Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(54.9918\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 51.9918 | 1.14887 | 0.574433 | − | 0.818552i | \(-0.305223\pi\) | ||||
0.574433 | + | 0.818552i | \(0.305223\pi\) | |||||||
\(3\) | 135.432 | 0.321776 | 0.160888 | − | 0.986973i | \(-0.448564\pi\) | ||||
0.160888 | + | 0.986973i | \(0.448564\pi\) | |||||||
\(4\) | 655.142 | 0.319894 | ||||||||
\(5\) | 3682.79 | 0.527037 | 0.263519 | − | 0.964654i | \(-0.415117\pi\) | ||||
0.263519 | + | 0.964654i | \(0.415117\pi\) | |||||||
\(6\) | 7041.33 | 0.369677 | ||||||||
\(7\) | −83752.5 | −1.88347 | −0.941735 | − | 0.336355i | \(-0.890806\pi\) | ||||
−0.941735 | + | 0.336355i | \(0.890806\pi\) | |||||||
\(8\) | −72417.1 | −0.781351 | ||||||||
\(9\) | −158805. | −0.896460 | ||||||||
\(10\) | 191474. | 0.605495 | ||||||||
\(11\) | 132980. | 0.248959 | 0.124479 | − | 0.992222i | \(-0.460274\pi\) | ||||
0.124479 | + | 0.992222i | \(0.460274\pi\) | |||||||
\(12\) | 88727.0 | 0.102934 | ||||||||
\(13\) | 193527. | 0.144561 | 0.0722807 | − | 0.997384i | \(-0.476972\pi\) | ||||
0.0722807 | + | 0.997384i | \(0.476972\pi\) | |||||||
\(14\) | −4.35444e6 | −2.16386 | ||||||||
\(15\) | 498766. | 0.169588 | ||||||||
\(16\) | −5.10682e6 | −1.21756 | ||||||||
\(17\) | 2.59769e6 | 0.443729 | 0.221865 | − | 0.975077i | \(-0.428786\pi\) | ||||
0.221865 | + | 0.975077i | \(0.428786\pi\) | |||||||
\(18\) | −8.25656e6 | −1.02991 | ||||||||
\(19\) | −4.52077e6 | −0.418859 | −0.209430 | − | 0.977824i | \(-0.567161\pi\) | ||||
−0.209430 | + | 0.977824i | \(0.567161\pi\) | |||||||
\(20\) | 2.41275e6 | 0.168596 | ||||||||
\(21\) | −1.13427e7 | −0.606055 | ||||||||
\(22\) | 6.91387e6 | 0.286020 | ||||||||
\(23\) | 7.42631e6 | 0.240586 | 0.120293 | − | 0.992738i | \(-0.461617\pi\) | ||||
0.120293 | + | 0.992738i | \(0.461617\pi\) | |||||||
\(24\) | −9.80757e6 | −0.251420 | ||||||||
\(25\) | −3.52652e7 | −0.722232 | ||||||||
\(26\) | 1.00618e7 | 0.166082 | ||||||||
\(27\) | −4.54986e7 | −0.610235 | ||||||||
\(28\) | −5.48698e7 | −0.602510 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | 2.59317e7 | 0.194834 | ||||||||
\(31\) | 4.28934e7 | 0.269092 | 0.134546 | − | 0.990907i | \(-0.457042\pi\) | ||||
0.134546 | + | 0.990907i | \(0.457042\pi\) | |||||||
\(32\) | −1.17202e8 | −0.617464 | ||||||||
\(33\) | 1.80097e7 | 0.0801088 | ||||||||
\(34\) | 1.35058e8 | 0.509786 | ||||||||
\(35\) | −3.08443e8 | −0.992659 | ||||||||
\(36\) | −1.04040e8 | −0.286772 | ||||||||
\(37\) | −8.25971e7 | −0.195819 | −0.0979096 | − | 0.995195i | \(-0.531216\pi\) | ||||
−0.0979096 | + | 0.995195i | \(0.531216\pi\) | |||||||
\(38\) | −2.35043e8 | −0.481213 | ||||||||
\(39\) | 2.62096e7 | 0.0465164 | ||||||||
\(40\) | −2.66697e8 | −0.411801 | ||||||||
\(41\) | −7.25750e8 | −0.978309 | −0.489154 | − | 0.872197i | \(-0.662695\pi\) | ||||
−0.489154 | + | 0.872197i | \(0.662695\pi\) | |||||||
\(42\) | −5.89729e8 | −0.696276 | ||||||||
\(43\) | −1.14606e8 | −0.118887 | −0.0594433 | − | 0.998232i | \(-0.518933\pi\) | ||||
−0.0594433 | + | 0.998232i | \(0.518933\pi\) | |||||||
\(44\) | 8.71209e7 | 0.0796403 | ||||||||
\(45\) | −5.84846e8 | −0.472468 | ||||||||
\(46\) | 3.86107e8 | 0.276401 | ||||||||
\(47\) | −3.13358e8 | −0.199298 | −0.0996490 | − | 0.995023i | \(-0.531772\pi\) | ||||
−0.0996490 | + | 0.995023i | \(0.531772\pi\) | |||||||
\(48\) | −6.91625e8 | −0.391782 | ||||||||
\(49\) | 5.03716e9 | 2.54746 | ||||||||
\(50\) | −1.83350e9 | −0.829748 | ||||||||
\(51\) | 3.51809e8 | 0.142781 | ||||||||
\(52\) | 1.26788e8 | 0.0462443 | ||||||||
\(53\) | −5.04903e8 | −0.165840 | −0.0829202 | − | 0.996556i | \(-0.526425\pi\) | ||||
−0.0829202 | + | 0.996556i | \(0.526425\pi\) | |||||||
\(54\) | −2.36555e9 | −0.701078 | ||||||||
\(55\) | 4.89737e8 | 0.131210 | ||||||||
\(56\) | 6.06512e9 | 1.47165 | ||||||||
\(57\) | −6.12256e8 | −0.134779 | ||||||||
\(58\) | 1.06641e9 | 0.213339 | ||||||||
\(59\) | 8.68166e9 | 1.58095 | 0.790473 | − | 0.612497i | \(-0.209835\pi\) | ||||
0.790473 | + | 0.612497i | \(0.209835\pi\) | |||||||
\(60\) | 3.26762e8 | 0.0542501 | ||||||||
\(61\) | 4.85120e9 | 0.735420 | 0.367710 | − | 0.929941i | \(-0.380142\pi\) | ||||
0.367710 | + | 0.929941i | \(0.380142\pi\) | |||||||
\(62\) | 2.23010e9 | 0.309151 | ||||||||
\(63\) | 1.33003e10 | 1.68846 | ||||||||
\(64\) | 4.36521e9 | 0.508178 | ||||||||
\(65\) | 7.12717e8 | 0.0761893 | ||||||||
\(66\) | 9.36357e8 | 0.0920343 | ||||||||
\(67\) | −1.44650e10 | −1.30890 | −0.654452 | − | 0.756104i | \(-0.727101\pi\) | ||||
−0.654452 | + | 0.756104i | \(0.727101\pi\) | |||||||
\(68\) | 1.70186e9 | 0.141946 | ||||||||
\(69\) | 1.00576e9 | 0.0774147 | ||||||||
\(70\) | −1.60365e10 | −1.14043 | ||||||||
\(71\) | −2.67681e10 | −1.76075 | −0.880374 | − | 0.474280i | \(-0.842708\pi\) | ||||
−0.880374 | + | 0.474280i | \(0.842708\pi\) | |||||||
\(72\) | 1.15002e10 | 0.700450 | ||||||||
\(73\) | 2.46174e10 | 1.38985 | 0.694924 | − | 0.719084i | \(-0.255438\pi\) | ||||
0.694924 | + | 0.719084i | \(0.255438\pi\) | |||||||
\(74\) | −4.29437e9 | −0.224970 | ||||||||
\(75\) | −4.77603e9 | −0.232397 | ||||||||
\(76\) | −2.96175e9 | −0.133990 | ||||||||
\(77\) | −1.11374e10 | −0.468906 | ||||||||
\(78\) | 1.36269e9 | 0.0534411 | ||||||||
\(79\) | −3.86002e10 | −1.41137 | −0.705685 | − | 0.708526i | \(-0.749360\pi\) | ||||
−0.705685 | + | 0.708526i | \(0.749360\pi\) | |||||||
\(80\) | −1.88073e10 | −0.641700 | ||||||||
\(81\) | 2.19699e10 | 0.700102 | ||||||||
\(82\) | −3.77330e10 | −1.12395 | ||||||||
\(83\) | 1.74415e9 | 0.0486020 | 0.0243010 | − | 0.999705i | \(-0.492264\pi\) | ||||
0.0243010 | + | 0.999705i | \(0.492264\pi\) | |||||||
\(84\) | −7.43111e9 | −0.193873 | ||||||||
\(85\) | 9.56673e9 | 0.233862 | ||||||||
\(86\) | −5.95859e9 | −0.136585 | ||||||||
\(87\) | 2.77786e9 | 0.0597522 | ||||||||
\(88\) | −9.63004e9 | −0.194524 | ||||||||
\(89\) | −2.10441e10 | −0.399471 | −0.199735 | − | 0.979850i | \(-0.564008\pi\) | ||||
−0.199735 | + | 0.979850i | \(0.564008\pi\) | |||||||
\(90\) | −3.04072e10 | −0.542803 | ||||||||
\(91\) | −1.62084e10 | −0.272277 | ||||||||
\(92\) | 4.86529e9 | 0.0769619 | ||||||||
\(93\) | 5.80912e9 | 0.0865873 | ||||||||
\(94\) | −1.62920e10 | −0.228967 | ||||||||
\(95\) | −1.66490e10 | −0.220754 | ||||||||
\(96\) | −1.58729e10 | −0.198685 | ||||||||
\(97\) | 1.02295e11 | 1.20951 | 0.604757 | − | 0.796410i | \(-0.293270\pi\) | ||||
0.604757 | + | 0.796410i | \(0.293270\pi\) | |||||||
\(98\) | 2.61891e11 | 2.92669 | ||||||||
\(99\) | −2.11180e10 | −0.223182 | ||||||||
\(100\) | −2.31037e10 | −0.231037 | ||||||||
\(101\) | 2.22830e10 | 0.210963 | 0.105481 | − | 0.994421i | \(-0.466362\pi\) | ||||
0.105481 | + | 0.994421i | \(0.466362\pi\) | |||||||
\(102\) | 1.82912e10 | 0.164037 | ||||||||
\(103\) | −1.18118e10 | −0.100395 | −0.0501976 | − | 0.998739i | \(-0.515985\pi\) | ||||
−0.0501976 | + | 0.998739i | \(0.515985\pi\) | |||||||
\(104\) | −1.40146e10 | −0.112953 | ||||||||
\(105\) | −4.17729e10 | −0.319414 | ||||||||
\(106\) | −2.62508e10 | −0.190528 | ||||||||
\(107\) | −2.30403e11 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(108\) | −2.98080e10 | −0.195210 | ||||||||
\(109\) | −7.31425e10 | −0.455328 | −0.227664 | − | 0.973740i | \(-0.573109\pi\) | ||||
−0.227664 | + | 0.973740i | \(0.573109\pi\) | |||||||
\(110\) | 2.54623e10 | 0.150743 | ||||||||
\(111\) | −1.11863e10 | −0.0630098 | ||||||||
\(112\) | 4.27710e11 | 2.29324 | ||||||||
\(113\) | −2.78421e11 | −1.42158 | −0.710788 | − | 0.703407i | \(-0.751661\pi\) | ||||
−0.710788 | + | 0.703407i | \(0.751661\pi\) | |||||||
