Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2535,2,Mod(1,2535)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2535, 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("2535.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2535 = 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2535.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: | \(20.2420769124\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.60168\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2535.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60168 | 1.83966 | 0.919832 | − | 0.392311i | \(-0.128324\pi\) | ||||
0.919832 | + | 0.392311i | \(0.128324\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.76873 | 2.38437 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.60168 | −1.06213 | ||||||||
\(7\) | 3.60168 | 1.36131 | 0.680653 | − | 0.732606i | \(-0.261696\pi\) | ||||
0.680653 | + | 0.732606i | \(0.261696\pi\) | |||||||
\(8\) | 7.20336 | 2.54677 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.60168 | 0.822723 | ||||||||
\(11\) | −5.20336 | −1.56887 | −0.784436 | − | 0.620210i | \(-0.787047\pi\) | ||||
−0.784436 | + | 0.620210i | \(0.787047\pi\) | |||||||
\(12\) | −4.76873 | −1.37662 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 9.37041 | 2.50435 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 9.20336 | 2.30084 | ||||||||
\(17\) | −2.93579 | −0.712034 | −0.356017 | − | 0.934480i | \(-0.615865\pi\) | ||||
−0.356017 | + | 0.934480i | \(0.615865\pi\) | |||||||
\(18\) | 2.60168 | 0.613222 | ||||||||
\(19\) | 6.76873 | 1.55285 | 0.776427 | − | 0.630207i | \(-0.217030\pi\) | ||||
0.776427 | + | 0.630207i | \(0.217030\pi\) | |||||||
\(20\) | 4.76873 | 1.06632 | ||||||||
\(21\) | −3.60168 | −0.785951 | ||||||||
\(22\) | −13.5375 | −2.88620 | ||||||||
\(23\) | 5.53747 | 1.15464 | 0.577321 | − | 0.816517i | \(-0.304098\pi\) | ||||
0.577321 | + | 0.816517i | \(0.304098\pi\) | |||||||
\(24\) | −7.20336 | −1.47038 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 17.1755 | 3.24586 | ||||||||
\(29\) | 1.83294 | 0.340369 | 0.170185 | − | 0.985412i | \(-0.445564\pi\) | ||||
0.170185 | + | 0.985412i | \(0.445564\pi\) | |||||||
\(30\) | −2.60168 | −0.474999 | ||||||||
\(31\) | 4.10284 | 0.736893 | 0.368446 | − | 0.929649i | \(-0.379890\pi\) | ||||
0.368446 | + | 0.929649i | \(0.379890\pi\) | |||||||
\(32\) | 9.53747 | 1.68600 | ||||||||
\(33\) | 5.20336 | 0.905788 | ||||||||
\(34\) | −7.63798 | −1.30990 | ||||||||
\(35\) | 3.60168 | 0.608795 | ||||||||
\(36\) | 4.76873 | 0.794789 | ||||||||
\(37\) | −3.53747 | −0.581556 | −0.290778 | − | 0.956791i | \(-0.593914\pi\) | ||||
−0.290778 | + | 0.956791i | \(0.593914\pi\) | |||||||
\(38\) | 17.6101 | 2.85673 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.20336 | 1.13895 | ||||||||
\(41\) | −5.37041 | −0.838718 | −0.419359 | − | 0.907821i | \(-0.637745\pi\) | ||||
−0.419359 | + | 0.907821i | \(0.637745\pi\) | |||||||
\(42\) | −9.37041 | −1.44589 | ||||||||
\(43\) | 3.16706 | 0.482971 | 0.241486 | − | 0.970404i | \(-0.422365\pi\) | ||||
0.241486 | + | 0.970404i | \(0.422365\pi\) | |||||||
\(44\) | −24.8134 | −3.74077 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 14.4067 | 2.12415 | ||||||||
\(47\) | 3.80504 | 0.555022 | 0.277511 | − | 0.960722i | \(-0.410491\pi\) | ||||
0.277511 | + | 0.960722i | \(0.410491\pi\) | |||||||
\(48\) | −9.20336 | −1.32839 | ||||||||
\(49\) | 5.97209 | 0.853156 | ||||||||
\(50\) | 2.60168 | 0.367933 | ||||||||
\(51\) | 2.93579 | 0.411093 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.20336 | −0.714736 | −0.357368 | − | 0.933964i | \(-0.616326\pi\) | ||||
−0.357368 | + | 0.933964i | \(0.616326\pi\) | |||||||
\(54\) | −2.60168 | −0.354044 | ||||||||
\(55\) | −5.20336 | −0.701621 | ||||||||
\(56\) | 25.9442 | 3.46694 | ||||||||
\(57\) | −6.76873 | −0.896541 | ||||||||
\(58\) | 4.76873 | 0.626165 | ||||||||
\(59\) | −7.37041 | −0.959546 | −0.479773 | − | 0.877393i | \(-0.659281\pi\) | ||||
−0.479773 | + | 0.877393i | \(0.659281\pi\) | |||||||
\(60\) | −4.76873 | −0.615641 | ||||||||
\(61\) | −3.43462 | −0.439759 | −0.219879 | − | 0.975527i | \(-0.570566\pi\) | ||||
−0.219879 | + | 0.975527i | \(0.570566\pi\) | |||||||
\(62\) | 10.6743 | 1.35564 | ||||||||
\(63\) | 3.60168 | 0.453769 | ||||||||
\(64\) | 6.40672 | 0.800840 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 13.5375 | 1.66635 | ||||||||
\(67\) | 3.50117 | 0.427735 | 0.213868 | − | 0.976863i | \(-0.431394\pi\) | ||||
0.213868 | + | 0.976863i | \(0.431394\pi\) | |||||||
\(68\) | −14.0000 | −1.69775 | ||||||||
\(69\) | −5.53747 | −0.666633 | ||||||||
\(70\) | 9.37041 | 1.11998 | ||||||||
\(71\) | −9.70452 | −1.15172 | −0.575858 | − | 0.817550i | \(-0.695332\pi\) | ||||
−0.575858 | + | 0.817550i | \(0.695332\pi\) | |||||||
\(72\) | 7.20336 | 0.848924 | ||||||||
\(73\) | −0.805037 | −0.0942225 | −0.0471113 | − | 0.998890i | \(-0.515002\pi\) | ||||
−0.0471113 | + | 0.998890i | \(0.515002\pi\) | |||||||
\(74\) | −9.20336 | −1.06987 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 32.2783 | 3.70257 | ||||||||
\(77\) | −18.7408 | −2.13572 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.10284 | −0.461606 | −0.230803 | − | 0.973000i | \(-0.574135\pi\) | ||||
−0.230803 | + | 0.973000i | \(0.574135\pi\) | |||||||
\(80\) | 9.20336 | 1.02897 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −13.9721 | −1.54296 | ||||||||
\(83\) | −11.5375 | −1.26640 | −0.633201 | − | 0.773988i | \(-0.718259\pi\) | ||||
−0.633201 | + | 0.773988i | \(0.718259\pi\) | |||||||
\(84\) | −17.1755 | −1.87400 | ||||||||
\(85\) | −2.93579 | −0.318431 | ||||||||
\(86\) | 8.23966 | 0.888506 | ||||||||
\(87\) | −1.83294 | −0.196512 | ||||||||
\(88\) | −37.4817 | −3.99556 | ||||||||
\(89\) | 9.83294 | 1.04229 | 0.521145 | − | 0.853468i | \(-0.325505\pi\) | ||||
0.521145 | + | 0.853468i | \(0.325505\pi\) | |||||||
\(90\) | 2.60168 | 0.274241 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 26.4067 | 2.75309 | ||||||||
\(93\) | −4.10284 | −0.425445 | ||||||||
\(94\) | 9.89949 | 1.02105 | ||||||||
\(95\) | 6.76873 | 0.694457 | ||||||||
\(96\) | −9.53747 | −0.973414 | ||||||||
\(97\) | −5.57377 | −0.565931 | −0.282965 | − | 0.959130i | \(-0.591318\pi\) | ||||
−0.282965 | + | 0.959130i | \(0.591318\pi\) | |||||||
\(98\) | 15.5375 | 1.56952 | ||||||||
\(99\) | −5.20336 | −0.522957 | ||||||||
\(100\) | 4.76873 | 0.476873 | ||||||||
\(101\) | 2.40672 | 0.239477 | 0.119739 | − | 0.992805i | \(-0.461794\pi\) | ||||
0.119739 | + | 0.992805i | \(0.461794\pi\) | |||||||
\(102\) | 7.63798 | 0.756273 | ||||||||
\(103\) | 18.4430 | 1.81724 | 0.908622 | − | 0.417619i | \(-0.137135\pi\) | ||||
0.908622 | + | 0.417619i | \(0.137135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.60168 | −0.351488 | ||||||||
\(106\) | −13.5375 | −1.31488 | ||||||||
\(107\) | 10.9358 | 1.05720 | 0.528601 | − | 0.848870i | \(-0.322717\pi\) | ||||
0.528601 | + | 0.848870i | \(0.322717\pi\) | |||||||
\(108\) | −4.76873 | −0.458872 | ||||||||
\(109\) | 13.8692 | 1.32843 | 0.664217 | − | 0.747540i | \(-0.268765\pi\) | ||||
0.664217 | + | 0.747540i | \(0.268765\pi\) | |||||||
\(110\) | −13.5375 | −1.29075 | ||||||||
