Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, 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("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.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: | \(64.1118877829\) |
Analytic rank: | \(0\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63529 | −1.86343 | −0.931716 | − | 0.363186i | \(-0.881689\pi\) | ||||
−0.931716 | + | 0.363186i | \(0.881689\pi\) | |||||||
\(3\) | −1.71677 | −0.991176 | −0.495588 | − | 0.868558i | \(-0.665047\pi\) | ||||
−0.495588 | + | 0.868558i | \(0.665047\pi\) | |||||||
\(4\) | 4.94476 | 2.47238 | ||||||||
\(5\) | −3.15507 | −1.41099 | −0.705494 | − | 0.708716i | \(-0.749275\pi\) | ||||
−0.705494 | + | 0.708716i | \(0.749275\pi\) | |||||||
\(6\) | 4.52418 | 1.84699 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −7.76032 | −2.74369 | ||||||||
\(9\) | −0.0527133 | −0.0175711 | ||||||||
\(10\) | 8.31452 | 2.62928 | ||||||||
\(11\) | 2.91781 | 0.879752 | 0.439876 | − | 0.898059i | \(-0.355022\pi\) | ||||
0.439876 | + | 0.898059i | \(0.355022\pi\) | |||||||
\(12\) | −8.48901 | −2.45056 | ||||||||
\(13\) | −0.0307174 | −0.00851949 | −0.00425974 | − | 0.999991i | \(-0.501356\pi\) | ||||
−0.00425974 | + | 0.999991i | \(0.501356\pi\) | |||||||
\(14\) | 2.63529 | 0.704311 | ||||||||
\(15\) | 5.41651 | 1.39854 | ||||||||
\(16\) | 10.5612 | 2.64029 | ||||||||
\(17\) | −3.68205 | −0.893029 | −0.446514 | − | 0.894776i | \(-0.647335\pi\) | ||||
−0.446514 | + | 0.894776i | \(0.647335\pi\) | |||||||
\(18\) | 0.138915 | 0.0327426 | ||||||||
\(19\) | −5.89519 | −1.35245 | −0.676224 | − | 0.736696i | \(-0.736385\pi\) | ||||
−0.676224 | + | 0.736696i | \(0.736385\pi\) | |||||||
\(20\) | −15.6011 | −3.48850 | ||||||||
\(21\) | 1.71677 | 0.374629 | ||||||||
\(22\) | −7.68927 | −1.63936 | ||||||||
\(23\) | 8.32560 | 1.73601 | 0.868004 | − | 0.496557i | \(-0.165403\pi\) | ||||
0.868004 | + | 0.496557i | \(0.165403\pi\) | |||||||
\(24\) | 13.3226 | 2.71947 | ||||||||
\(25\) | 4.95444 | 0.990889 | ||||||||
\(26\) | 0.0809495 | 0.0158755 | ||||||||
\(27\) | 5.24080 | 1.00859 | ||||||||
\(28\) | −4.94476 | −0.934473 | ||||||||
\(29\) | 4.04619 | 0.751358 | 0.375679 | − | 0.926750i | \(-0.377409\pi\) | ||||
0.375679 | + | 0.926750i | \(0.377409\pi\) | |||||||
\(30\) | −14.2741 | −2.60608 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −12.3111 | −2.17632 | ||||||||
\(33\) | −5.00919 | −0.871989 | ||||||||
\(34\) | 9.70328 | 1.66410 | ||||||||
\(35\) | 3.15507 | 0.533304 | ||||||||
\(36\) | −0.260655 | −0.0434425 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 15.5355 | 2.52020 | ||||||||
\(39\) | 0.0527347 | 0.00844431 | ||||||||
\(40\) | 24.4843 | 3.87131 | ||||||||
\(41\) | −0.941963 | −0.147110 | −0.0735550 | − | 0.997291i | \(-0.523434\pi\) | ||||
−0.0735550 | + | 0.997291i | \(0.523434\pi\) | |||||||
\(42\) | −4.52418 | −0.698096 | ||||||||
\(43\) | −9.88190 | −1.50698 | −0.753488 | − | 0.657461i | \(-0.771630\pi\) | ||||
−0.753488 | + | 0.657461i | \(0.771630\pi\) | |||||||
\(44\) | 14.4279 | 2.17508 | ||||||||
\(45\) | 0.166314 | 0.0247926 | ||||||||
\(46\) | −21.9404 | −3.23493 | ||||||||
\(47\) | 4.99629 | 0.728784 | 0.364392 | − | 0.931246i | \(-0.381277\pi\) | ||||
0.364392 | + | 0.931246i | \(0.381277\pi\) | |||||||
\(48\) | −18.1311 | −2.61699 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −13.0564 | −1.84646 | ||||||||
\(51\) | 6.32122 | 0.885148 | ||||||||
\(52\) | −0.151891 | −0.0210634 | ||||||||
\(53\) | −2.05341 | −0.282058 | −0.141029 | − | 0.990005i | \(-0.545041\pi\) | ||||
−0.141029 | + | 0.990005i | \(0.545041\pi\) | |||||||
\(54\) | −13.8110 | −1.87944 | ||||||||
\(55\) | −9.20588 | −1.24132 | ||||||||
\(56\) | 7.76032 | 1.03702 | ||||||||
\(57\) | 10.1207 | 1.34051 | ||||||||
\(58\) | −10.6629 | −1.40011 | ||||||||
\(59\) | −0.211513 | −0.0275367 | −0.0137684 | − | 0.999905i | \(-0.504383\pi\) | ||||
−0.0137684 | + | 0.999905i | \(0.504383\pi\) | |||||||
\(60\) | 26.7834 | 3.45772 | ||||||||
\(61\) | −2.55588 | −0.327247 | −0.163623 | − | 0.986523i | \(-0.552318\pi\) | ||||
−0.163623 | + | 0.986523i | \(0.552318\pi\) | |||||||
\(62\) | 2.63529 | 0.334682 | ||||||||
\(63\) | 0.0527133 | 0.00664125 | ||||||||
\(64\) | 11.3211 | 1.41514 | ||||||||
\(65\) | 0.0969156 | 0.0120209 | ||||||||
\(66\) | 13.2007 | 1.62489 | ||||||||
\(67\) | 13.4224 | 1.63981 | 0.819905 | − | 0.572500i | \(-0.194026\pi\) | ||||
0.819905 | + | 0.572500i | \(0.194026\pi\) | |||||||
\(68\) | −18.2069 | −2.20791 | ||||||||
\(69\) | −14.2931 | −1.72069 | ||||||||
\(70\) | −8.31452 | −0.993775 | ||||||||
\(71\) | 12.9686 | 1.53909 | 0.769545 | − | 0.638592i | \(-0.220483\pi\) | ||||
0.769545 | + | 0.638592i | \(0.220483\pi\) | |||||||
\(72\) | 0.409072 | 0.0482096 | ||||||||
\(73\) | −1.09398 | −0.128041 | −0.0640206 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640206 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(74\) | −2.63529 | −0.306346 | ||||||||
\(75\) | −8.50562 | −0.982145 | ||||||||
\(76\) | −29.1503 | −3.34377 | ||||||||
\(77\) | −2.91781 | −0.332515 | ||||||||
\(78\) | −0.138971 | −0.0157354 | ||||||||
\(79\) | 5.42088 | 0.609897 | 0.304949 | − | 0.952369i | \(-0.401361\pi\) | ||||
0.304949 | + | 0.952369i | \(0.401361\pi\) | |||||||
\(80\) | −33.3212 | −3.72542 | ||||||||
\(81\) | −8.83908 | −0.982120 | ||||||||
\(82\) | 2.48235 | 0.274129 | ||||||||
\(83\) | −14.6631 | −1.60948 | −0.804740 | − | 0.593628i | \(-0.797695\pi\) | ||||
−0.804740 | + | 0.593628i | \(0.797695\pi\) | |||||||
\(84\) | 8.48901 | 0.926226 | ||||||||
\(85\) | 11.6171 | 1.26005 | ||||||||
\(86\) | 26.0417 | 2.80815 | ||||||||
\(87\) | −6.94636 | −0.744728 | ||||||||
\(88\) | −22.6431 | −2.41376 | ||||||||
\(89\) | 8.61286 | 0.912962 | 0.456481 | − | 0.889733i | \(-0.349110\pi\) | ||||
0.456481 | + | 0.889733i | \(0.349110\pi\) | |||||||
\(90\) | −0.438286 | −0.0461994 | ||||||||
\(91\) | 0.0307174 | 0.00322006 | ||||||||
\(92\) | 41.1681 | 4.29207 | ||||||||
\(93\) | 1.71677 | 0.178020 | ||||||||
\(94\) | −13.1667 | −1.35804 | ||||||||
\(95\) | 18.5997 | 1.90829 | ||||||||
\(96\) | 21.1353 | 2.15712 | ||||||||
\(97\) | −8.08133 | −0.820535 | −0.410267 | − | 0.911965i | \(-0.634565\pi\) | ||||
−0.410267 | + | 0.911965i | \(0.634565\pi\) | |||||||
\(98\) | −2.63529 | −0.266205 | ||||||||
\(99\) | −0.153807 | −0.0154582 | ||||||||
\(100\) | 24.4986 | 2.44986 | ||||||||
\(101\) | 16.3437 | 1.62626 | 0.813131 | − | 0.582080i | \(-0.197761\pi\) | ||||
0.813131 | + | 0.582080i | \(0.197761\pi\) | |||||||
\(102\) | −16.6583 | −1.64941 | ||||||||
\(103\) | −20.0535 | −1.97593 | −0.987965 | − | 0.154679i | \(-0.950566\pi\) | ||||
−0.987965 | + | 0.154679i | \(0.950566\pi\) | |||||||
\(104\) | 0.238377 | 0.0233748 | ||||||||
\(105\) | −5.41651 | −0.528597 | ||||||||
\(106\) | 5.41135 | 0.525596 | ||||||||
\(107\) | −5.23674 | −0.506255 | −0.253127 | − | 0.967433i | \(-0.581459\pi\) | ||||
−0.253127 | + | 0.967433i | \(0.581459\pi\) | |||||||
\(108\) | 25.9145 | 2.49362 | ||||||||
\(109\) | 6.44359 | 0.617184 | 0.308592 | − | 0.951194i | \(-0.400142\pi\) | ||||
0.308592 | + | 0.951194i | \(0.400142\pi\) | |||||||
\(110\) | 24.2602 | 2.31312 | ||||||||
