Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [42,10,Mod(1,42)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("42.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 42 = 2 \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 42.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: | \(21.6315051189\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 42.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 1590.00 | 1.13771 | 0.568856 | − | 0.822437i | \(-0.307386\pi\) | ||||
0.568856 | + | 0.822437i | \(0.307386\pi\) | |||||||
\(6\) | 1296.00 | 0.408248 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −25440.0 | −0.804483 | ||||||||
\(11\) | −22668.0 | −0.466816 | −0.233408 | − | 0.972379i | \(-0.574988\pi\) | ||||
−0.233408 | + | 0.972379i | \(0.574988\pi\) | |||||||
\(12\) | −20736.0 | −0.288675 | ||||||||
\(13\) | −64186.0 | −0.623297 | −0.311649 | − | 0.950197i | \(-0.600881\pi\) | ||||
−0.311649 | + | 0.950197i | \(0.600881\pi\) | |||||||
\(14\) | −38416.0 | −0.267261 | ||||||||
\(15\) | −128790. | −0.656858 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 29946.0 | 0.0869598 | 0.0434799 | − | 0.999054i | \(-0.486156\pi\) | ||||
0.0434799 | + | 0.999054i | \(0.486156\pi\) | |||||||
\(18\) | −104976. | −0.235702 | ||||||||
\(19\) | 301484. | 0.530729 | 0.265365 | − | 0.964148i | \(-0.414508\pi\) | ||||
0.265365 | + | 0.964148i | \(0.414508\pi\) | |||||||
\(20\) | 407040. | 0.568856 | ||||||||
\(21\) | −194481. | −0.218218 | ||||||||
\(22\) | 362688. | 0.330089 | ||||||||
\(23\) | 1.23749e6 | 0.922074 | 0.461037 | − | 0.887381i | \(-0.347478\pi\) | ||||
0.461037 | + | 0.887381i | \(0.347478\pi\) | |||||||
\(24\) | 331776. | 0.204124 | ||||||||
\(25\) | 574975. | 0.294387 | ||||||||
\(26\) | 1.02698e6 | 0.440738 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 614656. | 0.188982 | ||||||||
\(29\) | 391806. | 0.102868 | 0.0514340 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514340 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(30\) | 2.06064e6 | 0.464469 | ||||||||
\(31\) | 6.80269e6 | 1.32298 | 0.661489 | − | 0.749954i | \(-0.269925\pi\) | ||||
0.661489 | + | 0.749954i | \(0.269925\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | 1.83611e6 | 0.269517 | ||||||||
\(34\) | −479136. | −0.0614899 | ||||||||
\(35\) | 3.81759e6 | 0.430014 | ||||||||
\(36\) | 1.67962e6 | 0.166667 | ||||||||
\(37\) | 1.92798e7 | 1.69120 | 0.845598 | − | 0.533820i | \(-0.179244\pi\) | ||||
0.845598 | + | 0.533820i | \(0.179244\pi\) | |||||||
\(38\) | −4.82374e6 | −0.375282 | ||||||||
\(39\) | 5.19907e6 | 0.359861 | ||||||||
\(40\) | −6.51264e6 | −0.402242 | ||||||||
\(41\) | −1.04874e7 | −0.579614 | −0.289807 | − | 0.957085i | \(-0.593591\pi\) | ||||
−0.289807 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(42\) | 3.11170e6 | 0.154303 | ||||||||
\(43\) | 3.84209e7 | 1.71380 | 0.856898 | − | 0.515486i | \(-0.172388\pi\) | ||||
0.856898 | + | 0.515486i | \(0.172388\pi\) | |||||||
\(44\) | −5.80301e6 | −0.233408 | ||||||||
\(45\) | 1.04320e7 | 0.379237 | ||||||||
\(46\) | −1.97998e7 | −0.652005 | ||||||||
\(47\) | −2928.00 | −8.75247e−5 0 | −4.37624e−5 | − | 1.00000i | \(-0.500014\pi\) | ||||
−4.37624e−5 | 1.00000i | \(0.500014\pi\) | ||||||||
\(48\) | −5.30842e6 | −0.144338 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −9.19960e6 | −0.208163 | ||||||||
\(51\) | −2.42563e6 | −0.0502063 | ||||||||
\(52\) | −1.64316e7 | −0.311649 | ||||||||
\(53\) | −6.81907e7 | −1.18709 | −0.593545 | − | 0.804801i | \(-0.702272\pi\) | ||||
−0.593545 | + | 0.804801i | \(0.702272\pi\) | |||||||
\(54\) | 8.50306e6 | 0.136083 | ||||||||
\(55\) | −3.60421e7 | −0.531102 | ||||||||
\(56\) | −9.83450e6 | −0.133631 | ||||||||
\(57\) | −2.44202e7 | −0.306417 | ||||||||
\(58\) | −6.26890e6 | −0.0727386 | ||||||||
\(59\) | 7.96367e7 | 0.855617 | 0.427808 | − | 0.903870i | \(-0.359286\pi\) | ||||
0.427808 | + | 0.903870i | \(0.359286\pi\) | |||||||
\(60\) | −3.29702e7 | −0.328429 | ||||||||
\(61\) | −3.72034e7 | −0.344031 | −0.172016 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172016 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(62\) | −1.08843e8 | −0.935487 | ||||||||
\(63\) | 1.57530e7 | 0.125988 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −1.02056e8 | −0.709132 | ||||||||
\(66\) | −2.93777e7 | −0.190577 | ||||||||
\(67\) | 5.82341e7 | 0.353053 | 0.176527 | − | 0.984296i | \(-0.443514\pi\) | ||||
0.176527 | + | 0.984296i | \(0.443514\pi\) | |||||||
\(68\) | 7.66618e6 | 0.0434799 | ||||||||
\(69\) | −1.00237e8 | −0.532360 | ||||||||
\(70\) | −6.10814e7 | −0.304066 | ||||||||
\(71\) | −4.93494e7 | −0.230472 | −0.115236 | − | 0.993338i | \(-0.536763\pi\) | ||||
−0.115236 | + | 0.993338i | \(0.536763\pi\) | |||||||
\(72\) | −2.68739e7 | −0.117851 | ||||||||
\(73\) | 3.45748e8 | 1.42497 | 0.712486 | − | 0.701686i | \(-0.247569\pi\) | ||||
0.712486 | + | 0.701686i | \(0.247569\pi\) | |||||||
\(74\) | −3.08476e8 | −1.19586 | ||||||||
\(75\) | −4.65730e7 | −0.169965 | ||||||||
\(76\) | 7.71799e7 | 0.265365 | ||||||||
\(77\) | −5.44259e7 | −0.176440 | ||||||||
\(78\) | −8.31851e7 | −0.254460 | ||||||||
\(79\) | 4.55982e8 | 1.31712 | 0.658561 | − | 0.752528i | \(-0.271166\pi\) | ||||
0.658561 | + | 0.752528i | \(0.271166\pi\) | |||||||
\(80\) | 1.04202e8 | 0.284428 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.67798e8 | 0.409849 | ||||||||
\(83\) | 4.46212e8 | 1.03202 | 0.516012 | − | 0.856581i | \(-0.327416\pi\) | ||||
0.516012 | + | 0.856581i | \(0.327416\pi\) | |||||||
\(84\) | −4.97871e7 | −0.109109 | ||||||||
\(85\) | 4.76141e7 | 0.0989352 | ||||||||
\(86\) | −6.14734e8 | −1.21184 | ||||||||
\(87\) | −3.17363e7 | −0.0593908 | ||||||||
\(88\) | 9.28481e7 | 0.165045 | ||||||||
\(89\) | −5.71902e8 | −0.966199 | −0.483099 | − | 0.875566i | \(-0.660489\pi\) | ||||
−0.483099 | + | 0.875566i | \(0.660489\pi\) | |||||||
\(90\) | −1.66912e8 | −0.268161 | ||||||||
\(91\) | −1.54111e8 | −0.235584 | ||||||||
\(92\) | 3.16797e8 | 0.461037 | ||||||||
\(93\) | −5.51018e8 | −0.763822 | ||||||||
\(94\) | 46848.0 | 6.18893e−5 0 | ||||||||
\(95\) | 4.79360e8 | 0.603817 | ||||||||
\(96\) | 8.49347e7 | 0.102062 | ||||||||
\(97\) | 2.44250e8 | 0.280132 | 0.140066 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140066 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(98\) | −9.22368e7 | −0.101015 | ||||||||
\(99\) | −1.48725e8 | −0.155605 | ||||||||
\(100\) | 1.47194e8 | 0.147194 | ||||||||
\(101\) | 1.31391e9 | 1.25637 | 0.628185 | − | 0.778064i | \(-0.283798\pi\) | ||||
0.628185 | + | 0.778064i | \(0.283798\pi\) | |||||||
\(102\) | 3.88100e7 | 0.0355012 | ||||||||
\(103\) | −1.53762e8 | −0.134611 | −0.0673056 | − | 0.997732i | \(-0.521440\pi\) | ||||
−0.0673056 | + | 0.997732i | \(0.521440\pi\) | |||||||
\(104\) | 2.62906e8 | 0.220369 | ||||||||
\(105\) | −3.09225e8 | −0.248269 | ||||||||
\(106\) | 1.09105e9 | 0.839399 | ||||||||
\(107\) | −2.11407e8 | −0.155917 | −0.0779584 | − | 0.996957i | \(-0.524840\pi\) | ||||
−0.0779584 | + | 0.996957i | \(0.524840\pi\) | |||||||
\(108\) | −1.36049e8 | −0.0962250 | ||||||||
\(109\) | 2.68503e9 | 1.82192 | 0.910960 | − | 0.412495i | \(-0.135343\pi\) | ||||
0.910960 | + | 0.412495i | \(0.135343\pi\) | |||||||
\(110\) | 5.76674e8 | 0.375546 | ||||||||
\(111\) | −1.56166e9 | −0.976413 | ||||||||
\(112\) | 1.57352e8 | 0.0944911 | ||||||||
\(113\) | 9.52202e8 | 0.549384 | 0.274692 | − | 0.961532i | \(-0.411424\pi\) | ||||
0.274692 | + | 0.961532i | \(0.411424\pi\) | |||||||
\(114\) | 3.90723e8 | 0.216669 | ||||||||