\(111\) | 3.53747 | 0.335762 | ||||||||
\(112\) | 33.1475 | 3.13215 | ||||||||
\(113\) | −11.2034 | −1.05392 | −0.526962 | − | 0.849889i | \(-0.676669\pi\) | ||||
−0.526962 | + | 0.849889i | \(0.676669\pi\) | |||||||
\(114\) | −17.6101 | −1.64933 | ||||||||
\(115\) | 5.53747 | 0.516372 | ||||||||
\(116\) | 8.74083 | 0.811565 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.1755 | −1.76524 | ||||||||
\(119\) | −10.5738 | −0.969296 | ||||||||
\(120\) | −7.20336 | −0.657574 | ||||||||
\(121\) | 16.0749 | 1.46136 | ||||||||
\(122\) | −8.93579 | −0.809008 | ||||||||
\(123\) | 5.37041 | 0.484234 | ||||||||
\(124\) | 19.5654 | 1.75702 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 9.37041 | 0.834783 | ||||||||
\(127\) | −3.19496 | −0.283507 | −0.141754 | − | 0.989902i | \(-0.545274\pi\) | ||||
−0.141754 | + | 0.989902i | \(0.545274\pi\) | |||||||
\(128\) | −2.40672 | −0.212726 | ||||||||
\(129\) | −3.16706 | −0.278844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.57377 | −0.399612 | −0.199806 | − | 0.979835i | \(-0.564031\pi\) | ||||
−0.199806 | + | 0.979835i | \(0.564031\pi\) | |||||||
\(132\) | 24.8134 | 2.15973 | ||||||||
\(133\) | 24.3788 | 2.11391 | ||||||||
\(134\) | 9.10891 | 0.786890 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −21.1475 | −1.81339 | ||||||||
\(137\) | 10.6743 | 0.911966 | 0.455983 | − | 0.889989i | \(-0.349288\pi\) | ||||
0.455983 | + | 0.889989i | \(0.349288\pi\) | |||||||
\(138\) | −14.4067 | −1.22638 | ||||||||
\(139\) | −16.1475 | −1.36962 | −0.684808 | − | 0.728723i | \(-0.740114\pi\) | ||||
−0.684808 | + | 0.728723i | \(0.740114\pi\) | |||||||
\(140\) | 17.1755 | 1.45159 | ||||||||
\(141\) | −3.80504 | −0.320442 | ||||||||
\(142\) | −25.2481 | −2.11877 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.20336 | 0.766947 | ||||||||
\(145\) | 1.83294 | 0.152218 | ||||||||
\(146\) | −2.09445 | −0.173338 | ||||||||
\(147\) | −5.97209 | −0.492570 | ||||||||
\(148\) | −16.8692 | −1.38664 | ||||||||
\(149\) | −9.66589 | −0.791861 | −0.395930 | − | 0.918281i | \(-0.629578\pi\) | ||||
−0.395930 | + | 0.918281i | \(0.629578\pi\) | |||||||
\(150\) | −2.60168 | −0.212426 | ||||||||
\(151\) | −18.7129 | −1.52284 | −0.761418 | − | 0.648261i | \(-0.775496\pi\) | ||||
−0.761418 | + | 0.648261i | \(0.775496\pi\) | |||||||
\(152\) | 48.7576 | 3.95477 | ||||||||
\(153\) | −2.93579 | −0.237345 | ||||||||
\(154\) | −48.7576 | −3.92900 | ||||||||
\(155\) | 4.10284 | 0.329548 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3704 | −0.827649 | −0.413825 | − | 0.910357i | \(-0.635807\pi\) | ||||
−0.413825 | + | 0.910357i | \(0.635807\pi\) | |||||||
\(158\) | −10.6743 | −0.849201 | ||||||||
\(159\) | 5.20336 | 0.412653 | ||||||||
\(160\) | 9.53747 | 0.754003 | ||||||||
\(161\) | 19.9442 | 1.57182 | ||||||||
\(162\) | 2.60168 | 0.204407 | ||||||||
\(163\) | −11.4733 | −0.898655 | −0.449327 | − | 0.893367i | \(-0.648336\pi\) | ||||
−0.449327 | + | 0.893367i | \(0.648336\pi\) | |||||||
\(164\) | −25.6101 | −1.99981 | ||||||||
\(165\) | 5.20336 | 0.405081 | ||||||||
\(166\) | −30.0168 | −2.32975 | ||||||||
\(167\) | −3.13075 | −0.242265 | −0.121132 | − | 0.992636i | \(-0.538653\pi\) | ||||
−0.121132 | + | 0.992636i | \(0.538653\pi\) | |||||||
\(168\) | −25.9442 | −2.00164 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −7.63798 | −0.585806 | ||||||||
\(171\) | 6.76873 | 0.517618 | ||||||||
\(172\) | 15.1028 | 1.15158 | ||||||||
\(173\) | 8.26757 | 0.628572 | 0.314286 | − | 0.949328i | \(-0.398235\pi\) | ||||
0.314286 | + | 0.949328i | \(0.398235\pi\) | |||||||
\(174\) | −4.76873 | −0.361517 | ||||||||
\(175\) | 3.60168 | 0.272261 | ||||||||
\(176\) | −47.8884 | −3.60972 | ||||||||
\(177\) | 7.37041 | 0.553994 | ||||||||
\(178\) | 25.5822 | 1.91746 | ||||||||
\(179\) | −18.4454 | −1.37867 | −0.689335 | − | 0.724443i | \(-0.742097\pi\) | ||||
−0.689335 | + | 0.724443i | \(0.742097\pi\) | |||||||
\(180\) | 4.76873 | 0.355440 | ||||||||
\(181\) | 21.1028 | 1.56856 | 0.784281 | − | 0.620406i | \(-0.213032\pi\) | ||||
0.784281 | + | 0.620406i | \(0.213032\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.43462 | 0.253895 | ||||||||
\(184\) | 39.8884 | 2.94061 | ||||||||
\(185\) | −3.53747 | −0.260080 | ||||||||
\(186\) | −10.6743 | −0.782677 | ||||||||
\(187\) | 15.2760 | 1.11709 | ||||||||
\(188\) | 18.1452 | 1.32338 | ||||||||
\(189\) | −3.60168 | −0.261984 | ||||||||
\(190\) | 17.6101 | 1.27757 | ||||||||
\(191\) | −8.70219 | −0.629669 | −0.314834 | − | 0.949147i | \(-0.601949\pi\) | ||||
−0.314834 | + | 0.949147i | \(0.601949\pi\) | |||||||
\(192\) | −6.40672 | −0.462365 | ||||||||
\(193\) | 19.2676 | 1.38691 | 0.693455 | − | 0.720500i | \(-0.256088\pi\) | ||||
0.693455 | + | 0.720500i | \(0.256088\pi\) | |||||||
\(194\) | −14.5012 | −1.04112 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.4793 | 2.03424 | ||||||||
\(197\) | −15.1475 | −1.07922 | −0.539609 | − | 0.841916i | \(-0.681428\pi\) | ||||
−0.539609 | + | 0.841916i | \(0.681428\pi\) | |||||||
\(198\) | −13.5375 | −0.962066 | ||||||||
\(199\) | −4.53747 | −0.321653 | −0.160826 | − | 0.986983i | \(-0.551416\pi\) | ||||
−0.160826 | + | 0.986983i | \(0.551416\pi\) | |||||||
\(200\) | 7.20336 | 0.509354 | ||||||||
\(201\) | −3.50117 | −0.246953 | ||||||||
\(202\) | 6.26150 | 0.440558 | ||||||||
\(203\) | 6.60168 | 0.463347 | ||||||||
\(204\) | 14.0000 | 0.980196 | ||||||||
\(205\) | −5.37041 | −0.375086 | ||||||||
\(206\) | 47.9828 | 3.34312 | ||||||||
\(207\) | 5.53747 | 0.384881 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.2201 | −2.43623 | ||||||||
\(210\) | −9.37041 | −0.646620 | ||||||||
\(211\) | −22.1475 | −1.52470 | −0.762350 | − | 0.647165i | \(-0.775954\pi\) | ||||
−0.762350 | + | 0.647165i | \(0.775954\pi\) | |||||||
\(212\) | −24.8134 | −1.70419 | ||||||||
\(213\) | 9.70452 | 0.664943 | ||||||||
\(214\) | 28.4514 | 1.94490 | ||||||||
\(215\) | 3.16706 | 0.215991 | ||||||||
\(216\) | −7.20336 | −0.490126 | ||||||||
\(217\) | 14.7771 | 1.00314 | ||||||||
\(218\) | 36.0833 | 2.44387 | ||||||||
\(219\) | 0.805037 | 0.0543994 | ||||||||
\(220\) | −24.8134 | −1.67292 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.20336 | 0.617689 | ||||||||
\(223\) | −7.61007 | −0.509608 | −0.254804 | − | 0.966993i | \(-0.582011\pi\) | ||||
−0.254804 | + | 0.966993i | \(0.582011\pi\) | |||||||
\(224\) | 34.3509 | 2.29517 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −29.1475 | −1.93887 | ||||||||
\(227\) | 23.3425 | 1.54930 | 0.774648 | − | 0.632392i | \(-0.217927\pi\) | ||||
0.774648 | + | 0.632392i | \(0.217927\pi\) | |||||||
\(228\) | −32.2783 | −2.13768 | ||||||||
\(229\) | 0.824549 | 0.0544877 | 0.0272439 | − | 0.999629i | \(-0.491327\pi\) | ||||
0.0272439 | + | 0.999629i | \(0.491327\pi\) | |||||||
\(230\) | 14.4067 | 0.949951 | ||||||||
\(231\) | 18.7408 | 1.23306 | ||||||||
\(232\) | 13.2034 | 0.866843 | ||||||||
\(233\) | −13.4044 | −0.878150 | −0.439075 | − | 0.898450i | \(-0.644694\pi\) | ||||
−0.439075 | + | 0.898450i | \(0.644694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.80504 | 0.248213 | ||||||||
\(236\) | −35.1475 | −2.28791 | ||||||||
\(237\) | 4.10284 | 0.266508 | ||||||||
