Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.3 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 40537.3i | − | 1.74952i | −0.484552 | − | 0.874762i | \(-0.661017\pi\) | ||
0.484552 | − | 0.874762i | \(-0.338983\pi\) | |||||||
\(3\) | −896293. | + | 8.23572e6i | −0.108191 | + | 0.994130i | ||||
\(4\) | −1.10640e9 | −2.06084 | ||||||||
\(5\) | 2.53522e10 | 1.85759 | 0.928797 | − | 0.370589i | \(-0.120844\pi\) | ||||
0.928797 | + | 0.370589i | \(0.120844\pi\) | |||||||
\(6\) | 3.33854e11 | + | 3.63333e10i | 1.73926 | + | 0.189283i | ||||
\(7\) | 3.38830e11 | − | 1.76213e12i | 0.188825 | − | 0.982011i | ||||
\(8\) | 2.30873e13i | 1.85596i | ||||||||
\(9\) | −6.70237e13 | − | 1.47632e13i | −0.976589 | − | 0.215112i | ||||
\(10\) | − | 1.02771e15i | − | 3.24991i | ||||||
\(11\) | − | 1.41931e15i | − | 1.12689i | −0.826152 | − | 0.563447i | \(-0.809475\pi\) | ||
0.826152 | − | 0.563447i | \(-0.190525\pi\) | |||||||
\(12\) | 9.91662e14 | − | 9.11203e15i | 0.222964 | − | 2.04874i | ||||
\(13\) | − | 2.20140e16i | − | 1.55068i | −0.631546 | − | 0.775338i | \(-0.717579\pi\) | ||
0.631546 | − | 0.775338i | \(-0.282421\pi\) | |||||||
\(14\) | −7.14320e16 | − | 1.37353e16i | −1.71805 | − | 0.330354i | ||||
\(15\) | −2.27230e16 | + | 2.08794e17i | −0.200975 | + | 1.84669i | ||||
\(16\) | 3.41903e17 | 1.18621 | ||||||||
\(17\) | 9.03848e17 | 1.30193 | 0.650963 | − | 0.759110i | \(-0.274365\pi\) | ||||
0.650963 | + | 0.759110i | \(0.274365\pi\) | |||||||
\(18\) | −5.98462e17 | + | 2.71696e18i | −0.376344 | + | 1.70857i | ||||
\(19\) | 2.84158e17i | 0.0815893i | 0.999168 | + | 0.0407947i | \(0.0129889\pi\) | ||||
−0.999168 | + | 0.0407947i | \(0.987011\pi\) | |||||||
\(20\) | −2.80498e19 | −3.82820 | ||||||||
\(21\) | 1.42087e19 | + | 4.36989e18i | 0.955817 | + | 0.293962i | ||||
\(22\) | −5.75350e19 | −1.97153 | ||||||||
\(23\) | − | 3.67708e19i | − | 0.661377i | −0.943740 | − | 0.330689i | \(-0.892719\pi\) | ||
0.943740 | − | 0.330689i | \(-0.107281\pi\) | |||||||
\(24\) | −1.90141e20 | − | 2.06930e19i | −1.84507 | − | 0.200799i | ||||
\(25\) | 4.56470e20 | 2.45066 | ||||||||
\(26\) | −8.92390e20 | −2.71295 | ||||||||
\(27\) | 1.81659e20 | − | 5.38756e20i | 0.319508 | − | 0.947584i | ||||
\(28\) | −3.74882e20 | + | 1.94963e21i | −0.389138 | + | 2.02376i | ||||
\(29\) | 1.16157e21i | 0.724895i | 0.932004 | + | 0.362448i | \(0.118059\pi\) | ||||
−0.932004 | + | 0.362448i | \(0.881941\pi\) | |||||||
\(30\) | 8.46394e21 | + | 9.21130e20i | 3.23083 | + | 0.351611i | ||||
\(31\) | 1.18888e21i | 0.282093i | 0.990003 | + | 0.141047i | \(0.0450468\pi\) | ||||
−0.990003 | + | 0.141047i | \(0.954953\pi\) | |||||||
\(32\) | − | 1.46491e21i | − | 0.219350i | ||||||
\(33\) | 1.16890e22 | + | 1.27212e21i | 1.12028 | + | 0.121920i | ||||
\(34\) | − | 3.66396e22i | − | 2.27775i | ||||||
\(35\) | 8.59008e21 | − | 4.46739e22i | 0.350761 | − | 1.82418i | ||||
\(36\) | 7.41553e22 | + | 1.63341e22i | 2.01259 | + | 0.443311i | ||||
\(37\) | −1.35607e21 | −0.0247375 | −0.0123688 | − | 0.999924i | \(-0.503937\pi\) | ||||
−0.0123688 | + | 0.999924i | \(0.503937\pi\) | |||||||
\(38\) | 1.15190e22 | 0.142743 | ||||||||
\(39\) | 1.81301e23 | + | 1.97310e22i | 1.54157 | + | 0.167769i | ||||
\(40\) | 5.85315e23i | 3.44762i | ||||||||
\(41\) | 1.70731e23 | 0.702984 | 0.351492 | − | 0.936191i | \(-0.385674\pi\) | ||||
0.351492 | + | 0.936191i | \(0.385674\pi\) | |||||||
\(42\) | 1.77144e23 | − | 5.75983e23i | 0.514293 | − | 1.67223i | ||||
\(43\) | −6.75136e23 | −1.39347 | −0.696737 | − | 0.717327i | \(-0.745365\pi\) | ||||
−0.696737 | + | 0.717327i | \(0.745365\pi\) | |||||||
\(44\) | 1.57033e24i | 2.32235i | ||||||||
\(45\) | −1.69920e24 | − | 3.74280e23i | −1.81411 | − | 0.399591i | ||||
\(46\) | −1.49059e24 | −1.15710 | ||||||||
\(47\) | 1.96537e24 | 1.11693 | 0.558464 | − | 0.829528i | \(-0.311391\pi\) | ||||
0.558464 | + | 0.829528i | \(0.311391\pi\) | |||||||
\(48\) | −3.06445e23 | + | 2.81582e24i | −0.128338 | + | 1.17925i | ||||
\(49\) | −2.99029e24 | − | 1.19412e24i | −0.928690 | − | 0.370857i | ||||
\(50\) | − | 1.85041e25i | − | 4.28748i | ||||||
\(51\) | −8.10112e23 | + | 7.44384e24i | −0.140857 | + | 1.29428i | ||||
\(52\) | 2.43564e25i | 3.19569i | ||||||||
\(53\) | 1.77266e24i | 0.176451i | 0.996101 | + | 0.0882257i | \(0.0281197\pi\) | ||||
−0.996101 | + | 0.0882257i | \(0.971880\pi\) | |||||||
\(54\) | −2.18397e25 | − | 7.36395e24i | −1.65782 | − | 0.558987i | ||||
\(55\) | − | 3.59826e25i | − | 2.09331i | ||||||
\(56\) | 4.06829e25 | + | 7.82268e24i | 1.82257 | + | 0.350452i | ||||
\(57\) | −2.34025e24 | − | 2.54689e23i | −0.0811104 | − | 0.00882724i | ||||
\(58\) | 4.70870e25 | 1.26822 | ||||||||
\(59\) | −4.83190e25 | −1.01570 | −0.507848 | − | 0.861447i | \(-0.669559\pi\) | ||||
−0.507848 | + | 0.861447i | \(0.669559\pi\) | |||||||
\(60\) | 2.51408e25 | − | 2.31010e26i | 0.414177 | − | 3.80573i | ||||
\(61\) | − | 7.56453e25i | − | 0.980617i | −0.871549 | − | 0.490309i | \(-0.836884\pi\) | ||
0.871549 | − | 0.490309i | \(-0.163116\pi\) | |||||||
\(62\) | 4.81939e25 | 0.493529 | ||||||||
\(63\) | −4.87243e25 | + | 1.13102e26i | −0.395647 | + | 0.918403i | ||||
\(64\) | 1.24174e26 | 0.802457 | ||||||||
\(65\) | − | 5.58105e26i | − | 2.88053i | ||||||
\(66\) | 5.15682e25 | − | 4.73842e26i | 0.213302 | − | 1.95996i | ||||
\(67\) | −1.04824e26 | −0.348639 | −0.174319 | − | 0.984689i | \(-0.555773\pi\) | ||||
−0.174319 | + | 0.984689i | \(0.555773\pi\) | |||||||
\(68\) | −1.00002e27 | −2.68306 | ||||||||
\(69\) | 3.02834e26 | + | 3.29574e25i | 0.657495 | + | 0.0715552i | ||||
\(70\) | −1.81096e27 | − | 3.48219e26i | −3.19144 | − | 0.613664i | ||||
\(71\) | 2.52140e26i | 0.361739i | 0.983507 | + | 0.180869i | \(0.0578911\pi\) | ||||
−0.983507 | + | 0.180869i | \(0.942109\pi\) | |||||||
\(72\) | 3.40844e26 | − | 1.54740e27i | 0.399240 | − | 1.81251i | ||||
\(73\) | 9.99284e26i | 0.958313i | 0.877729 | + | 0.479157i | \(0.159057\pi\) | ||||
−0.877729 | + | 0.479157i | \(0.840943\pi\) | |||||||
\(74\) | 5.49714e25i | 0.0432789i | ||||||||
\(75\) | −4.09131e26 | + | 3.75936e27i | −0.265139 | + | 2.43627i | ||||
\(76\) | − | 3.14394e26i | − | 0.168142i | ||||||
\(77\) | −2.50101e27 | − | 4.80904e26i | −1.10662 | − | 0.212786i | ||||
\(78\) | 7.99843e26 | − | 7.34948e27i | 0.293517 | − | 2.69702i | ||||
\(79\) | −2.17559e27 | −0.663720 | −0.331860 | − | 0.943329i | \(-0.607676\pi\) | ||||
−0.331860 | + | 0.943329i | \(0.607676\pi\) | |||||||
\(80\) | 8.66800e27 | 2.20350 | ||||||||
\(81\) | 4.27422e27 | + | 1.97897e27i | 0.907454 | + | 0.420152i | ||||
\(82\) | − | 6.92096e27i | − | 1.22989i | ||||||
\(83\) | 6.73274e27 | 1.00360 | 0.501798 | − | 0.864985i | \(-0.332672\pi\) | ||||
0.501798 | + | 0.864985i | \(0.332672\pi\) | |||||||
\(84\) | −1.57206e28 | − | 4.83486e27i | −1.96978 | − | 0.605807i | ||||
\(85\) | 2.29145e28 | 2.41845 | ||||||||
\(86\) | 2.73682e28i | 2.43792i | ||||||||
\(87\) | −9.56638e27 | − | 1.04111e27i | −0.720640 | − | 0.0784273i | ||||
\(88\) | 3.27681e28 | 2.09147 | ||||||||
\(89\) | −8.13678e27 | −0.440857 | −0.220428 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220428 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(90\) | −1.51723e28 | + | 6.88810e28i | −0.699094 | + | 3.17382i | ||||
\(91\) | −3.87916e28 | − | 7.45901e27i | −1.52278 | − | 0.292807i | ||||
\(92\) | 4.06833e28i | 1.36299i | ||||||||
\(93\) | −9.79126e27 | − | 1.06558e27i | −0.280437 | − | 0.0305200i | ||||
\(94\) | − | 7.96709e28i | − | 1.95409i | ||||||
\(95\) | 7.20404e27i | 0.151560i | ||||||||
\(96\) | 1.20646e28 | + | 1.31299e27i | 0.218062 | + | 0.0237317i | ||||
\(97\) | − | 1.01638e29i | − | 1.58075i | −0.612621 | − | 0.790377i | \(-0.709885\pi\) | ||
0.612621 | − | 0.790377i | \(-0.290115\pi\) | |||||||
\(98\) | −4.84066e28 | + | 1.21219e29i | −0.648823 | + | 1.62477i | ||||
\(99\) | −2.09536e28 | + | 9.51273e28i | −0.242409 | + | 1.10051i | ||||
\(100\) | −5.05040e29 | −5.05040 | ||||||||
\(101\) | 2.70459e28 | 0.234121 | 0.117061 | − | 0.993125i | \(-0.462653\pi\) | ||||
0.117061 | + | 0.993125i | \(0.462653\pi\) | |||||||
\(102\) | 3.01753e29 | + | 3.28398e28i | 2.26438 | + | 0.246432i | ||||
\(103\) | 7.33945e28i | 0.478106i | 0.971007 | + | 0.239053i | \(0.0768369\pi\) | ||||
−0.971007 | + | 0.239053i | \(0.923163\pi\) | |||||||
\(104\) | 5.08246e29 | 2.87800 | ||||||||
\(105\) | 3.60222e29 | + | 1.10786e29i | 1.77552 | + | 0.546061i | ||||
\(106\) | 7.18589e28 | 0.308706 | ||||||||
\(107\) | − | 2.13042e29i | − | 0.798732i | −0.916792 | − | 0.399366i | \(-0.869230\pi\) | ||
0.916792 | − | 0.399366i | \(-0.130770\pi\) | |||||||
\(108\) | −2.00988e29 | + | 5.96082e29i | −0.658454 | + | 1.95282i | ||||
\(109\) | 7.01375e28 | 0.201033 | 0.100516 | − | 0.994935i | \(-0.467951\pi\) | ||||
0.100516 | + | 0.994935i | \(0.467951\pi\) | |||||||
\(110\) | −1.45864e30 | −3.66230 | ||||||||
\(111\) | 1.21543e27 | − | 1.11682e28i | 0.00267638 | − | 0.0245923i | ||||
\(112\) | 1.15847e29 | − | 6.02477e29i | 0.223987 | − | 1.16488i | ||||
\(113\) | − | 3.32301e29i | − | 0.564800i | −0.959297 | − | 0.282400i | \(-0.908869\pi\) | ||
0.959297 | − | 0.282400i | \(-0.0911305\pi\) | |||||||
\(114\) | −1.03244e28 | + | 9.48674e28i | −0.0154435 | + | 0.141905i | ||||
\(115\) | − | 9.32221e29i | − | 1.22857i | ||||||