\(115\) | 1.96761e9 | 1.04905 | ||||||||
\(116\) | 1.00302e8 | 0.0514340 | ||||||||
\(117\) | −4.21124e8 | −0.207766 | ||||||||
\(118\) | −1.27419e9 | −0.605012 | ||||||||
\(119\) | 7.19003e7 | 0.0328677 | ||||||||
\(120\) | 5.27524e8 | 0.232234 | ||||||||
\(121\) | −1.84411e9 | −0.782082 | ||||||||
\(122\) | 5.95254e8 | 0.243267 | ||||||||
\(123\) | 8.49476e8 | 0.334640 | ||||||||
\(124\) | 1.74149e9 | 0.661489 | ||||||||
\(125\) | −2.19126e9 | −0.802784 | ||||||||
\(126\) | −2.52047e8 | −0.0890871 | ||||||||
\(127\) | −9.28823e8 | −0.316823 | −0.158411 | − | 0.987373i | \(-0.550637\pi\) | ||||
−0.158411 | + | 0.987373i | \(0.550637\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −3.11209e9 | −0.989461 | ||||||||
\(130\) | 1.63289e9 | 0.501432 | ||||||||
\(131\) | −4.75201e9 | −1.40980 | −0.704899 | − | 0.709308i | \(-0.749008\pi\) | ||||
−0.704899 | + | 0.709308i | \(0.749008\pi\) | |||||||
\(132\) | 4.70044e8 | 0.134758 | ||||||||
\(133\) | 7.23863e8 | 0.200597 | ||||||||
\(134\) | −9.31745e8 | −0.249646 | ||||||||
\(135\) | −8.44991e8 | −0.218953 | ||||||||
\(136\) | −1.22659e8 | −0.0307449 | ||||||||
\(137\) | −6.96787e9 | −1.68989 | −0.844943 | − | 0.534856i | \(-0.820366\pi\) | ||||
−0.844943 | + | 0.534856i | \(0.820366\pi\) | |||||||
\(138\) | 1.60378e9 | 0.376435 | ||||||||
\(139\) | −6.39056e9 | −1.45202 | −0.726009 | − | 0.687685i | \(-0.758627\pi\) | ||||
−0.726009 | + | 0.687685i | \(0.758627\pi\) | |||||||
\(140\) | 9.77303e8 | 0.215007 | ||||||||
\(141\) | 237168. | 5.05324e−5 0 | ||||||||
\(142\) | 7.89590e8 | 0.162969 | ||||||||
\(143\) | 1.45497e9 | 0.290965 | ||||||||
\(144\) | 4.29982e8 | 0.0833333 | ||||||||
\(145\) | 6.22972e8 | 0.117034 | ||||||||
\(146\) | −5.53196e9 | −1.00761 | ||||||||
\(147\) | −4.66949e8 | −0.0824786 | ||||||||
\(148\) | 4.93562e9 | 0.845598 | ||||||||
\(149\) | −1.00114e10 | −1.66402 | −0.832008 | − | 0.554763i | \(-0.812809\pi\) | ||||
−0.832008 | + | 0.554763i | \(0.812809\pi\) | |||||||
\(150\) | 7.45168e8 | 0.120183 | ||||||||
\(151\) | 4.95258e9 | 0.775238 | 0.387619 | − | 0.921820i | \(-0.373298\pi\) | ||||
0.387619 | + | 0.921820i | \(0.373298\pi\) | |||||||
\(152\) | −1.23488e9 | −0.187641 | ||||||||
\(153\) | 1.96476e8 | 0.0289866 | ||||||||
\(154\) | 8.70814e8 | 0.124762 | ||||||||
\(155\) | 1.08163e10 | 1.50517 | ||||||||
\(156\) | 1.33096e9 | 0.179930 | ||||||||
\(157\) | −4.30789e9 | −0.565869 | −0.282934 | − | 0.959139i | \(-0.591308\pi\) | ||||
−0.282934 | + | 0.959139i | \(0.591308\pi\) | |||||||
\(158\) | −7.29571e9 | −0.931345 | ||||||||
\(159\) | 5.52344e9 | 0.685367 | ||||||||
\(160\) | −1.66724e9 | −0.201121 | ||||||||
\(161\) | 2.97121e9 | 0.348511 | ||||||||
\(162\) | −6.88748e8 | −0.0785674 | ||||||||
\(163\) | −1.24554e10 | −1.38202 | −0.691011 | − | 0.722845i | \(-0.742834\pi\) | ||||
−0.691011 | + | 0.722845i | \(0.742834\pi\) | |||||||
\(164\) | −2.68476e9 | −0.289807 | ||||||||
\(165\) | 2.91941e9 | 0.306632 | ||||||||
\(166\) | −7.13940e9 | −0.729752 | ||||||||
\(167\) | 1.67083e10 | 1.66230 | 0.831149 | − | 0.556050i | \(-0.187684\pi\) | ||||
0.831149 | + | 0.556050i | \(0.187684\pi\) | |||||||
\(168\) | 7.96594e8 | 0.0771517 | ||||||||
\(169\) | −6.48466e9 | −0.611501 | ||||||||
\(170\) | −7.61826e8 | −0.0699577 | ||||||||
\(171\) | 1.97804e9 | 0.176910 | ||||||||
\(172\) | 9.83574e9 | 0.856898 | ||||||||
\(173\) | 2.07893e10 | 1.76455 | 0.882274 | − | 0.470736i | \(-0.156012\pi\) | ||||
0.882274 | + | 0.470736i | \(0.156012\pi\) | |||||||
\(174\) | 5.07781e8 | 0.0419957 | ||||||||
\(175\) | 1.38051e9 | 0.111268 | ||||||||
\(176\) | −1.48557e9 | −0.116704 | ||||||||
\(177\) | −6.45057e9 | −0.493990 | ||||||||
\(178\) | 9.15043e9 | 0.683206 | ||||||||
\(179\) | 1.30135e10 | 0.947447 | 0.473723 | − | 0.880674i | \(-0.342910\pi\) | ||||
0.473723 | + | 0.880674i | \(0.342910\pi\) | |||||||
\(180\) | 2.67059e9 | 0.189619 | ||||||||
\(181\) | 2.55798e9 | 0.177151 | 0.0885755 | − | 0.996069i | \(-0.471769\pi\) | ||||
0.0885755 | + | 0.996069i | \(0.471769\pi\) | |||||||
\(182\) | 2.46577e9 | 0.166583 | ||||||||
\(183\) | 3.01347e9 | 0.198627 | ||||||||
\(184\) | −5.06875e9 | −0.326002 | ||||||||
\(185\) | 3.06548e10 | 1.92409 | ||||||||
\(186\) | 8.81628e9 | 0.540104 | ||||||||
\(187\) | −6.78816e8 | −0.0405943 | ||||||||
\(188\) | −749568. | −4.37624e−5 0 | ||||||||
\(189\) | −1.27599e9 | −0.0727393 | ||||||||
\(190\) | −7.66975e9 | −0.426963 | ||||||||
\(191\) | −9.94011e9 | −0.540432 | −0.270216 | − | 0.962800i | \(-0.587095\pi\) | ||||
−0.270216 | + | 0.962800i | \(0.587095\pi\) | |||||||
\(192\) | −1.35895e9 | −0.0721688 | ||||||||
\(193\) | −1.07119e10 | −0.555724 | −0.277862 | − | 0.960621i | \(-0.589626\pi\) | ||||
−0.277862 | + | 0.960621i | \(0.589626\pi\) | |||||||
\(194\) | −3.90800e9 | −0.198083 | ||||||||
\(195\) | 8.26651e9 | 0.409418 | ||||||||
\(196\) | 1.47579e9 | 0.0714286 | ||||||||
\(197\) | −1.14767e10 | −0.542899 | −0.271449 | − | 0.962453i | \(-0.587503\pi\) | ||||
−0.271449 | + | 0.962453i | \(0.587503\pi\) | |||||||
\(198\) | 2.37960e9 | 0.110030 | ||||||||
\(199\) | 1.20785e10 | 0.545975 | 0.272987 | − | 0.962018i | \(-0.411988\pi\) | ||||
0.272987 | + | 0.962018i | \(0.411988\pi\) | |||||||
\(200\) | −2.35510e9 | −0.104082 | ||||||||
\(201\) | −4.71696e9 | −0.203835 | ||||||||
\(202\) | −2.10225e10 | −0.888388 | ||||||||
\(203\) | 9.40726e8 | 0.0388804 | ||||||||
\(204\) | −6.20960e8 | −0.0251031 | ||||||||
\(205\) | −1.66749e10 | −0.659433 | ||||||||
\(206\) | 2.46019e9 | 0.0951845 | ||||||||
\(207\) | 8.11916e9 | 0.307358 | ||||||||
\(208\) | −4.20649e9 | −0.155824 | ||||||||
\(209\) | −6.83404e9 | −0.247753 | ||||||||
\(210\) | 4.94760e9 | 0.175553 | ||||||||
\(211\) | −5.39229e10 | −1.87285 | −0.936423 | − | 0.350873i | \(-0.885885\pi\) | ||||
−0.936423 | + | 0.350873i | \(0.885885\pi\) | |||||||
\(212\) | −1.74568e10 | −0.593545 | ||||||||
\(213\) | 3.99730e9 | 0.133063 | ||||||||
\(214\) | 3.38251e9 | 0.110250 | ||||||||
\(215\) | 6.10892e10 | 1.94981 | ||||||||
\(216\) | 2.17678e9 | 0.0680414 | ||||||||
\(217\) | 1.63333e10 | 0.500039 | ||||||||
\(218\) | −4.29604e10 | −1.28829 | ||||||||
\(219\) | −2.80056e10 | −0.822708 | ||||||||
\(220\) | −9.22678e9 | −0.265551 | ||||||||
\(221\) | −1.92211e9 | −0.0542018 | ||||||||
\(222\) | 2.49866e10 | 0.690428 | ||||||||
\(223\) | 1.54752e10 | 0.419049 | 0.209525 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209525 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(224\) | −2.51763e9 | −0.0668153 | ||||||||
\(225\) | 3.77241e9 | 0.0981291 | ||||||||
\(226\) | −1.52352e10 | −0.388473 | ||||||||
\(227\) | 6.84122e10 | 1.71008 | 0.855041 | − | 0.518560i | \(-0.173532\pi\) | ||||
0.855041 | + | 0.518560i | \(0.173532\pi\) | |||||||
\(228\) | −6.25157e9 | −0.153208 | ||||||||
\(229\) | 6.07017e9 | 0.145862 | 0.0729309 | − | 0.997337i | \(-0.476765\pi\) | ||||
0.0729309 | + | 0.997337i | \(0.476765\pi\) | |||||||
\(230\) | −3.14817e10 | −0.741793 | ||||||||
\(231\) | 4.40850e9 | 0.101868 | ||||||||
\(232\) | −1.60484e9 | −0.0363693 | ||||||||
\(233\) | −2.11862e10 | −0.470924 | −0.235462 | − | 0.971884i | \(-0.575660\pi\) | ||||
−0.235462 | + | 0.971884i | \(0.575660\pi\) | |||||||
\(234\) | 6.73799e9 | 0.146913 | ||||||||
\(235\) | −4.65552e6 | −9.95779e−5 0 | ||||||||
\(236\) | 2.03870e10 | 0.427808 | ||||||||
\(237\) | −3.69345e10 | −0.760440 | ||||||||
\(238\) | −1.15041e9 | −0.0232410 | ||||||||
\(239\) | −3.06668e10 | −0.607965 | −0.303982 | − | 0.952678i | \(-0.598316\pi\) | ||||
−0.303982 | + | 0.952678i | \(0.598316\pi\) | |||||||