\(238\) | −27.5096 | −1.78318 | ||||||||
\(239\) | 12.7966 | 0.827746 | 0.413873 | − | 0.910335i | \(-0.364176\pi\) | ||||
0.413873 | + | 0.910335i | \(0.364176\pi\) | |||||||
\(240\) | −9.20336 | −0.594074 | ||||||||
\(241\) | 12.7687 | 0.822506 | 0.411253 | − | 0.911521i | \(-0.365091\pi\) | ||||
0.411253 | + | 0.911521i | \(0.365091\pi\) | |||||||
\(242\) | 41.8218 | 2.68841 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −16.3788 | −1.04855 | ||||||||
\(245\) | 5.97209 | 0.381543 | ||||||||
\(246\) | 13.9721 | 0.890828 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 29.5543 | 1.87670 | ||||||||
\(249\) | 11.5375 | 0.731157 | ||||||||
\(250\) | 2.60168 | 0.164545 | ||||||||
\(251\) | −8.40672 | −0.530627 | −0.265314 | − | 0.964162i | \(-0.585475\pi\) | ||||
−0.265314 | + | 0.964162i | \(0.585475\pi\) | |||||||
\(252\) | 17.1755 | 1.08195 | ||||||||
\(253\) | −28.8134 | −1.81149 | ||||||||
\(254\) | −8.31227 | −0.521558 | ||||||||
\(255\) | 2.93579 | 0.183846 | ||||||||
\(256\) | −19.0749 | −1.19218 | ||||||||
\(257\) | 6.13915 | 0.382950 | 0.191475 | − | 0.981498i | \(-0.438673\pi\) | ||||
0.191475 | + | 0.981498i | \(0.438673\pi\) | |||||||
\(258\) | −8.23966 | −0.512979 | ||||||||
\(259\) | −12.7408 | −0.791676 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83294 | 0.113456 | ||||||||
\(262\) | −11.8995 | −0.735153 | ||||||||
\(263\) | −4.73010 | −0.291670 | −0.145835 | − | 0.989309i | \(-0.546587\pi\) | ||||
−0.145835 | + | 0.989309i | \(0.546587\pi\) | |||||||
\(264\) | 37.4817 | 2.30684 | ||||||||
\(265\) | −5.20336 | −0.319640 | ||||||||
\(266\) | 63.4258 | 3.88889 | ||||||||
\(267\) | −9.83294 | −0.601766 | ||||||||
\(268\) | 16.6961 | 1.01988 | ||||||||
\(269\) | −5.44302 | −0.331867 | −0.165933 | − | 0.986137i | \(-0.553064\pi\) | ||||
−0.165933 | + | 0.986137i | \(0.553064\pi\) | |||||||
\(270\) | −2.60168 | −0.158333 | ||||||||
\(271\) | 25.4793 | 1.54776 | 0.773879 | − | 0.633333i | \(-0.218314\pi\) | ||||
0.773879 | + | 0.633333i | \(0.218314\pi\) | |||||||
\(272\) | −27.0191 | −1.63827 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 27.7711 | 1.67771 | ||||||||
\(275\) | −5.20336 | −0.313774 | ||||||||
\(276\) | −26.4067 | −1.58950 | ||||||||
\(277\) | −22.8134 | −1.37073 | −0.685363 | − | 0.728201i | \(-0.740357\pi\) | ||||
−0.685363 | + | 0.728201i | \(0.740357\pi\) | |||||||
\(278\) | −42.0107 | −2.51964 | ||||||||
\(279\) | 4.10284 | 0.245631 | ||||||||
\(280\) | 25.9442 | 1.55046 | ||||||||
\(281\) | −2.16706 | −0.129276 | −0.0646378 | − | 0.997909i | \(-0.520589\pi\) | ||||
−0.0646378 | + | 0.997909i | \(0.520589\pi\) | |||||||
\(282\) | −9.89949 | −0.589506 | ||||||||
\(283\) | −29.7469 | −1.76827 | −0.884135 | − | 0.467232i | \(-0.845251\pi\) | ||||
−0.884135 | + | 0.467232i | \(0.845251\pi\) | |||||||
\(284\) | −46.2783 | −2.74611 | ||||||||
\(285\) | −6.76873 | −0.400945 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.3425 | −1.14175 | ||||||||
\(288\) | 9.53747 | 0.562001 | ||||||||
\(289\) | −8.38114 | −0.493008 | ||||||||
\(290\) | 4.76873 | 0.280030 | ||||||||
\(291\) | 5.57377 | 0.326740 | ||||||||
\(292\) | −3.83901 | −0.224661 | ||||||||
\(293\) | 33.0857 | 1.93289 | 0.966443 | − | 0.256883i | \(-0.0826954\pi\) | ||||
0.966443 | + | 0.256883i | \(0.0826954\pi\) | |||||||
\(294\) | −15.5375 | −0.906164 | ||||||||
\(295\) | −7.37041 | −0.429122 | ||||||||
\(296\) | −25.4817 | −1.48109 | ||||||||
\(297\) | 5.20336 | 0.301929 | ||||||||
\(298\) | −25.1475 | −1.45676 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.76873 | −0.275323 | ||||||||
\(301\) | 11.4067 | 0.657472 | ||||||||
\(302\) | −48.6850 | −2.80151 | ||||||||
\(303\) | −2.40672 | −0.138262 | ||||||||
\(304\) | 62.2951 | 3.57287 | ||||||||
\(305\) | −3.43462 | −0.196666 | ||||||||
\(306\) | −7.63798 | −0.436634 | ||||||||
\(307\) | −14.3704 | −0.820163 | −0.410081 | − | 0.912049i | \(-0.634500\pi\) | ||||
−0.410081 | + | 0.912049i | \(0.634500\pi\) | |||||||
\(308\) | −89.3700 | −5.09233 | ||||||||
\(309\) | −18.4430 | −1.04919 | ||||||||
\(310\) | 10.6743 | 0.606259 | ||||||||
\(311\) | −8.70685 | −0.493720 | −0.246860 | − | 0.969051i | \(-0.579399\pi\) | ||||
−0.246860 | + | 0.969051i | \(0.579399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.16472 | −0.461497 | −0.230749 | − | 0.973013i | \(-0.574118\pi\) | ||||
−0.230749 | + | 0.973013i | \(0.574118\pi\) | |||||||
\(314\) | −26.9805 | −1.52260 | ||||||||
\(315\) | 3.60168 | 0.202932 | ||||||||
\(316\) | −19.5654 | −1.10064 | ||||||||
\(317\) | 13.4090 | 0.753127 | 0.376564 | − | 0.926391i | \(-0.377106\pi\) | ||||
0.376564 | + | 0.926391i | \(0.377106\pi\) | |||||||
\(318\) | 13.5375 | 0.759144 | ||||||||
\(319\) | −9.53747 | −0.533996 | ||||||||
\(320\) | 6.40672 | 0.358146 | ||||||||
\(321\) | −10.9358 | −0.610376 | ||||||||
\(322\) | 51.8884 | 2.89163 | ||||||||
\(323\) | −19.8716 | −1.10568 | ||||||||
\(324\) | 4.76873 | 0.264930 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.8497 | −1.65322 | ||||||||
\(327\) | −13.8692 | −0.766971 | ||||||||
\(328\) | −38.6850 | −2.13602 | ||||||||
\(329\) | 13.7045 | 0.755555 | ||||||||
\(330\) | 13.5375 | 0.745213 | ||||||||
\(331\) | 21.4793 | 1.18061 | 0.590305 | − | 0.807180i | \(-0.299007\pi\) | ||||
0.590305 | + | 0.807180i | \(0.299007\pi\) | |||||||
\(332\) | −55.0191 | −3.01957 | ||||||||
\(333\) | −3.53747 | −0.193852 | ||||||||
\(334\) | −8.14521 | −0.445686 | ||||||||
\(335\) | 3.50117 | 0.191289 | ||||||||
\(336\) | −33.1475 | −1.80835 | ||||||||
\(337\) | −7.44535 | −0.405574 | −0.202787 | − | 0.979223i | \(-0.565000\pi\) | ||||
−0.202787 | + | 0.979223i | \(0.565000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2034 | 0.608483 | ||||||||
\(340\) | −14.0000 | −0.759257 | ||||||||
\(341\) | −21.3486 | −1.15609 | ||||||||
\(342\) | 17.6101 | 0.952244 | ||||||||
\(343\) | −3.70219 | −0.199900 | ||||||||
\(344\) | 22.8134 | 1.23002 | ||||||||
\(345\) | −5.53747 | −0.298127 | ||||||||
\(346\) | 21.5096 | 1.15636 | ||||||||
\(347\) | −24.9465 | −1.33920 | −0.669600 | − | 0.742722i | \(-0.733534\pi\) | ||||
−0.669600 | + | 0.742722i | \(0.733534\pi\) | |||||||
\(348\) | −8.74083 | −0.468558 | ||||||||
\(349\) | 2.10284 | 0.112563 | 0.0562813 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562813 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(350\) | 9.37041 | 0.500870 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −49.6269 | −2.64512 | ||||||||
\(353\) | 18.5398 | 0.986774 | 0.493387 | − | 0.869810i | \(-0.335759\pi\) | ||||
0.493387 | + | 0.869810i | \(0.335759\pi\) | |||||||
\(354\) | 19.1755 | 1.01916 | ||||||||
\(355\) | −9.70452 | −0.515063 | ||||||||
\(356\) | 46.8907 | 2.48520 | ||||||||
\(357\) | 10.5738 | 0.559623 | ||||||||
\(358\) | −47.9889 | −2.53629 | ||||||||
\(359\) | −4.75801 | −0.251118 | −0.125559 | − | 0.992086i | \(-0.540072\pi\) | ||||
−0.125559 | + | 0.992086i | \(0.540072\pi\) | |||||||
\(360\) | 7.20336 | 0.379650 | ||||||||
\(361\) | 26.8158 | 1.41136 | ||||||||
\(362\) | 54.9028 | 2.88563 | ||||||||
\(363\) | −16.0749 | −0.843715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.805037 | −0.0421376 | ||||||||
