Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | −0.340721 | −0.196715 | −0.0983577 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983577 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.77081 | 0.791928 | 0.395964 | − | 0.918266i | \(-0.370410\pi\) | ||||
0.395964 | + | 0.918266i | \(0.370410\pi\) | |||||||
\(6\) | 0.340721 | 0.139099 | ||||||||
\(7\) | 4.18388 | 1.58136 | 0.790679 | − | 0.612230i | \(-0.209728\pi\) | ||||
0.790679 | + | 0.612230i | \(0.209728\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.88391 | −0.961303 | ||||||||
\(10\) | −1.77081 | −0.559978 | ||||||||
\(11\) | 2.61292 | 0.787824 | 0.393912 | − | 0.919148i | \(-0.371121\pi\) | ||||
0.393912 | + | 0.919148i | \(0.371121\pi\) | |||||||
\(12\) | −0.340721 | −0.0983577 | ||||||||
\(13\) | 3.00880 | 0.834490 | 0.417245 | − | 0.908794i | \(-0.362996\pi\) | ||||
0.417245 | + | 0.908794i | \(0.362996\pi\) | |||||||
\(14\) | −4.18388 | −1.11819 | ||||||||
\(15\) | −0.603351 | −0.155784 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.51698 | 0.852993 | 0.426496 | − | 0.904489i | \(-0.359748\pi\) | ||||
0.426496 | + | 0.904489i | \(0.359748\pi\) | |||||||
\(18\) | 2.88391 | 0.679744 | ||||||||
\(19\) | 7.65680 | 1.75659 | 0.878295 | − | 0.478119i | \(-0.158681\pi\) | ||||
0.878295 | + | 0.478119i | \(0.158681\pi\) | |||||||
\(20\) | 1.77081 | 0.395964 | ||||||||
\(21\) | −1.42554 | −0.311078 | ||||||||
\(22\) | −2.61292 | −0.557076 | ||||||||
\(23\) | 3.71765 | 0.775184 | 0.387592 | − | 0.921831i | \(-0.373307\pi\) | ||||
0.387592 | + | 0.921831i | \(0.373307\pi\) | |||||||
\(24\) | 0.340721 | 0.0695494 | ||||||||
\(25\) | −1.86425 | −0.372850 | ||||||||
\(26\) | −3.00880 | −0.590074 | ||||||||
\(27\) | 2.00477 | 0.385819 | ||||||||
\(28\) | 4.18388 | 0.790679 | ||||||||
\(29\) | −3.40065 | −0.631484 | −0.315742 | − | 0.948845i | \(-0.602253\pi\) | ||||
−0.315742 | + | 0.948845i | \(0.602253\pi\) | |||||||
\(30\) | 0.603351 | 0.110156 | ||||||||
\(31\) | 2.86692 | 0.514913 | 0.257457 | − | 0.966290i | \(-0.417116\pi\) | ||||
0.257457 | + | 0.966290i | \(0.417116\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.890276 | −0.154977 | ||||||||
\(34\) | −3.51698 | −0.603157 | ||||||||
\(35\) | 7.40884 | 1.25232 | ||||||||
\(36\) | −2.88391 | −0.480652 | ||||||||
\(37\) | −2.37182 | −0.389925 | −0.194963 | − | 0.980811i | \(-0.562459\pi\) | ||||
−0.194963 | + | 0.980811i | \(0.562459\pi\) | |||||||
\(38\) | −7.65680 | −1.24210 | ||||||||
\(39\) | −1.02516 | −0.164157 | ||||||||
\(40\) | −1.77081 | −0.279989 | ||||||||
\(41\) | −3.10570 | −0.485029 | −0.242514 | − | 0.970148i | \(-0.577972\pi\) | ||||
−0.242514 | + | 0.970148i | \(0.577972\pi\) | |||||||
\(42\) | 1.42554 | 0.219965 | ||||||||
\(43\) | −0.620433 | −0.0946151 | −0.0473076 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473076 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(44\) | 2.61292 | 0.393912 | ||||||||
\(45\) | −5.10684 | −0.761283 | ||||||||
\(46\) | −3.71765 | −0.548138 | ||||||||
\(47\) | 2.52070 | 0.367682 | 0.183841 | − | 0.982956i | \(-0.441147\pi\) | ||||
0.183841 | + | 0.982956i | \(0.441147\pi\) | |||||||
\(48\) | −0.340721 | −0.0491789 | ||||||||
\(49\) | 10.5049 | 1.50070 | ||||||||
\(50\) | 1.86425 | 0.263645 | ||||||||
\(51\) | −1.19831 | −0.167797 | ||||||||
\(52\) | 3.00880 | 0.417245 | ||||||||
\(53\) | 10.7851 | 1.48144 | 0.740721 | − | 0.671813i | \(-0.234484\pi\) | ||||
0.740721 | + | 0.671813i | \(0.234484\pi\) | |||||||
\(54\) | −2.00477 | −0.272815 | ||||||||
\(55\) | 4.62697 | 0.623900 | ||||||||
\(56\) | −4.18388 | −0.559095 | ||||||||
\(57\) | −2.60883 | −0.345548 | ||||||||
\(58\) | 3.40065 | 0.446527 | ||||||||
\(59\) | 10.6124 | 1.38162 | 0.690811 | − | 0.723036i | \(-0.257254\pi\) | ||||
0.690811 | + | 0.723036i | \(0.257254\pi\) | |||||||
\(60\) | −0.603351 | −0.0778922 | ||||||||
\(61\) | −12.7184 | −1.62843 | −0.814215 | − | 0.580563i | \(-0.802832\pi\) | ||||
−0.814215 | + | 0.580563i | \(0.802832\pi\) | |||||||
\(62\) | −2.86692 | −0.364099 | ||||||||
\(63\) | −12.0659 | −1.52016 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.32799 | 0.660856 | ||||||||
\(66\) | 0.890276 | 0.109585 | ||||||||
\(67\) | −16.2208 | −1.98169 | −0.990844 | − | 0.135015i | \(-0.956892\pi\) | ||||
−0.990844 | + | 0.135015i | \(0.956892\pi\) | |||||||
\(68\) | 3.51698 | 0.426496 | ||||||||
\(69\) | −1.26668 | −0.152491 | ||||||||
\(70\) | −7.40884 | −0.885526 | ||||||||
\(71\) | 8.12622 | 0.964404 | 0.482202 | − | 0.876060i | \(-0.339837\pi\) | ||||
0.482202 | + | 0.876060i | \(0.339837\pi\) | |||||||
\(72\) | 2.88391 | 0.339872 | ||||||||
\(73\) | −11.4257 | −1.33728 | −0.668640 | − | 0.743586i | \(-0.733123\pi\) | ||||
−0.668640 | + | 0.743586i | \(0.733123\pi\) | |||||||
\(74\) | 2.37182 | 0.275719 | ||||||||
\(75\) | 0.635189 | 0.0733453 | ||||||||
\(76\) | 7.65680 | 0.878295 | ||||||||
\(77\) | 10.9321 | 1.24583 | ||||||||
\(78\) | 1.02516 | 0.116077 | ||||||||
\(79\) | −12.7445 | −1.43387 | −0.716935 | − | 0.697140i | \(-0.754456\pi\) | ||||
−0.716935 | + | 0.697140i | \(0.754456\pi\) | |||||||
\(80\) | 1.77081 | 0.197982 | ||||||||
\(81\) | 7.96866 | 0.885407 | ||||||||
\(82\) | 3.10570 | 0.342967 | ||||||||
\(83\) | 4.18060 | 0.458881 | 0.229440 | − | 0.973323i | \(-0.426310\pi\) | ||||
0.229440 | + | 0.973323i | \(0.426310\pi\) | |||||||
\(84\) | −1.42554 | −0.155539 | ||||||||
\(85\) | 6.22789 | 0.675509 | ||||||||
\(86\) | 0.620433 | 0.0669030 | ||||||||
\(87\) | 1.15867 | 0.124223 | ||||||||
\(88\) | −2.61292 | −0.278538 | ||||||||
\(89\) | −7.88201 | −0.835491 | −0.417746 | − | 0.908564i | \(-0.637180\pi\) | ||||
−0.417746 | + | 0.908564i | \(0.637180\pi\) | |||||||
\(90\) | 5.10684 | 0.538308 | ||||||||
\(91\) | 12.5885 | 1.31963 | ||||||||
\(92\) | 3.71765 | 0.387592 | ||||||||
\(93\) | −0.976819 | −0.101291 | ||||||||
\(94\) | −2.52070 | −0.259990 | ||||||||
\(95\) | 13.5587 | 1.39109 | ||||||||
\(96\) | 0.340721 | 0.0347747 | ||||||||
\(97\) | 6.46877 | 0.656804 | 0.328402 | − | 0.944538i | \(-0.393490\pi\) | ||||
0.328402 | + | 0.944538i | \(0.393490\pi\) | |||||||
\(98\) | −10.5049 | −1.06115 | ||||||||
\(99\) | −7.53542 | −0.757338 | ||||||||
\(100\) | −1.86425 | −0.186425 | ||||||||
\(101\) | −1.69847 | −0.169004 | −0.0845020 | − | 0.996423i | \(-0.526930\pi\) | ||||
−0.0845020 | + | 0.996423i | \(0.526930\pi\) | |||||||
\(102\) | 1.19831 | 0.118650 | ||||||||
\(103\) | 14.3905 | 1.41794 | 0.708970 | − | 0.705239i | \(-0.249160\pi\) | ||||
0.708970 | + | 0.705239i | \(0.249160\pi\) | |||||||
\(104\) | −3.00880 | −0.295037 | ||||||||
\(105\) | −2.52435 | −0.246351 | ||||||||
\(106\) | −10.7851 | −1.04754 | ||||||||
\(107\) | 4.15309 | 0.401495 | 0.200747 | − | 0.979643i | \(-0.435663\pi\) | ||||
0.200747 | + | 0.979643i | \(0.435663\pi\) | |||||||
\(108\) | 2.00477 | 0.192909 | ||||||||
\(109\) | 2.33842 | 0.223980 | 0.111990 | − | 0.993709i | \(-0.464278\pi\) | ||||
0.111990 | + | 0.993709i | \(0.464278\pi\) | |||||||
\(110\) | −4.62697 | −0.441164 | ||||||||
\(111\) | 0.808130 | 0.0767043 | ||||||||
\(112\) | 4.18388 | 0.395340 | ||||||||
\(113\) | −11.3894 | −1.07142 | −0.535712 | − | 0.844401i | \(-0.679957\pi\) | ||||
