when I matched my answers with answer key of some coaching institutes i got 580-590 marks in neet 2021 which colleges can I get gender -female state -Bihar

Hello aspirant
Hope you are doing well
It is difficult to predict the cut off marks or ranks but according to previous year trends your expected rank would lie between 24534 - 29770but it may vary every year depending on the following factors
1. Level of question paper
2. Total no of candidates
3. Category of candidate
4. Total no of seats
5. Marks obtained by students
Here is the link for the expected marks vs ranks
https://medicine.careers360.com/articles/neet-result-marks-vs-rank
You have not mentioned your category so assuming that you are from general category so according to the cut off trends the cut off for various colleges are
1. Indira Gandhi Institute of Medical Sciences, Patna - 607 marks
2. Jawaharlal Nehru Medical College, Bhagalpur -596 marks
3. Government Medical College, Bettiah - 577 marks
4. Patna Medical College, Patna - 617 marks
Last cut off was 577 marks for general category
So you have chance to get seats in Medical College.
You can visit the given link to check previous year cut offs
https://medicine.careers360.com/articles/neet-cutoff-bihar
Further you can use college predictor tool to know about the colleges you can get
https://medicine.careers360.com/neet-college-predictor
Good luck
Hope it helps