Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1238167332\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.530451 | −0.375085 | −0.187543 | − | 0.982256i | \(-0.560052\pi\) | ||||
−0.187543 | + | 0.982256i | \(0.560052\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.71862 | −0.859311 | ||||||||
\(5\) | 3.35792 | 1.50171 | 0.750855 | − | 0.660467i | \(-0.229642\pi\) | ||||
0.750855 | + | 0.660467i | \(0.229642\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.91494 | 1.47971 | 0.739854 | − | 0.672767i | \(-0.234895\pi\) | ||||
0.739854 | + | 0.672767i | \(0.234895\pi\) | |||||||
\(8\) | 1.97255 | 0.697400 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.78121 | −0.563269 | ||||||||
\(11\) | −0.0181339 | −0.00546759 | −0.00273380 | − | 0.999996i | \(-0.500870\pi\) | ||||
−0.00273380 | + | 0.999996i | \(0.500870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.92757 | −1.64401 | −0.822006 | − | 0.569479i | \(-0.807145\pi\) | ||||
−0.822006 | + | 0.569479i | \(0.807145\pi\) | |||||||
\(14\) | −2.07668 | −0.555017 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.39091 | 0.597727 | ||||||||
\(17\) | 2.80172 | 0.679518 | 0.339759 | − | 0.940513i | \(-0.389655\pi\) | ||||
0.339759 | + | 0.940513i | \(0.389655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.42725 | 1.93334 | 0.966672 | − | 0.256020i | \(-0.0824112\pi\) | ||||
0.966672 | + | 0.256020i | \(0.0824112\pi\) | |||||||
\(20\) | −5.77100 | −1.29044 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.00961916 | 0.00205081 | ||||||||
\(23\) | −7.23843 | −1.50932 | −0.754658 | − | 0.656118i | \(-0.772197\pi\) | ||||
−0.754658 | + | 0.656118i | \(0.772197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.27566 | 1.25513 | ||||||||
\(26\) | 3.14428 | 0.616644 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.72830 | −1.27153 | ||||||||
\(29\) | 0.873804 | 0.162261 | 0.0811307 | − | 0.996703i | \(-0.474147\pi\) | ||||
0.0811307 | + | 0.996703i | \(0.474147\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.822902 | 0.147798 | 0.0738988 | − | 0.997266i | \(-0.476456\pi\) | ||||
0.0738988 | + | 0.997266i | \(0.476456\pi\) | |||||||
\(32\) | −5.21335 | −0.921598 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.48618 | −0.254877 | ||||||||
\(35\) | 13.1461 | 2.22209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.327675 | −0.0538695 | −0.0269347 | − | 0.999637i | \(-0.508575\pi\) | ||||
−0.0269347 | + | 0.999637i | \(0.508575\pi\) | |||||||
\(38\) | −4.47024 | −0.725168 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.62366 | 1.04729 | ||||||||
\(41\) | 8.66885 | 1.35385 | 0.676924 | − | 0.736053i | \(-0.263313\pi\) | ||||
0.676924 | + | 0.736053i | \(0.263313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00666 | −0.153515 | −0.0767574 | − | 0.997050i | \(-0.524457\pi\) | ||||
−0.0767574 | + | 0.997050i | \(0.524457\pi\) | |||||||
\(44\) | 0.0311654 | 0.00469836 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.83963 | 0.566122 | ||||||||
\(47\) | 7.71226 | 1.12495 | 0.562474 | − | 0.826815i | \(-0.309850\pi\) | ||||
0.562474 | + | 0.826815i | \(0.309850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.32675 | 1.18954 | ||||||||
\(50\) | −3.32892 | −0.470781 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.1872 | 1.41272 | ||||||||
\(53\) | 4.76237 | 0.654161 | 0.327081 | − | 0.944996i | \(-0.393935\pi\) | ||||
0.327081 | + | 0.944996i | \(0.393935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0608924 | −0.00821073 | ||||||||
\(56\) | 7.72239 | 1.03195 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.463510 | −0.0608618 | ||||||||
\(59\) | −11.5774 | −1.50725 | −0.753627 | − | 0.657302i | \(-0.771697\pi\) | ||||
−0.753627 | + | 0.657302i | \(0.771697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.56273 | 0.584198 | 0.292099 | − | 0.956388i | \(-0.405646\pi\) | ||||
0.292099 | + | 0.956388i | \(0.405646\pi\) | |||||||
\(62\) | −0.436509 | −0.0554367 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.01639 | −0.252049 | ||||||||
\(65\) | −19.9043 | −2.46883 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.44129 | 0.909098 | 0.454549 | − | 0.890722i | \(-0.349801\pi\) | ||||
0.454549 | + | 0.890722i | \(0.349801\pi\) | |||||||
\(68\) | −4.81511 | −0.583917 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.97334 | −0.833474 | ||||||||
\(71\) | 11.7175 | 1.39062 | 0.695309 | − | 0.718711i | \(-0.255268\pi\) | ||||
0.695309 | + | 0.718711i | \(0.255268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.83597 | −0.683049 | −0.341524 | − | 0.939873i | \(-0.610943\pi\) | ||||
−0.341524 | + | 0.939873i | \(0.610943\pi\) | |||||||
\(74\) | 0.173816 | 0.0202056 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.4833 | −1.66134 | ||||||||
\(77\) | −0.0709933 | −0.00809044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.209454 | −0.0235654 | −0.0117827 | − | 0.999931i | \(-0.503751\pi\) | ||||
−0.0117827 | + | 0.999931i | \(0.503751\pi\) | |||||||
\(80\) | 8.02848 | 0.897612 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.59840 | −0.507808 | ||||||||
\(83\) | 0.907761 | 0.0996397 | 0.0498199 | − | 0.998758i | \(-0.484135\pi\) | ||||
0.0498199 | + | 0.998758i | \(0.484135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.40798 | 1.02044 | ||||||||
\(86\) | 0.533985 | 0.0575811 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0357700 | −0.00381310 | ||||||||
\(89\) | 4.48048 | 0.474930 | 0.237465 | − | 0.971396i | \(-0.423684\pi\) | ||||
0.237465 | + | 0.971396i | \(0.423684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23.2061 | −2.43266 | ||||||||
\(92\) | 12.4401 | 1.29697 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.09097 | −0.421951 | ||||||||
\(95\) | 28.2981 | 2.90332 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.76631 | −0.687014 | −0.343507 | − | 0.939150i | \(-0.611615\pi\) | ||||
−0.343507 | + | 0.939150i | \(0.611615\pi\) | |||||||
\(98\) | −4.41693 | −0.446177 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.7855 | −1.07855 | ||||||||
\(101\) | −10.2494 | −1.01986 | −0.509929 | − | 0.860216i | \(-0.670328\pi\) | ||||
−0.509929 | + | 0.860216i | \(0.670328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.864367 | −0.0851686 | −0.0425843 | − | 0.999093i | \(-0.513559\pi\) | ||||
−0.0425843 | + | 0.999093i | \(0.513559\pi\) | |||||||
\(104\) | −11.6924 | −1.14653 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.52620 | −0.245366 | ||||||||
\(107\) | 11.8683 | 1.14735 | 0.573674 | − | 0.819084i | \(-0.305518\pi\) | ||||
0.573674 | + | 0.819084i | \(0.305518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6983 | −1.02472 | −0.512358 | − | 0.858772i | \(-0.671228\pi\) | ||||
