Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.98092 | −1.72103 | −0.860516 | − | 0.509423i | \(-0.829859\pi\) | ||||
−0.860516 | + | 0.509423i | \(0.829859\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.05916 | 1.36810 | 0.684049 | − | 0.729436i | \(-0.260218\pi\) | ||||
0.684049 | + | 0.729436i | \(0.260218\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.297244 | 0.112348 | 0.0561738 | − | 0.998421i | \(-0.482110\pi\) | ||||
0.0561738 | + | 0.998421i | \(0.482110\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.88586 | 1.96195 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.132067 | −0.0398198 | −0.0199099 | − | 0.999802i | \(-0.506338\pi\) | ||||
−0.0199099 | + | 0.999802i | \(0.506338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60162 | 0.998909 | 0.499455 | − | 0.866340i | \(-0.333534\pi\) | ||||
0.499455 | + | 0.866340i | \(0.333534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.11910 | −2.35454 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.86161 | 1.66419 | 0.832093 | − | 0.554636i | \(-0.187143\pi\) | ||||
0.832093 | + | 0.554636i | \(0.187143\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.04931 | −0.470145 | −0.235072 | − | 0.971978i | \(-0.575533\pi\) | ||||
−0.235072 | + | 0.971978i | \(0.575533\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.886059 | −0.193354 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.92554 | −1.86110 | −0.930552 | − | 0.366161i | \(-0.880672\pi\) | ||||
−0.930552 | + | 0.366161i | \(0.880672\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.35846 | 0.871691 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.60250 | −1.65555 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.43490 | −0.823541 | −0.411770 | − | 0.911288i | \(-0.635089\pi\) | ||||
−0.411770 | + | 0.911288i | \(0.635089\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.21683 | −0.398155 | −0.199077 | − | 0.979984i | \(-0.563795\pi\) | ||||
−0.199077 | + | 0.979984i | \(0.563795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.393681 | 0.0685311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.909317 | 0.153703 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.90972 | −0.971552 | −0.485776 | − | 0.874083i | \(-0.661463\pi\) | ||||
−0.485776 | + | 0.874083i | \(0.661463\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.7361 | −1.71916 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.20315 | −1.43729 | −0.718645 | − | 0.695377i | \(-0.755237\pi\) | ||||
−0.718645 | + | 0.695377i | \(0.755237\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.709880 | 0.108256 | 0.0541278 | − | 0.998534i | \(-0.482762\pi\) | ||||
0.0541278 | + | 0.998534i | \(0.482762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.0058 | 2.68414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.369774 | 0.0539370 | 0.0269685 | − | 0.999636i | \(-0.491415\pi\) | ||||
0.0269685 | + | 0.999636i | \(0.491415\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91165 | −0.987378 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.4539 | −2.86412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.1347 | −1.52947 | −0.764736 | − | 0.644344i | \(-0.777131\pi\) | ||||
−0.764736 | + | 0.644344i | \(0.777131\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.404015 | −0.0544773 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.10883 | 0.809134 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.23739 | 0.681851 | 0.340925 | − | 0.940090i | \(-0.389260\pi\) | ||||
0.340925 | + | 0.940090i | \(0.389260\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.397250 | 0.0508626 | 0.0254313 | − | 0.999677i | \(-0.491904\pi\) | ||||
0.0254313 | + | 0.999677i | \(0.491904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.74954 | 0.220421 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.0179 | 1.36661 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.96553 | −0.606636 | −0.303318 | − | 0.952889i | \(-0.598094\pi\) | ||||
−0.303318 | + | 0.952889i | \(0.598094\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 26.6063 | 3.20302 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.02363 | −0.358839 | −0.179419 | − | 0.983773i | \(-0.557422\pi\) | ||||
−0.179419 | + | 0.983773i | \(0.557422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.74973 | −1.14112 | −0.570560 | − | 0.821256i | \(-0.693274\pi\) | ||||
−0.570560 | + | 0.821256i | \(0.693274\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.9922 | −1.50021 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0392562 | −0.00447366 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.16717 | −0.468844 | −0.234422 | − | 0.972135i | \(-0.575320\pi\) | ||||
−0.234422 | + | 0.972135i | \(0.575320\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.98576 | 0.887306 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.18223 | 0.459059 | 0.229530 | − | 0.973302i | \(-0.426281\pi\) | ||||
0.229530 | + | 0.973302i | \(0.426281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 20.9908 | 2.27677 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.2201 | 1.41734 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9084 | 1.15629 | 0.578146 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578146 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07056 | 0.112225 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.60819 | 0.685237 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.26918 | −0.643204 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.82202 | −0.286532 | −0.143266 | − | 0.989684i | \(-0.545761\pi\) | ||||
−0.143266 | + | 0.989684i | \(0.545761\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.777329 | −0.0781245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.34157 | 0.133491 | 0.0667457 | − | 0.997770i | \(-0.478738\pi\) | ||||
0.0667457 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.83741 | 0.378111 | 0.189056 | − | 0.981966i | \(-0.439457\pi\) | ||||
0.189056 | + | 0.981966i | \(0.439457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.71060 | −0.264527 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.4717 | −1.39903 | −0.699514 | − | 0.714619i | \(-0.746600\pi\) | ||||
−0.699514 | + | 0.714619i | \(0.746600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6270 | −1.59258 | −0.796290 | − | 0.604915i | \(-0.793207\pi\) | ||||
