Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,10,Mod(1,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, 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("38.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(19.5713617742\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 34433x^{2} - 2723303x - 48270488 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-124.888\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −140.229 | −0.999525 | −0.499762 | − | 0.866163i | \(-0.666579\pi\) | ||||
−0.499762 | + | 0.866163i | \(0.666579\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | 1263.95 | 0.904407 | 0.452204 | − | 0.891915i | \(-0.350638\pi\) | ||||
0.452204 | + | 0.891915i | \(0.350638\pi\) | |||||||
\(6\) | 2243.67 | 0.706771 | ||||||||
\(7\) | −3487.42 | −0.548988 | −0.274494 | − | 0.961589i | \(-0.588510\pi\) | ||||
−0.274494 | + | 0.961589i | \(0.588510\pi\) | |||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −18.7042 | −0.000950271 0 | ||||||||
\(10\) | −20223.2 | −0.639512 | ||||||||
\(11\) | −49259.2 | −1.01443 | −0.507213 | − | 0.861821i | \(-0.669324\pi\) | ||||
−0.507213 | + | 0.861821i | \(0.669324\pi\) | |||||||
\(12\) | −35898.7 | −0.499762 | ||||||||
\(13\) | −68065.3 | −0.660969 | −0.330484 | − | 0.943811i | \(-0.607212\pi\) | ||||
−0.330484 | + | 0.943811i | \(0.607212\pi\) | |||||||
\(14\) | 55798.7 | 0.388193 | ||||||||
\(15\) | −177243. | −0.903977 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | 505716. | 1.46854 | 0.734271 | − | 0.678857i | \(-0.237524\pi\) | ||||
0.734271 | + | 0.678857i | \(0.237524\pi\) | |||||||
\(18\) | 299.267 | 0.000671943 0 | ||||||||
\(19\) | 130321. | 0.229416 | ||||||||
\(20\) | 323571. | 0.452204 | ||||||||
\(21\) | 489039. | 0.548727 | ||||||||
\(22\) | 788147. | 0.717307 | ||||||||
\(23\) | −585044. | −0.435926 | −0.217963 | − | 0.975957i | \(-0.569941\pi\) | ||||
−0.217963 | + | 0.975957i | \(0.569941\pi\) | |||||||
\(24\) | 574380. | 0.353385 | ||||||||
\(25\) | −355562. | −0.182048 | ||||||||
\(26\) | 1.08905e6 | 0.467375 | ||||||||
\(27\) | 2.76276e6 | 1.00047 | ||||||||
\(28\) | −892779. | −0.274494 | ||||||||
\(29\) | 2.62021e6 | 0.687932 | 0.343966 | − | 0.938982i | \(-0.388229\pi\) | ||||
0.343966 | + | 0.938982i | \(0.388229\pi\) | |||||||
\(30\) | 2.83588e6 | 0.639209 | ||||||||
\(31\) | 3.53093e6 | 0.686691 | 0.343345 | − | 0.939209i | \(-0.388440\pi\) | ||||
0.343345 | + | 0.939209i | \(0.388440\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | 6.90759e6 | 1.01394 | ||||||||
\(34\) | −8.09145e6 | −1.03842 | ||||||||
\(35\) | −4.40791e6 | −0.496509 | ||||||||
\(36\) | −4788.27 | −0.000475135 0 | ||||||||
\(37\) | 1.85431e7 | 1.62657 | 0.813287 | − | 0.581863i | \(-0.197676\pi\) | ||||
0.813287 | + | 0.581863i | \(0.197676\pi\) | |||||||
\(38\) | −2.08514e6 | −0.162221 | ||||||||
\(39\) | 9.54476e6 | 0.660655 | ||||||||
\(40\) | −5.17713e6 | −0.319756 | ||||||||
\(41\) | 2.18141e7 | 1.20562 | 0.602811 | − | 0.797884i | \(-0.294047\pi\) | ||||
0.602811 | + | 0.797884i | \(0.294047\pi\) | |||||||
\(42\) | −7.82462e6 | −0.388009 | ||||||||
\(43\) | −1.12704e7 | −0.502725 | −0.251362 | − | 0.967893i | \(-0.580879\pi\) | ||||
−0.251362 | + | 0.967893i | \(0.580879\pi\) | |||||||
\(44\) | −1.26104e7 | −0.507213 | ||||||||
\(45\) | −23641.1 | −0.000859432 0 | ||||||||
\(46\) | 9.36070e6 | 0.308246 | ||||||||
\(47\) | 1.54092e7 | 0.460616 | 0.230308 | − | 0.973118i | \(-0.426027\pi\) | ||||
0.230308 | + | 0.973118i | \(0.426027\pi\) | |||||||
\(48\) | −9.19008e6 | −0.249881 | ||||||||
\(49\) | −2.81915e7 | −0.698612 | ||||||||
\(50\) | 5.68899e6 | 0.128727 | ||||||||
\(51\) | −7.09162e7 | −1.46784 | ||||||||
\(52\) | −1.74247e7 | −0.330484 | ||||||||
\(53\) | 7.05741e6 | 0.122858 | 0.0614291 | − | 0.998111i | \(-0.480434\pi\) | ||||
0.0614291 | + | 0.998111i | \(0.480434\pi\) | |||||||
\(54\) | −4.42041e7 | −0.707442 | ||||||||
\(55\) | −6.22611e7 | −0.917454 | ||||||||
\(56\) | 1.42845e7 | 0.194097 | ||||||||
\(57\) | −1.82748e7 | −0.229307 | ||||||||
\(58\) | −4.19234e7 | −0.486442 | ||||||||
\(59\) | 2.90730e7 | 0.312360 | 0.156180 | − | 0.987729i | \(-0.450082\pi\) | ||||
0.156180 | + | 0.987729i | \(0.450082\pi\) | |||||||
\(60\) | −4.53741e7 | −0.451989 | ||||||||
\(61\) | 1.44284e8 | 1.33424 | 0.667121 | − | 0.744949i | \(-0.267526\pi\) | ||||
0.667121 | + | 0.744949i | \(0.267526\pi\) | |||||||
\(62\) | −5.64949e7 | −0.485564 | ||||||||
\(63\) | 65229.3 | 0.000521687 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −8.60310e7 | −0.597785 | ||||||||
\(66\) | −1.10521e8 | −0.716967 | ||||||||
\(67\) | 2.65266e7 | 0.160822 | 0.0804110 | − | 0.996762i | \(-0.474377\pi\) | ||||
0.0804110 | + | 0.996762i | \(0.474377\pi\) | |||||||
\(68\) | 1.29463e8 | 0.734271 | ||||||||
\(69\) | 8.20404e7 | 0.435719 | ||||||||
\(70\) | 7.05266e7 | 0.351085 | ||||||||
\(71\) | −4.27081e7 | −0.199456 | −0.0997281 | − | 0.995015i | \(-0.531797\pi\) | ||||
−0.0997281 | + | 0.995015i | \(0.531797\pi\) | |||||||
\(72\) | 76612.3 | 0.000335972 0 | ||||||||
\(73\) | 3.24644e8 | 1.33800 | 0.668998 | − | 0.743264i | \(-0.266723\pi\) | ||||
0.668998 | + | 0.743264i | \(0.266723\pi\) | |||||||
\(74\) | −2.96689e8 | −1.15016 | ||||||||
\(75\) | 4.98602e7 | 0.181961 | ||||||||
\(76\) | 3.33622e7 | 0.114708 | ||||||||
\(77\) | 1.71787e8 | 0.556908 | ||||||||
\(78\) | −1.52716e8 | −0.467153 | ||||||||
\(79\) | −8.88210e7 | −0.256563 | −0.128281 | − | 0.991738i | \(-0.540946\pi\) | ||||
−0.128281 | + | 0.991738i | \(0.540946\pi\) | |||||||
\(80\) | 8.28341e7 | 0.226102 | ||||||||
\(81\) | −3.87052e8 | −0.999049 | ||||||||
\(82\) | −3.49026e8 | −0.852503 | ||||||||
\(83\) | 6.29830e7 | 0.145671 | 0.0728353 | − | 0.997344i | \(-0.476795\pi\) | ||||
0.0728353 | + | 0.997344i | \(0.476795\pi\) | |||||||
\(84\) | 1.25194e8 | 0.274363 | ||||||||
\(85\) | 6.39198e8 | 1.32816 | ||||||||
\(86\) | 1.80326e8 | 0.355480 | ||||||||
\(87\) | −3.67431e8 | −0.687605 | ||||||||
\(88\) | 2.01766e8 | 0.358654 | ||||||||
\(89\) | −4.54329e7 | −0.0767565 | −0.0383783 | − | 0.999263i | \(-0.512219\pi\) | ||||
−0.0383783 | + | 0.999263i | \(0.512219\pi\) | |||||||
\(90\) | 378258. | 0.000607710 0 | ||||||||
\(91\) | 2.37372e8 | 0.362864 | ||||||||
\(92\) | −1.49771e8 | −0.217963 | ||||||||
\(93\) | −4.95140e8 | −0.686365 | ||||||||
\(94\) | −2.46547e8 | −0.325705 | ||||||||
\(95\) | 1.64719e8 | 0.207485 | ||||||||
\(96\) | 1.47041e8 | 0.176693 | ||||||||
\(97\) | 1.64830e9 | 1.89044 | 0.945219 | − | 0.326438i | \(-0.105848\pi\) | ||||
0.945219 | + | 0.326438i | \(0.105848\pi\) | |||||||
\(98\) | 4.51064e8 | 0.493994 | ||||||||
\(99\) | 921353. | 0.000963980 0 | ||||||||
\(100\) | −9.10238e7 | −0.0910238 | ||||||||
\(101\) | −8.97226e8 | −0.857938 | −0.428969 | − | 0.903319i | \(-0.641123\pi\) | ||||
−0.428969 | + | 0.903319i | \(0.641123\pi\) | |||||||
\(102\) | 1.13466e9 | 1.03792 | ||||||||
\(103\) | 1.67622e9 | 1.46745 | 0.733726 | − | 0.679445i | \(-0.237779\pi\) | ||||
0.733726 | + | 0.679445i | \(0.237779\pi\) | |||||||
\(104\) | 2.78796e8 | 0.233688 | ||||||||
\(105\) | 6.18119e8 | 0.496273 | ||||||||
\(106\) | −1.12919e8 | −0.0868738 | ||||||||
\(107\) | 3.08053e8 | 0.227195 | 0.113597 | − | 0.993527i | \(-0.463763\pi\) | ||||
0.113597 | + | 0.993527i | \(0.463763\pi\) | |||||||
\(108\) | 7.07266e8 | 0.500237 | ||||||||
\(109\) | −1.79569e8 | −0.121846 | −0.0609230 | − | 0.998142i | \(-0.519404\pi\) | ||||
−0.0609230 | + | 0.998142i | \(0.519404\pi\) | |||||||
\(110\) | 9.96177e8 | 0.648738 | ||||||||
\(111\) | −2.60028e9 | −1.62580 | ||||||||
