Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.161121.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.544588\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.42860 | −1.98053 | −0.990265 | − | 0.139196i | \(-0.955548\pi\) | ||||
−0.990265 | + | 0.139196i | \(0.955548\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.88401 | −0.712089 | −0.356045 | − | 0.934469i | \(-0.615875\pi\) | ||||
−0.356045 | + | 0.934469i | \(0.615875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.84527 | −0.556370 | −0.278185 | − | 0.960528i | \(-0.589733\pi\) | ||||
−0.278185 | + | 0.960528i | \(0.589733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.16786 | −1.43331 | −0.716653 | − | 0.697430i | \(-0.754327\pi\) | ||||
−0.716653 | + | 0.697430i | \(0.754327\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.42860 | 1.14346 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0891752 | 0.0216282 | 0.0108141 | − | 0.999942i | \(-0.496558\pi\) | ||||
0.0108141 | + | 0.999942i | \(0.496558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.45461 | −1.48079 | −0.740394 | − | 0.672173i | \(-0.765361\pi\) | ||||
−0.740394 | + | 0.672173i | \(0.765361\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.88401 | 0.411125 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.21151 | 0.669646 | 0.334823 | − | 0.942281i | \(-0.391324\pi\) | ||||
0.334823 | + | 0.942281i | \(0.391324\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.6125 | 2.92250 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.02095 | 0.560976 | 0.280488 | − | 0.959858i | \(-0.409504\pi\) | ||||
0.280488 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4636 | 1.87932 | 0.939661 | − | 0.342106i | \(-0.111140\pi\) | ||||
0.939661 | + | 0.342106i | \(0.111140\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.84527 | 0.321220 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.34353 | 1.41031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.51367 | −0.248845 | −0.124423 | − | 0.992229i | \(-0.539708\pi\) | ||||
−0.124423 | + | 0.992229i | \(0.539708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.16786 | 0.827519 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.82628 | −1.22226 | −0.611130 | − | 0.791531i | \(-0.709285\pi\) | ||||
−0.611130 | + | 0.791531i | \(0.709285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.61344 | 1.16104 | 0.580520 | − | 0.814246i | \(-0.302849\pi\) | ||||
0.580520 | + | 0.814246i | \(0.302849\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.42860 | −0.660177 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5711 | 1.68782 | 0.843910 | − | 0.536484i | \(-0.180248\pi\) | ||||
0.843910 | + | 0.536484i | \(0.180248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.45050 | −0.492929 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0891752 | −0.0124870 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.84132 | −0.390285 | −0.195142 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195142 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.17196 | 1.10191 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.45461 | 0.854934 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.92036 | 0.770766 | 0.385383 | − | 0.922757i | \(-0.374069\pi\) | ||||
0.385383 | + | 0.922757i | \(0.374069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29853 | 0.550370 | 0.275185 | − | 0.961391i | \(-0.411261\pi\) | ||||
0.275185 | + | 0.961391i | \(0.411261\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.88401 | −0.237363 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22.8864 | 2.83870 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.3364 | −1.62930 | −0.814649 | − | 0.579954i | \(-0.803071\pi\) | ||||
−0.814649 | + | 0.579954i | \(0.803071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.21151 | −0.386620 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9240 | 1.41511 | 0.707556 | − | 0.706657i | \(-0.249798\pi\) | ||||
0.707556 | + | 0.706657i | \(0.249798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.174243 | −0.0203936 | −0.0101968 | − | 0.999948i | \(-0.503246\pi\) | ||||
−0.0101968 | + | 0.999948i | \(0.503246\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.6125 | −1.68730 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.47651 | 0.396185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.45661 | −0.276390 | −0.138195 | − | 0.990405i | \(-0.544130\pi\) | ||||
−0.138195 | + | 0.990405i | \(0.544130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2161 | 1.23113 | 0.615565 | − | 0.788086i | \(-0.288928\pi\) | ||||
0.615565 | + | 0.788086i | \(0.288928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.394921 | −0.0428352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.02095 | −0.323879 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.3673 | −1.94693 | −0.973465 | − | 0.228835i | \(-0.926508\pi\) | ||||
−0.973465 | + | 0.228835i | \(0.926508\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.73630 | 1.02064 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4636 | −1.08503 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.5849 | 2.93275 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.13202 | −0.318009 | −0.159004 | − | 0.987278i | \(-0.550828\pi\) | ||||
−0.159004 | + | 0.987278i | \(0.550828\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.84527 | −0.185457 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.76183 | 0.175309 | 0.0876544 | − | 0.996151i | \(-0.472063\pi\) | ||||
0.0876544 | + | 0.996151i | \(0.472063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.99153 | −0.984494 | −0.492247 | − | 0.870455i | \(-0.663824\pi\) | ||||
−0.492247 | + | 0.870455i | \(0.663824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.34353 | −0.814245 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.65486 | −0.353329 | −0.176664 | − | 0.984271i | \(-0.556531\pi\) | ||||
−0.176664 | + | 0.984271i | \(0.556531\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.58240 | 0.822045 | 0.411022 | − | 0.911625i | \(-0.365172\pi\) | ||||
0.411022 | + | 0.911625i | \(0.365172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51367 | 0.143671 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.92953 | 0.651876 | 0.325938 | − | 0.945391i | \(-0.394320\pi\) | ||||
