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: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.892239 | −0.630908 | −0.315454 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315454 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.20391 | −0.601955 | ||||||||
\(5\) | −0.989381 | −0.442465 | −0.221232 | − | 0.975221i | \(-0.571008\pi\) | ||||
−0.221232 | + | 0.975221i | \(0.571008\pi\) | |||||||
\(6\) | −0.892239 | −0.364255 | ||||||||
\(7\) | 3.60802 | 1.36370 | 0.681852 | − | 0.731490i | \(-0.261175\pi\) | ||||
0.681852 | + | 0.731490i | \(0.261175\pi\) | |||||||
\(8\) | 2.85865 | 1.01069 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.882764 | 0.279155 | ||||||||
\(11\) | −0.219603 | −0.0662127 | −0.0331063 | − | 0.999452i | \(-0.510540\pi\) | ||||
−0.0331063 | + | 0.999452i | \(0.510540\pi\) | |||||||
\(12\) | −1.20391 | −0.347539 | ||||||||
\(13\) | −2.77618 | −0.769974 | −0.384987 | − | 0.922922i | \(-0.625794\pi\) | ||||
−0.384987 | + | 0.922922i | \(0.625794\pi\) | |||||||
\(14\) | −3.21922 | −0.860372 | ||||||||
\(15\) | −0.989381 | −0.255457 | ||||||||
\(16\) | −0.142779 | −0.0356948 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.892239 | −0.210303 | ||||||||
\(19\) | 4.91780 | 1.12822 | 0.564110 | − | 0.825700i | \(-0.309219\pi\) | ||||
0.564110 | + | 0.825700i | \(0.309219\pi\) | |||||||
\(20\) | 1.19113 | 0.266344 | ||||||||
\(21\) | 3.60802 | 0.787335 | ||||||||
\(22\) | 0.195938 | 0.0417741 | ||||||||
\(23\) | −3.55820 | −0.741936 | −0.370968 | − | 0.928646i | \(-0.620974\pi\) | ||||
−0.370968 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(24\) | 2.85865 | 0.583520 | ||||||||
\(25\) | −4.02112 | −0.804225 | ||||||||
\(26\) | 2.47701 | 0.485782 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.34373 | −0.820889 | ||||||||
\(29\) | 6.73135 | 1.24998 | 0.624990 | − | 0.780633i | \(-0.285103\pi\) | ||||
0.624990 | + | 0.780633i | \(0.285103\pi\) | |||||||
\(30\) | 0.882764 | 0.161170 | ||||||||
\(31\) | 0.993688 | 0.178472 | 0.0892358 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892358 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(32\) | −5.58991 | −0.988166 | ||||||||
\(33\) | −0.219603 | −0.0382279 | ||||||||
\(34\) | 0.892239 | 0.153018 | ||||||||
\(35\) | −3.56971 | −0.603391 | ||||||||
\(36\) | −1.20391 | −0.200652 | ||||||||
\(37\) | 1.79684 | 0.295399 | 0.147700 | − | 0.989032i | \(-0.452813\pi\) | ||||
0.147700 | + | 0.989032i | \(0.452813\pi\) | |||||||
\(38\) | −4.38785 | −0.711803 | ||||||||
\(39\) | −2.77618 | −0.444544 | ||||||||
\(40\) | −2.82830 | −0.447193 | ||||||||
\(41\) | 0.0934982 | 0.0146020 | 0.00730098 | − | 0.999973i | \(-0.497676\pi\) | ||||
0.00730098 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(42\) | −3.21922 | −0.496736 | ||||||||
\(43\) | −5.95800 | −0.908586 | −0.454293 | − | 0.890852i | \(-0.650108\pi\) | ||||
−0.454293 | + | 0.890852i | \(0.650108\pi\) | |||||||
\(44\) | 0.264382 | 0.0398571 | ||||||||
\(45\) | −0.989381 | −0.147488 | ||||||||
\(46\) | 3.17476 | 0.468093 | ||||||||
\(47\) | 1.73754 | 0.253446 | 0.126723 | − | 0.991938i | \(-0.459554\pi\) | ||||
0.126723 | + | 0.991938i | \(0.459554\pi\) | |||||||
\(48\) | −0.142779 | −0.0206084 | ||||||||
\(49\) | 6.01782 | 0.859688 | ||||||||
\(50\) | 3.58780 | 0.507392 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 3.34227 | 0.463490 | ||||||||
\(53\) | 6.41191 | 0.880743 | 0.440372 | − | 0.897816i | \(-0.354847\pi\) | ||||
0.440372 | + | 0.897816i | \(0.354847\pi\) | |||||||
\(54\) | −0.892239 | −0.121418 | ||||||||
\(55\) | 0.217271 | 0.0292968 | ||||||||
\(56\) | 10.3141 | 1.37828 | ||||||||
\(57\) | 4.91780 | 0.651378 | ||||||||
\(58\) | −6.00597 | −0.788622 | ||||||||
\(59\) | 11.9429 | 1.55483 | 0.777413 | − | 0.628990i | \(-0.216531\pi\) | ||||
0.777413 | + | 0.628990i | \(0.216531\pi\) | |||||||
\(60\) | 1.19113 | 0.153774 | ||||||||
\(61\) | −4.93840 | −0.632298 | −0.316149 | − | 0.948710i | \(-0.602390\pi\) | ||||
−0.316149 | + | 0.948710i | \(0.602390\pi\) | |||||||
\(62\) | −0.886607 | −0.112599 | ||||||||
\(63\) | 3.60802 | 0.454568 | ||||||||
\(64\) | 5.27309 | 0.659137 | ||||||||
\(65\) | 2.74670 | 0.340686 | ||||||||
\(66\) | 0.195938 | 0.0241183 | ||||||||
\(67\) | −5.94225 | −0.725961 | −0.362981 | − | 0.931797i | \(-0.618241\pi\) | ||||
−0.362981 | + | 0.931797i | \(0.618241\pi\) | |||||||
\(68\) | 1.20391 | 0.145996 | ||||||||
\(69\) | −3.55820 | −0.428357 | ||||||||
\(70\) | 3.18503 | 0.380684 | ||||||||
\(71\) | 11.2788 | 1.33855 | 0.669273 | − | 0.743016i | \(-0.266606\pi\) | ||||
0.669273 | + | 0.743016i | \(0.266606\pi\) | |||||||
\(72\) | 2.85865 | 0.336895 | ||||||||
\(73\) | 7.86008 | 0.919953 | 0.459976 | − | 0.887931i | \(-0.347858\pi\) | ||||
0.459976 | + | 0.887931i | \(0.347858\pi\) | |||||||
\(74\) | −1.60321 | −0.186370 | ||||||||
\(75\) | −4.02112 | −0.464319 | ||||||||
\(76\) | −5.92059 | −0.679138 | ||||||||
\(77\) | −0.792331 | −0.0902945 | ||||||||
\(78\) | 2.47701 | 0.280467 | ||||||||
\(79\) | 5.00470 | 0.563072 | 0.281536 | − | 0.959551i | \(-0.409156\pi\) | ||||
0.281536 | + | 0.959551i | \(0.409156\pi\) | |||||||
\(80\) | 0.141263 | 0.0157937 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.0834227 | −0.00921249 | ||||||||
\(83\) | 1.97285 | 0.216548 | 0.108274 | − | 0.994121i | \(-0.465468\pi\) | ||||
0.108274 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(84\) | −4.34373 | −0.473940 | ||||||||
\(85\) | 0.989381 | 0.107313 | ||||||||
\(86\) | 5.31596 | 0.573234 | ||||||||
\(87\) | 6.73135 | 0.721676 | ||||||||
\(88\) | −0.627768 | −0.0669203 | ||||||||
\(89\) | −6.03345 | −0.639544 | −0.319772 | − | 0.947495i | \(-0.603606\pi\) | ||||
−0.319772 | + | 0.947495i | \(0.603606\pi\) | |||||||
\(90\) | 0.882764 | 0.0930515 | ||||||||
\(91\) | −10.0165 | −1.05002 | ||||||||
\(92\) | 4.28375 | 0.446612 | ||||||||
\(93\) | 0.993688 | 0.103041 | ||||||||
\(94\) | −1.55030 | −0.159901 | ||||||||
\(95\) | −4.86558 | −0.499198 | ||||||||
\(96\) | −5.58991 | −0.570518 | ||||||||
\(97\) | −6.26191 | −0.635800 | −0.317900 | − | 0.948124i | \(-0.602978\pi\) | ||||
−0.317900 | + | 0.948124i | \(0.602978\pi\) | |||||||
\(98\) | −5.36933 | −0.542384 | ||||||||
\(99\) | −0.219603 | −0.0220709 | ||||||||
\(100\) | 4.84107 | 0.484107 | ||||||||
\(101\) | 13.5411 | 1.34739 | 0.673697 | − | 0.739008i | \(-0.264705\pi\) | ||||
0.673697 | + | 0.739008i | \(0.264705\pi\) | |||||||
\(102\) | 0.892239 | 0.0883448 | ||||||||
\(103\) | 13.0169 | 1.28259 | 0.641296 | − | 0.767293i | \(-0.278397\pi\) | ||||
0.641296 | + | 0.767293i | \(0.278397\pi\) | |||||||
\(104\) | −7.93613 | −0.778202 | ||||||||
\(105\) | −3.56971 | −0.348368 | ||||||||
\(106\) | −5.72095 | −0.555668 | ||||||||
\(107\) | 0.435274 | 0.0420795 | 0.0210397 | − | 0.999779i | \(-0.493302\pi\) | ||||
0.0210397 | + | 0.999779i | \(0.493302\pi\) | |||||||
\(108\) | −1.20391 | −0.115846 | ||||||||
\(109\) | −13.8854 | −1.32998 | −0.664991 | − | 0.746851i | \(-0.731565\pi\) | ||||
−0.664991 | + | 0.746851i | \(0.731565\pi\) | |||||||
\(110\) | −0.193857 | −0.0184836 | ||||||||
\(111\) | 1.79684 | 0.170549 | ||||||||
\(112\) | −0.515150 | −0.0486771 | ||||||||
