INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/9 -7/9 -2/3 -5/9 -7/15 -4/9 -5/12 -7/18 -41/108 -29/81 -19/54 -1/3 -17/54 -49/162 -7/24 -5/18 -29/108 -43/162 -19/72 -7/27 -5/21 -17/72 -2/9 -23/108 -5/24 -28/135 -5/26 -4/21 -14/81 -1/6 -3/20 -4/27 -3/22 -2/15 -3/23 -7/54 -2/17 -1/9 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 2/13 3/19 4/25 1/6 4/23 3/17 2/11 5/27 3/16 4/21 1/5 4/19 3/14 2/9 3/13 5/21 1/4 5/18 7/25 2/7 8/27 1/3 10/27 7/18 2/5 11/27 5/12 4/9 7/15 1/2 5/9 16/27 17/27 52/81 2/3 19/27 20/27 7/9 107/135 22/27 67/81 23/27 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -3/1 1/0 -8/9 -1/1 -7/8 -1/1 1/0 -13/15 0/1 -6/7 4/1 1/0 -11/13 1/0 -16/19 -4/1 1/0 -21/25 -13/4 -5/6 -3/1 -1/1 -24/29 -2/1 1/0 -19/23 1/0 -14/17 -2/1 1/0 -9/11 -3/2 -22/27 -1/1 -13/16 -1/1 -2/3 -17/21 0/1 -4/5 0/1 1/0 -15/19 3/2 -41/52 1/1 2/1 -26/33 1/1 -11/14 1/1 1/0 -18/23 4/1 1/0 -7/9 1/0 -24/31 -6/1 1/0 -41/53 1/0 -17/22 -6/1 -5/1 -27/35 1/0 -10/13 -4/1 1/0 -13/17 -5/2 -16/21 -1/1 -3/4 -2/1 -1/1 -14/19 -2/3 -1/2 -25/34 -1/2 -3/7 -36/49 -1/2 0/1 -11/15 0/1 -30/41 -1/2 0/1 -19/26 -1/3 0/1 -8/11 0/1 1/2 -21/29 -1/2 -13/18 -1/1 1/1 -18/25 0/1 1/0 -41/57 0/1 -23/32 -1/1 0/1 -5/7 1/0 -17/24 1/1 3/1 -12/17 6/1 1/0 -19/27 1/0 -7/10 -5/1 1/0 -30/43 -4/1 1/0 -23/33 -4/1 -39/56 -16/5 -3/1 -16/23 -5/2 -2/1 -9/13 1/0 -11/16 -3/1 -2/1 -13/19 1/0 -15/22 -4/1 -3/1 -2/3 -1/1 -13/20 1/1 1/0 -11/17 1/0 -20/31 2/1 1/0 -9/14 -1/1 1/0 -34/53 -1/2 0/1 -25/39 0/1 -66/103 0/1 1/0 -41/64 1/1 1/0 -16/25 0/1 1/0 -7/11 1/0 -19/30 1/1 3/1 -12/19 4/1 1/0 -17/27 1/0 -5/8 -3/1 1/0 -18/29 -2/1 1/0 -31/50 -3/1 -2/1 -13/21 -2/1 -60/97 -2/1 1/0 -47/76 -3/1 -2/1 -34/55 -2/1 -7/4 -21/34 -3/2 -1/1 -8/13 0/1 1/0 -19/31 1/0 -11/18 -3/1 -1/1 -14/23 -5/2 -2/1 -31/51 -2/1 -48/79 -2/1 1/0 -17/28 -3/1 -2/1 -3/5 -3/2 -16/27 -1/1 -13/22 -1/1 -8/9 -23/39 -4/5 -10/17 -3/4 -2/3 -17/29 -1/2 -24/41 -8/15 -1/2 -31/53 -1/2 -7/12 -1/1 -1/3 -32/55 -1/2 0/1 -25/43 -1/2 -18/31 -1/6 0/1 -11/19 1/0 -37/64 1/1 1/0 -26/45 -1/1 -15/26 -1/3 0/1 -19/33 0/1 -4/7 0/1 1/0 -13/23 1/0 -22/39 1/1 -31/55 1/0 -9/16 -1/1 0/1 -23/41 1/0 -14/25 0/1 1/0 -5/9 1/0 -16/29 -2/1 1/0 -27/49 1/0 -11/20 -1/1 1/0 -28/51 -3/1 -17/31 -3/2 -6/11 -2/1 1/0 -7/13 1/0 -8/15 -1/1 -1/2 -1/1 0/1 -9/19 -1/2 -8/17 -2/1 1/0 -7/15 0/1 -6/13 0/1 1/0 -11/24 -1/1 1/1 -5/11 1/0 -14/31 -2/1 -7/4 -9/20 -5/3 -3/2 -4/9 -1/1 -15/34 -11/13 -5/6 -26/59 -5/6 -4/5 -11/25 -3/4 -7/16 -5/7 -2/3 -24/55 -2/3 -5/8 -17/39 -2/3 -27/62 -1/1 -1/2 -10/23 -2/3 -1/2 -23/53 -1/2 -13/30 -1/1 -3/5 -3/7 -1/2 -17/40 -1/2 -1/3 -14/33 -1/3 -11/26 -1/3 0/1 -19/45 0/1 -27/64 1/3 1/2 -8/19 0/1 1/0 -21/50 -4/3 -1/1 -34/81 -1/1 -13/31 -3/4 -18/43 -2/3 -1/2 -41/98 -1/1 -1/2 -23/55 -1/2 -5/12 -1/1 -1/3 -22/53 -1/2 0/1 -39/94 -1/1 1/0 -56/135 -1/1 -17/41 -1/2 -12/29 -1/2 0/1 -19/46 -1/2 -1/3 -26/63 -1/3 -7/17 -1/2 -23/56 -1/3 -2/7 -16/39 -1/3 -9/22 -1/5 0/1 -11/27 0/1 -2/5 0/1 1/0 -13/33 0/1 -11/28 -1/5 0/1 -20/51 1/3 -9/23 1/0 -7/18 -1/1 1/1 -12/31 0/1 1/2 -5/13 1/0 -18/47 10/1 1/0 -31/81 1/0 -13/34 -9/1 1/0 -34/89 -4/1 1/0 -55/144 -5/1 -3/1 -21/55 1/0 -29/76 -5/1 -4/1 -8/21 -3/1 -19/50 -3/1 -2/1 -30/79 -2/1 1/0 -41/108 -3/1 -1/1 -11/29 1/0 -14/37 -5/2 -2/1 -3/8 -3/2 -1/1 -10/27 -1/1 -7/19 -7/8 -18/49 -5/6 -4/5 -29/79 -13/16 -11/30 -1/1 -7/9 -15/41 -3/4 -4/11 -3/4 -2/3 -9/25 -5/8 -32/89 -7/12 -4/7 -23/64 -5/9 -1/2 -14/39 -5/9 -19/53 -1/2 -24/67 -20/39 -1/2 -29/81 -1/2 -5/14 -1/2 -3/7 -6/17 -1/2 0/1 -19/54 -1/1 -1/3 -13/37 -1/2 -7/20 -1/1 -1/2 -8/23 0/1 1/0 -1/3 0/1 -6/19 0/1 1/0 -17/54 -1/1 1/1 -11/35 1/0 -5/16 -1/1 0/1 -9/29 1/0 -4/13 -4/1 1/0 -7/23 1/0 -24/79 -2/1 1/0 -41/135 -2/1 -17/56 -2/1 -1/1 -10/33 -1/1 -23/76 -3/1 -2/1 -36/119 -2/1 1/0 -49/162 -3/1 -1/1 -13/43 1/0 -3/10 -3/2 -1/1 -8/27 -1/1 -5/17 -5/6 -12/41 -3/4 -2/3 -7/24 -1/1 -5/7 -23/79 -11/16 -16/55 -2/3 -13/20 -9/31 -1/2 -2/7 -2/3 -1/2 -11/39 -2/5 -9/32 -1/3 -2/7 -16/57 -1/5 -23/82 -1/13 0/1 -53/189 0/1 -30/107 0/1 1/12 -7/25 1/0 -5/18 -1/1 -1/3 -8/29 -1/2 0/1 -3/11 -1/2 -10/37 -1/4 0/1 -17/63 0/1 -7/26 -1/3 0/1 -18/67 -1/2 0/1 -29/108 -1/1 -1/3 -11/41 -1/2 -4/15 -1/3 -17/64 -1/3 -1/4 -30/113 -1/4 0/1 -43/162 -1/3 -1/5 -13/49 -1/4 -9/34 -1/4 -1/5 -14/53 -1/2 0/1 -19/72 -1/3 -1/5 -24/91 -1/4 -2/9 -5/19 -1/6 -6/23 -1/12 0/1 -7/27 0/1 -1/4 0/1 1/1 -5/21 0/1 -9/38 1/1 2/1 -13/55 1/0 -17/72 -1/1 1/1 -4/17 2/1 1/0 -7/30 -3/1 -1/1 -3/13 1/0 -8/35 -2/1 1/0 -13/57 -2/1 -5/22 -2/1 -1/1 -2/9 -1/1 -7/32 -1/1 -2/3 -12/55 -11/16 -2/3 -5/23 -1/2 -8/37 -2/3 -1/2 -3/14 -1/2 -1/3 -13/61 -1/2 -23/108 -1/1 -1/3 -10/47 -1/2 0/1 -7/33 0/1 -11/52 -1/1 -4/5 -15/71 -1/2 -19/90 -1/1 -3/5 -4/19 -2/3 -1/2 -5/24 -1/1 -1/3 -11/53 -1/2 -28/135 -1/3 -17/82 -1/3 0/1 -6/29 -1/2 0/1 -1/5 -1/2 -5/26 -1/5 0/1 -4/21 -1/5 -7/37 -1/8 -17/90 -1/7 -1/9 -10/53 -1/6 0/1 -3/16 -1/11 0/1 -5/27 0/1 -2/11 0/1 1/6 -5/28 0/1 1/1 -8/45 1/3 -3/17 1/2 -4/23 1/2 2/3 -9/52 8/9 1/1 -14/81 1/1 -5/29 5/4 -1/6 -1/1 1/1 -4/25 0/1 1/0 -7/44 1/1 1/0 -3/19 1/0 -2/13 0/1 1/0 -3/20 -3/2 -1/1 -4/27 -1/1 -1/7 -1/2 -3/22 -1/3 0/1 -2/15 -1/1 -3/23 -1/2 -7/54 -1/1 -1/3 -4/31 -1/2 0/1 -1/8 -1/2 -1/3 -2/17 -1/6 0/1 -1/9 0/1 -1/10 1/2 1/1 -1/11 1/0 0/1 0/1 1/0 1/10 -1/1 -1/2 1/9 0/1 1/8 1/3 1/2 2/15 1/1 1/7 1/2 2/13 0/1 1/0 3/19 1/0 4/25 0/1 1/0 1/6 -1/1 1/1 5/29 -5/4 4/23 -2/3 -1/2 3/17 -1/2 2/11 -1/6 0/1 5/27 0/1 3/16 0/1 1/11 4/21 1/5 1/5 1/2 4/19 1/2 2/3 11/52 4/5 1/1 7/33 0/1 3/14 1/3 1/2 5/23 1/2 2/9 1/1 7/31 3/2 12/53 2/1 9/4 5/22 1/1 2/1 8/35 2/1 1/0 3/13 1/0 4/17 -2/1 1/0 5/21 0/1 1/4 -1/1 0/1 5/19 1/6 9/34 1/5 1/4 13/49 1/4 4/15 1/3 11/41 1/2 7/26 0/1 1/3 3/11 1/2 8/29 0/1 1/2 5/18 1/3 1/1 7/25 1/0 16/57 1/5 9/32 2/7 1/3 2/7 1/2 2/3 7/24 5/7 1/1 5/17 5/6 8/27 1/1 3/10 1/1 3/2 13/43 1/0 10/33 1/1 17/56 1/1 2/1 7/23 1/0 4/13 4/1 1/0 5/16 0/1 1/1 6/19 0/1 1/0 7/22 -1/1 0/1 1/3 0/1 7/20 1/2 1/1 6/17 0/1 1/2 11/31 1/2 5/14 3/7 1/2 19/53 1/2 14/39 5/9 37/103 1/2 23/64 1/2 5/9 9/25 5/8 4/11 2/3 3/4 11/30 7/9 1/1 7/19 7/8 10/27 1/1 3/8 1/1 3/2 11/29 1/0 19/50 2/1 3/1 8/21 3/1 37/97 1/0 29/76 4/1 5/1 21/55 1/0 13/34 9/1 1/0 5/13 1/0 12/31 -1/2 0/1 7/18 -1/1 1/1 9/23 1/0 20/51 -1/3 31/79 -1/8 11/28 0/1 1/5 2/5 0/1 1/0 11/27 0/1 9/22 0/1 1/5 16/39 1/3 7/17 1/2 12/29 0/1 1/2 17/41 1/2 22/53 0/1 1/2 5/12 1/3 1/1 23/55 1/2 18/43 1/2 2/3 13/31 3/4 8/19 0/1 1/0 27/64 -1/2 -1/3 19/45 0/1 11/26 0/1 1/3 14/33 1/3 3/7 1/2 10/23 1/2 2/3 17/39 2/3 24/55 5/8 2/3 7/16 2/3 5/7 18/41 14/19 3/4 11/25 3/4 4/9 1/1 13/29 5/4 22/49 4/3 3/2 9/20 3/2 5/3 23/51 2/1 14/31 7/4 2/1 5/11 1/0 6/13 0/1 1/0 7/15 0/1 1/2 0/1 1/1 10/19 3/2 2/1 9/17 3/2 8/15 1/1 7/13 1/0 13/24 -1/1 1/1 6/11 2/1 1/0 17/31 3/2 11/20 1/1 1/0 5/9 1/0 19/34 -1/1 1/0 33/59 1/0 14/25 0/1 1/0 9/16 0/1 1/1 31/55 1/0 22/39 -1/1 35/62 1/1 1/0 13/23 1/0 30/53 -1/6 0/1 17/30 1/3 1/1 4/7 0/1 1/0 23/40 1/1 1/0 19/33 0/1 15/26 0/1 1/3 26/45 1/1 37/64 -1/1 1/0 11/19 1/0 29/50 -1/7 0/1 47/81 0/1 18/31 0/1 1/6 25/43 1/2 57/98 1/1 1/0 32/55 0/1 1/2 7/12 1/3 1/1 31/53 1/2 55/94 15/31 1/2 79/135 1/2 24/41 1/2 8/15 17/29 1/2 27/46 3/5 5/8 37/63 2/3 10/17 2/3 3/4 33/56 4/5 1/1 23/39 4/5 13/22 8/9 1/1 16/27 1/1 3/5 3/2 20/33 3/1 17/28 2/1 3/1 31/51 2/1 14/23 2/1 5/2 11/18 1/1 3/1 19/31 1/0 8/13 0/1 1/0 29/47 1/2 50/81 1/1 21/34 1/1 3/2 55/89 1/0 89/144 1/1 5/3 34/55 7/4 2/1 47/76 2/1 3/1 13/21 2/1 31/50 2/1 3/1 49/79 1/0 67/108 1/1 3/1 18/29 2/1 1/0 23/37 1/0 5/8 3/1 1/0 17/27 1/0 12/19 -4/1 1/0 31/49 1/0 50/79 -2/1 1/0 19/30 -3/1 -1/1 26/41 -2/1 1/0 7/11 1/0 16/25 0/1 1/0 57/89 1/0 41/64 -1/1 1/0 25/39 0/1 34/53 0/1 1/2 43/67 1/2 52/81 1/1 9/14 1/1 1/0 11/17 1/0 35/54 -1/1 1/1 24/37 0/1 1/0 13/20 -1/1 1/0 15/23 -1/2 2/3 1/1 13/19 1/0 37/54 1/1 3/1 24/35 2/1 1/0 11/16 2/1 3/1 20/29 2/1 1/0 9/13 1/0 16/23 2/1 5/2 55/79 23/8 94/135 3/1 39/56 3/1 16/5 23/33 4/1 53/76 4/1 5/1 83/119 1/0 113/162 3/1 5/1 30/43 4/1 1/0 7/10 5/1 1/0 19/27 1/0 12/17 -6/1 1/0 29/41 1/0 17/24 -3/1 -1/1 56/79 -2/1 1/0 39/55 1/0 22/31 -2/1 1/0 5/7 1/0 28/39 -1/1 23/32 0/1 1/1 41/57 0/1 59/82 0/1 1/1 136/189 1/1 77/107 1/0 18/25 0/1 1/0 13/18 -1/1 1/1 21/29 1/2 8/11 -1/2 0/1 27/37 1/2 46/63 1/1 19/26 0/1 1/3 49/67 1/2 79/108 1/3 1/1 30/41 0/1 1/2 11/15 0/1 47/64 1/2 1/1 83/113 1/2 119/162 1/3 1/1 36/49 0/1 1/2 25/34 3/7 1/2 39/53 1/2 53/72 3/5 1/1 67/91 1/2 14/19 1/2 2/3 17/23 5/6 20/27 1/1 3/4 1/1 2/1 16/21 1/1 29/38 2/1 11/5 42/55 2/1 1/0 55/72 7/3 3/1 13/17 5/2 23/30 3/1 5/1 10/13 4/1 1/0 27/35 1/0 44/57 3/1 17/22 5/1 6/1 7/9 1/0 25/32 -5/1 -4/1 43/55 1/0 18/23 -4/1 1/0 29/37 1/0 11/14 -1/1 1/0 48/61 -2/1 1/0 85/108 -3/1 -1/1 37/47 1/0 26/33 -1/1 41/52 -2/1 -1/1 56/71 0/1 1/0 71/90 -3/1 -1/1 15/19 -3/2 19/24 -1/1 -1/3 42/53 -1/10 0/1 107/135 0/1 65/82 0/1 1/15 23/29 1/2 4/5 0/1 1/0 21/26 0/1 1/5 17/21 0/1 30/37 1/2 2/3 73/90 1/3 1/1 43/53 1/2 13/16 2/3 1/1 22/27 1/1 9/11 3/2 23/28 1/1 2/1 37/45 2/1 14/17 2/1 1/0 19/23 1/0 43/52 1/1 2/1 67/81 2/1 24/29 2/1 1/0 5/6 1/1 3/1 21/25 13/4 37/44 7/2 11/3 16/19 4/1 1/0 11/13 1/0 17/20 15/1 1/0 23/27 1/0 6/7 -4/1 1/0 19/22 -4/3 -1/1 13/15 0/1 20/23 0/1 1/0 47/54 -1/1 1/1 27/31 1/0 7/8 1/1 1/0 15/17 1/0 8/9 1/1 9/10 3/1 1/0 10/11 2/1 1/0 1/1 1/0 1/0 -1/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(271,248,-648,-593) (-1/1,-9/10) -> (-41/98,-23/55) Hyperbolic Matrix(593,530,1026,917) (-9/10,-8/9) -> (26/45,37/64) Hyperbolic Matrix(379,334,-918,-809) (-8/9,-7/8) -> (-19/46,-26/63) Hyperbolic