Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,2,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, 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("608.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(4.85490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.329727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.40617 | 1.52328 | 0.761642 | − | 0.647998i | \(-0.224394\pi\) | ||||
0.761642 | + | 0.647998i | \(0.224394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50407 | 0.946449 | 0.473224 | − | 0.880942i | \(-0.343090\pi\) | ||||
0.473224 | + | 0.880942i | \(0.343090\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.40617 | −0.423975 | −0.211988 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211988 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.22101 | 1.72540 | 0.862698 | − | 0.505719i | \(-0.168773\pi\) | ||||
0.862698 | + | 0.505719i | \(0.168773\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.31891 | −1.37334 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16352 | −0.767267 | −0.383633 | − | 0.923485i | \(-0.625327\pi\) | ||||
−0.383633 | + | 0.923485i | \(0.625327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.91023 | −0.853283 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.91023 | −1.64940 | −0.824699 | − | 0.565572i | \(-0.808655\pi\) | ||||
−0.824699 | + | 0.565572i | \(0.808655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.60197 | 1.32039 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.22101 | 1.15521 | 0.577606 | − | 0.816316i | \(-0.303987\pi\) | ||||
0.577606 | + | 0.816316i | \(0.303987\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.13124 | 1.46041 | 0.730207 | − | 0.683226i | \(-0.239424\pi\) | ||||
0.730207 | + | 0.683226i | \(0.239424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.19580 | 0.382240 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.52927 | 1.44171 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.13124 | −1.00797 | −0.503985 | − | 0.863712i | \(-0.668133\pi\) | ||||
−0.503985 | + | 0.863712i | \(0.668133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.71443 | −1.55555 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68923 | 0.263813 | 0.131906 | − | 0.991262i | \(-0.457890\pi\) | ||||
0.131906 | + | 0.991262i | \(0.457890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.71694 | 0.261831 | 0.130915 | − | 0.991394i | \(-0.458208\pi\) | ||||
0.130915 | + | 0.991394i | \(0.458208\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.91274 | −0.285135 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.84818 | 1.43650 | 0.718252 | − | 0.695783i | \(-0.244942\pi\) | ||||
0.718252 | + | 0.695783i | \(0.244942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.729644 | −0.104235 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.94001 | 0.691739 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.78713 | 0.382842 | 0.191421 | − | 0.981508i | \(-0.438690\pi\) | ||||
0.191421 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.78964 | −0.645834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.25078 | 1.20435 | 0.602174 | − | 0.798365i | \(-0.294301\pi\) | ||||
0.602174 | + | 0.798365i | \(0.294301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.52927 | 0.835988 | 0.417994 | − | 0.908450i | \(-0.362733\pi\) | ||||
0.417994 | + | 0.908450i | \(0.362733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.40617 | −0.177160 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 21.1898 | 2.62827 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.87233 | 0.228741 | 0.114370 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114370 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.3522 | 1.48704 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0081 | −1.54378 | −0.771891 | − | 0.635755i | \(-0.780689\pi\) | ||||
−0.771891 | + | 0.635755i | \(0.780689\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.28663 | −0.735794 | −0.367897 | − | 0.929867i | \(-0.619922\pi\) | ||||
−0.367897 | + | 0.929867i | \(0.619922\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.3093 | −1.19042 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.52114 | −0.401271 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.2543 | −1.26621 | −0.633106 | − | 0.774065i | \(-0.718220\pi\) | ||||
−0.633106 | + | 0.774065i | \(0.718220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.80420 | 0.198036 | 0.0990182 | − | 0.995086i | \(-0.468430\pi\) | ||||
0.0990182 | + | 0.995086i | \(0.468430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.7755 | −1.16877 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.71443 | −1.04150 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.57426 | −0.802870 | −0.401435 | − | 0.915888i | \(-0.631488\pi\) | ||||
−0.401435 | + | 0.915888i | \(0.631488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.5778 | 1.63300 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.6974 | −1.31666 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.40617 | 0.349465 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.81233 | 0.488618 | 0.244309 | − | 0.969697i | \(-0.421439\pi\) | ||||
0.244309 | + | 0.969697i | \(0.421439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.789637 | 0.0793615 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2462 | −1.61656 | −0.808279 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808279 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.68923 | 0.757642 | 0.378821 | − | 0.925470i | \(-0.376330\pi\) | ||||
0.378821 | + | 0.925470i | \(0.376330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.3189 | −1.29979 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.8886 | −1.14931 | −0.574657 | − | 0.818394i | \(-0.694865\pi\) | ||||
−0.574657 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65489 | −0.541640 | −0.270820 | − | 0.962630i | \(-0.587295\pi\) | ||||
−0.270820 | + | 0.962630i | \(0.587295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.57426 | 0.908748 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.81233 | −0.828995 | −0.414497 | − | 0.910051i | \(-0.636043\pi\) | ||||
