Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | 0.167528 | 0.0967223 | 0.0483611 | − | 0.998830i | \(-0.484600\pi\) | ||||
0.0483611 | + | 0.998830i | \(0.484600\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.89143 | −1.47082 | −0.735410 | − | 0.677622i | \(-0.763011\pi\) | ||||
−0.735410 | + | 0.677622i | \(0.763011\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97193 | −0.990645 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.80808 | 1.14818 | 0.574089 | − | 0.818793i | \(-0.305356\pi\) | ||||
0.574089 | + | 0.818793i | \(0.305356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.290451 | 0.0805567 | 0.0402784 | − | 0.999188i | \(-0.487176\pi\) | ||||
0.0402784 | + | 0.999188i | \(0.487176\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.167528 | −0.0432555 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.491694 | −0.119253 | −0.0596267 | − | 0.998221i | \(-0.518991\pi\) | ||||
−0.0596267 | + | 0.998221i | \(0.518991\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.25879 | −0.977033 | −0.488517 | − | 0.872555i | \(-0.662462\pi\) | ||||
−0.488517 | + | 0.872555i | \(0.662462\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.651922 | −0.142261 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.71853 | 1.81794 | 0.908970 | − | 0.416862i | \(-0.136870\pi\) | ||||
0.908970 | + | 0.416862i | \(0.136870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00047 | −0.192540 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00707 | 0.372704 | 0.186352 | − | 0.982483i | \(-0.440334\pi\) | ||||
0.186352 | + | 0.982483i | \(0.440334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.46257 | 0.442291 | 0.221146 | − | 0.975241i | \(-0.429020\pi\) | ||||
0.221146 | + | 0.975241i | \(0.429020\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.637959 | 0.111054 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.89143 | 0.657771 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.86566 | 1.45751 | 0.728753 | − | 0.684776i | \(-0.240100\pi\) | ||||
0.728753 | + | 0.684776i | \(0.240100\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0486587 | 0.00779163 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.82952 | −1.06659 | −0.533296 | − | 0.845929i | \(-0.679047\pi\) | ||||
−0.533296 | + | 0.845929i | \(0.679047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9057 | −1.66310 | −0.831549 | − | 0.555451i | \(-0.812545\pi\) | ||||
−0.831549 | + | 0.555451i | \(0.812545\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.97193 | 0.443030 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.14522 | 0.750507 | 0.375253 | − | 0.926922i | \(-0.377556\pi\) | ||||
0.375253 | + | 0.926922i | \(0.377556\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.14319 | 1.16331 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0823725 | −0.0115345 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.63701 | 0.636942 | 0.318471 | − | 0.947933i | \(-0.396831\pi\) | ||||
0.318471 | + | 0.947933i | \(0.396831\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.80808 | −0.513481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.713466 | −0.0945009 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0465 | 1.43814 | 0.719069 | − | 0.694939i | \(-0.244569\pi\) | ||||
0.719069 | + | 0.694939i | \(0.244569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.286775 | −0.0367177 | −0.0183589 | − | 0.999831i | \(-0.505844\pi\) | ||||
−0.0183589 | + | 0.999831i | \(0.505844\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.5651 | 1.45706 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.290451 | −0.0360261 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.22227 | −0.393664 | −0.196832 | − | 0.980437i | \(-0.563065\pi\) | ||||
−0.196832 | + | 0.980437i | \(0.563065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.46060 | 0.175835 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53421 | −0.300755 | −0.150378 | − | 0.988629i | \(-0.548049\pi\) | ||||
−0.150378 | + | 0.988629i | \(0.548049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.56543 | −0.651384 | −0.325692 | − | 0.945476i | \(-0.605597\pi\) | ||||
−0.325692 | + | 0.945476i | \(0.605597\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.167528 | 0.0193445 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.8188 | −1.68876 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6404 | −1.19713 | −0.598567 | − | 0.801073i | \(-0.704263\pi\) | ||||
−0.598567 | + | 0.801073i | \(0.704263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.74820 | 0.972022 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.47038 | 0.161395 | 0.0806975 | − | 0.996739i | \(-0.474285\pi\) | ||||
0.0806975 | + | 0.996739i | \(0.474285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.491694 | 0.0533317 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.336241 | 0.0360488 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.34625 | 0.884701 | 0.442350 | − | 0.896842i | \(-0.354145\pi\) | ||||
0.442350 | + | 0.896842i | \(0.354145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.13027 | −0.118484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.412550 | 0.0427794 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.25879 | 0.436942 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4387 | −1.05989 | −0.529943 | − | 0.848034i | \(-0.677787\pi\) | ||||
−0.529943 | + | 0.848034i | \(0.677787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.3174 | −1.13744 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.7396 | 1.06863 | 0.534314 | − | 0.845286i | \(-0.320570\pi\) | ||||
0.534314 | + | 0.845286i | \(0.320570\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8116 | −1.06530 | −0.532649 | − | 0.846336i | \(-0.678803\pi\) | ||||
−0.532649 | + | 0.846336i | \(0.678803\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.651922 | 0.0636211 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.52515 | −0.534136 | −0.267068 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267068 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.2933 | −1.08170 | −0.540849 | − | 0.841120i | \(-0.681897\pi\) | ||||
−0.540849 | + | 0.841120i | \(0.681897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.48525 | 0.140973 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8815 | 1.11772 | 0.558858 | − | 0.829264i | \(-0.311240\pi\) | ||||
