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 0/1 1/1 -9/10 0/1 1/2 -8/9 1/1 -7/8 1/1 1/0 -13/15 1/2 -6/7 1/2 1/1 -11/13 1/1 2/1 -16/19 1/1 2/1 -21/25 1/1 1/0 -5/6 1/0 -24/29 1/1 1/0 -19/23 0/1 1/0 -14/17 0/1 1/1 -9/11 0/1 1/1 -22/27 1/1 -13/16 1/1 2/1 -17/21 1/0 -4/5 1/1 1/0 -15/19 -3/1 1/0 -41/52 -1/1 1/0 -26/33 -2/1 -1/1 1/0 -11/14 -1/1 0/1 -18/23 -1/1 0/1 -7/9 0/1 -24/31 0/1 1/1 -41/53 0/1 1/1 -17/22 1/2 1/1 -27/35 1/1 1/0 -10/13 0/1 1/1 -13/17 0/1 1/0 -16/21 0/1 1/1 1/0 -3/4 0/1 1/0 -14/19 0/1 1/3 -25/34 1/3 2/5 -36/49 3/7 1/2 -11/15 1/2 -30/41 2/3 1/1 -19/26 0/1 1/1 -8/11 0/1 1/2 -21/29 1/2 1/1 -13/18 1/1 -18/25 1/1 1/0 -41/57 1/0 -23/32 3/1 1/0 -5/7 0/1 1/1 -17/24 1/0 -12/17 -1/1 0/1 -19/27 0/1 -7/10 0/1 1/2 -30/43 0/1 1/0 -23/33 1/2 -39/56 1/2 1/1 -16/23 0/1 1/1 -9/13 0/1 1/1 -11/16 0/1 1/1 -13/19 1/1 1/0 -15/22 1/2 1/1 -2/3 0/1 1/1 1/0 -13/20 0/1 1/1 -11/17 0/1 1/2 -20/31 0/1 1/1 -9/14 0/1 1/1 -34/53 0/1 1/2 -25/39 1/2 -66/103 3/7 1/2 -41/64 1/2 2/3 -16/25 1/2 1/1 -7/11 0/1 1/1 -19/30 1/2 -12/19 2/3 1/1 -17/27 1/1 -5/8 1/1 1/0 -18/29 1/1 1/0 -31/50 0/1 1/0 -13/21 1/0 -60/97 -1/2 0/1 -47/76 1/1 1/0 -34/55 0/1 1/0 -21/34 -1/1 0/1 -8/13 0/1 1/1 -19/31 0/1 1/0 -11/18 0/1 -14/23 0/1 1/1 -31/51 1/2 -48/79 1/2 1/1 -17/28 0/1 1/1 -3/5 1/2 1/1 -16/27 1/1 -13/22 1/1 5/4 -23/39 3/2 -10/17 1/1 2/1 -17/29 1/1 1/0 -24/41 0/1 1/1 -31/53 1/1 2/1 -7/12 1/0 -32/55 0/1 1/0 -25/43 0/1 1/1 -18/31 -1/1 0/1 -11/19 1/2 1/1 -37/64 1/2 2/3 -26/45 1/1 -15/26 0/1 1/1 -19/33 1/2 -4/7 1/1 1/0 -13/23 0/1 1/0 -22/39 0/1 1/2 1/1 -31/55 0/1 1/1 -9/16 0/1 1/1 -23/41 0/1 1/1 -14/25 1/2 1/1 -5/9 1/1 -16/29 1/1 3/2 -27/49 7/5 3/2 -11/20 1/1 2/1 -28/51 1/1 3/2 2/1 -17/31 3/2 2/1 -6/11 2/1 1/0 -7/13 0/1 1/1 -8/15 1/1 2/1 1/0 -1/2 1/1 1/0 -9/19 -1/1 1/0 -8/17 0/1 1/1 -7/15 1/0 -6/13 1/1 2/1 -11/24 1/0 -5/11 1/1 2/1 -14/31 2/1 3/1 -9/20 2/1 3/1 -4/9 1/0 -15/34 -2/1 -1/1 -26/59 -3/1 1/0 -11/25 -1/1 1/0 -7/16 -1/1 0/1 -24/55 0/1 1/0 -17/39 1/0 -27/62 -1/1 -1/2 -10/23 0/1 1/1 -23/53 0/1 1/1 -13/30 1/0 -3/7 0/1 1/1 -17/40 1/1 4/3 -14/33 1/1 3/2 2/1 -11/26 1/1 2/1 -19/45 2/1 -27/64 2/1 1/0 -8/19 1/1 2/1 -21/50 7/4 2/1 -34/81 2/1 -13/31 2/1 5/2 -18/43 2/1 1/0 -41/98 2/1 5/2 -23/55 2/1 3/1 -5/12 1/0 -22/53 2/1 1/0 -39/94 1/1 2/1 -56/135 2/1 -17/41 2/1 3/1 -12/29 3/1 1/0 -19/46 3/1 1/0 -26/63 3/1 -7/17 4/1 1/0 -23/56 5/1 1/0 -16/39 5/1 6/1 1/0 -9/22 9/1 1/0 -11/27 1/0 -2/5 -1/1 1/0 -13/33 1/0 -11/28 -1/1 0/1 -20/51 -1/1 0/1 1/0 -9/23 0/1 1/0 -7/18 0/1 -12/31 0/1 1/1 -5/13 0/1 1/1 -18/47 3/4 1/1 -31/81 1/1 -13/34 1/1 4/3 -34/89 1/1 2/1 -55/144 2/1 -21/55 1/1 2/1 -29/76 1/1 3/2 -8/21 1/1 2/1 1/0 -19/50 2/1 1/0 -30/79 3/1 1/0 -41/108 1/0 -11/29 1/1 1/0 -14/37 1/1 2/1 -3/8 3/1 1/0 -10/27 1/0 -7/19 -7/1 1/0 -18/49 -3/1 1/0 -29/79 -5/1 1/0 -11/30 1/0 -15/41 -4/1 -3/1 -4/11 -2/1 1/0 -9/25 -1/1 1/0 -32/89 -1/1 0/1 -23/64 0/1 1/0 -14/39 -2/1 -1/1 1/0 -19/53 -2/1 -1/1 -24/67 -4/3 -1/1 -29/81 -1/1 -5/14 -1/1 0/1 -6/17 -1/1 0/1 -19/54 0/1 -13/37 0/1 1/2 -7/20 0/1 1/1 -8/23 0/1 1/1 -1/3 1/0 -6/19 -2/1 -1/1 -17/54 -1/1 -11/35 -1/1 -1/2 -5/16 -1/1 0/1 -9/29 -1/1 1/0 -4/13 -1/1 0/1 -7/23 0/1 1/0 -24/79 1/1 1/0 -41/135 1/0 -17/56 -1/1 1/0 -10/33 -1/1 0/1 1/0 -23/76 -1/1 -1/2 -36/119 -1/4 0/1 -49/162 0/1 -13/43 0/1 1/1 -3/10 0/1 1/0 -8/27 1/0 -5/17 -2/1 1/0 -12/41 -2/1 -1/1 -7/24 1/0 -23/79 -3/1 1/0 -16/55 -2/1 1/0 -9/31 -2/1 1/0 -2/7 -1/1 1/0 -11/39 1/0 -9/32 -1/1 -1/2 -16/57 -1/1 0/1 1/0 -23/82 -1/1 0/1 -53/189 0/1 -30/107 0/1 1/0 -7/25 -1/1 1/0 -5/18 -1/1 -8/29 -1/1 -1/2 -3/11 -1/1 0/1 -10/37 -1/1 0/1 -17/63 0/1 -7/26 -1/1 0/1 -18/67 -2/1 -1/1 -29/108 -1/1 -11/41 -1/1 -2/3 -4/15 -1/1 -1/2 0/1 -17/64 -2/3 -1/2 -30/113 -7/13 -1/2 -43/162 -1/2 -13/49 -1/2 -3/7 -9/34 -1/3 0/1 -14/53 -1/2 0/1 -19/72 0/1 -24/91 -1/1 0/1 -5/19 -1/2 -1/3 -6/23 -1/5 0/1 -7/27 0/1 -1/4 0/1 1/0 -5/21 1/0 -9/38 -1/1 0/1 -13/55 -1/1 0/1 -17/72 0/1 -4/17 -1/1 0/1 -7/30 1/0 -3/13 -1/1 0/1 -8/35 -1/1 0/1 -13/57 -1/2 -5/22 -1/2 -1/3 -2/9 0/1 -7/32 1/2 1/1 -12/55 0/1 1/2 -5/23 0/1 1/2 -8/37 0/1 1/1 -3/14 0/1 1/1 -13/61 4/5 1/1 -23/108 1/1 -10/47 1/1 3/2 -7/33 1/0 -11/52 1/1 1/0 -15/71 0/1 1/0 -19/90 0/1 -4/19 0/1 1/1 -5/24 1/0 -11/53 0/1 1/1 -28/135 1/1 -17/82 1/1 2/1 -6/29 1/1 1/0 -1/5 -1/1 1/0 -5/26 -1/1 0/1 -4/21 -1/1 -1/2 0/1 -7/37 -1/2 0/1 -17/90 0/1 -10/53 -1/2 0/1 -3/16 -1/3 0/1 -5/27 0/1 -2/11 0/1 1/2 -5/28 0/1 1/1 -8/45 1/1 -3/17 0/1 1/0 -4/23 0/1 1/1 -9/52 1/2 1/1 -14/81 1/1 -5/29 1/1 1/0 -1/6 1/0 -4/25 -1/1 1/0 -7/44 -2/1 1/0 -3/19 -1/1 1/0 -2/13 -1/1 0/1 -3/20 -1/3 0/1 -4/27 0/1 -1/7 0/1 1/1 -3/22 3/1 1/0 -2/15 -1/1 0/1 1/0 -3/23 -1/2 0/1 -7/54 0/1 -4/31 0/1 1/3 -1/8 1/1 1/0 -2/17 -1/1 0/1 -1/9 0/1 -1/10 0/1 1/0 -1/11 0/1 1/1 0/1 0/1 1/0 1/10 0/1 1/0 1/9 0/1 1/8 -1/1 1/0 2/15 0/1 1/1 1/0 1/7 -1/1 0/1 2/13 0/1 1/1 3/19 1/1 1/0 4/25 1/1 1/0 1/6 1/0 5/29 -1/1 1/0 4/23 -1/1 0/1 3/17 0/1 1/0 2/11 -1/2 0/1 5/27 0/1 3/16 0/1 1/3 4/21 0/1 1/2 1/1 1/5 1/1 1/0 4/19 -1/1 0/1 11/52 -1/1 1/0 7/33 1/0 3/14 -1/1 0/1 5/23 -1/2 0/1 2/9 0/1 7/31 0/1 1/2 12/53 0/1 1/2 5/22 1/3 1/2 8/35 0/1 1/1 3/13 0/1 1/1 4/17 0/1 1/1 5/21 1/0 1/4 0/1 1/0 5/19 1/3 1/2 9/34 0/1 1/3 13/49 3/7 1/2 4/15 0/1 1/2 1/1 11/41 2/3 1/1 7/26 0/1 1/1 3/11 0/1 1/1 8/29 1/2 1/1 5/18 1/1 7/25 1/1 1/0 16/57 0/1 1/1 1/0 9/32 1/2 1/1 2/7 1/1 1/0 7/24 1/0 5/17 2/1 1/0 8/27 1/0 3/10 0/1 1/0 13/43 -1/1 0/1 10/33 0/1 1/1 1/0 17/56 1/1 1/0 7/23 0/1 1/0 4/13 0/1 1/1 5/16 0/1 1/1 6/19 1/1 2/1 7/22 3/1 1/0 1/3 1/0 7/20 -1/1 0/1 6/17 0/1 1/1 11/31 0/1 1/0 5/14 0/1 1/1 19/53 1/1 2/1 14/39 1/1 2/1 1/0 37/103 5/1 1/0 23/64 0/1 1/0 9/25 1/1 1/0 4/11 2/1 1/0 11/30 1/0 