−0.414497 | + | 0.910051i | \(0.636043\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.9436 | −2.51250 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.49342 | −0.322967 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.92167 | −0.726179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.02270 | −0.820245 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.63782 | −0.237844 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.45657 | 0.488051 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0504 | 1.06930 | 0.534650 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534650 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.68109 | −0.236057 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.920878 | 0.0804575 | 0.0402287 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402287 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50407 | 0.217130 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.9436 | 1.63040 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.525705 | −0.0449140 | −0.0224570 | − | 0.999748i | \(-0.507149\pi\) | ||||
−0.0224570 | + | 0.999748i | \(0.507149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.52927 | −0.384168 | −0.192084 | − | 0.981379i | \(-0.561525\pi\) | ||||
−0.192084 | + | 0.981379i | \(0.561525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.3785 | −1.29510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.74777 | −0.731525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.1898 | 1.75972 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.13938 | 0.0939743 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.9713 | −1.55419 | −0.777094 | − | 0.629384i | \(-0.783307\pi\) | ||||
−0.777094 | + | 0.629384i | \(0.783307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.55698 | 0.533600 | 0.266800 | − | 0.963752i | \(-0.414034\pi\) | ||||
0.266800 | + | 0.963752i | \(0.414034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.77648 | 0.143620 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.6964 | 2.22463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5651 | 1.40185 | 0.700925 | − | 0.713235i | \(-0.252771\pi\) | ||||
0.700925 | + | 0.713235i | \(0.252771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.35225 | −0.345156 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8078 | −1.56107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9436 | −1.79708 | −0.898540 | − | 0.438892i | \(-0.855371\pi\) | ||||
−0.898540 | + | 0.438892i | \(0.855371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.47927 | 0.582260 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.24621 | 0.483346 | 0.241673 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241673 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.7009 | 1.97699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.561553 | −0.0429430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9436 | −1.28820 | −0.644098 | − | 0.764943i | \(-0.722767\pi\) | ||||
−0.644098 | + | 0.764943i | \(0.722767\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.5318 | 1.24969 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.4456 | −1.08580 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2462 | 1.36379 | 0.681893 | − | 0.731452i | \(-0.261157\pi\) | ||||
0.681893 | + | 0.731452i | \(0.261157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9273 | 0.812220 | 0.406110 | − | 0.913824i | \(-0.366885\pi\) | ||||
0.406110 | + | 0.913824i | \(0.366885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1958 | −0.753695 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.8840 | −1.53542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.44844 | 0.325302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.9265 | 1.01300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5122 | −1.12242 | −0.561212 | − | 0.827672i | \(-0.689665\pi\) | ||||
−0.561212 | + | 0.827672i | \(0.689665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.56512 | −0.688512 | −0.344256 | − | 0.938876i | \(-0.611869\pi\) | ||||
−0.344256 | + | 0.938876i | \(0.611869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −33.0890 | −2.36955 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.1394 | 1.36362 | 0.681812 | − | 0.731527i | \(-0.261192\pi\) | ||||
0.681812 | + | 0.731527i | \(0.261192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.133749 | −0.00948125 | −0.00474062 | − | 0.999989i | \(-0.501509\pi\) | ||||
−0.00474062 | + | 0.999989i | \(0.501509\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.92374 | −0.206224 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5778 | 1.09335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.75379 | 0.401862 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.44201 | 0.308741 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.40617 | −0.0972666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0117 | −1.58419 | −0.792095 | − | 0.610397i | \(-0.791010\pi\) | ||||
−0.792095 | + | 0.610397i | \(0.791010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.3129 | 1.39182 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.84818 | 0.398843 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3612 | 1.38221 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.81690 | 0.663365 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.6803 | −1.32384 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.51471 | 0.503222 | 0.251611 | − | 0.967828i | \(-0.419040\pi\) | ||||
0.251611 | + | 0.967828i | \(0.419040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.70735 | −0.247157 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.81690 | 0.386081 | 0.193041 | − | 0.981191i | \(-0.438165\pi\) | ||||
0.193041 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.1702 | −1.72938 | −0.864688 | − | 0.502309i | \(-0.832484\pi\) | ||||
−0.864688 | + | 0.502309i | \(0.832484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.49844 | 0.361771 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.22352 | 0.145667 | 0.0728337 | − | 0.997344i | \(-0.476796\pi\) | ||||
0.0728337 | + | 0.997344i | \(0.476796\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.5445 | 2.18820 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.5743 | 1.14157 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.12873 | 0.525804 | 0.262902 | − | 0.964823i | \(-0.415320\pi\) | ||||
