Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, 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("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.72152 | −1.92440 | −0.962201 | − | 0.272339i | \(-0.912203\pi\) | ||||
−0.962201 | + | 0.272339i | \(0.912203\pi\) | |||||||
\(3\) | −2.92759 | −1.69025 | −0.845124 | − | 0.534571i | \(-0.820473\pi\) | ||||
−0.845124 | + | 0.534571i | \(0.820473\pi\) | |||||||
\(4\) | 5.40665 | 2.70333 | ||||||||
\(5\) | −3.58721 | −1.60425 | −0.802124 | − | 0.597157i | \(-0.796297\pi\) | ||||
−0.802124 | + | 0.597157i | \(0.796297\pi\) | |||||||
\(6\) | 7.96750 | 3.25272 | ||||||||
\(7\) | −4.23646 | −1.60123 | −0.800615 | − | 0.599179i | \(-0.795494\pi\) | ||||
−0.800615 | + | 0.599179i | \(0.795494\pi\) | |||||||
\(8\) | −9.27126 | −3.27789 | ||||||||
\(9\) | 5.57081 | 1.85694 | ||||||||
\(10\) | 9.76265 | 3.08722 | ||||||||
\(11\) | −0.812006 | −0.244829 | −0.122414 | − | 0.992479i | \(-0.539064\pi\) | ||||
−0.122414 | + | 0.992479i | \(0.539064\pi\) | |||||||
\(12\) | −15.8285 | −4.56929 | ||||||||
\(13\) | 5.74531 | 1.59346 | 0.796731 | − | 0.604334i | \(-0.206561\pi\) | ||||
0.796731 | + | 0.604334i | \(0.206561\pi\) | |||||||
\(14\) | 11.5296 | 3.08141 | ||||||||
\(15\) | 10.5019 | 2.71158 | ||||||||
\(16\) | 14.4186 | 3.60465 | ||||||||
\(17\) | −4.43616 | −1.07593 | −0.537964 | − | 0.842968i | \(-0.680806\pi\) | ||||
−0.537964 | + | 0.842968i | \(0.680806\pi\) | |||||||
\(18\) | −15.1610 | −3.57349 | ||||||||
\(19\) | 4.26293 | 0.977982 | 0.488991 | − | 0.872289i | \(-0.337365\pi\) | ||||
0.488991 | + | 0.872289i | \(0.337365\pi\) | |||||||
\(20\) | −19.3948 | −4.33681 | ||||||||
\(21\) | 12.4026 | 2.70647 | ||||||||
\(22\) | 2.20989 | 0.471149 | ||||||||
\(23\) | 6.91630 | 1.44215 | 0.721075 | − | 0.692858i | \(-0.243649\pi\) | ||||
0.721075 | + | 0.692858i | \(0.243649\pi\) | |||||||
\(24\) | 27.1425 | 5.54044 | ||||||||
\(25\) | 7.86806 | 1.57361 | ||||||||
\(26\) | −15.6360 | −3.06646 | ||||||||
\(27\) | −7.52628 | −1.44843 | ||||||||
\(28\) | −22.9050 | −4.32865 | ||||||||
\(29\) | 2.78340 | 0.516864 | 0.258432 | − | 0.966029i | \(-0.416794\pi\) | ||||
0.258432 | + | 0.966029i | \(0.416794\pi\) | |||||||
\(30\) | −28.5811 | −5.21816 | ||||||||
\(31\) | 9.64726 | 1.73270 | 0.866349 | − | 0.499439i | \(-0.166460\pi\) | ||||
0.866349 | + | 0.499439i | \(0.166460\pi\) | |||||||
\(32\) | −20.6979 | −3.65891 | ||||||||
\(33\) | 2.37722 | 0.413821 | ||||||||
\(34\) | 12.0731 | 2.07052 | ||||||||
\(35\) | 15.1970 | 2.56877 | ||||||||
\(36\) | 30.1194 | 5.01990 | ||||||||
\(37\) | 8.80524 | 1.44757 | 0.723786 | − | 0.690024i | \(-0.242400\pi\) | ||||
0.723786 | + | 0.690024i | \(0.242400\pi\) | |||||||
\(38\) | −11.6016 | −1.88203 | ||||||||
\(39\) | −16.8199 | −2.69334 | ||||||||
\(40\) | 33.2579 | 5.25854 | ||||||||
\(41\) | 3.79424 | 0.592561 | 0.296281 | − | 0.955101i | \(-0.404254\pi\) | ||||
0.296281 | + | 0.955101i | \(0.404254\pi\) | |||||||
\(42\) | −33.7539 | −5.20835 | ||||||||
\(43\) | −8.14223 | −1.24168 | −0.620839 | − | 0.783938i | \(-0.713208\pi\) | ||||
−0.620839 | + | 0.783938i | \(0.713208\pi\) | |||||||
\(44\) | −4.39023 | −0.661852 | ||||||||
\(45\) | −19.9836 | −2.97898 | ||||||||
\(46\) | −18.8228 | −2.77528 | ||||||||
\(47\) | 2.31756 | 0.338050 | 0.169025 | − | 0.985612i | \(-0.445938\pi\) | ||||
0.169025 | + | 0.985612i | \(0.445938\pi\) | |||||||
\(48\) | −42.2118 | −6.09275 | ||||||||
\(49\) | 10.9476 | 1.56394 | ||||||||
\(50\) | −21.4131 | −3.02826 | ||||||||
\(51\) | 12.9873 | 1.81858 | ||||||||
\(52\) | 31.0629 | 4.30765 | ||||||||
\(53\) | 1.94360 | 0.266974 | 0.133487 | − | 0.991051i | \(-0.457383\pi\) | ||||
0.133487 | + | 0.991051i | \(0.457383\pi\) | |||||||
\(54\) | 20.4829 | 2.78737 | ||||||||
\(55\) | 2.91283 | 0.392766 | ||||||||
\(56\) | 39.2773 | 5.24865 | ||||||||
\(57\) | −12.4801 | −1.65303 | ||||||||
\(58\) | −7.57507 | −0.994655 | ||||||||
\(59\) | −0.889207 | −0.115765 | −0.0578825 | − | 0.998323i | \(-0.518435\pi\) | ||||
−0.0578825 | + | 0.998323i | \(0.518435\pi\) | |||||||
\(60\) | 56.7801 | 7.33027 | ||||||||
\(61\) | −2.41942 | −0.309775 | −0.154887 | − | 0.987932i | \(-0.549501\pi\) | ||||
−0.154887 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(62\) | −26.2552 | −3.33441 | ||||||||
\(63\) | −23.6005 | −2.97338 | ||||||||
\(64\) | 27.4925 | 3.43657 | ||||||||
\(65\) | −20.6096 | −2.55631 | ||||||||
\(66\) | −6.46965 | −0.796359 | ||||||||
\(67\) | 0.0402207 | 0.00491374 | 0.00245687 | − | 0.999997i | \(-0.499218\pi\) | ||||
0.00245687 | + | 0.999997i | \(0.499218\pi\) | |||||||
\(68\) | −23.9848 | −2.90858 | ||||||||
\(69\) | −20.2481 | −2.43759 | ||||||||
\(70\) | −41.3590 | −4.94335 | ||||||||
\(71\) | −0.981324 | −0.116462 | −0.0582309 | − | 0.998303i | \(-0.518546\pi\) | ||||
−0.0582309 | + | 0.998303i | \(0.518546\pi\) | |||||||
\(72\) | −51.6484 | −6.08682 | ||||||||
\(73\) | 7.25877 | 0.849575 | 0.424788 | − | 0.905293i | \(-0.360349\pi\) | ||||
0.424788 | + | 0.905293i | \(0.360349\pi\) | |||||||
\(74\) | −23.9636 | −2.78571 | ||||||||
\(75\) | −23.0345 | −2.65979 | ||||||||
\(76\) | 23.0482 | 2.64381 | ||||||||
\(77\) | 3.44003 | 0.392027 | ||||||||
\(78\) | 45.7757 | 5.18308 | ||||||||
\(79\) | 2.14089 | 0.240869 | 0.120434 | − | 0.992721i | \(-0.461571\pi\) | ||||
0.120434 | + | 0.992721i | \(0.461571\pi\) | |||||||
\(80\) | −51.7225 | −5.78275 | ||||||||
\(81\) | 5.32146 | 0.591273 | ||||||||
\(82\) | −10.3261 | −1.14033 | ||||||||
\(83\) | 9.08648 | 0.997371 | 0.498685 | − | 0.866783i | \(-0.333816\pi\) | ||||
0.498685 | + | 0.866783i | \(0.333816\pi\) | |||||||
\(84\) | 67.0567 | 7.31648 | ||||||||
\(85\) | 15.9134 | 1.72606 | ||||||||
\(86\) | 22.1592 | 2.38949 | ||||||||
\(87\) | −8.14866 | −0.873628 | ||||||||
\(88\) | 7.52832 | 0.802521 | ||||||||
\(89\) | 3.14348 | 0.333208 | 0.166604 | − | 0.986024i | \(-0.446720\pi\) | ||||
0.166604 | + | 0.986024i | \(0.446720\pi\) | |||||||
\(90\) | 54.3858 | 5.73277 | ||||||||
\(91\) | −24.3397 | −2.55150 | ||||||||
\(92\) | 37.3941 | 3.89860 | ||||||||
\(93\) | −28.2432 | −2.92869 | ||||||||
\(94\) | −6.30727 | −0.650545 | ||||||||
\(95\) | −15.2920 | −1.56893 | ||||||||
\(96\) | 60.5951 | 6.18446 | ||||||||
\(97\) | 16.7830 | 1.70406 | 0.852030 | − | 0.523493i | \(-0.175371\pi\) | ||||
0.852030 | + | 0.523493i | \(0.175371\pi\) | |||||||
\(98\) | −29.7940 | −3.00964 | ||||||||
\(99\) | −4.52353 | −0.454631 | ||||||||
\(100\) | 42.5399 | 4.25399 | ||||||||
\(101\) | 11.6058 | 1.15482 | 0.577410 | − | 0.816455i | \(-0.304064\pi\) | ||||
0.577410 | + | 0.816455i | \(0.304064\pi\) | |||||||
\(102\) | −35.3451 | −3.49969 | ||||||||
\(103\) | −4.15549 | −0.409452 | −0.204726 | − | 0.978819i | \(-0.565630\pi\) | ||||
−0.204726 | + | 0.978819i | \(0.565630\pi\) | |||||||
\(104\) | −53.2663 | −5.22319 | ||||||||
\(105\) | −44.4908 | −4.34186 | ||||||||
\(106\) | −5.28954 | −0.513766 | ||||||||
\(107\) | 18.5577 | 1.79404 | 0.897018 | − | 0.441994i | \(-0.145729\pi\) | ||||
0.897018 | + | 0.441994i | \(0.145729\pi\) | |||||||
\(108\) | −40.6920 | −3.91559 | ||||||||
\(109\) | 3.88106 | 0.371738 | 0.185869 | − | 0.982574i | \(-0.440490\pi\) | ||||