7/19 7/1 1/0 10/27 1/0 3/8 -3/1 1/0 11/29 -1/1 1/0 19/50 -2/1 1/0 8/21 -2/1 -1/1 1/0 37/97 -3/1 -2/1 29/76 -3/2 -1/1 21/55 -2/1 -1/1 13/34 -4/3 -1/1 5/13 -1/1 0/1 12/31 -1/1 0/1 7/18 0/1 9/23 0/1 1/0 20/51 0/1 1/1 1/0 31/79 1/1 1/0 11/28 0/1 1/1 2/5 1/1 1/0 11/27 1/0 9/22 -9/1 1/0 16/39 -6/1 -5/1 1/0 7/17 -4/1 1/0 12/29 -3/1 1/0 17/41 -3/1 -2/1 22/53 -2/1 1/0 5/12 1/0 23/55 -3/1 -2/1 18/43 -2/1 1/0 13/31 -5/2 -2/1 8/19 -2/1 -1/1 27/64 -2/1 1/0 19/45 -2/1 11/26 -2/1 -1/1 14/33 -2/1 -3/2 -1/1 3/7 -1/1 0/1 10/23 -1/1 0/1 17/39 1/0 24/55 0/1 1/0 7/16 0/1 1/1 18/41 0/1 1/1 11/25 1/1 1/0 4/9 1/0 13/29 -3/1 1/0 22/49 -1/1 1/0 9/20 -3/1 -2/1 23/51 1/0 14/31 -3/1 -2/1 5/11 -2/1 -1/1 6/13 -2/1 -1/1 7/15 1/0 1/2 -1/1 1/0 10/19 -1/1 0/1 9/17 0/1 1/0 8/15 -2/1 -1/1 1/0 7/13 -1/1 0/1 13/24 1/0 6/11 -2/1 1/0 17/31 -2/1 -3/2 11/20 -2/1 -1/1 5/9 -1/1 19/34 -1/1 -2/3 33/59 -1/2 -1/3 14/25 -1/1 -1/2 9/16 -1/1 0/1 31/55 -1/1 0/1 22/39 -1/1 -1/2 0/1 35/62 -1/2 -1/3 13/23 0/1 1/0 30/53 0/1 1/0 17/30 1/0 4/7 -1/1 1/0 23/40 -1/1 -2/3 19/33 -1/2 15/26 -1/1 0/1 26/45 -1/1 37/64 -2/3 -1/2 11/19 -1/1 -1/2 29/50 -1/4 0/1 47/81 0/1 18/31 0/1 1/1 25/43 -1/1 0/1 57/98 0/1 1/0 32/55 0/1 1/0 7/12 1/0 31/53 -2/1 -1/1 55/94 -4/3 -1/1 79/135 -1/1 24/41 -1/1 0/1 17/29 -1/1 1/0 27/46 -3/1 1/0 37/63 -2/1 10/17 -2/1 -1/1 33/56 -3/2 -1/1 23/39 -3/2 13/22 -5/4 -1/1 16/27 -1/1 3/5 -1/1 -1/2 20/33 -1/1 0/1 1/0 17/28 -1/1 0/1 31/51 -1/2 14/23 -1/1 0/1 11/18 0/1 19/31 0/1 1/0 8/13 -1/1 0/1 29/47 -1/3 0/1 50/81 0/1 21/34 0/1 1/1 55/89 1/1 1/0 89/144 0/1 34/55 0/1 1/0 47/76 -1/1 1/0 13/21 1/0 31/50 0/1 1/0 49/79 1/1 1/0 67/108 1/0 18/29 -1/1 1/0 23/37 -2/1 1/0 5/8 -1/1 1/0 17/27 -1/1 12/19 -1/1 -2/3 31/49 -3/5 -1/2 50/79 -1/1 -1/2 19/30 -1/2 26/41 -1/1 0/1 7/11 -1/1 0/1 16/25 -1/1 -1/2 57/89 -1/1 -1/2 41/64 -2/3 -1/2 25/39 -1/2 34/53 -1/2 0/1 43/67 -1/3 0/1 52/81 0/1 9/14 -1/1 0/1 11/17 -1/2 0/1 35/54 0/1 24/37 0/1 1/1 13/20 -1/1 0/1 15/23 0/1 1/0 2/3 -1/1 0/1 1/0 13/19 -1/1 1/0 37/54 -1/1 24/35 -1/1 -2/3 11/16 -1/1 0/1 20/29 -1/1 -1/2 9/13 -1/1 0/1 16/23 -1/1 0/1 55/79 -1/1 1/0 94/135 -1/1 39/56 -1/1 -1/2 23/33 -1/2 53/76 -1/2 -1/3 83/119 -1/5 0/1 113/162 0/1 30/43 0/1 1/0 7/10 -1/2 0/1 19/27 0/1 12/17 0/1 1/1 29/41 0/1 1/1 17/24 1/0 56/79 -1/1 1/0 39/55 -1/1 0/1 22/31 -1/1 0/1 5/7 -1/1 0/1 28/39 0/1 1/1 1/0 23/32 -3/1 1/0 41/57 1/0 59/82 -2/1 -1/1 136/189 -1/1 77/107 -1/1 0/1 18/25 -1/1 1/0 13/18 -1/1 21/29 -1/1 -1/2 8/11 -1/2 0/1 27/37 0/1 1/0 46/63 -1/1 19/26 -1/1 0/1 49/67 -2/1 -1/1 79/108 -1/1 30/41 -1/1 -2/3 11/15 -1/2 47/64 -2/3 -1/2 83/113 -7/13 -1/2 119/162 -1/2 36/49 -1/2 -3/7 25/34 -2/5 -1/3 39/53 -1/3 0/1 53/72 0/1 67/91 -1/2 0/1 14/19 -1/3 0/1 17/23 -1/6 0/1 20/27 0/1 3/4 0/1 1/0 16/21 -1/1 0/1 1/0 29/38 0/1 1/1 42/55 0/1 1/0 55/72 0/1 13/17 0/1 1/0 23/30 1/0 10/13 -1/1 0/1 27/35 -1/1 1/0 44/57 -1/1 0/1 1/0 17/22 -1/1 -1/2 7/9 0/1 25/32 1/1 1/0 43/55 0/1 1/1 18/23 0/1 1/1 29/37 0/1 1/0 11/14 0/1 1/1 48/61 3/4 1/1 85/108 1/1 37/47 1/1 4/3 26/33 1/1 2/1 1/0 41/52 1/1 1/0 56/71 1/1 2/1 71/90 2/1 15/19 3/1 1/0 19/24 1/0 42/53 0/1 1/0 107/135 0/1 65/82 0/1 1/1 23/29 1/1 1/0 4/5 -1/1 1/0 21/26 -2/1 -1/1 17/21 1/0 30/37 -2/1 -1/1 73/90 -2/1 43/53 -2/1 -1/1 13/16 -2/1 -1/1 22/27 -1/1 9/11 -1/1 0/1 23/28 -1/1 0/1 37/45 0/1 14/17 -1/1 0/1 19/23 0/1 1/0 43/52 1/1 1/0 67/81 1/0 24/29 -1/1 1/0 5/6 1/0 21/25 -1/1 1/0 37/44 -2/1 1/0 16/19 -2/1 -1/1 11/13 -2/1 -1/1 17/20 -6/5 -1/1 23/27 -1/1 6/7 -1/1 -1/2 19/22 -1/1 1/0 13/15 -1/2 20/23 -1/3 0/1 47/54 0/1 27/31 0/1 1/2 7/8 -1/1 1/0 15/17 -2/1 1/0 8/9 -1/1 9/10 -1/2 0/1 10/11 0/1 1/0 1/1 -1/1 0/1 1/0 0/1 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,-2,1) Matrix(271,248,-648,-593) -> Matrix(1,2,0,1) Matrix(593,530,1026,917) -> Matrix(3,-2,-4,3) Matrix(379,334,-918,-809) -> Matrix(1,2,0,1) Matrix(541,470,-1242,-1079) -> Matrix(1,0,-2,1) Matrix(107,92,-378,-325) -> Matrix(1,0,-2,1) Matrix(269,228,-702,-595) -> Matrix(1,-2,2,-3) Matrix(161,136,702,593) -> Matrix(1,-2,2,-3) Matrix(971,816,-2700,-2269) -> Matrix(1,-2,0,1) Matrix(55,46,324,271) -> Matrix(1,-2,0,1) Matrix(53,44,324,269) -> Matrix(1,0,0,1) Matrix(755,624,-2484,-2053) -> Matrix(1,0,0,1) Matrix(325,268,918,757) -> Matrix(1,0,0,1) Matrix(161,132,-594,-487) -> Matrix(1,0,-2,1) Matrix(485,396,594,485) -> Matrix(1,0,-2,1) Matrix(703,572,864,703) -> Matrix(3,-4,-2,3) Matrix(269,218,-1134,-919) -> Matrix(1,-2,0,1) Matrix(107,86,-270,-217) -> Matrix(1,-2,0,1) Matrix(377,298,-1026,-811) -> Matrix(1,-4,0,1) Matrix(487,384,-1026,-809) -> Matrix(1,2,0,1) Matrix(1081,852,3564,2809) -> Matrix(1,2,0,1) Matrix(757,596,-1782,-1403) -> Matrix(3,4,2,3) Matrix(487,382,-756,-593) -> Matrix(1,0,2,1) Matrix(377,294,-486,-379) -> Matrix(1,0,2,1) Matrix(2375,1838,3348,2591) -> Matrix(1,0,-2,1) Matrix(1999,1546,5238,4051) -> Matrix(1,-2,0,1) Matrix(811,626,-1188,-917) -> Matrix(1,0,0,1) Matrix(109,84,702,541) -> Matrix(1,0,0,1) Matrix(269,206,-918,-703) -> Matrix(1,-2,0,1) Matrix(215,164,-1134,-865) -> Matrix(1,0,-2,1) Matrix(431,328,1134,863) -> Matrix(1,-2,0,1) Matrix(431,318,-1026,-757) -> Matrix(7,-2,4,-1) Matrix(1403,1032,-3672,-2701) -> Matrix(7,-2,4,-1) Matrix(1189,874,2646,1945) -> Matrix(9,-4,-2,1) Matrix(2215,1626,-3456,-2537) -> Matrix(1,0,0,1) Matrix(377,276,810,593) -> Matrix(1,0,-2,1) Matrix(755,552,-2808,-2053) -> Matrix(1,0,-2,1) Matrix(107,78,-594,-433) -> Matrix(1,0,0,1) Matrix(215,156,594,431) -> Matrix(3,-2,2,-1) Matrix(271,196,972,703) -> Matrix(3,-2,2,-1) Matrix(269,194,972,701) -> Matrix(1,-2,2,-3) Matrix(3511,2526,-5778,-4157) -> Matrix(1,-2,2,-3) Matrix(431,310,1350,971) -> Matrix(1,0,0,1) Matrix(53,38,-378,-271) -> Matrix(1,0,0,1) Matrix(163,116,-378,-269) -> Matrix(1,0,0,1) Matrix(215,152,-918,-649) -> Matrix(1,0,0,1) Matrix(647,456,918,647) -> Matrix(1,0,2,1) Matrix(379,266,540,379) -> Matrix(1,0,-4,1) Matrix(1943,1356,-4644,-3241) -> Matrix(1,2,0,1) Matrix(2539,1770,-4104,-2861) -> Matrix(1,0,-2,1) Matrix(755,526,3564,2483) -> Matrix(1,0,-2,1) Matrix(431,300,-2484,-1729) -> Matrix(1,0,0,1) Matrix(271,188,702,487) -> Matrix(1,0,-2,1) Matrix(485,334,-864,-595) -> Matrix(1,0,0,1) Matrix(271,186,-864,-593) -> Matrix(1,0,-2,1) Matrix(379,258,1350,919) -> Matrix(1,0,0,1) Matrix(593,386,-1080,-703) -> Matrix(3,-2,2,-1) Matrix(379,246,-1080,-701) -> Matrix(1,0,0,1) Matrix(161,104,918,593) -> Matrix(1,0,-2,1) Matrix(2375,1524,-5724,-3673) -> Matrix(3,-2,2,-1) Matrix(1837,1178,4212,2701) -> Matrix(1,0,-2,1) Matrix(3671,2352,-13824,-8857) -> Matrix(7,-4,-12,7) Matrix(431,276,-2700,-1729) -> Matrix(1,0,-2,1) Matrix(163,104,594,379) -> Matrix(1,0,0,1) Matrix(271,172,-594,-377) -> Matrix(3,-2,2,-1) Matrix(215,136,-1026,-649) -> Matrix(3,-2,2,-1) Matrix(647,408,1026,647) -> Matrix(5,-4,-6,5) Matrix(271,170,432,271) -> Matrix(1,-2,0,1) Matrix(647,402,-1566,-973) -> Matrix(1,2,0,1) Matrix(2051,1272,-5400,-3349) -> Matrix(1,2,0,1) Matrix(271,168,1134,703) -> Matrix(1,0,0,1) Matrix(4967,3072,-16416,-10153) -> Matrix(1,0,-2,1) Matrix(1187,734,5238,3239) -> Matrix(1,0,2,1) Matrix(971,600,-3672,-2269) -> Matrix(1,0,-2,1) Matrix(107,66,-702,-433) -> Matrix(1,0,-2,1) Matrix(215,132,702,431) -> Matrix(1,0,0,1) Matrix(379,232,972,595) -> Matrix(1,0,0,1) Matrix(377,230,972,593) -> Matrix(1,0,-2,1) Matrix(1243,756,2754,1675) -> Matrix(5,-2,-2,1) Matrix(1511,918,-7290,-4429) -> Matrix(3,-2,2,-1) Matrix(53,32,-270,-163) -> Matrix(1,0,-2,1) Matrix(161,96,270,161) -> Matrix(3,-2,-4,3) Matrix(703,416,1188,703) -> Matrix(9,-10,-8,9) Matrix(593,350,-2106,-1243) -> Matrix(3,-4,-2,3) Matrix(431,254,-918,-541) -> Matrix(1,-2,2,-3) Matrix(593,348,-1566,-919) -> Matrix(1,0,0,1) Matrix(973,570,2214,1297) -> Matrix(1,0,0,1) Matrix(2051,1200,-5724,-3349) -> Matrix(3,-4,-2,3) Matrix(541,316,1296,757) -> Matrix(1,-4,0,1) Matrix(539,314,1296,755) -> Matrix(1,-2,0,1) Matrix(55,32,-648,-377) -> Matrix(1,0,0,1) Matrix(757,440,1674,973) -> Matrix(1,-2,0,1) Matrix(269,156,-1026,-595) -> Matrix(1,0,-4,1) Matrix(325,188,-2052,-1187) -> Matrix(1,0,-2,1) Matrix(917,530,1026,593) -> Matrix(3,-2,-4,3) Matrix(433,250,-2430,-1403) -> Matrix(1,0,0,1) Matrix(701,404,-1782,-1027) -> Matrix(1,0,-2,1) Matrix(379,218,-1782,-1025) -> Matrix(3,-2,2,-1) Matrix(109,62,-378,-215) -> Matrix(1,-2,0,1) Matrix(163,92,-1242,-701) -> Matrix(1,0,-2,1) Matrix(1511,852,4212,2375) -> Matrix(3,-2,2,-1) Matrix(703,396,-2970,-1673) -> Matrix(1,0,-2,1) Matrix(917,514,2214,1241) -> Matrix(5,-2,-2,1) Matrix(269,150,-486,-271) -> Matrix(5,-4,4,-3) Matrix(3349,1846,5292,2917) -> Matrix(1,-2,0,1) Matrix(701,386,2646,1457) -> Matrix(1,-2,4,-7) Matrix(1079,592,2754,1511) -> Matrix(1,-2,2,-3) Matrix(701,384,1674,917) -> Matrix(1,-4,0,1) Matrix(217,118,-594,-323) -> Matrix(1,-4,0,1) Matrix(217,116,810,433) -> Matrix(1,-2,2,-3) Matrix(377,200,-918,-487) -> Matrix(1,4,0,1) Matrix(541,256,-2052,-971) -> Matrix(1,0,-2,1) Matrix(593,276,810,377) -> Matrix(1,0,-2,1) Matrix(539,248,702,323) -> Matrix(1,-2,0,1) Matrix(973,440,1674,757) -> Matrix(1,-2,0,1) Matrix(377,170,-1080,-487) -> Matrix(1,-2,0,1) Matrix(215,96,-486,-217) -> Matrix(1,-4,0,1) Matrix(2699,1190,3672,1619) -> Matrix(1,0,-2,1) Matrix(1457,642,1836,809) -> Matrix(1,2,0,1) Matrix(269,118,-864,-379) -> Matrix(1,0,0,1) Matrix(325,142,-1728,-755) -> Matrix(1,0,-2,1) Matrix(2701,1178,4212,1837) -> Matrix(1,0,-2,1) Matrix(271,118,-2106,-917) -> Matrix(1,0,2,1) Matrix(1943,844,2484,1079) -> Matrix(1,0,0,1) Matrix(595,258,-2862,-1241) -> Matrix(1,0,0,1) Matrix(541,230,-2538,-1079) -> Matrix(3,-4,4,-5) Matrix(269,114,-1404,-595) -> Matrix(1,-2,0,1) Matrix(757,320,-2808,-1187) -> Matrix(1,-2,0,1) Matrix(109,46,1026,433) -> Matrix(1,-2,0,1) Matrix(2485,1048,-6912,-2915) -> Matrix(1,-2,0,1) Matrix(1243,522,1674,703) -> Matrix(1,-2,4,-7) Matrix(1997,838,2700,1133) -> Matrix(1,-2,-8,17) Matrix(917,384,1674,701) -> Matrix(1,-4,0,1) Matrix(757,316,1296,541) -> Matrix(1,-4,0,1) Matrix(755,314,1296,539) -> Matrix(1,-2,0,1) Matrix(6103,2532,9504,3943) -> Matrix(1,-2,0,1) Matrix(7937,3292,12366,5129) -> Matrix(1,-2,-4,9) Matrix(1081,448,1566,649) -> Matrix(1,-2,-2,5) Matrix(2483,1024,3402,1403) -> Matrix(1,-4,0,1) Matrix(1027,422,-4860,-1997) -> Matrix(1,-4,0,1) Matrix(161,66,-1188,-487) -> Matrix(1,-6,0,1) Matrix(485,198,1188,485) -> Matrix(1,-18,0,1) Matrix(109,44,270,109) -> Matrix(1,2,0,1) Matrix(1621,636,-5778,-2267) -> Matrix(1,0,0,1) Matrix(811,318,1242,487) -> Matrix(1,0,0,1) Matrix(595,232,972,379) -> Matrix(1,0,0,1) Matrix(593,230,972,377) -> Matrix(1,0,-2,1) Matrix(487,188,702,271) -> Matrix(1,0,-2,1) Matrix(1567,600,1836,703) -> Matrix(5,-4,-6,5) Matrix(2159,826,2538,971) -> Matrix(9,-10,-8,9) Matrix(2267,866,-10746,-4105) -> Matrix(1,-2,2,-3) Matrix(2807,1072,-11880,-4537) -> Matrix(1,-2,0,1) Matrix(4643,1772,5940,2267) -> Matrix(1,-2,2,-3) Matrix(1243,474,-4104,-1565) -> Matrix(1,-2,0,1) Matrix(863,328,1134,431) -> Matrix(1,-2,0,1) Matrix(7237,2748,11664,4429) -> Matrix(1,-4,0,1) Matrix(7235,2746,11664,4427) -> Matrix(1,0,0,1) Matrix(53,20,-432,-163) -> Matrix(1,-2,0,1) Matrix(161,60,432,161) -> Matrix(1,-6,0,1) Matrix(379,140,1026,379) -> Matrix(1,14,0,1) Matrix(2375,872,5292,1943) -> Matrix(1,2,0,1) Matrix(1243,456,-4266,-1565) -> Matrix(1,2,0,1) Matrix(1567,574,2214,811) -> Matrix(1,4,0,1) Matrix(431,156,594,215) -> Matrix(1,2,-2,-3) Matrix(919,330,-3456,-1241) -> Matrix(1,2,-2,-3) Matrix(2375,852,4212,1511) -> Matrix(1,2,-2,-3) Matrix(7237,2592,12366,4429) -> Matrix(3,4,-4,-5) Matrix(5561,1990,9504,3401) -> Matrix(5,4,-4,-3) Matrix(163,58,-756,-269) -> Matrix(1,0,2,1) Matrix(1891,666,2916,1027) -> Matrix(1,0,2,1) Matrix(1889,664,2916,1025) -> Matrix(1,0,-4,1) Matrix(755,262,1242,431) -> Matrix(1,0,-2,1) Matrix(271,86,-1188,-377) -> Matrix(1,2,-2,-3) Matrix(1999,630,2916,919) -> Matrix(3,4,-4,-5) Matrix(1997,628,2916,917) -> Matrix(3,2,-2,-1) Matrix(917,284,1566,485) -> Matrix(1,0,0,1) Matrix(431,132,702,215) -> Matrix(1,0,0,1) Matrix(8533,2592,10314,3133) -> Matrix(1,-2,0,1) Matrix(9557,2902,11556,3509) -> Matrix(1,2,0,1) Matrix(2809,852,3564,1081) -> Matrix(1,2,0,1) Matrix(18307,5538,26244,7939) -> Matrix(1,0,4,1) Matrix(18305,5536,26244,7937) -> Matrix(1,0,-6,1) Matrix(53,16,-540,-163) -> Matrix(1,0,0,1) Matrix(161,48,540,161) -> Matrix(1,0,0,1) Matrix(271,80,918,271) -> Matrix(1,4,0,1) Matrix(1403,410,2214,647) -> Matrix(1,2,-2,-3) Matrix(2755,802,-9828,-2861) -> Matrix(1,2,0,1) Matrix(757,220,3348,973) -> Matrix(1,2,2,5) Matrix(2377,668,3078,865) -> Matrix(1,0,0,1) Matrix(21059,5906,26568,7451) -> Matrix(1,0,2,1) Matrix(19387,5436,24462,6859) -> Matrix(1,0,0,1) Matrix(703,196,972,271) -> Matrix(1,2,-2,-3) Matrix(701,194,972,269) -> Matrix(3,2,-2,-1) Matrix(379,104,594,163) -> Matrix(1,0,0,1) Matrix(1999,540,3402,919) -> Matrix(3,2,-2,-1) Matrix(8533,2292,11664,3133) -> Matrix(3,4,-4,-5) Matrix(8531,2290,11664,3131) -> Matrix(5,4,-4,-3) Matrix(433,116,810,217) -> Matrix(3,2,-2,-1) Matrix(19279,5118,26244,6967) -> Matrix(19,10,-40,-21) Matrix(19277,5116,26244,6965) -> Matrix(21,10,-40,-19) Matrix(2053,544,3672,973) -> Matrix(5,2,-8,-3) Matrix(1621,428,-8586,-2267) -> Matrix(1,0,0,1) Matrix(8803,2322,10854,2863) -> Matrix(3,2,-2,-1) Matrix(1567,408,2700,703) -> Matrix(1,0,6,1) Matrix(971,250,1674,431) -> Matrix(1,0,-4,1) Matrix(703,168,1134,271) -> Matrix(1,0,0,1) Matrix(5239,1236,6642,1567) -> Matrix(1,2,0,1) Matrix(379,88,702,163) -> Matrix(1,0,0,1) Matrix(593,136,702,161) -> Matrix(3,2,-2,-1) Matrix(2213,504,3078,701) -> Matrix(3,2,-2,-1) Matrix(107,24,-486,-109) -> Matrix(1,0,4,1) Matrix(3673,802,5940,1297) -> Matrix(1,0,-2,1) Matrix(1405,306,2484,541) -> Matrix(1,0,-2,1) Matrix(1025,222,1242,269) -> Matrix(1,0,-2,1) Matrix(9181,1956,11664,2485) -> Matrix(9,-8,8,-7) Matrix(9179,1954,11664,2483) -> Matrix(5,-6,6,-7) Matrix(2483,526,3564,755) -> Matrix(1,0,-2,1) Matrix(5075,1072,6642,1403) -> Matrix(1,0,0,1) Matrix(17603,3652,24462,5075) -> Matrix(1,0,-2,1) Matrix(19117,3964,26568,5509) -> Matrix(3,-4,-2,3) Matrix(1027,212,1836,379) -> Matrix(1,0,-2,1) Matrix(7991,1510,10854,2051) -> Matrix(1,0,0,1) Matrix(161,30,864,161) -> Matrix(1,0,6,1) Matrix(109,20,594,109) -> Matrix(1,0,-4,1) Matrix(811,144,918,163) -> Matrix(1,-2,0,1) Matrix(973,170,1242,217) -> Matrix(1,0,0,1) Matrix(8047,1392,11556,1999) -> Matrix(3,-2,-4,3) Matrix(7181,1240,10314,1781) -> Matrix(1,-2,0,1) Matrix(271,46,324,55) -> Matrix(1,-2,0,1) Matrix(269,44,324,53) -> Matrix(1,0,0,1) Matrix(541,84,702,109) -> Matrix(1,0,0,1) Matrix(1567,234,2538,379) -> Matrix(1,0,4,1) Matrix(1133,166,1836,269) -> Matrix(1,0,-4,1) Matrix(2539,330,2916,379) -> Matrix(1,0,4,1) Matrix(2537,328,2916,377) -> Matrix(1,0,-6,1) Matrix(755,88,918,107) -> Matrix(1,0,0,1) Matrix(433,46,1026,109) -> Matrix(1,-2,0,1) Matrix(377,-32,648,-55) -> Matrix(1,0,0,1) Matrix(539,-64,918,-109) -> Matrix(1,-2,0,1) Matrix(701,-92,1242,-163) -> Matrix(1,0,-2,1) Matrix(271,-38,378,-53) -> Matrix(1,0,0,1) Matrix(433,-66,702,-107) -> Matrix(1,0,-2,1) Matrix(1729,-276,2700,-431) -> Matrix(1,0,-2,1) Matrix(1729,-300,2484,-431) -> Matrix(1,0,0,1) Matrix(433,-78,594,-107) -> Matrix(1,0,0,1) Matrix(865,-164,1134,-215) -> Matrix(1,0,-2,1) Matrix(163,-32,270,-53) -> Matrix(1,0,-2,1) Matrix(649,-136,1026,-215) -> Matrix(1,2,-2,-3) Matrix(539,-114,1026,-217) -> Matrix(1,0,0,1) Matrix(1025,-218,1782,-379) -> Matrix(1,2,-2,-3) Matrix(269,-58,756,-163) -> Matrix(1,0,2,1) Matrix(109,-24,486,-107) -> Matrix(1,0,4,1) Matrix(377,-86,1188,-271) -> Matrix(3,-2,2,-1) Matrix(649,-152,918,-215) -> Matrix(1,0,0,1) Matrix(919,-218,1134,-269) -> Matrix(1,-2,0,1) Matrix(595,-156,1026,-269) -> Matrix(1,0,-4,1) Matrix(2269,-600,3672,-971) -> Matrix(1,0,-2,1) Matrix(1241,-330,3456,-919) -> Matrix(3,-2,2,-1) Matrix(2053,-552,2808,-755) -> Matrix(1,0,-2,1) Matrix(487,-132,594,-161) -> Matrix(1,0,-2,1) Matrix(2267,-636,5778,-1621) -> Matrix(1,0,0,1) Matrix(325,-92,378,-107) -> Matrix(1,0,-2,1) Matrix(215,-62,378,-109) -> Matrix(1,-2,0,1) Matrix(703,-206,918,-269) -> Matrix(1,-2,0,1) Matrix(2701,-816,4644,-1403) -> Matrix(1,0,0,1) 