\(114\) | −3.18322e10 | −0.154843 | ||||||||
\(115\) | 2.73495e10 | 0.126798 | ||||||||
\(116\) | 1.34377e10 | 0.0594028 | ||||||||
\(117\) | −3.07331e10 | −0.129594 | ||||||||
\(118\) | 4.51375e11 | 1.81629 | ||||||||
\(119\) | −2.17563e11 | −0.835751 | ||||||||
\(120\) | −3.61192e10 | −0.132508 | ||||||||
\(121\) | −2.67628e11 | −0.938020 | ||||||||
\(122\) | 2.52223e11 | 0.844899 | ||||||||
\(123\) | −9.82895e10 | −0.314796 | ||||||||
\(124\) | 2.81013e10 | 0.0860808 | ||||||||
\(125\) | −3.09698e11 | −0.907680 | ||||||||
\(126\) | 6.91508e11 | 1.93981 | ||||||||
\(127\) | 6.84159e11 | 1.83754 | 0.918769 | − | 0.394795i | \(-0.129184\pi\) | ||||
0.918769 | + | 0.394795i | \(0.129184\pi\) | |||||||
\(128\) | 4.66986e11 | 1.20129 | ||||||||
\(129\) | −1.55213e10 | −0.0382548 | ||||||||
\(130\) | 3.70554e10 | 0.0875313 | ||||||||
\(131\) | −3.46467e11 | −0.784638 | −0.392319 | − | 0.919829i | \(-0.628327\pi\) | ||||
−0.392319 | + | 0.919829i | \(0.628327\pi\) | |||||||
\(132\) | 1.17989e10 | 0.0256263 | ||||||||
\(133\) | 3.78626e11 | 0.788909 | ||||||||
\(134\) | −7.52062e11 | −1.50376 | ||||||||
\(135\) | −1.67561e11 | −0.321617 | ||||||||
\(136\) | −1.88117e11 | −0.346708 | ||||||||
\(137\) | −2.96772e11 | −0.525364 | −0.262682 | − | 0.964883i | \(-0.584607\pi\) | ||||
−0.262682 | + | 0.964883i | \(0.584607\pi\) | |||||||
\(138\) | 5.22911e10 | 0.0889391 | ||||||||
\(139\) | 3.77869e11 | 0.617674 | 0.308837 | − | 0.951115i | \(-0.400060\pi\) | ||||
0.308837 | + | 0.951115i | \(0.400060\pi\) | |||||||
\(140\) | −2.02074e11 | −0.317545 | ||||||||
\(141\) | −4.24386e10 | −0.0641292 | ||||||||
\(142\) | −1.39172e12 | −2.02286 | ||||||||
\(143\) | 2.57352e10 | 0.0359898 | ||||||||
\(144\) | 8.10991e11 | 1.09150 | ||||||||
\(145\) | 7.55382e10 | 0.0978684 | ||||||||
\(146\) | 1.27990e12 | 1.59675 | ||||||||
\(147\) | 6.82191e11 | 0.819711 | ||||||||
\(148\) | −5.41128e10 | −0.0626413 | ||||||||
\(149\) | −6.93233e11 | −0.773312 | −0.386656 | − | 0.922224i | \(-0.626370\pi\) | ||||
−0.386656 | + | 0.922224i | \(0.626370\pi\) | |||||||
\(150\) | −2.48314e11 | −0.266993 | ||||||||
\(151\) | −7.27671e11 | −0.754331 | −0.377165 | − | 0.926146i | \(-0.623101\pi\) | ||||
−0.377165 | + | 0.926146i | \(0.623101\pi\) | |||||||
\(152\) | 3.27381e11 | 0.327276 | ||||||||
\(153\) | −4.12527e11 | −0.397786 | ||||||||
\(154\) | −5.79054e11 | −0.538710 | ||||||||
\(155\) | 1.57967e11 | 0.141822 | ||||||||
\(156\) | 1.71710e10 | 0.0148803 | ||||||||
\(157\) | −1.94371e12 | −1.62623 | −0.813117 | − | 0.582101i | \(-0.802231\pi\) | ||||
−0.813117 | + | 0.582101i | \(0.802231\pi\) | |||||||
\(158\) | −2.00689e12 | −1.62147 | ||||||||
\(159\) | −6.83798e10 | −0.0533634 | ||||||||
\(160\) | −4.31631e11 | −0.325427 | ||||||||
\(161\) | −6.21972e11 | −0.453136 | ||||||||
\(162\) | 1.14226e12 | 0.804323 | ||||||||
\(163\) | 1.07427e12 | 0.731277 | 0.365638 | − | 0.930757i | \(-0.380851\pi\) | ||||
0.365638 | + | 0.930757i | \(0.380851\pi\) | |||||||
\(164\) | −4.75469e11 | −0.312955 | ||||||||
\(165\) | 6.63259e10 | 0.0422203 | ||||||||
\(166\) | 9.06813e10 | 0.0558371 | ||||||||
\(167\) | −2.05398e12 | −1.22365 | −0.611824 | − | 0.790994i | \(-0.709564\pi\) | ||||
−0.611824 | + | 0.790994i | \(0.709564\pi\) | |||||||
\(168\) | 8.21409e11 | 0.473542 | ||||||||
\(169\) | −1.75471e12 | −0.979102 | ||||||||
\(170\) | 4.97391e11 | 0.268676 | ||||||||
\(171\) | 7.17923e11 | 0.375491 | ||||||||
\(172\) | −7.50835e10 | −0.0380310 | ||||||||
\(173\) | 5.47972e10 | 0.0268847 | 0.0134423 | − | 0.999910i | \(-0.495721\pi\) | ||||
0.0134423 | + | 0.999910i | \(0.495721\pi\) | |||||||
\(174\) | 1.44426e11 | 0.0686473 | ||||||||
\(175\) | 2.95355e12 | 1.36030 | ||||||||
\(176\) | −6.79106e11 | −0.303122 | ||||||||
\(177\) | 1.17577e12 | 0.508710 | ||||||||
\(178\) | −1.09412e12 | −0.458938 | ||||||||
\(179\) | 1.01838e12 | 0.414209 | 0.207105 | − | 0.978319i | \(-0.433596\pi\) | ||||
0.207105 | + | 0.978319i | \(0.433596\pi\) | |||||||
\(180\) | −3.83157e11 | −0.151140 | ||||||||
\(181\) | 4.66142e12 | 1.78355 | 0.891777 | − | 0.452476i | \(-0.149459\pi\) | ||||
0.891777 | + | 0.452476i | \(0.149459\pi\) | |||||||
\(182\) | −8.42701e11 | −0.312810 | ||||||||
\(183\) | 6.57006e11 | 0.236640 | ||||||||
\(184\) | −5.37792e11 | −0.187982 | ||||||||
\(185\) | −3.04187e11 | −0.103204 | ||||||||
\(186\) | 3.02026e11 | 0.0994772 | ||||||||
\(187\) | 3.45441e11 | 0.110470 | ||||||||
\(188\) | −2.05294e11 | −0.0637541 | ||||||||
\(189\) | 3.81062e12 | 1.14936 | ||||||||
\(190\) | −8.65612e11 | −0.253617 | ||||||||
\(191\) | −3.44126e12 | −0.979567 | −0.489783 | − | 0.871844i | \(-0.662924\pi\) | ||||
−0.489783 | + | 0.871844i | \(0.662924\pi\) | |||||||
\(192\) | 5.91188e11 | 0.163519 | ||||||||
\(193\) | 1.88765e12 | 0.507408 | 0.253704 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253704 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(194\) | 5.31851e12 | 1.38957 | ||||||||
\(195\) | 9.65245e10 | 0.0245159 | ||||||||
\(196\) | 3.30006e12 | 0.814917 | ||||||||
\(197\) | 7.01609e12 | 1.68473 | 0.842366 | − | 0.538906i | \(-0.181162\pi\) | ||||
0.842366 | + | 0.538906i | \(0.181162\pi\) | |||||||
\(198\) | −1.09796e12 | −0.256406 | ||||||||
\(199\) | 1.98650e12 | 0.451228 | 0.225614 | − | 0.974217i | \(-0.427561\pi\) | ||||
0.225614 | + | 0.974217i | \(0.427561\pi\) | |||||||
\(200\) | 2.55381e12 | 0.564317 | ||||||||
\(201\) | −1.95902e12 | −0.421173 | ||||||||
\(202\) | 1.15853e12 | 0.242368 | ||||||||
\(203\) | −1.71786e12 | −0.349752 | ||||||||
\(204\) | 2.30485e11 | 0.0456748 | ||||||||
\(205\) | −2.67278e12 | −0.515605 | ||||||||
\(206\) | −6.14119e11 | −0.115341 | ||||||||
\(207\) | −1.17934e12 | −0.215676 | ||||||||
\(208\) | −9.88307e11 | −0.176012 | ||||||||
\(209\) | −6.01173e11 | −0.104279 | ||||||||
\(210\) | −2.17185e12 | −0.366963 | ||||||||
\(211\) | −6.11632e12 | −1.00678 | −0.503392 | − | 0.864058i | \(-0.667915\pi\) | ||||
−0.503392 | + | 0.864058i | \(0.667915\pi\) | |||||||
\(212\) | −3.30783e11 | −0.0530513 | ||||||||
\(213\) | −3.62525e12 | −0.566566 | ||||||||
\(214\) | −1.19790e13 | −1.82451 | ||||||||
\(215\) | −4.22071e11 | −0.0626576 | ||||||||
\(216\) | 3.29487e12 | 0.476808 | ||||||||
\(217\) | −3.59243e12 | −0.506827 | ||||||||
\(218\) | −3.80281e12 | −0.523111 | ||||||||
\(219\) | 3.33398e12 | 0.447219 | ||||||||
\(220\) | 3.20848e11 | 0.0419734 | ||||||||
\(221\) | 5.02722e11 | 0.0641462 | ||||||||
\(222\) | −5.81593e11 | −0.0723899 | ||||||||
\(223\) | −1.23957e13 | −1.50520 | −0.752600 | − | 0.658478i | \(-0.771201\pi\) | ||||
−0.752600 | + | 0.658478i | \(0.771201\pi\) | |||||||
\(224\) | 9.81600e12 | 1.16298 | ||||||||
\(225\) | 5.60030e12 | 0.647452 | ||||||||
\(226\) | −1.44756e13 | −1.63320 | ||||||||
\(227\) | 1.20542e13 | 1.32739 | 0.663694 | − | 0.748004i | \(-0.268988\pi\) | ||||
0.663694 | + | 0.748004i | \(0.268988\pi\) | |||||||
\(228\) | −4.01114e11 | −0.0431148 | ||||||||
\(229\) | 9.40324e12 | 0.986693 | 0.493347 | − | 0.869833i | \(-0.335773\pi\) | ||||
0.493347 | + | 0.869833i | \(0.335773\pi\) | |||||||
\(230\) | 1.42195e12 | 0.145674 | ||||||||
\(231\) | −1.50836e12 | −0.150883 | ||||||||
\(232\) | −1.48536e12 | −0.145093 | ||||||||
\(233\) | −1.26418e13 | −1.20601 | −0.603003 | − | 0.797739i | \(-0.706029\pi\) | ||||
−0.603003 | + | 0.797739i | \(0.706029\pi\) | |||||||
\(234\) | −1.59787e12 | −0.148886 | ||||||||
\(235\) | −1.15403e12 | −0.105037 | ||||||||
\(236\) | 5.68772e12 | 0.505734 | ||||||||
\(237\) | −5.22769e12 | −0.454144 | ||||||||
