.883184 | − | 0.469027i | \(-0.155395\pi\) | ||||
0.883184 | + | 0.469027i | \(0.155395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.4904 | 1.38670 | 0.693348 | − | 0.720603i | \(-0.256135\pi\) | ||||
0.693348 | + | 0.720603i | \(0.256135\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.0323 | 1.05328 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7723 | 0.447392 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.2272 | 1.75723 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.85919 | 0.274622 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 56.1720 | 1.96042 | 0.980208 | − | 0.197970i | \(-0.0634349\pi\) | ||||
0.980208 | + | 0.197970i | \(0.0634349\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.4527 | −1.27066 | −0.635331 | − | 0.772240i | \(-0.719137\pi\) | ||||
−0.635331 | + | 0.772240i | \(0.719137\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.32906 | 0.115903 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.8105 | 1.48867 | 0.744334 | − | 0.667808i | \(-0.232767\pi\) | ||||
0.744334 | + | 0.667808i | \(0.232767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.2448 | 1.01571 | 0.507857 | − | 0.861442i | \(-0.330438\pi\) | ||||
0.507857 | + | 0.861442i | \(0.330438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −54.3291 | −1.88465 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0405 | 0.347881 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.4043 | 0.671513 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 53.9527 | 1.86488 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.0705 | −0.761959 | −0.380979 | − | 0.924584i | \(-0.624413\pi\) | ||||
−0.380979 | + | 0.924584i | \(0.624413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.8040 | −0.751862 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −86.7969 | −2.98944 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.4883 | −0.842423 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.24288 | 0.180148 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.8421 | −1.33306 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.31725 | −0.0451547 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.9347 | −0.442875 | −0.221437 | − | 0.975175i | \(-0.571075\pi\) | ||||
−0.221437 | + | 0.975175i | \(0.571075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 49.7086 | 1.70000 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.6451 | −0.568586 | −0.284293 | − | 0.958738i | \(-0.591759\pi\) | ||||
−0.284293 | + | 0.958738i | \(0.591759\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3279 | 0.488860 | 0.244430 | − | 0.969667i | \(-0.421399\pi\) | ||||
0.244430 | + | 0.969667i | \(0.421399\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.2896 | 0.350667 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.0785 | −0.751562 | −0.375781 | − | 0.926708i | \(-0.622626\pi\) | ||||
−0.375781 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.646440 | 0.0219796 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.6355 | 1.27817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.9830 | −1.39025 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.55649 | −0.0866235 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.4493 | 0.759794 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.1734 | 0.512955 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.7181 | 1.61133 | 0.805663 | − | 0.592374i | \(-0.201809\pi\) | ||||
0.805663 | + | 0.592374i | \(0.201809\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.61181 | 0.290469 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.73988 | 0.0586179 | 0.0293090 | − | 0.999570i | \(-0.490669\pi\) | ||||
0.0293090 | + | 0.999570i | \(0.490669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.1934 | 0.443992 | 0.221996 | − | 0.975048i | \(-0.428743\pi\) | ||||
0.221996 | + | 0.975048i | \(0.428743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −86.3414 | −2.90233 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.7994 | 0.899836 | 0.449918 | − | 0.893070i | \(-0.351453\pi\) | ||||
0.449918 | + | 0.893070i | \(0.351453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.1042 | −0.573656 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.486438 | 0.0162963 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.8639 | 1.76902 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.7307 | −1.16092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.9475 | 0.398915 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.4011 | −0.913878 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00640 | 0.300047 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 38.5608 | 1.28322 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.9775 | −0.963245 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.7741 | −1.61952 | −0.809759 | − | 0.586762i | \(-0.800402\pi\) | ||||
−0.809759 | + | 0.586762i | \(0.800402\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43.7130 | 1.44987 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.3100 | 0.971083 | 0.485542 | − | 0.874213i | \(-0.338622\pi\) | ||||
0.485542 | + | 0.874213i | \(0.338622\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.4167 | 1.20522 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.57282 | −0.0519958 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.8460 | 0.358167 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.3685 | 0.902802 | 0.451401 | − | 0.892321i | \(-0.350924\pi\) | ||||
0.451401 | + | 0.892321i | \(0.350924\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 94.2419 | 3.10538 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.84717 | −0.126631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.171311 | 0.00563267 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.965466 | −0.0317100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.2898 | 1.42029 | 0.710146 | − | 0.704055i | \(-0.248629\pi\) | ||||
0.710146 | + | 0.704055i | \(0.248629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.2798 | −0.828514 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.38541 | −0.0453564 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6881 | −0.349538 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.3443 | −1.48134 | −0.740668 | − | 0.671872i | \(-0.765491\pi\) | ||||
−0.740668 | + | 0.671872i | \(0.765491\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −87.6353 | −2.85987 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6190 | 0.639562 | 0.319781 | − | 0.947491i | \(-0.396391\pi\) | ||||
0.319781 | + | 0.947491i | \(0.396391\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.68808 | 0.315487 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.7089 | 0.478480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.189029 | −0.00614263 | −0.00307132 | − | 0.999995i | \(-0.500978\pi\) | ||||
−0.00307132 | + | 0.999995i | \(0.500978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.5161 | 0.373830 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.9669 | −0.615045 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.1968 | −1.91757 | −0.958786 | − | 0.284129i | \(-0.908296\pi\) | ||||
−0.958786 | + | 0.284129i | \(0.908296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.2291 | −0.945831 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.9014 | −0.643322 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.4043 | −0.820348 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.3388 | 2.36577 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 40.6417 | 1.30966 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.9294 | −1.57509 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.37056 | 0.204864 | 0.102432 | − | 0.994740i | \(-0.467338\pi\) | ||||
0.102432 | + | 0.994740i | \(0.467338\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.4049 | 0.816124 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.0634 | −1.02896 | −0.514482 | − | 0.857501i | \(-0.672016\pi\) | ||||
−0.514482 | + | 0.857501i | \(0.672016\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.49045 | −0.0798403 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.55379 | −0.0497613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.9782 | −1.47097 | −0.735486 | − | 0.677540i | \(-0.763046\pi\) | ||||
−0.735486 | + | 0.677540i | \(0.763046\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −43.1455 | −1.37894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.9203 | −0.572152 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.9226 | 1.01817 | 0.509086 | − | 0.860716i | \(-0.329983\pi\) | ||||
0.509086 | + | 0.860716i | \(0.329983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.89291 | −0.0921756 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 40.5850 | 1.29184 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.3067 | 1.15449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.1835 | 1.56237 | 0.781183 | − | 0.624302i | \(-0.214617\pi\) | ||||
0.781183 | + | 0.624302i | \(0.214617\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.9674 | 1.96648 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 55.0501 | 1.74521 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.1515 | −1.27161 | −0.635806 | − | 0.771849i | \(-0.719332\pi\) | ||||
−0.635806 | + | 0.771849i | \(0.719332\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.01648 | 0.0637985 |
(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 | 8012.2.a.b.1.7 | ✓ | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8012.2.a.b.1.7 | ✓ | 88 | 1.1 | even | 1 | trivial |