−0.512358 | + | 0.858772i | \(0.671228\pi\) | |||||||
\(110\) | 0.0323004 | 0.00307972 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.36026 | 0.884461 | ||||||||
\(113\) | 5.67368 | 0.533735 | 0.266868 | − | 0.963733i | \(-0.414011\pi\) | ||||
0.266868 | + | 0.963733i | \(0.414011\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.3061 | −2.26655 | ||||||||
\(116\) | −1.50174 | −0.139433 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.14126 | 0.565349 | ||||||||
\(119\) | 10.9686 | 1.00549 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9997 | −0.999970 | ||||||||
\(122\) | −2.42030 | −0.219124 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.41426 | −0.127004 | ||||||||
\(125\) | 4.28355 | 0.383133 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.16460 | 0.458284 | 0.229142 | − | 0.973393i | \(-0.426408\pi\) | ||||
0.229142 | + | 0.973393i | \(0.426408\pi\) | |||||||
\(128\) | 11.4963 | 1.01614 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.5583 | 0.926020 | ||||||||
\(131\) | 0.843924 | 0.0737340 | 0.0368670 | − | 0.999320i | \(-0.488262\pi\) | ||||
0.0368670 | + | 0.999320i | \(0.488262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32.9922 | 2.86078 | ||||||||
\(134\) | −3.94723 | −0.340989 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.52653 | 0.473896 | ||||||||
\(137\) | 12.5066 | 1.06851 | 0.534255 | − | 0.845323i | \(-0.320592\pi\) | ||||
0.534255 | + | 0.845323i | \(0.320592\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.72761 | −0.570629 | −0.285314 | − | 0.958434i | \(-0.592098\pi\) | ||||
−0.285314 | + | 0.958434i | \(0.592098\pi\) | |||||||
\(140\) | −22.5931 | −1.90947 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.21558 | −0.521600 | ||||||||
\(143\) | 0.107490 | 0.00898878 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.93417 | 0.243669 | ||||||||
\(146\) | 3.09569 | 0.256201 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.563150 | 0.0462906 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.0650 | −1.55149 | −0.775745 | − | 0.631046i | \(-0.782626\pi\) | ||||
−0.775745 | + | 0.631046i | \(0.782626\pi\) | |||||||
\(152\) | 16.6231 | 1.34831 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0376584 | 0.00303460 | ||||||||
\(155\) | 2.76324 | 0.221949 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3633 | 1.06651 | 0.533255 | − | 0.845954i | \(-0.320969\pi\) | ||||
0.533255 | + | 0.845954i | \(0.320969\pi\) | |||||||
\(158\) | 0.111105 | 0.00883903 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −17.5060 | −1.38397 | ||||||||
\(161\) | −28.3380 | −2.23335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6010 | −1.37862 | −0.689308 | − | 0.724469i | \(-0.742085\pi\) | ||||
−0.689308 | + | 0.724469i | \(0.742085\pi\) | |||||||
\(164\) | −14.8985 | −1.16338 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.481522 | −0.0373734 | ||||||||
\(167\) | 21.0164 | 1.62630 | 0.813150 | − | 0.582054i | \(-0.197751\pi\) | ||||
0.813150 | + | 0.582054i | \(0.197751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.1360 | 1.70277 | ||||||||
\(170\) | −4.99047 | −0.382751 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.73007 | 0.131917 | ||||||||
\(173\) | −19.6201 | −1.49169 | −0.745843 | − | 0.666122i | \(-0.767953\pi\) | ||||
−0.745843 | + | 0.666122i | \(0.767953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.5688 | 1.85723 | ||||||||
\(176\) | −0.0433566 | −0.00326813 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.37667 | −0.178139 | ||||||||
\(179\) | −13.3659 | −0.999017 | −0.499508 | − | 0.866309i | \(-0.666486\pi\) | ||||
−0.499508 | + | 0.866309i | \(0.666486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.8820 | −1.32916 | −0.664578 | − | 0.747219i | \(-0.731389\pi\) | ||||
−0.664578 | + | 0.747219i | \(0.731389\pi\) | |||||||
\(182\) | 12.3097 | 0.912453 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.2781 | −1.05260 | ||||||||
\(185\) | −1.10031 | −0.0808963 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0508063 | −0.00371533 | ||||||||
\(188\) | −13.2545 | −0.966681 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.0107 | −1.08899 | ||||||||
\(191\) | −12.6985 | −0.918828 | −0.459414 | − | 0.888222i | \(-0.651941\pi\) | ||||
−0.459414 | + | 0.888222i | \(0.651941\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.4742 | −1.61773 | −0.808863 | − | 0.587998i | \(-0.799916\pi\) | ||||
−0.808863 | + | 0.587998i | \(0.799916\pi\) | |||||||
\(194\) | 3.58919 | 0.257689 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.3105 | −1.02218 | ||||||||
\(197\) | 19.1471 | 1.36418 | 0.682089 | − | 0.731270i | \(-0.261072\pi\) | ||||
0.682089 | + | 0.731270i | \(0.261072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.62488 | −0.398737 | −0.199369 | − | 0.979925i | \(-0.563889\pi\) | ||||
−0.199369 | + | 0.979925i | \(0.563889\pi\) | |||||||
\(200\) | 12.3790 | 0.875328 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.43682 | 0.382534 | ||||||||
\(203\) | 3.42089 | 0.240099 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.1094 | 2.03309 | ||||||||
\(206\) | 0.458504 | 0.0319455 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1723 | −0.982669 | ||||||||
\(209\) | −0.152819 | −0.0105707 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.28633 | 0.432769 | 0.216384 | − | 0.976308i | \(-0.430574\pi\) | ||||
0.216384 | + | 0.976308i | \(0.430574\pi\) | |||||||
\(212\) | −8.18471 | −0.562128 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.29552 | −0.430353 | ||||||||
\(215\) | −3.38030 | −0.230535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.22161 | 0.218697 | ||||||||
\(218\) | 5.67494 | 0.384356 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.104651 | 0.00705557 | ||||||||
\(221\) | −16.6074 | −1.11714 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5550 | 0.974676 | 0.487338 | − | 0.873213i | \(-0.337968\pi\) | ||||
0.487338 | + | 0.873213i | \(0.337968\pi\) | |||||||
\(224\) | −20.4099 | −1.36370 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00961 | −0.200196 | ||||||||
\(227\) | 22.2592 | 1.47740 | 0.738698 | − | 0.674036i | \(-0.235441\pi\) | ||||
0.738698 | + | 0.674036i | \(0.235441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.4305 | 1.28400 | 0.642001 | − | 0.766704i | \(-0.278104\pi\) | ||||
0.642001 | + | 0.766704i | \(0.278104\pi\) | |||||||
\(230\) | 12.8932 | 0.850151 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.72362 | 0.113161 | ||||||||
\(233\) | 25.4141 | 1.66493 | 0.832465 | − | 0.554077i | \(-0.186929\pi\) | ||||
