Suppose a, b, c, d are complex numbers such that

a + b + c + d = 1
a^2 + b^2 + c^2 + d^2 = 0
a^3 + b^3 + c^3 + d^3 = 1
a^4 + b^4 + c^4 + d^4 = 0

What is a^10 + b^10 + c^10 + d^10?