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): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -15/2 -22/3 -20/3 -32/5 -6/1 -28/5 -16/3 -5/1 -24/5 -14/3 -32/7 -30/7 -4/1 -15/4 -26/7 -18/5 -24/7 -10/3 -36/11 -20/7 -25/9 -36/13 -30/11 -8/3 -34/13 -44/17 -100/39 -5/2 -12/5 -16/7 -20/9 -15/7 -2/1 -28/15 -20/11 -30/17 -12/7 -100/59 -5/3 -30/19 -20/13 -10/7 -4/3 -5/4 -20/17 -10/9 0/1 1/1 10/9 20/17 5/4 4/3 10/7 3/2 20/13 30/19 5/3 100/59 12/7 30/17 20/11 28/15 2/1 15/7 20/9 120/53 16/7 40/17 160/67 12/5 80/33 5/2 100/39 80/31 44/17 8/3 30/11 25/9 120/43 20/7 3/1 10/3 200/59 24/7 7/2 18/5 40/11 11/3 160/43 15/4 34/9 4/1 80/19 30/7 13/3 520/119 40/9 9/2 32/7 14/3 80/17 24/5 5/1 16/3 38/7 11/2 28/5 17/3 40/7 6/1 19/3 32/5 13/2 20/3 7/1 80/11 22/3 15/2 38/5 8/1 17/2 26/3 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/2 -19/2 0/1 1/1 -9/1 -1/1 0/1 -17/2 -2/1 -1/1 -8/1 -1/1 -23/3 -1/1 -2/3 -15/2 -3/4 -22/3 -1/1 -2/3 -7/1 -2/3 -3/5 -20/3 -1/2 -13/2 -1/3 0/1 -32/5 -1/2 -1/4 -19/3 -1/7 0/1 -25/4 1/0 -6/1 -1/1 0/1 -17/3 -1/1 -6/7 -28/5 -3/4 -11/2 -1/1 -2/3 -16/3 -3/4 -1/2 -21/4 -1/1 -2/3 -5/1 -1/2 -24/5 0/1 -43/9 -1/1 0/1 -19/4 -1/3 0/1 -71/15 -1/1 0/1 -52/11 1/0 -33/7 -1/1 0/1 -14/3 -1/1 0/1 -23/5 -1/3 0/1 -32/7 -1/2 1/0 -41/9 -1/1 -4/5 -9/2 -1/1 0/1 -22/5 -1/1 -2/3 -13/3 -1/1 -2/3 -43/10 -2/3 -3/5 -30/7 -1/2 -17/4 -1/1 -2/3 -4/1 -1/2 -23/6 -1/3 0/1 -42/11 -1/3 0/1 -19/5 -1/3 0/1 -15/4 -1/2 -41/11 -2/5 -1/3 -67/18 -1/3 0/1 -26/7 -1/3 0/1 -63/17 -1/1 -2/3 -37/10 -2/5 -1/3 -48/13 -1/2 -1/4 -11/3 -1/3 0/1 -18/5 -1/1 0/1 -61/17 -1/3 0/1 -43/12 -1/1 0/1 -25/7 -1/2 -32/9 -1/2 1/0 -39/11 -4/3 -1/1 -7/2 -1/1 0/1 -38/11 -1/1 -2/3 -31/9 -1/1 0/1 -55/16 1/0 -24/7 -1/1 -41/12 -1/1 -4/5 -17/5 -1/1 -2/3 -10/3 -1/2 -23/7 -3/7 -2/5 -59/18 -2/5 -21/53 -36/11 -3/8 -13/4 -4/11 -1/3 -16/5 -1/2 -1/4 -19/6 -1/3 0/1 -22/7 -1/3 0/1 -25/8 -1/4 -3/1 -1/1 0/1 -20/7 -1/2 -37/13 -6/13 -5/11 -17/6 -3/7 -2/5 -14/5 -2/5 -1/3 -53/19 -1/3 -12/37 -39/14 -1/3 -2/7 -25/9 -1/4 -61/22 -1/11 0/1 -36/13 -1/2 -47/17 -1/1 0/1 -58/21 -1/3 0/1 -11/4 -1/3 0/1 -52/19 -1/4 -41/15 -2/5 -1/3 -30/11 -1/4 -19/7 -1/3 0/1 -8/3 0/1 -21/8 0/1 1/1 -34/13 0/1 1/1 -81/31 1/1 6/5 -47/18 1/1 2/1 -13/5 -2/1 -1/1 -44/17 1/0 -119/46 -1/1 -8/9 -75/29 -1/2 -31/12 -1/1 0/1 -18/7 -1/1 0/1 -59/23 0/1 1/1 -100/39 1/0 -41/16 -1/1 0/1 -23/9 -2/1 -1/1 -28/11 -1/2 -33/13 -1/1 0/1 -5/2 -1/2 -32/13 -1/2 -1/4 -27/11 -1/3 0/1 -22/9 -1/3 0/1 -61/25 -1/3 0/1 -100/41 -1/2 -39/16 -2/5 -1/3 -17/7 -1/3 0/1 -46/19 -1/3 0/1 -75/31 -1/4 -29/12 -1/3 0/1 -99/41 0/1 1/1 -70/29 -1/2 -41/17 -2/5 -1/3 -53/22 -1/3 -8/25 -12/5 -1/4 -67/28 -1/5 -6/31 -55/23 -1/6 -43/18 -1/5 0/1 -74/31 -1/5 0/1 -105/44 -1/4 -31/13 -1/5 0/1 -19/8 -1/7 0/1 -45/19 -1/8 -71/30 -1/9 0/1 -26/11 -1/11 0/1 -7/3 0/1 1/3 -44/19 1/2 -37/16 1/1 2/1 -30/13 1/0 -23/10 -2/1 -1/1 -39/17 -1/1 0/1 -16/7 -1/2 1/0 -41/18 -1/1 0/1 -25/11 -1/2 -34/15 -1/3 0/1 -43/19 0/1 1/3 -52/23 1/0 -9/4 -1/1 0/1 -20/9 -1/2 -31/14 -2/5 -1/3 -42/19 -1/3 0/1 -11/5 -1/3 0/1 -24/11 0/1 -37/17 -1/1 0/1 -13/6 -1/3 0/1 -41/19 -2/5 -1/3 -28/13 -1/4 -43/20 -1/1 0/1 -15/7 -1/4 -17/8 -1/7 0/1 -2/1 -1/1 0/1 -19/10 0/1 1/17 -17/9 0/1 1/5 -15/8 1/2 -43/23 -1/1 0/1 -28/15 1/2 -13/7 0/1 1/1 -37/20 -1/1 0/1 -24/13 0/1 -35/19 1/2 -11/6 0/1 1/1 -20/11 1/0 -29/16 -2/1 -1/1 -38/21 -2/1 -1/1 -9/5 -1/1 0/1 -52/29 -1/2 -43/24 -1/5 0/1 -120/67 0/1 -77/43 0/1 1/7 -34/19 0/1 1/1 -25/14 1/0 -41/23 -1/1 0/1 -16/9 -1/2 1/0 -39/22 -1/1 0/1 -23/13 -1/1 -2/3 -30/17 -1/2 -37/21 -2/5 -1/3 -7/4 -1/5 0/1 -40/23 0/1 -33/19 0/1 1/23 -26/15 0/1 1/9 -71/41 0/1 1/7 -45/26 1/6 -19/11 0/1 1/5 -50/29 1/4 -81/47 4/13 1/3 -31/18 0/1 1/3 -74/43 0/1 1/3 -117/68 0/1 1/3 -160/93 1/4 1/2 -43/25 0/1 1/3 -12/7 1/2 -53/31 8/9 1/1 -41/24 1/1 2/1 -70/41 1/0 -99/58 -1/3 0/1 -29/17 0/1 1/1 -75/44 1/2 -121/71 1/1 6/5 -46/27 0/1 1/1 -63/37 0/1 1/1 -80/47 1/2 1/0 -17/10 0/1 1/1 -39/23 1/1 2/1 -100/59 1/0 -61/36 0/1 1/1 -22/13 0/1 1/1 -5/3 1/0 -38/23 -1/1 -2/3 -33/20 -1/1 0/1 -28/17 1/0 -23/14 -1/1 -2/3 -41/25 -1/1 0/1 -100/61 -1/2 -59/36 -1/3 0/1 -18/11 -1/1 0/1 -49/30 -1/1 0/1 -80/49 -1/2 1/0 -31/19 -1/1 0/1 -75/46 1/0 -119/73 -8/7 -1/1 -163/100 -1/1 -4/5 -44/27 -1/2 -13/8 -1/1 -2/3 -60/37 -1/2 -47/29 -2/5 -1/3 -81/50 -6/17 -1/3 -115/71 -1/4 -34/21 -1/3 0/1 -55/34 -1/2 -21/13 -1/3 0/1 -8/5 0/1 -19/12 0/1 1/1 -49/31 0/1 1/3 -30/19 1/2 -71/45 2/3 1/1 -41/26 1/1 2/1 -11/7 0/1 1/1 -47/30 -1/1 0/1 -83/53 2/3 1/1 -119/76 1/1 10/9 -36/23 1/0 -61/39 0/1 1/9 -25/16 1/2 -39/25 2/3 1/1 -53/34 12/13 1/1 -120/77 1/1 -67/43 1/1 16/15 -14/9 1/1 2/1 -17/11 2/1 3/1 -20/13 1/0 -23/15 -4/1 -3/1 -3/2 -1/1 0/1 -22/15 0/1 1/1 -19/13 0/1 1/1 -16/11 1/2 1/0 -29/20 0/1 1/1 -42/29 0/1 1/1 -55/38 1/2 -13/9 1/1 4/3 -10/7 1/0 -27/19 -3/1 -8/3 -44/31 -5/2 -61/43 -23/11 -2/1 -200/141 -2/1 -139/98 -2/1 -49/25 -78/55 -2/1 -13/7 -17/12 -2/1 -1/1 -41/29 -4/3 -1/1 -65/46 -3/2 -24/17 -1/1 -55/39 -1/2 -31/22 -1/1 0/1 -38/27 -2/1 -1/1 -45/32 -1/2 -7/5 -1/1 0/1 -39/28 -1/1 -4/5 -32/23 -1/2 1/0 -57/41 -1/3 0/1 -25/18 1/0 -93/67 -6/5 -1/1 -68/49 -1/2 -43/31 -1/1 0/1 -61/44 0/1 1/1 -18/13 -1/1 0/1 -29/21 -1/3 0/1 -40/29 0/1 -11/8 0/1 1/1 -59/43 -1/3 0/1 -48/35 1/2 1/0 -85/62 1/2 -122/89 4/5 1/1 -159/116 1/1 14/13 -37/27 1/1 2/1 -63/46 -2/1 -1/1 -89/65 -1/1 0/1 -26/19 0/1 1/1 -93/68 0/1 1/1 -160/117 1/2 1/0 -67/49 0/1 1/1 -41/30 1/1 2/1 -56/41 1/1 -15/11 1/0 -34/25 0/1 1/1 -19/14 0/1 1/1 -4/3 1/0 -21/16 -2/1 -1/1 -80/61 -3/2 1/0 -59/45 -2/1 -1/1 -38/29 -2/1 -1/1 -55/42 1/0 -17/13 -2/1 -1/1 -30/23 1/0 -43/33 -3/1 -2/1 -13/10 -2/1 -1/1 -48/37 -3/2 1/0 -83/64 -4/3 -1/1 -201/155 -16/15 -1/1 -520/401 -1/1 -319/246 -1/1 -20/21 -118/91 -1/1 -2/3 -35/27 1/0 -22/17 -2/1 -1/1 -31/24 -4/3 -1/1 -40/31 -1/1 -9/7 -1/1 0/1 -41/32 -4/3 -1/1 -32/25 -1/2 1/0 -55/43 -1/2 -23/18 0/1 1/1 -14/11 -1/1 0/1 -47/37 -1/1 0/1 -80/63 -1/2 1/0 -33/26 -1/1 0/1 -52/41 -1/2 -71/56 -1/1 0/1 -19/15 0/1 1/1 -43/34 -1/1 0/1 -24/19 0/1 -29/23 0/1 1/1 -5/4 1/0 -21/17 -2/1 -1/1 -16/13 -3/2 1/0 -27/22 -6/5 -1/1 -65/53 1/0 -38/31 -2/1 -1/1 -11/9 -2/1 -1/1 -39/32 -1/1 0/1 -67/55 -2/1 -1/1 -28/23 -3/2 -17/14 -6/5 -1/1 -40/33 -1/1 -23/19 -1/1 -6/7 -6/5 -1/1 0/1 -31/26 -1/1 0/1 -25/21 -1/2 -19/16 0/1 1/5 -51/43 0/1 1/1 -32/27 1/2 1/0 -13/11 0/1 1/1 -20/17 1/0 -27/23 -6/1 -5/1 -7/6 -3/1 -2/1 -29/25 -2/1 -1/1 -80/69 -3/2 1/0 -51/44 -2/1 -1/1 -22/19 -2/1 -1/1 -37/32 -3/1 -2/1 -15/13 -3/2 -38/33 -2/1 -1/1 -23/20 -2/1 -1/1 -8/7 -1/1 -17/15 -1/1 -2/3 -26/23 -1/3 0/1 -9/8 -1/1 0/1 -19/17 -1/3 0/1 -10/9 1/0 -1/1 -1/1 0/1 0/1 -1/2 1/0 1/1 -1/1 0/1 10/9 -1/2 19/17 0/1 1/1 9/8 -1/1 0/1 17/15 -2/1 -1/1 8/7 -1/1 23/20 -1/1 -2/3 15/13 -3/4 22/19 -1/1 -2/3 7/6 -2/3 -3/5 20/17 -1/2 13/11 -1/3 0/1 32/27 -1/2 -1/4 19/16 -1/7 0/1 25/21 1/0 6/5 -1/1 0/1 17/14 -1/1 -6/7 28/23 -3/4 11/9 -1/1 -2/3 16/13 -3/4 -1/2 21/17 -1/1 -2/3 5/4 -1/2 24/19 0/1 43/34 -1/1 0/1 19/15 -1/3 0/1 71/56 -1/1 0/1 52/41 1/0 33/26 -1/1 0/1 14/11 -1/1 0/1 23/18 -1/3 0/1 32/25 -1/2 1/0 41/32 -1/1 -4/5 9/7 -1/1 0/1 22/17 -1/1 -2/3 13/10 -1/1 -2/3 43/33 -2/3 -3/5 30/23 -1/2 17/13 -1/1 -2/3 4/3 -1/2 23/17 -1/3 0/1 42/31 -1/3 0/1 19/14 -1/3 0/1 15/11 -1/2 41/30 -2/5 -1/3 67/49 -1/3 0/1 26/19 -1/3 0/1 63/46 -1/1 -2/3 37/27 -2/5 -1/3 48/35 -1/2 -1/4 11/8 -1/3 0/1 18/13 -1/1 0/1 61/44 -1/3 0/1 43/31 -1/1 0/1 25/18 -1/2 32/23 -1/2 1/0 39/28 -4/3 -1/1 7/5 -1/1 0/1 38/27 -1/1 -2/3 31/22 -1/1 0/1 55/39 1/0 24/17 -1/1 41/29 -1/1 -4/5 17/12 -1/1 -2/3 10/7 -1/2 23/16 -3/7 -2/5 59/41 -2/5 -21/53 36/25 -3/8 13/9 -4/11 -1/3 16/11 -1/2 -1/4 19/13 -1/3 0/1 22/15 -1/3 0/1 25/17 -1/4 3/2 -1/1 0/1 20/13 -1/2 37/24 -6/13 -5/11 17/11 -3/7 -2/5 14/9 -2/5 -1/3 53/34 -1/3 -12/37 39/25 -1/3 -2/7 25/16 -1/4 61/39 -1/11 0/1 36/23 -1/2 47/30 -1/1 0/1 58/37 -1/3 0/1 11/7 -1/3 0/1 52/33 -1/4 41/26 -2/5 -1/3 30/19 -1/4 19/12 -1/3 0/1 8/5 0/1 21/13 0/1 1/1 34/21 0/1 1/1 81/50 1/1 6/5 47/29 1/1 2/1 13/8 -2/1 -1/1 44/27 1/0 119/73 -1/1 -8/9 75/46 -1/2 31/19 -1/1 0/1 18/11 -1/1 0/1 59/36 0/1 1/1 100/61 1/0 41/25 -1/1 0/1 23/14 -2/1 -1/1 28/17 -1/2 33/20 -1/1 0/1 5/3 -1/2 32/19 -1/2 -1/4 27/16 -1/3 0/1 22/13 -1/3 0/1 61/36 -1/3 0/1 100/59 -1/2 39/23 -2/5 -1/3 17/10 -1/3 0/1 46/27 -1/3 0/1 75/44 -1/4 29/17 -1/3 0/1 99/58 0/1 1/1 70/41 -1/2 41/24 -2/5 -1/3 53/31 -1/3 -8/25 12/7 -1/4 67/39 -1/5 -6/31 55/32 -1/6 43/25 -1/5 0/1 74/43 -1/5 0/1 105/61 -1/4 31/18 -1/5 0/1 19/11 -1/7 0/1 45/26 -1/8 71/41 -1/9 0/1 26/15 -1/11 0/1 7/4 0/1 1/3 44/25 1/2 37/21 1/1 2/1 30/17 1/0 23/13 -2/1 -1/1 39/22 -1/1 0/1 16/9 -1/2 1/0 41/23 -1/1 0/1 25/14 -1/2 34/19 -1/3 0/1 43/24 0/1 1/3 52/29 1/0 9/5 -1/1 0/1 20/11 -1/2 31/17 -2/5 -1/3 42/23 -1/3 0/1 11/6 -1/3 0/1 24/13 0/1 37/20 -1/1 0/1 13/7 -1/3 0/1 41/22 -2/5 -1/3 28/15 -1/4 43/23 -1/1 0/1 15/8 -1/4 17/9 -1/7 0/1 2/1 -1/1 0/1 19/9 0/1 1/17 17/8 0/1 1/5 15/7 1/2 43/20 -1/1 0/1 28/13 1/2 13/6 0/1 1/1 37/17 -1/1 0/1 24/11 0/1 35/16 1/2 11/5 0/1 1/1 20/9 1/0 29/13 -2/1 -1/1 38/17 -2/1 -1/1 9/4 -1/1 0/1 52/23 -1/2 43/19 -1/5 0/1 120/53 0/1 77/34 0/1 1/7 34/15 0/1 1/1 25/11 1/0 41/18 -1/1 0/1 16/7 -1/2 1/0 39/17 -1/1 0/1 23/10 -1/1 -2/3 30/13 -1/2 37/16 -2/5 -1/3 7/3 -1/5 0/1 40/17 0/1 33/14 0/1 1/23 26/11 0/1 1/9 71/30 0/1 1/7 45/19 1/6 19/8 0/1 1/5 50/21 1/4 81/34 4/13 1/3 31/13 0/1 1/3 74/31 0/1 1/3 117/49 0/1 1/3 160/67 1/4 1/2 43/18 0/1 1/3 12/5 1/2 53/22 8/9 1/1 41/17 1/1 2/1 70/29 1/0 99/41 -1/3 0/1 29/12 0/1 1/1 75/31 1/2 121/50 1/1 6/5 46/19 0/1 1/1 63/26 0/1 1/1 80/33 1/2 1/0 17/7 0/1 1/1 39/16 1/1 2/1 100/41 1/0 61/25 0/1 1/1 22/9 0/1 1/1 5/2 1/0 38/15 -1/1 -2/3 33/13 -1/1 0/1 28/11 1/0 23/9 -1/1 -2/3 41/16 -1/1 0/1 100/39 -1/2 59/23 -1/3 0/1 18/7 -1/1 0/1 49/19 -1/1 0/1 80/31 -1/2 1/0 31/12 -1/1 0/1 75/29 1/0 119/46 -8/7 -1/1 163/63 -1/1 -4/5 44/17 -1/2 13/5 -1/1 -2/3 60/23 -1/2 47/18 -2/5 -1/3 81/31 -6/17 -1/3 115/44 -1/4 34/13 -1/3 0/1 55/21 -1/2 21/8 -1/3 0/1 8/3 0/1 19/7 0/1 1/1 49/18 0/1 1/3 30/11 1/2 71/26 2/3 1/1 41/15 1/1 2/1 11/4 0/1 1/1 47/17 -1/1 