Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32413 | −0.936301 | −0.468150 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468150 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.246682 | −0.123341 | ||||||||
\(5\) | 4.03355 | 1.80386 | 0.901929 | − | 0.431885i | \(-0.142151\pi\) | ||||
0.901929 | + | 0.431885i | \(0.142151\pi\) | |||||||
\(6\) | −1.32413 | −0.540573 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.97490 | 1.05178 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −5.34094 | −1.68895 | ||||||||
\(11\) | 4.32013 | 1.30257 | 0.651283 | − | 0.758835i | \(-0.274231\pi\) | ||||
0.651283 | + | 0.758835i | \(0.274231\pi\) | |||||||
\(12\) | −0.246682 | −0.0712109 | ||||||||
\(13\) | 1.67689 | 0.465085 | 0.232542 | − | 0.972586i | \(-0.425296\pi\) | ||||
0.232542 | + | 0.972586i | \(0.425296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.03355 | 1.04146 | ||||||||
\(16\) | −3.44578 | −0.861446 | ||||||||
\(17\) | −1.53497 | −0.372285 | −0.186143 | − | 0.982523i | \(-0.559599\pi\) | ||||
−0.186143 | + | 0.982523i | \(0.559599\pi\) | |||||||
\(18\) | −1.32413 | −0.312100 | ||||||||
\(19\) | 4.63220 | 1.06270 | 0.531350 | − | 0.847152i | \(-0.321685\pi\) | ||||
0.531350 | + | 0.847152i | \(0.321685\pi\) | |||||||
\(20\) | −0.995003 | −0.222489 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.72040 | −1.21959 | ||||||||
\(23\) | 1.68322 | 0.350977 | 0.175488 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175488 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(24\) | 2.97490 | 0.607248 | ||||||||
\(25\) | 11.2695 | 2.25390 | ||||||||
\(26\) | −2.22041 | −0.435459 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.19131 | 1.14970 | 0.574848 | − | 0.818260i | \(-0.305061\pi\) | ||||
0.574848 | + | 0.818260i | \(0.305061\pi\) | |||||||
\(30\) | −5.34094 | −0.975117 | ||||||||
\(31\) | −7.82172 | −1.40482 | −0.702411 | − | 0.711772i | \(-0.747893\pi\) | ||||
−0.702411 | + | 0.711772i | \(0.747893\pi\) | |||||||
\(32\) | −1.38713 | −0.245212 | ||||||||
\(33\) | 4.32013 | 0.752037 | ||||||||
\(34\) | 2.03250 | 0.348571 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.246682 | −0.0411136 | ||||||||
\(37\) | 5.18274 | 0.852038 | 0.426019 | − | 0.904714i | \(-0.359916\pi\) | ||||
0.426019 | + | 0.904714i | \(0.359916\pi\) | |||||||
\(38\) | −6.13364 | −0.995007 | ||||||||
\(39\) | 1.67689 | 0.268517 | ||||||||
\(40\) | 11.9994 | 1.89727 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.53487 | 0.691561 | 0.345780 | − | 0.938316i | \(-0.387614\pi\) | ||||
0.345780 | + | 0.938316i | \(0.387614\pi\) | |||||||
\(44\) | −1.06570 | −0.160660 | ||||||||
\(45\) | 4.03355 | 0.601286 | ||||||||
\(46\) | −2.22881 | −0.328620 | ||||||||
\(47\) | −7.25662 | −1.05849 | −0.529243 | − | 0.848470i | \(-0.677524\pi\) | ||||
−0.529243 | + | 0.848470i | \(0.677524\pi\) | |||||||
\(48\) | −3.44578 | −0.497356 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −14.9223 | −2.11033 | ||||||||
\(51\) | −1.53497 | −0.214939 | ||||||||
\(52\) | −0.413657 | −0.0573639 | ||||||||
\(53\) | −1.52553 | −0.209547 | −0.104774 | − | 0.994496i | \(-0.533412\pi\) | ||||
−0.104774 | + | 0.994496i | \(0.533412\pi\) | |||||||
\(54\) | −1.32413 | −0.180191 | ||||||||
\(55\) | 17.4254 | 2.34964 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.63220 | 0.613550 | ||||||||
\(58\) | −8.19809 | −1.07646 | ||||||||
\(59\) | 6.75314 | 0.879183 | 0.439592 | − | 0.898198i | \(-0.355123\pi\) | ||||
0.439592 | + | 0.898198i | \(0.355123\pi\) | |||||||
\(60\) | −0.995003 | −0.128454 | ||||||||
\(61\) | −1.19486 | −0.152986 | −0.0764931 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764931 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(62\) | 10.3570 | 1.31534 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.72831 | 1.09104 | ||||||||
\(65\) | 6.76380 | 0.838946 | ||||||||
\(66\) | −5.72040 | −0.704133 | ||||||||
\(67\) | 3.40655 | 0.416176 | 0.208088 | − | 0.978110i | \(-0.433276\pi\) | ||||
0.208088 | + | 0.978110i | \(0.433276\pi\) | |||||||
\(68\) | 0.378649 | 0.0459180 | ||||||||
\(69\) | 1.68322 | 0.202636 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.5966 | −1.96965 | −0.984825 | − | 0.173548i | \(-0.944477\pi\) | ||||
−0.984825 | + | 0.173548i | \(0.944477\pi\) | |||||||
\(72\) | 2.97490 | 0.350595 | ||||||||
\(73\) | −5.99200 | −0.701310 | −0.350655 | − | 0.936505i | \(-0.614041\pi\) | ||||
−0.350655 | + | 0.936505i | \(0.614041\pi\) | |||||||
\(74\) | −6.86262 | −0.797763 | ||||||||
\(75\) | 11.2695 | 1.30129 | ||||||||
\(76\) | −1.14268 | −0.131074 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.22041 | −0.251412 | ||||||||
\(79\) | 5.84022 | 0.657076 | 0.328538 | − | 0.944491i | \(-0.393444\pi\) | ||||
0.328538 | + | 0.944491i | \(0.393444\pi\) | |||||||
\(80\) | −13.8987 | −1.55393 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.32413 | 0.146226 | ||||||||
\(83\) | −0.0883750 | −0.00970042 | −0.00485021 | − | 0.999988i | \(-0.501544\pi\) | ||||
−0.00485021 | + | 0.999988i | \(0.501544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.19138 | −0.671549 | ||||||||
\(86\) | −6.00475 | −0.647509 | ||||||||
\(87\) | 6.19131 | 0.663778 | ||||||||
\(88\) | 12.8519 | 1.37002 | ||||||||
\(89\) | 10.4911 | 1.11206 | 0.556028 | − | 0.831164i | \(-0.312325\pi\) | ||||
0.556028 | + | 0.831164i | \(0.312325\pi\) | |||||||
\(90\) | −5.34094 | −0.562984 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.415221 | −0.0432898 | ||||||||
\(93\) | −7.82172 | −0.811074 | ||||||||
\(94\) | 9.60870 | 0.991062 | ||||||||
\(95\) | 18.6842 | 1.91696 | ||||||||
\(96\) | −1.38713 | −0.141573 | ||||||||
\(97\) | −2.82381 | −0.286714 | −0.143357 | − | 0.989671i | \(-0.545790\pi\) | ||||
−0.143357 | + | 0.989671i | \(0.545790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.32013 | 0.434189 | ||||||||
\(100\) | −2.77998 | −0.277998 | ||||||||
\(101\) | −8.90913 | −0.886491 | −0.443246 | − | 0.896400i | \(-0.646173\pi\) | ||||
−0.443246 | + | 0.896400i | \(0.646173\pi\) | |||||||
\(102\) | 2.03250 | 0.201247 | ||||||||
\(103\) | 13.2664 | 1.30717 | 0.653587 | − | 0.756852i | \(-0.273263\pi\) | ||||
0.653587 | + | 0.756852i | \(0.273263\pi\) | |||||||
\(104\) | 4.98856 | 0.489169 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.01999 | 0.196199 | ||||||||
\(107\) | −5.74268 | −0.555166 | −0.277583 | − | 0.960702i | \(-0.589533\pi\) | ||||
−0.277583 | + | 0.960702i | \(0.589533\pi\) | |||||||
\(108\) | −0.246682 | −0.0237370 | ||||||||
\(109\) | 4.22346 | 0.404534 | 0.202267 | − | 0.979330i | \(-0.435169\pi\) | ||||
0.202267 | + | 0.979330i | \(0.435169\pi\) | |||||||
\(110\) | −23.0735 | −2.19997 | ||||||||
\(111\) | 5.18274 | 0.491924 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5807 | −1.08942 | −0.544712 | − | 0.838623i | \(-0.683361\pi\) | ||||
−0.544712 | + | 0.838623i | \(0.683361\pi\) | |||||||