0.325938 | + | 0.945391i | \(0.394320\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.2225 | −1.32625 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.16786 | −0.477768 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.168007 | −0.0154012 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.59498 | −0.690452 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.82628 | 0.705672 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −42.5699 | −3.80756 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7672 | 1.13291 | 0.566454 | − | 0.824094i | \(-0.308315\pi\) | ||||
0.566454 | + | 0.824094i | \(0.308315\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.61344 | −0.670326 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.75251 | −0.153117 | −0.0765587 | − | 0.997065i | \(-0.524393\pi\) | ||||
−0.0765587 | + | 0.997065i | \(0.524393\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.1606 | 1.05445 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.42860 | 0.381153 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.7440 | 1.00335 | 0.501677 | − | 0.865055i | \(-0.332716\pi\) | ||||
0.501677 | + | 0.865055i | \(0.332716\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8695 | 1.09158 | 0.545789 | − | 0.837923i | \(-0.316230\pi\) | ||||
0.545789 | + | 0.837923i | \(0.316230\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.5711 | −0.974464 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.53609 | 0.797448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.3786 | −1.11103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.45050 | 0.284593 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.74986 | −0.716816 | −0.358408 | − | 0.933565i | \(-0.616680\pi\) | ||||
−0.358408 | + | 0.933565i | \(0.616680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.761158 | −0.0619422 | −0.0309711 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309711 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.0891752 | 0.00720939 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −46.3392 | −3.72205 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.5093 | 1.79643 | 0.898217 | − | 0.439552i | \(-0.144863\pi\) | ||||
0.898217 | + | 0.439552i | \(0.144863\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.84132 | 0.225331 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.05052 | −0.476848 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.9531 | −1.48452 | −0.742260 | − | 0.670112i | \(-0.766246\pi\) | ||||
−0.742260 | + | 0.670112i | \(0.766246\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.17196 | −0.636186 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7067 | 1.05436 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.45461 | −0.493596 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.76587 | −0.590428 | −0.295214 | − | 0.955431i | \(-0.595391\pi\) | ||||
−0.295214 | + | 0.955431i | \(0.595391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −27.5301 | −2.08108 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.92036 | −0.445002 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.63802 | 0.346662 | 0.173331 | − | 0.984864i | \(-0.444547\pi\) | ||||
0.173331 | + | 0.984864i | \(0.444547\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.9653 | −0.889375 | −0.444688 | − | 0.895686i | \(-0.646685\pi\) | ||||
−0.444688 | + | 0.895686i | \(0.646685\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.29853 | −0.317756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.70342 | 0.492846 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.164552 | −0.0120333 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.88401 | 0.137042 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.49863 | −0.180794 | −0.0903972 | − | 0.995906i | \(-0.528814\pi\) | ||||
−0.0903972 | + | 0.995906i | \(0.528814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.6727 | −1.41607 | −0.708036 | − | 0.706176i | \(-0.750419\pi\) | ||||
−0.708036 | + | 0.706176i | \(0.750419\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22.8864 | −1.63893 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.0553 | 1.50012 | 0.750062 | − | 0.661367i | \(-0.230023\pi\) | ||||
0.750062 | + | 0.661367i | \(0.230023\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.30427 | 0.0924572 | 0.0462286 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462286 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.3364 | 0.940676 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.69150 | −0.399465 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.6594 | 2.42072 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.21151 | 0.223215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.9105 | 0.823866 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2559 | 1.25679 | 0.628395 | − | 0.777894i | \(-0.283712\pi\) | ||||
0.628395 | + | 0.777894i | \(0.283712\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.9240 | −0.817016 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −33.7169 | −2.29947 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.7136 | −1.33825 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.174243 | 0.0117743 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.460844 | −0.0309997 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.16390 | −0.479730 | −0.239865 | − | 0.970806i | \(-0.577103\pi\) | ||||
−0.239865 | + | 0.970806i | \(0.577103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.6125 | 0.974166 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.58453 | −0.304286 | −0.152143 | − | 0.988359i | \(-0.548617\pi\) | ||||
−0.152143 | + | 0.988359i | \(0.548617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.62848 | −0.570186 | −0.285093 | − | 0.958500i | \(-0.592025\pi\) | ||||
−0.285093 | + | 0.958500i | \(0.592025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.47651 | −0.228738 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.3435 | 0.743139 | 0.371570 | − | 0.928405i | \(-0.378820\pi\) | ||||
0.371570 | + | 0.928405i | \(0.378820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −51.2438 | −3.34278 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.45661 | 0.159574 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.95726 | 0.514712 | 0.257356 | − | 0.966317i | \(-0.417149\pi\) | ||||
