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 -1/1 -8/17 -7/16 -2/5 -5/14 -4/13 -1/4 -2/11 0/1 1/8 1/5 5/22 2/7 4/11 5/13 8/19 1/2 10/17 8/13 7/11 11/16 5/7 4/5 1/1 8/7 5/4 47/34 7/5 16/11 3/2 11/7 50/31 13/8 17/10 35/19 2/1 37/17 56/25 113/49 19/8 17/7 5/2 136/53 13/5 137/52 79/29 11/4 119/43 20/7 3/1 41/13 16/5 55/17 10/3 7/2 11/3 85/23 19/5 107/28 4/1 17/4 73/17 13/3 22/5 9/2 37/8 14/3 19/4 67/14 5/1 68/13 21/4 16/3 11/2 17/3 23/4 6/1 19/3 13/2 20/3 47/7 7/1 15/2 23/3 8/1 17/2 26/3 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/2 -8/17 0/1 -7/15 0/1 1/2 -13/28 1/2 -6/13 0/1 1/0 -11/24 0/1 1/4 -5/11 1/2 -14/31 -1/1 1/0 -9/20 -1/2 0/1 -13/29 0/1 1/8 -17/38 1/4 -4/9 0/1 1/3 -15/34 1/2 2/3 -26/59 1/0 -11/25 0/1 1/2 -18/41 1/1 1/0 -7/16 0/1 -24/55 1/5 1/4 -17/39 0/1 1/5 -10/23 0/1 1/4 -13/30 1/4 3/11 -3/7 1/3 1/2 -14/33 0/1 1/2 -25/59 0/1 1/4 -11/26 1/2 -19/45 0/1 1/2 -8/19 0/1 1/4 -13/31 1/3 -5/12 2/5 1/2 -17/41 1/2 -12/29 7/15 1/2 -7/17 1/2 3/5 -9/22 0/1 1/2 -11/27 2/5 1/2 -13/32 1/2 2/3 -2/5 1/2 -13/33 0/1 1/2 -11/28 1/2 5/9 -9/23 1/2 2/3 -7/18 0/1 1/2 -19/49 1/2 -12/31 4/9 1/2 -5/13 1/2 4/7 -18/47 16/27 3/5 -13/34 5/8 -34/89 5/8 2/3 -21/55 9/14 2/3 -8/21 1/2 2/3 -11/29 2/3 -3/8 2/3 1/1 -13/35 0/1 1/1 -23/62 1/2 -10/27 1/2 1/1 -17/46 1/1 2/1 -7/19 1/2 -18/49 1/2 1/1 -11/30 1/2 2/3 -26/71 2/3 -15/41 1/2 2/3 -19/52 1/2 -4/11 2/3 3/4 -13/36 3/4 1/1 -22/61 3/4 -9/25 4/5 5/6 -14/39 4/5 1/1 -5/14 1/1 -16/45 1/1 4/3 -11/31 2/1 1/0 -6/17 0/1 1/2 -7/20 1/2 2/3 -1/3 0/1 1/1 -6/19 2/1 1/0 -5/16 0/1 1/0 -9/29 1/2 2/3 -4/13 1/1 -15/49 7/6 6/5 -11/36 1/1 4/3 -7/23 5/4 4/3 -17/56 3/2 -27/89 4/3 3/2 -10/33 1/1 3/2 -13/43 3/2 -3/10 3/2 2/1 -17/57 2/1 5/2 -14/47 1/0 -11/37 2/1 1/0 -19/64 2/1 -8/27 2/1 1/0 -21/71 3/1 1/0 -13/44 1/1 1/0 -5/17 1/0 -12/41 2/3 1/1 -19/65 3/2 2/1 -7/24 1/1 1/0 -16/55 1/0 -9/31 0/1 1/1 -2/7 1/1 2/1 -7/25 2/1 -5/18 2/1 1/0 -18/65 7/4 2/1 -13/47 2/1 9/4 -34/123 2/1 5/2 -55/199 2/1 -21/76 2/1 5/2 -8/29 5/2 -11/40 3/1 16/5 -14/51 3/1 7/2 -3/11 4/1 1/0 -7/26 -4/1 1/0 -18/67 -2/1 -1/1 -11/41 1/0 -4/15 0/1 1/0 -5/19 2/1 1/0 -6/23 5/1 1/0 -13/50 -5/1 1/0 -7/27 0/1 1/0 -1/4 1/0 -6/25 2/1 1/0 -11/46 -6/1 1/0 -5/21 -2/1 1/0 -4/17 0/1 1/0 -3/13 3/1 1/0 -5/22 -7/1 1/0 -7/31 1/0 -9/40 -3/1 1/0 -2/9 -2/1 1/0 -5/23 -1/1 -3/14 -1/2 0/1 -10/47 -1/1 1/0 -7/33 0/1 1/0 -4/19 1/0 -9/43 -1/2 0/1 -14/67 0/1 1/0 -19/91 0/1 -5/24 0/1 1/0 -6/29 1/1 1/0 -1/5 -1/1 1/0 -4/21 -3/5 -1/2 -3/16 -1/2 0/1 -5/27 -1/3 0/1 -2/11 0/1 -7/39 0/1 1/1 -5/28 1/2 1/1 -3/17 0/1 1/0 -13/74 -1/4 0/1 -10/57 0/1 1/4 -7/40 1/2 -4/23 2/1 1/0 -5/29 1/0 -1/6 -1/1 0/1 -4/25 -1/2 -3/19 -1/6 0/1 -2/13 0/1 1/4 -5/33 0/1 1/2 -3/20 1/3 1/2 -1/7 1/0 -2/15 -1/2 0/1 -3/23 -1/6 0/1 -1/8 0/1 1/2 -2/17 1/0 -3/26 1/1 1/0 -4/35 -1/1 1/0 -1/9 0/1 1/0 -1/10 0/1 0/1 0/1 1/0 1/9 -1/1 1/0 2/17 -1/2 0/1 1/8 0/1 1/7 0/1 1/0 2/13 1/0 1/6 -1/2 0/1 2/11 0/1 1/2 5/27 0/1 1/3 3/16 1/2 2/3 4/21 6/7 1/1 1/5 1/0 5/24 -8/7 -1/1 4/19 -1/1 -3/4 7/33 -2/3 -1/2 3/14 -1/2 -1/3 2/9 -1/4 0/1 5/22 0/1 8/35 0/1 1/16 3/13 0/1 1/6 4/17 1/2 1/4 0/1 1/1 4/15 -2/1 1/0 11/41 -6/5 -1/1 7/26 -1/2 3/11 0/1 1/0 5/18 -1/1 -1/2 2/7 0/1 7/24 1/3 1/2 19/65 1/2 12/41 0/1 1/2 17/58 1/2 5/17 0/1 1/3 8/27 1/2 2/3 19/64 6/7 1/1 11/37 1/0 3/10 0/1 1/2 4/13 1/2 3/5 5/16 3/4 6/19 10/11 1/1 1/3 1/1 1/0 5/14 0/1 1/0 9/25 0/1 1/2 13/36 0/1 1/1 4/11 1/0 19/52 -1/1 1/0 15/41 -1/1 -2/3 11/30 -1/2 0/1 7/19 0/1 1/0 3/8 0/1 1/2 11/29 1/2 2/3 19/50 3/4 27/71 3/4 1/1 8/21 0/1 1/1 21/55 2/3 1/1 34/89 1/2 13/34 2/3 3/4 5/13 1/1 7/18 1/1 4/3 16/41 3/2 25/64 3/2 8/5 9/23 1/1 2/1 2/5 2/1 1/0 7/17 1/0 5/12 7/1 1/0 8/19 1/0 11/26 -13/1 1/0 3/7 -3/1 1/0 13/30 -5/2 -2/1 10/23 -3/2 27/62 -5/4 -6/5 17/39 -10/9 -1/1 7/16 -1/1 -1/2 4/9 0/1 1/0 5/11 2/1 1/0 6/13 -2/1 1/0 7/15 0/1 1/1 8/17 1/1 2/1 1/2 1/0 7/13 0/1 1/0 6/11 -5/1 1/0 17/31 -7/2 28/51 -28/9 -3/1 11/20 -3/1 -5/2 5/9 -2/1 1/0 19/34 -2/1 -3/2 33/59 -2/1 -7/4 14/25 -3/2 37/66 -4/3 -1/1 23/41 -3/2 -1/1 9/16 -1/1 0/1 13/23 -1/1 4/7 0/1 1/0 11/19 1/0 7/12 4/1 1/0 10/17 1/0 13/22 -12/1 1/0 3/5 -4/1 1/0 11/18 -16/5 -3/1 19/31 -3/1 -17/6 27/44 -11/4 -19/7 35/57 -27/10 -8/3 8/13 -5/2 37/60 -13/6 -2/1 29/47 -3/1 -2/1 21/34 -5/2 -2/1 13/21 -9/4 -2/1 5/8 -2/1 1/0 17/27 -5/1 1/0 46/73 -9/2 -4/1 75/119 -4/1 -11/3 29/46 -7/2 41/65 -28/9 -3/1 12/19 -3/1 -5/2 31/49 -5/2 -2/1 50/79 -5/2 19/30 -3/1 -2/1 7/11 -2/1 16/25 -2/1 -3/2 9/14 -1/1 1/0 20/31 1/0 31/48 -3/1 -2/1 11/17 -2/1 1/0 2/3 -2/1 -1/1 11/16 -1/1 20/29 -1/1 -2/3 9/13 -1/1 0/1 16/23 1/0 7/10 -1/1 1/0 12/17 -1/1 -2/3 29/41 -2/3 -1/2 17/24 -1/2 0/1 22/31 0/1 1/0 5/7 1/0 23/32 -2/1 1/0 18/25 -2/1 -3/2 31/43 0/1 1/0 44/61 1/0 13/18 -1/1 1/0 8/11 -2/1 1/0 27/37 -3/1 -5/2 46/63 -5/2 -2/1 19/26 -2/1 11/15 -2/1 1/0 14/19 1/0 3/4 -2/1 -3/2 10/13 -3/2 -1/1 17/22 -3/2 41/53 -11/8 -4/3 24/31 -3/2 -4/3 7/9 -4/3 -5/4 18/23 -5/4 -6/5 47/60 -6/5 -7/6 29/37 -7/6 11/14 -4/3 -1/1 4/5 -1/1 13/16 -1/1 -4/5 48/59 -4/5 -3/4 35/43 -3/4 22/27 -1/1 -2/3 53/65 -1/1 -3/4 31/38 -3/4 9/11 -2/3 -1/2 23/28 -1/2 60/73 -1/3 0/1 37/45 -1/2 0/1 14/17 -1/1 -1/2 19/23 -1/2 24/29 -1/2 0/1 5/6 0/1 1/0 6/7 -2/1 1/0 13/15 -2/1 -3/2 7/8 -3/2 1/1 -1/1 0/1 10/9 -5/6 -4/5 9/8 -1/1 -3/4 8/7 -3/4 15/13 -3/4 -2/3 22/19 -7/10 -2/3 7/6 -2/3 -1/2 20/17 -5/9 -1/2 13/11 -1/2 6/5 -1/2 0/1 23/19 1/0 17/14 -1/1 1/0 11/9 -2/1 1/0 5/4 -1/1 19/15 -7/8 -6/7 52/41 -5/6 33/26 -1/1 -6/7 47/37 -5/6 14/11 -1/1 -4/5 9/7 -5/6 -4/5 31/24 -4/5 -3/4 22/17 -3/4 35/27 -4/5 -3/4 13/10 -1/1 -3/4 30/23 -4/5 -3/4 17/13 -3/4 4/3 -3/4 -2/3 23/17 -2/3 -5/8 19/14 -1/2 15/11 -2/3 -1/2 26/19 -2/3 63/46 -2/3 -5/8 37/27 -5/8 -3/5 11/8 -2/3 -1/2 29/21 -3/5 -1/2 47/34 -1/2 65/47 -1/2 -1/3 18/13 -1/1 -1/2 43/31 -1/2 0/1 25/18 -3/4 -2/3 57/41 -1/1 -1/2 32/23 -2/3 -1/2 7/5 -1/2 38/27 -1/4 0/1 69/49 -1/2 -1/3 31/22 -1/2 0/1 55/39 -1/4 0/1 79/56 0/1 24/17 0/1 1/0 41/29 -2/1 1/0 17/12 -2/1 -1/1 27/19 -3/4 -2/3 37/26 -2/3 47/33 -2/3 -1/2 10/7 -1/1 -1/2 33/23 -1/1 -4/5 23/16 -1/2 13/9 -1/1 0/1 16/11 -1/1 19/13 -1/1 -4/5 3/2 -1/1 -2/3 20/13 -1/2 17/11 -2/3 -1/2 31/20 -1/2 45/29 -1/2 0/1 14/9 -1/1 -1/2 11/7 -2/3 30/19 -2/3 -3/5 79/50 -5/8 49/31 -2/3 -5/8 19/12 -5/8 -3/5 46/29 -7/12 73/46 -4/7 -9/16 100/63 -4/7 -1/2 27/17 -5/9 -1/2 8/5 -2/3 -1/2 29/18 -7/10 -2/3 50/31 -2/3 71/44 -2/3 -25/38 21/13 -2/3 -9/14 55/34 -2/3 -5/8 89/55 -2/3 34/21 -2/3 -5/8 81/50 -5/8 -3/5 47/29 -2/3 -3/5 13/8 -5/8 57/35 -8/13 -27/44 101/62 -8/13 -11/18 44/27 -19/31 -11/18 31/19 -17/28 -3/5 49/30 -50/83 -3/5 67/41 -3/5 18/11 -3/5 -16/27 23/14 -3/5 -7/12 5/3 -4/7 -1/2 17/10 -1/2 29/17 -1/2 -12/25 12/7 -1/2 -4/9 31/18 -2/5 -1/3 81/47 -2/5 -3/8 50/29 -1/3 0/1 19/11 -1/2 45/26 -1/2 -5/11 26/15 -1/2 -2/5 7/4 -1/2 0/1 16/9 -1/1 0/1 57/32 -5/6 -4/5 41/23 -1/1 -3/4 25/14 -3/4 59/33 -7/10 -2/3 93/52 -3/4 -5/7 34/19 -3/4 -2/3 43/24 -7/10 -2/3 52/29 -2/3 9/5 -2/3 -1/2 11/6 -5/9 -1/2 35/19 -1/2 59/32 -1/2 -15/31 24/13 -1/2 -5/11 13/7 -1/2 0/1 15/8 -1/1 -1/2 17/9 -2/3 -1/2 2/1 -1/2 13/6 -2/3 -1/2 37/17 -1/2 61/28 -1/2 -14/29 24/11 -1/2 -6/13 11/5 -1/2 -2/5 20/9 -2/5 -1/3 29/13 -1/4 38/17 -1/4 0/1 47/21 -1/6 0/1 56/25 0/1 9/4 -1/2 0/1 25/11 0/1 16/7 -1/1 1/0 55/24 -12/11 -1/1 94/41 -1/1 39/17 -1/1 -10/11 101/44 -1/1 -7/8 62/27 -6/7 -5/6 23/10 -3/4 53/23 -5/7 -2/3 83/36 -15/22 -2/3 113/49 -2/3 30/13 -2/3 -5/8 7/3 -3/5 -1/2 19/8 -1/2 31/13 -1/2 -17/35 12/5 -1/2 -7/15 29/12 -1/2 -4/9 46/19 -1/2 -2/5 17/7 -1/2 56/23 -5/11 -4/9 39/16 -1/2 -4/9 61/25 -4/9 -3/7 22/9 -1/2 -3/7 5/2 -1/2 -2/5 