Conjugacy and the Class Equation · Challenge problem

In the alternating group $A_7$ (order $2520$), the $720$ seven-cycles of $S_7$ split into two $A_7$-conjugacy classes (the $S_7$-centralizer of a $7$-cycle is cyclic of odd order $7$, entirely even, so it satisfies the splitting criterion). How many elements does EACH of the two classes contain?