Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 15x^{7} + 15x^{6} + 66x^{5} - 59x^{4} - 77x^{3} + 34x^{2} + 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.94061\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.94061 | 1.12041 | 0.560207 | − | 0.828353i | \(-0.310722\pi\) | ||||
0.560207 | + | 0.828353i | \(0.310722\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.48281 | 0.663133 | 0.331566 | − | 0.943432i | \(-0.392423\pi\) | ||||
0.331566 | + | 0.943432i | \(0.392423\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.765982 | 0.255327 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.87756 | 0.742983 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.79179 | −1.40472 | −0.702358 | − | 0.711824i | \(-0.747869\pi\) | ||||
−0.702358 | + | 0.711824i | \(0.747869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.95626 | 0.678213 | 0.339106 | − | 0.940748i | \(-0.389875\pi\) | ||||
0.339106 | + | 0.940748i | \(0.389875\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.94061 | −0.423477 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.43248 | −0.715722 | −0.357861 | − | 0.933775i | \(-0.616494\pi\) | ||||
−0.357861 | + | 0.933775i | \(0.616494\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.80127 | −0.560255 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.33537 | −0.834342 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.27973 | −0.423335 | −0.211668 | − | 0.977342i | \(-0.567889\pi\) | ||||
−0.211668 | + | 0.977342i | \(0.567889\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.29356 | −0.771146 | −0.385573 | − | 0.922677i | \(-0.625996\pi\) | ||||
−0.385573 | + | 0.922677i | \(0.625996\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.94061 | 0.337818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.48281 | −0.250641 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.63237 | −1.25475 | −0.627377 | − | 0.778716i | \(-0.715871\pi\) | ||||
−0.627377 | + | 0.778716i | \(0.715871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.94061 | 0.310747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.26702 | −0.510222 | −0.255111 | − | 0.966912i | \(-0.582112\pi\) | ||||
−0.255111 | + | 0.966912i | \(0.582112\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24504 | −0.952360 | −0.476180 | − | 0.879348i | \(-0.657979\pi\) | ||||
−0.476180 | + | 0.879348i | \(0.657979\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.13581 | 0.169316 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.19672 | −0.758019 | −0.379010 | − | 0.925393i | \(-0.623735\pi\) | ||||
−0.379010 | + | 0.925393i | \(0.623735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.2396 | −1.57386 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.1806 | 1.94786 | 0.973928 | − | 0.226858i | \(-0.0728452\pi\) | ||||
0.973928 | + | 0.226858i | \(0.0728452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.48281 | 0.199942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.73696 | 0.759879 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.168206 | −0.0218986 | −0.0109493 | − | 0.999940i | \(-0.503485\pi\) | ||||
−0.0109493 | + | 0.999940i | \(0.503485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.15136 | −0.147416 | −0.0737080 | − | 0.997280i | \(-0.523483\pi\) | ||||
−0.0737080 | + | 0.997280i | \(0.523483\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.765982 | −0.0965047 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.48281 | 0.183920 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.79067 | −0.707443 | −0.353722 | − | 0.935351i | \(-0.615084\pi\) | ||||
−0.353722 | + | 0.935351i | \(0.615084\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.66112 | −0.801905 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.7993 | −1.63767 | −0.818836 | − | 0.574028i | \(-0.805380\pi\) | ||||
−0.818836 | + | 0.574028i | \(0.805380\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.12217 | −1.06767 | −0.533834 | − | 0.845589i | \(-0.679249\pi\) | ||||
−0.533834 | + | 0.845589i | \(0.679249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.43619 | −0.627717 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.90607 | −0.439467 | −0.219734 | − | 0.975560i | \(-0.570519\pi\) | ||||
−0.219734 | + | 0.975560i | \(0.570519\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.7112 | −1.19014 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.99115 | −0.218557 | −0.109278 | − | 0.994011i | \(-0.534854\pi\) | ||||
−0.109278 | + | 0.994011i | \(0.534854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.58813 | −0.931513 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.42408 | −0.474311 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.67678 | 0.177738 | 0.0888689 | − | 0.996043i | \(-0.471675\pi\) | ||||
0.0888689 | + | 0.996043i | \(0.471675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.33215 | −0.864003 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.38357 | 0.449745 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.7411 | 1.59827 | 0.799135 | − | 0.601152i | \(-0.205291\pi\) | ||||
0.799135 | + | 0.601152i | \(0.205291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.765982 | 0.0769841 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.19873 | −0.915308 | −0.457654 | − | 0.889130i | \(-0.651310\pi\) | ||||
−0.457654 | + | 0.889130i | \(0.651310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.1535 | 1.00045 | 0.500226 | − | 0.865895i | \(-0.333250\pi\) | ||||
0.500226 | + | 0.865895i | \(0.333250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.87756 | −0.280821 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.6142 | 1.70283 | 0.851416 | − | 0.524491i | \(-0.175744\pi\) | ||||
0.851416 | + | 0.524491i | \(0.175744\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.84109 | 0.367910 | 0.183955 | − | 0.982935i | \(-0.441110\pi\) | ||||
0.183955 | + | 0.982935i | \(0.441110\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.8115 | −1.40584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.521212 | 0.0490315 | 0.0245158 | − | 0.999699i | \(-0.492196\pi\) | ||||
