Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.08114 | −0.624199 | −0.312099 | − | 0.950049i | \(-0.601032\pi\) | ||||
−0.312099 | + | 0.950049i | \(0.601032\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.379081 | 0.169530 | 0.0847651 | − | 0.996401i | \(-0.472986\pi\) | ||||
0.0847651 | + | 0.996401i | \(0.472986\pi\) | |||||||
\(6\) | −1.08114 | −0.441375 | ||||||||
\(7\) | 0.614832 | 0.232385 | 0.116192 | − | 0.993227i | \(-0.462931\pi\) | ||||
0.116192 | + | 0.993227i | \(0.462931\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.83113 | −0.610376 | ||||||||
\(10\) | 0.379081 | 0.119876 | ||||||||
\(11\) | 5.27578 | 1.59071 | 0.795354 | − | 0.606145i | \(-0.207285\pi\) | ||||
0.795354 | + | 0.606145i | \(0.207285\pi\) | |||||||
\(12\) | −1.08114 | −0.312099 | ||||||||
\(13\) | −0.100390 | −0.0278431 | −0.0139216 | − | 0.999903i | \(-0.504432\pi\) | ||||
−0.0139216 | + | 0.999903i | \(0.504432\pi\) | |||||||
\(14\) | 0.614832 | 0.164321 | ||||||||
\(15\) | −0.409841 | −0.105821 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.27441 | −1.03670 | −0.518349 | − | 0.855169i | \(-0.673453\pi\) | ||||
−0.518349 | + | 0.855169i | \(0.673453\pi\) | |||||||
\(18\) | −1.83113 | −0.431601 | ||||||||
\(19\) | −3.59007 | −0.823619 | −0.411810 | − | 0.911270i | \(-0.635103\pi\) | ||||
−0.411810 | + | 0.911270i | \(0.635103\pi\) | |||||||
\(20\) | 0.379081 | 0.0847651 | ||||||||
\(21\) | −0.664722 | −0.145054 | ||||||||
\(22\) | 5.27578 | 1.12480 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.08114 | −0.220688 | ||||||||
\(25\) | −4.85630 | −0.971260 | ||||||||
\(26\) | −0.100390 | −0.0196881 | ||||||||
\(27\) | 5.22315 | 1.00519 | ||||||||
\(28\) | 0.614832 | 0.116192 | ||||||||
\(29\) | −6.70272 | −1.24466 | −0.622332 | − | 0.782754i | \(-0.713814\pi\) | ||||
−0.622332 | + | 0.782754i | \(0.713814\pi\) | |||||||
\(30\) | −0.409841 | −0.0748265 | ||||||||
\(31\) | −4.30760 | −0.773668 | −0.386834 | − | 0.922149i | \(-0.626431\pi\) | ||||
−0.386834 | + | 0.922149i | \(0.626431\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.70388 | −0.992919 | ||||||||
\(34\) | −4.27441 | −0.733056 | ||||||||
\(35\) | 0.233071 | 0.0393962 | ||||||||
\(36\) | −1.83113 | −0.305188 | ||||||||
\(37\) | 7.48078 | 1.22983 | 0.614916 | − | 0.788593i | \(-0.289190\pi\) | ||||
0.614916 | + | 0.788593i | \(0.289190\pi\) | |||||||
\(38\) | −3.59007 | −0.582387 | ||||||||
\(39\) | 0.108536 | 0.0173796 | ||||||||
\(40\) | 0.379081 | 0.0599380 | ||||||||
\(41\) | 8.15498 | 1.27359 | 0.636797 | − | 0.771031i | \(-0.280259\pi\) | ||||
0.636797 | + | 0.771031i | \(0.280259\pi\) | |||||||
\(42\) | −0.664722 | −0.102569 | ||||||||
\(43\) | −7.73581 | −1.17970 | −0.589850 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589850 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(44\) | 5.27578 | 0.795354 | ||||||||
\(45\) | −0.694145 | −0.103477 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −8.71811 | −1.27167 | −0.635834 | − | 0.771826i | \(-0.719344\pi\) | ||||
−0.635834 | + | 0.771826i | \(0.719344\pi\) | |||||||
\(48\) | −1.08114 | −0.156050 | ||||||||
\(49\) | −6.62198 | −0.945997 | ||||||||
\(50\) | −4.85630 | −0.686784 | ||||||||
\(51\) | 4.62126 | 0.647106 | ||||||||
\(52\) | −0.100390 | −0.0139216 | ||||||||
\(53\) | 1.61946 | 0.222450 | 0.111225 | − | 0.993795i | \(-0.464523\pi\) | ||||
0.111225 | + | 0.993795i | \(0.464523\pi\) | |||||||
\(54\) | 5.22315 | 0.710780 | ||||||||
\(55\) | 1.99995 | 0.269673 | ||||||||
\(56\) | 0.614832 | 0.0821604 | ||||||||
\(57\) | 3.88139 | 0.514102 | ||||||||
\(58\) | −6.70272 | −0.880110 | ||||||||
\(59\) | −7.31903 | −0.952857 | −0.476429 | − | 0.879213i | \(-0.658069\pi\) | ||||
−0.476429 | + | 0.879213i | \(0.658069\pi\) | |||||||
\(60\) | −0.409841 | −0.0529103 | ||||||||
\(61\) | 4.58610 | 0.587190 | 0.293595 | − | 0.955930i | \(-0.405148\pi\) | ||||
0.293595 | + | 0.955930i | \(0.405148\pi\) | |||||||
\(62\) | −4.30760 | −0.547066 | ||||||||
\(63\) | −1.12584 | −0.141842 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0380559 | −0.00472025 | ||||||||
\(66\) | −5.70388 | −0.702100 | ||||||||
\(67\) | −12.7060 | −1.55229 | −0.776145 | − | 0.630554i | \(-0.782828\pi\) | ||||
−0.776145 | + | 0.630554i | \(0.782828\pi\) | |||||||
\(68\) | −4.27441 | −0.518349 | ||||||||
\(69\) | 1.08114 | 0.130154 | ||||||||
\(70\) | 0.233071 | 0.0278573 | ||||||||
\(71\) | −3.66475 | −0.434926 | −0.217463 | − | 0.976069i | \(-0.569778\pi\) | ||||
−0.217463 | + | 0.976069i | \(0.569778\pi\) | |||||||
\(72\) | −1.83113 | −0.215800 | ||||||||
\(73\) | 2.16897 | 0.253859 | 0.126929 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126929 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(74\) | 7.48078 | 0.869623 | ||||||||
\(75\) | 5.25036 | 0.606259 | ||||||||
\(76\) | −3.59007 | −0.411810 | ||||||||
\(77\) | 3.24372 | 0.369656 | ||||||||
\(78\) | 0.108536 | 0.0122893 | ||||||||
\(79\) | 1.41071 | 0.158718 | 0.0793588 | − | 0.996846i | \(-0.474713\pi\) | ||||
0.0793588 | + | 0.996846i | \(0.474713\pi\) | |||||||
\(80\) | 0.379081 | 0.0423826 | ||||||||
\(81\) | −0.153594 | −0.0170660 | ||||||||
\(82\) | 8.15498 | 0.900567 | ||||||||
\(83\) | 12.3096 | 1.35116 | 0.675580 | − | 0.737287i | \(-0.263893\pi\) | ||||
0.675580 | + | 0.737287i | \(0.263893\pi\) | |||||||
\(84\) | −0.664722 | −0.0725271 | ||||||||
\(85\) | −1.62035 | −0.175752 | ||||||||
\(86\) | −7.73581 | −0.834174 | ||||||||
\(87\) | 7.24660 | 0.776918 | ||||||||
\(88\) | 5.27578 | 0.562400 | ||||||||
\(89\) | −0.0472708 | −0.00501070 | −0.00250535 | − | 0.999997i | \(-0.500797\pi\) | ||||
−0.00250535 | + | 0.999997i | \(0.500797\pi\) | |||||||
\(90\) | −0.694145 | −0.0731694 | ||||||||
\(91\) | −0.0617228 | −0.00647031 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 4.65714 | 0.482923 | ||||||||
\(94\) | −8.71811 | −0.899205 | ||||||||
\(95\) | −1.36093 | −0.139628 | ||||||||
\(96\) | −1.08114 | −0.110344 | ||||||||
\(97\) | 0.462560 | 0.0469658 | 0.0234829 | − | 0.999724i | \(-0.492524\pi\) | ||||
0.0234829 | + | 0.999724i | \(0.492524\pi\) | |||||||
\(98\) | −6.62198 | −0.668921 | ||||||||
\(99\) | −9.66063 | −0.970930 | ||||||||
\(100\) | −4.85630 | −0.485630 | ||||||||
\(101\) | −9.05936 | −0.901440 | −0.450720 | − | 0.892665i | \(-0.648833\pi\) | ||||
−0.450720 | + | 0.892665i | \(0.648833\pi\) | |||||||
\(102\) | 4.62126 | 0.457573 | ||||||||
\(103\) | 12.9499 | 1.27599 | 0.637994 | − | 0.770041i | \(-0.279764\pi\) | ||||
0.637994 | + | 0.770041i | \(0.279764\pi\) | |||||||
\(104\) | −0.100390 | −0.00984403 | ||||||||
\(105\) | −0.251984 | −0.0245911 | ||||||||
\(106\) | 1.61946 | 0.157296 | ||||||||
\(107\) | −17.3147 | −1.67387 | −0.836936 | − | 0.547301i | \(-0.815655\pi\) | ||||
−0.836936 | + | 0.547301i | \(0.815655\pi\) | |||||||
\(108\) | 5.22315 | 0.502597 | ||||||||
\(109\) | 2.98980 | 0.286371 | 0.143186 | − | 0.989696i | \(-0.454265\pi\) | ||||
0.143186 | + | 0.989696i | \(0.454265\pi\) | |||||||
\(110\) | 1.99995 | 0.190688 | ||||||||
\(111\) | −8.08780 | −0.767660 | ||||||||
\(112\) | 0.614832 | 0.0580961 | ||||||||
\(113\) | −12.3950 | −1.16602 | −0.583011 | − | 0.812464i | \(-0.698125\pi\) | ||||
