Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.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: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(62\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25455 | −1.59420 | −0.797102 | − | 0.603844i | \(-0.793635\pi\) | ||||
−0.797102 | + | 0.603844i | \(0.793635\pi\) | |||||||
\(3\) | 2.07382 | 1.19732 | 0.598660 | − | 0.801003i | \(-0.295700\pi\) | ||||
0.598660 | + | 0.801003i | \(0.295700\pi\) | |||||||
\(4\) | 3.08298 | 1.54149 | ||||||||
\(5\) | 1.31329 | 0.587320 | 0.293660 | − | 0.955910i | \(-0.405127\pi\) | ||||
0.293660 | + | 0.955910i | \(0.405127\pi\) | |||||||
\(6\) | −4.67552 | −1.90877 | ||||||||
\(7\) | −0.325302 | −0.122953 | −0.0614763 | − | 0.998109i | \(-0.519581\pi\) | ||||
−0.0614763 | + | 0.998109i | \(0.519581\pi\) | |||||||
\(8\) | −2.44162 | −0.863244 | ||||||||
\(9\) | 1.30073 | 0.433576 | ||||||||
\(10\) | −2.96087 | −0.936308 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 6.39354 | 1.84566 | ||||||||
\(13\) | −3.54069 | −0.982009 | −0.491005 | − | 0.871157i | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(14\) | 0.733408 | 0.196011 | ||||||||
\(15\) | 2.72352 | 0.703210 | ||||||||
\(16\) | −0.661206 | −0.165302 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.93255 | −0.691209 | ||||||||
\(19\) | 5.22856 | 1.19951 | 0.599756 | − | 0.800183i | \(-0.295264\pi\) | ||||
0.599756 | + | 0.800183i | \(0.295264\pi\) | |||||||
\(20\) | 4.04883 | 0.905347 | ||||||||
\(21\) | −0.674617 | −0.147214 | ||||||||
\(22\) | −2.25455 | −0.480671 | ||||||||
\(23\) | −1.98649 | −0.414212 | −0.207106 | − | 0.978318i | \(-0.566405\pi\) | ||||
−0.207106 | + | 0.978318i | \(0.566405\pi\) | |||||||
\(24\) | −5.06348 | −1.03358 | ||||||||
\(25\) | −3.27528 | −0.655055 | ||||||||
\(26\) | 7.98264 | 1.56552 | ||||||||
\(27\) | −3.52398 | −0.678191 | ||||||||
\(28\) | −1.00290 | −0.189530 | ||||||||
\(29\) | 0.424618 | 0.0788495 | 0.0394248 | − | 0.999223i | \(-0.487447\pi\) | ||||
0.0394248 | + | 0.999223i | \(0.487447\pi\) | |||||||
\(30\) | −6.14030 | −1.12106 | ||||||||
\(31\) | −5.82810 | −1.04676 | −0.523379 | − | 0.852100i | \(-0.675329\pi\) | ||||
−0.523379 | + | 0.852100i | \(0.675329\pi\) | |||||||
\(32\) | 6.37396 | 1.12677 | ||||||||
\(33\) | 2.07382 | 0.361006 | ||||||||
\(34\) | 2.25455 | 0.386651 | ||||||||
\(35\) | −0.427215 | −0.0722124 | ||||||||
\(36\) | 4.01011 | 0.668352 | ||||||||
\(37\) | 7.52448 | 1.23702 | 0.618508 | − | 0.785778i | \(-0.287737\pi\) | ||||
0.618508 | + | 0.785778i | \(0.287737\pi\) | |||||||
\(38\) | −11.7880 | −1.91227 | ||||||||
\(39\) | −7.34274 | −1.17578 | ||||||||
\(40\) | −3.20655 | −0.507000 | ||||||||
\(41\) | 5.24681 | 0.819414 | 0.409707 | − | 0.912217i | \(-0.365631\pi\) | ||||
0.409707 | + | 0.912217i | \(0.365631\pi\) | |||||||
\(42\) | 1.52096 | 0.234689 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 3.08298 | 0.464776 | ||||||||
\(45\) | 1.70823 | 0.254648 | ||||||||
\(46\) | 4.47864 | 0.660339 | ||||||||
\(47\) | −7.13969 | −1.04143 | −0.520716 | − | 0.853730i | \(-0.674335\pi\) | ||||
−0.520716 | + | 0.853730i | \(0.674335\pi\) | |||||||
\(48\) | −1.37122 | −0.197919 | ||||||||
\(49\) | −6.89418 | −0.984883 | ||||||||
\(50\) | 7.38426 | 1.04429 | ||||||||
\(51\) | −2.07382 | −0.290393 | ||||||||
\(52\) | −10.9159 | −1.51376 | ||||||||
\(53\) | −9.02173 | −1.23923 | −0.619615 | − | 0.784906i | \(-0.712711\pi\) | ||||
−0.619615 | + | 0.784906i | \(0.712711\pi\) | |||||||
\(54\) | 7.94498 | 1.08118 | ||||||||
\(55\) | 1.31329 | 0.177084 | ||||||||
\(56\) | 0.794264 | 0.106138 | ||||||||
\(57\) | 10.8431 | 1.43620 | ||||||||
\(58\) | −0.957320 | −0.125702 | ||||||||
\(59\) | 0.0984967 | 0.0128232 | 0.00641159 | − | 0.999979i | \(-0.497959\pi\) | ||||
0.00641159 | + | 0.999979i | \(0.497959\pi\) | |||||||
\(60\) | 8.39655 | 1.08399 | ||||||||
\(61\) | −0.224215 | −0.0287078 | −0.0143539 | − | 0.999897i | \(-0.504569\pi\) | ||||
−0.0143539 | + | 0.999897i | \(0.504569\pi\) | |||||||
\(62\) | 13.1397 | 1.66875 | ||||||||
\(63\) | −0.423129 | −0.0533093 | ||||||||
\(64\) | −13.0480 | −1.63100 | ||||||||
\(65\) | −4.64994 | −0.576754 | ||||||||
\(66\) | −4.67552 | −0.575517 | ||||||||
\(67\) | 11.7607 | 1.43679 | 0.718397 | − | 0.695633i | \(-0.244876\pi\) | ||||
0.718397 | + | 0.695633i | \(0.244876\pi\) | |||||||
\(68\) | −3.08298 | −0.373866 | ||||||||
\(69\) | −4.11963 | −0.495945 | ||||||||
\(70\) | 0.963175 | 0.115121 | ||||||||
\(71\) | 0.278786 | 0.0330858 | 0.0165429 | − | 0.999863i | \(-0.494734\pi\) | ||||
0.0165429 | + | 0.999863i | \(0.494734\pi\) | |||||||
\(72\) | −3.17589 | −0.374282 | ||||||||
\(73\) | −14.0167 | −1.64053 | −0.820265 | − | 0.571984i | \(-0.806174\pi\) | ||||
−0.820265 | + | 0.571984i | \(0.806174\pi\) | |||||||
\(74\) | −16.9643 | −1.97206 | ||||||||
\(75\) | −6.79233 | −0.784311 | ||||||||
\(76\) | 16.1195 | 1.84904 | ||||||||
\(77\) | −0.325302 | −0.0370716 | ||||||||
\(78\) | 16.5546 | 1.87443 | ||||||||
\(79\) | −2.68260 | −0.301816 | −0.150908 | − | 0.988548i | \(-0.548220\pi\) | ||||
−0.150908 | + | 0.988548i | \(0.548220\pi\) | |||||||
\(80\) | −0.868353 | −0.0970848 | ||||||||
\(81\) | −11.2103 | −1.24559 | ||||||||
\(82\) | −11.8292 | −1.30631 | ||||||||
\(83\) | 12.3668 | 1.35744 | 0.678719 | − | 0.734398i | \(-0.262536\pi\) | ||||
0.678719 | + | 0.734398i | \(0.262536\pi\) | |||||||
\(84\) | −2.07983 | −0.226928 | ||||||||
\(85\) | −1.31329 | −0.142446 | ||||||||
\(86\) | −2.25455 | −0.243114 | ||||||||
\(87\) | 0.880581 | 0.0944081 | ||||||||
\(88\) | −2.44162 | −0.260278 | ||||||||
\(89\) | 6.90487 | 0.731914 | 0.365957 | − | 0.930632i | \(-0.380742\pi\) | ||||
0.365957 | + | 0.930632i | \(0.380742\pi\) | |||||||
\(90\) | −3.85128 | −0.405961 | ||||||||
\(91\) | 1.15179 | 0.120741 | ||||||||
\(92\) | −6.12431 | −0.638504 | ||||||||
\(93\) | −12.0864 | −1.25330 | ||||||||
\(94\) | 16.0968 | 1.66025 | ||||||||
\(95\) | 6.86659 | 0.704498 | ||||||||
\(96\) | 13.2184 | 1.34910 | ||||||||
\(97\) | −6.24062 | −0.633639 | −0.316820 | − | 0.948486i | \(-0.602615\pi\) | ||||
−0.316820 | + | 0.948486i | \(0.602615\pi\) | |||||||
\(98\) | 15.5432 | 1.57010 | ||||||||
\(99\) | 1.30073 | 0.130728 | ||||||||
\(100\) | −10.0976 | −1.00976 | ||||||||
\(101\) | −16.3688 | −1.62876 | −0.814380 | − | 0.580332i | \(-0.802923\pi\) | ||||
−0.814380 | + | 0.580332i | \(0.802923\pi\) | |||||||
\(102\) | 4.67552 | 0.462946 | ||||||||
\(103\) | −2.95430 | −0.291095 | −0.145548 | − | 0.989351i | \(-0.546494\pi\) | ||||
−0.145548 | + | 0.989351i | \(0.546494\pi\) | |||||||
\(104\) | 8.64501 | 0.847713 | ||||||||
\(105\) | −0.885966 | −0.0864614 | ||||||||
\(106\) | 20.3399 | 1.97559 | ||||||||
\(107\) | 16.8977 | 1.63356 | 0.816781 | − | 0.576948i | \(-0.195757\pi\) | ||||
0.816781 | + | 0.576948i | \(0.195757\pi\) | |||||||
\(108\) | −10.8644 | −1.04542 | ||||||||
\(109\) | −0.557419 | −0.0533910 | −0.0266955 | − | 0.999644i | \(-0.508498\pi\) | ||||
−0.0266955 | + | 0.999644i | \(0.508498\pi\) | |||||||
\(110\) | −2.96087 | −0.282307 | ||||||||
\(111\) | 15.6044 | 1.48111 | ||||||||
\(112\) | 0.215091 | 0.0203242 | ||||||||