\(238\) | −1.13115e13 | −0.960166 | ||||||||
\(239\) | −1.22673e13 | −1.01756 | −0.508781 | − | 0.860896i | \(-0.669904\pi\) | ||||
−0.508781 | + | 0.860896i | \(0.669904\pi\) | |||||||
\(240\) | −2.54711e12 | −0.206484 | ||||||||
\(241\) | −2.89078e12 | −0.229046 | −0.114523 | − | 0.993421i | \(-0.536534\pi\) | ||||
−0.114523 | + | 0.993421i | \(0.536534\pi\) | |||||||
\(242\) | −1.39144e13 | −1.07766 | ||||||||
\(243\) | 1.10354e13 | 0.835511 | ||||||||
\(244\) | 3.17823e12 | 0.235256 | ||||||||
\(245\) | 1.85508e13 | 1.34261 | ||||||||
\(246\) | −5.11024e12 | −0.361658 | ||||||||
\(247\) | −8.74890e11 | −0.0605509 | ||||||||
\(248\) | −3.10621e12 | −0.210255 | ||||||||
\(249\) | 2.36213e11 | 0.0156389 | ||||||||
\(250\) | −1.61017e13 | −1.04280 | ||||||||
\(251\) | 2.68736e13 | 1.70263 | 0.851314 | − | 0.524657i | \(-0.175806\pi\) | ||||
0.851314 | + | 0.524657i | \(0.175806\pi\) | |||||||
\(252\) | 8.71362e12 | 0.540127 | ||||||||
\(253\) | 9.87552e11 | 0.0598959 | ||||||||
\(254\) | 3.55706e13 | 2.11109 | ||||||||
\(255\) | 1.29564e12 | 0.0752511 | ||||||||
\(256\) | 1.53394e13 | 0.871947 | ||||||||
\(257\) | −1.28426e13 | −0.714533 | −0.357266 | − | 0.934003i | \(-0.616291\pi\) | ||||
−0.357266 | + | 0.934003i | \(0.616291\pi\) | |||||||
\(258\) | −8.06982e11 | −0.0439496 | ||||||||
\(259\) | 6.91771e12 | 0.368820 | ||||||||
\(260\) | 4.66931e11 | 0.0243725 | ||||||||
\(261\) | −3.25728e12 | −0.166469 | ||||||||
\(262\) | −1.80134e13 | −0.901444 | ||||||||
\(263\) | 1.60237e13 | 0.785248 | 0.392624 | − | 0.919699i | \(-0.371567\pi\) | ||||
0.392624 | + | 0.919699i | \(0.371567\pi\) | |||||||
\(264\) | −1.30421e12 | −0.0625931 | ||||||||
\(265\) | −1.85945e12 | −0.0874041 | ||||||||
\(266\) | 1.96854e13 | 0.906350 | ||||||||
\(267\) | −2.85003e12 | −0.128540 | ||||||||
\(268\) | −9.47665e12 | −0.418710 | ||||||||
\(269\) | 3.10713e13 | 1.34500 | 0.672500 | − | 0.740097i | \(-0.265220\pi\) | ||||
0.672500 | + | 0.740097i | \(0.265220\pi\) | |||||||
\(270\) | −8.71181e12 | −0.369494 | ||||||||
\(271\) | −1.82362e13 | −0.757885 | −0.378943 | − | 0.925420i | \(-0.623712\pi\) | ||||
−0.378943 | + | 0.925420i | \(0.623712\pi\) | |||||||
\(272\) | −1.32659e13 | −0.540268 | ||||||||
\(273\) | −2.19512e12 | −0.0876122 | ||||||||
\(274\) | −1.54297e13 | −0.603573 | ||||||||
\(275\) | −4.68957e12 | −0.179806 | ||||||||
\(276\) | 6.58914e11 | 0.0247645 | ||||||||
\(277\) | −5.73318e12 | −0.211230 | −0.105615 | − | 0.994407i | \(-0.533681\pi\) | ||||
−0.105615 | + | 0.994407i | \(0.533681\pi\) | |||||||
\(278\) | 1.96461e13 | 0.709625 | ||||||||
\(279\) | −6.81169e12 | −0.241230 | ||||||||
\(280\) | 2.23365e13 | 0.775616 | ||||||||
\(281\) | −2.17147e13 | −0.739383 | −0.369692 | − | 0.929155i | \(-0.620537\pi\) | ||||
−0.369692 | + | 0.929155i | \(0.620537\pi\) | |||||||
\(282\) | −2.20646e12 | −0.0736759 | ||||||||
\(283\) | −5.22739e13 | −1.71182 | −0.855912 | − | 0.517121i | \(-0.827004\pi\) | ||||
−0.855912 | + | 0.517121i | \(0.827004\pi\) | |||||||
\(284\) | −1.75369e13 | −0.563252 | ||||||||
\(285\) | −2.25481e12 | −0.0710334 | ||||||||
\(286\) | 1.33802e12 | 0.0413475 | ||||||||
\(287\) | 6.07834e13 | 1.84262 | ||||||||
\(288\) | 1.86124e13 | 0.553532 | ||||||||
\(289\) | −2.75239e13 | −0.803104 | ||||||||
\(290\) | 3.92736e12 | 0.112438 | ||||||||
\(291\) | 1.38540e13 | 0.389192 | ||||||||
\(292\) | 1.61279e13 | 0.444603 | ||||||||
\(293\) | 4.99463e13 | 1.35124 | 0.675619 | − | 0.737251i | \(-0.263877\pi\) | ||||
0.675619 | + | 0.737251i | \(0.263877\pi\) | |||||||
\(294\) | 3.54683e13 | 0.941738 | ||||||||
\(295\) | 3.19727e13 | 0.833217 | ||||||||
\(296\) | 5.98144e12 | 0.153004 | ||||||||
\(297\) | −6.05041e12 | −0.151923 | ||||||||
\(298\) | −3.60424e13 | −0.888432 | ||||||||
\(299\) | 1.43719e12 | 0.0347794 | ||||||||
\(300\) | −3.12898e12 | −0.0743422 | ||||||||
\(301\) | 9.59859e12 | 0.223919 | ||||||||
\(302\) | −3.78329e13 | −0.866625 | ||||||||
\(303\) | 3.01782e12 | 0.0678827 | ||||||||
\(304\) | 2.30868e13 | 0.509987 | ||||||||
\(305\) | 1.78659e13 | 0.387594 | ||||||||
\(306\) | −2.14480e13 | −0.457003 | ||||||||
\(307\) | −5.28549e13 | −1.10618 | −0.553088 | − | 0.833123i | \(-0.686551\pi\) | ||||
−0.553088 | + | 0.833123i | \(0.686551\pi\) | |||||||
\(308\) | −7.29660e12 | −0.150000 | ||||||||
\(309\) | −1.59970e12 | −0.0323047 | ||||||||
\(310\) | 8.21298e12 | 0.162934 | ||||||||
\(311\) | −7.83474e13 | −1.52701 | −0.763506 | − | 0.645800i | \(-0.776524\pi\) | ||||
−0.763506 | + | 0.645800i | \(0.776524\pi\) | |||||||
\(312\) | −1.89803e12 | −0.0363456 | ||||||||
\(313\) | 8.71210e13 | 1.63919 | 0.819594 | − | 0.572944i | \(-0.194199\pi\) | ||||
0.819594 | + | 0.572944i | \(0.194199\pi\) | |||||||
\(314\) | −1.01057e14 | −1.86832 | ||||||||
\(315\) | 4.89823e13 | 0.889880 | ||||||||
\(316\) | −2.52886e13 | −0.451488 | ||||||||
\(317\) | 7.95836e13 | 1.39636 | 0.698180 | − | 0.715922i | \(-0.253993\pi\) | ||||
0.698180 | + | 0.715922i | \(0.253993\pi\) | |||||||
\(318\) | −3.55519e12 | −0.0613074 | ||||||||
\(319\) | 2.72758e12 | 0.0462304 | ||||||||
\(320\) | 1.60761e13 | 0.267829 | ||||||||
\(321\) | −3.12038e13 | −0.511011 | ||||||||
\(322\) | −3.23374e13 | −0.520593 | ||||||||
\(323\) | −1.17436e13 | −0.185860 | ||||||||
\(324\) | 1.43934e13 | 0.223958 | ||||||||
\(325\) | −6.82476e12 | −0.104407 | ||||||||
\(326\) | 5.58532e13 | 0.840139 | ||||||||
\(327\) | −9.90581e12 | −0.146513 | ||||||||
\(328\) | 5.25567e13 | 0.764403 | ||||||||
\(329\) | 2.62445e13 | 0.375372 | ||||||||
\(330\) | 3.44840e12 | 0.0485055 | ||||||||
\(331\) | −5.59223e13 | −0.773626 | −0.386813 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386813 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(332\) | 1.14266e12 | 0.0155475 | ||||||||
\(333\) | 1.31168e13 | 0.175544 | ||||||||
\(334\) | −1.06790e14 | −1.40581 | ||||||||
\(335\) | −5.32716e13 | −0.689841 | ||||||||
\(336\) | 5.79254e13 | 0.737909 | ||||||||
\(337\) | −8.02614e13 | −1.00587 | −0.502935 | − | 0.864324i | \(-0.667747\pi\) | ||||
−0.502935 | + | 0.864324i | \(0.667747\pi\) | |||||||
\(338\) | −9.12303e13 | −1.12486 | ||||||||
\(339\) | −3.77069e13 | −0.457428 | ||||||||
\(340\) | 6.26757e12 | 0.0748109 | ||||||||
\(341\) | 5.70397e12 | 0.0669928 | ||||||||
\(342\) | 3.73260e13 | 0.431388 | ||||||||
\(343\) | −2.56269e14 | −2.91460 | ||||||||
\(344\) | 8.29947e12 | 0.0928922 | ||||||||
\(345\) | 3.70399e12 | 0.0408004 | ||||||||
\(346\) | 2.84900e12 | 0.0308869 | ||||||||
\(347\) | 1.59883e13 | 0.170605 | 0.0853023 | − | 0.996355i | \(-0.472814\pi\) | ||||
0.0853023 | + | 0.996355i | \(0.472814\pi\) | |||||||
\(348\) | 1.81989e12 | 0.0191144 | ||||||||
\(349\) | −2.67236e13 | −0.276284 | −0.138142 | − | 0.990412i | \(-0.544113\pi\) | ||||
−0.138142 | + | 0.990412i | \(0.544113\pi\) | |||||||
\(350\) | 1.53560e14 | 1.56281 | ||||||||
\(351\) | −8.80519e12 | −0.0882164 | ||||||||
\(352\) | −1.55856e13 | −0.153723 | ||||||||
\(353\) | −9.23737e13 | −0.896989 | −0.448495 | − | 0.893786i | \(-0.648040\pi\) | ||||
−0.448495 | + | 0.893786i | \(0.648040\pi\) | |||||||
\(354\) | 6.11304e13 | 0.584439 | ||||||||
\(355\) | −9.85813e13 | −0.927980 | ||||||||
\(356\) | −1.37869e13 | −0.127788 | ||||||||
\(357\) | −2.94649e13 | −0.268924 | ||||||||
\(358\) | 5.29475e13 | 0.475871 | ||||||||
\(359\) | 5.10662e13 | 0.451975 | 0.225987 | − | 0.974130i | \(-0.427439\pi\) | ||||
0.225987 | + | 0.974130i | \(0.427439\pi\) | |||||||
\(360\) | 4.23528e13 | 0.369164 | ||||||||
\(361\) | −9.60529e13 | −0.824557 | ||||||||