0.558858 | + | 0.829264i | \(0.311240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.71853 | −0.813007 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.863202 | −0.0798031 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.91339 | 0.175400 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50144 | 0.318313 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.14413 | −0.103163 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41226 | 0.125318 | 0.0626590 | − | 0.998035i | \(-0.480042\pi\) | ||||
0.0626590 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.82700 | −0.160859 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.64353 | 0.143596 | 0.0717980 | − | 0.997419i | \(-0.477126\pi\) | ||||
0.0717980 | + | 0.997419i | \(0.477126\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.5728 | 1.43704 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00047 | 0.0861064 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.6338 | −0.908508 | −0.454254 | − | 0.890872i | \(-0.650094\pi\) | ||||
−0.454254 | + | 0.890872i | \(0.650094\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.89433 | 0.415131 | 0.207566 | − | 0.978221i | \(-0.433446\pi\) | ||||
0.207566 | + | 0.978221i | \(0.433446\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.861967 | 0.0725907 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.10606 | 0.0924935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00707 | −0.166678 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.36421 | 0.112518 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.51254 | −0.451605 | −0.225802 | − | 0.974173i | \(-0.572500\pi\) | ||||
−0.225802 | + | 0.974173i | \(0.572500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.40935 | −0.521586 | −0.260793 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260793 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.46128 | 0.118138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.46257 | −0.197799 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.5657 | −1.64132 | −0.820660 | − | 0.571417i | \(-0.806394\pi\) | ||||
−0.820660 | + | 0.571417i | \(0.806394\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.776828 | 0.0616065 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.9275 | −2.67386 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.7435 | 0.998145 | 0.499072 | − | 0.866560i | \(-0.333674\pi\) | ||||
0.499072 | + | 0.866560i | \(0.333674\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.637959 | −0.0496650 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.1650 | −1.25088 | −0.625442 | − | 0.780271i | \(-0.715081\pi\) | ||||
−0.625442 | + | 0.780271i | \(0.715081\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9156 | −0.993511 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.6568 | 0.967893 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.5417 | 1.02955 | 0.514777 | − | 0.857324i | \(-0.327875\pi\) | ||||
0.514777 | + | 0.857324i | \(0.327875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.89143 | −0.294164 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.85060 | 0.139100 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.44981 | −0.183108 | −0.0915538 | − | 0.995800i | \(-0.529183\pi\) | ||||
−0.0915538 | + | 0.995800i | \(0.529183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0186908 | −0.00138928 | −0.000694640 | − | 1.00000i | \(-0.500221\pi\) | ||||
−0.000694640 | 1.00000i | \(0.500221\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0480427 | −0.00355142 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.86566 | −0.651817 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.87241 | −0.136924 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.89324 | 0.283191 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.53162 | −0.400254 | −0.200127 | − | 0.979770i | \(-0.564135\pi\) | ||||
−0.200127 | + | 0.979770i | \(0.564135\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.1560 | 1.37888 | 0.689438 | − | 0.724345i | \(-0.257857\pi\) | ||||
0.689438 | + | 0.724345i | \(0.257857\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0486587 | −0.00348452 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4071 | −1.24020 | −0.620102 | − | 0.784521i | \(-0.712909\pi\) | ||||
−0.620102 | + | 0.784521i | \(0.712909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.65465 | −0.329959 | −0.164980 | − | 0.986297i | \(-0.552756\pi\) | ||||
−0.164980 | + | 0.986297i | \(0.552756\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.539821 | −0.0380760 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.81038 | −0.548181 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.82952 | 0.476994 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.9109 | −1.80093 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.2178 | −1.12181 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7612 | −1.77348 | −0.886738 | − | 0.462273i | \(-0.847034\pi\) | ||||
−0.886738 | + | 0.462273i | \(0.847034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.424551 | −0.0290897 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.9057 | 0.743760 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.58292 | −0.650531 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.932364 | −0.0630033 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.142813 | −0.00960666 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.14177 | 0.612178 | 0.306089 | − | 0.952003i | \(-0.400979\pi\) | ||||
0.306089 | + | 0.952003i | \(0.400979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.97193 | −0.198129 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.27798 | 0.217567 | 0.108784 | − | 0.994065i | \(-0.465304\pi\) | ||||
0.108784 | + | 0.994065i | \(0.465304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4092 | −1.21652 | −0.608258 | − | 0.793740i | \(-0.708131\pi\) | ||||
−0.608258 | + | 0.793740i | \(0.708131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.48257 | −0.163341 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.14449 | −0.468051 | −0.234025 | − | 0.972230i | \(-0.575190\pi\) | ||||