0.185869 | + | 0.982574i | \(0.440490\pi\) | |||||||
\(110\) | −7.92732 | −0.755841 | ||||||||
\(111\) | −25.7782 | −2.44675 | ||||||||
\(112\) | −61.0837 | −5.77187 | ||||||||
\(113\) | 9.87721 | 0.929170 | 0.464585 | − | 0.885528i | \(-0.346203\pi\) | ||||
0.464585 | + | 0.885528i | \(0.346203\pi\) | |||||||
\(114\) | 33.9648 | 3.18110 | ||||||||
\(115\) | −24.8102 | −2.31356 | ||||||||
\(116\) | 15.0489 | 1.39725 | ||||||||
\(117\) | 32.0060 | 2.95896 | ||||||||
\(118\) | 2.41999 | 0.222778 | ||||||||
\(119\) | 18.7936 | 1.72281 | ||||||||
\(120\) | −97.3658 | −8.88824 | ||||||||
\(121\) | −10.3406 | −0.940059 | ||||||||
\(122\) | 6.58449 | 0.596132 | ||||||||
\(123\) | −11.1080 | −1.00158 | ||||||||
\(124\) | 52.1594 | 4.68405 | ||||||||
\(125\) | −10.2883 | −0.920216 | ||||||||
\(126\) | 64.2291 | 5.72198 | ||||||||
\(127\) | −17.0789 | −1.51550 | −0.757752 | − | 0.652543i | \(-0.773702\pi\) | ||||
−0.757752 | + | 0.652543i | \(0.773702\pi\) | |||||||
\(128\) | −33.4255 | −2.95443 | ||||||||
\(129\) | 23.8371 | 2.09874 | ||||||||
\(130\) | 56.0894 | 4.91937 | ||||||||
\(131\) | 20.5294 | 1.79366 | 0.896831 | − | 0.442373i | \(-0.145863\pi\) | ||||
0.896831 | + | 0.442373i | \(0.145863\pi\) | |||||||
\(132\) | 12.8528 | 1.11869 | ||||||||
\(133\) | −18.0597 | −1.56597 | ||||||||
\(134\) | −0.109461 | −0.00945601 | ||||||||
\(135\) | 26.9983 | 2.32365 | ||||||||
\(136\) | 41.1288 | 3.52677 | ||||||||
\(137\) | −5.65378 | −0.483035 | −0.241518 | − | 0.970396i | \(-0.577645\pi\) | ||||
−0.241518 | + | 0.970396i | \(0.577645\pi\) | |||||||
\(138\) | 55.1056 | 4.69090 | ||||||||
\(139\) | −10.5136 | −0.891750 | −0.445875 | − | 0.895095i | \(-0.647107\pi\) | ||||
−0.445875 | + | 0.895095i | \(0.647107\pi\) | |||||||
\(140\) | 82.1652 | 6.94422 | ||||||||
\(141\) | −6.78486 | −0.571389 | ||||||||
\(142\) | 2.67069 | 0.224119 | ||||||||
\(143\) | −4.66522 | −0.390125 | ||||||||
\(144\) | 80.3232 | 6.69360 | ||||||||
\(145\) | −9.98463 | −0.829178 | ||||||||
\(146\) | −19.7549 | −1.63492 | ||||||||
\(147\) | −32.0500 | −2.64344 | ||||||||
\(148\) | 47.6069 | 3.91326 | ||||||||
\(149\) | −13.1181 | −1.07467 | −0.537336 | − | 0.843368i | \(-0.680569\pi\) | ||||
−0.537336 | + | 0.843368i | \(0.680569\pi\) | |||||||
\(150\) | 62.6887 | 5.11851 | ||||||||
\(151\) | 19.2207 | 1.56416 | 0.782079 | − | 0.623179i | \(-0.214159\pi\) | ||||
0.782079 | + | 0.623179i | \(0.214159\pi\) | |||||||
\(152\) | −39.5227 | −3.20572 | ||||||||
\(153\) | −24.7130 | −1.99793 | ||||||||
\(154\) | −9.36209 | −0.754418 | ||||||||
\(155\) | −34.6067 | −2.77968 | ||||||||
\(156\) | −90.9395 | −7.28099 | ||||||||
\(157\) | −12.8550 | −1.02594 | −0.512968 | − | 0.858407i | \(-0.671454\pi\) | ||||
−0.512968 | + | 0.858407i | \(0.671454\pi\) | |||||||
\(158\) | −5.82646 | −0.463528 | ||||||||
\(159\) | −5.69008 | −0.451252 | ||||||||
\(160\) | 74.2477 | 5.86980 | ||||||||
\(161\) | −29.3006 | −2.30921 | ||||||||
\(162\) | −14.4824 | −1.13785 | ||||||||
\(163\) | −1.47489 | −0.115523 | −0.0577613 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577613 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(164\) | 20.5142 | 1.60189 | ||||||||
\(165\) | −8.52759 | −0.663872 | ||||||||
\(166\) | −24.7290 | −1.91934 | ||||||||
\(167\) | −23.1226 | −1.78928 | −0.894642 | − | 0.446784i | \(-0.852569\pi\) | ||||
−0.894642 | + | 0.446784i | \(0.852569\pi\) | |||||||
\(168\) | −114.988 | −8.87151 | ||||||||
\(169\) | 20.0086 | 1.53912 | ||||||||
\(170\) | −43.3087 | −3.32163 | ||||||||
\(171\) | 23.7479 | 1.81605 | ||||||||
\(172\) | −44.0222 | −3.35666 | ||||||||
\(173\) | 16.3115 | 1.24014 | 0.620070 | − | 0.784546i | \(-0.287104\pi\) | ||||
0.620070 | + | 0.784546i | \(0.287104\pi\) | |||||||
\(174\) | 22.1767 | 1.68121 | ||||||||
\(175\) | −33.3327 | −2.51971 | ||||||||
\(176\) | −11.7080 | −0.882522 | ||||||||
\(177\) | 2.60324 | 0.195671 | ||||||||
\(178\) | −8.55503 | −0.641227 | ||||||||
\(179\) | 10.6670 | 0.797286 | 0.398643 | − | 0.917106i | \(-0.369481\pi\) | ||||
0.398643 | + | 0.917106i | \(0.369481\pi\) | |||||||
\(180\) | −108.045 | −8.05317 | ||||||||
\(181\) | −13.3600 | −0.993038 | −0.496519 | − | 0.868026i | \(-0.665389\pi\) | ||||
−0.496519 | + | 0.868026i | \(0.665389\pi\) | |||||||
\(182\) | 66.2410 | 4.91011 | ||||||||
\(183\) | 7.08308 | 0.523596 | ||||||||
\(184\) | −64.1229 | −4.72720 | ||||||||
\(185\) | −31.5862 | −2.32226 | ||||||||
\(186\) | 76.8645 | 5.63598 | ||||||||
\(187\) | 3.60219 | 0.263418 | ||||||||
\(188\) | 12.5302 | 0.913860 | ||||||||
\(189\) | 31.8847 | 2.31927 | ||||||||
\(190\) | 41.6174 | 3.01925 | ||||||||
\(191\) | −17.0514 | −1.23380 | −0.616899 | − | 0.787042i | \(-0.711611\pi\) | ||||
−0.616899 | + | 0.787042i | \(0.711611\pi\) | |||||||
\(192\) | −80.4869 | −5.80864 | ||||||||
\(193\) | 22.5712 | 1.62471 | 0.812355 | − | 0.583163i | \(-0.198185\pi\) | ||||
0.812355 | + | 0.583163i | \(0.198185\pi\) | |||||||
\(194\) | −45.6753 | −3.27930 | ||||||||
\(195\) | 60.3366 | 4.32079 | ||||||||
\(196\) | 59.1896 | 4.22783 | ||||||||
\(197\) | −3.45743 | −0.246332 | −0.123166 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123166 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(198\) | 12.3108 | 0.874894 | ||||||||
\(199\) | −23.4836 | −1.66471 | −0.832354 | − | 0.554245i | \(-0.813007\pi\) | ||||
−0.832354 | + | 0.554245i | \(0.813007\pi\) | |||||||
\(200\) | −72.9469 | −5.15812 | ||||||||
\(201\) | −0.117750 | −0.00830543 | ||||||||
\(202\) | −31.5853 | −2.22234 | ||||||||
\(203\) | −11.7917 | −0.827618 | ||||||||
\(204\) | 70.2178 | 4.91623 | ||||||||
\(205\) | −13.6107 | −0.950615 | ||||||||
\(206\) | 11.3092 | 0.787951 | ||||||||
\(207\) | 38.5294 | 2.67798 | ||||||||
\(208\) | 82.8392 | 5.74387 | ||||||||
\(209\) | −3.46152 | −0.239438 | ||||||||
\(210\) | 121.082 | 8.35548 | ||||||||
\(211\) | 1.69143 | 0.116443 | 0.0582214 | − | 0.998304i | \(-0.481457\pi\) | ||||
0.0582214 | + | 0.998304i | \(0.481457\pi\) | |||||||
\(212\) | 10.5084 | 0.721718 | ||||||||
\(213\) | 2.87292 | 0.196849 | ||||||||
\(214\) | −50.5050 | −3.45245 | ||||||||
\(215\) | 29.2079 | 1.99196 | ||||||||
\(216\) | 69.7781 | 4.74780 | ||||||||
\(217\) | −40.8702 | −2.77445 | ||||||||
\(218\) | −10.5624 | −0.715374 | ||||||||
\(219\) | −21.2507 | −1.43599 | ||||||||
\(220\) | 15.7487 | 1.06178 | ||||||||
\(221\) | −25.4871 | −1.71445 | ||||||||
\(222\) | 70.1557 | 4.70854 | ||||||||
\(223\) | 14.7662 | 0.988818 | 0.494409 | − | 0.869229i | \(-0.335384\pi\) | ||||
0.494409 | + | 0.869229i | \(0.335384\pi\) | |||||||
\(224\) | 87.6858 | 5.85875 | ||||||||
\(225\) | 43.8314 | 2.92210 | ||||||||
\(226\) | −26.8810 | −1.78810 | ||||||||
\(227\) | 13.9001 | 0.922584 | 0.461292 | − | 0.887248i | \(-0.347386\pi\) | ||||
0.461292 | + | 0.887248i | \(0.347386\pi\) | |||||||
\(228\) | −67.4757 | −4.46868 | ||||||||
\(229\) | 13.6588 | 0.902600 | 0.451300 | − | 0.892372i | \(-0.350960\pi\) | ||||
0.451300 | + | 0.892372i | \(0.350960\pi\) | |||||||
\(230\) | 67.5214 | 4.45223 | ||||||||
\(231\) | −10.0710 | −0.662623 | ||||||||
\(232\) | −25.8056 | −1.69422 | ||||||||