\(113\) | −10.8080 | −1.01673 | −0.508367 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508367 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(114\) | −4.38785 | −0.410960 | ||||||||
\(115\) | 3.52042 | 0.328280 | ||||||||
\(116\) | −8.10394 | −0.752432 | ||||||||
\(117\) | −2.77618 | −0.256658 | ||||||||
\(118\) | −10.6559 | −0.980953 | ||||||||
\(119\) | −3.60802 | −0.330747 | ||||||||
\(120\) | −2.82830 | −0.258187 | ||||||||
\(121\) | −10.9518 | −0.995616 | ||||||||
\(122\) | 4.40623 | 0.398922 | ||||||||
\(123\) | 0.0934982 | 0.00843045 | ||||||||
\(124\) | −1.19631 | −0.107432 | ||||||||
\(125\) | 8.92533 | 0.798306 | ||||||||
\(126\) | −3.21922 | −0.286791 | ||||||||
\(127\) | −9.20742 | −0.817027 | −0.408513 | − | 0.912752i | \(-0.633953\pi\) | ||||
−0.408513 | + | 0.912752i | \(0.633953\pi\) | |||||||
\(128\) | 6.47497 | 0.572312 | ||||||||
\(129\) | −5.95800 | −0.524573 | ||||||||
\(130\) | −2.45071 | −0.214942 | ||||||||
\(131\) | −9.10545 | −0.795547 | −0.397773 | − | 0.917484i | \(-0.630217\pi\) | ||||
−0.397773 | + | 0.917484i | \(0.630217\pi\) | |||||||
\(132\) | 0.264382 | 0.0230115 | ||||||||
\(133\) | 17.7435 | 1.53856 | ||||||||
\(134\) | 5.30190 | 0.458015 | ||||||||
\(135\) | −0.989381 | −0.0851524 | ||||||||
\(136\) | −2.85865 | −0.245127 | ||||||||
\(137\) | −2.08470 | −0.178108 | −0.0890538 | − | 0.996027i | \(-0.528384\pi\) | ||||
−0.0890538 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(138\) | 3.17476 | 0.270254 | ||||||||
\(139\) | 19.3869 | 1.64437 | 0.822186 | − | 0.569218i | \(-0.192754\pi\) | ||||
0.822186 | + | 0.569218i | \(0.192754\pi\) | |||||||
\(140\) | 4.29761 | 0.363214 | ||||||||
\(141\) | 1.73754 | 0.146327 | ||||||||
\(142\) | −10.0634 | −0.844500 | ||||||||
\(143\) | 0.609656 | 0.0509820 | ||||||||
\(144\) | −0.142779 | −0.0118983 | ||||||||
\(145\) | −6.65987 | −0.553072 | ||||||||
\(146\) | −7.01307 | −0.580406 | ||||||||
\(147\) | 6.01782 | 0.496341 | ||||||||
\(148\) | −2.16324 | −0.177817 | ||||||||
\(149\) | 16.5666 | 1.35719 | 0.678594 | − | 0.734513i | \(-0.262589\pi\) | ||||
0.678594 | + | 0.734513i | \(0.262589\pi\) | |||||||
\(150\) | 3.58780 | 0.292943 | ||||||||
\(151\) | 0.909183 | 0.0739882 | 0.0369941 | − | 0.999315i | \(-0.488222\pi\) | ||||
0.0369941 | + | 0.999315i | \(0.488222\pi\) | |||||||
\(152\) | 14.0583 | 1.14028 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.706948 | 0.0569675 | ||||||||
\(155\) | −0.983137 | −0.0789674 | ||||||||
\(156\) | 3.34227 | 0.267596 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −4.46538 | −0.355247 | ||||||||
\(159\) | 6.41191 | 0.508497 | ||||||||
\(160\) | 5.53056 | 0.437229 | ||||||||
\(161\) | −12.8381 | −1.01178 | ||||||||
\(162\) | −0.892239 | −0.0701009 | ||||||||
\(163\) | 8.99214 | 0.704319 | 0.352160 | − | 0.935940i | \(-0.385447\pi\) | ||||
0.352160 | + | 0.935940i | \(0.385447\pi\) | |||||||
\(164\) | −0.112563 | −0.00878973 | ||||||||
\(165\) | 0.217271 | 0.0169145 | ||||||||
\(166\) | −1.76025 | −0.136622 | ||||||||
\(167\) | 17.4735 | 1.35214 | 0.676069 | − | 0.736838i | \(-0.263682\pi\) | ||||
0.676069 | + | 0.736838i | \(0.263682\pi\) | |||||||
\(168\) | 10.3141 | 0.795748 | ||||||||
\(169\) | −5.29283 | −0.407141 | ||||||||
\(170\) | −0.882764 | −0.0677049 | ||||||||
\(171\) | 4.91780 | 0.376073 | ||||||||
\(172\) | 7.17290 | 0.546928 | ||||||||
\(173\) | 9.75269 | 0.741483 | 0.370742 | − | 0.928736i | \(-0.379104\pi\) | ||||
0.370742 | + | 0.928736i | \(0.379104\pi\) | |||||||
\(174\) | −6.00597 | −0.455311 | ||||||||
\(175\) | −14.5083 | −1.09672 | ||||||||
\(176\) | 0.0313547 | 0.00236345 | ||||||||
\(177\) | 11.9429 | 0.897680 | ||||||||
\(178\) | 5.38327 | 0.403493 | ||||||||
\(179\) | −12.3126 | −0.920289 | −0.460144 | − | 0.887844i | \(-0.652202\pi\) | ||||
−0.460144 | + | 0.887844i | \(0.652202\pi\) | |||||||
\(180\) | 1.19113 | 0.0887813 | ||||||||
\(181\) | 17.2539 | 1.28247 | 0.641235 | − | 0.767345i | \(-0.278423\pi\) | ||||
0.641235 | + | 0.767345i | \(0.278423\pi\) | |||||||
\(182\) | 8.93712 | 0.662463 | ||||||||
\(183\) | −4.93840 | −0.365057 | ||||||||
\(184\) | −10.1717 | −0.749864 | ||||||||
\(185\) | −1.77776 | −0.130704 | ||||||||
\(186\) | −0.886607 | −0.0650092 | ||||||||
\(187\) | 0.219603 | 0.0160589 | ||||||||
\(188\) | −2.09184 | −0.152563 | ||||||||
\(189\) | 3.60802 | 0.262445 | ||||||||
\(190\) | 4.34125 | 0.314948 | ||||||||
\(191\) | −18.5318 | −1.34092 | −0.670458 | − | 0.741948i | \(-0.733902\pi\) | ||||
−0.670458 | + | 0.741948i | \(0.733902\pi\) | |||||||
\(192\) | 5.27309 | 0.380553 | ||||||||
\(193\) | 13.6803 | 0.984729 | 0.492365 | − | 0.870389i | \(-0.336133\pi\) | ||||
0.492365 | + | 0.870389i | \(0.336133\pi\) | |||||||
\(194\) | 5.58712 | 0.401132 | ||||||||
\(195\) | 2.74670 | 0.196695 | ||||||||
\(196\) | −7.24491 | −0.517494 | ||||||||
\(197\) | 2.30949 | 0.164544 | 0.0822721 | − | 0.996610i | \(-0.473782\pi\) | ||||
0.0822721 | + | 0.996610i | \(0.473782\pi\) | |||||||
\(198\) | 0.195938 | 0.0139247 | ||||||||
\(199\) | −12.9433 | −0.917524 | −0.458762 | − | 0.888559i | \(-0.651707\pi\) | ||||
−0.458762 | + | 0.888559i | \(0.651707\pi\) | |||||||
\(200\) | −11.4950 | −0.812819 | ||||||||
\(201\) | −5.94225 | −0.419134 | ||||||||
\(202\) | −12.0819 | −0.850081 | ||||||||
\(203\) | 24.2869 | 1.70460 | ||||||||
\(204\) | 1.20391 | 0.0842906 | ||||||||
\(205\) | −0.0925054 | −0.00646086 | ||||||||
\(206\) | −11.6142 | −0.809198 | ||||||||
\(207\) | −3.55820 | −0.247312 | ||||||||
\(208\) | 0.396380 | 0.0274840 | ||||||||
\(209\) | −1.07996 | −0.0747025 | ||||||||
\(210\) | 3.18503 | 0.219788 | ||||||||
\(211\) | −25.7974 | −1.77597 | −0.887985 | − | 0.459873i | \(-0.847895\pi\) | ||||
−0.887985 | + | 0.459873i | \(0.847895\pi\) | |||||||
\(212\) | −7.71936 | −0.530168 | ||||||||
\(213\) | 11.2788 | 0.772810 | ||||||||
\(214\) | −0.388368 | −0.0265483 | ||||||||
\(215\) | 5.89473 | 0.402018 | ||||||||
\(216\) | 2.85865 | 0.194507 | ||||||||
\(217\) | 3.58525 | 0.243382 | ||||||||
\(218\) | 12.3891 | 0.839096 | ||||||||
\(219\) | 7.86008 | 0.531135 | ||||||||
\(220\) | −0.261575 | −0.0176354 | ||||||||
\(221\) | 2.77618 | 0.186746 | ||||||||
\(222\) | −1.60321 | −0.107601 | ||||||||
\(223\) | 18.8319 | 1.26108 | 0.630539 | − | 0.776158i | \(-0.282834\pi\) | ||||
0.630539 | + | 0.776158i | \(0.282834\pi\) | |||||||
\(224\) | −20.1685 | −1.34757 | ||||||||
\(225\) | −4.02112 | −0.268075 | ||||||||
\(226\) | 9.64333 | 0.641465 | ||||||||
\(227\) | −7.11795 | −0.472435 | −0.236218 | − | 0.971700i | \(-0.575908\pi\) | ||||
−0.236218 | + | 0.971700i | \(0.575908\pi\) | |||||||
\(228\) | −5.92059 | −0.392100 | ||||||||
\(229\) | −5.55949 | −0.367382 | −0.183691 | − | 0.982984i | \(-0.558805\pi\) | ||||
−0.183691 | + | 0.982984i | \(0.558805\pi\) | |||||||
\(230\) | −3.14105 | −0.207115 | ||||||||
\(231\) | −0.792331 | −0.0521316 | ||||||||
\(232\) | 19.2426 | 1.26334 | ||||||||
\(233\) | 5.61253 | 0.367689 | 0.183845 | − | 0.982955i | \(-0.441146\pi\) | ||||
0.183845 | + | 0.982955i | \(0.441146\pi\) | |||||||
\(234\) | 2.47701 | 0.161927 | ||||||||
\(235\) | −1.71909 | −0.112141 | ||||||||
\(236\) | −14.3781 | −0.935936 | ||||||||