0.0245158 | + | 0.999699i | \(0.492196\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.08972 | −0.474619 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.765982 | 0.0708151 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.79179 | 0.530933 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.34002 | −0.571660 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5678 | −1.03466 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.14711 | 0.811675 | 0.405837 | − | 0.913945i | \(-0.366980\pi\) | ||||
0.405837 | + | 0.913945i | \(0.366980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.1192 | −1.06704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.04167 | −0.265752 | −0.132876 | − | 0.991133i | \(-0.542421\pi\) | ||||
−0.132876 | + | 0.991133i | \(0.542421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.95626 | −0.256340 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.42852 | −0.553279 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.62644 | 0.651571 | 0.325785 | − | 0.945444i | \(-0.394371\pi\) | ||||
0.325785 | + | 0.945444i | \(0.394371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.988761 | 0.0838656 | 0.0419328 | − | 0.999120i | \(-0.486648\pi\) | ||||
0.0419328 | + | 0.999120i | \(0.486648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0848 | −0.849295 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38041 | −0.280728 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.94061 | 0.160059 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.93581 | −0.813973 | −0.406987 | − | 0.913434i | \(-0.633420\pi\) | ||||
−0.406987 | + | 0.913434i | \(0.633420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.758626 | −0.0617361 | −0.0308681 | − | 0.999523i | \(-0.509827\pi\) | ||||
−0.0308681 | + | 0.999523i | \(0.509827\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.43641 | −0.358663 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.36654 | −0.511372 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9992 | 1.51630 | 0.758152 | − | 0.652078i | \(-0.226103\pi\) | ||||
0.758152 | + | 0.652078i | \(0.226103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.5191 | 2.18240 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.43248 | 0.270518 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7933 | 0.845398 | 0.422699 | − | 0.906270i | \(-0.361083\pi\) | ||||
0.422699 | + | 0.906270i | \(0.361083\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.87756 | 0.224018 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5148 | 1.51010 | 0.755051 | − | 0.655667i | \(-0.227612\pi\) | ||||
0.755051 | + | 0.655667i | \(0.227612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.26444 | 0.173166 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.9031 | −1.66526 | −0.832632 | − | 0.553826i | \(-0.813167\pi\) | ||||
−0.832632 | + | 0.553826i | \(0.813167\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.80127 | 0.211756 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.326423 | −0.0245355 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.37316 | −0.102635 | −0.0513174 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513174 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9070 | 1.33102 | 0.665510 | − | 0.746389i | \(-0.268214\pi\) | ||||
0.665510 | + | 0.746389i | \(0.268214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.23434 | −0.165167 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.3174 | −0.832068 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.79179 | −0.423538 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.33537 | 0.315351 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7128 | 1.13694 | 0.568470 | − | 0.822704i | \(-0.307535\pi\) | ||||
0.568470 | + | 0.822704i | \(0.307535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.2046 | −1.88625 | −0.943125 | − | 0.332439i | \(-0.892128\pi\) | ||||
−0.943125 | + | 0.332439i | \(0.892128\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.87756 | 0.206066 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.39892 | 0.455904 | 0.227952 | − | 0.973672i | \(-0.426797\pi\) | ||||
0.227952 | + | 0.973672i | \(0.426797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.38441 | −0.665243 | −0.332621 | − | 0.943060i | \(-0.607933\pi\) | ||||
−0.332621 | + | 0.943060i | \(0.607933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.2375 | −0.792629 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.27973 | 0.160006 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.84436 | −0.338345 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.62922 | −0.182744 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.95626 | 0.204489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8018 | −0.743624 | −0.371812 | − | 0.928308i | \(-0.621263\pi\) | ||||
−0.371812 | + | 0.928308i | \(0.621263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −26.7790 | −1.83487 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.26021 | −0.631541 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.29356 | 0.291466 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.7026 | −1.19623 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.79179 | −0.389598 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.39924 | −0.428525 | −0.214262 | − | 0.976776i | \(-0.568735\pi\) | ||||
−0.214262 | + | 0.976776i | \(0.568735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.14573 | −0.143048 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.348915 | −0.0231583 | −0.0115792 | − | 0.999933i | \(-0.503686\pi\) | ||||
−0.0115792 | + | 0.999933i | \(0.503686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8710 | −0.982704 | −0.491352 | − | 0.870961i | \(-0.663497\pi\) | ||||
−0.491352 | + | 0.870961i | \(0.663497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.94061 | −0.127683 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.2376 | −0.801712 | −0.400856 | − | 0.916141i | \(-0.631287\pi\) | ||||
−0.400856 | + | 0.916141i | \(0.631287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.70574 | −0.502667 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.58018 | −0.492385 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5476 | −0.682264 | −0.341132 | − | 0.940015i | \(-0.610810\pi\) | ||||