−0.796290 | + | 0.604915i | \(0.793207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.6164 | 1.67207 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.49624 | −0.893331 | −0.446666 | − | 0.894701i | \(-0.647389\pi\) | ||||
−0.446666 | + | 0.894701i | \(0.647389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27.3046 | −2.54617 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.1986 | 1.95981 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.03957 | 0.186967 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9826 | −0.998414 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 27.4338 | 2.47362 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.96259 | −0.175539 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.61087 | 0.586620 | 0.293310 | − | 0.956017i | \(-0.405243\pi\) | ||||
0.293310 | + | 0.956017i | \(0.405243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.11609 | −0.186311 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4245 | 1.34765 | 0.673824 | − | 0.738892i | \(-0.264650\pi\) | ||||
0.673824 | + | 0.738892i | \(0.264650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.609146 | −0.0528197 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −26.3164 | −2.26496 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.1197 | −1.54807 | −0.774034 | − | 0.633144i | \(-0.781764\pi\) | ||||
−0.774034 | + | 0.633144i | \(0.781764\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6817 | −1.07565 | −0.537823 | − | 0.843058i | \(-0.680753\pi\) | ||||
−0.537823 | + | 0.843058i | \(0.680753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.10226 | −0.0928274 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.475656 | −0.0397763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5671 | −1.12668 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.6030 | 1.69931 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.8738 | 1.46428 | 0.732141 | − | 0.681153i | \(-0.238521\pi\) | ||||
0.732141 | + | 0.681153i | \(0.238521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0643 | 0.981775 | 0.490888 | − | 0.871223i | \(-0.336673\pi\) | ||||
0.490888 | + | 0.871223i | \(0.336673\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.3865 | 3.26505 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.78164 | −0.544715 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3399 | 1.62330 | 0.811651 | − | 0.584143i | \(-0.198569\pi\) | ||||
0.811651 | + | 0.584143i | \(0.198569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 33.1917 | 2.63227 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.65306 | −0.209091 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.8285 | 1.31811 | 0.659056 | − | 0.752094i | \(-0.270956\pi\) | ||||
0.659056 | + | 0.752094i | \(0.270956\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.20433 | 0.0937573 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.7134 | 1.21594 | 0.607969 | − | 0.793960i | \(-0.291984\pi\) | ||||
0.607969 | + | 0.793960i | \(0.291984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0283398 | −0.00217999 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0620 | −0.922402 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.03141 | −0.534588 | −0.267294 | − | 0.963615i | \(-0.586129\pi\) | ||||
−0.267294 | + | 0.963615i | \(0.586129\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.29552 | 0.0979325 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.6122 | −1.17349 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.47536 | 0.409248 | 0.204624 | − | 0.978841i | \(-0.434403\pi\) | ||||
0.204624 | + | 0.978841i | \(0.434403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7222 | −0.871305 | −0.435653 | − | 0.900115i | \(-0.643482\pi\) | ||||
−0.435653 | + | 0.900115i | \(0.643482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18417 | −0.0875362 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.0788 | −1.32918 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.906194 | −0.0662675 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.55704 | −0.185997 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1170 | −1.74505 | −0.872523 | − | 0.488573i | \(-0.837517\pi\) | ||||
−0.872523 | + | 0.488573i | \(0.837517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.15585 | 0.587071 | 0.293535 | − | 0.955948i | \(-0.405168\pi\) | ||||
0.293535 | + | 0.955948i | \(0.405168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −32.8435 | −2.35197 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.76635 | −0.695823 | −0.347912 | − | 0.937527i | \(-0.613109\pi\) | ||||
−0.347912 | + | 0.937527i | \(0.613109\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.217197 | −0.0153967 | −0.00769834 | − | 0.999970i | \(-0.502450\pi\) | ||||
−0.00769834 | + | 0.999970i | \(0.502450\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.8018 | 1.04404 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.31825 | −0.0925229 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.1539 | −1.96635 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −52.5345 | −3.65140 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.270647 | 0.0187211 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6428 | −0.939211 | −0.469606 | − | 0.882876i | \(-0.655604\pi\) | ||||
−0.469606 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.01319 | 0.617574 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.17164 | 0.148104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.658940 | −0.0447318 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.0631 | 1.96390 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.7129 | 1.66237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.3483 | 1.63048 | 0.815241 | − | 0.579121i | \(-0.196604\pi\) | ||||
0.815241 | + | 0.579121i | \(0.196604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.6533 | 1.71022 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9318 | 0.858312 | 0.429156 | − | 0.903230i | \(-0.358811\pi\) | ||||
0.429156 | + | 0.903230i | \(0.358811\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9500 | 1.25225 | 0.626125 | − | 0.779723i | \(-0.284640\pi\) | ||||
