Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23685 | 0.874586 | 0.437293 | − | 0.899319i | \(-0.355937\pi\) | ||||
0.437293 | + | 0.899319i | \(0.355937\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.470198 | −0.235099 | ||||||||
\(5\) | −0.403292 | −0.180358 | −0.0901789 | − | 0.995926i | \(-0.528744\pi\) | ||||
−0.0901789 | + | 0.995926i | \(0.528744\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.303505 | −0.114714 | −0.0573571 | − | 0.998354i | \(-0.518267\pi\) | ||||
−0.0573571 | + | 0.998354i | \(0.518267\pi\) | |||||||
\(8\) | −3.05527 | −1.08020 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.498813 | −0.157738 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.53056 | −0.979200 | −0.489600 | − | 0.871947i | \(-0.662857\pi\) | ||||
−0.489600 | + | 0.871947i | \(0.662857\pi\) | |||||||
\(14\) | −0.375391 | −0.100327 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.83852 | −0.709630 | ||||||||
\(17\) | 7.19973 | 1.74619 | 0.873096 | − | 0.487549i | \(-0.162109\pi\) | ||||
0.873096 | + | 0.487549i | \(0.162109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.67072 | 0.842122 | 0.421061 | − | 0.907032i | \(-0.361658\pi\) | ||||
0.421061 | + | 0.907032i | \(0.361658\pi\) | |||||||
\(20\) | 0.189627 | 0.0424019 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.23685 | 0.263698 | ||||||||
\(23\) | −3.45314 | −0.720030 | −0.360015 | − | 0.932946i | \(-0.617228\pi\) | ||||
−0.360015 | + | 0.932946i | \(0.617228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.83736 | −0.967471 | ||||||||
\(26\) | −4.36677 | −0.856395 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.142707 | 0.0269692 | ||||||||
\(29\) | 2.49100 | 0.462567 | 0.231283 | − | 0.972886i | \(-0.425708\pi\) | ||||
0.231283 | + | 0.972886i | \(0.425708\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.86904 | 0.515295 | 0.257648 | − | 0.966239i | \(-0.417053\pi\) | ||||
0.257648 | + | 0.966239i | \(0.417053\pi\) | |||||||
\(32\) | 2.59971 | 0.459568 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.90500 | 1.52720 | ||||||||
\(35\) | 0.122401 | 0.0206896 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00574 | 0.494141 | 0.247071 | − | 0.968997i | \(-0.420532\pi\) | ||||
0.247071 | + | 0.968997i | \(0.420532\pi\) | |||||||
\(38\) | 4.54014 | 0.736508 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.23217 | 0.194822 | ||||||||
\(41\) | 4.84782 | 0.757103 | 0.378551 | − | 0.925580i | \(-0.376422\pi\) | ||||
0.378551 | + | 0.925580i | \(0.376422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.93177 | −0.904586 | −0.452293 | − | 0.891869i | \(-0.649394\pi\) | ||||
−0.452293 | + | 0.891869i | \(0.649394\pi\) | |||||||
\(44\) | −0.470198 | −0.0708850 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.27103 | −0.629729 | ||||||||
\(47\) | −8.13596 | −1.18675 | −0.593376 | − | 0.804925i | \(-0.702205\pi\) | ||||
−0.593376 | + | 0.804925i | \(0.702205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90788 | −0.986841 | ||||||||
\(50\) | −5.98309 | −0.846137 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.66006 | 0.230209 | ||||||||
\(53\) | 1.91085 | 0.262475 | 0.131238 | − | 0.991351i | \(-0.458105\pi\) | ||||
0.131238 | + | 0.991351i | \(0.458105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.403292 | −0.0543799 | ||||||||
\(56\) | 0.927290 | 0.123914 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.08100 | 0.404555 | ||||||||
\(59\) | 1.68282 | 0.219084 | 0.109542 | − | 0.993982i | \(-0.465062\pi\) | ||||
0.109542 | + | 0.993982i | \(0.465062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 3.54858 | 0.450670 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.89249 | 1.11156 | ||||||||
\(65\) | 1.42385 | 0.176606 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0898202 | −0.0109733 | −0.00548664 | − | 0.999985i | \(-0.501746\pi\) | ||||
−0.00548664 | + | 0.999985i | \(0.501746\pi\) | |||||||
\(68\) | −3.38530 | −0.410528 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.151392 | 0.0180948 | ||||||||
\(71\) | −13.0923 | −1.55377 | −0.776886 | − | 0.629642i | \(-0.783202\pi\) | ||||
−0.776886 | + | 0.629642i | \(0.783202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0564 | −1.64518 | −0.822589 | − | 0.568637i | \(-0.807471\pi\) | ||||
−0.822589 | + | 0.568637i | \(0.807471\pi\) | |||||||
\(74\) | 3.71766 | 0.432169 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.72597 | −0.197982 | ||||||||
\(77\) | −0.303505 | −0.0345876 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46200 | 0.389505 | 0.194753 | − | 0.980852i | \(-0.437610\pi\) | ||||
0.194753 | + | 0.980852i | \(0.437610\pi\) | |||||||
\(80\) | 1.14475 | 0.127987 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.99604 | 0.662152 | ||||||||
\(83\) | −2.45660 | −0.269646 | −0.134823 | − | 0.990870i | \(-0.543047\pi\) | ||||
−0.134823 | + | 0.990870i | \(0.543047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.90360 | −0.314939 | ||||||||
\(86\) | −7.33671 | −0.791138 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.05527 | −0.325693 | ||||||||
\(89\) | −12.1773 | −1.29079 | −0.645397 | − | 0.763848i | \(-0.723308\pi\) | ||||
−0.645397 | + | 0.763848i | \(0.723308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07154 | 0.112328 | ||||||||
\(92\) | 1.62366 | 0.169278 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.0630 | −1.03792 | ||||||||
\(95\) | −1.48037 | −0.151883 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.70611 | −0.173229 | −0.0866145 | − | 0.996242i | \(-0.527605\pi\) | ||||
−0.0866145 | + | 0.996242i | \(0.527605\pi\) | |||||||
\(98\) | −8.54403 | −0.863077 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.27451 | 0.227451 | ||||||||
\(101\) | −3.09935 | −0.308397 | −0.154198 | − | 0.988040i | \(-0.549279\pi\) | ||||
−0.154198 | + | 0.988040i | \(0.549279\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.70468 | −0.167967 | −0.0839834 | − | 0.996467i | \(-0.526764\pi\) | ||||
−0.0839834 | + | 0.996467i | \(0.526764\pi\) | |||||||
\(104\) | 10.7868 | 1.05773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.36344 | 0.229557 | ||||||||
\(107\) | −11.9236 | −1.15270 | −0.576350 | − | 0.817203i | \(-0.695523\pi\) | ||||
−0.576350 | + | 0.817203i | \(0.695523\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.88221 | −0.371848 | −0.185924 | − | 0.982564i | \(-0.559528\pi\) | ||||
−0.185924 | + | 0.982564i | \(0.559528\pi\) | |||||||
\(110\) | −0.498813 | −0.0475599 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.861505 | 0.0814046 | ||||||||
\(113\) | −13.8764 | −1.30538 | −0.652692 | − | 0.757623i | \(-0.726361\pi\) | ||||
