Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.569311 | 0.402564 | 0.201282 | − | 0.979533i | \(-0.435489\pi\) | ||||
0.201282 | + | 0.979533i | \(0.435489\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.67588 | −0.837942 | ||||||||
\(5\) | 1.10171 | 0.492701 | 0.246351 | − | 0.969181i | \(-0.420769\pi\) | ||||
0.246351 | + | 0.969181i | \(0.420769\pi\) | |||||||
\(6\) | 0.569311 | 0.232420 | ||||||||
\(7\) | 2.67084 | 1.00948 | 0.504741 | − | 0.863271i | \(-0.331588\pi\) | ||||
0.504741 | + | 0.863271i | \(0.331588\pi\) | |||||||
\(8\) | −2.09272 | −0.739889 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.627218 | 0.198344 | ||||||||
\(11\) | −5.58292 | −1.68331 | −0.841656 | − | 0.540013i | \(-0.818419\pi\) | ||||
−0.841656 | + | 0.540013i | \(0.818419\pi\) | |||||||
\(12\) | −1.67588 | −0.483786 | ||||||||
\(13\) | 5.66739 | 1.57185 | 0.785925 | − | 0.618322i | \(-0.212187\pi\) | ||||
0.785925 | + | 0.618322i | \(0.212187\pi\) | |||||||
\(14\) | 1.52054 | 0.406381 | ||||||||
\(15\) | 1.10171 | 0.284461 | ||||||||
\(16\) | 2.16036 | 0.540090 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.569311 | 0.134188 | ||||||||
\(19\) | −8.17874 | −1.87633 | −0.938165 | − | 0.346187i | \(-0.887476\pi\) | ||||
−0.938165 | + | 0.346187i | \(0.887476\pi\) | |||||||
\(20\) | −1.84634 | −0.412855 | ||||||||
\(21\) | 2.67084 | 0.582825 | ||||||||
\(22\) | −3.17842 | −0.677641 | ||||||||
\(23\) | 1.82305 | 0.380133 | 0.190066 | − | 0.981771i | \(-0.439130\pi\) | ||||
0.190066 | + | 0.981771i | \(0.439130\pi\) | |||||||
\(24\) | −2.09272 | −0.427175 | ||||||||
\(25\) | −3.78623 | −0.757246 | ||||||||
\(26\) | 3.22651 | 0.632770 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.47602 | −0.845888 | ||||||||
\(29\) | −0.370279 | −0.0687591 | −0.0343796 | − | 0.999409i | \(-0.510946\pi\) | ||||
−0.0343796 | + | 0.999409i | \(0.510946\pi\) | |||||||
\(30\) | 0.627218 | 0.114514 | ||||||||
\(31\) | −0.983283 | −0.176603 | −0.0883015 | − | 0.996094i | \(-0.528144\pi\) | ||||
−0.0883015 | + | 0.996094i | \(0.528144\pi\) | |||||||
\(32\) | 5.41536 | 0.957310 | ||||||||
\(33\) | −5.58292 | −0.971861 | ||||||||
\(34\) | −0.569311 | −0.0976361 | ||||||||
\(35\) | 2.94250 | 0.497373 | ||||||||
\(36\) | −1.67588 | −0.279314 | ||||||||
\(37\) | −7.61191 | −1.25139 | −0.625695 | − | 0.780068i | \(-0.715184\pi\) | ||||
−0.625695 | + | 0.780068i | \(0.715184\pi\) | |||||||
\(38\) | −4.65625 | −0.755343 | ||||||||
\(39\) | 5.66739 | 0.907508 | ||||||||
\(40\) | −2.30558 | −0.364544 | ||||||||
\(41\) | −0.900065 | −0.140567 | −0.0702833 | − | 0.997527i | \(-0.522390\pi\) | ||||
−0.0702833 | + | 0.997527i | \(0.522390\pi\) | |||||||
\(42\) | 1.52054 | 0.234624 | ||||||||
\(43\) | −0.382632 | −0.0583508 | −0.0291754 | − | 0.999574i | \(-0.509288\pi\) | ||||
−0.0291754 | + | 0.999574i | \(0.509288\pi\) | |||||||
\(44\) | 9.35632 | 1.41052 | ||||||||
\(45\) | 1.10171 | 0.164234 | ||||||||
\(46\) | 1.03788 | 0.153028 | ||||||||
\(47\) | 11.8642 | 1.73057 | 0.865286 | − | 0.501279i | \(-0.167137\pi\) | ||||
0.865286 | + | 0.501279i | \(0.167137\pi\) | |||||||
\(48\) | 2.16036 | 0.311821 | ||||||||
\(49\) | 0.133374 | 0.0190535 | ||||||||
\(50\) | −2.15554 | −0.304840 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −9.49789 | −1.31712 | ||||||||
\(53\) | −6.33675 | −0.870419 | −0.435210 | − | 0.900329i | \(-0.643326\pi\) | ||||
−0.435210 | + | 0.900329i | \(0.643326\pi\) | |||||||
\(54\) | 0.569311 | 0.0774735 | ||||||||
\(55\) | −6.15077 | −0.829370 | ||||||||
\(56\) | −5.58932 | −0.746905 | ||||||||
\(57\) | −8.17874 | −1.08330 | ||||||||
\(58\) | −0.210804 | −0.0276799 | ||||||||
\(59\) | 2.76405 | 0.359849 | 0.179925 | − | 0.983680i | \(-0.442415\pi\) | ||||
0.179925 | + | 0.983680i | \(0.442415\pi\) | |||||||
\(60\) | −1.84634 | −0.238362 | ||||||||
\(61\) | 4.73721 | 0.606538 | 0.303269 | − | 0.952905i | \(-0.401922\pi\) | ||||
0.303269 | + | 0.952905i | \(0.401922\pi\) | |||||||
\(62\) | −0.559794 | −0.0710940 | ||||||||
\(63\) | 2.67084 | 0.336494 | ||||||||
\(64\) | −1.23769 | −0.154711 | ||||||||
\(65\) | 6.24383 | 0.774452 | ||||||||
\(66\) | −3.17842 | −0.391236 | ||||||||
\(67\) | −15.6969 | −1.91769 | −0.958844 | − | 0.283935i | \(-0.908360\pi\) | ||||
−0.958844 | + | 0.283935i | \(0.908360\pi\) | |||||||
\(68\) | 1.67588 | 0.203231 | ||||||||
\(69\) | 1.82305 | 0.219470 | ||||||||
\(70\) | 1.67520 | 0.200224 | ||||||||
\(71\) | −10.4123 | −1.23571 | −0.617855 | − | 0.786292i | \(-0.711998\pi\) | ||||
−0.617855 | + | 0.786292i | \(0.711998\pi\) | |||||||
\(72\) | −2.09272 | −0.246630 | ||||||||
\(73\) | −3.19989 | −0.374519 | −0.187259 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187259 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(74\) | −4.33354 | −0.503764 | ||||||||
\(75\) | −3.78623 | −0.437196 | ||||||||
\(76\) | 13.7066 | 1.57226 | ||||||||
\(77\) | −14.9111 | −1.69927 | ||||||||
\(78\) | 3.22651 | 0.365330 | ||||||||
\(79\) | 9.43468 | 1.06148 | 0.530742 | − | 0.847533i | \(-0.321913\pi\) | ||||
0.530742 | + | 0.847533i | \(0.321913\pi\) | |||||||
\(80\) | 2.38009 | 0.266103 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.512417 | −0.0565870 | ||||||||
\(83\) | −6.69273 | −0.734622 | −0.367311 | − | 0.930098i | \(-0.619722\pi\) | ||||
−0.367311 | + | 0.930098i | \(0.619722\pi\) | |||||||
\(84\) | −4.47602 | −0.488373 | ||||||||
\(85\) | −1.10171 | −0.119498 | ||||||||
\(86\) | −0.217837 | −0.0234899 | ||||||||
\(87\) | −0.370279 | −0.0396981 | ||||||||
\(88\) | 11.6835 | 1.24546 | ||||||||
\(89\) | −5.70127 | −0.604333 | −0.302166 | − | 0.953255i | \(-0.597710\pi\) | ||||
−0.302166 | + | 0.953255i | \(0.597710\pi\) | |||||||
\(90\) | 0.627218 | 0.0661145 | ||||||||
\(91\) | 15.1367 | 1.58675 | ||||||||
\(92\) | −3.05523 | −0.318529 | ||||||||
\(93\) | −0.983283 | −0.101962 | ||||||||
\(94\) | 6.75442 | 0.696666 | ||||||||
\(95\) | −9.01062 | −0.924470 | ||||||||
\(96\) | 5.41536 | 0.552703 | ||||||||
\(97\) | −6.95071 | −0.705738 | −0.352869 | − | 0.935673i | \(-0.614794\pi\) | ||||
−0.352869 | + | 0.935673i | \(0.614794\pi\) | |||||||
\(98\) | 0.0759316 | 0.00767025 | ||||||||
\(99\) | −5.58292 | −0.561104 | ||||||||
\(100\) | 6.34528 | 0.634528 | ||||||||
\(101\) | 4.56234 | 0.453970 | 0.226985 | − | 0.973898i | \(-0.427113\pi\) | ||||
0.226985 | + | 0.973898i | \(0.427113\pi\) | |||||||
\(102\) | −0.569311 | −0.0563702 | ||||||||
\(103\) | −17.3272 | −1.70730 | −0.853651 | − | 0.520846i | \(-0.825617\pi\) | ||||
−0.853651 | + | 0.520846i | \(0.825617\pi\) | |||||||
\(104\) | −11.8603 | −1.16300 | ||||||||
\(105\) | 2.94250 | 0.287158 | ||||||||
\(106\) | −3.60758 | −0.350399 | ||||||||
\(107\) | −1.92613 | −0.186206 | −0.0931030 | − | 0.995656i | \(-0.529679\pi\) | ||||
−0.0931030 | + | 0.995656i | \(0.529679\pi\) | |||||||
\(108\) | −1.67588 | −0.161262 | ||||||||
\(109\) | 5.30123 | 0.507766 | 0.253883 | − | 0.967235i | \(-0.418292\pi\) | ||||
0.253883 | + | 0.967235i | \(0.418292\pi\) | |||||||
\(110\) | −3.50170 | −0.333874 | ||||||||
\(111\) | −7.61191 | −0.722490 | ||||||||
\(112\) | 5.76997 | 0.545211 | ||||||||
\(113\) | −16.3132 | −1.53462 | −0.767309 | − | 0.641277i | \(-0.778405\pi\) | ||||
−0.767309 | + | 0.641277i | \(0.778405\pi\) | |||||||
\(114\) | −4.65625 | −0.436097 | ||||||||
\(115\) | 2.00848 | 0.187292 | ||||||||
\(116\) | 0.620545 | 0.0576162 | ||||||||
\(117\) | 5.66739 | 0.523950 | ||||||||
\(118\) | 1.57361 | 0.144862 | ||||||||
\(119\) | −2.67084 | −0.244835 | ||||||||
\(120\) | −2.30558 | −0.210470 | ||||||||
\(121\) | 20.1690 | 1.83354 | ||||||||
\(122\) | 2.69695 | 0.244170 | ||||||||
\(123\) | −0.900065 | −0.0811561 | ||||||||
\(124\) | 1.64787 | 0.147983 | ||||||||
\(125\) | −9.67990 | −0.865797 | ||||||||
\(126\) | 1.52054 | 0.135460 | ||||||||
\(127\) | 6.14179 | 0.544996 | 0.272498 | − | 0.962156i | \(-0.412150\pi\) | ||||
0.272498 | + | 0.962156i | \(0.412150\pi\) | |||||||
\(128\) | −11.5354 | −1.01959 | ||||||||
\(129\) | −0.382632 | −0.0336889 | ||||||||
\(130\) | 3.55469 | 0.311767 | ||||||||
\(131\) | −6.41089 | −0.560122 | −0.280061 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280061 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(132\) | 9.35632 | 0.814363 | ||||||||
\(133\) | −21.8441 | −1.89412 | ||||||||
\(134\) | −8.93645 | −0.771992 | ||||||||
\(135\) | 1.10171 | 0.0948204 | ||||||||
\(136\) | 2.09272 | 0.179449 | ||||||||
\(137\) | −15.9195 | −1.36010 | −0.680049 | − | 0.733167i | \(-0.738042\pi\) | ||||
−0.680049 | + | 0.733167i | \(0.738042\pi\) | |||||||
\(138\) | 1.03788 | 0.0883506 | ||||||||
\(139\) | 3.75752 | 0.318709 | 0.159354 | − | 0.987221i | \(-0.449059\pi\) | ||||
0.159354 | + | 0.987221i | \(0.449059\pi\) | |||||||
\(140\) | −4.93128 | −0.416770 | ||||||||
\(141\) | 11.8642 | 0.999146 | ||||||||
\(142\) | −5.92783 | −0.497452 | ||||||||
\(143\) | −31.6406 | −2.64592 | ||||||||
\(144\) | 2.16036 | 0.180030 | ||||||||
\(145\) | −0.407941 | −0.0338777 | ||||||||
\(146\) | −1.82173 | −0.150768 | ||||||||
\(147\) | 0.133374 | 0.0110005 | ||||||||
\(148\) | 12.7567 | 1.04859 | ||||||||
\(149\) | 19.6328 | 1.60838 | 0.804190 | − | 0.594372i | \(-0.202599\pi\) | ||||
0.804190 | + | 0.594372i | \(0.202599\pi\) | |||||||
\(150\) | −2.15554 | −0.175999 | ||||||||
\(151\) | 5.24765 | 0.427048 | 0.213524 | − | 0.976938i | \(-0.431506\pi\) | ||||
0.213524 | + | 0.976938i | \(0.431506\pi\) | |||||||
\(152\) | 17.1158 | 1.38828 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −8.48904 | −0.684066 | ||||||||
\(155\) | −1.08330 | −0.0870124 | ||||||||
\(156\) | −9.49789 | −0.760440 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 5.37127 | 0.427315 | ||||||||
\(159\) | −6.33675 | −0.502537 | ||||||||
\(160\) | 5.96617 | 0.471668 | ||||||||
\(161\) | 4.86908 | 0.383737 | ||||||||
\(162\) | 0.569311 | 0.0447293 | ||||||||
\(163\) | 24.9047 | 1.95068 | 0.975341 | − | 0.220702i | \(-0.0708347\pi\) | ||||
0.975341 | + | 0.220702i | \(0.0708347\pi\) | |||||||
\(164\) | 1.50841 | 0.117787 | ||||||||
\(165\) | −6.15077 | −0.478837 | ||||||||
\(166\) | −3.81024 | −0.295732 | ||||||||
\(167\) | 7.68036 | 0.594324 | 0.297162 | − | 0.954827i | \(-0.403960\pi\) | ||||
0.297162 | + | 0.954827i | \(0.403960\pi\) | |||||||
\(168\) | −5.58932 | −0.431226 | ||||||||
\(169\) | 19.1193 | 1.47071 | ||||||||
\(170\) | −0.627218 | −0.0481054 | ||||||||
\(171\) | −8.17874 | −0.625444 | ||||||||
\(172\) | 0.641247 | 0.0488946 | ||||||||
\(173\) | 6.82989 | 0.519267 | 0.259634 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259634 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(174\) | −0.210804 | −0.0159810 | ||||||||
\(175\) | −10.1124 | −0.764426 | ||||||||
\(176\) | −12.0611 | −0.909140 | ||||||||
\(177\) | 2.76405 | 0.207759 | ||||||||
\(178\) | −3.24579 | −0.243283 | ||||||||
\(179\) | −5.52492 | −0.412952 | −0.206476 | − | 0.978452i | \(-0.566200\pi\) | ||||
−0.206476 | + | 0.978452i | \(0.566200\pi\) | |||||||
\(180\) | −1.84634 | −0.137618 | ||||||||
\(181\) | 4.66759 | 0.346940 | 0.173470 | − | 0.984839i | \(-0.444502\pi\) | ||||
0.173470 | + | 0.984839i | \(0.444502\pi\) | |||||||
\(182\) | 8.61748 | 0.638770 | ||||||||
\(183\) | 4.73721 | 0.350185 | ||||||||
\(184\) | −3.81515 | −0.281256 | ||||||||
\(185\) | −8.38614 | −0.616561 | ||||||||
\(186\) | −0.559794 | −0.0410461 | ||||||||
\(187\) | 5.58292 | 0.408263 | ||||||||
\(188\) | −19.8830 | −1.45012 | ||||||||
\(189\) | 2.67084 | 0.194275 | ||||||||
\(190\) | −5.12985 | −0.372158 | ||||||||
\(191\) | 13.2139 | 0.956124 | 0.478062 | − | 0.878326i | \(-0.341339\pi\) | ||||
0.478062 | + | 0.878326i | \(0.341339\pi\) | |||||||
\(192\) | −1.23769 | −0.0893226 | ||||||||
\(193\) | −13.7389 | −0.988950 | −0.494475 | − | 0.869192i | \(-0.664640\pi\) | ||||
−0.494475 | + | 0.869192i | \(0.664640\pi\) | |||||||
\(194\) | −3.95712 | −0.284104 | ||||||||
\(195\) | 6.24383 | 0.447130 | ||||||||
\(196\) | −0.223520 | −0.0159657 | ||||||||
\(197\) | −20.9742 | −1.49435 | −0.747173 | − | 0.664629i | \(-0.768590\pi\) | ||||
−0.747173 | + | 0.664629i | \(0.768590\pi\) | |||||||
\(198\) | −3.17842 | −0.225880 | ||||||||
\(199\) | 20.8820 | 1.48029 | 0.740144 | − | 0.672449i | \(-0.234757\pi\) | ||||
0.740144 | + | 0.672449i | \(0.234757\pi\) | |||||||
\(200\) | 7.92353 | 0.560278 | ||||||||
\(201\) | −15.6969 | −1.10718 | ||||||||
\(202\) | 2.59739 | 0.182752 | ||||||||
\(203\) | −0.988956 | −0.0694111 | ||||||||
\(204\) | 1.67588 | 0.117335 | ||||||||
\(205\) | −0.991613 | −0.0692573 | ||||||||
\(206\) | −9.86458 | −0.687298 | ||||||||
\(207\) | 1.82305 | 0.126711 | ||||||||
\(208\) | 12.2436 | 0.848940 | ||||||||
\(209\) | 45.6612 | 3.15845 | ||||||||
\(210\) | 1.67520 | 0.115600 | ||||||||
\(211\) | −20.5762 | −1.41653 | −0.708263 | − | 0.705949i | \(-0.750521\pi\) | ||||
−0.708263 | + | 0.705949i | \(0.750521\pi\) | |||||||
\(212\) | 10.6197 | 0.729361 | ||||||||
\(213\) | −10.4123 | −0.713437 | ||||||||
\(214\) | −1.09657 | −0.0749598 | ||||||||
\(215\) | −0.421551 | −0.0287495 | ||||||||
\(216\) | −2.09272 | −0.142392 | ||||||||
\(217\) | −2.62619 | −0.178277 | ||||||||
\(218\) | 3.01805 | 0.204408 | ||||||||
\(219\) | −3.19989 | −0.216228 | ||||||||
\(220\) | 10.3080 | 0.694964 | ||||||||
\(221\) | −5.66739 | −0.381230 | ||||||||
\(222\) | −4.33354 | −0.290848 | ||||||||
\(223\) | 10.2001 | 0.683048 | 0.341524 | − | 0.939873i | \(-0.389057\pi\) | ||||
0.341524 | + | 0.939873i | \(0.389057\pi\) | |||||||
\(224\) | 14.4636 | 0.966387 | ||||||||
\(225\) | −3.78623 | −0.252415 | ||||||||
\(226\) | −9.28730 | −0.617782 | ||||||||
\(227\) | 11.9693 | 0.794432 | 0.397216 | − | 0.917725i | \(-0.369976\pi\) | ||||
0.397216 | + | 0.917725i | \(0.369976\pi\) | |||||||
\(228\) | 13.7066 | 0.907743 | ||||||||
\(229\) | 10.4011 | 0.687321 | 0.343661 | − | 0.939094i | \(-0.388333\pi\) | ||||
0.343661 | + | 0.939094i | \(0.388333\pi\) | |||||||
\(230\) | 1.14345 | 0.0753969 | ||||||||
\(231\) | −14.9111 | −0.981076 | ||||||||
\(232\) | 0.774892 | 0.0508741 | ||||||||
\(233\) | 11.6668 | 0.764317 | 0.382158 | − | 0.924097i | \(-0.375181\pi\) | ||||
0.382158 | + | 0.924097i | \(0.375181\pi\) | |||||||
\(234\) | 3.22651 | 0.210923 | ||||||||
\(235\) | 13.0709 | 0.852654 | ||||||||
\(236\) | −4.63224 | −0.301533 | ||||||||
\(237\) | 9.43468 | 0.612848 | ||||||||
\(238\) | −1.52054 | −0.0985619 | ||||||||
\(239\) | −15.6723 | −1.01376 | −0.506878 | − | 0.862018i | \(-0.669201\pi\) | ||||
−0.506878 | + | 0.862018i | \(0.669201\pi\) | |||||||
\(240\) | 2.38009 | 0.153634 | ||||||||
\(241\) | −22.4327 | −1.44502 | −0.722509 | − | 0.691361i | \(-0.757011\pi\) | ||||
−0.722509 | + | 0.691361i | \(0.757011\pi\) | |||||||
\(242\) | 11.4824 | 0.738118 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −7.93903 | −0.508244 | ||||||||
\(245\) | 0.146940 | 0.00938768 | ||||||||
\(246\) | −0.512417 | −0.0326705 | ||||||||
\(247\) | −46.3521 | −2.94931 | ||||||||
\(248\) | 2.05774 | 0.130667 | ||||||||
\(249\) | −6.69273 | −0.424134 | ||||||||
\(250\) | −5.51088 | −0.348539 | ||||||||
\(251\) | −25.6094 | −1.61645 | −0.808227 | − | 0.588872i | \(-0.799572\pi\) | ||||
−0.808227 | + | 0.588872i | \(0.799572\pi\) | |||||||
\(252\) | −4.47602 | −0.281963 | ||||||||
\(253\) | −10.1780 | −0.639883 | ||||||||
\(254\) | 3.49659 | 0.219396 | ||||||||
\(255\) | −1.10171 | −0.0689919 | ||||||||
\(256\) | −4.09183 | −0.255739 | ||||||||
\(257\) | −11.3502 | −0.708009 | −0.354004 | − | 0.935244i | \(-0.615180\pi\) | ||||
−0.354004 | + | 0.935244i | \(0.615180\pi\) | |||||||
\(258\) | −0.217837 | −0.0135619 | ||||||||
\(259\) | −20.3302 | −1.26326 | ||||||||
\(260\) | −10.4639 | −0.648946 | ||||||||
\(261\) | −0.370279 | −0.0229197 | ||||||||
\(262\) | −3.64979 | −0.225485 | ||||||||
\(263\) | −27.3107 | −1.68405 | −0.842024 | − | 0.539440i | \(-0.818636\pi\) | ||||
−0.842024 | + | 0.539440i | \(0.818636\pi\) | |||||||
\(264\) | 11.6835 | 0.719070 | ||||||||
\(265\) | −6.98128 | −0.428856 | ||||||||
\(266\) | −12.4361 | −0.762505 | ||||||||
\(267\) | −5.70127 | −0.348912 | ||||||||
\(268\) | 26.3063 | 1.60691 | ||||||||
\(269\) | −23.4956 | −1.43255 | −0.716275 | − | 0.697818i | \(-0.754154\pi\) | ||||
−0.716275 | + | 0.697818i | \(0.754154\pi\) | |||||||
\(270\) | 0.627218 | 0.0381713 | ||||||||
\(271\) | 26.4862 | 1.60892 | 0.804460 | − | 0.594007i | \(-0.202455\pi\) | ||||
0.804460 | + | 0.594007i | \(0.202455\pi\) | |||||||
\(272\) | −2.16036 | −0.130991 | ||||||||
\(273\) | 15.1367 | 0.916113 | ||||||||
\(274\) | −9.06317 | −0.547526 | ||||||||
\(275\) | 21.1382 | 1.27468 | ||||||||
\(276\) | −3.05523 | −0.183903 | ||||||||
\(277\) | −25.2646 | −1.51800 | −0.759002 | − | 0.651089i | \(-0.774313\pi\) | ||||
−0.759002 | + | 0.651089i | \(0.774313\pi\) | |||||||
\(278\) | 2.13920 | 0.128301 | ||||||||
\(279\) | −0.983283 | −0.0588676 | ||||||||
\(280\) | −6.15783 | −0.368001 | ||||||||
\(281\) | −17.7033 | −1.05609 | −0.528045 | − | 0.849217i | \(-0.677075\pi\) | ||||
−0.528045 | + | 0.849217i | \(0.677075\pi\) | |||||||
\(282\) | 6.75442 | 0.402220 | ||||||||
\(283\) | 4.60308 | 0.273625 | 0.136812 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136812 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(284\) | 17.4498 | 1.03545 | ||||||||
\(285\) | −9.01062 | −0.533743 | ||||||||
\(286\) | −18.0133 | −1.06515 | ||||||||
\(287\) | −2.40393 | −0.141899 | ||||||||
\(288\) | 5.41536 | 0.319103 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −0.232246 | −0.0136379 | ||||||||
\(291\) | −6.95071 | −0.407458 | ||||||||
\(292\) | 5.36264 | 0.313825 | ||||||||
\(293\) | −22.8712 | −1.33615 | −0.668074 | − | 0.744095i | \(-0.732881\pi\) | ||||
−0.668074 | + | 0.744095i | \(0.732881\pi\) | |||||||
\(294\) | 0.0759316 | 0.00442842 | ||||||||
\(295\) | 3.04519 | 0.177298 | ||||||||
\(296\) | 15.9296 | 0.925890 | ||||||||
\(297\) | −5.58292 | −0.323954 | ||||||||
\(298\) | 11.1772 | 0.647476 | ||||||||
\(299\) | 10.3319 | 0.597512 | ||||||||
\(300\) | 6.34528 | 0.366345 | ||||||||
\(301\) | −1.02195 | −0.0589041 | ||||||||
\(302\) | 2.98755 | 0.171914 | ||||||||
\(303\) | 4.56234 | 0.262100 | ||||||||
\(304\) | −17.6690 | −1.01339 | ||||||||
\(305\) | 5.21905 | 0.298842 | ||||||||
\(306\) | −0.569311 | −0.0325454 | ||||||||
\(307\) | −4.19223 | −0.239263 | −0.119632 | − | 0.992818i | \(-0.538171\pi\) | ||||
−0.119632 | + | 0.992818i | \(0.538171\pi\) | |||||||
\(308\) | 24.9892 | 1.42389 | ||||||||
\(309\) | −17.3272 | −0.985711 | ||||||||
\(310\) | −0.616733 | −0.0350281 | ||||||||
\(311\) | −2.94310 | −0.166888 | −0.0834439 | − | 0.996512i | \(-0.526592\pi\) | ||||
−0.0834439 | + | 0.996512i | \(0.526592\pi\) | |||||||
\(312\) | −11.8603 | −0.671456 | ||||||||
\(313\) | −1.06581 | −0.0602431 | −0.0301216 | − | 0.999546i | \(-0.509589\pi\) | ||||
−0.0301216 | + | 0.999546i | \(0.509589\pi\) | |||||||
\(314\) | 0.569311 | 0.0321281 | ||||||||
\(315\) | 2.94250 | 0.165791 | ||||||||
\(316\) | −15.8114 | −0.889463 | ||||||||
\(317\) | −10.0695 | −0.565560 | −0.282780 | − | 0.959185i | \(-0.591257\pi\) | ||||
−0.282780 | + | 0.959185i | \(0.591257\pi\) | |||||||
\(318\) | −3.60758 | −0.202303 | ||||||||
\(319\) | 2.06724 | 0.115743 | ||||||||
\(320\) | −1.36358 | −0.0762264 | ||||||||
\(321\) | −1.92613 | −0.107506 | ||||||||
\(322\) | 2.77202 | 0.154479 | ||||||||
\(323\) | 8.17874 | 0.455077 | ||||||||
\(324\) | −1.67588 | −0.0931047 | ||||||||
\(325\) | −21.4580 | −1.19028 | ||||||||
\(326\) | 14.1785 | 0.785274 | ||||||||
\(327\) | 5.30123 | 0.293159 | ||||||||
\(328\) | 1.88359 | 0.104004 | ||||||||
\(329\) | 31.6874 | 1.74698 | ||||||||
\(330\) | −3.50170 | −0.192762 | ||||||||
\(331\) | 18.9636 | 1.04234 | 0.521168 | − | 0.853454i | \(-0.325497\pi\) | ||||
0.521168 | + | 0.853454i | \(0.325497\pi\) | |||||||
\(332\) | 11.2162 | 0.615571 | ||||||||
\(333\) | −7.61191 | −0.417130 | ||||||||
\(334\) | 4.37251 | 0.239253 | ||||||||
\(335\) | −17.2935 | −0.944846 | ||||||||
\(336\) | 5.76997 | 0.314778 | ||||||||
\(337\) | −22.5790 | −1.22996 | −0.614978 | − | 0.788544i | \(-0.710835\pi\) | ||||
−0.614978 | + | 0.788544i | \(0.710835\pi\) | |||||||
\(338\) | 10.8848 | 0.592056 | ||||||||
\(339\) | −16.3132 | −0.886013 | ||||||||
\(340\) | 1.84634 | 0.100132 | ||||||||
\(341\) | 5.48959 | 0.297278 | ||||||||
\(342\) | −4.65625 | −0.251781 | ||||||||
\(343\) | −18.3396 | −0.990248 | ||||||||
\(344\) | 0.800743 | 0.0431731 | ||||||||
\(345\) | 2.00848 | 0.108133 | ||||||||
\(346\) | 3.88834 | 0.209038 | ||||||||
\(347\) | 23.8497 | 1.28032 | 0.640161 | − | 0.768241i | \(-0.278868\pi\) | ||||
0.640161 | + | 0.768241i | \(0.278868\pi\) | |||||||
\(348\) | 0.620545 | 0.0332647 | ||||||||
\(349\) | 33.6034 | 1.79875 | 0.899375 | − | 0.437177i | \(-0.144022\pi\) | ||||
0.899375 | + | 0.437177i | \(0.144022\pi\) | |||||||
\(350\) | −5.75711 | −0.307730 | ||||||||
\(351\) | 5.66739 | 0.302503 | ||||||||
\(352\) | −30.2335 | −1.61145 | ||||||||
\(353\) | 9.02875 | 0.480552 | 0.240276 | − | 0.970705i | \(-0.422762\pi\) | ||||
0.240276 | + | 0.970705i | \(0.422762\pi\) | |||||||
\(354\) | 1.57361 | 0.0836363 | ||||||||
\(355\) | −11.4713 | −0.608835 | ||||||||
\(356\) | 9.55466 | 0.506396 | ||||||||
\(357\) | −2.67084 | −0.141356 | ||||||||
\(358\) | −3.14540 | −0.166240 | ||||||||
\(359\) | −35.8080 | −1.88987 | −0.944937 | − | 0.327252i | \(-0.893878\pi\) | ||||
−0.944937 | + | 0.327252i | \(0.893878\pi\) | |||||||
\(360\) | −2.30558 | −0.121515 | ||||||||
\(361\) | 47.8917 | 2.52062 | ||||||||
\(362\) | 2.65731 | 0.139665 | ||||||||
\(363\) | 20.1690 | 1.05860 | ||||||||
\(364\) | −25.3673 | −1.32961 | ||||||||
\(365\) | −3.52536 | −0.184526 | ||||||||
\(366\) | 2.69695 | 0.140972 | ||||||||
\(367\) | 6.08980 | 0.317885 | 0.158943 | − | 0.987288i | \(-0.449192\pi\) | ||||
0.158943 | + | 0.987288i | \(0.449192\pi\) | |||||||
\(368\) | 3.93845 | 0.205306 | ||||||||
\(369\) | −0.900065 | −0.0468555 | ||||||||
\(370\) | −4.77432 | −0.248205 | ||||||||
\(371\) | −16.9244 | −0.878672 | ||||||||
\(372\) | 1.64787 | 0.0854381 | ||||||||
\(373\) | −20.3227 | −1.05227 | −0.526135 | − | 0.850401i | \(-0.676359\pi\) | ||||
−0.526135 | + | 0.850401i | \(0.676359\pi\) | |||||||
\(374\) | 3.17842 | 0.164352 | ||||||||
\(375\) | −9.67990 | −0.499868 | ||||||||
\(376\) | −24.8285 | −1.28043 | ||||||||
\(377\) | −2.09852 | −0.108079 | ||||||||
\(378\) | 1.52054 | 0.0782080 | ||||||||
\(379\) | 16.5189 | 0.848519 | 0.424260 | − | 0.905541i | \(-0.360534\pi\) | ||||
0.424260 | + | 0.905541i | \(0.360534\pi\) | |||||||
\(380\) | 15.1008 | 0.774653 | ||||||||
\(381\) | 6.14179 | 0.314654 | ||||||||
\(382\) | 7.52282 | 0.384901 | ||||||||
\(383\) | 0.851323 | 0.0435006 | 0.0217503 | − | 0.999763i | \(-0.493076\pi\) | ||||
0.0217503 | + | 0.999763i | \(0.493076\pi\) | |||||||
\(384\) | −11.5354 | −0.588661 | ||||||||
\(385\) | −16.4277 | −0.837234 | ||||||||
\(386\) | −7.82173 | −0.398115 | ||||||||
\(387\) | −0.382632 | −0.0194503 | ||||||||
\(388\) | 11.6486 | 0.591367 | ||||||||
\(389\) | −12.6242 | −0.640070 | −0.320035 | − | 0.947406i | \(-0.603695\pi\) | ||||
−0.320035 | + | 0.947406i | \(0.603695\pi\) | |||||||
\(390\) | 3.55469 | 0.179998 | ||||||||
\(391\) | −1.82305 | −0.0921958 | ||||||||
\(392\) | −0.279116 | −0.0140975 | ||||||||
\(393\) | −6.41089 | −0.323386 | ||||||||
\(394\) | −11.9408 | −0.601570 | ||||||||
\(395\) | 10.3943 | 0.522994 | ||||||||
\(396\) | 9.35632 | 0.470173 | ||||||||
\(397\) | −10.2699 | −0.515433 | −0.257717 | − | 0.966221i | \(-0.582970\pi\) | ||||
−0.257717 | + | 0.966221i | \(0.582970\pi\) | |||||||
\(398\) | 11.8884 | 0.595910 | ||||||||
\(399\) | −21.8441 | −1.09357 | ||||||||
\(400\) | −8.17961 | −0.408981 | ||||||||
\(401\) | −9.76594 | −0.487688 | −0.243844 | − | 0.969815i | \(-0.578408\pi\) | ||||
−0.243844 | + | 0.969815i | \(0.578408\pi\) | |||||||
\(402\) | −8.93645 | −0.445710 | ||||||||
\(403\) | −5.57265 | −0.277593 | ||||||||
\(404\) | −7.64596 | −0.380401 | ||||||||
\(405\) | 1.10171 | 0.0547446 | ||||||||
\(406\) | −0.563024 | −0.0279424 | ||||||||
\(407\) | 42.4966 | 2.10648 | ||||||||
\(408\) | 2.09272 | 0.103605 | ||||||||
\(409\) | −8.55321 | −0.422929 | −0.211464 | − | 0.977386i | \(-0.567823\pi\) | ||||
−0.211464 | + | 0.977386i | \(0.567823\pi\) | |||||||
\(410\) | −0.564537 | −0.0278805 | ||||||||
\(411\) | −15.9195 | −0.785253 | ||||||||
\(412\) | 29.0384 | 1.43062 | ||||||||
\(413\) | 7.38234 | 0.363261 | ||||||||
\(414\) | 1.03788 | 0.0510093 | ||||||||
\(415\) | −7.37346 | −0.361949 | ||||||||
\(416\) | 30.6910 | 1.50475 | ||||||||
\(417\) | 3.75752 | 0.184007 | ||||||||
\(418\) | 25.9954 | 1.27148 | ||||||||
\(419\) | −13.6583 | −0.667253 | −0.333626 | − | 0.942705i | \(-0.608272\pi\) | ||||
−0.333626 | + | 0.942705i | \(0.608272\pi\) | |||||||
\(420\) | −4.93128 | −0.240622 | ||||||||
\(421\) | 39.5480 | 1.92745 | 0.963725 | − | 0.266897i | \(-0.0859985\pi\) | ||||
0.963725 | + | 0.266897i | \(0.0859985\pi\) | |||||||
\(422\) | −11.7143 | −0.570242 | ||||||||
\(423\) | 11.8642 | 0.576857 | ||||||||
\(424\) | 13.2611 | 0.644014 | ||||||||
\(425\) | 3.78623 | 0.183659 | ||||||||
\(426\) | −5.92783 | −0.287204 | ||||||||
\(427\) | 12.6523 | 0.612289 | ||||||||
\(428\) | 3.22797 | 0.156030 | ||||||||
\(429\) | −31.6406 | −1.52762 | ||||||||
\(430\) | −0.239994 | −0.0115735 | ||||||||
\(431\) | −23.4392 | −1.12903 | −0.564514 | − | 0.825424i | \(-0.690936\pi\) | ||||
−0.564514 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(432\) | 2.16036 | 0.103940 | ||||||||
\(433\) | 2.14183 | 0.102930 | 0.0514648 | − | 0.998675i | \(-0.483611\pi\) | ||||
0.0514648 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(434\) | −1.49512 | −0.0717681 | ||||||||
\(435\) | −0.407941 | −0.0195593 | ||||||||
\(436\) | −8.88425 | −0.425478 | ||||||||
\(437\) | −14.9103 | −0.713255 | ||||||||
\(438\) | −1.82173 | −0.0870458 | ||||||||
\(439\) | −11.5639 | −0.551916 | −0.275958 | − | 0.961170i | \(-0.588995\pi\) | ||||
−0.275958 | + | 0.961170i | \(0.588995\pi\) | |||||||
\(440\) | 12.8719 | 0.613642 | ||||||||
\(441\) | 0.133374 | 0.00635117 | ||||||||
\(442\) | −3.22651 | −0.153469 | ||||||||
\(443\) | 32.3237 | 1.53575 | 0.767873 | − | 0.640602i | \(-0.221315\pi\) | ||||
0.767873 | + | 0.640602i | \(0.221315\pi\) | |||||||
\(444\) | 12.7567 | 0.605405 | ||||||||
\(445\) | −6.28116 | −0.297755 | ||||||||
\(446\) | 5.80702 | 0.274970 | ||||||||
\(447\) | 19.6328 | 0.928599 | ||||||||
\(448\) | −3.30567 | −0.156178 | ||||||||
\(449\) | 6.62478 | 0.312642 | 0.156321 | − | 0.987706i | \(-0.450036\pi\) | ||||
0.156321 | + | 0.987706i | \(0.450036\pi\) | |||||||
\(450\) | −2.15554 | −0.101613 | ||||||||
\(451\) | 5.02499 | 0.236617 | ||||||||
\(452\) | 27.3391 | 1.28592 | ||||||||
\(453\) | 5.24765 | 0.246556 | ||||||||
\(454\) | 6.81427 | 0.319810 | ||||||||
\(455\) | 16.6763 | 0.781795 | ||||||||
\(456\) | 17.1158 | 0.801522 | ||||||||
\(457\) | −7.37796 | −0.345127 | −0.172563 | − | 0.984998i | \(-0.555205\pi\) | ||||
−0.172563 | + | 0.984998i | \(0.555205\pi\) | |||||||
\(458\) | 5.92144 | 0.276691 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −3.36598 | −0.156940 | ||||||||
\(461\) | −21.1982 | −0.987301 | −0.493650 | − | 0.869660i | \(-0.664338\pi\) | ||||
−0.493650 | + | 0.869660i | \(0.664338\pi\) | |||||||
\(462\) | −8.48904 | −0.394946 | ||||||||
\(463\) | 7.83100 | 0.363937 | 0.181969 | − | 0.983304i | \(-0.441753\pi\) | ||||
0.181969 | + | 0.983304i | \(0.441753\pi\) | |||||||
\(464\) | −0.799936 | −0.0371361 | ||||||||
\(465\) | −1.08330 | −0.0502367 | ||||||||
\(466\) | 6.64203 | 0.307686 | ||||||||
\(467\) | −9.18216 | −0.424900 | −0.212450 | − | 0.977172i | \(-0.568144\pi\) | ||||
−0.212450 | + | 0.977172i | \(0.568144\pi\) | |||||||
\(468\) | −9.49789 | −0.439040 | ||||||||
\(469\) | −41.9240 | −1.93587 | ||||||||
\(470\) | 7.44144 | 0.343248 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −5.78440 | −0.266249 | ||||||||
\(473\) | 2.13620 | 0.0982227 | ||||||||
\(474\) | 5.37127 | 0.246711 | ||||||||
\(475\) | 30.9666 | 1.42084 | ||||||||
\(476\) | 4.47602 | 0.205158 | ||||||||
\(477\) | −6.33675 | −0.290140 | ||||||||
\(478\) | −8.92241 | −0.408102 | ||||||||
\(479\) | −15.2005 | −0.694529 | −0.347265 | − | 0.937767i | \(-0.612889\pi\) | ||||
−0.347265 | + | 0.937767i | \(0.612889\pi\) | |||||||
\(480\) | 5.96617 | 0.272317 | ||||||||
\(481\) | −43.1396 | −1.96700 | ||||||||
\(482\) | −12.7712 | −0.581712 | ||||||||
\(483\) | 4.86908 | 0.221551 | ||||||||
\(484\) | −33.8008 | −1.53640 | ||||||||
\(485\) | −7.65769 | −0.347718 | ||||||||
\(486\) | 0.569311 | 0.0258245 | ||||||||
\(487\) | 0.00509170 | 0.000230727 0 | 0.000115363 | − | 1.00000i | \(-0.499963\pi\) | ||||
0.000115363 | 1.00000i | \(0.499963\pi\) | ||||||||
\(488\) | −9.91368 | −0.448771 | ||||||||
\(489\) | 24.9047 | 1.12623 | ||||||||
\(490\) | 0.0836548 | 0.00377914 | ||||||||
\(491\) | −1.11204 | −0.0501855 | −0.0250928 | − | 0.999685i | \(-0.507988\pi\) | ||||
−0.0250928 | + | 0.999685i | \(0.507988\pi\) | |||||||
\(492\) | 1.50841 | 0.0680042 | ||||||||
\(493\) | 0.370279 | 0.0166765 | ||||||||
\(494\) | −26.3888 | −1.18729 | ||||||||
\(495\) | −6.15077 | −0.276457 | ||||||||
\(496\) | −2.12424 | −0.0953814 | ||||||||
\(497\) | −27.8095 | −1.24743 | ||||||||
\(498\) | −3.81024 | −0.170741 | ||||||||
\(499\) | 23.8754 | 1.06881 | 0.534405 | − | 0.845228i | \(-0.320536\pi\) | ||||
0.534405 | + | 0.845228i | \(0.320536\pi\) | |||||||
\(500\) | 16.2224 | 0.725488 | ||||||||
\(501\) | 7.68036 | 0.343133 | ||||||||
\(502\) | −14.5797 | −0.650726 | ||||||||
\(503\) | −13.3991 | −0.597435 | −0.298717 | − | 0.954342i | \(-0.596559\pi\) | ||||
−0.298717 | + | 0.954342i | \(0.596559\pi\) | |||||||
\(504\) | −5.58932 | −0.248968 | ||||||||
\(505\) | 5.02639 | 0.223671 | ||||||||
\(506\) | −5.79442 | −0.257594 | ||||||||
\(507\) | 19.1193 | 0.849117 | ||||||||
\(508\) | −10.2929 | −0.456675 | ||||||||
\(509\) | 5.38725 | 0.238786 | 0.119393 | − | 0.992847i | \(-0.461905\pi\) | ||||
0.119393 | + | 0.992847i | \(0.461905\pi\) | |||||||
\(510\) | −0.627218 | −0.0277737 | ||||||||
\(511\) | −8.54638 | −0.378070 | ||||||||
\(512\) | 20.7412 | 0.916640 | ||||||||
\(513\) | −8.17874 | −0.361100 | ||||||||
\(514\) | −6.46182 | −0.285019 | ||||||||
\(515\) | −19.0896 | −0.841189 | ||||||||
\(516\) | 0.641247 | 0.0282293 | ||||||||
\(517\) | −66.2368 | −2.91309 | ||||||||
\(518\) | −11.5742 | −0.508541 | ||||||||
\(519\) | 6.82989 | 0.299799 | ||||||||
\(520\) | −13.0666 | −0.573009 | ||||||||
\(521\) | −19.5475 | −0.856391 | −0.428195 | − | 0.903686i | \(-0.640850\pi\) | ||||
−0.428195 | + | 0.903686i | \(0.640850\pi\) | |||||||
\(522\) | −0.210804 | −0.00922665 | ||||||||
\(523\) | 11.0809 | 0.484532 | 0.242266 | − | 0.970210i | \(-0.422109\pi\) | ||||
0.242266 | + | 0.970210i | \(0.422109\pi\) | |||||||
\(524\) | 10.7439 | 0.469350 | ||||||||
\(525\) | −10.1124 | −0.441341 | ||||||||
\(526\) | −15.5483 | −0.677937 | ||||||||
\(527\) | 0.983283 | 0.0428325 | ||||||||
\(528\) | −12.0611 | −0.524892 | ||||||||
\(529\) | −19.6765 | −0.855499 | ||||||||
\(530\) | −3.97452 | −0.172642 | ||||||||
\(531\) | 2.76405 | 0.119950 | ||||||||
\(532\) | 36.6082 | 1.58716 | ||||||||
\(533\) | −5.10102 | −0.220950 | ||||||||
\(534\) | −3.24579 | −0.140459 | ||||||||
\(535\) | −2.12204 | −0.0917439 | ||||||||
\(536\) | 32.8494 | 1.41888 | ||||||||
\(537\) | −5.52492 | −0.238418 | ||||||||
\(538\) | −13.3763 | −0.576693 | ||||||||
\(539\) | −0.744619 | −0.0320730 | ||||||||
\(540\) | −1.84634 | −0.0794540 | ||||||||
\(541\) | −11.4194 | −0.490957 | −0.245479 | − | 0.969402i | \(-0.578945\pi\) | ||||
−0.245479 | + | 0.969402i | \(0.578945\pi\) | |||||||
\(542\) | 15.0789 | 0.647693 | ||||||||
\(543\) | 4.66759 | 0.200306 | ||||||||
\(544\) | −5.41536 | −0.232182 | ||||||||
\(545\) | 5.84043 | 0.250177 | ||||||||
\(546\) | 8.61748 | 0.368794 | ||||||||
\(547\) | 44.6050 | 1.90717 | 0.953586 | − | 0.301120i | \(-0.0973604\pi\) | ||||
0.953586 | + | 0.301120i | \(0.0973604\pi\) | |||||||
\(548\) | 26.6793 | 1.13968 | ||||||||
\(549\) | 4.73721 | 0.202179 | ||||||||
\(550\) | 12.0342 | 0.513141 | ||||||||
\(551\) | 3.02842 | 0.129015 | ||||||||
\(552\) | −3.81515 | −0.162383 | ||||||||
\(553\) | 25.1985 | 1.07155 | ||||||||
\(554\) | −14.3834 | −0.611093 | ||||||||
\(555\) | −8.38614 | −0.355972 | ||||||||
\(556\) | −6.29717 | −0.267060 | ||||||||
\(557\) | 33.1695 | 1.40544 | 0.702719 | − | 0.711468i | \(-0.251969\pi\) | ||||
0.702719 | + | 0.711468i | \(0.251969\pi\) | |||||||
\(558\) | −0.559794 | −0.0236980 | ||||||||
\(559\) | −2.16852 | −0.0917188 | ||||||||
\(560\) | 6.35685 | 0.268626 | ||||||||
\(561\) | 5.58292 | 0.235711 | ||||||||
\(562\) | −10.0787 | −0.425143 | ||||||||
\(563\) | 13.1059 | 0.552348 | 0.276174 | − | 0.961108i | \(-0.410933\pi\) | ||||
0.276174 | + | 0.961108i | \(0.410933\pi\) | |||||||
\(564\) | −19.8830 | −0.837227 | ||||||||
\(565\) | −17.9725 | −0.756108 | ||||||||
\(566\) | 2.62059 | 0.110152 | ||||||||
\(567\) | 2.67084 | 0.112165 | ||||||||
\(568\) | 21.7900 | 0.914288 | ||||||||
\(569\) | 7.89068 | 0.330794 | 0.165397 | − | 0.986227i | \(-0.447109\pi\) | ||||
0.165397 | + | 0.986227i | \(0.447109\pi\) | |||||||
\(570\) | −5.12985 | −0.214866 | ||||||||
\(571\) | −29.8410 | −1.24881 | −0.624403 | − | 0.781102i | \(-0.714658\pi\) | ||||
−0.624403 | + | 0.781102i | \(0.714658\pi\) | |||||||
\(572\) | 53.0259 | 2.21712 | ||||||||
\(573\) | 13.2139 | 0.552018 | ||||||||
\(574\) | −1.36858 | −0.0571236 | ||||||||
\(575\) | −6.90250 | −0.287854 | ||||||||
\(576\) | −1.23769 | −0.0515704 | ||||||||
\(577\) | 18.3241 | 0.762843 | 0.381421 | − | 0.924401i | \(-0.375435\pi\) | ||||
0.381421 | + | 0.924401i | \(0.375435\pi\) | |||||||
\(578\) | 0.569311 | 0.0236802 | ||||||||
\(579\) | −13.7389 | −0.570970 | ||||||||
\(580\) | 0.683663 | 0.0283876 | ||||||||
\(581\) | −17.8752 | −0.741588 | ||||||||
\(582\) | −3.95712 | −0.164028 | ||||||||
\(583\) | 35.3775 | 1.46519 | ||||||||
\(584\) | 6.69648 | 0.277102 | ||||||||
\(585\) | 6.24383 | 0.258151 | ||||||||
\(586\) | −13.0208 | −0.537885 | ||||||||
\(587\) | 19.4001 | 0.800728 | 0.400364 | − | 0.916356i | \(-0.368884\pi\) | ||||
0.400364 | + | 0.916356i | \(0.368884\pi\) | |||||||
\(588\) | −0.223520 | −0.00921782 | ||||||||
\(589\) | 8.04202 | 0.331365 | ||||||||
\(590\) | 1.73366 | 0.0713738 | ||||||||
\(591\) | −20.9742 | −0.862762 | ||||||||
\(592\) | −16.4444 | −0.675863 | ||||||||
\(593\) | −14.7220 | −0.604559 | −0.302280 | − | 0.953219i | \(-0.597748\pi\) | ||||
−0.302280 | + | 0.953219i | \(0.597748\pi\) | |||||||
\(594\) | −3.17842 | −0.130412 | ||||||||
\(595\) | −2.94250 | −0.120631 | ||||||||
\(596\) | −32.9023 | −1.34773 | ||||||||
\(597\) | 20.8820 | 0.854645 | ||||||||
\(598\) | 5.88210 | 0.240537 | ||||||||
\(599\) | 30.0065 | 1.22603 | 0.613016 | − | 0.790070i | \(-0.289956\pi\) | ||||
0.613016 | + | 0.790070i | \(0.289956\pi\) | |||||||
\(600\) | 7.92353 | 0.323477 | ||||||||
\(601\) | 7.46250 | 0.304402 | 0.152201 | − | 0.988350i | \(-0.451364\pi\) | ||||
0.152201 | + | 0.988350i | \(0.451364\pi\) | |||||||
\(602\) | −0.581806 | −0.0237127 | ||||||||
\(603\) | −15.6969 | −0.639229 | ||||||||
\(604\) | −8.79445 | −0.357841 | ||||||||
\(605\) | 22.2204 | 0.903388 | ||||||||
\(606\) | 2.59739 | 0.105512 | ||||||||
\(607\) | −9.36442 | −0.380090 | −0.190045 | − | 0.981775i | \(-0.560863\pi\) | ||||
−0.190045 | + | 0.981775i | \(0.560863\pi\) | |||||||
\(608\) | −44.2908 | −1.79623 | ||||||||
\(609\) | −0.988956 | −0.0400745 | ||||||||
\(610\) | 2.97126 | 0.120303 | ||||||||
\(611\) | 67.2390 | 2.72020 | ||||||||
\(612\) | 1.67588 | 0.0677436 | ||||||||
\(613\) | −21.0112 | −0.848634 | −0.424317 | − | 0.905514i | \(-0.639486\pi\) | ||||
−0.424317 | + | 0.905514i | \(0.639486\pi\) | |||||||
\(614\) | −2.38668 | −0.0963187 | ||||||||
\(615\) | −0.991613 | −0.0399857 | ||||||||
\(616\) | 31.2047 | 1.25727 | ||||||||
\(617\) | −16.4104 | −0.660658 | −0.330329 | − | 0.943866i | \(-0.607160\pi\) | ||||
−0.330329 | + | 0.943866i | \(0.607160\pi\) | |||||||
\(618\) | −9.86458 | −0.396812 | ||||||||
\(619\) | −6.70602 | −0.269538 | −0.134769 | − | 0.990877i | \(-0.543029\pi\) | ||||
−0.134769 | + | 0.990877i | \(0.543029\pi\) | |||||||
\(620\) | 1.81548 | 0.0729114 | ||||||||
\(621\) | 1.82305 | 0.0731566 | ||||||||
\(622\) | −1.67554 | −0.0671830 | ||||||||
\(623\) | −15.2272 | −0.610063 | ||||||||
\(624\) | 12.2436 | 0.490136 | ||||||||
\(625\) | 8.26667 | 0.330667 | ||||||||
\(626\) | −0.606778 | −0.0242517 | ||||||||
\(627\) | 45.6612 | 1.82353 | ||||||||
\(628\) | −1.67588 | −0.0668751 | ||||||||
\(629\) | 7.61191 | 0.303507 | ||||||||
\(630\) | 1.67520 | 0.0667414 | ||||||||
\(631\) | −2.95048 | −0.117457 | −0.0587283 | − | 0.998274i | \(-0.518705\pi\) | ||||
−0.0587283 | + | 0.998274i | \(0.518705\pi\) | |||||||
\(632\) | −19.7442 | −0.785381 | ||||||||
\(633\) | −20.5762 | −0.817831 | ||||||||
\(634\) | −5.73268 | −0.227674 | ||||||||
\(635\) | 6.76649 | 0.268520 | ||||||||
\(636\) | 10.6197 | 0.421097 | ||||||||
\(637\) | 0.755885 | 0.0299492 | ||||||||
\(638\) | 1.17690 | 0.0465940 | ||||||||
\(639\) | −10.4123 | −0.411903 | ||||||||
\(640\) | −12.7086 | −0.502353 | ||||||||
\(641\) | 12.8600 | 0.507940 | 0.253970 | − | 0.967212i | \(-0.418263\pi\) | ||||
0.253970 | + | 0.967212i | \(0.418263\pi\) | |||||||
\(642\) | −1.09657 | −0.0432781 | ||||||||
\(643\) | 34.9143 | 1.37688 | 0.688442 | − | 0.725291i | \(-0.258295\pi\) | ||||
0.688442 | + | 0.725291i | \(0.258295\pi\) | |||||||
\(644\) | −8.16002 | −0.321550 | ||||||||
\(645\) | −0.421551 | −0.0165985 | ||||||||
\(646\) | 4.65625 | 0.183198 | ||||||||
\(647\) | −14.9014 | −0.585834 | −0.292917 | − | 0.956138i | \(-0.594626\pi\) | ||||
−0.292917 | + | 0.956138i | \(0.594626\pi\) | |||||||
\(648\) | −2.09272 | −0.0822099 | ||||||||
\(649\) | −15.4315 | −0.605739 | ||||||||
\(650\) | −12.2163 | −0.479163 | ||||||||
\(651\) | −2.62619 | −0.102929 | ||||||||
\(652\) | −41.7373 | −1.63456 | ||||||||
\(653\) | −19.8946 | −0.778538 | −0.389269 | − | 0.921124i | \(-0.627272\pi\) | ||||
−0.389269 | + | 0.921124i | \(0.627272\pi\) | |||||||
\(654\) | 3.01805 | 0.118015 | ||||||||
\(655\) | −7.06296 | −0.275972 | ||||||||
\(656\) | −1.94446 | −0.0759185 | ||||||||
\(657\) | −3.19989 | −0.124840 | ||||||||
\(658\) | 18.0400 | 0.703271 | ||||||||
\(659\) | −33.0855 | −1.28883 | −0.644414 | − | 0.764677i | \(-0.722899\pi\) | ||||
−0.644414 | + | 0.764677i | \(0.722899\pi\) | |||||||
\(660\) | 10.3080 | 0.401238 | ||||||||
\(661\) | 9.48152 | 0.368788 | 0.184394 | − | 0.982852i | \(-0.440968\pi\) | ||||
0.184394 | + | 0.982852i | \(0.440968\pi\) | |||||||
\(662\) | 10.7962 | 0.419607 | ||||||||
\(663\) | −5.66739 | −0.220103 | ||||||||
\(664\) | 14.0060 | 0.543539 | ||||||||
\(665\) | −24.0659 | −0.933236 | ||||||||
\(666\) | −4.33354 | −0.167921 | ||||||||
\(667\) | −0.675039 | −0.0261376 | ||||||||
\(668\) | −12.8714 | −0.498009 | ||||||||
\(669\) | 10.2001 | 0.394358 | ||||||||
\(670\) | −9.84540 | −0.380361 | ||||||||
\(671\) | −26.4475 | −1.02099 | ||||||||
\(672\) | 14.4636 | 0.557944 | ||||||||
\(673\) | −33.0905 | −1.27555 | −0.637773 | − | 0.770225i | \(-0.720144\pi\) | ||||
−0.637773 | + | 0.770225i | \(0.720144\pi\) | |||||||
\(674\) | −12.8545 | −0.495136 | ||||||||
\(675\) | −3.78623 | −0.145732 | ||||||||
\(676\) | −32.0417 | −1.23237 | ||||||||
\(677\) | 34.1850 | 1.31384 | 0.656918 | − | 0.753962i | \(-0.271860\pi\) | ||||
0.656918 | + | 0.753962i | \(0.271860\pi\) | |||||||
\(678\) | −9.28730 | −0.356677 | ||||||||
\(679\) | −18.5642 | −0.712429 | ||||||||
\(680\) | 2.30558 | 0.0884149 | ||||||||
\(681\) | 11.9693 | 0.458665 | ||||||||
\(682\) | 3.12529 | 0.119673 | ||||||||
\(683\) | 4.10493 | 0.157071 | 0.0785355 | − | 0.996911i | \(-0.474976\pi\) | ||||
0.0785355 | + | 0.996911i | \(0.474976\pi\) | |||||||
\(684\) | 13.7066 | 0.524086 | ||||||||
\(685\) | −17.5388 | −0.670122 | ||||||||
\(686\) | −10.4410 | −0.398638 | ||||||||
\(687\) | 10.4011 | 0.396825 | ||||||||
\(688\) | −0.826622 | −0.0315147 | ||||||||
\(689\) | −35.9128 | −1.36817 | ||||||||
\(690\) | 1.14345 | 0.0435304 | ||||||||
\(691\) | 34.7293 | 1.32116 | 0.660582 | − | 0.750754i | \(-0.270310\pi\) | ||||
0.660582 | + | 0.750754i | \(0.270310\pi\) | |||||||
\(692\) | −11.4461 | −0.435116 | ||||||||
\(693\) | −14.9111 | −0.566425 | ||||||||
\(694\) | 13.5779 | 0.515411 | ||||||||
\(695\) | 4.13971 | 0.157028 | ||||||||
\(696\) | 0.774892 | 0.0293722 | ||||||||
\(697\) | 0.900065 | 0.0340924 | ||||||||
\(698\) | 19.1308 | 0.724112 | ||||||||
\(699\) | 11.6668 | 0.441278 | ||||||||
\(700\) | 16.9472 | 0.640545 | ||||||||
\(701\) | 37.0322 | 1.39869 | 0.699344 | − | 0.714785i | \(-0.253475\pi\) | ||||
0.699344 | + | 0.714785i | \(0.253475\pi\) | |||||||
\(702\) | 3.22651 | 0.121777 | ||||||||
\(703\) | 62.2558 | 2.34802 | ||||||||
\(704\) | 6.90992 | 0.260427 | ||||||||
\(705\) | 13.0709 | 0.492280 | ||||||||
\(706\) | 5.14017 | 0.193453 | ||||||||
\(707\) | 12.1853 | 0.458274 | ||||||||
\(708\) | −4.63224 | −0.174090 | ||||||||
\(709\) | 23.7078 | 0.890363 | 0.445182 | − | 0.895440i | \(-0.353139\pi\) | ||||
0.445182 | + | 0.895440i | \(0.353139\pi\) | |||||||
\(710\) | −6.53076 | −0.245095 | ||||||||
\(711\) | 9.43468 | 0.353828 | ||||||||
\(712\) | 11.9312 | 0.447139 | ||||||||
\(713\) | −1.79258 | −0.0671326 | ||||||||
\(714\) | −1.52054 | −0.0569047 | ||||||||
\(715\) | −34.8588 | −1.30365 | ||||||||
\(716\) | 9.25914 | 0.346030 | ||||||||
\(717\) | −15.6723 | −0.585292 | ||||||||
\(718\) | −20.3859 | −0.760795 | ||||||||
\(719\) | −13.0832 | −0.487922 | −0.243961 | − | 0.969785i | \(-0.578447\pi\) | ||||
−0.243961 | + | 0.969785i | \(0.578447\pi\) | |||||||
\(720\) | 2.38009 | 0.0887009 | ||||||||
\(721\) | −46.2782 | −1.72349 | ||||||||
\(722\) | 27.2653 | 1.01471 | ||||||||
\(723\) | −22.4327 | −0.834282 | ||||||||
\(724\) | −7.82235 | −0.290715 | ||||||||
\(725\) | 1.40196 | 0.0520676 | ||||||||
\(726\) | 11.4824 | 0.426152 | ||||||||
\(727\) | 24.4396 | 0.906413 | 0.453207 | − | 0.891405i | \(-0.350280\pi\) | ||||
0.453207 | + | 0.891405i | \(0.350280\pi\) | |||||||
\(728\) | −31.6769 | −1.17402 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.00703 | −0.0742834 | ||||||||
\(731\) | 0.382632 | 0.0141522 | ||||||||
\(732\) | −7.93903 | −0.293435 | ||||||||
\(733\) | −43.8336 | −1.61903 | −0.809516 | − | 0.587097i | \(-0.800271\pi\) | ||||
−0.809516 | + | 0.587097i | \(0.800271\pi\) | |||||||
\(734\) | 3.46699 | 0.127969 | ||||||||
\(735\) | 0.146940 | 0.00541998 | ||||||||
\(736\) | 9.87249 | 0.363905 | ||||||||
\(737\) | 87.6347 | 3.22807 | ||||||||
\(738\) | −0.512417 | −0.0188623 | ||||||||
\(739\) | −12.9690 | −0.477072 | −0.238536 | − | 0.971134i | \(-0.576668\pi\) | ||||
−0.238536 | + | 0.971134i | \(0.576668\pi\) | |||||||
\(740\) | 14.0542 | 0.516642 | ||||||||
\(741\) | −46.3521 | −1.70279 | ||||||||
\(742\) | −9.63526 | −0.353722 | ||||||||
\(743\) | 10.7100 | 0.392912 | 0.196456 | − | 0.980513i | \(-0.437057\pi\) | ||||
0.196456 | + | 0.980513i | \(0.437057\pi\) | |||||||
\(744\) | 2.05774 | 0.0754404 | ||||||||
\(745\) | 21.6297 | 0.792451 | ||||||||
\(746\) | −11.5700 | −0.423606 | ||||||||
\(747\) | −6.69273 | −0.244874 | ||||||||
\(748\) | −9.35632 | −0.342101 | ||||||||
\(749\) | −5.14438 | −0.187972 | ||||||||
\(750\) | −5.51088 | −0.201229 | ||||||||
\(751\) | 17.0558 | 0.622376 | 0.311188 | − | 0.950348i | \(-0.399273\pi\) | ||||
0.311188 | + | 0.950348i | \(0.399273\pi\) | |||||||
\(752\) | 25.6309 | 0.934664 | ||||||||
\(753\) | −25.6094 | −0.933260 | ||||||||
\(754\) | −1.19471 | −0.0435087 | ||||||||
\(755\) | 5.78140 | 0.210407 | ||||||||
\(756\) | −4.47602 | −0.162791 | ||||||||
\(757\) | −19.3246 | −0.702363 | −0.351182 | − | 0.936307i | \(-0.614220\pi\) | ||||
−0.351182 | + | 0.936307i | \(0.614220\pi\) | |||||||
\(758\) | 9.40440 | 0.341583 | ||||||||
\(759\) | −10.1780 | −0.369436 | ||||||||
\(760\) | 18.8567 | 0.684005 | ||||||||
\(761\) | −52.9253 | −1.91854 | −0.959270 | − | 0.282492i | \(-0.908839\pi\) | ||||
−0.959270 | + | 0.282492i | \(0.908839\pi\) | |||||||
\(762\) | 3.49659 | 0.126668 | ||||||||
\(763\) | 14.1587 | 0.512580 | ||||||||
\(764\) | −22.1450 | −0.801176 | ||||||||
\(765\) | −1.10171 | −0.0398325 | ||||||||
\(766\) | 0.484668 | 0.0175118 | ||||||||
\(767\) | 15.6650 | 0.565629 | ||||||||
\(768\) | −4.09183 | −0.147651 | ||||||||
\(769\) | −18.1482 | −0.654442 | −0.327221 | − | 0.944948i | \(-0.606112\pi\) | ||||
−0.327221 | + | 0.944948i | \(0.606112\pi\) | |||||||
\(770\) | −9.35248 | −0.337040 | ||||||||
\(771\) | −11.3502 | −0.408769 | ||||||||
\(772\) | 23.0249 | 0.828683 | ||||||||
\(773\) | 27.4209 | 0.986261 | 0.493131 | − | 0.869955i | \(-0.335852\pi\) | ||||
0.493131 | + | 0.869955i | \(0.335852\pi\) | |||||||
\(774\) | −0.217837 | −0.00782998 | ||||||||
\(775\) | 3.72294 | 0.133732 | ||||||||
\(776\) | 14.5459 | 0.522168 | ||||||||
\(777\) | −20.3302 | −0.729341 | ||||||||
\(778\) | −7.18707 | −0.257669 | ||||||||
\(779\) | 7.36139 | 0.263749 | ||||||||
\(780\) | −10.4639 | −0.374669 | ||||||||
\(781\) | 58.1309 | 2.08009 | ||||||||
\(782\) | −1.03788 | −0.0371147 | ||||||||
\(783\) | −0.370279 | −0.0132327 | ||||||||
\(784\) | 0.288137 | 0.0102906 | ||||||||
\(785\) | 1.10171 | 0.0393218 | ||||||||
\(786\) | −3.64979 | −0.130184 | ||||||||
\(787\) | 52.8139 | 1.88261 | 0.941306 | − | 0.337553i | \(-0.109599\pi\) | ||||
0.941306 | + | 0.337553i | \(0.109599\pi\) | |||||||
\(788\) | 35.1503 | 1.25218 | ||||||||
\(789\) | −27.3107 | −0.972285 | ||||||||
\(790\) | 5.91760 | 0.210539 | ||||||||
\(791\) | −43.5700 | −1.54917 | ||||||||
\(792\) | 11.6835 | 0.415155 | ||||||||
\(793\) | 26.8476 | 0.953387 | ||||||||
\(794\) | −5.84679 | −0.207495 | ||||||||
\(795\) | −6.98128 | −0.247600 | ||||||||
\(796\) | −34.9959 | −1.24040 | ||||||||
\(797\) | −40.3233 | −1.42832 | −0.714162 | − | 0.699980i | \(-0.753192\pi\) | ||||
−0.714162 | + | 0.699980i | \(0.753192\pi\) | |||||||
\(798\) | −12.4361 | −0.440232 | ||||||||
\(799\) | −11.8642 | −0.419725 | ||||||||
\(800\) | −20.5038 | −0.724919 | ||||||||
\(801\) | −5.70127 | −0.201444 | ||||||||
\(802\) | −5.55986 | −0.196325 | ||||||||
\(803\) | 17.8647 | 0.630432 | ||||||||
\(804\) | 26.3063 | 0.927751 | ||||||||
\(805\) | 5.36433 | 0.189068 | ||||||||
\(806\) | −3.17257 | −0.111749 | ||||||||
\(807\) | −23.4956 | −0.827083 | ||||||||
\(808\) | −9.54771 | −0.335887 | ||||||||
\(809\) | 10.1569 | 0.357098 | 0.178549 | − | 0.983931i | \(-0.442860\pi\) | ||||
0.178549 | + | 0.983931i | \(0.442860\pi\) | |||||||
\(810\) | 0.627218 | 0.0220382 | ||||||||
\(811\) | −2.32921 | −0.0817896 | −0.0408948 | − | 0.999163i | \(-0.513021\pi\) | ||||
−0.0408948 | + | 0.999163i | \(0.513021\pi\) | |||||||
\(812\) | 1.65738 | 0.0581625 | ||||||||
\(813\) | 26.4862 | 0.928910 | ||||||||
\(814\) | 24.1938 | 0.847993 | ||||||||
\(815\) | 27.4378 | 0.961103 | ||||||||
\(816\) | −2.16036 | −0.0756277 | ||||||||
\(817\) | 3.12945 | 0.109485 | ||||||||
\(818\) | −4.86944 | −0.170256 | ||||||||
\(819\) | 15.1367 | 0.528918 | ||||||||
\(820\) | 1.66183 | 0.0580336 | ||||||||
\(821\) | −46.3377 | −1.61720 | −0.808599 | − | 0.588360i | \(-0.799774\pi\) | ||||
−0.808599 | + | 0.588360i | \(0.799774\pi\) | |||||||
\(822\) | −9.06317 | −0.316114 | ||||||||
\(823\) | −36.8757 | −1.28541 | −0.642703 | − | 0.766116i | \(-0.722187\pi\) | ||||
−0.642703 | + | 0.766116i | \(0.722187\pi\) | |||||||
\(824\) | 36.2611 | 1.26321 | ||||||||
\(825\) | 21.1382 | 0.735938 | ||||||||
\(826\) | 4.20285 | 0.146236 | ||||||||
\(827\) | −10.0503 | −0.349484 | −0.174742 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174742 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(828\) | −3.05523 | −0.106176 | ||||||||
\(829\) | 29.4371 | 1.02239 | 0.511196 | − | 0.859464i | \(-0.329203\pi\) | ||||
0.511196 | + | 0.859464i | \(0.329203\pi\) | |||||||
\(830\) | −4.19780 | −0.145708 | ||||||||
\(831\) | −25.2646 | −0.876420 | ||||||||
\(832\) | −7.01447 | −0.243183 | ||||||||
\(833\) | −0.133374 | −0.00462115 | ||||||||
\(834\) | 2.13920 | 0.0740744 | ||||||||
\(835\) | 8.46155 | 0.292824 | ||||||||
\(836\) | −76.5229 | −2.64660 | ||||||||
\(837\) | −0.983283 | −0.0339872 | ||||||||
\(838\) | −7.77584 | −0.268612 | ||||||||
\(839\) | 40.3755 | 1.39392 | 0.696959 | − | 0.717111i | \(-0.254536\pi\) | ||||
0.696959 | + | 0.717111i | \(0.254536\pi\) | |||||||
\(840\) | −6.15783 | −0.212465 | ||||||||
\(841\) | −28.8629 | −0.995272 | ||||||||
\(842\) | 22.5151 | 0.775922 | ||||||||
\(843\) | −17.7033 | −0.609733 | ||||||||
\(844\) | 34.4834 | 1.18697 | ||||||||
\(845\) | 21.0640 | 0.724622 | ||||||||
\(846\) | 6.75442 | 0.232222 | ||||||||
\(847\) | 53.8680 | 1.85093 | ||||||||
\(848\) | −13.6896 | −0.470104 | ||||||||
\(849\) | 4.60308 | 0.157977 | ||||||||
\(850\) | 2.15554 | 0.0739345 | ||||||||
\(851\) | −13.8769 | −0.475694 | ||||||||
\(852\) | 17.4498 | 0.597819 | ||||||||
\(853\) | 22.3613 | 0.765638 | 0.382819 | − | 0.923823i | \(-0.374953\pi\) | ||||
0.382819 | + | 0.923823i | \(0.374953\pi\) | |||||||
\(854\) | 7.20312 | 0.246486 | ||||||||
\(855\) | −9.01062 | −0.308157 | ||||||||
\(856\) | 4.03086 | 0.137772 | ||||||||
\(857\) | −18.2212 | −0.622426 | −0.311213 | − | 0.950340i | \(-0.600735\pi\) | ||||
−0.311213 | + | 0.950340i | \(0.600735\pi\) | |||||||
\(858\) | −18.0133 | −0.614965 | ||||||||
\(859\) | 55.0141 | 1.87706 | 0.938529 | − | 0.345201i | \(-0.112189\pi\) | ||||
0.938529 | + | 0.345201i | \(0.112189\pi\) | |||||||
\(860\) | 0.706470 | 0.0240904 | ||||||||
\(861\) | −2.40393 | −0.0819256 | ||||||||
\(862\) | −13.3442 | −0.454506 | ||||||||
\(863\) | −27.1421 | −0.923930 | −0.461965 | − | 0.886898i | \(-0.652855\pi\) | ||||
−0.461965 | + | 0.886898i | \(0.652855\pi\) | |||||||
\(864\) | 5.41536 | 0.184234 | ||||||||
\(865\) | 7.52458 | 0.255843 | ||||||||
\(866\) | 1.21937 | 0.0414358 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 4.40119 | 0.149386 | ||||||||
\(869\) | −52.6730 | −1.78681 | ||||||||
\(870\) | −0.232246 | −0.00787387 | ||||||||
\(871\) | −88.9607 | −3.01432 | ||||||||
\(872\) | −11.0940 | −0.375690 | ||||||||
\(873\) | −6.95071 | −0.235246 | ||||||||
\(874\) | −8.48859 | −0.287131 | ||||||||
\(875\) | −25.8534 | −0.874006 | ||||||||
\(876\) | 5.36264 | 0.181187 | ||||||||
\(877\) | 17.8740 | 0.603561 | 0.301781 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301781 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(878\) | −6.58347 | −0.222181 | ||||||||
\(879\) | −22.8712 | −0.771425 | ||||||||
\(880\) | −13.2879 | −0.447934 | ||||||||
\(881\) | −13.0232 | −0.438764 | −0.219382 | − | 0.975639i | \(-0.570404\pi\) | ||||
−0.219382 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(882\) | 0.0759316 | 0.00255675 | ||||||||
\(883\) | −44.5019 | −1.49761 | −0.748804 | − | 0.662792i | \(-0.769371\pi\) | ||||
−0.748804 | + | 0.662792i | \(0.769371\pi\) | |||||||
\(884\) | 9.49789 | 0.319449 | ||||||||
\(885\) | 3.04519 | 0.102363 | ||||||||
\(886\) | 18.4023 | 0.618236 | ||||||||
\(887\) | −42.4944 | −1.42682 | −0.713410 | − | 0.700747i | \(-0.752850\pi\) | ||||
−0.713410 | + | 0.700747i | \(0.752850\pi\) | |||||||
\(888\) | 15.9296 | 0.534563 | ||||||||
\(889\) | 16.4037 | 0.550164 | ||||||||
\(890\) | −3.57593 | −0.119866 | ||||||||
\(891\) | −5.58292 | −0.187035 | ||||||||
\(892\) | −17.0942 | −0.572355 | ||||||||
\(893\) | −97.0342 | −3.24712 | ||||||||
\(894\) | 11.1772 | 0.373820 | ||||||||
\(895\) | −6.08688 | −0.203462 | ||||||||
\(896\) | −30.8091 | −1.02926 | ||||||||
\(897\) | 10.3319 | 0.344974 | ||||||||
\(898\) | 3.77156 | 0.125859 | ||||||||
\(899\) | 0.364089 | 0.0121431 | ||||||||
\(900\) | 6.34528 | 0.211509 | ||||||||
\(901\) | 6.33675 | 0.211108 | ||||||||
\(902\) | 2.86078 | 0.0952536 | ||||||||
\(903\) | −1.02195 | −0.0340083 | ||||||||
\(904\) | 34.1390 | 1.13545 | ||||||||
\(905\) | 5.14235 | 0.170937 | ||||||||
\(906\) | 2.98755 | 0.0992546 | ||||||||
\(907\) | 2.83718 | 0.0942069 | 0.0471035 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471035 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(908\) | −20.0592 | −0.665688 | ||||||||
\(909\) | 4.56234 | 0.151323 | ||||||||
\(910\) | 9.49399 | 0.314723 | ||||||||
\(911\) | 36.1695 | 1.19835 | 0.599175 | − | 0.800618i | \(-0.295496\pi\) | ||||
0.599175 | + | 0.800618i | \(0.295496\pi\) | |||||||
\(912\) | −17.6690 | −0.585079 | ||||||||
\(913\) | 37.3649 | 1.23660 | ||||||||
\(914\) | −4.20036 | −0.138935 | ||||||||
\(915\) | 5.21905 | 0.172537 | ||||||||
\(916\) | −17.4310 | −0.575936 | ||||||||
\(917\) | −17.1224 | −0.565433 | ||||||||
\(918\) | −0.569311 | −0.0187901 | ||||||||
\(919\) | 43.0251 | 1.41927 | 0.709634 | − | 0.704571i | \(-0.248860\pi\) | ||||
0.709634 | + | 0.704571i | \(0.248860\pi\) | |||||||
\(920\) | −4.20319 | −0.138575 | ||||||||
\(921\) | −4.19223 | −0.138139 | ||||||||
\(922\) | −12.0684 | −0.397452 | ||||||||
\(923\) | −59.0104 | −1.94235 | ||||||||
\(924\) | 24.9892 | 0.822085 | ||||||||
\(925\) | 28.8204 | 0.947609 | ||||||||
\(926\) | 4.45828 | 0.146508 | ||||||||
\(927\) | −17.3272 | −0.569101 | ||||||||
\(928\) | −2.00520 | −0.0658238 | ||||||||
\(929\) | −7.58073 | −0.248716 | −0.124358 | − | 0.992237i | \(-0.539687\pi\) | ||||
−0.124358 | + | 0.992237i | \(0.539687\pi\) | |||||||
\(930\) | −0.616733 | −0.0202235 | ||||||||
\(931\) | −1.09083 | −0.0357507 | ||||||||
\(932\) | −19.5522 | −0.640453 | ||||||||
\(933\) | −2.94310 | −0.0963527 | ||||||||
\(934\) | −5.22751 | −0.171049 | ||||||||
\(935\) | 6.15077 | 0.201152 | ||||||||
\(936\) | −11.8603 | −0.387665 | ||||||||
\(937\) | 30.5451 | 0.997865 | 0.498933 | − | 0.866641i | \(-0.333726\pi\) | ||||
0.498933 | + | 0.866641i | \(0.333726\pi\) | |||||||
\(938\) | −23.8678 | −0.779312 | ||||||||
\(939\) | −1.06581 | −0.0347814 | ||||||||
\(940\) | −21.9054 | −0.714475 | ||||||||
\(941\) | −9.27347 | −0.302307 | −0.151153 | − | 0.988510i | \(-0.548299\pi\) | ||||
−0.151153 | + | 0.988510i | \(0.548299\pi\) | |||||||
\(942\) | 0.569311 | 0.0185492 | ||||||||
\(943\) | −1.64087 | −0.0534340 | ||||||||
\(944\) | 5.97135 | 0.194351 | ||||||||
\(945\) | 2.94250 | 0.0957194 | ||||||||
\(946\) | 1.21616 | 0.0395409 | ||||||||
\(947\) | 52.3298 | 1.70049 | 0.850245 | − | 0.526387i | \(-0.176454\pi\) | ||||
0.850245 | + | 0.526387i | \(0.176454\pi\) | |||||||
\(948\) | −15.8114 | −0.513531 | ||||||||
\(949\) | −18.1350 | −0.588687 | ||||||||
\(950\) | 17.6296 | 0.571980 | ||||||||
\(951\) | −10.0695 | −0.326526 | ||||||||
\(952\) | 5.58932 | 0.181151 | ||||||||
\(953\) | −32.0217 | −1.03728 | −0.518642 | − | 0.854991i | \(-0.673562\pi\) | ||||
−0.518642 | + | 0.854991i | \(0.673562\pi\) | |||||||
\(954\) | −3.60758 | −0.116800 | ||||||||
\(955\) | 14.5579 | 0.471083 | ||||||||
\(956\) | 26.2650 | 0.849469 | ||||||||
\(957\) | 2.06724 | 0.0668243 | ||||||||
\(958\) | −8.65383 | −0.279592 | ||||||||
\(959\) | −42.5185 | −1.37299 | ||||||||
\(960\) | −1.36358 | −0.0440093 | ||||||||
\(961\) | −30.0332 | −0.968811 | ||||||||
\(962\) | −24.5599 | −0.791842 | ||||||||
\(963\) | −1.92613 | −0.0620687 | ||||||||
\(964\) | 37.5946 | 1.21084 | ||||||||
\(965\) | −15.1364 | −0.487257 | ||||||||
\(966\) | 2.77202 | 0.0891884 | ||||||||
\(967\) | −35.7784 | −1.15055 | −0.575277 | − | 0.817958i | \(-0.695106\pi\) | ||||
−0.575277 | + | 0.817958i | \(0.695106\pi\) | |||||||
\(968\) | −42.2080 | −1.35662 | ||||||||
\(969\) | 8.17874 | 0.262739 | ||||||||
\(970\) | −4.35961 | −0.139979 | ||||||||
\(971\) | −20.9514 | −0.672364 | −0.336182 | − | 0.941797i | \(-0.609136\pi\) | ||||
−0.336182 | + | 0.941797i | \(0.609136\pi\) | |||||||
\(972\) | −1.67588 | −0.0537540 | ||||||||
\(973\) | 10.0357 | 0.321731 | ||||||||
\(974\) | 0.00289876 | 9.28823e−5 0 | ||||||||
\(975\) | −21.4580 | −0.687207 | ||||||||
\(976\) | 10.2341 | 0.327585 | ||||||||
\(977\) | 20.2146 | 0.646723 | 0.323362 | − | 0.946275i | \(-0.395187\pi\) | ||||
0.323362 | + | 0.946275i | \(0.395187\pi\) | |||||||
\(978\) | 14.1785 | 0.453378 | ||||||||
\(979\) | 31.8297 | 1.01728 | ||||||||
\(980\) | −0.246255 | −0.00786633 | ||||||||
\(981\) | 5.30123 | 0.169255 | ||||||||
\(982\) | −0.633095 | −0.0202029 | ||||||||
\(983\) | −2.31944 | −0.0739786 | −0.0369893 | − | 0.999316i | \(-0.511777\pi\) | ||||
−0.0369893 | + | 0.999316i | \(0.511777\pi\) | |||||||
\(984\) | 1.88359 | 0.0600465 | ||||||||
\(985\) | −23.1075 | −0.736266 | ||||||||
\(986\) | 0.210804 | 0.00671337 | ||||||||
\(987\) | 31.6874 | 1.00862 | ||||||||
\(988\) | 77.6807 | 2.47135 | ||||||||
\(989\) | −0.697558 | −0.0221811 | ||||||||
\(990\) | −3.50170 | −0.111291 | ||||||||
\(991\) | 13.4184 | 0.426250 | 0.213125 | − | 0.977025i | \(-0.431636\pi\) | ||||
0.213125 | + | 0.977025i | \(0.431636\pi\) | |||||||
\(992\) | −5.32484 | −0.169064 | ||||||||
\(993\) | 18.9636 | 0.601792 | ||||||||
\(994\) | −15.8323 | −0.502169 | ||||||||
\(995\) | 23.0060 | 0.729339 | ||||||||
\(996\) | 11.2162 | 0.355400 | ||||||||
\(997\) | 13.6777 | 0.433178 | 0.216589 | − | 0.976263i | \(-0.430507\pi\) | ||||
0.216589 | + | 0.976263i | \(0.430507\pi\) | |||||||
\(998\) | 13.5925 | 0.430265 | ||||||||
\(999\) | −7.61191 | −0.240830 |
(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 | 8007.2.a.e.1.28 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.28 | ✓ | 46 | 1.1 | even | 1 | trivial |