Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8021,2,Mod(1,8021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8021, 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("8021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8021 = 13 \cdot 617 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8021.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: | \(64.0480074613\) |
Analytic rank: | \(0\) |
Dimension: | \(169\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8021.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75686 | −1.94939 | −0.974697 | − | 0.223529i | \(-0.928242\pi\) | ||||
−0.974697 | + | 0.223529i | \(0.928242\pi\) | |||||||
\(3\) | −1.90538 | −1.10007 | −0.550036 | − | 0.835141i | \(-0.685386\pi\) | ||||
−0.550036 | + | 0.835141i | \(0.685386\pi\) | |||||||
\(4\) | 5.60028 | 2.80014 | ||||||||
\(5\) | −0.896577 | −0.400962 | −0.200481 | − | 0.979698i | \(-0.564250\pi\) | ||||
−0.200481 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(6\) | 5.25287 | 2.14447 | ||||||||
\(7\) | 2.47327 | 0.934807 | 0.467403 | − | 0.884044i | \(-0.345190\pi\) | ||||
0.467403 | + | 0.884044i | \(0.345190\pi\) | |||||||
\(8\) | −9.92547 | −3.50918 | ||||||||
\(9\) | 0.630474 | 0.210158 | ||||||||
\(10\) | 2.47174 | 0.781632 | ||||||||
\(11\) | −0.829573 | −0.250126 | −0.125063 | − | 0.992149i | \(-0.539913\pi\) | ||||
−0.125063 | + | 0.992149i | \(0.539913\pi\) | |||||||
\(12\) | −10.6707 | −3.08035 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −6.81845 | −1.82231 | ||||||||
\(15\) | 1.70832 | 0.441087 | ||||||||
\(16\) | 16.1626 | 4.04064 | ||||||||
\(17\) | −2.26874 | −0.550251 | −0.275126 | − | 0.961408i | \(-0.588719\pi\) | ||||
−0.275126 | + | 0.961408i | \(0.588719\pi\) | |||||||
\(18\) | −1.73813 | −0.409681 | ||||||||
\(19\) | −3.69629 | −0.847987 | −0.423994 | − | 0.905665i | \(-0.639372\pi\) | ||||
−0.423994 | + | 0.905665i | \(0.639372\pi\) | |||||||
\(20\) | −5.02108 | −1.12275 | ||||||||
\(21\) | −4.71251 | −1.02835 | ||||||||
\(22\) | 2.28702 | 0.487594 | ||||||||
\(23\) | −5.25182 | −1.09508 | −0.547541 | − | 0.836779i | \(-0.684436\pi\) | ||||
−0.547541 | + | 0.836779i | \(0.684436\pi\) | |||||||
\(24\) | 18.9118 | 3.86035 | ||||||||
\(25\) | −4.19615 | −0.839230 | ||||||||
\(26\) | 2.75686 | 0.540665 | ||||||||
\(27\) | 4.51485 | 0.868883 | ||||||||
\(28\) | 13.8510 | 2.61759 | ||||||||
\(29\) | −6.49921 | −1.20687 | −0.603437 | − | 0.797411i | \(-0.706202\pi\) | ||||
−0.603437 | + | 0.797411i | \(0.706202\pi\) | |||||||
\(30\) | −4.70960 | −0.859852 | ||||||||
\(31\) | −2.31862 | −0.416436 | −0.208218 | − | 0.978082i | \(-0.566766\pi\) | ||||
−0.208218 | + | 0.978082i | \(0.566766\pi\) | |||||||
\(32\) | −24.7070 | −4.36762 | ||||||||
\(33\) | 1.58065 | 0.275156 | ||||||||
\(34\) | 6.25461 | 1.07266 | ||||||||
\(35\) | −2.21747 | −0.374822 | ||||||||
\(36\) | 3.53083 | 0.588472 | ||||||||
\(37\) | −7.02474 | −1.15486 | −0.577430 | − | 0.816440i | \(-0.695944\pi\) | ||||
−0.577430 | + | 0.816440i | \(0.695944\pi\) | |||||||
\(38\) | 10.1902 | 1.65306 | ||||||||
\(39\) | 1.90538 | 0.305105 | ||||||||
\(40\) | 8.89895 | 1.40705 | ||||||||
\(41\) | −5.48491 | −0.856599 | −0.428299 | − | 0.903637i | \(-0.640887\pi\) | ||||
−0.428299 | + | 0.903637i | \(0.640887\pi\) | |||||||
\(42\) | 12.9917 | 2.00467 | ||||||||
\(43\) | −9.24004 | −1.40909 | −0.704546 | − | 0.709658i | \(-0.748849\pi\) | ||||
−0.704546 | + | 0.709658i | \(0.748849\pi\) | |||||||
\(44\) | −4.64584 | −0.700387 | ||||||||
\(45\) | −0.565269 | −0.0842653 | ||||||||
\(46\) | 14.4785 | 2.13475 | ||||||||
\(47\) | 4.56715 | 0.666187 | 0.333093 | − | 0.942894i | \(-0.391908\pi\) | ||||
0.333093 | + | 0.942894i | \(0.391908\pi\) | |||||||
\(48\) | −30.7958 | −4.44500 | ||||||||
\(49\) | −0.882952 | −0.126136 | ||||||||
\(50\) | 11.5682 | 1.63599 | ||||||||
\(51\) | 4.32282 | 0.605316 | ||||||||
\(52\) | −5.60028 | −0.776619 | ||||||||
\(53\) | −10.1469 | −1.39378 | −0.696889 | − | 0.717179i | \(-0.745433\pi\) | ||||
−0.696889 | + | 0.717179i | \(0.745433\pi\) | |||||||
\(54\) | −12.4468 | −1.69380 | ||||||||
\(55\) | 0.743777 | 0.100291 | ||||||||
\(56\) | −24.5483 | −3.28041 | ||||||||
\(57\) | 7.04284 | 0.932847 | ||||||||
\(58\) | 17.9174 | 2.35267 | ||||||||
\(59\) | −2.24047 | −0.291685 | −0.145842 | − | 0.989308i | \(-0.546589\pi\) | ||||
−0.145842 | + | 0.989308i | \(0.546589\pi\) | |||||||
\(60\) | 9.56707 | 1.23510 | ||||||||
\(61\) | 8.47940 | 1.08568 | 0.542838 | − | 0.839837i | \(-0.317350\pi\) | ||||
0.542838 | + | 0.839837i | \(0.317350\pi\) | |||||||
\(62\) | 6.39211 | 0.811798 | ||||||||
\(63\) | 1.55933 | 0.196457 | ||||||||
\(64\) | 35.7886 | 4.47358 | ||||||||
\(65\) | 0.896577 | 0.111207 | ||||||||
\(66\) | −4.35764 | −0.536388 | ||||||||
\(67\) | −14.5732 | −1.78039 | −0.890197 | − | 0.455576i | \(-0.849433\pi\) | ||||
−0.890197 | + | 0.455576i | \(0.849433\pi\) | |||||||
\(68\) | −12.7056 | −1.54078 | ||||||||
\(69\) | 10.0067 | 1.20467 | ||||||||
\(70\) | 6.11327 | 0.730675 | ||||||||
\(71\) | −13.9707 | −1.65802 | −0.829008 | − | 0.559237i | \(-0.811094\pi\) | ||||
−0.829008 | + | 0.559237i | \(0.811094\pi\) | |||||||
\(72\) | −6.25775 | −0.737483 | ||||||||
\(73\) | −4.21314 | −0.493111 | −0.246556 | − | 0.969129i | \(-0.579299\pi\) | ||||
−0.246556 | + | 0.969129i | \(0.579299\pi\) | |||||||
\(74\) | 19.3662 | 2.25128 | ||||||||
\(75\) | 7.99526 | 0.923213 | ||||||||
\(76\) | −20.7003 | −2.37448 | ||||||||
\(77\) | −2.05176 | −0.233819 | ||||||||
\(78\) | −5.25287 | −0.594770 | ||||||||
\(79\) | −3.34200 | −0.376005 | −0.188002 | − | 0.982169i | \(-0.560201\pi\) | ||||
−0.188002 | + | 0.982169i | \(0.560201\pi\) | |||||||
\(80\) | −14.4910 | −1.62014 | ||||||||
\(81\) | −10.4939 | −1.16599 | ||||||||
\(82\) | 15.1211 | 1.66985 | ||||||||
\(83\) | 0.491916 | 0.0539948 | 0.0269974 | − | 0.999636i | \(-0.491405\pi\) | ||||
0.0269974 | + | 0.999636i | \(0.491405\pi\) | |||||||
\(84\) | −26.3914 | −2.87954 | ||||||||
\(85\) | 2.03410 | 0.220630 | ||||||||
\(86\) | 25.4735 | 2.74688 | ||||||||
\(87\) | 12.3835 | 1.32765 | ||||||||
\(88\) | 8.23390 | 0.877737 | ||||||||
\(89\) | −15.4847 | −1.64137 | −0.820687 | − | 0.571378i | \(-0.806409\pi\) | ||||
−0.820687 | + | 0.571378i | \(0.806409\pi\) | |||||||
\(90\) | 1.55837 | 0.164266 | ||||||||
\(91\) | −2.47327 | −0.259269 | ||||||||
\(92\) | −29.4117 | −3.06638 | ||||||||
\(93\) | 4.41785 | 0.458110 | ||||||||
\(94\) | −12.5910 | −1.29866 | ||||||||
\(95\) | 3.31401 | 0.340010 | ||||||||
\(96\) | 47.0762 | 4.80470 | ||||||||
\(97\) | 16.3692 | 1.66204 | 0.831019 | − | 0.556243i | \(-0.187758\pi\) | ||||
0.831019 | + | 0.556243i | \(0.187758\pi\) | |||||||
\(98\) | 2.43418 | 0.245889 | ||||||||
\(99\) | −0.523024 | −0.0525659 | ||||||||
\(100\) | −23.4996 | −2.34996 | ||||||||
\(101\) | 9.30569 | 0.925951 | 0.462976 | − | 0.886371i | \(-0.346782\pi\) | ||||
0.462976 | + | 0.886371i | \(0.346782\pi\) | |||||||
\(102\) | −11.9174 | −1.18000 | ||||||||
\(103\) | −1.23021 | −0.121216 | −0.0606081 | − | 0.998162i | \(-0.519304\pi\) | ||||
−0.0606081 | + | 0.998162i | \(0.519304\pi\) | |||||||
\(104\) | 9.92547 | 0.973272 | ||||||||
