| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$4$ |
$0$ |
$32$ |
$0$ |
$320$ |
$0$ |
$3584$ |
$0$ |
$43008$ |
$0$ |
$540672$ |
| $a_2$ |
$1$ |
$3$ |
$10$ |
$37$ |
$150$ |
$654$ |
$3012$ |
$14445$ |
$71398$ |
$361114$ |
$1859628$ |
$9716194$ |
$51373180$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$3$ |
$4$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$10$ |
$16$ |
$32$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$37$ |
$68$ |
$144$ |
$320$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$150$ |
$304$ |
$672$ |
$1536$ |
$3584$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$654$ |
$1416$ |
$3232$ |
$7552$ |
$17920$ |
$43008$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$3012$ |
$6816$ |
$15936$ |
$37888$ |
$91136$ |
$221184$ |
$540672$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&2&1&0&3&0&2&0&4\\0&4&0&0&8&0&4&0&12&0\\2&0&5&5&0&8&0&10&0&11\\1&0&5&10&0&9&0&20&0&13\\0&8&0&0&20&0&16&0&32&0\\3&0&8&9&0&14&0&21&0&20\\0&4&0&0&16&0&20&0&28&0\\2&0&10&20&0&21&0&49&0&32\\0&12&0&0&32&0&28&0&56&0\\4&0&11&13&0&20&0&32&0&30\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&4&5&10&20&14&20&49&56&30\end{bmatrix}$
$\mathrm{Pr}[a_i=n]=0$ for $i=1,2$ and $n\in\mathbb{Z}$.
