Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.30 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.44637 | 1.72984 | 0.864921 | − | 0.501907i | \(-0.167368\pi\) | ||||
0.864921 | + | 0.501907i | \(0.167368\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.98471 | 1.99236 | ||||||||
\(5\) | −1.74324 | −0.779599 | −0.389800 | − | 0.920900i | \(-0.627456\pi\) | ||||
−0.389800 | + | 0.920900i | \(0.627456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 4.85534 | 1.71662 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.26460 | −1.34858 | ||||||||
\(11\) | 0.135794 | 0.0409434 | 0.0204717 | − | 0.999790i | \(-0.493483\pi\) | ||||
0.0204717 | + | 0.999790i | \(0.493483\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.02529 | −0.561713 | −0.280857 | − | 0.959750i | \(-0.590619\pi\) | ||||
−0.280857 | + | 0.959750i | \(0.590619\pi\) | |||||||
\(14\) | −2.44637 | −0.653819 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.90851 | 0.977127 | ||||||||
\(17\) | −0.659283 | −0.159900 | −0.0799498 | − | 0.996799i | \(-0.525476\pi\) | ||||
−0.0799498 | + | 0.996799i | \(0.525476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26306 | −0.748598 | −0.374299 | − | 0.927308i | \(-0.622117\pi\) | ||||
−0.374299 | + | 0.927308i | \(0.622117\pi\) | |||||||
\(20\) | −6.94630 | −1.55324 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.332202 | 0.0708257 | ||||||||
\(23\) | 2.00548 | 0.418172 | 0.209086 | − | 0.977897i | \(-0.432951\pi\) | ||||
0.209086 | + | 0.977897i | \(0.432951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.96113 | −0.392225 | ||||||||
\(26\) | −4.95459 | −0.971676 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.98471 | −0.753040 | ||||||||
\(29\) | 6.31569 | 1.17279 | 0.586397 | − | 0.810024i | \(-0.300546\pi\) | ||||
0.586397 | + | 0.810024i | \(0.300546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.78434 | 1.21850 | 0.609252 | − | 0.792977i | \(-0.291470\pi\) | ||||
0.609252 | + | 0.792977i | \(0.291470\pi\) | |||||||
\(32\) | −0.149022 | −0.0263437 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.61285 | −0.276601 | ||||||||
\(35\) | 1.74324 | 0.294661 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.08417 | 0.342635 | 0.171317 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171317 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(38\) | −7.98265 | −1.29496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.46400 | −1.33828 | ||||||||
\(41\) | −2.96378 | −0.462865 | −0.231433 | − | 0.972851i | \(-0.574341\pi\) | ||||
−0.231433 | + | 0.972851i | \(0.574341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.48820 | −0.379447 | −0.189723 | − | 0.981838i | \(-0.560759\pi\) | ||||
−0.189723 | + | 0.981838i | \(0.560759\pi\) | |||||||
\(44\) | 0.541100 | 0.0815739 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.90615 | 0.723372 | ||||||||
\(47\) | −12.8855 | −1.87955 | −0.939773 | − | 0.341801i | \(-0.888963\pi\) | ||||
−0.939773 | + | 0.341801i | \(0.888963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −4.79763 | −0.678488 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.07018 | −1.11913 | ||||||||
\(53\) | −1.28176 | −0.176063 | −0.0880317 | − | 0.996118i | \(-0.528058\pi\) | ||||
−0.0880317 | + | 0.996118i | \(0.528058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.236721 | −0.0319195 | ||||||||
\(56\) | −4.85534 | −0.648822 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15.4505 | 2.02875 | ||||||||
\(59\) | −12.3426 | −1.60687 | −0.803434 | − | 0.595394i | \(-0.796996\pi\) | ||||
−0.803434 | + | 0.595394i | \(0.796996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9997 | −1.53640 | −0.768201 | − | 0.640209i | \(-0.778848\pi\) | ||||
−0.768201 | + | 0.640209i | \(0.778848\pi\) | |||||||
\(62\) | 16.5970 | 2.10782 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.18158 | −1.02270 | ||||||||
\(65\) | 3.53055 | 0.437911 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6878 | −1.67223 | −0.836113 | − | 0.548557i | \(-0.815177\pi\) | ||||
−0.836113 | + | 0.548557i | \(0.815177\pi\) | |||||||
\(68\) | −2.62705 | −0.318577 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.26460 | 0.509717 | ||||||||
\(71\) | 0.817936 | 0.0970712 | 0.0485356 | − | 0.998821i | \(-0.484545\pi\) | ||||
0.0485356 | + | 0.998821i | \(0.484545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.1195 | 1.18439 | 0.592196 | − | 0.805794i | \(-0.298261\pi\) | ||||
0.592196 | + | 0.805794i | \(0.298261\pi\) | |||||||
\(74\) | 5.09863 | 0.592704 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.0024 | −1.49147 | ||||||||
\(77\) | −0.135794 | −0.0154752 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.94496 | 0.443842 | 0.221921 | − | 0.975065i | \(-0.428767\pi\) | ||||
0.221921 | + | 0.975065i | \(0.428767\pi\) | |||||||
\(80\) | −6.81346 | −0.761768 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.25051 | −0.800684 | ||||||||
\(83\) | −17.3428 | −1.90362 | −0.951812 | − | 0.306684i | \(-0.900781\pi\) | ||||
−0.951812 | + | 0.306684i | \(0.900781\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.14929 | 0.124658 | ||||||||
\(86\) | −6.08704 | −0.656383 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.659325 | 0.0702843 | ||||||||
\(89\) | −12.4110 | −1.31556 | −0.657781 | − | 0.753209i | \(-0.728505\pi\) | ||||
−0.657781 | + | 0.753209i | \(0.728505\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.02529 | 0.212308 | ||||||||
\(92\) | 7.99127 | 0.833148 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −31.5227 | −3.25132 | ||||||||
\(95\) | 5.68829 | 0.583606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.98004 | 0.505647 | 0.252823 | − | 0.967512i | \(-0.418641\pi\) | ||||
0.252823 | + | 0.967512i | \(0.418641\pi\) | |||||||
\(98\) | 2.44637 | 0.247120 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.81452 | −0.781452 | ||||||||
\(101\) | 3.77619 | 0.375745 | 0.187873 | − | 0.982193i | \(-0.439841\pi\) | ||||
0.187873 | + | 0.982193i | \(0.439841\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.75563 | −0.370054 | −0.185027 | − | 0.982733i | \(-0.559237\pi\) | ||||
−0.185027 | + | 0.982733i | \(0.559237\pi\) | |||||||
\(104\) | −9.83344 | −0.964249 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.13566 | −0.304562 | ||||||||
\(107\) | 4.86491 | 0.470308 | 0.235154 | − | 0.971958i | \(-0.424440\pi\) | ||||
0.235154 | + | 0.971958i | \(0.424440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.59574 | −0.248627 | −0.124313 | − | 0.992243i | \(-0.539673\pi\) | ||||
−0.124313 | + | 0.992243i | \(0.539673\pi\) | |||||||