\(113\) | −8.82213 | −0.829916 | −0.414958 | − | 0.909841i | \(-0.636204\pi\) | ||||
−0.414958 | + | 0.909841i | \(0.636204\pi\) | |||||||
\(114\) | −24.4462 | −2.28960 | ||||||||
\(115\) | −2.60884 | −0.243275 | ||||||||
\(116\) | 1.30909 | 0.121546 | ||||||||
\(117\) | −4.60547 | −0.425776 | ||||||||
\(118\) | −0.222065 | −0.0204428 | ||||||||
\(119\) | 0.325302 | 0.0298204 | ||||||||
\(120\) | −6.64981 | −0.607042 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.505504 | 0.0457662 | ||||||||
\(123\) | 10.8809 | 0.981101 | ||||||||
\(124\) | −17.9679 | −1.61357 | ||||||||
\(125\) | −10.8678 | −0.972047 | ||||||||
\(126\) | 0.953964 | 0.0849859 | ||||||||
\(127\) | 4.17182 | 0.370189 | 0.185095 | − | 0.982721i | \(-0.440741\pi\) | ||||
0.185095 | + | 0.982721i | \(0.440741\pi\) | |||||||
\(128\) | 16.6693 | 1.47338 | ||||||||
\(129\) | 2.07382 | 0.182590 | ||||||||
\(130\) | 10.4835 | 0.919463 | ||||||||
\(131\) | −18.4481 | −1.61182 | −0.805910 | − | 0.592038i | \(-0.798324\pi\) | ||||
−0.805910 | + | 0.592038i | \(0.798324\pi\) | |||||||
\(132\) | 6.39354 | 0.556486 | ||||||||
\(133\) | −1.70086 | −0.147483 | ||||||||
\(134\) | −26.5150 | −2.29054 | ||||||||
\(135\) | −4.62800 | −0.398315 | ||||||||
\(136\) | 2.44162 | 0.209367 | ||||||||
\(137\) | −15.2031 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(138\) | 9.28789 | 0.790638 | ||||||||
\(139\) | −5.22427 | −0.443116 | −0.221558 | − | 0.975147i | \(-0.571114\pi\) | ||||
−0.221558 | + | 0.975147i | \(0.571114\pi\) | |||||||
\(140\) | −1.31709 | −0.111315 | ||||||||
\(141\) | −14.8064 | −1.24693 | ||||||||
\(142\) | −0.628535 | −0.0527455 | ||||||||
\(143\) | −3.54069 | −0.296087 | ||||||||
\(144\) | −0.860049 | −0.0716708 | ||||||||
\(145\) | 0.557645 | 0.0463099 | ||||||||
\(146\) | 31.6013 | 2.61534 | ||||||||
\(147\) | −14.2973 | −1.17922 | ||||||||
\(148\) | 23.1978 | 1.90685 | ||||||||
\(149\) | 18.3752 | 1.50536 | 0.752678 | − | 0.658388i | \(-0.228762\pi\) | ||||
0.752678 | + | 0.658388i | \(0.228762\pi\) | |||||||
\(150\) | 15.3136 | 1.25035 | ||||||||
\(151\) | −1.89912 | −0.154548 | −0.0772739 | − | 0.997010i | \(-0.524622\pi\) | ||||
−0.0772739 | + | 0.997010i | \(0.524622\pi\) | |||||||
\(152\) | −12.7662 | −1.03547 | ||||||||
\(153\) | −1.30073 | −0.105158 | ||||||||
\(154\) | 0.733408 | 0.0590997 | ||||||||
\(155\) | −7.65397 | −0.614782 | ||||||||
\(156\) | −22.6375 | −1.81245 | ||||||||
\(157\) | −7.88912 | −0.629621 | −0.314810 | − | 0.949155i | \(-0.601941\pi\) | ||||
−0.314810 | + | 0.949155i | \(0.601941\pi\) | |||||||
\(158\) | 6.04805 | 0.481157 | ||||||||
\(159\) | −18.7094 | −1.48375 | ||||||||
\(160\) | 8.37084 | 0.661773 | ||||||||
\(161\) | 0.646210 | 0.0509285 | ||||||||
\(162\) | 25.2741 | 1.98572 | ||||||||
\(163\) | 2.94099 | 0.230356 | 0.115178 | − | 0.993345i | \(-0.463256\pi\) | ||||
0.115178 | + | 0.993345i | \(0.463256\pi\) | |||||||
\(164\) | 16.1758 | 1.26312 | ||||||||
\(165\) | 2.72352 | 0.212026 | ||||||||
\(166\) | −27.8816 | −2.16403 | ||||||||
\(167\) | 13.9539 | 1.07978 | 0.539892 | − | 0.841734i | \(-0.318465\pi\) | ||||
0.539892 | + | 0.841734i | \(0.318465\pi\) | |||||||
\(168\) | 1.64716 | 0.127081 | ||||||||
\(169\) | −0.463547 | −0.0356575 | ||||||||
\(170\) | 2.96087 | 0.227088 | ||||||||
\(171\) | 6.80093 | 0.520080 | ||||||||
\(172\) | 3.08298 | 0.235075 | ||||||||
\(173\) | −7.60582 | −0.578260 | −0.289130 | − | 0.957290i | \(-0.593366\pi\) | ||||
−0.289130 | + | 0.957290i | \(0.593366\pi\) | |||||||
\(174\) | −1.98531 | −0.150506 | ||||||||
\(175\) | 1.06545 | 0.0805407 | ||||||||
\(176\) | −0.661206 | −0.0498403 | ||||||||
\(177\) | 0.204264 | 0.0153535 | ||||||||
\(178\) | −15.5673 | −1.16682 | ||||||||
\(179\) | −2.52249 | −0.188540 | −0.0942700 | − | 0.995547i | \(-0.530052\pi\) | ||||
−0.0942700 | + | 0.995547i | \(0.530052\pi\) | |||||||
\(180\) | 5.26643 | 0.392537 | ||||||||
\(181\) | 24.4917 | 1.82046 | 0.910228 | − | 0.414108i | \(-0.135906\pi\) | ||||
0.910228 | + | 0.414108i | \(0.135906\pi\) | |||||||
\(182\) | −2.59677 | −0.192485 | ||||||||
\(183\) | −0.464982 | −0.0343725 | ||||||||
\(184\) | 4.85026 | 0.357566 | ||||||||
\(185\) | 9.88180 | 0.726524 | ||||||||
\(186\) | 27.2494 | 1.99802 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | −22.0115 | −1.60535 | ||||||||
\(189\) | 1.14636 | 0.0833853 | ||||||||
\(190\) | −15.4811 | −1.12311 | ||||||||
\(191\) | −4.75117 | −0.343783 | −0.171891 | − | 0.985116i | \(-0.554988\pi\) | ||||
−0.171891 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(192\) | −27.0592 | −1.95283 | ||||||||
\(193\) | 9.58513 | 0.689952 | 0.344976 | − | 0.938611i | \(-0.387887\pi\) | ||||
0.344976 | + | 0.938611i | \(0.387887\pi\) | |||||||
\(194\) | 14.0698 | 1.01015 | ||||||||
\(195\) | −9.64313 | −0.690559 | ||||||||
\(196\) | −21.2546 | −1.51819 | ||||||||
\(197\) | −5.15260 | −0.367108 | −0.183554 | − | 0.983010i | \(-0.558760\pi\) | ||||
−0.183554 | + | 0.983010i | \(0.558760\pi\) | |||||||
\(198\) | −2.93255 | −0.208407 | ||||||||
\(199\) | −26.5657 | −1.88319 | −0.941595 | − | 0.336748i | \(-0.890673\pi\) | ||||
−0.941595 | + | 0.336748i | \(0.890673\pi\) | |||||||
\(200\) | 7.99699 | 0.565472 | ||||||||
\(201\) | 24.3895 | 1.72030 | ||||||||
\(202\) | 36.9043 | 2.59658 | ||||||||
\(203\) | −0.138129 | −0.00969475 | ||||||||
\(204\) | −6.39354 | −0.447637 | ||||||||
\(205\) | 6.89056 | 0.481258 | ||||||||
\(206\) | 6.66060 | 0.464066 | ||||||||
\(207\) | −2.58389 | −0.179593 | ||||||||
\(208\) | 2.34112 | 0.162328 | ||||||||
\(209\) | 5.22856 | 0.361667 | ||||||||
\(210\) | 1.99745 | 0.137837 | ||||||||
\(211\) | −4.08796 | −0.281427 | −0.140713 | − | 0.990050i | \(-0.544940\pi\) | ||||
−0.140713 | + | 0.990050i | \(0.544940\pi\) | |||||||
\(212\) | −27.8138 | −1.91026 | ||||||||
\(213\) | 0.578151 | 0.0396143 | ||||||||
\(214\) | −38.0966 | −2.60423 | ||||||||
\(215\) | 1.31329 | 0.0895654 | ||||||||
\(216\) | 8.60424 | 0.585444 | ||||||||
\(217\) | 1.89589 | 0.128702 | ||||||||
\(218\) | 1.25673 | 0.0851162 | ||||||||
\(219\) | −29.0681 | −1.96424 | ||||||||
\(220\) | 4.04883 | 0.272972 | ||||||||
\(221\) | 3.54069 | 0.238172 | ||||||||
\(222\) | −35.1809 | −2.36118 | ||||||||
\(223\) | 0.684309 | 0.0458247 | 0.0229123 | − | 0.999737i | \(-0.492706\pi\) | ||||
0.0229123 | + | 0.999737i | \(0.492706\pi\) | |||||||
\(224\) | −2.07346 | −0.138539 | ||||||||
\(225\) | −4.26025 | −0.284016 | ||||||||
\(226\) | 19.8899 | 1.32306 | ||||||||
\(227\) | −6.52355 | −0.432983 | −0.216492 | − | 0.976284i | \(-0.569461\pi\) | ||||
−0.216492 | + | 0.976284i | \(0.569461\pi\) | |||||||
\(228\) | 33.4290 | 2.21389 | ||||||||
\(229\) | −19.6404 | −1.29787 | −0.648937 | − | 0.760842i | \(-0.724786\pi\) | ||||
−0.648937 | + | 0.760842i | \(0.724786\pi\) | |||||||
\(230\) | 5.88174 | 0.387830 | ||||||||
\(231\) | −0.674617 | −0.0443866 | ||||||||
\(232\) | −1.03676 | −0.0680664 | ||||||||
\(233\) | −10.8315 | −0.709595 | −0.354798 | − | 0.934943i | \(-0.615450\pi\) | ||||
−0.354798 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(234\) | 10.3832 | 0.678774 | ||||||||
\(235\) | −9.37647 | −0.611653 | ||||||||
\(236\) | 0.303663 | 0.0197668 | ||||||||