0.832465 | + | 0.554077i | \(0.186929\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.8972 | 1.68935 | ||||||||
\(236\) | 19.8972 | 1.29520 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.81829 | −0.377144 | ||||||||
\(239\) | 21.7018 | 1.40377 | 0.701885 | − | 0.712290i | \(-0.252342\pi\) | ||||
0.701885 | + | 0.712290i | \(0.252342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7521 | 1.40118 | 0.700588 | − | 0.713566i | \(-0.252921\pi\) | ||||
0.700588 | + | 0.713566i | \(0.252921\pi\) | |||||||
\(242\) | 5.83478 | 0.375074 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.84162 | −0.502008 | ||||||||
\(245\) | 27.9606 | 1.78634 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −49.9531 | −3.17844 | ||||||||
\(248\) | 1.62321 | 0.103074 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.27221 | −0.143707 | ||||||||
\(251\) | 24.7699 | 1.56347 | 0.781733 | − | 0.623614i | \(-0.214336\pi\) | ||||
0.781733 | + | 0.623614i | \(0.214336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.131261 | 0.00825232 | ||||||||
\(254\) | −2.73956 | −0.171896 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.06543 | −0.129090 | ||||||||
\(257\) | −7.92098 | −0.494097 | −0.247049 | − | 0.969003i | \(-0.579461\pi\) | ||||
−0.247049 | + | 0.969003i | \(0.579461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.28283 | −0.0797111 | ||||||||
\(260\) | 34.2080 | 2.12149 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.447660 | −0.0276565 | ||||||||
\(263\) | −8.65342 | −0.533593 | −0.266796 | − | 0.963753i | \(-0.585965\pi\) | ||||
−0.266796 | + | 0.963753i | \(0.585965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9917 | 0.982360 | ||||||||
\(266\) | −17.5007 | −1.07304 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.7888 | −0.781198 | ||||||||
\(269\) | −23.4545 | −1.43005 | −0.715023 | − | 0.699101i | \(-0.753584\pi\) | ||||
−0.715023 | + | 0.699101i | \(0.753584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.4032 | 1.84686 | 0.923431 | − | 0.383766i | \(-0.125373\pi\) | ||||
0.923431 | + | 0.383766i | \(0.125373\pi\) | |||||||
\(272\) | 6.69866 | 0.406166 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.63413 | −0.400782 | ||||||||
\(275\) | −0.113802 | −0.00686254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.43685 | −0.506921 | −0.253460 | − | 0.967346i | \(-0.581569\pi\) | ||||
−0.253460 | + | 0.967346i | \(0.581569\pi\) | |||||||
\(278\) | 3.56867 | 0.214034 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 25.9312 | 1.54969 | ||||||||
\(281\) | 19.5511 | 1.16632 | 0.583162 | − | 0.812356i | \(-0.301815\pi\) | ||||
0.583162 | + | 0.812356i | \(0.301815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5020 | −1.27816 | −0.639081 | − | 0.769139i | \(-0.720685\pi\) | ||||
−0.639081 | + | 0.769139i | \(0.720685\pi\) | |||||||
\(284\) | −20.1380 | −1.19497 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0570182 | −0.00337156 | ||||||||
\(287\) | 33.9380 | 2.00330 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.15034 | −0.538255 | ||||||||
\(290\) | −1.55643 | −0.0913968 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.0298 | 0.586951 | ||||||||
\(293\) | −0.525326 | −0.0306899 | −0.0153449 | − | 0.999882i | \(-0.504885\pi\) | ||||
−0.0153449 | + | 0.999882i | \(0.504885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.8762 | −2.26346 | ||||||||
\(296\) | −0.646354 | −0.0375686 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.530451 | −0.0307282 | ||||||||
\(299\) | 42.9063 | 2.48133 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.94103 | −0.227157 | ||||||||
\(302\) | 10.1131 | 0.581941 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.1488 | 1.15561 | ||||||||
\(305\) | 15.3213 | 0.877296 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6144 | 1.23360 | 0.616799 | − | 0.787121i | \(-0.288429\pi\) | ||||
0.616799 | + | 0.787121i | \(0.288429\pi\) | |||||||
\(308\) | 0.122011 | 0.00695220 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.46576 | −0.0832498 | ||||||||
\(311\) | 2.46662 | 0.139869 | 0.0699345 | − | 0.997552i | \(-0.477721\pi\) | ||||
0.0699345 | + | 0.997552i | \(0.477721\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.4135 | 1.60603 | 0.803014 | − | 0.595960i | \(-0.203228\pi\) | ||||
0.803014 | + | 0.595960i | \(0.203228\pi\) | |||||||
\(314\) | −7.08859 | −0.400032 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.359972 | 0.0202500 | ||||||||
\(317\) | 22.7136 | 1.27572 | 0.637860 | − | 0.770152i | \(-0.279820\pi\) | ||||
0.637860 | + | 0.770152i | \(0.279820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0158455 | −0.000887178 0 | ||||||||
\(320\) | −6.77089 | −0.378504 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.0319 | 0.837695 | ||||||||
\(323\) | 23.6108 | 1.31374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −37.1994 | −2.06345 | ||||||||
\(326\) | 9.33645 | 0.517098 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.0997 | 0.944173 | ||||||||
\(329\) | 30.1930 | 1.66460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.79546 | 0.428477 | 0.214239 | − | 0.976781i | \(-0.431273\pi\) | ||||
0.214239 | + | 0.976781i | \(0.431273\pi\) | |||||||
\(332\) | −1.56010 | −0.0856215 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.1482 | −0.610001 | ||||||||
\(335\) | 24.9873 | 1.36520 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0560 | −1.41936 | −0.709679 | − | 0.704525i | \(-0.751160\pi\) | ||||
−0.709679 | + | 0.704525i | \(0.751160\pi\) | |||||||
\(338\) | −11.7421 | −0.638685 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −16.1688 | −0.876874 | ||||||||
\(341\) | −0.0149225 | −0.000808097 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.19415 | 0.280458 | ||||||||
\(344\) | −1.98569 | −0.107061 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.4075 | 0.559509 | ||||||||
\(347\) | −14.5930 | −0.783392 | −0.391696 | − | 0.920095i | \(-0.628111\pi\) | ||||
−0.391696 | + | 0.920095i | \(0.628111\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.52698 | −0.456439 | −0.228219 | − | 0.973610i | \(-0.573290\pi\) | ||||
−0.228219 | + | 0.973610i | \(0.573290\pi\) | |||||||
\(350\) | −13.0325 | −0.696619 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0945386 | 0.00503892 | ||||||||
\(353\) | 29.7193 | 1.58180 | 0.790900 | − | 0.611946i | \(-0.209613\pi\) | ||||
0.790900 | + | 0.611946i | \(0.209613\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.3466 | 2.08830 | ||||||||
\(356\) | −7.70025 | −0.408112 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.08997 | 0.374716 | ||||||||
\(359\) | −7.58639 | −0.400394 | −0.200197 | − | 0.979756i | \(-0.564158\pi\) | ||||
