Counting Powers of a Complex Number That Are Real

How many of the 2025 numbers in the list $$(1 + i)^1,\quad (1 + i)^{1 + 2},\quad (1 + i)^{1 + 2 + 3},\dots,\quad (1 + i)^{1 + 2 + 3 + \ldots + 2025} $$are positive real numbers? (Here, $ i = \sqrt{-1} $.)