−0.652692 | + | 0.757623i | \(0.726361\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.39263 | 0.129863 | ||||||||
\(116\) | −1.17126 | −0.108749 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.08140 | 0.191608 | ||||||||
\(119\) | −2.18516 | −0.200313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.23685 | 0.111979 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.34902 | −0.121145 | ||||||||
\(125\) | 3.96733 | 0.354849 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.9779 | 1.15160 | 0.575801 | − | 0.817590i | \(-0.304690\pi\) | ||||
0.575801 | + | 0.817590i | \(0.304690\pi\) | |||||||
\(128\) | 5.79927 | 0.512588 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.76109 | 0.154457 | ||||||||
\(131\) | 0.0196484 | 0.00171669 | 0.000858346 | − | 1.00000i | \(-0.499727\pi\) | ||||
0.000858346 | 1.00000i | \(0.499727\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.11408 | −0.0966033 | ||||||||
\(134\) | −0.111094 | −0.00959708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21.9971 | −1.88624 | ||||||||
\(137\) | −0.274897 | −0.0234860 | −0.0117430 | − | 0.999931i | \(-0.503738\pi\) | ||||
−0.0117430 | + | 0.999931i | \(0.503738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3695 | −1.21881 | −0.609404 | − | 0.792860i | \(-0.708591\pi\) | ||||
−0.609404 | + | 0.792860i | \(0.708591\pi\) | |||||||
\(140\) | −0.0575528 | −0.00486410 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.1932 | −1.35891 | ||||||||
\(143\) | −3.53056 | −0.295240 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00460 | −0.0834275 | ||||||||
\(146\) | −17.3857 | −1.43885 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.41329 | −0.116172 | ||||||||
\(149\) | −15.6059 | −1.27848 | −0.639242 | − | 0.769006i | \(-0.720752\pi\) | ||||
−0.639242 | + | 0.769006i | \(0.720752\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4498 | 1.66418 | 0.832091 | − | 0.554639i | \(-0.187143\pi\) | ||||
0.832091 | + | 0.554639i | \(0.187143\pi\) | |||||||
\(152\) | −11.2150 | −0.909660 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.375391 | −0.0302499 | ||||||||
\(155\) | −1.15706 | −0.0929375 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.7960 | −1.81932 | −0.909659 | − | 0.415356i | \(-0.863657\pi\) | ||||
−0.909659 | + | 0.415356i | \(0.863657\pi\) | |||||||
\(158\) | 4.28198 | 0.340656 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.04844 | −0.0828867 | ||||||||
\(161\) | 1.04805 | 0.0825977 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.52845 | 0.433022 | 0.216511 | − | 0.976280i | \(-0.430532\pi\) | ||||
0.216511 | + | 0.976280i | \(0.430532\pi\) | |||||||
\(164\) | −2.27944 | −0.177994 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.03844 | −0.235829 | ||||||||
\(167\) | 22.2926 | 1.72505 | 0.862526 | − | 0.506013i | \(-0.168881\pi\) | ||||
0.862526 | + | 0.506013i | \(0.168881\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.535178 | −0.0411675 | ||||||||
\(170\) | −3.59132 | −0.275441 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.78910 | 0.212667 | ||||||||
\(173\) | 2.92197 | 0.222153 | 0.111077 | − | 0.993812i | \(-0.464570\pi\) | ||||
0.111077 | + | 0.993812i | \(0.464570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.46816 | 0.110983 | ||||||||
\(176\) | −2.83852 | −0.213961 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.0615 | −1.12891 | ||||||||
\(179\) | −8.74757 | −0.653824 | −0.326912 | − | 0.945055i | \(-0.606008\pi\) | ||||
−0.326912 | + | 0.945055i | \(0.606008\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.9185 | −1.62919 | −0.814596 | − | 0.580028i | \(-0.803041\pi\) | ||||
−0.814596 | + | 0.580028i | \(0.803041\pi\) | |||||||
\(182\) | 1.32534 | 0.0982406 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.5503 | 0.777777 | ||||||||
\(185\) | −1.21219 | −0.0891222 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.19973 | 0.526497 | ||||||||
\(188\) | 3.82551 | 0.279004 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.83100 | −0.132835 | ||||||||
\(191\) | −1.79904 | −0.130174 | −0.0650869 | − | 0.997880i | \(-0.520732\pi\) | ||||
−0.0650869 | + | 0.997880i | \(0.520732\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.99299 | 0.503366 | 0.251683 | − | 0.967810i | \(-0.419016\pi\) | ||||
0.251683 | + | 0.967810i | \(0.419016\pi\) | |||||||
\(194\) | −2.11020 | −0.151504 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.24807 | 0.232005 | ||||||||
\(197\) | 19.7619 | 1.40798 | 0.703989 | − | 0.710211i | \(-0.251400\pi\) | ||||
0.703989 | + | 0.710211i | \(0.251400\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.95005 | −0.350900 | −0.175450 | − | 0.984488i | \(-0.556138\pi\) | ||||
−0.175450 | + | 0.984488i | \(0.556138\pi\) | |||||||
\(200\) | 14.7794 | 1.04506 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.83343 | −0.269720 | ||||||||
\(203\) | −0.756031 | −0.0530630 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.95509 | −0.136549 | ||||||||
\(206\) | −2.10843 | −0.146901 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.0215 | 0.694869 | ||||||||
\(209\) | 3.67072 | 0.253909 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.51717 | −0.586346 | −0.293173 | − | 0.956059i | \(-0.594711\pi\) | ||||
−0.293173 | + | 0.956059i | \(0.594711\pi\) | |||||||
\(212\) | −0.898477 | −0.0617076 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.7477 | −1.00813 | ||||||||
\(215\) | 2.39223 | 0.163149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.870770 | −0.0591117 | ||||||||
\(218\) | −4.80172 | −0.325213 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.189627 | 0.0127847 | ||||||||
\(221\) | −25.4191 | −1.70987 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.10025 | −0.341538 | −0.170769 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170769 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(224\) | −0.789026 | −0.0527190 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.1631 | −1.14167 | ||||||||
\(227\) | 13.1071 | 0.869951 | 0.434976 | − | 0.900442i | \(-0.356757\pi\) | ||||
0.434976 | + | 0.900442i | \(0.356757\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.15429 | 0.538851 | 0.269425 | − | 0.963021i | \(-0.413166\pi\) | ||||
0.269425 | + | 0.963021i | \(0.413166\pi\) | |||||||
\(230\) | 1.72247 | 0.113576 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.61067 | −0.499665 | ||||||||
\(233\) | −10.5083 | −0.688419 | −0.344209 | − | 0.938893i | \(-0.611853\pi\) | ||||
−0.344209 | + | 0.938893i | \(0.611853\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.28117 | 0.214040 | ||||||||
