Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.91738 | −0.394096 | −0.197048 | − | 0.980394i | \(-0.563136\pi\) | ||||
−0.197048 | + | 0.980394i | \(0.563136\pi\) | |||||||
\(3\) | 33.9373 | 0.241897 | 0.120949 | − | 0.992659i | \(-0.461406\pi\) | ||||
0.120949 | + | 0.992659i | \(0.461406\pi\) | |||||||
\(4\) | −432.480 | −0.844688 | ||||||||
\(5\) | −34.8748 | −0.0249544 | −0.0124772 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124772 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(6\) | −302.632 | −0.0953309 | ||||||||
\(7\) | −8539.90 | −1.34435 | −0.672174 | − | 0.740393i | \(-0.734639\pi\) | ||||
−0.672174 | + | 0.740393i | \(0.734639\pi\) | |||||||
\(8\) | 8422.29 | 0.726985 | ||||||||
\(9\) | −18531.3 | −0.941486 | ||||||||
\(10\) | 310.992 | 0.00983442 | ||||||||
\(11\) | −828.804 | −0.0170681 | −0.00853404 | − | 0.999964i | \(-0.502717\pi\) | ||||
−0.00853404 | + | 0.999964i | \(0.502717\pi\) | |||||||
\(12\) | −14677.2 | −0.204328 | ||||||||
\(13\) | 147504. | 1.43238 | 0.716190 | − | 0.697905i | \(-0.245884\pi\) | ||||
0.716190 | + | 0.697905i | \(0.245884\pi\) | |||||||
\(14\) | 76153.5 | 0.529802 | ||||||||
\(15\) | −1183.55 | −0.00603640 | ||||||||
\(16\) | 146325. | 0.558186 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 165250. | 0.371036 | ||||||||
\(19\) | 385867. | 0.679277 | 0.339638 | − | 0.940556i | \(-0.389695\pi\) | ||||
0.339638 | + | 0.940556i | \(0.389695\pi\) | |||||||
\(20\) | 15082.7 | 0.0210787 | ||||||||
\(21\) | −289821. | −0.325194 | ||||||||
\(22\) | 7390.76 | 0.00672646 | ||||||||
\(23\) | −1.98059e6 | −1.47577 | −0.737885 | − | 0.674927i | \(-0.764175\pi\) | ||||
−0.737885 | + | 0.674927i | \(0.764175\pi\) | |||||||
\(24\) | 285830. | 0.175856 | ||||||||
\(25\) | −1.95191e6 | −0.999377 | ||||||||
\(26\) | −1.31535e6 | −0.564496 | ||||||||
\(27\) | −1.29689e6 | −0.469640 | ||||||||
\(28\) | 3.69334e6 | 1.13555 | ||||||||
\(29\) | −2.63751e6 | −0.692473 | −0.346237 | − | 0.938147i | \(-0.612541\pi\) | ||||
−0.346237 | + | 0.938147i | \(0.612541\pi\) | |||||||
\(30\) | 10554.2 | 0.00237892 | ||||||||
\(31\) | −6.41699e6 | −1.24797 | −0.623984 | − | 0.781437i | \(-0.714487\pi\) | ||||
−0.623984 | + | 0.781437i | \(0.714487\pi\) | |||||||
\(32\) | −5.61705e6 | −0.946964 | ||||||||
\(33\) | −28127.3 | −0.00412873 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 297827. | 0.0335473 | ||||||||
\(36\) | 8.01441e6 | 0.795262 | ||||||||
\(37\) | −1.89325e7 | −1.66074 | −0.830369 | − | 0.557214i | \(-0.811870\pi\) | ||||
−0.830369 | + | 0.557214i | \(0.811870\pi\) | |||||||
\(38\) | −3.44092e6 | −0.267700 | ||||||||
\(39\) | 5.00588e6 | 0.346489 | ||||||||
\(40\) | −293725. | −0.0181414 | ||||||||
\(41\) | 9.32654e6 | 0.515458 | 0.257729 | − | 0.966217i | \(-0.417026\pi\) | ||||
0.257729 | + | 0.966217i | \(0.417026\pi\) | |||||||
\(42\) | 2.58444e6 | 0.128158 | ||||||||
\(43\) | −1.72009e7 | −0.767260 | −0.383630 | − | 0.923487i | \(-0.625326\pi\) | ||||
−0.383630 | + | 0.923487i | \(0.625326\pi\) | |||||||
\(44\) | 358441. | 0.0144172 | ||||||||
\(45\) | 646274. | 0.0234942 | ||||||||
\(46\) | 1.76616e7 | 0.581595 | ||||||||
\(47\) | 1.46297e7 | 0.437317 | 0.218658 | − | 0.975801i | \(-0.429832\pi\) | ||||
0.218658 | + | 0.975801i | \(0.429832\pi\) | |||||||
\(48\) | 4.96588e6 | 0.135024 | ||||||||
\(49\) | 3.25763e7 | 0.807271 | ||||||||
\(50\) | 1.74059e7 | 0.393851 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.37925e7 | −1.20991 | ||||||||
\(53\) | −9.96374e7 | −1.73453 | −0.867264 | − | 0.497849i | \(-0.834123\pi\) | ||||
−0.867264 | + | 0.497849i | \(0.834123\pi\) | |||||||
\(54\) | 1.15648e7 | 0.185083 | ||||||||
\(55\) | 28904.3 | 0.000425923 0 | ||||||||
\(56\) | −7.19255e7 | −0.977320 | ||||||||
\(57\) | 1.30953e7 | 0.164315 | ||||||||
\(58\) | 2.35197e7 | 0.272901 | ||||||||
\(59\) | 7.35572e7 | 0.790298 | 0.395149 | − | 0.918617i | \(-0.370693\pi\) | ||||
0.395149 | + | 0.918617i | \(0.370693\pi\) | |||||||
\(60\) | 511864. | 0.00509887 | ||||||||
\(61\) | 643588. | 0.00595146 | 0.00297573 | − | 0.999996i | \(-0.499053\pi\) | ||||
0.00297573 | + | 0.999996i | \(0.499053\pi\) | |||||||
\(62\) | 5.72227e7 | 0.491820 | ||||||||
\(63\) | 1.58255e8 | 1.26568 | ||||||||
\(64\) | −2.48292e7 | −0.184992 | ||||||||
\(65\) | −5.14417e6 | −0.0357441 | ||||||||
\(66\) | 250822. | 0.00162711 | ||||||||
\(67\) | −2.31463e8 | −1.40328 | −0.701642 | − | 0.712530i | \(-0.747549\pi\) | ||||
−0.701642 | + | 0.712530i | \(0.747549\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.72157e7 | −0.356985 | ||||||||
\(70\) | −2.65584e6 | −0.0132209 | ||||||||
\(71\) | −4.38074e7 | −0.204590 | −0.102295 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102295 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(72\) | −1.56076e8 | −0.684445 | ||||||||
\(73\) | 2.09768e8 | 0.864542 | 0.432271 | − | 0.901744i | \(-0.357712\pi\) | ||||
0.432271 | + | 0.901744i | \(0.357712\pi\) | |||||||
\(74\) | 1.68829e8 | 0.654490 | ||||||||
\(75\) | −6.62425e7 | −0.241747 | ||||||||
\(76\) | −1.66880e8 | −0.573777 | ||||||||
\(77\) | 7.07790e6 | 0.0229454 | ||||||||
\(78\) | −4.46393e7 | −0.136550 | ||||||||
\(79\) | 7.18393e7 | 0.207511 | 0.103755 | − | 0.994603i | \(-0.466914\pi\) | ||||
0.103755 | + | 0.994603i | \(0.466914\pi\) | |||||||
\(80\) | −5.10306e6 | −0.0139292 | ||||||||
\(81\) | 3.20738e8 | 0.827881 | ||||||||
\(82\) | −8.31683e7 | −0.203140 | ||||||||
\(83\) | −3.97394e8 | −0.919115 | −0.459557 | − | 0.888148i | \(-0.651992\pi\) | ||||
−0.459557 | + | 0.888148i | \(0.651992\pi\) | |||||||
\(84\) | 1.25342e8 | 0.274688 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.53387e8 | 0.302374 | ||||||||
\(87\) | −8.95099e7 | −0.167508 | ||||||||
\(88\) | −6.98042e6 | −0.0124082 | ||||||||
\(89\) | 2.63648e8 | 0.445420 | 0.222710 | − | 0.974885i | \(-0.428510\pi\) | ||||
0.222710 | + | 0.974885i | \(0.428510\pi\) | |||||||
\(90\) | −5.76307e6 | −0.00925896 | ||||||||
\(91\) | −1.25967e9 | −1.92562 | ||||||||
\(92\) | 8.56565e8 | 1.24657 | ||||||||
\(93\) | −2.17775e8 | −0.301881 | ||||||||
\(94\) | −1.30459e8 | −0.172345 | ||||||||
\(95\) | −1.34570e7 | −0.0169509 | ||||||||
\(96\) | −1.90627e8 | −0.229068 | ||||||||
\(97\) | −3.00392e8 | −0.344521 | −0.172261 | − | 0.985051i | \(-0.555107\pi\) | ||||
−0.172261 | + | 0.985051i | \(0.555107\pi\) | |||||||
\(98\) | −2.90495e8 | −0.318143 | ||||||||
\(99\) | 1.53588e7 | 0.0160694 | ||||||||
\(100\) | 8.44162e8 | 0.844162 | ||||||||
\(101\) | 1.66753e9 | 1.59451 | 0.797254 | − | 0.603644i | \(-0.206285\pi\) | ||||
0.797254 | + | 0.603644i | \(0.206285\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00995e8 | 0.175962 | 0.0879808 | − | 0.996122i | \(-0.471959\pi\) | ||||
0.0879808 | + | 0.996122i | \(0.471959\pi\) | |||||||
\(104\) | 1.24232e9 | 1.04132 | ||||||||
\(105\) | 1.01074e7 | 0.00811502 | ||||||||
\(106\) | 8.88505e8 | 0.683571 | ||||||||
\(107\) | 6.92487e8 | 0.510722 | 0.255361 | − | 0.966846i | \(-0.417806\pi\) | ||||
0.255361 | + | 0.966846i | \(0.417806\pi\) | |||||||
\(108\) | 5.60879e8 | 0.396700 | ||||||||
\(109\) | −9.89530e7 | −0.0671444 | −0.0335722 | − | 0.999436i | \(-0.510688\pi\) | ||||
−0.0335722 | + | 0.999436i | \(0.510688\pi\) | |||||||
\(110\) | −257751. | −0.000167855 0 | ||||||||
\(111\) | −6.42519e8 | −0.401728 | ||||||||
\(112\) | −1.24960e9 | −0.750397 | ||||||||
\(113\) | −2.44334e9 | −1.40972 | −0.704858 | − | 0.709349i | \(-0.748989\pi\) | ||||
−0.704858 | + | 0.709349i | \(0.748989\pi\) | |||||||
\(114\) | −1.16776e8 | −0.0647560 | ||||||||
\(115\) | 6.90725e7 | 0.0368269 | ||||||||
\(116\) | 1.14067e9 | 0.584924 | ||||||||
\(117\) | −2.73343e9 | −1.34857 | ||||||||
\(118\) | −6.55937e8 | −0.311454 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.96824e6 | −0.00438837 | ||||||||
\(121\) | −2.35726e9 | −0.999709 | ||||||||
\(122\) | −5.73911e6 | −0.00234545 | ||||||||
\(123\) | 3.16517e8 | 0.124688 | ||||||||
\(124\) | 2.77522e9 | 1.05414 | ||||||||
\(125\) | 1.36187e8 | 0.0498932 | ||||||||
\(126\) | −1.41122e9 | −0.498801 | ||||||||
\(127\) | 8.77474e8 | 0.299307 | 0.149654 | − | 0.988738i | \(-0.452184\pi\) | ||||
0.149654 | + | 0.988738i | \(0.452184\pi\) | |||||||
\(128\) | 3.09734e9 | 1.01987 | ||||||||
\(129\) | −5.83751e8 | −0.185598 | ||||||||
\(130\) | 4.58725e7 | 0.0140866 | ||||||||
\(131\) | 1.44575e9 | 0.428916 | 0.214458 | − | 0.976733i | \(-0.431202\pi\) | ||||
0.214458 | + | 0.976733i | \(0.431202\pi\) | |||||||
\(132\) | 1.21645e7 | 0.00348749 | ||||||||
\(133\) | −3.29527e9 | −0.913184 | ||||||||
\(134\) | 2.06405e9 | 0.553029 | ||||||||
\(135\) | 4.52287e7 | 0.0117196 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.23159e9 | −0.541218 | −0.270609 | − | 0.962689i | \(-0.587225\pi\) | ||||
−0.270609 | + | 0.962689i | \(0.587225\pi\) | |||||||
\(138\) | 5.99388e8 | 0.140686 | ||||||||
\(139\) | 7.93386e9 | 1.80268 | 0.901339 | − | 0.433115i | \(-0.142586\pi\) | ||||
0.901339 | + | 0.433115i | \(0.142586\pi\) | |||||||
\(140\) | −1.28804e8 | −0.0283370 | ||||||||
\(141\) | 4.96493e8 | 0.105786 | ||||||||
\(142\) | 3.90647e8 | 0.0806281 | ||||||||
\(143\) | −1.22252e8 | −0.0244480 | ||||||||
\(144\) | −2.71159e9 | −0.525524 | ||||||||
\(145\) | 9.19826e7 | 0.0172802 | ||||||||
\(146\) | −1.87058e9 | −0.340713 | ||||||||
\(147\) | 1.10555e9 | 0.195277 | ||||||||
\(148\) | 8.18795e9 | 1.40281 | ||||||||
\(149\) | 2.71032e9 | 0.450488 | 0.225244 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225244 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(150\) | 5.90709e8 | 0.0952715 | ||||||||
\(151\) | −2.22864e9 | −0.348853 | −0.174427 | − | 0.984670i | \(-0.555807\pi\) | ||||
−0.174427 | + | 0.984670i | \(0.555807\pi\) | |||||||
\(152\) | 3.24989e9 | 0.493824 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.31163e7 | −0.00904271 | ||||||||
\(155\) | 2.23791e8 | 0.0311423 | ||||||||
\(156\) | −2.16495e9 | −0.292675 | ||||||||
\(157\) | 2.51657e9 | 0.330568 | 0.165284 | − | 0.986246i | \(-0.447146\pi\) | ||||
0.165284 | + | 0.986246i | \(0.447146\pi\) | |||||||
\(158\) | −6.40618e8 | −0.0817791 | ||||||||
\(159\) | −3.38142e9 | −0.419578 | ||||||||
\(160\) | 1.95893e8 | 0.0236309 | ||||||||
\(161\) | 1.69140e10 | 1.98395 | ||||||||
\(162\) | −2.86014e9 | −0.326265 | ||||||||
\(163\) | −8.11516e9 | −0.900436 | −0.450218 | − | 0.892919i | \(-0.648654\pi\) | ||||
−0.450218 | + | 0.892919i | \(0.648654\pi\) | |||||||
\(164\) | −4.03355e9 | −0.435401 | ||||||||
\(165\) | 980935. | 0.000103030 0 | ||||||||
\(166\) | 3.54371e9 | 0.362220 | ||||||||
\(167\) | −1.50831e10 | −1.50060 | −0.750301 | − | 0.661096i | \(-0.770092\pi\) | ||||
−0.750301 | + | 0.661096i | \(0.770092\pi\) | |||||||
\(168\) | −2.44096e9 | −0.236411 | ||||||||
\(169\) | 1.11529e10 | 1.05171 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.15061e9 | −0.639529 | ||||||||
\(172\) | 7.43904e9 | 0.648096 | ||||||||
\(173\) | −2.04298e10 | −1.73403 | −0.867016 | − | 0.498281i | \(-0.833965\pi\) | ||||
−0.867016 | + | 0.498281i | \(0.833965\pi\) | |||||||
\(174\) | 7.98194e8 | 0.0660141 | ||||||||
\(175\) | 1.66691e10 | 1.34351 | ||||||||
\(176\) | −1.21275e8 | −0.00952717 | ||||||||
\(177\) | 2.49633e9 | 0.191171 | ||||||||
\(178\) | −2.35105e9 | −0.175538 | ||||||||
\(179\) | −7.07164e9 | −0.514851 | −0.257426 | − | 0.966298i | \(-0.582874\pi\) | ||||
−0.257426 | + | 0.966298i | \(0.582874\pi\) | |||||||
\(180\) | −2.79501e8 | −0.0198452 | ||||||||
\(181\) | 7.59530e9 | 0.526007 | 0.263003 | − | 0.964795i | \(-0.415287\pi\) | ||||
0.263003 | + | 0.964795i | \(0.415287\pi\) | |||||||
\(182\) | 1.12329e10 | 0.758879 | ||||||||
\(183\) | 2.18416e7 | 0.00143964 | ||||||||
\(184\) | −1.66811e10 | −1.07286 | ||||||||
\(185\) | 6.60268e8 | 0.0414426 | ||||||||
\(186\) | 1.94198e9 | 0.118970 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.32707e9 | −0.369396 | ||||||||
\(189\) | 1.10753e10 | 0.631360 | ||||||||
\(190\) | 1.20001e8 | 0.00668029 | ||||||||
\(191\) | 3.32722e10 | 1.80897 | 0.904484 | − | 0.426508i | \(-0.140256\pi\) | ||||
0.904484 | + | 0.426508i | \(0.140256\pi\) | |||||||
\(192\) | −8.42634e8 | −0.0447490 | ||||||||
\(193\) | 1.62233e10 | 0.841652 | 0.420826 | − | 0.907141i | \(-0.361740\pi\) | ||||
0.420826 | + | 0.907141i | \(0.361740\pi\) | |||||||
\(194\) | 2.67871e9 | 0.135775 | ||||||||
\(195\) | −1.74579e8 | −0.00864642 | ||||||||
\(196\) | −1.40886e10 | −0.681893 | ||||||||
\(197\) | −3.49292e10 | −1.65231 | −0.826154 | − | 0.563445i | \(-0.809476\pi\) | ||||
−0.826154 | + | 0.563445i | \(0.809476\pi\) | |||||||
\(198\) | −1.36960e8 | −0.00633287 | ||||||||
\(199\) | 2.91611e10 | 1.31815 | 0.659076 | − | 0.752076i | \(-0.270947\pi\) | ||||
0.659076 | + | 0.752076i | \(0.270947\pi\) | |||||||
\(200\) | −1.64395e10 | −0.726532 | ||||||||
\(201\) | −7.85524e9 | −0.339451 | ||||||||
\(202\) | −1.48700e10 | −0.628390 | ||||||||
\(203\) | 2.25241e10 | 0.930925 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.25261e8 | −0.0128629 | ||||||||
\(206\) | −1.79235e9 | −0.0693458 | ||||||||
\(207\) | 3.67028e10 | 1.38942 | ||||||||
\(208\) | 2.15835e10 | 0.799535 | ||||||||
\(209\) | −3.19808e8 | −0.0115940 | ||||||||
\(210\) | −9.01319e7 | −0.00319810 | ||||||||
\(211\) | −3.70370e10 | −1.28637 | −0.643183 | − | 0.765713i | \(-0.722386\pi\) | ||||
−0.643183 | + | 0.765713i | \(0.722386\pi\) | |||||||
\(212\) | 4.30912e10 | 1.46513 | ||||||||
\(213\) | −1.48670e9 | −0.0494898 | ||||||||
\(214\) | −6.17516e9 | −0.201273 | ||||||||
\(215\) | 5.99877e8 | 0.0191465 | ||||||||
\(216\) | −1.09228e10 | −0.341421 | ||||||||
\(217\) | 5.48005e10 | 1.67770 | ||||||||
\(218\) | 8.82401e8 | 0.0264613 | ||||||||
\(219\) | 7.11895e9 | 0.209131 | ||||||||
\(220\) | −1.25006e7 | −0.000359772 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 5.72958e9 | 0.158320 | ||||||||
\(223\) | 4.79718e10 | 1.29902 | 0.649508 | − | 0.760355i | \(-0.274975\pi\) | ||||
0.649508 | + | 0.760355i | \(0.274975\pi\) | |||||||
\(224\) | 4.79690e10 | 1.27305 | ||||||||
\(225\) | 3.61713e10 | 0.940899 | ||||||||
\(226\) | 2.17882e10 | 0.555563 | ||||||||
\(227\) | 1.11013e10 | 0.277497 | 0.138748 | − | 0.990328i | \(-0.455692\pi\) | ||||
0.138748 | + | 0.990328i | \(0.455692\pi\) | |||||||
\(228\) | −5.66345e9 | −0.138795 | ||||||||
\(229\) | 3.41722e10 | 0.821134 | 0.410567 | − | 0.911831i | \(-0.365331\pi\) | ||||
0.410567 | + | 0.911831i | \(0.365331\pi\) | |||||||
\(230\) | −6.15946e8 | −0.0145133 | ||||||||
\(231\) | 2.40205e8 | 0.00555044 | ||||||||
\(232\) | −2.22139e10 | −0.503417 | ||||||||
\(233\) | 8.01980e10 | 1.78263 | 0.891317 | − | 0.453381i | \(-0.149782\pi\) | ||||
0.891317 | + | 0.453381i | \(0.149782\pi\) | |||||||
\(234\) | 2.43751e10 | 0.531465 | ||||||||
\(235\) | −5.10208e8 | −0.0109130 | ||||||||
\(236\) | −3.18120e10 | −0.667556 | ||||||||
\(237\) | 2.43803e9 | 0.0501963 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.68969e10 | 0.929723 | 0.464861 | − | 0.885384i | \(-0.346104\pi\) | ||||
0.464861 | + | 0.885384i | \(0.346104\pi\) | |||||||
\(240\) | −1.73184e8 | −0.00336943 | ||||||||
\(241\) | −2.38227e9 | −0.0454899 | −0.0227449 | − | 0.999741i | \(-0.507241\pi\) | ||||
−0.0227449 | + | 0.999741i | \(0.507241\pi\) | |||||||
\(242\) | 2.10206e10 | 0.393981 | ||||||||
\(243\) | 3.64116e10 | 0.669903 | ||||||||
\(244\) | −2.78339e8 | −0.00502713 | ||||||||
\(245\) | −1.13609e9 | −0.0201449 | ||||||||
\(246\) | −2.82251e9 | −0.0491391 | ||||||||
\(247\) | 5.69169e10 | 0.972983 | ||||||||
\(248\) | −5.40457e10 | −0.907254 | ||||||||
\(249\) | −1.34865e10 | −0.222332 | ||||||||
\(250\) | −1.21443e9 | −0.0196627 | ||||||||
\(251\) | −9.82275e10 | −1.56207 | −0.781037 | − | 0.624485i | \(-0.785309\pi\) | ||||
−0.781037 | + | 0.624485i | \(0.785309\pi\) | |||||||
\(252\) | −6.84422e10 | −1.06911 | ||||||||
\(253\) | 1.64152e9 | 0.0251885 | ||||||||
\(254\) | −7.82477e9 | −0.117956 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.49076e10 | −0.216934 | ||||||||
\(257\) | 9.68357e10 | 1.38464 | 0.692319 | − | 0.721591i | \(-0.256589\pi\) | ||||
0.692319 | + | 0.721591i | \(0.256589\pi\) | |||||||
\(258\) | 5.20553e9 | 0.0731436 | ||||||||
\(259\) | 1.61682e11 | 2.23261 | ||||||||
\(260\) | 2.22475e9 | 0.0301926 | ||||||||
\(261\) | 4.88764e10 | 0.651954 | ||||||||
\(262\) | −1.28923e10 | −0.169034 | ||||||||
\(263\) | 6.80816e10 | 0.877463 | 0.438731 | − | 0.898618i | \(-0.355428\pi\) | ||||
0.438731 | + | 0.898618i | \(0.355428\pi\) | |||||||
\(264\) | −2.36897e8 | −0.00300152 | ||||||||
\(265\) | 3.47483e9 | 0.0432840 | ||||||||
\(266\) | 2.93852e10 | 0.359882 | ||||||||
\(267\) | 8.94749e9 | 0.107746 | ||||||||
\(268\) | 1.00103e11 | 1.18534 | ||||||||
\(269\) | −9.55603e10 | −1.11274 | −0.556368 | − | 0.830936i | \(-0.687805\pi\) | ||||
−0.556368 | + | 0.830936i | \(0.687805\pi\) | |||||||
\(270\) | −4.03321e8 | −0.00461864 | ||||||||
\(271\) | 1.38416e11 | 1.55893 | 0.779463 | − | 0.626449i | \(-0.215492\pi\) | ||||
0.779463 | + | 0.626449i | \(0.215492\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.27497e10 | −0.465802 | ||||||||
\(274\) | 1.98999e10 | 0.213292 | ||||||||
\(275\) | 1.61775e9 | 0.0170575 | ||||||||
\(276\) | 2.90695e10 | 0.301541 | ||||||||
\(277\) | 8.21346e10 | 0.838238 | 0.419119 | − | 0.907931i | \(-0.362339\pi\) | ||||
0.419119 | + | 0.907931i | \(0.362339\pi\) | |||||||
\(278\) | −7.07492e10 | −0.710428 | ||||||||
\(279\) | 1.18915e11 | 1.17494 | ||||||||
\(280\) | 2.50839e9 | 0.0243884 | ||||||||
\(281\) | −1.69825e11 | −1.62489 | −0.812444 | − | 0.583039i | \(-0.801864\pi\) | ||||
−0.812444 | + | 0.583039i | \(0.801864\pi\) | |||||||
\(282\) | −4.42742e9 | −0.0416898 | ||||||||
\(283\) | −8.41175e10 | −0.779556 | −0.389778 | − | 0.920909i | \(-0.627448\pi\) | ||||
−0.389778 | + | 0.920909i | \(0.627448\pi\) | |||||||
\(284\) | 1.89458e10 | 0.172815 | ||||||||
\(285\) | −4.56695e8 | −0.00410038 | ||||||||
\(286\) | 1.09017e9 | 0.00963486 | ||||||||
\(287\) | −7.96478e10 | −0.692955 | ||||||||
\(288\) | 1.04091e11 | 0.891553 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −8.20243e8 | −0.00681007 | ||||||||
\(291\) | −1.01945e10 | −0.0833389 | ||||||||
\(292\) | −9.07205e10 | −0.730269 | ||||||||
\(293\) | −1.20546e11 | −0.955536 | −0.477768 | − | 0.878486i | \(-0.658554\pi\) | ||||
−0.477768 | + | 0.878486i | \(0.658554\pi\) | |||||||
\(294\) | −9.85862e9 | −0.0769579 | ||||||||
\(295\) | −2.56529e9 | −0.0197214 | ||||||||
\(296\) | −1.59455e11 | −1.20733 | ||||||||
\(297\) | 1.07487e9 | 0.00801586 | ||||||||
\(298\) | −2.41690e10 | −0.177535 | ||||||||
\(299\) | −2.92144e11 | −2.11386 | ||||||||
\(300\) | 2.86486e10 | 0.204201 | ||||||||
\(301\) | 1.46894e11 | 1.03146 | ||||||||
\(302\) | 1.98736e10 | 0.137482 | ||||||||
\(303\) | 5.65913e10 | 0.385708 | ||||||||
\(304\) | 5.64621e10 | 0.379163 | ||||||||
\(305\) | −2.24450e7 | −0.000148515 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.75885e10 | −0.562762 | −0.281381 | − | 0.959596i | \(-0.590792\pi\) | ||||
−0.281381 | + | 0.959596i | \(0.590792\pi\) | |||||||
\(308\) | −3.06105e9 | −0.0193817 | ||||||||
\(309\) | 6.82123e9 | 0.0425647 | ||||||||
\(310\) | −1.99563e9 | −0.0122730 | ||||||||
\(311\) | 1.24191e10 | 0.0752780 | 0.0376390 | − | 0.999291i | \(-0.488016\pi\) | ||||
0.0376390 | + | 0.999291i | \(0.488016\pi\) | |||||||
\(312\) | 4.21610e10 | 0.251892 | ||||||||
\(313\) | 2.38814e9 | 0.0140640 | 0.00703201 | − | 0.999975i | \(-0.497762\pi\) | ||||
0.00703201 | + | 0.999975i | \(0.497762\pi\) | |||||||
\(314\) | −2.24412e10 | −0.130275 | ||||||||
\(315\) | −5.51911e9 | −0.0315843 | ||||||||
\(316\) | −3.10691e10 | −0.175282 | ||||||||
\(317\) | 6.54695e10 | 0.364144 | 0.182072 | − | 0.983285i | \(-0.441720\pi\) | ||||
0.182072 | + | 0.983285i | \(0.441720\pi\) | |||||||
\(318\) | 3.01534e10 | 0.165354 | ||||||||
\(319\) | 2.18598e9 | 0.0118192 | ||||||||
\(320\) | 8.65912e8 | 0.00461635 | ||||||||
\(321\) | 2.35011e10 | 0.123542 | ||||||||
\(322\) | −1.50829e11 | −0.781866 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.38713e11 | −0.699301 | ||||||||
\(325\) | −2.87914e11 | −1.43149 | ||||||||
\(326\) | 7.23659e10 | 0.354858 | ||||||||
\(327\) | −3.35819e9 | −0.0162421 | ||||||||
\(328\) | 7.85508e10 | 0.374730 | ||||||||
\(329\) | −1.24936e11 | −0.587906 | ||||||||
\(330\) | −8.74737e6 | −4.06036e−5 0 | ||||||||
\(331\) | 2.74512e10 | 0.125700 | 0.0628501 | − | 0.998023i | \(-0.479981\pi\) | ||||
0.0628501 | + | 0.998023i | \(0.479981\pi\) | |||||||
\(332\) | 1.71865e11 | 0.776365 | ||||||||
\(333\) | 3.50844e11 | 1.56356 | ||||||||
\(334\) | 1.34501e11 | 0.591382 | ||||||||
\(335\) | 8.07223e9 | 0.0350181 | ||||||||
\(336\) | −4.24081e10 | −0.181519 | ||||||||
\(337\) | −3.74823e11 | −1.58304 | −0.791519 | − | 0.611145i | \(-0.790709\pi\) | ||||
−0.791519 | + | 0.611145i | \(0.790709\pi\) | |||||||
\(338\) | −9.94546e10 | −0.414476 | ||||||||
\(339\) | −8.29204e10 | −0.341007 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.31843e9 | 0.0213004 | ||||||||
\(342\) | 6.37647e10 | 0.252036 | ||||||||
\(343\) | 6.64173e10 | 0.259094 | ||||||||
\(344\) | −1.44871e11 | −0.557786 | ||||||||
\(345\) | 2.34413e9 | 0.00890833 | ||||||||
\(346\) | 1.82180e11 | 0.683375 | ||||||||
\(347\) | −9.76618e10 | −0.361611 | −0.180806 | − | 0.983519i | \(-0.557871\pi\) | ||||
−0.180806 | + | 0.983519i | \(0.557871\pi\) | |||||||
\(348\) | 3.87113e10 | 0.141492 | ||||||||
\(349\) | 2.22229e11 | 0.801839 | 0.400920 | − | 0.916113i | \(-0.368691\pi\) | ||||
0.400920 | + | 0.916113i | \(0.368691\pi\) | |||||||
\(350\) | −1.48645e11 | −0.529472 | ||||||||
\(351\) | −1.91296e11 | −0.672704 | ||||||||
\(352\) | 4.65543e9 | 0.0161629 | ||||||||
\(353\) | −1.85396e9 | −0.00635500 | −0.00317750 | − | 0.999995i | \(-0.501011\pi\) | ||||
−0.00317750 | + | 0.999995i | \(0.501011\pi\) | |||||||
\(354\) | −2.22607e10 | −0.0753398 | ||||||||
\(355\) | 1.52777e9 | 0.00510541 | ||||||||
\(356\) | −1.14023e11 | −0.376241 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.30605e10 | 0.202901 | ||||||||
\(359\) | −2.26386e11 | −0.719323 | −0.359662 | − | 0.933083i | \(-0.617108\pi\) | ||||
−0.359662 | + | 0.933083i | \(0.617108\pi\) | |||||||
\(360\) | 5.44310e9 | 0.0170799 | ||||||||
\(361\) | −1.73794e11 | −0.538583 | ||||||||
\(362\) | −6.77301e10 | −0.207297 | ||||||||
\(363\) | −7.99990e10 | −0.241827 | ||||||||
\(364\) | 5.44782e11 | 1.62655 | ||||||||
\(365\) | −7.31561e9 | −0.0215741 | ||||||||
\(366\) | −1.94770e8 | −0.000567358 0 | ||||||||
\(367\) | 3.46886e11 | 0.998135 | 0.499067 | − | 0.866563i | \(-0.333676\pi\) | ||||
0.499067 | + | 0.866563i | \(0.333676\pi\) | |||||||
\(368\) | −2.89810e11 | −0.823754 | ||||||||
\(369\) | −1.72833e11 | −0.485296 | ||||||||
\(370\) | −5.88786e9 | −0.0163324 | ||||||||
\(371\) | 8.50894e11 | 2.33181 | ||||||||
\(372\) | 9.41835e10 | 0.254995 | ||||||||
\(373\) | 2.60856e11 | 0.697768 | 0.348884 | − | 0.937166i | \(-0.386561\pi\) | ||||
0.348884 | + | 0.937166i | \(0.386561\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.62182e9 | 0.0120690 | ||||||||
\(376\) | 1.23216e11 | 0.317922 | ||||||||
\(377\) | −3.89043e11 | −0.991885 | ||||||||
\(378\) | −9.87626e10 | −0.248817 | ||||||||
\(379\) | −8.02252e10 | −0.199726 | −0.0998629 | − | 0.995001i | \(-0.531840\pi\) | ||||
−0.0998629 | + | 0.995001i | \(0.531840\pi\) | |||||||
\(380\) | 5.81990e9 | 0.0143182 | ||||||||
\(381\) | 2.97791e10 | 0.0724017 | ||||||||
\(382\) | −2.96700e11 | −0.712907 | ||||||||
\(383\) | −5.97457e10 | −0.141877 | −0.0709386 | − | 0.997481i | \(-0.522599\pi\) | ||||
−0.0709386 | + | 0.997481i | \(0.522599\pi\) | |||||||
\(384\) | 1.05115e11 | 0.246704 | ||||||||
\(385\) | −2.46840e8 | −0.000572589 0 | ||||||||
\(386\) | −1.44670e11 | −0.331692 | ||||||||
\(387\) | 3.18754e11 | 0.722364 | ||||||||
\(388\) | 1.29914e11 | 0.291013 | ||||||||
\(389\) | 3.76555e11 | 0.833786 | 0.416893 | − | 0.908956i | \(-0.363119\pi\) | ||||
0.416893 | + | 0.908956i | \(0.363119\pi\) | |||||||
\(390\) | 1.55679e9 | 0.00340752 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.74367e11 | 0.586874 | ||||||||
\(393\) | 4.90647e10 | 0.103754 | ||||||||
\(394\) | 3.11477e11 | 0.651168 | ||||||||
\(395\) | −2.50538e9 | −0.00517829 | ||||||||
\(396\) | −6.64237e9 | −0.0135736 | ||||||||
\(397\) | −6.14963e11 | −1.24249 | −0.621244 | − | 0.783618i | \(-0.713372\pi\) | ||||
−0.621244 | + | 0.783618i | \(0.713372\pi\) | |||||||
\(398\) | −2.60041e11 | −0.519479 | ||||||||
\(399\) | −1.11832e11 | −0.220897 | ||||||||
\(400\) | −2.85613e11 | −0.557839 | ||||||||
\(401\) | −5.71865e9 | −0.0110444 | −0.00552222 | − | 0.999985i | \(-0.501758\pi\) | ||||
−0.00552222 | + | 0.999985i | \(0.501758\pi\) | |||||||
\(402\) | 7.00481e10 | 0.133776 | ||||||||
\(403\) | −9.46531e11 | −1.78757 | ||||||||
\(404\) | −7.21173e11 | −1.34686 | ||||||||
\(405\) | −1.11857e10 | −0.0206592 | ||||||||
\(406\) | −2.00856e11 | −0.366874 | ||||||||
\(407\) | 1.56914e10 | 0.0283456 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.18179e11 | 1.09234 | 0.546172 | − | 0.837673i | \(-0.316085\pi\) | ||||
0.546172 | + | 0.837673i | \(0.316085\pi\) | |||||||
\(410\) | 2.90048e9 | 0.00506923 | ||||||||
\(411\) | −7.57341e10 | −0.130919 | ||||||||
\(412\) | −8.69264e10 | −0.148633 | ||||||||
\(413\) | −6.28171e11 | −1.06244 | ||||||||
\(414\) | −3.27292e11 | −0.547563 | ||||||||
\(415\) | 1.38590e10 | 0.0229359 | ||||||||
\(416\) | −8.28537e11 | −1.35641 | ||||||||
\(417\) | 2.69254e11 | 0.436063 | ||||||||
\(418\) | 2.85185e9 | 0.00456913 | ||||||||
\(419\) | 5.15438e11 | 0.816983 | 0.408492 | − | 0.912762i | \(-0.366055\pi\) | ||||
0.408492 | + | 0.912762i | \(0.366055\pi\) | |||||||
\(420\) | −4.37127e9 | −0.00685466 | ||||||||
\(421\) | −1.89025e11 | −0.293258 | −0.146629 | − | 0.989192i | \(-0.546842\pi\) | ||||
−0.146629 | + | 0.989192i | \(0.546842\pi\) | |||||||
\(422\) | 3.30273e11 | 0.506952 | ||||||||
\(423\) | −2.71107e11 | −0.411727 | ||||||||
\(424\) | −8.39175e11 | −1.26097 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.32575e10 | 0.0195037 | ||||||||
\(427\) | −5.49618e9 | −0.00800083 | ||||||||
\(428\) | −2.99487e11 | −0.431401 | ||||||||
\(429\) | −4.14889e9 | −0.00591391 | ||||||||
\(430\) | −5.34933e9 | −0.00754555 | ||||||||
\(431\) | 1.00192e12 | 1.39858 | 0.699289 | − | 0.714840i | \(-0.253500\pi\) | ||||
0.699289 | + | 0.714840i | \(0.253500\pi\) | |||||||
\(432\) | −1.89767e11 | −0.262147 | ||||||||
\(433\) | −6.95832e11 | −0.951281 | −0.475640 | − | 0.879640i | \(-0.657784\pi\) | ||||
−0.475640 | + | 0.879640i | \(0.657784\pi\) | |||||||
\(434\) | −4.88676e11 | −0.661177 | ||||||||
\(435\) | 3.12164e9 | 0.00418004 | ||||||||
\(436\) | 4.27952e10 | 0.0567161 | ||||||||
\(437\) | −7.64244e11 | −1.00246 | ||||||||
\(438\) | −6.34824e10 | −0.0824176 | ||||||||
\(439\) | 8.70444e11 | 1.11854 | 0.559269 | − | 0.828987i | \(-0.311082\pi\) | ||||
0.559269 | + | 0.828987i | \(0.311082\pi\) | |||||||
\(440\) | 2.43441e8 | 0.000309639 0 | ||||||||
\(441\) | −6.03680e11 | −0.760034 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.60593e11 | −0.938286 | −0.469143 | − | 0.883122i | \(-0.655437\pi\) | ||||
−0.469143 | + | 0.883122i | \(0.655437\pi\) | |||||||
\(444\) | 2.77877e11 | 0.339335 | ||||||||
\(445\) | −9.19466e9 | −0.0111152 | ||||||||
\(446\) | −4.27783e11 | −0.511937 | ||||||||
\(447\) | 9.19810e10 | 0.108972 | ||||||||
\(448\) | 2.12039e11 | 0.248693 | ||||||||
\(449\) | 5.88029e11 | 0.682795 | 0.341397 | − | 0.939919i | \(-0.389100\pi\) | ||||
0.341397 | + | 0.939919i | \(0.389100\pi\) | |||||||
\(450\) | −3.22553e11 | −0.370805 | ||||||||
\(451\) | −7.72987e9 | −0.00879788 | ||||||||
\(452\) | 1.05670e12 | 1.19077 | ||||||||
\(453\) | −7.56338e10 | −0.0843867 | ||||||||
\(454\) | −9.89946e10 | −0.109360 | ||||||||
\(455\) | 4.39307e10 | 0.0480526 | ||||||||
\(456\) | 1.10292e11 | 0.119455 | ||||||||
\(457\) | 7.74899e11 | 0.831041 | 0.415520 | − | 0.909584i | \(-0.363599\pi\) | ||||
0.415520 | + | 0.909584i | \(0.363599\pi\) | |||||||
\(458\) | −3.04727e11 | −0.323606 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.98725e10 | −0.0311072 | ||||||||
\(461\) | −1.26161e12 | −1.30099 | −0.650493 | − | 0.759512i | \(-0.725438\pi\) | ||||
−0.650493 | + | 0.759512i | \(0.725438\pi\) | |||||||
\(462\) | −2.14200e9 | −0.00218741 | ||||||||
\(463\) | −1.80501e12 | −1.82543 | −0.912715 | − | 0.408596i | \(-0.866018\pi\) | ||||
−0.912715 | + | 0.408596i | \(0.866018\pi\) | |||||||
\(464\) | −3.85934e11 | −0.386529 | ||||||||
\(465\) | 7.59486e9 | 0.00753323 | ||||||||
\(466\) | −7.15156e11 | −0.702529 | ||||||||
\(467\) | 1.38727e12 | 1.34969 | 0.674846 | − | 0.737959i | \(-0.264210\pi\) | ||||
0.674846 | + | 0.737959i | \(0.264210\pi\) | |||||||
\(468\) | 1.18216e12 | 1.13912 | ||||||||
\(469\) | 1.97667e12 | 1.88650 | ||||||||
\(470\) | 4.54972e9 | 0.00430075 | ||||||||
\(471\) | 8.54055e10 | 0.0799635 | ||||||||
\(472\) | 6.19520e11 | 0.574535 | ||||||||
\(473\) | 1.42562e10 | 0.0130957 | ||||||||
\(474\) | −2.17408e10 | −0.0197822 | ||||||||
\(475\) | −7.53178e11 | −0.678854 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.84641e12 | 1.63303 | ||||||||
\(478\) | −4.18197e11 | −0.366400 | ||||||||
\(479\) | 2.10470e11 | 0.182675 | 0.0913376 | − | 0.995820i | \(-0.470886\pi\) | ||||
0.0913376 | + | 0.995820i | \(0.470886\pi\) | |||||||
\(480\) | 6.64809e9 | 0.00571625 | ||||||||
\(481\) | −2.79262e12 | −2.37881 | ||||||||
\(482\) | 2.12436e10 | 0.0179274 | ||||||||
\(483\) | 5.74015e11 | 0.479912 | ||||||||
\(484\) | 1.01947e12 | 0.844442 | ||||||||
\(485\) | 1.04761e10 | 0.00859731 | ||||||||
\(486\) | −3.24696e11 | −0.264006 | ||||||||
\(487\) | 1.10325e12 | 0.888778 | 0.444389 | − | 0.895834i | \(-0.353421\pi\) | ||||
0.444389 | + | 0.895834i | \(0.353421\pi\) | |||||||
\(488\) | 5.42048e9 | 0.00432662 | ||||||||
\(489\) | −2.75406e11 | −0.217813 | ||||||||
\(490\) | 1.01310e10 | 0.00793904 | ||||||||
\(491\) | 1.63476e12 | 1.26937 | 0.634684 | − | 0.772771i | \(-0.281130\pi\) | ||||
0.634684 | + | 0.772771i | \(0.281130\pi\) | |||||||
\(492\) | −1.36888e11 | −0.105322 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −5.07550e11 | −0.383449 | ||||||||
\(495\) | −5.35634e8 | −0.000401000 0 | ||||||||
\(496\) | −9.38968e11 | −0.696599 | ||||||||
\(497\) | 3.74111e11 | 0.275040 | ||||||||
\(498\) | 1.20264e11 | 0.0876200 | ||||||||
\(499\) | −4.41359e11 | −0.318669 | −0.159334 | − | 0.987225i | \(-0.550935\pi\) | ||||
−0.159334 | + | 0.987225i | \(0.550935\pi\) | |||||||
\(500\) | −5.88983e10 | −0.0421442 | ||||||||
\(501\) | −5.11878e11 | −0.362992 | ||||||||
\(502\) | 8.75932e11 | 0.615607 | ||||||||
\(503\) | 2.37298e11 | 0.165287 | 0.0826434 | − | 0.996579i | \(-0.473664\pi\) | ||||
0.0826434 | + | 0.996579i | \(0.473664\pi\) | |||||||
\(504\) | 1.33287e12 | 0.920133 | ||||||||
\(505\) | −5.81546e10 | −0.0397899 | ||||||||
\(506\) | −1.46380e10 | −0.00992671 | ||||||||
\(507\) | 3.78499e11 | 0.254407 | ||||||||
\(508\) | −3.79490e11 | −0.252821 | ||||||||
\(509\) | 9.67033e10 | 0.0638574 | 0.0319287 | − | 0.999490i | \(-0.489835\pi\) | ||||
0.0319287 | + | 0.999490i | \(0.489835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.79140e12 | −1.16225 | ||||||||
\(512\) | −1.45290e12 | −0.934375 | ||||||||
\(513\) | −5.00427e11 | −0.319016 | ||||||||
\(514\) | −8.63520e11 | −0.545681 | ||||||||
\(515\) | −7.00966e9 | −0.00439101 | ||||||||
\(516\) | 2.52461e11 | 0.156773 | ||||||||
\(517\) | −1.21252e10 | −0.00746415 | ||||||||
\(518\) | −1.44178e12 | −0.879863 | ||||||||
\(519\) | −6.93332e11 | −0.419458 | ||||||||
\(520\) | −4.33256e10 | −0.0259854 | ||||||||
\(521\) | −2.00394e12 | −1.19156 | −0.595779 | − | 0.803149i | \(-0.703156\pi\) | ||||
−0.595779 | + | 0.803149i | \(0.703156\pi\) | |||||||
\(522\) | −4.35849e11 | −0.256932 | ||||||||
\(523\) | −2.38851e12 | −1.39595 | −0.697975 | − | 0.716122i | \(-0.745916\pi\) | ||||
−0.697975 | + | 0.716122i | \(0.745916\pi\) | |||||||
\(524\) | −6.25258e11 | −0.362300 | ||||||||
\(525\) | 5.65704e11 | 0.324992 | ||||||||
\(526\) | −6.07109e11 | −0.345805 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −4.11574e9 | −0.00230460 | ||||||||
\(529\) | 2.12157e12 | 1.17790 | ||||||||
\(530\) | −3.09864e10 | −0.0170581 | ||||||||
\(531\) | −1.36311e12 | −0.744055 | ||||||||
\(532\) | 1.42514e12 | 0.771356 | ||||||||
\(533\) | 1.37570e12 | 0.738332 | ||||||||
\(534\) | −7.97882e10 | −0.0424622 | ||||||||
\(535\) | −2.41503e10 | −0.0127447 | ||||||||
\(536\) | −1.94945e12 | −1.02017 | ||||||||
\(537\) | −2.39992e11 | −0.124541 | ||||||||
\(538\) | 8.52147e11 | 0.438525 | ||||||||
\(539\) | −2.69994e10 | −0.0137786 | ||||||||
\(540\) | −1.95605e10 | −0.00989939 | ||||||||
\(541\) | −4.38039e10 | −0.0219849 | −0.0109925 | − | 0.999940i | \(-0.503499\pi\) | ||||
−0.0109925 | + | 0.999940i | \(0.503499\pi\) | |||||||
\(542\) | −1.23431e12 | −0.614366 | ||||||||
\(543\) | 2.57764e11 | 0.127240 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.45096e9 | 0.00167554 | ||||||||
\(546\) | 3.81215e11 | 0.183571 | ||||||||
\(547\) | −1.45378e12 | −0.694316 | −0.347158 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347158 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(548\) | 9.65119e11 | 0.457160 | ||||||||
\(549\) | −1.19265e10 | −0.00560321 | ||||||||
\(550\) | −1.44261e10 | −0.00672228 | ||||||||
\(551\) | −1.01773e12 | −0.470381 | ||||||||
\(552\) | −5.66110e11 | −0.259522 | ||||||||
\(553\) | −6.13501e11 | −0.278966 | ||||||||
\(554\) | −7.32426e11 | −0.330346 | ||||||||
\(555\) | 2.24077e10 | 0.0100249 | ||||||||
\(556\) | −3.43124e12 | −1.52270 | ||||||||
\(557\) | 2.18164e12 | 0.960363 | 0.480181 | − | 0.877169i | \(-0.340571\pi\) | ||||
0.480181 | + | 0.877169i | \(0.340571\pi\) | |||||||
\(558\) | −1.06041e12 | −0.463041 | ||||||||
\(559\) | −2.53720e12 | −1.09901 | ||||||||
\(560\) | 4.35796e10 | 0.0187257 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.51440e12 | 0.640362 | ||||||||
\(563\) | 5.13044e10 | 0.0215212 | 0.0107606 | − | 0.999942i | \(-0.496575\pi\) | ||||
0.0107606 | + | 0.999942i | \(0.496575\pi\) | |||||||
\(564\) | −2.14724e11 | −0.0893560 | ||||||||
\(565\) | 8.52110e10 | 0.0351785 | ||||||||
\(566\) | 7.50107e11 | 0.307220 | ||||||||
\(567\) | −2.73907e12 | −1.11296 | ||||||||
\(568\) | −3.68958e11 | −0.148734 | ||||||||
\(569\) | −3.00090e12 | −1.20018 | −0.600090 | − | 0.799933i | \(-0.704869\pi\) | ||||
−0.600090 | + | 0.799933i | \(0.704869\pi\) | |||||||
\(570\) | 4.07252e9 | 0.00161595 | ||||||||
\(571\) | −1.84446e12 | −0.726116 | −0.363058 | − | 0.931767i | \(-0.618267\pi\) | ||||
−0.363058 | + | 0.931767i | \(0.618267\pi\) | |||||||
\(572\) | 5.28715e10 | 0.0206509 | ||||||||
\(573\) | 1.12917e12 | 0.437585 | ||||||||
\(574\) | 7.10249e11 | 0.273091 | ||||||||
\(575\) | 3.86592e12 | 1.47485 | ||||||||
\(576\) | 4.60116e11 | 0.174167 | ||||||||
\(577\) | 3.01920e12 | 1.13397 | 0.566984 | − | 0.823729i | \(-0.308110\pi\) | ||||
0.566984 | + | 0.823729i | \(0.308110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.50576e11 | 0.203593 | ||||||||
\(580\) | −3.97806e10 | −0.0145964 | ||||||||
\(581\) | 3.39370e12 | 1.23561 | ||||||||
\(582\) | 9.09082e10 | 0.0328435 | ||||||||
\(583\) | 8.25799e10 | 0.0296051 | ||||||||
\(584\) | 1.76673e12 | 0.628509 | ||||||||
\(585\) | 9.53279e10 | 0.0336526 | ||||||||
\(586\) | 1.07495e12 | 0.376573 | ||||||||
\(587\) | 1.79991e12 | 0.625719 | 0.312860 | − | 0.949799i | \(-0.398713\pi\) | ||||
0.312860 | + | 0.949799i | \(0.398713\pi\) | |||||||
\(588\) | −4.78129e11 | −0.164948 | ||||||||
\(589\) | −2.47611e12 | −0.847716 | ||||||||
\(590\) | 2.28757e10 | 0.00777212 | ||||||||
\(591\) | −1.18540e12 | −0.399689 | ||||||||
\(592\) | −2.77031e12 | −0.927001 | ||||||||
\(593\) | 2.90587e12 | 0.965006 | 0.482503 | − | 0.875894i | \(-0.339728\pi\) | ||||
0.482503 | + | 0.875894i | \(0.339728\pi\) | |||||||
\(594\) | −9.58498e9 | −0.00315902 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.17216e12 | −0.380522 | ||||||||
\(597\) | 9.89650e11 | 0.318858 | ||||||||
\(598\) | 2.60516e12 | 0.833065 | ||||||||
\(599\) | 4.72811e12 | 1.50061 | 0.750303 | − | 0.661094i | \(-0.229908\pi\) | ||||
0.750303 | + | 0.661094i | \(0.229908\pi\) | |||||||
\(600\) | −5.57913e11 | −0.175746 | ||||||||
\(601\) | −2.89176e12 | −0.904121 | −0.452061 | − | 0.891987i | \(-0.649311\pi\) | ||||
−0.452061 | + | 0.891987i | \(0.649311\pi\) | |||||||
\(602\) | −1.30991e12 | −0.406496 | ||||||||
\(603\) | 4.28931e12 | 1.32117 | ||||||||
\(604\) | 9.63841e11 | 0.294672 | ||||||||
\(605\) | 8.22089e10 | 0.0249471 | ||||||||
\(606\) | −5.04646e11 | −0.152006 | ||||||||
\(607\) | 6.45254e12 | 1.92922 | 0.964610 | − | 0.263680i | \(-0.0849363\pi\) | ||||
0.964610 | + | 0.263680i | \(0.0849363\pi\) | |||||||
\(608\) | −2.16744e12 | −0.643250 | ||||||||
\(609\) | 7.64406e11 | 0.225188 | ||||||||
\(610\) | 2.00150e8 | 5.85291e−5 0 | ||||||||
\(611\) | 2.15794e12 | 0.626404 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.51234e12 | 0.718631 | 0.359316 | − | 0.933216i | \(-0.383010\pi\) | ||||
0.359316 | + | 0.933216i | \(0.383010\pi\) | |||||||
\(614\) | 7.81060e11 | 0.221782 | ||||||||
\(615\) | −1.10385e10 | −0.00311151 | ||||||||
\(616\) | 5.96121e10 | 0.0166810 | ||||||||
\(617\) | 4.19165e12 | 1.16440 | 0.582199 | − | 0.813046i | \(-0.302193\pi\) | ||||
0.582199 | + | 0.813046i | \(0.302193\pi\) | |||||||
\(618\) | −6.08274e10 | −0.0167746 | ||||||||
\(619\) | 5.81865e12 | 1.59299 | 0.796497 | − | 0.604642i | \(-0.206684\pi\) | ||||
0.796497 | + | 0.604642i | \(0.206684\pi\) | |||||||
\(620\) | −9.67853e10 | −0.0263055 | ||||||||
\(621\) | 2.56860e12 | 0.693081 | ||||||||
\(622\) | −1.10746e11 | −0.0296668 | ||||||||
\(623\) | −2.25153e12 | −0.598799 | ||||||||
\(624\) | 7.32487e11 | 0.193406 | ||||||||
\(625\) | 3.80757e12 | 0.998132 | ||||||||
\(626\) | −2.12959e10 | −0.00554258 | ||||||||
\(627\) | −1.08534e10 | −0.00280455 | ||||||||
\(628\) | −1.08837e12 | −0.279227 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 4.92160e10 | 0.0124473 | ||||||||
\(631\) | −3.40483e12 | −0.854995 | −0.427498 | − | 0.904017i | \(-0.640605\pi\) | ||||
−0.427498 | + | 0.904017i | \(0.640605\pi\) | |||||||
\(632\) | 6.05051e11 | 0.150857 | ||||||||
\(633\) | −1.25693e12 | −0.311169 | ||||||||
\(634\) | −5.83817e11 | −0.143508 | ||||||||
\(635\) | −3.06017e10 | −0.00746902 | ||||||||
\(636\) | 1.46240e12 | 0.354412 | ||||||||
\(637\) | 4.80513e12 | 1.15632 | ||||||||
\(638\) | −1.94932e10 | −0.00465790 | ||||||||
\(639\) | 8.11806e11 | 0.192619 | ||||||||
\(640\) | −1.08019e11 | −0.0254502 | ||||||||
\(641\) | −1.37939e12 | −0.322721 | −0.161360 | − | 0.986896i | \(-0.551588\pi\) | ||||
−0.161360 | + | 0.986896i | \(0.551588\pi\) | |||||||
\(642\) | −2.09568e11 | −0.0486875 | ||||||||
\(643\) | −6.11870e12 | −1.41159 | −0.705797 | − | 0.708414i | \(-0.749411\pi\) | ||||
−0.705797 | + | 0.708414i | \(0.749411\pi\) | |||||||
\(644\) | −7.31498e12 | −1.67582 | ||||||||
\(645\) | 2.03582e10 | 0.00463149 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.49553e12 | −0.784231 | −0.392116 | − | 0.919916i | \(-0.628257\pi\) | ||||
−0.392116 | + | 0.919916i | \(0.628257\pi\) | |||||||
\(648\) | 2.70135e12 | 0.601857 | ||||||||
\(649\) | −6.09645e10 | −0.0134889 | ||||||||
\(650\) | 2.56744e12 | 0.564144 | ||||||||
\(651\) | 1.85978e12 | 0.405832 | ||||||||
\(652\) | 3.50965e12 | 0.760588 | ||||||||
\(653\) | −5.24011e12 | −1.12780 | −0.563899 | − | 0.825844i | \(-0.690699\pi\) | ||||
−0.563899 | + | 0.825844i | \(0.690699\pi\) | |||||||
\(654\) | 2.99463e10 | 0.00640093 | ||||||||
\(655\) | −5.04201e10 | −0.0107033 | ||||||||
\(656\) | 1.36471e12 | 0.287722 | ||||||||
\(657\) | −3.88727e12 | −0.813954 | ||||||||
\(658\) | 1.11411e12 | 0.231691 | ||||||||
\(659\) | 6.99007e12 | 1.44377 | 0.721883 | − | 0.692015i | \(-0.243277\pi\) | ||||
0.721883 | + | 0.692015i | \(0.243277\pi\) | |||||||
\(660\) | −4.24235e8 | −8.70280e−5 0 | ||||||||
\(661\) | 5.79186e11 | 0.118008 | 0.0590040 | − | 0.998258i | \(-0.481208\pi\) | ||||
0.0590040 | + | 0.998258i | \(0.481208\pi\) | |||||||
\(662\) | −2.44793e11 | −0.0495380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.34697e12 | −0.668182 | ||||||||
\(665\) | 1.14922e11 | 0.0227879 | ||||||||
\(666\) | −3.12861e12 | −0.616193 | ||||||||
\(667\) | 5.22382e12 | 1.02193 | ||||||||
\(668\) | 6.52313e12 | 1.26754 | ||||||||
\(669\) | 1.62803e12 | 0.314229 | ||||||||
\(670\) | −7.19831e10 | −0.0138005 | ||||||||
\(671\) | −5.33408e8 | −0.000101580 0 | ||||||||
\(672\) | 1.62794e12 | 0.307947 | ||||||||
\(673\) | −8.24877e12 | −1.54996 | −0.774982 | − | 0.631984i | \(-0.782241\pi\) | ||||
−0.774982 | + | 0.631984i | \(0.782241\pi\) | |||||||
\(674\) | 3.34244e12 | 0.623869 | ||||||||
\(675\) | 2.53141e12 | 0.469348 | ||||||||
\(676\) | −4.82341e12 | −0.888370 | ||||||||
\(677\) | −3.10253e12 | −0.567633 | −0.283816 | − | 0.958879i | \(-0.591601\pi\) | ||||
−0.283816 | + | 0.958879i | \(0.591601\pi\) | |||||||
\(678\) | 7.39432e11 | 0.134389 | ||||||||
\(679\) | 2.56532e12 | 0.463157 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.76748e11 | 0.0671257 | ||||||||
\(682\) | −4.74264e10 | −0.00839442 | ||||||||
\(683\) | 6.90971e12 | 1.21497 | 0.607486 | − | 0.794330i | \(-0.292178\pi\) | ||||
0.607486 | + | 0.794330i | \(0.292178\pi\) | |||||||
\(684\) | 3.09250e12 | 0.540203 | ||||||||
\(685\) | 7.78262e10 | 0.0135057 | ||||||||
\(686\) | −5.92269e11 | −0.102108 | ||||||||
\(687\) | 1.15971e12 | 0.198630 | ||||||||
\(688\) | −2.51692e12 | −0.428274 | ||||||||
\(689\) | −1.46969e13 | −2.48450 | ||||||||
\(690\) | −2.09035e10 | −0.00351074 | ||||||||
\(691\) | 6.42061e12 | 1.07133 | 0.535667 | − | 0.844429i | \(-0.320060\pi\) | ||||
0.535667 | + | 0.844429i | \(0.320060\pi\) | |||||||
\(692\) | 8.83549e12 | 1.46472 | ||||||||
\(693\) | −1.31162e11 | −0.0216028 | ||||||||
\(694\) | 8.70887e11 | 0.142510 | ||||||||
\(695\) | −2.76692e11 | −0.0449846 | ||||||||
\(696\) | −7.53878e11 | −0.121775 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.98170e12 | −0.316002 | ||||||||
\(699\) | 2.72170e12 | 0.431215 | ||||||||
\(700\) | −7.20906e12 | −1.13485 | ||||||||
\(701\) | −1.11002e12 | −0.173620 | −0.0868102 | − | 0.996225i | \(-0.527667\pi\) | ||||
−0.0868102 | + | 0.996225i | \(0.527667\pi\) | |||||||
\(702\) | 1.70586e12 | 0.265110 | ||||||||
\(703\) | −7.30545e12 | −1.12810 | ||||||||
\(704\) | 2.05785e10 | 0.00315745 | ||||||||
\(705\) | −1.73151e10 | −0.00263982 | ||||||||
\(706\) | 1.65325e10 | 0.00250448 | ||||||||
\(707\) | −1.42405e13 | −2.14357 | ||||||||
\(708\) | −1.07961e12 | −0.161480 | ||||||||
\(709\) | 7.66189e12 | 1.13875 | 0.569374 | − | 0.822079i | \(-0.307186\pi\) | ||||
0.569374 | + | 0.822079i | \(0.307186\pi\) | |||||||
\(710\) | −1.36237e10 | −0.00201202 | ||||||||
\(711\) | −1.33127e12 | −0.195368 | ||||||||
\(712\) | 2.22052e12 | 0.323813 | ||||||||
\(713\) | 1.27094e13 | 1.84171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.26350e9 | 0.000610084 0 | ||||||||
\(716\) | 3.05835e12 | 0.434889 | ||||||||
\(717\) | 1.59155e12 | 0.224898 | ||||||||
\(718\) | 2.01877e12 | 0.283483 | ||||||||
\(719\) | −8.97215e12 | −1.25204 | −0.626018 | − | 0.779809i | \(-0.715316\pi\) | ||||
−0.626018 | + | 0.779809i | \(0.715316\pi\) | |||||||
\(720\) | 9.45661e10 | 0.0131141 | ||||||||
\(721\) | −1.71648e12 | −0.236554 | ||||||||
\(722\) | 1.54979e12 | 0.212253 | ||||||||
\(723\) | −8.08479e10 | −0.0110039 | ||||||||
\(724\) | −3.28482e12 | −0.444312 | ||||||||
\(725\) | 5.14818e12 | 0.692042 | ||||||||
\(726\) | 7.13381e11 | 0.0953031 | ||||||||
\(727\) | 8.45878e12 | 1.12306 | 0.561530 | − | 0.827456i | \(-0.310213\pi\) | ||||
0.561530 | + | 0.827456i | \(0.310213\pi\) | |||||||
\(728\) | −1.06093e13 | −1.39989 | ||||||||
\(729\) | −5.07737e12 | −0.665833 | ||||||||
\(730\) | 6.52361e10 | 0.00850227 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −9.44607e9 | −0.00121605 | ||||||||
\(733\) | −2.56649e12 | −0.328377 | −0.164188 | − | 0.986429i | \(-0.552501\pi\) | ||||
−0.164188 | + | 0.986429i | \(0.552501\pi\) | |||||||
\(734\) | −3.09331e12 | −0.393361 | ||||||||
\(735\) | −3.85558e10 | −0.00487301 | ||||||||
\(736\) | 1.11250e13 | 1.39750 | ||||||||
\(737\) | 1.91838e11 | 0.0239514 | ||||||||
\(738\) | 1.54121e12 | 0.191253 | ||||||||
\(739\) | 9.87426e12 | 1.21788 | 0.608940 | − | 0.793216i | \(-0.291595\pi\) | ||||
0.608940 | + | 0.793216i | \(0.291595\pi\) | |||||||
\(740\) | −2.85553e11 | −0.0350061 | ||||||||
\(741\) | 1.93161e12 | 0.235362 | ||||||||
\(742\) | −7.58774e12 | −0.918957 | ||||||||
\(743\) | −8.12358e12 | −0.977907 | −0.488954 | − | 0.872310i | \(-0.662621\pi\) | ||||
−0.488954 | + | 0.872310i | \(0.662621\pi\) | |||||||
\(744\) | −1.83417e12 | −0.219462 | ||||||||
\(745\) | −9.45219e10 | −0.0112416 | ||||||||
\(746\) | −2.32615e12 | −0.274988 | ||||||||