−0.535712 | + | 0.844401i | \(0.679957\pi\) | |||||||
\(114\) | 2.60883 | 0.244340 | ||||||||
\(115\) | 6.58324 | 0.613890 | ||||||||
\(116\) | −3.40065 | −0.315742 | ||||||||
\(117\) | −8.67710 | −0.802198 | ||||||||
\(118\) | −10.6124 | −0.976954 | ||||||||
\(119\) | 14.7146 | 1.34889 | ||||||||
\(120\) | 0.603351 | 0.0550781 | ||||||||
\(121\) | −4.17266 | −0.379333 | ||||||||
\(122\) | 12.7184 | 1.15147 | ||||||||
\(123\) | 1.05818 | 0.0954126 | ||||||||
\(124\) | 2.86692 | 0.257457 | ||||||||
\(125\) | −12.1552 | −1.08720 | ||||||||
\(126\) | 12.0659 | 1.07492 | ||||||||
\(127\) | −6.97942 | −0.619324 | −0.309662 | − | 0.950847i | \(-0.600216\pi\) | ||||
−0.309662 | + | 0.950847i | \(0.600216\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.211395 | 0.0186123 | ||||||||
\(130\) | −5.32799 | −0.467296 | ||||||||
\(131\) | −2.82079 | −0.246454 | −0.123227 | − | 0.992379i | \(-0.539324\pi\) | ||||
−0.123227 | + | 0.992379i | \(0.539324\pi\) | |||||||
\(132\) | −0.890276 | −0.0774886 | ||||||||
\(133\) | 32.0351 | 2.77780 | ||||||||
\(134\) | 16.2208 | 1.40126 | ||||||||
\(135\) | 3.55006 | 0.305541 | ||||||||
\(136\) | −3.51698 | −0.301579 | ||||||||
\(137\) | 11.1347 | 0.951298 | 0.475649 | − | 0.879635i | \(-0.342213\pi\) | ||||
0.475649 | + | 0.879635i | \(0.342213\pi\) | |||||||
\(138\) | 1.26668 | 0.107827 | ||||||||
\(139\) | −7.53677 | −0.639261 | −0.319630 | − | 0.947542i | \(-0.603559\pi\) | ||||
−0.319630 | + | 0.947542i | \(0.603559\pi\) | |||||||
\(140\) | 7.40884 | 0.626161 | ||||||||
\(141\) | −0.858855 | −0.0723286 | ||||||||
\(142\) | −8.12622 | −0.681937 | ||||||||
\(143\) | 7.86174 | 0.657432 | ||||||||
\(144\) | −2.88391 | −0.240326 | ||||||||
\(145\) | −6.02188 | −0.500090 | ||||||||
\(146\) | 11.4257 | 0.945600 | ||||||||
\(147\) | −3.57923 | −0.295210 | ||||||||
\(148\) | −2.37182 | −0.194963 | ||||||||
\(149\) | −16.0103 | −1.31161 | −0.655807 | − | 0.754929i | \(-0.727672\pi\) | ||||
−0.655807 | + | 0.754929i | \(0.727672\pi\) | |||||||
\(150\) | −0.635189 | −0.0518630 | ||||||||
\(151\) | 1.08999 | 0.0887017 | 0.0443509 | − | 0.999016i | \(-0.485878\pi\) | ||||
0.0443509 | + | 0.999016i | \(0.485878\pi\) | |||||||
\(152\) | −7.65680 | −0.621048 | ||||||||
\(153\) | −10.1426 | −0.819985 | ||||||||
\(154\) | −10.9321 | −0.880937 | ||||||||
\(155\) | 5.07675 | 0.407774 | ||||||||
\(156\) | −1.02516 | −0.0820786 | ||||||||
\(157\) | −18.3346 | −1.46326 | −0.731631 | − | 0.681701i | \(-0.761240\pi\) | ||||
−0.731631 | + | 0.681701i | \(0.761240\pi\) | |||||||
\(158\) | 12.7445 | 1.01390 | ||||||||
\(159\) | −3.67470 | −0.291423 | ||||||||
\(160\) | −1.77081 | −0.139994 | ||||||||
\(161\) | 15.5542 | 1.22584 | ||||||||
\(162\) | −7.96866 | −0.626077 | ||||||||
\(163\) | −8.94236 | −0.700420 | −0.350210 | − | 0.936671i | \(-0.613890\pi\) | ||||
−0.350210 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(164\) | −3.10570 | −0.242514 | ||||||||
\(165\) | −1.57651 | −0.122731 | ||||||||
\(166\) | −4.18060 | −0.324478 | ||||||||
\(167\) | 7.95624 | 0.615673 | 0.307836 | − | 0.951439i | \(-0.400395\pi\) | ||||
0.307836 | + | 0.951439i | \(0.400395\pi\) | |||||||
\(168\) | 1.42554 | 0.109983 | ||||||||
\(169\) | −3.94714 | −0.303626 | ||||||||
\(170\) | −6.22789 | −0.477657 | ||||||||
\(171\) | −22.0815 | −1.68862 | ||||||||
\(172\) | −0.620433 | −0.0473076 | ||||||||
\(173\) | −5.52887 | −0.420352 | −0.210176 | − | 0.977664i | \(-0.567404\pi\) | ||||
−0.210176 | + | 0.977664i | \(0.567404\pi\) | |||||||
\(174\) | −1.15867 | −0.0878387 | ||||||||
\(175\) | −7.79980 | −0.589609 | ||||||||
\(176\) | 2.61292 | 0.196956 | ||||||||
\(177\) | −3.61588 | −0.271786 | ||||||||
\(178\) | 7.88201 | 0.590782 | ||||||||
\(179\) | −4.59445 | −0.343406 | −0.171703 | − | 0.985149i | \(-0.554927\pi\) | ||||
−0.171703 | + | 0.985149i | \(0.554927\pi\) | |||||||
\(180\) | −5.10684 | −0.380641 | ||||||||
\(181\) | −10.1720 | −0.756081 | −0.378040 | − | 0.925789i | \(-0.623402\pi\) | ||||
−0.378040 | + | 0.925789i | \(0.623402\pi\) | |||||||
\(182\) | −12.5885 | −0.933118 | ||||||||
\(183\) | 4.33344 | 0.320337 | ||||||||
\(184\) | −3.71765 | −0.274069 | ||||||||
\(185\) | −4.20004 | −0.308793 | ||||||||
\(186\) | 0.976819 | 0.0716238 | ||||||||
\(187\) | 9.18958 | 0.672008 | ||||||||
\(188\) | 2.52070 | 0.183841 | ||||||||
\(189\) | 8.38773 | 0.610118 | ||||||||
\(190\) | −13.5587 | −0.983651 | ||||||||
\(191\) | −10.5694 | −0.764776 | −0.382388 | − | 0.924002i | \(-0.624898\pi\) | ||||
−0.382388 | + | 0.924002i | \(0.624898\pi\) | |||||||
\(192\) | −0.340721 | −0.0245894 | ||||||||
\(193\) | −12.4910 | −0.899123 | −0.449561 | − | 0.893249i | \(-0.648420\pi\) | ||||
−0.449561 | + | 0.893249i | \(0.648420\pi\) | |||||||
\(194\) | −6.46877 | −0.464431 | ||||||||
\(195\) | −1.81536 | −0.130001 | ||||||||
\(196\) | 10.5049 | 0.750348 | ||||||||
\(197\) | 19.3297 | 1.37718 | 0.688592 | − | 0.725149i | \(-0.258229\pi\) | ||||
0.688592 | + | 0.725149i | \(0.258229\pi\) | |||||||
\(198\) | 7.53542 | 0.535519 | ||||||||
\(199\) | −12.9496 | −0.917975 | −0.458988 | − | 0.888443i | \(-0.651788\pi\) | ||||
−0.458988 | + | 0.888443i | \(0.651788\pi\) | |||||||
\(200\) | 1.86425 | 0.131822 | ||||||||
\(201\) | 5.52677 | 0.389828 | ||||||||
\(202\) | 1.69847 | 0.119504 | ||||||||
\(203\) | −14.2279 | −0.998603 | ||||||||
\(204\) | −1.19831 | −0.0838984 | ||||||||
\(205\) | −5.49959 | −0.384108 | ||||||||
\(206\) | −14.3905 | −1.00263 | ||||||||
\(207\) | −10.7214 | −0.745187 | ||||||||
\(208\) | 3.00880 | 0.208623 | ||||||||
\(209\) | 20.0066 | 1.38388 | ||||||||
\(210\) | 2.52435 | 0.174197 | ||||||||
\(211\) | 3.73521 | 0.257143 | 0.128571 | − | 0.991700i | \(-0.458961\pi\) | ||||
0.128571 | + | 0.991700i | \(0.458961\pi\) | |||||||
\(212\) | 10.7851 | 0.740721 | ||||||||
\(213\) | −2.76877 | −0.189713 | ||||||||
\(214\) | −4.15309 | −0.283900 | ||||||||
\(215\) | −1.09867 | −0.0749284 | ||||||||
\(216\) | −2.00477 | −0.136407 | ||||||||
\(217\) | 11.9948 | 0.814262 | ||||||||
\(218\) | −2.33842 | −0.158378 | ||||||||
\(219\) | 3.89299 | 0.263064 | ||||||||
\(220\) | 4.62697 | 0.311950 | ||||||||
\(221\) | 10.5819 | 0.711814 | ||||||||
\(222\) | −0.808130 | −0.0542382 | ||||||||
\(223\) | 9.14690 | 0.612521 | 0.306261 | − | 0.951948i | \(-0.400922\pi\) | ||||
0.306261 | + | 0.951948i | \(0.400922\pi\) | |||||||
\(224\) | −4.18388 | −0.279547 | ||||||||
\(225\) | 5.37633 | 0.358422 | ||||||||
\(226\) | 11.3894 | 0.757611 | ||||||||
\(227\) | 6.78677 | 0.450454 | 0.225227 | − | 0.974306i | \(-0.427688\pi\) | ||||
0.225227 | + | 0.974306i | \(0.427688\pi\) | |||||||
\(228\) | −2.60883 | −0.172774 | ||||||||
\(229\) | 23.4843 | 1.55189 | 0.775944 | − | 0.630801i | \(-0.217274\pi\) | ||||
0.775944 | + | 0.630801i | \(0.217274\pi\) | |||||||
\(230\) | −6.58324 | −0.434086 | ||||||||
\(231\) | −3.72481 | −0.245075 | ||||||||
\(232\) | 3.40065 | 0.223263 | ||||||||
\(233\) | 5.17551 | 0.339059 | 0.169529 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169529 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(234\) | 8.67710 | 0.567240 | ||||||||
\(235\) | 4.46366 | 0.291177 | ||||||||