\(111\) | −1.71677 | −0.162948 | ||||||||
\(112\) | −10.5612 | −0.997937 | ||||||||
\(113\) | −10.9113 | −1.02645 | −0.513225 | − | 0.858254i | \(-0.671549\pi\) | ||||
−0.513225 | + | 0.858254i | \(0.671549\pi\) | |||||||
\(114\) | −26.6709 | −2.49796 | ||||||||
\(115\) | −26.2678 | −2.44949 | ||||||||
\(116\) | 20.0075 | 1.85765 | ||||||||
\(117\) | 0.00161922 | 0.000149697 0 | ||||||||
\(118\) | 0.557400 | 0.0513128 | ||||||||
\(119\) | 3.68205 | 0.337533 | ||||||||
\(120\) | −42.0338 | −3.83715 | ||||||||
\(121\) | −2.48640 | −0.226037 | ||||||||
\(122\) | 6.73549 | 0.609802 | ||||||||
\(123\) | 1.61713 | 0.145812 | ||||||||
\(124\) | −4.94476 | −0.444053 | ||||||||
\(125\) | 0.143730 | 0.0128556 | ||||||||
\(126\) | −0.138915 | −0.0123755 | ||||||||
\(127\) | −2.59075 | −0.229892 | −0.114946 | − | 0.993372i | \(-0.536670\pi\) | ||||
−0.114946 | + | 0.993372i | \(0.536670\pi\) | |||||||
\(128\) | −5.21213 | −0.460691 | ||||||||
\(129\) | 16.9649 | 1.49368 | ||||||||
\(130\) | −0.255401 | −0.0224001 | ||||||||
\(131\) | 0.701835 | 0.0613196 | 0.0306598 | − | 0.999530i | \(-0.490239\pi\) | ||||
0.0306598 | + | 0.999530i | \(0.490239\pi\) | |||||||
\(132\) | −24.7693 | −2.15589 | ||||||||
\(133\) | 5.89519 | 0.511177 | ||||||||
\(134\) | −35.3720 | −3.05567 | ||||||||
\(135\) | −16.5351 | −1.42311 | ||||||||
\(136\) | 28.5739 | 2.45019 | ||||||||
\(137\) | 2.14898 | 0.183600 | 0.0918001 | − | 0.995777i | \(-0.470738\pi\) | ||||
0.0918001 | + | 0.995777i | \(0.470738\pi\) | |||||||
\(138\) | 37.6665 | 3.20639 | ||||||||
\(139\) | −19.4665 | −1.65113 | −0.825564 | − | 0.564308i | \(-0.809143\pi\) | ||||
−0.825564 | + | 0.564308i | \(0.809143\pi\) | |||||||
\(140\) | 15.6011 | 1.31853 | ||||||||
\(141\) | −8.57747 | −0.722353 | ||||||||
\(142\) | −34.1761 | −2.86799 | ||||||||
\(143\) | −0.0896276 | −0.00749504 | ||||||||
\(144\) | −0.556714 | −0.0463928 | ||||||||
\(145\) | −12.7660 | −1.06016 | ||||||||
\(146\) | 2.88297 | 0.238596 | ||||||||
\(147\) | −1.71677 | −0.141597 | ||||||||
\(148\) | 4.94476 | 0.406457 | ||||||||
\(149\) | 16.6330 | 1.36262 | 0.681312 | − | 0.731993i | \(-0.261410\pi\) | ||||
0.681312 | + | 0.731993i | \(0.261410\pi\) | |||||||
\(150\) | 22.4148 | 1.83016 | ||||||||
\(151\) | −9.08362 | −0.739214 | −0.369607 | − | 0.929188i | \(-0.620508\pi\) | ||||
−0.369607 | + | 0.929188i | \(0.620508\pi\) | |||||||
\(152\) | 45.7485 | 3.71069 | ||||||||
\(153\) | 0.194093 | 0.0156915 | ||||||||
\(154\) | 7.68927 | 0.619619 | ||||||||
\(155\) | 3.15507 | 0.253421 | ||||||||
\(156\) | 0.260761 | 0.0208776 | ||||||||
\(157\) | 17.0886 | 1.36382 | 0.681908 | − | 0.731438i | \(-0.261150\pi\) | ||||
0.681908 | + | 0.731438i | \(0.261150\pi\) | |||||||
\(158\) | −14.2856 | −1.13650 | ||||||||
\(159\) | 3.52523 | 0.279569 | ||||||||
\(160\) | 38.8424 | 3.07076 | ||||||||
\(161\) | −8.32560 | −0.656149 | ||||||||
\(162\) | 23.2936 | 1.83012 | ||||||||
\(163\) | 7.49295 | 0.586893 | 0.293447 | − | 0.955975i | \(-0.405198\pi\) | ||||
0.293447 | + | 0.955975i | \(0.405198\pi\) | |||||||
\(164\) | −4.65779 | −0.363712 | ||||||||
\(165\) | 15.8043 | 1.23037 | ||||||||
\(166\) | 38.6414 | 2.99916 | ||||||||
\(167\) | −23.7939 | −1.84123 | −0.920615 | − | 0.390472i | \(-0.872312\pi\) | ||||
−0.920615 | + | 0.390472i | \(0.872312\pi\) | |||||||
\(168\) | −13.3226 | −1.02786 | ||||||||
\(169\) | −12.9991 | −0.999927 | ||||||||
\(170\) | −30.6145 | −2.34802 | ||||||||
\(171\) | 0.310755 | 0.0237640 | ||||||||
\(172\) | −48.8637 | −3.72582 | ||||||||
\(173\) | 1.45358 | 0.110514 | 0.0552569 | − | 0.998472i | \(-0.482402\pi\) | ||||
0.0552569 | + | 0.998472i | \(0.482402\pi\) | |||||||
\(174\) | 18.3057 | 1.38775 | ||||||||
\(175\) | −4.95444 | −0.374521 | ||||||||
\(176\) | 30.8155 | 2.32280 | ||||||||
\(177\) | 0.363119 | 0.0272937 | ||||||||
\(178\) | −22.6974 | −1.70124 | ||||||||
\(179\) | −12.9025 | −0.964379 | −0.482189 | − | 0.876067i | \(-0.660158\pi\) | ||||
−0.482189 | + | 0.876067i | \(0.660158\pi\) | |||||||
\(180\) | 0.822383 | 0.0612968 | ||||||||
\(181\) | −5.47227 | −0.406750 | −0.203375 | − | 0.979101i | \(-0.565191\pi\) | ||||
−0.203375 | + | 0.979101i | \(0.565191\pi\) | |||||||
\(182\) | −0.0809495 | −0.00600037 | ||||||||
\(183\) | 4.38785 | 0.324359 | ||||||||
\(184\) | −64.6093 | −4.76306 | ||||||||
\(185\) | −3.15507 | −0.231965 | ||||||||
\(186\) | −4.52418 | −0.331729 | ||||||||
\(187\) | −10.7435 | −0.785644 | ||||||||
\(188\) | 24.7055 | 1.80183 | ||||||||
\(189\) | −5.24080 | −0.381212 | ||||||||
\(190\) | −49.0156 | −3.55597 | ||||||||
\(191\) | 25.8131 | 1.86777 | 0.933886 | − | 0.357570i | \(-0.116395\pi\) | ||||
0.933886 | + | 0.357570i | \(0.116395\pi\) | |||||||
\(192\) | −19.4357 | −1.40265 | ||||||||
\(193\) | −13.0934 | −0.942486 | −0.471243 | − | 0.882003i | \(-0.656195\pi\) | ||||
−0.471243 | + | 0.882003i | \(0.656195\pi\) | |||||||
\(194\) | 21.2967 | 1.52901 | ||||||||
\(195\) | −0.166381 | −0.0119148 | ||||||||
\(196\) | 4.94476 | 0.353197 | ||||||||
\(197\) | −23.2418 | −1.65591 | −0.827956 | − | 0.560793i | \(-0.810496\pi\) | ||||
−0.827956 | + | 0.560793i | \(0.810496\pi\) | |||||||
\(198\) | 0.405327 | 0.0288053 | ||||||||
\(199\) | 3.19180 | 0.226261 | 0.113130 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113130 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(200\) | −38.4481 | −2.71869 | ||||||||
\(201\) | −23.0432 | −1.62534 | ||||||||
\(202\) | −43.0705 | −3.03043 | ||||||||
\(203\) | −4.04619 | −0.283987 | ||||||||
\(204\) | 31.2570 | 2.18842 | ||||||||
\(205\) | 2.97196 | 0.207570 | ||||||||
\(206\) | 52.8468 | 3.68201 | ||||||||
\(207\) | −0.438870 | −0.0305036 | ||||||||
\(208\) | −0.324412 | −0.0224939 | ||||||||
\(209\) | −17.2010 | −1.18982 | ||||||||
\(210\) | 14.2741 | 0.985006 | ||||||||
\(211\) | 10.9866 | 0.756350 | 0.378175 | − | 0.925734i | \(-0.376552\pi\) | ||||
0.378175 | + | 0.925734i | \(0.376552\pi\) | |||||||
\(212\) | −10.1537 | −0.697356 | ||||||||
\(213\) | −22.2641 | −1.52551 | ||||||||
\(214\) | 13.8003 | 0.943372 | ||||||||
\(215\) | 31.1781 | 2.12633 | ||||||||
\(216\) | −40.6702 | −2.76726 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | −16.9808 | −1.15008 | ||||||||
\(219\) | 1.87811 | 0.126911 | ||||||||
\(220\) | −45.5209 | −3.06902 | ||||||||
\(221\) | 0.113103 | 0.00760815 | ||||||||
\(222\) | 4.52418 | 0.303643 | ||||||||
\(223\) | 3.69938 | 0.247729 | 0.123864 | − | 0.992299i | \(-0.460471\pi\) | ||||
0.123864 | + | 0.992299i | \(0.460471\pi\) | |||||||
\(224\) | 12.3111 | 0.822572 | ||||||||
\(225\) | −0.261165 | −0.0174110 | ||||||||
\(226\) | 28.7545 | 1.91272 | ||||||||
\(227\) | −0.155384 | −0.0103132 | −0.00515661 | − | 0.999987i | \(-0.501641\pi\) | ||||
−0.00515661 | + | 0.999987i | \(0.501641\pi\) | |||||||
\(228\) | 50.0443 | 3.31426 | ||||||||
\(229\) | 28.5629 | 1.88749 | 0.943744 | − | 0.330676i | \(-0.107277\pi\) | ||||
0.943744 | + | 0.330676i | \(0.107277\pi\) | |||||||
\(230\) | 69.2234 | 4.56445 | ||||||||
\(231\) | 5.00919 | 0.329581 | ||||||||
\(232\) | −31.3997 | −2.06149 | ||||||||
\(233\) | −2.73029 | −0.178867 | −0.0894337 | − | 0.995993i | \(-0.528506\pi\) | ||||
−0.0894337 | + | 0.995993i | \(0.528506\pi\) | |||||||
