Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,10,Mod(1,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.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: | \(60.2591928312\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 1438x^{3} - 4164x^{2} + 396957x - 59580 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.150341\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.15034 | −0.139227 | −0.0696134 | − | 0.997574i | \(-0.522177\pi\) | ||||
−0.0696134 | + | 0.997574i | \(0.522177\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −502.075 | −0.980616 | ||||||||
\(5\) | −2554.62 | −1.82794 | −0.913968 | − | 0.405787i | \(-0.866998\pi\) | ||||
−0.913968 | + | 0.405787i | \(0.866998\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9399.91 | 1.47973 | 0.739865 | − | 0.672755i | \(-0.234889\pi\) | ||||
0.739865 | + | 0.672755i | \(0.234889\pi\) | |||||||
\(8\) | 3194.68 | 0.275755 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8047.92 | 0.254498 | ||||||||
\(11\) | −44094.1 | −0.908058 | −0.454029 | − | 0.890987i | \(-0.650014\pi\) | ||||
−0.454029 | + | 0.890987i | \(0.650014\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | −29612.9 | −0.206018 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 246998. | 0.942223 | ||||||||
\(17\) | −28289.4 | −0.0821492 | −0.0410746 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410746 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 273836. | 0.482058 | 0.241029 | − | 0.970518i | \(-0.422515\pi\) | ||||
0.241029 | + | 0.970518i | \(0.422515\pi\) | |||||||
\(20\) | 1.28261e6 | 1.79250 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 138911. | 0.126426 | ||||||||
\(23\) | 1.12921e6 | 0.841393 | 0.420697 | − | 0.907201i | \(-0.361786\pi\) | ||||
0.420697 | + | 0.907201i | \(0.361786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.57295e6 | 2.34135 | ||||||||
\(26\) | −89976.9 | −0.0386145 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.71947e6 | −1.45105 | ||||||||
\(29\) | 1.63691e6 | 0.429768 | 0.214884 | − | 0.976640i | \(-0.431063\pi\) | ||||
0.214884 | + | 0.976640i | \(0.431063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.65402e6 | 1.29407 | 0.647033 | − | 0.762462i | \(-0.276009\pi\) | ||||
0.647033 | + | 0.762462i | \(0.276009\pi\) | |||||||
\(32\) | −2.41381e6 | −0.406937 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 89121.2 | 0.0114374 | ||||||||
\(35\) | −2.40132e7 | −2.70485 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.71193e7 | −1.50169 | −0.750843 | − | 0.660481i | \(-0.770352\pi\) | ||||
−0.750843 | + | 0.660481i | \(0.770352\pi\) | |||||||
\(38\) | −862677. | −0.0671154 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.16119e6 | −0.504062 | ||||||||
\(41\) | 5.15179e6 | 0.284728 | 0.142364 | − | 0.989814i | \(-0.454530\pi\) | ||||
0.142364 | + | 0.989814i | \(0.454530\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.97275e7 | −0.879962 | −0.439981 | − | 0.898007i | \(-0.645015\pi\) | ||||
−0.439981 | + | 0.898007i | \(0.645015\pi\) | |||||||
\(44\) | 2.21386e7 | 0.890456 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.55739e6 | −0.117144 | ||||||||
\(47\) | −4.82947e7 | −1.44364 | −0.721821 | − | 0.692080i | \(-0.756695\pi\) | ||||
−0.721821 | + | 0.692080i | \(0.756695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.80048e7 | 1.18960 | ||||||||
\(50\) | −1.44063e7 | −0.325978 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.43398e7 | −0.271974 | ||||||||
\(53\) | 3.06731e7 | 0.533970 | 0.266985 | − | 0.963701i | \(-0.413973\pi\) | ||||
0.266985 | + | 0.963701i | \(0.413973\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12644e8 | 1.65987 | ||||||||
\(56\) | 3.00298e7 | 0.408043 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.15683e6 | −0.0598352 | ||||||||
\(59\) | 1.15154e7 | 0.123722 | 0.0618609 | − | 0.998085i | \(-0.480296\pi\) | ||||
0.0618609 | + | 0.998085i | \(0.480296\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.62567e7 | −0.335277 | −0.167639 | − | 0.985849i | \(-0.553614\pi\) | ||||
−0.167639 | + | 0.985849i | \(0.553614\pi\) | |||||||
\(62\) | −2.09624e7 | −0.180169 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.18859e8 | −0.885567 | ||||||||
\(65\) | −7.29624e7 | −0.506978 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.48390e7 | −0.393097 | −0.196548 | − | 0.980494i | \(-0.562973\pi\) | ||||
−0.196548 | + | 0.980494i | \(0.562973\pi\) | |||||||
\(68\) | 1.42034e7 | 0.0805568 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.56497e7 | 0.376588 | ||||||||
\(71\) | 1.47071e8 | 0.686853 | 0.343427 | − | 0.939180i | \(-0.388412\pi\) | ||||
0.343427 | + | 0.939180i | \(0.388412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.37321e8 | −1.39024 | −0.695122 | − | 0.718892i | \(-0.744650\pi\) | ||||
−0.695122 | + | 0.718892i | \(0.744650\pi\) | |||||||
\(74\) | 5.39317e7 | 0.209075 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.37486e8 | −0.472714 | ||||||||
\(77\) | −4.14481e8 | −1.34368 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04060e8 | −0.589436 | −0.294718 | − | 0.955584i | \(-0.595226\pi\) | ||||
−0.294718 | + | 0.955584i | \(0.595226\pi\) | |||||||
\(80\) | −6.30986e8 | −1.72232 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.62299e7 | −0.0396418 | ||||||||
\(83\) | −7.61700e8 | −1.76170 | −0.880851 | − | 0.473394i | \(-0.843029\pi\) | ||||
−0.880851 | + | 0.473394i | \(0.843029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.22685e7 | 0.150163 | ||||||||
\(86\) | 6.21484e7 | 0.122514 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.40867e8 | −0.250401 | ||||||||
\(89\) | 8.29058e8 | 1.40065 | 0.700326 | − | 0.713823i | \(-0.253038\pi\) | ||||
0.700326 | + | 0.713823i | \(0.253038\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.68471e8 | 0.410403 | ||||||||
\(92\) | −5.66948e8 | −0.825084 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.52145e8 | 0.200994 | ||||||||
\(95\) | −6.99547e8 | −0.881172 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00647e9 | 1.15432 | 0.577161 | − | 0.816631i | \(-0.304161\pi\) | ||||
0.577161 | + | 0.816631i | \(0.304161\pi\) | |||||||
\(98\) | −1.51231e8 | −0.165625 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29596e9 | −2.29596 | ||||||||
\(101\) | −1.59054e9 | −1.52089 | −0.760446 | − | 0.649401i | \(-0.775020\pi\) | ||||
−0.760446 | + | 0.649401i | \(0.775020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.13889e9 | 0.997040 | 0.498520 | − | 0.866878i | \(-0.333877\pi\) | ||||
0.498520 | + | 0.866878i | \(0.333877\pi\) | |||||||
\(104\) | 9.12434e7 | 0.0764806 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.66309e7 | −0.0743429 | ||||||||
\(107\) | 7.21432e8 | 0.532069 | 0.266035 | − | 0.963963i | \(-0.414286\pi\) | ||||
0.266035 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.86462e8 | −0.465798 | −0.232899 | − | 0.972501i | \(-0.574821\pi\) | ||||