Matrix(541,470,-1242,-1079) (-7/8,-13/15) -> (-17/39,-27/62) Hyperbolic Matrix(107,92,-378,-325) (-13/15,-6/7) -> (-2/7,-11/39) Hyperbolic Matrix(269,228,-702,-595) (-6/7,-11/13) -> (-5/13,-18/47) Hyperbolic Matrix(161,136,702,593) (-11/13,-16/19) -> (8/35,3/13) Hyperbolic Matrix(971,816,-2700,-2269) (-16/19,-21/25) -> (-9/25,-32/89) Hyperbolic Matrix(55,46,324,271) (-21/25,-5/6) -> (1/6,5/29) Hyperbolic Matrix(53,44,324,269) (-5/6,-24/29) -> (4/25,1/6) Hyperbolic Matrix(755,624,-2484,-2053) (-24/29,-19/23) -> (-7/23,-24/79) Hyperbolic Matrix(325,268,918,757) (-19/23,-14/17) -> (6/17,11/31) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(485,396,594,485) (-9/11,-22/27) -> (22/27,9/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(269,218,-1134,-919) (-13/16,-17/21) -> (-5/21,-9/38) Hyperbolic Matrix(107,86,-270,-217) (-17/21,-4/5) -> (-2/5,-13/33) Hyperbolic Matrix(377,298,-1026,-811) (-4/5,-15/19) -> (-7/19,-18/49) Hyperbolic Matrix(487,384,-1026,-809) (-15/19,-41/52) -> (-1/2,-9/19) Hyperbolic Matrix(1081,852,3564,2809) (-41/52,-26/33) -> (10/33,17/56) Hyperbolic Matrix(757,596,-1782,-1403) (-26/33,-11/14) -> (-17/40,-14/33) Hyperbolic Matrix(487,382,-756,-593) (-11/14,-18/23) -> (-20/31,-9/14) Hyperbolic Matrix(377,294,-486,-379) (-18/23,-7/9) -> (-7/9,-24/31) Parabolic Matrix(2375,1838,3348,2591) (-24/31,-41/53) -> (39/55,22/31) Hyperbolic Matrix(1999,1546,5238,4051) (-41/53,-17/22) -> (29/76,21/55) Hyperbolic Matrix(811,626,-1188,-917) (-17/22,-27/35) -> (-13/19,-15/22) Hyperbolic Matrix(109,84,702,541) (-27/35,-10/13) -> (2/13,3/19) Hyperbolic Matrix(269,206,-918,-703) (-10/13,-13/17) -> (-5/17,-12/41) Hyperbolic Matrix(215,164,-1134,-865) (-13/17,-16/21) -> (-4/21,-7/37) Hyperbolic Matrix(431,328,1134,863) (-16/21,-3/4) -> (19/50,8/21) Hyperbolic Matrix(431,318,-1026,-757) (-3/4,-14/19) -> (-8/19,-21/50) Hyperbolic Matrix(1403,1032,-3672,-2701) (-14/19,-25/34) -> (-13/34,-34/89) Hyperbolic Matrix(1189,874,2646,1945) (-25/34,-36/49) -> (22/49,9/20) Hyperbolic Matrix(2215,1626,-3456,-2537) (-36/49,-11/15) -> (-25/39,-66/103) Hyperbolic Matrix(377,276,810,593) (-11/15,-30/41) -> (6/13,7/15) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(107,78,-594,-433) (-19/26,-8/11) -> (-2/11,-5/28) Hyperbolic Matrix(215,156,594,431) (-8/11,-21/29) -> (9/25,4/11) Hyperbolic Matrix(271,196,972,703) (-21/29,-13/18) -> (5/18,7/25) Hyperbolic Matrix(269,194,972,701) (-13/18,-18/25) -> (8/29,5/18) Hyperbolic Matrix(3511,2526,-5778,-4157) (-18/25,-41/57) -> (-31/51,-48/79) Hyperbolic Matrix(431,310,1350,971) (-41/57,-23/32) -> (7/22,1/3) Hyperbolic Matrix(53,38,-378,-271) (-23/32,-5/7) -> (-1/7,-3/22) Hyperbolic Matrix(163,116,-378,-269) (-5/7,-17/24) -> (-13/30,-3/7) Hyperbolic Matrix(215,152,-918,-649) (-17/24,-12/17) -> (-4/17,-7/30) Hyperbolic Matrix(647,456,918,647) (-12/17,-19/27) -> (19/27,12/17) Hyperbolic Matrix(379,266,540,379) (-19/27,-7/10) -> (7/10,19/27) Hyperbolic Matrix(1943,1356,-4644,-3241) (-7/10,-30/43) -> (-18/43,-41/98) Hyperbolic Matrix(2539,1770,-4104,-2861) (-30/43,-23/33) -> (-13/21,-60/97) Hyperbolic Matrix(755,526,3564,2483) (-23/33,-39/56) -> (11/52,7/33) Hyperbolic Matrix(431,300,-2484,-1729) (-39/56,-16/23) -> (-4/23,-9/52) Hyperbolic Matrix(271,188,702,487) (-16/23,-9/13) -> (5/13,12/31) Hyperbolic Matrix(485,334,-864,-595) (-9/13,-11/16) -> (-9/16,-23/41) Hyperbolic Matrix(271,186,-864,-593) (-11/16,-13/19) -> (-11/35,-5/16) Hyperbolic Matrix(379,258,1350,919) (-15/22,-2/3) -> (16/57,9/32) Hyperbolic Matrix(593,386,-1080,-703) (-2/3,-13/20) -> (-11/20,-28/51) Hyperbolic Matrix(379,246,-1080,-701) (-13/20,-11/17) -> (-13/37,-7/20) Hyperbolic Matrix(161,104,918,593) (-11/17,-20/31) -> (4/23,3/17) Hyperbolic Matrix(2375,1524,-5724,-3673) (-9/14,-34/53) -> (-22/53,-39/94) Hyperbolic Matrix(1837,1178,4212,2701) (-34/53,-25/39) -> (17/39,24/55) Hyperbolic Matrix(3671,2352,-13824,-8857) (-66/103,-41/64) -> (-17/64,-30/113) Hyperbolic Matrix(431,276,-2700,-1729) (-41/64,-16/25) -> (-4/25,-7/44) Hyperbolic Matrix(163,104,594,379) (-16/25,-7/11) -> (3/11,8/29) Hyperbolic Matrix(271,172,-594,-377) (-7/11,-19/30) -> (-11/24,-5/11) Hyperbolic Matrix(215,136,-1026,-649) (-19/30,-12/19) -> (-4/19,-5/24) Hyperbolic Matrix(647,408,1026,647) (-12/19,-17/27) -> (17/27,12/19) Hyperbolic Matrix(271,170,432,271) (-17/27,-5/8) -> (5/8,17/27) Hyperbolic Matrix(647,402,-1566,-973) (-5/8,-18/29) -> (-12/29,-19/46) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(271,168,1134,703) (-31/50,-13/21) -> (5/21,1/4) Hyperbolic Matrix(4967,3072,-16416,-10153) (-60/97,-47/76) -> (-23/76,-36/119) Hyperbolic Matrix(1187,734,5238,3239) (-47/76,-34/55) -> (12/53,5/22) Hyperbolic Matrix(971,600,-3672,-2269) (-34/55,-21/34) -> (-9/34,-14/53) Hyperbolic Matrix(107,66,-702,-433) (-21/34,-8/13) -> (-2/13,-3/20) Hyperbolic Matrix(215,132,702,431) (-8/13,-19/31) -> (7/23,4/13) Hyperbolic Matrix(379,232,972,595) (-19/31,-11/18) -> (7/18,9/23) Hyperbolic Matrix(377,230,972,593) (-11/18,-14/23) -> (12/31,7/18) Hyperbolic Matrix(1243,756,2754,1675) (-14/23,-31/51) -> (23/51,14/31) Hyperbolic Matrix(1511,918,-7290,-4429) (-48/79,-17/28) -> (-17/82,-6/29) Hyperbolic Matrix(53,32,-270,-163) (-17/28,-3/5) -> (-1/5,-5/26) Hyperbolic Matrix(161,96,270,161) (-3/5,-16/27) -> (16/27,3/5) Hyperbolic Matrix(703,416,1188,703) (-16/27,-13/22) -> (13/22,16/27) Hyperbolic Matrix(593,350,-2106,-1243) (-13/22,-23/39) -> (-11/39,-9/32) Hyperbolic Matrix(431,254,-918,-541) (-23/39,-10/17) -> (-8/17,-7/15) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(973,570,2214,1297) (-17/29,-24/41) -> (18/41,11/25) Hyperbolic Matrix(2051,1200,-5724,-3349) (-24/41,-31/53) -> (-19/53,-24/67) Hyperbolic Matrix(541,316,1296,757) (-31/53,-7/12) -> (5/12,23/55) Hyperbolic Matrix(539,314,1296,755) (-7/12,-32/55) -> (22/53,5/12) Hyperbolic Matrix(55,32,-648,-377) (-32/55,-25/43) -> (-1/11,0/1) Hyperbolic Matrix(757,440,1674,973) (-25/43,-18/31) -> (14/31,5/11) Hyperbolic Matrix(269,156,-1026,-595) (-18/31,-11/19) -> (-5/19,-6/23) Hyperbolic Matrix(325,188,-2052,-1187) (-11/19,-37/64) -> (-7/44,-3/19) Hyperbolic Matrix(917,530,1026,593) (-37/64,-26/45) -> (8/9,9/10) Hyperbolic Matrix(433,250,-2430,-1403) (-26/45,-15/26) -> (-5/28,-8/45) Hyperbolic Matrix(701,404,-1782,-1027) (-15/26,-19/33) -> (-13/33,-11/28) Hyperbolic Matrix(379,218,-1782,-1025) (-19/33,-4/7) -> (-10/47,-7/33) Hyperbolic Matrix(109,62,-378,-215) (-4/7,-13/23) -> (-9/31,-2/7) Hyperbolic Matrix(163,92,-1242,-701) (-13/23,-22/39) -> (-2/15,-3/23) Hyperbolic Matrix(1511,852,4212,2375) (-22/39,-31/55) -> (19/53,14/39) Hyperbolic Matrix(703,396,-2970,-1673) (-31/55,-9/16) -> (-9/38,-13/55) Hyperbolic Matrix(917,514,2214,1241) (-23/41,-14/25) -> (12/29,17/41) Hyperbolic Matrix(269,150,-486,-271) (-14/25,-5/9) -> (-5/9,-16/29) Parabolic Matrix(3349,1846,5292,2917) (-16/29,-27/49) -> (31/49,50/79) Hyperbolic Matrix(701,386,2646,1457) (-27/49,-11/20) -> (9/34,13/49) Hyperbolic Matrix(1079,592,2754,1511) (-28/51,-17/31) -> (9/23,20/51) Hyperbolic Matrix(701,384,1674,917) (-17/31,-6/11) -> (18/43,13/31) Hyperbolic Matrix(217,118,-594,-323) (-6/11,-7/13) -> (-15/41,-4/11) Hyperbolic Matrix(217,116,810,433) (-7/13,-8/15) -> (4/15,11/41) Hyperbolic Matrix(377,200,-918,-487) (-8/15,-1/2) -> (-23/56,-16/39) Hyperbolic Matrix(541,256,-2052,-971) (-9/19,-8/17) -> (-24/91,-5/19) Hyperbolic Matrix(593,276,810,377) (-7/15,-6/13) -> (30/41,11/15) Hyperbolic Matrix(539,248,702,323) (-6/13,-11/24) -> (23/30,10/13) Hyperbolic Matrix(973,440,1674,757) (-5/11,-14/31) -> (18/31,25/43) Hyperbolic Matrix(377,170,-1080,-487) (-14/31,-9/20) -> (-7/20,-8/23) Hyperbolic Matrix(215,96,-486,-217) (-9/20,-4/9) -> (-4/9,-15/34) Parabolic Matrix(2699,1190,3672,1619) (-15/34,-26/59) -> (36/49,25/34) Hyperbolic Matrix(1457,642,1836,809) (-26/59,-11/25) -> (23/29,4/5) Hyperbolic Matrix(269,118,-864,-379) (-11/25,-7/16) -> (-5/16,-9/29) Hyperbolic Matrix(325,142,-1728,-755) (-7/16,-24/55) -> (-10/53,-3/16) Hyperbolic Matrix(2701,1178,4212,1837) (-24/55,-17/39) -> (25/39,34/53) Hyperbolic Matrix(271,118,-2106,-917) (-27/62,-10/23) -> (-4/31,-1/8) Hyperbolic Matrix(1943,844,2484,1079) (-10/23,-23/53) -> (43/55,18/23) Hyperbolic Matrix(595,258,-2862,-1241) (-23/53,-13/30) -> (-5/24,-11/53) Hyperbolic Matrix(541,230,-2538,-1079) (-3/7,-17/40) -> (-3/14,-13/61) Hyperbolic Matrix(269,114,-1404,-595) (-14/33,-11/26) -> (-5/26,-4/21) Hyperbolic Matrix(757,320,-2808,-1187) (-11/26,-19/45) -> (-17/63,-7/26) Hyperbolic Matrix(109,46,1026,433) (-19/45,-27/64) -> (1/10,1/9) Hyperbolic Matrix(2485,1048,-6912,-2915) (-27/64,-8/19) -> (-32/89,-23/64) Hyperbolic Matrix(1243,522,1674,703) (-21/50,-34/81) -> (20/27,3/4) Hyperbolic Matrix(1997,838,2700,1133) (-34/81,-13/31) -> (17/23,20/27) Hyperbolic Matrix(917,384,1674,701) (-13/31,-18/43) -> (6/11,17/31) Hyperbolic Matrix(757,316,1296,541) (-23/55,-5/12) -> (7/12,31/53) Hyperbolic Matrix(755,314,1296,539) (-5/12,-22/53) -> (32/55,7/12) Hyperbolic Matrix(6103,2532,9504,3943) (-39/94,-56/135) -> (52/81,9/14) Hyperbolic Matrix(7937,3292,12366,5129) (-56/135,-17/41) -> (43/67,52/81) Hyperbolic Matrix(1081,448,1566,649) (-17/41,-12/29) -> (20/29,9/13) Hyperbolic Matrix(2483,1024,3402,1403) (-26/63,-7/17) -> (27/37,46/63) Hyperbolic Matrix(1027,422,-4860,-1997) (-7/17,-23/56) -> (-11/52,-15/71) Hyperbolic