Let $S ^ { 1 } = \{ z \in \mathbb { C } | | z \mid = 1 \}$ be the unit circle in the complex plane. Let $f : S ^ { 1 } \rightarrow S ^ { 1 }$ be the map given by $f ( z ) = z ^ { 2 }$. We define $f ^ { ( 1 ) } : = f$ and $f ^ { ( k + 1 ) } : = f \circ f ^ { ( k ) }$ for $k \geq 1$. The smallest positive integer $n$ such that $f ^ { ( n ) } ( z ) = z$ is called the period of $z$. Determine the total number of points in $S ^ { 1 }$ of period 2025. (Hint: $2025 = 3 ^ { 4 } \times 5 ^ { 2 }$)