Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.242773.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 7x^{3} + 4x^{2} + 6x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 502) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.71702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.71702 | 1.56867 | 0.784336 | − | 0.620336i | \(-0.213004\pi\) | ||||
0.784336 | + | 0.620336i | \(0.213004\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20324 | −0.985319 | −0.492660 | − | 0.870222i | \(-0.663975\pi\) | ||||
−0.492660 | + | 0.870222i | \(0.663975\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45833 | −0.929160 | −0.464580 | − | 0.885531i | \(-0.653795\pi\) | ||||
−0.464580 | + | 0.885531i | \(0.653795\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.38220 | 1.46073 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.626744 | −0.188970 | −0.0944852 | − | 0.995526i | \(-0.530120\pi\) | ||||
−0.0944852 | + | 0.995526i | \(0.530120\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.36311 | 0.655410 | 0.327705 | − | 0.944780i | \(-0.393725\pi\) | ||||
0.327705 | + | 0.944780i | \(0.393725\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.98625 | −1.54564 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70155 | −0.412686 | −0.206343 | − | 0.978480i | \(-0.566156\pi\) | ||||
−0.206343 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.16481 | −0.267226 | −0.133613 | − | 0.991034i | \(-0.542658\pi\) | ||||
−0.133613 | + | 0.991034i | \(0.542658\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.67932 | −1.45755 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.01908 | 0.838036 | 0.419018 | − | 0.907978i | \(-0.362374\pi\) | ||||
0.419018 | + | 0.907978i | \(0.362374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.145728 | −0.0291456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.75545 | 0.722737 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.57129 | −1.03456 | −0.517281 | − | 0.855815i | \(-0.673056\pi\) | ||||
−0.517281 | + | 0.855815i | \(0.673056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.20191 | −0.215870 | −0.107935 | − | 0.994158i | \(-0.534424\pi\) | ||||
−0.107935 | + | 0.994158i | \(0.534424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.70287 | −0.296432 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.41629 | 0.915519 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.8149 | −1.77796 | −0.888980 | − | 0.457946i | \(-0.848585\pi\) | ||||
−0.888980 | + | 0.457946i | \(0.848585\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.42063 | 1.02812 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.14126 | 0.490582 | 0.245291 | − | 0.969450i | \(-0.421117\pi\) | ||||
0.245291 | + | 0.969450i | \(0.421117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.97210 | 0.605740 | 0.302870 | − | 0.953032i | \(-0.402055\pi\) | ||||
0.302870 | + | 0.953032i | \(0.402055\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.65503 | −1.43929 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.37859 | −0.346953 | −0.173476 | − | 0.984838i | \(-0.555500\pi\) | ||||
−0.173476 | + | 0.984838i | \(0.555500\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.956632 | −0.136662 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.62314 | −0.647368 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.2463 | −1.81952 | −0.909758 | − | 0.415140i | \(-0.863733\pi\) | ||||
−0.909758 | + | 0.415140i | \(0.863733\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.38087 | 0.186196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.16481 | −0.419189 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.59425 | 0.337743 | 0.168871 | − | 0.985638i | \(-0.445988\pi\) | ||||
0.168871 | + | 0.985638i | \(0.445988\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.891376 | 0.114129 | 0.0570645 | − | 0.998370i | \(-0.481826\pi\) | ||||
0.0570645 | + | 0.998370i | \(0.481826\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.7729 | −1.35725 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.20651 | −0.645788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.69273 | −0.328970 | −0.164485 | − | 0.986380i | \(-0.552596\pi\) | ||||
−0.164485 | + | 0.986380i | \(0.552596\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.9199 | 1.31460 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5924 | −1.37576 | −0.687880 | − | 0.725824i | \(-0.741459\pi\) | ||||
−0.687880 | + | 0.725824i | \(0.741459\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.11857 | −0.716124 | −0.358062 | − | 0.933698i | \(-0.616562\pi\) | ||||
−0.358062 | + | 0.933698i | \(0.616562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.395946 | −0.0457199 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.54074 | 0.175584 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.82465 | −0.205290 | −0.102645 | − | 0.994718i | \(-0.532731\pi\) | ||||
−0.102645 | + | 0.994718i | \(0.532731\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.94295 | −0.326994 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.7422 | 1.39863 | 0.699317 | − | 0.714812i | \(-0.253488\pi\) | ||||
0.699317 | + | 0.714812i | \(0.253488\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.74892 | 0.406627 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.1373 | −1.62289 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.93573 | 0.947186 | 0.473593 | − | 0.880744i | \(-0.342957\pi\) | ||||
0.473593 | + | 0.880744i | \(0.342957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.80931 | −0.608981 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.26562 | −0.338629 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56636 | 0.263303 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.22438 | −0.428921 | −0.214461 | − | 0.976733i | \(-0.568799\pi\) | ||||
−0.214461 | + | 0.976733i | \(0.568799\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.74651 | −0.276035 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4203 | −1.23586 | −0.617932 | − | 0.786231i | \(-0.712029\pi\) | ||||
−0.617932 | + | 0.786231i | \(0.712029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.45378 | 0.931509 | 0.465755 | − | 0.884914i | \(-0.345783\pi\) | ||||
0.465755 | + | 0.884914i | \(0.345783\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.7162 | 1.43615 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.05091 | 0.778311 | 0.389155 | − | 0.921172i | \(-0.372767\pi\) | ||||
