Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,2,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.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: | \(7.84929451869\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45073 | −1.02582 | −0.512910 | − | 0.858443i | \(-0.671432\pi\) | ||||
−0.512910 | + | 0.858443i | \(0.671432\pi\) | |||||||
\(3\) | 1.34954 | 0.779159 | 0.389580 | − | 0.920993i | \(-0.372620\pi\) | ||||
0.389580 | + | 0.920993i | \(0.372620\pi\) | |||||||
\(4\) | 0.104610 | 0.0523052 | ||||||||
\(5\) | 3.00144 | 1.34228 | 0.671142 | − | 0.741329i | \(-0.265804\pi\) | ||||
0.671142 | + | 0.741329i | \(0.265804\pi\) | |||||||
\(6\) | −1.95782 | −0.799276 | ||||||||
\(7\) | −1.88776 | −0.713507 | −0.356754 | − | 0.934199i | \(-0.616116\pi\) | ||||
−0.356754 | + | 0.934199i | \(0.616116\pi\) | |||||||
\(8\) | 2.74969 | 0.972164 | ||||||||
\(9\) | −1.17873 | −0.392911 | ||||||||
\(10\) | −4.35427 | −1.37694 | ||||||||
\(11\) | 3.71907 | 1.12134 | 0.560671 | − | 0.828039i | \(-0.310543\pi\) | ||||
0.560671 | + | 0.828039i | \(0.310543\pi\) | |||||||
\(12\) | 0.141176 | 0.0407541 | ||||||||
\(13\) | 2.53528 | 0.703160 | 0.351580 | − | 0.936158i | \(-0.385645\pi\) | ||||
0.351580 | + | 0.936158i | \(0.385645\pi\) | |||||||
\(14\) | 2.73863 | 0.731929 | ||||||||
\(15\) | 4.05057 | 1.04585 | ||||||||
\(16\) | −4.19828 | −1.04957 | ||||||||
\(17\) | 3.78744 | 0.918588 | 0.459294 | − | 0.888284i | \(-0.348102\pi\) | ||||
0.459294 | + | 0.888284i | \(0.348102\pi\) | |||||||
\(18\) | 1.71002 | 0.403056 | ||||||||
\(19\) | −6.83647 | −1.56839 | −0.784197 | − | 0.620512i | \(-0.786925\pi\) | ||||
−0.784197 | + | 0.620512i | \(0.786925\pi\) | |||||||
\(20\) | 0.313982 | 0.0702084 | ||||||||
\(21\) | −2.54762 | −0.555936 | ||||||||
\(22\) | −5.39535 | −1.15029 | ||||||||
\(23\) | 3.18416 | 0.663944 | 0.331972 | − | 0.943289i | \(-0.392286\pi\) | ||||
0.331972 | + | 0.943289i | \(0.392286\pi\) | |||||||
\(24\) | 3.71083 | 0.757470 | ||||||||
\(25\) | 4.00862 | 0.801724 | ||||||||
\(26\) | −3.67800 | −0.721315 | ||||||||
\(27\) | −5.63938 | −1.08530 | ||||||||
\(28\) | −0.197480 | −0.0373202 | ||||||||
\(29\) | 8.32393 | 1.54572 | 0.772858 | − | 0.634580i | \(-0.218827\pi\) | ||||
0.772858 | + | 0.634580i | \(0.218827\pi\) | |||||||
\(30\) | −5.87627 | −1.07286 | ||||||||
\(31\) | 3.36062 | 0.603586 | 0.301793 | − | 0.953373i | \(-0.402415\pi\) | ||||
0.301793 | + | 0.953373i | \(0.402415\pi\) | |||||||
\(32\) | 0.591169 | 0.104505 | ||||||||
\(33\) | 5.01904 | 0.873703 | ||||||||
\(34\) | −5.49454 | −0.942305 | ||||||||
\(35\) | −5.66600 | −0.957729 | ||||||||
\(36\) | −0.123308 | −0.0205513 | ||||||||
\(37\) | 7.28659 | 1.19791 | 0.598954 | − | 0.800783i | \(-0.295583\pi\) | ||||
0.598954 | + | 0.800783i | \(0.295583\pi\) | |||||||
\(38\) | 9.91785 | 1.60889 | ||||||||
\(39\) | 3.42147 | 0.547873 | ||||||||
\(40\) | 8.25303 | 1.30492 | ||||||||
\(41\) | 9.17250 | 1.43250 | 0.716252 | − | 0.697842i | \(-0.245856\pi\) | ||||
0.716252 | + | 0.697842i | \(0.245856\pi\) | |||||||
\(42\) | 3.69590 | 0.570290 | ||||||||
\(43\) | −9.55198 | −1.45666 | −0.728332 | − | 0.685225i | \(-0.759704\pi\) | ||||
−0.728332 | + | 0.685225i | \(0.759704\pi\) | |||||||
\(44\) | 0.389054 | 0.0586520 | ||||||||
\(45\) | −3.53789 | −0.527398 | ||||||||
\(46\) | −4.61936 | −0.681087 | ||||||||
\(47\) | −0.876620 | −0.127868 | −0.0639341 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639341 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(48\) | −5.66576 | −0.817782 | ||||||||
\(49\) | −3.43635 | −0.490908 | ||||||||
\(50\) | −5.81542 | −0.822424 | ||||||||
\(51\) | 5.11131 | 0.715726 | ||||||||
\(52\) | 0.265217 | 0.0367789 | ||||||||
\(53\) | −0.975272 | −0.133964 | −0.0669819 | − | 0.997754i | \(-0.521337\pi\) | ||||
−0.0669819 | + | 0.997754i | \(0.521337\pi\) | |||||||
\(54\) | 8.18121 | 1.11332 | ||||||||
\(55\) | 11.1625 | 1.50516 | ||||||||
\(56\) | −5.19077 | −0.693646 | ||||||||
\(57\) | −9.22611 | −1.22203 | ||||||||
\(58\) | −12.0758 | −1.58562 | ||||||||
\(59\) | −5.04391 | −0.656662 | −0.328331 | − | 0.944563i | \(-0.606486\pi\) | ||||
−0.328331 | + | 0.944563i | \(0.606486\pi\) | |||||||
\(60\) | 0.423732 | 0.0547036 | ||||||||
\(61\) | −2.70474 | −0.346306 | −0.173153 | − | 0.984895i | \(-0.555396\pi\) | ||||
−0.173153 | + | 0.984895i | \(0.555396\pi\) | |||||||
\(62\) | −4.87535 | −0.619170 | ||||||||
\(63\) | 2.22517 | 0.280345 | ||||||||
\(64\) | 7.53893 | 0.942366 | ||||||||
\(65\) | 7.60948 | 0.943839 | ||||||||
\(66\) | −7.28126 | −0.896262 | ||||||||
\(67\) | −14.7687 | −1.80429 | −0.902145 | − | 0.431434i | \(-0.858008\pi\) | ||||
−0.902145 | + | 0.431434i | \(0.858008\pi\) | |||||||
\(68\) | 0.396205 | 0.0480470 | ||||||||
\(69\) | 4.29717 | 0.517318 | ||||||||
\(70\) | 8.21982 | 0.982457 | ||||||||
\(71\) | 14.7189 | 1.74681 | 0.873407 | − | 0.486991i | \(-0.161905\pi\) | ||||
0.873407 | + | 0.486991i | \(0.161905\pi\) | |||||||
\(72\) | −3.24116 | −0.381974 | ||||||||
\(73\) | 0.866554 | 0.101423 | 0.0507113 | − | 0.998713i | \(-0.483851\pi\) | ||||
0.0507113 | + | 0.998713i | \(0.483851\pi\) | |||||||
\(74\) | −10.5709 | −1.22884 | ||||||||
\(75\) | 5.40981 | 0.624671 | ||||||||
\(76\) | −0.715166 | −0.0820352 | ||||||||
\(77\) | −7.02072 | −0.800085 | ||||||||
\(78\) | −4.96362 | −0.562019 | ||||||||
\(79\) | 17.3763 | 1.95499 | 0.977495 | − | 0.210960i | \(-0.0676591\pi\) | ||||
0.977495 | + | 0.210960i | \(0.0676591\pi\) | |||||||
\(80\) | −12.6009 | −1.40882 | ||||||||
\(81\) | −4.07439 | −0.452710 | ||||||||
\(82\) | −13.3068 | −1.46949 | ||||||||
\(83\) | 0.894889 | 0.0982269 | 0.0491134 | − | 0.998793i | \(-0.484360\pi\) | ||||
0.0491134 | + | 0.998793i | \(0.484360\pi\) | |||||||
\(84\) | −0.266507 | −0.0290783 | ||||||||
\(85\) | 11.3677 | 1.23301 | ||||||||
\(86\) | 13.8573 | 1.49427 | ||||||||
\(87\) | 11.2335 | 1.20436 | ||||||||
\(88\) | 10.2263 | 1.09013 | ||||||||
\(89\) | 8.23898 | 0.873330 | 0.436665 | − | 0.899624i | \(-0.356159\pi\) | ||||
0.436665 | + | 0.899624i | \(0.356159\pi\) | |||||||
\(90\) | 5.13252 | 0.541015 | ||||||||
\(91\) | −4.78600 | −0.501709 | ||||||||
\(92\) | 0.333097 | 0.0347278 | ||||||||
\(93\) | 4.53531 | 0.470289 | ||||||||
\(94\) | 1.27174 | 0.131170 | ||||||||
\(95\) | −20.5192 | −2.10523 | ||||||||
\(96\) | 0.797809 | 0.0814260 | ||||||||
\(97\) | −1.04131 | −0.105729 | −0.0528643 | − | 0.998602i | \(-0.516835\pi\) | ||||
−0.0528643 | + | 0.998602i | \(0.516835\pi\) | |||||||
\(98\) | 4.98521 | 0.503582 | ||||||||
\(99\) | −4.38379 | −0.440587 | ||||||||
\(100\) | 0.419344 | 0.0419344 | ||||||||
\(101\) | −7.70973 | −0.767147 | −0.383574 | − | 0.923510i | \(-0.625307\pi\) | ||||
−0.383574 | + | 0.923510i | \(0.625307\pi\) | |||||||
\(102\) | −7.41512 | −0.734206 | ||||||||
\(103\) | 9.99278 | 0.984618 | 0.492309 | − | 0.870421i | \(-0.336153\pi\) | ||||
0.492309 | + | 0.870421i | \(0.336153\pi\) | |||||||
\(104\) | 6.97124 | 0.683586 | ||||||||
\(105\) | −7.64651 | −0.746223 | ||||||||
\(106\) | 1.41485 | 0.137423 | ||||||||
\(107\) | 13.9840 | 1.35188 | 0.675941 | − | 0.736956i | \(-0.263738\pi\) | ||||
0.675941 | + | 0.736956i | \(0.263738\pi\) | |||||||