\(233\) | 6.02562 | 0.394751 | 0.197376 | − | 0.980328i | \(-0.436758\pi\) | ||||
0.197376 | + | 0.980328i | \(0.436758\pi\) | |||||||
\(234\) | −87.1048 | −5.69422 | ||||||||
\(235\) | −8.31356 | −0.542317 | ||||||||
\(236\) | −4.80764 | −0.312950 | ||||||||
\(237\) | −6.26765 | −0.407127 | ||||||||
\(238\) | −51.1471 | −3.31538 | ||||||||
\(239\) | −8.55872 | −0.553617 | −0.276809 | − | 0.960925i | \(-0.589277\pi\) | ||||
−0.276809 | + | 0.960925i | \(0.589277\pi\) | |||||||
\(240\) | 151.422 | 9.77428 | ||||||||
\(241\) | 26.3532 | 1.69756 | 0.848781 | − | 0.528745i | \(-0.177337\pi\) | ||||
0.848781 | + | 0.528745i | \(0.177337\pi\) | |||||||
\(242\) | 28.1422 | 1.80905 | ||||||||
\(243\) | 6.99975 | 0.449034 | ||||||||
\(244\) | −13.0810 | −0.837423 | ||||||||
\(245\) | −39.2712 | −2.50894 | ||||||||
\(246\) | 30.2306 | 1.92743 | ||||||||
\(247\) | 24.4918 | 1.55838 | ||||||||
\(248\) | −89.4422 | −5.67959 | ||||||||
\(249\) | −26.6015 | −1.68580 | ||||||||
\(250\) | 27.9999 | 1.77087 | ||||||||
\(251\) | −28.7461 | −1.81444 | −0.907219 | − | 0.420659i | \(-0.861799\pi\) | ||||
−0.907219 | + | 0.420659i | \(0.861799\pi\) | |||||||
\(252\) | −127.600 | −8.03802 | ||||||||
\(253\) | −5.61608 | −0.353080 | ||||||||
\(254\) | 46.4804 | 2.91644 | ||||||||
\(255\) | −46.5881 | −2.91746 | ||||||||
\(256\) | 35.9831 | 2.24895 | ||||||||
\(257\) | −11.0973 | −0.692234 | −0.346117 | − | 0.938191i | \(-0.612500\pi\) | ||||
−0.346117 | + | 0.938191i | \(0.612500\pi\) | |||||||
\(258\) | −64.8732 | −4.03883 | ||||||||
\(259\) | −37.3030 | −2.31790 | ||||||||
\(260\) | −111.429 | −6.91053 | ||||||||
\(261\) | 15.5058 | 0.959783 | ||||||||
\(262\) | −55.8711 | −3.45173 | ||||||||
\(263\) | −2.42736 | −0.149678 | −0.0748389 | − | 0.997196i | \(-0.523844\pi\) | ||||
−0.0748389 | + | 0.997196i | \(0.523844\pi\) | |||||||
\(264\) | −22.0399 | −1.35646 | ||||||||
\(265\) | −6.97210 | −0.428293 | ||||||||
\(266\) | 49.1498 | 3.01357 | ||||||||
\(267\) | −9.20283 | −0.563204 | ||||||||
\(268\) | 0.217459 | 0.0132834 | ||||||||
\(269\) | 20.0193 | 1.22060 | 0.610300 | − | 0.792171i | \(-0.291049\pi\) | ||||
0.610300 | + | 0.792171i | \(0.291049\pi\) | |||||||
\(270\) | −73.4764 | −4.47163 | ||||||||
\(271\) | 2.02599 | 0.123070 | 0.0615350 | − | 0.998105i | \(-0.480400\pi\) | ||||
0.0615350 | + | 0.998105i | \(0.480400\pi\) | |||||||
\(272\) | −63.9632 | −3.87834 | ||||||||
\(273\) | 71.2569 | 4.31266 | ||||||||
\(274\) | 15.3869 | 0.929555 | ||||||||
\(275\) | −6.38891 | −0.385266 | ||||||||
\(276\) | −109.475 | −6.58960 | ||||||||
\(277\) | 4.70577 | 0.282742 | 0.141371 | − | 0.989957i | \(-0.454849\pi\) | ||||
0.141371 | + | 0.989957i | \(0.454849\pi\) | |||||||
\(278\) | 28.6129 | 1.71609 | ||||||||
\(279\) | 53.7430 | 3.21751 | ||||||||
\(280\) | −140.896 | −8.42014 | ||||||||
\(281\) | 18.4735 | 1.10204 | 0.551019 | − | 0.834493i | \(-0.314239\pi\) | ||||
0.551019 | + | 0.834493i | \(0.314239\pi\) | |||||||
\(282\) | 18.4651 | 1.09958 | ||||||||
\(283\) | 6.06426 | 0.360483 | 0.180241 | − | 0.983622i | \(-0.442312\pi\) | ||||
0.180241 | + | 0.983622i | \(0.442312\pi\) | |||||||
\(284\) | −5.30568 | −0.314834 | ||||||||
\(285\) | 44.7688 | 2.65187 | ||||||||
\(286\) | 12.6965 | 0.750759 | ||||||||
\(287\) | −16.0741 | −0.948827 | ||||||||
\(288\) | −115.304 | −6.79436 | ||||||||
\(289\) | 2.67956 | 0.157621 | ||||||||
\(290\) | 27.1733 | 1.59567 | ||||||||
\(291\) | −49.1339 | −2.88028 | ||||||||
\(292\) | 39.2457 | 2.29668 | ||||||||
\(293\) | 28.1158 | 1.64254 | 0.821272 | − | 0.570536i | \(-0.193265\pi\) | ||||
0.821272 | + | 0.570536i | \(0.193265\pi\) | |||||||
\(294\) | 87.2246 | 5.08704 | ||||||||
\(295\) | 3.18977 | 0.185716 | ||||||||
\(296\) | −81.6357 | −4.74498 | ||||||||
\(297\) | 6.11138 | 0.354618 | ||||||||
\(298\) | 35.7010 | 2.06810 | ||||||||
\(299\) | 39.7363 | 2.29801 | ||||||||
\(300\) | −124.539 | −7.19029 | ||||||||
\(301\) | 34.4942 | 1.98821 | ||||||||
\(302\) | −52.3094 | −3.01007 | ||||||||
\(303\) | −33.9770 | −1.95193 | ||||||||
\(304\) | 61.4654 | 3.52528 | ||||||||
\(305\) | 8.67896 | 0.496956 | ||||||||
\(306\) | 67.2569 | 3.84482 | ||||||||
\(307\) | 5.80774 | 0.331465 | 0.165733 | − | 0.986171i | \(-0.447001\pi\) | ||||
0.165733 | + | 0.986171i | \(0.447001\pi\) | |||||||
\(308\) | 18.5990 | 1.05978 | ||||||||
\(309\) | 12.1656 | 0.692076 | ||||||||
\(310\) | 94.1827 | 5.34922 | ||||||||
\(311\) | −3.27688 | −0.185815 | −0.0929073 | − | 0.995675i | \(-0.529616\pi\) | ||||
−0.0929073 | + | 0.995675i | \(0.529616\pi\) | |||||||
\(312\) | 155.942 | 8.82848 | ||||||||
\(313\) | 17.6891 | 0.999847 | 0.499924 | − | 0.866070i | \(-0.333361\pi\) | ||||
0.499924 | + | 0.866070i | \(0.333361\pi\) | |||||||
\(314\) | 34.9850 | 1.97432 | ||||||||
\(315\) | 84.6598 | 4.77004 | ||||||||
\(316\) | 11.5750 | 0.651147 | ||||||||
\(317\) | −28.9691 | −1.62707 | −0.813534 | − | 0.581517i | \(-0.802459\pi\) | ||||
−0.813534 | + | 0.581517i | \(0.802459\pi\) | |||||||
\(318\) | 15.4856 | 0.868391 | ||||||||
\(319\) | −2.26014 | −0.126543 | ||||||||
\(320\) | −98.6214 | −5.51310 | ||||||||
\(321\) | −54.3293 | −3.03236 | ||||||||
\(322\) | 79.7421 | 4.44385 | ||||||||
\(323\) | −18.9110 | −1.05224 | ||||||||
\(324\) | 28.7713 | 1.59841 | ||||||||
\(325\) | 45.2044 | 2.50749 | ||||||||
\(326\) | 4.01395 | 0.222312 | ||||||||
\(327\) | −11.3622 | −0.628330 | ||||||||
\(328\) | −35.1774 | −1.94235 | ||||||||
\(329\) | −9.81823 | −0.541296 | ||||||||
\(330\) | 23.2080 | 1.27756 | ||||||||
\(331\) | −21.1733 | −1.16379 | −0.581895 | − | 0.813264i | \(-0.697689\pi\) | ||||
−0.581895 | + | 0.813264i | \(0.697689\pi\) | |||||||
\(332\) | 49.1274 | 2.69622 | ||||||||
\(333\) | 49.0523 | 2.68805 | ||||||||
\(334\) | 62.9287 | 3.44330 | ||||||||
\(335\) | −0.144280 | −0.00788286 | ||||||||
\(336\) | 178.828 | 9.75589 | ||||||||
\(337\) | 15.7193 | 0.856283 | 0.428141 | − | 0.903712i | \(-0.359169\pi\) | ||||
0.428141 | + | 0.903712i | \(0.359169\pi\) | |||||||
\(338\) | −54.4536 | −2.96189 | ||||||||
\(339\) | −28.9165 | −1.57053 | ||||||||
\(340\) | 86.0385 | 4.66609 | ||||||||
\(341\) | −7.83363 | −0.424215 | ||||||||
\(342\) | −64.6304 | −3.49481 | ||||||||
\(343\) | −16.7237 | −0.902993 | ||||||||
\(344\) | 75.4888 | 4.07008 | ||||||||
\(345\) | 72.6342 | 3.91050 | ||||||||
\(346\) | −44.3920 | −2.38653 | ||||||||
\(347\) | 1.71236 | 0.0919241 | 0.0459621 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459621 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(348\) | −44.0570 | −2.36170 | ||||||||
\(349\) | 30.4210 | 1.62840 | 0.814200 | − | 0.580584i | \(-0.197176\pi\) | ||||
0.814200 | + | 0.580584i | \(0.197176\pi\) | |||||||
\(350\) | 90.7155 | 4.84895 | ||||||||
\(351\) | −43.2408 | −2.30802 | ||||||||
\(352\) | 16.8068 | 0.895806 | ||||||||
\(353\) | 3.10716 | 0.165378 | 0.0826888 | − | 0.996575i | \(-0.473649\pi\) | ||||
0.0826888 | + | 0.996575i | \(0.473649\pi\) | |||||||
\(354\) | −7.08476 | −0.376551 | ||||||||
\(355\) | 3.52021 | 0.186834 | ||||||||
\(356\) | 16.9957 | 0.900771 | ||||||||
\(357\) | −55.0201 | −2.91197 | ||||||||