\(237\) | −5.56323 | −0.361371 | ||||||||
\(238\) | −0.733408 | −0.0475398 | ||||||||
\(239\) | −11.5067 | −0.744307 | −0.372154 | − | 0.928171i | \(-0.621381\pi\) | ||||
−0.372154 | + | 0.928171i | \(0.621381\pi\) | |||||||
\(240\) | −1.80081 | −0.116242 | ||||||||
\(241\) | −10.1150 | −0.651566 | −0.325783 | − | 0.945445i | \(-0.605628\pi\) | ||||
−0.325783 | + | 0.945445i | \(0.605628\pi\) | |||||||
\(242\) | −2.25455 | −0.144928 | ||||||||
\(243\) | −12.6762 | −0.813177 | ||||||||
\(244\) | −0.691251 | −0.0442528 | ||||||||
\(245\) | −9.05404 | −0.578441 | ||||||||
\(246\) | −24.5316 | −1.56408 | ||||||||
\(247\) | −18.5127 | −1.17793 | ||||||||
\(248\) | 14.2300 | 0.903607 | ||||||||
\(249\) | 25.6466 | 1.62529 | ||||||||
\(250\) | 24.5020 | 1.54964 | ||||||||
\(251\) | −24.3533 | −1.53717 | −0.768584 | − | 0.639749i | \(-0.779038\pi\) | ||||
−0.768584 | + | 0.639749i | \(0.779038\pi\) | |||||||
\(252\) | −1.30450 | −0.0821756 | ||||||||
\(253\) | −1.98649 | −0.124890 | ||||||||
\(254\) | −9.40556 | −0.590157 | ||||||||
\(255\) | −2.72352 | −0.170553 | ||||||||
\(256\) | −11.4858 | −0.717865 | ||||||||
\(257\) | −4.70560 | −0.293528 | −0.146764 | − | 0.989172i | \(-0.546886\pi\) | ||||
−0.146764 | + | 0.989172i | \(0.546886\pi\) | |||||||
\(258\) | −4.67552 | −0.291085 | ||||||||
\(259\) | −2.44773 | −0.152094 | ||||||||
\(260\) | −14.3356 | −0.889059 | ||||||||
\(261\) | 0.552312 | 0.0341873 | ||||||||
\(262\) | 41.5921 | 2.56957 | ||||||||
\(263\) | −9.53630 | −0.588034 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(264\) | −5.06348 | −0.311636 | ||||||||
\(265\) | −11.8481 | −0.727824 | ||||||||
\(266\) | 3.83466 | 0.235118 | ||||||||
\(267\) | 14.3194 | 0.876336 | ||||||||
\(268\) | 36.2579 | 2.21480 | ||||||||
\(269\) | −26.7296 | −1.62973 | −0.814867 | − | 0.579648i | \(-0.803190\pi\) | ||||
−0.814867 | + | 0.579648i | \(0.803190\pi\) | |||||||
\(270\) | 10.4340 | 0.634996 | ||||||||
\(271\) | −21.7486 | −1.32113 | −0.660567 | − | 0.750767i | \(-0.729684\pi\) | ||||
−0.660567 | + | 0.750767i | \(0.729684\pi\) | |||||||
\(272\) | 0.661206 | 0.0400915 | ||||||||
\(273\) | 2.38861 | 0.144565 | ||||||||
\(274\) | 34.2762 | 2.07070 | ||||||||
\(275\) | −3.27528 | −0.197507 | ||||||||
\(276\) | −12.7007 | −0.764493 | ||||||||
\(277\) | −29.6604 | −1.78212 | −0.891060 | − | 0.453886i | \(-0.850037\pi\) | ||||
−0.891060 | + | 0.453886i | \(0.850037\pi\) | |||||||
\(278\) | 11.7783 | 0.706418 | ||||||||
\(279\) | −7.58078 | −0.453849 | ||||||||
\(280\) | 1.04310 | 0.0623369 | ||||||||
\(281\) | 2.49934 | 0.149098 | 0.0745492 | − | 0.997217i | \(-0.476248\pi\) | ||||
0.0745492 | + | 0.997217i | \(0.476248\pi\) | |||||||
\(282\) | 33.3818 | 1.98786 | ||||||||
\(283\) | 15.1833 | 0.902554 | 0.451277 | − | 0.892384i | \(-0.350969\pi\) | ||||
0.451277 | + | 0.892384i | \(0.350969\pi\) | |||||||
\(284\) | 0.859490 | 0.0510013 | ||||||||
\(285\) | 14.2401 | 0.843509 | ||||||||
\(286\) | 7.98264 | 0.472023 | ||||||||
\(287\) | −1.70680 | −0.100749 | ||||||||
\(288\) | 8.29079 | 0.488540 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −1.25724 | −0.0738274 | ||||||||
\(291\) | −12.9419 | −0.758669 | ||||||||
\(292\) | −43.2132 | −2.52886 | ||||||||
\(293\) | 6.97776 | 0.407645 | 0.203823 | − | 0.979008i | \(-0.434663\pi\) | ||||
0.203823 | + | 0.979008i | \(0.434663\pi\) | |||||||
\(294\) | 32.2339 | 1.87992 | ||||||||
\(295\) | 0.129354 | 0.00753131 | ||||||||
\(296\) | −18.3719 | −1.06785 | ||||||||
\(297\) | −3.52398 | −0.204482 | ||||||||
\(298\) | −41.4278 | −2.39985 | ||||||||
\(299\) | 7.03355 | 0.406760 | ||||||||
\(300\) | −20.9406 | −1.20901 | ||||||||
\(301\) | −0.325302 | −0.0187501 | ||||||||
\(302\) | 4.28164 | 0.246381 | ||||||||
\(303\) | −33.9460 | −1.95015 | ||||||||
\(304\) | −3.45715 | −0.198281 | ||||||||
\(305\) | −0.294459 | −0.0168607 | ||||||||
\(306\) | 2.93255 | 0.167643 | ||||||||
\(307\) | 24.5376 | 1.40043 | 0.700217 | − | 0.713930i | \(-0.253087\pi\) | ||||
0.700217 | + | 0.713930i | \(0.253087\pi\) | |||||||
\(308\) | −1.00290 | −0.0571454 | ||||||||
\(309\) | −6.12668 | −0.348534 | ||||||||
\(310\) | 17.2562 | 0.980088 | ||||||||
\(311\) | 7.57324 | 0.429439 | 0.214719 | − | 0.976676i | \(-0.431116\pi\) | ||||
0.214719 | + | 0.976676i | \(0.431116\pi\) | |||||||
\(312\) | 17.9282 | 1.01498 | ||||||||
\(313\) | 13.1084 | 0.740932 | 0.370466 | − | 0.928846i | \(-0.379198\pi\) | ||||
0.370466 | + | 0.928846i | \(0.379198\pi\) | |||||||
\(314\) | 17.7864 | 1.00374 | ||||||||
\(315\) | −0.555690 | −0.0313096 | ||||||||
\(316\) | −8.27040 | −0.465246 | ||||||||
\(317\) | −4.28748 | −0.240809 | −0.120404 | − | 0.992725i | \(-0.538419\pi\) | ||||
−0.120404 | + | 0.992725i | \(0.538419\pi\) | |||||||
\(318\) | 42.1813 | 2.36541 | ||||||||
\(319\) | 0.424618 | 0.0237740 | ||||||||
\(320\) | −17.1357 | −0.957917 | ||||||||
\(321\) | 35.0428 | 1.95590 | ||||||||
\(322\) | −1.45691 | −0.0811904 | ||||||||
\(323\) | −5.22856 | −0.290925 | ||||||||
\(324\) | −34.5611 | −1.92006 | ||||||||
\(325\) | 11.5967 | 0.643271 | ||||||||
\(326\) | −6.63059 | −0.367234 | ||||||||
\(327\) | −1.15599 | −0.0639262 | ||||||||
\(328\) | −12.8107 | −0.707354 | ||||||||
\(329\) | 2.32255 | 0.128047 | ||||||||
\(330\) | −6.14030 | −0.338012 | ||||||||
\(331\) | 8.90844 | 0.489652 | 0.244826 | − | 0.969567i | \(-0.421269\pi\) | ||||
0.244826 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(332\) | 38.1267 | 2.09247 | ||||||||
\(333\) | 9.78730 | 0.536341 | ||||||||
\(334\) | −31.4597 | −1.72140 | ||||||||
\(335\) | 15.4451 | 0.843858 | ||||||||
\(336\) | 0.446061 | 0.0243346 | ||||||||
\(337\) | 11.3994 | 0.620967 | 0.310484 | − | 0.950579i | \(-0.399509\pi\) | ||||
0.310484 | + | 0.950579i | \(0.399509\pi\) | |||||||
\(338\) | 1.04509 | 0.0568453 | ||||||||
\(339\) | −18.2955 | −0.993675 | ||||||||
\(340\) | −4.04883 | −0.219579 | ||||||||
\(341\) | −5.82810 | −0.315609 | ||||||||
\(342\) | −15.3330 | −0.829114 | ||||||||
\(343\) | 4.51980 | 0.244046 | ||||||||
\(344\) | −2.44162 | −0.131643 | ||||||||
\(345\) | −5.41025 | −0.291278 | ||||||||
\(346\) | 17.1477 | 0.921865 | ||||||||
\(347\) | −22.0429 | −1.18333 | −0.591663 | − | 0.806186i | \(-0.701528\pi\) | ||||
−0.591663 | + | 0.806186i | \(0.701528\pi\) | |||||||
\(348\) | 2.71481 | 0.145529 | ||||||||
\(349\) | −1.37949 | −0.0738422 | −0.0369211 | − | 0.999318i | \(-0.511755\pi\) | ||||
−0.0369211 | + | 0.999318i | \(0.511755\pi\) | |||||||
\(350\) | −2.40211 | −0.128398 | ||||||||
\(351\) | 12.4773 | 0.665990 | ||||||||
\(352\) | 6.37396 | 0.339733 | ||||||||
\(353\) | 12.0503 | 0.641375 | 0.320688 | − | 0.947185i | \(-0.396086\pi\) | ||||
0.320688 | + | 0.947185i | \(0.396086\pi\) | |||||||
\(354\) | −0.460524 | −0.0244766 | ||||||||
\(355\) | 0.366126 | 0.0194319 | ||||||||
\(356\) | 21.2875 | 1.12824 | ||||||||
\(357\) | 0.674617 | 0.0357045 | ||||||||
\(358\) | 5.68707 | 0.300571 | ||||||||
\(359\) | −15.7103 | −0.829159 | −0.414579 | − | 0.910013i | \(-0.636071\pi\) | ||||
−0.414579 | + | 0.910013i | \(0.636071\pi\) | |||||||
\(360\) | −4.17085 | −0.219823 | ||||||||
\(361\) | 8.33780 | 0.438831 | ||||||||
\(362\) | −55.2177 | −2.90218 | ||||||||
