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

$\displaystyle \zeta_1 + \zeta_2 + \zeta_3 = 1$

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

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


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