−0.583011 | + | 0.812464i | \(0.698125\pi\) | |||||||
\(114\) | 3.88139 | 0.363525 | ||||||||
\(115\) | −0.379081 | −0.0353495 | ||||||||
\(116\) | −6.70272 | −0.622332 | ||||||||
\(117\) | 0.183826 | 0.0169948 | ||||||||
\(118\) | −7.31903 | −0.673772 | ||||||||
\(119\) | −2.62805 | −0.240913 | ||||||||
\(120\) | −0.409841 | −0.0374132 | ||||||||
\(121\) | 16.8339 | 1.53035 | ||||||||
\(122\) | 4.58610 | 0.415206 | ||||||||
\(123\) | −8.81671 | −0.794976 | ||||||||
\(124\) | −4.30760 | −0.386834 | ||||||||
\(125\) | −3.73634 | −0.334188 | ||||||||
\(126\) | −1.12584 | −0.100297 | ||||||||
\(127\) | 15.5795 | 1.38246 | 0.691229 | − | 0.722636i | \(-0.257070\pi\) | ||||
0.691229 | + | 0.722636i | \(0.257070\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.36353 | 0.736368 | ||||||||
\(130\) | −0.0380559 | −0.00333772 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −5.70388 | −0.496459 | ||||||||
\(133\) | −2.20729 | −0.191396 | ||||||||
\(134\) | −12.7060 | −1.09764 | ||||||||
\(135\) | 1.98000 | 0.170411 | ||||||||
\(136\) | −4.27441 | −0.366528 | ||||||||
\(137\) | −4.52366 | −0.386483 | −0.193241 | − | 0.981151i | \(-0.561900\pi\) | ||||
−0.193241 | + | 0.981151i | \(0.561900\pi\) | |||||||
\(138\) | 1.08114 | 0.0920331 | ||||||||
\(139\) | −13.2164 | −1.12100 | −0.560501 | − | 0.828154i | \(-0.689391\pi\) | ||||
−0.560501 | + | 0.828154i | \(0.689391\pi\) | |||||||
\(140\) | 0.233071 | 0.0196981 | ||||||||
\(141\) | 9.42554 | 0.793774 | ||||||||
\(142\) | −3.66475 | −0.307539 | ||||||||
\(143\) | −0.529635 | −0.0442903 | ||||||||
\(144\) | −1.83113 | −0.152594 | ||||||||
\(145\) | −2.54087 | −0.211008 | ||||||||
\(146\) | 2.16897 | 0.179505 | ||||||||
\(147\) | 7.15932 | 0.590491 | ||||||||
\(148\) | 7.48078 | 0.614916 | ||||||||
\(149\) | 19.2562 | 1.57753 | 0.788764 | − | 0.614697i | \(-0.210722\pi\) | ||||
0.788764 | + | 0.614697i | \(0.210722\pi\) | |||||||
\(150\) | 5.25036 | 0.428690 | ||||||||
\(151\) | 8.36267 | 0.680545 | 0.340272 | − | 0.940327i | \(-0.389481\pi\) | ||||
0.340272 | + | 0.940327i | \(0.389481\pi\) | |||||||
\(152\) | −3.59007 | −0.291193 | ||||||||
\(153\) | 7.82699 | 0.632775 | ||||||||
\(154\) | 3.24372 | 0.261386 | ||||||||
\(155\) | −1.63293 | −0.131160 | ||||||||
\(156\) | 0.108536 | 0.00868982 | ||||||||
\(157\) | −6.72793 | −0.536948 | −0.268474 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268474 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(158\) | 1.41071 | 0.112230 | ||||||||
\(159\) | −1.75087 | −0.138853 | ||||||||
\(160\) | 0.379081 | 0.0299690 | ||||||||
\(161\) | −0.614832 | −0.0484555 | ||||||||
\(162\) | −0.153594 | −0.0120675 | ||||||||
\(163\) | 0.451346 | 0.0353521 | 0.0176761 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176761 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(164\) | 8.15498 | 0.636797 | ||||||||
\(165\) | −2.16223 | −0.168330 | ||||||||
\(166\) | 12.3096 | 0.955414 | ||||||||
\(167\) | −1.79938 | −0.139240 | −0.0696200 | − | 0.997574i | \(-0.522179\pi\) | ||||
−0.0696200 | + | 0.997574i | \(0.522179\pi\) | |||||||
\(168\) | −0.664722 | −0.0512844 | ||||||||
\(169\) | −12.9899 | −0.999225 | ||||||||
\(170\) | −1.62035 | −0.124275 | ||||||||
\(171\) | 6.57388 | 0.502717 | ||||||||
\(172\) | −7.73581 | −0.589850 | ||||||||
\(173\) | 4.48264 | 0.340809 | 0.170404 | − | 0.985374i | \(-0.445493\pi\) | ||||
0.170404 | + | 0.985374i | \(0.445493\pi\) | |||||||
\(174\) | 7.24660 | 0.549364 | ||||||||
\(175\) | −2.98581 | −0.225706 | ||||||||
\(176\) | 5.27578 | 0.397677 | ||||||||
\(177\) | 7.91293 | 0.594772 | ||||||||
\(178\) | −0.0472708 | −0.00354310 | ||||||||
\(179\) | −26.4904 | −1.97999 | −0.989993 | − | 0.141113i | \(-0.954932\pi\) | ||||
−0.989993 | + | 0.141113i | \(0.954932\pi\) | |||||||
\(180\) | −0.694145 | −0.0517386 | ||||||||
\(181\) | 0.316097 | 0.0234953 | 0.0117477 | − | 0.999931i | \(-0.496261\pi\) | ||||
0.0117477 | + | 0.999931i | \(0.496261\pi\) | |||||||
\(182\) | −0.0617228 | −0.00457520 | ||||||||
\(183\) | −4.95824 | −0.366523 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 2.83582 | 0.208494 | ||||||||
\(186\) | 4.65714 | 0.341478 | ||||||||
\(187\) | −22.5509 | −1.64908 | ||||||||
\(188\) | −8.71811 | −0.635834 | ||||||||
\(189\) | 3.21136 | 0.233592 | ||||||||
\(190\) | −1.36093 | −0.0987322 | ||||||||
\(191\) | 9.18166 | 0.664362 | 0.332181 | − | 0.943216i | \(-0.392216\pi\) | ||||
0.332181 | + | 0.943216i | \(0.392216\pi\) | |||||||
\(192\) | −1.08114 | −0.0780249 | ||||||||
\(193\) | −9.13123 | −0.657280 | −0.328640 | − | 0.944455i | \(-0.606590\pi\) | ||||
−0.328640 | + | 0.944455i | \(0.606590\pi\) | |||||||
\(194\) | 0.462560 | 0.0332098 | ||||||||
\(195\) | 0.0411439 | 0.00294637 | ||||||||
\(196\) | −6.62198 | −0.472999 | ||||||||
\(197\) | −25.9547 | −1.84920 | −0.924599 | − | 0.380941i | \(-0.875600\pi\) | ||||
−0.924599 | + | 0.380941i | \(0.875600\pi\) | |||||||
\(198\) | −9.66063 | −0.686551 | ||||||||
\(199\) | −15.7517 | −1.11661 | −0.558306 | − | 0.829635i | \(-0.688548\pi\) | ||||
−0.558306 | + | 0.829635i | \(0.688548\pi\) | |||||||
\(200\) | −4.85630 | −0.343392 | ||||||||
\(201\) | 13.7371 | 0.968938 | ||||||||
\(202\) | −9.05936 | −0.637415 | ||||||||
\(203\) | −4.12104 | −0.289241 | ||||||||
\(204\) | 4.62126 | 0.323553 | ||||||||
\(205\) | 3.09140 | 0.215913 | ||||||||
\(206\) | 12.9499 | 0.902260 | ||||||||
\(207\) | 1.83113 | 0.127272 | ||||||||
\(208\) | −0.100390 | −0.00696078 | ||||||||
\(209\) | −18.9405 | −1.31014 | ||||||||
\(210\) | −0.251984 | −0.0173885 | ||||||||
\(211\) | 5.85101 | 0.402800 | 0.201400 | − | 0.979509i | \(-0.435451\pi\) | ||||
0.201400 | + | 0.979509i | \(0.435451\pi\) | |||||||
\(212\) | 1.61946 | 0.111225 | ||||||||
\(213\) | 3.96213 | 0.271480 | ||||||||
\(214\) | −17.3147 | −1.18361 | ||||||||
\(215\) | −2.93250 | −0.199995 | ||||||||
\(216\) | 5.22315 | 0.355390 | ||||||||
\(217\) | −2.64845 | −0.179789 | ||||||||
\(218\) | 2.98980 | 0.202495 | ||||||||
\(219\) | −2.34497 | −0.158458 | ||||||||
\(220\) | 1.99995 | 0.134837 | ||||||||
\(221\) | 0.429107 | 0.0288649 | ||||||||
\(222\) | −8.08780 | −0.542818 | ||||||||
\(223\) | −8.04417 | −0.538678 | −0.269339 | − | 0.963045i | \(-0.586805\pi\) | ||||
−0.269339 | + | 0.963045i | \(0.586805\pi\) | |||||||
\(224\) | 0.614832 | 0.0410802 | ||||||||
\(225\) | 8.89250 | 0.592833 | ||||||||
\(226\) | −12.3950 | −0.824502 | ||||||||
\(227\) | 7.78958 | 0.517013 | 0.258506 | − | 0.966010i | \(-0.416770\pi\) | ||||
0.258506 | + | 0.966010i | \(0.416770\pi\) | |||||||
\(228\) | 3.88139 | 0.257051 | ||||||||
\(229\) | −0.972106 | −0.0642386 | −0.0321193 | − | 0.999484i | \(-0.510226\pi\) | ||||
−0.0321193 | + | 0.999484i | \(0.510226\pi\) | |||||||
\(230\) | −0.379081 | −0.0249959 | ||||||||
\(231\) | −3.50693 | −0.230739 | ||||||||
\(232\) | −6.70272 | −0.440055 | ||||||||
\(233\) | 19.7699 | 1.29517 | 0.647583 | − | 0.761995i | \(-0.275780\pi\) | ||||
0.647583 | + | 0.761995i | \(0.275780\pi\) | |||||||
\(234\) | 0.183826 | 0.0120171 | ||||||||
\(235\) | −3.30487 | −0.215586 | ||||||||
\(236\) | −7.31903 | −0.476429 | ||||||||
\(237\) | −1.52518 | −0.0990714 | ||||||||
\(238\) | −2.62805 | −0.170351 | ||||||||