−0.341132 | + | 0.940015i | \(0.610810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.47743 | 0.224001 | 0.112000 | − | 0.993708i | \(-0.464274\pi\) | ||||
0.112000 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.78024 | −0.499103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.48281 | 0.0947333 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.95626 | 0.188102 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.86404 | −0.244874 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.53585 | −0.538778 | −0.269389 | − | 0.963031i | \(-0.586822\pi\) | ||||
−0.269389 | + | 0.963031i | \(0.586822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.43248 | −0.215798 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.6662 | −1.04368 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.28668 | 0.579287 | 0.289643 | − | 0.957135i | \(-0.406463\pi\) | ||||
0.289643 | + | 0.957135i | \(0.406463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.63237 | 0.474252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.74623 | −0.108089 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.11390 | −0.315336 | −0.157668 | − | 0.987492i | \(-0.550398\pi\) | ||||
−0.157668 | + | 0.987492i | \(0.550398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0271 | 1.29169 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.25397 | 0.199140 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.99275 | −0.487326 | −0.243663 | − | 0.969860i | \(-0.578349\pi\) | ||||
−0.243663 | + | 0.969860i | \(0.578349\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00230 | −0.121631 | −0.0608156 | − | 0.998149i | \(-0.519370\pi\) | ||||
−0.0608156 | + | 0.998149i | \(0.519370\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.94061 | −0.117451 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.80127 | −0.168923 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.240867 | 0.0144723 | 0.00723614 | − | 0.999974i | \(-0.497697\pi\) | ||||
0.00723614 | + | 0.999974i | \(0.497697\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.28879 | −0.196895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9760 | 0.953050 | 0.476525 | − | 0.879161i | \(-0.341896\pi\) | ||||
0.476525 | + | 0.879161i | \(0.341896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.81423 | −0.167289 | −0.0836443 | − | 0.996496i | \(-0.526656\pi\) | ||||
−0.0836443 | + | 0.996496i | \(0.526656\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.50682 | 0.503901 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.26702 | 0.192846 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.5449 | 0.973227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 30.5475 | 1.79072 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.4426 | −1.48637 | −0.743187 | − | 0.669084i | \(-0.766687\pi\) | ||||
−0.743187 | + | 0.669084i | \(0.766687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.249418 | −0.0145217 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.33537 | −0.251563 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.43248 | −0.198506 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.24504 | 0.359958 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.8512 | −1.02552 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.70724 | −0.0977564 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.3465 | 1.50367 | 0.751837 | − | 0.659349i | \(-0.229168\pi\) | ||||
0.751837 | + | 0.659349i | \(0.229168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.7040 | 1.12092 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.26643 | 0.525451 | 0.262726 | − | 0.964871i | \(-0.415379\pi\) | ||||
0.262726 | + | 0.964871i | \(0.415379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.51183 | 0.537641 | 0.268820 | − | 0.963190i | \(-0.413366\pi\) | ||||
0.268820 | + | 0.963190i | \(0.413366\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.13581 | −0.0639954 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.9336 | −0.614090 | −0.307045 | − | 0.951695i | \(-0.599340\pi\) | ||||
−0.307045 | + | 0.951695i | \(0.599340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.27973 | −0.127640 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 34.1824 | 1.90788 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1221 | −0.952696 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.80127 | −0.155387 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.45408 | 0.412212 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.19672 | 0.286504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.6026 | 1.79200 | 0.896000 | − | 0.444055i | \(-0.146461\pi\) | ||||
0.896000 | + | 0.444055i | \(0.146461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.84626 | −0.320373 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.58647 | −0.469129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5266 | −0.954737 | −0.477369 | − | 0.878703i | \(-0.658409\pi\) | ||||
−0.477369 | + | 0.878703i | \(0.658409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.01147 | 0.0549356 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.29356 | −0.232509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.87718 | −0.531770 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.7223 | −1.32716 | −0.663580 | − | 0.748105i | \(-0.730964\pi\) | ||||
−0.663580 | + | 0.748105i | \(0.730964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0093 | −0.642843 | −0.321421 | − | 0.946936i | \(-0.604161\pi\) | ||||
−0.321421 | + | 0.946936i | \(0.604161\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.33537 | −0.231405 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.20619 | −0.117423 | −0.0587117 | − | 0.998275i | \(-0.518699\pi\) | ||||
−0.0587117 | + | 0.998275i | \(0.518699\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4617 | −1.08599 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.2396 | 0.594864 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.70435 | 0.301064 | 0.150532 | − | 0.988605i | \(-0.451901\pi\) | ||||
0.150532 | + | 0.988605i | \(0.451901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2605 | −0.540027 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94061 | 0.101856 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5264 | −0.708006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2589 | 0.587710 | 0.293855 | − | 0.955850i | \(-0.405062\pi\) | ||||