\(108\) | −0.589938 | −0.0567668 | ||||||||
\(109\) | 3.47527 | 0.332870 | 0.166435 | − | 0.986052i | \(-0.446774\pi\) | ||||
0.166435 | + | 0.986052i | \(0.446774\pi\) | |||||||
\(110\) | −16.1938 | −1.54402 | ||||||||
\(111\) | 9.83357 | 0.933361 | ||||||||
\(112\) | 7.92535 | 0.748875 | ||||||||
\(113\) | 19.1675 | 1.80313 | 0.901565 | − | 0.432643i | \(-0.142419\pi\) | ||||
0.901565 | + | 0.432643i | \(0.142419\pi\) | |||||||
\(114\) | 13.3846 | 1.25358 | ||||||||
\(115\) | 9.55707 | 0.891201 | ||||||||
\(116\) | 0.870770 | 0.0808490 | ||||||||
\(117\) | −2.98842 | −0.276279 | ||||||||
\(118\) | 7.31735 | 0.673616 | ||||||||
\(119\) | −7.14978 | −0.655419 | ||||||||
\(120\) | 11.1378 | 1.01674 | ||||||||
\(121\) | 2.83147 | 0.257406 | ||||||||
\(122\) | 3.92384 | 0.355248 | ||||||||
\(123\) | 12.3787 | 1.11615 | ||||||||
\(124\) | 0.351557 | 0.0315707 | ||||||||
\(125\) | −2.97556 | −0.266142 | ||||||||
\(126\) | −3.22811 | −0.287583 | ||||||||
\(127\) | 13.9984 | 1.24216 | 0.621078 | − | 0.783749i | \(-0.286695\pi\) | ||||
0.621078 | + | 0.783749i | \(0.286695\pi\) | |||||||
\(128\) | −12.1193 | −1.07120 | ||||||||
\(129\) | −12.8908 | −1.13497 | ||||||||
\(130\) | −11.0393 | −0.968209 | ||||||||
\(131\) | −16.5816 | −1.44874 | −0.724372 | − | 0.689409i | \(-0.757870\pi\) | ||||
−0.724372 | + | 0.689409i | \(0.757870\pi\) | |||||||
\(132\) | 0.525045 | 0.0456993 | ||||||||
\(133\) | 12.9056 | 1.11906 | ||||||||
\(134\) | 21.4254 | 1.85087 | ||||||||
\(135\) | −16.9262 | −1.45678 | ||||||||
\(136\) | 10.4143 | 0.893018 | ||||||||
\(137\) | −18.1996 | −1.55489 | −0.777447 | − | 0.628948i | \(-0.783486\pi\) | ||||
−0.777447 | + | 0.628948i | \(0.783486\pi\) | |||||||
\(138\) | −6.23402 | −0.530675 | ||||||||
\(139\) | 2.55559 | 0.216763 | 0.108381 | − | 0.994109i | \(-0.465433\pi\) | ||||
0.108381 | + | 0.994109i | \(0.465433\pi\) | |||||||
\(140\) | −0.592723 | −0.0500942 | ||||||||
\(141\) | −1.18304 | −0.0996297 | ||||||||
\(142\) | −21.3531 | −1.79192 | ||||||||
\(143\) | 9.42887 | 0.788482 | ||||||||
\(144\) | 4.94865 | 0.412387 | ||||||||
\(145\) | 24.9837 | 2.07479 | ||||||||
\(146\) | −1.25713 | −0.104041 | ||||||||
\(147\) | −4.63751 | −0.382495 | ||||||||
\(148\) | 0.762254 | 0.0626569 | ||||||||
\(149\) | −2.49663 | −0.204532 | −0.102266 | − | 0.994757i | \(-0.532609\pi\) | ||||
−0.102266 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(150\) | −7.84816 | −0.640799 | ||||||||
\(151\) | −12.5137 | −1.01835 | −0.509175 | − | 0.860663i | \(-0.670049\pi\) | ||||
−0.509175 | + | 0.860663i | \(0.670049\pi\) | |||||||
\(152\) | −18.7982 | −1.52473 | ||||||||
\(153\) | −4.46438 | −0.360923 | ||||||||
\(154\) | 10.1851 | 0.820743 | ||||||||
\(155\) | 10.0867 | 0.810183 | ||||||||
\(156\) | 0.357921 | 0.0286566 | ||||||||
\(157\) | −21.6510 | −1.72793 | −0.863967 | − | 0.503548i | \(-0.832028\pi\) | ||||
−0.863967 | + | 0.503548i | \(0.832028\pi\) | |||||||
\(158\) | −25.2083 | −2.00547 | ||||||||
\(159\) | −1.31617 | −0.104379 | ||||||||
\(160\) | 1.77436 | 0.140275 | ||||||||
\(161\) | −6.01095 | −0.473729 | ||||||||
\(162\) | 5.91083 | 0.464399 | ||||||||
\(163\) | 16.8642 | 1.32091 | 0.660453 | − | 0.750867i | \(-0.270364\pi\) | ||||
0.660453 | + | 0.750867i | \(0.270364\pi\) | |||||||
\(164\) | 0.959540 | 0.0749275 | ||||||||
\(165\) | 15.0643 | 1.17276 | ||||||||
\(166\) | −1.29824 | −0.100763 | ||||||||
\(167\) | 1.93831 | 0.149991 | 0.0749955 | − | 0.997184i | \(-0.476106\pi\) | ||||
0.0749955 | + | 0.997184i | \(0.476106\pi\) | |||||||
\(168\) | −7.00517 | −0.540460 | ||||||||
\(169\) | −6.57237 | −0.505567 | ||||||||
\(170\) | −16.4915 | −1.26484 | ||||||||
\(171\) | 8.05837 | 0.616239 | ||||||||
\(172\) | −0.999237 | −0.0761911 | ||||||||
\(173\) | −11.7282 | −0.891682 | −0.445841 | − | 0.895112i | \(-0.647095\pi\) | ||||
−0.445841 | + | 0.895112i | \(0.647095\pi\) | |||||||
\(174\) | −16.2968 | −1.23545 | ||||||||
\(175\) | −7.56732 | −0.572036 | ||||||||
\(176\) | −15.6137 | −1.17693 | ||||||||
\(177\) | −6.80698 | −0.511644 | ||||||||
\(178\) | −11.9525 | −0.895879 | ||||||||
\(179\) | −4.38674 | −0.327880 | −0.163940 | − | 0.986470i | \(-0.552420\pi\) | ||||
−0.163940 | + | 0.986470i | \(0.552420\pi\) | |||||||
\(180\) | −0.370101 | −0.0275857 | ||||||||
\(181\) | 7.45034 | 0.553780 | 0.276890 | − | 0.960902i | \(-0.410696\pi\) | ||||
0.276890 | + | 0.960902i | \(0.410696\pi\) | |||||||
\(182\) | 6.94319 | 0.514663 | ||||||||
\(183\) | −3.65016 | −0.269828 | ||||||||
\(184\) | 8.75548 | 0.645462 | ||||||||
\(185\) | 21.8702 | 1.60793 | ||||||||
\(186\) | −6.57950 | −0.482432 | ||||||||
\(187\) | 14.0857 | 1.03005 | ||||||||
\(188\) | −0.0917036 | −0.00668818 | ||||||||
\(189\) | 10.6458 | 0.774369 | ||||||||
\(190\) | 29.7678 | 2.15958 | ||||||||
\(191\) | −8.59358 | −0.621809 | −0.310905 | − | 0.950441i | \(-0.600632\pi\) | ||||
−0.310905 | + | 0.950441i | \(0.600632\pi\) | |||||||
\(192\) | 10.1741 | 0.734253 | ||||||||
\(193\) | 10.9955 | 0.791471 | 0.395736 | − | 0.918364i | \(-0.370490\pi\) | ||||
0.395736 | + | 0.918364i | \(0.370490\pi\) | |||||||
\(194\) | 1.51065 | 0.108458 | ||||||||
\(195\) | 10.2693 | 0.735401 | ||||||||
\(196\) | −0.359479 | −0.0256770 | ||||||||
\(197\) | 4.71964 | 0.336260 | 0.168130 | − | 0.985765i | \(-0.446227\pi\) | ||||
0.168130 | + | 0.985765i | \(0.446227\pi\) | |||||||
\(198\) | 6.35968 | 0.451963 | ||||||||
\(199\) | −14.3633 | −1.01819 | −0.509093 | − | 0.860712i | \(-0.670019\pi\) | ||||
−0.509093 | + | 0.860712i | \(0.670019\pi\) | |||||||
\(200\) | 11.0225 | 0.779407 | ||||||||
\(201\) | −19.9311 | −1.40583 | ||||||||
\(202\) | 11.1847 | 0.786954 | ||||||||
\(203\) | −15.7136 | −1.10288 | ||||||||
\(204\) | 0.534696 | 0.0374362 | ||||||||
\(205\) | 27.5307 | 1.92283 | ||||||||
\(206\) | −14.4968 | −1.01004 | ||||||||
\(207\) | −3.75328 | −0.260871 | ||||||||
\(208\) | −10.6438 | −0.738015 | ||||||||
\(209\) | −25.4253 | −1.75870 | ||||||||
\(210\) | 11.0930 | 0.765490 | ||||||||
\(211\) | −13.5723 | −0.934353 | −0.467177 | − | 0.884164i | \(-0.654729\pi\) | ||||
−0.467177 | + | 0.884164i | \(0.654729\pi\) | |||||||
\(212\) | −0.102024 | −0.00700701 | ||||||||
\(213\) | 19.8638 | 1.36105 | ||||||||
\(214\) | −20.2869 | −1.38679 | ||||||||
\(215\) | −28.6697 | −1.95525 | ||||||||
\(216\) | −15.5066 | −1.05509 | ||||||||
\(217\) | −6.34406 | −0.430663 | ||||||||
\(218\) | −5.04167 | −0.341465 | ||||||||
\(219\) | 1.16945 | 0.0790243 | ||||||||
\(220\) | 1.16772 | 0.0787276 | ||||||||
\(221\) | 9.60220 | 0.645914 | ||||||||
\(222\) | −14.2658 | −0.957460 | ||||||||
\(223\) | −20.2102 | −1.35338 | −0.676689 | − | 0.736269i | \(-0.736586\pi\) | ||||
−0.676689 | + | 0.736269i | \(0.736586\pi\) | |||||||
\(224\) | −1.11599 | −0.0745650 | ||||||||
\(225\) | −4.72509 | −0.315006 | ||||||||
\(226\) | −27.8069 | −1.84969 | ||||||||
\(227\) | −11.3411 | −0.752733 | −0.376367 | − | 0.926471i | \(-0.622827\pi\) | ||||
−0.376367 | + | 0.926471i | \(0.622827\pi\) | |||||||
\(228\) | −0.965148 | −0.0639185 | ||||||||
\(229\) | −26.4406 | −1.74724 | −0.873622 | − | 0.486605i | \(-0.838235\pi\) | ||||
−0.873622 | + | 0.486605i | \(0.838235\pi\) | |||||||
\(230\) | −13.8647 | −0.914211 | ||||||||