0.262902 | + | 0.964823i | \(0.415320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.9517 | 1.67170 | 0.835848 | − | 0.548960i | \(-0.184976\pi\) | ||||
0.835848 | + | 0.548960i | \(0.184976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.48529 | −0.158779 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.22101 | 0.395833 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.81735 | −0.178542 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.53741 | −0.0970403 | −0.0485202 | − | 0.998822i | \(-0.515451\pi\) | ||||
−0.0485202 | + | 0.998822i | \(0.515451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1231 | 0.699304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.8265 | 1.05372 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.370318 | −0.0230998 | −0.0115499 | − | 0.999933i | \(-0.503677\pi\) | ||||
−0.0115499 | + | 0.999933i | \(0.503677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.3530 | −0.953992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.49342 | −0.216238 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.9067 | −1.16584 | −0.582919 | − | 0.812530i | \(-0.698090\pi\) | ||||
−0.582919 | + | 0.812530i | \(0.698090\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.49342 | 0.583176 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.8276 | 0.723838 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.1898 | −0.926138 | −0.463069 | − | 0.886322i | \(-0.653252\pi\) | ||||
−0.463069 | + | 0.886322i | \(0.653252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.4027 | −1.72534 | −0.862669 | − | 0.505768i | \(-0.831209\pi\) | ||||
−0.862669 | + | 0.505768i | \(0.831209\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.3256 | −1.47225 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.28347 | −0.559814 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.4647 | 1.71028 | 0.855139 | − | 0.518398i | \(-0.173471\pi\) | ||||
0.855139 | + | 0.518398i | \(0.173471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.56612 | −0.273367 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.1394 | −1.61900 | −0.809500 | − | 0.587120i | \(-0.800262\pi\) | ||||
−0.809500 | + | 0.587120i | \(0.800262\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.9117 | −1.59974 | −0.799868 | − | 0.600175i | \(-0.795097\pi\) | ||||
−0.799868 | + | 0.600175i | \(0.795097\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.31891 | −0.315065 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.22994 | 0.249685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.99213 | −0.411302 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.51471 | −0.440520 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2714 | 0.600062 | 0.300031 | − | 0.953929i | \(-0.403003\pi\) | ||||
0.300031 | + | 0.953929i | \(0.403003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.5097 | 1.83457 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.82047 | −0.453790 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −49.2096 | −2.84587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.29933 | 0.247809 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.3693 | 1.45743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.2398 | 1.27345 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.05854 | 0.288706 | 0.144353 | − | 0.989526i | \(-0.453890\pi\) | ||||
0.144353 | + | 0.989526i | \(0.453890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.0071 | −0.683062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4222 | −0.761105 | −0.380553 | − | 0.924759i | \(-0.624266\pi\) | ||||
−0.380553 | + | 0.924759i | \(0.624266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.94001 | 0.392272 | 0.196136 | − | 0.980577i | \(-0.437161\pi\) | ||||
0.196136 | + | 0.980577i | \(0.437161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.78964 | −0.269865 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.60448 | 0.314779 | 0.157389 | − | 0.987537i | \(-0.449692\pi\) | ||||
0.157389 | + | 0.987537i | \(0.449692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.74777 | −0.489781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.5647 | 1.03618 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.16352 | −0.176023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.0709 | 2.27820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.83040 | 0.488322 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 24.6605 | 1.35958 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.11140 | 0.225983 | 0.112992 | − | 0.993596i | \(-0.463957\pi\) | ||||
0.112992 | + | 0.993596i | \(0.463957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.44302 | 0.188676 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.37745 | 0.348437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.632801 | −0.0344709 | −0.0172354 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172354 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7609 | 0.747391 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4339 | −0.619179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.3556 | −1.04510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 42.0738 | 2.26518 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.02871 | −0.162590 | −0.0812949 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812949 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0954 | 1.02215 | 0.511076 | − | 0.859535i | \(-0.329247\pi\) | ||||
0.511076 | + | 0.859535i | \(0.329247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 34.5985 | 1.84673 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.2025 | 0.809147 | 0.404573 | − | 0.914506i | \(-0.367420\pi\) | ||||
0.404573 | + | 0.914506i | \(0.367420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44.3079 | −2.35162 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.3701 | 0.654696 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.9411 | −1.84412 | −0.922059 | − | 0.387048i | \(-0.873495\pi\) | ||||
−0.922059 | + | 0.387048i | \(0.873495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0894 | 0.739503 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.4133 | −1.12082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.60839 | 0.397155 | 0.198577 | − | 0.980085i | \(-0.436368\pi\) | ||||
0.198577 | + | 0.980085i | \(0.436368\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.948590 | −0.0493816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.97916 | 0.362340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.38739 | 0.486060 | 0.243030 | − | 0.970019i | \(-0.421859\pi\) | ||||
0.243030 | + | 0.970019i | \(0.421859\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.52073 | −0.440009 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 38.7009 | 1.99320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.0046 | 0.565267 | 0.282633 | − | 0.959228i | \(-0.408792\pi\) | ||||
0.282633 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8173 | −0.964042 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6923 | 1.05733 | 0.528665 | − | 0.848831i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.9936 | −0.611249 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.964152 | −0.0490106 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4306 | −0.731659 | −0.365830 | − | 0.930682i | \(-0.619215\pi\) | ||||
−0.365830 | + | 0.930682i | \(0.619215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.0242 | 1.26553 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.43800 | −0.0725375 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.3342 | −1.92880 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2739 | −0.716388 | −0.358194 | − | 0.933647i | \(-0.616607\pi\) | ||||
−0.358194 | + | 0.933647i | \(0.616607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.91023 | −0.195757 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.38559 | 0.268943 | 0.134472 | − | 0.990917i | \(-0.457066\pi\) | ||||
0.134472 | + | 0.990917i | \(0.457066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.5845 | 2.51979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −23.8432 | −1.18478 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.62155 | 0.427354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.07983 | 0.251182 | 0.125591 | − | 0.992082i | \(-0.459917\pi\) | ||||
0.125591 | + | 0.992082i | \(0.459917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.820916 | 0.0404928 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.1646 | 1.13985 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.14539 | 0.301666 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.07270 | 0.346351 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.30576 | 0.210350 | 0.105175 | − | 0.994454i | \(-0.466460\pi\) | ||||
0.105175 | + | 0.994454i | \(0.466460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8670 | −0.870782 | −0.435391 | − | 0.900241i | \(-0.643390\pi\) | ||||
−0.435391 | + | 0.900241i | \(0.643390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.53027 | −0.268891 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.8855 | −1.01309 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.3497 | 0.791219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.6601 | 0.659516 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.1958 | −0.876461 | −0.438230 | − | 0.898863i | \(-0.644395\pi\) | ||||
−0.438230 | + | 0.898863i | \(0.644395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6074 | −0.798100 | −0.399050 | − | 0.916929i | \(-0.630660\pi\) | ||||
−0.399050 | + | 0.916929i | \(0.630660\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.0890 | −1.58649 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.91023 | −0.378398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6084 | −0.554038 | −0.277019 | − | 0.960864i | \(-0.589347\pi\) | ||||
−0.277019 | + | 0.960864i | \(0.589347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.409734 | 0.0195111 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.8140 | 1.13144 | 0.565720 | − | 0.824598i | \(-0.308598\pi\) | ||||
0.565720 | + | 0.824598i | \(0.308598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.7992 | −1.22300 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.6247 | 1.40120 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.72336 | 0.175716 | 0.0878582 | − | 0.996133i | \(-0.471998\pi\) | ||||
0.0878582 | + | 0.996133i | \(0.471998\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.37533 | −0.111850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.2391 | −0.481074 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 53.0607 | 2.48752 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7719 | 1.25234 | 0.626169 | − | 0.779688i | \(-0.284622\pi\) | ||||
0.626169 | + | 0.779688i | \(0.284622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.5941 | −0.821222 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.76735 | 0.361761 | 0.180881 | − | 0.983505i | \(-0.442105\pi\) | ||||
0.180881 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.7928 | −0.641004 | −0.320502 | − | 0.947248i | \(-0.603852\pi\) | ||||
−0.320502 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −43.2493 | −2.00564 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7282 | 1.28311 | 0.641554 | − | 0.767078i | \(-0.278290\pi\) | ||||
0.641554 | + | 0.767078i | \(0.278290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.68843 | 0.216492 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −27.4289 | −1.26386 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.41430 | −0.111010 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.60197 | 0.302919 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.56512 | −0.0716619 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0163 | 0.640420 | 0.320210 | − | 0.947347i | \(-0.396247\pi\) | ||||
0.320210 | + | 0.947347i | \(0.396247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.1425 | −1.73915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.9309 | 1.40740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.3916 | 0.744304 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.5764 | −1.70275 | −0.851374 | − | 0.524559i | \(-0.824230\pi\) | ||||