\(236\) | −0.791258 | −0.0515065 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.70271 | −0.175191 | ||||||||
\(239\) | −21.1592 | −1.36868 | −0.684338 | − | 0.729165i | \(-0.739909\pi\) | ||||
−0.684338 | + | 0.729165i | \(0.739909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.1626 | −1.87853 | −0.939264 | − | 0.343194i | \(-0.888491\pi\) | ||||
−0.939264 | + | 0.343194i | \(0.888491\pi\) | |||||||
\(242\) | 1.23685 | 0.0795078 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.470198 | −0.0301013 | ||||||||
\(245\) | 2.78590 | 0.177984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.9597 | −0.824606 | ||||||||
\(248\) | −8.76570 | −0.556622 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.90700 | 0.310346 | ||||||||
\(251\) | −24.0553 | −1.51835 | −0.759177 | − | 0.650884i | \(-0.774398\pi\) | ||||
−0.759177 | + | 0.650884i | \(0.774398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.45314 | −0.217097 | ||||||||
\(254\) | 16.0517 | 1.00718 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.6121 | −0.663259 | ||||||||
\(257\) | 12.6806 | 0.790993 | 0.395497 | − | 0.918467i | \(-0.370573\pi\) | ||||
0.395497 | + | 0.918467i | \(0.370573\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.912259 | −0.0566850 | ||||||||
\(260\) | −0.669489 | −0.0415199 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0243022 | 0.00150140 | ||||||||
\(263\) | −25.0698 | −1.54587 | −0.772934 | − | 0.634487i | \(-0.781211\pi\) | ||||
−0.772934 | + | 0.634487i | \(0.781211\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.770630 | −0.0473394 | ||||||||
\(266\) | −1.37796 | −0.0844879 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.0422332 | 0.00257981 | ||||||||
\(269\) | −4.34238 | −0.264760 | −0.132380 | − | 0.991199i | \(-0.542262\pi\) | ||||
−0.132380 | + | 0.991199i | \(0.542262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.9773 | 1.09204 | 0.546021 | − | 0.837771i | \(-0.316142\pi\) | ||||
0.546021 | + | 0.837771i | \(0.316142\pi\) | |||||||
\(272\) | −20.4366 | −1.23915 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.340007 | −0.0205406 | ||||||||
\(275\) | −4.83736 | −0.291704 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.1868 | 0.912485 | 0.456242 | − | 0.889856i | \(-0.349195\pi\) | ||||
0.456242 | + | 0.889856i | \(0.349195\pi\) | |||||||
\(278\) | −17.7730 | −1.06595 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.373969 | −0.0223489 | ||||||||
\(281\) | 21.9272 | 1.30807 | 0.654034 | − | 0.756465i | \(-0.273075\pi\) | ||||
0.654034 | + | 0.756465i | \(0.273075\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5407 | −1.28046 | −0.640230 | − | 0.768183i | \(-0.721161\pi\) | ||||
−0.640230 | + | 0.768183i | \(0.721161\pi\) | |||||||
\(284\) | 6.15598 | 0.365290 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.36677 | −0.258213 | ||||||||
\(287\) | −1.47134 | −0.0868504 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.8362 | 2.04919 | ||||||||
\(290\) | −1.24254 | −0.0729645 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.60929 | 0.386779 | ||||||||
\(293\) | −29.3795 | −1.71637 | −0.858183 | − | 0.513344i | \(-0.828407\pi\) | ||||
−0.858183 | + | 0.513344i | \(0.828407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.678668 | −0.0395136 | ||||||||
\(296\) | −9.18335 | −0.533771 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.3022 | −1.11814 | ||||||||
\(299\) | 12.1915 | 0.705054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.80032 | 0.103769 | ||||||||
\(302\) | 25.2934 | 1.45547 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.4194 | −0.597595 | ||||||||
\(305\) | −0.403292 | −0.0230924 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.0803 | 1.54555 | 0.772777 | − | 0.634678i | \(-0.218867\pi\) | ||||
0.772777 | + | 0.634678i | \(0.218867\pi\) | |||||||
\(308\) | 0.142707 | 0.00813151 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.43112 | −0.0812819 | ||||||||
\(311\) | −29.9461 | −1.69809 | −0.849044 | − | 0.528321i | \(-0.822822\pi\) | ||||
−0.849044 | + | 0.528321i | \(0.822822\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.01342 | 0.283376 | 0.141688 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141688 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(314\) | −28.1953 | −1.59115 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62782 | −0.0915723 | ||||||||
\(317\) | −4.61539 | −0.259226 | −0.129613 | − | 0.991565i | \(-0.541374\pi\) | ||||
−0.129613 | + | 0.991565i | \(0.541374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.49100 | 0.139469 | ||||||||
\(320\) | −3.58627 | −0.200479 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.29628 | 0.0722388 | ||||||||
\(323\) | 26.4282 | 1.47051 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0786 | 0.947348 | ||||||||
\(326\) | 6.83787 | 0.378715 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.8114 | −0.817823 | ||||||||
\(329\) | 2.46931 | 0.136137 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.66498 | 0.256410 | 0.128205 | − | 0.991748i | \(-0.459078\pi\) | ||||
0.128205 | + | 0.991748i | \(0.459078\pi\) | |||||||
\(332\) | 1.15509 | 0.0633936 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 27.5726 | 1.50871 | ||||||||
\(335\) | 0.0362238 | 0.00197912 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.6742 | 1.07172 | 0.535861 | − | 0.844306i | \(-0.319987\pi\) | ||||
0.535861 | + | 0.844306i | \(0.319987\pi\) | |||||||
\(338\) | −0.661936 | −0.0360046 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.36526 | 0.0740419 | ||||||||
\(341\) | 2.86904 | 0.155367 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.22112 | 0.227919 | ||||||||
\(344\) | 18.1231 | 0.977134 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.61404 | 0.194292 | ||||||||
\(347\) | −3.66629 | −0.196817 | −0.0984083 | − | 0.995146i | \(-0.531375\pi\) | ||||
−0.0984083 | + | 0.995146i | \(0.531375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1270 | 0.542084 | 0.271042 | − | 0.962567i | \(-0.412632\pi\) | ||||
0.271042 | + | 0.962567i | \(0.412632\pi\) | |||||||
\(350\) | 1.81590 | 0.0970639 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59971 | 0.138565 | ||||||||
\(353\) | 16.6514 | 0.886265 | 0.443133 | − | 0.896456i | \(-0.353867\pi\) | ||||
0.443133 | + | 0.896456i | \(0.353867\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.28003 | 0.280235 | ||||||||
\(356\) | 5.72575 | 0.303464 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.8194 | −0.571825 | ||||||||
\(359\) | −11.9942 | −0.633027 | −0.316514 | − | 0.948588i | \(-0.602512\pi\) | ||||
−0.316514 | + | 0.948588i | \(0.602512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.52579 | −0.290831 | ||||||||