\(116\) | − | 1.28517e30i | − | 1.49389i | ||||||
\(117\) | −3.24998e29 | + | 1.47546e30i | −0.333569 | + | 1.51437i | ||||
\(118\) | 1.95872e30i | 1.77699i | ||||||||
\(119\) | 3.06251e29 | − | 1.59270e30i | 0.245836 | − | 1.27850i | ||||
\(120\) | −4.82049e30 | − | 5.24614e29i | −3.42739 | − | 0.373002i | ||||
\(121\) | −4.28128e29 | −0.269890 | ||||||||
\(122\) | −3.06646e30 | −1.71561 | ||||||||
\(123\) | −1.53025e29 | + | 1.40609e30i | −0.0760566 | + | 0.698857i | ||||
\(124\) | − | 1.31538e30i | − | 0.581348i | ||||||
\(125\) | 6.85031e30 | 2.69473 | ||||||||
\(126\) | 4.58486e30 | + | 1.97515e30i | 1.60677 | + | 0.692194i | ||||
\(127\) | −1.74410e28 | −0.00545026 | −0.00272513 | − | 0.999996i | \(-0.500867\pi\) | ||||
−0.00272513 | + | 0.999996i | \(0.500867\pi\) | |||||||
\(128\) | − | 5.82016e30i | − | 1.62327i | ||||||
\(129\) | 6.05120e29 | − | 5.56023e30i | 0.150761 | − | 1.38529i | ||||
\(130\) | −2.26241e31 | −5.03955 | ||||||||
\(131\) | −6.50358e29 | −0.129634 | −0.0648170 | − | 0.997897i | \(-0.520646\pi\) | ||||
−0.0648170 | + | 0.997897i | \(0.520646\pi\) | |||||||
\(132\) | −1.29328e31 | − | 1.40747e30i | −2.30871 | − | 0.251257i | ||||
\(133\) | 5.00724e29 | + | 9.62813e28i | 0.0801216 | + | 0.0154061i | ||||
\(134\) | 4.24928e30i | 0.609952i | ||||||||
\(135\) | 4.60545e30 | − | 1.36587e31i | 0.593516 | − | 1.76023i | ||||
\(136\) | 2.08674e31i | 2.41632i | ||||||||
\(137\) | 1.06805e31i | 1.11209i | 0.831151 | + | 0.556047i | \(0.187683\pi\) | ||||
−0.831151 | + | 0.556047i | \(0.812317\pi\) | |||||||
\(138\) | 1.33600e30 | − | 1.22761e31i | 0.125188 | − | 1.15030i | ||||
\(139\) | − | 6.22380e30i | − | 0.525220i | −0.964902 | − | 0.262610i | \(-0.915417\pi\) | ||
0.964902 | − | 0.262610i | \(-0.0845832\pi\) | |||||||
\(140\) | −9.50410e30 | + | 4.94273e31i | −0.722860 | + | 3.75933i | ||||
\(141\) | −1.76155e30 | + | 1.61862e31i | −0.120842 | + | 1.11037i | ||||
\(142\) | 1.02211e31 | 0.632871 | ||||||||
\(143\) | −3.12447e31 | −1.74745 | ||||||||
\(144\) | −2.29156e31 | − | 5.04759e30i | −1.15844 | − | 0.255169i | ||||
\(145\) | 2.94484e31i | 1.34656i | ||||||||
\(146\) | 4.05083e31 | 1.67659 | ||||||||
\(147\) | 1.25146e31 | − | 2.35569e31i | 0.469156 | − | 0.883115i | ||||
\(148\) | 1.50036e30 | 0.0509800 | ||||||||
\(149\) | − | 7.49140e30i | − | 0.230867i | −0.993315 | − | 0.115434i | \(-0.963174\pi\) | ||
0.993315 | − | 0.115434i | \(-0.0368257\pi\) | |||||||
\(150\) | 1.52394e32 | + | 1.65851e31i | 4.26232 | + | 0.463868i | ||||
\(151\) | −3.37654e31 | −0.857643 | −0.428821 | − | 0.903389i | \(-0.641071\pi\) | ||||
−0.428821 | + | 0.903389i | \(0.641071\pi\) | |||||||
\(152\) | −6.56046e30 | −0.151427 | ||||||||
\(153\) | −6.05792e31 | − | 1.33437e31i | −1.27145 | − | 0.280060i | ||||
\(154\) | −1.94946e31 | + | 1.01384e32i | −0.372274 | + | 1.93606i | ||||
\(155\) | 3.01407e31i | 0.524015i | ||||||||
\(156\) | −2.00593e32 | − | 2.18305e31i | −3.17693 | − | 0.345746i | ||||
\(157\) | 2.00568e31i | 0.289545i | 0.989465 | + | 0.144772i | \(0.0462450\pi\) | ||||
−0.989465 | + | 0.144772i | \(0.953755\pi\) | |||||||
\(158\) | 8.81927e31i | 1.16119i | ||||||||
\(159\) | −1.45991e31 | − | 1.58882e30i | −0.175416 | − | 0.0190905i | ||||
\(160\) | − | 3.71387e31i | − | 0.407462i | ||||||
\(161\) | −6.47949e31 | − | 1.24590e31i | −0.649480 | − | 0.124885i | ||||
\(162\) | 8.02222e31 | − | 1.73266e32i | 0.735067 | − | 1.58761i | ||||
\(163\) | −1.57676e32 | −1.32144 | −0.660719 | − | 0.750634i | \(-0.729748\pi\) | ||||
−0.660719 | + | 0.750634i | \(0.729748\pi\) | |||||||
\(164\) | −1.88897e32 | −1.44874 | ||||||||
\(165\) | 2.96343e32 | + | 3.22510e31i | 2.08102 | + | 0.226478i | ||||
\(166\) | − | 2.72927e32i | − | 1.75582i | ||||||
\(167\) | −1.17503e32 | −0.692885 | −0.346443 | − | 0.938071i | \(-0.612611\pi\) | ||||
−0.346443 | + | 0.938071i | \(0.612611\pi\) | |||||||
\(168\) | −1.00889e32 | + | 3.28041e32i | −0.545582 | + | 1.77396i | ||||
\(169\) | −2.83080e32 | −1.40460 | ||||||||
\(170\) | − | 9.28894e32i | − | 4.23114i | ||||||
\(171\) | 4.19510e30 | − | 1.90453e31i | 0.0175509 | − | 0.0796793i | ||||
\(172\) | 7.46973e32 | 2.87172 | ||||||||
\(173\) | 4.13553e31 | 0.146171 | 0.0730857 | − | 0.997326i | \(-0.476715\pi\) | ||||
0.0730857 | + | 0.997326i | \(0.476715\pi\) | |||||||
\(174\) | −4.22038e31 | + | 3.87796e32i | −0.137210 | + | 1.26078i | ||||
\(175\) | 1.54666e32 | − | 8.04359e32i | 0.462745 | − | 2.40657i | ||||
\(176\) | − | 4.85266e32i | − | 1.33674i | ||||||
\(177\) | 4.33080e31 | − | 3.97942e32i | 0.109889 | − | 1.00973i | ||||
\(178\) | 3.29843e32i | 0.771290i | ||||||||
\(179\) | − | 4.08045e32i | − | 0.879709i | −0.898069 | − | 0.439855i | \(-0.855030\pi\) | ||
0.898069 | − | 0.439855i | \(-0.144970\pi\) | |||||||
\(180\) | 1.88000e33 | + | 4.14105e32i | 3.73858 | + | 0.823492i | ||||
\(181\) | 2.24904e32i | 0.412723i | 0.978476 | + | 0.206361i | \(0.0661622\pi\) | ||||
−0.978476 | + | 0.206361i | \(0.933838\pi\) | |||||||
\(182\) | −3.02368e32 | + | 1.57251e33i | −0.512273 | + | 2.66414i | ||||
\(183\) | 6.22994e32 | + | 6.78004e31i | 0.974861 | + | 0.106094i | ||||
\(184\) | 8.48940e32 | 1.22749 | ||||||||
\(185\) | −3.43793e31 | −0.0459523 | ||||||||
\(186\) | −4.31959e31 | + | 3.96912e32i | −0.0533955 | + | 0.490632i | ||||
\(187\) | − | 1.28284e33i | − | 1.46713i | ||||||
\(188\) | −2.17449e33 | −2.30181 | ||||||||
\(189\) | −8.87807e32 | − | 5.02653e32i | −0.870206 | − | 0.492688i | ||||
\(190\) | 2.92033e32 | 0.265158 | ||||||||
\(191\) | 1.73131e33i | 1.45677i | 0.685167 | + | 0.728386i | \(0.259729\pi\) | ||||
−0.685167 | + | 0.728386i | \(0.740271\pi\) | |||||||
\(192\) | −1.11296e32 | + | 1.02266e33i | −0.0868187 | + | 0.797747i | ||||
\(193\) | −2.27621e33 | −1.64676 | −0.823382 | − | 0.567488i | \(-0.807915\pi\) | ||||
−0.823382 | + | 0.567488i | \(0.807915\pi\) | |||||||
\(194\) | −4.12012e33 | −2.76557 | ||||||||
\(195\) | 4.59639e33 | + | 5.00225e32i | 2.86362 | + | 0.311648i | ||||
\(196\) | 3.30847e33 | + | 1.32118e33i | 1.91388 | + | 0.764275i | ||||
\(197\) | − | 3.08387e33i | − | 1.65705i | −0.559953 | − | 0.828524i | \(-0.689181\pi\) | ||
0.559953 | − | 0.828524i | \(-0.310819\pi\) | |||||||
\(198\) | 3.85621e33 | + | 8.49402e32i | 1.92537 | + | 0.424100i | ||||
\(199\) | 2.22436e33i | 1.03237i | 0.856477 | + | 0.516185i | \(0.172648\pi\) | ||||
−0.856477 | + | 0.516185i | \(0.827352\pi\) | |||||||
\(200\) | 1.05387e34i | 4.54832i | ||||||||
\(201\) | 9.39529e31 | − | 8.63300e32i | 0.0377196 | − | 0.346592i | ||||
\(202\) | − | 1.09637e33i | − | 0.409601i | ||||||
\(203\) | 2.04684e33 | + | 3.93575e32i | 0.711855 | + | 0.136879i | ||||
\(204\) | 8.96311e32 | − | 8.23589e33i | 0.290283 | − | 2.66731i | ||||
\(205\) | 4.32840e33 | 1.30586 | ||||||||
\(206\) | 2.97522e33 | 0.836458 | ||||||||
\(207\) | −5.42856e32 | + | 2.46451e33i | −0.142270 | + | 0.645894i | ||||
\(208\) | − | 7.52667e33i | − | 1.83943i | ||||||
\(209\) | 4.03309e32 | 0.0919425 | ||||||||
\(210\) | 4.49098e33 | − | 1.46024e34i | 0.955348 | − | 3.10632i | ||||
\(211\) | 5.33777e33 | 1.05990 | 0.529949 | − | 0.848029i | \(-0.322211\pi\) | ||||
0.529949 | + | 0.848029i | \(0.322211\pi\) | |||||||
\(212\) | − | 1.96128e33i | − | 0.363638i | ||||||
\(213\) | −2.07655e33 | − | 2.25991e32i | −0.359615 | − | 0.0391369i | ||||
\(214\) | −8.63617e33 | −1.39740 | ||||||||
\(215\) | −1.71162e34 | −2.58851 | ||||||||
\(216\) | 1.24384e34 | + | 4.19401e33i | 1.75868 | + | 0.592994i | ||||
\(217\) | 2.09496e33 | + | 4.02827e32i | 0.277019 | + | 0.0532663i | ||||
\(218\) | − | 2.84319e33i | − | 0.351711i | ||||||
\(219\) | −8.22982e33 | − | 8.95651e32i | −0.952688 | − | 0.103681i | ||||
\(220\) | 3.98113e34i | 4.31397i | ||||||||
\(221\) | − | 1.98973e34i | − | 2.01886i | ||||||
\(222\) | −4.52729e32 | − | 4.92704e31i | −0.0430249 | − | 0.00468240i | ||||
\(223\) | 1.01051e33i | 0.0899746i | 0.998988 | + | 0.0449873i | \(0.0143247\pi\) | ||||
−0.998988 | + | 0.0449873i | \(0.985675\pi\) | |||||||
\(224\) | −2.58136e33 | − | 4.96356e32i | −0.215404 | − | 0.0414187i | ||||
\(225\) | −3.05943e34 | − | 6.73897e33i | −2.39328 | − | 0.527166i | ||||
\(226\) | −1.34706e34 | −0.988132 | ||||||||
\(227\) | −2.00462e34 | −1.37930 | −0.689649 | − | 0.724144i | \(-0.742235\pi\) | ||||
−0.689649 | + | 0.724144i | \(0.742235\pi\) | |||||||
\(228\) | 2.58926e33 | + | 2.81789e32i | 0.167155 | + | 0.0181915i | ||||
\(229\) | − | 2.74288e34i | − | 1.66185i | −0.556382 | − | 0.830927i | \(-0.687811\pi\) | ||
0.556382 | − | 0.830927i | \(-0.312189\pi\) | |||||||
\(230\) | −3.77897e34 | −2.14942 | ||||||||
\(231\) | 6.20222e33 | − | 2.01665e34i | 0.331264 | − | 1.07710i | ||||
\(232\) | −2.68176e34 | −1.34538 | ||||||||
\(233\) | 1.74777e34i | 0.823804i | 0.911228 | + | 0.411902i | \(0.135135\pi\) | ||||
−0.911228 | + | 0.411902i | \(0.864865\pi\) | |||||||
\(234\) | 5.98113e34 | + | 1.31746e34i | 2.64944 | + | 0.583588i | ||||
\(235\) | 4.98265e34 | 2.07480 | ||||||||
\(236\) | 5.34603e34 | 2.09319 | ||||||||
\(237\) | 1.94997e33 | − | 1.79176e34i | 0.0718086 | − | 0.659824i | ||||
\(238\) | −6.45637e34 | − | 1.24146e34i | −2.23678 | − | 0.430097i | ||||
\(239\) | − | 3.55379e34i | − | 1.15857i | −0.815125 | − | 0.579285i | \(-0.803332\pi\) | ||
0.815125 | − | 0.579285i | \(-0.196668\pi\) | |||||||