\(358\) | −29.0303 | −1.53430 | ||||||||
\(359\) | 14.1718 | 0.747961 | 0.373981 | − | 0.927437i | \(-0.377993\pi\) | ||||
0.373981 | + | 0.927437i | \(0.377993\pi\) | |||||||
\(360\) | 185.274 | 9.76477 | ||||||||
\(361\) | −0.827461 | −0.0435506 | ||||||||
\(362\) | 36.3594 | 1.91101 | ||||||||
\(363\) | 30.2732 | 1.58893 | ||||||||
\(364\) | −131.597 | −6.89753 | ||||||||
\(365\) | −26.0387 | −1.36293 | ||||||||
\(366\) | −19.2767 | −1.00761 | ||||||||
\(367\) | −11.9927 | −0.626015 | −0.313007 | − | 0.949751i | \(-0.601336\pi\) | ||||
−0.313007 | + | 0.949751i | \(0.601336\pi\) | |||||||
\(368\) | 99.7234 | 5.19844 | ||||||||
\(369\) | 21.1370 | 1.10035 | ||||||||
\(370\) | 85.9624 | 4.46897 | ||||||||
\(371\) | −8.23398 | −0.427487 | ||||||||
\(372\) | −152.701 | −7.91720 | ||||||||
\(373\) | 23.7254 | 1.22846 | 0.614228 | − | 0.789128i | \(-0.289467\pi\) | ||||
0.614228 | + | 0.789128i | \(0.289467\pi\) | |||||||
\(374\) | −9.80342 | −0.506923 | ||||||||
\(375\) | 30.1200 | 1.55539 | ||||||||
\(376\) | −21.4867 | −1.10809 | ||||||||
\(377\) | 15.9915 | 0.823603 | ||||||||
\(378\) | −86.7748 | −4.46322 | ||||||||
\(379\) | −13.6922 | −0.703320 | −0.351660 | − | 0.936128i | \(-0.614383\pi\) | ||||
−0.351660 | + | 0.936128i | \(0.614383\pi\) | |||||||
\(380\) | −82.6785 | −4.24132 | ||||||||
\(381\) | 50.0000 | 2.56158 | ||||||||
\(382\) | 46.4057 | 2.37432 | ||||||||
\(383\) | 27.5624 | 1.40837 | 0.704187 | − | 0.710014i | \(-0.251312\pi\) | ||||
0.704187 | + | 0.710014i | \(0.251312\pi\) | |||||||
\(384\) | 97.8564 | 4.99371 | ||||||||
\(385\) | −12.3401 | −0.628909 | ||||||||
\(386\) | −61.4279 | −3.12660 | ||||||||
\(387\) | −45.3588 | −2.30572 | ||||||||
\(388\) | 90.7401 | 4.60663 | ||||||||
\(389\) | 23.2389 | 1.17826 | 0.589129 | − | 0.808039i | \(-0.299471\pi\) | ||||
0.589129 | + | 0.808039i | \(0.299471\pi\) | |||||||
\(390\) | −164.207 | −8.31494 | ||||||||
\(391\) | −30.6819 | −1.55165 | ||||||||
\(392\) | −101.498 | −5.12641 | ||||||||
\(393\) | −60.1018 | −3.03173 | ||||||||
\(394\) | 9.40945 | 0.474041 | ||||||||
\(395\) | −7.67981 | −0.386413 | ||||||||
\(396\) | −24.4571 | −1.22902 | ||||||||
\(397\) | −2.53242 | −0.127099 | −0.0635493 | − | 0.997979i | \(-0.520242\pi\) | ||||
−0.0635493 | + | 0.997979i | \(0.520242\pi\) | |||||||
\(398\) | 63.9110 | 3.20357 | ||||||||
\(399\) | 52.8715 | 2.64688 | ||||||||
\(400\) | 113.446 | 5.67232 | ||||||||
\(401\) | 15.6560 | 0.781823 | 0.390912 | − | 0.920428i | \(-0.372160\pi\) | ||||
0.390912 | + | 0.920428i | \(0.372160\pi\) | |||||||
\(402\) | 0.320458 | 0.0159830 | ||||||||
\(403\) | 55.4265 | 2.76099 | ||||||||
\(404\) | 62.7485 | 3.12185 | ||||||||
\(405\) | −19.0892 | −0.948549 | ||||||||
\(406\) | 32.0914 | 1.59267 | ||||||||
\(407\) | −7.14990 | −0.354407 | ||||||||
\(408\) | −120.409 | −5.96111 | ||||||||
\(409\) | 10.6639 | 0.527298 | 0.263649 | − | 0.964619i | \(-0.415074\pi\) | ||||
0.263649 | + | 0.964619i | \(0.415074\pi\) | |||||||
\(410\) | 37.0419 | 1.82937 | ||||||||
\(411\) | 16.5520 | 0.816449 | ||||||||
\(412\) | −22.4673 | −1.10688 | ||||||||
\(413\) | 3.76709 | 0.185366 | ||||||||
\(414\) | −104.858 | −5.15351 | ||||||||
\(415\) | −32.5951 | −1.60003 | ||||||||
\(416\) | −118.916 | −5.83033 | ||||||||
\(417\) | 30.7795 | 1.50728 | ||||||||
\(418\) | 9.42058 | 0.460776 | ||||||||
\(419\) | −17.6880 | −0.864113 | −0.432057 | − | 0.901847i | \(-0.642212\pi\) | ||||
−0.432057 | + | 0.901847i | \(0.642212\pi\) | |||||||
\(420\) | −240.546 | −11.7375 | ||||||||
\(421\) | −5.54481 | −0.270238 | −0.135119 | − | 0.990829i | \(-0.543142\pi\) | ||||
−0.135119 | + | 0.990829i | \(0.543142\pi\) | |||||||
\(422\) | −4.60325 | −0.224083 | ||||||||
\(423\) | 12.9107 | 0.627738 | ||||||||
\(424\) | −18.0196 | −0.875111 | ||||||||
\(425\) | −34.9040 | −1.69309 | ||||||||
\(426\) | −7.81870 | −0.378817 | ||||||||
\(427\) | 10.2498 | 0.496021 | ||||||||
\(428\) | 100.335 | 4.84987 | ||||||||
\(429\) | 13.6579 | 0.659408 | ||||||||
\(430\) | −79.4897 | −3.83333 | ||||||||
\(431\) | −14.7614 | −0.711031 | −0.355515 | − | 0.934670i | \(-0.615695\pi\) | ||||
−0.355515 | + | 0.934670i | \(0.615695\pi\) | |||||||
\(432\) | −108.518 | −5.22109 | ||||||||
\(433\) | −23.9551 | −1.15121 | −0.575603 | − | 0.817729i | \(-0.695233\pi\) | ||||
−0.575603 | + | 0.817729i | \(0.695233\pi\) | |||||||
\(434\) | 111.229 | 5.33916 | ||||||||
\(435\) | 29.2309 | 1.40152 | ||||||||
\(436\) | 20.9836 | 1.00493 | ||||||||
\(437\) | 29.4837 | 1.41040 | ||||||||
\(438\) | 57.8342 | 2.76343 | ||||||||
\(439\) | 17.5216 | 0.836261 | 0.418130 | − | 0.908387i | \(-0.362686\pi\) | ||||
0.418130 | + | 0.908387i | \(0.362686\pi\) | |||||||
\(440\) | −27.0056 | −1.28744 | ||||||||
\(441\) | 60.9867 | 2.90413 | ||||||||
\(442\) | 69.3637 | 3.29929 | ||||||||
\(443\) | −29.6975 | −1.41097 | −0.705485 | − | 0.708724i | \(-0.749271\pi\) | ||||
−0.705485 | + | 0.708724i | \(0.749271\pi\) | |||||||
\(444\) | −139.374 | −6.61438 | ||||||||
\(445\) | −11.2763 | −0.534549 | ||||||||
\(446\) | −40.1865 | −1.90288 | ||||||||
\(447\) | 38.4043 | 1.81646 | ||||||||
\(448\) | −116.471 | −5.50273 | ||||||||
\(449\) | 11.7012 | 0.552213 | 0.276106 | − | 0.961127i | \(-0.410956\pi\) | ||||
0.276106 | + | 0.961127i | \(0.410956\pi\) | |||||||
\(450\) | −119.288 | −5.62329 | ||||||||
\(451\) | −3.08095 | −0.145076 | ||||||||
\(452\) | 53.4027 | 2.51185 | ||||||||
\(453\) | −56.2704 | −2.64381 | ||||||||
\(454\) | −37.8294 | −1.77542 | ||||||||
\(455\) | 87.3117 | 4.09324 | ||||||||
\(456\) | 115.706 | 5.41845 | ||||||||
\(457\) | −21.8411 | −1.02168 | −0.510841 | − | 0.859675i | \(-0.670666\pi\) | ||||
−0.510841 | + | 0.859675i | \(0.670666\pi\) | |||||||
\(458\) | −37.1727 | −1.73697 | ||||||||
\(459\) | 33.3878 | 1.55841 | ||||||||
\(460\) | −134.140 | −6.25432 | ||||||||
\(461\) | −4.01641 | −0.187063 | −0.0935315 | − | 0.995616i | \(-0.529816\pi\) | ||||
−0.0935315 | + | 0.995616i | \(0.529816\pi\) | |||||||
\(462\) | 27.4084 | 1.27515 | ||||||||
\(463\) | −19.4102 | −0.902070 | −0.451035 | − | 0.892506i | \(-0.648945\pi\) | ||||
−0.451035 | + | 0.892506i | \(0.648945\pi\) | |||||||
\(464\) | 40.1327 | 1.86311 | ||||||||
\(465\) | 101.314 | 4.69834 | ||||||||
\(466\) | −16.3988 | −0.759660 | ||||||||
\(467\) | 19.9888 | 0.924971 | 0.462486 | − | 0.886627i | \(-0.346958\pi\) | ||||
0.462486 | + | 0.886627i | \(0.346958\pi\) | |||||||
\(468\) | 173.045 | 7.99902 | ||||||||
\(469\) | −0.170393 | −0.00786803 | ||||||||
\(470\) | 22.6255 | 1.04364 | ||||||||
\(471\) | 37.6341 | 1.73409 | ||||||||
\(472\) | 8.24408 | 0.379464 | ||||||||
\(473\) | 6.61154 | 0.303999 | ||||||||
\(474\) | 17.0575 | 0.783477 | ||||||||
\(475\) | 33.5410 | 1.53896 | ||||||||
\(476\) | 101.611 | 4.65731 | ||||||||
\(477\) | 10.8274 | 0.495754 | ||||||||
\(478\) | 23.2927 | 1.06538 | ||||||||
\(479\) | 15.4074 | 0.703980 | 0.351990 | − | 0.936004i | \(-0.385505\pi\) | ||||
0.351990 | + | 0.936004i | \(0.385505\pi\) | |||||||
\(480\) | −217.367 | −9.92141 | ||||||||
\(481\) | 50.5888 | 2.30665 | ||||||||
\(482\) | −71.7208 | −3.26679 | ||||||||
\(483\) | 85.7803 | 3.90314 | ||||||||