\(366\) | 8.93579 | 0.467081 | ||||||||
\(367\) | −10.2420 | −0.534628 | −0.267314 | − | 0.963610i | \(-0.586136\pi\) | ||||
−0.267314 | + | 0.963610i | \(0.586136\pi\) | |||||||
\(368\) | 50.9633 | 2.65665 | ||||||||
\(369\) | −5.37041 | −0.279573 | ||||||||
\(370\) | −9.20336 | −0.478460 | ||||||||
\(371\) | −18.7408 | −0.972975 | ||||||||
\(372\) | −19.5654 | −1.01442 | ||||||||
\(373\) | −23.3402 | −1.20851 | −0.604254 | − | 0.796792i | \(-0.706529\pi\) | ||||
−0.604254 | + | 0.796792i | \(0.706529\pi\) | |||||||
\(374\) | 39.7432 | 2.05507 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 27.4090 | 1.41351 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.37041 | −0.481962 | ||||||||
\(379\) | −35.6571 | −1.83158 | −0.915791 | − | 0.401655i | \(-0.868435\pi\) | ||||
−0.915791 | + | 0.401655i | \(0.868435\pi\) | |||||||
\(380\) | 32.2783 | 1.65584 | ||||||||
\(381\) | 3.19496 | 0.163683 | ||||||||
\(382\) | −22.6403 | −1.15838 | ||||||||
\(383\) | −30.6185 | −1.56453 | −0.782265 | − | 0.622945i | \(-0.785936\pi\) | ||||
−0.782265 | + | 0.622945i | \(0.785936\pi\) | |||||||
\(384\) | 2.40672 | 0.122817 | ||||||||
\(385\) | −18.7408 | −0.955121 | ||||||||
\(386\) | 50.1280 | 2.55145 | ||||||||
\(387\) | 3.16706 | 0.160990 | ||||||||
\(388\) | −26.5798 | −1.34939 | ||||||||
\(389\) | 25.0191 | 1.26852 | 0.634260 | − | 0.773120i | \(-0.281305\pi\) | ||||
0.634260 | + | 0.773120i | \(0.281305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.2568 | −0.822144 | ||||||||
\(392\) | 43.0191 | 2.17279 | ||||||||
\(393\) | 4.57377 | 0.230716 | ||||||||
\(394\) | −39.4090 | −1.98540 | ||||||||
\(395\) | −4.10284 | −0.206437 | ||||||||
\(396\) | −24.8134 | −1.24692 | ||||||||
\(397\) | 10.8329 | 0.543690 | 0.271845 | − | 0.962341i | \(-0.412366\pi\) | ||||
0.271845 | + | 0.962341i | \(0.412366\pi\) | |||||||
\(398\) | −11.8050 | −0.591733 | ||||||||
\(399\) | −24.3788 | −1.22047 | ||||||||
\(400\) | 9.20336 | 0.460168 | ||||||||
\(401\) | −24.4793 | −1.22244 | −0.611220 | − | 0.791461i | \(-0.709321\pi\) | ||||
−0.611220 | + | 0.791461i | \(0.709321\pi\) | |||||||
\(402\) | −9.10891 | −0.454311 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11.4770 | 0.571002 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 17.1755 | 0.852403 | ||||||||
\(407\) | 18.4067 | 0.912387 | ||||||||
\(408\) | 21.1475 | 1.04696 | ||||||||
\(409\) | 26.7106 | 1.32075 | 0.660377 | − | 0.750934i | \(-0.270397\pi\) | ||||
0.660377 | + | 0.750934i | \(0.270397\pi\) | |||||||
\(410\) | −13.9721 | −0.690032 | ||||||||
\(411\) | −10.6743 | −0.526524 | ||||||||
\(412\) | 87.9499 | 4.33298 | ||||||||
\(413\) | −26.5459 | −1.30624 | ||||||||
\(414\) | 14.4067 | 0.708051 | ||||||||
\(415\) | −11.5375 | −0.566352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.1475 | 0.790749 | ||||||||
\(418\) | −91.6315 | −4.48184 | ||||||||
\(419\) | 15.0363 | 0.734571 | 0.367286 | − | 0.930108i | \(-0.380287\pi\) | ||||
0.367286 | + | 0.930108i | \(0.380287\pi\) | |||||||
\(420\) | −17.1755 | −0.838076 | ||||||||
\(421\) | −5.90182 | −0.287637 | −0.143818 | − | 0.989604i | \(-0.545938\pi\) | ||||
−0.143818 | + | 0.989604i | \(0.545938\pi\) | |||||||
\(422\) | −57.6208 | −2.80494 | ||||||||
\(423\) | 3.80504 | 0.185007 | ||||||||
\(424\) | −37.4817 | −1.82027 | ||||||||
\(425\) | −2.93579 | −0.142407 | ||||||||
\(426\) | 25.2481 | 1.22327 | ||||||||
\(427\) | −12.3704 | −0.598646 | ||||||||
\(428\) | 52.1499 | 2.52076 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.23966 | 0.397352 | ||||||||
\(431\) | 39.3486 | 1.89535 | 0.947677 | − | 0.319231i | \(-0.103425\pi\) | ||||
0.947677 | + | 0.319231i | \(0.103425\pi\) | |||||||
\(432\) | −9.20336 | −0.442797 | ||||||||
\(433\) | 12.4151 | 0.596632 | 0.298316 | − | 0.954467i | \(-0.403575\pi\) | ||||
0.298316 | + | 0.954467i | \(0.403575\pi\) | |||||||
\(434\) | 38.4454 | 1.84544 | ||||||||
\(435\) | −1.83294 | −0.0878830 | ||||||||
\(436\) | 66.1388 | 3.16747 | ||||||||
\(437\) | 37.4817 | 1.79299 | ||||||||
\(438\) | 2.09445 | 0.100077 | ||||||||
\(439\) | 31.8413 | 1.51970 | 0.759852 | − | 0.650096i | \(-0.225271\pi\) | ||||
0.759852 | + | 0.650096i | \(0.225271\pi\) | |||||||
\(440\) | −37.4817 | −1.78687 | ||||||||
\(441\) | 5.97209 | 0.284385 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.06421 | −0.0505622 | −0.0252811 | − | 0.999680i | \(-0.508048\pi\) | ||||
−0.0252811 | + | 0.999680i | \(0.508048\pi\) | |||||||
\(444\) | 16.8692 | 0.800579 | ||||||||
\(445\) | 9.83294 | 0.466126 | ||||||||
\(446\) | −19.7990 | −0.937509 | ||||||||
\(447\) | 9.66589 | 0.457181 | ||||||||
\(448\) | 23.0749 | 1.09019 | ||||||||
\(449\) | 15.4044 | 0.726978 | 0.363489 | − | 0.931599i | \(-0.381585\pi\) | ||||
0.363489 | + | 0.931599i | \(0.381585\pi\) | |||||||
\(450\) | 2.60168 | 0.122644 | ||||||||
\(451\) | 27.9442 | 1.31584 | ||||||||
\(452\) | −53.4258 | −2.51294 | ||||||||
\(453\) | 18.7129 | 0.879210 | ||||||||
\(454\) | 60.7297 | 2.85019 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −48.7576 | −2.28328 | ||||||||
\(457\) | −9.57377 | −0.447842 | −0.223921 | − | 0.974607i | \(-0.571886\pi\) | ||||
−0.223921 | + | 0.974607i | \(0.571886\pi\) | |||||||
\(458\) | 2.14521 | 0.100239 | ||||||||
\(459\) | 2.93579 | 0.137031 | ||||||||
\(460\) | 26.4067 | 1.23122 | ||||||||
\(461\) | 16.3727 | 0.762555 | 0.381277 | − | 0.924461i | \(-0.375484\pi\) | ||||
0.381277 | + | 0.924461i | \(0.375484\pi\) | |||||||
\(462\) | 48.7576 | 2.26841 | ||||||||
\(463\) | −24.6487 | −1.14552 | −0.572761 | − | 0.819722i | \(-0.694128\pi\) | ||||
−0.572761 | + | 0.819722i | \(0.694128\pi\) | |||||||
\(464\) | 16.8692 | 0.783135 | ||||||||
\(465\) | −4.10284 | −0.190265 | ||||||||
\(466\) | −34.8739 | −1.61550 | ||||||||
\(467\) | −20.3402 | −0.941231 | −0.470616 | − | 0.882338i | \(-0.655968\pi\) | ||||
−0.470616 | + | 0.882338i | \(0.655968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.6101 | 0.582279 | ||||||||
\(470\) | 9.89949 | 0.456629 | ||||||||
\(471\) | 10.3704 | 0.477843 | ||||||||
\(472\) | −53.0917 | −2.44374 | ||||||||
\(473\) | −16.4793 | −0.757720 | ||||||||
\(474\) | 10.6743 | 0.490286 | ||||||||
\(475\) | 6.76873 | 0.310571 | ||||||||
\(476\) | −50.4235 | −2.31116 | ||||||||
\(477\) | −5.20336 | −0.238245 | ||||||||
\(478\) | 33.2928 | 1.52278 | ||||||||
\(479\) | −0.162393 | −0.00741993 | −0.00370996 | − | 0.999993i | \(-0.501181\pi\) | ||||
−0.00370996 | + | 0.999993i | \(0.501181\pi\) | |||||||
\(480\) | −9.53747 | −0.435324 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 33.2201 | 1.51314 | ||||||||
\(483\) | −19.9442 | −0.907492 | ||||||||
\(484\) | 76.6571 | 3.48441 | ||||||||
\(485\) | −5.57377 | −0.253092 | ||||||||
\(486\) | −2.60168 | −0.118015 | ||||||||
\(487\) | 2.56305 | 0.116143 | 0.0580713 | − | 0.998312i | \(-0.481505\pi\) | ||||
0.0580713 | + | 0.998312i | \(0.481505\pi\) | |||||||
\(488\) | −24.7408 | −1.11996 | ||||||||
\(489\) | 11.4733 | 0.518839 | ||||||||
\(490\) | 15.5375 | 0.701911 | ||||||||
\(491\) | 28.4407 | 1.28351 | 0.641755 | − | 0.766910i | \(-0.278207\pi\) | ||||
0.641755 | + | 0.766910i | \(0.278207\pi\) | |||||||
\(492\) | 25.6101 | 1.15459 | ||||||||