Matrix(161,66,-1188,-487) (-16/39,-9/22) -> (-3/22,-2/15) Hyperbolic Matrix(485,198,1188,485) (-9/22,-11/27) -> (11/27,9/22) Hyperbolic Matrix(109,44,270,109) (-11/27,-2/5) -> (2/5,11/27) Hyperbolic Matrix(1621,636,-5778,-2267) (-11/28,-20/51) -> (-16/57,-23/82) Hyperbolic Matrix(811,318,1242,487) (-20/51,-9/23) -> (15/23,2/3) Hyperbolic Matrix(595,232,972,379) (-9/23,-7/18) -> (11/18,19/31) Hyperbolic Matrix(593,230,972,377) (-7/18,-12/31) -> (14/23,11/18) Hyperbolic Matrix(487,188,702,271) (-12/31,-5/13) -> (9/13,16/23) Hyperbolic Matrix(1567,600,1836,703) (-18/47,-31/81) -> (23/27,6/7) Hyperbolic Matrix(2159,826,2538,971) (-31/81,-13/34) -> (17/20,23/27) Hyperbolic Matrix(2267,866,-10746,-4105) (-34/89,-55/144) -> (-19/90,-4/19) Hyperbolic Matrix(2807,1072,-11880,-4537) (-55/144,-21/55) -> (-13/55,-17/72) Hyperbolic Matrix(4643,1772,5940,2267) (-21/55,-29/76) -> (25/32,43/55) Hyperbolic Matrix(1243,474,-4104,-1565) (-29/76,-8/21) -> (-10/33,-23/76) Hyperbolic Matrix(863,328,1134,431) (-8/21,-19/50) -> (3/4,16/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(53,20,-432,-163) (-14/37,-3/8) -> (-1/8,-2/17) Hyperbolic Matrix(161,60,432,161) (-3/8,-10/27) -> (10/27,3/8) Hyperbolic Matrix(379,140,1026,379) (-10/27,-7/19) -> (7/19,10/27) Hyperbolic Matrix(2375,872,5292,1943) (-18/49,-29/79) -> (13/29,22/49) Hyperbolic Matrix(1243,456,-4266,-1565) (-29/79,-11/30) -> (-7/24,-23/79) Hyperbolic Matrix(1567,574,2214,811) (-11/30,-15/41) -> (29/41,17/24) Hyperbolic Matrix(431,156,594,215) (-4/11,-9/25) -> (21/29,8/11) Hyperbolic Matrix(919,330,-3456,-1241) (-23/64,-14/39) -> (-4/15,-17/64) Hyperbolic Matrix(2375,852,4212,1511) (-14/39,-19/53) -> (31/55,22/39) Hyperbolic Matrix(7237,2592,12366,4429) (-24/67,-29/81) -> (79/135,24/41) Hyperbolic Matrix(5561,1990,9504,3401) (-29/81,-5/14) -> (55/94,79/135) Hyperbolic Matrix(163,58,-756,-269) (-5/14,-6/17) -> (-8/37,-3/14) Hyperbolic Matrix(1891,666,2916,1027) (-6/17,-19/54) -> (35/54,24/37) Hyperbolic Matrix(1889,664,2916,1025) (-19/54,-13/37) -> (11/17,35/54) Hyperbolic Matrix(755,262,1242,431) (-8/23,-1/3) -> (31/51,14/23) Hyperbolic Matrix(271,86,-1188,-377) (-1/3,-6/19) -> (-8/35,-13/57) Hyperbolic Matrix(1999,630,2916,919) (-6/19,-17/54) -> (37/54,24/35) Hyperbolic Matrix(1997,628,2916,917) (-17/54,-11/35) -> (13/19,37/54) Hyperbolic Matrix(917,284,1566,485) (-9/29,-4/13) -> (24/41,17/29) Hyperbolic Matrix(431,132,702,215) (-4/13,-7/23) -> (19/31,8/13) Hyperbolic Matrix(8533,2592,10314,3133) (-24/79,-41/135) -> (67/81,24/29) Hyperbolic Matrix(9557,2902,11556,3509) (-41/135,-17/56) -> (43/52,67/81) Hyperbolic Matrix(2809,852,3564,1081) (-17/56,-10/33) -> (26/33,41/52) Hyperbolic Matrix(18307,5538,26244,7939) (-36/119,-49/162) -> (113/162,30/43) Hyperbolic Matrix(18305,5536,26244,7937) (-49/162,-13/43) -> (83/119,113/162) Hyperbolic Matrix(53,16,-540,-163) (-13/43,-3/10) -> (-1/10,-1/11) Hyperbolic Matrix(161,48,540,161) (-3/10,-8/27) -> (8/27,3/10) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(1403,410,2214,647) (-12/41,-7/24) -> (19/30,26/41) Hyperbolic Matrix(2755,802,-9828,-2861) (-23/79,-16/55) -> (-30/107,-7/25) Hyperbolic Matrix(757,220,3348,973) (-16/55,-9/31) -> (7/31,12/53) Hyperbolic Matrix(2377,668,3078,865) (-9/32,-16/57) -> (44/57,17/22) Hyperbolic Matrix(21059,5906,26568,7451) (-23/82,-53/189) -> (107/135,65/82) Hyperbolic Matrix(19387,5436,24462,6859) (-53/189,-30/107) -> (42/53,107/135) Hyperbolic Matrix(703,196,972,271) (-7/25,-5/18) -> (13/18,21/29) Hyperbolic Matrix(701,194,972,269) (-5/18,-8/29) -> (18/25,13/18) Hyperbolic Matrix(379,104,594,163) (-8/29,-3/11) -> (7/11,16/25) Hyperbolic Matrix(1999,540,3402,919) (-10/37,-17/63) -> (37/63,10/17) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) Hyperbolic Matrix(433,116,810,217) (-11/41,-4/15) -> (8/15,7/13) Hyperbolic Matrix(19279,5118,26244,6967) (-30/113,-43/162) -> (119/162,36/49) Hyperbolic Matrix(19277,5116,26244,6965) (-43/162,-13/49) -> (83/113,119/162) Hyperbolic Matrix(2053,544,3672,973) (-13/49,-9/34) -> (19/34,33/59) Hyperbolic Matrix(1621,428,-8586,-2267) (-14/53,-19/72) -> (-17/90,-10/53) Hyperbolic Matrix(8803,2322,10854,2863) (-19/72,-24/91) -> (30/37,73/90) Hyperbolic Matrix(1567,408,2700,703) (-6/23,-7/27) -> (47/81,18/31) Hyperbolic Matrix(971,250,1674,431) (-7/27,-1/4) -> (29/50,47/81) Hyperbolic Matrix(703,168,1134,271) (-1/4,-5/21) -> (13/21,31/50) Hyperbolic Matrix(5239,1236,6642,1567) (-17/72,-4/17) -> (56/71,71/90) Hyperbolic Matrix(379,88,702,163) (-7/30,-3/13) -> (7/13,13/24) Hyperbolic Matrix(593,136,702,161) (-3/13,-8/35) -> (16/19,11/13) Hyperbolic Matrix(2213,504,3078,701) (-13/57,-5/22) -> (23/32,41/57) Hyperbolic Matrix(107,24,-486,-109) (-5/22,-2/9) -> (-2/9,-7/32) Parabolic Matrix(3673,802,5940,1297) (-7/32,-12/55) -> (34/55,47/76) Hyperbolic Matrix(1405,306,2484,541) (-12/55,-5/23) -> (13/23,30/53) Hyperbolic Matrix(1025,222,1242,269) (-5/23,-8/37) -> (14/17,19/23) Hyperbolic Matrix(9181,1956,11664,2485) (-13/61,-23/108) -> (85/108,37/47) Hyperbolic Matrix(9179,1954,11664,2483) (-23/108,-10/47) -> (48/61,85/108) Hyperbolic Matrix(2483,526,3564,755) (-7/33,-11/52) -> (39/56,23/33) Hyperbolic Matrix(5075,1072,6642,1403) (-15/71,-19/90) -> (55/72,13/17) Hyperbolic Matrix(17603,3652,24462,5075) (-11/53,-28/135) -> (136/189,77/107) Hyperbolic Matrix(19117,3964,26568,5509) (-28/135,-17/82) -> (59/82,136/189) Hyperbolic Matrix(1027,212,1836,379) (-6/29,-1/5) -> (33/59,14/25) Hyperbolic Matrix(7991,1510,10854,2051) (-7/37,-17/90) -> (53/72,67/91) Hyperbolic Matrix(161,30,864,161) (-3/16,-5/27) -> (5/27,3/16) Hyperbolic Matrix(109,20,594,109) (-5/27,-2/11) -> (2/11,5/27) Hyperbolic Matrix(811,144,918,163) (-8/45,-3/17) -> (15/17,8/9) Hyperbolic Matrix(973,170,1242,217) (-3/17,-4/23) -> (18/23,29/37) Hyperbolic Matrix(8047,1392,11556,1999) (-9/52,-14/81) -> (94/135,39/56) Hyperbolic Matrix(7181,1240,10314,1781) (-14/81,-5/29) -> (55/79,94/135) Hyperbolic Matrix(271,46,324,55) (-5/29,-1/6) -> (5/6,21/25) Hyperbolic Matrix(269,44,324,53) (-1/6,-4/25) -> (24/29,5/6) Hyperbolic Matrix(541,84,702,109) (-3/19,-2/13) -> (10/13,27/35) Hyperbolic Matrix(1567,234,2538,379) (-3/20,-4/27) -> (50/81,21/34) Hyperbolic Matrix(1133,166,1836,269) (-4/27,-1/7) -> (29/47,50/81) Hyperbolic Matrix(2539,330,2916,379) (-3/23,-7/54) -> (47/54,27/31) Hyperbolic Matrix(2537,328,2916,377) (-7/54,-4/31) -> (20/23,47/54) Hyperbolic Matrix(755,88,918,107) (-2/17,-1/9) -> (37/45,14/17) Hyperbolic Matrix(433,46,1026,109) (-1/9,-1/10) -> (27/64,19/45) Hyperbolic Matrix(377,-32,648,-55) (0/1,1/10) -> (57/98,32/55) Hyperbolic Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(701,-92,1242,-163) (1/8,2/15) -> (22/39,35/62) Hyperbolic Matrix(271,-38,378,-53) (2/15,1/7) -> (5/7,28/39) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(1729,-300,2484,-431) (5/29,4/23) -> (16/23,55/79) Hyperbolic Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(865,-164,1134,-215) (3/16,4/21) -> (16/21,29/38) Hyperbolic Matrix(163,-32,270,-53) (4/21,1/5) -> (3/5,20/33) Hyperbolic Matrix(649,-136,1026,-215) (1/5,4/19) -> (12/19,31/49) Hyperbolic Matrix(539,-114,1026,-217) (4/19,11/52) -> (1/2,10/19) Hyperbolic Matrix(1025,-218,1782,-379) (7/33,3/14) -> (23/40,19/33) Hyperbolic Matrix(269,-58,756,-163) (3/14,5/23) -> (11/31,5/14) Hyperbolic Matrix(109,-24,486,-107) (5/23,2/9) -> (2/9,7/31) Parabolic Matrix(377,-86,1188,-271) (5/22,8/35) -> (6/19,7/22) Hyperbolic Matrix(649,-152,918,-215) (3/13,4/17) -> (12/17,29/41) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(2269,-600,3672,-971) (5/19,9/34) -> (21/34,55/89) Hyperbolic Matrix(1241,-330,3456,-919) (13/49,4/15) -> (14/39,37/103) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(703,-206,918,-269) (7/24,5/17) -> (13/17,23/30) Hyperbolic Matrix(2701,-816,4644,-1403) (3/10,13/43) -> (25/43,57/98) Hyperbolic Matrix(1565,-474,4104,-1243) (13/43,10/33) -> (8/21,37/97) Hyperbolic Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(379,-118,864,-269) (4/13,5/16) -> (7/16,18/41) Hyperbolic Matrix(593,-186,864,-271) (5/16,6/19) -> (24/35,11/16) Hyperbolic Matrix(487,-170,1080,-377) (1/3,7/20) -> (9/20,23/51) Hyperbolic Matrix(701,-246,1080,-379) (7/20,6/17) -> (24/37,13/20) Hyperbolic Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(10153,-3648,13824,-4967) (37/103,23/64) -> (47/64,83/113) Hyperbolic Matrix(2269,-816,2700,-971) (23/64,9/25) -> (21/25,37/44) Hyperbolic Matrix(323,-118,594,-217) (4/11,11/30) -> (13/24,6/11) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(11449,-4368,16416,-6263) (37/97,29/76) -> (53/76,83/119) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(1513,-620,2106,-863) (9/22,16/39) -> (28/39,23/32) Hyperbolic Matrix(487,-200,918,-377) (16/39,7/17) -> (9/17,8/15) Hyperbolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(3673,-1524,5724,-2375) (17/41,22/53) -> (34/53,43/67) Hyperbolic Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1727,-728,2052,-865) (8/19,27/64) -> (37/44,16/19) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(1081,-458,1782,-755) (11/26,14/33) -> (20/33,17/28) Hyperbolic Matrix(1403,-596,1782,-757) (14/33,3/7) -> (37/47,26/33) Hyperbolic Matrix(269,-116,378,-163) (3/7,10/23) -> (22/31,5/7) Hyperbolic Matrix(1079,-470,1242,-541) (10/23,17/39) -> (13/15,20/23) Hyperbolic Matrix(2267,-990,2970,-1297) (24/55,7/16) -> (29/38,42/55) Hyperbolic