\(484\) | −55.9083 | −2.54129 | ||||||||
\(485\) | −60.2043 | −2.73373 | ||||||||
\(486\) | −19.0499 | −0.864123 | ||||||||
\(487\) | −4.73181 | −0.214419 | −0.107209 | − | 0.994236i | \(-0.534192\pi\) | ||||
−0.107209 | + | 0.994236i | \(0.534192\pi\) | |||||||
\(488\) | 22.4311 | 1.01541 | ||||||||
\(489\) | 4.31789 | 0.195262 | ||||||||
\(490\) | 106.877 | 4.82822 | ||||||||
\(491\) | 0.750374 | 0.0338639 | 0.0169320 | − | 0.999857i | \(-0.494610\pi\) | ||||
0.0169320 | + | 0.999857i | \(0.494610\pi\) | |||||||
\(492\) | −60.0571 | −2.70758 | ||||||||
\(493\) | −12.3476 | −0.556109 | ||||||||
\(494\) | −66.6549 | −2.99895 | ||||||||
\(495\) | 16.2268 | 0.729342 | ||||||||
\(496\) | 139.100 | 6.24577 | ||||||||
\(497\) | 4.15734 | 0.186482 | ||||||||
\(498\) | 72.3965 | 3.24416 | ||||||||
\(499\) | 41.9809 | 1.87932 | 0.939661 | − | 0.342107i | \(-0.111141\pi\) | ||||
0.939661 | + | 0.342107i | \(0.111141\pi\) | |||||||
\(500\) | −55.6254 | −2.48764 | ||||||||
\(501\) | 67.6937 | 3.02433 | ||||||||
\(502\) | 78.2330 | 3.49171 | ||||||||
\(503\) | 9.47672 | 0.422546 | 0.211273 | − | 0.977427i | \(-0.432239\pi\) | ||||
0.211273 | + | 0.977427i | \(0.432239\pi\) | |||||||
\(504\) | 218.806 | 9.74640 | ||||||||
\(505\) | −41.6324 | −1.85262 | ||||||||
\(506\) | 15.2842 | 0.679468 | ||||||||
\(507\) | −58.5769 | −2.60149 | ||||||||
\(508\) | −92.3395 | −4.09690 | ||||||||
\(509\) | 4.03027 | 0.178639 | 0.0893193 | − | 0.996003i | \(-0.471531\pi\) | ||||
0.0893193 | + | 0.996003i | \(0.471531\pi\) | |||||||
\(510\) | 126.790 | 5.61437 | ||||||||
\(511\) | −30.7515 | −1.36036 | ||||||||
\(512\) | −31.0776 | −1.37345 | ||||||||
\(513\) | −32.0840 | −1.41654 | ||||||||
\(514\) | 30.2016 | 1.33214 | ||||||||
\(515\) | 14.9066 | 0.656863 | ||||||||
\(516\) | 128.879 | 5.67359 | ||||||||
\(517\) | −1.88187 | −0.0827645 | ||||||||
\(518\) | 101.521 | 4.46056 | ||||||||
\(519\) | −47.7535 | −2.09614 | ||||||||
\(520\) | 191.077 | 8.37929 | ||||||||
\(521\) | −40.8989 | −1.79182 | −0.895908 | − | 0.444240i | \(-0.853474\pi\) | ||||
−0.895908 | + | 0.444240i | \(0.853474\pi\) | |||||||
\(522\) | −42.1992 | −1.84701 | ||||||||
\(523\) | 14.2369 | 0.622535 | 0.311267 | − | 0.950322i | \(-0.399247\pi\) | ||||
0.311267 | + | 0.950322i | \(0.399247\pi\) | |||||||
\(524\) | 110.995 | 4.84886 | ||||||||
\(525\) | 97.5846 | 4.25894 | ||||||||
\(526\) | 6.60611 | 0.288040 | ||||||||
\(527\) | −42.7968 | −1.86426 | ||||||||
\(528\) | 34.2762 | 1.49168 | ||||||||
\(529\) | 24.8353 | 1.07979 | ||||||||
\(530\) | 18.9747 | 0.824208 | ||||||||
\(531\) | −4.95360 | −0.214968 | ||||||||
\(532\) | −97.6425 | −4.23334 | ||||||||
\(533\) | 21.7991 | 0.944224 | ||||||||
\(534\) | 25.0457 | 1.08383 | ||||||||
\(535\) | −66.5702 | −2.87808 | ||||||||
\(536\) | −0.372897 | −0.0161067 | ||||||||
\(537\) | −31.2285 | −1.34761 | ||||||||
\(538\) | −54.4829 | −2.34892 | ||||||||
\(539\) | −8.88948 | −0.382897 | ||||||||
\(540\) | 145.971 | 6.28157 | ||||||||
\(541\) | 34.2061 | 1.47064 | 0.735318 | − | 0.677722i | \(-0.237033\pi\) | ||||
0.735318 | + | 0.677722i | \(0.237033\pi\) | |||||||
\(542\) | −5.51376 | −0.236836 | ||||||||
\(543\) | 39.1125 | 1.67848 | ||||||||
\(544\) | 91.8193 | 3.93672 | ||||||||
\(545\) | −13.9222 | −0.596361 | ||||||||
\(546\) | −193.927 | −8.29930 | ||||||||
\(547\) | 3.59229 | 0.153595 | 0.0767975 | − | 0.997047i | \(-0.475530\pi\) | ||||
0.0767975 | + | 0.997047i | \(0.475530\pi\) | |||||||
\(548\) | −30.5680 | −1.30580 | ||||||||
\(549\) | −13.4781 | −0.575232 | ||||||||
\(550\) | 17.3875 | 0.741406 | ||||||||
\(551\) | 11.8654 | 0.505484 | ||||||||
\(552\) | 187.726 | 7.99014 | ||||||||
\(553\) | −9.06977 | −0.385686 | ||||||||
\(554\) | −12.8068 | −0.544110 | ||||||||
\(555\) | 92.4716 | 3.92520 | ||||||||
\(556\) | −56.8432 | −2.41069 | ||||||||
\(557\) | −22.3462 | −0.946837 | −0.473419 | − | 0.880837i | \(-0.656980\pi\) | ||||
−0.473419 | + | 0.880837i | \(0.656980\pi\) | |||||||
\(558\) | −146.262 | −6.19178 | ||||||||
\(559\) | −46.7796 | −1.97857 | ||||||||
\(560\) | 219.120 | 9.25951 | ||||||||
\(561\) | −10.5458 | −0.445242 | ||||||||
\(562\) | −50.2760 | −2.12077 | ||||||||
\(563\) | −35.0493 | −1.47715 | −0.738576 | − | 0.674170i | \(-0.764502\pi\) | ||||
−0.738576 | + | 0.674170i | \(0.764502\pi\) | |||||||
\(564\) | −36.6834 | −1.54465 | ||||||||
\(565\) | −35.4316 | −1.49062 | ||||||||
\(566\) | −16.5040 | −0.693714 | ||||||||
\(567\) | −22.5441 | −0.946765 | ||||||||
\(568\) | 9.09812 | 0.381748 | ||||||||
\(569\) | 15.3310 | 0.642711 | 0.321355 | − | 0.946959i | \(-0.395862\pi\) | ||||
0.321355 | + | 0.946959i | \(0.395862\pi\) | |||||||
\(570\) | −121.839 | −5.10327 | ||||||||
\(571\) | −17.4641 | −0.730851 | −0.365425 | − | 0.930841i | \(-0.619076\pi\) | ||||
−0.365425 | + | 0.930841i | \(0.619076\pi\) | |||||||
\(572\) | −25.2232 | −1.05464 | ||||||||
\(573\) | 49.9197 | 2.08542 | ||||||||
\(574\) | 43.7461 | 1.82593 | ||||||||
\(575\) | 54.4179 | 2.26938 | ||||||||
\(576\) | 153.156 | 6.38148 | ||||||||
\(577\) | 11.6577 | 0.485317 | 0.242658 | − | 0.970112i | \(-0.421981\pi\) | ||||
0.242658 | + | 0.970112i | \(0.421981\pi\) | |||||||
\(578\) | −7.29246 | −0.303326 | ||||||||
\(579\) | −66.0793 | −2.74616 | ||||||||
\(580\) | −53.9834 | −2.24154 | ||||||||
\(581\) | −38.4945 | −1.59702 | ||||||||
\(582\) | 133.719 | 5.54282 | ||||||||
\(583\) | −1.57821 | −0.0653630 | ||||||||
\(584\) | −67.2980 | −2.78481 | ||||||||
\(585\) | −114.812 | −4.74690 | ||||||||
\(586\) | −76.5177 | −3.16092 | ||||||||
\(587\) | 12.9078 | 0.532761 | 0.266380 | − | 0.963868i | \(-0.414172\pi\) | ||||
0.266380 | + | 0.963868i | \(0.414172\pi\) | |||||||
\(588\) | −173.283 | −7.14608 | ||||||||
\(589\) | 41.1255 | 1.69455 | ||||||||
\(590\) | −8.68102 | −0.357392 | ||||||||
\(591\) | 10.1220 | 0.416361 | ||||||||
\(592\) | 126.959 | 5.21799 | ||||||||
\(593\) | 38.6077 | 1.58543 | 0.792713 | − | 0.609595i | \(-0.208668\pi\) | ||||
0.792713 | + | 0.609595i | \(0.208668\pi\) | |||||||
\(594\) | −16.6322 | −0.682428 | ||||||||
\(595\) | −67.4166 | −2.76381 | ||||||||
\(596\) | −70.9247 | −2.90519 | ||||||||
\(597\) | 68.7504 | 2.81377 | ||||||||
\(598\) | −108.143 | −4.42230 | ||||||||
\(599\) | −23.3478 | −0.953967 | −0.476983 | − | 0.878912i | \(-0.658270\pi\) | ||||
−0.476983 | + | 0.878912i | \(0.658270\pi\) | |||||||
\(600\) | 213.559 | 8.71850 | ||||||||
\(601\) | 16.0281 | 0.653800 | 0.326900 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326900 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(602\) | −93.8765 | −3.82612 | ||||||||
\(603\) | 0.224062 | 0.00912450 | ||||||||
\(604\) | 103.920 | 4.22843 | ||||||||
\(605\) | 37.0940 | 1.50809 | ||||||||
\(606\) | 92.4691 | 3.75630 | ||||||||
\(607\) | −14.5367 | −0.590025 | −0.295013 | − | 0.955493i | \(-0.595324\pi\) | ||||
−0.295013 | + | 0.955493i | \(0.595324\pi\) | |||||||
\(608\) | −88.2337 | −3.57835 | ||||||||
\(609\) | 34.5214 | 1.39888 | ||||||||
\(610\) | −23.6199 | −0.956343 | ||||||||
\(611\) | 13.3151 | 0.538670 | ||||||||
\(612\) | −133.615 | −5.40105 | ||||||||
\(613\) | 17.1730 | 0.693611 | 0.346805 | − | 0.937937i | \(-0.387266\pi\) | ||||
