Dealing with Z[Sqrt(-13)], let J = (7, -1+Sqrt(-13) ). ie - J is the ideal generate by 7 & -1+Sqrt(-13)
Find an integer N s.t. J^2 = (49, n+Sqrt(-13) )
Not being an algebraist, I'm not 100% sure of this, but it looks to me as though J^2 should contain the elements , and . Therefore it will also contain . So I would go for n=6.