\(747\) | 7.36421e12 | 0.865333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.91377e12 | −0.686588 | ||||||||
\(750\) | −4.12145e10 | −0.00475636 | ||||||||
\(751\) | 8.29551e11 | 0.0951619 | 0.0475810 | − | 0.998867i | \(-0.484849\pi\) | ||||
0.0475810 | + | 0.998867i | \(0.484849\pi\) | |||||||
\(752\) | 2.14070e12 | 0.244104 | ||||||||
\(753\) | −3.33357e12 | −0.377862 | ||||||||
\(754\) | 3.46924e12 | 0.390898 | ||||||||
\(755\) | 7.77231e10 | 0.00870541 | ||||||||
\(756\) | −4.78985e12 | −0.533303 | ||||||||
\(757\) | −3.65926e12 | −0.405007 | −0.202503 | − | 0.979282i | \(-0.564908\pi\) | ||||
−0.202503 | + | 0.979282i | \(0.564908\pi\) | |||||||
\(758\) | 7.15398e11 | 0.0787112 | ||||||||
\(759\) | 5.57086e10 | 0.00609305 | ||||||||
\(760\) | −1.13339e11 | −0.0123231 | ||||||||
\(761\) | −2.33882e12 | −0.252793 | −0.126396 | − | 0.991980i | \(-0.540341\pi\) | ||||
−0.126396 | + | 0.991980i | \(0.540341\pi\) | |||||||
\(762\) | −2.65551e11 | −0.0285332 | ||||||||
\(763\) | 8.45049e11 | 0.0902654 | ||||||||
\(764\) | −1.43896e13 | −1.52801 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.32775e11 | 0.0559132 | ||||||||
\(767\) | 1.08500e13 | 1.13201 | ||||||||
\(768\) | −5.05924e11 | −0.0524759 | ||||||||
\(769\) | 7.17500e12 | 0.739866 | 0.369933 | − | 0.929058i | \(-0.379381\pi\) | ||||
0.369933 | + | 0.929058i | \(0.379381\pi\) | |||||||
\(770\) | 2.20117e9 | 0.000225655 0 | ||||||||
\(771\) | 3.28634e12 | 0.334941 | ||||||||
\(772\) | −7.01628e12 | −0.710933 | ||||||||
\(773\) | 1.41219e13 | 1.42261 | 0.711303 | − | 0.702886i | \(-0.248106\pi\) | ||||
0.711303 | + | 0.702886i | \(0.248106\pi\) | |||||||
\(774\) | −2.84245e12 | −0.284681 | ||||||||
\(775\) | 1.25254e13 | 1.24719 | ||||||||
\(776\) | −2.52999e12 | −0.250462 | ||||||||
\(777\) | 5.48705e12 | 0.540062 | ||||||||
\(778\) | −3.35788e12 | −0.328592 | ||||||||
\(779\) | 3.59881e12 | 0.350139 | ||||||||
\(780\) | 7.55020e10 | 0.00730353 | ||||||||
\(781\) | 3.63077e10 | 0.00349196 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.42055e12 | 0.325214 | ||||||||
\(784\) | 4.76674e12 | 0.450608 | ||||||||
\(785\) | −8.77648e10 | −0.00824910 | ||||||||
\(786\) | −4.37529e11 | −0.0408889 | ||||||||
\(787\) | 5.29148e12 | 0.491689 | 0.245845 | − | 0.969309i | \(-0.420935\pi\) | ||||
0.245845 | + | 0.969309i | \(0.420935\pi\) | |||||||
\(788\) | 1.51062e13 | 1.39568 | ||||||||
\(789\) | 2.31050e12 | 0.212256 | ||||||||
\(790\) | 2.23414e10 | 0.00204075 | ||||||||
\(791\) | 2.08659e13 | 1.89515 | ||||||||
\(792\) | 1.29356e11 | 0.0116822 | ||||||||
\(793\) | 9.49317e10 | 0.00852475 | ||||||||
\(794\) | 5.48386e12 | 0.489659 | ||||||||
\(795\) | 1.17926e11 | 0.0104703 | ||||||||
\(796\) | −1.26116e13 | −1.11343 | ||||||||
\(797\) | 1.06101e13 | 0.931444 | 0.465722 | − | 0.884931i | \(-0.345795\pi\) | ||||
0.465722 | + | 0.884931i | \(0.345795\pi\) | |||||||
\(798\) | 9.97252e11 | 0.0870547 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 1.09640e13 | 0.946374 | ||||||||
\(801\) | −4.88573e12 | −0.419356 | ||||||||
\(802\) | 5.09954e10 | 0.00435257 | ||||||||
\(803\) | −1.73856e11 | −0.0147561 | ||||||||
\(804\) | 3.39724e12 | 0.286730 | ||||||||
\(805\) | −5.89872e11 | −0.0495081 | ||||||||
\(806\) | 8.44058e12 | 0.704473 | ||||||||
\(807\) | −3.24306e12 | −0.269168 | ||||||||
\(808\) | 1.40444e13 | 1.15918 | ||||||||
\(809\) | 8.09411e11 | 0.0664356 | 0.0332178 | − | 0.999448i | \(-0.489424\pi\) | ||||
0.0332178 | + | 0.999448i | \(0.489424\pi\) | |||||||
\(810\) | 9.97468e10 | 0.00814172 | ||||||||
\(811\) | −3.97455e11 | −0.0322622 | −0.0161311 | − | 0.999870i | \(-0.505135\pi\) | ||||
−0.0161311 | + | 0.999870i | \(0.505135\pi\) | |||||||
\(812\) | −9.74122e12 | −0.786341 | ||||||||
\(813\) | 4.69747e12 | 0.377100 | ||||||||
\(814\) | −1.39926e11 | −0.0111709 | ||||||||
\(815\) | 2.83014e11 | 0.0224698 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.63726e12 | −0.521182 | ||||||||
\(818\) | −5.51253e12 | −0.430488 | ||||||||
\(819\) | 2.33433e13 | 1.81294 | ||||||||
\(820\) | 1.40669e11 | 0.0108652 | ||||||||
\(821\) | −1.51125e13 | −1.16089 | −0.580447 | − | 0.814298i | \(-0.697122\pi\) | ||||
−0.580447 | + | 0.814298i | \(0.697122\pi\) | |||||||
\(822\) | 6.75349e11 | 0.0515947 | ||||||||
\(823\) | −2.13194e13 | −1.61986 | −0.809928 | − | 0.586530i | \(-0.800494\pi\) | ||||
−0.809928 | + | 0.586530i | \(0.800494\pi\) | |||||||
\(824\) | 1.69284e12 | 0.127921 | ||||||||
\(825\) | 5.49020e10 | 0.00412615 | ||||||||
\(826\) | 5.60164e12 | 0.418702 | ||||||||
\(827\) | −9.73433e12 | −0.723655 | −0.361827 | − | 0.932245i | \(-0.617847\pi\) | ||||
−0.361827 | + | 0.932245i | \(0.617847\pi\) | |||||||
\(828\) | −1.58732e13 | −1.17362 | ||||||||
\(829\) | 1.44405e13 | 1.06191 | 0.530954 | − | 0.847400i | \(-0.321834\pi\) | ||||
0.530954 | + | 0.847400i | \(0.321834\pi\) | |||||||
\(830\) | −1.23586e11 | −0.00903896 | ||||||||
\(831\) | 2.78743e12 | 0.202768 | ||||||||
\(832\) | −3.66240e12 | −0.264979 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.40104e12 | −0.171851 | ||||||||
\(835\) | 5.26019e11 | 0.0374466 | ||||||||
\(836\) | 1.38311e11 | 0.00979327 | ||||||||
\(837\) | 8.32212e12 | 0.586097 | ||||||||
\(838\) | −4.59635e12 | −0.321970 | ||||||||
\(839\) | −2.39510e13 | −1.66877 | −0.834383 | − | 0.551185i | \(-0.814176\pi\) | ||||
−0.834383 | + | 0.551185i | \(0.814176\pi\) | |||||||
\(840\) | 8.51278e10 | 0.00589949 | ||||||||
\(841\) | −7.55069e12 | −0.520481 | ||||||||
\(842\) | 1.68561e12 | 0.115572 | ||||||||
\(843\) | −5.76340e12 | −0.393057 | ||||||||
\(844\) | 1.60178e13 | 1.08658 | ||||||||
\(845\) | −3.88955e11 | −0.0262448 | ||||||||
\(846\) | 2.41757e12 | 0.162260 | ||||||||
\(847\) | 2.01308e13 | 1.34396 | ||||||||
\(848\) | −1.45795e13 | −0.968190 | ||||||||
\(849\) | −2.85472e12 | −0.188573 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.74975e13 | 2.45087 | ||||||||
\(852\) | 6.42970e11 | 0.0418035 | ||||||||
\(853\) | 8.01694e12 | 0.518487 | 0.259244 | − | 0.965812i | \(-0.416527\pi\) | ||||
0.259244 | + | 0.965812i | \(0.416527\pi\) | |||||||
\(854\) | 4.90115e10 | 0.00315310 | ||||||||
\(855\) | 2.49376e11 | 0.0159590 | ||||||||
\(856\) | 5.83232e12 | 0.371287 | ||||||||
\(857\) | −4.38404e12 | −0.277626 | −0.138813 | − | 0.990319i | \(-0.544329\pi\) | ||||
−0.138813 | + | 0.990319i | \(0.544329\pi\) | |||||||
\(858\) | 3.69972e10 | 0.00233065 | ||||||||
\(859\) | −3.16658e13 | −1.98436 | −0.992181 | − | 0.124805i | \(-0.960169\pi\) | ||||
−0.992181 | + | 0.124805i | \(0.960169\pi\) | |||||||
\(860\) | −2.59435e11 | −0.0161728 | ||||||||
\(861\) | −2.70303e12 | −0.167624 | ||||||||
\(862\) | −8.93452e12 | −0.551174 | ||||||||
\(863\) | −1.32337e13 | −0.812141 | −0.406071 | − | 0.913842i | \(-0.633101\pi\) | ||||
−0.406071 | + | 0.913842i | \(0.633101\pi\) | |||||||
\(864\) | 7.28468e12 | 0.444732 | ||||||||
\(865\) | 7.12485e11 | 0.0432716 | ||||||||
\(866\) | 6.20500e12 | 0.374896 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.37001e13 | −1.41714 | ||||||||
\(869\) | −5.95407e10 | −0.00354181 | ||||||||
\(870\) | −2.78368e10 | −0.00164734 | ||||||||
\(871\) | −3.41417e13 | −2.01004 | ||||||||
\(872\) | −8.33411e11 | −0.0488129 | ||||||||
\(873\) | 5.56665e12 | 0.324362 | ||||||||
\(874\) | 6.81505e12 | 0.395064 | ||||||||
\(875\) | −1.16303e12 | −0.0670738 | ||||||||
\(876\) | −3.07881e12 | −0.176650 | ||||||||
\(877\) | −6.75147e12 | −0.385390 | −0.192695 | − | 0.981259i | \(-0.561723\pi\) | ||||