\(239\) | −13.9374 | −0.901534 | −0.450767 | − | 0.892642i | \(-0.648849\pi\) | ||||
−0.450767 | + | 0.892642i | \(0.648849\pi\) | |||||||
\(240\) | −0.409841 | −0.0264551 | ||||||||
\(241\) | 9.00899 | 0.580320 | 0.290160 | − | 0.956978i | \(-0.406291\pi\) | ||||
0.290160 | + | 0.956978i | \(0.406291\pi\) | |||||||
\(242\) | 16.8339 | 1.08212 | ||||||||
\(243\) | −15.5034 | −0.994542 | ||||||||
\(244\) | 4.58610 | 0.293595 | ||||||||
\(245\) | −2.51027 | −0.160375 | ||||||||
\(246\) | −8.81671 | −0.562133 | ||||||||
\(247\) | 0.360407 | 0.0229321 | ||||||||
\(248\) | −4.30760 | −0.273533 | ||||||||
\(249\) | −13.3085 | −0.843392 | ||||||||
\(250\) | −3.73634 | −0.236307 | ||||||||
\(251\) | 9.80227 | 0.618714 | 0.309357 | − | 0.950946i | \(-0.399886\pi\) | ||||
0.309357 | + | 0.950946i | \(0.399886\pi\) | |||||||
\(252\) | −1.12584 | −0.0709209 | ||||||||
\(253\) | −5.27578 | −0.331686 | ||||||||
\(254\) | 15.5795 | 0.977546 | ||||||||
\(255\) | 1.75183 | 0.109704 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.10256 | 0.318289 | 0.159145 | − | 0.987255i | \(-0.449126\pi\) | ||||
0.159145 | + | 0.987255i | \(0.449126\pi\) | |||||||
\(258\) | 8.36353 | 0.520691 | ||||||||
\(259\) | 4.59942 | 0.285794 | ||||||||
\(260\) | −0.0380559 | −0.00236012 | ||||||||
\(261\) | 12.2735 | 0.759712 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 0.989009 | 0.0609849 | 0.0304925 | − | 0.999535i | \(-0.490292\pi\) | ||||
0.0304925 | + | 0.999535i | \(0.490292\pi\) | |||||||
\(264\) | −5.70388 | −0.351050 | ||||||||
\(265\) | 0.613907 | 0.0377120 | ||||||||
\(266\) | −2.20729 | −0.135338 | ||||||||
\(267\) | 0.0511066 | 0.00312767 | ||||||||
\(268\) | −12.7060 | −0.776145 | ||||||||
\(269\) | −8.24587 | −0.502759 | −0.251380 | − | 0.967889i | \(-0.580884\pi\) | ||||
−0.251380 | + | 0.967889i | \(0.580884\pi\) | |||||||
\(270\) | 1.98000 | 0.120499 | ||||||||
\(271\) | −0.251100 | −0.0152532 | −0.00762661 | − | 0.999971i | \(-0.502428\pi\) | ||||
−0.00762661 | + | 0.999971i | \(0.502428\pi\) | |||||||
\(272\) | −4.27441 | −0.259174 | ||||||||
\(273\) | 0.0667313 | 0.00403876 | ||||||||
\(274\) | −4.52366 | −0.273285 | ||||||||
\(275\) | −25.6208 | −1.54499 | ||||||||
\(276\) | 1.08114 | 0.0650772 | ||||||||
\(277\) | −30.6713 | −1.84286 | −0.921429 | − | 0.388547i | \(-0.872977\pi\) | ||||
−0.921429 | + | 0.388547i | \(0.872977\pi\) | |||||||
\(278\) | −13.2164 | −0.792668 | ||||||||
\(279\) | 7.88777 | 0.472228 | ||||||||
\(280\) | 0.233071 | 0.0139287 | ||||||||
\(281\) | −8.71800 | −0.520072 | −0.260036 | − | 0.965599i | \(-0.583734\pi\) | ||||
−0.260036 | + | 0.965599i | \(0.583734\pi\) | |||||||
\(282\) | 9.42554 | 0.561283 | ||||||||
\(283\) | 25.7018 | 1.52782 | 0.763908 | − | 0.645325i | \(-0.223278\pi\) | ||||
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(284\) | −3.66475 | −0.217463 | ||||||||
\(285\) | 1.47136 | 0.0871559 | ||||||||
\(286\) | −0.529635 | −0.0313180 | ||||||||
\(287\) | 5.01394 | 0.295964 | ||||||||
\(288\) | −1.83113 | −0.107900 | ||||||||
\(289\) | 1.27061 | 0.0747417 | ||||||||
\(290\) | −2.54087 | −0.149205 | ||||||||
\(291\) | −0.500094 | −0.0293160 | ||||||||
\(292\) | 2.16897 | 0.126929 | ||||||||
\(293\) | −17.2397 | −1.00715 | −0.503576 | − | 0.863951i | \(-0.667983\pi\) | ||||
−0.503576 | + | 0.863951i | \(0.667983\pi\) | |||||||
\(294\) | 7.15932 | 0.417540 | ||||||||
\(295\) | −2.77451 | −0.161538 | ||||||||
\(296\) | 7.48078 | 0.434811 | ||||||||
\(297\) | 27.5562 | 1.59897 | ||||||||
\(298\) | 19.2562 | 1.11548 | ||||||||
\(299\) | 0.100390 | 0.00580569 | ||||||||
\(300\) | 5.25036 | 0.303130 | ||||||||
\(301\) | −4.75622 | −0.274144 | ||||||||
\(302\) | 8.36267 | 0.481218 | ||||||||
\(303\) | 9.79448 | 0.562678 | ||||||||
\(304\) | −3.59007 | −0.205905 | ||||||||
\(305\) | 1.73850 | 0.0995465 | ||||||||
\(306\) | 7.82699 | 0.447439 | ||||||||
\(307\) | −15.5417 | −0.887012 | −0.443506 | − | 0.896271i | \(-0.646265\pi\) | ||||
−0.443506 | + | 0.896271i | \(0.646265\pi\) | |||||||
\(308\) | 3.24372 | 0.184828 | ||||||||
\(309\) | −14.0007 | −0.796470 | ||||||||
\(310\) | −1.63293 | −0.0927442 | ||||||||
\(311\) | −15.0946 | −0.855935 | −0.427967 | − | 0.903794i | \(-0.640770\pi\) | ||||
−0.427967 | + | 0.903794i | \(0.640770\pi\) | |||||||
\(312\) | 0.108536 | 0.00614463 | ||||||||
\(313\) | −5.25969 | −0.297295 | −0.148648 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148648 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(314\) | −6.72793 | −0.379679 | ||||||||
\(315\) | −0.426783 | −0.0240465 | ||||||||
\(316\) | 1.41071 | 0.0793588 | ||||||||
\(317\) | 4.28608 | 0.240730 | 0.120365 | − | 0.992730i | \(-0.461593\pi\) | ||||
0.120365 | + | 0.992730i | \(0.461593\pi\) | |||||||
\(318\) | −1.75087 | −0.0981840 | ||||||||
\(319\) | −35.3621 | −1.97990 | ||||||||
\(320\) | 0.379081 | 0.0211913 | ||||||||
\(321\) | 18.7196 | 1.04483 | ||||||||
\(322\) | −0.614832 | −0.0342632 | ||||||||
\(323\) | 15.3455 | 0.853844 | ||||||||
\(324\) | −0.153594 | −0.00853300 | ||||||||
\(325\) | 0.487523 | 0.0270429 | ||||||||
\(326\) | 0.451346 | 0.0249977 | ||||||||
\(327\) | −3.23241 | −0.178753 | ||||||||
\(328\) | 8.15498 | 0.450284 | ||||||||
\(329\) | −5.36017 | −0.295516 | ||||||||
\(330\) | −2.16223 | −0.119027 | ||||||||
\(331\) | −17.1562 | −0.942991 | −0.471495 | − | 0.881869i | \(-0.656286\pi\) | ||||
−0.471495 | + | 0.881869i | \(0.656286\pi\) | |||||||
\(332\) | 12.3096 | 0.675580 | ||||||||
\(333\) | −13.6983 | −0.750660 | ||||||||
\(334\) | −1.79938 | −0.0984576 | ||||||||
\(335\) | −4.81662 | −0.263160 | ||||||||
\(336\) | −0.664722 | −0.0362636 | ||||||||
\(337\) | −9.74530 | −0.530860 | −0.265430 | − | 0.964130i | \(-0.585514\pi\) | ||||
−0.265430 | + | 0.964130i | \(0.585514\pi\) | |||||||
\(338\) | −12.9899 | −0.706559 | ||||||||
\(339\) | 13.4008 | 0.727830 | ||||||||
\(340\) | −1.62035 | −0.0878758 | ||||||||
\(341\) | −22.7260 | −1.23068 | ||||||||
\(342\) | 6.57388 | 0.355475 | ||||||||
\(343\) | −8.37523 | −0.452220 | ||||||||
\(344\) | −7.73581 | −0.417087 | ||||||||
\(345\) | 0.409841 | 0.0220651 | ||||||||
\(346\) | 4.48264 | 0.240988 | ||||||||
\(347\) | 20.3165 | 1.09065 | 0.545325 | − | 0.838225i | \(-0.316406\pi\) | ||||
0.545325 | + | 0.838225i | \(0.316406\pi\) | |||||||
\(348\) | 7.24660 | 0.388459 | ||||||||
\(349\) | 16.5982 | 0.888483 | 0.444242 | − | 0.895907i | \(-0.353473\pi\) | ||||
0.444242 | + | 0.895907i | \(0.353473\pi\) | |||||||
\(350\) | −2.98581 | −0.159598 | ||||||||
\(351\) | −0.524350 | −0.0279878 | ||||||||
\(352\) | 5.27578 | 0.281200 | ||||||||
\(353\) | −15.2653 | −0.812491 | −0.406246 | − | 0.913764i | \(-0.633162\pi\) | ||||
−0.406246 | + | 0.913764i | \(0.633162\pi\) | |||||||
\(354\) | 7.91293 | 0.420568 | ||||||||
\(355\) | −1.38924 | −0.0737331 | ||||||||
\(356\) | −0.0472708 | −0.00250535 | ||||||||
\(357\) | 2.84130 | 0.150377 | ||||||||
\(358\) | −26.4904 | −1.40006 | ||||||||
\(359\) | −0.668603 | −0.0352875 | −0.0176438 | − | 0.999844i | \(-0.505616\pi\) | ||||
−0.0176438 | + | 0.999844i | \(0.505616\pi\) | |||||||
\(360\) | −0.694145 | −0.0365847 | ||||||||
\(361\) | −6.11137 | −0.321651 | ||||||||