\(112\) | −2.28551e8 | −0.137247 | ||||||||
\(113\) | −2.30787e9 | −1.33155 | −0.665776 | − | 0.746152i | \(-0.731899\pi\) | ||||
−0.665776 | + | 0.746152i | \(0.731899\pi\) | |||||||
\(114\) | 2.92397e8 | 0.162144 | ||||||||
\(115\) | −7.39465e8 | −0.394255 | ||||||||
\(116\) | 6.70775e8 | 0.343966 | ||||||||
\(117\) | 1.27311e6 | 0.000628099 0 | ||||||||
\(118\) | −4.65168e8 | −0.220872 | ||||||||
\(119\) | −1.76364e9 | −0.806212 | ||||||||
\(120\) | 7.25986e8 | 0.319604 | ||||||||
\(121\) | 6.85222e7 | 0.0290601 | ||||||||
\(122\) | −2.30855e9 | −0.943452 | ||||||||
\(123\) | −3.05899e9 | −1.20505 | ||||||||
\(124\) | 9.03918e8 | 0.343345 | ||||||||
\(125\) | −2.91806e9 | −1.06905 | ||||||||
\(126\) | −1.04367e6 | −0.000368889 0 | ||||||||
\(127\) | −4.51313e9 | −1.53943 | −0.769717 | − | 0.638385i | \(-0.779603\pi\) | ||||
−0.769717 | + | 0.638385i | \(0.779603\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | 1.58044e9 | 0.502486 | ||||||||
\(130\) | 1.37650e9 | 0.422698 | ||||||||
\(131\) | −2.53716e9 | −0.752708 | −0.376354 | − | 0.926476i | \(-0.622822\pi\) | ||||
−0.376354 | + | 0.926476i | \(0.622822\pi\) | |||||||
\(132\) | 1.76834e9 | 0.506972 | ||||||||
\(133\) | −4.54484e8 | −0.125946 | ||||||||
\(134\) | −4.24426e8 | −0.113718 | ||||||||
\(135\) | 3.49198e9 | 0.904836 | ||||||||
\(136\) | −2.07141e9 | −0.519208 | ||||||||
\(137\) | 4.04090e9 | 0.980021 | 0.490010 | − | 0.871717i | \(-0.336993\pi\) | ||||
0.490010 | + | 0.871717i | \(0.336993\pi\) | |||||||
\(138\) | −1.31265e9 | −0.308100 | ||||||||
\(139\) | −1.86522e9 | −0.423803 | −0.211901 | − | 0.977291i | \(-0.567966\pi\) | ||||
−0.211901 | + | 0.977291i | \(0.567966\pi\) | |||||||
\(140\) | −1.12843e9 | −0.248254 | ||||||||
\(141\) | −2.16082e9 | −0.460397 | ||||||||
\(142\) | 6.83329e8 | 0.141037 | ||||||||
\(143\) | 3.35284e9 | 0.670504 | ||||||||
\(144\) | −1.22580e6 | −0.000237568 0 | ||||||||
\(145\) | 3.31181e9 | 0.622171 | ||||||||
\(146\) | −5.19431e9 | −0.946106 | ||||||||
\(147\) | 3.95328e9 | 0.698280 | ||||||||
\(148\) | 4.74702e9 | 0.813287 | ||||||||
\(149\) | −7.60481e9 | −1.26401 | −0.632004 | − | 0.774965i | \(-0.717768\pi\) | ||||
−0.632004 | + | 0.774965i | \(0.717768\pi\) | |||||||
\(150\) | −7.97763e8 | −0.128666 | ||||||||
\(151\) | 1.74653e9 | 0.273388 | 0.136694 | − | 0.990613i | \(-0.456352\pi\) | ||||
0.136694 | + | 0.990613i | \(0.456352\pi\) | |||||||
\(152\) | −5.33795e8 | −0.0811107 | ||||||||
\(153\) | −9.45900e6 | −0.00139551 | ||||||||
\(154\) | −2.74860e9 | −0.393793 | ||||||||
\(155\) | 4.46291e9 | 0.621048 | ||||||||
\(156\) | 2.44346e9 | 0.330327 | ||||||||
\(157\) | 1.06564e10 | 1.39979 | 0.699893 | − | 0.714248i | \(-0.253231\pi\) | ||||
0.699893 | + | 0.714248i | \(0.253231\pi\) | |||||||
\(158\) | 1.42114e9 | 0.181417 | ||||||||
\(159\) | −9.89657e8 | −0.122800 | ||||||||
\(160\) | −1.32535e9 | −0.159878 | ||||||||
\(161\) | 2.04029e9 | 0.239318 | ||||||||
\(162\) | 6.19283e9 | 0.706434 | ||||||||
\(163\) | 9.11348e9 | 1.01121 | 0.505603 | − | 0.862766i | \(-0.331270\pi\) | ||||
0.505603 | + | 0.862766i | \(0.331270\pi\) | |||||||
\(164\) | 5.58442e9 | 0.602811 | ||||||||
\(165\) | 8.73083e9 | 0.917018 | ||||||||
\(166\) | −1.00773e9 | −0.103005 | ||||||||
\(167\) | 1.15546e10 | 1.14956 | 0.574778 | − | 0.818309i | \(-0.305088\pi\) | ||||
0.574778 | + | 0.818309i | \(0.305088\pi\) | |||||||
\(168\) | −2.00310e9 | −0.194004 | ||||||||
\(169\) | −5.97161e9 | −0.563120 | ||||||||
\(170\) | −1.02272e10 | −0.939151 | ||||||||
\(171\) | −2.43755e6 | −0.000218007 0 | ||||||||
\(172\) | −2.88522e9 | −0.251362 | ||||||||
\(173\) | −2.52786e9 | −0.214558 | −0.107279 | − | 0.994229i | \(-0.534214\pi\) | ||||
−0.107279 | + | 0.994229i | \(0.534214\pi\) | |||||||
\(174\) | 5.87890e9 | 0.486210 | ||||||||
\(175\) | 1.23999e9 | 0.0999419 | ||||||||
\(176\) | −3.22825e9 | −0.253606 | ||||||||
\(177\) | −4.07689e9 | −0.312212 | ||||||||
\(178\) | 7.26926e8 | 0.0542751 | ||||||||
\(179\) | −1.73068e10 | −1.26002 | −0.630009 | − | 0.776588i | \(-0.716949\pi\) | ||||
−0.630009 | + | 0.776588i | \(0.716949\pi\) | |||||||
\(180\) | −6.05212e6 | −0.000429716 0 | ||||||||
\(181\) | 1.08688e10 | 0.752711 | 0.376355 | − | 0.926475i | \(-0.377177\pi\) | ||||
0.376355 | + | 0.926475i | \(0.377177\pi\) | |||||||
\(182\) | −3.79796e9 | −0.256583 | ||||||||
\(183\) | −2.02329e10 | −1.33361 | ||||||||
\(184\) | 2.39634e9 | 0.154123 | ||||||||
\(185\) | 2.34375e10 | 1.47108 | ||||||||
\(186\) | 7.92224e9 | 0.485333 | ||||||||
\(187\) | −2.49112e10 | −1.48973 | ||||||||
\(188\) | 3.94475e9 | 0.230308 | ||||||||
\(189\) | −9.63489e9 | −0.549248 | ||||||||
\(190\) | −2.63550e9 | −0.146714 | ||||||||
\(191\) | −5.33871e9 | −0.290259 | −0.145130 | − | 0.989413i | \(-0.546360\pi\) | ||||
−0.145130 | + | 0.989413i | \(0.546360\pi\) | |||||||
\(192\) | −2.35266e9 | −0.124941 | ||||||||
\(193\) | 2.75948e10 | 1.43159 | 0.715797 | − | 0.698309i | \(-0.246064\pi\) | ||||
0.715797 | + | 0.698309i | \(0.246064\pi\) | |||||||
\(194\) | −2.63727e10 | −1.33674 | ||||||||
\(195\) | 1.20641e10 | 0.597501 | ||||||||
\(196\) | −7.21703e9 | −0.349306 | ||||||||
\(197\) | −9.61053e9 | −0.454621 | −0.227310 | − | 0.973822i | \(-0.572993\pi\) | ||||
−0.227310 | + | 0.973822i | \(0.572993\pi\) | |||||||
\(198\) | −1.47417e7 | −0.000681636 0 | ||||||||
\(199\) | 2.88815e10 | 1.30551 | 0.652756 | − | 0.757568i | \(-0.273612\pi\) | ||||
0.652756 | + | 0.757568i | \(0.273612\pi\) | |||||||
\(200\) | 1.45638e9 | 0.0643635 | ||||||||
\(201\) | −3.71982e9 | −0.160746 | ||||||||
\(202\) | 1.43556e10 | 0.606654 | ||||||||
\(203\) | −9.13778e9 | −0.377666 | ||||||||
\(204\) | −1.81546e10 | −0.733922 | ||||||||
\(205\) | 2.75719e10 | 1.09037 | ||||||||
\(206\) | −2.68196e10 | −1.03765 | ||||||||
\(207\) | 1.09428e7 | 0.000414248 0 | ||||||||
\(208\) | −4.46073e9 | −0.165242 | ||||||||
\(209\) | −6.41951e9 | −0.232725 | ||||||||
\(210\) | −9.88990e9 | −0.350918 | ||||||||
\(211\) | 2.26589e10 | 0.786986 | 0.393493 | − | 0.919328i | \(-0.371267\pi\) | ||||
0.393493 | + | 0.919328i | \(0.371267\pi\) | |||||||
\(212\) | 1.80670e9 | 0.0614291 | ||||||||
\(213\) | 5.98893e9 | 0.199361 | ||||||||
\(214\) | −4.92884e9 | −0.160651 | ||||||||
\(215\) | −1.42452e10 | −0.454668 | ||||||||
\(216\) | −1.13163e10 | −0.353721 | ||||||||
\(217\) | −1.23138e10 | −0.376985 | ||||||||
\(218\) | 2.87310e9 | 0.0861581 | ||||||||
\(219\) | −4.55247e10 | −1.33736 | ||||||||
\(220\) | −1.59388e10 | −0.458727 | ||||||||
\(221\) | −3.44217e10 | −0.970660 | ||||||||
\(222\) | 4.16045e10 | 1.14961 | ||||||||
\(223\) | −5.84566e10 | −1.58293 | −0.791465 | − | 0.611214i | \(-0.790681\pi\) | ||||
−0.791465 | + | 0.611214i | \(0.790681\pi\) | |||||||
\(224\) | 3.65682e9 | 0.0970483 | ||||||||
\(225\) | 6.65049e6 | 0.000172995 0 | ||||||||
\(226\) | 3.69259e10 | 0.941549 | ||||||||
\(227\) | −4.82187e9 | −0.120531 | −0.0602656 | − | 0.998182i | \(-0.519195\pi\) | ||||
−0.0602656 | + | 0.998182i | \(0.519195\pi\) | |||||||
\(228\) | −4.67836e9 | −0.114653 | ||||||||
\(229\) | −7.15833e9 | −0.172009 | −0.0860046 | − | 0.996295i | \(-0.527410\pi\) | ||||
−0.0860046 | + | 0.996295i | \(0.527410\pi\) | |||||||
\(230\) | 1.18314e10 | 0.278780 | ||||||||
\(231\) | −2.40897e10 | −0.556643 | ||||||||
\(232\) | −1.07324e10 | −0.243221 | ||||||||
\(233\) | 4.52737e10 | 1.00634 | 0.503169 | − | 0.864188i | \(-0.332167\pi\) | ||||
0.503169 | + | 0.864188i | \(0.332167\pi\) | |||||||
\(234\) | −2.03697e7 | −0.000444133 0 | ||||||||
\(235\) | 1.94764e10 | 0.416585 | ||||||||
\(236\) | 7.44268e9 | 0.156180 | ||||||||