\(240\) | −8.44038e9 | −0.164214 | ||||||||
\(241\) | −5.87077e10 | −1.12103 | −0.560516 | − | 0.828143i | \(-0.689397\pi\) | ||||
−0.560516 | + | 0.828143i | \(0.689397\pi\) | |||||||
\(242\) | 2.95058e10 | 0.553016 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −9.52406e9 | −0.172016 | ||||||||
\(245\) | 9.16603e9 | 0.162530 | ||||||||
\(246\) | −1.35916e10 | −0.236626 | ||||||||
\(247\) | −1.93511e10 | −0.330802 | ||||||||
\(248\) | −2.78638e10 | −0.467744 | ||||||||
\(249\) | −3.61432e10 | −0.595840 | ||||||||
\(250\) | 3.50601e10 | 0.567654 | ||||||||
\(251\) | −8.13561e10 | −1.29377 | −0.646887 | − | 0.762586i | \(-0.723929\pi\) | ||||
−0.646887 | + | 0.762586i | \(0.723929\pi\) | |||||||
\(252\) | 4.03276e9 | 0.0629941 | ||||||||
\(253\) | −2.80514e10 | −0.430439 | ||||||||
\(254\) | 1.48612e10 | 0.224027 | ||||||||
\(255\) | −3.85675e9 | −0.0571203 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | −3.38969e9 | −0.0484686 | −0.0242343 | − | 0.999706i | \(-0.507715\pi\) | ||||
−0.0242343 | + | 0.999706i | \(0.507715\pi\) | |||||||
\(258\) | 4.97935e10 | 0.699654 | ||||||||
\(259\) | 4.62907e10 | 0.639212 | ||||||||
\(260\) | −2.61263e10 | −0.354566 | ||||||||
\(261\) | 2.57064e9 | 0.0342893 | ||||||||
\(262\) | 7.60322e10 | 0.996878 | ||||||||
\(263\) | 7.18542e10 | 0.926086 | 0.463043 | − | 0.886336i | \(-0.346758\pi\) | ||||
0.463043 | + | 0.886336i | \(0.346758\pi\) | |||||||
\(264\) | −7.52070e9 | −0.0952885 | ||||||||
\(265\) | −1.08423e11 | −1.35057 | ||||||||
\(266\) | −1.15818e10 | −0.141843 | ||||||||
\(267\) | 4.63240e10 | 0.557835 | ||||||||
\(268\) | 1.49079e10 | 0.176527 | ||||||||
\(269\) | 1.39264e10 | 0.162164 | 0.0810820 | − | 0.996707i | \(-0.474162\pi\) | ||||
0.0810820 | + | 0.996707i | \(0.474162\pi\) | |||||||
\(270\) | 1.35199e10 | 0.154823 | ||||||||
\(271\) | 1.31656e11 | 1.48279 | 0.741394 | − | 0.671070i | \(-0.234165\pi\) | ||||
0.741394 | + | 0.671070i | \(0.234165\pi\) | |||||||
\(272\) | 1.96254e9 | 0.0217400 | ||||||||
\(273\) | 1.24830e10 | 0.136015 | ||||||||
\(274\) | 1.11486e11 | 1.19493 | ||||||||
\(275\) | −1.30335e10 | −0.137425 | ||||||||
\(276\) | −2.56606e10 | −0.266180 | ||||||||
\(277\) | −3.63674e10 | −0.371154 | −0.185577 | − | 0.982630i | \(-0.559415\pi\) | ||||
−0.185577 | + | 0.982630i | \(0.559415\pi\) | |||||||
\(278\) | 1.02249e11 | 1.02673 | ||||||||
\(279\) | 4.46324e10 | 0.440993 | ||||||||
\(280\) | −1.56368e10 | −0.152033 | ||||||||
\(281\) | −1.16969e11 | −1.11916 | −0.559580 | − | 0.828776i | \(-0.689038\pi\) | ||||
−0.559580 | + | 0.828776i | \(0.689038\pi\) | |||||||
\(282\) | −3.79469e6 | −3.57318e−5 0 | ||||||||
\(283\) | 1.57635e11 | 1.46087 | 0.730437 | − | 0.682980i | \(-0.239316\pi\) | ||||
0.730437 | + | 0.682980i | \(0.239316\pi\) | |||||||
\(284\) | −1.26334e10 | −0.115236 | ||||||||
\(285\) | −3.88281e10 | −0.348614 | ||||||||
\(286\) | −2.32795e10 | −0.205744 | ||||||||
\(287\) | −2.51801e10 | −0.219073 | ||||||||
\(288\) | −6.87971e9 | −0.0589256 | ||||||||
\(289\) | −1.17691e11 | −0.992438 | ||||||||
\(290\) | −9.96754e9 | −0.0827556 | ||||||||
\(291\) | −1.97843e10 | −0.161734 | ||||||||
\(292\) | 8.85114e10 | 0.712486 | ||||||||
\(293\) | −1.34540e11 | −1.06647 | −0.533235 | − | 0.845967i | \(-0.679024\pi\) | ||||
−0.533235 | + | 0.845967i | \(0.679024\pi\) | |||||||
\(294\) | 7.47118e9 | 0.0583212 | ||||||||
\(295\) | 1.26622e11 | 0.973445 | ||||||||
\(296\) | −7.89699e10 | −0.597928 | ||||||||
\(297\) | 1.20467e10 | 0.0898389 | ||||||||
\(298\) | 1.60183e11 | 1.17664 | ||||||||
\(299\) | −7.94294e10 | −0.574726 | ||||||||
\(300\) | −1.19227e10 | −0.0849823 | ||||||||
\(301\) | 9.22485e10 | 0.647754 | ||||||||
\(302\) | −7.92412e10 | −0.548176 | ||||||||
\(303\) | −1.06426e11 | −0.725366 | ||||||||
\(304\) | 1.97581e10 | 0.132682 | ||||||||
\(305\) | −5.91534e10 | −0.391408 | ||||||||
\(306\) | −3.14361e9 | −0.0204966 | ||||||||
\(307\) | 2.81460e11 | 1.80840 | 0.904199 | − | 0.427111i | \(-0.140469\pi\) | ||||
0.904199 | + | 0.427111i | \(0.140469\pi\) | |||||||
\(308\) | −1.39330e10 | −0.0882200 | ||||||||
\(309\) | 1.24547e10 | 0.0777178 | ||||||||
\(310\) | −1.73060e11 | −1.06431 | ||||||||
\(311\) | 1.84533e11 | 1.11854 | 0.559270 | − | 0.828986i | \(-0.311082\pi\) | ||||
0.559270 | + | 0.828986i | \(0.311082\pi\) | |||||||
\(312\) | −2.12954e10 | −0.127230 | ||||||||
\(313\) | −1.61632e10 | −0.0951872 | −0.0475936 | − | 0.998867i | \(-0.515155\pi\) | ||||
−0.0475936 | + | 0.998867i | \(0.515155\pi\) | |||||||
\(314\) | 6.89262e10 | 0.400130 | ||||||||
\(315\) | 2.50472e10 | 0.143338 | ||||||||
\(316\) | 1.16731e11 | 0.658561 | ||||||||
\(317\) | −8.95885e9 | −0.0498294 | −0.0249147 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249147 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(318\) | −8.83751e10 | −0.484627 | ||||||||
\(319\) | −8.88146e9 | −0.0480204 | ||||||||
\(320\) | 2.66758e10 | 0.142214 | ||||||||
\(321\) | 1.71240e10 | 0.0900185 | ||||||||
\(322\) | −4.75393e10 | −0.246435 | ||||||||
\(323\) | 9.02824e9 | 0.0461521 | ||||||||
\(324\) | 1.10200e10 | 0.0555556 | ||||||||
\(325\) | −3.69053e10 | −0.183491 | ||||||||
\(326\) | 1.99287e11 | 0.977237 | ||||||||
\(327\) | −2.17487e11 | −1.05189 | ||||||||
\(328\) | 4.29562e10 | 0.204924 | ||||||||
\(329\) | −7.03013e6 | −3.30812e−5 0 | ||||||||
\(330\) | −4.67106e10 | −0.216822 | ||||||||
\(331\) | −3.77109e10 | −0.172680 | −0.0863398 | − | 0.996266i | \(-0.527517\pi\) | ||||
−0.0863398 | + | 0.996266i | \(0.527517\pi\) | |||||||
\(332\) | 1.14230e11 | 0.516012 | ||||||||
\(333\) | 1.26495e11 | 0.563732 | ||||||||
\(334\) | −2.67333e11 | −1.17542 | ||||||||
\(335\) | 9.25921e10 | 0.401673 | ||||||||
\(336\) | −1.27455e10 | −0.0545545 | ||||||||
\(337\) | 2.02981e11 | 0.857278 | 0.428639 | − | 0.903476i | \(-0.358993\pi\) | ||||
0.428639 | + | 0.903476i | \(0.358993\pi\) | |||||||
\(338\) | 1.03755e11 | 0.432396 | ||||||||
\(339\) | −7.71284e10 | −0.317187 | ||||||||
\(340\) | 1.21892e10 | 0.0494676 | ||||||||
\(341\) | −1.54203e11 | −0.617588 | ||||||||
\(342\) | −3.16486e10 | −0.125094 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | −1.57372e11 | −0.605919 | ||||||||
\(345\) | −1.59376e11 | −0.605672 | ||||||||
\(346\) | −3.32630e11 | −1.24772 | ||||||||
\(347\) | −1.88559e11 | −0.698177 | −0.349089 | − | 0.937090i | \(-0.613509\pi\) | ||||
−0.349089 | + | 0.937090i | \(0.613509\pi\) | |||||||
\(348\) | −8.12449e9 | −0.0296954 | ||||||||
\(349\) | −1.40280e11 | −0.506154 | −0.253077 | − | 0.967446i | \(-0.581443\pi\) | ||||
−0.253077 | + | 0.967446i | \(0.581443\pi\) | |||||||
\(350\) | −2.20882e10 | −0.0786783 | ||||||||
\(351\) | 3.41111e10 | 0.119954 | ||||||||
\(352\) | 2.37691e10 | 0.0825223 | ||||||||
\(353\) | 7.44306e10 | 0.255132 | 0.127566 | − | 0.991830i | \(-0.459283\pi\) | ||||
0.127566 | + | 0.991830i | \(0.459283\pi\) | |||||||
\(354\) | 1.03209e11 | 0.349304 | ||||||||
\(355\) | −7.84655e10 | −0.262211 | ||||||||
\(356\) | −1.46407e11 | −0.483099 | ||||||||
\(357\) | −5.82393e9 | −0.0189762 | ||||||||
\(358\) | −2.08216e11 | −0.669946 | ||||||||
\(359\) | −2.31256e11 | −0.734798 | −0.367399 | − | 0.930063i | \(-0.619752\pi\) | ||||
−0.367399 | + | 0.930063i | \(0.619752\pi\) | |||||||
\(360\) | −4.27294e10 | −0.134081 | ||||||||
\(361\) | −2.31795e11 | −0.718326 | ||||||||
\(362\) | −4.09277e10 | −0.125265 | ||||||||
\(363\) | 1.49373e11 | 0.451536 | ||||||||
\(364\) | −3.94523e10 | −0.117792 | ||||||||
\(365\) | 5.49739e11 | 1.62121 | ||||||||
\(366\) | −4.82156e10 | −0.140450 | ||||||||