\(234\) | −0.00426711 | −0.000278950 0 | ||||||||
\(235\) | −15.7636 | −1.02831 | ||||||||
\(236\) | −1.04588 | −0.0680813 | ||||||||
\(237\) | −9.30639 | −0.604515 | ||||||||
\(238\) | −9.70328 | −0.628970 | ||||||||
\(239\) | −6.23443 | −0.403271 | −0.201636 | − | 0.979461i | \(-0.564626\pi\) | ||||
−0.201636 | + | 0.979461i | \(0.564626\pi\) | |||||||
\(240\) | 57.2047 | 3.69255 | ||||||||
\(241\) | 3.34339 | 0.215367 | 0.107683 | − | 0.994185i | \(-0.465657\pi\) | ||||
0.107683 | + | 0.994185i | \(0.465657\pi\) | |||||||
\(242\) | 6.55239 | 0.421204 | ||||||||
\(243\) | −0.547749 | −0.0351381 | ||||||||
\(244\) | −12.6382 | −0.809079 | ||||||||
\(245\) | −3.15507 | −0.201570 | ||||||||
\(246\) | −4.26161 | −0.271710 | ||||||||
\(247\) | 0.181085 | 0.0115222 | ||||||||
\(248\) | 7.76032 | 0.492781 | ||||||||
\(249\) | 25.1730 | 1.59528 | ||||||||
\(250\) | −0.378772 | −0.0239556 | ||||||||
\(251\) | −9.76237 | −0.616196 | −0.308098 | − | 0.951355i | \(-0.599692\pi\) | ||||
−0.308098 | + | 0.951355i | \(0.599692\pi\) | |||||||
\(252\) | 0.260655 | 0.0164197 | ||||||||
\(253\) | 24.2925 | 1.52726 | ||||||||
\(254\) | 6.82739 | 0.428388 | ||||||||
\(255\) | −19.9439 | −1.24893 | ||||||||
\(256\) | −8.90671 | −0.556669 | ||||||||
\(257\) | 1.76103 | 0.109850 | 0.0549249 | − | 0.998490i | \(-0.482508\pi\) | ||||
0.0549249 | + | 0.998490i | \(0.482508\pi\) | |||||||
\(258\) | −44.7075 | −2.78337 | ||||||||
\(259\) | −1.00000 | −0.0621370 | ||||||||
\(260\) | 0.479225 | 0.0297203 | ||||||||
\(261\) | −0.213288 | −0.0132022 | ||||||||
\(262\) | −1.84954 | −0.114265 | ||||||||
\(263\) | −25.5470 | −1.57530 | −0.787648 | − | 0.616125i | \(-0.788701\pi\) | ||||
−0.787648 | + | 0.616125i | \(0.788701\pi\) | |||||||
\(264\) | 38.8729 | 2.39246 | ||||||||
\(265\) | 6.47866 | 0.397981 | ||||||||
\(266\) | −15.5355 | −0.952545 | ||||||||
\(267\) | −14.7863 | −0.904905 | ||||||||
\(268\) | 66.3707 | 4.05424 | ||||||||
\(269\) | 22.0236 | 1.34281 | 0.671403 | − | 0.741093i | \(-0.265692\pi\) | ||||
0.671403 | + | 0.741093i | \(0.265692\pi\) | |||||||
\(270\) | 43.5747 | 2.65187 | ||||||||
\(271\) | −2.44701 | −0.148645 | −0.0743227 | − | 0.997234i | \(-0.523679\pi\) | ||||
−0.0743227 | + | 0.997234i | \(0.523679\pi\) | |||||||
\(272\) | −38.8868 | −2.35786 | ||||||||
\(273\) | −0.0527347 | −0.00319165 | ||||||||
\(274\) | −5.66320 | −0.342127 | ||||||||
\(275\) | 14.4561 | 0.871736 | ||||||||
\(276\) | −70.6761 | −4.25420 | ||||||||
\(277\) | 26.8285 | 1.61197 | 0.805985 | − | 0.591936i | \(-0.201636\pi\) | ||||
0.805985 | + | 0.591936i | \(0.201636\pi\) | |||||||
\(278\) | 51.3000 | 3.07677 | ||||||||
\(279\) | 0.0527133 | 0.00315586 | ||||||||
\(280\) | −24.4843 | −1.46322 | ||||||||
\(281\) | −22.4358 | −1.33841 | −0.669205 | − | 0.743078i | \(-0.733365\pi\) | ||||
−0.669205 | + | 0.743078i | \(0.733365\pi\) | |||||||
\(282\) | 22.6041 | 1.34606 | ||||||||
\(283\) | −25.4290 | −1.51160 | −0.755798 | − | 0.654805i | \(-0.772751\pi\) | ||||
−0.755798 | + | 0.654805i | \(0.772751\pi\) | |||||||
\(284\) | 64.1267 | 3.80522 | ||||||||
\(285\) | −31.9313 | −1.89145 | ||||||||
\(286\) | 0.236195 | 0.0139665 | ||||||||
\(287\) | 0.941963 | 0.0556023 | ||||||||
\(288\) | 0.648960 | 0.0382404 | ||||||||
\(289\) | −3.44250 | −0.202500 | ||||||||
\(290\) | 33.6421 | 1.97553 | ||||||||
\(291\) | 13.8738 | 0.813294 | ||||||||
\(292\) | −5.40949 | −0.316567 | ||||||||
\(293\) | 7.43809 | 0.434538 | 0.217269 | − | 0.976112i | \(-0.430285\pi\) | ||||
0.217269 | + | 0.976112i | \(0.430285\pi\) | |||||||
\(294\) | 4.52418 | 0.263856 | ||||||||
\(295\) | 0.667339 | 0.0388540 | ||||||||
\(296\) | −7.76032 | −0.451059 | ||||||||
\(297\) | 15.2916 | 0.887310 | ||||||||
\(298\) | −43.8327 | −2.53916 | ||||||||
\(299\) | −0.255741 | −0.0147899 | ||||||||
\(300\) | −42.0583 | −2.42824 | ||||||||
\(301\) | 9.88190 | 0.569584 | ||||||||
\(302\) | 23.9380 | 1.37748 | ||||||||
\(303\) | −28.0584 | −1.61191 | ||||||||
\(304\) | −62.2600 | −3.57086 | ||||||||
\(305\) | 8.06397 | 0.461741 | ||||||||
\(306\) | −0.511492 | −0.0292400 | ||||||||
\(307\) | −27.6917 | −1.58045 | −0.790224 | − | 0.612818i | \(-0.790036\pi\) | ||||
−0.790224 | + | 0.612818i | \(0.790036\pi\) | |||||||
\(308\) | −14.4279 | −0.822104 | ||||||||
\(309\) | 34.4272 | 1.95849 | ||||||||
\(310\) | −8.31452 | −0.472233 | ||||||||
\(311\) | 7.38443 | 0.418733 | 0.209366 | − | 0.977837i | \(-0.432860\pi\) | ||||
0.209366 | + | 0.977837i | \(0.432860\pi\) | |||||||
\(312\) | −0.409238 | −0.0231685 | ||||||||
\(313\) | −25.6010 | −1.44705 | −0.723527 | − | 0.690297i | \(-0.757480\pi\) | ||||
−0.723527 | + | 0.690297i | \(0.757480\pi\) | |||||||
\(314\) | −45.0334 | −2.54138 | ||||||||
\(315\) | −0.166314 | −0.00937073 | ||||||||
\(316\) | 26.8050 | 1.50790 | ||||||||
\(317\) | −20.8879 | −1.17318 | −0.586590 | − | 0.809884i | \(-0.699530\pi\) | ||||
−0.586590 | + | 0.809884i | \(0.699530\pi\) | |||||||
\(318\) | −9.29002 | −0.520958 | ||||||||
\(319\) | 11.8060 | 0.661009 | ||||||||
\(320\) | −35.7188 | −1.99674 | ||||||||
\(321\) | 8.99026 | 0.501787 | ||||||||
\(322\) | 21.9404 | 1.22269 | ||||||||
\(323\) | 21.7064 | 1.20777 | ||||||||
\(324\) | −43.7072 | −2.42818 | ||||||||
\(325\) | −0.152188 | −0.00844187 | ||||||||
\(326\) | −19.7461 | −1.09364 | ||||||||
\(327\) | −11.0621 | −0.611738 | ||||||||
\(328\) | 7.30993 | 0.403623 | ||||||||
\(329\) | −4.99629 | −0.275455 | ||||||||
\(330\) | −41.6490 | −2.29270 | ||||||||
\(331\) | −24.3817 | −1.34014 | −0.670069 | − | 0.742299i | \(-0.733735\pi\) | ||||
−0.670069 | + | 0.742299i | \(0.733735\pi\) | |||||||
\(332\) | −72.5053 | −3.97925 | ||||||||
\(333\) | −0.0527133 | −0.00288867 | ||||||||
\(334\) | 62.7040 | 3.43101 | ||||||||
\(335\) | −42.3486 | −2.31375 | ||||||||
\(336\) | 18.1311 | 0.989130 | ||||||||
\(337\) | −10.5971 | −0.577261 | −0.288630 | − | 0.957441i | \(-0.593200\pi\) | ||||
−0.288630 | + | 0.957441i | \(0.593200\pi\) | |||||||
\(338\) | 34.2563 | 1.86330 | ||||||||
\(339\) | 18.7322 | 1.01739 | ||||||||
\(340\) | 57.4439 | 3.11533 | ||||||||
\(341\) | −2.91781 | −0.158008 | ||||||||
\(342\) | −0.818929 | −0.0442826 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 76.6867 | 4.13467 | ||||||||
\(345\) | 45.0957 | 2.42787 | ||||||||
\(346\) | −3.83061 | −0.205935 | ||||||||
\(347\) | 12.1532 | 0.652416 | 0.326208 | − | 0.945298i | \(-0.394229\pi\) | ||||
0.326208 | + | 0.945298i | \(0.394229\pi\) | |||||||
\(348\) | −34.3481 | −1.84125 | ||||||||
\(349\) | −2.61459 | −0.139956 | −0.0699778 | − | 0.997549i | \(-0.522293\pi\) | ||||
−0.0699778 | + | 0.997549i | \(0.522293\pi\) | |||||||
\(350\) | 13.0564 | 0.697894 | ||||||||
\(351\) | −0.160984 | −0.00859268 | ||||||||
\(352\) | −35.9215 | −1.91462 | ||||||||
\(353\) | −20.6057 | −1.09673 | −0.548366 | − | 0.836239i | \(-0.684750\pi\) | ||||
−0.548366 | + | 0.836239i | \(0.684750\pi\) | |||||||
\(354\) | −0.956925 | −0.0508600 | ||||||||
\(355\) | −40.9168 | −2.17164 | ||||||||
\(356\) | 42.5886 | 2.25719 | ||||||||
\(357\) | −6.32122 | −0.334555 | ||||||||
\(358\) | 34.0019 | 1.79705 | ||||||||
\(359\) | 24.5795 | 1.29726 | 0.648629 | − | 0.761105i | \(-0.275343\pi\) | ||||
