python3 -c 'import math
s=math.sqrt(3);b=math.sqrt(2)
def f(j,m):return math.sqrt(1/3)*(math.sin((j+1)*m*math.pi/6)-math.sin(j*m*math.pi/6))
def C(r,p,q,t):return sum(f(j,r)*f(j,p)*f(j,q)*f(j,t) for j in range(6))
w=[0,math.sqrt(2-s),1,math.sqrt(2),math.sqrt(3),math.sqrt(2+s)];a=[0,0,2,math.sqrt(3),2,0]
T=(3,4,4);P=(2,2);O=sum(w[i] for i in T)
for p in range(1,6):
 print(p,C(1,p,*P),C(p,*T),w[p]**2-O**2,C(1,p,*P)*C(p,*T)*math.prod(a[i] for i in T)*math.prod(a[i] for i in P)/(w[p]**2-O**2))'