\(240\) | −7.76906e33 | + | 7.13872e34i | −0.238400 | + | 2.19057i | ||||
\(241\) | 5.61592e34i | 1.62246i | 0.584728 | + | 0.811229i | \(0.301201\pi\) | ||||
−0.584728 | + | 0.811229i | \(0.698799\pi\) | |||||||
\(242\) | 1.73552e34i | 0.472179i | ||||||||
\(243\) | −2.01292e34 | + | 3.34276e34i | −0.515865 | + | 0.856670i | ||||
\(244\) | 8.36943e34i | 2.02089i | ||||||||
\(245\) | −7.58106e34 | − | 3.02737e34i | −1.72513 | − | 0.688901i | ||||
\(246\) | 5.69991e34 | + | 6.20321e33i | 1.22267 | + | 0.133063i | ||||
\(247\) | 6.25548e33 | 0.126519 | ||||||||
\(248\) | −2.74480e34 | −0.523554 | ||||||||
\(249\) | −6.03450e33 | + | 5.54489e34i | −0.108580 | + | 0.997706i | ||||
\(250\) | − | 2.77693e35i | − | 4.71449i | ||||||
\(251\) | 1.02385e35 | 1.64047 | 0.820237 | − | 0.572024i | \(-0.193842\pi\) | ||||
0.820237 | + | 0.572024i | \(0.193842\pi\) | |||||||
\(252\) | 5.39088e34 | − | 1.25137e35i | 0.815364 | − | 1.89268i | ||||
\(253\) | −5.21891e34 | −0.745302 | ||||||||
\(254\) | 7.07011e32i | 0.00953537i | ||||||||
\(255\) | −2.05381e34 | + | 1.88718e35i | −0.261655 | + | 2.40425i | ||||
\(256\) | −1.69268e35 | −2.03749 | ||||||||
\(257\) | 1.38355e35 | 1.57385 | 0.786927 | − | 0.617046i | \(-0.211671\pi\) | ||||
0.786927 | + | 0.617046i | \(0.211671\pi\) | |||||||
\(258\) | −2.25397e35 | − | 2.45299e34i | −2.42361 | − | 0.263761i | ||||
\(259\) | −4.59476e32 | + | 2.38957e33i | −0.00467107 | + | 0.0242925i | ||||
\(260\) | 6.17489e35i | 5.93630i | ||||||||
\(261\) | 1.71486e34 | − | 7.78529e34i | 0.155934 | − | 0.707925i | ||||
\(262\) | 2.63638e34i | 0.226798i | ||||||||
\(263\) | − | 1.90296e35i | − | 1.54907i | −0.632531 | − | 0.774535i | \(-0.717984\pi\) | ||
0.632531 | − | 0.774535i | \(-0.282016\pi\) | |||||||
\(264\) | −2.93698e34 | + | 2.69869e35i | −0.226279 | + | 2.07920i | ||||
\(265\) | 4.49408e34i | 0.327775i | ||||||||
\(266\) | 3.90299e33 | − | 2.02980e34i | 0.0269534 | − | 0.140175i | ||||
\(267\) | 7.29294e33 | − | 6.70122e34i | 0.0476968 | − | 0.438269i | ||||
\(268\) | 1.15978e35 | 0.718488 | ||||||||
\(269\) | 8.92185e34 | 0.523657 | 0.261828 | − | 0.965114i | \(-0.415675\pi\) | ||||
0.261828 | + | 0.965114i | \(0.415675\pi\) | |||||||
\(270\) | −5.53685e35 | − | 1.86693e35i | −3.07956 | − | 1.03837i | ||||
\(271\) | − | 1.16122e35i | − | 0.612152i | −0.952007 | − | 0.306076i | \(-0.900984\pi\) | ||
0.952007 | − | 0.306076i | \(-0.0990162\pi\) | |||||||
\(272\) | 3.09028e35 | 1.54436 | ||||||||
\(273\) | 9.61989e34 | − | 3.12791e35i | 0.455839 | − | 1.48216i | ||||
\(274\) | 4.32957e35 | 1.94564 | ||||||||
\(275\) | − | 6.47872e35i | − | 2.76163i | ||||||
\(276\) | −3.35057e35 | − | 3.64642e34i | −1.35499 | − | 0.147464i | ||||
\(277\) | −2.67170e35 | −1.02525 | −0.512626 | − | 0.858612i | \(-0.671327\pi\) | ||||
−0.512626 | + | 0.858612i | \(0.671327\pi\) | |||||||
\(278\) | −2.52296e35 | −0.918885 | ||||||||
\(279\) | 1.75517e34 | − | 7.96830e34i | 0.0606817 | − | 0.275489i | ||||
\(280\) | 1.03140e36 | + | 1.98322e35i | 3.38560 | + | 0.650998i | ||||
\(281\) | − | 8.53294e34i | − | 0.265985i | −0.991117 | − | 0.132993i | \(-0.957541\pi\) | ||
0.991117 | − | 0.132993i | \(-0.0424586\pi\) | |||||||
\(282\) | 6.56147e35 | + | 7.14084e34i | 1.94262 | + | 0.211416i | ||||
\(283\) | − | 4.51797e34i | − | 0.127069i | −0.997980 | − | 0.0635345i | \(-0.979763\pi\) | ||
0.997980 | − | 0.0635345i | \(-0.0202373\pi\) | |||||||
\(284\) | − | 2.78968e35i | − | 0.745485i | ||||||
\(285\) | −5.93305e34 | − | 6.45693e33i | −0.150670 | − | 0.0163974i | ||||
\(286\) | 1.26658e36i | 3.05720i | ||||||||
\(287\) | 5.78486e34 | − | 3.00849e35i | 0.132741 | − | 0.690338i | ||||
\(288\) | −2.16268e34 | + | 9.81838e34i | −0.0471847 | + | 0.214214i | ||||
\(289\) | 3.34973e35 | 0.695009 | ||||||||
\(290\) | 1.19376e36 | 2.35584 | ||||||||
\(291\) | 8.37059e35 | + | 9.10971e34i | 1.57148 | + | 0.171024i | ||||
\(292\) | − | 1.10561e36i | − | 1.97493i | ||||||
\(293\) | −6.15925e34 | −0.104700 | −0.0523501 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523501 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(294\) | −9.54935e35 | − | 5.07310e35i | −1.54503 | − | 0.820800i | ||||
\(295\) | −1.22499e36 | −1.88675 | ||||||||
\(296\) | − | 3.13080e34i | − | 0.0459119i | ||||||
\(297\) | −7.64661e35 | − | 2.57830e35i | −1.06783 | − | 0.360051i | ||||
\(298\) | −3.03681e35 | −0.403908 | ||||||||
\(299\) | −8.09474e35 | −1.02558 | ||||||||
\(300\) | 4.52664e35 | − | 4.15937e36i | 0.546409 | − | 5.02076i | ||||
\(301\) | −2.28756e35 | + | 1.18968e36i | −0.263123 | + | 1.36841i | ||||
\(302\) | 1.36876e36i | 1.50047i | ||||||||
\(303\) | −2.42410e34 | + | 2.22742e35i | −0.0253299 | + | 0.232747i | ||||
\(304\) | 9.71546e34i | 0.0967824i | ||||||||
\(305\) | − | 1.91778e36i | − | 1.82159i | ||||||
\(306\) | −5.40918e35 | + | 2.45572e36i | −0.489972 | + | 2.22443i | ||||
\(307\) | 4.68306e35i | 0.404598i | 0.979324 | + | 0.202299i | \(0.0648412\pi\) | ||||
−0.979324 | + | 0.202299i | \(0.935159\pi\) | |||||||
\(308\) | 2.76712e36 | + | 5.32074e35i | 2.28057 | + | 0.438517i | ||||
\(309\) | −6.04457e35 | − | 6.57830e34i | −0.475299 | − | 0.0517268i | ||||
\(310\) | 1.22182e36 | 0.916777 | ||||||||
\(311\) | −1.53662e36 | −1.10037 | −0.550186 | − | 0.835042i | \(-0.685443\pi\) | ||||
−0.550186 | + | 0.835042i | \(0.685443\pi\) | |||||||
\(312\) | −4.55537e35 | + | 4.18577e36i | −0.311374 | + | 2.86110i | ||||
\(313\) | 1.19248e36i | 0.778141i | 0.921208 | + | 0.389071i | \(0.127204\pi\) | ||||
−0.921208 | + | 0.389071i | \(0.872796\pi\) | |||||||
\(314\) | 8.13048e35 | 0.506566 | ||||||||
\(315\) | −1.23527e36 | + | 2.86739e36i | −0.734952 | + | 1.70602i | ||||
\(316\) | 2.40708e36 | 1.36782 | ||||||||
\(317\) | − | 6.75081e34i | − | 0.0366435i | −0.999832 | − | 0.0183217i | \(-0.994168\pi\) | ||
0.999832 | − | 0.0183217i | \(-0.00583231\pi\) | |||||||
\(318\) | −6.44066e34 | + | 5.91809e35i | −0.0333993 | + | 0.306894i | ||||
\(319\) | 1.64863e36 | 0.816880 | ||||||||
\(320\) | 3.14809e36 | 1.49064 | ||||||||
\(321\) | 1.75456e36 | + | 1.90948e35i | 0.794044 | + | 0.0864157i | ||||
\(322\) | −5.05056e35 | + | 2.62661e36i | −0.218489 | + | 1.13628i | ||||
\(323\) | 2.56836e35i | 0.106223i | ||||||||
\(324\) | −4.72902e36 | − | 2.18954e36i | −1.87011 | − | 0.865866i | ||||
\(325\) | − | 1.00488e37i | − | 3.80017i | ||||||
\(326\) | 6.39178e36i | 2.31189i | ||||||||
\(327\) | −6.28638e34 | + | 5.77633e35i | −0.0217499 | + | 0.199853i | ||||
\(328\) | 3.94171e36i | 1.30471i | ||||||||
\(329\) | 6.65926e35 | − | 3.46324e36i | 0.210904 | − | 1.09684i | ||||
\(330\) | 1.30737e36 | − | 1.20129e37i | 0.396228 | − | 3.64080i | ||||
\(331\) | 4.49145e36 | 1.30281 | 0.651405 | − | 0.758730i | \(-0.274180\pi\) | ||||
0.651405 | + | 0.758730i | \(0.274180\pi\) | |||||||
\(332\) | −7.44912e36 | −2.06825 | ||||||||
\(333\) | 9.08887e34 | + | 2.00199e34i | 0.0241584 | + | 0.00532134i | ||||
\(334\) | 4.76327e36i | 1.21222i | ||||||||
\(335\) | −2.65752e36 | −0.647629 | ||||||||
\(336\) | 4.85800e36 | + | 1.49408e36i | 1.13380 | + | 0.348702i | ||||
\(337\) | −4.28477e36 | −0.957842 | −0.478921 | − | 0.877858i | \(-0.658972\pi\) | ||||
−0.478921 | + | 0.877858i | \(0.658972\pi\) | |||||||
\(338\) | 1.14753e37i | 2.45738i | ||||||||
\(339\) | 2.73674e36 | + | 2.97839e35i | 0.561485 | + | 0.0611064i | ||||
\(340\) | −2.53527e37 | −4.98403 | ||||||||
\(341\) | 1.68739e36 | 0.317889 | ||||||||
\(342\) | −7.72047e35 | − | 1.70058e35i | −0.139401 | − | 0.0307057i | ||||
\(343\) | −3.11740e36 | + | 4.86468e36i | −0.539545 | + | 0.841957i | ||||
\(344\) | − | 1.55871e37i | − | 2.58623i | ||||||
\(345\) | 7.67751e36 | + | 8.35543e35i | 1.22136 | + | 0.132920i | ||||
\(346\) | − | 1.67643e36i | − | 0.255731i | ||||||
\(347\) | 1.36597e36i | 0.199831i | 0.994996 | + | 0.0999157i | \(0.0318573\pi\) | ||||
−0.994996 | + | 0.0999157i | \(0.968143\pi\) | |||||||
\(348\) | 1.05843e37 | + | 1.15189e36i | 1.48512 | + | 0.161626i | ||||
\(349\) | − | 6.00688e36i | − | 0.808500i | −0.914648 | − | 0.404250i | \(-0.867533\pi\) | ||
0.914648 | − | 0.404250i | \(-0.132467\pi\) | |||||||
\(350\) | −3.26066e37 | − | 6.26973e36i | −4.21035 | − | 0.809585i | ||||
\(351\) | −1.18602e37 | − | 3.99904e36i | −1.46940 | − | 0.495453i | ||||
\(352\) | −2.07916e36 | −0.247184 | ||||||||
\(353\) | 4.96737e36 | 0.566752 | 0.283376 | − | 0.959009i | \(-0.408546\pi\) | ||||
0.283376 | + | 0.959009i | \(0.408546\pi\) | |||||||
\(354\) | −1.61315e37 | − | 1.75559e36i | −1.76656 | − | 0.192254i | ||||
\(355\) | 6.39230e36i | 0.671964i | ||||||||
\(356\) | 9.00256e36 | 0.908534 | ||||||||
\(357\) | 1.28425e37 | + | 3.94972e36i | 1.24440 | + | 0.382716i | ||||
\(358\) | −1.65411e37 | −1.53907 | ||||||||
\(359\) | − | 2.42934e36i | − | 0.217080i | −0.994092 | − | 0.108540i | \(-0.965382\pi\) | ||
0.994092 | − | 0.108540i | \(-0.0346175\pi\) | |||||||
\(360\) | 8.64114e36 | − | 3.92300e37i | 0.741626 | − | 3.36691i | ||||
\(361\) | 1.20491e37 | 0.993343 | ||||||||
\(362\) | 9.11702e36 | 0.722069 | ||||||||
\(363\) | 3.83728e35 | − | 3.52594e36i | 0.0291997 | − | 0.268305i | ||||
\(364\) | 4.29192e37 | + | 8.25268e36i | 3.13820 | + | 0.603427i | ||||
\(365\) | 2.53341e37i | 1.78016i | ||||||||