\(493\) | −5.38114 | −0.242354 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.20336 | −0.233874 | ||||||||
\(496\) | 37.7599 | 1.69547 | ||||||||
\(497\) | −34.9526 | −1.56784 | ||||||||
\(498\) | 30.0168 | 1.34508 | ||||||||
\(499\) | −27.8605 | −1.24721 | −0.623603 | − | 0.781741i | \(-0.714332\pi\) | ||||
−0.623603 | + | 0.781741i | \(0.714332\pi\) | |||||||
\(500\) | 4.76873 | 0.213264 | ||||||||
\(501\) | 3.13075 | 0.139872 | ||||||||
\(502\) | −21.8716 | −0.976176 | ||||||||
\(503\) | 31.4258 | 1.40121 | 0.700604 | − | 0.713550i | \(-0.252914\pi\) | ||||
0.700604 | + | 0.713550i | \(0.252914\pi\) | |||||||
\(504\) | 25.9442 | 1.15565 | ||||||||
\(505\) | 2.40672 | 0.107097 | ||||||||
\(506\) | −74.9633 | −3.33253 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.2359 | −0.675985 | ||||||||
\(509\) | 16.2225 | 0.719049 | 0.359524 | − | 0.933136i | \(-0.382939\pi\) | ||||
0.359524 | + | 0.933136i | \(0.382939\pi\) | |||||||
\(510\) | 7.63798 | 0.338216 | ||||||||
\(511\) | −2.89949 | −0.128266 | ||||||||
\(512\) | −44.8134 | −1.98049 | ||||||||
\(513\) | −6.76873 | −0.298847 | ||||||||
\(514\) | 15.9721 | 0.704499 | ||||||||
\(515\) | 18.4430 | 0.812697 | ||||||||
\(516\) | −15.1028 | −0.664866 | ||||||||
\(517\) | −19.7990 | −0.870758 | ||||||||
\(518\) | −33.1475 | −1.45642 | ||||||||
\(519\) | −8.26757 | −0.362906 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.0386 | −0.877909 | −0.438954 | − | 0.898509i | \(-0.644651\pi\) | ||||
−0.438954 | + | 0.898509i | \(0.644651\pi\) | |||||||
\(522\) | 4.76873 | 0.208722 | ||||||||
\(523\) | −13.2592 | −0.579783 | −0.289892 | − | 0.957059i | \(-0.593619\pi\) | ||||
−0.289892 | + | 0.957059i | \(0.593619\pi\) | |||||||
\(524\) | −21.8111 | −0.952822 | ||||||||
\(525\) | −3.60168 | −0.157190 | ||||||||
\(526\) | −12.3062 | −0.536576 | ||||||||
\(527\) | −12.0451 | −0.524692 | ||||||||
\(528\) | 47.8884 | 2.08407 | ||||||||
\(529\) | 7.66356 | 0.333198 | ||||||||
\(530\) | −13.5375 | −0.588030 | ||||||||
\(531\) | −7.37041 | −0.319849 | ||||||||
\(532\) | 116.256 | 5.04034 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −25.5822 | −1.10705 | ||||||||
\(535\) | 10.9358 | 0.472795 | ||||||||
\(536\) | 25.2201 | 1.08934 | ||||||||
\(537\) | 18.4454 | 0.795976 | ||||||||
\(538\) | −14.1610 | −0.610524 | ||||||||
\(539\) | −31.0749 | −1.33849 | ||||||||
\(540\) | −4.76873 | −0.205214 | ||||||||
\(541\) | 35.6850 | 1.53422 | 0.767109 | − | 0.641516i | \(-0.221694\pi\) | ||||
0.767109 | + | 0.641516i | \(0.221694\pi\) | |||||||
\(542\) | 66.2890 | 2.84736 | ||||||||
\(543\) | −21.1028 | −0.905610 | ||||||||
\(544\) | −28.0000 | −1.20049 | ||||||||
\(545\) | 13.8692 | 0.594093 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.627256 | −0.0268195 | −0.0134098 | − | 0.999910i | \(-0.504269\pi\) | ||||
−0.0134098 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(548\) | 50.9028 | 2.17446 | ||||||||
\(549\) | −3.43462 | −0.146586 | ||||||||
\(550\) | −13.5375 | −0.577240 | ||||||||
\(551\) | 12.4067 | 0.528544 | ||||||||
\(552\) | −39.8884 | −1.69776 | ||||||||
\(553\) | −14.7771 | −0.628387 | ||||||||
\(554\) | −59.3532 | −2.52168 | ||||||||
\(555\) | 3.53747 | 0.150157 | ||||||||
\(556\) | −77.0033 | −3.26567 | ||||||||
\(557\) | 9.20802 | 0.390156 | 0.195078 | − | 0.980788i | \(-0.437504\pi\) | ||||
0.195078 | + | 0.980788i | \(0.437504\pi\) | |||||||
\(558\) | 10.6743 | 0.451879 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 33.1475 | 1.40074 | ||||||||
\(561\) | −15.2760 | −0.644952 | ||||||||
\(562\) | −5.63798 | −0.237824 | ||||||||
\(563\) | 2.66822 | 0.112452 | 0.0562260 | − | 0.998418i | \(-0.482093\pi\) | ||||
0.0562260 | + | 0.998418i | \(0.482093\pi\) | |||||||
\(564\) | −18.1452 | −0.764051 | ||||||||
\(565\) | −11.2034 | −0.471329 | ||||||||
\(566\) | −77.3919 | −3.25302 | ||||||||
\(567\) | 3.60168 | 0.151256 | ||||||||
\(568\) | −69.9052 | −2.93316 | ||||||||
\(569\) | −26.1838 | −1.09768 | −0.548842 | − | 0.835926i | \(-0.684931\pi\) | ||||
−0.548842 | + | 0.835926i | \(0.684931\pi\) | |||||||
\(570\) | −17.6101 | −0.737605 | ||||||||
\(571\) | −19.2481 | −0.805506 | −0.402753 | − | 0.915309i | \(-0.631947\pi\) | ||||
−0.402753 | + | 0.915309i | \(0.631947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.70219 | 0.363539 | ||||||||
\(574\) | −50.3230 | −2.10044 | ||||||||
\(575\) | 5.53747 | 0.230928 | ||||||||
\(576\) | 6.40672 | 0.266947 | ||||||||
\(577\) | 23.8716 | 0.993787 | 0.496893 | − | 0.867812i | \(-0.334474\pi\) | ||||
0.496893 | + | 0.867812i | \(0.334474\pi\) | |||||||
\(578\) | −21.8050 | −0.906970 | ||||||||
\(579\) | −19.2676 | −0.800733 | ||||||||
\(580\) | 8.74083 | 0.362943 | ||||||||
\(581\) | −41.5543 | −1.72396 | ||||||||
\(582\) | 14.5012 | 0.601093 | ||||||||
\(583\) | 27.0749 | 1.12133 | ||||||||
\(584\) | −5.79897 | −0.239963 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 86.0783 | 3.55586 | ||||||||
\(587\) | 28.8753 | 1.19181 | 0.595906 | − | 0.803054i | \(-0.296793\pi\) | ||||
0.595906 | + | 0.803054i | \(0.296793\pi\) | |||||||
\(588\) | −28.4793 | −1.17447 | ||||||||
\(589\) | 27.7711 | 1.14429 | ||||||||
\(590\) | −19.1755 | −0.789441 | ||||||||
\(591\) | 15.1475 | 0.623087 | ||||||||
\(592\) | −32.5566 | −1.33807 | ||||||||
\(593\) | −8.74083 | −0.358943 | −0.179471 | − | 0.983763i | \(-0.557439\pi\) | ||||
−0.179471 | + | 0.983763i | \(0.557439\pi\) | |||||||
\(594\) | 13.5375 | 0.555449 | ||||||||
\(595\) | −10.5738 | −0.433482 | ||||||||
\(596\) | −46.0941 | −1.88809 | ||||||||
\(597\) | 4.53747 | 0.185706 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.5929 | 0.882262 | 0.441131 | − | 0.897443i | \(-0.354577\pi\) | ||||
0.441131 | + | 0.897443i | \(0.354577\pi\) | |||||||
\(600\) | −7.20336 | −0.294076 | ||||||||
\(601\) | 30.2504 | 1.23394 | 0.616970 | − | 0.786987i | \(-0.288360\pi\) | ||||
0.616970 | + | 0.786987i | \(0.288360\pi\) | |||||||
\(602\) | 29.6766 | 1.20953 | ||||||||
\(603\) | 3.50117 | 0.142578 | ||||||||
\(604\) | −89.2369 | −3.63100 | ||||||||
\(605\) | 16.0749 | 0.653539 | ||||||||
\(606\) | −6.26150 | −0.254356 | ||||||||
\(607\) | −22.5072 | −0.913540 | −0.456770 | − | 0.889585i | \(-0.650994\pi\) | ||||
−0.456770 | + | 0.889585i | \(0.650994\pi\) | |||||||
\(608\) | 64.5566 | 2.61812 | ||||||||
\(609\) | −6.60168 | −0.267514 | ||||||||
\(610\) | −8.93579 | −0.361800 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −14.0000 | −0.565916 | ||||||||
\(613\) | 18.7771 | 0.758401 | 0.379201 | − | 0.925315i | \(-0.376199\pi\) | ||||
0.379201 | + | 0.925315i | \(0.376199\pi\) | |||||||
\(614\) | −37.3872 | −1.50882 | ||||||||
\(615\) | 5.37041 | 0.216556 | ||||||||
\(616\) | −134.997 | −5.43918 | ||||||||
\(617\) | −3.61007 | −0.145336 | −0.0726681 | − | 0.997356i | \(-0.523151\pi\) | ||||
−0.0726681 | + | 0.997356i | \(0.523151\pi\) | |||||||
\(618\) | −47.9828 | −1.93015 | ||||||||
\(619\) | 2.87158 | 0.115419 | 0.0577093 | − | 0.998333i | \(-0.481620\pi\) | ||||
0.0577093 | + | 0.998333i | \(0.481620\pi\) | |||||||
\(620\) | 19.5654 | 0.785764 | ||||||||
\(621\) | −5.53747 | −0.222211 | ||||||||
\(622\) | −22.6524 | −0.908280 | ||||||||
