Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, 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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10273.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.38266\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.38266 | −1.37563 | −0.687816 | − | 0.725885i | \(-0.741430\pi\) | ||||
−0.687816 | + | 0.725885i | \(0.741430\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.61326 | −1.16869 | −0.584344 | − | 0.811506i | \(-0.698648\pi\) | ||||
−0.584344 | + | 0.811506i | \(0.698648\pi\) | |||||||
\(6\) | 2.38266 | 0.972718 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.67708 | 0.892361 | ||||||||
\(10\) | 2.61326 | 0.826387 | ||||||||
\(11\) | −3.93618 | −1.18680 | −0.593401 | − | 0.804907i | \(-0.702215\pi\) | ||||
−0.593401 | + | 0.804907i | \(0.702215\pi\) | |||||||
\(12\) | −2.38266 | −0.687816 | ||||||||
\(13\) | 1.76940 | 0.490743 | 0.245372 | − | 0.969429i | \(-0.421090\pi\) | ||||
0.245372 | + | 0.969429i | \(0.421090\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 6.22653 | 1.60768 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.61734 | −0.634797 | −0.317399 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317399 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(18\) | −2.67708 | −0.630995 | ||||||||
\(19\) | −0.510304 | −0.117072 | −0.0585359 | − | 0.998285i | \(-0.518643\pi\) | ||||
−0.0585359 | + | 0.998285i | \(0.518643\pi\) | |||||||
\(20\) | −2.61326 | −0.584344 | ||||||||
\(21\) | −2.38266 | −0.519940 | ||||||||
\(22\) | 3.93618 | 0.839196 | ||||||||
\(23\) | −6.44241 | −1.34334 | −0.671668 | − | 0.740853i | \(-0.734422\pi\) | ||||
−0.671668 | + | 0.740853i | \(0.734422\pi\) | |||||||
\(24\) | 2.38266 | 0.486359 | ||||||||
\(25\) | 1.82915 | 0.365829 | ||||||||
\(26\) | −1.76940 | −0.347008 | ||||||||
\(27\) | 0.769400 | 0.148071 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.06382 | 0.754633 | 0.377316 | − | 0.926084i | \(-0.376847\pi\) | ||||
0.377316 | + | 0.926084i | \(0.376847\pi\) | |||||||
\(30\) | −6.22653 | −1.13680 | ||||||||
\(31\) | 4.60919 | 0.827835 | 0.413918 | − | 0.910314i | \(-0.364160\pi\) | ||||
0.413918 | + | 0.910314i | \(0.364160\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 9.37859 | 1.63260 | ||||||||
\(34\) | 2.61734 | 0.448870 | ||||||||
\(35\) | −2.61326 | −0.441722 | ||||||||
\(36\) | 2.67708 | 0.446181 | ||||||||
\(37\) | 4.31884 | 0.710013 | 0.355007 | − | 0.934864i | \(-0.384479\pi\) | ||||
0.355007 | + | 0.934864i | \(0.384479\pi\) | |||||||
\(38\) | 0.510304 | 0.0827823 | ||||||||
\(39\) | −4.21588 | −0.675082 | ||||||||
\(40\) | 2.61326 | 0.413193 | ||||||||
\(41\) | −11.8751 | −1.85458 | −0.927291 | − | 0.374342i | \(-0.877869\pi\) | ||||
−0.927291 | + | 0.374342i | \(0.877869\pi\) | |||||||
\(42\) | 2.38266 | 0.367653 | ||||||||
\(43\) | 8.97125 | 1.36810 | 0.684051 | − | 0.729434i | \(-0.260217\pi\) | ||||
0.684051 | + | 0.729434i | \(0.260217\pi\) | |||||||
\(44\) | −3.93618 | −0.593401 | ||||||||
\(45\) | −6.99593 | −1.04289 | ||||||||
\(46\) | 6.44241 | 0.949882 | ||||||||
\(47\) | 11.4571 | 1.67119 | 0.835597 | − | 0.549343i | \(-0.185122\pi\) | ||||
0.835597 | + | 0.549343i | \(0.185122\pi\) | |||||||
\(48\) | −2.38266 | −0.343908 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.82915 | −0.258680 | ||||||||
\(51\) | 6.23623 | 0.873247 | ||||||||
\(52\) | 1.76940 | 0.245372 | ||||||||
\(53\) | −8.70151 | −1.19524 | −0.597622 | − | 0.801778i | \(-0.703888\pi\) | ||||
−0.597622 | + | 0.801778i | \(0.703888\pi\) | |||||||
\(54\) | −0.769400 | −0.104702 | ||||||||
\(55\) | 10.2863 | 1.38700 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.21588 | 0.161048 | ||||||||
\(58\) | −4.06382 | −0.533606 | ||||||||
\(59\) | −9.05975 | −1.17948 | −0.589739 | − | 0.807594i | \(-0.700770\pi\) | ||||
−0.589739 | + | 0.807594i | \(0.700770\pi\) | |||||||
\(60\) | 6.22653 | 0.803841 | ||||||||
\(61\) | 6.05975 | 0.775871 | 0.387936 | − | 0.921686i | \(-0.373188\pi\) | ||||
0.387936 | + | 0.921686i | \(0.373188\pi\) | |||||||
\(62\) | −4.60919 | −0.585368 | ||||||||
\(63\) | 2.67708 | 0.337281 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.62391 | −0.573525 | ||||||||
\(66\) | −9.37859 | −1.15442 | ||||||||
\(67\) | −9.84386 | −1.20262 | −0.601310 | − | 0.799016i | \(-0.705354\pi\) | ||||
−0.601310 | + | 0.799016i | \(0.705354\pi\) | |||||||
\(68\) | −2.61734 | −0.317399 | ||||||||
\(69\) | 15.3501 | 1.84793 | ||||||||
\(70\) | 2.61326 | 0.312345 | ||||||||
\(71\) | −7.39920 | −0.878123 | −0.439062 | − | 0.898457i | \(-0.644689\pi\) | ||||
−0.439062 | + | 0.898457i | \(0.644689\pi\) | |||||||
\(72\) | −2.67708 | −0.315497 | ||||||||
\(73\) | −0.662367 | −0.0775242 | −0.0387621 | − | 0.999248i | \(-0.512341\pi\) | ||||
−0.0387621 | + | 0.999248i | \(0.512341\pi\) | |||||||
\(74\) | −4.31884 | −0.502055 | ||||||||
\(75\) | −4.35824 | −0.503246 | ||||||||
\(76\) | −0.510304 | −0.0585359 | ||||||||
\(77\) | −3.93618 | −0.448569 | ||||||||
\(78\) | 4.21588 | 0.477355 | ||||||||
\(79\) | 14.1195 | 1.58857 | 0.794284 | − | 0.607547i | \(-0.207846\pi\) | ||||
0.794284 | + | 0.607547i | \(0.207846\pi\) | |||||||
\(80\) | −2.61326 | −0.292172 | ||||||||
\(81\) | −9.86447 | −1.09605 | ||||||||
\(82\) | 11.8751 | 1.31139 | ||||||||
\(83\) | −8.90768 | −0.977745 | −0.488873 | − | 0.872355i | \(-0.662592\pi\) | ||||
−0.488873 | + | 0.872355i | \(0.662592\pi\) | |||||||
\(84\) | −2.38266 | −0.259970 | ||||||||
\(85\) | 6.83979 | 0.741880 | ||||||||
\(86\) | −8.97125 | −0.967394 | ||||||||
\(87\) | −9.68272 | −1.03810 | ||||||||
\(88\) | 3.93618 | 0.419598 | ||||||||
\(89\) | 16.3272 | 1.73068 | 0.865342 | − | 0.501183i | \(-0.167101\pi\) | ||||
0.865342 | + | 0.501183i | \(0.167101\pi\) | |||||||
\(90\) | 6.99593 | 0.737435 | ||||||||
\(91\) | 1.76940 | 0.185483 | ||||||||
\(92\) | −6.44241 | −0.671668 | ||||||||
\(93\) | −10.9821 | −1.13880 | ||||||||
\(94\) | −11.4571 | −1.18171 | ||||||||
\(95\) | 1.33356 | 0.136820 | ||||||||
\(96\) | 2.38266 | 0.243180 | ||||||||
\(97\) | 4.26593 | 0.433139 | 0.216570 | − | 0.976267i | \(-0.430513\pi\) | ||||
0.216570 | + | 0.976267i | \(0.430513\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −10.5375 | −1.05906 | ||||||||
\(100\) | 1.82915 | 0.182915 | ||||||||
\(101\) | 12.9593 | 1.28950 | 0.644749 | − | 0.764395i | \(-0.276962\pi\) | ||||
0.644749 | + | 0.764395i | \(0.276962\pi\) | |||||||
\(102\) | −6.23623 | −0.617479 | ||||||||
\(103\) | −11.1668 | −1.10030 | −0.550148 | − | 0.835067i | \(-0.685429\pi\) | ||||
−0.550148 | + | 0.835067i | \(0.685429\pi\) | |||||||
\(104\) | −1.76940 | −0.173504 | ||||||||
\(105\) | 6.22653 | 0.607647 | ||||||||
\(106\) | 8.70151 | 0.845165 | ||||||||
\(107\) | 11.7925 | 1.14002 | 0.570012 | − | 0.821636i | \(-0.306938\pi\) | ||||
0.570012 | + | 0.821636i | \(0.306938\pi\) | |||||||
\(108\) | 0.769400 | 0.0740355 | ||||||||
\(109\) | 6.73683 | 0.645271 | 0.322636 | − | 0.946523i | \(-0.395431\pi\) | ||||
0.322636 | + | 0.946523i | \(0.395431\pi\) | |||||||
\(110\) | −10.2863 | −0.980758 | ||||||||