\(236\) | 10.6124 | 0.690811 | ||||||||
\(237\) | 4.34233 | 0.282064 | ||||||||
\(238\) | −14.7146 | −0.953808 | ||||||||
\(239\) | 12.2861 | 0.794721 | 0.397360 | − | 0.917663i | \(-0.369926\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369926\pi\) | |||||||
\(240\) | −0.603351 | −0.0389461 | ||||||||
\(241\) | 7.08381 | 0.456308 | 0.228154 | − | 0.973625i | \(-0.426731\pi\) | ||||
0.228154 | + | 0.973625i | \(0.426731\pi\) | |||||||
\(242\) | 4.17266 | 0.268229 | ||||||||
\(243\) | −8.72941 | −0.559992 | ||||||||
\(244\) | −12.7184 | −0.814215 | ||||||||
\(245\) | 18.6021 | 1.18844 | ||||||||
\(246\) | −1.05818 | −0.0674669 | ||||||||
\(247\) | 23.0378 | 1.46586 | ||||||||
\(248\) | −2.86692 | −0.182049 | ||||||||
\(249\) | −1.42442 | −0.0902690 | ||||||||
\(250\) | 12.1552 | 0.768765 | ||||||||
\(251\) | −30.6666 | −1.93566 | −0.967830 | − | 0.251605i | \(-0.919042\pi\) | ||||
−0.967830 | + | 0.251605i | \(0.919042\pi\) | |||||||
\(252\) | −12.0659 | −0.760082 | ||||||||
\(253\) | 9.71392 | 0.610709 | ||||||||
\(254\) | 6.97942 | 0.437928 | ||||||||
\(255\) | −2.12197 | −0.132883 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.71507 | 0.606010 | 0.303005 | − | 0.952989i | \(-0.402010\pi\) | ||||
0.303005 | + | 0.952989i | \(0.402010\pi\) | |||||||
\(258\) | −0.211395 | −0.0131608 | ||||||||
\(259\) | −9.92343 | −0.616612 | ||||||||
\(260\) | 5.32799 | 0.330428 | ||||||||
\(261\) | 9.80716 | 0.607048 | ||||||||
\(262\) | 2.82079 | 0.174269 | ||||||||
\(263\) | 21.7138 | 1.33893 | 0.669464 | − | 0.742845i | \(-0.266524\pi\) | ||||
0.669464 | + | 0.742845i | \(0.266524\pi\) | |||||||
\(264\) | 0.890276 | 0.0547927 | ||||||||
\(265\) | 19.0982 | 1.17320 | ||||||||
\(266\) | −32.0351 | −1.96420 | ||||||||
\(267\) | 2.68557 | 0.164354 | ||||||||
\(268\) | −16.2208 | −0.990844 | ||||||||
\(269\) | −25.7944 | −1.57271 | −0.786355 | − | 0.617775i | \(-0.788034\pi\) | ||||
−0.786355 | + | 0.617775i | \(0.788034\pi\) | |||||||
\(270\) | −3.55006 | −0.216050 | ||||||||
\(271\) | −18.1386 | −1.10184 | −0.550920 | − | 0.834558i | \(-0.685723\pi\) | ||||
−0.550920 | + | 0.834558i | \(0.685723\pi\) | |||||||
\(272\) | 3.51698 | 0.213248 | ||||||||
\(273\) | −4.28915 | −0.259591 | ||||||||
\(274\) | −11.1347 | −0.672669 | ||||||||
\(275\) | −4.87113 | −0.293740 | ||||||||
\(276\) | −1.26668 | −0.0762453 | ||||||||
\(277\) | 16.5732 | 0.995785 | 0.497893 | − | 0.867239i | \(-0.334107\pi\) | ||||
0.497893 | + | 0.867239i | \(0.334107\pi\) | |||||||
\(278\) | 7.53677 | 0.452026 | ||||||||
\(279\) | −8.26792 | −0.494988 | ||||||||
\(280\) | −7.40884 | −0.442763 | ||||||||
\(281\) | 11.4974 | 0.685875 | 0.342937 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342937 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(282\) | 0.858855 | 0.0511441 | ||||||||
\(283\) | −4.92943 | −0.293024 | −0.146512 | − | 0.989209i | \(-0.546805\pi\) | ||||
−0.146512 | + | 0.989209i | \(0.546805\pi\) | |||||||
\(284\) | 8.12622 | 0.482202 | ||||||||
\(285\) | −4.61973 | −0.273649 | ||||||||
\(286\) | −7.86174 | −0.464874 | ||||||||
\(287\) | −12.9939 | −0.767004 | ||||||||
\(288\) | 2.88391 | 0.169936 | ||||||||
\(289\) | −4.63085 | −0.272403 | ||||||||
\(290\) | 6.02188 | 0.353617 | ||||||||
\(291\) | −2.20405 | −0.129203 | ||||||||
\(292\) | −11.4257 | −0.668640 | ||||||||
\(293\) | 17.1886 | 1.00417 | 0.502084 | − | 0.864819i | \(-0.332567\pi\) | ||||
0.502084 | + | 0.864819i | \(0.332567\pi\) | |||||||
\(294\) | 3.57923 | 0.208745 | ||||||||
\(295\) | 18.7926 | 1.09414 | ||||||||
\(296\) | 2.37182 | 0.137859 | ||||||||
\(297\) | 5.23830 | 0.303957 | ||||||||
\(298\) | 16.0103 | 0.927451 | ||||||||
\(299\) | 11.1857 | 0.646884 | ||||||||
\(300\) | 0.635189 | 0.0366727 | ||||||||
\(301\) | −2.59582 | −0.149620 | ||||||||
\(302\) | −1.08999 | −0.0627216 | ||||||||
\(303\) | 0.578704 | 0.0332457 | ||||||||
\(304\) | 7.65680 | 0.439147 | ||||||||
\(305\) | −22.5219 | −1.28960 | ||||||||
\(306\) | 10.1426 | 0.579817 | ||||||||
\(307\) | 28.0058 | 1.59838 | 0.799188 | − | 0.601082i | \(-0.205263\pi\) | ||||
0.799188 | + | 0.601082i | \(0.205263\pi\) | |||||||
\(308\) | 10.9321 | 0.622916 | ||||||||
\(309\) | −4.90315 | −0.278931 | ||||||||
\(310\) | −5.07675 | −0.288340 | ||||||||
\(311\) | −4.19907 | −0.238108 | −0.119054 | − | 0.992888i | \(-0.537986\pi\) | ||||
−0.119054 | + | 0.992888i | \(0.537986\pi\) | |||||||
\(312\) | 1.02516 | 0.0580383 | ||||||||
\(313\) | 29.7464 | 1.68137 | 0.840683 | − | 0.541527i | \(-0.182154\pi\) | ||||
0.840683 | + | 0.541527i | \(0.182154\pi\) | |||||||
\(314\) | 18.3346 | 1.03468 | ||||||||
\(315\) | −21.3664 | −1.20386 | ||||||||
\(316\) | −12.7445 | −0.716935 | ||||||||
\(317\) | −9.87969 | −0.554899 | −0.277449 | − | 0.960740i | \(-0.589489\pi\) | ||||
−0.277449 | + | 0.960740i | \(0.589489\pi\) | |||||||
\(318\) | 3.67470 | 0.206067 | ||||||||
\(319\) | −8.88561 | −0.497499 | ||||||||
\(320\) | 1.77081 | 0.0989910 | ||||||||
\(321\) | −1.41505 | −0.0789802 | ||||||||
\(322\) | −15.5542 | −0.866803 | ||||||||
\(323\) | 26.9288 | 1.49836 | ||||||||
\(324\) | 7.96866 | 0.442703 | ||||||||
\(325\) | −5.60915 | −0.311140 | ||||||||
\(326\) | 8.94236 | 0.495272 | ||||||||
\(327\) | −0.796748 | −0.0440603 | ||||||||
\(328\) | 3.10570 | 0.171484 | ||||||||
\(329\) | 10.5463 | 0.581436 | ||||||||
\(330\) | 1.57651 | 0.0867838 | ||||||||
\(331\) | 21.8518 | 1.20109 | 0.600543 | − | 0.799593i | \(-0.294951\pi\) | ||||
0.600543 | + | 0.799593i | \(0.294951\pi\) | |||||||
\(332\) | 4.18060 | 0.229440 | ||||||||
\(333\) | 6.84012 | 0.374836 | ||||||||
\(334\) | −7.95624 | −0.435346 | ||||||||
\(335\) | −28.7239 | −1.56935 | ||||||||
\(336\) | −1.42554 | −0.0777694 | ||||||||
\(337\) | −24.9243 | −1.35772 | −0.678858 | − | 0.734270i | \(-0.737525\pi\) | ||||
−0.678858 | + | 0.734270i | \(0.737525\pi\) | |||||||
\(338\) | 3.94714 | 0.214696 | ||||||||
\(339\) | 3.88061 | 0.210766 | ||||||||
\(340\) | 6.22789 | 0.337755 | ||||||||
\(341\) | 7.49101 | 0.405661 | ||||||||
\(342\) | 22.0815 | 1.19403 | ||||||||
\(343\) | 14.6640 | 0.791779 | ||||||||
\(344\) | 0.620433 | 0.0334515 | ||||||||
\(345\) | −2.24305 | −0.120762 | ||||||||
\(346\) | 5.52887 | 0.297234 | ||||||||
\(347\) | −14.4684 | −0.776707 | −0.388353 | − | 0.921511i | \(-0.626956\pi\) | ||||
−0.388353 | + | 0.921511i | \(0.626956\pi\) | |||||||
\(348\) | 1.15867 | 0.0621114 | ||||||||
\(349\) | 29.7908 | 1.59467 | 0.797334 | − | 0.603539i | \(-0.206243\pi\) | ||||
0.797334 | + | 0.603539i | \(0.206243\pi\) | |||||||
\(350\) | 7.79980 | 0.416917 | ||||||||
\(351\) | 6.03195 | 0.321962 | ||||||||
\(352\) | −2.61292 | −0.139269 | ||||||||
\(353\) | −24.6869 | −1.31395 | −0.656975 | − | 0.753912i | \(-0.728164\pi\) | ||||
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(354\) | 3.61588 | 0.192182 | ||||||||
\(355\) | 14.3899 | 0.763739 | ||||||||
\(356\) | −7.88201 | −0.417746 | ||||||||
\(357\) | −5.01358 | −0.265347 | ||||||||
\(358\) | 4.59445 | 0.242824 | ||||||||
\(359\) | 7.76955 | 0.410061 | 0.205031 | − | 0.978756i | \(-0.434271\pi\) | ||||
0.205031 | + | 0.978756i | \(0.434271\pi\) | |||||||
\(360\) | 5.10684 | 0.269154 | ||||||||