\(363\) | 2.07382 | 0.108847 | ||||||||
\(364\) | 3.55095 | 0.186120 | ||||||||
\(365\) | −18.4079 | −0.963516 | ||||||||
\(366\) | 1.04832 | 0.0547968 | ||||||||
\(367\) | 14.7856 | 0.771803 | 0.385902 | − | 0.922540i | \(-0.373890\pi\) | ||||
0.385902 | + | 0.922540i | \(0.373890\pi\) | |||||||
\(368\) | 1.31348 | 0.0684699 | ||||||||
\(369\) | 6.82467 | 0.355278 | ||||||||
\(370\) | −22.2790 | −1.15823 | ||||||||
\(371\) | 2.93478 | 0.152366 | ||||||||
\(372\) | −37.2622 | −1.93195 | ||||||||
\(373\) | 21.2815 | 1.10191 | 0.550957 | − | 0.834534i | \(-0.314263\pi\) | ||||
0.550957 | + | 0.834534i | \(0.314263\pi\) | |||||||
\(374\) | 2.25455 | 0.116580 | ||||||||
\(375\) | −22.5379 | −1.16385 | ||||||||
\(376\) | 17.4324 | 0.899009 | ||||||||
\(377\) | −1.50344 | −0.0774310 | ||||||||
\(378\) | −2.58452 | −0.132933 | ||||||||
\(379\) | −7.57927 | −0.389321 | −0.194660 | − | 0.980871i | \(-0.562360\pi\) | ||||
−0.194660 | + | 0.980871i | \(0.562360\pi\) | |||||||
\(380\) | 21.1696 | 1.08598 | ||||||||
\(381\) | 8.65160 | 0.443235 | ||||||||
\(382\) | 10.7117 | 0.548060 | ||||||||
\(383\) | −12.4305 | −0.635171 | −0.317585 | − | 0.948230i | \(-0.602872\pi\) | ||||
−0.317585 | + | 0.948230i | \(0.602872\pi\) | |||||||
\(384\) | 34.5692 | 1.76410 | ||||||||
\(385\) | −0.427215 | −0.0217729 | ||||||||
\(386\) | −21.6101 | −1.09993 | ||||||||
\(387\) | 1.30073 | 0.0661197 | ||||||||
\(388\) | −19.2397 | −0.976747 | ||||||||
\(389\) | −8.68606 | −0.440401 | −0.220200 | − | 0.975455i | \(-0.570671\pi\) | ||||
−0.220200 | + | 0.975455i | \(0.570671\pi\) | |||||||
\(390\) | 21.7409 | 1.10089 | ||||||||
\(391\) | 1.98649 | 0.100461 | ||||||||
\(392\) | 16.8330 | 0.850194 | ||||||||
\(393\) | −38.2581 | −1.92987 | ||||||||
\(394\) | 11.6168 | 0.585245 | ||||||||
\(395\) | −3.52302 | −0.177263 | ||||||||
\(396\) | 4.01011 | 0.201516 | ||||||||
\(397\) | 7.48503 | 0.375663 | 0.187832 | − | 0.982201i | \(-0.439854\pi\) | ||||
0.187832 | + | 0.982201i | \(0.439854\pi\) | |||||||
\(398\) | 59.8935 | 3.00219 | ||||||||
\(399\) | −3.52727 | −0.176585 | ||||||||
\(400\) | 2.16563 | 0.108282 | ||||||||
\(401\) | 31.7349 | 1.58477 | 0.792383 | − | 0.610024i | \(-0.208840\pi\) | ||||
0.792383 | + | 0.610024i | \(0.208840\pi\) | |||||||
\(402\) | −54.9873 | −2.74252 | ||||||||
\(403\) | 20.6355 | 1.02793 | ||||||||
\(404\) | −50.4648 | −2.51072 | ||||||||
\(405\) | −14.7223 | −0.731558 | ||||||||
\(406\) | 0.311418 | 0.0154554 | ||||||||
\(407\) | 7.52448 | 0.372975 | ||||||||
\(408\) | 5.06348 | 0.250680 | ||||||||
\(409\) | 17.1220 | 0.846629 | 0.423315 | − | 0.905983i | \(-0.360866\pi\) | ||||
0.423315 | + | 0.905983i | \(0.360866\pi\) | |||||||
\(410\) | −15.5351 | −0.767224 | ||||||||
\(411\) | −31.5286 | −1.55519 | ||||||||
\(412\) | −9.10803 | −0.448720 | ||||||||
\(413\) | −0.0320412 | −0.00157664 | ||||||||
\(414\) | 5.82549 | 0.286307 | ||||||||
\(415\) | 16.2412 | 0.797250 | ||||||||
\(416\) | −22.5682 | −1.10650 | ||||||||
\(417\) | −10.8342 | −0.530552 | ||||||||
\(418\) | −11.7880 | −0.576571 | ||||||||
\(419\) | 6.19243 | 0.302520 | 0.151260 | − | 0.988494i | \(-0.451667\pi\) | ||||
0.151260 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(420\) | −2.73141 | −0.133279 | ||||||||
\(421\) | −12.2466 | −0.596862 | −0.298431 | − | 0.954431i | \(-0.596463\pi\) | ||||
−0.298431 | + | 0.954431i | \(0.596463\pi\) | |||||||
\(422\) | 9.21649 | 0.448651 | ||||||||
\(423\) | −9.28680 | −0.451540 | ||||||||
\(424\) | 22.0276 | 1.06976 | ||||||||
\(425\) | 3.27528 | 0.158874 | ||||||||
\(426\) | −1.30347 | −0.0631532 | ||||||||
\(427\) | 0.0729377 | 0.00352970 | ||||||||
\(428\) | 52.0952 | 2.51812 | ||||||||
\(429\) | −7.34274 | −0.354511 | ||||||||
\(430\) | −2.96087 | −0.142786 | ||||||||
\(431\) | −23.0747 | −1.11147 | −0.555735 | − | 0.831359i | \(-0.687563\pi\) | ||||
−0.555735 | + | 0.831359i | \(0.687563\pi\) | |||||||
\(432\) | 2.33008 | 0.112106 | ||||||||
\(433\) | −18.7038 | −0.898849 | −0.449424 | − | 0.893318i | \(-0.648371\pi\) | ||||
−0.449424 | + | 0.893318i | \(0.648371\pi\) | |||||||
\(434\) | −4.27438 | −0.205177 | ||||||||
\(435\) | 1.15645 | 0.0554478 | ||||||||
\(436\) | −1.71851 | −0.0823017 | ||||||||
\(437\) | −10.3865 | −0.496853 | ||||||||
\(438\) | 65.5354 | 3.13140 | ||||||||
\(439\) | −6.12026 | −0.292104 | −0.146052 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146052 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(440\) | −3.20655 | −0.152866 | ||||||||
\(441\) | −8.96745 | −0.427022 | ||||||||
\(442\) | −7.98264 | −0.379695 | ||||||||
\(443\) | −2.57359 | −0.122275 | −0.0611375 | − | 0.998129i | \(-0.519473\pi\) | ||||
−0.0611375 | + | 0.998129i | \(0.519473\pi\) | |||||||
\(444\) | 48.1080 | 2.28311 | ||||||||
\(445\) | 9.06807 | 0.429868 | ||||||||
\(446\) | −1.54281 | −0.0730539 | ||||||||
\(447\) | 38.1069 | 1.80239 | ||||||||
\(448\) | 4.24453 | 0.200535 | ||||||||
\(449\) | −35.0213 | −1.65276 | −0.826378 | − | 0.563116i | \(-0.809602\pi\) | ||||
−0.826378 | + | 0.563116i | \(0.809602\pi\) | |||||||
\(450\) | 9.60492 | 0.452780 | ||||||||
\(451\) | 5.24681 | 0.247063 | ||||||||
\(452\) | −27.1984 | −1.27931 | ||||||||
\(453\) | −3.93842 | −0.185043 | ||||||||
\(454\) | 14.7076 | 0.690264 | ||||||||
\(455\) | 1.51263 | 0.0709133 | ||||||||
\(456\) | −26.4747 | −1.23979 | ||||||||
\(457\) | 23.2333 | 1.08681 | 0.543405 | − | 0.839471i | \(-0.317135\pi\) | ||||
0.543405 | + | 0.839471i | \(0.317135\pi\) | |||||||
\(458\) | 44.2802 | 2.06908 | ||||||||
\(459\) | 3.52398 | 0.164485 | ||||||||
\(460\) | −8.04298 | −0.375006 | ||||||||
\(461\) | 6.53965 | 0.304582 | 0.152291 | − | 0.988336i | \(-0.451335\pi\) | ||||
0.152291 | + | 0.988336i | \(0.451335\pi\) | |||||||
\(462\) | 1.52096 | 0.0707613 | ||||||||
\(463\) | 10.5315 | 0.489438 | 0.244719 | − | 0.969594i | \(-0.421304\pi\) | ||||
0.244719 | + | 0.969594i | \(0.421304\pi\) | |||||||
\(464\) | −0.280760 | −0.0130339 | ||||||||
\(465\) | −15.8730 | −0.736091 | ||||||||
\(466\) | 24.4201 | 1.13124 | ||||||||
\(467\) | −12.0092 | −0.555719 | −0.277859 | − | 0.960622i | \(-0.589625\pi\) | ||||
−0.277859 | + | 0.960622i | \(0.589625\pi\) | |||||||
\(468\) | −14.1986 | −0.656328 | ||||||||
\(469\) | −3.82577 | −0.176657 | ||||||||
\(470\) | 21.1397 | 0.975100 | ||||||||
\(471\) | −16.3606 | −0.753858 | ||||||||
\(472\) | −0.240492 | −0.0110695 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 12.5426 | 0.576099 | ||||||||
\(475\) | −17.1250 | −0.785748 | ||||||||
\(476\) | 1.00290 | 0.0459678 | ||||||||
\(477\) | −11.7348 | −0.537300 | ||||||||
\(478\) | 25.9424 | 1.18658 | ||||||||
\(479\) | 25.4205 | 1.16149 | 0.580745 | − | 0.814085i | \(-0.302761\pi\) | ||||
0.580745 | + | 0.814085i | \(0.302761\pi\) | |||||||
\(480\) | 17.3596 | 0.792355 | ||||||||
\(481\) | −26.6418 | −1.21476 | ||||||||
\(482\) | 22.8048 | 1.03873 | ||||||||
\(483\) | 1.34012 | 0.0609777 | ||||||||
\(484\) | 3.08298 | 0.140135 | ||||||||
\(485\) | −8.19573 | −0.372149 | ||||||||
\(486\) | 28.5790 | 1.29637 | ||||||||
\(487\) | 31.9900 | 1.44961 | 0.724803 | − | 0.688956i | \(-0.241931\pi\) | ||||
0.724803 | + | 0.688956i | \(0.241931\pi\) | |||||||