\(367\) | −2.94257e11 | −0.846701 | −0.423351 | − | 0.905966i | \(-0.639146\pi\) | ||||
−0.423351 | + | 0.905966i | \(0.639146\pi\) | |||||||
\(368\) | 8.11000e10 | 0.230518 | ||||||||
\(369\) | −6.88076e10 | −0.193205 | ||||||||
\(370\) | −4.90477e11 | −1.36054 | ||||||||
\(371\) | −1.63726e11 | −0.448678 | ||||||||
\(372\) | −1.41061e11 | −0.381911 | ||||||||
\(373\) | 2.70035e11 | 0.722322 | 0.361161 | − | 0.932503i | \(-0.382380\pi\) | ||||
0.361161 | + | 0.932503i | \(0.382380\pi\) | |||||||
\(374\) | 1.08611e10 | 0.0287045 | ||||||||
\(375\) | 1.77492e11 | 0.463487 | ||||||||
\(376\) | 1.19931e7 | 3.09447e−5 0 | ||||||||
\(377\) | −2.51485e10 | −0.0641173 | ||||||||
\(378\) | 2.04158e10 | 0.0514344 | ||||||||
\(379\) | 1.88183e11 | 0.468494 | 0.234247 | − | 0.972177i | \(-0.424737\pi\) | ||||
0.234247 | + | 0.972177i | \(0.424737\pi\) | |||||||
\(380\) | 1.22716e11 | 0.301908 | ||||||||
\(381\) | 7.52346e10 | 0.182918 | ||||||||
\(382\) | 1.59042e11 | 0.382143 | ||||||||
\(383\) | −2.82829e11 | −0.671628 | −0.335814 | − | 0.941928i | \(-0.609011\pi\) | ||||
−0.335814 | + | 0.941928i | \(0.609011\pi\) | |||||||
\(384\) | 2.17433e10 | 0.0510310 | ||||||||
\(385\) | −8.65371e10 | −0.200738 | ||||||||
\(386\) | 1.71391e11 | 0.392956 | ||||||||
\(387\) | 2.52079e11 | 0.571265 | ||||||||
\(388\) | 6.25281e10 | 0.140066 | ||||||||
\(389\) | −7.58058e11 | −1.67853 | −0.839265 | − | 0.543722i | \(-0.817014\pi\) | ||||
−0.839265 | + | 0.543722i | \(0.817014\pi\) | |||||||
\(390\) | −1.32264e11 | −0.289502 | ||||||||
\(391\) | 3.70578e10 | 0.0801834 | ||||||||
\(392\) | −2.36126e10 | −0.0505076 | ||||||||
\(393\) | 3.84913e11 | 0.813947 | ||||||||
\(394\) | 1.83627e11 | 0.383887 | ||||||||
\(395\) | 7.25011e11 | 1.49850 | ||||||||
\(396\) | −3.80735e10 | −0.0778027 | ||||||||
\(397\) | 5.58142e11 | 1.12768 | 0.563842 | − | 0.825882i | \(-0.309323\pi\) | ||||
0.563842 | + | 0.825882i | \(0.309323\pi\) | |||||||
\(398\) | −1.93255e11 | −0.386063 | ||||||||
\(399\) | −5.86329e10 | −0.115815 | ||||||||
\(400\) | 3.76816e10 | 0.0735968 | ||||||||
\(401\) | 7.13587e11 | 1.37815 | 0.689076 | − | 0.724689i | \(-0.258017\pi\) | ||||
0.689076 | + | 0.724689i | \(0.258017\pi\) | |||||||
\(402\) | 7.54713e10 | 0.144133 | ||||||||
\(403\) | −4.36637e11 | −0.824609 | ||||||||
\(404\) | 3.36360e11 | 0.628185 | ||||||||
\(405\) | 6.84443e10 | 0.126412 | ||||||||
\(406\) | −1.50516e10 | −0.0274926 | ||||||||
\(407\) | −4.37034e11 | −0.789478 | ||||||||
\(408\) | 9.93536e9 | 0.0177506 | ||||||||
\(409\) | −6.71417e11 | −1.18642 | −0.593208 | − | 0.805049i | \(-0.702139\pi\) | ||||
−0.593208 | + | 0.805049i | \(0.702139\pi\) | |||||||
\(410\) | 2.66798e11 | 0.466290 | ||||||||
\(411\) | 5.64398e11 | 0.975657 | ||||||||
\(412\) | −3.93630e10 | −0.0673056 | ||||||||
\(413\) | 1.91208e11 | 0.323393 | ||||||||
\(414\) | −1.29907e11 | −0.217335 | ||||||||
\(415\) | 7.09477e11 | 1.17415 | ||||||||
\(416\) | 6.73039e10 | 0.110184 | ||||||||
\(417\) | 5.17635e11 | 0.838323 | ||||||||
\(418\) | 1.09345e11 | 0.175188 | ||||||||
\(419\) | 7.85557e11 | 1.24513 | 0.622565 | − | 0.782568i | \(-0.286091\pi\) | ||||
0.622565 | + | 0.782568i | \(0.286091\pi\) | |||||||
\(420\) | −7.91615e10 | −0.124134 | ||||||||
\(421\) | 8.41170e11 | 1.30501 | 0.652506 | − | 0.757784i | \(-0.273718\pi\) | ||||
0.652506 | + | 0.757784i | \(0.273718\pi\) | |||||||
\(422\) | 8.62766e11 | 1.32430 | ||||||||
\(423\) | −1.92106e7 | −2.91749e−5 0 | ||||||||
\(424\) | 2.79309e11 | 0.419700 | ||||||||
\(425\) | 1.72182e10 | 0.0255999 | ||||||||
\(426\) | −6.39568e10 | −0.0940900 | ||||||||
\(427\) | −8.93253e10 | −0.130032 | ||||||||
\(428\) | −5.41202e10 | −0.0779584 | ||||||||
\(429\) | −1.17852e11 | −0.167989 | ||||||||
\(430\) | −9.77427e11 | −1.37872 | ||||||||
\(431\) | −9.91535e11 | −1.38408 | −0.692039 | − | 0.721861i | \(-0.743287\pi\) | ||||
−0.692039 | + | 0.721861i | \(0.743287\pi\) | |||||||
\(432\) | −3.48285e10 | −0.0481125 | ||||||||
\(433\) | −2.09922e11 | −0.286987 | −0.143493 | − | 0.989651i | \(-0.545834\pi\) | ||||
−0.143493 | + | 0.989651i | \(0.545834\pi\) | |||||||
\(434\) | −2.61332e11 | −0.353581 | ||||||||
\(435\) | −5.04607e10 | −0.0675696 | ||||||||
\(436\) | 6.87367e11 | 0.910960 | ||||||||
\(437\) | 3.73083e11 | 0.489372 | ||||||||
\(438\) | 4.48089e11 | 0.581742 | ||||||||
\(439\) | −1.05061e12 | −1.35005 | −0.675026 | − | 0.737794i | \(-0.735868\pi\) | ||||
−0.675026 | + | 0.737794i | \(0.735868\pi\) | |||||||
\(440\) | 1.47629e11 | 0.187773 | ||||||||
\(441\) | 3.78229e10 | 0.0476190 | ||||||||
\(442\) | 3.07538e10 | 0.0383265 | ||||||||
\(443\) | −1.71164e11 | −0.211153 | −0.105576 | − | 0.994411i | \(-0.533669\pi\) | ||||
−0.105576 | + | 0.994411i | \(0.533669\pi\) | |||||||
\(444\) | −3.99785e11 | −0.488206 | ||||||||
\(445\) | −9.09324e11 | −1.09926 | ||||||||
\(446\) | −2.47604e11 | −0.296313 | ||||||||
\(447\) | 8.10925e11 | 0.960720 | ||||||||
\(448\) | 4.02821e10 | 0.0472456 | ||||||||
\(449\) | −8.92199e11 | −1.03598 | −0.517992 | − | 0.855385i | \(-0.673320\pi\) | ||||
−0.517992 | + | 0.855385i | \(0.673320\pi\) | |||||||
\(450\) | −6.03586e10 | −0.0693877 | ||||||||
\(451\) | 2.37727e11 | 0.270573 | ||||||||
\(452\) | 2.43764e11 | 0.274692 | ||||||||
\(453\) | −4.01159e11 | −0.447584 | ||||||||
\(454\) | −1.09459e12 | −1.20921 | ||||||||
\(455\) | −2.45036e11 | −0.268027 | ||||||||
\(456\) | 1.00025e11 | 0.108335 | ||||||||
\(457\) | 1.93571e11 | 0.207595 | 0.103798 | − | 0.994598i | \(-0.466901\pi\) | ||||
0.103798 | + | 0.994598i | \(0.466901\pi\) | |||||||
\(458\) | −9.71228e10 | −0.103140 | ||||||||
\(459\) | −1.59145e10 | −0.0167354 | ||||||||
\(460\) | 5.03707e11 | 0.524527 | ||||||||
\(461\) | 1.20264e12 | 1.24017 | 0.620087 | − | 0.784533i | \(-0.287097\pi\) | ||||
0.620087 | + | 0.784533i | \(0.287097\pi\) | |||||||
\(462\) | −7.05359e10 | −0.0720313 | ||||||||
\(463\) | −1.28520e12 | −1.29974 | −0.649870 | − | 0.760045i | \(-0.725177\pi\) | ||||
−0.649870 | + | 0.760045i | \(0.725177\pi\) | |||||||
\(464\) | 2.56774e10 | 0.0257170 | ||||||||
\(465\) | −8.76118e11 | −0.869009 | ||||||||
\(466\) | 3.38979e11 | 0.332994 | ||||||||
\(467\) | −1.37619e12 | −1.33891 | −0.669457 | − | 0.742851i | \(-0.733473\pi\) | ||||
−0.669457 | + | 0.742851i | \(0.733473\pi\) | |||||||
\(468\) | −1.07808e11 | −0.103883 | ||||||||
\(469\) | 1.39820e11 | 0.133442 | ||||||||
\(470\) | 7.44883e7 | 7.04122e−5 0 | ||||||||
\(471\) | 3.48939e11 | 0.326705 | ||||||||
\(472\) | −3.26192e11 | −0.302506 | ||||||||
\(473\) | −8.70924e11 | −0.800028 | ||||||||
\(474\) | 5.90953e11 | 0.537712 | ||||||||
\(475\) | 1.73346e11 | 0.156240 | ||||||||
\(476\) | 1.84065e10 | 0.0164339 | ||||||||
\(477\) | −4.47399e11 | −0.395697 | ||||||||
\(478\) | 4.90669e11 | 0.429896 | ||||||||
\(479\) | −1.15599e12 | −1.00333 | −0.501665 | − | 0.865062i | \(-0.667279\pi\) | ||||
−0.501665 | + | 0.865062i | \(0.667279\pi\) | |||||||
\(480\) | 1.35046e11 | 0.116117 | ||||||||
\(481\) | −1.23749e12 | −1.05412 | ||||||||
\(482\) | 9.39323e11 | 0.792690 | ||||||||
\(483\) | −2.40668e11 | −0.201213 | ||||||||
\(484\) | −4.72092e11 | −0.391041 | ||||||||
\(485\) | 3.88358e11 | 0.318709 | ||||||||
\(486\) | 5.57886e10 | 0.0453609 | ||||||||
\(487\) | −6.72883e11 | −0.542075 | −0.271038 | − | 0.962569i | \(-0.587367\pi\) | ||||
−0.271038 | + | 0.962569i | \(0.587367\pi\) | |||||||
\(488\) | 1.52385e11 | 0.121633 | ||||||||
\(489\) | 1.00889e12 | 0.797910 | ||||||||
\(490\) | −1.46657e11 | −0.114926 | ||||||||
\(491\) | −7.90636e11 | −0.613917 | −0.306958 | − | 0.951723i | \(-0.599311\pi\) | ||||
