The four typical nasal vowels are /œ̃, ɔ̃, ɛ̃, ã/ as in un bon vin blanc.

In what is called Parisian French, /œ̃/ has been absorbed into /ɛ̃/, leaving only three distinct nasals. Hence, brun sounds like brin and so on. And yup, it affects un, which is otherwise /œ̃/, not /ã/.

You don’t need to emulate this pronunciation. You can if you want, but it probably won’t please your teacher. And it may not even please Parisians, because when you make a distinction between sounds, people who don’t make that distinction usually don’t hear it anyway.

And it goes without saying that Parisian is only one of many interesting dialects of the language. Others have other variations of the classic four nasal vowels.

Added based on comments: in some accents, including Parisian, /ɛ̃/ is realized [æ᷈] (tongue a little bit lower / mouth more open). Thus /œ̃/ and /ɛ̃/ are both realized [æ᷈].