I wonder if there is a relationship to e^(πi) = -1. Are there any other pair of numbers (other than multiple of these e and π) that have this relationship? Pe

I wonder if there is a relationship to e^(πi) = -1. Are there any other pair of numbers (other than multiple of these e and π) that have this relationship? Perhaps these two numbers sharing that relationship are why they appear so commonly in our current mathematical equations.