# examples for languages of natural numbers

I need to find examples for language $$L_i$$ $$i\in[1,3]$$ of natural numbers that is:

1. $$L_1\in$$ $$RE \backslash R$$

2. $$L_2\in$$ $$coRE\backslash R$$

3. $$L_3\in$$ $$\overline{ R \cup RE}$$

My idea was in any case to take a language in the desired language class, and find some sort of function from the language to the natural numbers. But I do not know if this is the right way to approach the problem, and how exactly to find such function.