0.648629 | + | 0.761105i | \(0.275343\pi\) | |||||||
\(360\) | −1.29065 | −0.0680232 | ||||||||
\(361\) | 15.7532 | 0.829116 | ||||||||
\(362\) | 14.4210 | 0.757952 | ||||||||
\(363\) | 4.26857 | 0.224042 | ||||||||
\(364\) | 0.151891 | 0.00796123 | ||||||||
\(365\) | 3.45159 | 0.180665 | ||||||||
\(366\) | −11.5633 | −0.604421 | ||||||||
\(367\) | −1.27829 | −0.0667263 | −0.0333632 | − | 0.999443i | \(-0.510622\pi\) | ||||
−0.0333632 | + | 0.999443i | \(0.510622\pi\) | |||||||
\(368\) | 87.9281 | 4.58357 | ||||||||
\(369\) | 0.0496540 | 0.00258488 | ||||||||
\(370\) | 8.31452 | 0.432251 | ||||||||
\(371\) | 2.05341 | 0.106608 | ||||||||
\(372\) | 8.48901 | 0.440134 | ||||||||
\(373\) | −28.2010 | −1.46019 | −0.730096 | − | 0.683345i | \(-0.760525\pi\) | ||||
−0.730096 | + | 0.683345i | \(0.760525\pi\) | |||||||
\(374\) | 28.3123 | 1.46399 | ||||||||
\(375\) | −0.246752 | −0.0127422 | ||||||||
\(376\) | −38.7728 | −1.99956 | ||||||||
\(377\) | −0.124289 | −0.00640119 | ||||||||
\(378\) | 13.8110 | 0.710363 | ||||||||
\(379\) | 20.5998 | 1.05814 | 0.529071 | − | 0.848578i | \(-0.322541\pi\) | ||||
0.529071 | + | 0.848578i | \(0.322541\pi\) | |||||||
\(380\) | 91.9711 | 4.71802 | ||||||||
\(381\) | 4.44772 | 0.227863 | ||||||||
\(382\) | −68.0251 | −3.48047 | ||||||||
\(383\) | 22.6238 | 1.15602 | 0.578011 | − | 0.816029i | \(-0.303829\pi\) | ||||
0.578011 | + | 0.816029i | \(0.303829\pi\) | |||||||
\(384\) | 8.94801 | 0.456626 | ||||||||
\(385\) | 9.20588 | 0.469175 | ||||||||
\(386\) | 34.5050 | 1.75626 | ||||||||
\(387\) | 0.520908 | 0.0264792 | ||||||||
\(388\) | −39.9603 | −2.02868 | ||||||||
\(389\) | 4.52612 | 0.229483 | 0.114742 | − | 0.993395i | \(-0.463396\pi\) | ||||
0.114742 | + | 0.993395i | \(0.463396\pi\) | |||||||
\(390\) | 0.438464 | 0.0222025 | ||||||||
\(391\) | −30.6553 | −1.55030 | ||||||||
\(392\) | −7.76032 | −0.391955 | ||||||||
\(393\) | −1.20489 | −0.0607785 | ||||||||
\(394\) | 61.2490 | 3.08568 | ||||||||
\(395\) | −17.1032 | −0.860558 | ||||||||
\(396\) | −0.760540 | −0.0382186 | ||||||||
\(397\) | −13.4606 | −0.675568 | −0.337784 | − | 0.941224i | \(-0.609677\pi\) | ||||
−0.337784 | + | 0.941224i | \(0.609677\pi\) | |||||||
\(398\) | −8.41132 | −0.421621 | ||||||||
\(399\) | −10.1207 | −0.506667 | ||||||||
\(400\) | 52.3247 | 2.61624 | ||||||||
\(401\) | 6.90612 | 0.344875 | 0.172438 | − | 0.985020i | \(-0.444836\pi\) | ||||
0.172438 | + | 0.985020i | \(0.444836\pi\) | |||||||
\(402\) | 60.7254 | 3.02871 | ||||||||
\(403\) | 0.0307174 | 0.00153015 | ||||||||
\(404\) | 80.8159 | 4.02074 | ||||||||
\(405\) | 27.8879 | 1.38576 | ||||||||
\(406\) | 10.6629 | 0.529190 | ||||||||
\(407\) | 2.91781 | 0.144630 | ||||||||
\(408\) | −49.0547 | −2.42857 | ||||||||
\(409\) | −3.56735 | −0.176394 | −0.0881971 | − | 0.996103i | \(-0.528111\pi\) | ||||
−0.0881971 | + | 0.996103i | \(0.528111\pi\) | |||||||
\(410\) | −7.83197 | −0.386794 | ||||||||
\(411\) | −3.68930 | −0.181980 | ||||||||
\(412\) | −99.1598 | −4.88525 | ||||||||
\(413\) | 0.211513 | 0.0104079 | ||||||||
\(414\) | 1.15655 | 0.0568413 | ||||||||
\(415\) | 46.2629 | 2.27096 | ||||||||
\(416\) | 0.378167 | 0.0185411 | ||||||||
\(417\) | 33.4195 | 1.63656 | ||||||||
\(418\) | 45.3297 | 2.21715 | ||||||||
\(419\) | 0.534638 | 0.0261188 | 0.0130594 | − | 0.999915i | \(-0.495843\pi\) | ||||
0.0130594 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(420\) | −26.7834 | −1.30689 | ||||||||
\(421\) | −29.8011 | −1.45242 | −0.726209 | − | 0.687474i | \(-0.758720\pi\) | ||||
−0.726209 | + | 0.687474i | \(0.758720\pi\) | |||||||
\(422\) | −28.9529 | −1.40941 | ||||||||
\(423\) | −0.263371 | −0.0128055 | ||||||||
\(424\) | 15.9351 | 0.773879 | ||||||||
\(425\) | −18.2425 | −0.884892 | ||||||||
\(426\) | 58.6723 | 2.84268 | ||||||||
\(427\) | 2.55588 | 0.123688 | ||||||||
\(428\) | −25.8945 | −1.25166 | ||||||||
\(429\) | 0.153870 | 0.00742890 | ||||||||
\(430\) | −82.1633 | −3.96227 | ||||||||
\(431\) | −2.06961 | −0.0996897 | −0.0498449 | − | 0.998757i | \(-0.515873\pi\) | ||||
−0.0498449 | + | 0.998757i | \(0.515873\pi\) | |||||||
\(432\) | 55.3489 | 2.66298 | ||||||||
\(433\) | 22.4412 | 1.07846 | 0.539228 | − | 0.842160i | \(-0.318716\pi\) | ||||
0.539228 | + | 0.842160i | \(0.318716\pi\) | |||||||
\(434\) | −2.63529 | −0.126498 | ||||||||
\(435\) | 21.9162 | 1.05080 | ||||||||
\(436\) | 31.8621 | 1.52592 | ||||||||
\(437\) | −49.0810 | −2.34786 | ||||||||
\(438\) | −4.94938 | −0.236491 | ||||||||
\(439\) | 18.3921 | 0.877808 | 0.438904 | − | 0.898534i | \(-0.355367\pi\) | ||||
0.438904 | + | 0.898534i | \(0.355367\pi\) | |||||||
\(440\) | 71.4405 | 3.40579 | ||||||||
\(441\) | −0.0527133 | −0.00251016 | ||||||||
\(442\) | −0.298060 | −0.0141773 | ||||||||
\(443\) | −19.2915 | −0.916568 | −0.458284 | − | 0.888806i | \(-0.651536\pi\) | ||||
−0.458284 | + | 0.888806i | \(0.651536\pi\) | |||||||
\(444\) | −8.48901 | −0.402870 | ||||||||
\(445\) | −27.1742 | −1.28818 | ||||||||
\(446\) | −9.74895 | −0.461626 | ||||||||
\(447\) | −28.5549 | −1.35060 | ||||||||
\(448\) | −11.3211 | −0.534871 | ||||||||
\(449\) | −6.25959 | −0.295408 | −0.147704 | − | 0.989032i | \(-0.547188\pi\) | ||||
−0.147704 | + | 0.989032i | \(0.547188\pi\) | |||||||
\(450\) | 0.688246 | 0.0324442 | ||||||||
\(451\) | −2.74847 | −0.129420 | ||||||||
\(452\) | −53.9539 | −2.53778 | ||||||||
\(453\) | 15.5945 | 0.732691 | ||||||||
\(454\) | 0.409483 | 0.0192180 | ||||||||
\(455\) | −0.0969156 | −0.00454347 | ||||||||
\(456\) | −78.5395 | −3.67795 | ||||||||
\(457\) | 11.8843 | 0.555926 | 0.277963 | − | 0.960592i | \(-0.410341\pi\) | ||||
0.277963 | + | 0.960592i | \(0.410341\pi\) | |||||||
\(458\) | −75.2715 | −3.51721 | ||||||||
\(459\) | −19.2969 | −0.900701 | ||||||||
\(460\) | −129.888 | −6.05607 | ||||||||
\(461\) | −9.98204 | −0.464910 | −0.232455 | − | 0.972607i | \(-0.574676\pi\) | ||||
−0.232455 | + | 0.972607i | \(0.574676\pi\) | |||||||
\(462\) | −13.2007 | −0.614152 | ||||||||
\(463\) | −19.7536 | −0.918029 | −0.459014 | − | 0.888429i | \(-0.651797\pi\) | ||||
−0.459014 | + | 0.888429i | \(0.651797\pi\) | |||||||
\(464\) | 42.7325 | 1.98381 | ||||||||
\(465\) | −5.41651 | −0.251185 | ||||||||
\(466\) | 7.19512 | 0.333307 | ||||||||
\(467\) | 1.23145 | 0.0569849 | 0.0284924 | − | 0.999594i | \(-0.490929\pi\) | ||||
0.0284924 | + | 0.999594i | \(0.490929\pi\) | |||||||
\(468\) | 0.00800665 | 0.000370108 0 | ||||||||
\(469\) | −13.4224 | −0.619790 | ||||||||
\(470\) | 41.5418 | 1.91618 | ||||||||
\(471\) | −29.3371 | −1.35178 | ||||||||
\(472\) | 1.64141 | 0.0755521 | ||||||||
\(473\) | −28.8335 | −1.32577 | ||||||||
\(474\) | 24.5251 | 1.12647 | ||||||||
\(475\) | −29.2074 | −1.34013 | ||||||||
\(476\) | 18.2069 | 0.834511 | ||||||||
\(477\) | 0.108242 | 0.00495607 | ||||||||
\(478\) | 16.4295 | 0.751469 | ||||||||
\(479\) | −23.4862 | −1.07311 | −0.536556 | − | 0.843865i | \(-0.680275\pi\) | ||||
−0.536556 | + | 0.843865i | \(0.680275\pi\) | |||||||
\(480\) | −66.6834 | −3.04367 | ||||||||
\(481\) | −0.0307174 | −0.00140060 | ||||||||
\(482\) | −8.81082 | −0.401322 | ||||||||
\(483\) | 14.2931 | 0.650359 | ||||||||
\(484\) | −12.2947 | −0.558849 | ||||||||