0.257356 | + | 0.966317i | \(0.417149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9868 | −1.60954 | −0.804770 | − | 0.593586i | \(-0.797712\pi\) | ||||
−0.804770 | + | 0.593586i | \(0.797712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.2809 | 0.976260 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 33.3565 | 2.12242 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.2161 | −0.710794 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7487 | 0.804689 | 0.402344 | − | 0.915488i | \(-0.368195\pi\) | ||||
0.402344 | + | 0.915488i | \(0.368195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.92610 | −0.372571 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.394921 | 0.0247309 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1781 | 0.884404 | 0.442202 | − | 0.896916i | \(-0.354197\pi\) | ||||
0.442202 | + | 0.896916i | \(0.354197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.85177 | 0.177200 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.02095 | 0.186992 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.65792 | 0.472208 | 0.236104 | − | 0.971728i | \(-0.424129\pi\) | ||||
0.236104 | + | 0.971728i | \(0.424129\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.5830 | 0.772970 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.3673 | 1.12406 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.2060 | 1.17101 | 0.585506 | − | 0.810668i | \(-0.300896\pi\) | ||||
0.585506 | + | 0.810668i | \(0.300896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.299771 | 0.0182098 | 0.00910489 | − | 0.999959i | \(-0.497102\pi\) | ||||
0.00910489 | + | 0.999959i | \(0.497102\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.73630 | −0.589268 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.9640 | −1.62599 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4831 | −0.689955 | −0.344978 | − | 0.938611i | \(-0.612113\pi\) | ||||
−0.344978 | + | 0.938611i | \(0.612113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.4636 | 0.626441 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.8670 | 0.648274 | 0.324137 | − | 0.946010i | \(-0.394926\pi\) | ||||
0.324137 | + | 0.946010i | \(0.394926\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.59764 | −0.570521 | −0.285260 | − | 0.958450i | \(-0.592080\pi\) | ||||
−0.285260 | + | 0.958450i | \(0.592080\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.5849 | −1.69322 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7448 | 0.870358 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9920 | −0.999532 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.13202 | 0.183602 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.9508 | 1.86659 | 0.933294 | − | 0.359114i | \(-0.116921\pi\) | ||||
0.933294 | + | 0.359114i | \(0.116921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.2189 | −1.52652 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.84527 | 0.107073 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.5966 | −0.959807 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3438 | −0.826764 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.76183 | −0.101215 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −19.0365 | −1.09002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5965 | −0.661847 | −0.330924 | − | 0.943658i | \(-0.607360\pi\) | ||||
−0.330924 | + | 0.943658i | \(0.607360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.99153 | 0.568398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.68667 | −0.322461 | −0.161231 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161231 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.50704 | 0.367800 | 0.183900 | − | 0.982945i | \(-0.441128\pi\) | ||||
0.183900 | + | 0.982945i | \(0.441128\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.34353 | 0.470105 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.1953 | 1.30278 | 0.651390 | − | 0.758743i | \(-0.274186\pi\) | ||||
0.651390 | + | 0.758743i | \(0.274186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.57446 | −0.312110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.65486 | 0.203994 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.575591 | −0.0320267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −75.5152 | −4.18883 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.58240 | −0.474608 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.8001 | −1.20188 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.7232 | 1.08409 | 0.542044 | − | 0.840350i | \(-0.317651\pi\) | ||||
0.542044 | + | 0.840350i | \(0.317651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.51367 | −0.0829484 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 59.0615 | 3.22687 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8567 | −0.645874 | −0.322937 | − | 0.946420i | \(-0.604670\pi\) | ||||
−0.322937 | + | 0.946420i | \(0.604670\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.92953 | −0.376361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3082 | −1.04560 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6889 | 1.06310 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.2225 | 0.765713 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4703 | 0.937857 | 0.468928 | − | 0.883236i | \(-0.344640\pi\) | ||||
0.468928 | + | 0.883236i | \(0.344640\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.2137 | 1.61730 | 0.808650 | − | 0.588290i | \(-0.200199\pi\) | ||||
0.808650 | + | 0.588290i | \(0.200199\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.16786 | 0.275840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.6819 | −1.26046 | −0.630229 | − | 0.776409i | \(-0.717039\pi\) | ||||
−0.630229 | + | 0.776409i | \(0.717039\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −52.8064 | −2.80267 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.168007 | 0.00889188 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.7084 | −1.14573 | −0.572863 | − | 0.819651i | \(-0.694167\pi\) | ||||
−0.572863 | + | 0.819651i | \(0.694167\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.6620 | 1.19274 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.59498 | 0.398633 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.771653 | 0.0403902 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.4853 | −1.59132 | −0.795661 | − | 0.605742i | \(-0.792876\pi\) | ||||