0.293855 | + | 0.955850i | \(0.405062\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.50248 | −0.130274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.1806 | −0.736220 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2812 | −1.20546 | −0.602728 | − | 0.797946i | \(-0.705920\pi\) | ||||
−0.602728 | + | 0.797946i | \(0.705920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22.4486 | −1.15924 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.27973 | −0.117412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6533 | 0.649959 | 0.324979 | − | 0.945721i | \(-0.394643\pi\) | ||||
0.324979 | + | 0.945721i | \(0.394643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.7510 | 0.909412 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.42398 | −0.379348 | −0.189674 | − | 0.981847i | \(-0.560743\pi\) | ||||
−0.189674 | + | 0.981847i | \(0.560743\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.48281 | −0.0755710 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.78359 | −0.243164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.13672 | −0.159038 | −0.0795191 | − | 0.996833i | \(-0.525338\pi\) | ||||
−0.0795191 | + | 0.996833i | \(0.525338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8802 | 1.00539 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.90271 | −0.297752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.79196 | −0.291425 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.4590 | −1.22756 | −0.613781 | − | 0.789476i | \(-0.710352\pi\) | ||||
−0.613781 | + | 0.789476i | \(0.710352\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.73696 | −0.287207 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.3681 | 1.36670 | 0.683348 | − | 0.730092i | \(-0.260523\pi\) | ||||
0.683348 | + | 0.730092i | \(0.260523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.29356 | −0.213878 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.8827 | −0.789218 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.63237 | −0.378322 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.22204 | −0.0604258 | −0.0302129 | − | 0.999543i | \(-0.509619\pi\) | ||||
−0.0302129 | + | 0.999543i | \(0.509619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8000 | 0.730029 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.168206 | 0.00827688 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.95249 | −0.144932 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.91880 | 0.0939642 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.4860 | −0.561129 | −0.280564 | − | 0.959835i | \(-0.590522\pi\) | ||||
−0.280564 | + | 0.959835i | \(0.590522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.53451 | −0.464684 | −0.232342 | − | 0.972634i | \(-0.574639\pi\) | ||||
−0.232342 | + | 0.972634i | \(0.574639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.98059 | −0.193543 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.2244 | 0.786999 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.15136 | 0.0557180 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.94061 | 0.0936937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3980 | 0.549021 | 0.274511 | − | 0.961584i | \(-0.411484\pi\) | ||||
0.274511 | + | 0.961584i | \(0.411484\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.42472 | −0.404866 | −0.202433 | − | 0.979296i | \(-0.564885\pi\) | ||||
−0.202433 | + | 0.979296i | \(0.564885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.56007 | −0.314531 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10.1473 | −0.485412 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.1048 | −1.00728 | −0.503639 | − | 0.863914i | \(-0.668006\pi\) | ||||
−0.503639 | + | 0.863914i | \(0.668006\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.765982 | 0.0364754 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.7455 | 1.41325 | 0.706625 | − | 0.707588i | \(-0.250217\pi\) | ||||
0.706625 | + | 0.707588i | \(0.250217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.48634 | 0.117864 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.2816 | −0.911987 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.8937 | 0.938842 | 0.469421 | − | 0.882974i | \(-0.344463\pi\) | ||||
0.469421 | + | 0.882974i | \(0.344463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.26702 | −0.153838 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.47220 | −0.0691700 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.48281 | −0.0695152 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.2292 | 0.572059 | 0.286030 | − | 0.958221i | \(-0.407664\pi\) | ||||
0.286030 | + | 0.958221i | \(0.407664\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.1095 | 1.17201 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.8744 | −1.53111 | −0.765556 | − | 0.643369i | \(-0.777536\pi\) | ||||
−0.765556 | + | 0.643369i | \(0.777536\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.3571 | 0.620758 | 0.310379 | − | 0.950613i | \(-0.399544\pi\) | ||||
0.310379 | + | 0.950613i | \(0.399544\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −12.3550 | −0.572949 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5317 | −1.18147 | −0.590733 | − | 0.806867i | \(-0.701161\pi\) | ||||
−0.590733 | + | 0.806867i | \(0.701161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.79067 | 0.267388 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.8702 | 1.69889 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24504 | −0.287147 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.28130 | −0.379972 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8621 | 0.497341 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.9584 | 1.73437 | 0.867183 | − | 0.497990i | \(-0.165929\pi\) | ||||
0.867183 | + | 0.497990i | \(0.165929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.63237 | −0.348006 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.66112 | 0.303092 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 23.3411 | 1.05987 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.5736 | −0.977593 | −0.488796 | − | 0.872398i | \(-0.662564\pi\) | ||||