0.389155 | + | 0.921172i | \(0.372767\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.57817 | 0.821640 | 0.410820 | − | 0.911717i | \(-0.365243\pi\) | ||||
0.410820 | + | 0.911717i | \(0.365243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −29.3843 | −2.78904 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.06827 | −0.288638 | −0.144319 | − | 0.989531i | \(-0.546099\pi\) | ||||
−0.144319 | + | 0.989531i | \(0.546099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.85501 | −0.825734 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3556 | 0.957378 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.18296 | 0.383451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6072 | −0.964290 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.53485 | 0.769562 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3373 | 1.01404 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.0241 | −1.42191 | −0.710954 | − | 0.703239i | \(-0.751737\pi\) | ||||
−0.710954 | + | 0.703239i | \(0.751737\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7923 | 0.950208 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3865 | −0.994840 | −0.497420 | − | 0.867510i | \(-0.665719\pi\) | ||||
−0.497420 | + | 0.867510i | \(0.665719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.86348 | 0.248295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.27417 | −0.712127 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3251 | 0.967567 | 0.483783 | − | 0.875188i | \(-0.339262\pi\) | ||||
0.483783 | + | 0.875188i | \(0.339262\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7412 | −0.911060 | −0.455530 | − | 0.890220i | \(-0.650550\pi\) | ||||
−0.455530 | + | 0.890220i | \(0.650550\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.46267 | −0.544255 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.48107 | −0.123853 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.2749 | 1.01937 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.59919 | −0.214377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.5934 | −1.44131 | −0.720655 | − | 0.693294i | \(-0.756159\pi\) | ||||
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.1563 | 1.72167 | 0.860836 | − | 0.508883i | \(-0.169941\pi\) | ||||
0.860836 | + | 0.508883i | \(0.169941\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.45651 | −0.602823 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.64810 | 0.212701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.3583 | −1.94400 | −0.972002 | − | 0.234972i | \(-0.924500\pi\) | ||||
−0.972002 | + | 0.234972i | \(0.924500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −35.9904 | −2.85422 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.88021 | −0.778670 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.4677 | 1.44650 | 0.723249 | − | 0.690587i | \(-0.242648\pi\) | ||||
0.723249 | + | 0.690587i | \(0.242648\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.75184 | 0.292081 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5586 | −0.817049 | −0.408524 | − | 0.912747i | \(-0.633957\pi\) | ||||
−0.408524 | + | 0.912747i | \(0.633957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.41569 | −0.570438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.10442 | −0.390345 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9856 | −1.13933 | −0.569667 | − | 0.821876i | \(-0.692928\pi\) | ||||
−0.569667 | + | 0.821876i | \(0.692928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.358247 | 0.0270809 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.04863 | 0.529807 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.59403 | −0.343374 | −0.171687 | − | 0.985152i | \(-0.554922\pi\) | ||||
−0.171687 | + | 0.985152i | \(0.554922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.46292 | 0.183068 | 0.0915338 | − | 0.995802i | \(-0.470823\pi\) | ||||
0.0915338 | + | 0.995802i | \(0.470823\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.42189 | 0.179031 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.8278 | 1.75186 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.06643 | 0.0779853 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.23213 | −0.671538 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.9040 | 1.00606 | 0.503028 | − | 0.864270i | \(-0.332219\pi\) | ||||
0.503028 | + | 0.864270i | \(0.332219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.786222 | −0.0565935 | −0.0282967 | − | 0.999600i | \(-0.509008\pi\) | ||||
−0.0282967 | + | 0.999600i | \(0.509008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.1462 | −1.01303 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.95082 | 0.423978 | 0.211989 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211989 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.0310 | −1.06552 | −0.532758 | − | 0.846267i | \(-0.678845\pi\) | ||||
−0.532758 | + | 0.846267i | \(0.678845\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.31621 | −0.516045 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.6961 | 0.961274 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.92094 | −0.483380 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.6124 | 1.22415 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.730037 | 0.0504977 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.12711 | 0.490651 | 0.245325 | − | 0.969441i | \(-0.421105\pi\) | ||||
0.245325 | + | 0.969441i | \(0.421105\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.4967 | −2.15812 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.75150 | −0.596848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.95470 | 0.200578 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.6243 | −1.12336 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.02095 | −0.270478 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.1880 | −1.35189 | −0.675945 | − | 0.736952i | \(-0.736264\pi\) | ||||
−0.675945 | + | 0.736952i | \(0.736264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.638608 | −0.0425739 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.351443 | −0.0233261 | −0.0116630 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116630 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1399 | −0.736147 | −0.368074 | − | 0.929797i | \(-0.619983\pi\) | ||||