\(488\) | 0.547449 | 0.0247819 | ||||||||
\(489\) | 6.09908 | 0.275810 | ||||||||
\(490\) | 20.4127 | 0.922153 | ||||||||
\(491\) | −24.1436 | −1.08958 | −0.544792 | − | 0.838571i | \(-0.683391\pi\) | ||||
−0.544792 | + | 0.838571i | \(0.683391\pi\) | |||||||
\(492\) | 33.5457 | 1.51236 | ||||||||
\(493\) | −0.424618 | −0.0191238 | ||||||||
\(494\) | 41.7377 | 1.87787 | ||||||||
\(495\) | 1.70823 | 0.0767792 | ||||||||
\(496\) | 3.85358 | 0.173031 | ||||||||
\(497\) | −0.0906895 | −0.00406798 | ||||||||
\(498\) | −57.8215 | −2.59104 | ||||||||
\(499\) | 6.08353 | 0.272336 | 0.136168 | − | 0.990686i | \(-0.456521\pi\) | ||||
0.136168 | + | 0.990686i | \(0.456521\pi\) | |||||||
\(500\) | −33.5052 | −1.49840 | ||||||||
\(501\) | 28.9378 | 1.29285 | ||||||||
\(502\) | 54.9057 | 2.45056 | ||||||||
\(503\) | −8.19577 | −0.365431 | −0.182716 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182716 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(504\) | 1.03312 | 0.0460189 | ||||||||
\(505\) | −21.4970 | −0.956603 | ||||||||
\(506\) | 4.47864 | 0.199100 | ||||||||
\(507\) | −0.961314 | −0.0426934 | ||||||||
\(508\) | 12.8616 | 0.570642 | ||||||||
\(509\) | 18.0880 | 0.801736 | 0.400868 | − | 0.916136i | \(-0.368709\pi\) | ||||
0.400868 | + | 0.916136i | \(0.368709\pi\) | |||||||
\(510\) | 6.14030 | 0.271897 | ||||||||
\(511\) | 4.55966 | 0.201707 | ||||||||
\(512\) | −7.44333 | −0.328952 | ||||||||
\(513\) | −18.4253 | −0.813499 | ||||||||
\(514\) | 10.6090 | 0.467943 | ||||||||
\(515\) | −3.87984 | −0.170966 | ||||||||
\(516\) | 6.39354 | 0.281460 | ||||||||
\(517\) | −7.13969 | −0.314003 | ||||||||
\(518\) | 5.51851 | 0.242469 | ||||||||
\(519\) | −15.7731 | −0.692362 | ||||||||
\(520\) | 11.3534 | 0.497879 | ||||||||
\(521\) | 23.4661 | 1.02807 | 0.514035 | − | 0.857769i | \(-0.328150\pi\) | ||||
0.514035 | + | 0.857769i | \(0.328150\pi\) | |||||||
\(522\) | −1.24521 | −0.0545015 | ||||||||
\(523\) | 27.5348 | 1.20401 | 0.602007 | − | 0.798491i | \(-0.294368\pi\) | ||||
0.602007 | + | 0.798491i | \(0.294368\pi\) | |||||||
\(524\) | −56.8751 | −2.48460 | ||||||||
\(525\) | 2.20956 | 0.0964330 | ||||||||
\(526\) | 21.5000 | 0.937446 | ||||||||
\(527\) | 5.82810 | 0.253876 | ||||||||
\(528\) | −1.37122 | −0.0596748 | ||||||||
\(529\) | −19.0538 | −0.828428 | ||||||||
\(530\) | 26.7121 | 1.16030 | ||||||||
\(531\) | 0.128117 | 0.00555982 | ||||||||
\(532\) | −5.24371 | −0.227344 | ||||||||
\(533\) | −18.5773 | −0.804672 | ||||||||
\(534\) | −32.2839 | −1.39706 | ||||||||
\(535\) | 22.1915 | 0.959423 | ||||||||
\(536\) | −28.7151 | −1.24030 | ||||||||
\(537\) | −5.23119 | −0.225743 | ||||||||
\(538\) | 60.2632 | 2.59813 | ||||||||
\(539\) | −6.89418 | −0.296953 | ||||||||
\(540\) | −14.2680 | −0.613998 | ||||||||
\(541\) | −3.29811 | −0.141797 | −0.0708984 | − | 0.997484i | \(-0.522587\pi\) | ||||
−0.0708984 | + | 0.997484i | \(0.522587\pi\) | |||||||
\(542\) | 49.0333 | 2.10616 | ||||||||
\(543\) | 50.7914 | 2.17967 | ||||||||
\(544\) | −6.37396 | −0.273281 | ||||||||
\(545\) | −0.732051 | −0.0313576 | ||||||||
\(546\) | −5.38522 | −0.230466 | ||||||||
\(547\) | −9.36368 | −0.400362 | −0.200181 | − | 0.979759i | \(-0.564153\pi\) | ||||
−0.200181 | + | 0.979759i | \(0.564153\pi\) | |||||||
\(548\) | −46.8709 | −2.00223 | ||||||||
\(549\) | −0.291643 | −0.0124470 | ||||||||
\(550\) | 7.38426 | 0.314866 | ||||||||
\(551\) | 2.22014 | 0.0945810 | ||||||||
\(552\) | 10.0586 | 0.428121 | ||||||||
\(553\) | 0.872655 | 0.0371091 | ||||||||
\(554\) | 66.8707 | 2.84106 | ||||||||
\(555\) | 20.4931 | 0.869882 | ||||||||
\(556\) | −16.1063 | −0.683059 | ||||||||
\(557\) | −14.7220 | −0.623789 | −0.311895 | − | 0.950117i | \(-0.600964\pi\) | ||||
−0.311895 | + | 0.950117i | \(0.600964\pi\) | |||||||
\(558\) | 17.0912 | 0.723529 | ||||||||
\(559\) | −3.54069 | −0.149755 | ||||||||
\(560\) | 0.282477 | 0.0119368 | ||||||||
\(561\) | −2.07382 | −0.0875567 | ||||||||
\(562\) | −5.63488 | −0.237693 | ||||||||
\(563\) | −11.3946 | −0.480223 | −0.240112 | − | 0.970745i | \(-0.577184\pi\) | ||||
−0.240112 | + | 0.970745i | \(0.577184\pi\) | |||||||
\(564\) | −45.6479 | −1.92212 | ||||||||
\(565\) | −11.5860 | −0.487426 | ||||||||
\(566\) | −34.2315 | −1.43886 | ||||||||
\(567\) | 3.64673 | 0.153148 | ||||||||
\(568\) | −0.680689 | −0.0285611 | ||||||||
\(569\) | 39.7435 | 1.66613 | 0.833066 | − | 0.553173i | \(-0.186583\pi\) | ||||
0.833066 | + | 0.553173i | \(0.186583\pi\) | |||||||
\(570\) | −32.1049 | −1.34473 | ||||||||
\(571\) | 27.2361 | 1.13979 | 0.569897 | − | 0.821716i | \(-0.306983\pi\) | ||||
0.569897 | + | 0.821716i | \(0.306983\pi\) | |||||||
\(572\) | −10.9159 | −0.456415 | ||||||||
\(573\) | −9.85307 | −0.411618 | ||||||||
\(574\) | 3.84805 | 0.160614 | ||||||||
\(575\) | 6.50631 | 0.271332 | ||||||||
\(576\) | −16.9719 | −0.707161 | ||||||||
\(577\) | 4.27206 | 0.177848 | 0.0889241 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889241 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(578\) | −2.25455 | −0.0937767 | ||||||||
\(579\) | 19.8778 | 0.826094 | ||||||||
\(580\) | 1.71921 | 0.0713862 | ||||||||
\(581\) | −4.02296 | −0.166900 | ||||||||
\(582\) | 29.1782 | 1.20947 | ||||||||
\(583\) | −9.02173 | −0.373642 | ||||||||
\(584\) | 34.2235 | 1.41618 | ||||||||
\(585\) | −6.04830 | −0.250067 | ||||||||
\(586\) | −15.7317 | −0.649870 | ||||||||
\(587\) | −0.194556 | −0.00803017 | −0.00401509 | − | 0.999992i | \(-0.501278\pi\) | ||||
−0.00401509 | + | 0.999992i | \(0.501278\pi\) | |||||||
\(588\) | −44.0782 | −1.81775 | ||||||||
\(589\) | −30.4726 | −1.25560 | ||||||||
\(590\) | −0.291636 | −0.0120064 | ||||||||
\(591\) | −10.6856 | −0.439545 | ||||||||
\(592\) | −4.97523 | −0.204481 | ||||||||
\(593\) | −23.5786 | −0.968258 | −0.484129 | − | 0.874997i | \(-0.660864\pi\) | ||||
−0.484129 | + | 0.874997i | \(0.660864\pi\) | |||||||
\(594\) | 7.94498 | 0.325987 | ||||||||
\(595\) | 0.427215 | 0.0175141 | ||||||||
\(596\) | 56.6504 | 2.32049 | ||||||||
\(597\) | −55.0924 | −2.25478 | ||||||||
\(598\) | −15.8575 | −0.648459 | ||||||||
\(599\) | 22.7353 | 0.928938 | 0.464469 | − | 0.885590i | \(-0.346245\pi\) | ||||
0.464469 | + | 0.885590i | \(0.346245\pi\) | |||||||
\(600\) | 16.5843 | 0.677052 | ||||||||
\(601\) | −10.7132 | −0.436999 | −0.218500 | − | 0.975837i | \(-0.570116\pi\) | ||||
−0.218500 | + | 0.975837i | \(0.570116\pi\) | |||||||
\(602\) | 0.733408 | 0.0298915 | ||||||||
\(603\) | 15.2974 | 0.622960 | ||||||||
\(604\) | −5.85493 | −0.238234 | ||||||||
\(605\) | 1.31329 | 0.0533927 | ||||||||
\(606\) | 76.5329 | 3.10894 | ||||||||
\(607\) | 9.43946 | 0.383136 | 0.191568 | − | 0.981479i | \(-0.438643\pi\) | ||||
0.191568 | + | 0.981479i | \(0.438643\pi\) | |||||||
\(608\) | 33.3266 | 1.35157 | ||||||||
\(609\) | −0.286454 | −0.0116077 | ||||||||
\(610\) | 0.663872 | 0.0268794 | ||||||||
\(611\) | 25.2794 | 1.02270 | ||||||||
\(612\) | −4.01011 | −0.162099 | ||||||||
\(613\) | 29.3134 | 1.18396 | 0.591978 | − | 0.805954i | \(-0.298347\pi\) | ||||
0.591978 | + | 0.805954i | \(0.298347\pi\) | |||||||
\(614\) | −55.3211 | −2.23258 | ||||||||
\(615\) | 14.2898 | 0.576220 | ||||||||