−0.234025 | + | 0.972230i | \(0.575190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.14522 | −0.335637 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.78256 | −0.115790 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.6506 | 0.947671 | 0.473836 | − | 0.880613i | \(-0.342869\pi\) | ||||
0.473836 | + | 0.880613i | \(0.342869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.98268 | 0.514210 | 0.257105 | − | 0.966383i | \(-0.417231\pi\) | ||||
0.257105 | + | 0.966383i | \(0.417231\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.46696 | 0.286556 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.14319 | −0.520250 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23697 | −0.0787066 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.246329 | 0.0156105 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0627 | −0.824510 | −0.412255 | − | 0.911069i | \(-0.635259\pi\) | ||||
−0.412255 | + | 0.911069i | \(0.635259\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.2008 | 2.08732 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0823725 | 0.00515837 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2393 | 0.763464 | 0.381732 | − | 0.924273i | \(-0.375328\pi\) | ||||
0.381732 | + | 0.924273i | \(0.375328\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.5001 | −2.14373 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.96489 | −0.369217 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.1594 | 1.61306 | 0.806528 | − | 0.591196i | \(-0.201344\pi\) | ||||
0.806528 | + | 0.591196i | \(0.201344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.63701 | −0.284849 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.39823 | 0.0855703 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.10981 | 0.494464 | 0.247232 | − | 0.968956i | \(-0.420479\pi\) | ||||
0.247232 | + | 0.968956i | \(0.420479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.350519 | −0.0212925 | −0.0106463 | − | 0.999943i | \(-0.503389\pi\) | ||||
−0.0106463 | + | 0.999943i | \(0.503389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.189352 | −0.0114601 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.80808 | 0.229636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3250 | −0.980871 | −0.490436 | − | 0.871477i | \(-0.663162\pi\) | ||||
−0.490436 | + | 0.871477i | \(0.663162\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.31861 | −0.438154 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.2566 | −1.32772 | −0.663860 | − | 0.747857i | \(-0.731083\pi\) | ||||
−0.663860 | + | 0.747857i | \(0.731083\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.5738 | −1.16354 | −0.581771 | − | 0.813353i | \(-0.697640\pi\) | ||||
−0.581771 | + | 0.813353i | \(0.697640\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.713466 | 0.0422621 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.5766 | 1.56876 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7582 | −0.985779 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.74877 | −0.102514 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5087 | −1.02287 | −0.511435 | − | 0.859322i | \(-0.670886\pi\) | ||||
−0.511435 | + | 0.859322i | \(0.670886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0465 | −0.643154 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.80985 | −0.221070 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.53231 | 0.146447 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.4386 | 2.44612 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.79918 | 0.103360 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.286775 | 0.0164207 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.18354 | 0.352913 | 0.176457 | − | 0.984308i | \(-0.443536\pi\) | ||||
0.176457 | + | 0.984308i | \(0.443536\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.81124 | −0.103038 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.7369 | −0.892359 | −0.446180 | − | 0.894943i | \(-0.647216\pi\) | ||||
−0.446180 | + | 0.894943i | \(0.647216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0198 | 0.962018 | 0.481009 | − | 0.876716i | \(-0.340270\pi\) | ||||
0.481009 | + | 0.876716i | \(0.340270\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.5651 | −0.651617 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.64336 | −0.485460 | −0.242730 | − | 0.970094i | \(-0.578043\pi\) | ||||
−0.242730 | + | 0.970094i | \(0.578043\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.64309 | 0.427931 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.925617 | −0.0516629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.09402 | 0.116514 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.290451 | 0.0161113 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.89194 | −0.104624 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.0222 | −1.10386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1262 | −0.776447 | −0.388223 | − | 0.921565i | \(-0.626911\pi\) | ||||
−0.388223 | + | 0.921565i | \(0.626911\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −26.3482 | −1.44387 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.22227 | 0.176052 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7314 | −0.693522 | −0.346761 | − | 0.937954i | \(-0.612718\pi\) | ||||
−0.346761 | + | 0.937954i | \(0.612718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.99048 | 0.108108 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.37767 | 0.507829 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.44866 | −0.240205 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.46060 | −0.0786359 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45968 | 0.0783595 | 0.0391798 | − | 0.999232i | \(-0.487525\pi\) | ||||
0.0391798 | + | 0.999232i | \(0.487525\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.7787 | −1.54049 | −0.770244 | − | 0.637749i | \(-0.779866\pi\) | ||||
−0.770244 | + | 0.637749i | \(0.779866\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.290587 | −0.0155104 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.6016 | 1.41586 | 0.707930 | − | 0.706282i | \(-0.249629\pi\) | ||||
0.707930 | + | 0.706282i | \(0.249629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53421 | 0.134502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.320546 | 0.0169651 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8903 | −0.627549 | −0.313774 | − | 0.949498i | \(-0.601594\pi\) | ||||
