High resolution photoelectron spectra of C(2)N(-), C(4)N(-), and C(6)N(-) anions are reported, obtained using slow electron velocity-map imaging. The spectra show well resolved transitions to the X (2)Pi neutral ground state of all three species and to the a (4)Sigma(-) excited state of C(2)N and C(4)N. This study yields the adiabatic electron affinity of C(2)N, C(4)N, and C(6)N, the spin-orbit splitting in the X (2)Pi state of each radical, and the term energy of the a (4)Sigma(-) state in C(2)N and C(4)N. Relatively little vibrational activity is observed, indicating small geometry changes upon photodetachment. This result, plus the observation of transitions to neutral quartet states, indicates that the C(2n)N(-) (n=1-3) anions all have linear (3)Sigma(-) ground states.