n=5: orbit of rho under G has 24 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1)  reduced (1, 1)  (4 orbit elements)
    factors (5, 5)  reduced (1, 1)  (20 orbit elements)
    Conjecture 1.7 for n=5: TRUE (0 violating patterns)
n=7: orbit of rho under G has 48 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1)  reduced (1, 1, 1)  (6 orbit elements)
    factors (7, 7, 7)  reduced (1, 1, 1)  (42 orbit elements)
    Conjecture 1.7 for n=7: TRUE (0 violating patterns)
n=9: orbit of rho under G has 72 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1)  reduced (1, 1, 1, 1)  (6 orbit elements)
    factors (3, 3, 1, 3)  reduced (3, 3, 1, 3)  (12 orbit elements)
    factors (9, 9, 3, 9)  reduced (3, 3, 1, 3)  (54 orbit elements)
    Conjecture 1.7 for n=9: TRUE (0 violating patterns)
n=11: orbit of rho under G has 120 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1)  (10 orbit elements)
    factors (11, 11, 11, 11, 11)  reduced (1, 1, 1, 1, 1)  (110 orbit elements)
    Conjecture 1.7 for n=11: TRUE (0 violating patterns)
n=13: orbit of rho under G has 168 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1)  (12 orbit elements)
    factors (13, 13, 13, 13, 13, 13)  reduced (1, 1, 1, 1, 1, 1)  (156 orbit elements)
    Conjecture 1.7 for n=13: TRUE (0 violating patterns)
n=15: orbit of rho under G has 192 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1)  (8 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3)  (24 orbit elements)
    factors (5, 5, 5, 5, 1, 5, 5)  reduced (5, 5, 5, 5, 1, 5, 5)  (40 orbit elements)
    factors (15, 15, 5, 15, 3, 5, 15)  reduced (15, 15, 5, 15, 3, 5, 15)  (120 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=15: FALSE (1 violating patterns)
n=17: orbit of rho under G has 288 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1)  (16 orbit elements)
    factors (17, 17, 17, 17, 17, 17, 17, 17)  reduced (1, 1, 1, 1, 1, 1, 1, 1)  (272 orbit elements)
    Conjecture 1.7 for n=17: TRUE (0 violating patterns)
n=19: orbit of rho under G has 360 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1)  (18 orbit elements)
    factors (19, 19, 19, 19, 19, 19, 19, 19, 19)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1)  (342 orbit elements)
    Conjecture 1.7 for n=19: TRUE (0 violating patterns)
n=21: orbit of rho under G has 384 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (12 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  (36 orbit elements)
    factors (7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  reduced (7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  (84 orbit elements)
    factors (21, 21, 7, 21, 21, 7, 3, 21, 7, 21)  reduced (21, 21, 7, 21, 21, 7, 3, 21, 7, 21)  (252 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=21: FALSE (1 violating patterns)
n=23: orbit of rho under G has 528 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (22 orbit elements)
    factors (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (506 orbit elements)
    Conjecture 1.7 for n=23: TRUE (0 violating patterns)
n=25: orbit of rho under G has 600 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (20 orbit elements)
    factors (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  reduced (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  (80 orbit elements)
    factors (25, 25, 25, 25, 5, 25, 25, 25, 25, 5, 25, 25)  reduced (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  (500 orbit elements)
    Conjecture 1.7 for n=25: TRUE (0 violating patterns)
n=27: orbit of rho under G has 648 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (18 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  (36 orbit elements)
    factors (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9)  reduced (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9)  (108 orbit elements)
    factors (27, 27, 9, 27, 27, 9, 27, 27, 3, 27, 27, 9, 27)  reduced (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9)  (486 orbit elements)
    Conjecture 1.7 for n=27: TRUE (0 violating patterns)
n=29: orbit of rho under G has 840 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (28 orbit elements)
    factors (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (812 orbit elements)
    Conjecture 1.7 for n=29: TRUE (0 violating patterns)
n=31: orbit of rho under G has 960 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (30 orbit elements)
    factors (31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (930 orbit elements)
    Conjecture 1.7 for n=31: TRUE (0 violating patterns)