\(114\) | −6.13364 | −0.574468 | ||||||||
\(115\) | 6.78937 | 0.633112 | ||||||||
\(116\) | −1.52728 | −0.141805 | ||||||||
\(117\) | 1.67689 | 0.155028 | ||||||||
\(118\) | −8.94203 | −0.823180 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 11.9994 | 1.09539 | ||||||||
\(121\) | 7.66349 | 0.696681 | ||||||||
\(122\) | 1.58215 | 0.143241 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 1.92947 | 0.173272 | ||||||||
\(125\) | 25.2883 | 2.26186 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8178 | −0.959923 | −0.479961 | − | 0.877290i | \(-0.659349\pi\) | ||||
−0.479961 | + | 0.877290i | \(0.659349\pi\) | |||||||
\(128\) | −8.78315 | −0.776328 | ||||||||
\(129\) | 4.53487 | 0.399273 | ||||||||
\(130\) | −8.95615 | −0.785506 | ||||||||
\(131\) | 5.17202 | 0.451881 | 0.225941 | − | 0.974141i | \(-0.427454\pi\) | ||||
0.225941 | + | 0.974141i | \(0.427454\pi\) | |||||||
\(132\) | −1.06570 | −0.0927570 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.51071 | −0.389666 | ||||||||
\(135\) | 4.03355 | 0.347152 | ||||||||
\(136\) | −4.56638 | −0.391564 | ||||||||
\(137\) | −11.4202 | −0.975692 | −0.487846 | − | 0.872930i | \(-0.662217\pi\) | ||||
−0.487846 | + | 0.872930i | \(0.662217\pi\) | |||||||
\(138\) | −2.22881 | −0.189729 | ||||||||
\(139\) | −15.9859 | −1.35591 | −0.677954 | − | 0.735105i | \(-0.737133\pi\) | ||||
−0.677954 | + | 0.735105i | \(0.737133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.25662 | −0.611118 | ||||||||
\(142\) | 21.9760 | 1.84419 | ||||||||
\(143\) | 7.24436 | 0.605804 | ||||||||
\(144\) | −3.44578 | −0.287149 | ||||||||
\(145\) | 24.9729 | 2.07389 | ||||||||
\(146\) | 7.93418 | 0.656637 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.27849 | −0.105091 | ||||||||
\(149\) | 0.835425 | 0.0684407 | 0.0342203 | − | 0.999414i | \(-0.489105\pi\) | ||||
0.0342203 | + | 0.999414i | \(0.489105\pi\) | |||||||
\(150\) | −14.9223 | −1.21840 | ||||||||
\(151\) | −0.560915 | −0.0456466 | −0.0228233 | − | 0.999740i | \(-0.507266\pi\) | ||||
−0.0228233 | + | 0.999740i | \(0.507266\pi\) | |||||||
\(152\) | 13.7803 | 1.11773 | ||||||||
\(153\) | −1.53497 | −0.124095 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.5493 | −2.53410 | ||||||||
\(156\) | −0.413657 | −0.0331191 | ||||||||
\(157\) | 14.4460 | 1.15292 | 0.576458 | − | 0.817127i | \(-0.304434\pi\) | ||||
0.576458 | + | 0.817127i | \(0.304434\pi\) | |||||||
\(158\) | −7.73320 | −0.615221 | ||||||||
\(159\) | −1.52553 | −0.120982 | ||||||||
\(160\) | −5.59505 | −0.442328 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.32413 | −0.104033 | ||||||||
\(163\) | 19.5921 | 1.53457 | 0.767286 | − | 0.641305i | \(-0.221607\pi\) | ||||
0.767286 | + | 0.641305i | \(0.221607\pi\) | |||||||
\(164\) | 0.246682 | 0.0192626 | ||||||||
\(165\) | 17.4254 | 1.35657 | ||||||||
\(166\) | 0.117020 | 0.00908251 | ||||||||
\(167\) | 2.54730 | 0.197116 | 0.0985579 | − | 0.995131i | \(-0.468577\pi\) | ||||
0.0985579 | + | 0.995131i | \(0.468577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1881 | −0.783696 | ||||||||
\(170\) | 8.19818 | 0.628772 | ||||||||
\(171\) | 4.63220 | 0.354234 | ||||||||
\(172\) | −1.11867 | −0.0852977 | ||||||||
\(173\) | 1.24963 | 0.0950079 | 0.0475039 | − | 0.998871i | \(-0.484873\pi\) | ||||
0.0475039 | + | 0.998871i | \(0.484873\pi\) | |||||||
\(174\) | −8.19809 | −0.621496 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.8862 | −1.12209 | ||||||||
\(177\) | 6.75314 | 0.507597 | ||||||||
\(178\) | −13.8916 | −1.04122 | ||||||||
\(179\) | −14.2508 | −1.06515 | −0.532576 | − | 0.846382i | \(-0.678776\pi\) | ||||
−0.532576 | + | 0.846382i | \(0.678776\pi\) | |||||||
\(180\) | −0.995003 | −0.0741631 | ||||||||
\(181\) | −24.2245 | −1.80059 | −0.900297 | − | 0.435275i | \(-0.856651\pi\) | ||||
−0.900297 | + | 0.435275i | \(0.856651\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.19486 | −0.0883267 | ||||||||
\(184\) | 5.00742 | 0.369152 | ||||||||
\(185\) | 20.9048 | 1.53695 | ||||||||
\(186\) | 10.3570 | 0.759409 | ||||||||
\(187\) | −6.63127 | −0.484926 | ||||||||
\(188\) | 1.79008 | 0.130555 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.7403 | −1.79485 | ||||||||
\(191\) | −22.1282 | −1.60114 | −0.800571 | − | 0.599238i | \(-0.795470\pi\) | ||||
−0.800571 | + | 0.599238i | \(0.795470\pi\) | |||||||
\(192\) | 8.72831 | 0.629911 | ||||||||
\(193\) | −23.9356 | −1.72293 | −0.861463 | − | 0.507821i | \(-0.830451\pi\) | ||||
−0.861463 | + | 0.507821i | \(0.830451\pi\) | |||||||
\(194\) | 3.73909 | 0.268451 | ||||||||
\(195\) | 6.76380 | 0.484366 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2050 | 1.65329 | 0.826643 | − | 0.562727i | \(-0.190248\pi\) | ||||
0.826643 | + | 0.562727i | \(0.190248\pi\) | |||||||
\(198\) | −5.72040 | −0.406531 | ||||||||
\(199\) | −17.0966 | −1.21194 | −0.605972 | − | 0.795486i | \(-0.707216\pi\) | ||||
−0.605972 | + | 0.795486i | \(0.707216\pi\) | |||||||
\(200\) | 33.5256 | 2.37062 | ||||||||
\(201\) | 3.40655 | 0.240279 | ||||||||
\(202\) | 11.7968 | 0.830022 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.378649 | 0.0265108 | ||||||||
\(205\) | −4.03355 | −0.281715 | ||||||||
\(206\) | −17.5664 | −1.22391 | ||||||||
\(207\) | 1.68322 | 0.116992 | ||||||||
\(208\) | −5.77819 | −0.400645 | ||||||||
\(209\) | 20.0117 | 1.38424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4613 | 1.40861 | 0.704306 | − | 0.709897i | \(-0.251258\pi\) | ||||
0.704306 | + | 0.709897i | \(0.251258\pi\) | |||||||
\(212\) | 0.376319 | 0.0258457 | ||||||||
\(213\) | −16.5966 | −1.13718 | ||||||||
\(214\) | 7.60405 | 0.519802 | ||||||||
\(215\) | 18.2916 | 1.24748 | ||||||||
\(216\) | 2.97490 | 0.202416 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.59240 | −0.378765 | ||||||||
\(219\) | −5.99200 | −0.404902 | ||||||||
\(220\) | −4.29854 | −0.289807 | ||||||||
\(221\) | −2.57397 | −0.173144 | ||||||||
\(222\) | −6.86262 | −0.460589 | ||||||||
\(223\) | −20.1256 | −1.34771 | −0.673854 | − | 0.738865i | \(-0.735362\pi\) | ||||
−0.673854 | + | 0.738865i | \(0.735362\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2695 | 0.751300 | ||||||||
\(226\) | 15.3344 | 1.02003 | ||||||||
\(227\) | −7.05161 | −0.468032 | −0.234016 | − | 0.972233i | \(-0.575187\pi\) | ||||
−0.234016 | + | 0.972233i | \(0.575187\pi\) | |||||||
\(228\) | −1.14268 | −0.0756759 | ||||||||
\(229\) | 15.7618 | 1.04157 | 0.520783 | − | 0.853689i | \(-0.325640\pi\) | ||||
0.520783 | + | 0.853689i | \(0.325640\pi\) | |||||||
\(230\) | −8.99000 | −0.592783 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.4185 | 1.20923 | ||||||||
\(233\) | 18.7319 | 1.22717 | 0.613583 | − | 0.789630i | \(-0.289728\pi\) | ||||
0.613583 | + | 0.789630i | \(0.289728\pi\) | |||||||
\(234\) | −2.22041 | −0.145153 | ||||||||
\(235\) | −29.2699 | −1.90936 | ||||||||
\(236\) | −1.66588 | −0.108439 | ||||||||