−0.313774 | + | 0.949498i | \(0.601594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.862722 | −0.0454064 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.586590 | 0.0307880 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.56543 | 0.291308 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7937 | −0.615628 | −0.307814 | − | 0.951447i | \(-0.599597\pi\) | ||||
−0.307814 | + | 0.951447i | \(0.599597\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.2969 | 1.05661 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.0446 | −0.936827 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.7122 | −1.33133 | −0.665665 | − | 0.746251i | \(-0.731852\pi\) | ||||
−0.665665 | + | 0.746251i | \(0.731852\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.167528 | −0.00865110 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.582957 | 0.0300238 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.9527 | −0.819435 | −0.409718 | − | 0.912212i | \(-0.634373\pi\) | ||||
−0.409718 | + | 0.912212i | \(0.634373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.236593 | 0.0121210 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.21784 | 0.0622287 | 0.0311143 | − | 0.999516i | \(-0.490094\pi\) | ||||
0.0311143 | + | 0.999516i | \(0.490094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.8188 | 0.755238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 32.4109 | 1.64754 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.1756 | −0.921540 | −0.460770 | − | 0.887520i | \(-0.652427\pi\) | ||||
−0.460770 | + | 0.887520i | \(0.652427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.28685 | −0.216795 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.275337 | 0.0138889 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.6404 | 0.535375 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.47535 | 0.274800 | 0.137400 | − | 0.990516i | \(-0.456125\pi\) | ||||
0.137400 | + | 0.990516i | \(0.456125\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.77640 | 0.138994 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.715258 | 0.0356295 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.74820 | −0.434701 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.7611 | 1.67348 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.6852 | −1.31950 | −0.659749 | − | 0.751486i | \(-0.729337\pi\) | ||||
−0.659749 | + | 0.751486i | \(0.729337\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.78146 | −0.0878729 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −42.9868 | −2.11524 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.47038 | −0.0721781 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.819936 | 0.0401525 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.4873 | 0.952017 | 0.476008 | − | 0.879441i | \(-0.342083\pi\) | ||||
0.476008 | + | 0.879441i | \(0.342083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.4824 | −1.63183 | −0.815915 | − | 0.578172i | \(-0.803766\pi\) | ||||
−0.815915 | + | 0.578172i | \(0.803766\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.2912 | −0.743486 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.491694 | −0.0238507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.11596 | 0.0540052 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.185296 | 0.00894618 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.86253 | 0.137883 | 0.0689416 | − | 0.997621i | \(-0.478038\pi\) | ||||
0.0689416 | + | 0.997621i | \(0.478038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.577693 | 0.0277622 | 0.0138811 | − | 0.999904i | \(-0.495581\pi\) | ||||
0.0138811 | + | 0.999904i | \(0.495581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.336241 | −0.0161215 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.1304 | −1.77619 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4584 | −0.928698 | −0.464349 | − | 0.885652i | \(-0.653712\pi\) | ||||
−0.464349 | + | 0.885652i | \(0.653712\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.2010 | −1.15243 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6336 | 0.837796 | 0.418898 | − | 0.908033i | \(-0.362417\pi\) | ||||
0.418898 | + | 0.908033i | \(0.362417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.34625 | −0.395650 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.923504 | −0.0436803 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.39251 | 0.207296 | 0.103648 | − | 0.994614i | \(-0.466949\pi\) | ||||
0.103648 | + | 0.994614i | \(0.466949\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.0073 | −1.22464 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.07374 | −0.0504489 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.13027 | 0.0529879 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4326 | −0.768683 | −0.384342 | − | 0.923191i | \(-0.625572\pi\) | ||||
−0.384342 | + | 0.923191i | \(0.625572\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.491923 | 0.0229610 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.9029 | −0.647522 | −0.323761 | − | 0.946139i | \(-0.604947\pi\) | ||||
−0.323761 | + | 0.946139i | \(0.604947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.6555 | −1.00642 | −0.503208 | − | 0.864165i | \(-0.667847\pi\) | ||||
−0.503208 | + | 0.864165i | \(0.667847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.412550 | −0.0191315 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6077 | 0.537142 | 0.268571 | − | 0.963260i | \(-0.413449\pi\) | ||||
0.268571 | + | 0.963260i | \(0.413449\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.5392 | 0.579008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.44532 | −0.158752 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −41.5296 | −1.90953 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.25879 | −0.195407 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.7809 | −0.630983 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.0285 | 1.23496 | 0.617482 | − | 0.786585i | \(-0.288153\pi\) | ||||
0.617482 | + | 0.786585i | \(0.288153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.57504 | 0.117412 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.68381 | −0.258622 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.4387 | 0.473995 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.7965 | 1.71272 | 0.856361 | − | 0.516378i | \(-0.172720\pi\) | ||||