−0.192695 | + | 0.981259i | \(0.561723\pi\) | |||||||
\(878\) | −7.76208e12 | −0.440811 | ||||||||
\(879\) | −4.09099e12 | −0.231142 | ||||||||
\(880\) | 4.22943e9 | 0.000237744 0 | ||||||||
\(881\) | 2.18093e13 | 1.21969 | 0.609846 | − | 0.792520i | \(-0.291231\pi\) | ||||
0.609846 | + | 0.792520i | \(0.291231\pi\) | |||||||
\(882\) | 5.38324e12 | 0.299527 | ||||||||
\(883\) | 5.52011e12 | 0.305580 | 0.152790 | − | 0.988259i | \(-0.451174\pi\) | ||||
0.152790 | + | 0.988259i | \(0.451174\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.70590e10 | −0.00477055 | ||||||||
\(886\) | 6.78249e12 | 0.369775 | ||||||||
\(887\) | −2.50221e13 | −1.35727 | −0.678636 | − | 0.734475i | \(-0.737429\pi\) | ||||
−0.678636 | + | 0.734475i | \(0.737429\pi\) | |||||||
\(888\) | −5.41148e12 | −0.292050 | ||||||||
\(889\) | −7.49354e12 | −0.402373 | ||||||||
\(890\) | 8.19923e10 | 0.00438044 | ||||||||
\(891\) | −2.65829e11 | −0.0141303 | ||||||||
\(892\) | −2.07469e13 | −1.09726 | ||||||||
\(893\) | 5.64513e12 | 0.297059 | ||||||||
\(894\) | −8.20229e11 | −0.0429454 | ||||||||
\(895\) | 2.46622e11 | 0.0128478 | ||||||||
\(896\) | −2.64510e13 | −1.37106 | ||||||||
\(897\) | −9.91458e12 | −0.511338 | ||||||||
\(898\) | −5.24368e12 | −0.269087 | ||||||||
\(899\) | 1.69249e13 | 0.864185 | ||||||||
\(900\) | −1.56434e13 | −0.794767 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 6.89302e10 | 0.00346721 | ||||||||
\(903\) | 4.98518e12 | 0.249509 | ||||||||
\(904\) | −2.05785e13 | −1.02484 | ||||||||
\(905\) | −2.64884e11 | −0.0131262 | ||||||||
\(906\) | 6.74455e11 | 0.0332565 | ||||||||
\(907\) | 1.30935e13 | 0.642427 | 0.321214 | − | 0.947007i | \(-0.395909\pi\) | ||||
0.321214 | + | 0.947007i | \(0.395909\pi\) | |||||||
\(908\) | −4.80110e12 | −0.234398 | ||||||||
\(909\) | −3.09014e13 | −1.50121 | ||||||||
\(910\) | −3.91746e11 | −0.0189373 | ||||||||
\(911\) | 2.89525e13 | 1.39269 | 0.696343 | − | 0.717709i | \(-0.254809\pi\) | ||||
0.696343 | + | 0.717709i | \(0.254809\pi\) | |||||||
\(912\) | 1.91617e12 | 0.0917186 | ||||||||
\(913\) | 3.29362e11 | 0.0156875 | ||||||||
\(914\) | −6.91007e12 | −0.327510 | ||||||||
\(915\) | −7.61721e8 | −3.59254e−5 0 | ||||||||
\(916\) | −1.47788e13 | −0.693602 | ||||||||
\(917\) | −1.23465e13 | −0.576612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.28385e13 | 0.593738 | 0.296869 | − | 0.954918i | \(-0.404057\pi\) | ||||
0.296869 | + | 0.954918i | \(0.404057\pi\) | |||||||
\(920\) | 5.81748e11 | 0.0267726 | ||||||||
\(921\) | −2.97252e12 | −0.136131 | ||||||||
\(922\) | 1.12503e13 | 0.512714 | ||||||||
\(923\) | −6.46176e12 | −0.293051 | ||||||||
\(924\) | −1.03884e11 | −0.00468839 | ||||||||
\(925\) | 3.69546e13 | 1.65970 | ||||||||
\(926\) | 1.60960e13 | 0.719395 | ||||||||
\(927\) | −3.72469e12 | −0.165665 | ||||||||
\(928\) | 1.48150e13 | 0.655747 | ||||||||
\(929\) | 3.18274e13 | 1.40194 | 0.700972 | − | 0.713189i | \(-0.252750\pi\) | ||||
0.700972 | + | 0.713189i | \(0.252750\pi\) | |||||||
\(930\) | −6.77262e10 | −0.00296882 | ||||||||
\(931\) | 1.25701e13 | 0.548361 | ||||||||
\(932\) | −3.46841e13 | −1.50577 | ||||||||
\(933\) | 4.21470e11 | 0.0182095 | ||||||||
\(934\) | −1.23708e13 | −0.531908 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.30218e13 | −0.980386 | ||||||||
\(937\) | −4.48583e13 | −1.90114 | −0.950570 | − | 0.310509i | \(-0.899501\pi\) | ||||
−0.950570 | + | 0.310509i | \(0.899501\pi\) | |||||||
\(938\) | −1.76268e13 | −0.743463 | ||||||||
\(939\) | 8.10468e10 | 0.00340205 | ||||||||
\(940\) | 2.20655e11 | 0.00921804 | ||||||||
\(941\) | −4.15108e13 | −1.72587 | −0.862934 | − | 0.505317i | \(-0.831376\pi\) | ||||
−0.862934 | + | 0.505317i | \(0.831376\pi\) | |||||||
\(942\) | −7.61593e11 | −0.0315133 | ||||||||
\(943\) | −1.84720e13 | −0.760697 | ||||||||
\(944\) | 1.07633e13 | 0.441134 | ||||||||
\(945\) | −3.86248e11 | −0.0157552 | ||||||||
\(946\) | −1.27128e11 | −0.00516095 | ||||||||
\(947\) | −3.14548e12 | −0.127090 | −0.0635451 | − | 0.997979i | \(-0.520241\pi\) | ||||
−0.0635451 | + | 0.997979i | \(0.520241\pi\) | |||||||
\(948\) | −1.05440e12 | −0.0424002 | ||||||||
\(949\) | 3.09416e13 | 1.23835 | ||||||||
\(950\) | 6.71637e12 | 0.267534 | ||||||||
\(951\) | 2.22186e12 | 0.0880854 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.48692e12 | −0.294026 | −0.147013 | − | 0.989135i | \(-0.546966\pi\) | ||||
−0.147013 | + | 0.989135i | \(0.546966\pi\) | |||||||
\(954\) | −1.64651e13 | −0.643572 | ||||||||
\(955\) | −1.16036e12 | −0.0451416 | ||||||||
\(956\) | −2.02820e13 | −0.785326 | ||||||||
\(957\) | 7.41861e10 | 0.00285903 | ||||||||
\(958\) | −1.87684e12 | −0.0719916 | ||||||||
\(959\) | 1.90576e13 | 0.727585 | ||||||||
\(960\) | 2.93867e10 | 0.00111668 | ||||||||
\(961\) | 1.47381e13 | 0.557427 | ||||||||
\(962\) | 2.49029e13 | 0.937479 | ||||||||
\(963\) | −1.28327e13 | −0.480837 | ||||||||
\(964\) | 1.03029e12 | 0.0384248 | ||||||||
\(965\) | −5.65786e11 | −0.0210029 | ||||||||
\(966\) | −5.11871e12 | −0.189131 | ||||||||
\(967\) | 2.43528e13 | 0.895633 | 0.447817 | − | 0.894125i | \(-0.352202\pi\) | ||||
0.447817 | + | 0.894125i | \(0.352202\pi\) | |||||||
\(968\) | −1.98535e13 | −0.726773 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.34195e10 | −0.00338817 | ||||||||
\(971\) | −1.44805e12 | −0.0522753 | −0.0261376 | − | 0.999658i | \(-0.508321\pi\) | ||||
−0.0261376 | + | 0.999658i | \(0.508321\pi\) | |||||||
\(972\) | −1.57473e13 | −0.565859 | ||||||||
\(973\) | −6.77544e13 | −2.42343 | ||||||||
\(974\) | −9.83809e12 | −0.350264 | ||||||||
\(975\) | −9.77102e12 | −0.346273 | ||||||||
\(976\) | 9.41731e10 | 0.00332202 | ||||||||
\(977\) | 2.93210e13 | 1.02956 | 0.514782 | − | 0.857321i | \(-0.327873\pi\) | ||||
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(978\) | 2.45590e12 | 0.0858393 | ||||||||
\(979\) | −2.18512e11 | −0.00760246 | ||||||||
\(980\) | 4.91337e11 | 0.0170162 | ||||||||
\(981\) | 1.83372e12 | 0.0632155 | ||||||||
\(982\) | −1.45778e13 | −0.500253 | ||||||||
\(983\) | 3.94450e13 | 1.34741 | 0.673706 | − | 0.738999i | \(-0.264701\pi\) | ||||
0.673706 | + | 0.738999i | \(0.264701\pi\) | |||||||
\(984\) | 2.66580e12 | 0.0906462 | ||||||||
\(985\) | 1.21815e12 | 0.0412323 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.24000e12 | −0.142213 | ||||||||
\(988\) | −2.46155e13 | −0.821867 | ||||||||
\(989\) | 3.40678e13 | 1.13230 | ||||||||
\(990\) | 4.77645e9 | 0.000158033 0 | ||||||||
\(991\) | −5.47857e13 | −1.80441 | −0.902207 | − | 0.431304i | \(-0.858054\pi\) | ||||
−0.902207 | + | 0.431304i | \(0.858054\pi\) | |||||||
\(992\) | 3.60446e13 | 1.18178 | ||||||||
\(993\) | 9.31620e11 | 0.0304066 | ||||||||
\(994\) | −3.33608e12 | −0.108392 | ||||||||
\(995\) | −1.01699e12 | −0.0328936 | ||||||||
\(996\) | 5.83263e12 | 0.187801 | ||||||||
\(997\) | 4.35512e12 | 0.139596 | 0.0697979 | − | 0.997561i | \(-0.477765\pi\) | ||||
0.0697979 | + | 0.997561i | \(0.477765\pi\) | |||||||
\(998\) | 3.93577e12 | 0.125586 | ||||||||
\(999\) | 2.45534e13 | 0.779950 |
(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 | 289.10.a.i.1.20 | 52 | ||
17.10 | odd | 16 | 17.10.d.a.15.9 | yes | 52 | ||
17.12 | odd | 16 | 17.10.d.a.8.9 | ✓ | 52 | ||
17.16 | even | 2 | inner | 289.10.a.i.1.19 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.d.a.8.9 | ✓ | 52 | 17.12 | odd | 16 | ||
17.10.d.a.15.9 | yes | 52 | 17.10 | odd | 16 | ||
289.10.a.i.1.19 | 52 | 17.16 | even | 2 | inner | ||
289.10.a.i.1.20 | 52 | 1.1 | even | 1 | trivial |