\(366\) | 2.74845e36 | − | 2.52545e37i | 0.185614 | − | 1.70554i | ||||
\(367\) | 1.82108e37i | 1.18214i | 0.806618 | + | 0.591072i | \(0.201295\pi\) | ||||
−0.806618 | + | 0.591072i | \(0.798705\pi\) | |||||||
\(368\) | − | 1.25720e37i | − | 0.784535i | ||||||
\(369\) | −1.14430e37 | − | 2.52053e36i | −0.686526 | − | 0.151220i | ||||
\(370\) | 1.39365e36i | 0.0803947i | ||||||||
\(371\) | 3.12366e36 | + | 6.00630e35i | 0.173277 | + | 0.0333185i | ||||
\(372\) | 1.08331e37 | + | 1.17896e36i | 0.577936 | + | 0.0628968i | ||||
\(373\) | 2.96683e37 | 1.52235 | 0.761175 | − | 0.648547i | \(-0.224623\pi\) | ||||
0.761175 | + | 0.648547i | \(0.224623\pi\) | |||||||
\(374\) | −5.20029e37 | −2.56678 | ||||||||
\(375\) | −6.13988e36 | + | 5.64172e37i | −0.291546 | + | 2.67891i | ||||
\(376\) | 4.53752e37i | 2.07298i | ||||||||
\(377\) | 2.55709e37 | 1.12408 | ||||||||
\(378\) | −2.03762e37 | + | 3.59893e37i | −0.861969 | + | 1.52245i | ||||
\(379\) | 7.48995e36 | 0.304937 | 0.152469 | − | 0.988308i | \(-0.451278\pi\) | ||||
0.152469 | + | 0.988308i | \(0.451278\pi\) | |||||||
\(380\) | − | 7.97058e36i | − | 0.312340i | ||||||
\(381\) | 1.56322e34 | − | 1.43639e35i | 0.000589670 | − | 0.00541827i | ||||
\(382\) | 7.01827e37 | 2.54866 | ||||||||
\(383\) | −3.26768e37 | −1.14250 | −0.571251 | − | 0.820776i | \(-0.693542\pi\) | ||||
−0.571251 | + | 0.820776i | \(0.693542\pi\) | |||||||
\(384\) | 4.79332e37 | + | 5.21657e36i | 1.61374 | + | 0.175623i | ||||
\(385\) | −6.34060e37 | − | 1.21920e37i | −2.05565 | − | 0.395270i | ||||
\(386\) | 9.22714e37i | 2.88105i | ||||||||
\(387\) | 4.52501e37 | + | 9.96719e36i | 1.36085 | + | 0.299753i | ||||
\(388\) | 1.12452e38i | 3.25768i | ||||||||
\(389\) | − | 2.80009e37i | − | 0.781452i | −0.920507 | − | 0.390726i | \(-0.872224\pi\) | ||
0.920507 | − | 0.390726i | \(-0.127776\pi\) | |||||||
\(390\) | 2.02778e37 | − | 1.86325e38i | 0.545235 | − | 5.00997i | ||||
\(391\) | − | 3.32352e37i | − | 0.861064i | ||||||
\(392\) | 2.75691e37 | − | 6.90379e37i | 0.688296 | − | 1.72361i | ||||
\(393\) | 5.82911e35 | − | 5.35616e36i | 0.0140252 | − | 0.128873i | ||||
\(394\) | −1.25012e38 | −2.89905 | ||||||||
\(395\) | −5.51561e37 | −1.23292 | ||||||||
\(396\) | 2.31831e37 | − | 1.05249e38i | 0.499565 | − | 2.26798i | ||||
\(397\) | 7.23184e37i | 1.50240i | 0.660073 | + | 0.751201i | \(0.270525\pi\) | ||||
−0.660073 | + | 0.751201i | \(0.729475\pi\) | |||||||
\(398\) | 9.01696e37 | 1.80616 | ||||||||
\(399\) | −1.24174e36 | + | 4.03752e36i | −0.0239841 | + | 0.0779845i | ||||
\(400\) | 1.56068e38 | 2.90700 | ||||||||
\(401\) | 6.54810e37i | 1.17631i | 0.808748 | + | 0.588155i | \(0.200145\pi\) | ||||
−0.808748 | + | 0.588155i | \(0.799855\pi\) | |||||||
\(402\) | −3.49959e37 | − | 3.80860e36i | −0.606372 | − | 0.0659914i | ||||
\(403\) | 2.61720e37 | 0.437435 | ||||||||
\(404\) | −2.99237e37 | −0.482486 | ||||||||
\(405\) | 1.08361e38 | + | 5.01713e37i | 1.68568 | + | 0.780473i | ||||
\(406\) | 1.59545e37 | − | 8.29735e37i | 0.239472 | − | 1.24541i | ||||
\(407\) | 1.92468e36i | 0.0278766i | ||||||||
\(408\) | −1.71858e38 | − | 1.87033e37i | −2.40214 | − | 0.261425i | ||||
\(409\) | − | 9.85984e36i | − | 0.133009i | −0.997786 | − | 0.0665046i | \(-0.978815\pi\) | ||
0.997786 | − | 0.0665046i | \(-0.0211847\pi\) | |||||||
\(410\) | − | 1.75462e38i | − | 2.28463i | ||||||
\(411\) | −8.79612e37 | − | 9.57282e36i | −1.10557 | − | 0.120319i | ||||
\(412\) | − | 8.12040e37i | − | 0.985298i | ||||||
\(413\) | −1.63719e37 | + | 8.51444e37i | −0.191789 | + | 0.997425i | ||||
\(414\) | 9.99048e37 | + | 2.20059e37i | 1.13001 | + | 0.248905i | ||||
\(415\) | 1.70690e38 | 1.86428 | ||||||||
\(416\) | −3.22486e37 | −0.340140 | ||||||||
\(417\) | 5.12575e37 | + | 5.57835e36i | 0.522137 | + | 0.0568241i | ||||
\(418\) | − | 1.63491e37i | − | 0.160856i | ||||||
\(419\) | −5.25615e37 | −0.499533 | −0.249767 | − | 0.968306i | \(-0.580354\pi\) | ||||
−0.249767 | + | 0.968306i | \(0.580354\pi\) | |||||||
\(420\) | −3.98551e38 | − | 1.22574e38i | −3.65906 | − | 1.12534i | ||||
\(421\) | 3.20373e37 | 0.284162 | 0.142081 | − | 0.989855i | \(-0.454621\pi\) | ||||
0.142081 | + | 0.989855i | \(0.454621\pi\) | |||||||
\(422\) | − | 2.16379e38i | − | 1.85432i | ||||||
\(423\) | −1.31726e38 | − | 2.90152e37i | −1.09078 | − | 0.240265i | ||||
\(424\) | −4.09260e37 | −0.327487 | ||||||||
\(425\) | 4.12580e38 | 3.19057 | ||||||||
\(426\) | −9.16106e36 | + | 8.41778e37i | −0.0684710 | + | 0.629156i | ||||
\(427\) | −1.33297e38 | − | 2.56309e37i | −0.962977 | − | 0.185165i | ||||
\(428\) | 2.35711e38i | 1.64606i | ||||||||
\(429\) | 2.80044e37 | − | 2.57323e38i | 0.189058 | − | 1.73719i | ||||
\(430\) | 6.93845e38i | 4.52866i | ||||||||
\(431\) | − | 2.30202e37i | − | 0.145274i | −0.997358 | − | 0.0726371i | \(-0.976859\pi\) | ||
0.997358 | − | 0.0726371i | \(-0.0231415\pi\) | |||||||
\(432\) | 6.21096e37 | − | 1.84202e38i | 0.379005 | − | 1.12404i | ||||
\(433\) | 3.08651e37i | 0.182135i | 0.995845 | + | 0.0910676i | \(0.0290279\pi\) | ||||
−0.995845 | + | 0.0910676i | \(0.970972\pi\) | |||||||
\(434\) | 1.63295e37 | − | 8.49240e37i | 0.0931908 | − | 0.484651i | ||||
\(435\) | −2.42529e38 | − | 2.63944e37i | −1.33866 | − | 0.145686i | ||||
\(436\) | −7.76005e37 | −0.414295 | ||||||||
\(437\) | 1.04487e37 | 0.0539613 | ||||||||
\(438\) | −3.63073e37 | + | 3.33615e38i | −0.181393 | + | 1.66675i | ||||
\(439\) | − | 3.14943e38i | − | 1.52229i | −0.648585 | − | 0.761143i | \(-0.724639\pi\) | ||
0.648585 | − | 0.761143i | \(-0.275361\pi\) | |||||||
\(440\) | 8.30743e38 | 3.88511 | ||||||||
\(441\) | 1.82791e38 | + | 1.24181e38i | 0.827173 | + | 0.561947i | ||||
\(442\) | −8.06585e38 | −3.53205 | ||||||||
\(443\) | 3.05724e38i | 1.29561i | 0.761805 | + | 0.647807i | \(0.224314\pi\) | ||||
−0.761805 | + | 0.647807i | \(0.775686\pi\) | |||||||
\(444\) | −1.34476e36 | + | 1.23565e37i | −0.00551559 | + | 0.0506808i | ||||
\(445\) | −2.06285e38 | −0.818933 | ||||||||
\(446\) | 4.09634e37 | 0.157413 | ||||||||
\(447\) | 6.16970e37 | + | 6.71449e36i | 0.229512 | + | 0.0249778i | ||||
\(448\) | 4.20739e37 | − | 2.18811e38i | 0.151524 | − | 0.788021i | ||||
\(449\) | − | 2.65621e38i | − | 0.926170i | −0.886314 | − | 0.463085i | \(-0.846742\pi\) | ||
0.886314 | − | 0.463085i | \(-0.153258\pi\) | |||||||
\(450\) | −2.73180e38 | + | 1.24021e39i | −0.922290 | + | 4.18711i | ||||
\(451\) | − | 2.42319e38i | − | 0.792188i | ||||||
\(452\) | 3.67659e38i | 1.16396i | ||||||||
\(453\) | 3.02637e37 | − | 2.78082e38i | 0.0927893 | − | 0.852608i | ||||
\(454\) | 8.12621e38i | 2.41311i | ||||||||
\(455\) | −9.83453e38 | − | 1.89102e38i | −2.82871 | − | 0.543916i | ||||
\(456\) | 5.88009e36 | − | 5.40301e37i | 0.0163830 | − | 0.150538i | ||||
\(457\) | 3.78952e38 | 1.02282 | 0.511410 | − | 0.859337i | \(-0.329123\pi\) | ||||
0.511410 | + | 0.859337i | \(0.329123\pi\) | |||||||
\(458\) | −1.11189e39 | −2.90745 | ||||||||
\(459\) | 1.64192e38 | − | 4.86954e38i | 0.415975 | − | 1.23368i | ||||
\(460\) | 1.03141e39i | 2.53188i | ||||||||
\(461\) | 6.92235e38 | 1.64661 | 0.823304 | − | 0.567600i | \(-0.192128\pi\) | ||||
0.823304 | + | 0.567600i | \(0.192128\pi\) | |||||||
\(462\) | −8.17498e38 | − | 2.51422e38i | −1.88442 | − | 0.579554i | ||||
\(463\) | 7.45245e38 | 1.66485 | 0.832424 | − | 0.554139i | \(-0.186952\pi\) | ||||
0.832424 | + | 0.554139i | \(0.186952\pi\) | |||||||
\(464\) | 3.97145e38i | 0.859881i | ||||||||
\(465\) | −2.48230e38 | − | 2.70149e37i | −0.520939 | − | 0.0566938i | ||||
\(466\) | 7.08500e38 | 1.44127 | ||||||||
\(467\) | 4.66425e38 | 0.919787 | 0.459893 | − | 0.887974i | \(-0.347888\pi\) | ||||
0.459893 | + | 0.887974i | \(0.347888\pi\) | |||||||
\(468\) | 3.59579e38 | − | 1.63246e39i | 0.687432 | − | 3.12088i | ||||
\(469\) | −3.55174e37 | + | 1.84713e38i | −0.0658318 | + | 0.342367i | ||||
\(470\) | − | 2.01983e39i | − | 3.62991i | ||||||
\(471\) | −1.65182e38 | − | 1.79767e37i | −0.287845 | − | 0.0313262i | ||||
\(472\) | − | 1.11556e39i | − | 1.88509i | ||||||
\(473\) | 9.58227e38i | 1.57030i | ||||||||
\(474\) | −7.26330e38 | − | 7.90465e37i | −1.15438 | − | 0.125631i | ||||
\(475\) | 1.29710e38i | 0.199947i | ||||||||
\(476\) | −3.38837e38 | + | 1.76217e39i | −0.506629 | + | 2.63479i | ||||
\(477\) | 2.61702e37 | − | 1.18810e38i | 0.0379568 | − | 0.172321i | ||||
\(478\) | −1.44061e39 | −2.02695 | ||||||||
\(479\) | −8.86151e38 | −1.20960 | −0.604802 | − | 0.796376i | \(-0.706748\pi\) | ||||
−0.604802 | + | 0.796376i | \(0.706748\pi\) | |||||||
\(480\) | 3.05864e38 | + | 3.32872e37i | 0.405071 | + | 0.0440838i | ||||
\(481\) | 2.98525e37i | 0.0383599i | ||||||||
\(482\) | 2.27654e39 | 2.83853 | ||||||||
\(483\) | 1.60684e38 | − | 5.22466e38i | 0.194420 | − | 0.632156i | ||||
\(484\) | 4.73683e38 | 0.556199 | ||||||||
\(485\) | − | 2.57674e39i | − | 2.93640i | ||||||
\(486\) | 1.35506e39 | + | 8.15984e38i | 1.49877 | + | 0.902518i | ||||
\(487\) | 1.52650e39 | 1.63880 | 0.819399 | − | 0.573223i | \(-0.194307\pi\) | ||||
0.819399 | + | 0.573223i | \(0.194307\pi\) | |||||||
\(488\) | 1.74645e39 | 1.81999 | ||||||||
\(489\) | 1.41324e38 | − | 1.29858e39i | 0.142968 | − | 1.31368i | ||||
\(490\) | −1.22721e39 | + | 3.07316e39i | −1.20525 | + | 3.01816i | ||||
\(491\) | − | 9.61324e38i | − | 0.916617i | −0.888793 | − | 0.458309i | \(-0.848455\pi\) | ||
0.888793 | − | 0.458309i | \(-0.151545\pi\) | |||||||
\(492\) | 1.69307e38 | − | 1.55570e39i | 0.156740 | − | 1.44023i | ||||
\(493\) | 1.04988e39i | 0.943760i | ||||||||
\(494\) | − | 2.53580e38i | − | 0.221348i | ||||||
\(495\) | −5.31220e38 | + | 2.41169e39i | −0.450297 | + | 2.04431i | ||||
\(496\) | 4.06481e38i | 0.334623i | ||||||||
\(497\) | 4.44303e38 | + | 8.54324e37i | 0.355231 | + | 0.0683054i | ||||
\(498\) | 2.24775e39 | + | 2.44623e38i | 1.74551 | + | 0.189964i | ||||
\(499\) | −2.19901e39 | −1.65871 | −0.829354 | − | 0.558723i | \(-0.811291\pi\) | ||||
−0.829354 | + | 0.558723i | \(0.811291\pi\) | |||||||
\(500\) | −7.57921e39 | −5.55340 | ||||||||
\(501\) | 1.05317e38 | − | 9.67724e38i | 0.0749641 | − | 0.688818i | ||||
\(502\) | − | 4.15043e39i | − | 2.87005i | ||||||
\(503\) | −1.09841e39 | −0.737954 | −0.368977 | − | 0.929438i | \(-0.620292\pi\) | ||||
−0.368977 | + | 0.929438i | \(0.620292\pi\) | |||||||
\(504\) | −2.61123e39 | − | 1.12492e39i | −1.70452 | − | 0.734306i | ||||
\(505\) | 6.85673e38 | 0.434902 | ||||||||
\(506\) | 2.11561e39i | 1.30392i | ||||||||
\(507\) | 2.53723e38 | − | 2.33137e39i | 0.151965 | − | 1.39635i | ||||
\(508\) | 1.92968e37 | 0.0112321 | ||||||||
\(509\) | −6.04238e38 | −0.341822 | −0.170911 | − | 0.985286i | \(-0.554671\pi\) | ||||
−0.170911 | + | 0.985286i | \(0.554671\pi\) | |||||||
\(510\) | 7.65011e39 | + | 8.32561e38i | 4.20630 | + | 0.457771i | ||||
\(511\) | 1.76087e39 | + | 3.38587e38i | 0.941074 | + | 0.180954i | ||||
\(512\) | 3.73700e39i | 1.94137i | ||||||||
\(513\) | 1.53092e38 | + | 5.16198e37i | 0.0773127 | + | 0.0260684i | ||||
\(514\) | − | 5.60854e39i | − | 2.75350i | ||||||
\(515\) | 1.86071e39i | 0.888126i | ||||||||
\(516\) | −6.69507e38 | + | 6.15186e39i | −0.310695 | + | 2.85487i | ||||
\(517\) | − | 2.78947e39i | − | 1.25866i | ||||||
\(518\) | 9.68666e37 | + | 1.86259e37i | 0.0425004 | + | 0.00817215i | ||||
\(519\) | −3.70665e37 | + | 3.40591e38i | −0.0158145 | + | 0.145313i | ||||
\(520\) | 1.28852e40 | 5.34615 | ||||||||
\(521\) | −2.48661e38 | −0.100337 | −0.0501684 | − | 0.998741i | \(-0.515976\pi\) | ||||
−0.0501684 | + | 0.998741i | \(0.515976\pi\) | |||||||
\(522\) | −3.15595e39 | − | 6.95157e38i | −1.23853 | − | 0.272810i | ||||
\(523\) | 1.18620e39i | 0.452777i | 0.974037 | + | 0.226389i | \(0.0726919\pi\) | ||||
−0.974037 | + | 0.226389i | \(0.927308\pi\) | |||||||
\(524\) | 7.19559e38 | 0.267154 | ||||||||
\(525\) | 6.48585e39 | + | 1.99472e39i | 2.34238 | + | 0.720399i | ||||
\(526\) | −7.71408e39 | −2.71014 | ||||||||
\(527\) | 1.07456e39i | 0.367264i | ||||||||
\(528\) | 3.99651e39 | + | 4.34940e38i | 1.32889 | + | 0.144623i | ||||
\(529\) | 1.73897e39 | 0.562580 | ||||||||
\(530\) | 1.82178e39 | 0.573451 | ||||||||
\(531\) | 3.23852e39 | + | 7.13345e38i | 0.991918 | + | 0.218489i | ||||
\(532\) | −5.54003e38 | − | 1.06526e38i | −0.165118 | − | 0.0317495i | ||||
\(533\) | − | 3.75847e39i | − | 1.09010i | ||||||
\(534\) | −2.71650e39 | − | 2.95636e38i | −0.766762 | − | 0.0834467i | ||||
\(535\) | − | 5.40109e39i | − | 1.48372i | ||||||
\(536\) | − | 2.42010e39i | − | 0.647060i | ||||||
\(537\) | 3.36054e39 | + | 3.65728e38i | 0.874545 | + | 0.0951767i | ||||
\(538\) | − | 3.61668e39i | − | 0.916151i | ||||||
\(539\) | −1.69483e39 | + | 4.24415e39i | −0.417916 | + | 1.04654i | ||||
\(540\) | −5.09548e39 | + | 1.51120e40i | −1.22314 | + | 3.62754i | ||||
\(541\) | −1.96022e39 | −0.458084 | −0.229042 | − | 0.973417i | \(-0.573559\pi\) | ||||
−0.229042 | + | 0.973417i | \(0.573559\pi\) | |||||||
\(542\) | −4.70727e39 | −1.07098 | ||||||||
\(543\) | −1.85225e39 | − | 2.01580e38i | −0.410300 | − | 0.0446529i | ||||
\(544\) | − | 1.32406e39i | − | 0.285577i | ||||||
\(545\) | 1.77814e39 | 0.373437 | ||||||||
\(546\) | −1.26797e40 | − | 3.89965e39i | −2.59308 | − | 0.797503i | ||||
\(547\) | 5.39261e39 | 1.07395 | 0.536973 | − | 0.843599i | \(-0.319568\pi\) | ||||
0.536973 | + | 0.843599i | \(0.319568\pi\) | |||||||
\(548\) | − | 1.18169e40i | − | 2.29185i | ||||||
\(549\) | −1.11677e39 | + | 5.07003e39i | −0.210943 | + | 0.957661i | ||||
\(550\) | −2.62630e40 | −4.83154 | ||||||||
\(551\) | −3.30071e38 | −0.0591437 | ||||||||
\(552\) | −7.60899e38 | + | 6.99163e39i | −0.132804 | + | 1.22029i | ||||
\(553\) | −7.37155e38 | + | 3.83368e39i | −0.125327 | + | 0.651780i | ||||
\(554\) | 1.08304e40i | 1.79370i | ||||||||
\(555\) | 3.08139e37 | − | 2.83138e38i | 0.00497163 | − | 0.0456826i | ||||
\(556\) | 6.88604e39i | 1.08239i | ||||||||
\(557\) | 1.86146e39i | 0.285071i | 0.989790 | + | 0.142536i | \(0.0455256\pi\) | ||||
−0.989790 | + | 0.142536i | \(0.954474\pi\) | |||||||
\(558\) | −3.23014e39 | − | 7.11498e38i | −0.481975 | − | 0.106164i | ||||
\(559\) | 1.48625e40i | 2.16083i | ||||||||
\(560\) | 2.93698e39 | − | 1.52741e40i | 0.416077 | − | 2.16387i | ||||
\(561\) | 1.05651e40 | + | 1.14980e39i | 1.45852 | + | 0.158731i | ||||
\(562\) | −3.45903e39 | −0.465348 | ||||||||
\(563\) | −9.81277e38 | −0.128653 | −0.0643265 | − | 0.997929i | \(-0.520490\pi\) | ||||
−0.0643265 | + | 0.997929i | \(0.520490\pi\) | |||||||
\(564\) | 1.94898e39 | − | 1.79085e40i | 0.249035 | − | 2.28830i | ||||
\(565\) | − | 8.42457e39i | − | 1.04917i | ||||||
\(566\) | −1.83146e39 | −0.222310 | ||||||||
\(567\) | 4.93544e39 | − | 6.86120e39i | 0.583944 | − | 0.811794i | ||||
\(568\) | −5.82123e39 | −0.671373 | ||||||||
\(569\) | 1.20996e40i | 1.36033i | 0.733061 | + | 0.680163i | \(0.238091\pi\) | ||||
−0.733061 | + | 0.680163i | \(0.761909\pi\) | |||||||
\(570\) | −2.61747e38 | + | 2.40510e39i | −0.0286877 | + | 0.263601i | ||||
\(571\) | 1.66810e40 | 1.78238 | 0.891189 | − | 0.453633i | \(-0.149872\pi\) | ||||
0.891189 | + | 0.453633i | \(0.149872\pi\) | |||||||
\(572\) | 3.45693e40 | 3.60121 | ||||||||
\(573\) | −1.42586e40 | − | 1.55176e39i | −1.44822 | − | 0.157610i | ||||
\(574\) | −1.21956e40 | − | 2.34503e39i | −1.20776 | − | 0.232234i | ||||
\(575\) | − | 1.67848e40i | − | 1.62081i | ||||||
\(576\) | −8.32261e39 | − | 1.83321e39i | −0.783671 | − | 0.172618i | ||||
\(577\) | 1.46760e40i | 1.34760i | 0.738916 | + | 0.673798i | \(0.235338\pi\) | ||||
−0.738916 | + | 0.673798i | \(0.764662\pi\) | |||||||
\(578\) | − | 1.35789e40i | − | 1.21594i | ||||||
\(579\) | 2.04015e39 | − | 1.87462e40i | 0.178165 | − | 1.63710i | ||||
\(580\) | − | 3.25819e40i | − | 2.77504i | ||||||
\(581\) | 2.28125e39 | − | 1.18640e40i | 0.189504 | − | 0.985543i | ||||
\(582\) | 3.69283e39 | − | 3.39321e40i | 0.299210 | − | 2.74934i | ||||
\(583\) | 2.51595e39 | 0.198842 | ||||||||
\(584\) | −2.30708e40 | −1.77859 | ||||||||
\(585\) | −8.23943e39 | + | 3.74062e40i | −0.619636 | + | 2.81309i | ||||
\(586\) | 2.49680e39i | 0.183176i | ||||||||
\(587\) | 1.75156e40 | 1.25364 | 0.626819 | − | 0.779165i | \(-0.284356\pi\) | ||||
0.626819 | + | 0.779165i | \(0.284356\pi\) | |||||||
\(588\) | −1.38462e40 | + | 2.60635e40i | −0.966854 | + | 1.81996i | ||||
\(589\) | −3.37830e38 | −0.0230158 | ||||||||
\(590\) | 4.96580e40i | 3.30092i | ||||||||
\(591\) | 2.53978e40 | + | 2.76405e39i | 1.64732 | + | 0.179278i | ||||
\(592\) | −4.63644e38 | −0.0293440 | ||||||||
\(593\) | −2.04282e40 | −1.26164 | −0.630822 | − | 0.775928i | \(-0.717282\pi\) | ||||
−0.630822 | + | 0.775928i | \(0.717282\pi\) | |||||||
\(594\) | −1.04517e40 | + | 3.09973e40i | −0.629919 | + | 1.86819i | ||||
\(595\) | 7.76413e39 | − | 4.03784e40i | 0.456664 | − | 2.37494i | ||||
\(596\) | 8.28851e39i | 0.475780i | ||||||||
\(597\) | −1.83192e40 | − | 1.99368e39i | −1.02631 | − | 0.111693i | ||||
\(598\) | 3.28139e40i | 1.79428i | ||||||||
\(599\) | 3.07821e40i | 1.64289i | 0.570287 | + | 0.821445i | \(0.306832\pi\) | ||||
−0.570287 | + | 0.821445i | \(0.693168\pi\) | |||||||
\(600\) | −8.67936e40 | − | 9.44574e39i | −4.52162 | − | 0.492088i | ||||
\(601\) | − | 2.87869e40i | − | 1.46391i | −0.681351 | − | 0.731957i | \(-0.738607\pi\) | ||
0.681351 | − | 0.731957i | \(-0.261393\pi\) | |||||||
\(602\) | 4.82263e40 | + | 9.27316e39i | 2.39406 | + | 0.460340i | ||||
\(603\) | 7.02568e39 | + | 1.54754e39i | 0.340477 | + | 0.0749964i | ||||
\(604\) | 3.73582e40 | 1.76746 | ||||||||
\(605\) | −1.08540e40 | −0.501345 | ||||||||
\(606\) | 9.02937e39 | + | 9.82666e38i | 0.407197 | + | 0.0443152i | ||||
\(607\) | − | 6.50759e39i | − | 0.286539i | −0.989684 | − | 0.143270i | \(-0.954238\pi\) | ||
0.989684 | − | 0.143270i | \(-0.0457616\pi\) | |||||||
\(608\) | 4.16267e38 | 0.0178966 | ||||||||
\(609\) | −5.07594e39 | + | 1.65044e40i | −0.213091 | + | 0.692867i | ||||
\(610\) | −7.77415e40 | −3.18692 | ||||||||
\(611\) | − | 4.32658e40i | − | 1.73200i | ||||||
\(612\) | 6.70251e40 | + | 1.47635e40i | 2.62024 | + | 0.577158i | ||||
\(613\) | 2.10947e40 | 0.805370 | 0.402685 | − | 0.915339i | \(-0.368077\pi\) | ||||
0.402685 | + | 0.915339i | \(0.368077\pi\) | |||||||
\(614\) | 1.89839e40 | 0.707854 | ||||||||
\(615\) | −3.87951e39 | + | 3.56474e40i | −0.141282 | + | 1.29819i | ||||
\(616\) | 1.11028e40 | − | 5.77416e40i | 0.394923 | − | 2.05385i | ||||
\(617\) | 2.77271e40i | 0.963317i | 0.876359 | + | 0.481659i | \(0.159965\pi\) | ||||
−0.876359 | + | 0.481659i | \(0.840035\pi\) | |||||||
\(618\) | −2.66667e39 | + | 2.45031e40i | −0.0904973 | + | 0.831548i | ||||
