Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.745749504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.24337\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 3.24337 | 1.87256 | 0.936281 | − | 0.351252i | \(-0.114244\pi\) | ||||
0.936281 | + | 0.351252i | \(0.114244\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.24337 | 1.32410 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.51947 | 2.50649 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.24337 | 0.936281 | ||||||||
\(13\) | 2.14515 | 0.594959 | 0.297479 | − | 0.954728i | \(-0.403854\pi\) | ||||
0.297479 | + | 0.954728i | \(0.403854\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −3.24337 | −0.837435 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.43942 | 0.349111 | 0.174555 | − | 0.984647i | \(-0.444151\pi\) | ||||
0.174555 | + | 0.984647i | \(0.444151\pi\) | |||||||
\(18\) | 7.51947 | 1.77236 | ||||||||
\(19\) | −0.633832 | −0.145411 | −0.0727056 | − | 0.997353i | \(-0.523163\pi\) | ||||
−0.0727056 | + | 0.997353i | \(0.523163\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −3.24337 | −0.707762 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.61769 | −1.17137 | −0.585684 | − | 0.810539i | \(-0.699174\pi\) | ||||
−0.585684 | + | 0.810539i | \(0.699174\pi\) | |||||||
\(24\) | 3.24337 | 0.662051 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.14515 | 0.420699 | ||||||||
\(27\) | 14.6583 | 2.82100 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −1.19605 | −0.222101 | −0.111050 | − | 0.993815i | \(-0.535421\pi\) | ||||
−0.111050 | + | 0.993815i | \(0.535421\pi\) | |||||||
\(30\) | −3.24337 | −0.592156 | ||||||||
\(31\) | 6.95889 | 1.24985 | 0.624927 | − | 0.780683i | \(-0.285129\pi\) | ||||
0.624927 | + | 0.780683i | \(0.285129\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.43942 | 0.246859 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 7.51947 | 1.25324 | ||||||||
\(37\) | 4.80395 | 0.789765 | 0.394882 | − | 0.918732i | \(-0.370785\pi\) | ||||
0.394882 | + | 0.918732i | \(0.370785\pi\) | |||||||
\(38\) | −0.633832 | −0.102821 | ||||||||
\(39\) | 6.95754 | 1.11410 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.93663 | −1.39567 | −0.697834 | − | 0.716260i | \(-0.745853\pi\) | ||||
−0.697834 | + | 0.716260i | \(0.745853\pi\) | |||||||
\(42\) | −3.24337 | −0.500463 | ||||||||
\(43\) | 9.70747 | 1.48038 | 0.740188 | − | 0.672400i | \(-0.234736\pi\) | ||||
0.740188 | + | 0.672400i | \(0.234736\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.51947 | −1.12094 | ||||||||
\(46\) | −5.61769 | −0.828283 | ||||||||
\(47\) | 8.29874 | 1.21050 | 0.605248 | − | 0.796037i | \(-0.293074\pi\) | ||||
0.605248 | + | 0.796037i | \(0.293074\pi\) | |||||||
\(48\) | 3.24337 | 0.468141 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.66858 | 0.653732 | ||||||||
\(52\) | 2.14515 | 0.297479 | ||||||||
\(53\) | 14.1537 | 1.94416 | 0.972079 | − | 0.234652i | \(-0.0753952\pi\) | ||||
0.972079 | + | 0.234652i | \(0.0753952\pi\) | |||||||
\(54\) | 14.6583 | 1.99475 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −2.05576 | −0.272291 | ||||||||
\(58\) | −1.19605 | −0.157049 | ||||||||
\(59\) | −1.19248 | −0.155248 | −0.0776238 | − | 0.996983i | \(-0.524733\pi\) | ||||
−0.0776238 | + | 0.996983i | \(0.524733\pi\) | |||||||
\(60\) | −3.24337 | −0.418718 | ||||||||
\(61\) | −4.19441 | −0.537039 | −0.268520 | − | 0.963274i | \(-0.586534\pi\) | ||||
−0.268520 | + | 0.963274i | \(0.586534\pi\) | |||||||
\(62\) | 6.95889 | 0.883780 | ||||||||
\(63\) | −7.51947 | −0.947364 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.14515 | −0.266074 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0099 | −1.46724 | −0.733621 | − | 0.679559i | \(-0.762171\pi\) | ||||
−0.733621 | + | 0.679559i | \(0.762171\pi\) | |||||||
\(68\) | 1.43942 | 0.174555 | ||||||||
\(69\) | −18.2203 | −2.19346 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −5.71591 | −0.678353 | −0.339177 | − | 0.940723i | \(-0.610148\pi\) | ||||
−0.339177 | + | 0.940723i | \(0.610148\pi\) | |||||||
\(72\) | 7.51947 | 0.886178 | ||||||||
\(73\) | 6.43981 | 0.753723 | 0.376861 | − | 0.926270i | \(-0.377003\pi\) | ||||
0.376861 | + | 0.926270i | \(0.377003\pi\) | |||||||
\(74\) | 4.80395 | 0.558448 | ||||||||
\(75\) | 3.24337 | 0.374512 | ||||||||
\(76\) | −0.633832 | −0.0727056 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.95754 | 0.787786 | ||||||||
\(79\) | −7.69133 | −0.865342 | −0.432671 | − | 0.901552i | \(-0.642429\pi\) | ||||
−0.432671 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 24.9840 | 2.77600 | ||||||||
\(82\) | −8.93663 | −0.986886 | ||||||||
\(83\) | 11.5685 | 1.26981 | 0.634906 | − | 0.772590i | \(-0.281039\pi\) | ||||
0.634906 | + | 0.772590i | \(0.281039\pi\) | |||||||
\(84\) | −3.24337 | −0.353881 | ||||||||
\(85\) | −1.43942 | −0.156127 | ||||||||
\(86\) | 9.70747 | 1.04678 | ||||||||
\(87\) | −3.87923 | −0.415897 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.7855 | 1.77926 | 0.889629 | − | 0.456684i | \(-0.150963\pi\) | ||||
0.889629 | + | 0.456684i | \(0.150963\pi\) | |||||||
\(90\) | −7.51947 | −0.792622 | ||||||||
\(91\) | −2.14515 | −0.224873 | ||||||||
\(92\) | −5.61769 | −0.585684 | ||||||||
\(93\) | 22.5703 | 2.34043 | ||||||||
\(94\) | 8.29874 | 0.855950 | ||||||||
\(95\) | 0.633832 | 0.0650298 | ||||||||
\(96\) | 3.24337 | 0.331025 | ||||||||
\(97\) | −2.96529 | −0.301080 | −0.150540 | − | 0.988604i | \(-0.548101\pi\) | ||||
−0.150540 | + | 0.988604i | \(0.548101\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −15.5584 | −1.54812 | −0.774060 | − | 0.633113i | \(-0.781777\pi\) | ||||
−0.774060 | + | 0.633113i | \(0.781777\pi\) | |||||||
\(102\) | 4.66858 | 0.462258 | ||||||||
\(103\) | 0.404673 | 0.0398736 | 0.0199368 | − | 0.999801i | \(-0.493653\pi\) | ||||
0.0199368 | + | 0.999801i | \(0.493653\pi\) | |||||||
\(104\) | 2.14515 | 0.210350 | ||||||||
\(105\) | 3.24337 | 0.316521 | ||||||||
\(106\) | 14.1537 | 1.37473 | ||||||||
\(107\) | −8.17962 | −0.790754 | −0.395377 | − | 0.918519i | \(-0.629386\pi\) | ||||
−0.395377 | + | 0.918519i | \(0.629386\pi\) | |||||||
\(108\) | 14.6583 | 1.41050 | ||||||||
\(109\) | −1.34828 | −0.129142 | −0.0645709 | − | 0.997913i | \(-0.520568\pi\) | ||||
−0.0645709 | + | 0.997913i | \(0.520568\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.5810 | 1.47888 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 12.6845 | 1.19326 | 0.596630 | − | 0.802516i | \(-0.296506\pi\) | ||||
0.596630 | + | 0.802516i | \(0.296506\pi\) | |||||||
\(114\) | −2.05576 | −0.192539 | ||||||||
\(115\) | 5.61769 | 0.523852 | ||||||||
\(116\) | −1.19605 | −0.111050 | ||||||||
\(117\) | 16.1304 | 1.49126 | ||||||||
\(118\) | −1.19248 | −0.109777 | ||||||||
\(119\) | −1.43942 | −0.131952 | ||||||||
\(120\) | −3.24337 | −0.296078 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.19441 | −0.379744 | ||||||||
