Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(1,21)]
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([0, 0]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3 x^{7} - 2857317313 x^{6} - 1405020216555 x^{5} + \cdots - 19\!\cdots\!94 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{16}\cdot 5^{2}\cdot 7^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-239.721\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2672.72 | −0.115350 | −0.0576751 | − | 0.998335i | \(-0.518369\pi\) | ||||
−0.0576751 | + | 0.998335i | \(0.518369\pi\) | |||||||
\(3\) | 4.78297e6 | 0.577350 | ||||||||
\(4\) | −5.29727e8 | −0.986694 | ||||||||
\(5\) | 1.94732e10 | 1.42683 | 0.713417 | − | 0.700740i | \(-0.247147\pi\) | ||||
0.713417 | + | 0.700740i | \(0.247147\pi\) | |||||||
\(6\) | −1.27835e10 | −0.0665975 | ||||||||
\(7\) | −6.78223e11 | −0.377964 | ||||||||
\(8\) | 2.85072e12 | 0.229166 | ||||||||
\(9\) | 2.28768e13 | 0.333333 | ||||||||
\(10\) | −5.20466e13 | −0.164586 | ||||||||
\(11\) | −2.34539e15 | −1.86218 | −0.931089 | − | 0.364791i | \(-0.881140\pi\) | ||||
−0.931089 | + | 0.364791i | \(0.881140\pi\) | |||||||
\(12\) | −2.53367e15 | −0.569668 | ||||||||
\(13\) | −1.06675e16 | −0.751422 | −0.375711 | − | 0.926737i | \(-0.622602\pi\) | ||||
−0.375711 | + | 0.926737i | \(0.622602\pi\) | |||||||
\(14\) | 1.81270e15 | 0.0435983 | ||||||||
\(15\) | 9.31399e16 | 0.823783 | ||||||||
\(16\) | 2.76776e17 | 0.960260 | ||||||||
\(17\) | −1.80413e17 | −0.259872 | −0.129936 | − | 0.991522i | \(-0.541477\pi\) | ||||
−0.129936 | + | 0.991522i | \(0.541477\pi\) | |||||||
\(18\) | −6.11433e16 | −0.0384501 | ||||||||
\(19\) | 3.63408e18 | 1.04344 | 0.521720 | − | 0.853117i | \(-0.325291\pi\) | ||||
0.521720 | + | 0.853117i | \(0.325291\pi\) | |||||||
\(20\) | −1.03155e19 | −1.40785 | ||||||||
\(21\) | −3.24392e18 | −0.218218 | ||||||||
\(22\) | 6.26858e18 | 0.214803 | ||||||||
\(23\) | 1.42481e19 | 0.256273 | 0.128136 | − | 0.991757i | \(-0.459101\pi\) | ||||
0.128136 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(24\) | 1.36349e19 | 0.132309 | ||||||||
\(25\) | 1.92943e20 | 1.03585 | ||||||||
\(26\) | 2.85113e19 | 0.0866768 | ||||||||
\(27\) | 1.09419e20 | 0.192450 | ||||||||
\(28\) | 3.59273e20 | 0.372935 | ||||||||
\(29\) | 1.38009e21 | 0.861267 | 0.430634 | − | 0.902527i | \(-0.358290\pi\) | ||||
0.430634 | + | 0.902527i | \(0.358290\pi\) | |||||||
\(30\) | −2.48937e20 | −0.0950236 | ||||||||
\(31\) | −1.39623e21 | −0.331293 | −0.165647 | − | 0.986185i | \(-0.552971\pi\) | ||||
−0.165647 | + | 0.986185i | \(0.552971\pi\) | |||||||
\(32\) | −2.27021e21 | −0.339932 | ||||||||
\(33\) | −1.12179e22 | −1.07513 | ||||||||
\(34\) | 4.82194e20 | 0.0299763 | ||||||||
\(35\) | −1.32072e22 | −0.539292 | ||||||||
\(36\) | −1.21185e22 | −0.328898 | ||||||||
\(37\) | 1.35650e22 | 0.247454 | 0.123727 | − | 0.992316i | \(-0.460515\pi\) | ||||
0.123727 | + | 0.992316i | \(0.460515\pi\) | |||||||
\(38\) | −9.71289e21 | −0.120361 | ||||||||
\(39\) | −5.10223e22 | −0.433834 | ||||||||
\(40\) | 5.55128e22 | 0.326981 | ||||||||
\(41\) | −4.23543e23 | −1.74394 | −0.871969 | − | 0.489561i | \(-0.837157\pi\) | ||||
−0.871969 | + | 0.489561i | \(0.837157\pi\) | |||||||
\(42\) | 8.67009e21 | 0.0251715 | ||||||||
\(43\) | 3.71448e23 | 0.766664 | 0.383332 | − | 0.923611i | \(-0.374776\pi\) | ||||
0.383332 | + | 0.923611i | \(0.374776\pi\) | |||||||
\(44\) | 1.24242e24 | 1.83740 | ||||||||
\(45\) | 4.45485e23 | 0.475611 | ||||||||
\(46\) | −3.80811e22 | −0.0295611 | ||||||||
\(47\) | 2.04365e24 | 1.16142 | 0.580708 | − | 0.814112i | \(-0.302776\pi\) | ||||
0.580708 | + | 0.814112i | \(0.302776\pi\) | |||||||
\(48\) | 1.32381e24 | 0.554406 | ||||||||
\(49\) | 4.59987e23 | 0.142857 | ||||||||
\(50\) | −5.15682e23 | −0.119486 | ||||||||
\(51\) | −8.62910e23 | −0.150037 | ||||||||
\(52\) | 5.65087e24 | 0.741424 | ||||||||
\(53\) | 1.15964e25 | 1.15431 | 0.577157 | − | 0.816633i | \(-0.304162\pi\) | ||||
0.577157 | + | 0.816633i | \(0.304162\pi\) | |||||||
\(54\) | −2.92446e23 | −0.0221992 | ||||||||
\(55\) | −4.56724e25 | −2.65702 | ||||||||
\(56\) | −1.93342e24 | −0.0866165 | ||||||||
\(57\) | 1.73817e25 | 0.602430 | ||||||||
\(58\) | −3.68861e24 | −0.0993474 | ||||||||
\(59\) | −2.23571e25 | −0.469961 | −0.234981 | − | 0.972000i | \(-0.575503\pi\) | ||||
−0.234981 | + | 0.972000i | \(0.575503\pi\) | |||||||
\(60\) | −4.93388e25 | −0.812822 | ||||||||
\(61\) | −4.97521e25 | −0.644954 | −0.322477 | − | 0.946577i | \(-0.604516\pi\) | ||||
−0.322477 | + | 0.946577i | \(0.604516\pi\) | |||||||
\(62\) | 3.73174e24 | 0.0382148 | ||||||||
\(63\) | −1.55156e25 | −0.125988 | ||||||||
\(64\) | −1.42525e26 | −0.921049 | ||||||||
\(65\) | −2.07731e26 | −1.07215 | ||||||||
\(66\) | 2.99824e25 | 0.124016 | ||||||||
\(67\) | 5.48772e26 | 1.82519 | 0.912593 | − | 0.408869i | \(-0.134077\pi\) | ||||
0.912593 | + | 0.408869i | \(0.134077\pi\) | |||||||
\(68\) | 9.55698e25 | 0.256414 | ||||||||
\(69\) | 6.81480e25 | 0.147959 | ||||||||
\(70\) | 3.52992e25 | 0.0622075 | ||||||||
\(71\) | 1.06838e27 | 1.53279 | 0.766393 | − | 0.642372i | \(-0.222050\pi\) | ||||
0.766393 | + | 0.642372i | \(0.222050\pi\) | |||||||
\(72\) | 6.52153e25 | 0.0763886 | ||||||||
\(73\) | −1.06623e27 | −1.02251 | −0.511257 | − | 0.859428i | \(-0.670820\pi\) | ||||
−0.511257 | + | 0.859428i | \(0.670820\pi\) | |||||||
\(74\) | −3.62554e25 | −0.0285439 | ||||||||
\(75\) | 9.22839e26 | 0.598050 | ||||||||
\(76\) | −1.92507e27 | −1.02956 | ||||||||
\(77\) | 1.59070e27 | 0.703837 | ||||||||
\(78\) | 1.36368e26 | 0.0500429 | ||||||||
\(79\) | −5.67748e27 | −1.73206 | −0.866029 | − | 0.499994i | \(-0.833336\pi\) | ||||
−0.866029 | + | 0.499994i | \(0.833336\pi\) | |||||||
\(80\) | 5.38973e27 | 1.37013 | ||||||||
\(81\) | 5.23348e26 | 0.111111 | ||||||||
\(82\) | 1.13201e27 | 0.201164 | ||||||||
\(83\) | −5.28365e27 | −0.787592 | −0.393796 | − | 0.919198i | \(-0.628838\pi\) | ||||
−0.393796 | + | 0.919198i | \(0.628838\pi\) | |||||||
\(84\) | 1.71839e27 | 0.215314 | ||||||||
\(85\) | −3.51323e27 | −0.370793 | ||||||||
\(86\) | −9.92776e26 | −0.0884349 | ||||||||
\(87\) | 6.60095e27 | 0.497253 | ||||||||
\(88\) | −6.68605e27 | −0.426748 | ||||||||
\(89\) | 2.36536e28 | 1.28157 | 0.640784 | − | 0.767721i | \(-0.278609\pi\) | ||||
0.640784 | + | 0.767721i | \(0.278609\pi\) | |||||||
\(90\) | −1.19066e27 | −0.0548619 | ||||||||
\(91\) | 7.23494e27 | 0.284011 | ||||||||
\(92\) | −7.54759e27 | −0.252863 | ||||||||
\(93\) | −6.67813e27 | −0.191272 | ||||||||
\(94\) | −5.46211e27 | −0.133970 | ||||||||
\(95\) | 7.07674e28 | 1.48882 | ||||||||
\(96\) | −1.08584e28 | −0.196260 | ||||||||
\(97\) | 2.86997e28 | 0.446362 | 0.223181 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223181 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(98\) | −1.22942e27 | −0.0164786 | ||||||||
\(99\) | −5.36550e28 | −0.620726 | ||||||||
\(100\) | −1.02207e29 | −1.02207 | ||||||||
\(101\) | 1.00238e29 | 0.867704 | 0.433852 | − | 0.900984i | \(-0.357154\pi\) | ||||
0.433852 | + | 0.900984i | \(0.357154\pi\) | |||||||
\(102\) | 2.30632e27 | 0.0173068 | ||||||||
\(103\) | −2.20235e28 | −0.143465 | −0.0717327 | − | 0.997424i | \(-0.522853\pi\) | ||||
−0.0717327 | + | 0.997424i | \(0.522853\pi\) | |||||||
\(104\) | −3.04101e28 | −0.172200 | ||||||||
\(105\) | −6.31696e28 | −0.311361 | ||||||||
\(106\) | −3.09940e28 | −0.133150 | ||||||||
\(107\) | 2.29131e29 | 0.859053 | 0.429526 | − | 0.903054i | \(-0.358681\pi\) | ||||
0.429526 | + | 0.903054i | \(0.358681\pi\) | |||||||
\(108\) | −5.79622e28 | −0.189889 | ||||||||