n=33: orbit of rho under G has 960 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (20 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  (60 orbit elements)
    factors (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 11, 11, 11, 11, 11)  reduced (11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 11, 11, 11, 11, 11)  (220 orbit elements)
    factors (33, 33, 11, 33, 33, 11, 33, 33, 11, 33, 3, 11, 33, 33, 11, 33)  reduced (33, 33, 11, 33, 33, 11, 33, 33, 11, 33, 3, 11, 33, 33, 11, 33)  (660 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=33: FALSE (1 violating patterns)
n=35: orbit of rho under G has 1152 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (24 orbit elements)
    factors (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  reduced (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  (120 orbit elements)
    factors (7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  reduced (7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  (168 orbit elements)
    factors (35, 35, 35, 35, 7, 35, 5, 35, 35, 7, 35, 35, 35, 5, 7, 35, 35)  reduced (35, 35, 35, 35, 7, 35, 5, 35, 35, 7, 35, 35, 35, 5, 7, 35, 35)  (840 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=35: FALSE (1 violating patterns)
n=37: orbit of rho under G has 1368 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (36 orbit elements)
    factors (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (1332 orbit elements)
    Conjecture 1.7 for n=37: TRUE (0 violating patterns)
n=39: orbit of rho under G has 1344 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (24 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  (72 orbit elements)
    factors (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 1, 13, 13, 13, 13, 13, 13)  reduced (13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 1, 13, 13, 13, 13, 13, 13)  (312 orbit elements)
    factors (39, 39, 13, 39, 39, 13, 39, 39, 13, 39, 39, 13, 3, 39, 13, 39, 39, 13, 39)  reduced (39, 39, 13, 39, 39, 13, 39, 39, 13, 39, 39, 13, 3, 39, 13, 39, 39, 13, 39)  (936 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=39: FALSE (1 violating patterns)
n=41: orbit of rho under G has 1680 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (40 orbit elements)
    factors (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (1640 orbit elements)
    Conjecture 1.7 for n=41: TRUE (0 violating patterns)
n=43: orbit of rho under G has 1848 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (42 orbit elements)
    factors (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (1806 orbit elements)
    Conjecture 1.7 for n=43: TRUE (0 violating patterns)
n=45: orbit of rho under G has 1728 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (24 orbit elements)
    factors (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  reduced (3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3)  (48 orbit elements)
    factors (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  reduced (5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1, 5, 5)  (120 orbit elements)
    factors (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9)  reduced (9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 3, 9)  (216 orbit elements)
    factors (15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15)  reduced (15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15)  (240 orbit elements)
    factors (45, 45, 15, 45, 9, 15, 45, 45, 5, 9, 45, 15, 45, 45, 3, 45, 45, 5, 45, 9, 15, 45)  reduced (45, 45, 15, 45, 9, 15, 45, 45, 5, 9, 45, 15, 45, 45, 3, 45, 45, 5, 45, 9, 15, 45)  (1080 orbit elements)   <-- reduced factor = n
    Conjecture 1.7 for n=45: FALSE (1 violating patterns)
n=47: orbit of rho under G has 2208 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (46 orbit elements)
    factors (47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (2162 orbit elements)
    Conjecture 1.7 for n=47: TRUE (0 violating patterns)
n=49: orbit of rho under G has 2352 elements; factor patterns (d_1..d_m) for the cylinders C_1..C_m [preclosed length of C_j proportional to sin(2j pi/n)]:
    factors (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  reduced (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)  (42 orbit elements)
    factors (7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  reduced (7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  (252 orbit elements)
    factors (49, 49, 49, 49, 49, 49, 7, 49, 49, 49, 49, 49, 49, 7, 49, 49, 49, 49, 49, 49, 7, 49, 49, 49)  reduced (7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7)  (2058 orbit elements)
    Conjecture 1.7 for n=49: TRUE (0 violating patterns)