\(123\) | −28.9848 | −2.61347 | ||||||||
\(124\) | 6.95889 | 0.624927 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.51947 | −0.669887 | ||||||||
\(127\) | 12.6218 | 1.12000 | 0.560001 | − | 0.828492i | \(-0.310801\pi\) | ||||
0.560001 | + | 0.828492i | \(0.310801\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 31.4850 | 2.77210 | ||||||||
\(130\) | −2.14515 | −0.188143 | ||||||||
\(131\) | 4.14932 | 0.362528 | 0.181264 | − | 0.983434i | \(-0.441981\pi\) | ||||
0.181264 | + | 0.983434i | \(0.441981\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.633832 | 0.0549602 | ||||||||
\(134\) | −12.0099 | −1.03750 | ||||||||
\(135\) | −14.6583 | −1.26159 | ||||||||
\(136\) | 1.43942 | 0.123429 | ||||||||
\(137\) | 20.8283 | 1.77948 | 0.889742 | − | 0.456463i | \(-0.150884\pi\) | ||||
0.889742 | + | 0.456463i | \(0.150884\pi\) | |||||||
\(138\) | −18.2203 | −1.55101 | ||||||||
\(139\) | −18.4862 | −1.56798 | −0.783988 | − | 0.620776i | \(-0.786818\pi\) | ||||
−0.783988 | + | 0.620776i | \(0.786818\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 26.9159 | 2.26673 | ||||||||
\(142\) | −5.71591 | −0.479668 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.51947 | 0.626622 | ||||||||
\(145\) | 1.19605 | 0.0993264 | ||||||||
\(146\) | 6.43981 | 0.532962 | ||||||||
\(147\) | 3.24337 | 0.267509 | ||||||||
\(148\) | 4.80395 | 0.394882 | ||||||||
\(149\) | −15.4372 | −1.26467 | −0.632333 | − | 0.774697i | \(-0.717902\pi\) | ||||
−0.632333 | + | 0.774697i | \(0.717902\pi\) | |||||||
\(150\) | 3.24337 | 0.264820 | ||||||||
\(151\) | −11.4606 | −0.932648 | −0.466324 | − | 0.884614i | \(-0.654422\pi\) | ||||
−0.466324 | + | 0.884614i | \(0.654422\pi\) | |||||||
\(152\) | −0.633832 | −0.0514106 | ||||||||
\(153\) | 10.8237 | 0.875043 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.95889 | −0.558951 | ||||||||
\(156\) | 6.95754 | 0.557049 | ||||||||
\(157\) | −10.2685 | −0.819514 | −0.409757 | − | 0.912195i | \(-0.634387\pi\) | ||||
−0.409757 | + | 0.912195i | \(0.634387\pi\) | |||||||
\(158\) | −7.69133 | −0.611889 | ||||||||
\(159\) | 45.9057 | 3.64056 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.61769 | 0.442736 | ||||||||
\(162\) | 24.9840 | 1.96293 | ||||||||
\(163\) | −2.90989 | −0.227920 | −0.113960 | − | 0.993485i | \(-0.536354\pi\) | ||||
−0.113960 | + | 0.993485i | \(0.536354\pi\) | |||||||
\(164\) | −8.93663 | −0.697834 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.5685 | 0.897892 | ||||||||
\(167\) | 11.7960 | 0.912798 | 0.456399 | − | 0.889775i | \(-0.349139\pi\) | ||||
0.456399 | + | 0.889775i | \(0.349139\pi\) | |||||||
\(168\) | −3.24337 | −0.250232 | ||||||||
\(169\) | −8.39831 | −0.646024 | ||||||||
\(170\) | −1.43942 | −0.110399 | ||||||||
\(171\) | −4.76608 | −0.364472 | ||||||||
\(172\) | 9.70747 | 0.740188 | ||||||||
\(173\) | 0.146508 | 0.0111388 | 0.00556939 | − | 0.999984i | \(-0.498227\pi\) | ||||
0.00556939 | + | 0.999984i | \(0.498227\pi\) | |||||||
\(174\) | −3.87923 | −0.294084 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.86766 | −0.290711 | ||||||||
\(178\) | 16.7855 | 1.25813 | ||||||||
\(179\) | 10.2987 | 0.769764 | 0.384882 | − | 0.922966i | \(-0.374242\pi\) | ||||
0.384882 | + | 0.922966i | \(0.374242\pi\) | |||||||
\(180\) | −7.51947 | −0.560468 | ||||||||
\(181\) | −19.8342 | −1.47426 | −0.737131 | − | 0.675750i | \(-0.763820\pi\) | ||||
−0.737131 | + | 0.675750i | \(0.763820\pi\) | |||||||
\(182\) | −2.14515 | −0.159009 | ||||||||
\(183\) | −13.6040 | −1.00564 | ||||||||
\(184\) | −5.61769 | −0.414141 | ||||||||
\(185\) | −4.80395 | −0.353194 | ||||||||
\(186\) | 22.5703 | 1.65493 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.29874 | 0.605248 | ||||||||
\(189\) | −14.6583 | −1.06624 | ||||||||
\(190\) | 0.633832 | 0.0459830 | ||||||||
\(191\) | 5.95268 | 0.430720 | 0.215360 | − | 0.976535i | \(-0.430907\pi\) | ||||
0.215360 | + | 0.976535i | \(0.430907\pi\) | |||||||
\(192\) | 3.24337 | 0.234070 | ||||||||
\(193\) | −14.9671 | −1.07736 | −0.538678 | − | 0.842512i | \(-0.681076\pi\) | ||||
−0.538678 | + | 0.842512i | \(0.681076\pi\) | |||||||
\(194\) | −2.96529 | −0.212896 | ||||||||
\(195\) | −6.95754 | −0.498240 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −19.1531 | −1.36460 | −0.682301 | − | 0.731071i | \(-0.739021\pi\) | ||||
−0.682301 | + | 0.731071i | \(0.739021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.268053 | −0.0190018 | −0.00950089 | − | 0.999955i | \(-0.503024\pi\) | ||||
−0.00950089 | + | 0.999955i | \(0.503024\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −38.9525 | −2.74750 | ||||||||
\(202\) | −15.5584 | −1.09469 | ||||||||
\(203\) | 1.19605 | 0.0839461 | ||||||||
\(204\) | 4.66858 | 0.326866 | ||||||||
\(205\) | 8.93663 | 0.624162 | ||||||||
\(206\) | 0.404673 | 0.0281949 | ||||||||
\(207\) | −42.2420 | −2.93602 | ||||||||
\(208\) | 2.14515 | 0.148740 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.24337 | 0.223814 | ||||||||
\(211\) | −9.35228 | −0.643837 | −0.321919 | − | 0.946767i | \(-0.604328\pi\) | ||||
−0.321919 | + | 0.946767i | \(0.604328\pi\) | |||||||
\(212\) | 14.1537 | 0.972079 | ||||||||
\(213\) | −18.5388 | −1.27026 | ||||||||
\(214\) | −8.17962 | −0.559147 | ||||||||
\(215\) | −9.70747 | −0.662044 | ||||||||
\(216\) | 14.6583 | 0.997373 | ||||||||
\(217\) | −6.95889 | −0.472400 | ||||||||
\(218\) | −1.34828 | −0.0913171 | ||||||||
\(219\) | 20.8867 | 1.41139 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.08778 | 0.207707 | ||||||||
\(222\) | 15.5810 | 1.04573 | ||||||||
\(223\) | −13.8365 | −0.926559 | −0.463280 | − | 0.886212i | \(-0.653327\pi\) | ||||
−0.463280 | + | 0.886212i | \(0.653327\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 7.51947 | 0.501298 | ||||||||
\(226\) | 12.6845 | 0.843763 | ||||||||
\(227\) | 25.8686 | 1.71696 | 0.858481 | − | 0.512846i | \(-0.171409\pi\) | ||||
0.858481 | + | 0.512846i | \(0.171409\pi\) | |||||||
\(228\) | −2.05576 | −0.136146 | ||||||||
\(229\) | 11.1800 | 0.738796 | 0.369398 | − | 0.929271i | \(-0.379564\pi\) | ||||
0.369398 | + | 0.929271i | \(0.379564\pi\) | |||||||
\(230\) | 5.61769 | 0.370419 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.19605 | −0.0785244 | ||||||||
\(233\) | 2.87302 | 0.188218 | 0.0941088 | − | 0.995562i | \(-0.470000\pi\) | ||||
0.0941088 | + | 0.995562i | \(0.470000\pi\) | |||||||
\(234\) | 16.1304 | 1.05448 | ||||||||
\(235\) | −8.29874 | −0.541350 | ||||||||
\(236\) | −1.19248 | −0.0776238 | ||||||||
\(237\) | −24.9458 | −1.62041 | ||||||||
\(238\) | −1.43942 | −0.0933038 | ||||||||
\(239\) | 8.22791 | 0.532219 | 0.266110 | − | 0.963943i | \(-0.414262\pi\) | ||||
0.266110 | + | 0.963943i | \(0.414262\pi\) | |||||||
\(240\) | −3.24337 | −0.209359 | ||||||||
\(241\) | −6.54207 | −0.421412 | −0.210706 | − | 0.977550i | \(-0.567576\pi\) | ||||
−0.210706 | + | 0.977550i | \(0.567576\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 37.0575 | 2.37724 | ||||||||
