I dont think 586 is enough to get any seat in any of the top seven IIT even if you are OBC.
IIT Delhi
IIT Bombay
IIT Kanpur
IIT Madras
IIT Kharagpur
IIT Roorkee
IIT Guwahati
IIT Hyderabad
IIT Patna
These are the cutoffs of previous year. But you can be eligible for top NITs.
Best of Luck!
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