Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4024,2,Mod(1,4024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4024, 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("4024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4024 = 2^{3} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4024.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1318017734\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4024.1 |
$q$-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 | ||||||||
\(3\) | 0.0147975 | 0.00854334 | 0.00427167 | − | 0.999991i | \(-0.498640\pi\) | ||||
0.00427167 | + | 0.999991i | \(0.498640\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.88853 | −1.29179 | −0.645896 | − | 0.763425i | \(-0.723516\pi\) | ||||
−0.645896 | + | 0.763425i | \(0.723516\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.61248 | −0.609459 | −0.304729 | − | 0.952439i | \(-0.598566\pi\) | ||||
−0.304729 | + | 0.952439i | \(0.598566\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99978 | −0.999927 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.67687 | −1.10862 | −0.554309 | − | 0.832311i | \(-0.687018\pi\) | ||||
−0.554309 | + | 0.832311i | \(0.687018\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.42310 | −1.50410 | −0.752049 | − | 0.659108i | \(-0.770934\pi\) | ||||
−0.752049 | + | 0.659108i | \(0.770934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0427431 | −0.0110362 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.739860 | −0.179442 | −0.0897212 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897212 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.07178 | −0.475298 | −0.237649 | − | 0.971351i | \(-0.576377\pi\) | ||||
−0.237649 | + | 0.971351i | \(0.576377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0238606 | −0.00520681 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.75750 | −0.574978 | −0.287489 | − | 0.957784i | \(-0.592820\pi\) | ||||
−0.287489 | + | 0.957784i | \(0.592820\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.34363 | 0.668727 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.0887818 | −0.0170861 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0289230 | 0.00537086 | 0.00268543 | − | 0.999996i | \(-0.499145\pi\) | ||||
0.00268543 | + | 0.999996i | \(0.499145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.10947 | 0.558477 | 0.279238 | − | 0.960222i | \(-0.409918\pi\) | ||||
0.279238 | + | 0.960222i | \(0.409918\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0544085 | −0.00947131 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.65769 | 0.787294 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.40122 | −0.230359 | −0.115180 | − | 0.993345i | \(-0.536744\pi\) | ||||
−0.115180 | + | 0.993345i | \(0.536744\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0802483 | −0.0128500 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.0456 | −1.72503 | −0.862513 | − | 0.506035i | \(-0.831111\pi\) | ||||
−0.862513 | + | 0.506035i | \(0.831111\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.99763 | −0.762131 | −0.381066 | − | 0.924548i | \(-0.624443\pi\) | ||||
−0.381066 | + | 0.924548i | \(0.624443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.66497 | 1.29170 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.39726 | −1.07900 | −0.539500 | − | 0.841985i | \(-0.681387\pi\) | ||||
−0.539500 | + | 0.841985i | \(0.681387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.39992 | −0.628560 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0109481 | −0.00153304 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.42772 | 1.02028 | 0.510138 | − | 0.860093i | \(-0.329594\pi\) | ||||
0.510138 | + | 0.860093i | \(0.329594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.6208 | 1.43210 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0306571 | −0.00406063 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.1711 | 1.71473 | 0.857365 | − | 0.514710i | \(-0.172100\pi\) | ||||
0.857365 | + | 0.514710i | \(0.172100\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.31482 | −0.424419 | −0.212210 | − | 0.977224i | \(-0.568066\pi\) | ||||
−0.212210 | + | 0.977224i | \(0.568066\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.83707 | 0.609414 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.6648 | 1.94298 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0846196 | 0.0103379 | 0.00516897 | − | 0.999987i | \(-0.498355\pi\) | ||||
0.00516897 | + | 0.999987i | \(0.498355\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0408041 | −0.00491223 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.58897 | −0.781967 | −0.390983 | − | 0.920398i | \(-0.627865\pi\) | ||||
−0.390983 | + | 0.920398i | \(0.627865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.88606 | −0.922994 | −0.461497 | − | 0.887142i | \(-0.652687\pi\) | ||||
−0.461497 | + | 0.887142i | \(0.652687\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0494774 | 0.00571316 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.92887 | 0.675657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.88374 | 0.774481 | 0.387241 | − | 0.921979i | \(-0.373428\pi\) | ||||
0.387241 | + | 0.921979i | \(0.373428\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99803 | 0.999781 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.85024 | 0.532383 | 0.266192 | − | 0.963920i | \(-0.414235\pi\) | ||||
0.266192 | + | 0.963920i | \(0.414235\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.13711 | 0.231802 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.000427988 0 | 4.58851e−5 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.6708 | 1.13110 | 0.565552 | − | 0.824713i | \(-0.308663\pi\) | ||||
0.565552 | + | 0.824713i | \(0.308663\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.74462 | 0.916685 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0460123 | 0.00477126 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.98439 | 0.613986 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.7602 | −1.19407 | −0.597034 | − | 0.802216i | \(-0.703654\pi\) | ||||
−0.597034 | + | 0.802216i | \(0.703654\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.0298 | 1.10854 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6147 | 1.15571 | 0.577854 | − | 0.816140i | \(-0.303890\pi\) | ||||