\(237\) | 1.24553e10 | 0.256441 | ||||||||
\(238\) | 2.82183e10 | 0.570078 | ||||||||
\(239\) | −7.05422e10 | −1.39849 | −0.699244 | − | 0.714883i | \(-0.746480\pi\) | ||||
−0.699244 | + | 0.714883i | \(0.746480\pi\) | |||||||
\(240\) | −1.16158e10 | −0.225994 | ||||||||
\(241\) | 7.83138e10 | 1.49542 | 0.747708 | − | 0.664028i | \(-0.231154\pi\) | ||||
0.747708 | + | 0.664028i | \(0.231154\pi\) | |||||||
\(242\) | −1.09635e9 | −0.0205486 | ||||||||
\(243\) | −1.03301e8 | −0.00190054 | ||||||||
\(244\) | 3.69368e10 | 0.667121 | ||||||||
\(245\) | −3.56326e10 | −0.631830 | ||||||||
\(246\) | 4.89438e10 | 0.852098 | ||||||||
\(247\) | −8.87034e9 | −0.151637 | ||||||||
\(248\) | −1.44627e10 | −0.242782 | ||||||||
\(249\) | −8.83207e9 | −0.145601 | ||||||||
\(250\) | 4.66889e10 | 0.755934 | ||||||||
\(251\) | 1.03661e11 | 1.64848 | 0.824240 | − | 0.566241i | \(-0.191603\pi\) | ||||
0.824240 | + | 0.566241i | \(0.191603\pi\) | |||||||
\(252\) | 1.66987e7 | 0.000260844 0 | ||||||||
\(253\) | 2.88188e10 | 0.442215 | ||||||||
\(254\) | 7.22101e10 | 1.08854 | ||||||||
\(255\) | −8.96344e10 | −1.32753 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 1.07294e11 | 1.53419 | 0.767093 | − | 0.641536i | \(-0.221703\pi\) | ||||
0.767093 | + | 0.641536i | \(0.221703\pi\) | |||||||
\(258\) | −2.52870e10 | −0.355311 | ||||||||
\(259\) | −6.46674e10 | −0.892969 | ||||||||
\(260\) | −2.20239e10 | −0.298892 | ||||||||
\(261\) | −4.90090e7 | −0.000653722 0 | ||||||||
\(262\) | 4.05945e10 | 0.532245 | ||||||||
\(263\) | −1.18240e11 | −1.52393 | −0.761963 | − | 0.647620i | \(-0.775764\pi\) | ||||
−0.761963 | + | 0.647620i | \(0.775764\pi\) | |||||||
\(264\) | −2.82935e10 | −0.358483 | ||||||||
\(265\) | 8.92019e9 | 0.111114 | ||||||||
\(266\) | 7.27174e9 | 0.0890576 | ||||||||
\(267\) | 6.37103e9 | 0.0767201 | ||||||||
\(268\) | 6.79082e9 | 0.0804110 | ||||||||
\(269\) | 1.08142e11 | 1.25924 | 0.629620 | − | 0.776903i | \(-0.283211\pi\) | ||||
0.629620 | + | 0.776903i | \(0.283211\pi\) | |||||||
\(270\) | −5.58717e10 | −0.639816 | ||||||||
\(271\) | −1.22183e11 | −1.37609 | −0.688047 | − | 0.725667i | \(-0.741532\pi\) | ||||
−0.688047 | + | 0.725667i | \(0.741532\pi\) | |||||||
\(272\) | 3.31426e10 | 0.367135 | ||||||||
\(273\) | −3.32866e10 | −0.362691 | ||||||||
\(274\) | −6.46544e10 | −0.692979 | ||||||||
\(275\) | 1.75147e10 | 0.184674 | ||||||||
\(276\) | 2.10023e10 | 0.217860 | ||||||||
\(277\) | 1.18944e11 | 1.21390 | 0.606951 | − | 0.794740i | \(-0.292393\pi\) | ||||
0.606951 | + | 0.794740i | \(0.292393\pi\) | |||||||
\(278\) | 2.98436e10 | 0.299674 | ||||||||
\(279\) | −6.60431e7 | −0.000652542 0 | ||||||||
\(280\) | 1.80548e10 | 0.175542 | ||||||||
\(281\) | −4.73680e10 | −0.453218 | −0.226609 | − | 0.973986i | \(-0.572764\pi\) | ||||
−0.226609 | + | 0.973986i | \(0.572764\pi\) | |||||||
\(282\) | 3.45731e10 | 0.325550 | ||||||||
\(283\) | 1.59829e11 | 1.48121 | 0.740603 | − | 0.671943i | \(-0.234540\pi\) | ||||
0.740603 | + | 0.671943i | \(0.234540\pi\) | |||||||
\(284\) | −1.09333e10 | −0.0997281 | ||||||||
\(285\) | −2.30984e10 | −0.207387 | ||||||||
\(286\) | −5.36455e10 | −0.474118 | ||||||||
\(287\) | −7.60750e10 | −0.661871 | ||||||||
\(288\) | 1.96128e7 | 0.000167986 0 | ||||||||
\(289\) | 1.37161e11 | 1.15662 | ||||||||
\(290\) | −5.29890e10 | −0.439941 | ||||||||
\(291\) | −2.31140e11 | −1.88954 | ||||||||
\(292\) | 8.31089e10 | 0.668998 | ||||||||
\(293\) | 1.32731e11 | 1.05212 | 0.526062 | − | 0.850446i | \(-0.323668\pi\) | ||||
0.526062 | + | 0.850446i | \(0.323668\pi\) | |||||||
\(294\) | −6.32525e10 | −0.493759 | ||||||||
\(295\) | 3.67467e10 | 0.282501 | ||||||||
\(296\) | −7.59524e10 | −0.575081 | ||||||||
\(297\) | −1.36091e11 | −1.01491 | ||||||||
\(298\) | 1.21677e11 | 0.893789 | ||||||||
\(299\) | 3.98212e10 | 0.288134 | ||||||||
\(300\) | 1.27642e10 | 0.0909805 | ||||||||
\(301\) | 3.93045e10 | 0.275990 | ||||||||
\(302\) | −2.79444e10 | −0.193314 | ||||||||
\(303\) | 1.25818e11 | 0.857530 | ||||||||
\(304\) | 8.54072e9 | 0.0573539 | ||||||||
\(305\) | 1.82368e11 | 1.20670 | ||||||||
\(306\) | 1.51344e8 | 0.000986776 0 | ||||||||
\(307\) | 2.41951e11 | 1.55455 | 0.777274 | − | 0.629162i | \(-0.216602\pi\) | ||||
0.777274 | + | 0.629162i | \(0.216602\pi\) | |||||||
\(308\) | 4.39776e10 | 0.278454 | ||||||||
\(309\) | −2.35056e11 | −1.46676 | ||||||||
\(310\) | −7.14065e10 | −0.439147 | ||||||||
\(311\) | −1.75276e11 | −1.06243 | −0.531217 | − | 0.847236i | \(-0.678265\pi\) | ||||
−0.531217 | + | 0.847236i | \(0.678265\pi\) | |||||||
\(312\) | −3.90954e10 | −0.233577 | ||||||||
\(313\) | −2.56460e11 | −1.51032 | −0.755161 | − | 0.655539i | \(-0.772442\pi\) | ||||
−0.755161 | + | 0.655539i | \(0.772442\pi\) | |||||||
\(314\) | −1.70502e11 | −0.989798 | ||||||||
\(315\) | 8.24464e7 | 0.000471818 0 | ||||||||
\(316\) | −2.27382e10 | −0.128281 | ||||||||
\(317\) | −2.91020e10 | −0.161866 | −0.0809331 | − | 0.996720i | \(-0.525790\pi\) | ||||
−0.0809331 | + | 0.996720i | \(0.525790\pi\) | |||||||
\(318\) | 1.58345e10 | 0.0868325 | ||||||||
\(319\) | −1.29070e11 | −0.697856 | ||||||||
\(320\) | 2.12055e10 | 0.113051 | ||||||||
\(321\) | −4.31980e10 | −0.227087 | ||||||||
\(322\) | −3.26447e10 | −0.169224 | ||||||||
\(323\) | 6.59054e10 | 0.336907 | ||||||||
\(324\) | −9.90853e10 | −0.499524 | ||||||||
\(325\) | 2.42014e10 | 0.120328 | ||||||||
\(326\) | −1.45816e11 | −0.715031 | ||||||||
\(327\) | 2.51808e10 | 0.121788 | ||||||||
\(328\) | −8.93508e10 | −0.426251 | ||||||||
\(329\) | −5.37382e10 | −0.252873 | ||||||||
\(330\) | −1.39693e11 | −0.648430 | ||||||||
\(331\) | −1.45683e11 | −0.667088 | −0.333544 | − | 0.942734i | \(-0.608245\pi\) | ||||
−0.333544 | + | 0.942734i | \(0.608245\pi\) | |||||||
\(332\) | 1.61236e10 | 0.0728353 | ||||||||
\(333\) | −3.46833e8 | −0.00154569 | ||||||||
\(334\) | −1.84873e11 | −0.812859 | ||||||||
\(335\) | 3.35283e10 | 0.145449 | ||||||||
\(336\) | 3.20496e10 | 0.137182 | ||||||||
\(337\) | −4.16729e10 | −0.176002 | −0.0880012 | − | 0.996120i | \(-0.528048\pi\) | ||||
−0.0880012 | + | 0.996120i | \(0.528048\pi\) | |||||||
\(338\) | 9.55457e10 | 0.398186 | ||||||||
\(339\) | 3.23631e11 | 1.33092 | ||||||||
\(340\) | 1.63635e11 | 0.664080 | ||||||||
\(341\) | −1.73931e11 | −0.696597 | ||||||||
\(342\) | 3.90008e7 | 0.000154154 0 | ||||||||
\(343\) | 2.39045e11 | 0.932518 | ||||||||
\(344\) | 4.61635e10 | 0.177740 | ||||||||
\(345\) | 1.03695e11 | 0.394067 | ||||||||
\(346\) | 4.04457e10 | 0.151716 | ||||||||
\(347\) | −5.79909e10 | −0.214722 | −0.107361 | − | 0.994220i | \(-0.534240\pi\) | ||||
−0.107361 | + | 0.994220i | \(0.534240\pi\) | |||||||
\(348\) | −9.40624e10 | −0.343803 | ||||||||
\(349\) | −1.06762e11 | −0.385214 | −0.192607 | − | 0.981276i | \(-0.561694\pi\) | ||||
−0.192607 | + | 0.981276i | \(0.561694\pi\) | |||||||
\(350\) | −1.98399e10 | −0.0706696 | ||||||||
\(351\) | −1.88048e11 | −0.661282 | ||||||||
\(352\) | 5.16520e10 | 0.179327 | ||||||||
\(353\) | −4.27202e11 | −1.46436 | −0.732180 | − | 0.681112i | \(-0.761497\pi\) | ||||
−0.732180 | + | 0.681112i | \(0.761497\pi\) | |||||||
\(354\) | 6.52302e10 | 0.220767 | ||||||||
\(355\) | −5.39808e10 | −0.180390 | ||||||||
\(356\) | −1.16308e10 | −0.0383783 | ||||||||
\(357\) | 2.47314e11 | 0.805828 | ||||||||
\(358\) | 2.76908e11 | 0.890968 | ||||||||
\(359\) | 4.29892e11 | 1.36595 | 0.682975 | − | 0.730442i | \(-0.260686\pi\) | ||||
0.682975 | + | 0.730442i | \(0.260686\pi\) | |||||||
\(360\) | 9.68340e7 | 0.000303855 0 | ||||||||
\(361\) | 1.69836e10 | 0.0526316 | ||||||||
\(362\) | −1.73901e11 | −0.532247 | ||||||||