−0.306958 | + | 0.951723i | \(0.599311\pi\) | |||||||
\(492\) | 2.17466e11 | 0.167320 | ||||||||
\(493\) | 1.17330e10 | 0.00894538 | ||||||||
\(494\) | 3.09617e11 | 0.233912 | ||||||||
\(495\) | −2.36472e11 | −0.177034 | ||||||||
\(496\) | 4.45821e11 | 0.330745 | ||||||||
\(497\) | −1.18488e11 | −0.0871104 | ||||||||
\(498\) | 5.78291e11 | 0.421322 | ||||||||
\(499\) | 2.73134e11 | 0.197207 | 0.0986037 | − | 0.995127i | \(-0.468562\pi\) | ||||
0.0986037 | + | 0.995127i | \(0.468562\pi\) | |||||||
\(500\) | −5.60962e11 | −0.401392 | ||||||||
\(501\) | −1.35337e12 | −0.959728 | ||||||||
\(502\) | 1.30170e12 | 0.914836 | ||||||||
\(503\) | 1.57083e12 | 1.09414 | 0.547072 | − | 0.837086i | \(-0.315742\pi\) | ||||
0.547072 | + | 0.837086i | \(0.315742\pi\) | |||||||
\(504\) | −6.45241e10 | −0.0445435 | ||||||||
\(505\) | 2.08911e12 | 1.42939 | ||||||||
\(506\) | 4.48822e11 | 0.304367 | ||||||||
\(507\) | 5.25257e11 | 0.353050 | ||||||||
\(508\) | −2.37779e11 | −0.158411 | ||||||||
\(509\) | −1.24142e12 | −0.819767 | −0.409883 | − | 0.912138i | \(-0.634431\pi\) | ||||
−0.409883 | + | 0.912138i | \(0.634431\pi\) | |||||||
\(510\) | 6.17079e10 | 0.0403901 | ||||||||
\(511\) | 8.30140e11 | 0.538589 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | −1.60221e11 | −0.102139 | ||||||||
\(514\) | 5.42350e10 | 0.0342725 | ||||||||
\(515\) | −2.44481e11 | −0.153149 | ||||||||
\(516\) | −7.96695e11 | −0.494730 | ||||||||
\(517\) | 6.63719e7 | 4.08580e−5 0 | ||||||||
\(518\) | −7.40651e11 | −0.451991 | ||||||||
\(519\) | −1.68394e12 | −1.01876 | ||||||||
\(520\) | 4.18020e11 | 0.250716 | ||||||||
\(521\) | 6.88837e11 | 0.409587 | 0.204794 | − | 0.978805i | \(-0.434348\pi\) | ||||
0.204794 | + | 0.978805i | \(0.434348\pi\) | |||||||
\(522\) | −4.11302e10 | −0.0242462 | ||||||||
\(523\) | −4.93203e11 | −0.288249 | −0.144125 | − | 0.989560i | \(-0.546037\pi\) | ||||
−0.144125 | + | 0.989560i | \(0.546037\pi\) | |||||||
\(524\) | −1.21652e12 | −0.704899 | ||||||||
\(525\) | −1.11822e11 | −0.0642406 | ||||||||
\(526\) | −1.14967e12 | −0.654841 | ||||||||
\(527\) | 2.03713e11 | 0.115046 | ||||||||
\(528\) | 1.20331e11 | 0.0673791 | ||||||||
\(529\) | −2.69776e11 | −0.149780 | ||||||||
\(530\) | 1.73477e12 | 0.954994 | ||||||||
\(531\) | 5.22496e11 | 0.285206 | ||||||||
\(532\) | 1.85309e11 | 0.100298 | ||||||||
\(533\) | 6.73142e11 | 0.361272 | ||||||||
\(534\) | −7.41185e11 | −0.394449 | ||||||||
\(535\) | −3.36137e11 | −0.177388 | ||||||||
\(536\) | −2.38527e11 | −0.124823 | ||||||||
\(537\) | −1.05409e12 | −0.547009 | ||||||||
\(538\) | −2.22823e11 | −0.114667 | ||||||||
\(539\) | −1.30677e11 | −0.0666881 | ||||||||
\(540\) | −2.16318e11 | −0.109476 | ||||||||
\(541\) | 3.70983e12 | 1.86194 | 0.930972 | − | 0.365091i | \(-0.118962\pi\) | ||||
0.930972 | + | 0.365091i | \(0.118962\pi\) | |||||||
\(542\) | −2.10650e12 | −1.04849 | ||||||||
\(543\) | −2.07196e11 | −0.102278 | ||||||||
\(544\) | −3.14007e10 | −0.0153725 | ||||||||
\(545\) | 4.26919e12 | 2.07282 | ||||||||
\(546\) | −1.99727e11 | −0.0961769 | ||||||||
\(547\) | 3.35488e12 | 1.60226 | 0.801132 | − | 0.598487i | \(-0.204231\pi\) | ||||
0.801132 | + | 0.598487i | \(0.204231\pi\) | |||||||
\(548\) | −1.78378e12 | −0.844943 | ||||||||
\(549\) | −2.44091e11 | −0.114677 | ||||||||
\(550\) | 2.08537e11 | 0.0971740 | ||||||||
\(551\) | 1.18123e11 | 0.0545950 | ||||||||
\(552\) | 4.10569e11 | 0.188218 | ||||||||
\(553\) | 1.09481e12 | 0.497825 | ||||||||
\(554\) | 5.81879e11 | 0.262445 | ||||||||
\(555\) | −2.48304e12 | −1.11088 | ||||||||
\(556\) | −1.63598e12 | −0.726009 | ||||||||
\(557\) | 4.39669e12 | 1.93543 | 0.967714 | − | 0.252050i | \(-0.0811048\pi\) | ||||
0.967714 | + | 0.252050i | \(0.0811048\pi\) | |||||||
\(558\) | −7.14119e11 | −0.311829 | ||||||||
\(559\) | −2.46608e12 | −1.06820 | ||||||||
\(560\) | 2.50190e11 | 0.107504 | ||||||||
\(561\) | 5.49841e10 | 0.0234371 | ||||||||
\(562\) | 1.87150e12 | 0.791366 | ||||||||
\(563\) | 2.18836e9 | 0.000917974 0 | 0.000458987 | − | 1.00000i | \(-0.499854\pi\) | ||||
0.000458987 | 1.00000i | \(0.499854\pi\) | ||||||||
\(564\) | 6.07150e7 | 2.52662e−5 0 | ||||||||
\(565\) | 1.51400e12 | 0.625041 | ||||||||
\(566\) | −2.52215e12 | −1.03299 | ||||||||
\(567\) | 1.03355e11 | 0.0419961 | ||||||||
\(568\) | 2.02135e11 | 0.0814843 | ||||||||
\(569\) | −6.93422e11 | −0.277327 | −0.138664 | − | 0.990340i | \(-0.544281\pi\) | ||||
−0.138664 | + | 0.990340i | \(0.544281\pi\) | |||||||
\(570\) | 6.21250e11 | 0.246507 | ||||||||
\(571\) | −1.71495e12 | −0.675131 | −0.337565 | − | 0.941302i | \(-0.609603\pi\) | ||||
−0.337565 | + | 0.941302i | \(0.609603\pi\) | |||||||
\(572\) | 3.72472e11 | 0.145483 | ||||||||
\(573\) | 8.05149e11 | 0.312018 | ||||||||
\(574\) | 4.02882e11 | 0.154908 | ||||||||
\(575\) | 7.11525e11 | 0.271447 | ||||||||
\(576\) | 1.10075e11 | 0.0416667 | ||||||||
\(577\) | 6.18396e11 | 0.232261 | 0.116130 | − | 0.993234i | \(-0.462951\pi\) | ||||
0.116130 | + | 0.993234i | \(0.462951\pi\) | |||||||
\(578\) | 1.88306e12 | 0.701760 | ||||||||
\(579\) | 8.67665e11 | 0.320848 | ||||||||
\(580\) | 1.59481e11 | 0.0585170 | ||||||||
\(581\) | 1.07136e12 | 0.390069 | ||||||||
\(582\) | 3.16548e11 | 0.114363 | ||||||||
\(583\) | 1.54575e12 | 0.554153 | ||||||||
\(584\) | −1.41618e12 | −0.503804 | ||||||||
\(585\) | −6.69588e11 | −0.236377 | ||||||||
\(586\) | 2.15265e12 | 0.754108 | ||||||||
\(587\) | −4.54366e12 | −1.57955 | −0.789776 | − | 0.613395i | \(-0.789803\pi\) | ||||
−0.789776 | + | 0.613395i | \(0.789803\pi\) | |||||||
\(588\) | −1.19539e11 | −0.0412393 | ||||||||
\(589\) | 2.05090e12 | 0.702144 | ||||||||
\(590\) | −2.02596e12 | −0.688329 | ||||||||
\(591\) | 9.29613e11 | 0.313443 | ||||||||
\(592\) | 1.26352e12 | 0.422799 | ||||||||
\(593\) | 4.23622e12 | 1.40680 | 0.703400 | − | 0.710795i | \(-0.251664\pi\) | ||||
0.703400 | + | 0.710795i | \(0.251664\pi\) | |||||||
\(594\) | −1.92747e11 | −0.0635257 | ||||||||
\(595\) | 1.14322e11 | 0.0373940 | ||||||||
\(596\) | −2.56292e12 | −0.832008 | ||||||||
\(597\) | −9.78355e11 | −0.315219 | ||||||||
\(598\) | 1.27087e12 | 0.406393 | ||||||||
\(599\) | −3.37403e12 | −1.07085 | −0.535424 | − | 0.844583i | \(-0.679848\pi\) | ||||
−0.535424 | + | 0.844583i | \(0.679848\pi\) | |||||||
\(600\) | 1.90763e11 | 0.0600915 | ||||||||
\(601\) | −3.09334e12 | −0.967146 | −0.483573 | − | 0.875304i | \(-0.660661\pi\) | ||||
−0.483573 | + | 0.875304i | \(0.660661\pi\) | |||||||
\(602\) | −1.47598e12 | −0.458031 | ||||||||
\(603\) | 3.82074e11 | 0.117684 | ||||||||
\(604\) | 1.26786e12 | 0.387619 | ||||||||
\(605\) | −2.93213e12 | −0.889784 | ||||||||
\(606\) | 1.70282e12 | 0.512911 | ||||||||
\(607\) | 4.37823e11 | 0.130903 | 0.0654514 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654514 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(608\) | −3.16129e11 | −0.0938206 | ||||||||
\(609\) | −7.61988e10 | −0.0224476 | ||||||||
\(610\) | 9.46454e11 | 0.276768 | ||||||||
\(611\) | 1.87937e8 | 5.45539e−5 0 | ||||||||
\(612\) | 5.02978e10 | 0.0144933 | ||||||||
\(613\) | −2.16858e12 | −0.620303 | −0.310152 | − | 0.950687i | \(-0.600380\pi\) | ||||
−0.310152 | + | 0.950687i | \(0.600380\pi\) | |||||||
\(614\) | −4.50336e12 | −1.27873 | ||||||||
\(615\) | 1.35067e12 | 0.380724 | ||||||||
\(616\) | 2.22928e11 | 0.0623810 | ||||||||
\(617\) | 1.32098e12 | 0.366956 | 0.183478 | − | 0.983024i | \(-0.441264\pi\) | ||||
0.183478 | + | 0.983024i | \(0.441264\pi\) | |||||||
\(618\) | −1.99275e11 | −0.0549548 | ||||||||
\(619\) | 3.97904e12 | 1.08936 | 0.544678 | − | 0.838645i | \(-0.316652\pi\) | ||||