\(237\) | 5.84022 | 0.379363 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8693 | −1.09119 | −0.545593 | − | 0.838050i | \(-0.683696\pi\) | ||||
−0.545593 | + | 0.838050i | \(0.683696\pi\) | |||||||
\(240\) | −13.8987 | −0.897159 | ||||||||
\(241\) | −16.2267 | −1.04525 | −0.522627 | − | 0.852561i | \(-0.675048\pi\) | ||||
−0.522627 | + | 0.852561i | \(0.675048\pi\) | |||||||
\(242\) | −10.1474 | −0.652303 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.294750 | 0.0188695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.32413 | 0.0844234 | ||||||||
\(247\) | 7.76768 | 0.494246 | ||||||||
\(248\) | −23.2688 | −1.47757 | ||||||||
\(249\) | −0.0883750 | −0.00560054 | ||||||||
\(250\) | −33.4850 | −2.11778 | ||||||||
\(251\) | −4.47161 | −0.282246 | −0.141123 | − | 0.989992i | \(-0.545071\pi\) | ||||
−0.141123 | + | 0.989992i | \(0.545071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.27174 | 0.457170 | ||||||||
\(254\) | 14.3241 | 0.898776 | ||||||||
\(255\) | −6.19138 | −0.387719 | ||||||||
\(256\) | −5.82659 | −0.364162 | ||||||||
\(257\) | −14.3874 | −0.897459 | −0.448730 | − | 0.893668i | \(-0.648123\pi\) | ||||
−0.448730 | + | 0.893668i | \(0.648123\pi\) | |||||||
\(258\) | −6.00475 | −0.373839 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.66851 | −0.103476 | ||||||||
\(261\) | 6.19131 | 0.383232 | ||||||||
\(262\) | −6.84842 | −0.423097 | ||||||||
\(263\) | 7.34706 | 0.453039 | 0.226520 | − | 0.974007i | \(-0.427265\pi\) | ||||
0.226520 | + | 0.974007i | \(0.427265\pi\) | |||||||
\(264\) | 12.8519 | 0.790982 | ||||||||
\(265\) | −6.15328 | −0.377993 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4911 | 0.642046 | ||||||||
\(268\) | −0.840333 | −0.0513315 | ||||||||
\(269\) | 11.1262 | 0.678375 | 0.339187 | − | 0.940719i | \(-0.389848\pi\) | ||||
0.339187 | + | 0.940719i | \(0.389848\pi\) | |||||||
\(270\) | −5.34094 | −0.325039 | ||||||||
\(271\) | 9.36079 | 0.568627 | 0.284314 | − | 0.958731i | \(-0.408234\pi\) | ||||
0.284314 | + | 0.958731i | \(0.408234\pi\) | |||||||
\(272\) | 5.28918 | 0.320703 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.1218 | 0.913541 | ||||||||
\(275\) | 48.6857 | 2.93586 | ||||||||
\(276\) | −0.415221 | −0.0249934 | ||||||||
\(277\) | 9.20675 | 0.553180 | 0.276590 | − | 0.960988i | \(-0.410796\pi\) | ||||
0.276590 | + | 0.960988i | \(0.410796\pi\) | |||||||
\(278\) | 21.1674 | 1.26954 | ||||||||
\(279\) | −7.82172 | −0.468274 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6540 | 0.993493 | 0.496747 | − | 0.867896i | \(-0.334528\pi\) | ||||
0.496747 | + | 0.867896i | \(0.334528\pi\) | |||||||
\(282\) | 9.60870 | 0.572190 | ||||||||
\(283\) | −28.8253 | −1.71348 | −0.856742 | − | 0.515745i | \(-0.827515\pi\) | ||||
−0.856742 | + | 0.515745i | \(0.827515\pi\) | |||||||
\(284\) | 4.09407 | 0.242938 | ||||||||
\(285\) | 18.6842 | 1.10676 | ||||||||
\(286\) | −9.59247 | −0.567215 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.38713 | −0.0817374 | ||||||||
\(289\) | −14.6439 | −0.861404 | ||||||||
\(290\) | −33.0674 | −1.94178 | ||||||||
\(291\) | −2.82381 | −0.165535 | ||||||||
\(292\) | 1.47812 | 0.0865002 | ||||||||
\(293\) | −3.68402 | −0.215223 | −0.107611 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107611 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.2391 | 1.58592 | ||||||||
\(296\) | 15.4181 | 0.896160 | ||||||||
\(297\) | 4.32013 | 0.250679 | ||||||||
\(298\) | −1.10621 | −0.0640811 | ||||||||
\(299\) | 2.82258 | 0.163234 | ||||||||
\(300\) | −2.77998 | −0.160502 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.742723 | 0.0427389 | ||||||||
\(303\) | −8.90913 | −0.511816 | ||||||||
\(304\) | −15.9616 | −0.915459 | ||||||||
\(305\) | −4.81953 | −0.275965 | ||||||||
\(306\) | 2.03250 | 0.116190 | ||||||||
\(307\) | −33.3876 | −1.90553 | −0.952764 | − | 0.303711i | \(-0.901774\pi\) | ||||
−0.952764 | + | 0.303711i | \(0.901774\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.2664 | 0.754697 | ||||||||
\(310\) | 41.7753 | 2.37268 | ||||||||
\(311\) | 20.4085 | 1.15726 | 0.578629 | − | 0.815591i | \(-0.303588\pi\) | ||||
0.578629 | + | 0.815591i | \(0.303588\pi\) | |||||||
\(312\) | 4.98856 | 0.282422 | ||||||||
\(313\) | 11.2547 | 0.636156 | 0.318078 | − | 0.948065i | \(-0.396963\pi\) | ||||
0.318078 | + | 0.948065i | \(0.396963\pi\) | |||||||
\(314\) | −19.1284 | −1.07948 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.44068 | −0.0810443 | ||||||||
\(317\) | 22.7904 | 1.28004 | 0.640020 | − | 0.768359i | \(-0.278926\pi\) | ||||
0.640020 | + | 0.768359i | \(0.278926\pi\) | |||||||
\(318\) | 2.01999 | 0.113276 | ||||||||
\(319\) | 26.7472 | 1.49756 | ||||||||
\(320\) | 35.2060 | 1.96808 | ||||||||
\(321\) | −5.74268 | −0.320525 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.11030 | −0.395628 | ||||||||
\(324\) | −0.246682 | −0.0137045 | ||||||||
\(325\) | 18.8977 | 1.04825 | ||||||||
\(326\) | −25.9425 | −1.43682 | ||||||||
\(327\) | 4.22346 | 0.233558 | ||||||||
\(328\) | −2.97490 | −0.164261 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −23.0735 | −1.27016 | ||||||||
\(331\) | −10.1035 | −0.555339 | −0.277670 | − | 0.960677i | \(-0.589562\pi\) | ||||
−0.277670 | + | 0.960677i | \(0.589562\pi\) | |||||||
\(332\) | 0.0218005 | 0.00119646 | ||||||||
\(333\) | 5.18274 | 0.284013 | ||||||||
\(334\) | −3.37295 | −0.184560 | ||||||||
\(335\) | 13.7405 | 0.750722 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.8588 | −1.73546 | −0.867730 | − | 0.497036i | \(-0.834422\pi\) | ||||
−0.867730 | + | 0.497036i | \(0.834422\pi\) | |||||||
\(338\) | 13.4903 | 0.733775 | ||||||||
\(339\) | −11.5807 | −0.628980 | ||||||||
\(340\) | 1.52730 | 0.0828295 | ||||||||
\(341\) | −33.7908 | −1.82987 | ||||||||
\(342\) | −6.13364 | −0.331669 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.4908 | 0.727373 | ||||||||
\(345\) | 6.78937 | 0.365527 | ||||||||
\(346\) | −1.65468 | −0.0889559 | ||||||||
\(347\) | 9.88435 | 0.530620 | 0.265310 | − | 0.964163i | \(-0.414526\pi\) | ||||
0.265310 | + | 0.964163i | \(0.414526\pi\) | |||||||
\(348\) | −1.52728 | −0.0818709 | ||||||||
\(349\) | −13.0448 | −0.698274 | −0.349137 | − | 0.937072i | \(-0.613525\pi\) | ||||
−0.349137 | + | 0.937072i | \(0.613525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.67689 | 0.0895056 | ||||||||
\(352\) | −5.99258 | −0.319405 | ||||||||
\(353\) | −5.78886 | −0.308110 | −0.154055 | − | 0.988062i | \(-0.549233\pi\) | ||||
−0.154055 | + | 0.988062i | \(0.549233\pi\) | |||||||
\(354\) | −8.94203 | −0.475263 | ||||||||
\(355\) | −66.9431 | −3.55297 | ||||||||
\(356\) | −2.58797 | −0.137162 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.8698 | 0.997302 | ||||||||
\(359\) | −14.4069 | −0.760367 | −0.380184 | − | 0.924911i | \(-0.624139\pi\) | ||||
−0.380184 | + | 0.924911i | \(0.624139\pi\) | |||||||
\(360\) | 11.9994 | 0.632423 | ||||||||
\(361\) | 2.45732 | 0.129333 | ||||||||
\(362\) | 32.0764 | 1.68590 | ||||||||