\(623\) | 35.4151 | 1.41888 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −21.2420 | −0.849001 | ||||||||
\(627\) | 35.2201 | 1.40656 | ||||||||
\(628\) | −49.4537 | −1.97342 | ||||||||
\(629\) | 10.3853 | 0.414088 | ||||||||
\(630\) | 9.37041 | 0.373326 | ||||||||
\(631\) | 16.9889 | 0.676317 | 0.338158 | − | 0.941089i | \(-0.390196\pi\) | ||||
0.338158 | + | 0.941089i | \(0.390196\pi\) | |||||||
\(632\) | −29.5543 | −1.17561 | ||||||||
\(633\) | 22.1475 | 0.880286 | ||||||||
\(634\) | 34.8860 | 1.38550 | ||||||||
\(635\) | −3.19496 | −0.126788 | ||||||||
\(636\) | 24.8134 | 0.983917 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.8134 | −0.982373 | ||||||||
\(639\) | −9.70452 | −0.383905 | ||||||||
\(640\) | −2.40672 | −0.0951338 | ||||||||
\(641\) | −16.6124 | −0.656151 | −0.328075 | − | 0.944652i | \(-0.606400\pi\) | ||||
−0.328075 | + | 0.944652i | \(0.606400\pi\) | |||||||
\(642\) | −28.4514 | −1.12289 | ||||||||
\(643\) | 45.3402 | 1.78804 | 0.894021 | − | 0.448025i | \(-0.147872\pi\) | ||||
0.894021 | + | 0.448025i | \(0.147872\pi\) | |||||||
\(644\) | 95.1085 | 3.74780 | ||||||||
\(645\) | −3.16706 | −0.124703 | ||||||||
\(646\) | −51.6995 | −2.03409 | ||||||||
\(647\) | 4.86925 | 0.191430 | 0.0957149 | − | 0.995409i | \(-0.469486\pi\) | ||||
0.0957149 | + | 0.995409i | \(0.469486\pi\) | |||||||
\(648\) | 7.20336 | 0.282975 | ||||||||
\(649\) | 38.3509 | 1.50540 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7771 | −0.579161 | ||||||||
\(652\) | −54.7129 | −2.14272 | ||||||||
\(653\) | 19.2699 | 0.754089 | 0.377045 | − | 0.926195i | \(-0.376940\pi\) | ||||
0.377045 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(654\) | −36.0833 | −1.41097 | ||||||||
\(655\) | −4.57377 | −0.178712 | ||||||||
\(656\) | −49.4258 | −1.92975 | ||||||||
\(657\) | −0.805037 | −0.0314075 | ||||||||
\(658\) | 35.6548 | 1.38997 | ||||||||
\(659\) | 0.334110 | 0.0130151 | 0.00650755 | − | 0.999979i | \(-0.497929\pi\) | ||||
0.00650755 | + | 0.999979i | \(0.497929\pi\) | |||||||
\(660\) | 24.8134 | 0.965862 | ||||||||
\(661\) | −13.6682 | −0.531632 | −0.265816 | − | 0.964024i | \(-0.585641\pi\) | ||||
−0.265816 | + | 0.964024i | \(0.585641\pi\) | |||||||
\(662\) | 55.8823 | 2.17193 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −83.1085 | −3.22524 | ||||||||
\(665\) | 24.3788 | 0.945370 | ||||||||
\(666\) | −9.20336 | −0.356623 | ||||||||
\(667\) | 10.1499 | 0.393005 | ||||||||
\(668\) | −14.9297 | −0.577648 | ||||||||
\(669\) | 7.61007 | 0.294222 | ||||||||
\(670\) | 9.10891 | 0.351908 | ||||||||
\(671\) | 17.8716 | 0.689925 | ||||||||
\(672\) | −34.3509 | −1.32511 | ||||||||
\(673\) | −21.8800 | −0.843411 | −0.421706 | − | 0.906733i | \(-0.638568\pi\) | ||||
−0.421706 | + | 0.906733i | \(0.638568\pi\) | |||||||
\(674\) | −19.3704 | −0.746120 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.0749 | −0.656243 | −0.328122 | − | 0.944636i | \(-0.606416\pi\) | ||||
−0.328122 | + | 0.944636i | \(0.606416\pi\) | |||||||
\(678\) | 29.1475 | 1.11940 | ||||||||
\(679\) | −20.0749 | −0.770405 | ||||||||
\(680\) | −21.1475 | −0.810971 | ||||||||
\(681\) | −23.3425 | −0.894487 | ||||||||
\(682\) | −55.5421 | −2.12682 | ||||||||
\(683\) | −26.7301 | −1.02280 | −0.511399 | − | 0.859343i | \(-0.670873\pi\) | ||||
−0.511399 | + | 0.859343i | \(0.670873\pi\) | |||||||
\(684\) | 32.2783 | 1.23419 | ||||||||
\(685\) | 10.6743 | 0.407843 | ||||||||
\(686\) | −9.63192 | −0.367748 | ||||||||
\(687\) | −0.824549 | −0.0314585 | ||||||||
\(688\) | 29.1475 | 1.11124 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −14.4067 | −0.548454 | ||||||||
\(691\) | 48.7153 | 1.85322 | 0.926608 | − | 0.376029i | \(-0.122711\pi\) | ||||
0.926608 | + | 0.376029i | \(0.122711\pi\) | |||||||
\(692\) | 39.4258 | 1.49875 | ||||||||
\(693\) | −18.7408 | −0.711905 | ||||||||
\(694\) | −64.9028 | −2.46368 | ||||||||
\(695\) | −16.1475 | −0.612511 | ||||||||
\(696\) | −13.2034 | −0.500472 | ||||||||
\(697\) | 15.7664 | 0.597195 | ||||||||
\(698\) | 5.47093 | 0.207078 | ||||||||
\(699\) | 13.4044 | 0.507000 | ||||||||
\(700\) | 17.1755 | 0.649171 | ||||||||
\(701\) | 22.9419 | 0.866502 | 0.433251 | − | 0.901273i | \(-0.357366\pi\) | ||||
0.433251 | + | 0.901273i | \(0.357366\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.9442 | −0.903072 | ||||||||
\(704\) | −33.3364 | −1.25641 | ||||||||
\(705\) | −3.80504 | −0.143306 | ||||||||
\(706\) | 48.2346 | 1.81533 | ||||||||
\(707\) | 8.66822 | 0.326002 | ||||||||
\(708\) | 35.1475 | 1.32093 | ||||||||
\(709\) | −7.14521 | −0.268344 | −0.134172 | − | 0.990958i | \(-0.542837\pi\) | ||||
−0.134172 | + | 0.990958i | \(0.542837\pi\) | |||||||
\(710\) | −25.2481 | −0.947543 | ||||||||
\(711\) | −4.10284 | −0.153869 | ||||||||
\(712\) | 70.8302 | 2.65447 | ||||||||
\(713\) | 22.7194 | 0.850847 | ||||||||
\(714\) | 27.5096 | 1.02952 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −87.9610 | −3.28726 | ||||||||
\(717\) | −12.7966 | −0.477899 | ||||||||
\(718\) | −12.3788 | −0.461973 | ||||||||
\(719\) | 41.9782 | 1.56552 | 0.782761 | − | 0.622323i | \(-0.213811\pi\) | ||||
0.782761 | + | 0.622323i | \(0.213811\pi\) | |||||||
\(720\) | 9.20336 | 0.342989 | ||||||||
\(721\) | 66.4258 | 2.47383 | ||||||||
\(722\) | 69.7660 | 2.59642 | ||||||||
\(723\) | −12.7687 | −0.474874 | ||||||||
\(724\) | 100.634 | 3.74003 | ||||||||
\(725\) | 1.83294 | 0.0680739 | ||||||||
\(726\) | −41.8218 | −1.55215 | ||||||||
\(727\) | −11.4965 | −0.426382 | −0.213191 | − | 0.977011i | \(-0.568386\pi\) | ||||
−0.213191 | + | 0.977011i | \(0.568386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.09445 | −0.0775190 | ||||||||
\(731\) | −9.29781 | −0.343892 | ||||||||
\(732\) | 16.3788 | 0.605378 | ||||||||
\(733\) | 46.1136 | 1.70324 | 0.851622 | − | 0.524157i | \(-0.175619\pi\) | ||||
0.851622 | + | 0.524157i | \(0.175619\pi\) | |||||||
\(734\) | −26.6464 | −0.983536 | ||||||||
\(735\) | −5.97209 | −0.220284 | ||||||||
\(736\) | 52.8134 | 1.94673 | ||||||||
\(737\) | −18.2178 | −0.671062 | ||||||||
\(738\) | −13.9721 | −0.514320 | ||||||||
\(739\) | −11.6101 | −0.427084 | −0.213542 | − | 0.976934i | \(-0.568500\pi\) | ||||
−0.213542 | + | 0.976934i | \(0.568500\pi\) | |||||||
\(740\) | −16.8692 | −0.620126 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −48.7576 | −1.78995 | ||||||||
\(743\) | 13.4151 | 0.492153 | 0.246076 | − | 0.969250i | \(-0.420859\pi\) | ||||
0.246076 | + | 0.969250i | \(0.420859\pi\) | |||||||
\(744\) | −29.5543 | −1.08351 | ||||||||
\(745\) | −9.66589 | −0.354131 | ||||||||
\(746\) | −60.7236 | −2.22325 | ||||||||
\(747\) | −11.5375 | −0.422134 | ||||||||
\(748\) | 72.8470 | 2.66355 | ||||||||
\(749\) | 39.3872 | 1.43918 | ||||||||
\(750\) | −2.60168 | −0.0949999 | ||||||||
\(751\) | 44.1731 | 1.61190 | 0.805950 | − | 0.591984i | \(-0.201655\pi\) | ||||
0.805950 | + | 0.591984i | \(0.201655\pi\) | |||||||
\(752\) | 35.0191 | 1.27702 | ||||||||
\(753\) | 8.40672 | 0.306358 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.7129 | −0.681033 | ||||||||
\(756\) | −17.1755 | −0.624665 | ||||||||
\(757\) | 7.97209 | 0.289751 | 0.144875 | − | 0.989450i | \(-0.453722\pi\) | ||||
