Need ideas for a character's appearance?

-like for what would suit their personality and match best



it's a character for an anime or cartoon i made up, but the character will be a minor not the main one



i mainly want hairstyle ideas[i decided most of the rest..] but other ideas are ok too.



i already chose the hair to be black or purple or any color that won't be bright like

yellow/blonde/pink/etc.



character's traits/personality[this is just *main* stuff, not every detail]:

anti-social, quiet, cold, distant



so i just wanna know what would match her personality best with black/purple hair