0.577854 | + | 0.816140i | \(0.303890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.99357 | 0.196432 | 0.0982162 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982162 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0689222 | 0.00672612 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.10156 | −0.589861 | −0.294930 | − | 0.955519i | \(-0.595296\pi\) | ||||
−0.294930 | + | 0.955519i | \(0.595296\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2132 | 1.07403 | 0.537014 | − | 0.843573i | \(-0.319552\pi\) | ||||
0.537014 | + | 0.843573i | \(0.319552\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0207346 | −0.00196804 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.70315 | −0.536507 | −0.268254 | − | 0.963348i | \(-0.586447\pi\) | ||||
−0.268254 | + | 0.963348i | \(0.586447\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.96513 | 0.742752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.2681 | 1.50399 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.19301 | 0.109363 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.51939 | 0.229035 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.163447 | −0.0147375 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.78447 | 0.427936 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1852 | −1.34747 | −0.673735 | − | 0.738973i | \(-0.735311\pi\) | ||||
−0.673735 | + | 0.738973i | \(0.735311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.0739524 | −0.00651115 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.76214 | 0.590811 | 0.295406 | − | 0.955372i | \(-0.404545\pi\) | ||||
0.295406 | + | 0.955372i | \(0.404545\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.34069 | 0.289674 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.256449 | 0.0220716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.2609 | −1.30383 | −0.651914 | − | 0.758293i | \(-0.726034\pi\) | ||||
−0.651914 | + | 0.758293i | \(0.726034\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.8633 | −1.76960 | −0.884802 | − | 0.465966i | \(-0.845707\pi\) | ||||
−0.884802 | + | 0.465966i | \(0.845707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.109461 | −0.00921827 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.9400 | 1.66747 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0835450 | −0.00693804 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0651078 | −0.00537000 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.90707 | −0.729696 | −0.364848 | − | 0.931067i | \(-0.618879\pi\) | ||||
−0.364848 | + | 0.931067i | \(0.618879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.1837 | −1.64252 | −0.821262 | − | 0.570552i | \(-0.806729\pi\) | ||||
−0.821262 | + | 0.570552i | \(0.806729\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.21942 | 0.179429 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.98180 | −0.721436 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.58543 | 0.445766 | 0.222883 | − | 0.974845i | \(-0.428453\pi\) | ||||
0.222883 | + | 0.974845i | \(0.428453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.109912 | 0.00871656 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.44640 | 0.350425 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.9753 | 1.40793 | 0.703966 | − | 0.710234i | \(-0.251411\pi\) | ||||
0.703966 | + | 0.710234i | \(0.251411\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.157161 | 0.0122350 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.70835 | 0.441726 | 0.220863 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220863 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.4100 | 1.26231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.21487 | 0.475263 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.02020 | −0.0775641 | −0.0387821 | − | 0.999248i | \(-0.512348\pi\) | ||||
−0.0387821 | + | 0.999248i | \(0.512348\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.39153 | −0.407561 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.194899 | 0.0146495 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −26.3011 | −1.96584 | −0.982920 | − | 0.184033i | \(-0.941085\pi\) | ||||
−0.982920 | + | 0.184033i | \(0.941085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.91194 | 0.513760 | 0.256880 | − | 0.966443i | \(-0.417305\pi\) | ||||
0.256880 | + | 0.966443i | \(0.417305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0490510 | −0.00362596 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.04748 | 0.297576 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.72037 | 0.198933 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.143158 | 0.0104132 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6600 | 1.78434 | 0.892168 | − | 0.451704i | \(-0.149184\pi\) | ||||
0.892168 | + | 0.451704i | \(0.149184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.62448 | 0.116933 | 0.0584664 | − | 0.998289i | \(-0.481379\pi\) | ||||
0.0584664 | + | 0.998289i | \(0.481379\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.231800 | 0.0165996 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8372 | 1.55584 | 0.777919 | − | 0.628365i | \(-0.216275\pi\) | ||||
0.777919 | + | 0.628365i | \(0.216275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0279 | −1.41974 | −0.709869 | − | 0.704334i | \(-0.751246\pi\) | ||||
−0.709869 | + | 0.704334i | \(0.751246\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.00125216 | 8.83205e−5 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0466376 | −0.00327332 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.9055 | 2.22837 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.27189 | 0.574936 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.61765 | 0.526924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.88027 | −0.680186 | −0.340093 | − | 0.940392i | \(-0.610459\pi\) | ||||
−0.340093 | + | 0.940392i | \(0.610459\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0975003 | −0.00668061 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4358 | 0.984515 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.01394 | −0.340368 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.116694 | −0.00788545 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.01234 | 0.269899 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7872 | −0.990227 | −0.495113 | − | 0.868828i | \(-0.664874\pi\) | ||||
−0.495113 | + | 0.868828i | \(0.664874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0302 | −0.668678 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.51449 | 0.233265 | 0.116632 | − | 0.993175i | \(-0.462790\pi\) | ||||