0.856361 | + | 0.516378i | \(0.172720\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.13488 | 0.0965428 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.1387 | 1.13449 | 0.567247 | − | 0.823548i | \(-0.308009\pi\) | ||||
0.567247 | + | 0.823548i | \(0.308009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.986866 | −0.0444462 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3174 | 0.508677 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.86169 | 0.442357 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.85404 | −0.262063 | −0.131031 | − | 0.991378i | \(-0.541829\pi\) | ||||
−0.131031 | + | 0.991378i | \(0.541829\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.70808 | −0.120988 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.83758 | 0.438636 | 0.219318 | − | 0.975653i | \(-0.429617\pi\) | ||||
0.219318 | + | 0.975653i | \(0.429617\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7396 | −0.477905 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.16373 | −0.0960946 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5931 | 0.646826 | 0.323413 | − | 0.946258i | \(-0.395170\pi\) | ||||
0.323413 | + | 0.946258i | \(0.395170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6574 | 0.958069 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.26077 | 0.188118 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.8116 | 0.476416 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.5934 | 0.861715 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.26861 | 0.0995809 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.6354 | 1.34216 | 0.671081 | − | 0.741384i | \(-0.265830\pi\) | ||||
0.671081 | + | 0.741384i | \(0.265830\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4840 | 0.502162 | 0.251081 | − | 0.967966i | \(-0.419214\pi\) | ||||
0.251081 | + | 0.967966i | \(0.419214\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.651922 | −0.0284522 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.21083 | −0.0527447 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.0128 | 2.30491 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.8296 | −1.42468 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.98364 | −0.0859211 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.52515 | 0.238873 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.410412 | −0.0177106 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.0099 | 1.33569 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0130 | 1.03240 | 0.516201 | − | 0.856468i | \(-0.327346\pi\) | ||||
0.516201 | + | 0.856468i | \(0.327346\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.00313124 | −0.000134374 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2933 | 0.483750 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.9079 | 1.40704 | 0.703520 | − | 0.710676i | \(-0.251611\pi\) | ||||
0.703520 | + | 0.710676i | \(0.251611\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.852275 | 0.0363742 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.54770 | −0.364144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 41.4062 | 1.76077 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.48525 | −0.0630452 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.4795 | −1.50331 | −0.751657 | − | 0.659554i | \(-0.770745\pi\) | ||||
−0.751657 | + | 0.659554i | \(0.770745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.16756 | −0.133974 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.313681 | −0.0132436 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.6742 | 1.54564 | 0.772818 | − | 0.634628i | \(-0.218847\pi\) | ||||
0.772818 | + | 0.634628i | \(0.218847\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.8815 | −0.499857 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34.0430 | −1.42967 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.5530 | −0.568172 | −0.284086 | − | 0.958799i | \(-0.591690\pi\) | ||||
−0.284086 | + | 0.958799i | \(0.591690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.7913 | −1.41412 | −0.707060 | − | 0.707154i | \(-0.749979\pi\) | ||||
−0.707060 | + | 0.707154i | \(0.749979\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.926700 | −0.0387135 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.71853 | 0.363588 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.2813 | 1.88509 | 0.942543 | − | 0.334086i | \(-0.108428\pi\) | ||||
0.942543 | + | 0.334086i | \(0.108428\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.20916 | 0.133368 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.72187 | −0.237383 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6581 | 0.731323 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.863202 | 0.0356890 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.5132 | 1.34196 | 0.670981 | − | 0.741474i | \(-0.265873\pi\) | ||||
0.670981 | + | 0.741474i | \(0.265873\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4876 | −0.432133 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.91617 | −0.119955 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.39687 | −0.0573626 | −0.0286813 | − | 0.999589i | \(-0.509131\pi\) | ||||
−0.0286813 | + | 0.999589i | \(0.509131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.91339 | −0.0784414 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.779784 | −0.0319144 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.4307 | −0.957354 | −0.478677 | − | 0.877991i | \(-0.658883\pi\) | ||||
−0.478677 | + | 0.877991i | \(0.658883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.40119 | −0.342692 | −0.171346 | − | 0.985211i | \(-0.554812\pi\) | ||||
−0.171346 | + | 0.985211i | \(0.554812\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.57639 | 0.389981 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50144 | −0.142354 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.33107 | −0.0946151 | −0.0473075 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473075 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.30846 | −0.0530213 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.49443 | 0.0604584 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.8865 | 1.61100 | 0.805500 | − | 0.592596i | \(-0.201897\pi\) | ||||