0/1 83/30 2/3 1/1 119/43 1/1 10/9 36/13 1/0 61/22 0/1 1/9 25/9 1/2 39/14 2/3 1/1 53/19 12/13 1/1 120/43 1/1 67/24 1/1 16/15 14/5 1/1 2/1 17/6 2/1 3/1 20/7 1/0 23/8 -4/1 -3/1 3/1 -1/1 0/1 22/7 0/1 1/1 19/6 0/1 1/1 16/5 1/2 1/0 29/9 0/1 1/1 42/13 0/1 1/1 55/17 1/2 13/4 1/1 4/3 10/3 1/0 27/8 -3/1 -8/3 44/13 -5/2 61/18 -23/11 -2/1 200/59 -2/1 139/41 -2/1 -49/25 78/23 -2/1 -13/7 17/5 -2/1 -1/1 41/12 -4/3 -1/1 65/19 -3/2 24/7 -1/1 55/16 -1/2 31/9 -1/1 0/1 38/11 -2/1 -1/1 45/13 -1/2 7/2 -1/1 0/1 39/11 -1/1 -4/5 32/9 -1/2 1/0 57/16 -1/3 0/1 25/7 1/0 93/26 -6/5 -1/1 68/19 -1/2 43/12 -1/1 0/1 61/17 0/1 1/1 18/5 -1/1 0/1 29/8 -1/3 0/1 40/11 0/1 11/3 0/1 1/1 59/16 -1/3 0/1 48/13 1/2 1/0 85/23 1/2 122/33 4/5 1/1 159/43 1/1 14/13 37/10 1/1 2/1 63/17 -2/1 -1/1 89/24 -1/1 0/1 26/7 0/1 1/1 93/25 0/1 1/1 160/43 1/2 1/0 67/18 0/1 1/1 41/11 1/1 2/1 56/15 1/1 15/4 1/0 34/9 0/1 1/1 19/5 0/1 1/1 4/1 1/0 21/5 -2/1 -1/1 80/19 -3/2 1/0 59/14 -2/1 -1/1 38/9 -2/1 -1/1 55/13 1/0 17/4 -2/1 -1/1 30/7 1/0 43/10 -3/1 -2/1 13/3 -2/1 -1/1 48/11 -3/2 1/0 83/19 -4/3 -1/1 201/46 -16/15 -1/1 520/119 -1/1 319/73 -1/1 -20/21 118/27 -1/1 -2/3 35/8 1/0 22/5 -2/1 -1/1 31/7 -4/3 -1/1 40/9 -1/1 9/2 -1/1 0/1 41/9 -4/3 -1/1 32/7 -1/2 1/0 55/12 -1/2 23/5 0/1 1/1 14/3 -1/1 0/1 47/10 -1/1 0/1 80/17 -1/2 1/0 33/7 -1/1 0/1 52/11 -1/2 71/15 -1/1 0/1 19/4 0/1 1/1 43/9 -1/1 0/1 24/5 0/1 29/6 0/1 1/1 5/1 1/0 21/4 -2/1 -1/1 16/3 -3/2 1/0 27/5 -6/5 -1/1 65/12 1/0 38/7 -2/1 -1/1 11/2 -2/1 -1/1 39/7 -1/1 0/1 67/12 -2/1 -1/1 28/5 -3/2 17/3 -6/5 -1/1 40/7 -1/1 23/4 -1/1 -6/7 6/1 -1/1 0/1 31/5 -1/1 0/1 25/4 -1/2 19/3 0/1 1/5 51/8 0/1 1/1 32/5 1/2 1/0 13/2 0/1 1/1 20/3 1/0 27/4 -6/1 -5/1 7/1 -3/1 -2/1 29/4 -2/1 -1/1 80/11 -3/2 1/0 51/7 -2/1 -1/1 22/3 -2/1 -1/1 37/5 -3/1 -2/1 15/2 -3/2 38/5 -2/1 -1/1 23/3 -2/1 -1/1 8/1 -1/1 17/2 -1/1 -2/3 26/3 -1/3 0/1 9/1 -1/1 0/1 19/2 -1/3 0/1 10/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,480,24,281) (-10/1,1/0) -> (70/41,41/24) Hyperbolic Matrix(239,2320,140,1359) (-10/1,-19/2) -> (99/58,70/41) Hyperbolic Matrix(161,1520,34,321) (-19/2,-9/1) -> (71/15,19/4) Hyperbolic Matrix(241,2080,-176,-1519) (-9/1,-17/2) -> (-63/46,-89/65) Hyperbolic Matrix(39,320,34,279) (-17/2,-8/1) -> (8/7,23/20) Hyperbolic Matrix(41,320,36,281) (-8/1,-23/3) -> (17/15,8/7) Hyperbolic Matrix(199,1520,-152,-1161) (-23/3,-15/2) -> (-55/42,-17/13) Hyperbolic Matrix(119,880,-38,-281) (-15/2,-22/3) -> (-22/7,-25/8) Hyperbolic Matrix(199,1440,-72,-521) (-22/3,-7/1) -> (-47/17,-58/21) Hyperbolic Matrix(201,1360,-124,-839) (-7/1,-20/3) -> (-60/37,-47/29) Hyperbolic Matrix(159,1040,-98,-641) (-20/3,-13/2) -> (-13/8,-60/37) Hyperbolic Matrix(199,1280,118,759) (-13/2,-32/5) -> (32/19,27/16) Hyperbolic Matrix(439,2800,-320,-2041) (-32/5,-19/3) -> (-59/43,-48/35) Hyperbolic Matrix(319,2000,204,1279) (-19/3,-25/4) -> (25/16,61/39) Hyperbolic Matrix(401,2480,-168,-1039) (-25/4,-6/1) -> (-74/31,-105/44) Hyperbolic Matrix(41,240,-34,-199) (-6/1,-17/3) -> (-23/19,-6/5) Hyperbolic Matrix(199,1120,78,439) (-17/3,-28/5) -> (28/11,23/9) Hyperbolic Matrix(159,880,-58,-321) (-28/5,-11/2) -> (-11/4,-52/19) Hyperbolic Matrix(119,640,-82,-441) (-11/2,-16/3) -> (-16/11,-29/20) Hyperbolic Matrix(121,640,38,201) (-16/3,-21/4) -> (19/6,16/5) Hyperbolic Matrix(199,1040,84,439) (-21/4,-5/1) -> (45/19,19/8) Hyperbolic Matrix(199,960,-108,-521) (-5/1,-24/5) -> (-24/13,-35/19) Hyperbolic Matrix(401,1920,184,881) (-24/5,-43/9) -> (37/17,24/11) Hyperbolic Matrix(721,3440,520,2481) (-43/9,-19/4) -> (61/44,43/31) Hyperbolic Matrix(321,1520,34,161) (-19/4,-71/15) -> (9/1,19/2) Hyperbolic Matrix(879,4160,490,2319) (-71/15,-52/11) -> (52/29,9/5) Hyperbolic Matrix(559,2640,220,1039) (-52/11,-33/7) -> (33/13,28/11) Hyperbolic Matrix(239,1120,-188,-881) (-33/7,-14/3) -> (-14/11,-47/37) Hyperbolic Matrix(121,560,78,361) (-14/3,-23/5) -> (17/11,14/9) Hyperbolic Matrix(559,2560,-402,-1841) (-23/5,-32/7) -> (-32/23,-57/41) Hyperbolic Matrix(561,2560,158,721) (-32/7,-41/9) -> (39/11,32/9) Hyperbolic Matrix(721,3280,264,1201) (-41/9,-9/2) -> (71/26,41/15) Hyperbolic Matrix(199,880,-154,-681) (-9/2,-22/5) -> (-22/17,-31/24) Hyperbolic Matrix(201,880,-82,-359) (-22/5,-13/3) -> (-27/11,-22/9) Hyperbolic Matrix(241,1040,130,561) (-13/3,-43/10) -> (37/20,13/7) Hyperbolic Matrix(559,2400,242,1039) (-43/10,-30/7) -> (30/13,37/16) Hyperbolic Matrix(281,1200,122,521) (-30/7,-17/4) -> (23/10,30/13) Hyperbolic Matrix(39,160,-10,-41) (-17/4,-4/1) -> (-4/1,-23/6) Parabolic Matrix(481,1840,-418,-1599) (-23/6,-42/11) -> (-38/33,-23/20) Hyperbolic Matrix(839,3200,-640,-2441) (-42/11,-19/5) -> (-59/45,-38/29) Hyperbolic Matrix(359,1360,-222,-841) (-19/5,-15/4) -> (-55/34,-21/13) Hyperbolic Matrix(879,3280,-622,-2321) (-15/4,-41/11) -> (-41/29,-65/46) Hyperbolic Matrix(881,3280,-408,-1519) (-41/11,-67/18) -> (-13/6,-41/19) Hyperbolic Matrix(1119,4160,-818,-3041) (-67/18,-26/7) -> (-26/19,-93/68) Hyperbolic Matrix(561,2080,-496,-1839) (-26/7,-63/17) -> (-17/15,-26/23) Hyperbolic Matrix(799,2960,518,1919) (-63/17,-37/10) -> (37/24,17/11) Hyperbolic Matrix(1559,5760,-1202,-4441) (-37/10,-48/13) -> (-48/37,-83/64) Hyperbolic Matrix(759,2800,-640,-2361) (-48/13,-11/3) -> (-51/43,-32/27) Hyperbolic Matrix(199,720,-144,-521) (-11/3,-18/5) -> (-18/13,-29/21) Hyperbolic Matrix(601,2160,234,841) (-18/5,-61/17) -> (59/23,18/7) Hyperbolic Matrix(959,3440,758,2719) (-61/17,-43/12) -> (43/34,19/15) Hyperbolic Matrix(961,3440,-402,-1439) (-43/12,-25/7) -> (-55/23,-43/18) Hyperbolic Matrix(719,2560,-562,-2001) (-25/7,-32/9) -> (-32/25,-55/43) Hyperbolic Matrix(721,2560,158,561) (-32/9,-39/11) -> (41/9,32/7) Hyperbolic Matrix(679,2400,260,919) (-39/11,-7/2) -> (47/18,81/31) Hyperbolic Matrix(439,1520,-266,-921) (-7/2,-38/11) -> (-38/23,-33/20) Hyperbolic Matrix(719,2480,394,1359) (-38/11,-31/9) -> (31/17,42/23) Hyperbolic Matrix(1441,4960,-604,-2079) (-31/9,-55/16) -> (-105/44,-31/13) Hyperbolic Matrix(1001,3440,268,921) (-55/16,-24/7) -> (56/15,15/4) Hyperbolic Matrix(959,3280,-702,-2401) (-24/7,-41/12) -> (-41/30,-56/41) Hyperbolic Matrix(399,1360,164,559) (-41/12,-17/5) -> (17/7,39/16) Hyperbolic Matrix(119,400,-36,-121) (-17/5,-10/3) -> (-10/3,-23/7) Parabolic Matrix(439,1440,-232,-761) (-23/7,-59/18) -> (-19/10,-17/9) Hyperbolic Matrix(1319,4320,476,1559) (-59/18,-36/11) -> (36/13,61/22) Hyperbolic Matrix(319,1040,196,639) (-36/11,-13/4) -> (13/8,44/27) Hyperbolic Matrix(199,640,-162,-521) (-13/4,-16/5) -> (-16/13,-27/22) Hyperbolic Matrix(201,640,38,121) (-16/5,-19/6) -> (21/4,16/3) Hyperbolic Matrix(559,1760,330,1039) (-19/6,-22/7) -> (22/13,61/36) Hyperbolic Matrix(359,1120,192,599) (-25/8,-3/1) -> (43/23,15/8) Hyperbolic Matrix(279,800,-98,-281) (-3/1,-20/7) -> (-20/7,-37/13) Parabolic Matrix(1041,2960,760,2161) (-37/13,-17/6) -> (63/46,37/27) Hyperbolic Matrix(199,560,156,439) (-17/6,-14/5) -> (14/11,23/18) Hyperbolic Matrix(601,1680,-386,-1079) (-14/5,-53/19) -> (-67/43,-14/9) Hyperbolic Matrix(1521,4240,890,2481) (-53/19,-39/14) -> (41/24,53/31) Hyperbolic Matrix(719,2000,316,879) (-39/14,-25/9) -> (25/11,41/18) Hyperbolic Matrix(721,2000,606,1681) (-25/9,-61/22) -> (19/16,25/21) Hyperbolic Matrix(1761,4880,520,1441) (-61/22,-36/13) -> (44/13,61/18) Hyperbolic Matrix(839,2320,-362,-1001) (-36/13,-47/17) -> (-7/3,-44/19) Hyperbolic Matrix(1159,3200,-1000,-2761) (-58/21,-11/4) -> (-51/44,-22/19) Hyperbolic Matrix(1199,3280,-556,-1521) (-52/19,-41/15) -> (-41/19,-28/13) Hyperbolic Matrix(1641,4480,-952,-2599) (-41/15,-30/11) -> (-50/29,-81/47) Hyperbolic Matrix(559,1520,-324,-881) (-30/11,-19/7) -> (-19/11,-50/29) Hyperbolic Matrix(119,320,74,199) (-19/7,-8/3) -> (8/5,21/13) Hyperbolic Matrix(121,320,76,201) (-8/3,-21/8) -> (19/12,8/5) Hyperbolic Matrix(519,1360,-382,-1001) (-21/8,-34/13) -> (-34/25,-19/14) Hyperbolic Matrix(2999,7840,-1760,-4601) (-34/13,-81/31) -> (-121/71,-46/27) Hyperbolic Matrix(919,2400,260,679) (-81/31,-47/18) -> (7/2,39/11) Hyperbolic Matrix(521,1360,-444,-1159) (-47/18,-13/5) -> (-27/23,-7/6) Hyperbolic Matrix(401,1040,278,721) (-13/5,-44/17) -> (36/25,13/9) Hyperbolic Matrix(3679,9520,-2350,-6081) (-44/17,-119/46) -> (-119/76,-36/23) Hyperbolic Matrix(6959,18000,2876,7439) (-119/46,-75/29) -> (75/31,121/50) Hyperbolic Matrix(2599,6720,1098,2839) (-75/29,-31/12) -> (71/30,45/19) Hyperbolic Matrix(559,1440,-342,-881) (-31/12,-18/7) -> (-18/11,-49/30) Hyperbolic Matrix(841,2160,234,601) (-18/7,-59/23) -> (61/17,18/5) Hyperbolic Matrix(4679,12000,1918,4919) (-59/23,-100/39) -> (100/41,61/25) Hyperbolic Matrix(3121,8000,1280,3281) (-100/39,-41/16) -> (39/16,100/41) Hyperbolic Matrix(719,1840,406,1039) (-41/16,-23/9) -> (23/13,39/22) Hyperbolic Matrix(439,1120,78,199) (-23/9,-28/11) -> (28/5,17/3) Hyperbolic Matrix(1039,2640,220,559) (-28/11,-33/13) -> (33/7,52/11) Hyperbolic Matrix(599,1520,-426,-1081) (-33/13,-5/2) -> (-45/32,-7/5) Hyperbolic Matrix(1201,2960,-876,-2159) (-5/2,-32/13) -> (-48/35,-85/62) Hyperbolic Matrix(521,1280,440,1081) (-32/13,-27/11) -> (13/11,32/27) Hyperbolic Matrix(721,1760,492,1201) (-22/9,-61/25) -> (19/13,22/15) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(3281,8000,1280,3121) (-100/41,-39/16) -> (41/16,100/39) Hyperbolic Matrix(559,1360,164,399) (-39/16,-17/7) -> (17/5,41/12) Hyperbolic Matrix(1519,3680,-892,-2161) (-17/7,-46/19) -> (-46/27,-63/37) Hyperbolic Matrix(3239,7840,-2000,-4841) (-46/19,-75/31) -> (-115/71,-34/21) Hyperbolic Matrix(959,2320,198,479) (-75/31,-29/12) -> (29/6,5/1) Hyperbolic Matrix(2319,5600,364,879) (-29/12,-99/41) -> (19/3,51/8) Hyperbolic Matrix(961,2320,862,2081) (-99/41,-70/29) -> (10/9,19/17) Hyperbolic Matrix(199,480,182,439) (-70/29,-41/17) -> (1/1,10/9) Hyperbolic Matrix(1759,4240,1128,2719) (-41/17,-53/22) -> (53/34,39/25) Hyperbolic Matrix(599,1440,-250,-601) (-53/22,-12/5) -> (-12/5,-67/28) Parabolic Matrix(1839,4400,568,1359) (-67/28,-55/23) -> (55/17,13/4) Hyperbolic