\(485\) | 25.4971 | 1.15776 | ||||||||
\(486\) | 1.44348 | 0.0654775 | ||||||||
\(487\) | 15.3945 | 0.697592 | 0.348796 | − | 0.937199i | \(-0.386591\pi\) | ||||
0.348796 | + | 0.937199i | \(0.386591\pi\) | |||||||
\(488\) | 19.8344 | 0.897862 | ||||||||
\(489\) | −12.8636 | −0.581714 | ||||||||
\(490\) | 8.31452 | 0.375612 | ||||||||
\(491\) | −29.8889 | −1.34887 | −0.674434 | − | 0.738336i | \(-0.735612\pi\) | ||||
−0.674434 | + | 0.738336i | \(0.735612\pi\) | |||||||
\(492\) | 7.99633 | 0.360502 | ||||||||
\(493\) | −14.8983 | −0.670985 | ||||||||
\(494\) | −0.477212 | −0.0214708 | ||||||||
\(495\) | 0.485272 | 0.0218114 | ||||||||
\(496\) | −10.5612 | −0.474210 | ||||||||
\(497\) | −12.9686 | −0.581722 | ||||||||
\(498\) | −66.3383 | −2.97269 | ||||||||
\(499\) | 29.9586 | 1.34113 | 0.670566 | − | 0.741850i | \(-0.266051\pi\) | ||||
0.670566 | + | 0.741850i | \(0.266051\pi\) | |||||||
\(500\) | 0.710713 | 0.0317841 | ||||||||
\(501\) | 40.8486 | 1.82498 | ||||||||
\(502\) | 25.7267 | 1.14824 | ||||||||
\(503\) | −1.48938 | −0.0664083 | −0.0332042 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332042 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(504\) | −0.409072 | −0.0182215 | ||||||||
\(505\) | −51.5656 | −2.29464 | ||||||||
\(506\) | −64.0178 | −2.84594 | ||||||||
\(507\) | 22.3163 | 0.991104 | ||||||||
\(508\) | −12.8107 | −0.568381 | ||||||||
\(509\) | −9.82058 | −0.435289 | −0.217645 | − | 0.976028i | \(-0.569837\pi\) | ||||
−0.217645 | + | 0.976028i | \(0.569837\pi\) | |||||||
\(510\) | 52.5579 | 2.32730 | ||||||||
\(511\) | 1.09398 | 0.0483950 | ||||||||
\(512\) | 33.8960 | 1.49801 | ||||||||
\(513\) | −30.8955 | −1.36407 | ||||||||
\(514\) | −4.64082 | −0.204698 | ||||||||
\(515\) | 63.2701 | 2.78801 | ||||||||
\(516\) | 83.8875 | 3.69294 | ||||||||
\(517\) | 14.5782 | 0.641149 | ||||||||
\(518\) | 2.63529 | 0.115788 | ||||||||
\(519\) | −2.49546 | −0.109539 | ||||||||
\(520\) | −0.752096 | −0.0329816 | ||||||||
\(521\) | −3.83043 | −0.167814 | −0.0839071 | − | 0.996474i | \(-0.526740\pi\) | ||||
−0.0839071 | + | 0.996474i | \(0.526740\pi\) | |||||||
\(522\) | 0.562076 | 0.0246014 | ||||||||
\(523\) | −14.4193 | −0.630514 | −0.315257 | − | 0.949006i | \(-0.602091\pi\) | ||||
−0.315257 | + | 0.949006i | \(0.602091\pi\) | |||||||
\(524\) | 3.47041 | 0.151606 | ||||||||
\(525\) | 8.50562 | 0.371216 | ||||||||
\(526\) | 67.3238 | 2.93546 | ||||||||
\(527\) | 3.68205 | 0.160393 | ||||||||
\(528\) | −52.9029 | −2.30230 | ||||||||
\(529\) | 46.3156 | 2.01372 | ||||||||
\(530\) | −17.0732 | −0.741611 | ||||||||
\(531\) | 0.0111496 | 0.000483850 0 | ||||||||
\(532\) | 29.1503 | 1.26383 | ||||||||
\(533\) | 0.0289347 | 0.00125330 | ||||||||
\(534\) | 38.9662 | 1.68623 | ||||||||
\(535\) | 16.5223 | 0.714320 | ||||||||
\(536\) | −104.162 | −4.49912 | ||||||||
\(537\) | 22.1506 | 0.955868 | ||||||||
\(538\) | −58.0387 | −2.50223 | ||||||||
\(539\) | 2.91781 | 0.125679 | ||||||||
\(540\) | −81.7620 | −3.51848 | ||||||||
\(541\) | −27.4267 | −1.17916 | −0.589582 | − | 0.807708i | \(-0.700708\pi\) | ||||
−0.589582 | + | 0.807708i | \(0.700708\pi\) | |||||||
\(542\) | 6.44859 | 0.276991 | ||||||||
\(543\) | 9.39460 | 0.403161 | ||||||||
\(544\) | 45.3302 | 1.94352 | ||||||||
\(545\) | −20.3300 | −0.870840 | ||||||||
\(546\) | 0.138971 | 0.00594742 | ||||||||
\(547\) | −17.9831 | −0.768901 | −0.384450 | − | 0.923146i | \(-0.625609\pi\) | ||||
−0.384450 | + | 0.923146i | \(0.625609\pi\) | |||||||
\(548\) | 10.6262 | 0.453930 | ||||||||
\(549\) | 0.134729 | 0.00575008 | ||||||||
\(550\) | −38.0961 | −1.62442 | ||||||||
\(551\) | −23.8530 | −1.01617 | ||||||||
\(552\) | 110.919 | 4.72103 | ||||||||
\(553\) | −5.42088 | −0.230519 | ||||||||
\(554\) | −70.7010 | −3.00380 | ||||||||
\(555\) | 5.41651 | 0.229918 | ||||||||
\(556\) | −96.2574 | −4.08222 | ||||||||
\(557\) | 11.3799 | 0.482180 | 0.241090 | − | 0.970503i | \(-0.422495\pi\) | ||||
0.241090 | + | 0.970503i | \(0.422495\pi\) | |||||||
\(558\) | −0.138915 | −0.00588074 | ||||||||
\(559\) | 0.303547 | 0.0128387 | ||||||||
\(560\) | 33.3212 | 1.40808 | ||||||||
\(561\) | 18.4441 | 0.778711 | ||||||||
\(562\) | 59.1250 | 2.49404 | ||||||||
\(563\) | 22.6930 | 0.956396 | 0.478198 | − | 0.878252i | \(-0.341290\pi\) | ||||
0.478198 | + | 0.878252i | \(0.341290\pi\) | |||||||
\(564\) | −42.4136 | −1.78593 | ||||||||
\(565\) | 34.4259 | 1.44831 | ||||||||
\(566\) | 67.0128 | 2.81676 | ||||||||
\(567\) | 8.83908 | 0.371207 | ||||||||
\(568\) | −100.640 | −4.22278 | ||||||||
\(569\) | −42.2509 | −1.77125 | −0.885624 | − | 0.464402i | \(-0.846269\pi\) | ||||
−0.885624 | + | 0.464402i | \(0.846269\pi\) | |||||||
\(570\) | 84.1484 | 3.52459 | ||||||||
\(571\) | −32.6900 | −1.36803 | −0.684017 | − | 0.729466i | \(-0.739769\pi\) | ||||
−0.684017 | + | 0.729466i | \(0.739769\pi\) | |||||||
\(572\) | −0.443187 | −0.0185306 | ||||||||
\(573\) | −44.3151 | −1.85129 | ||||||||
\(574\) | −2.48235 | −0.103611 | ||||||||
\(575\) | 41.2487 | 1.72019 | ||||||||
\(576\) | −0.596772 | −0.0248655 | ||||||||
\(577\) | −1.97451 | −0.0821999 | −0.0411000 | − | 0.999155i | \(-0.513086\pi\) | ||||
−0.0411000 | + | 0.999155i | \(0.513086\pi\) | |||||||
\(578\) | 9.07199 | 0.377345 | ||||||||
\(579\) | 22.4784 | 0.934169 | ||||||||
\(580\) | −63.1248 | −2.62112 | ||||||||
\(581\) | 14.6631 | 0.608326 | ||||||||
\(582\) | −36.5614 | −1.51552 | ||||||||
\(583\) | −5.99147 | −0.248141 | ||||||||
\(584\) | 8.48966 | 0.351305 | ||||||||
\(585\) | −0.00510874 | −0.000211220 0 | ||||||||
\(586\) | −19.6015 | −0.809732 | ||||||||
\(587\) | 35.4273 | 1.46224 | 0.731122 | − | 0.682247i | \(-0.238997\pi\) | ||||
0.731122 | + | 0.682247i | \(0.238997\pi\) | |||||||
\(588\) | −8.48901 | −0.350081 | ||||||||
\(589\) | 5.89519 | 0.242907 | ||||||||
\(590\) | −1.75863 | −0.0724018 | ||||||||
\(591\) | 39.9008 | 1.64130 | ||||||||
\(592\) | 10.5612 | 0.434061 | ||||||||
\(593\) | 34.6176 | 1.42157 | 0.710786 | − | 0.703408i | \(-0.248339\pi\) | ||||
0.710786 | + | 0.703408i | \(0.248339\pi\) | |||||||
\(594\) | −40.2979 | −1.65344 | ||||||||
\(595\) | −11.6171 | −0.476255 | ||||||||
\(596\) | 82.2461 | 3.36893 | ||||||||
\(597\) | −5.47957 | −0.224264 | ||||||||
\(598\) | 0.673953 | 0.0275600 | ||||||||
\(599\) | 43.6696 | 1.78429 | 0.892146 | − | 0.451748i | \(-0.149199\pi\) | ||||
0.892146 | + | 0.451748i | \(0.149199\pi\) | |||||||
\(600\) | 66.0063 | 2.69470 | ||||||||
\(601\) | 3.28076 | 0.133825 | 0.0669124 | − | 0.997759i | \(-0.478685\pi\) | ||||
0.0669124 | + | 0.997759i | \(0.478685\pi\) | |||||||
\(602\) | −26.0417 | −1.06138 | ||||||||
\(603\) | −0.707540 | −0.0288133 | ||||||||
\(604\) | −44.9164 | −1.82762 | ||||||||
\(605\) | 7.84476 | 0.318935 | ||||||||
\(606\) | 73.9420 | 3.00369 | ||||||||
\(607\) | −41.9500 | −1.70270 | −0.851348 | − | 0.524601i | \(-0.824214\pi\) | ||||
−0.851348 | + | 0.524601i | \(0.824214\pi\) | |||||||
\(608\) | 72.5764 | 2.94336 | ||||||||
\(609\) | 6.94636 | 0.281481 | ||||||||
\(610\) | −21.2509 | −0.860424 | ||||||||
\(611\) | −0.153473 | −0.00620887 | ||||||||
\(612\) | 0.959744 | 0.0387954 | ||||||||
\(613\) | 37.0642 | 1.49701 | 0.748505 | − | 0.663130i | \(-0.230772\pi\) | ||||