\(616\) | 0.794264 | 0.0320018 | ||||||||
\(617\) | 9.08556 | 0.365771 | 0.182885 | − | 0.983134i | \(-0.441456\pi\) | ||||
0.182885 | + | 0.983134i | \(0.441456\pi\) | |||||||
\(618\) | 13.8129 | 0.555635 | ||||||||
\(619\) | −23.6629 | −0.951093 | −0.475546 | − | 0.879691i | \(-0.657750\pi\) | ||||
−0.475546 | + | 0.879691i | \(0.657750\pi\) | |||||||
\(620\) | −23.5970 | −0.947679 | ||||||||
\(621\) | 7.00037 | 0.280915 | ||||||||
\(622\) | −17.0742 | −0.684613 | ||||||||
\(623\) | −2.24617 | −0.0899907 | ||||||||
\(624\) | 4.85507 | 0.194358 | ||||||||
\(625\) | 2.10383 | 0.0841531 | ||||||||
\(626\) | −29.5535 | −1.18120 | ||||||||
\(627\) | 10.8431 | 0.433031 | ||||||||
\(628\) | −24.3220 | −0.970553 | ||||||||
\(629\) | −7.52448 | −0.300021 | ||||||||
\(630\) | 1.25283 | 0.0499139 | ||||||||
\(631\) | 22.6880 | 0.903196 | 0.451598 | − | 0.892222i | \(-0.350854\pi\) | ||||
0.451598 | + | 0.892222i | \(0.350854\pi\) | |||||||
\(632\) | 6.54990 | 0.260541 | ||||||||
\(633\) | −8.47768 | −0.336958 | ||||||||
\(634\) | 9.66631 | 0.383898 | ||||||||
\(635\) | 5.47880 | 0.217419 | ||||||||
\(636\) | −57.6808 | −2.28719 | ||||||||
\(637\) | 24.4101 | 0.967164 | ||||||||
\(638\) | −0.957320 | −0.0379007 | ||||||||
\(639\) | 0.362624 | 0.0143452 | ||||||||
\(640\) | 21.8916 | 0.865343 | ||||||||
\(641\) | −2.39573 | −0.0946255 | −0.0473128 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473128 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(642\) | −79.0055 | −3.11810 | ||||||||
\(643\) | 14.1495 | 0.558003 | 0.279001 | − | 0.960291i | \(-0.409997\pi\) | ||||
0.279001 | + | 0.960291i | \(0.409997\pi\) | |||||||
\(644\) | 1.99225 | 0.0785056 | ||||||||
\(645\) | 2.72352 | 0.107239 | ||||||||
\(646\) | 11.7880 | 0.463793 | ||||||||
\(647\) | 29.6761 | 1.16669 | 0.583343 | − | 0.812226i | \(-0.301744\pi\) | ||||
0.583343 | + | 0.812226i | \(0.301744\pi\) | |||||||
\(648\) | 27.3713 | 1.07525 | ||||||||
\(649\) | 0.0984967 | 0.00386634 | ||||||||
\(650\) | −26.1454 | −1.02551 | ||||||||
\(651\) | 3.93174 | 0.154097 | ||||||||
\(652\) | 9.06699 | 0.355091 | ||||||||
\(653\) | −49.8595 | −1.95115 | −0.975577 | − | 0.219657i | \(-0.929506\pi\) | ||||
−0.975577 | + | 0.219657i | \(0.929506\pi\) | |||||||
\(654\) | 2.60622 | 0.101911 | ||||||||
\(655\) | −24.2277 | −0.946654 | ||||||||
\(656\) | −3.46922 | −0.135450 | ||||||||
\(657\) | −18.2319 | −0.711294 | ||||||||
\(658\) | −5.23631 | −0.204132 | ||||||||
\(659\) | −10.1834 | −0.396690 | −0.198345 | − | 0.980132i | \(-0.563557\pi\) | ||||
−0.198345 | + | 0.980132i | \(0.563557\pi\) | |||||||
\(660\) | 8.39655 | 0.326835 | ||||||||
\(661\) | 17.6302 | 0.685733 | 0.342867 | − | 0.939384i | \(-0.388602\pi\) | ||||
0.342867 | + | 0.939384i | \(0.388602\pi\) | |||||||
\(662\) | −20.0845 | −0.780606 | ||||||||
\(663\) | 7.34274 | 0.285169 | ||||||||
\(664\) | −30.1952 | −1.17180 | ||||||||
\(665\) | −2.23372 | −0.0866198 | ||||||||
\(666\) | −22.0659 | −0.855037 | ||||||||
\(667\) | −0.843500 | −0.0326604 | ||||||||
\(668\) | 43.0195 | 1.66447 | ||||||||
\(669\) | 1.41913 | 0.0548668 | ||||||||
\(670\) | −34.8218 | −1.34528 | ||||||||
\(671\) | −0.224215 | −0.00865574 | ||||||||
\(672\) | −4.29998 | −0.165876 | ||||||||
\(673\) | −2.06113 | −0.0794508 | −0.0397254 | − | 0.999211i | \(-0.512648\pi\) | ||||
−0.0397254 | + | 0.999211i | \(0.512648\pi\) | |||||||
\(674\) | −25.7006 | −0.989949 | ||||||||
\(675\) | 11.5420 | 0.444253 | ||||||||
\(676\) | −1.42911 | −0.0549656 | ||||||||
\(677\) | −9.07207 | −0.348668 | −0.174334 | − | 0.984687i | \(-0.555777\pi\) | ||||
−0.174334 | + | 0.984687i | \(0.555777\pi\) | |||||||
\(678\) | 41.2480 | 1.58412 | ||||||||
\(679\) | 2.03009 | 0.0779075 | ||||||||
\(680\) | 3.20655 | 0.122966 | ||||||||
\(681\) | −13.5287 | −0.518420 | ||||||||
\(682\) | 13.1397 | 0.503146 | ||||||||
\(683\) | 33.2896 | 1.27379 | 0.636895 | − | 0.770951i | \(-0.280219\pi\) | ||||
0.636895 | + | 0.770951i | \(0.280219\pi\) | |||||||
\(684\) | 20.9671 | 0.801697 | ||||||||
\(685\) | −19.9661 | −0.762865 | ||||||||
\(686\) | −10.1901 | −0.389060 | ||||||||
\(687\) | −40.7307 | −1.55397 | ||||||||
\(688\) | −0.661206 | −0.0252082 | ||||||||
\(689\) | 31.9431 | 1.21693 | ||||||||
\(690\) | 12.1977 | 0.464357 | ||||||||
\(691\) | −0.528484 | −0.0201045 | −0.0100522 | − | 0.999949i | \(-0.503200\pi\) | ||||
−0.0100522 | + | 0.999949i | \(0.503200\pi\) | |||||||
\(692\) | −23.4486 | −0.891381 | ||||||||
\(693\) | −0.423129 | −0.0160733 | ||||||||
\(694\) | 49.6968 | 1.88646 | ||||||||
\(695\) | −6.86096 | −0.260251 | ||||||||
\(696\) | −2.15004 | −0.0814972 | ||||||||
\(697\) | −5.24681 | −0.198737 | ||||||||
\(698\) | 3.11012 | 0.117720 | ||||||||
\(699\) | −22.4626 | −0.849613 | ||||||||
\(700\) | 3.28477 | 0.124153 | ||||||||
\(701\) | −40.2495 | −1.52020 | −0.760102 | − | 0.649804i | \(-0.774851\pi\) | ||||
−0.760102 | + | 0.649804i | \(0.774851\pi\) | |||||||
\(702\) | −28.1307 | −1.06172 | ||||||||
\(703\) | 39.3422 | 1.48382 | ||||||||
\(704\) | −13.0480 | −0.491764 | ||||||||
\(705\) | −19.4451 | −0.732345 | ||||||||
\(706\) | −27.1681 | −1.02248 | ||||||||
\(707\) | 5.32481 | 0.200260 | ||||||||
\(708\) | 0.629743 | 0.0236672 | ||||||||
\(709\) | −19.5235 | −0.733222 | −0.366611 | − | 0.930374i | \(-0.619482\pi\) | ||||
−0.366611 | + | 0.930374i | \(0.619482\pi\) | |||||||
\(710\) | −0.825447 | −0.0309785 | ||||||||
\(711\) | −3.48933 | −0.130860 | ||||||||
\(712\) | −16.8591 | −0.631820 | ||||||||
\(713\) | 11.5775 | 0.433580 | ||||||||
\(714\) | −1.52096 | −0.0569203 | ||||||||
\(715\) | −4.64994 | −0.173898 | ||||||||
\(716\) | −7.77679 | −0.290632 | ||||||||
\(717\) | −23.8628 | −0.891174 | ||||||||
\(718\) | 35.4196 | 1.32185 | ||||||||
\(719\) | −26.8303 | −1.00060 | −0.500301 | − | 0.865852i | \(-0.666777\pi\) | ||||
−0.500301 | + | 0.865852i | \(0.666777\pi\) | |||||||
\(720\) | −1.12949 | −0.0420937 | ||||||||
\(721\) | 0.961038 | 0.0357909 | ||||||||
\(722\) | −18.7979 | −0.699587 | ||||||||
\(723\) | −20.9767 | −0.780133 | ||||||||
\(724\) | 75.5074 | 2.80621 | ||||||||
\(725\) | −1.39074 | −0.0516508 | ||||||||
\(726\) | −4.67552 | −0.173525 | ||||||||
\(727\) | 30.6278 | 1.13592 | 0.567961 | − | 0.823055i | \(-0.307732\pi\) | ||||
0.567961 | + | 0.823055i | \(0.307732\pi\) | |||||||
\(728\) | −2.81224 | −0.104228 | ||||||||
\(729\) | 7.34278 | 0.271955 | ||||||||
\(730\) | 41.5016 | 1.53604 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | −1.43353 | −0.0529848 | ||||||||
\(733\) | 29.0359 | 1.07247 | 0.536233 | − | 0.844070i | \(-0.319847\pi\) | ||||
0.536233 | + | 0.844070i | \(0.319847\pi\) | |||||||
\(734\) | −33.3349 | −1.23041 | ||||||||
\(735\) | −18.7764 | −0.692579 | ||||||||
\(736\) | −12.6618 | −0.466721 | ||||||||
\(737\) | 11.7607 | 0.433210 | ||||||||
\(738\) | −15.3865 | −0.566386 | ||||||||
\(739\) | 16.6320 | 0.611820 | 0.305910 | − | 0.952060i | \(-0.401039\pi\) | ||||
0.305910 | + | 0.952060i | \(0.401039\pi\) | |||||||
\(740\) | 30.4654 | 1.11993 | ||||||||
\(741\) | −38.3919 | −1.41036 | ||||||||
\(742\) | −6.61660 | −0.242903 | ||||||||
\(743\) | 40.0253 | 1.46839 | 0.734193 | − | 0.678940i | \(-0.237561\pi\) | ||||
