C NCLFORTSTART
      subroutine ftslow(npts,r, kmax,a0,a,b)
      implicit none
      integer npts, kmax
      real r(npts)
      real a(kmax),b(kmax), a0
C NCLEND
      integer n, k
      real pi, arg, coef

      a0 = 0.0
      do n=1,npts
         a0 = a0+r(n)
      end do
      a0 = a0/npts            !  average

      pi  = 4.0*atan(1.0)
      arg = (2.0/npts)*pi
      do k=1,kmax
         a(k) = 0.0
         b(k) = 0.0
        do n=1,npts
           coef = (2.0/npts)*r(n)
           a(k) = a(k) + coef*cos(k*(n-1)*arg) 
           b(k) = b(k) + coef*sin(k*(n-1)*arg) 
        end do
      end do

      if (mod(npts,2).eq.0) then
          a(kmax) = a(kmax)/2.0
          b(kmax) = 0.0              ! numerical 
      end if

      return
      end