−0.368074 | + | 0.929797i | \(0.619983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.18622 | 0.275433 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.93861 | −0.127002 | −0.0635012 | − | 0.997982i | \(-0.520227\pi\) | ||||
−0.0635012 | + | 0.997982i | \(0.520227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.24060 | 0.341859 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.95762 | −0.322032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.9507 | 1.80798 | 0.903989 | − | 0.427555i | \(-0.140625\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.52706 | 0.0983665 | 0.0491832 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491832 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.2624 | −1.23568 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.10769 | 0.134655 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.75258 | −0.175142 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 34.6207 | 2.19400 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.51893 | −0.158364 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.1859 | 0.637865 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.1502 | −1.06980 | −0.534900 | − | 0.844915i | \(-0.679651\pi\) | ||||
−0.534900 | + | 0.844915i | \(0.679651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.5866 | 1.65201 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.4145 | −1.51122 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.67331 | −0.534819 | −0.267410 | − | 0.963583i | \(-0.586168\pi\) | ||||
−0.267410 | + | 0.963583i | \(0.586168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.1847 | 1.79280 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.2786 | 1.48582 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.5263 | 1.06860 | 0.534299 | − | 0.845296i | \(-0.320576\pi\) | ||||
0.534299 | + | 0.845296i | \(0.320576\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.3676 | −1.29799 | −0.648994 | − | 0.760793i | \(-0.724810\pi\) | ||||
−0.648994 | + | 0.760793i | \(0.724810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −15.7840 | −0.955291 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.0913341 | 0.00550765 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.52213 | −0.151540 | −0.0757700 | − | 0.997125i | \(-0.524141\pi\) | ||||
−0.0757700 | + | 0.997125i | \(0.524141\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.26702 | −0.315328 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.12510 | 0.186428 | 0.0932139 | − | 0.995646i | \(-0.470286\pi\) | ||||
0.0932139 | + | 0.995646i | \(0.470286\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.34841 | −0.317930 | −0.158965 | − | 0.987284i | \(-0.550816\pi\) | ||||
−0.158965 | + | 0.987284i | \(0.550816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.97284 | 0.413035 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.72223 | −0.455829 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.1047 | −0.829691 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4777 | −0.672837 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.8829 | 0.986310 | 0.493155 | − | 0.869941i | \(-0.335844\pi\) | ||||
0.493155 | + | 0.869941i | \(0.335844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.71576 | −0.332784 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.35371 | −0.136576 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.49755 | 0.549257 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.76473 | −0.562830 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.7462 | −1.93867 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.96392 | −0.112454 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.42984 | 0.0816051 | 0.0408025 | − | 0.999167i | \(-0.487009\pi\) | ||||
0.0408025 | + | 0.999167i | \(0.487009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.6861 | 1.46123 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.8314 | 1.29465 | 0.647324 | − | 0.762215i | \(-0.275888\pi\) | ||||
0.647324 | + | 0.762215i | \(0.275888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5505 | 0.992011 | 0.496006 | − | 0.868319i | \(-0.334800\pi\) | ||||
0.496006 | + | 0.868319i | \(0.334800\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.7352 | 1.33733 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.4561 | 1.42976 | 0.714879 | − | 0.699248i | \(-0.246482\pi\) | ||||
0.714879 | + | 0.699248i | \(0.246482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.49177 | 0.195502 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.8745 | 1.22091 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.98198 | 0.110280 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.344372 | −0.0191023 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.3071 | 1.28888 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.84734 | 0.322374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.40015 | 0.241854 | 0.120927 | − | 0.992661i | \(-0.461413\pi\) | ||||
0.120927 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −47.3930 | −2.59712 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.93274 | 0.324140 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.63055 | 0.361189 | 0.180595 | − | 0.983558i | \(-0.442198\pi\) | ||||
0.180595 | + | 0.983558i | \(0.442198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.33655 | −0.452779 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.753291 | 0.0407930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5600 | 1.05614 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.0592 | −1.29531 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4024 | 0.773159 | 0.386580 | − | 0.922256i | \(-0.373656\pi\) | ||||
0.386580 | + | 0.922256i | \(0.373656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.4842 | 0.882380 | 0.441190 | − | 0.897414i | \(-0.354557\pi\) | ||||
0.441190 | + | 0.897414i | \(0.354557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.87456 | 0.473689 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.46606 | 0.503827 | 0.251914 | − | 0.967750i | \(-0.418940\pi\) | ||||
0.251914 | + | 0.967750i | \(0.418940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.5408 | 1.35556 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.3652 | 0.601509 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.7828 | 1.46632 | 0.733160 | − | 0.680057i | \(-0.238045\pi\) | ||||