−0.200197 | + | 0.979756i | \(0.564158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.0185 | 2.73782 | ||||||||
\(362\) | 9.48550 | 0.498547 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 39.8825 | 2.09041 | ||||||||
\(365\) | −19.5967 | −1.02574 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.18734 | 0.0619786 | 0.0309893 | − | 0.999520i | \(-0.490134\pi\) | ||||
0.0309893 | + | 0.999520i | \(0.490134\pi\) | |||||||
\(368\) | −17.3064 | −0.902159 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.583659 | 0.0303430 | ||||||||
\(371\) | 18.6444 | 0.967968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9023 | 0.823389 | 0.411695 | − | 0.911322i | \(-0.364937\pi\) | ||||
0.411695 | + | 0.911322i | \(0.364937\pi\) | |||||||
\(374\) | 0.0269502 | 0.00139356 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.2128 | 0.784539 | ||||||||
\(377\) | −5.17953 | −0.266759 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0065 | −0.514001 | −0.257000 | − | 0.966411i | \(-0.582734\pi\) | ||||
−0.257000 | + | 0.966411i | \(0.582734\pi\) | |||||||
\(380\) | −48.6337 | −2.49485 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.73591 | 0.344639 | ||||||||
\(383\) | −34.7613 | −1.77622 | −0.888111 | − | 0.459630i | \(-0.847982\pi\) | ||||
−0.888111 | + | 0.459630i | \(0.847982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.238390 | −0.0121495 | ||||||||
\(386\) | 11.9214 | 0.606785 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.6287 | 0.590359 | ||||||||
\(389\) | −13.7771 | −0.698527 | −0.349264 | − | 0.937024i | \(-0.613568\pi\) | ||||
−0.349264 | + | 0.937024i | \(0.613568\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.2801 | −1.02561 | ||||||||
\(392\) | 16.4249 | 0.829582 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.1566 | −0.511683 | ||||||||
\(395\) | −0.703330 | −0.0353884 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0908 | −0.556629 | −0.278315 | − | 0.960490i | \(-0.589776\pi\) | ||||
−0.278315 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(398\) | 2.98372 | 0.149560 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.0045 | 0.750225 | ||||||||
\(401\) | 4.79005 | 0.239203 | 0.119602 | − | 0.992822i | \(-0.461838\pi\) | ||||
0.119602 | + | 0.992822i | \(0.461838\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.87781 | −0.242981 | ||||||||
\(404\) | 17.6149 | 0.876375 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.81461 | −0.0900577 | ||||||||
\(407\) | 0.00594205 | 0.000294536 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.7677 | −1.57081 | −0.785406 | − | 0.618981i | \(-0.787546\pi\) | ||||
−0.785406 | + | 0.618981i | \(0.787546\pi\) | |||||||
\(410\) | −15.4411 | −0.762580 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.48552 | 0.0731863 | ||||||||
\(413\) | −45.3250 | −2.23030 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.04819 | 0.149630 | ||||||||
\(416\) | 30.9025 | 1.51512 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0810631 | 0.00396492 | ||||||||
\(419\) | 38.3410 | 1.87308 | 0.936541 | − | 0.350557i | \(-0.114008\pi\) | ||||
0.936541 | + | 0.350557i | \(0.114008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.145307 | −0.00708184 | −0.00354092 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354092 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(422\) | −3.33459 | −0.162325 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.39398 | 0.456212 | ||||||||
\(425\) | 17.5827 | 0.852884 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.8628 | 0.864443 | ||||||||
\(428\) | −20.3970 | −0.985928 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.79308 | 0.0864701 | ||||||||
\(431\) | 0.439138 | 0.0211526 | 0.0105763 | − | 0.999944i | \(-0.496633\pi\) | ||||
0.0105763 | + | 0.999944i | \(0.496633\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.35091 | 0.161034 | 0.0805171 | − | 0.996753i | \(-0.474343\pi\) | ||||
0.0805171 | + | 0.996753i | \(0.474343\pi\) | |||||||
\(434\) | −1.70891 | −0.0820301 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.3864 | 0.880549 | ||||||||
\(437\) | −61.0000 | −2.91803 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.64091 | 0.221498 | 0.110749 | − | 0.993848i | \(-0.464675\pi\) | ||||
0.110749 | + | 0.993848i | \(0.464675\pi\) | |||||||
\(440\) | −0.120113 | −0.00572616 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.80941 | 0.419021 | ||||||||
\(443\) | 18.0312 | 0.856689 | 0.428344 | − | 0.903616i | \(-0.359097\pi\) | ||||
0.428344 | + | 0.903616i | \(0.359097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.0451 | 0.713207 | ||||||||
\(446\) | −7.72071 | −0.365586 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.89405 | −0.372959 | ||||||||
\(449\) | 7.47507 | 0.352770 | 0.176385 | − | 0.984321i | \(-0.443560\pi\) | ||||
0.176385 | + | 0.984321i | \(0.443560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.157201 | −0.00740228 | ||||||||
\(452\) | −9.75092 | −0.458644 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.8074 | −0.554149 | ||||||||
\(455\) | −77.9242 | −3.65314 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.32153 | 0.108597 | 0.0542983 | − | 0.998525i | \(-0.482708\pi\) | ||||
0.0542983 | + | 0.998525i | \(0.482708\pi\) | |||||||
\(458\) | −10.3069 | −0.481610 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 41.7730 | 1.94768 | ||||||||
\(461\) | −28.3889 | −1.32220 | −0.661101 | − | 0.750297i | \(-0.729911\pi\) | ||||
−0.661101 | + | 0.750297i | \(0.729911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.0681 | −1.76917 | −0.884587 | − | 0.466375i | \(-0.845560\pi\) | ||||
−0.884587 | + | 0.466375i | \(0.845560\pi\) | |||||||
\(464\) | 2.08918 | 0.0969879 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.4809 | −0.624491 | ||||||||
\(467\) | −33.2327 | −1.53783 | −0.768913 | − | 0.639354i | \(-0.779202\pi\) | ||||
−0.768913 | + | 0.639354i | \(0.779202\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.1322 | 1.34520 | ||||||||
\(470\) | −13.7372 | −0.633648 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.8370 | −1.05116 | ||||||||
\(473\) | 0.0182548 | 0.000839356 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 52.8865 | 2.42660 | ||||||||
\(476\) | −18.8508 | −0.864027 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.5117 | −0.526533 | ||||||||
\(479\) | −21.6861 | −0.990862 | −0.495431 | − | 0.868647i | \(-0.664990\pi\) | ||||
−0.495431 | + | 0.868647i | \(0.664990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94232 | 0.0885620 | ||||||||
\(482\) | −11.5384 | −0.525560 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.9043 | 0.859285 | ||||||||