\(363\) | −9.60883e9 | −0.0290463 | ||||||||
\(364\) | 6.07673e10 | 0.181432 | ||||||||
\(365\) | 4.10333e11 | 1.21009 | ||||||||
\(366\) | 3.23727e11 | 0.943004 | ||||||||
\(367\) | 1.40582e11 | 0.404512 | 0.202256 | − | 0.979333i | \(-0.435173\pi\) | ||||
0.202256 | + | 0.979333i | \(0.435173\pi\) | |||||||
\(368\) | −3.83414e10 | −0.108982 | ||||||||
\(369\) | −4.08016e8 | −0.00114567 | ||||||||
\(370\) | −3.74999e11 | −1.04021 | ||||||||
\(371\) | −2.46121e10 | −0.0674476 | ||||||||
\(372\) | −1.26756e11 | −0.343182 | ||||||||
\(373\) | 4.31647e11 | 1.15462 | 0.577310 | − | 0.816525i | \(-0.304102\pi\) | ||||
0.577310 | + | 0.816525i | \(0.304102\pi\) | |||||||
\(374\) | 3.98579e11 | 1.05340 | ||||||||
\(375\) | 4.09198e11 | 1.06854 | ||||||||
\(376\) | −6.31160e10 | −0.162852 | ||||||||
\(377\) | −1.78346e11 | −0.454702 | ||||||||
\(378\) | 1.54158e11 | 0.388377 | ||||||||
\(379\) | 7.16332e11 | 1.78336 | 0.891678 | − | 0.452670i | \(-0.149528\pi\) | ||||
0.891678 | + | 0.452670i | \(0.149528\pi\) | |||||||
\(380\) | 4.21680e10 | 0.103743 | ||||||||
\(381\) | 6.32874e11 | 1.53870 | ||||||||
\(382\) | 8.54194e10 | 0.205244 | ||||||||
\(383\) | −1.03271e11 | −0.245236 | −0.122618 | − | 0.992454i | \(-0.539129\pi\) | ||||
−0.122618 | + | 0.992454i | \(0.539129\pi\) | |||||||
\(384\) | 3.76426e10 | 0.0883463 | ||||||||
\(385\) | 2.17130e11 | 0.503671 | ||||||||
\(386\) | −4.41517e11 | −1.01229 | ||||||||
\(387\) | 2.10803e8 | 0.000477725 0 | ||||||||
\(388\) | 4.21964e11 | 0.945219 | ||||||||
\(389\) | −3.49935e11 | −0.774845 | −0.387422 | − | 0.921902i | \(-0.626634\pi\) | ||||
−0.387422 | + | 0.921902i | \(0.626634\pi\) | |||||||
\(390\) | −1.93025e11 | −0.422497 | ||||||||
\(391\) | −2.95866e11 | −0.640176 | ||||||||
\(392\) | 1.15473e11 | 0.246997 | ||||||||
\(393\) | 3.55784e11 | 0.752351 | ||||||||
\(394\) | 1.53769e11 | 0.321466 | ||||||||
\(395\) | −1.12265e11 | −0.232037 | ||||||||
\(396\) | 2.35866e8 | 0.000481990 0 | ||||||||
\(397\) | −2.83640e11 | −0.573073 | −0.286536 | − | 0.958069i | \(-0.592504\pi\) | ||||
−0.286536 | + | 0.958069i | \(0.592504\pi\) | |||||||
\(398\) | −4.62104e11 | −0.923137 | ||||||||
\(399\) | 6.37320e10 | 0.125887 | ||||||||
\(400\) | −2.33021e10 | −0.0455119 | ||||||||
\(401\) | −9.94065e11 | −1.91984 | −0.959920 | − | 0.280275i | \(-0.909574\pi\) | ||||
−0.959920 | + | 0.280275i | \(0.909574\pi\) | |||||||
\(402\) | 5.95171e10 | 0.113664 | ||||||||
\(403\) | −2.40334e11 | −0.453881 | ||||||||
\(404\) | −2.29690e11 | −0.428969 | ||||||||
\(405\) | −4.89213e11 | −0.903547 | ||||||||
\(406\) | 1.46204e11 | 0.267051 | ||||||||
\(407\) | −9.13417e11 | −1.65004 | ||||||||
\(408\) | 2.90473e11 | 0.518961 | ||||||||
\(409\) | 2.41111e11 | 0.426051 | 0.213026 | − | 0.977047i | \(-0.431668\pi\) | ||||
0.213026 | + | 0.977047i | \(0.431668\pi\) | |||||||
\(410\) | −4.41151e11 | −0.771010 | ||||||||
\(411\) | −5.66653e11 | −0.979555 | ||||||||
\(412\) | 4.29113e11 | 0.733726 | ||||||||
\(413\) | −1.01390e11 | −0.171482 | ||||||||
\(414\) | −1.75084e8 | −0.000292918 0 | ||||||||
\(415\) | 7.96072e10 | 0.131745 | ||||||||
\(416\) | 7.13717e10 | 0.116844 | ||||||||
\(417\) | 2.61559e11 | 0.423602 | ||||||||
\(418\) | 1.02712e11 | 0.164562 | ||||||||
\(419\) | 7.03102e11 | 1.11444 | 0.557218 | − | 0.830366i | \(-0.311869\pi\) | ||||
0.557218 | + | 0.830366i | \(0.311869\pi\) | |||||||
\(420\) | 1.58238e11 | 0.248136 | ||||||||
\(421\) | −2.68270e11 | −0.416200 | −0.208100 | − | 0.978108i | \(-0.566728\pi\) | ||||
−0.208100 | + | 0.978108i | \(0.566728\pi\) | |||||||
\(422\) | −3.62542e11 | −0.556483 | ||||||||
\(423\) | −2.88216e8 | −0.000437710 0 | ||||||||
\(424\) | −2.89071e10 | −0.0434369 | ||||||||
\(425\) | −1.79813e11 | −0.267344 | ||||||||
\(426\) | −9.58229e10 | −0.140970 | ||||||||
\(427\) | −5.03180e11 | −0.732483 | ||||||||
\(428\) | 7.88615e10 | 0.113597 | ||||||||
\(429\) | −4.70168e11 | −0.670185 | ||||||||
\(430\) | 2.27923e11 | 0.321499 | ||||||||
\(431\) | 5.95908e10 | 0.0831825 | 0.0415912 | − | 0.999135i | \(-0.486757\pi\) | ||||
0.0415912 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(432\) | 1.81060e11 | 0.250119 | ||||||||
\(433\) | −1.16290e12 | −1.58982 | −0.794909 | − | 0.606729i | \(-0.792481\pi\) | ||||
−0.794909 | + | 0.606729i | \(0.792481\pi\) | |||||||
\(434\) | 1.97021e11 | 0.266569 | ||||||||
\(435\) | −4.64414e11 | −0.621875 | ||||||||
\(436\) | −4.59696e10 | −0.0609230 | ||||||||
\(437\) | −7.62435e10 | −0.100008 | ||||||||
\(438\) | 7.28395e11 | 0.945657 | ||||||||
\(439\) | −1.32465e12 | −1.70220 | −0.851100 | − | 0.525004i | \(-0.824064\pi\) | ||||
−0.851100 | + | 0.525004i | \(0.824064\pi\) | |||||||
\(440\) | 2.55021e11 | 0.324369 | ||||||||
\(441\) | 5.27300e8 | 0.000663871 0 | ||||||||
\(442\) | 5.50747e11 | 0.686360 | ||||||||
\(443\) | 7.48682e11 | 0.923593 | 0.461797 | − | 0.886986i | \(-0.347205\pi\) | ||||
0.461797 | + | 0.886986i | \(0.347205\pi\) | |||||||
\(444\) | −6.65673e11 | −0.812900 | ||||||||
\(445\) | −5.74248e10 | −0.0694192 | ||||||||
\(446\) | 9.35306e11 | 1.11930 | ||||||||
\(447\) | 1.06642e12 | 1.26341 | ||||||||
\(448\) | −5.85091e10 | −0.0686235 | ||||||||
\(449\) | 8.07450e11 | 0.937577 | 0.468788 | − | 0.883310i | \(-0.344691\pi\) | ||||
0.468788 | + | 0.883310i | \(0.344691\pi\) | |||||||
\(450\) | −1.06408e8 | −0.000122326 0 | ||||||||
\(451\) | −1.07455e12 | −1.22301 | ||||||||
\(452\) | −5.90814e11 | −0.665776 | ||||||||
\(453\) | −2.44914e11 | −0.273258 | ||||||||
\(454\) | 7.71500e10 | 0.0852284 | ||||||||
\(455\) | 3.00026e11 | 0.328177 | ||||||||
\(456\) | 7.48537e10 | 0.0810722 | ||||||||
\(457\) | −2.09593e11 | −0.224778 | −0.112389 | − | 0.993664i | \(-0.535850\pi\) | ||||
−0.112389 | + | 0.993664i | \(0.535850\pi\) | |||||||
\(458\) | 1.14533e11 | 0.121629 | ||||||||
\(459\) | 1.39717e12 | 1.46924 | ||||||||
\(460\) | −1.89303e11 | −0.197127 | ||||||||
\(461\) | 1.12823e12 | 1.16343 | 0.581717 | − | 0.813391i | \(-0.302381\pi\) | ||||
0.581717 | + | 0.813391i | \(0.302381\pi\) | |||||||
\(462\) | 3.85434e11 | 0.393606 | ||||||||
\(463\) | −9.75512e11 | −0.986548 | −0.493274 | − | 0.869874i | \(-0.664200\pi\) | ||||
−0.493274 | + | 0.869874i | \(0.664200\pi\) | |||||||
\(464\) | 1.71718e11 | 0.171983 | ||||||||
\(465\) | −6.25831e11 | −0.620753 | ||||||||
\(466\) | −7.24379e11 | −0.711589 | ||||||||
\(467\) | −5.15878e11 | −0.501904 | −0.250952 | − | 0.968000i | \(-0.580744\pi\) | ||||
−0.250952 | + | 0.968000i | \(0.580744\pi\) | |||||||
\(468\) | 3.25915e8 | 0.000314050 0 | ||||||||
\(469\) | −9.25095e10 | −0.0882894 | ||||||||
\(470\) | −3.11622e11 | −0.294570 | ||||||||
\(471\) | −1.49434e12 | −1.39912 | ||||||||
\(472\) | −1.19083e11 | −0.110436 | ||||||||
\(473\) | 5.55170e11 | 0.509977 | ||||||||
\(474\) | −1.99285e11 | −0.181331 | ||||||||
\(475\) | −4.63372e10 | −0.0417646 | ||||||||
\(476\) | −4.51492e11 | −0.403106 | ||||||||
\(477\) | −1.32003e8 | −0.000116749 0 | ||||||||
\(478\) | 1.12868e12 | 0.988880 | ||||||||
\(479\) | 1.89215e12 | 1.64228 | 0.821139 | − | 0.570728i | \(-0.193339\pi\) | ||||
0.821139 | + | 0.570728i | \(0.193339\pi\) | |||||||
\(480\) | 1.85852e11 | 0.159802 | ||||||||
\(481\) | −1.26214e12 | −1.07511 | ||||||||
\(482\) | −1.25302e12 | −1.05742 | ||||||||
\(483\) | −2.86109e11 | −0.239204 | ||||||||
\(484\) | 1.75417e10 | 0.0145300 | ||||||||
\(485\) | 2.08336e12 | 1.70973 | ||||||||
\(486\) | 1.65282e9 | 0.00134389 | ||||||||
\(487\) | 1.35254e12 | 1.08960 | 0.544802 | − | 0.838565i | \(-0.316605\pi\) | ||||
0.544802 | + | 0.838565i | \(0.316605\pi\) | |||||||
\(488\) | −5.90989e11 | −0.471726 | ||||||||
\(489\) | −1.27798e12 | −1.01073 | ||||||||
\(490\) | 5.70122e11 | 0.446771 | ||||||||
\(491\) | 9.23267e11 | 0.716903 | 0.358452 | − | 0.933548i | \(-0.383305\pi\) | ||||
0.358452 | + | 0.933548i | \(0.383305\pi\) | |||||||
\(492\) | −7.83100e11 | −0.602524 | ||||||||
\(493\) | 1.32508e12 | 1.01026 | ||||||||
\(494\) | 1.41925e11 | 0.107223 | ||||||||
\(495\) | 1.16454e9 | 0.000871830 0 | ||||||||
\(496\) | 2.31403e11 | 0.171673 | ||||||||
\(497\) | 1.48941e11 | 0.109499 | ||||||||
\(498\) | 1.41313e11 | 0.102956 | ||||||||
\(499\) | 1.98116e12 | 1.43043 | 0.715214 | − | 0.698905i | \(-0.246329\pi\) | ||||
0.715214 | + | 0.698905i | \(0.246329\pi\) | |||||||
\(500\) | −7.47023e11 | −0.534526 | ||||||||
\(501\) | −1.62029e12 | −1.14901 | ||||||||
\(502\) | −1.65858e12 | −1.16565 | ||||||||
\(503\) | 2.56937e12 | 1.78966 | 0.894830 | − | 0.446406i | \(-0.147296\pi\) | ||||
0.894830 | + | 0.446406i | \(0.147296\pi\) | |||||||
\(504\) | −2.67179e8 | −0.000184444 0 | ||||||||
\(505\) | −1.13405e12 | −0.775925 | ||||||||
\(506\) | −4.61101e11 | −0.312693 | ||||||||
\(507\) | 8.37395e11 | 0.562853 | ||||||||
\(508\) | −1.15536e12 | −0.769717 | ||||||||
\(509\) | 1.56900e11 | 0.103608 | 0.0518040 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518040 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(510\) | 1.43415e12 | 0.938705 | ||||||||
\(511\) | −1.13217e12 | −0.734544 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 3.60046e11 | 0.229525 | ||||||||
\(514\) | −1.71671e12 | −1.08483 | ||||||||
\(515\) | 2.11866e12 | 1.32717 | ||||||||
\(516\) | 4.04592e11 | 0.251243 | ||||||||
\(517\) | −7.59044e11 | −0.467261 | ||||||||
\(518\) | 1.03468e12 | 0.631424 | ||||||||
\(519\) | 3.54480e11 | 0.214456 | ||||||||
\(520\) | 3.52383e11 | 0.211349 | ||||||||
\(521\) | −1.30379e12 | −0.775241 | −0.387621 | − | 0.921819i | \(-0.626703\pi\) | ||||
−0.387621 | + | 0.921819i | \(0.626703\pi\) | |||||||
\(522\) | 7.84143e8 | 0.000462251 0 | ||||||||
\(523\) | 2.30458e12 | 1.34690 | 0.673449 | − | 0.739234i | \(-0.264812\pi\) | ||||
0.673449 | + | 0.739234i | \(0.264812\pi\) | |||||||
\(524\) | −6.49513e11 | −0.376354 | ||||||||
\(525\) | −1.73883e11 | −0.0998944 | ||||||||
\(526\) | 1.89184e12 | 1.07758 | ||||||||
\(527\) | 1.78565e12 | 1.00843 | ||||||||
\(528\) | 4.52696e11 | 0.253486 | ||||||||
\(529\) | −1.45888e12 | −0.809968 | ||||||||
\(530\) | −1.42723e11 | −0.0785693 | ||||||||
\(531\) | −5.43786e8 | −0.000296827 0 | ||||||||
\(532\) | −1.16348e11 | −0.0629732 | ||||||||
\(533\) | −1.48479e12 | −0.796878 | ||||||||
\(534\) | −1.01936e11 | −0.0542493 | ||||||||
\(535\) | 3.89362e11 | 0.205476 | ||||||||
\(536\) | −1.08653e11 | −0.0568592 | ||||||||
\(537\) | 2.42692e12 | 1.25942 | ||||||||
\(538\) | −1.73027e12 | −0.890417 | ||||||||
\(539\) | 1.38869e12 | 0.708691 | ||||||||
\(540\) | 8.93947e11 | 0.452418 | ||||||||
\(541\) | 5.93525e11 | 0.297887 | 0.148943 | − | 0.988846i | \(-0.452413\pi\) | ||||
0.148943 | + | 0.988846i | \(0.452413\pi\) | |||||||
\(542\) | 1.95492e12 | 0.973045 | ||||||||
\(543\) | −1.52413e12 | −0.752353 | ||||||||
\(544\) | −5.30281e11 | −0.259604 | ||||||||
\(545\) | −2.26965e11 | −0.110198 | ||||||||
\(546\) | 5.32585e11 | 0.256462 | ||||||||
\(547\) | −2.57843e12 | −1.23144 | −0.615719 | − | 0.787966i | \(-0.711134\pi\) | ||||
−0.615719 | + | 0.787966i | \(0.711134\pi\) | |||||||
\(548\) | 1.03447e12 | 0.490010 | ||||||||
\(549\) | −2.69872e9 | −0.00126789 | ||||||||
\(550\) | −2.80235e11 | −0.130584 | ||||||||
\(551\) | 3.41469e11 | 0.157822 | ||||||||
\(552\) | −3.36037e11 | −0.154050 | ||||||||
\(553\) | 3.09756e11 | 0.140850 | ||||||||
\(554\) | −1.90310e12 | −0.858358 | ||||||||
\(555\) | −3.28662e12 | −1.47039 | ||||||||
\(556\) | −4.77497e11 | −0.211901 | ||||||||
\(557\) | −3.49163e12 | −1.53702 | −0.768510 | − | 0.639838i | \(-0.779001\pi\) | ||||
−0.768510 | + | 0.639838i | \(0.779001\pi\) | |||||||
\(558\) | 1.05669e9 | 0.000461417 0 | ||||||||
\(559\) | 7.67122e11 | 0.332285 | ||||||||
\(560\) | −2.88877e11 | −0.124127 | ||||||||
\(561\) | 3.49328e12 | 1.48902 | ||||||||
\(562\) | 7.57888e11 | 0.320473 | ||||||||
\(563\) | −1.40676e12 | −0.590109 | −0.295054 | − | 0.955480i | \(-0.595338\pi\) | ||||
−0.295054 | + | 0.955480i | \(0.595338\pi\) | |||||||
\(564\) | −5.53170e11 | −0.230199 | ||||||||
\(565\) | −2.91702e12 | −1.20427 | ||||||||
\(566\) | −2.55726e12 | −1.04737 | ||||||||
\(567\) | 1.34981e12 | 0.548466 | ||||||||
\(568\) | 1.74932e11 | 0.0705184 | ||||||||
\(569\) | 2.81635e12 | 1.12637 | 0.563185 | − | 0.826331i | \(-0.309576\pi\) | ||||
0.563185 | + | 0.826331i | \(0.309576\pi\) | |||||||
\(570\) | 3.69575e11 | 0.146644 | ||||||||
\(571\) | −1.85246e11 | −0.0729266 | −0.0364633 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364633 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(572\) | 8.58328e11 | 0.335252 | ||||||||
\(573\) | 7.48645e11 | 0.290121 | ||||||||
\(574\) | 1.21720e12 | 0.468014 | ||||||||
\(575\) | 2.08019e11 | 0.0793593 | ||||||||
\(576\) | −3.13804e8 | −0.000118784 0 | ||||||||
\(577\) | −2.36440e12 | −0.888034 | −0.444017 | − | 0.896018i | \(-0.646447\pi\) | ||||
−0.444017 | + | 0.896018i | \(0.646447\pi\) | |||||||
\(578\) | −2.19457e12 | −0.817850 | ||||||||
\(579\) | −3.86961e12 | −1.43091 | ||||||||
\(580\) | 8.47824e11 | 0.311085 | ||||||||
\(581\) | −2.19648e11 | −0.0799714 | ||||||||
\(582\) | 3.69823e12 | 1.33611 | ||||||||
\(583\) | −3.47642e11 | −0.124630 | ||||||||
\(584\) | −1.32974e12 | −0.473053 | ||||||||
\(585\) | 1.60914e9 | 0.000568058 0 | ||||||||
\(586\) | −2.12369e12 | −0.743964 | ||||||||
\(587\) | 8.75403e11 | 0.304324 | 0.152162 | − | 0.988356i | \(-0.451376\pi\) | ||||
0.152162 | + | 0.988356i | \(0.451376\pi\) | |||||||
\(588\) | 1.01204e12 | 0.349140 | ||||||||
\(589\) | 4.60154e11 | 0.157538 | ||||||||
\(590\) | −5.87947e11 | −0.199758 | ||||||||
\(591\) | 1.34768e12 | 0.454405 | ||||||||
\(592\) | 1.21524e12 | 0.406643 | ||||||||
\(593\) | −2.10579e12 | −0.699307 | −0.349654 | − | 0.936879i | \(-0.613701\pi\) | ||||
−0.349654 | + | 0.936879i | \(0.613701\pi\) | |||||||
\(594\) | 2.17746e12 | 0.717648 | ||||||||
\(595\) | −2.22915e12 | −0.729144 | ||||||||
\(596\) | −1.94683e12 | −0.632004 | ||||||||
\(597\) | −4.05004e12 | −1.30489 | ||||||||
\(598\) | −6.37139e11 | −0.203741 | ||||||||
\(599\) | 5.86647e12 | 1.86190 | 0.930950 | − | 0.365147i | \(-0.118981\pi\) | ||||
0.930950 | + | 0.365147i | \(0.118981\pi\) | |||||||
\(600\) | −2.04227e11 | −0.0643330 | ||||||||
\(601\) | −8.97472e11 | −0.280599 | −0.140299 | − | 0.990109i | \(-0.544807\pi\) | ||||
−0.140299 | + | 0.990109i | \(0.544807\pi\) | |||||||
\(602\) | −6.28872e11 | −0.195154 | ||||||||
\(603\) | −4.96159e8 | −0.000152825 0 | ||||||||
\(604\) | 4.47111e11 | 0.136694 | ||||||||
\(605\) | 8.66084e10 | 0.0262822 | ||||||||
\(606\) | −2.01308e12 | −0.606365 | ||||||||
\(607\) | −4.20534e12 | −1.25734 | −0.628669 | − | 0.777673i | \(-0.716400\pi\) | ||||
−0.628669 | + | 0.777673i | \(0.716400\pi\) | |||||||
\(608\) | −1.36651e11 | −0.0405554 | ||||||||
\(609\) | 1.28139e12 | 0.377487 | ||||||||
\(610\) | −2.91788e12 | −0.853265 | ||||||||
\(611\) | −1.04883e12 | −0.304453 | ||||||||
\(612\) | −2.42150e9 | −0.000697756 0 | ||||||||
\(613\) | 4.66333e12 | 1.33390 | 0.666951 | − | 0.745102i | \(-0.267599\pi\) | ||||
0.666951 | + | 0.745102i | \(0.267599\pi\) | |||||||
\(614\) | −3.87121e12 | −1.09923 | ||||||||
\(615\) | −3.86640e12 | −1.08985 | ||||||||
\(616\) | −7.03641e11 | −0.196897 | ||||||||
\(617\) | 3.80910e12 | 1.05813 | 0.529065 | − | 0.848581i | \(-0.322543\pi\) | ||||