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(1,0,0,1) Matrix(593,-186,864,-271) -> Matrix(1,0,-2,1) Matrix(487,-170,1080,-377) -> Matrix(1,-2,0,1) Matrix(701,-246,1080,-379) -> Matrix(1,0,0,1) Matrix(3349,-1200,5724,-2051) -> Matrix(3,-4,-2,3) Matrix(10153,-3648,13824,-4967) -> Matrix(1,2,-2,-3) Matrix(2269,-816,2700,-971) -> Matrix(1,-2,0,1) Matrix(323,-118,594,-217) -> Matrix(1,-4,0,1) Matrix(811,-298,1026,-377) -> Matrix(1,-4,0,1) Matrix(919,-348,1566,-593) -> Matrix(1,0,0,1) Matrix(3349,-1272,5400,-2051) -> Matrix(1,2,0,1) Matrix(11449,-4368,16416,-6263) -> Matrix(1,2,-4,-7) Matrix(2701,-1032,3672,-1403) -> Matrix(1,2,-4,-7) Matrix(595,-228,702,-269) -> Matrix(3,2,-2,-1) Matrix(5779,-2268,7290,-2861) -> Matrix(1,0,0,1) Matrix(217,-86,270,-107) -> Matrix(1,-2,0,1) Matrix(1513,-620,2106,-863) -> Matrix(1,6,0,1) Matrix(487,-200,918,-377) -> Matrix(1,4,0,1) Matrix(973,-402,1566,-647) -> Matrix(1,2,0,1) Matrix(3673,-1524,5724,-2375) -> Matrix(1,2,-2,-3) Matrix(593,-248,648,-271) -> Matrix(1,2,0,1) Matrix(757,-318,1026,-431) -> Matrix(1,2,-4,-7) Matrix(1727,-728,2052,-865) -> Matrix(1,0,0,1) Matrix(1997,-844,2430,-1027) -> Matrix(1,2,-2,-3) Matrix(1081,-458,1782,-755) -> Matrix(1,2,-2,-3) Matrix(1403,-596,1782,-757) -> Matrix(3,4,2,3) Matrix(269,-116,378,-163) -> Matrix(1,0,0,1) Matrix(1079,-470,1242,-541) -> Matrix(1,0,-2,1) Matrix(2267,-990,2970,-1297) -> Matrix(1,0,0,1) Matrix(217,-96,486,-215) -> Matrix(1,-4,0,1) Matrix(377,-172,594,-271) -> Matrix(1,2,-2,-3) Matrix(541,-254,918,-431) -> Matrix(3,2,-2,-1) Matrix(1511,-796,2052,-1081) -> Matrix(1,0,-2,1) Matrix(703,-386,1080,-593) -> Matrix(1,2,-2,-3) Matrix(271,-150,486,-269) -> Matrix(3,4,-4,-5) Matrix(595,-334,864,-485) -> Matrix(1,0,0,1) Matrix(1403,-790,1728,-973) -> Matrix(3,2,-2,-1) Matrix(1835,-1036,2106,-1189) -> Matrix(1,0,2,1) Matrix(2267,-1284,2862,-1621) -> Matrix(1,0,0,1) Matrix(1997,-1148,2538,-1459) -> Matrix(3,2,4,3) Matrix(1135,-654,1404,-809) -> Matrix(3,2,-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(3,4,2,3) Matrix(1027,-606,1188,-701) -> Matrix(3,4,-4,-5) Matrix(4157,-2526,5778,-3511) -> Matrix(3,2,-2,-1) Matrix(8479,-5240,10746,-6641) -> Matrix(1,2,0,1) Matrix(9073,-5608,11880,-7343) -> Matrix(1,0,0,1) Matrix(2861,-1770,4104,-2539) -> Matrix(1,0,-2,1) Matrix(379,-236,432,-269) -> Matrix(1,0,0,1) Matrix(3023,-1914,4266,-2701) -> Matrix(3,2,-2,-1) Matrix(2537,-1626,3456,-2215) -> Matrix(1,0,0,1) Matrix(593,-382,756,-487) -> Matrix(1,0,2,1) Matrix(917,-626,1188,-811) -> Matrix(1,0,0,1) Matrix(487,-340,540,-377) -> Matrix(1,0,0,1) Matrix(7073,-5014,9828,-6967) -> Matrix(1,0,0,1) Matrix(6965,-5126,8586,-6319) -> Matrix(7,2,-4,-1) Matrix(379,-294,486,-377) -> Matrix(1,0,2,1) 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): 52 Degree of the the map X: 52 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 972 Minimal number of generators: 163 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -7/9 -2/3 -5/9 -4/9 -5/12 -41/108 -1/3 -29/108 -7/27 -2/9 -4/21 -1/6 -2/17 -1/9 0/1 1/10 1/9 1/8 2/15 1/7 2/13 1/6 4/23 2/11 5/27 4/21 1/5 4/19 2/9 3/13 1/4 4/15 3/11 2/7 8/27 1/3 10/27 2/5 11/27 5/12 4/9 1/2 5/9 14/25 26/45 16/27 50/81 17/27 52/81 2/3 94/135 19/27 136/189 20/27 7/9 22/27 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 0/1 1/1 -6/7 1/2 1/1 -11/13 1/1 2/1 -5/6 1/0 -14/17 0/1 1/1 -9/11 0/1 1/1 -4/5 1/1 1/0 -7/9 0/1 -10/13 0/1 1/1 -3/4 0/1 1/0 -11/15 1/2 -30/41 2/3 1/1 -19/26 0/1 1/1 -8/11 0/1 1/2 -13/18 1/1 -18/25 1/1 1/0 -23/32 3/1 1/0 -5/7 0/1 1/1 -17/24 1/0 -12/17 -1/1 0/1 -19/27 0/1 -7/10 0/1 1/2 -16/23 0/1 1/1 -9/13 0/1 1/1 -2/3 0/1 1/1 1/0 -9/14 0/1 1/1 -16/25 1/2 1/1 -7/11 0/1 1/1 -19/30 1/2 -12/19 2/3 1/1 -17/27 1/1 -5/8 1/1 1/0 -18/29 1/1 1/0 -31/50 0/1 1/0 -13/21 1/0 -8/13 0/1 1/1 -11/18 0/1 -14/23 0/1 1/1 -17/28 0/1 1/1 -3/5 1/2 1/1 -10/17 1/1 2/1 -17/29 1/1 1/0 -7/12 1/0 -18/31 -1/1 0/1 -11/19 1/2 1/1 -4/7 1/1 1/0 -5/9 1/1 -6/11 2/1 1/0 -1/2 1/1 1/0 -6/13 1/1 2/1 -5/11 1/1 2/1 -4/9 1/0 -7/16 -1/1 0/1 -10/23 0/1 1/1 -13/30 1/0 -3/7 0/1 1/1 -11/26 1/1 2/1 -19/45 2/1 -27/64 2/1 1/0 -8/19 1/1 2/1 -5/12 1/0 -12/29 3/1 1/0 -19/46 3/1 1/0 -7/17 4/1 1/0 -16/39 5/1 6/1 1/0 -9/22 9/1 1/0 -11/27 1/0 -2/5 -1/1 1/0 -5/13 0/1 1/1 -18/47 3/4 1/1 -31/81 1/1 -13/34 1/1 4/3 -8/21 1/1 2/1 1/0 -19/50 2/1 1/0 -30/79 3/1 1/0 -41/108 1/0 -11/29 1/1 1/0 -14/37 1/1 2/1 -3/8 3/1 1/0 -4/11 -2/1 1/0 -5/14 -1/1 0/1 -6/17 -1/1 0/1 -1/3 1/0 -5/16 -1/1 0/1 -4/13 -1/1 0/1 -3/10 0/1 1/0 -2/7 -1/1 1/0 -3/11 -1/1 0/1 -10/37 -1/1 0/1 -17/63 0/1 -7/26 -1/1 0/1 -18/67 -2/1 -1/1 -29/108 -1/1 -11/41 -1/1 -2/3 -4/15 -1/1 -1/2 0/1 -5/19 -1/2 -1/3 -6/23 -1/5 0/1 -7/27 0/1 -1/4 0/1 1/0 -4/17 -1/1 0/1 -3/13 -1/1 0/1 -2/9 0/1 -3/14 0/1 1/1 -4/19 0/1 1/1 -5/24 1/0 -1/5 -1/1 1/0 -4/21 -1/1 -1/2 0/1 -3/16 -1/3 0/1 -5/27 0/1 -2/11 0/1 1/2 -5/28 0/1 1/1 -3/17 0/1 1/0 -1/6 1/0 -1/7 0/1 1/1 -1/8 1/1 1/0 -2/17 -1/1 0/1 -1/9 0/1 -1/10 0/1 1/0 0/1 0/1 1/0 1/10 0/1 1/0 1/9 0/1 1/8 -1/1 1/0 2/15 0/1 1/1 1/0 1/7 -1/1 0/1 2/13 0/1 1/1 1/6 1/0 5/29 -1/1 1/0 4/23 -1/1 0/1 3/17 0/1 1/0 2/11 -1/2 0/1 5/27 0/1 3/16 0/1 1/3 4/21 0/1 1/2 1/1 1/5 1/1 1/0 4/19 -1/1 0/1 11/52 -1/1 1/0 7/33 1/0 3/14 -1/1 0/1 2/9 0/1 3/13 0/1 1/1 4/17 0/1 1/1 5/21 1/0 1/4 0/1 1/0 5/19 1/3 1/2 9/34 0/1 1/3 13/49 3/7 1/2 4/15 0/1 1/2 1/1 11/41 2/3 1/1 7/26 0/1 1/1 3/11 0/1 1/1 8/29 1/2 1/1 5/18 1/1 2/7 1/1 1/0 5/17 2/1 1/0 8/27 1/0 3/10 0/1 1/0 13/43 -1/1 0/1 10/33 0/1 1/1 1/0 7/23 0/1 1/0 4/13 0/1 1/1 5/16 0/1 1/1 1/3 1/0 6/17 0/1 1/1 5/14 0/1 1/1 14/39 1/1 2/1 1/0 23/64 0/1 1/0 9/25 1/1 1/0 4/11 2/1 1/0 7/19 7/1 1/0 10/27 1/0 3/8 -3/1 1/0 11/29 -1/1 1/0 19/50 -2/1 1/0 8/21 -2/1 -1/1 1/0 29/76 -3/2 -1/1 21/55 -2/1 -1/1 13/34 -4/3 -1/1 5/13 -1/1 0/1 12/31 -1/1 0/1 7/18 0/1 2/5 1/1 1/0 11/27 1/0 9/22 -9/1 1/0 16/39 -6/1 -5/1 1/0 7/17 -4/1 1/0 12/29 -3/1 1/0 17/41 -3/1 -2/1 22/53 -2/1 1/0 5/12 1/0 13/31 -5/2 -2/1 8/19 -2/1 -1/1 27/64 -2/1 1/0 19/45 -2/1 11/26 -2/1 -1/1 14/33 -2/1 -3/2 -1/1 3/7 -1/1 0/1 10/23 -1/1 0/1 17/39 1/0 24/55 0/1 1/0 7/16 0/1 1/1 4/9 1/0 5/11 -2/1 -1/1 6/13 -2/1 -1/1 7/15 1/0 1/2 -1/1 1/0 10/19 -1/1 0/1 9/17 0/1 1/0 8/15 -2/1 -1/1 1/0 7/13 -1/1 0/1 6/11 -2/1 1/0 5/9 -1/1 14/25 -1/1 -1/2 9/16 -1/1 0/1 4/7 -1/1 1/0 15/26 -1/1 0/1 26/45 -1/1 37/64 -2/3 -1/2 11/19 -1/1 -1/2 29/50 -1/4 0/1 47/81 0/1 18/31 0/1 1/1 25/43 -1/1 0/1 