\(110\) | −0.579107 | −0.0552156 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.90851 | −0.369319 | ||||||||
\(113\) | 2.63918 | 0.248274 | 0.124137 | − | 0.992265i | \(-0.460384\pi\) | ||||
0.124137 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.49603 | −0.326007 | ||||||||
\(116\) | 25.1662 | 2.33662 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −30.1945 | −2.77963 | ||||||||
\(119\) | 0.659283 | 0.0604363 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9816 | −0.998324 | ||||||||
\(122\) | −29.3556 | −2.65773 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 27.0336 | 2.42769 | ||||||||
\(125\) | 12.1349 | 1.08538 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −19.7171 | −1.74276 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.63703 | 0.757518 | ||||||||
\(131\) | −12.4783 | −1.09023 | −0.545115 | − | 0.838361i | \(-0.683514\pi\) | ||||
−0.545115 | + | 0.838361i | \(0.683514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.26306 | 0.282943 | ||||||||
\(134\) | −33.4853 | −2.89269 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.20104 | −0.274487 | ||||||||
\(137\) | −12.4812 | −1.06634 | −0.533171 | − | 0.846007i | \(-0.679000\pi\) | ||||
−0.533171 | + | 0.846007i | \(0.679000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.12288 | 0.519336 | 0.259668 | − | 0.965698i | \(-0.416387\pi\) | ||||
0.259668 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(140\) | 6.94630 | 0.587069 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00097 | 0.167918 | ||||||||
\(143\) | −0.275022 | −0.0229985 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.0097 | −0.914310 | ||||||||
\(146\) | 24.7559 | 2.04881 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.30480 | 0.682650 | ||||||||
\(149\) | 3.76846 | 0.308725 | 0.154362 | − | 0.988014i | \(-0.450668\pi\) | ||||
0.154362 | + | 0.988014i | \(0.450668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.0889 | −1.06516 | −0.532579 | − | 0.846381i | \(-0.678777\pi\) | ||||
−0.532579 | + | 0.846381i | \(0.678777\pi\) | |||||||
\(152\) | −15.8433 | −1.28506 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.332202 | −0.0267696 | ||||||||
\(155\) | −11.8267 | −0.949944 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1694 | 1.29046 | 0.645230 | − | 0.763988i | \(-0.276762\pi\) | ||||
0.645230 | + | 0.763988i | \(0.276762\pi\) | |||||||
\(158\) | 9.65081 | 0.767777 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.259781 | 0.0205375 | ||||||||
\(161\) | −2.00548 | −0.158054 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.0079 | −1.33216 | −0.666080 | − | 0.745880i | \(-0.732029\pi\) | ||||
−0.666080 | + | 0.745880i | \(0.732029\pi\) | |||||||
\(164\) | −11.8098 | −0.922193 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −42.4269 | −3.29297 | ||||||||
\(167\) | 6.66021 | 0.515382 | 0.257691 | − | 0.966227i | \(-0.417038\pi\) | ||||
0.257691 | + | 0.966227i | \(0.417038\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.89822 | −0.684478 | ||||||||
\(170\) | 2.81158 | 0.215638 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.91475 | −0.755993 | ||||||||
\(173\) | 18.1392 | 1.37910 | 0.689548 | − | 0.724240i | \(-0.257809\pi\) | ||||
0.689548 | + | 0.724240i | \(0.257809\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.96113 | 0.148247 | ||||||||
\(176\) | 0.530752 | 0.0400069 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −30.3618 | −2.27572 | ||||||||
\(179\) | 18.5858 | 1.38917 | 0.694583 | − | 0.719413i | \(-0.255589\pi\) | ||||
0.694583 | + | 0.719413i | \(0.255589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.8637 | −1.62512 | −0.812558 | − | 0.582880i | \(-0.801926\pi\) | ||||
−0.812558 | + | 0.582880i | \(0.801926\pi\) | |||||||
\(182\) | 4.95459 | 0.367259 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.73729 | 0.717843 | ||||||||
\(185\) | −3.63319 | −0.267118 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0895266 | −0.00654684 | ||||||||
\(188\) | −51.3451 | −3.74472 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.9156 | 1.00955 | ||||||||
\(191\) | 18.6935 | 1.35262 | 0.676308 | − | 0.736619i | \(-0.263579\pi\) | ||||
0.676308 | + | 0.736619i | \(0.263579\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7789 | −1.20777 | −0.603886 | − | 0.797071i | \(-0.706382\pi\) | ||||
−0.603886 | + | 0.797071i | \(0.706382\pi\) | |||||||
\(194\) | 12.1830 | 0.874689 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.98471 | 0.284622 | ||||||||
\(197\) | 11.4210 | 0.813709 | 0.406855 | − | 0.913493i | \(-0.366626\pi\) | ||||
0.406855 | + | 0.913493i | \(0.366626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0173 | −0.780992 | −0.390496 | − | 0.920605i | \(-0.627697\pi\) | ||||
−0.390496 | + | 0.920605i | \(0.627697\pi\) | |||||||
\(200\) | −9.52193 | −0.673302 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.23795 | 0.649980 | ||||||||
\(203\) | −6.31569 | −0.443275 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.16658 | 0.360849 | ||||||||
\(206\) | −9.18766 | −0.640135 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.91585 | −0.548865 | ||||||||
\(209\) | −0.443104 | −0.0306501 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.44988 | 0.650557 | 0.325278 | − | 0.945618i | \(-0.394542\pi\) | ||||
0.325278 | + | 0.945618i | \(0.394542\pi\) | |||||||
\(212\) | −5.10745 | −0.350781 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.9014 | 0.813560 | ||||||||
\(215\) | 4.33752 | 0.295816 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.78434 | −0.460551 | ||||||||
\(218\) | −6.35013 | −0.430085 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.943265 | −0.0635949 | ||||||||
\(221\) | 1.33524 | 0.0898177 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9005 | −0.997811 | −0.498906 | − | 0.866656i | \(-0.666265\pi\) | ||||
−0.498906 | + | 0.866656i | \(0.666265\pi\) | |||||||
\(224\) | 0.149022 | 0.00995698 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.45641 | 0.429474 | ||||||||
\(227\) | 10.5921 | 0.703025 | 0.351513 | − | 0.936183i | \(-0.385667\pi\) | ||||
0.351513 | + | 0.936183i | \(0.385667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.6836 | 1.43289 | 0.716447 | − | 0.697641i | \(-0.245767\pi\) | ||||
0.716447 | + | 0.697641i | \(0.245767\pi\) | |||||||
\(230\) | −8.55258 | −0.563940 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 30.6648 | 2.01324 | ||||||||
\(233\) | 9.95372 | 0.652090 | 0.326045 | − | 0.945354i | \(-0.394284\pi\) | ||||
0.326045 | + | 0.945354i | \(0.394284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.4625 | 1.46529 | ||||||||