−0.488796 | + | 0.872398i | \(0.662564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.9457 | 0.947196 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.34145 | −0.376445 | −0.188222 | − | 0.982126i | \(-0.560273\pi\) | ||||
−0.188222 | + | 0.982126i | \(0.560273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.2037 | 0.594666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.13581 | 0.0510507 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.7993 | 0.618982 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.74508 | −0.122887 | −0.0614434 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614434 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.8707 | 1.69194 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.0724 | −0.939571 | −0.469785 | − | 0.882781i | \(-0.655669\pi\) | ||||
−0.469785 | + | 0.882781i | \(0.655669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.6400 | −0.606971 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.94061 | 0.0861857 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.7906 | 0.655582 | 0.327791 | − | 0.944750i | \(-0.393696\pi\) | ||||
0.327791 | + | 0.944750i | \(0.393696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.12217 | 0.403541 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.8165 | −0.565861 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.0557 | 0.663432 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.19672 | −0.228551 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −42.5055 | −1.86579 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.1380 | 0.926072 | 0.463036 | − | 0.886339i | \(-0.346760\pi\) | ||||
0.463036 | + | 0.886339i | \(0.346760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.93936 | 0.347164 | 0.173582 | − | 0.984819i | \(-0.444466\pi\) | ||||
0.173582 | + | 0.984819i | \(0.444466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.43619 | 0.237255 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 24.8674 | 1.08324 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2181 | −0.487742 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.128843 | −0.00559131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.26702 | −0.141510 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.1186 | 1.12920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.66477 | −0.114993 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0689 | −0.733851 | −0.366926 | − | 0.930250i | \(-0.619590\pi\) | ||||
−0.366926 | + | 0.930250i | \(0.619590\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.7507 | 1.49129 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.69561 | 0.243973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.50646 | −0.192683 | −0.0963413 | − | 0.995348i | \(-0.530714\pi\) | ||||
−0.0963413 | + | 0.995348i | \(0.530714\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.881918 | −0.0376394 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.73948 | −0.287112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.90607 | 0.166103 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.9626 | −0.932261 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.6886 | 1.85114 | 0.925572 | − | 0.378572i | \(-0.123585\pi\) | ||||
0.925572 | + | 0.378572i | \(0.123585\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.24504 | −0.264137 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.2396 | −0.474538 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.2961 | −0.433930 | −0.216965 | − | 0.976179i | \(-0.569616\pi\) | ||||
−0.216965 | + | 0.976179i | \(0.569616\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.772859 | 0.0325144 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.7112 | 0.449829 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.17191 | −0.342584 | −0.171292 | − | 0.985220i | \(-0.554794\pi\) | ||||
−0.171292 | + | 0.985220i | \(0.554794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.795651 | 0.0332970 | 0.0166485 | − | 0.999861i | \(-0.494700\pi\) | ||||
0.0166485 | + | 0.999861i | \(0.494700\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.4925 | 1.27384 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.61533 | 0.400987 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4885 | 0.436641 | 0.218320 | − | 0.975877i | \(-0.429942\pi\) | ||||
0.218320 | + | 0.975877i | \(0.429942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −50.8530 | −2.11338 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.99115 | 0.0826066 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1806 | 0.587301 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.13581 | 0.0469598 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.33437 | −0.137624 | −0.0688122 | − | 0.997630i | \(-0.521921\pi\) | ||||
−0.0688122 | + | 0.997630i | \(0.521921\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.6929 | −0.523001 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.4178 | 0.510802 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.52003 | −0.390941 | −0.195470 | − | 0.980710i | \(-0.562623\pi\) | ||||
−0.195470 | + | 0.980710i | \(0.562623\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.58813 | 0.352079 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.2115 | −0.745347 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.09126 | 0.330600 | 0.165300 | − | 0.986243i | \(-0.447141\pi\) | ||||
0.165300 | + | 0.986243i | \(0.447141\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45651 | −0.0594124 | −0.0297062 | − | 0.999559i | \(-0.509457\pi\) | ||||
−0.0297062 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.43555 | −0.180630 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.48281 | 0.0602848 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4429 | 1.19505 | 0.597525 | − | 0.801850i | \(-0.296151\pi\) | ||||
0.597525 | + | 0.801850i | \(0.296151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.42408 | 0.179273 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.19672 | −0.210237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.76454 | 0.394386 | 0.197193 | − | 0.980365i | \(-0.436817\pi\) | ||||
0.197193 | + | 0.980365i | \(0.436817\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.40104 | −0.379086 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.7235 | 0.834298 | 0.417149 | − | 0.908838i | \(-0.363029\pi\) | ||||