57/98 0/1 1/0 32/55 0/1 1/0 7/12 1/0 24/41 -1/1 0/1 17/29 -1/1 1/0 27/46 -3/1 1/0 37/63 -2/1 10/17 -2/1 -1/1 13/22 -5/4 -1/1 16/27 -1/1 3/5 -1/1 -1/2 20/33 -1/1 0/1 1/0 17/28 -1/1 0/1 31/51 -1/2 14/23 -1/1 0/1 11/18 0/1 8/13 -1/1 0/1 29/47 -1/3 0/1 50/81 0/1 21/34 0/1 1/1 13/21 1/0 31/50 0/1 1/0 49/79 1/1 1/0 67/108 1/0 18/29 -1/1 1/0 23/37 -2/1 1/0 5/8 -1/1 1/0 17/27 -1/1 12/19 -1/1 -2/3 31/49 -3/5 -1/2 50/79 -1/1 -1/2 19/30 -1/2 7/11 -1/1 0/1 16/25 -1/1 -1/2 25/39 -1/2 34/53 -1/2 0/1 43/67 -1/3 0/1 52/81 0/1 9/14 -1/1 0/1 2/3 -1/1 0/1 1/0 9/13 -1/1 0/1 16/23 -1/1 0/1 55/79 -1/1 1/0 94/135 -1/1 39/56 -1/1 -1/2 23/33 -1/2 7/10 -1/2 0/1 19/27 0/1 12/17 0/1 1/1 17/24 1/0 56/79 -1/1 1/0 39/55 -1/1 0/1 22/31 -1/1 0/1 5/7 -1/1 0/1 28/39 0/1 1/1 1/0 23/32 -3/1 1/0 41/57 1/0 59/82 -2/1 -1/1 136/189 -1/1 77/107 -1/1 0/1 18/25 -1/1 1/0 13/18 -1/1 8/11 -1/2 0/1 27/37 0/1 1/0 46/63 -1/1 19/26 -1/1 0/1 49/67 -2/1 -1/1 79/108 -1/1 30/41 -1/1 -2/3 11/15 -1/2 14/19 -1/3 0/1 17/23 -1/6 0/1 20/27 0/1 3/4 0/1 1/0 16/21 -1/1 0/1 1/0 29/38 0/1 1/1 42/55 0/1 1/0 13/17 0/1 1/0 10/13 -1/1 0/1 7/9 0/1 18/23 0/1 1/1 11/14 0/1 1/1 4/5 -1/1 1/0 13/16 -2/1 -1/1 22/27 -1/1 9/11 -1/1 0/1 23/28 -1/1 0/1 37/45 0/1 14/17 -1/1 0/1 19/23 0/1 1/0 5/6 1/0 21/25 -1/1 1/0 37/44 -2/1 1/0 16/19 -2/1 -1/1 11/13 -2/1 -1/1 17/20 -6/5 -1/1 23/27 -1/1 6/7 -1/1 -1/2 7/8 -1/1 1/0 15/17 -2/1 1/0 8/9 -1/1 9/10 -1/2 0/1 1/1 -1/1 0/1 1/0 0/1 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(109,94,189,163) (-1/1,-6/7) -> (4/7,15/26) Hyperbolic Matrix(269,228,-702,-595) (-6/7,-11/13) -> (-5/13,-18/47) Hyperbolic Matrix(109,92,513,433) (-11/13,-5/6) -> (7/33,3/14) Hyperbolic Matrix(109,90,459,379) (-5/6,-14/17) -> (4/17,5/21) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(109,88,135,109) (-9/11,-4/5) -> (4/5,13/16) Hyperbolic Matrix(53,42,135,107) (-4/5,-7/9) -> (7/18,2/5) Hyperbolic Matrix(215,166,-351,-271) (-7/9,-10/13) -> (-8/13,-11/18) Hyperbolic Matrix(107,82,351,269) (-10/13,-3/4) -> (7/23,4/13) Hyperbolic Matrix(215,158,513,377) (-3/4,-11/15) -> (5/12,13/31) 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(163,118,-297,-215) (-8/11,-13/18) -> (-5/9,-6/11) Hyperbolic Matrix(269,194,972,701) (-13/18,-18/25) -> (8/29,5/18) Hyperbolic Matrix(2375,1708,3753,2699) (-18/25,-23/32) -> (31/49,50/79) Hyperbolic Matrix(379,272,1431,1027) (-23/32,-5/7) -> (9/34,13/49) Hyperbolic Matrix(163,116,-378,-269) (-5/7,-17/24) -> (-13/30,-3/7) Hyperbolic Matrix(161,114,-459,-325) (-17/24,-12/17) -> (-6/17,-1/3) 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(109,76,621,433) (-7/10,-16/23) -> (4/23,3/17) Hyperbolic Matrix(271,188,702,487) (-16/23,-9/13) -> (5/13,12/31) Hyperbolic Matrix(53,36,-81,-55) (-9/13,-2/3) -> (-2/3,-9/14) Parabolic Matrix(593,380,1431,917) (-9/14,-16/25) -> (12/29,17/41) Hyperbolic Matrix(163,104,594,379) (-16/25,-7/11) -> (3/11,8/29) Hyperbolic Matrix(161,102,-513,-325) (-7/11,-19/30) -> (-1/3,-5/16) 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(55,34,351,217) (-13/21,-8/13) -> (2/13,1/6) Hyperbolic Matrix(377,230,972,593) (-11/18,-14/23) -> (12/31,7/18) Hyperbolic Matrix(1513,920,2133,1297) (-14/23,-17/28) -> (39/55,22/31) Hyperbolic Matrix(917,556,2403,1457) (-17/28,-3/5) -> (29/76,21/55) Hyperbolic Matrix(271,160,459,271) (-3/5,-10/17) -> (10/17,13/22) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(215,126,459,269) (-17/29,-7/12) -> (7/15,1/2) Hyperbolic Matrix(647,376,1485,863) (-7/12,-18/31) -> (10/23,17/39) Hyperbolic Matrix(269,156,-1026,-595) (-18/31,-11/19) -> (-5/19,-6/23) Hyperbolic Matrix(163,94,189,109) (-11/19,-4/7) -> (6/7,7/8) Hyperbolic Matrix(53,30,189,107) (-4/7,-5/9) -> (5/18,2/7) Hyperbolic Matrix(107,58,297,161) (-6/11,-1/2) -> (9/25,4/11) Hyperbolic Matrix(269,126,459,215) (-1/2,-6/13) -> (24/41,17/29) Hyperbolic Matrix(109,50,-351,-161) (-6/13,-5/11) -> (-5/16,-4/13) Hyperbolic Matrix(107,48,-243,-109) (-5/11,-4/9) -> (-4/9,-7/16) Parabolic Matrix(863,376,1485,647) (-7/16,-10/23) -> (18/31,25/43) Hyperbolic Matrix(1133,492,1863,809) (-10/23,-13/30) -> (31/51,14/23) Hyperbolic Matrix(485,206,1269,539) (-3/7,-11/26) -> (21/55,13/34) 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(811,342,1539,649) (-27/64,-8/19) -> (10/19,9/17) Hyperbolic Matrix(377,158,513,215) (-8/19,-5/12) -> (11/15,14/19) Hyperbolic Matrix(917,380,1431,593) (-5/12,-12/29) -> (16/25,25/39) Hyperbolic Matrix(1889,780,3267,1349) (-19/46,-7/17) -> (37/64,11/19) Hyperbolic Matrix(1135,466,3159,1297) (-7/17,-16/39) -> (14/39,23/64) Hyperbolic Matrix(595,244,2241,919) (-16/39,-9/22) -> (13/49,4/15) 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(107,42,135,53) (-2/5,-5/13) -> (11/14,4/5) 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(539,206,1269,485) (-13/34,-8/21) -> (14/33,3/7) 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(109,40,297,109) (-3/8,-4/11) -> (4/11,7/19) Hyperbolic Matrix(161,58,297,107) (-4/11,-5/14) -> (7/13,6/11) Hyperbolic Matrix(107,38,-459,-163) (-5/14,-6/17) -> (-4/17,-3/13) Hyperbolic Matrix(269,82,351,107) (-4/13,-3/10) -> (13/17,10/13) Hyperbolic Matrix(55,16,189,55) (-3/10,-2/7) -> (2/7,5/17) Hyperbolic Matrix(107,30,189,53) (-2/7,-3/11) -> (9/16,4/7) 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(53,14,405,107) (-4/15,-5/19) -> (1/8,2/15) 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(379,90,459,109) (-1/4,-4/17) -> (14/17,19/23) Hyperbolic Matrix(53,12,-243,-55) (-3/13,-2/9) -> (-2/9,-3/14) Parabolic Matrix(433,92,513,109) (-3/14,-4/19) -> (16/19,11/13) Hyperbolic