0.805500 | + | 0.592596i | \(0.201897\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.14413 | 0.0461360 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.77020 | 0.272558 | 0.136279 | − | 0.990670i | \(-0.456486\pi\) | ||||
0.136279 | + | 0.990670i | \(0.456486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.15830 | −0.247523 | −0.123762 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123762 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.72259 | −0.350026 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.4788 | −1.30124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.71693 | −0.108504 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.35920 | −0.173813 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.5305 | −1.41445 | −0.707223 | − | 0.706991i | \(-0.750052\pi\) | ||||
−0.707223 | + | 0.706991i | \(0.750052\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.31572 | −0.171535 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.41226 | −0.0560439 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.36520 | 0.0937127 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.53151 | 0.297942 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.4406 | −1.12334 | −0.561669 | − | 0.827362i | \(-0.689841\pi\) | ||||
−0.561669 | + | 0.827362i | \(0.689841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.2090 | 1.27020 | 0.635099 | − | 0.772431i | \(-0.280959\pi\) | ||||
0.635099 | + | 0.772431i | \(0.280959\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.82700 | 0.0719382 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.6222 | −0.417602 | −0.208801 | − | 0.977958i | \(-0.566956\pi\) | ||||
−0.208801 | + | 0.977958i | \(0.566956\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.0661 | 1.65124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.60541 | −0.0629209 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.188320 | −0.00736951 | −0.00368476 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368476 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.64353 | −0.0642181 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.5401 | 0.645290 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.2043 | −0.903910 | −0.451955 | − | 0.892041i | \(-0.649273\pi\) | ||||
−0.451955 | + | 0.892041i | \(0.649273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.3302 | 1.68535 | 0.842676 | − | 0.538422i | \(-0.180979\pi\) | ||||
0.842676 | + | 0.538422i | \(0.180979\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0239252 | −0.000929178 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.5728 | −0.642664 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.4987 | 0.677554 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.53150 | 0.0592112 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.09206 | −0.0421585 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.2392 | −1.78239 | −0.891196 | − | 0.453619i | \(-0.850133\pi\) | ||||
−0.891196 | + | 0.453619i | \(0.850133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00047 | −0.0385079 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2254 | −0.662024 | −0.331012 | − | 0.943626i | \(-0.607390\pi\) | ||||
−0.331012 | + | 0.943626i | \(0.607390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.6213 | 1.55890 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.549153 | 0.0210436 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.8786 | −0.416259 | −0.208130 | − | 0.978101i | \(-0.566738\pi\) | ||||
−0.208130 | + | 0.978101i | \(0.566738\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6338 | 0.406297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.08406 | −0.117664 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.34682 | 0.0513099 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8085 | 1.21005 | 0.605027 | − | 0.796205i | \(-0.293162\pi\) | ||||
0.605027 | + | 0.796205i | \(0.293162\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.0406 | 1.67297 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.89433 | −0.185652 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.35803 | 0.127195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.19690 | −0.0452710 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9457 | −1.13103 | −0.565517 | − | 0.824737i | \(-0.691323\pi\) | ||||
−0.565517 | + | 0.824737i | \(0.691323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.7570 | −1.42403 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.861967 | −0.0324636 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −41.7923 | −1.57176 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.1642 | −1.02017 | −0.510087 | − | 0.860123i | \(-0.670387\pi\) | ||||
−0.510087 | + | 0.860123i | \(0.670387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.6224 | 1.18593 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.4700 | 0.804059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.10606 | −0.0413643 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.45439 | 0.0916609 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.4084 | 0.872987 | 0.436493 | − | 0.899707i | \(-0.356220\pi\) | ||||
0.436493 | + | 0.899707i | \(0.356220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.0725 | 1.56686 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.33732 | 0.0497355 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00707 | 0.0745408 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.6260 | −1.02459 | −0.512296 | − | 0.858809i | \(-0.671205\pi\) | ||||
−0.512296 | + | 0.858809i | \(0.671205\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.4963 | −0.944306 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.36225 | 0.198330 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6431 | −1.50119 | −0.750593 | − | 0.660765i | \(-0.770232\pi\) | ||||
−0.750593 | + | 0.660765i | \(0.770232\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.36421 | −0.0503197 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2707 | −0.451996 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.2296 | −1.07523 | −0.537613 | − | 0.843192i | \(-0.680674\pi\) | ||||
−0.537613 | + | 0.843192i | \(0.680674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.207227 | −0.00761268 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.6987 | 1.19960 | 0.599800 | − | 0.800150i | \(-0.295247\pi\) | ||||