Matrix(217,-96,486,-215) (11/25,4/9) -> (4/9,13/29) Parabolic Matrix(377,-172,594,-271) (5/11,6/13) -> (26/41,7/11) Hyperbolic Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(1511,-796,2052,-1081) (10/19,9/17) -> (67/91,14/19) Hyperbolic Matrix(703,-386,1080,-593) (17/31,11/20) -> (13/20,15/23) Hyperbolic Matrix(271,-150,486,-269) (11/20,5/9) -> (5/9,19/34) Parabolic Matrix(595,-334,864,-485) (14/25,9/16) -> (11/16,20/29) Hyperbolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1835,-1036,2106,-1189) (35/62,13/23) -> (27/31,7/8) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1997,-1148,2538,-1459) (4/7,23/40) -> (11/14,48/61) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(4157,-2526,5778,-3511) (17/28,31/51) -> (41/57,59/82) Hyperbolic Matrix(8479,-5240,10746,-6641) (55/89,89/144) -> (71/90,15/19) Hyperbolic Matrix(9073,-5608,11880,-7343) (89/144,34/55) -> (42/55,55/72) Hyperbolic Matrix(2861,-1770,4104,-2539) (47/76,13/21) -> (23/33,53/76) Hyperbolic Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(3023,-1914,4266,-2701) (50/79,19/30) -> (17/24,56/79) Hyperbolic Matrix(2537,-1626,3456,-2215) (41/64,25/39) -> (11/15,47/64) Hyperbolic Matrix(593,-382,756,-487) (9/14,11/17) -> (29/37,11/14) Hyperbolic Matrix(917,-626,1188,-811) (2/3,13/19) -> (27/35,44/57) Hyperbolic Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(7073,-5014,9828,-6967) (56/79,39/55) -> (77/107,18/25) Hyperbolic Matrix(6965,-5126,8586,-6319) (39/53,53/72) -> (73/90,43/53) Hyperbolic Matrix(379,-294,486,-377) (17/22,7/9) -> (7/9,25/32) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,0,1) Matrix(271,248,-648,-593) -> Matrix(1,4,-2,-7) Matrix(593,530,1026,917) -> Matrix(1,2,0,1) Matrix(379,334,-918,-809) -> Matrix(1,0,-2,1) Matrix(541,470,-1242,-1079) -> Matrix(1,2,-2,-3) Matrix(107,92,-378,-325) -> Matrix(1,-2,-2,5) Matrix(269,228,-702,-595) -> Matrix(1,6,0,1) Matrix(161,136,702,593) -> Matrix(1,6,0,1) Matrix(971,816,-2700,-2269) -> Matrix(7,24,-12,-41) Matrix(55,46,324,271) -> Matrix(1,2,0,1) Matrix(53,44,324,269) -> Matrix(1,2,0,1) Matrix(755,624,-2484,-2053) -> Matrix(1,0,0,1) Matrix(325,268,918,757) -> Matrix(1,2,2,5) Matrix(161,132,-594,-487) -> Matrix(1,2,-4,-7) Matrix(485,396,594,485) -> Matrix(5,6,4,5) Matrix(703,572,864,703) -> Matrix(5,4,6,5) Matrix(269,218,-1134,-919) -> Matrix(1,0,2,1) Matrix(107,86,-270,-217) -> Matrix(1,0,0,1) Matrix(377,298,-1026,-811) -> Matrix(5,-4,-6,5) Matrix(487,384,-1026,-809) -> Matrix(1,-2,0,1) Matrix(1081,852,3564,2809) -> Matrix(1,0,0,1) Matrix(757,596,-1782,-1403) -> Matrix(1,-2,-2,5) Matrix(487,382,-756,-593) -> Matrix(1,-2,0,1) Matrix(377,294,-486,-379) -> Matrix(1,-10,0,1) Matrix(2375,1838,3348,2591) -> Matrix(1,4,0,1) Matrix(1999,1546,5238,4051) -> Matrix(1,10,0,1) Matrix(811,626,-1188,-917) -> Matrix(1,2,0,1) Matrix(109,84,702,541) -> Matrix(1,4,0,1) Matrix(269,206,-918,-703) -> Matrix(3,10,-4,-13) Matrix(215,164,-1134,-865) -> Matrix(1,2,-6,-11) Matrix(431,328,1134,863) -> Matrix(1,4,0,1) Matrix(431,318,-1026,-757) -> Matrix(3,2,-2,-1) Matrix(1403,1032,-3672,-2701) -> Matrix(11,6,-2,-1) Matrix(1189,874,2646,1945) -> Matrix(11,4,8,3) Matrix(2215,1626,-3456,-2537) -> Matrix(1,0,2,1) Matrix(377,276,810,593) -> Matrix(1,0,2,1) Matrix(755,552,-2808,-2053) -> Matrix(1,0,0,1) Matrix(107,78,-594,-433) -> Matrix(1,0,4,1) Matrix(215,156,594,431) -> Matrix(1,-2,2,-3) Matrix(271,196,972,703) -> Matrix(1,0,2,1) Matrix(269,194,972,701) -> Matrix(1,0,2,1) Matrix(3511,2526,-5778,-4157) -> Matrix(1,-2,0,1) Matrix(431,310,1350,971) -> Matrix(1,0,0,1) Matrix(53,38,-378,-271) -> Matrix(1,0,-2,1) Matrix(163,116,-378,-269) -> Matrix(1,0,-2,1) Matrix(215,152,-918,-649) -> Matrix(1,-4,0,1) Matrix(647,456,918,647) -> Matrix(1,-12,0,1) Matrix(379,266,540,379) -> Matrix(1,10,0,1) Matrix(1943,1356,-4644,-3241) -> Matrix(1,6,-2,-11) Matrix(2539,1770,-4104,-2861) -> Matrix(1,2,0,1) Matrix(755,526,3564,2483) -> Matrix(1,4,0,1) Matrix(431,300,-2484,-1729) -> Matrix(3,8,4,11) Matrix(271,188,702,487) -> Matrix(1,2,0,1) Matrix(485,334,-864,-595) -> Matrix(1,2,0,1) Matrix(271,186,-864,-593) -> Matrix(1,2,0,1) Matrix(379,258,1350,919) -> Matrix(1,2,4,9) Matrix(593,386,-1080,-703) -> Matrix(1,-2,0,1) Matrix(379,246,-1080,-701) -> Matrix(1,0,-2,1) Matrix(161,104,918,593) -> Matrix(1,0,-2,1) Matrix(2375,1524,-5724,-3673) -> Matrix(1,0,0,1) Matrix(1837,1178,4212,2701) -> Matrix(1,-2,2,-3) Matrix(3671,2352,-13824,-8857) -> Matrix(1,0,-4,1) Matrix(431,276,-2700,-1729) -> Matrix(1,0,0,1) Matrix(163,104,594,379) -> Matrix(1,0,2,1) Matrix(271,172,-594,-377) -> Matrix(1,-2,0,1) Matrix(215,136,-1026,-649) -> Matrix(1,-2,-2,5) Matrix(647,408,1026,647) -> Matrix(1,-8,0,1) Matrix(271,170,432,271) -> Matrix(1,6,0,1) Matrix(647,402,-1566,-973) -> Matrix(1,2,-2,-3) Matrix(2051,1272,-5400,-3349) -> Matrix(1,0,0,1) Matrix(271,168,1134,703) -> Matrix(1,2,0,1) Matrix(4967,3072,-16416,-10153) -> Matrix(1,0,0,1) Matrix(1187,734,5238,3239) -> Matrix(1,4,0,1) Matrix(971,600,-3672,-2269) -> Matrix(1,2,-6,-11) Matrix(107,66,-702,-433) -> Matrix(1,0,0,1) Matrix(215,132,702,431) -> Matrix(1,4,0,1) Matrix(379,232,972,595) -> Matrix(1,2,0,1) Matrix(377,230,972,593) -> Matrix(1,2,0,1) Matrix(1243,756,2754,1675) -> Matrix(3,4,2,3) Matrix(1511,918,-7290,-4429) -> Matrix(1,2,-2,-3) Matrix(53,32,-270,-163) -> Matrix(1,2,-4,-7) Matrix(161,96,270,161) -> Matrix(5,6,4,5) Matrix(703,416,1188,703) -> Matrix(17,16,18,17) Matrix(593,350,-2106,-1243) -> Matrix(7,6,-20,-17) Matrix(431,254,-918,-541) -> Matrix(5,4,-4,-3) Matrix(593,348,-1566,-919) -> Matrix(7,4,-2,-1) Matrix(973,570,2214,1297) -> Matrix(17,10,22,13) Matrix(2051,1200,-5724,-3349) -> Matrix(25,12,-48,-23) Matrix(541,316,1296,757) -> Matrix(1,0,4,1) Matrix(539,314,1296,755) -> Matrix(1,0,4,1) Matrix(55,32,-648,-377) -> Matrix(1,0,2,1) Matrix(757,440,1674,973) -> Matrix(5,2,2,1) Matrix(269,156,-1026,-595) -> Matrix(1,0,-6,1) Matrix(325,188,-2052,-1187) -> Matrix(1,0,0,1) Matrix(917,530,1026,593) -> Matrix(1,2,0,1) Matrix(433,250,-2430,-1403) -> Matrix(1,0,4,1) Matrix(701,404,-1782,-1027) -> Matrix(1,0,-2,1) Matrix(379,218,-1782,-1025) -> Matrix(1,0,-2,1) Matrix(109,62,-378,-215) -> Matrix(1,2,-2,-3) Matrix(163,92,-1242,-701) -> Matrix(1,0,-2,1) Matrix(1511,852,4212,2375) -> Matrix(1,-6,2,-11) Matrix(703,396,-2970,-1673) -> Matrix(1,2,0,1) Matrix(917,514,2214,1241) -> Matrix(1,0,2,1) Matrix(269,150,-486,-271) -> Matrix(1,-2,0,1) Matrix(3349,1846,5292,2917) -> Matrix(1,0,0,1) Matrix(701,386,2646,1457) -> Matrix(1,2,4,9) Matrix(1079,592,2754,1511) -> Matrix(1,2,-2,-3) Matrix(701,384,1674,917) -> Matrix(1,0,2,1) Matrix(217,118,-594,-323) -> Matrix(3,4,-4,-5) Matrix(217,116,810,433) -> Matrix(1,2,2,5) Matrix(377,200,-918,-487) -> Matrix(1,2,-4,-7) Matrix(541,256,-2052,-971) -> Matrix(1,0,-4,1) Matrix(593,276,810,377) -> Matrix(1,0,2,1) Matrix(539,248,702,323) -> Matrix(1,4,0,1) Matrix(973,440,1674,757) -> Matrix(1,2,2,5) Matrix(377,170,-1080,-487) -> Matrix(1,2,-4,-7) Matrix(215,96,-486,-217) -> Matrix(7,8,-8,-9) Matrix(2699,1190,3672,1619) -> Matrix(5,4,16,13) Matrix(1457,642,1836,809) -> Matrix(5,4,6,5) Matrix(269,118,-864,-379) -> Matrix(3,2,4,3) Matrix(325,142,-1728,-755) -> Matrix(3,2,-26,-17) Matrix(2701,1178,4212,1837) -> Matrix(3,2,-2,-1) Matrix(271,118,-2106,-917) -> Matrix(3,2,-8,-5) Matrix(1943,844,2484,1079) -> Matrix(11,6,-2,-1) Matrix(595,258,-2862,-1241) -> Matrix(3,2,-8,-5) Matrix(541,230,-2538,-1079) -> Matrix(1,0,0,1) Matrix(269,114,-1404,-595) -> Matrix(1,0,-2,1) Matrix(757,320,-2808,-1187) -> Matrix(1,0,0,1) Matrix(109,46,1026,433) -> Matrix(1,0,-4,1) Matrix(2485,1048,-6912,-2915) -> Matrix(7,-4,-12,7) Matrix(1243,522,1674,703) -> Matrix(5,6,4,5) Matrix(1997,838,2700,1133) -> Matrix(9,8,10,9) Matrix(917,384,1674,701) -> Matrix(1,0,2,1) Matrix(757,316,1296,541) -> Matrix(1,0,4,1) Matrix(755,314,1296,539) -> Matrix(1,0,4,1) Matrix(6103,2532,9504,3943) -> Matrix(1,2,0,1) Matrix(7937,3292,12366,5129) -> Matrix(3,2,4,3) Matrix(1081,448,1566,649) -> Matrix(5,2,2,1) Matrix(2483,1024,3402,1403) -> Matrix(1,0,4,1) Matrix(1027,422,-4860,-1997) -> Matrix(5,2,-8,-3) Matrix(161,66,-1188,-487) -> Matrix(1,0,2,1) Matrix(485,198,1188,485) -> Matrix(1,0,10,1) Matrix(109,44,270,109) -> Matrix(1,0,0,1) Matrix(1621,636,-5778,-2267) -> Matrix(1,0,-8,1) Matrix(811,318,1242,487) -> Matrix(1,0,-2,1) Matrix(595,232,972,379) -> Matrix(1,2,0,1) Matrix(593,230,972,377) -> Matrix(1,2,0,1) Matrix(487,188,702,271) -> Matrix(1,2,0,1) Matrix(1567,600,1836,703) -> Matrix(1,-14,0,1) Matrix(2159,826,2538,971) -> Matrix(1,24,0,1) Matrix(2267,866,-10746,-4105) -> Matrix(1,6,-2,-11) Matrix(2807,1072,-11880,-4537) -> Matrix(1,4,0,1) Matrix(4643,1772,5940,2267) -> Matrix(1,0,0,1) Matrix(1243,474,-4104,-1565) -> Matrix(1,2,0,1) Matrix(863,328,1134,431) -> Matrix(1,4,0,1) Matrix(7237,2748,11664,4429) -> Matrix(1,4,0,1) Matrix(7235,2746,11664,4427) -> Matrix(1,4,0,1) Matrix(53,20,-432,-163) -> Matrix(1,2,-4,-7) Matrix(161,60,432,161) -> Matrix(5,6,4,5) Matrix(379,140,1026,379) -> Matrix(15,14,16,15) Matrix(2375,872,5292,1943) -> Matrix(39,32,28,23) Matrix(1243,456,-4266,-1565) -> Matrix(23,18,-32,-25) Matrix(1567,574,2214,811) -> Matrix(13,10,-4,-3) Matrix(431,156,594,215) -> Matrix(3,2,-2,-1) Matrix(919,330,-3456,-1241) -> Matrix(7,4,-30,-17) Matrix(2375,852,4212,1511) -> Matrix(11