0.734193 | + | 0.678940i | \(0.237561\pi\) | |||||||
\(744\) | 29.5105 | 1.08191 | ||||||||
\(745\) | 24.1319 | 0.884126 | ||||||||
\(746\) | −47.9801 | −1.75668 | ||||||||
\(747\) | 16.0859 | 0.588552 | ||||||||
\(748\) | −3.08298 | −0.112725 | ||||||||
\(749\) | −5.49685 | −0.200850 | ||||||||
\(750\) | 50.8127 | 1.85542 | ||||||||
\(751\) | 8.24102 | 0.300719 | 0.150360 | − | 0.988631i | \(-0.451957\pi\) | ||||
0.150360 | + | 0.988631i | \(0.451957\pi\) | |||||||
\(752\) | 4.72081 | 0.172150 | ||||||||
\(753\) | −50.5044 | −1.84048 | ||||||||
\(754\) | 3.38957 | 0.123441 | ||||||||
\(755\) | −2.49408 | −0.0907690 | ||||||||
\(756\) | 3.53420 | 0.128537 | ||||||||
\(757\) | −23.8527 | −0.866941 | −0.433471 | − | 0.901168i | \(-0.642711\pi\) | ||||
−0.433471 | + | 0.901168i | \(0.642711\pi\) | |||||||
\(758\) | 17.0878 | 0.620657 | ||||||||
\(759\) | −4.11963 | −0.149533 | ||||||||
\(760\) | −16.7656 | −0.608153 | ||||||||
\(761\) | −22.2992 | −0.808344 | −0.404172 | − | 0.914683i | \(-0.632440\pi\) | ||||
−0.404172 | + | 0.914683i | \(0.632440\pi\) | |||||||
\(762\) | −19.5054 | −0.706607 | ||||||||
\(763\) | 0.181329 | 0.00656456 | ||||||||
\(764\) | −14.6478 | −0.529937 | ||||||||
\(765\) | −1.70823 | −0.0617612 | ||||||||
\(766\) | 28.0252 | 1.01259 | ||||||||
\(767\) | −0.348746 | −0.0125925 | ||||||||
\(768\) | −23.8196 | −0.859514 | ||||||||
\(769\) | 19.8319 | 0.715157 | 0.357578 | − | 0.933883i | \(-0.383602\pi\) | ||||
0.357578 | + | 0.933883i | \(0.383602\pi\) | |||||||
\(770\) | 0.963175 | 0.0347104 | ||||||||
\(771\) | −9.75858 | −0.351447 | ||||||||
\(772\) | 29.5507 | 1.06355 | ||||||||
\(773\) | −43.0339 | −1.54782 | −0.773910 | − | 0.633295i | \(-0.781702\pi\) | ||||
−0.773910 | + | 0.633295i | \(0.781702\pi\) | |||||||
\(774\) | −2.93255 | −0.105408 | ||||||||
\(775\) | 19.0887 | 0.685685 | ||||||||
\(776\) | 15.2372 | 0.546985 | ||||||||
\(777\) | −5.07614 | −0.182106 | ||||||||
\(778\) | 19.5831 | 0.702089 | ||||||||
\(779\) | 27.4332 | 0.982897 | ||||||||
\(780\) | −29.7295 | −1.06449 | ||||||||
\(781\) | 0.278786 | 0.00997573 | ||||||||
\(782\) | −4.47864 | −0.160156 | ||||||||
\(783\) | −1.49635 | −0.0534750 | ||||||||
\(784\) | 4.55847 | 0.162803 | ||||||||
\(785\) | −10.3607 | −0.369789 | ||||||||
\(786\) | 86.2546 | 3.07660 | ||||||||
\(787\) | 16.1532 | 0.575800 | 0.287900 | − | 0.957661i | \(-0.407043\pi\) | ||||
0.287900 | + | 0.957661i | \(0.407043\pi\) | |||||||
\(788\) | −15.8853 | −0.565892 | ||||||||
\(789\) | −19.7766 | −0.704065 | ||||||||
\(790\) | 7.94282 | 0.282593 | ||||||||
\(791\) | 2.86985 | 0.102040 | ||||||||
\(792\) | −3.17589 | −0.112850 | ||||||||
\(793\) | 0.793876 | 0.0281914 | ||||||||
\(794\) | −16.8753 | −0.598884 | ||||||||
\(795\) | −24.5709 | −0.871438 | ||||||||
\(796\) | −81.9013 | −2.90291 | ||||||||
\(797\) | −30.8393 | −1.09238 | −0.546192 | − | 0.837660i | \(-0.683923\pi\) | ||||
−0.546192 | + | 0.837660i | \(0.683923\pi\) | |||||||
\(798\) | 7.95240 | 0.281512 | ||||||||
\(799\) | 7.13969 | 0.252584 | ||||||||
\(800\) | −20.8765 | −0.738096 | ||||||||
\(801\) | 8.98135 | 0.317341 | ||||||||
\(802\) | −71.5478 | −2.52644 | ||||||||
\(803\) | −14.0167 | −0.494638 | ||||||||
\(804\) | 75.1923 | 2.65183 | ||||||||
\(805\) | 0.848659 | 0.0299113 | ||||||||
\(806\) | −46.5236 | −1.63872 | ||||||||
\(807\) | −55.4324 | −1.95131 | ||||||||
\(808\) | 39.9665 | 1.40602 | ||||||||
\(809\) | −31.3557 | −1.10241 | −0.551204 | − | 0.834371i | \(-0.685831\pi\) | ||||
−0.551204 | + | 0.834371i | \(0.685831\pi\) | |||||||
\(810\) | 33.1922 | 1.16625 | ||||||||
\(811\) | 41.0527 | 1.44156 | 0.720778 | − | 0.693166i | \(-0.243785\pi\) | ||||
0.720778 | + | 0.693166i | \(0.243785\pi\) | |||||||
\(812\) | −0.425848 | −0.0149443 | ||||||||
\(813\) | −45.1027 | −1.58182 | ||||||||
\(814\) | −16.9643 | −0.594598 | ||||||||
\(815\) | 3.86236 | 0.135293 | ||||||||
\(816\) | 1.37122 | 0.0480024 | ||||||||
\(817\) | 5.22856 | 0.182924 | ||||||||
\(818\) | −38.6024 | −1.34970 | ||||||||
\(819\) | 1.49817 | 0.0523502 | ||||||||
\(820\) | 21.2435 | 0.741854 | ||||||||
\(821\) | 1.64628 | 0.0574554 | 0.0287277 | − | 0.999587i | \(-0.490854\pi\) | ||||
0.0287277 | + | 0.999587i | \(0.490854\pi\) | |||||||
\(822\) | 71.0826 | 2.47929 | ||||||||
\(823\) | −35.7731 | −1.24697 | −0.623486 | − | 0.781835i | \(-0.714284\pi\) | ||||
−0.623486 | + | 0.781835i | \(0.714284\pi\) | |||||||
\(824\) | 7.21327 | 0.251286 | ||||||||
\(825\) | −6.79233 | −0.236479 | ||||||||
\(826\) | 0.0722383 | 0.00251349 | ||||||||
\(827\) | −35.5788 | −1.23720 | −0.618599 | − | 0.785707i | \(-0.712299\pi\) | ||||
−0.618599 | + | 0.785707i | \(0.712299\pi\) | |||||||
\(828\) | −7.96606 | −0.276840 | ||||||||
\(829\) | −5.52846 | −0.192011 | −0.0960057 | − | 0.995381i | \(-0.530607\pi\) | ||||
−0.0960057 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(830\) | −36.6166 | −1.27098 | ||||||||
\(831\) | −61.5103 | −2.13377 | ||||||||
\(832\) | 46.1988 | 1.60165 | ||||||||
\(833\) | 6.89418 | 0.238869 | ||||||||
\(834\) | 24.4262 | 0.845809 | ||||||||
\(835\) | 18.3254 | 0.634178 | ||||||||
\(836\) | 16.1195 | 0.557505 | ||||||||
\(837\) | 20.5381 | 0.709902 | ||||||||
\(838\) | −13.9611 | −0.482279 | ||||||||
\(839\) | 39.0304 | 1.34748 | 0.673739 | − | 0.738969i | \(-0.264687\pi\) | ||||
0.673739 | + | 0.738969i | \(0.264687\pi\) | |||||||
\(840\) | 2.16319 | 0.0746373 | ||||||||
\(841\) | −28.8197 | −0.993783 | ||||||||
\(842\) | 27.6105 | 0.951520 | ||||||||
\(843\) | 5.18319 | 0.178518 | ||||||||
\(844\) | −12.6031 | −0.433816 | ||||||||
\(845\) | −0.608771 | −0.0209423 | ||||||||
\(846\) | 20.9375 | 0.719847 | ||||||||
\(847\) | −0.325302 | −0.0111775 | ||||||||
\(848\) | 5.96522 | 0.204846 | ||||||||
\(849\) | 31.4875 | 1.08065 | ||||||||
\(850\) | −7.38426 | −0.253278 | ||||||||
\(851\) | −14.9473 | −0.512388 | ||||||||
\(852\) | 1.78243 | 0.0610649 | ||||||||
\(853\) | −31.3143 | −1.07218 | −0.536091 | − | 0.844160i | \(-0.680100\pi\) | ||||
−0.536091 | + | 0.844160i | \(0.680100\pi\) | |||||||
\(854\) | −0.164441 | −0.00562707 | ||||||||
\(855\) | 8.93157 | 0.305453 | ||||||||
\(856\) | −41.2578 | −1.41016 | ||||||||
\(857\) | −7.47999 | −0.255512 | −0.127756 | − | 0.991806i | \(-0.540777\pi\) | ||||
−0.127756 | + | 0.991806i | \(0.540777\pi\) | |||||||
\(858\) | 16.5546 | 0.565163 | ||||||||
\(859\) | 10.1188 | 0.345250 | 0.172625 | − | 0.984988i | \(-0.444775\pi\) | ||||
0.172625 | + | 0.984988i | \(0.444775\pi\) | |||||||
\(860\) | 4.04883 | 0.138064 | ||||||||
\(861\) | −3.53959 | −0.120629 | ||||||||
\(862\) | 52.0231 | 1.77191 | ||||||||
\(863\) | 29.8717 | 1.01684 | 0.508422 | − | 0.861108i | \(-0.330229\pi\) | ||||
0.508422 | + | 0.861108i | \(0.330229\pi\) | |||||||
\(864\) | −22.4617 | −0.764164 | ||||||||
\(865\) | −9.98863 | −0.339624 | ||||||||
\(866\) | 42.1686 | 1.43295 | ||||||||
\(867\) | 2.07382 | 0.0704306 | ||||||||
\(868\) | 5.84499 | 0.198392 | ||||||||
\(869\) | −2.68260 | −0.0910010 | ||||||||
\(870\) | −2.60728 | −0.0883951 | ||||||||
\(871\) | −41.6408 | −1.41095 | ||||||||
\(872\) | 1.36101 | 0.0460895 | ||||||||