0.748505 | + | 0.663130i | \(0.230772\pi\) | |||||||
\(614\) | 72.9757 | 2.94506 | ||||||||
\(615\) | −5.10215 | −0.205739 | ||||||||
\(616\) | 22.6431 | 0.912317 | ||||||||
\(617\) | 7.59001 | 0.305562 | 0.152781 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152781 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(618\) | −90.7256 | −3.64952 | ||||||||
\(619\) | 47.5164 | 1.90985 | 0.954923 | − | 0.296853i | \(-0.0959373\pi\) | ||||
0.954923 | + | 0.296853i | \(0.0959373\pi\) | |||||||
\(620\) | 15.6011 | 0.626554 | ||||||||
\(621\) | 43.6328 | 1.75092 | ||||||||
\(622\) | −19.4601 | −0.780280 | ||||||||
\(623\) | −8.61286 | −0.345067 | ||||||||
\(624\) | 0.556940 | 0.0222954 | ||||||||
\(625\) | −25.2257 | −1.00903 | ||||||||
\(626\) | 67.4661 | 2.69649 | ||||||||
\(627\) | 29.5301 | 1.17932 | ||||||||
\(628\) | 84.4990 | 3.37188 | ||||||||
\(629\) | −3.68205 | −0.146813 | ||||||||
\(630\) | 0.438286 | 0.0174617 | ||||||||
\(631\) | 35.2433 | 1.40301 | 0.701506 | − | 0.712664i | \(-0.252511\pi\) | ||||
0.701506 | + | 0.712664i | \(0.252511\pi\) | |||||||
\(632\) | −42.0678 | −1.67337 | ||||||||
\(633\) | −18.8614 | −0.749675 | ||||||||
\(634\) | 55.0456 | 2.18614 | ||||||||
\(635\) | 8.17399 | 0.324375 | ||||||||
\(636\) | 17.4314 | 0.691202 | ||||||||
\(637\) | −0.0307174 | −0.00121707 | ||||||||
\(638\) | −31.1123 | −1.23175 | ||||||||
\(639\) | −0.683618 | −0.0270435 | ||||||||
\(640\) | 16.4446 | 0.650030 | ||||||||
\(641\) | −19.6869 | −0.777586 | −0.388793 | − | 0.921325i | \(-0.627108\pi\) | ||||
−0.388793 | + | 0.921325i | \(0.627108\pi\) | |||||||
\(642\) | −23.6920 | −0.935047 | ||||||||
\(643\) | 39.3743 | 1.55277 | 0.776386 | − | 0.630257i | \(-0.217051\pi\) | ||||
0.776386 | + | 0.630257i | \(0.217051\pi\) | |||||||
\(644\) | −41.1681 | −1.62225 | ||||||||
\(645\) | −53.5255 | −2.10756 | ||||||||
\(646\) | −57.2026 | −2.25061 | ||||||||
\(647\) | −26.6643 | −1.04828 | −0.524141 | − | 0.851631i | \(-0.675614\pi\) | ||||
−0.524141 | + | 0.851631i | \(0.675614\pi\) | |||||||
\(648\) | 68.5941 | 2.69463 | ||||||||
\(649\) | −0.617155 | −0.0242255 | ||||||||
\(650\) | 0.401060 | 0.0157309 | ||||||||
\(651\) | −1.71677 | −0.0672854 | ||||||||
\(652\) | 37.0509 | 1.45102 | ||||||||
\(653\) | −0.346561 | −0.0135620 | −0.00678099 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00678099 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(654\) | 29.1520 | 1.13993 | ||||||||
\(655\) | −2.21434 | −0.0865213 | ||||||||
\(656\) | −9.94823 | −0.388413 | ||||||||
\(657\) | 0.0576675 | 0.00224982 | ||||||||
\(658\) | 13.1667 | 0.513291 | ||||||||
\(659\) | −15.8594 | −0.617795 | −0.308898 | − | 0.951095i | \(-0.599960\pi\) | ||||
−0.308898 | + | 0.951095i | \(0.599960\pi\) | |||||||
\(660\) | 78.1487 | 3.04194 | ||||||||
\(661\) | −6.31293 | −0.245545 | −0.122772 | − | 0.992435i | \(-0.539178\pi\) | ||||
−0.122772 | + | 0.992435i | \(0.539178\pi\) | |||||||
\(662\) | 64.2528 | 2.49726 | ||||||||
\(663\) | −0.194172 | −0.00754101 | ||||||||
\(664\) | 113.790 | 4.41590 | ||||||||
\(665\) | −18.5997 | −0.721265 | ||||||||
\(666\) | 0.138915 | 0.00538284 | ||||||||
\(667\) | 33.6870 | 1.30436 | ||||||||
\(668\) | −117.655 | −4.55222 | ||||||||
\(669\) | −6.35097 | −0.245543 | ||||||||
\(670\) | 111.601 | 4.31152 | ||||||||
\(671\) | −7.45756 | −0.287896 | ||||||||
\(672\) | −21.1353 | −0.815313 | ||||||||
\(673\) | 5.93953 | 0.228952 | 0.114476 | − | 0.993426i | \(-0.463481\pi\) | ||||
0.114476 | + | 0.993426i | \(0.463481\pi\) | |||||||
\(674\) | 27.9265 | 1.07569 | ||||||||
\(675\) | 25.9652 | 0.999402 | ||||||||
\(676\) | −64.2773 | −2.47220 | ||||||||
\(677\) | 36.8244 | 1.41528 | 0.707638 | − | 0.706575i | \(-0.249761\pi\) | ||||
0.707638 | + | 0.706575i | \(0.249761\pi\) | |||||||
\(678\) | −49.3648 | −1.89584 | ||||||||
\(679\) | 8.08133 | 0.310133 | ||||||||
\(680\) | −90.1525 | −3.45719 | ||||||||
\(681\) | 0.266759 | 0.0102222 | ||||||||
\(682\) | 7.68927 | 0.294438 | ||||||||
\(683\) | 30.5136 | 1.16757 | 0.583785 | − | 0.811908i | \(-0.301571\pi\) | ||||
0.583785 | + | 0.811908i | \(0.301571\pi\) | |||||||
\(684\) | 1.53661 | 0.0587537 | ||||||||
\(685\) | −6.78019 | −0.259058 | ||||||||
\(686\) | 2.63529 | 0.100616 | ||||||||
\(687\) | −49.0358 | −1.87083 | ||||||||
\(688\) | −104.364 | −3.97886 | ||||||||
\(689\) | 0.0630756 | 0.00240299 | ||||||||
\(690\) | −118.840 | −4.52418 | ||||||||
\(691\) | −7.84131 | −0.298297 | −0.149149 | − | 0.988815i | \(-0.547653\pi\) | ||||
−0.149149 | + | 0.988815i | \(0.547653\pi\) | |||||||
\(692\) | 7.18762 | 0.273232 | ||||||||
\(693\) | 0.153807 | 0.00584265 | ||||||||
\(694\) | −32.0271 | −1.21573 | ||||||||
\(695\) | 61.4182 | 2.32972 | ||||||||
\(696\) | 53.9059 | 2.04330 | ||||||||
\(697\) | 3.46836 | 0.131373 | ||||||||
\(698\) | 6.89020 | 0.260798 | ||||||||
\(699\) | 4.68728 | 0.177289 | ||||||||
\(700\) | −24.4986 | −0.925959 | ||||||||
\(701\) | 36.5833 | 1.38173 | 0.690866 | − | 0.722983i | \(-0.257229\pi\) | ||||
0.690866 | + | 0.722983i | \(0.257229\pi\) | |||||||
\(702\) | 0.424240 | 0.0160119 | ||||||||
\(703\) | −5.89519 | −0.222341 | ||||||||
\(704\) | 33.0328 | 1.24497 | ||||||||
\(705\) | 27.0625 | 1.01923 | ||||||||
\(706\) | 54.3021 | 2.04368 | ||||||||
\(707\) | −16.3437 | −0.614669 | ||||||||
\(708\) | 1.79554 | 0.0674805 | ||||||||
\(709\) | 4.67072 | 0.175412 | 0.0877062 | − | 0.996146i | \(-0.472046\pi\) | ||||
0.0877062 | + | 0.996146i | \(0.472046\pi\) | |||||||
\(710\) | 107.828 | 4.04670 | ||||||||
\(711\) | −0.285753 | −0.0107166 | ||||||||
\(712\) | −66.8385 | −2.50488 | ||||||||
\(713\) | −8.32560 | −0.311796 | ||||||||
\(714\) | 16.6583 | 0.623420 | ||||||||
\(715\) | 0.282781 | 0.0105754 | ||||||||
\(716\) | −63.7999 | −2.38431 | ||||||||
\(717\) | 10.7031 | 0.399713 | ||||||||
\(718\) | −64.7743 | −2.41735 | ||||||||
\(719\) | −1.94794 | −0.0726461 | −0.0363230 | − | 0.999340i | \(-0.511565\pi\) | ||||
−0.0363230 | + | 0.999340i | \(0.511565\pi\) | |||||||
\(720\) | 1.75647 | 0.0654598 | ||||||||
\(721\) | 20.0535 | 0.746831 | ||||||||
\(722\) | −41.5143 | −1.54500 | ||||||||
\(723\) | −5.73983 | −0.213466 | ||||||||
\(724\) | −27.0591 | −1.00564 | ||||||||
\(725\) | 20.0466 | 0.744513 | ||||||||
\(726\) | −11.2489 | −0.417487 | ||||||||
\(727\) | 0.410968 | 0.0152420 | 0.00762098 | − | 0.999971i | \(-0.497574\pi\) | ||||
0.00762098 | + | 0.999971i | \(0.497574\pi\) | |||||||
\(728\) | −0.238377 | −0.00883484 | ||||||||
\(729\) | 27.4576 | 1.01695 | ||||||||
\(730\) | −9.09595 | −0.336656 | ||||||||
\(731\) | 36.3857 | 1.34577 | ||||||||
\(732\) | 21.6969 | 0.801939 | ||||||||
\(733\) | −23.5920 | −0.871391 | −0.435695 | − | 0.900094i | \(-0.643498\pi\) | ||||
−0.435695 | + | 0.900094i | \(0.643498\pi\) | |||||||
\(734\) | 3.36867 | 0.124340 | ||||||||
\(735\) | 5.41651 | 0.199791 | ||||||||
\(736\) | −102.498 | −3.77811 | ||||||||
\(737\) | 39.1640 | 1.44263 | ||||||||
\(738\) | −0.130853 | −0.00481676 | ||||||||
\(739\) | 33.1133 | 1.21809 | 0.609046 | − | 0.793135i | \(-0.291553\pi\) | ||||
0.609046 | + | 0.793135i | \(0.291553\pi\) | |||||||
\(740\) | −15.6011 | −0.573506 | ||||||||
\(741\) | −0.310881 | −0.0114205 | ||||||||