\(231\) | −9.47476 | −0.623394 | ||||||||
\(232\) | 22.8883 | 1.50269 | ||||||||
\(233\) | 18.1239 | 1.18734 | 0.593668 | − | 0.804710i | \(-0.297679\pi\) | ||||
0.593668 | + | 0.804710i | \(0.297679\pi\) | |||||||
\(234\) | 4.33538 | 0.283412 | ||||||||
\(235\) | −2.63112 | −0.171635 | ||||||||
\(236\) | −0.527646 | −0.0343468 | ||||||||
\(237\) | 23.4501 | 1.52325 | ||||||||
\(238\) | 10.3724 | 0.672342 | ||||||||
\(239\) | −12.4814 | −0.807355 | −0.403678 | − | 0.914901i | \(-0.632268\pi\) | ||||
−0.403678 | + | 0.914901i | \(0.632268\pi\) | |||||||
\(240\) | −17.0054 | −1.09769 | ||||||||
\(241\) | 27.2423 | 1.75483 | 0.877414 | − | 0.479734i | \(-0.159267\pi\) | ||||
0.877414 | + | 0.479734i | \(0.159267\pi\) | |||||||
\(242\) | −4.10769 | −0.264052 | ||||||||
\(243\) | 11.4196 | 0.732566 | ||||||||
\(244\) | −0.282944 | −0.0181136 | ||||||||
\(245\) | −10.3140 | −0.658937 | ||||||||
\(246\) | −17.9581 | −1.14497 | ||||||||
\(247\) | −17.3323 | −1.10283 | ||||||||
\(248\) | 9.24069 | 0.586784 | ||||||||
\(249\) | 1.20769 | 0.0765344 | ||||||||
\(250\) | 4.31673 | 0.273014 | ||||||||
\(251\) | −6.05155 | −0.381970 | −0.190985 | − | 0.981593i | \(-0.561168\pi\) | ||||
−0.190985 | + | 0.981593i | \(0.561168\pi\) | |||||||
\(252\) | 0.232776 | 0.0146635 | ||||||||
\(253\) | 11.8421 | 0.744508 | ||||||||
\(254\) | −20.3078 | −1.27423 | ||||||||
\(255\) | 15.3413 | 0.960707 | ||||||||
\(256\) | 2.50390 | 0.156494 | ||||||||
\(257\) | −4.35090 | −0.271402 | −0.135701 | − | 0.990750i | \(-0.543329\pi\) | ||||
−0.135701 | + | 0.990750i | \(0.543329\pi\) | |||||||
\(258\) | 18.7011 | 1.16428 | ||||||||
\(259\) | −13.7554 | −0.854716 | ||||||||
\(260\) | 0.796031 | 0.0493677 | ||||||||
\(261\) | −9.81169 | −0.607329 | ||||||||
\(262\) | 24.0554 | 1.48615 | ||||||||
\(263\) | 2.50475 | 0.154450 | 0.0772249 | − | 0.997014i | \(-0.475394\pi\) | ||||
0.0772249 | + | 0.997014i | \(0.475394\pi\) | |||||||
\(264\) | 13.8008 | 0.849383 | ||||||||
\(265\) | −2.92722 | −0.179817 | ||||||||
\(266\) | −18.7226 | −1.14795 | ||||||||
\(267\) | 11.1189 | 0.680463 | ||||||||
\(268\) | −1.54497 | −0.0943738 | ||||||||
\(269\) | −22.2360 | −1.35575 | −0.677877 | − | 0.735175i | \(-0.737100\pi\) | ||||
−0.677877 | + | 0.735175i | \(0.737100\pi\) | |||||||
\(270\) | 24.5554 | 1.49439 | ||||||||
\(271\) | −26.7130 | −1.62270 | −0.811350 | − | 0.584560i | \(-0.801267\pi\) | ||||
−0.811350 | + | 0.584560i | \(0.801267\pi\) | |||||||
\(272\) | −15.9007 | −0.964122 | ||||||||
\(273\) | −6.45892 | −0.390911 | ||||||||
\(274\) | 26.4026 | 1.59504 | ||||||||
\(275\) | 14.9083 | 0.899006 | ||||||||
\(276\) | 0.449529 | 0.0270585 | ||||||||
\(277\) | −13.6054 | −0.817470 | −0.408735 | − | 0.912653i | \(-0.634030\pi\) | ||||
−0.408735 | + | 0.912653i | \(0.634030\pi\) | |||||||
\(278\) | −3.70747 | −0.222359 | ||||||||
\(279\) | −3.96128 | −0.237156 | ||||||||
\(280\) | −15.5798 | −0.931069 | ||||||||
\(281\) | 15.6871 | 0.935812 | 0.467906 | − | 0.883778i | \(-0.345008\pi\) | ||||
0.467906 | + | 0.883778i | \(0.345008\pi\) | |||||||
\(282\) | 1.71626 | 0.102202 | ||||||||
\(283\) | −17.3203 | −1.02958 | −0.514792 | − | 0.857315i | \(-0.672131\pi\) | ||||
−0.514792 | + | 0.857315i | \(0.672131\pi\) | |||||||
\(284\) | 1.53975 | 0.0913675 | ||||||||
\(285\) | −27.6916 | −1.64031 | ||||||||
\(286\) | −13.6787 | −0.808840 | ||||||||
\(287\) | −17.3155 | −1.02210 | ||||||||
\(288\) | −0.696831 | −0.0410612 | ||||||||
\(289\) | −2.65533 | −0.156196 | ||||||||
\(290\) | −36.2446 | −2.12836 | ||||||||
\(291\) | −1.40529 | −0.0823795 | ||||||||
\(292\) | 0.0906507 | 0.00530493 | ||||||||
\(293\) | −25.3088 | −1.47856 | −0.739278 | − | 0.673400i | \(-0.764833\pi\) | ||||
−0.739278 | + | 0.673400i | \(0.764833\pi\) | |||||||
\(294\) | 6.72776 | 0.392371 | ||||||||
\(295\) | −15.1390 | −0.881426 | ||||||||
\(296\) | 20.0359 | 1.16456 | ||||||||
\(297\) | −20.9732 | −1.21699 | ||||||||
\(298\) | 3.62194 | 0.209813 | ||||||||
\(299\) | 8.07274 | 0.466859 | ||||||||
\(300\) | 0.565922 | 0.0326735 | ||||||||
\(301\) | 18.0319 | 1.03934 | ||||||||
\(302\) | 18.1539 | 1.04464 | ||||||||
\(303\) | −10.4046 | −0.597730 | ||||||||
\(304\) | 28.7014 | 1.64614 | ||||||||
\(305\) | −8.11810 | −0.464841 | ||||||||
\(306\) | 6.47659 | 0.370242 | ||||||||
\(307\) | −23.1877 | −1.32339 | −0.661695 | − | 0.749773i | \(-0.730163\pi\) | ||||
−0.661695 | + | 0.749773i | \(0.730163\pi\) | |||||||
\(308\) | −0.734441 | −0.0418486 | ||||||||
\(309\) | 13.4857 | 0.767174 | ||||||||
\(310\) | −14.6331 | −0.831102 | ||||||||
\(311\) | 12.0104 | 0.681050 | 0.340525 | − | 0.940235i | \(-0.389395\pi\) | ||||
0.340525 | + | 0.940235i | \(0.389395\pi\) | |||||||
\(312\) | 9.40799 | 0.532622 | ||||||||
\(313\) | −22.6132 | −1.27817 | −0.639087 | − | 0.769135i | \(-0.720688\pi\) | ||||
−0.639087 | + | 0.769135i | \(0.720688\pi\) | |||||||
\(314\) | 31.4096 | 1.77255 | ||||||||
\(315\) | 6.67870 | 0.376302 | ||||||||
\(316\) | 1.81775 | 0.102256 | ||||||||
\(317\) | 12.8214 | 0.720122 | 0.360061 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360061 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(318\) | 1.90941 | 0.107074 | ||||||||
\(319\) | 30.9573 | 1.73327 | ||||||||
\(320\) | 22.6276 | 1.26492 | ||||||||
\(321\) | 18.8720 | 1.05333 | ||||||||
\(322\) | 8.72025 | 0.485960 | ||||||||
\(323\) | −25.8927 | −1.44071 | ||||||||
\(324\) | −0.426224 | −0.0236791 | ||||||||
\(325\) | 10.1630 | 0.563740 | ||||||||
\(326\) | −24.4654 | −1.35501 | ||||||||
\(327\) | 4.69002 | 0.259359 | ||||||||
\(328\) | 25.2216 | 1.39263 | ||||||||
\(329\) | 1.65485 | 0.0912349 | ||||||||
\(330\) | −21.8543 | −1.20304 | ||||||||
\(331\) | −29.0189 | −1.59502 | −0.797512 | − | 0.603303i | \(-0.793851\pi\) | ||||
−0.797512 | + | 0.603303i | \(0.793851\pi\) | |||||||
\(332\) | 0.0936148 | 0.00513778 | ||||||||
\(333\) | −8.58895 | −0.470671 | ||||||||
\(334\) | −2.81196 | −0.153864 | ||||||||
\(335\) | −44.3274 | −2.42187 | ||||||||
\(336\) | 10.6956 | 0.583493 | ||||||||
\(337\) | 10.1690 | 0.553940 | 0.276970 | − | 0.960879i | \(-0.410670\pi\) | ||||
0.276970 | + | 0.960879i | \(0.410670\pi\) | |||||||
\(338\) | 9.53471 | 0.518620 | ||||||||
\(339\) | 25.8674 | 1.40493 | ||||||||
\(340\) | 1.18919 | 0.0644926 | ||||||||
\(341\) | 12.4984 | 0.676826 | ||||||||
\(342\) | −11.6905 | −0.632150 | ||||||||
\(343\) | 19.7014 | 1.06377 | ||||||||
\(344\) | −26.2650 | −1.41611 | ||||||||
\(345\) | 12.8977 | 0.694388 | ||||||||
\(346\) | 17.0145 | 0.914705 | ||||||||
\(347\) | 3.37958 | 0.181426 | 0.0907128 | − | 0.995877i | \(-0.471085\pi\) | ||||
0.0907128 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(348\) | 1.17514 | 0.0629942 | ||||||||
\(349\) | 11.1240 | 0.595453 | 0.297727 | − | 0.954651i | \(-0.403772\pi\) | ||||
0.297727 | + | 0.954651i | \(0.403772\pi\) | |||||||
\(350\) | 10.9781 | 0.586805 | ||||||||
\(351\) | −14.2974 | −0.763139 | ||||||||
\(352\) | 2.19860 | 0.117186 | ||||||||
\(353\) | 12.2734 | 0.653245 | 0.326623 | − | 0.945155i | \(-0.394089\pi\) | ||||
0.326623 | + | 0.945155i | \(0.394089\pi\) | |||||||
\(354\) | 9.87507 | 0.524854 | ||||||||
\(355\) | 44.1779 | 2.34472 | ||||||||
\(356\) | 0.861884 | 0.0456797 | ||||||||