\(111\) | −10.2903 | −0.976717 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 9.77779 | 0.919817 | 0.459909 | − | 0.887966i | \(-0.347882\pi\) | ||||
0.459909 | + | 0.887966i | \(0.347882\pi\) | |||||||
\(114\) | −1.21588 | −0.113878 | ||||||||
\(115\) | 16.8357 | 1.56994 | ||||||||
\(116\) | 4.06382 | 0.377316 | ||||||||
\(117\) | 4.73683 | 0.437920 | ||||||||
\(118\) | 9.05975 | 0.834017 | ||||||||
\(119\) | −2.61734 | −0.239931 | ||||||||
\(120\) | −6.22653 | −0.568402 | ||||||||
\(121\) | 4.49351 | 0.408501 | ||||||||
\(122\) | −6.05975 | −0.548624 | ||||||||
\(123\) | 28.2944 | 2.55122 | ||||||||
\(124\) | 4.60919 | 0.413918 | ||||||||
\(125\) | 8.28627 | 0.741147 | ||||||||
\(126\) | −2.67708 | −0.238494 | ||||||||
\(127\) | 2.61734 | 0.232251 | 0.116126 | − | 0.993235i | \(-0.462953\pi\) | ||||
0.116126 | + | 0.993235i | \(0.462953\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −21.3755 | −1.88200 | ||||||||
\(130\) | 4.62391 | 0.405544 | ||||||||
\(131\) | 20.0378 | 1.75071 | 0.875356 | − | 0.483478i | \(-0.160627\pi\) | ||||
0.875356 | + | 0.483478i | \(0.160627\pi\) | |||||||
\(132\) | 9.37859 | 0.816301 | ||||||||
\(133\) | −0.510304 | −0.0442490 | ||||||||
\(134\) | 9.84386 | 0.850380 | ||||||||
\(135\) | −2.01064 | −0.173049 | ||||||||
\(136\) | 2.61734 | 0.224435 | ||||||||
\(137\) | 9.50216 | 0.811824 | 0.405912 | − | 0.913912i | \(-0.366954\pi\) | ||||
0.405912 | + | 0.913912i | \(0.366954\pi\) | |||||||
\(138\) | −15.3501 | −1.30669 | ||||||||
\(139\) | −3.92528 | −0.332938 | −0.166469 | − | 0.986047i | \(-0.553236\pi\) | ||||
−0.166469 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(140\) | −2.61326 | −0.220861 | ||||||||
\(141\) | −27.2985 | −2.29895 | ||||||||
\(142\) | 7.39920 | 0.620927 | ||||||||
\(143\) | −6.96467 | −0.582415 | ||||||||
\(144\) | 2.67708 | 0.223090 | ||||||||
\(145\) | −10.6198 | −0.881929 | ||||||||
\(146\) | 0.662367 | 0.0548179 | ||||||||
\(147\) | −2.38266 | −0.196519 | ||||||||
\(148\) | 4.31884 | 0.355007 | ||||||||
\(149\) | 5.29416 | 0.433715 | 0.216857 | − | 0.976203i | \(-0.430419\pi\) | ||||
0.216857 | + | 0.976203i | \(0.430419\pi\) | |||||||
\(150\) | 4.35824 | 0.355849 | ||||||||
\(151\) | −7.84360 | −0.638303 | −0.319152 | − | 0.947704i | \(-0.603398\pi\) | ||||
−0.319152 | + | 0.947704i | \(0.603398\pi\) | |||||||
\(152\) | 0.510304 | 0.0413911 | ||||||||
\(153\) | −7.00683 | −0.566469 | ||||||||
\(154\) | 3.93618 | 0.317186 | ||||||||
\(155\) | −12.0450 | −0.967480 | ||||||||
\(156\) | −4.21588 | −0.337541 | ||||||||
\(157\) | 17.0066 | 1.35727 | 0.678636 | − | 0.734475i | \(-0.262571\pi\) | ||||
0.678636 | + | 0.734475i | \(0.262571\pi\) | |||||||
\(158\) | −14.1195 | −1.12329 | ||||||||
\(159\) | 20.7328 | 1.64421 | ||||||||
\(160\) | 2.61326 | 0.206597 | ||||||||
\(161\) | −6.44241 | −0.507733 | ||||||||
\(162\) | 9.86447 | 0.775026 | ||||||||
\(163\) | 0.495587 | 0.0388174 | 0.0194087 | − | 0.999812i | \(-0.493822\pi\) | ||||
0.0194087 | + | 0.999812i | \(0.493822\pi\) | |||||||
\(164\) | −11.8751 | −0.927291 | ||||||||
\(165\) | −24.5087 | −1.90800 | ||||||||
\(166\) | 8.90768 | 0.691370 | ||||||||
\(167\) | 7.55627 | 0.584722 | 0.292361 | − | 0.956308i | \(-0.405559\pi\) | ||||
0.292361 | + | 0.956308i | \(0.405559\pi\) | |||||||
\(168\) | 2.38266 | 0.183826 | ||||||||
\(169\) | −9.86923 | −0.759171 | ||||||||
\(170\) | −6.83979 | −0.524588 | ||||||||
\(171\) | −1.36613 | −0.104470 | ||||||||
\(172\) | 8.97125 | 0.684051 | ||||||||
\(173\) | 12.1410 | 0.923066 | 0.461533 | − | 0.887123i | \(-0.347300\pi\) | ||||
0.461533 | + | 0.887123i | \(0.347300\pi\) | |||||||
\(174\) | 9.68272 | 0.734045 | ||||||||
\(175\) | 1.82915 | 0.138271 | ||||||||
\(176\) | −3.93618 | −0.296701 | ||||||||
\(177\) | 21.5863 | 1.62253 | ||||||||
\(178\) | −16.3272 | −1.22378 | ||||||||
\(179\) | −10.2509 | −0.766192 | −0.383096 | − | 0.923709i | \(-0.625142\pi\) | ||||
−0.383096 | + | 0.923709i | \(0.625142\pi\) | |||||||
\(180\) | −6.99593 | −0.521446 | ||||||||
\(181\) | 21.8045 | 1.62071 | 0.810357 | − | 0.585937i | \(-0.199273\pi\) | ||||
0.810357 | + | 0.585937i | \(0.199273\pi\) | |||||||
\(182\) | −1.76940 | −0.131157 | ||||||||
\(183\) | −14.4383 | −1.06731 | ||||||||
\(184\) | 6.44241 | 0.474941 | ||||||||
\(185\) | −11.2863 | −0.829783 | ||||||||
\(186\) | 10.9821 | 0.805250 | ||||||||
\(187\) | 10.3023 | 0.753379 | ||||||||
\(188\) | 11.4571 | 0.835597 | ||||||||
\(189\) | 0.769400 | 0.0559656 | ||||||||
\(190\) | −1.33356 | −0.0967466 | ||||||||
\(191\) | −0.944326 | −0.0683290 | −0.0341645 | − | 0.999416i | \(-0.510877\pi\) | ||||
−0.0341645 | + | 0.999416i | \(0.510877\pi\) | |||||||
\(192\) | −2.38266 | −0.171954 | ||||||||
\(193\) | −20.6651 | −1.48751 | −0.743754 | − | 0.668453i | \(-0.766957\pi\) | ||||
−0.743754 | + | 0.668453i | \(0.766957\pi\) | |||||||
\(194\) | −4.26593 | −0.306276 | ||||||||
\(195\) | 11.0172 | 0.788959 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 5.81036 | 0.413971 | 0.206985 | − | 0.978344i | \(-0.433635\pi\) | ||||
0.206985 | + | 0.978344i | \(0.433635\pi\) | |||||||
\(198\) | 10.5375 | 0.748866 | ||||||||
\(199\) | −1.59949 | −0.113385 | −0.0566923 | − | 0.998392i | \(-0.518055\pi\) | ||||
−0.0566923 | + | 0.998392i | \(0.518055\pi\) | |||||||
\(200\) | −1.82915 | −0.129340 | ||||||||
\(201\) | 23.4546 | 1.65436 | ||||||||
\(202\) | −12.9593 | −0.911812 | ||||||||
\(203\) | 4.06382 | 0.285224 | ||||||||
\(204\) | 6.23623 | 0.436624 | ||||||||
\(205\) | 31.0328 | 2.16743 | ||||||||
\(206\) | 11.1668 | 0.778026 | ||||||||
\(207\) | −17.2469 | −1.19874 | ||||||||
\(208\) | 1.76940 | 0.122686 | ||||||||
\(209\) | 2.00865 | 0.138941 | ||||||||
\(210\) | −6.22653 | −0.429671 | ||||||||
\(211\) | −11.0145 | −0.758266 | −0.379133 | − | 0.925342i | \(-0.623778\pi\) | ||||
−0.379133 | + | 0.925342i | \(0.623778\pi\) | |||||||
\(212\) | −8.70151 | −0.597622 | ||||||||
\(213\) | 17.6298 | 1.20797 | ||||||||
\(214\) | −11.7925 | −0.806119 | ||||||||
\(215\) | −23.4442 | −1.59888 | ||||||||
\(216\) | −0.769400 | −0.0523510 | ||||||||
\(217\) | 4.60919 | 0.312892 | ||||||||
\(218\) | −6.73683 | −0.456276 | ||||||||
\(219\) | 1.57820 | 0.106645 | ||||||||
\(220\) | 10.2863 | 0.693501 | ||||||||
\(221\) | −4.63111 | −0.311522 | ||||||||
\(222\) | 10.2903 | 0.690643 | ||||||||
\(223\) | 2.20524 | 0.147674 | 0.0738369 | − | 0.997270i | \(-0.476476\pi\) | ||||
0.0738369 | + | 0.997270i | \(0.476476\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.89678 | 0.326452 | ||||||||
\(226\) | −9.77779 | −0.650409 | ||||||||
\(227\) | 10.7465 | 0.713273 | 0.356636 | − | 0.934243i | \(-0.383924\pi\) | ||||
0.356636 | + | 0.934243i | \(0.383924\pi\) | |||||||
\(228\) | 1.21588 | 0.0805238 | ||||||||
\(229\) | −21.9052 | −1.44753 | −0.723767 | − | 0.690044i | \(-0.757591\pi\) | ||||
−0.723767 | + | 0.690044i | \(0.757591\pi\) | |||||||
\(230\) | −16.8357 | −1.11011 | ||||||||
\(231\) | 9.37859 | 0.617066 | ||||||||
\(232\) | −4.06382 | −0.266803 | ||||||||
\(233\) | −14.1342 | −0.925963 | −0.462982 | − | 0.886368i | \(-0.653220\pi\) | ||||
−0.462982 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(234\) | −4.73683 | −0.309656 | ||||||||