\(742\) | −5.41135 | −0.198657 | ||||||||
\(743\) | 43.8621 | 1.60915 | 0.804573 | − | 0.593854i | \(-0.202394\pi\) | ||||
0.804573 | + | 0.593854i | \(0.202394\pi\) | |||||||
\(744\) | −13.3226 | −0.488432 | ||||||||
\(745\) | −52.4781 | −1.92265 | ||||||||
\(746\) | 74.3178 | 2.72097 | ||||||||
\(747\) | 0.772938 | 0.0282803 | ||||||||
\(748\) | −53.1242 | −1.94241 | ||||||||
\(749\) | 5.23674 | 0.191346 | ||||||||
\(750\) | 0.650262 | 0.0237442 | ||||||||
\(751\) | −37.0041 | −1.35030 | −0.675149 | − | 0.737681i | \(-0.735921\pi\) | ||||
−0.675149 | + | 0.737681i | \(0.735921\pi\) | |||||||
\(752\) | 52.7667 | 1.92420 | ||||||||
\(753\) | 16.7597 | 0.610758 | ||||||||
\(754\) | 0.327537 | 0.0119282 | ||||||||
\(755\) | 28.6594 | 1.04302 | ||||||||
\(756\) | −25.9145 | −0.942501 | ||||||||
\(757\) | −9.15847 | −0.332870 | −0.166435 | − | 0.986052i | \(-0.553226\pi\) | ||||
−0.166435 | + | 0.986052i | \(0.553226\pi\) | |||||||
\(758\) | −54.2865 | −1.97178 | ||||||||
\(759\) | −41.7045 | −1.51378 | ||||||||
\(760\) | −144.340 | −5.23575 | ||||||||
\(761\) | −19.0128 | −0.689214 | −0.344607 | − | 0.938747i | \(-0.611988\pi\) | ||||
−0.344607 | + | 0.938747i | \(0.611988\pi\) | |||||||
\(762\) | −11.7210 | −0.424608 | ||||||||
\(763\) | −6.44359 | −0.233274 | ||||||||
\(764\) | 127.640 | 4.61785 | ||||||||
\(765\) | −0.612376 | −0.0221405 | ||||||||
\(766\) | −59.6203 | −2.15417 | ||||||||
\(767\) | 0.00649715 | 0.000234599 0 | ||||||||
\(768\) | 15.2907 | 0.551757 | ||||||||
\(769\) | 27.3612 | 0.986670 | 0.493335 | − | 0.869839i | \(-0.335778\pi\) | ||||
0.493335 | + | 0.869839i | \(0.335778\pi\) | |||||||
\(770\) | −24.2602 | −0.874276 | ||||||||
\(771\) | −3.02327 | −0.108880 | ||||||||
\(772\) | −64.7439 | −2.33019 | ||||||||
\(773\) | −29.3331 | −1.05504 | −0.527519 | − | 0.849543i | \(-0.676878\pi\) | ||||
−0.527519 | + | 0.849543i | \(0.676878\pi\) | |||||||
\(774\) | −1.37274 | −0.0493423 | ||||||||
\(775\) | −4.95444 | −0.177969 | ||||||||
\(776\) | 62.7137 | 2.25129 | ||||||||
\(777\) | 1.71677 | 0.0615886 | ||||||||
\(778\) | −11.9276 | −0.427627 | ||||||||
\(779\) | 5.55305 | 0.198959 | ||||||||
\(780\) | −0.822717 | −0.0294580 | ||||||||
\(781\) | 37.8399 | 1.35402 | ||||||||
\(782\) | 80.7856 | 2.88889 | ||||||||
\(783\) | 21.2052 | 0.757814 | ||||||||
\(784\) | 10.5612 | 0.377185 | ||||||||
\(785\) | −53.9156 | −1.92433 | ||||||||
\(786\) | 3.17523 | 0.113257 | ||||||||
\(787\) | −18.4009 | −0.655922 | −0.327961 | − | 0.944691i | \(-0.606361\pi\) | ||||
−0.327961 | + | 0.944691i | \(0.606361\pi\) | |||||||
\(788\) | −114.925 | −4.09405 | ||||||||
\(789\) | 43.8582 | 1.56139 | ||||||||
\(790\) | 45.0721 | 1.60359 | ||||||||
\(791\) | 10.9113 | 0.387962 | ||||||||
\(792\) | 1.19359 | 0.0424125 | ||||||||
\(793\) | 0.0785101 | 0.00278797 | ||||||||
\(794\) | 35.4726 | 1.25888 | ||||||||
\(795\) | −11.1223 | −0.394469 | ||||||||
\(796\) | 15.7827 | 0.559403 | ||||||||
\(797\) | 8.85858 | 0.313787 | 0.156893 | − | 0.987616i | \(-0.449852\pi\) | ||||
0.156893 | + | 0.987616i | \(0.449852\pi\) | |||||||
\(798\) | 26.6709 | 0.944139 | ||||||||
\(799\) | −18.3966 | −0.650825 | ||||||||
\(800\) | −60.9948 | −2.15649 | ||||||||
\(801\) | −0.454012 | −0.0160417 | ||||||||
\(802\) | −18.1996 | −0.642652 | ||||||||
\(803\) | −3.19203 | −0.112644 | ||||||||
\(804\) | −113.943 | −4.01846 | ||||||||
\(805\) | 26.2678 | 0.925819 | ||||||||
\(806\) | −0.0809495 | −0.00285132 | ||||||||
\(807\) | −37.8095 | −1.33096 | ||||||||
\(808\) | −126.833 | −4.46195 | ||||||||
\(809\) | 3.73318 | 0.131252 | 0.0656259 | − | 0.997844i | \(-0.479096\pi\) | ||||
0.0656259 | + | 0.997844i | \(0.479096\pi\) | |||||||
\(810\) | −73.4927 | −2.58227 | ||||||||
\(811\) | 14.7047 | 0.516352 | 0.258176 | − | 0.966098i | \(-0.416878\pi\) | ||||
0.258176 | + | 0.966098i | \(0.416878\pi\) | |||||||
\(812\) | −20.0075 | −0.702124 | ||||||||
\(813\) | 4.20095 | 0.147334 | ||||||||
\(814\) | −7.68927 | −0.269509 | ||||||||
\(815\) | −23.6408 | −0.828100 | ||||||||
\(816\) | 66.7595 | 2.33705 | ||||||||
\(817\) | 58.2557 | 2.03811 | ||||||||
\(818\) | 9.40101 | 0.328699 | ||||||||
\(819\) | −0.00161922 | −5.65800e−5 0 | ||||||||
\(820\) | 14.6956 | 0.513193 | ||||||||
\(821\) | 30.9000 | 1.07842 | 0.539208 | − | 0.842173i | \(-0.318724\pi\) | ||||
0.539208 | + | 0.842173i | \(0.318724\pi\) | |||||||
\(822\) | 9.72239 | 0.339107 | ||||||||
\(823\) | −0.903887 | −0.0315075 | −0.0157538 | − | 0.999876i | \(-0.505015\pi\) | ||||
−0.0157538 | + | 0.999876i | \(0.505015\pi\) | |||||||
\(824\) | 155.621 | 5.42133 | ||||||||
\(825\) | −24.8178 | −0.864044 | ||||||||
\(826\) | −0.557400 | −0.0193944 | ||||||||
\(827\) | 26.8039 | 0.932062 | 0.466031 | − | 0.884768i | \(-0.345684\pi\) | ||||
0.466031 | + | 0.884768i | \(0.345684\pi\) | |||||||
\(828\) | −2.17011 | −0.0754165 | ||||||||
\(829\) | 29.8044 | 1.03515 | 0.517574 | − | 0.855638i | \(-0.326835\pi\) | ||||
0.517574 | + | 0.855638i | \(0.326835\pi\) | |||||||
\(830\) | −121.916 | −4.23178 | ||||||||
\(831\) | −46.0583 | −1.59775 | ||||||||
\(832\) | −0.347755 | −0.0120562 | ||||||||
\(833\) | −3.68205 | −0.127576 | ||||||||
\(834\) | −88.0701 | −3.04962 | ||||||||
\(835\) | 75.0714 | 2.59795 | ||||||||
\(836\) | −85.0550 | −2.94169 | ||||||||
\(837\) | −5.24080 | −0.181148 | ||||||||
\(838\) | −1.40893 | −0.0486706 | ||||||||
\(839\) | −25.2381 | −0.871317 | −0.435659 | − | 0.900112i | \(-0.643484\pi\) | ||||
−0.435659 | + | 0.900112i | \(0.643484\pi\) | |||||||
\(840\) | 42.0338 | 1.45031 | ||||||||
\(841\) | −12.6284 | −0.435461 | ||||||||
\(842\) | 78.5347 | 2.70648 | ||||||||
\(843\) | 38.5171 | 1.32660 | ||||||||
\(844\) | 54.3262 | 1.86999 | ||||||||
\(845\) | 41.0129 | 1.41089 | ||||||||
\(846\) | 0.694060 | 0.0238623 | ||||||||
\(847\) | 2.48640 | 0.0854338 | ||||||||
\(848\) | −21.6865 | −0.744716 | ||||||||
\(849\) | 43.6556 | 1.49826 | ||||||||
\(850\) | 48.0744 | 1.64894 | ||||||||
\(851\) | 8.32560 | 0.285398 | ||||||||
\(852\) | −110.091 | −3.77164 | ||||||||
\(853\) | 56.0810 | 1.92018 | 0.960089 | − | 0.279694i | \(-0.0902331\pi\) | ||||
0.960089 | + | 0.279694i | \(0.0902331\pi\) | |||||||
\(854\) | −6.73549 | −0.230484 | ||||||||
\(855\) | −0.980451 | −0.0335307 | ||||||||
\(856\) | 40.6388 | 1.38900 | ||||||||
\(857\) | −3.81599 | −0.130352 | −0.0651759 | − | 0.997874i | \(-0.520761\pi\) | ||||
−0.0651759 | + | 0.997874i | \(0.520761\pi\) | |||||||
\(858\) | −0.405491 | −0.0138432 | ||||||||
\(859\) | 26.6296 | 0.908590 | 0.454295 | − | 0.890851i | \(-0.349891\pi\) | ||||
0.454295 | + | 0.890851i | \(0.349891\pi\) | |||||||
\(860\) | 154.168 | 5.25709 | ||||||||
\(861\) | −1.61713 | −0.0551117 | ||||||||
\(862\) | 5.45403 | 0.185765 | ||||||||
\(863\) | 13.7822 | 0.469152 | 0.234576 | − | 0.972098i | \(-0.424630\pi\) | ||||
0.234576 | + | 0.972098i | \(0.424630\pi\) | |||||||
\(864\) | −64.5201 | −2.19502 | ||||||||
\(865\) | −4.58615 | −0.155934 | ||||||||
\(866\) | −59.1391 | −2.00963 | ||||||||
\(867\) | 5.90996 | 0.200713 | ||||||||
\(868\) | 4.94476 | 0.167836 | ||||||||
\(869\) | 15.8171 | 0.536558 | ||||||||
\(870\) | −57.7557 | −1.95810 | ||||||||
\(871\) | −0.412302 | −0.0139703 | ||||||||