\(237\) | 5.00470 | 0.325090 | ||||||||
\(238\) | 3.21922 | 0.208671 | ||||||||
\(239\) | −11.4166 | −0.738478 | −0.369239 | − | 0.929335i | \(-0.620382\pi\) | ||||
−0.369239 | + | 0.929335i | \(0.620382\pi\) | |||||||
\(240\) | 0.141263 | 0.00911848 | ||||||||
\(241\) | 12.2964 | 0.792081 | 0.396040 | − | 0.918233i | \(-0.370384\pi\) | ||||
0.396040 | + | 0.918233i | \(0.370384\pi\) | |||||||
\(242\) | 9.77160 | 0.628142 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.94539 | 0.380615 | ||||||||
\(245\) | −5.95392 | −0.380382 | ||||||||
\(246\) | −0.0834227 | −0.00531884 | ||||||||
\(247\) | −13.6527 | −0.868699 | ||||||||
\(248\) | 2.84061 | 0.180379 | ||||||||
\(249\) | 1.97285 | 0.125024 | ||||||||
\(250\) | −7.96353 | −0.503658 | ||||||||
\(251\) | 28.2372 | 1.78232 | 0.891159 | − | 0.453691i | \(-0.149893\pi\) | ||||
0.891159 | + | 0.453691i | \(0.149893\pi\) | |||||||
\(252\) | −4.34373 | −0.273630 | ||||||||
\(253\) | 0.781390 | 0.0491256 | ||||||||
\(254\) | 8.21522 | 0.515469 | ||||||||
\(255\) | 0.989381 | 0.0619575 | ||||||||
\(256\) | −16.3234 | −1.02021 | ||||||||
\(257\) | 13.1349 | 0.819330 | 0.409665 | − | 0.912236i | \(-0.365646\pi\) | ||||
0.409665 | + | 0.912236i | \(0.365646\pi\) | |||||||
\(258\) | 5.31596 | 0.330957 | ||||||||
\(259\) | 6.48304 | 0.402837 | ||||||||
\(260\) | −3.30678 | −0.205078 | ||||||||
\(261\) | 6.73135 | 0.416660 | ||||||||
\(262\) | 8.12423 | 0.501917 | ||||||||
\(263\) | 4.67604 | 0.288337 | 0.144169 | − | 0.989553i | \(-0.453949\pi\) | ||||
0.144169 | + | 0.989553i | \(0.453949\pi\) | |||||||
\(264\) | −0.627768 | −0.0386364 | ||||||||
\(265\) | −6.34382 | −0.389698 | ||||||||
\(266\) | −15.8314 | −0.970688 | ||||||||
\(267\) | −6.03345 | −0.369241 | ||||||||
\(268\) | 7.15393 | 0.436996 | ||||||||
\(269\) | −16.2954 | −0.993548 | −0.496774 | − | 0.867880i | \(-0.665482\pi\) | ||||
−0.496774 | + | 0.867880i | \(0.665482\pi\) | |||||||
\(270\) | 0.882764 | 0.0537233 | ||||||||
\(271\) | 3.98510 | 0.242078 | 0.121039 | − | 0.992648i | \(-0.461377\pi\) | ||||
0.121039 | + | 0.992648i | \(0.461377\pi\) | |||||||
\(272\) | 0.142779 | 0.00865725 | ||||||||
\(273\) | −10.0165 | −0.606227 | ||||||||
\(274\) | 1.86005 | 0.112369 | ||||||||
\(275\) | 0.883050 | 0.0532499 | ||||||||
\(276\) | 4.28375 | 0.257852 | ||||||||
\(277\) | −21.3862 | −1.28497 | −0.642485 | − | 0.766298i | \(-0.722096\pi\) | ||||
−0.642485 | + | 0.766298i | \(0.722096\pi\) | |||||||
\(278\) | −17.2977 | −1.03745 | ||||||||
\(279\) | 0.993688 | 0.0594905 | ||||||||
\(280\) | −10.2046 | −0.609839 | ||||||||
\(281\) | 14.8841 | 0.887914 | 0.443957 | − | 0.896048i | \(-0.353574\pi\) | ||||
0.443957 | + | 0.896048i | \(0.353574\pi\) | |||||||
\(282\) | −1.55030 | −0.0923188 | ||||||||
\(283\) | 4.58113 | 0.272320 | 0.136160 | − | 0.990687i | \(-0.456524\pi\) | ||||
0.136160 | + | 0.990687i | \(0.456524\pi\) | |||||||
\(284\) | −13.5787 | −0.805745 | ||||||||
\(285\) | −4.86558 | −0.288212 | ||||||||
\(286\) | −0.543959 | −0.0321650 | ||||||||
\(287\) | 0.337343 | 0.0199128 | ||||||||
\(288\) | −5.58991 | −0.329389 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 5.94219 | 0.348938 | ||||||||
\(291\) | −6.26191 | −0.367080 | ||||||||
\(292\) | −9.46283 | −0.553770 | ||||||||
\(293\) | −16.3215 | −0.953510 | −0.476755 | − | 0.879036i | \(-0.658187\pi\) | ||||
−0.476755 | + | 0.879036i | \(0.658187\pi\) | |||||||
\(294\) | −5.36933 | −0.313146 | ||||||||
\(295\) | −11.8160 | −0.687956 | ||||||||
\(296\) | 5.13655 | 0.298556 | ||||||||
\(297\) | −0.219603 | −0.0127426 | ||||||||
\(298\) | −14.7814 | −0.856261 | ||||||||
\(299\) | 9.87819 | 0.571271 | ||||||||
\(300\) | 4.84107 | 0.279499 | ||||||||
\(301\) | −21.4966 | −1.23904 | ||||||||
\(302\) | −0.811208 | −0.0466798 | ||||||||
\(303\) | 13.5411 | 0.777918 | ||||||||
\(304\) | −0.702158 | −0.0402715 | ||||||||
\(305\) | 4.88596 | 0.279770 | ||||||||
\(306\) | 0.892239 | 0.0510059 | ||||||||
\(307\) | 15.1210 | 0.863003 | 0.431502 | − | 0.902112i | \(-0.357984\pi\) | ||||
0.431502 | + | 0.902112i | \(0.357984\pi\) | |||||||
\(308\) | 0.953896 | 0.0543532 | ||||||||
\(309\) | 13.0169 | 0.740505 | ||||||||
\(310\) | 0.877192 | 0.0498212 | ||||||||
\(311\) | −14.0721 | −0.797953 | −0.398977 | − | 0.916961i | \(-0.630635\pi\) | ||||
−0.398977 | + | 0.916961i | \(0.630635\pi\) | |||||||
\(312\) | −7.93613 | −0.449295 | ||||||||
\(313\) | −18.0182 | −1.01845 | −0.509226 | − | 0.860633i | \(-0.670068\pi\) | ||||
−0.509226 | + | 0.860633i | \(0.670068\pi\) | |||||||
\(314\) | 0.892239 | 0.0503519 | ||||||||
\(315\) | −3.56971 | −0.201130 | ||||||||
\(316\) | −6.02521 | −0.338944 | ||||||||
\(317\) | 30.4718 | 1.71147 | 0.855734 | − | 0.517417i | \(-0.173106\pi\) | ||||
0.855734 | + | 0.517417i | \(0.173106\pi\) | |||||||
\(318\) | −5.72095 | −0.320815 | ||||||||
\(319\) | −1.47822 | −0.0827646 | ||||||||
\(320\) | −5.21710 | −0.291645 | ||||||||
\(321\) | 0.435274 | 0.0242946 | ||||||||
\(322\) | 11.4546 | 0.638340 | ||||||||
\(323\) | −4.91780 | −0.273633 | ||||||||
\(324\) | −1.20391 | −0.0668839 | ||||||||
\(325\) | 11.1634 | 0.619232 | ||||||||
\(326\) | −8.02314 | −0.444360 | ||||||||
\(327\) | −13.8854 | −0.767866 | ||||||||
\(328\) | 0.267279 | 0.0147580 | ||||||||
\(329\) | 6.26907 | 0.345625 | ||||||||
\(330\) | −0.193857 | −0.0106715 | ||||||||
\(331\) | 3.00303 | 0.165062 | 0.0825308 | − | 0.996589i | \(-0.473700\pi\) | ||||
0.0825308 | + | 0.996589i | \(0.473700\pi\) | |||||||
\(332\) | −2.37513 | −0.130352 | ||||||||
\(333\) | 1.79684 | 0.0984664 | ||||||||
\(334\) | −15.5905 | −0.853074 | ||||||||
\(335\) | 5.87915 | 0.321212 | ||||||||
\(336\) | −0.515150 | −0.0281037 | ||||||||
\(337\) | −29.6425 | −1.61473 | −0.807366 | − | 0.590051i | \(-0.799108\pi\) | ||||
−0.807366 | + | 0.590051i | \(0.799108\pi\) | |||||||
\(338\) | 4.72247 | 0.256868 | ||||||||
\(339\) | −10.8080 | −0.587011 | ||||||||
\(340\) | −1.19113 | −0.0645979 | ||||||||
\(341\) | −0.218217 | −0.0118171 | ||||||||
\(342\) | −4.38785 | −0.237268 | ||||||||
\(343\) | −3.54374 | −0.191344 | ||||||||
\(344\) | −17.0319 | −0.918296 | ||||||||
\(345\) | 3.52042 | 0.189533 | ||||||||
\(346\) | −8.70172 | −0.467808 | ||||||||
\(347\) | 12.8339 | 0.688957 | 0.344479 | − | 0.938794i | \(-0.388056\pi\) | ||||
0.344479 | + | 0.938794i | \(0.388056\pi\) | |||||||
\(348\) | −8.10394 | −0.434417 | ||||||||
\(349\) | −13.3069 | −0.712302 | −0.356151 | − | 0.934428i | \(-0.615911\pi\) | ||||
−0.356151 | + | 0.934428i | \(0.615911\pi\) | |||||||
\(350\) | 12.9449 | 0.691932 | ||||||||
\(351\) | −2.77618 | −0.148181 | ||||||||
\(352\) | 1.22756 | 0.0654291 | ||||||||
\(353\) | 27.5704 | 1.46743 | 0.733713 | − | 0.679459i | \(-0.237786\pi\) | ||||
0.733713 | + | 0.679459i | \(0.237786\pi\) | |||||||
\(354\) | −10.6559 | −0.566353 | ||||||||
\(355\) | −11.1590 | −0.592260 | ||||||||
\(356\) | 7.26373 | 0.384977 | ||||||||
\(357\) | −3.60802 | −0.190957 | ||||||||
\(358\) | 10.9858 | 0.580617 | ||||||||
\(359\) | −3.57962 | −0.188925 | −0.0944625 | − | 0.995528i | \(-0.530113\pi\) | ||||
−0.0944625 | + | 0.995528i | \(0.530113\pi\) | |||||||
\(360\) | −2.82830 | −0.149064 | ||||||||