\(362\) | 0.316097 | 0.0166137 | ||||||||
\(363\) | −18.1999 | −0.955246 | ||||||||
\(364\) | −0.0617228 | −0.00323516 | ||||||||
\(365\) | 0.822215 | 0.0430367 | ||||||||
\(366\) | −4.95824 | −0.259171 | ||||||||
\(367\) | 13.8383 | 0.722353 | 0.361176 | − | 0.932498i | \(-0.382375\pi\) | ||||
0.361176 | + | 0.932498i | \(0.382375\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −14.9328 | −0.777371 | ||||||||
\(370\) | 2.83582 | 0.147427 | ||||||||
\(371\) | 0.995696 | 0.0516940 | ||||||||
\(372\) | 4.65714 | 0.241461 | ||||||||
\(373\) | −11.2191 | −0.580906 | −0.290453 | − | 0.956889i | \(-0.593806\pi\) | ||||
−0.290453 | + | 0.956889i | \(0.593806\pi\) | |||||||
\(374\) | −22.5509 | −1.16608 | ||||||||
\(375\) | 4.03952 | 0.208600 | ||||||||
\(376\) | −8.71811 | −0.449602 | ||||||||
\(377\) | 0.672884 | 0.0346553 | ||||||||
\(378\) | 3.21136 | 0.165174 | ||||||||
\(379\) | 9.03697 | 0.464198 | 0.232099 | − | 0.972692i | \(-0.425441\pi\) | ||||
0.232099 | + | 0.972692i | \(0.425441\pi\) | |||||||
\(380\) | −1.36093 | −0.0698142 | ||||||||
\(381\) | −16.8437 | −0.862929 | ||||||||
\(382\) | 9.18166 | 0.469775 | ||||||||
\(383\) | −13.2562 | −0.677359 | −0.338679 | − | 0.940902i | \(-0.609980\pi\) | ||||
−0.338679 | + | 0.940902i | \(0.609980\pi\) | |||||||
\(384\) | −1.08114 | −0.0551719 | ||||||||
\(385\) | 1.22963 | 0.0626679 | ||||||||
\(386\) | −9.13123 | −0.464767 | ||||||||
\(387\) | 14.1653 | 0.720060 | ||||||||
\(388\) | 0.462560 | 0.0234829 | ||||||||
\(389\) | −5.85650 | −0.296937 | −0.148468 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148468 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(390\) | 0.0411439 | 0.00208340 | ||||||||
\(391\) | 4.27441 | 0.216166 | ||||||||
\(392\) | −6.62198 | −0.334461 | ||||||||
\(393\) | −1.08114 | −0.0545365 | ||||||||
\(394\) | −25.9547 | −1.30758 | ||||||||
\(395\) | 0.534775 | 0.0269074 | ||||||||
\(396\) | −9.66063 | −0.485465 | ||||||||
\(397\) | −23.3470 | −1.17175 | −0.585876 | − | 0.810401i | \(-0.699249\pi\) | ||||
−0.585876 | + | 0.810401i | \(0.699249\pi\) | |||||||
\(398\) | −15.7517 | −0.789564 | ||||||||
\(399\) | 2.38640 | 0.119469 | ||||||||
\(400\) | −4.85630 | −0.242815 | ||||||||
\(401\) | −8.27895 | −0.413431 | −0.206716 | − | 0.978401i | \(-0.566277\pi\) | ||||
−0.206716 | + | 0.978401i | \(0.566277\pi\) | |||||||
\(402\) | 13.7371 | 0.685143 | ||||||||
\(403\) | 0.432439 | 0.0215413 | ||||||||
\(404\) | −9.05936 | −0.450720 | ||||||||
\(405\) | −0.0582246 | −0.00289320 | ||||||||
\(406\) | −4.12104 | −0.204524 | ||||||||
\(407\) | 39.4670 | 1.95630 | ||||||||
\(408\) | 4.62126 | 0.228786 | ||||||||
\(409\) | 20.9817 | 1.03748 | 0.518740 | − | 0.854932i | \(-0.326401\pi\) | ||||
0.518740 | + | 0.854932i | \(0.326401\pi\) | |||||||
\(410\) | 3.09140 | 0.152673 | ||||||||
\(411\) | 4.89073 | 0.241242 | ||||||||
\(412\) | 12.9499 | 0.637994 | ||||||||
\(413\) | −4.49997 | −0.221429 | ||||||||
\(414\) | 1.83113 | 0.0899950 | ||||||||
\(415\) | 4.66635 | 0.229062 | ||||||||
\(416\) | −0.100390 | −0.00492201 | ||||||||
\(417\) | 14.2889 | 0.699728 | ||||||||
\(418\) | −18.9405 | −0.926408 | ||||||||
\(419\) | −9.20606 | −0.449745 | −0.224873 | − | 0.974388i | \(-0.572197\pi\) | ||||
−0.224873 | + | 0.974388i | \(0.572197\pi\) | |||||||
\(420\) | −0.251984 | −0.0122955 | ||||||||
\(421\) | −27.5113 | −1.34082 | −0.670409 | − | 0.741991i | \(-0.733881\pi\) | ||||
−0.670409 | + | 0.741991i | \(0.733881\pi\) | |||||||
\(422\) | 5.85101 | 0.284823 | ||||||||
\(423\) | 15.9640 | 0.776195 | ||||||||
\(424\) | 1.61946 | 0.0786480 | ||||||||
\(425\) | 20.7578 | 1.00690 | ||||||||
\(426\) | 3.96213 | 0.191966 | ||||||||
\(427\) | 2.81968 | 0.136454 | ||||||||
\(428\) | −17.3147 | −0.836936 | ||||||||
\(429\) | 0.572612 | 0.0276459 | ||||||||
\(430\) | −2.93250 | −0.141418 | ||||||||
\(431\) | 35.7431 | 1.72168 | 0.860842 | − | 0.508872i | \(-0.169937\pi\) | ||||
0.860842 | + | 0.508872i | \(0.169937\pi\) | |||||||
\(432\) | 5.22315 | 0.251299 | ||||||||
\(433\) | 38.9427 | 1.87147 | 0.935733 | − | 0.352708i | \(-0.114739\pi\) | ||||
0.935733 | + | 0.352708i | \(0.114739\pi\) | |||||||
\(434\) | −2.64845 | −0.127130 | ||||||||
\(435\) | 2.74705 | 0.131711 | ||||||||
\(436\) | 2.98980 | 0.143186 | ||||||||
\(437\) | 3.59007 | 0.171737 | ||||||||
\(438\) | −2.34497 | −0.112047 | ||||||||
\(439\) | 13.5949 | 0.648848 | 0.324424 | − | 0.945912i | \(-0.394830\pi\) | ||||
0.324424 | + | 0.945912i | \(0.394830\pi\) | |||||||
\(440\) | 1.99995 | 0.0953439 | ||||||||
\(441\) | 12.1257 | 0.577414 | ||||||||
\(442\) | 0.429107 | 0.0204106 | ||||||||
\(443\) | −15.2013 | −0.722236 | −0.361118 | − | 0.932520i | \(-0.617605\pi\) | ||||
−0.361118 | + | 0.932520i | \(0.617605\pi\) | |||||||
\(444\) | −8.08780 | −0.383830 | ||||||||
\(445\) | −0.0179195 | −0.000849465 0 | ||||||||
\(446\) | −8.04417 | −0.380903 | ||||||||
\(447\) | −20.8187 | −0.984691 | ||||||||
\(448\) | 0.614832 | 0.0290481 | ||||||||
\(449\) | −29.9533 | −1.41358 | −0.706791 | − | 0.707422i | \(-0.749858\pi\) | ||||
−0.706791 | + | 0.707422i | \(0.749858\pi\) | |||||||
\(450\) | 8.89250 | 0.419196 | ||||||||
\(451\) | 43.0239 | 2.02592 | ||||||||
\(452\) | −12.3950 | −0.583011 | ||||||||
\(453\) | −9.04126 | −0.424795 | ||||||||
\(454\) | 7.78958 | 0.365583 | ||||||||
\(455\) | −0.0233980 | −0.00109691 | ||||||||
\(456\) | 3.88139 | 0.181763 | ||||||||
\(457\) | 31.0148 | 1.45081 | 0.725406 | − | 0.688321i | \(-0.241652\pi\) | ||||
0.725406 | + | 0.688321i | \(0.241652\pi\) | |||||||
\(458\) | −0.972106 | −0.0454235 | ||||||||
\(459\) | −22.3259 | −1.04208 | ||||||||
\(460\) | −0.379081 | −0.0176747 | ||||||||
\(461\) | 4.55154 | 0.211986 | 0.105993 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105993 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(462\) | −3.50693 | −0.163157 | ||||||||
\(463\) | 5.14068 | 0.238908 | 0.119454 | − | 0.992840i | \(-0.461886\pi\) | ||||
0.119454 | + | 0.992840i | \(0.461886\pi\) | |||||||
\(464\) | −6.70272 | −0.311166 | ||||||||
\(465\) | 1.76543 | 0.0818700 | ||||||||
\(466\) | 19.7699 | 0.915821 | ||||||||
\(467\) | −11.6226 | −0.537830 | −0.268915 | − | 0.963164i | \(-0.586665\pi\) | ||||
−0.268915 | + | 0.963164i | \(0.586665\pi\) | |||||||
\(468\) | 0.183826 | 0.00849738 | ||||||||
\(469\) | −7.81208 | −0.360728 | ||||||||
\(470\) | −3.30487 | −0.152442 | ||||||||
\(471\) | 7.27387 | 0.335162 | ||||||||
\(472\) | −7.31903 | −0.336886 | ||||||||
\(473\) | −40.8125 | −1.87656 | ||||||||
\(474\) | −1.52518 | −0.0700541 | ||||||||
\(475\) | 17.4345 | 0.799948 | ||||||||
\(476\) | −2.62805 | −0.120456 | ||||||||
\(477\) | −2.96544 | −0.135778 | ||||||||
\(478\) | −13.9374 | −0.637481 | ||||||||
\(479\) | 28.5323 | 1.30367 | 0.651837 | − | 0.758359i | \(-0.273999\pi\) | ||||
0.651837 | + | 0.758359i | \(0.273999\pi\) | |||||||
\(480\) | −0.409841 | −0.0187066 | ||||||||
\(481\) | −0.750994 | −0.0342424 | ||||||||
\(482\) | 9.00899 | 0.410348 | ||||||||
\(483\) | 0.664722 | 0.0302459 | ||||||||
\(484\) | 16.8339 | 0.765177 | ||||||||
\(485\) | 0.175348 | 0.00796212 | ||||||||
\(486\) | −15.5034 | −0.703248 | ||||||||
\(487\) | 27.6020 | 1.25076 | 0.625382 | − | 0.780318i | \(-0.284943\pi\) | ||||
