What does the left paw mean in maneki-neko?

Could you please explain the significance of the left paw in the Japanese figurine known as the maneki-neko? I'm particularly curious about the traditional beliefs and superstitions associated with this gesture, and how it's interpreted in different contexts. I've heard that it's often used as a symbol of good luck and prosperity, but I'd like to know more about the specifics behind this symbolism.