\(363\) | 7.66349 | 0.402229 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.1690 | −1.26506 | ||||||||
\(366\) | 1.58215 | 0.0827003 | ||||||||
\(367\) | −9.22050 | −0.481306 | −0.240653 | − | 0.970611i | \(-0.577362\pi\) | ||||
−0.240653 | + | 0.970611i | \(0.577362\pi\) | |||||||
\(368\) | −5.80003 | −0.302347 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | −27.6807 | −1.43905 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.92947 | 0.100039 | ||||||||
\(373\) | 28.0620 | 1.45299 | 0.726497 | − | 0.687170i | \(-0.241147\pi\) | ||||
0.726497 | + | 0.687170i | \(0.241147\pi\) | |||||||
\(374\) | 8.78065 | 0.454037 | ||||||||
\(375\) | 25.2883 | 1.30588 | ||||||||
\(376\) | −21.5877 | −1.11330 | ||||||||
\(377\) | 10.3821 | 0.534706 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2699 | 1.29803 | 0.649015 | − | 0.760776i | \(-0.275181\pi\) | ||||
0.649015 | + | 0.760776i | \(0.275181\pi\) | |||||||
\(380\) | −4.60906 | −0.236440 | ||||||||
\(381\) | −10.8178 | −0.554212 | ||||||||
\(382\) | 29.3006 | 1.49915 | ||||||||
\(383\) | −8.13954 | −0.415911 | −0.207956 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207956 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(384\) | −8.78315 | −0.448213 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.6939 | 1.61318 | ||||||||
\(387\) | 4.53487 | 0.230520 | ||||||||
\(388\) | 0.696583 | 0.0353636 | ||||||||
\(389\) | −17.2736 | −0.875805 | −0.437902 | − | 0.899023i | \(-0.644278\pi\) | ||||
−0.437902 | + | 0.899023i | \(0.644278\pi\) | |||||||
\(390\) | −8.95615 | −0.453512 | ||||||||
\(391\) | −2.58370 | −0.130663 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.17202 | 0.260894 | ||||||||
\(394\) | −30.7264 | −1.54797 | ||||||||
\(395\) | 23.5568 | 1.18527 | ||||||||
\(396\) | −1.06570 | −0.0535533 | ||||||||
\(397\) | 7.38909 | 0.370848 | 0.185424 | − | 0.982659i | \(-0.440634\pi\) | ||||
0.185424 | + | 0.982659i | \(0.440634\pi\) | |||||||
\(398\) | 22.6381 | 1.13474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −38.8323 | −1.94161 | ||||||||
\(401\) | 15.2580 | 0.761948 | 0.380974 | − | 0.924586i | \(-0.375589\pi\) | ||||
0.380974 | + | 0.924586i | \(0.375589\pi\) | |||||||
\(402\) | −4.51071 | −0.224974 | ||||||||
\(403\) | −13.1161 | −0.653361 | ||||||||
\(404\) | 2.19772 | 0.109341 | ||||||||
\(405\) | 4.03355 | 0.200429 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.3901 | 1.10984 | ||||||||
\(408\) | −4.56638 | −0.226069 | ||||||||
\(409\) | 18.3573 | 0.907709 | 0.453854 | − | 0.891076i | \(-0.350049\pi\) | ||||
0.453854 | + | 0.891076i | \(0.350049\pi\) | |||||||
\(410\) | 5.34094 | 0.263770 | ||||||||
\(411\) | −11.4202 | −0.563316 | ||||||||
\(412\) | −3.27257 | −0.161228 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.22881 | −0.109540 | ||||||||
\(415\) | −0.356465 | −0.0174982 | ||||||||
\(416\) | −2.32606 | −0.114044 | ||||||||
\(417\) | −15.9859 | −0.782833 | ||||||||
\(418\) | −26.4981 | −1.29606 | ||||||||
\(419\) | −23.9322 | −1.16917 | −0.584583 | − | 0.811334i | \(-0.698742\pi\) | ||||
−0.584583 | + | 0.811334i | \(0.698742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6662 | 1.10468 | 0.552341 | − | 0.833619i | \(-0.313735\pi\) | ||||
0.552341 | + | 0.833619i | \(0.313735\pi\) | |||||||
\(422\) | −27.0934 | −1.31888 | ||||||||
\(423\) | −7.25662 | −0.352829 | ||||||||
\(424\) | −4.53828 | −0.220398 | ||||||||
\(425\) | −17.2984 | −0.839093 | ||||||||
\(426\) | 21.9760 | 1.06474 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.41662 | 0.0684747 | ||||||||
\(429\) | 7.24436 | 0.349761 | ||||||||
\(430\) | −24.2204 | −1.16801 | ||||||||
\(431\) | 35.5576 | 1.71275 | 0.856376 | − | 0.516353i | \(-0.172711\pi\) | ||||
0.856376 | + | 0.516353i | \(0.172711\pi\) | |||||||
\(432\) | −3.44578 | −0.165785 | ||||||||
\(433\) | 28.7162 | 1.38001 | 0.690007 | − | 0.723803i | \(-0.257608\pi\) | ||||
0.690007 | + | 0.723803i | \(0.257608\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 24.9729 | 1.19736 | ||||||||
\(436\) | −1.04185 | −0.0498955 | ||||||||
\(437\) | 7.79704 | 0.372983 | ||||||||
\(438\) | 7.93418 | 0.379110 | ||||||||
\(439\) | −10.1913 | −0.486404 | −0.243202 | − | 0.969976i | \(-0.578198\pi\) | ||||
−0.243202 | + | 0.969976i | \(0.578198\pi\) | |||||||
\(440\) | 51.8389 | 2.47132 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.40827 | 0.162115 | ||||||||
\(443\) | −11.5843 | −0.550386 | −0.275193 | − | 0.961389i | \(-0.588742\pi\) | ||||
−0.275193 | + | 0.961389i | \(0.588742\pi\) | |||||||
\(444\) | −1.27849 | −0.0606744 | ||||||||
\(445\) | 42.3164 | 2.00599 | ||||||||
\(446\) | 26.6489 | 1.26186 | ||||||||
\(447\) | 0.835425 | 0.0395143 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.2850 | −1.61801 | −0.809004 | − | 0.587803i | \(-0.799993\pi\) | ||||
−0.809004 | + | 0.587803i | \(0.799993\pi\) | |||||||
\(450\) | −14.9223 | −0.703443 | ||||||||
\(451\) | −4.32013 | −0.203427 | ||||||||
\(452\) | 2.85676 | 0.134371 | ||||||||
\(453\) | −0.560915 | −0.0263541 | ||||||||
\(454\) | 9.33725 | 0.438219 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.7803 | 0.645323 | ||||||||
\(457\) | 1.34031 | 0.0626970 | 0.0313485 | − | 0.999509i | \(-0.490020\pi\) | ||||
0.0313485 | + | 0.999509i | \(0.490020\pi\) | |||||||
\(458\) | −20.8706 | −0.975219 | ||||||||
\(459\) | −1.53497 | −0.0716463 | ||||||||
\(460\) | −1.67481 | −0.0780885 | ||||||||
\(461\) | −28.1737 | −1.31218 | −0.656089 | − | 0.754683i | \(-0.727791\pi\) | ||||
−0.656089 | + | 0.754683i | \(0.727791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4603 | −1.18324 | −0.591620 | − | 0.806217i | \(-0.701512\pi\) | ||||
−0.591620 | + | 0.806217i | \(0.701512\pi\) | |||||||
\(464\) | −21.3339 | −0.990402 | ||||||||
\(465\) | −31.5493 | −1.46306 | ||||||||
\(466\) | −24.8034 | −1.14900 | ||||||||
\(467\) | −6.52537 | −0.301958 | −0.150979 | − | 0.988537i | \(-0.548243\pi\) | ||||
−0.150979 | + | 0.988537i | \(0.548243\pi\) | |||||||
\(468\) | −0.413657 | −0.0191213 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 38.7572 | 1.78773 | ||||||||
\(471\) | 14.4460 | 0.665637 | ||||||||
\(472\) | 20.0899 | 0.924712 | ||||||||
\(473\) | 19.5912 | 0.900804 | ||||||||
\(474\) | −7.73320 | −0.355198 | ||||||||
\(475\) | 52.2026 | 2.39522 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.52553 | −0.0698490 | ||||||||
\(478\) | 22.3372 | 1.02168 | ||||||||
\(479\) | 6.79632 | 0.310532 | 0.155266 | − | 0.987873i | \(-0.450377\pi\) | ||||
0.155266 | + | 0.987873i | \(0.450377\pi\) | |||||||
\(480\) | −5.59505 | −0.255378 | ||||||||
\(481\) | 8.69087 | 0.396270 | ||||||||
\(482\) | 21.4863 | 0.978673 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.89044 | −0.0859292 | ||||||||
\(485\) | −11.3900 | −0.517192 | ||||||||
\(486\) | −1.32413 | −0.0600637 | ||||||||
\(487\) | 4.67769 | 0.211967 | 0.105983 | − | 0.994368i | \(-0.466201\pi\) | ||||
0.105983 | + | 0.994368i | \(0.466201\pi\) | |||||||