0.529065 | + | 0.848581i | \(0.322543\pi\) | |||||||
\(618\) | 3.76089e12 | 1.03715 | ||||||||
\(619\) | −3.62001e12 | −0.991063 | −0.495532 | − | 0.868590i | \(-0.665027\pi\) | ||||
−0.495532 | + | 0.868590i | \(0.665027\pi\) | |||||||
\(620\) | 1.14250e12 | 0.310524 | ||||||||
\(621\) | −1.61633e12 | −0.436133 | ||||||||
\(622\) | 2.80442e12 | 0.751254 | ||||||||
\(623\) | 1.58443e11 | 0.0421384 | ||||||||
\(624\) | 6.25526e11 | 0.165164 | ||||||||
\(625\) | −2.99382e12 | −0.784811 | ||||||||
\(626\) | 4.10336e12 | 1.06796 | ||||||||
\(627\) | 9.00204e11 | 0.232615 | ||||||||
\(628\) | 2.72804e12 | 0.699893 | ||||||||
\(629\) | 9.37752e12 | 2.38869 | ||||||||
\(630\) | −1.31914e9 | −0.000333625 0 | ||||||||
\(631\) | −7.16358e11 | −0.179886 | −0.0899431 | − | 0.995947i | \(-0.528669\pi\) | ||||
−0.0899431 | + | 0.995947i | \(0.528669\pi\) | |||||||
\(632\) | 3.63811e11 | 0.0907086 | ||||||||
\(633\) | −3.17744e12 | −0.786612 | ||||||||
\(634\) | 4.65632e11 | 0.114457 | ||||||||
\(635\) | −5.70436e12 | −1.39228 | ||||||||
\(636\) | −2.53352e11 | −0.0613999 | ||||||||
\(637\) | 1.91887e12 | 0.461761 | ||||||||
\(638\) | 2.06511e12 | 0.493459 | ||||||||
\(639\) | 7.98820e8 | 0.000189537 0 | ||||||||
\(640\) | −3.39288e11 | −0.0799391 | ||||||||
\(641\) | −4.92458e12 | −1.15215 | −0.576074 | − | 0.817397i | \(-0.695416\pi\) | ||||
−0.576074 | + | 0.817397i | \(0.695416\pi\) | |||||||
\(642\) | 6.91169e11 | 0.160574 | ||||||||
\(643\) | 3.16432e12 | 0.730013 | 0.365007 | − | 0.931005i | \(-0.381067\pi\) | ||||
0.365007 | + | 0.931005i | \(0.381067\pi\) | |||||||
\(644\) | 5.22315e11 | 0.119659 | ||||||||
\(645\) | 1.99759e12 | 0.454452 | ||||||||
\(646\) | −1.05449e12 | −0.238229 | ||||||||
\(647\) | 8.63261e12 | 1.93675 | 0.968374 | − | 0.249504i | \(-0.0802677\pi\) | ||||
0.968374 | + | 0.249504i | \(0.0802677\pi\) | |||||||
\(648\) | 1.58536e12 | 0.353217 | ||||||||
\(649\) | −1.43211e12 | −0.316866 | ||||||||
\(650\) | −3.87223e11 | −0.0850846 | ||||||||
\(651\) | 1.72676e12 | 0.376806 | ||||||||
\(652\) | 2.33305e12 | 0.505603 | ||||||||
\(653\) | −4.53346e12 | −0.975710 | −0.487855 | − | 0.872925i | \(-0.662220\pi\) | ||||
−0.487855 | + | 0.872925i | \(0.662220\pi\) | |||||||
\(654\) | −4.02893e11 | −0.0861172 | ||||||||
\(655\) | −3.20684e12 | −0.680755 | ||||||||
\(656\) | 1.42961e12 | 0.301405 | ||||||||
\(657\) | −6.07221e9 | −0.00127146 | ||||||||
\(658\) | 8.59812e11 | 0.178808 | ||||||||
\(659\) | 2.67609e12 | 0.552734 | 0.276367 | − | 0.961052i | \(-0.410869\pi\) | ||||
0.276367 | + | 0.961052i | \(0.410869\pi\) | |||||||
\(660\) | 2.23509e12 | 0.458509 | ||||||||
\(661\) | 1.23915e12 | 0.252475 | 0.126238 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126238 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(662\) | 2.33093e12 | 0.471703 | ||||||||
\(663\) | 4.82694e12 | 0.970199 | ||||||||
\(664\) | −2.57978e11 | −0.0515023 | ||||||||
\(665\) | −5.74444e11 | −0.113907 | ||||||||
\(666\) | 5.54933e9 | 0.00109296 | ||||||||
\(667\) | −1.53294e12 | −0.299888 | ||||||||
\(668\) | 2.95797e12 | 0.574778 | ||||||||
\(669\) | 8.19734e12 | 1.58218 | ||||||||
\(670\) | −5.36452e11 | −0.102848 | ||||||||
\(671\) | −7.10733e12 | −1.35349 | ||||||||
\(672\) | −5.12794e11 | −0.0970021 | ||||||||
\(673\) | −5.79692e11 | −0.108926 | −0.0544628 | − | 0.998516i | \(-0.517345\pi\) | ||||
−0.0544628 | + | 0.998516i | \(0.517345\pi\) | |||||||
\(674\) | 6.66766e11 | 0.124453 | ||||||||
\(675\) | −9.82331e11 | −0.182134 | ||||||||
\(676\) | −1.52873e12 | −0.281560 | ||||||||
\(677\) | 6.09981e12 | 1.11601 | 0.558004 | − | 0.829838i | \(-0.311567\pi\) | ||||
0.558004 | + | 0.829838i | \(0.311567\pi\) | |||||||
\(678\) | −5.17810e12 | −0.941102 | ||||||||
\(679\) | −5.74829e12 | −1.03783 | ||||||||
\(680\) | −2.61816e12 | −0.469575 | ||||||||
\(681\) | 6.76168e11 | 0.120474 | ||||||||
\(682\) | 2.78289e12 | 0.492569 | ||||||||
\(683\) | −1.92035e12 | −0.337665 | −0.168833 | − | 0.985645i | \(-0.554000\pi\) | ||||
−0.168833 | + | 0.985645i | \(0.554000\pi\) | |||||||
\(684\) | −6.24012e8 | −0.000109004 0 | ||||||||
\(685\) | 5.10748e12 | 0.886338 | ||||||||
\(686\) | −3.82473e12 | −0.659389 | ||||||||
\(687\) | 1.00381e12 | 0.171928 | ||||||||
\(688\) | −7.38615e11 | −0.125681 | ||||||||
\(689\) | −4.80365e11 | −0.0812054 | ||||||||
\(690\) | −1.65912e12 | −0.278648 | ||||||||
\(691\) | −1.22588e12 | −0.204549 | −0.102275 | − | 0.994756i | \(-0.532612\pi\) | ||||
−0.102275 | + | 0.994756i | \(0.532612\pi\) | |||||||
\(692\) | −6.47132e11 | −0.107279 | ||||||||
\(693\) | −3.21314e9 | −0.000529213 0 | ||||||||
\(694\) | 9.27854e11 | 0.151832 | ||||||||
\(695\) | −2.35754e12 | −0.383290 | ||||||||
\(696\) | 1.50500e12 | 0.243105 | ||||||||
\(697\) | 1.10318e13 | 1.77051 | ||||||||
\(698\) | 1.70819e12 | 0.272388 | ||||||||
\(699\) | −6.34870e12 | −1.00586 | ||||||||
\(700\) | 3.17438e11 | 0.0499710 | ||||||||
\(701\) | −7.54657e10 | −0.0118037 | −0.00590186 | − | 0.999983i | \(-0.501879\pi\) | ||||
−0.00590186 | + | 0.999983i | \(0.501879\pi\) | |||||||
\(702\) | 3.00877e12 | 0.467597 | ||||||||
\(703\) | 2.41655e12 | 0.373162 | ||||||||
\(704\) | −8.26432e11 | −0.126803 | ||||||||
\(705\) | −2.73116e12 | −0.416387 | ||||||||
\(706\) | 6.83524e12 | 1.03546 | ||||||||
\(707\) | 3.12900e12 | 0.470997 | ||||||||
\(708\) | −1.04368e12 | −0.156106 | ||||||||
\(709\) | −2.48251e12 | −0.368964 | −0.184482 | − | 0.982836i | \(-0.559061\pi\) | ||||
−0.184482 | + | 0.982836i | \(0.559061\pi\) | |||||||
\(710\) | 8.63692e11 | 0.127555 | ||||||||
\(711\) | 1.66132e9 | 0.000243804 0 | ||||||||
\(712\) | 1.86093e11 | 0.0271375 | ||||||||
\(713\) | −2.06575e12 | −0.299347 | ||||||||
\(714\) | −3.95703e12 | −0.569807 | ||||||||
\(715\) | 4.23782e12 | 0.606409 | ||||||||
\(716\) | −4.43053e12 | −0.630009 | ||||||||
\(717\) | 9.89210e12 | 1.39782 | ||||||||
\(718\) | −6.87828e12 | −0.965872 | ||||||||
\(719\) | −5.21696e12 | −0.728010 | −0.364005 | − | 0.931397i | \(-0.618591\pi\) | ||||
−0.364005 | + | 0.931397i | \(0.618591\pi\) | |||||||
\(720\) | −1.54934e9 | −0.000214858 0 | ||||||||
\(721\) | −5.84569e12 | −0.805614 | ||||||||
\(722\) | −2.71737e11 | −0.0372161 | ||||||||
\(723\) | −1.09819e13 | −1.49470 | ||||||||
\(724\) | 2.78241e12 | 0.376355 | ||||||||
\(725\) | −9.31648e11 | −0.125236 | ||||||||
\(726\) | 1.53741e11 | 0.0205388 | ||||||||
\(727\) | 1.23462e13 | 1.63919 | 0.819595 | − | 0.572944i | \(-0.194199\pi\) | ||||
0.819595 | + | 0.572944i | \(0.194199\pi\) | |||||||
\(728\) | −9.72277e11 | −0.128292 | ||||||||
\(729\) | 7.63283e12 | 1.00095 | ||||||||
\(730\) | −6.56533e12 | −0.855665 | ||||||||
\(731\) | −5.69961e12 | −0.738273 | ||||||||
\(732\) | −5.17962e12 | −0.666804 | ||||||||
\(733\) | −7.23773e12 | −0.926050 | −0.463025 | − | 0.886345i | \(-0.653236\pi\) | ||||
−0.463025 | + | 0.886345i | \(0.653236\pi\) | |||||||
\(734\) | −2.24931e12 | −0.286033 | ||||||||
\(735\) | 4.99674e12 | 0.631530 | ||||||||
\(736\) | 6.13463e11 | 0.0770616 | ||||||||
\(737\) | −1.30668e12 | −0.163142 | ||||||||
\(738\) | 6.52825e9 | 0.000810109 0 | ||||||||
\(739\) | −1.58616e12 | −0.195636 | −0.0978179 | − | 0.995204i | \(-0.531186\pi\) | ||||
−0.0978179 | + | 0.995204i | \(0.531186\pi\) | |||||||
\(740\) | 5.99999e12 | 0.735542 | ||||||||
\(741\) | 1.24388e12 | 0.151565 | ||||||||
\(742\) | 3.93794e11 | 0.0476927 | ||||||||
\(743\) | −1.32982e13 | −1.60082 | −0.800408 | − | 0.599455i | \(-0.795384\pi\) | ||||
−0.800408 | + | 0.599455i | \(0.795384\pi\) | |||||||
\(744\) | 2.02809e12 | 0.242667 | ||||||||