0.346805 | + | 0.937937i | \(0.387266\pi\) | |||||||
\(614\) | −15.8059 | −0.637873 | ||||||||
\(615\) | 39.8467 | 1.60677 | ||||||||
\(616\) | −31.8934 | −1.28502 | ||||||||
\(617\) | −16.3183 | −0.656952 | −0.328476 | − | 0.944512i | \(-0.606535\pi\) | ||||
−0.328476 | + | 0.944512i | \(0.606535\pi\) | |||||||
\(618\) | −33.1088 | −1.33183 | ||||||||
\(619\) | 10.2398 | 0.411571 | 0.205786 | − | 0.978597i | \(-0.434025\pi\) | ||||
0.205786 | + | 0.978597i | \(0.434025\pi\) | |||||||
\(620\) | −187.106 | −7.51438 | ||||||||
\(621\) | −52.0540 | −2.08886 | ||||||||
\(622\) | 8.91808 | 0.357582 | ||||||||
\(623\) | −13.3172 | −0.533543 | ||||||||
\(624\) | −242.520 | −9.70856 | ||||||||
\(625\) | −2.43393 | −0.0973574 | ||||||||
\(626\) | −48.1412 | −1.92411 | ||||||||
\(627\) | 10.1339 | 0.404710 | ||||||||
\(628\) | −69.5023 | −2.77344 | ||||||||
\(629\) | −39.0615 | −1.55748 | ||||||||
\(630\) | −230.403 | −9.17948 | ||||||||
\(631\) | −36.7811 | −1.46423 | −0.732116 | − | 0.681180i | \(-0.761467\pi\) | ||||
−0.732116 | + | 0.681180i | \(0.761467\pi\) | |||||||
\(632\) | −19.8487 | −0.789540 | ||||||||
\(633\) | −4.95182 | −0.196817 | ||||||||
\(634\) | 78.8400 | 3.13114 | ||||||||
\(635\) | 61.2654 | 2.43124 | ||||||||
\(636\) | −30.7643 | −1.21988 | ||||||||
\(637\) | 62.8971 | 2.49207 | ||||||||
\(638\) | 6.15100 | 0.243520 | ||||||||
\(639\) | −5.46677 | −0.216262 | ||||||||
\(640\) | 119.904 | 4.73964 | ||||||||
\(641\) | −20.5764 | −0.812721 | −0.406360 | − | 0.913713i | \(-0.633202\pi\) | ||||
−0.406360 | + | 0.913713i | \(0.633202\pi\) | |||||||
\(642\) | 147.858 | 5.83549 | ||||||||
\(643\) | −44.2443 | −1.74483 | −0.872413 | − | 0.488770i | \(-0.837446\pi\) | ||||
−0.872413 | + | 0.488770i | \(0.837446\pi\) | |||||||
\(644\) | −158.418 | −6.24255 | ||||||||
\(645\) | −85.5088 | −3.36691 | ||||||||
\(646\) | 51.4667 | 2.02493 | ||||||||
\(647\) | −23.6724 | −0.930658 | −0.465329 | − | 0.885138i | \(-0.654064\pi\) | ||||
−0.465329 | + | 0.885138i | \(0.654064\pi\) | |||||||
\(648\) | −49.3367 | −1.93813 | ||||||||
\(649\) | 0.722041 | 0.0283426 | ||||||||
\(650\) | −123.025 | −4.82542 | ||||||||
\(651\) | 119.651 | 4.68950 | ||||||||
\(652\) | −7.97425 | −0.312296 | ||||||||
\(653\) | 30.3736 | 1.18861 | 0.594306 | − | 0.804239i | \(-0.297427\pi\) | ||||
0.594306 | + | 0.804239i | \(0.297427\pi\) | |||||||
\(654\) | 30.9224 | 1.20916 | ||||||||
\(655\) | −73.6432 | −2.87748 | ||||||||
\(656\) | 54.7076 | 2.13597 | ||||||||
\(657\) | 40.4372 | 1.57761 | ||||||||
\(658\) | 26.7205 | 1.04167 | ||||||||
\(659\) | 48.8388 | 1.90249 | 0.951246 | − | 0.308434i | \(-0.0998050\pi\) | ||||
0.951246 | + | 0.308434i | \(0.0998050\pi\) | |||||||
\(660\) | −46.1057 | −1.79466 | ||||||||
\(661\) | −36.0454 | −1.40200 | −0.701002 | − | 0.713159i | \(-0.747264\pi\) | ||||
−0.701002 | + | 0.713159i | \(0.747264\pi\) | |||||||
\(662\) | 57.6235 | 2.23960 | ||||||||
\(663\) | 74.6160 | 2.89784 | ||||||||
\(664\) | −84.2431 | −3.26927 | ||||||||
\(665\) | 64.7839 | 2.51221 | ||||||||
\(666\) | −133.497 | −5.17289 | ||||||||
\(667\) | 19.2508 | 0.745395 | ||||||||
\(668\) | −125.016 | −4.83702 | ||||||||
\(669\) | −43.2294 | −1.67135 | ||||||||
\(670\) | 0.392660 | 0.0151698 | ||||||||
\(671\) | 1.96458 | 0.0758418 | ||||||||
\(672\) | −256.708 | −9.90274 | ||||||||
\(673\) | −12.3602 | −0.476451 | −0.238225 | − | 0.971210i | \(-0.576566\pi\) | ||||
−0.238225 | + | 0.971210i | \(0.576566\pi\) | |||||||
\(674\) | −42.7802 | −1.64783 | ||||||||
\(675\) | −59.2172 | −2.27927 | ||||||||
\(676\) | 108.179 | 4.16074 | ||||||||
\(677\) | −4.89405 | −0.188094 | −0.0940469 | − | 0.995568i | \(-0.529980\pi\) | ||||
−0.0940469 | + | 0.995568i | \(0.529980\pi\) | |||||||
\(678\) | 78.6967 | 3.02233 | ||||||||
\(679\) | −71.1006 | −2.72859 | ||||||||
\(680\) | −147.538 | −5.65781 | ||||||||
\(681\) | −40.6939 | −1.55940 | ||||||||
\(682\) | 21.3193 | 0.816360 | ||||||||
\(683\) | −10.0611 | −0.384976 | −0.192488 | − | 0.981299i | \(-0.561656\pi\) | ||||
−0.192488 | + | 0.981299i | \(0.561656\pi\) | |||||||
\(684\) | 128.397 | 4.90938 | ||||||||
\(685\) | 20.2813 | 0.774909 | ||||||||
\(686\) | 45.5137 | 1.73772 | ||||||||
\(687\) | −39.9875 | −1.52562 | ||||||||
\(688\) | −117.400 | −4.47581 | ||||||||
\(689\) | 11.1666 | 0.425413 | ||||||||
\(690\) | −197.675 | −7.52537 | ||||||||
\(691\) | 21.1330 | 0.803939 | 0.401970 | − | 0.915653i | \(-0.368326\pi\) | ||||
0.401970 | + | 0.915653i | \(0.368326\pi\) | |||||||
\(692\) | 88.1906 | 3.35251 | ||||||||
\(693\) | 19.1637 | 0.727969 | ||||||||
\(694\) | −4.66021 | −0.176899 | ||||||||
\(695\) | 37.7144 | 1.43059 | ||||||||
\(696\) | 75.5484 | 2.86365 | ||||||||
\(697\) | −16.8319 | −0.637553 | ||||||||
\(698\) | −82.7913 | −3.13370 | ||||||||
\(699\) | −17.6406 | −0.667227 | ||||||||
\(700\) | −180.218 | −6.81161 | ||||||||
\(701\) | −22.3977 | −0.845949 | −0.422974 | − | 0.906142i | \(-0.639014\pi\) | ||||
−0.422974 | + | 0.906142i | \(0.639014\pi\) | |||||||
\(702\) | 117.680 | 4.44156 | ||||||||
\(703\) | 37.5361 | 1.41570 | ||||||||
\(704\) | −22.3241 | −0.841370 | ||||||||
\(705\) | 24.3387 | 0.916649 | ||||||||
\(706\) | −8.45619 | −0.318253 | ||||||||
\(707\) | −49.1674 | −1.84913 | ||||||||
\(708\) | 14.0748 | 0.528964 | ||||||||
\(709\) | −11.1195 | −0.417601 | −0.208801 | − | 0.977958i | \(-0.566956\pi\) | ||||
−0.208801 | + | 0.977958i | \(0.566956\pi\) | |||||||
\(710\) | −9.58032 | −0.359543 | ||||||||
\(711\) | 11.9265 | 0.447277 | ||||||||
\(712\) | −29.1440 | −1.09222 | ||||||||
\(713\) | 66.7234 | 2.49881 | ||||||||
\(714\) | 149.738 | 5.60381 | ||||||||
\(715\) | 16.7351 | 0.625858 | ||||||||
\(716\) | 57.6725 | 2.15532 | ||||||||
\(717\) | 25.0564 | 0.935750 | ||||||||
\(718\) | −38.5689 | −1.43938 | ||||||||
\(719\) | 29.1072 | 1.08551 | 0.542757 | − | 0.839890i | \(-0.317380\pi\) | ||||
0.542757 | + | 0.839890i | \(0.317380\pi\) | |||||||
\(720\) | −288.136 | −10.7382 | ||||||||
\(721\) | 17.6045 | 0.655627 | ||||||||
\(722\) | 2.25195 | 0.0838089 | ||||||||
\(723\) | −77.1516 | −2.86930 | ||||||||
\(724\) | −72.2327 | −2.68451 | ||||||||
\(725\) | 21.8999 | 0.813344 | ||||||||
\(726\) | −82.3891 | −3.05774 | ||||||||
\(727\) | −19.7599 | −0.732854 | −0.366427 | − | 0.930447i | \(-0.619419\pi\) | ||||
−0.366427 | + | 0.930447i | \(0.619419\pi\) | |||||||
\(728\) | 225.660 | 8.36352 | ||||||||
\(729\) | −36.4568 | −1.35025 | ||||||||
\(730\) | 70.8648 | 2.62282 | ||||||||
\(731\) | 36.1203 | 1.33596 | ||||||||
\(732\) | 38.2957 | 1.41545 | ||||||||
\(733\) | −3.19649 | −0.118065 | −0.0590326 | − | 0.998256i | \(-0.518802\pi\) | ||||
−0.0590326 | + | 0.998256i | \(0.518802\pi\) | |||||||
\(734\) | 32.6384 | 1.20471 | ||||||||
\(735\) | 114.970 | 4.24073 | ||||||||
\(736\) | −143.153 | −5.27669 | ||||||||
\(737\) | −0.0326594 | −0.00120303 | ||||||||
\(738\) | −57.5247 | −2.11751 | ||||||||
\(739\) | 23.4764 | 0.863595 | 0.431797 | − | 0.901971i | \(-0.357880\pi\) | ||||
0.431797 | + | 0.901971i | \(0.357880\pi\) | |||||||
\(740\) | −170.776 | −6.27784 | ||||||||
\(741\) | −71.7021 | −2.63404 | ||||||||
