Consider equations of the form: a² + b² = N, 0 a b, a, b and N integer.

For N=65 there are two solutions:

a=1, b=8 and a=4, b=7.

We call S(N) the sum of the values of a of all solutions of a² + b² = N, 0 a b, a, b and N integer.

Thus S(65) = 1 + 4 = 5.

Find S(N), for all squarefree N only divisible by primes of the form 4k+1 with 4k+1 150.