n = 15 (m = 7): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_30)
j= 1  simple preclosed piece: 2 segments, length 3.8271 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 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 6.9924 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 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 8.9487 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 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 9.3577 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 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 8.1487 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -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= 6  simple preclosed piece: 2 segments, length 5.5306 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  5 = n/gcd(n,j); closed trajectory: 10 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 1.9563 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 15 = n/gcd(n,j); closed trajectory: 30 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [15, 15, 5, 15, 3, 5, 15] ; gcd = 1 ; a quotient equals n: True
DONE [0.1s]