0.625382 | + | 0.780318i | \(0.284943\pi\) | |||||||
\(488\) | 4.58610 | 0.207603 | ||||||||
\(489\) | −0.487970 | −0.0220668 | ||||||||
\(490\) | −2.51027 | −0.113402 | ||||||||
\(491\) | 8.63792 | 0.389824 | 0.194912 | − | 0.980821i | \(-0.437558\pi\) | ||||
0.194912 | + | 0.980821i | \(0.437558\pi\) | |||||||
\(492\) | −8.81671 | −0.397488 | ||||||||
\(493\) | 28.6502 | 1.29034 | ||||||||
\(494\) | 0.360407 | 0.0162155 | ||||||||
\(495\) | −3.66216 | −0.164602 | ||||||||
\(496\) | −4.30760 | −0.193417 | ||||||||
\(497\) | −2.25321 | −0.101070 | ||||||||
\(498\) | −13.3085 | −0.596368 | ||||||||
\(499\) | 0.577779 | 0.0258649 | 0.0129325 | − | 0.999916i | \(-0.495883\pi\) | ||||
0.0129325 | + | 0.999916i | \(0.495883\pi\) | |||||||
\(500\) | −3.73634 | −0.167094 | ||||||||
\(501\) | 1.94539 | 0.0869135 | ||||||||
\(502\) | 9.80227 | 0.437497 | ||||||||
\(503\) | 37.5020 | 1.67213 | 0.836065 | − | 0.548630i | \(-0.184851\pi\) | ||||
0.836065 | + | 0.548630i | \(0.184851\pi\) | |||||||
\(504\) | −1.12584 | −0.0501487 | ||||||||
\(505\) | −3.43423 | −0.152821 | ||||||||
\(506\) | −5.27578 | −0.234537 | ||||||||
\(507\) | 14.0440 | 0.623715 | ||||||||
\(508\) | 15.5795 | 0.691229 | ||||||||
\(509\) | 11.3872 | 0.504730 | 0.252365 | − | 0.967632i | \(-0.418792\pi\) | ||||
0.252365 | + | 0.967632i | \(0.418792\pi\) | |||||||
\(510\) | 1.75183 | 0.0775724 | ||||||||
\(511\) | 1.33355 | 0.0589928 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −18.7515 | −0.827898 | ||||||||
\(514\) | 5.10256 | 0.225064 | ||||||||
\(515\) | 4.90905 | 0.216318 | ||||||||
\(516\) | 8.36353 | 0.368184 | ||||||||
\(517\) | −45.9949 | −2.02285 | ||||||||
\(518\) | 4.59942 | 0.202087 | ||||||||
\(519\) | −4.84638 | −0.212732 | ||||||||
\(520\) | −0.0380559 | −0.00166886 | ||||||||
\(521\) | −35.2190 | −1.54297 | −0.771486 | − | 0.636246i | \(-0.780486\pi\) | ||||
−0.771486 | + | 0.636246i | \(0.780486\pi\) | |||||||
\(522\) | 12.2735 | 0.537198 | ||||||||
\(523\) | −19.4966 | −0.852526 | −0.426263 | − | 0.904599i | \(-0.640170\pi\) | ||||
−0.426263 | + | 0.904599i | \(0.640170\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 3.22809 | 0.140885 | ||||||||
\(526\) | 0.989009 | 0.0431228 | ||||||||
\(527\) | 18.4125 | 0.802060 | ||||||||
\(528\) | −5.70388 | −0.248230 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.613907 | 0.0266664 | ||||||||
\(531\) | 13.4021 | 0.581601 | ||||||||
\(532\) | −2.20729 | −0.0956982 | ||||||||
\(533\) | −0.818677 | −0.0354608 | ||||||||
\(534\) | 0.0511066 | 0.00221160 | ||||||||
\(535\) | −6.56366 | −0.283772 | ||||||||
\(536\) | −12.7060 | −0.548818 | ||||||||
\(537\) | 28.6400 | 1.23591 | ||||||||
\(538\) | −8.24587 | −0.355505 | ||||||||
\(539\) | −34.9361 | −1.50481 | ||||||||
\(540\) | 1.98000 | 0.0852054 | ||||||||
\(541\) | 12.0331 | 0.517343 | 0.258671 | − | 0.965965i | \(-0.416715\pi\) | ||||
0.258671 | + | 0.965965i | \(0.416715\pi\) | |||||||
\(542\) | −0.251100 | −0.0107857 | ||||||||
\(543\) | −0.341747 | −0.0146658 | ||||||||
\(544\) | −4.27441 | −0.183264 | ||||||||
\(545\) | 1.13338 | 0.0485486 | ||||||||
\(546\) | 0.0667313 | 0.00285584 | ||||||||
\(547\) | −26.0326 | −1.11307 | −0.556536 | − | 0.830824i | \(-0.687870\pi\) | ||||
−0.556536 | + | 0.830824i | \(0.687870\pi\) | |||||||
\(548\) | −4.52366 | −0.193241 | ||||||||
\(549\) | −8.39773 | −0.358407 | ||||||||
\(550\) | −25.6208 | −1.09247 | ||||||||
\(551\) | 24.0632 | 1.02513 | ||||||||
\(552\) | 1.08114 | 0.0460166 | ||||||||
\(553\) | 0.867352 | 0.0368835 | ||||||||
\(554\) | −30.6713 | −1.30310 | ||||||||
\(555\) | −3.06593 | −0.130142 | ||||||||
\(556\) | −13.2164 | −0.560501 | ||||||||
\(557\) | −3.15232 | −0.133568 | −0.0667841 | − | 0.997767i | \(-0.521274\pi\) | ||||
−0.0667841 | + | 0.997767i | \(0.521274\pi\) | |||||||
\(558\) | 7.88777 | 0.333916 | ||||||||
\(559\) | 0.776597 | 0.0328465 | ||||||||
\(560\) | 0.233071 | 0.00984905 | ||||||||
\(561\) | 24.3808 | 1.02936 | ||||||||
\(562\) | −8.71800 | −0.367747 | ||||||||
\(563\) | 43.3718 | 1.82790 | 0.913952 | − | 0.405823i | \(-0.133015\pi\) | ||||
0.913952 | + | 0.405823i | \(0.133015\pi\) | |||||||
\(564\) | 9.42554 | 0.396887 | ||||||||
\(565\) | −4.69870 | −0.197676 | ||||||||
\(566\) | 25.7018 | 1.08033 | ||||||||
\(567\) | −0.0944345 | −0.00396588 | ||||||||
\(568\) | −3.66475 | −0.153770 | ||||||||
\(569\) | −19.9713 | −0.837240 | −0.418620 | − | 0.908161i | \(-0.637486\pi\) | ||||
−0.418620 | + | 0.908161i | \(0.637486\pi\) | |||||||
\(570\) | 1.47136 | 0.0616285 | ||||||||
\(571\) | −13.0736 | −0.547112 | −0.273556 | − | 0.961856i | \(-0.588200\pi\) | ||||
−0.273556 | + | 0.961856i | \(0.588200\pi\) | |||||||
\(572\) | −0.529635 | −0.0221451 | ||||||||
\(573\) | −9.92671 | −0.414694 | ||||||||
\(574\) | 5.01394 | 0.209278 | ||||||||
\(575\) | 4.85630 | 0.202522 | ||||||||
\(576\) | −1.83113 | −0.0762970 | ||||||||
\(577\) | −26.2810 | −1.09409 | −0.547045 | − | 0.837103i | \(-0.684247\pi\) | ||||
−0.547045 | + | 0.837103i | \(0.684247\pi\) | |||||||
\(578\) | 1.27061 | 0.0528504 | ||||||||
\(579\) | 9.87217 | 0.410274 | ||||||||
\(580\) | −2.54087 | −0.105504 | ||||||||
\(581\) | 7.56836 | 0.313989 | ||||||||
\(582\) | −0.500094 | −0.0207296 | ||||||||
\(583\) | 8.54393 | 0.353853 | ||||||||
\(584\) | 2.16897 | 0.0897526 | ||||||||
\(585\) | 0.0696851 | 0.00288112 | ||||||||
\(586\) | −17.2397 | −0.712164 | ||||||||
\(587\) | 17.3173 | 0.714762 | 0.357381 | − | 0.933959i | \(-0.383670\pi\) | ||||
0.357381 | + | 0.933959i | \(0.383670\pi\) | |||||||
\(588\) | 7.15932 | 0.295245 | ||||||||
\(589\) | 15.4646 | 0.637208 | ||||||||
\(590\) | −2.77451 | −0.114225 | ||||||||
\(591\) | 28.0608 | 1.15427 | ||||||||
\(592\) | 7.48078 | 0.307458 | ||||||||
\(593\) | 32.9152 | 1.35166 | 0.675832 | − | 0.737055i | \(-0.263784\pi\) | ||||
0.675832 | + | 0.737055i | \(0.263784\pi\) | |||||||
\(594\) | 27.5562 | 1.13064 | ||||||||
\(595\) | −0.996242 | −0.0408420 | ||||||||
\(596\) | 19.2562 | 0.788764 | ||||||||
\(597\) | 17.0299 | 0.696988 | ||||||||
\(598\) | 0.100390 | 0.00410524 | ||||||||
\(599\) | 11.7553 | 0.480309 | 0.240154 | − | 0.970735i | \(-0.422802\pi\) | ||||
0.240154 | + | 0.970735i | \(0.422802\pi\) | |||||||
\(600\) | 5.25036 | 0.214345 | ||||||||
\(601\) | 5.69853 | 0.232448 | 0.116224 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116224 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(602\) | −4.75622 | −0.193849 | ||||||||
\(603\) | 23.2664 | 0.947480 | ||||||||
\(604\) | 8.36267 | 0.340272 | ||||||||
\(605\) | 6.38141 | 0.259441 | ||||||||
\(606\) | 9.79448 | 0.397874 | ||||||||
\(607\) | −17.3964 | −0.706099 | −0.353050 | − | 0.935605i | \(-0.614855\pi\) | ||||
−0.353050 | + | 0.935605i | \(0.614855\pi\) | |||||||
\(608\) | −3.59007 | −0.145597 | ||||||||
\(609\) | 4.45544 | 0.180544 | ||||||||
\(610\) | 1.73850 | 0.0703900 | ||||||||
\(611\) | 0.875210 | 0.0354072 | ||||||||
\(612\) | 7.82699 | 0.316387 | ||||||||
\(613\) | 17.7128 | 0.715414 | 0.357707 | − | 0.933834i | \(-0.383559\pi\) | ||||
0.357707 | + | 0.933834i | \(0.383559\pi\) | |||||||
\(614\) | −15.5417 | −0.627212 | ||||||||
\(615\) | −3.34225 | −0.134772 | ||||||||