0.417149 | + | 0.908838i | \(0.363029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.45591 | 0.380065 | 0.190033 | − | 0.981778i | \(-0.439141\pi\) | ||||
0.190033 | + | 0.981778i | \(0.439141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.8811 | 0.597157 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.67678 | −0.0671786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.14649 | −0.125860 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.73696 | 0.229112 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 44.2051 | 1.76257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.0835 | −1.83455 | −0.917277 | − | 0.398251i | \(-0.869617\pi\) | ||||
−0.917277 | + | 0.398251i | \(0.869617\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.9620 | −0.833167 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13.5634 | 0.538248 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.5700 | −0.418142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.9594 | 1.10433 | 0.552165 | − | 0.833735i | \(-0.313802\pi\) | ||||
0.552165 | + | 0.833735i | \(0.313802\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.59170 | 0.0627706 | 0.0313853 | − | 0.999507i | \(-0.490008\pi\) | ||||
0.0313853 | + | 0.999507i | \(0.490008\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.9705 | −0.707587 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.37164 | 0.289809 | 0.144904 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144904 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.168206 | −0.00660267 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.33215 | 0.326563 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.8422 | −1.40262 | −0.701308 | − | 0.712859i | \(-0.747400\pi\) | ||||
−0.701308 | + | 0.712859i | \(0.747400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.51022 | −0.176229 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.98742 | −0.272605 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.9918 | −0.622952 | −0.311476 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311476 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2939 | −0.633758 | −0.316879 | − | 0.948466i | \(-0.602635\pi\) | ||||
−0.316879 | + | 0.948466i | \(0.602635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.2396 | −0.436511 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.38357 | −0.169988 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.82514 | 0.302991 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.4184 | −0.480125 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.15136 | −0.0444476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0502 | −0.425955 | −0.212978 | − | 0.977057i | \(-0.568316\pi\) | ||||
−0.212978 | + | 0.977057i | \(0.568316\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.1445 | 0.467444 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.6267 | −1.90731 | −0.953655 | − | 0.300902i | \(-0.902712\pi\) | ||||
−0.953655 | + | 0.300902i | \(0.902712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.7411 | −0.604089 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.677110 | −0.0259469 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.449062 | −0.0171829 | −0.00859144 | − | 0.999963i | \(-0.502735\pi\) | ||||
−0.00859144 | + | 0.999963i | \(0.502735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3086 | 0.432078 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.8589 | −1.10104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.1806 | 0.540238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7961 | 1.39979 | 0.699895 | − | 0.714246i | \(-0.253230\pi\) | ||||
0.699895 | + | 0.714246i | \(0.253230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.765982 | −0.0290973 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.46614 | 0.0556140 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.9219 | 0.716717 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.7485 | −0.898249 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1007 | −0.985809 | −0.492905 | − | 0.870083i | \(-0.664065\pi\) | ||||
−0.492905 | + | 0.870083i | \(0.664065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.5633 | −0.850990 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.9539 | −0.563196 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.19873 | 0.345954 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3394 | 1.32720 | 0.663600 | − | 0.748087i | \(-0.269028\pi\) | ||||
0.663600 | + | 0.748087i | \(0.269028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.99198 | −0.112208 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.7376 | 0.551927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48281 | 0.0554539 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.4687 | −0.764419 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.79535 | 0.365305 | 0.182652 | − | 0.983178i | \(-0.441532\pi\) | ||||
0.182652 | + | 0.983178i | \(0.441532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.1535 | −0.378135 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.74835 | 0.250974 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.38615 | 0.237176 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7322 | −1.17688 | −0.588441 | − | 0.808540i | \(-0.700258\pi\) | ||||
−0.588441 | + | 0.808540i | \(0.700258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.0352 | 0.630934 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.1700 | 1.33779 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.15992 | −0.264458 | −0.132229 | − | 0.991219i | \(-0.542213\pi\) | ||||
−0.132229 | + | 0.991219i | \(0.542213\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.87756 | 0.106140 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.79067 | −0.213302 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.5138 | 1.60068 | 0.800341 | − | 0.599545i | \(-0.204652\pi\) | ||||
0.800341 | + | 0.599545i | \(0.204652\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.73696 | 0.210753 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4006 | −0.895170 | −0.447585 | − | 0.894241i | \(-0.647716\pi\) | ||||