0.599800 | + | 0.800150i | \(0.295247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.51254 | 0.201964 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.36987 | −0.159885 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.5007 | 0.785619 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.97400 | −0.108523 | −0.0542613 | − | 0.998527i | \(-0.517280\pi\) | ||||
−0.0542613 | + | 0.998527i | \(0.517280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.18836 | −0.0797484 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.40935 | 0.233260 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8433 | 1.19371 | 0.596855 | − | 0.802349i | \(-0.296417\pi\) | ||||
0.596855 | + | 0.802349i | \(0.296417\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.56207 | 0.201890 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.9171 | 1.48324 | 0.741622 | − | 0.670818i | \(-0.234057\pi\) | ||||
0.741622 | + | 0.670818i | \(0.234057\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.9469 | 1.59098 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.46128 | −0.0528328 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.20848 | 0.115852 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5503 | −0.452574 | −0.226287 | − | 0.974061i | \(-0.572659\pi\) | ||||
−0.226287 | + | 0.974061i | \(0.572659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.05042 | 0.0738440 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.4109 | −0.554291 | −0.277145 | − | 0.960828i | \(-0.589388\pi\) | ||||
−0.277145 | + | 0.960828i | \(0.589388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.46257 | 0.0884583 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.77973 | −0.207346 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.0855 | 1.04210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.65047 | −0.345321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00801 | −0.0717603 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.5657 | 0.734020 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.87593 | −0.173808 | −0.0869040 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869040 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.38242 | 0.156018 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.2359 | −1.64396 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.0832941 | −0.00295786 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.776828 | −0.0275512 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.3984 | −1.43098 | −0.715492 | − | 0.698621i | \(-0.753797\pi\) | ||||
−0.715492 | + | 0.698621i | \(0.753797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.52987 | −0.0895005 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.8045 | −0.876424 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.1936 | −0.747905 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.9275 | 1.19579 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.35862 | 0.0478257 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.4863 | −1.38827 | −0.694133 | − | 0.719847i | \(-0.744212\pi\) | ||||
−0.694133 | + | 0.719847i | \(0.744212\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.4821 | 0.824569 | 0.412284 | − | 0.911055i | \(-0.364731\pi\) | ||||
0.412284 | + | 0.911055i | \(0.364731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0587218 | −0.00205946 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.7435 | −0.446384 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.4449 | 1.62490 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.35909 | 0.117376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.3493 | 0.849795 | 0.424897 | − | 0.905242i | \(-0.360310\pi\) | ||||
0.424897 | + | 0.905242i | \(0.360310\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.2922 | 1.23021 | 0.615104 | − | 0.788446i | \(-0.289114\pi\) | ||||
0.615104 | + | 0.788446i | \(0.289114\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.637959 | 0.0222109 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.54431 | −0.227568 | −0.113784 | − | 0.993506i | \(-0.536297\pi\) | ||||
−0.113784 | + | 0.993506i | \(0.536297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35532 | 0.324924 | 0.162462 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162462 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.73488 | −0.0948721 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00396 | −0.138729 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.1650 | 0.559412 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.46372 | −0.0851586 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9419 | −0.584899 | −0.292450 | − | 0.956281i | \(-0.594470\pi\) | ||||
−0.292450 | + | 0.956281i | \(0.594470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9717 | −0.861092 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.72861 | −0.128420 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.9156 | 0.444311 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.6256 | −0.468182 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.27916 | −0.112540 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77.2956 | 2.64966 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.8745 | −0.954405 | −0.477203 | − | 0.878793i | \(-0.658349\pi\) | ||||
−0.477203 | + | 0.878793i | \(0.658349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6568 | −0.432855 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.66296 | −0.125124 | −0.0625621 | − | 0.998041i | \(-0.519927\pi\) | ||||
−0.0625621 | + | 0.998041i | \(0.519927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.603877 | −0.0206040 | −0.0103020 | − | 0.999947i | \(-0.503279\pi\) | ||||
−0.0103020 | + | 0.999947i | \(0.503279\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.45232 | 0.151734 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.87184 | 0.199880 | 0.0999399 | − | 0.994993i | \(-0.468135\pi\) | ||||
0.0999399 | + | 0.994993i | \(0.468135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5417 | −0.460431 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.80747 | −0.0953468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.5193 | −1.37452 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.935914 | −0.0317122 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 31.0230 | 1.04997 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.89143 | 0.131554 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.2888 | −1.52930 | −0.764648 | − | 0.644448i | \(-0.777087\pi\) | ||||
