Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,100,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 100, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 100);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 100 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(62.0676682981\) |
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: | \( x^{8} - x^{7} + \cdots + 23\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{109}\cdot 3^{44}\cdot 5^{13}\cdot 7^{9}\cdot 11^{3}\cdot 13\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.10181e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53931e15 | −1.93349 | −0.966744 | − | 0.255744i | \(-0.917680\pi\) | ||||
−0.966744 | + | 0.255744i | \(0.917680\pi\) | |||||||
\(3\) | 1.09471e23 | 0.264118 | 0.132059 | − | 0.991242i | \(-0.457841\pi\) | ||||
0.132059 | + | 0.991242i | \(0.457841\pi\) | |||||||
\(4\) | 1.73565e30 | 2.73838 | ||||||||
\(5\) | −1.42424e34 | −0.358565 | −0.179282 | − | 0.983798i | \(-0.557378\pi\) | ||||
−0.179282 | + | 0.983798i | \(0.557378\pi\) | |||||||
\(6\) | −1.68510e38 | −0.510669 | ||||||||
\(7\) | −4.25157e41 | −0.625455 | −0.312728 | − | 0.949843i | \(-0.601243\pi\) | ||||
−0.312728 | + | 0.949843i | \(0.601243\pi\) | |||||||
\(8\) | −1.69606e45 | −3.36114 | ||||||||
\(9\) | −1.59809e47 | −0.930242 | ||||||||
\(10\) | 2.19235e49 | 0.693281 | ||||||||
\(11\) | −5.04571e51 | −1.42556 | −0.712778 | − | 0.701390i | \(-0.752563\pi\) | ||||
−0.712778 | + | 0.701390i | \(0.752563\pi\) | |||||||
\(12\) | 1.90004e53 | 0.723255 | ||||||||
\(13\) | −1.33313e55 | −0.965334 | −0.482667 | − | 0.875804i | \(-0.660332\pi\) | ||||
−0.482667 | + | 0.875804i | \(0.660332\pi\) | |||||||
\(14\) | 6.54449e56 | 1.20931 | ||||||||
\(15\) | −1.55913e57 | −0.0947034 | ||||||||
\(16\) | 1.51066e60 | 3.76034 | ||||||||
\(17\) | 8.54293e60 | 1.05776 | 0.528878 | − | 0.848698i | \(-0.322613\pi\) | ||||
0.528878 | + | 0.848698i | \(0.322613\pi\) | |||||||
\(18\) | 2.45995e62 | 1.79861 | ||||||||
\(19\) | −3.57926e63 | −1.80090 | −0.900451 | − | 0.434957i | \(-0.856763\pi\) | ||||
−0.900451 | + | 0.434957i | \(0.856763\pi\) | |||||||
\(20\) | −2.47199e64 | −0.981887 | ||||||||
\(21\) | −4.65425e64 | −0.165194 | ||||||||
\(22\) | 7.76692e66 | 2.75630 | ||||||||
\(23\) | −1.32632e67 | −0.521340 | −0.260670 | − | 0.965428i | \(-0.583943\pi\) | ||||
−0.260670 | + | 0.965428i | \(0.583943\pi\) | |||||||
\(24\) | −1.85670e68 | −0.887737 | ||||||||
\(25\) | −1.37488e69 | −0.871431 | ||||||||
\(26\) | 2.05211e70 | 1.86646 | ||||||||
\(27\) | −3.63008e70 | −0.509811 | ||||||||
\(28\) | −7.37926e71 | −1.71273 | ||||||||
\(29\) | −1.57811e71 | −0.0644817 | −0.0322409 | − | 0.999480i | \(-0.510264\pi\) | ||||
−0.0322409 | + | 0.999480i | \(0.510264\pi\) | |||||||
\(30\) | 2.39999e72 | 0.183108 | ||||||||
\(31\) | −3.89706e73 | −0.586588 | −0.293294 | − | 0.956022i | \(-0.594752\pi\) | ||||
−0.293294 | + | 0.956022i | \(0.594752\pi\) | |||||||
\(32\) | −1.25037e75 | −3.90944 | ||||||||
\(33\) | −5.52360e74 | −0.376515 | ||||||||
\(34\) | −1.31502e76 | −2.04516 | ||||||||
\(35\) | 6.05525e75 | 0.224266 | ||||||||
\(36\) | −2.77372e77 | −2.54735 | ||||||||
\(37\) | −1.80202e77 | −0.426357 | −0.213179 | − | 0.977013i | \(-0.568382\pi\) | ||||
−0.213179 | + | 0.977013i | \(0.568382\pi\) | |||||||
\(38\) | 5.50960e78 | 3.48202 | ||||||||
\(39\) | −1.45940e78 | −0.254962 | ||||||||
\(40\) | 2.41559e79 | 1.20519 | ||||||||
\(41\) | 2.13003e79 | 0.313029 | 0.156514 | − | 0.987676i | \(-0.449974\pi\) | ||||
0.156514 | + | 0.987676i | \(0.449974\pi\) | |||||||
\(42\) | 7.16433e79 | 0.319401 | ||||||||
\(43\) | 8.43003e79 | 0.117257 | 0.0586287 | − | 0.998280i | \(-0.481327\pi\) | ||||
0.0586287 | + | 0.998280i | \(0.481327\pi\) | |||||||
\(44\) | −8.75761e81 | −3.90371 | ||||||||
\(45\) | 2.27606e81 | 0.333552 | ||||||||
\(46\) | 2.04162e82 | 1.00800 | ||||||||
\(47\) | 2.19872e82 | 0.374391 | 0.187195 | − | 0.982323i | \(-0.440060\pi\) | ||||
0.187195 | + | 0.982323i | \(0.440060\pi\) | |||||||
\(48\) | 1.65374e83 | 0.993174 | ||||||||
\(49\) | −2.81310e83 | −0.608805 | ||||||||
\(50\) | 2.11636e84 | 1.68490 | ||||||||
\(51\) | 9.35205e83 | 0.279372 | ||||||||
\(52\) | −2.31386e85 | −2.64345 | ||||||||
\(53\) | −2.60808e85 | −1.16056 | −0.580278 | − | 0.814418i | \(-0.697056\pi\) | ||||
−0.580278 | + | 0.814418i | \(0.697056\pi\) | |||||||
\(54\) | 5.58782e85 | 0.985715 | ||||||||
\(55\) | 7.18630e85 | 0.511154 | ||||||||
\(56\) | 7.21091e86 | 2.10224 | ||||||||
\(57\) | −3.91826e86 | −0.475651 | ||||||||
\(58\) | 2.42920e86 | 0.124675 | ||||||||
\(59\) | 3.91766e87 | 0.862684 | 0.431342 | − | 0.902188i | \(-0.358040\pi\) | ||||
0.431342 | + | 0.902188i | \(0.358040\pi\) | |||||||
\(60\) | −2.70611e87 | −0.259334 | ||||||||
\(61\) | −3.67456e88 | −1.55374 | −0.776869 | − | 0.629662i | \(-0.783193\pi\) | ||||
−0.776869 | + | 0.629662i | \(0.783193\pi\) | |||||||
\(62\) | 5.99879e88 | 1.13416 | ||||||||
\(63\) | 6.79437e88 | 0.581825 | ||||||||
\(64\) | 9.67216e89 | 3.79852 | ||||||||
\(65\) | 1.89870e89 | 0.346135 | ||||||||
\(66\) | 8.50254e89 | 0.727987 | ||||||||
\(67\) | −3.53225e90 | −1.43664 | −0.718322 | − | 0.695711i | \(-0.755089\pi\) | ||||
−0.718322 | + | 0.695711i | \(0.755089\pi\) | |||||||
\(68\) | 1.48276e91 | 2.89654 | ||||||||
\(69\) | −1.45194e90 | −0.137695 | ||||||||
\(70\) | −9.32092e90 | −0.433617 | ||||||||
\(71\) | 1.43616e91 | 0.331065 | 0.165533 | − | 0.986204i | \(-0.447066\pi\) | ||||
0.165533 | + | 0.986204i | \(0.447066\pi\) | |||||||
\(72\) | 2.71045e92 | 3.12667 | ||||||||
\(73\) | −5.96639e91 | −0.347720 | −0.173860 | − | 0.984770i | \(-0.555624\pi\) | ||||
−0.173860 | + | 0.984770i | \(0.555624\pi\) | |||||||
\(74\) | 2.77387e92 | 0.824357 | ||||||||
\(75\) | −1.50509e92 | −0.230161 | ||||||||
\(76\) | −6.21236e93 | −4.93155 | ||||||||
\(77\) | 2.14522e93 | 0.891622 | ||||||||
\(78\) | 2.24647e93 | 0.492966 | ||||||||
\(79\) | −1.81922e93 | −0.212493 | −0.106247 | − | 0.994340i | \(-0.533883\pi\) | ||||
−0.106247 | + | 0.994340i | \(0.533883\pi\) | |||||||
\(80\) | −2.15154e94 | −1.34833 | ||||||||
\(81\) | 2.34800e94 | 0.795591 | ||||||||
\(82\) | −3.27878e94 | −0.605238 | ||||||||
\(83\) | −6.69942e93 | −0.0678690 | −0.0339345 | − | 0.999424i | \(-0.510804\pi\) | ||||
−0.0339345 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(84\) | −8.07816e94 | −0.452364 | ||||||||
\(85\) | −1.21672e95 | −0.379274 | ||||||||
\(86\) | −1.29764e95 | −0.226716 | ||||||||
\(87\) | −1.72758e94 | −0.0170308 | ||||||||
\(88\) | 8.55782e96 | 4.79149 | ||||||||
\(89\) | −5.60112e95 | −0.179254 | −0.0896271 | − | 0.995975i | \(-0.528568\pi\) | ||||
−0.0896271 | + | 0.995975i | \(0.528568\pi\) | |||||||
\(90\) | −3.50356e96 | −0.644919 | ||||||||
\(91\) | 5.66791e96 | 0.603774 | ||||||||
\(92\) | −2.30203e97 | −1.42763 | ||||||||
\(93\) | −4.26616e96 | −0.154929 | ||||||||
\(94\) | −3.38451e97 | −0.723881 | ||||||||
\(95\) | 5.09772e97 | 0.645740 | ||||||||
\(96\) | −1.36880e98 | −1.03255 | ||||||||
\(97\) | −2.13029e98 | −0.962139 | −0.481070 | − | 0.876682i | \(-0.659752\pi\) | ||||
−0.481070 | + | 0.876682i | \(0.659752\pi\) | |||||||
\(98\) | 4.33023e98 | 1.17712 | ||||||||
\(99\) | 8.06348e98 | 1.32611 | ||||||||
\(100\) | −2.38631e99 | −2.38631 | ||||||||
\(101\) | −1.55937e99 | −0.952888 | −0.476444 | − | 0.879205i | \(-0.658075\pi\) | ||||
−0.476444 | + | 0.879205i | \(0.658075\pi\) | |||||||
\(102\) | −1.43957e99 | −0.540163 | ||||||||
\(103\) | 2.08933e99 | 0.483686 | 0.241843 | − | 0.970315i | \(-0.422248\pi\) | ||||
0.241843 | + | 0.970315i | \(0.422248\pi\) | |||||||
\(104\) | 2.26107e100 | 3.24462 | ||||||||
\(105\) | 6.62876e98 | 0.0592328 | ||||||||
\(106\) | 4.01465e100 | 2.24392 | ||||||||
