Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,22,Mod(1,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(22.3581875430\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4963x + 96223 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(21.2235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 201833. | 1.97342 | 0.986708 | − | 0.162503i | \(-0.0519569\pi\) | ||||
0.986708 | + | 0.162503i | \(0.0519569\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.11555e7 | −0.968811 | −0.484406 | − | 0.874844i | \(-0.660964\pi\) | ||||
−0.484406 | + | 0.874844i | \(0.660964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.32981e8 | 0.980761 | 0.490381 | − | 0.871508i | \(-0.336858\pi\) | ||||
0.490381 | + | 0.871508i | \(0.336858\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.02761e10 | 2.89437 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59634e9 | −0.0650551 | −0.0325275 | − | 0.999471i | \(-0.510356\pi\) | ||||
−0.0325275 | + | 0.999471i | \(0.510356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.30207e10 | −0.126788 | −0.0633940 | − | 0.997989i | \(-0.520192\pi\) | ||||
−0.0633940 | + | 0.997989i | \(0.520192\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.26988e12 | −1.91187 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.35490e13 | 1.63003 | 0.815013 | − | 0.579443i | \(-0.196730\pi\) | ||||
0.815013 | + | 0.579443i | \(0.196730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.39028e13 | 0.520221 | 0.260111 | − | 0.965579i | \(-0.416241\pi\) | ||||
0.260111 | + | 0.965579i | \(0.416241\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.47940e14 | 1.93545 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.80711e14 | −1.41292 | −0.706458 | − | 0.707754i | \(-0.749708\pi\) | ||||
−0.706458 | + | 0.707754i | \(0.749708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.92803e13 | −0.0614052 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.99948e15 | 3.73838 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.19637e15 | 0.528063 | 0.264031 | − | 0.964514i | \(-0.414948\pi\) | ||||
0.264031 | + | 0.964514i | \(0.414948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.88487e15 | 0.851292 | 0.425646 | − | 0.904890i | \(-0.360047\pi\) | ||||
0.425646 | + | 0.904890i | \(0.360047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.12953e15 | −0.128381 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.55066e16 | −0.950173 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.72004e16 | 0.929944 | 0.464972 | − | 0.885325i | \(-0.346064\pi\) | ||||
0.464972 | + | 0.885325i | \(0.346064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.27197e16 | −0.250205 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.89865e16 | −0.802663 | −0.401332 | − | 0.915933i | \(-0.631453\pi\) | ||||
−0.401332 | + | 0.915933i | \(0.631453\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24557e16 | 0.229020 | 0.114510 | − | 0.993422i | \(-0.463470\pi\) | ||||
0.114510 | + | 0.993422i | \(0.463470\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.40508e17 | −2.80410 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.07417e17 | −0.575196 | −0.287598 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287598 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.12844e16 | −0.0381069 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73464e18 | 3.21672 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.38971e17 | −0.501862 | −0.250931 | − | 0.968005i | \(-0.580737\pi\) | ||||
−0.250931 | + | 0.968005i | \(0.580737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.18394e17 | 0.0630261 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.80603e18 | 1.02661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.04610e18 | −0.775887 | −0.387944 | − | 0.921683i | \(-0.626814\pi\) | ||||
−0.387944 | + | 0.921683i | \(0.626814\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.64497e18 | −1.01321 | −0.506604 | − | 0.862179i | \(-0.669099\pi\) | ||||
−0.506604 | + | 0.862179i | \(0.669099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.21918e19 | 2.83869 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.33324e18 | 0.122834 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.96718e18 | −0.265886 | −0.132943 | − | 0.991124i | \(-0.542443\pi\) | ||||
−0.132943 | + | 0.991124i | \(0.542443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.66566e19 | −2.78827 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.61878e19 | −0.954743 | −0.477371 | − | 0.878702i | \(-0.658410\pi\) | ||||
−0.477371 | + | 0.878702i | \(0.658410\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.37659e19 | 0.374899 | 0.187449 | − | 0.982274i | \(-0.439978\pi\) | ||||
0.187449 | + | 0.982274i | \(0.439978\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.90972e18 | −0.121178 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.10201e18 | −0.0638035 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.18258e20 | −1.40523 | −0.702615 | − | 0.711570i | \(-0.747984\pi\) | ||||
−0.702615 | + | 0.711570i | \(0.747984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.90526e20 | 4.48301 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.60950e19 | −0.113860 | −0.0569301 | − | 0.998378i | \(-0.518131\pi\) | ||||
−0.0569301 | + | 0.998378i | \(0.518131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.86637e20 | −1.57919 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.41466e20 | 1.04209 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.30103e20 | −0.782217 | −0.391109 | − | 0.920345i | \(-0.627908\pi\) | ||||
−0.391109 | + | 0.920345i | \(0.627908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.61930e19 | −0.124349 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.84094e20 | 1.67995 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.94120e20 | −0.503996 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.72050e20 | 0.374581 | 0.187290 | − | 0.982305i | \(-0.440029\pi\) | ||||
0.187290 | + | 0.982305i | \(0.440029\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.69436e20 | −0.188293 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.18197e21 | −1.06471 | −0.532357 | − | 0.846520i | \(-0.678693\pi\) | ||||
−0.532357 | + | 0.846520i | \(0.678693\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.39849e21 | −1.75852 | −0.879258 | − | 0.476345i | \(-0.841961\pi\) | ||||
−0.879258 | + | 0.476345i | \(0.841961\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.12974e21 | −1.87509 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.01203e20 | 0.197167 | 0.0985835 | − | 0.995129i | \(-0.468569\pi\) | ||||