−0.795661 | + | 0.605742i | \(0.792876\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.82628 | −0.407420 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.35307 | 0.277918 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.3119 | 1.46593 | 0.732967 | − | 0.680264i | \(-0.238135\pi\) | ||||
0.732967 | + | 0.680264i | \(0.238135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 42.5699 | 2.19830 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.6118 | −0.804049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.0469 | −1.13247 | −0.566237 | − | 0.824243i | \(-0.691601\pi\) | ||||
−0.566237 | + | 0.824243i | \(0.691601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.7672 | −0.654084 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.3210 | −1.03835 | −0.519177 | − | 0.854667i | \(-0.673761\pi\) | ||||
−0.519177 | + | 0.854667i | \(0.673761\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.3961 | −0.784656 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.61344 | 0.387013 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.81405 | −0.294784 | −0.147392 | − | 0.989078i | \(-0.547088\pi\) | ||||
−0.147392 | + | 0.989078i | \(0.547088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.286387 | 0.0144832 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.75251 | 0.0884024 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.8793 | 0.547399 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.3084 | −1.27019 | −0.635096 | − | 0.772433i | \(-0.719039\pi\) | ||||
−0.635096 | + | 0.772433i | \(0.719039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.1606 | −0.608789 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.2771 | −1.06253 | −0.531265 | − | 0.847206i | \(-0.678283\pi\) | ||||
−0.531265 | + | 0.847206i | \(0.678283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −54.0745 | −2.69364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.42860 | −0.220059 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.79312 | 0.138450 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −39.4470 | −1.95053 | −0.975263 | − | 0.221047i | \(-0.929053\pi\) | ||||
−0.975263 | + | 0.221047i | \(0.929053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.7440 | −0.579287 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.1540 | −0.548854 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −49.6718 | −2.43829 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8695 | −0.630223 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.0752 | −0.736474 | −0.368237 | − | 0.929732i | \(-0.620038\pi\) | ||||
−0.368237 | + | 0.929732i | \(0.620038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.2233 | −0.985624 | −0.492812 | − | 0.870136i | \(-0.664031\pi\) | ||||
−0.492812 | + | 0.870136i | \(0.664031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.5711 | 0.562607 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.30307 | 0.0632082 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.09848 | −0.391913 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.53609 | −0.460407 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.4054 | −1.56091 | −0.780456 | − | 0.625211i | \(-0.785013\pi\) | ||||
−0.780456 | + | 0.625211i | \(0.785013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.6597 | −0.608387 | −0.304194 | − | 0.952610i | \(-0.598387\pi\) | ||||
−0.304194 | + | 0.952610i | \(0.598387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.3786 | 0.641453 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.7290 | −0.991604 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.4985 | −1.59879 | −0.799397 | − | 0.600803i | \(-0.794848\pi\) | ||||
−0.799397 | + | 0.600803i | \(0.794848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.45050 | −0.164310 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.7875 | 1.22520 | 0.612601 | − | 0.790392i | \(-0.290123\pi\) | ||||
0.612601 | + | 0.790392i | \(0.290123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 81.3414 | 3.85595 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.74986 | 0.413854 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.134437 | 0.00634446 | 0.00317223 | − | 0.999995i | \(-0.498990\pi\) | ||||
0.00317223 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.4416 | 0.680028 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.761158 | 0.0357623 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −43.1182 | −2.02141 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.7011 | −0.500578 | −0.250289 | − | 0.968171i | \(-0.580526\pi\) | ||||
−0.250289 | + | 0.968171i | \(0.580526\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0891752 | −0.00416234 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.23604 | −0.290441 | −0.145221 | − | 0.989399i | \(-0.546389\pi\) | ||||
−0.145221 | + | 0.989399i | \(0.546389\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0329 | 1.16338 | 0.581689 | − | 0.813411i | \(-0.302392\pi\) | ||||
0.581689 | + | 0.813411i | \(0.302392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 46.3392 | 2.14893 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.25511 | 0.289452 | 0.144726 | − | 0.989472i | \(-0.453770\pi\) | ||||
0.144726 | + | 0.989472i | \(0.453770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.1259 | 1.16021 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.5093 | −1.03717 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.0489 | −0.645967 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −94.3179 | −4.32760 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.84132 | −0.130095 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 39.8726 | 1.82183 | 0.910913 | − | 0.412598i | \(-0.135378\pi\) | ||||
0.910913 | + | 0.412598i | \(0.135378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.82241 | 0.356671 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.05052 | 0.275308 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8705 | 0.629826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.81602 | 0.172921 | 0.0864603 | − | 0.996255i | \(-0.472444\pi\) | ||||
