Classifying all Hecke Characters of a given field and a given conductor

Question

I'm rather very new to this topics and in the hopes of understanding Tate's Thesis I have come to the issue of Hecke Character. Given the following definition: Let $F$ be a number field and let $\mathbb{I}_F$ be the idele group of $F$. A Hecke Character of $F$ is a continuous (not necessarily unitary) homomorphism: \begin{align*} \chi : \mathbb{I}_F/F^\times \to \mathbb{C}^\times \end{align*} where $F^\times$ is the group of non-zero of $F$ and $\mathbb{C}^\times$ is the group of non-zero complex numbers.

I would be thankful if you could guide me on how I can Classify all the Dirichlet Characters in the following cases

1. Field $\mathbb{Q}$ with conductor 25. (I know that in this case I can simplify things to the case of Dirichlet Characters mod 25 but I'm not sure how to proceed from here)
2. Field $\mathbb{Q}(i)$ with conductor 2.
3. Field $\mathbb{Q}(\sqrt{5})$ with conductor $(5)$