Matrix(4959,11840,-2882,-6881) (-43/18,-74/31) -> (-74/43,-117/68) Hyperbolic Matrix(639,1520,-404,-961) (-31/13,-19/8) -> (-19/12,-49/31) Hyperbolic Matrix(439,1040,84,199) (-19/8,-45/19) -> (5/1,21/4) Hyperbolic Matrix(2839,6720,1098,2599) (-45/19,-71/30) -> (31/12,75/29) Hyperbolic Matrix(879,2080,-778,-1841) (-71/30,-26/11) -> (-26/23,-9/8) Hyperbolic Matrix(441,1040,-254,-599) (-26/11,-7/3) -> (-33/19,-26/15) Hyperbolic Matrix(3801,8800,-2332,-5399) (-44/19,-37/16) -> (-163/100,-44/27) Hyperbolic Matrix(1039,2400,242,559) (-37/16,-30/13) -> (30/7,43/10) Hyperbolic Matrix(521,1200,122,281) (-30/13,-23/10) -> (17/4,30/7) Hyperbolic Matrix(801,1840,488,1121) (-23/10,-39/17) -> (41/25,23/14) Hyperbolic Matrix(559,1280,314,719) (-39/17,-16/7) -> (16/9,41/23) Hyperbolic Matrix(561,1280,316,721) (-16/7,-41/18) -> (39/22,16/9) Hyperbolic Matrix(879,2000,316,719) (-41/18,-25/11) -> (25/9,39/14) Hyperbolic Matrix(1199,2720,458,1039) (-25/11,-34/15) -> (34/13,55/21) Hyperbolic Matrix(1801,4080,-1006,-2279) (-34/15,-43/19) -> (-77/43,-34/19) Hyperbolic Matrix(1521,3440,814,1841) (-43/19,-52/23) -> (28/15,43/23) Hyperbolic Matrix(1841,4160,1452,3281) (-52/23,-9/4) -> (71/56,52/41) Hyperbolic Matrix(359,800,-162,-361) (-9/4,-20/9) -> (-20/9,-31/14) Parabolic Matrix(1121,2480,796,1761) (-31/14,-42/19) -> (38/27,31/22) Hyperbolic Matrix(761,1680,236,521) (-42/19,-11/5) -> (29/9,42/13) Hyperbolic Matrix(439,960,-348,-761) (-11/5,-24/11) -> (-24/19,-29/23) Hyperbolic Matrix(881,1920,184,401) (-24/11,-37/17) -> (43/9,24/5) Hyperbolic Matrix(479,1040,368,799) (-37/17,-13/6) -> (13/10,43/33) Hyperbolic Matrix(1599,3440,892,1919) (-28/13,-43/20) -> (43/24,52/29) Hyperbolic Matrix(521,1120,354,761) (-43/20,-15/7) -> (25/17,3/2) Hyperbolic Matrix(599,1280,168,359) (-15/7,-17/8) -> (57/16,25/7) Hyperbolic Matrix(641,1360,-452,-959) (-17/8,-2/1) -> (-78/55,-17/12) Hyperbolic Matrix(919,1760,-648,-1241) (-2/1,-19/10) -> (-139/98,-78/55) Hyperbolic Matrix(679,1280,148,279) (-17/9,-15/8) -> (55/12,23/5) Hyperbolic Matrix(641,1200,86,161) (-15/8,-43/23) -> (37/5,15/2) Hyperbolic Matrix(1841,3440,814,1521) (-43/23,-28/15) -> (52/23,43/19) Hyperbolic Matrix(1201,2240,-986,-1839) (-28/15,-13/7) -> (-67/55,-28/23) Hyperbolic Matrix(561,1040,130,241) (-13/7,-37/20) -> (43/10,13/3) Hyperbolic Matrix(1039,1920,822,1519) (-37/20,-24/13) -> (24/19,43/34) Hyperbolic Matrix(1001,1840,414,761) (-35/19,-11/6) -> (29/12,75/31) Hyperbolic Matrix(439,800,-242,-441) (-11/6,-20/11) -> (-20/11,-29/16) Parabolic Matrix(839,1520,154,279) (-29/16,-38/21) -> (38/7,11/2) Hyperbolic Matrix(841,1520,244,441) (-38/21,-9/5) -> (31/9,38/11) Hyperbolic Matrix(2319,4160,490,879) (-9/5,-52/29) -> (52/11,71/15) Hyperbolic Matrix(1919,3440,892,1599) (-52/29,-43/24) -> (43/20,28/13) Hyperbolic Matrix(8039,14400,3550,6359) (-43/24,-120/67) -> (120/53,77/34) Hyperbolic Matrix(8041,14400,3552,6361) (-120/67,-77/43) -> (43/19,120/53) Hyperbolic Matrix(761,1360,202,361) (-34/19,-25/14) -> (15/4,34/9) Hyperbolic Matrix(1121,2000,718,1281) (-25/14,-41/23) -> (39/25,25/16) Hyperbolic Matrix(719,1280,314,559) (-41/23,-16/9) -> (16/7,39/17) Hyperbolic Matrix(721,1280,316,561) (-16/9,-39/22) -> (41/18,16/7) Hyperbolic Matrix(1039,1840,406,719) (-39/22,-23/13) -> (23/9,41/16) Hyperbolic Matrix(679,1200,520,919) (-23/13,-30/17) -> (30/23,17/13) Hyperbolic Matrix(1361,2400,1044,1841) (-30/17,-37/21) -> (43/33,30/23) Hyperbolic Matrix(1319,2320,-842,-1481) (-37/21,-7/4) -> (-47/30,-83/53) Hyperbolic Matrix(919,1600,390,679) (-7/4,-40/23) -> (40/17,33/14) Hyperbolic Matrix(921,1600,392,681) (-40/23,-33/19) -> (7/3,40/17) Hyperbolic Matrix(2401,4160,-1754,-3039) (-26/15,-71/41) -> (-89/65,-26/19) Hyperbolic Matrix(3881,6720,2380,4121) (-71/41,-45/26) -> (75/46,31/19) Hyperbolic Matrix(601,1040,486,841) (-45/26,-19/11) -> (21/17,5/4) Hyperbolic Matrix(1161,2000,256,441) (-81/47,-31/18) -> (9/2,41/9) Hyperbolic Matrix(1441,2480,-1208,-2079) (-31/18,-74/43) -> (-6/5,-31/26) Hyperbolic Matrix(14879,25600,6230,10719) (-117/68,-160/93) -> (160/67,43/18) Hyperbolic Matrix(14881,25600,6232,10721) (-160/93,-43/25) -> (117/49,160/67) Hyperbolic Matrix(2001,3440,-1442,-2479) (-43/25,-12/7) -> (-68/49,-43/31) Hyperbolic Matrix(2759,4720,-1988,-3401) (-12/7,-53/31) -> (-93/67,-68/49) Hyperbolic Matrix(2481,4240,890,1521) (-53/31,-41/24) -> (39/14,53/19) Hyperbolic Matrix(281,480,24,41) (-41/24,-70/41) -> (10/1,1/0) Hyperbolic Matrix(1359,2320,140,239) (-70/41,-99/58) -> (19/2,10/1) Hyperbolic Matrix(1641,2800,446,761) (-99/58,-29/17) -> (11/3,59/16) Hyperbolic Matrix(1079,1840,492,839) (-29/17,-75/44) -> (35/16,11/5) Hyperbolic Matrix(10561,18000,6478,11041) (-75/44,-121/71) -> (119/73,75/46) Hyperbolic Matrix(3759,6400,1550,2639) (-63/37,-80/47) -> (80/33,17/7) Hyperbolic Matrix(3761,6400,1552,2641) (-80/47,-17/10) -> (63/26,80/33) Hyperbolic Matrix(801,1360,566,961) (-17/10,-39/23) -> (41/29,17/12) Hyperbolic Matrix(4719,8000,2878,4879) (-39/23,-100/59) -> (100/61,41/25) Hyperbolic Matrix(7081,12000,4320,7321) (-100/59,-61/36) -> (59/36,100/61) Hyperbolic Matrix(1039,1760,330,559) (-61/36,-22/13) -> (22/7,19/6) Hyperbolic Matrix(521,880,-402,-679) (-22/13,-5/3) -> (-35/27,-22/17) Hyperbolic Matrix(1159,1920,-894,-1481) (-5/3,-38/23) -> (-118/91,-35/27) Hyperbolic Matrix(1601,2640,1262,2081) (-33/20,-28/17) -> (52/41,33/26) Hyperbolic Matrix(681,1120,560,921) (-28/17,-23/14) -> (17/14,28/23) Hyperbolic Matrix(1121,1840,488,801) (-23/14,-41/25) -> (39/17,23/10) Hyperbolic Matrix(4879,8000,2878,4719) (-41/25,-100/61) -> (100/59,39/23) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(3919,6400,1518,2479) (-49/30,-80/49) -> (80/31,31/12) Hyperbolic Matrix(3921,6400,1520,2481) (-80/49,-31/19) -> (49/19,80/31) Hyperbolic Matrix(4121,6720,2380,3881) (-31/19,-75/46) -> (45/26,71/41) Hyperbolic Matrix(12121,19760,4638,7561) (-75/46,-119/73) -> (81/31,115/44) Hyperbolic Matrix(26159,42640,-20172,-32881) (-119/73,-163/100) -> (-83/64,-201/155) Hyperbolic Matrix(1081,1760,320,521) (-44/27,-13/8) -> (27/8,44/13) Hyperbolic Matrix(1481,2400,1062,1721) (-47/29,-81/50) -> (39/28,7/5) Hyperbolic Matrix(12199,19760,4716,7639) (-81/50,-115/71) -> (75/29,119/46) Hyperbolic Matrix(1681,2720,940,1521) (-34/21,-55/34) -> (25/14,34/19) Hyperbolic Matrix(199,320,74,119) (-21/13,-8/5) -> (8/3,19/7) Hyperbolic Matrix(201,320,76,121) (-8/5,-19/12) -> (21/8,8/3) Hyperbolic Matrix(2279,3600,-1444,-2281) (-49/31,-30/19) -> (-30/19,-71/45) Parabolic Matrix(2079,3280,1622,2559) (-71/45,-41/26) -> (41/32,9/7) Hyperbolic Matrix(559,880,-458,-721) (-41/26,-11/7) -> (-11/9,-39/32) Hyperbolic Matrix(919,1440,-792,-1241) (-11/7,-47/30) -> (-7/6,-29/25) Hyperbolic Matrix(11239,17600,-8200,-12841) (-83/53,-119/76) -> (-159/116,-37/27) Hyperbolic Matrix(2761,4320,1918,3001) (-36/23,-61/39) -> (59/41,36/25) Hyperbolic Matrix(1279,2000,204,319) (-61/39,-25/16) -> (25/4,19/3) Hyperbolic Matrix(1281,2000,718,1121) (-25/16,-39/25) -> (41/23,25/14) Hyperbolic Matrix(2719,4240,1128,1759) (-39/25,-53/34) -> (53/22,41/17) Hyperbolic Matrix(9239,14400,3310,5159) (-53/34,-120/77) -> (120/43,67/24) Hyperbolic Matrix(9241,14400,3312,5161) (-120/77,-67/43) -> (53/19,120/43) Hyperbolic Matrix(361,560,78,121) (-14/9,-17/11) -> (23/5,14/3) Hyperbolic Matrix(519,800,-338,-521) (-17/11,-20/13) -> (-20/13,-23/15) Parabolic Matrix(681,1040,184,281) (-23/15,-3/2) -> (37/10,63/17) Hyperbolic Matrix(599,880,-518,-761) (-3/2,-22/15) -> (-22/19,-37/32) Hyperbolic Matrix(1201,1760,492,721) (-22/15,-19/13) -> (61/25,22/9) Hyperbolic Matrix(439,640,356,519) (-19/13,-16/11) -> (16/13,21/17) Hyperbolic Matrix(1159,1680,634,919) (-29/20,-42/29) -> (42/23,11/6) Hyperbolic Matrix(1879,2720,248,359) (-42/29,-55/38) -> (15/2,38/5) Hyperbolic Matrix(3041,4400,1770,2561) (-55/38,-13/9) -> (67/39,55/32) Hyperbolic Matrix(279,400,-196,-281) (-13/9,-10/7) -> (-10/7,-27/19) Parabolic Matrix(1239,1760,478,679) (-27/19,-44/31) -> (44/17,13/5) Hyperbolic Matrix(3439,4880,2198,3119) (-44/31,-61/43) -> (61/39,36/23) Hyperbolic Matrix(28199,40000,8318,11799) (-61/43,-200/141) -> (200/59,139/41) Hyperbolic Matrix(28201,40000,8320,11801) (-200/141,-139/98) -> (61/18,200/59) Hyperbolic Matrix(961,1360,566,801) (-17/12,-41/29) -> (39/23,17/10) Hyperbolic Matrix(2039,2880,594,839) (-65/46,-24/17) -> (24/7,55/16) Hyperbolic Matrix(2041,2880,596,841) (-24/17,-55/39) -> (65/19,24/7) Hyperbolic Matrix(1759,2480,-1476,-2081) (-55/39,-31/22) -> (-31/26,-25/21) Hyperbolic Matrix(1079,1520,482,679) (-31/22,-38/27) -> (38/17,9/4) Hyperbolic Matrix(6199,8720,-4522,-6361) (-38/27,-45/32) -> (-85/62,-122/89) Hyperbolic Matrix(1721,2400,1062,1481) (-7/5,-39/28) -> (81/50,47/29) Hyperbolic Matrix(1839,2560,1436,1999) (-39/28,-32/23) -> (32/25,41/32) Hyperbolic Matrix(921,1280,490,681) (-57/41,-25/18) -> (15/8,17/9) Hyperbolic Matrix(4841,6720,894,1241) (-25/18,-93/67) -> (27/5,65/12) Hyperbolic Matrix(2481,3440,520,721) (-43/31,-61/44) -> (19/4,43/9) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(1159,1600,318,439) (-29/21,-40/29) -> (40/11,11/3) Hyperbolic Matrix(1161,1600,320,441) (-40/29,-11/8) -> (29/8,40/11) Hyperbolic Matrix(2039,2800,844,1159) (-11/8,-59/43) -> (99/41,29/12) Hyperbolic Matrix(42079,57680,-32450,-44481) (-122/89,-159/116) -> (-319/246,-118/91) Hyperbolic Matrix(759,1040,262,359) (-37/27,-63/46) -> (23/8,3/1) Hyperbolic Matrix(18719,25600,5030,6879) (-93/68,-160/117) -> (160/43,67/18) Hyperbolic Matrix(18721,25600,5032,6881) (-160/117,-67/49) -> (93/25,160/43) Hyperbolic Matrix(3921,5360,-3218,-4399) (-67/49,-41/30) -> (-39/32,-67/55) Hyperbolic Matrix(2519,3440,1786,2439) (-56/41,-15/11) -> (55/39,24/17) Hyperbolic Matrix(999,1360,440,599) (-15/11,-34/25) -> (34/15,25/11) Hyperbolic Matrix(119,160,-90,-121) (-19/14,-4/3) -> (-4/3,-21/16) Parabolic