\(105\) | 4.22513 | 0.412331 | ||||||||
\(106\) | 27.9735 | 2.71702 | ||||||||
\(107\) | −17.2946 | −1.67193 | −0.835966 | − | 0.548782i | \(-0.815092\pi\) | ||||
−0.835966 | + | 0.548782i | \(0.815092\pi\) | |||||||
\(108\) | 25.2844 | 2.43299 | ||||||||
\(109\) | 17.4148 | 1.66804 | 0.834020 | − | 0.551735i | \(-0.186034\pi\) | ||||
0.834020 | + | 0.551735i | \(0.186034\pi\) | |||||||
\(110\) | −2.05049 | −0.195506 | ||||||||
\(111\) | 13.3848 | 1.27043 | ||||||||
\(112\) | 39.9743 | 3.77722 | ||||||||
\(113\) | 1.71682 | 0.161505 | 0.0807526 | − | 0.996734i | \(-0.474268\pi\) | ||||
0.0807526 | + | 0.996734i | \(0.474268\pi\) | |||||||
\(114\) | −19.4161 | −1.81849 | ||||||||
\(115\) | 4.70867 | 0.439085 | ||||||||
\(116\) | −36.3974 | −3.37941 | ||||||||
\(117\) | −0.630474 | −0.0582873 | ||||||||
\(118\) | 6.17667 | 0.568609 | ||||||||
\(119\) | −5.61121 | −0.514379 | ||||||||
\(120\) | −16.9559 | −1.54785 | ||||||||
\(121\) | −10.3118 | −0.937437 | ||||||||
\(122\) | −23.3765 | −2.11641 | ||||||||
\(123\) | 10.4508 | 0.942320 | ||||||||
\(124\) | −12.9849 | −1.16608 | ||||||||
\(125\) | 8.24506 | 0.737461 | ||||||||
\(126\) | −4.29885 | −0.382972 | ||||||||
\(127\) | −8.86184 | −0.786362 | −0.393181 | − | 0.919461i | \(-0.628625\pi\) | ||||
−0.393181 | + | 0.919461i | \(0.628625\pi\) | |||||||
\(128\) | −49.2503 | −4.35315 | ||||||||
\(129\) | 17.6058 | 1.55010 | ||||||||
\(130\) | −2.47174 | −0.216786 | ||||||||
\(131\) | 5.06912 | 0.442891 | 0.221445 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221445 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(132\) | 8.85209 | 0.770476 | ||||||||
\(133\) | −9.14191 | −0.792705 | ||||||||
\(134\) | 40.1761 | 3.47069 | ||||||||
\(135\) | −4.04791 | −0.348389 | ||||||||
\(136\) | 22.5183 | 1.93093 | ||||||||
\(137\) | −9.67626 | −0.826699 | −0.413349 | − | 0.910572i | \(-0.635641\pi\) | ||||
−0.413349 | + | 0.910572i | \(0.635641\pi\) | |||||||
\(138\) | −27.5871 | −2.34837 | ||||||||
\(139\) | 18.4780 | 1.56728 | 0.783641 | − | 0.621214i | \(-0.213360\pi\) | ||||
0.783641 | + | 0.621214i | \(0.213360\pi\) | |||||||
\(140\) | −12.4185 | −1.04955 | ||||||||
\(141\) | −8.70215 | −0.732853 | ||||||||
\(142\) | 38.5152 | 3.23213 | ||||||||
\(143\) | 0.829573 | 0.0693724 | ||||||||
\(144\) | 10.1901 | 0.849173 | ||||||||
\(145\) | 5.82704 | 0.483910 | ||||||||
\(146\) | 11.6151 | 0.961268 | ||||||||
\(147\) | 1.68236 | 0.138759 | ||||||||
\(148\) | −39.3405 | −3.23377 | ||||||||
\(149\) | 23.0464 | 1.88804 | 0.944019 | − | 0.329891i | \(-0.107012\pi\) | ||||
0.944019 | + | 0.329891i | \(0.107012\pi\) | |||||||
\(150\) | −22.0418 | −1.79971 | ||||||||
\(151\) | 5.42506 | 0.441485 | 0.220743 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220743 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(152\) | 36.6874 | 2.97574 | ||||||||
\(153\) | −1.43038 | −0.115640 | ||||||||
\(154\) | 5.65640 | 0.455806 | ||||||||
\(155\) | 2.07882 | 0.166975 | ||||||||
\(156\) | 10.6707 | 0.854337 | ||||||||
\(157\) | −4.01511 | −0.320441 | −0.160220 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160220 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(158\) | 9.21344 | 0.732982 | ||||||||
\(159\) | 19.3336 | 1.53326 | ||||||||
\(160\) | 22.1517 | 1.75125 | ||||||||
\(161\) | −12.9892 | −1.02369 | ||||||||
\(162\) | 28.9303 | 2.27298 | ||||||||
\(163\) | −7.57930 | −0.593657 | −0.296828 | − | 0.954931i | \(-0.595929\pi\) | ||||
−0.296828 | + | 0.954931i | \(0.595929\pi\) | |||||||
\(164\) | −30.7170 | −2.39860 | ||||||||
\(165\) | −1.41718 | −0.110327 | ||||||||
\(166\) | −1.35614 | −0.105257 | ||||||||
\(167\) | −15.9189 | −1.23184 | −0.615921 | − | 0.787808i | \(-0.711216\pi\) | ||||
−0.615921 | + | 0.787808i | \(0.711216\pi\) | |||||||
\(168\) | 46.7739 | 3.60868 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −5.60774 | −0.430094 | ||||||||
\(171\) | −2.33042 | −0.178211 | ||||||||
\(172\) | −51.7468 | −3.94566 | ||||||||
\(173\) | 7.54878 | 0.573923 | 0.286962 | − | 0.957942i | \(-0.407355\pi\) | ||||
0.286962 | + | 0.957942i | \(0.407355\pi\) | |||||||
\(174\) | −34.1395 | −2.58811 | ||||||||
\(175\) | −10.3782 | −0.784518 | ||||||||
\(176\) | −13.4080 | −1.01067 | ||||||||
\(177\) | 4.26895 | 0.320874 | ||||||||
\(178\) | 42.6891 | 3.19968 | ||||||||
\(179\) | −11.8518 | −0.885844 | −0.442922 | − | 0.896560i | \(-0.646058\pi\) | ||||
−0.442922 | + | 0.896560i | \(0.646058\pi\) | |||||||
\(180\) | −3.16566 | −0.235954 | ||||||||
\(181\) | 8.31162 | 0.617798 | 0.308899 | − | 0.951095i | \(-0.400040\pi\) | ||||
0.308899 | + | 0.951095i | \(0.400040\pi\) | |||||||
\(182\) | 6.81845 | 0.505417 | ||||||||
\(183\) | −16.1565 | −1.19432 | ||||||||
\(184\) | 52.1268 | 3.84284 | ||||||||
\(185\) | 6.29822 | 0.463054 | ||||||||
\(186\) | −12.1794 | −0.893036 | ||||||||
\(187\) | 1.88209 | 0.137632 | ||||||||
\(188\) | 25.5773 | 1.86542 | ||||||||
\(189\) | 11.1664 | 0.812238 | ||||||||
\(190\) | −9.13627 | −0.662814 | ||||||||
\(191\) | 6.50624 | 0.470775 | 0.235388 | − | 0.971902i | \(-0.424364\pi\) | ||||
0.235388 | + | 0.971902i | \(0.424364\pi\) | |||||||
\(192\) | −68.1910 | −4.92126 | ||||||||
\(193\) | 21.8143 | 1.57023 | 0.785114 | − | 0.619351i | \(-0.212604\pi\) | ||||
0.785114 | + | 0.619351i | \(0.212604\pi\) | |||||||
\(194\) | −45.1276 | −3.23997 | ||||||||
\(195\) | −1.70832 | −0.122335 | ||||||||
\(196\) | −4.94478 | −0.353198 | ||||||||
\(197\) | −19.7563 | −1.40758 | −0.703788 | − | 0.710410i | \(-0.748510\pi\) | ||||
−0.703788 | + | 0.710410i | \(0.748510\pi\) | |||||||
\(198\) | 1.44190 | 0.102472 | ||||||||
\(199\) | 14.2734 | 1.01182 | 0.505908 | − | 0.862588i | \(-0.331158\pi\) | ||||
0.505908 | + | 0.862588i | \(0.331158\pi\) | |||||||
\(200\) | 41.6487 | 2.94501 | ||||||||
\(201\) | 27.7674 | 1.95856 | ||||||||
\(202\) | −25.6545 | −1.80504 | ||||||||
\(203\) | −16.0743 | −1.12819 | ||||||||
\(204\) | 24.2090 | 1.69497 | ||||||||
\(205\) | 4.91764 | 0.343463 | ||||||||
\(206\) | 3.39152 | 0.236298 | ||||||||
\(207\) | −3.31114 | −0.230140 | ||||||||
\(208\) | −16.1626 | −1.12067 | ||||||||
\(209\) | 3.06634 | 0.212103 | ||||||||
\(210\) | −11.6481 | −0.803795 | ||||||||
\(211\) | 14.7070 | 1.01247 | 0.506235 | − | 0.862396i | \(-0.331037\pi\) | ||||
0.506235 | + | 0.862396i | \(0.331037\pi\) | |||||||
\(212\) | −56.8252 | −3.90277 | ||||||||
\(213\) | 26.6195 | 1.82394 | ||||||||
\(214\) | 47.6788 | 3.25925 | ||||||||
\(215\) | 8.28441 | 0.564992 | ||||||||
\(216\) | −44.8120 | −3.04907 | ||||||||
\(217\) | −5.73456 | −0.389287 | ||||||||
\(218\) | −48.0103 | −3.25167 | ||||||||
\(219\) | 8.02764 | 0.542458 | ||||||||
\(220\) | 4.16536 | 0.280828 | ||||||||
\(221\) | 2.26874 | 0.152612 | ||||||||
\(222\) | −36.9000 | −2.47657 | ||||||||
\(223\) | 11.3078 | 0.757227 | 0.378613 | − | 0.925555i | \(-0.376401\pi\) | ||||
0.378613 | + | 0.925555i | \(0.376401\pi\) | |||||||
\(224\) | −61.1070 | −4.08288 | ||||||||
\(225\) | −2.64556 | −0.176371 | ||||||||
\(226\) | −4.73304 | −0.314837 | ||||||||
\(227\) | 24.8073 | 1.64652 | 0.823260 | − | 0.567664i | \(-0.192153\pi\) | ||||
0.823260 | + | 0.567664i | \(0.192153\pi\) | |||||||
\(228\) | 39.4419 | 2.61210 | ||||||||
