Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, 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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.59774\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.59774 | 1.49980 | 0.749902 | − | 0.661549i | \(-0.230101\pi\) | ||||
0.749902 | + | 0.661549i | \(0.230101\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.59774 | −0.714529 | −0.357264 | − | 0.934003i | \(-0.616291\pi\) | ||||
−0.357264 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.34596 | −1.64262 | −0.821310 | − | 0.570482i | \(-0.806756\pi\) | ||||
−0.821310 | + | 0.570482i | \(0.806756\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.74823 | 1.24941 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.74823 | 0.527111 | 0.263555 | − | 0.964644i | \(-0.415105\pi\) | ||||
0.263555 | + | 0.964644i | \(0.415105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.748228 | −0.207521 | −0.103761 | − | 0.994602i | \(-0.533088\pi\) | ||||
−0.103761 | + | 0.994602i | \(0.533088\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.15049 | −1.07165 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.2897 | −2.46361 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94370 | 0.405289 | 0.202645 | − | 0.979252i | \(-0.435046\pi\) | ||||
0.202645 | + | 0.979252i | \(0.435046\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.44724 | −0.489448 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.94370 | 0.374065 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.28966 | 1.35366 | 0.676828 | − | 0.736141i | \(-0.263354\pi\) | ||||
0.676828 | + | 0.736141i | \(0.263354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.654037 | −0.117468 | −0.0587342 | − | 0.998274i | \(-0.518706\pi\) | ||||
−0.0587342 | + | 0.998274i | \(0.518706\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54143 | 0.790562 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.94370 | 1.17370 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.84951 | −0.632855 | −0.316428 | − | 0.948617i | \(-0.602483\pi\) | ||||
−0.316428 | + | 0.948617i | \(0.602483\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.94370 | −0.311241 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.54143 | 0.709253 | 0.354626 | − | 0.935008i | \(-0.384608\pi\) | ||||
0.354626 | + | 0.935008i | \(0.384608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4402 | −1.59211 | −0.796054 | − | 0.605225i | \(-0.793083\pi\) | ||||
−0.796054 | + | 0.605225i | \(0.793083\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.98868 | −0.892739 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.59774 | −1.10824 | −0.554122 | − | 0.832436i | \(-0.686946\pi\) | ||||
−0.554122 | + | 0.832436i | \(0.686946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.8874 | 1.69820 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.79321 | 1.09127 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.59774 | −0.906269 | −0.453134 | − | 0.891442i | \(-0.649694\pi\) | ||||
−0.453134 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.79321 | −0.376636 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.59774 | −0.344078 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.74823 | −0.878544 | −0.439272 | − | 0.898354i | \(-0.644764\pi\) | ||||
−0.439272 | + | 0.898354i | \(0.644764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.09419 | −1.16439 | −0.582196 | − | 0.813049i | \(-0.697806\pi\) | ||||
−0.582196 | + | 0.813049i | \(0.697806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.2897 | −2.05230 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.19547 | 0.148280 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.40226 | 0.904331 | 0.452165 | − | 0.891934i | \(-0.350652\pi\) | ||||
0.452165 | + | 0.891934i | \(0.350652\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.04921 | 0.607854 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.69901 | 0.201636 | 0.100818 | − | 0.994905i | \(-0.467854\pi\) | ||||
0.100818 | + | 0.994905i | \(0.467854\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.6848 | −1.95281 | −0.976406 | − | 0.215941i | \(-0.930718\pi\) | ||||
−0.976406 | + | 0.215941i | \(0.930718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.35729 | −0.734076 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.59774 | −0.865842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.654037 | −0.0735849 | −0.0367924 | − | 0.999323i | \(-0.511714\pi\) | ||||
−0.0367924 | + | 0.999323i | \(0.511714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.19547 | −0.688386 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.5793 | −1.38076 | −0.690380 | − | 0.723447i | \(-0.742557\pi\) | ||||
−0.690380 | + | 0.723447i | \(0.742557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.79321 | −0.519896 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.9366 | 2.03022 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.5414 | −1.54139 | −0.770694 | − | 0.637205i | \(-0.780091\pi\) | ||||
−0.770694 | + | 0.637205i | \(0.780091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.25177 | 0.340878 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.69901 | −0.176180 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.59774 | 0.163924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5793 | −1.07417 | −0.537084 | − | 0.843529i | \(-0.680474\pi\) | ||||
−0.537084 | + | 0.843529i | \(0.680474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.55276 | 0.658577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.80453 | 0.478069 | 0.239034 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239034 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5793 | 1.23948 | 0.619739 | − | 0.784808i | \(-0.287239\pi\) | ||||
0.619739 | + | 0.784808i | \(0.287239\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 18.0379 | 1.76032 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.44015 | 0.525920 | 0.262960 | − | 0.964807i | \(-0.415301\pi\) | ||||
0.262960 | + | 0.964807i | \(0.415301\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.7861 | −1.41625 | −0.708127 | − | 0.706085i | \(-0.750459\pi\) | ||||
−0.708127 | + | 0.706085i | \(0.750459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0379 | 1.32057 | 0.660287 | − | 0.751014i | \(-0.270435\pi\) | ||||