28/11 -3/8 23/9 -2/5 -1/3 41/16 -3/8 59/23 -3/8 -4/11 136/53 -4/11 77/30 -4/11 -5/14 18/7 -4/11 -1/3 31/12 -3/8 -4/11 13/5 -1/3 34/13 -3/10 -2/7 89/34 -1/4 55/21 -1/3 -2/7 21/8 -1/3 0/1 92/35 -5/16 -4/13 71/27 -1/3 -3/10 192/73 -1/3 -2/7 121/46 -1/3 -4/13 50/19 -3/10 79/30 -3/10 -2/7 108/41 -7/24 -2/7 137/52 -2/7 29/11 -2/7 -1/4 8/3 -1/4 0/1 27/10 -1/2 -1/3 73/27 -1/4 0/1 46/17 0/1 19/7 -1/2 0/1 49/18 -1/4 0/1 79/29 0/1 109/40 0/1 1/4 30/11 0/1 1/0 41/15 -2/1 -1/1 93/34 -3/4 -2/3 52/19 -1/1 -1/2 11/4 -1/2 47/17 -1/2 -1/3 83/30 -2/5 -1/3 119/43 -1/3 155/56 -1/3 -2/7 36/13 -1/3 0/1 25/9 -1/4 0/1 39/14 -1/2 0/1 53/19 0/1 120/43 0/1 1/0 67/24 -1/1 1/0 14/5 -1/2 0/1 17/6 -1/1 -1/2 20/7 -1/2 23/8 -1/2 -3/7 3/1 -1/2 -1/3 22/7 -12/35 -1/3 41/13 -1/3 19/6 -1/3 -10/31 16/5 -3/10 29/9 -2/7 -5/18 42/13 -2/7 -1/4 55/17 -2/7 68/21 -2/7 -5/18 13/4 -3/11 -1/4 23/7 -1/4 33/10 -1/4 -2/9 10/3 -1/4 0/1 37/11 -1/2 27/8 -2/7 -1/4 44/13 -1/4 105/31 -1/4 -2/9 166/49 -2/9 -3/14 61/18 -2/9 -1/5 17/5 -1/5 0/1 7/2 0/1 25/7 -1/1 0/1 118/33 -1/6 0/1 211/59 0/1 93/26 0/1 1/4 68/19 1/0 43/12 0/1 1/0 190/53 0/1 147/41 0/1 1/2 104/29 0/1 1/1 61/17 1/0 18/5 -1/1 1/0 47/13 -3/4 29/8 -3/5 -1/2 11/3 -1/2 0/1 48/13 -1/6 0/1 85/23 0/1 122/33 0/1 1/10 37/10 0/1 1/2 26/7 1/0 67/18 -5/4 -1/1 108/29 -16/15 -1/1 41/11 -1/1 -6/7 56/15 -1/1 -3/4 127/34 -3/4 -2/3 71/19 -2/3 15/4 -2/3 -1/2 19/5 -1/2 42/11 -1/2 -2/5 107/28 -2/5 172/45 -2/5 -7/18 65/17 -2/5 -3/8 23/6 -2/5 -1/3 27/7 -1/4 0/1 4/1 -1/3 0/1 21/5 -1/4 0/1 17/4 -1/4 30/7 -1/6 -1/7 103/24 -1/8 0/1 73/17 0/1 43/10 -1/6 0/1 13/3 -1/8 0/1 22/5 0/1 31/7 0/1 1/12 9/2 0/1 1/2 23/5 0/1 1/0 37/8 0/1 51/11 0/1 1/2 14/3 1/1 1/0 33/7 -2/1 1/0 19/4 -3/2 -1/1 43/9 -14/13 -1/1 67/14 -1/1 91/19 -1/1 -30/31 24/5 -1/1 -8/9 29/6 -4/5 -3/4 5/1 -1/2 26/5 -5/14 -1/3 47/9 -16/47 -1/3 68/13 -1/3 21/4 -1/3 -6/19 37/7 -1/3 -3/10 16/3 -2/7 -1/4 43/8 -1/4 27/5 -1/5 0/1 11/2 -1/4 0/1 17/3 -1/8 0/1 23/4 0/1 29/5 0/1 1/8 6/1 0/1 1/0 19/3 -1/1 0/1 13/2 -1/2 20/3 -1/1 -1/2 47/7 -1/2 74/11 -1/2 -3/7 27/4 -1/2 -1/3 7/1 -1/2 0/1 15/2 -1/3 -1/4 23/3 -1/4 0/1 8/1 0/1 17/2 0/1 1/0 26/3 -1/1 -4/5 9/1 -1/1 -1/2 10/1 0/1 1/0 1/0 -1/2 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(1123,530,820,387) (-1/2,-8/17) -> (26/19,63/46) Hyperbolic Matrix(1931,906,714,335) (-8/17,-7/15) -> (73/27,46/17) Hyperbolic Matrix(1011,470,-3332,-1549) (-7/15,-13/28) -> (-17/56,-27/89) Hyperbolic Matrix(2109,976,806,373) (-13/28,-6/13) -> (34/13,89/34) Hyperbolic Matrix(497,228,-1794,-823) (-6/13,-11/24) -> (-5/18,-18/65) Hyperbolic Matrix(297,136,998,457) (-11/24,-5/11) -> (11/37,3/10) Hyperbolic Matrix(593,268,1082,489) (-5/11,-14/31) -> (6/11,17/31) Hyperbolic Matrix(293,132,-1374,-619) (-14/31,-9/20) -> (-3/14,-10/47) Hyperbolic Matrix(881,396,198,89) (-9/20,-13/29) -> (31/7,9/2) Hyperbolic Matrix(2543,1138,1562,699) (-13/29,-17/38) -> (13/8,57/35) Hyperbolic Matrix(1851,826,1172,523) (-17/38,-4/9) -> (30/19,79/50) Hyperbolic Matrix(675,298,-2512,-1109) (-4/9,-15/34) -> (-7/26,-18/67) Hyperbolic Matrix(1933,852,4440,1957) (-15/34,-26/59) -> (10/23,27/62) Hyperbolic Matrix(1353,596,-4538,-1999) (-26/59,-11/25) -> (-17/57,-14/47) Hyperbolic Matrix(387,170,1828,803) (-11/25,-18/41) -> (4/19,7/33) Hyperbolic Matrix(671,294,-1536,-673) (-18/41,-7/16) -> (-7/16,-24/55) Parabolic Matrix(4213,1838,1726,753) (-24/55,-17/39) -> (61/25,22/9) Hyperbolic Matrix(193,84,1050,457) (-17/39,-10/23) -> (2/11,5/27) Hyperbolic Matrix(1815,788,1048,455) (-10/23,-13/30) -> (45/26,26/15) Hyperbolic Matrix(759,328,1238,535) (-13/30,-3/7) -> (19/31,27/44) Hyperbolic Matrix(749,318,-2532,-1075) (-3/7,-14/33) -> (-8/27,-21/71) Hyperbolic Matrix(2435,1032,-8808,-3733) (-14/33,-25/59) -> (-13/47,-34/123) Hyperbolic Matrix(2063,874,2528,1071) (-25/59,-11/26) -> (31/38,9/11) Hyperbolic Matrix(653,276,750,317) (-11/26,-19/45) -> (13/15,7/8) Hyperbolic Matrix(185,78,-1212,-511) (-19/45,-8/19) -> (-2/13,-5/33) Hyperbolic Matrix(371,156,654,275) (-8/19,-13/31) -> (13/23,4/7) Hyperbolic Matrix(463,194,1210,507) (-13/31,-5/12) -> (13/34,5/13) Hyperbolic Matrix(279,116,-926,-385) (-5/12,-17/41) -> (-13/43,-3/10) Hyperbolic Matrix(1197,496,1016,421) (-17/41,-12/29) -> (20/17,13/11) Hyperbolic Matrix(1103,456,462,191) (-12/29,-7/17) -> (31/13,12/5) Hyperbolic Matrix(459,188,730,299) (-7/17,-9/22) -> (5/8,17/27) Hyperbolic Matrix(1097,448,1550,633) (-9/22,-11/27) -> (29/41,17/24) Hyperbolic Matrix(457,186,-1914,-779) (-11/27,-13/32) -> (-11/46,-5/21) Hyperbolic Matrix(637,258,1632,661) (-13/32,-2/5) -> (16/41,25/64) Hyperbolic Matrix(1607,634,2228,879) (-2/5,-13/33) -> (31/43,44/61) Hyperbolic Matrix(625,246,-2406,-947) (-13/33,-11/28) -> (-13/50,-7/27) Hyperbolic Matrix(265,104,1246,489) (-11/28,-9/23) -> (7/33,3/14) Hyperbolic Matrix(267,104,706,275) (-9/23,-7/18) -> (3/8,11/29) Hyperbolic Matrix(2031,788,616,239) (-7/18,-19/49) -> (23/7,33/10) Hyperbolic Matrix(351,136,-2026,-785) (-19/49,-12/31) -> (-4/23,-5/29) Hyperbolic Matrix(1055,408,618,239) (-12/31,-5/13) -> (29/17,12/7) Hyperbolic Matrix(1049,402,-3588,-1375) (-5/13,-18/47) -> (-12/41,-19/65) Hyperbolic Matrix(439,168,1398,535) (-18/47,-13/34) -> (5/16,6/19) Hyperbolic Matrix(1921,734,6556,2505) (-13/34,-34/89) -> (12/41,17/58) Hyperbolic Matrix(1571,600,-7512,-2869) (-34/89,-21/55) -> (-9/43,-14/67) Hyperbolic Matrix(173,66,-1308,-499) (-21/55,-8/21) -> (-2/15,-3/23) Hyperbolic Matrix(611,232,956,363) (-8/21,-11/29) -> (7/11,16/25) Hyperbolic Matrix(607,230,958,363) (-11/29,-3/8) -> (19/30,7/11) Hyperbolic Matrix(257,96,174,65) (-3/8,-13/35) -> (19/13,3/2) Hyperbolic Matrix(6525,2422,2492,925) (-13/35,-23/62) -> (89/34,55/21) Hyperbolic Matrix(3521,1306,1286,477) (-23/62,-10/27) -> (52/19,11/4) Hyperbolic Matrix(941,348,-3426,-1267) (-10/27,-17/46) -> (-11/40,-14/51) Hyperbolic Matrix(1543,570,1968,727) (-17/46,-7/19) -> (29/37,11/14) Hyperbolic Matrix(1197,440,1450,533) (-7/19,-18/49) -> (14/17,19/23) Hyperbolic Matrix(425,156,-2046,-751) (-18/49,-11/30) -> (-5/24,-6/29) Hyperbolic Matrix(1447,530,172,63) (-11/30,-26/71) -> (8/1,17/2) Hyperbolic Matrix(1961,718,254,93) (-26/71,-15/41) -> (23/3,8/1) Hyperbolic Matrix(5787,2116,3662,1339) (-15/41,-19/52) -> (79/50,49/31) Hyperbolic Matrix(597,218,-3404,-1243) (-19/52,-4/11) -> (-10/57,-7/40) Hyperbolic Matrix(171,62,-764,-277) (-4/11,-13/36) -> (-9/40,-2/9) Hyperbolic Matrix(255,92,-2198,-793) (-13/36,-22/61) -> (-2/17,-3/26) Hyperbolic Matrix(2363,852,4224,1523) (-22/61,-9/25) -> (33/59,14/25) Hyperbolic Matrix(1431,514,2024,727) (-9/25,-14/39) -> (12/17,29/41) Hyperbolic Matrix(419,150,-1176,-421) (-14/39,-5/14) -> (-5/14,-16/45) Parabolic Matrix(5195,1846,3014,1071) (-16/45,-11/31) -> (81/47,50/29) Hyperbolic Matrix(1085,384,1506,533) (-11/31,-6/17) -> (18/25,31/43) Hyperbolic Matrix(1413,496,584,205) (-6/17,-7/20) -> (29/12,46/19) Hyperbolic Matrix(333,116,910,317) (-7/20,-1/3) -> (15/41,11/30) Hyperbolic Matrix(869,276,318,101) (-1/3,-6/19) -> (30/11,41/15) Hyperbolic Matrix(787,248,238,75) (-6/19,-5/16) -> (33/10,10/3) Hyperbolic Matrix(1413,440,1018,317) (-5/16,-9/29) -> (43/31,25/18) Hyperbolic Matrix(311,96,-1014,-313) (-9/29,-4/13) -> (-4/13,-15/49) Parabolic Matrix(2099,642,546,167) (-15/49,-11/36) -> (23/6,27/7) Hyperbolic Matrix(1867,570,1320,403) (-11/36,-7/23) -> (41/29,17/12) Hyperbolic Matrix(3879,1178,2170,659) (-7/23,-17/56) -> (25/14,59/33) Hyperbolic Matrix(389,118,-3412,-1035) (-27/89,-10/33) -> (-4/35,-1/9) Hyperbolic