,6,-2,-1) Matrix(7237,2592,12366,4429) -> Matrix(55,28,108,55) Matrix(5561,1990,9504,3401) -> Matrix(37,18,76,37) Matrix(163,58,-756,-269) -> Matrix(5,2,-8,-3) Matrix(1891,666,2916,1027) -> Matrix(1,0,2,1) Matrix(1889,664,2916,1025) -> Matrix(1,0,2,1) Matrix(755,262,1242,431) -> Matrix(5,2,2,1) Matrix(271,86,-1188,-377) -> Matrix(1,-2,0,1) Matrix(1999,630,2916,919) -> Matrix(1,2,0,1) Matrix(1997,628,2916,917) -> Matrix(1,2,0,1) Matrix(917,284,1566,485) -> Matrix(1,-4,2,-7) Matrix(431,132,702,215) -> Matrix(1,4,0,1) Matrix(8533,2592,10314,3133) -> Matrix(1,4,0,1) Matrix(9557,2902,11556,3509) -> Matrix(3,4,2,3) Matrix(2809,852,3564,1081) -> Matrix(1,0,0,1) Matrix(18307,5538,26244,7939) -> Matrix(1,6,0,1) Matrix(18305,5536,26244,7937) -> Matrix(1,6,0,1) Matrix(53,16,-540,-163) -> Matrix(1,2,0,1) Matrix(161,48,540,161) -> Matrix(5,6,4,5) Matrix(271,80,918,271) -> Matrix(11,10,12,11) Matrix(1403,410,2214,647) -> Matrix(5,4,-4,-3) Matrix(2755,802,-9828,-2861) -> Matrix(3,2,16,11) Matrix(757,220,3348,973) -> Matrix(13,8,8,5) Matrix(2377,668,3078,865) -> Matrix(17,4,4,1) Matrix(21059,5906,26568,7451) -> Matrix(1,0,28,1) Matrix(19387,5436,24462,6859) -> Matrix(1,0,-22,1) Matrix(703,196,972,271) -> Matrix(1,0,2,1) Matrix(701,194,972,269) -> Matrix(1,0,2,1) Matrix(379,104,594,163) -> Matrix(1,0,2,1) Matrix(1999,540,3402,919) -> Matrix(11,2,16,3) Matrix(8533,2292,11664,3133) -> Matrix(1,0,4,1) Matrix(8531,2290,11664,3131) -> Matrix(1,0,4,1) Matrix(433,116,810,217) -> Matrix(5,2,2,1) Matrix(19279,5118,26244,6967) -> Matrix(1,0,6,1) Matrix(19277,5116,26244,6965) -> Matrix(1,0,6,1) Matrix(2053,544,3672,973) -> Matrix(1,0,4,1) Matrix(1621,428,-8586,-2267) -> Matrix(1,0,-4,1) Matrix(8803,2322,10854,2863) -> Matrix(1,0,6,1) Matrix(1567,408,2700,703) -> Matrix(1,0,18,1) Matrix(971,250,1674,431) -> Matrix(1,0,-8,1) Matrix(703,168,1134,271) -> Matrix(1,2,0,1) Matrix(5239,1236,6642,1567) -> Matrix(1,-2,0,1) Matrix(379,88,702,163) -> Matrix(1,2,0,1) Matrix(593,136,702,161) -> Matrix(1,6,0,1) Matrix(2213,504,3078,701) -> Matrix(1,2,0,1) Matrix(107,24,-486,-109) -> Matrix(3,4,-4,-5) Matrix(3673,802,5940,1297) -> Matrix(11,8,4,3) Matrix(1405,306,2484,541) -> Matrix(3,2,-2,-1) Matrix(1025,222,1242,269) -> Matrix(1,0,2,1) Matrix(9181,1956,11664,2485) -> Matrix(3,2,-2,-1) Matrix(9179,1954,11664,2483) -> Matrix(3,2,-2,-1) Matrix(2483,526,3564,755) -> Matrix(1,4,0,1) Matrix(5075,1072,6642,1403) -> Matrix(11,8,4,3) Matrix(17603,3652,24462,5075) -> Matrix(5,2,2,1) Matrix(19117,3964,26568,5509) -> Matrix(1,0,4,1) Matrix(1027,212,1836,379) -> Matrix(1,0,2,1) Matrix(7991,1510,10854,2051) -> Matrix(15,2,22,3) Matrix(161,30,864,161) -> Matrix(1,0,22,1) Matrix(109,20,594,109) -> Matrix(1,0,-12,1) Matrix(811,144,918,163) -> Matrix(1,0,-2,1) Matrix(973,170,1242,217) -> Matrix(5,-2,-2,1) Matrix(8047,1392,11556,1999) -> Matrix(43,-40,14,-13) Matrix(7181,1240,10314,1781) -> Matrix(35,-38,12,-13) Matrix(271,46,324,55) -> Matrix(1,2,0,1) Matrix(269,44,324,53) -> Matrix(1,2,0,1) Matrix(541,84,702,109) -> Matrix(1,4,0,1) Matrix(1567,234,2538,379) -> Matrix(5,6,4,5) Matrix(1133,166,1836,269) -> Matrix(3,2,4,3) Matrix(2539,330,2916,379) -> Matrix(1,0,2,1) Matrix(2537,328,2916,377) -> Matrix(1,0,2,1) Matrix(755,88,918,107) -> Matrix(13,2,6,1) Matrix(433,46,1026,109) -> Matrix(1,0,-4,1) Matrix(377,-32,648,-55) -> Matrix(1,0,2,1) Matrix(539,-64,918,-109) -> Matrix(9,-2,14,-3) Matrix(701,-92,1242,-163) -> Matrix(1,0,-2,1) Matrix(271,-38,378,-53) -> Matrix(1,0,-2,1) Matrix(433,-66,702,-107) -> Matrix(1,0,0,1) Matrix(1729,-276,2700,-431) -> Matrix(1,0,0,1) Matrix(1729,-300,2484,-431) -> Matrix(11,8,4,3) Matrix(433,-78,594,-107) -> Matrix(1,0,4,1) Matrix(865,-164,1134,-215) -> Matrix(11,-2,6,-1) Matrix(163,-32,270,-53) -> Matrix(7,-2,4,-1) Matrix(649,-136,1026,-215) -> Matrix(5,-2,-2,1) Matrix(539,-114,1026,-217) -> Matrix(5,-4,4,-3) Matrix(1025,-218,1782,-379) -> Matrix(1,0,-2,1) Matrix(269,-58,756,-163) -> Matrix(3,-2,8,-5) Matrix(109,-24,486,-107) -> Matrix(5,-4,4,-3) Matrix(377,-86,1188,-271) -> Matrix(1,-2,0,1) Matrix(649,-152,918,-215) -> Matrix(1,-4,0,1) Matrix(919,-218,1134,-269) -> Matrix(1,0,2,1) Matrix(595,-156,1026,-269) -> Matrix(1,0,-6,1) Matrix(2269,-600,3672,-971) -> Matrix(11,-2,6,-1) Matrix(1241,-330,3456,-919) -> Matrix(17,-4,30,-7) Matrix(2053,-552,2808,-755) -> Matrix(1,0,0,1) Matrix(487,-132,594,-161) -> Matrix(7,-2,4,-1) Matrix(2267,-636,5778,-1621) -> Matrix(1,0,-8,1) Matrix(325,-92,378,-107) -> Matrix(5,-2,-2,1) Matrix(215,-62,378,-109) -> Matrix(3,-2,2,-1) Matrix(703,-206,918,-269) -> Matrix(13,-10,4,-3) Matrix(2701,-816,4644,-1403) -> Matrix(1,-2,2,-3) Matrix(1565,-474,4104,-1243) -> Matrix(1,2,0,1) Matrix(2053,-624,2484,-755) -> Matrix(1,0,0,1) Matrix(379,-118,864,-269) -> Matrix(3,2,4,3) Matrix(593,-186,864,-271) -> Matrix(1,2,0,1) Matrix(487,-170,1080,-377) -> Matrix(7,-2,4,-1) Matrix(701,-246,1080,-379) -> Matrix(1,0,-2,1) Matrix(3349,-1200,5724,-2051) -> Matrix(23,-12,48,-25) Matrix(10153,-3648,13824,-4967) -> Matrix(7,-4,16,-9) Matrix(2269,-816,2700,-971) -> Matrix(41,-24,12,-7) Matrix(323,-118,594,-217) -> Matrix(5,-4,4,-3) Matrix(811,-298,1026,-377) -> Matrix(5,-4,-6,5) Matrix(919,-348,1566,-593) -> Matrix(1,-4,2,-7) Matrix(3349,-1272,5400,-2051) -> Matrix(1,0,0,1) Matrix(11449,-4368,16416,-6263) -> Matrix(1,0,0,1) Matrix(2701,-1032,3672,-1403) -> Matrix(1,-6,2,-11) Matrix(595,-228,702,-269) -> Matrix(1,6,0,1) Matrix(5779,-2268,7290,-2861) -> Matrix(1,0,10,1) Matrix(217,-86,270,-107) -> Matrix(1,0,0,1) Matrix(1513,-620,2106,-863) -> Matrix(1,0,-4,1) Matrix(487,-200,918,-377) -> Matrix(7,-2,4,-1) Matrix(973,-402,1566,-647) -> Matrix(3,-2,2,-1) Matrix(3673,-1524,5724,-2375) -> Matrix(1,0,0,1) Matrix(593,-248,648,-271) -> Matrix(7,-4,2,-1) Matrix(757,-318,1026,-431) -> Matrix(1,-2,2,-3) Matrix(1727,-728,2052,-865) -> Matrix(1,4,0,1) Matrix(1997,-844,2430,-1027) -> Matrix(7,-2,4,-1) Matrix(1081,-458,1782,-755) -> Matrix(3,-2,2,-1) Matrix(1403,-596,1782,-757) -> Matrix(5,-2,-2,1) Matrix(269,-116,378,-163) -> Matrix(1,0,-2,1) Matrix(1079,-470,1242,-541) -> Matrix(3,-2,2,-1) Matrix(2267,-990,2970,-1297) -> Matrix(19,-12,8,-5) Matrix(217,-96,486,-215) -> Matrix(9,-8,8,-7) Matrix(377,-172,594,-271) -> Matrix(1,-2,0,1) Matrix(541,-254,918,-431) -> Matrix(3,-4,4,-5) Matrix(1511,-796,2052,-1081) -> Matrix(3,-4,4,-5) Matrix(703,-386,1080,-593) -> Matrix(1,-2,0,1) Matrix(271,-150,486,-269) -> Matrix(1,-2,0,1) Matrix(595,-334,864,-485) -> Matrix(1,2,0,1) Matrix(1403,-790,1728,-973) -> Matrix(1,-2,2,-3) Matrix(1835,-1036,2106,-1189) -> Matrix(1,0,0,1) Matrix(2267,-1284,2862,-1621) -> Matrix(1,0,-4,1) Matrix(1997,-1148,2538,-1459) -> Matrix(1,-2,0,1) Matrix(1135,-654,1404,-809) -> Matrix(1,0,2,1) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(4427,-2560,6912,-3997) -> Matrix(1,0,0,1) Matrix(3833,-2258,4860,-2863) -> Matrix(3,-2,-4,3) Matrix(1027,-606,1188,-701) -> Matrix(5,-4,-6,5) Matrix(4157,-2526,5778,-3511) -> Matrix(1,-2,0,1) Matrix(8479,-5240,10746,-6641) -> Matrix(3,-4,-2,3) Matrix(9073,-5608,11880,-7343) -> Matrix(9,-16,4,-7) Matrix(2861,-1770,4104,-2539) -> Matrix(1,2,0,1) Matrix(379,-236,432,-269) -> Matrix(1,-2,0,1) Matrix(3023,-1914,4266,-2701) -> Matrix(1,0,0,1) Matrix(2537,-1626,3456,-2215) -> Matrix(1,0,2,1) Matrix(593,-382,756,-487) -> Matrix(1,-2,0,1) Matrix(917,-626,1188,-811) -> Matrix(1,2,0,1) Matrix(487,-340,540,-377) -> Matrix(1,-2,0,1) Matrix(7073,-5014,9828,-6967) -> Matrix(1,2,0,1) Matrix(6965,-5126,8586,-6319) -> Matrix(3,-2,8,-5) Matrix(379,-294,486,-377) -> Matrix(1,-10,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 Degree of the the map X: 81 Degree of the the map Y: 324 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (0/1,1/0) 0 27 1/10 (-1/1,-1/2) 0 27 1/9 0/1 7 3 1/8 (1/3,1/2) 0 27 2/15 1/1 1 9 1/7 1/2 1 27 2/13 (0/1,1/0) 0 27 3/19 1/0 1 27 4/25 (0/1,1/0) 0 27 1/6 0 9 5/29 -5/4 1 27 4/23 (-2/3,-1/2) 0 27 3/17 -1/2 1 27 2/11 (-1/6,0/1) 0 27 5/27 0/1 17 1 3/16 (0/1,1/11) 0 27 4/21 1/5 1 9 1/5 1/2 1 27 4/19 (1/2,2/3) 0 27 11/52 (4/5,1/1) 0 27 7/33 0/1 1 9 3/14 (1/3,1/2) 0 27 5/23 1/2 1 27 2/9 1/1 2 3 7/31 3/2 1 27 12/53 (2/1,9/4) 0 27 5/22 (1/1,2/1) 0 27 8/35 (2/1,1/0) 0 27 3/13 1/0 1 27 4/17 (-2/1,1/0) 0 27 5/21 0/1 1 9 1/4 (-1/1,0/1) 0 27 5/19 1/6 1 27 9/34 (1/5,1/4) 0 27 13/49 1/4 1 27 4/15 1/3 1 9 11/41 1/2 1 27 7/26 (0/1,1/3) 0 27 3/11 1/2 1 27 8/29 (0/1,1/2) 0 27 5/18 0 3 7/25 1/0 1 27 16/57 1/5 1 9 9/32 (2/7,1/3) 0 27 2/7 (1/2,2/3) 0 27 7/24 0 9 5/17 5/6 1 27 8/27 1/1 8 1 3/10 (1/1,3/2) 0 27 13/43 1/0 1 27 10/33 1/1 1 9 17/56 (1/1,2/1) 0 27 7/23 1/0 1 27 4/13 (4/1,1/0) 0 27 5/16 (0/1,1/1) 0 27 6/19 (0/1,1/0) 0 27 7/22 (-1/1,0/1) 0 27 1/3 0/1 1 9 7/20 (1/2,1/1) 0 27 6/17 (0/1,1/2) 0 27 11/31 1/2 1 27 5/14 (3/7,1/2) 0 27 19/53 1/2 1 27 14/39 5/9 1 9 37/103 1/2 1 27 23/64 (1/2,5/9) 0 27 9/25 5/8 1 27 4/11 (2/3,3/4) 0 27 11/30 0 9 7/19 7/8 1 27 10/27 1/1 10 1 3/8 (1/1,3/2) 0 27 11/29 1/0 1 27 19/50 (2/1,3/1) 0 27 8/21 3/1 1 9 37/97 1/0 1 27 29/76 (4/1,5/1) 0 27 21/55 1/0 1 27 13/34 (9/1,1/0) 0 27 5/13 1/0 1 27 12/31 (-1/2,0/1) 0 27 7/18 0 3 9/23 1/0 1 27 20/51 -1/3 1 9 31/79 -1/8 1 27 11/28 (0/1,1/5) 0 27 2/5 (0/1,1/0) 0 27 11/27 0/1 5 1 9/22 (0/1,1/5) 0 27 16/39 1/3 1 9 7/17 1/2 1 27 12/29 (0/1,1/2) 0 27 17/41 1/2 1 27 22/53 (0/1,1/2) 0 27 5/12 0 9 23/55 1/2 1 27 18/43 (1/2,2/3) 0 27 13/31 3/4 1 27 