0.733160 | + | 0.680057i | \(0.238045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6432 | −0.928591 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −28.8199 | −1.51266 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4807 | 0.705611 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.7430 | −1.08277 | −0.541387 | − | 0.840774i | \(-0.682100\pi\) | ||||
−0.541387 | + | 0.840774i | \(0.682100\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.7656 | 0.716608 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.5637 | 1.69062 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.38553 | 0.434187 | 0.217093 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217093 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.8036 | 1.59069 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.1656 | −0.678063 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.80599 | −0.0927672 | −0.0463836 | − | 0.998924i | \(-0.514770\pi\) | ||||
−0.0463836 | + | 0.998924i | \(0.514770\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.5378 | −2.23051 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0809 | 0.821697 | 0.410848 | − | 0.911704i | \(-0.365233\pi\) | ||||
0.410848 | + | 0.911704i | \(0.365233\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.39462 | −0.173006 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.4065 | 0.884824 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.4083 | 1.89668 | 0.948339 | − | 0.317259i | \(-0.102762\pi\) | ||||
0.948339 | + | 0.317259i | \(0.102762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.83865 | −0.345846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −30.9373 | −1.56058 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.02015 | 0.202276 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8883 | 1.19892 | 0.599461 | − | 0.800404i | \(-0.295382\pi\) | ||||
0.599461 | + | 0.800404i | \(0.295382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.78013 | 0.389494 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.6539 | 1.63066 | 0.815329 | − | 0.578997i | \(-0.196556\pi\) | ||||
0.815329 | + | 0.578997i | \(0.196556\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.84026 | −0.141483 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.48403 | 0.322194 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.77817 | 0.335982 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.586640 | −0.0290075 | −0.0145037 | − | 0.999895i | \(-0.504617\pi\) | ||||
−0.0145037 | + | 0.999895i | \(0.504617\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.7705 | 1.51779 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.37752 | −0.313817 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.0741 | −1.37810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.1842 | −1.42915 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.6938 | −1.20637 | −0.603185 | − | 0.797601i | \(-0.706102\pi\) | ||||
−0.603185 | + | 0.797601i | \(0.706102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.3992 | 1.87146 | 0.935731 | − | 0.352714i | \(-0.114741\pi\) | ||||
0.935731 | + | 0.352714i | \(0.114741\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.4234 | −0.506805 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.247963 | 0.0120280 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.19129 | −0.106044 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.02409 | −0.194285 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1175 | 0.583679 | 0.291840 | − | 0.956467i | \(-0.405733\pi\) | ||||
0.291840 | + | 0.956467i | \(0.405733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.18656 | 0.441478 | 0.220739 | − | 0.975333i | \(-0.429153\pi\) | ||||
0.220739 | + | 0.975333i | \(0.429153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 33.3511 | 1.59906 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.68146 | −0.223945 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.5692 | 0.790806 | 0.395403 | − | 0.918508i | \(-0.370605\pi\) | ||||
0.395403 | + | 0.918508i | \(0.370605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.19215 | −0.199626 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.6364 | −1.17051 | −0.585255 | − | 0.810849i | \(-0.699006\pi\) | ||||
−0.585255 | + | 0.810849i | \(0.699006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.6876 | −0.933281 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −47.8017 | −2.26094 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9412 | 1.46021 | 0.730103 | − | 0.683337i | \(-0.239472\pi\) | ||||
0.730103 | + | 0.683337i | \(0.239472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.96876 | −0.0927054 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 57.4820 | 2.70074 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.7993 | 0.600041 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.8381 | 1.44255 | 0.721273 | − | 0.692651i | \(-0.243557\pi\) | ||||
0.721273 | + | 0.692651i | \(0.243557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.39008 | −0.298263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.6619 | −1.42807 | −0.714033 | − | 0.700112i | \(-0.753133\pi\) | ||||
−0.714033 | + | 0.700112i | \(0.753133\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.9205 | 1.90173 | 0.950867 | − | 0.309598i | \(-0.100195\pi\) | ||||
0.950867 | + | 0.309598i | \(0.100195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.19495 | 0.333658 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5509 | −1.18236 | −0.591178 | − | 0.806541i | \(-0.701337\pi\) | ||||
−0.591178 | + | 0.806541i | \(0.701337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.61961 | 0.305665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −66.1820 | −3.04950 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.48949 | −0.114467 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.169745 | 0.00778845 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −58.0477 | −2.65782 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8475 | 0.541324 | 0.270662 | − | 0.962674i | \(-0.412757\pi\) | ||||
0.270662 | + | 0.962674i | \(0.412757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.5569 | −1.16529 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.8447 | −1.22148 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.30734 | 0.422624 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.07419 | 0.229933 | 0.114967 | − | 0.993369i | \(-0.463324\pi\) | ||||