0.0985835 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.25100e21 | 1.71994 | 0.859970 | − | 0.510345i | \(-0.170482\pi\) | ||||
0.859970 | + | 0.510345i | \(0.170482\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.48993e21 | 1.83517 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.36941e21 | −0.933748 | −0.466874 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466874 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.93859e21 | 1.36885 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.90802e21 | −0.366971 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.93118e21 | 1.59867 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.36893e21 | −0.995768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.39237e22 | −1.58399 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.07072e22 | 1.02830 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.15394e20 | −0.00938093 | −0.00469046 | − | 0.999989i | \(-0.501493\pi\) | ||||
−0.00469046 | + | 0.999989i | \(0.501493\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.55063e21 | 0.451951 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.13322e22 | 0.665223 | 0.332611 | − | 0.943064i | \(-0.392070\pi\) | ||||
0.332611 | + | 0.943064i | \(0.392070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01905e22 | 0.510213 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −8.46111e22 | −3.62178 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.18696e21 | 0.263621 | 0.131810 | − | 0.991275i | \(-0.457921\pi\) | ||||
0.131810 | + | 0.991275i | \(0.457921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.34620e22 | 0.739109 | 0.369555 | − | 0.929209i | \(-0.379510\pi\) | ||||
0.369555 | + | 0.929209i | \(0.379510\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.18635e22 | −1.13510 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.52686e20 | 0.00824820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.53098e22 | −0.511593 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.29590e21 | −0.0752007 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.57122e22 | −0.390557 | −0.195278 | − | 0.980748i | \(-0.562561\pi\) | ||||
−0.195278 | + | 0.980748i | \(0.562561\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.38339e23 | 1.82679 | 0.913393 | − | 0.407078i | \(-0.133452\pi\) | ||||
0.913393 | + | 0.407078i | \(0.133452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.10212e23 | 4.71790 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.21865e22 | −0.824741 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.14060e23 | −1.00043 | −0.500215 | − | 0.865901i | \(-0.666746\pi\) | ||||
−0.500215 | + | 0.865901i | \(0.666746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.28965e23 | −0.990382 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.05756e23 | −1.38573 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.59877e22 | 0.390385 | 0.195192 | − | 0.980765i | \(-0.437467\pi\) | ||||
0.195192 | + | 0.980765i | \(0.437467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.38957e22 | 0.124377 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.09416e22 | 0.0960477 | 0.0480239 | − | 0.998846i | \(-0.484708\pi\) | ||||
0.0480239 | + | 0.998846i | \(0.484708\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.43093e23 | −0.983925 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.20922e23 | 1.50571 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.69739e23 | −0.537400 | −0.268700 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268700 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.14619e22 | −0.0602238 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.14804e23 | −1.53115 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.58531e23 | 1.23620 | 0.618102 | − | 0.786098i | \(-0.287902\pi\) | ||||
0.618102 | + | 0.786098i | \(0.287902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.50056e23 | −0.492506 | −0.246253 | − | 0.969206i | \(-0.579199\pi\) | ||||
−0.246253 | + | 0.969206i | \(0.579199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.13934e24 | −1.99948 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.75439e23 | −0.900940 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.58250e22 | −0.106041 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.93154e24 | 3.66646 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.66807e23 | −0.186794 | −0.0933971 | − | 0.995629i | \(-0.529773\pi\) | ||||
−0.0933971 | + | 0.995629i | \(0.529773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.33244e24 | 1.33750 | 0.668751 | − | 0.743487i | \(-0.266829\pi\) | ||||
0.668751 | + | 0.743487i | \(0.266829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.69091e23 | 0.242402 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.38870e23 | −0.517032 | −0.258516 | − | 0.966007i | \(-0.583233\pi\) | ||||
−0.258516 | + | 0.966007i | \(0.583233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.84623e24 | 1.34378 | 0.671889 | − | 0.740652i | \(-0.265483\pi\) | ||||
0.671889 | + | 0.740652i | \(0.265483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00707e23 | −0.524705 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.76915e23 | 0.517904 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.45945e24 | 0.777629 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.49883e24 | −4.08951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.78046e22 | −0.0338430 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.35146e24 | 1.31907 | 0.659536 | − | 0.751673i | \(-0.270753\pi\) | ||||
0.659536 | + | 0.751673i | \(0.270753\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.28556e24 | −1.88410 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.86619e23 | −0.221877 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.84754e24 | 0.834915 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.77841e24 | 0.739831 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.53869e23 | −0.206668 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.56926e22 | 0.0100611 | 0.00503054 | − | 0.999987i | \(-0.498399\pi\) | ||||
0.00503054 | + | 0.999987i | \(0.498399\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.86493e23 | −0.177729 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.05295e24 | −1.10585 | −0.552924 | − | 0.833232i | \(-0.686488\pi\) | ||||
−0.552924 | + | 0.833232i | \(0.686488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.16931e24 | 0.861311 | 0.430655 | − | 0.902516i | \(-0.358282\pi\) | ||||
0.430655 | + | 0.902516i | \(0.358282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.27921e23 | −0.125911 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.21547e24 | 0.724530 | 0.362265 | − | 0.932075i | \(-0.382003\pi\) | ||||