\(244\) | −4.19441 | −0.268520 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −28.9848 | −1.84801 | ||||||||
\(247\) | −1.35967 | −0.0865136 | ||||||||
\(248\) | 6.95889 | 0.441890 | ||||||||
\(249\) | 37.5211 | 2.37780 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −11.0809 | −0.699422 | −0.349711 | − | 0.936858i | \(-0.613720\pi\) | ||||
−0.349711 | + | 0.936858i | \(0.613720\pi\) | |||||||
\(252\) | −7.51947 | −0.473682 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.6218 | 0.791960 | ||||||||
\(255\) | −4.66858 | −0.292358 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.1347 | 1.13121 | 0.565606 | − | 0.824676i | \(-0.308642\pi\) | ||||
0.565606 | + | 0.824676i | \(0.308642\pi\) | |||||||
\(258\) | 31.4850 | 1.96017 | ||||||||
\(259\) | −4.80395 | −0.298503 | ||||||||
\(260\) | −2.14515 | −0.133037 | ||||||||
\(261\) | −8.99365 | −0.556693 | ||||||||
\(262\) | 4.14932 | 0.256346 | ||||||||
\(263\) | −17.9268 | −1.10541 | −0.552706 | − | 0.833376i | \(-0.686405\pi\) | ||||
−0.552706 | + | 0.833376i | \(0.686405\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.1537 | −0.869454 | ||||||||
\(266\) | 0.633832 | 0.0388628 | ||||||||
\(267\) | 54.4416 | 3.33177 | ||||||||
\(268\) | −12.0099 | −0.733621 | ||||||||
\(269\) | 6.06753 | 0.369944 | 0.184972 | − | 0.982744i | \(-0.440781\pi\) | ||||
0.184972 | + | 0.982744i | \(0.440781\pi\) | |||||||
\(270\) | −14.6583 | −0.892077 | ||||||||
\(271\) | 21.2185 | 1.28893 | 0.644466 | − | 0.764633i | \(-0.277080\pi\) | ||||
0.644466 | + | 0.764633i | \(0.277080\pi\) | |||||||
\(272\) | 1.43942 | 0.0872777 | ||||||||
\(273\) | −6.95754 | −0.421089 | ||||||||
\(274\) | 20.8283 | 1.25829 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.2203 | −1.09673 | ||||||||
\(277\) | −5.01421 | −0.301275 | −0.150637 | − | 0.988589i | \(-0.548133\pi\) | ||||
−0.150637 | + | 0.988589i | \(0.548133\pi\) | |||||||
\(278\) | −18.4862 | −1.10873 | ||||||||
\(279\) | 52.3272 | 3.13274 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 4.76751 | 0.284406 | 0.142203 | − | 0.989838i | \(-0.454581\pi\) | ||||
0.142203 | + | 0.989838i | \(0.454581\pi\) | |||||||
\(282\) | 26.9159 | 1.60282 | ||||||||
\(283\) | 9.65019 | 0.573644 | 0.286822 | − | 0.957984i | \(-0.407401\pi\) | ||||
0.286822 | + | 0.957984i | \(0.407401\pi\) | |||||||
\(284\) | −5.71591 | −0.339177 | ||||||||
\(285\) | 2.05576 | 0.121772 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.93663 | 0.527513 | ||||||||
\(288\) | 7.51947 | 0.443089 | ||||||||
\(289\) | −14.9281 | −0.878122 | ||||||||
\(290\) | 1.19605 | 0.0702344 | ||||||||
\(291\) | −9.61756 | −0.563791 | ||||||||
\(292\) | 6.43981 | 0.376861 | ||||||||
\(293\) | −28.5011 | −1.66505 | −0.832526 | − | 0.553986i | \(-0.813106\pi\) | ||||
−0.832526 | + | 0.553986i | \(0.813106\pi\) | |||||||
\(294\) | 3.24337 | 0.189157 | ||||||||
\(295\) | 1.19248 | 0.0694288 | ||||||||
\(296\) | 4.80395 | 0.279224 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.4372 | −0.894253 | ||||||||
\(299\) | −12.0508 | −0.696916 | ||||||||
\(300\) | 3.24337 | 0.187256 | ||||||||
\(301\) | −9.70747 | −0.559530 | ||||||||
\(302\) | −11.4606 | −0.659482 | ||||||||
\(303\) | −50.4617 | −2.89895 | ||||||||
\(304\) | −0.633832 | −0.0363528 | ||||||||
\(305\) | 4.19441 | 0.240171 | ||||||||
\(306\) | 10.8237 | 0.618749 | ||||||||
\(307\) | −0.552191 | −0.0315152 | −0.0157576 | − | 0.999876i | \(-0.505016\pi\) | ||||
−0.0157576 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.31251 | 0.0746659 | ||||||||
\(310\) | −6.95889 | −0.395238 | ||||||||
\(311\) | −30.4747 | −1.72806 | −0.864032 | − | 0.503437i | \(-0.832069\pi\) | ||||
−0.864032 | + | 0.503437i | \(0.832069\pi\) | |||||||
\(312\) | 6.95754 | 0.393893 | ||||||||
\(313\) | −33.4678 | −1.89171 | −0.945856 | − | 0.324587i | \(-0.894775\pi\) | ||||
−0.945856 | + | 0.324587i | \(0.894775\pi\) | |||||||
\(314\) | −10.2685 | −0.579484 | ||||||||
\(315\) | 7.51947 | 0.423674 | ||||||||
\(316\) | −7.69133 | −0.432671 | ||||||||
\(317\) | −20.2125 | −1.13525 | −0.567623 | − | 0.823288i | \(-0.692137\pi\) | ||||
−0.567623 | + | 0.823288i | \(0.692137\pi\) | |||||||
\(318\) | 45.9057 | 2.57426 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −26.5296 | −1.48074 | ||||||||
\(322\) | 5.61769 | 0.313061 | ||||||||
\(323\) | −0.912352 | −0.0507646 | ||||||||
\(324\) | 24.9840 | 1.38800 | ||||||||
\(325\) | 2.14515 | 0.118992 | ||||||||
\(326\) | −2.90989 | −0.161164 | ||||||||
\(327\) | −4.37298 | −0.241826 | ||||||||
\(328\) | −8.93663 | −0.493443 | ||||||||
\(329\) | −8.29874 | −0.457524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.3667 | −1.06449 | −0.532244 | − | 0.846591i | \(-0.678651\pi\) | ||||
−0.532244 | + | 0.846591i | \(0.678651\pi\) | |||||||
\(332\) | 11.5685 | 0.634906 | ||||||||
\(333\) | 36.1232 | 1.97954 | ||||||||
\(334\) | 11.7960 | 0.645446 | ||||||||
\(335\) | 12.0099 | 0.656170 | ||||||||
\(336\) | −3.24337 | −0.176941 | ||||||||
\(337\) | 0.0549787 | 0.00299488 | 0.00149744 | − | 0.999999i | \(-0.499523\pi\) | ||||
0.00149744 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(338\) | −8.39831 | −0.456808 | ||||||||
\(339\) | 41.1407 | 2.23446 | ||||||||
\(340\) | −1.43942 | −0.0780636 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.76608 | −0.257720 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 9.70747 | 0.523392 | ||||||||
\(345\) | 18.2203 | 0.980945 | ||||||||
\(346\) | 0.146508 | 0.00787631 | ||||||||
\(347\) | 22.9466 | 1.23184 | 0.615920 | − | 0.787809i | \(-0.288784\pi\) | ||||
0.615920 | + | 0.787809i | \(0.288784\pi\) | |||||||
\(348\) | −3.87923 | −0.207949 | ||||||||
\(349\) | −21.7380 | −1.16361 | −0.581804 | − | 0.813329i | \(-0.697653\pi\) | ||||
−0.581804 | + | 0.813329i | \(0.697653\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 31.4444 | 1.67838 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.3596 | −0.551384 | −0.275692 | − | 0.961246i | \(-0.588907\pi\) | ||||
−0.275692 | + | 0.961246i | \(0.588907\pi\) | |||||||
\(354\) | −3.86766 | −0.205564 | ||||||||
\(355\) | 5.71591 | 0.303369 | ||||||||
\(356\) | 16.7855 | 0.889629 | ||||||||
\(357\) | −4.66858 | −0.247087 | ||||||||
\(358\) | 10.2987 | 0.544305 | ||||||||
\(359\) | 33.6387 | 1.77538 | 0.887690 | − | 0.460442i | \(-0.152309\pi\) | ||||
0.887690 | + | 0.460442i | \(0.152309\pi\) | |||||||
\(360\) | −7.51947 | −0.396311 | ||||||||
\(361\) | −18.5983 | −0.978856 | ||||||||
\(362\) | −19.8342 | −1.04246 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.14515 | −0.112437 | ||||||||
\(365\) | −6.43981 | −0.337075 | ||||||||
\(366\) | −13.6040 | −0.711095 | ||||||||
\(367\) | −23.1345 | −1.20761 | −0.603806 | − | 0.797131i | \(-0.706350\pi\) | ||||
−0.603806 | + | 0.797131i | \(0.706350\pi\) | |||||||
\(368\) | −5.61769 | −0.292842 | ||||||||
\(369\) | −67.1987 | −3.49823 | ||||||||