Matrix(4879,6400,1158,1519) (-21/16,-80/61) -> (80/19,59/14) Hyperbolic Matrix(4881,6400,1160,1521) (-80/61,-59/45) -> (21/5,80/19) Hyperbolic Matrix(3481,4560,642,841) (-38/29,-55/42) -> (65/12,38/7) Hyperbolic Matrix(919,1200,520,679) (-17/13,-30/23) -> (30/17,23/13) Hyperbolic Matrix(1841,2400,1044,1361) (-30/23,-43/33) -> (37/21,30/17) Hyperbolic Matrix(799,1040,368,479) (-43/33,-13/10) -> (13/6,37/17) Hyperbolic Matrix(801,1040,124,161) (-13/10,-48/37) -> (32/5,13/2) Hyperbolic Matrix(208519,270400,47718,61879) (-201/155,-520/401) -> (520/119,319/73) Hyperbolic Matrix(208521,270400,47720,61881) (-520/401,-319/246) -> (201/46,520/119) Hyperbolic Matrix(1239,1600,278,359) (-31/24,-40/31) -> (40/9,9/2) Hyperbolic Matrix(1241,1600,280,361) (-40/31,-9/7) -> (31/7,40/9) Hyperbolic Matrix(1559,2000,654,839) (-9/7,-41/32) -> (81/34,31/13) Hyperbolic Matrix(1999,2560,1436,1839) (-41/32,-32/25) -> (32/23,39/28) Hyperbolic Matrix(1001,1280,470,601) (-55/43,-23/18) -> (17/8,15/7) Hyperbolic Matrix(439,560,156,199) (-23/18,-14/11) -> (14/5,17/6) Hyperbolic Matrix(5039,6400,1070,1359) (-47/37,-80/63) -> (80/17,33/7) Hyperbolic Matrix(5041,6400,1072,1361) (-80/63,-33/26) -> (47/10,80/17) Hyperbolic Matrix(2081,2640,1262,1601) (-33/26,-52/41) -> (28/17,33/20) Hyperbolic Matrix(3281,4160,1452,1841) (-52/41,-71/56) -> (9/4,52/23) Hyperbolic Matrix(1199,1520,1072,1359) (-71/56,-19/15) -> (19/17,9/8) Hyperbolic Matrix(2719,3440,758,959) (-19/15,-43/34) -> (43/12,61/17) Hyperbolic Matrix(1519,1920,822,1039) (-43/34,-24/19) -> (24/13,37/20) Hyperbolic Matrix(1841,2320,1080,1361) (-29/23,-5/4) -> (75/44,29/17) Hyperbolic Matrix(841,1040,486,601) (-5/4,-21/17) -> (19/11,45/26) Hyperbolic Matrix(519,640,356,439) (-21/17,-16/13) -> (16/11,19/13) Hyperbolic Matrix(5479,6720,1532,1879) (-27/22,-65/53) -> (25/7,93/26) Hyperbolic Matrix(3719,4560,880,1079) (-65/53,-38/31) -> (38/9,55/13) Hyperbolic Matrix(1241,1520,556,681) (-38/31,-11/9) -> (29/13,38/17) Hyperbolic Matrix(921,1120,560,681) (-28/23,-17/14) -> (23/14,28/17) Hyperbolic Matrix(1319,1600,230,279) (-17/14,-40/33) -> (40/7,23/4) Hyperbolic Matrix(1321,1600,232,281) (-40/33,-23/19) -> (17/3,40/7) Hyperbolic Matrix(1681,2000,606,721) (-25/21,-19/16) -> (61/22,25/9) Hyperbolic Matrix(4721,5600,2766,3281) (-19/16,-51/43) -> (29/17,99/58) Hyperbolic Matrix(879,1040,202,239) (-32/27,-13/11) -> (13/3,48/11) Hyperbolic Matrix(679,800,-578,-681) (-13/11,-20/17) -> (-20/17,-27/23) Parabolic Matrix(5519,6400,758,879) (-29/25,-80/69) -> (80/11,51/7) Hyperbolic Matrix(5521,6400,760,881) (-80/69,-51/44) -> (29/4,80/11) Hyperbolic Matrix(1039,1200,484,559) (-37/32,-15/13) -> (15/7,43/20) Hyperbolic Matrix(2361,2720,730,841) (-15/13,-38/33) -> (42/13,55/17) Hyperbolic Matrix(279,320,34,39) (-23/20,-8/7) -> (8/1,17/2) Hyperbolic Matrix(281,320,36,41) (-8/7,-17/15) -> (23/3,8/1) Hyperbolic Matrix(1359,1520,1072,1199) (-9/8,-19/17) -> (19/15,71/56) Hyperbolic Matrix(2081,2320,862,961) (-19/17,-10/9) -> (70/29,99/41) Hyperbolic Matrix(439,480,182,199) (-10/9,-1/1) -> (41/17,70/29) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(1839,-2080,496,-561) (9/8,17/15) -> (63/17,89/24) Hyperbolic Matrix(1321,-1520,312,-359) (23/20,15/13) -> (55/13,17/4) Hyperbolic Matrix(761,-880,518,-599) (15/13,22/19) -> (22/15,25/17) Hyperbolic Matrix(1241,-1440,792,-919) (22/19,7/6) -> (47/30,58/37) Hyperbolic Matrix(1159,-1360,444,-521) (7/6,20/17) -> (60/23,47/18) Hyperbolic Matrix(881,-1040,338,-399) (20/17,13/11) -> (13/5,60/23) Hyperbolic Matrix(2361,-2800,640,-759) (32/27,19/16) -> (59/16,48/13) Hyperbolic Matrix(2079,-2480,1208,-1441) (25/21,6/5) -> (74/43,105/61) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(721,-880,458,-559) (28/23,11/9) -> (11/7,52/33) Hyperbolic Matrix(521,-640,162,-199) (11/9,16/13) -> (16/5,29/9) Hyperbolic Matrix(761,-960,348,-439) (5/4,24/19) -> (24/11,35/16) Hyperbolic Matrix(881,-1120,188,-239) (33/26,14/11) -> (14/3,47/10) Hyperbolic Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(681,-880,154,-199) (9/7,22/17) -> (22/5,31/7) Hyperbolic Matrix(679,-880,402,-521) (22/17,13/10) -> (27/16,22/13) Hyperbolic Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(1359,-1840,178,-241) (23/17,42/31) -> (38/5,23/3) Hyperbolic Matrix(2361,-3200,560,-759) (42/31,19/14) -> (59/14,38/9) Hyperbolic Matrix(1001,-1360,382,-519) (19/14,15/11) -> (55/21,21/8) Hyperbolic Matrix(2401,-3280,702,-959) (15/11,41/30) -> (41/12,65/19) Hyperbolic Matrix(2399,-3280,1288,-1761) (41/30,67/49) -> (13/7,41/22) Hyperbolic Matrix(3041,-4160,818,-1119) (67/49,26/19) -> (26/7,93/25) Hyperbolic Matrix(1519,-2080,176,-241) (26/19,63/46) -> (17/2,26/3) Hyperbolic Matrix(4201,-5760,962,-1319) (37/27,48/35) -> (48/11,83/19) Hyperbolic Matrix(2041,-2800,320,-439) (48/35,11/8) -> (51/8,32/5) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(2479,-3440,1442,-2001) (43/31,25/18) -> (55/32,43/25) Hyperbolic Matrix(1841,-2560,402,-559) (25/18,32/23) -> (32/7,55/12) Hyperbolic Matrix(1081,-1520,426,-599) (7/5,38/27) -> (38/15,33/13) Hyperbolic Matrix(3519,-4960,2044,-2881) (31/22,55/39) -> (105/61,31/18) Hyperbolic Matrix(2321,-3280,622,-879) (24/17,41/29) -> (41/11,56/15) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(1001,-1440,472,-679) (23/16,59/41) -> (19/9,17/8) Hyperbolic Matrix(441,-640,82,-119) (13/9,16/11) -> (16/3,27/5) Hyperbolic Matrix(521,-800,338,-519) (3/2,20/13) -> (20/13,37/24) Parabolic Matrix(1079,-1680,386,-601) (14/9,53/34) -> (67/24,14/5) Hyperbolic Matrix(1481,-2320,842,-1319) (36/23,47/30) -> (7/4,44/25) Hyperbolic Matrix(2041,-3200,280,-439) (58/37,11/7) -> (51/7,22/3) Hyperbolic Matrix(2081,-3280,1116,-1759) (52/33,41/26) -> (41/22,28/15) Hyperbolic Matrix(2839,-4480,1192,-1881) (41/26,30/19) -> (50/21,81/34) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(4841,-7840,2000,-3239) (34/21,81/50) -> (121/50,46/19) Hyperbolic Matrix(839,-1360,124,-201) (47/29,13/8) -> (27/4,7/1) Hyperbolic Matrix(5841,-9520,2110,-3439) (44/27,119/73) -> (119/43,36/13) Hyperbolic Matrix(881,-1440,342,-559) (31/19,18/11) -> (18/7,49/19) Hyperbolic Matrix(921,-1520,266,-439) (33/20,5/3) -> (45/13,7/2) Hyperbolic Matrix(1759,-2960,476,-801) (5/3,32/19) -> (48/13,85/23) Hyperbolic Matrix(2161,-3680,892,-1519) (17/10,46/27) -> (46/19,63/26) Hyperbolic Matrix(4601,-7840,1760,-2999) (46/27,75/44) -> (115/44,34/13) Hyperbolic Matrix(841,-1440,490,-839) (53/31,12/7) -> (12/7,67/39) Parabolic Matrix(6881,-11840,2882,-4959) (43/25,74/43) -> (74/31,117/49) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(1201,-2080,138,-239) (71/41,26/15) -> (26/3,9/1) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(4999,-8800,1932,-3401) (44/25,37/21) -> (163/63,44/17) Hyperbolic Matrix(2279,-4080,1006,-1801) (34/19,43/24) -> (77/34,34/15) Hyperbolic Matrix(441,-800,242,-439) (9/5,20/11) -> (20/11,31/17) Parabolic Matrix(521,-960,108,-199) (11/6,24/13) -> (24/5,29/6) Hyperbolic Matrix(719,-1360,212,-401) (17/9,2/1) -> (78/23,17/5) Hyperbolic Matrix(841,-1760,248,-519) (2/1,19/9) -> (139/41,78/23) Hyperbolic Matrix(1039,-2240,186,-401) (28/13,13/6) -> (67/12,28/5) Hyperbolic Matrix(361,-800,162,-359) (11/5,20/9) -> (20/9,29/13) Parabolic Matrix(1001,-2320,362,-839) (37/16,7/3) -> (47/17,83/30) Hyperbolic Matrix(1759,-4160,474,-1121) (26/11,71/30) -> (89/24,26/7) Hyperbolic Matrix(1039,-2480,168,-401) (31/13,74/31) -> (6/1,31/5) Hyperbolic Matrix(1439,-3440,402,-961) (43/18,12/5) -> (68/19,43/12) Hyperbolic Matrix(1961,-4720,548,-1319) (12/5,53/22) -> (93/26,68/19) Hyperbolic Matrix(359,-880,82,-201) (22/9,5/2) -> (35/8,22/5) Hyperbolic Matrix(761,-1920,174,-439) (5/2,38/15) -> (118/27,35/8) Hyperbolic Matrix(16481,-42640,3772,-9759) (119/46,163/63) -> (83/19,201/46) Hyperbolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(321,-880,58,-159) (41/15,11/4) -> (11/2,39/7) Hyperbolic Matrix(521,-1440,72,-199) (11/4,47/17) -> (7/1,29/4) Hyperbolic Matrix(6361,-17600,1720,-4759) (83/30,119/43) -> (159/43,37/10) Hyperbolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(281,-880,38,-119) (3/1,22/7) -> (22/3,37/5) Hyperbolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(721,-2480,116,-399) (55/16,31/9) -> (31/5,25/4) Hyperbolic Matrix(2521,-8720,682,-2359) (38/11,45/13) -> (85/23,122/33) Hyperbolic Matrix(15601,-57680,3570,-13199) (122/33,159/43) -> (319/73,118/27) Hyperbolic