\(229\) | 19.4057 | 1.28237 | 0.641183 | − | 0.767388i | \(-0.278444\pi\) | ||||
0.641183 | + | 0.767388i | \(0.278444\pi\) | |||||||
\(230\) | −12.9811 | −0.855951 | ||||||||
\(231\) | 3.90937 | 0.257218 | ||||||||
\(232\) | 64.5077 | 4.23514 | ||||||||
\(233\) | 4.98730 | 0.326729 | 0.163365 | − | 0.986566i | \(-0.447765\pi\) | ||||
0.163365 | + | 0.986566i | \(0.447765\pi\) | |||||||
\(234\) | 1.73813 | 0.113625 | ||||||||
\(235\) | −4.09480 | −0.267115 | ||||||||
\(236\) | −12.5473 | −0.816758 | ||||||||
\(237\) | 6.36779 | 0.413632 | ||||||||
\(238\) | 15.4693 | 1.00273 | ||||||||
\(239\) | −22.3202 | −1.44378 | −0.721888 | − | 0.692010i | \(-0.756725\pi\) | ||||
−0.721888 | + | 0.692010i | \(0.756725\pi\) | |||||||
\(240\) | 27.6109 | 1.78227 | ||||||||
\(241\) | −14.2876 | −0.920342 | −0.460171 | − | 0.887830i | \(-0.652212\pi\) | ||||
−0.460171 | + | 0.887830i | \(0.652212\pi\) | |||||||
\(242\) | 28.4282 | 1.82743 | ||||||||
\(243\) | 6.45037 | 0.413791 | ||||||||
\(244\) | 47.4870 | 3.04005 | ||||||||
\(245\) | 0.791635 | 0.0505757 | ||||||||
\(246\) | −28.8115 | −1.83695 | ||||||||
\(247\) | 3.69629 | 0.235189 | ||||||||
\(248\) | 23.0134 | 1.46135 | ||||||||
\(249\) | −0.937288 | −0.0593982 | ||||||||
\(250\) | −22.7305 | −1.43760 | ||||||||
\(251\) | −14.6923 | −0.927369 | −0.463685 | − | 0.886000i | \(-0.653473\pi\) | ||||
−0.463685 | + | 0.886000i | \(0.653473\pi\) | |||||||
\(252\) | 8.73268 | 0.550107 | ||||||||
\(253\) | 4.35677 | 0.273908 | ||||||||
\(254\) | 24.4309 | 1.53293 | ||||||||
\(255\) | −3.87574 | −0.242708 | ||||||||
\(256\) | 64.1988 | 4.01243 | ||||||||
\(257\) | −7.53700 | −0.470145 | −0.235073 | − | 0.971978i | \(-0.575533\pi\) | ||||
−0.235073 | + | 0.971978i | \(0.575533\pi\) | |||||||
\(258\) | −48.5367 | −3.02176 | ||||||||
\(259\) | −17.3740 | −1.07957 | ||||||||
\(260\) | 5.02108 | 0.311394 | ||||||||
\(261\) | −4.09758 | −0.253634 | ||||||||
\(262\) | −13.9749 | −0.863369 | ||||||||
\(263\) | −23.9422 | −1.47634 | −0.738170 | − | 0.674614i | \(-0.764310\pi\) | ||||
−0.738170 | + | 0.674614i | \(0.764310\pi\) | |||||||
\(264\) | −15.6887 | −0.965573 | ||||||||
\(265\) | 9.09744 | 0.558851 | ||||||||
\(266\) | 25.2030 | 1.54529 | ||||||||
\(267\) | 29.5042 | 1.80563 | ||||||||
\(268\) | −81.6137 | −4.98535 | ||||||||
\(269\) | −25.6418 | −1.56341 | −0.781704 | − | 0.623649i | \(-0.785649\pi\) | ||||
−0.781704 | + | 0.623649i | \(0.785649\pi\) | |||||||
\(270\) | 11.1595 | 0.679147 | ||||||||
\(271\) | 26.7658 | 1.62591 | 0.812954 | − | 0.582327i | \(-0.197858\pi\) | ||||
0.812954 | + | 0.582327i | \(0.197858\pi\) | |||||||
\(272\) | −36.6687 | −2.22337 | ||||||||
\(273\) | 4.71251 | 0.285214 | ||||||||
\(274\) | 26.6761 | 1.61156 | ||||||||
\(275\) | 3.48101 | 0.209913 | ||||||||
\(276\) | 56.0404 | 3.37324 | ||||||||
\(277\) | −28.5995 | −1.71838 | −0.859189 | − | 0.511658i | \(-0.829032\pi\) | ||||
−0.859189 | + | 0.511658i | \(0.829032\pi\) | |||||||
\(278\) | −50.9412 | −3.05525 | ||||||||
\(279\) | −1.46183 | −0.0875173 | ||||||||
\(280\) | 22.0095 | 1.31532 | ||||||||
\(281\) | −7.13971 | −0.425919 | −0.212960 | − | 0.977061i | \(-0.568310\pi\) | ||||
−0.212960 | + | 0.977061i | \(0.568310\pi\) | |||||||
\(282\) | 23.9906 | 1.42862 | ||||||||
\(283\) | −9.76934 | −0.580727 | −0.290363 | − | 0.956916i | \(-0.593776\pi\) | ||||
−0.290363 | + | 0.956916i | \(0.593776\pi\) | |||||||
\(284\) | −78.2397 | −4.64267 | ||||||||
\(285\) | −6.31445 | −0.374036 | ||||||||
\(286\) | −2.28702 | −0.135234 | ||||||||
\(287\) | −13.5656 | −0.800754 | ||||||||
\(288\) | −15.5771 | −0.917891 | ||||||||
\(289\) | −11.8528 | −0.697224 | ||||||||
\(290\) | −16.0643 | −0.943331 | ||||||||
\(291\) | −31.1895 | −1.82836 | ||||||||
\(292\) | −23.5948 | −1.38078 | ||||||||
\(293\) | −5.95696 | −0.348009 | −0.174005 | − | 0.984745i | \(-0.555671\pi\) | ||||
−0.174005 | + | 0.984745i | \(0.555671\pi\) | |||||||
\(294\) | −4.63803 | −0.270495 | ||||||||
\(295\) | 2.00876 | 0.116954 | ||||||||
\(296\) | 69.7238 | 4.05261 | ||||||||
\(297\) | −3.74540 | −0.217330 | ||||||||
\(298\) | −63.5358 | −3.68053 | ||||||||
\(299\) | 5.25182 | 0.303721 | ||||||||
\(300\) | 44.7757 | 2.58513 | ||||||||
\(301\) | −22.8531 | −1.31723 | ||||||||
\(302\) | −14.9561 | −0.860629 | ||||||||
\(303\) | −17.7309 | −1.01861 | ||||||||
\(304\) | −59.7416 | −3.42641 | ||||||||
\(305\) | −7.60244 | −0.435314 | ||||||||
\(306\) | 3.94337 | 0.225427 | ||||||||
\(307\) | −6.31397 | −0.360357 | −0.180179 | − | 0.983634i | \(-0.557668\pi\) | ||||
−0.180179 | + | 0.983634i | \(0.557668\pi\) | |||||||
\(308\) | −11.4904 | −0.654727 | ||||||||
\(309\) | 2.34402 | 0.133347 | ||||||||
\(310\) | −5.73102 | −0.325500 | ||||||||
\(311\) | 32.7829 | 1.85895 | 0.929474 | − | 0.368888i | \(-0.120261\pi\) | ||||
0.929474 | + | 0.368888i | \(0.120261\pi\) | |||||||
\(312\) | −18.9118 | −1.07067 | ||||||||
\(313\) | −17.2502 | −0.975037 | −0.487518 | − | 0.873113i | \(-0.662098\pi\) | ||||
−0.487518 | + | 0.873113i | \(0.662098\pi\) | |||||||
\(314\) | 11.0691 | 0.624665 | ||||||||
\(315\) | −1.39806 | −0.0787718 | ||||||||
\(316\) | −18.7162 | −1.05287 | ||||||||
\(317\) | 8.77899 | 0.493077 | 0.246539 | − | 0.969133i | \(-0.420707\pi\) | ||||
0.246539 | + | 0.969133i | \(0.420707\pi\) | |||||||
\(318\) | −53.3001 | −2.98892 | ||||||||
\(319\) | 5.39157 | 0.301870 | ||||||||
\(320\) | −32.0873 | −1.79373 | ||||||||
\(321\) | 32.9528 | 1.83924 | ||||||||
\(322\) | 35.8093 | 1.99557 | ||||||||
\(323\) | 8.38594 | 0.466606 | ||||||||
\(324\) | −58.7689 | −3.26494 | ||||||||
\(325\) | 4.19615 | 0.232760 | ||||||||
\(326\) | 20.8951 | 1.15727 | ||||||||
\(327\) | −33.1819 | −1.83496 | ||||||||
\(328\) | 54.4403 | 3.00596 | ||||||||
\(329\) | 11.2958 | 0.622756 | ||||||||
\(330\) | 3.90696 | 0.215071 | ||||||||
\(331\) | −25.3258 | −1.39203 | −0.696015 | − | 0.718027i | \(-0.745045\pi\) | ||||
−0.696015 | + | 0.718027i | \(0.745045\pi\) | |||||||
\(332\) | 2.75487 | 0.151193 | ||||||||
\(333\) | −4.42891 | −0.242703 | ||||||||
\(334\) | 43.8862 | 2.40135 | ||||||||
\(335\) | 13.0660 | 0.713869 | ||||||||
\(336\) | −76.1663 | −4.15521 | ||||||||
\(337\) | −15.4794 | −0.843218 | −0.421609 | − | 0.906778i | \(-0.638534\pi\) | ||||
−0.421609 | + | 0.906778i | \(0.638534\pi\) | |||||||
\(338\) | −2.75686 | −0.149953 | ||||||||
\(339\) | −3.27120 | −0.177667 | ||||||||
\(340\) | 11.3916 | 0.617794 | ||||||||
\(341\) | 1.92346 | 0.104161 | ||||||||
\(342\) | 6.42463 | 0.347404 | ||||||||
\(343\) | −19.4966 | −1.05272 | ||||||||
\(344\) | 91.7117 | 4.94476 | ||||||||
\(345\) | −8.97180 | −0.483026 | ||||||||
\(346\) | −20.8109 | −1.11880 | ||||||||
\(347\) | −18.0490 | −0.968920 | −0.484460 | − | 0.874813i | \(-0.660984\pi\) | ||||
−0.484460 | + | 0.874813i | \(0.660984\pi\) | |||||||
\(348\) | 69.3509 | 3.71760 | ||||||||
\(349\) | −13.7918 | −0.738257 | −0.369128 | − | 0.929378i | \(-0.620344\pi\) | ||||
−0.369128 | + | 0.929378i | \(0.620344\pi\) | |||||||
\(350\) | 28.6112 | 1.52933 | ||||||||
\(351\) | −4.51485 | −0.240985 | ||||||||
\(352\) | 20.4963 | 1.09245 | ||||||||
\(353\) | 35.4270 | 1.88559 | 0.942794 | − | 0.333376i | \(-0.108188\pi\) | ||||