\(370\) | −4.80395 | −0.249746 | ||||||||
\(371\) | −14.1537 | −0.734823 | ||||||||
\(372\) | 22.5703 | 1.17021 | ||||||||
\(373\) | −20.5321 | −1.06311 | −0.531555 | − | 0.847024i | \(-0.678392\pi\) | ||||
−0.531555 | + | 0.847024i | \(0.678392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.24337 | −0.167487 | ||||||||
\(376\) | 8.29874 | 0.427975 | ||||||||
\(377\) | −2.56571 | −0.132141 | ||||||||
\(378\) | −14.6583 | −0.753943 | ||||||||
\(379\) | 21.0362 | 1.08056 | 0.540278 | − | 0.841487i | \(-0.318319\pi\) | ||||
0.540278 | + | 0.841487i | \(0.318319\pi\) | |||||||
\(380\) | 0.633832 | 0.0325149 | ||||||||
\(381\) | 40.9371 | 2.09727 | ||||||||
\(382\) | 5.95268 | 0.304565 | ||||||||
\(383\) | 11.3755 | 0.581263 | 0.290632 | − | 0.956835i | \(-0.406135\pi\) | ||||
0.290632 | + | 0.956835i | \(0.406135\pi\) | |||||||
\(384\) | 3.24337 | 0.165513 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9671 | −0.761805 | ||||||||
\(387\) | 72.9951 | 3.71055 | ||||||||
\(388\) | −2.96529 | −0.150540 | ||||||||
\(389\) | 25.9812 | 1.31730 | 0.658649 | − | 0.752450i | \(-0.271128\pi\) | ||||
0.658649 | + | 0.752450i | \(0.271128\pi\) | |||||||
\(390\) | −6.95754 | −0.352309 | ||||||||
\(391\) | −8.08622 | −0.408938 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 13.4578 | 0.678856 | ||||||||
\(394\) | −19.1531 | −0.964920 | ||||||||
\(395\) | 7.69133 | 0.386993 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.16936 | 0.359820 | 0.179910 | − | 0.983683i | \(-0.442419\pi\) | ||||
0.179910 | + | 0.983683i | \(0.442419\pi\) | |||||||
\(398\) | −0.268053 | −0.0134363 | ||||||||
\(399\) | 2.05576 | 0.102916 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −26.2702 | −1.31187 | −0.655937 | − | 0.754816i | \(-0.727726\pi\) | ||||
−0.655937 | + | 0.754816i | \(0.727726\pi\) | |||||||
\(402\) | −38.9525 | −1.94278 | ||||||||
\(403\) | 14.9279 | 0.743611 | ||||||||
\(404\) | −15.5584 | −0.774060 | ||||||||
\(405\) | −24.9840 | −1.24147 | ||||||||
\(406\) | 1.19605 | 0.0593589 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.66858 | 0.231129 | ||||||||
\(409\) | 36.5385 | 1.80671 | 0.903356 | − | 0.428891i | \(-0.141096\pi\) | ||||
0.903356 | + | 0.428891i | \(0.141096\pi\) | |||||||
\(410\) | 8.93663 | 0.441349 | ||||||||
\(411\) | 67.5541 | 3.33220 | ||||||||
\(412\) | 0.404673 | 0.0199368 | ||||||||
\(413\) | 1.19248 | 0.0586781 | ||||||||
\(414\) | −42.2420 | −2.07608 | ||||||||
\(415\) | −11.5685 | −0.567877 | ||||||||
\(416\) | 2.14515 | 0.105175 | ||||||||
\(417\) | −59.9575 | −2.93613 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.9411 | −0.876480 | −0.438240 | − | 0.898858i | \(-0.644398\pi\) | ||||
−0.438240 | + | 0.898858i | \(0.644398\pi\) | |||||||
\(420\) | 3.24337 | 0.158260 | ||||||||
\(421\) | 36.8460 | 1.79576 | 0.897882 | − | 0.440237i | \(-0.145106\pi\) | ||||
0.897882 | + | 0.440237i | \(0.145106\pi\) | |||||||
\(422\) | −9.35228 | −0.455262 | ||||||||
\(423\) | 62.4021 | 3.03409 | ||||||||
\(424\) | 14.1537 | 0.687364 | ||||||||
\(425\) | 1.43942 | 0.0698222 | ||||||||
\(426\) | −18.5388 | −0.898208 | ||||||||
\(427\) | 4.19441 | 0.202982 | ||||||||
\(428\) | −8.17962 | −0.395377 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.70747 | −0.468136 | ||||||||
\(431\) | 31.8543 | 1.53437 | 0.767185 | − | 0.641426i | \(-0.221657\pi\) | ||||
0.767185 | + | 0.641426i | \(0.221657\pi\) | |||||||
\(432\) | 14.6583 | 0.705249 | ||||||||
\(433\) | 25.0278 | 1.20276 | 0.601380 | − | 0.798963i | \(-0.294618\pi\) | ||||
0.601380 | + | 0.798963i | \(0.294618\pi\) | |||||||
\(434\) | −6.95889 | −0.334037 | ||||||||
\(435\) | 3.87923 | 0.185995 | ||||||||
\(436\) | −1.34828 | −0.0645709 | ||||||||
\(437\) | 3.56067 | 0.170330 | ||||||||
\(438\) | 20.8867 | 0.998005 | ||||||||
\(439\) | −40.3537 | −1.92598 | −0.962988 | − | 0.269544i | \(-0.913127\pi\) | ||||
−0.962988 | + | 0.269544i | \(0.913127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.51947 | 0.358070 | ||||||||
\(442\) | 3.08778 | 0.146871 | ||||||||
\(443\) | −0.519900 | −0.0247012 | −0.0123506 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123506 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(444\) | 15.5810 | 0.739442 | ||||||||
\(445\) | −16.7855 | −0.795708 | ||||||||
\(446\) | −13.8365 | −0.655176 | ||||||||
\(447\) | −50.0686 | −2.36816 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 23.0974 | 1.09003 | 0.545016 | − | 0.838426i | \(-0.316524\pi\) | ||||
0.545016 | + | 0.838426i | \(0.316524\pi\) | |||||||
\(450\) | 7.51947 | 0.354471 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.6845 | 0.596630 | ||||||||
\(453\) | −37.1709 | −1.74644 | ||||||||
\(454\) | 25.8686 | 1.21407 | ||||||||
\(455\) | 2.14515 | 0.100566 | ||||||||
\(456\) | −2.05576 | −0.0962696 | ||||||||
\(457\) | −20.3786 | −0.953273 | −0.476637 | − | 0.879100i | \(-0.658144\pi\) | ||||
−0.476637 | + | 0.879100i | \(0.658144\pi\) | |||||||
\(458\) | 11.1800 | 0.522407 | ||||||||
\(459\) | 21.0995 | 0.984840 | ||||||||
\(460\) | 5.61769 | 0.261926 | ||||||||
\(461\) | −12.1816 | −0.567354 | −0.283677 | − | 0.958920i | \(-0.591554\pi\) | ||||
−0.283677 | + | 0.958920i | \(0.591554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4172 | −0.530601 | −0.265301 | − | 0.964166i | \(-0.585471\pi\) | ||||
−0.265301 | + | 0.964166i | \(0.585471\pi\) | |||||||
\(464\) | −1.19605 | −0.0555252 | ||||||||
\(465\) | −22.5703 | −1.04667 | ||||||||
\(466\) | 2.87302 | 0.133090 | ||||||||
\(467\) | 22.7698 | 1.05366 | 0.526831 | − | 0.849970i | \(-0.323380\pi\) | ||||
0.526831 | + | 0.849970i | \(0.323380\pi\) | |||||||
\(468\) | 16.1304 | 0.745629 | ||||||||
\(469\) | 12.0099 | 0.554565 | ||||||||
\(470\) | −8.29874 | −0.382792 | ||||||||
\(471\) | −33.3045 | −1.53459 | ||||||||
\(472\) | −1.19248 | −0.0548883 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −24.9458 | −1.14580 | ||||||||
\(475\) | −0.633832 | −0.0290822 | ||||||||
\(476\) | −1.43942 | −0.0659758 | ||||||||
\(477\) | 106.428 | 4.87301 | ||||||||
\(478\) | 8.22791 | 0.376336 | ||||||||
\(479\) | −15.9269 | −0.727719 | −0.363859 | − | 0.931454i | \(-0.618541\pi\) | ||||
−0.363859 | + | 0.931454i | \(0.618541\pi\) | |||||||
\(480\) | −3.24337 | −0.148039 | ||||||||
\(481\) | 10.3052 | 0.469878 | ||||||||
\(482\) | −6.54207 | −0.297983 | ||||||||
\(483\) | 18.2203 | 0.829050 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.96529 | 0.134647 | ||||||||
\(486\) | 37.0575 | 1.68096 | ||||||||
\(487\) | 4.57953 | 0.207518 | 0.103759 | − | 0.994602i | \(-0.466913\pi\) | ||||
0.103759 | + | 0.994602i | \(0.466913\pi\) | |||||||
\(488\) | −4.19441 | −0.189872 | ||||||||
\(489\) | −9.43784 | −0.426794 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −28.0073 | −1.26395 | −0.631975 | − | 0.774989i | \(-0.717756\pi\) | ||||
−0.631975 | + | 0.774989i | \(0.717756\pi\) | |||||||
\(492\) | −28.9848 | −1.30674 | ||||||||