Matrix(1439,-5360,258,-961) (67/18,41/11) -> (39/7,67/12) Hyperbolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(121,-800,18,-119) (13/2,20/3) -> (20/3,27/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,480,24,281) -> Matrix(3,2,-8,-5) Matrix(239,2320,140,1359) -> Matrix(1,0,0,1) Matrix(161,1520,34,321) -> Matrix(1,0,0,1) Matrix(241,2080,-176,-1519) -> Matrix(1,0,0,1) Matrix(39,320,34,279) -> Matrix(3,4,-4,-5) Matrix(41,320,36,281) -> Matrix(5,4,-4,-3) Matrix(199,1520,-152,-1161) -> Matrix(5,4,-4,-3) Matrix(119,880,-38,-281) -> Matrix(3,2,-8,-5) Matrix(199,1440,-72,-521) -> Matrix(3,2,-8,-5) Matrix(201,1360,-124,-839) -> Matrix(7,4,-16,-9) Matrix(159,1040,-98,-641) -> Matrix(5,2,-8,-3) Matrix(199,1280,118,759) -> Matrix(1,0,0,1) Matrix(439,2800,-320,-2041) -> Matrix(1,0,4,1) Matrix(319,2000,204,1279) -> Matrix(1,0,-4,1) Matrix(401,2480,-168,-1039) -> Matrix(1,0,-4,1) Matrix(41,240,-34,-199) -> Matrix(1,0,0,1) Matrix(199,1120,78,439) -> Matrix(5,4,-4,-3) Matrix(159,880,-58,-321) -> Matrix(3,2,-8,-5) Matrix(119,640,-82,-441) -> Matrix(3,2,4,3) Matrix(121,640,38,201) -> Matrix(3,2,4,3) Matrix(199,1040,84,439) -> Matrix(3,2,16,11) Matrix(199,960,-108,-521) -> Matrix(1,0,4,1) Matrix(401,1920,184,881) -> Matrix(1,0,0,1) Matrix(721,3440,520,2481) -> Matrix(1,0,0,1) Matrix(321,1520,34,161) -> Matrix(1,0,0,1) Matrix(879,4160,490,2319) -> Matrix(1,0,0,1) Matrix(559,2640,220,1039) -> Matrix(1,0,0,1) Matrix(239,1120,-188,-881) -> Matrix(1,0,0,1) Matrix(121,560,78,361) -> Matrix(3,2,-8,-5) Matrix(559,2560,-402,-1841) -> Matrix(1,0,0,1) Matrix(561,2560,158,721) -> Matrix(1,0,0,1) Matrix(721,3280,264,1201) -> Matrix(3,2,4,3) Matrix(199,880,-154,-681) -> Matrix(5,4,-4,-3) Matrix(201,880,-82,-359) -> Matrix(3,2,-8,-5) Matrix(241,1040,130,561) -> Matrix(3,2,-8,-5) Matrix(559,2400,242,1039) -> Matrix(7,4,-16,-9) Matrix(281,1200,122,521) -> Matrix(1,0,0,1) Matrix(39,160,-10,-41) -> Matrix(3,2,-8,-5) Matrix(481,1840,-418,-1599) -> Matrix(7,2,-4,-1) Matrix(839,3200,-640,-2441) -> Matrix(7,2,-4,-1) Matrix(359,1360,-222,-841) -> Matrix(1,0,0,1) Matrix(879,3280,-622,-2321) -> Matrix(7,2,-4,-1) Matrix(881,3280,-408,-1519) -> Matrix(1,0,0,1) Matrix(1119,4160,-818,-3041) -> Matrix(1,0,4,1) Matrix(561,2080,-496,-1839) -> Matrix(1,0,0,1) Matrix(799,2960,518,1919) -> Matrix(7,4,-16,-9) Matrix(1559,5760,-1202,-4441) -> Matrix(7,2,-4,-1) Matrix(759,2800,-640,-2361) -> Matrix(1,0,4,1) Matrix(199,720,-144,-521) -> Matrix(1,0,0,1) Matrix(601,2160,234,841) -> Matrix(1,0,0,1) Matrix(959,3440,758,2719) -> Matrix(1,0,0,1) Matrix(961,3440,-402,-1439) -> Matrix(1,0,-4,1) Matrix(719,2560,-562,-2001) -> Matrix(1,0,0,1) Matrix(721,2560,158,561) -> Matrix(1,0,0,1) Matrix(679,2400,260,919) -> Matrix(3,2,-8,-5) Matrix(439,1520,-266,-921) -> Matrix(1,0,0,1) Matrix(719,2480,394,1359) -> Matrix(3,2,-8,-5) Matrix(1441,4960,-604,-2079) -> Matrix(1,0,-4,1) Matrix(1001,3440,268,921) -> Matrix(1,2,0,1) Matrix(959,3280,-702,-2401) -> Matrix(3,2,4,3) Matrix(399,1360,164,559) -> Matrix(3,2,4,3) Matrix(119,400,-36,-121) -> Matrix(7,4,-16,-9) Matrix(439,1440,-232,-761) -> Matrix(5,2,32,13) Matrix(1319,4320,476,1559) -> Matrix(5,2,-8,-3) Matrix(319,1040,196,639) -> Matrix(5,2,-8,-3) Matrix(199,640,-162,-521) -> Matrix(7,2,-4,-1) Matrix(201,640,38,121) -> Matrix(7,2,-4,-1) Matrix(559,1760,330,1039) -> Matrix(1,0,0,1) Matrix(359,1120,192,599) -> Matrix(1,0,0,1) Matrix(279,800,-98,-281) -> Matrix(11,6,-24,-13) Matrix(1041,2960,760,2161) -> Matrix(9,4,-16,-7) Matrix(199,560,156,439) -> Matrix(5,2,-8,-3) Matrix(601,1680,-386,-1079) -> Matrix(11,4,8,3) Matrix(1521,4240,890,2481) -> Matrix(13,4,-36,-11) Matrix(719,2000,316,879) -> Matrix(7,2,-4,-1) Matrix(721,2000,606,1681) -> Matrix(1,0,4,1) Matrix(1761,4880,520,1441) -> Matrix(1,-2,0,1) Matrix(839,2320,-362,-1001) -> Matrix(1,0,4,1) Matrix(1159,3200,-1000,-2761) -> Matrix(7,2,-4,-1) Matrix(1199,3280,-556,-1521) -> Matrix(1,0,0,1) Matrix(1641,4480,-952,-2599) -> Matrix(7,2,24,7) Matrix(559,1520,-324,-881) -> Matrix(1,0,8,1) Matrix(119,320,74,199) -> Matrix(1,0,4,1) Matrix(121,320,76,201) -> Matrix(1,0,-4,1) Matrix(519,1360,-382,-1001) -> Matrix(1,0,0,1) Matrix(2999,7840,-1760,-4601) -> Matrix(1,0,0,1) Matrix(919,2400,260,679) -> Matrix(1,-2,0,1) Matrix(521,1360,-444,-1159) -> Matrix(1,-4,0,1) Matrix(401,1040,278,721) -> Matrix(3,2,-8,-5) Matrix(3679,9520,-2350,-6081) -> Matrix(1,2,0,1) Matrix(6959,18000,2876,7439) -> Matrix(3,2,4,3) Matrix(2599,6720,1098,2839) -> Matrix(1,0,8,1) Matrix(559,1440,-342,-881) -> Matrix(1,0,0,1) Matrix(841,2160,234,601) -> Matrix(1,0,0,1) Matrix(4679,12000,1918,4919) -> Matrix(1,0,0,1) Matrix(3121,8000,1280,3281) -> Matrix(1,2,0,1) Matrix(719,1840,406,1039) -> Matrix(1,0,0,1) Matrix(439,1120,78,199) -> Matrix(5,4,-4,-3) Matrix(1039,2640,220,559) -> Matrix(1,0,0,1) Matrix(599,1520,-426,-1081) -> Matrix(1,0,0,1) Matrix(1201,2960,-876,-2159) -> Matrix(1,0,4,1) Matrix(521,1280,440,1081) -> Matrix(1,0,0,1) Matrix(721,1760,492,1201) -> Matrix(1,0,0,1) Matrix(4919,12000,1918,4679) -> Matrix(1,0,0,1) Matrix(3281,8000,1280,3121) -> Matrix(5,2,-8,-3) Matrix(559,1360,164,399) -> Matrix(7,2,-4,-1) Matrix(1519,3680,-892,-2161) -> Matrix(1,0,4,1) Matrix(3239,7840,-2000,-4841) -> Matrix(1,0,0,1) Matrix(959,2320,198,479) -> Matrix(1,0,4,1) Matrix(2319,5600,364,879) -> Matrix(1,0,4,1) Matrix(961,2320,862,2081) -> Matrix(1,0,0,1) Matrix(199,480,182,439) -> Matrix(5,2,-8,-3) Matrix(1759,4240,1128,2719) -> Matrix(11,4,-36,-13) Matrix(599,1440,-250,-601) -> Matrix(7,2,-32,-9) Matrix(1839,4400,568,1359) -> Matrix(11,2,16,3) Matrix(4959,11840,-2882,-6881) -> Matrix(1,0,8,1) Matrix(639,1520,-404,-961) -> Matrix(1,0,8,1) Matrix(439,1040,84,199) -> Matrix(15,2,-8,-1) Matrix(2839,6720,1098,2599) -> Matrix(1,0,8,1) Matrix(879,2080,-778,-1841) -> Matrix(1,0,8,1) Matrix(441,1040,-254,-599) -> Matrix(1,0,20,1) Matrix(3801,8800,-2332,-5399) -> Matrix(3,-2,-4,3) Matrix(1039,2400,242,559) -> Matrix(1,-4,0,1) Matrix(521,1200,122,281) -> Matrix(1,0,0,1) Matrix(801,1840,488,1121) -> Matrix(1,0,0,1) Matrix(559,1280,314,719) -> Matrix(1,0,0,1) Matrix(561,1280,316,721) -> Matrix(1,0,0,1) Matrix(879,2000,316,719) -> Matrix(3,2,4,3) Matrix(1199,2720,458,1039) -> Matrix(1,0,0,1) Matrix(1801,4080,-1006,-2279) -> Matrix(1,0,4,1) Matrix(1521,3440,814,1841) -> Matrix(1,0,-4,1) Matrix(1841,4160,1452,3281) -> Matrix(1,0,0,1) Matrix(359,800,-162,-361) -> Matrix(3,2,-8,-5) Matrix(1121,2480,796,1761) -> Matrix(5,2,-8,-3) Matrix(761,1680,236,521) -> Matrix(1,0,4,1) Matrix(439,960,-348,-761) -> Matrix(1,0,4,1) Matrix(881,1920,184,401) -> Matrix(1,0,0,1) Matrix(479,1040,368,799) -> Matrix(5,2,-8,-3) Matrix(1599,3440,892,1919) -> Matrix(1,0,4,1) Matrix(521,1120,354,761) -> Matrix(1,0,0,1) Matrix(599,1280,168,359) -> Matrix(1,0,4,1) Matrix(641,1360,-452,-959) -> Matrix(15,2,-8,-1) Matrix(919,1760,-648,-1241) -> Matrix(15,2,-8,-1) Matrix(679,1280,148,279) -> Matrix(1,0,-4,1) Matrix(641,1200,86,161) -> Matrix(1,-2,0,1) Matrix(1841,3440,814,1521) -> Matrix(1,0,-4,1) Matrix(1201,2240,-986,-1839) -> Matrix(1,-2,0,1) Matrix(561,1040,130,241) -> Matrix(1,-2,0,1) Matrix(1039,1920,822,1519) -> Matrix(1,0,0,1) Matrix(1001,1840,414,761) -> Matrix(1,0,0,1) Matrix(439,800,-242,-441) -> Matrix(1,-2,0,1) Matrix(839,1520,154,279) -> Matrix(1,0,0,1) Matrix(841,1520,244,441) -> Matrix(1,0,0,1) Matrix(2319,4160,490,879) -> Matrix(1,0,0,1) Matrix(1919,3440,892,1599) -> Matrix(1,0,4,1) Matrix(8039,14400,3550,6359) -> Matrix(1,0,12,1) Matrix(8041,14400,3552,6361) -> Matrix(1,0,-12,1) Matrix(761,1360,202,361) -> Matrix(1,0,0,1) Matrix(1121,2000,718,1281) -> Matrix(1,2,-4,-7) Matrix(719,1280,314,559) -> Matrix(1,0,0,1) Matrix(721,1280,316,561) -> Matrix(1,0,0,1) Matrix(1039,1840,406,719) -> Matrix(1,0,0,1) Matrix(679,1200,520,919) -> Matrix(1,0,0,1) Matrix(1361,2400,1044,1841) -> Matrix(9,4,-16,-7) Matrix(1319,2320,-842,-1481) -> Matrix(1,0,4,1) Matrix(919,1600,390,679) -> Matrix(1,0,28,1) Matrix(921,1600,392,681) -> Matrix(1,0,-28,1) Matrix(2401,4160,-1754,-3039) -> Matrix(1,0,-8,1) Matrix(3881,6720,2380,4121) -> Matrix(1,0,-8,1) Matrix(601,1040,486,841) -> Matrix(11,-2,-16,3) Matrix(1161,2000,256,441) -> Matrix(1,0,-4,1) Matrix(1441,2480,-1208,-2079) -> Matrix(1,0,-4,1) Matrix(14879,25600,6230,10719) -> Matrix(1,0,0,1) Matrix(14881,25600,6232,10721) -> Matrix(1,0,0,1) Matrix(2001,3440,-1442,-2479) -> Matrix(1,0,-4,1) Matrix(2759,4720,-1988,-3401) -> Matrix(3,-2,-4,3) Matrix(2481,4240,890,1521) -> Matrix(3,-4,4,-5) Matrix(281,480,24,41) -> Matrix(1,-2,0,1) Matrix(1359,2320,140,239) -> Matrix(1,0,0,1) Matrix(1641,2800,446,761) -> Matrix(1,0,0,1) Matrix(1079,1840,492,839) -> Matrix(1,0,0,1) Matrix(10561,18000,6478,11041) -> Matrix(3,-2,-4,3) Matrix(3759,6400,1550,2639) -> Matrix(1,0,0,1) Matrix(3761,6400,1552,2641) -> Matrix(1,0,0,1) Matrix(801,1360,566,961) -> Matrix(3,-2,-4,3) Matrix(4719,8000,2878,4879) -> Matrix(1,-2,0,1) Matrix(7081,12000,4320,7321) -> Matrix(1,0,0,1) Matrix(1039,1760,330,559) -> Matrix(1,0,0,1) Matrix(521,880,-402,-679) -> Matrix(1,-2,0,1) Matrix(1159,1920,-894,-1481) -> Matrix(1,0,0,1) Matrix(1601,2640,1262,2081) -> Matrix(1,0,0,1) Matrix(681,1120,560,921) -> Matrix(3,4,-4,-5) Matrix(1121,1840,488,801) -> Matrix(1,0,0,1) Matrix(4879,8000,2878,4719) -> Matrix(3,2,-8,-5) Matrix(7321,12000,4320,7081) -> Matrix(1,0,0,1) Matrix(1319,2160,952,1559) -> Matrix(1,0,0,1) Matrix(3919,6400,1518,2479) -> Matrix(1,0,0,1) Matrix(3921,6400,1520,2481) -> Matrix(1,0,0,1) Matrix(4121,6720,2380,3881) -> Matrix(1,0,-8,1) Matrix(12121,19760,4638,7561) -> Matrix(1,2,-4,-7) Matrix(26159,42640,-20172,-32881) -> Matrix(9,8,-8,-7) Matrix(1081,1760,320,521) -> Matrix(1,-2,0,1) Matrix(1481,2400,1062,1721) -> Matrix(5,2,-8,-3) Matrix(12199,19760,4716,7639) -> Matrix(7,2,-4,-1) Matrix(1681,2720,940,1521) -> Matrix(1,0,0,1) Matrix(199,320,74,119) -> Matrix(1,0,4,1) Matrix(201,320,76,121) -> Matrix(1,0,-4,1) Matrix(2279,3600,-1444,-2281) -> Matrix(5,-2,8,-3) Matrix(2079,3280,1622,2559) -> Matrix(3,-2,-4,3) Matrix(559,880,-458,-721) -> Matrix(1,-2,0,1) Matrix(919,1440,-792,-1241) -> Matrix(1,-2,0,1) Matrix(11239,17600,-8200,-12841) -> Matrix(5,-4,4,-3) Matrix(2761,4320,1918,3001) -> Matrix(3,2,-8,-5) Matrix(1279,2000,204,319) -> Matrix(1,0,-4,1) Matrix(1281,2000,718,1121) -> Matrix(3,-2,-4,3) Matrix(2719,4240,1128,1759) -> Matrix(5,-4,4,-3) Matrix(9239,14400,3310,5159) -> Matrix(29,-28,28,-27) Matrix(9241,14400,3312,5161) -> Matrix(27,-28,28,-29) Matrix(361,560,78,121) -> Matrix(1,-2,0,1) Matrix(519,800,-338,-521) -> Matrix(1,-6,0,1) Matrix(681,1040,184,281) -> Matrix(1,2,0,1) Matrix(599,880,-518,-761) -> Matrix(1,-2,0,1) Matrix(1201,1760,492,721) -> Matrix(1,0,0,1) Matrix(439,640,356,519) -> Matrix(3,-2,-4,3) Matrix(1159,1680,634,919) -> Matrix(1,0,-4,1) Matrix(1879,2720,248,359) -> Matrix(1,-2,0,1) Matrix(3041,4400,1770,2561) -> Matrix(3,-2,-16,11) Matrix(279,400,-196,-281) -> Matrix(1,-4,0,1) Matrix(1239,1760,478,679) -> Matrix(1,2,0,1) Matrix(3439,4880,2198,3119) -> Matrix(1,2,0,1) Matrix(28199,40000,8318,11799) -> Matrix(71,144,-36,-73) Matrix(28201,40000,8320,11801) -> Matrix(73,144,-36,-71) Matrix(961,1360,566,801) -> Matrix(1,2,-4,-7) Matrix(2039,2880,594,839) -> Matrix(3,4,-4,-5) Matrix(2041,2880,596,841) -> Matrix(5,4,-4,-3) Matrix(1759,2480,-1476,-2081) -> Matrix(1,0,0,1) Matrix(1079,1520,482,679) -> Matrix(1,0,0,1) Matrix(6199,8720,-4522,-6361) -> Matrix(3,2,4,3) Matrix(1721,2400,1062,1481) -> Matrix(1,2,0,1) Matrix(1839,2560,1436,1999) -> Matrix(1,0,0,1) Matrix(921,1280,490,681) -> Matrix(1,0,-4,1) Matrix(4841,6720,894,1241) -> Matrix(1,0,0,1) Matrix(2481,3440,520,721) -> Matrix(1,0,0,1) Matrix(1559,2160,952,1319) -> Matrix(1,0,0,1) Matrix(1159,1600,318,439) -> Matrix(1,0,4,1) Matrix(1161,1600,320,441) -> Matrix(1,0,-4,1) Matrix(2039,2800,844,1159) -> Matrix(1,0,0,1) Matrix(42079,57680,-32450,-44481) -> Matrix(7,-6,-8,7) Matrix(759,1040,262,359) -> Matrix(1,-2,0,1) Matrix(18719,25600,5030,6879) -> Matrix(1,0,0,1) Matrix(18721,25600,5032,6881) -> Matrix(1,0,0,1) Matrix(3921,5360,-3218,-4399) -> Matrix(1,-2,0,1) Matrix(2519,3440,1786,2439) -> Matrix(1,-2,0,1) Matrix(999,1360,440,599) -> Matrix(1,0,0,1) Matrix(119,160,-90,-121) -> Matrix(1,-2,0,1) Matrix(4879,6400,1158,1519) -> Matrix(1,0,0,1) Matrix(4881,6400,1160,1521) -> Matrix(1,0,0,1) Matrix(3481,4560,642,841) -> Matrix(1,0,0,1) Matrix(919,1200,520,679) -> Matrix(1,0,0,1) Matrix(1841,2400,1044,1361) -> Matrix(1,4,0,1) Matrix(799,1040,368,479) -> Matrix(1,2,0,1) Matrix(801,1040,124,161) -> Matrix(1,2,0,1) Matrix(208519,270400,47718,61879) -> Matrix(35,36,-36,-37) Matrix(208521,270400,47720,61881) -> Matrix(37,36,-36,-35) Matrix(1239,1600,278,359) -> Matrix(3,4,-4,-5) Matrix(1241,1600,280,361) -> Matrix(5,4,-4,-3) Matrix(1559,2000,654,839) -> Matrix(1,0,4,1) Matrix(1999,2560,1436,1839) -> Matrix(1,0,0,1) Matrix(1001,1280,470,601) -> Matrix(1,0,4,1) Matrix(439,560,156,199) -> Matrix(1,2,0,1) Matrix(5039,6400,1070,1359) -> Matrix(1,0,0,1) Matrix(5041,6400,1072,1361) -> Matrix(1,0,0,1) Matrix(2081,2640,1262,1601) -> Matrix(1,0,0,1) Matrix(3281,4160,1452,1841) -> Matrix(1,0,0,1) Matrix(1199,1520,1072,1359) -> Matrix(1,0,0,1) Matrix(2719,3440,758,959) -> Matrix(1,0,0,1) Matrix(1519,1920,822,1039) -> Matrix(1,0,0,1) Matrix(1841,2320,1080,1361) -> Matrix(1,0,-4,1) Matrix(841,1040,486,601) -> Matrix(1,2,-8,-15) Matrix(519,640,356,439) -> Matrix(1,2,-4,-7) Matrix(5479,6720,1532,1879) -> Matrix(1,0,0,1) Matrix(3719,4560,880,1079) -> Matrix(1,0,0,1) Matrix(1241,1520,556,681) -> Matrix(1,0,0,1) Matrix(921,1120,560,681) -> Matrix(3,4,-4,-5) Matrix(1319,1600,230,279) -> Matrix(11,12,-12,-13) Matrix(1321,1600,232,281) -> Matrix(13,12,-12,-11) Matrix(1681,2000,606,721) -> Matrix(1,0,4,1) Matrix(4721,5600,2766,3281) -> Matrix(1,0,-4,1) Matrix(879,1040,202,239) -> Matrix(1,-2,0,1) Matrix(679,800,-578,-681) -> Matrix(1,-6,0,1) Matrix(5519,6400,758,879) -> Matrix(1,0,0,1) Matrix(5521,6400,760,881) -> Matrix(1,0,0,1) Matrix(1039,1200,484,559) -> Matrix(1,2,0,1) Matrix(2361,2720,730,841) -> Matrix(1,2,0,1) Matrix(279,320,34,39) -> Matrix(3,4,-4,-5) Matrix(281,320,36,41) -> Matrix(5,4,-4,-3) Matrix(1359,1520,1072,1199) -> Matrix(1,0,0,1) Matrix(2081,2320,862,961) -> Matrix(1,0,0,1) Matrix(439,480,182,199) -> Matrix(1,2,0,1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(1839,-2080,496,-561) -> Matrix(1,0,0,1) Matrix(1321,-1520,312,-359) -> Matrix(5,4,-4,-3) Matrix(761,-880,518,-599) -> Matrix(3,2,-8,-5) Matrix(1241,-1440,792,-919) -> Matrix(3,2,-8,-5) Matrix(1159,-1360,444,-521) -> Matrix(7,4,-16,-9) Matrix(881,-1040,338,-399) -> Matrix(5,2,-8,-3) Matrix(2361,-2800,640,-759) -> Matrix(1,0,4,1) Matrix(2079,-2480,1208,-1441) -> Matrix(1,0,-4,1) Matrix(199,-240,34,-41) -> Matrix(1,0,0,1) Matrix(721,-880,458,-559) -> Matrix(3,2,-8,-5) Matrix(521,-640,162,-199) -> Matrix(3,2,4,3) Matrix(761,-960,348,-439) -> Matrix(1,0,4,1) Matrix(881,-1120,188,-239) -> Matrix(1,0,0,1) Matrix(2001,-2560,562,-719) -> Matrix(1,0,0,1) Matrix(681,-880,154,-199) -> Matrix(5,4,-4,-3) Matrix(679,-880,402,-521) -> Matrix(3,2,-8,-5) Matrix(121,-160,90,-119) -> Matrix(3,2,-8,-5) Matrix(1359,-1840,178,-241) -> Matrix(7,2,-4,-1) Matrix(2361,-3200,560,-759) -> Matrix(7,2,-4,-1) Matrix(1001,-1360,382,-519) -> Matrix(1,0,0,1) Matrix(2401,-3280,702,-959) -> Matrix(7,2,-4,-1) Matrix(2399,-3280,1288,-1761) -> Matrix(1,0,0,1) Matrix(3041,-4160,818,-1119) -> Matrix(1,0,4,1) Matrix(1519,-2080,176,-241) -> Matrix(1,0,0,1) Matrix(4201,-5760,962,-1319) -> Matrix(7,2,-4,-1) Matrix(2041,-2800,320,-439) -> Matrix(1,0,4,1) Matrix(521,-720,144,-199) -> Matrix(1,0,0,1) Matrix(2479,-3440,1442,-2001) -> Matrix(1,0,-4,1) Matrix(1841,-2560,402,-559) -> Matrix(1,0,0,1) Matrix(1081,-1520,426,-599) -> Matrix(1,0,0,1) Matrix(3519,-4960,2044,-2881) -> Matrix(1,0,-4,1) Matrix(2321,-3280,622,-879) -> Matrix(3,2,4,3) Matrix(281,-400,196,-279) -> Matrix(7,4,-16,-9) Matrix(1001,-1440,472,-679) -> Matrix(5,2,32,13) Matrix(441,-640,82,-119) -> Matrix(7,2,-4,-1) Matrix(521,-800,338,-519) -> Matrix(11,6,-24,-13) Matrix(1079,-1680,386,-601) -> Matrix(11,4,8,3) Matrix(1481,-2320,842,-1319) -> Matrix(1,0,4,1) Matrix(2041,-3200,280,-439) -> Matrix(7,2,-4,-1) Matrix(2081,-3280,1116,-1759) -> Matrix(1,0,0,1) Matrix(2839,-4480,1192,-1881) -> Matrix(7,2,24,7) Matrix(961,-1520,404,-639) -> Matrix(1,0,8,1) Matrix(841,-1360,222,-359) -> Matrix(1,0,0,1) Matrix(4841,-7840,2000,-3239) -> Matrix(1,0,0,1) Matrix(839,-1360,124,-201) -> Matrix(1,-4,0,1) Matrix(5841,-9520,2110,-3439) -> Matrix(1,2,0,1) Matrix(881,-1440,342,-559) -> Matrix(1,0,0,1) Matrix(921,-1520,266,-439) -> Matrix(1,0,0,1) Matrix(1759,-2960,476,-801) -> Matrix(1,0,4,1) Matrix(2161,-3680,892,-1519) -> Matrix(1,0,4,1) Matrix(4601,-7840,1760,-2999) -> Matrix(1,0,0,1) Matrix(841,-1440,490,-839) -> Matrix(7,2,-32,-9) Matrix(6881,-11840,2882,-4959) -> Matrix(1,0,8,1) Matrix(881,-1520,324,-559) -> Matrix(1,0,8,1) Matrix(1201,-2080,138,-239) -> Matrix(1,0,8,1) Matrix(599,-1040,254,-441) -> Matrix(1,0,20,1) Matrix(4999,-8800,1932,-3401) -> Matrix(3,-2,-4,3) Matrix(2279,-4080,1006,-1801) -> Matrix(1,0,4,1) Matrix(441,-800,242,-439) -> Matrix(3,2,-8,-5) Matrix(521,-960,108,-199) -> Matrix(1,0,4,1) Matrix(719,-1360,212,-401) -> Matrix(15,2,-8,-1) Matrix(841,-1760,248,-519) -> Matrix(15,2,-8,-1) Matrix(1039,-2240,186,-401) -> Matrix(1,-2,0,1) Matrix(361,-800,162,-359) -> Matrix(1,-2,0,1) Matrix(1001,-2320,362,-839) -> Matrix(1,0,4,1) Matrix(1759,-4160,474,-1121) -> Matrix(1,0,-8,1) Matrix(1039,-2480,168,-401) -> Matrix(1,0,-4,1) Matrix(1439,-3440,402,-961) -> Matrix(1,0,-4,1) Matrix(1961,-4720,548,-1319) -> Matrix(3,-2,-4,3) Matrix(359,-880,82,-201) -> Matrix(1,-2,0,1) Matrix(761,-1920,174,-439) -> Matrix(1,0,0,1) Matrix(16481,-42640,3772,-9759) -> Matrix(9,8,-8,-7) Matrix(1321,-3600,484,-1319) -> Matrix(5,-2,8,-3) Matrix(321,-880,58,-159) -> Matrix(1,-2,0,1) Matrix(521,-1440,72,-199) -> Matrix(1,-2,0,1) Matrix(6361,-17600,1720,-4759) -> Matrix(5,-4,4,-3) Matrix(281,-800,98,-279) -> Matrix(1,-6,0,1) Matrix(281,-880,38,-119) -> Matrix(1,-2,0,1) Matrix(121,-400,36,-119) -> Matrix(1,-4,0,1) Matrix(721,-2480,116,-399) -> Matrix(1,0,0,1) Matrix(2521,-8720,682,-2359) -> Matrix(3,2,4,3) Matrix(15601,-57680,3570,-13199) -> Matrix(7,-6,-8,7) Matrix(1439,-5360,258,-961) -> Matrix(1,-2,0,1) Matrix(41,-160,10,-39) -> Matrix(1,-2,0,1) Matrix(121,-800,18,-119) -> Matrix(1,-6,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 Degree of the the map X: 96 Degree of the the map Y: 384 ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 20/17 5/4 4/3 10/7 20/13 30/19 8/5 5/3 12/7 20/11 2/1 20/9 40/17 12/5 80/33 100/41 5/2 28/11 100/39 80/31 8/3 30/11 36/13 20/7 3/1 16/5 10/3 44/13 200/59 24/7 18/5 40/11 4/1 9/2 32/7 14/3 80/17 24/5 5/1 16/3 28/5 40/7 6/1 32/5 20/3 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/2 1/0 1/1 -1/1 0/1 7/6 -2/3 -3/5 20/17 -1/2 13/11 -1/3 0/1 19/16 -1/7 0/1 25/21 1/0 6/5 -1/1 0/1 17/14 -1/1 -6/7 28/23 -3/4 11/9 -1/1 -2/3 5/4 -1/2 24/19 0/1 19/15 -1/3 0/1 52/41 1/0 33/26 -1/1 0/1 14/11 -1/1 0/1 23/18 -1/3 0/1 32/25 -1/2 1/0 41/32 -1/1 -4/5 9/7 -1/1 0/1 4/3 -1/2 11/8 -1/3 0/1 18/13 -1/1 0/1 25/18 -1/2 32/23 -1/2 1/0 39/28 -4/3 -1/1 7/5 -1/1 0/1 24/17 -1/1 41/29 -1/1 -4/5 17/12 -1/1 -2/3 10/7 -1/2 23/16 -3/7 -2/5 59/41 -2/5 -21/53 36/25 -3/8 13/9 -4/11 -1/3 3/2 -1/1 0/1 20/13 -1/2 17/11 -3/7 -2/5 14/9 -2/5 -1/3 25/16 -1/4 61/39 -1/11 0/1 36/23 -1/2 11/7 -1/3 0/1 52/33 -1/4 41/26 -2/5 -1/3 30/19 -1/4 19/12 -1/3 0/1 8/5 0/1 21/13 0/1 1/1 13/8 -2/1 -1/1 44/27 1/0 31/19 -1/1 0/1 18/11 -1/1 0/1 41/25 -1/1 0/1 23/14 -2/1 -1/1 28/17 -1/2 5/3 -1/2 22/13 -1/3 0/1 39/23 -2/5 -1/3 17/10 -1/3 0/1 46/27 -1/3 0/1 75/44 -1/4 29/17 -1/3 0/1 12/7 -1/4 31/18 -1/5 0/1 19/11 -1/7 0/1 45/26 -1/8 26/15 -1/11 0/1 7/4 0/1 1/3 16/9 -1/2 1/0 41/23 -1/1 0/1 25/14 -1/2 9/5 -1/1 0/1 20/11 -1/2 11/6 -1/3 0/1 24/13 0/1 13/7 -1/3 0/1 15/8 -1/4 17/9 -1/7 0/1 2/1 -1/1 0/1 19/9 0/1 1/17 17/8 0/1 1/5 15/7 1/2 28/13 1/2 13/6 0/1 1/1 11/5 0/1 1/1 20/9 1/0 9/4 -1/1 0/1 16/7 -1/2 1/0 39/17 -1/1 0/1 23/10 -1/1 -2/3 7/3 -1/5 0/1 40/17 0/1 33/14 0/1 1/23 26/11 0/1 1/9 19/8 0/1 1/5 50/21 1/4 81/34 4/13 1/3 31/13 0/1 1/3 12/5 1/2 29/12 0/1 1/1 75/31 1/2 46/19 0/1 1/1 63/26 0/1 1/1 80/33 1/2 1/0 17/7 0/1 1/1 39/16 1/1 2/1 100/41 1/0 61/25 0/1 1/1 22/9 0/1 1/1 5/2 1/0 33/13 -1/1 0/1 28/11 1/0 23/9 -1/1 -2/3 41/16 -1/1 0/1 100/39 -1/2 59/23 -1/3 0/1 18/7 -1/1 0/1 49/19 -1/1 0/1 80/31 -1/2 1/0 31/12 -1/1 0/1 44/17 -1/2 13/5 -1/1 -2/3 21/8 -1/3 0/1 8/3 0/1 19/7 0/1 1/1 49/18 0/1 1/3 30/11 1/2 71/26 2/3 1/1 41/15 1/1 2/1 11/4 0/1 1/1 36/13 1/0 61/22 0/1 1/9 25/9 1/2 39/14 2/3 1/1 14/5 1/1 2/1 17/6 2/1 3/1 20/7 1/0 3/1 -1/1 0/1 19/6 0/1 1/1 16/5 1/2 1/0 13/4 1/1 4/3 10/3 1/0 27/8 -3/1 -8/3 44/13 -5/2 61/18 -23/11 -2/1 200/59 -2/1 139/41 -2/1 -49/25 78/23 -2/1 -13/7 17/5 -2/1 -1/1 41/12 -4/3 -1/1 24/7 -1/1 55/16 -1/2 31/9 -1/1 0/1 7/2 -1/1 0/1 32/9 -1/2 1/0 57/16 -1/3 0/1 25/7 1/0 18/5 -1/1 0/1 29/8 -1/3 0/1 40/11 0/1 11/3 0/1 1/1 4/1 1/0 9/2 -1/1 0/1 41/9 -4/3 -1/1 32/7 -1/2 1/0 55/12 -1/2 23/5 0/1 1/1 14/3 -1/1 0/1 47/10 -1/1 0/1 80/17 -1/2 1/0 33/7 -1/1 0/1 52/11 -1/2 19/4 0/1 1/1 24/5 0/1 29/6 0/1 1/1 5/1 1/0 21/4 -2/1 -1/1 16/3 -3/2 1/0 11/2 -2/1 -1/1 39/7 -1/1 0/1 28/5 -3/2 17/3 -6/5 -1/1 40/7 -1/1 23/4 -1/1 -6/7 6/1 -1/1 0/1 25/4 -1/2 19/3 0/1 1/5 32/5 1/2 1/0 13/2 0/1 1/1 20/3 1/0 7/1 -3/1 -2/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(139,-160,53,-61) (1/1,7/6) -> (13/5,21/8) Hyperbolic Matrix(341,-400,289,-339) (7/6,20/17) -> (20/17,13/11) Parabolic Matrix(541,-640,388,-459) (13/11,19/16) -> (39/28,7/5) Hyperbolic Matrix(1681,-2000,1075,-1279) (19/16,25/21) -> (25/16,61/39) Hyperbolic Matrix(1341,-1600,787,-939) (25/21,6/5) -> (46/27,75/44) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(921,-1120,361,-439) (17/14,28/23) -> (28/11,23/9) Hyperbolic Matrix(721,-880,458,-559) (28/23,11/9) -> (11/7,52/33) Hyperbolic Matrix(261,-320,146,-179) (11/9,5/4) -> (25/14,9/5) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(1139,-1440,333,-421) (24/19,19/15) -> (41/12,24/7) Hyperbolic Matrix(2461,-3120,1561,-1979) (19/15,52/41) -> (52/33,41/26) Hyperbolic Matrix(2081,-2640,819,-1039) (52/41,33/26) -> (33/13,28/11) Hyperbolic Matrix(881,-1120,188,-239) (33/26,14/11) -> (14/3,47/10) Hyperbolic Matrix(439,-560,283,-361) (14/11,23/18) -> (17/11,14/9) Hyperbolic Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(1499,-1920,235,-301) (32/25,41/32) -> (19/3,32/5) Hyperbolic Matrix(2559,-3280,937,-1201) (41/32,9/7) -> (71/26,41/15) Hyperbolic Matrix(61,-80,45,-59) (9/7,4/3) -> (4/3,11/8) Parabolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(461,-640,273,-379) (18/13,25/18) -> (5/3,22/13) Hyperbolic Matrix(1841,-2560,402,-559) (25/18,32/23) -> (32/7,55/12) Hyperbolic Matrix(1839,-2560,403,-561) (32/23,39/28) -> (41/9,32/7) Hyperbolic Matrix(341,-480,184,-259) (7/5,24/17) -> (24/13,13/7) Hyperbolic Matrix(1019,-1440,213,-301) (24/17,41/29) -> (19/4,24/5) Hyperbolic Matrix(961,-1360,395,-559) (41/29,17/12) -> (17/7,39/16) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(1001,-1440,472,-679) (23/16,59/41) -> (19/9,17/8) Hyperbolic Matrix(3001,-4320,1083,-1559) (59/41,36/25) -> (36/13,61/22) Hyperbolic Matrix(721,-1040,443,-639) (36/25,13/9) -> (13/8,44/27) Hyperbolic Matrix(221,-320,96,-139) (13/9,3/2) -> (23/10,7/3) Hyperbolic Matrix(261,-400,169,-259) (3/2,20/13) -> (20/13,17/11) Parabolic Matrix(821,-1280,474,-739) (14/9,25/16) -> (45/26,26/15) Hyperbolic Matrix(3119,-4880,921,-1441) (61/39,36/23) -> (44/13,61/18) Hyperbolic Matrix(1021,-1600,395,-619) (36/23,11/7) -> (31/12,44/17) Hyperbolic Matrix(2839,-4480,1192,-1881) (41/26,30/19) -> (50/21,81/34) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(201,-320,125,-199) (19/12,8/5) -> (8/5,21/13) Parabolic Matrix(99,-160,13,-21) (21/13,13/8) -> (7/1,1/0) Hyperbolic Matrix(981,-1600,355,-579) (44/27,31/19) -> (11/4,36/13) Hyperbolic Matrix(881,-1440,342,-559) (31/19,18/11) -> (18/7,49/19) Hyperbolic Matrix(1221,-2000,500,-819) (18/11,41/25) -> (61/25,22/9) Hyperbolic Matrix(341,-560,109,-179) (41/25,23/14) -> (3/1,19/6) Hyperbolic Matrix(681,-1120,121,-199) (23/14,28/17) -> (28/5,17/3) Hyperbolic Matrix(339,-560,158,-261) (28/17,5/3) -> (15/7,28/13) Hyperbolic Matrix(1181,-2000,460,-779) (22/13,39/23) -> (59/23,18/7) Hyperbolic Matrix(801,-1360,235,-399) (39/23,17/10) -> (17/5,41/12) Hyperbolic Matrix(2161,-3680,892,-1519) (17/10,46/27) -> (46/19,63/26) Hyperbolic Matrix(1361,-2320,281,-479) (75/44,29/17) -> (29/6,5/1) Hyperbolic Matrix(421,-720,245,-419) (29/17,12/7) -> (12/7,31/18) Parabolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(601,-1040,115,-199) (19/11,45/26) -> (5/1,21/4) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(181,-320,56,-99) (7/4,16/9) -> (16/5,13/4) Hyperbolic Matrix(539,-960,169,-301) (16/9,41/23) -> (19/6,16/5) Hyperbolic Matrix(1121,-2000,403,-719) (41/23,25/14) -> (25/9,39/14) Hyperbolic Matrix(221,-400,121,-219) (9/5,20/11) -> (20/11,11/6) Parabolic Matrix(521,-960,108,-199) (11/6,24/13) -> (24/5,29/6) Hyperbolic Matrix(299,-560,118,-221) (13/7,15/8) -> (5/2,33/13) Hyperbolic Matrix(681,-1280,191,-359) (15/8,17/9) -> (57/16,25/7) Hyperbolic Matrix(719,-1360,212,-401) (17/9,2/1) -> (78/23,17/5) Hyperbolic Matrix(841,-1760,248,-519) (2/1,19/9) -> (139/41,78/23) Hyperbolic Matrix(601,-1280,131,-279) (17/8,15/7) -> (55/12,23/5) Hyperbolic Matrix(741,-1600,157,-339) (28/13,13/6) -> (33/7,52/11) Hyperbolic Matrix(221,-480,64,-139) (13/6,11/5) -> (31/9,7/2) Hyperbolic Matrix(181,-400,81,-179) (11/5,20/9) -> (20/9,9/4) Parabolic Matrix(141,-320,26,-59) (9/4,16/7) -> (16/3,11/2) Hyperbolic Matrix(419,-960,79,-181) (16/7,39/17) -> (21/4,16/3) Hyperbolic Matrix(801,-1840,313,-719) (39/17,23/10) -> (23/9,41/16) Hyperbolic Matrix(681,-1600,289,-679) (7/3,40/17) -> (40/17,33/14) Parabolic Matrix(541,-1280,194,-459) (26/11,19/8) -> (39/14,14/5) Hyperbolic Matrix(839,-2000,185,-441) (81/34,31/13) -> (9/2,41/9) Hyperbolic Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(1621,-3920,471,-1139) (29/12,75/31) -> (55/16,31/9) Hyperbolic Matrix(661,-1600,107,-259) (75/31,46/19) -> (6/1,25/4) Hyperbolic Matrix(2641,-6400,1089,-2639) (63/26,80/33) -> (80/33,17/7) Parabolic Matrix(4101,-10000,1681,-4099) (39/16,100/41) -> (100/41,61/25) Parabolic Matrix(261,-640,73,-179) (22/9,5/2) -> (25/7,18/5) Hyperbolic Matrix(3901,-10000,1521,-3899) (41/16,100/39) -> (100/39,59/23) Parabolic Matrix(2481,-6400,961,-2479) (49/19,80/31) -> (80/31,31/12) Parabolic Matrix(679,-1760,201,-521) (44/17,13/5) -> (27/8,44/13) Hyperbolic Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(321,-880,58,-159) (41/15,11/4) -> (11/2,39/7) Hyperbolic Matrix(721,-2000,115,-319) (61/22,25/9) -> (25/4,19/3) Hyperbolic Matrix(199,-560,43,-121) (14/5,17/6) -> (23/5,14/3) Hyperbolic Matrix(141,-400,49,-139) (17/6,20/7) -> (20/7,3/1) Parabolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(11801,-40000,3481,-11799) (61/18,200/59) -> (200/59,139/41) Parabolic Matrix(181,-640,28,-99) (7/2,32/9) -> (32/5,13/2) Hyperbolic Matrix(441,-1600,121,-439) (29/8,40/11) -> (40/11,11/3) Parabolic Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(1361,-6400,289,-1359) (47/10,80/17) -> (80/17,33/7) Parabolic Matrix(541,-2560,97,-459) (52/11,19/4) -> (39/7,28/5) Hyperbolic Matrix(281,-1600,49,-279) (17/3,40/7) -> (40/7,23/4) Parabolic Matrix(61,-400,9,-59) (13/2,20/3) -> (20/3,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,0,1) Matrix(139,-160,53,-61) -> Matrix(1,1,-4,-3) Matrix(341,-400,289,-339) -> Matrix(5,3,-12,-7) Matrix(541,-640,388,-459) -> Matrix(3,1,-4,-1) Matrix(1681,-2000,1075,-1279) -> Matrix(1,0,-4,1) Matrix(1341,-1600,787,-939) -> Matrix(1,1,-4,-3) Matrix(199,-240,34,-41) -> Matrix(1,0,0,1) Matrix(921,-1120,361,-439) -> Matrix(5,4,-4,-3) Matrix(721,-880,458,-559) -> Matrix(3,2,-8,-5) Matrix(261,-320,146,-179) -> Matrix(1,1,-4,-3) Matrix(1141,-1440,332,-419) -> Matrix(3,1,-4,-1) Matrix(1139,-1440,333,-421) -> Matrix(1,-1,0,1) Matrix(2461,-3120,1561,-1979) -> Matrix(1,1,-4,-3) Matrix(2081,-2640,819,-1039) -> Matrix(1,0,0,1) Matrix(881,-1120,188,-239) -> Matrix(1,0,0,1) Matrix(439,-560,283,-361) -> Matrix(3,2,-8,-5) Matrix(2001,-2560,562,-719) -> Matrix(1,0,0,1) Matrix(1499,-1920,235,-301) -> Matrix(1,1,0,1) Matrix(2559,-3280,937,-1201) -> Matrix(3,2,4,3) Matrix(61,-80,45,-59) -> Matrix(1,1,-4,-3) Matrix(521,-720,144,-199) -> Matrix(1,0,0,1) Matrix(461,-640,273,-379) -> Matrix(1,1,-4,-3) Matrix(1841,-2560,402,-559) -> Matrix(1,0,0,1) Matrix(1839,-2560,403,-561) -> Matrix(1,0,0,1) Matrix(341,-480,184,-259) -> Matrix(1,1,-4,-3) Matrix(1019,-1440,213,-301) -> Matrix(1,1,-4,-3) Matrix(961,-1360,395,-559) -> Matrix(3,2,4,3) Matrix(281,-400,196,-279) -> Matrix(7,4,-16,-9) Matrix(1001,-1440,472,-679) -> Matrix(5,2,32,13) Matrix(3001,-4320,1083,-1559) -> Matrix(5,2,-8,-3) Matrix(721,-1040,443,-639) -> Matrix(5,2,-8,-3) Matrix(221,-320,96,-139) -> Matrix(3,1,-4,-1) Matrix(261,-400,169,-259) -> Matrix(5,3,-12,-7) Matrix(821,-1280,474,-739) -> Matrix(3,1,-28,-9) Matrix(3119,-4880,921,-1441) -> Matrix(1,-2,0,1) Matrix(1021,-1600,395,-619) -> Matrix(3,1,-4,-1) Matrix(2839,-4480,1192,-1881) -> Matrix(7,2,24,7) Matrix(961,-1520,404,-639) -> Matrix(1,0,8,1) Matrix(201,-320,125,-199) -> Matrix(1,0,4,1) Matrix(99,-160,13,-21) -> Matrix(1,-1,0,1) Matrix(981,-1600,355,-579) -> Matrix(1,1,0,1) Matrix(881,-1440,342,-559) -> Matrix(1,0,0,1) Matrix(1221,-2000,500,-819) -> Matrix(1,1,0,1) Matrix(341,-560,109,-179) -> Matrix(1,1,0,1) Matrix(681,-1120,121,-199) -> Matrix(5,4,-4,-3) Matrix(339,-560,158,-261) -> Matrix(1,1,0,1) Matrix(1181,-2000,460,-779) -> Matrix(3,1,-4,-1) Matrix(801,-1360,235,-399) -> Matrix(7,2,-4,-1) Matrix(2161,-3680,892,-1519) -> Matrix(1,0,4,1) Matrix(1361,-2320,281,-479) -> Matrix(1,0,4,1) Matrix(421,-720,245,-419) -> Matrix(3,1,-16,-5) Matrix(881,-1520,324,-559) -> Matrix(1,0,8,1) Matrix(601,-1040,115,-199) -> Matrix(15,2,-8,-1) Matrix(599,-1040,254,-441) -> Matrix(1,0,20,1) Matrix(181,-320,56,-99) -> Matrix(1,1,0,1) Matrix(539,-960,169,-301) -> Matrix(1,1,0,1) Matrix(1121,-2000,403,-719) -> Matrix(3,2,4,3) Matrix(221,-400,121,-219) -> Matrix(1,1,-4,-3) Matrix(521,-960,108,-199) -> Matrix(1,0,4,1) Matrix(299,-560,118,-221) -> Matrix(3,1,-4,-1) Matrix(681,-1280,191,-359) -> Matrix(1,0,4,1) Matrix(719,-1360,212,-401) -> Matrix(15,2,-8,-1) Matrix(841,-1760,248,-519) -> Matrix(15,2,-8,-1) Matrix(601,-1280,131,-279) -> Matrix(1,0,-4,1) Matrix(741,-1600,157,-339) -> Matrix(1,-1,0,1) Matrix(221,-480,64,-139) -> Matrix(1,-1,0,1) Matrix(181,-400,81,-179) -> Matrix(1,-1,0,1) Matrix(141,-320,26,-59) -> Matrix(1,-1,0,1) Matrix(419,-960,79,-181) -> Matrix(1,-1,0,1) Matrix(801,-1840,313,-719) -> Matrix(1,0,0,1) Matrix(681,-1600,289,-679) -> Matrix(1,0,28,1) Matrix(541,-1280,194,-459) -> Matrix(7,-1,8,-1) Matrix(839,-2000,185,-441) -> Matrix(1,0,-4,1) Matrix(301,-720,125,-299) -> Matrix(3,-1,4,-1) Matrix(1621,-3920,471,-1139) -> Matrix(1,-1,0,1) Matrix(661,-1600,107,-259) -> Matrix(1,-1,0,1) Matrix(2641,-6400,1089,-2639) -> Matrix(1,0,0,1) Matrix(4101,-10000,1681,-4099) -> Matrix(1,-1,0,1) Matrix(261,-640,73,-179) -> Matrix(1,-1,0,1) Matrix(3901,-10000,1521,-3899) -> Matrix(1,1,-4,-3) Matrix(2481,-6400,961,-2479) -> Matrix(1,0,0,1) Matrix(679,-1760,201,-521) -> Matrix(1,-2,0,1) Matrix(121,-320,45,-119) -> Matrix(1,0,4,1) Matrix(1321,-3600,484,-1319) -> Matrix(5,-2,8,-3) Matrix(321,-880,58,-159) -> Matrix(1,-2,0,1) Matrix(721,-2000,115,-319) -> Matrix(1,0,-4,1) Matrix(199,-560,43,-121) -> Matrix(1,-2,0,1) Matrix(141,-400,49,-139) -> Matrix(1,-3,0,1) Matrix(121,-400,36,-119) -> Matrix(1,-4,0,1) Matrix(11801,-40000,3481,-11799) -> Matrix(71,144,-36,-73) Matrix(181,-640,28,-99) -> Matrix(1,1,0,1) Matrix(441,-1600,121,-439) -> Matrix(1,0,4,1) Matrix(21,-80,5,-19) -> Matrix(1,-1,0,1) Matrix(1361,-6400,289,-1359) -> Matrix(1,0,0,1) Matrix(541,-2560,97,-459) -> Matrix(1,-1,0,1) Matrix(281,-1600,49,-279) -> Matrix(11,12,-12,-13) Matrix(61,-400,9,-59) -> Matrix(1,-3,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of 