\(362\) | 2.42355e14 | 2.04906 | ||||||||
\(363\) | −3.62453e13 | −0.301832 | ||||||||
\(364\) | −1.06188e13 | −0.0870997 | ||||||||
\(365\) | 9.06607e13 | 0.732501 | ||||||||
\(366\) | 3.41589e13 | 0.271868 | ||||||||
\(367\) | 5.30370e13 | 0.415830 | 0.207915 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207915 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(368\) | −3.79249e13 | −0.292928 | ||||||||
\(369\) | 1.15253e14 | 0.877015 | ||||||||
\(370\) | −1.58152e13 | −0.118568 | ||||||||
\(371\) | 4.22869e13 | 0.312356 | ||||||||
\(372\) | 3.80580e12 | 0.0276987 | ||||||||
\(373\) | 2.07858e14 | 1.49062 | 0.745312 | − | 0.666716i | \(-0.232301\pi\) | ||||
0.745312 | + | 0.666716i | \(0.232301\pi\) | |||||||
\(374\) | 1.79601e13 | 0.126916 | ||||||||
\(375\) | −4.19429e13 | −0.292069 | ||||||||
\(376\) | 2.26925e13 | 0.155722 | ||||||||
\(377\) | 3.96946e12 | 0.0268444 | ||||||||
\(378\) | 1.98121e14 | 1.32046 | ||||||||
\(379\) | 1.89936e14 | 1.24765 | 0.623823 | − | 0.781566i | \(-0.285579\pi\) | ||||
0.623823 | + | 0.781566i | \(0.285579\pi\) | |||||||
\(380\) | −1.09075e13 | −0.0706179 | ||||||||
\(381\) | 9.26567e13 | 0.591275 | ||||||||
\(382\) | −1.78917e14 | −1.12539 | ||||||||
\(383\) | −2.53366e14 | −1.57092 | −0.785462 | − | 0.618910i | \(-0.787574\pi\) | ||||
−0.785462 | + | 0.618910i | \(0.787574\pi\) | |||||||
\(384\) | 6.32446e13 | 0.386547 | ||||||||
\(385\) | −4.10168e13 | −0.247131 | ||||||||
\(386\) | 9.81425e13 | 0.582944 | ||||||||
\(387\) | 1.82001e13 | 0.106577 | ||||||||
\(388\) | 6.70179e13 | 0.386916 | ||||||||
\(389\) | 2.50859e14 | 1.42793 | 0.713964 | − | 0.700182i | \(-0.246898\pi\) | ||||
0.713964 | + | 0.700182i | \(0.246898\pi\) | |||||||
\(390\) | 5.01848e12 | 0.0281654 | ||||||||
\(391\) | 1.92912e13 | 0.106755 | ||||||||
\(392\) | −3.64777e14 | −1.99046 | ||||||||
\(393\) | −4.69225e13 | −0.252477 | ||||||||
\(394\) | 3.64779e14 | 1.93553 | ||||||||
\(395\) | −1.42156e14 | −0.743844 | ||||||||
\(396\) | −1.38353e13 | −0.0713943 | ||||||||
\(397\) | −8.33694e13 | −0.424286 | −0.212143 | − | 0.977239i | \(-0.568044\pi\) | ||||
−0.212143 | + | 0.977239i | \(0.568044\pi\) | |||||||
\(398\) | 1.03281e14 | 0.518401 | ||||||||
\(399\) | 5.12780e13 | 0.253852 | ||||||||
\(400\) | 1.80093e14 | 0.879362 | ||||||||
\(401\) | −8.55764e13 | −0.412154 | −0.206077 | − | 0.978536i | \(-0.566070\pi\) | ||||
−0.206077 | + | 0.978536i | \(0.566070\pi\) | |||||||
\(402\) | −1.01853e14 | −0.483872 | ||||||||
\(403\) | 8.30101e12 | 0.0389003 | ||||||||
\(404\) | 1.45985e13 | 0.0674857 | ||||||||
\(405\) | 8.09105e13 | 0.368980 | ||||||||
\(406\) | −8.93146e13 | −0.401818 | ||||||||
\(407\) | −1.09838e13 | −0.0487508 | ||||||||
\(408\) | −2.54770e13 | −0.111562 | ||||||||
\(409\) | 2.89966e14 | 1.25276 | 0.626382 | − | 0.779516i | \(-0.284535\pi\) | ||||
0.626382 | + | 0.779516i | \(0.284535\pi\) | |||||||
\(410\) | −1.38963e14 | −0.592361 | ||||||||
\(411\) | −4.01923e13 | −0.169049 | ||||||||
\(412\) | −7.73844e12 | −0.0321158 | ||||||||
\(413\) | −7.27111e14 | −2.97766 | ||||||||
\(414\) | −6.13158e13 | −0.247782 | ||||||||
\(415\) | 6.42332e12 | 0.0256150 | ||||||||
\(416\) | −2.26818e13 | −0.0892615 | ||||||||
\(417\) | 5.11754e13 | 0.198753 | ||||||||
\(418\) | −3.12560e13 | −0.119802 | ||||||||
\(419\) | 1.15977e14 | 0.438727 | 0.219364 | − | 0.975643i | \(-0.429602\pi\) | ||||
0.219364 | + | 0.975643i | \(0.429602\pi\) | |||||||
\(420\) | −2.73672e13 | −0.102178 | ||||||||
\(421\) | −1.29586e14 | −0.477535 | −0.238767 | − | 0.971077i | \(-0.576743\pi\) | ||||
−0.238767 | + | 0.971077i | \(0.576743\pi\) | |||||||
\(422\) | −3.17998e14 | −1.15666 | ||||||||
\(423\) | 4.97629e13 | 0.178663 | ||||||||
\(424\) | 3.65636e13 | 0.129580 | ||||||||
\(425\) | −9.16081e13 | −0.320475 | ||||||||
\(426\) | −1.88483e14 | −0.650908 | ||||||||
\(427\) | −4.06301e14 | −1.38514 | ||||||||
\(428\) | −1.50947e14 | −0.508022 | ||||||||
\(429\) | 3.48536e12 | 0.0115806 | ||||||||
\(430\) | −2.19442e13 | −0.0719853 | ||||||||
\(431\) | 8.77012e13 | 0.284041 | 0.142020 | − | 0.989864i | \(-0.454640\pi\) | ||||
0.142020 | + | 0.989864i | \(0.454640\pi\) | |||||||
\(432\) | 2.32353e14 | 0.742999 | ||||||||
\(433\) | 3.21721e14 | 1.01577 | 0.507886 | − | 0.861424i | \(-0.330427\pi\) | ||||
0.507886 | + | 0.861424i | \(0.330427\pi\) | |||||||
\(434\) | −1.86777e14 | −0.582276 | ||||||||
\(435\) | 1.02303e13 | 0.0314917 | ||||||||
\(436\) | −4.79188e13 | −0.145656 | ||||||||
\(437\) | −3.35727e13 | −0.100772 | ||||||||
\(438\) | 1.73339e14 | 0.513795 | ||||||||
\(439\) | 4.76314e14 | 1.39424 | 0.697121 | − | 0.716954i | \(-0.254464\pi\) | ||||
0.697121 | + | 0.716954i | \(0.254464\pi\) | |||||||
\(440\) | −3.54654e13 | −0.102521 | ||||||||
\(441\) | −7.99928e14 | −2.28370 | ||||||||
\(442\) | 2.61374e13 | 0.0736954 | ||||||||
\(443\) | 6.68817e13 | 0.186246 | 0.0931230 | − | 0.995655i | \(-0.470315\pi\) | ||||
0.0931230 | + | 0.995655i | \(0.470315\pi\) | |||||||
\(444\) | −7.32859e12 | −0.0201564 | ||||||||
\(445\) | −7.75008e13 | −0.210536 | ||||||||
\(446\) | −6.44474e14 | −1.72927 | ||||||||
\(447\) | −9.38856e13 | −0.248833 | ||||||||
\(448\) | −3.65598e14 | −0.957138 | ||||||||
\(449\) | 3.99733e14 | 1.03375 | 0.516874 | − | 0.856062i | \(-0.327096\pi\) | ||||
0.516874 | + | 0.856062i | \(0.327096\pi\) | |||||||
\(450\) | 2.91170e14 | 0.743836 | ||||||||
\(451\) | −9.65104e13 | −0.243558 | ||||||||
\(452\) | −1.82405e14 | −0.454753 | ||||||||
\(453\) | −9.85497e13 | −0.242725 | ||||||||
\(454\) | 6.26721e14 | 1.52499 | ||||||||
\(455\) | −5.96919e13 | −0.143500 | ||||||||
\(456\) | 4.43378e13 | 0.105309 | ||||||||
\(457\) | 4.42060e14 | 1.03739 | 0.518695 | − | 0.854959i | \(-0.326418\pi\) | ||||
0.518695 | + | 0.854959i | \(0.326418\pi\) | |||||||
\(458\) | 4.88891e14 | 1.13358 | ||||||||
\(459\) | −1.18191e14 | −0.270779 | ||||||||
\(460\) | 1.79178e13 | 0.0405618 | ||||||||
\(461\) | 6.61295e14 | 1.47925 | 0.739623 | − | 0.673022i | \(-0.235004\pi\) | ||||
0.739623 | + | 0.673022i | \(0.235004\pi\) | |||||||
\(462\) | −7.84223e13 | −0.173344 | ||||||||
\(463\) | −1.41874e14 | −0.309890 | −0.154945 | − | 0.987923i | \(-0.549520\pi\) | ||||
−0.154945 | + | 0.987923i | \(0.549520\pi\) | |||||||
\(464\) | −1.04747e14 | −0.226096 | ||||||||
\(465\) | 2.13937e13 | 0.0456347 | ||||||||
\(466\) | −6.57267e14 | −1.38554 | ||||||||
\(467\) | 3.99126e14 | 0.831509 | 0.415755 | − | 0.909477i | \(-0.363518\pi\) | ||||
0.415755 | + | 0.909477i | \(0.363518\pi\) | |||||||
\(468\) | −2.01345e13 | −0.0414562 | ||||||||
\(469\) | 1.21148e15 | 2.46528 | ||||||||
\(470\) | −6.00001e13 | −0.120674 | ||||||||
\(471\) | −2.63240e14 | −0.523282 | ||||||||
\(472\) | −6.28701e14 | −1.23527 | ||||||||
\(473\) | −1.52404e13 | −0.0295978 | ||||||||
\(474\) | −2.71797e14 | −0.521751 | ||||||||
\(475\) | 1.59426e14 | 0.302513 | ||||||||
\(476\) | −1.42535e14 | −0.267351 | ||||||||
\(477\) | 8.01812e13 | 0.148669 | ||||||||
\(478\) | −6.37799e14 | −1.16904 | ||||||||
\(479\) | 3.65975e14 | 0.663141 | 0.331570 | − | 0.943431i | \(-0.392422\pi\) | ||||
0.331570 | + | 0.943431i | \(0.392422\pi\) | |||||||
\(480\) | −5.84566e13 | −0.104714 | ||||||||
\(481\) | −1.59847e13 | −0.0283079 | ||||||||
\(482\) | −1.50297e14 | −0.263143 | ||||||||
\(483\) | −8.42347e13 | −0.145808 | ||||||||
\(484\) | −1.75334e14 | −0.300066 | ||||||||
\(485\) | 3.76731e14 | 0.637459 | ||||||||
\(486\) | 5.73748e14 | 0.959890 | ||||||||
\(487\) | 5.80639e14 | 0.960499 | 0.480249 | − | 0.877132i | \(-0.340546\pi\) | ||||
0.480249 | + | 0.877132i | \(0.340546\pi\) | |||||||
\(488\) | −3.51310e14 | −0.574621 | ||||||||
\(489\) | 1.45490e14 | 0.235307 | ||||||||
\(490\) | 9.64488e14 | 1.54248 | ||||||||
\(491\) | 6.75492e14 | 1.06825 | 0.534124 | − | 0.845406i | \(-0.320642\pi\) | ||||
0.534124 | + | 0.845406i | \(0.320642\pi\) | |||||||
\(492\) | −6.43936e13 | −0.100701 | ||||||||
\(493\) | 5.32816e13 | 0.0823985 | ||||||||
\(494\) | −4.54871e13 | −0.0695648 | ||||||||
\(495\) | −7.77729e13 | −0.117625 | ||||||||
\(496\) | −2.19049e14 | −0.327636 | ||||||||
\(497\) | 2.24190e15 | 3.31632 | ||||||||
\(498\) | 1.22811e13 | 0.0179670 | ||||||||
\(499\) | −5.89501e14 | −0.852965 | −0.426483 | − | 0.904496i | \(-0.640247\pi\) | ||||
−0.426483 | + | 0.904496i | \(0.640247\pi\) | |||||||
\(500\) | −2.02896e14 | −0.290361 | ||||||||
\(501\) | −2.78174e14 | −0.393740 | ||||||||
\(502\) | 1.39720e15 | 1.95609 | ||||||||
\(503\) | −9.33902e14 | −1.29324 | −0.646618 | − | 0.762814i | \(-0.723817\pi\) | ||||
−0.646618 | + | 0.762814i | \(0.723817\pi\) | |||||||
\(504\) | −9.63173e14 | −1.31928 | ||||||||
\(505\) | 8.20635e13 | 0.111185 | ||||||||
\(506\) | 5.13446e13 | 0.0688124 | ||||||||
\(507\) | −2.37643e14 | −0.315051 | ||||||||
\(508\) | 4.48221e14 | 0.587817 | ||||||||
\(509\) | −5.80951e14 | −0.753688 | −0.376844 | − | 0.926277i | \(-0.622991\pi\) | ||||
−0.376844 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(510\) | 6.73625e13 | 0.0864534 | ||||||||
\(511\) | −2.06177e15 | −2.61774 | ||||||||
\(512\) | −1.58862e14 | −0.199543 | ||||||||
\(513\) | 2.05689e14 | 0.255602 | ||||||||
\(514\) | −6.67711e14 | −0.820902 | ||||||||
\(515\) | −4.35005e13 | −0.0529120 | ||||||||
\(516\) | −1.01687e13 | −0.0122375 | ||||||||
\(517\) | −4.16704e13 | −0.0496169 | ||||||||
\(518\) | 3.59664e14 | 0.423724 | ||||||||
\(519\) | 7.42128e12 | 0.00865084 | ||||||||
\(520\) | −5.16129e13 | −0.0595306 | ||||||||
\(521\) | 6.16566e14 | 0.703675 | 0.351837 | − | 0.936061i | \(-0.385557\pi\) | ||||
0.351837 | + | 0.936061i | \(0.385557\pi\) | |||||||
\(522\) | −1.69352e14 | −0.191250 | ||||||||
\(523\) | −9.25923e14 | −1.03470 | −0.517351 | − | 0.855773i | \(-0.673082\pi\) | ||||
−0.517351 | + | 0.855773i | \(0.673082\pi\) | |||||||
\(524\) | −2.26985e14 | −0.251001 | ||||||||
\(525\) | 4.00004e14 | 0.437712 | ||||||||
\(526\) | 8.33101e14 | 0.902145 | ||||||||
\(527\) | 1.11424e14 | 0.119404 | ||||||||
\(528\) | −9.19725e13 | −0.0975374 | ||||||||
\(529\) | −8.97660e14 | −0.942118 | ||||||||
\(530\) | −9.66760e13 | −0.100416 | ||||||||
\(531\) | −1.37869e15 | −1.41725 | ||||||||
\(532\) | 2.48054e14 | 0.252367 | ||||||||
\(533\) | −1.40452e14 | −0.141426 | ||||||||
\(534\) | −1.48178e14 | −0.147675 | ||||||||
\(535\) | −8.48524e14 | −0.836986 | ||||||||
\(536\) | 1.04752e15 | 1.02271 | ||||||||
\(537\) | 1.37921e14 | 0.133282 | ||||||||
\(538\) | 1.61545e15 | 1.54523 | ||||||||
\(539\) | 6.69843e14 | 0.634212 | ||||||||
\(540\) | −1.09777e14 | −0.102883 | ||||||||
\(541\) | 1.71163e15 | 1.58790 | 0.793952 | − | 0.607980i | \(-0.208020\pi\) | ||||
0.793952 | + | 0.607980i | \(0.208020\pi\) | |||||||
\(542\) | −9.48133e14 | −0.870709 | ||||||||
\(543\) | 6.31304e14 | 0.573904 | ||||||||
\(544\) | −3.04456e14 | −0.273987 | ||||||||
\(545\) | −2.69368e14 | −0.239975 | ||||||||
\(546\) | −1.14128e14 | −0.100655 | ||||||||
\(547\) | 3.09884e14 | 0.270563 | 0.135282 | − | 0.990807i | \(-0.456806\pi\) | ||||
0.135282 | + | 0.990807i | \(0.456806\pi\) | |||||||
\(548\) | −1.94428e14 | −0.168060 | ||||||||
\(549\) | −7.70397e14 | −0.659275 | ||||||||
\(550\) | −2.43819e14 | −0.206573 | ||||||||
\(551\) | −9.27262e13 | −0.0777802 | ||||||||
\(552\) | −7.28341e13 | −0.0604880 | ||||||||
\(553\) | 3.23287e15 | 2.65827 | ||||||||
\(554\) | −2.98078e14 | −0.242676 | ||||||||
\(555\) | −4.11966e13 | −0.0332085 | ||||||||
\(556\) | 2.47558e14 | 0.197590 | ||||||||
\(557\) | −1.41441e15 | −1.11782 | −0.558911 | − | 0.829227i | \(-0.688781\pi\) | ||||
−0.558911 | + | 0.829227i | \(0.688781\pi\) | |||||||
\(558\) | −3.54152e14 | −0.277141 | ||||||||
\(559\) | −2.21794e13 | −0.0171864 | ||||||||
\(560\) | 1.57516e15 | 1.20862 | ||||||||
\(561\) | 4.67837e13 | 0.0355466 | ||||||||
\(562\) | −1.12899e15 | −0.849452 | ||||||||
\(563\) | 1.58073e14 | 0.117778 | 0.0588888 | − | 0.998265i | \(-0.481244\pi\) | ||||
0.0588888 | + | 0.998265i | \(0.481244\pi\) | |||||||
\(564\) | −2.78033e13 | −0.0205145 | ||||||||
\(565\) | −1.02536e15 | −0.749223 | ||||||||
\(566\) | −2.71781e15 | −1.96666 | ||||||||
\(567\) | −1.84004e15 | −1.31862 | ||||||||
\(568\) | 1.93847e15 | 1.37576 | ||||||||
\(569\) | −7.94297e14 | −0.558297 | −0.279149 | − | 0.960248i | \(-0.590052\pi\) | ||||
−0.279149 | + | 0.960248i | \(0.590052\pi\) | |||||||
\(570\) | −1.17231e14 | −0.0816078 | ||||||||
\(571\) | −2.46506e15 | −1.69953 | −0.849764 | − | 0.527164i | \(-0.823255\pi\) | ||||
−0.849764 | + | 0.527164i | \(0.823255\pi\) | |||||||
\(572\) | 1.68602e13 | 0.0115129 | ||||||||
\(573\) | −4.66055e14 | −0.315201 | ||||||||
\(574\) | 3.16024e15 | 2.11692 | ||||||||
\(575\) | −2.61890e14 | −0.173759 | ||||||||
\(576\) | −6.93219e14 | −0.455561 | ||||||||
\(577\) | −7.32129e14 | −0.476563 | −0.238282 | − | 0.971196i | \(-0.576584\pi\) | ||||
−0.238282 | + | 0.971196i | \(0.576584\pi\) | |||||||
\(578\) | −1.43102e15 | −0.922659 | ||||||||
\(579\) | 2.55648e14 | 0.163272 | ||||||||
\(580\) | 4.94882e13 | 0.0313075 | ||||||||
\(581\) | −1.46077e14 | −0.0915403 | ||||||||
\(582\) | 7.20294e14 | 0.447130 | ||||||||
\(583\) | −6.71421e13 | −0.0412874 | ||||||||
\(584\) | −1.78272e15 | −1.08596 | ||||||||
\(585\) | −1.13183e14 | −0.0683007 | ||||||||
\(586\) | 2.59680e15 | 1.55239 | ||||||||
\(587\) | −1.85488e15 | −1.09851 | −0.549256 | − | 0.835654i | \(-0.685089\pi\) | ||||
−0.549256 | + | 0.835654i | \(0.685089\pi\) | |||||||
\(588\) | 4.46932e14 | 0.262220 | ||||||||
\(589\) | −1.93911e14 | −0.112712 | ||||||||
\(590\) | 1.66232e15 | 0.957255 | ||||||||
\(591\) | 9.50200e14 | 0.542106 | ||||||||
\(592\) | 4.21809e14 | 0.238422 | ||||||||
\(593\) | 2.47471e15 | 1.38587 | 0.692936 | − | 0.720999i | \(-0.256317\pi\) | ||||
0.692936 | + | 0.720999i | \(0.256317\pi\) | |||||||
\(594\) | −3.14571e14 | −0.174539 | ||||||||
\(595\) | −8.01238e14 | −0.440472 | ||||||||
\(596\) | −4.54166e14 | −0.247377 | ||||||||
\(597\) | 2.69035e14 | 0.145194 | ||||||||
\(598\) | 7.47220e13 | 0.0399569 | ||||||||
\(599\) | −1.41526e15 | −0.749877 | −0.374938 | − | 0.927050i | \(-0.622336\pi\) | ||||
−0.374938 | + | 0.927050i | \(0.622336\pi\) | |||||||
\(600\) | 3.45866e14 | 0.181583 | ||||||||
\(601\) | −3.03423e15 | −1.57848 | −0.789240 | − | 0.614084i | \(-0.789525\pi\) | ||||
−0.789240 | + | 0.614084i | \(0.789525\pi\) | |||||||
\(602\) | 4.99047e14 | 0.257253 | ||||||||
\(603\) | 2.29712e15 | 1.17338 | ||||||||
\(604\) | −4.76728e14 | −0.241306 | ||||||||
\(605\) | −9.85616e14 | −0.494371 | ||||||||
\(606\) | 1.56902e14 | 0.0779882 | ||||||||
\(607\) | 3.26634e14 | 0.160888 | 0.0804440 | − | 0.996759i | \(-0.474366\pi\) | ||||
0.0804440 | + | 0.996759i | \(0.474366\pi\) | |||||||
\(608\) | 5.29846e14 | 0.258630 | ||||||||
\(609\) | −2.32653e14 | −0.112542 | ||||||||
\(610\) | 9.28882e14 | 0.445293 | ||||||||
\(611\) | −6.06432e13 | −0.0288108 | ||||||||
\(612\) | −2.70264e14 | −0.127249 | ||||||||
\(613\) | 1.34079e15 | 0.625645 | 0.312822 | − | 0.949812i | \(-0.398726\pi\) | ||||
0.312822 | + | 0.949812i | \(0.398726\pi\) | |||||||
\(614\) | −2.74802e15 | −1.27085 | ||||||||
\(615\) | −3.61979e14 | −0.165909 | ||||||||
\(616\) | 8.06540e14 | 0.366380 | ||||||||
\(617\) | 1.57502e15 | 0.709117 | 0.354558 | − | 0.935034i | \(-0.384631\pi\) | ||||
0.354558 | + | 0.935034i | \(0.384631\pi\) | |||||||
\(618\) | −8.31711e13 | −0.0371138 | ||||||||
\(619\) | 1.74802e15 | 0.773121 | 0.386561 | − | 0.922264i | \(-0.373663\pi\) | ||||
0.386561 | + | 0.922264i | \(0.373663\pi\) | |||||||
\(620\) | 1.03491e14 | 0.0453678 | ||||||||
\(621\) | −3.37886e14 | −0.146814 | ||||||||
\(622\) | −4.07342e15 | −1.75433 | ||||||||
\(623\) | 1.76250e15 | 0.752391 | ||||||||
\(624\) | −1.33848e14 | −0.0566365 | ||||||||
\(625\) | 5.81384e14 | 0.243850 | ||||||||
\(626\) | 4.52957e15 | 1.88321 | ||||||||
\(627\) | −8.14179e13 | −0.0335543 | ||||||||
\(628\) | −1.27340e15 | −0.520222 | ||||||||
\(629\) | −2.14561e14 | −0.0868907 | ||||||||
\(630\) | 2.54668e15 | 1.02235 | ||||||||
\(631\) | −4.49331e15 | −1.78815 | −0.894077 | − | 0.447913i | \(-0.852167\pi\) | ||||
−0.894077 | + | 0.447913i | \(0.852167\pi\) | |||||||
\(632\) | 2.79532e15 | 1.10278 | ||||||||
\(633\) | −8.28343e14 | −0.323959 | ||||||||
\(634\) | 4.13769e15 | 1.60423 | ||||||||
\(635\) | 2.51961e15 | 0.968451 | ||||||||
\(636\) | −4.47985e13 | −0.0170706 | ||||||||
\(637\) | 9.74826e14 | 0.368265 | ||||||||
\(638\) | 1.41811e14 | 0.0531126 | ||||||||
\(639\) | 4.25092e15 | 1.57844 | ||||||||
\(640\) | 1.71981e15 | 0.633126 | ||||||||
\(641\) | −1.93652e15 | −0.706809 | −0.353405 | − | 0.935471i | \(-0.614976\pi\) | ||||
−0.353405 | + | 0.935471i | \(0.614976\pi\) | |||||||
\(642\) | −1.62234e15 | −0.587083 | ||||||||
\(643\) | 1.70043e15 | 0.610095 | 0.305048 | − | 0.952337i | \(-0.401328\pi\) | ||||
0.305048 | + | 0.952337i | \(0.401328\pi\) | |||||||
\(644\) | −4.07480e14 | −0.144955 | ||||||||
\(645\) | −5.71618e13 | −0.0201617 | ||||||||
\(646\) | −6.10568e14 | −0.213528 | ||||||||
\(647\) | 2.04196e14 | 0.0708068 | 0.0354034 | − | 0.999373i | \(-0.488728\pi\) | ||||
0.0354034 | + | 0.999373i | \(0.488728\pi\) | |||||||
\(648\) | −1.59100e15 | −0.547025 | ||||||||
\(649\) | 1.15449e15 | 0.393590 | ||||||||
\(650\) | −3.54831e14 | −0.119950 | ||||||||
\(651\) | −4.86529e14 | −0.163085 | ||||||||
\(652\) | 7.03800e14 | 0.233931 | ||||||||
\(653\) | 2.57221e15 | 0.847783 | 0.423891 | − | 0.905713i | \(-0.360664\pi\) | ||||
0.423891 | + | 0.905713i | \(0.360664\pi\) | |||||||
\(654\) | −5.15021e14 | −0.168324 | ||||||||
\(655\) | −1.27596e15 | −0.413533 | ||||||||
\(656\) | 3.70628e15 | 1.19115 | ||||||||
\(657\) | −3.90938e15 | −1.24594 | ||||||||
\(658\) | 1.36450e15 | 0.431252 | ||||||||
\(659\) | −1.82638e14 | −0.0572429 | −0.0286215 | − | 0.999590i | \(-0.509112\pi\) | ||||
−0.0286215 | + | 0.999590i | \(0.509112\pi\) | |||||||
\(660\) | 4.34529e13 | 0.0135060 | ||||||||
\(661\) | 1.53812e15 | 0.474114 | 0.237057 | − | 0.971496i | \(-0.423817\pi\) | ||||
0.237057 | + | 0.971496i | \(0.423817\pi\) | |||||||
\(662\) | −2.90750e15 | −0.888793 | ||||||||
\(663\) | 6.80845e13 | 0.0206407 | ||||||||
\(664\) | −1.26306e14 | −0.0379752 | ||||||||
\(665\) | 1.39440e15 | 0.415784 | ||||||||
\(666\) | 6.81968e14 | 0.201677 | ||||||||
\(667\) | 1.52322e14 | 0.0446757 | ||||||||
\(668\) | −1.34565e15 | −0.391437 | ||||||||
\(669\) | −1.67877e15 | −0.484337 | ||||||||
\(670\) | −2.76968e15 | −0.792535 | ||||||||
\(671\) | 6.45114e14 | 0.183089 | ||||||||
\(672\) | 1.32940e15 | 0.374217 | ||||||||
\(673\) | 5.36855e15 | 1.49890 | 0.749452 | − | 0.662058i | \(-0.230317\pi\) | ||||
0.749452 | + | 0.662058i | \(0.230317\pi\) | |||||||
\(674\) | −4.17293e15 | −1.15561 | ||||||||
\(675\) | 1.60452e15 | 0.440731 | ||||||||
\(676\) | −1.14958e15 | −0.313208 | ||||||||
\(677\) | 1.47849e15 | 0.399558 | 0.199779 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199779 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(678\) | −1.96045e15 | −0.525524 | ||||||||
\(679\) | −8.56749e15 | −2.27808 | ||||||||
\(680\) | −6.92795e14 | −0.182728 | ||||||||
\(681\) | 1.63253e15 | 0.427121 | ||||||||
\(682\) | 2.96559e14 | 0.0769657 | ||||||||
\(683\) | −5.89943e15 | −1.51879 | −0.759393 | − | 0.650632i | \(-0.774504\pi\) | ||||
−0.759393 | + | 0.650632i | \(0.774504\pi\) | |||||||
\(684\) | 4.70341e14 | 0.120117 | ||||||||
\(685\) | −1.09295e15 | −0.276886 | ||||||||
\(686\) | −1.33239e16 | −3.34848 | ||||||||
\(687\) | 1.27350e15 | 0.317494 | ||||||||
\(688\) | 5.85275e14 | 0.144752 | ||||||||
\(689\) | −9.77122e13 | −0.0239741 | ||||||||
\(690\) | 1.92577e14 | 0.0468742 | ||||||||
\(691\) | −2.68896e15 | −0.649314 | −0.324657 | − | 0.945832i | \(-0.605249\pi\) | ||||
−0.324657 | + | 0.945832i | \(0.605249\pi\) | |||||||
\(692\) | 3.59000e13 | 0.00860024 | ||||||||
\(693\) | 1.76868e15 | 0.420356 | ||||||||
\(694\) | 8.31260e14 | 0.196002 | ||||||||
\(695\) | 1.39161e15 | 0.325537 | ||||||||
\(696\) | −2.01165e14 | −0.0466875 | ||||||||
\(697\) | −1.88527e15 | −0.434104 | ||||||||
\(698\) | −1.38941e15 | −0.317413 | ||||||||
\(699\) | −1.71209e15 | −0.388064 | ||||||||
\(700\) | 1.93500e15 | 0.435152 | ||||||||
\(701\) | 1.81744e14 | 0.0405520 | 0.0202760 | − | 0.999794i | \(-0.493546\pi\) | ||||
0.0202760 | + | 0.999794i | \(0.493546\pi\) | |||||||
\(702\) | −4.57797e14 | −0.101349 | ||||||||
\(703\) | 3.73403e14 | 0.0820206 | ||||||||
\(704\) | 5.80487e14 | 0.126515 | ||||||||
\(705\) | −1.56292e14 | −0.0337985 | ||||||||
\(706\) | −4.80267e15 | −1.03052 | ||||||||
\(707\) | −1.86626e15 | −0.397342 | ||||||||
\(708\) | 7.70298e14 | 0.162733 | ||||||||
\(709\) | 1.92897e15 | 0.404362 | 0.202181 | − | 0.979348i | \(-0.435197\pi\) | ||||
0.202181 | + | 0.979348i | \(0.435197\pi\) | |||||||
\(710\) | −5.12541e15 | −1.06612 | ||||||||
\(711\) | 6.12992e15 | 1.26524 | ||||||||
\(712\) | 1.52395e15 | 0.312127 | ||||||||
\(713\) | 3.18539e14 | 0.0647397 | ||||||||
\(714\) | −1.53193e15 | −0.308958 | ||||||||
\(715\) | 9.47773e13 | 0.0189680 | ||||||||
\(716\) | 6.67186e14 | 0.132503 | ||||||||
\(717\) | −1.66138e15 | −0.327427 | ||||||||
\(718\) | 2.65502e15 | 0.519258 | ||||||||
\(719\) | −5.16510e15 | −1.00247 | −0.501234 | − | 0.865312i | \(-0.667120\pi\) | ||||
−0.501234 | + | 0.865312i | \(0.667120\pi\) | |||||||
\(720\) | 2.98670e15 | 0.575259 | ||||||||
\(721\) | 9.89272e14 | 0.189091 | ||||||||
\(722\) | −4.99396e15 | −0.947306 | ||||||||
\(723\) | −3.91504e14 | −0.0737013 | ||||||||
\(724\) | 3.05389e15 | 0.570547 | ||||||||
\(725\) | −7.23330e14 | −0.134115 | ||||||||
\(726\) | −1.88446e15 | −0.346764 | ||||||||
\(727\) | −1.46638e15 | −0.267797 | −0.133899 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133899 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(728\) | 1.17376e15 | 0.212744 | ||||||||
\(729\) | −2.39737e15 | −0.431255 | ||||||||
\(730\) | 4.71361e15 | 0.841546 | ||||||||
\(731\) | −2.97712e14 | −0.0527534 | ||||||||
\(732\) | 4.30433e14 | 0.0756997 | ||||||||
\(733\) | 5.01638e15 | 0.875626 | 0.437813 | − | 0.899066i | \(-0.355753\pi\) | ||||
0.437813 | + | 0.899066i | \(0.355753\pi\) | |||||||
\(734\) | 2.75749e15 | 0.477733 | ||||||||
\(735\) | 2.51236e15 | 0.432018 | ||||||||
\(736\) | −8.70382e14 | −0.148553 | ||||||||
\(737\) | −1.92356e15 | −0.325863 | ||||||||
\(738\) | 5.99220e15 | 1.00757 | ||||||||
\(739\) | −6.41227e15 | −1.07021 | −0.535103 | − | 0.844787i | \(-0.679727\pi\) | ||||
−0.535103 | + | 0.844787i | \(0.679727\pi\) | |||||||
\(740\) | −1.99286e14 | −0.0330143 | ||||||||
\(741\) | −1.18488e14 | −0.0194838 | ||||||||
\(742\) | 2.19857e15 | 0.358855 | ||||||||
\(743\) | 9.01527e15 | 1.46063 | 0.730315 | − | 0.683110i | \(-0.239373\pi\) | ||||
0.730315 | + | 0.683110i | \(0.239373\pi\) | |||||||
\(744\) | −4.20680e14 | −0.0676551 | ||||||||
\(745\) | −2.55303e15 | −0.407564 | ||||||||
\(746\) | 1.08069e16 | 1.71253 | ||||||||
\(747\) | −2.76980e14 | −0.0435697 | ||||||||
\(748\) | 2.26313e14 | 0.0353387 | ||||||||
\(749\) | 1.92968e16 | 2.99113 | ||||||||
\(750\) | −2.18068e15 | −0.335549 | ||||||||
\(751\) | −4.51349e15 | −0.689434 | −0.344717 | − | 0.938707i | \(-0.612025\pi\) | ||||
−0.344717 | + | 0.938707i | \(0.612025\pi\) | |||||||
\(752\) | 1.60027e15 | 0.242658 | ||||||||
\(753\) | 3.63953e15 | 0.547864 | ||||||||
\(754\) | 2.06379e14 | 0.0308406 | ||||||||
\(755\) | −2.67986e15 | −0.397560 | ||||||||
\(756\) | 2.49650e15 | 0.367673 | ||||||||
\(757\) | −1.27132e15 | −0.185878 | −0.0929389 | − | 0.995672i | \(-0.529626\pi\) | ||||
−0.0929389 | + | 0.995672i | \(0.529626\pi\) | |||||||
\(758\) | 9.87509e15 | 1.43338 | ||||||||
\(759\) | 1.33746e14 | 0.0192730 | ||||||||
\(760\) | 1.20568e15 | 0.172487 | ||||||||
\(761\) | −8.49793e15 | −1.20697 | −0.603486 | − | 0.797373i | \(-0.706222\pi\) | ||||
−0.603486 | + | 0.797373i | \(0.706222\pi\) | |||||||
\(762\) | 4.81739e15 | 0.679296 | ||||||||
\(763\) | 6.12587e15 | 0.857597 | ||||||||
\(764\) | −2.25451e15 | −0.313357 | ||||||||
\(765\) | −1.51925e15 | −0.209648 | ||||||||
\(766\) | −1.31729e16 | −1.80478 | ||||||||
\(767\) | 1.68013e15 | 0.228544 | ||||||||
\(768\) | 2.07745e15 | 0.280571 | ||||||||
\(769\) | −3.91757e15 | −0.525317 | −0.262659 | − | 0.964889i | \(-0.584599\pi\) | ||||
−0.262659 | + | 0.964889i | \(0.584599\pi\) | |||||||
\(770\) | −2.13253e15 | −0.283920 | ||||||||
\(771\) | −1.73930e15 | −0.229919 | ||||||||
\(772\) | 1.23668e15 | 0.162317 | ||||||||
\(773\) | 1.11302e16 | 1.45049 | 0.725244 | − | 0.688492i | \(-0.241727\pi\) | ||||
0.725244 | + | 0.688492i | \(0.241727\pi\) | |||||||
\(774\) | 9.46256e14 | 0.122443 | ||||||||
\(775\) | −1.51264e15 | −0.194347 | ||||||||
\(776\) | −7.40793e15 | −0.945055 | ||||||||
\(777\) | 9.36877e14 | 0.118677 | ||||||||
\(778\) | 1.30426e16 | 1.64050 | ||||||||
\(779\) | 3.28095e15 | 0.409773 | ||||||||
\(780\) | 6.32372e13 | 0.00784247 | ||||||||
\(781\) | −3.55963e15 | −0.438353 | ||||||||
\(782\) | 1.00299e15 | 0.122647 | ||||||||
\(783\) | −9.33228e14 | −0.113318 | ||||||||
\(784\) | −2.57239e16 | −3.10169 | ||||||||
\(785\) | −7.15826e15 | −0.857086 | ||||||||
\(786\) | −2.43958e15 | −0.290063 | ||||||||
\(787\) | −2.14922e15 | −0.253758 | −0.126879 | − | 0.991918i | \(-0.540496\pi\) | ||||
−0.126879 | + | 0.991918i | \(0.540496\pi\) | |||||||
\(788\) | 4.59654e15 | 0.538935 | ||||||||
\(789\) | 2.17012e15 | 0.252674 | ||||||||
\(790\) | −7.39095e15 | −0.854578 | ||||||||
\(791\) | 2.33184e16 | 2.67749 | ||||||||
\(792\) | 1.52930e15 | 0.174383 | ||||||||
\(793\) | 9.38838e14 | 0.106313 | ||||||||
\(794\) | −4.33452e15 | −0.487448 | ||||||||
\(795\) | −2.51828e14 | −0.0281245 | ||||||||
\(796\) | 1.30144e15 | 0.144345 | ||||||||
\(797\) | −1.56355e16 | −1.72223 | −0.861116 | − | 0.508409i | \(-0.830234\pi\) | ||||
−0.861116 | + | 0.508409i | \(0.830234\pi\) | |||||||
\(798\) | 2.66603e15 | 0.291642 | ||||||||
\(799\) | −8.14007e14 | −0.0884343 | ||||||||
\(800\) | 4.13317e15 | 0.445952 | ||||||||
\(801\) | 3.34191e15 | 0.358110 | ||||||||
\(802\) | −4.44927e15 | −0.473510 | ||||||||
\(803\) | 3.27363e15 | 0.346014 | ||||||||
\(804\) | −1.28344e15 | −0.134731 | ||||||||
\(805\) | −2.29059e15 | −0.238820 | ||||||||
\(806\) | 4.31584e14 | 0.0446913 | ||||||||
\(807\) | 4.20804e15 | 0.432789 | ||||||||
\(808\) | −1.61367e15 | −0.164836 | ||||||||
\(809\) | −1.58636e16 | −1.60948 | −0.804740 | − | 0.593628i | \(-0.797695\pi\) | ||||
−0.804740 | + | 0.593628i | \(0.797695\pi\) | |||||||
\(810\) | 4.20668e15 | 0.423908 | ||||||||
\(811\) | 1.03213e16 | 1.03305 | 0.516524 | − | 0.856273i | \(-0.327226\pi\) | ||||
0.516524 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(812\) | −1.12544e15 | −0.111883 | ||||||||
\(813\) | −2.46976e15 | −0.243869 | ||||||||
\(814\) | −5.71065e14 | −0.0560082 | ||||||||
\(815\) | 3.95631e15 | 0.385410 | ||||||||
\(816\) | −1.79663e15 | −0.173845 | ||||||||
\(817\) | 5.18110e14 | 0.0497967 | ||||||||
\(818\) | 1.50759e16 | 1.43926 | ||||||||
\(819\) | 2.57397e15 | 0.244086 | ||||||||
\(820\) | −1.75105e15 | −0.164939 | ||||||||
\(821\) | 1.30461e16 | 1.22065 | 0.610327 | − | 0.792149i | \(-0.291038\pi\) | ||||
0.610327 | + | 0.792149i | \(0.291038\pi\) | |||||||
\(822\) | −2.08967e15 | −0.194215 | ||||||||
\(823\) | −9.40594e15 | −0.868366 | −0.434183 | − | 0.900825i | \(-0.642963\pi\) | ||||
−0.434183 | + | 0.900825i | \(0.642963\pi\) | |||||||
\(824\) | 8.55380e14 | 0.0784440 | ||||||||
\(825\) | −6.35117e14 | −0.0578571 | ||||||||
\(826\) | −3.78038e16 | −3.42094 | ||||||||
\(827\) | −5.58618e15 | −0.502151 | −0.251076 | − | 0.967967i | \(-0.580784\pi\) | ||||
−0.251076 | + | 0.967967i | \(0.580784\pi\) | |||||||
\(828\) | −7.72634e14 | −0.0689933 | ||||||||
\(829\) | 1.46565e15 | 0.130011 | 0.0650054 | − | 0.997885i | \(-0.479294\pi\) | ||||
0.0650054 | + | 0.997885i | \(0.479294\pi\) | |||||||
\(830\) | 3.33960e14 | 0.0294283 | ||||||||
\(831\) | −7.76454e14 | −0.0679688 | ||||||||
\(832\) | 8.44786e14 | 0.0734629 | ||||||||
\(833\) | 1.30850e16 | 1.13038 | ||||||||
\(834\) | 2.66070e15 | 0.228340 | ||||||||
\(835\) | −7.56438e15 | −0.644908 | ||||||||
\(836\) | −3.93854e14 | −0.0333580 | ||||||||
\(837\) | −1.95159e15 | −0.164209 | ||||||||
\(838\) | 6.02984e15 | 0.504039 | ||||||||
\(839\) | −2.31777e16 | −1.92477 | −0.962387 | − | 0.271684i | \(-0.912420\pi\) | ||||
−0.962387 | + | 0.271684i | \(0.912420\pi\) | |||||||
\(840\) | 3.02507e15 | 0.249574 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | −6.73738e15 | −0.548623 | ||||||||
\(843\) | −2.94086e15 | −0.237915 | ||||||||
\(844\) | −4.00706e15 | −0.322064 | ||||||||
\(845\) | −6.46221e15 | −0.516023 | ||||||||
\(846\) | 2.58726e15 | 0.205260 | ||||||||
\(847\) | 2.24145e16 | 1.76673 | ||||||||
\(848\) | 2.57845e15 | 0.201921 | ||||||||
\(849\) | −7.07953e15 | −0.550823 | ||||||||
\(850\) | −4.76286e15 | −0.368183 | ||||||||
\(851\) | −6.13391e14 | −0.0471113 | ||||||||
\(852\) | −2.37506e15 | −0.181241 | ||||||||
\(853\) | −1.62059e16 | −1.22872 | −0.614359 | − | 0.789027i | \(-0.710585\pi\) | ||||
−0.614359 | + | 0.789027i | \(0.710585\pi\) | |||||||
\(854\) | −2.11243e16 | −1.59134 | ||||||||
\(855\) | 2.64395e15 | 0.197898 | ||||||||
\(856\) | 1.66851e16 | 1.24086 | ||||||||
\(857\) | −1.76845e15 | −0.130677 | −0.0653383 | − | 0.997863i | \(-0.520813\pi\) | ||||
−0.0653383 | + | 0.997863i | \(0.520813\pi\) | |||||||
\(858\) | 1.81210e14 | 0.0133046 | ||||||||
\(859\) | 2.15096e16 | 1.56917 | 0.784586 | − | 0.620020i | \(-0.212875\pi\) | ||||
0.784586 | + | 0.620020i | \(0.212875\pi\) | |||||||
\(860\) | −2.76517e14 | −0.0200438 | ||||||||
\(861\) | 8.23200e15 | 0.592909 | ||||||||
\(862\) | 4.55974e15 | 0.326325 | ||||||||
\(863\) | 2.05957e16 | 1.46459 | 0.732297 | − | 0.680986i | \(-0.238448\pi\) | ||||
0.732297 | + | 0.680986i | \(0.238448\pi\) | |||||||
\(864\) | 5.33254e15 | 0.376798 | ||||||||
\(865\) | 2.01806e14 | 0.0141692 | ||||||||
\(866\) | 1.67269e16 | 1.16699 | ||||||||
\(867\) | −3.72761e15 | −0.258419 | ||||||||
\(868\) | −2.35355e15 | −0.162131 | ||||||||
\(869\) | −5.13306e15 | −0.351373 | ||||||||
\(870\) | 5.31889e14 | 0.0361797 | ||||||||
\(871\) | −2.79937e15 | −0.189217 | ||||||||
\(872\) | 5.29677e15 | 0.355771 | ||||||||
\(873\) | −1.62450e16 | −1.08428 | ||||||||
