\zeta_1, \zeta_2,  \zeta_3 are complex numbers such that

\zeta_1 + \zeta_2 + \zeta_3 = 1

\zeta_1^{2} + \zeta_2^{2} + \zeta_3^{2} = 3

\zeta_1^{3} + \zeta_2^{3} + \zeta_3^{3} = 7


Compute \zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}.