\(742\) | 22.4089 | 0.822657 | ||||||||
\(743\) | 22.2324 | 0.815626 | 0.407813 | − | 0.913065i | \(-0.366291\pi\) | ||||
0.407813 | + | 0.913065i | \(0.366291\pi\) | |||||||
\(744\) | 261.851 | 9.59991 | ||||||||
\(745\) | 47.0572 | 1.72404 | ||||||||
\(746\) | −64.5692 | −2.36405 | ||||||||
\(747\) | 50.6190 | 1.85205 | ||||||||
\(748\) | 19.4758 | 0.712106 | ||||||||
\(749\) | −78.6187 | −2.87266 | ||||||||
\(750\) | −81.9722 | −2.99320 | ||||||||
\(751\) | 53.0732 | 1.93667 | 0.968334 | − | 0.249659i | \(-0.0803184\pi\) | ||||
0.968334 | + | 0.249659i | \(0.0803184\pi\) | |||||||
\(752\) | 33.4159 | 1.21855 | ||||||||
\(753\) | 84.1569 | 3.06685 | ||||||||
\(754\) | −43.5211 | −1.58494 | ||||||||
\(755\) | −68.9486 | −2.50930 | ||||||||
\(756\) | 172.390 | 6.26975 | ||||||||
\(757\) | −24.7941 | −0.901158 | −0.450579 | − | 0.892737i | \(-0.648782\pi\) | ||||
−0.450579 | + | 0.892737i | \(0.648782\pi\) | |||||||
\(758\) | 37.2635 | 1.35347 | ||||||||
\(759\) | 16.4416 | 0.596792 | ||||||||
\(760\) | 141.776 | 5.14276 | ||||||||
\(761\) | −14.2001 | −0.514753 | −0.257377 | − | 0.966311i | \(-0.582858\pi\) | ||||
−0.257377 | + | 0.966311i | \(0.582858\pi\) | |||||||
\(762\) | −136.076 | −4.92951 | ||||||||
\(763\) | −16.4420 | −0.595239 | ||||||||
\(764\) | −92.1911 | −3.33536 | ||||||||
\(765\) | 88.6507 | 3.20517 | ||||||||
\(766\) | −75.0116 | −2.71028 | ||||||||
\(767\) | −5.10877 | −0.184467 | ||||||||
\(768\) | −105.344 | −3.80127 | ||||||||
\(769\) | −53.0620 | −1.91346 | −0.956732 | − | 0.290971i | \(-0.906022\pi\) | ||||
−0.956732 | + | 0.290971i | \(0.906022\pi\) | |||||||
\(770\) | 33.5838 | 1.21027 | ||||||||
\(771\) | 32.4885 | 1.17005 | ||||||||
\(772\) | 122.035 | 4.39212 | ||||||||
\(773\) | 41.3255 | 1.48637 | 0.743187 | − | 0.669084i | \(-0.233313\pi\) | ||||
0.743187 | + | 0.669084i | \(0.233313\pi\) | |||||||
\(774\) | 123.445 | 4.43713 | ||||||||
\(775\) | 75.9052 | 2.72659 | ||||||||
\(776\) | −155.600 | −5.58571 | ||||||||
\(777\) | 109.208 | 3.91782 | ||||||||
\(778\) | −63.2450 | −2.26744 | ||||||||
\(779\) | 16.1746 | 0.579515 | ||||||||
\(780\) | 326.219 | 11.6805 | ||||||||
\(781\) | 0.796841 | 0.0285132 | ||||||||
\(782\) | 83.5012 | 2.98600 | ||||||||
\(783\) | −20.9486 | −0.748643 | ||||||||
\(784\) | 157.848 | 5.63744 | ||||||||
\(785\) | 46.1134 | 1.64586 | ||||||||
\(786\) | 163.568 | 5.83428 | ||||||||
\(787\) | 13.6572 | 0.486826 | 0.243413 | − | 0.969923i | \(-0.421733\pi\) | ||||
0.243413 | + | 0.969923i | \(0.421733\pi\) | |||||||
\(788\) | −18.6931 | −0.665915 | ||||||||
\(789\) | 7.10634 | 0.252992 | ||||||||
\(790\) | 20.9007 | 0.743614 | ||||||||
\(791\) | −41.8444 | −1.48781 | ||||||||
\(792\) | 41.9388 | 1.49023 | ||||||||
\(793\) | −13.9003 | −0.493614 | ||||||||
\(794\) | 6.89203 | 0.244589 | ||||||||
\(795\) | 20.4115 | 0.723921 | ||||||||
\(796\) | −126.968 | −4.50025 | ||||||||
\(797\) | 31.8186 | 1.12707 | 0.563537 | − | 0.826091i | \(-0.309440\pi\) | ||||
0.563537 | + | 0.826091i | \(0.309440\pi\) | |||||||
\(798\) | −143.891 | −5.09367 | ||||||||
\(799\) | −10.2811 | −0.363718 | ||||||||
\(800\) | −162.852 | −5.75770 | ||||||||
\(801\) | 17.5117 | 0.618746 | ||||||||
\(802\) | −42.6081 | −1.50454 | ||||||||
\(803\) | −5.89416 | −0.208001 | ||||||||
\(804\) | −0.636633 | −0.0224523 | ||||||||
\(805\) | 105.107 | 3.70455 | ||||||||
\(806\) | −150.844 | −5.31325 | ||||||||
\(807\) | −58.6084 | −2.06311 | ||||||||
\(808\) | −107.600 | −3.78537 | ||||||||
\(809\) | −27.7781 | −0.976627 | −0.488314 | − | 0.872668i | \(-0.662388\pi\) | ||||
−0.488314 | + | 0.872668i | \(0.662388\pi\) | |||||||
\(810\) | 51.9515 | 1.82539 | ||||||||
\(811\) | −22.4548 | −0.788496 | −0.394248 | − | 0.919004i | \(-0.628995\pi\) | ||||
−0.394248 | + | 0.919004i | \(0.628995\pi\) | |||||||
\(812\) | −63.7539 | −2.23732 | ||||||||
\(813\) | −5.93127 | −0.208019 | ||||||||
\(814\) | 19.4586 | 0.682023 | ||||||||
\(815\) | 5.29075 | 0.185327 | ||||||||
\(816\) | 187.258 | 6.55536 | ||||||||
\(817\) | −34.7097 | −1.21434 | ||||||||
\(818\) | −29.0221 | −1.01473 | ||||||||
\(819\) | −135.592 | −4.73797 | ||||||||
\(820\) | −73.5886 | −2.56982 | ||||||||
\(821\) | −6.25950 | −0.218458 | −0.109229 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109229 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(822\) | −45.0465 | −1.57118 | ||||||||
\(823\) | 45.8724 | 1.59901 | 0.799505 | − | 0.600659i | \(-0.205095\pi\) | ||||
0.799505 | + | 0.600659i | \(0.205095\pi\) | |||||||
\(824\) | 38.5266 | 1.34214 | ||||||||
\(825\) | 18.7041 | 0.651194 | ||||||||
\(826\) | −10.2522 | −0.356719 | ||||||||
\(827\) | −11.2671 | −0.391796 | −0.195898 | − | 0.980624i | \(-0.562762\pi\) | ||||
−0.195898 | + | 0.980624i | \(0.562762\pi\) | |||||||
\(828\) | 208.315 | 7.23945 | ||||||||
\(829\) | −17.4260 | −0.605229 | −0.302615 | − | 0.953113i | \(-0.597860\pi\) | ||||
−0.302615 | + | 0.953113i | \(0.597860\pi\) | |||||||
\(830\) | 88.7081 | 3.07910 | ||||||||
\(831\) | −13.7766 | −0.477904 | ||||||||
\(832\) | 157.953 | 5.47604 | ||||||||
\(833\) | −48.5652 | −1.68268 | ||||||||
\(834\) | −83.7668 | −2.90061 | ||||||||
\(835\) | 82.9457 | 2.87046 | ||||||||
\(836\) | −18.7152 | −0.647280 | ||||||||
\(837\) | −72.6079 | −2.50970 | ||||||||
\(838\) | 48.1381 | 1.66290 | ||||||||
\(839\) | −20.2186 | −0.698022 | −0.349011 | − | 0.937119i | \(-0.613482\pi\) | ||||
−0.349011 | + | 0.937119i | \(0.613482\pi\) | |||||||
\(840\) | 412.486 | 14.2321 | ||||||||
\(841\) | −21.2527 | −0.732851 | ||||||||
\(842\) | 15.0903 | 0.520046 | ||||||||
\(843\) | −54.0830 | −1.86272 | ||||||||
\(844\) | 9.14497 | 0.314783 | ||||||||
\(845\) | −71.7749 | −2.46913 | ||||||||
\(846\) | −35.1366 | −1.20802 | ||||||||
\(847\) | 43.8077 | 1.50525 | ||||||||
\(848\) | 28.0240 | 0.962348 | ||||||||
\(849\) | −17.7537 | −0.609305 | ||||||||
\(850\) | 94.9918 | 3.25819 | ||||||||
\(851\) | 60.8997 | 2.08761 | ||||||||
\(852\) | 15.5329 | 0.532148 | ||||||||
\(853\) | 23.9744 | 0.820867 | 0.410433 | − | 0.911891i | \(-0.365377\pi\) | ||||
0.410433 | + | 0.911891i | \(0.365377\pi\) | |||||||
\(854\) | −27.8949 | −0.954544 | ||||||||
\(855\) | −85.1888 | −2.91339 | ||||||||
\(856\) | −172.053 | −5.88065 | ||||||||
\(857\) | 18.3770 | 0.627745 | 0.313872 | − | 0.949465i | \(-0.398374\pi\) | ||||
0.313872 | + | 0.949465i | \(0.398374\pi\) | |||||||
\(858\) | −37.1701 | −1.26897 | ||||||||
\(859\) | −11.1695 | −0.381098 | −0.190549 | − | 0.981678i | \(-0.561027\pi\) | ||||
−0.190549 | + | 0.981678i | \(0.561027\pi\) | |||||||
\(860\) | 157.917 | 5.38492 | ||||||||
\(861\) | 47.0586 | 1.60375 | ||||||||
\(862\) | 40.1733 | 1.36831 | ||||||||
\(863\) | −17.4980 | −0.595638 | −0.297819 | − | 0.954622i | \(-0.596259\pi\) | ||||
−0.297819 | + | 0.954622i | \(0.596259\pi\) | |||||||
\(864\) | 155.778 | 5.29968 | ||||||||
\(865\) | −58.5128 | −1.98949 | ||||||||
\(866\) | 65.1941 | 2.21539 | ||||||||
\(867\) | −7.84465 | −0.266418 | ||||||||
\(868\) | −220.971 | −7.50024 | ||||||||
\(869\) | −1.73841 | −0.0589716 | ||||||||
\(870\) | −79.5525 | −2.69708 | ||||||||
\(871\) | 0.231080 | 0.00782986 | ||||||||