\(361\) | 5.18472 | 0.272880 | ||||||||
\(362\) | −15.3946 | −0.809120 | ||||||||
\(363\) | −10.9518 | −0.574819 | ||||||||
\(364\) | 12.0590 | 0.632063 | ||||||||
\(365\) | −7.77662 | −0.407047 | ||||||||
\(366\) | 4.40623 | 0.230318 | ||||||||
\(367\) | 37.8608 | 1.97632 | 0.988160 | − | 0.153429i | \(-0.0490317\pi\) | ||||
0.988160 | + | 0.153429i | \(0.0490317\pi\) | |||||||
\(368\) | 0.508036 | 0.0264832 | ||||||||
\(369\) | 0.0934982 | 0.00486732 | ||||||||
\(370\) | 1.58619 | 0.0824620 | ||||||||
\(371\) | 23.1343 | 1.20107 | ||||||||
\(372\) | −1.19631 | −0.0620259 | ||||||||
\(373\) | 23.2424 | 1.20345 | 0.601724 | − | 0.798704i | \(-0.294481\pi\) | ||||
0.601724 | + | 0.798704i | \(0.294481\pi\) | |||||||
\(374\) | −0.195938 | −0.0101317 | ||||||||
\(375\) | 8.92533 | 0.460902 | ||||||||
\(376\) | 4.96701 | 0.256154 | ||||||||
\(377\) | −18.6874 | −0.962452 | ||||||||
\(378\) | −3.21922 | −0.165579 | ||||||||
\(379\) | −6.52900 | −0.335372 | −0.167686 | − | 0.985840i | \(-0.553630\pi\) | ||||
−0.167686 | + | 0.985840i | \(0.553630\pi\) | |||||||
\(380\) | 5.85772 | 0.300495 | ||||||||
\(381\) | −9.20742 | −0.471711 | ||||||||
\(382\) | 16.5348 | 0.845994 | ||||||||
\(383\) | 25.9296 | 1.32494 | 0.662470 | − | 0.749089i | \(-0.269508\pi\) | ||||
0.662470 | + | 0.749089i | \(0.269508\pi\) | |||||||
\(384\) | 6.47497 | 0.330424 | ||||||||
\(385\) | 0.783918 | 0.0399521 | ||||||||
\(386\) | −12.2061 | −0.621273 | ||||||||
\(387\) | −5.95800 | −0.302862 | ||||||||
\(388\) | 7.53878 | 0.382723 | ||||||||
\(389\) | 15.4376 | 0.782717 | 0.391359 | − | 0.920238i | \(-0.372005\pi\) | ||||
0.391359 | + | 0.920238i | \(0.372005\pi\) | |||||||
\(390\) | −2.45071 | −0.124097 | ||||||||
\(391\) | 3.55820 | 0.179946 | ||||||||
\(392\) | 17.2028 | 0.868875 | ||||||||
\(393\) | −9.10545 | −0.459309 | ||||||||
\(394\) | −2.06062 | −0.103812 | ||||||||
\(395\) | −4.95155 | −0.249140 | ||||||||
\(396\) | 0.264382 | 0.0132857 | ||||||||
\(397\) | 4.36306 | 0.218976 | 0.109488 | − | 0.993988i | \(-0.465079\pi\) | ||||
0.109488 | + | 0.993988i | \(0.465079\pi\) | |||||||
\(398\) | 11.5485 | 0.578873 | ||||||||
\(399\) | 17.7435 | 0.888287 | ||||||||
\(400\) | 0.574132 | 0.0287066 | ||||||||
\(401\) | 7.15335 | 0.357221 | 0.178611 | − | 0.983920i | \(-0.442840\pi\) | ||||
0.178611 | + | 0.983920i | \(0.442840\pi\) | |||||||
\(402\) | 5.30190 | 0.264435 | ||||||||
\(403\) | −2.75866 | −0.137418 | ||||||||
\(404\) | −16.3023 | −0.811071 | ||||||||
\(405\) | −0.989381 | −0.0491628 | ||||||||
\(406\) | −21.6697 | −1.07545 | ||||||||
\(407\) | −0.394591 | −0.0195592 | ||||||||
\(408\) | −2.85865 | −0.141524 | ||||||||
\(409\) | −19.4140 | −0.959960 | −0.479980 | − | 0.877279i | \(-0.659356\pi\) | ||||
−0.479980 | + | 0.877279i | \(0.659356\pi\) | |||||||
\(410\) | 0.0825369 | 0.00407621 | ||||||||
\(411\) | −2.08470 | −0.102830 | ||||||||
\(412\) | −15.6712 | −0.772063 | ||||||||
\(413\) | 43.0901 | 2.12032 | ||||||||
\(414\) | 3.17476 | 0.156031 | ||||||||
\(415\) | −1.95190 | −0.0958150 | ||||||||
\(416\) | 15.5186 | 0.760862 | ||||||||
\(417\) | 19.3869 | 0.949379 | ||||||||
\(418\) | 0.963583 | 0.0471304 | ||||||||
\(419\) | −22.5842 | −1.10331 | −0.551655 | − | 0.834072i | \(-0.686004\pi\) | ||||
−0.551655 | + | 0.834072i | \(0.686004\pi\) | |||||||
\(420\) | 4.29761 | 0.209702 | ||||||||
\(421\) | 16.4010 | 0.799334 | 0.399667 | − | 0.916660i | \(-0.369126\pi\) | ||||
0.399667 | + | 0.916660i | \(0.369126\pi\) | |||||||
\(422\) | 23.0175 | 1.12047 | ||||||||
\(423\) | 1.73754 | 0.0844819 | ||||||||
\(424\) | 18.3294 | 0.890155 | ||||||||
\(425\) | 4.02112 | 0.195053 | ||||||||
\(426\) | −10.0634 | −0.487572 | ||||||||
\(427\) | −17.8179 | −0.862267 | ||||||||
\(428\) | −0.524030 | −0.0253300 | ||||||||
\(429\) | 0.609656 | 0.0294345 | ||||||||
\(430\) | −5.25951 | −0.253636 | ||||||||
\(431\) | −6.10254 | −0.293949 | −0.146974 | − | 0.989140i | \(-0.546953\pi\) | ||||
−0.146974 | + | 0.989140i | \(0.546953\pi\) | |||||||
\(432\) | −0.142779 | −0.00686946 | ||||||||
\(433\) | 2.88811 | 0.138794 | 0.0693968 | − | 0.997589i | \(-0.477893\pi\) | ||||
0.0693968 | + | 0.997589i | \(0.477893\pi\) | |||||||
\(434\) | −3.19890 | −0.153552 | ||||||||
\(435\) | −6.65987 | −0.319316 | ||||||||
\(436\) | 16.7168 | 0.800590 | ||||||||
\(437\) | −17.4985 | −0.837066 | ||||||||
\(438\) | −7.01307 | −0.335097 | ||||||||
\(439\) | 33.2795 | 1.58834 | 0.794171 | − | 0.607694i | \(-0.207905\pi\) | ||||
0.794171 | + | 0.607694i | \(0.207905\pi\) | |||||||
\(440\) | 0.621102 | 0.0296099 | ||||||||
\(441\) | 6.01782 | 0.286563 | ||||||||
\(442\) | −2.47701 | −0.117820 | ||||||||
\(443\) | 35.6344 | 1.69304 | 0.846520 | − | 0.532356i | \(-0.178693\pi\) | ||||
0.846520 | + | 0.532356i | \(0.178693\pi\) | |||||||
\(444\) | −2.16324 | −0.102663 | ||||||||
\(445\) | 5.96938 | 0.282976 | ||||||||
\(446\) | −16.8026 | −0.795624 | ||||||||
\(447\) | 16.5666 | 0.783573 | ||||||||
\(448\) | 19.0254 | 0.898867 | ||||||||
\(449\) | 39.3240 | 1.85582 | 0.927908 | − | 0.372810i | \(-0.121606\pi\) | ||||
0.927908 | + | 0.372810i | \(0.121606\pi\) | |||||||
\(450\) | 3.58780 | 0.169131 | ||||||||
\(451\) | −0.0205325 | −0.000966835 0 | ||||||||
\(452\) | 13.0119 | 0.612028 | ||||||||
\(453\) | 0.909183 | 0.0427171 | ||||||||
\(454\) | 6.35091 | 0.298063 | ||||||||
\(455\) | 9.91015 | 0.464595 | ||||||||
\(456\) | 14.0583 | 0.658339 | ||||||||
\(457\) | 14.6188 | 0.683840 | 0.341920 | − | 0.939729i | \(-0.388923\pi\) | ||||
0.341920 | + | 0.939729i | \(0.388923\pi\) | |||||||
\(458\) | 4.96039 | 0.231784 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | −4.23826 | −0.197610 | ||||||||
\(461\) | 12.7576 | 0.594183 | 0.297091 | − | 0.954849i | \(-0.403983\pi\) | ||||
0.297091 | + | 0.954849i | \(0.403983\pi\) | |||||||
\(462\) | 0.706948 | 0.0328902 | ||||||||
\(463\) | 12.7574 | 0.592888 | 0.296444 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296444 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(464\) | −0.961095 | −0.0446177 | ||||||||
\(465\) | −0.983137 | −0.0455919 | ||||||||
\(466\) | −5.00772 | −0.231978 | ||||||||
\(467\) | −0.394515 | −0.0182560 | −0.00912798 | − | 0.999958i | \(-0.502906\pi\) | ||||
−0.00912798 | + | 0.999958i | \(0.502906\pi\) | |||||||
\(468\) | 3.34227 | 0.154497 | ||||||||
\(469\) | −21.4398 | −0.989996 | ||||||||
\(470\) | 1.53383 | 0.0707505 | ||||||||
\(471\) | −1.00000 | −0.0460776 | ||||||||
\(472\) | 34.1405 | 1.57144 | ||||||||
\(473\) | 1.30839 | 0.0601600 | ||||||||
\(474\) | −4.46538 | −0.205102 | ||||||||
\(475\) | −19.7751 | −0.907342 | ||||||||
\(476\) | 4.34373 | 0.199095 | ||||||||
\(477\) | 6.41191 | 0.293581 | ||||||||
\(478\) | 10.1863 | 0.465911 | ||||||||
\(479\) | 38.1001 | 1.74084 | 0.870420 | − | 0.492311i | \(-0.163848\pi\) | ||||
0.870420 | + | 0.492311i | \(0.163848\pi\) | |||||||
\(480\) | 5.53056 | 0.252434 | ||||||||
\(481\) | −4.98836 | −0.227449 | ||||||||
\(482\) | −10.9713 | −0.499730 | ||||||||
\(483\) | −12.8381 | −0.584152 | ||||||||
\(484\) | 13.1850 | 0.599316 | ||||||||
\(485\) | 6.19542 | 0.281319 | ||||||||
\(486\) | −0.892239 | −0.0404728 | ||||||||