0.114967 | + | 0.993369i | \(0.463324\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 50.1770 | 2.26908 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.5821 | −1.87658 | −0.938288 | − | 0.345856i | \(-0.887589\pi\) | ||||
−0.938288 | + | 0.345856i | \(0.887589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.47981 | 0.426949 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.05123 | 0.271983 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.4978 | 1.27830 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.6802 | −1.55250 | −0.776250 | − | 0.630425i | \(-0.782881\pi\) | ||||
−0.776250 | + | 0.630425i | \(0.782881\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.6879 | −1.28168 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.2335 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.3649 | 1.21772 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.1486 | −0.894830 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.3844 | 0.504604 | 0.252302 | − | 0.967649i | \(-0.418812\pi\) | ||||
0.252302 | + | 0.967649i | \(0.418812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.0414 | 0.665394 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.37438 | −0.193134 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.8290 | −0.917834 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.49076 | 0.0655637 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −40.7161 | −1.78724 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3861 | −0.586456 | −0.293228 | − | 0.956043i | \(-0.594729\pi\) | ||||
−0.293228 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.2928 | 1.23716 | 0.618580 | − | 0.785722i | \(-0.287708\pi\) | ||||
0.618580 | + | 0.785722i | \(0.287708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.973364 | 0.0424811 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.04511 | 0.0890865 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.84699 | −0.297695 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.3685 | 0.493351 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.42314 | 0.321532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.7381 | −0.766885 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.4821 | −0.538641 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.599563 | 0.0258250 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.1435 | −1.85488 | −0.927442 | − | 0.373967i | \(-0.877997\pi\) | ||||
−0.927442 | + | 0.373967i | \(0.877997\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.69181 | 0.287173 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.8998 | −0.809577 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.56283 | 0.152336 | 0.0761679 | − | 0.997095i | \(-0.475731\pi\) | ||||
0.0761679 | + | 0.997095i | \(0.475731\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.90618 | 0.166712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.48949 | 0.276462 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.48560 | 0.190747 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 64.7407 | 2.74809 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.3898 | −1.75374 | −0.876872 | − | 0.480724i | \(-0.840374\pi\) | ||||
−0.876872 | + | 0.480724i | \(0.840374\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.38654 | 0.397008 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.89752 | 0.122333 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.18917 | 0.0922625 | 0.0461313 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461313 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.76014 | 0.284401 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.23473 | 0.303830 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.6584 | 0.488747 | 0.244373 | − | 0.969681i | \(-0.421418\pi\) | ||||
0.244373 | + | 0.969681i | \(0.421418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0137 | −0.586456 | −0.293228 | − | 0.956043i | \(-0.594729\pi\) | ||||
−0.293228 | + | 0.956043i | \(0.594729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.7773 | 1.57817 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.585692 | −0.0244251 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.4746 | −1.26867 | −0.634337 | − | 0.773057i | \(-0.718727\pi\) | ||||
−0.634337 | + | 0.773057i | \(0.718727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.13618 | −0.0887766 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.3244 | −1.29956 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.30202 | 0.343834 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.8159 | −0.943323 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.45165 | −0.266288 | −0.133144 | − | 0.991097i | \(-0.542507\pi\) | ||||
−0.133144 | + | 0.991097i | \(0.542507\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.40000 | 0.0576860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.1685 | 0.665083 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.47035 | −0.0603802 | −0.0301901 | − | 0.999544i | \(-0.509611\pi\) | ||||
−0.0301901 | + | 0.999544i | \(0.509611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.21606 | −0.377822 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −40.8394 | −1.67145 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.8677 | 1.54723 | 0.773616 | − | 0.633655i | \(-0.218446\pi\) | ||||
0.773616 | + | 0.633655i | \(0.218446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.6304 | −1.65735 | −0.828675 | − | 0.559730i | \(-0.810905\pi\) | ||||
−0.828675 | + | 0.559730i | \(0.810905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.8001 | −0.480536 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.3702 | 0.950134 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.8417 | 1.65771 | 0.828857 | − | 0.559460i | \(-0.188992\pi\) | ||||
0.828857 | + | 0.559460i | \(0.188992\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 37.2124 | 1.50792 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.62087 | −0.227396 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9266 | 0.845216 | 0.422608 | − | 0.906313i | \(-0.361115\pi\) | ||||
0.422608 | + | 0.906313i | \(0.361115\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.8043 | −0.758264 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.4425 | −0.500917 | −0.250458 | − | 0.968127i | \(-0.580581\pi\) | ||||