\(493\) | −1.72162 | −0.0775378 | ||||||||
\(494\) | −1.35967 | −0.0611744 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.95889 | 0.312463 | ||||||||
\(497\) | 5.71591 | 0.256393 | ||||||||
\(498\) | 37.5211 | 1.68136 | ||||||||
\(499\) | 27.8295 | 1.24582 | 0.622910 | − | 0.782294i | \(-0.285950\pi\) | ||||
0.622910 | + | 0.782294i | \(0.285950\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 38.2587 | 1.70927 | ||||||||
\(502\) | −11.0809 | −0.494566 | ||||||||
\(503\) | −30.4709 | −1.35863 | −0.679316 | − | 0.733846i | \(-0.737723\pi\) | ||||
−0.679316 | + | 0.733846i | \(0.737723\pi\) | |||||||
\(504\) | −7.51947 | −0.334944 | ||||||||
\(505\) | 15.5584 | 0.692340 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −27.2389 | −1.20972 | ||||||||
\(508\) | 12.6218 | 0.560001 | ||||||||
\(509\) | −25.7729 | −1.14236 | −0.571181 | − | 0.820824i | \(-0.693515\pi\) | ||||
−0.571181 | + | 0.820824i | \(0.693515\pi\) | |||||||
\(510\) | −4.66858 | −0.206728 | ||||||||
\(511\) | −6.43981 | −0.284880 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.29092 | −0.410204 | ||||||||
\(514\) | 18.1347 | 0.799888 | ||||||||
\(515\) | −0.404673 | −0.0178320 | ||||||||
\(516\) | 31.4850 | 1.38605 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.80395 | −0.211074 | ||||||||
\(519\) | 0.475179 | 0.0208581 | ||||||||
\(520\) | −2.14515 | −0.0940713 | ||||||||
\(521\) | 3.08204 | 0.135027 | 0.0675133 | − | 0.997718i | \(-0.478493\pi\) | ||||
0.0675133 | + | 0.997718i | \(0.478493\pi\) | |||||||
\(522\) | −8.99365 | −0.393641 | ||||||||
\(523\) | −10.0632 | −0.440033 | −0.220016 | − | 0.975496i | \(-0.570611\pi\) | ||||
−0.220016 | + | 0.975496i | \(0.570611\pi\) | |||||||
\(524\) | 4.14932 | 0.181264 | ||||||||
\(525\) | −3.24337 | −0.141552 | ||||||||
\(526\) | −17.9268 | −0.781644 | ||||||||
\(527\) | 10.0168 | 0.436338 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.55841 | 0.372105 | ||||||||
\(530\) | −14.1537 | −0.614797 | ||||||||
\(531\) | −8.96681 | −0.389126 | ||||||||
\(532\) | 0.633832 | 0.0274801 | ||||||||
\(533\) | −19.1705 | −0.830365 | ||||||||
\(534\) | 54.4416 | 2.35592 | ||||||||
\(535\) | 8.17962 | 0.353636 | ||||||||
\(536\) | −12.0099 | −0.518748 | ||||||||
\(537\) | 33.4027 | 1.44143 | ||||||||
\(538\) | 6.06753 | 0.261590 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −14.6583 | −0.630794 | ||||||||
\(541\) | 21.7416 | 0.934744 | 0.467372 | − | 0.884061i | \(-0.345201\pi\) | ||||
0.467372 | + | 0.884061i | \(0.345201\pi\) | |||||||
\(542\) | 21.2185 | 0.911413 | ||||||||
\(543\) | −64.3296 | −2.76065 | ||||||||
\(544\) | 1.43942 | 0.0617147 | ||||||||
\(545\) | 1.34828 | 0.0577540 | ||||||||
\(546\) | −6.95754 | −0.297755 | ||||||||
\(547\) | 33.5075 | 1.43268 | 0.716338 | − | 0.697753i | \(-0.245817\pi\) | ||||
0.716338 | + | 0.697753i | \(0.245817\pi\) | |||||||
\(548\) | 20.8283 | 0.889742 | ||||||||
\(549\) | −31.5397 | −1.34608 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.758094 | 0.0322959 | ||||||||
\(552\) | −18.2203 | −0.775506 | ||||||||
\(553\) | 7.69133 | 0.327069 | ||||||||
\(554\) | −5.01421 | −0.213034 | ||||||||
\(555\) | −15.5810 | −0.661377 | ||||||||
\(556\) | −18.4862 | −0.783988 | ||||||||
\(557\) | −27.9709 | −1.18517 | −0.592583 | − | 0.805509i | \(-0.701892\pi\) | ||||
−0.592583 | + | 0.805509i | \(0.701892\pi\) | |||||||
\(558\) | 52.3272 | 2.21519 | ||||||||
\(559\) | 20.8240 | 0.880763 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.76751 | 0.201105 | ||||||||
\(563\) | 19.1724 | 0.808019 | 0.404009 | − | 0.914755i | \(-0.367616\pi\) | ||||
0.404009 | + | 0.914755i | \(0.367616\pi\) | |||||||
\(564\) | 26.9159 | 1.13336 | ||||||||
\(565\) | −12.6845 | −0.533642 | ||||||||
\(566\) | 9.65019 | 0.405628 | ||||||||
\(567\) | −24.9840 | −1.04923 | ||||||||
\(568\) | −5.71591 | −0.239834 | ||||||||
\(569\) | 39.8416 | 1.67025 | 0.835124 | − | 0.550062i | \(-0.185396\pi\) | ||||
0.835124 | + | 0.550062i | \(0.185396\pi\) | |||||||
\(570\) | 2.05576 | 0.0861061 | ||||||||
\(571\) | 47.3425 | 1.98122 | 0.990610 | − | 0.136718i | \(-0.0436555\pi\) | ||||
0.990610 | + | 0.136718i | \(0.0436555\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.3067 | 0.806551 | ||||||||
\(574\) | 8.93663 | 0.373008 | ||||||||
\(575\) | −5.61769 | −0.234274 | ||||||||
\(576\) | 7.51947 | 0.313311 | ||||||||
\(577\) | −11.3882 | −0.474097 | −0.237048 | − | 0.971498i | \(-0.576180\pi\) | ||||
−0.237048 | + | 0.971498i | \(0.576180\pi\) | |||||||
\(578\) | −14.9281 | −0.620926 | ||||||||
\(579\) | −48.5439 | −2.01741 | ||||||||
\(580\) | 1.19605 | 0.0496632 | ||||||||
\(581\) | −11.5685 | −0.479944 | ||||||||
\(582\) | −9.61756 | −0.398661 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.43981 | 0.266481 | ||||||||
\(585\) | −16.1304 | −0.666911 | ||||||||
\(586\) | −28.5011 | −1.17737 | ||||||||
\(587\) | −22.3027 | −0.920529 | −0.460265 | − | 0.887782i | \(-0.652245\pi\) | ||||
−0.460265 | + | 0.887782i | \(0.652245\pi\) | |||||||
\(588\) | 3.24337 | 0.133754 | ||||||||
\(589\) | −4.41077 | −0.181743 | ||||||||
\(590\) | 1.19248 | 0.0490936 | ||||||||
\(591\) | −62.1207 | −2.55530 | ||||||||
\(592\) | 4.80395 | 0.197441 | ||||||||
\(593\) | −14.0840 | −0.578361 | −0.289180 | − | 0.957275i | \(-0.593383\pi\) | ||||
−0.289180 | + | 0.957275i | \(0.593383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.43942 | 0.0590105 | ||||||||
\(596\) | −15.4372 | −0.632333 | ||||||||
\(597\) | −0.869397 | −0.0355820 | ||||||||
\(598\) | −12.0508 | −0.492794 | ||||||||
\(599\) | −22.5478 | −0.921280 | −0.460640 | − | 0.887587i | \(-0.652380\pi\) | ||||
−0.460640 | + | 0.887587i | \(0.652380\pi\) | |||||||
\(600\) | 3.24337 | 0.132410 | ||||||||
\(601\) | 38.4433 | 1.56814 | 0.784068 | − | 0.620675i | \(-0.213141\pi\) | ||||
0.784068 | + | 0.620675i | \(0.213141\pi\) | |||||||
\(602\) | −9.70747 | −0.395647 | ||||||||
\(603\) | −90.3080 | −3.67762 | ||||||||
\(604\) | −11.4606 | −0.466324 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −50.4617 | −2.04987 | ||||||||
\(607\) | 24.2061 | 0.982497 | 0.491248 | − | 0.871020i | \(-0.336541\pi\) | ||||
0.491248 | + | 0.871020i | \(0.336541\pi\) | |||||||
\(608\) | −0.633832 | −0.0257053 | ||||||||
\(609\) | 3.87923 | 0.157194 | ||||||||
\(610\) | 4.19441 | 0.169827 | ||||||||
\(611\) | 17.8021 | 0.720195 | ||||||||
\(612\) | 10.8237 | 0.437521 | ||||||||
\(613\) | −26.3266 | −1.06332 | −0.531662 | − | 0.846957i | \(-0.678432\pi\) | ||||
−0.531662 | + | 0.846957i | \(0.678432\pi\) | |||||||
\(614\) | −0.552191 | −0.0222846 | ||||||||
\(615\) | 28.9848 | 1.16878 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.7839 | −1.44061 | −0.720303 | − | 0.693660i | \(-0.755997\pi\) | ||||
−0.720303 | + | 0.693660i | \(0.755997\pi\) | |||||||
\(618\) | 1.31251 | 0.0527968 | ||||||||
\(619\) | −8.17683 | −0.328654 | −0.164327 | − | 0.986406i | \(-0.552545\pi\) | ||||
