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.