−0.851374 | + | 0.524559i | \(0.824230\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 35.8276 | 1.62018 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.24309 | 0.236617 | 0.118309 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118309 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6803 | −0.886356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.68963 | 0.120890 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.5733 | −1.46111 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0542 | 1.30065 | 0.650323 | − | 0.759658i | \(-0.274633\pi\) | ||||
0.650323 | + | 0.759658i | \(0.274633\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.75379 | −0.435767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.5512 | −1.40680 | −0.703399 | − | 0.710796i | \(-0.748335\pi\) | ||||
−0.703399 | + | 0.710796i | \(0.748335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.3373 | −2.46248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.1334 | −1.78239 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5097 | 0.776104 | 0.388052 | − | 0.921638i | \(-0.373148\pi\) | ||||
0.388052 | + | 0.921638i | \(0.373148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.7421 | −0.696391 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56155 | 0.245549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.1908 | 1.15410 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8482 | −0.609042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.4583 | 1.16139 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.8780 | −1.65947 | −0.829733 | − | 0.558161i | \(-0.811507\pi\) | ||||
−0.829733 | + | 0.558161i | \(0.811507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.3739 | 1.24070 | 0.620352 | − | 0.784324i | \(-0.286990\pi\) | ||||
0.620352 | + | 0.784324i | \(0.286990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25.8152 | −1.12667 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.7234 | −1.12053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.5718 | 1.72051 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.19480 | −0.225435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5087 | 0.455182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.4945 | −1.75073 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.4924 | −1.22954 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.02600 | 0.0441930 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.5868 | 1.65898 | 0.829488 | − | 0.558524i | \(-0.188632\pi\) | ||||
0.829488 | + | 0.558524i | \(0.188632\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.0636 | −0.732267 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.2615 | −0.825071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3947 | −0.572717 | −0.286359 | − | 0.958123i | \(-0.592445\pi\) | ||||
−0.286359 | + | 0.958123i | \(0.592445\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.66653 | −0.156484 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.22101 | 0.265024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.1816 | −1.19841 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 32.6115 | 1.38428 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.46471 | 0.189176 | 0.0945879 | − | 0.995517i | \(-0.469847\pi\) | ||||
0.0945879 | + | 0.995517i | \(0.469847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.6811 | 0.451762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.94647 | −0.293280 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.1171 | −0.932124 | −0.466062 | − | 0.884752i | \(-0.654328\pi\) | ||||
−0.466062 | + | 0.884752i | \(0.654328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0163 | −1.26279 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.5285 | −0.736127 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.70238 | 0.280978 | 0.140489 | − | 0.990082i | \(-0.455132\pi\) | ||||
0.140489 | + | 0.990082i | \(0.455132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37533 | −0.266799 | −0.133400 | − | 0.991062i | \(-0.542589\pi\) | ||||
−0.133400 | + | 0.991062i | \(0.542589\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.2231 | 1.01194 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52.2231 | −2.17785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.5654 | 1.85528 | 0.927641 | − | 0.373474i | \(-0.121834\pi\) | ||||
0.927641 | + | 0.373474i | \(0.121834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9364 | 0.620737 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.51783 | 0.187431 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.91917 | −0.162315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.8992 | −0.491971 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.6311 | −1.22301 | −0.611503 | − | 0.791242i | \(-0.709435\pi\) | ||||
−0.611503 | + | 0.791242i | \(0.709435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.13124 | 0.335042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.8871 | −1.22939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.6572 | 1.79279 | 0.896393 | − | 0.443259i | \(-0.146178\pi\) | ||||
0.896393 | + | 0.443259i | \(0.146178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.9825 | −1.10618 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.208857 | 0.00854794 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5661 | −0.513438 | −0.256719 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256719 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.9213 | −1.54684 | −0.773421 | − | 0.633893i | \(-0.781456\pi\) | ||||
−0.773421 | + | 0.633893i | \(0.781456\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.05141 | −0.0428167 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.7328 | −1.24947 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.93332 | 0.0784710 | 0.0392355 | − | 0.999230i | \(-0.487508\pi\) | ||||
0.0392355 | + | 0.999230i | \(0.487508\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.3256 | −0.985723 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.2656 | 2.47854 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4306 | 0.744404 | 0.372202 | − | 0.928152i | \(-0.378603\pi\) | ||||
0.372202 | + | 0.928152i | \(0.378603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.98485 | −0.362304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.5314 | 1.22915 | 0.614574 | − | 0.788859i | \(-0.289328\pi\) | ||||
0.614574 | + | 0.788859i | \(0.289328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9094 | 1.16197 | 0.580984 | − | 0.813915i | \(-0.302668\pi\) | ||||