0.626125 | + | 0.779723i | \(0.284640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.117019 | 0.00769931 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.90095 | 0.321072 | 0.160536 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160536 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.13120 | 0.0737911 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.4220 | 0.806895 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.9952 | 1.16401 | 0.582006 | − | 0.813184i | \(-0.302268\pi\) | ||||
0.582006 | + | 0.813184i | \(0.302268\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.92465 | 0.446056 | 0.223028 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223028 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.00263 | 0.128469 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.1438 | −1.35083 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.38085 | −0.469632 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.4669 | −0.790056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.2014 | 1.59070 | 0.795349 | − | 0.606152i | \(-0.207288\pi\) | ||||
0.795349 | + | 0.606152i | \(0.207288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.17877 | 0.0741087 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −62.5717 | −3.91839 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7985 | −0.673593 | −0.336796 | − | 0.941578i | \(-0.609343\pi\) | ||||
−0.336796 | + | 0.941578i | \(0.609343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.75663 | −0.109152 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.1032 | −1.61575 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.2806 | −1.43554 | −0.717771 | − | 0.696279i | \(-0.754838\pi\) | ||||
−0.717771 | + | 0.696279i | \(0.754838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.0629 | −2.09247 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −32.5171 | −1.99002 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.0946 | 0.798392 | 0.399196 | − | 0.916866i | \(-0.369289\pi\) | ||||
0.399196 | + | 0.916866i | \(0.369289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.5126 | −0.760086 | −0.380043 | − | 0.924969i | \(-0.624091\pi\) | ||||
−0.380043 | + | 0.924969i | \(0.624091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.19125 | −0.193143 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.575609 | −0.0347105 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2064 | 1.21409 | 0.607043 | − | 0.794669i | \(-0.292355\pi\) | ||||
0.607043 | + | 0.794669i | \(0.292355\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.0480 | −0.781161 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.31394 | −0.436313 | −0.218157 | − | 0.975914i | \(-0.570004\pi\) | ||||
−0.218157 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2538 | −1.08507 | −0.542536 | − | 0.840032i | \(-0.682536\pi\) | ||||
−0.542536 | + | 0.840032i | \(0.682536\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.6879 | 1.10697 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.73558 | −0.161476 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.0817 | 1.76951 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.41219 | 0.493132 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.3113 | −0.836077 | −0.418038 | − | 0.908429i | \(-0.637282\pi\) | ||||
−0.418038 | + | 0.908429i | \(0.637282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0220 | 0.932838 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.13611 | 0.0659237 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −32.1464 | −1.85907 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.211008 | 0.0121623 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.99912 | −0.229743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.21525 | 0.0695850 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.15472 | −0.351268 | −0.175634 | − | 0.984456i | \(-0.556198\pi\) | ||||
−0.175634 | + | 0.984456i | \(0.556198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4390 | −0.650742 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.08231 | −0.458306 | −0.229153 | − | 0.973390i | \(-0.573596\pi\) | ||||
−0.229153 | + | 0.973390i | \(0.573596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6435 | −1.39294 | −0.696468 | − | 0.717588i | \(-0.745246\pi\) | ||||
−0.696468 | + | 0.717588i | \(0.745246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.35211 | 0.301557 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.7784 | −0.998535 | −0.499268 | − | 0.866448i | \(-0.666398\pi\) | ||||
−0.499268 | + | 0.866448i | \(0.666398\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.585705 | 0.0327932 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 43.1388 | 2.40777 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0616 | −0.782408 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.6975 | 0.870740 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 49.5638 | 2.74088 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.109913 | 0.00605970 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.50558 | 0.522474 | 0.261237 | − | 0.965275i | \(-0.415870\pi\) | ||||
0.261237 | + | 0.965275i | \(0.415870\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −34.7838 | −1.90614 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.1903 | −0.829937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2528 | −1.70245 | −0.851224 | − | 0.524803i | \(-0.824139\pi\) | ||||
−0.851224 | + | 0.524803i | \(0.824139\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 28.3075 | 1.53745 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.292771 | 0.0158544 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.13515 | −0.223277 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 81.3928 | 4.38204 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.1380 | −1.51053 | −0.755264 | − | 0.655421i | \(-0.772491\pi\) | ||||
−0.755264 | + | 0.655421i | \(0.772491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.77830 | 0.362834 | 0.181417 | − | 0.983406i | \(-0.441932\pi\) | ||||
0.181417 | + | 0.983406i | \(0.441932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −30.9829 | −1.65375 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.35060 | −0.178334 | −0.0891672 | − | 0.996017i | \(-0.528421\pi\) | ||||
−0.0891672 | + | 0.996017i | \(0.528421\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.24977 | −0.490927 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.07980 | −0.321777 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.0690 | −0.900867 | −0.450434 | − | 0.892810i | \(-0.648731\pi\) | ||||