\(872\) | −35.9824 | −1.21852 | ||||||||
\(873\) | 93.4951 | 3.16433 | ||||||||
\(874\) | −80.2404 | −2.71417 | ||||||||
\(875\) | 43.5860 | 1.47348 | ||||||||
\(876\) | −114.895 | −3.88195 | ||||||||
\(877\) | −7.43542 | −0.251076 | −0.125538 | − | 0.992089i | \(-0.540066\pi\) | ||||
−0.125538 | + | 0.992089i | \(0.540066\pi\) | |||||||
\(878\) | −47.6853 | −1.60930 | ||||||||
\(879\) | −82.3118 | −2.77631 | ||||||||
\(880\) | 41.9989 | 1.41578 | ||||||||
\(881\) | −21.9400 | −0.739176 | −0.369588 | − | 0.929196i | \(-0.620501\pi\) | ||||
−0.369588 | + | 0.929196i | \(0.620501\pi\) | |||||||
\(882\) | −165.976 | −5.58872 | ||||||||
\(883\) | −20.6143 | −0.693727 | −0.346863 | − | 0.937916i | \(-0.612753\pi\) | ||||
−0.346863 | + | 0.937916i | \(0.612753\pi\) | |||||||
\(884\) | −137.800 | −4.63472 | ||||||||
\(885\) | −9.33836 | −0.313905 | ||||||||
\(886\) | 80.8222 | 2.71528 | ||||||||
\(887\) | −10.1581 | −0.341075 | −0.170538 | − | 0.985351i | \(-0.554550\pi\) | ||||
−0.170538 | + | 0.985351i | \(0.554550\pi\) | |||||||
\(888\) | 238.996 | 8.02018 | ||||||||
\(889\) | 72.3539 | 2.42667 | ||||||||
\(890\) | 30.6887 | 1.02869 | ||||||||
\(891\) | −4.32106 | −0.144761 | ||||||||
\(892\) | 79.8357 | 2.67310 | ||||||||
\(893\) | 9.87957 | 0.330607 | ||||||||
\(894\) | −104.518 | −3.49561 | ||||||||
\(895\) | −38.2646 | −1.27904 | ||||||||
\(896\) | 141.606 | 4.73072 | ||||||||
\(897\) | −116.332 | −3.88420 | ||||||||
\(898\) | −31.8450 | −1.06268 | ||||||||
\(899\) | 26.8522 | 0.895570 | ||||||||
\(900\) | 236.981 | 7.89938 | ||||||||
\(901\) | −8.62214 | −0.287245 | ||||||||
\(902\) | 8.38485 | 0.279185 | ||||||||
\(903\) | −100.985 | −3.36057 | ||||||||
\(904\) | −91.5743 | −3.04571 | ||||||||
\(905\) | 47.9250 | 1.59308 | ||||||||
\(906\) | 153.141 | 5.08776 | ||||||||
\(907\) | −8.96702 | −0.297745 | −0.148873 | − | 0.988856i | \(-0.547564\pi\) | ||||
−0.148873 | + | 0.988856i | \(0.547564\pi\) | |||||||
\(908\) | 75.1532 | 2.49405 | ||||||||
\(909\) | 64.6536 | 2.14442 | ||||||||
\(910\) | −237.620 | −7.87704 | ||||||||
\(911\) | −38.6670 | −1.28109 | −0.640547 | − | 0.767919i | \(-0.721292\pi\) | ||||
−0.640547 | + | 0.767919i | \(0.721292\pi\) | |||||||
\(912\) | −179.946 | −5.95860 | ||||||||
\(913\) | −7.37827 | −0.244185 | ||||||||
\(914\) | 59.4409 | 1.96613 | ||||||||
\(915\) | −25.4085 | −0.839978 | ||||||||
\(916\) | 73.8485 | 2.44002 | ||||||||
\(917\) | −86.9719 | −2.87207 | ||||||||
\(918\) | −90.8655 | −2.99901 | ||||||||
\(919\) | −11.9509 | −0.394224 | −0.197112 | − | 0.980381i | \(-0.563156\pi\) | ||||
−0.197112 | + | 0.980381i | \(0.563156\pi\) | |||||||
\(920\) | 230.022 | 7.58360 | ||||||||
\(921\) | −17.0027 | −0.560258 | ||||||||
\(922\) | 10.9307 | 0.359984 | ||||||||
\(923\) | −5.63801 | −0.185577 | ||||||||
\(924\) | −54.4504 | −1.79129 | ||||||||
\(925\) | 69.2801 | 2.27792 | ||||||||
\(926\) | 52.8253 | 1.73595 | ||||||||
\(927\) | −23.1494 | −0.760326 | ||||||||
\(928\) | −57.6105 | −1.89116 | ||||||||
\(929\) | −26.9891 | −0.885483 | −0.442741 | − | 0.896649i | \(-0.645994\pi\) | ||||
−0.442741 | + | 0.896649i | \(0.645994\pi\) | |||||||
\(930\) | −275.729 | −9.04150 | ||||||||
\(931\) | 46.6686 | 1.52950 | ||||||||
\(932\) | 32.5784 | 1.06714 | ||||||||
\(933\) | 9.59337 | 0.314073 | ||||||||
\(934\) | −54.3998 | −1.78002 | ||||||||
\(935\) | −12.9218 | −0.422588 | ||||||||
\(936\) | −296.736 | −9.69912 | ||||||||
\(937\) | 1.75980 | 0.0574903 | 0.0287451 | − | 0.999587i | \(-0.490849\pi\) | ||||
0.0287451 | + | 0.999587i | \(0.490849\pi\) | |||||||
\(938\) | 0.463728 | 0.0151413 | ||||||||
\(939\) | −51.7865 | −1.68999 | ||||||||
\(940\) | −44.9485 | −1.46606 | ||||||||
\(941\) | 29.1840 | 0.951370 | 0.475685 | − | 0.879616i | \(-0.342200\pi\) | ||||
0.475685 | + | 0.879616i | \(0.342200\pi\) | |||||||
\(942\) | −102.422 | −3.33708 | ||||||||
\(943\) | 26.2421 | 0.854562 | ||||||||
\(944\) | −12.8211 | −0.417292 | ||||||||
\(945\) | −114.377 | −3.72069 | ||||||||
\(946\) | −17.9934 | −0.585016 | ||||||||
\(947\) | 18.9016 | 0.614220 | 0.307110 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307110 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(948\) | −33.8870 | −1.10060 | ||||||||
\(949\) | 41.7039 | 1.35377 | ||||||||
\(950\) | −91.2823 | −2.96159 | ||||||||
\(951\) | 84.8099 | 2.75015 | ||||||||
\(952\) | −174.241 | −5.64717 | ||||||||
\(953\) | 7.67814 | 0.248719 | 0.124360 | − | 0.992237i | \(-0.460312\pi\) | ||||
0.124360 | + | 0.992237i | \(0.460312\pi\) | |||||||
\(954\) | −29.4670 | −0.954030 | ||||||||
\(955\) | 61.1670 | 1.97932 | ||||||||
\(956\) | −46.2740 | −1.49661 | ||||||||
\(957\) | 6.61676 | 0.213889 | ||||||||
\(958\) | −41.9314 | −1.35474 | ||||||||
\(959\) | 23.9520 | 0.773451 | ||||||||
\(960\) | 288.723 | 9.31851 | ||||||||
\(961\) | 62.0695 | 2.00224 | ||||||||
\(962\) | −137.678 | −4.43893 | ||||||||
\(963\) | 103.381 | 3.33141 | ||||||||
\(964\) | 142.483 | 4.58906 | ||||||||
\(965\) | −80.9675 | −2.60644 | ||||||||
\(966\) | −233.453 | −7.51121 | ||||||||
\(967\) | 3.75610 | 0.120788 | 0.0603941 | − | 0.998175i | \(-0.480764\pi\) | ||||
0.0603941 | + | 0.998175i | \(0.480764\pi\) | |||||||
\(968\) | 95.8709 | 3.08141 | ||||||||
\(969\) | 55.3639 | 1.77854 | ||||||||
\(970\) | 163.847 | 5.26081 | ||||||||
\(971\) | 4.51861 | 0.145009 | 0.0725046 | − | 0.997368i | \(-0.476901\pi\) | ||||
0.0725046 | + | 0.997368i | \(0.476901\pi\) | |||||||
\(972\) | 37.8452 | 1.21389 | ||||||||
\(973\) | 44.5403 | 1.42790 | ||||||||
\(974\) | 12.8777 | 0.412628 | ||||||||
\(975\) | −132.340 | −4.23828 | ||||||||
\(976\) | −34.8846 | −1.11663 | ||||||||
\(977\) | −33.4235 | −1.06931 | −0.534656 | − | 0.845070i | \(-0.679559\pi\) | ||||
−0.534656 | + | 0.845070i | \(0.679559\pi\) | |||||||
\(978\) | −11.7512 | −0.375763 | ||||||||
\(979\) | −2.55252 | −0.0815790 | ||||||||
\(980\) | −212.326 | −6.78249 | ||||||||
\(981\) | 21.6206 | 0.690294 | ||||||||
\(982\) | −2.04216 | −0.0651678 | ||||||||
\(983\) | 6.74209 | 0.215039 | 0.107520 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107520 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(984\) | 102.985 | 3.28305 | ||||||||
\(985\) | 12.4025 | 0.395177 | ||||||||
\(986\) | 33.6042 | 1.07018 | ||||||||
\(987\) | 28.7438 | 0.914924 | ||||||||
\(988\) | 132.419 | 4.21280 | ||||||||
\(989\) | −56.3141 | −1.79069 | ||||||||
\(990\) | −44.1616 | −1.40355 | ||||||||
\(991\) | −36.3277 | −1.15399 | −0.576994 | − | 0.816749i | \(-0.695774\pi\) | ||||
−0.576994 | + | 0.816749i | \(0.695774\pi\) | |||||||
\(992\) | −199.678 | −6.33978 | ||||||||
\(993\) | 61.9869 | 1.96709 | ||||||||
\(994\) | −11.3143 | −0.358867 | ||||||||
\(995\) | 84.2405 | 2.67060 | ||||||||
\(996\) | −143.825 | −4.55728 | ||||||||
\(997\) | −16.4234 | −0.520133 | −0.260067 | − | 0.965591i | \(-0.583745\pi\) | ||||
−0.260067 | + | 0.965591i | \(0.583745\pi\) | |||||||
\(998\) | −114.252 | −3.61657 | ||||||||
\(999\) | −66.2706 | −2.09671 |
(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 | 4019.2.a.b.1.5 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.5 | ✓ | 186 | 1.1 | even | 1 | trivial |