0.144875 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(758\) | −92.7683 | −3.36950 | ||||||||
\(759\) | 28.8134 | 1.04586 | ||||||||
\(760\) | 48.7576 | 1.76862 | ||||||||
\(761\) | 13.6659 | 0.495388 | 0.247694 | − | 0.968838i | \(-0.420327\pi\) | ||||
0.247694 | + | 0.968838i | \(0.420327\pi\) | |||||||
\(762\) | 8.31227 | 0.301122 | ||||||||
\(763\) | 49.9526 | 1.80840 | ||||||||
\(764\) | −41.4984 | −1.50136 | ||||||||
\(765\) | −2.93579 | −0.106144 | ||||||||
\(766\) | −79.6594 | −2.87821 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 19.0749 | 0.688308 | ||||||||
\(769\) | 16.4904 | 0.594660 | 0.297330 | − | 0.954775i | \(-0.403904\pi\) | ||||
0.297330 | + | 0.954775i | \(0.403904\pi\) | |||||||
\(770\) | −48.7576 | −1.75710 | ||||||||
\(771\) | −6.13915 | −0.221096 | ||||||||
\(772\) | 91.8819 | 3.30690 | ||||||||
\(773\) | −45.7041 | −1.64386 | −0.821932 | − | 0.569586i | \(-0.807104\pi\) | ||||
−0.821932 | + | 0.569586i | \(0.807104\pi\) | |||||||
\(774\) | 8.23966 | 0.296169 | ||||||||
\(775\) | 4.10284 | 0.147379 | ||||||||
\(776\) | −40.1499 | −1.44130 | ||||||||
\(777\) | 12.7408 | 0.457075 | ||||||||
\(778\) | 65.0917 | 2.33365 | ||||||||
\(779\) | −36.3509 | −1.30241 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.4961 | 1.80689 | ||||||||
\(782\) | −42.2951 | −1.51247 | ||||||||
\(783\) | −1.83294 | −0.0655041 | ||||||||
\(784\) | 54.9633 | 1.96298 | ||||||||
\(785\) | −10.3704 | −0.370136 | ||||||||
\(786\) | 11.8995 | 0.424441 | ||||||||
\(787\) | −48.8218 | −1.74031 | −0.870155 | − | 0.492778i | \(-0.835982\pi\) | ||||
−0.870155 | + | 0.492778i | \(0.835982\pi\) | |||||||
\(788\) | −72.2346 | −2.57325 | ||||||||
\(789\) | 4.73010 | 0.168396 | ||||||||
\(790\) | −10.6743 | −0.379774 | ||||||||
\(791\) | −40.3509 | −1.43471 | ||||||||
\(792\) | −37.4817 | −1.33185 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.1838 | 1.00021 | ||||||||
\(795\) | 5.20336 | 0.184544 | ||||||||
\(796\) | −21.6380 | −0.766938 | ||||||||
\(797\) | 13.7492 | 0.487022 | 0.243511 | − | 0.969898i | \(-0.421701\pi\) | ||||
0.243511 | + | 0.969898i | \(0.421701\pi\) | |||||||
\(798\) | −63.4258 | −2.24525 | ||||||||
\(799\) | −11.1708 | −0.395194 | ||||||||
\(800\) | 9.53747 | 0.337200 | ||||||||
\(801\) | 9.83294 | 0.347430 | ||||||||
\(802\) | −63.6873 | −2.24888 | ||||||||
\(803\) | 4.18890 | 0.147823 | ||||||||
\(804\) | −16.6961 | −0.588827 | ||||||||
\(805\) | 19.9442 | 0.702940 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.44302 | 0.191603 | ||||||||
\(808\) | 17.3364 | 0.609894 | ||||||||
\(809\) | 20.3341 | 0.714909 | 0.357455 | − | 0.933931i | \(-0.383645\pi\) | ||||
0.357455 | + | 0.933931i | \(0.383645\pi\) | |||||||
\(810\) | 2.60168 | 0.0914137 | ||||||||
\(811\) | 22.4817 | 0.789438 | 0.394719 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394719 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(812\) | 31.4817 | 1.10479 | ||||||||
\(813\) | −25.4793 | −0.893599 | ||||||||
\(814\) | 47.8884 | 1.67849 | ||||||||
\(815\) | −11.4733 | −0.401891 | ||||||||
\(816\) | 27.0191 | 0.945858 | ||||||||
\(817\) | 21.4370 | 0.749984 | ||||||||
\(818\) | 69.4924 | 2.42974 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −25.6101 | −0.894343 | ||||||||
\(821\) | −32.6077 | −1.13802 | −0.569009 | − | 0.822331i | \(-0.692673\pi\) | ||||
−0.569009 | + | 0.822331i | \(0.692673\pi\) | |||||||
\(822\) | −27.7711 | −0.968627 | ||||||||
\(823\) | 33.4817 | 1.16710 | 0.583549 | − | 0.812078i | \(-0.301664\pi\) | ||||
0.583549 | + | 0.812078i | \(0.301664\pi\) | |||||||
\(824\) | 132.852 | 4.62811 | ||||||||
\(825\) | 5.20336 | 0.181158 | ||||||||
\(826\) | −69.0638 | −2.40304 | ||||||||
\(827\) | −51.0298 | −1.77448 | −0.887241 | − | 0.461306i | \(-0.847381\pi\) | ||||
−0.887241 | + | 0.461306i | \(0.847381\pi\) | |||||||
\(828\) | 26.4067 | 0.917697 | ||||||||
\(829\) | 21.1946 | 0.736118 | 0.368059 | − | 0.929802i | \(-0.380022\pi\) | ||||
0.368059 | + | 0.929802i | \(0.380022\pi\) | |||||||
\(830\) | −30.0168 | −1.04190 | ||||||||
\(831\) | 22.8134 | 0.791389 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.5328 | −0.607476 | ||||||||
\(834\) | 42.0107 | 1.45471 | ||||||||
\(835\) | −3.13075 | −0.108344 | ||||||||
\(836\) | −167.956 | −5.80886 | ||||||||
\(837\) | −4.10284 | −0.141815 | ||||||||
\(838\) | 39.1196 | 1.35137 | ||||||||
\(839\) | 53.8837 | 1.86027 | 0.930136 | − | 0.367215i | \(-0.119689\pi\) | ||||
0.930136 | + | 0.367215i | \(0.119689\pi\) | |||||||
\(840\) | −25.9442 | −0.895159 | ||||||||
\(841\) | −25.6403 | −0.884149 | ||||||||
\(842\) | −15.3546 | −0.529156 | ||||||||
\(843\) | 2.16706 | 0.0746373 | ||||||||
\(844\) | −105.616 | −3.63544 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.89949 | 0.340351 | ||||||||
\(847\) | 57.8968 | 1.98936 | ||||||||
\(848\) | −47.8884 | −1.64449 | ||||||||
\(849\) | 29.7469 | 1.02091 | ||||||||
\(850\) | −7.63798 | −0.261981 | ||||||||
\(851\) | −19.5886 | −0.671489 | ||||||||
\(852\) | 46.2783 | 1.58547 | ||||||||
\(853\) | −4.06421 | −0.139156 | −0.0695780 | − | 0.997577i | \(-0.522165\pi\) | ||||
−0.0695780 | + | 0.997577i | \(0.522165\pi\) | |||||||
\(854\) | −32.1838 | −1.10131 | ||||||||
\(855\) | 6.76873 | 0.231486 | ||||||||
\(856\) | 78.7744 | 2.69245 | ||||||||
\(857\) | −39.2141 | −1.33953 | −0.669764 | − | 0.742574i | \(-0.733605\pi\) | ||||
−0.669764 | + | 0.742574i | \(0.733605\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.64031 | −0.192445 | −0.0962225 | − | 0.995360i | \(-0.530676\pi\) | ||||
−0.0962225 | + | 0.995360i | \(0.530676\pi\) | |||||||
\(860\) | 15.1028 | 0.515003 | ||||||||
\(861\) | 19.3425 | 0.659191 | ||||||||
\(862\) | 102.372 | 3.48682 | ||||||||
\(863\) | −9.66589 | −0.329031 | −0.164515 | − | 0.986375i | \(-0.552606\pi\) | ||||
−0.164515 | + | 0.986375i | \(0.552606\pi\) | |||||||
\(864\) | −9.53747 | −0.324471 | ||||||||
\(865\) | 8.26757 | 0.281106 | ||||||||
\(866\) | 32.3001 | 1.09760 | ||||||||
\(867\) | 8.38114 | 0.284638 | ||||||||
\(868\) | 70.4682 | 2.39185 | ||||||||
\(869\) | 21.3486 | 0.724201 | ||||||||
\(870\) | −4.76873 | −0.161675 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 99.9052 | 3.38322 | ||||||||
\(873\) | −5.57377 | −0.188644 | ||||||||
\(874\) | 97.5152 | 3.29850 | ||||||||
\(875\) | 3.60168 | 0.121759 | ||||||||
\(876\) | 3.83901 | 0.129708 | ||||||||
\(877\) | 15.8716 | 0.535945 | 0.267973 | − | 0.963427i | \(-0.413646\pi\) | ||||
0.267973 | + | 0.963427i | \(0.413646\pi\) | |||||||
\(878\) | 82.8410 | 2.79575 | ||||||||
\(879\) | −33.0857 | −1.11595 | ||||||||
\(880\) | −47.8884 | −1.61432 | ||||||||
\(881\) | −29.2034 | −0.983886 | −0.491943 | − | 0.870627i | \(-0.663713\pi\) | ||||
−0.491943 | + | 0.870627i | \(0.663713\pi\) | |||||||
\(882\) | 15.5375 | 0.523174 | ||||||||
\(883\) | 30.4598 | 1.02505 | 0.512527 | − | 0.858671i | \(-0.328709\pi\) | ||||
0.512527 | + | 0.858671i | \(0.328709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.37041 | 0.247754 | ||||||||
\(886\) | −2.76873 | −0.0930174 | ||||||||
\(887\) | 11.5993 | 0.389468 | 0.194734 | − | 0.980856i | \(-0.437616\pi\) | ||||
0.194734 | + | 0.980856i | \(0.437616\pi\) | |||||||