\(361\) | 39.6266 | 2.08561 | ||||||||
\(362\) | 10.1720 | 0.534630 | ||||||||
\(363\) | 1.42171 | 0.0746207 | ||||||||
\(364\) | 12.5885 | 0.659814 | ||||||||
\(365\) | −20.2327 | −1.05903 | ||||||||
\(366\) | −4.33344 | −0.226513 | ||||||||
\(367\) | 7.80521 | 0.407429 | 0.203714 | − | 0.979030i | \(-0.434699\pi\) | ||||
0.203714 | + | 0.979030i | \(0.434699\pi\) | |||||||
\(368\) | 3.71765 | 0.193796 | ||||||||
\(369\) | 8.95655 | 0.466259 | ||||||||
\(370\) | 4.20004 | 0.218350 | ||||||||
\(371\) | 45.1234 | 2.34269 | ||||||||
\(372\) | −0.976819 | −0.0506457 | ||||||||
\(373\) | 33.6045 | 1.73997 | 0.869987 | − | 0.493075i | \(-0.164127\pi\) | ||||
0.869987 | + | 0.493075i | \(0.164127\pi\) | |||||||
\(374\) | −9.18958 | −0.475182 | ||||||||
\(375\) | 4.14155 | 0.213869 | ||||||||
\(376\) | −2.52070 | −0.129995 | ||||||||
\(377\) | −10.2319 | −0.526967 | ||||||||
\(378\) | −8.38773 | −0.431418 | ||||||||
\(379\) | −14.0025 | −0.719263 | −0.359631 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359631 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(380\) | 13.5587 | 0.695547 | ||||||||
\(381\) | 2.37804 | 0.121831 | ||||||||
\(382\) | 10.5694 | 0.540778 | ||||||||
\(383\) | −20.9251 | −1.06922 | −0.534612 | − | 0.845098i | \(-0.679542\pi\) | ||||
−0.534612 | + | 0.845098i | \(0.679542\pi\) | |||||||
\(384\) | 0.340721 | 0.0173874 | ||||||||
\(385\) | 19.3587 | 0.986610 | ||||||||
\(386\) | 12.4910 | 0.635776 | ||||||||
\(387\) | 1.78927 | 0.0909538 | ||||||||
\(388\) | 6.46877 | 0.328402 | ||||||||
\(389\) | 13.3813 | 0.678458 | 0.339229 | − | 0.940704i | \(-0.389834\pi\) | ||||
0.339229 | + | 0.940704i | \(0.389834\pi\) | |||||||
\(390\) | 1.81536 | 0.0919243 | ||||||||
\(391\) | 13.0749 | 0.661226 | ||||||||
\(392\) | −10.5049 | −0.530576 | ||||||||
\(393\) | 0.961103 | 0.0484812 | ||||||||
\(394\) | −19.3297 | −0.973817 | ||||||||
\(395\) | −22.5681 | −1.13552 | ||||||||
\(396\) | −7.53542 | −0.378669 | ||||||||
\(397\) | −34.1292 | −1.71290 | −0.856449 | − | 0.516232i | \(-0.827334\pi\) | ||||
−0.856449 | + | 0.516232i | \(0.827334\pi\) | |||||||
\(398\) | 12.9496 | 0.649107 | ||||||||
\(399\) | −10.9150 | −0.546436 | ||||||||
\(400\) | −1.86425 | −0.0932125 | ||||||||
\(401\) | 25.3458 | 1.26571 | 0.632855 | − | 0.774270i | \(-0.281883\pi\) | ||||
0.632855 | + | 0.774270i | \(0.281883\pi\) | |||||||
\(402\) | −5.52677 | −0.275650 | ||||||||
\(403\) | 8.62597 | 0.429690 | ||||||||
\(404\) | −1.69847 | −0.0845020 | ||||||||
\(405\) | 14.1109 | 0.701178 | ||||||||
\(406\) | 14.2279 | 0.706119 | ||||||||
\(407\) | −6.19738 | −0.307193 | ||||||||
\(408\) | 1.19831 | 0.0593252 | ||||||||
\(409\) | 32.1256 | 1.58851 | 0.794254 | − | 0.607586i | \(-0.207862\pi\) | ||||
0.794254 | + | 0.607586i | \(0.207862\pi\) | |||||||
\(410\) | 5.49959 | 0.271605 | ||||||||
\(411\) | −3.79381 | −0.187135 | ||||||||
\(412\) | 14.3905 | 0.708970 | ||||||||
\(413\) | 44.4012 | 2.18484 | ||||||||
\(414\) | 10.7214 | 0.526927 | ||||||||
\(415\) | 7.40303 | 0.363401 | ||||||||
\(416\) | −3.00880 | −0.147518 | ||||||||
\(417\) | 2.56794 | 0.125752 | ||||||||
\(418\) | −20.0066 | −0.978554 | ||||||||
\(419\) | 36.7157 | 1.79368 | 0.896839 | − | 0.442357i | \(-0.145857\pi\) | ||||
0.896839 | + | 0.442357i | \(0.145857\pi\) | |||||||
\(420\) | −2.52435 | −0.123176 | ||||||||
\(421\) | −15.2841 | −0.744902 | −0.372451 | − | 0.928052i | \(-0.621482\pi\) | ||||
−0.372451 | + | 0.928052i | \(0.621482\pi\) | |||||||
\(422\) | −3.73521 | −0.181827 | ||||||||
\(423\) | −7.26946 | −0.353453 | ||||||||
\(424\) | −10.7851 | −0.523769 | ||||||||
\(425\) | −6.55653 | −0.318038 | ||||||||
\(426\) | 2.76877 | 0.134148 | ||||||||
\(427\) | −53.2125 | −2.57513 | ||||||||
\(428\) | 4.15309 | 0.200747 | ||||||||
\(429\) | −2.67866 | −0.129327 | ||||||||
\(430\) | 1.09867 | 0.0529824 | ||||||||
\(431\) | −9.38721 | −0.452166 | −0.226083 | − | 0.974108i | \(-0.572592\pi\) | ||||
−0.226083 | + | 0.974108i | \(0.572592\pi\) | |||||||
\(432\) | 2.00477 | 0.0964546 | ||||||||
\(433\) | 5.89835 | 0.283457 | 0.141728 | − | 0.989906i | \(-0.454734\pi\) | ||||
0.141728 | + | 0.989906i | \(0.454734\pi\) | |||||||
\(434\) | −11.9948 | −0.575771 | ||||||||
\(435\) | 2.05178 | 0.0983755 | ||||||||
\(436\) | 2.33842 | 0.111990 | ||||||||
\(437\) | 28.4653 | 1.36168 | ||||||||
\(438\) | −3.89299 | −0.186014 | ||||||||
\(439\) | 4.09609 | 0.195496 | 0.0977479 | − | 0.995211i | \(-0.468836\pi\) | ||||
0.0977479 | + | 0.995211i | \(0.468836\pi\) | |||||||
\(440\) | −4.62697 | −0.220582 | ||||||||
\(441\) | −30.2951 | −1.44262 | ||||||||
\(442\) | −10.5819 | −0.503329 | ||||||||
\(443\) | 39.8409 | 1.89290 | 0.946450 | − | 0.322851i | \(-0.104641\pi\) | ||||
0.946450 | + | 0.322851i | \(0.104641\pi\) | |||||||
\(444\) | 0.808130 | 0.0383522 | ||||||||
\(445\) | −13.9575 | −0.661649 | ||||||||
\(446\) | −9.14690 | −0.433118 | ||||||||
\(447\) | 5.45504 | 0.258015 | ||||||||
\(448\) | 4.18388 | 0.197670 | ||||||||
\(449\) | 16.5522 | 0.781148 | 0.390574 | − | 0.920571i | \(-0.372276\pi\) | ||||
0.390574 | + | 0.920571i | \(0.372276\pi\) | |||||||
\(450\) | −5.37633 | −0.253442 | ||||||||
\(451\) | −8.11493 | −0.382117 | ||||||||
\(452\) | −11.3894 | −0.535712 | ||||||||
\(453\) | −0.371381 | −0.0174490 | ||||||||
\(454\) | −6.78677 | −0.318519 | ||||||||
\(455\) | 22.2917 | 1.04505 | ||||||||
\(456\) | 2.60883 | 0.122170 | ||||||||
\(457\) | −35.3162 | −1.65202 | −0.826012 | − | 0.563653i | \(-0.809395\pi\) | ||||
−0.826012 | + | 0.563653i | \(0.809395\pi\) | |||||||
\(458\) | −23.4843 | −1.09735 | ||||||||
\(459\) | 7.05074 | 0.329101 | ||||||||
\(460\) | 6.58324 | 0.306945 | ||||||||
\(461\) | −28.5573 | −1.33004 | −0.665022 | − | 0.746824i | \(-0.731578\pi\) | ||||
−0.665022 | + | 0.746824i | \(0.731578\pi\) | |||||||
\(462\) | 3.72481 | 0.173294 | ||||||||
\(463\) | 36.6034 | 1.70110 | 0.850552 | − | 0.525891i | \(-0.176268\pi\) | ||||
0.850552 | + | 0.525891i | \(0.176268\pi\) | |||||||
\(464\) | −3.40065 | −0.157871 | ||||||||
\(465\) | −1.72976 | −0.0802155 | ||||||||
\(466\) | −5.17551 | −0.239751 | ||||||||
\(467\) | 12.6389 | 0.584859 | 0.292429 | − | 0.956287i | \(-0.405536\pi\) | ||||
0.292429 | + | 0.956287i | \(0.405536\pi\) | |||||||
\(468\) | −8.67710 | −0.401099 | ||||||||
\(469\) | −67.8659 | −3.13376 | ||||||||
\(470\) | −4.46366 | −0.205894 | ||||||||
\(471\) | 6.24699 | 0.287846 | ||||||||
\(472\) | −10.6124 | −0.488477 | ||||||||
\(473\) | −1.62114 | −0.0745401 | ||||||||
\(474\) | −4.34233 | −0.199450 | ||||||||
\(475\) | −14.2742 | −0.654944 | ||||||||
\(476\) | 14.7146 | 0.674444 | ||||||||
\(477\) | −31.1031 | −1.42411 | ||||||||
\(478\) | −12.2861 | −0.561952 | ||||||||
\(479\) | 15.6466 | 0.714910 | 0.357455 | − | 0.933930i | \(-0.383645\pi\) | ||||
0.357455 | + | 0.933930i | \(0.383645\pi\) | |||||||
\(480\) | 0.603351 | 0.0275391 | ||||||||
\(481\) | −7.13634 | −0.325389 | ||||||||
\(482\) | −7.08381 | −0.322659 | ||||||||
\(483\) | −5.29965 | −0.241142 | ||||||||
\(484\) | −4.17266 | −0.189667 | ||||||||
\(485\) | 11.4549 | 0.520142 | ||||||||
\(486\) | 8.72941 | 0.395974 | ||||||||
\(487\) | −31.0411 | −1.40661 | −0.703303 | − | 0.710890i | \(-0.748292\pi\) | ||||