\(357\) | −9.64894 | −0.510676 | ||||||||
\(358\) | 6.36396 | 0.336346 | ||||||||
\(359\) | 12.7857 | 0.674802 | 0.337401 | − | 0.941361i | \(-0.390452\pi\) | ||||
0.337401 | + | 0.941361i | \(0.390452\pi\) | |||||||
\(360\) | −9.72812 | −0.512717 | ||||||||
\(361\) | 27.7373 | 1.45986 | ||||||||
\(362\) | −10.8084 | −0.568078 | ||||||||
\(363\) | 3.82119 | 0.200560 | ||||||||
\(364\) | −0.500666 | −0.0262420 | ||||||||
\(365\) | 2.60091 | 0.136138 | ||||||||
\(366\) | 5.29539 | 0.276794 | ||||||||
\(367\) | −16.8725 | −0.880739 | −0.440369 | − | 0.897817i | \(-0.645152\pi\) | ||||
−0.440369 | + | 0.897817i | \(0.645152\pi\) | |||||||
\(368\) | −13.3680 | −0.696856 | ||||||||
\(369\) | −10.8119 | −0.562847 | ||||||||
\(370\) | −31.7278 | −1.64945 | ||||||||
\(371\) | 1.84108 | 0.0955842 | ||||||||
\(372\) | 0.474441 | 0.0245986 | ||||||||
\(373\) | 25.0777 | 1.29847 | 0.649236 | − | 0.760587i | \(-0.275089\pi\) | ||||
0.649236 | + | 0.760587i | \(0.275089\pi\) | |||||||
\(374\) | −20.4346 | −1.05665 | ||||||||
\(375\) | −4.01565 | −0.207367 | ||||||||
\(376\) | −2.41044 | −0.124309 | ||||||||
\(377\) | 21.1035 | 1.08688 | ||||||||
\(378\) | −15.4442 | −0.794363 | ||||||||
\(379\) | −20.7014 | −1.06336 | −0.531679 | − | 0.846946i | \(-0.678439\pi\) | ||||
−0.531679 | + | 0.846946i | \(0.678439\pi\) | |||||||
\(380\) | −2.14653 | −0.110114 | ||||||||
\(381\) | 18.8914 | 0.967837 | ||||||||
\(382\) | 12.4669 | 0.637864 | ||||||||
\(383\) | −4.51458 | −0.230684 | −0.115342 | − | 0.993326i | \(-0.536796\pi\) | ||||
−0.115342 | + | 0.993326i | \(0.536796\pi\) | |||||||
\(384\) | −16.3555 | −0.834637 | ||||||||
\(385\) | −21.0722 | −1.07394 | ||||||||
\(386\) | −15.9514 | −0.811907 | ||||||||
\(387\) | 11.2592 | 0.572339 | ||||||||
\(388\) | −0.108932 | −0.00553016 | ||||||||
\(389\) | 5.10467 | 0.258817 | 0.129408 | − | 0.991591i | \(-0.458692\pi\) | ||||
0.129408 | + | 0.991591i | \(0.458692\pi\) | |||||||
\(390\) | −14.8980 | −0.754389 | ||||||||
\(391\) | 12.0598 | 0.609891 | ||||||||
\(392\) | −9.44892 | −0.477242 | ||||||||
\(393\) | −22.3776 | −1.12880 | ||||||||
\(394\) | −6.84691 | −0.344942 | ||||||||
\(395\) | 52.1539 | 2.62415 | ||||||||
\(396\) | −0.458590 | −0.0230450 | ||||||||
\(397\) | −9.63939 | −0.483787 | −0.241893 | − | 0.970303i | \(-0.577768\pi\) | ||||
−0.241893 | + | 0.970303i | \(0.577768\pi\) | |||||||
\(398\) | 20.8372 | 1.04447 | ||||||||
\(399\) | 17.4167 | 0.871926 | ||||||||
\(400\) | −16.8293 | −0.841465 | ||||||||
\(401\) | −31.9040 | −1.59321 | −0.796605 | − | 0.604500i | \(-0.793373\pi\) | ||||
−0.796605 | + | 0.604500i | \(0.793373\pi\) | |||||||
\(402\) | 28.9145 | 1.44213 | ||||||||
\(403\) | 8.52012 | 0.424417 | ||||||||
\(404\) | −0.806519 | −0.0401258 | ||||||||
\(405\) | −12.2290 | −0.607665 | ||||||||
\(406\) | 22.7962 | 1.13135 | ||||||||
\(407\) | 27.0993 | 1.34326 | ||||||||
\(408\) | 14.0545 | 0.695803 | ||||||||
\(409\) | −1.73766 | −0.0859217 | −0.0429609 | − | 0.999077i | \(-0.513679\pi\) | ||||
−0.0429609 | + | 0.999077i | \(0.513679\pi\) | |||||||
\(410\) | −39.9395 | −1.97247 | ||||||||
\(411\) | −24.5611 | −1.21151 | ||||||||
\(412\) | 1.04535 | 0.0515007 | ||||||||
\(413\) | 9.52171 | 0.468533 | ||||||||
\(414\) | 5.44499 | 0.267607 | ||||||||
\(415\) | 2.68595 | 0.131848 | ||||||||
\(416\) | 1.49878 | 0.0734837 | ||||||||
\(417\) | 3.44889 | 0.168893 | ||||||||
\(418\) | 36.8852 | 1.80411 | ||||||||
\(419\) | 14.5746 | 0.712015 | 0.356008 | − | 0.934483i | \(-0.384138\pi\) | ||||
0.356008 | + | 0.934483i | \(0.384138\pi\) | |||||||
\(420\) | −0.799905 | −0.0390314 | ||||||||
\(421\) | −11.9750 | −0.583624 | −0.291812 | − | 0.956476i | \(-0.594258\pi\) | ||||
−0.291812 | + | 0.956476i | \(0.594258\pi\) | |||||||
\(422\) | 19.6897 | 0.958478 | ||||||||
\(423\) | 1.03330 | 0.0502408 | ||||||||
\(424\) | −2.68170 | −0.130235 | ||||||||
\(425\) | 15.1824 | 0.736454 | ||||||||
\(426\) | −28.8170 | −1.39619 | ||||||||
\(427\) | 5.10590 | 0.247092 | ||||||||
\(428\) | 1.46287 | 0.0707105 | ||||||||
\(429\) | 12.7247 | 0.614353 | ||||||||
\(430\) | 41.5919 | 2.00574 | ||||||||
\(431\) | −27.2432 | −1.31226 | −0.656128 | − | 0.754649i | \(-0.727807\pi\) | ||||
−0.656128 | + | 0.754649i | \(0.727807\pi\) | |||||||
\(432\) | 23.6757 | 1.13910 | ||||||||
\(433\) | 7.04691 | 0.338653 | 0.169326 | − | 0.985560i | \(-0.445841\pi\) | ||||
0.169326 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(434\) | 9.20350 | 0.441782 | ||||||||
\(435\) | 33.7166 | 1.61659 | ||||||||
\(436\) | 0.363549 | 0.0174109 | ||||||||
\(437\) | −21.7684 | −1.04133 | ||||||||
\(438\) | −1.69656 | −0.0810646 | ||||||||
\(439\) | −3.95251 | −0.188643 | −0.0943214 | − | 0.995542i | \(-0.530068\pi\) | ||||
−0.0943214 | + | 0.995542i | \(0.530068\pi\) | |||||||
\(440\) | 30.6936 | 1.46326 | ||||||||
\(441\) | 4.05054 | 0.192883 | ||||||||
\(442\) | −13.9302 | −0.662591 | ||||||||
\(443\) | 27.4494 | 1.30416 | 0.652080 | − | 0.758150i | \(-0.273896\pi\) | ||||
0.652080 | + | 0.758150i | \(0.273896\pi\) | |||||||
\(444\) | 1.02869 | 0.0488197 | ||||||||
\(445\) | 24.7288 | 1.17226 | ||||||||
\(446\) | 29.3195 | 1.38832 | ||||||||
\(447\) | −3.36932 | −0.159363 | ||||||||
\(448\) | −14.2317 | −0.672385 | ||||||||
\(449\) | −30.1810 | −1.42433 | −0.712166 | − | 0.702011i | \(-0.752286\pi\) | ||||
−0.712166 | + | 0.702011i | \(0.752286\pi\) | |||||||
\(450\) | 6.85482 | 0.323139 | ||||||||
\(451\) | 34.1132 | 1.60633 | ||||||||
\(452\) | 2.00513 | 0.0943132 | ||||||||
\(453\) | −16.8878 | −0.793456 | ||||||||
\(454\) | 16.4528 | 0.772168 | ||||||||
\(455\) | −14.3649 | −0.673436 | ||||||||
\(456\) | −25.3690 | −1.18801 | ||||||||
\(457\) | −16.0684 | −0.751648 | −0.375824 | − | 0.926691i | \(-0.622640\pi\) | ||||
−0.375824 | + | 0.926691i | \(0.622640\pi\) | |||||||
\(458\) | 38.3581 | 1.79236 | ||||||||
\(459\) | −21.3588 | −0.996943 | ||||||||
\(460\) | 0.999769 | 0.0466145 | ||||||||
\(461\) | 0.892613 | 0.0415731 | 0.0207866 | − | 0.999784i | \(-0.493383\pi\) | ||||
0.0207866 | + | 0.999784i | \(0.493383\pi\) | |||||||
\(462\) | 13.7453 | 0.639489 | ||||||||
\(463\) | 42.3928 | 1.97016 | 0.985081 | − | 0.172090i | \(-0.0550519\pi\) | ||||
0.985081 | + | 0.172090i | \(0.0550519\pi\) | |||||||
\(464\) | −34.9462 | −1.62234 | ||||||||
\(465\) | 13.6124 | 0.631262 | ||||||||
\(466\) | −26.2928 | −1.21799 | ||||||||
\(467\) | −32.4692 | −1.50250 | −0.751248 | − | 0.660020i | \(-0.770548\pi\) | ||||
−0.751248 | + | 0.660020i | \(0.770548\pi\) | |||||||
\(468\) | −0.312620 | −0.0144508 | ||||||||
\(469\) | 27.8799 | 1.28737 | ||||||||
\(470\) | 3.81704 | 0.176067 | ||||||||
\(471\) | −29.2189 | −1.34634 | ||||||||
\(472\) | −13.8692 | −0.638383 | ||||||||
\(473\) | −35.5245 | −1.63342 | ||||||||
\(474\) | −34.0197 | −1.56258 | ||||||||
\(475\) | −27.4048 | −1.25742 | ||||||||
\(476\) | −0.747942 | −0.0342819 | ||||||||
\(477\) | 1.14959 | 0.0526359 | ||||||||
\(478\) | 18.1071 | 0.828200 | ||||||||
\(479\) | 14.1845 | 0.648106 | 0.324053 | − | 0.946039i | \(-0.394954\pi\) | ||||
0.324053 | + | 0.946039i | \(0.394954\pi\) | |||||||
\(480\) | 2.39457 | 0.109297 | ||||||||
\(481\) | 18.4735 | 0.842321 | ||||||||
\(482\) | −39.5211 | −1.80014 | ||||||||