\(616\) | 3.24372 | 0.130693 | ||||||||
\(617\) | −37.4340 | −1.50704 | −0.753519 | − | 0.657426i | \(-0.771645\pi\) | ||||
−0.753519 | + | 0.657426i | \(0.771645\pi\) | |||||||
\(618\) | −14.0007 | −0.563190 | ||||||||
\(619\) | 31.8540 | 1.28032 | 0.640160 | − | 0.768242i | \(-0.278868\pi\) | ||||
0.640160 | + | 0.768242i | \(0.278868\pi\) | |||||||
\(620\) | −1.63293 | −0.0655801 | ||||||||
\(621\) | −5.22315 | −0.209598 | ||||||||
\(622\) | −15.0946 | −0.605237 | ||||||||
\(623\) | −0.0290636 | −0.00116441 | ||||||||
\(624\) | 0.108536 | 0.00434491 | ||||||||
\(625\) | 22.8651 | 0.914605 | ||||||||
\(626\) | −5.25969 | −0.210219 | ||||||||
\(627\) | 20.4774 | 0.817787 | ||||||||
\(628\) | −6.72793 | −0.268474 | ||||||||
\(629\) | −31.9759 | −1.27496 | ||||||||
\(630\) | −0.426783 | −0.0170034 | ||||||||
\(631\) | −42.0682 | −1.67471 | −0.837355 | − | 0.546659i | \(-0.815899\pi\) | ||||
−0.837355 | + | 0.546659i | \(0.815899\pi\) | |||||||
\(632\) | 1.41071 | 0.0561152 | ||||||||
\(633\) | −6.32579 | −0.251428 | ||||||||
\(634\) | 4.28608 | 0.170222 | ||||||||
\(635\) | 5.90590 | 0.234368 | ||||||||
\(636\) | −1.75087 | −0.0694266 | ||||||||
\(637\) | 0.664779 | 0.0263395 | ||||||||
\(638\) | −35.3621 | −1.40000 | ||||||||
\(639\) | 6.71063 | 0.265468 | ||||||||
\(640\) | 0.379081 | 0.0149845 | ||||||||
\(641\) | −3.99106 | −0.157637 | −0.0788187 | − | 0.996889i | \(-0.525115\pi\) | ||||
−0.0788187 | + | 0.996889i | \(0.525115\pi\) | |||||||
\(642\) | 18.7196 | 0.738805 | ||||||||
\(643\) | 41.3942 | 1.63243 | 0.816213 | − | 0.577750i | \(-0.196069\pi\) | ||||
0.816213 | + | 0.577750i | \(0.196069\pi\) | |||||||
\(644\) | −0.614832 | −0.0242278 | ||||||||
\(645\) | 3.17046 | 0.124837 | ||||||||
\(646\) | 15.3455 | 0.603759 | ||||||||
\(647\) | 15.8086 | 0.621501 | 0.310750 | − | 0.950492i | \(-0.399420\pi\) | ||||
0.310750 | + | 0.950492i | \(0.399420\pi\) | |||||||
\(648\) | −0.153594 | −0.00603374 | ||||||||
\(649\) | −38.6136 | −1.51572 | ||||||||
\(650\) | 0.487523 | 0.0191222 | ||||||||
\(651\) | 2.86336 | 0.112224 | ||||||||
\(652\) | 0.451346 | 0.0176761 | ||||||||
\(653\) | 42.4282 | 1.66034 | 0.830171 | − | 0.557508i | \(-0.188243\pi\) | ||||
0.830171 | + | 0.557508i | \(0.188243\pi\) | |||||||
\(654\) | −3.23241 | −0.126397 | ||||||||
\(655\) | 0.379081 | 0.0148119 | ||||||||
\(656\) | 8.15498 | 0.318399 | ||||||||
\(657\) | −3.97166 | −0.154949 | ||||||||
\(658\) | −5.36017 | −0.208961 | ||||||||
\(659\) | 13.1469 | 0.512130 | 0.256065 | − | 0.966660i | \(-0.417574\pi\) | ||||
0.256065 | + | 0.966660i | \(0.417574\pi\) | |||||||
\(660\) | −2.16223 | −0.0841649 | ||||||||
\(661\) | 35.4668 | 1.37950 | 0.689749 | − | 0.724049i | \(-0.257721\pi\) | ||||
0.689749 | + | 0.724049i | \(0.257721\pi\) | |||||||
\(662\) | −17.1562 | −0.666795 | ||||||||
\(663\) | −0.463927 | −0.0180174 | ||||||||
\(664\) | 12.3096 | 0.477707 | ||||||||
\(665\) | −0.836742 | −0.0324475 | ||||||||
\(666\) | −13.6983 | −0.530796 | ||||||||
\(667\) | 6.70272 | 0.259530 | ||||||||
\(668\) | −1.79938 | −0.0696200 | ||||||||
\(669\) | 8.69691 | 0.336242 | ||||||||
\(670\) | −4.81662 | −0.186082 | ||||||||
\(671\) | 24.1953 | 0.934048 | ||||||||
\(672\) | −0.664722 | −0.0256422 | ||||||||
\(673\) | −19.3611 | −0.746317 | −0.373159 | − | 0.927768i | \(-0.621725\pi\) | ||||
−0.373159 | + | 0.927768i | \(0.621725\pi\) | |||||||
\(674\) | −9.74530 | −0.375375 | ||||||||
\(675\) | −25.3651 | −0.976305 | ||||||||
\(676\) | −12.9899 | −0.499612 | ||||||||
\(677\) | 13.7856 | 0.529824 | 0.264912 | − | 0.964273i | \(-0.414657\pi\) | ||||
0.264912 | + | 0.964273i | \(0.414657\pi\) | |||||||
\(678\) | 13.4008 | 0.514653 | ||||||||
\(679\) | 0.284396 | 0.0109141 | ||||||||
\(680\) | −1.62035 | −0.0621376 | ||||||||
\(681\) | −8.42166 | −0.322719 | ||||||||
\(682\) | −22.7260 | −0.870223 | ||||||||
\(683\) | 17.3188 | 0.662687 | 0.331343 | − | 0.943510i | \(-0.392498\pi\) | ||||
0.331343 | + | 0.943510i | \(0.392498\pi\) | |||||||
\(684\) | 6.57388 | 0.251359 | ||||||||
\(685\) | −1.71484 | −0.0655205 | ||||||||
\(686\) | −8.37523 | −0.319768 | ||||||||
\(687\) | 1.05099 | 0.0400977 | ||||||||
\(688\) | −7.73581 | −0.294925 | ||||||||
\(689\) | −0.162577 | −0.00619370 | ||||||||
\(690\) | 0.409841 | 0.0156024 | ||||||||
\(691\) | −6.95936 | −0.264746 | −0.132373 | − | 0.991200i | \(-0.542260\pi\) | ||||
−0.132373 | + | 0.991200i | \(0.542260\pi\) | |||||||
\(692\) | 4.48264 | 0.170404 | ||||||||
\(693\) | −5.93966 | −0.225629 | ||||||||
\(694\) | 20.3165 | 0.771205 | ||||||||
\(695\) | −5.01009 | −0.190044 | ||||||||
\(696\) | 7.24660 | 0.274682 | ||||||||
\(697\) | −34.8578 | −1.32033 | ||||||||
\(698\) | 16.5982 | 0.628252 | ||||||||
\(699\) | −21.3741 | −0.808442 | ||||||||
\(700\) | −2.98581 | −0.112853 | ||||||||
\(701\) | −8.33027 | −0.314630 | −0.157315 | − | 0.987548i | \(-0.550284\pi\) | ||||
−0.157315 | + | 0.987548i | \(0.550284\pi\) | |||||||
\(702\) | −0.524350 | −0.0197903 | ||||||||
\(703\) | −26.8565 | −1.01291 | ||||||||
\(704\) | 5.27578 | 0.198839 | ||||||||
\(705\) | 3.57304 | 0.134569 | ||||||||
\(706\) | −15.2653 | −0.574518 | ||||||||
\(707\) | −5.56998 | −0.209481 | ||||||||
\(708\) | 7.91293 | 0.297386 | ||||||||
\(709\) | 15.9516 | 0.599076 | 0.299538 | − | 0.954084i | \(-0.403167\pi\) | ||||
0.299538 | + | 0.954084i | \(0.403167\pi\) | |||||||
\(710\) | −1.38924 | −0.0521372 | ||||||||
\(711\) | −2.58320 | −0.0968774 | ||||||||
\(712\) | −0.0472708 | −0.00177155 | ||||||||
\(713\) | 4.30760 | 0.161321 | ||||||||
\(714\) | 2.84130 | 0.106333 | ||||||||
\(715\) | −0.200774 | −0.00750854 | ||||||||
\(716\) | −26.4904 | −0.989993 | ||||||||
\(717\) | 15.0683 | 0.562737 | ||||||||
\(718\) | −0.668603 | −0.0249520 | ||||||||
\(719\) | 8.10670 | 0.302329 | 0.151164 | − | 0.988509i | \(-0.451698\pi\) | ||||
0.151164 | + | 0.988509i | \(0.451698\pi\) | |||||||
\(720\) | −0.694145 | −0.0258693 | ||||||||
\(721\) | 7.96199 | 0.296520 | ||||||||
\(722\) | −6.11137 | −0.227442 | ||||||||
\(723\) | −9.74002 | −0.362235 | ||||||||
\(724\) | 0.316097 | 0.0117477 | ||||||||
\(725\) | 32.5504 | 1.20889 | ||||||||
\(726\) | −18.1999 | −0.675461 | ||||||||
\(727\) | 38.7631 | 1.43764 | 0.718821 | − | 0.695195i | \(-0.244682\pi\) | ||||
0.718821 | + | 0.695195i | \(0.244682\pi\) | |||||||
\(728\) | −0.0617228 | −0.00228760 | ||||||||
\(729\) | 17.2222 | 0.637858 | ||||||||
\(730\) | 0.822215 | 0.0304315 | ||||||||
\(731\) | 33.0661 | 1.22299 | ||||||||
\(732\) | −4.95824 | −0.183262 | ||||||||
\(733\) | −36.6878 | −1.35509 | −0.677547 | − | 0.735480i | \(-0.736957\pi\) | ||||
−0.677547 | + | 0.735480i | \(0.736957\pi\) | |||||||
\(734\) | 13.8383 | 0.510780 | ||||||||
\(735\) | 2.71396 | 0.100106 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −67.0344 | −2.46924 | ||||||||
\(738\) | −14.9328 | −0.549684 | ||||||||
\(739\) | 42.8080 | 1.57472 | 0.787359 | − | 0.616495i | \(-0.211448\pi\) | ||||
0.787359 | + | 0.616495i | \(0.211448\pi\) | |||||||
\(740\) | 2.83582 | 0.104247 | ||||||||
\(741\) | −0.389652 | −0.0143142 | ||||||||
\(742\) | 0.995696 | 0.0365532 | ||||||||
\(743\) | −37.6738 | −1.38212 | −0.691058 | − | 0.722799i | \(-0.742855\pi\) | ||||