\(109\) | 6.79956e29 | 1.94893 | 0.974466 | − | 0.224534i | \(-0.0720861\pi\) | ||||
0.974466 | + | 0.224534i | \(0.0720861\pi\) | |||||||
\(110\) | 1.22070e29 | 0.306488 | ||||||||
\(111\) | 6.48809e28 | 0.142868 | ||||||||
\(112\) | −1.87716e29 | −0.362944 | ||||||||
\(113\) | 8.64483e29 | 1.46933 | 0.734664 | − | 0.678431i | \(-0.237340\pi\) | ||||
0.734664 | + | 0.678431i | \(0.237340\pi\) | |||||||
\(114\) | −4.64564e28 | −0.0694905 | ||||||||
\(115\) | 2.77456e29 | 0.365658 | ||||||||
\(116\) | −7.31074e29 | −0.849808 | ||||||||
\(117\) | −2.44038e29 | −0.250474 | ||||||||
\(118\) | 5.97544e28 | 0.0542101 | ||||||||
\(119\) | 1.22360e29 | 0.0982222 | ||||||||
\(120\) | 2.65516e29 | 0.188783 | ||||||||
\(121\) | 3.91455e30 | 2.46771 | ||||||||
\(122\) | 1.32973e29 | 0.0743956 | ||||||||
\(123\) | −2.02579e30 | −1.00686 | ||||||||
\(124\) | 7.39622e29 | 0.326885 | ||||||||
\(125\) | 1.30047e29 | 0.0511572 | ||||||||
\(126\) | 4.14688e28 | 0.0145328 | ||||||||
\(127\) | 1.93309e30 | 0.604084 | 0.302042 | − | 0.953295i | \(-0.402332\pi\) | ||||
0.302042 | + | 0.953295i | \(0.402332\pi\) | |||||||
\(128\) | 1.59974e30 | 0.446175 | ||||||||
\(129\) | 1.77662e30 | 0.442634 | ||||||||
\(130\) | 5.55207e29 | 0.123673 | ||||||||
\(131\) | 1.56740e30 | 0.312425 | 0.156212 | − | 0.987723i | \(-0.450072\pi\) | ||||
0.156212 | + | 0.987723i | \(0.450072\pi\) | |||||||
\(132\) | 5.94245e30 | 1.06082 | ||||||||
\(133\) | −2.46472e30 | −0.394383 | ||||||||
\(134\) | −1.46671e30 | −0.210536 | ||||||||
\(135\) | 2.13074e30 | 0.274594 | ||||||||
\(136\) | −5.14307e29 | −0.0595537 | ||||||||
\(137\) | 5.59686e30 | 0.582768 | 0.291384 | − | 0.956606i | \(-0.405884\pi\) | ||||
0.291384 | + | 0.956606i | \(0.405884\pi\) | |||||||
\(138\) | −1.82141e29 | −0.0170671 | ||||||||
\(139\) | −9.85701e29 | −0.0831822 | −0.0415911 | − | 0.999135i | \(-0.513243\pi\) | ||||
−0.0415911 | + | 0.999135i | \(0.513243\pi\) | |||||||
\(140\) | 6.99622e30 | 0.532117 | ||||||||
\(141\) | 9.77471e30 | 0.670543 | ||||||||
\(142\) | −2.85549e30 | −0.176807 | ||||||||
\(143\) | 2.50195e31 | 1.39928 | ||||||||
\(144\) | 6.33175e30 | 0.320087 | ||||||||
\(145\) | 2.68749e31 | 1.22889 | ||||||||
\(146\) | 2.84973e30 | 0.117947 | ||||||||
\(147\) | 2.20010e30 | 0.0824786 | ||||||||
\(148\) | −7.18575e30 | −0.244161 | ||||||||
\(149\) | −2.84172e31 | −0.875752 | −0.437876 | − | 0.899035i | \(-0.644269\pi\) | ||||
−0.437876 | + | 0.899035i | \(0.644269\pi\) | |||||||
\(150\) | −2.46649e30 | −0.0689853 | ||||||||
\(151\) | 2.81089e31 | 0.713967 | 0.356984 | − | 0.934111i | \(-0.383805\pi\) | ||||
0.356984 | + | 0.934111i | \(0.383805\pi\) | |||||||
\(152\) | 1.03598e31 | 0.239121 | ||||||||
\(153\) | −4.12727e30 | −0.0866239 | ||||||||
\(154\) | −4.25149e30 | −0.0811878 | ||||||||
\(155\) | −2.71891e31 | −0.472700 | ||||||||
\(156\) | 2.70279e31 | 0.428061 | ||||||||
\(157\) | 9.89253e31 | 1.42811 | 0.714056 | − | 0.700088i | \(-0.246856\pi\) | ||||
0.714056 | + | 0.700088i | \(0.246856\pi\) | |||||||
\(158\) | 1.51743e31 | 0.199793 | ||||||||
\(159\) | 5.54653e31 | 0.666443 | ||||||||
\(160\) | −4.42084e31 | −0.485026 | ||||||||
\(161\) | −9.66336e30 | −0.0968619 | ||||||||
\(162\) | −1.39876e30 | −0.0128167 | ||||||||
\(163\) | 4.69173e31 | 0.393199 | 0.196600 | − | 0.980484i | \(-0.437010\pi\) | ||||
0.196600 | + | 0.980484i | \(0.437010\pi\) | |||||||
\(164\) | 2.24362e32 | 1.72073 | ||||||||
\(165\) | −2.18450e32 | −1.53403 | ||||||||
\(166\) | 1.41217e31 | 0.0908490 | ||||||||
\(167\) | −1.40088e32 | −0.826058 | −0.413029 | − | 0.910718i | \(-0.635529\pi\) | ||||
−0.413029 | + | 0.910718i | \(0.635529\pi\) | |||||||
\(168\) | −9.24751e30 | −0.0500081 | ||||||||
\(169\) | −8.77426e31 | −0.435365 | ||||||||
\(170\) | 9.38988e30 | 0.0427711 | ||||||||
\(171\) | 8.31362e31 | 0.347813 | ||||||||
\(172\) | −1.96766e32 | −0.756463 | ||||||||
\(173\) | −3.03186e31 | −0.107162 | −0.0535810 | − | 0.998564i | \(-0.517064\pi\) | ||||
−0.0535810 | + | 0.998564i | \(0.517064\pi\) | |||||||
\(174\) | −1.76425e31 | −0.0573583 | ||||||||
\(175\) | −1.30858e32 | −0.391516 | ||||||||
\(176\) | −6.49148e32 | −1.78818 | ||||||||
\(177\) | −1.06933e32 | −0.271332 | ||||||||
\(178\) | −6.32194e31 | −0.147829 | ||||||||
\(179\) | −8.79328e31 | −0.189575 | −0.0947877 | − | 0.995498i | \(-0.530217\pi\) | ||||
−0.0947877 | + | 0.995498i | \(0.530217\pi\) | |||||||
\(180\) | −2.35986e32 | −0.469283 | ||||||||
\(181\) | 1.39286e32 | 0.255605 | 0.127802 | − | 0.991800i | \(-0.459208\pi\) | ||||
0.127802 | + | 0.991800i | \(0.459208\pi\) | |||||||
\(182\) | −1.93370e31 | −0.0327607 | ||||||||
\(183\) | −2.37963e32 | −0.372364 | ||||||||
\(184\) | 4.06172e31 | 0.0587289 | ||||||||
\(185\) | 2.64154e32 | 0.353076 | ||||||||
\(186\) | 1.78488e31 | 0.0220633 | ||||||||
\(187\) | 4.23139e32 | 0.483927 | ||||||||
\(188\) | −1.08258e33 | −1.14596 | ||||||||
\(189\) | −7.42105e31 | −0.0727393 | ||||||||
\(190\) | −1.89141e32 | −0.171735 | ||||||||
\(191\) | 2.33825e33 | 1.96746 | 0.983732 | − | 0.179644i | \(-0.0574947\pi\) | ||||
0.983732 | + | 0.179644i | \(0.0574947\pi\) | |||||||
\(192\) | −6.81694e32 | −0.531768 | ||||||||
\(193\) | −1.92217e33 | −1.39063 | −0.695315 | − | 0.718705i | \(-0.744735\pi\) | ||||
−0.695315 | + | 0.718705i | \(0.744735\pi\) | |||||||
\(194\) | −7.67062e31 | −0.0514879 | ||||||||
\(195\) | −9.93570e32 | −0.619009 | ||||||||
\(196\) | −2.43668e32 | −0.140956 | ||||||||
\(197\) | −8.31047e32 | −0.446545 | −0.223272 | − | 0.974756i | \(-0.571674\pi\) | ||||
−0.223272 | + | 0.974756i | \(0.571674\pi\) | |||||||
\(198\) | 1.43405e32 | 0.0716010 | ||||||||
\(199\) | 3.47494e33 | 1.61279 | 0.806394 | − | 0.591378i | \(-0.201416\pi\) | ||||
0.806394 | + | 0.591378i | \(0.201416\pi\) | |||||||
\(200\) | 5.50026e32 | 0.237382 | ||||||||
\(201\) | 2.62476e33 | 1.05377 | ||||||||
\(202\) | −2.67908e32 | −0.100090 | ||||||||
\(203\) | −9.36012e32 | −0.325528 | ||||||||
\(204\) | 4.57107e32 | 0.148041 | ||||||||
\(205\) | −8.24775e33 | −2.48831 | ||||||||
\(206\) | 5.88627e31 | 0.0165488 | ||||||||
\(207\) | 3.25950e32 | 0.0854242 | ||||||||
\(208\) | −2.95251e33 | −0.721561 | ||||||||
\(209\) | −8.52334e33 | −1.94307 | ||||||||
\(210\) | 1.68835e32 | 0.0359155 | ||||||||
\(211\) | −8.10783e33 | −1.60994 | −0.804969 | − | 0.593317i | \(-0.797818\pi\) | ||||
−0.804969 | + | 0.593317i | \(0.797818\pi\) | |||||||
\(212\) | −6.14294e33 | −1.13895 | ||||||||
\(213\) | 5.11005e33 | 0.884954 | ||||||||
\(214\) | −6.12404e32 | −0.0990920 | ||||||||
\(215\) | 7.23329e33 | 1.09390 | ||||||||
\(216\) | 3.11923e32 | 0.0441030 | ||||||||
\(217\) | 9.46956e32 | 0.125217 | ||||||||
\(218\) | −1.81733e33 | −0.224810 | ||||||||
\(219\) | −5.09974e33 | −0.590348 | ||||||||
\(220\) | 2.41939e34 | 2.62167 | ||||||||
\(221\) | 1.92456e33 | 0.195273 | ||||||||
\(222\) | −1.73409e32 | −0.0164798 | ||||||||
\(223\) | 1.50914e34 | 1.34372 | 0.671858 | − | 0.740680i | \(-0.265496\pi\) | ||||
0.671858 | + | 0.740680i | \(0.265496\pi\) | |||||||
\(224\) | 1.53971e33 | 0.128482 | ||||||||
\(225\) | 4.41391e33 | 0.345285 | ||||||||
\(226\) | −2.31052e33 | −0.169487 | ||||||||
\(227\) | 5.78815e33 | 0.398258 | 0.199129 | − | 0.979973i | \(-0.436189\pi\) | ||||
0.199129 | + | 0.979973i | \(0.436189\pi\) | |||||||
\(228\) | −9.20757e33 | −0.594415 | ||||||||
\(229\) | 1.93852e34 | 1.17451 | 0.587253 | − | 0.809404i | \(-0.300209\pi\) | ||||
0.587253 | + | 0.809404i | \(0.300209\pi\) | |||||||
\(230\) | −7.41562e32 | −0.0421788 | ||||||||
\(231\) | 7.60826e33 | 0.406361 | ||||||||
\(232\) | 3.93426e33 | 0.197373 | ||||||||
\(233\) | −6.44258e33 | −0.303668 | −0.151834 | − | 0.988406i | \(-0.548518\pi\) | ||||
−0.151834 | + | 0.988406i | \(0.548518\pi\) | |||||||
\(234\) | 6.52246e32 | 0.0288923 | ||||||||
\(235\) | 3.97965e34 | 1.65715 | ||||||||
\(236\) | 1.18432e34 | 0.463708 | ||||||||
\(237\) | −2.71552e34 | −1.00000 | ||||||||
\(238\) | −3.27035e32 | −0.0113300 | ||||||||
\(239\) | 2.07853e34 | 0.677620 | 0.338810 | − | 0.940855i | \(-0.389976\pi\) | ||||
0.338810 | + | 0.940855i | \(0.389976\pi\) | |||||||
\(240\) | 2.57789e34 | 0.791046 | ||||||||
\(241\) | −4.38919e34 | −1.26805 | −0.634026 | − | 0.773312i | \(-0.718599\pi\) | ||||
−0.634026 | + | 0.773312i | \(0.718599\pi\) | |||||||
\(242\) | −1.04625e34 | −0.284651 | ||||||||
\(243\) | 2.50316e33 | 0.0641500 | ||||||||
\(244\) | 2.63551e34 | 0.636373 | ||||||||
\(245\) | 8.95743e33 | 0.203833 | ||||||||
\(246\) | 5.41437e33 | 0.116142 | ||||||||
\(247\) | −3.87666e34 | −0.784064 | ||||||||
\(248\) | −3.98026e33 | −0.0759211 | ||||||||
\(249\) | −2.52715e34 | −0.454717 | ||||||||
\(250\) | −3.47580e32 | −0.00590099 | ||||||||
\(251\) | −2.43361e34 | −0.389925 | −0.194963 | − | 0.980811i | \(-0.562459\pi\) | ||||
−0.194963 | + | 0.980811i | \(0.562459\pi\) | |||||||
\(252\) | 8.21902e33 | 0.124312 | ||||||||
\(253\) | −3.34173e34 | −0.477225 | ||||||||
\(254\) | −5.16660e33 | −0.0696813 | ||||||||
\(255\) | −1.68037e34 | −0.214078 | ||||||||
\(256\) | 7.22421e34 | 0.869582 | ||||||||
\(257\) | 1.41213e35 | 1.60637 | 0.803184 | − | 0.595731i | \(-0.203138\pi\) | ||||
0.803184 | + | 0.595731i | \(0.203138\pi\) | |||||||
\(258\) | −4.74842e33 | −0.0510579 | ||||||||
\(259\) | −9.20009e33 | −0.0935288 | ||||||||
\(260\) | 1.10041e35 | 1.05789 | ||||||||
\(261\) | 3.15721e34 | 0.287089 | ||||||||
\(262\) | −4.18922e33 | −0.0360383 | ||||||||
\(263\) | 1.27035e35 | 1.03411 | 0.517054 | − | 0.855953i | \(-0.327028\pi\) | ||||
0.517054 | + | 0.855953i | \(0.327028\pi\) | |||||||
\(264\) | −3.19792e34 | −0.246383 | ||||||||
\(265\) | 2.25820e35 | 1.64701 | ||||||||
\(266\) | 6.58751e33 | 0.0454922 | ||||||||
\(267\) | 1.13134e35 | 0.739913 | ||||||||
\(268\) | −2.90700e35 | −1.80090 | ||||||||
\(269\) | −1.61544e35 | −0.948160 | −0.474080 | − | 0.880482i | \(-0.657219\pi\) | ||||
−0.474080 | + | 0.880482i | \(0.657219\pi\) | |||||||
\(270\) | −5.69488e33 | −0.0316745 | ||||||||
\(271\) | −1.92714e35 | −1.01592 | −0.507960 | − | 0.861381i | \(-0.669600\pi\) | ||||
−0.507960 | + | 0.861381i | \(0.669600\pi\) | |||||||
\(272\) | −4.99340e34 | −0.249544 | ||||||||
\(273\) | 3.46045e34 | 0.163974 | ||||||||
\(274\) | −1.49588e34 | −0.0672225 | ||||||||
\(275\) | −4.52526e35 | −1.92894 | ||||||||
\(276\) | −3.60999e34 | −0.145990 | ||||||||
\(277\) | 1.24537e35 | 0.477906 | 0.238953 | − | 0.971031i | \(-0.423196\pi\) | ||||
0.238953 | + | 0.971031i | \(0.423196\pi\) | |||||||
\(278\) | 2.63450e33 | 0.00959509 | ||||||||
\(279\) | −3.19413e34 | −0.110431 | ||||||||
\(280\) | −3.76500e34 | −0.123587 | ||||||||
\(281\) | 9.35141e34 | 0.291498 | 0.145749 | − | 0.989322i | \(-0.453441\pi\) | ||||
0.145749 | + | 0.989322i | \(0.453441\pi\) | |||||||
\(282\) | −2.61251e34 | −0.0773474 | ||||||||
\(283\) | −3.30375e35 | −0.929188 | −0.464594 | − | 0.885524i | \(-0.653800\pi\) | ||||
−0.464594 | + | 0.885524i | \(0.653800\pi\) | |||||||
\(284\) | −5.65953e35 | −1.51239 | ||||||||
\(285\) | 3.38478e35 | 0.859568 | ||||||||
\(286\) | −6.68700e34 | −0.161408 | ||||||||
\(287\) | 2.87256e35 | 0.659147 | ||||||||
\(288\) | −5.19352e34 | −0.113311 | ||||||||
\(289\) | −4.49420e35 | −0.932467 | ||||||||
\(290\) | −7.18292e34 | −0.141752 | ||||||||
\(291\) | 1.37270e35 | 0.257707 | ||||||||
\(292\) | 5.64811e35 | 1.00891 | ||||||||
\(293\) | −7.63998e35 | −1.29871 | −0.649355 | − | 0.760486i | \(-0.724961\pi\) | ||||
−0.649355 | + | 0.760486i | \(0.724961\pi\) | |||||||
\(294\) | −5.88026e33 | −0.00951393 | ||||||||
\(295\) | −4.35366e35 | −0.670556 | ||||||||
\(296\) | 3.86700e34 | 0.0567080 | ||||||||
\(297\) | −2.56630e35 | −0.358376 | ||||||||
\(298\) | 7.59513e34 | 0.101018 | ||||||||
\(299\) | −1.51991e35 | −0.192569 | ||||||||
\(300\) | −4.88853e35 | −0.590093 | ||||||||
\(301\) | −2.51924e35 | −0.289772 | ||||||||
\(302\) | −7.51273e34 | −0.0823563 | ||||||||
\(303\) | 4.79434e35 | 0.500969 | ||||||||
\(304\) | 1.00583e36 | 1.00197 | ||||||||
\(305\) | −9.68835e35 | −0.920242 | ||||||||
\(306\) | 1.10311e34 | 0.00999209 | ||||||||
\(307\) | 1.73065e36 | 1.49521 | 0.747604 | − | 0.664144i | \(-0.231204\pi\) | ||||
0.747604 | + | 0.664144i | \(0.231204\pi\) | |||||||
\(308\) | −8.42637e35 | −0.694472 | ||||||||
\(309\) | −1.05338e35 | −0.0828297 | ||||||||
\(310\) | 7.26690e34 | 0.0545261 | ||||||||
\(311\) | −1.05243e36 | −0.753648 | −0.376824 | − | 0.926285i | \(-0.622984\pi\) | ||||
−0.376824 | + | 0.926285i | \(0.622984\pi\) | |||||||
\(312\) | −1.45450e35 | −0.0994199 | ||||||||
\(313\) | 5.43426e34 | 0.0354607 | 0.0177304 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177304 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(314\) | −2.64400e35 | −0.164733 | ||||||||
\(315\) | −3.02138e35 | −0.179764 | ||||||||
\(316\) | 3.00751e36 | 1.70901 | ||||||||
\(317\) | 2.67754e36 | 1.45337 | 0.726686 | − | 0.686970i | \(-0.241059\pi\) | ||||
0.726686 | + | 0.686970i | \(0.241059\pi\) | |||||||
\(318\) | −1.48243e35 | −0.0768744 | ||||||||
\(319\) | −3.23686e36 | −1.60383 | ||||||||
\(320\) | −2.77543e36 | −1.31418 | ||||||||
\(321\) | 1.09593e36 | 0.495974 | ||||||||
\(322\) | 2.58275e34 | 0.0111730 | ||||||||
\(323\) | −6.55636e35 | −0.271160 | ||||||||
\(324\) | −2.77232e35 | −0.109633 | ||||||||
\(325\) | −2.05822e36 | −0.778363 | ||||||||
\(326\) | −1.25397e35 | −0.0453556 | ||||||||
\(327\) | 3.25221e36 | 1.12522 | ||||||||
\(328\) | −1.20740e36 | −0.399651 | ||||||||
\(329\) | −1.38605e36 | −0.438974 | ||||||||
\(330\) | 5.83855e35 | 0.176951 | ||||||||
\(331\) | 5.14201e36 | 1.49151 | 0.745756 | − | 0.666219i | \(-0.232089\pi\) | ||||
0.745756 | + | 0.666219i | \(0.232089\pi\) | |||||||
\(332\) | 2.79889e36 | 0.777113 | ||||||||
\(333\) | 3.10323e35 | 0.0824847 | ||||||||
\(334\) | 3.74415e35 | 0.0952860 | ||||||||
\(335\) | 1.06864e37 | 2.60424 | ||||||||
\(336\) | −8.97839e35 | −0.209546 | ||||||||
\(337\) | −8.50236e35 | −0.190067 | −0.0950333 | − | 0.995474i | \(-0.530296\pi\) | ||||
−0.0950333 | + | 0.995474i | \(0.530296\pi\) | |||||||
\(338\) | 2.34511e35 | 0.0502194 | ||||||||
\(339\) | 4.13479e36 | 0.848317 | ||||||||
\(340\) | 1.86105e36 | 0.365860 | ||||||||
\(341\) | 3.27471e36 | 0.616927 | ||||||||
\(342\) | −2.22200e35 | −0.0401204 | ||||||||
\(343\) | −3.11973e35 | −0.0539949 | ||||||||
\(344\) | 1.05889e36 | 0.175693 | ||||||||
\(345\) | 1.32706e36 | 0.211113 | ||||||||
\(346\) | 8.10331e34 | 0.0123612 | ||||||||
\(347\) | −9.07198e36 | −1.32717 | −0.663583 | − | 0.748103i | \(-0.730965\pi\) | ||||
−0.663583 | + | 0.748103i | \(0.730965\pi\) | |||||||
\(348\) | −3.49671e36 | −0.490637 | ||||||||
\(349\) | −7.98276e36 | −1.07445 | −0.537223 | − | 0.843440i | \(-0.680527\pi\) | ||||
−0.537223 | + | 0.843440i | \(0.680527\pi\) | |||||||
\(350\) | 3.49748e35 | 0.0451615 | ||||||||
\(351\) | −1.16723e36 | −0.144611 | ||||||||
\(352\) | 5.32454e36 | 0.633014 | ||||||||
\(353\) | −2.38372e35 | −0.0271970 | −0.0135985 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135985 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(354\) | 2.85803e35 | 0.0312982 | ||||||||
\(355\) | 2.08049e37 | 2.18703 | ||||||||
\(356\) | −1.25299e37 | −1.26452 | ||||||||
\(357\) | 5.85246e35 | 0.0567086 | ||||||||
\(358\) | 2.35020e35 | 0.0218676 | ||||||||
\(359\) | −6.70211e36 | −0.598883 | −0.299442 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299442 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(360\) | 1.26995e36 | 0.108994 | ||||||||
\(361\) | 1.07673e36 | 0.0887675 | ||||||||
\(362\) | −3.72273e35 | −0.0294841 | ||||||||
\(363\) | 1.87232e37 | 1.42473 | ||||||||
\(364\) | −3.83255e36 | −0.280232 | ||||||||
\(365\) | −2.07629e37 | −1.45896 | ||||||||
\(366\) | 6.36008e35 | 0.0429523 | ||||||||
\(367\) | 6.00718e36 | 0.389953 | 0.194977 | − | 0.980808i | \(-0.437537\pi\) | ||||
0.194977 | + | 0.980808i | \(0.437537\pi\) | |||||||
\(368\) | 3.94352e36 | 0.246088 | ||||||||
\(369\) | −9.68930e36 | −0.581313 | ||||||||
\(370\) | −7.06011e35 | −0.0407274 | ||||||||
\(371\) | −7.86496e36 | −0.436289 | ||||||||
\(372\) | 3.53759e36 | 0.188727 | ||||||||
\(373\) | 6.08471e36 | 0.312221 | 0.156110 | − | 0.987740i | \(-0.450104\pi\) | ||||
0.156110 | + | 0.987740i | \(0.450104\pi\) | |||||||
\(374\) | −1.13093e36 | −0.0558212 | ||||||||
\(375\) | 6.22013e35 | 0.0295356 | ||||||||
\(376\) | 5.82587e36 | 0.266157 | ||||||||
\(377\) | −1.47222e37 | −0.647175 | ||||||||
\(378\) | 1.98344e35 | 0.00839050 | ||||||||
\(379\) | 3.06661e37 | 1.24850 | 0.624252 | − | 0.781223i | \(-0.285404\pi\) | ||||
0.624252 | + | 0.781223i | \(0.285404\pi\) | |||||||
\(380\) | −3.74874e37 | −1.46901 | ||||||||
\(381\) | 9.24590e36 | 0.348768 | ||||||||
\(382\) | −6.24948e36 | −0.226947 | ||||||||
\(383\) | −1.06910e37 | −0.373798 | −0.186899 | − | 0.982379i | \(-0.559844\pi\) | ||||
−0.186899 | + | 0.982379i | \(0.559844\pi\) | |||||||
\(384\) | 7.65152e36 | 0.257599 | ||||||||
\(385\) | 3.09761e37 | 1.00426 | ||||||||
\(386\) | 5.13743e36 | 0.160409 | ||||||||
\(387\) | 8.49753e36 | 0.255555 | ||||||||
\(388\) | −1.52030e37 | −0.440422 | ||||||||
\(389\) | −3.13590e37 | −0.875172 | −0.437586 | − | 0.899176i | \(-0.644166\pi\) | ||||
−0.437586 | + | 0.899176i | \(0.644166\pi\) | |||||||
\(390\) | 2.65554e36 | 0.0714028 | ||||||||
\(391\) | −2.57054e36 | −0.0665979 | ||||||||
\(392\) | 1.31129e36 | 0.0327380 | ||||||||
\(393\) | 7.49682e36 | 0.180379 | ||||||||
\(394\) | 2.22116e36 | 0.0515091 | ||||||||
\(395\) | −1.10559e38 | −2.47136 | ||||||||
\(396\) | 2.84225e37 | 0.612467 | ||||||||
\(397\) | −8.36014e37 | −1.73681 | −0.868403 | − | 0.495859i | \(-0.834853\pi\) | ||||
−0.868403 | + | 0.495859i | \(0.834853\pi\) | |||||||
\(398\) | −9.28754e36 | −0.186036 | ||||||||
\(399\) | −1.17887e37 | −0.227697 | ||||||||
\(400\) | 5.34019e37 | 0.994689 | ||||||||
\(401\) | −4.15145e37 | −0.745772 | −0.372886 | − | 0.927877i | \(-0.621632\pi\) | ||||
−0.372886 | + | 0.927877i | \(0.621632\pi\) | |||||||
\(402\) | −7.01525e36 | −0.121553 | ||||||||
\(403\) | 1.48943e37 | 0.248941 | ||||||||
\(404\) | −5.30987e37 | −0.856158 | ||||||||
\(405\) | 1.01913e37 | 0.158537 | ||||||||
\(406\) | 2.50170e36 | 0.0375498 | ||||||||
\(407\) | −3.18152e37 | −0.460803 | ||||||||
\(408\) | −2.45992e36 | −0.0343833 | ||||||||
\(409\) | 1.92537e37 | 0.259733 | 0.129866 | − | 0.991532i | \(-0.458545\pi\) | ||||
0.129866 | + | 0.991532i | \(0.458545\pi\) | |||||||
\(410\) | 2.20439e37 | 0.287027 | ||||||||
\(411\) | 2.67696e37 | 0.336462 | ||||||||
\(412\) | 1.16665e37 | 0.141556 | ||||||||
\(413\) | 1.51631e37 | 0.177629 | ||||||||
\(414\) | −8.71173e35 | −0.00985370 | ||||||||
\(415\) | −1.02890e38 | −1.12376 | ||||||||
\(416\) | 2.42175e37 | 0.255433 | ||||||||
\(417\) | −4.71458e36 | −0.0480253 | ||||||||
\(418\) | 2.27805e37 | 0.224134 | ||||||||
\(419\) | 3.02161e37 | 0.287167 | 0.143584 | − | 0.989638i | \(-0.454137\pi\) | ||||
0.143584 | + | 0.989638i | \(0.454137\pi\) | |||||||
\(420\) | 3.34627e37 | 0.307218 | ||||||||
\(421\) | −1.00326e38 | −0.889863 | −0.444931 | − | 0.895565i | \(-0.646772\pi\) | ||||
−0.444931 | + | 0.895565i | \(0.646772\pi\) | |||||||
\(422\) | 2.16700e37 | 0.185707 | ||||||||
\(423\) | 4.67521e37 | 0.387138 | ||||||||
\(424\) | 3.30581e37 | 0.264529 | ||||||||
\(425\) | −3.48094e37 | −0.269189 | ||||||||
\(426\) | −1.36577e37 | −0.102080 | ||||||||
\(427\) | 3.37430e37 | 0.243770 | ||||||||
\(428\) | −1.21377e38 | −0.847622 | ||||||||
\(429\) | 1.19667e38 | 0.807876 | ||||||||
\(430\) | −1.93326e37 | −0.126182 | ||||||||
\(431\) | 1.97532e38 | 1.24657 | 0.623287 | − | 0.781994i | \(-0.285797\pi\) | ||||
0.623287 | + | 0.781994i | \(0.285797\pi\) | |||||||
\(432\) | 3.02846e37 | 0.184802 | ||||||||
\(433\) | 2.49009e37 | 0.146940 | 0.0734700 | − | 0.997297i | \(-0.476593\pi\) | ||||
0.0734700 | + | 0.997297i | \(0.476593\pi\) | |||||||
\(434\) | −2.53095e36 | −0.0144438 | ||||||||
\(435\) | 1.28542e38 | 0.709497 | ||||||||
\(436\) | −3.60192e38 | −1.92300 | ||||||||
\(437\) | 5.17786e37 | 0.267405 | ||||||||
\(438\) | 1.36302e37 | 0.0680969 | ||||||||
\(439\) | 3.60571e38 | 1.74283 | 0.871416 | − | 0.490545i | \(-0.163202\pi\) | ||||
0.871416 | + | 0.490545i | \(0.163202\pi\) | |||||||
\(440\) | −1.30199e38 | −0.608898 | ||||||||
\(441\) | 1.05230e37 | 0.0476190 | ||||||||
\(442\) | −5.14380e36 | −0.0225248 | ||||||||
\(443\) | 7.19114e36 | 0.0304750 | 0.0152375 | − | 0.999884i | \(-0.495150\pi\) | ||||
0.0152375 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(444\) | −3.43692e37 | −0.140967 | ||||||||
\(445\) | 4.60612e38 | 1.82858 | ||||||||
\(446\) | −4.03350e37 | −0.154998 | ||||||||
\(447\) | −1.35919e38 | −0.505615 | ||||||||
\(448\) | 9.66640e37 | 0.348124 | ||||||||
\(449\) | 6.39610e37 | 0.223020 | 0.111510 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111510 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(450\) | −1.17972e37 | −0.0398287 | ||||||||
\(451\) | 9.93373e38 | 3.24752 | ||||||||
\(452\) | −4.57940e38 | −1.44978 | ||||||||
\(453\) | 1.34444e38 | 0.412209 | ||||||||
\(454\) | −1.54701e37 | −0.0459392 | ||||||||
\(455\) | 1.40888e38 | 0.405236 | ||||||||
\(456\) | 4.95504e37 | 0.138056 | ||||||||
\(457\) | 3.36298e38 | 0.907695 | 0.453847 | − | 0.891079i | \(-0.350051\pi\) | ||||
0.453847 | + | 0.891079i | \(0.350051\pi\) | |||||||
\(458\) | −5.18112e37 | −0.135480 | ||||||||
\(459\) | −1.97406e37 | −0.0500123 | ||||||||
\(460\) | −1.46976e38 | −0.360793 | ||||||||
\(461\) | −3.00963e38 | −0.715896 | −0.357948 | − | 0.933742i | \(-0.616523\pi\) | ||||
−0.357948 | + | 0.933742i | \(0.616523\pi\) | |||||||
\(462\) | −2.03348e37 | −0.0468738 | ||||||||
\(463\) | −2.02310e37 | −0.0451952 | −0.0225976 | − | 0.999745i | \(-0.507194\pi\) | ||||
−0.0225976 | + | 0.999745i | \(0.507194\pi\) | |||||||
\(464\) | 3.81977e38 | 0.827041 | ||||||||
\(465\) | −1.30045e38 | −0.272914 | ||||||||
\(466\) | 1.72192e37 | 0.0350282 | ||||||||
\(467\) | −9.23292e38 | −1.82072 | −0.910362 | − | 0.413812i | \(-0.864197\pi\) | ||||
−0.910362 | + | 0.413812i | \(0.864197\pi\) | |||||||
\(468\) | 1.29274e38 | 0.247141 | ||||||||
\(469\) | −3.72190e38 | −0.689856 | ||||||||
\(470\) | −1.06365e38 | −0.191152 | ||||||||
\(471\) | 4.73157e38 | 0.824521 | ||||||||
\(472\) | −6.37339e37 | −0.107699 | ||||||||
\(473\) | −8.71190e38 | −1.42767 | ||||||||
\(474\) | 7.25782e37 | 0.115351 | ||||||||
\(475\) | 7.01170e38 | 1.08085 | ||||||||
\(476\) | −6.48176e37 | −0.0969153 | ||||||||
\(477\) | 2.65289e38 | 0.384771 | ||||||||
\(478\) | −5.55532e37 | −0.0781636 | ||||||||
\(479\) | 3.71292e38 | 0.506817 | 0.253408 | − | 0.967359i | \(-0.418448\pi\) | ||||
0.253408 | + | 0.967359i | \(0.418448\pi\) | |||||||
\(480\) | −2.11448e38 | −0.280030 | ||||||||
\(481\) | −1.44705e38 | −0.185942 | ||||||||
\(482\) | 1.17311e38 | 0.146270 | ||||||||
\(483\) | −4.62196e37 | −0.0559232 | ||||||||
\(484\) | −2.07364e39 | −2.43487 | ||||||||
\(485\) | 5.58876e38 | 0.636884 | ||||||||
\(486\) | −6.69024e36 | −0.00739972 | ||||||||
\(487\) | 3.31078e38 | 0.355435 | 0.177718 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177718 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(488\) | −1.41829e38 | −0.147801 | ||||||||
\(489\) | 2.24404e38 | 0.227014 | ||||||||
\(490\) | −2.39407e37 | −0.0235122 | ||||||||
\(491\) | 4.67267e38 | 0.445536 | 0.222768 | − | 0.974871i | \(-0.428491\pi\) | ||||
0.222768 | + | 0.974871i | \(0.428491\pi\) | |||||||
\(492\) | 1.07312e39 | 0.993466 | ||||||||
\(493\) | −2.48987e38 | −0.223819 | ||||||||
\(494\) | 1.03612e38 | 0.0904420 | ||||||||
\(495\) | −1.04484e39 | −0.885673 | ||||||||
\(496\) | −3.86443e38 | −0.318128 | ||||||||
\(497\) | −7.24603e38 | −0.579339 | ||||||||
\(498\) | 6.75437e37 | 0.0524517 | ||||||||
\(499\) | −8.77872e38 | −0.662176 | −0.331088 | − | 0.943600i | \(-0.607416\pi\) | ||||
−0.331088 | + | 0.943600i | \(0.607416\pi\) | |||||||
\(500\) | −6.88897e37 | −0.0504765 | ||||||||
\(501\) | −6.70034e38 | −0.476925 | ||||||||
\(502\) | 6.50435e37 | 0.0449780 | ||||||||
\(503\) | 1.58017e39 | 1.06161 | 0.530807 | − | 0.847492i | \(-0.321889\pi\) | ||||
0.530807 | + | 0.847492i | \(0.321889\pi\) | |||||||
\(504\) | −4.42305e37 | −0.0288722 | ||||||||
\(505\) | 1.95195e39 | 1.23807 | ||||||||
\(506\) | 8.93150e37 | 0.0550481 | ||||||||
\(507\) | −4.19670e38 | −0.251358 | ||||||||
\(508\) | −1.02401e39 | −0.596047 | ||||||||
\(509\) | 5.38247e38 | 0.304490 | 0.152245 | − | 0.988343i | \(-0.451350\pi\) | ||||
0.152245 | + | 0.988343i | \(0.451350\pi\) | |||||||
\(510\) | 4.49115e37 | 0.0246939 | ||||||||
\(511\) | 7.23141e38 | 0.386474 | ||||||||
\(512\) | −1.05194e39 | −0.546482 | ||||||||
\(513\) | 3.97638e38 | 0.200810 | ||||||||
\(514\) | −3.77424e38 | −0.185295 | ||||||||
\(515\) | −4.28869e38 | −0.204701 | ||||||||
\(516\) | −9.41126e38 | −0.436744 | ||||||||
\(517\) | −4.79316e39 | −2.16276 | ||||||||
\(518\) | 2.45893e37 | 0.0107886 | ||||||||
\(519\) | −1.45013e38 | −0.0618700 | ||||||||
\(520\) | −5.92182e38 | −0.245701 | ||||||||
\(521\) | −2.42785e39 | −0.979661 | −0.489830 | − | 0.871818i | \(-0.662941\pi\) | ||||
−0.489830 | + | 0.871818i | \(0.662941\pi\) | |||||||
\(522\) | −8.43835e37 | −0.0331158 | ||||||||
\(523\) | 8.33744e38 | 0.318242 | 0.159121 | − | 0.987259i | \(-0.449134\pi\) | ||||
0.159121 | + | 0.987259i | \(0.449134\pi\) | |||||||
\(524\) | −8.30294e38 | −0.308268 | ||||||||
\(525\) | −6.25891e38 | −0.226042 | ||||||||
\(526\) | −3.39530e38 | −0.119285 | ||||||||
\(527\) | 2.51898e38 | 0.0860937 | ||||||||
\(528\) | −3.10486e39 | −1.03240 | ||||||||
\(529\) | −2.88805e39 | −0.934324 | ||||||||
\(530\) | −6.03554e38 | −0.189983 | ||||||||
\(531\) | −5.11459e38 | −0.156654 | ||||||||
\(532\) | 1.30563e39 | 0.389136 | ||||||||
\(533\) | 4.51814e39 | 1.31043 | ||||||||
\(534\) | −3.02376e38 | −0.0853492 | ||||||||
\(535\) | 4.46193e39 | 1.22573 | ||||||||
\(536\) | 1.56439e39 | 0.418270 | ||||||||
\(537\) | −4.20580e38 | −0.109451 | ||||||||
\(538\) | 4.31761e38 | 0.109371 | ||||||||
\(539\) | −1.07885e39 | −0.266026 | ||||||||
\(540\) | −1.12871e39 | −0.270941 | ||||||||
\(541\) | −5.64635e39 | −1.31949 | −0.659747 | − | 0.751488i | \(-0.729337\pi\) | ||||
−0.659747 | + | 0.751488i | \(0.729337\pi\) | |||||||
\(542\) | 5.15071e38 | 0.117187 | ||||||||
\(543\) | 6.66202e38 | 0.147573 | ||||||||
\(544\) | 4.09576e38 | 0.0883387 | ||||||||
\(545\) | 1.32410e40 | 2.78080 | ||||||||
\(546\) | −9.24882e37 | −0.0189144 | ||||||||
\(547\) | 4.46905e39 | 0.890019 | 0.445010 | − | 0.895526i | \(-0.353200\pi\) | ||||
0.445010 | + | 0.895526i | \(0.353200\pi\) | |||||||
\(548\) | −2.96481e39 | −0.575014 | ||||||||
\(549\) | −1.13817e39 | −0.214985 | ||||||||
\(550\) | 1.20948e39 | 0.222504 | ||||||||
\(551\) | 5.01538e39 | 0.898681 | ||||||||
\(552\) | 1.94271e38 | 0.0339071 | ||||||||
\(553\) | 3.85059e39 | 0.654656 | ||||||||
\(554\) | −3.32853e38 | −0.0551265 | ||||||||
\(555\) | 1.26344e39 | 0.203848 | ||||||||
\(556\) | 5.22153e38 | 0.0820754 | ||||||||
\(557\) | 1.23118e40 | 1.88547 | 0.942736 | − | 0.333540i | \(-0.108243\pi\) | ||||
0.942736 | + | 0.333540i | \(0.108243\pi\) | |||||||
\(558\) | 8.53701e37 | 0.0127383 | ||||||||
\(559\) | −3.96242e39 | −0.576089 | ||||||||
\(560\) | −3.65544e39 | −0.517861 | ||||||||
\(561\) | 2.02386e39 | 0.279396 | ||||||||
\(562\) | −2.49937e38 | −0.0336244 | ||||||||
\(563\) | −9.45065e39 | −1.23905 | −0.619527 | − | 0.784976i | \(-0.712675\pi\) | ||||
−0.619527 | + | 0.784976i | \(0.712675\pi\) | |||||||
\(564\) | −5.17793e39 | −0.661621 | ||||||||
\(565\) | 1.68343e40 | 2.09649 | ||||||||
\(566\) | 8.83000e38 | 0.107182 | ||||||||
\(567\) | −3.54946e38 | −0.0419961 | ||||||||
\(568\) | 3.04566e39 | 0.351262 | ||||||||
\(569\) | 1.58490e40 | 1.78187 | 0.890934 | − | 0.454133i | \(-0.150051\pi\) | ||||
0.890934 | + | 0.454133i | \(0.150051\pi\) | |||||||
\(570\) | −9.04658e38 | −0.0991514 | ||||||||
\(571\) | 2.09571e39 | 0.223928 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(572\) | −1.32535e40 | −1.38066 | ||||||||
\(573\) | 1.11838e40 | 1.13592 | ||||||||
\(574\) | −7.67756e38 | −0.0760328 | ||||||||
\(575\) | 2.74906e39 | 0.265461 | ||||||||
\(576\) | −3.26052e39 | −0.307016 | ||||||||
\(577\) | −8.37574e39 | −0.769084 | −0.384542 | − | 0.923108i | \(-0.625641\pi\) | ||||
−0.384542 | + | 0.923108i | \(0.625641\pi\) | |||||||
\(578\) | 1.20117e39 | 0.107560 | ||||||||
\(579\) | −9.19369e39 | −0.802880 | ||||||||
\(580\) | −1.42364e40 | −1.21253 | ||||||||
\(581\) | 3.58349e39 | 0.297682 | ||||||||
\(582\) | −3.66884e38 | −0.0297266 | ||||||||
\(583\) | −2.71981e40 | −2.14954 | ||||||||
\(584\) | −3.03952e39 | −0.234325 | ||||||||
\(585\) | −4.75222e39 | −0.357385 | ||||||||
\(586\) | 2.04195e39 | 0.149806 | ||||||||
\(587\) | 2.19066e40 | 1.56791 | 0.783956 | − | 0.620817i | \(-0.213199\pi\) | ||||
0.783956 | + | 0.620817i | \(0.213199\pi\) | |||||||
\(588\) | −1.16545e39 | −0.0813812 | ||||||||
\(589\) | −5.07402e39 | −0.345685 | ||||||||
\(590\) | 1.16361e39 | 0.0773489 | ||||||||
\(591\) | −3.97487e39 | −0.257813 | ||||||||
\(592\) | 3.75446e39 | 0.237620 | ||||||||
\(593\) | 8.92945e39 | 0.551482 | 0.275741 | − | 0.961232i | \(-0.411077\pi\) | ||||
0.275741 | + | 0.961232i | \(0.411077\pi\) | |||||||
\(594\) | 6.85901e38 | 0.0413388 | ||||||||
\(595\) | 2.38275e39 | 0.140147 | ||||||||
\(596\) | 1.50534e40 | 0.864099 | ||||||||
\(597\) | 1.66205e40 | 0.931144 | ||||||||
\(598\) | 4.06230e38 | 0.0222129 | ||||||||
\(599\) | −1.76630e40 | −0.942706 | −0.471353 | − | 0.881945i | \(-0.656234\pi\) | ||||
−0.471353 | + | 0.881945i | \(0.656234\pi\) | |||||||
\(600\) | 2.63076e39 | 0.137053 | ||||||||
\(601\) | −3.56607e40 | −1.81347 | −0.906735 | − | 0.421702i | \(-0.861433\pi\) | ||||
−0.906735 | + | 0.421702i | \(0.861433\pi\) | |||||||
\(602\) | 6.73324e38 | 0.0334253 | ||||||||
\(603\) | 1.25541e40 | 0.608395 | ||||||||
\(604\) | −1.48901e40 | −0.704467 | ||||||||
\(605\) | 7.62290e40 | 3.52101 | ||||||||
\(606\) | −1.28139e39 | −0.0577869 | ||||||||
\(607\) | 2.55200e40 | 1.12368 | 0.561842 | − | 0.827245i | \(-0.310093\pi\) | ||||
0.561842 | + | 0.827245i | \(0.310093\pi\) | |||||||
\(608\) | −8.25014e39 | −0.354699 | ||||||||
\(609\) | −4.47692e39 | −0.187944 | ||||||||
\(610\) | 2.58943e39 | 0.106150 | ||||||||
\(611\) | −2.18006e40 | −0.872713 | ||||||||
\(612\) | 2.18633e39 | 0.0854713 | ||||||||
\(613\) | 9.39524e39 | 0.358700 | 0.179350 | − | 0.983785i | \(-0.442601\pi\) | ||||