0.580984 | + | 0.813915i | \(0.302668\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −43.9932 | −1.76539 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9665 | −0.759875 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.4238 | −0.576954 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.19580 | 0.0876919 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3963 | 0.773382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.5314 | 1.29505 | 0.647527 | − | 0.762042i | \(-0.275803\pi\) | ||||
0.647527 | + | 0.762042i | \(0.275803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 35.9340 | 1.42825 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41.0457 | 1.62885 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.53912 | −0.179846 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.30476 | 0.288972 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.1312 | −1.19011 | −0.595056 | − | 0.803684i | \(-0.702870\pi\) | ||||
−0.595056 | + | 0.803684i | \(0.702870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1752 | 0.795633 | 0.397817 | − | 0.917465i | \(-0.369768\pi\) | ||||
0.397817 | + | 0.917465i | \(0.369768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.13224 | −0.359582 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.2741 | 0.561174 | 0.280587 | − | 0.959829i | \(-0.409471\pi\) | ||||
0.280587 | + | 0.959829i | \(0.409471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.0081 | −0.510614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.7951 | −1.24615 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.21538 | 0.360626 | 0.180313 | − | 0.983609i | \(-0.442289\pi\) | ||||
0.180313 | + | 0.983609i | \(0.442289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.13666 | 0.122560 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.53027 | 0.137729 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1511 | −0.473339 | −0.236669 | − | 0.971590i | \(-0.576056\pi\) | ||||
−0.236669 | + | 0.971590i | \(0.576056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6924 | 0.532574 | 0.266287 | − | 0.963894i | \(-0.414203\pi\) | ||||
0.266287 | + | 0.963894i | \(0.414203\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.7318 | 1.19352 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.52927 | 0.330751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −49.2096 | −1.90540 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.7346 | −0.453687 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.18124 | −0.354438 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.5341 | 1.56247 | 0.781237 | − | 0.624234i | \(-0.214589\pi\) | ||||
0.781237 | + | 0.624234i | \(0.214589\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 36.7172 | 1.41325 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.5653 | 0.444492 | 0.222246 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222246 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0504 | 0.462452 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.08340 | −0.348077 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.2625 | 1.69366 | 0.846828 | − | 0.531866i | \(-0.178509\pi\) | ||||
0.846828 | + | 0.531866i | \(0.178509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.79064 | −0.0684168 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.8662 | 1.55914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.3387 | 0.660554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.6676 | −1.24274 | −0.621368 | − | 0.783519i | \(-0.713423\pi\) | ||||
−0.621368 | + | 0.783519i | \(0.713423\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.97730 | 0.0751116 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4275 | −0.585197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.34391 | −0.202415 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.47214 | −0.131328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.73150 | −0.329784 | −0.164892 | − | 0.986312i | \(-0.552728\pi\) | ||||
−0.164892 | + | 0.986312i | \(0.552728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.13124 | −0.231244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −52.3816 | −1.97280 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.6816 | −1.52999 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3058 | 0.537264 | 0.268632 | − | 0.963243i | \(-0.413428\pi\) | ||||
0.268632 | + | 0.963243i | \(0.413428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.31991 | 0.237015 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −64.3200 | −2.40880 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29.7964 | −1.11432 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.6934 | −0.474045 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4959 | −0.801663 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.2543 | 0.717069 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −40.5250 | −1.50714 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.0709 | 1.52533 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.6002 | −1.76539 | −0.882696 | − | 0.469944i | \(-0.844274\pi\) | ||||
−0.882696 | + | 0.469944i | \(0.844274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.43158 | −0.200894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.7239 | −1.83659 | −0.918297 | − | 0.395892i | \(-0.870435\pi\) | ||||
−0.918297 | + | 0.395892i | \(0.870435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.88091 | 0.143149 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.63280 | −0.0969805 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.5283 | 1.30693 | 0.653464 | − | 0.756957i | \(-0.273315\pi\) | ||||
0.653464 | + | 0.756957i | \(0.273315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.71443 | −0.356869 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.3612 | 0.746979 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −64.6194 | −2.36747 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.01315 | −0.0370693 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.7699 | −1.08777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.9868 | 0.692840 | 0.346420 | − | 0.938080i | \(-0.387397\pi\) | ||||