\(745\) | −9.61208e12 | −1.14318 | ||||||||
\(746\) | −6.90636e12 | −0.816440 | ||||||||
\(747\) | −1.17805e9 | −0.000138426 0 | ||||||||
\(748\) | −6.37726e12 | −0.744864 | ||||||||
\(749\) | −1.07431e12 | −0.124727 | ||||||||
\(750\) | −6.54716e12 | −0.755575 | ||||||||
\(751\) | −7.69495e12 | −0.882726 | −0.441363 | − | 0.897329i | \(-0.645505\pi\) | ||||
−0.441363 | + | 0.897329i | \(0.645505\pi\) | |||||||
\(752\) | 1.00986e12 | 0.115154 | ||||||||
\(753\) | −1.45363e13 | −1.64770 | ||||||||
\(754\) | 2.85353e12 | 0.321523 | ||||||||
\(755\) | 2.20752e12 | 0.247254 | ||||||||
\(756\) | −2.46653e12 | −0.274624 | ||||||||
\(757\) | 1.46042e13 | 1.61640 | 0.808198 | − | 0.588911i | \(-0.200443\pi\) | ||||
0.808198 | + | 0.588911i | \(0.200443\pi\) | |||||||
\(758\) | −1.14613e13 | −1.26102 | ||||||||
\(759\) | −4.04124e12 | −0.442005 | ||||||||
\(760\) | −6.74689e11 | −0.0733571 | ||||||||
\(761\) | −2.14254e12 | −0.231578 | −0.115789 | − | 0.993274i | \(-0.536940\pi\) | ||||
−0.115789 | + | 0.993274i | \(0.536940\pi\) | |||||||
\(762\) | −1.01260e13 | −1.08803 | ||||||||
\(763\) | 6.26231e11 | 0.0668920 | ||||||||
\(764\) | −1.36671e12 | −0.145130 | ||||||||
\(765\) | −1.19557e10 | −0.00126211 | ||||||||
\(766\) | 1.65234e12 | 0.173408 | ||||||||
\(767\) | −1.97886e12 | −0.206460 | ||||||||
\(768\) | −6.02281e11 | −0.0624703 | ||||||||
\(769\) | 1.37576e13 | 1.41865 | 0.709326 | − | 0.704881i | \(-0.249000\pi\) | ||||
0.709326 | + | 0.704881i | \(0.249000\pi\) | |||||||
\(770\) | −3.47408e12 | −0.356149 | ||||||||
\(771\) | −1.50458e13 | −1.53346 | ||||||||
\(772\) | 7.06428e12 | 0.715797 | ||||||||
\(773\) | 1.78934e13 | 1.80254 | 0.901270 | − | 0.433257i | \(-0.142636\pi\) | ||||
0.901270 | + | 0.433257i | \(0.142636\pi\) | |||||||
\(774\) | −3.37285e9 | −0.000337802 0 | ||||||||
\(775\) | −1.25546e12 | −0.125010 | ||||||||
\(776\) | −6.75142e12 | −0.668371 | ||||||||
\(777\) | 9.06827e12 | 0.892545 | ||||||||
\(778\) | 5.59897e12 | 0.547898 | ||||||||
\(779\) | 2.84284e12 | 0.276588 | ||||||||
\(780\) | 3.08840e12 | 0.298750 | ||||||||
\(781\) | 2.10377e12 | 0.202334 | ||||||||
\(782\) | 4.73385e12 | 0.452673 | ||||||||
\(783\) | 7.23902e12 | 0.688259 | ||||||||
\(784\) | −1.84756e12 | −0.174653 | ||||||||
\(785\) | 1.34691e13 | 1.26598 | ||||||||
\(786\) | −5.69255e12 | −0.531992 | ||||||||
\(787\) | 1.90983e13 | 1.77464 | 0.887318 | − | 0.461158i | \(-0.152566\pi\) | ||||
0.887318 | + | 0.461158i | \(0.152566\pi\) | |||||||
\(788\) | −2.46030e12 | −0.227310 | ||||||||
\(789\) | 1.65807e13 | 1.52320 | ||||||||
\(790\) | 1.79624e12 | 0.164075 | ||||||||
\(791\) | 8.04850e12 | 0.731006 | ||||||||
\(792\) | −3.77386e9 | −0.000340818 0 | ||||||||
\(793\) | −9.82076e12 | −0.881893 | ||||||||
\(794\) | 4.53823e12 | 0.405224 | ||||||||
\(795\) | −1.25087e12 | −0.111061 | ||||||||
\(796\) | 7.39367e12 | 0.652756 | ||||||||
\(797\) | −4.39907e10 | −0.00386188 | −0.00193094 | − | 0.999998i | \(-0.500615\pi\) | ||||
−0.00193094 | + | 0.999998i | \(0.500615\pi\) | |||||||
\(798\) | −1.01971e12 | −0.0890153 | ||||||||
\(799\) | 7.79267e12 | 0.676434 | ||||||||
\(800\) | 3.72833e11 | 0.0321818 | ||||||||
\(801\) | 8.49785e8 | 7.29395e−5 0 | ||||||||
\(802\) | 1.59050e13 | 1.35753 | ||||||||
\(803\) | −1.59917e13 | −1.35730 | ||||||||
\(804\) | −9.52273e11 | −0.0803728 | ||||||||
\(805\) | 2.57882e12 | 0.216441 | ||||||||
\(806\) | 3.84534e12 | 0.320943 | ||||||||
\(807\) | −1.51647e13 | −1.25864 | ||||||||
\(808\) | 3.67504e12 | 0.303327 | ||||||||
\(809\) | −1.85839e13 | −1.52535 | −0.762675 | − | 0.646782i | \(-0.776114\pi\) | ||||
−0.762675 | + | 0.646782i | \(0.776114\pi\) | |||||||
\(810\) | 7.82741e12 | 0.638904 | ||||||||
\(811\) | 1.29810e13 | 1.05369 | 0.526847 | − | 0.849960i | \(-0.323374\pi\) | ||||
0.526847 | + | 0.849960i | \(0.323374\pi\) | |||||||
\(812\) | −2.33927e12 | −0.188833 | ||||||||
\(813\) | 1.71336e13 | 1.37544 | ||||||||
\(814\) | 1.46147e13 | 1.16675 | ||||||||
\(815\) | 1.15190e13 | 0.914543 | ||||||||
\(816\) | −4.64757e12 | −0.366961 | ||||||||
\(817\) | −1.46877e12 | −0.115333 | ||||||||
\(818\) | −3.85777e12 | −0.301264 | ||||||||
\(819\) | −4.43985e9 | −0.000344819 0 | ||||||||
\(820\) | 7.05842e12 | 0.545186 | ||||||||
\(821\) | −4.47787e12 | −0.343975 | −0.171987 | − | 0.985099i | \(-0.555019\pi\) | ||||
−0.171987 | + | 0.985099i | \(0.555019\pi\) | |||||||
\(822\) | 9.06644e12 | 0.692650 | ||||||||
\(823\) | 1.13315e13 | 0.860973 | 0.430487 | − | 0.902597i | \(-0.358342\pi\) | ||||
0.430487 | + | 0.902597i | \(0.358342\pi\) | |||||||
\(824\) | −6.86581e12 | −0.518823 | ||||||||
\(825\) | −2.45607e12 | −0.184586 | ||||||||
\(826\) | 1.62223e12 | 0.121256 | ||||||||
\(827\) | −1.46669e13 | −1.09034 | −0.545171 | − | 0.838325i | \(-0.683535\pi\) | ||||
−0.545171 | + | 0.838325i | \(0.683535\pi\) | |||||||
\(828\) | 2.80135e9 | 0.000207124 0 | ||||||||
\(829\) | −2.45530e13 | −1.80555 | −0.902774 | − | 0.430115i | \(-0.858473\pi\) | ||||
−0.902774 | + | 0.430115i | \(0.858473\pi\) | |||||||
\(830\) | −1.27371e12 | −0.0931581 | ||||||||
\(831\) | −1.66794e13 | −1.21332 | ||||||||
\(832\) | −1.14195e12 | −0.0826211 | ||||||||
\(833\) | −1.42569e13 | −1.02594 | ||||||||
\(834\) | −4.18495e12 | −0.299532 | ||||||||
\(835\) | 1.46044e13 | 1.03967 | ||||||||
\(836\) | −1.64339e12 | −0.116363 | ||||||||
\(837\) | 9.75510e12 | 0.687017 | ||||||||
\(838\) | −1.12496e13 | −0.788025 | ||||||||
\(839\) | 8.71743e12 | 0.607379 | 0.303689 | − | 0.952771i | \(-0.401781\pi\) | ||||
0.303689 | + | 0.952771i | \(0.401781\pi\) | |||||||
\(840\) | −2.53182e12 | −0.175459 | ||||||||
\(841\) | −7.64163e12 | −0.526749 | ||||||||
\(842\) | 4.29231e12 | 0.294298 | ||||||||
\(843\) | 6.64239e12 | 0.453002 | ||||||||
\(844\) | 5.80067e12 | 0.393493 | ||||||||
\(845\) | −7.54780e12 | −0.509290 | ||||||||
\(846\) | 4.61146e9 | 0.000309508 0 | ||||||||
\(847\) | −2.38965e11 | −0.0159536 | ||||||||
\(848\) | 4.62514e11 | 0.0307145 | ||||||||
\(849\) | −2.24127e13 | −1.48050 | ||||||||
\(850\) | 2.87701e12 | 0.189041 | ||||||||
\(851\) | −1.08485e13 | −0.709066 | ||||||||
\(852\) | 1.53317e12 | 0.0996807 | ||||||||
\(853\) | 1.30680e12 | 0.0845159 | 0.0422580 | − | 0.999107i | \(-0.486545\pi\) | ||||
0.0422580 | + | 0.999107i | \(0.486545\pi\) | |||||||
\(854\) | 8.05087e12 | 0.517944 | ||||||||
\(855\) | −3.08093e9 | −0.000197167 0 | ||||||||
\(856\) | −1.26178e12 | −0.0803254 | ||||||||
\(857\) | −1.57408e12 | −0.0996811 | −0.0498405 | − | 0.998757i | \(-0.515871\pi\) | ||||
−0.0498405 | + | 0.998757i | \(0.515871\pi\) | |||||||
\(858\) | 7.52268e12 | 0.473893 | ||||||||
\(859\) | 1.39034e13 | 0.871265 | 0.435633 | − | 0.900125i | \(-0.356525\pi\) | ||||
0.435633 | + | 0.900125i | \(0.356525\pi\) | |||||||
\(860\) | −3.64676e12 | −0.227334 | ||||||||
\(861\) | 1.06680e13 | 0.661557 | ||||||||
\(862\) | −9.53453e11 | −0.0588189 | ||||||||
\(863\) | 2.53344e11 | 0.0155476 | 0.00777378 | − | 0.999970i | \(-0.497526\pi\) | ||||
0.00777378 | + | 0.999970i | \(0.497526\pi\) | |||||||
\(864\) | −2.89696e12 | −0.176861 | ||||||||
\(865\) | −3.19508e12 | −0.194048 | ||||||||
\(866\) | 1.86064e13 | 1.12417 | ||||||||
\(867\) | −1.92339e13 | −1.15607 | ||||||||
\(868\) | −3.15234e12 | −0.188492 | ||||||||
\(869\) | 4.37525e12 | 0.260264 | ||||||||
\(870\) | 7.43062e12 | 0.439732 | ||||||||
\(871\) | −1.80554e12 | −0.106298 | ||||||||
\(872\) | 7.35513e11 | 0.0430791 | ||||||||
\(873\) | −3.08300e10 | −0.00179643 | ||||||||
\(874\) | 1.21990e12 | 0.0707166 | ||||||||
\(875\) | 1.01765e13 | 0.586897 | ||||||||