0.179350 | + | 0.983785i | \(0.442601\pi\) | |||||||
\(614\) | −4.62553e39 | −0.172473 | ||||||||
\(615\) | −3.94487e40 | −1.43663 | ||||||||
\(616\) | 4.53464e39 | 0.161295 | ||||||||
\(617\) | −4.84847e40 | −1.68450 | −0.842248 | − | 0.539091i | \(-0.818768\pi\) | ||||
−0.842248 | + | 0.539091i | \(0.818768\pi\) | |||||||
\(618\) | 2.81539e38 | 0.00955444 | ||||||||
\(619\) | 5.52968e40 | 1.83310 | 0.916549 | − | 0.399923i | \(-0.130963\pi\) | ||||
0.916549 | + | 0.399923i | \(0.130963\pi\) | |||||||
\(620\) | 1.44028e40 | 0.466411 | ||||||||
\(621\) | 1.55901e39 | 0.0493197 | ||||||||
\(622\) | 2.81286e39 | 0.0869335 | ||||||||
\(623\) | −1.60424e40 | −0.484387 | ||||||||
\(624\) | −1.41218e40 | −0.416593 | ||||||||
\(625\) | −3.34059e40 | −0.962861 | ||||||||
\(626\) | −1.45243e38 | −0.00409041 | ||||||||
\(627\) | −4.07669e40 | −1.12183 | ||||||||
\(628\) | −5.24035e40 | −1.40911 | ||||||||
\(629\) | −2.44730e39 | −0.0643062 | ||||||||
\(630\) | 8.07532e38 | 0.0207358 | ||||||||
\(631\) | −5.95042e40 | −1.49321 | −0.746606 | − | 0.665266i | \(-0.768318\pi\) | ||||
−0.746606 | + | 0.665266i | \(0.768318\pi\) | |||||||
\(632\) | −1.61849e40 | −0.396928 | ||||||||
\(633\) | −3.87795e40 | −0.929498 | ||||||||
\(634\) | −7.15632e39 | −0.167647 | ||||||||
\(635\) | 3.76435e40 | 0.861928 | ||||||||
\(636\) | −2.93815e40 | −0.657576 | ||||||||
\(637\) | −4.90691e39 | −0.107346 | ||||||||
\(638\) | 8.65123e39 | 0.185003 | ||||||||
\(639\) | 2.44412e40 | 0.510929 | ||||||||
\(640\) | 3.11522e40 | 0.636618 | ||||||||
\(641\) | 2.12073e40 | 0.423686 | 0.211843 | − | 0.977304i | \(-0.432053\pi\) | ||||
0.211843 | + | 0.977304i | \(0.432053\pi\) | |||||||
\(642\) | −2.92911e39 | −0.0572108 | ||||||||
\(643\) | −1.69538e39 | −0.0323748 | −0.0161874 | − | 0.999869i | \(-0.505153\pi\) | ||||
−0.0161874 | + | 0.999869i | \(0.505153\pi\) | |||||||
\(644\) | 5.11895e39 | 0.0955731 | ||||||||
\(645\) | 3.45966e40 | 0.631565 | ||||||||
\(646\) | 1.75233e39 | 0.0312784 | ||||||||
\(647\) | −9.52815e40 | −1.66302 | −0.831508 | − | 0.555513i | \(-0.812522\pi\) | ||||
−0.831508 | + | 0.555513i | \(0.812522\pi\) | |||||||
\(648\) | 1.49192e39 | 0.0254629 | ||||||||
\(649\) | 5.24362e40 | 0.875151 | ||||||||
\(650\) | 5.50104e39 | 0.0897845 | ||||||||
\(651\) | 4.52926e39 | 0.0722941 | ||||||||
\(652\) | −2.48534e40 | −0.387967 | ||||||||
\(653\) | 5.05290e40 | 0.771436 | 0.385718 | − | 0.922617i | \(-0.373954\pi\) | ||||
0.385718 | + | 0.922617i | \(0.373954\pi\) | |||||||
\(654\) | −8.69225e39 | −0.129794 | ||||||||
\(655\) | 3.05223e40 | 0.445778 | ||||||||
\(656\) | −1.17226e41 | −1.67463 | ||||||||
\(657\) | −2.43919e40 | −0.340838 | ||||||||
\(658\) | 3.70453e39 | 0.0506357 | ||||||||
\(659\) | 1.12152e40 | 0.149958 | 0.0749788 | − | 0.997185i | \(-0.476111\pi\) | ||||
0.0749788 | + | 0.997185i | \(0.476111\pi\) | |||||||
\(660\) | 1.15719e41 | 1.51362 | ||||||||
\(661\) | −3.04968e40 | −0.390242 | −0.195121 | − | 0.980779i | \(-0.562510\pi\) | ||||
−0.195121 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(662\) | −1.37431e40 | −0.172046 | ||||||||
\(663\) | 9.20510e39 | 0.112741 | ||||||||
\(664\) | −1.50622e40 | −0.180489 | ||||||||
\(665\) | −4.79961e40 | −0.562719 | ||||||||
\(666\) | −8.29408e38 | −0.00951463 | ||||||||
\(667\) | 1.96637e40 | 0.220719 | ||||||||
\(668\) | 7.42082e40 | 0.815067 | ||||||||
\(669\) | 7.21815e40 | 0.775795 | ||||||||
\(670\) | −2.85617e40 | −0.300399 | ||||||||
\(671\) | 1.16688e41 | 1.20102 | ||||||||
\(672\) | 7.36439e39 | 0.0741793 | ||||||||
\(673\) | 1.41854e41 | 1.39838 | 0.699188 | − | 0.714938i | \(-0.253545\pi\) | ||||
0.699188 | + | 0.714938i | \(0.253545\pi\) | |||||||
\(674\) | 2.27244e39 | 0.0219242 | ||||||||
\(675\) | 2.11116e40 | 0.199350 | ||||||||
\(676\) | 4.64796e40 | 0.429572 | ||||||||
\(677\) | −1.27467e41 | −1.15308 | −0.576542 | − | 0.817068i | \(-0.695598\pi\) | ||||
−0.576542 | + | 0.817068i | \(0.695598\pi\) | |||||||
\(678\) | −1.10511e40 | −0.0978536 | ||||||||
\(679\) | −1.94648e40 | −0.168709 | ||||||||
\(680\) | −1.00152e40 | −0.0849732 | ||||||||
\(681\) | 2.76845e40 | 0.229934 | ||||||||
\(682\) | −8.75238e39 | −0.0711627 | ||||||||
\(683\) | −1.29019e41 | −1.02696 | −0.513482 | − | 0.858101i | \(-0.671645\pi\) | ||||
−0.513482 | + | 0.858101i | \(0.671645\pi\) | |||||||
\(684\) | −4.40395e40 | −0.343186 | ||||||||
\(685\) | 1.08989e41 | 0.831514 | ||||||||
\(686\) | 8.33818e38 | 0.00622833 | ||||||||
\(687\) | 9.27187e40 | 0.678101 | ||||||||
\(688\) | 1.02808e41 | 0.736197 | ||||||||
\(689\) | −1.23705e41 | −0.867377 | ||||||||
\(690\) | −3.54687e39 | −0.0243519 | ||||||||
\(691\) | −2.21087e41 | −1.48638 | −0.743192 | − | 0.669079i | \(-0.766689\pi\) | ||||
−0.743192 | + | 0.669079i | \(0.766689\pi\) | |||||||
\(692\) | 1.60606e40 | 0.105736 | ||||||||
\(693\) | 3.63901e40 | 0.234612 | ||||||||
\(694\) | 2.42469e40 | 0.153089 | ||||||||
\(695\) | −1.91948e40 | −0.118687 | ||||||||
\(696\) | 1.88175e40 | 0.113953 | ||||||||
\(697\) | 7.64126e40 | 0.453200 | ||||||||
\(698\) | 2.13357e40 | 0.123938 | ||||||||
\(699\) | −3.08147e40 | −0.175323 | ||||||||
\(700\) | 6.93192e40 | 0.386306 | ||||||||
\(701\) | 4.29431e40 | 0.234413 | 0.117207 | − | 0.993108i | \(-0.462606\pi\) | ||||
0.117207 | + | 0.993108i | \(0.462606\pi\) | |||||||
\(702\) | 3.11967e39 | 0.0166810 | ||||||||
\(703\) | 4.92963e40 | 0.258203 | ||||||||
\(704\) | 3.34278e41 | 1.71516 | ||||||||
\(705\) | 1.90345e41 | 0.956754 | ||||||||
\(706\) | 6.37101e38 | 0.00313719 | ||||||||
\(707\) | −6.79836e40 | −0.327961 | ||||||||
\(708\) | 5.66456e40 | 0.267722 | ||||||||
\(709\) | 1.08342e41 | 0.501680 | 0.250840 | − | 0.968029i | \(-0.419293\pi\) | ||||
0.250840 | + | 0.968029i | \(0.419293\pi\) | |||||||
\(710\) | −5.56057e40 | −0.252275 | ||||||||
\(711\) | −1.29882e41 | −0.577353 | ||||||||
\(712\) | 6.74297e40 | 0.293691 | ||||||||
\(713\) | −1.98936e40 | −0.0849014 | ||||||||
\(714\) | −1.56420e39 | −0.00654136 | ||||||||
\(715\) | 4.87210e41 | 1.99654 | ||||||||
\(716\) | 4.65804e40 | 0.187053 | ||||||||
\(717\) | 9.94153e40 | 0.391224 | ||||||||
\(718\) | 1.79129e40 | 0.0690814 | ||||||||
\(719\) | −3.17789e41 | −1.20108 | −0.600538 | − | 0.799596i | \(-0.705047\pi\) | ||||
−0.600538 | + | 0.799596i | \(0.705047\pi\) | |||||||
\(720\) | 1.23300e41 | 0.456710 | ||||||||
\(721\) | 1.49369e40 | 0.0542248 | ||||||||
\(722\) | −2.87781e39 | −0.0102394 | ||||||||
\(723\) | −2.09934e41 | −0.732110 | ||||||||
\(724\) | −7.37837e40 | −0.252204 | ||||||||
\(725\) | 2.66279e41 | 0.892147 | ||||||||
\(726\) | −5.00418e40 | −0.164343 | ||||||||
\(727\) | −4.95180e41 | −1.59410 | −0.797048 | − | 0.603916i | \(-0.793606\pi\) | ||||
−0.797048 | + | 0.603916i | \(0.793606\pi\) | |||||||
\(728\) | 2.06248e40 | 0.0650856 | ||||||||
\(729\) | 1.19725e40 | 0.0370370 | ||||||||
\(730\) | 5.54936e40 | 0.168291 | ||||||||
\(731\) | −6.70141e40 | −0.199234 | ||||||||
\(732\) | 1.26055e41 | 0.367410 | ||||||||
\(733\) | 3.31979e41 | 0.948643 | 0.474321 | − | 0.880352i | \(-0.342693\pi\) | ||||
0.474321 | + | 0.880352i | \(0.342693\pi\) | |||||||
\(734\) | −1.60555e40 | −0.0449812 | ||||||||
\(735\) | 4.28431e40 | 0.117683 | ||||||||
\(736\) | −3.23461e40 | −0.0871152 | ||||||||
\(737\) | −1.28708e42 | −3.39882 | ||||||||
\(738\) | 2.58968e40 | 0.0670546 | ||||||||
\(739\) | −2.21021e41 | −0.561163 | −0.280581 | − | 0.959830i | \(-0.590527\pi\) | ||||
−0.280581 | + | 0.959830i | \(0.590527\pi\) | |||||||
\(740\) | −1.39930e41 | −0.348378 | ||||||||
\(741\) | −1.85419e41 | −0.452680 | ||||||||
\(742\) | 2.10208e40 | 0.0503261 | ||||||||