−0.703303 | + | 0.710890i | \(0.748292\pi\) | |||||||
\(488\) | 12.7184 | 0.575737 | ||||||||
\(489\) | 3.04685 | 0.137783 | ||||||||
\(490\) | −18.6021 | −0.840356 | ||||||||
\(491\) | −20.2397 | −0.913404 | −0.456702 | − | 0.889620i | \(-0.650969\pi\) | ||||
−0.456702 | + | 0.889620i | \(0.650969\pi\) | |||||||
\(492\) | 1.05818 | 0.0477063 | ||||||||
\(493\) | −11.9600 | −0.538652 | ||||||||
\(494\) | −23.0378 | −1.03652 | ||||||||
\(495\) | −13.3438 | −0.599757 | ||||||||
\(496\) | 2.86692 | 0.128728 | ||||||||
\(497\) | 33.9991 | 1.52507 | ||||||||
\(498\) | 1.42442 | 0.0638298 | ||||||||
\(499\) | 12.9574 | 0.580052 | 0.290026 | − | 0.957019i | \(-0.406336\pi\) | ||||
0.290026 | + | 0.957019i | \(0.406336\pi\) | |||||||
\(500\) | −12.1552 | −0.543599 | ||||||||
\(501\) | −2.71086 | −0.121112 | ||||||||
\(502\) | 30.6666 | 1.36872 | ||||||||
\(503\) | 4.89600 | 0.218302 | 0.109151 | − | 0.994025i | \(-0.465187\pi\) | ||||
0.109151 | + | 0.994025i | \(0.465187\pi\) | |||||||
\(504\) | 12.0659 | 0.537459 | ||||||||
\(505\) | −3.00766 | −0.133839 | ||||||||
\(506\) | −9.71392 | −0.431836 | ||||||||
\(507\) | 1.34487 | 0.0597279 | ||||||||
\(508\) | −6.97942 | −0.309662 | ||||||||
\(509\) | 41.8912 | 1.85679 | 0.928397 | − | 0.371590i | \(-0.121187\pi\) | ||||
0.928397 | + | 0.371590i | \(0.121187\pi\) | |||||||
\(510\) | 2.12197 | 0.0939625 | ||||||||
\(511\) | −47.8039 | −2.11472 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 15.3501 | 0.677725 | ||||||||
\(514\) | −9.71507 | −0.428514 | ||||||||
\(515\) | 25.4828 | 1.12291 | ||||||||
\(516\) | 0.211395 | 0.00930613 | ||||||||
\(517\) | 6.58638 | 0.289668 | ||||||||
\(518\) | 9.92343 | 0.436010 | ||||||||
\(519\) | 1.88380 | 0.0826898 | ||||||||
\(520\) | −5.32799 | −0.233648 | ||||||||
\(521\) | 5.44798 | 0.238680 | 0.119340 | − | 0.992853i | \(-0.461922\pi\) | ||||
0.119340 | + | 0.992853i | \(0.461922\pi\) | |||||||
\(522\) | −9.80716 | −0.429248 | ||||||||
\(523\) | −22.8803 | −1.00049 | −0.500243 | − | 0.865885i | \(-0.666756\pi\) | ||||
−0.500243 | + | 0.865885i | \(0.666756\pi\) | |||||||
\(524\) | −2.82079 | −0.123227 | ||||||||
\(525\) | 2.65756 | 0.115985 | ||||||||
\(526\) | −21.7138 | −0.946765 | ||||||||
\(527\) | 10.0829 | 0.439217 | ||||||||
\(528\) | −0.890276 | −0.0387443 | ||||||||
\(529\) | −9.17906 | −0.399090 | ||||||||
\(530\) | −19.0982 | −0.829575 | ||||||||
\(531\) | −30.6053 | −1.32816 | ||||||||
\(532\) | 32.0351 | 1.38890 | ||||||||
\(533\) | −9.34442 | −0.404752 | ||||||||
\(534\) | −2.68557 | −0.116216 | ||||||||
\(535\) | 7.35432 | 0.317955 | ||||||||
\(536\) | 16.2208 | 0.700632 | ||||||||
\(537\) | 1.56543 | 0.0675532 | ||||||||
\(538\) | 25.7944 | 1.11207 | ||||||||
\(539\) | 27.4484 | 1.18228 | ||||||||
\(540\) | 3.55006 | 0.152770 | ||||||||
\(541\) | −18.0039 | −0.774048 | −0.387024 | − | 0.922070i | \(-0.626497\pi\) | ||||
−0.387024 | + | 0.922070i | \(0.626497\pi\) | |||||||
\(542\) | 18.1386 | 0.779119 | ||||||||
\(543\) | 3.46582 | 0.148733 | ||||||||
\(544\) | −3.51698 | −0.150789 | ||||||||
\(545\) | 4.14088 | 0.177376 | ||||||||
\(546\) | 4.28915 | 0.183559 | ||||||||
\(547\) | 14.7664 | 0.631366 | 0.315683 | − | 0.948865i | \(-0.397766\pi\) | ||||
0.315683 | + | 0.948865i | \(0.397766\pi\) | |||||||
\(548\) | 11.1347 | 0.475649 | ||||||||
\(549\) | 36.6788 | 1.56541 | ||||||||
\(550\) | 4.87113 | 0.207706 | ||||||||
\(551\) | −26.0381 | −1.10926 | ||||||||
\(552\) | 1.26668 | 0.0539136 | ||||||||
\(553\) | −53.3216 | −2.26746 | ||||||||
\(554\) | −16.5732 | −0.704126 | ||||||||
\(555\) | 1.43104 | 0.0607443 | ||||||||
\(556\) | −7.53677 | −0.319630 | ||||||||
\(557\) | −17.1405 | −0.726264 | −0.363132 | − | 0.931738i | \(-0.618293\pi\) | ||||
−0.363132 | + | 0.931738i | \(0.618293\pi\) | |||||||
\(558\) | 8.26792 | 0.350009 | ||||||||
\(559\) | −1.86676 | −0.0789554 | ||||||||
\(560\) | 7.40884 | 0.313081 | ||||||||
\(561\) | −3.13108 | −0.132194 | ||||||||
\(562\) | −11.4974 | −0.484987 | ||||||||
\(563\) | −34.4595 | −1.45230 | −0.726148 | − | 0.687538i | \(-0.758691\pi\) | ||||
−0.726148 | + | 0.687538i | \(0.758691\pi\) | |||||||
\(564\) | −0.858855 | −0.0361643 | ||||||||
\(565\) | −20.1684 | −0.848491 | ||||||||
\(566\) | 4.92943 | 0.207199 | ||||||||
\(567\) | 33.3399 | 1.40015 | ||||||||
\(568\) | −8.12622 | −0.340968 | ||||||||
\(569\) | 30.0681 | 1.26052 | 0.630260 | − | 0.776384i | \(-0.282948\pi\) | ||||
0.630260 | + | 0.776384i | \(0.282948\pi\) | |||||||
\(570\) | 4.61973 | 0.193499 | ||||||||
\(571\) | 4.55022 | 0.190421 | 0.0952104 | − | 0.995457i | \(-0.469648\pi\) | ||||
0.0952104 | + | 0.995457i | \(0.469648\pi\) | |||||||
\(572\) | 7.86174 | 0.328716 | ||||||||
\(573\) | 3.60122 | 0.150443 | ||||||||
\(574\) | 12.9939 | 0.542354 | ||||||||
\(575\) | −6.93063 | −0.289027 | ||||||||
\(576\) | −2.88391 | −0.120163 | ||||||||
\(577\) | 8.77684 | 0.365384 | 0.182692 | − | 0.983170i | \(-0.441519\pi\) | ||||
0.182692 | + | 0.983170i | \(0.441519\pi\) | |||||||
\(578\) | 4.63085 | 0.192618 | ||||||||
\(579\) | 4.25595 | 0.176871 | ||||||||
\(580\) | −6.02188 | −0.250045 | ||||||||
\(581\) | 17.4912 | 0.725655 | ||||||||
\(582\) | 2.20405 | 0.0913607 | ||||||||
\(583\) | 28.1805 | 1.16712 | ||||||||
\(584\) | 11.4257 | 0.472800 | ||||||||
\(585\) | −15.3655 | −0.635283 | ||||||||
\(586\) | −17.1886 | −0.710054 | ||||||||
\(587\) | −26.6817 | −1.10127 | −0.550637 | − | 0.834745i | \(-0.685615\pi\) | ||||
−0.550637 | + | 0.834745i | \(0.685615\pi\) | |||||||
\(588\) | −3.57923 | −0.147605 | ||||||||
\(589\) | 21.9514 | 0.904491 | ||||||||
\(590\) | −18.7926 | −0.773677 | ||||||||
\(591\) | −6.58604 | −0.270914 | ||||||||
\(592\) | −2.37182 | −0.0974813 | ||||||||
\(593\) | −9.35126 | −0.384010 | −0.192005 | − | 0.981394i | \(-0.561499\pi\) | ||||
−0.192005 | + | 0.981394i | \(0.561499\pi\) | |||||||
\(594\) | −5.23830 | −0.214930 | ||||||||
\(595\) | 26.0567 | 1.06822 | ||||||||
\(596\) | −16.0103 | −0.655807 | ||||||||
\(597\) | 4.41222 | 0.180580 | ||||||||
\(598\) | −11.1857 | −0.457416 | ||||||||
\(599\) | −5.22874 | −0.213640 | −0.106820 | − | 0.994278i | \(-0.534067\pi\) | ||||
−0.106820 | + | 0.994278i | \(0.534067\pi\) | |||||||
\(600\) | −0.635189 | −0.0259315 | ||||||||
\(601\) | 14.8639 | 0.606311 | 0.303155 | − | 0.952941i | \(-0.401960\pi\) | ||||
0.303155 | + | 0.952941i | \(0.401960\pi\) | |||||||
\(602\) | 2.59582 | 0.105798 | ||||||||
\(603\) | 46.7793 | 1.90500 | ||||||||
\(604\) | 1.08999 | 0.0443509 | ||||||||
\(605\) | −7.38897 | −0.300404 | ||||||||
\(606\) | −0.578704 | −0.0235083 | ||||||||
\(607\) | −18.5494 | −0.752898 | −0.376449 | − | 0.926437i | \(-0.622855\pi\) | ||||
−0.376449 | + | 0.926437i | \(0.622855\pi\) | |||||||
\(608\) | −7.65680 | −0.310524 | ||||||||
\(609\) | 4.84775 | 0.196441 | ||||||||
\(610\) | 22.5219 | 0.911885 | ||||||||
\(611\) | 7.58427 | 0.306827 | ||||||||
\(612\) | −10.1426 | −0.409992 | ||||||||
\(613\) | 4.32618 | 0.174733 | 0.0873663 | − | 0.996176i | \(-0.472155\pi\) | ||||
0.0873663 | + | 0.996176i | \(0.472155\pi\) | |||||||
\(614\) | −28.0058 | −1.13022 | ||||||||
\(615\) | 1.87383 | 0.0755599 | ||||||||