\(485\) | −22.7207 | −1.03170 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.9044 | −1.76292 | −0.881462 | − | 0.472254i | \(-0.843440\pi\) | ||||
−0.881462 | + | 0.472254i | \(0.843440\pi\) | |||||||
\(488\) | 9.00020 | 0.407420 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.8317 | −0.670029 | ||||||||
\(491\) | −5.59325 | −0.252420 | −0.126210 | − | 0.992004i | \(-0.540281\pi\) | ||||
−0.126210 | + | 0.992004i | \(0.540281\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.44816 | 0.110259 | ||||||||
\(494\) | 26.4976 | 1.19218 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.96748 | 0.0883426 | ||||||||
\(497\) | 45.8735 | 2.05771 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.8271 | −0.977115 | −0.488558 | − | 0.872532i | \(-0.662477\pi\) | ||||
−0.488558 | + | 0.872532i | \(0.662477\pi\) | |||||||
\(500\) | −7.36181 | −0.329230 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.1392 | −0.586433 | ||||||||
\(503\) | 25.7315 | 1.14731 | 0.573655 | − | 0.819097i | \(-0.305525\pi\) | ||||
0.573655 | + | 0.819097i | \(0.305525\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.4169 | −1.53153 | ||||||||
\(506\) | −0.0696276 | −0.00309532 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.87600 | −0.393809 | ||||||||
\(509\) | 13.2495 | 0.587273 | 0.293637 | − | 0.955917i | \(-0.405134\pi\) | ||||
0.293637 | + | 0.955917i | \(0.405134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.8475 | −1.01071 | ||||||||
\(512\) | −21.8970 | −0.967719 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.20169 | 0.185328 | ||||||||
\(515\) | −2.90248 | −0.127898 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.139854 | −0.00615076 | ||||||||
\(518\) | 0.680477 | 0.0298985 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −39.2622 | −1.72176 | ||||||||
\(521\) | −41.7311 | −1.82827 | −0.914136 | − | 0.405407i | \(-0.867130\pi\) | ||||
−0.914136 | + | 0.405407i | \(0.867130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0286 | 0.700881 | 0.350441 | − | 0.936585i | \(-0.386032\pi\) | ||||
0.350441 | + | 0.936585i | \(0.386032\pi\) | |||||||
\(524\) | −1.45039 | −0.0633605 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.59021 | 0.200143 | ||||||||
\(527\) | 2.30554 | 0.100431 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.3948 | 1.27804 | ||||||||
\(530\) | −8.48279 | −0.368469 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −56.7011 | −2.45830 | ||||||||
\(533\) | −51.3852 | −2.22574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.8527 | 1.72298 | ||||||||
\(536\) | 14.6783 | 0.634005 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.4415 | 0.536389 | ||||||||
\(539\) | −0.150997 | −0.00650390 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.8842 | 1.58578 | 0.792888 | − | 0.609368i | \(-0.208577\pi\) | ||||
0.792888 | + | 0.609368i | \(0.208577\pi\) | |||||||
\(542\) | −16.1274 | −0.692730 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14.6064 | −0.626243 | ||||||||
\(545\) | −35.9242 | −1.53882 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9918 | 0.983058 | 0.491529 | − | 0.870861i | \(-0.336438\pi\) | ||||
0.491529 | + | 0.870861i | \(0.336438\pi\) | |||||||
\(548\) | −21.4941 | −0.918182 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0603665 | 0.00257404 | ||||||||
\(551\) | 7.36376 | 0.313707 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.819999 | −0.0348699 | ||||||||
\(554\) | 4.47533 | 0.190139 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.5622 | 0.490347 | ||||||||
\(557\) | 16.3802 | 0.694050 | 0.347025 | − | 0.937856i | \(-0.387192\pi\) | ||||
0.347025 | + | 0.937856i | \(0.387192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.96706 | 0.252380 | ||||||||
\(560\) | 31.4310 | 1.32820 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.3709 | −0.437471 | ||||||||
\(563\) | 10.8411 | 0.456897 | 0.228448 | − | 0.973556i | \(-0.426635\pi\) | ||||
0.228448 | + | 0.973556i | \(0.426635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.0518 | 0.801515 | ||||||||
\(566\) | 11.4058 | 0.479420 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 23.1134 | 0.969816 | ||||||||
\(569\) | −14.2012 | −0.595347 | −0.297673 | − | 0.954668i | \(-0.596211\pi\) | ||||
−0.297673 | + | 0.954668i | \(0.596211\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.2664 | −1.68510 | −0.842548 | − | 0.538621i | \(-0.818946\pi\) | ||||
−0.842548 | + | 0.538621i | \(0.818946\pi\) | |||||||
\(572\) | −0.184735 | −0.00772416 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.0024 | −0.751408 | ||||||||
\(575\) | −45.4259 | −1.89439 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.7821 | −0.865171 | −0.432585 | − | 0.901593i | \(-0.642399\pi\) | ||||
−0.432585 | + | 0.901593i | \(0.642399\pi\) | |||||||
\(578\) | 4.85380 | 0.201892 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.04273 | −0.209388 | ||||||||
\(581\) | 3.55383 | 0.147438 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0863605 | −0.00357669 | ||||||||
\(584\) | −11.5117 | −0.476358 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.278659 | 0.0115113 | ||||||||
\(587\) | −10.0202 | −0.413577 | −0.206789 | − | 0.978386i | \(-0.566301\pi\) | ||||
−0.206789 | + | 0.978386i | \(0.566301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.93480 | 0.285743 | ||||||||
\(590\) | 20.6219 | 0.848989 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.783441 | −0.0321992 | ||||||||
\(593\) | −3.38206 | −0.138885 | −0.0694423 | − | 0.997586i | \(-0.522122\pi\) | ||||
−0.0694423 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.8317 | 1.50995 | ||||||||
\(596\) | −1.71862 | −0.0703975 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.7596 | −0.930711 | ||||||||
\(599\) | −14.6166 | −0.597217 | −0.298609 | − | 0.954376i | \(-0.596523\pi\) | ||||
−0.298609 | + | 0.954376i | \(0.596523\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.46074 | 0.345121 | 0.172560 | − | 0.984999i | \(-0.444796\pi\) | ||||
0.172560 | + | 0.984999i | \(0.444796\pi\) | |||||||
\(602\) | 2.09052 | 0.0852032 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 32.7656 | 1.33321 | ||||||||
\(605\) | −36.9361 | −1.50166 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.0077 | −0.527967 | −0.263983 | − | 0.964527i | \(-0.585036\pi\) | ||||
−0.263983 | + | 0.964527i | \(0.585036\pi\) | |||||||
\(608\) | −43.9342 | −1.78177 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.12720 | −0.329061 | ||||||||
\(611\) | −45.7149 | −1.84943 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6052 | 0.872626 | 0.436313 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436313 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(614\) | −11.4654 | −0.462704 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.140037 | −0.00564227 | ||||||||
