Computation of the center of the Burnside group $B_0(2,5)$

Let $B_0(2,5)=\langle a_1,a_2 \rangle$ be the largest two generator Burnside group of exponent five. It has the order $5^{34}$. There is a power commutator presentation of $B_0(2,5)$. In this case every element of the group can be represented uniquely as $a_1^{\alpha_1}\cdot a_2^{\alpha_2}\cdot\ldots\cdot a_{34}^{\alpha_{34}}$, $\alpha_i \in \mathbb{Z}_5$, $i=1,\ldots,34$. Here $a_1$ and $a_2$ are generators of $B_0(2,5)$, commutators $a_3,\ldots,a_{34}$ are defined recursively by $a_1$ and $a_2$. Using a supercomputer, we have calculated the elements of the center of $B_0(2,5)$ in the form of group words of the smallest length for the symmetric generating set $\{ a_1,a_1^{-1},a_2,a_2^{-1}\}$.