\(488\) | −3.55459 | −0.160909 | ||||||||
\(489\) | 19.5921 | 0.885986 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9925 | 1.39867 | 0.699336 | − | 0.714793i | \(-0.253479\pi\) | ||||
0.699336 | + | 0.714793i | \(0.253479\pi\) | |||||||
\(492\) | 0.246682 | 0.0111213 | ||||||||
\(493\) | −9.50347 | −0.428015 | ||||||||
\(494\) | −10.2854 | −0.462763 | ||||||||
\(495\) | 17.4254 | 0.783215 | ||||||||
\(496\) | 26.9519 | 1.21018 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.117020 | 0.00524379 | ||||||||
\(499\) | −15.1164 | −0.676702 | −0.338351 | − | 0.941020i | \(-0.609869\pi\) | ||||
−0.338351 | + | 0.941020i | \(0.609869\pi\) | |||||||
\(500\) | −6.23817 | −0.278980 | ||||||||
\(501\) | 2.54730 | 0.113805 | ||||||||
\(502\) | 5.92099 | 0.264267 | ||||||||
\(503\) | 31.9345 | 1.42389 | 0.711944 | − | 0.702237i | \(-0.247815\pi\) | ||||
0.711944 | + | 0.702237i | \(0.247815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.9354 | −1.59910 | ||||||||
\(506\) | −9.62873 | −0.428049 | ||||||||
\(507\) | −10.1881 | −0.452467 | ||||||||
\(508\) | 2.66855 | 0.118398 | ||||||||
\(509\) | 31.6661 | 1.40357 | 0.701787 | − | 0.712387i | \(-0.252386\pi\) | ||||
0.701787 | + | 0.712387i | \(0.252386\pi\) | |||||||
\(510\) | 8.19818 | 0.363022 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 25.2815 | 1.11729 | ||||||||
\(513\) | 4.63220 | 0.204517 | ||||||||
\(514\) | 19.0507 | 0.840292 | ||||||||
\(515\) | 53.5105 | 2.35795 | ||||||||
\(516\) | −1.11867 | −0.0492467 | ||||||||
\(517\) | −31.3495 | −1.37875 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.24963 | 0.0548528 | ||||||||
\(520\) | 20.1216 | 0.882391 | ||||||||
\(521\) | 33.2889 | 1.45841 | 0.729207 | − | 0.684294i | \(-0.239889\pi\) | ||||
0.729207 | + | 0.684294i | \(0.239889\pi\) | |||||||
\(522\) | −8.19809 | −0.358821 | ||||||||
\(523\) | 28.6126 | 1.25114 | 0.625570 | − | 0.780168i | \(-0.284866\pi\) | ||||
0.625570 | + | 0.780168i | \(0.284866\pi\) | |||||||
\(524\) | −1.27584 | −0.0557354 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.72846 | −0.424181 | ||||||||
\(527\) | 12.0061 | 0.522994 | ||||||||
\(528\) | −14.8862 | −0.647840 | ||||||||
\(529\) | −20.1668 | −0.876815 | ||||||||
\(530\) | 8.14774 | 0.353915 | ||||||||
\(531\) | 6.75314 | 0.293061 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.67689 | −0.0726340 | ||||||||
\(534\) | −13.8916 | −0.601148 | ||||||||
\(535\) | −23.1634 | −1.00144 | ||||||||
\(536\) | 10.1341 | 0.437727 | ||||||||
\(537\) | −14.2508 | −0.614966 | ||||||||
\(538\) | −14.7325 | −0.635163 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.995003 | −0.0428181 | ||||||||
\(541\) | −26.4485 | −1.13711 | −0.568554 | − | 0.822646i | \(-0.692497\pi\) | ||||
−0.568554 | + | 0.822646i | \(0.692497\pi\) | |||||||
\(542\) | −12.3949 | −0.532406 | ||||||||
\(543\) | −24.2245 | −1.03957 | ||||||||
\(544\) | 2.12920 | 0.0912889 | ||||||||
\(545\) | 17.0355 | 0.729721 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.0439 | 1.07080 | 0.535401 | − | 0.844598i | \(-0.320161\pi\) | ||||
0.535401 | + | 0.844598i | \(0.320161\pi\) | |||||||
\(548\) | 2.81715 | 0.120343 | ||||||||
\(549\) | −1.19486 | −0.0509954 | ||||||||
\(550\) | −64.4661 | −2.74884 | ||||||||
\(551\) | 28.6794 | 1.22178 | ||||||||
\(552\) | 5.00742 | 0.213130 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.1909 | −0.517943 | ||||||||
\(555\) | 20.9048 | 0.887361 | ||||||||
\(556\) | 3.94343 | 0.167239 | ||||||||
\(557\) | −9.72009 | −0.411853 | −0.205927 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205927 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(558\) | 10.3570 | 0.438445 | ||||||||
\(559\) | 7.60446 | 0.321634 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.63127 | −0.279972 | ||||||||
\(562\) | −22.0520 | −0.930208 | ||||||||
\(563\) | −24.0850 | −1.01506 | −0.507531 | − | 0.861634i | \(-0.669442\pi\) | ||||
−0.507531 | + | 0.861634i | \(0.669442\pi\) | |||||||
\(564\) | 1.79008 | 0.0753758 | ||||||||
\(565\) | −46.7115 | −1.96517 | ||||||||
\(566\) | 38.1684 | 1.60434 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −49.3731 | −2.07165 | ||||||||
\(569\) | −17.7779 | −0.745289 | −0.372644 | − | 0.927974i | \(-0.621549\pi\) | ||||
−0.372644 | + | 0.927974i | \(0.621549\pi\) | |||||||
\(570\) | −24.7403 | −1.03626 | ||||||||
\(571\) | −39.5045 | −1.65321 | −0.826607 | − | 0.562780i | \(-0.809732\pi\) | ||||
−0.826607 | + | 0.562780i | \(0.809732\pi\) | |||||||
\(572\) | −1.78705 | −0.0747204 | ||||||||
\(573\) | −22.1282 | −0.924419 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.9691 | 0.791066 | ||||||||
\(576\) | 8.72831 | 0.363680 | ||||||||
\(577\) | −15.7384 | −0.655200 | −0.327600 | − | 0.944817i | \(-0.606240\pi\) | ||||
−0.327600 | + | 0.944817i | \(0.606240\pi\) | |||||||
\(578\) | 19.3904 | 0.806533 | ||||||||
\(579\) | −23.9356 | −0.994732 | ||||||||
\(580\) | −6.16037 | −0.255795 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.73909 | 0.154990 | ||||||||
\(583\) | −6.59046 | −0.272949 | ||||||||
\(584\) | −17.8256 | −0.737627 | ||||||||
\(585\) | 6.76380 | 0.279649 | ||||||||
\(586\) | 4.87812 | 0.201513 | ||||||||
\(587\) | 43.9906 | 1.81569 | 0.907843 | − | 0.419310i | \(-0.137728\pi\) | ||||
0.907843 | + | 0.419310i | \(0.137728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.2318 | −1.49290 | ||||||||
\(590\) | −36.0681 | −1.48490 | ||||||||
\(591\) | 23.2050 | 0.954525 | ||||||||
\(592\) | −17.8586 | −0.733984 | ||||||||
\(593\) | −42.6855 | −1.75288 | −0.876442 | − | 0.481507i | \(-0.840090\pi\) | ||||
−0.876442 | + | 0.481507i | \(0.840090\pi\) | |||||||
\(594\) | −5.72040 | −0.234711 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.206084 | −0.00844154 | ||||||||
\(597\) | −17.0966 | −0.699716 | ||||||||
\(598\) | −3.73746 | −0.152836 | ||||||||
\(599\) | 43.1503 | 1.76307 | 0.881537 | − | 0.472114i | \(-0.156509\pi\) | ||||
0.881537 | + | 0.472114i | \(0.156509\pi\) | |||||||
\(600\) | 33.5256 | 1.36868 | ||||||||
\(601\) | 37.9513 | 1.54806 | 0.774032 | − | 0.633146i | \(-0.218237\pi\) | ||||
0.774032 | + | 0.633146i | \(0.218237\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.40655 | 0.138725 | ||||||||
\(604\) | 0.138367 | 0.00563009 | ||||||||
\(605\) | 30.9110 | 1.25671 | ||||||||
\(606\) | 11.7968 | 0.479214 | ||||||||
\(607\) | −45.1372 | −1.83206 | −0.916031 | − | 0.401107i | \(-0.868626\pi\) | ||||
−0.916031 | + | 0.401107i | \(0.868626\pi\) | |||||||
\(608\) | −6.42547 | −0.260587 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.38168 | 0.258387 | ||||||||
\(611\) | −12.1685 | −0.492286 | ||||||||
\(612\) | 0.378649 | 0.0153060 | ||||||||
\(613\) | −0.969393 | −0.0391534 | −0.0195767 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195767 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(614\) | 44.2094 | 1.78415 | ||||||||