\(617\) | 35.3363 | 1.42258 | 0.711292 | − | 0.702896i | \(-0.248110\pi\) | ||||
0.711292 | + | 0.702896i | \(0.248110\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.4083 | −0.659505 | −0.329752 | − | 0.944067i | \(-0.606965\pi\) | ||||
−0.329752 | + | 0.944067i | \(0.606965\pi\) | |||||||
\(620\) | −4.74897 | −0.190723 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.30842 | −0.0524628 | ||||||||
\(623\) | 17.5408 | 0.702757 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.9944 | −0.679777 | ||||||||
\(626\) | −15.0720 | −0.602398 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.9665 | −0.916464 | ||||||||
\(629\) | −0.918056 | −0.0366053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.317511 | 0.0126399 | 0.00631996 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00631996 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(632\) | −0.413157 | −0.0164345 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.0484 | −0.478504 | ||||||||
\(635\) | 17.3423 | 0.688210 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49.3574 | −1.95561 | ||||||||
\(638\) | 0.00840526 | 0.000332767 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 38.6037 | 1.52594 | ||||||||
\(641\) | −18.1436 | −0.716628 | −0.358314 | − | 0.933601i | \(-0.616648\pi\) | ||||
−0.358314 | + | 0.933601i | \(0.616648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.2642 | 1.03576 | 0.517879 | − | 0.855454i | \(-0.326722\pi\) | ||||
0.517879 | + | 0.855454i | \(0.326722\pi\) | |||||||
\(644\) | 48.7023 | 1.91914 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.5244 | −0.492765 | ||||||||
\(647\) | 19.7059 | 0.774720 | 0.387360 | − | 0.921929i | \(-0.373387\pi\) | ||||
0.387360 | + | 0.921929i | \(0.373387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.209945 | 0.00824105 | ||||||||
\(650\) | 19.7324 | 0.773969 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.2494 | 1.18466 | ||||||||
\(653\) | 34.9563 | 1.36795 | 0.683974 | − | 0.729507i | \(-0.260250\pi\) | ||||
0.683974 | + | 0.729507i | \(0.260250\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.83383 | 0.110727 | ||||||||
\(656\) | 20.7264 | 0.809231 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.0159 | −0.624365 | ||||||||
\(659\) | −38.8782 | −1.51448 | −0.757239 | − | 0.653137i | \(-0.773452\pi\) | ||||
−0.757239 | + | 0.653137i | \(0.773452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.7519 | −0.923840 | −0.461920 | − | 0.886922i | \(-0.652839\pi\) | ||||
−0.461920 | + | 0.886922i | \(0.652839\pi\) | |||||||
\(662\) | −4.13511 | −0.160715 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.79060 | 0.0694887 | ||||||||
\(665\) | 110.785 | 4.29607 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.32496 | −0.244904 | ||||||||
\(668\) | −36.1193 | −1.39750 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.2545 | −0.512066 | ||||||||
\(671\) | −0.0827404 | −0.00319416 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.61288 | −0.0621720 | −0.0310860 | − | 0.999517i | \(-0.509897\pi\) | ||||
−0.0310860 | + | 0.999517i | \(0.509897\pi\) | |||||||
\(674\) | 13.8214 | 0.532380 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −38.0435 | −1.46321 | ||||||||
\(677\) | −26.4378 | −1.01609 | −0.508044 | − | 0.861331i | \(-0.669631\pi\) | ||||
−0.508044 | + | 0.861331i | \(0.669631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.4897 | −1.01658 | ||||||||
\(680\) | 18.5577 | 0.711654 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.00791563 | 0.000303105 0 | ||||||||
\(683\) | −26.1063 | −0.998931 | −0.499465 | − | 0.866334i | \(-0.666470\pi\) | ||||
−0.499465 | + | 0.866334i | \(0.666470\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 41.9962 | 1.60459 | ||||||||
\(686\) | −2.75524 | −0.105196 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.40684 | −0.0917599 | ||||||||
\(689\) | −28.2292 | −1.07545 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.4534 | −0.397664 | −0.198832 | − | 0.980034i | \(-0.563715\pi\) | ||||
−0.198832 | + | 0.980034i | \(0.563715\pi\) | |||||||
\(692\) | 33.7195 | 1.28182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.74085 | 0.293839 | ||||||||
\(695\) | −22.5908 | −0.856918 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.2877 | 0.919964 | ||||||||
\(698\) | 4.52314 | 0.171203 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −42.2245 | −1.59594 | ||||||||
\(701\) | 44.1917 | 1.66910 | 0.834548 | − | 0.550936i | \(-0.185729\pi\) | ||||
0.834548 | + | 0.550936i | \(0.185729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.76140 | −0.104148 | ||||||||
\(704\) | 0.0365651 | 0.00137810 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.7646 | −0.593309 | ||||||||
\(707\) | −40.1260 | −1.50909 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.6858 | −0.851984 | −0.425992 | − | 0.904727i | \(-0.640075\pi\) | ||||
−0.425992 | + | 0.904727i | \(0.640075\pi\) | |||||||
\(710\) | −20.8714 | −0.783291 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.83795 | 0.331216 | ||||||||
\(713\) | −5.95652 | −0.223073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.360944 | 0.0134985 | ||||||||
\(716\) | 22.9710 | 0.858466 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.02421 | 0.150182 | ||||||||
\(719\) | −43.1259 | −1.60833 | −0.804163 | − | 0.594409i | \(-0.797386\pi\) | ||||
−0.804163 | + | 0.594409i | \(0.797386\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.38394 | −0.126025 | ||||||||
\(722\) | −27.5932 | −1.02691 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 30.7324 | 1.14216 | ||||||||
\(725\) | 5.48369 | 0.203659 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.5706 | −0.614570 | −0.307285 | − | 0.951617i | \(-0.599421\pi\) | ||||
−0.307285 | + | 0.951617i | \(0.599421\pi\) | |||||||
\(728\) | −45.7750 | −1.69653 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.3951 | 0.384740 | ||||||||
\(731\) | −2.82039 | −0.104316 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.6534 | 1.90786 | 0.953931 | − | 0.300026i | \(-0.0969954\pi\) | ||||
0.953931 | + | 0.300026i | \(0.0969954\pi\) | |||||||
\(734\) | −0.629825 | −0.0232473 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.7364 | 1.39098 | ||||||||
\(737\) | −0.134940 | −0.00497057 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.9045 | 0.805768 | 0.402884 | − | 0.915251i | \(-0.368008\pi\) | ||||
0.402884 | + | 0.915251i | \(0.368008\pi\) | |||||||
\(740\) | 1.89102 | 0.0695151 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.88992 | −0.363070 | ||||||||