\(107\) | −4.67376e100 | −1.64123 | −0.820615 | − | 0.571481i | \(-0.806369\pi\) | ||||
−0.820615 | + | 0.571481i | \(0.806369\pi\) | |||||||
\(108\) | −6.30056e100 | −1.39606 | ||||||||
\(109\) | 9.73243e100 | 1.36650 | 0.683250 | − | 0.730185i | \(-0.260566\pi\) | ||||
0.683250 | + | 0.730185i | \(0.260566\pi\) | |||||||
\(110\) | −1.10620e101 | −0.988311 | ||||||||
\(111\) | −1.97269e100 | −0.112609 | ||||||||
\(112\) | −6.42268e101 | −2.35193 | ||||||||
\(113\) | 2.10873e101 | 0.497323 | 0.248661 | − | 0.968591i | \(-0.420009\pi\) | ||||
0.248661 | + | 0.968591i | \(0.420009\pi\) | |||||||
\(114\) | 6.03142e101 | 0.919665 | ||||||||
\(115\) | 1.88900e101 | 0.186934 | ||||||||
\(116\) | −2.73905e101 | −0.176575 | ||||||||
\(117\) | 2.13046e102 | 0.897994 | ||||||||
\(118\) | −6.03049e102 | −1.66799 | ||||||||
\(119\) | −3.63209e102 | −0.661579 | ||||||||
\(120\) | 2.64438e102 | 0.318311 | ||||||||
\(121\) | 1.29314e103 | 1.03221 | ||||||||
\(122\) | 5.65629e103 | 3.00414 | ||||||||
\(123\) | 2.33177e102 | 0.0826765 | ||||||||
\(124\) | −6.76395e103 | −1.60630 | ||||||||
\(125\) | 4.20521e103 | 0.671030 | ||||||||
\(126\) | −1.04587e104 | −1.12495 | ||||||||
\(127\) | 1.76385e104 | 1.28285 | 0.641426 | − | 0.767185i | \(-0.278343\pi\) | ||||
0.641426 | + | 0.767185i | \(0.278343\pi\) | |||||||
\(128\) | −6.96330e104 | −3.43496 | ||||||||
\(129\) | 9.22846e102 | 0.0309698 | ||||||||
\(130\) | −2.92269e104 | −0.669248 | ||||||||
\(131\) | 8.92579e104 | 1.39868 | 0.699338 | − | 0.714791i | \(-0.253478\pi\) | ||||
0.699338 | + | 0.714791i | \(0.253478\pi\) | |||||||
\(132\) | −9.58706e104 | −1.03104 | ||||||||
\(133\) | 1.52175e105 | 1.12638 | ||||||||
\(134\) | 5.43724e105 | 2.77773 | ||||||||
\(135\) | 5.17010e104 | 0.182800 | ||||||||
\(136\) | −1.44893e106 | −3.55526 | ||||||||
\(137\) | 3.33189e105 | 0.568883 | 0.284441 | − | 0.958693i | \(-0.408192\pi\) | ||||
0.284441 | + | 0.958693i | \(0.408192\pi\) | |||||||
\(138\) | 2.23499e105 | 0.266232 | ||||||||
\(139\) | 1.60870e106 | 1.34043 | 0.670213 | − | 0.742169i | \(-0.266203\pi\) | ||||
0.670213 | + | 0.742169i | \(0.266203\pi\) | |||||||
\(140\) | 1.05098e106 | 0.614126 | ||||||||
\(141\) | 2.40696e105 | 0.0988834 | ||||||||
\(142\) | −2.21069e106 | −0.640111 | ||||||||
\(143\) | 6.72660e106 | 1.37614 | ||||||||
\(144\) | −2.41416e107 | −3.49803 | ||||||||
\(145\) | 2.24761e105 | 0.0231209 | ||||||||
\(146\) | 9.18413e106 | 0.672313 | ||||||||
\(147\) | −3.07953e106 | −0.160796 | ||||||||
\(148\) | −3.12768e107 | −1.16753 | ||||||||
\(149\) | −7.50937e106 | −0.200855 | −0.100428 | − | 0.994944i | \(-0.532021\pi\) | ||||
−0.100428 | + | 0.994944i | \(0.532021\pi\) | |||||||
\(150\) | 2.31681e107 | 0.445013 | ||||||||
\(151\) | −4.40125e107 | −0.608439 | −0.304219 | − | 0.952602i | \(-0.598396\pi\) | ||||
−0.304219 | + | 0.952602i | \(0.598396\pi\) | |||||||
\(152\) | 6.07063e108 | 6.05308 | ||||||||
\(153\) | −1.36523e108 | −0.983968 | ||||||||
\(154\) | −3.30216e108 | −1.72394 | ||||||||
\(155\) | 5.55035e107 | 0.210330 | ||||||||
\(156\) | −2.53301e108 | −0.698183 | ||||||||
\(157\) | −7.75028e108 | −1.55699 | −0.778493 | − | 0.627653i | \(-0.784016\pi\) | ||||
−0.778493 | + | 0.627653i | \(0.784016\pi\) | |||||||
\(158\) | 2.80035e108 | 0.410854 | ||||||||
\(159\) | −2.85510e108 | −0.306524 | ||||||||
\(160\) | 1.78083e109 | 1.40179 | ||||||||
\(161\) | 5.63895e108 | 0.326075 | ||||||||
\(162\) | −3.61431e109 | −1.53827 | ||||||||
\(163\) | −2.45335e109 | −0.769968 | −0.384984 | − | 0.922923i | \(-0.625793\pi\) | ||||
−0.384984 | + | 0.922923i | \(0.625793\pi\) | |||||||
\(164\) | 3.69699e109 | 0.857192 | ||||||||
\(165\) | 7.86693e108 | 0.135005 | ||||||||
\(166\) | 1.03125e109 | 0.131224 | ||||||||
\(167\) | −9.13307e109 | −0.863280 | −0.431640 | − | 0.902046i | \(-0.642065\pi\) | ||||
−0.431640 | + | 0.902046i | \(0.642065\pi\) | |||||||
\(168\) | 7.89387e109 | 0.555240 | ||||||||
\(169\) | −1.29936e109 | −0.0681300 | ||||||||
\(170\) | 1.87291e110 | 0.733322 | ||||||||
\(171\) | 5.71997e110 | 1.67527 | ||||||||
\(172\) | 1.46316e110 | 0.321096 | ||||||||
\(173\) | −7.23256e108 | −0.0119127 | −0.00595635 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595635 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(174\) | 2.65928e109 | 0.0329288 | ||||||||
\(175\) | 5.84538e110 | 0.545041 | ||||||||
\(176\) | −7.62235e111 | −5.36058 | ||||||||
\(177\) | 4.28871e110 | 0.227850 | ||||||||
\(178\) | 8.62186e110 | 0.346586 | ||||||||
\(179\) | 1.89280e111 | 0.576607 | 0.288303 | − | 0.957539i | \(-0.406909\pi\) | ||||
0.288303 | + | 0.957539i | \(0.406909\pi\) | |||||||
\(180\) | 3.95045e111 | 0.913392 | ||||||||
\(181\) | 7.66036e111 | 1.34636 | 0.673178 | − | 0.739481i | \(-0.264929\pi\) | ||||
0.673178 | + | 0.739481i | \(0.264929\pi\) | |||||||
\(182\) | −8.72468e111 | −1.16739 | ||||||||
\(183\) | −4.02258e111 | −0.410370 | ||||||||
\(184\) | 2.24952e112 | 1.75229 | ||||||||
\(185\) | 2.56651e111 | 0.152877 | ||||||||
\(186\) | 6.56695e111 | 0.299553 | ||||||||
\(187\) | −4.31051e112 | −1.50789 | ||||||||
\(188\) | 3.81621e112 | 1.02522 | ||||||||
\(189\) | 1.54335e112 | 0.318864 | ||||||||
\(190\) | −7.84699e112 | −1.24853 | ||||||||
\(191\) | −6.08896e112 | −0.747121 | −0.373561 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373561 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(192\) | 1.05882e113 | 1.00326 | ||||||||
\(193\) | −7.56005e112 | −0.553908 | −0.276954 | − | 0.960883i | \(-0.589325\pi\) | ||||
−0.276954 | + | 0.960883i | \(0.589325\pi\) | |||||||
\(194\) | 3.27918e113 | 1.86029 | ||||||||
\(195\) | 2.07853e112 | 0.0914204 | ||||||||
\(196\) | −4.88256e113 | −1.66714 | ||||||||
\(197\) | −4.51135e113 | −1.19737 | −0.598685 | − | 0.800984i | \(-0.704310\pi\) | ||||
−0.598685 | + | 0.800984i | \(0.704310\pi\) | |||||||
\(198\) | −1.24122e114 | −2.56402 | ||||||||
\(199\) | 5.34960e113 | 0.861181 | 0.430590 | − | 0.902547i | \(-0.358305\pi\) | ||||
0.430590 | + | 0.902547i | \(0.358305\pi\) | |||||||
\(200\) | 2.33187e114 | 2.92900 | ||||||||
\(201\) | −3.86680e113 | −0.379443 | ||||||||
\(202\) | 2.40036e114 | 1.84240 | ||||||||
\(203\) | 6.70945e112 | 0.0403304 | ||||||||
\(204\) | 1.62319e114 | 0.765027 | ||||||||
\(205\) | −3.03367e113 | −0.112241 | ||||||||
\(206\) | −3.21612e114 | −0.935201 | ||||||||
\(207\) | 2.11957e114 | 0.484972 | ||||||||
\(208\) | −2.01391e115 | −3.62999 | ||||||||
\(209\) | 1.80599e115 | 2.56729 | ||||||||
\(210\) | −1.02037e114 | −0.114526 | ||||||||
\(211\) | −6.81741e114 | −0.604836 | −0.302418 | − | 0.953175i | \(-0.597794\pi\) | ||||
−0.302418 | + | 0.953175i | \(0.597794\pi\) | |||||||
\(212\) | −4.52673e115 | −3.17804 | ||||||||
\(213\) | 1.57218e114 | 0.0874402 | ||||||||
\(214\) | 7.19438e115 | 3.17330 | ||||||||
\(215\) | −1.20064e114 | −0.0420444 | ||||||||
\(216\) | 6.15682e115 | 1.71355 | ||||||||
\(217\) | 1.65686e115 | 0.366885 | ||||||||
\(218\) | −1.49812e116 | −2.64211 | ||||||||
\(219\) | −6.53148e114 | −0.0918392 | ||||||||
\(220\) | 1.24729e116 | 1.39973 | ||||||||
\(221\) | −1.13889e116 | −1.02109 | ||||||||
\(222\) | 3.03659e115 | 0.217728 | ||||||||
\(223\) | −1.16918e116 | −0.671105 | −0.335553 | − | 0.942021i | \(-0.608923\pi\) | ||||
−0.335553 | + | 0.942021i | \(0.608923\pi\) | |||||||
\(224\) | 5.31604e116 | 2.44518 | ||||||||
\(225\) | 2.19717e116 | 0.810642 | ||||||||
\(226\) | −3.24599e116 | −0.961568 | ||||||||
\(227\) | −1.47452e116 | −0.351051 | −0.175526 | − | 0.984475i | \(-0.556162\pi\) | ||||
−0.175526 | + | 0.984475i | \(0.556162\pi\) | |||||||
\(228\) | −6.80075e116 | −1.30251 | ||||||||
\(229\) | −6.46968e116 | −0.997760 | −0.498880 | − | 0.866671i | \(-0.666255\pi\) | ||||
−0.498880 | + | 0.866671i | \(0.666255\pi\) | |||||||
\(230\) | −2.90776e116 | −0.361435 | ||||||||
\(231\) | 2.34840e116 | 0.235493 | ||||||||
\(232\) | 2.67657e116 | 0.216732 | ||||||||
\(233\) | 1.37974e117 | 0.902983 | 0.451492 | − | 0.892275i | \(-0.350892\pi\) | ||||
0.451492 | + | 0.892275i | \(0.350892\pi\) | |||||||
\(234\) | −3.27944e117 | −1.73626 | ||||||||
\(235\) | −3.13150e116 | −0.134243 | ||||||||
\(236\) | 6.79970e117 | 2.36236 | ||||||||
\(237\) | −1.99153e116 | −0.0561233 | ||||||||
\(238\) | 5.59091e117 | 1.27916 | ||||||||
\(239\) | 4.89334e117 | 0.909722 | 0.454861 | − | 0.890562i | \(-0.349689\pi\) | ||||
0.454861 | + | 0.890562i | \(0.349689\pi\) | |||||||
\(240\) | −2.35532e117 | −0.356117 | ||||||||
\(241\) | 6.47362e117 | 0.796717 | 0.398358 | − | 0.917230i | \(-0.369580\pi\) | ||||
0.398358 | + | 0.917230i | \(0.369580\pi\) | |||||||
\(242\) | −1.99054e118 | −1.99577 | ||||||||
\(243\) | 8.80659e117 | 0.719941 | ||||||||
\(244\) | −6.37776e118 | −4.25473 | ||||||||
\(245\) | 4.00652e117 | 0.218296 | ||||||||
\(246\) | −3.58932e117 | −0.159854 | ||||||||
\(247\) | 4.77163e118 | 1.73847 | ||||||||
\(248\) | 6.60964e118 | 1.97160 | ||||||||
\(249\) | −7.33393e116 | −0.0179254 | ||||||||
\(250\) | −6.47312e118 | −1.29743 | ||||||||
\(251\) | −6.92152e118 | −1.13855 | −0.569275 | − | 0.822147i | \(-0.692776\pi\) | ||||
−0.569275 | + | 0.822147i | \(0.692776\pi\) | |||||||
\(252\) | 1.17927e119 | 1.59326 | ||||||||
\(253\) | 6.69223e118 | 0.743199 | ||||||||
\(254\) | −2.71511e119 | −2.48038 | ||||||||
\(255\) | −1.33196e118 | −0.100173 | ||||||||
\(256\) | 4.58823e119 | 2.84293 | ||||||||
\(257\) | −1.47015e119 | −0.751057 | −0.375529 | − | 0.926811i | \(-0.622539\pi\) | ||||
−0.375529 | + | 0.926811i | \(0.622539\pi\) | |||||||
\(258\) | −1.42055e118 | −0.0598798 | ||||||||
\(259\) | 7.66141e118 | 0.266668 | ||||||||
\(260\) | 3.29549e119 | 0.947849 | ||||||||
\(261\) | 2.52196e118 | 0.0599836 | ||||||||
\(262\) | −1.37396e120 | −2.70433 | ||||||||
\(263\) | 6.72240e119 | 1.09576 | 0.547879 | − | 0.836558i | \(-0.315435\pi\) | ||||
0.547879 | + | 0.836558i | \(0.315435\pi\) | |||||||
\(264\) | 9.36834e119 | 1.26552 | ||||||||
\(265\) | 3.71454e119 | 0.416135 | ||||||||
\(266\) | −2.34244e120 | −2.17785 | ||||||||
\(267\) | −6.13161e118 | −0.0473442 | ||||||||
\(268\) | −6.13077e120 | −3.93408 | ||||||||
\(269\) | 3.58420e120 | 1.91273 | 0.956366 | − | 0.292171i | \(-0.0943777\pi\) | ||||
0.956366 | + | 0.292171i | \(0.0943777\pi\) | |||||||
\(270\) | −7.95839e119 | −0.353443 | ||||||||
\(271\) | 1.94223e120 | 0.718326 | 0.359163 | − | 0.933275i | \(-0.383062\pi\) | ||||
0.359163 | + | 0.933275i | \(0.383062\pi\) | |||||||
\(272\) | 1.29055e121 | 3.97752 | ||||||||
\(273\) | 6.20473e119 | 0.159467 | ||||||||
\(274\) | −5.12882e120 | −1.09993 | ||||||||
\(275\) | 6.93722e120 | 1.24227 | ||||||||
\(276\) | −2.52007e120 | −0.377061 | ||||||||
\(277\) | 3.85718e120 | 0.482527 | 0.241264 | − | 0.970460i | \(-0.422438\pi\) | ||||
0.241264 | + | 0.970460i | \(0.422438\pi\) | |||||||
\(278\) | −2.47629e121 | −2.59170 | ||||||||
\(279\) | 6.22784e120 | 0.545669 | ||||||||
\(280\) | −1.02701e121 | −0.753790 | ||||||||
\(281\) | 5.10363e120 | 0.313990 | 0.156995 | − | 0.987599i | \(-0.449819\pi\) | ||||
0.156995 | + | 0.987599i | \(0.449819\pi\) | |||||||
\(282\) | −3.70506e120 | −0.191190 | ||||||||
\(283\) | −1.19050e121 | −0.515587 | −0.257793 | − | 0.966200i | \(-0.582995\pi\) | ||||
−0.257793 | + | 0.966200i | \(0.582995\pi\) | |||||||
\(284\) | 2.49267e121 | 0.906582 | ||||||||
\(285\) | 5.58054e120 | 0.170552 | ||||||||
\(286\) | −1.03543e122 | −2.66075 | ||||||||
\(287\) | −9.05596e120 | −0.195786 | ||||||||
\(288\) | 1.99820e122 | 3.63673 | ||||||||
\(289\) | 7.75228e120 | 0.118846 | ||||||||
\(290\) | −3.45977e120 | −0.0447040 | ||||||||
\(291\) | −2.33206e121 | −0.254118 | ||||||||
\(292\) | −1.03556e122 | −0.952190 | ||||||||
\(293\) | −1.17765e122 | −0.914259 | −0.457130 | − | 0.889400i | \(-0.651122\pi\) | ||||
−0.457130 | + | 0.889400i | \(0.651122\pi\) | |||||||
\(294\) | 4.74036e121 | 0.310898 | ||||||||
\(295\) | −5.57968e121 | −0.309328 | ||||||||
\(296\) | 3.05633e122 | 1.43305 | ||||||||
\(297\) | 1.83163e122 | 0.726765 | ||||||||
\(298\) | 1.15593e122 | 0.388352 | ||||||||
\(299\) | 1.76816e122 | 0.503267 | ||||||||
\(300\) | −2.61232e122 | −0.630267 | ||||||||
\(301\) | −3.58409e121 | −0.0733393 | ||||||||
\(302\) | 6.77489e122 | 1.17641 | ||||||||
\(303\) | −1.70706e122 | −0.251675 | ||||||||
\(304\) | −5.40704e123 | −6.77201 | ||||||||
\(305\) | 5.23345e122 | 0.557116 | ||||||||
\(306\) | 2.10152e123 | 1.90249 | ||||||||
\(307\) | −2.98902e122 | −0.230239 | −0.115120 | − | 0.993352i | \(-0.536725\pi\) | ||||
−0.115120 | + | 0.993352i | \(0.536725\pi\) | |||||||
\(308\) | 3.72336e123 | 2.44160 | ||||||||
\(309\) | 2.28721e122 | 0.127750 | ||||||||
\(310\) | −8.54372e122 | −0.406671 | ||||||||
\(311\) | 5.98572e122 | 0.242928 | 0.121464 | − | 0.992596i | \(-0.461241\pi\) | ||||
0.121464 | + | 0.992596i | \(0.461241\pi\) | |||||||
\(312\) | 2.47522e123 | 0.856963 | ||||||||
\(313\) | −4.50272e123 | −1.33055 | −0.665274 | − | 0.746599i | \(-0.731685\pi\) | ||||
−0.665274 | + | 0.746599i | \(0.731685\pi\) | |||||||
\(314\) | 1.19301e124 | 3.01041 | ||||||||
\(315\) | −9.67681e122 | −0.208622 | ||||||||
\(316\) | −3.15755e123 | −0.581887 | ||||||||
\(317\) | −9.72485e123 | −1.53267 | −0.766336 | − | 0.642440i | \(-0.777922\pi\) | ||||
−0.766336 | + | 0.642440i | \(0.777922\pi\) | |||||||
\(318\) | 4.39489e123 | 0.592660 | ||||||||
\(319\) | 7.96269e122 | 0.0919223 | ||||||||
\(320\) | −1.37755e124 | −1.36202 | ||||||||
\(321\) | −5.11642e123 | −0.433478 | ||||||||
\(322\) | −8.68009e123 | −0.630462 | ||||||||
\(323\) | −3.05774e124 | −1.90491 | ||||||||
\(324\) | 4.07532e124 | 2.17863 | ||||||||
\(325\) | 1.83289e124 | 0.841222 | ||||||||
\(326\) | 3.77647e124 | 1.48872 | ||||||||
\(327\) | 1.06542e124 | 0.360917 | ||||||||
\(328\) | −3.61265e124 | −1.05213 | ||||||||
\(329\) | −9.34800e123 | −0.234165 | ||||||||
\(330\) | −1.21097e124 | −0.261031 | ||||||||
\(331\) | −7.03877e124 | −1.30620 | −0.653102 | − | 0.757270i | \(-0.726533\pi\) | ||||
−0.653102 | + | 0.757270i | \(0.726533\pi\) | |||||||
\(332\) | −1.16279e124 | −0.185851 | ||||||||
\(333\) | 2.87978e124 | 0.396615 | ||||||||
\(334\) | 1.40586e125 | 1.66914 | ||||||||
\(335\) | 5.03077e124 | 0.515130 | ||||||||
\(336\) | −7.03098e124 | −0.621186 | ||||||||
\(337\) | 1.61739e125 | 1.23349 | 0.616744 | − | 0.787164i | \(-0.288451\pi\) | ||||
0.616744 | + | 0.787164i | \(0.288451\pi\) | |||||||
\(338\) | 2.00012e124 | 0.131729 | ||||||||
\(339\) | 2.30845e124 | 0.131352 | ||||||||
\(340\) | −2.11180e125 | −1.03860 | ||||||||
\(341\) | 1.96634e125 | 0.836215 | ||||||||
\(342\) | −8.80481e125 | −3.23912 | ||||||||
\(343\) | 3.16052e125 | 1.00624 | ||||||||
\(344\) | −1.42978e125 | −0.394119 | ||||||||
\(345\) | 2.06791e124 | 0.0493726 | ||||||||
\(346\) | 1.11332e124 | 0.0230331 | ||||||||
\(347\) | 5.65213e124 | 0.101369 | 0.0506843 | − | 0.998715i | \(-0.483860\pi\) | ||||
0.0506843 | + | 0.998715i | \(0.483860\pi\) | |||||||
\(348\) | −2.99848e124 | −0.0466367 | ||||||||
\(349\) | −1.31636e126 | −1.77630 | −0.888152 | − | 0.459550i | \(-0.848011\pi\) | ||||
−0.888152 | + | 0.459550i | \(0.848011\pi\) | |||||||
\(350\) | −8.99786e125 | −1.05383 | ||||||||
\(351\) | 4.83938e125 | 0.492138 | ||||||||
\(352\) | 6.30901e126 | 5.57313 | ||||||||
\(353\) | 1.02761e126 | 0.788823 | 0.394411 | − | 0.918934i | \(-0.370949\pi\) | ||||
0.394411 | + | 0.918934i | \(0.370949\pi\) | |||||||
\(354\) | −6.60166e125 | −0.440546 | ||||||||
\(355\) | −2.04543e125 | −0.118708 | ||||||||