\(872\) | −50.0043 | −1.69336 | ||||||||
\(873\) | 0.425993 | 0.0144177 | ||||||||
\(874\) | 129.343 | 4.37508 | ||||||||
\(875\) | −0.143730 | −0.00485897 | ||||||||
\(876\) | 9.28684 | 0.313773 | ||||||||
\(877\) | 22.7788 | 0.769184 | 0.384592 | − | 0.923087i | \(-0.374342\pi\) | ||||
0.384592 | + | 0.923087i | \(0.374342\pi\) | |||||||
\(878\) | −48.4686 | −1.63574 | ||||||||
\(879\) | −12.7695 | −0.430703 | ||||||||
\(880\) | −97.2248 | −3.27745 | ||||||||
\(881\) | 22.0245 | 0.742024 | 0.371012 | − | 0.928628i | \(-0.379011\pi\) | ||||
0.371012 | + | 0.928628i | \(0.379011\pi\) | |||||||
\(882\) | 0.138915 | 0.00467751 | ||||||||
\(883\) | 20.6836 | 0.696057 | 0.348029 | − | 0.937484i | \(-0.386851\pi\) | ||||
0.348029 | + | 0.937484i | \(0.386851\pi\) | |||||||
\(884\) | 0.559269 | 0.0188102 | ||||||||
\(885\) | −1.14567 | −0.0385111 | ||||||||
\(886\) | 50.8388 | 1.70796 | ||||||||
\(887\) | 32.4413 | 1.08927 | 0.544636 | − | 0.838673i | \(-0.316668\pi\) | ||||
0.544636 | + | 0.838673i | \(0.316668\pi\) | |||||||
\(888\) | 13.3226 | 0.447079 | ||||||||
\(889\) | 2.59075 | 0.0868910 | ||||||||
\(890\) | 71.6119 | 2.40043 | ||||||||
\(891\) | −25.7907 | −0.864022 | ||||||||
\(892\) | 18.2926 | 0.612480 | ||||||||
\(893\) | −29.4541 | −0.985643 | ||||||||
\(894\) | 75.2505 | 2.51675 | ||||||||
\(895\) | 40.7083 | 1.36073 | ||||||||
\(896\) | 5.21213 | 0.174125 | ||||||||
\(897\) | 0.439048 | 0.0146594 | ||||||||
\(898\) | 16.4958 | 0.550473 | ||||||||
\(899\) | −4.04619 | −0.134948 | ||||||||
\(900\) | −1.29140 | −0.0430467 | ||||||||
\(901\) | 7.56078 | 0.251886 | ||||||||
\(902\) | 7.24301 | 0.241166 | ||||||||
\(903\) | −16.9649 | −0.564557 | ||||||||
\(904\) | 84.6753 | 2.81626 | ||||||||
\(905\) | 17.2654 | 0.573920 | ||||||||
\(906\) | −41.0959 | −1.36532 | ||||||||
\(907\) | 37.0471 | 1.23013 | 0.615065 | − | 0.788476i | \(-0.289130\pi\) | ||||
0.615065 | + | 0.788476i | \(0.289130\pi\) | |||||||
\(908\) | −0.768339 | −0.0254982 | ||||||||
\(909\) | −0.861532 | −0.0285752 | ||||||||
\(910\) | 0.255401 | 0.00846646 | ||||||||
\(911\) | 10.1122 | 0.335033 | 0.167517 | − | 0.985869i | \(-0.446425\pi\) | ||||
0.167517 | + | 0.985869i | \(0.446425\pi\) | |||||||
\(912\) | 106.886 | 3.53935 | ||||||||
\(913\) | −42.7840 | −1.41594 | ||||||||
\(914\) | −31.3187 | −1.03593 | ||||||||
\(915\) | −13.8439 | −0.457667 | ||||||||
\(916\) | 141.237 | 4.66659 | ||||||||
\(917\) | −0.701835 | −0.0231766 | ||||||||
\(918\) | 50.8529 | 1.67840 | ||||||||
\(919\) | 14.4004 | 0.475027 | 0.237513 | − | 0.971384i | \(-0.423668\pi\) | ||||
0.237513 | + | 0.971384i | \(0.423668\pi\) | |||||||
\(920\) | 203.847 | 6.72062 | ||||||||
\(921\) | 47.5401 | 1.56650 | ||||||||
\(922\) | 26.3056 | 0.866328 | ||||||||
\(923\) | −0.398363 | −0.0131123 | ||||||||
\(924\) | 24.7693 | 0.814850 | ||||||||
\(925\) | 4.95444 | 0.162901 | ||||||||
\(926\) | 52.0566 | 1.71068 | ||||||||
\(927\) | 1.05709 | 0.0347192 | ||||||||
\(928\) | −49.8132 | −1.63520 | ||||||||
\(929\) | 2.76064 | 0.0905737 | 0.0452869 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452869 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(930\) | 14.2741 | 0.468066 | ||||||||
\(931\) | −5.89519 | −0.193207 | ||||||||
\(932\) | −13.5007 | −0.442229 | ||||||||
\(933\) | −12.6773 | −0.415038 | ||||||||
\(934\) | −3.24524 | −0.106187 | ||||||||
\(935\) | 33.8965 | 1.10853 | ||||||||
\(936\) | −0.0125656 | −0.000410721 0 | ||||||||
\(937\) | 50.1341 | 1.63781 | 0.818905 | − | 0.573929i | \(-0.194581\pi\) | ||||
0.818905 | + | 0.573929i | \(0.194581\pi\) | |||||||
\(938\) | 35.3720 | 1.15494 | ||||||||
\(939\) | 43.9509 | 1.43428 | ||||||||
\(940\) | −77.9475 | −2.54237 | ||||||||
\(941\) | 10.5373 | 0.343506 | 0.171753 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171753 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(942\) | 77.3118 | 2.51895 | ||||||||
\(943\) | −7.84241 | −0.255384 | ||||||||
\(944\) | −2.23383 | −0.0727049 | ||||||||
\(945\) | 16.5351 | 0.537885 | ||||||||
\(946\) | 75.9847 | 2.47047 | ||||||||
\(947\) | 3.20529 | 0.104158 | 0.0520790 | − | 0.998643i | \(-0.483415\pi\) | ||||
0.0520790 | + | 0.998643i | \(0.483415\pi\) | |||||||
\(948\) | −46.0179 | −1.49459 | ||||||||
\(949\) | 0.0336044 | 0.00109084 | ||||||||
\(950\) | 76.9699 | 2.49723 | ||||||||
\(951\) | 35.8596 | 1.16283 | ||||||||
\(952\) | −28.5739 | −0.926085 | ||||||||
\(953\) | 34.9760 | 1.13298 | 0.566492 | − | 0.824067i | \(-0.308300\pi\) | ||||
0.566492 | + | 0.824067i | \(0.308300\pi\) | |||||||
\(954\) | −0.285250 | −0.00923531 | ||||||||
\(955\) | −81.4421 | −2.63541 | ||||||||
\(956\) | −30.8278 | −0.997041 | ||||||||
\(957\) | −20.2681 | −0.655176 | ||||||||
\(958\) | 61.8930 | 1.99967 | ||||||||
\(959\) | −2.14898 | −0.0693943 | ||||||||
\(960\) | 61.3209 | 1.97912 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0.0809495 | 0.00260992 | ||||||||
\(963\) | 0.276046 | 0.00889545 | ||||||||
\(964\) | 16.5323 | 0.532469 | ||||||||
\(965\) | 41.3107 | 1.32984 | ||||||||
\(966\) | −37.6665 | −1.21190 | ||||||||
\(967\) | −6.39790 | −0.205743 | −0.102871 | − | 0.994695i | \(-0.532803\pi\) | ||||
−0.102871 | + | 0.994695i | \(0.532803\pi\) | |||||||
\(968\) | 19.2953 | 0.620173 | ||||||||
\(969\) | −37.2648 | −1.19712 | ||||||||
\(970\) | −67.1924 | −2.15742 | ||||||||
\(971\) | −57.8957 | −1.85796 | −0.928980 | − | 0.370130i | \(-0.879313\pi\) | ||||
−0.928980 | + | 0.370130i | \(0.879313\pi\) | |||||||
\(972\) | −2.70849 | −0.0868748 | ||||||||
\(973\) | 19.4665 | 0.624068 | ||||||||
\(974\) | −40.5690 | −1.29992 | ||||||||
\(975\) | 0.261271 | 0.00836737 | ||||||||
\(976\) | −26.9931 | −0.864027 | ||||||||
\(977\) | 58.5842 | 1.87428 | 0.937138 | − | 0.348959i | \(-0.113465\pi\) | ||||
0.937138 | + | 0.348959i | \(0.113465\pi\) | |||||||
\(978\) | 33.8995 | 1.08399 | ||||||||
\(979\) | 25.1307 | 0.803180 | ||||||||
\(980\) | −15.6011 | −0.498358 | ||||||||
\(981\) | −0.339663 | −0.0108446 | ||||||||
\(982\) | 78.7660 | 2.51352 | ||||||||
\(983\) | 2.21812 | 0.0707469 | 0.0353735 | − | 0.999374i | \(-0.488738\pi\) | ||||
0.0353735 | + | 0.999374i | \(0.488738\pi\) | |||||||
\(984\) | −12.5494 | −0.400062 | ||||||||
\(985\) | 73.3295 | 2.33647 | ||||||||
\(986\) | 39.2613 | 1.25033 | ||||||||
\(987\) | 8.57747 | 0.273024 | ||||||||
\(988\) | 0.895423 | 0.0284872 | ||||||||
\(989\) | −82.2728 | −2.61612 | ||||||||
\(990\) | −1.27883 | −0.0406440 | ||||||||
\(991\) | −25.6608 | −0.815141 | −0.407571 | − | 0.913174i | \(-0.633624\pi\) | ||||
−0.407571 | + | 0.913174i | \(0.633624\pi\) | |||||||
\(992\) | 12.3111 | 0.390879 | ||||||||
\(993\) | 41.8576 | 1.32831 | ||||||||
\(994\) | 34.1761 | 1.08400 | ||||||||
\(995\) | −10.0703 | −0.319251 | ||||||||
\(996\) | 124.475 | 3.94413 | ||||||||
\(997\) | 14.0269 | 0.444235 | 0.222118 | − | 0.975020i | \(-0.428703\pi\) | ||||
0.222118 | + | 0.975020i | \(0.428703\pi\) | |||||||
\(998\) | −78.9497 | −2.49911 | ||||||||
\(999\) | 5.24080 | 0.165811 |
(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 | 8029.2.a.h.1.4 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8029.2.a.h.1.4 | ✓ | 71 | 1.1 | even | 1 | trivial |