\(743\) | −47.9102 | −1.75765 | −0.878827 | − | 0.477140i | \(-0.841673\pi\) | ||||
−0.878827 | + | 0.477140i | \(0.841673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.35792 | 0.123025 | ||||||||
\(746\) | −8.43538 | −0.308841 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0873169 | 0.00319262 | ||||||||
\(749\) | 46.4635 | 1.69774 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.2207 | −0.993299 | −0.496650 | − | 0.867951i | \(-0.665437\pi\) | ||||
−0.496650 | + | 0.867951i | \(0.665437\pi\) | |||||||
\(752\) | 18.4393 | 0.672412 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.74749 | 0.100058 | ||||||||
\(755\) | −64.0189 | −2.32989 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.9698 | 0.507742 | 0.253871 | − | 0.967238i | \(-0.418296\pi\) | ||||
0.253871 | + | 0.967238i | \(0.418296\pi\) | |||||||
\(758\) | 5.30797 | 0.192794 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 55.8192 | 2.02478 | ||||||||
\(761\) | 7.46960 | 0.270773 | 0.135386 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135386 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.8834 | −1.51628 | ||||||||
\(764\) | 21.8239 | 0.789559 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.4392 | 0.666234 | ||||||||
\(767\) | 68.6260 | 2.47794 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.6443 | 0.852635 | 0.426318 | − | 0.904574i | \(-0.359811\pi\) | ||||
0.426318 | + | 0.904574i | \(0.359811\pi\) | |||||||
\(770\) | 0.126454 | 0.00455709 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 38.6246 | 1.39013 | ||||||||
\(773\) | −30.3897 | −1.09304 | −0.546521 | − | 0.837445i | \(-0.684048\pi\) | ||||
−0.546521 | + | 0.837445i | \(0.684048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.16425 | 0.185505 | ||||||||
\(776\) | −13.3468 | −0.479124 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.30808 | 0.262007 | ||||||||
\(779\) | 73.0546 | 2.61745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.212485 | −0.00760333 | ||||||||
\(782\) | 10.7576 | 0.384690 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.9085 | 0.711017 | ||||||||
\(785\) | 44.8731 | 1.60159 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.7757 | −0.384112 | −0.192056 | − | 0.981384i | \(-0.561516\pi\) | ||||
−0.192056 | + | 0.981384i | \(0.561516\pi\) | |||||||
\(788\) | −32.9067 | −1.17225 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.373082 | 0.0132737 | ||||||||
\(791\) | 22.2121 | 0.789772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.0459 | −0.960428 | ||||||||
\(794\) | 5.88310 | 0.208783 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.66704 | 0.342639 | ||||||||
\(797\) | −8.93814 | −0.316605 | −0.158303 | − | 0.987391i | \(-0.550602\pi\) | ||||
−0.158303 | + | 0.987391i | \(0.550602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.6076 | 0.764422 | ||||||||
\(800\) | −32.7172 | −1.15673 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.54088 | −0.0897217 | ||||||||
\(803\) | 0.105829 | 0.00373463 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −95.1569 | −3.35384 | ||||||||
\(806\) | 2.58744 | 0.0911385 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.2175 | −0.711249 | ||||||||
\(809\) | −37.5114 | −1.31883 | −0.659416 | − | 0.751778i | \(-0.729196\pi\) | ||||
−0.659416 | + | 0.751778i | \(0.729196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.39395 | −0.154292 | −0.0771462 | − | 0.997020i | \(-0.524581\pi\) | ||||
−0.0771462 | + | 0.997020i | \(0.524581\pi\) | |||||||
\(812\) | −5.87922 | −0.206320 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.00315196 | −0.000110476 0 | ||||||||
\(815\) | −59.1028 | −2.07028 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.48340 | −0.296797 | ||||||||
\(818\) | 16.8512 | 0.589188 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −50.0280 | −1.74705 | ||||||||
\(821\) | −13.9328 | −0.486257 | −0.243128 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243128 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.6850 | 0.546746 | 0.273373 | − | 0.961908i | \(-0.411861\pi\) | ||||
0.273373 | + | 0.961908i | \(0.411861\pi\) | |||||||
\(824\) | −1.70500 | −0.0593966 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0427 | 0.836551 | ||||||||
\(827\) | 32.1864 | 1.11923 | 0.559616 | − | 0.828752i | \(-0.310949\pi\) | ||||
0.559616 | + | 0.828752i | \(0.310949\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.2221 | −1.46643 | −0.733217 | − | 0.679994i | \(-0.761982\pi\) | ||||
−0.733217 | + | 0.679994i | \(0.761982\pi\) | |||||||
\(830\) | −1.61692 | −0.0561240 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.9523 | 0.414371 | ||||||||
\(833\) | 23.3293 | 0.808311 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 70.5716 | 2.44223 | ||||||||
\(836\) | 0.262639 | 0.00908354 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.3380 | −0.702566 | ||||||||
\(839\) | 7.36583 | 0.254297 | 0.127148 | − | 0.991884i | \(-0.459418\pi\) | ||||
0.127148 | + | 0.991884i | \(0.459418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2365 | −0.973671 | ||||||||
\(842\) | 0.0770783 | 0.00265629 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.8038 | −0.371883 | ||||||||
\(845\) | 74.3312 | 2.55707 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.0630 | −1.47966 | ||||||||
\(848\) | 11.3864 | 0.391010 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.32673 | −0.319904 | ||||||||
\(851\) | 2.37185 | 0.0813061 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.4496 | 1.31649 | 0.658245 | − | 0.752804i | \(-0.271299\pi\) | ||||
0.658245 | + | 0.752804i | \(0.271299\pi\) | |||||||
\(854\) | −9.47535 | −0.324240 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.4107 | 0.800160 | ||||||||
\(857\) | 1.92317 | 0.0656942 | 0.0328471 | − | 0.999460i | \(-0.489543\pi\) | ||||
0.0328471 | + | 0.999460i | \(0.489543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1582 | −0.790149 | −0.395075 | − | 0.918649i | \(-0.629281\pi\) | ||||
−0.395075 | + | 0.918649i | \(0.629281\pi\) | |||||||
\(860\) | 5.80946 | 0.198101 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.232941 | −0.00793401 | ||||||||
\(863\) | −9.21594 | −0.313714 | −0.156857 | − | 0.987621i | \(-0.550136\pi\) | ||||
−0.156857 | + | 0.987621i | \(0.550136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −65.8827 | −2.24008 | ||||||||
\(866\) | −1.77749 | −0.0604015 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.53673 | −0.187929 | ||||||||
\(869\) | 0.00379822 | 0.000128846 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.1087 | −1.49457 | ||||||||