\(235\) | −29.9405 | −1.95310 | ||||||||
\(236\) | −9.05975 | −0.589739 | ||||||||
\(237\) | −33.6420 | −2.18528 | ||||||||
\(238\) | 2.61734 | 0.169657 | ||||||||
\(239\) | −17.0234 | −1.10115 | −0.550575 | − | 0.834786i | \(-0.685592\pi\) | ||||
−0.550575 | + | 0.834786i | \(0.685592\pi\) | |||||||
\(240\) | 6.22653 | 0.401921 | ||||||||
\(241\) | −18.1722 | −1.17057 | −0.585286 | − | 0.810827i | \(-0.699018\pi\) | ||||
−0.585286 | + | 0.810827i | \(0.699018\pi\) | |||||||
\(242\) | −4.49351 | −0.288854 | ||||||||
\(243\) | 21.1955 | 1.35969 | ||||||||
\(244\) | 6.05975 | 0.387936 | ||||||||
\(245\) | −2.61326 | −0.166955 | ||||||||
\(246\) | −28.2944 | −1.80399 | ||||||||
\(247\) | −0.902932 | −0.0574522 | ||||||||
\(248\) | −4.60919 | −0.292684 | ||||||||
\(249\) | 21.2240 | 1.34502 | ||||||||
\(250\) | −8.28627 | −0.524070 | ||||||||
\(251\) | 20.5716 | 1.29847 | 0.649234 | − | 0.760588i | \(-0.275089\pi\) | ||||
0.649234 | + | 0.760588i | \(0.275089\pi\) | |||||||
\(252\) | 2.67708 | 0.168640 | ||||||||
\(253\) | 25.3585 | 1.59427 | ||||||||
\(254\) | −2.61734 | −0.164226 | ||||||||
\(255\) | −16.2969 | −1.02055 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.29035 | −0.267625 | −0.133812 | − | 0.991007i | \(-0.542722\pi\) | ||||
−0.133812 | + | 0.991007i | \(0.542722\pi\) | |||||||
\(258\) | 21.3755 | 1.33078 | ||||||||
\(259\) | 4.31884 | 0.268360 | ||||||||
\(260\) | −4.62391 | −0.286763 | ||||||||
\(261\) | 10.8792 | 0.673405 | ||||||||
\(262\) | −20.0378 | −1.23794 | ||||||||
\(263\) | 21.4345 | 1.32171 | 0.660855 | − | 0.750514i | \(-0.270194\pi\) | ||||
0.660855 | + | 0.750514i | \(0.270194\pi\) | |||||||
\(264\) | −9.37859 | −0.577212 | ||||||||
\(265\) | 22.7393 | 1.39687 | ||||||||
\(266\) | 0.510304 | 0.0312888 | ||||||||
\(267\) | −38.9023 | −2.38078 | ||||||||
\(268\) | −9.84386 | −0.601310 | ||||||||
\(269\) | 5.98095 | 0.364665 | 0.182332 | − | 0.983237i | \(-0.441635\pi\) | ||||
0.182332 | + | 0.983237i | \(0.441635\pi\) | |||||||
\(270\) | 2.01064 | 0.122364 | ||||||||
\(271\) | −23.0641 | −1.40104 | −0.700521 | − | 0.713632i | \(-0.747049\pi\) | ||||
−0.700521 | + | 0.713632i | \(0.747049\pi\) | |||||||
\(272\) | −2.61734 | −0.158699 | ||||||||
\(273\) | −4.21588 | −0.255157 | ||||||||
\(274\) | −9.50216 | −0.574046 | ||||||||
\(275\) | −7.19985 | −0.434167 | ||||||||
\(276\) | 15.3501 | 0.923967 | ||||||||
\(277\) | 9.54762 | 0.573661 | 0.286831 | − | 0.957981i | \(-0.407398\pi\) | ||||
0.286831 | + | 0.957981i | \(0.407398\pi\) | |||||||
\(278\) | 3.92528 | 0.235422 | ||||||||
\(279\) | 12.3392 | 0.738728 | ||||||||
\(280\) | 2.61326 | 0.156172 | ||||||||
\(281\) | −6.01272 | −0.358689 | −0.179344 | − | 0.983786i | \(-0.557398\pi\) | ||||
−0.179344 | + | 0.983786i | \(0.557398\pi\) | |||||||
\(282\) | 27.2985 | 1.62560 | ||||||||
\(283\) | −29.7178 | −1.76654 | −0.883269 | − | 0.468866i | \(-0.844663\pi\) | ||||
−0.883269 | + | 0.468866i | \(0.844663\pi\) | |||||||
\(284\) | −7.39920 | −0.439062 | ||||||||
\(285\) | −3.17742 | −0.188214 | ||||||||
\(286\) | 6.96467 | 0.411830 | ||||||||
\(287\) | −11.8751 | −0.700966 | ||||||||
\(288\) | −2.67708 | −0.157749 | ||||||||
\(289\) | −10.1495 | −0.597032 | ||||||||
\(290\) | 10.6198 | 0.623618 | ||||||||
\(291\) | −10.1643 | −0.595840 | ||||||||
\(292\) | −0.662367 | −0.0387621 | ||||||||
\(293\) | 2.20956 | 0.129084 | 0.0645418 | − | 0.997915i | \(-0.479441\pi\) | ||||
0.0645418 | + | 0.997915i | \(0.479441\pi\) | |||||||
\(294\) | 2.38266 | 0.138960 | ||||||||
\(295\) | 23.6755 | 1.37844 | ||||||||
\(296\) | −4.31884 | −0.251028 | ||||||||
\(297\) | −3.02849 | −0.175731 | ||||||||
\(298\) | −5.29416 | −0.306683 | ||||||||
\(299\) | −11.3992 | −0.659233 | ||||||||
\(300\) | −4.35824 | −0.251623 | ||||||||
\(301\) | 8.97125 | 0.517094 | ||||||||
\(302\) | 7.84360 | 0.451349 | ||||||||
\(303\) | −30.8776 | −1.77387 | ||||||||
\(304\) | −0.510304 | −0.0292680 | ||||||||
\(305\) | −15.8357 | −0.906751 | ||||||||
\(306\) | 7.00683 | 0.400554 | ||||||||
\(307\) | −5.01222 | −0.286062 | −0.143031 | − | 0.989718i | \(-0.545685\pi\) | ||||
−0.143031 | + | 0.989718i | \(0.545685\pi\) | |||||||
\(308\) | −3.93618 | −0.224285 | ||||||||
\(309\) | 26.6067 | 1.51360 | ||||||||
\(310\) | 12.0450 | 0.684112 | ||||||||
\(311\) | −5.93920 | −0.336781 | −0.168390 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168390 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(312\) | 4.21588 | 0.238677 | ||||||||
\(313\) | −17.9396 | −1.01400 | −0.507002 | − | 0.861945i | \(-0.669246\pi\) | ||||
−0.507002 | + | 0.861945i | \(0.669246\pi\) | |||||||
\(314\) | −17.0066 | −0.959736 | ||||||||
\(315\) | −6.99593 | −0.394176 | ||||||||
\(316\) | 14.1195 | 0.794284 | ||||||||
\(317\) | 25.9572 | 1.45790 | 0.728951 | − | 0.684566i | \(-0.240008\pi\) | ||||
0.728951 | + | 0.684566i | \(0.240008\pi\) | |||||||
\(318\) | −20.7328 | −1.16264 | ||||||||
\(319\) | −15.9959 | −0.895600 | ||||||||
\(320\) | −2.61326 | −0.146086 | ||||||||
\(321\) | −28.0976 | −1.56825 | ||||||||
\(322\) | 6.44241 | 0.359022 | ||||||||
\(323\) | 1.33564 | 0.0743169 | ||||||||
\(324\) | −9.86447 | −0.548026 | ||||||||
\(325\) | 3.23649 | 0.179528 | ||||||||
\(326\) | −0.495587 | −0.0274480 | ||||||||
\(327\) | −16.0516 | −0.887656 | ||||||||
\(328\) | 11.8751 | 0.655694 | ||||||||
\(329\) | 11.4571 | 0.631652 | ||||||||
\(330\) | 24.5087 | 1.34916 | ||||||||
\(331\) | −15.8973 | −0.873794 | −0.436897 | − | 0.899512i | \(-0.643923\pi\) | ||||
−0.436897 | + | 0.899512i | \(0.643923\pi\) | |||||||
\(332\) | −8.90768 | −0.488873 | ||||||||
\(333\) | 11.5619 | 0.633589 | ||||||||
\(334\) | −7.55627 | −0.413461 | ||||||||
\(335\) | 25.7246 | 1.40549 | ||||||||
\(336\) | −2.38266 | −0.129985 | ||||||||
\(337\) | −27.5044 | −1.49826 | −0.749130 | − | 0.662423i | \(-0.769528\pi\) | ||||
−0.749130 | + | 0.662423i | \(0.769528\pi\) | |||||||
\(338\) | 9.86923 | 0.536815 | ||||||||
\(339\) | −23.2972 | −1.26533 | ||||||||
\(340\) | 6.83979 | 0.370940 | ||||||||
\(341\) | −18.1426 | −0.982477 | ||||||||
\(342\) | 1.36613 | 0.0738717 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.97125 | −0.483697 | ||||||||
\(345\) | −40.1138 | −2.15966 | ||||||||
\(346\) | −12.1410 | −0.652707 | ||||||||
\(347\) | −13.8129 | −0.741513 | −0.370756 | − | 0.928730i | \(-0.620902\pi\) | ||||
−0.370756 | + | 0.928730i | \(0.620902\pi\) | |||||||
\(348\) | −9.68272 | −0.519048 | ||||||||
\(349\) | 27.5712 | 1.47585 | 0.737927 | − | 0.674880i | \(-0.235805\pi\) | ||||
0.737927 | + | 0.674880i | \(0.235805\pi\) | |||||||
\(350\) | −1.82915 | −0.0977720 | ||||||||
\(351\) | 1.36138 | 0.0726648 | ||||||||
\(352\) | 3.93618 | 0.209799 | ||||||||
\(353\) | 15.4180 | 0.820617 | 0.410308 | − | 0.911947i | \(-0.365421\pi\) | ||||
0.410308 | + | 0.911947i | \(0.365421\pi\) | |||||||
\(354\) | −21.5863 | −1.14730 | ||||||||
\(355\) | 19.3361 | 1.02625 | ||||||||
\(356\) | 16.3272 | 0.865342 | ||||||||
\(357\) | 6.23623 | 0.330056 | ||||||||
\(358\) | 10.2509 | 0.541779 | ||||||||
\(359\) | −13.2973 | −0.701804 | −0.350902 | − | 0.936412i | \(-0.614125\pi\) | ||||