−0.250458 | + | 0.968127i | \(0.580581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.47560 | 0.179890 | 0.0899448 | − | 0.995947i | \(-0.471331\pi\) | ||||
0.0899448 | + | 0.995947i | \(0.471331\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0935 | 0.605680 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.9669 | −0.880087 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2501 | −0.970005 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.98352 | 0.0792143 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.4021 | 0.733738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.47879 | −0.178298 | −0.0891488 | − | 0.996018i | \(-0.528415\pi\) | ||||
−0.0891488 | + | 0.996018i | \(0.528415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3645 | 0.769670 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 35.3049 | 1.40103 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.26063 | −0.0895694 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −50.8000 | −2.00962 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.20664 | −0.126655 | −0.0633274 | − | 0.997993i | \(-0.520171\pi\) | ||||
−0.0633274 | + | 0.997993i | \(0.520171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.8300 | 1.09751 | 0.548753 | − | 0.835984i | \(-0.315103\pi\) | ||||
0.548753 | + | 0.835984i | \(0.315103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.7780 | −0.936258 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.44508 | −0.253382 | −0.126691 | − | 0.991942i | \(-0.540436\pi\) | ||||
−0.126691 | + | 0.991942i | \(0.540436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.62593 | −0.0638233 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.02796 | 0.314641 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4765 | 0.840442 | 0.420221 | − | 0.907422i | \(-0.361953\pi\) | ||||
0.420221 | + | 0.907422i | \(0.361953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.0871 | 0.980236 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.8128 | −1.04607 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.90000 | 0.190877 | 0.0954385 | − | 0.995435i | \(-0.469575\pi\) | ||||
0.0954385 | + | 0.995435i | \(0.469575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00081 | 0.194509 | 0.0972546 | − | 0.995260i | \(-0.468994\pi\) | ||||
0.0972546 | + | 0.995260i | \(0.468994\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.9250 | −0.424292 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.30894 | −0.244650 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.3915 | −0.867001 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −54.8512 | −2.12067 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.558664 | −0.0215670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.9370 | −1.26963 | −0.634813 | − | 0.772665i | \(-0.718923\pi\) | ||||
−0.634813 | + | 0.772665i | \(0.718923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.547274 | −0.0210646 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.4198 | 1.01539 | 0.507697 | − | 0.861536i | \(-0.330497\pi\) | ||||
0.507697 | + | 0.861536i | \(0.330497\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.3849 | 0.398536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.954877 | −0.0365910 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0624 | −0.920723 | −0.460362 | − | 0.887731i | \(-0.652280\pi\) | ||||
−0.460362 | + | 0.887731i | \(0.652280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24.9519 | −0.953362 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.2674 | −1.15477 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.3025 | −1.19253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.3594 | 1.00276 | 0.501379 | − | 0.865228i | \(-0.332826\pi\) | ||||
0.501379 | + | 0.865228i | \(0.332826\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.75182 | 0.256481 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6655 | 0.897685 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.34499 | −0.202456 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.26724 | −0.199225 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6977 | −1.08390 | −0.541948 | − | 0.840412i | \(-0.682313\pi\) | ||||
−0.541948 | + | 0.840412i | \(0.682313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.5973 | 0.475116 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.2388 | 0.536265 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.5331 | 1.14832 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.4638 | −0.505644 | −0.252822 | − | 0.967513i | \(-0.581359\pi\) | ||||
−0.252822 | + | 0.967513i | \(0.581359\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.99599 | −0.299873 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.83059 | −0.180907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.26315 | 0.122035 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 75.9425 | 2.83613 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9723 | 0.782135 | 0.391067 | − | 0.920362i | \(-0.372106\pi\) | ||||
0.391067 | + | 0.920362i | \(0.372106\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2405 | −0.865521 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.14905 | 0.154305 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.811893 | 0.0301529 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9166 | −0.924104 | −0.462052 | − | 0.886853i | \(-0.652887\pi\) | ||||
−0.462052 | + | 0.886853i | \(0.652887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.5075 | −1.61139 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.75872 | −0.249980 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.5799 | −1.01869 | −0.509343 | − | 0.860564i | \(-0.670112\pi\) | ||||
−0.509343 | + | 0.860564i | \(0.670112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.72664 | 0.211230 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.68765 | 0.0621655 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.3870 | −1.04423 | −0.522116 | − | 0.852874i | \(-0.674857\pi\) | ||||
−0.522116 | + | 0.852874i | \(0.674857\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.47881 | −0.274741 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.74424 | −0.174049 | −0.0870246 | − | 0.996206i | \(-0.527736\pi\) | ||||
