n = 27 (m = 13): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_54)
j= 1  simple preclosed piece: 2 segments, length 3.9461 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 2  simple preclosed piece: 2 segments, length 7.6794 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 3  simple preclosed piece: 2 segments, length 10.9988 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 4  simple preclosed piece: 2 segments, length 13.7252 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 5  simple preclosed piece: 2 segments, length 15.7117 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 6  simple preclosed piece: 2 segments, length 16.8511 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 7  simple preclosed piece: 2 segments, length 17.0821 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 8  simple preclosed piece: 2 segments, length 16.3922 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j= 9  simple preclosed piece: 2 segments, length 14.8186 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  3 = n/gcd(n,j); closed trajectory: 6 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=10  simple preclosed piece: 2 segments, length 12.4462 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=11  simple preclosed piece: 2 segments, length 9.4027 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=12  simple preclosed piece: 2 segments, length 5.8523 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  9 = n/gcd(n,j); closed trajectory: 18 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=13  simple preclosed piece: 2 segments, length 1.9865 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 27 = n/gcd(n,j); closed trajectory: 54 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [27, 27, 9, 27, 27, 9, 27, 27, 3, 27, 27, 9, 27] ; gcd = 3 ; a quotient equals n: False
DONE [0.6s]