\(362\) | −27.1100 | −1.42487 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.503837 | −0.0264082 | ||||||||
\(365\) | 5.66884 | 0.296720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.28210 | 0.484522 | 0.242261 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242261 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(368\) | 9.80181 | 0.510955 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.49930 | −0.0779450 | ||||||||
\(371\) | −0.579952 | −0.0301096 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6865 | 0.553327 | 0.276663 | − | 0.960967i | \(-0.410771\pi\) | ||||
0.276663 | + | 0.960967i | \(0.410771\pi\) | |||||||
\(374\) | 8.90500 | 0.460467 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.8575 | 1.28193 | ||||||||
\(377\) | −8.79461 | −0.452945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.1527 | 1.65157 | 0.825787 | − | 0.563982i | \(-0.190731\pi\) | ||||
0.825787 | + | 0.563982i | \(0.190731\pi\) | |||||||
\(380\) | 0.696069 | 0.0357076 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.22514 | −0.113848 | ||||||||
\(383\) | −22.4294 | −1.14609 | −0.573046 | − | 0.819524i | \(-0.694238\pi\) | ||||
−0.573046 | + | 0.819524i | \(0.694238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.122401 | 0.00623815 | ||||||||
\(386\) | 8.64929 | 0.440237 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.802209 | 0.0407260 | ||||||||
\(389\) | −23.7359 | −1.20346 | −0.601729 | − | 0.798700i | \(-0.705521\pi\) | ||||
−0.601729 | + | 0.798700i | \(0.705521\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.8617 | −1.25731 | ||||||||
\(392\) | 21.1054 | 1.06599 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.4426 | 1.23140 | ||||||||
\(395\) | −1.39620 | −0.0702503 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5028 | 0.677686 | 0.338843 | − | 0.940843i | \(-0.389964\pi\) | ||||
0.338843 | + | 0.940843i | \(0.389964\pi\) | |||||||
\(398\) | −6.12248 | −0.306892 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.7309 | 0.686546 | ||||||||
\(401\) | 28.6582 | 1.43112 | 0.715561 | − | 0.698550i | \(-0.246171\pi\) | ||||
0.715561 | + | 0.698550i | \(0.246171\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.1293 | −0.504577 | ||||||||
\(404\) | 1.45731 | 0.0725037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.935098 | −0.0464081 | ||||||||
\(407\) | 3.00574 | 0.148989 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.4603 | 0.962252 | 0.481126 | − | 0.876651i | \(-0.340228\pi\) | ||||
0.481126 | + | 0.876651i | \(0.340228\pi\) | |||||||
\(410\) | −2.41816 | −0.119424 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.801536 | 0.0394888 | ||||||||
\(413\) | −0.510744 | −0.0251321 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.990726 | 0.0486328 | ||||||||
\(416\) | −9.17842 | −0.450009 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.54014 | 0.222066 | ||||||||
\(419\) | −17.3821 | −0.849169 | −0.424585 | − | 0.905388i | \(-0.639580\pi\) | ||||
−0.424585 | + | 0.905388i | \(0.639580\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5440 | 0.513885 | 0.256943 | − | 0.966427i | \(-0.417285\pi\) | ||||
0.256943 | + | 0.966427i | \(0.417285\pi\) | |||||||
\(422\) | −10.5345 | −0.512810 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.83815 | −0.283526 | ||||||||
\(425\) | −34.8277 | −1.68939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.303505 | −0.0146876 | ||||||||
\(428\) | 5.60646 | 0.270998 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.95884 | 0.142688 | ||||||||
\(431\) | 32.8548 | 1.58256 | 0.791281 | − | 0.611453i | \(-0.209415\pi\) | ||||
0.791281 | + | 0.611453i | \(0.209415\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.53171 | 0.410008 | 0.205004 | − | 0.978761i | \(-0.434279\pi\) | ||||
0.205004 | + | 0.978761i | \(0.434279\pi\) | |||||||
\(434\) | −1.07701 | −0.0516983 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.82541 | 0.0874211 | ||||||||
\(437\) | −12.6755 | −0.606353 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.2501 | 0.680122 | 0.340061 | − | 0.940403i | \(-0.389552\pi\) | ||||
0.340061 | + | 0.940403i | \(0.389552\pi\) | |||||||
\(440\) | 1.23217 | 0.0587412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −31.4396 | −1.49543 | ||||||||
\(443\) | 8.82606 | 0.419339 | 0.209669 | − | 0.977772i | \(-0.432761\pi\) | ||||
0.209669 | + | 0.977772i | \(0.432761\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.91102 | 0.232805 | ||||||||
\(446\) | −6.30825 | −0.298704 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.69892 | −0.127512 | ||||||||
\(449\) | −10.0380 | −0.473721 | −0.236860 | − | 0.971544i | \(-0.576118\pi\) | ||||
−0.236860 | + | 0.971544i | \(0.576118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.84782 | 0.228275 | ||||||||
\(452\) | 6.52467 | 0.306895 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.2116 | 0.760848 | ||||||||
\(455\) | −0.432144 | −0.0202592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.9769 | −0.981260 | −0.490630 | − | 0.871368i | \(-0.663233\pi\) | ||||
−0.490630 | + | 0.871368i | \(0.663233\pi\) | |||||||
\(458\) | 10.0857 | 0.471272 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.654810 | −0.0305307 | ||||||||
\(461\) | 24.8875 | 1.15913 | 0.579564 | − | 0.814927i | \(-0.303223\pi\) | ||||
0.579564 | + | 0.814927i | \(0.303223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9458 | 1.01991 | 0.509954 | − | 0.860202i | \(-0.329663\pi\) | ||||
0.509954 | + | 0.860202i | \(0.329663\pi\) | |||||||
\(464\) | −7.07074 | −0.328251 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.9972 | −0.602082 | ||||||||
\(467\) | −11.5803 | −0.535871 | −0.267936 | − | 0.963437i | \(-0.586341\pi\) | ||||
−0.267936 | + | 0.963437i | \(0.586341\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0272609 | 0.00125879 | ||||||||
\(470\) | 4.05832 | 0.187196 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.14146 | −0.236655 | ||||||||
\(473\) | −5.93177 | −0.272743 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.7566 | −0.814728 | ||||||||
\(476\) | 1.02746 | 0.0470934 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.1708 | −1.19702 | ||||||||
\(479\) | −21.6662 | −0.989952 | −0.494976 | − | 0.868907i | \(-0.664823\pi\) | ||||
−0.494976 | + | 0.868907i | \(0.664823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6119 | −0.483863 | ||||||||
\(482\) | −36.0698 | −1.64294 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.470198 | −0.0213726 | ||||||||