8/19 (0/1,1/0) 0 27 27/64 (-1/2,-1/3) 0 27 19/45 0/1 7 3 11/26 (0/1,1/3) 0 27 14/33 1/3 1 9 3/7 1/2 1 27 10/23 (1/2,2/3) 0 27 17/39 2/3 1 9 24/55 (5/8,2/3) 0 27 7/16 (2/3,5/7) 0 27 18/41 (14/19,3/4) 0 27 11/25 3/4 1 27 4/9 1/1 4 3 13/29 5/4 1 27 22/49 (4/3,3/2) 0 27 9/20 (3/2,5/3) 0 27 23/51 2/1 1 9 14/31 (7/4,2/1) 0 27 5/11 1/0 1 27 6/13 (0/1,1/0) 0 27 7/15 0/1 1 9 1/2 (0/1,1/1) 0 27 10/19 (3/2,2/1) 0 27 9/17 3/2 1 27 8/15 1/1 1 9 7/13 1/0 1 27 13/24 0 9 6/11 (2/1,1/0) 0 27 17/31 3/2 1 27 11/20 (1/1,1/0) 0 27 5/9 1/0 1 3 19/34 (-1/1,1/0) 0 27 33/59 1/0 1 27 14/25 (0/1,1/0) 0 27 9/16 (0/1,1/1) 0 27 31/55 1/0 1 27 22/39 -1/1 1 9 35/62 (1/1,1/0) 0 27 13/23 1/0 1 27 30/53 (-1/6,0/1) 0 27 17/30 0 9 4/7 (0/1,1/0) 0 27 23/40 (1/1,1/0) 0 27 19/33 0/1 1 9 15/26 (0/1,1/3) 0 27 26/45 1/1 1 3 37/64 (-1/1,1/0) 0 27 11/19 1/0 1 27 29/50 (-1/7,0/1) 0 27 47/81 0/1 13 1 18/31 (0/1,1/6) 0 27 25/43 1/2 1 27 57/98 (1/1,1/0) 0 27 32/55 (0/1,1/2) 0 27 7/12 0 9 31/53 1/2 1 27 55/94 (15/31,1/2) 0 27 79/135 1/2 23 1 24/41 (1/2,8/15) 0 27 17/29 1/2 1 27 27/46 (3/5,5/8) 0 27 37/63 2/3 7 3 10/17 (2/3,3/4) 0 27 33/56 (4/5,1/1) 0 27 23/39 4/5 1 9 13/22 (8/9,1/1) 0 27 16/27 1/1 11 1 3/5 3/2 1 27 20/33 3/1 1 9 17/28 (2/1,3/1) 0 27 31/51 2/1 1 9 14/23 (2/1,5/2) 0 27 11/18 0 3 19/31 1/0 1 27 8/13 (0/1,1/0) 0 27 29/47 1/2 1 27 50/81 1/1 4 1 21/34 (1/1,3/2) 0 27 55/89 1/0 1 27 89/144 0 3 34/55 (7/4,2/1) 0 27 47/76 (2/1,3/1) 0 27 13/21 2/1 1 9 31/50 (2/1,3/1) 0 27 49/79 1/0 1 27 67/108 (2/1,1/0) 0 1 18/29 (2/1,1/0) 0 27 23/37 1/0 1 27 5/8 (3/1,1/0) 0 27 17/27 1/0 7 1 12/19 (-4/1,1/0) 0 27 31/49 1/0 1 27 50/79 (-2/1,1/0) 0 27 19/30 0 9 26/41 (-2/1,1/0) 0 27 7/11 1/0 1 27 16/25 (0/1,1/0) 0 27 57/89 1/0 1 27 41/64 (-1/1,1/0) 0 27 25/39 0/1 1 9 34/53 (0/1,1/2) 0 27 43/67 1/2 1 27 52/81 1/1 2 1 9/14 (1/1,1/0) 0 27 11/17 1/0 1 27 35/54 (0/1,1/0) 0 1 24/37 (0/1,1/0) 0 27 13/20 (-1/1,1/0) 0 27 15/23 -1/2 1 27 2/3 1/1 1 9 13/19 1/0 1 27 37/54 (2/1,1/0) 0 1 24/35 (2/1,1/0) 0 27 11/16 (2/1,3/1) 0 27 20/29 (2/1,1/0) 0 27 9/13 1/0 1 27 16/23 (2/1,5/2) 0 27 55/79 23/8 1 27 94/135 3/1 13 1 39/56 (3/1,16/5) 0 27 23/33 4/1 1 9 53/76 (4/1,5/1) 0 27 83/119 1/0 1 27 113/162 (4/1,1/0) 0 1 30/43 (4/1,1/0) 0 27 7/10 (5/1,1/0) 0 27 19/27 1/0 11 1 12/17 (-6/1,1/0) 0 27 29/41 1/0 1 27 17/24 0 9 56/79 (-2/1,1/0) 0 27 39/55 1/0 1 27 22/31 (-2/1,1/0) 0 27 5/7 1/0 1 27 28/39 -1/1 1 9 23/32 (0/1,1/1) 0 27 41/57 0/1 1 9 59/82 (0/1,1/1) 0 27 136/189 1/1 1 1 77/107 1/0 1 27 18/25 (0/1,1/0) 0 27 13/18 0 3 21/29 1/2 1 27 8/11 (-1/2,0/1) 0 27 27/37 1/2 1 27 46/63 1/1 1 3 19/26 (0/1,1/3) 0 27 49/67 1/2 1 27 79/108 (0/1,1/2) 0 1 30/41 (0/1,1/2) 0 27 11/15 0/1 1 9 47/64 (1/2,1/1) 0 27 83/113 1/2 1 27 119/162 (0/1,1/2) 0 1 36/49 (0/1,1/2) 0 27 25/34 (3/7,1/2) 0 27 39/53 1/2 1 27 53/72 0 3 67/91 1/2 1 27 14/19 (1/2,2/3) 0 27 17/23 5/6 1 27 20/27 1/1 7 1 3/4 (1/1,2/1) 0 27 16/21 1/1 1 9 29/38 (2/1,11/5) 0 27 42/55 (2/1,1/0) 0 27 55/72 0 3 13/17 5/2 1 27 23/30 0 9 10/13 (4/1,1/0) 0 27 27/35 1/0 1 27 44/57 3/1 1 9 17/22 (5/1,6/1) 0 27 7/9 1/0 5 3 25/32 (-5/1,-4/1) 0 27 43/55 1/0 1 27 18/23 (-4/1,1/0) 0 27 29/37 1/0 1 27 11/14 (-1/1,1/0) 0 27 48/61 (-2/1,1/0) 0 27 85/108 (-2/1,1/0) 0 1 37/47 1/0 1 27 26/33 -1/1 1 9 41/52 (-2/1,-1/1) 0 27 56/71 (0/1,1/0) 0 27 71/90 0 3 15/19 -3/2 1 27 19/24 0 9 42/53 (-1/10,0/1) 0 27 107/135 0/1 25 1 65/82 (0/1,1/15) 0 27 23/29 1/2 1 27 4/5 (0/1,1/0) 0 27 21/26 (0/1,1/5) 0 27 17/21 0/1 1 9 30/37 (1/2,2/3) 0 27 73/90 0 3 43/53 1/2 1 27 13/16 (2/3,1/1) 0 27 22/27 1/1 5 1 9/11 3/2 1 27 23/28 (1/1,2/1) 0 27 37/45 2/1 7 3 14/17 (2/1,1/0) 0 27 19/23 1/0 1 27 43/52 (1/1,2/1) 0 27 67/81 2/1 1 1 24/29 (2/1,1/0) 0 27 5/6 0 9 21/25 13/4 1 27 37/44 (7/2,11/3) 0 27 16/19 (4/1,1/0) 0 27 11/13 1/0 1 27 17/20 (15/1,1/0) 0 27 23/27 1/0 19 1 6/7 (-4/1,1/0) 0 27 19/22 (-4/3,-1/1) 0 27 13/15 0/1 1 9 20/23 (0/1,1/0) 0 27 47/54 (0/1,1/0) 0 1 27/31 1/0 1 27 7/8 (1/1,1/0) 0 27 15/17 1/0 1 27 8/9 1/1 1 3 9/10 (3/1,1/0) 0 27 10/11 (2/1,1/0) 0 27 1/1 1/0 1 27 1/0 (0/1,1/0) 0 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(377,-32,648,-55) (0/1,1/10) -> (57/98,32/55) Hyperbolic Matrix(433,-46,1026,-109) (1/10,1/9) -> (27/64,19/45) Glide Reflection Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(701,-92,1242,-163) (1/8,2/15) -> (22/39,35/62) Hyperbolic Matrix(271,-38,378,-53) (2/15,1/7) -> (5/7,28/39) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(541,-84,702,-109) (2/13,3/19) -> (10/13,27/35) Glide Reflection Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(269,-44,324,-53) (4/25,1/6) -> (24/29,5/6) Glide Reflection Matrix(271,-46,324,-55) (1/6,5/29) -> (5/6,21/25) Glide Reflection Matrix(1729,-300,2484,-431) (5/29,4/23) -> (16/23,55/79) Hyperbolic Matrix(973,-170,1242,-217) (4/23,3/17) -> (18/23,29/37) Glide Reflection Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(109,-20,594,-109) (2/11,5/27) -> (2/11,5/27) Reflection Matrix(161,-30,864,-161) (5/27,3/16) -> (5/27,3/16) Reflection Matrix(865,-164,1134,-215) (3/16,4/21) -> (16/21,29/38) Hyperbolic Matrix(163,-32,270,-53) (4/21,1/5) -> (3/5,20/33) Hyperbolic Matrix(649,-136,1026,-215) (1/5,4/19) -> (12/19,31/49) Hyperbolic Matrix(539,-114,1026,-217) (4/19,11/52) -> (1/2,10/19) Hyperbolic Matrix(2483,-526,3564,-755) (11/52,7/33) -> (39/56,23/33) Glide Reflection Matrix(1025,-218,1782,-379) (7/33,3/14) -> (23/40,19/33) Hyperbolic Matrix(269,-58,756,-163) (3/14,5/23) -> (11/31,5/14) Hyperbolic Matrix(109,-24,486,-107) (5/23,2/9) -> (2/9,7/31) Parabolic Matrix(1619,-366,2862,-647) (7/31,12/53) -> (13/23,30/53) Glide Reflection Matrix(3239,-734,5238,-1187) (12/53,5/22) -> (34/55,47/76) Glide Reflection Matrix(377,-86,1188,-271) (5/22,8/35) -> (6/19,7/22) Hyperbolic Matrix(593,-136,702,-161) (8/35,3/13) -> (16/19,11/13) Glide Reflection Matrix(649,-152,918,-215) (3/13,4/17) -> (12/17,29/41) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(703,-168,1134,-271) (5/21,1/4) -> (13/21,31/50) Glide Reflection Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(2269,-600,3672,-971) (5/19,9/34) -> (21/34,55/89) Hyperbolic Matrix(2053,-544,3672,-973) (9/34,13/49) -> (19/34,33/59) Glide Reflection Matrix(1241,-330,3456,-919) (13/49,4/15) -> (14/39,37/103) Hyperbolic Matrix(433,-116,810,-217) (4/15,11/41) -> (8/15,7/13) Glide Reflection Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(379,-104,594,-163) (3/11,8/29) -> (7/11,16/25) Glide Reflection Matrix(701,-194,972,-269) (8/29,5/18) -> (18/25,13/18) Glide Reflection Matrix(703,-196,972,-271) (5/18,7/25) -> (13/18,21/29) Glide Reflection Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(2377,-668,3078,-865) (16/57,9/32) -> (44/57,17/22) Glide Reflection Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(703,-206,918,-269) (7/24,5/17) -> (13/17,23/30) Hyperbolic Matrix(271,-80,918,-271) (5/17,8/27) -> (5/17,8/27) Reflection Matrix(161,-48,540,-161) (8/27,3/10) -> (8/27,3/10) Reflection Matrix(2701,-816,4644,-1403) (3/10,13/43) -> (25/43,57/98) Hyperbolic Matrix(1565,-474,4104,-1243) (13/43,10/33) -> (8/21,37/97) Hyperbolic Matrix(2809,-852,3564,-1081) (10/33,17/56) -> (26/33,41/52) Glide Reflection Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(431,-132,702,-215) (7/23,4/13) -> (19/31,8/13) Glide Reflection Matrix(379,-118,864,-269) (4/13,5/16) -> (7/16,18/41) Hyperbolic Matrix(593,-186,864,-271) (5/16,6/19) -> (24/35,11/16) Hyperbolic Matrix(971,-310,1350,-431) (7/22,1/3) -> (23/32,41/57) Glide Reflection Matrix(487,-170,1080,-377) (1/3,7/20) -> (9/20,23/51) Hyperbolic Matrix(701,-246,1080,-379) (7/20,6/17) -> (24/37,13/20) Hyperbolic Matrix(757,-268,918,-325) (6/17,11/31) -> (14/17,19/23) Glide Reflection Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(2375,-852,4212,-1511) (19/53,14/39) -> (31/55,22/39) Glide Reflection Matrix(10153,-3648,13824,-4967) (37/103,23/64) -> (47/64,83/113) Hyperbolic Matrix(2269,-816,2700,-971) (23/64,9/25) -> (21/25,37/44) Hyperbolic Matrix(431,-156,594,-215) (9/25,4/11) -> (21/29,8/11) Glide Reflection Matrix(323,-118,594,-217) (4/11,11/30) -> (13/24,6/11) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(379,-140,1026,-379) (7/19,10/27) -> (7/19,10/27) Reflection Matrix(161,-60,432,-161) (10/27,3/8) -> (10/27,3/8) Reflection Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(863,-328,1134,-431) (19/50,8/21) -> (3/4,16/21) Glide Reflection Matrix(11449,-4368,16416,-6263) (37/97,29/76) -> (53/76,83/119) Hyperbolic Matrix(4643,-1772,5940,-2267) (29/76,21/55) -> (25/32,43/55) Glide Reflection Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(487,-188,702,-271) (5/13,12/31) -> (9/13,16/23) Glide Reflection Matrix(593,-230,972,-377) (12/31,7/18) -> (14/23,11/18) Glide Reflection Matrix(595,-232,972,-379) (7/18,9/23) -> (11/18,19/31) Glide Reflection Matrix(811,-318,1242,-487) (9/23,20/51) -> (15/23,2/3) Glide Reflection Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(109,-44,270,-109) (2/5,11/27) -> (2/5,11/27) Reflection Matrix(485,-198,1188,-485) (11/27,9/22) -> (11/27,9/22) Reflection Matrix(1513,-620,2106,-863) (9/22,16/39) -> (28/39,23/32) Hyperbolic Matrix(487,-200,918,-377) (16/39,7/17) -> (9/17,8/15) Hyperbolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(1081,-448,1566,-649) (12/29,17/41) -> (20/29,9/13) Glide Reflection Matrix(3673,-1524,5724,-2375) (17/41,22/53) -> (34/53,43/67) Hyperbolic