−0.691058 | + | 0.722799i | \(0.742855\pi\) | |||||||
\(744\) | 4.65714 | 0.170739 | ||||||||
\(745\) | 7.29965 | 0.267438 | ||||||||
\(746\) | −11.2191 | −0.410762 | ||||||||
\(747\) | −22.5405 | −0.824715 | ||||||||
\(748\) | −22.5509 | −0.824542 | ||||||||
\(749\) | −10.6456 | −0.388982 | ||||||||
\(750\) | 4.03952 | 0.147502 | ||||||||
\(751\) | −29.6729 | −1.08278 | −0.541389 | − | 0.840772i | \(-0.682101\pi\) | ||||
−0.541389 | + | 0.840772i | \(0.682101\pi\) | |||||||
\(752\) | −8.71811 | −0.317917 | ||||||||
\(753\) | −10.5977 | −0.386201 | ||||||||
\(754\) | 0.672884 | 0.0245050 | ||||||||
\(755\) | 3.17013 | 0.115373 | ||||||||
\(756\) | 3.21136 | 0.116796 | ||||||||
\(757\) | −40.2256 | −1.46202 | −0.731012 | − | 0.682365i | \(-0.760951\pi\) | ||||
−0.731012 | + | 0.682365i | \(0.760951\pi\) | |||||||
\(758\) | 9.03697 | 0.328238 | ||||||||
\(759\) | 5.70388 | 0.207038 | ||||||||
\(760\) | −1.36093 | −0.0493661 | ||||||||
\(761\) | 22.2108 | 0.805142 | 0.402571 | − | 0.915389i | \(-0.368117\pi\) | ||||
0.402571 | + | 0.915389i | \(0.368117\pi\) | |||||||
\(762\) | −16.8437 | −0.610183 | ||||||||
\(763\) | 1.83823 | 0.0665483 | ||||||||
\(764\) | 9.18166 | 0.332181 | ||||||||
\(765\) | 2.96706 | 0.107274 | ||||||||
\(766\) | −13.2562 | −0.478965 | ||||||||
\(767\) | 0.734756 | 0.0265305 | ||||||||
\(768\) | −1.08114 | −0.0390124 | ||||||||
\(769\) | 1.36151 | 0.0490974 | 0.0245487 | − | 0.999699i | \(-0.492185\pi\) | ||||
0.0245487 | + | 0.999699i | \(0.492185\pi\) | |||||||
\(770\) | 1.22963 | 0.0443129 | ||||||||
\(771\) | −5.51661 | −0.198676 | ||||||||
\(772\) | −9.13123 | −0.328640 | ||||||||
\(773\) | −19.4923 | −0.701090 | −0.350545 | − | 0.936546i | \(-0.614004\pi\) | ||||
−0.350545 | + | 0.936546i | \(0.614004\pi\) | |||||||
\(774\) | 14.1653 | 0.509160 | ||||||||
\(775\) | 20.9190 | 0.751433 | ||||||||
\(776\) | 0.462560 | 0.0166049 | ||||||||
\(777\) | −4.97264 | −0.178392 | ||||||||
\(778\) | −5.85650 | −0.209966 | ||||||||
\(779\) | −29.2770 | −1.04896 | ||||||||
\(780\) | 0.0411439 | 0.00147319 | ||||||||
\(781\) | −19.3344 | −0.691841 | ||||||||
\(782\) | 4.27441 | 0.152853 | ||||||||
\(783\) | −35.0093 | −1.25113 | ||||||||
\(784\) | −6.62198 | −0.236499 | ||||||||
\(785\) | −2.55043 | −0.0910288 | ||||||||
\(786\) | −1.08114 | −0.0385631 | ||||||||
\(787\) | −29.4836 | −1.05098 | −0.525488 | − | 0.850801i | \(-0.676117\pi\) | ||||
−0.525488 | + | 0.850801i | \(0.676117\pi\) | |||||||
\(788\) | −25.9547 | −0.924599 | ||||||||
\(789\) | −1.06926 | −0.0380667 | ||||||||
\(790\) | 0.534775 | 0.0190264 | ||||||||
\(791\) | −7.62083 | −0.270965 | ||||||||
\(792\) | −9.66063 | −0.343276 | ||||||||
\(793\) | −0.460398 | −0.0163492 | ||||||||
\(794\) | −23.3470 | −0.828554 | ||||||||
\(795\) | −0.663722 | −0.0235398 | ||||||||
\(796\) | −15.7517 | −0.558306 | ||||||||
\(797\) | 22.5052 | 0.797174 | 0.398587 | − | 0.917130i | \(-0.369501\pi\) | ||||
0.398587 | + | 0.917130i | \(0.369501\pi\) | |||||||
\(798\) | 2.38640 | 0.0844777 | ||||||||
\(799\) | 37.2648 | 1.31833 | ||||||||
\(800\) | −4.85630 | −0.171696 | ||||||||
\(801\) | 0.0865589 | 0.00305841 | ||||||||
\(802\) | −8.27895 | −0.292340 | ||||||||
\(803\) | 11.4430 | 0.403815 | ||||||||
\(804\) | 13.7371 | 0.484469 | ||||||||
\(805\) | −0.233071 | −0.00821468 | ||||||||
\(806\) | 0.432439 | 0.0152320 | ||||||||
\(807\) | 8.91497 | 0.313822 | ||||||||
\(808\) | −9.05936 | −0.318707 | ||||||||
\(809\) | −18.2134 | −0.640349 | −0.320175 | − | 0.947359i | \(-0.603742\pi\) | ||||
−0.320175 | + | 0.947359i | \(0.603742\pi\) | |||||||
\(810\) | −0.0582246 | −0.00204580 | ||||||||
\(811\) | −9.21285 | −0.323507 | −0.161753 | − | 0.986831i | \(-0.551715\pi\) | ||||
−0.161753 | + | 0.986831i | \(0.551715\pi\) | |||||||
\(812\) | −4.12104 | −0.144620 | ||||||||
\(813\) | 0.271475 | 0.00952105 | ||||||||
\(814\) | 39.4670 | 1.38332 | ||||||||
\(815\) | 0.171097 | 0.00599325 | ||||||||
\(816\) | 4.62126 | 0.161776 | ||||||||
\(817\) | 27.7721 | 0.971624 | ||||||||
\(818\) | 20.9817 | 0.733609 | ||||||||
\(819\) | 0.113022 | 0.00394932 | ||||||||
\(820\) | 3.09140 | 0.107956 | ||||||||
\(821\) | 15.1297 | 0.528031 | 0.264015 | − | 0.964518i | \(-0.414953\pi\) | ||||
0.264015 | + | 0.964518i | \(0.414953\pi\) | |||||||
\(822\) | 4.89073 | 0.170584 | ||||||||
\(823\) | −38.9952 | −1.35929 | −0.679643 | − | 0.733543i | \(-0.737865\pi\) | ||||
−0.679643 | + | 0.733543i | \(0.737865\pi\) | |||||||
\(824\) | 12.9499 | 0.451130 | ||||||||
\(825\) | 27.6998 | 0.964382 | ||||||||
\(826\) | −4.49997 | −0.156574 | ||||||||
\(827\) | −22.2480 | −0.773639 | −0.386820 | − | 0.922155i | \(-0.626426\pi\) | ||||
−0.386820 | + | 0.922155i | \(0.626426\pi\) | |||||||
\(828\) | 1.83113 | 0.0636361 | ||||||||
\(829\) | −3.16991 | −0.110096 | −0.0550478 | − | 0.998484i | \(-0.517531\pi\) | ||||
−0.0550478 | + | 0.998484i | \(0.517531\pi\) | |||||||
\(830\) | 4.66635 | 0.161972 | ||||||||
\(831\) | 33.1601 | 1.15031 | ||||||||
\(832\) | −0.100390 | −0.00348039 | ||||||||
\(833\) | 28.3051 | 0.980713 | ||||||||
\(834\) | 14.2889 | 0.494782 | ||||||||
\(835\) | −0.682110 | −0.0236054 | ||||||||
\(836\) | −18.9405 | −0.655069 | ||||||||
\(837\) | −22.4992 | −0.777687 | ||||||||
\(838\) | −9.20606 | −0.318018 | ||||||||
\(839\) | −24.3391 | −0.840279 | −0.420139 | − | 0.907460i | \(-0.638019\pi\) | ||||
−0.420139 | + | 0.907460i | \(0.638019\pi\) | |||||||
\(840\) | −0.251984 | −0.00869426 | ||||||||
\(841\) | 15.9264 | 0.549187 | ||||||||
\(842\) | −27.5113 | −0.948102 | ||||||||
\(843\) | 9.42541 | 0.324629 | ||||||||
\(844\) | 5.85101 | 0.201400 | ||||||||
\(845\) | −4.92423 | −0.169399 | ||||||||
\(846\) | 15.9640 | 0.548853 | ||||||||
\(847\) | 10.3500 | 0.355631 | ||||||||
\(848\) | 1.61946 | 0.0556125 | ||||||||
\(849\) | −27.7874 | −0.953661 | ||||||||
\(850\) | 20.7578 | 0.711987 | ||||||||
\(851\) | −7.48078 | −0.256438 | ||||||||
\(852\) | 3.96213 | 0.135740 | ||||||||
\(853\) | −12.6255 | −0.432290 | −0.216145 | − | 0.976361i | \(-0.569348\pi\) | ||||
−0.216145 | + | 0.976361i | \(0.569348\pi\) | |||||||
\(854\) | 2.81968 | 0.0964875 | ||||||||
\(855\) | 2.49203 | 0.0852258 | ||||||||
\(856\) | −17.3147 | −0.591803 | ||||||||
\(857\) | −13.1920 | −0.450630 | −0.225315 | − | 0.974286i | \(-0.572341\pi\) | ||||
−0.225315 | + | 0.974286i | \(0.572341\pi\) | |||||||
\(858\) | 0.572612 | 0.0195486 | ||||||||
\(859\) | −24.6661 | −0.841595 | −0.420797 | − | 0.907155i | \(-0.638250\pi\) | ||||
−0.420797 | + | 0.907155i | \(0.638250\pi\) | |||||||
\(860\) | −2.93250 | −0.0999974 | ||||||||
\(861\) | −5.42080 | −0.184740 | ||||||||
\(862\) | 35.7431 | 1.21741 | ||||||||
\(863\) | 47.5123 | 1.61734 | 0.808668 | − | 0.588265i | \(-0.200189\pi\) | ||||
0.808668 | + | 0.588265i | \(0.200189\pi\) | |||||||
\(864\) | 5.22315 | 0.177695 | ||||||||
\(865\) | 1.69928 | 0.0577773 | ||||||||
\(866\) | 38.9427 | 1.32333 | ||||||||
\(867\) | −1.37371 | −0.0466537 | ||||||||
\(868\) | −2.64845 | −0.0898943 | ||||||||
\(869\) | 7.44262 | 0.252474 | ||||||||
\(870\) | 2.74705 | 0.0931337 | ||||||||
\(871\) | 1.27556 | 0.0432206 | ||||||||
\(872\) | 2.98980 | 0.101248 | ||||||||