\(615\) | −4.03355 | −0.162648 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.4830 | 1.91160 | 0.955798 | − | 0.294025i | \(-0.0949951\pi\) | ||||
0.955798 | + | 0.294025i | \(0.0949951\pi\) | |||||||
\(618\) | −17.5664 | −0.706623 | ||||||||
\(619\) | 30.0585 | 1.20815 | 0.604076 | − | 0.796927i | \(-0.293542\pi\) | ||||
0.604076 | + | 0.796927i | \(0.293542\pi\) | |||||||
\(620\) | 7.78263 | 0.312558 | ||||||||
\(621\) | 1.68322 | 0.0675455 | ||||||||
\(622\) | −27.0235 | −1.08354 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.77819 | −0.231313 | ||||||||
\(625\) | 45.6542 | 1.82617 | ||||||||
\(626\) | −14.9027 | −0.595633 | ||||||||
\(627\) | 20.0117 | 0.799191 | ||||||||
\(628\) | −3.56357 | −0.142202 | ||||||||
\(629\) | −7.95536 | −0.317201 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.9101 | 1.42956 | 0.714780 | − | 0.699350i | \(-0.246527\pi\) | ||||
0.714780 | + | 0.699350i | \(0.246527\pi\) | |||||||
\(632\) | 17.3740 | 0.691103 | ||||||||
\(633\) | 20.4613 | 0.813262 | ||||||||
\(634\) | −30.1775 | −1.19850 | ||||||||
\(635\) | −43.6340 | −1.73156 | ||||||||
\(636\) | 0.376319 | 0.0149220 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −35.4168 | −1.40216 | ||||||||
\(639\) | −16.5966 | −0.656550 | ||||||||
\(640\) | −35.4272 | −1.40038 | ||||||||
\(641\) | 24.6578 | 0.973924 | 0.486962 | − | 0.873423i | \(-0.338105\pi\) | ||||
0.486962 | + | 0.873423i | \(0.338105\pi\) | |||||||
\(642\) | 7.60405 | 0.300108 | ||||||||
\(643\) | 4.55930 | 0.179801 | 0.0899007 | − | 0.995951i | \(-0.471345\pi\) | ||||
0.0899007 | + | 0.995951i | \(0.471345\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.2916 | 0.720231 | ||||||||
\(646\) | 9.41495 | 0.370426 | ||||||||
\(647\) | 27.0812 | 1.06467 | 0.532335 | − | 0.846534i | \(-0.321315\pi\) | ||||
0.532335 | + | 0.846534i | \(0.321315\pi\) | |||||||
\(648\) | 2.97490 | 0.116865 | ||||||||
\(649\) | 29.1744 | 1.14520 | ||||||||
\(650\) | −25.0230 | −0.981481 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.83302 | −0.189276 | ||||||||
\(653\) | 38.7977 | 1.51827 | 0.759136 | − | 0.650932i | \(-0.225622\pi\) | ||||
0.759136 | + | 0.650932i | \(0.225622\pi\) | |||||||
\(654\) | −5.59240 | −0.218680 | ||||||||
\(655\) | 20.8616 | 0.815129 | ||||||||
\(656\) | 3.44578 | 0.134535 | ||||||||
\(657\) | −5.99200 | −0.233770 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.7303 | −1.82035 | −0.910176 | − | 0.414222i | \(-0.864054\pi\) | ||||
−0.910176 | + | 0.414222i | \(0.864054\pi\) | |||||||
\(660\) | −4.29854 | −0.167320 | ||||||||
\(661\) | −23.1898 | −0.901978 | −0.450989 | − | 0.892529i | \(-0.648929\pi\) | ||||
−0.450989 | + | 0.892529i | \(0.648929\pi\) | |||||||
\(662\) | 13.3784 | 0.519965 | ||||||||
\(663\) | −2.57397 | −0.0999647 | ||||||||
\(664\) | −0.262907 | −0.0102028 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.86262 | −0.265921 | ||||||||
\(667\) | 10.4214 | 0.403517 | ||||||||
\(668\) | −0.628372 | −0.0243125 | ||||||||
\(669\) | −20.1256 | −0.778100 | ||||||||
\(670\) | −18.1941 | −0.702901 | ||||||||
\(671\) | −5.16195 | −0.199275 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.4829 | 1.09794 | 0.548968 | − | 0.835844i | \(-0.315021\pi\) | ||||
0.548968 | + | 0.835844i | \(0.315021\pi\) | |||||||
\(674\) | 42.1852 | 1.62491 | ||||||||
\(675\) | 11.2695 | 0.433763 | ||||||||
\(676\) | 2.51321 | 0.0966618 | ||||||||
\(677\) | 44.6726 | 1.71691 | 0.858454 | − | 0.512891i | \(-0.171426\pi\) | ||||
0.858454 | + | 0.512891i | \(0.171426\pi\) | |||||||
\(678\) | 15.3344 | 0.588914 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −18.4187 | −0.706325 | ||||||||
\(681\) | −7.05161 | −0.270218 | ||||||||
\(682\) | 44.7434 | 1.71331 | ||||||||
\(683\) | 11.0672 | 0.423473 | 0.211736 | − | 0.977327i | \(-0.432088\pi\) | ||||
0.211736 | + | 0.977327i | \(0.432088\pi\) | |||||||
\(684\) | −1.14268 | −0.0436915 | ||||||||
\(685\) | −46.0638 | −1.76001 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.7618 | 0.601349 | ||||||||
\(688\) | −15.6262 | −0.595742 | ||||||||
\(689\) | −2.55813 | −0.0974571 | ||||||||
\(690\) | −8.99000 | −0.342243 | ||||||||
\(691\) | 29.2076 | 1.11111 | 0.555555 | − | 0.831480i | \(-0.312506\pi\) | ||||
0.555555 | + | 0.831480i | \(0.312506\pi\) | |||||||
\(692\) | −0.308262 | −0.0117184 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0882 | −0.496819 | ||||||||
\(695\) | −64.4799 | −2.44586 | ||||||||
\(696\) | 18.4185 | 0.698151 | ||||||||
\(697\) | 1.53497 | 0.0581412 | ||||||||
\(698\) | 17.2730 | 0.653795 | ||||||||
\(699\) | 18.7319 | 0.708505 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9978 | 0.641999 | 0.321000 | − | 0.947079i | \(-0.395981\pi\) | ||||
0.321000 | + | 0.947079i | \(0.395981\pi\) | |||||||
\(702\) | −2.22041 | −0.0838041 | ||||||||
\(703\) | 24.0075 | 0.905461 | ||||||||
\(704\) | 37.7074 | 1.42115 | ||||||||
\(705\) | −29.2699 | −1.10237 | ||||||||
\(706\) | 7.66519 | 0.288483 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.66588 | −0.0626074 | ||||||||
\(709\) | 44.0489 | 1.65429 | 0.827145 | − | 0.561988i | \(-0.189963\pi\) | ||||
0.827145 | + | 0.561988i | \(0.189963\pi\) | |||||||
\(710\) | 88.6413 | 3.32665 | ||||||||
\(711\) | 5.84022 | 0.219025 | ||||||||
\(712\) | 31.2100 | 1.16964 | ||||||||
\(713\) | −13.1657 | −0.493059 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.2205 | 1.09278 | ||||||||
\(716\) | 3.51540 | 0.131377 | ||||||||
\(717\) | −16.8693 | −0.629997 | ||||||||
\(718\) | 19.0766 | 0.711933 | ||||||||
\(719\) | −36.5360 | −1.36256 | −0.681282 | − | 0.732021i | \(-0.738577\pi\) | ||||
−0.681282 | + | 0.732021i | \(0.738577\pi\) | |||||||
\(720\) | −13.8987 | −0.517975 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.25381 | −0.121094 | ||||||||
\(723\) | −16.2267 | −0.603478 | ||||||||
\(724\) | 5.97575 | 0.222087 | ||||||||
\(725\) | 69.7729 | 2.59130 | ||||||||
\(726\) | −10.1474 | −0.376607 | ||||||||
\(727\) | 50.5977 | 1.87656 | 0.938282 | − | 0.345870i | \(-0.112416\pi\) | ||||
0.938282 | + | 0.345870i | \(0.112416\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 32.0029 | 1.18448 | ||||||||
\(731\) | −6.96089 | −0.257458 | ||||||||
\(732\) | 0.294750 | 0.0108943 | ||||||||
\(733\) | 8.66771 | 0.320149 | 0.160075 | − | 0.987105i | \(-0.448827\pi\) | ||||
0.160075 | + | 0.987105i | \(0.448827\pi\) | |||||||
\(734\) | 12.2091 | 0.450647 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.33485 | −0.0860638 | ||||||||
\(737\) | 14.7167 | 0.542097 | ||||||||
\(738\) | 1.32413 | 0.0487419 | ||||||||
\(739\) | −6.55816 | −0.241246 | −0.120623 | − | 0.992698i | \(-0.538489\pi\) | ||||
−0.120623 | + | 0.992698i | \(0.538489\pi\) | |||||||
\(740\) | −5.15684 | −0.189569 | ||||||||
\(741\) | 7.76768 | 0.285353 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3630 | 1.15060 | 0.575298 | − | 0.817944i | \(-0.304886\pi\) | ||||
0.575298 | + | 0.817944i | \(0.304886\pi\) | |||||||
