The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves

For a partition lambda = {lambda(1) =lambda(2) >= lambda(3) >= 0} of non-negative integers, we calculate the Euler characteristic of the local system V-lambda on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some lambda of low degree, we make a guess for the motivic Euler characteristic of V-lambda using counting curves over finite fields.