\(485\) | 0.688060 | 0.0312432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.2365 | 0.509173 | 0.254587 | − | 0.967050i | \(-0.418061\pi\) | ||||
0.254587 | + | 0.967050i | \(0.418061\pi\) | |||||||
\(488\) | −3.05527 | −0.138306 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.44574 | 0.155663 | ||||||||
\(491\) | −40.3512 | −1.82102 | −0.910512 | − | 0.413482i | \(-0.864313\pi\) | ||||
−0.910512 | + | 0.413482i | \(0.864313\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.9345 | 0.807730 | ||||||||
\(494\) | −16.0292 | −0.721189 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.14383 | −0.365669 | ||||||||
\(497\) | 3.97358 | 0.178240 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.3298 | −1.62635 | −0.813173 | − | 0.582022i | \(-0.802262\pi\) | ||||
−0.813173 | + | 0.582022i | \(0.802262\pi\) | |||||||
\(500\) | −1.86543 | −0.0834245 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −29.7528 | −1.32793 | ||||||||
\(503\) | 5.74480 | 0.256148 | 0.128074 | − | 0.991765i | \(-0.459121\pi\) | ||||
0.128074 | + | 0.991765i | \(0.459121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.24994 | 0.0556217 | ||||||||
\(506\) | −4.27103 | −0.189870 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.10218 | −0.270740 | ||||||||
\(509\) | −40.4047 | −1.79091 | −0.895453 | − | 0.445156i | \(-0.853148\pi\) | ||||
−0.895453 | + | 0.445156i | \(0.853148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.26619 | 0.188725 | ||||||||
\(512\) | −24.7242 | −1.09267 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.6840 | 0.691792 | ||||||||
\(515\) | 0.687483 | 0.0302941 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.13596 | −0.357819 | ||||||||
\(518\) | −1.12833 | −0.0495759 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.35023 | −0.190770 | ||||||||
\(521\) | −26.7769 | −1.17312 | −0.586559 | − | 0.809907i | \(-0.699518\pi\) | ||||
−0.586559 | + | 0.809907i | \(0.699518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.37927 | −0.322673 | −0.161336 | − | 0.986899i | \(-0.551580\pi\) | ||||
−0.161336 | + | 0.986899i | \(0.551580\pi\) | |||||||
\(524\) | −0.00923865 | −0.000403592 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.0076 | −1.35199 | ||||||||
\(527\) | 20.6563 | 0.899805 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0758 | −0.481556 | ||||||||
\(530\) | −0.953155 | −0.0414024 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.523840 | 0.0227113 | ||||||||
\(533\) | −17.1155 | −0.741355 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.80870 | 0.207898 | ||||||||
\(536\) | 0.274425 | 0.0118533 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.37088 | −0.231555 | ||||||||
\(539\) | −6.90788 | −0.297544 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7137 | 1.14851 | 0.574256 | − | 0.818676i | \(-0.305291\pi\) | ||||
0.574256 | + | 0.818676i | \(0.305291\pi\) | |||||||
\(542\) | 22.2352 | 0.955085 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.7172 | 0.802494 | ||||||||
\(545\) | 1.56567 | 0.0670657 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2664 | −0.524472 | −0.262236 | − | 0.965004i | \(-0.584460\pi\) | ||||
−0.262236 | + | 0.965004i | \(0.584460\pi\) | |||||||
\(548\) | 0.129256 | 0.00552154 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.98309 | −0.255120 | ||||||||
\(551\) | 9.14377 | 0.389538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.05073 | −0.0446818 | ||||||||
\(554\) | 18.7838 | 0.798047 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.75653 | 0.286541 | ||||||||
\(557\) | −18.9900 | −0.804632 | −0.402316 | − | 0.915501i | \(-0.631795\pi\) | ||||
−0.402316 | + | 0.915501i | \(0.631795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.9424 | 0.885770 | ||||||||
\(560\) | −0.347438 | −0.0146819 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.1207 | 1.14402 | ||||||||
\(563\) | −12.4311 | −0.523907 | −0.261953 | − | 0.965081i | \(-0.584367\pi\) | ||||
−0.261953 | + | 0.965081i | \(0.584367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.59626 | 0.235436 | ||||||||
\(566\) | −26.6426 | −1.11987 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 40.0005 | 1.67838 | ||||||||
\(569\) | −24.3719 | −1.02172 | −0.510861 | − | 0.859663i | \(-0.670673\pi\) | ||||
−0.510861 | + | 0.859663i | \(0.670673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.3684 | −0.936088 | −0.468044 | − | 0.883705i | \(-0.655041\pi\) | ||||
−0.468044 | + | 0.883705i | \(0.655041\pi\) | |||||||
\(572\) | 1.66006 | 0.0694106 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.81983 | −0.0759582 | ||||||||
\(575\) | 16.7041 | 0.696609 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.888594 | −0.0369927 | −0.0184963 | − | 0.999829i | \(-0.505888\pi\) | ||||
−0.0184963 | + | 0.999829i | \(0.505888\pi\) | |||||||
\(578\) | 43.0872 | 1.79219 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.472361 | 0.0196137 | ||||||||
\(581\) | 0.745590 | 0.0309323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.91085 | 0.0791392 | ||||||||
\(584\) | 42.9461 | 1.77712 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −36.3380 | −1.50111 | ||||||||
\(587\) | −38.8288 | −1.60264 | −0.801319 | − | 0.598238i | \(-0.795868\pi\) | ||||
−0.801319 | + | 0.598238i | \(0.795868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5315 | 0.433942 | ||||||||
\(590\) | −0.839411 | −0.0345580 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.53186 | −0.350657 | ||||||||
\(593\) | 27.1156 | 1.11350 | 0.556751 | − | 0.830679i | \(-0.312048\pi\) | ||||
0.556751 | + | 0.830679i | \(0.312048\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.881256 | 0.0361280 | ||||||||
\(596\) | 7.33785 | 0.300570 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.0791 | 0.616630 | ||||||||
\(599\) | 13.0804 | 0.534451 | 0.267225 | − | 0.963634i | \(-0.413893\pi\) | ||||
0.267225 | + | 0.963634i | \(0.413893\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.30686 | −0.379635 | −0.189817 | − | 0.981819i | \(-0.560790\pi\) | ||||
−0.189817 | + | 0.981819i | \(0.560790\pi\) | |||||||
\(602\) | 2.22673 | 0.0907548 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.61546 | −0.391248 | ||||||||
\(605\) | −0.403292 | −0.0163962 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.2161 | 1.30761 | 0.653805 | − | 0.756663i | \(-0.273172\pi\) | ||||
0.653805 | + | 0.756663i | \(0.273172\pi\) | |||||||
\(608\) | 9.54282 | 0.387012 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.498813 | −0.0201963 | ||||||||
\(611\) | 28.7245 | 1.16207 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.00638 | 0.282985 | 0.141492 | − | 0.989939i | \(-0.454810\pi\) | ||||
0.141492 | + | 0.989939i | \(0.454810\pi\) | |||||||