0.660287 | + | 0.751014i | \(0.270435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.10552 | −0.289591 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.80453 | −0.259279 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.0379 | −1.19518 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.94370 | −0.722154 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.7974 | 1.06374 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8987 | 1.06425 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.54852 | −0.669823 | −0.334911 | − | 0.942250i | \(-0.608706\pi\) | ||||
−0.334911 | + | 0.942250i | \(0.608706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −27.1208 | −2.38785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0492139 | 0.00429984 | 0.00214992 | − | 0.999998i | \(-0.499316\pi\) | ||||
0.00214992 | + | 0.999998i | \(0.499316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.34596 | 0.376843 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.10552 | −0.267280 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3909 | 1.48581 | 0.742904 | − | 0.669398i | \(-0.233448\pi\) | ||||
0.742904 | + | 0.669398i | \(0.233448\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.25177 | −0.699906 | −0.349953 | − | 0.936767i | \(-0.613802\pi\) | ||||
−0.349953 | + | 0.936767i | \(0.613802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.7369 | −1.66215 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.30807 | −0.109387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6469 | −0.967226 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 30.8803 | 2.54696 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.28966 | 0.515269 | 0.257635 | − | 0.966242i | \(-0.417057\pi\) | ||||
0.257635 | + | 0.966242i | \(0.417057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.1884 | −1.80566 | −0.902832 | − | 0.429992i | \(-0.858516\pi\) | ||||
−0.902832 | + | 0.429992i | \(0.858516\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.2447 | 0.909079 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.04498 | 0.0839346 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.99291 | 0.717713 | 0.358856 | − | 0.933393i | \(-0.383167\pi\) | ||||
0.358856 | + | 0.933393i | \(0.383167\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.1392 | −1.35922 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.44724 | −0.665736 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9929 | −1.33099 | −0.665494 | − | 0.746403i | \(-0.731779\pi\) | ||||
−0.665494 | + | 0.746403i | \(0.731779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.25601 | −0.564879 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.3389 | 1.26434 | 0.632170 | − | 0.774830i | \(-0.282164\pi\) | ||||
0.632170 | + | 0.774830i | \(0.282164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4402 | −0.956935 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.74823 | −0.286634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.3839 | 1.77784 | 0.888921 | − | 0.458061i | \(-0.151456\pi\) | ||||
0.888921 | + | 0.458061i | \(0.151456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.6356 | 0.803978 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.5301 | −1.31764 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.54143 | −0.339443 | −0.169721 | − | 0.985492i | \(-0.554287\pi\) | ||||
−0.169721 | + | 0.985492i | \(0.554287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0900 | 0.898639 | 0.449320 | − | 0.893371i | \(-0.351666\pi\) | ||||
0.449320 | + | 0.893371i | \(0.351666\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.6243 | −1.74636 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.15049 | 0.452193 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.24468 | 0.383529 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.44724 | −0.614446 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5485 | −0.907979 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.7298 | 0.772349 | 0.386175 | − | 0.922426i | \(-0.373796\pi\) | ||||
0.386175 | + | 0.922426i | \(0.373796\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.10552 | 0.222391 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.38385 | −0.668572 | −0.334286 | − | 0.942472i | \(-0.608495\pi\) | ||||
−0.334286 | + | 0.942472i | \(0.608495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.2404 | −0.796814 | −0.398407 | − | 0.917209i | \(-0.630437\pi\) | ||||
−0.398407 | + | 0.917209i | \(0.630437\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.2291 | 1.35632 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −31.6806 | −2.22354 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.25601 | −0.506782 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.28543 | 0.506372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.74823 | −0.120927 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.44015 | −0.374516 | −0.187258 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187258 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.41359 | 0.302414 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.6806 | 1.13761 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.84242 | 0.192956 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43.3428 | −2.92883 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24468 | −0.150994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4217 | −1.70237 | −0.851183 | − | 0.524869i | \(-0.824114\pi\) | ||||
−0.851183 | + | 0.524869i | \(0.824114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.17282 | −0.611521 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.74114 | 0.248308 | 0.124154 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124154 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.29675 | 0.350019 | 0.175010 | − | 0.984567i | \(-0.444004\pi\) | ||||
0.175010 | + | 0.984567i | \(0.444004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.7369 | −1.29859 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.93661 | 0.650969 | 0.325485 | − | 0.945547i | \(-0.394473\pi\) | ||||
0.325485 | + | 0.945547i | \(0.394473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1392 | 0.791872 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.69901 | −0.110363 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.8424 | −1.80098 | −0.900488 | − | 0.434880i | \(-0.856791\pi\) | ||||