Matrix(2787,844,776,235) (-10/33,-13/43) -> (61/17,18/5) Hyperbolic Matrix(771,230,-4388,-1309) (-3/10,-17/57) -> (-3/17,-13/74) Hyperbolic Matrix(3307,984,5226,1555) (-14/47,-11/37) -> (31/49,50/79) Hyperbolic Matrix(4377,1300,3074,913) (-11/37,-19/64) -> (37/26,47/33) Hyperbolic Matrix(155,46,1304,387) (-19/64,-8/27) -> (2/17,1/8) Hyperbolic Matrix(1765,522,612,181) (-21/71,-13/44) -> (23/8,3/1) Hyperbolic Matrix(1301,384,1074,317) (-13/44,-5/17) -> (23/19,17/14) Hyperbolic Matrix(1529,448,686,201) (-5/17,-12/41) -> (20/9,29/13) Hyperbolic Matrix(3507,1024,1298,379) (-19/65,-7/24) -> (27/10,73/27) Hyperbolic Matrix(1141,332,3124,909) (-7/24,-16/55) -> (4/11,19/52) Hyperbolic Matrix(2209,642,5784,1681) (-16/55,-9/31) -> (21/55,34/89) Hyperbolic Matrix(683,198,990,287) (-9/31,-2/7) -> (20/29,9/13) Hyperbolic Matrix(827,232,524,147) (-2/7,-7/25) -> (11/7,30/19) Hyperbolic Matrix(675,188,298,83) (-7/25,-5/18) -> (9/4,25/11) Hyperbolic Matrix(2167,600,372,103) (-18/65,-13/47) -> (29/5,6/1) Hyperbolic Matrix(20297,5610,6270,1733) (-34/123,-55/199) -> (55/17,68/21) Hyperbolic Matrix(30669,8476,8210,2269) (-55/199,-21/76) -> (127/34,71/19) Hyperbolic Matrix(6415,1772,1792,495) (-21/76,-8/29) -> (68/19,43/12) Hyperbolic Matrix(1191,328,374,103) (-8/29,-11/40) -> (19/6,16/5) Hyperbolic Matrix(2755,756,594,163) (-14/51,-3/11) -> (51/11,14/3) Hyperbolic Matrix(221,60,372,101) (-3/11,-7/26) -> (13/22,3/5) Hyperbolic Matrix(3247,872,3988,1071) (-18/67,-11/41) -> (35/43,22/27) Hyperbolic Matrix(2141,574,884,237) (-11/41,-4/15) -> (46/19,17/7) Hyperbolic Matrix(587,156,222,59) (-4/15,-5/19) -> (29/11,8/3) Hyperbolic Matrix(1025,268,218,57) (-5/19,-6/23) -> (14/3,33/7) Hyperbolic Matrix(2557,666,1386,361) (-6/23,-13/50) -> (59/32,24/13) Hyperbolic Matrix(1017,262,656,169) (-7/27,-1/4) -> (31/20,45/29) Hyperbolic Matrix(1139,274,212,51) (-1/4,-6/25) -> (16/3,43/8) Hyperbolic Matrix(2629,630,1206,289) (-6/25,-11/46) -> (61/28,24/11) Hyperbolic Matrix(1201,284,850,201) (-5/21,-4/17) -> (24/17,41/29) Hyperbolic Matrix(563,132,354,83) (-4/17,-3/13) -> (27/17,8/5) Hyperbolic Matrix(209,48,492,113) (-3/13,-5/22) -> (11/26,3/7) Hyperbolic Matrix(1813,410,1048,237) (-5/22,-7/31) -> (19/11,45/26) Hyperbolic Matrix(977,220,3344,753) (-7/31,-9/40) -> (7/24,19/65) Hyperbolic Matrix(899,196,344,75) (-2/9,-5/23) -> (13/5,34/13) Hyperbolic Matrix(895,194,346,75) (-5/23,-3/14) -> (31/12,13/5) Hyperbolic Matrix(2539,540,1782,379) (-10/47,-7/33) -> (47/33,10/7) Hyperbolic Matrix(549,116,478,101) (-7/33,-4/19) -> (8/7,15/13) Hyperbolic Matrix(2597,544,2048,429) (-4/19,-9/43) -> (19/15,52/41) Hyperbolic Matrix(14471,3022,5186,1083) (-14/67,-19/91) -> (53/19,120/43) Hyperbolic Matrix(11125,2322,2592,541) (-19/91,-5/24) -> (103/24,73/17) Hyperbolic Matrix(1975,408,1428,295) (-6/29,-1/5) -> (65/47,18/13) Hyperbolic Matrix(871,168,534,103) (-1/5,-4/21) -> (44/27,31/19) Hyperbolic Matrix(467,88,398,75) (-4/21,-3/16) -> (7/6,20/17) Hyperbolic Matrix(729,136,134,25) (-3/16,-5/27) -> (27/5,11/2) Hyperbolic Matrix(131,24,-726,-133) (-5/27,-2/11) -> (-2/11,-7/39) Parabolic Matrix(4475,802,2762,495) (-7/39,-5/28) -> (81/50,47/29) Hyperbolic Matrix(1247,222,264,47) (-5/28,-3/17) -> (33/7,19/4) Hyperbolic Matrix(11137,1956,3012,529) (-13/74,-10/57) -> (122/33,37/10) Hyperbolic Matrix(3009,526,1310,229) (-7/40,-4/23) -> (62/27,23/10) Hyperbolic Matrix(1239,212,976,167) (-5/29,-1/6) -> (33/26,47/37) Hyperbolic Matrix(775,126,1224,199) (-1/6,-4/25) -> (50/79,19/30) Hyperbolic Matrix(1027,164,1672,267) (-4/25,-3/19) -> (35/57,8/13) Hyperbolic Matrix(191,30,834,131) (-3/19,-2/13) -> (8/35,3/13) Hyperbolic Matrix(955,144,126,19) (-5/33,-3/20) -> (15/2,23/3) Hyperbolic Matrix(1143,170,316,47) (-3/20,-1/7) -> (47/13,29/8) Hyperbolic Matrix(625,84,186,25) (-1/7,-2/15) -> (10/3,37/11) Hyperbolic Matrix(1801,234,1116,145) (-3/23,-1/8) -> (71/44,21/13) Hyperbolic Matrix(493,60,1290,157) (-1/8,-2/17) -> (34/89,13/34) Hyperbolic Matrix(2869,330,426,49) (-3/26,-4/35) -> (74/11,27/4) Hyperbolic Matrix(843,88,182,19) (-1/9,-1/10) -> (37/8,51/11) Hyperbolic Matrix(479,46,656,63) (-1/10,0/1) -> (46/63,19/26) Hyperbolic Matrix(345,-32,248,-23) (0/1,1/9) -> (57/41,32/23) Hyperbolic Matrix(2035,-234,774,-89) (1/9,2/17) -> (92/35,71/27) Hyperbolic Matrix(475,-64,334,-45) (1/8,1/7) -> (27/19,37/26) Hyperbolic Matrix(609,-92,470,-71) (1/7,2/13) -> (22/17,35/27) Hyperbolic Matrix(233,-38,92,-15) (2/13,1/6) -> (5/2,28/11) Hyperbolic Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(819,-152,2096,-389) (5/27,3/16) -> (25/64,9/23) Hyperbolic Matrix(1453,-276,816,-155) (3/16,4/21) -> (16/9,57/32) Hyperbolic Matrix(497,-96,906,-175) (4/21,1/5) -> (17/31,28/51) Hyperbolic Matrix(359,-74,1208,-249) (1/5,5/24) -> (19/64,11/37) Hyperbolic Matrix(1429,-300,624,-131) (5/24,4/19) -> (16/7,55/24) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(221,-50,968,-219) (2/9,5/22) -> (5/22,8/35) Parabolic Matrix(701,-164,218,-51) (3/13,4/17) -> (16/5,29/9) Hyperbolic Matrix(131,-32,86,-21) (4/17,1/4) -> (3/2,20/13) Hyperbolic Matrix(513,-136,298,-79) (1/4,4/15) -> (12/7,31/18) Hyperbolic Matrix(425,-114,384,-103) (4/15,11/41) -> (1/1,10/9) Hyperbolic Matrix(2255,-606,3576,-961) (11/41,7/26) -> (29/46,41/65) Hyperbolic Matrix(807,-218,596,-161) (7/26,3/11) -> (23/17,19/14) Hyperbolic Matrix(211,-58,382,-105) (3/11,5/18) -> (11/20,5/9) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(4555,-1332,5598,-1637) (19/65,12/41) -> (48/59,35/43) Hyperbolic Matrix(4843,-1420,7684,-2253) (17/58,5/17) -> (75/119,29/46) Hyperbolic Matrix(291,-86,626,-185) (5/17,8/27) -> (6/13,7/15) Hyperbolic Matrix(6455,-1916,2456,-729) (8/27,19/64) -> (21/8,92/35) Hyperbolic Matrix(497,-152,206,-63) (3/10,4/13) -> (12/5,29/12) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(123,-40,40,-13) (6/19,1/3) -> (3/1,22/7) Hyperbolic Matrix(439,-156,318,-113) (1/3,5/14) -> (11/8,29/21) Hyperbolic Matrix(1669,-600,1032,-371) (5/14,9/25) -> (21/13,55/34) Hyperbolic Matrix(3691,-1332,2142,-773) (9/25,13/36) -> (31/18,81/47) Hyperbolic Matrix(911,-330,1626,-589) (13/36,4/11) -> (14/25,37/66) Hyperbolic Matrix(6169,-2256,2688,-983) (19/52,15/41) -> (39/17,101/44) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(2543,-966,3288,-1249) (11/29,19/50) -> (17/22,41/53) Hyperbolic Matrix(4851,-1844,5948,-2261) (19/50,27/71) -> (53/65,31/38) Hyperbolic Matrix(2035,-774,234,-89) (27/71,8/21) -> (26/3,9/1) Hyperbolic Matrix(587,-224,1250,-477) (8/21,21/55) -> (7/15,8/17) Hyperbolic Matrix(351,-136,622,-241) (5/13,7/18) -> (9/16,13/23) Hyperbolic Matrix(1631,-636,2526,-985) (7/18,16/41) -> (20/31,31/48) Hyperbolic Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(497,-206,152,-63) (7/17,5/12) -> (13/4,23/7) Hyperbolic Matrix(305,-128,722,-303) (5/12,8/19) -> (8/19,11/26) Parabolic Matrix(1885,-816,1356,-587) (3/7,13/30) -> (25/18,57/41) Hyperbolic Matrix(1091,-474,1770,-769) (13/30,10/23) -> (8/13,37/60) Hyperbolic Matrix(6169,-2688,2256,-983) (27/62,17/39) -> (41/15,93/34) Hyperbolic Matrix(1429,-624,300,-131) (17/39,7/16) -> (19/4,43/9) Hyperbolic Matrix(337,-148,526,-231) (7/16,4/9) -> (16/25,9/14) Hyperbolic Matrix(261,-118,334,-151) (4/9,5/11) -> (7/9,18/23) Hyperbolic Matrix(407,-186,186,-85) (5/11,6/13) -> (24/11,11/5) Hyperbolic Matrix(511,-244,622,-297) (8/17,1/2) -> (23/28,60/73) Hyperbolic