\(487\) | 8.44055 | 0.382478 | 0.191239 | − | 0.981544i | \(-0.438749\pi\) | ||||
0.191239 | + | 0.981544i | \(0.438749\pi\) | |||||||
\(488\) | −14.1172 | −0.639055 | ||||||||
\(489\) | 8.99214 | 0.406639 | ||||||||
\(490\) | 5.31231 | 0.239986 | ||||||||
\(491\) | 7.86877 | 0.355113 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(492\) | −0.112563 | −0.00507475 | ||||||||
\(493\) | −6.73135 | −0.303165 | ||||||||
\(494\) | 12.1814 | 0.548069 | ||||||||
\(495\) | 0.217271 | 0.00976560 | ||||||||
\(496\) | −0.141878 | −0.00637050 | ||||||||
\(497\) | 40.6941 | 1.82538 | ||||||||
\(498\) | −1.76025 | −0.0788787 | ||||||||
\(499\) | 6.91656 | 0.309628 | 0.154814 | − | 0.987944i | \(-0.450522\pi\) | ||||
0.154814 | + | 0.987944i | \(0.450522\pi\) | |||||||
\(500\) | −10.7453 | −0.480544 | ||||||||
\(501\) | 17.4735 | 0.780657 | ||||||||
\(502\) | −25.1943 | −1.12448 | ||||||||
\(503\) | −6.55482 | −0.292265 | −0.146133 | − | 0.989265i | \(-0.546683\pi\) | ||||
−0.146133 | + | 0.989265i | \(0.546683\pi\) | |||||||
\(504\) | 10.3141 | 0.459426 | ||||||||
\(505\) | −13.3974 | −0.596174 | ||||||||
\(506\) | −0.697186 | −0.0309937 | ||||||||
\(507\) | −5.29283 | −0.235063 | ||||||||
\(508\) | 11.0849 | 0.491813 | ||||||||
\(509\) | −17.3609 | −0.769510 | −0.384755 | − | 0.923019i | \(-0.625714\pi\) | ||||
−0.384755 | + | 0.923019i | \(0.625714\pi\) | |||||||
\(510\) | −0.882764 | −0.0390895 | ||||||||
\(511\) | 28.3593 | 1.25454 | ||||||||
\(512\) | 1.61443 | 0.0713485 | ||||||||
\(513\) | 4.91780 | 0.217126 | ||||||||
\(514\) | −11.7194 | −0.516921 | ||||||||
\(515\) | −12.8787 | −0.567502 | ||||||||
\(516\) | 7.17290 | 0.315769 | ||||||||
\(517\) | −0.381568 | −0.0167813 | ||||||||
\(518\) | −5.78442 | −0.254153 | ||||||||
\(519\) | 9.75269 | 0.428096 | ||||||||
\(520\) | 7.85186 | 0.344327 | ||||||||
\(521\) | −37.5898 | −1.64684 | −0.823419 | − | 0.567434i | \(-0.807936\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(522\) | −6.00597 | −0.262874 | ||||||||
\(523\) | 3.38403 | 0.147973 | 0.0739867 | − | 0.997259i | \(-0.476428\pi\) | ||||
0.0739867 | + | 0.997259i | \(0.476428\pi\) | |||||||
\(524\) | 10.9621 | 0.478883 | ||||||||
\(525\) | −14.5083 | −0.633194 | ||||||||
\(526\) | −4.17215 | −0.181914 | ||||||||
\(527\) | −0.993688 | −0.0432857 | ||||||||
\(528\) | 0.0313547 | 0.00136454 | ||||||||
\(529\) | −10.3392 | −0.449532 | ||||||||
\(530\) | 5.66020 | 0.245863 | ||||||||
\(531\) | 11.9429 | 0.518276 | ||||||||
\(532\) | −21.3616 | −0.926143 | ||||||||
\(533\) | −0.259568 | −0.0112431 | ||||||||
\(534\) | 5.38327 | 0.232957 | ||||||||
\(535\) | −0.430652 | −0.0186187 | ||||||||
\(536\) | −16.9868 | −0.733719 | ||||||||
\(537\) | −12.3126 | −0.531329 | ||||||||
\(538\) | 14.5394 | 0.626837 | ||||||||
\(539\) | −1.32153 | −0.0569223 | ||||||||
\(540\) | 1.19113 | 0.0512579 | ||||||||
\(541\) | −10.9698 | −0.471630 | −0.235815 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235815 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(542\) | −3.55566 | −0.152729 | ||||||||
\(543\) | 17.2539 | 0.740434 | ||||||||
\(544\) | 5.58991 | 0.239665 | ||||||||
\(545\) | 13.7380 | 0.588470 | ||||||||
\(546\) | 8.93712 | 0.382473 | ||||||||
\(547\) | 16.0799 | 0.687528 | 0.343764 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343764 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(548\) | 2.50979 | 0.107213 | ||||||||
\(549\) | −4.93840 | −0.210766 | ||||||||
\(550\) | −0.787891 | −0.0335958 | ||||||||
\(551\) | 33.1034 | 1.41025 | ||||||||
\(552\) | −10.1717 | −0.432934 | ||||||||
\(553\) | 18.0570 | 0.767864 | ||||||||
\(554\) | 19.0816 | 0.810697 | ||||||||
\(555\) | −1.77776 | −0.0754618 | ||||||||
\(556\) | −23.3401 | −0.989839 | ||||||||
\(557\) | −10.2436 | −0.434037 | −0.217019 | − | 0.976167i | \(-0.569633\pi\) | ||||
−0.217019 | + | 0.976167i | \(0.569633\pi\) | |||||||
\(558\) | −0.886607 | −0.0375331 | ||||||||
\(559\) | 16.5405 | 0.699588 | ||||||||
\(560\) | 0.509680 | 0.0215379 | ||||||||
\(561\) | 0.219603 | 0.00927163 | ||||||||
\(562\) | −13.2802 | −0.560192 | ||||||||
\(563\) | 5.66551 | 0.238773 | 0.119386 | − | 0.992848i | \(-0.461907\pi\) | ||||
0.119386 | + | 0.992848i | \(0.461907\pi\) | |||||||
\(564\) | −2.09184 | −0.0880823 | ||||||||
\(565\) | 10.6933 | 0.449869 | ||||||||
\(566\) | −4.08746 | −0.171809 | ||||||||
\(567\) | 3.60802 | 0.151523 | ||||||||
\(568\) | 32.2421 | 1.35285 | ||||||||
\(569\) | 8.01376 | 0.335954 | 0.167977 | − | 0.985791i | \(-0.446277\pi\) | ||||
0.167977 | + | 0.985791i | \(0.446277\pi\) | |||||||
\(570\) | 4.34125 | 0.181835 | ||||||||
\(571\) | 25.7496 | 1.07759 | 0.538794 | − | 0.842438i | \(-0.318880\pi\) | ||||
0.538794 | + | 0.842438i | \(0.318880\pi\) | |||||||
\(572\) | −0.733972 | −0.0306889 | ||||||||
\(573\) | −18.5318 | −0.774178 | ||||||||
\(574\) | −0.300991 | −0.0125631 | ||||||||
\(575\) | 14.3080 | 0.596683 | ||||||||
\(576\) | 5.27309 | 0.219712 | ||||||||
\(577\) | −14.9926 | −0.624152 | −0.312076 | − | 0.950057i | \(-0.601024\pi\) | ||||
−0.312076 | + | 0.950057i | \(0.601024\pi\) | |||||||
\(578\) | −0.892239 | −0.0371122 | ||||||||
\(579\) | 13.6803 | 0.568534 | ||||||||
\(580\) | 8.01789 | 0.332925 | ||||||||
\(581\) | 7.11808 | 0.295308 | ||||||||
\(582\) | 5.58712 | 0.231593 | ||||||||
\(583\) | −1.40807 | −0.0583164 | ||||||||
\(584\) | 22.4692 | 0.929784 | ||||||||
\(585\) | 2.74670 | 0.113562 | ||||||||
\(586\) | 14.5626 | 0.601577 | ||||||||
\(587\) | 29.7529 | 1.22803 | 0.614016 | − | 0.789293i | \(-0.289553\pi\) | ||||
0.614016 | + | 0.789293i | \(0.289553\pi\) | |||||||
\(588\) | −7.24491 | −0.298775 | ||||||||
\(589\) | 4.88675 | 0.201355 | ||||||||
\(590\) | 10.5427 | 0.434037 | ||||||||
\(591\) | 2.30949 | 0.0949997 | ||||||||
\(592\) | −0.256551 | −0.0105442 | ||||||||
\(593\) | −33.1252 | −1.36029 | −0.680145 | − | 0.733078i | \(-0.738083\pi\) | ||||
−0.680145 | + | 0.733078i | \(0.738083\pi\) | |||||||
\(594\) | 0.195938 | 0.00803943 | ||||||||
\(595\) | 3.56971 | 0.146344 | ||||||||
\(596\) | −19.9447 | −0.816967 | ||||||||
\(597\) | −12.9433 | −0.529733 | ||||||||
\(598\) | −8.81371 | −0.360419 | ||||||||
\(599\) | −22.1396 | −0.904600 | −0.452300 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452300 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(600\) | −11.4950 | −0.469281 | ||||||||
\(601\) | 12.6996 | 0.518028 | 0.259014 | − | 0.965874i | \(-0.416602\pi\) | ||||
0.259014 | + | 0.965874i | \(0.416602\pi\) | |||||||
\(602\) | 19.1801 | 0.781722 | ||||||||
\(603\) | −5.94225 | −0.241987 | ||||||||
\(604\) | −1.09457 | −0.0445376 | ||||||||
\(605\) | 10.8355 | 0.440525 | ||||||||
\(606\) | −12.0819 | −0.490795 | ||||||||
\(607\) | 6.50596 | 0.264069 | 0.132034 | − | 0.991245i | \(-0.457849\pi\) | ||||
0.132034 | + | 0.991245i | \(0.457849\pi\) | |||||||
\(608\) | −27.4900 | −1.11487 | ||||||||
\(609\) | 24.2869 | 0.984153 | ||||||||
\(610\) | −4.35945 | −0.176509 | ||||||||
\(611\) | −4.82371 | −0.195146 | ||||||||
\(612\) | 1.20391 | 0.0486652 | ||||||||
\(613\) | −13.4815 | −0.544512 | −0.272256 | − | 0.962225i | \(-0.587770\pi\) | ||||
−0.272256 | + | 0.962225i | \(0.587770\pi\) | |||||||