\(619\) | − | 3.62054e39i | − | 0.120021i | −0.998198 | − | 0.0600107i | \(-0.980887\pi\) | ||
0.998198 | − | 0.0600107i | \(-0.0191135\pi\) | |||||||
\(620\) | − | 3.33478e40i | − | 1.07991i | ||||||
\(621\) | −1.98105e40 | − | 6.67973e39i | −0.626710 | − | 0.211315i | ||||
\(622\) | 6.22903e40i | 1.92513i | ||||||||
\(623\) | −2.75698e39 | + | 1.43381e40i | −0.0832448 | + | 0.432926i | ||||
\(624\) | 6.19875e40 | + | 6.74610e39i | 1.82864 | + | 0.199011i | ||||
\(625\) | 8.86463e40 | 2.55506 | ||||||||
\(626\) | 4.83400e40 | 1.36138 | ||||||||
\(627\) | −3.61483e38 | + | 3.32154e39i | −0.00994736 | + | 0.0914028i | ||||
\(628\) | − | 2.21909e40i | − | 0.596705i | ||||||
\(629\) | −1.22568e39 | −0.0322064 | ||||||||
\(630\) | 1.16236e41 | + | 5.00745e40i | 2.98472 | + | 1.28582i | ||||
\(631\) | −3.16287e40 | −0.793699 | −0.396849 | − | 0.917884i | \(-0.629896\pi\) | ||||
−0.396849 | + | 0.917884i | \(0.629896\pi\) | |||||||
\(632\) | − | 5.02286e40i | − | 1.23184i | ||||||
\(633\) | −4.78421e39 | + | 4.39604e40i | −0.114672 | + | 1.05368i | ||||
\(634\) | −2.73660e39 | −0.0641086 | ||||||||
\(635\) | −4.42168e38 | −0.0101244 | ||||||||
\(636\) | 1.61525e40 | + | 1.75788e39i | 0.361503 | + | 0.0393424i | ||||
\(637\) | −2.62875e40 | + | 6.58285e40i | −0.575079 | + | 1.44010i | ||||
\(638\) | − | 6.68311e40i | − | 1.42915i | ||||||
\(639\) | 3.72239e39 | − | 1.68993e40i | 0.0778144 | − | 0.353270i | ||||
\(640\) | − | 1.47554e41i | − | 3.01537i | ||||||
\(641\) | 3.32279e40i | 0.663838i | 0.943308 | + | 0.331919i | \(0.107696\pi\) | ||||
−0.943308 | + | 0.331919i | \(0.892304\pi\) | |||||||
\(642\) | 7.74053e39 | − | 7.11250e40i | 0.151187 | − | 1.38920i | ||||
\(643\) | − | 6.25407e40i | − | 1.19427i | −0.802140 | − | 0.597136i | \(-0.796305\pi\) | ||
0.802140 | − | 0.597136i | \(-0.203695\pi\) | |||||||
\(644\) | 7.16893e40 | + | 1.37847e40i | 1.33847 | + | 0.257367i | ||||
\(645\) | 1.53411e40 | − | 1.40964e41i | 0.280054 | − | 2.57331i | ||||
\(646\) | 1.04114e40 | 0.185840 | ||||||||
\(647\) | −2.46712e40 | −0.430604 | −0.215302 | − | 0.976547i | \(-0.569074\pi\) | ||||
−0.215302 | + | 0.976547i | \(0.569074\pi\) | |||||||
\(648\) | −4.56892e40 | + | 9.86804e40i | −0.779787 | + | 1.68420i | ||||
\(649\) | 6.85796e40i | 1.14458i | ||||||||
\(650\) | −4.07350e41 | −6.64850 | ||||||||
\(651\) | −5.19527e39 | + | 1.68924e40i | −0.0829246 | + | 0.269630i | ||||
\(652\) | 1.74454e41 | 2.72327 | ||||||||
\(653\) | − | 8.56660e40i | − | 1.30788i | −0.756547 | − | 0.653939i | \(-0.773115\pi\) | ||
0.756547 | − | 0.653939i | \(-0.226885\pi\) | |||||||
\(654\) | 2.34157e40 | + | 2.54833e39i | 0.349647 | + | 0.0380521i | ||||
\(655\) | −1.64880e40 | −0.240807 | ||||||||
\(656\) | 5.83733e40 | 0.833889 | ||||||||
\(657\) | 1.47527e40 | − | 6.69757e40i | 0.206145 | − | 0.935879i | ||||
\(658\) | −1.40390e41 | − | 2.69949e40i | −1.91894 | − | 0.368982i | ||||
\(659\) | − | 2.34042e39i | − | 0.0312935i | −0.999878 | − | 0.0156468i | \(-0.995019\pi\) | ||
0.999878 | − | 0.0156468i | \(-0.00498073\pi\) | |||||||
\(660\) | −3.27875e41 | − | 3.56826e40i | −4.28865 | − | 0.466734i | ||||
\(661\) | 4.64889e40i | 0.594878i | 0.954741 | + | 0.297439i | \(0.0961325\pi\) | ||||
−0.954741 | + | 0.297439i | \(0.903868\pi\) | |||||||
\(662\) | − | 1.82072e41i | − | 2.27930i | ||||||
\(663\) | 1.63869e41 | + | 1.78338e40i | 2.00701 | + | 0.218423i | ||||
\(664\) | 1.55441e41i | 1.86264i | ||||||||
\(665\) | 1.26945e40 | + | 2.44094e39i | 0.148833 | + | 0.0286183i | ||||
\(666\) | 8.11555e38 | − | 3.68438e39i | 0.00930982 | − | 0.0422657i | ||||
\(667\) | 4.27119e40 | 0.479429 | ||||||||
\(668\) | 1.30006e41 | 1.42792 | ||||||||
\(669\) | −8.32227e39 | − | 9.05713e38i | −0.0894465 | − | 0.00973446i | ||||
\(670\) | 1.07729e41i | 1.13304i | ||||||||
\(671\) | −1.07364e41 | −1.10505 | ||||||||
\(672\) | 6.40150e39 | − | 2.08145e40i | 0.0644803 | − | 0.209658i | ||||
\(673\) | −1.84928e41 | −1.82299 | −0.911497 | − | 0.411307i | \(-0.865072\pi\) | ||||
−0.911497 | + | 0.411307i | \(0.865072\pi\) | |||||||
\(674\) | 1.73693e41i | 1.67577i | ||||||||
\(675\) | 8.29217e40 | − | 2.45926e41i | 0.783003 | − | 2.32220i | ||||
\(676\) | 3.13201e41 | 2.89465 | ||||||||
\(677\) | −1.58660e41 | −1.43527 | −0.717633 | − | 0.696422i | \(-0.754774\pi\) | ||||
−0.717633 | + | 0.696422i | \(0.754774\pi\) | |||||||
\(678\) | 1.20736e40 | − | 1.10940e41i | 0.106907 | − | 0.982332i | ||||
\(679\) | −1.79099e41 | − | 3.44378e40i | −1.55232 | − | 0.298486i | ||||
\(680\) | 5.29036e41i | 4.48855i | ||||||||
\(681\) | 1.79673e40 | − | 1.65095e41i | 0.149228 | − | 1.37120i | ||||
\(682\) | − | 6.84021e40i | − | 0.556155i | ||||||
\(683\) | 1.21940e41i | 0.970609i | 0.874345 | + | 0.485304i | \(0.161291\pi\) | ||||
−0.874345 | + | 0.485304i | \(0.838709\pi\) | |||||||
\(684\) | −4.64147e39 | + | 2.10718e40i | −0.0361695 | + | 0.164206i | ||||
\(685\) | 2.70773e41i | 2.06582i | ||||||||
\(686\) | 1.97201e41 | + | 1.26371e41i | 1.47302 | + | 0.943948i | ||||
\(687\) | 2.25896e41 | + | 2.45843e40i | 1.65210 | + | 0.179798i | ||||
\(688\) | −2.30831e41 | −1.65296 | ||||||||
\(689\) | 3.90234e40 | 0.273619 | ||||||||
\(690\) | 3.38707e40 | − | 3.11226e41i | 0.232548 | − | 2.13680i | ||||
\(691\) | − | 1.29754e41i | − | 0.872348i | −0.899862 | − | 0.436174i | \(-0.856333\pi\) | ||
0.899862 | − | 0.436174i | \(-0.143667\pi\) | |||||||
\(692\) | −4.57557e40 | −0.301236 | ||||||||
\(693\) | 1.60527e41 | + | 6.91549e40i | 1.03494 | + | 0.445852i | ||||
\(694\) | 5.53727e40 | 0.349610 | ||||||||
\(695\) | − | 1.57787e41i | − | 0.975645i | ||||||
\(696\) | 2.40364e40 | − | 2.20862e41i | 0.145558 | − | 1.33748i | ||||
\(697\) | 1.54314e41 | 0.915232 | ||||||||
\(698\) | −2.43503e41 | −1.41449 | ||||||||
\(699\) | −1.43942e41 | − | 1.56652e40i | −0.818969 | − | 0.0891283i | ||||
\(700\) | −1.71123e41 | + | 8.89946e41i | −0.953643 | + | 4.95955i | ||||
\(701\) | − | 1.30986e41i | − | 0.715013i | −0.933911 | − | 0.357507i | \(-0.883627\pi\) | ||
0.933911 | − | 0.357507i | \(-0.116373\pi\) | |||||||
\(702\) | −1.62110e41 | + | 4.80781e41i | −0.866808 | + | 2.57074i | ||||
\(703\) | − | 3.85338e38i | − | 0.00201832i | ||||||
\(704\) | − | 1.76242e41i | − | 0.904284i | ||||||
\(705\) | −4.46591e40 | + | 4.10357e41i | −0.224475 | + | 2.06262i | ||||
\(706\) | − | 2.01364e41i | − | 0.991547i | ||||||
\(707\) | 9.16394e39 | − | 4.76583e40i | 0.0442080 | − | 0.229910i | ||||
\(708\) | −4.79161e40 | + | 4.40284e41i | −0.226464 | + | 2.08090i | ||||
\(709\) | 2.32302e41 | 1.07568 | 0.537840 | − | 0.843047i | \(-0.319241\pi\) | ||||
0.537840 | + | 0.843047i | \(0.319241\pi\) | |||||||
\(710\) | 2.59127e41 | 1.17562 | ||||||||
\(711\) | 1.45816e41 | + | 3.21188e40i | 0.648182 | + | 0.142774i | ||||
\(712\) | − | 1.87857e41i | − | 0.818213i | ||||||
\(713\) | 4.37160e40 | 0.186570 | ||||||||
\(714\) | 1.60111e41 | − | 5.20601e41i | 0.669571 | − | 2.17711i | ||||
\(715\) | −7.92123e41 | −3.24605 | ||||||||
\(716\) | 4.51463e41i | 1.81294i | ||||||||
\(717\) | 2.92680e41 | + | 3.18524e40i | 1.15177 | + | 0.125347i | ||||
\(718\) | −9.84790e40 | −0.379786 | ||||||||
\(719\) | −9.86131e40 | −0.372705 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(720\) | −5.80961e41 | − | 1.27968e41i | −2.15192 | − | 0.474001i | ||||
\(721\) | 1.29331e41 | + | 2.48682e40i | 0.469505 | + | 0.0902784i | ||||
\(722\) | − | 4.88437e41i | − | 1.73788i | ||||||
\(723\) | −4.62511e41 | − | 5.03351e40i | −1.61293 | − | 0.175536i | ||||
\(724\) | − | 2.48835e41i | − | 0.850555i | ||||||
\(725\) | 5.30223e41i | 1.77647i | ||||||||
\(726\) | −1.42932e41 | − | 1.55553e40i | −0.469407 | − | 0.0510855i | ||||
\(727\) | − | 9.34355e40i | − | 0.300790i | −0.988626 | − | 0.150395i | \(-0.951946\pi\) | ||
0.988626 | − | 0.150395i | \(-0.0480545\pi\) | |||||||
\(728\) | 1.72209e41 | − | 8.95595e41i | 0.543438 | − | 2.82622i | ||||
\(729\) | −2.57258e41 | − | 1.95739e41i | −0.795830 | − | 0.605521i | ||||
\(730\) | 1.02698e42 | 3.11443 | ||||||||
\(731\) | −6.10220e41 | −1.81420 | ||||||||
\(732\) | −6.89283e41 | − | 7.50146e40i | −2.00903 | − | 0.218643i | ||||
\(733\) | − | 3.34929e41i | − | 0.957072i | −0.878068 | − | 0.478536i | \(-0.841168\pi\) | ||
0.878068 | − | 0.478536i | \(-0.158832\pi\) | |||||||
\(734\) | 7.38217e41 | 2.06819 | ||||||||
\(735\) | 3.17274e41 | − | 5.97220e41i | 0.871501 | − | 1.64047i | ||||
\(736\) | −5.38660e40 | −0.145073 | ||||||||
\(737\) | 1.48777e41i | 0.392879i | ||||||||
\(738\) | −1.02176e41 | + | 4.63868e41i | −0.264564 | + | 1.20110i | ||||
\(739\) | −3.87117e41 | −0.982875 | −0.491437 | − | 0.870913i | \(-0.663528\pi\) | ||||
−0.491437 | + | 0.870913i | \(0.663528\pi\) | |||||||
\(740\) | 3.80374e40 | 0.0947002 | ||||||||
\(741\) | −5.60674e39 | + | 5.15183e40i | −0.0136882 | + | 0.125776i | ||||
\(742\) | 2.43479e40 | − | 1.26625e41i | 0.0582915 | − | 0.303153i | ||||
\(743\) | − | 7.69793e40i | − | 0.180733i | −0.995909 | − | 0.0903663i | \(-0.971196\pi\) | ||
0.995909 | − | 0.0903663i | \(-0.0288038\pi\) | |||||||
\(744\) | 2.46015e40 | − | 2.26054e41i | 0.0566439 | − | 0.520481i | ||||
\(745\) | − | 1.89924e41i | − | 0.428857i | ||||||
\(746\) | − | 1.20267e42i | − | 2.66339i | ||||||
\(747\) | −4.51253e41 | − | 9.93969e40i | −0.980102 | − | 0.215886i | ||||
\(748\) | 1.41934e42i | 3.02352i | ||||||||