\(236\) | −49.1816 | −3.20145 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.61285 | 0.104545 | ||||||||
\(239\) | 23.4606 | 1.51754 | 0.758771 | − | 0.651357i | \(-0.225800\pi\) | ||||
0.758771 | + | 0.651357i | \(0.225800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.49046 | 0.611334 | 0.305667 | − | 0.952138i | \(-0.401121\pi\) | ||||
0.305667 | + | 0.952138i | \(0.401121\pi\) | |||||||
\(242\) | −26.8649 | −1.72694 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −47.8153 | −3.06106 | ||||||||
\(245\) | −1.74324 | −0.111371 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.60863 | 0.420497 | ||||||||
\(248\) | 32.9403 | 2.09171 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.6864 | 1.87753 | ||||||||
\(251\) | 12.1739 | 0.768409 | 0.384204 | − | 0.923248i | \(-0.374476\pi\) | ||||
0.384204 | + | 0.923248i | \(0.374476\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.272333 | 0.0171214 | ||||||||
\(254\) | −2.44637 | −0.153499 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.8721 | −1.99201 | ||||||||
\(257\) | 5.54656 | 0.345985 | 0.172993 | − | 0.984923i | \(-0.444656\pi\) | ||||
0.172993 | + | 0.984923i | \(0.444656\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.08417 | −0.129504 | ||||||||
\(260\) | 14.0682 | 0.872475 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −30.5264 | −1.88593 | ||||||||
\(263\) | 28.9806 | 1.78702 | 0.893509 | − | 0.449046i | \(-0.148236\pi\) | ||||
0.893509 | + | 0.449046i | \(0.148236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.23441 | 0.137259 | ||||||||
\(266\) | 7.98265 | 0.489447 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −54.5418 | −3.33167 | ||||||||
\(269\) | 3.14968 | 0.192039 | 0.0960197 | − | 0.995379i | \(-0.469389\pi\) | ||||
0.0960197 | + | 0.995379i | \(0.469389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.19663 | −0.558655 | −0.279328 | − | 0.960196i | \(-0.590112\pi\) | ||||
−0.279328 | + | 0.960196i | \(0.590112\pi\) | |||||||
\(272\) | −2.57681 | −0.156242 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.5336 | −1.84460 | ||||||||
\(275\) | −0.266309 | −0.0160590 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1167 | 0.667935 | 0.333967 | − | 0.942585i | \(-0.391612\pi\) | ||||
0.333967 | + | 0.942585i | \(0.391612\pi\) | |||||||
\(278\) | 14.9788 | 0.898370 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.46400 | 0.505821 | ||||||||
\(281\) | 14.0895 | 0.840511 | 0.420255 | − | 0.907406i | \(-0.361940\pi\) | ||||
0.420255 | + | 0.907406i | \(0.361940\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.6269 | 1.46392 | 0.731960 | − | 0.681348i | \(-0.238606\pi\) | ||||
0.731960 | + | 0.681348i | \(0.238606\pi\) | |||||||
\(284\) | 3.25924 | 0.193400 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.672804 | −0.0397837 | ||||||||
\(287\) | 2.96378 | 0.174947 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.5653 | −0.974432 | ||||||||
\(290\) | −26.9339 | −1.58161 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 40.3231 | 2.35973 | ||||||||
\(293\) | 5.37284 | 0.313884 | 0.156942 | − | 0.987608i | \(-0.449836\pi\) | ||||
0.156942 | + | 0.987608i | \(0.449836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.5160 | 1.25271 | ||||||||
\(296\) | 10.1193 | 0.588174 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.21905 | 0.534045 | ||||||||
\(299\) | −4.06168 | −0.234893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.48820 | 0.143417 | ||||||||
\(302\) | −32.0202 | −1.84255 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.7537 | −0.731475 | ||||||||
\(305\) | 20.9183 | 1.19778 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.1371 | −0.578554 | −0.289277 | − | 0.957245i | \(-0.593415\pi\) | ||||
−0.289277 | + | 0.957245i | \(0.593415\pi\) | |||||||
\(308\) | −0.541100 | −0.0308320 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.9325 | −1.64325 | ||||||||
\(311\) | −7.81567 | −0.443186 | −0.221593 | − | 0.975139i | \(-0.571126\pi\) | ||||
−0.221593 | + | 0.975139i | \(0.571126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.2066 | −0.972574 | −0.486287 | − | 0.873799i | \(-0.661649\pi\) | ||||
−0.486287 | + | 0.873799i | \(0.661649\pi\) | |||||||
\(314\) | 39.5563 | 2.23229 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.7195 | 0.884292 | ||||||||
\(317\) | −19.2484 | −1.08110 | −0.540548 | − | 0.841313i | \(-0.681783\pi\) | ||||
−0.540548 | + | 0.841313i | \(0.681783\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.857633 | 0.0480182 | ||||||||
\(320\) | 14.2624 | 0.797294 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.90615 | −0.273409 | ||||||||
\(323\) | 2.15128 | 0.119700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.97184 | 0.220318 | ||||||||
\(326\) | −41.6075 | −2.30443 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.3902 | −0.794564 | ||||||||
\(329\) | 12.8855 | 0.710401 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.8190 | 1.52907 | 0.764536 | − | 0.644581i | \(-0.222968\pi\) | ||||
0.764536 | + | 0.644581i | \(0.222968\pi\) | |||||||
\(332\) | −69.1062 | −3.79270 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.2933 | 0.891530 | ||||||||
\(335\) | 23.8610 | 1.30367 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.9358 | 1.57623 | 0.788115 | − | 0.615528i | \(-0.211057\pi\) | ||||
0.788115 | + | 0.615528i | \(0.211057\pi\) | |||||||
\(338\) | −21.7683 | −1.18404 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.57957 | 0.248362 | ||||||||
\(341\) | 0.921273 | 0.0498897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −12.0810 | −0.651366 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 44.3751 | 2.38562 | ||||||||
\(347\) | 20.6974 | 1.11109 | 0.555547 | − | 0.831485i | \(-0.312509\pi\) | ||||
0.555547 | + | 0.831485i | \(0.312509\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.7409 | −1.37788 | −0.688938 | − | 0.724820i | \(-0.741923\pi\) | ||||
−0.688938 | + | 0.724820i | \(0.741923\pi\) | |||||||
\(350\) | 4.79763 | 0.256444 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0202364 | −0.00107860 | ||||||||
\(353\) | −28.8035 | −1.53306 | −0.766529 | − | 0.642210i | \(-0.778018\pi\) | ||||
−0.766529 | + | 0.642210i | \(0.778018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42586 | −0.0756766 | ||||||||
\(356\) | −49.4542 | −2.62107 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 45.4676 | 2.40304 | ||||||||
\(359\) | 8.09394 | 0.427182 | 0.213591 | − | 0.976923i | \(-0.431484\pi\) | ||||
0.213591 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.35243 | −0.439602 | ||||||||