−0.164327 | + | 0.986406i | \(0.552545\pi\) | |||||||
\(620\) | −6.95889 | −0.279476 | ||||||||
\(621\) | −82.3459 | −3.30443 | ||||||||
\(622\) | −30.4747 | −1.22193 | ||||||||
\(623\) | −16.7855 | −0.672496 | ||||||||
\(624\) | 6.95754 | 0.278524 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −33.4678 | −1.33764 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.2685 | −0.409757 | ||||||||
\(629\) | 6.91491 | 0.275716 | ||||||||
\(630\) | 7.51947 | 0.299583 | ||||||||
\(631\) | 20.1283 | 0.801293 | 0.400647 | − | 0.916233i | \(-0.368785\pi\) | ||||
0.400647 | + | 0.916233i | \(0.368785\pi\) | |||||||
\(632\) | −7.69133 | −0.305945 | ||||||||
\(633\) | −30.3329 | −1.20563 | ||||||||
\(634\) | −20.2125 | −0.802741 | ||||||||
\(635\) | −12.6218 | −0.500880 | ||||||||
\(636\) | 45.9057 | 1.82028 | ||||||||
\(637\) | 2.14515 | 0.0849941 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −42.9806 | −1.70029 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 8.58218 | 0.338976 | 0.169488 | − | 0.985532i | \(-0.445789\pi\) | ||||
0.169488 | + | 0.985532i | \(0.445789\pi\) | |||||||
\(642\) | −26.5296 | −1.04704 | ||||||||
\(643\) | −12.5152 | −0.493550 | −0.246775 | − | 0.969073i | \(-0.579371\pi\) | ||||
−0.246775 | + | 0.969073i | \(0.579371\pi\) | |||||||
\(644\) | 5.61769 | 0.221368 | ||||||||
\(645\) | −31.4850 | −1.23972 | ||||||||
\(646\) | −0.912352 | −0.0358960 | ||||||||
\(647\) | 16.7526 | 0.658611 | 0.329305 | − | 0.944223i | \(-0.393185\pi\) | ||||
0.329305 | + | 0.944223i | \(0.393185\pi\) | |||||||
\(648\) | 24.9840 | 0.981464 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.14515 | 0.0841399 | ||||||||
\(651\) | −22.5703 | −0.884599 | ||||||||
\(652\) | −2.90989 | −0.113960 | ||||||||
\(653\) | −27.3451 | −1.07010 | −0.535048 | − | 0.844822i | \(-0.679707\pi\) | ||||
−0.535048 | + | 0.844822i | \(0.679707\pi\) | |||||||
\(654\) | −4.37298 | −0.170997 | ||||||||
\(655\) | −4.14932 | −0.162127 | ||||||||
\(656\) | −8.93663 | −0.348917 | ||||||||
\(657\) | 48.4239 | 1.88920 | ||||||||
\(658\) | −8.29874 | −0.323519 | ||||||||
\(659\) | −12.7483 | −0.496604 | −0.248302 | − | 0.968683i | \(-0.579873\pi\) | ||||
−0.248302 | + | 0.968683i | \(0.579873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.892400 | −0.0347103 | −0.0173552 | − | 0.999849i | \(-0.505525\pi\) | ||||
−0.0173552 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(662\) | −19.3667 | −0.752707 | ||||||||
\(663\) | 10.0148 | 0.388944 | ||||||||
\(664\) | 11.5685 | 0.448946 | ||||||||
\(665\) | −0.633832 | −0.0245790 | ||||||||
\(666\) | 36.1232 | 1.39974 | ||||||||
\(667\) | 6.71903 | 0.260162 | ||||||||
\(668\) | 11.7960 | 0.456399 | ||||||||
\(669\) | −44.8769 | −1.73504 | ||||||||
\(670\) | 12.0099 | 0.463982 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −3.24337 | −0.125116 | ||||||||
\(673\) | −16.8765 | −0.650541 | −0.325271 | − | 0.945621i | \(-0.605455\pi\) | ||||
−0.325271 | + | 0.945621i | \(0.605455\pi\) | |||||||
\(674\) | 0.0549787 | 0.00211770 | ||||||||
\(675\) | 14.6583 | 0.564199 | ||||||||
\(676\) | −8.39831 | −0.323012 | ||||||||
\(677\) | 19.6250 | 0.754248 | 0.377124 | − | 0.926163i | \(-0.376913\pi\) | ||||
0.377124 | + | 0.926163i | \(0.376913\pi\) | |||||||
\(678\) | 41.1407 | 1.58000 | ||||||||
\(679\) | 2.96529 | 0.113798 | ||||||||
\(680\) | −1.43942 | −0.0551993 | ||||||||
\(681\) | 83.9016 | 3.21512 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.3107 | −0.547585 | −0.273792 | − | 0.961789i | \(-0.588278\pi\) | ||||
−0.273792 | + | 0.961789i | \(0.588278\pi\) | |||||||
\(684\) | −4.76608 | −0.182236 | ||||||||
\(685\) | −20.8283 | −0.795810 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 36.2609 | 1.38344 | ||||||||
\(688\) | 9.70747 | 0.370094 | ||||||||
\(689\) | 30.3619 | 1.15669 | ||||||||
\(690\) | 18.2203 | 0.693633 | ||||||||
\(691\) | −6.52873 | −0.248365 | −0.124182 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124182 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(692\) | 0.146508 | 0.00556939 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.9466 | 0.871042 | ||||||||
\(695\) | 18.4862 | 0.701220 | ||||||||
\(696\) | −3.87923 | −0.147042 | ||||||||
\(697\) | −12.8636 | −0.487243 | ||||||||
\(698\) | −21.7380 | −0.822795 | ||||||||
\(699\) | 9.31826 | 0.352449 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −0.193487 | −0.00730791 | −0.00365395 | − | 0.999993i | \(-0.501163\pi\) | ||||
−0.00365395 | + | 0.999993i | \(0.501163\pi\) | |||||||
\(702\) | 31.4444 | 1.18679 | ||||||||
\(703\) | −3.04490 | −0.114841 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26.9159 | −1.01371 | ||||||||
\(706\) | −10.3596 | −0.389888 | ||||||||
\(707\) | 15.5584 | 0.585134 | ||||||||
\(708\) | −3.86766 | −0.145355 | ||||||||
\(709\) | −19.2772 | −0.723970 | −0.361985 | − | 0.932184i | \(-0.617901\pi\) | ||||
−0.361985 | + | 0.932184i | \(0.617901\pi\) | |||||||
\(710\) | 5.71591 | 0.214514 | ||||||||
\(711\) | −57.8347 | −2.16897 | ||||||||
\(712\) | 16.7855 | 0.629063 | ||||||||
\(713\) | −39.0929 | −1.46404 | ||||||||
\(714\) | −4.66858 | −0.174717 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.2987 | 0.384882 | ||||||||
\(717\) | 26.6862 | 0.996613 | ||||||||
\(718\) | 33.6387 | 1.25538 | ||||||||
\(719\) | −41.7245 | −1.55606 | −0.778030 | − | 0.628227i | \(-0.783781\pi\) | ||||
−0.778030 | + | 0.628227i | \(0.783781\pi\) | |||||||
\(720\) | −7.51947 | −0.280234 | ||||||||
\(721\) | −0.404673 | −0.0150708 | ||||||||
\(722\) | −18.5983 | −0.692155 | ||||||||
\(723\) | −21.2184 | −0.789120 | ||||||||
\(724\) | −19.8342 | −0.737131 | ||||||||
\(725\) | −1.19605 | −0.0444201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.81130 | 0.104265 | 0.0521326 | − | 0.998640i | \(-0.483398\pi\) | ||||
0.0521326 | + | 0.998640i | \(0.483398\pi\) | |||||||
\(728\) | −2.14515 | −0.0795047 | ||||||||
\(729\) | 45.2392 | 1.67553 | ||||||||
\(730\) | −6.43981 | −0.238348 | ||||||||
\(731\) | 13.9731 | 0.516816 | ||||||||
\(732\) | −13.6040 | −0.502820 | ||||||||
\(733\) | 50.4642 | 1.86394 | 0.931969 | − | 0.362539i | \(-0.118090\pi\) | ||||
0.931969 | + | 0.362539i | \(0.118090\pi\) | |||||||
\(734\) | −23.1345 | −0.853911 | ||||||||
\(735\) | −3.24337 | −0.119634 | ||||||||
\(736\) | −5.61769 | −0.207071 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −67.1987 | −2.47362 | ||||||||
\(739\) | −22.9651 | −0.844783 | −0.422392 | − | 0.906413i | \(-0.638809\pi\) | ||||
−0.422392 | + | 0.906413i | \(0.638809\pi\) | |||||||
\(740\) | −4.80395 | −0.176597 | ||||||||
\(741\) | −4.40991 | −0.162002 | ||||||||
\(742\) | −14.1537 | −0.519598 | ||||||||
\(743\) | −45.8455 | −1.68191 | −0.840954 | − | 0.541107i | \(-0.818006\pi\) | ||||
−0.840954 | + | 0.541107i | \(0.818006\pi\) | |||||||
\(744\) | 22.5703 | 0.827466 | ||||||||
\(745\) | 15.4372 | 0.565575 | ||||||||
\(746\) | −20.5321 | −0.751733 | ||||||||