\(749\) | −3.75408e41 | − | 7.21851e40i | −0.784364 | − | 0.150821i | ||||
\(750\) | 2.28700e42 | + | 2.48894e41i | 4.68682 | + | 0.510067i | ||||
\(751\) | 6.59473e41 | 1.32562 | 0.662809 | − | 0.748789i | \(-0.269364\pi\) | ||||
0.662809 | + | 0.748789i | \(0.269364\pi\) | |||||||
\(752\) | 6.71966e41 | 1.32492 | ||||||||
\(753\) | −9.17673e40 | + | 8.43217e41i | −0.177485 | + | 1.63084i | ||||
\(754\) | − | 1.03658e42i | − | 1.96660i | ||||||
\(755\) | −8.56028e41 | −1.59315 | ||||||||
\(756\) | 9.82273e41 | + | 5.56137e41i | 1.79335 | + | 1.01535i | ||||
\(757\) | 2.53641e41 | 0.454286 | 0.227143 | − | 0.973861i | \(-0.427062\pi\) | ||||
0.227143 | + | 0.973861i | \(0.427062\pi\) | |||||||
\(758\) | − | 3.03622e41i | − | 0.533495i | ||||||
\(759\) | 4.67767e40 | − | 4.29815e41i | 0.0806351 | − | 0.740927i | ||||
\(760\) | −1.66322e41 | −0.281289 | ||||||||
\(761\) | 7.53557e41 | 1.25037 | 0.625185 | − | 0.780477i | \(-0.285024\pi\) | ||||
0.625185 | + | 0.780477i | \(0.285024\pi\) | |||||||
\(762\) | −5.82274e39 | − | 6.33689e38i | −0.00947939 | − | 0.00103164i | ||||
\(763\) | 2.37647e40 | − | 1.23591e41i | 0.0379600 | − | 0.197416i | ||||
\(764\) | − | 1.91553e42i | − | 3.00217i | ||||||
\(765\) | −1.53582e42 | − | 3.38293e41i | −2.36183 | − | 0.520238i | ||||
\(766\) | 1.32463e42i | 1.99884i | ||||||||
\(767\) | 1.06370e42i | 1.57502i | ||||||||
\(768\) | 1.51714e41 | − | 1.39404e42i | 0.220438 | − | 2.02553i | ||||
\(769\) | − | 6.57063e40i | − | 0.0936862i | −0.998902 | − | 0.0468431i | \(-0.985084\pi\) | ||
0.998902 | − | 0.0468431i | \(-0.0149161\pi\) | |||||||
\(770\) | −4.94230e41 | + | 2.57031e42i | −0.691534 | + | 3.59642i | ||||
\(771\) | −1.24007e41 | + | 1.13945e42i | −0.170277 | + | 1.56462i | ||||
\(772\) | 2.51841e42 | 3.39371 | ||||||||
\(773\) | 1.43189e42 | 1.89369 | 0.946844 | − | 0.321694i | \(-0.104252\pi\) | ||||
0.946844 | + | 0.321694i | \(0.104252\pi\) | |||||||
\(774\) | 4.04043e41 | − | 1.83432e42i | 0.524426 | − | 2.38084i | ||||
\(775\) | 5.42687e41i | 0.691313i | ||||||||
\(776\) | 2.34654e42 | 2.93382 | ||||||||
\(777\) | −1.92680e40 | − | 5.92587e39i | −0.0236446 | − | 0.00727189i | ||||
\(778\) | −1.13508e42 | −1.36717 | ||||||||
\(779\) | 4.85145e40i | 0.0573560i | ||||||||
\(780\) | −5.08547e42 | − | 5.53451e41i | −5.90145 | − | 0.642255i | ||||
\(781\) | 3.57864e41 | 0.407641 | ||||||||
\(782\) | −1.34727e42 | −1.50645 | ||||||||
\(783\) | 6.25804e41 | + | 2.11010e41i | 0.686899 | + | 0.231610i | ||||
\(784\) | −1.02239e42 | − | 4.08274e41i | −1.10163 | − | 0.439916i | ||||
\(785\) | 5.08483e41i | 0.537857i | ||||||||
\(786\) | −2.17125e41 | − | 2.36297e40i | −0.225467 | − | 0.0245375i | ||||
\(787\) | 1.17907e42i | 1.20201i | 0.799246 | + | 0.601004i | \(0.205233\pi\) | ||||
−0.799246 | + | 0.601004i | \(0.794767\pi\) | |||||||
\(788\) | 3.41200e42i | 3.41491i | ||||||||
\(789\) | 1.56722e42 | + | 1.70561e41i | 1.53998 | + | 0.167596i | ||||
\(790\) | 2.23588e42i | 2.15703i | ||||||||
\(791\) | −5.85558e41 | − | 1.12594e41i | −0.554640 | − | 0.106648i | ||||
\(792\) | −2.19624e42 | − | 4.83762e41i | −2.04251 | − | 0.449901i | ||||
\(793\) | −1.66526e42 | −1.52062 | ||||||||
\(794\) | 2.93159e42 | 2.62849 | ||||||||
\(795\) | −3.70120e41 | − | 4.02801e40i | −0.325851 | − | 0.0354624i | ||||
\(796\) | − | 2.46104e42i | − | 2.12755i | ||||||
\(797\) | −7.12284e41 | −0.604655 | −0.302328 | − | 0.953204i | \(-0.597764\pi\) | ||||
−0.302328 | + | 0.953204i | \(0.597764\pi\) | |||||||
\(798\) | 1.63670e41 | + | 5.03369e40i | 0.136436 | + | 0.0419608i | ||||
\(799\) | 1.77640e42 | 1.45416 | ||||||||
\(800\) | − | 6.68688e41i | − | 0.537550i | ||||||
\(801\) | 5.45357e41 | + | 1.20125e41i | 0.430536 | + | 0.0948336i | ||||
\(802\) | 2.65442e42 | 2.05798 | ||||||||
\(803\) | 1.41829e42 | 1.07992 | ||||||||
\(804\) | −1.03950e41 | + | 9.55158e41i | −0.0777340 | + | 0.714270i | ||||
\(805\) | −1.64269e42 | − | 3.15864e41i | −1.20647 | − | 0.231985i | ||||
\(806\) | − | 1.06094e42i | − | 0.765304i | ||||||
\(807\) | −7.99659e40 | + | 7.34778e41i | −0.0566550 | + | 0.520583i | ||||
\(808\) | 6.24417e41i | 0.434520i | ||||||||
\(809\) | 2.10855e41i | 0.144122i | 0.997400 | + | 0.0720609i | \(0.0229576\pi\) | ||||
−0.997400 | + | 0.0720609i | \(0.977042\pi\) | |||||||
\(810\) | 2.03381e42 | − | 4.39267e42i | 1.36546 | − | 2.94914i | ||||
\(811\) | − | 2.50434e42i | − | 1.65154i | −0.564004 | − | 0.825772i | \(-0.690740\pi\) | ||
0.564004 | − | 0.825772i | \(-0.309260\pi\) | |||||||
\(812\) | −2.26463e42 | − | 4.35453e41i | −1.46702 | − | 0.282084i | ||||
\(813\) | 9.56347e41 | + | 1.04079e41i | 0.608559 | + | 0.0662295i | ||||
\(814\) | 7.80213e40 | 0.0487708 | ||||||||
\(815\) | −3.99745e42 | −2.45469 | ||||||||
\(816\) | −2.76980e41 | + | 2.54507e42i | −0.167086 | + | 1.53530i | ||||
\(817\) | − | 1.91846e41i | − | 0.113693i | ||||||
\(818\) | −3.99691e41 | −0.232703 | ||||||||
\(819\) | 2.48984e42 | + | 1.07262e42i | 1.42415 | + | 0.613521i | ||||
\(820\) | −4.78895e42 | −2.69116 | ||||||||
\(821\) | − | 2.58842e42i | − | 1.42909i | −0.699590 | − | 0.714544i | \(-0.746634\pi\) | ||
0.699590 | − | 0.714544i | \(-0.253366\pi\) | |||||||
\(822\) | −3.88056e41 | + | 3.56571e42i | −0.210501 | + | 1.93422i | ||||
\(823\) | −3.55304e42 | −1.89366 | −0.946832 | − | 0.321729i | \(-0.895736\pi\) | ||||
−0.946832 | + | 0.321729i | \(0.895736\pi\) | |||||||
\(824\) | −1.69448e42 | −0.887346 | ||||||||
\(825\) | 5.33569e42 | + | 5.80683e41i | 2.74542 | + | 0.298784i | ||||
\(826\) | 3.45152e42 | + | 6.63674e41i | 1.74502 | + | 0.335540i | ||||
\(827\) | 3.04056e42i | 1.51051i | 0.655431 | + | 0.755255i | \(0.272487\pi\) | ||||
−0.655431 | + | 0.755255i | \(0.727513\pi\) | |||||||
\(828\) | 6.00618e41 | − | 2.72675e42i | 0.293196 | − | 1.33108i | ||||
\(829\) | 2.58916e42i | 1.24199i | 0.783814 | + | 0.620995i | \(0.213271\pi\) | ||||
−0.783814 | + | 0.620995i | \(0.786729\pi\) | |||||||
\(830\) | − | 6.91931e42i | − | 3.26160i | ||||||
\(831\) | 2.39462e41 | − | 2.20034e42i | 0.110923 | − | 1.01923i | ||||
\(832\) | − | 2.73358e42i | − | 1.24435i | ||||||
\(833\) | −2.70277e42 | − | 1.07931e42i | −1.20908 | − | 0.482828i | ||||
\(834\) | 2.26131e41 | − | 2.07784e42i | 0.0994152 | − | 0.913491i | ||||
\(835\) | −2.97897e42 | −1.28710 | ||||||||
\(836\) | −4.46222e41 | −0.189479 | ||||||||
\(837\) | 6.40515e41 | + | 2.15970e41i | 0.267307 | + | 0.0901310i | ||||
\(838\) | 2.13070e42i | 0.873946i | ||||||||
\(839\) | 2.13343e42 | 0.860062 | 0.430031 | − | 0.902814i | \(-0.358503\pi\) | ||||
0.430031 | + | 0.902814i | \(0.358503\pi\) | |||||||
\(840\) | −2.55776e42 | + | 8.31657e42i | −1.01347 | + | 3.29530i | ||||
\(841\) | 1.21844e42 | 0.474527 | ||||||||
\(842\) | − | 1.29871e42i | − | 0.497149i | ||||||
\(843\) | 7.02749e41 | + | 7.64802e40i | 0.264424 | + | 0.0287772i | ||||
\(844\) | −5.90573e42 | −2.18428 | ||||||||
\(845\) | −7.17670e42 | −2.60917 | ||||||||
\(846\) | −1.17620e42 | + | 5.33984e42i | −0.420350 | + | 1.90835i | ||||
\(847\) | −1.45063e41 | + | 7.54418e41i | −0.0509620 | + | 0.265034i | ||||
\(848\) | 6.06077e41i | 0.209309i | ||||||||
\(849\) | 3.72087e41 | + | 4.04942e40i | 0.126323 | + | 0.0137477i | ||||
\(850\) | − | 1.67249e43i | − | 5.58198i | ||||||
\(851\) | 4.98637e40i | 0.0163608i | ||||||||
\(852\) | 2.29750e42 | + | 2.50037e41i | 0.741109 | + | 0.0806548i | ||||
\(853\) | 5.00613e42i | 1.58760i | 0.608178 | + | 0.793801i | \(0.291901\pi\) | ||||
−0.608178 | + | 0.793801i | \(0.708099\pi\) | |||||||
\(854\) | −1.03901e42 | + | 5.40350e42i | −0.323951 | + | 1.68475i | ||||
\(855\) | 1.06355e41 | − | 4.82842e41i | 0.0326024 | − | 0.148012i | ||||
\(856\) | 4.91858e42 | 1.48242 | ||||||||
\(857\) | −4.67549e42 | −1.38550 | −0.692748 | − | 0.721179i | \(-0.743600\pi\) | ||||
−0.692748 | + | 0.721179i | \(0.743600\pi\) | |||||||
\(858\) | −1.04312e43 | − | 1.13522e42i | −3.03926 | − | 0.330762i | ||||
\(859\) | − | 2.01030e42i | − | 0.575918i | −0.957643 | − | 0.287959i | \(-0.907023\pi\) | ||
0.957643 | − | 0.287959i | \(-0.0929767\pi\) | |||||||
\(860\) | 1.89374e43 | 5.33449 | ||||||||
\(861\) | 2.42586e42 | + | 7.46074e41i | 0.671924 | + | 0.206650i | ||||
\(862\) | −9.33177e41 | −0.254161 | ||||||||
\(863\) | − | 8.04899e41i | − | 0.215568i | −0.994174 | − | 0.107784i | \(-0.965624\pi\) | ||
0.994174 | − | 0.107784i | \(-0.0343755\pi\) | |||||||
\(864\) | −7.89230e41 | − | 2.66114e41i | −0.207852 | − | 0.0700839i | ||||
\(865\) | 1.04845e42 | 0.271527 | ||||||||
\(866\) | 1.25119e42 | 0.318650 | ||||||||
\(867\) | −3.00233e41 | + | 2.75874e42i | −0.0751938 | + | 0.690929i | ||||
\(868\) | −2.31787e42 | − | 4.45690e41i | −0.570890 | − | 0.109773i | ||||
\(869\) | 3.08784e42i | 0.747942i | ||||||||
\(870\) | −1.06996e42 | + | 9.83147e42i | −0.254881 | + | 2.34201i | ||||
\(871\) | 2.30760e42i | 0.540626i | ||||||||
\(872\) | 1.61929e42i | 0.373109i | ||||||||
\(873\) | −1.50050e42 | + | 6.81213e42i | −0.340039 | + | 1.54375i | ||||
\(874\) | − | 4.23564e41i | − | 0.0944067i | ||||||
\(875\) | 2.32109e42 | − | 1.20711e43i | 0.508833 | − | 2.64625i | ||||
\(876\) | 9.10551e42 | + | 9.90952e41i | 1.96334 | + | 0.213670i | ||||
\(877\) | 4.94014e42 | 1.04772 | 0.523860 | − | 0.851804i | \(-0.324491\pi\) | ||||