−0.900488 | + | 0.434880i | \(0.856791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.84951 | 0.376800 | 0.188400 | − | 0.982092i | \(-0.439670\pi\) | ||||
0.188400 | + | 0.982092i | \(0.439670\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.9253 | −1.40651 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.9929 | −1.21341 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.748228 | 0.0476086 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32.6778 | −2.07087 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.2447 | 0.962236 | 0.481118 | − | 0.876656i | \(-0.340231\pi\) | ||||
0.481118 | + | 0.876656i | \(0.340231\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.39803 | 0.213632 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.4515 | −0.779742 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.58641 | 0.473227 | 0.236614 | − | 0.971604i | \(-0.423962\pi\) | ||||
0.236614 | + | 0.971604i | \(0.423962\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.7298 | 1.03954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.3233 | 1.69127 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.79321 | 0.172236 | 0.0861182 | − | 0.996285i | \(-0.472554\pi\) | ||||
0.0861182 | + | 0.996285i | \(0.472554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5414 | 0.647555 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −37.7748 | −2.31178 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.0308 | −1.52615 | −0.763077 | − | 0.646307i | \(-0.776313\pi\) | ||||
−0.763077 | + | 0.646307i | \(0.776313\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.5301 | 1.67234 | 0.836168 | − | 0.548474i | \(-0.184791\pi\) | ||||
0.836168 | + | 0.548474i | \(0.184791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.44724 | 0.511250 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.27834 | −0.257993 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4023 | 0.625012 | 0.312506 | − | 0.949916i | \(-0.398832\pi\) | ||||
0.312506 | + | 0.949916i | \(0.398832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.45148 | −0.146766 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.8874 | −0.828453 | −0.414226 | − | 0.910174i | \(-0.635948\pi\) | ||||
−0.414226 | + | 0.910174i | \(0.635948\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.3346 | 1.62488 | 0.812438 | − | 0.583048i | \(-0.198140\pi\) | ||||
0.812438 | + | 0.583048i | \(0.198140\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.15049 | 0.245854 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.7369 | −1.16503 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.4823 | −1.61104 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1321 | 0.591923 | 0.295961 | − | 0.955200i | \(-0.404360\pi\) | ||||
0.295961 | + | 0.955200i | \(0.404360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.7819 | 0.627745 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.39803 | 0.197174 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.45433 | −0.0841061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 45.3725 | 2.61523 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.4809 | 0.717009 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.5301 | 0.831992 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1208 | 0.977133 | 0.488567 | − | 0.872527i | \(-0.337520\pi\) | ||||
0.488567 | + | 0.872527i | \(0.337520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.6778 | 1.85897 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.2404 | −1.77148 | −0.885742 | − | 0.464179i | \(-0.846350\pi\) | ||||
−0.885742 | + | 0.464179i | \(0.846350\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2291 | −1.42603 | −0.713017 | − | 0.701147i | \(-0.752672\pi\) | ||||
−0.713017 | + | 0.701147i | \(0.752672\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.0266 | 1.46643 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.6427 | 0.653920 | 0.326960 | − | 0.945038i | \(-0.393976\pi\) | ||||
0.326960 | + | 0.945038i | \(0.393976\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.7440 | 0.713527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.1321 | 0.788776 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.83110 | 0.101571 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −38.4104 | −2.12410 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.0195 | 1.82042 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.5977 | 0.692434 | 0.346217 | − | 0.938154i | \(-0.387466\pi\) | ||||
0.346217 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.4288 | −0.790695 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8269 | −0.646170 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.49646 | −0.299411 | −0.149706 | − | 0.988731i | \(-0.547833\pi\) | ||||
−0.149706 | + | 0.988731i | \(0.547833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.4667 | 1.98060 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.14341 | −0.0619189 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.2404 | −1.14688 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.06731 | −0.434329 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3417 | 0.555173 | 0.277586 | − | 0.960701i | \(-0.410465\pi\) | ||||
0.277586 | + | 0.960701i | \(0.410465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6806 | 1.64230 | 0.821148 | − | 0.570716i | \(-0.193334\pi\) | ||||
0.821148 | + | 0.570716i | \(0.193334\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.45433 | −0.0776264 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.3276 | 1.24160 | 0.620800 | − | 0.783969i | \(-0.286808\pi\) | ||||
0.620800 | + | 0.783969i | \(0.286808\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.71457 | −0.144075 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.8690 | −1.79254 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1576 | −0.641653 | −0.320826 | − | 0.947138i | \(-0.603961\pi\) | ||||
−0.320826 | + | 0.947138i | \(0.603961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.6356 | −1.08309 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.6580 | 1.39534 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.08287 | −0.474122 | −0.237061 | − | 0.971495i | \(-0.576184\pi\) | ||||