−0.350902 | + | 0.936412i | \(0.614125\pi\) | |||||||
\(360\) | 6.99593 | 0.368718 | ||||||||
\(361\) | −18.7396 | −0.986294 | ||||||||
\(362\) | −21.8045 | −1.14602 | ||||||||
\(363\) | −10.7065 | −0.561946 | ||||||||
\(364\) | 1.76940 | 0.0927417 | ||||||||
\(365\) | 1.73094 | 0.0906015 | ||||||||
\(366\) | 14.4383 | 0.754704 | ||||||||
\(367\) | 28.7975 | 1.50322 | 0.751609 | − | 0.659609i | \(-0.229278\pi\) | ||||
0.751609 | + | 0.659609i | \(0.229278\pi\) | |||||||
\(368\) | −6.44241 | −0.335834 | ||||||||
\(369\) | −31.7907 | −1.65496 | ||||||||
\(370\) | 11.2863 | 0.586745 | ||||||||
\(371\) | −8.70151 | −0.451760 | ||||||||
\(372\) | −10.9821 | −0.569398 | ||||||||
\(373\) | 3.49940 | 0.181192 | 0.0905960 | − | 0.995888i | \(-0.471123\pi\) | ||||
0.0905960 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(374\) | −10.3023 | −0.532720 | ||||||||
\(375\) | −19.7434 | −1.01954 | ||||||||
\(376\) | −11.4571 | −0.590856 | ||||||||
\(377\) | 7.19052 | 0.370331 | ||||||||
\(378\) | −0.769400 | −0.0395736 | ||||||||
\(379\) | −5.91921 | −0.304049 | −0.152025 | − | 0.988377i | \(-0.548579\pi\) | ||||
−0.152025 | + | 0.988377i | \(0.548579\pi\) | |||||||
\(380\) | 1.33356 | 0.0684102 | ||||||||
\(381\) | −6.23623 | −0.319492 | ||||||||
\(382\) | 0.944326 | 0.0483159 | ||||||||
\(383\) | −2.97031 | −0.151776 | −0.0758878 | − | 0.997116i | \(-0.524179\pi\) | ||||
−0.0758878 | + | 0.997116i | \(0.524179\pi\) | |||||||
\(384\) | 2.38266 | 0.121590 | ||||||||
\(385\) | 10.2863 | 0.524237 | ||||||||
\(386\) | 20.6651 | 1.05183 | ||||||||
\(387\) | 24.0168 | 1.22084 | ||||||||
\(388\) | 4.26593 | 0.216570 | ||||||||
\(389\) | 6.70990 | 0.340205 | 0.170103 | − | 0.985426i | \(-0.445590\pi\) | ||||
0.170103 | + | 0.985426i | \(0.445590\pi\) | |||||||
\(390\) | −11.0172 | −0.557878 | ||||||||
\(391\) | 16.8620 | 0.852746 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −47.7434 | −2.40834 | ||||||||
\(394\) | −5.81036 | −0.292722 | ||||||||
\(395\) | −36.8980 | −1.85654 | ||||||||
\(396\) | −10.5375 | −0.529528 | ||||||||
\(397\) | 13.5622 | 0.680666 | 0.340333 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340333 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(398\) | 1.59949 | 0.0801750 | ||||||||
\(399\) | 1.21588 | 0.0608703 | ||||||||
\(400\) | 1.82915 | 0.0914574 | ||||||||
\(401\) | −13.1430 | −0.656332 | −0.328166 | − | 0.944620i | \(-0.606431\pi\) | ||||
−0.328166 | + | 0.944620i | \(0.606431\pi\) | |||||||
\(402\) | −23.4546 | −1.16981 | ||||||||
\(403\) | 8.15550 | 0.406254 | ||||||||
\(404\) | 12.9593 | 0.644749 | ||||||||
\(405\) | 25.7785 | 1.28094 | ||||||||
\(406\) | −4.06382 | −0.201684 | ||||||||
\(407\) | −16.9997 | −0.842646 | ||||||||
\(408\) | −6.23623 | −0.308739 | ||||||||
\(409\) | 18.8416 | 0.931658 | 0.465829 | − | 0.884875i | \(-0.345756\pi\) | ||||
0.465829 | + | 0.884875i | \(0.345756\pi\) | |||||||
\(410\) | −31.0328 | −1.53260 | ||||||||
\(411\) | −22.6404 | −1.11677 | ||||||||
\(412\) | −11.1668 | −0.550148 | ||||||||
\(413\) | −9.05975 | −0.445801 | ||||||||
\(414\) | 17.2469 | 0.847638 | ||||||||
\(415\) | 23.2781 | 1.14268 | ||||||||
\(416\) | −1.76940 | −0.0867520 | ||||||||
\(417\) | 9.35261 | 0.457999 | ||||||||
\(418\) | −2.00865 | −0.0982463 | ||||||||
\(419\) | −12.8973 | −0.630074 | −0.315037 | − | 0.949079i | \(-0.602017\pi\) | ||||
−0.315037 | + | 0.949079i | \(0.602017\pi\) | |||||||
\(420\) | 6.22653 | 0.303823 | ||||||||
\(421\) | −16.5184 | −0.805059 | −0.402530 | − | 0.915407i | \(-0.631869\pi\) | ||||
−0.402530 | + | 0.915407i | \(0.631869\pi\) | |||||||
\(422\) | 11.0145 | 0.536175 | ||||||||
\(423\) | 30.6717 | 1.49131 | ||||||||
\(424\) | 8.70151 | 0.422582 | ||||||||
\(425\) | −4.78749 | −0.232228 | ||||||||
\(426\) | −17.6298 | −0.854167 | ||||||||
\(427\) | 6.05975 | 0.293252 | ||||||||
\(428\) | 11.7925 | 0.570012 | ||||||||
\(429\) | 16.5945 | 0.801189 | ||||||||
\(430\) | 23.4442 | 1.13058 | ||||||||
\(431\) | 1.00000 | 0.0481683 | ||||||||
\(432\) | 0.769400 | 0.0370178 | ||||||||
\(433\) | 8.93592 | 0.429433 | 0.214716 | − | 0.976676i | \(-0.431117\pi\) | ||||
0.214716 | + | 0.976676i | \(0.431117\pi\) | |||||||
\(434\) | −4.60919 | −0.221248 | ||||||||
\(435\) | 25.3035 | 1.21321 | ||||||||
\(436\) | 6.73683 | 0.322636 | ||||||||
\(437\) | 3.28759 | 0.157267 | ||||||||
\(438\) | −1.57820 | −0.0754092 | ||||||||
\(439\) | −10.6669 | −0.509101 | −0.254551 | − | 0.967059i | \(-0.581928\pi\) | ||||
−0.254551 | + | 0.967059i | \(0.581928\pi\) | |||||||
\(440\) | −10.2863 | −0.490379 | ||||||||
\(441\) | 2.67708 | 0.127480 | ||||||||
\(442\) | 4.63111 | 0.220280 | ||||||||
\(443\) | −29.5100 | −1.40206 | −0.701032 | − | 0.713130i | \(-0.747277\pi\) | ||||
−0.701032 | + | 0.713130i | \(0.747277\pi\) | |||||||
\(444\) | −10.2903 | −0.488358 | ||||||||
\(445\) | −42.6674 | −2.02263 | ||||||||
\(446\) | −2.20524 | −0.104421 | ||||||||
\(447\) | −12.6142 | −0.596631 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −8.80065 | −0.415328 | −0.207664 | − | 0.978200i | \(-0.566586\pi\) | ||||
−0.207664 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(450\) | −4.89678 | −0.230836 | ||||||||
\(451\) | 46.7426 | 2.20102 | ||||||||
\(452\) | 9.77779 | 0.459909 | ||||||||
\(453\) | 18.6887 | 0.878070 | ||||||||
\(454\) | −10.7465 | −0.504360 | ||||||||
\(455\) | −4.62391 | −0.216772 | ||||||||
\(456\) | −1.21588 | −0.0569390 | ||||||||
\(457\) | −2.87643 | −0.134554 | −0.0672769 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672769 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(458\) | 21.9052 | 1.02356 | ||||||||
\(459\) | −2.01378 | −0.0939951 | ||||||||
\(460\) | 16.8357 | 0.784969 | ||||||||
\(461\) | −31.0928 | −1.44814 | −0.724068 | − | 0.689728i | \(-0.757730\pi\) | ||||
−0.724068 | + | 0.689728i | \(0.757730\pi\) | |||||||
\(462\) | −9.37859 | −0.436332 | ||||||||
\(463\) | 11.3344 | 0.526756 | 0.263378 | − | 0.964693i | \(-0.415163\pi\) | ||||
0.263378 | + | 0.964693i | \(0.415163\pi\) | |||||||
\(464\) | 4.06382 | 0.188658 | ||||||||
\(465\) | 28.6993 | 1.33090 | ||||||||
\(466\) | 14.1342 | 0.654755 | ||||||||
\(467\) | 37.9010 | 1.75385 | 0.876924 | − | 0.480629i | \(-0.159592\pi\) | ||||
0.876924 | + | 0.480629i | \(0.159592\pi\) | |||||||
\(468\) | 4.73683 | 0.218960 | ||||||||
\(469\) | −9.84386 | −0.454547 | ||||||||
\(470\) | 29.9405 | 1.38105 | ||||||||
\(471\) | −40.5209 | −1.86711 | ||||||||
\(472\) | 9.05975 | 0.417009 | ||||||||
\(473\) | −35.3124 | −1.62367 | ||||||||
\(474\) | 33.6420 | 1.54523 | ||||||||
\(475\) | −0.933422 | −0.0428283 | ||||||||
\(476\) | −2.61734 | −0.119965 | ||||||||
\(477\) | −23.2947 | −1.06659 | ||||||||
\(478\) | 17.0234 | 0.778631 | ||||||||
\(479\) | −21.0034 | −0.959669 | −0.479834 | − | 0.877359i | \(-0.659303\pi\) | ||||
−0.479834 | + | 0.877359i | \(0.659303\pi\) | |||||||
\(480\) | −6.22653 | −0.284201 | ||||||||
\(481\) | 7.64176 | 0.348434 | ||||||||
\(482\) | 18.1722 | 0.827719 | ||||||||
\(483\) | 15.3501 | 0.698454 | ||||||||
\(484\) | 4.49351 | 0.204250 | ||||||||
\(485\) | −11.1480 | −0.506204 | ||||||||
\(486\) | −21.1955 | −0.961448 | ||||||||
