Amir and Amani can exclude up to $500,000 of long-term capital gains from the sale of their primary residence, given that they meet the ownership and use tests. They are married and file a joint return, so they qualify for the higher exclusion amount.
Since they had a long-term capital gain of $650,000 from the sale of their home, they can exclude $500,000 from taxable income. This means that the amount of the long-term capital gain that they will need to report on their tax return will be:
\[ 650,000 - 500,000 = 150,000 \]
Therefore, they will need to report $150,000 of the long-term capital gain on their return.