−0.232899 | + | 0.972501i | \(0.574821\pi\) | |||||||
\(110\) | −3.54866e8 | −0.231098 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.32176e9 | 1.39424 | ||||||||
\(113\) | 8.33795e8 | 0.481068 | 0.240534 | − | 0.970641i | \(-0.422677\pi\) | ||||
0.240534 | + | 0.970641i | \(0.422677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.88470e9 | −1.53801 | ||||||||
\(116\) | −8.21852e8 | −0.421437 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.62775e7 | −0.0172254 | ||||||||
\(119\) | −2.65918e8 | −0.121559 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.13658e8 | −0.175431 | ||||||||
\(122\) | 1.14221e8 | 0.0466796 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.34082e9 | −1.26898 | ||||||||
\(125\) | −6.69264e9 | −2.45190 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.01307e8 | −0.136886 | −0.0684431 | − | 0.997655i | \(-0.521803\pi\) | ||||
−0.0684431 | + | 0.997655i | \(0.521803\pi\) | |||||||
\(128\) | 1.61031e9 | 0.530232 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.29857e8 | 0.0705849 | ||||||||
\(131\) | 3.78377e9 | 1.12255 | 0.561273 | − | 0.827631i | \(-0.310312\pi\) | ||||
0.561273 | + | 0.827631i | \(0.310312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.57404e9 | 0.713317 | ||||||||
\(134\) | 2.04265e8 | 0.0547296 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −9.03756e7 | −0.0226530 | ||||||||
\(137\) | −1.45518e9 | −0.352919 | −0.176459 | − | 0.984308i | \(-0.556464\pi\) | ||||
−0.176459 | + | 0.984308i | \(0.556464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.50381e9 | 0.341685 | 0.170842 | − | 0.985298i | \(-0.445351\pi\) | ||||
0.170842 | + | 0.985298i | \(0.445351\pi\) | |||||||
\(140\) | 1.20564e10 | 2.65242 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.63323e8 | −0.0956283 | ||||||||
\(143\) | −1.25937e9 | −0.251850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.18168e9 | −0.785588 | ||||||||
\(146\) | 1.06268e9 | 0.193559 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.59520e9 | 1.47258 | ||||||||
\(149\) | 4.28624e9 | 0.712423 | 0.356212 | − | 0.934405i | \(-0.384068\pi\) | ||||
0.356212 | + | 0.934405i | \(0.384068\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.79918e8 | 0.0751226 | 0.0375613 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375613 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(152\) | 8.74820e8 | 0.132930 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.30576e9 | 0.187076 | ||||||||
\(155\) | −1.69985e10 | −2.36547 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24624e9 | −1.08320 | −0.541598 | − | 0.840637i | \(-0.682181\pi\) | ||||
−0.541598 | + | 0.840637i | \(0.682181\pi\) | |||||||
\(158\) | 6.42860e8 | 0.0820652 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.16635e9 | 0.743855 | ||||||||
\(161\) | 1.06145e10 | 1.24504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.93537e9 | −0.658573 | −0.329286 | − | 0.944230i | \(-0.606808\pi\) | ||||
−0.329286 | + | 0.944230i | \(0.606808\pi\) | |||||||
\(164\) | −2.58659e9 | −0.279209 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.39961e9 | 0.245276 | ||||||||
\(167\) | 7.41172e9 | 0.737386 | 0.368693 | − | 0.929551i | \(-0.379805\pi\) | ||||
0.368693 | + | 0.929551i | \(0.379805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −2.27671e8 | −0.0209068 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.90469e9 | 0.862905 | ||||||||
\(173\) | −5.63923e9 | −0.478643 | −0.239322 | − | 0.970940i | \(-0.576925\pi\) | ||||
−0.239322 | + | 0.970940i | \(0.576925\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.29853e10 | 3.46457 | ||||||||
\(176\) | −1.08912e10 | −0.855593 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.61182e9 | −0.195008 | ||||||||
\(179\) | −1.23881e10 | −0.901916 | −0.450958 | − | 0.892545i | \(-0.648918\pi\) | ||||
−0.450958 | + | 0.892545i | \(0.648918\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.45852e10 | −1.70263 | −0.851314 | − | 0.524657i | \(-0.824194\pi\) | ||||
−0.851314 | + | 0.524657i | \(0.824194\pi\) | |||||||
\(182\) | −8.45775e8 | −0.0571391 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.60746e9 | 0.232018 | ||||||||
\(185\) | 4.37334e10 | 2.74499 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.24739e9 | 0.0745962 | ||||||||
\(188\) | 2.42476e10 | 1.41566 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.20381e9 | 0.122683 | ||||||||
\(191\) | 1.06604e10 | 0.579592 | 0.289796 | − | 0.957088i | \(-0.406413\pi\) | ||||
0.289796 | + | 0.957088i | \(0.406413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.09640e10 | −1.08759 | −0.543797 | − | 0.839217i | \(-0.683014\pi\) | ||||
−0.543797 | + | 0.839217i | \(0.683014\pi\) | |||||||
\(194\) | −3.17071e9 | −0.160712 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.41020e10 | −1.16654 | ||||||||
\(197\) | −1.27051e10 | −0.601009 | −0.300504 | − | 0.953780i | \(-0.597155\pi\) | ||||
−0.300504 | + | 0.953780i | \(0.597155\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.57825e9 | 0.116543 | 0.0582715 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582715 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(200\) | 1.46091e10 | 0.645638 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.01075e9 | 0.211749 | ||||||||
\(203\) | 1.53868e10 | 0.635941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.31608e10 | −0.520465 | ||||||||
\(206\) | −3.58788e9 | −0.138815 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.05452e9 | 0.261326 | ||||||||
\(209\) | −1.20746e10 | −0.437737 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.94301e10 | 0.674846 | 0.337423 | − | 0.941353i | \(-0.390445\pi\) | ||||
0.337423 | + | 0.941353i | \(0.390445\pi\) | |||||||
\(212\) | −1.54002e10 | −0.523620 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.27276e9 | −0.0740783 | ||||||||
\(215\) | 5.03962e10 | 1.60851 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.25472e10 | 1.91487 | ||||||||
\(218\) | 2.16259e9 | 0.0648515 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.65556e10 | −1.62770 | ||||||||
\(221\) | −8.07973e8 | −0.0227841 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.56077e9 | 0.258893 | 0.129447 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129447 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(224\) | −2.26896e10 | −0.602158 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.62674e9 | −0.0669775 | ||||||||
\(227\) | 2.02032e10 | 0.505015 | 0.252507 | − | 0.967595i | \(-0.418745\pi\) | ||||
0.252507 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.45816e10 | −0.590678 | −0.295339 | − | 0.955392i | \(-0.595433\pi\) | ||||
−0.295339 | + | 0.955392i | \(0.595433\pi\) | |||||||
\(230\) | 9.08778e9 | 0.214132 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.22941e9 | 0.118510 | ||||||||
\(233\) | −7.93260e10 | −1.76325 | −0.881625 | − | 0.471951i | \(-0.843550\pi\) | ||||
−0.881625 | + | 0.471951i | \(0.843550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.23375e11 | 2.63888 | ||||||||