\(362\) | −53.4866 | −2.81120 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.07018 | 0.422993 | ||||||||
\(365\) | −17.6406 | −0.923351 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.7470 | −0.874186 | −0.437093 | − | 0.899416i | \(-0.643992\pi\) | ||||
−0.437093 | + | 0.899416i | \(0.643992\pi\) | |||||||
\(368\) | 7.83845 | 0.408607 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.88812 | −0.462072 | ||||||||
\(371\) | 1.28176 | 0.0665457 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6227 | 1.01603 | 0.508013 | − | 0.861349i | \(-0.330380\pi\) | ||||
0.508013 | + | 0.861349i | \(0.330380\pi\) | |||||||
\(374\) | −0.219015 | −0.0113250 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −62.5635 | −3.22647 | ||||||||
\(377\) | −12.7911 | −0.658774 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.60545 | −0.442032 | −0.221016 | − | 0.975270i | \(-0.570937\pi\) | ||||
−0.221016 | + | 0.975270i | \(0.570937\pi\) | |||||||
\(380\) | 22.6662 | 1.16275 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 45.7312 | 2.33981 | ||||||||
\(383\) | −36.7316 | −1.87690 | −0.938448 | − | 0.345420i | \(-0.887736\pi\) | ||||
−0.938448 | + | 0.345420i | \(0.887736\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.236721 | 0.0120644 | ||||||||
\(386\) | −41.0473 | −2.08925 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.8440 | 1.00743 | ||||||||
\(389\) | 5.24504 | 0.265934 | 0.132967 | − | 0.991120i | \(-0.457550\pi\) | ||||
0.132967 | + | 0.991120i | \(0.457550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.32218 | −0.0668655 | ||||||||
\(392\) | 4.85534 | 0.245231 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.9398 | 1.40759 | ||||||||
\(395\) | −6.87699 | −0.346019 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.4181 | 0.573058 | 0.286529 | − | 0.958072i | \(-0.407499\pi\) | ||||
0.286529 | + | 0.958072i | \(0.407499\pi\) | |||||||
\(398\) | −26.9522 | −1.35099 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.66508 | −0.383254 | ||||||||
\(401\) | −3.11844 | −0.155728 | −0.0778638 | − | 0.996964i | \(-0.524810\pi\) | ||||
−0.0778638 | + | 0.996964i | \(0.524810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.7402 | −0.684450 | ||||||||
\(404\) | 15.0470 | 0.748618 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.4505 | −0.766796 | ||||||||
\(407\) | 0.283017 | 0.0140286 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.6880 | −1.22075 | −0.610373 | − | 0.792114i | \(-0.708980\pi\) | ||||
−0.610373 | + | 0.792114i | \(0.708980\pi\) | |||||||
\(410\) | 12.6393 | 0.624213 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.9651 | −0.737279 | ||||||||
\(413\) | 12.3426 | 0.607339 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.2327 | 1.48406 | ||||||||
\(416\) | 0.301813 | 0.0147976 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.08400 | −0.0530199 | ||||||||
\(419\) | 0.509385 | 0.0248851 | 0.0124425 | − | 0.999923i | \(-0.496039\pi\) | ||||
0.0124425 | + | 0.999923i | \(0.496039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9127 | 1.31165 | 0.655823 | − | 0.754915i | \(-0.272322\pi\) | ||||
0.655823 | + | 0.754915i | \(0.272322\pi\) | |||||||
\(422\) | 23.1179 | 1.12536 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.22338 | −0.302234 | ||||||||
\(425\) | 1.29294 | 0.0627166 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9997 | 0.580705 | ||||||||
\(428\) | 19.3853 | 0.937022 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.6112 | 0.511715 | ||||||||
\(431\) | 5.41933 | 0.261040 | 0.130520 | − | 0.991446i | \(-0.458335\pi\) | ||||
0.130520 | + | 0.991446i | \(0.458335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.57950 | −0.268134 | −0.134067 | − | 0.990972i | \(-0.542804\pi\) | ||||
−0.134067 | + | 0.990972i | \(0.542804\pi\) | |||||||
\(434\) | −16.5970 | −0.796681 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.3433 | −0.495353 | ||||||||
\(437\) | −6.54401 | −0.313043 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.5614 | −1.55407 | −0.777035 | − | 0.629457i | \(-0.783277\pi\) | ||||
−0.777035 | + | 0.629457i | \(0.783277\pi\) | |||||||
\(440\) | −1.14936 | −0.0547936 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.26648 | 0.155371 | ||||||||
\(443\) | −28.6399 | −1.36072 | −0.680361 | − | 0.732878i | \(-0.738177\pi\) | ||||
−0.680361 | + | 0.732878i | \(0.738177\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.6353 | 1.02561 | ||||||||
\(446\) | −36.4521 | −1.72606 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.18158 | 0.386543 | ||||||||
\(449\) | −40.1926 | −1.89681 | −0.948403 | − | 0.317066i | \(-0.897302\pi\) | ||||
−0.948403 | + | 0.317066i | \(0.897302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.402464 | −0.0189513 | ||||||||
\(452\) | 10.5164 | 0.494649 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.9123 | 1.21612 | ||||||||
\(455\) | −3.53055 | −0.165515 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.1798 | 0.990750 | 0.495375 | − | 0.868679i | \(-0.335031\pi\) | ||||
0.495375 | + | 0.868679i | \(0.335031\pi\) | |||||||
\(458\) | 53.0461 | 2.47868 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.9307 | −0.649521 | ||||||||
\(461\) | 1.87919 | 0.0875224 | 0.0437612 | − | 0.999042i | \(-0.486066\pi\) | ||||
0.0437612 | + | 0.999042i | \(0.486066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.08778 | 0.236449 | 0.118225 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118225 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(464\) | 24.6849 | 1.14597 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.3505 | 1.12801 | ||||||||
\(467\) | 7.80477 | 0.361162 | 0.180581 | − | 0.983560i | \(-0.442202\pi\) | ||||
0.180581 | + | 0.983560i | \(0.442202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6878 | 0.632042 | ||||||||
\(470\) | 54.9515 | 2.53472 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −59.9274 | −2.75838 | ||||||||
\(473\) | −0.337882 | −0.0155358 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.39927 | 0.293619 | ||||||||
\(476\) | 2.62705 | 0.120411 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 57.3933 | 2.62511 | ||||||||
\(479\) | 11.7028 | 0.534717 | 0.267358 | − | 0.963597i | \(-0.413849\pi\) | ||||
0.267358 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.22103 | −0.192462 | ||||||||
\(482\) | 23.2172 | 1.05751 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −43.7584 | −1.98902 | ||||||||
\(485\) | −8.68139 | −0.394202 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.1856 | −1.73035 | −0.865177 | − | 0.501466i | \(-0.832794\pi\) | ||||