0.346420 | + | 0.938080i | \(0.387397\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.40074 | 0.0874880 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3342 | 0.812824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4738 | −0.816826 | −0.408413 | − | 0.912797i | \(-0.633918\pi\) | ||||
−0.408413 | + | 0.912797i | \(0.633918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −17.3693 | −0.630466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.40973 | −0.0511028 | −0.0255514 | − | 0.999674i | \(-0.508134\pi\) | ||||
−0.0255514 | + | 0.999674i | \(0.508134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1602 | −0.512634 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.05100 | 0.218774 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.5492 | 2.07798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.114116 | −0.00411512 | −0.00205756 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205756 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.578272 | 0.0208260 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.1799 | −1.66097 | −0.830487 | − | 0.557038i | \(-0.811938\pi\) | ||||
−0.830487 | + | 0.557038i | \(0.811938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 53.6822 | 1.92832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.9746 | 0.860084 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.68923 | 0.0605228 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.2916 | 0.654525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 34.5985 | 1.23645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 59.8297 | 2.13541 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6847 | 0.452159 | 0.226080 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226080 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.5238 | 1.05108 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.0667 | −0.784601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.6186 | 1.44241 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.8245 | −0.525770 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.2796 | 1.39135 | 0.695677 | − | 0.718355i | \(-0.255105\pi\) | ||||
0.695677 | + | 0.718355i | \(0.255105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.1549 | −1.10218 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.25335 | 0.150285 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.84004 | 0.311958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −67.4685 | −2.37795 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.7197 | 0.834971 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.09896 | −0.0386374 | −0.0193187 | − | 0.999813i | \(-0.506150\pi\) | ||||
−0.0193187 | + | 0.999813i | \(0.506150\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.5627 | 1.28389 | 0.641944 | − | 0.766751i | \(-0.278128\pi\) | ||||
0.641944 | + | 0.766751i | \(0.278128\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 44.3522 | 1.55550 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −78.1496 | −2.73746 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.71694 | 0.0600681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.74777 | −0.305672 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8823 | −0.624097 | −0.312049 | − | 0.950066i | \(-0.601015\pi\) | ||||
−0.312049 | + | 0.950066i | \(0.601015\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.31328 | −0.289783 | −0.144891 | − | 0.989448i | \(-0.546283\pi\) | ||||
−0.144891 | + | 0.989448i | \(0.546283\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.4966 | 0.504708 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.280204 | 0.00974363 | 0.00487182 | − | 0.999988i | \(-0.498449\pi\) | ||||
0.00487182 | + | 0.999988i | \(0.498449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.04148 | 0.209829 | 0.104915 | − | 0.994481i | \(-0.466543\pi\) | ||||
0.104915 | + | 0.994481i | \(0.466543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −44.4491 | −1.54192 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.30824 | 0.0799759 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.2756 | 0.736274 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 45.2223 | 1.56311 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.5942 | 1.02171 | 0.510853 | − | 0.859668i | \(-0.329330\pi\) | ||||
0.510853 | + | 0.859668i | \(0.329330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.70093 | 0.334515 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.3796 | 1.45963 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 87.5416 | 3.01152 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.5934 | −0.776320 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 42.0241 | 1.44226 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.4996 | 1.66254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.2331 | 0.521570 | 0.260785 | − | 0.965397i | \(-0.416019\pi\) | ||||
0.260785 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.91274 | −0.0654144 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.25535 | −0.0770412 | −0.0385206 | − | 0.999258i | \(-0.512265\pi\) | ||||
−0.0385206 | + | 0.999258i | \(0.512265\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.91686 | −0.0654025 | −0.0327013 | − | 0.999465i | \(-0.510411\pi\) | ||||
−0.0327013 | + | 0.999465i | \(0.510411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.60527 | −0.225107 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.8530 | −1.22045 | −0.610225 | − | 0.792228i | \(-0.708921\pi\) | ||||
−0.610225 | + | 0.792228i | \(0.708921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.7126 | −1.96229 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.9186 | 0.370814 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.8255 | 0.536843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6478 | 0.394669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.70238 | −0.0914617 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.6636 | 0.461915 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.2323 | 1.62869 | 0.814344 | − | 0.580383i | \(-0.197097\pi\) | ||||
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.0394 | −0.540994 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.77336 | 0.160819 | 0.0804094 | − | 0.996762i | \(-0.474377\pi\) | ||||