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): 24 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 1 2/1 (-1/1,0/1) 0 20 17/8 (0/1,1/5) 0 40 15/7 1/2 1 8 13/6 (0/1,1/1) 0 40 11/5 (0/1,1/1) 0 40 20/9 1/0 2 2 9/4 (-1/1,0/1) 0 40 16/7 0 5 7/3 (-1/5,0/1) 0 40 40/17 0/1 28 1 26/11 (0/1,1/9) 0 20 19/8 (0/1,1/5) 0 40 31/13 (0/1,1/3) 0 40 12/5 1/2 2 10 29/12 (0/1,1/1) 0 40 75/31 1/2 2 8 46/19 (0/1,1/1) 0 20 80/33 (0/1,1/1) 0 1 17/7 (0/1,1/1) 0 40 39/16 (1/1,2/1) 0 40 22/9 (0/1,1/1) 0 20 5/2 1/0 1 8 33/13 (-1/1,0/1) 0 40 28/11 1/0 2 10 23/9 (-1/1,-2/3) 0 40 41/16 (-1/1,0/1) 0 40 100/39 -1/2 2 2 59/23 (-1/3,0/1) 0 40 18/7 (-1/1,0/1) 0 20 80/31 (-1/1,0/1) 0 1 31/12 (-1/1,0/1) 0 40 44/17 -1/2 2 10 13/5 (-1/1,-2/3) 0 40 21/8 (-1/3,0/1) 0 40 8/3 0/1 4 5 19/7 (0/1,1/1) 0 40 49/18 (0/1,1/3) 0 40 30/11 1/2 2 4 71/26 (2/3,1/1) 0 40 41/15 (1/1,2/1) 0 40 11/4 (0/1,1/1) 0 40 36/13 1/0 2 10 61/22 (0/1,1/9) 0 40 25/9 1/2 2 8 39/14 (2/3,1/1) 0 40 14/5 (1/1,2/1) 0 20 17/6 (2/1,3/1) 0 40 20/7 1/0 6 2 3/1 (-1/1,0/1) 0 40 19/6 (0/1,1/1) 0 40 16/5 0 5 13/4 (1/1,4/3) 0 40 10/3 1/0 4 4 27/8 (-3/1,-8/3) 0 40 44/13 -5/2 2 10 61/18 (-23/11,-2/1) 0 40 200/59 -2/1 36 1 78/23 (-2/1,-13/7) 0 20 17/5 (-2/1,-1/1) 0 40 41/12 (-4/3,-1/1) 0 40 24/7 -1/1 4 5 31/9 (-1/1,0/1) 0 40 7/2 (-1/1,0/1) 0 40 32/9 0 5 25/7 1/0 1 8 18/5 (-1/1,0/1) 0 20 40/11 0/1 4 1 11/3 (0/1,1/1) 0 40 4/1 1/0 2 10 9/2 (-1/1,0/1) 0 40 41/9 (-4/3,-1/1) 0 40 32/7 0 5 55/12 -1/2 1 8 23/5 (0/1,1/1) 0 40 14/3 (-1/1,0/1) 0 20 80/17 (-1/1,0/1) 0 1 33/7 (-1/1,0/1) 0 40 52/11 -1/2 2 10 19/4 (0/1,1/1) 0 40 24/5 0/1 4 5 29/6 (0/1,1/1) 0 40 5/1 1/0 2 8 21/4 (-2/1,-1/1) 0 40 16/3 0 5 11/2 (-2/1,-1/1) 0 40 39/7 (-1/1,0/1) 0 40 28/5 -3/2 2 10 17/3 (-6/5,-1/1) 0 40 40/7 -1/1 12 1 6/1 (-1/1,0/1) 0 20 25/4 -1/2 2 8 19/3 (0/1,1/5) 0 40 32/5 0 5 13/2 (0/1,1/1) 0 40 20/3 1/0 6 2 7/1 (-3/1,-2/1) 0 40 1/0 (-1/1,0/1) 0 40 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(641,-1360,189,-401) (2/1,17/8) -> (78/23,17/5) Glide Reflection Matrix(601,-1280,131,-279) (17/8,15/7) -> (55/12,23/5) Hyperbolic Matrix(261,-560,103,-221) (15/7,13/6) -> (5/2,33/13) Glide Reflection Matrix(221,-480,64,-139) (13/6,11/5) -> (31/9,7/2) Hyperbolic Matrix(181,-400,81,-179) (11/5,20/9) -> (20/9,9/4) Parabolic Matrix(141,-320,26,-59) (9/4,16/7) -> (16/3,11/2) Hyperbolic Matrix(139,-320,43,-99) (16/7,7/3) -> (16/5,13/4) Glide Reflection Matrix(239,-560,102,-239) (7/3,40/17) -> (7/3,40/17) Reflection Matrix(441,-1040,187,-441) (40/17,26/11) -> (40/17,26/11) Reflection Matrix(541,-1280,194,-459) (26/11,19/8) -> (39/14,14/5) Hyperbolic Matrix(639,-1520,235,-559) (19/8,31/13) -> (19/7,49/18) Glide Reflection Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(959,-2320,198,-479) (29/12,75/31) -> (29/6,5/1) Glide Reflection Matrix(661,-1600,107,-259) (75/31,46/19) -> (6/1,25/4) Hyperbolic Matrix(1519,-3680,627,-1519) (46/19,80/33) -> (46/19,80/33) Reflection Matrix(1121,-2720,462,-1121) (80/33,17/7) -> (80/33,17/7) Reflection Matrix(559,-1360,164,-399) (17/7,39/16) -> (17/5,41/12) Glide Reflection Matrix(819,-2000,319,-779) (39/16,22/9) -> (59/23,18/7) Glide Reflection Matrix(261,-640,73,-179) (22/9,5/2) -> (25/7,18/5) Hyperbolic Matrix(1039,-2640,220,-559) (33/13,28/11) -> (33/7,52/11) Glide Reflection Matrix(439,-1120,78,-199) (28/11,23/9) -> (28/5,17/3) Glide Reflection Matrix(219,-560,70,-179) (23/9,41/16) -> (3/1,19/6) Glide Reflection Matrix(3901,-10000,1521,-3899) (41/16,100/39) -> (100/39,59/23) Parabolic Matrix(559,-1440,217,-559) (18/7,80/31) -> (18/7,80/31) Reflection Matrix(1921,-4960,744,-1921) (80/31,31/12) -> (80/31,31/12) Reflection Matrix(619,-1600,224,-579) (31/12,44/17) -> (11/4,36/13) Glide Reflection Matrix(679,-1760,201,-521) (44/17,13/5) -> (27/8,44/13) Hyperbolic Matrix(61,-160,8,-21) (13/5,21/8) -> (7/1,1/0) Glide Reflection Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(1201,-3280,264,-721) (71/26,41/15) -> (9/2,41/9) Glide Reflection Matrix(321,-880,58,-159) (41/15,11/4) -> (11/2,39/7) Hyperbolic Matrix(1761,-4880,520,-1441) (36/13,61/22) -> (44/13,61/18) Glide Reflection Matrix(721,-2000,115,-319) (61/22,25/9) -> (25/4,19/3) Hyperbolic Matrix(259,-720,50,-139) (25/9,39/14) -> (5/1,21/4) Glide Reflection Matrix(199,-560,43,-121) (14/5,17/6) -> (23/5,14/3) Hyperbolic Matrix(141,-400,49,-139) (17/6,20/7) -> (20/7,3/1) Parabolic Matrix(201,-640,38,-121) (19/6,16/5) -> (21/4,16/3) Glide Reflection Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(7199,-24400,2124,-7199) (61/18,200/59) -> (61/18,200/59) Reflection Matrix(4601,-15600,1357,-4601) (200/59,78/23) -> (200/59,78/23) Reflection Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection Matrix(419,-1440,87,-299) (24/7,31/9) -> (24/5,29/6) Glide Reflection Matrix(181,-640,28,-99) (7/2,32/9) -> (32/5,13/2) Hyperbolic Matrix(719,-2560,157,-559) (32/9,25/7) -> (32/7,55/12) Glide Reflection Matrix(199,-720,55,-199) (18/5,40/11) -> (18/5,40/11) Reflection Matrix(241,-880,66,-241) (40/11,11/3) -> (40/11,11/3) Reflection Matrix(21,-80,5,-19) (11/3,4/1) -> (4/1,9/2) Parabolic Matrix(421,-1920,66,-301) (41/9,32/7) -> (19/3,32/5) Glide Reflection Matrix(239,-1120,51,-239) (14/3,80/17) -> (14/3,80/17) Reflection Matrix(1121,-5280,238,-1121) (80/17,33/7) -> (80/17,33/7) Reflection Matrix(541,-2560,97,-459) (52/11,19/4) -> (39/7,28/5) Hyperbolic Matrix(239,-1360,42,-239) (17/3,40/7) -> (17/3,40/7) Reflection Matrix(41,-240,7,-41) (40/7,6/1) -> (40/7,6/1) Reflection Matrix(61,-400,9,-59) (13/2,20/3) -> (20/3,7/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(-1,0,2,1) (0/1,2/1) -> (-1/1,0/1) Matrix(641,-1360,189,-401) -> Matrix(11,-2,-6,1) Matrix(601,-1280,131,-279) -> Matrix(1,0,-4,1) 0/1 Matrix(261,-560,103,-221) -> Matrix(1,-1,-2,1) Matrix(221,-480,64,-139) -> Matrix(1,-1,0,1) 1/0 Matrix(181,-400,81,-179) -> Matrix(1,-1,0,1) 1/0 Matrix(141,-320,26,-59) -> Matrix(1,-1,0,1) 1/0 Matrix(139,-320,43,-99) -> Matrix(1,1,2,1) Matrix(239,-560,102,-239) -> Matrix(-1,0,10,1) (7/3,40/17) -> (-1/5,0/1) Matrix(441,-1040,187,-441) -> Matrix(1,0,18,-1) (40/17,26/11) -> (0/1,1/9) Matrix(541,-1280,194,-459) -> Matrix(7,-1,8,-1) Matrix(639,-1520,235,-559) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(301,-720,125,-299) -> Matrix(3,-1,4,-1) 1/2 Matrix(959,-2320,198,-479) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(661,-1600,107,-259) -> Matrix(1,-1,0,1) 1/0 Matrix(1519,-3680,627,-1519) -> Matrix(1,0,2,-1) (46/19,80/33) -> (0/1,1/1) Matrix(1121,-2720,462,-1121) -> Matrix(1,0,2,-1) (80/33,17/7) -> (0/1,1/1) Matrix(559,-1360,164,-399) -> Matrix(3,-2,-2,1) Matrix(819,-2000,319,-779) -> Matrix(1,-1,-2,1) Matrix(261,-640,73,-179) -> Matrix(1,-1,0,1) 1/0 Matrix(1039,-2640,220,-559) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(439,-1120,78,-199) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(219,-560,70,-179) -> Matrix(1,1,2,1) Matrix(3901,-10000,1521,-3899) -> Matrix(1,1,-4,-3) -1/2 Matrix(559,-1440,217,-559) -> Matrix(-1,0,2,1) (18/7,80/31) -> (-1/1,0/1) Matrix(1921,-4960,744,-1921) -> Matrix(-1,0,2,1) (80/31,31/12) -> (-1/1,0/1) Matrix(619,-1600,224,-579) -> Matrix(1,1,2,1) Matrix(679,-1760,201,-521) -> Matrix(1,-2,0,1) 1/0 Matrix(61,-160,8,-21) -> Matrix(3,1,-2,-1) Matrix(121,-320,45,-119) -> Matrix(1,0,4,1) 0/1 Matrix(1321,-3600,484,-1319) -> Matrix(5,-2,8,-3) 1/2 Matrix(1201,-3280,264,-721) -> Matrix(3,-2,-2,1) Matrix(321,-880,58,-159) -> Matrix(1,-2,0,1) 1/0 Matrix(1761,-4880,520,-1441) -> Matrix(5,2,-2,-1) Matrix(721,-2000,115,-319) -> Matrix(1,0,-4,1) 0/1 Matrix(259,-720,50,-139) -> Matrix(5,-3,-2,1) Matrix(199,-560,43,-121) -> Matrix(1,-2,0,1) 1/0 Matrix(141,-400,49,-139) -> Matrix(1,-3,0,1) 1/0 Matrix(201,-640,38,-121) -> Matrix(3,-2,-2,1) Matrix(121,-400,36,-119) -> Matrix(1,-4,0,1) 1/0 Matrix(7199,-24400,2124,-7199) -> Matrix(45,92,-22,-45) (61/18,200/59) -> (-23/11,-2/1) Matrix(4601,-15600,1357,-4601) -> Matrix(27,52,-14,-27) (200/59,78/23) -> (-2/1,-13/7) Matrix(421,-1440,88,-301) -> Matrix(1,1,-2,-3) Matrix(419,-1440,87,-299) -> Matrix(1,1,2,1) Matrix(181,-640,28,-99) -> Matrix(1,1,0,1) 1/0 Matrix(719,-2560,157,-559) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(199,-720,55,-199) -> Matrix(-1,0,2,1) (18/5,40/11) -> (-1/1,0/1) Matrix(241,-880,66,-241) -> Matrix(1,0,2,-1) (40/11,11/3) -> (0/1,1/1) Matrix(21,-80,5,-19) -> Matrix(1,-1,0,1) 1/0 Matrix(421,-1920,66,-301) -> Matrix(1,1,2,1) Matrix(239,-1120,51,-239) -> Matrix(-1,0,2,1) (14/3,80/17) -> (-1/1,0/1) Matrix(1121,-5280,238,-1121) -> Matrix(-1,0,2,1) (80/17,33/7) -> (-1/1,0/1) Matrix(541,-2560,97,-459) -> Matrix(1,-1,0,1) 1/0 Matrix(239,-1360,42,-239) -> Matrix(11,12,-10,-11) (17/3,40/7) -> (-6/5,-1/1) Matrix(41,-240,7,-41) -> Matrix(-1,0,2,1) (40/7,6/1) -> (-1/1,0/1) Matrix(61,-400,9,-59) -> Matrix(1,-3,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.