−0.764648 | + | 0.644448i | \(0.777087\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.93320 | −0.0989343 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.5944 | −0.424318 | −0.212159 | − | 0.977235i | \(-0.568049\pi\) | ||||
−0.212159 | + | 0.977235i | \(0.568049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7247 | 0.596483 | 0.298242 | − | 0.954490i | \(-0.403600\pi\) | ||||
0.298242 | + | 0.954490i | \(0.403600\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.85060 | −0.0622074 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.7875 | 0.362210 | 0.181105 | − | 0.983464i | \(-0.442033\pi\) | ||||
0.181105 | + | 0.983464i | \(0.442033\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.49571 | −0.184320 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.3138 | 1.11605 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.9124 | −0.733270 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.44981 | 0.0818882 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.424233 | 0.0141647 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.94257 | 0.164844 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.27999 | −0.0759575 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.10965 | 0.236594 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.0186908 | 0.000621305 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9256 | −1.02687 | −0.513433 | − | 0.858129i | \(-0.671627\pi\) | ||||
−0.513433 | + | 0.858129i | \(0.671627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.9173 | −1.05863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.10261 | 0.202188 | 0.101094 | − | 0.994877i | \(-0.467766\pi\) | ||||
0.101094 | + | 0.994877i | \(0.467766\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.59931 | 0.185310 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0480427 | 0.00158824 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.39568 | −0.211204 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9989 | −0.560741 | −0.280371 | − | 0.959892i | \(-0.590457\pi\) | ||||
−0.280371 | + | 0.959892i | \(0.590457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.03592 | 0.0341346 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.736065 | −0.0242279 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.86566 | 0.291501 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.1314 | 1.05533 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.3858 | −0.636027 | −0.318014 | − | 0.948086i | \(-0.603016\pi\) | ||||
−0.318014 | + | 0.948086i | \(0.603016\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.6801 | −1.13660 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.63637 | −0.0863110 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.87241 | 0.0612343 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.3467 | 1.64475 | 0.822377 | − | 0.568943i | \(-0.192648\pi\) | ||||
0.822377 | + | 0.568943i | \(0.192648\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.85130 | 0.0930485 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.47031 | −0.178327 | −0.0891634 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891634 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.5434 | −1.93900 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.89324 | −0.126647 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.3468 | −0.856156 | −0.428078 | − | 0.903742i | \(-0.640809\pi\) | ||||
−0.428078 | + | 0.903742i | \(0.640809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.61649 | −0.0524733 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.44800 | −0.0469548 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5156 | 0.405419 | 0.202709 | − | 0.979239i | \(-0.435025\pi\) | ||||
0.202709 | + | 0.979239i | \(0.435025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.53162 | 0.178999 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.28043 | 0.0413904 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.3807 | 1.33625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.9357 | −0.804378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.4204 | 0.529139 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.1560 | −0.616652 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.4452 | −0.979051 | −0.489525 | − | 0.871989i | \(-0.662830\pi\) | ||||
−0.489525 | + | 0.871989i | \(0.662830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.350807 | 0.0112695 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0458 | 0.579119 | 0.289559 | − | 0.957160i | \(-0.406491\pi\) | ||||
0.289559 | + | 0.957160i | \(0.406491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.0459 | −0.610584 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0486587 | 0.00155833 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.921257 | 0.0294736 | 0.0147368 | − | 0.999891i | \(-0.495309\pi\) | ||||
0.0147368 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.7832 | 1.01579 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.5628 | 1.07158 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.4193 | −1.03402 | −0.517008 | − | 0.855981i | \(-0.672954\pi\) | ||||
−0.517008 | + | 0.855981i | \(0.672954\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.4071 | 0.554636 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.35428 | −0.106768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −95.0814 | −3.02341 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.9063 | −0.378215 | −0.189108 | − | 0.981956i | \(-0.560559\pi\) | ||||
−0.189108 | + | 0.981956i | \(0.560559\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.36653 | −0.0750997 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.65465 | 0.147562 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44.5748 | −1.41170 | −0.705849 | − | 0.708362i | \(-0.749434\pi\) | ||||
−0.705849 | + | 0.708362i | \(0.749434\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.86979 | −0.280628 |
(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 | 8020.2.a.c.1.15 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.15 | ✓ | 28 | 1.1 | even | 1 | trivial |