HMMT 2015 U10

Let $b(x)=x^{2}+x+1$. The polynomial $x^{2015}+x^{2014}+\cdots+x+1$ has a unique "base $b(x)$ " representation $$x^{2015}+x^{2014}+\cdots+x+1=\sum_{k=0}^{N} a_{k}(x) b(x)^{k}$$ where

• $N$ is a nonnegative integer;
• each "digit" $a_{k}(x)$ (for $0 \leq k \leq N$ ) is either the zero polynomial (i.e. $a_{k}(x)=0$ ) or a nonzero polynomial of degree less than $\operatorname{deg} b=2$; and
• the "leading digit $a_{N}(x)$ " is nonzero (i.e. not the zero polynomial).

Find $a_{N}(0)$ (the "leading digit evaluated at 0 ").