−0.865177 | + | 0.501466i | \(0.832794\pi\) | |||||||
\(488\) | −58.2625 | −2.63742 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.26460 | −0.192655 | ||||||||
\(491\) | 26.7718 | 1.20820 | 0.604098 | − | 0.796910i | \(-0.293534\pi\) | ||||
0.604098 | + | 0.796910i | \(0.293534\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.16383 | −0.187529 | ||||||||
\(494\) | 16.1671 | 0.727394 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.5167 | 1.19063 | ||||||||
\(497\) | −0.817936 | −0.0366895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.8339 | −1.38032 | −0.690158 | − | 0.723659i | \(-0.742459\pi\) | ||||
−0.690158 | + | 0.723659i | \(0.742459\pi\) | |||||||
\(500\) | 48.3540 | 2.16246 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.7818 | 1.32923 | ||||||||
\(503\) | 34.5237 | 1.53934 | 0.769669 | − | 0.638444i | \(-0.220421\pi\) | ||||
0.769669 | + | 0.638444i | \(0.220421\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.58280 | −0.292931 | ||||||||
\(506\) | 0.666225 | 0.0296173 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.98471 | −0.176793 | ||||||||
\(509\) | −9.52278 | −0.422090 | −0.211045 | − | 0.977476i | \(-0.567687\pi\) | ||||
−0.211045 | + | 0.977476i | \(0.567687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.1195 | −0.447658 | ||||||||
\(512\) | −38.5367 | −1.70310 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.5689 | 0.598500 | ||||||||
\(515\) | 6.54696 | 0.288493 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.74977 | −0.0769550 | ||||||||
\(518\) | −5.09863 | −0.224021 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.1420 | 0.751727 | ||||||||
\(521\) | 28.8103 | 1.26220 | 0.631102 | − | 0.775700i | \(-0.282603\pi\) | ||||
0.631102 | + | 0.775700i | \(0.282603\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7577 | 0.689036 | 0.344518 | − | 0.938780i | \(-0.388042\pi\) | ||||
0.344518 | + | 0.938780i | \(0.388042\pi\) | |||||||
\(524\) | −49.7222 | −2.17213 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 70.8971 | 3.09126 | ||||||||
\(527\) | −4.47280 | −0.194838 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.9780 | −0.825132 | ||||||||
\(530\) | 5.46620 | 0.237436 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.0024 | 0.563724 | ||||||||
\(533\) | 6.00251 | 0.259998 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48069 | −0.366652 | ||||||||
\(536\) | −66.4587 | −2.87058 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.70528 | 0.332198 | ||||||||
\(539\) | 0.135794 | 0.00584906 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.14738 | −0.350283 | −0.175142 | − | 0.984543i | \(-0.556038\pi\) | ||||
−0.175142 | + | 0.984543i | \(0.556038\pi\) | |||||||
\(542\) | −22.4983 | −0.966386 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0982479 | 0.00421235 | ||||||||
\(545\) | 4.52498 | 0.193829 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.1907 | 1.71843 | 0.859215 | − | 0.511614i | \(-0.170952\pi\) | ||||
0.859215 | + | 0.511614i | \(0.170952\pi\) | |||||||
\(548\) | −49.7341 | −2.12453 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.651490 | −0.0277796 | ||||||||
\(551\) | −20.6085 | −0.877951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.94496 | −0.167757 | ||||||||
\(554\) | 27.1954 | 1.15542 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.3979 | 1.03470 | ||||||||
\(557\) | −40.1085 | −1.69945 | −0.849727 | − | 0.527223i | \(-0.823233\pi\) | ||||
−0.849727 | + | 0.527223i | \(0.823233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.03931 | 0.213140 | ||||||||
\(560\) | 6.81346 | 0.287921 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 34.4682 | 1.45395 | ||||||||
\(563\) | 28.1913 | 1.18812 | 0.594062 | − | 0.804419i | \(-0.297523\pi\) | ||||
0.594062 | + | 0.804419i | \(0.297523\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.60072 | −0.193554 | ||||||||
\(566\) | 60.2465 | 2.53235 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.97136 | 0.166634 | ||||||||
\(569\) | 1.73907 | 0.0729056 | 0.0364528 | − | 0.999335i | \(-0.488394\pi\) | ||||
0.0364528 | + | 0.999335i | \(0.488394\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.7736 | −1.79002 | −0.895009 | − | 0.446048i | \(-0.852831\pi\) | ||||
−0.895009 | + | 0.446048i | \(0.852831\pi\) | |||||||
\(572\) | −1.09588 | −0.0458211 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.25051 | 0.302630 | ||||||||
\(575\) | −3.93300 | −0.164018 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.7296 | −0.529940 | −0.264970 | − | 0.964257i | \(-0.585362\pi\) | ||||
−0.264970 | + | 0.964257i | \(0.585362\pi\) | |||||||
\(578\) | −40.5249 | −1.68561 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −43.8707 | −1.82163 | ||||||||
\(581\) | 17.3428 | 0.719502 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.174055 | −0.00720864 | ||||||||
\(584\) | 49.1334 | 2.03315 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.1439 | 0.542971 | ||||||||
\(587\) | −1.89439 | −0.0781898 | −0.0390949 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390949 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.1377 | −0.912169 | ||||||||
\(590\) | 52.6361 | 2.16700 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.14598 | 0.334798 | ||||||||
\(593\) | −21.0493 | −0.864391 | −0.432196 | − | 0.901780i | \(-0.642261\pi\) | ||||
−0.432196 | + | 0.901780i | \(0.642261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.14929 | −0.0471161 | ||||||||
\(596\) | 15.0162 | 0.615089 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.93635 | −0.406328 | ||||||||
\(599\) | −11.2389 | −0.459208 | −0.229604 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229604 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.58370 | −0.390927 | −0.195464 | − | 0.980711i | \(-0.562621\pi\) | ||||
−0.195464 | + | 0.980711i | \(0.562621\pi\) | |||||||
\(602\) | 6.08704 | 0.248089 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −52.1554 | −2.12217 | ||||||||
\(605\) | 19.1435 | 0.778292 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.46115 | −0.384016 | −0.192008 | − | 0.981393i | \(-0.561500\pi\) | ||||
−0.192008 | + | 0.981393i | \(0.561500\pi\) | |||||||
\(608\) | 0.486269 | 0.0197208 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 51.1738 | 2.07197 | ||||||||
\(611\) | 26.0968 | 1.05577 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.9848 | 0.564839 | 0.282420 | − | 0.959291i | \(-0.408863\pi\) | ||||
0.282420 | + | 0.959291i | \(0.408863\pi\) | |||||||