0.0804094 | + | 0.996762i | \(0.474377\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.2144 | −0.747573 | −0.373787 | − | 0.927515i | \(-0.621941\pi\) | ||||
−0.373787 | + | 0.927515i | \(0.621941\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −49.2041 | −1.65398 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.1729 | 1.41603 | 0.708014 | − | 0.706198i | \(-0.249591\pi\) | ||||
0.708014 | + | 0.706198i | \(0.249591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.1750 | 1.01204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.84316 | 0.329758 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.84818 | 0.329557 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62.1496 | 2.07743 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 76.8434 | 2.56573 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.5845 | 1.68709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.81714 | −0.293742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.71363 | −0.223416 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.2202 | 1.23724 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.7564 | −0.888430 | −0.444215 | − | 0.895920i | \(-0.646517\pi\) | ||||
−0.444215 | + | 0.895920i | \(0.646517\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.12311 | 0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1281 | −0.368691 | −0.184346 | − | 0.982861i | \(-0.559017\pi\) | ||||
−0.184346 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.53700 | −0.0839625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.7286 | −1.14809 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.30594 | 0.0761489 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.45195 | −0.179843 | −0.0899216 | − | 0.995949i | \(-0.528662\pi\) | ||||
−0.0899216 | + | 0.995949i | \(0.528662\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.89918 | −0.260287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −80.9237 | −2.66364 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.4783 | −1.33092 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.31791 | −0.141819 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.94402 | −0.0637813 | −0.0318906 | − | 0.999491i | \(-0.510153\pi\) | ||||
−0.0318906 | + | 0.999491i | \(0.510153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.729644 | −0.0239131 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.9595 | 0.686184 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.1521 | 0.495527 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2897 | −0.368820 | −0.184410 | − | 0.982849i | \(-0.559037\pi\) | ||||
−0.184410 | + | 0.982849i | \(0.559037\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.8372 | −0.353658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.4229 | 1.67634 | 0.838170 | − | 0.545409i | \(-0.183626\pi\) | ||||
0.838170 | + | 0.545409i | \(0.183626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3622 | −0.435133 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 47.4360 | 1.54309 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.94045 | −0.0630563 | −0.0315281 | − | 0.999503i | \(-0.510037\pi\) | ||||
−0.0315281 | + | 0.999503i | \(0.510037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.1092 | −1.26954 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.75169 | −0.283793 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.4523 | −0.759693 | −0.379847 | − | 0.925049i | \(-0.624023\pi\) | ||||
−0.379847 | + | 0.925049i | \(0.624023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52.8371 | −1.70977 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.6601 | 0.441569 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31640 | −0.0425088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.1171 | 1.13281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.67608 | 0.215134 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −32.5804 | −1.04880 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.0194 | 1.89794 | 0.948968 | − | 0.315373i | \(-0.102130\pi\) | ||||
0.948968 | + | 0.315373i | \(0.102130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.94001 | 0.158696 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.7743 | 1.27642 | 0.638209 | − | 0.769863i | \(-0.279676\pi\) | ||||
0.638209 | + | 0.769863i | \(0.279676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3416 | −0.363595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −64.1344 | −2.05394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.9538 | −1.34222 | −0.671111 | − | 0.741357i | \(-0.734183\pi\) | ||||
−0.671111 | + | 0.741357i | \(0.734183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6507 | 0.340397 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.17552 | 0.101386 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.93132 | 0.252970 | 0.126485 | − | 0.991969i | \(-0.459630\pi\) | ||||
0.126485 | + | 0.991969i | \(0.459630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.1919 | 2.07719 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −38.5087 | −1.22575 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.5814 | −0.431863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8408 | 0.789093 | 0.394546 | − | 0.918876i | \(-0.370902\pi\) | ||||
0.394546 | + | 0.918876i | \(0.370902\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.42017 | −0.203738 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.455573 | −0.0144426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1157 | 0.890433 | 0.445216 | − | 0.895423i | \(-0.353127\pi\) | ||||
0.445216 | + | 0.895423i | \(0.353127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.0992 | −1.07885 |
(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 | 608.2.a.j.1.2 | yes | 4 | |
3.2 | odd | 2 | 5472.2.a.bs.1.1 | 4 | |||
4.3 | odd | 2 | 608.2.a.i.1.4 | ✓ | 4 | ||
8.3 | odd | 2 | 1216.2.a.x.1.1 | 4 | |||
8.5 | even | 2 | 1216.2.a.w.1.3 | 4 | |||
12.11 | even | 2 | 5472.2.a.bt.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.i.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
608.2.a.j.1.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1216.2.a.w.1.3 | 4 | 8.5 | even | 2 | |||
1216.2.a.x.1.1 | 4 | 8.3 | odd | 2 | |||
5472.2.a.bs.1.1 | 4 | 3.2 | odd | 2 | |||
5472.2.a.bt.1.1 | 4 | 12.11 | even | 2 |