n = 21 (m = 10): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_42)
j= 1  simple preclosed piece: 2 segments, length 3.9111 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 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 7.4748 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 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 10.3742 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 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 12.3519 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 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 13.2320 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 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 12.9364 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 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 11.4914 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -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= 8  simple preclosed piece: 2 segments, length 9.0253 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 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 5.7573 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor  7 = n/gcd(n,j); closed trajectory: 14 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 1.9777 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 21 = n/gcd(n,j); closed trajectory: 42 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [21, 21, 7, 21, 21, 7, 3, 21, 7, 21] ; gcd = 1 ; a quotient equals n: True
DONE [0.4s]