0.0864603 | + | 0.996255i | \(0.472444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.9531 | 0.857088 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4535 | 0.742535 | 0.371267 | − | 0.928526i | \(-0.378923\pi\) | ||||
0.371267 | + | 0.928526i | \(0.378923\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.269393 | 0.0121329 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.17196 | 0.367302 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.4649 | −1.00769 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.3871 | −0.644057 | −0.322028 | − | 0.946730i | \(-0.604365\pi\) | ||||
−0.322028 | + | 0.946730i | \(0.604365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.7487 | −1.72772 | −0.863860 | − | 0.503732i | \(-0.831960\pi\) | ||||
−0.863860 | + | 0.503732i | \(0.831960\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.80244 | −0.347204 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.7067 | −0.608737 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.9491 | 0.618282 | 0.309141 | − | 0.951016i | \(-0.399958\pi\) | ||||
0.309141 | + | 0.951016i | \(0.399958\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.328276 | 0.0145221 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.45461 | 0.284978 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.2485 | 1.94982 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.3518 | −0.939053 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.76587 | 0.340884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7198 | 1.52110 | 0.760550 | − | 0.649279i | \(-0.224929\pi\) | ||||
0.760550 | + | 0.649279i | \(0.224929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.18919 | 0.314362 | 0.157181 | − | 0.987570i | \(-0.449759\pi\) | ||||
0.157181 | + | 0.987570i | \(0.449759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 27.5301 | 1.20151 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.933096 | 0.0406463 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.6862 | −0.551575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.92036 | 0.256922 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.4451 | 1.75187 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1859 | 0.699778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.63802 | −0.200145 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.36711 | 0.274251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5805 | 0.540878 | 0.270439 | − | 0.962737i | \(-0.412831\pi\) | ||||
0.270439 | + | 0.962737i | \(0.412831\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.9653 | 0.513481 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.0080 | −1.62808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.54235 | −0.0659462 | −0.0329731 | − | 0.999456i | \(-0.510498\pi\) | ||||
−0.0329731 | + | 0.999456i | \(0.510498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.29853 | 0.183457 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.4990 | −0.830686 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.62828 | 0.196815 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.70342 | −0.284545 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.4661 | −1.12140 | −0.560702 | − | 0.828017i | \(-0.689469\pi\) | ||||
−0.560702 | + | 0.828017i | \(0.689469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −39.3452 | −1.66412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.164552 | 0.00694740 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.2657 | −1.73914 | −0.869572 | − | 0.493806i | \(-0.835605\pi\) | ||||
−0.869572 | + | 0.493806i | \(0.835605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.6881 | −1.29106 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.88401 | −0.0791210 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.6241 | −1.03229 | −0.516147 | − | 0.856500i | \(-0.672634\pi\) | ||||
−0.516147 | + | 0.856500i | \(0.672634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.5529 | 1.48784 | 0.743921 | − | 0.668268i | \(-0.232964\pi\) | ||||
0.743921 | + | 0.668268i | \(0.232964\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.49863 | 0.104382 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.9281 | 1.95704 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.6068 | −0.566459 | −0.283229 | − | 0.959052i | \(-0.591406\pi\) | ||||
−0.283229 | + | 0.959052i | \(0.591406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.6727 | 0.817569 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.1313 | −0.876675 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.24299 | 0.217143 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.8864 | 0.946234 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.46542 | −0.184308 | −0.0921538 | − | 0.995745i | \(-0.529375\pi\) | ||||
−0.0921538 | + | 0.995745i | \(0.529375\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −67.5386 | −2.78288 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.0553 | −0.866097 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.7574 | 1.46838 | 0.734191 | − | 0.678943i | \(-0.237562\pi\) | ||||
0.734191 | + | 0.678943i | \(0.237562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.744036 | 0.0305025 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.30427 | −0.0533802 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4065 | −0.711210 | −0.355605 | − | 0.934636i | \(-0.615725\pi\) | ||||
−0.355605 | + | 0.934636i | \(0.615725\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6763 | 1.41447 | 0.707237 | − | 0.706976i | \(-0.249941\pi\) | ||||
0.707237 | + | 0.706976i | \(0.249941\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.3364 | −0.543099 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.6351 | 1.36746 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9382 | 0.931034 | 0.465517 | − | 0.885039i | \(-0.345868\pi\) | ||||
0.465517 | + | 0.885039i | \(0.345868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.69150 | 0.230631 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −59.7979 | −2.41916 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.1586 | 0.773810 | 0.386905 | − | 0.922120i | \(-0.373544\pi\) | ||||
0.386905 | + | 0.922120i | \(0.373544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −34.6594 | −1.39760 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.9411 | 0.722283 | 0.361141 | − | 0.932511i | \(-0.382387\pi\) | ||||