0.942794 | + | 0.333376i | \(0.108188\pi\) | |||||||
\(354\) | −11.7689 | −0.625510 | ||||||||
\(355\) | 12.5258 | 0.664801 | ||||||||
\(356\) | −86.7186 | −4.59607 | ||||||||
\(357\) | 10.6915 | 0.565853 | ||||||||
\(358\) | 32.6737 | 1.72686 | ||||||||
\(359\) | −16.5285 | −0.872342 | −0.436171 | − | 0.899864i | \(-0.643666\pi\) | ||||
−0.436171 | + | 0.899864i | \(0.643666\pi\) | |||||||
\(360\) | 5.61055 | 0.295702 | ||||||||
\(361\) | −5.33743 | −0.280917 | ||||||||
\(362\) | −22.9140 | −1.20433 | ||||||||
\(363\) | 19.6479 | 1.03125 | ||||||||
\(364\) | −13.8510 | −0.725989 | ||||||||
\(365\) | 3.77741 | 0.197719 | ||||||||
\(366\) | 44.5412 | 2.32820 | ||||||||
\(367\) | −11.7670 | −0.614232 | −0.307116 | − | 0.951672i | \(-0.599364\pi\) | ||||
−0.307116 | + | 0.951672i | \(0.599364\pi\) | |||||||
\(368\) | −84.8830 | −4.42483 | ||||||||
\(369\) | −3.45809 | −0.180021 | ||||||||
\(370\) | −17.3633 | −0.902676 | ||||||||
\(371\) | −25.0959 | −1.30291 | ||||||||
\(372\) | 24.7412 | 1.28277 | ||||||||
\(373\) | 8.31865 | 0.430723 | 0.215362 | − | 0.976534i | \(-0.430907\pi\) | ||||
0.215362 | + | 0.976534i | \(0.430907\pi\) | |||||||
\(374\) | −5.18866 | −0.268299 | ||||||||
\(375\) | −15.7100 | −0.811259 | ||||||||
\(376\) | −45.3311 | −2.33777 | ||||||||
\(377\) | 6.49921 | 0.334726 | ||||||||
\(378\) | −30.7843 | −1.58337 | ||||||||
\(379\) | −20.1478 | −1.03492 | −0.517462 | − | 0.855706i | \(-0.673123\pi\) | ||||
−0.517462 | + | 0.855706i | \(0.673123\pi\) | |||||||
\(380\) | 18.5594 | 0.952077 | ||||||||
\(381\) | 16.8852 | 0.865054 | ||||||||
\(382\) | −17.9368 | −0.917727 | ||||||||
\(383\) | 33.0288 | 1.68769 | 0.843846 | − | 0.536585i | \(-0.180286\pi\) | ||||
0.843846 | + | 0.536585i | \(0.180286\pi\) | |||||||
\(384\) | 93.8405 | 4.78878 | ||||||||
\(385\) | 1.83956 | 0.0937525 | ||||||||
\(386\) | −60.1390 | −3.06100 | ||||||||
\(387\) | −5.82560 | −0.296132 | ||||||||
\(388\) | 91.6720 | 4.65394 | ||||||||
\(389\) | 12.0130 | 0.609083 | 0.304541 | − | 0.952499i | \(-0.401497\pi\) | ||||
0.304541 | + | 0.952499i | \(0.401497\pi\) | |||||||
\(390\) | 4.70960 | 0.238480 | ||||||||
\(391\) | 11.9150 | 0.602570 | ||||||||
\(392\) | 8.76371 | 0.442634 | ||||||||
\(393\) | −9.65860 | −0.487212 | ||||||||
\(394\) | 54.4653 | 2.74392 | ||||||||
\(395\) | 2.99637 | 0.150764 | ||||||||
\(396\) | −2.92908 | −0.147192 | ||||||||
\(397\) | −19.5818 | −0.982780 | −0.491390 | − | 0.870940i | \(-0.663511\pi\) | ||||
−0.491390 | + | 0.870940i | \(0.663511\pi\) | |||||||
\(398\) | −39.3498 | −1.97243 | ||||||||
\(399\) | 17.4188 | 0.872032 | ||||||||
\(400\) | −67.8205 | −3.39103 | ||||||||
\(401\) | −5.12431 | −0.255896 | −0.127948 | − | 0.991781i | \(-0.540839\pi\) | ||||
−0.127948 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(402\) | −76.5508 | −3.81801 | ||||||||
\(403\) | 2.31862 | 0.115499 | ||||||||
\(404\) | 52.1145 | 2.59279 | ||||||||
\(405\) | 9.40861 | 0.467518 | ||||||||
\(406\) | 44.3145 | 2.19929 | ||||||||
\(407\) | 5.82753 | 0.288860 | ||||||||
\(408\) | −42.9060 | −2.12416 | ||||||||
\(409\) | 3.81835 | 0.188805 | 0.0944026 | − | 0.995534i | \(-0.469906\pi\) | ||||
0.0944026 | + | 0.995534i | \(0.469906\pi\) | |||||||
\(410\) | −13.5573 | −0.669545 | ||||||||
\(411\) | 18.4370 | 0.909428 | ||||||||
\(412\) | −6.88952 | −0.339422 | ||||||||
\(413\) | −5.54129 | −0.272669 | ||||||||
\(414\) | 9.12835 | 0.448634 | ||||||||
\(415\) | −0.441041 | −0.0216499 | ||||||||
\(416\) | 24.7070 | 1.21136 | ||||||||
\(417\) | −35.2076 | −1.72412 | ||||||||
\(418\) | −8.45348 | −0.413473 | ||||||||
\(419\) | −3.62208 | −0.176950 | −0.0884750 | − | 0.996078i | \(-0.528199\pi\) | ||||
−0.0884750 | + | 0.996078i | \(0.528199\pi\) | |||||||
\(420\) | 23.6619 | 1.15458 | ||||||||
\(421\) | 12.9561 | 0.631444 | 0.315722 | − | 0.948852i | \(-0.397753\pi\) | ||||
0.315722 | + | 0.948852i | \(0.397753\pi\) | |||||||
\(422\) | −40.5450 | −1.97370 | ||||||||
\(423\) | 2.87947 | 0.140004 | ||||||||
\(424\) | 100.712 | 4.89102 | ||||||||
\(425\) | 9.51999 | 0.461787 | ||||||||
\(426\) | −73.3862 | −3.55557 | ||||||||
\(427\) | 20.9718 | 1.01490 | ||||||||
\(428\) | −96.8545 | −4.68164 | ||||||||
\(429\) | −1.58065 | −0.0763146 | ||||||||
\(430\) | −22.8390 | −1.10139 | ||||||||
\(431\) | 31.7530 | 1.52949 | 0.764745 | − | 0.644334i | \(-0.222865\pi\) | ||||
0.764745 | + | 0.644334i | \(0.222865\pi\) | |||||||
\(432\) | 72.9715 | 3.51084 | ||||||||
\(433\) | −5.35980 | −0.257576 | −0.128788 | − | 0.991672i | \(-0.541109\pi\) | ||||
−0.128788 | + | 0.991672i | \(0.541109\pi\) | |||||||
\(434\) | 15.8094 | 0.758875 | ||||||||
\(435\) | −11.1027 | −0.532335 | ||||||||
\(436\) | 97.5280 | 4.67074 | ||||||||
\(437\) | 19.4123 | 0.928615 | ||||||||
\(438\) | −22.1311 | −1.05746 | ||||||||
\(439\) | −30.2345 | −1.44302 | −0.721508 | − | 0.692406i | \(-0.756551\pi\) | ||||
−0.721508 | + | 0.692406i | \(0.756551\pi\) | |||||||
\(440\) | −7.38233 | −0.351939 | ||||||||
\(441\) | −0.556678 | −0.0265085 | ||||||||
\(442\) | −6.25461 | −0.297501 | ||||||||
\(443\) | 21.0515 | 1.00019 | 0.500093 | − | 0.865971i | \(-0.333299\pi\) | ||||
0.500093 | + | 0.865971i | \(0.333299\pi\) | |||||||
\(444\) | 74.9586 | 3.55738 | ||||||||
\(445\) | 13.8832 | 0.658128 | ||||||||
\(446\) | −31.1740 | −1.47613 | ||||||||
\(447\) | −43.9122 | −2.07698 | ||||||||
\(448\) | 88.5148 | 4.18193 | ||||||||
\(449\) | −26.9075 | −1.26984 | −0.634921 | − | 0.772577i | \(-0.718967\pi\) | ||||
−0.634921 | + | 0.772577i | \(0.718967\pi\) | |||||||
\(450\) | 7.29345 | 0.343816 | ||||||||
\(451\) | 4.55013 | 0.214257 | ||||||||
\(452\) | 9.61469 | 0.452237 | ||||||||
\(453\) | −10.3368 | −0.485666 | ||||||||
\(454\) | −68.3904 | −3.20972 | ||||||||
\(455\) | 2.21747 | 0.103957 | ||||||||
\(456\) | −69.9035 | −3.27353 | ||||||||
\(457\) | −28.6732 | −1.34128 | −0.670638 | − | 0.741784i | \(-0.733980\pi\) | ||||
−0.670638 | + | 0.741784i | \(0.733980\pi\) | |||||||
\(458\) | −53.4989 | −2.49984 | ||||||||
\(459\) | −10.2430 | −0.478104 | ||||||||
\(460\) | 26.3699 | 1.22950 | ||||||||
\(461\) | 2.13682 | 0.0995219 | 0.0497609 | − | 0.998761i | \(-0.484154\pi\) | ||||
0.0497609 | + | 0.998761i | \(0.484154\pi\) | |||||||
\(462\) | −10.7776 | −0.501419 | ||||||||
\(463\) | 5.53612 | 0.257285 | 0.128643 | − | 0.991691i | \(-0.458938\pi\) | ||||
0.128643 | + | 0.991691i | \(0.458938\pi\) | |||||||
\(464\) | −105.044 | −4.87654 | ||||||||
\(465\) | −3.96094 | −0.183684 | ||||||||
\(466\) | −13.7493 | −0.636924 | ||||||||
\(467\) | −40.5622 | −1.87699 | −0.938496 | − | 0.345289i | \(-0.887781\pi\) | ||||
−0.938496 | + | 0.345289i | \(0.887781\pi\) | |||||||
\(468\) | −3.53083 | −0.163213 | ||||||||
\(469\) | −36.0433 | −1.66432 | ||||||||
\(470\) | 11.2888 | 0.520713 | ||||||||
\(471\) | 7.65031 | 0.352508 | ||||||||
\(472\) | 22.2377 | 1.02357 | ||||||||
\(473\) | 7.66529 | 0.352450 | ||||||||
\(474\) | −17.5551 | −0.806333 | ||||||||
\(475\) | 15.5102 | 0.711656 | ||||||||
\(476\) | −31.4243 | −1.44033 | ||||||||
\(477\) | −6.39733 | −0.292913 | ||||||||
\(478\) | 61.5338 | 2.81449 | ||||||||
\(479\) | 37.2373 | 1.70142 | 0.850708 | − | 0.525638i | \(-0.176174\pi\) | ||||