\(747\) | 86.9892 | 3.18277 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.17962 | 0.298877 | ||||||||
\(750\) | −3.24337 | −0.118431 | ||||||||
\(751\) | −3.84194 | −0.140194 | −0.0700972 | − | 0.997540i | \(-0.522331\pi\) | ||||
−0.0700972 | + | 0.997540i | \(0.522331\pi\) | |||||||
\(752\) | 8.29874 | 0.302624 | ||||||||
\(753\) | −35.9396 | −1.30971 | ||||||||
\(754\) | −2.56571 | −0.0934376 | ||||||||
\(755\) | 11.4606 | 0.417093 | ||||||||
\(756\) | −14.6583 | −0.533118 | ||||||||
\(757\) | −26.9122 | −0.978140 | −0.489070 | − | 0.872245i | \(-0.662664\pi\) | ||||
−0.489070 | + | 0.872245i | \(0.662664\pi\) | |||||||
\(758\) | 21.0362 | 0.764068 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.633832 | 0.0229915 | ||||||||
\(761\) | 0.765350 | 0.0277439 | 0.0138720 | − | 0.999904i | \(-0.495584\pi\) | ||||
0.0138720 | + | 0.999904i | \(0.495584\pi\) | |||||||
\(762\) | 40.9371 | 1.48300 | ||||||||
\(763\) | 1.34828 | 0.0488110 | ||||||||
\(764\) | 5.95268 | 0.215360 | ||||||||
\(765\) | −10.8237 | −0.391331 | ||||||||
\(766\) | 11.3755 | 0.411015 | ||||||||
\(767\) | −2.55805 | −0.0923659 | ||||||||
\(768\) | 3.24337 | 0.117035 | ||||||||
\(769\) | −42.2441 | −1.52336 | −0.761681 | − | 0.647952i | \(-0.775626\pi\) | ||||
−0.761681 | + | 0.647952i | \(0.775626\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 58.8176 | 2.11826 | ||||||||
\(772\) | −14.9671 | −0.538678 | ||||||||
\(773\) | 31.5640 | 1.13528 | 0.567639 | − | 0.823277i | \(-0.307857\pi\) | ||||
0.567639 | + | 0.823277i | \(0.307857\pi\) | |||||||
\(774\) | 72.9951 | 2.62375 | ||||||||
\(775\) | 6.95889 | 0.249971 | ||||||||
\(776\) | −2.96529 | −0.106448 | ||||||||
\(777\) | −15.5810 | −0.558966 | ||||||||
\(778\) | 25.9812 | 0.931470 | ||||||||
\(779\) | 5.66433 | 0.202946 | ||||||||
\(780\) | −6.95754 | −0.249120 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.08622 | −0.289163 | ||||||||
\(783\) | −17.5321 | −0.626545 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 10.2685 | 0.366498 | ||||||||
\(786\) | 13.4578 | 0.480024 | ||||||||
\(787\) | −20.4895 | −0.730370 | −0.365185 | − | 0.930935i | \(-0.618994\pi\) | ||||
−0.365185 | + | 0.930935i | \(0.618994\pi\) | |||||||
\(788\) | −19.1531 | −0.682301 | ||||||||
\(789\) | −58.1432 | −2.06995 | ||||||||
\(790\) | 7.69133 | 0.273645 | ||||||||
\(791\) | −12.6845 | −0.451010 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.99766 | −0.319516 | ||||||||
\(794\) | 7.16936 | 0.254431 | ||||||||
\(795\) | −45.9057 | −1.62811 | ||||||||
\(796\) | −0.268053 | −0.00950089 | ||||||||
\(797\) | −6.13739 | −0.217397 | −0.108699 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108699 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(798\) | 2.05576 | 0.0727729 | ||||||||
\(799\) | 11.9454 | 0.422597 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 126.218 | 4.45969 | ||||||||
\(802\) | −26.2702 | −0.927634 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −38.9525 | −1.37375 | ||||||||
\(805\) | −5.61769 | −0.197997 | ||||||||
\(806\) | 14.9279 | 0.525813 | ||||||||
\(807\) | 19.6793 | 0.692743 | ||||||||
\(808\) | −15.5584 | −0.547343 | ||||||||
\(809\) | 31.7238 | 1.11535 | 0.557674 | − | 0.830060i | \(-0.311694\pi\) | ||||
0.557674 | + | 0.830060i | \(0.311694\pi\) | |||||||
\(810\) | −24.9840 | −0.877848 | ||||||||
\(811\) | −9.91528 | −0.348173 | −0.174086 | − | 0.984730i | \(-0.555697\pi\) | ||||
−0.174086 | + | 0.984730i | \(0.555697\pi\) | |||||||
\(812\) | 1.19605 | 0.0419731 | ||||||||
\(813\) | 68.8196 | 2.41361 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.90989 | 0.101929 | ||||||||
\(816\) | 4.66858 | 0.163433 | ||||||||
\(817\) | −6.15291 | −0.215263 | ||||||||
\(818\) | 36.5385 | 1.27754 | ||||||||
\(819\) | −16.1304 | −0.563643 | ||||||||
\(820\) | 8.93663 | 0.312081 | ||||||||
\(821\) | 15.9145 | 0.555419 | 0.277710 | − | 0.960665i | \(-0.410425\pi\) | ||||
0.277710 | + | 0.960665i | \(0.410425\pi\) | |||||||
\(822\) | 67.5541 | 2.35622 | ||||||||
\(823\) | −5.51317 | −0.192177 | −0.0960885 | − | 0.995373i | \(-0.530633\pi\) | ||||
−0.0960885 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(824\) | 0.404673 | 0.0140975 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.19248 | 0.0414917 | ||||||||
\(827\) | 18.8463 | 0.655350 | 0.327675 | − | 0.944790i | \(-0.393735\pi\) | ||||
0.327675 | + | 0.944790i | \(0.393735\pi\) | |||||||
\(828\) | −42.2420 | −1.46801 | ||||||||
\(829\) | −23.0204 | −0.799532 | −0.399766 | − | 0.916617i | \(-0.630909\pi\) | ||||
−0.399766 | + | 0.916617i | \(0.630909\pi\) | |||||||
\(830\) | −11.5685 | −0.401550 | ||||||||
\(831\) | −16.2630 | −0.564156 | ||||||||
\(832\) | 2.14515 | 0.0743699 | ||||||||
\(833\) | 1.43942 | 0.0498730 | ||||||||
\(834\) | −59.9575 | −2.07616 | ||||||||
\(835\) | −11.7960 | −0.408216 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 102.006 | 3.52583 | ||||||||
\(838\) | −17.9411 | −0.619765 | ||||||||
\(839\) | 41.3387 | 1.42717 | 0.713585 | − | 0.700569i | \(-0.247070\pi\) | ||||
0.713585 | + | 0.700569i | \(0.247070\pi\) | |||||||
\(840\) | 3.24337 | 0.111907 | ||||||||
\(841\) | −27.5695 | −0.950671 | ||||||||
\(842\) | 36.8460 | 1.26980 | ||||||||
\(843\) | 15.4628 | 0.532567 | ||||||||
\(844\) | −9.35228 | −0.321919 | ||||||||
\(845\) | 8.39831 | 0.288911 | ||||||||
\(846\) | 62.4021 | 2.14543 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.1537 | 0.486040 | ||||||||
\(849\) | 31.2992 | 1.07418 | ||||||||
\(850\) | 1.43942 | 0.0493717 | ||||||||
\(851\) | −26.9871 | −0.925106 | ||||||||
\(852\) | −18.5388 | −0.635129 | ||||||||
\(853\) | −19.8786 | −0.680630 | −0.340315 | − | 0.940312i | \(-0.610534\pi\) | ||||
−0.340315 | + | 0.940312i | \(0.610534\pi\) | |||||||
\(854\) | 4.19441 | 0.143530 | ||||||||
\(855\) | 4.76608 | 0.162997 | ||||||||
\(856\) | −8.17962 | −0.279574 | ||||||||
\(857\) | −30.9589 | −1.05753 | −0.528767 | − | 0.848767i | \(-0.677346\pi\) | ||||
−0.528767 | + | 0.848767i | \(0.677346\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.3155 | −1.30731 | −0.653654 | − | 0.756793i | \(-0.726765\pi\) | ||||
−0.653654 | + | 0.756793i | \(0.726765\pi\) | |||||||
\(860\) | −9.70747 | −0.331022 | ||||||||
\(861\) | 28.9848 | 0.987801 | ||||||||
\(862\) | 31.8543 | 1.08496 | ||||||||
\(863\) | 33.7087 | 1.14746 | 0.573729 | − | 0.819045i | \(-0.305496\pi\) | ||||
0.573729 | + | 0.819045i | \(0.305496\pi\) | |||||||
\(864\) | 14.6583 | 0.498686 | ||||||||
\(865\) | −0.146508 | −0.00498141 | ||||||||
\(866\) | 25.0278 | 0.850480 | ||||||||
\(867\) | −48.4173 | −1.64434 | ||||||||
\(868\) | −6.95889 | −0.236200 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.87923 | 0.131518 | ||||||||
\(871\) | −25.7631 | −0.872948 | ||||||||
\(872\) | −1.34828 | −0.0456585 | ||||||||
\(873\) | −22.2974 | −0.754654 | ||||||||
\(874\) | 3.56067 | 0.120442 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 20.8867 | 0.705696 | ||||||||