0.361141 | + | 0.932511i | \(0.382387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.33510 | 0.134049 | 0.0670245 | − | 0.997751i | \(-0.478649\pi\) | ||||
0.0670245 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.21151 | −0.128873 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.6042 | 1.38639 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 115.462 | 4.61850 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.9105 | −0.475659 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.134982 | −0.00538207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.5155 | −1.41385 | −0.706925 | − | 0.707289i | \(-0.749918\pi\) | ||||
−0.706925 | + | 0.707289i | \(0.749918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.2559 | −0.725609 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −56.5409 | −2.24376 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.8317 | 0.706517 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.9240 | 0.471704 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9112 | 0.549461 | 0.274730 | − | 0.961521i | \(-0.411411\pi\) | ||||
0.274730 | + | 0.961521i | \(0.411411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.57110 | −0.338011 | −0.169006 | − | 0.985615i | \(-0.554056\pi\) | ||||
−0.169006 | + | 0.985615i | \(0.554056\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.7169 | 1.32760 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.5038 | 1.74963 | 0.874813 | − | 0.484461i | \(-0.160984\pi\) | ||||
0.874813 | + | 0.484461i | \(0.160984\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.9247 | −0.428831 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.7136 | 0.772637 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.37382 | 0.171161 | 0.0855805 | − | 0.996331i | \(-0.472726\pi\) | ||||
0.0855805 | + | 0.996331i | \(0.472726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.76116 | 0.303254 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.174243 | −0.00679788 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.68235 | −0.377171 | −0.188585 | − | 0.982057i | \(-0.560390\pi\) | ||||
−0.188585 | + | 0.982057i | \(0.560390\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8248 | 0.809992 | 0.404996 | − | 0.914318i | \(-0.367273\pi\) | ||||
0.404996 | + | 0.914318i | \(0.367273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.460844 | 0.0178977 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −53.8542 | −2.08838 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.70179 | 0.375655 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.16390 | 0.276972 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.93195 | −0.306209 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.75633 | 0.376079 | 0.188039 | − | 0.982161i | \(-0.439787\pi\) | ||||
0.188039 | + | 0.982161i | \(0.439787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.6125 | −0.562435 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.4827 | −0.825647 | −0.412823 | − | 0.910811i | \(-0.635457\pi\) | ||||
−0.412823 | + | 0.910811i | \(0.635457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.90077 | 0.226451 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.58453 | 0.175679 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.4925 | 0.631068 | 0.315534 | − | 0.948914i | \(-0.397816\pi\) | ||||
0.315534 | + | 0.948914i | \(0.397816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −52.0093 | −1.98717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.62848 | 0.329197 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.6835 | 0.559397 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0700 | −0.915666 | −0.457833 | − | 0.889038i | \(-0.651374\pi\) | ||||
−0.457833 | + | 0.889038i | \(0.651374\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.47651 | 0.132062 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −56.9939 | −2.16190 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.697910 | −0.0264352 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.3435 | −0.429052 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.5056 | −0.585640 | −0.292820 | − | 0.956168i | \(-0.594594\pi\) | ||||
−0.292820 | + | 0.956168i | \(0.594594\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.77013 | 0.368487 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 51.2438 | 1.92995 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.31931 | −0.124835 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.9477 | −1.23738 | −0.618689 | − | 0.785636i | \(-0.712336\pi\) | ||||
−0.618689 | + | 0.785636i | \(0.712336\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.45661 | −0.0921301 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.6040 | 1.25848 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.2315 | −1.57937 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.95726 | −0.297169 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.1464 | 1.23615 | 0.618076 | − | 0.786119i | \(-0.287913\pi\) | ||||
0.618076 | + | 0.786119i | \(0.287913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8242 | 0.701048 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.9868 | 0.929269 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.1435 | 1.63945 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.57131 | 0.132453 | 0.0662263 | − | 0.997805i | \(-0.478904\pi\) | ||||
0.0662263 | + | 0.997805i | \(0.478904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.678930 | 0.0251111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.4545 | −0.423081 | −0.211541 | − | 0.977369i | \(-0.567848\pi\) | ||||
−0.211541 | + | 0.977369i | \(0.567848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.2809 | −0.563644 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.6092 | 0.906493 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.93622 | 0.0712251 | 0.0356126 | − | 0.999366i | \(-0.488662\pi\) | ||||
0.0356126 | + | 0.999366i | \(0.488662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −33.3565 | −1.22538 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 47.0852 | 1.72739 | 0.863695 | − | 0.504015i | \(-0.168144\pi\) | ||||