−0.237061 | + | 0.971495i | \(0.576184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.0223 | 0.886147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.6735 | 1.48865 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.1321 | 0.938844 | 0.469422 | − | 0.882974i | \(-0.344462\pi\) | ||||
0.469422 | + | 0.882974i | \(0.344462\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.9097 | 1.59617 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.45433 | −0.280912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6427 | 1.21444 | 0.607222 | − | 0.794532i | \(-0.292284\pi\) | ||||
0.607222 | + | 0.794532i | \(0.292284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.6091 | −1.00460 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9253 | 1.12033 | 0.560165 | − | 0.828381i | \(-0.310738\pi\) | ||||
0.560165 | + | 0.828381i | \(0.310738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1392 | 0.618669 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −39.1321 | −1.98920 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.2599 | 1.48354 | 0.741769 | − | 0.670656i | \(-0.233987\pi\) | ||||
0.741769 | + | 0.670656i | \(0.233987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.83110 | 0.294891 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.127845 | 0.00644892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.04498 | 0.0525785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.10128 | 0.306214 | 0.153107 | − | 0.988210i | \(-0.451072\pi\) | ||||
0.153107 | + | 0.988210i | \(0.451072\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.2897 | 0.565190 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.0379 | 0.800894 | 0.400447 | − | 0.916320i | \(-0.368855\pi\) | ||||
0.400447 | + | 0.916320i | \(0.368855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.489369 | 0.0243772 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.89872 | 0.491871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.72982 | −0.333585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.5343 | −1.26259 | −0.631296 | − | 0.775542i | \(-0.717477\pi\) | ||||
−0.631296 | + | 0.775542i | \(0.717477\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.1771 | 2.22842 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.3276 | 1.44311 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0984 | 0.986593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.4359 | −1.04972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.1586 | −1.71761 | −0.858806 | − | 0.512301i | \(-0.828793\pi\) | ||||
−0.858806 | + | 0.512301i | \(0.828793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.89872 | −0.141275 | −0.0706375 | − | 0.997502i | \(-0.522503\pi\) | ||||
−0.0706375 | + | 0.997502i | \(0.522503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −28.4780 | −1.38465 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.34173 | −0.356126 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.5230 | 1.91265 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.39803 | −0.164058 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.9774 | −1.25129 | −0.625643 | − | 0.780110i | \(-0.715163\pi\) | ||||
−0.625643 | + | 0.780110i | \(0.715163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.9324 | 1.48652 | 0.743258 | − | 0.669005i | \(-0.233280\pi\) | ||||
0.743258 | + | 0.669005i | \(0.233280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.2557 | −1.45065 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94370 | −0.0929797 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1278 | −0.483376 | −0.241688 | − | 0.970354i | \(-0.577701\pi\) | ||||
−0.241688 | + | 0.970354i | \(0.577701\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44.5567 | 2.12175 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3276 | −0.680723 | −0.340361 | − | 0.940295i | \(-0.610549\pi\) | ||||
−0.340361 | + | 0.940295i | \(0.610549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.2334 | 1.10137 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.3389 | 0.772802 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.61615 | 0.312235 | 0.156118 | − | 0.987738i | \(-0.450102\pi\) | ||||
0.156118 | + | 0.987738i | \(0.450102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.93946 | 0.373855 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −57.6395 | −2.70814 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.19547 | −0.243567 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.5864 | 1.80500 | 0.902498 | − | 0.430694i | \(-0.141731\pi\) | ||||
0.902498 | + | 0.430694i | \(0.141731\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.83110 | 0.272172 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.1841 | 1.54554 | 0.772770 | − | 0.634686i | \(-0.218871\pi\) | ||||
0.772770 | + | 0.634686i | \(0.218871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2826 | −0.617294 | −0.308647 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308647 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.71457 | 0.125885 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.8311 | 0.963948 | 0.481974 | − | 0.876185i | \(-0.339920\pi\) | ||||
0.481974 | + | 0.876185i | \(0.339920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.1700 | −1.48547 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.3612 | 1.07643 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.2518 | −0.839217 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.44724 | 0.112287 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.7298 | −1.13230 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.6848 | −1.17357 | −0.586785 | − | 0.809743i | \(-0.699607\pi\) | ||||
−0.586785 | + | 0.809743i | \(0.699607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88031 | 0.131331 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.9437 | −0.998473 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.9030 | 0.767524 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.51063 | −0.430968 | −0.215484 | − | 0.976507i | \(-0.569133\pi\) | ||||
−0.215484 | + | 0.976507i | \(0.569133\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −44.1431 | −1.99622 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89448 | −0.311144 | −0.155572 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155572 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.8690 | 0.984930 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.4696 | −0.470572 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.38385 | −0.331211 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.1321 | −1.30413 | −0.652066 | − | 0.758163i | \(-0.726097\pi\) | ||||
−0.652066 | + | 0.758163i | \(0.726097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 42.4441 | 1.89626 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.1533 | −0.586479 | −0.293239 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293239 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.67637 | −0.341594 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.3162 | −1.43521 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.5651 | −1.44342 | −0.721712 | − | 0.692193i | \(-0.756645\pi\) | ||||
−0.721712 | + | 0.692193i | \(0.756645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.5117 | 3.20773 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.94370 | −0.0858164 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.0984 | −0.885643 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.2826 | −0.584167 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 60.7451 | 2.66641 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0450 | 0.571511 | 0.285755 | − | 0.958303i | \(-0.407756\pi\) | ||||
0.285755 | + | 0.958303i | \(0.407756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9437 | −0.522261 | −0.261131 | − | 0.965303i | \(-0.584095\pi\) | ||||
−0.261131 | + | 0.965303i | \(0.584095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.6285 | 1.20581 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.96211 | −0.0854709 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2220 | −0.835741 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.2939 | −1.09766 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.39803 | −0.147185 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.69193 | −0.375785 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.7974 | −0.509097 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.7819 | 0.895139 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.48513 | −0.0638508 | −0.0319254 | − | 0.999490i | \(-0.510164\pi\) | ||||
−0.0319254 | + | 0.999490i | \(0.510164\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 31.4065 | 1.34778 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.6243 | 1.01195 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.01418 | −0.257148 | −0.128574 | − | 0.991700i | \(-0.541040\pi\) | ||||
−0.128574 | + | 0.991700i | \(0.541040\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.0871 | −1.45480 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.28966 | −0.310550 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.84242 | 0.120872 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.9774 | 0.678201 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.3584 | 1.15921 | 0.579605 | − | 0.814897i | \(-0.303207\pi\) | ||||
0.579605 | + | 0.814897i | \(0.303207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.81162 | 0.330396 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.6243 | 0.575218 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1434 | 0.891088 | 0.445544 | − | 0.895260i | \(-0.353010\pi\) | ||||
0.445544 | + | 0.895260i | \(0.353010\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.4288 | −0.943588 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 26.9253 | 1.13076 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.18130 | −0.384225 | −0.192113 | − | 0.981373i | \(-0.561534\pi\) | ||||
−0.192113 | + | 0.981373i | \(0.561534\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.5977 | −1.36179 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.75670 | −0.198368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.79744 | −0.199720 | −0.0998601 | − | 0.995001i | \(-0.531840\pi\) | ||||
−0.0998601 | + | 0.995001i | \(0.531840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.8732 | 1.15837 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 54.6693 | 2.26806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.5343 | −0.477704 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.48090 | 0.185262 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.64980 | 0.0680945 | 0.0340473 | − | 0.999420i | \(-0.489160\pi\) | ||||
0.0340473 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.654037 | 0.0269491 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3768 | −1.00273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.8874 | −0.816678 | −0.408339 | − | 0.912830i | \(-0.633892\pi\) | ||||
−0.408339 | + | 0.912830i | \(0.633892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.8311 | 0.853992 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.1997 | −1.19506 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.25462 | 0.0921214 | 0.0460607 | − | 0.998939i | \(-0.485333\pi\) | ||||
0.0460607 | + | 0.998939i | \(0.485333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7677 | 1.01030 | 0.505148 | − | 0.863033i | \(-0.331438\pi\) | ||||
0.505148 | + | 0.863033i | \(0.331438\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.7454 | 1.12988 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.6919 | 0.516000 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 45.9774 | 1.86616 | 0.933082 | − | 0.359665i | \(-0.117109\pi\) | ||||
0.933082 | + | 0.359665i | \(0.117109\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −82.2978 | −3.33488 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.68484 | 0.229984 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.326485 | 0.0131866 | 0.00659330 | − | 0.999978i | \(-0.497901\pi\) | ||||
0.00659330 | + | 0.999978i | \(0.497901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.8492 | −0.760073 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.9140 | −1.52636 | −0.763179 | − | 0.646187i | \(-0.776363\pi\) | ||||
−0.763179 | + | 0.646187i | \(0.776363\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.76771 | 0.191630 | 0.0958151 | − | 0.995399i | \(-0.469454\pi\) | ||||
0.0958151 | + | 0.995399i | \(0.469454\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.77796 | 0.151604 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 63.1965 | 2.53192 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.77479 | −0.270992 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.54143 | −0.181367 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.5485 | −0.460470 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.9958 | −0.437734 | −0.218867 | − | 0.975755i | \(-0.570236\pi\) | ||||