\(483\) | −8.11203 | −0.369110 | ||||||||
\(484\) | 0.296201 | 0.0134637 | ||||||||
\(485\) | −3.12542 | −0.141918 | ||||||||
\(486\) | −16.5667 | −0.751481 | ||||||||
\(487\) | −23.8548 | −1.08096 | −0.540482 | − | 0.841356i | \(-0.681758\pi\) | ||||
−0.540482 | + | 0.841356i | \(0.681758\pi\) | |||||||
\(488\) | −7.43720 | −0.336666 | ||||||||
\(489\) | 22.7590 | 1.02920 | ||||||||
\(490\) | 14.9628 | 0.675950 | ||||||||
\(491\) | 22.9375 | 1.03515 | 0.517576 | − | 0.855637i | \(-0.326834\pi\) | ||||
0.517576 | + | 0.855637i | \(0.326834\pi\) | |||||||
\(492\) | 1.29494 | 0.0583804 | ||||||||
\(493\) | 31.5264 | 1.41988 | ||||||||
\(494\) | 25.1445 | 1.13131 | ||||||||
\(495\) | −13.1577 | −0.591393 | ||||||||
\(496\) | −14.1088 | −0.633505 | ||||||||
\(497\) | −27.7858 | −1.24636 | ||||||||
\(498\) | −1.75203 | −0.0785104 | ||||||||
\(499\) | 22.1577 | 0.991917 | 0.495958 | − | 0.868346i | \(-0.334817\pi\) | ||||
0.495958 | + | 0.868346i | \(0.334817\pi\) | |||||||
\(500\) | −0.311275 | −0.0139206 | ||||||||
\(501\) | 2.61583 | 0.116867 | ||||||||
\(502\) | 8.77915 | 0.391832 | ||||||||
\(503\) | 13.4364 | 0.599100 | 0.299550 | − | 0.954081i | \(-0.403164\pi\) | ||||
0.299550 | + | 0.954081i | \(0.403164\pi\) | |||||||
\(504\) | 6.11853 | 0.272541 | ||||||||
\(505\) | −23.1403 | −1.02973 | ||||||||
\(506\) | −17.1797 | −0.763731 | ||||||||
\(507\) | −8.86969 | −0.393917 | ||||||||
\(508\) | 1.46438 | 0.0649712 | ||||||||
\(509\) | 4.24178 | 0.188014 | 0.0940068 | − | 0.995572i | \(-0.470032\pi\) | ||||
0.0940068 | + | 0.995572i | \(0.470032\pi\) | |||||||
\(510\) | −22.2560 | −0.985512 | ||||||||
\(511\) | −1.63585 | −0.0723657 | ||||||||
\(512\) | 20.6061 | 0.910668 | ||||||||
\(513\) | 38.5534 | 1.70218 | ||||||||
\(514\) | 6.31197 | 0.278409 | ||||||||
\(515\) | 29.9927 | 1.32164 | ||||||||
\(516\) | −1.34851 | −0.0593650 | ||||||||
\(517\) | −3.26021 | −0.143384 | ||||||||
\(518\) | 19.9553 | 0.876785 | ||||||||
\(519\) | −15.8278 | −0.694762 | ||||||||
\(520\) | 20.9237 | 0.917566 | ||||||||
\(521\) | −0.576744 | −0.0252676 | −0.0126338 | − | 0.999920i | \(-0.504022\pi\) | ||||
−0.0126338 | + | 0.999920i | \(0.504022\pi\) | |||||||
\(522\) | 14.2341 | 0.623009 | ||||||||
\(523\) | −1.02123 | −0.0446554 | −0.0223277 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223277 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(524\) | −1.73461 | −0.0757769 | ||||||||
\(525\) | −10.2124 | −0.445707 | ||||||||
\(526\) | −3.63372 | −0.158438 | ||||||||
\(527\) | 12.7281 | 0.554447 | ||||||||
\(528\) | −21.0713 | −0.917012 | ||||||||
\(529\) | −12.8611 | −0.559178 | ||||||||
\(530\) | 4.24659 | 0.184460 | ||||||||
\(531\) | 5.94543 | 0.258010 | ||||||||
\(532\) | 1.35006 | 0.0585327 | ||||||||
\(533\) | 23.2548 | 1.00728 | ||||||||
\(534\) | −16.1304 | −0.698032 | ||||||||
\(535\) | 41.9720 | 1.81461 | ||||||||
\(536\) | −40.6095 | −1.75406 | ||||||||
\(537\) | −5.92009 | −0.255471 | ||||||||
\(538\) | 32.2584 | 1.39076 | ||||||||
\(539\) | −12.7800 | −0.550475 | ||||||||
\(540\) | −1.77066 | −0.0761972 | ||||||||
\(541\) | −15.6894 | −0.674539 | −0.337269 | − | 0.941408i | \(-0.609503\pi\) | ||||
−0.337269 | + | 0.941408i | \(0.609503\pi\) | |||||||
\(542\) | 38.7533 | 1.66460 | ||||||||
\(543\) | 10.0546 | 0.431482 | ||||||||
\(544\) | 2.23902 | 0.0959970 | ||||||||
\(545\) | 10.4308 | 0.446806 | ||||||||
\(546\) | 9.37013 | 0.401005 | ||||||||
\(547\) | −11.2159 | −0.479557 | −0.239779 | − | 0.970828i | \(-0.577075\pi\) | ||||
−0.239779 | + | 0.970828i | \(0.577075\pi\) | |||||||
\(548\) | −1.90387 | −0.0813292 | ||||||||
\(549\) | 3.18816 | 0.136068 | ||||||||
\(550\) | −21.6279 | −0.922218 | ||||||||
\(551\) | −56.9063 | −2.42429 | ||||||||
\(552\) | 11.8159 | 0.502918 | ||||||||
\(553\) | −32.8024 | −1.39490 | ||||||||
\(554\) | 19.7377 | 0.838577 | ||||||||
\(555\) | 29.5148 | 1.25284 | ||||||||
\(556\) | 0.267342 | 0.0113378 | ||||||||
\(557\) | 14.3333 | 0.607322 | 0.303661 | − | 0.952780i | \(-0.401791\pi\) | ||||
0.303661 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(558\) | 5.74674 | 0.243279 | ||||||||
\(559\) | −24.2169 | −1.02427 | ||||||||
\(560\) | 23.7874 | 1.00520 | ||||||||
\(561\) | 19.0093 | 0.802573 | ||||||||
\(562\) | −22.7577 | −0.959975 | ||||||||
\(563\) | 26.9834 | 1.13722 | 0.568608 | − | 0.822609i | \(-0.307482\pi\) | ||||
0.568608 | + | 0.822609i | \(0.307482\pi\) | |||||||
\(564\) | −0.123758 | −0.00521115 | ||||||||
\(565\) | 57.5302 | 2.42031 | ||||||||
\(566\) | 25.1270 | 1.05617 | ||||||||
\(567\) | 7.69148 | 0.323012 | ||||||||
\(568\) | 40.4725 | 1.69819 | ||||||||
\(569\) | 3.08488 | 0.129325 | 0.0646625 | − | 0.997907i | \(-0.479403\pi\) | ||||
0.0646625 | + | 0.997907i | \(0.479403\pi\) | |||||||
\(570\) | 40.1729 | 1.68266 | ||||||||
\(571\) | −8.77746 | −0.367325 | −0.183663 | − | 0.982989i | \(-0.558795\pi\) | ||||
−0.183663 | + | 0.982989i | \(0.558795\pi\) | |||||||
\(572\) | 0.986359 | 0.0412417 | ||||||||
\(573\) | −11.5974 | −0.484488 | ||||||||
\(574\) | 25.1201 | 1.04849 | ||||||||
\(575\) | 12.7641 | 0.532300 | ||||||||
\(576\) | −8.88639 | −0.370266 | ||||||||
\(577\) | 26.3403 | 1.09656 | 0.548280 | − | 0.836295i | \(-0.315283\pi\) | ||||
0.548280 | + | 0.836295i | \(0.315283\pi\) | |||||||
\(578\) | 3.85216 | 0.160229 | ||||||||
\(579\) | 14.8389 | 0.616682 | ||||||||
\(580\) | 2.61356 | 0.108522 | ||||||||
\(581\) | −1.68934 | −0.0700856 | ||||||||
\(582\) | 2.03869 | 0.0845064 | ||||||||
\(583\) | −3.62710 | −0.150219 | ||||||||
\(584\) | 2.38276 | 0.0985993 | ||||||||
\(585\) | −8.96954 | −0.370845 | ||||||||
\(586\) | 36.7162 | 1.51673 | ||||||||
\(587\) | 4.65092 | 0.191964 | 0.0959820 | − | 0.995383i | \(-0.469401\pi\) | ||||
0.0959820 | + | 0.995383i | \(0.469401\pi\) | |||||||
\(588\) | −0.485132 | −0.0200065 | ||||||||
\(589\) | −22.9748 | −0.946660 | ||||||||
\(590\) | 21.9625 | 0.904184 | ||||||||
\(591\) | 6.36936 | 0.262000 | ||||||||
\(592\) | −30.5911 | −1.25729 | ||||||||
\(593\) | 23.3624 | 0.959380 | 0.479690 | − | 0.877438i | \(-0.340749\pi\) | ||||
0.479690 | + | 0.877438i | \(0.340749\pi\) | |||||||
\(594\) | 30.4265 | 1.24841 | ||||||||
\(595\) | −21.4596 | −0.879758 | ||||||||
\(596\) | −0.261174 | −0.0106981 | ||||||||
\(597\) | −19.3839 | −0.793329 | ||||||||
\(598\) | −11.7113 | −0.478913 | ||||||||
\(599\) | −35.6661 | −1.45728 | −0.728638 | − | 0.684899i | \(-0.759846\pi\) | ||||
−0.728638 | + | 0.684899i | \(0.759846\pi\) | |||||||
\(600\) | 14.8753 | 0.607282 | ||||||||
\(601\) | 38.0829 | 1.55343 | 0.776717 | − | 0.629850i | \(-0.216883\pi\) | ||||
0.776717 | + | 0.629850i | \(0.216883\pi\) | |||||||
\(602\) | −26.1593 | −1.06617 | ||||||||
\(603\) | 17.4084 | 0.708925 | ||||||||
\(604\) | −1.30906 | −0.0532650 | ||||||||
\(605\) | 8.49847 | 0.345512 | ||||||||
\(606\) | 15.0943 | 0.613163 | ||||||||
\(607\) | 32.9253 | 1.33640 | 0.668199 | − | 0.743983i | \(-0.267065\pi\) | ||||
0.668199 | + | 0.743983i | \(0.267065\pi\) | |||||||
\(608\) | −4.04151 | −0.163905 | ||||||||
\(609\) | −21.2062 | −0.859318 | ||||||||
\(610\) | 11.7771 | 0.476843 | ||||||||
\(611\) | −2.22248 | −0.0899117 | ||||||||
\(612\) | −0.467020 | −0.0188782 | ||||||||
\(613\) | 33.2601 | 1.34336 | 0.671680 | − | 0.740841i | \(-0.265573\pi\) | ||||
0.671680 | + | 0.740841i | \(0.265573\pi\) | |||||||
\(614\) | 33.6390 | 1.35756 | ||||||||
\(615\) | 37.1538 | 1.49819 | ||||||||
\(616\) | −19.3048 | −0.777814 | ||||||||
\(617\) | 25.9173 | 1.04339 | 0.521695 | − | 0.853132i | \(-0.325300\pi\) | ||||
0.521695 | + | 0.853132i | \(0.325300\pi\) | |||||||
\(618\) | −19.5641 | −0.786982 | ||||||||
\(619\) | −36.2632 | −1.45754 | −0.728771 | − | 0.684758i | \(-0.759908\pi\) | ||||
−0.728771 | + | 0.684758i | \(0.759908\pi\) | |||||||
\(620\) | 1.05517 | 0.0423768 | ||||||||
\(621\) | −17.9567 | −0.720578 | ||||||||
\(622\) | −17.4239 | −0.698634 | ||||||||
\(623\) | −15.5532 | −0.623127 | ||||||||
\(624\) | −14.3643 | −0.575031 | ||||||||
\(625\) | −28.9741 | −1.15896 | ||||||||
\(626\) | 32.8056 | 1.31118 | ||||||||
\(627\) | −34.3125 | −1.37031 | ||||||||
\(628\) | −2.26492 | −0.0903800 | ||||||||
\(629\) | 27.5975 | 1.10038 | ||||||||
\(630\) | −9.68898 | −0.386018 | ||||||||
\(631\) | 26.2694 | 1.04577 | 0.522884 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522884 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(632\) | 47.7796 | 1.90057 | ||||||||
\(633\) | −18.3164 | −0.728010 | ||||||||
\(634\) | −18.6004 | −0.738715 | ||||||||
\(635\) | 42.0152 | 1.66732 | ||||||||
\(636\) | −0.137685 | −0.00545958 | ||||||||
\(637\) | −8.71211 | −0.345186 | ||||||||
\(638\) | −44.9106 | −1.77803 | ||||||||
\(639\) | −17.3497 | −0.686343 | ||||||||
\(640\) | −36.3752 | −1.43786 | ||||||||
\(641\) | 1.87771 | 0.0741651 | 0.0370826 | − | 0.999312i | \(-0.488194\pi\) | ||||
0.0370826 | + | 0.999312i | \(0.488194\pi\) | |||||||
\(642\) | −27.3781 | −1.08053 | ||||||||
\(643\) | −38.7911 | −1.52977 | −0.764886 | − | 0.644165i | \(-0.777205\pi\) | ||||
−0.764886 | + | 0.644165i | \(0.777205\pi\) | |||||||
\(644\) | −0.628808 | −0.0247785 | ||||||||
\(645\) | −38.6909 | −1.52345 | ||||||||
\(646\) | 37.5632 | 1.47791 | ||||||||
\(647\) | −14.5299 | −0.571227 | −0.285614 | − | 0.958345i | \(-0.592197\pi\) | ||||
−0.285614 | + | 0.958345i | \(0.592197\pi\) | |||||||
\(648\) | −11.2033 | −0.440108 | ||||||||
\(649\) | −18.7587 | −0.736342 | ||||||||
\(650\) | −14.7437 | −0.578295 | ||||||||
\(651\) | −8.56158 | −0.335555 | ||||||||
\(652\) | 1.76417 | 0.0690904 | ||||||||
\(653\) | −44.2710 | −1.73246 | −0.866230 | − | 0.499646i | \(-0.833464\pi\) | ||||
−0.866230 | + | 0.499646i | \(0.833464\pi\) | |||||||
\(654\) | −6.80395 | −0.266055 | ||||||||
\(655\) | −49.7687 | −1.94463 | ||||||||
\(656\) | −38.5087 | −1.50351 | ||||||||
\(657\) | −1.02144 | −0.0398500 | ||||||||
\(658\) | −2.40074 | −0.0935905 | ||||||||
\(659\) | 31.8325 | 1.24002 | 0.620009 | − | 0.784595i | \(-0.287129\pi\) | ||||
0.620009 | + | 0.784595i | \(0.287129\pi\) | |||||||
\(660\) | 1.57589 | 0.0613413 | ||||||||
\(661\) | 12.3380 | 0.479892 | 0.239946 | − | 0.970786i | \(-0.422870\pi\) | ||||
0.239946 | + | 0.970786i | \(0.422870\pi\) | |||||||
\(662\) | 42.0986 | 1.63621 | ||||||||
\(663\) | 12.9586 | 0.503270 | ||||||||
\(664\) | 2.46067 | 0.0954926 | ||||||||
\(665\) | 38.7354 | 1.50210 | ||||||||
\(666\) | 12.4602 | 0.482824 | ||||||||
\(667\) | 26.5048 | 1.02627 | ||||||||
\(668\) | 0.202768 | 0.00784531 | ||||||||
\(669\) | −27.2746 | −1.05450 | ||||||||
\(670\) | 64.3070 | 2.48440 | ||||||||
\(671\) | −10.0591 | −0.388327 | ||||||||
\(672\) | −1.50607 | −0.0580980 | ||||||||
\(673\) | −44.0425 | −1.69771 | −0.848856 | − | 0.528624i | \(-0.822708\pi\) | ||||
−0.848856 | + | 0.528624i | \(0.822708\pi\) | |||||||
\(674\) | −14.7524 | −0.568243 | ||||||||
\(675\) | −22.6061 | −0.870111 | ||||||||
\(676\) | −0.687538 | −0.0264438 | ||||||||
\(677\) | 50.5185 | 1.94158 | 0.970792 | − | 0.239921i | \(-0.0771216\pi\) | ||||
0.970792 | + | 0.239921i | \(0.0771216\pi\) | |||||||
\(678\) | −37.5266 | −1.44120 | ||||||||
\(679\) | 1.96574 | 0.0754382 | ||||||||
\(680\) | 31.2578 | 1.19868 | ||||||||
\(681\) | −15.3053 | −0.586499 | ||||||||
\(682\) | −18.1318 | −0.694301 | ||||||||
\(683\) | 33.9742 | 1.29999 | 0.649993 | − | 0.759941i | \(-0.274772\pi\) | ||||
0.649993 | + | 0.759941i | \(0.274772\pi\) | |||||||
\(684\) | 0.842990 | 0.0322325 | ||||||||
\(685\) | −54.6249 | −2.08711 | ||||||||
\(686\) | −28.5813 | −1.09124 | ||||||||
\(687\) | −35.6827 | −1.36138 | ||||||||
\(688\) | 40.1019 | 1.52887 | ||||||||
\(689\) | −2.47259 | −0.0941980 | ||||||||
\(690\) | −18.7110 | −0.712316 | ||||||||
\(691\) | −33.8904 | −1.28925 | −0.644626 | − | 0.764498i | \(-0.722987\pi\) | ||||
−0.644626 | + | 0.764498i | \(0.722987\pi\) | |||||||
\(692\) | −1.22690 | −0.0466396 | ||||||||
\(693\) | 8.27555 | 0.314362 | ||||||||
\(694\) | −4.90285 | −0.186110 | ||||||||
\(695\) | 7.67046 | 0.290957 | ||||||||
\(696\) | 30.8887 | 1.17083 | ||||||||
\(697\) | 34.7403 | 1.31588 | ||||||||
\(698\) | −16.1379 | −0.610827 | ||||||||
\(699\) | 24.4590 | 0.925124 | ||||||||
\(700\) | −0.791621 | −0.0299205 | ||||||||
\(701\) | −16.8977 | −0.638216 | −0.319108 | − | 0.947718i | \(-0.603383\pi\) | ||||
−0.319108 | + | 0.947718i | \(0.603383\pi\) | |||||||
\(702\) | 20.7416 | 0.782842 | ||||||||
\(703\) | −49.8146 | −1.87879 | ||||||||
\(704\) | 28.0378 | 1.05671 | ||||||||
\(705\) | −3.55081 | −0.133731 | ||||||||
\(706\) | −17.8053 | −0.670111 | ||||||||
\(707\) | 14.5541 | 0.547365 | ||||||||
\(708\) | −0.712082 | −0.0267617 | ||||||||
\(709\) | −1.62126 | −0.0608879 | −0.0304439 | − | 0.999536i | \(-0.509692\pi\) | ||||
−0.0304439 | + | 0.999536i | \(0.509692\pi\) | |||||||
\(710\) | −64.0901 | −2.40526 | ||||||||
\(711\) | −20.4820 | −0.768137 | ||||||||
\(712\) | 22.6547 | 0.849020 | ||||||||
\(713\) | 10.7008 | 0.400747 | ||||||||
\(714\) | 13.9980 | 0.523861 | ||||||||
\(715\) | 28.3002 | 1.05837 | ||||||||
\(716\) | −0.458899 | −0.0171499 | ||||||||
\(717\) | −16.8442 | −0.629058 | ||||||||
\(718\) | −18.5485 | −0.692225 | ||||||||
\(719\) | 1.96204 | 0.0731718 | 0.0365859 | − | 0.999331i | \(-0.488352\pi\) | ||||
0.0365859 | + | 0.999331i | \(0.488352\pi\) | |||||||
\(720\) | 14.8531 | 0.553541 | ||||||||
\(721\) | −18.8640 | −0.702532 | ||||||||
\(722\) | −40.2393 | −1.49755 | ||||||||
\(723\) | 36.7646 | 1.36729 | ||||||||
\(724\) | 0.779384 | 0.0289656 | ||||||||
\(725\) | 33.3675 | 1.23924 | ||||||||
\(726\) | −5.54350 | −0.205739 | ||||||||
\(727\) | −20.1524 | −0.747411 | −0.373706 | − | 0.927547i | \(-0.621913\pi\) | ||||
−0.373706 | + | 0.927547i | \(0.621913\pi\) | |||||||
\(728\) | −13.1600 | −0.487744 | ||||||||
\(729\) | 27.6344 | 1.02350 | ||||||||
\(730\) | −3.77321 | −0.139653 | ||||||||
\(731\) | −36.1775 | −1.33807 | ||||||||
\(732\) | −0.381845 | −0.0141134 | ||||||||
\(733\) | −29.6504 | −1.09516 | −0.547581 | − | 0.836753i | \(-0.684451\pi\) | ||||
−0.547581 | + | 0.836753i | \(0.684451\pi\) | |||||||
\(734\) | 24.4774 | 0.903479 | ||||||||
\(735\) | −13.9192 | −0.513417 | ||||||||
\(736\) | 1.88238 | 0.0693855 | ||||||||
\(737\) | −54.9260 | −2.02322 | ||||||||
\(738\) | 15.6852 | 0.577379 | ||||||||
\(739\) | −25.6486 | −0.943498 | −0.471749 | − | 0.881733i | \(-0.656377\pi\) | ||||
−0.471749 | + | 0.881733i | \(0.656377\pi\) | |||||||
\(740\) | 2.28786 | 0.0841033 | ||||||||
\(741\) | −23.3908 | −0.859281 | ||||||||
\(742\) | −2.67091 | −0.0980521 | ||||||||
\(743\) | 15.5400 | 0.570106 | 0.285053 | − | 0.958512i | \(-0.407989\pi\) | ||||
0.285053 | + | 0.958512i | \(0.407989\pi\) | |||||||
\(744\) | 12.4707 | 0.457198 | ||||||||
\(745\) | −7.49349 | −0.274540 | ||||||||
\(746\) | −36.3809 | −1.33200 | ||||||||
\(747\) | −1.05484 | −0.0385944 | ||||||||
\(748\) | 1.47352 | 0.0538770 | ||||||||
\(749\) | −26.3984 | −0.964577 | ||||||||
\(750\) | 5.82561 | 0.212721 | ||||||||
\(751\) | −18.9200 | −0.690401 | −0.345201 | − | 0.938529i | \(-0.612189\pi\) | ||||
−0.345201 | + | 0.938529i | \(0.612189\pi\) | |||||||
\(752\) | 3.68029 | 0.134207 | ||||||||
\(753\) | −8.16682 | −0.297616 | ||||||||
\(754\) | −30.6154 | −1.11495 | ||||||||
\(755\) | −37.5590 | −1.36691 | ||||||||
\(756\) | 1.11366 | 0.0405035 | ||||||||
\(757\) | 11.1265 | 0.404401 | 0.202200 | − | 0.979344i | \(-0.435191\pi\) | ||||
0.202200 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(758\) | 30.0321 | 1.09081 | ||||||||
\(759\) | 15.9815 | 0.580090 | ||||||||
\(760\) | −56.4216 | −2.04663 | ||||||||
\(761\) | 33.0965 | 1.19975 | 0.599874 | − | 0.800094i | \(-0.295217\pi\) | ||||
0.599874 | + | 0.800094i | \(0.295217\pi\) | |||||||
\(762\) | −27.4063 | −0.992825 | ||||||||
\(763\) | −6.56048 | −0.237505 | ||||||||
\(764\) | −0.898978 | −0.0325239 | ||||||||
\(765\) | −13.3995 | −0.484461 | ||||||||
\(766\) | 6.54943 | 0.236641 | ||||||||
\(767\) | −12.7877 | −0.461738 | ||||||||
\(768\) | 3.37912 | 0.121934 | ||||||||
\(769\) | −5.34626 | −0.192791 | −0.0963956 | − | 0.995343i | \(-0.530731\pi\) | ||||
−0.0963956 | + | 0.995343i | \(0.530731\pi\) | |||||||
\(770\) | 30.5701 | 1.10167 | ||||||||
\(771\) | −5.87173 | −0.211465 | ||||||||
\(772\) | 1.15024 | 0.0413981 | ||||||||
\(773\) | −29.8702 | −1.07436 | −0.537178 | − | 0.843469i | \(-0.680510\pi\) | ||||
−0.537178 | + | 0.843469i | \(0.680510\pi\) | |||||||
\(774\) | −16.3341 | −0.587116 | ||||||||
\(775\) | 13.4715 | 0.483909 | ||||||||
\(776\) | −2.86327 | −0.102786 | ||||||||
\(777\) | −18.5634 | −0.665960 | ||||||||
\(778\) | −7.40548 | −0.265499 | ||||||||
\(779\) | −62.7075 | −2.24673 | ||||||||
\(780\) | 1.07428 | 0.0384653 | ||||||||
\(781\) | 54.7407 | 1.95877 | ||||||||
\(782\) | −17.4955 | −0.625638 | ||||||||
\(783\) | −46.9418 | −1.67756 | ||||||||
\(784\) | 14.4268 | 0.515242 | ||||||||
\(785\) | −64.9840 | −2.31938 | ||||||||
\(786\) | 32.4639 | 1.15795 | ||||||||
\(787\) | −0.289779 | −0.0103295 | −0.00516474 | − | 0.999987i | \(-0.501644\pi\) | ||||
−0.00516474 | + | 0.999987i | \(0.501644\pi\) | |||||||
\(788\) | 0.493724 | 0.0175882 | ||||||||
\(789\) | 3.38027 | 0.120341 | ||||||||
\(790\) | −75.6611 | −2.69190 | ||||||||
\(791\) | −36.1838 | −1.28655 | ||||||||
\(792\) | −12.0541 | −0.428323 | ||||||||
\(793\) | −6.85726 | −0.243509 | ||||||||
\(794\) | 13.9841 | 0.496278 | ||||||||
\(795\) | −3.95041 | −0.140106 | ||||||||
\(796\) | −1.50255 | −0.0532564 | ||||||||
\(797\) | 18.9669 | 0.671842 | 0.335921 | − | 0.941890i | \(-0.390952\pi\) | ||||
0.335921 | + | 0.941890i | \(0.390952\pi\) | |||||||
\(798\) | −25.2669 | −0.894438 | ||||||||
\(799\) | −3.32014 | −0.117458 | ||||||||
\(800\) | 2.36977 | 0.0837842 | ||||||||
\(801\) | −9.71156 | −0.343141 | ||||||||
\(802\) | 46.2840 | 1.63435 | ||||||||
\(803\) | 3.22277 | 0.113729 | ||||||||
\(804\) | −2.08500 | −0.0735322 | ||||||||
\(805\) | −18.0415 | −0.635878 | ||||||||
\(806\) | −12.3604 | −0.435375 | ||||||||
\(807\) | −30.0085 | −1.05635 | ||||||||
\(808\) | −21.1994 | −0.745793 | ||||||||
\(809\) | −10.5686 | −0.371572 | −0.185786 | − | 0.982590i | \(-0.559483\pi\) | ||||
−0.185786 | + | 0.982590i | \(0.559483\pi\) | |||||||
\(810\) | 17.7410 | 0.623354 | ||||||||
\(811\) | −2.54431 | −0.0893427 | −0.0446714 | − | 0.999002i | \(-0.514224\pi\) | ||||
−0.0446714 | + | 0.999002i | \(0.514224\pi\) | |||||||
\(812\) | −1.64381 | −0.0576863 | ||||||||
\(813\) | −36.0504 | −1.26434 | ||||||||
\(814\) | −39.3138 | −1.37795 | ||||||||
\(815\) | 50.6169 | 1.77303 | ||||||||
\(816\) | −21.4587 | −0.751204 | ||||||||
\(817\) | 65.3018 | 2.28462 | ||||||||
\(818\) | 2.52087 | 0.0881402 | ||||||||
\(819\) | 5.64142 | 0.197127 | ||||||||
\(820\) | 2.88000 | 0.100574 | ||||||||
\(821\) | −7.11300 | −0.248246 | −0.124123 | − | 0.992267i | \(-0.539612\pi\) | ||||
−0.124123 | + | 0.992267i | \(0.539612\pi\) | |||||||
\(822\) | 35.6315 | 1.24279 | ||||||||
\(823\) | 27.0899 | 0.944294 | 0.472147 | − | 0.881520i | \(-0.343479\pi\) | ||||
0.472147 | + | 0.881520i | \(0.343479\pi\) | |||||||
\(824\) | 27.4771 | 0.957210 | ||||||||
\(825\) | 20.1194 | 0.700469 | ||||||||
\(826\) | −13.8134 | −0.480630 | ||||||||
\(827\) | 31.8819 | 1.10864 | 0.554321 | − | 0.832303i | \(-0.312978\pi\) | ||||
0.554321 | + | 0.832303i | \(0.312978\pi\) | |||||||
\(828\) | −0.392632 | −0.0136449 | ||||||||
\(829\) | 14.9781 | 0.520210 | 0.260105 | − | 0.965580i | \(-0.416243\pi\) | ||||
0.260105 | + | 0.965580i | \(0.416243\pi\) | |||||||
\(830\) | −3.89659 | −0.135252 | ||||||||
\(831\) | −18.3611 | −0.636939 | ||||||||
\(832\) | 19.1133 | 0.662634 | ||||||||
\(833\) | −13.0150 | −0.450942 | ||||||||
\(834\) | −5.00339 | −0.173253 | ||||||||
\(835\) | 5.81772 | 0.201330 | ||||||||
\(836\) | −2.65975 | −0.0919894 | ||||||||
\(837\) | −18.9518 | −0.655071 | ||||||||
\(838\) | −21.1438 | −0.730399 | ||||||||
\(839\) | −42.8497 | −1.47934 | −0.739669 | − | 0.672971i | \(-0.765018\pi\) | ||||
−0.739669 | + | 0.672971i | \(0.765018\pi\) | |||||||
\(840\) | −21.0256 | −0.725451 | ||||||||
\(841\) | 40.2878 | 1.38924 | ||||||||
\(842\) | 17.3724 | 0.598692 | ||||||||
\(843\) | 21.1704 | 0.729147 | ||||||||
\(844\) | −1.41980 | −0.0488716 | ||||||||
\(845\) | −19.7265 | −0.678614 | ||||||||
\(846\) | −1.49904 | −0.0515380 | ||||||||
\(847\) | −5.34514 | −0.183661 | ||||||||
\(848\) | 4.09446 | 0.140604 | ||||||||
\(849\) | −23.3745 | −0.802210 | ||||||||
\(850\) | −22.0255 | −0.755469 | ||||||||
\(851\) | 23.2017 | 0.795344 | ||||||||
\(852\) | 2.07796 | 0.0711899 | ||||||||
\(853\) | 27.5834 | 0.944438 | 0.472219 | − | 0.881481i | \(-0.343453\pi\) | ||||
0.472219 | + | 0.881481i | \(0.343453\pi\) | |||||||
\(854\) | −7.40727 | −0.253472 | ||||||||
\(855\) | 24.1867 | 0.827167 | ||||||||
\(856\) | 38.4516 | 1.31425 | ||||||||
\(857\) | 29.6751 | 1.01368 | 0.506842 | − | 0.862039i | \(-0.330813\pi\) | ||||
0.506842 | + | 0.862039i | \(0.330813\pi\) | |||||||
\(858\) | −18.4600 | −0.630215 | ||||||||
\(859\) | 32.9086 | 1.12283 | 0.561414 | − | 0.827535i | \(-0.310257\pi\) | ||||
0.561414 | + | 0.827535i | \(0.310257\pi\) | |||||||
\(860\) | −2.99915 | −0.102270 | ||||||||
\(861\) | −23.3680 | −0.796380 | ||||||||
\(862\) | 39.5224 | 1.34614 | ||||||||
\(863\) | −16.3490 | −0.556526 | −0.278263 | − | 0.960505i | \(-0.589759\pi\) | ||||
−0.278263 | + | 0.960505i | \(0.589759\pi\) | |||||||
\(864\) | −3.33383 | −0.113419 | ||||||||
\(865\) | −35.2016 | −1.19689 | ||||||||
\(866\) | −10.2231 | −0.347397 | ||||||||
\(867\) | −3.58348 | −0.121701 | ||||||||
\(868\) | −0.663655 | −0.0225259 | ||||||||
\(869\) | 64.6237 | 2.19221 | ||||||||
\(870\) | −48.9137 | −1.65833 | ||||||||
\(871\) | −37.4429 | −1.26870 | ||||||||
\(872\) | 9.55592 | 0.323604 | ||||||||
\(873\) | 1.22742 | 0.0415420 | ||||||||
\(874\) | 31.5801 | 1.06821 | ||||||||
\(875\) | 5.61715 | 0.189894 | ||||||||
\(876\) | 0.122337 | 0.00413338 | ||||||||
\(877\) | −2.26530 | −0.0764937 | −0.0382469 | − | 0.999268i | \(-0.512177\pi\) | ||||
−0.0382469 | + | 0.999268i | \(0.512177\pi\) | |||||||
\(878\) | 5.73401 | 0.193514 | ||||||||
\(879\) | −34.1553 | −1.15203 | ||||||||
\(880\) | −46.8635 | −1.57977 | ||||||||
\(881\) | −15.7439 | −0.530424 | −0.265212 | − | 0.964190i | \(-0.585442\pi\) | ||||
−0.265212 | + | 0.964190i | \(0.585442\pi\) | |||||||
\(882\) | −5.87623 | −0.197863 | ||||||||
\(883\) | −33.7073 | −1.13434 | −0.567170 | − | 0.823601i | \(-0.691962\pi\) | ||||
−0.567170 | + | 0.823601i | \(0.691962\pi\) | |||||||
\(884\) | 1.00449 | 0.0337847 | ||||||||
\(885\) | −20.4307 | −0.686771 | ||||||||
\(886\) | −39.8216 | −1.33783 | ||||||||
\(887\) | 15.1671 | 0.509260 | 0.254630 | − | 0.967039i | \(-0.418046\pi\) | ||||
0.254630 | + | 0.967039i | \(0.418046\pi\) | |||||||
\(888\) | 27.0393 | 0.907380 | ||||||||
\(889\) | −26.4256 | −0.886287 | ||||||||
\(890\) | −35.8747 | −1.20252 | ||||||||
\(891\) | −15.1529 | −0.507642 | ||||||||
\(892\) | −2.11420 | −0.0707887 | ||||||||
\(893\) | 5.99299 | 0.200548 | ||||||||
\(894\) | 4.88796 | 0.163478 | ||||||||
\(895\) | −13.1665 | −0.440108 | ||||||||
\(896\) | 22.8783 | 0.764311 | ||||||||
\(897\) | 10.8945 | 0.363757 | ||||||||
\(898\) | 43.7845 | 1.46111 | ||||||||
\(899\) | 27.9736 | 0.932972 | ||||||||
\(900\) | −0.494294 | −0.0164765 | ||||||||
\(901\) | −3.69378 | −0.123058 | ||||||||
\(902\) | −49.4889 | −1.64780 | ||||||||
\(903\) | 24.3348 | 0.809811 | ||||||||
\(904\) | 52.7049 | 1.75294 | ||||||||
\(905\) | 22.3617 | 0.743329 | ||||||||
\(906\) | 24.4995 | 0.813943 | ||||||||
\(907\) | 1.18154 | 0.0392325 | 0.0196162 | − | 0.999808i | \(-0.493756\pi\) | ||||
0.0196162 | + | 0.999808i | \(0.493756\pi\) | |||||||
\(908\) | −1.18639 | −0.0393719 | ||||||||
\(909\) | 9.08772 | 0.301421 | ||||||||
\(910\) | 20.8395 | 0.690824 | ||||||||
\(911\) | 11.1032 | 0.367867 | 0.183934 | − | 0.982939i | \(-0.441117\pi\) | ||||
0.183934 | + | 0.982939i | \(0.441117\pi\) | |||||||
\(912\) | 38.7338 | 1.28260 | ||||||||
\(913\) | 3.32815 | 0.110146 | ||||||||
\(914\) | 23.3109 | 0.771055 | ||||||||
\(915\) | −10.9557 | −0.362185 | ||||||||
\(916\) | −2.76596 | −0.0913900 | ||||||||
\(917\) | 31.3022 | 1.03369 | ||||||||
\(918\) | 30.9858 | 1.02268 | ||||||||
\(919\) | −35.2464 | −1.16267 | −0.581336 | − | 0.813664i | \(-0.697470\pi\) | ||||
−0.581336 | + | 0.813664i | \(0.697470\pi\) | |||||||
\(920\) | 26.2790 | 0.866393 | ||||||||
\(921\) | −31.2928 | −1.03113 | ||||||||
\(922\) | −1.29494 | −0.0426465 | ||||||||
\(923\) | 37.3165 | 1.22829 | ||||||||
\(924\) | −0.991159 | −0.0326067 | ||||||||
\(925\) | 29.2092 | 0.960392 | ||||||||
\(926\) | −61.5005 | −2.02103 | ||||||||
\(927\) | −11.7788 | −0.386867 | ||||||||
\(928\) | 4.92085 | 0.161535 | ||||||||
\(929\) | 11.9488 | 0.392028 | 0.196014 | − | 0.980601i | \(-0.437200\pi\) | ||||
0.196014 | + | 0.980601i | \(0.437200\pi\) | |||||||
\(930\) | −19.7479 | −0.647560 | ||||||||
\(931\) | 23.4925 | 0.769936 | ||||||||
\(932\) | 1.89595 | 0.0621039 | ||||||||
\(933\) | 16.2086 | 0.530646 | ||||||||
\(934\) | 47.1040 | 1.54129 | ||||||||
\(935\) | 42.2774 | 1.38262 | ||||||||
\(936\) | −8.21723 | −0.268589 | ||||||||
\(937\) | −15.5796 | −0.508964 | −0.254482 | − | 0.967078i | \(-0.581905\pi\) | ||||
−0.254482 | + | 0.967078i | \(0.581905\pi\) | |||||||
\(938\) | −40.4461 | −1.32061 | ||||||||
\(939\) | −30.5175 | −0.995901 | ||||||||
\(940\) | −0.275243 | −0.00897743 | ||||||||
\(941\) | −14.4050 | −0.469591 | −0.234795 | − | 0.972045i | \(-0.575442\pi\) | ||||
−0.234795 | + | 0.972045i | \(0.575442\pi\) | |||||||
\(942\) | 42.3887 | 1.38110 | ||||||||
\(943\) | 29.2067 | 0.951103 | ||||||||
\(944\) | 21.1758 | 0.689212 | ||||||||
\(945\) | 31.9527 | 1.03942 | ||||||||
\(946\) | 51.5363 | 1.67559 | ||||||||
\(947\) | 44.5130 | 1.44648 | 0.723240 | − | 0.690597i | \(-0.242652\pi\) | ||||
0.723240 | + | 0.690597i | \(0.242652\pi\) | |||||||
\(948\) | 2.45313 | 0.0796738 | ||||||||
\(949\) | 2.19696 | 0.0713162 | ||||||||
\(950\) | 39.7569 | 1.28988 | ||||||||
\(951\) | 17.3030 | 0.561090 | ||||||||
\(952\) | −19.6597 | −0.637175 | ||||||||
\(953\) | −26.4208 | −0.855852 | −0.427926 | − | 0.903814i | \(-0.640756\pi\) | ||||
−0.427926 | + | 0.903814i | \(0.640756\pi\) | |||||||
\(954\) | −1.66773 | −0.0539949 | ||||||||
\(955\) | −25.7931 | −0.834644 | ||||||||
\(956\) | −1.30569 | −0.0422289 | ||||||||
\(957\) | 41.7782 | 1.35050 | ||||||||
\(958\) | −20.5778 | −0.664840 | ||||||||
\(959\) | 34.3565 | 1.10943 | ||||||||
\(960\) | 30.5369 | 0.985576 | ||||||||
\(961\) | −19.7062 | −0.635684 | ||||||||
\(962\) | −26.8001 | −0.864069 | ||||||||
\(963\) | −16.4834 | −0.531169 | ||||||||
\(964\) | 2.84983 | 0.0917867 | ||||||||
\(965\) | 33.0022 | 1.06238 | ||||||||
\(966\) | 11.7683 | 0.378640 | ||||||||
\(967\) | 43.1537 | 1.38773 | 0.693864 | − | 0.720106i | \(-0.255907\pi\) | ||||
0.693864 | + | 0.720106i | \(0.255907\pi\) | |||||||
\(968\) | 7.78567 | 0.250241 | ||||||||
\(969\) | −34.9433 | −1.12254 | ||||||||
\(970\) | 4.53413 | 0.145582 | ||||||||
\(971\) | 11.9071 | 0.382115 | 0.191058 | − | 0.981579i | \(-0.438808\pi\) | ||||
0.191058 | + | 0.981579i | \(0.438808\pi\) | |||||||
\(972\) | 1.19461 | 0.0383171 | ||||||||
\(973\) | −4.82436 | −0.154662 | ||||||||
\(974\) | 34.6068 | 1.10887 | ||||||||
\(975\) | 13.7154 | 0.439243 | ||||||||
\(976\) | 11.3552 | 0.363472 | ||||||||
\(977\) | 9.60316 | 0.307232 | 0.153616 | − | 0.988131i | \(-0.450908\pi\) | ||||
0.153616 | + | 0.988131i | \(0.450908\pi\) | |||||||
\(978\) | −33.0171 | −1.05577 | ||||||||
\(979\) | 30.6413 | 0.979301 | ||||||||
\(980\) | −1.07895 | −0.0344659 | ||||||||
\(981\) | −4.09641 | −0.130788 | ||||||||
\(982\) | −33.2760 | −1.06188 | ||||||||
\(983\) | 1.00000 | 0.0318950 | ||||||||
\(984\) | 34.0376 | 1.08508 | ||||||||
\(985\) | 14.1657 | 0.451357 | ||||||||
\(986\) | −45.7361 | −1.45654 | ||||||||
\(987\) | 2.23329 | 0.0710865 | ||||||||
\(988\) | −1.81315 | −0.0576838 | ||||||||
\(989\) | −30.4151 | −0.967143 | ||||||||
\(990\) | 19.0882 | 0.606662 | ||||||||
\(991\) | 34.4460 | 1.09421 | 0.547106 | − | 0.837063i | \(-0.315729\pi\) | ||||
0.547106 | + | 0.837063i | \(0.315729\pi\) | |||||||
\(992\) | 1.98670 | 0.0630777 | ||||||||
\(993\) | −39.1623 | −1.24278 | ||||||||
\(994\) | 40.3097 | 1.27854 | ||||||||
\(995\) | −43.1105 | −1.36669 | ||||||||
\(996\) | 0.126337 | 0.00400315 | ||||||||
\(997\) | −30.7018 | −0.972337 | −0.486168 | − | 0.873865i | \(-0.661606\pi\) | ||||
−0.486168 | + | 0.873865i | \(0.661606\pi\) | |||||||
\(998\) | −32.1449 | −1.01753 | ||||||||
\(999\) | −41.0919 | −1.30009 |
(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 | 983.2.a.b.1.15 | ✓ | 54 | |
3.2 | odd | 2 | 8847.2.a.g.1.40 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.2.a.b.1.15 | ✓ | 54 | 1.1 | even | 1 | trivial | |
8847.2.a.g.1.40 | 54 | 3.2 | odd | 2 |