Matrix(755,-314,1296,-539) (22/53,5/12) -> (32/55,7/12) Glide Reflection Matrix(757,-316,1296,-541) (5/12,23/55) -> (7/12,31/53) Glide Reflection Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(917,-384,1674,-701) (18/43,13/31) -> (6/11,17/31) Glide Reflection Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1727,-728,2052,-865) (8/19,27/64) -> (37/44,16/19) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(1081,-458,1782,-755) (11/26,14/33) -> (20/33,17/28) Hyperbolic Matrix(1403,-596,1782,-757) (14/33,3/7) -> (37/47,26/33) Hyperbolic Matrix(269,-116,378,-163) (3/7,10/23) -> (22/31,5/7) Hyperbolic Matrix(1079,-470,1242,-541) (10/23,17/39) -> (13/15,20/23) Hyperbolic Matrix(2701,-1178,4212,-1837) (17/39,24/55) -> (25/39,34/53) Glide Reflection Matrix(2267,-990,2970,-1297) (24/55,7/16) -> (29/38,42/55) Hyperbolic Matrix(1297,-570,2214,-973) (18/41,11/25) -> (24/41,17/29) Glide Reflection Matrix(217,-96,486,-215) (11/25,4/9) -> (4/9,13/29) Parabolic Matrix(1243,-558,1566,-703) (13/29,22/49) -> (23/29,4/5) Glide Reflection Matrix(1945,-874,2646,-1189) (22/49,9/20) -> (36/49,25/34) Glide Reflection Matrix(1675,-756,2754,-1243) (23/51,14/31) -> (31/51,14/23) Glide Reflection Matrix(973,-440,1674,-757) (14/31,5/11) -> (18/31,25/43) Glide Reflection Matrix(377,-172,594,-271) (5/11,6/13) -> (26/41,7/11) Hyperbolic Matrix(593,-276,810,-377) (6/13,7/15) -> (30/41,11/15) Glide Reflection Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(1511,-796,2052,-1081) (10/19,9/17) -> (67/91,14/19) Hyperbolic Matrix(917,-496,1296,-701) (7/13,13/24) -> (29/41,17/24) Glide Reflection Matrix(703,-386,1080,-593) (17/31,11/20) -> (13/20,15/23) Hyperbolic Matrix(271,-150,486,-269) (11/20,5/9) -> (5/9,19/34) Parabolic Matrix(3725,-2084,5886,-3293) (33/59,14/25) -> (31/49,50/79) Glide Reflection Matrix(595,-334,864,-485) (14/25,9/16) -> (11/16,20/29) Hyperbolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1835,-1036,2106,-1189) (35/62,13/23) -> (27/31,7/8) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1997,-1148,2538,-1459) (4/7,23/40) -> (11/14,48/61) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(917,-530,1026,-593) (26/45,37/64) -> (8/9,9/10) Glide Reflection Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(4699,-2726,8100,-4699) (29/50,47/81) -> (29/50,47/81) Reflection Matrix(2915,-1692,5022,-2915) (47/81,18/31) -> (47/81,18/31) Reflection Matrix(14851,-8690,25380,-14851) (55/94,79/135) -> (55/94,79/135) Reflection Matrix(6479,-3792,11070,-6479) (79/135,24/41) -> (79/135,24/41) Reflection Matrix(1511,-888,1836,-1079) (37/63,10/17) -> (37/45,14/17) Glide Reflection Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(703,-416,1188,-703) (13/22,16/27) -> (13/22,16/27) Reflection Matrix(161,-96,270,-161) (16/27,3/5) -> (16/27,3/5) Reflection Matrix(4157,-2526,5778,-3511) (17/28,31/51) -> (41/57,59/82) Hyperbolic Matrix(4699,-2900,7614,-4699) (29/47,50/81) -> (29/47,50/81) Reflection Matrix(3401,-2100,5508,-3401) (50/81,21/34) -> (50/81,21/34) Reflection Matrix(8479,-5240,10746,-6641) (55/89,89/144) -> (71/90,15/19) Hyperbolic Matrix(9073,-5608,11880,-7343) (89/144,34/55) -> (42/55,55/72) Hyperbolic Matrix(2861,-1770,4104,-2539) (47/76,13/21) -> (23/33,53/76) Hyperbolic Matrix(10585,-6566,17064,-10585) (49/79,67/108) -> (49/79,67/108) Reflection Matrix(3887,-2412,6264,-3887) (67/108,18/29) -> (67/108,18/29) Reflection Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(271,-170,432,-271) (5/8,17/27) -> (5/8,17/27) Reflection Matrix(647,-408,1026,-647) (17/27,12/19) -> (17/27,12/19) Reflection Matrix(3023,-1914,4266,-2701) (50/79,19/30) -> (17/24,56/79) Hyperbolic Matrix(1243,-788,1620,-1027) (19/30,26/41) -> (23/30,10/13) Glide Reflection Matrix(2537,-1626,3456,-2215) (41/64,25/39) -> (11/15,47/64) Hyperbolic Matrix(6967,-4472,10854,-6967) (43/67,52/81) -> (43/67,52/81) Reflection Matrix(1457,-936,2268,-1457) (52/81,9/14) -> (52/81,9/14) Reflection Matrix(593,-382,756,-487) (9/14,11/17) -> (29/37,11/14) Hyperbolic Matrix(1189,-770,1836,-1189) (11/17,35/54) -> (11/17,35/54) Reflection Matrix(2591,-1680,3996,-2591) (35/54,24/37) -> (35/54,24/37) Reflection Matrix(917,-626,1188,-811) (2/3,13/19) -> (27/35,44/57) Hyperbolic Matrix(1405,-962,2052,-1405) (13/19,37/54) -> (13/19,37/54) Reflection Matrix(2591,-1776,3780,-2591) (37/54,24/35) -> (37/54,24/35) Reflection Matrix(14851,-10340,21330,-14851) (55/79,94/135) -> (55/79,94/135) Reflection Matrix(10529,-7332,15120,-10529) (94/135,39/56) -> (94/135,39/56) Reflection Matrix(26893,-18758,38556,-26893) (83/119,113/162) -> (83/119,113/162) Reflection Matrix(9719,-6780,13932,-9719) (113/162,30/43) -> (113/162,30/43) Reflection Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(379,-266,540,-379) (7/10,19/27) -> (7/10,19/27) Reflection Matrix(647,-456,918,-647) (19/27,12/17) -> (19/27,12/17) Reflection Matrix(7073,-5014,9828,-6967) (56/79,39/55) -> (77/107,18/25) Hyperbolic Matrix(2323,-1648,2970,-2107) (39/55,22/31) -> (43/55,18/23) Glide Reflection Matrix(22303,-16048,30996,-22303) (59/82,136/189) -> (59/82,136/189) Reflection Matrix(29105,-20944,40446,-29105) (136/189,77/107) -> (136/189,77/107) Reflection Matrix(1241,-906,1404,-1025) (27/37,46/63) -> (15/17,8/9) Glide Reflection Matrix(10585,-7742,14472,-10585) (49/67,79/108) -> (49/67,79/108) Reflection Matrix(6479,-4740,8856,-6479) (79/108,30/41) -> (79/108,30/41) Reflection Matrix(26893,-19754,36612,-26893) (83/113,119/162) -> (83/113,119/162) Reflection Matrix(11663,-8568,15876,-11663) (119/162,36/49) -> (119/162,36/49) Reflection Matrix(6965,-5126,8586,-6319) (39/53,53/72) -> (73/90,43/53) Hyperbolic Matrix(5941,-4374,7776,-5725) (53/72,67/91) -> (55/72,13/17) Glide Reflection Matrix(919,-680,1242,-919) (17/23,20/27) -> (17/23,20/27) Reflection Matrix(161,-120,216,-161) (20/27,3/4) -> (20/27,3/4) Reflection Matrix(379,-294,486,-377) (17/22,7/9) -> (7/9,25/32) Parabolic Matrix(10369,-8160,13176,-10369) (48/61,85/108) -> (48/61,85/108) Reflection Matrix(7991,-6290,10152,-7991) (85/108,37/47) -> (85/108,37/47) Reflection Matrix(7883,-6218,9720,-7667) (56/71,71/90) -> (30/37,73/90) Glide Reflection Matrix(11341,-8988,14310,-11341) (42/53,107/135) -> (42/53,107/135) Reflection Matrix(17549,-13910,22140,-17549) (107/135,65/82) -> (107/135,65/82) Reflection Matrix(703,-572,864,-703) (13/16,22/27) -> (13/16,22/27) Reflection Matrix(485,-396,594,-485) (22/27,9/11) -> (22/27,9/11) Reflection Matrix(6967,-5762,8424,-6967) (43/52,67/81) -> (43/52,67/81) Reflection Matrix(3887,-3216,4698,-3887) (67/81,24/29) -> (67/81,24/29) Reflection Matrix(919,-782,1080,-919) (17/20,23/27) -> (17/20,23/27) Reflection Matrix(323,-276,378,-323) (23/27,6/7) -> (23/27,6/7) Reflection Matrix(2161,-1880,2484,-2161) (20/23,47/54) -> (20/23,47/54) Reflection Matrix(2915,-2538,3348,-2915) (47/54,27/31) -> (47/54,27/31) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(377,-32,648,-55) -> Matrix(1,0,2,1) 0/1 Matrix(433,-46,1026,-109) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(539,-64,918,-109) -> Matrix(9,-2,14,-3) Matrix(701,-92,1242,-163) -> Matrix(1,0,-2,1) 0/1 Matrix(271,-38,378,-53) -> Matrix(1,0,-2,1) 0/1 Matrix(433,-66,702,-107) -> Matrix(1,0,0,1) Matrix(541,-84,702,-109) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1729,-276,2700,-431) -> Matrix(1,0,0,1) Matrix(269,-44,324,-53) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(271,-46,324,-55) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1729,-300,2484,-431) -> Matrix(11,8,4,3) Matrix(973,-170,1242,-217) -> Matrix(5,2,-2,-1) Matrix(433,-78,594,-107) -> Matrix(1,0,4,1) 0/1 Matrix(109,-20,594,-109) -> Matrix(-1,0,12,1) (2/11,5/27) -> (-1/6,0/1) Matrix(161,-30,864,-161) -> Matrix(1,0,22,-1) (5/27,3/16) -> (0/1,1/11) Matrix(865,-164,1134,-215) -> Matrix(11,-2,6,-1) Matrix(163,-32,270,-53) -> Matrix(7,-2,4,-1) Matrix(649,-136,1026,-215) -> Matrix(5,-2,-2,1) Matrix(539,-114,1026,-217) -> Matrix(5,-4,4,-3) 1/1 Matrix(2483,-526,3564,-755) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1025,-218,1782,-379) -> Matrix(1,0,-2,1) 0/1 Matrix(269,-58,756,-163) -> Matrix(3,-2,8,-5) 1/2 Matrix(109,-24,486,-107) -> Matrix(5,-4,4,-3) 1/1 Matrix(1619,-366,2862,-647) -> Matrix(1,-2,-2,3) Matrix(3239,-734,5238,-1187) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(377,-86,1188,-271) -> Matrix(1,-2,0,1) 1/0 Matrix(593,-136,702,-161) -> Matrix(-1,6,0,1) *** -> (3/1,1/0) Matrix(649,-152,918,-215) -> Matrix(1,-4,0,1) 1/0 Matrix(919,-218,1134,-269) -> Matrix(1,0,2,1) 0/1 Matrix(703,-168,1134,-271) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(595,-156,1026,-269) -> Matrix(1,0,-6,1) 0/1 Matrix(2269,-600,3672,-971) -> Matrix(11,-2,6,-1) Matrix(2053,-544,3672,-973) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1241,-330,3456,-919) -> Matrix(17,-4,30,-7) Matrix(433,-116,810,-217) -> Matrix(5,-2,2,-1) Matrix(2053,-552,2808,-755) -> Matrix(1,0,0,1) Matrix(487,-132,594,-161) -> Matrix(7,-2,4,-1) Matrix(379,-104,594,-163) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(701,-194,972,-269) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(703,-196,972,-271) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(2267,-636,5778,-1621) -> Matrix(1,0,-8,1) 0/1 Matrix(2377,-668,3078,-865) -> Matrix(17,-4,4,-1) Matrix(325,-92,378,-107) -> Matrix(5,-2,-2,1) Matrix(215,-62,378,-109) -> Matrix(3,-2,2,-1) 