\(487\) | −30.1820 | −1.36768 | −0.683838 | − | 0.729633i | \(-0.739691\pi\) | ||||
−0.683838 | + | 0.729633i | \(0.739691\pi\) | |||||||
\(488\) | −6.05975 | −0.274312 | ||||||||
\(489\) | −1.18082 | −0.0533984 | ||||||||
\(490\) | 2.61326 | 0.118055 | ||||||||
\(491\) | −1.49758 | −0.0675849 | −0.0337925 | − | 0.999429i | \(-0.510759\pi\) | ||||
−0.0337925 | + | 0.999429i | \(0.510759\pi\) | |||||||
\(492\) | 28.2944 | 1.27561 | ||||||||
\(493\) | −10.6364 | −0.479039 | ||||||||
\(494\) | 0.902932 | 0.0406248 | ||||||||
\(495\) | 27.5372 | 1.23771 | ||||||||
\(496\) | 4.60919 | 0.206959 | ||||||||
\(497\) | −7.39920 | −0.331899 | ||||||||
\(498\) | −21.2240 | −0.951071 | ||||||||
\(499\) | 13.6529 | 0.611188 | 0.305594 | − | 0.952162i | \(-0.401145\pi\) | ||||
0.305594 | + | 0.952162i | \(0.401145\pi\) | |||||||
\(500\) | 8.28627 | 0.370573 | ||||||||
\(501\) | −18.0041 | −0.804362 | ||||||||
\(502\) | −20.5716 | −0.918156 | ||||||||
\(503\) | −44.0099 | −1.96231 | −0.981153 | − | 0.193231i | \(-0.938103\pi\) | ||||
−0.981153 | + | 0.193231i | \(0.938103\pi\) | |||||||
\(504\) | −2.67708 | −0.119247 | ||||||||
\(505\) | −33.8660 | −1.50702 | ||||||||
\(506\) | −25.3585 | −1.12732 | ||||||||
\(507\) | 23.5150 | 1.04434 | ||||||||
\(508\) | 2.61734 | 0.116126 | ||||||||
\(509\) | −40.4846 | −1.79445 | −0.897223 | − | 0.441578i | \(-0.854419\pi\) | ||||
−0.897223 | + | 0.441578i | \(0.854419\pi\) | |||||||
\(510\) | 16.2969 | 0.721640 | ||||||||
\(511\) | −0.662367 | −0.0293014 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.392628 | −0.0173349 | ||||||||
\(514\) | 4.29035 | 0.189239 | ||||||||
\(515\) | 29.1817 | 1.28590 | ||||||||
\(516\) | −21.3755 | −0.941002 | ||||||||
\(517\) | −45.0973 | −1.98338 | ||||||||
\(518\) | −4.31884 | −0.189759 | ||||||||
\(519\) | −28.9280 | −1.26980 | ||||||||
\(520\) | 4.62391 | 0.202772 | ||||||||
\(521\) | 29.5814 | 1.29598 | 0.647992 | − | 0.761647i | \(-0.275609\pi\) | ||||
0.647992 | + | 0.761647i | \(0.275609\pi\) | |||||||
\(522\) | −10.8792 | −0.476169 | ||||||||
\(523\) | −19.0348 | −0.832334 | −0.416167 | − | 0.909288i | \(-0.636627\pi\) | ||||
−0.416167 | + | 0.909288i | \(0.636627\pi\) | |||||||
\(524\) | 20.0378 | 0.875356 | ||||||||
\(525\) | −4.35824 | −0.190209 | ||||||||
\(526\) | −21.4345 | −0.934590 | ||||||||
\(527\) | −12.0638 | −0.525508 | ||||||||
\(528\) | 9.37859 | 0.408151 | ||||||||
\(529\) | 18.5047 | 0.804550 | ||||||||
\(530\) | −22.7393 | −0.987733 | ||||||||
\(531\) | −24.2537 | −1.05252 | ||||||||
\(532\) | −0.510304 | −0.0221245 | ||||||||
\(533\) | −21.0118 | −0.910123 | ||||||||
\(534\) | 38.9023 | 1.68347 | ||||||||
\(535\) | −30.8169 | −1.33233 | ||||||||
\(536\) | 9.84386 | 0.425190 | ||||||||
\(537\) | 24.4246 | 1.05400 | ||||||||
\(538\) | −5.98095 | −0.257857 | ||||||||
\(539\) | −3.93618 | −0.169543 | ||||||||
\(540\) | −2.01064 | −0.0865243 | ||||||||
\(541\) | −36.1532 | −1.55435 | −0.777175 | − | 0.629285i | \(-0.783348\pi\) | ||||
−0.777175 | + | 0.629285i | \(0.783348\pi\) | |||||||
\(542\) | 23.0641 | 0.990686 | ||||||||
\(543\) | −51.9527 | −2.22950 | ||||||||
\(544\) | 2.61734 | 0.112217 | ||||||||
\(545\) | −17.6051 | −0.754120 | ||||||||
\(546\) | 4.21588 | 0.180423 | ||||||||
\(547\) | 31.6407 | 1.35286 | 0.676429 | − | 0.736508i | \(-0.263527\pi\) | ||||
0.676429 | + | 0.736508i | \(0.263527\pi\) | |||||||
\(548\) | 9.50216 | 0.405912 | ||||||||
\(549\) | 16.2225 | 0.692357 | ||||||||
\(550\) | 7.19985 | 0.307003 | ||||||||
\(551\) | −2.07379 | −0.0883462 | ||||||||
\(552\) | −15.3501 | −0.653343 | ||||||||
\(553\) | 14.1195 | 0.600422 | ||||||||
\(554\) | −9.54762 | −0.405640 | ||||||||
\(555\) | 26.8914 | 1.14148 | ||||||||
\(556\) | −3.92528 | −0.166469 | ||||||||
\(557\) | −6.23987 | −0.264392 | −0.132196 | − | 0.991224i | \(-0.542203\pi\) | ||||
−0.132196 | + | 0.991224i | \(0.542203\pi\) | |||||||
\(558\) | −12.3392 | −0.522360 | ||||||||
\(559\) | 15.8737 | 0.671387 | ||||||||
\(560\) | −2.61326 | −0.110431 | ||||||||
\(561\) | −24.5469 | −1.03637 | ||||||||
\(562\) | 6.01272 | 0.253631 | ||||||||
\(563\) | −35.8441 | −1.51065 | −0.755325 | − | 0.655351i | \(-0.772521\pi\) | ||||
−0.755325 | + | 0.655351i | \(0.772521\pi\) | |||||||
\(564\) | −27.2985 | −1.14947 | ||||||||
\(565\) | −25.5519 | −1.07498 | ||||||||
\(566\) | 29.7178 | 1.24913 | ||||||||
\(567\) | −9.86447 | −0.414269 | ||||||||
\(568\) | 7.39920 | 0.310463 | ||||||||
\(569\) | −34.6952 | −1.45450 | −0.727249 | − | 0.686374i | \(-0.759201\pi\) | ||||
−0.727249 | + | 0.686374i | \(0.759201\pi\) | |||||||
\(570\) | 3.17742 | 0.133088 | ||||||||
\(571\) | −12.0991 | −0.506334 | −0.253167 | − | 0.967423i | \(-0.581472\pi\) | ||||
−0.253167 | + | 0.967423i | \(0.581472\pi\) | |||||||
\(572\) | −6.96467 | −0.291208 | ||||||||
\(573\) | 2.25001 | 0.0939955 | ||||||||
\(574\) | 11.8751 | 0.495658 | ||||||||
\(575\) | −11.7841 | −0.491432 | ||||||||
\(576\) | 2.67708 | 0.111545 | ||||||||
\(577\) | −9.42049 | −0.392180 | −0.196090 | − | 0.980586i | \(-0.562824\pi\) | ||||
−0.196090 | + | 0.980586i | \(0.562824\pi\) | |||||||
\(578\) | 10.1495 | 0.422166 | ||||||||
\(579\) | 49.2380 | 2.04626 | ||||||||
\(580\) | −10.6198 | −0.440965 | ||||||||
\(581\) | −8.90768 | −0.369553 | ||||||||
\(582\) | 10.1643 | 0.421322 | ||||||||
\(583\) | 34.2507 | 1.41852 | ||||||||
\(584\) | 0.662367 | 0.0274089 | ||||||||
\(585\) | −12.3786 | −0.511792 | ||||||||
\(586\) | −2.20956 | −0.0912759 | ||||||||
\(587\) | 20.1188 | 0.830392 | 0.415196 | − | 0.909732i | \(-0.363713\pi\) | ||||
0.415196 | + | 0.909732i | \(0.363713\pi\) | |||||||
\(588\) | −2.38266 | −0.0982594 | ||||||||
\(589\) | −2.35209 | −0.0969162 | ||||||||
\(590\) | −23.6755 | −0.974705 | ||||||||
\(591\) | −13.8441 | −0.569471 | ||||||||
\(592\) | 4.31884 | 0.177503 | ||||||||
\(593\) | 40.6217 | 1.66813 | 0.834066 | − | 0.551665i | \(-0.186007\pi\) | ||||
0.834066 | + | 0.551665i | \(0.186007\pi\) | |||||||
\(594\) | 3.02849 | 0.124261 | ||||||||
\(595\) | 6.83979 | 0.280404 | ||||||||
\(596\) | 5.29416 | 0.216857 | ||||||||
\(597\) | 3.81104 | 0.155975 | ||||||||
\(598\) | 11.3992 | 0.466148 | ||||||||
\(599\) | 23.0043 | 0.939931 | 0.469965 | − | 0.882685i | \(-0.344266\pi\) | ||||
0.469965 | + | 0.882685i | \(0.344266\pi\) | |||||||
\(600\) | 4.35824 | 0.177924 | ||||||||
\(601\) | −4.46226 | −0.182019 | −0.0910096 | − | 0.995850i | \(-0.529009\pi\) | ||||
−0.0910096 | + | 0.995850i | \(0.529009\pi\) | |||||||
\(602\) | −8.97125 | −0.365641 | ||||||||
\(603\) | −26.3529 | −1.07317 | ||||||||
\(604\) | −7.84360 | −0.319152 | ||||||||
\(605\) | −11.7427 | −0.477410 | ||||||||
\(606\) | 30.8776 | 1.25432 | ||||||||
\(607\) | 25.6061 | 1.03932 | 0.519659 | − | 0.854374i | \(-0.326059\pi\) | ||||
0.519659 | + | 0.854374i | \(0.326059\pi\) | |||||||
\(608\) | 0.510304 | 0.0206956 | ||||||||
\(609\) | −9.68272 | −0.392363 | ||||||||
\(610\) | 15.8357 | 0.641169 | ||||||||
\(611\) | 20.2722 | 0.820127 | ||||||||
\(612\) | −7.00683 | −0.283234 | ||||||||
\(613\) | 4.35667 | 0.175964 | 0.0879820 | − | 0.996122i | \(-0.471958\pi\) | ||||
0.0879820 | + | 0.996122i | \(0.471958\pi\) | |||||||