\(744\) | −23.2688 | −0.853076 | ||||||||
\(745\) | 3.36973 | 0.123457 | ||||||||
\(746\) | −37.1577 | −1.36044 | ||||||||
\(747\) | −0.0883750 | −0.00323347 | ||||||||
\(748\) | 1.63581 | 0.0598112 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −33.4850 | −1.22270 | ||||||||
\(751\) | 35.9531 | 1.31195 | 0.655973 | − | 0.754785i | \(-0.272259\pi\) | ||||
0.655973 | + | 0.754785i | \(0.272259\pi\) | |||||||
\(752\) | 25.0047 | 0.911829 | ||||||||
\(753\) | −4.47161 | −0.162955 | ||||||||
\(754\) | −13.7473 | −0.500646 | ||||||||
\(755\) | −2.26248 | −0.0823399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.1675 | 0.587617 | 0.293808 | − | 0.955864i | \(-0.405077\pi\) | ||||
0.293808 | + | 0.955864i | \(0.405077\pi\) | |||||||
\(758\) | −33.4607 | −1.21535 | ||||||||
\(759\) | 7.27174 | 0.263947 | ||||||||
\(760\) | 55.5836 | 2.01623 | ||||||||
\(761\) | 17.6078 | 0.638281 | 0.319140 | − | 0.947707i | \(-0.396606\pi\) | ||||
0.319140 | + | 0.947707i | \(0.396606\pi\) | |||||||
\(762\) | 14.3241 | 0.518909 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.45863 | 0.197486 | ||||||||
\(765\) | −6.19138 | −0.223850 | ||||||||
\(766\) | 10.7778 | 0.389418 | ||||||||
\(767\) | 11.3242 | 0.408895 | ||||||||
\(768\) | −5.82659 | −0.210249 | ||||||||
\(769\) | −26.5362 | −0.956920 | −0.478460 | − | 0.878109i | \(-0.658805\pi\) | ||||
−0.478460 | + | 0.878109i | \(0.658805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3874 | −0.518148 | ||||||||
\(772\) | 5.90449 | 0.212507 | ||||||||
\(773\) | 26.1052 | 0.938940 | 0.469470 | − | 0.882949i | \(-0.344445\pi\) | ||||
0.469470 | + | 0.882949i | \(0.344445\pi\) | |||||||
\(774\) | −6.00475 | −0.215836 | ||||||||
\(775\) | −88.1468 | −3.16633 | ||||||||
\(776\) | −8.40054 | −0.301562 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.8724 | 0.820017 | ||||||||
\(779\) | −4.63220 | −0.165966 | ||||||||
\(780\) | −1.66851 | −0.0597421 | ||||||||
\(781\) | −71.6993 | −2.56560 | ||||||||
\(782\) | 3.42115 | 0.122340 | ||||||||
\(783\) | 6.19131 | 0.221259 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.2686 | 2.07970 | ||||||||
\(786\) | −6.84842 | −0.244275 | ||||||||
\(787\) | −5.59220 | −0.199340 | −0.0996701 | − | 0.995021i | \(-0.531779\pi\) | ||||
−0.0996701 | + | 0.995021i | \(0.531779\pi\) | |||||||
\(788\) | −5.72424 | −0.203918 | ||||||||
\(789\) | 7.34706 | 0.261562 | ||||||||
\(790\) | −31.1922 | −1.10977 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.8519 | 0.456673 | ||||||||
\(793\) | −2.00365 | −0.0711516 | ||||||||
\(794\) | −9.78411 | −0.347225 | ||||||||
\(795\) | −6.15328 | −0.218234 | ||||||||
\(796\) | 4.21741 | 0.149482 | ||||||||
\(797\) | −54.8608 | −1.94327 | −0.971634 | − | 0.236489i | \(-0.924003\pi\) | ||||
−0.971634 | + | 0.236489i | \(0.924003\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.1387 | 0.394059 | ||||||||
\(800\) | −15.6323 | −0.552684 | ||||||||
\(801\) | 10.4911 | 0.370685 | ||||||||
\(802\) | −20.2036 | −0.713412 | ||||||||
\(803\) | −25.8862 | −0.913503 | ||||||||
\(804\) | −0.840333 | −0.0296363 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.3674 | 0.611742 | ||||||||
\(807\) | 11.1262 | 0.391660 | ||||||||
\(808\) | −26.5037 | −0.932398 | ||||||||
\(809\) | −54.6666 | −1.92197 | −0.960987 | − | 0.276593i | \(-0.910795\pi\) | ||||
−0.960987 | + | 0.276593i | \(0.910795\pi\) | |||||||
\(810\) | −5.34094 | −0.187661 | ||||||||
\(811\) | −11.9720 | −0.420394 | −0.210197 | − | 0.977659i | \(-0.567411\pi\) | ||||
−0.210197 | + | 0.977659i | \(0.567411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.36079 | 0.328297 | ||||||||
\(814\) | −29.6474 | −1.03914 | ||||||||
\(815\) | 79.0257 | 2.76815 | ||||||||
\(816\) | 5.28918 | 0.185158 | ||||||||
\(817\) | 21.0064 | 0.734922 | ||||||||
\(818\) | −24.3074 | −0.849888 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.995003 | 0.0347470 | ||||||||
\(821\) | −9.62125 | −0.335784 | −0.167892 | − | 0.985805i | \(-0.553696\pi\) | ||||
−0.167892 | + | 0.985805i | \(0.553696\pi\) | |||||||
\(822\) | 15.1218 | 0.527433 | ||||||||
\(823\) | −44.0763 | −1.53640 | −0.768201 | − | 0.640209i | \(-0.778848\pi\) | ||||
−0.768201 | + | 0.640209i | \(0.778848\pi\) | |||||||
\(824\) | 39.4661 | 1.37487 | ||||||||
\(825\) | 48.6857 | 1.69502 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7234 | 0.546758 | 0.273379 | − | 0.961906i | \(-0.411859\pi\) | ||||
0.273379 | + | 0.961906i | \(0.411859\pi\) | |||||||
\(828\) | −0.415221 | −0.0144299 | ||||||||
\(829\) | 17.0066 | 0.590664 | 0.295332 | − | 0.955395i | \(-0.404570\pi\) | ||||
0.295332 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(830\) | 0.472005 | 0.0163835 | ||||||||
\(831\) | 9.20675 | 0.319379 | ||||||||
\(832\) | 14.6364 | 0.507425 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 21.1674 | 0.732967 | ||||||||
\(835\) | 10.2746 | 0.355569 | ||||||||
\(836\) | −4.93652 | −0.170733 | ||||||||
\(837\) | −7.82172 | −0.270358 | ||||||||
\(838\) | 31.6893 | 1.09469 | ||||||||
\(839\) | 26.9183 | 0.929325 | 0.464662 | − | 0.885488i | \(-0.346176\pi\) | ||||
0.464662 | + | 0.885488i | \(0.346176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.33227 | 0.321803 | ||||||||
\(842\) | −30.0129 | −1.03431 | ||||||||
\(843\) | 16.6540 | 0.573593 | ||||||||
\(844\) | −5.04742 | −0.173739 | ||||||||
\(845\) | −41.0940 | −1.41368 | ||||||||
\(846\) | 9.60870 | 0.330354 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.25663 | 0.180513 | ||||||||
\(849\) | −28.8253 | −0.989281 | ||||||||
\(850\) | 22.9053 | 0.785644 | ||||||||
\(851\) | 8.72372 | 0.299045 | ||||||||
\(852\) | 4.09407 | 0.140261 | ||||||||
\(853\) | 24.3943 | 0.835246 | 0.417623 | − | 0.908620i | \(-0.362863\pi\) | ||||
0.417623 | + | 0.908620i | \(0.362863\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.6842 | 0.638987 | ||||||||
\(856\) | −17.0839 | −0.583915 | ||||||||
\(857\) | 31.1527 | 1.06416 | 0.532078 | − | 0.846695i | \(-0.321411\pi\) | ||||
0.532078 | + | 0.846695i | \(0.321411\pi\) | |||||||
\(858\) | −9.59247 | −0.327481 | ||||||||
\(859\) | −51.4913 | −1.75686 | −0.878430 | − | 0.477871i | \(-0.841409\pi\) | ||||
−0.878430 | + | 0.477871i | \(0.841409\pi\) | |||||||
\(860\) | −4.51220 | −0.153865 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −47.0829 | −1.60365 | ||||||||
\(863\) | −31.1056 | −1.05885 | −0.529424 | − | 0.848358i | \(-0.677592\pi\) | ||||
−0.529424 | + | 0.848358i | \(0.677592\pi\) | |||||||
\(864\) | −1.38713 | −0.0471911 | ||||||||
\(865\) | 5.04046 | 0.171381 | ||||||||
\(866\) | −38.0240 | −1.29211 | ||||||||
\(867\) | −14.6439 | −0.497332 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.2305 | 0.855885 | ||||||||
\(870\) | −33.0674 | −1.12109 | ||||||||
\(871\) | 5.71239 | 0.193557 | ||||||||
\(872\) | 12.5643 | 0.425482 | ||||||||
\(873\) | −2.82381 | −0.0955715 | ||||||||
\(874\) | −10.3243 | −0.349224 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.47812 | 0.0499409 | ||||||||
\(877\) | 22.9723 | 0.775720 | 0.387860 | − | 0.921718i | \(-0.373214\pi\) | ||||
0.387860 | + | 0.921718i | \(0.373214\pi\) | |||||||
\(878\) | 13.4946 | 0.455421 | ||||||||
\(879\) | −3.68402 | −0.124259 | ||||||||
\(880\) | −60.0443 | −2.02409 | ||||||||
\(881\) | 0.746180 | 0.0251394 | 0.0125697 | − | 0.999921i | \(-0.495999\pi\) | ||||
0.0125697 | + | 0.999921i | \(0.495999\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.0939 | −0.507951 | −0.253976 | − | 0.967211i | \(-0.581738\pi\) | ||||
−0.253976 | + | 0.967211i | \(0.581738\pi\) | |||||||
\(884\) | 0.634952 | 0.0213557 | ||||||||
\(885\) | 27.2391 | 0.915632 | ||||||||
\(886\) | 15.3391 | 0.515327 | ||||||||
\(887\) | −21.7017 | −0.728670 | −0.364335 | − | 0.931268i | \(-0.618704\pi\) | ||||
−0.364335 | + | 0.931268i | \(0.618704\pi\) | |||||||
\(888\) | 15.4181 | 0.517398 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −56.0324 | −1.87821 | ||||||||
\(891\) | 4.32013 | 0.144730 | ||||||||
\(892\) | 4.96461 | 0.166227 | ||||||||
\(893\) | −33.6141 | −1.12485 | ||||||||
\(894\) | −1.10621 | −0.0369972 | ||||||||
\(895\) | −57.4811 | −1.92138 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.82258 | 0.0942431 | ||||||||
\(898\) | 45.3978 | 1.51494 | ||||||||
\(899\) | −48.4266 | −1.61512 | ||||||||
\(900\) | −2.77998 | −0.0926660 | ||||||||
\(901\) | 2.34164 | 0.0780112 | ||||||||
\(902\) | 5.72040 | 0.190469 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.4515 | −1.14584 | ||||||||
\(905\) | −97.7108 | −3.24802 | ||||||||
\(906\) | 0.742723 | 0.0246753 | ||||||||
\(907\) | 25.6962 | 0.853227 | 0.426613 | − | 0.904434i | \(-0.359707\pi\) | ||||
0.426613 | + | 0.904434i | \(0.359707\pi\) | |||||||
\(908\) | 1.73950 | 0.0577275 | ||||||||
\(909\) | −8.90913 | −0.295497 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.86146 | −0.194199 | −0.0970994 | − | 0.995275i | \(-0.530956\pi\) | ||||
−0.0970994 | + | 0.995275i | \(0.530956\pi\) | |||||||
\(912\) | −15.9616 | −0.528541 | ||||||||
\(913\) | −0.381791 | −0.0126354 | ||||||||
\(914\) | −1.77474 | −0.0587033 | ||||||||
\(915\) | −4.81953 | −0.159329 | ||||||||
\(916\) | −3.88814 | −0.128468 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.03250 | 0.0670825 | ||||||||
\(919\) | −32.8094 | −1.08228 | −0.541141 | − | 0.840932i | \(-0.682008\pi\) | ||||
−0.541141 | + | 0.840932i | \(0.682008\pi\) | |||||||
\(920\) | 20.1977 | 0.665897 | ||||||||
\(921\) | −33.3876 | −1.10016 | ||||||||
\(922\) | 37.3056 | 1.22859 | ||||||||
\(923\) | −27.8306 | −0.916054 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 58.4069 | 1.92041 | ||||||||
\(926\) | 33.7127 | 1.10787 | ||||||||
\(927\) | 13.2664 | 0.435724 | ||||||||
\(928\) | −8.58815 | −0.281920 | ||||||||
\(929\) | −36.4771 | −1.19678 | −0.598388 | − | 0.801207i | \(-0.704192\pi\) | ||||
−0.598388 | + | 0.801207i | \(0.704192\pi\) | |||||||
\(930\) | 41.7753 | 1.36987 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.62081 | −0.151360 | ||||||||
\(933\) | 20.4085 | 0.668143 | ||||||||
\(934\) | 8.64043 | 0.282723 | ||||||||
\(935\) | −26.7475 | −0.874738 | ||||||||
\(936\) | 4.98856 | 0.163056 | ||||||||
\(937\) | −37.8363 | −1.23606 | −0.618029 | − | 0.786155i | \(-0.712069\pi\) | ||||
−0.618029 | + | 0.786155i | \(0.712069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.2547 | 0.367285 | ||||||||
\(940\) | 7.22036 | 0.235502 | ||||||||
\(941\) | −41.6898 | −1.35905 | −0.679524 | − | 0.733653i | \(-0.737814\pi\) | ||||
−0.679524 | + | 0.733653i | \(0.737814\pi\) | |||||||
\(942\) | −19.1284 | −0.623236 | ||||||||
\(943\) | −1.68322 | −0.0548133 | ||||||||
\(944\) | −23.2699 | −0.757369 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.9413 | −0.843423 | ||||||||
\(947\) | 14.2571 | 0.463293 | 0.231646 | − | 0.972800i | \(-0.425589\pi\) | ||||
0.231646 | + | 0.972800i | \(0.425589\pi\) | |||||||
\(948\) | −1.44068 | −0.0467910 | ||||||||
\(949\) | −10.0479 | −0.326169 | ||||||||
\(950\) | −69.1230 | −2.24265 | ||||||||
\(951\) | 22.7904 | 0.739031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.06503 | −0.0668930 | −0.0334465 | − | 0.999441i | \(-0.510648\pi\) | ||||
−0.0334465 | + | 0.999441i | \(0.510648\pi\) | |||||||
\(954\) | 2.01999 | 0.0653997 | ||||||||
\(955\) | −89.2552 | −2.88823 | ||||||||
\(956\) | 4.16136 | 0.134588 | ||||||||
\(957\) | 26.7472 | 0.864615 | ||||||||
\(958\) | −8.99921 | −0.290751 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 35.2060 | 1.13627 | ||||||||
\(961\) | 30.1792 | 0.973524 | ||||||||
\(962\) | −11.5078 | −0.371027 | ||||||||
\(963\) | −5.74268 | −0.185055 | ||||||||
\(964\) | 4.00284 | 0.128923 | ||||||||
\(965\) | −96.5456 | −3.10791 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1249 | −0.743645 | −0.371823 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(968\) | 22.7981 | 0.732758 | ||||||||
\(969\) | −7.11030 | −0.228416 | ||||||||
\(970\) | 15.0818 | 0.484247 | ||||||||
\(971\) | −41.3802 | −1.32795 | −0.663977 | − | 0.747753i | \(-0.731133\pi\) | ||||
−0.663977 | + | 0.747753i | \(0.731133\pi\) | |||||||
\(972\) | −0.246682 | −0.00791232 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.19387 | −0.198464 | ||||||||
\(975\) | 18.8977 | 0.605210 | ||||||||
\(976\) | 4.11723 | 0.131789 | ||||||||
\(977\) | −14.3806 | −0.460076 | −0.230038 | − | 0.973182i | \(-0.573885\pi\) | ||||
−0.230038 | + | 0.973182i | \(0.573885\pi\) | |||||||
\(978\) | −25.9425 | −0.829549 | ||||||||
\(979\) | 45.3229 | 1.44853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.22346 | 0.134845 | ||||||||
\(982\) | −41.0381 | −1.30958 | ||||||||
\(983\) | 49.7977 | 1.58830 | 0.794151 | − | 0.607721i | \(-0.207916\pi\) | ||||
0.794151 | + | 0.607721i | \(0.207916\pi\) | |||||||
\(984\) | −2.97490 | −0.0948363 | ||||||||
\(985\) | 93.5983 | 2.98229 | ||||||||
\(986\) | 12.5838 | 0.400751 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.91615 | −0.0609607 | ||||||||
\(989\) | 7.63320 | 0.242722 | ||||||||
\(990\) | −23.0735 | −0.733325 | ||||||||
\(991\) | 29.1147 | 0.924860 | 0.462430 | − | 0.886656i | \(-0.346978\pi\) | ||||
0.462430 | + | 0.886656i | \(0.346978\pi\) | |||||||
\(992\) | 10.8497 | 0.344480 | ||||||||
\(993\) | −10.1035 | −0.320625 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −68.9598 | −2.18617 | ||||||||
\(996\) | 0.0218005 | 0.000690775 0 | ||||||||
\(997\) | −3.91838 | −0.124096 | −0.0620481 | − | 0.998073i | \(-0.519763\pi\) | ||||
−0.0620481 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(998\) | 20.0161 | 0.633597 | ||||||||
\(999\) | 5.18274 | 0.163975 |
(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 | 6027.2.a.bo.1.6 | yes | 24 | |
7.6 | odd | 2 | 6027.2.a.bn.1.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6027.2.a.bn.1.6 | ✓ | 24 | 7.6 | odd | 2 | ||
6027.2.a.bo.1.6 | yes | 24 | 1.1 | even | 1 | trivial |