\(888\) | 25.4817 | 0.855108 | ||||||||
\(889\) | −11.5072 | −0.385940 | ||||||||
\(890\) | 25.5822 | 0.857516 | ||||||||
\(891\) | −5.20336 | −0.174319 | ||||||||
\(892\) | −36.2904 | −1.21509 | ||||||||
\(893\) | 25.7553 | 0.861868 | ||||||||
\(894\) | 25.1475 | 0.841060 | ||||||||
\(895\) | −18.4454 | −0.616560 | ||||||||
\(896\) | −8.66822 | −0.289585 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.0773 | 1.33740 | ||||||||
\(899\) | 7.52029 | 0.250816 | ||||||||
\(900\) | 4.76873 | 0.158958 | ||||||||
\(901\) | 15.2760 | 0.508916 | ||||||||
\(902\) | 72.7018 | 2.42071 | ||||||||
\(903\) | −11.4067 | −0.379592 | ||||||||
\(904\) | −80.7018 | −2.68410 | ||||||||
\(905\) | 21.1028 | 0.701482 | ||||||||
\(906\) | 48.6850 | 1.61745 | ||||||||
\(907\) | 42.9186 | 1.42509 | 0.712545 | − | 0.701627i | \(-0.247543\pi\) | ||||
0.712545 | + | 0.701627i | \(0.247543\pi\) | |||||||
\(908\) | 111.314 | 3.69409 | ||||||||
\(909\) | 2.40672 | 0.0798257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.0726 | 1.39393 | 0.696964 | − | 0.717106i | \(-0.254534\pi\) | ||||
0.696964 | + | 0.717106i | \(0.254534\pi\) | |||||||
\(912\) | −62.2951 | −2.06280 | ||||||||
\(913\) | 60.0336 | 1.98682 | ||||||||
\(914\) | −24.9079 | −0.823880 | ||||||||
\(915\) | 3.43462 | 0.113545 | ||||||||
\(916\) | 3.93206 | 0.129919 | ||||||||
\(917\) | −16.4733 | −0.543995 | ||||||||
\(918\) | 7.63798 | 0.252091 | ||||||||
\(919\) | 39.1150 | 1.29028 | 0.645142 | − | 0.764063i | \(-0.276798\pi\) | ||||
0.645142 | + | 0.764063i | \(0.276798\pi\) | |||||||
\(920\) | 39.8884 | 1.31508 | ||||||||
\(921\) | 14.3704 | 0.473521 | ||||||||
\(922\) | 42.5966 | 1.40285 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 89.3700 | 2.94006 | ||||||||
\(925\) | −3.53747 | −0.116311 | ||||||||
\(926\) | −64.1280 | −2.10738 | ||||||||
\(927\) | 18.4430 | 0.605748 | ||||||||
\(928\) | 17.4817 | 0.573863 | ||||||||
\(929\) | 10.4625 | 0.343265 | 0.171632 | − | 0.985161i | \(-0.445096\pi\) | ||||
0.171632 | + | 0.985161i | \(0.445096\pi\) | |||||||
\(930\) | −10.6743 | −0.350024 | ||||||||
\(931\) | 40.4235 | 1.32483 | ||||||||
\(932\) | −63.9220 | −2.09383 | ||||||||
\(933\) | 8.70685 | 0.285050 | ||||||||
\(934\) | −52.9186 | −1.73155 | ||||||||
\(935\) | 15.2760 | 0.499577 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.6269 | 1.29455 | 0.647277 | − | 0.762255i | \(-0.275908\pi\) | ||||
0.647277 | + | 0.762255i | \(0.275908\pi\) | |||||||
\(938\) | 32.8074 | 1.07120 | ||||||||
\(939\) | 8.16472 | 0.266446 | ||||||||
\(940\) | 18.1452 | 0.591832 | ||||||||
\(941\) | 15.3146 | 0.499242 | 0.249621 | − | 0.968344i | \(-0.419694\pi\) | ||||
0.249621 | + | 0.968344i | \(0.419694\pi\) | |||||||
\(942\) | 26.9805 | 0.879072 | ||||||||
\(943\) | −29.7385 | −0.968419 | ||||||||
\(944\) | −67.8326 | −2.20776 | ||||||||
\(945\) | −3.60168 | −0.117163 | ||||||||
\(946\) | −42.8739 | −1.39395 | ||||||||
\(947\) | −33.2867 | −1.08167 | −0.540836 | − | 0.841128i | \(-0.681892\pi\) | ||||
−0.540836 | + | 0.841128i | \(0.681892\pi\) | |||||||
\(948\) | 19.5654 | 0.635454 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 17.6101 | 0.571346 | ||||||||
\(951\) | −13.4090 | −0.434818 | ||||||||
\(952\) | −76.1667 | −2.46858 | ||||||||
\(953\) | 23.4090 | 0.758293 | 0.379147 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379147 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(954\) | −13.5375 | −0.438292 | ||||||||
\(955\) | −8.70219 | −0.281596 | ||||||||
\(956\) | 61.0238 | 1.97365 | ||||||||
\(957\) | 9.53747 | 0.308303 | ||||||||
\(958\) | −0.422495 | −0.0136502 | ||||||||
\(959\) | 38.4454 | 1.24147 | ||||||||
\(960\) | −6.40672 | −0.206776 | ||||||||
\(961\) | −14.1667 | −0.456989 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.9358 | 0.352401 | ||||||||
\(964\) | 60.8907 | 1.96116 | ||||||||
\(965\) | 19.2676 | 0.620245 | ||||||||
\(966\) | −51.8884 | −1.66948 | ||||||||
\(967\) | 27.8669 | 0.896140 | 0.448070 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448070 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(968\) | 115.794 | 3.72175 | ||||||||
\(969\) | 19.8716 | 0.638367 | ||||||||
\(970\) | −14.5012 | −0.465604 | ||||||||
\(971\) | −4.51835 | −0.145001 | −0.0725003 | − | 0.997368i | \(-0.523098\pi\) | ||||
−0.0725003 | + | 0.997368i | \(0.523098\pi\) | |||||||
\(972\) | −4.76873 | −0.152957 | ||||||||
\(973\) | −58.1583 | −1.86447 | ||||||||
\(974\) | 6.66822 | 0.213664 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.6101 | −1.01181 | ||||||||
\(977\) | −42.4840 | −1.35918 | −0.679592 | − | 0.733591i | \(-0.737843\pi\) | ||||
−0.679592 | + | 0.733591i | \(0.737843\pi\) | |||||||
\(978\) | 29.8497 | 0.954489 | ||||||||
\(979\) | −51.1643 | −1.63522 | ||||||||
\(980\) | 28.4793 | 0.909739 | ||||||||
\(981\) | 13.8692 | 0.442811 | ||||||||
\(982\) | 73.9935 | 2.36123 | ||||||||
\(983\) | 9.87158 | 0.314854 | 0.157427 | − | 0.987531i | \(-0.449680\pi\) | ||||
0.157427 | + | 0.987531i | \(0.449680\pi\) | |||||||
\(984\) | 38.6850 | 1.23323 | ||||||||
\(985\) | −15.1475 | −0.482641 | ||||||||
\(986\) | −14.0000 | −0.445851 | ||||||||
\(987\) | −13.7045 | −0.436220 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.5375 | 0.557659 | ||||||||
\(990\) | −13.5375 | −0.430249 | ||||||||
\(991\) | 21.1196 | 0.670887 | 0.335444 | − | 0.942060i | \(-0.391114\pi\) | ||||
0.335444 | + | 0.942060i | \(0.391114\pi\) | |||||||
\(992\) | 39.1308 | 1.24240 | ||||||||
\(993\) | −21.4793 | −0.681626 | ||||||||
\(994\) | −90.9354 | −2.88430 | ||||||||
\(995\) | −4.53747 | −0.143847 | ||||||||
\(996\) | 55.0191 | 1.74335 | ||||||||
\(997\) | 17.0833 | 0.541035 | 0.270517 | − | 0.962715i | \(-0.412805\pi\) | ||||
0.270517 | + | 0.962715i | \(0.412805\pi\) | |||||||
\(998\) | −72.4840 | −2.29444 | ||||||||
\(999\) | 3.53747 | 0.111921 |
(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 | 2535.2.a.bb.1.3 | 3 | ||
3.2 | odd | 2 | 7605.2.a.bv.1.1 | 3 | |||
13.3 | even | 3 | 195.2.i.d.61.1 | yes | 6 | ||
13.9 | even | 3 | 195.2.i.d.16.1 | ✓ | 6 | ||
13.12 | even | 2 | 2535.2.a.ba.1.1 | 3 | |||
39.29 | odd | 6 | 585.2.j.f.451.3 | 6 | |||
39.35 | odd | 6 | 585.2.j.f.406.3 | 6 | |||
39.38 | odd | 2 | 7605.2.a.bw.1.3 | 3 | |||
65.3 | odd | 12 | 975.2.bb.k.724.6 | 12 | |||
65.9 | even | 6 | 975.2.i.l.601.3 | 6 | |||
65.22 | odd | 12 | 975.2.bb.k.874.6 | 12 | |||
65.29 | even | 6 | 975.2.i.l.451.3 | 6 | |||
65.42 | odd | 12 | 975.2.bb.k.724.1 | 12 | |||
65.48 | odd | 12 | 975.2.bb.k.874.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.d.16.1 | ✓ | 6 | 13.9 | even | 3 | ||
195.2.i.d.61.1 | yes | 6 | 13.3 | even | 3 | ||
585.2.j.f.406.3 | 6 | 39.35 | odd | 6 | |||
585.2.j.f.451.3 | 6 | 39.29 | odd | 6 | |||
975.2.i.l.451.3 | 6 | 65.29 | even | 6 | |||
975.2.i.l.601.3 | 6 | 65.9 | even | 6 | |||
975.2.bb.k.724.1 | 12 | 65.42 | odd | 12 | |||
975.2.bb.k.724.6 | 12 | 65.3 | odd | 12 | |||
975.2.bb.k.874.1 | 12 | 65.48 | odd | 12 | |||
975.2.bb.k.874.6 | 12 | 65.22 | odd | 12 | |||
2535.2.a.ba.1.1 | 3 | 13.12 | even | 2 | |||
2535.2.a.bb.1.3 | 3 | 1.1 | even | 1 | trivial | ||
7605.2.a.bv.1.1 | 3 | 3.2 | odd | 2 | |||
7605.2.a.bw.1.3 | 3 | 39.38 | odd | 2 |