\(616\) | −10.9321 | −0.440468 | ||||||||
\(617\) | −17.8360 | −0.718050 | −0.359025 | − | 0.933328i | \(-0.616891\pi\) | ||||
−0.359025 | + | 0.933328i | \(0.616891\pi\) | |||||||
\(618\) | 4.90315 | 0.197234 | ||||||||
\(619\) | −13.5013 | −0.542661 | −0.271331 | − | 0.962486i | \(-0.587464\pi\) | ||||
−0.271331 | + | 0.962486i | \(0.587464\pi\) | |||||||
\(620\) | 5.07675 | 0.203887 | ||||||||
\(621\) | 7.45305 | 0.299080 | ||||||||
\(622\) | 4.19907 | 0.168368 | ||||||||
\(623\) | −32.9774 | −1.32121 | ||||||||
\(624\) | −1.02516 | −0.0410393 | ||||||||
\(625\) | −12.2033 | −0.488133 | ||||||||
\(626\) | −29.7464 | −1.18891 | ||||||||
\(627\) | −6.81666 | −0.272231 | ||||||||
\(628\) | −18.3346 | −0.731631 | ||||||||
\(629\) | −8.34165 | −0.332604 | ||||||||
\(630\) | 21.3664 | 0.851259 | ||||||||
\(631\) | −16.1175 | −0.641627 | −0.320814 | − | 0.947142i | \(-0.603956\pi\) | ||||
−0.320814 | + | 0.947142i | \(0.603956\pi\) | |||||||
\(632\) | 12.7445 | 0.506950 | ||||||||
\(633\) | −1.27267 | −0.0505839 | ||||||||
\(634\) | 9.87969 | 0.392373 | ||||||||
\(635\) | −12.3592 | −0.490460 | ||||||||
\(636\) | −3.67470 | −0.145711 | ||||||||
\(637\) | 31.6070 | 1.25232 | ||||||||
\(638\) | 8.88561 | 0.351785 | ||||||||
\(639\) | −23.4353 | −0.927085 | ||||||||
\(640\) | −1.77081 | −0.0699972 | ||||||||
\(641\) | 39.4889 | 1.55972 | 0.779858 | − | 0.625956i | \(-0.215291\pi\) | ||||
0.779858 | + | 0.625956i | \(0.215291\pi\) | |||||||
\(642\) | 1.41505 | 0.0558474 | ||||||||
\(643\) | −17.5498 | −0.692097 | −0.346049 | − | 0.938217i | \(-0.612477\pi\) | ||||
−0.346049 | + | 0.938217i | \(0.612477\pi\) | |||||||
\(644\) | 15.5542 | 0.612922 | ||||||||
\(645\) | 0.374339 | 0.0147396 | ||||||||
\(646\) | −26.9288 | −1.05950 | ||||||||
\(647\) | −17.7761 | −0.698851 | −0.349426 | − | 0.936964i | \(-0.613623\pi\) | ||||
−0.349426 | + | 0.936964i | \(0.613623\pi\) | |||||||
\(648\) | −7.96866 | −0.313038 | ||||||||
\(649\) | 27.7294 | 1.08847 | ||||||||
\(650\) | 5.60915 | 0.220009 | ||||||||
\(651\) | −4.08689 | −0.160178 | ||||||||
\(652\) | −8.94236 | −0.350210 | ||||||||
\(653\) | 17.9052 | 0.700685 | 0.350342 | − | 0.936622i | \(-0.386065\pi\) | ||||
0.350342 | + | 0.936622i | \(0.386065\pi\) | |||||||
\(654\) | 0.796748 | 0.0311553 | ||||||||
\(655\) | −4.99507 | −0.195173 | ||||||||
\(656\) | −3.10570 | −0.121257 | ||||||||
\(657\) | 32.9507 | 1.28553 | ||||||||
\(658\) | −10.5463 | −0.411138 | ||||||||
\(659\) | −11.7277 | −0.456845 | −0.228422 | − | 0.973562i | \(-0.573357\pi\) | ||||
−0.228422 | + | 0.973562i | \(0.573357\pi\) | |||||||
\(660\) | −1.57651 | −0.0613654 | ||||||||
\(661\) | −43.4397 | −1.68961 | −0.844804 | − | 0.535075i | \(-0.820283\pi\) | ||||
−0.844804 | + | 0.535075i | \(0.820283\pi\) | |||||||
\(662\) | −21.8518 | −0.849296 | ||||||||
\(663\) | −3.60547 | −0.140025 | ||||||||
\(664\) | −4.18060 | −0.162239 | ||||||||
\(665\) | 56.7280 | 2.19982 | ||||||||
\(666\) | −6.84012 | −0.265049 | ||||||||
\(667\) | −12.6424 | −0.489517 | ||||||||
\(668\) | 7.95624 | 0.307836 | ||||||||
\(669\) | −3.11654 | −0.120492 | ||||||||
\(670\) | 28.7239 | 1.10970 | ||||||||
\(671\) | −33.2323 | −1.28292 | ||||||||
\(672\) | 1.42554 | 0.0549913 | ||||||||
\(673\) | 13.2021 | 0.508903 | 0.254451 | − | 0.967086i | \(-0.418105\pi\) | ||||
0.254451 | + | 0.967086i | \(0.418105\pi\) | |||||||
\(674\) | 24.9243 | 0.960050 | ||||||||
\(675\) | −3.73739 | −0.143852 | ||||||||
\(676\) | −3.94714 | −0.151813 | ||||||||
\(677\) | −42.6568 | −1.63943 | −0.819717 | − | 0.572769i | \(-0.805869\pi\) | ||||
−0.819717 | + | 0.572769i | \(0.805869\pi\) | |||||||
\(678\) | −3.88061 | −0.149034 | ||||||||
\(679\) | 27.0646 | 1.03864 | ||||||||
\(680\) | −6.22789 | −0.238829 | ||||||||
\(681\) | −2.31240 | −0.0886112 | ||||||||
\(682\) | −7.49101 | −0.286846 | ||||||||
\(683\) | 31.7498 | 1.21487 | 0.607436 | − | 0.794369i | \(-0.292198\pi\) | ||||
0.607436 | + | 0.794369i | \(0.292198\pi\) | |||||||
\(684\) | −22.0815 | −0.844308 | ||||||||
\(685\) | 19.7173 | 0.753360 | ||||||||
\(686\) | −14.6640 | −0.559872 | ||||||||
\(687\) | −8.00161 | −0.305281 | ||||||||
\(688\) | −0.620433 | −0.0236538 | ||||||||
\(689\) | 32.4501 | 1.23625 | ||||||||
\(690\) | 2.24305 | 0.0853914 | ||||||||
\(691\) | −30.9580 | −1.17770 | −0.588848 | − | 0.808244i | \(-0.700418\pi\) | ||||
−0.588848 | + | 0.808244i | \(0.700418\pi\) | |||||||
\(692\) | −5.52887 | −0.210176 | ||||||||
\(693\) | −31.5273 | −1.19762 | ||||||||
\(694\) | 14.4684 | 0.549215 | ||||||||
\(695\) | −13.3462 | −0.506248 | ||||||||
\(696\) | −1.15867 | −0.0439194 | ||||||||
\(697\) | −10.9227 | −0.413726 | ||||||||
\(698\) | −29.7908 | −1.12760 | ||||||||
\(699\) | −1.76340 | −0.0666981 | ||||||||
\(700\) | −7.79980 | −0.294805 | ||||||||
\(701\) | −10.2901 | −0.388653 | −0.194327 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194327 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(702\) | −6.03195 | −0.227661 | ||||||||
\(703\) | −18.1606 | −0.684939 | ||||||||
\(704\) | 2.61292 | 0.0984780 | ||||||||
\(705\) | −1.52086 | −0.0572791 | ||||||||
\(706\) | 24.6869 | 0.929103 | ||||||||
\(707\) | −7.10619 | −0.267256 | ||||||||
\(708\) | −3.61588 | −0.135893 | ||||||||
\(709\) | −31.0416 | −1.16579 | −0.582895 | − | 0.812547i | \(-0.698080\pi\) | ||||
−0.582895 | + | 0.812547i | \(0.698080\pi\) | |||||||
\(710\) | −14.3899 | −0.540045 | ||||||||
\(711\) | 36.7540 | 1.37838 | ||||||||
\(712\) | 7.88201 | 0.295391 | ||||||||
\(713\) | 10.6582 | 0.399153 | ||||||||
\(714\) | 5.01358 | 0.187629 | ||||||||
\(715\) | 13.9216 | 0.520639 | ||||||||
\(716\) | −4.59445 | −0.171703 | ||||||||
\(717\) | −4.18613 | −0.156334 | ||||||||
\(718\) | −7.76955 | −0.289957 | ||||||||
\(719\) | 18.6707 | 0.696298 | 0.348149 | − | 0.937439i | \(-0.386810\pi\) | ||||
0.348149 | + | 0.937439i | \(0.386810\pi\) | |||||||
\(720\) | −5.10684 | −0.190321 | ||||||||
\(721\) | 60.2082 | 2.24227 | ||||||||
\(722\) | −39.6266 | −1.47475 | ||||||||
\(723\) | −2.41360 | −0.0897628 | ||||||||
\(724\) | −10.1720 | −0.378040 | ||||||||
\(725\) | 6.33965 | 0.235449 | ||||||||
\(726\) | −1.42171 | −0.0527648 | ||||||||
\(727\) | −15.1315 | −0.561196 | −0.280598 | − | 0.959825i | \(-0.590533\pi\) | ||||
−0.280598 | + | 0.959825i | \(0.590533\pi\) | |||||||
\(728\) | −12.5885 | −0.466559 | ||||||||
\(729\) | −20.9317 | −0.775248 | ||||||||
\(730\) | 20.2327 | 0.748847 | ||||||||
\(731\) | −2.18205 | −0.0807060 | ||||||||
\(732\) | 4.33344 | 0.160169 | ||||||||
\(733\) | −20.6092 | −0.761219 | −0.380610 | − | 0.924736i | \(-0.624286\pi\) | ||||
−0.380610 | + | 0.924736i | \(0.624286\pi\) | |||||||
\(734\) | −7.80521 | −0.288096 | ||||||||
\(735\) | −6.33812 | −0.233785 | ||||||||
\(736\) | −3.71765 | −0.137034 | ||||||||
\(737\) | −42.3836 | −1.56122 | ||||||||
\(738\) | −8.95655 | −0.329695 | ||||||||
\(739\) | 12.2839 | 0.451869 | 0.225934 | − | 0.974143i | \(-0.427456\pi\) | ||||
0.225934 | + | 0.974143i | \(0.427456\pi\) | |||||||
\(740\) | −4.20004 | −0.154396 | ||||||||
\(741\) | −7.84945 | −0.288357 | ||||||||
\(742\) | −45.1234 | −1.65653 | ||||||||
\(743\) | −12.9805 | −0.476210 | −0.238105 | − | 0.971239i | \(-0.576526\pi\) | ||||