0.116632 | + | 0.993175i | \(0.462790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.697824 | 0.0461135 | 0.0230568 | − | 0.999734i | \(-0.492660\pi\) | ||||
0.0230568 | + | 0.999734i | \(0.492660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.0877324 | 0.00577237 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.532456 | −0.0348824 | −0.0174412 | − | 0.999848i | \(-0.505552\pi\) | ||||
−0.0174412 | + | 0.999848i | \(0.505552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3672 | 1.39384 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.101862 | 0.00661666 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7798 | −1.34414 | −0.672068 | − | 0.740490i | \(-0.734594\pi\) | ||||
−0.672068 | + | 0.740490i | \(0.734594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.9898 | 0.707917 | 0.353959 | − | 0.935261i | \(-0.384835\pi\) | ||||
0.353959 | + | 0.935261i | \(0.384835\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.399494 | 0.0256275 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.7093 | 0.811969 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.2354 | 0.714894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0717715 | 0.00454833 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5002 | −0.662765 | −0.331383 | − | 0.943496i | \(-0.607515\pi\) | ||||
−0.331383 | + | 0.943496i | \(0.607515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1390 | 0.637431 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0316239 | 0.00198037 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.3616 | −1.08299 | −0.541495 | − | 0.840704i | \(-0.682141\pi\) | ||||
−0.541495 | + | 0.840704i | \(0.682141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.25944 | 0.140394 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0867626 | −0.00537047 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.78239 | −0.171569 | −0.0857847 | − | 0.996314i | \(-0.527340\pi\) | ||||
−0.0857847 | + | 0.996314i | \(0.527340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.4552 | −1.31798 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.157901 | 0.00966341 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.9762 | −1.40089 | −0.700443 | − | 0.713708i | \(-0.747014\pi\) | ||||
−0.700443 | + | 0.713708i | \(0.747014\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.22861 | −0.196124 | −0.0980621 | − | 0.995180i | \(-0.531264\pi\) | ||||
−0.0980621 | + | 0.995180i | \(0.531264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.129399 | 0.00783155 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.2941 | −0.741363 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.8434 | 1.91328 | 0.956641 | − | 0.291270i | \(-0.0940776\pi\) | ||||
0.956641 | + | 0.291270i | \(0.0940776\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.32772 | −0.558436 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0084 | 0.597050 | 0.298525 | − | 0.954402i | \(-0.403505\pi\) | ||||
0.298525 | + | 0.954402i | \(0.403505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.0070 | −1.12985 | −0.564925 | − | 0.825142i | \(-0.691095\pi\) | ||||
−0.564925 | + | 0.825142i | \(0.691095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.0885541 | 0.00524549 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.8107 | 1.05133 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4526 | −0.967800 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.174022 | −0.0102013 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.7160 | −0.626033 | −0.313017 | − | 0.949748i | \(-0.601340\pi\) | ||||
−0.313017 | + | 0.949748i | \(0.601340\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.0451 | −2.21507 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.326439 | 0.0189419 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.9542 | 0.864823 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.05856 | 0.464488 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.171869 | 0.00987360 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.57497 | 0.548261 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.596611 | −0.0340504 | −0.0170252 | − | 0.999855i | \(-0.505420\pi\) | ||||
−0.0170252 | + | 0.999855i | \(0.505420\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0294999 | 0.00167819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.82381 | 0.386943 | 0.193471 | − | 0.981106i | \(-0.438025\pi\) | ||||
0.193471 | + | 0.981106i | \(0.438025\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1226 | 0.628684 | 0.314342 | − | 0.949310i | \(-0.398216\pi\) | ||||
0.314342 | + | 0.949310i | \(0.398216\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −13.9721 | −0.787236 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.76165 | 0.548269 | 0.274134 | − | 0.961691i | \(-0.411609\pi\) | ||||
0.274134 | + | 0.961691i | \(0.411609\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.106346 | −0.00595424 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0902879 | −0.00503938 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.53282 | 0.0852886 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.1329 | −1.00583 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.165927 | 0.00917580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.9279 | 0.657606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.83632 | 0.375758 | 0.187879 | − | 0.982192i | \(-0.439839\pi\) | ||||
0.187879 | + | 0.982192i | \(0.439839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.20336 | 0.230343 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.244427 | −0.0133545 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.1341 | 1.64151 | 0.820754 | − | 0.571282i | \(-0.193554\pi\) | ||||
0.820754 | + | 0.571282i | \(0.193554\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0843924 | −0.00458357 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.4331 | −0.619137 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3821 | 0.992540 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.117864 | 0.00634558 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.89878 | 0.531394 | 0.265697 | − | 0.964057i | \(-0.414398\pi\) | ||||
0.265697 | + | 0.964057i | \(0.414398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.2313 | 1.83236 | 0.916179 | − | 0.400769i | \(-0.131257\pi\) | ||||