\(614\) | 33.4943 | 1.35172 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.927290 | 0.0373616 | ||||||||
\(617\) | 33.8218 | 1.36161 | 0.680807 | − | 0.732463i | \(-0.261629\pi\) | ||||
0.680807 | + | 0.732463i | \(0.261629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.7967 | 0.715309 | 0.357655 | − | 0.933854i | \(-0.383577\pi\) | ||||
0.357655 | + | 0.933854i | \(0.383577\pi\) | |||||||
\(620\) | 0.544048 | 0.0218495 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −37.0389 | −1.48513 | ||||||||
\(623\) | 3.69588 | 0.148072 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.5868 | 0.903471 | ||||||||
\(626\) | 6.20086 | 0.247836 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.7186 | 0.427720 | ||||||||
\(629\) | 21.6405 | 0.862865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.5090 | 1.61264 | 0.806319 | − | 0.591480i | \(-0.201456\pi\) | ||||
0.806319 | + | 0.591480i | \(0.201456\pi\) | |||||||
\(632\) | −10.5773 | −0.420744 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.70856 | −0.226716 | ||||||||
\(635\) | −5.23388 | −0.207700 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.3887 | 0.966314 | ||||||||
\(638\) | 3.08100 | 0.121978 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.33880 | −0.0924493 | ||||||||
\(641\) | 10.7585 | 0.424936 | 0.212468 | − | 0.977168i | \(-0.431850\pi\) | ||||
0.212468 | + | 0.977168i | \(0.431850\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.6131 | −1.40445 | −0.702223 | − | 0.711957i | \(-0.747809\pi\) | ||||
−0.702223 | + | 0.711957i | \(0.747809\pi\) | |||||||
\(644\) | −0.492790 | −0.0194186 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.6878 | 1.28608 | ||||||||
\(647\) | 28.1304 | 1.10592 | 0.552961 | − | 0.833207i | \(-0.313498\pi\) | ||||
0.552961 | + | 0.833207i | \(0.313498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.68282 | 0.0660564 | ||||||||
\(650\) | 21.1236 | 0.828537 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.59946 | −0.101803 | ||||||||
\(653\) | −13.3332 | −0.521769 | −0.260884 | − | 0.965370i | \(-0.584014\pi\) | ||||
−0.260884 | + | 0.965370i | \(0.584014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.00792406 | −0.000309619 0 | ||||||||
\(656\) | −13.7606 | −0.537263 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.05417 | 0.119064 | ||||||||
\(659\) | 19.3913 | 0.755378 | 0.377689 | − | 0.925932i | \(-0.376719\pi\) | ||||
0.377689 | + | 0.925932i | \(0.376719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.7209 | −1.03932 | −0.519661 | − | 0.854373i | \(-0.673942\pi\) | ||||
−0.519661 | + | 0.854373i | \(0.673942\pi\) | |||||||
\(662\) | 5.76989 | 0.224253 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.50556 | 0.291272 | ||||||||
\(665\) | 0.449301 | 0.0174232 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.60178 | −0.333062 | ||||||||
\(668\) | −10.4819 | −0.405558 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0448034 | 0.00173091 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.3889 | −1.59543 | −0.797713 | − | 0.603038i | \(-0.793957\pi\) | ||||
−0.797713 | + | 0.603038i | \(0.793957\pi\) | |||||||
\(674\) | 24.3341 | 0.937314 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.251640 | 0.00967844 | ||||||||
\(677\) | 26.0151 | 0.999840 | 0.499920 | − | 0.866072i | \(-0.333363\pi\) | ||||
0.499920 | + | 0.866072i | \(0.333363\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.517813 | 0.0198718 | ||||||||
\(680\) | 8.87126 | 0.340197 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.54858 | 0.135882 | ||||||||
\(683\) | 14.8239 | 0.567220 | 0.283610 | − | 0.958940i | \(-0.408468\pi\) | ||||
0.283610 | + | 0.958940i | \(0.408468\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.110864 | 0.00423589 | ||||||||
\(686\) | 5.22089 | 0.199335 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.8374 | 0.641921 | ||||||||
\(689\) | −6.74635 | −0.257016 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.7801 | −1.85568 | −0.927841 | − | 0.372975i | \(-0.878338\pi\) | ||||
−0.927841 | + | 0.372975i | \(0.878338\pi\) | |||||||
\(692\) | −1.37390 | −0.0522280 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.53465 | −0.172133 | ||||||||
\(695\) | 5.79512 | 0.219821 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.9030 | 1.32205 | ||||||||
\(698\) | 12.5256 | 0.474099 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.690327 | −0.0260919 | ||||||||
\(701\) | −51.2249 | −1.93474 | −0.967369 | − | 0.253371i | \(-0.918461\pi\) | ||||
−0.967369 | + | 0.253371i | \(0.918461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0333 | 0.416127 | ||||||||
\(704\) | 8.89249 | 0.335148 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.5953 | 0.775115 | ||||||||
\(707\) | 0.940668 | 0.0353775 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.1294 | 0.943753 | 0.471876 | − | 0.881665i | \(-0.343577\pi\) | ||||
0.471876 | + | 0.881665i | \(0.343577\pi\) | |||||||
\(710\) | 6.53061 | 0.245089 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37.2050 | 1.39432 | ||||||||
\(713\) | −9.90722 | −0.371028 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.42385 | 0.0532488 | ||||||||
\(716\) | 4.11309 | 0.153713 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.8350 | −0.553637 | ||||||||
\(719\) | −3.40870 | −0.127123 | −0.0635615 | − | 0.997978i | \(-0.520246\pi\) | ||||
−0.0635615 | + | 0.997978i | \(0.520246\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.517378 | 0.0192682 | ||||||||
\(722\) | −6.83458 | −0.254357 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.3061 | 0.383021 | ||||||||
\(725\) | −12.0498 | −0.447520 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.1314 | 1.37713 | 0.688563 | − | 0.725176i | \(-0.258242\pi\) | ||||
0.688563 | + | 0.725176i | \(0.258242\pi\) | |||||||
\(728\) | −3.27385 | −0.121337 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.01151 | 0.259508 | ||||||||
\(731\) | −42.7071 | −1.57958 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.2953 | 0.528009 | 0.264004 | − | 0.964521i | \(-0.414957\pi\) | ||||
0.264004 | + | 0.964521i | \(0.414957\pi\) | |||||||
\(734\) | 11.4806 | 0.423756 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.97718 | −0.330903 | ||||||||
\(737\) | −0.0898202 | −0.00330857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.9653 | 1.28622 | 0.643110 | − | 0.765774i | \(-0.277644\pi\) | ||||
0.643110 | + | 0.765774i | \(0.277644\pi\) | |||||||
\(740\) | 0.569970 | 0.0209525 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.717315 | −0.0263335 | ||||||||