\(743\) | −2.82062e41 | −0.662227 | −0.331113 | − | 0.943591i | \(-0.607424\pi\) | ||||
−0.331113 | + | 0.943591i | \(0.607424\pi\) | |||||||
\(744\) | −1.90375e40 | −0.0438331 | ||||||||
\(745\) | −5.53376e41 | −1.24955 | ||||||||
\(746\) | −1.62627e40 | −0.0360148 | ||||||||
\(747\) | −1.20873e41 | −0.262531 | ||||||||
\(748\) | −2.24149e41 | −0.477488 | ||||||||
\(749\) | −1.55402e41 | −0.324691 | ||||||||
\(750\) | −1.66247e39 | −0.00340694 | ||||||||
\(751\) | 3.22452e41 | 0.648166 | 0.324083 | − | 0.946029i | \(-0.394944\pi\) | ||||
0.324083 | + | 0.946029i | \(0.394944\pi\) | |||||||
\(752\) | 5.65633e41 | 1.11526 | ||||||||
\(753\) | −1.16399e41 | −0.225123 | ||||||||
\(754\) | 3.93482e40 | 0.0746519 | ||||||||
\(755\) | 5.47372e41 | 1.01871 | ||||||||
\(756\) | 3.93113e40 | 0.0717715 | ||||||||
\(757\) | 7.91119e41 | 1.41694 | 0.708470 | − | 0.705741i | \(-0.249386\pi\) | ||||
0.708470 | + | 0.705741i | \(0.249386\pi\) | |||||||
\(758\) | −8.19619e40 | −0.144015 | ||||||||
\(759\) | −1.59834e41 | −0.275526 | ||||||||
\(760\) | 2.01738e41 | 0.341186 | ||||||||
\(761\) | −7.23142e41 | −1.19990 | −0.599951 | − | 0.800037i | \(-0.704813\pi\) | ||||
−0.599951 | + | 0.800037i | \(0.704813\pi\) | |||||||
\(762\) | −2.47117e40 | −0.0402305 | ||||||||
\(763\) | −4.61162e41 | −0.736627 | ||||||||
\(764\) | −1.23863e42 | −1.94128 | ||||||||
\(765\) | −8.03714e40 | −0.123598 | ||||||||
\(766\) | 2.85741e40 | 0.0431177 | ||||||||
\(767\) | 2.38495e41 | 0.353139 | ||||||||
\(768\) | 3.45532e41 | 0.502054 | ||||||||
\(769\) | −7.92719e41 | −1.13028 | −0.565142 | − | 0.824994i | \(-0.691179\pi\) | ||||
−0.565142 | + | 0.824994i | \(0.691179\pi\) | |||||||
\(770\) | −8.27904e40 | −0.115842 | ||||||||
\(771\) | 6.75419e41 | 0.927437 | ||||||||
\(772\) | 1.01823e42 | 1.37213 | ||||||||
\(773\) | 8.00140e41 | 1.05819 | 0.529095 | − | 0.848563i | \(-0.322532\pi\) | ||||
0.529095 | + | 0.848563i | \(0.322532\pi\) | |||||||
\(774\) | −2.27115e40 | −0.0294783 | ||||||||
\(775\) | −2.69393e41 | −0.343171 | ||||||||
\(776\) | 8.18147e40 | 0.102291 | ||||||||
\(777\) | −4.40037e40 | −0.0539989 | ||||||||
\(778\) | 8.38140e40 | 0.100951 | ||||||||
\(779\) | −1.53919e42 | −1.81970 | ||||||||
\(780\) | 5.26321e41 | 0.610772 | ||||||||
\(781\) | −2.50578e42 | −2.85432 | ||||||||
\(782\) | 6.87033e39 | 0.00768209 | ||||||||
\(783\) | 1.51009e41 | 0.165751 | ||||||||
\(784\) | 1.27313e41 | 0.137180 | ||||||||
\(785\) | 1.92640e42 | 2.03768 | ||||||||
\(786\) | −2.00369e40 | −0.0208067 | ||||||||
\(787\) | 9.37568e41 | 0.955804 | 0.477902 | − | 0.878413i | \(-0.341397\pi\) | ||||
0.477902 | + | 0.878413i | \(0.341397\pi\) | |||||||
\(788\) | 4.40228e41 | 0.440603 | ||||||||
\(789\) | 6.07606e41 | 0.597043 | ||||||||
\(790\) | 2.95493e41 | 0.285072 | ||||||||
\(791\) | −5.86312e41 | −0.555354 | ||||||||
\(792\) | −1.52955e41 | −0.142249 | ||||||||
\(793\) | 5.30731e41 | 0.484633 | ||||||||
\(794\) | 2.23443e41 | 0.200341 | ||||||||
\(795\) | 1.08009e42 | 0.950903 | ||||||||
\(796\) | −1.84077e42 | −1.59133 | ||||||||
\(797\) | −1.97737e42 | −1.67858 | −0.839289 | − | 0.543686i | \(-0.817028\pi\) | ||||
−0.839289 | + | 0.543686i | \(0.817028\pi\) | |||||||
\(798\) | 3.15078e40 | 0.0262650 | ||||||||
\(799\) | −3.68701e41 | −0.301819 | ||||||||
\(800\) | −4.38021e41 | −0.352120 | ||||||||
\(801\) | 5.41118e41 | 0.427189 | ||||||||
\(802\) | 1.10957e41 | 0.0860251 | ||||||||
\(803\) | 2.50072e42 | 1.90410 | ||||||||
\(804\) | −1.39041e42 | −1.03975 | ||||||||
\(805\) | −1.88177e41 | −0.138206 | ||||||||
\(806\) | −3.98083e40 | −0.0287154 | ||||||||
\(807\) | −7.72658e41 | −0.547420 | ||||||||
\(808\) | 2.85750e41 | 0.198848 | ||||||||
\(809\) | −6.85121e41 | −0.468289 | −0.234144 | − | 0.972202i | \(-0.575229\pi\) | ||||
−0.234144 | + | 0.972202i | \(0.575229\pi\) | |||||||
\(810\) | −2.72384e40 | −0.0182873 | ||||||||
\(811\) | −6.85487e41 | −0.452061 | −0.226030 | − | 0.974120i | \(-0.572575\pi\) | ||||
−0.226030 | + | 0.974120i | \(0.572575\pi\) | |||||||
\(812\) | 4.95831e41 | 0.321197 | ||||||||
\(813\) | −9.21746e41 | −0.586541 | ||||||||
\(814\) | 8.50332e40 | 0.0531538 | ||||||||
\(815\) | 9.13632e41 | 0.561030 | ||||||||
\(816\) | −2.38833e41 | −0.144074 | ||||||||
\(817\) | 1.34987e42 | 0.799968 | ||||||||
\(818\) | −5.14598e40 | −0.0299602 | ||||||||
\(819\) | 1.65512e41 | 0.0946703 | ||||||||
\(820\) | 4.36906e42 | 2.45520 | ||||||||
\(821\) | −7.85106e41 | −0.433463 | −0.216732 | − | 0.976231i | \(-0.569540\pi\) | ||||
−0.216732 | + | 0.976231i | \(0.569540\pi\) | |||||||
\(822\) | −7.15477e40 | −0.0388109 | ||||||||
\(823\) | 6.55490e41 | 0.349356 | 0.174678 | − | 0.984626i | \(-0.444112\pi\) | ||||
0.174678 | + | 0.984626i | \(0.444112\pi\) | |||||||
\(824\) | −6.27829e40 | −0.0328773 | ||||||||
\(825\) | −2.16442e42 | −1.11368 | ||||||||
\(826\) | −4.05268e40 | −0.0204895 | ||||||||
\(827\) | 2.86888e41 | 0.142522 | 0.0712612 | − | 0.997458i | \(-0.477298\pi\) | ||||
0.0712612 | + | 0.997458i | \(0.477298\pi\) | |||||||
\(828\) | −1.72665e41 | −0.0842875 | ||||||||
\(829\) | 8.78790e41 | 0.421545 | 0.210773 | − | 0.977535i | \(-0.432402\pi\) | ||||
0.210773 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(830\) | 2.74996e41 | 0.129626 | ||||||||
\(831\) | 5.95657e41 | 0.275919 | ||||||||
\(832\) | 1.52039e42 | 0.692096 | ||||||||
\(833\) | −8.29876e40 | −0.0371245 | ||||||||
\(834\) | 1.26007e40 | 0.00553973 | ||||||||
\(835\) | −2.72796e42 | −1.17865 | ||||||||
\(836\) | 4.51505e42 | 1.91722 | ||||||||
\(837\) | −1.52774e41 | −0.0637574 | ||||||||
\(838\) | −8.07592e40 | −0.0331248 | ||||||||
\(839\) | 4.67265e42 | 1.88371 | 0.941856 | − | 0.336016i | \(-0.109080\pi\) | ||||
0.941856 | + | 0.336016i | \(0.109080\pi\) | |||||||
\(840\) | −1.80079e41 | −0.0713532 | ||||||||
\(841\) | −6.63024e41 | −0.258219 | ||||||||
\(842\) | 2.68143e41 | 0.102646 | ||||||||
\(843\) | 4.47275e41 | 0.168296 | ||||||||
\(844\) | 4.29494e42 | 1.58852 | ||||||||
\(845\) | −1.70863e42 | −0.621193 | ||||||||
\(846\) | −1.24955e41 | −0.0446565 | ||||||||
\(847\) | −2.65494e42 | −0.932706 | ||||||||
\(848\) | 3.20961e42 | 1.10844 | ||||||||
\(849\) | −1.58017e42 | −0.536467 | ||||||||
\(850\) | 9.30358e40 | 0.0310510 | ||||||||
\(851\) | 1.93275e41 | 0.0634156 | ||||||||
\(852\) | −2.70693e42 | −0.873179 | ||||||||
\(853\) | 1.89245e42 | 0.600156 | 0.300078 | − | 0.953915i | \(-0.402987\pi\) | ||||
0.300078 | + | 0.953915i | \(0.402987\pi\) | |||||||
\(854\) | −9.01857e40 | −0.0281189 | ||||||||
\(855\) | 1.61893e42 | 0.496272 | ||||||||
\(856\) | 6.53189e41 | 0.196865 | ||||||||
\(857\) | −1.78935e42 | −0.530240 | −0.265120 | − | 0.964215i | \(-0.585412\pi\) | ||||
−0.265120 | + | 0.964215i | \(0.585412\pi\) | |||||||
\(858\) | −3.19837e41 | −0.0931887 | ||||||||
\(859\) | −5.36533e42 | −1.53708 | −0.768538 | − | 0.639804i | \(-0.779016\pi\) | ||||
−0.768538 | + | 0.639804i | \(0.779016\pi\) | |||||||
\(860\) | −3.83167e42 | −1.07935 | ||||||||
\(861\) | 1.37394e42 | 0.380559 | ||||||||
\(862\) | −5.27949e41 | −0.143793 | ||||||||
\(863\) | 2.68416e42 | 0.718871 | 0.359436 | − | 0.933170i | \(-0.382969\pi\) | ||||
0.359436 | + | 0.933170i | \(0.382969\pi\) | |||||||
\(864\) | −2.48405e41 | −0.0654200 | ||||||||
\(865\) | −5.90401e41 | −0.152902 | ||||||||
\(866\) | −6.65531e40 | −0.0169496 | ||||||||
\(867\) | −2.14956e42 | −0.538360 | ||||||||
\(868\) | −5.01629e41 | −0.123551 | ||||||||
\(869\) | 1.33159e43 | 3.22540 | ||||||||
\(870\) | −3.43557e41 | −0.0818407 | ||||||||
\(871\) | −5.85402e42 | −1.37149 | ||||||||
\(872\) | 1.93837e42 | 0.446629 | ||||||||
