Hello Dear,

As the percentile mentioned by you the General AIR rank must be between 573996 - 400110. As your category must be little less. There is a very less chance that you can get any government colleges on your rank. but as you know cut off depends upon the number of seats available, the difficulty level of paper and number of candidates writing the examination. And, hence varies every year depending on these factors. You can check the rank vs percentile vs marks below:

https://engineering.careers360.com/articles/jee-main-marks-vs-percentile

You can check our predictors link to know more about the college which you can get

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Good Luck