\p 300

x = exp(log(2)/3)*exp(2*I*Pi/3)
t = (x*(x+1) + 3)/15
s = (x - 8)/15

f(z, n, j) = sin(Pi*j*n*(2*z-t-s))/(j*sin(Pi*j*t*n)*sin(Pi*j*s*n))

g(z, n) = suminf(j = 1, n*f(z, 1, j) - f(z, n, j))

exp(-g(-1/3, 5)/(2*I))
algdep(%, 6)