| $x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
| $a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$16$ |
$0$ |
$160$ |
$0$ |
$1792$ |
$0$ |
$21504$ |
$0$ |
$270336$ |
| $a_2$ |
$1$ |
$1$ |
$6$ |
$17$ |
$78$ |
$322$ |
$1516$ |
$7205$ |
$35734$ |
$180494$ |
$929940$ |
$4857866$ |
$25687052$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=2\right)\colon$ |
$1$ |
$2$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=4\right)\colon$ |
$6$ |
$8$ |
$16$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=6\right)\colon$ |
$17$ |
$34$ |
$72$ |
$160$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=8\right)\colon$ |
$78$ |
$152$ |
$336$ |
$768$ |
$1792$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=10\right)\colon$ |
$322$ |
$708$ |
$1616$ |
$3776$ |
$8960$ |
$21504$ |
| $\left(\mathrm{E}\left[a_1^{e_1}a_2^{e_2}\right]:\sum ie_i=12\right)\colon$ |
$1516$ |
$3408$ |
$7968$ |
$18944$ |
$45568$ |
$110592$ |
$270336$ |
$\mathrm{E}\left[\chi_i\chi_j\right] = \begin{bmatrix}1&0&0&1&0&3&0&0&0&0\\0&2&0&0&4&0&2&0&6&0\\0&0&5&1&0&0&0&8&0&11\\1&0&1&6&0&7&0&8&0&3\\0&4&0&0&10&0&8&0&16&0\\3&0&0&7&0&14&0&5&0&0\\0&2&0&0&8&0&10&0&14&0\\0&0&8&8&0&5&0&29&0&24\\0&6&0&0&16&0&14&0&28&0\\0&0&11&3&0&0&0&24&0&30\end{bmatrix}$
$\ \ \ \mathrm{E}\left[\chi_i^2\right] = \begin{bmatrix}1&2&5&6&10&14&10&29&28&30\end{bmatrix}$
| $-$ | $a_2\in\mathbb{Z}$ | $a_2=-2$ | $a_2=-1$ | $a_2=0$ | $a_2=1$ | $a_2=2$ |
|---|
| $-$ | $1$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
| $a_1=0$ | $1/2$ | $0$ | $0$ | $0$ | $0$ | $0$ | $0$ |
|---|