0.863695 | + | 0.504015i | \(0.168144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.7496 | 1.41968 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.2161 | 0.410377 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.88580 | 0.251602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9219 | 1.42028 | 0.710141 | − | 0.704060i | \(-0.248631\pi\) | ||||
0.710141 | + | 0.704060i | \(0.248631\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.7487 | −0.464587 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.37087 | 0.122678 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1383 | 0.913669 | 0.456834 | − | 0.889552i | \(-0.348983\pi\) | ||||
0.456834 | + | 0.889552i | \(0.348983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.92610 | 0.215104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.6330 | −0.892945 | −0.446473 | − | 0.894797i | \(-0.647320\pi\) | ||||
−0.446473 | + | 0.894797i | \(0.647320\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.1693 | −0.585369 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.394921 | −0.0142784 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −30.5956 | −1.10474 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.50988 | 0.198692 | 0.0993458 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993458 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.1781 | −0.510611 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.73543 | −0.134354 | −0.0671771 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671771 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 152.900 | 5.49232 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.85177 | −0.102307 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 50.5156 | 1.80991 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.0029 | −0.787326 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.02095 | −0.107960 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −99.6845 | −3.55789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.4386 | −0.728557 | −0.364279 | − | 0.931290i | \(-0.618684\pi\) | ||||
−0.364279 | + | 0.931290i | \(0.618684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.65792 | −0.272629 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.0553 | −0.464194 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.2142 | −0.788848 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.5830 | −0.446275 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0001 | 0.425065 | 0.212533 | − | 0.977154i | \(-0.431829\pi\) | ||||
0.212533 | + | 0.977154i | \(0.431829\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.03186 | 0.0365045 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.3673 | −0.648977 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.321526 | 0.0113464 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.7953 | 0.944411 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −19.2060 | −0.676084 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.91890 | 0.102623 | 0.0513116 | − | 0.998683i | \(-0.483660\pi\) | ||||
0.0513116 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.1192 | 0.355333 | 0.177667 | − | 0.984091i | \(-0.443145\pi\) | ||||
0.177667 | + | 0.984091i | \(0.443145\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.299771 | −0.0105134 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 83.9356 | 2.94014 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −49.1418 | −1.71925 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.73630 | 0.340214 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.3896 | 1.72371 | 0.861855 | − | 0.507155i | \(-0.169303\pi\) | ||||
0.861855 | + | 0.507155i | \(0.169303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1619 | −1.01652 | −0.508261 | − | 0.861203i | \(-0.669711\pi\) | ||||
−0.508261 | + | 0.861203i | \(0.669711\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 26.9640 | 0.938766 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0347 | 0.557583 | 0.278791 | − | 0.960352i | \(-0.410066\pi\) | ||||
0.278791 | + | 0.960352i | \(0.410066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.0995 | −0.871743 | −0.435871 | − | 0.900009i | \(-0.643560\pi\) | ||||
−0.435871 | + | 0.900009i | \(0.643560\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.4831 | 0.398346 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.307699 | −0.0106611 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.42860 | −0.153258 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.4636 | −0.361676 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.9491 | −1.06848 | −0.534241 | − | 0.845332i | \(-0.679402\pi\) | ||||
−0.534241 | + | 0.845332i | \(0.679402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.8739 | −0.685306 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.8670 | −0.374281 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −60.7016 | −2.08820 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.3090 | 0.491664 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.59764 | 0.329390 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.86115 | −0.166638 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.7371 | −1.32633 | −0.663166 | − | 0.748472i | \(-0.730788\pi\) | ||||
−0.663166 | + | 0.748472i | \(0.730788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.5849 | 0.977582 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.5386 | −1.55557 | −0.777784 | − | 0.628532i | \(-0.783656\pi\) | ||||
−0.777784 | + | 0.628532i | \(0.783656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4128 | 0.696477 | 0.348238 | − | 0.937406i | \(-0.386780\pi\) | ||||
0.348238 | + | 0.937406i | \(0.386780\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.7448 | −0.502501 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.2563 | −0.927815 | −0.463907 | − | 0.885884i | \(-0.653553\pi\) | ||||
−0.463907 | + | 0.885884i | \(0.653553\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.3919 | 1.16936 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9920 | 0.577080 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.53311 | 0.153775 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68.9205 | 2.33528 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.13202 | −0.106003 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 80.2021 | 2.71133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.1311 | −1.82788 | −0.913939 | − | 0.405851i | \(-0.866975\pi\) | ||||