−0.450434 | + | 0.892810i | \(0.648731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8003 | −0.778964 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.7381 | 1.71830 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −29.8260 | −1.56116 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.2072 | −1.21140 | −0.605702 | − | 0.795692i | \(-0.707108\pi\) | ||||
−0.605702 | + | 0.795692i | \(0.707108\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −54.1684 | −2.81990 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.30973 | −0.171833 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.0032 | 0.932171 | 0.466085 | − | 0.884740i | \(-0.345664\pi\) | ||||
0.466085 | + | 0.884740i | \(0.345664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.85031 | 0.302109 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.9728 | −0.822643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5805 | −1.10852 | −0.554259 | − | 0.832345i | \(-0.686998\pi\) | ||||
−0.554259 | + | 0.832345i | \(0.686998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.7064 | −1.00959 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.4335 | −1.45288 | −0.726442 | − | 0.687227i | \(-0.758828\pi\) | ||||
−0.726442 | + | 0.687227i | \(0.758828\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.120091 | −0.00612040 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.17825 | 0.212392 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.10098 | −0.106524 | −0.0532619 | − | 0.998581i | \(-0.516962\pi\) | ||||
−0.0532619 | + | 0.998581i | \(0.516962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −61.2436 | −3.09722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −45.9793 | −2.31935 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.7480 | −0.641424 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9121 | 1.20011 | 0.600056 | − | 0.799958i | \(-0.295145\pi\) | ||||
0.600056 | + | 0.799958i | \(0.295145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.81581 | 0.0909044 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.2924 | 0.563918 | 0.281959 | − | 0.959426i | \(-0.409016\pi\) | ||||
0.281959 | + | 0.959426i | \(0.409016\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.98418 | −0.397720 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 24.4297 | 1.21392 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.780480 | 0.0386870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.18638 | 0.454237 | 0.227119 | − | 0.973867i | \(-0.427069\pi\) | ||||
0.227119 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 54.0132 | 2.66427 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55678 | 0.0766043 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.7941 | 0.628038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 37.8030 | 1.85122 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.50817 | −0.317945 | −0.158973 | − | 0.987283i | \(-0.550818\pi\) | ||||
−0.158973 | + | 0.987283i | \(0.550818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.9286 | −1.11747 | −0.558735 | − | 0.829346i | \(-0.688713\pi\) | ||||
−0.558735 | + | 0.829346i | \(0.688713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.17644 | 0.105822 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.9060 | 1.45066 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.118080 | 0.00571430 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.41789 | 0.0684564 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.03628 | 0.0499159 | 0.0249580 | − | 0.999689i | \(-0.492055\pi\) | ||||
0.0249580 | + | 0.999689i | \(0.492055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5581 | 0.603503 | 0.301751 | − | 0.953387i | \(-0.402429\pi\) | ||||
0.301751 | + | 0.953387i | \(0.402429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.4423 | 1.93906 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2912 | 0.874988 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2191 | −0.535457 | −0.267729 | − | 0.963494i | \(-0.586273\pi\) | ||||
−0.267729 | + | 0.963494i | \(0.586273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −40.6810 | −1.93719 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.5728 | −0.549839 | −0.274920 | − | 0.961467i | \(-0.588651\pi\) | ||||
−0.274920 | + | 0.961467i | \(0.588651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.3706 | 1.58192 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −53.2804 | −2.52008 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.3019 | −0.958107 | −0.479053 | − | 0.877786i | \(-0.659020\pi\) | ||||
−0.479053 | + | 0.877786i | \(0.659020\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.21543 | 0.0572326 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −35.9625 | −1.68967 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.27501 | 0.153535 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.1861 | 0.850708 | 0.425354 | − | 0.905027i | \(-0.360150\pi\) | ||||
0.425354 | + | 0.905027i | \(0.360150\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.0270 | −2.75515 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3340 | 0.760750 | 0.380375 | − | 0.924832i | \(-0.375795\pi\) | ||||
0.380375 | + | 0.924832i | \(0.375795\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0699 | −0.467988 | −0.233994 | − | 0.972238i | \(-0.575180\pi\) | ||||
−0.233994 | + | 0.972238i | \(0.575180\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.2155 | 0.937471 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.21270 | −0.241215 | −0.120608 | − | 0.992700i | \(-0.538484\pi\) | ||||
−0.120608 | + | 0.992700i | \(0.538484\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.47597 | −0.0681541 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −60.6316 | −2.79376 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0937519 | −0.00431071 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.93184 | −0.409821 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −65.5374 | −3.00075 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.14836 | 0.235235 | 0.117617 | − | 0.993059i | \(-0.462474\pi\) | ||||