1/1 Matrix(703,-206,918,-269) -> Matrix(13,-10,4,-3) Matrix(271,-80,918,-271) -> Matrix(11,-10,12,-11) (5/17,8/27) -> (5/6,1/1) Matrix(161,-48,540,-161) -> Matrix(5,-6,4,-5) (8/27,3/10) -> (1/1,3/2) Matrix(2701,-816,4644,-1403) -> Matrix(1,-2,2,-3) 1/1 Matrix(1565,-474,4104,-1243) -> Matrix(1,2,0,1) 1/0 Matrix(2809,-852,3564,-1081) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2053,-624,2484,-755) -> Matrix(1,0,0,1) Matrix(431,-132,702,-215) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(379,-118,864,-269) -> Matrix(3,2,4,3) Matrix(593,-186,864,-271) -> Matrix(1,2,0,1) 1/0 Matrix(971,-310,1350,-431) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(487,-170,1080,-377) -> Matrix(7,-2,4,-1) Matrix(701,-246,1080,-379) -> Matrix(1,0,-2,1) 0/1 Matrix(757,-268,918,-325) -> Matrix(5,-2,2,-1) Matrix(3349,-1200,5724,-2051) -> Matrix(23,-12,48,-25) 1/2 Matrix(2375,-852,4212,-1511) -> Matrix(11,-6,-2,1) Matrix(10153,-3648,13824,-4967) -> Matrix(7,-4,16,-9) 1/2 Matrix(2269,-816,2700,-971) -> Matrix(41,-24,12,-7) Matrix(431,-156,594,-215) -> Matrix(3,-2,-2,1) Matrix(323,-118,594,-217) -> Matrix(5,-4,4,-3) 1/1 Matrix(811,-298,1026,-377) -> Matrix(5,-4,-6,5) Matrix(379,-140,1026,-379) -> Matrix(15,-14,16,-15) (7/19,10/27) -> (7/8,1/1) Matrix(161,-60,432,-161) -> Matrix(5,-6,4,-5) (10/27,3/8) -> (1/1,3/2) Matrix(919,-348,1566,-593) -> Matrix(1,-4,2,-7) Matrix(3349,-1272,5400,-2051) -> Matrix(1,0,0,1) Matrix(863,-328,1134,-431) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(11449,-4368,16416,-6263) -> Matrix(1,0,0,1) Matrix(4643,-1772,5940,-2267) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2701,-1032,3672,-1403) -> Matrix(1,-6,2,-11) Matrix(595,-228,702,-269) -> Matrix(1,6,0,1) 1/0 Matrix(487,-188,702,-271) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(593,-230,972,-377) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(595,-232,972,-379) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(811,-318,1242,-487) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(5779,-2268,7290,-2861) -> Matrix(1,0,10,1) 0/1 Matrix(217,-86,270,-107) -> Matrix(1,0,0,1) Matrix(109,-44,270,-109) -> Matrix(1,0,0,-1) (2/5,11/27) -> (0/1,1/0) Matrix(485,-198,1188,-485) -> Matrix(1,0,10,-1) (11/27,9/22) -> (0/1,1/5) Matrix(1513,-620,2106,-863) -> Matrix(1,0,-4,1) 0/1 Matrix(487,-200,918,-377) -> Matrix(7,-2,4,-1) Matrix(973,-402,1566,-647) -> Matrix(3,-2,2,-1) 1/1 Matrix(1081,-448,1566,-649) -> Matrix(5,-2,2,-1) Matrix(3673,-1524,5724,-2375) -> Matrix(1,0,0,1) Matrix(755,-314,1296,-539) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(757,-316,1296,-541) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(593,-248,648,-271) -> Matrix(7,-4,2,-1) Matrix(917,-384,1674,-701) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(757,-318,1026,-431) -> Matrix(1,-2,2,-3) 1/1 Matrix(1727,-728,2052,-865) -> Matrix(1,4,0,1) 1/0 Matrix(1997,-844,2430,-1027) -> Matrix(7,-2,4,-1) Matrix(1081,-458,1782,-755) -> Matrix(3,-2,2,-1) 1/1 Matrix(1403,-596,1782,-757) -> Matrix(5,-2,-2,1) Matrix(269,-116,378,-163) -> Matrix(1,0,-2,1) 0/1 Matrix(1079,-470,1242,-541) -> Matrix(3,-2,2,-1) 1/1 Matrix(2701,-1178,4212,-1837) -> Matrix(3,-2,-2,1) Matrix(2267,-990,2970,-1297) -> Matrix(19,-12,8,-5) Matrix(1297,-570,2214,-973) -> Matrix(13,-10,22,-17) Matrix(217,-96,486,-215) -> Matrix(9,-8,8,-7) 1/1 Matrix(1243,-558,1566,-703) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1945,-874,2646,-1189) -> Matrix(3,-4,8,-11) Matrix(1675,-756,2754,-1243) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(973,-440,1674,-757) -> Matrix(1,-2,2,-5) Matrix(377,-172,594,-271) -> Matrix(1,-2,0,1) 1/0 Matrix(593,-276,810,-377) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(541,-254,918,-431) -> Matrix(3,-4,4,-5) 1/1 Matrix(1511,-796,2052,-1081) -> Matrix(3,-4,4,-5) 1/1 Matrix(917,-496,1296,-701) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(703,-386,1080,-593) -> Matrix(1,-2,0,1) 1/0 Matrix(271,-150,486,-269) -> Matrix(1,-2,0,1) 1/0 Matrix(3725,-2084,5886,-3293) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(595,-334,864,-485) -> Matrix(1,2,0,1) 1/0 Matrix(1403,-790,1728,-973) -> Matrix(1,-2,2,-3) 1/1 Matrix(1835,-1036,2106,-1189) -> Matrix(1,0,0,1) Matrix(2267,-1284,2862,-1621) -> Matrix(1,0,-4,1) 0/1 Matrix(1997,-1148,2538,-1459) -> Matrix(1,-2,0,1) 1/0 Matrix(1135,-654,1404,-809) -> Matrix(1,0,2,1) 0/1 Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(917,-530,1026,-593) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(4427,-2560,6912,-3997) -> Matrix(1,0,0,1) Matrix(4699,-2726,8100,-4699) -> Matrix(-1,0,14,1) (29/50,47/81) -> (-1/7,0/1) Matrix(2915,-1692,5022,-2915) -> Matrix(1,0,12,-1) (47/81,18/31) -> (0/1,1/6) Matrix(14851,-8690,25380,-14851) -> Matrix(61,-30,124,-61) (55/94,79/135) -> (15/31,1/2) Matrix(6479,-3792,11070,-6479) -> Matrix(31,-16,60,-31) (79/135,24/41) -> (1/2,8/15) Matrix(1511,-888,1836,-1079) -> Matrix(11,-8,4,-3) Matrix(3833,-2258,4860,-2863) -> Matrix(3,-2,-4,3) Matrix(1027,-606,1188,-701) -> Matrix(5,-4,-6,5) Matrix(703,-416,1188,-703) -> Matrix(17,-16,18,-17) (13/22,16/27) -> (8/9,1/1) Matrix(161,-96,270,-161) -> Matrix(5,-6,4,-5) (16/27,3/5) -> (1/1,3/2) Matrix(4157,-2526,5778,-3511) -> Matrix(1,-2,0,1) 1/0 Matrix(4699,-2900,7614,-4699) -> Matrix(3,-2,4,-3) (29/47,50/81) -> (1/2,1/1) Matrix(3401,-2100,5508,-3401) -> Matrix(5,-6,4,-5) (50/81,21/34) -> (1/1,3/2) Matrix(8479,-5240,10746,-6641) -> Matrix(3,-4,-2,3) Matrix(9073,-5608,11880,-7343) -> Matrix(9,-16,4,-7) 2/1 Matrix(2861,-1770,4104,-2539) -> Matrix(1,2,0,1) 1/0 Matrix(10585,-6566,17064,-10585) -> Matrix(-1,4,0,1) (49/79,67/108) -> (2/1,1/0) Matrix(3887,-2412,6264,-3887) -> Matrix(-1,4,0,1) (67/108,18/29) -> (2/1,1/0) Matrix(379,-236,432,-269) -> Matrix(1,-2,0,1) 1/0 Matrix(271,-170,432,-271) -> Matrix(-1,6,0,1) (5/8,17/27) -> (3/1,1/0) Matrix(647,-408,1026,-647) -> Matrix(1,8,0,-1) (17/27,12/19) -> (-4/1,1/0) Matrix(3023,-1914,4266,-2701) -> Matrix(1,0,0,1) Matrix(1243,-788,1620,-1027) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(2537,-1626,3456,-2215) -> Matrix(1,0,2,1) 0/1 Matrix(6967,-4472,10854,-6967) -> Matrix(3,-2,4,-3) (43/67,52/81) -> (1/2,1/1) Matrix(1457,-936,2268,-1457) -> Matrix(-1,2,0,1) (52/81,9/14) -> (1/1,1/0) Matrix(593,-382,756,-487) -> Matrix(1,-2,0,1) 1/0 Matrix(1189,-770,1836,-1189) -> Matrix(1,0,0,-1) (11/17,35/54) -> (0/1,1/0) Matrix(2591,-1680,3996,-2591) -> Matrix(1,0,0,-1) (35/54,24/37) -> (0/1,1/0) Matrix(917,-626,1188,-811) -> Matrix(1,2,0,1) 1/0 Matrix(1405,-962,2052,-1405) -> Matrix(-1,4,0,1) (13/19,37/54) -> (2/1,1/0) Matrix(2591,-1776,3780,-2591) -> Matrix(-1,4,0,1) (37/54,24/35) -> (2/1,1/0) Matrix(14851,-10340,21330,-14851) -> Matrix(47,-138,16,-47) (55/79,94/135) -> (23/8,3/1) Matrix(10529,-7332,15120,-10529) -> Matrix(31,-96,10,-31) (94/135,39/56) -> (3/1,16/5) Matrix(26893,-18758,38556,-26893) -> Matrix(-1,8,0,1) (83/119,113/162) -> (4/1,1/0) Matrix(9719,-6780,13932,-9719) -> Matrix(-1,8,0,1) (113/162,30/43) -> (4/1,1/0) Matrix(487,-340,540,-377) -> Matrix(1,-2,0,1) 1/0 Matrix(379,-266,540,-379) -> Matrix(-1,10,0,1) (7/10,19/27) -> (5/1,1/0) Matrix(647,-456,918,-647) -> Matrix(1,12,0,-1) (19/27,12/17) -> (-6/1,1/0) Matrix(7073,-5014,9828,-6967) -> Matrix(1,2,0,1) 1/0 Matrix(2323,-1648,2970,-2107) -> Matrix(1,6,0,-1) *** -> (-3/1,1/0) Matrix(22303,-16048,30996,-22303) -> Matrix(1,0,2,-1) (59/82,136/189) -> (0/1,1/1) Matrix(29105,-20944,40446,-29105) -> Matrix(-1,2,0,1) (136/189,77/107) -> (1/1,1/0) Matrix(1241,-906,1404,-1025) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(10585,-7742,14472,-10585) -> Matrix(1,0,4,-1) (49/67,79/108) -> (0/1,1/2) Matrix(6479,-4740,8856,-6479) -> Matrix(1,0,4,-1) (79/108,30/41) -> (0/1,1/2) Matrix(26893,-19754,36612,-26893) -> Matrix(1,0,4,-1) (83/113,119/162) -> (0/1,1/2) Matrix(11663,-8568,15876,-11663) -> Matrix(1,0,4,-1) (119/162,36/49) -> (0/1,1/2) Matrix(6965,-5126,8586,-6319) -> Matrix(3,-2,8,-5) 1/2 Matrix(5941,-4374,7776,-5725) -> Matrix(11,-8,4,-3) Matrix(919,-680,1242,-919) -> Matrix(11,-10,12,-11) (17/23,20/27) -> (5/6,1/1) Matrix(161,-120,216,-161) -> Matrix(3,-4,2,-3) (20/27,3/4) -> (1/1,2/1) Matrix(379,-294,486,-377) -> Matrix(1,-10,0,1) 1/0 Matrix(10369,-8160,13176,-10369) -> Matrix(1,4,0,-1) (48/61,85/108) -> (-2/1,1/0) Matrix(7991,-6290,10152,-7991) -> Matrix(1,4,0,-1) (85/108,37/47) -> (-2/1,1/0) Matrix(7883,-6218,9720,-7667) -> Matrix(1,2,2,3) Matrix(11341,-8988,14310,-11341) -> Matrix(-1,0,20,1) (42/53,107/135) -> (-1/10,0/1) Matrix(17549,-13910,22140,-17549) -> Matrix(1,0,30,-1) (107/135,65/82) -> (0/1,1/15) Matrix(703,-572,864,-703) -> Matrix(5,-4,6,-5) (13/16,22/27) -> (2/3,1/1) Matrix(485,-396,594,-485) -> Matrix(5,-6,4,-5) (22/27,9/11) -> (1/1,3/2) Matrix(6967,-5762,8424,-6967) -> Matrix(3,-4,2,-3) (43/52,67/81) -> (1/1,2/1) Matrix(3887,-3216,4698,-3887) -> Matrix(-1,4,0,1) (67/81,24/29) -> (2/1,1/0) Matrix(919,-782,1080,-919) -> Matrix(-1,30,0,1) (17/20,23/27) -> (15/1,1/0) Matrix(323,-276,378,-323) -> Matrix(1,8,0,-1) (23/27,6/7) -> (-4/1,1/0) Matrix(2161,-1880,2484,-2161) -> Matrix(1,0,0,-1) (20/23,47/54) -> (0/1,1/0) Matrix(2915,-2538,3348,-2915) -> Matrix(1,0,0,-1) (47/54,27/31) -> (0/1,1/0) Matrix(-1,2,0,1) -> Matrix(1,0,0,-1) (1/1,1/0) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.