−0.913939 | + | 0.405851i | \(0.866975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.9508 | −1.07767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 49.1257 | 1.65509 | 0.827543 | − | 0.561403i | \(-0.189738\pi\) | ||||
0.827543 | + | 0.561403i | \(0.189738\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.8325 | 1.20586 | 0.602930 | − | 0.797794i | \(-0.294000\pi\) | ||||
0.602930 | + | 0.797794i | \(0.294000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 26.2189 | 0.881339 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.2790 | 1.08382 | 0.541911 | − | 0.840436i | \(-0.317701\pi\) | ||||
0.541911 | + | 0.840436i | \(0.317701\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0536 | −0.806731 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.84527 | −0.0618189 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −74.6870 | −2.49931 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.5399 | −0.686574 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.5966 | 0.554145 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.6101 | 1.05425 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.253375 | −0.00844114 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.3438 | 0.477332 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 52.9896 | 1.76143 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9281 | 0.429269 | 0.214635 | − | 0.976694i | \(-0.431144\pi\) | ||||
0.214635 | + | 0.976694i | \(0.431144\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.76183 | 0.0584362 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.4084 | −1.37192 | −0.685961 | − | 0.727638i | \(-0.740618\pi\) | ||||
−0.685961 | + | 0.727638i | \(0.740618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.6968 | −0.684964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.0365 | 0.629326 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.30175 | 0.109033 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.204782 | 0.00675514 | 0.00337757 | − | 0.999994i | \(-0.498925\pi\) | ||||
0.00337757 | + | 0.999994i | \(0.498925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.5965 | 0.382118 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −61.6212 | −2.02829 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.1184 | −0.727250 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.99153 | −0.328165 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.8315 | 0.978741 | 0.489371 | − | 0.872076i | \(-0.337227\pi\) | ||||
0.489371 | + | 0.872076i | \(0.337227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.2716 | 0.729923 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.68667 | 0.186173 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.728736 | 0.0238322 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.7370 | 0.906128 | 0.453064 | − | 0.891478i | \(-0.350331\pi\) | ||||
0.453064 | + | 0.891478i | \(0.350331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.50704 | −0.212349 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.2119 | −1.53906 | −0.769532 | − | 0.638609i | \(-0.779510\pi\) | ||||
−0.769532 | + | 0.638609i | \(0.779510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.1341 | −0.818481 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.34353 | −0.271415 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.6942 | −0.542487 | −0.271244 | − | 0.962511i | \(-0.587435\pi\) | ||||
−0.271244 | + | 0.962511i | \(0.587435\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.900464 | 0.0292303 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.1953 | −0.752160 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.0236 | 0.389482 | 0.194741 | − | 0.980855i | \(-0.437613\pi\) | ||||
0.194741 | + | 0.980855i | \(0.437613\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0654 | 0.358069 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.57446 | 0.180197 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.1258 | −0.714478 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.4875 | 2.53185 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.65486 | −0.117776 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 87.1225 | 2.80457 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.3542 | 1.29770 | 0.648852 | − | 0.760914i | \(-0.275249\pi\) | ||||
0.648852 | + | 0.760914i | \(0.275249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.575591 | 0.0184906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.5121 | −0.947088 | −0.473544 | − | 0.880770i | \(-0.657026\pi\) | ||||
−0.473544 | + | 0.880770i | \(0.657026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.2463 | −0.777301 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 75.5152 | 2.41842 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.577211 | −0.0184666 | −0.00923330 | − | 0.999957i | \(-0.502939\pi\) | ||||
−0.00923330 | + | 0.999957i | \(0.502939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.8926 | 1.08321 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.58240 | 0.274015 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.6804 | 1.32940 | 0.664698 | − | 0.747112i | \(-0.268560\pi\) | ||||
0.664698 | + | 0.747112i | \(0.268560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −93.2453 | −2.97104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.8001 | 0.693905 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.4506 | 0.777485 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.68185 | 0.275788 | 0.137894 | − | 0.990447i | \(-0.455967\pi\) | ||||
0.137894 | + | 0.990447i | \(0.455967\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.7232 | −0.625898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.77609 | −0.183114 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.2583 | 1.05330 | 0.526650 | − | 0.850082i | \(-0.323448\pi\) | ||||
0.526650 | + | 0.850082i | \(0.323448\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.51367 | 0.0478903 |
(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 | 8016.2.a.q.1.1 | 5 | ||
4.3 | odd | 2 | 2004.2.a.b.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 6012.2.a.f.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.b.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
6012.2.a.f.1.5 | 5 | 12.11 | even | 2 | |||
8016.2.a.q.1.1 | 5 | 1.1 | even | 1 | trivial |