0.117617 | + | 0.993059i | \(0.462474\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.2846 | −0.970493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.90856 | 0.359852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.63300 | −0.392004 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.00118 | 0.271940 | 0.135970 | − | 0.990713i | \(-0.456585\pi\) | ||||
0.135970 | + | 0.990713i | \(0.456585\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −50.1645 | −2.26851 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.9781 | 0.675951 | 0.337976 | − | 0.941155i | \(-0.390258\pi\) | ||||
0.337976 | + | 0.941155i | \(0.390258\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.4306 | −1.37053 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.37797 | −0.106882 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.898756 | −0.0403147 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4259 | 0.914391 | 0.457195 | − | 0.889366i | \(-0.348854\pi\) | ||||
0.457195 | + | 0.889366i | \(0.348854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −46.8403 | −2.09267 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.5387 | 0.603662 | 0.301831 | − | 0.953361i | \(-0.402402\pi\) | ||||
0.301831 | + | 0.953361i | \(0.402402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.10408 | 0.182629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0844786 | 0.00375183 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3012 | 0.456594 | 0.228297 | − | 0.973591i | \(-0.426684\pi\) | ||||
0.228297 | + | 0.973591i | \(0.426684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.89805 | −0.128202 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.6292 | 0.778349 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.7392 | 0.517293 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0488350 | −0.00214776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.9600 | 0.920043 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.8230 | 0.693220 | 0.346610 | − | 0.938009i | \(-0.387333\pi\) | ||||
0.346610 | + | 0.938009i | \(0.387333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.7200 | −1.29956 | −0.649782 | − | 0.760121i | \(-0.725140\pi\) | ||||
−0.649782 | + | 0.760121i | \(0.725140\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.86185 | −0.168545 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.2110 | −0.662603 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.6652 | 2.46371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.8266 | 1.33776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.1462 | −1.43572 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −44.2711 | −1.91401 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.3216 | −0.704329 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.912802 | 0.0393172 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.91261 | −0.340190 | −0.170095 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170095 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.9429 | 1.49954 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −50.8647 | −2.17881 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2010 | 1.24855 | 0.624273 | − | 0.781206i | \(-0.285395\pi\) | ||||
0.624273 | + | 0.781206i | \(0.285395\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.33816 | 0.0997900 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.08851 | 0.387183 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23867 | −0.0526735 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 53.8913 | 2.28756 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.1567 | −0.938810 | −0.469405 | − | 0.882983i | \(-0.655532\pi\) | ||||
−0.469405 | + | 0.882983i | \(0.655532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.55672 | 0.108138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.70129 | 0.114049 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.409756 | 0.0172692 | 0.00863458 | − | 0.999963i | \(-0.497251\pi\) | ||||
0.00863458 | + | 0.999963i | \(0.497251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.0505 | −1.22216 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.37372 | 0.0996868 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.87091 | −0.204199 | −0.102100 | − | 0.994774i | \(-0.532556\pi\) | ||||
−0.102100 | + | 0.994774i | \(0.532556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.2933 | −1.81177 | −0.905884 | − | 0.423525i | \(-0.860793\pi\) | ||||
−0.905884 | + | 0.423525i | \(0.860793\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 71.8908 | 3.00328 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.9016 | −1.62231 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.2488 | 0.551553 | 0.275776 | − | 0.961222i | \(-0.411065\pi\) | ||||
0.275776 | + | 0.961222i | \(0.411065\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.3119 | −1.01037 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24314 | 0.0515742 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.47053 | 0.0609032 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 64.8500 | 2.68122 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.15537 | 0.212785 | 0.106392 | − | 0.994324i | \(-0.466070\pi\) | ||||
0.106392 | + | 0.994324i | \(0.466070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.54298 | 0.187190 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.1127 | 1.19753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 43.3018 | 1.77819 | 0.889095 | − | 0.457722i | \(-0.151335\pi\) | ||||
0.889095 | + | 0.457722i | \(0.151335\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.23938 | 0.255790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.647446 | 0.0264982 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.2368 | 0.499983 | 0.249992 | − | 0.968248i | \(-0.419572\pi\) | ||||
0.249992 | + | 0.968248i | \(0.419572\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2617 | −1.03045 | −0.515224 | − | 0.857056i | \(-0.672291\pi\) | ||||
−0.515224 | + | 0.857056i | \(0.672291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.2264 | −1.19019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.5974 | −1.36593 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.9595 | −0.688365 | −0.344182 | − | 0.938903i | \(-0.611844\pi\) | ||||
−0.344182 | + | 0.938903i | \(0.611844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.92959 | 0.159235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.33178 | 0.0538782 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3245 | 1.14402 | 0.572008 | − | 0.820248i | \(-0.306165\pi\) | ||||