−0.0870246 | + | 0.996206i | \(0.527736\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.7626 | 1.42015 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 55.8387 | 2.04303 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.7918 | −0.723175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.57930 | 0.130611 | 0.0653053 | − | 0.997865i | \(-0.479198\pi\) | ||||
0.0653053 | + | 0.997865i | \(0.479198\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.71702 | 0.0990137 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.6123 | −1.69640 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.2557 | −0.990626 | −0.495313 | − | 0.868714i | \(-0.664947\pi\) | ||||
−0.495313 | + | 0.868714i | \(0.664947\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.84399 | −0.248421 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.4975 | −1.21428 | −0.607141 | − | 0.794594i | \(-0.707684\pi\) | ||||
−0.607141 | + | 0.794594i | \(0.707684\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.0879 | −0.763435 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.4285 | 0.593973 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.13051 | 0.221360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.5722 | −1.75156 | −0.875778 | − | 0.482713i | \(-0.839651\pi\) | ||||
−0.875778 | + | 0.482713i | \(0.839651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −46.5974 | −1.67816 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.2684 | 0.477230 | 0.238615 | − | 0.971114i | \(-0.423307\pi\) | ||||
0.238615 | + | 0.971114i | \(0.423307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.175152 | 0.00629166 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 72.2362 | 2.59146 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.65896 | −0.131096 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.26544 | 0.259978 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.9227 | −0.747717 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 53.6672 | 1.91547 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.60077 | −0.128354 | −0.0641768 | − | 0.997939i | \(-0.520442\pi\) | ||||
−0.0641768 | + | 0.997939i | \(0.520442\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23.5656 | −0.838956 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.54281 | 0.268191 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.10642 | 0.0748013 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 79.2955 | 2.81232 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.2720 | 1.49735 | 0.748675 | − | 0.662937i | \(-0.230690\pi\) | ||||
0.748675 | + | 0.662937i | \(0.230690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.04728 | 0.143182 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.1581 | 1.38358 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.83477 | 0.135326 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.7685 | 0.767239 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 47.6193 | 1.67628 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.6696 | 1.53534 | 0.767671 | − | 0.640844i | \(-0.221415\pi\) | ||||
0.767671 | + | 0.640844i | \(0.221415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.28785 | −0.255911 | −0.127955 | − | 0.991780i | \(-0.540841\pi\) | ||||
−0.127955 | + | 0.991780i | \(0.540841\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −58.0561 | −2.03612 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.6887 | −1.42526 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.62674 | −0.161869 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.4575 | −0.889557 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.79241 | −0.132356 | −0.0661780 | − | 0.997808i | \(-0.521081\pi\) | ||||
−0.0661780 | + | 0.997808i | \(0.521081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5848 | 0.996404 | 0.498202 | − | 0.867061i | \(-0.333994\pi\) | ||||
0.498202 | + | 0.867061i | \(0.333994\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.248156 | 0.00863970 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.25556 | 0.217527 | 0.108763 | − | 0.994068i | \(-0.465311\pi\) | ||||
0.108763 | + | 0.994068i | \(0.465311\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.99888 | 0.208350 | 0.104175 | − | 0.994559i | \(-0.466780\pi\) | ||||
0.104175 | + | 0.994559i | \(0.466780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.85267 | −0.237717 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.62775 | 0.0563983 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.2631 | 0.805054 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.51373 | −0.156017 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.5373 | −0.432837 | −0.216419 | − | 0.976301i | \(-0.569438\pi\) | ||||
−0.216419 | + | 0.976301i | \(0.569438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.03929 | 0.0703204 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.49096 | 0.292444 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.3386 | 0.562063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.0759 | 0.895980 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.5317 | −0.498728 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.4660 | −1.48999 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.2563 | −1.03595 | −0.517977 | − | 0.855394i | \(-0.673315\pi\) | ||||
−0.517977 | + | 0.855394i | \(0.673315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.2463 | 0.384614 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13.7501 | 0.469695 | 0.234848 | − | 0.972032i | \(-0.424541\pi\) | ||||
0.234848 | + | 0.972032i | \(0.424541\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5314 | −0.905238 | −0.452619 | − | 0.891704i | \(-0.649510\pi\) | ||||
−0.452619 | + | 0.891704i | \(0.649510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.9815 | −0.715046 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.34872 | 0.0799514 | 0.0399757 | − | 0.999201i | \(-0.487272\pi\) | ||||
0.0399757 | + | 0.999201i | \(0.487272\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.0169 | 1.12261 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.3229 | −1.30151 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.14359 | 0.0387936 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.36323 | −0.215610 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.5121 | −0.626539 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.8707 | −0.942203 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.0685 | −1.01534 | −0.507670 | − | 0.861552i | \(-0.669493\pi\) | ||||