0.523860 | + | 0.851804i | \(0.324491\pi\) | |||||||
\(878\) | −1.27669e43 | −2.66328 | ||||||||
\(879\) | 5.52049e40 | − | 5.07259e41i | 0.0113276 | − | 0.104086i | ||||
\(880\) | − | 1.23026e43i | − | 2.48312i | ||||||
\(881\) | 1.13033e42 | 0.224417 | 0.112208 | − | 0.993685i | \(-0.464208\pi\) | ||||
0.112208 | + | 0.993685i | \(0.464208\pi\) | |||||||
\(882\) | 5.03396e42 | − | 7.40988e42i | 0.983141 | − | 1.44716i | ||||
\(883\) | −6.29335e41 | −0.120907 | −0.0604535 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604535 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(884\) | 2.20145e43i | 4.16055i | ||||||||
\(885\) | 1.09795e42 | − | 1.00887e43i | 0.204130 | − | 1.87568i | ||||
\(886\) | 1.23932e43 | 2.26671 | ||||||||
\(887\) | −2.75262e42 | −0.495283 | −0.247641 | − | 0.968852i | \(-0.579655\pi\) | ||||
−0.247641 | + | 0.968852i | \(0.579655\pi\) | |||||||
\(888\) | 2.57844e41 | + | 2.80611e40i | 0.0456424 | + | 0.00496726i | ||||
\(889\) | −5.90953e39 | + | 3.07333e40i | −0.00102915 | + | 0.00535221i | ||||
\(890\) | 8.36226e42i | 1.43274i | ||||||||
\(891\) | 2.80877e42 | − | 6.06644e42i | 0.473467 | − | 1.02260i | ||||
\(892\) | − | 1.11803e42i | − | 0.185423i | ||||||
\(893\) | 5.58477e41i | 0.0911295i | ||||||||
\(894\) | 2.72187e41 | − | 2.50103e42i | 0.0436992 | − | 0.401537i | ||||
\(895\) | − | 1.03448e43i | − | 1.63414i | ||||||
\(896\) | −1.02559e43 | − | 1.97204e42i | −1.59407 | − | 0.306514i | ||||
\(897\) | 7.25526e41 | − | 6.66660e42i | 0.110959 | − | 1.01956i | ||||
\(898\) | −1.07676e43 | −1.62036 | ||||||||
\(899\) | −1.38097e42 | −0.204488 | ||||||||
\(900\) | 3.38497e43 | + | 7.45602e42i | 4.93217 | + | 1.08640i | ||||
\(901\) | 1.60221e42i | 0.229727i | ||||||||
\(902\) | −9.82298e42 | −1.38595 | ||||||||
\(903\) | −9.59281e42 | − | 2.95027e42i | −1.33191 | − | 0.409628i | ||||
\(904\) | 7.67195e42 | 1.04825 | ||||||||
\(905\) | 5.70182e42i | 0.766671i | ||||||||
\(906\) | −1.12727e43 | − | 1.22681e42i | −1.49166 | − | 0.162337i | ||||
\(907\) | 5.70163e42 | 0.742495 | 0.371247 | − | 0.928534i | \(-0.378930\pi\) | ||||
0.371247 | + | 0.928534i | \(0.378930\pi\) | |||||||
\(908\) | 2.21792e43 | 2.84251 | ||||||||
\(909\) | −1.81271e42 | − | 3.99284e41i | −0.228640 | − | 0.0503623i | ||||
\(910\) | −7.66571e42 | + | 3.98665e43i | −0.951595 | + | 4.94890i | ||||
\(911\) | 9.54791e42i | 1.16652i | 0.812286 | + | 0.583260i | \(0.198223\pi\) | ||||
−0.812286 | + | 0.583260i | \(0.801777\pi\) | |||||||
\(912\) | −8.00138e41 | − | 8.70790e40i | −0.0962143 | − | 0.0104710i | ||||
\(913\) | − | 9.55583e42i | − | 1.13095i | ||||||
\(914\) | − | 1.53617e43i | − | 1.78945i | ||||||
\(915\) | 1.57943e43 | + | 1.71889e42i | 1.81090 | + | 0.197080i | ||||
\(916\) | 3.03474e43i | 3.42481i | ||||||||
\(917\) | −2.20361e41 | + | 1.14601e42i | −0.0244781 | + | 0.127302i | ||||
\(918\) | −1.97398e43 | − | 6.65590e42i | −2.15836 | − | 0.727759i | ||||
\(919\) | 7.31122e42 | 0.786892 | 0.393446 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393446 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(920\) | 2.15225e43 | 2.28018 | ||||||||
\(921\) | −3.85684e42 | − | 4.19739e41i | −0.402223 | − | 0.0437739i | ||||
\(922\) | − | 2.80614e43i | − | 2.88078i | ||||||
\(923\) | 5.55061e42 | 0.560940 | ||||||||
\(924\) | −6.86216e42 | + | 2.23123e43i | −0.682680 | + | 2.21974i | ||||
\(925\) | −6.19004e41 | −0.0606232 | ||||||||
\(926\) | − | 3.02102e43i | − | 2.91269i | ||||||
\(927\) | 1.08354e42 | − | 4.91917e42i | 0.102846 | − | 0.466913i | ||||
\(928\) | 1.70160e42 | 0.159005 | ||||||||
\(929\) | −5.29124e42 | −0.486776 | −0.243388 | − | 0.969929i | \(-0.578259\pi\) | ||||
−0.243388 | + | 0.969929i | \(0.578259\pi\) | |||||||
\(930\) | −1.09511e42 | + | 1.00626e43i | −0.0991871 | + | 0.911396i | ||||
\(931\) | 3.39320e41 | − | 8.49717e41i | 0.0302579 | − | 0.0757712i | ||||
\(932\) | − | 1.93374e43i | − | 1.69773i | ||||||
\(933\) | 1.37726e42 | − | 1.26551e43i | 0.119050 | − | 1.09391i | ||||
\(934\) | − | 1.89076e43i | − | 1.60919i | ||||||
\(935\) | − | 3.25228e43i | − | 2.72533i | ||||||
\(936\) | −3.40645e43 | − | 7.50335e42i | −2.81062 | − | 0.619092i | ||||
\(937\) | − | 8.95227e42i | − | 0.727293i | −0.931537 | − | 0.363646i | \(-0.881532\pi\) | ||
0.931537 | − | 0.363646i | \(-0.118468\pi\) | |||||||
\(938\) | 7.48778e42 | + | 1.43978e42i | 0.598980 | + | 0.115174i | ||||
\(939\) | −9.82094e42 | − | 1.06881e42i | −0.773574 | − | 0.0841880i | ||||
\(940\) | −5.51282e43 | −4.27583 | ||||||||
\(941\) | 2.40860e43 | 1.83956 | 0.919782 | − | 0.392430i | \(-0.128365\pi\) | ||||
0.919782 | + | 0.392430i | \(0.128365\pi\) | |||||||
\(942\) | −7.28729e41 | + | 6.69603e42i | −0.0548060 | + | 0.503593i | ||||
\(943\) | − | 6.27790e42i | − | 0.464938i | ||||||
\(944\) | −1.65204e43 | −1.20483 | ||||||||
\(945\) | −2.25079e43 | − | 1.27434e43i | −1.61649 | − | 0.915214i | ||||
\(946\) | 3.88439e43 | 2.74727 | ||||||||
\(947\) | 1.12201e43i | 0.781488i | 0.920499 | + | 0.390744i | \(0.127782\pi\) | ||||
−0.920499 | + | 0.390744i | \(0.872218\pi\) | |||||||
\(948\) | −2.15745e42 | + | 1.98241e43i | −0.147986 | + | 1.35979i | ||||
\(949\) | 2.19983e43 | 1.48603 | ||||||||
\(950\) | 5.25809e42 | 0.349813 | ||||||||
\(951\) | 5.55977e41 | + | 6.05070e40i | 0.0364284 | + | 0.00396450i | ||||
\(952\) | 3.67711e43 | + | 7.07051e42i | 2.37286 | + | 0.456263i | ||||
\(953\) | − | 1.19102e42i | − | 0.0756957i | −0.999284 | − | 0.0378478i | \(-0.987950\pi\) | ||
0.999284 | − | 0.0378478i | \(-0.0120502\pi\) | |||||||
\(954\) | −4.81625e42 | − | 1.06087e42i | −0.301479 | − | 0.0664064i | ||||
\(955\) | 4.38926e43i | 2.70609i | ||||||||
\(956\) | 3.93193e43i | 2.38762i | ||||||||
\(957\) | −1.47766e42 | + | 1.35777e43i | −0.0883792 | + | 0.812085i | ||||
\(958\) | 3.59222e43i | 2.11623i | ||||||||
\(959\) | 1.88203e43 | + | 3.61886e42i | 1.09209 | + | 0.209991i | ||||
\(960\) | −2.82161e42 | + | 2.59268e43i | −0.161274 | + | 1.48189i | ||||
\(961\) | 1.63485e43 | 0.920423 | ||||||||
\(962\) | 1.21014e42 | 0.0671116 | ||||||||
\(963\) | −3.14519e42 | + | 1.42789e43i | −0.171817 | + | 0.780033i | ||||
\(964\) | − | 6.21347e43i | − | 3.34362i | ||||||
\(965\) | −5.77069e43 | −3.05902 | ||||||||
\(966\) | −2.11794e43 | − | 6.51371e42i | −1.10597 | − | 0.340142i | ||||
\(967\) | −3.71332e42 | −0.191020 | −0.0955099 | − | 0.995428i | \(-0.530448\pi\) | ||||
−0.0955099 | + | 0.995428i | \(0.530448\pi\) | |||||||
\(968\) | − | 9.88435e42i | − | 0.500905i | ||||||
\(969\) | −2.11523e42 | − | 2.30200e41i | −0.105600 | − | 0.0114924i | ||||
\(970\) | −1.04454e44 | −5.13730 | ||||||||
\(971\) | −7.89413e42 | −0.382495 | −0.191247 | − | 0.981542i | \(-0.561253\pi\) | ||||
−0.191247 | + | 0.981542i | \(0.561253\pi\) | |||||||
\(972\) | 2.22710e43 | − | 3.69844e43i | 1.06311 | − | 1.76546i | ||||
\(973\) | −1.09671e43 | − | 2.10881e42i | −0.515772 | − | 0.0991747i | ||||
\(974\) | − | 6.18800e43i | − | 2.86712i | ||||||
\(975\) | 8.27587e43 | + | 9.00662e42i | 3.77787 | + | 0.411145i | ||||
\(976\) | − | 2.58634e43i | − | 1.16322i | ||||||
\(977\) | 5.83677e42i | 0.258644i | 0.991603 | + | 0.129322i | \(0.0412800\pi\) | ||||
−0.991603 | + | 0.129322i | \(0.958720\pi\) | |||||||
\(978\) | −5.26409e43 | − | 5.72891e42i | −2.29832 | − | 0.250126i | ||||
\(979\) | 1.15486e43i | 0.496799i | ||||||||
\(980\) | 8.38771e43 | + | 3.34949e43i | 3.55521 | + | 1.41971i | ||||
\(981\) | −4.70088e42 | − | 1.03546e42i | −0.196326 | − | 0.0432445i | ||||
\(982\) | −3.89695e43 | −1.60364 | ||||||||
\(983\) | −1.53736e43 | −0.623375 | −0.311687 | − | 0.950185i | \(-0.600894\pi\) | ||||
−0.311687 | + | 0.950185i | \(0.600894\pi\) | |||||||
\(984\) | −3.24628e43 | − | 3.53293e42i | −1.29705 | − | 0.141158i | ||||
\(985\) | − | 7.81828e43i | − | 3.07812i | ||||||
\(986\) | 4.25595e43 | 1.65113 | ||||||||
\(987\) | 2.79254e43 | + | 8.58845e42i | 1.06758 | + | 0.328334i | ||||
\(988\) | −6.92108e42 | −0.260734 | ||||||||
\(989\) | 2.48253e43i | 0.921612i | ||||||||
\(990\) | 9.77634e43 | + | 2.15342e43i | 3.57656 | + | 0.787805i | ||||
\(991\) | 9.62473e42 | 0.346993 | 0.173497 | − | 0.984834i | \(-0.444493\pi\) | ||||
0.173497 | + | 0.984834i | \(0.444493\pi\) | |||||||
\(992\) | 1.74160e42 | 0.0618770 | ||||||||
\(993\) | −4.02566e42 | + | 3.69904e43i | −0.140953 | + | 1.29516i | ||||
\(994\) | 3.46320e42 | − | 1.80108e43i | 0.119502 | − | 0.621486i | ||||
\(995\) | 5.63925e43i | 1.91772i | ||||||||
\(996\) | 6.67660e42 | − | 6.13489e43i | 0.223766 | − | 2.05611i | ||||
\(997\) | 3.99552e43i | 1.31976i | 0.751373 | + | 0.659878i | \(0.229392\pi\) | ||||
−0.751373 | + | 0.659878i | \(0.770608\pi\) | |||||||
\(998\) | 8.91421e43i | 2.90195i | ||||||||
\(999\) | −2.46341e41 | + | 7.30590e41i | −0.00790383 | + | 0.0234409i |
(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 | 21.30.c.a.20.3 | ✓ | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.74 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.73 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.4 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.3 | ✓ | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.4 | yes | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.73 | yes | 76 | 7.6 | odd | 2 | inner | |
21.30.c.a.20.74 | yes | 76 | 3.2 | odd | 2 | inner |