0.544678 | + | 0.838645i | \(0.316652\pi\) | |||||||
\(620\) | 2.76897e12 | 0.752584 | ||||||||
\(621\) | −6.57652e11 | −0.177453 | ||||||||
\(622\) | −2.95252e12 | −0.790927 | ||||||||
\(623\) | −1.37314e12 | −0.365189 | ||||||||
\(624\) | 3.40726e11 | 0.0899652 | ||||||||
\(625\) | −4.60710e12 | −1.20772 | ||||||||
\(626\) | 2.58612e11 | 0.0673075 | ||||||||
\(627\) | 5.53557e11 | 0.143040 | ||||||||
\(628\) | −1.10282e12 | −0.282934 | ||||||||
\(629\) | 5.77352e11 | 0.147066 | ||||||||
\(630\) | −4.00755e11 | −0.101355 | ||||||||
\(631\) | 3.79318e12 | 0.952515 | 0.476257 | − | 0.879306i | \(-0.341993\pi\) | ||||
0.476257 | + | 0.879306i | \(0.341993\pi\) | |||||||
\(632\) | −1.86770e12 | −0.465673 | ||||||||
\(633\) | 4.36775e12 | 1.08129 | ||||||||
\(634\) | 1.43342e11 | 0.0352347 | ||||||||
\(635\) | −1.47683e12 | −0.360453 | ||||||||
\(636\) | 1.41400e12 | 0.342683 | ||||||||
\(637\) | −3.70020e11 | −0.0890425 | ||||||||
\(638\) | 1.42103e11 | 0.0339556 | ||||||||
\(639\) | −3.23781e11 | −0.0768242 | ||||||||
\(640\) | −4.26812e11 | −0.100560 | ||||||||
\(641\) | 7.02589e12 | 1.64377 | 0.821884 | − | 0.569655i | \(-0.192923\pi\) | ||||
0.821884 | + | 0.569655i | \(0.192923\pi\) | |||||||
\(642\) | −2.73984e11 | −0.0636527 | ||||||||
\(643\) | −6.14886e12 | −1.41855 | −0.709276 | − | 0.704931i | \(-0.750978\pi\) | ||||
−0.709276 | + | 0.704931i | \(0.750978\pi\) | |||||||
\(644\) | 7.60629e11 | 0.174256 | ||||||||
\(645\) | −4.94822e12 | −1.12572 | ||||||||
\(646\) | −1.44452e11 | −0.0326345 | ||||||||
\(647\) | 2.17149e12 | 0.487179 | 0.243589 | − | 0.969878i | \(-0.421675\pi\) | ||||
0.243589 | + | 0.969878i | \(0.421675\pi\) | |||||||
\(648\) | −1.76319e11 | −0.0392837 | ||||||||
\(649\) | −1.80520e12 | −0.399416 | ||||||||
\(650\) | 5.90486e11 | 0.129748 | ||||||||
\(651\) | −1.32299e12 | −0.288698 | ||||||||
\(652\) | −3.18859e12 | −0.691011 | ||||||||
\(653\) | −5.47584e12 | −1.17853 | −0.589266 | − | 0.807939i | \(-0.700583\pi\) | ||||
−0.589266 | + | 0.807939i | \(0.700583\pi\) | |||||||
\(654\) | 3.47979e12 | 0.743795 | ||||||||
\(655\) | −7.55570e12 | −1.60394 | ||||||||
\(656\) | −6.87299e11 | −0.144903 | ||||||||
\(657\) | 2.26845e12 | 0.474991 | ||||||||
\(658\) | 1.12482e8 | 2.33920e−5 0 | ||||||||
\(659\) | −4.67490e12 | −0.965580 | −0.482790 | − | 0.875736i | \(-0.660376\pi\) | ||||
−0.482790 | + | 0.875736i | \(0.660376\pi\) | |||||||
\(660\) | 7.47369e11 | 0.153316 | ||||||||
\(661\) | 3.34777e11 | 0.0682103 | 0.0341051 | − | 0.999418i | \(-0.489142\pi\) | ||||
0.0341051 | + | 0.999418i | \(0.489142\pi\) | |||||||
\(662\) | 6.03375e11 | 0.122103 | ||||||||
\(663\) | 1.55691e11 | 0.0312934 | ||||||||
\(664\) | −1.82769e12 | −0.364876 | ||||||||
\(665\) | 1.15094e12 | 0.228221 | ||||||||
\(666\) | −2.02391e12 | −0.398619 | ||||||||
\(667\) | 4.84855e11 | 0.0948519 | ||||||||
\(668\) | 4.27733e12 | 0.831149 | ||||||||
\(669\) | −1.25349e12 | −0.241938 | ||||||||
\(670\) | −1.48147e12 | −0.284026 | ||||||||
\(671\) | 8.43326e11 | 0.160599 | ||||||||
\(672\) | 2.03928e11 | 0.0385758 | ||||||||
\(673\) | −2.47029e12 | −0.464173 | −0.232087 | − | 0.972695i | \(-0.574555\pi\) | ||||
−0.232087 | + | 0.972695i | \(0.574555\pi\) | |||||||
\(674\) | −3.24770e12 | −0.606187 | ||||||||
\(675\) | −3.05565e11 | −0.0566548 | ||||||||
\(676\) | −1.66007e12 | −0.305750 | ||||||||
\(677\) | −4.48933e12 | −0.821359 | −0.410679 | − | 0.911780i | \(-0.634708\pi\) | ||||
−0.410679 | + | 0.911780i | \(0.634708\pi\) | |||||||
\(678\) | 1.23405e12 | 0.224285 | ||||||||
\(679\) | 5.86445e11 | 0.105880 | ||||||||
\(680\) | −1.95028e11 | −0.0349789 | ||||||||
\(681\) | −5.54139e12 | −0.987317 | ||||||||
\(682\) | 2.46725e12 | 0.436701 | ||||||||
\(683\) | 8.32962e12 | 1.46464 | 0.732322 | − | 0.680958i | \(-0.238437\pi\) | ||||
0.732322 | + | 0.680958i | \(0.238437\pi\) | |||||||
\(684\) | 5.06377e11 | 0.0884549 | ||||||||
\(685\) | −1.10789e13 | −1.92260 | ||||||||
\(686\) | −2.21461e11 | −0.0381802 | ||||||||
\(687\) | −4.91684e11 | −0.0842133 | ||||||||
\(688\) | 2.51795e12 | 0.428449 | ||||||||
\(689\) | 4.37689e12 | 0.739910 | ||||||||
\(690\) | 2.55002e12 | 0.428274 | ||||||||
\(691\) | 1.06352e13 | 1.77458 | 0.887292 | − | 0.461209i | \(-0.152584\pi\) | ||||
0.887292 | + | 0.461209i | \(0.152584\pi\) | |||||||
\(692\) | 5.32207e12 | 0.882274 | ||||||||
\(693\) | −3.57088e11 | −0.0588133 | ||||||||
\(694\) | 3.01695e12 | 0.493686 | ||||||||
\(695\) | −1.01610e13 | −1.65198 | ||||||||
\(696\) | 1.29992e11 | 0.0209978 | ||||||||
\(697\) | −3.14054e11 | −0.0504031 | ||||||||
\(698\) | 2.24449e12 | 0.357905 | ||||||||
\(699\) | 1.71608e12 | 0.271888 | ||||||||
\(700\) | 3.53412e11 | 0.0556340 | ||||||||
\(701\) | 5.02284e12 | 0.785630 | 0.392815 | − | 0.919618i | \(-0.371501\pi\) | ||||
0.392815 | + | 0.919618i | \(0.371501\pi\) | |||||||
\(702\) | −5.45777e11 | −0.0848200 | ||||||||
\(703\) | 5.81254e12 | 0.897567 | ||||||||
\(704\) | −3.80306e11 | −0.0583521 | ||||||||
\(705\) | 3.77097e8 | 5.74913e−5 0 | ||||||||
\(706\) | −1.19089e12 | −0.180406 | ||||||||
\(707\) | 3.15469e12 | 0.474864 | ||||||||
\(708\) | −1.65135e12 | −0.246995 | ||||||||
\(709\) | −1.03005e13 | −1.53091 | −0.765456 | − | 0.643488i | \(-0.777487\pi\) | ||||
−0.765456 | + | 0.643488i | \(0.777487\pi\) | |||||||
\(710\) | 1.25545e12 | 0.185411 | ||||||||
\(711\) | 2.99170e12 | 0.439040 | ||||||||
\(712\) | 2.34251e12 | 0.341603 | ||||||||
\(713\) | 8.41824e12 | 1.21988 | ||||||||
\(714\) | 9.31828e10 | 0.0134182 | ||||||||
\(715\) | 2.31340e12 | 0.331035 | ||||||||
\(716\) | 3.33145e12 | 0.473723 | ||||||||
\(717\) | 2.48401e12 | 0.351009 | ||||||||
\(718\) | 3.70010e12 | 0.519581 | ||||||||
\(719\) | −5.03660e11 | −0.0702841 | −0.0351421 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351421 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(720\) | 6.83671e11 | 0.0948093 | ||||||||
\(721\) | −3.69182e11 | −0.0508782 | ||||||||
\(722\) | 3.70872e12 | 0.507933 | ||||||||
\(723\) | 4.75532e12 | 0.647228 | ||||||||
\(724\) | 6.54843e11 | 0.0885755 | ||||||||
\(725\) | 2.25279e11 | 0.0302830 | ||||||||
\(726\) | −2.38997e12 | −0.319284 | ||||||||
\(727\) | −1.04863e13 | −1.39225 | −0.696126 | − | 0.717920i | \(-0.745094\pi\) | ||||
−0.696126 | + | 0.717920i | \(0.745094\pi\) | |||||||
\(728\) | 6.31237e11 | 0.0832916 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −8.79582e12 | −1.14637 | ||||||||
\(731\) | 1.15055e12 | 0.149031 | ||||||||
\(732\) | 7.71449e11 | 0.0993133 | ||||||||
\(733\) | 1.29295e13 | 1.65430 | 0.827150 | − | 0.561981i | \(-0.189961\pi\) | ||||
0.827150 | + | 0.561981i | \(0.189961\pi\) | |||||||
\(734\) | 4.70812e12 | 0.598708 | ||||||||
\(735\) | −7.42449e11 | −0.0938369 | ||||||||
\(736\) | −1.29760e12 | −0.163001 | ||||||||
\(737\) | −1.32005e12 | −0.164811 | ||||||||
\(738\) | 1.10092e12 | 0.136616 | ||||||||
\(739\) | −5.31822e12 | −0.655944 | −0.327972 | − | 0.944687i | \(-0.606365\pi\) | ||||
−0.327972 | + | 0.944687i | \(0.606365\pi\) | |||||||
\(740\) | 7.84764e12 | 0.962047 | ||||||||
\(741\) | 1.56744e12 | 0.190989 | ||||||||
\(742\) | 2.61961e12 | 0.317263 | ||||||||
\(743\) | −2.50527e11 | −0.0301582 | −0.0150791 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150791 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(744\) | 2.25697e12 | 0.270052 | ||||||||
\(745\) | −1.59182e13 | −1.89317 | ||||||||
\(746\) | −4.32057e12 | −0.510759 | ||||||||
\(747\) | 2.92760e12 | 0.344008 | ||||||||
\(748\) | −1.73777e11 | −0.0202971 | ||||||||