−0.447585 | + | 0.894241i | \(0.647716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7329 | −0.539772 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.52518 | −0.0558035 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.6142 | −0.643610 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.2199 | 0.993267 | 0.496634 | − | 0.867960i | \(-0.334569\pi\) | ||||
0.496634 | + | 0.867960i | \(0.334569\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.5648 | −0.603654 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.12490 | −0.0409393 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.0231333 | −0.000840793 0 | −0.000420397 | − | 1.00000i | \(-0.500134\pi\) | ||||
−0.000420397 | 1.00000i | \(0.500134\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.66112 | −0.241784 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.1675 | −0.658573 | −0.329287 | − | 0.944230i | \(-0.606808\pi\) | ||||
−0.329287 | + | 0.944230i | \(0.606808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.84109 | −0.139057 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.57835 | −0.237841 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.168206 | −0.00607357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.70549 | −0.349989 | −0.174994 | − | 0.984569i | \(-0.555991\pi\) | ||||
−0.174994 | + | 0.984569i | \(0.555991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0219 | 0.649041 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.85918 | −0.0668701 | −0.0334350 | − | 0.999441i | \(-0.510645\pi\) | ||||
−0.0334350 | + | 0.999441i | \(0.510645\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.0274 | 0.432039 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.8115 | 0.531359 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.65815 | −0.346039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7993 | −0.493776 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.88347 | 0.353206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.1722 | 1.00551 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.36669 | 0.155656 | 0.0778278 | − | 0.996967i | \(-0.475202\pi\) | ||||
0.0778278 | + | 0.996967i | \(0.475202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.92410 | −0.353307 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.521212 | −0.0185322 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.15136 | −0.0408858 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.8056 | 1.44722 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.65681 | 0.0941090 | 0.0470545 | − | 0.998892i | \(-0.485017\pi\) | ||||
0.0470545 | + | 0.998892i | \(0.485017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0983 | 1.06480 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.28438 | 0.0453814 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.12217 | −0.321914 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.08972 | 0.179389 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.5108 | −0.546007 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.01799 | −0.106107 | −0.0530534 | − | 0.998592i | \(-0.516895\pi\) | ||||
−0.0530534 | + | 0.998592i | \(0.516895\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0562 | 0.598924 | 0.299462 | − | 0.954108i | \(-0.403193\pi\) | ||||
0.299462 | + | 0.954108i | \(0.403193\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.88570 | −0.136277 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.0044 | 0.560611 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.4620 | −0.645903 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.765982 | −0.0267656 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.8148 | 1.21504 | 0.607522 | − | 0.794303i | \(-0.292164\pi\) | ||||
0.607522 | + | 0.794303i | \(0.292164\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.0235 | −1.46485 | −0.732423 | − | 0.680850i | \(-0.761611\pi\) | ||||
−0.732423 | + | 0.680850i | \(0.761611\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.43619 | −0.189264 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.1011 | −1.77696 | −0.888479 | − | 0.458917i | \(-0.848237\pi\) | ||||
−0.888479 | + | 0.458917i | \(0.848237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.6271 | −0.473289 | −0.236644 | − | 0.971596i | \(-0.576048\pi\) | ||||
−0.236644 | + | 0.971596i | \(0.576048\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.467430 | 0.0162150 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.79179 | −0.200674 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.9367 | 1.00140 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.6142 | 0.643399 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.9272 | 1.44749 | 0.723744 | − | 0.690068i | \(-0.242419\pi\) | ||||
0.723744 | + | 0.690068i | \(0.242419\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.8028 | −0.820787 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.0033 | 1.06781 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.48281 | 0.0510102 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.46134 | −0.187433 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 26.1980 | 0.898055 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.6996 | −1.18809 | −0.594047 | − | 0.804431i | \(-0.702471\pi\) | ||||
−0.594047 | + | 0.804431i | \(0.702471\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.35774 | 0.114832 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.8623 | −1.90822 | −0.954111 | − | 0.299454i | \(-0.903196\pi\) | ||||
−0.954111 | + | 0.299454i | \(0.903196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.17540 | −0.313061 | −0.156530 | − | 0.987673i | \(-0.550031\pi\) | ||||
−0.156530 | + | 0.987673i | \(0.550031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.34002 | 0.216067 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.5768 | 1.07489 | 0.537444 | − | 0.843299i | \(-0.319390\pi\) | ||||
0.537444 | + | 0.843299i | \(0.319390\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.4782 | −1.10429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 32.1072 | 1.09042 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.90607 | −0.132504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.79067 | −0.196209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0574 | 0.408082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.5678 | 0.391063 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.82613 | −0.196734 | −0.0983672 | − | 0.995150i | \(-0.531362\pi\) | ||||
