| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$10$ |
$0$ |
$70$ |
$0$ |
$588$ |
$0$ |
$5544$ |
$0$ |
$56628$ |
| $a_2$ |
$1$ |
$2$ |
$5$ |
$14$ |
$44$ |
$152$ |
$569$ |
$2270$ |
$9524$ |
$41576$ |
$187348$ |
$866296$ |
$4092400$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$2$ |
$2$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$5$ |
$6$ |
$10$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$14$ |
$20$ |
$36$ |
$70$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$44$ |
$72$ |
$138$ |
$280$ |
$588$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$152$ |
$276$ |
$556$ |
$1168$ |
$2520$ |
$5544$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$569$ |
$1114$ |
$2334$ |
$5044$ |
$11130$ |
$24948$ |
$56628$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&1&0&0&1&0&0&0&1\\0&2&0&0&2&0&0&0&2&0\\1&0&2&1&0&2&0&1&0&2\\0&0&1&3&0&1&0&3&0&1\\0&2&0&0&4&0&2&0&4&0\\1&0&2&1&0&3&0&2&0&3\\0&0&0&0&2&0&4&0&2&0\\0&0&1&3&0&2&0&6&0&2\\0&2&0&0&4&0&2&0&6&0\\1&0&2&1&0&3&0&2&0&4\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&2&3&4&3&4&6&6&4\end{bmatrix}$
$\mathrm{Pr}[a_i=n]=0$ for $i=1,2$ and $n\in\mathbb{Z}$.