−0.507670 | + | 0.861552i | \(0.669493\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 45.8712 | 1.54720 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.8148 | 1.64461 | 0.822306 | − | 0.569046i | \(-0.192687\pi\) | ||||
0.822306 | + | 0.569046i | \(0.192687\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.5925 | −0.861257 | −0.430628 | − | 0.902529i | \(-0.641708\pi\) | ||||
−0.430628 | + | 0.902529i | \(0.641708\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15.5298 | −0.522030 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.1440 | 1.18002 | 0.590010 | − | 0.807396i | \(-0.299124\pi\) | ||||
0.590010 | + | 0.807396i | \(0.299124\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.3924 | 1.32118 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.84448 | 0.0617922 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.77060 | 0.0927146 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.1218 | 0.338333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.8050 | 0.861605 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.69621 | 0.223331 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.5391 | 0.750888 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −26.5310 | −0.882895 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.42642 | −0.180380 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.1004 | 0.534605 | 0.267303 | − | 0.963613i | \(-0.413868\pi\) | ||||
0.267303 | + | 0.963613i | \(0.413868\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −54.4281 | −1.80527 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.4451 | 1.43940 | 0.719700 | − | 0.694285i | \(-0.244279\pi\) | ||||
0.719700 | + | 0.694285i | \(0.244279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.98607 | −0.264300 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.33600 | −0.176403 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.9917 | 0.924366 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.79550 | −0.0592281 | −0.0296140 | − | 0.999561i | \(-0.509428\pi\) | ||||
−0.0296140 | + | 0.999561i | \(0.509428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.88489 | 0.128012 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27.3941 | −0.901687 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.57603 | 0.0518197 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.4283 | 1.36068 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.80958 | 0.256224 | 0.128112 | − | 0.991760i | \(-0.459108\pi\) | ||||
0.128112 | + | 0.991760i | \(0.459108\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.11429 | 0.0365195 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 62.0333 | 2.03088 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.34961 | −0.0768405 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.0439 | 0.818148 | 0.409074 | − | 0.912501i | \(-0.365852\pi\) | ||||
0.409074 | + | 0.912501i | \(0.365852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47.6850 | 1.55614 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.1353 | −1.17798 | −0.588988 | − | 0.808142i | \(-0.700474\pi\) | ||||
−0.588988 | + | 0.808142i | \(0.700474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.6250 | 0.411125 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.3406 | 0.661680 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.5097 | −0.796457 | −0.398229 | − | 0.917286i | \(-0.630375\pi\) | ||||
−0.398229 | + | 0.917286i | \(0.630375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4589 | −0.469355 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 69.1648 | 2.24282 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9614 | 1.32687 | 0.663435 | − | 0.748234i | \(-0.269098\pi\) | ||||
0.663435 | + | 0.748234i | \(0.269098\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.6338 | −0.991286 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.48721 | 0.306678 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27.8407 | −0.899024 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5554 | −0.953400 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 35.2807 | 1.13690 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.73224 | 0.0557627 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.7541 | −1.27841 | −0.639203 | − | 0.769038i | \(-0.720735\pi\) | ||||
−0.639203 | + | 0.769038i | \(0.720735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.38507 | 0.172993 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.1119 | 0.773788 | 0.386894 | − | 0.922124i | \(-0.373548\pi\) | ||||
0.386894 | + | 0.922124i | \(0.373548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.4055 | 0.846520 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.935665 | −0.0299653 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.53652 | 0.145136 | 0.0725680 | − | 0.997363i | \(-0.476881\pi\) | ||||
0.0725680 | + | 0.997363i | \(0.476881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.60041 | −0.178990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.5912 | 1.20020 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.03811 | −0.160691 | −0.0803453 | − | 0.996767i | \(-0.525602\pi\) | ||||
−0.0803453 | + | 0.996767i | \(0.525602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1111 | −0.417754 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.8873 | 0.505700 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.9642 | 0.507632 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.4826 | −0.364757 | −0.182379 | − | 0.983228i | \(-0.558380\pi\) | ||||
−0.182379 | + | 0.983228i | \(0.558380\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.9553 | 0.379390 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.1168 | 1.04987 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.91042 | 0.187185 | 0.0935925 | − | 0.995611i | \(-0.470165\pi\) | ||||
0.0935925 | + | 0.995611i | \(0.470165\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.6149 | −1.28500 |
(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 | 4016.2.a.e.1.5 | 5 | ||
4.3 | odd | 2 | 502.2.a.c.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 4518.2.a.v.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
502.2.a.c.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
4016.2.a.e.1.5 | 5 | 1.1 | even | 1 | trivial | ||
4518.2.a.v.1.3 | 5 | 12.11 | even | 2 |