\(749\) | −5.07589e11 | −0.0589310 | ||||||||
\(750\) | −2.83987e12 | −0.327735 | ||||||||
\(751\) | 1.43882e13 | 1.65054 | 0.825269 | − | 0.564739i | \(-0.191023\pi\) | ||||
0.825269 | + | 0.564739i | \(0.191023\pi\) | |||||||
\(752\) | −1.91889e8 | −2.18812e−5 0 | ||||||||
\(753\) | 6.58984e12 | 0.746960 | ||||||||
\(754\) | 4.02375e11 | 0.0453378 | ||||||||
\(755\) | 7.87460e12 | 0.881997 | ||||||||
\(756\) | −3.26653e11 | −0.0363696 | ||||||||
\(757\) | −4.39087e12 | −0.485981 | −0.242991 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242991 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(758\) | −3.01093e12 | −0.331276 | ||||||||
\(759\) | 2.27216e12 | 0.248514 | ||||||||
\(760\) | −1.96346e12 | −0.213481 | ||||||||
\(761\) | −4.31046e12 | −0.465900 | −0.232950 | − | 0.972489i | \(-0.574838\pi\) | ||||
−0.232950 | + | 0.972489i | \(0.574838\pi\) | |||||||
\(762\) | −1.20375e12 | −0.129342 | ||||||||
\(763\) | 6.44675e12 | 0.688621 | ||||||||
\(764\) | −2.54467e12 | −0.270216 | ||||||||
\(765\) | 3.12396e11 | 0.0329784 | ||||||||
\(766\) | 4.52526e12 | 0.474913 | ||||||||
\(767\) | −5.11156e12 | −0.533303 | ||||||||
\(768\) | −3.47892e11 | −0.0360844 | ||||||||
\(769\) | −1.27531e13 | −1.31506 | −0.657530 | − | 0.753428i | \(-0.728399\pi\) | ||||
−0.657530 | + | 0.753428i | \(0.728399\pi\) | |||||||
\(770\) | 1.38459e12 | 0.141943 | ||||||||
\(771\) | 2.74565e11 | 0.0279834 | ||||||||
\(772\) | −2.74225e12 | −0.277862 | ||||||||
\(773\) | 1.26121e13 | 1.27051 | 0.635256 | − | 0.772301i | \(-0.280894\pi\) | ||||
0.635256 | + | 0.772301i | \(0.280894\pi\) | |||||||
\(774\) | −4.03327e12 | −0.403946 | ||||||||
\(775\) | 3.91138e12 | 0.389468 | ||||||||
\(776\) | −1.00045e12 | −0.0990415 | ||||||||
\(777\) | −3.74955e12 | −0.369049 | ||||||||
\(778\) | 1.21289e13 | 1.18690 | ||||||||
\(779\) | −3.16177e12 | −0.307618 | ||||||||
\(780\) | 2.11623e12 | 0.204709 | ||||||||
\(781\) | 1.11865e12 | 0.107588 | ||||||||
\(782\) | −5.92925e11 | −0.0566982 | ||||||||
\(783\) | −2.08222e11 | −0.0197969 | ||||||||
\(784\) | 3.77802e11 | 0.0357143 | ||||||||
\(785\) | −6.84954e12 | −0.643795 | ||||||||
\(786\) | −6.15861e12 | −0.575548 | ||||||||
\(787\) | 2.63165e12 | 0.244535 | 0.122267 | − | 0.992497i | \(-0.460983\pi\) | ||||
0.122267 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(788\) | −2.93803e12 | −0.271449 | ||||||||
\(789\) | −5.82019e12 | −0.534676 | ||||||||
\(790\) | −1.16002e13 | −1.05960 | ||||||||
\(791\) | 2.28624e12 | 0.207648 | ||||||||
\(792\) | 6.09177e11 | 0.0550148 | ||||||||
\(793\) | 2.38794e12 | 0.214434 | ||||||||
\(794\) | −8.93028e12 | −0.797394 | ||||||||
\(795\) | 8.78228e12 | 0.779749 | ||||||||
\(796\) | 3.09209e12 | 0.272987 | ||||||||
\(797\) | 2.11384e10 | 0.00185571 | 0.000927854 | − | 1.00000i | \(-0.499705\pi\) | ||||
0.000927854 | 1.00000i | \(0.499705\pi\) | ||||||||
\(798\) | 9.38127e11 | 0.0818933 | ||||||||
\(799\) | −8.76819e7 | −7.61113e−6 0 | ||||||||
\(800\) | −6.02905e11 | −0.0520408 | ||||||||
\(801\) | −3.75225e12 | −0.322066 | ||||||||
\(802\) | −1.14174e13 | −0.974500 | ||||||||
\(803\) | −7.83741e12 | −0.665200 | ||||||||
\(804\) | −1.20754e12 | −0.101918 | ||||||||
\(805\) | 4.72422e12 | 0.396505 | ||||||||
\(806\) | 6.98620e12 | 0.583087 | ||||||||
\(807\) | −1.12804e12 | −0.0936254 | ||||||||
\(808\) | −5.38176e12 | −0.444194 | ||||||||
\(809\) | 6.73901e12 | 0.553131 | 0.276565 | − | 0.960995i | \(-0.410804\pi\) | ||||
0.276565 | + | 0.960995i | \(0.410804\pi\) | |||||||
\(810\) | −1.09511e12 | −0.0893870 | ||||||||
\(811\) | −1.43465e12 | −0.116454 | −0.0582269 | − | 0.998303i | \(-0.518545\pi\) | ||||
−0.0582269 | + | 0.998303i | \(0.518545\pi\) | |||||||
\(812\) | 2.40826e11 | 0.0194402 | ||||||||
\(813\) | −1.06641e13 | −0.856088 | ||||||||
\(814\) | 6.99254e12 | 0.558245 | ||||||||
\(815\) | −1.98041e13 | −1.57234 | ||||||||
\(816\) | −1.58966e11 | −0.0125516 | ||||||||
\(817\) | 1.15833e13 | 0.909562 | ||||||||
\(818\) | 1.07427e13 | 0.838923 | ||||||||
\(819\) | −1.01112e12 | −0.0785281 | ||||||||
\(820\) | −4.26877e12 | −0.329717 | ||||||||
\(821\) | −1.38553e13 | −1.06432 | −0.532160 | − | 0.846644i | \(-0.678619\pi\) | ||||
−0.532160 | + | 0.846644i | \(0.678619\pi\) | |||||||
\(822\) | −9.03036e12 | −0.689893 | ||||||||
\(823\) | 3.12155e12 | 0.237176 | 0.118588 | − | 0.992944i | \(-0.462163\pi\) | ||||
0.118588 | + | 0.992944i | \(0.462163\pi\) | |||||||
\(824\) | 6.29809e11 | 0.0475922 | ||||||||
\(825\) | 1.05572e12 | 0.0793422 | ||||||||
\(826\) | −3.05932e12 | −0.228673 | ||||||||
\(827\) | −9.34575e12 | −0.694767 | −0.347384 | − | 0.937723i | \(-0.612930\pi\) | ||||
−0.347384 | + | 0.937723i | \(0.612930\pi\) | |||||||
\(828\) | 2.07850e12 | 0.153679 | ||||||||
\(829\) | −1.11481e13 | −0.819799 | −0.409899 | − | 0.912131i | \(-0.634436\pi\) | ||||
−0.409899 | + | 0.912131i | \(0.634436\pi\) | |||||||
\(830\) | −1.13516e13 | −0.830247 | ||||||||
\(831\) | 2.94576e12 | 0.214286 | ||||||||
\(832\) | −1.07686e12 | −0.0779122 | ||||||||
\(833\) | 1.72633e11 | 0.0124228 | ||||||||
\(834\) | −8.28216e12 | −0.592784 | ||||||||
\(835\) | 2.65662e13 | 1.89122 | ||||||||
\(836\) | −1.74951e12 | −0.123877 | ||||||||
\(837\) | −3.61523e12 | −0.254607 | ||||||||
\(838\) | −1.25689e13 | −0.880440 | ||||||||
\(839\) | −2.44315e13 | −1.70224 | −0.851121 | − | 0.524970i | \(-0.824077\pi\) | ||||
−0.851121 | + | 0.524970i | \(0.824077\pi\) | |||||||
\(840\) | 1.26658e12 | 0.0877763 | ||||||||
\(841\) | −1.43536e13 | −0.989418 | ||||||||
\(842\) | −1.34587e13 | −0.922783 | ||||||||
\(843\) | 9.47449e12 | 0.646147 | ||||||||
\(844\) | −1.38043e13 | −0.936423 | ||||||||
\(845\) | −1.03106e13 | −0.695711 | ||||||||
\(846\) | 3.07370e8 | 2.06298e−5 0 | ||||||||
\(847\) | −4.42771e12 | −0.295599 | ||||||||
\(848\) | −4.46894e12 | −0.296772 | ||||||||
\(849\) | −1.27684e13 | −0.843436 | ||||||||
\(850\) | −2.75491e11 | −0.0181018 | ||||||||
\(851\) | 2.38585e13 | 1.55941 | ||||||||
\(852\) | 1.02331e12 | 0.0665317 | ||||||||
\(853\) | 1.67379e13 | 1.08251 | 0.541253 | − | 0.840859i | \(-0.317950\pi\) | ||||
0.541253 | + | 0.840859i | \(0.317950\pi\) | |||||||
\(854\) | 1.42920e12 | 0.0919462 | ||||||||
\(855\) | 3.14508e12 | 0.201272 | ||||||||
\(856\) | 8.65924e11 | 0.0551249 | ||||||||
\(857\) | −1.79355e13 | −1.13579 | −0.567896 | − | 0.823100i | \(-0.692242\pi\) | ||||
−0.567896 | + | 0.823100i | \(0.692242\pi\) | |||||||
\(858\) | 1.88564e12 | 0.118786 | ||||||||
\(859\) | 1.78417e13 | 1.11807 | 0.559033 | − | 0.829145i | \(-0.311172\pi\) | ||||
0.559033 | + | 0.829145i | \(0.311172\pi\) | |||||||
\(860\) | 1.56388e13 | 0.974903 | ||||||||
\(861\) | 2.03959e12 | 0.126482 | ||||||||
\(862\) | 1.58646e13 | 0.978690 | ||||||||
\(863\) | 1.32676e13 | 0.814225 | 0.407112 | − | 0.913378i | \(-0.366536\pi\) | ||||
0.407112 | + | 0.913378i | \(0.366536\pi\) | |||||||
\(864\) | 5.57256e11 | 0.0340207 | ||||||||
\(865\) | 3.30551e13 | 2.00755 | ||||||||
\(866\) | 3.35875e12 | 0.202930 | ||||||||
\(867\) | 9.53298e12 | 0.572984 | ||||||||
\(868\) | 4.18131e12 | 0.250020 | ||||||||
\(869\) | −1.03362e13 | −0.614854 | ||||||||
\(870\) | 8.07371e11 | 0.0477789 | ||||||||
\(871\) | −3.73781e12 | −0.220057 | ||||||||
\(872\) | −1.09979e13 | −0.644146 | ||||||||
\(873\) | 1.60253e12 | 0.0933772 | ||||||||
\(874\) | −5.96933e12 | −0.346038 | ||||||||
\(875\) | −5.26121e12 | −0.303424 | ||||||||
\(876\) | −7.16942e12 | −0.411354 | ||||||||
\(877\) | 2.51717e13 | 1.43686 | 0.718430 | − | 0.695599i | \(-0.244861\pi\) | ||||
0.718430 | + | 0.695599i | \(0.244861\pi\) | |||||||
