python3 -c 'import math
x=[3,0,-1,0,-1]
for m in range(1,6):
 e=[math.sqrt(1/3)*math.sin(j*m*math.pi/6) for j in range(1,6)]
 print(m,sum(x[j]*e[j] for j in range(5)),2*math.sin(m*math.pi/12))'