−0.238105 | + | 0.971239i | \(0.576526\pi\) | |||||||
\(744\) | 0.976819 | 0.0358119 | ||||||||
\(745\) | −28.3511 | −1.03870 | ||||||||
\(746\) | −33.6045 | −1.23035 | ||||||||
\(747\) | −12.0565 | −0.441124 | ||||||||
\(748\) | 9.18958 | 0.336004 | ||||||||
\(749\) | 17.3761 | 0.634907 | ||||||||
\(750\) | −4.14155 | −0.151228 | ||||||||
\(751\) | 0.596847 | 0.0217793 | 0.0108896 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108896 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(752\) | 2.52070 | 0.0919204 | ||||||||
\(753\) | 10.4488 | 0.380774 | ||||||||
\(754\) | 10.2319 | 0.372622 | ||||||||
\(755\) | 1.93015 | 0.0702454 | ||||||||
\(756\) | 8.38773 | 0.305059 | ||||||||
\(757\) | −5.90667 | −0.214682 | −0.107341 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107341 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(758\) | 14.0025 | 0.508595 | ||||||||
\(759\) | −3.30974 | −0.120136 | ||||||||
\(760\) | −13.5587 | −0.491826 | ||||||||
\(761\) | 13.8249 | 0.501154 | 0.250577 | − | 0.968097i | \(-0.419380\pi\) | ||||
0.250577 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(762\) | −2.37804 | −0.0861472 | ||||||||
\(763\) | 9.78366 | 0.354192 | ||||||||
\(764\) | −10.5694 | −0.382388 | ||||||||
\(765\) | −17.9607 | −0.649369 | ||||||||
\(766\) | 20.9251 | 0.756055 | ||||||||
\(767\) | 31.9307 | 1.15295 | ||||||||
\(768\) | −0.340721 | −0.0122947 | ||||||||
\(769\) | 20.3738 | 0.734698 | 0.367349 | − | 0.930083i | \(-0.380266\pi\) | ||||
0.367349 | + | 0.930083i | \(0.380266\pi\) | |||||||
\(770\) | −19.3587 | −0.697639 | ||||||||
\(771\) | −3.31013 | −0.119211 | ||||||||
\(772\) | −12.4910 | −0.449561 | ||||||||
\(773\) | −0.199155 | −0.00716311 | −0.00358156 | − | 0.999994i | \(-0.501140\pi\) | ||||
−0.00358156 | + | 0.999994i | \(0.501140\pi\) | |||||||
\(774\) | −1.78927 | −0.0643140 | ||||||||
\(775\) | −5.34464 | −0.191985 | ||||||||
\(776\) | −6.46877 | −0.232215 | ||||||||
\(777\) | 3.38112 | 0.121297 | ||||||||
\(778\) | −13.3813 | −0.479743 | ||||||||
\(779\) | −23.7797 | −0.851996 | ||||||||
\(780\) | −1.81536 | −0.0650003 | ||||||||
\(781\) | 21.2331 | 0.759781 | ||||||||
\(782\) | −13.0749 | −0.467558 | ||||||||
\(783\) | −6.81752 | −0.243638 | ||||||||
\(784\) | 10.5049 | 0.375174 | ||||||||
\(785\) | −32.4670 | −1.15880 | ||||||||
\(786\) | −0.961103 | −0.0342814 | ||||||||
\(787\) | −1.42241 | −0.0507036 | −0.0253518 | − | 0.999679i | \(-0.508071\pi\) | ||||
−0.0253518 | + | 0.999679i | \(0.508071\pi\) | |||||||
\(788\) | 19.3297 | 0.688592 | ||||||||
\(789\) | −7.39834 | −0.263388 | ||||||||
\(790\) | 22.5681 | 0.802936 | ||||||||
\(791\) | −47.6519 | −1.69431 | ||||||||
\(792\) | 7.53542 | 0.267759 | ||||||||
\(793\) | −38.2672 | −1.35891 | ||||||||
\(794\) | 34.1292 | 1.21120 | ||||||||
\(795\) | −6.50717 | −0.230786 | ||||||||
\(796\) | −12.9496 | −0.458988 | ||||||||
\(797\) | −37.2638 | −1.31995 | −0.659976 | − | 0.751286i | \(-0.729434\pi\) | ||||
−0.659976 | + | 0.751286i | \(0.729434\pi\) | |||||||
\(798\) | 10.9150 | 0.386389 | ||||||||
\(799\) | 8.86524 | 0.313630 | ||||||||
\(800\) | 1.86425 | 0.0659112 | ||||||||
\(801\) | 22.7310 | 0.803160 | ||||||||
\(802\) | −25.3458 | −0.894992 | ||||||||
\(803\) | −29.8545 | −1.05354 | ||||||||
\(804\) | 5.52677 | 0.194914 | ||||||||
\(805\) | 27.5435 | 0.970780 | ||||||||
\(806\) | −8.62597 | −0.303837 | ||||||||
\(807\) | 8.78868 | 0.309376 | ||||||||
\(808\) | 1.69847 | 0.0597519 | ||||||||
\(809\) | 47.7828 | 1.67995 | 0.839977 | − | 0.542622i | \(-0.182568\pi\) | ||||
0.839977 | + | 0.542622i | \(0.182568\pi\) | |||||||
\(810\) | −14.1109 | −0.495808 | ||||||||
\(811\) | 37.6399 | 1.32172 | 0.660858 | − | 0.750511i | \(-0.270193\pi\) | ||||
0.660858 | + | 0.750511i | \(0.270193\pi\) | |||||||
\(812\) | −14.2279 | −0.499302 | ||||||||
\(813\) | 6.18020 | 0.216749 | ||||||||
\(814\) | 6.19738 | 0.217218 | ||||||||
\(815\) | −15.8352 | −0.554682 | ||||||||
\(816\) | −1.19831 | −0.0419492 | ||||||||
\(817\) | −4.75053 | −0.166200 | ||||||||
\(818\) | −32.1256 | −1.12324 | ||||||||
\(819\) | −36.3040 | −1.26856 | ||||||||
\(820\) | −5.49959 | −0.192054 | ||||||||
\(821\) | 51.9505 | 1.81309 | 0.906543 | − | 0.422115i | \(-0.138712\pi\) | ||||
0.906543 | + | 0.422115i | \(0.138712\pi\) | |||||||
\(822\) | 3.79381 | 0.132324 | ||||||||
\(823\) | 10.6966 | 0.372861 | 0.186430 | − | 0.982468i | \(-0.440308\pi\) | ||||
0.186430 | + | 0.982468i | \(0.440308\pi\) | |||||||
\(824\) | −14.3905 | −0.501317 | ||||||||
\(825\) | 1.65970 | 0.0577832 | ||||||||
\(826\) | −44.4012 | −1.54491 | ||||||||
\(827\) | 22.3864 | 0.778450 | 0.389225 | − | 0.921143i | \(-0.372743\pi\) | ||||
0.389225 | + | 0.921143i | \(0.372743\pi\) | |||||||
\(828\) | −10.7214 | −0.372593 | ||||||||
\(829\) | 25.5571 | 0.887634 | 0.443817 | − | 0.896117i | \(-0.353624\pi\) | ||||
0.443817 | + | 0.896117i | \(0.353624\pi\) | |||||||
\(830\) | −7.40303 | −0.256963 | ||||||||
\(831\) | −5.64683 | −0.195886 | ||||||||
\(832\) | 3.00880 | 0.104311 | ||||||||
\(833\) | 36.9454 | 1.28008 | ||||||||
\(834\) | −2.56794 | −0.0889204 | ||||||||
\(835\) | 14.0890 | 0.487568 | ||||||||
\(836\) | 20.0066 | 0.691942 | ||||||||
\(837\) | 5.74751 | 0.198663 | ||||||||
\(838\) | −36.7157 | −1.26832 | ||||||||
\(839\) | −24.5235 | −0.846645 | −0.423322 | − | 0.905979i | \(-0.639136\pi\) | ||||
−0.423322 | + | 0.905979i | \(0.639136\pi\) | |||||||
\(840\) | 2.52435 | 0.0870983 | ||||||||
\(841\) | −17.4356 | −0.601228 | ||||||||
\(842\) | 15.2841 | 0.526725 | ||||||||
\(843\) | −3.91739 | −0.134922 | ||||||||
\(844\) | 3.73521 | 0.128571 | ||||||||
\(845\) | −6.98961 | −0.240450 | ||||||||
\(846\) | 7.26946 | 0.249929 | ||||||||
\(847\) | −17.4579 | −0.599862 | ||||||||
\(848\) | 10.7851 | 0.370360 | ||||||||
\(849\) | 1.67956 | 0.0576423 | ||||||||
\(850\) | 6.55653 | 0.224887 | ||||||||
\(851\) | −8.81761 | −0.302264 | ||||||||
\(852\) | −2.76877 | −0.0948566 | ||||||||
\(853\) | −22.0767 | −0.755892 | −0.377946 | − | 0.925828i | \(-0.623370\pi\) | ||||
−0.377946 | + | 0.925828i | \(0.623370\pi\) | |||||||
\(854\) | 53.2125 | 1.82089 | ||||||||
\(855\) | −39.1021 | −1.33726 | ||||||||
\(856\) | −4.15309 | −0.141950 | ||||||||
\(857\) | −5.33040 | −0.182083 | −0.0910415 | − | 0.995847i | \(-0.529020\pi\) | ||||
−0.0910415 | + | 0.995847i | \(0.529020\pi\) | |||||||
\(858\) | 2.67866 | 0.0914480 | ||||||||
\(859\) | −42.1337 | −1.43758 | −0.718792 | − | 0.695225i | \(-0.755305\pi\) | ||||
−0.718792 | + | 0.695225i | \(0.755305\pi\) | |||||||
\(860\) | −1.09867 | −0.0374642 | ||||||||
\(861\) | 4.42729 | 0.150882 | ||||||||
\(862\) | 9.38721 | 0.319730 | ||||||||
\(863\) | −36.0412 | −1.22686 | −0.613429 | − | 0.789750i | \(-0.710210\pi\) | ||||
−0.613429 | + | 0.789750i | \(0.710210\pi\) | |||||||
\(864\) | −2.00477 | −0.0682037 | ||||||||
\(865\) | −9.79055 | −0.332889 | ||||||||
\(866\) | −5.89835 | −0.200434 | ||||||||
\(867\) | 1.57783 | 0.0535859 | ||||||||
\(868\) | 11.9948 | 0.407131 | ||||||||
\(869\) | −33.3004 | −1.12964 | ||||||||
\(870\) | −2.05178 | −0.0695620 | ||||||||
\(871\) | −48.8051 | −1.65370 | ||||||||
\(872\) | −2.33842 | −0.0791888 | ||||||||