\(873\) | 6.56557e41 | 0.148787 | ||||||||
\(874\) | −1.38390e41 | −0.0308453 | ||||||||
\(875\) | −8.82011e40 | −0.0193356 | ||||||||
\(876\) | 2.70147e42 | 0.582493 | ||||||||
\(877\) | 2.15557e41 | 0.0457160 | 0.0228580 | − | 0.999739i | \(-0.492723\pi\) | ||||
0.0228580 | + | 0.999739i | \(0.492723\pi\) | |||||||
\(878\) | −9.63706e41 | −0.201036 | ||||||||
\(879\) | −3.65418e42 | −0.749810 | ||||||||
\(880\) | −1.26410e43 | −2.55143 | ||||||||
\(881\) | −1.18085e42 | −0.234446 | −0.117223 | − | 0.993106i | \(-0.537399\pi\) | ||||
−0.117223 | + | 0.993106i | \(0.537399\pi\) | |||||||
\(882\) | −2.81251e40 | −0.00549287 | ||||||||
\(883\) | 8.24508e42 | 1.58404 | 0.792018 | − | 0.610498i | \(-0.209031\pi\) | ||||
0.792018 | + | 0.610498i | \(0.209031\pi\) | |||||||
\(884\) | −1.01949e42 | −0.192675 | ||||||||
\(885\) | −2.08234e42 | −0.387146 | ||||||||
\(886\) | −1.92199e40 | −0.00351530 | ||||||||
\(887\) | −6.80014e42 | −1.22356 | −0.611780 | − | 0.791028i | \(-0.709546\pi\) | ||||
−0.611780 | + | 0.791028i | \(0.709546\pi\) | |||||||
\(888\) | 1.84957e41 | 0.0327404 | ||||||||
\(889\) | −1.31106e42 | −0.228322 | ||||||||
\(890\) | −1.23109e42 | −0.210928 | ||||||||
\(891\) | −1.22745e42 | −0.206909 | ||||||||
\(892\) | −7.99430e42 | −1.32584 | ||||||||
\(893\) | 7.42679e42 | 1.21187 | ||||||||
\(894\) | 3.63273e41 | 0.0583229 | ||||||||
\(895\) | −1.71234e42 | −0.270493 | ||||||||
\(896\) | −1.08498e42 | −0.168638 | ||||||||
\(897\) | −7.26969e41 | −0.111180 | ||||||||
\(898\) | −1.70950e41 | −0.0257254 | ||||||||
\(899\) | −1.92693e42 | −0.285332 | ||||||||
\(900\) | −2.33817e42 | −0.340690 | ||||||||
\(901\) | −2.09215e42 | −0.299973 | ||||||||
\(902\) | −2.65501e42 | −0.374603 | ||||||||
\(903\) | −1.20495e42 | −0.167300 | ||||||||
\(904\) | 2.46440e42 | 0.336720 | ||||||||
\(905\) | 2.71236e42 | 0.364705 | ||||||||
\(906\) | −3.59331e41 | −0.0475484 | ||||||||
\(907\) | −1.57296e42 | −0.204839 | −0.102420 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102420 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(908\) | −3.06614e42 | −0.392959 | ||||||||
\(909\) | 2.29312e42 | 0.289235 | ||||||||
\(910\) | −3.76554e41 | −0.0467441 | ||||||||
\(911\) | −1.50764e42 | −0.184196 | −0.0920981 | − | 0.995750i | \(-0.529357\pi\) | ||||
−0.0920981 | + | 0.995750i | \(0.529357\pi\) | |||||||
\(912\) | 4.81084e42 | 0.578490 | ||||||||
\(913\) | 1.23922e43 | 1.46664 | ||||||||
\(914\) | −8.98832e41 | −0.104703 | ||||||||
\(915\) | −4.63391e42 | −0.531302 | ||||||||
\(916\) | −1.02689e43 | −1.15888 | ||||||||
\(917\) | −1.06305e42 | −0.118086 | ||||||||
\(918\) | 5.27612e40 | 0.00576893 | ||||||||
\(919\) | 1.99622e42 | 0.214849 | 0.107424 | − | 0.994213i | \(-0.465740\pi\) | ||||
0.107424 | + | 0.994213i | \(0.465740\pi\) | |||||||
\(920\) | 7.90949e41 | 0.0837963 | ||||||||
\(921\) | 8.27763e42 | 0.863259 | ||||||||
\(922\) | 8.04390e41 | 0.0825788 | ||||||||
\(923\) | −1.13970e43 | −1.15177 | ||||||||
\(924\) | −4.03030e42 | −0.400954 | ||||||||
\(925\) | 2.61727e42 | 0.256326 | ||||||||
\(926\) | 5.40717e40 | 0.00521328 | ||||||||
\(927\) | −5.03827e41 | −0.0478218 | ||||||||
\(928\) | −3.13311e42 | −0.292772 | ||||||||
\(929\) | −9.33009e42 | −0.858338 | −0.429169 | − | 0.903224i | \(-0.641193\pi\) | ||||
−0.429169 | + | 0.903224i | \(0.641193\pi\) | |||||||
\(930\) | 3.47574e41 | 0.0314807 | ||||||||
\(931\) | 1.67163e42 | 0.149063 | ||||||||
\(932\) | 3.41281e42 | 0.299628 | ||||||||
\(933\) | −5.03375e42 | −0.435119 | ||||||||
\(934\) | 2.46770e42 | 0.210021 | ||||||||
\(935\) | 8.23990e42 | 0.690484 | ||||||||
\(936\) | −6.95685e41 | −0.0574001 | ||||||||
\(937\) | 3.45465e42 | 0.280660 | 0.140330 | − | 0.990105i | \(-0.455184\pi\) | ||||
0.140330 | + | 0.990105i | \(0.455184\pi\) | |||||||
\(938\) | 9.94759e41 | 0.0795750 | ||||||||
\(939\) | 2.59919e41 | 0.0204733 | ||||||||
\(940\) | −2.10813e43 | −1.63510 | ||||||||
\(941\) | 2.35450e43 | 1.79825 | 0.899124 | − | 0.437694i | \(-0.144205\pi\) | ||||
0.899124 | + | 0.437694i | \(0.144205\pi\) | |||||||
\(942\) | −1.26462e42 | −0.0951088 | ||||||||
\(943\) | −6.03466e42 | −0.446923 | ||||||||
\(944\) | −6.18792e42 | −0.451285 | ||||||||
\(945\) | −1.44512e42 | −0.103787 | ||||||||
\(946\) | 2.32845e42 | 0.164682 | ||||||||
\(947\) | −5.81953e42 | −0.405334 | −0.202667 | − | 0.979248i | \(-0.564961\pi\) | ||||
−0.202667 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(948\) | 1.43848e43 | 0.986698 | ||||||||
\(949\) | 1.13740e43 | 0.768339 | ||||||||
\(950\) | −1.87403e42 | −0.124677 | ||||||||
\(951\) | 1.28066e43 | 0.839105 | ||||||||
\(952\) | 3.48815e41 | 0.0225092 | ||||||||
\(953\) | 2.14066e43 | 1.36051 | 0.680253 | − | 0.732977i | \(-0.261870\pi\) | ||||
0.680253 | + | 0.732977i | \(0.261870\pi\) | |||||||
\(954\) | −7.09043e41 | −0.0443835 | ||||||||
\(955\) | 4.55333e43 | 2.80724 | ||||||||
\(956\) | −1.10105e43 | −0.668604 | ||||||||
\(957\) | −1.54818e43 | −0.925974 | ||||||||
\(958\) | −9.92361e41 | −0.0584615 | ||||||||
\(959\) | −3.79592e42 | −0.220266 | ||||||||
\(960\) | −1.32748e43 | −0.758744 | ||||||||
\(961\) | −1.58124e43 | −0.890245 | ||||||||
\(962\) | 3.86755e41 | 0.0214485 | ||||||||
\(963\) | 5.24179e42 | 0.286351 | ||||||||
\(964\) | 2.32507e43 | 1.25118 | ||||||||
\(965\) | −3.74309e43 | −1.98420 | ||||||||
\(966\) | 1.23532e41 | 0.00645076 | ||||||||
\(967\) | 2.74428e43 | 1.41171 | 0.705853 | − | 0.708358i | \(-0.250564\pi\) | ||||
0.705853 | + | 0.708358i | \(0.250564\pi\) | |||||||
\(968\) | 1.11593e43 | 0.565514 | ||||||||
\(969\) | −3.13589e42 | −0.156555 | ||||||||
\(970\) | −1.49372e42 | −0.0734647 | ||||||||
\(971\) | 1.57511e42 | 0.0763189 | 0.0381594 | − | 0.999272i | \(-0.487851\pi\) | ||||
0.0381594 | + | 0.999272i | \(0.487851\pi\) | |||||||
\(972\) | −1.32599e42 | −0.0632965 | ||||||||
\(973\) | 6.68525e41 | 0.0314399 | ||||||||
\(974\) | −8.84879e41 | −0.0409996 | ||||||||
\(975\) | −9.84439e42 | −0.449388 | ||||||||
\(976\) | −1.37702e43 | −0.619324 | ||||||||
\(977\) | 3.21646e42 | 0.142530 | 0.0712652 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712652 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(978\) | −5.99769e41 | −0.0261861 | ||||||||
\(979\) | −5.54769e43 | −2.38651 | ||||||||
\(980\) | −4.74500e42 | −0.201121 | ||||||||
\(981\) | 1.55552e43 | 0.649644 | ||||||||
\(982\) | −1.24887e42 | −0.0513928 | ||||||||
\(983\) | 6.59024e42 | 0.267224 | 0.133612 | − | 0.991034i | \(-0.457342\pi\) | ||||
0.133612 | + | 0.991034i | \(0.457342\pi\) | |||||||
\(984\) | −5.77496e42 | −0.230739 | ||||||||
\(985\) | −1.61832e43 | −0.637145 | ||||||||
\(986\) | 6.65473e41 | 0.0258176 | ||||||||
\(987\) | −6.62944e42 | −0.253442 | ||||||||
\(988\) | 2.05357e43 | 0.773632 | ||||||||
\(989\) | 5.29241e42 | 0.196475 | ||||||||
\(990\) | 2.79256e42 | 0.102163 | ||||||||
\(991\) | 1.96287e43 | 0.707659 | 0.353830 | − | 0.935310i | \(-0.384879\pi\) | ||||
0.353830 | + | 0.935310i | \(0.384879\pi\) | |||||||
\(992\) | 3.16974e42 | 0.112617 | ||||||||
\(993\) | 2.45941e43 | 0.861125 | ||||||||
\(994\) | 1.93666e42 | 0.0668269 | ||||||||
\(995\) | 6.76683e43 | 2.30118 | ||||||||
\(996\) | 1.33870e43 | 0.448666 | ||||||||
\(997\) | 5.40710e43 | 1.78601 | 0.893007 | − | 0.450043i | \(-0.148591\pi\) | ||||
0.893007 | + | 0.450043i | \(0.148591\pi\) | |||||||
\(998\) | 2.34631e42 | 0.0763822 | ||||||||
\(999\) | 1.48427e42 | 0.0476225 |
(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.a.d.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.a.d.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial |