n = 39 (m = 19): trajectories parallel to the side X_0 X_(n-1); exact arithmetic in Q(zeta_78)
j= 1  simple preclosed piece: 2 segments, length 3.9741 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 35 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 7.8453 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 31 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 11.5133 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 27 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 14.8831 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 23 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 17.8674 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 19 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 20.3890 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 15 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 22.3825 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 11 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 23.7963 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  7 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 24.5938 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  3 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 24.7544 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 38 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 24.2738 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 34 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 23.1645 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 30 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 21.4553 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 26 = -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=14  simple preclosed piece: 2 segments, length 19.1904 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 22 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 16.4285 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 18 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 13.2411 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 14 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 9.7108 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b = 10 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 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 5.9289 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  6 = -4j mod n; factor 13 = n/gcd(n,j); closed trajectory: 26 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 1.9935 = lambda sin(2j pi/n)/sin(pi/n) (exact); x_2 = r^b x_0 with b =  2 = -4j mod n; factor 39 = n/gcd(n,j); closed trajectory: 78 segments   [t = 3/10, 1/7, 5/9; midpoint t = 1/2: 1 segment, half the length, same factor]
factors d_1..d_m: [39, 39, 13, 39, 39, 13, 39, 39, 13, 39, 39, 13, 3, 39, 13, 39, 39, 13, 39] ; gcd = 1 ; a quotient equals n: True
DONE [2.7s]