\(877\) | 32.7548 | 1.10605 | 0.553025 | − | 0.833165i | \(-0.313473\pi\) | ||||
0.553025 | + | 0.833165i | \(0.313473\pi\) | |||||||
\(878\) | −40.3537 | −1.36187 | ||||||||
\(879\) | −92.4397 | −3.11791 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −41.6696 | −1.40389 | −0.701943 | − | 0.712233i | \(-0.747684\pi\) | ||||
−0.701943 | + | 0.712233i | \(0.747684\pi\) | |||||||
\(882\) | 7.51947 | 0.253194 | ||||||||
\(883\) | −19.7448 | −0.664467 | −0.332234 | − | 0.943197i | \(-0.607802\pi\) | ||||
−0.332234 | + | 0.943197i | \(0.607802\pi\) | |||||||
\(884\) | 3.08778 | 0.103853 | ||||||||
\(885\) | 3.86766 | 0.130010 | ||||||||
\(886\) | −0.519900 | −0.0174664 | ||||||||
\(887\) | −25.1277 | −0.843704 | −0.421852 | − | 0.906665i | \(-0.638620\pi\) | ||||
−0.421852 | + | 0.906665i | \(0.638620\pi\) | |||||||
\(888\) | 15.5810 | 0.522864 | ||||||||
\(889\) | −12.6218 | −0.423321 | ||||||||
\(890\) | −16.7855 | −0.562651 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.8365 | −0.463280 | ||||||||
\(893\) | −5.26001 | −0.176020 | ||||||||
\(894\) | −50.0686 | −1.67455 | ||||||||
\(895\) | −10.2987 | −0.344249 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −39.0853 | −1.30502 | ||||||||
\(898\) | 23.0974 | 0.770769 | ||||||||
\(899\) | −8.32317 | −0.277593 | ||||||||
\(900\) | 7.51947 | 0.250649 | ||||||||
\(901\) | 20.3731 | 0.678727 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −31.4850 | −1.04775 | ||||||||
\(904\) | 12.6845 | 0.421881 | ||||||||
\(905\) | 19.8342 | 0.659310 | ||||||||
\(906\) | −37.1709 | −1.23492 | ||||||||
\(907\) | 15.1970 | 0.504608 | 0.252304 | − | 0.967648i | \(-0.418812\pi\) | ||||
0.252304 | + | 0.967648i | \(0.418812\pi\) | |||||||
\(908\) | 25.8686 | 0.858481 | ||||||||
\(909\) | −116.991 | −3.88034 | ||||||||
\(910\) | 2.14515 | 0.0711112 | ||||||||
\(911\) | −31.4976 | −1.04356 | −0.521781 | − | 0.853080i | \(-0.674732\pi\) | ||||
−0.521781 | + | 0.853080i | \(0.674732\pi\) | |||||||
\(912\) | −2.05576 | −0.0680729 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −20.3786 | −0.674066 | ||||||||
\(915\) | 13.6040 | 0.449736 | ||||||||
\(916\) | 11.1800 | 0.369398 | ||||||||
\(917\) | −4.14932 | −0.137023 | ||||||||
\(918\) | 21.0995 | 0.696387 | ||||||||
\(919\) | 3.67799 | 0.121326 | 0.0606628 | − | 0.998158i | \(-0.480679\pi\) | ||||
0.0606628 | + | 0.998158i | \(0.480679\pi\) | |||||||
\(920\) | 5.61769 | 0.185210 | ||||||||
\(921\) | −1.79096 | −0.0590142 | ||||||||
\(922\) | −12.1816 | −0.401180 | ||||||||
\(923\) | −12.2615 | −0.403592 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.80395 | 0.157953 | ||||||||
\(926\) | −11.4172 | −0.375192 | ||||||||
\(927\) | 3.04293 | 0.0999429 | ||||||||
\(928\) | −1.19605 | −0.0392622 | ||||||||
\(929\) | 57.4781 | 1.88579 | 0.942897 | − | 0.333084i | \(-0.108089\pi\) | ||||
0.942897 | + | 0.333084i | \(0.108089\pi\) | |||||||
\(930\) | −22.5703 | −0.740109 | ||||||||
\(931\) | −0.633832 | −0.0207730 | ||||||||
\(932\) | 2.87302 | 0.0941088 | ||||||||
\(933\) | −98.8410 | −3.23591 | ||||||||
\(934\) | 22.7698 | 0.745052 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16.1304 | 0.527239 | ||||||||
\(937\) | −18.0162 | −0.588564 | −0.294282 | − | 0.955719i | \(-0.595081\pi\) | ||||
−0.294282 | + | 0.955719i | \(0.595081\pi\) | |||||||
\(938\) | 12.0099 | 0.392137 | ||||||||
\(939\) | −108.549 | −3.54235 | ||||||||
\(940\) | −8.29874 | −0.270675 | ||||||||
\(941\) | −27.4433 | −0.894625 | −0.447312 | − | 0.894378i | \(-0.647619\pi\) | ||||
−0.447312 | + | 0.894378i | \(0.647619\pi\) | |||||||
\(942\) | −33.3045 | −1.08512 | ||||||||
\(943\) | 50.2032 | 1.63484 | ||||||||
\(944\) | −1.19248 | −0.0388119 | ||||||||
\(945\) | 14.6583 | 0.476835 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.524970 | 0.0170592 | 0.00852961 | − | 0.999964i | \(-0.497285\pi\) | ||||
0.00852961 | + | 0.999964i | \(0.497285\pi\) | |||||||
\(948\) | −24.9458 | −0.810204 | ||||||||
\(949\) | 13.8144 | 0.448434 | ||||||||
\(950\) | −0.633832 | −0.0205642 | ||||||||
\(951\) | −65.5567 | −2.12582 | ||||||||
\(952\) | −1.43942 | −0.0466519 | ||||||||
\(953\) | 47.1112 | 1.52608 | 0.763040 | − | 0.646351i | \(-0.223706\pi\) | ||||
0.763040 | + | 0.646351i | \(0.223706\pi\) | |||||||
\(954\) | 106.428 | 3.44574 | ||||||||
\(955\) | −5.95268 | −0.192624 | ||||||||
\(956\) | 8.22791 | 0.266110 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.9269 | −0.514575 | ||||||||
\(959\) | −20.8283 | −0.672582 | ||||||||
\(960\) | −3.24337 | −0.104679 | ||||||||
\(961\) | 17.4261 | 0.562134 | ||||||||
\(962\) | 10.3052 | 0.332254 | ||||||||
\(963\) | −61.5064 | −1.98202 | ||||||||
\(964\) | −6.54207 | −0.210706 | ||||||||
\(965\) | 14.9671 | 0.481808 | ||||||||
\(966\) | 18.2203 | 0.586227 | ||||||||
\(967\) | −30.5133 | −0.981243 | −0.490621 | − | 0.871373i | \(-0.663230\pi\) | ||||
−0.490621 | + | 0.871373i | \(0.663230\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.95910 | −0.0950599 | ||||||||
\(970\) | 2.96529 | 0.0952099 | ||||||||
\(971\) | 39.5470 | 1.26912 | 0.634562 | − | 0.772872i | \(-0.281180\pi\) | ||||
0.634562 | + | 0.772872i | \(0.281180\pi\) | |||||||
\(972\) | 37.0575 | 1.18862 | ||||||||
\(973\) | 18.4862 | 0.592639 | ||||||||
\(974\) | 4.57953 | 0.146737 | ||||||||
\(975\) | 6.95754 | 0.222820 | ||||||||
\(976\) | −4.19441 | −0.134260 | ||||||||
\(977\) | −31.0366 | −0.992950 | −0.496475 | − | 0.868051i | \(-0.665373\pi\) | ||||
−0.496475 | + | 0.868051i | \(0.665373\pi\) | |||||||
\(978\) | −9.43784 | −0.301789 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −10.1384 | −0.323693 | ||||||||
\(982\) | −28.0073 | −0.893748 | ||||||||
\(983\) | −51.0988 | −1.62980 | −0.814900 | − | 0.579602i | \(-0.803208\pi\) | ||||
−0.814900 | + | 0.579602i | \(0.803208\pi\) | |||||||
\(984\) | −28.9848 | −0.924003 | ||||||||
\(985\) | 19.1531 | 0.610269 | ||||||||
\(986\) | −1.72162 | −0.0548275 | ||||||||
\(987\) | −26.9159 | −0.856743 | ||||||||
\(988\) | −1.35967 | −0.0432568 | ||||||||
\(989\) | −54.5336 | −1.73407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.89709 | −0.282625 | −0.141313 | − | 0.989965i | \(-0.545132\pi\) | ||||
−0.141313 | + | 0.989965i | \(0.545132\pi\) | |||||||
\(992\) | 6.95889 | 0.220945 | ||||||||
\(993\) | −62.8133 | −1.99332 | ||||||||
\(994\) | 5.71591 | 0.181298 | ||||||||
\(995\) | 0.268053 | 0.00849786 | ||||||||
\(996\) | 37.5211 | 1.18890 | ||||||||
\(997\) | −26.9013 | −0.851974 | −0.425987 | − | 0.904729i | \(-0.640073\pi\) | ||||
−0.425987 | + | 0.904729i | \(0.640073\pi\) | |||||||
\(998\) | 27.8295 | 0.880928 | ||||||||
\(999\) | 70.4179 | 2.22792 |
(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 | 8470.2.a.dd.1.6 | yes | 6 | |
11.10 | odd | 2 | 8470.2.a.cx.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cx.1.6 | ✓ | 6 | 11.10 | odd | 2 | ||
8470.2.a.dd.1.6 | yes | 6 | 1.1 | even | 1 | trivial |