\(743\) | 23.7805 | 0.872422 | 0.436211 | − | 0.899844i | \(-0.356320\pi\) | ||||
0.436211 | + | 0.899844i | \(0.356320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.29373 | 0.230584 | ||||||||
\(746\) | 13.2176 | 0.483932 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.38530 | −0.123779 | ||||||||
\(749\) | 3.61888 | 0.132231 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.735996 | 0.0268569 | 0.0134284 | − | 0.999910i | \(-0.495725\pi\) | ||||
0.0134284 | + | 0.999910i | \(0.495725\pi\) | |||||||
\(752\) | 23.0941 | 0.842154 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.8776 | −0.396140 | ||||||||
\(755\) | −8.24725 | −0.300148 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.9323 | 1.70578 | 0.852892 | − | 0.522087i | \(-0.174846\pi\) | ||||
0.852892 | + | 0.522087i | \(0.174846\pi\) | |||||||
\(758\) | 39.7681 | 1.44444 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.52294 | 0.164064 | ||||||||
\(761\) | 7.29456 | 0.264427 | 0.132214 | − | 0.991221i | \(-0.457791\pi\) | ||||
0.132214 | + | 0.991221i | \(0.457791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.17827 | 0.0426563 | ||||||||
\(764\) | 0.845904 | 0.0306037 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.7419 | −1.00236 | ||||||||
\(767\) | −5.94129 | −0.214527 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.6811 | −1.25063 | −0.625316 | − | 0.780372i | \(-0.715030\pi\) | ||||
−0.625316 | + | 0.780372i | \(0.715030\pi\) | |||||||
\(770\) | 0.151392 | 0.00545580 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.28809 | −0.118341 | ||||||||
\(773\) | 15.5742 | 0.560165 | 0.280083 | − | 0.959976i | \(-0.409638\pi\) | ||||
0.280083 | + | 0.959976i | \(0.409638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.8786 | −0.498533 | ||||||||
\(776\) | 5.21262 | 0.187122 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.3578 | −1.05253 | ||||||||
\(779\) | 17.7950 | 0.637573 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.0923 | −0.468480 | ||||||||
\(782\) | −30.7503 | −1.09963 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.6082 | 0.700291 | ||||||||
\(785\) | 9.19344 | 0.328128 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.43019 | 0.0866271 | 0.0433135 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433135 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(788\) | −9.29201 | −0.331014 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.72689 | −0.0614399 | ||||||||
\(791\) | 4.21157 | 0.149746 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.53056 | −0.125374 | ||||||||
\(794\) | 16.7010 | 0.592695 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.32750 | 0.0824962 | ||||||||
\(797\) | 16.5071 | 0.584712 | 0.292356 | − | 0.956310i | \(-0.405561\pi\) | ||||
0.292356 | + | 0.956310i | \(0.405561\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.5768 | −2.07230 | ||||||||
\(800\) | −12.5757 | −0.444619 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.4459 | 1.25164 | ||||||||
\(803\) | −14.0564 | −0.496040 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.422669 | −0.0148971 | ||||||||
\(806\) | −12.5285 | −0.441296 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.46934 | 0.333130 | ||||||||
\(809\) | −26.1046 | −0.917788 | −0.458894 | − | 0.888491i | \(-0.651754\pi\) | ||||
−0.458894 | + | 0.888491i | \(0.651754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.3961 | −0.997122 | −0.498561 | − | 0.866855i | \(-0.666138\pi\) | ||||
−0.498561 | + | 0.866855i | \(0.666138\pi\) | |||||||
\(812\) | 0.355484 | 0.0124750 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.71766 | 0.130304 | ||||||||
\(815\) | −2.22958 | −0.0780988 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.7739 | −0.761771 | ||||||||
\(818\) | 24.0696 | 0.841573 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.919279 | 0.0321026 | ||||||||
\(821\) | 7.36854 | 0.257164 | 0.128582 | − | 0.991699i | \(-0.458957\pi\) | ||||
0.128582 | + | 0.991699i | \(0.458957\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5592 | −0.856080 | −0.428040 | − | 0.903760i | \(-0.640796\pi\) | ||||
−0.428040 | + | 0.903760i | \(0.640796\pi\) | |||||||
\(824\) | 5.20825 | 0.181438 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.631715 | −0.0219802 | ||||||||
\(827\) | −31.8506 | −1.10755 | −0.553776 | − | 0.832666i | \(-0.686814\pi\) | ||||
−0.553776 | + | 0.832666i | \(0.686814\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0544 | 0.974370 | 0.487185 | − | 0.873299i | \(-0.338024\pi\) | ||||
0.487185 | + | 0.873299i | \(0.338024\pi\) | |||||||
\(830\) | 1.22538 | 0.0425336 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −31.3954 | −1.08844 | ||||||||
\(833\) | −49.7349 | −1.72321 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.99042 | −0.311126 | ||||||||
\(836\) | −1.72597 | −0.0596938 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21.4990 | −0.742672 | ||||||||
\(839\) | −8.53067 | −0.294511 | −0.147256 | − | 0.989098i | \(-0.547044\pi\) | ||||
−0.147256 | + | 0.989098i | \(0.547044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7949 | −0.786032 | ||||||||
\(842\) | 13.0414 | 0.449437 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00475 | 0.137849 | ||||||||
\(845\) | 0.215833 | 0.00742488 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.303505 | −0.0104286 | ||||||||
\(848\) | −5.42398 | −0.186260 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −43.0767 | −1.47752 | ||||||||
\(851\) | −10.3793 | −0.355797 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 47.7707 | 1.63564 | 0.817818 | − | 0.575477i | \(-0.195183\pi\) | ||||
0.817818 | + | 0.575477i | \(0.195183\pi\) | |||||||
\(854\) | −0.375391 | −0.0128456 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 36.4298 | 1.24515 | ||||||||
\(857\) | −20.2990 | −0.693399 | −0.346700 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346700 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.8031 | 1.39218 | 0.696091 | − | 0.717953i | \(-0.254921\pi\) | ||||
0.696091 | + | 0.717953i | \(0.254921\pi\) | |||||||
\(860\) | −1.12482 | −0.0383562 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.6366 | 1.38409 | ||||||||
\(863\) | 13.1014 | 0.445979 | 0.222989 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222989 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.17841 | −0.0400671 | ||||||||
\(866\) | 10.5525 | 0.358587 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.409434 | 0.0138971 | ||||||||
\(869\) | 3.46200 | 0.117440 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.317115 | 0.0107450 | ||||||||
\(872\) | 11.8612 | 0.401671 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.6778 | −0.530308 | ||||||||