\(614\) | 5.01222 | 0.202277 | ||||||||
\(615\) | −73.9407 | −2.98158 | ||||||||
\(616\) | 3.93618 | 0.158593 | ||||||||
\(617\) | −41.7099 | −1.67918 | −0.839589 | − | 0.543223i | \(-0.817204\pi\) | ||||
−0.839589 | + | 0.543223i | \(0.817204\pi\) | |||||||
\(618\) | −26.6067 | −1.07028 | ||||||||
\(619\) | −15.6482 | −0.628952 | −0.314476 | − | 0.949265i | \(-0.601829\pi\) | ||||
−0.314476 | + | 0.949265i | \(0.601829\pi\) | |||||||
\(620\) | −12.0450 | −0.483740 | ||||||||
\(621\) | −4.95679 | −0.198909 | ||||||||
\(622\) | 5.93920 | 0.238140 | ||||||||
\(623\) | 16.3272 | 0.654137 | ||||||||
\(624\) | −4.21588 | −0.168770 | ||||||||
\(625\) | −30.8000 | −1.23200 | ||||||||
\(626\) | 17.9396 | 0.717009 | ||||||||
\(627\) | −4.78594 | −0.191132 | ||||||||
\(628\) | 17.0066 | 0.678636 | ||||||||
\(629\) | −11.3039 | −0.450715 | ||||||||
\(630\) | 6.99593 | 0.278724 | ||||||||
\(631\) | 41.2127 | 1.64065 | 0.820326 | − | 0.571895i | \(-0.193792\pi\) | ||||
0.820326 | + | 0.571895i | \(0.193792\pi\) | |||||||
\(632\) | −14.1195 | −0.561643 | ||||||||
\(633\) | 26.2437 | 1.04310 | ||||||||
\(634\) | −25.9572 | −1.03089 | ||||||||
\(635\) | −6.83979 | −0.271429 | ||||||||
\(636\) | 20.7328 | 0.822107 | ||||||||
\(637\) | 1.76940 | 0.0701062 | ||||||||
\(638\) | 15.9959 | 0.633285 | ||||||||
\(639\) | −19.8083 | −0.783603 | ||||||||
\(640\) | 2.61326 | 0.103298 | ||||||||
\(641\) | −28.6468 | −1.13148 | −0.565740 | − | 0.824584i | \(-0.691409\pi\) | ||||
−0.565740 | + | 0.824584i | \(0.691409\pi\) | |||||||
\(642\) | 28.0976 | 1.10892 | ||||||||
\(643\) | −38.1967 | −1.50633 | −0.753166 | − | 0.657831i | \(-0.771474\pi\) | ||||
−0.753166 | + | 0.657831i | \(0.771474\pi\) | |||||||
\(644\) | −6.44241 | −0.253867 | ||||||||
\(645\) | 55.8597 | 2.19947 | ||||||||
\(646\) | −1.33564 | −0.0525500 | ||||||||
\(647\) | −34.5209 | −1.35716 | −0.678579 | − | 0.734527i | \(-0.737404\pi\) | ||||
−0.678579 | + | 0.734527i | \(0.737404\pi\) | |||||||
\(648\) | 9.86447 | 0.387513 | ||||||||
\(649\) | 35.6608 | 1.39981 | ||||||||
\(650\) | −3.23649 | −0.126946 | ||||||||
\(651\) | −10.9821 | −0.430424 | ||||||||
\(652\) | 0.495587 | 0.0194087 | ||||||||
\(653\) | 20.0758 | 0.785625 | 0.392813 | − | 0.919619i | \(-0.371502\pi\) | ||||
0.392813 | + | 0.919619i | \(0.371502\pi\) | |||||||
\(654\) | 16.0516 | 0.627667 | ||||||||
\(655\) | −52.3641 | −2.04604 | ||||||||
\(656\) | −11.8751 | −0.463645 | ||||||||
\(657\) | −1.77321 | −0.0691796 | ||||||||
\(658\) | −11.4571 | −0.446645 | ||||||||
\(659\) | 2.19621 | 0.0855523 | 0.0427762 | − | 0.999085i | \(-0.486380\pi\) | ||||
0.0427762 | + | 0.999085i | \(0.486380\pi\) | |||||||
\(660\) | −24.5087 | −0.954001 | ||||||||
\(661\) | −6.40958 | −0.249304 | −0.124652 | − | 0.992201i | \(-0.539781\pi\) | ||||
−0.124652 | + | 0.992201i | \(0.539781\pi\) | |||||||
\(662\) | 15.8973 | 0.617865 | ||||||||
\(663\) | 11.0344 | 0.428540 | ||||||||
\(664\) | 8.90768 | 0.345685 | ||||||||
\(665\) | 1.33356 | 0.0517132 | ||||||||
\(666\) | −11.5619 | −0.448015 | ||||||||
\(667\) | −26.1808 | −1.01372 | ||||||||
\(668\) | 7.55627 | 0.292361 | ||||||||
\(669\) | −5.25434 | −0.203145 | ||||||||
\(670\) | −25.7246 | −0.993828 | ||||||||
\(671\) | −23.8523 | −0.920806 | ||||||||
\(672\) | 2.38266 | 0.0919132 | ||||||||
\(673\) | 24.3145 | 0.937255 | 0.468628 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468628 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(674\) | 27.5044 | 1.05943 | ||||||||
\(675\) | 1.40734 | 0.0541687 | ||||||||
\(676\) | −9.86923 | −0.379586 | ||||||||
\(677\) | 8.27719 | 0.318118 | 0.159059 | − | 0.987269i | \(-0.449154\pi\) | ||||
0.159059 | + | 0.987269i | \(0.449154\pi\) | |||||||
\(678\) | 23.2972 | 0.894723 | ||||||||
\(679\) | 4.26593 | 0.163711 | ||||||||
\(680\) | −6.83979 | −0.262294 | ||||||||
\(681\) | −25.6054 | −0.981200 | ||||||||
\(682\) | 18.1426 | 0.694716 | ||||||||
\(683\) | −21.5950 | −0.826309 | −0.413154 | − | 0.910661i | \(-0.635573\pi\) | ||||
−0.413154 | + | 0.910661i | \(0.635573\pi\) | |||||||
\(684\) | −1.36613 | −0.0522352 | ||||||||
\(685\) | −24.8316 | −0.948768 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 52.1926 | 1.99127 | ||||||||
\(688\) | 8.97125 | 0.342026 | ||||||||
\(689\) | −15.3964 | −0.586558 | ||||||||
\(690\) | 40.1138 | 1.52711 | ||||||||
\(691\) | −32.9106 | −1.25198 | −0.625988 | − | 0.779832i | \(-0.715304\pi\) | ||||
−0.625988 | + | 0.779832i | \(0.715304\pi\) | |||||||
\(692\) | 12.1410 | 0.461533 | ||||||||
\(693\) | −10.5375 | −0.400286 | ||||||||
\(694\) | 13.8129 | 0.524329 | ||||||||
\(695\) | 10.2578 | 0.389100 | ||||||||
\(696\) | 9.68272 | 0.367022 | ||||||||
\(697\) | 31.0812 | 1.17728 | ||||||||
\(698\) | −27.5712 | −1.04359 | ||||||||
\(699\) | 33.6771 | 1.27378 | ||||||||
\(700\) | 1.82915 | 0.0691353 | ||||||||
\(701\) | 28.4402 | 1.07417 | 0.537085 | − | 0.843528i | \(-0.319525\pi\) | ||||
0.537085 | + | 0.843528i | \(0.319525\pi\) | |||||||
\(702\) | −1.36138 | −0.0513818 | ||||||||
\(703\) | −2.20392 | −0.0831226 | ||||||||
\(704\) | −3.93618 | −0.148350 | ||||||||
\(705\) | 71.3381 | 2.68675 | ||||||||
\(706\) | −15.4180 | −0.580264 | ||||||||
\(707\) | 12.9593 | 0.487384 | ||||||||
\(708\) | 21.5863 | 0.811264 | ||||||||
\(709\) | −37.4596 | −1.40683 | −0.703413 | − | 0.710781i | \(-0.748341\pi\) | ||||
−0.703413 | + | 0.710781i | \(0.748341\pi\) | |||||||
\(710\) | −19.3361 | −0.725669 | ||||||||
\(711\) | 37.7991 | 1.41758 | ||||||||
\(712\) | −16.3272 | −0.611889 | ||||||||
\(713\) | −29.6943 | −1.11206 | ||||||||
\(714\) | −6.23623 | −0.233385 | ||||||||
\(715\) | 18.2005 | 0.680661 | ||||||||
\(716\) | −10.2509 | −0.383096 | ||||||||
\(717\) | 40.5609 | 1.51478 | ||||||||
\(718\) | 13.2973 | 0.496251 | ||||||||
\(719\) | −17.6605 | −0.658627 | −0.329313 | − | 0.944221i | \(-0.606817\pi\) | ||||
−0.329313 | + | 0.944221i | \(0.606817\pi\) | |||||||
\(720\) | −6.99593 | −0.260723 | ||||||||
\(721\) | −11.1668 | −0.415873 | ||||||||
\(722\) | 18.7396 | 0.697415 | ||||||||
\(723\) | 43.2981 | 1.61027 | ||||||||
\(724\) | 21.8045 | 0.810357 | ||||||||
\(725\) | 7.43333 | 0.276067 | ||||||||
\(726\) | 10.7065 | 0.397356 | ||||||||
\(727\) | −29.8960 | −1.10878 | −0.554390 | − | 0.832257i | \(-0.687049\pi\) | ||||
−0.554390 | + | 0.832257i | \(0.687049\pi\) | |||||||
\(728\) | −1.76940 | −0.0655783 | ||||||||
\(729\) | −20.9084 | −0.774384 | ||||||||
\(730\) | −1.73094 | −0.0640650 | ||||||||
\(731\) | −23.4808 | −0.868468 | ||||||||
\(732\) | −14.4383 | −0.533656 | ||||||||
\(733\) | 41.4747 | 1.53190 | 0.765952 | − | 0.642898i | \(-0.222268\pi\) | ||||
0.765952 | + | 0.642898i | \(0.222268\pi\) | |||||||
\(734\) | −28.7975 | −1.06294 | ||||||||
\(735\) | 6.22653 | 0.229669 | ||||||||
\(736\) | 6.44241 | 0.237470 | ||||||||
\(737\) | 38.7472 | 1.42727 | ||||||||
\(738\) | 31.7907 | 1.17023 | ||||||||
\(739\) | −44.7271 | −1.64531 | −0.822657 | − | 0.568538i | \(-0.807509\pi\) | ||||
−0.822657 | + | 0.568538i | \(0.807509\pi\) | |||||||
\(740\) | −11.2863 | −0.414892 | ||||||||
\(741\) | 2.15138 | 0.0790330 | ||||||||
\(742\) | 8.70151 | 0.319442 | ||||||||