\(873\) | −0.847005 | −0.0286668 | ||||||||
\(874\) | 3.59007 | 0.121436 | ||||||||
\(875\) | −2.29722 | −0.0776601 | ||||||||
\(876\) | −2.34497 | −0.0792291 | ||||||||
\(877\) | −32.4295 | −1.09506 | −0.547532 | − | 0.836785i | \(-0.684433\pi\) | ||||
−0.547532 | + | 0.836785i | \(0.684433\pi\) | |||||||
\(878\) | 13.5949 | 0.458804 | ||||||||
\(879\) | 18.6386 | 0.628663 | ||||||||
\(880\) | 1.99995 | 0.0674183 | ||||||||
\(881\) | −23.3163 | −0.785548 | −0.392774 | − | 0.919635i | \(-0.628484\pi\) | ||||
−0.392774 | + | 0.919635i | \(0.628484\pi\) | |||||||
\(882\) | 12.1257 | 0.408293 | ||||||||
\(883\) | −11.7070 | −0.393972 | −0.196986 | − | 0.980406i | \(-0.563115\pi\) | ||||
−0.196986 | + | 0.980406i | \(0.563115\pi\) | |||||||
\(884\) | 0.429107 | 0.0144324 | ||||||||
\(885\) | 2.99964 | 0.100832 | ||||||||
\(886\) | −15.2013 | −0.510698 | ||||||||
\(887\) | 50.3212 | 1.68962 | 0.844809 | − | 0.535067i | \(-0.179714\pi\) | ||||
0.844809 | + | 0.535067i | \(0.179714\pi\) | |||||||
\(888\) | −8.08780 | −0.271409 | ||||||||
\(889\) | 9.57878 | 0.321262 | ||||||||
\(890\) | −0.0179195 | −0.000600662 0 | ||||||||
\(891\) | −0.810329 | −0.0271470 | ||||||||
\(892\) | −8.04417 | −0.269339 | ||||||||
\(893\) | 31.2987 | 1.04737 | ||||||||
\(894\) | −20.8187 | −0.696282 | ||||||||
\(895\) | −10.0420 | −0.335668 | ||||||||
\(896\) | 0.614832 | 0.0205401 | ||||||||
\(897\) | −0.108536 | −0.00362391 | ||||||||
\(898\) | −29.9533 | −0.999554 | ||||||||
\(899\) | 28.8726 | 0.962956 | ||||||||
\(900\) | 8.89250 | 0.296417 | ||||||||
\(901\) | −6.92225 | −0.230613 | ||||||||
\(902\) | 43.0239 | 1.43254 | ||||||||
\(903\) | 5.14217 | 0.171121 | ||||||||
\(904\) | −12.3950 | −0.412251 | ||||||||
\(905\) | 0.119826 | 0.00398317 | ||||||||
\(906\) | −9.04126 | −0.300376 | ||||||||
\(907\) | 14.1432 | 0.469617 | 0.234808 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234808 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(908\) | 7.78958 | 0.258506 | ||||||||
\(909\) | 16.5888 | 0.550217 | ||||||||
\(910\) | −0.0233980 | −0.000775635 0 | ||||||||
\(911\) | −30.7231 | −1.01790 | −0.508951 | − | 0.860796i | \(-0.669966\pi\) | ||||
−0.508951 | + | 0.860796i | \(0.669966\pi\) | |||||||
\(912\) | 3.88139 | 0.128526 | ||||||||
\(913\) | 64.9430 | 2.14930 | ||||||||
\(914\) | 31.0148 | 1.02588 | ||||||||
\(915\) | −1.87957 | −0.0621368 | ||||||||
\(916\) | −0.972106 | −0.0321193 | ||||||||
\(917\) | 0.614832 | 0.0203035 | ||||||||
\(918\) | −22.3259 | −0.736864 | ||||||||
\(919\) | 25.6938 | 0.847560 | 0.423780 | − | 0.905765i | \(-0.360703\pi\) | ||||
0.423780 | + | 0.905765i | \(0.360703\pi\) | |||||||
\(920\) | −0.379081 | −0.0124979 | ||||||||
\(921\) | 16.8028 | 0.553672 | ||||||||
\(922\) | 4.55154 | 0.149897 | ||||||||
\(923\) | 0.367904 | 0.0121097 | ||||||||
\(924\) | −3.50693 | −0.115370 | ||||||||
\(925\) | −36.3289 | −1.19449 | ||||||||
\(926\) | 5.14068 | 0.168933 | ||||||||
\(927\) | −23.7128 | −0.778832 | ||||||||
\(928\) | −6.70272 | −0.220027 | ||||||||
\(929\) | −8.91222 | −0.292401 | −0.146200 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146200 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(930\) | 1.76543 | 0.0578909 | ||||||||
\(931\) | 23.7734 | 0.779142 | ||||||||
\(932\) | 19.7699 | 0.647583 | ||||||||
\(933\) | 16.3194 | 0.534274 | ||||||||
\(934\) | −11.6226 | −0.380303 | ||||||||
\(935\) | −8.54861 | −0.279570 | ||||||||
\(936\) | 0.183826 | 0.00600855 | ||||||||
\(937\) | 50.7293 | 1.65726 | 0.828628 | − | 0.559800i | \(-0.189122\pi\) | ||||
0.828628 | + | 0.559800i | \(0.189122\pi\) | |||||||
\(938\) | −7.81208 | −0.255074 | ||||||||
\(939\) | 5.68648 | 0.185571 | ||||||||
\(940\) | −3.30487 | −0.107793 | ||||||||
\(941\) | 31.5893 | 1.02978 | 0.514891 | − | 0.857256i | \(-0.327832\pi\) | ||||
0.514891 | + | 0.857256i | \(0.327832\pi\) | |||||||
\(942\) | 7.27387 | 0.236995 | ||||||||
\(943\) | −8.15498 | −0.265563 | ||||||||
\(944\) | −7.31903 | −0.238214 | ||||||||
\(945\) | 1.21736 | 0.0396009 | ||||||||
\(946\) | −40.8125 | −1.32693 | ||||||||
\(947\) | −12.7920 | −0.415685 | −0.207842 | − | 0.978162i | \(-0.566644\pi\) | ||||
−0.207842 | + | 0.978162i | \(0.566644\pi\) | |||||||
\(948\) | −1.52518 | −0.0495357 | ||||||||
\(949\) | −0.217742 | −0.00706821 | ||||||||
\(950\) | 17.4345 | 0.565649 | ||||||||
\(951\) | −4.63388 | −0.150264 | ||||||||
\(952\) | −2.62805 | −0.0851754 | ||||||||
\(953\) | 23.4487 | 0.759578 | 0.379789 | − | 0.925073i | \(-0.375997\pi\) | ||||
0.379789 | + | 0.925073i | \(0.375997\pi\) | |||||||
\(954\) | −2.96544 | −0.0960096 | ||||||||
\(955\) | 3.48060 | 0.112629 | ||||||||
\(956\) | −13.9374 | −0.450767 | ||||||||
\(957\) | 38.2315 | 1.23585 | ||||||||
\(958\) | 28.5323 | 0.921837 | ||||||||
\(959\) | −2.78129 | −0.0898126 | ||||||||
\(960\) | −0.409841 | −0.0132276 | ||||||||
\(961\) | −12.4446 | −0.401437 | ||||||||
\(962\) | −0.750994 | −0.0242130 | ||||||||
\(963\) | 31.7053 | 1.02169 | ||||||||
\(964\) | 9.00899 | 0.290160 | ||||||||
\(965\) | −3.46147 | −0.111429 | ||||||||
\(966\) | 0.664722 | 0.0213871 | ||||||||
\(967\) | 48.7326 | 1.56714 | 0.783568 | − | 0.621306i | \(-0.213398\pi\) | ||||
0.783568 | + | 0.621306i | \(0.213398\pi\) | |||||||
\(968\) | 16.8339 | 0.541062 | ||||||||
\(969\) | −16.5907 | −0.532969 | ||||||||
\(970\) | 0.175348 | 0.00563007 | ||||||||
\(971\) | 37.2671 | 1.19596 | 0.597979 | − | 0.801512i | \(-0.295971\pi\) | ||||
0.597979 | + | 0.801512i | \(0.295971\pi\) | |||||||
\(972\) | −15.5034 | −0.497271 | ||||||||
\(973\) | −8.12587 | −0.260504 | ||||||||
\(974\) | 27.6020 | 0.884424 | ||||||||
\(975\) | −0.527082 | −0.0168801 | ||||||||
\(976\) | 4.58610 | 0.146798 | ||||||||
\(977\) | 25.3556 | 0.811197 | 0.405599 | − | 0.914051i | \(-0.367063\pi\) | ||||
0.405599 | + | 0.914051i | \(0.367063\pi\) | |||||||
\(978\) | −0.487970 | −0.0156036 | ||||||||
\(979\) | −0.249391 | −0.00797056 | ||||||||
\(980\) | −2.51027 | −0.0801876 | ||||||||
\(981\) | −5.47471 | −0.174794 | ||||||||
\(982\) | 8.63792 | 0.275647 | ||||||||
\(983\) | 41.5682 | 1.32582 | 0.662909 | − | 0.748700i | \(-0.269321\pi\) | ||||
0.662909 | + | 0.748700i | \(0.269321\pi\) | |||||||
\(984\) | −8.81671 | −0.281067 | ||||||||
\(985\) | −9.83895 | −0.313495 | ||||||||
\(986\) | 28.6502 | 0.912408 | ||||||||
\(987\) | 5.79512 | 0.184461 | ||||||||
\(988\) | 0.360407 | 0.0114661 | ||||||||
\(989\) | 7.73581 | 0.245985 | ||||||||
\(990\) | −3.66216 | −0.116391 | ||||||||
\(991\) | −22.0387 | −0.700082 | −0.350041 | − | 0.936734i | \(-0.613832\pi\) | ||||
−0.350041 | + | 0.936734i | \(0.613832\pi\) | |||||||
\(992\) | −4.30760 | −0.136767 | ||||||||
\(993\) | 18.5483 | 0.588614 | ||||||||
\(994\) | −2.25321 | −0.0714674 | ||||||||
\(995\) | −5.97119 | −0.189299 | ||||||||
\(996\) | −13.3085 | −0.421696 | ||||||||
\(997\) | 49.9169 | 1.58088 | 0.790441 | − | 0.612538i | \(-0.209851\pi\) | ||||
0.790441 | + | 0.612538i | \(0.209851\pi\) | |||||||
\(998\) | 0.577779 | 0.0182893 | ||||||||
\(999\) | 39.0732 | 1.23622 |
(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 | 6026.2.a.g.1.8 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.g.1.8 | ✓ | 21 | 1.1 | even | 1 | trivial |