On R. Chapman's "evil determinant": case p=1 (mod 4)
  For p=1 (mod 4), we prove the formula (conjectured by R. Chapman) for the determinant of the matrix C with C(i,j)=LegendreSymbol(j-i,p), i,j=0,...,(p-1)/2. 
Maxim Vsemirnov
math.NT