\(356\) | −9.72160e125 | −0.490866 | ||||||||
\(357\) | −3.97609e125 | −0.174735 | ||||||||
\(358\) | −2.91361e126 | −1.11486 | ||||||||
\(359\) | −5.03591e126 | −1.67843 | −0.839213 | − | 0.543802i | \(-0.816984\pi\) | ||||
−0.839213 | + | 0.543802i | \(0.816984\pi\) | |||||||
\(360\) | −3.86032e126 | −1.12111 | ||||||||
\(361\) | 8.86102e126 | 2.24325 | ||||||||
\(362\) | −1.17917e127 | −2.60316 | ||||||||
\(363\) | 1.41561e126 | 0.272625 | ||||||||
\(364\) | 9.83753e126 | 1.65336 | ||||||||
\(365\) | 8.49757e125 | 0.124680 | ||||||||
\(366\) | 6.19201e126 | 0.793446 | ||||||||
\(367\) | 8.30488e126 | 0.929744 | 0.464872 | − | 0.885378i | \(-0.346100\pi\) | ||||
0.464872 | + | 0.885378i | \(0.346100\pi\) | |||||||
\(368\) | −2.00362e127 | −1.96042 | ||||||||
\(369\) | −3.40397e126 | −0.291192 | ||||||||
\(370\) | −3.95065e126 | −0.295586 | ||||||||
\(371\) | 1.10885e127 | 0.725876 | ||||||||
\(372\) | −7.40458e126 | −0.424253 | ||||||||
\(373\) | −1.36455e127 | −0.684544 | −0.342272 | − | 0.939601i | \(-0.611196\pi\) | ||||
−0.342272 | + | 0.939601i | \(0.611196\pi\) | |||||||
\(374\) | 6.63522e127 | 2.91549 | ||||||||
\(375\) | 4.60349e126 | 0.177231 | ||||||||
\(376\) | −3.72915e127 | −1.25838 | ||||||||
\(377\) | 2.10383e126 | 0.0622464 | ||||||||
\(378\) | −2.37570e127 | −0.616521 | ||||||||
\(379\) | −2.89152e127 | −0.658394 | −0.329197 | − | 0.944261i | \(-0.606778\pi\) | ||||
−0.329197 | + | 0.944261i | \(0.606778\pi\) | |||||||
\(380\) | 8.84789e127 | 1.76828 | ||||||||
\(381\) | 1.93090e127 | 0.338824 | ||||||||
\(382\) | 9.37280e127 | 1.44455 | ||||||||
\(383\) | −1.41040e128 | −1.90987 | −0.954937 | − | 0.296810i | \(-0.904077\pi\) | ||||
−0.954937 | + | 0.296810i | \(0.904077\pi\) | |||||||
\(384\) | −7.62281e127 | −0.907235 | ||||||||
\(385\) | −3.05531e127 | −0.319704 | ||||||||
\(386\) | 1.16373e128 | 1.07098 | ||||||||
\(387\) | −1.34719e127 | −0.109078 | ||||||||
\(388\) | −3.69745e128 | −2.63470 | ||||||||
\(389\) | −1.19485e128 | −0.749562 | −0.374781 | − | 0.927113i | \(-0.622282\pi\) | ||||
−0.374781 | + | 0.927113i | \(0.622282\pi\) | |||||||
\(390\) | −3.19951e127 | −0.176760 | ||||||||
\(391\) | −1.13307e128 | −0.551450 | ||||||||
\(392\) | 4.77117e128 | 2.04628 | ||||||||
\(393\) | 9.77117e127 | 0.369416 | ||||||||
\(394\) | 6.94438e128 | 2.31510 | ||||||||
\(395\) | 2.59101e127 | 0.0761927 | ||||||||
\(396\) | 1.39954e129 | 3.63140 | ||||||||
\(397\) | −8.36626e128 | −1.91602 | −0.958012 | − | 0.286727i | \(-0.907433\pi\) | ||||
−0.958012 | + | 0.286727i | \(0.907433\pi\) | |||||||
\(398\) | −8.23470e128 | −1.66508 | ||||||||
\(399\) | 1.66588e128 | 0.297498 | ||||||||
\(400\) | −2.07697e129 | −3.27688 | ||||||||
\(401\) | 1.41593e129 | 1.97421 | 0.987107 | − | 0.160059i | \(-0.0511685\pi\) | ||||
0.987107 | + | 0.160059i | \(0.0511685\pi\) | |||||||
\(402\) | 5.95221e128 | 0.733650 | ||||||||
\(403\) | 5.19530e128 | 0.566254 | ||||||||
\(404\) | −2.70653e129 | −2.60937 | ||||||||
\(405\) | −3.34412e128 | −0.285271 | ||||||||
\(406\) | −1.03279e128 | −0.0779784 | ||||||||
\(407\) | 9.09246e128 | 0.607796 | ||||||||
\(408\) | −1.58616e129 | −0.939008 | ||||||||
\(409\) | 1.37636e129 | 0.721819 | 0.360909 | − | 0.932601i | \(-0.382466\pi\) | ||||
0.360909 | + | 0.932601i | \(0.382466\pi\) | |||||||
\(410\) | 4.66976e128 | 0.217017 | ||||||||
\(411\) | 3.64746e128 | 0.150252 | ||||||||
\(412\) | 3.62635e129 | 1.32452 | ||||||||
\(413\) | −1.66562e129 | −0.539571 | ||||||||
\(414\) | −3.26268e129 | −0.937688 | ||||||||
\(415\) | 9.54158e127 | 0.0243354 | ||||||||
\(416\) | 1.66691e130 | 3.77392 | ||||||||
\(417\) | 1.76107e129 | 0.354031 | ||||||||
\(418\) | −2.77998e130 | −4.96382 | ||||||||
\(419\) | 1.18071e129 | 0.187305 | 0.0936526 | − | 0.995605i | \(-0.470146\pi\) | ||||
0.0936526 | + | 0.995605i | \(0.470146\pi\) | |||||||
\(420\) | 1.15052e129 | 0.162202 | ||||||||
\(421\) | −9.31891e128 | −0.116789 | −0.0583944 | − | 0.998294i | \(-0.518598\pi\) | ||||
−0.0583944 | + | 0.998294i | \(0.518598\pi\) | |||||||
\(422\) | 1.04941e130 | 1.16944 | ||||||||
\(423\) | −3.51374e129 | −0.348274 | ||||||||
\(424\) | 4.42346e130 | 3.90079 | ||||||||
\(425\) | −1.17455e130 | −0.921761 | ||||||||
\(426\) | −2.42007e129 | −0.169065 | ||||||||
\(427\) | 1.56226e130 | 0.971794 | ||||||||
\(428\) | −8.11204e130 | −4.49431 | ||||||||
\(429\) | 7.36370e129 | 0.363463 | ||||||||
\(430\) | 1.84816e129 | 0.0812924 | ||||||||
\(431\) | 8.65057e129 | 0.339172 | 0.169586 | − | 0.985515i | \(-0.445757\pi\) | ||||
0.169586 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(432\) | −5.48381e130 | −1.91707 | ||||||||
\(433\) | −8.67048e129 | −0.270329 | −0.135164 | − | 0.990823i | \(-0.543156\pi\) | ||||
−0.135164 | + | 0.990823i | \(0.543156\pi\) | |||||||
\(434\) | −2.55043e130 | −0.709368 | ||||||||
\(435\) | 2.46048e128 | 0.00610664 | ||||||||
\(436\) | 1.68921e131 | 3.74199 | ||||||||
\(437\) | 4.74725e130 | 0.938881 | ||||||||
\(438\) | 1.00540e130 | 0.177570 | ||||||||
\(439\) | −2.50512e130 | −0.395216 | −0.197608 | − | 0.980281i | \(-0.563317\pi\) | ||||
−0.197608 | + | 0.980281i | \(0.563317\pi\) | |||||||
\(440\) | −1.21884e131 | −1.71806 | ||||||||
\(441\) | 4.49557e130 | 0.566336 | ||||||||
\(442\) | 1.75310e131 | 1.97426 | ||||||||
\(443\) | −2.67742e130 | −0.269607 | −0.134804 | − | 0.990872i | \(-0.543040\pi\) | ||||
−0.134804 | + | 0.990872i | \(0.543040\pi\) | |||||||
\(444\) | −3.42391e130 | −0.308365 | ||||||||
\(445\) | 7.97733e129 | 0.0642743 | ||||||||
\(446\) | 1.79973e131 | 1.29758 | ||||||||
\(447\) | −8.22060e129 | −0.0530495 | ||||||||
\(448\) | −4.11219e131 | −2.37581 | ||||||||
\(449\) | −2.52889e131 | −1.30839 | −0.654194 | − | 0.756327i | \(-0.726992\pi\) | ||||
−0.654194 | + | 0.756327i | \(0.726992\pi\) | |||||||
\(450\) | −3.38213e131 | −1.56737 | ||||||||
\(451\) | −1.07475e131 | −0.446240 | ||||||||
\(452\) | 3.66003e131 | 1.36186 | ||||||||
\(453\) | −4.81810e130 | −0.160700 | ||||||||
\(454\) | 2.26974e131 | 0.678754 | ||||||||
\(455\) | −8.07246e130 | −0.216492 | ||||||||
\(456\) | 6.64560e131 | 1.59873 | ||||||||
\(457\) | −3.01784e131 | −0.651395 | −0.325698 | − | 0.945474i | \(-0.605599\pi\) | ||||
−0.325698 | + | 0.945474i | \(0.605599\pi\) | |||||||
\(458\) | 9.95885e131 | 1.92916 | ||||||||
\(459\) | −3.10115e131 | −0.539256 | ||||||||
\(460\) | 3.27865e131 | 0.511896 | ||||||||
\(461\) | −2.92541e131 | −0.410196 | −0.205098 | − | 0.978741i | \(-0.565751\pi\) | ||||
−0.205098 | + | 0.978741i | \(0.565751\pi\) | |||||||
\(462\) | −3.61491e131 | −0.455324 | ||||||||
\(463\) | −9.30561e131 | −1.05314 | −0.526569 | − | 0.850132i | \(-0.676522\pi\) | ||||
−0.526569 | + | 0.850132i | \(0.676522\pi\) | |||||||
\(464\) | −2.38399e131 | −0.242473 | ||||||||
\(465\) | 6.07604e130 | 0.0555519 | ||||||||
\(466\) | −2.12385e132 | −1.74591 | ||||||||
\(467\) | 2.03544e132 | 1.50478 | 0.752388 | − | 0.658720i | \(-0.228902\pi\) | ||||
0.752388 | + | 0.658720i | \(0.228902\pi\) | |||||||
\(468\) | 3.69774e132 | 2.45905 | ||||||||
\(469\) | 1.50176e132 | 0.898557 | ||||||||
\(470\) | 4.82035e131 | 0.259558 | ||||||||
\(471\) | −8.48433e131 | −0.411228 | ||||||||
\(472\) | −6.64457e132 | −2.89960 | ||||||||
\(473\) | −4.25355e131 | −0.167157 | ||||||||
\(474\) | 3.06558e131 | 0.108514 | ||||||||
\(475\) | 4.92104e132 | 1.56936 | ||||||||
\(476\) | −6.30405e132 | −1.81165 | ||||||||
\(477\) | 4.16794e132 | 1.07960 | ||||||||
\(478\) | −7.53237e132 | −1.75894 | ||||||||
\(479\) | −5.32664e131 | −0.112162 | −0.0560810 | − | 0.998426i | \(-0.517860\pi\) | ||||
−0.0560810 | + | 0.998426i | \(0.517860\pi\) | |||||||
\(480\) | 1.94949e132 | 0.370238 | ||||||||
\(481\) | 2.40233e132 | 0.411577 | ||||||||
\(482\) | −9.96492e132 | −1.54044 | ||||||||
\(483\) | 6.17302e131 | 0.0861222 | ||||||||
\(484\) | 2.24444e133 | 2.82658 | ||||||||
\(485\) | 3.03404e132 | 0.344989 | ||||||||
\(486\) | −1.35561e133 | −1.39200 | ||||||||
\(487\) | −1.86038e133 | −1.72552 | −0.862758 | − | 0.505617i | \(-0.831265\pi\) | ||||
−0.862758 | + | 0.505617i | \(0.831265\pi\) | |||||||
\(488\) | 6.23226e133 | 5.22233 | ||||||||
\(489\) | −2.68571e132 | −0.203362 | ||||||||
\(490\) | −6.16728e132 | −0.422073 | ||||||||
\(491\) | 1.36922e133 | 0.847106 | 0.423553 | − | 0.905871i | \(-0.360783\pi\) | ||||
0.423553 | + | 0.905871i | \(0.360783\pi\) | |||||||
\(492\) | 4.04714e132 | 0.226400 | ||||||||
\(493\) | −1.34817e132 | −0.0682059 | ||||||||
\(494\) | −7.34503e133 | −3.36132 | ||||||||
\(495\) | −1.14843e133 | −0.475497 | ||||||||
\(496\) | −5.88713e133 | −2.20577 | ||||||||
\(497\) | −6.10592e132 | −0.207066 | ||||||||
\(498\) | 1.12892e132 | 0.0346586 | ||||||||
\(499\) | −3.35713e132 | −0.0933236 | −0.0466618 | − | 0.998911i | \(-0.514858\pi\) | ||||
−0.0466618 | + | 0.998911i | \(0.514858\pi\) | |||||||
\(500\) | 7.29878e133 | 1.83753 | ||||||||
\(501\) | −9.99809e132 | −0.228008 | ||||||||
\(502\) | 1.06544e134 | 2.20137 | ||||||||
\(503\) | 5.31160e133 | 0.994512 | 0.497256 | − | 0.867604i | \(-0.334341\pi\) | ||||
0.497256 | + | 0.867604i | \(0.334341\pi\) | |||||||
\(504\) | −1.15237e134 | −1.95559 | ||||||||
\(505\) | 2.22092e133 | 0.341672 | ||||||||
\(506\) | −1.03014e134 | −1.43697 | ||||||||
\(507\) | −1.42243e132 | −0.0179943 | ||||||||
\(508\) | 3.06143e134 | 3.51294 | ||||||||
\(509\) | −1.65463e134 | −1.72255 | −0.861273 | − | 0.508143i | \(-0.830332\pi\) | ||||
−0.861273 | + | 0.508143i | \(0.830332\pi\) | |||||||
\(510\) | 2.05029e133 | 0.193683 | ||||||||
\(511\) | 2.53665e133 | 0.217484 | ||||||||
\(512\) | −2.64920e134 | −2.06182 | ||||||||
\(513\) | 1.29930e134 | 0.918120 | ||||||||
\(514\) | 2.26302e134 | 1.45216 | ||||||||
\(515\) | −2.97570e133 | −0.173433 | ||||||||
\(516\) | 1.60174e133 | 0.0848071 | ||||||||
\(517\) | −1.10941e134 | −0.533715 | ||||||||
\(518\) | −1.17933e134 | −0.515599 | ||||||||
\(519\) | −7.91757e131 | −0.00314636 | ||||||||
\(520\) | −3.22031e134 | −1.16341 | ||||||||
\(521\) | 6.72181e133 | 0.220810 | 0.110405 | − | 0.993887i | \(-0.464785\pi\) | ||||
0.110405 | + | 0.993887i | \(0.464785\pi\) | |||||||
\(522\) | −3.88207e133 | −0.115978 | ||||||||
\(523\) | −1.66421e134 | −0.452246 | −0.226123 | − | 0.974099i | \(-0.572605\pi\) | ||||
−0.226123 | + | 0.974099i | \(0.572605\pi\) | |||||||
\(524\) | 1.54921e135 | 3.83011 | ||||||||
\(525\) | 6.39901e133 | 0.143955 | ||||||||
\(526\) | −1.03479e135 | −2.11864 | ||||||||
\(527\) | −3.32923e134 | −0.620467 | ||||||||
\(528\) | −8.34428e134 | −1.41583 | ||||||||
\(529\) | −4.71313e134 | −0.728205 | ||||||||
\(530\) | −5.71783e134 | −0.804592 | ||||||||
\(531\) | −6.26075e134 | −0.802505 | ||||||||
\(532\) | 2.64123e135 | 3.08447 | ||||||||
\(533\) | −2.83961e134 | −0.302177 | ||||||||
\(534\) | 9.43846e133 | 0.0915396 | ||||||||
\(535\) | 6.65656e134 | 0.588488 | ||||||||
\(536\) | 5.99091e135 | 4.82876 | ||||||||
\(537\) | 2.07207e134 | 0.152292 | ||||||||
\(538\) | −5.51720e135 | −3.69825 | ||||||||
\(539\) | 1.41941e135 | 0.867886 | ||||||||
\(540\) | 8.97351e134 | 0.500577 | ||||||||
\(541\) | 1.65804e135 | 0.843978 | 0.421989 | − | 0.906601i | \(-0.361332\pi\) | ||||
0.421989 | + | 0.906601i | \(0.361332\pi\) | |||||||
\(542\) | −2.98970e135 | −1.38887 | ||||||||
\(543\) | 8.38589e134 | 0.355597 | ||||||||
\(544\) | −1.06818e136 | −4.13524 | ||||||||
\(545\) | −1.38613e135 | −0.489979 | ||||||||
\(546\) | −9.55101e134 | −0.308328 | ||||||||
\(547\) | 2.22724e135 | 0.656740 | 0.328370 | − | 0.944549i | \(-0.393501\pi\) | ||||
0.328370 | + | 0.944549i | \(0.393501\pi\) | |||||||
\(548\) | 5.78301e135 | 1.55782 | ||||||||
\(549\) | 5.87225e135 | 1.44535 | ||||||||
\(550\) | −1.06785e136 | −2.40192 | ||||||||
\(551\) | 5.64847e134 | 0.116125 | ||||||||
\(552\) | 2.46257e135 | 0.462812 | ||||||||
\(553\) | 7.73456e134 | 0.132905 | ||||||||
\(554\) | −5.93741e135 | −0.932961 | ||||||||
\(555\) | 2.80958e134 | 0.0403775 | ||||||||
\(556\) | 2.79215e136 | 3.67060 | ||||||||
\(557\) | 4.12341e135 | 0.495934 | 0.247967 | − | 0.968768i | \(-0.420238\pi\) | ||||
0.247967 | + | 0.968768i | \(0.420238\pi\) | |||||||
\(558\) | −9.58658e135 | −1.05504 | ||||||||
\(559\) | −1.12384e135 | −0.113193 | ||||||||
\(560\) | 9.14743e135 | 0.843319 | ||||||||
\(561\) | −4.71877e135 | −0.398261 | ||||||||
\(562\) | −7.85607e135 | −0.607097 | ||||||||
\(563\) | −1.98383e136 | −1.40391 | −0.701955 | − | 0.712221i | \(-0.747689\pi\) | ||||
−0.701955 | + | 0.712221i | \(0.747689\pi\) | |||||||
\(564\) | 4.17765e135 | 0.270780 | ||||||||
\(565\) | −3.00334e135 | −0.178322 | ||||||||
\(566\) | 1.83255e136 | 0.996881 | ||||||||
\(567\) | −9.98270e135 | −0.497607 | ||||||||
\(568\) | −2.43580e136 | −1.11276 | ||||||||
\(569\) | −9.86907e135 | −0.413256 | −0.206628 | − | 0.978420i | \(-0.566249\pi\) | ||||
−0.206628 | + | 0.978420i | \(0.566249\pi\) | |||||||
\(570\) | −8.59019e135 | −0.329760 | ||||||||
\(571\) | −8.98219e134 | −0.0316151 | −0.0158076 | − | 0.999875i | \(-0.505032\pi\) | ||||
−0.0158076 | + | 0.999875i | \(0.505032\pi\) | |||||||
\(572\) | 1.16751e137 | 3.76839 | ||||||||
\(573\) | −6.66566e135 | −0.197328 | ||||||||
\(574\) | 1.39399e136 | 0.378549 | ||||||||
\(575\) | 1.82353e136 | 0.454312 | ||||||||
\(576\) | −1.54569e137 | −3.53355 | ||||||||
\(577\) | −5.82852e136 | −1.22280 | −0.611400 | − | 0.791322i | \(-0.709393\pi\) | ||||
−0.611400 | + | 0.791322i | \(0.709393\pi\) | |||||||
\(578\) | −1.19332e136 | −0.229788 | ||||||||
\(579\) | −8.27608e135 | −0.146297 | ||||||||
\(580\) | 3.90107e135 | 0.0633137 | ||||||||
\(581\) | 2.84830e135 | 0.0424490 | ||||||||
\(582\) | 3.58976e136 | 0.491335 | ||||||||
\(583\) | 1.31596e137 | 1.65444 | ||||||||
\(584\) | 1.01193e137 | 1.16874 | ||||||||
\(585\) | −3.03429e136 | −0.321989 | ||||||||
\(586\) | 1.81277e137 | 1.76771 | ||||||||
\(587\) | −1.52532e137 | −1.36702 | −0.683511 | − | 0.729941i | \(-0.739548\pi\) | ||||
−0.683511 | + | 0.729941i | \(0.739548\pi\) | |||||||
\(588\) | −5.34500e136 | −0.440322 | ||||||||
\(589\) | 1.39486e137 | 1.05639 | ||||||||
\(590\) | 8.58887e136 | 0.598083 | ||||||||
\(591\) | −4.93863e136 | −0.316247 | ||||||||
\(592\) | −2.72224e137 | −1.60325 | ||||||||
\(593\) | 2.39449e137 | 1.29720 | 0.648599 | − | 0.761130i | \(-0.275355\pi\) | ||||
0.648599 | + | 0.761130i | \(0.275355\pi\) | |||||||
\(594\) | −2.81945e137 | −1.40519 | ||||||||
\(595\) | 5.17296e136 | 0.237219 | ||||||||
\(596\) | −1.30337e137 | −0.550018 | ||||||||
\(597\) | 5.85628e136 | 0.227453 | ||||||||
\(598\) | −2.72175e137 | −0.973061 | ||||||||
\(599\) | −3.10264e137 | −1.02118 | −0.510591 | − | 0.859824i | \(-0.670573\pi\) | ||||
−0.510591 | + | 0.859824i | \(0.670573\pi\) | |||||||
\(600\) | 2.55273e137 | 0.773601 | ||||||||
\(601\) | −5.55438e137 | −1.55006 | −0.775031 | − | 0.631923i | \(-0.782266\pi\) | ||||
−0.775031 | + | 0.631923i | \(0.782266\pi\) | |||||||
\(602\) | 5.51703e136 | 0.141801 | ||||||||
\(603\) | 5.64484e137 | 1.33643 | ||||||||
\(604\) | −7.63904e137 | −1.66614 | ||||||||
\(605\) | −1.84173e137 | −0.370114 | ||||||||
\(606\) | 2.62770e137 | 0.486611 | ||||||||
\(607\) | 2.49301e137 | 0.425485 | 0.212742 | − | 0.977108i | \(-0.431761\pi\) | ||||
0.212742 | + | 0.977108i | \(0.431761\pi\) | |||||||
\(608\) | 4.47540e138 | 7.04053 | ||||||||
\(609\) | 7.34491e135 | 0.0106520 | ||||||||
\(610\) | −8.05591e137 | −1.07718 | ||||||||
\(611\) | −2.93118e137 | −0.361412 | ||||||||
\(612\) | −2.36957e138 | −2.69448 | ||||||||
\(613\) | −1.14723e137 | −0.120325 | −0.0601625 | − | 0.998189i | \(-0.519162\pi\) | ||||
−0.0601625 | + | 0.998189i | \(0.519162\pi\) | |||||||
\(614\) | 4.60103e137 | 0.445165 | ||||||||
\(615\) | −3.32099e136 | −0.0296449 | ||||||||
\(616\) | −3.63842e138 | −2.99686 | ||||||||
\(617\) | 1.08609e138 | 0.825560 | 0.412780 | − | 0.910831i | \(-0.364558\pi\) | ||||
0.412780 | + | 0.910831i | \(0.364558\pi\) | |||||||
\(618\) | −3.52073e137 | −0.247003 | ||||||||
\(619\) | 1.41284e138 | 0.914968 | 0.457484 | − | 0.889218i | \(-0.348751\pi\) | ||||
0.457484 | + | 0.889218i | \(0.348751\pi\) | |||||||
\(620\) | 9.63349e137 | 0.575963 | ||||||||
\(621\) | 4.81465e137 | 0.265785 | ||||||||
\(622\) | −9.21389e137 | −0.469698 | ||||||||
\(623\) | 2.38135e137 | 0.112116 | ||||||||
\(624\) | −2.20465e138 | −0.958745 | ||||||||
\(625\) | 1.57025e138 | 0.630824 | ||||||||
\(626\) | 6.93109e138 | 2.57260 | ||||||||
\(627\) | 1.97704e138 | 0.678066 | ||||||||
\(628\) | −1.34518e139 | −4.26362 | ||||||||
\(629\) | −1.53945e138 | −0.450982 | ||||||||
\(630\) | 1.48956e138 | 0.403368 | ||||||||
\(631\) | −3.56283e138 | −0.891953 | −0.445976 | − | 0.895045i | \(-0.647144\pi\) | ||||
−0.445976 | + | 0.895045i | \(0.647144\pi\) | |||||||
\(632\) | 3.08551e138 | 0.714219 | ||||||||
\(633\) | −7.46310e137 | −0.159748 | ||||||||
\(634\) | 1.49696e139 | 2.96340 | ||||||||
\(635\) | −2.51214e138 | −0.459986 | ||||||||
\(636\) | −4.95547e138 | −0.839378 | ||||||||
\(637\) | 3.75023e138 | 0.587701 | ||||||||
\(638\) | −1.22571e138 | −0.177731 | ||||||||
\(639\) | −2.29510e138 | −0.307971 | ||||||||
\(640\) | 9.91741e138 | 1.23166 | ||||||||
\(641\) | −1.38569e139 | −1.59292 | −0.796461 | − | 0.604690i | \(-0.793297\pi\) | ||||
−0.796461 | + | 0.604690i | \(0.793297\pi\) | |||||||
\(642\) | 7.87577e138 | 0.838126 | ||||||||
\(643\) | −4.00774e138 | −0.394872 | −0.197436 | − | 0.980316i | \(-0.563262\pi\) | ||||
−0.197436 | + | 0.980316i | \(0.563262\pi\) | |||||||
\(644\) | 9.78726e138 | 0.892916 | ||||||||
\(645\) | −1.31435e137 | −0.0111047 | ||||||||
\(646\) | 4.70681e139 | 3.68313 | ||||||||
\(647\) | −6.39338e138 | −0.463414 | −0.231707 | − | 0.972786i | \(-0.574431\pi\) | ||||
−0.231707 | + | 0.972786i | \(0.574431\pi\) | |||||||
\(648\) | −3.98235e139 | −2.67409 | ||||||||
\(649\) | −1.97674e139 | −1.22980 | ||||||||
\(650\) | −2.82139e139 | −1.62649 | ||||||||
\(651\) | 1.81379e138 | 0.0969009 | ||||||||
\(652\) | −4.25816e139 | −2.10846 | ||||||||
\(653\) | 2.80881e139 | 1.28920 | 0.644599 | − | 0.764521i | \(-0.277024\pi\) | ||||
0.644599 | + | 0.764521i | \(0.277024\pi\) | |||||||
\(654\) | −1.64001e139 | −0.697829 | ||||||||
\(655\) | −1.27125e139 | −0.501516 | ||||||||
\(656\) | 3.21775e139 | 1.17710 | ||||||||
\(657\) | 9.53480e138 | 0.323464 | ||||||||
\(658\) | 1.43895e139 | 0.452755 | ||||||||
\(659\) | 4.04659e138 | 0.118103 | 0.0590515 | − | 0.998255i | \(-0.481192\pi\) | ||||
0.0590515 | + | 0.998255i | \(0.481192\pi\) | |||||||
\(660\) | 1.36543e139 | 0.369695 | ||||||||
\(661\) | 5.46130e139 | 1.37191 | 0.685953 | − | 0.727646i | \(-0.259386\pi\) | ||||
0.685953 | + | 0.727646i | \(0.259386\pi\) | |||||||
\(662\) | 1.08349e140 | 2.52553 | ||||||||
\(663\) | −1.24675e139 | −0.269687 | ||||||||
\(664\) | 1.13626e139 | 0.228117 | ||||||||
\(665\) | −2.16733e139 | −0.403882 | ||||||||
\(666\) | −4.43288e139 | −0.766852 | ||||||||
\(667\) | 2.09308e138 | 0.0336169 | ||||||||
\(668\) | −1.58519e140 | −2.36399 | ||||||||
\(669\) | −1.27992e139 | −0.177251 | ||||||||
\(670\) | −7.74393e139 | −0.995998 | ||||||||
\(671\) | 1.85407e140 | 2.21494 | ||||||||
\(672\) | 5.81954e139 | 0.645817 | ||||||||
\(673\) | 2.88994e139 | 0.297950 | 0.148975 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148975 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(674\) | −2.48967e140 | −2.38494 | ||||||||
\(675\) | 4.99091e139 | 0.444266 | ||||||||
\(676\) | −2.25524e139 | −0.186566 | ||||||||
\(677\) | −1.30300e140 | −1.00185 | −0.500927 | − | 0.865490i | \(-0.667007\pi\) | ||||
−0.500927 | + | 0.865490i | \(0.667007\pi\) | |||||||
\(678\) | −3.55343e139 | −0.253967 | ||||||||
\(679\) | 9.05708e139 | 0.601775 | ||||||||
\(680\) | 2.06362e140 | 1.27479 | ||||||||
\(681\) | −1.61417e139 | −0.0927189 | ||||||||
\(682\) | −3.02682e140 | −1.61681 | ||||||||
\(683\) | −1.78510e140 | −0.886824 | −0.443412 | − | 0.896318i | \(-0.646232\pi\) | ||||
−0.443412 | + | 0.896318i | \(0.646232\pi\) | |||||||
\(684\) | 9.92788e140 | 4.58754 | ||||||||
\(685\) | −4.74541e139 | −0.203981 | ||||||||
\(686\) | −4.86503e140 | −1.94555 | ||||||||
\(687\) | −7.08243e139 | −0.263526 | ||||||||
\(688\) | 1.27349e140 | 0.440928 | ||||||||
\(689\) | 3.47692e140 | 1.12032 | ||||||||
\(690\) | −3.18316e139 | −0.0954614 | ||||||||
\(691\) | −3.94939e140 | −1.10247 | −0.551235 | − | 0.834350i | \(-0.685843\pi\) | ||||
−0.551235 | + | 0.834350i | \(0.685843\pi\) | |||||||
\(692\) | −1.25532e139 | −0.0326215 | ||||||||
\(693\) | −3.42824e140 | −0.829424 | ||||||||
\(694\) | −8.70039e139 | −0.195995 | ||||||||
\(695\) | −2.29118e140 | −0.480630 | ||||||||
\(696\) | 2.93007e139 | 0.0572428 | ||||||||
\(697\) | 1.81967e140 | 0.331108 | ||||||||
\(698\) | 2.02629e141 | 3.43446 | ||||||||
\(699\) | 1.51042e140 | 0.238494 | ||||||||
\(700\) | 1.01456e141 | 1.49253 | ||||||||
\(701\) | 9.14278e139 | 0.125325 | 0.0626623 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626623 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(702\) | −7.44931e140 | −0.951544 | ||||||||
\(703\) | 6.44989e140 | 0.767828 | ||||||||
\(704\) | −4.88029e141 | −5.41501 | ||||||||
\(705\) | −3.42809e139 | −0.0354561 | ||||||||
\(706\) | −1.58181e141 | −1.52518 | ||||||||
\(707\) | 6.62978e140 | 0.595989 | ||||||||
\(708\) | 7.44371e140 | 0.623941 | ||||||||
\(709\) | −9.83283e140 | −0.768581 | −0.384291 | − | 0.923212i | \(-0.625554\pi\) | ||||
−0.384291 | + | 0.923212i | \(0.625554\pi\) | |||||||
\(710\) | 3.14855e140 | 0.229521 | ||||||||
\(711\) | 2.90728e140 | 0.197670 | ||||||||
\(712\) | 9.49982e140 | 0.602498 | ||||||||
\(713\) | 5.16875e140 | 0.305812 | ||||||||
\(714\) | 6.12044e140 | 0.337848 | ||||||||
\(715\) | −9.58029e140 | −0.493435 | ||||||||
\(716\) | 3.28525e141 | 1.57897 | ||||||||
\(717\) | 5.35679e140 | 0.240274 | ||||||||
\(718\) | 7.75183e141 | 3.24522 | ||||||||
\(719\) | −4.55372e141 | −1.77945 | −0.889727 | − | 0.456494i | \(-0.849105\pi\) | ||||
−0.889727 | + | 0.456494i | \(0.849105\pi\) | |||||||
\(720\) | 3.43835e141 | 1.25427 | ||||||||
\(721\) | −8.88291e140 | −0.302524 | ||||||||
\(722\) | −1.36399e142 | −4.33730 | ||||||||
\(723\) | 7.08676e140 | 0.210427 | ||||||||
\(724\) | 1.32957e142 | 3.68683 | ||||||||
\(725\) | 2.16971e140 | 0.0561914 | ||||||||
\(726\) | −2.17907e141 | −0.527118 | ||||||||
\(727\) | 2.67121e141 | 0.603608 | 0.301804 | − | 0.953370i | \(-0.402411\pi\) | ||||
0.301804 | + | 0.953370i | \(0.402411\pi\) | |||||||
\(728\) | −9.61310e141 | −2.02937 | ||||||||
\(729\) | −3.06962e141 | −0.605442 | ||||||||
\(730\) | −1.30804e141 | −0.241068 | ||||||||
\(731\) | 7.20172e140 | 0.124030 | ||||||||
\(732\) | −6.98181e141 | −1.12375 | ||||||||
\(733\) | −7.44783e141 | −1.12043 | −0.560213 | − | 0.828349i | \(-0.689281\pi\) | ||||
−0.560213 | + | 0.828349i | \(0.689281\pi\) | |||||||
\(734\) | −1.27838e142 | −1.79765 | ||||||||
\(735\) | 4.38599e140 | 0.0576560 | ||||||||
\(736\) | 1.65839e142 | 2.03815 | ||||||||
\(737\) | 1.78227e142 | 2.04802 | ||||||||
\(738\) | 5.23976e141 | 0.563017 | ||||||||
\(739\) | 6.83854e141 | 0.687169 | 0.343585 | − | 0.939122i | \(-0.388359\pi\) | ||||
0.343585 | + | 0.939122i | \(0.388359\pi\) | |||||||
\(740\) | 4.45457e141 | 0.418635 | ||||||||
\(741\) | 5.22356e141 | 0.459162 | ||||||||
\(742\) | −1.70686e142 | −1.40347 | ||||||||