\(878\) | 1.68097e13 | 0.954632 | ||||||||
\(879\) | 1.08978e13 | 0.615727 | ||||||||
\(880\) | −2.36206e12 | −0.132776 | ||||||||
\(881\) | 2.12069e13 | 1.18601 | 0.593003 | − | 0.805201i | \(-0.297942\pi\) | ||||
0.593003 | + | 0.805201i | \(0.297942\pi\) | |||||||
\(882\) | −6.05166e11 | −0.0336718 | ||||||||
\(883\) | 2.79753e13 | 1.54864 | 0.774322 | − | 0.632792i | \(-0.218091\pi\) | ||||
0.774322 | + | 0.632792i | \(0.218091\pi\) | |||||||
\(884\) | −4.92061e11 | −0.0271009 | ||||||||
\(885\) | −1.02564e13 | −0.562019 | ||||||||
\(886\) | 2.73863e12 | 0.149307 | ||||||||
\(887\) | −7.69155e12 | −0.417213 | −0.208606 | − | 0.978000i | \(-0.566893\pi\) | ||||
−0.208606 | + | 0.978000i | \(0.566893\pi\) | |||||||
\(888\) | 6.39656e12 | 0.345214 | ||||||||
\(889\) | −2.23010e12 | −0.119748 | ||||||||
\(890\) | 1.45492e13 | 0.777291 | ||||||||
\(891\) | −9.75783e11 | −0.0518685 | ||||||||
\(892\) | 3.96166e12 | 0.209525 | ||||||||
\(893\) | −8.82745e8 | −4.64519e−5 0 | ||||||||
\(894\) | −1.29748e13 | −0.679332 | ||||||||
\(895\) | 2.06914e13 | 1.07792 | ||||||||
\(896\) | −6.44514e11 | −0.0334077 | ||||||||
\(897\) | 6.43378e12 | 0.331818 | ||||||||
\(898\) | 1.42752e13 | 0.732552 | ||||||||
\(899\) | 2.66533e12 | 0.136092 | ||||||||
\(900\) | 9.65737e11 | 0.0490645 | ||||||||
\(901\) | −2.04204e12 | −0.103229 | ||||||||
\(902\) | −3.80364e12 | −0.191324 | ||||||||
\(903\) | −7.47213e12 | −0.373981 | ||||||||
\(904\) | −3.90022e12 | −0.194237 | ||||||||
\(905\) | 4.06719e12 | 0.201547 | ||||||||
\(906\) | 6.41854e12 | 0.316489 | ||||||||
\(907\) | −8.03188e12 | −0.394080 | −0.197040 | − | 0.980395i | \(-0.563133\pi\) | ||||
−0.197040 | + | 0.980395i | \(0.563133\pi\) | |||||||
\(908\) | 1.75135e13 | 0.855041 | ||||||||
\(909\) | 8.62053e12 | 0.418790 | ||||||||
\(910\) | 3.92057e12 | 0.189524 | ||||||||
\(911\) | −3.70764e13 | −1.78347 | −0.891733 | − | 0.452561i | \(-0.850510\pi\) | ||||
−0.891733 | + | 0.452561i | \(0.850510\pi\) | |||||||
\(912\) | −1.60040e12 | −0.0766042 | ||||||||
\(913\) | −1.01147e13 | −0.481766 | ||||||||
\(914\) | −3.09713e12 | −0.146792 | ||||||||
\(915\) | 4.79142e12 | 0.225980 | ||||||||
\(916\) | 1.55396e12 | 0.0729309 | ||||||||
\(917\) | −1.14096e13 | −0.532853 | ||||||||
\(918\) | 2.54633e11 | 0.0118337 | ||||||||
\(919\) | −2.32387e13 | −1.07471 | −0.537357 | − | 0.843355i | \(-0.680577\pi\) | ||||
−0.537357 | + | 0.843355i | \(0.680577\pi\) | |||||||
\(920\) | −8.05931e12 | −0.370897 | ||||||||
\(921\) | −2.27983e13 | −1.04408 | ||||||||
\(922\) | −1.92423e13 | −0.876936 | ||||||||
\(923\) | 3.16754e12 | 0.143653 | ||||||||
\(924\) | 1.12857e12 | 0.0509338 | ||||||||
\(925\) | 1.10854e13 | 0.497867 | ||||||||
\(926\) | 2.05632e13 | 0.919055 | ||||||||
\(927\) | −1.00883e12 | −0.0448704 | ||||||||
\(928\) | −4.10838e11 | −0.0181847 | ||||||||
\(929\) | −1.47386e13 | −0.649211 | −0.324605 | − | 0.945850i | \(-0.605231\pi\) | ||||
−0.324605 | + | 0.945850i | \(0.605231\pi\) | |||||||
\(930\) | 1.40179e13 | 0.614482 | ||||||||
\(931\) | 1.73800e12 | 0.0758185 | ||||||||
\(932\) | −5.42366e12 | −0.235462 | ||||||||
\(933\) | −1.49471e13 | −0.645789 | ||||||||
\(934\) | 2.20191e13 | 0.946756 | ||||||||
\(935\) | −1.07932e12 | −0.0461846 | ||||||||
\(936\) | 1.72493e12 | 0.0734563 | ||||||||
\(937\) | −3.86396e13 | −1.63759 | −0.818795 | − | 0.574087i | \(-0.805357\pi\) | ||||
−0.818795 | + | 0.574087i | \(0.805357\pi\) | |||||||
\(938\) | −2.23712e12 | −0.0943575 | ||||||||
\(939\) | 1.30922e12 | 0.0549564 | ||||||||
\(940\) | −1.19181e9 | −4.97889e−5 0 | ||||||||
\(941\) | 4.12643e13 | 1.71562 | 0.857810 | − | 0.513967i | \(-0.171825\pi\) | ||||
0.857810 | + | 0.513967i | \(0.171825\pi\) | |||||||
\(942\) | −5.58302e12 | −0.231015 | ||||||||
\(943\) | −1.29780e13 | −0.534447 | ||||||||
\(944\) | 5.21907e12 | 0.213904 | ||||||||
\(945\) | −2.02882e12 | −0.0827563 | ||||||||
\(946\) | 1.39348e13 | 0.565705 | ||||||||
\(947\) | 3.25255e13 | 1.31416 | 0.657081 | − | 0.753820i | \(-0.271791\pi\) | ||||
0.657081 | + | 0.753820i | \(0.271791\pi\) | |||||||
\(948\) | −9.45524e12 | −0.380220 | ||||||||
\(949\) | −2.21922e13 | −0.888181 | ||||||||
\(950\) | −2.77353e12 | −0.110478 | ||||||||
\(951\) | 7.25667e11 | 0.0287690 | ||||||||
\(952\) | −2.94504e11 | −0.0116205 | ||||||||
\(953\) | 2.30788e13 | 0.906349 | 0.453174 | − | 0.891422i | \(-0.350291\pi\) | ||||
0.453174 | + | 0.891422i | \(0.350291\pi\) | |||||||
\(954\) | 7.15838e12 | 0.279800 | ||||||||
\(955\) | −1.58048e13 | −0.614855 | ||||||||
\(956\) | −7.85071e12 | −0.303982 | ||||||||
\(957\) | 7.19398e11 | 0.0277246 | ||||||||
\(958\) | 1.84958e13 | 0.709461 | ||||||||
\(959\) | −1.67299e13 | −0.638717 | ||||||||
\(960\) | −2.16074e12 | −0.0821072 | ||||||||
\(961\) | 1.98369e13 | 0.750273 | ||||||||
\(962\) | 1.97999e13 | 0.745374 | ||||||||
\(963\) | −1.38704e12 | −0.0519722 | ||||||||
\(964\) | −1.50292e13 | −0.560516 | ||||||||
\(965\) | −1.70319e13 | −0.632254 | ||||||||
\(966\) | 3.85069e12 | 0.142279 | ||||||||
\(967\) | −1.53358e13 | −0.564011 | −0.282005 | − | 0.959413i | \(-0.591000\pi\) | ||||
−0.282005 | + | 0.959413i | \(0.591000\pi\) | |||||||
\(968\) | 7.55347e12 | 0.276508 | ||||||||
\(969\) | −7.31287e11 | −0.0266459 | ||||||||
\(970\) | −6.21373e12 | −0.225361 | ||||||||
\(971\) | 1.98971e13 | 0.718297 | 0.359149 | − | 0.933280i | \(-0.383067\pi\) | ||||
0.359149 | + | 0.933280i | \(0.383067\pi\) | |||||||
\(972\) | −8.92617e11 | −0.0320750 | ||||||||
\(973\) | −1.53437e13 | −0.548811 | ||||||||
\(974\) | 1.07661e13 | 0.383305 | ||||||||
\(975\) | 2.98933e12 | 0.105938 | ||||||||
\(976\) | −2.43816e12 | −0.0860078 | ||||||||
\(977\) | 1.16887e13 | 0.410432 | 0.205216 | − | 0.978717i | \(-0.434210\pi\) | ||||
0.205216 | + | 0.978717i | \(0.434210\pi\) | |||||||
\(978\) | −1.61422e13 | −0.564208 | ||||||||
\(979\) | 1.29639e13 | 0.451037 | ||||||||
\(980\) | 2.34650e12 | 0.0812651 | ||||||||
\(981\) | 1.76165e13 | 0.607306 | ||||||||
\(982\) | 1.26502e13 | 0.434105 | ||||||||
\(983\) | −3.68758e13 | −1.25965 | −0.629826 | − | 0.776736i | \(-0.716874\pi\) | ||||
−0.629826 | + | 0.776736i | \(0.716874\pi\) | |||||||
\(984\) | −3.47945e12 | −0.118313 | ||||||||
\(985\) | −1.82479e13 | −0.617662 | ||||||||
\(986\) | −1.87728e11 | −0.00632534 | ||||||||
\(987\) | 5.69440e8 | 1.90995e−5 0 | ||||||||
\(988\) | −4.95387e12 | −0.165401 | ||||||||
\(989\) | 4.75454e13 | 1.58025 | ||||||||
\(990\) | 3.78356e12 | 0.125182 | ||||||||
\(991\) | −4.10347e13 | −1.35151 | −0.675756 | − | 0.737126i | \(-0.736183\pi\) | ||||
−0.675756 | + | 0.737126i | \(0.736183\pi\) | |||||||
\(992\) | −7.13314e12 | −0.233872 | ||||||||
\(993\) | 3.05458e12 | 0.0996966 | ||||||||
\(994\) | 1.89581e12 | 0.0615964 | ||||||||
\(995\) | 1.92047e13 | 0.621162 | ||||||||
\(996\) | −9.25266e12 | −0.297920 | ||||||||
\(997\) | −4.99823e11 | −0.0160209 | −0.00801047 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00801047 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(998\) | −4.37014e12 | −0.139447 | ||||||||
\(999\) | −1.02461e13 | −0.325471 |
(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 | 42.10.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 126.10.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 336.10.a.g.1.1 | 1 | |||
7.6 | odd | 2 | 294.10.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.10.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
126.10.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
294.10.a.e.1.1 | 1 | 7.6 | odd | 2 | |||
336.10.a.g.1.1 | 1 | 4.3 | odd | 2 |