0.572008 | + | 0.820248i | \(0.306165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 83.9244 | 3.38416 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.8076 | 1.92466 | 0.962331 | − | 0.271881i | \(-0.0876456\pi\) | ||||
0.962331 | + | 0.271881i | \(0.0876456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.9193 | 1.40353 | 0.701763 | − | 0.712411i | \(-0.252397\pi\) | ||||
0.701763 | + | 0.712411i | \(0.252397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 76.7820 | 3.08115 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.24247 | 0.129907 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7961 | −1.11185 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.806776 | −0.0322195 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.5502 | −1.61684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9559 | 0.515766 | 0.257883 | − | 0.966176i | \(-0.416975\pi\) | ||||
0.257883 | + | 0.966176i | \(0.416975\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40.6681 | 1.61641 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.2237 | 0.802553 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.8931 | −0.986301 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.7967 | −0.704025 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.61478 | −0.261268 | −0.130634 | − | 0.991431i | \(-0.541701\pi\) | ||||
−0.130634 | + | 0.991431i | \(0.541701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.03171 | −0.0801227 | −0.0400613 | − | 0.999197i | \(-0.512755\pi\) | ||||
−0.0400613 | + | 0.999197i | \(0.512755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.47346 | −0.254892 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.8630 | −0.898839 | −0.449420 | − | 0.893321i | \(-0.648369\pi\) | ||||
−0.449420 | + | 0.893321i | \(0.648369\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.691688 | −0.0271511 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.96424 | 0.0769848 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.75304 | −0.264267 | −0.132133 | − | 0.991232i | \(-0.542183\pi\) | ||||
−0.132133 | + | 0.991232i | \(0.542183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 47.1861 | 1.84371 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −57.3855 | −2.23882 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.72239 | −0.183958 | −0.0919790 | − | 0.995761i | \(-0.529319\pi\) | ||||
−0.0919790 | + | 0.995761i | \(0.529319\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.4057 | 1.84387 | 0.921934 | − | 0.387346i | \(-0.126608\pi\) | ||||
0.921934 | + | 0.387346i | \(0.126608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −73.6671 | −2.86099 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.86348 | −0.0722625 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39.5839 | 1.53269 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −72.5802 | −2.80611 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0524637 | −0.00202534 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4380 | 0.440902 | 0.220451 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220451 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −37.4936 | −1.44313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.02734 | 0.346949 | 0.173475 | − | 0.984838i | \(-0.444501\pi\) | ||||
0.173475 | + | 0.984838i | \(0.444501\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.838828 | −0.0321912 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.5485 | −1.47718 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.4228 | 0.513610 | 0.256805 | − | 0.966463i | \(-0.417330\pi\) | ||||
0.256805 | + | 0.966463i | \(0.417330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.4309 | −2.11791 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −56.4883 | −2.15516 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.1030 | −1.52780 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.9348 | 1.40506 | 0.702532 | − | 0.711652i | \(-0.252053\pi\) | ||||
0.702532 | + | 0.711652i | \(0.252053\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.231056 | −0.00877711 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.7953 | −1.47159 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −63.1484 | −2.39192 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.6093 | −0.552576 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.7399 | 1.72757 | 0.863785 | − | 0.503860i | \(-0.168087\pi\) | ||||
0.863785 | + | 0.503860i | \(0.168087\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1109 | 0.456770 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.37200 | −0.126997 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.398774 | 0.0149975 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.9620 | −0.411687 | −0.205843 | − | 0.978585i | \(-0.565994\pi\) | ||||
−0.205843 | + | 0.978585i | \(0.565994\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.5274 | −0.919849 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.7864 | 0.741007 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.45511 | −0.0544179 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −53.6422 | −2.00330 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.8983 | 1.74901 | 0.874506 | − | 0.485015i | \(-0.161186\pi\) | ||||
0.874506 | + | 0.485015i | \(0.161186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.14065 | 0.0424799 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.6418 | −0.767677 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.3293 | −0.717873 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −47.1700 | −1.74944 | −0.874719 | − | 0.484631i | \(-0.838954\pi\) | ||||
−0.874719 | + | 0.484631i | \(0.838954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9270 | −1.10841 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.87092 | 0.180157 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 50.1170 | 1.85111 | 0.925557 | − | 0.378609i | \(-0.123597\pi\) | ||||
0.925557 | + | 0.378609i | \(0.123597\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 63.0280 | 2.32482 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.655783 | 0.0241561 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.1130 | 1.29165 | 0.645827 | − | 0.763484i | \(-0.276513\pi\) | ||||