\(743\) | −1.02755e142 | −0.790420 | −0.395210 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395210 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(744\) | 7.23566e141 | 0.520736 | ||||||||
\(745\) | 1.06951e141 | 0.0720197 | ||||||||
\(746\) | 2.10046e142 | 1.32356 | ||||||||
\(747\) | 1.07062e141 | 0.0631346 | ||||||||
\(748\) | −7.48156e142 | −4.12917 | ||||||||
\(749\) | 1.98708e142 | 1.02652 | ||||||||
\(750\) | −7.08621e141 | −0.342674 | ||||||||
\(751\) | 2.68344e142 | 1.21483 | 0.607413 | − | 0.794386i | \(-0.292207\pi\) | ||||
0.607413 | + | 0.794386i | \(0.292207\pi\) | |||||||
\(752\) | 3.32151e142 | 1.40784 | ||||||||
\(753\) | −7.57707e141 | −0.300711 | ||||||||
\(754\) | −3.23845e141 | −0.120353 | ||||||||
\(755\) | 6.26843e141 | 0.218165 | ||||||||
\(756\) | 2.67873e142 | 0.873172 | ||||||||
\(757\) | −7.90246e141 | −0.241277 | −0.120639 | − | 0.992697i | \(-0.538494\pi\) | ||||
−0.120639 | + | 0.992697i | \(0.538494\pi\) | |||||||
\(758\) | 4.45096e142 | 1.27300 | ||||||||
\(759\) | 7.32606e141 | 0.196292 | ||||||||
\(760\) | −8.64604e142 | −2.17042 | ||||||||
\(761\) | −2.76766e142 | −0.650988 | −0.325494 | − | 0.945544i | \(-0.605531\pi\) | ||||
−0.325494 | + | 0.945544i | \(0.605531\pi\) | |||||||
\(762\) | −2.97226e142 | −0.655113 | ||||||||
\(763\) | −4.13781e142 | −0.854684 | ||||||||
\(764\) | −1.05683e143 | −2.04590 | ||||||||
\(765\) | 1.94442e142 | 0.352816 | ||||||||
\(766\) | 2.17105e143 | 3.69272 | ||||||||
\(767\) | −5.22276e142 | −0.832779 | ||||||||
\(768\) | 5.02279e142 | 0.750870 | ||||||||
\(769\) | −1.15768e143 | −1.62269 | −0.811347 | − | 0.584566i | \(-0.801265\pi\) | ||||
−0.811347 | + | 0.584566i | \(0.801265\pi\) | |||||||
\(770\) | 4.70307e142 | 0.618145 | ||||||||
\(771\) | −1.60939e142 | −0.198368 | ||||||||
\(772\) | −1.31216e143 | −1.51681 | ||||||||
\(773\) | −2.07069e142 | −0.224507 | −0.112253 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112253 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(774\) | 2.07375e142 | 0.210901 | ||||||||
\(775\) | 5.35798e142 | 0.511171 | ||||||||
\(776\) | 3.61310e143 | 3.23388 | ||||||||
\(777\) | 8.38704e141 | 0.0704317 | ||||||||
\(778\) | 1.83924e143 | 1.44927 | ||||||||
\(779\) | −7.62392e142 | −0.563734 | ||||||||
\(780\) | 3.60761e142 | 0.250344 | ||||||||
\(781\) | −7.24643e142 | −0.471952 | ||||||||
\(782\) | 1.74414e143 | 1.06622 | ||||||||
\(783\) | 5.72866e141 | 0.0328735 | ||||||||
\(784\) | −4.24963e143 | −2.28932 | ||||||||
\(785\) | 1.10383e143 | 0.558280 | ||||||||
\(786\) | −1.50409e143 | −0.714261 | ||||||||
\(787\) | 1.34529e143 | 0.599885 | 0.299943 | − | 0.953957i | \(-0.403032\pi\) | ||||
0.299943 | + | 0.953957i | \(0.403032\pi\) | |||||||
\(788\) | −7.83015e143 | −3.27886 | ||||||||
\(789\) | 7.35909e142 | 0.289409 | ||||||||
\(790\) | −3.98837e142 | −0.147318 | ||||||||
\(791\) | −8.96542e142 | −0.311053 | ||||||||
\(792\) | −1.36761e144 | −4.45724 | ||||||||
\(793\) | 4.89867e143 | 1.49988 | ||||||||
\(794\) | 1.28783e144 | 3.70461 | ||||||||
\(795\) | 4.06635e142 | 0.109909 | ||||||||
\(796\) | 9.28506e143 | 2.35824 | ||||||||
\(797\) | −3.26321e143 | −0.778859 | −0.389429 | − | 0.921056i | \(-0.627328\pi\) | ||||
−0.389429 | + | 0.921056i | \(0.627328\pi\) | |||||||
\(798\) | −2.56430e143 | −0.575209 | ||||||||
\(799\) | 1.87835e143 | 0.396014 | ||||||||
\(800\) | 1.71911e144 | 3.40681 | ||||||||
\(801\) | 8.95106e142 | 0.166750 | ||||||||
\(802\) | −2.17955e144 | −3.81712 | ||||||||
\(803\) | 3.01047e143 | 0.495695 | ||||||||
\(804\) | −6.71143e143 | −1.03906 | ||||||||
\(805\) | −8.03121e142 | −0.116919 | ||||||||
\(806\) | −7.99719e143 | −1.09485 | ||||||||
\(807\) | 3.92367e143 | 0.505187 | ||||||||
\(808\) | 2.64479e144 | 3.20279 | ||||||||
\(809\) | −9.17846e143 | −1.04549 | −0.522743 | − | 0.852490i | \(-0.675091\pi\) | ||||
−0.522743 | + | 0.852490i | \(0.675091\pi\) | |||||||
\(810\) | 5.14764e143 | 0.551569 | ||||||||
\(811\) | −7.89187e143 | −0.795513 | −0.397757 | − | 0.917491i | \(-0.630211\pi\) | ||||
−0.397757 | + | 0.917491i | \(0.630211\pi\) | |||||||
\(812\) | 1.16453e143 | 0.110440 | ||||||||
\(813\) | 2.12619e143 | 0.189723 | ||||||||
\(814\) | −1.39961e144 | −1.17517 | ||||||||
\(815\) | 3.49415e143 | 0.276083 | ||||||||
\(816\) | 1.41278e144 | 1.05054 | ||||||||
\(817\) | −3.01733e143 | −0.211169 | ||||||||
\(818\) | −2.11865e144 | −1.39563 | ||||||||
\(819\) | −9.05781e143 | −0.561655 | ||||||||
\(820\) | −5.26540e143 | −0.307359 | ||||||||
\(821\) | 3.00742e144 | 1.65275 | 0.826376 | − | 0.563118i | \(-0.190398\pi\) | ||||
0.826376 | + | 0.563118i | \(0.190398\pi\) | |||||||
\(822\) | −5.61458e143 | −0.290511 | ||||||||
\(823\) | 1.16005e144 | 0.565178 | 0.282589 | − | 0.959241i | \(-0.408807\pi\) | ||||
0.282589 | + | 0.959241i | \(0.408807\pi\) | |||||||
\(824\) | −3.54362e144 | −1.62574 | ||||||||
\(825\) | 7.59426e143 | 0.328107 | ||||||||
\(826\) | 2.56391e144 | 1.04325 | ||||||||
\(827\) | −3.90585e144 | −1.49690 | −0.748450 | − | 0.663192i | \(-0.769201\pi\) | ||||
−0.748450 | + | 0.663192i | \(0.769201\pi\) | |||||||
\(828\) | 3.67885e144 | 1.32804 | ||||||||
\(829\) | 4.28000e143 | 0.145544 | 0.0727720 | − | 0.997349i | \(-0.476815\pi\) | ||||
0.0727720 | + | 0.997349i | \(0.476815\pi\) | |||||||
\(830\) | −1.46875e143 | −0.0470523 | ||||||||
\(831\) | 4.22251e143 | 0.127444 | ||||||||
\(832\) | −1.28943e145 | −3.66685 | ||||||||
\(833\) | −2.40321e144 | −0.643967 | ||||||||
\(834\) | −2.71083e144 | −0.684514 | ||||||||
\(835\) | 1.30077e144 | 0.309542 | ||||||||
\(836\) | 3.13458e145 | 7.03021 | ||||||||
\(837\) | 1.41466e144 | 0.299049 | ||||||||
\(838\) | −1.81748e144 | −0.362152 | ||||||||
\(839\) | 5.82834e144 | 1.09478 | 0.547391 | − | 0.836877i | \(-0.315621\pi\) | ||||
0.547391 | + | 0.836877i | \(0.315621\pi\) | |||||||
\(840\) | −1.12428e144 | −0.199089 | ||||||||
\(841\) | −5.96475e144 | −0.995842 | ||||||||
\(842\) | 1.43447e144 | 0.225810 | ||||||||
\(843\) | 5.58700e143 | 0.0829304 | ||||||||
\(844\) | −1.18327e145 | −1.65627 | ||||||||
\(845\) | 1.85060e143 | 0.0244290 | ||||||||
\(846\) | 5.40874e144 | 0.673384 | ||||||||
\(847\) | −5.49786e144 | −0.645601 | ||||||||
\(848\) | −3.93993e145 | −4.36409 | ||||||||
\(849\) | −1.30326e144 | −0.136176 | ||||||||
\(850\) | 1.80799e145 | 1.78221 | ||||||||
\(851\) | 2.39005e144 | 0.222277 | ||||||||
\(852\) | 2.72876e144 | 0.239445 | ||||||||
\(853\) | −1.78007e145 | −1.47388 | −0.736938 | − | 0.675960i | \(-0.763729\pi\) | ||||
−0.736938 | + | 0.675960i | \(0.763729\pi\) | |||||||
\(854\) | −2.40481e145 | −1.87895 | ||||||||
\(855\) | −8.14660e144 | −0.600695 | ||||||||
\(856\) | 7.92697e145 | 5.51640 | ||||||||
\(857\) | 7.01094e143 | 0.0460496 | 0.0230248 | − | 0.999735i | \(-0.492670\pi\) | ||||
0.0230248 | + | 0.999735i | \(0.492670\pi\) | |||||||
\(858\) | −1.13350e145 | −0.702751 | ||||||||
\(859\) | 1.71574e145 | 1.00413 | 0.502064 | − | 0.864830i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864830i | \(0.332574\pi\) | |||||||
\(860\) | −2.08389e144 | −0.115134 | ||||||||
\(861\) | −9.91367e143 | −0.0517105 | ||||||||
\(862\) | −1.33159e145 | −0.655785 | ||||||||
\(863\) | −2.85672e145 | −1.32841 | −0.664206 | − | 0.747549i | \(-0.731230\pi\) | ||||
−0.664206 | + | 0.747549i | \(0.731230\pi\) | |||||||
\(864\) | 4.53894e145 | 1.99308 | ||||||||
\(865\) | 1.03009e143 | 0.00427147 | ||||||||
\(866\) | 1.33466e145 | 0.522678 | ||||||||
\(867\) | 8.48651e143 | 0.0313895 | ||||||||
\(868\) | 2.87574e145 | 1.00467 | ||||||||
\(869\) | 9.17928e144 | 0.302921 | ||||||||
\(870\) | −3.78745e143 | −0.0118071 | ||||||||
\(871\) | 4.70896e145 | 1.38684 | ||||||||
\(872\) | −1.65068e146 | −4.59299 | ||||||||