−0.218867 | + | 0.975755i | \(0.570236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.1321 | −0.561700 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.0605 | 0.478608 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.89448 | −0.352412 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.36829 | 0.251926 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.1586 | −0.993707 | −0.496853 | − | 0.867834i | \(-0.665511\pi\) | ||||
−0.496853 | + | 0.867834i | \(0.665511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.9069 | 1.45547 | 0.727733 | − | 0.685861i | \(-0.240574\pi\) | ||||
0.727733 | + | 0.685861i | \(0.240574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 43.3318 | 1.70619 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.3531 | −0.682219 | −0.341109 | − | 0.940024i | \(-0.610803\pi\) | ||||
−0.341109 | + | 0.940024i | \(0.610803\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.7974 | −0.463090 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.38385 | 0.289396 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.4780 | −0.566570 | −0.283285 | − | 0.959036i | \(-0.591424\pi\) | ||||
−0.283285 | + | 0.959036i | \(0.591424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0786309 | −0.00307236 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −62.5386 | −2.43986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.5301 | 1.85151 | 0.925755 | − | 0.378124i | \(-0.123431\pi\) | ||||
0.925755 | + | 0.378124i | \(0.123431\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.22204 | 0.319800 | 0.159900 | − | 0.987133i | \(-0.448883\pi\) | ||||
0.159900 | + | 0.987133i | \(0.448883\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.83110 | −0.226461 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.94370 | −0.269265 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.1689 | 0.548622 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −66.0390 | −2.55321 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.8987 | −0.613763 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9016 | 0.612961 | 0.306480 | − | 0.951877i | \(-0.400849\pi\) | ||||
0.306480 | + | 0.951877i | \(0.400849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.75670 | −0.183086 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.9816 | −0.844821 | −0.422411 | − | 0.906405i | \(-0.638816\pi\) | ||||
−0.422411 | + | 0.906405i | \(0.638816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.9774 | 1.76445 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.71849 | 0.372413 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.30807 | 0.0500520 | 0.0250260 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250260 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.7861 | −1.06165 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.7596 | 0.524960 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.93661 | 0.188070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.2291 | −1.68256 | −0.841278 | − | 0.540603i | \(-0.818196\pi\) | ||||
−0.841278 | + | 0.540603i | \(0.818196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −28.4780 | −1.08179 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1841 | 0.500103 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.6243 | 0.516057 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.8127 | 0.976325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5793 | −0.928348 | −0.464174 | − | 0.885744i | \(-0.653649\pi\) | ||||
−0.464174 | + | 0.885744i | \(0.653649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.84951 | 0.145187 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 31.5343 | 1.18765 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.8803 | −0.785285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.39803 | −0.352950 | −0.176475 | − | 0.984305i | \(-0.556470\pi\) | ||||
−0.176475 | + | 0.984305i | \(0.556470\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.45148 | −0.0919376 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.27125 | −0.0476087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.08995 | 0.0781599 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −72.3272 | −2.70111 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.3460 | −0.907951 | −0.453976 | − | 0.891014i | \(-0.649995\pi\) | ||||
−0.453976 | + | 0.891014i | \(0.649995\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −54.6693 | −2.03599 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.1955 | 0.565126 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.8396 | −0.662545 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.1137 | 1.07977 | 0.539883 | − | 0.841740i | \(-0.318468\pi\) | ||||
0.539883 | + | 0.841740i | \(0.318468\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.3697 | −1.42110 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.3205 | −1.15843 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.91713 | −0.181618 | −0.0908092 | − | 0.995868i | \(-0.528945\pi\) | ||||
−0.0908092 | + | 0.995868i | \(0.528945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −49.3386 | −1.81988 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9408 | 0.476682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.7114 | −1.90223 | −0.951117 | − | 0.308830i | \(-0.900063\pi\) | ||||
−0.951117 | + | 0.308830i | \(0.900063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.94370 | 0.0714035 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0379 | −0.661746 | −0.330873 | − | 0.943675i | \(-0.607343\pi\) | ||||
−0.330873 | + | 0.943675i | \(0.607343\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.0492 | −0.368175 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −47.1502 | −1.72513 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.6427 | −0.863886 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.9171 | 0.398372 | 0.199186 | − | 0.979962i | \(-0.436170\pi\) | ||||
0.199186 | + | 0.979962i | \(0.436170\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.6017 | 1.44316 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.4512 | 1.29020 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.4710 | 1.21652 | 0.608261 | − | 0.793737i | \(-0.291867\pi\) | ||||