\(874\) | −1.74550e15 | −0.115773 | ||||||||
\(875\) | 2.59380e16 | 1.70959 | ||||||||
\(876\) | 2.18423e15 | 0.143062 | ||||||||
\(877\) | 5.19470e15 | 0.338114 | 0.169057 | − | 0.985606i | \(-0.445928\pi\) | ||||
0.169057 | + | 0.985606i | \(0.445928\pi\) | |||||||
\(878\) | 2.47644e16 | 1.60180 | ||||||||
\(879\) | 6.76431e15 | 0.434795 | ||||||||
\(880\) | −2.50100e15 | −0.159757 | ||||||||
\(881\) | −1.55161e16 | −0.984952 | −0.492476 | − | 0.870326i | \(-0.663908\pi\) | ||||
−0.492476 | + | 0.870326i | \(0.663908\pi\) | |||||||
\(882\) | −4.15897e16 | −2.62366 | ||||||||
\(883\) | −1.33984e16 | −0.839977 | −0.419989 | − | 0.907529i | \(-0.637966\pi\) | ||||
−0.419989 | + | 0.907529i | \(0.637966\pi\) | |||||||
\(884\) | 3.29355e14 | 0.0205199 | ||||||||
\(885\) | 4.33012e15 | 0.268109 | ||||||||
\(886\) | 3.47730e15 | 0.213972 | ||||||||
\(887\) | 4.71681e15 | 0.288449 | 0.144224 | − | 0.989545i | \(-0.453931\pi\) | ||||
0.144224 | + | 0.989545i | \(0.453931\pi\) | |||||||
\(888\) | 8.10076e14 | 0.0492328 | ||||||||
\(889\) | −5.73000e16 | −3.46095 | ||||||||
\(890\) | −4.02940e15 | −0.241878 | ||||||||
\(891\) | 2.92157e15 | 0.174296 | ||||||||
\(892\) | −8.12095e15 | −0.481504 | ||||||||
\(893\) | 1.41662e15 | 0.0834777 | ||||||||
\(894\) | −4.88128e15 | −0.285876 | ||||||||
\(895\) | 3.75049e15 | 0.218304 | ||||||||
\(896\) | −3.91112e16 | −2.26260 | ||||||||
\(897\) | 1.94641e14 | 0.0111912 | ||||||||
\(898\) | 2.07828e16 | 1.18764 | ||||||||
\(899\) | 8.79792e14 | 0.0499691 | ||||||||
\(900\) | 3.66899e15 | 0.207116 | ||||||||
\(901\) | −1.31158e15 | −0.0735883 | ||||||||
\(902\) | −5.01774e15 | −0.279816 | ||||||||
\(903\) | 1.29995e15 | 0.0720518 | ||||||||
\(904\) | 2.01624e16 | 1.11075 | ||||||||
\(905\) | 1.71670e16 | 0.939999 | ||||||||
\(906\) | −5.12377e15 | −0.278859 | ||||||||
\(907\) | −4.70220e15 | −0.254367 | −0.127183 | − | 0.991879i | \(-0.540594\pi\) | ||||
−0.127183 | + | 0.991879i | \(0.540594\pi\) | |||||||
\(908\) | 7.89724e15 | 0.424623 | ||||||||
\(909\) | −3.53866e15 | −0.189120 | ||||||||
\(910\) | −3.10349e15 | −0.164863 | ||||||||
\(911\) | 7.70359e15 | 0.406763 | 0.203382 | − | 0.979100i | \(-0.434807\pi\) | ||||
0.203382 | + | 0.979100i | \(0.434807\pi\) | |||||||
\(912\) | 3.12668e15 | 0.164101 | ||||||||
\(913\) | 2.31937e14 | 0.0120999 | ||||||||
\(914\) | 2.29835e16 | 1.19182 | ||||||||
\(915\) | 2.41961e15 | 0.124718 | ||||||||
\(916\) | 6.16046e15 | 0.315637 | ||||||||
\(917\) | 2.90175e16 | 1.47784 | ||||||||
\(918\) | −6.14496e15 | −0.311089 | ||||||||
\(919\) | 2.83879e16 | 1.42856 | 0.714280 | − | 0.699860i | \(-0.246754\pi\) | ||||
0.714280 | + | 0.699860i | \(0.246754\pi\) | |||||||
\(920\) | −1.98057e15 | −0.0990735 | ||||||||
\(921\) | −7.15823e15 | −0.355941 | ||||||||
\(922\) | 3.43819e16 | 1.69945 | ||||||||
\(923\) | −5.18035e15 | −0.254536 | ||||||||
\(924\) | −9.88190e14 | −0.0482664 | ||||||||
\(925\) | 2.91280e15 | 0.141427 | ||||||||
\(926\) | −7.37627e15 | −0.356022 | ||||||||
\(927\) | 1.87578e15 | 0.0900004 | ||||||||
\(928\) | −2.40396e15 | −0.114660 | ||||||||
\(929\) | −2.43302e13 | −0.00115361 | −0.000576804 | − | 1.00000i | \(-0.500184\pi\) | ||||
−0.000576804 | 1.00000i | \(0.500184\pi\) | ||||||||
\(930\) | 1.11230e15 | 0.0524282 | ||||||||
\(931\) | −2.27719e16 | −1.06703 | ||||||||
\(932\) | −8.28214e15 | −0.385794 | ||||||||
\(933\) | −1.06107e16 | −0.491356 | ||||||||
\(934\) | 2.07512e16 | 0.955293 | ||||||||
\(935\) | 1.27219e15 | 0.0582219 | ||||||||
\(936\) | 2.22560e15 | 0.101258 | ||||||||
\(937\) | −6.94518e15 | −0.314135 | −0.157067 | − | 0.987588i | \(-0.550204\pi\) | ||||
−0.157067 | + | 0.987588i | \(0.550204\pi\) | |||||||
\(938\) | 6.29871e16 | 2.83228 | ||||||||
\(939\) | 1.17989e16 | 0.527451 | ||||||||
\(940\) | −7.56054e14 | −0.0336008 | ||||||||
\(941\) | −3.11414e16 | −1.37593 | −0.687963 | − | 0.725745i | \(-0.741495\pi\) | ||||
−0.687963 | + | 0.725745i | \(0.741495\pi\) | |||||||
\(942\) | −1.36863e16 | −0.601181 | ||||||||
\(943\) | −5.38965e15 | −0.235367 | ||||||||
\(944\) | −4.43357e16 | −1.92490 | ||||||||
\(945\) | 1.40337e16 | 0.605755 | ||||||||
\(946\) | −7.92375e14 | −0.0340039 | ||||||||
\(947\) | −3.66620e16 | −1.56420 | −0.782098 | − | 0.623155i | \(-0.785851\pi\) | ||||
−0.782098 | + | 0.623155i | \(0.785851\pi\) | |||||||
\(948\) | −3.42488e15 | −0.145278 | ||||||||
\(949\) | 4.76413e15 | 0.200918 | ||||||||
\(950\) | 8.28884e15 | 0.347547 | ||||||||
\(951\) | 1.07781e16 | 0.449315 | ||||||||
\(952\) | 1.57553e16 | 0.653015 | ||||||||
\(953\) | 1.01542e16 | 0.418440 | 0.209220 | − | 0.977869i | \(-0.432908\pi\) | ||||
0.209220 | + | 0.977869i | \(0.432908\pi\) | |||||||
\(954\) | 4.16876e15 | 0.170801 | ||||||||
\(955\) | −1.26734e16 | −0.516268 | ||||||||
\(956\) | −8.03683e15 | −0.325512 | ||||||||
\(957\) | 3.69400e14 | 0.0148758 | ||||||||
\(958\) | 1.90277e16 | 0.761860 | ||||||||
\(959\) | 2.48554e16 | 0.989507 | ||||||||
\(960\) | 2.17722e15 | 0.0861808 | ||||||||
\(961\) | −2.35686e16 | −0.927589 | ||||||||
\(962\) | −8.31074e14 | −0.0325220 | ||||||||
\(963\) | 3.65892e16 | 1.42367 | ||||||||
\(964\) | −1.89388e15 | −0.0732702 | ||||||||
\(965\) | 6.95183e15 | 0.267423 | ||||||||
\(966\) | −4.37951e15 | −0.167514 | ||||||||
\(967\) | −3.28531e16 | −1.24949 | −0.624743 | − | 0.780830i | \(-0.714796\pi\) | ||||
−0.624743 | + | 0.780830i | \(0.714796\pi\) | |||||||
\(968\) | 1.93808e16 | 0.732923 | ||||||||
\(969\) | −1.59045e15 | −0.0598052 | ||||||||
\(970\) | 1.95869e16 | 0.732355 | ||||||||
\(971\) | −2.39850e16 | −0.891732 | −0.445866 | − | 0.895100i | \(-0.647104\pi\) | ||||
−0.445866 | + | 0.895100i | \(0.647104\pi\) | |||||||
\(972\) | 7.22973e15 | 0.267274 | ||||||||
\(973\) | −3.16475e16 | −1.16337 | ||||||||
\(974\) | 3.01884e16 | 1.10348 | ||||||||
\(975\) | −9.24289e14 | −0.0335956 | ||||||||
\(976\) | −2.47742e16 | −0.895419 | ||||||||
\(977\) | −1.64069e16 | −0.589667 | −0.294834 | − | 0.955549i | \(-0.595264\pi\) | ||||
−0.294834 | + | 0.955549i | \(0.595264\pi\) | |||||||
\(978\) | 7.56429e15 | 0.270336 | ||||||||
\(979\) | −2.79845e15 | −0.0994517 | ||||||||
\(980\) | 1.21534e16 | 0.429491 | ||||||||
\(981\) | 1.16154e16 | 0.408183 | ||||||||
\(982\) | 3.51200e16 | 1.22727 | ||||||||
\(983\) | −4.35578e16 | −1.51364 | −0.756818 | − | 0.653626i | \(-0.773247\pi\) | ||||
−0.756818 | + | 0.653626i | \(0.773247\pi\) | |||||||
\(984\) | 7.11784e15 | 0.245966 | ||||||||
\(985\) | 2.58387e16 | 0.887917 | ||||||||
\(986\) | 2.77020e15 | 0.0946648 | ||||||||
\(987\) | 3.55434e15 | 0.120786 | ||||||||
\(988\) | −5.73178e14 | −0.0193698 | ||||||||
\(989\) | −8.51103e14 | −0.0286024 | ||||||||
\(990\) | −4.04355e15 | −0.135135 | ||||||||
\(991\) | −2.49086e16 | −0.827835 | −0.413918 | − | 0.910314i | \(-0.635840\pi\) | ||||
−0.413918 | + | 0.910314i | \(0.635840\pi\) | |||||||
\(992\) | −5.02721e15 | −0.166155 | ||||||||
\(993\) | −7.57365e15 | −0.248934 | ||||||||
\(994\) | 1.16560e17 | 3.81000 | ||||||||
\(995\) | 7.31584e15 | 0.237814 | ||||||||
\(996\) | 1.54753e14 | 0.00500279 | ||||||||
\(997\) | −2.41171e16 | −0.775358 | −0.387679 | − | 0.921795i | \(-0.626723\pi\) | ||||
−0.387679 | + | 0.921795i | \(0.626723\pi\) | |||||||
\(998\) | −3.06492e16 | −0.979943 | ||||||||
\(999\) | 3.75805e15 | 0.119496 |
(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 | 29.12.a.a.1.9 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.3 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.9 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.3 | 11 | 3.2 | odd | 2 |