\(873\) | 3.40439e145 | 0.895022 | ||||||||
\(874\) | −7.30749e145 | −1.81532 | ||||||||
\(875\) | −1.78787e145 | −0.419699 | ||||||||
\(876\) | −1.13364e145 | −0.251490 | ||||||||
\(877\) | −8.76907e143 | −0.0183854 | −0.00919271 | − | 0.999958i | \(-0.502926\pi\) | ||||
−0.00919271 | + | 0.999958i | \(0.502926\pi\) | |||||||
\(878\) | 3.85616e145 | 0.764145 | ||||||||
\(879\) | −1.28919e145 | −0.241472 | ||||||||
\(880\) | 1.08561e146 | 1.92212 | ||||||||
\(881\) | 1.00378e146 | 1.68008 | 0.840041 | − | 0.542523i | \(-0.182531\pi\) | ||||
0.840041 | + | 0.542523i | \(0.182531\pi\) | |||||||
\(882\) | −6.92008e145 | −1.09500 | ||||||||
\(883\) | 6.84113e145 | 1.02347 | 0.511733 | − | 0.859145i | \(-0.329004\pi\) | ||||
0.511733 | + | 0.859145i | \(0.329004\pi\) | |||||||
\(884\) | −1.97671e146 | −2.79612 | ||||||||
\(885\) | −6.10815e144 | −0.0816992 | ||||||||
\(886\) | 4.12138e145 | 0.521283 | ||||||||
\(887\) | 1.28947e146 | 1.54238 | 0.771192 | − | 0.636603i | \(-0.219661\pi\) | ||||
0.771192 | + | 0.636603i | \(0.219661\pi\) | |||||||
\(888\) | 3.34580e145 | 0.378493 | ||||||||
\(889\) | −7.49912e145 | −0.802367 | ||||||||
\(890\) | −1.22796e145 | −0.124274 | ||||||||
\(891\) | −1.18473e146 | −1.13416 | ||||||||
\(892\) | −2.02929e146 | −1.83774 | ||||||||
\(893\) | −7.86978e145 | −0.674241 | ||||||||
\(894\) | 1.26541e145 | 0.102571 | ||||||||
\(895\) | −2.69580e145 | −0.206751 | ||||||||
\(896\) | 2.96050e146 | 2.14841 | ||||||||
\(897\) | 1.93563e145 | 0.132922 | ||||||||
\(898\) | 3.89275e146 | 2.52975 | ||||||||
\(899\) | 6.14999e144 | 0.0378242 | ||||||||
\(900\) | 3.81353e146 | 2.21984 | ||||||||
\(901\) | −2.22807e146 | −1.22758 | ||||||||
\(902\) | 1.65437e146 | 0.862800 | ||||||||
\(903\) | −3.92354e144 | −0.0193702 | ||||||||
\(904\) | −3.57653e146 | −1.67157 | ||||||||
\(905\) | −1.09102e146 | −0.482756 | ||||||||
\(906\) | 7.41655e145 | 0.310711 | ||||||||
\(907\) | −3.83792e146 | −1.52242 | −0.761210 | − | 0.648505i | \(-0.775395\pi\) | ||||
−0.761210 | + | 0.648505i | \(0.775395\pi\) | |||||||
\(908\) | −2.55926e146 | −0.961311 | ||||||||
\(909\) | 2.49201e146 | 0.886416 | ||||||||
\(910\) | 1.24260e146 | 0.418585 | ||||||||
\(911\) | −6.33858e145 | −0.202224 | −0.101112 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101112 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(912\) | −5.91916e146 | −1.78861 | ||||||||
\(913\) | 3.38033e145 | 0.0967511 | ||||||||
\(914\) | 4.64540e146 | 1.25947 | ||||||||
\(915\) | 5.72912e145 | 0.147144 | ||||||||
\(916\) | −1.12291e147 | −2.73225 | ||||||||
\(917\) | −3.79486e146 | −0.874810 | ||||||||
\(918\) | 4.77364e146 | 1.04265 | ||||||||
\(919\) | 8.77393e146 | 1.81583 | 0.907917 | − | 0.419150i | \(-0.137672\pi\) | ||||
0.907917 | + | 0.419150i | \(0.137672\pi\) | |||||||
\(920\) | −3.20385e146 | −0.628311 | ||||||||
\(921\) | −3.27212e145 | −0.0608103 | ||||||||
\(922\) | 4.50312e146 | 0.793109 | ||||||||
\(923\) | −1.91459e146 | −0.319588 | ||||||||
\(924\) | 4.07601e146 | 0.644870 | ||||||||
\(925\) | 2.47755e146 | 0.371541 | ||||||||
\(926\) | 1.43242e147 | 2.03623 | ||||||||
\(927\) | −3.33892e146 | −0.449945 | ||||||||
\(928\) | 1.97322e146 | 0.252088 | ||||||||
\(929\) | −3.48231e146 | −0.421783 | −0.210892 | − | 0.977509i | \(-0.567637\pi\) | ||||
−0.210892 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(930\) | −9.35291e145 | −0.107409 | ||||||||
\(931\) | 1.00688e147 | 1.09640 | ||||||||
\(932\) | 2.39476e147 | 2.47271 | ||||||||
\(933\) | 6.55264e145 | 0.0641616 | ||||||||
\(934\) | −3.13317e147 | −2.90947 | ||||||||
\(935\) | 6.13920e146 | 0.540676 | ||||||||
\(936\) | −3.61339e147 | −3.01828 | ||||||||
\(937\) | −7.60769e146 | −0.602758 | −0.301379 | − | 0.953504i | \(-0.597447\pi\) | ||||
−0.301379 | + | 0.953504i | \(0.597447\pi\) | |||||||
\(938\) | −2.31168e147 | −1.73735 | ||||||||
\(939\) | −4.92919e146 | −0.351422 | ||||||||
\(940\) | −5.43520e146 | −0.367610 | ||||||||
\(941\) | 8.96692e146 | 0.575383 | 0.287691 | − | 0.957723i | \(-0.407112\pi\) | ||||
0.287691 | + | 0.957723i | \(0.407112\pi\) | |||||||
\(942\) | 1.30600e147 | 0.795105 | ||||||||
\(943\) | −2.82510e146 | −0.163194 | ||||||||
\(944\) | 5.91825e147 | 3.24399 | ||||||||
\(945\) | −2.19810e146 | −0.114334 | ||||||||
\(946\) | 6.54754e146 | 0.323196 | ||||||||
\(947\) | 1.17443e147 | 0.550180 | 0.275090 | − | 0.961418i | \(-0.411292\pi\) | ||||
0.275090 | + | 0.961418i | \(0.411292\pi\) | |||||||
\(948\) | −3.45660e146 | −0.153687 | ||||||||
\(949\) | 7.95399e146 | 0.335666 | ||||||||
\(950\) | −7.57501e147 | −3.03434 | ||||||||
\(951\) | −1.06459e147 | −0.404806 | ||||||||
\(952\) | 6.16023e147 | 2.22366 | ||||||||
\(953\) | −2.75038e147 | −0.942527 | −0.471264 | − | 0.881992i | \(-0.656202\pi\) | ||||
−0.471264 | + | 0.881992i | \(0.656202\pi\) | |||||||
\(954\) | −6.41576e147 | −2.08739 | ||||||||
\(955\) | 8.67213e146 | 0.267892 | ||||||||
\(956\) | 8.49314e147 | 2.49117 | ||||||||
\(957\) | 8.71685e145 | 0.0242783 | ||||||||
\(958\) | 8.19936e146 | 0.216864 | ||||||||
\(959\) | −1.41658e147 | −0.355811 | ||||||||
\(960\) | −1.50802e147 | −0.359733 | ||||||||
\(961\) | −2.89504e147 | −0.655914 | ||||||||
\(962\) | −3.69794e147 | −0.795780 | ||||||||
\(963\) | 7.46907e147 | 1.52674 | ||||||||
\(964\) | 1.12360e148 | 2.18171 | ||||||||
\(965\) | 1.07673e147 | 0.198612 | ||||||||
\(966\) | −9.50220e146 | −0.166516 | ||||||||
\(967\) | 8.89246e147 | 1.48051 | 0.740255 | − | 0.672326i | \(-0.234705\pi\) | ||||
0.740255 | + | 0.672326i | \(0.234705\pi\) | |||||||
\(968\) | −2.19323e148 | −3.46940 | ||||||||
\(969\) | −3.34734e147 | −0.503122 | ||||||||
\(970\) | −4.67034e147 | −0.667033 | ||||||||
\(971\) | 6.23935e146 | 0.0846813 | 0.0423406 | − | 0.999103i | \(-0.486519\pi\) | ||||
0.0423406 | + | 0.999103i | \(0.486519\pi\) | |||||||
\(972\) | 1.52852e148 | 1.97147 | ||||||||
\(973\) | −6.83951e147 | −0.838377 | ||||||||
\(974\) | 2.86371e148 | 3.33627 | ||||||||
\(975\) | 2.00649e147 | 0.222182 | ||||||||
\(976\) | −5.55100e148 | −5.84259 | ||||||||
\(977\) | 9.53759e147 | 0.954241 | 0.477120 | − | 0.878838i | \(-0.341681\pi\) | ||||
0.477120 | + | 0.878838i | \(0.341681\pi\) | |||||||
\(978\) | 4.13414e147 | 0.393199 | ||||||||
\(979\) | 2.82616e147 | 0.255537 | ||||||||
\(980\) | 6.95394e147 | 0.597778 | ||||||||
\(981\) | −1.55532e148 | −1.27117 | ||||||||
\(982\) | −2.10765e148 | −1.63787 | ||||||||
\(983\) | −1.49619e148 | −1.10558 | −0.552788 | − | 0.833322i | \(-0.686436\pi\) | ||||
−0.552788 | + | 0.833322i | \(0.686436\pi\) | |||||||
\(984\) | −3.95481e147 | −0.277887 | ||||||||
\(985\) | 6.42525e147 | 0.429335 | ||||||||
\(986\) | 2.07525e147 | 0.131875 | ||||||||
\(987\) | −1.02334e147 | −0.0618471 | ||||||||
\(988\) | 8.28190e148 | 4.76060 | ||||||||
\(989\) | −1.11809e147 | −0.0611310 | ||||||||
\(990\) | 1.76779e148 | 0.919368 | ||||||||
\(991\) | −1.65465e148 | −0.818577 | −0.409289 | − | 0.912405i | \(-0.634223\pi\) | ||||
−0.409289 | + | 0.912405i | \(0.634223\pi\) | |||||||
\(992\) | 4.87277e148 | 2.29323 | ||||||||
\(993\) | −7.70543e147 | −0.344992 | ||||||||
\(994\) | 9.39891e147 | 0.400361 | ||||||||
\(995\) | −7.61912e147 | −0.308789 | ||||||||
\(996\) | −1.27292e147 | −0.0490866 | ||||||||
\(997\) | −3.26412e148 | −1.19772 | −0.598860 | − | 0.800854i | \(-0.704379\pi\) | ||||
−0.598860 | + | 0.800854i | \(0.704379\pi\) | |||||||
\(998\) | 5.16767e147 | 0.180440 | ||||||||
\(999\) | 6.54147e147 | 0.217362 |
(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 | 1.100.a.a.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 9.100.a.d.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.100.a.a.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
9.100.a.d.1.8 | 8 | 3.2 | odd | 2 |