Matrix(317,-170,386,-207) (1/2,7/13) -> (9/11,23/28) Hyperbolic Matrix(455,-246,246,-133) (7/13,6/11) -> (24/13,13/7) Hyperbolic Matrix(5577,-3064,1498,-823) (28/51,11/20) -> (67/18,108/29) Hyperbolic Matrix(2149,-1200,1524,-851) (5/9,19/34) -> (31/22,55/39) Hyperbolic Matrix(7897,-4416,4848,-2711) (19/34,33/59) -> (57/35,101/62) Hyperbolic Matrix(6505,-3648,2352,-1319) (37/66,23/41) -> (47/17,83/30) Hyperbolic Matrix(1453,-816,276,-155) (23/41,9/16) -> (21/4,37/7) Hyperbolic Matrix(205,-118,172,-99) (4/7,11/19) -> (13/11,6/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(341,-200,578,-339) (7/12,10/17) -> (10/17,13/22) Parabolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(7897,-4848,4416,-2711) (27/44,35/57) -> (59/33,93/52) Hyperbolic Matrix(7081,-4368,3072,-1895) (37/60,29/47) -> (53/23,83/36) Hyperbolic Matrix(3907,-2412,1602,-989) (29/47,21/34) -> (39/16,61/25) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(6063,-3820,4306,-2713) (17/27,46/73) -> (38/27,69/49) Hyperbolic Matrix(15867,-10000,4438,-2797) (46/73,75/119) -> (25/7,118/33) Hyperbolic Matrix(2583,-1630,496,-313) (41/65,12/19) -> (26/5,47/9) Hyperbolic Matrix(1389,-878,1688,-1067) (12/19,31/49) -> (37/45,14/17) Hyperbolic Matrix(1019,-656,1412,-909) (9/14,20/31) -> (44/61,13/18) Hyperbolic Matrix(3511,-2268,918,-593) (31/48,11/17) -> (65/17,23/6) Hyperbolic Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(353,-242,512,-351) (2/3,11/16) -> (11/16,20/29) Parabolic Matrix(893,-620,350,-243) (9/13,16/23) -> (28/11,23/9) Hyperbolic Matrix(287,-200,254,-177) (16/23,7/10) -> (9/8,8/7) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(2149,-1524,1200,-851) (17/24,22/31) -> (34/19,43/24) Hyperbolic Matrix(757,-538,916,-651) (22/31,5/7) -> (19/23,24/29) Hyperbolic Matrix(1257,-902,1604,-1151) (5/7,23/32) -> (47/60,29/37) Hyperbolic Matrix(345,-248,32,-23) (23/32,18/25) -> (10/1,1/0) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(999,-728,188,-137) (8/11,27/37) -> (37/7,16/3) Hyperbolic Matrix(5401,-3942,3402,-2483) (27/37,46/63) -> (100/63,27/17) Hyperbolic Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(623,-458,404,-297) (11/15,14/19) -> (20/13,17/11) Hyperbolic Matrix(807,-596,218,-161) (14/19,3/4) -> (37/10,26/7) Hyperbolic Matrix(153,-116,62,-47) (3/4,10/13) -> (22/9,5/2) Hyperbolic Matrix(609,-470,92,-71) (10/13,17/22) -> (13/2,20/3) Hyperbolic Matrix(3471,-2686,1552,-1201) (41/53,24/31) -> (38/17,47/21) Hyperbolic Matrix(1277,-990,396,-307) (24/31,7/9) -> (29/9,42/13) Hyperbolic Matrix(8297,-6498,3150,-2467) (18/23,47/60) -> (79/30,108/41) Hyperbolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(6255,-5086,1846,-1501) (13/16,48/59) -> (166/49,61/18) Hyperbolic Matrix(14397,-11738,5474,-4463) (22/27,53/65) -> (71/27,192/73) Hyperbolic Matrix(15411,-12668,4298,-3533) (60/73,37/45) -> (147/41,104/29) Hyperbolic Matrix(2717,-2252,1712,-1419) (24/29,5/6) -> (73/46,100/63) Hyperbolic Matrix(205,-172,118,-99) (5/6,6/7) -> (26/15,7/4) Hyperbolic Matrix(435,-376,376,-325) (6/7,13/15) -> (15/13,22/19) Hyperbolic Matrix(287,-254,200,-177) (7/8,1/1) -> (33/23,23/16) Hyperbolic Matrix(715,-796,256,-285) (10/9,9/8) -> (67/24,14/5) Hyperbolic Matrix(2251,-2608,826,-957) (22/19,7/6) -> (109/40,30/11) Hyperbolic Matrix(757,-916,538,-651) (6/5,23/19) -> (7/5,38/27) Hyperbolic Matrix(317,-386,170,-207) (17/14,11/9) -> (13/7,15/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(6261,-7942,2380,-3019) (52/41,33/26) -> (121/46,50/19) Hyperbolic Matrix(4519,-5742,1260,-1601) (47/37,14/11) -> (104/29,61/17) Hyperbolic Matrix(261,-334,118,-151) (14/11,9/7) -> (11/5,20/9) Hyperbolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(2543,-3288,966,-1249) (31/24,22/17) -> (50/19,79/30) Hyperbolic Matrix(799,-1036,118,-153) (35/27,13/10) -> (27/4,7/1) Hyperbolic Matrix(2203,-2872,1360,-1773) (13/10,30/23) -> (34/21,81/50) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(849,-1148,230,-311) (4/3,23/17) -> (11/3,48/13) Hyperbolic Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(4011,-5494,2848,-3901) (63/46,37/27) -> (69/49,31/22) Hyperbolic Matrix(1867,-2560,1048,-1437) (37/27,11/8) -> (57/32,41/23) Hyperbolic Matrix(3197,-4418,2312,-3195) (29/21,47/34) -> (47/34,65/47) Parabolic Matrix(1019,-1412,656,-909) (18/13,43/31) -> (45/29,14/9) Hyperbolic Matrix(857,-1194,384,-535) (32/23,7/5) -> (29/13,38/17) Hyperbolic Matrix(6967,-9826,2644,-3729) (55/39,79/56) -> (137/52,29/11) Hyperbolic Matrix(8377,-11820,3180,-4487) (79/56,24/17) -> (108/41,137/52) Hyperbolic Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(353,-512,242,-351) (13/9,16/11) -> (16/11,19/13) Parabolic Matrix(1631,-2526,636,-985) (17/11,31/20) -> (41/16,59/23) Hyperbolic Matrix(337,-526,148,-231) (14/9,11/7) -> (25/11,16/7) Hyperbolic Matrix(669,-1058,356,-563) (49/31,19/12) -> (15/8,17/9) Hyperbolic Matrix(2255,-3576,606,-961) (19/12,46/29) -> (26/7,67/18) Hyperbolic Matrix(5825,-9242,1628,-2583) (46/29,73/46) -> (93/26,68/19) Hyperbolic Matrix(3101,-5000,1922,-3099) (29/18,50/31) -> (50/31,71/44) Parabolic Matrix(3239,-5240,866,-1401) (55/34,89/55) -> (71/19,15/4) Hyperbolic Matrix(3465,-5608,1072,-1735) (89/55,34/21) -> (42/13,55/17) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(6901,-11244,1848,-3011) (101/62,44/27) -> (56/15,127/34) Hyperbolic Matrix(2009,-3282,636,-1039) (49/30,67/41) -> (41/13,19/6) Hyperbolic Matrix(1353,-2212,430,-703) (67/41,18/11) -> (22/7,41/13) Hyperbolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(341,-578,200,-339) (5/3,17/10) -> (17/10,29/17) Parabolic Matrix(1109,-1914,456,-787) (50/29,19/11) -> (17/7,56/23) Hyperbolic Matrix(351,-622,136,-241) (7/4,16/9) -> (18/7,31/12) Hyperbolic Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(7513,-13438,2692,-4815) (93/52,34/19) -> (120/43,67/24) Hyperbolic Matrix(1605,-2876,716,-1283) (43/24,52/29) -> (56/25,9/4) Hyperbolic Matrix(1643,-2948,734,-1317) (52/29,9/5) -> (47/21,56/25) Hyperbolic Matrix(211,-382,58,-105) (9/5,11/6) -> (29/8,11/3) Hyperbolic Matrix(1331,-2450,722,-1329) (11/6,35/19) -> (35/19,59/32) Parabolic Matrix(501,-958,148,-283) (17/9,2/1) -> (44/13,105/31) Hyperbolic Matrix(291,-626,86,-185) (2/1,13/6) -> (27/8,44/13) Hyperbolic Matrix(1259,-2738,578,-1257) (13/6,37/17) -> (37/17,61/28) Parabolic Matrix(2493,-5714,476,-1091) (55/24,94/41) -> (68/13,21/4) Hyperbolic Matrix(3083,-7070,590,-1353) (94/41,39/17) -> (47/9,68/13) Hyperbolic Matrix(3343,-7674,1032,-2369) (101/44,62/27) -> (68/21,13/4) Hyperbolic Matrix(12153,-28022,3398,-7835) (83/36,113/49) -> (211/59,93/26) Hyperbolic Matrix(8525,-19664,2384,-5499) (113/49,30/13) -> (118/33,211/59) Hyperbolic Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(305,-722,128,-303) (7/3,19/8) -> (19/8,31/13) Parabolic Matrix(2059,-5014,802,-1953) (56/23,39/16) -> (77/30,18/7) Hyperbolic Matrix(819,-2096,152,-389) (23/9,41/16) -> (43/8,27/5) Hyperbolic Matrix(12161,-31202,3392,-8703) (59/23,136/53) -> (190/53,147/41) Hyperbolic Matrix(7979,-20478,2226,-5713) (136/53,77/30) -> (43/12,190/53) Hyperbolic Matrix(1417,-3712,418,-1095) (55/21,21/8) -> (61/18,17/5) Hyperbolic Matrix(12971,-34116,4686,-12325) (192/73,121/46) -> (155/56,36/13) Hyperbolic Matrix(4583,-12482,1682,-4581) (49/18,79/29) -> (79/29,109/40) Parabolic Matrix(2977,-8146,694,-1899) (93/34,52/19) -> (30/7,103/24) Hyperbolic Matrix(10235,-28322,3698,-10233) (83/30,119/43) -> (119/43,155/56) Parabolic