\(873\) | −18.6553 | −0.631388 | ||||||||
\(874\) | −28.4653 | −0.962854 | ||||||||
\(875\) | −50.8561 | −1.71925 | ||||||||
\(876\) | 3.89299 | 0.131532 | ||||||||
\(877\) | −19.8349 | −0.669778 | −0.334889 | − | 0.942258i | \(-0.608699\pi\) | ||||
−0.334889 | + | 0.942258i | \(0.608699\pi\) | |||||||
\(878\) | −4.09609 | −0.138236 | ||||||||
\(879\) | −5.85652 | −0.197535 | ||||||||
\(880\) | 4.62697 | 0.155975 | ||||||||
\(881\) | 3.74473 | 0.126163 | 0.0630815 | − | 0.998008i | \(-0.479907\pi\) | ||||
0.0630815 | + | 0.998008i | \(0.479907\pi\) | |||||||
\(882\) | 30.2951 | 1.02009 | ||||||||
\(883\) | 20.5729 | 0.692332 | 0.346166 | − | 0.938173i | \(-0.387483\pi\) | ||||
0.346166 | + | 0.938173i | \(0.387483\pi\) | |||||||
\(884\) | 10.5819 | 0.355907 | ||||||||
\(885\) | −6.40302 | −0.215235 | ||||||||
\(886\) | −39.8409 | −1.33848 | ||||||||
\(887\) | −51.3374 | −1.72374 | −0.861871 | − | 0.507128i | \(-0.830707\pi\) | ||||
−0.861871 | + | 0.507128i | \(0.830707\pi\) | |||||||
\(888\) | −0.808130 | −0.0271191 | ||||||||
\(889\) | −29.2011 | −0.979373 | ||||||||
\(890\) | 13.9575 | 0.467857 | ||||||||
\(891\) | 20.8214 | 0.697545 | ||||||||
\(892\) | 9.14690 | 0.306261 | ||||||||
\(893\) | 19.3005 | 0.645866 | ||||||||
\(894\) | −5.45504 | −0.182444 | ||||||||
\(895\) | −8.13588 | −0.271953 | ||||||||
\(896\) | −4.18388 | −0.139774 | ||||||||
\(897\) | −3.81119 | −0.127252 | ||||||||
\(898\) | −16.5522 | −0.552355 | ||||||||
\(899\) | −9.74937 | −0.325160 | ||||||||
\(900\) | 5.37633 | 0.179211 | ||||||||
\(901\) | 37.9308 | 1.26366 | ||||||||
\(902\) | 8.11493 | 0.270198 | ||||||||
\(903\) | 0.884450 | 0.0294326 | ||||||||
\(904\) | 11.3894 | 0.378806 | ||||||||
\(905\) | −18.0127 | −0.598761 | ||||||||
\(906\) | 0.371381 | 0.0123383 | ||||||||
\(907\) | 32.2707 | 1.07153 | 0.535765 | − | 0.844367i | \(-0.320023\pi\) | ||||
0.535765 | + | 0.844367i | \(0.320023\pi\) | |||||||
\(908\) | 6.78677 | 0.225227 | ||||||||
\(909\) | 4.89823 | 0.162464 | ||||||||
\(910\) | −22.2917 | −0.738963 | ||||||||
\(911\) | −14.6828 | −0.486464 | −0.243232 | − | 0.969968i | \(-0.578208\pi\) | ||||
−0.243232 | + | 0.969968i | \(0.578208\pi\) | |||||||
\(912\) | −2.60883 | −0.0863871 | ||||||||
\(913\) | 10.9236 | 0.361517 | ||||||||
\(914\) | 35.3162 | 1.16816 | ||||||||
\(915\) | 7.67368 | 0.253684 | ||||||||
\(916\) | 23.4843 | 0.775944 | ||||||||
\(917\) | −11.8019 | −0.389731 | ||||||||
\(918\) | −7.05074 | −0.232709 | ||||||||
\(919\) | 12.8944 | 0.425346 | 0.212673 | − | 0.977123i | \(-0.431783\pi\) | ||||
0.212673 | + | 0.977123i | \(0.431783\pi\) | |||||||
\(920\) | −6.58324 | −0.217043 | ||||||||
\(921\) | −9.54217 | −0.314425 | ||||||||
\(922\) | 28.5573 | 0.940483 | ||||||||
\(923\) | 24.4501 | 0.804786 | ||||||||
\(924\) | −3.72481 | −0.122537 | ||||||||
\(925\) | 4.42167 | 0.145384 | ||||||||
\(926\) | −36.6034 | −1.20286 | ||||||||
\(927\) | −41.5009 | −1.36307 | ||||||||
\(928\) | 3.40065 | 0.111632 | ||||||||
\(929\) | −19.1605 | −0.628635 | −0.314318 | − | 0.949318i | \(-0.601776\pi\) | ||||
−0.314318 | + | 0.949318i | \(0.601776\pi\) | |||||||
\(930\) | 1.72976 | 0.0567209 | ||||||||
\(931\) | 80.4337 | 2.63611 | ||||||||
\(932\) | 5.17551 | 0.169529 | ||||||||
\(933\) | 1.43071 | 0.0468395 | ||||||||
\(934\) | −12.6389 | −0.413558 | ||||||||
\(935\) | 16.2729 | 0.532182 | ||||||||
\(936\) | 8.67710 | 0.283620 | ||||||||
\(937\) | 38.5521 | 1.25944 | 0.629722 | − | 0.776821i | \(-0.283169\pi\) | ||||
0.629722 | + | 0.776821i | \(0.283169\pi\) | |||||||
\(938\) | 67.8659 | 2.21590 | ||||||||
\(939\) | −10.1352 | −0.330751 | ||||||||
\(940\) | 4.46366 | 0.145589 | ||||||||
\(941\) | 36.2593 | 1.18202 | 0.591011 | − | 0.806664i | \(-0.298729\pi\) | ||||
0.591011 | + | 0.806664i | \(0.298729\pi\) | |||||||
\(942\) | −6.24699 | −0.203538 | ||||||||
\(943\) | −11.5459 | −0.375986 | ||||||||
\(944\) | 10.6124 | 0.345405 | ||||||||
\(945\) | 14.8530 | 0.483169 | ||||||||
\(946\) | 1.62114 | 0.0527078 | ||||||||
\(947\) | −30.5207 | −0.991789 | −0.495894 | − | 0.868383i | \(-0.665160\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665160\pi\) | |||||||
\(948\) | 4.34233 | 0.141032 | ||||||||
\(949\) | −34.3777 | −1.11595 | ||||||||
\(950\) | 14.2742 | 0.463116 | ||||||||
\(951\) | 3.36622 | 0.109157 | ||||||||
\(952\) | −14.7146 | −0.476904 | ||||||||
\(953\) | −57.2412 | −1.85422 | −0.927112 | − | 0.374786i | \(-0.877716\pi\) | ||||
−0.927112 | + | 0.374786i | \(0.877716\pi\) | |||||||
\(954\) | 31.1031 | 1.00700 | ||||||||
\(955\) | −18.7164 | −0.605647 | ||||||||
\(956\) | 12.2861 | 0.397360 | ||||||||
\(957\) | 3.02751 | 0.0978657 | ||||||||
\(958\) | −15.6466 | −0.505517 | ||||||||
\(959\) | 46.5861 | 1.50434 | ||||||||
\(960\) | −0.603351 | −0.0194731 | ||||||||
\(961\) | −22.7808 | −0.734864 | ||||||||
\(962\) | 7.13634 | 0.230085 | ||||||||
\(963\) | −11.9771 | −0.385958 | ||||||||
\(964\) | 7.08381 | 0.228154 | ||||||||
\(965\) | −22.1191 | −0.712040 | ||||||||
\(966\) | 5.29965 | 0.170513 | ||||||||
\(967\) | −10.2808 | −0.330607 | −0.165303 | − | 0.986243i | \(-0.552860\pi\) | ||||
−0.165303 | + | 0.986243i | \(0.552860\pi\) | |||||||
\(968\) | 4.17266 | 0.134114 | ||||||||
\(969\) | −9.17521 | −0.294750 | ||||||||
\(970\) | −11.4549 | −0.367796 | ||||||||
\(971\) | 16.8974 | 0.542264 | 0.271132 | − | 0.962542i | \(-0.412602\pi\) | ||||
0.271132 | + | 0.962542i | \(0.412602\pi\) | |||||||
\(972\) | −8.72941 | −0.279996 | ||||||||
\(973\) | −31.5330 | −1.01090 | ||||||||
\(974\) | 31.0411 | 0.994621 | ||||||||
\(975\) | 1.91116 | 0.0612060 | ||||||||
\(976\) | −12.7184 | −0.407108 | ||||||||
\(977\) | −22.1223 | −0.707755 | −0.353878 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353878 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(978\) | −3.04685 | −0.0974276 | ||||||||
\(979\) | −20.5950 | −0.658220 | ||||||||
\(980\) | 18.6021 | 0.594221 | ||||||||
\(981\) | −6.74378 | −0.215312 | ||||||||
\(982\) | 20.2397 | 0.645874 | ||||||||
\(983\) | 14.2082 | 0.453170 | 0.226585 | − | 0.973991i | \(-0.427244\pi\) | ||||
0.226585 | + | 0.973991i | \(0.427244\pi\) | |||||||
\(984\) | −1.05818 | −0.0337335 | ||||||||
\(985\) | 34.2291 | 1.09063 | ||||||||
\(986\) | 11.9600 | 0.380884 | ||||||||
\(987\) | −3.59335 | −0.114378 | ||||||||
\(988\) | 23.0378 | 0.732929 | ||||||||
\(989\) | −2.30655 | −0.0733441 | ||||||||
\(990\) | 13.3438 | 0.424092 | ||||||||
\(991\) | 22.5726 | 0.717043 | 0.358521 | − | 0.933522i | \(-0.383281\pi\) | ||||
0.358521 | + | 0.933522i | \(0.383281\pi\) | |||||||
\(992\) | −2.86692 | −0.0910247 | ||||||||
\(993\) | −7.44538 | −0.236272 | ||||||||
\(994\) | −33.9991 | −1.07839 | ||||||||
\(995\) | −22.9313 | −0.726971 | ||||||||
\(996\) | −1.42442 | −0.0451345 | ||||||||
\(997\) | −36.2712 | −1.14872 | −0.574360 | − | 0.818603i | \(-0.694749\pi\) | ||||
−0.574360 | + | 0.818603i | \(0.694749\pi\) | |||||||
\(998\) | −12.9574 | −0.410158 | ||||||||
\(999\) | −4.75497 | −0.150440 |
(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 | 4006.2.a.h.1.20 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.h.1.20 | ✓ | 42 | 1.1 | even | 1 | trivial |