\(743\) | 2.97600 | 0.109179 | 0.0545894 | − | 0.998509i | \(-0.482615\pi\) | ||||
0.0545894 | + | 0.998509i | \(0.482615\pi\) | |||||||
\(744\) | 10.9821 | 0.402625 | ||||||||
\(745\) | −13.8350 | −0.506877 | ||||||||
\(746\) | −3.49940 | −0.128122 | ||||||||
\(747\) | −23.8466 | −0.872502 | ||||||||
\(748\) | 10.3023 | 0.376690 | ||||||||
\(749\) | 11.7925 | 0.430889 | ||||||||
\(750\) | 19.7434 | 0.720927 | ||||||||
\(751\) | 7.18212 | 0.262079 | 0.131040 | − | 0.991377i | \(-0.458169\pi\) | ||||
0.131040 | + | 0.991377i | \(0.458169\pi\) | |||||||
\(752\) | 11.4571 | 0.417798 | ||||||||
\(753\) | −49.0152 | −1.78621 | ||||||||
\(754\) | −7.19052 | −0.261863 | ||||||||
\(755\) | 20.4974 | 0.745977 | ||||||||
\(756\) | 0.769400 | 0.0279828 | ||||||||
\(757\) | 11.2660 | 0.409471 | 0.204736 | − | 0.978817i | \(-0.434367\pi\) | ||||
0.204736 | + | 0.978817i | \(0.434367\pi\) | |||||||
\(758\) | 5.91921 | 0.214995 | ||||||||
\(759\) | −60.4207 | −2.19313 | ||||||||
\(760\) | −1.33356 | −0.0483733 | ||||||||
\(761\) | 48.7344 | 1.76662 | 0.883310 | − | 0.468790i | \(-0.155310\pi\) | ||||
0.883310 | + | 0.468790i | \(0.155310\pi\) | |||||||
\(762\) | 6.23623 | 0.225915 | ||||||||
\(763\) | 6.73683 | 0.243890 | ||||||||
\(764\) | −0.944326 | −0.0341645 | ||||||||
\(765\) | 18.3107 | 0.662025 | ||||||||
\(766\) | 2.97031 | 0.107322 | ||||||||
\(767\) | −16.0303 | −0.578821 | ||||||||
\(768\) | −2.38266 | −0.0859770 | ||||||||
\(769\) | 45.5354 | 1.64205 | 0.821024 | − | 0.570894i | \(-0.193403\pi\) | ||||
0.821024 | + | 0.570894i | \(0.193403\pi\) | |||||||
\(770\) | −10.2863 | −0.370692 | ||||||||
\(771\) | 10.2225 | 0.368153 | ||||||||
\(772\) | −20.6651 | −0.743754 | ||||||||
\(773\) | 24.1468 | 0.868500 | 0.434250 | − | 0.900792i | \(-0.357013\pi\) | ||||
0.434250 | + | 0.900792i | \(0.357013\pi\) | |||||||
\(774\) | −24.0168 | −0.863265 | ||||||||
\(775\) | 8.43089 | 0.302846 | ||||||||
\(776\) | −4.26593 | −0.153138 | ||||||||
\(777\) | −10.2903 | −0.369164 | ||||||||
\(778\) | −6.70990 | −0.240561 | ||||||||
\(779\) | 6.05992 | 0.217119 | ||||||||
\(780\) | 11.0172 | 0.394480 | ||||||||
\(781\) | 29.1246 | 1.04216 | ||||||||
\(782\) | −16.8620 | −0.602982 | ||||||||
\(783\) | 3.12670 | 0.111739 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −44.4427 | −1.58623 | ||||||||
\(786\) | 47.7434 | 1.70295 | ||||||||
\(787\) | −15.1832 | −0.541223 | −0.270611 | − | 0.962689i | \(-0.587226\pi\) | ||||
−0.270611 | + | 0.962689i | \(0.587226\pi\) | |||||||
\(788\) | 5.81036 | 0.206985 | ||||||||
\(789\) | −51.0713 | −1.81818 | ||||||||
\(790\) | 36.8980 | 1.31277 | ||||||||
\(791\) | 9.77779 | 0.347658 | ||||||||
\(792\) | 10.5375 | 0.374433 | ||||||||
\(793\) | 10.7221 | 0.380753 | ||||||||
\(794\) | −13.5622 | −0.481303 | ||||||||
\(795\) | −54.1802 | −1.92157 | ||||||||
\(796\) | −1.59949 | −0.0566923 | ||||||||
\(797\) | 38.3843 | 1.35964 | 0.679821 | − | 0.733379i | \(-0.262058\pi\) | ||||
0.679821 | + | 0.733379i | \(0.262058\pi\) | |||||||
\(798\) | −1.21588 | −0.0430418 | ||||||||
\(799\) | −29.9872 | −1.06087 | ||||||||
\(800\) | −1.82915 | −0.0646701 | ||||||||
\(801\) | 43.7094 | 1.54439 | ||||||||
\(802\) | 13.1430 | 0.464097 | ||||||||
\(803\) | 2.60720 | 0.0920060 | ||||||||
\(804\) | 23.4546 | 0.827180 | ||||||||
\(805\) | 16.8357 | 0.593381 | ||||||||
\(806\) | −8.15550 | −0.287265 | ||||||||
\(807\) | −14.2506 | −0.501645 | ||||||||
\(808\) | −12.9593 | −0.455906 | ||||||||
\(809\) | 29.7430 | 1.04571 | 0.522855 | − | 0.852422i | \(-0.324867\pi\) | ||||
0.522855 | + | 0.852422i | \(0.324867\pi\) | |||||||
\(810\) | −25.7785 | −0.905763 | ||||||||
\(811\) | −52.4383 | −1.84136 | −0.920679 | − | 0.390320i | \(-0.872364\pi\) | ||||
−0.920679 | + | 0.390320i | \(0.872364\pi\) | |||||||
\(812\) | 4.06382 | 0.142612 | ||||||||
\(813\) | 54.9539 | 1.92732 | ||||||||
\(814\) | 16.9997 | 0.595841 | ||||||||
\(815\) | −1.29510 | −0.0453654 | ||||||||
\(816\) | 6.23623 | 0.218312 | ||||||||
\(817\) | −4.57807 | −0.160166 | ||||||||
\(818\) | −18.8416 | −0.658781 | ||||||||
\(819\) | 4.73683 | 0.165518 | ||||||||
\(820\) | 31.0328 | 1.08371 | ||||||||
\(821\) | 9.03281 | 0.315247 | 0.157624 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157624 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(822\) | 22.6404 | 0.789676 | ||||||||
\(823\) | 13.7443 | 0.479096 | 0.239548 | − | 0.970885i | \(-0.423001\pi\) | ||||
0.239548 | + | 0.970885i | \(0.423001\pi\) | |||||||
\(824\) | 11.1668 | 0.389013 | ||||||||
\(825\) | 17.1548 | 0.597254 | ||||||||
\(826\) | 9.05975 | 0.315229 | ||||||||
\(827\) | 46.6119 | 1.62086 | 0.810428 | − | 0.585838i | \(-0.199235\pi\) | ||||
0.810428 | + | 0.585838i | \(0.199235\pi\) | |||||||
\(828\) | −17.2469 | −0.599370 | ||||||||
\(829\) | 25.9939 | 0.902806 | 0.451403 | − | 0.892320i | \(-0.350924\pi\) | ||||
0.451403 | + | 0.892320i | \(0.350924\pi\) | |||||||
\(830\) | −23.2781 | −0.807996 | ||||||||
\(831\) | −22.7488 | −0.789146 | ||||||||
\(832\) | 1.76940 | 0.0613429 | ||||||||
\(833\) | −2.61734 | −0.0906853 | ||||||||
\(834\) | −9.35261 | −0.323854 | ||||||||
\(835\) | −19.7465 | −0.683357 | ||||||||
\(836\) | 2.00865 | 0.0694706 | ||||||||
\(837\) | 3.54631 | 0.122578 | ||||||||
\(838\) | 12.8973 | 0.445530 | ||||||||
\(839\) | −23.6709 | −0.817211 | −0.408605 | − | 0.912711i | \(-0.633985\pi\) | ||||
−0.408605 | + | 0.912711i | \(0.633985\pi\) | |||||||
\(840\) | −6.22653 | −0.214836 | ||||||||
\(841\) | −12.4854 | −0.430530 | ||||||||
\(842\) | 16.5184 | 0.569263 | ||||||||
\(843\) | 14.3263 | 0.493424 | ||||||||
\(844\) | −11.0145 | −0.379133 | ||||||||
\(845\) | 25.7909 | 0.887234 | ||||||||
\(846\) | −30.6717 | −1.05451 | ||||||||
\(847\) | 4.49351 | 0.154399 | ||||||||
\(848\) | −8.70151 | −0.298811 | ||||||||
\(849\) | 70.8075 | 2.43011 | ||||||||
\(850\) | 4.78749 | 0.164210 | ||||||||
\(851\) | −27.8238 | −0.953786 | ||||||||
\(852\) | 17.6298 | 0.603987 | ||||||||
\(853\) | −0.141838 | −0.00485645 | −0.00242822 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242822 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(854\) | −6.05975 | −0.207360 | ||||||||
\(855\) | 3.57005 | 0.122093 | ||||||||
\(856\) | −11.7925 | −0.403060 | ||||||||
\(857\) | 36.4607 | 1.24548 | 0.622738 | − | 0.782431i | \(-0.286020\pi\) | ||||
0.622738 | + | 0.782431i | \(0.286020\pi\) | |||||||
\(858\) | −16.5945 | −0.566526 | ||||||||
\(859\) | −32.1398 | −1.09660 | −0.548299 | − | 0.836283i | \(-0.684724\pi\) | ||||
−0.548299 | + | 0.836283i | \(0.684724\pi\) | |||||||
\(860\) | −23.4442 | −0.799442 | ||||||||
\(861\) | 28.2944 | 0.964271 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | 47.2395 | 1.60805 | 0.804026 | − | 0.594595i | \(-0.202688\pi\) | ||||
0.804026 | + | 0.594595i | \(0.202688\pi\) | |||||||
\(864\) | −0.769400 | −0.0261755 | ||||||||
\(865\) | −31.7277 | −1.07878 | ||||||||
\(866\) | −8.93592 | −0.303655 | ||||||||
\(867\) | 24.1830 | 0.821296 | ||||||||
\(868\) | 4.60919 | 0.156446 | ||||||||
\(869\) | −55.5769 | −1.88532 | ||||||||
\(870\) | −25.3035 | −0.857869 | ||||||||
\(871\) | −17.4177 | −0.590177 | ||||||||