Matrix(757,156,1053,217) (-5/24,-1/5) -> (23/32,41/57) Hyperbolic Matrix(649,124,1701,325) (-1/5,-4/21) -> (8/21,29/76) Hyperbolic Matrix(433,82,1431,271) (-4/21,-3/16) -> (13/43,10/33) 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(269,48,297,53) (-5/28,-3/17) -> (9/10,1/1) Hyperbolic Matrix(433,76,621,109) (-3/17,-1/6) -> (23/33,7/10) Hyperbolic Matrix(217,34,351,55) (-1/6,-1/7) -> (21/34,13/21) Hyperbolic Matrix(107,14,405,53) (-1/7,-1/8) -> (5/19,9/34) 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(433,42,567,55) (-1/10,0/1) -> (42/55,13/17) 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(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(269,-46,1269,-217) (1/6,5/29) -> (11/52,7/33) 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(55,-12,243,-53) (3/14,2/9) -> (2/9,3/13) Parabolic Matrix(163,-38,459,-107) (3/13,4/17) -> (6/17,5/14) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(649,-174,1809,-485) (4/15,11/41) -> (5/14,14/39) 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(217,-64,729,-215) (5/17,8/27) -> (8/27,3/10) Parabolic Matrix(2701,-816,4644,-1403) (3/10,13/43) -> (25/43,57/98) Hyperbolic Matrix(811,-246,2133,-647) (10/33,7/23) -> (19/50,8/21) Hyperbolic Matrix(161,-50,351,-109) (4/13,5/16) -> (5/11,6/13) Hyperbolic Matrix(325,-102,513,-161) (5/16,1/3) -> (19/30,7/11) Hyperbolic Matrix(325,-114,459,-161) (1/3,6/17) -> (12/17,17/24) Hyperbolic Matrix(2269,-816,2700,-971) (23/64,9/25) -> (21/25,37/44) Hyperbolic Matrix(271,-100,729,-269) (7/19,10/27) -> (10/27,3/8) Parabolic 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(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) 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(1189,-494,2727,-1133) (22/53,5/12) -> (17/39,24/55) 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(269,-116,378,-163) (3/7,10/23) -> (22/31,5/7) Hyperbolic Matrix(2267,-990,2970,-1297) (24/55,7/16) -> (29/38,42/55) Hyperbolic Matrix(109,-48,243,-107) (7/16,4/9) -> (4/9,5/11) Parabolic Matrix(215,-118,297,-163) (6/11,5/9) -> (13/18,8/11) Hyperbolic Matrix(487,-272,675,-377) (5/9,14/25) -> (18/25,13/18) Hyperbolic Matrix(431,-242,675,-379) (14/25,9/16) -> (7/11,16/25) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4159,-2404,5697,-3293) (26/45,37/64) -> (27/37,46/63) Hyperbolic Matrix(1783,-1038,2781,-1619) (32/55,7/12) -> (25/39,34/53) Hyperbolic Matrix(811,-474,1107,-647) (7/12,24/41) -> (30/41,11/15) Hyperbolic Matrix(433,-256,729,-431) (13/22,16/27) -> (16/27,3/5) Parabolic Matrix(4157,-2526,5778,-3511) (17/28,31/51) -> (41/57,59/82) Hyperbolic Matrix(485,-296,621,-379) (14/23,11/18) -> (7/9,18/23) Hyperbolic Matrix(271,-166,351,-215) (11/18,8/13) -> (10/13,7/9) Hyperbolic Matrix(4051,-2500,6561,-4049) (29/47,50/81) -> (50/81,21/34) Parabolic Matrix(649,-402,783,-485) (13/21,31/50) -> (19/23,5/6) 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(4213,-2704,6561,-4211) (43/67,52/81) -> (52/81,9/14) Parabolic Matrix(55,-36,81,-53) (9/14,2/3) -> (2/3,9/13) Parabolic Matrix(487,-338,621,-431) (9/13,16/23) -> (18/23,11/14) Hyperbolic Matrix(12691,-8836,18225,-12689) (55/79,94/135) -> (94/135,39/56) Parabolic Matrix(973,-678,1161,-809) (39/56,23/33) -> (5/6,21/25) Hyperbolic Matrix(7073,-5014,9828,-6967) (56/79,39/55) -> (77/107,18/25) Hyperbolic Matrix(25705,-18496,35721,-25703) (59/82,136/189) -> (136/189,77/107) Parabolic Matrix(541,-400,729,-539) (17/23,20/27) -> (20/27,3/4) Parabolic Matrix(595,-484,729,-593) (13/16,22/27) -> (22/27,9/11) Parabolic Matrix(217,-192,243,-215) (15/17,8/9) -> (8/9,9/10) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(109,94,189,163) -> Matrix(1,0,-2,1) Matrix(269,228,-702,-595) -> Matrix(1,-2,2,-3) Matrix(109,92,513,433) -> Matrix(1,-2,0,1) Matrix(109,90,459,379) -> Matrix(1,0,0,1) Matrix(161,132,-594,-487) -> Matrix(1,0,-2,1) Matrix(109,88,135,109) -> Matrix(1,-2,0,1) Matrix(53,42,135,107) -> Matrix(1,0,0,1) Matrix(215,166,-351,-271) -> Matrix(1,0,0,1) Matrix(107,82,351,269) -> Matrix(1,0,0,1) Matrix(215,158,513,377) -> Matrix(5,-2,-2,1) Matrix(377,276,810,593) -> Matrix(1,0,-2,1) Matrix(755,552,-2808,-2053) -> Matrix(1,0,-2,1) Matrix(107,78,-594,-433) -> Matrix(1,0,0,1) Matrix(163,118,-297,-215) -> Matrix(3,-2,2,-1) Matrix(269,194,972,701) -> Matrix(1,-2,2,-3) Matrix(2375,1708,3753,2699) -> Matrix(1,0,-2,1) Matrix(379,272,1431,1027) -> Matrix(1,0,2,1) Matrix(163,116,-378,-269) -> Matrix(1,0,0,1) Matrix(161,114,-459,-325) -> Matrix(1,0,0,1) Matrix(647,456,918,647) -> Matrix(1,0,2,1) Matrix(379,266,540,379) -> Matrix(1,0,-4,1) Matrix(109,76,621,433) -> Matrix(1,0,-2,1) Matrix(271,188,702,487) -> Matrix(1,0,-2,1) Matrix(53,36,-81,-55) -> Matrix(1,0,0,1) Matrix(593,380,1431,917) -> Matrix(5,-2,-2,1) Matrix(163,104,594,379) -> Matrix(1,0,0,1) Matrix(161,102,-513,-325) -> Matrix(1,0,-2,1) Matrix(215,136,-1026,-649) -> Matrix(3,-2,2,-1) Matrix(647,408,1026,647) -> Matrix(5,-4,-6,5) Matrix(271,170,432,271) -> Matrix(1,-2,0,1) Matrix(647,402,-1566,-973) -> Matrix(1,2,0,1) Matrix(2051,1272,-5400,-3349) -> Matrix(1,2,0,1) Matrix(271,168,1134,703) -> Matrix(1,0,0,1) Matrix(55,34,351,217) -> Matrix(1,0,0,1) Matrix(377,230,972,593) -> Matrix(1,0,-2,1) Matrix(1513,920,2133,1297) -> Matrix(1,0,-2,1) Matrix(917,556,2403,1457) -> Matrix(1,-2,0,1) Matrix(271,160,459,271) -> Matrix(3,-4,-2,3) Matrix(593,348,-1566,-919) -> Matrix(1,0,0,1) Matrix(215,126,459,269) -> Matrix(1,-2,0,1) Matrix(647,376,1485,863) -> Matrix(1,0,0,1) Matrix(269,156,-1026,-595) -> Matrix(1,0,-4,1) Matrix(163,94,189,109) -> Matrix(1,0,-2,1) Matrix(53,30,189,107) -> Matrix