\(614\) | −13.4916 | −0.544476 | ||||||||
\(615\) | −0.0925054 | −0.00373018 | ||||||||
\(616\) | −2.26500 | −0.0912594 | ||||||||
\(617\) | 3.49246 | 0.140601 | 0.0703006 | − | 0.997526i | \(-0.477604\pi\) | ||||
0.0703006 | + | 0.997526i | \(0.477604\pi\) | |||||||
\(618\) | −11.6142 | −0.467191 | ||||||||
\(619\) | 42.2390 | 1.69773 | 0.848863 | − | 0.528612i | \(-0.177287\pi\) | ||||
0.848863 | + | 0.528612i | \(0.177287\pi\) | |||||||
\(620\) | 1.18361 | 0.0475349 | ||||||||
\(621\) | −3.55820 | −0.142786 | ||||||||
\(622\) | 12.5556 | 0.503435 | ||||||||
\(623\) | −21.7688 | −0.872149 | ||||||||
\(624\) | 0.396380 | 0.0158679 | ||||||||
\(625\) | 11.2751 | 0.451002 | ||||||||
\(626\) | 16.0766 | 0.642549 | ||||||||
\(627\) | −1.07996 | −0.0431295 | ||||||||
\(628\) | 1.20391 | 0.0480413 | ||||||||
\(629\) | −1.79684 | −0.0716448 | ||||||||
\(630\) | 3.18503 | 0.126895 | ||||||||
\(631\) | 20.0697 | 0.798963 | 0.399482 | − | 0.916741i | \(-0.369190\pi\) | ||||
0.399482 | + | 0.916741i | \(0.369190\pi\) | |||||||
\(632\) | 14.3067 | 0.569089 | ||||||||
\(633\) | −25.7974 | −1.02536 | ||||||||
\(634\) | −27.1881 | −1.07978 | ||||||||
\(635\) | 9.10965 | 0.361506 | ||||||||
\(636\) | −7.71936 | −0.306093 | ||||||||
\(637\) | −16.7065 | −0.661937 | ||||||||
\(638\) | 1.31893 | 0.0522168 | ||||||||
\(639\) | 11.2788 | 0.446182 | ||||||||
\(640\) | −6.40621 | −0.253228 | ||||||||
\(641\) | −12.2217 | −0.482729 | −0.241364 | − | 0.970435i | \(-0.577595\pi\) | ||||
−0.241364 | + | 0.970435i | \(0.577595\pi\) | |||||||
\(642\) | −0.388368 | −0.0153277 | ||||||||
\(643\) | −6.11753 | −0.241252 | −0.120626 | − | 0.992698i | \(-0.538490\pi\) | ||||
−0.120626 | + | 0.992698i | \(0.538490\pi\) | |||||||
\(644\) | 15.4559 | 0.609046 | ||||||||
\(645\) | 5.89473 | 0.232105 | ||||||||
\(646\) | 4.38785 | 0.172638 | ||||||||
\(647\) | 48.1369 | 1.89246 | 0.946228 | − | 0.323501i | \(-0.104860\pi\) | ||||
0.946228 | + | 0.323501i | \(0.104860\pi\) | |||||||
\(648\) | 2.85865 | 0.112298 | ||||||||
\(649\) | −2.62268 | −0.102949 | ||||||||
\(650\) | −9.96038 | −0.390678 | ||||||||
\(651\) | 3.58525 | 0.140517 | ||||||||
\(652\) | −10.8257 | −0.423969 | ||||||||
\(653\) | −18.4826 | −0.723282 | −0.361641 | − | 0.932318i | \(-0.617783\pi\) | ||||
−0.361641 | + | 0.932318i | \(0.617783\pi\) | |||||||
\(654\) | 12.3891 | 0.484452 | ||||||||
\(655\) | 9.00876 | 0.352001 | ||||||||
\(656\) | −0.0133496 | −0.000521214 0 | ||||||||
\(657\) | 7.86008 | 0.306651 | ||||||||
\(658\) | −5.59350 | −0.218057 | ||||||||
\(659\) | −18.9864 | −0.739604 | −0.369802 | − | 0.929111i | \(-0.620574\pi\) | ||||
−0.369802 | + | 0.929111i | \(0.620574\pi\) | |||||||
\(660\) | −0.261575 | −0.0101818 | ||||||||
\(661\) | −4.50535 | −0.175238 | −0.0876189 | − | 0.996154i | \(-0.527926\pi\) | ||||
−0.0876189 | + | 0.996154i | \(0.527926\pi\) | |||||||
\(662\) | −2.67942 | −0.104139 | ||||||||
\(663\) | 2.77618 | 0.107818 | ||||||||
\(664\) | 5.63969 | 0.218862 | ||||||||
\(665\) | −17.5551 | −0.680758 | ||||||||
\(666\) | −1.60321 | −0.0621232 | ||||||||
\(667\) | −23.9515 | −0.927405 | ||||||||
\(668\) | −21.0365 | −0.813926 | ||||||||
\(669\) | 18.8319 | 0.728084 | ||||||||
\(670\) | −5.24560 | −0.202655 | ||||||||
\(671\) | 1.08449 | 0.0418661 | ||||||||
\(672\) | −20.1685 | −0.778018 | ||||||||
\(673\) | −8.05013 | −0.310310 | −0.155155 | − | 0.987890i | \(-0.549588\pi\) | ||||
−0.155155 | + | 0.987890i | \(0.549588\pi\) | |||||||
\(674\) | 26.4482 | 1.01875 | ||||||||
\(675\) | −4.02112 | −0.154773 | ||||||||
\(676\) | 6.37209 | 0.245080 | ||||||||
\(677\) | 37.9685 | 1.45925 | 0.729625 | − | 0.683848i | \(-0.239695\pi\) | ||||
0.729625 | + | 0.683848i | \(0.239695\pi\) | |||||||
\(678\) | 9.64333 | 0.370350 | ||||||||
\(679\) | −22.5931 | −0.867044 | ||||||||
\(680\) | 2.82830 | 0.108460 | ||||||||
\(681\) | −7.11795 | −0.272761 | ||||||||
\(682\) | 0.194701 | 0.00745549 | ||||||||
\(683\) | 27.6502 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(684\) | −5.92059 | −0.226379 | ||||||||
\(685\) | 2.06256 | 0.0788063 | ||||||||
\(686\) | 3.16186 | 0.120720 | ||||||||
\(687\) | −5.55949 | −0.212108 | ||||||||
\(688\) | 0.850677 | 0.0324318 | ||||||||
\(689\) | −17.8006 | −0.678149 | ||||||||
\(690\) | −3.14105 | −0.119578 | ||||||||
\(691\) | 6.55651 | 0.249421 | 0.124711 | − | 0.992193i | \(-0.460200\pi\) | ||||
0.124711 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(692\) | −11.7414 | −0.446340 | ||||||||
\(693\) | −0.792331 | −0.0300982 | ||||||||
\(694\) | −11.4509 | −0.434669 | ||||||||
\(695\) | −19.1810 | −0.727577 | ||||||||
\(696\) | 19.2426 | 0.729388 | ||||||||
\(697\) | −0.0934982 | −0.00354150 | ||||||||
\(698\) | 11.8729 | 0.449397 | ||||||||
\(699\) | 5.61253 | 0.212285 | ||||||||
\(700\) | 17.4667 | 0.660179 | ||||||||
\(701\) | 1.60435 | 0.0605955 | 0.0302977 | − | 0.999541i | \(-0.490354\pi\) | ||||
0.0302977 | + | 0.999541i | \(0.490354\pi\) | |||||||
\(702\) | 2.47701 | 0.0934889 | ||||||||
\(703\) | 8.83650 | 0.333275 | ||||||||
\(704\) | −1.15799 | −0.0436432 | ||||||||
\(705\) | −1.71909 | −0.0647445 | ||||||||
\(706\) | −24.5994 | −0.925811 | ||||||||
\(707\) | 48.8567 | 1.83745 | ||||||||
\(708\) | −14.3781 | −0.540363 | ||||||||
\(709\) | −40.2894 | −1.51310 | −0.756550 | − | 0.653935i | \(-0.773117\pi\) | ||||
−0.756550 | + | 0.653935i | \(0.773117\pi\) | |||||||
\(710\) | 9.95652 | 0.373661 | ||||||||
\(711\) | 5.00470 | 0.187691 | ||||||||
\(712\) | −17.2475 | −0.646378 | ||||||||
\(713\) | −3.53574 | −0.132414 | ||||||||
\(714\) | 3.21922 | 0.120476 | ||||||||
\(715\) | −0.603183 | −0.0225578 | ||||||||
\(716\) | 14.8233 | 0.553973 | ||||||||
\(717\) | −11.4166 | −0.426360 | ||||||||
\(718\) | 3.19387 | 0.119194 | ||||||||
\(719\) | 28.4225 | 1.05998 | 0.529990 | − | 0.848004i | \(-0.322196\pi\) | ||||
0.529990 | + | 0.848004i | \(0.322196\pi\) | |||||||
\(720\) | 0.141263 | 0.00526456 | ||||||||
\(721\) | 46.9652 | 1.74908 | ||||||||
\(722\) | −4.62600 | −0.172162 | ||||||||
\(723\) | 12.2964 | 0.457308 | ||||||||
\(724\) | −20.7721 | −0.771989 | ||||||||
\(725\) | −27.0676 | −1.00527 | ||||||||
\(726\) | 9.77160 | 0.362658 | ||||||||
\(727\) | 41.6640 | 1.54523 | 0.772617 | − | 0.634873i | \(-0.218947\pi\) | ||||
0.772617 | + | 0.634873i | \(0.218947\pi\) | |||||||
\(728\) | −28.6337 | −1.06124 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.93860 | 0.256809 | ||||||||
\(731\) | 5.95800 | 0.220365 | ||||||||
\(732\) | 5.94539 | 0.219748 | ||||||||
\(733\) | −40.5778 | −1.49878 | −0.749389 | − | 0.662131i | \(-0.769652\pi\) | ||||
−0.749389 | + | 0.662131i | \(0.769652\pi\) | |||||||
\(734\) | −33.7809 | −1.24688 | ||||||||
\(735\) | −5.95392 | −0.219613 | ||||||||
\(736\) | 19.8900 | 0.733156 | ||||||||
\(737\) | 1.30493 | 0.0480678 | ||||||||
\(738\) | −0.0834227 | −0.00307083 | ||||||||
\(739\) | −14.1032 | −0.518793 | −0.259396 | − | 0.965771i | \(-0.583524\pi\) | ||||
−0.259396 | + | 0.965771i | \(0.583524\pi\) | |||||||
\(740\) | 2.14027 | 0.0786778 | ||||||||
\(741\) | −13.6527 | −0.501544 | ||||||||
\(742\) | −20.6413 | −0.757766 | ||||||||
\(743\) | 18.0932 | 0.663775 | 0.331887 | − | 0.943319i | \(-0.392315\pi\) | ||||
0.331887 | + | 0.943319i | \(0.392315\pi\) | |||||||
\(744\) | 2.84061 | 0.104142 | ||||||||
\(745\) | −16.3907 | −0.600508 | ||||||||
\(746\) | −20.7378 | −0.759265 | ||||||||
\(747\) | 1.97285 | 0.0721827 | ||||||||
\(748\) | −0.264382 | −0.00966676 | ||||||||
\(749\) | 1.57048 | 0.0573840 | ||||||||
\(750\) | −7.96353 | −0.290787 | ||||||||
\(751\) | 50.4062 | 1.83935 | 0.919674 | − | 0.392683i | \(-0.128453\pi\) | ||||
0.919674 | + | 0.392683i | \(0.128453\pi\) | |||||||
\(752\) | −0.248084 | −0.00904668 | ||||||||
\(753\) | 28.2372 | 1.02902 | ||||||||
\(754\) | 16.6736 | 0.607218 | ||||||||
\(755\) | −0.899529 | −0.0327372 | ||||||||
\(756\) | −4.34373 | −0.157980 | ||||||||
\(757\) | −46.7539 | −1.69930 | −0.849650 | − | 0.527348i | \(-0.823187\pi\) | ||||
−0.849650 | + | 0.527348i | \(0.823187\pi\) | |||||||
\(758\) | 5.82543 | 0.211589 | ||||||||
\(759\) | 0.781390 | 0.0283627 | ||||||||
\(760\) | −13.9090 | −0.504532 | ||||||||
\(761\) | 37.0638 | 1.34356 | 0.671781 | − | 0.740750i | \(-0.265530\pi\) | ||||
0.671781 | + | 0.740750i | \(0.265530\pi\) | |||||||
\(762\) | 8.21522 | 0.297606 | ||||||||
\(763\) | −50.0989 | −1.81370 | ||||||||
\(764\) | 22.3107 | 0.807171 | ||||||||
\(765\) | 0.989381 | 0.0357712 | ||||||||
\(766\) | −23.1354 | −0.835915 | ||||||||
\(767\) | −33.1555 | −1.19718 | ||||||||
\(768\) | −16.3234 | −0.589020 | ||||||||
\(769\) | −20.6870 | −0.745991 | −0.372995 | − | 0.927833i | \(-0.621669\pi\) | ||||
−0.372995 | + | 0.927833i | \(0.621669\pi\) | |||||||
\(770\) | −0.699442 | −0.0252061 | ||||||||
\(771\) | 13.1349 | 0.473040 | ||||||||
\(772\) | −16.4698 | −0.592763 | ||||||||
\(773\) | 10.9866 | 0.395161 | 0.197581 | − | 0.980287i | \(-0.436692\pi\) | ||||
0.197581 | + | 0.980287i | \(0.436692\pi\) | |||||||
\(774\) | 5.31596 | 0.191078 | ||||||||
\(775\) | −3.99574 | −0.143531 | ||||||||
\(776\) | −17.9006 | −0.642595 | ||||||||
\(777\) | 6.48304 | 0.232578 | ||||||||
\(778\) | −13.7740 | −0.493823 | ||||||||
\(779\) | 0.459805 | 0.0164742 | ||||||||
\(780\) | −3.30678 | −0.118402 | ||||||||
\(781\) | −2.47685 | −0.0886288 | ||||||||
\(782\) | −3.17476 | −0.113529 | ||||||||
\(783\) | 6.73135 | 0.240559 | ||||||||
\(784\) | −0.859218 | −0.0306864 | ||||||||
\(785\) | 0.989381 | 0.0353125 | ||||||||
\(786\) | 8.12423 | 0.289782 | ||||||||
\(787\) | 41.4498 | 1.47752 | 0.738762 | − | 0.673966i | \(-0.235411\pi\) | ||||
0.738762 | + | 0.673966i | \(0.235411\pi\) | |||||||
\(788\) | −2.78042 | −0.0990483 | ||||||||
\(789\) | 4.67604 | 0.166472 | ||||||||
\(790\) | 4.41797 | 0.157184 | ||||||||
\(791\) | −38.9956 | −1.38652 | ||||||||
\(792\) | −0.627768 | −0.0223068 | ||||||||
\(793\) | 13.7099 | 0.486853 | ||||||||
\(794\) | −3.89289 | −0.138154 | ||||||||
\(795\) | −6.34382 | −0.224992 | ||||||||
\(796\) | 15.5825 | 0.552308 | ||||||||
\(797\) | 41.1032 | 1.45595 | 0.727974 | − | 0.685604i | \(-0.240462\pi\) | ||||
0.727974 | + | 0.685604i | \(0.240462\pi\) | |||||||
\(798\) | −15.8314 | −0.560427 | ||||||||
\(799\) | −1.73754 | −0.0614696 | ||||||||
\(800\) | 22.4777 | 0.794708 | ||||||||
\(801\) | −6.03345 | −0.213181 | ||||||||
\(802\) | −6.38249 | −0.225374 | ||||||||
\(803\) | −1.72609 | −0.0609126 | ||||||||
\(804\) | 7.15393 | 0.252300 | ||||||||
\(805\) | 12.7017 | 0.447677 | ||||||||
\(806\) | 2.46138 | 0.0866984 | ||||||||
\(807\) | −16.2954 | −0.573625 | ||||||||
\(808\) | 38.7094 | 1.36179 | ||||||||
\(809\) | 13.4962 | 0.474500 | 0.237250 | − | 0.971449i | \(-0.423754\pi\) | ||||
0.237250 | + | 0.971449i | \(0.423754\pi\) | |||||||
\(810\) | 0.882764 | 0.0310172 | ||||||||
\(811\) | −8.99366 | −0.315810 | −0.157905 | − | 0.987454i | \(-0.550474\pi\) | ||||
−0.157905 | + | 0.987454i | \(0.550474\pi\) | |||||||
\(812\) | −29.2392 | −1.02609 | ||||||||
\(813\) | 3.98510 | 0.139764 | ||||||||
\(814\) | 0.352070 | 0.0123400 | ||||||||
\(815\) | −8.89666 | −0.311636 | ||||||||
\(816\) | 0.142779 | 0.00499827 | ||||||||
\(817\) | −29.3002 | −1.02509 | ||||||||
\(818\) | 17.3219 | 0.605647 | ||||||||
\(819\) | −10.0165 | −0.350005 | ||||||||
\(820\) | 0.111368 | 0.00388915 | ||||||||
\(821\) | −18.1826 | −0.634576 | −0.317288 | − | 0.948329i | \(-0.602772\pi\) | ||||
−0.317288 | + | 0.948329i | \(0.602772\pi\) | |||||||
\(822\) | 1.86005 | 0.0648765 | ||||||||
\(823\) | −15.8361 | −0.552013 | −0.276007 | − | 0.961156i | \(-0.589011\pi\) | ||||
−0.276007 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(824\) | 37.2108 | 1.29630 | ||||||||
\(825\) | 0.883050 | 0.0307438 | ||||||||
\(826\) | −38.4466 | −1.33773 | ||||||||
\(827\) | 18.8956 | 0.657064 | 0.328532 | − | 0.944493i | \(-0.393446\pi\) | ||||
0.328532 | + | 0.944493i | \(0.393446\pi\) | |||||||
\(828\) | 4.28375 | 0.148871 | ||||||||
\(829\) | −14.9754 | −0.520118 | −0.260059 | − | 0.965593i | \(-0.583742\pi\) | ||||
−0.260059 | + | 0.965593i | \(0.583742\pi\) | |||||||
\(830\) | 1.74156 | 0.0604504 | ||||||||
\(831\) | −21.3862 | −0.741878 | ||||||||
\(832\) | −14.6391 | −0.507518 | ||||||||
\(833\) | −6.01782 | −0.208505 | ||||||||
\(834\) | −17.2977 | −0.598971 | ||||||||
\(835\) | −17.2879 | −0.598273 | ||||||||
\(836\) | 1.30018 | 0.0449675 | ||||||||
\(837\) | 0.993688 | 0.0343469 | ||||||||
\(838\) | 20.1505 | 0.696087 | ||||||||
\(839\) | 52.1989 | 1.80210 | 0.901052 | − | 0.433710i | \(-0.142796\pi\) | ||||
0.901052 | + | 0.433710i | \(0.142796\pi\) | |||||||
\(840\) | −10.2046 | −0.352091 | ||||||||
\(841\) | 16.3111 | 0.562451 | ||||||||
\(842\) | −14.6336 | −0.504306 | ||||||||
\(843\) | 14.8841 | 0.512637 | ||||||||
\(844\) | 31.0578 | 1.06905 | ||||||||
\(845\) | 5.23663 | 0.180145 | ||||||||
\(846\) | −1.55030 | −0.0533003 | ||||||||
\(847\) | −39.5142 | −1.35773 | ||||||||
\(848\) | −0.915486 | −0.0314379 | ||||||||
\(849\) | 4.58113 | 0.157224 | ||||||||
\(850\) | −3.58780 | −0.123061 | ||||||||
\(851\) | −6.39352 | −0.219167 | ||||||||
\(852\) | −13.5787 | −0.465197 | ||||||||
\(853\) | 42.1342 | 1.44265 | 0.721324 | − | 0.692598i | \(-0.243534\pi\) | ||||
0.721324 | + | 0.692598i | \(0.243534\pi\) | |||||||
\(854\) | 15.8978 | 0.544011 | ||||||||
\(855\) | −4.86558 | −0.166399 | ||||||||
\(856\) | 1.24430 | 0.0425292 | ||||||||
\(857\) | 15.9513 | 0.544887 | 0.272443 | − | 0.962172i | \(-0.412168\pi\) | ||||
0.272443 | + | 0.962172i | \(0.412168\pi\) | |||||||
\(858\) | −0.543959 | −0.0185705 | ||||||||
\(859\) | 3.59920 | 0.122803 | 0.0614016 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614016 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(860\) | −7.09673 | −0.241997 | ||||||||
\(861\) | 0.337343 | 0.0114966 | ||||||||
\(862\) | 5.44492 | 0.185455 | ||||||||
\(863\) | −0.0465595 | −0.00158490 | −0.000792452 | − | 1.00000i | \(-0.500252\pi\) | ||||
−0.000792452 | 1.00000i | \(0.500252\pi\) | ||||||||
\(864\) | −5.58991 | −0.190173 | ||||||||
\(865\) | −9.64913 | −0.328080 | ||||||||
\(866\) | −2.57688 | −0.0875660 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −4.31632 | −0.146505 | ||||||||
\(869\) | −1.09904 | −0.0372825 | ||||||||
\(870\) | 5.94219 | 0.201459 | ||||||||
\(871\) | 16.4967 | 0.558971 | ||||||||
\(872\) | −39.6936 | −1.34419 | ||||||||
\(873\) | −6.26191 | −0.211933 | ||||||||
\(874\) | 15.6128 | 0.528112 | ||||||||
\(875\) | 32.2028 | 1.08865 | ||||||||
\(876\) | −9.46283 | −0.319720 | ||||||||
\(877\) | −46.6436 | −1.57504 | −0.787522 | − | 0.616286i | \(-0.788636\pi\) | ||||
−0.787522 | + | 0.616286i | \(0.788636\pi\) | |||||||
\(878\) | −29.6932 | −1.00210 | ||||||||
\(879\) | −16.3215 | −0.550509 | ||||||||
\(880\) | −0.0310217 | −0.00104574 | ||||||||
\(881\) | 17.9980 | 0.606369 | 0.303184 | − | 0.952932i | \(-0.401950\pi\) | ||||
0.303184 | + | 0.952932i | \(0.401950\pi\) | |||||||
\(882\) | −5.36933 | −0.180795 | ||||||||
\(883\) | −44.2503 | −1.48914 | −0.744570 | − | 0.667545i | \(-0.767345\pi\) | ||||
−0.744570 | + | 0.667545i | \(0.767345\pi\) | |||||||
\(884\) | −3.34227 | −0.112413 | ||||||||
\(885\) | −11.8160 | −0.397192 | ||||||||
\(886\) | −31.7944 | −1.06815 | ||||||||
\(887\) | −33.7261 | −1.13241 | −0.566206 | − | 0.824264i | \(-0.691589\pi\) | ||||
−0.566206 | + | 0.824264i | \(0.691589\pi\) | |||||||
\(888\) | 5.13655 | 0.172371 | ||||||||
\(889\) | −33.2206 | −1.11418 | ||||||||
\(890\) | −5.32611 | −0.178532 | ||||||||
\(891\) | −0.219603 | −0.00735697 | ||||||||
\(892\) | −22.6719 | −0.759112 | ||||||||
\(893\) | 8.54485 | 0.285942 | ||||||||
\(894\) | −14.7814 | −0.494363 | ||||||||
\(895\) | 12.1819 | 0.407195 | ||||||||
\(896\) | 23.3618 | 0.780464 | ||||||||
\(897\) | 9.87819 | 0.329823 | ||||||||
\(898\) | −35.0864 | −1.17085 | ||||||||
\(899\) | 6.68886 | 0.223086 | ||||||||
\(900\) | 4.84107 | 0.161369 | ||||||||
\(901\) | −6.41191 | −0.213612 | ||||||||
\(902\) | 0.0183198 | 0.000609984 0 | ||||||||
\(903\) | −21.4966 | −0.715362 | ||||||||
\(904\) | −30.8964 | −1.02760 | ||||||||
\(905\) | −17.0706 | −0.567448 | ||||||||
\(906\) | −0.811208 | −0.0269506 | ||||||||
\(907\) | −43.4126 | −1.44149 | −0.720745 | − | 0.693200i | \(-0.756200\pi\) | ||||
−0.720745 | + | 0.693200i | \(0.756200\pi\) | |||||||
\(908\) | 8.56938 | 0.284385 | ||||||||
\(909\) | 13.5411 | 0.449131 | ||||||||
\(910\) | −8.84222 | −0.293117 | ||||||||
\(911\) | −26.5779 | −0.880566 | −0.440283 | − | 0.897859i | \(-0.645122\pi\) | ||||
−0.440283 | + | 0.897859i | \(0.645122\pi\) | |||||||
\(912\) | −0.702158 | −0.0232508 | ||||||||
\(913\) | −0.433243 | −0.0143382 | ||||||||
\(914\) | −13.0435 | −0.431440 | ||||||||
\(915\) | 4.88596 | 0.161525 | ||||||||
\(916\) | 6.69313 | 0.221147 | ||||||||
\(917\) | −32.8526 | −1.08489 | ||||||||
\(918\) | 0.892239 | 0.0294483 | ||||||||
\(919\) | −33.5636 | −1.10716 | −0.553581 | − | 0.832796i | \(-0.686739\pi\) | ||||
−0.553581 | + | 0.832796i | \(0.686739\pi\) | |||||||
\(920\) | 10.0636 | 0.331788 | ||||||||
\(921\) | 15.1210 | 0.498255 | ||||||||
\(922\) | −11.3829 | −0.374875 | ||||||||
\(923\) | −31.3120 | −1.03065 | ||||||||
\(924\) | 0.953896 | 0.0313809 | ||||||||
\(925\) | −7.22533 | −0.237567 | ||||||||
\(926\) | −11.3827 | −0.374058 | ||||||||
\(927\) | 13.0169 | 0.427531 | ||||||||
\(928\) | −37.6276 | −1.23519 | ||||||||
\(929\) | −29.9598 | −0.982951 | −0.491475 | − | 0.870892i | \(-0.663542\pi\) | ||||
−0.491475 | + | 0.870892i | \(0.663542\pi\) | |||||||
\(930\) | 0.877192 | 0.0287643 | ||||||||
\(931\) | 29.5944 | 0.969917 | ||||||||
\(932\) | −6.75698 | −0.221332 | ||||||||
\(933\) | −14.0721 | −0.460699 | ||||||||
\(934\) | 0.352001 | 0.0115178 | ||||||||
\(935\) | −0.217271 | −0.00710552 | ||||||||
\(936\) | −7.93613 | −0.259401 | ||||||||
\(937\) | 11.3522 | 0.370859 | 0.185429 | − | 0.982658i | \(-0.440632\pi\) | ||||
0.185429 | + | 0.982658i | \(0.440632\pi\) | |||||||
\(938\) | 19.1294 | 0.624596 | ||||||||
\(939\) | −18.0182 | −0.588003 | ||||||||
\(940\) | 2.06963 | 0.0675037 | ||||||||
\(941\) | −29.7945 | −0.971274 | −0.485637 | − | 0.874160i | \(-0.661412\pi\) | ||||
−0.485637 | + | 0.874160i | \(0.661412\pi\) | |||||||
\(942\) | 0.892239 | 0.0290707 | ||||||||
\(943\) | −0.332685 | −0.0108337 | ||||||||
\(944\) | −1.70519 | −0.0554992 | ||||||||
\(945\) | −3.56971 | −0.116123 | ||||||||
\(946\) | −1.16740 | −0.0379554 | ||||||||
\(947\) | −19.3568 | −0.629011 | −0.314506 | − | 0.949256i | \(-0.601839\pi\) | ||||
−0.314506 | + | 0.949256i | \(0.601839\pi\) | |||||||
\(948\) | −6.02521 | −0.195690 | ||||||||
\(949\) | −21.8210 | −0.708339 | ||||||||
\(950\) | 17.6441 | 0.572449 | ||||||||
\(951\) | 30.4718 | 0.988116 | ||||||||
\(952\) | −10.3141 | −0.334281 | ||||||||
\(953\) | 14.0591 | 0.455420 | 0.227710 | − | 0.973729i | \(-0.426876\pi\) | ||||
0.227710 | + | 0.973729i | \(0.426876\pi\) | |||||||
\(954\) | −5.72095 | −0.185223 | ||||||||
\(955\) | 18.3350 | 0.593308 | ||||||||
\(956\) | 13.7445 | 0.444530 | ||||||||
\(957\) | −1.47822 | −0.0477841 | ||||||||
\(958\) | −33.9944 | −1.09831 | ||||||||
\(959\) | −7.52163 | −0.242886 | ||||||||
\(960\) | −5.21710 | −0.168381 | ||||||||
\(961\) | −30.0126 | −0.968148 | ||||||||
\(962\) | 4.45080 | 0.143500 | ||||||||
\(963\) | 0.435274 | 0.0140265 | ||||||||
\(964\) | −14.8038 | −0.476797 | ||||||||
\(965\) | −13.5350 | −0.435708 | ||||||||
\(966\) | 11.4546 | 0.368546 | ||||||||
\(967\) | 19.9898 | 0.642828 | 0.321414 | − | 0.946939i | \(-0.395842\pi\) | ||||
0.321414 | + | 0.946939i | \(0.395842\pi\) | |||||||
\(968\) | −31.3073 | −1.00626 | ||||||||
\(969\) | −4.91780 | −0.157982 | ||||||||
\(970\) | −5.52779 | −0.177487 | ||||||||
\(971\) | 32.0285 | 1.02784 | 0.513921 | − | 0.857837i | \(-0.328192\pi\) | ||||
0.513921 | + | 0.857837i | \(0.328192\pi\) | |||||||
\(972\) | −1.20391 | −0.0386154 | ||||||||
\(973\) | 69.9482 | 2.24244 | ||||||||
\(974\) | −7.53099 | −0.241308 | ||||||||
\(975\) | 11.1634 | 0.357514 | ||||||||
\(976\) | 0.705100 | 0.0225697 | ||||||||
\(977\) | 51.1067 | 1.63505 | 0.817523 | − | 0.575895i | \(-0.195346\pi\) | ||||
0.817523 | + | 0.575895i | \(0.195346\pi\) | |||||||
\(978\) | −8.02314 | −0.256552 | ||||||||
\(979\) | 1.32496 | 0.0423459 | ||||||||
\(980\) | 7.16798 | 0.228973 | ||||||||
\(981\) | −13.8854 | −0.443327 | ||||||||
\(982\) | −7.02082 | −0.224043 | ||||||||
\(983\) | −49.2635 | −1.57126 | −0.785631 | − | 0.618695i | \(-0.787662\pi\) | ||||
−0.785631 | + | 0.618695i | \(0.787662\pi\) | |||||||
\(984\) | 0.267279 | 0.00852054 | ||||||||
\(985\) | −2.28497 | −0.0728051 | ||||||||
\(986\) | 6.00597 | 0.191269 | ||||||||
\(987\) | 6.26907 | 0.199547 | ||||||||
\(988\) | 16.4366 | 0.522918 | ||||||||
\(989\) | 21.1997 | 0.674113 | ||||||||
\(990\) | −0.193857 | −0.00616119 | ||||||||
\(991\) | −29.3376 | −0.931941 | −0.465970 | − | 0.884800i | \(-0.654295\pi\) | ||||
−0.465970 | + | 0.884800i | \(0.654295\pi\) | |||||||
\(992\) | −5.55463 | −0.176360 | ||||||||
\(993\) | 3.00303 | 0.0952983 | ||||||||
\(994\) | −36.3089 | −1.15165 | ||||||||
\(995\) | 12.8058 | 0.405972 | ||||||||
\(996\) | −2.37513 | −0.0752589 | ||||||||
\(997\) | −50.3103 | −1.59334 | −0.796671 | − | 0.604413i | \(-0.793408\pi\) | ||||
−0.796671 | + | 0.604413i | \(0.793408\pi\) | |||||||
\(998\) | −6.17122 | −0.195347 | ||||||||
\(999\) | 1.79684 | 0.0568496 |
(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.h.1.20 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.h.1.20 | ✓ | 56 | 1.1 | even | 1 | trivial |