\(872\) | −6.73683 | −0.228138 | ||||||||
\(873\) | 11.4202 | 0.386517 | ||||||||
\(874\) | −3.28759 | −0.111204 | ||||||||
\(875\) | 8.28627 | 0.280127 | ||||||||
\(876\) | 1.57820 | 0.0533224 | ||||||||
\(877\) | 44.6371 | 1.50729 | 0.753644 | − | 0.657282i | \(-0.228294\pi\) | ||||
0.753644 | + | 0.657282i | \(0.228294\pi\) | |||||||
\(878\) | 10.6669 | 0.359989 | ||||||||
\(879\) | −5.26463 | −0.177571 | ||||||||
\(880\) | 10.2863 | 0.346750 | ||||||||
\(881\) | −22.0713 | −0.743602 | −0.371801 | − | 0.928312i | \(-0.621260\pi\) | ||||
−0.371801 | + | 0.928312i | \(0.621260\pi\) | |||||||
\(882\) | −2.67708 | −0.0901421 | ||||||||
\(883\) | −31.9181 | −1.07413 | −0.537064 | − | 0.843542i | \(-0.680467\pi\) | ||||
−0.537064 | + | 0.843542i | \(0.680467\pi\) | |||||||
\(884\) | −4.63111 | −0.155761 | ||||||||
\(885\) | −56.4108 | −1.89623 | ||||||||
\(886\) | 29.5100 | 0.991409 | ||||||||
\(887\) | 53.8899 | 1.80945 | 0.904723 | − | 0.425999i | \(-0.140077\pi\) | ||||
0.904723 | + | 0.425999i | \(0.140077\pi\) | |||||||
\(888\) | 10.2903 | 0.345321 | ||||||||
\(889\) | 2.61734 | 0.0877827 | ||||||||
\(890\) | 42.6674 | 1.43021 | ||||||||
\(891\) | 38.8283 | 1.30080 | ||||||||
\(892\) | 2.20524 | 0.0738369 | ||||||||
\(893\) | −5.84662 | −0.195650 | ||||||||
\(894\) | 12.6142 | 0.421882 | ||||||||
\(895\) | 26.7884 | 0.895439 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 27.1605 | 0.906861 | ||||||||
\(898\) | 8.80065 | 0.293682 | ||||||||
\(899\) | 18.7309 | 0.624711 | ||||||||
\(900\) | 4.89678 | 0.163226 | ||||||||
\(901\) | 22.7748 | 0.758738 | ||||||||
\(902\) | −46.7426 | −1.55636 | ||||||||
\(903\) | −21.3755 | −0.711331 | ||||||||
\(904\) | −9.77779 | −0.325204 | ||||||||
\(905\) | −56.9808 | −1.89411 | ||||||||
\(906\) | −18.6887 | −0.620889 | ||||||||
\(907\) | −47.7372 | −1.58509 | −0.792544 | − | 0.609815i | \(-0.791244\pi\) | ||||
−0.792544 | + | 0.609815i | \(0.791244\pi\) | |||||||
\(908\) | 10.7465 | 0.356636 | ||||||||
\(909\) | 34.6931 | 1.15070 | ||||||||
\(910\) | 4.62391 | 0.153281 | ||||||||
\(911\) | 23.6674 | 0.784135 | 0.392067 | − | 0.919937i | \(-0.371760\pi\) | ||||
0.392067 | + | 0.919937i | \(0.371760\pi\) | |||||||
\(912\) | 1.21588 | 0.0402619 | ||||||||
\(913\) | 35.0622 | 1.16039 | ||||||||
\(914\) | 2.87643 | 0.0951439 | ||||||||
\(915\) | 37.7312 | 1.24735 | ||||||||
\(916\) | −21.9052 | −0.723767 | ||||||||
\(917\) | 20.0378 | 0.661707 | ||||||||
\(918\) | 2.01378 | 0.0664646 | ||||||||
\(919\) | −12.1321 | −0.400202 | −0.200101 | − | 0.979775i | \(-0.564127\pi\) | ||||
−0.200101 | + | 0.979775i | \(0.564127\pi\) | |||||||
\(920\) | −16.8357 | −0.555057 | ||||||||
\(921\) | 11.9424 | 0.393516 | ||||||||
\(922\) | 31.0928 | 1.02399 | ||||||||
\(923\) | −13.0921 | −0.430933 | ||||||||
\(924\) | 9.37859 | 0.308533 | ||||||||
\(925\) | 7.89980 | 0.259744 | ||||||||
\(926\) | −11.3344 | −0.372473 | ||||||||
\(927\) | −29.8944 | −0.981861 | ||||||||
\(928\) | −4.06382 | −0.133401 | ||||||||
\(929\) | −17.7527 | −0.582449 | −0.291224 | − | 0.956655i | \(-0.594063\pi\) | ||||
−0.291224 | + | 0.956655i | \(0.594063\pi\) | |||||||
\(930\) | −28.6993 | −0.941086 | ||||||||
\(931\) | −0.510304 | −0.0167245 | ||||||||
\(932\) | −14.1342 | −0.462982 | ||||||||
\(933\) | 14.1511 | 0.463286 | ||||||||
\(934\) | −37.9010 | −1.24016 | ||||||||
\(935\) | −26.9226 | −0.880465 | ||||||||
\(936\) | −4.73683 | −0.154828 | ||||||||
\(937\) | 8.44423 | 0.275861 | 0.137930 | − | 0.990442i | \(-0.455955\pi\) | ||||
0.137930 | + | 0.990442i | \(0.455955\pi\) | |||||||
\(938\) | 9.84386 | 0.321414 | ||||||||
\(939\) | 42.7439 | 1.39490 | ||||||||
\(940\) | −29.9405 | −0.976551 | ||||||||
\(941\) | 18.8649 | 0.614978 | 0.307489 | − | 0.951552i | \(-0.400511\pi\) | ||||
0.307489 | + | 0.951552i | \(0.400511\pi\) | |||||||
\(942\) | 40.5209 | 1.32024 | ||||||||
\(943\) | 76.5044 | 2.49133 | ||||||||
\(944\) | −9.05975 | −0.294870 | ||||||||
\(945\) | −2.01064 | −0.0654063 | ||||||||
\(946\) | 35.3124 | 1.14811 | ||||||||
\(947\) | −25.1991 | −0.818860 | −0.409430 | − | 0.912341i | \(-0.634272\pi\) | ||||
−0.409430 | + | 0.912341i | \(0.634272\pi\) | |||||||
\(948\) | −33.6420 | −1.09264 | ||||||||
\(949\) | −1.17199 | −0.0380445 | ||||||||
\(950\) | 0.933422 | 0.0302842 | ||||||||
\(951\) | −61.8473 | −2.00554 | ||||||||
\(952\) | 2.61734 | 0.0848284 | ||||||||
\(953\) | −12.6032 | −0.408259 | −0.204129 | − | 0.978944i | \(-0.565436\pi\) | ||||
−0.204129 | + | 0.978944i | \(0.565436\pi\) | |||||||
\(954\) | 23.2947 | 0.754193 | ||||||||
\(955\) | 2.46777 | 0.0798552 | ||||||||
\(956\) | −17.0234 | −0.550575 | ||||||||
\(957\) | 38.1129 | 1.23202 | ||||||||
\(958\) | 21.0034 | 0.678588 | ||||||||
\(959\) | 9.50216 | 0.306841 | ||||||||
\(960\) | 6.22653 | 0.200960 | ||||||||
\(961\) | −9.75536 | −0.314689 | ||||||||
\(962\) | −7.64176 | −0.246380 | ||||||||
\(963\) | 31.5695 | 1.01731 | ||||||||
\(964\) | −18.1722 | −0.585286 | ||||||||
\(965\) | 54.0034 | 1.73843 | ||||||||
\(966\) | −15.3501 | −0.493881 | ||||||||
\(967\) | −6.30646 | −0.202802 | −0.101401 | − | 0.994846i | \(-0.532333\pi\) | ||||
−0.101401 | + | 0.994846i | \(0.532333\pi\) | |||||||
\(968\) | −4.49351 | −0.144427 | ||||||||
\(969\) | −3.18238 | −0.102233 | ||||||||
\(970\) | 11.1480 | 0.357940 | ||||||||
\(971\) | −20.1034 | −0.645148 | −0.322574 | − | 0.946544i | \(-0.604548\pi\) | ||||
−0.322574 | + | 0.946544i | \(0.604548\pi\) | |||||||
\(972\) | 21.1955 | 0.679847 | ||||||||
\(973\) | −3.92528 | −0.125839 | ||||||||
\(974\) | 30.1820 | 0.967094 | ||||||||
\(975\) | −7.71147 | −0.246965 | ||||||||
\(976\) | 6.05975 | 0.193968 | ||||||||
\(977\) | −40.0374 | −1.28091 | −0.640455 | − | 0.767996i | \(-0.721254\pi\) | ||||
−0.640455 | + | 0.767996i | \(0.721254\pi\) | |||||||
\(978\) | 1.18082 | 0.0377584 | ||||||||
\(979\) | −64.2669 | −2.05398 | ||||||||
\(980\) | −2.61326 | −0.0834776 | ||||||||
\(981\) | 18.0351 | 0.575815 | ||||||||
\(982\) | 1.49758 | 0.0477898 | ||||||||
\(983\) | 20.4105 | 0.650993 | 0.325496 | − | 0.945543i | \(-0.394469\pi\) | ||||
0.325496 | + | 0.945543i | \(0.394469\pi\) | |||||||
\(984\) | −28.2944 | −0.901993 | ||||||||
\(985\) | −15.1840 | −0.483802 | ||||||||
\(986\) | 10.6364 | 0.338732 | ||||||||
\(987\) | −27.2985 | −0.868920 | ||||||||
\(988\) | −0.902932 | −0.0287261 | ||||||||
\(989\) | −57.7964 | −1.83782 | ||||||||
\(990\) | −27.5372 | −0.875190 | ||||||||
\(991\) | 44.8529 | 1.42480 | 0.712400 | − | 0.701773i | \(-0.247608\pi\) | ||||
0.712400 | + | 0.701773i | \(0.247608\pi\) | |||||||
\(992\) | −4.60919 | −0.146342 | ||||||||
\(993\) | 37.8779 | 1.20202 | ||||||||
\(994\) | 7.39920 | 0.234688 | ||||||||
\(995\) | 4.17988 | 0.132511 | ||||||||
\(996\) | 21.2240 | 0.672509 | ||||||||
\(997\) | 50.7816 | 1.60827 | 0.804135 | − | 0.594447i | \(-0.202629\pi\) | ||||
0.804135 | + | 0.594447i | \(0.202629\pi\) | |||||||
\(998\) | −13.6529 | −0.432175 | ||||||||
\(999\) | 3.32292 | 0.105132 |
(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 | 6034.2.a.j.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.j.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |