Set 256 color prompt in zsh/kitty/tmux

This problem is only for the Kitty terminal (works in alacritty, Hyper; problem exists both on macos and arch linux) currently set my terminal with

PS1='%B%F{magenta}%3~ ${vim_mode}%f%b '

this sets the prompt to magenta in both the base terminal and tmux. however, if I use a 256 color number like 170 in place of magenta, the prompt color gets set in the base terminal but not tmux. is there a way to fix this?