0.850708 | + | 0.525638i | \(0.176174\pi\) | |||||||
\(480\) | −42.2075 | −1.92650 | ||||||||
\(481\) | 7.02474 | 0.320300 | ||||||||
\(482\) | 39.3888 | 1.79411 | ||||||||
\(483\) | 24.7493 | 1.12613 | ||||||||
\(484\) | −57.7490 | −2.62495 | ||||||||
\(485\) | −14.6762 | −0.666414 | ||||||||
\(486\) | −17.7828 | −0.806643 | ||||||||
\(487\) | −24.2374 | −1.09830 | −0.549151 | − | 0.835723i | \(-0.685049\pi\) | ||||
−0.549151 | + | 0.835723i | \(0.685049\pi\) | |||||||
\(488\) | −84.1620 | −3.80984 | ||||||||
\(489\) | 14.4414 | 0.653065 | ||||||||
\(490\) | −2.18243 | −0.0985920 | ||||||||
\(491\) | −33.4164 | −1.50806 | −0.754030 | − | 0.656839i | \(-0.771893\pi\) | ||||
−0.754030 | + | 0.656839i | \(0.771893\pi\) | |||||||
\(492\) | 58.5276 | 2.63863 | ||||||||
\(493\) | 14.7450 | 0.664083 | ||||||||
\(494\) | −10.1902 | −0.458477 | ||||||||
\(495\) | 0.468932 | 0.0210769 | ||||||||
\(496\) | −37.4748 | −1.68267 | ||||||||
\(497\) | −34.5532 | −1.54992 | ||||||||
\(498\) | 2.58397 | 0.115791 | ||||||||
\(499\) | 17.3723 | 0.777689 | 0.388845 | − | 0.921303i | \(-0.372874\pi\) | ||||
0.388845 | + | 0.921303i | \(0.372874\pi\) | |||||||
\(500\) | 46.1746 | 2.06499 | ||||||||
\(501\) | 30.3316 | 1.35511 | ||||||||
\(502\) | 40.5046 | 1.80781 | ||||||||
\(503\) | −23.6472 | −1.05438 | −0.527189 | − | 0.849748i | \(-0.676754\pi\) | ||||
−0.527189 | + | 0.849748i | \(0.676754\pi\) | |||||||
\(504\) | −15.4771 | −0.689404 | ||||||||
\(505\) | −8.34327 | −0.371271 | ||||||||
\(506\) | −12.0110 | −0.533955 | ||||||||
\(507\) | −1.90538 | −0.0846209 | ||||||||
\(508\) | −49.6288 | −2.20192 | ||||||||
\(509\) | −9.68169 | −0.429133 | −0.214567 | − | 0.976709i | \(-0.568834\pi\) | ||||
−0.214567 | + | 0.976709i | \(0.568834\pi\) | |||||||
\(510\) | 10.6849 | 0.473134 | ||||||||
\(511\) | −10.4202 | −0.460964 | ||||||||
\(512\) | −78.4867 | −3.46865 | ||||||||
\(513\) | −16.6882 | −0.736802 | ||||||||
\(514\) | 20.7785 | 0.916499 | ||||||||
\(515\) | 1.10298 | 0.0486030 | ||||||||
\(516\) | 98.5973 | 4.34051 | ||||||||
\(517\) | −3.78878 | −0.166630 | ||||||||
\(518\) | 47.8978 | 2.10451 | ||||||||
\(519\) | −14.3833 | −0.631357 | ||||||||
\(520\) | −8.89895 | −0.390245 | ||||||||
\(521\) | 6.18500 | 0.270970 | 0.135485 | − | 0.990779i | \(-0.456741\pi\) | ||||
0.135485 | + | 0.990779i | \(0.456741\pi\) | |||||||
\(522\) | 11.2965 | 0.494433 | ||||||||
\(523\) | −9.44238 | −0.412887 | −0.206443 | − | 0.978459i | \(-0.566189\pi\) | ||||
−0.206443 | + | 0.978459i | \(0.566189\pi\) | |||||||
\(524\) | 28.3885 | 1.24016 | ||||||||
\(525\) | 19.7744 | 0.863026 | ||||||||
\(526\) | 66.0054 | 2.87797 | ||||||||
\(527\) | 5.26035 | 0.229144 | ||||||||
\(528\) | 25.5474 | 1.11181 | ||||||||
\(529\) | 4.58166 | 0.199203 | ||||||||
\(530\) | −25.0804 | −1.08942 | ||||||||
\(531\) | −1.41256 | −0.0612999 | ||||||||
\(532\) | −51.1973 | −2.21968 | ||||||||
\(533\) | 5.48491 | 0.237578 | ||||||||
\(534\) | −81.3390 | −3.51988 | ||||||||
\(535\) | 15.5059 | 0.670380 | ||||||||
\(536\) | 144.645 | 6.24773 | ||||||||
\(537\) | 22.5822 | 0.974492 | ||||||||
\(538\) | 70.6909 | 3.04770 | ||||||||
\(539\) | 0.732473 | 0.0315499 | ||||||||
\(540\) | −22.6694 | −0.975537 | ||||||||
\(541\) | 26.2027 | 1.12654 | 0.563271 | − | 0.826272i | \(-0.309543\pi\) | ||||
0.563271 | + | 0.826272i | \(0.309543\pi\) | |||||||
\(542\) | −73.7897 | −3.16954 | ||||||||
\(543\) | −15.8368 | −0.679622 | ||||||||
\(544\) | 56.0539 | 2.40329 | ||||||||
\(545\) | −15.6138 | −0.668820 | ||||||||
\(546\) | −12.9917 | −0.555995 | ||||||||
\(547\) | −12.0358 | −0.514612 | −0.257306 | − | 0.966330i | \(-0.582835\pi\) | ||||
−0.257306 | + | 0.966330i | \(0.582835\pi\) | |||||||
\(548\) | −54.1898 | −2.31487 | ||||||||
\(549\) | 5.34604 | 0.228163 | ||||||||
\(550\) | −9.59667 | −0.409203 | ||||||||
\(551\) | 24.0230 | 1.02341 | ||||||||
\(552\) | −99.3214 | −4.22740 | ||||||||
\(553\) | −8.26567 | −0.351492 | ||||||||
\(554\) | 78.8449 | 3.34980 | ||||||||
\(555\) | −12.0005 | −0.509393 | ||||||||
\(556\) | 103.482 | 4.38861 | ||||||||
\(557\) | −21.6892 | −0.918999 | −0.459500 | − | 0.888178i | \(-0.651971\pi\) | ||||
−0.459500 | + | 0.888178i | \(0.651971\pi\) | |||||||
\(558\) | 4.03006 | 0.170606 | ||||||||
\(559\) | 9.24004 | 0.390812 | ||||||||
\(560\) | −35.8401 | −1.51452 | ||||||||
\(561\) | −3.58609 | −0.151405 | ||||||||
\(562\) | 19.6832 | 0.830285 | ||||||||
\(563\) | 43.0617 | 1.81483 | 0.907416 | − | 0.420233i | \(-0.138052\pi\) | ||||
0.907416 | + | 0.420233i | \(0.138052\pi\) | |||||||
\(564\) | −48.7345 | −2.05209 | ||||||||
\(565\) | −1.53926 | −0.0647574 | ||||||||
\(566\) | 26.9327 | 1.13207 | ||||||||
\(567\) | −25.9543 | −1.08998 | ||||||||
\(568\) | 138.666 | 5.81828 | ||||||||
\(569\) | 31.2329 | 1.30935 | 0.654675 | − | 0.755910i | \(-0.272805\pi\) | ||||
0.654675 | + | 0.755910i | \(0.272805\pi\) | |||||||
\(570\) | 17.4081 | 0.729143 | ||||||||
\(571\) | 22.9090 | 0.958712 | 0.479356 | − | 0.877620i | \(-0.340870\pi\) | ||||
0.479356 | + | 0.877620i | \(0.340870\pi\) | |||||||
\(572\) | 4.64584 | 0.194252 | ||||||||
\(573\) | −12.3969 | −0.517887 | ||||||||
\(574\) | 37.3986 | 1.56099 | ||||||||
\(575\) | 22.0374 | 0.919025 | ||||||||
\(576\) | 22.5638 | 0.940158 | ||||||||
\(577\) | −37.8639 | −1.57630 | −0.788148 | − | 0.615485i | \(-0.788960\pi\) | ||||
−0.788148 | + | 0.615485i | \(0.788960\pi\) | |||||||
\(578\) | 32.6765 | 1.35916 | ||||||||
\(579\) | −41.5646 | −1.72736 | ||||||||
\(580\) | 32.6331 | 1.35501 | ||||||||
\(581\) | 1.21664 | 0.0504747 | ||||||||
\(582\) | 85.9851 | 3.56420 | ||||||||
\(583\) | 8.41756 | 0.348620 | ||||||||
\(584\) | 41.8174 | 1.73042 | ||||||||
\(585\) | 0.565269 | 0.0233710 | ||||||||
\(586\) | 16.4225 | 0.678407 | ||||||||
\(587\) | 8.26364 | 0.341077 | 0.170539 | − | 0.985351i | \(-0.445449\pi\) | ||||
0.170539 | + | 0.985351i | \(0.445449\pi\) | |||||||
\(588\) | 9.42168 | 0.388544 | ||||||||
\(589\) | 8.57029 | 0.353133 | ||||||||
\(590\) | −5.53786 | −0.227990 | ||||||||
\(591\) | 37.6432 | 1.54843 | ||||||||
\(592\) | −113.538 | −4.66637 | ||||||||
\(593\) | 15.2281 | 0.625345 | 0.312673 | − | 0.949861i | \(-0.398776\pi\) | ||||
0.312673 | + | 0.949861i | \(0.398776\pi\) | |||||||
\(594\) | 10.3255 | 0.423662 | ||||||||
\(595\) | 5.03088 | 0.206246 | ||||||||
\(596\) | 129.067 | 5.28677 | ||||||||
\(597\) | −27.1963 | −1.11307 | ||||||||
\(598\) | −14.4785 | −0.592072 | ||||||||
\(599\) | −21.1014 | −0.862179 | −0.431089 | − | 0.902309i | \(-0.641871\pi\) | ||||
−0.431089 | + | 0.902309i | \(0.641871\pi\) | |||||||
\(600\) | −79.3567 | −3.23972 | ||||||||
\(601\) | −46.0284 | −1.87754 | −0.938770 | − | 0.344546i | \(-0.888033\pi\) | ||||
−0.938770 | + | 0.344546i | \(0.888033\pi\) | |||||||
\(602\) | 63.0027 | 2.56780 | ||||||||
\(603\) | −9.18799 | −0.374164 | ||||||||
\(604\) | 30.3819 | 1.23622 | ||||||||
\(605\) | 9.24533 | 0.375876 | ||||||||
\(606\) | 48.8816 | 1.98568 | ||||||||
\(607\) | 28.4268 | 1.15381 | 0.576904 | − | 0.816812i | \(-0.304261\pi\) | ||||
0.576904 | + | 0.816812i | \(0.304261\pi\) | |||||||
\(608\) | 91.3243 | 3.70369 | ||||||||
\(609\) | 30.6276 | 1.24109 | ||||||||
\(610\) | 20.9589 | 0.848600 | ||||||||
\(611\) | −4.56715 | −0.184767 | ||||||||
\(612\) | −8.01055 | −0.323807 | ||||||||
\(613\) | 31.3037 | 1.26435 | 0.632173 | − | 0.774827i | \(-0.282163\pi\) | ||||
0.632173 | + | 0.774827i | \(0.282163\pi\) | |||||||
\(614\) | 17.4067 | 0.702478 | ||||||||
\(615\) | −9.36998 | −0.377834 | ||||||||
\(616\) | 20.3646 | 0.820514 | ||||||||
\(617\) | 1.00000 | 0.0402585 | ||||||||
\(618\) | −6.46213 | −0.259945 | ||||||||
\(619\) | −6.63834 | −0.266818 | −0.133409 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133409 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(620\) | 11.6420 | 0.467553 | ||||||||
\(621\) | −23.7112 | −0.951497 | ||||||||
\(622\) | −90.3779 | −3.62382 | ||||||||
\(623\) | −38.2978 | −1.53437 | ||||||||
\(624\) | 30.7958 | 1.23282 | ||||||||
\(625\) | 13.5884 | 0.543536 | ||||||||
\(626\) | 47.5563 | 1.90073 | ||||||||
\(627\) | −5.84255 | −0.233329 | ||||||||
\(628\) | −22.4857 | −0.897278 | ||||||||
\(629\) | 15.9373 | 0.635463 | ||||||||
\(630\) | 3.85426 | 0.153557 | ||||||||
\(631\) | 23.7435 | 0.945212 | 0.472606 | − | 0.881274i | \(-0.343313\pi\) | ||||
0.472606 | + | 0.881274i | \(0.343313\pi\) | |||||||
\(632\) | 33.1710 | 1.31947 | ||||||||
\(633\) | −28.0224 | −1.11379 | ||||||||
\(634\) | −24.2024 | −0.961202 | ||||||||
\(635\) | 7.94533 | 0.315301 | ||||||||
\(636\) | 108.274 | 4.29333 | ||||||||
\(637\) | 0.882952 | 0.0349838 | ||||||||
\(638\) | −14.8638 | −0.588464 | ||||||||
\(639\) | −8.80815 | −0.348445 | ||||||||
\(640\) | 44.1567 | 1.74545 | ||||||||
\(641\) | −26.0610 | −1.02935 | −0.514674 | − | 0.857386i | \(-0.672087\pi\) | ||||
−0.514674 | + | 0.857386i | \(0.672087\pi\) | |||||||
\(642\) | −90.8462 | −3.58541 | ||||||||
\(643\) | −11.2452 | −0.443466 | −0.221733 | − | 0.975107i | \(-0.571171\pi\) | ||||
−0.221733 | + | 0.975107i | \(0.571171\pi\) | |||||||
\(644\) | −72.7429 | −2.86647 | ||||||||
\(645\) | −15.7850 | −0.621532 | ||||||||
\(646\) | −23.1189 | −0.909599 | ||||||||
\(647\) | −16.4529 | −0.646831 | −0.323416 | − | 0.946257i | \(-0.604831\pi\) | ||||
−0.323416 | + | 0.946257i | \(0.604831\pi\) | |||||||
\(648\) | 104.157 | 4.09168 | ||||||||
\(649\) | 1.85864 | 0.0729579 | ||||||||
\(650\) | −11.5682 | −0.453742 | ||||||||
\(651\) | 10.9265 | 0.428244 | ||||||||
\(652\) | −42.4462 | −1.66232 | ||||||||
\(653\) | −18.6852 | −0.731209 | −0.365604 | − | 0.930770i | \(-0.619138\pi\) | ||||
−0.365604 | + | 0.930770i | \(0.619138\pi\) | |||||||
\(654\) | 91.4778 | 3.57707 | ||||||||
\(655\) | −4.54486 | −0.177582 | ||||||||
\(656\) | −88.6502 | −3.46121 | ||||||||
\(657\) | −2.65628 | −0.103631 | ||||||||
\(658\) | −31.1409 | −1.21400 | ||||||||
\(659\) | 19.7470 | 0.769234 | 0.384617 | − | 0.923076i | \(-0.374333\pi\) | ||||
0.384617 | + | 0.923076i | \(0.374333\pi\) | |||||||
\(660\) | −7.93659 | −0.308931 | ||||||||
\(661\) | 40.6988 | 1.58300 | 0.791500 | − | 0.611169i | \(-0.209300\pi\) | ||||
0.791500 | + | 0.611169i | \(0.209300\pi\) | |||||||
\(662\) | 69.8196 | 2.71362 | ||||||||
\(663\) | −4.32282 | −0.167884 | ||||||||
\(664\) | −4.88250 | −0.189478 | ||||||||
\(665\) | 8.19643 | 0.317844 | ||||||||
\(666\) | 12.2099 | 0.473124 | ||||||||
\(667\) | 34.1327 | 1.32162 | ||||||||
\(668\) | −89.1503 | −3.44933 | ||||||||
\(669\) | −21.5457 | −0.833004 | ||||||||
\(670\) | −36.0210 | −1.39161 | ||||||||
\(671\) | −7.03429 | −0.271556 | ||||||||
\(672\) | 116.432 | 4.49147 | ||||||||
\(673\) | −3.18889 | −0.122923 | −0.0614613 | − | 0.998109i | \(-0.519576\pi\) | ||||
−0.0614613 | + | 0.998109i | \(0.519576\pi\) | |||||||
\(674\) | 42.6746 | 1.64376 | ||||||||
\(675\) | −18.9450 | −0.729192 | ||||||||
\(676\) | 5.60028 | 0.215395 | ||||||||
\(677\) | −22.9844 | −0.883362 | −0.441681 | − | 0.897172i | \(-0.645618\pi\) | ||||
−0.441681 | + | 0.897172i | \(0.645618\pi\) | |||||||
\(678\) | 9.01824 | 0.346344 | ||||||||
\(679\) | 40.4854 | 1.55369 | ||||||||
\(680\) | −20.1894 | −0.774229 | ||||||||
\(681\) | −47.2674 | −1.81129 | ||||||||
\(682\) | −5.30272 | −0.203052 | ||||||||
\(683\) | 25.7789 | 0.986404 | 0.493202 | − | 0.869915i | \(-0.335826\pi\) | ||||
0.493202 | + | 0.869915i | \(0.335826\pi\) | |||||||
\(684\) | −13.0510 | −0.499017 | ||||||||
\(685\) | 8.67552 | 0.331474 | ||||||||
\(686\) | 53.7495 | 2.05217 | ||||||||
\(687\) | −36.9753 | −1.41070 | ||||||||
\(688\) | −149.343 | −5.69364 | ||||||||
\(689\) | 10.1469 | 0.386564 | ||||||||
\(690\) | 24.7340 | 0.941607 | ||||||||
\(691\) | −30.1322 | −1.14628 | −0.573141 | − | 0.819457i | \(-0.694275\pi\) | ||||
−0.573141 | + | 0.819457i | \(0.694275\pi\) | |||||||
\(692\) | 42.2753 | 1.60707 | ||||||||
\(693\) | −1.29358 | −0.0491390 | ||||||||
\(694\) | 49.7585 | 1.88881 | ||||||||
\(695\) | −16.5669 | −0.628420 | ||||||||
\(696\) | −122.912 | −4.65896 | ||||||||
\(697\) | 12.4438 | 0.471344 | ||||||||
\(698\) | 38.0220 | 1.43915 | ||||||||
\(699\) | −9.50271 | −0.359425 | ||||||||
\(700\) | −58.1208 | −2.19676 | ||||||||
\(701\) | 32.5446 | 1.22919 | 0.614597 | − | 0.788841i | \(-0.289319\pi\) | ||||
0.614597 | + | 0.788841i | \(0.289319\pi\) | |||||||
\(702\) | 12.4468 | 0.469774 | ||||||||
\(703\) | 25.9655 | 0.979307 | ||||||||
\(704\) | −29.6893 | −1.11896 | ||||||||
\(705\) | 7.80215 | 0.293846 | ||||||||
\(706\) | −97.6672 | −3.67575 | ||||||||
\(707\) | 23.0155 | 0.865586 | ||||||||
\(708\) | 23.9073 | 0.898492 | ||||||||
\(709\) | 5.36266 | 0.201399 | 0.100699 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100699 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(710\) | −34.5319 | −1.29596 | ||||||||
\(711\) | −2.10705 | −0.0790204 | ||||||||
\(712\) | 153.693 | 5.75988 | ||||||||
\(713\) | 12.1770 | 0.456031 | ||||||||
\(714\) | −29.4749 | −1.10307 | ||||||||
\(715\) | −0.743777 | −0.0278157 | ||||||||
\(716\) | −66.3733 | −2.48049 | ||||||||
\(717\) | 42.5285 | 1.58826 | ||||||||
\(718\) | 45.5668 | 1.70054 | ||||||||
\(719\) | −49.1337 | −1.83238 | −0.916188 | − | 0.400748i | \(-0.868750\pi\) | ||||
−0.916188 | + | 0.400748i | \(0.868750\pi\) | |||||||
\(720\) | −9.13619 | −0.340486 | ||||||||
\(721\) | −3.04264 | −0.113314 | ||||||||
\(722\) | 14.7145 | 0.547619 | ||||||||
\(723\) | 27.2232 | 1.01244 | ||||||||
\(724\) | 46.5474 | 1.72992 | ||||||||
\(725\) | 27.2717 | 1.01284 | ||||||||
\(726\) | −54.1666 | −2.01031 | ||||||||
\(727\) | −9.75190 | −0.361678 | −0.180839 | − | 0.983513i | \(-0.557881\pi\) | ||||
−0.180839 | + | 0.983513i | \(0.557881\pi\) | |||||||
\(728\) | 24.5483 | 0.909821 | ||||||||
\(729\) | 19.1914 | 0.710791 | ||||||||
\(730\) | −10.4138 | −0.385432 | ||||||||
\(731\) | 20.9633 | 0.775355 | ||||||||
\(732\) | −90.4808 | −3.34427 | ||||||||
\(733\) | −11.5395 | −0.426222 | −0.213111 | − | 0.977028i | \(-0.568360\pi\) | ||||
−0.213111 | + | 0.977028i | \(0.568360\pi\) | |||||||
\(734\) | 32.4400 | 1.19738 | ||||||||
\(735\) | −1.50837 | −0.0556369 | ||||||||
\(736\) | 129.757 | 4.78290 | ||||||||
\(737\) | 12.0895 | 0.445322 | ||||||||
\(738\) | 9.53347 | 0.350932 | ||||||||
\(739\) | 23.7484 | 0.873600 | 0.436800 | − | 0.899559i | \(-0.356112\pi\) | ||||
0.436800 | + | 0.899559i | \(0.356112\pi\) | |||||||
\(740\) | 35.2718 | 1.29662 | ||||||||
\(741\) | −7.04284 | −0.258725 | ||||||||
\(742\) | 69.1858 | 2.53989 | ||||||||
\(743\) | 19.7555 | 0.724758 | 0.362379 | − | 0.932031i | \(-0.381965\pi\) | ||||
0.362379 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(744\) | −43.8492 | −1.60759 | ||||||||
\(745\) | −20.6629 | −0.757031 | ||||||||
\(746\) | −22.9333 | −0.839649 | ||||||||
\(747\) | 0.310140 | 0.0113474 | ||||||||
\(748\) | 10.5402 | 0.385389 | ||||||||
\(749\) | −42.7741 | −1.56293 | ||||||||
\(750\) | 43.3102 | 1.58146 | ||||||||
\(751\) | 11.2707 | 0.411275 | 0.205638 | − | 0.978628i | \(-0.434073\pi\) | ||||
0.205638 | + | 0.978628i | \(0.434073\pi\) | |||||||
\(752\) | 73.8168 | 2.69182 | ||||||||
\(753\) | 27.9944 | 1.02017 | ||||||||
\(754\) | −17.9174 | −0.652514 | ||||||||
\(755\) | −4.86399 | −0.177019 | ||||||||
\(756\) | 62.5351 | 2.27438 | ||||||||
\(757\) | −21.6872 | −0.788234 | −0.394117 | − | 0.919060i | \(-0.628950\pi\) | ||||
−0.394117 | + | 0.919060i | \(0.628950\pi\) | |||||||
\(758\) | 55.5447 | 2.01747 | ||||||||
\(759\) | −8.30131 | −0.301318 | ||||||||
\(760\) | −32.8931 | −1.19316 | ||||||||
\(761\) | −28.3931 | −1.02925 | −0.514624 | − | 0.857416i | \(-0.672068\pi\) | ||||
−0.514624 | + | 0.857416i | \(0.672068\pi\) | |||||||
\(762\) | −46.5501 | −1.68633 | ||||||||
\(763\) | 43.0715 | 1.55929 | ||||||||
\(764\) | 36.4368 | 1.31824 | ||||||||
\(765\) | 1.28245 | 0.0463671 | ||||||||
\(766\) | −91.0558 | −3.28998 | ||||||||
\(767\) | 2.24047 | 0.0808988 | ||||||||
\(768\) | −122.323 | −4.41396 | ||||||||
\(769\) | 11.4571 | 0.413155 | 0.206578 | − | 0.978430i | \(-0.433767\pi\) | ||||
0.206578 | + | 0.978430i | \(0.433767\pi\) | |||||||
\(770\) | −5.07140 | −0.182761 | ||||||||
\(771\) | 14.3609 | 0.517194 | ||||||||
\(772\) | 122.166 | 4.39686 | ||||||||
\(773\) | 39.3912 | 1.41680 | 0.708402 | − | 0.705809i | \(-0.249416\pi\) | ||||
0.708402 | + | 0.705809i | \(0.249416\pi\) | |||||||
\(774\) | 16.0604 | 0.577278 | ||||||||
\(775\) | 9.72927 | 0.349486 | ||||||||
\(776\) | −162.472 | −5.83240 | ||||||||
\(777\) | 33.1042 | 1.18761 | ||||||||
\(778\) | −33.1181 | −1.18734 | ||||||||
\(779\) | 20.2738 | 0.726385 | ||||||||
\(780\) | −9.56707 | −0.342556 | ||||||||
\(781\) | 11.5897 | 0.414712 | ||||||||
\(782\) | −32.8481 | −1.17465 | ||||||||
\(783\) | −29.3429 | −1.04863 | ||||||||
\(784\) | −14.2708 | −0.509670 | ||||||||
\(785\) | 3.59986 | 0.128484 | ||||||||
\(786\) | 26.6274 | 0.949768 | ||||||||
\(787\) | −15.5583 | −0.554594 | −0.277297 | − | 0.960784i | \(-0.589439\pi\) | ||||
−0.277297 | + | 0.960784i | \(0.589439\pi\) | |||||||
\(788\) | −110.641 | −3.94141 | ||||||||
\(789\) | 45.6190 | 1.62408 | ||||||||
\(790\) | −8.26056 | −0.293898 | ||||||||
\(791\) | 4.24616 | 0.150976 | ||||||||
\(792\) | 5.19126 | 0.184463 | ||||||||
\(793\) | −8.47940 | −0.301112 | ||||||||
\(794\) | 53.9842 | 1.91583 | ||||||||
\(795\) | −17.3341 | −0.614777 | ||||||||
\(796\) | 79.9351 | 2.83323 | ||||||||
\(797\) | 39.1590 | 1.38708 | 0.693542 | − | 0.720416i | \(-0.256049\pi\) | ||||
0.693542 | + | 0.720416i | \(0.256049\pi\) | |||||||
\(798\) | −48.0213 | −1.69993 | ||||||||
\(799\) | −10.3617 | −0.366570 | ||||||||
\(800\) | 103.674 | 3.66544 | ||||||||
\(801\) | −9.76269 | −0.344948 | ||||||||
\(802\) | 14.1270 | 0.498842 | ||||||||
\(803\) | 3.49511 | 0.123340 | ||||||||
\(804\) | 155.505 | 5.48424 | ||||||||
\(805\) | 11.6458 | 0.410460 | ||||||||
\(806\) | −6.39211 | −0.225152 | ||||||||
\(807\) | 48.8574 | 1.71986 | ||||||||
\(808\) | −92.3634 | −3.24933 | ||||||||
\(809\) | −3.98605 | −0.140142 | −0.0700711 | − | 0.997542i | \(-0.522323\pi\) | ||||
−0.0700711 | + | 0.997542i | \(0.522323\pi\) | |||||||
\(810\) | −25.9382 | −0.911377 | ||||||||
\(811\) | −27.1271 | −0.952562 | −0.476281 | − | 0.879293i | \(-0.658016\pi\) | ||||
−0.476281 | + | 0.879293i | \(0.658016\pi\) | |||||||
\(812\) | −90.0205 | −3.15910 | ||||||||
\(813\) | −50.9991 | −1.78862 | ||||||||
\(814\) | −16.0657 | −0.563102 | ||||||||
\(815\) | 6.79543 | 0.238033 | ||||||||
\(816\) | 69.8679 | 2.44586 | ||||||||
\(817\) | 34.1539 | 1.19489 | ||||||||
\(818\) | −10.5267 | −0.368056 | ||||||||
\(819\) | −1.55933 | −0.0544874 | ||||||||
\(820\) | 27.5402 | 0.961745 | ||||||||
\(821\) | 51.9286 | 1.81232 | 0.906161 | − | 0.422934i | \(-0.139000\pi\) | ||||
0.906161 | + | 0.422934i | \(0.139000\pi\) | |||||||
\(822\) | −50.8281 | −1.77283 | ||||||||
\(823\) | −29.8238 | −1.03959 | −0.519796 | − | 0.854290i | \(-0.673992\pi\) | ||||
−0.519796 | + | 0.854290i | \(0.673992\pi\) | |||||||
\(824\) | 12.2104 | 0.425370 | ||||||||
\(825\) | −6.63265 | −0.230919 | ||||||||
\(826\) | 15.2766 | 0.531539 | ||||||||
\(827\) | 25.2158 | 0.876839 | 0.438419 | − | 0.898770i | \(-0.355538\pi\) | ||||
0.438419 | + | 0.898770i | \(0.355538\pi\) | |||||||
\(828\) | −18.5433 | −0.644424 | ||||||||
\(829\) | 5.19751 | 0.180517 | 0.0902586 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902586 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(830\) | 1.21589 | 0.0422041 | ||||||||
\(831\) | 54.4930 | 1.89034 | ||||||||
\(832\) | −35.7886 | −1.24075 | ||||||||
\(833\) | 2.00319 | 0.0694065 | ||||||||
\(834\) | 97.0623 | 3.36099 | ||||||||
\(835\) | 14.2725 | 0.493921 | ||||||||
\(836\) | 17.1724 | 0.593919 | ||||||||
\(837\) | −10.4682 | −0.361834 | ||||||||
\(838\) | 9.98556 | 0.344946 | ||||||||
\(839\) | 17.9428 | 0.619453 | 0.309727 | − | 0.950826i | \(-0.399762\pi\) | ||||
0.309727 | + | 0.950826i | \(0.399762\pi\) | |||||||
\(840\) | −41.9364 | −1.44694 | ||||||||
\(841\) | 13.2397 | 0.456543 | ||||||||
\(842\) | −35.7183 | −1.23093 | ||||||||
\(843\) | 13.6039 | 0.468542 | ||||||||
\(844\) | 82.3631 | 2.83505 | ||||||||
\(845\) | −0.896577 | −0.0308432 | ||||||||
\(846\) | −7.93829 | −0.272924 | ||||||||
\(847\) | −25.5039 | −0.876323 | ||||||||
\(848\) | −163.999 | −5.63176 | ||||||||
\(849\) | 18.6143 | 0.638841 | ||||||||
\(850\) | −26.2453 | −0.900205 | ||||||||
\(851\) | 36.8927 | 1.26467 | ||||||||
\(852\) | 149.076 | 5.10728 | ||||||||
\(853\) | −15.3351 | −0.525064 | −0.262532 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262532 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(854\) | −57.8164 | −1.97844 | ||||||||
\(855\) | 2.08940 | 0.0714559 | ||||||||
\(856\) | 171.657 | 5.86711 | ||||||||
\(857\) | −21.4849 | −0.733909 | −0.366955 | − | 0.930239i | \(-0.619600\pi\) | ||||
−0.366955 | + | 0.930239i | \(0.619600\pi\) | |||||||
\(858\) | 4.35764 | 0.148767 | ||||||||
\(859\) | 19.0104 | 0.648627 | 0.324314 | − | 0.945950i | \(-0.394867\pi\) | ||||
0.324314 | + | 0.945950i | \(0.394867\pi\) | |||||||
\(860\) | 46.3950 | 1.58206 | ||||||||
\(861\) | 25.8477 | 0.880887 | ||||||||
\(862\) | −87.5386 | −2.98158 | ||||||||
\(863\) | −24.3660 | −0.829429 | −0.414714 | − | 0.909952i | \(-0.636119\pi\) | ||||
−0.414714 | + | 0.909952i | \(0.636119\pi\) | |||||||
\(864\) | −111.548 | −3.79495 | ||||||||
\(865\) | −6.76807 | −0.230121 | ||||||||
\(866\) | 14.7762 | 0.502116 | ||||||||
\(867\) | 22.5841 | 0.766996 | ||||||||
\(868\) | −32.1151 | −1.09006 | ||||||||
\(869\) | 2.77244 | 0.0940485 | ||||||||
\(870\) | 30.6087 | 1.03773 | ||||||||
\(871\) | 14.5732 | 0.493792 | ||||||||
\(872\) | −172.850 | −5.85345 | ||||||||
\(873\) | 10.3203 | 0.349291 | ||||||||
\(874\) | −53.5169 | −1.81024 | ||||||||
\(875\) | 20.3922 | 0.689383 | ||||||||
\(876\) | 44.9570 | 1.51896 | ||||||||
\(877\) | −52.0935 | −1.75907 | −0.879537 | − | 0.475831i | \(-0.842147\pi\) | ||||
−0.879537 | + | 0.475831i | \(0.842147\pi\) | |||||||
\(878\) | 83.3524 | 2.81301 | ||||||||
\(879\) | 11.3503 | 0.382835 | ||||||||
\(880\) | 12.0213 | 0.405239 | ||||||||
\(881\) | −18.6743 | −0.629153 | −0.314576 | − | 0.949232i | \(-0.601862\pi\) | ||||
−0.314576 | + | 0.949232i | \(0.601862\pi\) | |||||||
\(882\) | 1.53468 | 0.0516755 | ||||||||
\(883\) | 38.9810 | 1.31181 | 0.655907 | − | 0.754841i | \(-0.272286\pi\) | ||||
0.655907 | + | 0.754841i | \(0.272286\pi\) | |||||||
\(884\) | 12.7056 | 0.427335 | ||||||||
\(885\) | −3.82745 | −0.128658 | ||||||||
\(886\) | −58.0360 | −1.94976 | ||||||||
\(887\) | −21.2810 | −0.714547 | −0.357273 | − | 0.934000i | \(-0.616294\pi\) | ||||
−0.357273 | + | 0.934000i | \(0.616294\pi\) | |||||||
\(888\) | −132.850 | −4.45817 | ||||||||
\(889\) | −21.9177 | −0.735096 | ||||||||
\(890\) | −38.2741 | −1.28295 | ||||||||
\(891\) | 8.70548 | 0.291644 | ||||||||
\(892\) | 63.3269 | 2.12034 | ||||||||
\(893\) | −16.8815 | −0.564918 | ||||||||
\(894\) | 121.060 | 4.04885 | ||||||||
\(895\) | 10.6260 | 0.355189 | ||||||||
\(896\) | −121.809 | −4.06935 | ||||||||
\(897\) | −10.0067 | −0.334115 | ||||||||
\(898\) | 74.1802 | 2.47542 | ||||||||
\(899\) | 15.0692 | 0.502585 | ||||||||
\(900\) | −14.8159 | −0.493863 | ||||||||
\(901\) | 23.0206 | 0.766928 | ||||||||
\(902\) | −12.5441 | −0.417672 | ||||||||
\(903\) | 43.5438 | 1.44905 | ||||||||
\(904\) | −17.0403 | −0.566751 | ||||||||
\(905\) | −7.45201 | −0.247713 | ||||||||
\(906\) | 28.4971 | 0.946754 | ||||||||
\(907\) | 36.2069 | 1.20223 | 0.601116 | − | 0.799162i | \(-0.294723\pi\) | ||||
0.601116 | + | 0.799162i | \(0.294723\pi\) | |||||||
\(908\) | 138.928 | 4.61049 | ||||||||
\(909\) | 5.86700 | 0.194596 | ||||||||
\(910\) | −6.11327 | −0.202653 | ||||||||
\(911\) | −23.8016 | −0.788582 | −0.394291 | − | 0.918986i | \(-0.629010\pi\) | ||||
−0.394291 | + | 0.918986i | \(0.629010\pi\) | |||||||
\(912\) | 113.830 | 3.76930 | ||||||||
\(913\) | −0.408081 | −0.0135055 | ||||||||
\(914\) | 79.0481 | 2.61468 | ||||||||
\(915\) | 14.4855 | 0.478877 | ||||||||
\(916\) | 108.677 | 3.59080 | ||||||||
\(917\) | 12.5373 | 0.414018 | ||||||||
\(918\) | 28.2386 | 0.932013 | ||||||||
\(919\) | 56.0665 | 1.84946 | 0.924732 | − | 0.380619i | \(-0.124289\pi\) | ||||
0.924732 | + | 0.380619i | \(0.124289\pi\) | |||||||
\(920\) | −46.7357 | −1.54083 | ||||||||
\(921\) | 12.0305 | 0.396419 | ||||||||
\(922\) | −5.89093 | −0.194007 | ||||||||
\(923\) | 13.9707 | 0.459851 | ||||||||
\(924\) | 21.8936 | 0.720246 | ||||||||
\(925\) | 29.4768 | 0.969193 | ||||||||
\(926\) | −15.2623 | −0.501551 | ||||||||
\(927\) | −0.775615 | −0.0254745 | ||||||||
\(928\) | 160.576 | 5.27117 | ||||||||
\(929\) | 44.0479 | 1.44517 | 0.722583 | − | 0.691284i | \(-0.242955\pi\) | ||||
0.722583 | + | 0.691284i | \(0.242955\pi\) | |||||||
\(930\) | 10.9198 | 0.358073 | ||||||||
\(931\) | 3.26365 | 0.106962 | ||||||||
\(932\) | 27.9303 | 0.914887 | ||||||||
\(933\) | −62.4639 | −2.04498 | ||||||||
\(934\) | 111.824 | 3.65900 | ||||||||
\(935\) | −1.68744 | −0.0551851 | ||||||||
\(936\) | 6.25775 | 0.204541 | ||||||||
\(937\) | −59.5467 | −1.94531 | −0.972653 | − | 0.232262i | \(-0.925387\pi\) | ||||
−0.972653 | + | 0.232262i | \(0.925387\pi\) | |||||||
\(938\) | 99.3663 | 3.24443 | ||||||||
\(939\) | 32.8681 | 1.07261 | ||||||||
\(940\) | −22.9320 | −0.747960 | ||||||||
\(941\) | −47.9447 | −1.56295 | −0.781477 | − | 0.623934i | \(-0.785533\pi\) | ||||
−0.781477 | + | 0.623934i | \(0.785533\pi\) | |||||||
\(942\) | −21.0908 | −0.687177 | ||||||||
\(943\) | 28.8058 | 0.938045 | ||||||||
\(944\) | −36.2118 | −1.17859 | ||||||||
\(945\) | −10.0116 | −0.325676 | ||||||||
\(946\) | −21.1321 | −0.687065 | ||||||||
\(947\) | 35.8937 | 1.16639 | 0.583194 | − | 0.812333i | \(-0.301803\pi\) | ||||
0.583194 | + | 0.812333i | \(0.301803\pi\) | |||||||
\(948\) | 35.6614 | 1.15823 | ||||||||
\(949\) | 4.21314 | 0.136764 | ||||||||
\(950\) | −42.7594 | −1.38730 | ||||||||
\(951\) | −16.7273 | −0.542420 | ||||||||
\(952\) | 55.6939 | 1.80505 | ||||||||
\(953\) | 9.76399 | 0.316287 | 0.158143 | − | 0.987416i | \(-0.449449\pi\) | ||||
0.158143 | + | 0.987416i | \(0.449449\pi\) | |||||||
\(954\) | 17.6365 | 0.571004 | ||||||||
\(955\) | −5.83335 | −0.188763 | ||||||||
\(956\) | −125.000 | −4.04277 | ||||||||
\(957\) | −10.2730 | −0.332079 | ||||||||
\(958\) | −102.658 | −3.31673 | ||||||||
\(959\) | −23.9320 | −0.772804 | ||||||||
\(960\) | 61.1385 | 1.97324 | ||||||||
\(961\) | −25.6240 | −0.826581 | ||||||||
\(962\) | −19.3662 | −0.624392 | ||||||||
\(963\) | −10.9038 | −0.351370 | ||||||||
\(964\) | −80.0143 | −2.57709 | ||||||||
\(965\) | −19.5582 | −0.629601 | ||||||||
\(966\) | −68.2304 | −2.19528 | ||||||||
\(967\) | −45.6133 | −1.46682 | −0.733412 | − | 0.679785i | \(-0.762073\pi\) | ||||
−0.733412 | + | 0.679785i | \(0.762073\pi\) | |||||||
\(968\) | 102.350 | 3.28964 | ||||||||
\(969\) | −15.9784 | −0.513300 | ||||||||
\(970\) | 40.4603 | 1.29910 | ||||||||
\(971\) | 10.1981 | 0.327273 | 0.163637 | − | 0.986521i | \(-0.447678\pi\) | ||||
0.163637 | + | 0.986521i | \(0.447678\pi\) | |||||||
\(972\) | 36.1239 | 1.15867 | ||||||||
\(973\) | 45.7010 | 1.46511 | ||||||||
\(974\) | 66.8191 | 2.14102 | ||||||||
\(975\) | −7.99526 | −0.256053 | ||||||||
\(976\) | 137.049 | 4.38683 | ||||||||
\(977\) | 7.28968 | 0.233218 | 0.116609 | − | 0.993178i | \(-0.462798\pi\) | ||||
0.116609 | + | 0.993178i | \(0.462798\pi\) | |||||||
\(978\) | −39.8131 | −1.27308 | ||||||||
\(979\) | 12.8457 | 0.410550 | ||||||||
\(980\) | 4.43338 | 0.141619 | ||||||||
\(981\) | 10.9796 | 0.350552 | ||||||||
\(982\) | 92.1243 | 2.93981 | ||||||||
\(983\) | 57.3648 | 1.82965 | 0.914826 | − | 0.403849i | \(-0.132328\pi\) | ||||
0.914826 | + | 0.403849i | \(0.132328\pi\) | |||||||
\(984\) | −103.729 | −3.30677 | ||||||||
\(985\) | 17.7130 | 0.564384 | ||||||||
\(986\) | −40.6500 | −1.29456 | ||||||||
\(987\) | −21.5227 | −0.685076 | ||||||||
\(988\) | 20.7003 | 0.658563 | ||||||||
\(989\) | 48.5271 | 1.54307 | ||||||||
\(990\) | −1.29278 | −0.0410872 | ||||||||
\(991\) | −30.2611 | −0.961276 | −0.480638 | − | 0.876919i | \(-0.659595\pi\) | ||||
−0.480638 | + | 0.876919i | \(0.659595\pi\) | |||||||
\(992\) | 57.2861 | 1.81884 | ||||||||
\(993\) | 48.2552 | 1.53133 | ||||||||
\(994\) | 95.2584 | 3.02141 | ||||||||
\(995\) | −12.7972 | −0.405699 | ||||||||
\(996\) | −5.24907 | −0.166323 | ||||||||
\(997\) | −54.9786 | −1.74119 | −0.870595 | − | 0.492001i | \(-0.836266\pi\) | ||||
−0.870595 | + | 0.492001i | \(0.836266\pi\) | |||||||
\(998\) | −47.8929 | −1.51602 | ||||||||
\(999\) | −31.7156 | −1.00344 |
(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 | 8021.2.a.c.1.5 | ✓ | 169 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8021.2.a.c.1.5 | ✓ | 169 | 1.1 | even | 1 | trivial |