\(873\) | −8.11735 | −0.274731 | ||||||||
\(874\) | 23.4168 | 0.792086 | ||||||||
\(875\) | 3.53532 | 0.119516 | ||||||||
\(876\) | −89.6163 | −3.02785 | ||||||||
\(877\) | 13.7855 | 0.465503 | 0.232752 | − | 0.972536i | \(-0.425227\pi\) | ||||
0.232752 | + | 0.972536i | \(0.425227\pi\) | |||||||
\(878\) | 13.7984 | 0.465673 | ||||||||
\(879\) | 14.4706 | 0.488082 | ||||||||
\(880\) | −0.868353 | −0.0292722 | ||||||||
\(881\) | −9.75647 | −0.328704 | −0.164352 | − | 0.986402i | \(-0.552553\pi\) | ||||
−0.164352 | + | 0.986402i | \(0.552553\pi\) | |||||||
\(882\) | 20.2175 | 0.680760 | ||||||||
\(883\) | 24.1636 | 0.813171 | 0.406586 | − | 0.913613i | \(-0.366719\pi\) | ||||
0.406586 | + | 0.913613i | \(0.366719\pi\) | |||||||
\(884\) | 10.9159 | 0.367140 | ||||||||
\(885\) | 0.268258 | 0.00901739 | ||||||||
\(886\) | 5.80228 | 0.194931 | ||||||||
\(887\) | 37.4053 | 1.25595 | 0.627973 | − | 0.778235i | \(-0.283885\pi\) | ||||
0.627973 | + | 0.778235i | \(0.283885\pi\) | |||||||
\(888\) | −38.1001 | −1.27855 | ||||||||
\(889\) | −1.35710 | −0.0455157 | ||||||||
\(890\) | −20.4444 | −0.685297 | ||||||||
\(891\) | −11.2103 | −0.375559 | ||||||||
\(892\) | 2.10971 | 0.0706382 | ||||||||
\(893\) | −37.3303 | −1.24921 | ||||||||
\(894\) | −85.9137 | −2.87339 | ||||||||
\(895\) | −3.31276 | −0.110733 | ||||||||
\(896\) | −5.42257 | −0.181155 | ||||||||
\(897\) | 14.5863 | 0.487023 | ||||||||
\(898\) | 78.9570 | 2.63483 | ||||||||
\(899\) | −2.47472 | −0.0825364 | ||||||||
\(900\) | −13.1342 | −0.437808 | ||||||||
\(901\) | 9.02173 | 0.300557 | ||||||||
\(902\) | −11.8292 | −0.393868 | ||||||||
\(903\) | −0.674617 | −0.0224499 | ||||||||
\(904\) | 21.5403 | 0.716420 | ||||||||
\(905\) | 32.1647 | 1.06919 | ||||||||
\(906\) | 8.87935 | 0.294997 | ||||||||
\(907\) | −7.36050 | −0.244402 | −0.122201 | − | 0.992505i | \(-0.538995\pi\) | ||||
−0.122201 | + | 0.992505i | \(0.538995\pi\) | |||||||
\(908\) | −20.1120 | −0.667439 | ||||||||
\(909\) | −21.2914 | −0.706192 | ||||||||
\(910\) | −3.41030 | −0.113050 | ||||||||
\(911\) | −7.68868 | −0.254737 | −0.127369 | − | 0.991855i | \(-0.540653\pi\) | ||||
−0.127369 | + | 0.991855i | \(0.540653\pi\) | |||||||
\(912\) | −7.16951 | −0.237406 | ||||||||
\(913\) | 12.3668 | 0.409283 | ||||||||
\(914\) | −52.3806 | −1.73260 | ||||||||
\(915\) | −0.610655 | −0.0201876 | ||||||||
\(916\) | −60.5509 | −2.00066 | ||||||||
\(917\) | 6.00121 | 0.198177 | ||||||||
\(918\) | −7.94498 | −0.262224 | ||||||||
\(919\) | 0.433699 | 0.0143064 | 0.00715321 | − | 0.999974i | \(-0.497723\pi\) | ||||
0.00715321 | + | 0.999974i | \(0.497723\pi\) | |||||||
\(920\) | 6.36979 | 0.210006 | ||||||||
\(921\) | 50.8865 | 1.67677 | ||||||||
\(922\) | −14.7439 | −0.485566 | ||||||||
\(923\) | −0.987092 | −0.0324905 | ||||||||
\(924\) | −2.07983 | −0.0684214 | ||||||||
\(925\) | −24.6448 | −0.810314 | ||||||||
\(926\) | −23.7436 | −0.780265 | ||||||||
\(927\) | −3.84274 | −0.126212 | ||||||||
\(928\) | 2.70650 | 0.0888451 | ||||||||
\(929\) | −15.2402 | −0.500015 | −0.250008 | − | 0.968244i | \(-0.580433\pi\) | ||||
−0.250008 | + | 0.968244i | \(0.580433\pi\) | |||||||
\(930\) | 35.7863 | 1.17348 | ||||||||
\(931\) | −36.0466 | −1.18138 | ||||||||
\(932\) | −33.3933 | −1.09383 | ||||||||
\(933\) | 15.7055 | 0.514176 | ||||||||
\(934\) | 27.0753 | 0.885929 | ||||||||
\(935\) | −1.31329 | −0.0429491 | ||||||||
\(936\) | 11.2448 | 0.367548 | ||||||||
\(937\) | 12.4759 | 0.407569 | 0.203784 | − | 0.979016i | \(-0.434676\pi\) | ||||
0.203784 | + | 0.979016i | \(0.434676\pi\) | |||||||
\(938\) | 8.62537 | 0.281628 | ||||||||
\(939\) | 27.1845 | 0.887133 | ||||||||
\(940\) | −28.9074 | −0.942857 | ||||||||
\(941\) | −23.3479 | −0.761119 | −0.380560 | − | 0.924756i | \(-0.624269\pi\) | ||||
−0.380560 | + | 0.924756i | \(0.624269\pi\) | |||||||
\(942\) | 36.8858 | 1.20180 | ||||||||
\(943\) | −10.4227 | −0.339411 | ||||||||
\(944\) | −0.0651266 | −0.00211969 | ||||||||
\(945\) | 1.50550 | 0.0489738 | ||||||||
\(946\) | −2.25455 | −0.0733016 | ||||||||
\(947\) | −42.3225 | −1.37530 | −0.687649 | − | 0.726043i | \(-0.741357\pi\) | ||||
−0.687649 | + | 0.726043i | \(0.741357\pi\) | |||||||
\(948\) | −17.1513 | −0.557049 | ||||||||
\(949\) | 49.6287 | 1.61102 | ||||||||
\(950\) | 38.6090 | 1.25264 | ||||||||
\(951\) | −8.89145 | −0.288325 | ||||||||
\(952\) | −0.794264 | −0.0257422 | ||||||||
\(953\) | −27.0693 | −0.876859 | −0.438430 | − | 0.898765i | \(-0.644465\pi\) | ||||
−0.438430 | + | 0.898765i | \(0.644465\pi\) | |||||||
\(954\) | 26.4567 | 0.856566 | ||||||||
\(955\) | −6.23965 | −0.201910 | ||||||||
\(956\) | −35.4749 | −1.14734 | ||||||||
\(957\) | 0.880581 | 0.0284651 | ||||||||
\(958\) | −57.3116 | −1.85165 | ||||||||
\(959\) | 4.94561 | 0.159702 | ||||||||
\(960\) | −35.5364 | −1.14693 | ||||||||
\(961\) | 2.96678 | 0.0957025 | ||||||||
\(962\) | 60.0652 | 1.93658 | ||||||||
\(963\) | 21.9793 | 0.708273 | ||||||||
\(964\) | −31.1844 | −1.00438 | ||||||||
\(965\) | 12.5880 | 0.405223 | ||||||||
\(966\) | −3.02137 | −0.0972109 | ||||||||
\(967\) | −54.1184 | −1.74033 | −0.870164 | − | 0.492761i | \(-0.835988\pi\) | ||||
−0.870164 | + | 0.492761i | \(0.835988\pi\) | |||||||
\(968\) | −2.44162 | −0.0784767 | ||||||||
\(969\) | −10.8431 | −0.348330 | ||||||||
\(970\) | 18.4776 | 0.593281 | ||||||||
\(971\) | −38.5443 | −1.23695 | −0.618473 | − | 0.785806i | \(-0.712249\pi\) | ||||
−0.618473 | + | 0.785806i | \(0.712249\pi\) | |||||||
\(972\) | −39.0803 | −1.25350 | ||||||||
\(973\) | 1.69946 | 0.0544823 | ||||||||
\(974\) | −72.1229 | −2.31097 | ||||||||
\(975\) | 24.0495 | 0.770201 | ||||||||
\(976\) | 0.148253 | 0.00474545 | ||||||||
\(977\) | −33.7275 | −1.07904 | −0.539520 | − | 0.841973i | \(-0.681394\pi\) | ||||
−0.539520 | + | 0.841973i | \(0.681394\pi\) | |||||||
\(978\) | −13.7506 | −0.439697 | ||||||||
\(979\) | 6.90487 | 0.220680 | ||||||||
\(980\) | −27.9134 | −0.891660 | ||||||||
\(981\) | −0.725050 | −0.0231491 | ||||||||
\(982\) | 54.4328 | 1.73702 | ||||||||
\(983\) | −36.5986 | −1.16731 | −0.583657 | − | 0.812000i | \(-0.698379\pi\) | ||||
−0.583657 | + | 0.812000i | \(0.698379\pi\) | |||||||
\(984\) | −26.5671 | −0.846929 | ||||||||
\(985\) | −6.76684 | −0.215610 | ||||||||
\(986\) | 0.957320 | 0.0304873 | ||||||||
\(987\) | 4.81656 | 0.153313 | ||||||||
\(988\) | −57.0741 | −1.81577 | ||||||||
\(989\) | −1.98649 | −0.0631668 | ||||||||
\(990\) | −3.85128 | −0.122402 | ||||||||
\(991\) | −2.11266 | −0.0671108 | −0.0335554 | − | 0.999437i | \(-0.510683\pi\) | ||||
−0.0335554 | + | 0.999437i | \(0.510683\pi\) | |||||||
\(992\) | −37.1481 | −1.17945 | ||||||||
\(993\) | 18.4745 | 0.586271 | ||||||||
\(994\) | 0.204464 | 0.00648519 | ||||||||
\(995\) | −34.8883 | −1.10603 | ||||||||
\(996\) | 79.0679 | 2.50536 | ||||||||
\(997\) | 2.70245 | 0.0855876 | 0.0427938 | − | 0.999084i | \(-0.486374\pi\) | ||||
0.0427938 | + | 0.999084i | \(0.486374\pi\) | |||||||
\(998\) | −13.7156 | −0.434160 | ||||||||
\(999\) | −26.5161 | −0.838933 |
(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 | 8041.2.a.d.1.8 | ✓ | 62 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.d.1.8 | ✓ | 62 | 1.1 | even | 1 | trivial |