0.916179 | + | 0.400769i | \(0.131257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.481472 | 0.0256991 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.0633 | −1.17431 | −0.587156 | − | 0.809474i | \(-0.699753\pi\) | ||||
−0.587156 | + | 0.809474i | \(0.699753\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.0325 | 1.01014 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.0176535 | 0.000934323 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2127 | 1.70012 | 0.850061 | − | 0.526684i | \(-0.176565\pi\) | ||||
0.850061 | + | 0.526684i | \(0.176565\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.7077 | −0.774092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.0372806 | 0.00195672 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.7792 | 1.19232 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.17329 | −0.322243 | −0.161121 | − | 0.986935i | \(-0.551511\pi\) | ||||
−0.161121 | + | 0.986935i | \(0.551511\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 33.1343 | 1.72490 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9770 | −0.621816 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.28364 | −0.428911 | −0.214455 | − | 0.976734i | \(-0.568798\pi\) | ||||
−0.214455 | + | 0.976734i | \(0.568798\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.0707983 | 0.00365601 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.156852 | −0.00807830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7329 | −1.06498 | −0.532489 | − | 0.846437i | \(-0.678743\pi\) | ||||
−0.532489 | + | 0.846437i | \(0.678743\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.224703 | −0.0115119 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.29514 | −0.474959 | −0.237480 | − | 0.971393i | \(-0.576321\pi\) | ||||
−0.237480 | + | 0.971393i | \(0.576321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1257 | −0.872808 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.9918 | 0.762076 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.814216 | 0.0412824 | 0.0206412 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206412 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.04016 | 0.103175 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.100063 | 0.00504750 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.8839 | −1.00047 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.9942 | −1.35480 | −0.677401 | − | 0.735614i | \(-0.736894\pi\) | ||||
−0.677401 | + | 0.735614i | \(0.736894\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0494338 | 0.00247479 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.4537 | 1.72054 | 0.860269 | − | 0.509841i | \(-0.170296\pi\) | ||||
0.860269 | + | 0.509841i | \(0.170296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.8629 | −0.840003 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −25.9911 | −1.29151 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.15211 | 0.255381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.3626 | −1.60023 | −0.800115 | − | 0.599847i | \(-0.795228\pi\) | ||||
−0.800115 | + | 0.599847i | \(0.795228\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.225824 | −0.0111391 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.2381 | −1.04506 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.0101 | −0.687729 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.308725 | −0.0151183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.2742 | −0.746193 | −0.373096 | − | 0.927793i | \(-0.621704\pi\) | ||||
−0.373096 | + | 0.927793i | \(0.621704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.04350 | −0.294542 | −0.147271 | − | 0.989096i | \(-0.547049\pi\) | ||||
−0.147271 | + | 0.989096i | \(0.547049\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.1901 | 1.07892 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.47382 | −0.119998 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.34507 | 0.258666 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.295063 | 0.0142458 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.6695 | 0.562101 | 0.281050 | − | 0.959693i | \(-0.409317\pi\) | ||||
0.281050 | + | 0.959693i | \(0.409317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6689 | 0.849113 | 0.424556 | − | 0.905402i | \(-0.360430\pi\) | ||||
0.424556 | + | 0.905402i | \(0.360430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.00123626 | −5.92740e−5 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.71291 | 0.273286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.5165 | −1.55193 | −0.775965 | − | 0.630777i | \(-0.782736\pi\) | ||||
−0.775965 | + | 0.630777i | \(0.782736\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.1988 | 0.628514 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.6653 | −1.07686 | −0.538431 | − | 0.842669i | \(-0.680983\pi\) | ||||
−0.538431 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.8230 | −1.46115 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.131802 | −0.00623404 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.5743 | 1.44289 | 0.721446 | − | 0.692470i | \(-0.243478\pi\) | ||||
0.721446 | + | 0.692470i | \(0.243478\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.6131 | 1.91240 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.298668 | −0.0140326 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.2591 | −1.18417 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.74447 | −0.175159 | −0.0875794 | − | 0.996158i | \(-0.527913\pi\) | ||||
−0.0875794 | + | 0.996158i | \(0.527913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0656861 | 0.00306596 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.56887 | 0.399092 | 0.199546 | − | 0.979888i | \(-0.436053\pi\) | ||||
0.199546 | + | 0.979888i | \(0.436053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.7295 | −0.545116 | −0.272558 | − | 0.962139i | \(-0.587870\pi\) | ||||
−0.272558 | + | 0.962139i | \(0.587870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.132908 | −0.00616347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.8900 | −1.70707 | −0.853533 | − | 0.521038i | \(-0.825545\pi\) | ||||
−0.853533 | + | 0.521038i | \(0.825545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.136447 | −0.00630054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0826504 | 0.00380833 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.3756 | 0.844913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.92726 | −0.317844 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.2815 | −1.02020 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.7603 | 0.537342 | 0.268671 | − | 0.963232i | \(-0.413416\pi\) | ||||
0.268671 | + | 0.963232i | \(0.413416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.59896 | 0.346483 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.0657956 | 0.00299380 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 33.9698 | 1.54249 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.5200 | −1.47362 | −0.736810 | − | 0.676100i | \(-0.763669\pi\) | ||||
−0.736810 | + | 0.676100i | \(0.763669\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.265989 | 0.0120284 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.68312 | −0.166217 | −0.0831085 | − | 0.996541i | \(-0.526485\pi\) | ||||
−0.0831085 | + | 0.996541i | \(0.526485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0213990 | −0.000963760 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.8600 | −1.43200 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.6246 | 0.476576 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.7311 | −0.928052 | −0.464026 | − | 0.885822i | \(-0.653596\pi\) | ||||
−0.464026 | + | 0.885822i | \(0.653596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0844694 | 0.00377381 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.5495 | −1.49293 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.242827 | 0.0107843 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.0782 | 0.934273 | 0.467137 | − | 0.884185i | \(-0.345286\pi\) | ||||
0.467137 | + | 0.884185i | \(0.345286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7161 | 0.562526 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.183936 | 0.00812097 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.75850 | −0.253750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.1988 | 1.19620 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0150964 | −0.000662657 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2059 | −0.490939 | −0.245470 | − | 0.969404i | \(-0.578942\pi\) | ||||
−0.245470 | + | 0.969404i | \(0.578942\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2726 | −0.449191 | −0.224596 | − | 0.974452i | \(-0.572106\pi\) | ||||
−0.224596 | + | 0.974452i | \(0.572106\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0797811 | −0.00348193 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.30057 | −0.100214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3962 | −0.669400 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −39.5104 | −1.71460 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 59.9012 | 2.59461 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.6246 | 0.761977 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.389191 | −0.0167948 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.1779 | 0.696834 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6431 | 0.801532 | 0.400766 | − | 0.916181i | \(-0.368744\pi\) | ||||
0.400766 | + | 0.916181i | \(0.368744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.102279 | 0.00438923 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.3897 | −1.38742 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8545 | −1.23373 | −0.616865 | − | 0.787069i | \(-0.711598\pi\) | ||||
−0.616865 | + | 0.787069i | \(0.711598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.94373 | 0.424388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0599219 | −0.00255276 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0999 | −0.472014 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.0598925 | 0.00254230 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.96301 | 0.295032 | 0.147516 | − | 0.989060i | \(-0.452872\pi\) | ||||
0.147516 | + | 0.989060i | \(0.452872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.1026 | 1.14632 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0402547 | 0.00169955 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.8136 | −0.877190 | −0.438595 | − | 0.898685i | \(-0.644524\pi\) | ||||
−0.438595 | + | 0.898685i | \(0.644524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.4738 | 0.693056 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.5091 | −0.609325 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0034 | 0.587055 | 0.293528 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293528 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.7234 | −0.867247 | −0.433623 | − | 0.901094i | \(-0.642765\pi\) | ||||
−0.433623 | + | 0.901094i | \(0.642765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.364907 | 0.0152442 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.22006 | −0.384503 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6902 | 0.736455 | 0.368227 | − | 0.929736i | \(-0.379965\pi\) | ||||
0.368227 | + | 0.929736i | \(0.379965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0240383 | 0.000998997 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.82090 | −0.324466 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.3108 | −1.13110 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −46.9910 | −1.94284 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.7140 | 0.607312 | 0.303656 | − | 0.952782i | \(-0.401793\pi\) | ||||
0.303656 | + | 0.952782i | \(0.401793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.44211 | −0.265443 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.323136 | 0.0132921 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.57943 | −0.188054 | −0.0940272 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940272 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.44604 | −0.141274 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.296362 | −0.0121293 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.3967 | −0.465658 | −0.232829 | − | 0.972518i | \(-0.574798\pi\) | ||||
−0.232829 | + | 0.972518i | \(0.574798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.43329 | −0.344001 | −0.172001 | − | 0.985097i | \(-0.555023\pi\) | ||||
−0.172001 | + | 0.985097i | \(0.555023\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.253840 | −0.0103372 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.27733 | −0.295866 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.34250 | 0.135668 | 0.0678340 | − | 0.997697i | \(-0.478391\pi\) | ||||
0.0678340 | + | 0.997697i | \(0.478391\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.000690120 0 | −2.79651e−5 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.1161 | 1.62292 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.11500 | −0.287372 | −0.143686 | − | 0.989623i | \(-0.545896\pi\) | ||||
−0.143686 | + | 0.989623i | \(0.545896\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.472121 | 0.0190378 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.5827 | −0.748113 | −0.374056 | − | 0.927406i | \(-0.622033\pi\) | ||||
−0.374056 | + | 0.927406i | \(0.622033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.89042 | −0.276949 | −0.138475 | − | 0.990366i | \(-0.544220\pi\) | ||||
−0.138475 | + | 0.990366i | \(0.544220\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.244815 | 0.00982411 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2064 | −0.689361 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.5383 | −1.22153 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.112722 | 0.00450169 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.03671 | 0.0413362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.84998 | −0.153265 | −0.0766326 | − | 0.997059i | \(-0.524417\pi\) | ||||
−0.0766326 | + | 0.997059i | \(0.524417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.146203 | −0.00581106 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43.8630 | 1.74065 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.8612 | 0.945416 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.7655 | 0.781910 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.4694 | 0.571507 | 0.285753 | − | 0.958303i | \(-0.407756\pi\) | ||||
0.285753 | + | 0.958303i | \(0.407756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.7064 | 0.461654 | 0.230827 | − | 0.972995i | \(-0.425857\pi\) | ||||
0.230827 | + | 0.972995i | \(0.425857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.213614 | 0.00841105 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0476 | 0.591583 | 0.295791 | − | 0.955253i | \(-0.404417\pi\) | ||||
0.295791 | + | 0.955253i | \(0.404417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.4284 | −1.90098 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.0741938 | −0.00290788 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.61956 | 0.102511 | 0.0512557 | − | 0.998686i | \(-0.483678\pi\) | ||||
0.0512557 | + | 0.998686i | \(0.483678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5327 | −0.763205 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.6565 | 0.922926 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.8485 | 1.08482 | 0.542411 | − | 0.840113i | \(-0.317512\pi\) | ||||
0.542411 | + | 0.840113i | \(0.317512\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.7901 | 1.08091 | 0.540456 | − | 0.841373i | \(-0.318252\pi\) | ||||
0.540456 | + | 0.841373i | \(0.318252\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0593725 | 0.00230584 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.64969 | −0.374199 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0797550 | −0.00308813 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.218814 | −0.00845985 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.1882 | 0.470519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.9820 | −0.500420 | −0.250210 | − | 0.968192i | \(-0.580500\pi\) | ||||
−0.250210 | + | 0.968192i | \(0.580500\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.296854 | −0.0114259 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.6855 | −1.52524 | −0.762619 | − | 0.646848i | \(-0.776087\pi\) | ||||
−0.762619 | + | 0.646848i | \(0.776087\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.9631 | 0.727735 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0520056 | 0.00199286 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.7927 | −0.948665 | −0.474332 | − | 0.880346i | \(-0.657310\pi\) | ||||
−0.474332 | + | 0.880346i | \(0.657310\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.0817 | 1.68428 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0103261 | 0.000393964 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.2813 | −1.53459 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.29980 | 0.0874883 | 0.0437442 | − | 0.999043i | \(-0.486071\pi\) | ||||
0.0437442 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −17.7853 | −0.675608 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 60.2645 | 2.28596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.17217 | 0.309543 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.00787902 | −0.000298012 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.7107 | 1.53762 | 0.768811 | − | 0.639476i | \(-0.220849\pi\) | ||||
0.768811 | + | 0.639476i | \(0.220849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.90302 | 0.109489 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.316182 | 0.0119081 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.7284 | −0.704356 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.3053 | −0.725027 | −0.362513 | − | 0.931979i | \(-0.618081\pi\) | ||||
−0.362513 | + | 0.931979i | \(0.618081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.6497 | −0.774425 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.57434 | −0.321112 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −57.5975 | −2.15402 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.307490 | −0.0114834 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.1852 | 1.23760 | 0.618800 | − | 0.785549i | \(-0.287619\pi\) | ||||
0.618800 | + | 0.785549i | \(0.287619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.21459 | −0.119717 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.162622 | 0.00604798 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.0967078 | 0.00359164 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9838 | −0.444453 | −0.222227 | − | 0.974995i | \(-0.571332\pi\) | ||||
−0.222227 | + | 0.974995i | \(0.571332\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9882 | −0.999562 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.69755 | 0.136759 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.1288 | −0.928154 | −0.464077 | − | 0.885795i | \(-0.653614\pi\) | ||||
−0.464077 | + | 0.885795i | \(0.653614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.188066 | 0.00693693 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.311136 | −0.0114608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.3059 | −0.379109 | −0.189554 | − | 0.981870i | \(-0.560704\pi\) | ||||
−0.189554 | + | 0.981870i | \(0.560704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.166257 | 0.00610759 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.0598 | 1.46965 | 0.734825 | − | 0.678256i | \(-0.237264\pi\) | ||||
0.734825 | + | 0.678256i | \(0.237264\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.7284 | 0.942615 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.5497 | −0.532345 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.83863 | 0.359496 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0804 | 0.586784 | 0.293392 | − | 0.955992i | \(-0.405216\pi\) | ||||
0.293392 | + | 0.955992i | \(0.405216\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.155376 | −0.00566223 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 58.3012 | 2.12180 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0819 | 1.74757 | 0.873783 | − | 0.486316i | \(-0.161659\pi\) | ||||
0.873783 | + | 0.486316i | \(0.161659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.150031 | 0.00544579 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.8538 | −1.84345 | −0.921724 | − | 0.387846i | \(-0.873219\pi\) | ||||
−0.921724 | + | 0.387846i | \(0.873219\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.0810 | −0.654576 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.41087 | −0.231785 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −71.4281 | −2.57912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.8297 | −0.895382 | −0.447691 | − | 0.894188i | \(-0.647753\pi\) | ||||
−0.447691 | + | 0.894188i | \(0.647753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.256909 | −0.00925235 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.62167 | −0.346067 | −0.173034 | − | 0.984916i | \(-0.555357\pi\) | ||||
−0.173034 | + | 0.984916i | \(0.555357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3969 | 0.373468 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0334340 | 0.00119944 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.8839 | 0.819901 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.2268 | 0.866903 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.00256783 | −9.17669e−5 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.1337 | −0.575837 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.9875 | 0.748124 | 0.374062 | − | 0.927404i | \(-0.377965\pi\) | ||||
0.374062 | + | 0.927404i | \(0.377965\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0411724 | −0.00146578 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.19620 | 0.326979 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.9766 | 0.638368 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.317484 | −0.0112600 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.0687051 | −0.00243366 | −0.00121683 | − | 0.999999i | \(-0.500387\pi\) | ||||
−0.00121683 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.47293 | 0.193619 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0101 | −1.13102 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.9960 | 1.02325 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.8436 | −0.452676 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.339991 | −0.0119683 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.3414 | 1.48864 | 0.744322 | − | 0.667821i | \(-0.232773\pi\) | ||||
0.744322 | + | 0.667821i | \(0.232773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6941 | 1.04270 | 0.521350 | − | 0.853343i | \(-0.325429\pi\) | ||||
0.521350 | + | 0.853343i | \(0.325429\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0477754 | −0.00167556 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.9222 | −1.81875 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3540 | 0.362239 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.2319 | −0.916618 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5816 | −1.06731 | −0.533653 | − | 0.845704i | \(-0.679181\pi\) | ||||
−0.533653 | + | 0.845704i | \(0.679181\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.7249 | −1.41958 | −0.709791 | − | 0.704413i | \(-0.751210\pi\) | ||||
−0.709791 | + | 0.704413i | \(0.751210\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.181922 | −0.00633371 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.2206 | 0.946552 | 0.473276 | − | 0.880914i | \(-0.343071\pi\) | ||||
0.473276 | + | 0.880914i | \(0.343071\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7317 | 0.476922 | 0.238461 | − | 0.971152i | \(-0.423357\pi\) | ||||
0.238461 | + | 0.971152i | \(0.423357\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.471202 | 0.0163458 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.25533 | 0.112790 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.4888 | −0.570618 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.276064 | −0.00954216 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.483965 | −0.0167083 | −0.00835416 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835416 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9992 | −0.999971 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.148099 | 0.00510080 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −47.4009 | −1.63064 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.06245 | −0.139587 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.281256 | −0.00965269 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.86386 | 0.132452 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.1760 | 0.690813 | 0.345406 | − | 0.938453i | \(-0.387741\pi\) | ||||
0.345406 | + | 0.938453i | \(0.387741\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.9519 | −0.613941 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 36.4272 | 1.24433 | 0.622164 | − | 0.782887i | \(-0.286254\pi\) | ||||
0.622164 | + | 0.782887i | \(0.286254\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.32321 | −0.0792671 | −0.0396335 | − | 0.999214i | \(-0.512619\pi\) | ||||
−0.0396335 | + | 0.999214i | \(0.512619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.263554 | 0.00898189 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.1351 | 1.84278 | 0.921391 | − | 0.388637i | \(-0.127054\pi\) | ||||
0.921391 | + | 0.388637i | \(0.127054\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.94687 | 0.100197 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.243457 | −0.00826825 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −25.3106 | −0.858604 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.458901 | −0.0155493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2781 | 1.19398 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.71485 | −0.260809 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3820 | 0.586948 | 0.293474 | − | 0.955967i | \(-0.405189\pi\) | ||||
0.293474 | + | 0.955967i | \(0.405189\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.158569 | −0.00534842 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.7985 | −1.03763 | −0.518814 | − | 0.854887i | \(-0.673626\pi\) | ||||
−0.518814 | + | 0.854887i | \(0.673626\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.53905 | 0.321015 | 0.160507 | − | 0.987035i | \(-0.448687\pi\) | ||||
0.160507 | + | 0.987035i | \(0.448687\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.562973 | −0.0189241 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.0798 | −1.07714 | −0.538568 | − | 0.842582i | \(-0.681034\pi\) | ||||
−0.538568 | + | 0.842582i | \(0.681034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24.4858 | 0.821227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.0846 | −1.10838 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.3255 | 0.512847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 75.9718 | 2.53946 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.221285 | 0.00738848 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0899350 | 0.00299950 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.49547 | −0.183081 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.119247 | 0.00396828 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.9654 | −0.663671 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.9792 | −1.09506 | −0.547529 | − | 0.836787i | \(-0.684431\pi\) | ||||
−0.547529 | + | 0.836787i | \(0.684431\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.8416 | −1.15562 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.7684 | −0.853744 | −0.426872 | − | 0.904312i | \(-0.640385\pi\) | ||||
−0.426872 | + | 0.904312i | \(0.640385\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.8337 | −0.590210 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.141686 | 0.00468398 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.9038 | −0.360075 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.3018 | −1.36242 | −0.681211 | − | 0.732088i | \(-0.738546\pi\) | ||||
−0.681211 | + | 0.732088i | \(0.738546\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.00882836 | −0.000290904 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.7326 | 1.17615 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.68517 | −0.154047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.98028 | −0.196418 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.0830 | 0.888565 | 0.444283 | − | 0.895887i | \(-0.353459\pi\) | ||||
0.444283 | + | 0.895887i | \(0.353459\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.11565 | 0.298753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.100975 | 0.00330578 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.85789 | −0.256980 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.5951 | 1.55486 | 0.777432 | − | 0.628967i | \(-0.216522\pi\) | ||||
0.777432 | + | 0.628967i | \(0.216522\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.164586 | 0.00537106 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.5267 | −0.799547 | −0.399773 | − | 0.916614i | \(-0.630911\pi\) | ||||
−0.399773 | + | 0.916614i | \(0.630911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.4581 | 0.991852 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.413518 | −0.0134517 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.57604 | 0.213693 | 0.106846 | − | 0.994276i | \(-0.465925\pi\) | ||||
0.106846 | + | 0.994276i | \(0.465925\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42.7669 | 1.38827 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.144448 | 0.00468405 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.7339 | −1.74061 | −0.870306 | − | 0.492512i | \(-0.836079\pi\) | ||||
−0.870306 | + | 0.492512i | \(0.836079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −71.2313 | −2.30499 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.00157366 | −5.08691e−5 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.6079 | 0.794630 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.3312 | −0.688104 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.3034 | 0.589817 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.69237 | −0.151053 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.8475 | −0.509622 | −0.254811 | − | 0.966991i | \(-0.582013\pi\) | ||||
−0.254811 | + | 0.966991i | \(0.582013\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0226820 | 0.000728650 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6150 | −0.404833 | −0.202417 | − | 0.979299i | \(-0.564880\pi\) | ||||
−0.202417 | + | 0.979299i | \(0.564880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.6416 | 1.07850 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.268321 | −0.00859315 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.18447 | 0.293837 | 0.146919 | − | 0.989149i | \(-0.453064\pi\) | ||||
0.146919 | + | 0.989149i | \(0.453064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39.2352 | −1.25396 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.6371 | −1.07395 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.1655 | −1.02592 | −0.512960 | − | 0.858413i | \(-0.671451\pi\) | ||||
−0.512960 | + | 0.858413i | \(0.671451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.0776 | −2.00982 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.176503 | 0.00561815 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.7809 | 0.438209 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.8856 | 1.55290 | 0.776451 | − | 0.630177i | \(-0.217018\pi\) | ||||
0.776451 | + | 0.630177i | \(0.217018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.101160 | 0.00321023 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.8512 | 1.83401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.95639 | −0.283652 | −0.141826 | − | 0.989892i | \(-0.545297\pi\) | ||||
−0.141826 | + | 0.989892i | \(0.545297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.124403 | 0.00393593 |
(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 | 4024.2.a.f.1.17 | ✓ | 33 | |
4.3 | odd | 2 | 8048.2.a.y.1.17 | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.17 | ✓ | 33 | 1.1 | even | 1 | trivial | |
8048.2.a.y.1.17 | 33 | 4.3 | odd | 2 |