−0.0983672 | + | 0.995150i | \(0.531362\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.3743 | −1.66535 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.72891 | −0.327775 | −0.163888 | − | 0.986479i | \(-0.552403\pi\) | ||||
−0.163888 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.2868 | 1.65863 | 0.829317 | − | 0.558778i | \(-0.188730\pi\) | ||||
0.829317 | + | 0.558778i | \(0.188730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.484024 | −0.0162703 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.0688 | 1.47969 | 0.739843 | − | 0.672779i | \(-0.234900\pi\) | ||||
0.739843 | + | 0.672779i | \(0.234900\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.14711 | −0.306784 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.7112 | −0.358839 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3629 | −0.514098 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.03613 | −0.0680605 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.66112 | −0.222408 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.78817 | 0.326454 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −82.1311 | −2.73618 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.1192 | 0.403302 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.5528 | 0.882643 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.30139 | −0.176030 | −0.0880148 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880148 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.04607 | −0.233703 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0252 | 1.12730 | 0.563652 | − | 0.826012i | \(-0.309396\pi\) | ||||
0.563652 | + | 0.826012i | \(0.309396\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.99115 | −0.0658973 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.31310 | −0.109528 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.04167 | 0.100445 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.1096 | −0.498418 | −0.249209 | − | 0.968450i | \(-0.580171\pi\) | ||||
−0.249209 | + | 0.968450i | \(0.580171\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.1284 | 1.68474 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.7993 | −0.454208 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.3804 | 0.702982 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.77738 | 0.255443 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.6738 | −0.973567 | −0.486784 | − | 0.873523i | \(-0.661830\pi\) | ||||
−0.486784 | + | 0.873523i | \(0.661830\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.95626 | 0.0968875 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.9826 | 0.588723 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.58813 | −0.280862 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0825 | 1.14610 | 0.573048 | − | 0.819522i | \(-0.305761\pi\) | ||||
0.573048 | + | 0.819522i | \(0.305761\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4588 | 0.602380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0092 | −0.456687 | −0.228344 | − | 0.973581i | \(-0.573331\pi\) | ||||
−0.228344 | + | 0.973581i | \(0.573331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.2140 | 0.365177 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.42852 | 0.209120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.54068 | −0.0825609 | −0.0412804 | − | 0.999148i | \(-0.513144\pi\) | ||||
−0.0412804 | + | 0.999148i | \(0.513144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.12217 | −0.296118 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.2178 | −0.688035 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.3206 | −1.27372 | −0.636860 | − | 0.770980i | \(-0.719767\pi\) | ||||
−0.636860 | + | 0.770980i | \(0.719767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.2991 | 0.753943 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.42408 | −0.143010 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.62644 | −0.246271 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5653 | −0.405333 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.4922 | 0.434780 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38.8565 | −1.25083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.9114 | −0.383045 | −0.191523 | − | 0.981488i | \(-0.561343\pi\) | ||||
−0.191523 | + | 0.981488i | \(0.561343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.2273 | −1.06741 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.8806 | 0.926824 | 0.463412 | − | 0.886143i | \(-0.346625\pi\) | ||||
0.463412 | + | 0.886143i | \(0.346625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.988761 | −0.0316982 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.43619 | −0.174097 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.545671 | −0.0174576 | −0.00872878 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872878 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.67678 | 0.0535900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.94221 | 0.0939375 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.4237 | −0.778995 | −0.389497 | − | 0.921028i | \(-0.627351\pi\) | ||||
−0.389497 | + | 0.921028i | \(0.627351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.48839 | 0.302325 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0848 | 0.321003 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.4360 | 0.681625 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5724 | −0.685270 | −0.342635 | − | 0.939469i | \(-0.611319\pi\) | ||||
−0.342635 | + | 0.939469i | \(0.611319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 63.2690 | 2.00778 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.9153 | −0.441144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.1961 | −1.62140 | −0.810699 | − | 0.585463i | \(-0.800913\pi\) | ||||
−0.810699 | + | 0.585463i | \(0.800913\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.0891 | 1.04689 |
(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 | 8008.2.a.p.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.p.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |