Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.22794 | −1.86365 | −0.931825 | − | 0.362908i | \(-0.881784\pi\) | ||||
−0.931825 | + | 0.362908i | \(0.881784\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.50843 | 0.674590 | 0.337295 | − | 0.941399i | \(-0.390488\pi\) | ||||
0.337295 | + | 0.941399i | \(0.390488\pi\) | |||||||
\(6\) | 3.22794 | 1.31780 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.41957 | 2.47319 | ||||||||
\(10\) | −1.50843 | −0.477007 | ||||||||
\(11\) | 2.69181 | 0.811611 | 0.405805 | − | 0.913960i | \(-0.366991\pi\) | ||||
0.405805 | + | 0.913960i | \(0.366991\pi\) | |||||||
\(12\) | −3.22794 | −0.931825 | ||||||||
\(13\) | 2.34378 | 0.650048 | 0.325024 | − | 0.945706i | \(-0.394628\pi\) | ||||
0.325024 | + | 0.945706i | \(0.394628\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −4.86911 | −1.25720 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.99039 | −0.482741 | −0.241370 | − | 0.970433i | \(-0.577597\pi\) | ||||
−0.241370 | + | 0.970433i | \(0.577597\pi\) | |||||||
\(18\) | −7.41957 | −1.74881 | ||||||||
\(19\) | −3.26883 | −0.749922 | −0.374961 | − | 0.927041i | \(-0.622344\pi\) | ||||
−0.374961 | + | 0.927041i | \(0.622344\pi\) | |||||||
\(20\) | 1.50843 | 0.337295 | ||||||||
\(21\) | −3.22794 | −0.704393 | ||||||||
\(22\) | −2.69181 | −0.573895 | ||||||||
\(23\) | 5.95775 | 1.24228 | 0.621139 | − | 0.783701i | \(-0.286670\pi\) | ||||
0.621139 | + | 0.783701i | \(0.286670\pi\) | |||||||
\(24\) | 3.22794 | 0.658900 | ||||||||
\(25\) | −2.72464 | −0.544929 | ||||||||
\(26\) | −2.34378 | −0.459653 | ||||||||
\(27\) | −14.2661 | −2.74551 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −7.07809 | −1.31437 | −0.657184 | − | 0.753730i | \(-0.728252\pi\) | ||||
−0.657184 | + | 0.753730i | \(0.728252\pi\) | |||||||
\(30\) | 4.86911 | 0.888974 | ||||||||
\(31\) | 9.75321 | 1.75173 | 0.875864 | − | 0.482558i | \(-0.160292\pi\) | ||||
0.875864 | + | 0.482558i | \(0.160292\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.68898 | −1.51256 | ||||||||
\(34\) | 1.99039 | 0.341349 | ||||||||
\(35\) | 1.50843 | 0.254971 | ||||||||
\(36\) | 7.41957 | 1.23660 | ||||||||
\(37\) | 2.88944 | 0.475021 | 0.237511 | − | 0.971385i | \(-0.423669\pi\) | ||||
0.237511 | + | 0.971385i | \(0.423669\pi\) | |||||||
\(38\) | 3.26883 | 0.530275 | ||||||||
\(39\) | −7.56558 | −1.21146 | ||||||||
\(40\) | −1.50843 | −0.238503 | ||||||||
\(41\) | 8.32408 | 1.30000 | 0.650001 | − | 0.759933i | \(-0.274768\pi\) | ||||
0.650001 | + | 0.759933i | \(0.274768\pi\) | |||||||
\(42\) | 3.22794 | 0.498081 | ||||||||
\(43\) | 3.75276 | 0.572290 | 0.286145 | − | 0.958186i | \(-0.407626\pi\) | ||||
0.286145 | + | 0.958186i | \(0.407626\pi\) | |||||||
\(44\) | 2.69181 | 0.405805 | ||||||||
\(45\) | 11.1919 | 1.66839 | ||||||||
\(46\) | −5.95775 | −0.878423 | ||||||||
\(47\) | 8.78196 | 1.28098 | 0.640490 | − | 0.767966i | \(-0.278731\pi\) | ||||
0.640490 | + | 0.767966i | \(0.278731\pi\) | |||||||
\(48\) | −3.22794 | −0.465913 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.72464 | 0.385323 | ||||||||
\(51\) | 6.42486 | 0.899660 | ||||||||
\(52\) | 2.34378 | 0.325024 | ||||||||
\(53\) | −3.37076 | −0.463009 | −0.231504 | − | 0.972834i | \(-0.574365\pi\) | ||||
−0.231504 | + | 0.972834i | \(0.574365\pi\) | |||||||
\(54\) | 14.2661 | 1.94137 | ||||||||
\(55\) | 4.06040 | 0.547504 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 10.5516 | 1.39759 | ||||||||
\(58\) | 7.07809 | 0.929398 | ||||||||
\(59\) | −0.771012 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(60\) | −4.86911 | −0.628599 | ||||||||
\(61\) | 11.1625 | 1.42922 | 0.714609 | − | 0.699524i | \(-0.246605\pi\) | ||||
0.714609 | + | 0.699524i | \(0.246605\pi\) | |||||||
\(62\) | −9.75321 | −1.23866 | ||||||||
\(63\) | 7.41957 | 0.934778 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.53543 | 0.438516 | ||||||||
\(66\) | 8.68898 | 1.06954 | ||||||||
\(67\) | −1.49141 | −0.182205 | −0.0911025 | − | 0.995842i | \(-0.529039\pi\) | ||||
−0.0911025 | + | 0.995842i | \(0.529039\pi\) | |||||||
\(68\) | −1.99039 | −0.241370 | ||||||||
\(69\) | −19.2312 | −2.31517 | ||||||||
\(70\) | −1.50843 | −0.180292 | ||||||||
\(71\) | 14.9001 | 1.76832 | 0.884160 | − | 0.467184i | \(-0.154732\pi\) | ||||
0.884160 | + | 0.467184i | \(0.154732\pi\) | |||||||
\(72\) | −7.41957 | −0.874405 | ||||||||
\(73\) | −12.1773 | −1.42524 | −0.712620 | − | 0.701550i | \(-0.752492\pi\) | ||||
−0.712620 | + | 0.701550i | \(0.752492\pi\) | |||||||
\(74\) | −2.88944 | −0.335891 | ||||||||
\(75\) | 8.79498 | 1.01556 | ||||||||
\(76\) | −3.26883 | −0.374961 | ||||||||
\(77\) | 2.69181 | 0.306760 | ||||||||
\(78\) | 7.56558 | 0.856633 | ||||||||
\(79\) | 2.71302 | 0.305239 | 0.152619 | − | 0.988285i | \(-0.451229\pi\) | ||||
0.152619 | + | 0.988285i | \(0.451229\pi\) | |||||||
\(80\) | 1.50843 | 0.168647 | ||||||||
\(81\) | 23.7914 | 2.64348 | ||||||||
\(82\) | −8.32408 | −0.919240 | ||||||||
\(83\) | −7.89882 | −0.867008 | −0.433504 | − | 0.901152i | \(-0.642723\pi\) | ||||
−0.433504 | + | 0.901152i | \(0.642723\pi\) | |||||||
\(84\) | −3.22794 | −0.352197 | ||||||||
\(85\) | −3.00236 | −0.325652 | ||||||||
\(86\) | −3.75276 | −0.404670 | ||||||||
\(87\) | 22.8476 | 2.44952 | ||||||||
\(88\) | −2.69181 | −0.286948 | ||||||||
\(89\) | 10.1594 | 1.07690 | 0.538449 | − | 0.842658i | \(-0.319010\pi\) | ||||
0.538449 | + | 0.842658i | \(0.319010\pi\) | |||||||
\(90\) | −11.1919 | −1.17973 | ||||||||
\(91\) | 2.34378 | 0.245695 | ||||||||
\(92\) | 5.95775 | 0.621139 | ||||||||
\(93\) | −31.4827 | −3.26461 | ||||||||
\(94\) | −8.78196 | −0.905790 | ||||||||
\(95\) | −4.93080 | −0.505889 | ||||||||
\(96\) | 3.22794 | 0.329450 | ||||||||
\(97\) | −12.8948 | −1.30927 | −0.654637 | − | 0.755944i | \(-0.727178\pi\) | ||||
−0.654637 | + | 0.755944i | \(0.727178\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 19.9721 | 2.00727 | ||||||||
\(100\) | −2.72464 | −0.272464 | ||||||||
\(101\) | −15.7843 | −1.57059 | −0.785297 | − | 0.619119i | \(-0.787490\pi\) | ||||
−0.785297 | + | 0.619119i | \(0.787490\pi\) | |||||||
\(102\) | −6.42486 | −0.636156 | ||||||||
\(103\) | −0.299389 | −0.0294997 | −0.0147498 | − | 0.999891i | \(-0.504695\pi\) | ||||
−0.0147498 | + | 0.999891i | \(0.504695\pi\) | |||||||
\(104\) | −2.34378 | −0.229827 | ||||||||
\(105\) | −4.86911 | −0.475176 | ||||||||
\(106\) | 3.37076 | 0.327397 | ||||||||
\(107\) | −0.402137 | −0.0388760 | −0.0194380 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194380 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(108\) | −14.2661 | −1.37276 | ||||||||
\(109\) | 12.5157 | 1.19878 | 0.599392 | − | 0.800456i | \(-0.295409\pi\) | ||||
0.599392 | + | 0.800456i | \(0.295409\pi\) | |||||||
\(110\) | −4.06040 | −0.387144 | ||||||||
\(111\) | −9.32693 | −0.885273 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 13.0313 | 1.22588 | 0.612941 | − | 0.790129i | \(-0.289986\pi\) | ||||
0.612941 | + | 0.790129i | \(0.289986\pi\) | |||||||
\(114\) | −10.5516 | −0.988247 | ||||||||
\(115\) | 8.98684 | 0.838027 | ||||||||
\(116\) | −7.07809 | −0.657184 | ||||||||
\(117\) | 17.3899 | 1.60769 | ||||||||
\(118\) | 0.771012 | 0.0709774 | ||||||||
\(119\) | −1.99039 | −0.182459 | ||||||||
\(120\) | 4.86911 | 0.444487 | ||||||||
\(121\) | −3.75417 | −0.341288 | ||||||||
\(122\) | −11.1625 | −1.01061 | ||||||||
\(123\) | −26.8696 | −2.42275 | ||||||||
\(124\) | 9.75321 | 0.875864 | ||||||||
\(125\) | −11.6521 | −1.04219 | ||||||||
\(126\) | −7.41957 | −0.660988 | ||||||||
\(127\) | −7.23989 | −0.642436 | −0.321218 | − | 0.947005i | \(-0.604092\pi\) | ||||
−0.321218 | + | 0.947005i | \(0.604092\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.1137 | −1.06655 | ||||||||
\(130\) | −3.53543 | −0.310077 | ||||||||
\(131\) | −4.12405 | −0.360320 | −0.180160 | − | 0.983637i | \(-0.557662\pi\) | ||||
−0.180160 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(132\) | −8.68898 | −0.756279 | ||||||||
\(133\) | −3.26883 | −0.283444 | ||||||||
\(134\) | 1.49141 | 0.128838 | ||||||||
\(135\) | −21.5194 | −1.85209 | ||||||||
\(136\) | 1.99039 | 0.170675 | ||||||||
\(137\) | −3.14143 | −0.268390 | −0.134195 | − | 0.990955i | \(-0.542845\pi\) | ||||
−0.134195 | + | 0.990955i | \(0.542845\pi\) | |||||||
\(138\) | 19.2312 | 1.63707 | ||||||||
\(139\) | −3.62990 | −0.307884 | −0.153942 | − | 0.988080i | \(-0.549197\pi\) | ||||
−0.153942 | + | 0.988080i | \(0.549197\pi\) | |||||||
\(140\) | 1.50843 | 0.127485 | ||||||||
\(141\) | −28.3476 | −2.38730 | ||||||||
\(142\) | −14.9001 | −1.25039 | ||||||||
\(143\) | 6.30901 | 0.527586 | ||||||||
\(144\) | 7.41957 | 0.618298 | ||||||||
\(145\) | −10.6768 | −0.886659 | ||||||||
\(146\) | 12.1773 | 1.00780 | ||||||||
\(147\) | −3.22794 | −0.266236 | ||||||||
\(148\) | 2.88944 | 0.237511 | ||||||||
\(149\) | 10.4225 | 0.853842 | 0.426921 | − | 0.904289i | \(-0.359598\pi\) | ||||
0.426921 | + | 0.904289i | \(0.359598\pi\) | |||||||
\(150\) | −8.79498 | −0.718107 | ||||||||
\(151\) | 14.6673 | 1.19361 | 0.596804 | − | 0.802387i | \(-0.296437\pi\) | ||||
0.596804 | + | 0.802387i | \(0.296437\pi\) | |||||||
\(152\) | 3.26883 | 0.265137 | ||||||||
\(153\) | −14.7679 | −1.19391 | ||||||||
\(154\) | −2.69181 | −0.216912 | ||||||||
\(155\) | 14.7120 | 1.18170 | ||||||||
\(156\) | −7.56558 | −0.605731 | ||||||||
\(157\) | 7.59333 | 0.606013 | 0.303007 | − | 0.952988i | \(-0.402010\pi\) | ||||
0.303007 | + | 0.952988i | \(0.402010\pi\) | |||||||
\(158\) | −2.71302 | −0.215837 | ||||||||
\(159\) | 10.8806 | 0.862887 | ||||||||
\(160\) | −1.50843 | −0.119252 | ||||||||
\(161\) | 5.95775 | 0.469537 | ||||||||
\(162\) | −23.7914 | −1.86923 | ||||||||
\(163\) | 6.15575 | 0.482155 | 0.241078 | − | 0.970506i | \(-0.422499\pi\) | ||||
0.241078 | + | 0.970506i | \(0.422499\pi\) | |||||||
\(164\) | 8.32408 | 0.650001 | ||||||||
\(165\) | −13.1067 | −1.02036 | ||||||||
\(166\) | 7.89882 | 0.613068 | ||||||||
\(167\) | 13.7924 | 1.06729 | 0.533645 | − | 0.845709i | \(-0.320822\pi\) | ||||
0.533645 | + | 0.845709i | \(0.320822\pi\) | |||||||
\(168\) | 3.22794 | 0.249041 | ||||||||
\(169\) | −7.50669 | −0.577437 | ||||||||
\(170\) | 3.00236 | 0.230271 | ||||||||
\(171\) | −24.2534 | −1.85470 | ||||||||
\(172\) | 3.75276 | 0.286145 | ||||||||
\(173\) | −21.6024 | −1.64240 | −0.821201 | − | 0.570640i | \(-0.806695\pi\) | ||||
−0.821201 | + | 0.570640i | \(0.806695\pi\) | |||||||
\(174\) | −22.8476 | −1.73207 | ||||||||
\(175\) | −2.72464 | −0.205964 | ||||||||
\(176\) | 2.69181 | 0.202903 | ||||||||
\(177\) | 2.48878 | 0.187068 | ||||||||
\(178\) | −10.1594 | −0.761482 | ||||||||
\(179\) | 5.76165 | 0.430646 | 0.215323 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215323 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(180\) | 11.1919 | 0.834194 | ||||||||
\(181\) | −12.1495 | −0.903062 | −0.451531 | − | 0.892255i | \(-0.649122\pi\) | ||||
−0.451531 | + | 0.892255i | \(0.649122\pi\) | |||||||
\(182\) | −2.34378 | −0.173733 | ||||||||
\(183\) | −36.0320 | −2.66356 | ||||||||
\(184\) | −5.95775 | −0.439211 | ||||||||
\(185\) | 4.35851 | 0.320444 | ||||||||
\(186\) | 31.4827 | 2.30843 | ||||||||
\(187\) | −5.35775 | −0.391798 | ||||||||
\(188\) | 8.78196 | 0.640490 | ||||||||
\(189\) | −14.2661 | −1.03771 | ||||||||
\(190\) | 4.93080 | 0.357718 | ||||||||
\(191\) | 3.57067 | 0.258365 | 0.129182 | − | 0.991621i | \(-0.458765\pi\) | ||||
0.129182 | + | 0.991621i | \(0.458765\pi\) | |||||||
\(192\) | −3.22794 | −0.232956 | ||||||||
\(193\) | 1.06836 | 0.0769019 | 0.0384510 | − | 0.999260i | \(-0.487758\pi\) | ||||
0.0384510 | + | 0.999260i | \(0.487758\pi\) | |||||||
\(194\) | 12.8948 | 0.925796 | ||||||||
\(195\) | −11.4121 | −0.817240 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.859221 | 0.0612170 | 0.0306085 | − | 0.999531i | \(-0.490255\pi\) | ||||
0.0306085 | + | 0.999531i | \(0.490255\pi\) | |||||||
\(198\) | −19.9721 | −1.41935 | ||||||||
\(199\) | −1.00002 | −0.0708897 | −0.0354448 | − | 0.999372i | \(-0.511285\pi\) | ||||
−0.0354448 | + | 0.999372i | \(0.511285\pi\) | |||||||
\(200\) | 2.72464 | 0.192661 | ||||||||
\(201\) | 4.81418 | 0.339566 | ||||||||
\(202\) | 15.7843 | 1.11058 | ||||||||
\(203\) | −7.07809 | −0.496784 | ||||||||
\(204\) | 6.42486 | 0.449830 | ||||||||
\(205\) | 12.5563 | 0.876968 | ||||||||
\(206\) | 0.299389 | 0.0208594 | ||||||||
\(207\) | 44.2040 | 3.07239 | ||||||||
\(208\) | 2.34378 | 0.162512 | ||||||||
\(209\) | −8.79907 | −0.608644 | ||||||||
\(210\) | 4.86911 | 0.336001 | ||||||||
\(211\) | 22.3911 | 1.54147 | 0.770733 | − | 0.637158i | \(-0.219890\pi\) | ||||
0.770733 | + | 0.637158i | \(0.219890\pi\) | |||||||
\(212\) | −3.37076 | −0.231504 | ||||||||
\(213\) | −48.0967 | −3.29553 | ||||||||
\(214\) | 0.402137 | 0.0274895 | ||||||||
\(215\) | 5.66076 | 0.386061 | ||||||||
\(216\) | 14.2661 | 0.970685 | ||||||||
\(217\) | 9.75321 | 0.662091 | ||||||||
\(218\) | −12.5157 | −0.847668 | ||||||||
\(219\) | 39.3074 | 2.65615 | ||||||||
\(220\) | 4.06040 | 0.273752 | ||||||||
\(221\) | −4.66504 | −0.313805 | ||||||||
\(222\) | 9.32693 | 0.625983 | ||||||||
\(223\) | −8.48735 | −0.568355 | −0.284178 | − | 0.958772i | \(-0.591721\pi\) | ||||
−0.284178 | + | 0.958772i | \(0.591721\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −20.2157 | −1.34771 | ||||||||
\(226\) | −13.0313 | −0.866829 | ||||||||
\(227\) | 24.5082 | 1.62666 | 0.813332 | − | 0.581800i | \(-0.197651\pi\) | ||||
0.813332 | + | 0.581800i | \(0.197651\pi\) | |||||||
\(228\) | 10.5516 | 0.698796 | ||||||||
\(229\) | −23.2995 | −1.53967 | −0.769837 | − | 0.638241i | \(-0.779662\pi\) | ||||
−0.769837 | + | 0.638241i | \(0.779662\pi\) | |||||||
\(230\) | −8.98684 | −0.592575 | ||||||||
\(231\) | −8.68898 | −0.571693 | ||||||||
\(232\) | 7.07809 | 0.464699 | ||||||||
\(233\) | −0.337960 | −0.0221405 | −0.0110703 | − | 0.999939i | \(-0.503524\pi\) | ||||
−0.0110703 | + | 0.999939i | \(0.503524\pi\) | |||||||
\(234\) | −17.3899 | −1.13681 | ||||||||
\(235\) | 13.2470 | 0.864136 | ||||||||
\(236\) | −0.771012 | −0.0501886 | ||||||||
\(237\) | −8.75747 | −0.568859 | ||||||||
\(238\) | 1.99039 | 0.129018 | ||||||||
\(239\) | −30.5154 | −1.97388 | −0.986940 | − | 0.161088i | \(-0.948500\pi\) | ||||
−0.986940 | + | 0.161088i | \(0.948500\pi\) | |||||||
\(240\) | −4.86911 | −0.314300 | ||||||||
\(241\) | −1.29495 | −0.0834152 | −0.0417076 | − | 0.999130i | \(-0.513280\pi\) | ||||
−0.0417076 | + | 0.999130i | \(0.513280\pi\) | |||||||
\(242\) | 3.75417 | 0.241327 | ||||||||
\(243\) | −33.9987 | −2.18102 | ||||||||
\(244\) | 11.1625 | 0.714609 | ||||||||
\(245\) | 1.50843 | 0.0963699 | ||||||||
\(246\) | 26.8696 | 1.71314 | ||||||||
\(247\) | −7.66143 | −0.487485 | ||||||||
\(248\) | −9.75321 | −0.619329 | ||||||||
\(249\) | 25.4969 | 1.61580 | ||||||||
\(250\) | 11.6521 | 0.736942 | ||||||||
\(251\) | −24.5643 | −1.55048 | −0.775242 | − | 0.631665i | \(-0.782372\pi\) | ||||
−0.775242 | + | 0.631665i | \(0.782372\pi\) | |||||||
\(252\) | 7.41957 | 0.467389 | ||||||||
\(253\) | 16.0371 | 1.00825 | ||||||||
\(254\) | 7.23989 | 0.454271 | ||||||||
\(255\) | 9.69144 | 0.606901 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.1892 | −1.63364 | −0.816819 | − | 0.576894i | \(-0.804264\pi\) | ||||
−0.816819 | + | 0.576894i | \(0.804264\pi\) | |||||||
\(258\) | 12.1137 | 0.754163 | ||||||||
\(259\) | 2.88944 | 0.179541 | ||||||||
\(260\) | 3.53543 | 0.219258 | ||||||||
\(261\) | −52.5164 | −3.25068 | ||||||||
\(262\) | 4.12405 | 0.254785 | ||||||||
\(263\) | 0.277761 | 0.0171275 | 0.00856374 | − | 0.999963i | \(-0.497274\pi\) | ||||
0.00856374 | + | 0.999963i | \(0.497274\pi\) | |||||||
\(264\) | 8.68898 | 0.534770 | ||||||||
\(265\) | −5.08454 | −0.312341 | ||||||||
\(266\) | 3.26883 | 0.200425 | ||||||||
\(267\) | −32.7940 | −2.00696 | ||||||||
\(268\) | −1.49141 | −0.0911025 | ||||||||
\(269\) | 25.1147 | 1.53127 | 0.765634 | − | 0.643276i | \(-0.222425\pi\) | ||||
0.765634 | + | 0.643276i | \(0.222425\pi\) | |||||||
\(270\) | 21.5194 | 1.30963 | ||||||||
\(271\) | −18.0708 | −1.09772 | −0.548862 | − | 0.835913i | \(-0.684939\pi\) | ||||
−0.548862 | + | 0.835913i | \(0.684939\pi\) | |||||||
\(272\) | −1.99039 | −0.120685 | ||||||||
\(273\) | −7.56558 | −0.457890 | ||||||||
\(274\) | 3.14143 | 0.189780 | ||||||||
\(275\) | −7.33422 | −0.442270 | ||||||||
\(276\) | −19.2312 | −1.15758 | ||||||||
\(277\) | 18.3269 | 1.10116 | 0.550580 | − | 0.834783i | \(-0.314407\pi\) | ||||
0.550580 | + | 0.834783i | \(0.314407\pi\) | |||||||
\(278\) | 3.62990 | 0.217707 | ||||||||
\(279\) | 72.3646 | 4.33236 | ||||||||
\(280\) | −1.50843 | −0.0901458 | ||||||||
\(281\) | 11.1314 | 0.664041 | 0.332020 | − | 0.943272i | \(-0.392270\pi\) | ||||
0.332020 | + | 0.943272i | \(0.392270\pi\) | |||||||
\(282\) | 28.3476 | 1.68808 | ||||||||
\(283\) | −16.8138 | −0.999478 | −0.499739 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499739 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(284\) | 14.9001 | 0.884160 | ||||||||
\(285\) | 15.9163 | 0.942801 | ||||||||
\(286\) | −6.30901 | −0.373060 | ||||||||
\(287\) | 8.32408 | 0.491355 | ||||||||
\(288\) | −7.41957 | −0.437203 | ||||||||
\(289\) | −13.0383 | −0.766961 | ||||||||
\(290\) | 10.6768 | 0.626962 | ||||||||
\(291\) | 41.6237 | 2.44003 | ||||||||
\(292\) | −12.1773 | −0.712620 | ||||||||
\(293\) | −12.0673 | −0.704981 | −0.352490 | − | 0.935815i | \(-0.614665\pi\) | ||||
−0.352490 | + | 0.935815i | \(0.614665\pi\) | |||||||
\(294\) | 3.22794 | 0.188257 | ||||||||
\(295\) | −1.16302 | −0.0677134 | ||||||||
\(296\) | −2.88944 | −0.167945 | ||||||||
\(297\) | −38.4016 | −2.22829 | ||||||||
\(298\) | −10.4225 | −0.603758 | ||||||||
\(299\) | 13.9637 | 0.807540 | ||||||||
\(300\) | 8.79498 | 0.507778 | ||||||||
\(301\) | 3.75276 | 0.216305 | ||||||||
\(302\) | −14.6673 | −0.844008 | ||||||||
\(303\) | 50.9506 | 2.92704 | ||||||||
\(304\) | −3.26883 | −0.187480 | ||||||||
\(305\) | 16.8379 | 0.964136 | ||||||||
\(306\) | 14.7679 | 0.844222 | ||||||||
\(307\) | −10.1488 | −0.579221 | −0.289611 | − | 0.957145i | \(-0.593526\pi\) | ||||
−0.289611 | + | 0.957145i | \(0.593526\pi\) | |||||||
\(308\) | 2.69181 | 0.153380 | ||||||||
\(309\) | 0.966408 | 0.0549770 | ||||||||
\(310\) | −14.7120 | −0.835586 | ||||||||
\(311\) | 2.91875 | 0.165507 | 0.0827536 | − | 0.996570i | \(-0.473629\pi\) | ||||
0.0827536 | + | 0.996570i | \(0.473629\pi\) | |||||||
\(312\) | 7.56558 | 0.428317 | ||||||||
\(313\) | 28.3749 | 1.60384 | 0.801921 | − | 0.597430i | \(-0.203812\pi\) | ||||
0.801921 | + | 0.597430i | \(0.203812\pi\) | |||||||
\(314\) | −7.59333 | −0.428516 | ||||||||
\(315\) | 11.1919 | 0.630592 | ||||||||
\(316\) | 2.71302 | 0.152619 | ||||||||
\(317\) | 17.2455 | 0.968606 | 0.484303 | − | 0.874900i | \(-0.339073\pi\) | ||||
0.484303 | + | 0.874900i | \(0.339073\pi\) | |||||||
\(318\) | −10.8806 | −0.610153 | ||||||||
\(319\) | −19.0528 | −1.06675 | ||||||||
\(320\) | 1.50843 | 0.0843237 | ||||||||
\(321\) | 1.29807 | 0.0724513 | ||||||||
\(322\) | −5.95775 | −0.332013 | ||||||||
\(323\) | 6.50626 | 0.362018 | ||||||||
\(324\) | 23.7914 | 1.32174 | ||||||||
\(325\) | −6.38597 | −0.354230 | ||||||||
\(326\) | −6.15575 | −0.340935 | ||||||||
\(327\) | −40.3998 | −2.23411 | ||||||||
\(328\) | −8.32408 | −0.459620 | ||||||||
\(329\) | 8.78196 | 0.484165 | ||||||||
\(330\) | 13.1067 | 0.721501 | ||||||||
\(331\) | 31.9632 | 1.75685 | 0.878427 | − | 0.477877i | \(-0.158593\pi\) | ||||
0.878427 | + | 0.477877i | \(0.158593\pi\) | |||||||
\(332\) | −7.89882 | −0.433504 | ||||||||
\(333\) | 21.4384 | 1.17482 | ||||||||
\(334\) | −13.7924 | −0.754688 | ||||||||
\(335\) | −2.24969 | −0.122914 | ||||||||
\(336\) | −3.22794 | −0.176098 | ||||||||
\(337\) | 18.6668 | 1.01684 | 0.508422 | − | 0.861108i | \(-0.330229\pi\) | ||||
0.508422 | + | 0.861108i | \(0.330229\pi\) | |||||||
\(338\) | 7.50669 | 0.408310 | ||||||||
\(339\) | −42.0642 | −2.28461 | ||||||||
\(340\) | −3.00236 | −0.162826 | ||||||||
\(341\) | 26.2538 | 1.42172 | ||||||||
\(342\) | 24.2534 | 1.31147 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.75276 | −0.202335 | ||||||||
\(345\) | −29.0090 | −1.56179 | ||||||||
\(346\) | 21.6024 | 1.16135 | ||||||||
\(347\) | −10.9018 | −0.585242 | −0.292621 | − | 0.956229i | \(-0.594527\pi\) | ||||
−0.292621 | + | 0.956229i | \(0.594527\pi\) | |||||||
\(348\) | 22.8476 | 1.22476 | ||||||||
\(349\) | −28.8675 | −1.54524 | −0.772622 | − | 0.634866i | \(-0.781055\pi\) | ||||
−0.772622 | + | 0.634866i | \(0.781055\pi\) | |||||||
\(350\) | 2.72464 | 0.145638 | ||||||||
\(351\) | −33.4366 | −1.78472 | ||||||||
\(352\) | −2.69181 | −0.143474 | ||||||||
\(353\) | 15.6173 | 0.831224 | 0.415612 | − | 0.909542i | \(-0.363567\pi\) | ||||
0.415612 | + | 0.909542i | \(0.363567\pi\) | |||||||
\(354\) | −2.48878 | −0.132277 | ||||||||
\(355\) | 22.4758 | 1.19289 | ||||||||
\(356\) | 10.1594 | 0.538449 | ||||||||
\(357\) | 6.42486 | 0.340040 | ||||||||
\(358\) | −5.76165 | −0.304513 | ||||||||
\(359\) | 1.07679 | 0.0568310 | 0.0284155 | − | 0.999596i | \(-0.490954\pi\) | ||||
0.0284155 | + | 0.999596i | \(0.490954\pi\) | |||||||
\(360\) | −11.1919 | −0.589865 | ||||||||
\(361\) | −8.31473 | −0.437617 | ||||||||
\(362\) | 12.1495 | 0.638562 | ||||||||
\(363\) | 12.1182 | 0.636042 | ||||||||
\(364\) | 2.34378 | 0.122848 | ||||||||
\(365\) | −18.3685 | −0.961452 | ||||||||
\(366\) | 36.0320 | 1.88342 | ||||||||
\(367\) | 2.73231 | 0.142625 | 0.0713127 | − | 0.997454i | \(-0.477281\pi\) | ||||
0.0713127 | + | 0.997454i | \(0.477281\pi\) | |||||||
\(368\) | 5.95775 | 0.310569 | ||||||||
\(369\) | 61.7611 | 3.21515 | ||||||||
\(370\) | −4.35851 | −0.226588 | ||||||||
\(371\) | −3.37076 | −0.175001 | ||||||||
\(372\) | −31.4827 | −1.63230 | ||||||||
\(373\) | −31.8728 | −1.65031 | −0.825154 | − | 0.564907i | \(-0.808912\pi\) | ||||
−0.825154 | + | 0.564907i | \(0.808912\pi\) | |||||||
\(374\) | 5.35775 | 0.277043 | ||||||||
\(375\) | 37.6121 | 1.94228 | ||||||||
\(376\) | −8.78196 | −0.452895 | ||||||||
\(377\) | −16.5895 | −0.854402 | ||||||||
\(378\) | 14.2661 | 0.733769 | ||||||||
\(379\) | 33.5657 | 1.72415 | 0.862077 | − | 0.506777i | \(-0.169163\pi\) | ||||
0.862077 | + | 0.506777i | \(0.169163\pi\) | |||||||
\(380\) | −4.93080 | −0.252945 | ||||||||
\(381\) | 23.3699 | 1.19728 | ||||||||
\(382\) | −3.57067 | −0.182692 | ||||||||
\(383\) | 29.1282 | 1.48838 | 0.744190 | − | 0.667968i | \(-0.232836\pi\) | ||||
0.744190 | + | 0.667968i | \(0.232836\pi\) | |||||||
\(384\) | 3.22794 | 0.164725 | ||||||||
\(385\) | 4.06040 | 0.206937 | ||||||||
\(386\) | −1.06836 | −0.0543779 | ||||||||
\(387\) | 27.8438 | 1.41538 | ||||||||
\(388\) | −12.8948 | −0.654637 | ||||||||
\(389\) | 23.5239 | 1.19271 | 0.596355 | − | 0.802721i | \(-0.296615\pi\) | ||||
0.596355 | + | 0.802721i | \(0.296615\pi\) | |||||||
\(390\) | 11.4121 | 0.577876 | ||||||||
\(391\) | −11.8583 | −0.599698 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 13.3122 | 0.671511 | ||||||||
\(394\) | −0.859221 | −0.0432869 | ||||||||
\(395\) | 4.09240 | 0.205911 | ||||||||
\(396\) | 19.9721 | 1.00363 | ||||||||
\(397\) | −19.2102 | −0.964131 | −0.482065 | − | 0.876135i | \(-0.660113\pi\) | ||||
−0.482065 | + | 0.876135i | \(0.660113\pi\) | |||||||
\(398\) | 1.00002 | 0.0501266 | ||||||||
\(399\) | 10.5516 | 0.528240 | ||||||||
\(400\) | −2.72464 | −0.136232 | ||||||||
\(401\) | 28.4563 | 1.42104 | 0.710521 | − | 0.703676i | \(-0.248460\pi\) | ||||
0.710521 | + | 0.703676i | \(0.248460\pi\) | |||||||
\(402\) | −4.81418 | −0.240110 | ||||||||
\(403\) | 22.8594 | 1.13871 | ||||||||
\(404\) | −15.7843 | −0.785297 | ||||||||
\(405\) | 35.8875 | 1.78327 | ||||||||
\(406\) | 7.07809 | 0.351279 | ||||||||
\(407\) | 7.77782 | 0.385532 | ||||||||
\(408\) | −6.42486 | −0.318078 | ||||||||
\(409\) | 30.0035 | 1.48358 | 0.741789 | − | 0.670634i | \(-0.233978\pi\) | ||||
0.741789 | + | 0.670634i | \(0.233978\pi\) | |||||||
\(410\) | −12.5563 | −0.620110 | ||||||||
\(411\) | 10.1403 | 0.500185 | ||||||||
\(412\) | −0.299389 | −0.0147498 | ||||||||
\(413\) | −0.771012 | −0.0379390 | ||||||||
\(414\) | −44.2040 | −2.17251 | ||||||||
\(415\) | −11.9148 | −0.584875 | ||||||||
\(416\) | −2.34378 | −0.114913 | ||||||||
\(417\) | 11.7171 | 0.573788 | ||||||||
\(418\) | 8.79907 | 0.430377 | ||||||||
\(419\) | 8.81082 | 0.430437 | 0.215218 | − | 0.976566i | \(-0.430954\pi\) | ||||
0.215218 | + | 0.976566i | \(0.430954\pi\) | |||||||
\(420\) | −4.86911 | −0.237588 | ||||||||
\(421\) | −12.3383 | −0.601332 | −0.300666 | − | 0.953730i | \(-0.597209\pi\) | ||||
−0.300666 | + | 0.953730i | \(0.597209\pi\) | |||||||
\(422\) | −22.3911 | −1.08998 | ||||||||
\(423\) | 65.1584 | 3.16811 | ||||||||
\(424\) | 3.37076 | 0.163698 | ||||||||
\(425\) | 5.42311 | 0.263059 | ||||||||
\(426\) | 48.0967 | 2.33029 | ||||||||
\(427\) | 11.1625 | 0.540194 | ||||||||
\(428\) | −0.402137 | −0.0194380 | ||||||||
\(429\) | −20.3651 | −0.983236 | ||||||||
\(430\) | −5.66076 | −0.272986 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −14.2661 | −0.686378 | ||||||||
\(433\) | −33.2119 | −1.59606 | −0.798032 | − | 0.602615i | \(-0.794125\pi\) | ||||
−0.798032 | + | 0.602615i | \(0.794125\pi\) | |||||||
\(434\) | −9.75321 | −0.468169 | ||||||||
\(435\) | 34.4640 | 1.65242 | ||||||||
\(436\) | 12.5157 | 0.599392 | ||||||||
\(437\) | −19.4749 | −0.931611 | ||||||||
\(438\) | −39.3074 | −1.87818 | ||||||||
\(439\) | 32.5701 | 1.55448 | 0.777242 | − | 0.629202i | \(-0.216618\pi\) | ||||
0.777242 | + | 0.629202i | \(0.216618\pi\) | |||||||
\(440\) | −4.06040 | −0.193572 | ||||||||
\(441\) | 7.41957 | 0.353313 | ||||||||
\(442\) | 4.66504 | 0.221894 | ||||||||
\(443\) | 13.5122 | 0.641983 | 0.320992 | − | 0.947082i | \(-0.395984\pi\) | ||||
0.320992 | + | 0.947082i | \(0.395984\pi\) | |||||||
\(444\) | −9.32693 | −0.442636 | ||||||||
\(445\) | 15.3248 | 0.726465 | ||||||||
\(446\) | 8.48735 | 0.401888 | ||||||||
\(447\) | −33.6431 | −1.59126 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −35.3651 | −1.66898 | −0.834491 | − | 0.551022i | \(-0.814238\pi\) | ||||
−0.834491 | + | 0.551022i | \(0.814238\pi\) | |||||||
\(450\) | 20.2157 | 0.952977 | ||||||||
\(451\) | 22.4068 | 1.05510 | ||||||||
\(452\) | 13.0313 | 0.612941 | ||||||||
\(453\) | −47.3451 | −2.22447 | ||||||||
\(454\) | −24.5082 | −1.15023 | ||||||||
\(455\) | 3.53543 | 0.165743 | ||||||||
\(456\) | −10.5516 | −0.494123 | ||||||||
\(457\) | 17.9663 | 0.840429 | 0.420214 | − | 0.907425i | \(-0.361955\pi\) | ||||
0.420214 | + | 0.907425i | \(0.361955\pi\) | |||||||
\(458\) | 23.2995 | 1.08871 | ||||||||
\(459\) | 28.3951 | 1.32537 | ||||||||
\(460\) | 8.98684 | 0.419014 | ||||||||
\(461\) | 4.93636 | 0.229909 | 0.114954 | − | 0.993371i | \(-0.463328\pi\) | ||||
0.114954 | + | 0.993371i | \(0.463328\pi\) | |||||||
\(462\) | 8.68898 | 0.404248 | ||||||||
\(463\) | −26.3298 | −1.22365 | −0.611824 | − | 0.790994i | \(-0.709564\pi\) | ||||
−0.611824 | + | 0.790994i | \(0.709564\pi\) | |||||||
\(464\) | −7.07809 | −0.328592 | ||||||||
\(465\) | −47.4894 | −2.20227 | ||||||||
\(466\) | 0.337960 | 0.0156557 | ||||||||
\(467\) | −16.2673 | −0.752763 | −0.376381 | − | 0.926465i | \(-0.622832\pi\) | ||||
−0.376381 | + | 0.926465i | \(0.622832\pi\) | |||||||
\(468\) | 17.3899 | 0.803847 | ||||||||
\(469\) | −1.49141 | −0.0688670 | ||||||||
\(470\) | −13.2470 | −0.611036 | ||||||||
\(471\) | −24.5108 | −1.12940 | ||||||||
\(472\) | 0.771012 | 0.0354887 | ||||||||
\(473\) | 10.1017 | 0.464477 | ||||||||
\(474\) | 8.75747 | 0.402244 | ||||||||
\(475\) | 8.90641 | 0.408654 | ||||||||
\(476\) | −1.99039 | −0.0912295 | ||||||||
\(477\) | −25.0096 | −1.14511 | ||||||||
\(478\) | 30.5154 | 1.39574 | ||||||||
\(479\) | −21.2767 | −0.972156 | −0.486078 | − | 0.873915i | \(-0.661573\pi\) | ||||
−0.486078 | + | 0.873915i | \(0.661573\pi\) | |||||||
\(480\) | 4.86911 | 0.222243 | ||||||||
\(481\) | 6.77222 | 0.308787 | ||||||||
\(482\) | 1.29495 | 0.0589835 | ||||||||
\(483\) | −19.2312 | −0.875052 | ||||||||
\(484\) | −3.75417 | −0.170644 | ||||||||
\(485\) | −19.4509 | −0.883222 | ||||||||
\(486\) | 33.9987 | 1.54221 | ||||||||
\(487\) | 5.98714 | 0.271303 | 0.135652 | − | 0.990757i | \(-0.456687\pi\) | ||||
0.135652 | + | 0.990757i | \(0.456687\pi\) | |||||||
\(488\) | −11.1625 | −0.505305 | ||||||||
\(489\) | −19.8704 | −0.898569 | ||||||||
\(490\) | −1.50843 | −0.0681438 | ||||||||
\(491\) | 36.4413 | 1.64457 | 0.822286 | − | 0.569075i | \(-0.192699\pi\) | ||||
0.822286 | + | 0.569075i | \(0.192699\pi\) | |||||||
\(492\) | −26.8696 | −1.21137 | ||||||||
\(493\) | 14.0882 | 0.634499 | ||||||||
\(494\) | 7.66143 | 0.344704 | ||||||||
\(495\) | 30.1264 | 1.35408 | ||||||||
\(496\) | 9.75321 | 0.437932 | ||||||||
\(497\) | 14.9001 | 0.668362 | ||||||||
\(498\) | −25.4969 | −1.14254 | ||||||||
\(499\) | 6.63243 | 0.296908 | 0.148454 | − | 0.988919i | \(-0.452570\pi\) | ||||
0.148454 | + | 0.988919i | \(0.452570\pi\) | |||||||
\(500\) | −11.6521 | −0.521096 | ||||||||
\(501\) | −44.5211 | −1.98905 | ||||||||
\(502\) | 24.5643 | 1.09636 | ||||||||
\(503\) | 42.5396 | 1.89675 | 0.948373 | − | 0.317156i | \(-0.102728\pi\) | ||||
0.948373 | + | 0.317156i | \(0.102728\pi\) | |||||||
\(504\) | −7.41957 | −0.330494 | ||||||||
\(505\) | −23.8094 | −1.05951 | ||||||||
\(506\) | −16.0371 | −0.712937 | ||||||||
\(507\) | 24.2311 | 1.07614 | ||||||||
\(508\) | −7.23989 | −0.321218 | ||||||||
\(509\) | −7.20298 | −0.319266 | −0.159633 | − | 0.987176i | \(-0.551031\pi\) | ||||
−0.159633 | + | 0.987176i | \(0.551031\pi\) | |||||||
\(510\) | −9.69144 | −0.429144 | ||||||||
\(511\) | −12.1773 | −0.538690 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 46.6335 | 2.05892 | ||||||||
\(514\) | 26.1892 | 1.15516 | ||||||||
\(515\) | −0.451607 | −0.0199002 | ||||||||
\(516\) | −12.1137 | −0.533274 | ||||||||
\(517\) | 23.6393 | 1.03966 | ||||||||
\(518\) | −2.88944 | −0.126955 | ||||||||
\(519\) | 69.7312 | 3.06086 | ||||||||
\(520\) | −3.53543 | −0.155039 | ||||||||
\(521\) | 24.9797 | 1.09438 | 0.547190 | − | 0.837009i | \(-0.315698\pi\) | ||||
0.547190 | + | 0.837009i | \(0.315698\pi\) | |||||||
\(522\) | 52.5164 | 2.29858 | ||||||||
\(523\) | 2.44361 | 0.106852 | 0.0534258 | − | 0.998572i | \(-0.482986\pi\) | ||||
0.0534258 | + | 0.998572i | \(0.482986\pi\) | |||||||
\(524\) | −4.12405 | −0.180160 | ||||||||
\(525\) | 8.79498 | 0.383844 | ||||||||
\(526\) | −0.277761 | −0.0121110 | ||||||||
\(527\) | −19.4127 | −0.845631 | ||||||||
\(528\) | −8.68898 | −0.378140 | ||||||||
\(529\) | 12.4948 | 0.543253 | ||||||||
\(530\) | 5.08454 | 0.220858 | ||||||||
\(531\) | −5.72058 | −0.248252 | ||||||||
\(532\) | −3.26883 | −0.141722 | ||||||||
\(533\) | 19.5098 | 0.845064 | ||||||||
\(534\) | 32.7940 | 1.41914 | ||||||||
\(535\) | −0.606595 | −0.0262254 | ||||||||
\(536\) | 1.49141 | 0.0644192 | ||||||||
\(537\) | −18.5982 | −0.802574 | ||||||||
\(538\) | −25.1147 | −1.08277 | ||||||||
\(539\) | 2.69181 | 0.115944 | ||||||||
\(540\) | −21.5194 | −0.926047 | ||||||||
\(541\) | −34.0698 | −1.46478 | −0.732388 | − | 0.680887i | \(-0.761594\pi\) | ||||
−0.732388 | + | 0.680887i | \(0.761594\pi\) | |||||||
\(542\) | 18.0708 | 0.776208 | ||||||||
\(543\) | 39.2177 | 1.68299 | ||||||||
\(544\) | 1.99039 | 0.0853373 | ||||||||
\(545\) | 18.8790 | 0.808687 | ||||||||
\(546\) | 7.56558 | 0.323777 | ||||||||
\(547\) | 9.86277 | 0.421702 | 0.210851 | − | 0.977518i | \(-0.432377\pi\) | ||||
0.210851 | + | 0.977518i | \(0.432377\pi\) | |||||||
\(548\) | −3.14143 | −0.134195 | ||||||||
\(549\) | 82.8214 | 3.53473 | ||||||||
\(550\) | 7.33422 | 0.312732 | ||||||||
\(551\) | 23.1371 | 0.985673 | ||||||||
\(552\) | 19.2312 | 0.818536 | ||||||||
\(553\) | 2.71302 | 0.115369 | ||||||||
\(554\) | −18.3269 | −0.778637 | ||||||||
\(555\) | −14.0690 | −0.597196 | ||||||||
\(556\) | −3.62990 | −0.153942 | ||||||||
\(557\) | 8.01471 | 0.339594 | 0.169797 | − | 0.985479i | \(-0.445689\pi\) | ||||
0.169797 | + | 0.985479i | \(0.445689\pi\) | |||||||
\(558\) | −72.3646 | −3.06344 | ||||||||
\(559\) | 8.79564 | 0.372016 | ||||||||
\(560\) | 1.50843 | 0.0637427 | ||||||||
\(561\) | 17.2945 | 0.730174 | ||||||||
\(562\) | −11.1314 | −0.469548 | ||||||||
\(563\) | −41.3772 | −1.74384 | −0.871920 | − | 0.489648i | \(-0.837125\pi\) | ||||
−0.871920 | + | 0.489648i | \(0.837125\pi\) | |||||||
\(564\) | −28.3476 | −1.19365 | ||||||||
\(565\) | 19.6568 | 0.826967 | ||||||||
\(566\) | 16.8138 | 0.706738 | ||||||||
\(567\) | 23.7914 | 0.999143 | ||||||||
\(568\) | −14.9001 | −0.625195 | ||||||||
\(569\) | 19.7446 | 0.827736 | 0.413868 | − | 0.910337i | \(-0.364178\pi\) | ||||
0.413868 | + | 0.910337i | \(0.364178\pi\) | |||||||
\(570\) | −15.9163 | −0.666661 | ||||||||
\(571\) | 17.1819 | 0.719042 | 0.359521 | − | 0.933137i | \(-0.382940\pi\) | ||||
0.359521 | + | 0.933137i | \(0.382940\pi\) | |||||||
\(572\) | 6.30901 | 0.263793 | ||||||||
\(573\) | −11.5259 | −0.481502 | ||||||||
\(574\) | −8.32408 | −0.347440 | ||||||||
\(575\) | −16.2328 | −0.676953 | ||||||||
\(576\) | 7.41957 | 0.309149 | ||||||||
\(577\) | 27.5181 | 1.14559 | 0.572797 | − | 0.819697i | \(-0.305858\pi\) | ||||
0.572797 | + | 0.819697i | \(0.305858\pi\) | |||||||
\(578\) | 13.0383 | 0.542323 | ||||||||
\(579\) | −3.44858 | −0.143318 | ||||||||
\(580\) | −10.6768 | −0.443329 | ||||||||
\(581\) | −7.89882 | −0.327698 | ||||||||
\(582\) | −41.6237 | −1.72536 | ||||||||
\(583\) | −9.07343 | −0.375783 | ||||||||
\(584\) | 12.1773 | 0.503898 | ||||||||
\(585\) | 26.2314 | 1.08453 | ||||||||
\(586\) | 12.0673 | 0.498497 | ||||||||
\(587\) | 17.8475 | 0.736646 | 0.368323 | − | 0.929698i | \(-0.379932\pi\) | ||||
0.368323 | + | 0.929698i | \(0.379932\pi\) | |||||||
\(588\) | −3.22794 | −0.133118 | ||||||||
\(589\) | −31.8816 | −1.31366 | ||||||||
\(590\) | 1.16302 | 0.0478806 | ||||||||
\(591\) | −2.77351 | −0.114087 | ||||||||
\(592\) | 2.88944 | 0.118755 | ||||||||
\(593\) | −31.4173 | −1.29015 | −0.645077 | − | 0.764117i | \(-0.723175\pi\) | ||||
−0.645077 | + | 0.764117i | \(0.723175\pi\) | |||||||
\(594\) | 38.4016 | 1.57564 | ||||||||
\(595\) | −3.00236 | −0.123085 | ||||||||
\(596\) | 10.4225 | 0.426921 | ||||||||
\(597\) | 3.22801 | 0.132114 | ||||||||
\(598\) | −13.9637 | −0.571017 | ||||||||
\(599\) | 40.9431 | 1.67289 | 0.836445 | − | 0.548051i | \(-0.184630\pi\) | ||||
0.836445 | + | 0.548051i | \(0.184630\pi\) | |||||||
\(600\) | −8.79498 | −0.359054 | ||||||||
\(601\) | −11.0768 | −0.451832 | −0.225916 | − | 0.974147i | \(-0.572538\pi\) | ||||
−0.225916 | + | 0.974147i | \(0.572538\pi\) | |||||||
\(602\) | −3.75276 | −0.152951 | ||||||||
\(603\) | −11.0656 | −0.450628 | ||||||||
\(604\) | 14.6673 | 0.596804 | ||||||||
\(605\) | −5.66290 | −0.230230 | ||||||||
\(606\) | −50.9506 | −2.06973 | ||||||||
\(607\) | −9.89165 | −0.401490 | −0.200745 | − | 0.979644i | \(-0.564336\pi\) | ||||
−0.200745 | + | 0.979644i | \(0.564336\pi\) | |||||||
\(608\) | 3.26883 | 0.132569 | ||||||||
\(609\) | 22.8476 | 0.925832 | ||||||||
\(610\) | −16.8379 | −0.681747 | ||||||||
\(611\) | 20.5830 | 0.832699 | ||||||||
\(612\) | −14.7679 | −0.596955 | ||||||||
\(613\) | 4.41319 | 0.178247 | 0.0891235 | − | 0.996021i | \(-0.471593\pi\) | ||||
0.0891235 | + | 0.996021i | \(0.471593\pi\) | |||||||
\(614\) | 10.1488 | 0.409571 | ||||||||
\(615\) | −40.5308 | −1.63436 | ||||||||
\(616\) | −2.69181 | −0.108456 | ||||||||
\(617\) | −19.5141 | −0.785606 | −0.392803 | − | 0.919623i | \(-0.628495\pi\) | ||||
−0.392803 | + | 0.919623i | \(0.628495\pi\) | |||||||
\(618\) | −0.966408 | −0.0388746 | ||||||||
\(619\) | −15.0744 | −0.605892 | −0.302946 | − | 0.953008i | \(-0.597970\pi\) | ||||
−0.302946 | + | 0.953008i | \(0.597970\pi\) | |||||||
\(620\) | 14.7120 | 0.590849 | ||||||||
\(621\) | −84.9939 | −3.41069 | ||||||||
\(622\) | −2.91875 | −0.117031 | ||||||||
\(623\) | 10.1594 | 0.407029 | ||||||||
\(624\) | −7.56558 | −0.302866 | ||||||||
\(625\) | −3.95309 | −0.158123 | ||||||||
\(626\) | −28.3749 | −1.13409 | ||||||||
\(627\) | 28.4028 | 1.13430 | ||||||||
\(628\) | 7.59333 | 0.303007 | ||||||||
\(629\) | −5.75112 | −0.229312 | ||||||||
\(630\) | −11.1919 | −0.445896 | ||||||||
\(631\) | −19.6002 | −0.780273 | −0.390136 | − | 0.920757i | \(-0.627572\pi\) | ||||
−0.390136 | + | 0.920757i | \(0.627572\pi\) | |||||||
\(632\) | −2.71302 | −0.107918 | ||||||||
\(633\) | −72.2770 | −2.87275 | ||||||||
\(634\) | −17.2455 | −0.684908 | ||||||||
\(635\) | −10.9209 | −0.433381 | ||||||||
\(636\) | 10.8806 | 0.431443 | ||||||||
\(637\) | 2.34378 | 0.0928640 | ||||||||
\(638\) | 19.0528 | 0.754309 | ||||||||
\(639\) | 110.553 | 4.37339 | ||||||||
\(640\) | −1.50843 | −0.0596259 | ||||||||
\(641\) | 21.8799 | 0.864203 | 0.432102 | − | 0.901825i | \(-0.357772\pi\) | ||||
0.432102 | + | 0.901825i | \(0.357772\pi\) | |||||||
\(642\) | −1.29807 | −0.0512308 | ||||||||
\(643\) | −8.12830 | −0.320549 | −0.160274 | − | 0.987072i | \(-0.551238\pi\) | ||||
−0.160274 | + | 0.987072i | \(0.551238\pi\) | |||||||
\(644\) | 5.95775 | 0.234768 | ||||||||
\(645\) | −18.2726 | −0.719482 | ||||||||
\(646\) | −6.50626 | −0.255985 | ||||||||
\(647\) | −21.1450 | −0.831295 | −0.415648 | − | 0.909526i | \(-0.636445\pi\) | ||||
−0.415648 | + | 0.909526i | \(0.636445\pi\) | |||||||
\(648\) | −23.7914 | −0.934613 | ||||||||
\(649\) | −2.07542 | −0.0814672 | ||||||||
\(650\) | 6.38597 | 0.250478 | ||||||||
\(651\) | −31.4827 | −1.23391 | ||||||||
\(652\) | 6.15575 | 0.241078 | ||||||||
\(653\) | 22.3846 | 0.875979 | 0.437989 | − | 0.898980i | \(-0.355691\pi\) | ||||
0.437989 | + | 0.898980i | \(0.355691\pi\) | |||||||
\(654\) | 40.3998 | 1.57976 | ||||||||
\(655\) | −6.22084 | −0.243068 | ||||||||
\(656\) | 8.32408 | 0.325001 | ||||||||
\(657\) | −90.3500 | −3.52489 | ||||||||
\(658\) | −8.78196 | −0.342356 | ||||||||
\(659\) | 24.2136 | 0.943228 | 0.471614 | − | 0.881805i | \(-0.343671\pi\) | ||||
0.471614 | + | 0.881805i | \(0.343671\pi\) | |||||||
\(660\) | −13.1067 | −0.510178 | ||||||||
\(661\) | 29.3944 | 1.14331 | 0.571656 | − | 0.820494i | \(-0.306301\pi\) | ||||
0.571656 | + | 0.820494i | \(0.306301\pi\) | |||||||
\(662\) | −31.9632 | −1.24228 | ||||||||
\(663\) | 15.0585 | 0.584822 | ||||||||
\(664\) | 7.89882 | 0.306534 | ||||||||
\(665\) | −4.93080 | −0.191208 | ||||||||
\(666\) | −21.4384 | −0.830722 | ||||||||
\(667\) | −42.1695 | −1.63281 | ||||||||
\(668\) | 13.7924 | 0.533645 | ||||||||
\(669\) | 27.3966 | 1.05922 | ||||||||
\(670\) | 2.24969 | 0.0869130 | ||||||||
\(671\) | 30.0474 | 1.15997 | ||||||||
\(672\) | 3.22794 | 0.124520 | ||||||||
\(673\) | −43.0873 | −1.66089 | −0.830446 | − | 0.557099i | \(-0.811914\pi\) | ||||
−0.830446 | + | 0.557099i | \(0.811914\pi\) | |||||||
\(674\) | −18.6668 | −0.719017 | ||||||||
\(675\) | 38.8701 | 1.49611 | ||||||||
\(676\) | −7.50669 | −0.288719 | ||||||||
\(677\) | −22.7507 | −0.874382 | −0.437191 | − | 0.899369i | \(-0.644027\pi\) | ||||
−0.437191 | + | 0.899369i | \(0.644027\pi\) | |||||||
\(678\) | 42.0642 | 1.61547 | ||||||||
\(679\) | −12.8948 | −0.494859 | ||||||||
\(680\) | 3.00236 | 0.115135 | ||||||||
\(681\) | −79.1108 | −3.03153 | ||||||||
\(682\) | −26.2538 | −1.00531 | ||||||||
\(683\) | 20.4017 | 0.780648 | 0.390324 | − | 0.920678i | \(-0.372363\pi\) | ||||
0.390324 | + | 0.920678i | \(0.372363\pi\) | |||||||
\(684\) | −24.2534 | −0.927350 | ||||||||
\(685\) | −4.73861 | −0.181053 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 75.2093 | 2.86941 | ||||||||
\(688\) | 3.75276 | 0.143072 | ||||||||
\(689\) | −7.90032 | −0.300978 | ||||||||
\(690\) | 29.0090 | 1.10435 | ||||||||
\(691\) | 10.7276 | 0.408096 | 0.204048 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204048 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(692\) | −21.6024 | −0.821201 | ||||||||
\(693\) | 19.9721 | 0.758676 | ||||||||
\(694\) | 10.9018 | 0.413829 | ||||||||
\(695\) | −5.47544 | −0.207695 | ||||||||
\(696\) | −22.8476 | −0.866036 | ||||||||
\(697\) | −16.5682 | −0.627564 | ||||||||
\(698\) | 28.8675 | 1.09265 | ||||||||
\(699\) | 1.09091 | 0.0412621 | ||||||||
\(700\) | −2.72464 | −0.102982 | ||||||||
\(701\) | 44.5397 | 1.68224 | 0.841121 | − | 0.540847i | \(-0.181896\pi\) | ||||
0.841121 | + | 0.540847i | \(0.181896\pi\) | |||||||
\(702\) | 33.4366 | 1.26198 | ||||||||
\(703\) | −9.44510 | −0.356229 | ||||||||
\(704\) | 2.69181 | 0.101451 | ||||||||
\(705\) | −42.7603 | −1.61045 | ||||||||
\(706\) | −15.6173 | −0.587764 | ||||||||
\(707\) | −15.7843 | −0.593629 | ||||||||
\(708\) | 2.48878 | 0.0935340 | ||||||||
\(709\) | −4.98936 | −0.187379 | −0.0936896 | − | 0.995601i | \(-0.529866\pi\) | ||||
−0.0936896 | + | 0.995601i | \(0.529866\pi\) | |||||||
\(710\) | −22.4758 | −0.843501 | ||||||||
\(711\) | 20.1295 | 0.754914 | ||||||||
\(712\) | −10.1594 | −0.380741 | ||||||||
\(713\) | 58.1072 | 2.17613 | ||||||||
\(714\) | −6.42486 | −0.240444 | ||||||||
\(715\) | 9.51669 | 0.355904 | ||||||||
\(716\) | 5.76165 | 0.215323 | ||||||||
\(717\) | 98.5019 | 3.67862 | ||||||||
\(718\) | −1.07679 | −0.0401856 | ||||||||
\(719\) | −10.0762 | −0.375778 | −0.187889 | − | 0.982190i | \(-0.560164\pi\) | ||||
−0.187889 | + | 0.982190i | \(0.560164\pi\) | |||||||
\(720\) | 11.1919 | 0.417097 | ||||||||
\(721\) | −0.299389 | −0.0111498 | ||||||||
\(722\) | 8.31473 | 0.309442 | ||||||||
\(723\) | 4.18002 | 0.155457 | ||||||||
\(724\) | −12.1495 | −0.451531 | ||||||||
\(725\) | 19.2853 | 0.716237 | ||||||||
\(726\) | −12.1182 | −0.449750 | ||||||||
\(727\) | −11.9306 | −0.442482 | −0.221241 | − | 0.975219i | \(-0.571011\pi\) | ||||
−0.221241 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(728\) | −2.34378 | −0.0868663 | ||||||||
\(729\) | 38.3715 | 1.42117 | ||||||||
\(730\) | 18.3685 | 0.679849 | ||||||||
\(731\) | −7.46945 | −0.276268 | ||||||||
\(732\) | −36.0320 | −1.33178 | ||||||||
\(733\) | 30.7298 | 1.13503 | 0.567516 | − | 0.823363i | \(-0.307905\pi\) | ||||
0.567516 | + | 0.823363i | \(0.307905\pi\) | |||||||
\(734\) | −2.73231 | −0.100851 | ||||||||
\(735\) | −4.86911 | −0.179600 | ||||||||
\(736\) | −5.95775 | −0.219606 | ||||||||
\(737\) | −4.01459 | −0.147879 | ||||||||
\(738\) | −61.7611 | −2.27346 | ||||||||
\(739\) | −15.7916 | −0.580902 | −0.290451 | − | 0.956890i | \(-0.593805\pi\) | ||||
−0.290451 | + | 0.956890i | \(0.593805\pi\) | |||||||
\(740\) | 4.35851 | 0.160222 | ||||||||
\(741\) | 24.7306 | 0.908502 | ||||||||
\(742\) | 3.37076 | 0.123744 | ||||||||
\(743\) | 19.9736 | 0.732760 | 0.366380 | − | 0.930465i | \(-0.380597\pi\) | ||||
0.366380 | + | 0.930465i | \(0.380597\pi\) | |||||||
\(744\) | 31.4827 | 1.15421 | ||||||||
\(745\) | 15.7216 | 0.575993 | ||||||||
\(746\) | 31.8728 | 1.16694 | ||||||||
\(747\) | −58.6059 | −2.14428 | ||||||||
\(748\) | −5.35775 | −0.195899 | ||||||||
\(749\) | −0.402137 | −0.0146938 | ||||||||
\(750\) | −37.6121 | −1.37340 | ||||||||
\(751\) | −3.13621 | −0.114442 | −0.0572210 | − | 0.998362i | \(-0.518224\pi\) | ||||
−0.0572210 | + | 0.998362i | \(0.518224\pi\) | |||||||
\(752\) | 8.78196 | 0.320245 | ||||||||
\(753\) | 79.2919 | 2.88956 | ||||||||
\(754\) | 16.5895 | 0.604154 | ||||||||
\(755\) | 22.1246 | 0.805195 | ||||||||
\(756\) | −14.2661 | −0.518853 | ||||||||
\(757\) | −13.0861 | −0.475624 | −0.237812 | − | 0.971311i | \(-0.576430\pi\) | ||||
−0.237812 | + | 0.971311i | \(0.576430\pi\) | |||||||
\(758\) | −33.5657 | −1.21916 | ||||||||
\(759\) | −51.7668 | −1.87902 | ||||||||
\(760\) | 4.93080 | 0.178859 | ||||||||
\(761\) | 20.9009 | 0.757658 | 0.378829 | − | 0.925467i | \(-0.376327\pi\) | ||||
0.378829 | + | 0.925467i | \(0.376327\pi\) | |||||||
\(762\) | −23.3699 | −0.846602 | ||||||||
\(763\) | 12.5157 | 0.453098 | ||||||||
\(764\) | 3.57067 | 0.129182 | ||||||||
\(765\) | −22.2763 | −0.805400 | ||||||||
\(766\) | −29.1282 | −1.05244 | ||||||||
\(767\) | −1.80708 | −0.0652500 | ||||||||
\(768\) | −3.22794 | −0.116478 | ||||||||
\(769\) | 15.3750 | 0.554436 | 0.277218 | − | 0.960807i | \(-0.410588\pi\) | ||||
0.277218 | + | 0.960807i | \(0.410588\pi\) | |||||||
\(770\) | −4.06040 | −0.146327 | ||||||||
\(771\) | 84.5371 | 3.04453 | ||||||||
\(772\) | 1.06836 | 0.0384510 | ||||||||
\(773\) | −0.368057 | −0.0132381 | −0.00661905 | − | 0.999978i | \(-0.502107\pi\) | ||||
−0.00661905 | + | 0.999978i | \(0.502107\pi\) | |||||||
\(774\) | −27.8438 | −1.00083 | ||||||||
\(775\) | −26.5740 | −0.954567 | ||||||||
\(776\) | 12.8948 | 0.462898 | ||||||||
\(777\) | −9.32693 | −0.334602 | ||||||||
\(778\) | −23.5239 | −0.843373 | ||||||||
\(779\) | −27.2100 | −0.974900 | ||||||||
\(780\) | −11.4121 | −0.408620 | ||||||||
\(781\) | 40.1083 | 1.43519 | ||||||||
\(782\) | 11.8583 | 0.424051 | ||||||||
\(783\) | 100.977 | 3.60861 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 11.4540 | 0.408810 | ||||||||
\(786\) | −13.3122 | −0.474830 | ||||||||
\(787\) | 17.1667 | 0.611928 | 0.305964 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305964 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(788\) | 0.859221 | 0.0306085 | ||||||||
\(789\) | −0.896595 | −0.0319196 | ||||||||
\(790\) | −4.09240 | −0.145601 | ||||||||
\(791\) | 13.0313 | 0.463340 | ||||||||
\(792\) | −19.9721 | −0.709676 | ||||||||
\(793\) | 26.1626 | 0.929061 | ||||||||
\(794\) | 19.2102 | 0.681744 | ||||||||
\(795\) | 16.4126 | 0.582094 | ||||||||
\(796\) | −1.00002 | −0.0354448 | ||||||||
\(797\) | 45.2551 | 1.60302 | 0.801508 | − | 0.597984i | \(-0.204031\pi\) | ||||
0.801508 | + | 0.597984i | \(0.204031\pi\) | |||||||
\(798\) | −10.5516 | −0.373522 | ||||||||
\(799\) | −17.4795 | −0.618382 | ||||||||
\(800\) | 2.72464 | 0.0963307 | ||||||||
\(801\) | 75.3787 | 2.66338 | ||||||||
\(802\) | −28.4563 | −1.00483 | ||||||||
\(803\) | −32.7788 | −1.15674 | ||||||||
\(804\) | 4.81418 | 0.169783 | ||||||||
\(805\) | 8.98684 | 0.316745 | ||||||||
\(806\) | −22.8594 | −0.805188 | ||||||||
\(807\) | −81.0686 | −2.85375 | ||||||||
\(808\) | 15.7843 | 0.555289 | ||||||||
\(809\) | 6.78879 | 0.238681 | 0.119341 | − | 0.992853i | \(-0.461922\pi\) | ||||
0.119341 | + | 0.992853i | \(0.461922\pi\) | |||||||
\(810\) | −35.8875 | −1.26096 | ||||||||
\(811\) | −0.0664774 | −0.00233434 | −0.00116717 | − | 0.999999i | \(-0.500372\pi\) | ||||
−0.00116717 | + | 0.999999i | \(0.500372\pi\) | |||||||
\(812\) | −7.07809 | −0.248392 | ||||||||
\(813\) | 58.3314 | 2.04577 | ||||||||
\(814\) | −7.77782 | −0.272612 | ||||||||
\(815\) | 9.28550 | 0.325257 | ||||||||
\(816\) | 6.42486 | 0.224915 | ||||||||
\(817\) | −12.2671 | −0.429173 | ||||||||
\(818\) | −30.0035 | −1.04905 | ||||||||
\(819\) | 17.3899 | 0.607651 | ||||||||
\(820\) | 12.5563 | 0.438484 | ||||||||
\(821\) | 6.30860 | 0.220172 | 0.110086 | − | 0.993922i | \(-0.464887\pi\) | ||||
0.110086 | + | 0.993922i | \(0.464887\pi\) | |||||||
\(822\) | −10.1403 | −0.353684 | ||||||||
\(823\) | −12.2833 | −0.428169 | −0.214084 | − | 0.976815i | \(-0.568677\pi\) | ||||
−0.214084 | + | 0.976815i | \(0.568677\pi\) | |||||||
\(824\) | 0.299389 | 0.0104297 | ||||||||
\(825\) | 23.6744 | 0.824237 | ||||||||
\(826\) | 0.771012 | 0.0268269 | ||||||||
\(827\) | −20.1290 | −0.699954 | −0.349977 | − | 0.936758i | \(-0.613811\pi\) | ||||
−0.349977 | + | 0.936758i | \(0.613811\pi\) | |||||||
\(828\) | 44.2040 | 1.53619 | ||||||||
\(829\) | −16.0295 | −0.556728 | −0.278364 | − | 0.960476i | \(-0.589792\pi\) | ||||
−0.278364 | + | 0.960476i | \(0.589792\pi\) | |||||||
\(830\) | 11.9148 | 0.413569 | ||||||||
\(831\) | −59.1582 | −2.05218 | ||||||||
\(832\) | 2.34378 | 0.0812560 | ||||||||
\(833\) | −1.99039 | −0.0689630 | ||||||||
\(834\) | −11.7171 | −0.405730 | ||||||||
\(835\) | 20.8049 | 0.719982 | ||||||||
\(836\) | −8.79907 | −0.304322 | ||||||||
\(837\) | −139.140 | −4.80939 | ||||||||
\(838\) | −8.81082 | −0.304365 | ||||||||
\(839\) | 35.4121 | 1.22256 | 0.611280 | − | 0.791414i | \(-0.290655\pi\) | ||||
0.611280 | + | 0.791414i | \(0.290655\pi\) | |||||||
\(840\) | 4.86911 | 0.168000 | ||||||||
\(841\) | 21.0993 | 0.727562 | ||||||||
\(842\) | 12.3383 | 0.425206 | ||||||||
\(843\) | −35.9313 | −1.23754 | ||||||||
\(844\) | 22.3911 | 0.770733 | ||||||||
\(845\) | −11.3233 | −0.389533 | ||||||||
\(846\) | −65.1584 | −2.24019 | ||||||||
\(847\) | −3.75417 | −0.128995 | ||||||||
\(848\) | −3.37076 | −0.115752 | ||||||||
\(849\) | 54.2740 | 1.86268 | ||||||||
\(850\) | −5.42311 | −0.186011 | ||||||||
\(851\) | 17.2146 | 0.590108 | ||||||||
\(852\) | −48.0967 | −1.64776 | ||||||||
\(853\) | 23.1897 | 0.794000 | 0.397000 | − | 0.917819i | \(-0.370051\pi\) | ||||
0.397000 | + | 0.917819i | \(0.370051\pi\) | |||||||
\(854\) | −11.1625 | −0.381975 | ||||||||
\(855\) | −36.5844 | −1.25116 | ||||||||
\(856\) | 0.402137 | 0.0137448 | ||||||||
\(857\) | 32.6339 | 1.11475 | 0.557377 | − | 0.830260i | \(-0.311808\pi\) | ||||
0.557377 | + | 0.830260i | \(0.311808\pi\) | |||||||
\(858\) | 20.3651 | 0.695253 | ||||||||
\(859\) | 51.3605 | 1.75240 | 0.876199 | − | 0.481950i | \(-0.160071\pi\) | ||||
0.876199 | + | 0.481950i | \(0.160071\pi\) | |||||||
\(860\) | 5.66076 | 0.193030 | ||||||||
\(861\) | −26.8696 | −0.915713 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −29.2470 | −0.995579 | −0.497789 | − | 0.867298i | \(-0.665855\pi\) | ||||
−0.497789 | + | 0.867298i | \(0.665855\pi\) | |||||||
\(864\) | 14.2661 | 0.485343 | ||||||||
\(865\) | −32.5857 | −1.10795 | ||||||||
\(866\) | 33.2119 | 1.12859 | ||||||||
\(867\) | 42.0869 | 1.42935 | ||||||||
\(868\) | 9.75321 | 0.331045 | ||||||||
\(869\) | 7.30294 | 0.247735 | ||||||||
\(870\) | −34.4640 | −1.16844 | ||||||||
\(871\) | −3.49554 | −0.118442 | ||||||||
\(872\) | −12.5157 | −0.423834 | ||||||||
\(873\) | −95.6743 | −3.23808 | ||||||||
\(874\) | 19.4749 | 0.658748 | ||||||||
\(875\) | −11.6521 | −0.393912 | ||||||||
\(876\) | 39.3074 | 1.32807 | ||||||||
\(877\) | −34.8175 | −1.17571 | −0.587853 | − | 0.808968i | \(-0.700026\pi\) | ||||
−0.587853 | + | 0.808968i | \(0.700026\pi\) | |||||||
\(878\) | −32.5701 | −1.09919 | ||||||||
\(879\) | 38.9526 | 1.31384 | ||||||||
\(880\) | 4.06040 | 0.136876 | ||||||||
\(881\) | 50.2851 | 1.69415 | 0.847074 | − | 0.531475i | \(-0.178362\pi\) | ||||
0.847074 | + | 0.531475i | \(0.178362\pi\) | |||||||
\(882\) | −7.41957 | −0.249830 | ||||||||
\(883\) | −27.8694 | −0.937879 | −0.468940 | − | 0.883230i | \(-0.655364\pi\) | ||||
−0.468940 | + | 0.883230i | \(0.655364\pi\) | |||||||
\(884\) | −4.66504 | −0.156902 | ||||||||
\(885\) | 3.75414 | 0.126194 | ||||||||
\(886\) | −13.5122 | −0.453951 | ||||||||
\(887\) | −2.43896 | −0.0818923 | −0.0409461 | − | 0.999161i | \(-0.513037\pi\) | ||||
−0.0409461 | + | 0.999161i | \(0.513037\pi\) | |||||||
\(888\) | 9.32693 | 0.312991 | ||||||||
\(889\) | −7.23989 | −0.242818 | ||||||||
\(890\) | −15.3248 | −0.513688 | ||||||||
\(891\) | 64.0418 | 2.14548 | ||||||||
\(892\) | −8.48735 | −0.284178 | ||||||||
\(893\) | −28.7068 | −0.960635 | ||||||||
\(894\) | 33.6431 | 1.12519 | ||||||||
\(895\) | 8.69104 | 0.290509 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −45.0738 | −1.50497 | ||||||||
\(898\) | 35.3651 | 1.18015 | ||||||||
\(899\) | −69.0340 | −2.30241 | ||||||||
\(900\) | −20.2157 | −0.673857 | ||||||||
\(901\) | 6.70913 | 0.223513 | ||||||||
\(902\) | −22.4068 | −0.746065 | ||||||||
\(903\) | −12.1137 | −0.403117 | ||||||||
\(904\) | −13.0313 | −0.433415 | ||||||||
\(905\) | −18.3266 | −0.609196 | ||||||||
\(906\) | 47.3451 | 1.57294 | ||||||||
\(907\) | 20.2124 | 0.671140 | 0.335570 | − | 0.942015i | \(-0.391071\pi\) | ||||
0.335570 | + | 0.942015i | \(0.391071\pi\) | |||||||
\(908\) | 24.5082 | 0.813332 | ||||||||
\(909\) | −117.113 | −3.88438 | ||||||||
\(910\) | −3.53543 | −0.117198 | ||||||||
\(911\) | 20.5060 | 0.679394 | 0.339697 | − | 0.940535i | \(-0.389675\pi\) | ||||
0.339697 | + | 0.940535i | \(0.389675\pi\) | |||||||
\(912\) | 10.5516 | 0.349398 | ||||||||
\(913\) | −21.2621 | −0.703673 | ||||||||
\(914\) | −17.9663 | −0.594273 | ||||||||
\(915\) | −54.3517 | −1.79681 | ||||||||
\(916\) | −23.2995 | −0.769837 | ||||||||
\(917\) | −4.12405 | −0.136188 | ||||||||
\(918\) | −28.3951 | −0.937179 | ||||||||
\(919\) | 2.76912 | 0.0913448 | 0.0456724 | − | 0.998956i | \(-0.485457\pi\) | ||||
0.0456724 | + | 0.998956i | \(0.485457\pi\) | |||||||
\(920\) | −8.98684 | −0.296287 | ||||||||
\(921\) | 32.7596 | 1.07947 | ||||||||
\(922\) | −4.93636 | −0.162570 | ||||||||
\(923\) | 34.9227 | 1.14949 | ||||||||
\(924\) | −8.68898 | −0.285847 | ||||||||
\(925\) | −7.87270 | −0.258853 | ||||||||
\(926\) | 26.3298 | 0.865250 | ||||||||
\(927\) | −2.22134 | −0.0729583 | ||||||||
\(928\) | 7.07809 | 0.232350 | ||||||||
\(929\) | 38.6933 | 1.26949 | 0.634743 | − | 0.772724i | \(-0.281106\pi\) | ||||
0.634743 | + | 0.772724i | \(0.281106\pi\) | |||||||
\(930\) | 47.4894 | 1.55724 | ||||||||
\(931\) | −3.26883 | −0.107132 | ||||||||
\(932\) | −0.337960 | −0.0110703 | ||||||||
\(933\) | −9.42154 | −0.308447 | ||||||||
\(934\) | 16.2673 | 0.532284 | ||||||||
\(935\) | −8.08178 | −0.264303 | ||||||||
\(936\) | −17.3899 | −0.568405 | ||||||||
\(937\) | −47.2698 | −1.54424 | −0.772119 | − | 0.635478i | \(-0.780803\pi\) | ||||
−0.772119 | + | 0.635478i | \(0.780803\pi\) | |||||||
\(938\) | 1.49141 | 0.0486963 | ||||||||
\(939\) | −91.5922 | −2.98900 | ||||||||
\(940\) | 13.2470 | 0.432068 | ||||||||
\(941\) | 43.8583 | 1.42974 | 0.714869 | − | 0.699258i | \(-0.246486\pi\) | ||||
0.714869 | + | 0.699258i | \(0.246486\pi\) | |||||||
\(942\) | 24.5108 | 0.798604 | ||||||||
\(943\) | 49.5928 | 1.61496 | ||||||||
\(944\) | −0.771012 | −0.0250943 | ||||||||
\(945\) | −21.5194 | −0.700026 | ||||||||
\(946\) | −10.1017 | −0.328435 | ||||||||
\(947\) | −10.1254 | −0.329032 | −0.164516 | − | 0.986374i | \(-0.552606\pi\) | ||||
−0.164516 | + | 0.986374i | \(0.552606\pi\) | |||||||
\(948\) | −8.75747 | −0.284429 | ||||||||
\(949\) | −28.5408 | −0.926475 | ||||||||
\(950\) | −8.90641 | −0.288962 | ||||||||
\(951\) | −55.6675 | −1.80514 | ||||||||
\(952\) | 1.99039 | 0.0645090 | ||||||||
\(953\) | −18.5160 | −0.599790 | −0.299895 | − | 0.953972i | \(-0.596952\pi\) | ||||
−0.299895 | + | 0.953972i | \(0.596952\pi\) | |||||||
\(954\) | 25.0096 | 0.809715 | ||||||||
\(955\) | 5.38611 | 0.174290 | ||||||||
\(956\) | −30.5154 | −0.986940 | ||||||||
\(957\) | 61.5014 | 1.98806 | ||||||||
\(958\) | 21.2767 | 0.687418 | ||||||||
\(959\) | −3.14143 | −0.101442 | ||||||||
\(960\) | −4.86911 | −0.157150 | ||||||||
\(961\) | 64.1251 | 2.06855 | ||||||||
\(962\) | −6.77222 | −0.218345 | ||||||||
\(963\) | −2.98368 | −0.0961479 | ||||||||
\(964\) | −1.29495 | −0.0417076 | ||||||||
\(965\) | 1.61154 | 0.0518772 | ||||||||
\(966\) | 19.2312 | 0.618755 | ||||||||
\(967\) | −8.85459 | −0.284744 | −0.142372 | − | 0.989813i | \(-0.545473\pi\) | ||||
−0.142372 | + | 0.989813i | \(0.545473\pi\) | |||||||
\(968\) | 3.75417 | 0.120664 | ||||||||
\(969\) | −21.0018 | −0.674675 | ||||||||
\(970\) | 19.4509 | 0.624532 | ||||||||
\(971\) | −34.8884 | −1.11962 | −0.559811 | − | 0.828620i | \(-0.689126\pi\) | ||||
−0.559811 | + | 0.828620i | \(0.689126\pi\) | |||||||
\(972\) | −33.9987 | −1.09051 | ||||||||
\(973\) | −3.62990 | −0.116369 | ||||||||
\(974\) | −5.98714 | −0.191840 | ||||||||
\(975\) | 20.6135 | 0.660161 | ||||||||
\(976\) | 11.1625 | 0.357305 | ||||||||
\(977\) | 7.99558 | 0.255801 | 0.127901 | − | 0.991787i | \(-0.459176\pi\) | ||||
0.127901 | + | 0.991787i | \(0.459176\pi\) | |||||||
\(978\) | 19.8704 | 0.635384 | ||||||||
\(979\) | 27.3473 | 0.874022 | ||||||||
\(980\) | 1.50843 | 0.0481850 | ||||||||
\(981\) | 92.8609 | 2.96482 | ||||||||
\(982\) | −36.4413 | −1.16289 | ||||||||
\(983\) | −43.1930 | −1.37764 | −0.688822 | − | 0.724931i | \(-0.741872\pi\) | ||||
−0.688822 | + | 0.724931i | \(0.741872\pi\) | |||||||
\(984\) | 26.8696 | 0.856571 | ||||||||
\(985\) | 1.29607 | 0.0412963 | ||||||||
\(986\) | −14.0882 | −0.448658 | ||||||||
\(987\) | −28.3476 | −0.902314 | ||||||||
\(988\) | −7.66143 | −0.243743 | ||||||||
\(989\) | 22.3580 | 0.710943 | ||||||||
\(990\) | −30.1264 | −0.957481 | ||||||||
\(991\) | 1.25519 | 0.0398723 | 0.0199362 | − | 0.999801i | \(-0.493654\pi\) | ||||
0.0199362 | + | 0.999801i | \(0.493654\pi\) | |||||||
\(992\) | −9.75321 | −0.309665 | ||||||||
\(993\) | −103.175 | −3.27416 | ||||||||
\(994\) | −14.9001 | −0.472603 | ||||||||
\(995\) | −1.50846 | −0.0478214 | ||||||||
\(996\) | 25.4969 | 0.807900 | ||||||||
\(997\) | −17.6419 | −0.558725 | −0.279362 | − | 0.960186i | \(-0.590123\pi\) | ||||
−0.279362 | + | 0.960186i | \(0.590123\pi\) | |||||||
\(998\) | −6.63243 | −0.209946 | ||||||||
\(999\) | −41.2211 | −1.30418 |
(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 | 6034.2.a.p.1.1 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.1 | ✓ | 27 | 1.1 | even | 1 | trivial |