\(872\) | −21.1030 | −0.714637 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.3575 | 1.09451 | ||||||||
\(875\) | 16.7699 | 0.566925 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.5672 | −1.20102 | −0.600509 | − | 0.799618i | \(-0.705035\pi\) | ||||
−0.600509 | + | 0.799618i | \(0.705035\pi\) | |||||||
\(878\) | −2.46177 | −0.0830807 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.145588 | −0.00490777 | ||||||||
\(881\) | 13.3847 | 0.450943 | 0.225471 | − | 0.974250i | \(-0.427608\pi\) | ||||
0.225471 | + | 0.974250i | \(0.427608\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.2966 | −1.62531 | −0.812655 | − | 0.582745i | \(-0.801979\pi\) | ||||
−0.812655 | + | 0.582745i | \(0.801979\pi\) | |||||||
\(884\) | 28.5419 | 0.959967 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.56467 | −0.321331 | ||||||||
\(887\) | 11.8976 | 0.399481 | 0.199741 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199741 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2191 | 0.678127 | ||||||||
\(890\) | −7.98069 | −0.267513 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.0146 | −0.837550 | ||||||||
\(893\) | 64.9931 | 2.17491 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.8818 | −1.50023 | ||||||||
\(896\) | 45.0073 | 1.50359 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.96516 | −0.132319 | ||||||||
\(899\) | 0.719055 | 0.0239818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.3428 | 0.444514 | ||||||||
\(902\) | 0.0833871 | 0.00277649 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.1916 | 0.372227 | ||||||||
\(905\) | −60.0463 | −1.99601 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.28699 | 0.241961 | 0.120980 | − | 0.992655i | \(-0.461396\pi\) | ||||
0.120980 | + | 0.992655i | \(0.461396\pi\) | |||||||
\(908\) | −38.2552 | −1.26954 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.3349 | 1.37024 | ||||||||
\(911\) | −43.2137 | −1.43173 | −0.715867 | − | 0.698236i | \(-0.753968\pi\) | ||||
−0.715867 | + | 0.698236i | \(0.753968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.0164613 | −0.000544789 0 | ||||||||
\(914\) | −1.23146 | −0.0407330 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.3937 | −1.10336 | ||||||||
\(917\) | 3.30391 | 0.109105 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.3602 | −1.29837 | −0.649187 | − | 0.760629i | \(-0.724891\pi\) | ||||
−0.649187 | + | 0.760629i | \(0.724891\pi\) | |||||||
\(920\) | −47.9448 | −1.58069 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.0589 | 0.495939 | ||||||||
\(923\) | −69.4565 | −2.28619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.05638 | −0.0676133 | ||||||||
\(926\) | 20.1932 | 0.663591 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.55544 | −0.149540 | ||||||||
\(929\) | 52.3627 | 1.71797 | 0.858983 | − | 0.512004i | \(-0.171097\pi\) | ||||
0.858983 | + | 0.512004i | \(0.171097\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70.1716 | 2.29978 | ||||||||
\(932\) | −43.6772 | −1.43069 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.6283 | 0.576816 | ||||||||
\(935\) | −0.170604 | −0.00557934 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.642958 | −0.0210045 | −0.0105023 | − | 0.999945i | \(-0.503343\pi\) | ||||
−0.0105023 | + | 0.999945i | \(0.503343\pi\) | |||||||
\(938\) | −15.4532 | −0.504564 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −44.5075 | −1.45167 | ||||||||
\(941\) | 6.85566 | 0.223488 | 0.111744 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111744 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −62.7488 | −2.04338 | ||||||||
\(944\) | −27.6806 | −0.900926 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.00968326 | −0.000314830 0 | ||||||||
\(947\) | −23.8132 | −0.773826 | −0.386913 | − | 0.922116i | \(-0.626459\pi\) | ||||
−0.386913 | + | 0.922116i | \(0.626459\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.5931 | 1.12294 | ||||||||
\(950\) | −28.0537 | −0.910181 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.6360 | 0.701227 | ||||||||
\(953\) | −8.89776 | −0.288227 | −0.144113 | − | 0.989561i | \(-0.546033\pi\) | ||||
−0.144113 | + | 0.989561i | \(0.546033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −42.6405 | −1.37981 | ||||||||
\(956\) | −37.2971 | −1.20628 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.5034 | 0.371658 | ||||||||
\(959\) | 48.9625 | 1.58108 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3228 | −0.978156 | ||||||||
\(962\) | −1.03030 | −0.0332183 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.3836 | −1.20405 | ||||||||
\(965\) | −75.4665 | −2.42935 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.99362 | 0.0641105 | 0.0320552 | − | 0.999486i | \(-0.489795\pi\) | ||||
0.0320552 | + | 0.999486i | \(0.489795\pi\) | |||||||
\(968\) | −21.6973 | −0.697379 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 12.0522 | 0.386974 | ||||||||
\(971\) | −24.8965 | −0.798965 | −0.399483 | − | 0.916741i | \(-0.630810\pi\) | ||||
−0.399483 | + | 0.916741i | \(0.630810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.3382 | −0.844364 | ||||||||
\(974\) | 20.6368 | 0.661247 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.9091 | 0.349191 | ||||||||
\(977\) | 49.8050 | 1.59340 | 0.796701 | − | 0.604374i | \(-0.206577\pi\) | ||||
0.796701 | + | 0.604374i | \(0.206577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0812488 | −0.00259672 | ||||||||
\(980\) | −48.0537 | −1.53502 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.96694 | 0.0946789 | ||||||||
\(983\) | 18.3355 | 0.584812 | 0.292406 | − | 0.956294i | \(-0.405544\pi\) | ||||
0.292406 | + | 0.956294i | \(0.405544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.2946 | 2.04860 | ||||||||
\(986\) | −1.29863 | −0.0413567 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 85.8505 | 2.73127 | ||||||||
\(989\) | 7.28666 | 0.231702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1904 | −0.355476 | −0.177738 | − | 0.984078i | \(-0.556878\pi\) | ||||
−0.177738 | + | 0.984078i | \(0.556878\pi\) | |||||||
\(992\) | −4.29008 | −0.136210 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.3336 | −0.771815 | ||||||||
\(995\) | −18.8879 | −0.598787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.9659 | −1.20239 | −0.601195 | − | 0.799102i | \(-0.705309\pi\) | ||||
−0.601195 | + | 0.799102i | \(0.705309\pi\) | |||||||
\(998\) | 11.5782 | 0.366501 | ||||||||
\(999\) | 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 | 4023.2.a.f.1.10 | yes | 25 | |
3.2 | odd | 2 | 4023.2.a.e.1.16 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.16 | ✓ | 25 | 3.2 | odd | 2 | ||
4023.2.a.f.1.10 | yes | 25 | 1.1 | even | 1 | trivial |