(1,0,0,1) Matrix(107,58,297,161) -> Matrix(1,0,0,1) Matrix(269,126,459,215) -> Matrix(1,-2,0,1) Matrix(109,50,-351,-161) -> Matrix(1,-2,0,1) Matrix(107,48,-243,-109) -> Matrix(1,-2,0,1) Matrix(863,376,1485,647) -> Matrix(1,0,0,1) Matrix(1133,492,1863,809) -> Matrix(1,0,-2,1) Matrix(485,206,1269,539) -> Matrix(3,-4,-2,3) Matrix(757,320,-2808,-1187) -> Matrix(1,-2,0,1) Matrix(109,46,1026,433) -> Matrix(1,-2,0,1) Matrix(811,342,1539,649) -> Matrix(1,-2,0,1) Matrix(377,158,513,215) -> Matrix(1,-2,-2,5) Matrix(917,380,1431,593) -> Matrix(1,-2,-2,5) Matrix(1889,780,3267,1349) -> Matrix(1,-2,-2,5) Matrix(1135,466,3159,1297) -> Matrix(1,-4,0,1) Matrix(595,244,2241,919) -> Matrix(1,-6,2,-11) Matrix(485,198,1188,485) -> Matrix(1,-18,0,1) Matrix(109,44,270,109) -> Matrix(1,2,0,1) Matrix(107,42,135,53) -> Matrix(1,0,0,1) Matrix(1567,600,1836,703) -> Matrix(5,-4,-6,5) Matrix(2159,826,2538,971) -> Matrix(9,-10,-8,9) Matrix(539,206,1269,485) -> Matrix(3,-4,-2,3) Matrix(863,328,1134,431) -> Matrix(1,-2,0,1) Matrix(7237,2748,11664,4429) -> Matrix(1,-4,0,1) Matrix(7235,2746,11664,4427) -> Matrix(1,0,0,1) Matrix(53,20,-432,-163) -> Matrix(1,-2,0,1) Matrix(109,40,297,109) -> Matrix(1,4,0,1) Matrix(161,58,297,107) -> Matrix(1,0,0,1) Matrix(107,38,-459,-163) -> Matrix(1,0,0,1) Matrix(269,82,351,107) -> Matrix(1,0,0,1) Matrix(55,16,189,55) -> Matrix(1,2,0,1) Matrix(107,30,189,53) -> Matrix(1,0,0,1) Matrix(1999,540,3402,919) -> Matrix(3,2,-2,-1) Matrix(8533,2292,11664,3133) -> Matrix(3,4,-4,-5) Matrix(8531,2290,11664,3131) -> Matrix(5,4,-4,-3) Matrix(433,116,810,217) -> Matrix(3,2,-2,-1) Matrix(53,14,405,107) -> Matrix(1,0,2,1) Matrix(1567,408,2700,703) -> Matrix(1,0,6,1) Matrix(971,250,1674,431) -> Matrix(1,0,-4,1) Matrix(379,90,459,109) -> Matrix(1,0,0,1) Matrix(53,12,-243,-55) -> Matrix(1,0,2,1) Matrix(433,92,513,109) -> Matrix(1,-2,0,1) Matrix(757,156,1053,217) -> Matrix(1,-2,0,1) Matrix(649,124,1701,325) -> Matrix(3,2,-2,-1) Matrix(433,82,1431,271) -> Matrix(1,0,2,1) Matrix(161,30,864,161) -> Matrix(1,0,6,1) Matrix(109,20,594,109) -> Matrix(1,0,-4,1) Matrix(269,48,297,53) -> Matrix(1,0,-2,1) Matrix(433,76,621,109) -> Matrix(1,0,-2,1) Matrix(217,34,351,55) -> Matrix(1,0,0,1) Matrix(107,14,405,53) -> Matrix(1,0,2,1) Matrix(755,88,918,107) -> Matrix(1,0,0,1) Matrix(433,46,1026,109) -> Matrix(1,-2,0,1) Matrix(433,42,567,55) -> Matrix(1,0,0,1) Matrix(377,-32,648,-55) -> Matrix(1,0,0,1) Matrix(539,-64,918,-109) -> Matrix(1,-2,0,1) Matrix(271,-38,378,-53) -> Matrix(1,0,0,1) Matrix(433,-66,702,-107) -> Matrix(1,0,-2,1) Matrix(269,-46,1269,-217) -> Matrix(1,0,0,1) Matrix(1729,-300,2484,-431) -> Matrix(1,0,0,1) Matrix(433,-78,594,-107) -> Matrix(1,0,0,1) Matrix(865,-164,1134,-215) -> Matrix(1,0,-2,1) Matrix(163,-32,270,-53) -> Matrix(1,0,-2,1) Matrix(649,-136,1026,-215) -> Matrix(1,2,-2,-3) Matrix(539,-114,1026,-217) -> Matrix(1,0,0,1) Matrix(55,-12,243,-53) -> Matrix(1,0,2,1) Matrix(163,-38,459,-107) -> Matrix(1,0,0,1) Matrix(595,-156,1026,-269) -> Matrix(1,0,-4,1) Matrix(649,-174,1809,-485) -> Matrix(3,-2,2,-1) Matrix(2053,-552,2808,-755) -> Matrix(1,0,-2,1) Matrix(487,-132,594,-161) -> Matrix(1,0,-2,1) Matrix(217,-64,729,-215) -> Matrix(1,-2,0,1) Matrix(2701,-816,4644,-1403) -> Matrix(1,0,0,1) Matrix(811,-246,2133,-647) -> Matrix(1,-2,0,1) Matrix(161,-50,351,-109) -> Matrix(1,-2,0,1) Matrix(325,-102,513,-161) -> Matrix(1,0,-2,1) Matrix(325,-114,459,-161) -> Matrix(1,0,0,1) Matrix(2269,-816,2700,-971) -> Matrix(1,-2,0,1) Matrix(271,-100,729,-269) -> Matrix(1,-10,0,1) Matrix(919,-348,1566,-593) -> Matrix(1,0,0,1) Matrix(3349,-1272,5400,-2051) -> Matrix(1,2,0,1) Matrix(595,-228,702,-269) -> Matrix(3,2,-2,-1) Matrix(1513,-620,2106,-863) -> Matrix(1,6,0,1) Matrix(487,-200,918,-377) -> Matrix(1,4,0,1) Matrix(973,-402,1566,-647) -> Matrix(1,2,0,1) Matrix(3673,-1524,5724,-2375) -> Matrix(1,2,-2,-3) Matrix(1189,-494,2727,-1133) -> Matrix(1,2,0,1) Matrix(757,-318,1026,-431) -> Matrix(1,2,-4,-7) Matrix(1727,-728,2052,-865) -> Matrix(1,0,0,1) Matrix(1997,-844,2430,-1027) -> Matrix(1,2,-2,-3) Matrix(1081,-458,1782,-755) -> Matrix(1,2,-2,-3) Matrix(269,-116,378,-163) -> Matrix(1,0,0,1) Matrix(2267,-990,2970,-1297) -> Matrix(1,0,0,1) Matrix(109,-48,243,-107) -> Matrix(1,-2,0,1) Matrix(215,-118,297,-163) -> Matrix(1,2,-2,-3) Matrix(487,-272,675,-377) -> Matrix(3,2,-2,-1) Matrix(431,-242,675,-379) -> Matrix(1,0,0,1) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(4159,-2404,5697,-3293) -> Matrix(3,2,-2,-1) Matrix(1783,-1038,2781,-1619) -> Matrix(1,0,-2,1) Matrix(811,-474,1107,-647) -> Matrix(1,2,-2,-3) Matrix(433,-256,729,-431) -> Matrix(5,6,-6,-7) Matrix(4157,-2526,5778,-3511) -> Matrix(3,2,-2,-1) Matrix(485,-296,621,-379) -> Matrix(1,0,2,1) Matrix(271,-166,351,-215) -> Matrix(1,0,0,1) Matrix(4051,-2500,6561,-4049) -> Matrix(1,0,4,1) Matrix(649,-402,783,-485) -> Matrix(1,0,0,1) Matrix(379,-236,432,-269) -> Matrix(1,0,0,1) Matrix(3023,-1914,4266,-2701) -> Matrix(3,2,-2,-1) Matrix(4213,-2704,6561,-4211) -> Matrix(1,0,2,1) Matrix(55,-36,81,-53) -> Matrix(1,0,0,1) Matrix(487,-338,621,-431) -> Matrix(1,0,2,1) Matrix(12691,-8836,18225,-12689) -> Matrix(1,2,-2,-3) Matrix(973,-678,1161,-809) -> Matrix(3,2,-2,-1) Matrix(7073,-5014,9828,-6967) -> Matrix(1,0,0,1) Matrix(25705,-18496,35721,-25703) -> Matrix(1,2,-2,-3) Matrix(541,-400,729,-539) -> Matrix(1,0,6,1) Matrix(595,-484,729,-593) -> Matrix(1,2,-2,-3) Matrix(217,-192,243,-215) -> Matrix(1,2,-2,-3) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 26 Imminent integer overflow caused the modular group computation to abort.