0.362265 | + | 0.932075i | \(0.382003\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.38801e24 | 0.557257 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.38684e25 | −2.77310 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.57703e24 | 0.167749 | 0.0838747 | − | 0.996476i | \(-0.473270\pi\) | ||||
0.0838747 | + | 0.996476i | \(0.473270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.93088e24 | 0.967851 | 0.483926 | − | 0.875109i | \(-0.339211\pi\) | ||||
0.483926 | + | 0.875109i | \(0.339211\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.71684e25 | 5.10846 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.50284e23 | 0.0369184 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.76162e23 | −0.0659578 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.24850e24 | −0.224693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.38505e25 | −1.51679 | −0.758393 | − | 0.651798i | \(-0.774015\pi\) | ||||
−0.758393 | + | 0.651798i | \(0.774015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.57095e24 | 0.0919174 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.78528e25 | −3.11639 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.76190e25 | −1.86685 | −0.933425 | − | 0.358772i | \(-0.883195\pi\) | ||||
−0.933425 | + | 0.358772i | \(0.883195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.99374e25 | 0.912054 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.62214e25 | 1.52841 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.52809e25 | −0.984592 | −0.492296 | − | 0.870428i | \(-0.663842\pi\) | ||||
−0.492296 | + | 0.870428i | \(0.663842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.35178e25 | 0.486209 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.64424e25 | −1.54364 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.38239e25 | 1.34683 | 0.673414 | − | 0.739266i | \(-0.264827\pi\) | ||||
0.673414 | + | 0.739266i | \(0.264827\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.43576e24 | 0.0692560 | 0.0346280 | − | 0.999400i | \(-0.488975\pi\) | ||||
0.0346280 | + | 0.999400i | \(0.488975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.32326e24 | −0.245392 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.63862e23 | 0.00399472 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.43475e25 | 1.00192 | 0.500958 | − | 0.865472i | \(-0.332981\pi\) | ||||
0.500958 | + | 0.865472i | \(0.332981\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.17619e26 | 2.46396 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.89794e25 | −1.72931 | −0.864655 | − | 0.502365i | \(-0.832463\pi\) | ||||
−0.864655 | + | 0.502365i | \(0.832463\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.34320e25 | −0.422719 | −0.211359 | − | 0.977408i | \(-0.567789\pi\) | ||||
−0.211359 | + | 0.977408i | \(0.567789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.93631e25 | −0.994594 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.05658e25 | −0.787221 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.14484e26 | 1.65698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.49086e25 | 0.739204 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.82209e25 | 0.729405 | 0.364703 | − | 0.931124i | \(-0.381171\pi\) | ||||
0.364703 | + | 0.931124i | \(0.381171\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.44420e25 | 0.751688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.23824e25 | −0.243201 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.76906e25 | 0.179141 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.37894e25 | 0.224614 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.38561e26 | −2.10112 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.19422e26 | 0.981607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.92535e26 | 1.47760 | 0.738799 | − | 0.673926i | \(-0.235393\pi\) | ||||
0.738799 | + | 0.673926i | \(0.235393\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.84093e26 | −3.47028 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.71812e26 | 1.15098 | 0.575491 | − | 0.817808i | \(-0.304811\pi\) | ||||
0.575491 | + | 0.817808i | \(0.304811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.10727e25 | −0.194609 | −0.0973045 | − | 0.995255i | \(-0.531022\pi\) | ||||
−0.0973045 | + | 0.995255i | \(0.531022\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.69480e26 | −2.75015 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.10055e26 | −1.15136 | −0.575680 | − | 0.817675i | \(-0.695262\pi\) | ||||
−0.575680 | + | 0.817675i | \(0.695262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.69528e24 | −0.0343532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.09759e25 | 0.389093 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.88369e26 | 0.847974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.84526e24 | 0.00778544 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.57992e26 | 3.39416 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.52033e26 | −0.564130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.36914e26 | −0.824891 | −0.412446 | − | 0.910982i | \(-0.635325\pi\) | ||||
−0.412446 | + | 0.910982i | \(0.635325\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.23523e26 | 2.69160 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.39278e25 | 0.257594 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.34353e25 | −0.182902 | −0.0914508 | − | 0.995810i | \(-0.529150\pi\) | ||||
−0.0914508 | + | 0.995810i | \(0.529150\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.80057e26 | −1.84267 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.17411e25 | −0.0553809 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.25005e26 | −1.01814 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.19860e27 | 2.70131 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.30760e26 | −0.489442 | −0.244721 | − | 0.969593i | \(-0.578696\pi\) | ||||
−0.244721 | + | 0.969593i | \(0.578696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.64125e26 | −1.32612 | −0.663060 | − | 0.748566i | \(-0.730742\pi\) | ||||
−0.663060 | + | 0.748566i | \(0.730742\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.52050e26 | −0.473982 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.72081e26 | −1.36782 | −0.683909 | − | 0.729567i | \(-0.739722\pi\) | ||||
−0.683909 | + | 0.729567i | \(0.739722\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.54017e26 | 0.924965 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.00444e27 | 3.15483 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.35001e26 | 1.23935 | 0.619677 | − | 0.784857i | \(-0.287264\pi\) | ||||
0.619677 | + | 0.784857i | \(0.287264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.20923e26 | −0.729370 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.48729e27 | −1.96506 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.91225e26 | −0.363206 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.88336e26 | −0.575075 | −0.287538 | − | 0.957769i | \(-0.592837\pi\) | ||||
−0.287538 | + | 0.957769i | \(0.592837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.08864e27 | −2.32321 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.68353e26 | −0.492207 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.33813e27 | −1.32909 | −0.664547 | − | 0.747247i | \(-0.731375\pi\) | ||||
−0.664547 | + | 0.747247i | \(0.731375\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.16106e27 | 2.02927 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.53960e25 | −0.0669520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.26568e25 | 0.0610329 | 0.0305165 | − | 0.999534i | \(-0.490285\pi\) | ||||
0.0305165 | + | 0.999534i | \(0.490285\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.32904e25 | −0.0185125 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.24472e27 | 0.936449 | 0.468225 | − | 0.883610i | \(-0.344894\pi\) | ||||
0.468225 | + | 0.883610i | \(0.344894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.67803e25 | 0.0618135 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.82635e26 | 0.662868 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.14241e27 | 1.36909 | 0.684544 | − | 0.728972i | \(-0.260002\pi\) | ||||
0.684544 | + | 0.728972i | \(0.260002\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.80336e27 | −2.30309 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.28722e27 | 1.31276 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.50182e27 | 1.36140 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.44762e27 | 1.26312 | 0.631560 | − | 0.775327i | \(-0.282415\pi\) | ||||
0.631560 | + | 0.775327i | \(0.282415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.05677e27 | 1.00686 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.80970e27 | 1.30510 | 0.652550 | − | 0.757746i | \(-0.273699\pi\) | ||||
0.652550 | + | 0.757746i | \(0.273699\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.44827e26 | −0.107934 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.03774e28 | −4.34319 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.52223e26 | −0.0604976 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.81600e27 | −1.44050 | −0.720250 | − | 0.693714i | \(-0.755973\pi\) | ||||
−0.720250 | + | 0.693714i | \(0.755973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.45057e27 | 0.520233 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23274e27 | −0.760960 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.40499e26 | 0.110309 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.73539e27 | 1.45857 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.13782e26 | −0.121206 | −0.0606031 | − | 0.998162i | \(-0.519302\pi\) | ||||
−0.0606031 | + | 0.998162i | \(0.519302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.16773e27 | 1.16128 | 0.580641 | − | 0.814160i | \(-0.302802\pi\) | ||||
0.580641 | + | 0.814160i | \(0.302802\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.27978e27 | −1.66483 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.96719e26 | −0.100092 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.13766e27 | −0.993715 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.11835e25 | 0.0162771 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.31148e27 | 0.721125 | 0.360563 | − | 0.932735i | \(-0.382585\pi\) | ||||
0.360563 | + | 0.932735i | \(0.382585\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.71199e27 | 1.59972 | 0.799859 | − | 0.600188i | \(-0.204908\pi\) | ||||
0.799859 | + | 0.600188i | \(0.204908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.10835e27 | −1.00959 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.90265e27 | −0.735029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.40474e27 | −1.32933 | −0.664665 | − | 0.747142i | \(-0.731426\pi\) | ||||
−0.664665 | + | 0.747142i | \(0.731426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.44411e26 | −0.110295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.59541e27 | 0.423611 | 0.211805 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211805 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.86795e27 | 0.757821 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.18958e27 | −0.770731 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.63721e27 | −1.22402 | −0.612008 | − | 0.790852i | \(-0.709638\pi\) | ||||
−0.612008 | + | 0.790852i | \(0.709638\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.86072e26 | 0.0522173 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.79214e28 | 3.60501 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.77238e26 | 0.120470 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.22330e27 | −0.850385 | −0.425193 | − | 0.905103i | \(-0.639794\pi\) | ||||
−0.425193 | + | 0.905103i | \(0.639794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.41890e28 | 6.09366 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.67275e27 | −0.716878 | −0.358439 | − | 0.933553i | \(-0.616691\pi\) | ||||
−0.358439 | + | 0.933553i | \(0.616691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.22059e27 | −0.741263 | −0.370632 | − | 0.928780i | \(-0.620859\pi\) | ||||
−0.370632 | + | 0.928780i | \(0.620859\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.65879e28 | −1.62756 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.14336e27 | −0.294827 | −0.147413 | − | 0.989075i | \(-0.547095\pi\) | ||||
−0.147413 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.90787e27 | −0.260771 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.30210e28 | −1.97427 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.81634e26 | −0.0148989 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.07076e26 | −0.0319443 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.93456e28 | −1.45257 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.98918e28 | 1.42939 | 0.714696 | − | 0.699435i | \(-0.246565\pi\) | ||||
0.714696 | + | 0.699435i | \(0.246565\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.71419e27 | −0.117906 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.15282e28 | −2.73463 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.75536e27 | −0.362898 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.49710e28 | 0.904058 | 0.452029 | − | 0.892003i | \(-0.350700\pi\) | ||||
0.452029 | + | 0.892003i | \(0.350700\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.33185e28 | 0.770392 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.87261e27 | −0.325444 | −0.162722 | − | 0.986672i | \(-0.552027\pi\) | ||||
−0.162722 | + | 0.986672i | \(0.552027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.62096e28 | 0.860756 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.58450e27 | 0.182421 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.91952e28 | −0.936375 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.56403e28 | 1.66681 | 0.833404 | − | 0.552665i | \(-0.186389\pi\) | ||||
0.833404 | + | 0.552665i | \(0.186389\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.22670e27 | 0.189542 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.66833e28 | −0.717495 | −0.358748 | − | 0.933435i | \(-0.616796\pi\) | ||||
−0.358748 | + | 0.933435i | \(0.616796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.50053e28 | 1.03151 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.90641e28 | −1.94169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.66847e28 | −1.39299 | −0.696495 | − | 0.717562i | \(-0.745258\pi\) | ||||
−0.696495 | + | 0.717562i | \(0.745258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00901e28 | 0.367686 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56037e28 | 1.94478 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.07413e28 | 1.70367 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.16078e27 | 0.0374194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.42589e28 | −1.06051 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.16512e28 | −0.941009 | −0.470505 | − | 0.882398i | \(-0.655928\pi\) | ||||
−0.470505 | + | 0.882398i | \(0.655928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.41639e28 | 1.26125 | 0.630623 | − | 0.776090i | \(-0.282800\pi\) | ||||
0.630623 | + | 0.776090i | \(0.282800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.33171e27 | −0.118847 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.26362e28 | 1.38763 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.93269e28 | 0.996334 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.22243e28 | −2.24571 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.34758e27 | 0.101768 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.48766e27 | −0.191018 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.12730e29 | 2.43954 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.19115e26 | 0.00247905 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.65965e28 | 1.73352 | 0.866760 | − | 0.498725i | \(-0.166198\pi\) | ||||
0.866760 | + | 0.498725i | \(0.166198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.04694e28 | −0.971919 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.99322e28 | −1.66630 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.71643e28 | −1.19749 | −0.598745 | − | 0.800940i | \(-0.704334\pi\) | ||||
−0.598745 | + | 0.800940i | \(0.704334\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.70908e29 | −2.93260 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.66328e28 | 0.274710 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.66811e28 | −1.37820 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.16142e29 | −1.77793 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.28272e28 | 0.926122 | 0.463061 | − | 0.886326i | \(-0.346751\pi\) | ||||
0.463061 | + | 0.886326i | \(0.346751\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.04538e27 | −0.0290369 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.53040e28 | −0.209264 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.00019e28 | 1.18553 | 0.592766 | − | 0.805375i | \(-0.298036\pi\) | ||||
0.592766 | + | 0.805375i | \(0.298036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.12816e28 | 0.904625 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.59547e29 | 4.39676 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.19277e29 | −1.40565 | −0.702824 | − | 0.711364i | \(-0.748078\pi\) | ||||
−0.702824 | + | 0.711364i | \(0.748078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.14674e29 | −1.30253 | −0.651265 | − | 0.758851i | \(-0.725761\pi\) | ||||
−0.651265 | + | 0.758851i | \(0.725761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.36671e28 | −0.368623 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.21928e27 | 0.0867604 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.51949e28 | −0.256429 | −0.128214 | − | 0.991746i | \(-0.540925\pi\) | ||||
−0.128214 | + | 0.991746i | \(0.540925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.68929e29 | 2.63945 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.17974e28 | −0.111670 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.57590e27 | 0.0326487 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.03653e28 | 0.355526 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.22050e28 | −0.358644 | −0.179322 | − | 0.983790i | \(-0.557390\pi\) | ||||
−0.179322 | + | 0.983790i | \(0.557390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.40104e28 | 0.442860 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.28945e29 | −1.02032 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.61710e29 | −1.23499 | −0.617495 | − | 0.786575i | \(-0.711852\pi\) | ||||
−0.617495 | + | 0.786575i | \(0.711852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.10100e29 | −1.54881 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.72629e29 | 2.65183 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.18099e28 | −0.562113 | −0.281057 | − | 0.959691i | \(-0.590685\pi\) | ||||
−0.281057 | + | 0.959691i | \(0.590685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.09704e28 | 0.139131 | 0.0695657 | − | 0.997577i | \(-0.477839\pi\) | ||||
0.0695657 | + | 0.997577i | \(0.477839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.20111e29 | −0.769574 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.55894e29 | 0.964711 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.39211e29 | 0.832131 | 0.416066 | − | 0.909335i | \(-0.363409\pi\) | ||||
0.416066 | + | 0.909335i | \(0.363409\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.76990e29 | 1.02204 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.30715e28 | 0.0729280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.57634e29 | −0.849795 | −0.424898 | − | 0.905241i | \(-0.639690\pi\) | ||||
−0.424898 | + | 0.905241i | \(0.639690\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.94564e29 | 1.53459 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.96390e29 | 0.988836 | 0.494418 | − | 0.869224i | \(-0.335381\pi\) | ||||
0.494418 | + | 0.869224i | \(0.335381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.32870e29 | −1.13334 | −0.566671 | − | 0.823944i | \(-0.691769\pi\) | ||||
−0.566671 | + | 0.823944i | \(0.691769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.12270e30 | −5.28202 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.68661e29 | −0.767168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.12554e29 | −0.934824 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.57035e28 | −0.0667864 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.68539e29 | 1.51583 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.44143e29 | −0.971261 | −0.485631 | − | 0.874164i | \(-0.661410\pi\) | ||||
−0.485631 | + | 0.874164i | \(0.661410\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.76435e29 | 2.60308 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.44123e27 | 0.00908835 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.34136e27 | 0.00483150 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.92865e29 | −2.76338 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.44014e28 | −0.116029 | −0.0580145 | − | 0.998316i | \(-0.518477\pi\) | ||||
−0.0580145 | + | 0.998316i | \(0.518477\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.55690e29 | 1.48749 | 0.743745 | − | 0.668463i | \(-0.233048\pi\) | ||||
0.743745 | + | 0.668463i | \(0.233048\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.38582e29 | −0.437855 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.99700e29 | 1.52832 | 0.764161 | − | 0.645026i | \(-0.223153\pi\) | ||||
0.764161 | + | 0.645026i | \(0.223153\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.70470e28 | 0.0504754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.74726e29 | 1.64763 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.87688e29 | 0.798607 | 0.399303 | − | 0.916819i | \(-0.369252\pi\) | ||||
0.399303 | + | 0.916819i | \(0.369252\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.39740e29 | −0.644475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.16778e29 | 1.08510 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.60817e29 | 1.16207 | 0.581034 | − | 0.813879i | \(-0.302648\pi\) | ||||
0.581034 | + | 0.813879i | \(0.302648\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.94237e29 | 0.718756 | 0.359378 | − | 0.933192i | \(-0.382989\pi\) | ||||
0.359378 | + | 0.933192i | \(0.382989\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.72339e29 | −0.407841 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.15585e29 | −0.494300 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.35833e29 | −0.746109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.22226e27 | 0.0198547 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.15912e28 | 0.0659143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.64032e29 | −0.938403 | −0.469202 | − | 0.883091i | \(-0.655458\pi\) | ||||
−0.469202 | + | 0.883091i | \(0.655458\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.17106e29 | −0.229556 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.90684e29 | −0.742411 | −0.371206 | − | 0.928551i | \(-0.621056\pi\) | ||||
−0.371206 | + | 0.928551i | \(0.621056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.99408e29 | 0.367374 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.22168e30 | −2.18230 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.80255e29 | 0.312227 | 0.156113 | − | 0.987739i | \(-0.450103\pi\) | ||||
0.156113 | + | 0.987739i | \(0.450103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52044e29 | −0.255399 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.04334e30 | 1.69972 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.02684e28 | 0.0636301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.69163e28 | −0.148552 | −0.0742758 | − | 0.997238i | \(-0.523665\pi\) | ||||
−0.0742758 | + | 0.997238i | \(0.523665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.24193e29 | −0.184671 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.96350e29 | −0.716057 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.34700e29 | −1.30836 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.05265e30 | 1.42980 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.44452e29 | 0.717663 | 0.358831 | − | 0.933402i | \(-0.383175\pi\) | ||||
0.358831 | + | 0.933402i | \(0.383175\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.78160e29 | 0.483777 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.85645e29 | 1.09970 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.66363e29 | −1.04423 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.34223e30 | 1.57052 | 0.785258 | − | 0.619168i | \(-0.212530\pi\) | ||||
0.785258 | + | 0.619168i | \(0.212530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.58041e30 | −4.06725 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.09052e30 | −1.20281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.46126e27 | −0.00799095 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.18296e29 | 0.331039 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.27979e29 | −0.937313 | −0.468657 | − | 0.883380i | \(-0.655262\pi\) | ||||
−0.468657 | + | 0.883380i | \(0.655262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.75805e30 | −1.72469 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00438e30 | 1.90997 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.50300e28 | −0.0324258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.97796e29 | 0.177871 | 0.0889357 | − | 0.996037i | \(-0.471653\pi\) | ||||
0.0889357 | + | 0.996037i | \(0.471653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.40738e30 | 5.59811 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.39744e29 | 0.373308 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.95031e28 | −0.0738323 | −0.0369161 | − | 0.999318i | \(-0.511753\pi\) | ||||
−0.0369161 | + | 0.999318i | \(0.511753\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.08821e28 | 0.0728553 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.22017e28 | 0.0172973 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.59180e29 | 0.120537 | 0.0602687 | − | 0.998182i | \(-0.480804\pi\) | ||||
0.0602687 | + | 0.998182i | \(0.480804\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.76838e29 | −0.130162 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.50012e28 | 0.0679746 | 0.0339873 | − | 0.999422i | \(-0.489179\pi\) | ||||
0.0339873 | + | 0.999422i | \(0.489179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.43956e29 | 0.378376 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.87295e29 | −0.329553 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.94074e29 | 0.193374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.97935e30 | 1.90503 | 0.952516 | − | 0.304488i | \(-0.0984855\pi\) | ||||
0.952516 | + | 0.304488i | \(0.0984855\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.81382e30 | −2.99325 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.92664e30 | −1.76981 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.10128e29 | 0.476482 | 0.238241 | − | 0.971206i | \(-0.423429\pi\) | ||||
0.238241 | + | 0.971206i | \(0.423429\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.17070e29 | 0.181391 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.84872e29 | 0.492426 | 0.246213 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246213 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.11590e30 | 1.68685 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.67826e30 | −4.57075 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.91968e29 | 0.0983732 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.59763e29 | 0.129524 | 0.0647620 | − | 0.997901i | \(-0.479371\pi\) | ||||
0.0647620 | + | 0.997901i | \(0.479371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.59275e30 | −3.68407 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.97566e30 | 1.87726 | 0.938630 | − | 0.344925i | \(-0.112096\pi\) | ||||
0.938630 | + | 0.344925i | \(0.112096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.13750e29 | −0.0522738 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.02402e30 | 1.79986 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.59102e29 | −0.417562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.46556e29 | 0.0621109 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.78484e30 | 1.97410 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.41300e30 | 0.969228 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.54080e30 | 0.602577 | 0.301288 | − | 0.953533i | \(-0.402583\pi\) | ||||
0.301288 | + | 0.953533i | \(0.402583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.10251e30 | −1.94301 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.46971e30 | −0.915784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.55750e29 | 0.128463 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.72833e30 | 0.959493 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.29587e29 | 0.0443862 | 0.0221931 | − | 0.999754i | \(-0.492935\pi\) | ||||
0.0221931 | + | 0.999754i | \(0.492935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.81029e30 | −0.937585 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.96663e30 | −2.26403 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.70386e28 | −0.0243891 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.35287e30 | 1.34251 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.84510e30 | 2.65785 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.25920e30 | −0.661449 | −0.330724 | − | 0.943727i | \(-0.607293\pi\) | ||||
−0.330724 | + | 0.943727i | \(0.607293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.17856e30 | 1.19209 | 0.596043 | − | 0.802953i | \(-0.296739\pi\) | ||||
0.596043 | + | 0.802953i | \(0.296739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.91617e29 | 0.136671 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.39600e30 | −0.378209 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.51224e29 | 0.119141 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.39855e30 | −0.359911 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.32971e29 | −0.0333543 | −0.0166772 | − | 0.999861i | \(-0.505309\pi\) | ||||
−0.0166772 | + | 0.999861i | \(0.505309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.12434e30 | −0.274915 | −0.137457 | − | 0.990508i | \(-0.543893\pi\) | ||||
−0.137457 | + | 0.990508i | \(0.543893\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.30728e28 | 0.00788324 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.53339e30 | −0.821077 | −0.410539 | − | 0.911843i | \(-0.634659\pi\) | ||||
−0.410539 | + | 0.911843i | \(0.634659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.22988e30 | 0.731751 | 0.365875 | − | 0.930664i | \(-0.380770\pi\) | ||||
0.365875 | + | 0.930664i | \(0.380770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.95077e30 | 1.97720 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.88384e29 | −0.0621152 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.43031e29 | −0.0930521 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.55374e31 | 3.18245 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.24571e30 | 0.248838 | 0.124419 | − | 0.992230i | \(-0.460293\pi\) | ||||
0.124419 | + | 0.992230i | \(0.460293\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.70155e30 | −0.721150 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.79590e31 | −3.41265 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.14276e30 | 0.953237 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.40129e30 | −0.976611 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.72934e30 | −0.834200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.63544e30 | −1.31393 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.54885e30 | −1.09951 | −0.549757 | − | 0.835325i | \(-0.685280\pi\) | ||||
−0.549757 | + | 0.835325i | \(0.685280\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.90483e30 | −1.45875 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.91673e30 | 0.306381 | 0.153191 | − | 0.988197i | \(-0.451045\pi\) | ||||
0.153191 | + | 0.988197i | \(0.451045\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.28266e30 | −0.356051 | −0.178026 | − | 0.984026i | \(-0.556971\pi\) | ||||
−0.178026 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.02058e31 | −1.55352 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.87662e30 | −1.17011 | −0.585055 | − | 0.810994i | \(-0.698927\pi\) | ||||
−0.585055 | + | 0.810994i | \(0.698927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.59092e30 | 0.520639 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.31067e31 | 3.26992 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.61814e29 | 0.0914173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.50014e29 | 0.0337112 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.23662e30 | 1.08418 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.84817e30 | 1.00852 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.25742e31 | −1.57756 | −0.788778 | − | 0.614678i | \(-0.789286\pi\) | ||||
−0.788778 | + | 0.614678i | \(0.789286\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.17509e31 | 1.43942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.18000e29 | −0.0619560 | −0.0309780 | − | 0.999520i | \(-0.509862\pi\) | ||||
−0.0309780 | + | 0.999520i | \(0.509862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.26502e30 | −0.498120 | −0.249060 | − | 0.968488i | \(-0.580122\pi\) | ||||
−0.249060 | + | 0.968488i | \(0.580122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.30065e31 | 1.48339 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.39563e31 | 1.55444 | 0.777218 | − | 0.629232i | \(-0.216630\pi\) | ||||
0.777218 | + | 0.629232i | \(0.216630\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.45819e28 | −0.00920045 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.74515e30 | −0.291643 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.88366e30 | −0.299229 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.18160e31 | −1.19765 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.57054e30 | 0.353520 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.64773e30 | 0.449536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.65743e30 | −0.818048 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.80149e30 | 0.443256 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.29006e30 | 0.477145 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.99799e30 | −0.704862 | −0.352431 | − | 0.935838i | \(-0.614645\pi\) | ||||
−0.352431 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.57855e31 | −3.08168 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.04758e30 | 0.508907 | 0.254454 | − | 0.967085i | \(-0.418104\pi\) | ||||
0.254454 | + | 0.967085i | \(0.418104\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.00733e28 | 0.00740718 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.41034e31 | 1.93712 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.30632e30 | 0.652425 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.36741e31 | 1.81744 | 0.908719 | − | 0.417408i | \(-0.137061\pi\) | ||||
0.908719 | + | 0.417408i | \(0.137061\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.88598e31 | 2.91591 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.65037e30 | 0.121050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.96435e29 | −0.0571034 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.26169e31 | −5.08980 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.41968e31 | −1.65803 | −0.829016 | − | 0.559226i | \(-0.811099\pi\) | ||||
−0.829016 | + | 0.559226i | \(0.811099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.95912e29 | −0.0198240 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.46773e31 | 2.27137 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.60412e30 | 0.102734 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.58736e30 | −0.537767 | −0.268883 | − | 0.963173i | \(-0.586655\pi\) | ||||
−0.268883 | + | 0.963173i | \(0.586655\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.27148e30 | −0.384044 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.47302e30 | −0.327745 | −0.163872 | − | 0.986482i | \(-0.552399\pi\) | ||||
−0.163872 | + | 0.986482i | \(0.552399\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.93652e31 | 1.13410 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.20183e31 | −3.55211 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.44243e31 | 1.36819 | 0.684096 | − | 0.729392i | \(-0.260197\pi\) | ||||
0.684096 | + | 0.729392i | \(0.260197\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.67536e29 | −0.0475327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.23960e31 | −2.27211 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.04469e31 | 0.547661 | 0.273831 | − | 0.961778i | \(-0.411709\pi\) | ||||
0.273831 | + | 0.961778i | \(0.411709\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.52889e30 | 0.180968 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.35133e30 | −0.0677931 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.26791e30 | 0.258549 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.73329e30 | −0.275301 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.21469e31 | 0.570675 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.81884e31 | −1.29579 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.41008e31 | −1.53386 | −0.766931 | − | 0.641729i | \(-0.778217\pi\) | ||||
−0.766931 | + | 0.641729i | \(0.778217\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.80190e31 | 1.67340 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.17245e31 | 1.36645 | 0.683224 | − | 0.730209i | \(-0.260577\pi\) | ||||
0.683224 | + | 0.730209i | \(0.260577\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.71972e31 | 0.724890 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.72435e29 | 0.0153639 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.33987e31 | 0.944710 | 0.472355 | − | 0.881408i | \(-0.343404\pi\) | ||||
0.472355 | + | 0.881408i | \(0.343404\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.28774e30 | 0.0508872 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.28704e32 | 4.97814 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.15166e28 | 0.000436024 0 | 0.000218012 | − | 1.00000i | \(-0.499931\pi\) | ||||
0.000218012 | 1.00000i | \(0.499931\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35156e31 | 0.500906 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.06852e31 | −1.11326 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.11067e30 | −0.323586 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.52057e31 | −0.528730 | −0.264365 | − | 0.964423i | \(-0.585162\pi\) | ||||
−0.264365 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.78170e31 | −1.62785 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.90579e31 | −1.30187 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.15395e31 | −1.35569 | −0.677847 | − | 0.735203i | \(-0.737087\pi\) | ||||
−0.677847 | + | 0.735203i | \(0.737087\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.08787e32 | 3.47649 |
(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 | 8.22.a.b.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 72.22.a.f.1.2 | 3 | |||
4.3 | odd | 2 | 16.22.a.f.1.1 | 3 | |||
8.3 | odd | 2 | 64.22.a.m.1.3 | 3 | |||
8.5 | even | 2 | 64.22.a.l.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.22.a.b.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.22.a.f.1.1 | 3 | 4.3 | odd | 2 | |||
64.22.a.l.1.1 | 3 | 8.5 | even | 2 | |||
64.22.a.m.1.3 | 3 | 8.3 | odd | 2 | |||
72.22.a.f.1.2 | 3 | 3.2 | odd | 2 |