\(876\) | −1.16543e13 | −0.668680 | ||||||||
\(877\) | −4.95849e12 | −0.283042 | −0.141521 | − | 0.989935i | \(-0.545199\pi\) | ||||
−0.141521 | + | 0.989935i | \(0.545199\pi\) | |||||||
\(878\) | 2.11944e13 | 1.20364 | ||||||||
\(879\) | −1.86127e13 | −1.05162 | ||||||||
\(880\) | −4.08034e12 | −0.229364 | ||||||||
\(881\) | −1.32981e13 | −0.743702 | −0.371851 | − | 0.928292i | \(-0.621277\pi\) | ||||
−0.371851 | + | 0.928292i | \(0.621277\pi\) | |||||||
\(882\) | −8.43679e9 | −0.000469428 0 | ||||||||
\(883\) | 1.27657e13 | 0.706677 | 0.353338 | − | 0.935496i | \(-0.385046\pi\) | ||||
0.353338 | + | 0.935496i | \(0.385046\pi\) | |||||||
\(884\) | −8.81196e12 | −0.485330 | ||||||||
\(885\) | −5.15297e12 | −0.282366 | ||||||||
\(886\) | −1.19789e13 | −0.653079 | ||||||||
\(887\) | 1.14862e13 | 0.623044 | 0.311522 | − | 0.950239i | \(-0.399161\pi\) | ||||
0.311522 | + | 0.950239i | \(0.399161\pi\) | |||||||
\(888\) | 1.06508e13 | 0.574807 | ||||||||
\(889\) | 1.57392e13 | 0.845131 | ||||||||
\(890\) | 9.18797e11 | 0.0490868 | ||||||||
\(891\) | 1.90659e13 | 1.01346 | ||||||||
\(892\) | −1.49649e13 | −0.791465 | ||||||||
\(893\) | 2.00814e12 | 0.105673 | ||||||||
\(894\) | −1.70627e13 | −0.893365 | ||||||||
\(895\) | −2.18748e13 | −1.13957 | ||||||||
\(896\) | 9.36146e11 | 0.0485241 | ||||||||
\(897\) | −5.58410e12 | −0.287997 | ||||||||
\(898\) | −1.29192e13 | −0.662967 | ||||||||
\(899\) | 9.25179e12 | 0.472397 | ||||||||
\(900\) | 1.70253e9 | 8.64973e−5 0 | ||||||||
\(901\) | 3.56904e12 | 0.180422 | ||||||||
\(902\) | 1.71928e13 | 0.864801 | ||||||||
\(903\) | −5.51165e12 | −0.275859 | ||||||||
\(904\) | 9.45303e12 | 0.470775 | ||||||||
\(905\) | 1.37376e13 | 0.680757 | ||||||||
\(906\) | 3.91863e12 | 0.193222 | ||||||||
\(907\) | 1.87998e13 | 0.922400 | 0.461200 | − | 0.887296i | \(-0.347419\pi\) | ||||
0.461200 | + | 0.887296i | \(0.347419\pi\) | |||||||
\(908\) | −1.23440e12 | −0.0602656 | ||||||||
\(909\) | 1.67819e10 | 0.000815273 0 | ||||||||
\(910\) | −4.80042e12 | −0.232056 | ||||||||
\(911\) | −1.56523e12 | −0.0752914 | −0.0376457 | − | 0.999291i | \(-0.511986\pi\) | ||||
−0.0376457 | + | 0.999291i | \(0.511986\pi\) | |||||||
\(912\) | −1.19766e12 | −0.0573267 | ||||||||
\(913\) | −3.10249e12 | −0.147772 | ||||||||
\(914\) | 3.35349e12 | 0.158942 | ||||||||
\(915\) | −2.55733e13 | −1.20613 | ||||||||
\(916\) | −1.83253e12 | −0.0860046 | ||||||||
\(917\) | 8.84813e12 | 0.413228 | ||||||||
\(918\) | −2.23547e13 | −1.03891 | ||||||||
\(919\) | 2.72891e13 | 1.26203 | 0.631014 | − | 0.775771i | \(-0.282639\pi\) | ||||
0.631014 | + | 0.775771i | \(0.282639\pi\) | |||||||
\(920\) | 3.02885e12 | 0.139390 | ||||||||
\(921\) | −3.39286e13 | −1.55381 | ||||||||
\(922\) | −1.80516e13 | −0.822673 | ||||||||
\(923\) | 2.90694e12 | 0.131834 | ||||||||
\(924\) | −6.16695e12 | −0.278321 | ||||||||
\(925\) | −6.59320e12 | −0.296114 | ||||||||
\(926\) | 1.56082e13 | 0.697595 | ||||||||
\(927\) | −3.13524e10 | −0.00139448 | ||||||||
\(928\) | −2.74749e12 | −0.121610 | ||||||||
\(929\) | −3.27413e13 | −1.44220 | −0.721100 | − | 0.692831i | \(-0.756363\pi\) | ||||
−0.721100 | + | 0.692831i | \(0.756363\pi\) | |||||||
\(930\) | 1.00133e13 | 0.438939 | ||||||||
\(931\) | −3.67395e12 | −0.160273 | ||||||||
\(932\) | 1.15901e13 | 0.503169 | ||||||||
\(933\) | 2.45789e13 | 1.06193 | ||||||||
\(934\) | 8.25404e12 | 0.354900 | ||||||||
\(935\) | −3.14864e13 | −1.34732 | ||||||||
\(936\) | −5.21464e9 | −0.000222067 0 | ||||||||
\(937\) | −2.41823e13 | −1.02487 | −0.512435 | − | 0.858726i | \(-0.671256\pi\) | ||||
−0.512435 | + | 0.858726i | \(0.671256\pi\) | |||||||
\(938\) | 1.48015e12 | 0.0624300 | ||||||||
\(939\) | 3.59632e13 | 1.50961 | ||||||||
\(940\) | 4.98596e12 | 0.208292 | ||||||||
\(941\) | 7.48541e12 | 0.311216 | 0.155608 | − | 0.987819i | \(-0.450266\pi\) | ||||
0.155608 | + | 0.987819i | \(0.450266\pi\) | |||||||
\(942\) | 2.39094e13 | 0.989328 | ||||||||
\(943\) | −1.27622e13 | −0.525562 | ||||||||
\(944\) | 1.90533e12 | 0.0780900 | ||||||||
\(945\) | −1.21780e13 | −0.496744 | ||||||||
\(946\) | −8.88272e12 | −0.360608 | ||||||||
\(947\) | −4.31138e13 | −1.74197 | −0.870986 | − | 0.491307i | \(-0.836519\pi\) | ||||
−0.870986 | + | 0.491307i | \(0.836519\pi\) | |||||||
\(948\) | 3.18856e12 | 0.128220 | ||||||||
\(949\) | −2.20970e13 | −0.884374 | ||||||||
\(950\) | 7.41394e11 | 0.0295320 | ||||||||
\(951\) | 4.08096e12 | 0.161789 | ||||||||
\(952\) | 7.22388e12 | 0.285039 | ||||||||
\(953\) | −9.69686e12 | −0.380814 | −0.190407 | − | 0.981705i | \(-0.560981\pi\) | ||||
−0.190407 | + | 0.981705i | \(0.560981\pi\) | |||||||
\(954\) | 2.11205e9 | 8.25537e−5 0 | ||||||||
\(955\) | −6.74785e12 | −0.262513 | ||||||||
\(956\) | −1.80588e13 | −0.699244 | ||||||||
\(957\) | 1.80994e13 | 0.697525 | ||||||||
\(958\) | −3.02745e13 | −1.16127 | ||||||||
\(959\) | −1.40923e13 | −0.538019 | ||||||||
\(960\) | −2.97364e12 | −0.112997 | ||||||||
\(961\) | −1.39722e13 | −0.528456 | ||||||||
\(962\) | 2.01942e13 | 0.760221 | ||||||||
\(963\) | −5.76187e9 | −0.000215896 0 | ||||||||
\(964\) | 2.00483e13 | 0.747708 | ||||||||
\(965\) | 3.48784e13 | 1.29474 | ||||||||
\(966\) | 4.57774e12 | 0.169143 | ||||||||
\(967\) | 2.84710e13 | 1.04709 | 0.523545 | − | 0.851998i | \(-0.324609\pi\) | ||||
0.523545 | + | 0.851998i | \(0.324609\pi\) | |||||||
\(968\) | −2.80667e11 | −0.0102743 | ||||||||
\(969\) | −9.24187e12 | −0.336746 | ||||||||
\(970\) | −3.33337e13 | −1.20896 | ||||||||
\(971\) | 3.67091e13 | 1.32522 | 0.662609 | − | 0.748965i | \(-0.269449\pi\) | ||||
0.662609 | + | 0.748965i | \(0.269449\pi\) | |||||||
\(972\) | −2.64451e10 | −0.000950271 0 | ||||||||
\(973\) | 6.50481e12 | 0.232663 | ||||||||
\(974\) | −2.16406e13 | −0.770467 | ||||||||
\(975\) | −3.39375e12 | −0.120271 | ||||||||
\(976\) | 9.45582e12 | 0.333561 | ||||||||
\(977\) | −4.89209e13 | −1.71778 | −0.858892 | − | 0.512157i | \(-0.828847\pi\) | ||||
−0.858892 | + | 0.512157i | \(0.828847\pi\) | |||||||
\(978\) | 2.04476e13 | 0.714691 | ||||||||
\(979\) | 2.23799e12 | 0.0778638 | ||||||||
\(980\) | −9.12195e12 | −0.315915 | ||||||||
\(981\) | 3.35868e9 | 0.000115787 0 | ||||||||
\(982\) | −1.47723e13 | −0.506927 | ||||||||
\(983\) | −1.06278e13 | −0.363038 | −0.181519 | − | 0.983387i | \(-0.558101\pi\) | ||||
−0.181519 | + | 0.983387i | \(0.558101\pi\) | |||||||
\(984\) | 1.25296e13 | 0.426049 | ||||||||
\(985\) | −1.21472e13 | −0.411162 | ||||||||
\(986\) | −2.12013e13 | −0.714360 | ||||||||
\(987\) | 7.53568e12 | 0.252753 | ||||||||
\(988\) | −2.27081e12 | −0.0758183 | ||||||||
\(989\) | 6.59366e12 | 0.219151 | ||||||||
\(990\) | −1.86327e10 | −0.000616477 0 | ||||||||
\(991\) | −9.73679e12 | −0.320689 | −0.160345 | − | 0.987061i | \(-0.551261\pi\) | ||||
−0.160345 | + | 0.987061i | \(0.551261\pi\) | |||||||
\(992\) | −3.70245e12 | −0.121391 | ||||||||
\(993\) | 2.04291e13 | 0.666771 | ||||||||
\(994\) | −2.38305e12 | −0.0774275 | ||||||||
\(995\) | 3.65047e13 | 1.18072 | ||||||||
\(996\) | −2.26101e12 | −0.0728007 | ||||||||
\(997\) | 1.04996e13 | 0.336547 | 0.168273 | − | 0.985740i | \(-0.446181\pi\) | ||||
0.168273 | + | 0.985740i | \(0.446181\pi\) | |||||||
\(998\) | −3.16985e13 | −1.01147 | ||||||||
\(999\) | 5.12300e13 | 1.62735 |
(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 | 38.10.a.d.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 342.10.a.l.1.2 | 4 | |||
4.3 | odd | 2 | 304.10.a.e.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.10.a.d.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
304.10.a.e.1.4 | 4 | 4.3 | odd | 2 | |||
342.10.a.l.1.2 | 4 | 3.2 | odd | 2 |