Lusztig's conjecture for uniform almost characters in type F4

Let $\operatorname{\bf{G}}_0$ be a simple group of type $F_4$, and let $F_0$ be the generalized Frobenius map defining a Ree group of type $F_4$. Write $\operatorname{\bf{G}}_0^{F_0^2}$ for the fixed-point group and $\langle F_0\rangle$ for the cyclic group generated by $F_0$. Lusztig's conjecture for type $F_4$. The values of the uniform almost characters of $\operatorname{\bf{G}}_0^{F_0^2}\rtimes\langle F_0\rangle$ on the coset $\operatorname{\bf{G}}_0^{F_0^2}F_0$ are given in Table~, after replacing each $u_i$ by its Shintani correspondent $N_{F_0/F_0^2}(u_i)$. This is a conjectural extension of the algorithm for uniform almost characters from the disconnected case of type $B_2$ to disconnected type $F_4$; the source does not report a resolution of this specific assertion.