Matrix(387,-1072,100,-277) (36/13,25/9) -> (27/7,4/1) Hyperbolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(359,-1208,74,-249) (37/11,27/8) -> (29/6,5/1) Hyperbolic Matrix(8517,-28850,2228,-7547) (105/31,166/49) -> (172/45,65/17) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(363,-1312,70,-253) (18/5,47/13) -> (5/1,26/5) Hyperbolic Matrix(3911,-14450,1058,-3909) (48/13,85/23) -> (85/23,122/33) Parabolic Matrix(2903,-10812,606,-2257) (108/29,41/11) -> (91/19,24/5) Hyperbolic Matrix(5993,-22898,1568,-5991) (42/11,107/28) -> (107/28,172/45) Parabolic Matrix(221,-968,50,-219) (13/3,22/5) -> (22/5,31/7) Parabolic Matrix(1877,-8978,392,-1875) (43/9,67/14) -> (67/14,91/19) Parabolic Matrix(241,-1162,28,-135) (24/5,29/6) -> (17/2,26/3) Hyperbolic Matrix(185,-1058,32,-183) (17/3,23/4) -> (23/4,29/5) Parabolic Matrix(659,-4418,98,-657) (20/3,47/7) -> (47/7,74/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(1123,530,820,387) -> Matrix(1,2,-2,-3) Matrix(1931,906,714,335) -> Matrix(1,0,-6,1) Matrix(1011,470,-3332,-1549) -> Matrix(5,-4,4,-3) Matrix(2109,976,806,373) -> Matrix(3,-2,-10,7) Matrix(497,228,-1794,-823) -> Matrix(7,-2,4,-1) Matrix(297,136,998,457) -> Matrix(1,0,-2,1) Matrix(593,268,1082,489) -> Matrix(1,-4,0,1) Matrix(293,132,-1374,-619) -> Matrix(1,0,0,1) Matrix(881,396,198,89) -> Matrix(1,0,4,1) Matrix(2543,1138,1562,699) -> Matrix(37,-8,-60,13) Matrix(1851,826,1172,523) -> Matrix(3,-2,-4,3) Matrix(675,298,-2512,-1109) -> Matrix(5,-2,-2,1) Matrix(1933,852,4440,1957) -> Matrix(3,-4,-2,3) Matrix(1353,596,-4538,-1999) -> Matrix(1,2,0,1) Matrix(387,170,1828,803) -> Matrix(3,-2,-4,3) Matrix(671,294,-1536,-673) -> Matrix(1,0,4,1) Matrix(4213,1838,1726,753) -> Matrix(17,-4,-38,9) Matrix(193,84,1050,457) -> Matrix(1,0,-2,1) Matrix(1815,788,1048,455) -> Matrix(9,-2,-22,5) Matrix(759,328,1238,535) -> Matrix(45,-14,-16,5) Matrix(749,318,-2532,-1075) -> Matrix(3,-2,2,-1) Matrix(2435,1032,-8808,-3733) -> Matrix(1,2,0,1) Matrix(2063,874,2528,1071) -> Matrix(7,-2,-10,3) Matrix(653,276,750,317) -> Matrix(1,-2,0,1) Matrix(185,78,-1212,-511) -> Matrix(1,0,0,1) Matrix(371,156,654,275) -> Matrix(1,0,-4,1) Matrix(463,194,1210,507) -> Matrix(11,-4,14,-5) Matrix(279,116,-926,-385) -> Matrix(19,-8,12,-5) Matrix(1197,496,1016,421) -> Matrix(5,-2,-12,5) Matrix(1103,456,462,191) -> Matrix(29,-14,-60,29) Matrix(459,188,730,299) -> Matrix(5,-2,-2,1) Matrix(1097,448,1550,633) -> Matrix(1,0,-4,1) Matrix(457,186,-1914,-779) -> Matrix(9,-4,-2,1) Matrix(637,258,1632,661) -> Matrix(7,-2,4,-1) Matrix(1607,634,2228,879) -> Matrix(1,0,-2,1) Matrix(625,246,-2406,-947) -> Matrix(1,0,-2,1) Matrix(265,104,1246,489) -> Matrix(7,-4,-12,7) Matrix(267,104,706,275) -> Matrix(1,0,0,1) Matrix(2031,788,616,239) -> Matrix(5,-2,-22,9) Matrix(351,136,-2026,-785) -> Matrix(5,-2,-2,1) Matrix(1055,408,618,239) -> Matrix(17,-8,-36,17) Matrix(1049,402,-3588,-1375) -> Matrix(17,-10,12,-7) Matrix(439,168,1398,535) -> Matrix(23,-14,28,-17) Matrix(1921,734,6556,2505) -> Matrix(3,-2,14,-9) Matrix(1571,600,-7512,-2869) -> Matrix(3,-2,8,-5) Matrix(173,66,-1308,-499) -> Matrix(3,-2,-4,3) Matrix(611,232,956,363) -> Matrix(13,-8,-8,5) Matrix(607,230,958,363) -> Matrix(11,-8,-4,3) Matrix(257,96,174,65) -> Matrix(5,-4,-6,5) Matrix(6525,2422,2492,925) -> Matrix(3,-2,-10,7) Matrix(3521,1306,1286,477) -> Matrix(3,-2,-4,3) Matrix(941,348,-3426,-1267) -> Matrix(13,-10,4,-3) Matrix(1543,570,1968,727) -> Matrix(5,-6,-4,5) Matrix(1197,440,1450,533) -> Matrix(3,-2,-4,3) Matrix(425,156,-2046,-751) -> Matrix(3,-2,2,-1) Matrix(1447,530,172,63) -> Matrix(3,-2,2,-1) Matrix(1961,718,254,93) -> Matrix(3,-2,-10,7) Matrix(5787,2116,3662,1339) -> Matrix(19,-12,-30,19) Matrix(597,218,-3404,-1243) -> Matrix(3,-2,8,-5) Matrix(171,62,-764,-277) -> Matrix(11,-8,-4,3) Matrix(255,92,-2198,-793) -> Matrix(5,-4,4,-3) Matrix(2363,852,4224,1523) -> Matrix(23,-18,-14,11) Matrix(1431,514,2024,727) -> Matrix(7,-6,-8,7) Matrix(419,150,-1176,-421) -> Matrix(9,-8,8,-7) Matrix(5195,1846,3014,1071) -> Matrix(3,-4,-8,11) Matrix(1085,384,1506,533) -> Matrix(1,-2,0,1) Matrix(1413,496,584,205) -> Matrix(5,-2,-12,5) Matrix(333,116,910,317) -> Matrix(3,-2,-4,3) Matrix(869,276,318,101) -> Matrix(1,-2,0,1) Matrix(787,248,238,75) -> Matrix(1,-2,-4,9) Matrix(1413,440,1018,317) -> Matrix(3,-2,-4,3) Matrix(311,96,-1014,-313) -> Matrix(9,-8,8,-7) Matrix(2099,642,546,167) -> Matrix(5,-6,-14,17) Matrix(1867,570,1320,403) -> Matrix(5,-6,-4,5) Matrix(3879,1178,2170,659) -> Matrix(13,-18,-18,25) Matrix(389,118,-3412,-1035) -> Matrix(3,-4,-2,3) Matrix(2787,844,776,235) -> Matrix(3,-4,-2,3) Matrix(771,230,-4388,-1309) -> Matrix(1,-2,-2,5) Matrix(3307,984,5226,1555) -> Matrix(5,-12,-2,5) Matrix(4377,1300,3074,913) -> Matrix(1,0,-2,1) Matrix(155,46,1304,387) -> Matrix(1,-2,-2,5) Matrix(1765,522,612,181) -> Matrix(1,-4,-2,9) Matrix(1301,384,1074,317) -> Matrix(1,-2,0,1) Matrix(1529,448,686,201) -> Matrix(1,0,-4,1) Matrix(3507,1024,1298,379) -> Matrix(1,-2,-2,5) Matrix(1141,332,3124,909) -> Matrix(1,-2,0,1) Matrix(2209,642,5784,1681) -> Matrix(1,-2,2,-3) Matrix(683,198,990,287) -> Matrix(1,0,-2,1) Matrix(827,232,524,147) -> Matrix(5,-8,-8,13) Matrix(675,188,298,83) -> Matrix(1,-2,-2,5) Matrix(2167,600,372,103) -> Matrix(1,-2,4,-7) Matrix(20297,5610,6270,1733) -> Matrix(1,0,-4,1) Matrix(30669,8476,8210,2269) -> Matrix(7,-16,-10,23) Matrix(6415,1772,1792,495) -> Matrix(1,-2,-2,5) Matrix(1191,328,374,103) -> Matrix(5,-14,-16,45) Matrix(2755,756,594,163) -> Matrix(1,-4,2,-7) Matrix(221,60,372,101) -> Matrix(1,-8,0,1) Matrix(3247,872,3988,1071) -> Matrix(3,4,-4,-5) Matrix(2141,574,884,237) -> Matrix(1,-2,-2,5) Matrix(587,156,222,59) -> Matrix(1,0,-4,1) Matrix(1025,268,218,57) -> Matrix(1,-4,0,1) Matrix(2557,666,1386,361) -> Matrix(1,-10,-2,21) Matrix(1017,262,656,169) -> Matrix(1,0,-2,1) Matrix(1139,274,212,51) -> Matrix(1,0,-4,1) Matrix(2629,630,1206,289) -> Matrix(1,-8,-2,17) Matrix(1201,284,850,201) -> Matrix(1,0,0,1) Matrix(563,132,354,83) -> Matrix(1,2,-2,-3) Matrix(209,48,492,113) -> Matrix(1,-6,0,1) Matrix(1813,410,1048,237) -> Matrix(1,2,-2,-3) Matrix(977,220,3344,753) -> Matrix(1,4,2,9) Matrix(899,196,344,75) -> Matrix(3,4,-10,-13) Matrix(895,194,346,75) -> Matrix(5,4,-14,-11) Matrix(2539,540,1782,379) -> Matrix(1,2,-2,-3) Matrix(549,116,478,101) -> Matrix(3,-2,-4,3) Matrix(2597,544,2048,429) -> Matrix(5,6,-6,-7) Matrix(14471,3022,5186,1083) -> Matrix(1,0,0,1) Matrix(11125,2322,2592,541) -> Matrix(1,0,-8,1) Matrix(1975,408,1428,295) -> Matrix(1,0,-2,1) Matrix(871,168,534,103) -> Matrix(17,14,-28,-23) Matrix(467,88,398,75) -> Matrix(5,2,-8,-3) Matrix(729,136,134,25) -> Matrix(1,0,-2,1) Matrix(131,24,-726,-133) -> Matrix(1,0,4,1) Matrix(4475,802,2762,495) -> Matrix(1,2,-2,-3) Matrix(1247,222,264,47) -> Matrix(1,-2,0,1) Matrix(11137,1956,3012,529) -> Matrix(1,0,6,1) Matrix(3009,526,1310,229) -> Matrix(5,-4,-6,5) Matrix(1239,212,976,167) -> Matrix(5,6,-6,-7) Matrix(775,126,1224,199) -> Matrix(1,-2,0,1) Matrix(1027,164,1672,267) -> Matrix(21,8,-8,-3) Matrix(191,30,834,131) -> Matrix(1,0,12,1) Matrix(955,144,126,19) -> Matrix(1,0,-6,1) Matrix(1143,170,316,47) -> Matrix(3,-2,-4,3) Matrix(625,84,186,25) -> Matrix(1,0,-2,1) Matrix(1801,234,1116,145) -> Matrix(21,2,-32,-3) Matrix(493,60,1290,157) -> Matrix(1,-2,2,-3) Matrix(2869,330,426,49) -> Matrix(1,-2,-2,5) Matrix(843,88,182,19) -> Matrix(1,0,2,1) Matrix(479,46,656,63) -> Matrix(5,-2,-2,1) Matrix(345,-32,248,-23) -> Matrix(1,2,-2,-3) Matrix(2035,-234,774,-89) -> Matrix(3,4,-10,-13) Matrix(475,-64,334,-45) -> Matrix(3,-2,-4,3) Matrix(609,-92,470,-71) -> Matrix(3,4,-4,-5) Matrix(233,-38,92,-15) -> Matrix(3,2,-8,-5) Matrix(367,-66,228,-41) -> Matrix(3,-2,-4,3) Matrix(819,-152,2096,-389) -> Matrix(7,-2,4,-1) Matrix(1453,-276,816,-155) -> Matrix(7,-6,-8,7) Matrix(497,-96,906,-175) -> Matrix(7,-10,-2,3) Matrix(359,-74,1208,-249) -> Matrix(1,2,0,1) Matrix(1429,-300,624,-131) -> Matrix(5,4,-4,-3) Matrix(355,-78,132,-29) -> Matrix(1,0,0,1) Matrix(221,-50,968,-219) -> Matrix(1,0,20,1) Matrix(701,-164,218,-51) -> Matrix(7,-2,-24,7) Matrix(131,-32,86,-21) -> Matrix(3,-2,-4,3) Matrix(513,-136,298,-79) -> Matrix(1,-2,-2,5) Matrix(425,-114,384,-103) -> Matrix(5,6,-6,-7) Matrix(2255,-606,3576,-961) -> Matrix(13,10,-4,-3) Matrix(807,-218,596,-161) -> Matrix(5,2,-8,-3) Matrix(211,-58,382,-105) -> Matrix(1,-2,0,1) Matrix(85,-24,294,-83) -> Matrix(1,0,4,1) Matrix(4555,-1332,5598,-1637) -> Matrix(5,-4,-6,5) Matrix(4843,-1420,7684,-2253) -> Matrix(1,-4,0,1) Matrix(291,-86,626,-185) -> Matrix(1,0,-2,1) Matrix(6455,-1916,2456,-729) -> Matrix(7,-6,-22,19) Matrix(497,-152,206,-63) -> Matrix(9,-4,-20,9) Matrix(701,-218,164,-51) -> Matrix(3,-2,-16,11) Matrix(123,-40,40,-13) -> Matrix(1,-2,-2,5) Matrix(439,-156,318,-113) -> Matrix(1,2,-2,-3) Matrix(1669,-600,1032,-371) -> Matrix(5,2,-8,-3) Matrix(3691,-1332,2142,-773) -> Matrix(1,-2,-2,5) Matrix(911,-330,1626,-589) -> Matrix(3,-4,-2,3) Matrix(6169,-2256,2688,-983) -> Matrix(7,8,-8,-9) Matrix(1501,-552,552,-203) -> Matrix(1,0,-2,1) Matrix(355,-132,78,-29) -> Matrix(1,0,0,1) Matrix(2543,-966,3288,-1249) -> Matrix(25,-18,-18,13) Matrix(4851,-1844,5948,-2261) -> Matrix(7,-6,-8,7) Matrix(2035,-774,234,-89) -> Matrix(5,-4,-6,5) Matrix(587,-224,1250,-477) -> Matrix(3,-2,2,-1) Matrix(351,-136,622,-241) -> Matrix(3,-4,-2,3) Matrix(1631,-636,2526,-985) -> Matrix(7,-10,-2,3) Matrix(233,-92,38,-15) -> Matrix(1,-2,0,1) Matrix(153,-62,116,-47) -> Matrix(3,-8,-4,11) Matrix(497,-206,152,-63) -> Matrix(1,-4,-4,17) Matrix(305,-128,722,-303) -> Matrix(1,-20,0,1) Matrix(1885,-816,1356,-587) -> Matrix(1,4,-2,-7) Matrix(1091,-474,1770,-769) -> Matrix(9,16,-4,-7) Matrix(6169,-2688,2256,-983) -> Matrix(7,8,-8,-9) Matrix(1429,-624,300,-131) -> Matrix(5,4,-4,-3) Matrix(337,-148,526,-231) -> Matrix(3,2,-2,-1) Matrix(261,-118,334,-151) -> Matrix(5,-6,-4,5) Matrix(407,-186,186,-85) -> Matrix(1,-4,-2,9) Matrix(511,-244,622,-297) -> Matrix(1,-2,-2,5) Matrix(317,-170,386,-207) -> Matrix(1,2,-2,-3) Matrix(455,-246,246,-133) -> Matrix(1,0,-2,1) Matrix(5577,-3064,1498,-823) -> Matrix(7,20,-6,-17) Matrix(2149,-1200,1524,-851) -> Matrix(1,2,-4,-7) Matrix(7897,-4416,4848,-2711) -> Matrix(5,2,-8,-3) Matrix(6505,-3648,2352,-1319) -> Matrix(1,2,-4,-7) Matrix(1453,-816,276,-155) -> Matrix(5,6,-16,-19) Matrix(205,-118,172,-99) -> Matrix(1,0,-2,1) Matrix(513,-298,136,-79) -> Matrix(1,-2,-2,5) Matrix(341,-200,578,-339) -> Matrix(1,-16,0,1) Matrix(571,-348,402,-245) -> Matrix(3,10,-4,-13) Matrix(2077,-1272,1272,-779) -> Matrix(35,102,-58,-169) Matrix(7897,-4848,4416,-2711) -> Matrix(1,2,0,1) Matrix(7081,-4368,3072,-1895) -> Matrix(3,4,-4,-5) Matrix(3907,-2412,1602,-989) -> Matrix(7,18,-16,-41) Matrix(1669,-1032,600,-371) -> Matrix(1,2,0,1) Matrix(367,-228,66,-41) -> Matrix(1,2,-4,-7) Matrix(6063,-3820,4306,-2713) -> Matrix(1,4,-2,-7) Matrix(15867,-10000,4438,-2797) -> Matrix(1,4,-4,-15) Matrix(2583,-1630,496,-313) -> Matrix(7,20,-20,-57) Matrix(1389,-878,1688,-1067) -> Matrix(1,2,0,1) Matrix(1019,-656,1412,-909) -> Matrix(1,0,0,1) Matrix(3511,-2268,918,-593) -> Matrix(3,8,-8,-21) Matrix(131,-86,32,-21) -> Matrix(1,2,-4,-7) Matrix(353,-242,512,-351) -> Matrix(3,4,-4,-5) Matrix(893,-620,350,-243) -> Matrix(3,2,-8,-5) Matrix(287,-200,254,-177) -> Matrix(3,4,-4,-5) Matrix(571,-402,348,-245) -> Matrix(7,10,-12,-17) Matrix(2149,-1524,1200,-851) -> Matrix(3,-2,-4,3) Matrix(757,-538,916,-651) -> Matrix(1,0,-2,1) Matrix(1257,-902,1604,-1151) -> Matrix(7,20,-6,-17) Matrix(345,-248,32,-23) -> Matrix(1,2,-2,-3) Matrix(439,-318,156,-113) -> Matrix(1,2,-2,-3) Matrix(999,-728,188,-137) -> Matrix(1,4,-4,-15) Matrix(5401,-3942,3402,-2483) -> Matrix(9,22,-16,-39) Matrix(1153,-844,250,-183) -> Matrix(1,2,0,1) Matrix(623,-458,404,-297) -> Matrix(1,4,-2,-7) Matrix(807,-596,218,-161) -> Matrix(1,2,0,1) Matrix(153,-116,62,-47) -> Matrix(5,8,-12,-19) Matrix(609,-470,92,-71) -> Matrix(3,4,-4,-5) Matrix(3471,-2686,1552,-1201) -> Matrix(3,4,-10,-13) Matrix(1277,-990,396,-307) -> Matrix(7,10,-26,-37) Matrix(8297,-6498,3150,-2467) -> Matrix(27,32,-92,-109) Matrix(121,-96,150,-119) -> Matrix(7,8,-8,-9) Matrix(6255,-5086,1846,-1501) -> Matrix(7,6,-34,-29) Matrix(14397,-11738,5474,-4463) -> Matrix(1,0,-2,1) Matrix(15411,-12668,4298,-3533) -> Matrix(1,0,4,1) Matrix(2717,-2252,1712,-1419) -> Matrix(9,4,-16,-7) Matrix(205,-172,118,-99) -> Matrix(1,0,-2,1) Matrix(435,-376,376,-325) -> Matrix(7,12,-10,-17) Matrix(287,-254,200,-177) -> Matrix(3,4,-4,-5) Matrix(715,-796,256,-285) -> Matrix(5,4,-4,-3) Matrix(2251,-2608,826,-957) -> Matrix(3,2,10,7) Matrix(757,-916,538,-651) -> Matrix(1,0,-2,1) Matrix(317,-386,170,-207) -> Matrix(1,2,-2,-3) Matrix(121,-150,96,-119) -> Matrix(7,8,-8,-9) Matrix(6261,-7942,2380,-3019) -> Matrix(3,2,-8,-5) Matrix(4519,-5742,1260,-1601) -> Matrix(5,4,6,5) Matrix(261,-334,118,-151) -> Matrix(7,6,-20,-17) Matrix(613,-790,142,-183) -> Matrix(5,4,-34,-27) Matrix(2543,-3288,966,-1249) -> Matrix(23,18,-78,-61) Matrix(799,-1036,118,-153) -> Matrix(5,4,-14,-11) Matrix(2203,-2872,1360,-1773) -> Matrix(17,14,-28,-23) Matrix(983,-1284,258,-337) -> Matrix(13,10,-30,-23) Matrix(849,-1148,230,-311) -> Matrix(3,2,-14,-9) Matrix(481,-654,114,-155) -> Matrix(3,2,-14,-9) Matrix(867,-1184,320,-437) -> Matrix(3,2,-8,-5) Matrix(4011,-5494,2848,-3901) -> Matrix(3,2,-14,-9) Matrix(1867,-2560,1048,-1437) -> Matrix(23,14,-28,-17) Matrix(3197,-4418,2312,-3195) -> Matrix(7,4,-16,-9) Matrix(1019,-1412,656,-909) -> Matrix(1,0,0,1) Matrix(857,-1194,384,-535) -> Matrix(3,2,-14,-9) Matrix(6967,-9826,2644,-3729) -> Matrix(9,2,-32,-7) Matrix(8377,-11820,3180,-4487) -> Matrix(7,-2,-24,7) Matrix(1575,-2258,422,-605) -> Matrix(1,2,-2,-3) Matrix(421,-606,66,-95) -> Matrix(1,0,0,1) Matrix(353,-512,242,-351) -> Matrix(3,4,-4,-5) Matrix(1631,-2526,636,-985) -> Matrix(17,10,-46,-27) Matrix(337,-526,148,-231) -> Matrix(3,2,-2,-1) Matrix(669,-1058,356,-563) -> Matrix(13,8,-18,-11) Matrix(2255,-3576,606,-961) -> Matrix(17,10,-12,-7) Matrix(5825,-9242,1628,-2583) -> Matrix(7,4,12,7) Matrix(3101,-5000,1922,-3099) -> Matrix(95,64,-144,-97) Matrix(3239,-5240,866,-1401) -> Matrix(13,8,-18,-11) Matrix(3465,-5608,1072,-1735) -> Matrix(13,8,-44,-27) Matrix(1091,-1770,474,-769) -> Matrix(25,16,-36,-23) Matrix(6901,-11244,1848,-3011) -> Matrix(75,46,-106,-65) Matrix(2009,-3282,636,-1039) -> Matrix(133,80,-404,-243) Matrix(1353,-2212,430,-703) -> Matrix(87,52,-256,-153) Matrix(143,-236,20,-33) -> Matrix(7,4,-16,-9) Matrix(341,-578,200,-339) -> Matrix(31,16,-64,-33) Matrix(1109,-1914,456,-787) -> Matrix(7,4,-16,-9) Matrix(351,-622,136,-241) -> Matrix(5,4,-14,-11) Matrix(911,-1626,330,-589) -> Matrix(5,4,-14,-11) Matrix(7513,-13438,2692,-4815) -> Matrix(3,2,4,3) Matrix(1605,-2876,716,-1283) -> Matrix(3,2,4,3) Matrix(1643,-2948,734,-1317) -> Matrix(3,2,-20,-13) Matrix(211,-382,58,-105) -> Matrix(3,2,-8,-5) Matrix(1331,-2450,722,-1329) -> Matrix(39,20,-80,-41) Matrix(501,-958,148,-283) -> Matrix(7,4,-30,-17) Matrix(291,-626,86,-185) -> Matrix(1,0,-2,1) Matrix(1259,-2738,578,-1257) -> Matrix(31,16,-64,-33) Matrix(2493,-5714,476,-1091) -> Matrix(17,18,-52,-55) Matrix(3083,-7070,590,-1353) -> Matrix(27,26,-80,-77) Matrix(3343,-7674,1032,-2369) -> Matrix(23,20,-84,-73) Matrix(12153,-28022,3398,-7835) -> Matrix(3,2,34,23) Matrix(8525,-19664,2384,-5499) -> Matrix(3,2,-26,-17) Matrix(147,-340,16,-37) -> Matrix(3,2,-8,-5) Matrix(305,-722,128,-303) -> Matrix(39,20,-80,-41) Matrix(2059,-5014,802,-1953) -> Matrix(53,24,-148,-67) Matrix(819,-2096,152,-389) -> Matrix(5,2,-28,-11) Matrix(12161,-31202,3392,-8703) -> Matrix(11,4,30,11) Matrix(7979,-20478,2226,-5713) -> Matrix(11,4,-14,-5) Matrix(1417,-3712,418,-1095) -> Matrix(7,2,-32,-9) Matrix(12971,-34116,4686,-12325) -> Matrix(7,2,-18,-5) Matrix(4583,-12482,1682,-4581) -> Matrix(1,0,8,1) Matrix(2977,-8146,694,-1899) -> Matrix(3,2,-20,-13) Matrix(10235,-28322,3698,-10233) -> Matrix(11,4,-36,-13) Matrix(387,-1072,100,-277) -> Matrix(1,0,0,1) Matrix(1839,-5126,428,-1193) -> Matrix(1,0,-4,1) Matrix(281,-800,98,-279) -> Matrix(7,4,-16,-9) Matrix(359,-1208,74,-249) -> Matrix(5,2,-8,-3) Matrix(8517,-28850,2228,-7547) -> Matrix(35,8,-92,-21) Matrix(85,-294,24,-83) -> Matrix(1,0,4,1) Matrix(363,-1312,70,-253) -> Matrix(5,4,-14,-11) Matrix(3911,-14450,1058,-3909) -> Matrix(1,0,16,1) Matrix(2903,-10812,606,-2257) -> Matrix(23,24,-24,-25) Matrix(5993,-22898,1568,-5991) -> Matrix(39,16,-100,-41) Matrix(221,-968,50,-219) -> Matrix(1,0,20,1) Matrix(1877,-8978,392,-1875) -> Matrix(43,44,-44,-45) Matrix(241,-1162,28,-135) -> Matrix(5,4,-4,-3) Matrix(185,-1058,32,-183) -> Matrix(1,0,16,1) Matrix(659,-4418,98,-657) -> Matrix(7,4,-16,-9) 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): 96 Degree of the the map X: 96 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): 324 Minimal number of generators: 55 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: 30 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/5 2/7 1/2 5/7 4/5 1/1 5/4 16/11 67/41 17/10 2/1 19/8 46/17 79/29 11/4 20/7 3/1 7/2 4/1 22/5 9/2 5/1 11/2 23/4 6/1 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/0 1/6 -1/2 0/1 1/5 1/0 3/14 -1/2 -1/3 2/9 -1/4 0/1 1/4 0/1 1/1 2/7 0/1 3/10 0/1 1/2 1/3 1/1 1/0 4/11 1/0 11/30 -1/2 0/1 7/19 0/1 1/0 3/8 0/1 1/2 2/5 2/1 1/0 3/7 -3/1 1/0 10/23 -3/2 7/16 -1/1 -1/2 4/9 0/1 1/0 1/2 1/0 5/9 -2/1 1/0 4/7 0/1 1/0 3/5 -4/1 1/0 11/18 -16/5 -3/1 19/31 -3/1 -17/6 8/13 -5/2 13/21 -9/4 -2/1 5/8 -2/1 1/0 7/11 -2/1 2/3 -2/1 -1/1 7/10 -1/1 1/0 12/17 -1/1 -2/3 5/7 1/0 13/18 -1/1 1/0 8/11 -2/1 1/0 3/4 -2/1 -3/2 7/9 -4/3 -5/4 4/5 -1/1 5/6 0/1 1/0 6/7 -2/1 1/0 7/8 -3/2 1/1 -1/1 0/1 6/5 -1/2 0/1 5/4 -1/1 4/3 -3/4 -2/3 15/11 -2/3 -1/2 26/19 -2/3 11/8 -2/3 -1/2 7/5 -1/2 17/12 -2/1 -1/1 27/19 -3/4 -2/3 37/26 -2/3 10/7 -1/1 -1/2 13/9 -1/1 0/1 16/11 -1/1 3/2 -1/1 -2/3 8/5 -2/3 -1/2 13/8 -5/8 31/19 -17/28 -3/5 49/30 -50/83 -3/5 67/41 -3/5 18/11 -3/5 -16/27 23/14 -3/5 -7/12 5/3 -4/7 -1/2 17/10 -1/2 12/7 -1/2 -4/9 7/4 -1/2 0/1 16/9 -1/1 0/1 25/14 -3/4 9/5 -2/3 -1/2 2/1 -1/2 9/4 -1/2 0/1 7/3 -3/5 -1/2 19/8 -1/2 12/5 -1/2 -7/15 5/2 -1/2 -2/5 13/5 -1/3 8/3 -1/4 0/1 27/10 -1/2 -1/3 46/17 0/1 19/7 -1/2 0/1 49/18 -1/4 0/1 79/29 0/1 30/11 0/1 1/0 11/4 -1/2 14/5 -1/2 0/1 17/6 -1/1 -1/2 20/7 -1/2 3/1 -1/2 -1/3 13/4 -3/11 -1/4 10/3 -1/4 0/1 7/2 0/1 11/3 -1/2 0/1 4/1 -1/3 0/1 13/3 -1/8 0/1 22/5 0/1 9/2 0/1 1/2 23/5 0/1 1/0 14/3 1/1 1/0 19/4 -3/2 -1/1 5/1 -1/2 11/2 -1/4 0/1 17/3 -1/8 0/1 23/4 0/1 6/1 0/1 1/0 7/1 -1/2 0/1 15/2 -1/3 -1/4 8/1 0/1 9/1 -1/1 -1/2 1/0 -1/2 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(94,-15,69,-11) (0/1,1/6) -> (4/3,15/11) Hyperbolic Matrix(113,-21,183,-34) (1/6,1/5) -> (8/13,13/21) Hyperbolic Matrix(155,-33,357,-76) (1/5,3/14) -> (3/7,10/23) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(88,-21,21,-5) (2/9,1/4) -> (4/1,13/3) Hyperbolic Matrix(42,-11,65,-17) (1/4,2/7) -> (7/11,2/3) Hyperbolic Matrix(105,-31,166,-49) (2/7,3/10) -> (5/8,7/11) Hyperbolic Matrix(82,-25,187,-57) (3/10,1/3) -> (7/16,4/9) Hyperbolic Matrix(158,-57,219,-79) (1/3,4/11) -> (5/7,13/18) Hyperbolic Matrix(276,-101,317,-116) (4/11,11/30) -> (6/7,7/8) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(59,-23,77,-30) (3/8,2/5) -> (3/4,7/9) Hyperbolic Matrix(95,-39,39,-16) (2/5,3/7) -> (12/5,5/2) Hyperbolic Matrix(565,-246,921,-401) (10/23,7/16) -> (19/31,8/13) Hyperbolic Matrix(19,-9,36,-17) (4/9,1/2) -> (1/2,5/9) Parabolic Matrix(87,-49,103,-58) (5/9,4/7) -> (5/6,6/7) Hyperbolic Matrix(119,-69,69,-40) (4/7,3/5) -> (12/7,7/4) Hyperbolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(160,-111,111,-77) (2/3,7/10) -> (10/7,13/9) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(126,-89,143,-101) (12/17,5/7) -> (7/8,1/1) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(94,-69,15,-11) (8/11,3/4) -> (6/1,7/1) Hyperbolic Matrix(61,-48,75,-59) (7/9,4/5) -> (4/5,5/6) Parabolic Matrix(87,-103,49,-58) (1/1,6/5) -> (7/4,16/9) Hyperbolic Matrix(97,-118,37,-45) (6/5,5/4) -> (13/5,8/3) Hyperbolic Matrix(59,-77,23,-30) (5/4,4/3) -> (5/2,13/5) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(809,-1109,569,-780) (26/19,11/8) -> (27/19,37/26) Hyperbolic Matrix(158,-219,57,-79) (11/8,7/5) -> (11/4,14/5) Hyperbolic Matrix(380,-537,213,-301) (7/5,17/12) -> (16/9,25/14) Hyperbolic Matrix(1024,-1459,379,-540) (37/26,10/7) -> (27/10,46/17) Hyperbolic Matrix(177,-256,121,-175) (13/9,16/11) -> (16/11,3/2) Parabolic Matrix(42,-65,11,-17) (3/2,8/5) -> (11/3,4/1) Hyperbolic Matrix(113,-183,21,-34) (8/5,13/8) -> (5/1,11/2) Hyperbolic Matrix(247,-402,51,-83) (13/8,31/19) -> (19/4,5/1) Hyperbolic Matrix(2748,-4489,1681,-2746) (49/30,67/41) -> (67/41,18/11) Parabolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(171,-289,100,-169) (5/3,17/10) -> (17/10,12/7) Parabolic Matrix(475,-849,174,-311) (25/14,9/5) -> (30/11,11/4) Hyperbolic Matrix(19,-36,9,-17) (9/5,2/1) -> (2/1,9/4) Parabolic Matrix(82,-187,25,-57) (9/4,7/3) -> (13/4,10/3) Hyperbolic Matrix(153,-361,64,-151) (7/3,19/8) -> (19/8,12/5) Parabolic Matrix(2292,-6241,841,-2290) (49/18,79/29) -> (79/29,30/11) Parabolic Matrix(141,-400,49,-139) (17/6,20/7) -> (20/7,3/1) Parabolic Matrix(90,-289,19,-61) (3/1,13/4) -> (14/3,19/4) Hyperbolic Matrix(43,-147,12,-41) (10/3,7/2) -> (7/2,11/3) Parabolic Matrix(111,-484,25,-109) (13/3,22/5) -> (22/5,9/2) Parabolic Matrix(48,-221,5,-23) (23/5,14/3) -> (9/1,1/0) Hyperbolic Matrix(93,-529,16,-91) (17/3,23/4) -> (23/4,6/1) Parabolic Matrix(25,-192,3,-23) (15/2,8/1) -> (8/1,9/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,2,1) Matrix(94,-15,69,-11) -> Matrix(1,2,-2,-3) Matrix(113,-21,183,-34) -> Matrix(5,-2,-2,1) Matrix(155,-33,357,-76) -> Matrix(3,2,-2,-1) Matrix(355,-78,132,-29) -> Matrix(1,0,0,1) Matrix(88,-21,21,-5) -> Matrix(1,0,-4,1) Matrix(42,-11,65,-17) -> Matrix(1,-2,0,1) Matrix(105,-31,166,-49) -> Matrix(5,-2,-2,1) Matrix(82,-25,187,-57) -> Matrix(1,0,-2,1) Matrix(158,-57,219,-79) -> Matrix(1,-2,0,1) Matrix(276,-101,317,-116) -> Matrix(3,2,-2,-1) Matrix(1501,-552,552,-203) -> Matrix(1,0,-2,1) Matrix(355,-132,78,-29) -> Matrix(1,0,0,1) Matrix(59,-23,77,-30) -> Matrix(3,-4,-2,3) Matrix(95,-39,39,-16) -> Matrix(1,-4,-2,9) Matrix(565,-246,921,-401) -> Matrix(11,14,-4,-5) Matrix(19,-9,36,-17) -> Matrix(1,-2,0,1) Matrix(87,-49,103,-58) -> Matrix(1,0,0,1) Matrix(119,-69,69,-40) -> Matrix(1,0,-2,1) Matrix(571,-348,402,-245) -> Matrix(3,10,-4,-13) Matrix(2077,-1272,1272,-779) -> Matrix(35,102,-58,-169) Matrix(367,-228,66,-41) -> Matrix(1,2,-4,-7) Matrix(160,-111,111,-77) -> Matrix(1,2,-2,-3) Matrix(571,-402,348,-245) -> Matrix(7,10,-12,-17) Matrix(126,-89,143,-101) -> Matrix(3,2,-2,-1) Matrix(439,-318,156,-113) -> Matrix(1,2,-2,-3) Matrix(94,-69,15,-11) -> Matrix(1,2,-2,-3) Matrix(61,-48,75,-59) -> Matrix(3,4,-4,-5) Matrix(87,-103,49,-58) -> Matrix(1,0,0,1) Matrix(97,-118,37,-45) -> Matrix(1,0,-2,1) Matrix(59,-77,23,-30) -> Matrix(5,4,-14,-11) Matrix(867,-1184,320,-437) -> Matrix(3,2,-8,-5) Matrix(809,-1109,569,-780) -> Matrix(13,8,-18,-11) Matrix(158,-219,57,-79) -> Matrix(3,2,-8,-5) Matrix(380,-537,213,-301) -> Matrix(1,2,-2,-3) Matrix(1024,-1459,379,-540) -> Matrix(3,2,-8,-5) Matrix(177,-256,121,-175) -> Matrix(1,2,-2,-3) Matrix(42,-65,11,-17) -> Matrix(3,2,-8,-5) Matrix(113,-183,21,-34) -> Matrix(3,2,-14,-9) Matrix(247,-402,51,-83) -> Matrix(13,8,-18,-11) Matrix(2748,-4489,1681,-2746) -> Matrix(329,198,-550,-331) Matrix(143,-236,20,-33) -> Matrix(7,4,-16,-9) Matrix(171,-289,100,-169) -> Matrix(15,8,-32,-17) Matrix(475,-849,174,-311) -> Matrix(3,2,-2,-1) Matrix(19,-36,9,-17) -> Matrix(3,2,-8,-5) Matrix(82,-187,25,-57) -> Matrix(1,0,-2,1) Matrix(153,-361,64,-151) -> Matrix(19,10,-40,-21) Matrix(2292,-6241,841,-2290) -> Matrix(1,0,4,1) Matrix(141,-400,49,-139) -> Matrix(3,2,-8,-5) Matrix(90,-289,19,-61) -> Matrix(7,2,-4,-1) Matrix(43,-147,12,-41) -> Matrix(1,0,2,1) Matrix(111,-484,25,-109) -> Matrix(1,0,10,1) Matrix(48,-221,5,-23) -> Matrix(1,0,-2,1) Matrix(93,-529,16,-91) -> Matrix(1,0,8,1) Matrix(25,-192,3,-23) -> 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 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): 16 ----------------------------------------------------------------------- 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 -1/1 0/1 2 1 1/1 (-1/1,0/1) 0 27 6/5 (-1/2,0/1) 0 27 5/4 -1/1 4 3 4/3 (-3/4,-2/3) 0 27 11/8 (-2/3,-1/2) 0 27 7/5 -1/2 2 9 17/12 (-2/1,-1/1) 0 27 10/7 (-1/1,-1/2) 0 27 16/11 -1/1 2 1 3/2 (-1/1,-2/3) 0 27 8/5 (-2/3,-1/2) 0 27 13/8 -5/8 2 9 31/19 (-17/28,-3/5) 0 27 67/41 -3/5 22 1 18/11 (-3/5,-16/27) 0 27 23/14 (-3/5,-7/12) 0 27 5/3 (-4/7,-1/2) 0 27 17/10 -1/2 8 1 7/4 (-1/2,0/1) 0 27 16/9 (-1/1,0/1) 0 27 25/14 -3/4 2 9 9/5 (-2/3,-1/2) 0 27 2/1 -1/2 2 9 9/4 (-1/2,0/1) 0 27 7/3 (-3/5,-1/2) 0 27 19/8 -1/2 10 1 5/2 (-1/2,-2/5) 0 27 13/5 -1/3 4 3 8/3 (-1/4,0/1) 0 27 19/7 (-1/2,0/1) 0 27 79/29 0/1 4 1 30/11 (0/1,1/0) 0 27 11/4 -1/2 2 9 14/5 (-1/2,0/1) 0 27 20/7 -1/2 2 1 3/1 (-1/2,-1/3) 0 27 13/4 (-3/11,-1/4) 0 27 10/3 (-1/4,0/1) 0 27 7/2 0/1 2 3 11/3 (-1/2,0/1) 0 27 4/1 (-1/3,0/1) 0 27 22/5 0/1 10 1 9/2 (0/1,1/2) 0 27 23/5 (0/1,1/0) 0 27 14/3 (1/1,1/0) 0 27 19/4 (-3/2,-1/1) 0 27 5/1 -1/2 2 9 11/2 (-1/4,0/1) 0 27 23/4 0/1 8 1 6/1 (0/1,1/0) 0 27 7/1 (-1/2,0/1) 0 27 15/2 (-1/3,-1/4) 0 27 8/1 0/1 2 3 9/1 (-1/1,-1/2) 0 27 1/0 (-1/2,0/1) 0 27 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(87,-103,49,-58) (1/1,6/5) -> (7/4,16/9) Hyperbolic Matrix(97,-118,37,-45) (6/5,5/4) -> (13/5,8/3) Hyperbolic Matrix(59,-77,23,-30) (5/4,4/3) -> (5/2,13/5) Hyperbolic Matrix(69,-94,11,-15) (4/3,11/8) -> (6/1,7/1) Glide Reflection Matrix(158,-219,57,-79) (11/8,7/5) -> (11/4,14/5) Hyperbolic Matrix(380,-537,213,-301) (7/5,17/12) -> (16/9,25/14) Hyperbolic Matrix(402,-571,245,-348) (17/12,10/7) -> (18/11,23/14) Glide Reflection Matrix(111,-160,77,-111) (10/7,16/11) -> (10/7,16/11) Reflection Matrix(65,-96,44,-65) (16/11,3/2) -> (16/11,3/2) Reflection Matrix(42,-65,11,-17) (3/2,8/5) -> (11/3,4/1) Hyperbolic Matrix(113,-183,21,-34) (8/5,13/8) -> (5/1,11/2) Hyperbolic Matrix(247,-402,51,-83) (13/8,31/19) -> (19/4,5/1) Hyperbolic Matrix(1272,-2077,779,-1272) (31/19,67/41) -> (31/19,67/41) Reflection Matrix(1475,-2412,902,-1475) (67/41,18/11) -> (67/41,18/11) Reflection Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(101,-170,60,-101) (5/3,17/10) -> (5/3,17/10) Reflection Matrix(69,-119,40,-69) (17/10,7/4) -> (17/10,7/4) Reflection Matrix(475,-849,174,-311) (25/14,9/5) -> (30/11,11/4) Hyperbolic Matrix(19,-36,9,-17) (9/5,2/1) -> (2/1,9/4) Parabolic Matrix(82,-187,25,-57) (9/4,7/3) -> (13/4,10/3) Hyperbolic Matrix(113,-266,48,-113) (7/3,19/8) -> (7/3,19/8) Reflection Matrix(39,-95,16,-39) (19/8,5/2) -> (19/8,5/2) Reflection Matrix(132,-355,29,-78) (8/3,19/7) -> (9/2,23/5) Glide Reflection Matrix(552,-1501,203,-552) (19/7,79/29) -> (19/7,79/29) Reflection Matrix(1739,-4740,638,-1739) (79/29,30/11) -> (79/29,30/11) Reflection Matrix(99,-280,35,-99) (14/5,20/7) -> (14/5,20/7) Reflection Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(90,-289,19,-61) (3/1,13/4) -> (14/3,19/4) Hyperbolic Matrix(43,-147,12,-41) (10/3,7/2) -> (7/2,11/3) Parabolic Matrix(21,-88,5,-21) (4/1,22/5) -> (4/1,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(48,-221,5,-23) (23/5,14/3) -> (9/1,1/0) Hyperbolic Matrix(45,-253,8,-45) (11/2,23/4) -> (11/2,23/4) Reflection Matrix(47,-276,8,-47) (23/4,6/1) -> (23/4,6/1) Reflection Matrix(25,-192,3,-23) (15/2,8/1) -> (8/1,9/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,4,1) (-1/1,1/0) -> (-1/2,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(87,-103,49,-58) -> Matrix(1,0,0,1) Matrix(97,-118,37,-45) -> Matrix(1,0,-2,1) 0/1 Matrix(59,-77,23,-30) -> Matrix(5,4,-14,-11) Matrix(69,-94,11,-15) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(158,-219,57,-79) -> Matrix(3,2,-8,-5) -1/2 Matrix(380,-537,213,-301) -> Matrix(1,2,-2,-3) -1/1 Matrix(402,-571,245,-348) -> Matrix(13,10,-22,-17) Matrix(111,-160,77,-111) -> Matrix(3,2,-4,-3) (10/7,16/11) -> (-1/1,-1/2) Matrix(65,-96,44,-65) -> Matrix(5,4,-6,-5) (16/11,3/2) -> (-1/1,-2/3) Matrix(42,-65,11,-17) -> Matrix(3,2,-8,-5) -1/2 Matrix(113,-183,21,-34) -> Matrix(3,2,-14,-9) Matrix(247,-402,51,-83) -> Matrix(13,8,-18,-11) -2/3 Matrix(1272,-2077,779,-1272) -> Matrix(169,102,-280,-169) (31/19,67/41) -> (-17/28,-3/5) Matrix(1475,-2412,902,-1475) -> Matrix(161,96,-270,-161) (67/41,18/11) -> (-3/5,-16/27) Matrix(143,-236,20,-33) -> Matrix(7,4,-16,-9) -1/2 Matrix(101,-170,60,-101) -> Matrix(15,8,-28,-15) (5/3,17/10) -> (-4/7,-1/2) Matrix(69,-119,40,-69) -> Matrix(-1,0,4,1) (17/10,7/4) -> (-1/2,0/1) Matrix(475,-849,174,-311) -> Matrix(3,2,-2,-1) -1/1 Matrix(19,-36,9,-17) -> Matrix(3,2,-8,-5) -1/2 Matrix(82,-187,25,-57) -> Matrix(1,0,-2,1) 0/1 Matrix(113,-266,48,-113) -> Matrix(11,6,-20,-11) (7/3,19/8) -> (-3/5,-1/2) Matrix(39,-95,16,-39) -> Matrix(9,4,-20,-9) (19/8,5/2) -> (-1/2,-2/5) Matrix(132,-355,29,-78) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(552,-1501,203,-552) -> Matrix(-1,0,4,1) (19/7,79/29) -> (-1/2,0/1) Matrix(1739,-4740,638,-1739) -> Matrix(1,0,0,-1) (79/29,30/11) -> (0/1,1/0) Matrix(99,-280,35,-99) -> Matrix(-1,0,4,1) (14/5,20/7) -> (-1/2,0/1) Matrix(41,-120,14,-41) -> Matrix(5,2,-12,-5) (20/7,3/1) -> (-1/2,-1/3) Matrix(90,-289,19,-61) -> Matrix(7,2,-4,-1) Matrix(43,-147,12,-41) -> Matrix(1,0,2,1) 0/1 Matrix(21,-88,5,-21) -> Matrix(-1,0,6,1) (4/1,22/5) -> (-1/3,0/1) Matrix(89,-396,20,-89) -> Matrix(1,0,4,-1) (22/5,9/2) -> (0/1,1/2) Matrix(48,-221,5,-23) -> Matrix(1,0,-2,1) 0/1 Matrix(45,-253,8,-45) -> Matrix(-1,0,8,1) (11/2,23/4) -> (-1/4,0/1) Matrix(47,-276,8,-47) -> Matrix(1,0,0,-1) (23/4,6/1) -> (0/1,1/0) Matrix(25,-192,3,-23) -> Matrix(1,0,2,1) 0/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.