\(614\) | −24.7990 | −1.00081 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.659325 | −0.0265650 | ||||||||
\(617\) | 33.5946 | 1.35247 | 0.676233 | − | 0.736688i | \(-0.263611\pi\) | ||||
0.676233 | + | 0.736688i | \(0.263611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.8830 | 0.758971 | 0.379486 | − | 0.925198i | \(-0.376101\pi\) | ||||
0.379486 | + | 0.925198i | \(0.376101\pi\) | |||||||
\(620\) | −47.1260 | −1.89263 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.1200 | −0.766642 | ||||||||
\(623\) | 12.4110 | 0.497236 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.3484 | −0.453934 | ||||||||
\(626\) | −42.0936 | −1.68240 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 64.4305 | 2.57106 | ||||||||
\(629\) | −1.37405 | −0.0547871 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.1723 | −1.24095 | −0.620474 | − | 0.784227i | \(-0.713060\pi\) | ||||
−0.620474 | + | 0.784227i | \(0.713060\pi\) | |||||||
\(632\) | 19.1541 | 0.761909 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −47.0886 | −1.87013 | ||||||||
\(635\) | 1.74324 | 0.0691782 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.02529 | −0.0802448 | ||||||||
\(638\) | 2.09809 | 0.0830640 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 34.3716 | 1.35866 | ||||||||
\(641\) | 25.0094 | 0.987812 | 0.493906 | − | 0.869515i | \(-0.335569\pi\) | ||||
0.493906 | + | 0.869515i | \(0.335569\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4838 | 0.492313 | 0.246157 | − | 0.969230i | \(-0.420832\pi\) | ||||
0.246157 | + | 0.969230i | \(0.420832\pi\) | |||||||
\(644\) | −7.99127 | −0.314900 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.26282 | 0.207063 | ||||||||
\(647\) | 9.50215 | 0.373568 | 0.186784 | − | 0.982401i | \(-0.440194\pi\) | ||||
0.186784 | + | 0.982401i | \(0.440194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.67605 | −0.0657907 | ||||||||
\(650\) | 9.71658 | 0.381116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −67.7715 | −2.65414 | ||||||||
\(653\) | −1.75747 | −0.0687752 | −0.0343876 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343876 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7525 | 0.849942 | ||||||||
\(656\) | −11.5840 | −0.452278 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 31.5227 | 1.22888 | ||||||||
\(659\) | −28.7980 | −1.12181 | −0.560905 | − | 0.827880i | \(-0.689547\pi\) | ||||
−0.560905 | + | 0.827880i | \(0.689547\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.6135 | −1.11293 | −0.556467 | − | 0.830870i | \(-0.687843\pi\) | ||||
−0.556467 | + | 0.830870i | \(0.687843\pi\) | |||||||
\(662\) | 68.0556 | 2.64506 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −84.2053 | −3.26780 | ||||||||
\(665\) | −5.68829 | −0.220582 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.6660 | 0.490430 | ||||||||
\(668\) | 26.5390 | 1.02683 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 58.3728 | 2.25514 | ||||||||
\(671\) | −1.62948 | −0.0629055 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.74566 | 0.260026 | 0.130013 | − | 0.991512i | \(-0.458498\pi\) | ||||
0.130013 | + | 0.991512i | \(0.458498\pi\) | |||||||
\(674\) | 70.7875 | 2.72663 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −35.4568 | −1.36372 | ||||||||
\(677\) | 6.45811 | 0.248205 | 0.124103 | − | 0.992269i | \(-0.460395\pi\) | ||||
0.124103 | + | 0.992269i | \(0.460395\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.98004 | −0.191116 | ||||||||
\(680\) | 5.58017 | 0.213990 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.25377 | 0.0863014 | ||||||||
\(683\) | 14.7524 | 0.564485 | 0.282243 | − | 0.959343i | \(-0.408922\pi\) | ||||
0.282243 | + | 0.959343i | \(0.408922\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.7577 | 0.831319 | ||||||||
\(686\) | −2.44637 | −0.0934027 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.72514 | −0.370768 | ||||||||
\(689\) | 2.59593 | 0.0988972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.3145 | 1.79993 | 0.899963 | − | 0.435965i | \(-0.143593\pi\) | ||||
0.899963 | + | 0.435965i | \(0.143593\pi\) | |||||||
\(692\) | 72.2794 | 2.74765 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 50.6335 | 1.92202 | ||||||||
\(695\) | −10.6736 | −0.404874 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.95397 | 0.0740120 | ||||||||
\(698\) | −62.9716 | −2.38351 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 7.81452 | 0.295361 | ||||||||
\(701\) | −31.6000 | −1.19352 | −0.596758 | − | 0.802421i | \(-0.703545\pi\) | ||||
−0.596758 | + | 0.802421i | \(0.703545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.80076 | −0.256495 | ||||||||
\(704\) | −1.11101 | −0.0418728 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −70.4640 | −2.65195 | ||||||||
\(707\) | −3.77619 | −0.142018 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2336 | 1.36078 | 0.680390 | − | 0.732850i | \(-0.261810\pi\) | ||||
0.680390 | + | 0.732850i | \(0.261810\pi\) | |||||||
\(710\) | −3.48817 | −0.130909 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −60.2595 | −2.25832 | ||||||||
\(713\) | 13.6059 | 0.509544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.479428 | 0.0179296 | ||||||||
\(716\) | 74.0589 | 2.76771 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.8008 | 0.738958 | ||||||||
\(719\) | 23.9301 | 0.892441 | 0.446221 | − | 0.894923i | \(-0.352770\pi\) | ||||
0.446221 | + | 0.894923i | \(0.352770\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.75563 | 0.139867 | ||||||||
\(722\) | −20.4331 | −0.760442 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −87.1206 | −3.23781 | ||||||||
\(725\) | −12.3859 | −0.460000 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.7407 | −0.435439 | −0.217719 | − | 0.976011i | \(-0.569862\pi\) | ||||
−0.217719 | + | 0.976011i | \(0.569862\pi\) | |||||||
\(728\) | 9.83344 | 0.364452 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −43.1554 | −1.59725 | ||||||||
\(731\) | 1.64043 | 0.0606733 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.6643 | 0.652446 | 0.326223 | − | 0.945293i | \(-0.394224\pi\) | ||||
0.326223 | + | 0.945293i | \(0.394224\pi\) | |||||||
\(734\) | −40.9693 | −1.51221 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.298862 | −0.0110162 | ||||||||
\(737\) | −1.85872 | −0.0684667 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.3601 | −1.48467 | −0.742335 | − | 0.670029i | \(-0.766282\pi\) | ||||
−0.742335 | + | 0.670029i | \(0.766282\pi\) | |||||||
\(740\) | −14.4772 | −0.532194 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.13566 | 0.115114 | ||||||||
