n = 45 (m = 22): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_90)
j= 1  simple preclosed piece: 2 segments, length 3.9805 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 41 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 7.8836 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 37 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 11.6332 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 33 = -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= 4  simple preclosed piece: 2 segments, length 15.1564 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 29 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 18.3846 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 25 = -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= 6  simple preclosed piece: 2 segments, length 21.2549 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 21 = -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= 7  simple preclosed piece: 2 segments, length 23.7116 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 17 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 25.7067 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 13 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 27.2015 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  9 = -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=10  simple preclosed piece: 2 segments, length 28.1668 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  5 = -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=11  simple preclosed piece: 2 segments, length 28.5839 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  1 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 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 28.4447 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 42 = -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=13  simple preclosed piece: 2 segments, length 27.7518 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=14  simple preclosed piece: 2 segments, length 26.5187 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=15  simple preclosed piece: 2 segments, length 24.7695 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -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=16  simple preclosed piece: 2 segments, length 22.5382 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=17  simple preclosed piece: 2 segments, length 19.8682 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=18  simple preclosed piece: 2 segments, length 16.8114 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -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=19  simple preclosed piece: 2 segments, length 13.4275 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
j=20  simple preclosed piece: 2 segments, length 9.7822 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -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=21  simple preclosed piece: 2 segments, length 5.9466 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -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=22  simple preclosed piece: 2 segments, length 1.9951 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 45 = n/gcd(n,j); closed trajectory: 90 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [45, 45, 15, 45, 9, 15, 45, 45, 5, 9, 45, 15, 45, 45, 3, 45, 45, 5, 45, 9, 15, 45] ; gcd = 1 ; a quotient equals n: True
DONE [2.7s]