\(236\) | −5.78161e9 | −0.121324 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.37732e8 | 0.0169242 | ||||||||
\(239\) | 2.62515e10 | 0.520431 | 0.260215 | − | 0.965551i | \(-0.416206\pi\) | ||||
0.260215 | + | 0.965551i | \(0.416206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00766e11 | −1.92415 | −0.962074 | − | 0.272787i | \(-0.912055\pi\) | ||||
−0.962074 | + | 0.272787i | \(0.912055\pi\) | |||||||
\(242\) | 1.30316e9 | 0.0244247 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.82036e10 | 0.328778 | ||||||||
\(245\) | −1.22634e11 | −2.17452 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.82103e9 | 0.133699 | ||||||||
\(248\) | 2.12575e10 | 0.356845 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.10841e10 | 0.341370 | ||||||||
\(251\) | 8.72780e10 | 1.38795 | 0.693973 | − | 0.720001i | \(-0.255858\pi\) | ||||
0.693973 | + | 0.720001i | \(0.255858\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.97914e10 | −0.764034 | ||||||||
\(254\) | 1.26425e9 | 0.0190582 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.57827e10 | 0.811744 | ||||||||
\(257\) | −4.84205e10 | −0.692358 | −0.346179 | − | 0.938169i | \(-0.612521\pi\) | ||||
−0.346179 | + | 0.938169i | \(0.612521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.60920e11 | −2.22209 | ||||||||
\(260\) | 3.66326e10 | 0.497151 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.19202e10 | −0.156288 | ||||||||
\(263\) | 4.40656e9 | 0.0567935 | 0.0283968 | − | 0.999597i | \(-0.490960\pi\) | ||||
0.0283968 | + | 0.999597i | \(0.490960\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.83582e10 | −0.976063 | ||||||||
\(266\) | −8.10909e9 | −0.0993127 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.25540e10 | 0.385477 | ||||||||
\(269\) | −1.41879e11 | −1.65209 | −0.826045 | − | 0.563604i | \(-0.809414\pi\) | ||||
−0.826045 | + | 0.563604i | \(0.809414\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.09707e10 | −0.799313 | −0.399657 | − | 0.916665i | \(-0.630871\pi\) | ||||
−0.399657 | + | 0.916665i | \(0.630871\pi\) | |||||||
\(272\) | −6.98743e9 | −0.0774029 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.58432e9 | 0.0491357 | ||||||||
\(275\) | −2.01640e11 | −2.12608 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22293e11 | 1.24808 | 0.624039 | − | 0.781393i | \(-0.285491\pi\) | ||||
0.624039 | + | 0.781393i | \(0.285491\pi\) | |||||||
\(278\) | −4.73751e9 | −0.0475717 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.67145e10 | −0.745876 | ||||||||
\(281\) | 9.91936e10 | 0.949085 | 0.474543 | − | 0.880233i | \(-0.342613\pi\) | ||||
0.474543 | + | 0.880233i | \(0.342613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.89673e11 | 1.75779 | 0.878893 | − | 0.477019i | \(-0.158283\pi\) | ||||
0.878893 | + | 0.477019i | \(0.158283\pi\) | |||||||
\(284\) | −7.38406e10 | −0.673539 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.96745e9 | 0.0350642 | ||||||||
\(287\) | 4.84264e10 | 0.421321 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.17788e11 | −0.993252 | ||||||||
\(290\) | 1.31737e10 | 0.109375 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.69361e11 | 1.36329 | ||||||||
\(293\) | −1.95772e11 | −1.55183 | −0.775917 | − | 0.630835i | \(-0.782713\pi\) | ||||
−0.775917 | + | 0.630835i | \(0.782713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.94175e10 | −0.226155 | ||||||||
\(296\) | −5.46908e10 | −0.414097 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.35031e10 | −0.0991884 | ||||||||
\(299\) | 3.22513e10 | 0.233360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.85437e11 | −1.30211 | ||||||||
\(302\) | −1.51190e9 | −0.0104591 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.76370e10 | 0.454207 | ||||||||
\(305\) | 9.26220e10 | 0.612865 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.17504e10 | −0.461001 | −0.230500 | − | 0.973072i | \(-0.574036\pi\) | ||||
−0.230500 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(308\) | 2.08101e11 | 1.31763 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.35510e10 | 0.329337 | ||||||||
\(311\) | −2.11023e10 | −0.127911 | −0.0639554 | − | 0.997953i | \(-0.520372\pi\) | ||||
−0.0639554 | + | 0.997953i | \(0.520372\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.44667e11 | −0.851963 | −0.425982 | − | 0.904732i | \(-0.640071\pi\) | ||||
−0.425982 | + | 0.904732i | \(0.640071\pi\) | |||||||
\(314\) | 2.59785e10 | 0.150810 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.02454e11 | 0.578010 | ||||||||
\(317\) | −5.78709e10 | −0.321880 | −0.160940 | − | 0.986964i | \(-0.551453\pi\) | ||||
−0.160940 | + | 0.986964i | \(0.551453\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.21781e10 | −0.390254 | ||||||||
\(320\) | 3.03639e11 | 1.61876 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.34392e10 | −0.173342 | ||||||||
\(323\) | −7.74665e9 | −0.0396007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.30608e11 | 0.649373 | ||||||||
\(326\) | 1.86984e10 | 0.0916909 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.64583e10 | 0.0785151 | ||||||||
\(329\) | −4.53966e11 | −2.13620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00283e11 | −0.459199 | −0.229600 | − | 0.973285i | \(-0.573742\pi\) | ||||
−0.229600 | + | 0.973285i | \(0.573742\pi\) | |||||||
\(332\) | 3.82431e11 | 1.72755 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.33495e10 | −0.102664 | ||||||||
\(335\) | 1.65639e11 | 0.718555 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.73297e10 | −0.242128 | −0.121064 | − | 0.992645i | \(-0.538631\pi\) | ||||
−0.121064 | + | 0.992645i | \(0.538631\pi\) | |||||||
\(338\) | −2.56983e9 | −0.0107097 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.62843e10 | −0.147253 | ||||||||
\(341\) | −2.93403e11 | −1.17509 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.19204e10 | 0.280562 | ||||||||
\(344\) | −6.30231e10 | −0.242654 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.77655e10 | 0.0666399 | ||||||||
\(347\) | 2.34072e10 | 0.0866695 | 0.0433347 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433347 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.92804e11 | 1.41730 | 0.708649 | − | 0.705562i | \(-0.249305\pi\) | ||||
0.708649 | + | 0.705562i | \(0.249305\pi\) | |||||||
\(350\) | −1.35418e11 | −0.482360 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.06435e11 | 0.369523 | ||||||||
\(353\) | −2.16422e11 | −0.741849 | −0.370925 | − | 0.928663i | \(-0.620959\pi\) | ||||
−0.370925 | + | 0.928663i | \(0.620959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.75710e11 | −1.25552 | ||||||||
\(356\) | −4.16250e11 | −1.37350 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.90267e10 | 0.125571 | ||||||||
\(359\) | −3.49576e11 | −1.11075 | −0.555376 | − | 0.831600i | \(-0.687426\pi\) | ||||
−0.555376 | + | 0.831600i | \(0.687426\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47701e11 | −0.767620 | ||||||||
\(362\) | 7.74517e10 | 0.237051 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.34793e11 | −0.402448 | ||||||||
\(365\) | 8.61727e11 | 2.54128 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.83237e9 | −0.00527248 | −0.00263624 | − | 0.999997i | \(-0.500839\pi\) | ||||
−0.00263624 | + | 0.999997i | \(0.500839\pi\) | |||||||
\(368\) | 2.78913e11 | 0.792780 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.37775e11 | −0.382175 | ||||||||
\(371\) | 2.88325e11 | 0.790132 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.52030e10 | 0.147663 | 0.0738317 | − | 0.997271i | \(-0.476477\pi\) | ||||
0.0738317 | + | 0.997271i | \(0.476477\pi\) | |||||||
\(374\) | −3.92972e9 | −0.0103858 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.54286e11 | −0.398091 | ||||||||
\(377\) | 4.67518e10 | 0.119196 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.25258e11 | 0.560795 | 0.280397 | − | 0.959884i | \(-0.409534\pi\) | ||||
0.280397 | + | 0.959884i | \(0.409534\pi\) | |||||||
\(380\) | 3.51225e11 | 0.864091 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.35838e10 | −0.0806947 | ||||||||
\(383\) | −4.64079e11 | −1.10204 | −0.551020 | − | 0.834492i | \(-0.685761\pi\) | ||||
−0.551020 | + | 0.834492i | \(0.685761\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.05884e12 | 2.45616 | ||||||||
\(386\) | 6.60438e10 | 0.151422 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.05322e11 | −1.13195 | ||||||||
\(389\) | 2.63061e11 | 0.582482 | 0.291241 | − | 0.956650i | \(-0.405932\pi\) | ||||
0.291241 | + | 0.956650i | \(0.405932\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.19446e10 | −0.0691198 | ||||||||
\(392\) | 1.53360e11 | 0.328039 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.00255e10 | 0.0836765 | ||||||||
\(395\) | 5.21296e11 | 1.07745 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.80382e10 | −0.0364449 | −0.0182224 | − | 0.999834i | \(-0.505801\pi\) | ||||
−0.0182224 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(398\) | −8.12236e9 | −0.0162259 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.12951e12 | 2.20607 | ||||||||
\(401\) | −7.18792e10 | −0.138821 | −0.0694103 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694103 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90046e11 | 0.358910 | ||||||||
\(404\) | 7.98571e11 | 1.49141 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.84737e10 | −0.0885399 | ||||||||
\(407\) | 7.54862e11 | 1.36362 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.31862e11 | 0.939819 | 0.469910 | − | 0.882715i | \(-0.344287\pi\) | ||||
0.469910 | + | 0.882715i | \(0.344287\pi\) | |||||||
\(410\) | 4.14612e10 | 0.0724626 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.71806e11 | −0.977713 | ||||||||
\(413\) | 1.08244e11 | 0.183075 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.94585e12 | 3.22028 | ||||||||
\(416\) | −6.89407e10 | −0.112864 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.80390e10 | 0.0609446 | ||||||||
\(419\) | −1.45942e11 | −0.231322 | −0.115661 | − | 0.993289i | \(-0.536899\pi\) | ||||
−0.115661 | + | 0.993289i | \(0.536899\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.66247e11 | 0.568204 | 0.284102 | − | 0.958794i | \(-0.408305\pi\) | ||||
0.284102 | + | 0.958794i | \(0.408305\pi\) | |||||||
\(422\) | −6.12115e10 | −0.0939565 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.79910e10 | 0.147245 | ||||||||
\(425\) | −1.29366e11 | −0.192340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.40810e11 | −0.496120 | ||||||||
\(428\) | −3.62213e11 | −0.521756 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.58765e11 | −0.223948 | ||||||||
\(431\) | −7.66389e11 | −1.06980 | −0.534899 | − | 0.844916i | \(-0.679650\pi\) | ||||
−0.534899 | + | 0.844916i | \(0.679650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.24176e12 | −1.69763 | −0.848813 | − | 0.528694i | \(-0.822682\pi\) | ||||
−0.848813 | + | 0.528694i | \(0.822682\pi\) | |||||||
\(434\) | −1.97045e11 | −0.266601 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.44656e11 | 0.456769 | ||||||||
\(437\) | 3.09218e11 | 0.405601 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.48429e12 | −1.90734 | −0.953671 | − | 0.300852i | \(-0.902729\pi\) | ||||
−0.953671 | + | 0.300852i | \(0.902729\pi\) | |||||||
\(440\) | 3.59861e11 | 0.457717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.54539e9 | 0.00317215 | ||||||||
\(443\) | −1.03343e12 | −1.27487 | −0.637433 | − | 0.770506i | \(-0.720004\pi\) | ||||
−0.637433 | + | 0.770506i | \(0.720004\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.11793e12 | −2.56030 | ||||||||
\(446\) | −3.01197e10 | −0.0360449 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.11726e12 | −1.31040 | ||||||||
\(449\) | 5.83072e11 | 0.677039 | 0.338519 | − | 0.940959i | \(-0.390074\pi\) | ||||
0.338519 | + | 0.940959i | \(0.390074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.27163e11 | −0.258550 | ||||||||
\(452\) | −4.18628e11 | −0.471743 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.36470e10 | −0.0703116 | ||||||||
\(455\) | −6.85841e11 | −0.750191 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.39681e11 | 0.793271 | 0.396635 | − | 0.917976i | \(-0.370178\pi\) | ||||
0.396635 | + | 0.917976i | \(0.370178\pi\) | |||||||
\(458\) | 7.74405e10 | 0.0822382 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.44834e12 | 1.50820 | ||||||||
\(461\) | −1.45843e12 | −1.50394 | −0.751971 | − | 0.659197i | \(-0.770896\pi\) | ||||
−0.751971 | + | 0.659197i | \(0.770896\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.63194e12 | −1.65040 | −0.825200 | − | 0.564841i | \(-0.808937\pi\) | ||||
−0.825200 | + | 0.564841i | \(0.808937\pi\) | |||||||
\(464\) | 4.04314e11 | 0.404937 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.49904e11 | 0.245492 | ||||||||
\(467\) | 8.24440e11 | 0.802109 | 0.401054 | − | 0.916054i | \(-0.368644\pi\) | ||||
0.401054 | + | 0.916054i | \(0.368644\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.09481e11 | −0.581677 | ||||||||
\(470\) | −3.88672e11 | −0.367403 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.67882e10 | 0.0341169 | ||||||||
\(473\) | 8.69866e11 | 0.799056 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.25224e12 | 1.12867 | ||||||||
\(476\) | 1.33511e11 | 0.119202 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.27011e10 | −0.0724579 | ||||||||
\(479\) | 1.80073e11 | 0.156293 | 0.0781463 | − | 0.996942i | \(-0.475100\pi\) | ||||
0.0781463 | + | 0.996942i | \(0.475100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.88945e11 | −0.416493 | ||||||||
\(482\) | 3.17448e11 | 0.267893 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.07688e11 | 0.172031 | ||||||||
\(485\) | −2.57114e12 | −2.11003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.22045e11 | −0.581680 | −0.290840 | − | 0.956772i | \(-0.593935\pi\) | ||||