0.645827 | + | 0.763484i | \(0.276513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.0017 | 0.808252 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −46.4629 | −1.70456 | −0.852280 | − | 0.523087i | \(-0.824780\pi\) | ||||
−0.852280 | + | 0.523087i | \(0.824780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.6789 | 2.00328 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.6160 | 0.900653 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.30161 | −0.157177 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −75.1232 | −2.73764 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36.9065 | 1.34316 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.7374 | 0.899097 | 0.449548 | − | 0.893256i | \(-0.351585\pi\) | ||||
0.449548 | + | 0.893256i | \(0.351585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.51382 | −0.127543 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.95100 | −0.106974 | −0.0534869 | − | 0.998569i | \(-0.517034\pi\) | ||||
−0.0534869 | + | 0.998569i | \(0.517034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.94229 | −0.178923 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 123.549 | 4.46691 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.8631 | 0.681107 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.49197 | 0.270167 | 0.135084 | − | 0.990834i | \(-0.456870\pi\) | ||||
0.135084 | + | 0.990834i | \(0.456870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 32.1894 | 1.15927 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3565 | 1.27169 | 0.635843 | − | 0.771819i | \(-0.280653\pi\) | ||||
0.635843 | + | 0.771819i | \(0.280653\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.66196 | −0.347068 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.23636 | 0.187853 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.8601 | 0.675735 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.399323 | 0.0142889 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.1513 | 1.36342 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 62.2230 | 2.22084 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3186 | −1.08074 | −0.540372 | − | 0.841427i | \(-0.681716\pi\) | ||||
−0.540372 | + | 0.841427i | \(0.681716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 69.3975 | 2.47062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.82270 | −0.100364 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.43074 | 0.0508071 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 101.539 | 3.60120 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −49.6831 | −1.75987 | −0.879933 | − | 0.475099i | \(-0.842412\pi\) | ||||
−0.879933 | + | 0.475099i | \(0.842412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.53724 | 0.0897612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 64.2055 | 2.26859 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.28762 | 0.0454391 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.11614 | −0.286056 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −39.0339 | −1.37406 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.6256 | 1.04158 | 0.520791 | − | 0.853685i | \(-0.325637\pi\) | ||||
0.520791 | + | 0.853685i | \(0.325637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −52.0726 | −1.82852 | −0.914258 | − | 0.405134i | \(-0.867225\pi\) | ||||
−0.914258 | + | 0.405134i | \(0.867225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.2990 | 1.30813 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 51.4812 | 1.80331 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.45477 | −0.0508958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.30116 | 0.220180 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.0722 | −0.840124 | −0.420062 | − | 0.907495i | \(-0.637992\pi\) | ||||
−0.420062 | + | 0.907495i | \(0.637992\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.7874 | −1.90977 | −0.954884 | − | 0.296980i | \(-0.904020\pi\) | ||||
−0.954884 | + | 0.296980i | \(0.904020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.71584 | 0.0597380 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.2267 | 0.564257 | 0.282128 | − | 0.959377i | \(-0.408960\pi\) | ||||
0.282128 | + | 0.959377i | \(0.408960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.2588 | −0.842544 | −0.421272 | − | 0.906934i | \(-0.638416\pi\) | ||||
−0.421272 | + | 0.906934i | \(0.638416\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −60.2337 | −2.08948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −47.4250 | −1.64318 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.0698 | 1.66352 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.0703 | 0.659166 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.6871 | 1.43920 | 0.719599 | − | 0.694390i | \(-0.244326\pi\) | ||||
0.719599 | + | 0.694390i | \(0.244326\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.33163 | −0.321780 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.8022 | 0.750909 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0866960 | −0.00298243 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.26450 | −0.112170 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 54.4129 | 1.86745 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52.7474 | 1.80816 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.71850 | 0.0930798 | 0.0465399 | − | 0.998916i | \(-0.485181\pi\) | ||||
0.0465399 | + | 0.998916i | \(0.485181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.8995 | −1.26194 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.75359 | −0.0599015 | −0.0299507 | − | 0.999551i | \(-0.509535\pi\) | ||||
−0.0299507 | + | 0.999551i | \(0.509535\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7566 | 0.469369 | 0.234685 | − | 0.972072i | \(-0.424594\pi\) | ||||
0.234685 | + | 0.972072i | \(0.424594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.15454 | 0.277906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.16644 | 0.312029 | 0.156015 | − | 0.987755i | \(-0.450135\pi\) | ||||
0.156015 | + | 0.987755i | \(0.450135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.5102 | −0.731369 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −89.6711 | −3.04539 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.550347 | 0.0186692 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.8839 | −0.605974 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.6100 | −0.562163 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.583368 | −0.0197214 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.39218 | 0.148313 | 0.0741567 | − | 0.997247i | \(-0.476374\pi\) | ||||
0.0741567 | + | 0.997247i | \(0.476374\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 42.6609 | 1.43892 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.9220 | −0.435352 | −0.217676 | − | 0.976021i | \(-0.569848\pi\) | ||||
−0.217676 | + | 0.976021i | \(0.569848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.8403 | −1.37438 | −0.687192 | − | 0.726476i | \(-0.741157\pi\) | ||||
−0.687192 | + | 0.726476i | \(0.741157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −47.7603 | −1.60544 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.7519 | −0.998972 | −0.499486 | − | 0.866322i | \(-0.666478\pi\) | ||||
−0.499486 | + | 0.866322i | \(0.666478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.96504 | 0.0659054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.05466 | −0.0353323 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.757782 | −0.0253582 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.7500 | 0.559891 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 95.8257 | 3.19953 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.83144 | 0.327897 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −76.4022 | −2.54533 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.628996 | −0.0209317 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −35.8601 | −1.19203 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8703 | 0.892214 | 0.446107 | − | 0.894980i | \(-0.352810\pi\) | ||||
0.446107 | + | 0.894980i | \(0.352810\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.89631 | 0.261904 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.290314 | −0.00961854 | −0.00480927 | − | 0.999988i | \(-0.501531\pi\) | ||||
−0.00480927 | + | 0.999988i | \(0.501531\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.552335 | −0.0182796 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.62256 | −0.119758 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.58485 | 0.151405 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.2476 | 0.667908 | 0.333954 | − | 0.942589i | \(-0.391617\pi\) | ||||
0.333954 | + | 0.942589i | \(0.391617\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.3467 | 0.604544 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.8900 | −0.358448 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.7573 | −0.846893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.5864 | 0.741836 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.86011 | 0.192264 | 0.0961320 | − | 0.995369i | \(-0.469353\pi\) | ||||
0.0961320 | + | 0.995369i | \(0.469353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.1641 | 0.464211 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 24.0927 | 0.788759 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.77219 | −0.0906604 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.8764 | −1.10670 | −0.553348 | − | 0.832950i | \(-0.686650\pi\) | ||||
−0.553348 | + | 0.832950i | \(0.686650\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 73.4603 | 2.39729 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5147 | 1.74453 | 0.872265 | − | 0.489033i | \(-0.162650\pi\) | ||||
0.872265 | + | 0.489033i | \(0.162650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 82.1431 | 2.67495 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.82240 | −0.254463 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.2206 | −1.53446 | −0.767231 | − | 0.641371i | \(-0.778366\pi\) | ||||
−0.767231 | + | 0.641371i | \(0.778366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.1148 | −1.13987 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.9960 | 1.71851 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.3831 | −1.27574 | −0.637872 | − | 0.770142i | \(-0.720185\pi\) | ||||
−0.637872 | + | 0.770142i | \(0.720185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −73.7778 | −2.38739 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.74594 | −0.0564382 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.38596 | −0.173922 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.0857 | −0.841473 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −85.1781 | −2.74483 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.9500 | 0.803170 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.23083 | −0.168212 | −0.0841061 | − | 0.996457i | \(-0.526803\pi\) | ||||
−0.0841061 | + | 0.996457i | \(0.526803\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.9164 | 1.34655 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.7138 | 1.59539 | 0.797697 | − | 0.603059i | \(-0.206052\pi\) | ||||
0.797697 | + | 0.603059i | \(0.206052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.76955 | −0.120846 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −46.7929 | −1.49857 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.7627 | 0.536286 | 0.268143 | − | 0.963379i | \(-0.413590\pi\) | ||||
0.268143 | + | 0.963379i | \(0.413590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.44065 | −0.0460433 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −97.8643 | −3.12457 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.31366 | −0.0737942 | −0.0368971 | − | 0.999319i | \(-0.511747\pi\) | ||||
−0.0368971 | + | 0.999319i | \(0.511747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −29.8768 | −0.951954 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.327641 | −0.0104289 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.33606 | −0.201475 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7561 | −0.881702 | −0.440851 | − | 0.897580i | \(-0.645323\pi\) | ||||
−0.440851 | + | 0.897580i | \(0.645323\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −28.3353 | −0.899194 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.664440 | −0.0210642 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.8153 | 1.22929 | 0.614646 | − | 0.788803i | \(-0.289299\pi\) | ||||
0.614646 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50.8384 | 1.60846 |
(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 | 6008.2.a.b.1.6 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.6 | ✓ | 44 | 1.1 | even | 1 | trivial |