0.608261 | + | 0.793737i | \(0.291867\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.82718 | 0.320406 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.3399 | −1.86107 | −0.930536 | − | 0.366201i | \(-0.880658\pi\) | ||||
−0.930536 | + | 0.366201i | \(0.880658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.2599 | 2.32637 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17.9660 | −0.649563 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.04921 | 0.182317 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.7974 | 0.605731 | 0.302866 | − | 0.953033i | \(-0.402057\pi\) | ||||
0.302866 | + | 0.953033i | \(0.402057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7075 | 0.709748 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.62145 | 0.310092 | 0.155046 | − | 0.987907i | \(-0.450447\pi\) | ||||
0.155046 | + | 0.987907i | \(0.450447\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.60059 | 0.0574948 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 43.4596 | 1.55911 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.54143 | −0.162714 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.97026 | 0.106284 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1689 | 0.506355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.3683 | −0.512826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.0124 | −0.891595 | −0.445798 | − | 0.895134i | \(-0.647080\pi\) | ||||
−0.445798 | + | 0.895134i | \(0.647080\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.25601 | 0.258321 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −61.0082 | −2.16920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.80453 | 0.241636 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.3839 | 0.971205 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −48.0574 | −1.70228 | −0.851140 | − | 0.524939i | \(-0.824088\pi\) | ||||
−0.851140 | + | 0.524939i | \(0.824088\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.7932 | −0.806366 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −54.5046 | −1.92583 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.1689 | −1.02935 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.4965 | 0.475688 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −65.0234 | −2.28893 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.20965 | 0.218320 | 0.109160 | − | 0.994024i | \(-0.465184\pi\) | ||||
0.109160 | + | 0.994024i | \(0.465184\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.6130 | −0.934508 | −0.467254 | − | 0.884123i | \(-0.654757\pi\) | ||||
−0.467254 | + | 0.884123i | \(0.654757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 71.5159 | 2.50817 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.1502 | 0.951029 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4402 | 0.365255 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.1884 | 0.425897 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4993 | 0.889932 | 0.444966 | − | 0.895547i | \(-0.353216\pi\) | ||||
0.444966 | + | 0.895547i | \(0.353216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.0166 | −1.18575 | −0.592873 | − | 0.805296i | \(-0.702006\pi\) | ||||
−0.592873 | + | 0.805296i | \(0.702006\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1140 | −0.386939 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.6048 | −0.890367 | −0.445183 | − | 0.895439i | \(-0.646862\pi\) | ||||
−0.445183 | + | 0.895439i | \(0.646862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0350 | 0.661114 | 0.330557 | − | 0.943786i | \(-0.392763\pi\) | ||||
0.330557 | + | 0.943786i | \(0.392763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0223 | 0.937394 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.6622 | 1.23562 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.1052 | −0.903408 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.27125 | −0.0439408 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6848 | 0.541501 | 0.270750 | − | 0.962650i | \(-0.412728\pi\) | ||||
0.270750 | + | 0.962650i | \(0.412728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1392 | 0.832385 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.0758 | −1.24252 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.8761 | 0.683758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 34.5230 | 1.18623 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71.0082 | 2.43699 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.48228 | −0.256489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.57224 | 0.122311 | 0.0611555 | − | 0.998128i | \(-0.480521\pi\) | ||||
0.0611555 | + | 0.998128i | \(0.480521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.98868 | 0.204808 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 56.7309 | 1.93789 | 0.968945 | − | 0.247276i | \(-0.0795355\pi\) | ||||
0.968945 | + | 0.247276i | \(0.0795355\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.6059 | −0.634825 | −0.317412 | − | 0.948288i | \(-0.602814\pi\) | ||||
−0.317412 | + | 0.948288i | \(0.602814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −51.2713 | −1.74732 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.9395 | 0.610666 | 0.305333 | − | 0.952246i | \(-0.401232\pi\) | ||||
0.305333 | + | 0.952246i | \(0.401232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.3612 | −1.27032 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.7819 | −0.705790 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.14341 | −0.0387874 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.53858 | −0.187668 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.6537 | −1.34208 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −51.7114 | −1.74816 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.6201 | −1.94569 | −0.972846 | − | 0.231455i | \(-0.925651\pi\) | ||||
−0.972846 | + | 0.231455i | \(0.925651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.3205 | 0.887767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3431 | 0.516923 | 0.258461 | − | 0.966022i | \(-0.416785\pi\) | ||||
0.258461 | + | 0.966022i | \(0.416785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.8608 | −0.601065 | −0.300532 | − | 0.953772i | \(-0.597164\pi\) | ||||
−0.300532 | + | 0.953772i | \(0.597164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 28.0085 | 0.941495 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.1445 | 1.65011 | 0.825055 | − | 0.565053i | \(-0.191144\pi\) | ||||
0.825055 | + | 0.565053i | \(0.191144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.8056 | 1.10026 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8311 | −0.362855 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.59774 | 0.254249 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.25601 | 0.242542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.77796 | −0.126143 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.76771 | −0.159012 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.7932 | −0.659407 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 117.866 | 3.92233 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.3165 | −0.642104 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.19971 | 0.305471 | 0.152736 | − | 0.988267i | \(-0.451192\pi\) | ||||
0.152736 | + | 0.988267i | \(0.451192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.0085 | 0.597303 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.2939 | −0.838024 | −0.419012 | − | 0.907981i | \(-0.637624\pi\) | ||||
−0.419012 | + | 0.907981i | \(0.637624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9915 | −0.727813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 37.7454 | 1.24782 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.213882 | −0.00706301 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44.8155 | −1.47833 | −0.739164 | − | 0.673525i | \(-0.764779\pi\) | ||||
−0.739164 | + | 0.673525i | \(0.764779\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 44.4752 | 1.46551 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.27125 | −0.0418437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.42068 | 0.309750 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 47.1502 | 1.54861 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.65119 | −0.185409 | −0.0927047 | − | 0.995694i | \(-0.529551\pi\) | ||||
−0.0927047 | + | 0.995694i | \(0.529551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.8874 | −0.389594 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −81.1544 | −2.65688 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.37962 | −0.274043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.58641 | −0.280506 | −0.140253 | − | 0.990116i | \(-0.544792\pi\) | ||||
−0.140253 | + | 0.990116i | \(0.544792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.5386 | −2.13877 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.8155 | −1.13495 | −0.567477 | − | 0.823389i | \(-0.692080\pi\) | ||||
−0.567477 | + | 0.823389i | \(0.692080\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.82718 | 0.287452 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.4965 | 0.439040 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.6551 | −0.606209 | −0.303105 | − | 0.952957i | \(-0.598023\pi\) | ||||
−0.303105 | + | 0.952957i | \(0.598023\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.4841 | 0.405250 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.2447 | 0.980751 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 37.7227 | 1.22196 | 0.610980 | − | 0.791646i | \(-0.290776\pi\) | ||||
0.610980 | + | 0.791646i | \(0.290776\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0492 | 0.648777 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 33.1055 | 1.07015 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.5804 | −2.44062 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.5722 | −0.986201 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.3909 | 0.657089 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.1434 | −0.551866 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.3683 | 0.847947 | 0.423974 | − | 0.905675i | \(-0.360635\pi\) | ||||
0.423974 | + | 0.905675i | \(0.360635\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.79321 | −0.250354 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.978737 | 0.0314092 | 0.0157046 | − | 0.999877i | \(-0.495001\pi\) | ||||
0.0157046 | + | 0.999877i | \(0.495001\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.8619 | 1.14968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.75670 | 0.152336 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.254623 | −0.00814611 | −0.00407306 | − | 0.999992i | \(-0.501296\pi\) | ||||
−0.00407306 | + | 0.999992i | \(0.501296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.4217 | −0.812482 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −55.4217 | −1.76948 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.3754 | 1.57483 | 0.787415 | − | 0.616423i | \(-0.211419\pi\) | ||||
0.787415 | + | 0.616423i | \(0.211419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.9929 | 0.477714 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 85.7759 | 2.73028 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.2925 | −0.645264 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.6101 | −1.19473 | −0.597363 | − | 0.801971i | \(-0.703785\pi\) | ||||
−0.597363 | + | 0.801971i | \(0.703785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.7256 | 1.03851 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.9593 | 0.569347 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.3867 | −0.613983 | −0.306992 | − | 0.951712i | \(-0.599322\pi\) | ||||
−0.306992 | + | 0.951712i | \(0.599322\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.48228 | −0.236729 |
(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 | 4864.2.a.bf.1.3 | 3 | ||
4.3 | odd | 2 | 4864.2.a.bd.1.1 | 3 | |||
8.3 | odd | 2 | 4864.2.a.be.1.3 | 3 | |||
8.5 | even | 2 | 4864.2.a.bc.1.1 | 3 | |||
16.3 | odd | 4 | 2432.2.c.f.1217.2 | ✓ | 6 | ||
16.5 | even | 4 | 2432.2.c.g.1217.2 | yes | 6 | ||
16.11 | odd | 4 | 2432.2.c.f.1217.5 | yes | 6 | ||
16.13 | even | 4 | 2432.2.c.g.1217.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.f.1217.2 | ✓ | 6 | 16.3 | odd | 4 | ||
2432.2.c.f.1217.5 | yes | 6 | 16.11 | odd | 4 | ||
2432.2.c.g.1217.2 | yes | 6 | 16.5 | even | 4 | ||
2432.2.c.g.1217.5 | yes | 6 | 16.13 | even | 4 | ||
4864.2.a.bc.1.1 | 3 | 8.5 | even | 2 | |||
4864.2.a.bd.1.1 | 3 | 4.3 | odd | 2 | |||
4864.2.a.be.1.3 | 3 | 8.3 | odd | 2 | |||
4864.2.a.bf.1.3 | 3 | 1.1 | even | 1 | trivial |