−0.290840 | + | 0.956772i | \(0.593935\pi\) | |||||||
\(488\) | −1.15829e11 | −0.0924543 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.86339e11 | 0.302751 | ||||||||
\(491\) | −1.98313e12 | −1.53987 | −0.769937 | − | 0.638119i | \(-0.779713\pi\) | ||||
−0.769937 | + | 0.638119i | \(0.779713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.63072e10 | −0.0353051 | ||||||||
\(494\) | −2.46389e10 | −0.0186145 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.64353e12 | 1.21930 | ||||||||
\(497\) | 1.38245e12 | 1.01636 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.27327e11 | −0.597344 | −0.298672 | − | 0.954356i | \(-0.596544\pi\) | ||||
−0.298672 | + | 0.954356i | \(0.596544\pi\) | |||||||
\(500\) | 3.36021e12 | 2.40437 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.74955e11 | −0.193239 | ||||||||
\(503\) | −4.94554e11 | −0.344475 | −0.172238 | − | 0.985055i | \(-0.555100\pi\) | ||||
−0.172238 | + | 0.985055i | \(0.555100\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.06322e12 | 2.78009 | ||||||||
\(506\) | 1.56860e11 | 0.106374 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.01486e11 | 0.134233 | ||||||||
\(509\) | 2.31118e12 | 1.52617 | 0.763087 | − | 0.646296i | \(-0.223683\pi\) | ||||
0.763087 | + | 0.646296i | \(0.223683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.17079e12 | −2.05719 | ||||||||
\(512\) | −1.00022e12 | −0.643248 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.52541e11 | 0.0963947 | ||||||||
\(515\) | −2.90942e12 | −1.82252 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.12951e12 | 1.31091 | ||||||||
\(518\) | 5.06954e11 | 0.309374 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.33092e11 | −0.139802 | ||||||||
\(521\) | −2.20997e12 | −1.31406 | −0.657031 | − | 0.753864i | \(-0.728188\pi\) | ||||
−0.657031 | + | 0.753864i | \(0.728188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.43867e12 | 1.42527 | 0.712633 | − | 0.701537i | \(-0.247503\pi\) | ||||
0.712633 | + | 0.701537i | \(0.247503\pi\) | |||||||
\(524\) | −1.89974e12 | −1.10079 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.38822e10 | −0.00790718 | ||||||||
\(527\) | −1.88238e11 | −0.106307 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.26040e11 | −0.292057 | ||||||||
\(530\) | 2.46855e11 | 0.135894 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.29236e12 | −0.699490 | ||||||||
\(533\) | 1.47140e11 | 0.0789694 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.84298e12 | −0.972588 | ||||||||
\(536\) | −2.07140e11 | −0.108398 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.46968e11 | 0.230015 | ||||||||
\(539\) | −2.11673e12 | −1.08023 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.84418e12 | −0.925585 | −0.462792 | − | 0.886467i | \(-0.653152\pi\) | ||||
−0.462792 | + | 0.886467i | \(0.653152\pi\) | |||||||
\(542\) | 2.23582e11 | 0.111286 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.82851e10 | 0.0334296 | ||||||||
\(545\) | 1.75365e12 | 0.851448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.62022e12 | −1.25140 | −0.625698 | − | 0.780065i | \(-0.715186\pi\) | ||||
−0.625698 | + | 0.780065i | \(0.715186\pi\) | |||||||
\(548\) | 7.30611e11 | 0.346078 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.35235e11 | 0.296007 | ||||||||
\(551\) | 4.48245e11 | 0.207173 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.91815e12 | −0.872206 | ||||||||
\(554\) | −3.85264e11 | −0.173766 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.55025e11 | −0.335062 | ||||||||
\(557\) | −2.45908e12 | −1.08249 | −0.541245 | − | 0.840865i | \(-0.682047\pi\) | ||||
−0.541245 | + | 0.840865i | \(0.682047\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.63437e11 | −0.244058 | ||||||||
\(560\) | −5.93122e12 | −2.54858 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.12494e11 | −0.132138 | ||||||||
\(563\) | 1.30659e12 | 0.548091 | 0.274046 | − | 0.961717i | \(-0.411638\pi\) | ||||
0.274046 | + | 0.961717i | \(0.411638\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.13003e12 | −0.879361 | ||||||||
\(566\) | −5.97534e11 | −0.244731 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.69845e11 | 0.189403 | ||||||||
\(569\) | 2.68810e12 | 1.07508 | 0.537539 | − | 0.843239i | \(-0.319354\pi\) | ||||
0.537539 | + | 0.843239i | \(0.319354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.99602e12 | 1.17946 | 0.589729 | − | 0.807601i | \(-0.299235\pi\) | ||||
0.589729 | + | 0.807601i | \(0.299235\pi\) | |||||||
\(572\) | 6.32299e11 | 0.246968 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.52560e11 | −0.0586592 | ||||||||
\(575\) | 5.16381e12 | 1.97000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.04343e11 | 0.226982 | 0.113491 | − | 0.993539i | \(-0.463797\pi\) | ||||
0.113491 | + | 0.993539i | \(0.463797\pi\) | |||||||
\(578\) | 3.71071e11 | 0.138287 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.09952e12 | 0.770360 | ||||||||
\(581\) | −7.15991e12 | −2.60684 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.35250e12 | −0.484876 | ||||||||
\(584\) | −1.07763e12 | −0.383366 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.16747e11 | 0.216057 | ||||||||
\(587\) | 7.41276e11 | 0.257697 | 0.128848 | − | 0.991664i | \(-0.458872\pi\) | ||||
0.128848 | + | 0.991664i | \(0.458872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.82211e12 | 0.623816 | ||||||||
\(590\) | 9.26752e10 | 0.0314869 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.22845e12 | −1.41492 | ||||||||
\(593\) | 5.55536e12 | 1.84487 | 0.922435 | − | 0.386152i | \(-0.126196\pi\) | ||||
0.922435 | + | 0.386152i | \(0.126196\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.79318e11 | 0.222201 | ||||||||
\(596\) | −2.15201e12 | −0.698614 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.01603e11 | −0.0324900 | ||||||||
\(599\) | 3.35363e12 | 1.06437 | 0.532187 | − | 0.846627i | \(-0.321370\pi\) | ||||
0.532187 | + | 0.846627i | \(0.321370\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.88646e12 | 0.589809 | 0.294905 | − | 0.955527i | \(-0.404712\pi\) | ||||
0.294905 | + | 0.955527i | \(0.404712\pi\) | |||||||
\(602\) | 5.84189e11 | 0.181288 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.40955e11 | −0.0736664 | ||||||||
\(605\) | 1.05674e12 | 0.320677 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.01740e12 | 0.304188 | 0.152094 | − | 0.988366i | \(-0.451398\pi\) | ||||
0.152094 | + | 0.988366i | \(0.451398\pi\) | |||||||
\(608\) | −6.60987e11 | −0.196168 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.91791e11 | −0.0853272 | ||||||||
\(611\) | −1.37935e12 | −0.400394 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.21446e11 | −0.149155 | −0.0745774 | − | 0.997215i | \(-0.523761\pi\) | ||||
−0.0745774 | + | 0.997215i | \(0.523761\pi\) | |||||||
\(614\) | 2.26038e11 | 0.0641836 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.32413e12 | −0.370526 | ||||||||
\(617\) | −1.14541e12 | −0.318183 | −0.159092 | − | 0.987264i | \(-0.550857\pi\) | ||||
−0.159092 | + | 0.987264i | \(0.550857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.10612e12 | −0.302827 | −0.151414 | − | 0.988470i | \(-0.548383\pi\) | ||||
−0.151414 | + | 0.988470i | \(0.548383\pi\) | |||||||
\(620\) | 8.53452e12 | 2.31962 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.64793e10 | 0.0178086 | ||||||||
\(623\) | 7.79308e12 | 2.07259 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.16561e12 | 2.14057 | ||||||||
\(626\) | 4.55751e11 | 0.118616 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.14023e12 | 1.06220 | ||||||||
\(629\) | 4.84295e11 | 0.123362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.20443e12 | 0.804671 | 0.402336 | − | 0.915492i | \(-0.368198\pi\) | ||||
0.402336 | + | 0.915492i | \(0.368198\pi\) | |||||||
\(632\) | −6.51908e11 | −0.162540 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.82313e11 | 0.0448143 | ||||||||
\(635\) | 1.02518e12 | 0.250219 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.37106e12 | 0.329937 | ||||||||
\(638\) | 2.27386e11 | 0.0543338 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.11374e12 | −0.969230 | ||||||||
\(641\) | 4.90467e12 | 1.14749 | 0.573745 | − | 0.819034i | \(-0.305490\pi\) | ||||
0.573745 | + | 0.819034i | \(0.305490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.53529e12 | 0.354194 | 0.177097 | − | 0.984193i | \(-0.443329\pi\) | ||||
0.177097 | + | 0.984193i | \(0.443329\pi\) | |||||||
\(644\) | −5.32926e12 | −1.22090 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.44046e10 | 0.00551347 | ||||||||
\(647\) | 6.61326e11 | 0.148370 | 0.0741850 | − | 0.997244i | \(-0.476364\pi\) | ||||
0.0741850 | + | 0.997244i | \(0.476364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.07763e11 | −0.112347 | ||||||||
\(650\) | −4.11460e11 | −0.0904101 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.98000e12 | 0.645807 | ||||||||
\(653\) | −4.61469e12 | −0.993192 | −0.496596 | − | 0.867982i | \(-0.665417\pi\) | ||||
−0.496596 | + | 0.867982i | \(0.665417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.66610e12 | −2.05194 | ||||||||
\(656\) | 1.27248e12 | 0.268278 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.43015e12 | 0.297416 | ||||||||
\(659\) | 9.04687e12 | 1.86859 | 0.934294 | − | 0.356502i | \(-0.116031\pi\) | ||||
0.934294 | + | 0.356502i | \(0.116031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.59295e12 | 0.732057 | 0.366028 | − | 0.930604i | \(-0.380717\pi\) | ||||
0.366028 | + | 0.930604i | \(0.380717\pi\) | |||||||
\(662\) | 3.15926e11 | 0.0639328 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.43339e12 | −0.485797 | ||||||||
\(665\) | −6.57568e12 | −1.30390 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.84841e12 | 0.361604 | ||||||||
\(668\) | −3.72124e12 | −0.723093 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.21819e11 | −0.100042 | ||||||||
\(671\) | 1.59871e12 | 0.304451 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.13714e12 | 0.401573 | 0.200786 | − | 0.979635i | \(-0.435650\pi\) | ||||
0.200786 | + | 0.979635i | \(0.435650\pi\) | |||||||
\(674\) | 1.80608e11 | 0.0337107 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.09558e11 | −0.0754320 | ||||||||
\(677\) | 2.55166e12 | 0.466847 | 0.233423 | − | 0.972375i | \(-0.425007\pi\) | ||||
0.233423 | + | 0.972375i | \(0.425007\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.46070e12 | 1.70809 | ||||||||
\(680\) | 2.30875e11 | 0.0414083 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.24320e11 | 0.163604 | ||||||||
\(683\) | −7.63188e12 | −1.34196 | −0.670978 | − | 0.741477i | \(-0.734126\pi\) | ||||
−0.670978 | + | 0.741477i | \(0.734126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.71743e12 | 0.645113 | ||||||||
\(686\) | −2.26574e11 | −0.0390617 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.87266e12 | −0.829121 | ||||||||
\(689\) | 8.76056e11 | 0.148097 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.36970e12 | −0.395405 | −0.197703 | − | 0.980262i | \(-0.563348\pi\) | ||||
−0.197703 | + | 0.980262i | \(0.563348\pi\) | |||||||
\(692\) | 2.83132e12 | 0.469365 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.37405e10 | −0.0120667 | ||||||||
\(695\) | −3.84165e12 | −0.624578 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.45741e11 | −0.0233902 | ||||||||
\(698\) | −1.23747e12 | −0.197326 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.15819e13 | −3.39741 | ||||||||
\(701\) | 1.72803e12 | 0.270284 | 0.135142 | − | 0.990826i | \(-0.456851\pi\) | ||||
0.135142 | + | 0.990826i | \(0.456851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.68789e12 | −0.723900 | ||||||||
\(704\) | 5.24097e12 | 0.804146 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.81804e11 | 0.103285 | ||||||||
\(707\) | −1.49509e13 | −2.25051 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.26440e12 | −0.485172 | −0.242586 | − | 0.970130i | \(-0.577996\pi\) | ||||
−0.242586 | + | 0.970130i | \(0.577996\pi\) | |||||||
\(710\) | 1.18361e12 | 0.174802 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.64858e12 | 0.386236 | ||||||||
\(713\) | 7.51378e12 | 1.08882 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.21721e12 | 0.460365 | ||||||||
\(716\) | 6.21976e12 | 0.884433 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.10128e12 | 0.154646 | ||||||||
\(719\) | 6.17850e11 | 0.0862191 | 0.0431095 | − | 0.999070i | \(-0.486274\pi\) | ||||
0.0431095 | + | 0.999070i | \(0.486274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.07054e13 | 1.47535 | ||||||||
\(722\) | 7.80344e11 | 0.106873 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.23436e13 | 1.66962 | ||||||||
\(725\) | 7.48550e12 | 1.00624 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.84000e12 | 0.775368 | 0.387684 | − | 0.921792i | \(-0.373275\pi\) | ||||
0.387684 | + | 0.921792i | \(0.373275\pi\) | |||||||
\(728\) | 8.57680e11 | 0.113171 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.71473e12 | −0.353813 | ||||||||
\(731\) | 5.58079e11 | 0.0722882 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.18908e10 | −0.00919826 | −0.00459913 | − | 0.999989i | \(-0.501464\pi\) | ||||
−0.00459913 | + | 0.999989i | \(0.501464\pi\) | |||||||
\(734\) | 5.77258e9 | 0.000734070 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.72569e12 | −0.342394 | ||||||||
\(737\) | 2.85902e12 | 0.356954 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.01033e13 | −1.24613 | −0.623067 | − | 0.782168i | \(-0.714114\pi\) | ||||
−0.623067 | + | 0.782168i | \(0.714114\pi\) | |||||||
\(740\) | −2.19574e13 | −2.69178 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.08322e11 | −0.110007 | ||||||||
\(743\) | 6.09193e12 | 0.733340 | 0.366670 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366670 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.09497e13 | −1.30226 | ||||||||
\(746\) | −1.73908e11 | −0.0205587 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.26286e11 | −0.0731502 | ||||||||
\(749\) | 6.78139e12 | 0.787319 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.43572e13 | −1.64698 | −0.823491 | − | 0.567330i | \(-0.807976\pi\) | ||||
−0.823491 | + | 0.567330i | \(0.807976\pi\) | |||||||
\(752\) | −1.19287e13 | −1.36023 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.47284e11 | −0.0165953 | ||||||||
\(755\) | −1.22601e12 | −0.137319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.33786e13 | 1.48074 | 0.740370 | − | 0.672200i | \(-0.234651\pi\) | ||||
0.740370 | + | 0.672200i | \(0.234651\pi\) | |||||||
\(758\) | −7.09640e11 | −0.0780776 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.23483e12 | −0.242987 | ||||||||
\(761\) | −1.00649e13 | −1.08788 | −0.543938 | − | 0.839126i | \(-0.683067\pi\) | ||||
−0.543938 | + | 0.839126i | \(0.683067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.45269e12 | −0.689255 | ||||||||
\(764\) | −5.35231e12 | −0.568357 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.46201e12 | 0.153433 | ||||||||
\(767\) | 3.28892e11 | 0.0343142 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.34623e12 | 0.448172 | 0.224086 | − | 0.974569i | \(-0.428060\pi\) | ||||
0.224086 | + | 0.974569i | \(0.428060\pi\) | |||||||
\(770\) | −3.33571e12 | −0.341963 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.05255e13 | 1.06651 | ||||||||
\(773\) | −2.50017e12 | −0.251862 | −0.125931 | − | 0.992039i | \(-0.540192\pi\) | ||||
−0.125931 | + | 0.992039i | \(0.540192\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.04285e13 | 3.02986 | ||||||||
\(776\) | 3.21534e12 | 0.318310 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.28731e11 | −0.0810971 | ||||||||
\(779\) | 1.41075e12 | 0.137256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.48495e12 | −0.623702 | ||||||||
\(782\) | 1.00636e11 | 0.00962332 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.18571e13 | 1.12087 | ||||||||
\(785\) | 2.10660e13 | 1.98001 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.47010e13 | −1.36603 | −0.683013 | − | 0.730406i | \(-0.739331\pi\) | ||||
−0.683013 | + | 0.730406i | \(0.739331\pi\) | |||||||
\(788\) | 6.37893e12 | 0.589359 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.64226e12 | −0.150010 | ||||||||
\(791\) | 7.83761e12 | 0.711851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.03553e12 | −0.0929892 | ||||||||
\(794\) | 5.68266e10 | 0.00507410 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.29448e12 | −0.114284 | ||||||||
\(797\) | −8.96898e12 | −0.787373 | −0.393687 | − | 0.919245i | \(-0.628801\pi\) | ||||
−0.393687 | + | 0.919245i | \(0.628801\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36623e12 | 0.118594 | ||||||||
\(800\) | −1.10382e13 | −0.952782 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.26444e11 | 0.0193275 | ||||||||
\(803\) | 1.48739e13 | 1.26242 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.71159e13 | −2.27584 | ||||||||
\(806\) | −5.98708e11 | −0.0499698 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.08127e12 | −0.419393 | ||||||||
\(809\) | −1.74450e13 | −1.43187 | −0.715934 | − | 0.698168i | \(-0.753999\pi\) | ||||
−0.715934 | + | 0.698168i | \(0.753999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.34611e12 | −0.677470 | −0.338735 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338735 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(812\) | −7.72534e12 | −0.623614 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.37807e12 | −0.189852 | ||||||||
\(815\) | 1.51626e13 | 1.20383 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.40210e12 | −0.424193 | ||||||||
\(818\) | −1.67555e12 | −0.130848 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.60774e12 | 0.510376 | ||||||||
\(821\) | −1.88288e13 | −1.44637 | −0.723183 | − | 0.690657i | \(-0.757322\pi\) | ||||
−0.723183 | + | 0.690657i | \(0.757322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.02178e12 | 0.305576 | 0.152788 | − | 0.988259i | \(-0.451175\pi\) | ||||
0.152788 | + | 0.988259i | \(0.451175\pi\) | |||||||
\(824\) | 3.63838e12 | 0.274938 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.41006e11 | −0.0254889 | ||||||||
\(827\) | −3.84013e12 | −0.285477 | −0.142738 | − | 0.989760i | \(-0.545591\pi\) | ||||
−0.142738 | + | 0.989760i | \(0.545591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.81041e13 | 1.33132 | 0.665660 | − | 0.746255i | \(-0.268150\pi\) | ||||
0.665660 | + | 0.746255i | \(0.268150\pi\) | |||||||
\(830\) | −6.13010e12 | −0.448349 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.39473e12 | −0.245612 | ||||||||
\(833\) | −1.35803e12 | −0.0977249 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.89341e13 | −1.34789 | ||||||||
\(836\) | 6.06234e12 | 0.429252 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.59766e11 | 0.0322062 | ||||||||
\(839\) | −1.83543e13 | −1.27882 | −0.639410 | − | 0.768866i | \(-0.720821\pi\) | ||||
−0.639410 | + | 0.768866i | \(0.720821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.18277e13 | −0.815300 | ||||||||
\(842\) | −1.15380e12 | −0.0791092 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.75538e12 | −0.661764 | ||||||||
\(845\) | −2.08388e12 | −0.140610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.88835e12 | −0.259591 | ||||||||
\(848\) | 7.57621e12 | 0.503119 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.07546e11 | 0.0267789 | ||||||||
\(851\) | −1.93313e13 | −1.26351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.20116e13 | −0.776835 | −0.388418 | − | 0.921483i | \(-0.626978\pi\) | ||||
−0.388418 | + | 0.921483i | \(0.626978\pi\) | |||||||
\(854\) | 1.07367e12 | 0.0690732 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.30475e12 | 0.146721 | ||||||||
\(857\) | 6.17723e12 | 0.391183 | 0.195592 | − | 0.980685i | \(-0.437337\pi\) | ||||
0.195592 | + | 0.980685i | \(0.437337\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.76160e13 | 1.73058 | 0.865291 | − | 0.501269i | \(-0.167133\pi\) | ||||
0.865291 | + | 0.501269i | \(0.167133\pi\) | |||||||
\(860\) | −2.53027e13 | −1.57733 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.41439e12 | 0.148944 | ||||||||
\(863\) | −9.27582e12 | −0.569251 | −0.284626 | − | 0.958639i | \(-0.591869\pi\) | ||||
−0.284626 | + | 0.958639i | \(0.591869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.44061e13 | 0.874929 | ||||||||
\(866\) | 3.91197e12 | 0.236355 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.14034e13 | −1.87775 | ||||||||
\(869\) | 8.99785e12 | 0.535242 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.85187e12 | −0.109025 | ||||||||
\(872\) | −2.19303e12 | −0.128446 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.74143e11 | −0.0564704 | ||||||||
\(875\) | −6.29103e13 | −3.62815 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.19078e13 | −1.25055 | −0.625274 | − | 0.780405i | \(-0.715013\pi\) | ||||
−0.625274 | + | 0.780405i | \(0.715013\pi\) | |||||||
\(878\) | 4.67602e12 | 0.265553 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.78228e13 | 1.56397 | ||||||||
\(881\) | −2.92416e12 | −0.163534 | −0.0817672 | − | 0.996651i | \(-0.526056\pi\) | ||||
−0.0817672 | + | 0.996651i | \(0.526056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.35851e13 | 1.85919 | 0.929594 | − | 0.368585i | \(-0.120158\pi\) | ||||
0.929594 | + | 0.368585i | \(0.120158\pi\) | |||||||
\(884\) | 4.05663e11 | 0.0223424 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.25566e12 | 0.177495 | ||||||||
\(887\) | 3.31699e13 | 1.79924 | 0.899619 | − | 0.436676i | \(-0.143844\pi\) | ||||
0.899619 | + | 0.436676i | \(0.143844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.77225e12 | −0.202555 | ||||||||
\(890\) | 6.67219e12 | 0.356462 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.80023e12 | −0.253875 | ||||||||
\(893\) | −1.32248e13 | −0.695920 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.16469e13 | 1.64864 | ||||||||
\(896\) | 1.51368e13 | 0.784601 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.83688e12 | −0.0942619 | ||||||||
\(899\) | 1.08920e13 | 0.556148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.67724e11 | −0.0438652 | ||||||||
\(902\) | 7.15642e11 | 0.0359970 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.66371e12 | 0.132657 | ||||||||
\(905\) | 6.28057e13 | 3.11229 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.27086e13 | 1.11418 | 0.557092 | − | 0.830451i | \(-0.311917\pi\) | ||||
0.557092 | + | 0.830451i | \(0.311917\pi\) | |||||||
\(908\) | −1.01435e13 | −0.495226 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.16063e12 | 0.104447 | ||||||||
\(911\) | −4.92090e12 | −0.236707 | −0.118354 | − | 0.992972i | \(-0.537762\pi\) | ||||
−0.118354 | + | 0.992972i | \(0.537762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.35865e13 | 1.59973 | ||||||||
\(914\) | −2.33025e12 | −0.110444 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.23418e13 | 0.579229 | ||||||||
\(917\) | 3.55671e13 | 1.66107 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.41621e12 | −0.435468 | −0.217734 | − | 0.976008i | \(-0.569867\pi\) | ||||
−0.217734 | + | 0.976008i | \(0.569867\pi\) | |||||||
\(920\) | −9.21569e12 | −0.424114 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.59455e12 | 0.209389 | ||||||||
\(923\) | 4.20049e12 | 0.190499 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.82858e13 | −3.51597 | ||||||||
\(926\) | 5.14116e12 | 0.229780 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.95118e12 | −0.174889 | ||||||||
\(929\) | 3.87518e13 | 1.70695 | 0.853476 | − | 0.521131i | \(-0.174490\pi\) | ||||
0.853476 | + | 0.521131i | \(0.174490\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.31454e13 | 0.573458 | ||||||||
\(932\) | 3.98276e13 | 1.72907 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.59727e12 | −0.111675 | ||||||||
\(935\) | −3.18662e12 | −0.136357 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.41425e13 | 0.599373 | 0.299687 | − | 0.954038i | \(-0.403118\pi\) | ||||
0.299687 | + | 0.954038i | \(0.403118\pi\) | |||||||
\(938\) | 1.92007e12 | 0.0809850 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.19433e13 | −2.58773 | ||||||||
\(941\) | 2.29704e13 | 0.955027 | 0.477514 | − | 0.878624i | \(-0.341538\pi\) | ||||
0.477514 | + | 0.878624i | \(0.341538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.81744e12 | 0.239568 | ||||||||
\(944\) | 2.84429e12 | 0.116574 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.74038e12 | −0.111250 | ||||||||
\(947\) | 1.50510e12 | 0.0608120 | 0.0304060 | − | 0.999538i | \(-0.490320\pi\) | ||||
0.0304060 | + | 0.999538i | \(0.490320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.63423e12 | −0.385584 | ||||||||
\(950\) | −3.94498e12 | −0.157141 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.49523e11 | −0.0335204 | ||||||||
\(953\) | −2.42253e13 | −0.951373 | −0.475686 | − | 0.879615i | \(-0.657800\pi\) | ||||
−0.475686 | + | 0.879615i | \(0.657800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.72332e13 | −1.05946 | ||||||||
\(956\) | −1.31802e13 | −0.510343 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.67291e11 | −0.0217601 | ||||||||
\(959\) | −1.36786e13 | −0.522225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.78364e13 | 0.674608 | ||||||||
\(962\) | 1.54034e12 | 0.0579869 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.05923e13 | 1.88685 | ||||||||
\(965\) | 5.35551e13 | 1.98805 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41172e13 | 0.886967 | 0.443484 | − | 0.896282i | \(-0.353742\pi\) | ||||
0.443484 | + | 0.896282i | \(0.353742\pi\) | |||||||
\(968\) | −1.32151e12 | −0.0483760 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.09996e12 | 0.293772 | ||||||||
\(971\) | −3.13584e13 | −1.13206 | −0.566028 | − | 0.824386i | \(-0.691521\pi\) | ||||
−0.566028 | + | 0.824386i | \(0.691521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.41357e13 | 0.505602 | ||||||||
\(974\) | 2.27469e12 | 0.0809854 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.95534e12 | −0.315906 | ||||||||
\(977\) | −4.44366e13 | −1.56033 | −0.780163 | − | 0.625576i | \(-0.784864\pi\) | ||||
−0.780163 | + | 0.625576i | \(0.784864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.65566e13 | −1.27187 | ||||||||
\(980\) | 6.15714e13 | 2.13237 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.24755e12 | 0.214392 | ||||||||
\(983\) | −1.53216e13 | −0.523376 | −0.261688 | − | 0.965153i | \(-0.584279\pi\) | ||||
−0.261688 | + | 0.965153i | \(0.584279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.24567e13 | 1.09861 | ||||||||
\(986\) | 1.45883e11 | 0.00491541 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.92675e12 | −0.131107 | ||||||||
\(989\) | −2.22765e13 | −0.740394 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.32887e13 | 0.767034 | 0.383517 | − | 0.923534i | \(-0.374713\pi\) | ||||
0.383517 | + | 0.923534i | \(0.374713\pi\) | |||||||
\(992\) | −1.60615e13 | −0.526604 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.35520e12 | −0.141504 | ||||||||
\(995\) | −6.58644e12 | −0.213033 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.12247e13 | −0.359788 | −0.179894 | − | 0.983686i | \(-0.557575\pi\) | ||||
−0.179894 | + | 0.983686i | \(0.557575\pi\) | |||||||
\(998\) | 2.60636e12 | 0.0831663 | ||||||||
\(999\) | 0 | 0 |
(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 | 117.10.a.e.1.3 | 5 | ||
3.2 | odd | 2 | 13.10.a.b.1.3 | ✓ | 5 | ||
12.11 | even | 2 | 208.10.a.h.1.4 | 5 | |||
15.14 | odd | 2 | 325.10.a.b.1.3 | 5 | |||
39.38 | odd | 2 | 169.10.a.b.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.b.1.3 | ✓ | 5 | 3.2 | odd | 2 | ||
117.10.a.e.1.3 | 5 | 1.1 | even | 1 | trivial | ||
169.10.a.b.1.3 | 5 | 39.38 | odd | 2 | |||
208.10.a.h.1.4 | 5 | 12.11 | even | 2 | |||
325.10.a.b.1.3 | 5 | 15.14 | odd | 2 |