\(743\) | 31.8055 | 1.16683 | 0.583415 | − | 0.812174i | \(-0.301716\pi\) | ||||
0.583415 | + | 0.812174i | \(0.301716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.56932 | −0.240681 | ||||||||
\(746\) | 48.0044 | 1.75756 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.356738 | −0.0130436 | ||||||||
\(749\) | −4.86491 | −0.177760 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5089 | −0.675398 | −0.337699 | − | 0.941254i | \(-0.609649\pi\) | ||||
−0.337699 | + | 0.941254i | \(0.609649\pi\) | |||||||
\(752\) | −50.3631 | −1.83655 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −31.2917 | −1.13958 | ||||||||
\(755\) | 22.8170 | 0.830396 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.3991 | 0.523343 | 0.261671 | − | 0.965157i | \(-0.415726\pi\) | ||||
0.261671 | + | 0.965157i | \(0.415726\pi\) | |||||||
\(758\) | −21.0521 | −0.764646 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 27.6185 | 1.00183 | ||||||||
\(761\) | 50.0061 | 1.81272 | 0.906360 | − | 0.422507i | \(-0.138850\pi\) | ||||
0.906360 | + | 0.422507i | \(0.138850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.59574 | 0.0939720 | ||||||||
\(764\) | 74.4883 | 2.69489 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −89.8589 | −3.24674 | ||||||||
\(767\) | 24.9973 | 0.902599 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.2862 | −0.551233 | −0.275617 | − | 0.961268i | \(-0.588882\pi\) | ||||
−0.275617 | + | 0.961268i | \(0.588882\pi\) | |||||||
\(770\) | 0.579107 | 0.0208696 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −66.8591 | −2.40631 | ||||||||
\(773\) | −16.9843 | −0.610884 | −0.305442 | − | 0.952211i | \(-0.598804\pi\) | ||||
−0.305442 | + | 0.952211i | \(0.598804\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.3049 | −0.477928 | ||||||||
\(776\) | 24.1798 | 0.868003 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.8313 | 0.460024 | ||||||||
\(779\) | 9.67101 | 0.346500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.111071 | 0.00397443 | ||||||||
\(782\) | −3.23454 | −0.115667 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.90851 | 0.139590 | ||||||||
\(785\) | −28.1871 | −1.00604 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.8926 | −1.84977 | −0.924885 | − | 0.380247i | \(-0.875839\pi\) | ||||
−0.924885 | + | 0.380247i | \(0.875839\pi\) | |||||||
\(788\) | 45.5092 | 1.62120 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.8236 | −0.598559 | ||||||||
\(791\) | −2.63918 | −0.0938386 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.3028 | 0.863017 | ||||||||
\(794\) | 27.9329 | 0.991300 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −43.9006 | −1.55601 | ||||||||
\(797\) | −7.38115 | −0.261454 | −0.130727 | − | 0.991418i | \(-0.541731\pi\) | ||||
−0.130727 | + | 0.991418i | \(0.541731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.49520 | 0.300538 | ||||||||
\(800\) | 0.292252 | 0.0103327 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.62885 | −0.269384 | ||||||||
\(803\) | 1.37416 | 0.0484931 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.49603 | 0.123219 | ||||||||
\(806\) | −33.6137 | −1.18399 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.3347 | 0.645012 | ||||||||
\(809\) | −3.29935 | −0.115999 | −0.0579995 | − | 0.998317i | \(-0.518472\pi\) | ||||
−0.0579995 | + | 0.998317i | \(0.518472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1011 | −0.495157 | −0.247579 | − | 0.968868i | \(-0.579635\pi\) | ||||
−0.247579 | + | 0.968868i | \(0.579635\pi\) | |||||||
\(812\) | −25.1662 | −0.883161 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.692364 | 0.0242673 | ||||||||
\(815\) | 29.6488 | 1.03855 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.11914 | 0.284053 | ||||||||
\(818\) | −60.3960 | −2.11170 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.5873 | 0.718941 | ||||||||
\(821\) | −37.3111 | −1.30217 | −0.651084 | − | 0.759006i | \(-0.725685\pi\) | ||||
−0.651084 | + | 0.759006i | \(0.725685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.25210 | −0.148219 | −0.0741094 | − | 0.997250i | \(-0.523611\pi\) | ||||
−0.0741094 | + | 0.997250i | \(0.523611\pi\) | |||||||
\(824\) | −18.2349 | −0.635242 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.1945 | 1.05060 | ||||||||
\(827\) | 25.0081 | 0.869617 | 0.434809 | − | 0.900523i | \(-0.356816\pi\) | ||||
0.434809 | + | 0.900523i | \(0.356816\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.7303 | 1.69247 | 0.846236 | − | 0.532808i | \(-0.178863\pi\) | ||||
0.846236 | + | 0.532808i | \(0.178863\pi\) | |||||||
\(830\) | 73.9602 | 2.56720 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.5700 | 0.574463 | ||||||||
\(833\) | −0.659283 | −0.0228428 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6103 | −0.401792 | ||||||||
\(836\) | −1.76564 | −0.0610660 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.24614 | 0.0430473 | ||||||||
\(839\) | −1.50639 | −0.0520062 | −0.0260031 | − | 0.999662i | \(-0.508278\pi\) | ||||
−0.0260031 | + | 0.999662i | \(0.508278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8880 | 0.375447 | ||||||||
\(842\) | 65.8384 | 2.26894 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37.6551 | 1.29614 | ||||||||
\(845\) | 15.5117 | 0.533619 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9816 | 0.377331 | ||||||||
\(848\) | −5.00978 | −0.172036 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.16300 | 0.108490 | ||||||||
\(851\) | 4.17976 | 0.143280 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.9103 | −0.373562 | −0.186781 | − | 0.982402i | \(-0.559805\pi\) | ||||
−0.186781 | + | 0.982402i | \(0.559805\pi\) | |||||||
\(854\) | 29.3556 | 1.00453 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.6208 | 0.807341 | ||||||||
\(857\) | 34.0924 | 1.16457 | 0.582286 | − | 0.812984i | \(-0.302158\pi\) | ||||
0.582286 | + | 0.812984i | \(0.302158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9172 | 1.70315 | 0.851576 | − | 0.524230i | \(-0.175647\pi\) | ||||
0.851576 | + | 0.524230i | \(0.175647\pi\) | |||||||
\(860\) | 17.2838 | 0.589371 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.2577 | 0.451558 | ||||||||
\(863\) | 31.8199 | 1.08316 | 0.541582 | − | 0.840648i | \(-0.317826\pi\) | ||||
0.541582 | + | 0.840648i | \(0.317826\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.6209 | −1.07514 | ||||||||
\(866\) | −13.6495 | −0.463829 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −27.0336 | −0.917582 | ||||||||
\(869\) | 0.535701 | 0.0181724 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.7216 | 0.939312 | ||||||||
\(872\) | −12.6032 | −0.426797 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.0091 | −0.541515 | ||||||||
\(875\) | −12.1349 | −0.410234 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.8062 | 1.14156 | 0.570778 | − | 0.821105i | \(-0.306642\pi\) | ||||
0.570778 | + | 0.821105i | \(0.306642\pi\) | |||||||
\(878\) | −79.6571 | −2.68830 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.925226 | −0.0311894 | ||||||||
\(881\) | −42.2270 | −1.42266 | −0.711332 | − | 0.702856i | \(-0.751908\pi\) | ||||
−0.711332 | + | 0.702856i | \(0.751908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.1525 | −0.745492 | −0.372746 | − | 0.927933i | \(-0.621584\pi\) | ||||
−0.372746 | + | 0.927933i | \(0.621584\pi\) | |||||||
\(884\) | 5.32053 | 0.178949 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −70.0636 | −2.35383 | ||||||||
\(887\) | −23.5438 | −0.790524 | −0.395262 | − | 0.918568i | \(-0.629346\pi\) | ||||
−0.395262 | + | 0.918568i | \(0.629346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 52.9279 | 1.77415 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −59.3742 | −1.98800 | ||||||||
\(893\) | 42.0462 | 1.40702 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.3994 | −1.08299 | ||||||||
\(896\) | 19.7171 | 0.658702 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −98.3259 | −3.28118 | ||||||||
\(899\) | 42.8478 | 1.42905 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.845043 | 0.0281525 | ||||||||
\(902\) | −0.984575 | −0.0327828 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.8141 | 0.426191 | ||||||||
\(905\) | 38.1136 | 1.26694 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5277 | −0.847633 | −0.423817 | − | 0.905748i | \(-0.639310\pi\) | ||||
−0.423817 | + | 0.905748i | \(0.639310\pi\) | |||||||
\(908\) | 42.2067 | 1.40068 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.63703 | −0.286315 | ||||||||
\(911\) | −54.1250 | −1.79324 | −0.896621 | − | 0.442799i | \(-0.853986\pi\) | ||||
−0.896621 | + | 0.442799i | \(0.853986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.35505 | −0.0779408 | ||||||||
\(914\) | 51.8136 | 1.71384 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 86.4031 | 2.85484 | ||||||||
\(917\) | 12.4783 | 0.412068 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.2896 | −1.69189 | −0.845944 | − | 0.533272i | \(-0.820962\pi\) | ||||
−0.845944 | + | 0.533272i | \(0.820962\pi\) | |||||||
\(920\) | −16.9744 | −0.559630 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.59718 | 0.151400 | ||||||||
\(923\) | −1.65656 | −0.0545262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.08731 | −0.134390 | ||||||||
\(926\) | 12.4466 | 0.409020 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.941180 | −0.0308958 | ||||||||
\(929\) | −44.9274 | −1.47402 | −0.737011 | − | 0.675881i | \(-0.763763\pi\) | ||||
−0.737011 | + | 0.675881i | \(0.763763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.26306 | −0.106943 | ||||||||
\(932\) | 39.6627 | 1.29920 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.0933 | 0.624753 | ||||||||
\(935\) | 0.156066 | 0.00510391 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4048 | 0.764603 | 0.382301 | − | 0.924038i | \(-0.375132\pi\) | ||||
0.382301 | + | 0.924038i | \(0.375132\pi\) | |||||||
\(938\) | 33.4853 | 1.09333 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 89.5066 | 2.91938 | ||||||||
\(941\) | 18.7843 | 0.612349 | 0.306175 | − | 0.951975i | \(-0.400951\pi\) | ||||
0.306175 | + | 0.951975i | \(0.400951\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.94382 | −0.193557 | ||||||||
\(944\) | −48.2411 | −1.57011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.826584 | −0.0268746 | ||||||||
\(947\) | 16.1089 | 0.523468 | 0.261734 | − | 0.965140i | \(-0.415706\pi\) | ||||
0.261734 | + | 0.965140i | \(0.415706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.4948 | −0.665289 | ||||||||
\(950\) | 15.6550 | 0.507914 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.20104 | 0.103746 | ||||||||
\(953\) | 7.01631 | 0.227280 | 0.113640 | − | 0.993522i | \(-0.463749\pi\) | ||||
0.113640 | + | 0.993522i | \(0.463749\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.5872 | −1.05450 | ||||||||
\(956\) | 93.4839 | 3.02348 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.6295 | 0.924976 | ||||||||
\(959\) | 12.4812 | 0.403039 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0273 | 0.484751 | ||||||||
\(962\) | −10.3262 | −0.332930 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.8168 | 1.21800 | ||||||||
\(965\) | 29.2496 | 0.941577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.73407 | −0.0879218 | −0.0439609 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439609 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(968\) | −53.3192 | −1.71374 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21.2379 | −0.681907 | ||||||||
\(971\) | 35.6649 | 1.14454 | 0.572271 | − | 0.820065i | \(-0.306063\pi\) | ||||
0.572271 | + | 0.820065i | \(0.306063\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.12288 | −0.196291 | ||||||||
\(974\) | −93.4160 | −2.99324 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.9009 | −1.50126 | ||||||||
\(977\) | 46.1434 | 1.47626 | 0.738129 | − | 0.674660i | \(-0.235710\pi\) | ||||
0.738129 | + | 0.674660i | \(0.235710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.68534 | −0.0538636 | ||||||||
\(980\) | −6.94630 | −0.221891 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 65.4937 | 2.08999 | ||||||||
\(983\) | −29.5575 | −0.942736 | −0.471368 | − | 0.881937i | \(-0.656240\pi\) | ||||
−0.471368 | + | 0.881937i | \(0.656240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.9094 | −0.634367 | ||||||||
\(986\) | −10.1863 | −0.324396 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.3335 | 0.837780 | ||||||||
\(989\) | −4.99004 | −0.158674 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.8251 | 0.597998 | 0.298999 | − | 0.954254i | \(-0.403347\pi\) | ||||
0.298999 | + | 0.954254i | \(0.403347\pi\) | |||||||
\(992\) | −1.01102 | −0.0320999 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00097 | −0.0634670 | ||||||||
\(995\) | 19.2057 | 0.608861 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.27591 | −0.262101 | −0.131050 | − | 0.991376i | \(-0.541835\pi\) | ||||
−0.131050 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(998\) | −75.4311 | −2.38773 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.z.1.30 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.3 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.30 | yes | 32 | 1.1 | even | 1 | trivial |