\(875\) | −1.20410 | −0.0407062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.8525 | −0.602836 | −0.301418 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301418 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(878\) | 17.6253 | 0.594825 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.14475 | 0.0385896 | ||||||||
\(881\) | −23.6982 | −0.798412 | −0.399206 | − | 0.916861i | \(-0.630714\pi\) | ||||
−0.399206 | + | 0.916861i | \(0.630714\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45.6569 | 1.53648 | 0.768239 | − | 0.640163i | \(-0.221133\pi\) | ||||
0.768239 | + | 0.640163i | \(0.221133\pi\) | |||||||
\(884\) | 11.9520 | 0.401989 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.9165 | 0.366748 | ||||||||
\(887\) | −23.1922 | −0.778716 | −0.389358 | − | 0.921086i | \(-0.627303\pi\) | ||||
−0.389358 | + | 0.921086i | \(0.627303\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.93886 | −0.132105 | ||||||||
\(890\) | 6.07420 | 0.203608 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.39813 | 0.0802952 | ||||||||
\(893\) | −29.8649 | −0.999390 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.52783 | 0.117922 | ||||||||
\(896\) | −1.76011 | −0.0588011 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.4155 | −0.414310 | ||||||||
\(899\) | 7.14678 | 0.238359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.7576 | 0.458332 | ||||||||
\(902\) | 5.99604 | 0.199646 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 42.3962 | 1.41008 | ||||||||
\(905\) | 8.83958 | 0.293837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.587437 | −0.0195055 | −0.00975277 | − | 0.999952i | \(-0.503104\pi\) | ||||
−0.00975277 | + | 0.999952i | \(0.503104\pi\) | |||||||
\(908\) | −6.16295 | −0.204525 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.534499 | −0.0177185 | ||||||||
\(911\) | −0.0732945 | −0.00242836 | −0.00121418 | − | 0.999999i | \(-0.500386\pi\) | ||||
−0.00121418 | + | 0.999999i | \(0.500386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.45660 | −0.0813015 | ||||||||
\(914\) | −25.9454 | −0.858196 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.83413 | −0.126683 | ||||||||
\(917\) | −0.00596340 | −0.000196929 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5785 | 0.612849 | 0.306424 | − | 0.951895i | \(-0.400867\pi\) | ||||
0.306424 | + | 0.951895i | \(0.400867\pi\) | |||||||
\(920\) | −4.25485 | −0.140278 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.7822 | 1.01376 | ||||||||
\(923\) | 46.2231 | 1.52145 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.5398 | −0.478067 | ||||||||
\(926\) | 27.1437 | 0.891997 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.47587 | 0.212581 | ||||||||
\(929\) | −8.28707 | −0.271890 | −0.135945 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135945 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −25.3569 | −0.831040 | ||||||||
\(932\) | 4.94096 | 0.161847 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.3231 | −0.468666 | ||||||||
\(935\) | −2.90360 | −0.0949577 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.3030 | 1.25131 | 0.625653 | − | 0.780102i | \(-0.284833\pi\) | ||||
0.625653 | + | 0.780102i | \(0.284833\pi\) | |||||||
\(938\) | 0.0337177 | 0.00110092 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.54280 | −0.0503205 | ||||||||
\(941\) | 8.69924 | 0.283587 | 0.141793 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141793 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.7402 | −0.545137 | ||||||||
\(944\) | −4.77671 | −0.155469 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.33671 | −0.238537 | ||||||||
\(947\) | 16.1962 | 0.526306 | 0.263153 | − | 0.964754i | \(-0.415238\pi\) | ||||
0.263153 | + | 0.964754i | \(0.415238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.6269 | 1.61096 | ||||||||
\(950\) | −21.9623 | −0.712550 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.67624 | 0.216378 | ||||||||
\(953\) | 13.7098 | 0.444104 | 0.222052 | − | 0.975035i | \(-0.428724\pi\) | ||||
0.222052 | + | 0.975035i | \(0.428724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.725538 | 0.0234779 | ||||||||
\(956\) | 9.94901 | 0.321774 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.7978 | −0.865799 | ||||||||
\(959\) | 0.0834327 | 0.00269418 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.7686 | −0.734471 | ||||||||
\(962\) | −13.1254 | −0.423180 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.7122 | 0.441640 | ||||||||
\(965\) | −2.82022 | −0.0907860 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.8355 | 0.959444 | 0.479722 | − | 0.877420i | \(-0.340737\pi\) | ||||
0.479722 | + | 0.877420i | \(0.340737\pi\) | |||||||
\(968\) | −3.05527 | −0.0982000 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.851028 | 0.0273249 | ||||||||
\(971\) | 45.1242 | 1.44811 | 0.724053 | − | 0.689745i | \(-0.242277\pi\) | ||||
0.724053 | + | 0.689745i | \(0.242277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.36123 | 0.139815 | ||||||||
\(974\) | 13.8979 | 0.445316 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.83852 | −0.0908588 | ||||||||
\(977\) | −60.1493 | −1.92435 | −0.962173 | − | 0.272439i | \(-0.912170\pi\) | ||||
−0.962173 | + | 0.272439i | \(0.912170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.1773 | −0.389189 | ||||||||
\(980\) | −1.30992 | −0.0418439 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −49.9085 | −1.59264 | ||||||||
\(983\) | 13.5937 | 0.433573 | 0.216786 | − | 0.976219i | \(-0.430442\pi\) | ||||
0.216786 | + | 0.976219i | \(0.430442\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.96983 | −0.253940 | ||||||||
\(986\) | 22.1823 | 0.706430 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.09362 | 0.193864 | ||||||||
\(989\) | 20.4832 | 0.651329 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.1950 | −0.641517 | −0.320758 | − | 0.947161i | \(-0.603938\pi\) | ||||
−0.320758 | + | 0.947161i | \(0.603938\pi\) | |||||||
\(992\) | 7.45868 | 0.236813 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.91473 | 0.155886 | ||||||||
\(995\) | 1.99632 | 0.0632875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.4389 | −1.24904 | −0.624522 | − | 0.781007i | \(-0.714706\pi\) | ||||
−0.624522 | + | 0.781007i | \(0.714706\pi\) | |||||||
\(998\) | −44.9346 | −1.42238 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.m.1.19 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.p.1.7 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.m.1.19 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.p.1.7 | yes | 25 | 3.2 | odd | 2 |