\[\large \cfrac { 1 }{ 503 } ,\cfrac { 4 }{ 524 } ,\cfrac { 9 }{ 581 } ,\cfrac { 16 }{ 692 } , \dots, \frac{ n^2 } { 500 + 3 n ^ 3 }, \ldots \]

Find the largest term of the sequence above. Give your answer to 3 decimal places.

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