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): 2016 Minimal number of generators: 337 Number of equivalence classes of cusps: 96 Genus: 121 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -20/3 -13/2 -6/1 -16/3 -24/5 -14/3 -13/3 -4/1 -18/5 -13/4 -39/14 -13/5 -12/5 -13/6 -2/1 -13/7 -13/8 -39/25 -26/17 -13/9 -13/10 -13/11 -26/23 0/1 1/1 13/11 26/21 13/10 26/19 13/9 3/2 39/25 13/8 130/79 26/15 13/7 2/1 13/6 104/47 26/11 208/87 12/5 5/2 130/51 13/5 208/79 52/19 39/14 26/9 3/1 13/4 104/31 52/15 7/2 104/29 18/5 26/7 208/55 4/1 25/6 21/5 13/3 22/5 9/2 23/5 14/3 52/11 19/4 24/5 5/1 26/5 21/4 16/3 27/5 11/2 17/3 23/4 52/9 6/1 19/3 13/2 20/3 7/1 22/3 37/5 52/7 15/2 8/1 17/2 26/3 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -2/3 -9/1 -1/1 1/0 -8/1 -2/3 0/1 -15/2 -1/1 0/1 -7/1 -1/1 -1/2 -20/3 -2/5 0/1 -13/2 0/1 -32/5 -2/1 0/1 -19/3 -1/1 -1/2 -6/1 0/1 -17/3 1/1 1/0 -11/2 0/1 1/0 -16/3 -2/1 0/1 -37/7 -1/1 -1/2 -21/4 -1/1 0/1 -26/5 0/1 -5/1 0/1 1/0 -24/5 -4/1 -2/1 -43/9 -3/2 -1/1 -19/4 -2/1 -1/1 -14/3 0/1 -51/11 1/3 1/2 -37/8 0/1 1/1 -23/5 2/1 1/0 -9/2 -2/1 1/0 -31/7 -4/3 -1/1 -53/12 -4/3 -1/1 -22/5 0/1 -13/3 -2/1 0/1 -17/4 -2/1 -1/1 -21/5 -1/1 0/1 -25/6 0/1 1/0 -4/1 -2/1 0/1 -27/7 -5/3 -3/2 -23/6 -2/1 -1/1 -19/5 -3/2 -1/1 -53/14 -2/1 -1/1 -87/23 -9/8 -1/1 -34/9 -2/1 -15/4 -6/5 -1/1 -26/7 -1/1 -11/3 -1/1 -3/4 -29/8 -2/3 -3/5 -18/5 -2/3 -25/7 -3/8 -1/3 -32/9 -2/11 0/1 -7/2 0/1 1/0 -31/9 -2/1 -1/1 -24/7 -2/3 0/1 -41/12 0/1 1/0 -17/5 1/1 1/0 -27/8 0/1 1/0 -64/19 -2/1 0/1 -37/11 -1/1 1/0 -47/14 6/1 1/0 -10/3 -2/1 -43/13 -1/1 -1/2 -33/10 -1/1 0/1 -23/7 -2/1 1/0 -13/4 -2/1 0/1 -16/5 -2/1 0/1 -51/16 -4/3 -1/1 -35/11 -1/1 -3/4 -19/6 -1/1 0/1 -3/1 -2/1 -1/1 -20/7 -4/5 -2/3 -37/13 -1/2 -1/3 -17/6 -1/1 -2/3 -31/11 -1/1 0/1 -45/16 -2/3 -1/2 -14/5 0/1 -53/19 -1/4 -1/5 -39/14 0/1 -64/23 0/1 2/7 -25/9 1/2 1/1 -11/4 0/1 1/0 -30/11 -2/1 -49/18 0/1 1/0 -19/7 -1/1 1/0 -46/17 0/1 -73/27 0/1 1/1 -27/10 0/1 1/0 -35/13 1/1 1/0 -8/3 -2/1 0/1 -37/14 -1/1 0/1 -29/11 -2/1 1/0 -79/30 0/1 1/0 -50/19 -2/1 -21/8 -1/1 0/1 -13/5 -2/1 0/1 -31/12 -1/1 0/1 -49/19 -3/1 -2/1 -67/26 -4/3 -1/1 -18/7 0/1 -23/9 -2/1 -3/2 -51/20 -8/7 -1/1 -130/51 -1/1 -79/31 -1/1 -11/12 -28/11 -2/3 0/1 -5/2 0/1 1/0 -37/15 -7/1 1/0 -32/13 -14/3 -4/1 -27/11 -13/4 -3/1 -49/20 -8/3 -5/2 -22/9 -2/1 -17/7 -1/1 1/0 -46/19 -2/1 -29/12 -2/1 -5/3 -41/17 -1/1 1/0 -53/22 -2/1 -1/1 -12/5 -2/1 0/1 -55/23 -3/1 -2/1 -98/41 -2/1 -43/18 -2/1 -3/2 -31/13 -1/1 0/1 -50/21 -2/1 -69/29 -5/4 -1/1 -19/8 -2/1 -1/1 -26/11 -1/1 -7/3 -1/1 1/0 -37/16 -2/1 -1/1 -30/13 0/1 -53/23 5/1 1/0 -23/10 -2/1 -1/1 -16/7 -2/1 0/1 -41/18 0/1 1/0 -25/11 1/2 1/1 -34/15 4/1 -9/4 -4/1 1/0 -29/13 0/1 1/0 -20/9 -6/1 -4/1 -51/23 -25/7 -7/2 -31/14 -16/5 -3/1 -42/19 -8/3 -53/24 -3/1 -2/1 -11/5 -3/1 -5/2 -24/11 -12/5 -2/1 -13/6 -2/1 -28/13 -2/1 -12/7 -15/7 -5/3 -3/2 -17/8 -4/3 -1/1 -2/1 -2/1 -17/9 -1/1 -1/2 -15/8 -3/1 -2/1 -13/7 -2/1 -37/20 -2/1 -13/7 -61/33 -15/8 -13/7 -24/13 -2/1 -20/11 -11/6 -2/1 -7/4 -42/23 -22/13 -73/40 -62/37 -5/3 -104/57 -5/3 -31/17 -5/3 -18/11 -51/28 -5/3 -18/11 -71/39 -5/3 -13/8 -20/11 -2/1 -8/5 -9/5 -11/7 -3/2 -25/14 -3/2 -10/7 -16/9 -2/1 -4/3 -39/22 -2/1 -4/3 -23/13 -3/2 -4/3 -53/30 -1/1 -2/3 -30/17 -2/1 -7/4 -2/1 -3/2 -26/15 -3/2 -19/11 -3/2 -1/1 -69/40 -1/1 0/1 -50/29 -2/1 -31/18 -4/3 -1/1 -43/25 -3/2 -1/1 -98/57 -2/1 -153/89 -7/3 -2/1 -208/121 -2/1 -55/32 -2/1 -7/4 -12/7 -2/1 -4/3 -29/17 -2/1 1/0 -17/10 -2/1 -5/3 -39/23 -2/1 -8/5 -22/13 -8/5 -27/16 -3/2 -4/3 -5/3 -3/2 -4/3 -28/17 -2/1 -8/5 -79/48 -32/21 -3/2 -130/79 -3/2 -51/31 -3/2 -25/17 -23/14 -7/5 -4/3 -18/11 -4/3 -13/8 -2/1 -4/3 -34/21 -4/3 -55/34 -4/3 -5/4 -131/81 -11/10 -1/1 -76/47 -2/1 0/1 -21/13 -4/3 -1/1 -50/31 -2/1 -129/80 -8/5 -3/2 -208/129 -3/2 -79/49 -3/2 -7/5 -29/18 -4/3 -1/1 -37/23 -3/2 -1/1 -8/5 -2/1 -4/3 -27/17 -1/1 1/0 -73/46 -3/1 -2/1 -119/75 -3/1 -5/2 -46/29 -2/1 -19/12 -2/1 -5/3 -49/31 -5/3 -8/5 -79/50 -3/2 -10/7 -30/19 -2/1 -41/26 -8/5 -3/2 -52/33 -3/2 -11/7 -3/2 -1/1 -25/16 -3/2 -4/3 -64/41 -2/1 -4/3 -39/25 -2/1 -4/3 -92/59 -2/1 -4/3 -53/34 -4/3 -1/1 -14/9 -2/1 -31/20 -2/1 -1/1 -17/11 -7/4 -5/3 -37/24 -8/5 -11/7 -20/13 -2/1 -8/5 -23/15 -20/13 -3/2 -26/17 -3/2 -3/2 -3/2 -4/3 -19/13 -3/2 -1/1 -35/24 -6/5 -1/1 -51/35 -3/1 1/0 -16/11 -2/1 -4/3 -13/9 -2/1 -4/3 -36/25 -2/1 -4/3 -23/16 -4/3 -1/1 -33/23 -3/2 -1/1 -43/30 -2/1 -3/2 -10/7 -2/1 -57/40 -26/17 -3/2 -104/73 -3/2 -47/33 -3/2 -22/15 -37/26 -10/7 -7/5 -101/71 -15/11 -4/3 -64/45 -18/13 -4/3 -27/19 -3/2 -1/1 -44/31 -4/3 -6/5 -61/43 -7/6 -1/1 -78/55 -1/1 -17/12 -2/1 -1/1 -24/17 -2/1 -8/5 -79/56 -3/2 -22/15 -55/39 -7/5 -4/3 -31/22 -2/1 -1/1 -38/27 -2/1 -45/32 -8/5 -3/2 -52/37 -3/2 -7/5 -3/2 -1/1 -32/23 -2/1 -8/5 -89/64 -8/5 -11/7 -57/41 -3/2 -4/3 -25/18 -3/2 -4/3 -43/31 -17/11 -3/2 -104/75 -3/2 -61/44 -3/2 -28/19 -18/13 -4/3 -29/21 -2/1 1/0 -40/29 -2/1 -4/3 -91/66 -2/1 -51/37 -7/4 -5/3 -11/8 -8/5 -3/2 -26/19 -3/2 -15/11 -3/2 -19/13 -64/47 -22/15 -16/11 -49/36 -16/11 -29/20 -34/25 -16/11 -121/89 -107/74 -13/9 -208/153 -13/9 -87/64 -13/9 -88/61 -53/39 -59/41 -23/16 -19/14 -10/7 -7/5 -23/17 -3/2 -4/3 -27/20 -3/2 -10/7 -4/3 -10/7 -4/3 -25/19 -11/8 -15/11 -21/16 -7/5 -4/3 -17/13 -15/11 -19/14 -13/10 -4/3 -35/27 -25/19 -21/16 -22/17 -4/3 -53/41 -13/10 -61/47 -31/24 -9/7 -14/11 -9/7 -9/7 -5/4 -32/25 -4/3 -6/5 -55/43 -10/9 -1/1 -78/61 -1/1 -23/18 -2/1 -1/1 -37/29 -3/2 -1/1 -88/69 -4/3 -6/5 -51/40 -2/1 -1/1 -14/11 -4/3 -33/26 -6/5 -1/1 -52/41 -1/1 -19/15 -3/2 -1/1 -43/34 -3/2 -4/3 -110/87 -4/3 -67/53 -3/2 -1/1 -24/19 -4/3 -6/5 -5/4 -3/2 -4/3 -26/21 -4/3 -21/17 -4/3 -1/1 -58/47 -4/3 -95/77 -5/4 -1/1 -37/30 -4/3 -1/1 -53/43 -9/7 -5/4 -16/13 -2/1 -4/3 -27/22 -3/2 -10/7 -11/9 -3/2 -7/5 -28/23 -2/1 -4/3 -17/14 -7/5 -4/3 -23/19 -19/14 -4/3 -52/43 -4/3 -29/24 -4/3 -9/7 -6/5 -4/3 -19/16 -23/17 -4/3 -13/11 -4/3 -33/28 -4/3 -57/43 -53/45 -139/105 -45/34 -20/17 -4/3 -70/53 -7/6 -4/3 -13/10 -22/19 -4/3 -37/32 -22/17 -9/7 -52/45 -9/7 -15/13 -9/7 -5/4 -8/7 -4/3 -14/11 -17/15 -19/15 -5/4 -26/23 -5/4 -9/8 -5/4 -6/5 -10/9 -6/5 -11/10 -2/1 -3/2 -1/1 -5/4 -1/1 0/1 -1/1 1/1 -1/1 -5/6 10/9 -6/7 9/8 -6/7 -5/6 8/7 -14/17 -4/5 15/13 -5/6 -9/11 7/6 -13/16 -4/5 20/17 -70/87 -4/5 13/11 -4/5 32/27 -4/5 -90/113 19/16 -4/5 -23/29 6/5 -4/5 17/14 -4/5 -7/9 11/9 -7/9 -3/4 16/13 -4/5 -2/3 37/30 -1/1 -4/5 21/17 -1/1 -4/5 26/21 -4/5 5/4 -4/5 -3/4 24/19 -6/7 -4/5 43/34 -4/5 -3/4 19/15 -1/1 -3/4 14/11 -4/5 51/40 -1/1 -2/3 37/29 -1/1 -3/4 23/18 -1/1 -2/3 9/7 -5/6 -9/11 31/24 -14/17 -9/11 53/41 -61/75 -13/16 22/17 -4/5 13/10 -4/5 17/13 -19/24 -15/19 21/16 -4/5 -7/9 25/19 -15/19 -11/14 4/3 -4/5 -10/13 27/20 -10/13 -3/4 23/17 -4/5 -3/4 19/14 -7/9 -10/13 53/39 -23/30 -59/77 87/64 -88/115 -13/17 34/25 -16/21 15/11 -19/25 -3/4 26/19 -3/4 11/8 -3/4 -8/11 29/21 -2/3 -1/2 18/13 -4/5 25/18 -4/5 -3/4 32/23 -8/11 -2/3 7/5 -1/1 -3/4 31/22 -1/1 -2/3 24/17 -8/11 -2/3 41/29 -1/1 -3/4 17/12 -1/1 -2/3 27/19 -1/1 -3/4 64/45 -4/5 -18/23 37/26 -7/9 -10/13 47/33 -22/29 -3/4 10/7 -2/3 43/30 -3/4 -2/3 33/23 -1/1 -3/4 23/16 -1/1 -4/5 13/9 -4/5 -2/3 16/11 -4/5 -2/3 51/35 -3/5 -1/2 35/24 -1/1 -6/7 19/13 -1/1 -3/4 3/2 -4/5 -3/4 20/13 -8/11 -2/3 37/24 -11/15 -8/11 17/11 -5/7 -7/10 31/20 -1/1 -2/3 45/29 -1/1 -3/4 14/9 -2/3 53/34 -1/1 -4/5 39/25 -4/5 -2/3 64/41 -4/5 -2/3 25/16 -4/5 -3/4 11/7 -1/1 -3/4 30/19 -2/3 49/31 -8/11 -5/7 19/12 -5/7 -2/3 46/29 -2/3 73/46 -2/3 -3/5 27/17 -1/1 -1/2 35/22 -1/1 0/1 8/5 -4/5 -2/3 37/23 -1/1 -3/4 29/18 -1/1 -4/5 79/49 -7/9 -3/4 50/31 -2/3 21/13 -1/1 -4/5 13/8 -4/5 -2/3 31/19 -1/1 -4/5 49/30 -5/6 -4/5 67/41 -7/9 -3/4 18/11 -4/5 23/14 -4/5 -7/9 51/31 -25/33 -3/4 130/79 -3/4 79/48 -3/4 -32/43 28/17 -8/11 -2/3 5/3 -4/5 -3/4 37/22 -11/15 -8/11 32/19 -8/11 -2/3 27/16 -4/5 -3/4 49/29 -14/19 -11/15 22/13 -8/11 17/10 -5/7 -2/3 46/27 -2/3 29/17 -2/3 -1/2 41/24 -3/4 -8/11 53/31 -5/7 -7/10 12/7 -4/5 -2/3 55/32 -7/10 -2/3 98/57 -2/3 43/25 -1/1 -3/4 31/18 -1/1 -4/5 50/29 -2/3 69/40 -1/1 0/1 19/11 -1/1 -3/4 26/15 -3/4 7/4 -3/4 -2/3 37/21 -1/1 -1/2 30/17 -2/3 53/30 -2/1 -1/1 23/13 -4/5 -3/4 16/9 -4/5 -2/3 41/23 -7/9 -3/4 25/14 -10/13 -3/4 34/19 -10/13 9/5 -3/4 -11/15 29/16 -18/25 -5/7 20/11 -8/11 -2/3 51/28 -18/25 -5/7 31/17 -18/25 -5/7 42/23 -22/31 53/29 -5/7 -17/24 11/6 -7/10 -2/3 24/13 -20/29 -2/3 13/7 -2/3 28/15 -2/3 -12/19 15/8 -2/3 -3/5 17/9 -1/1 1/0 2/1 -2/3 17/8 -1/1 -4/5 15/7 -3/4 -5/7 13/6 -2/3 37/17 -9/14 -7/11 61/28 -2/3 -9/14 24/11 -2/3 -12/19 11/5 -5/8 -3/5 42/19 -8/13 73/33 -32/53 -3/5 104/47 -3/5 31/14 -3/5 -16/27 51/23 -7/12 -25/43 71/32 -19/33 -4/7 20/9 -4/7 -6/11 9/4 -4/7 -1/2 25/11 -1/3 -1/4 16/7 -2/3 0/1 39/17 -2/3 0/1 23/10 -1/1 -2/3 53/23 -1/2 -5/11 30/13 0/1 7/3 -1/1 -1/2 26/11 -1/1 19/8 -1/1 -2/3 69/29 -1/1 -5/6 50/21 -2/3 31/13 -1/1 0/1 43/18 -3/4 -2/3 98/41 -2/3 153/64 -11/16 -2/3 208/87 -2/3 55/23 -2/3 -3/5 12/5 -2/3 0/1 29/12 -5/7 -2/3 17/7 -1/1 -1/2 39/16 -2/3 22/9 -2/3 27/11 -3/5 -13/22 5/2 -1/2 0/1 28/11 -2/1 0/1 79/31 -11/10 -1/1 130/51 -1/1 51/20 -1/1 -8/9 23/9 -3/4 -2/3 18/7 0/1 13/5 -2/3 0/1 34/13 0/1 55/21 -2/3 -3/5 131/50 -8/15 -1/2 76/29 -2/5 0/1 21/8 -1/1 0/1 50/19 -2/3 129/49 -5/9 -1/2 208/79 -1/2 79/30 -1/2 0/1 29/11 -2/3 -1/2 37/14 -1/1 0/1 8/3 -2/3 0/1 27/10 -1/2 0/1 73/27 -1/3 0/1 119/44 -1/3 0/1 46/17 0/1 19/7 -1/1 -1/2 49/18 -1/2 0/1 79/29 -1/1 -7/8 30/11 -2/3 41/15 -3/5 -1/2 52/19 -1/2 11/4 -1/2 0/1 25/9 -1/3 -1/4 64/23 -2/11 0/1 39/14 0/1 92/33 0/1 2/9 53/19 1/3 1/2 14/5 0/1 31/11 -1/1 0/1 17/6 -2/1 -1/1 37/13 1/1 1/0 20/7 -2/1 -4/3 23/8 -6/5 -1/1 26/9 -1/1 3/1 -1/1 -2/3 19/6 -1/1 0/1 35/11 -3/2 -1/1 51/16 -1/1 -4/5 16/5 -2/3 0/1 13/4 -2/3 0/1 36/11 -2/3 0/1 23/7 -2/3 -1/2 33/10 -1/1 0/1 43/13 -1/1 1/0 10/3 -2/3 57/17 -10/19 -1/2 104/31 -1/2 47/14 -1/2 -6/13 37/11 -1/1 -1/2 101/30 -1/4 0/1 64/19 -2/3 0/1 27/8 -1/2 0/1 44/13 -2/3 0/1 61/18 -4/7 -1/2 78/23 -1/2 17/5 -1/2 -1/3 24/7 -2/1 0/1 79/23 -1/1 -9/10 55/16 -3/4 -2/3 31/9 -1/1 -2/3 38/11 -2/3 45/13 -3/5 -1/2 52/15 -1/2 7/2 -1/2 0/1 32/9 0/1 2/7 89/25 3/7 1/2 57/16 1/2 4/7 25/7 1/1 3/2 43/12 6/1 1/0 104/29 1/0 61/17 -9/1 1/0 18/5 -2/1 29/8 -3/1 -2/1 40/11 -2/1 -4/3 91/25 -2/1 -4/3 51/14 -2/1 -1/1 11/3 -3/2 -1/1 26/7 -1/1 15/4 -1/1 -6/7 64/17 -4/5 -2/3 49/13 -4/5 -7/9 34/9 -2/3 121/32 -6/5 -1/1 208/55 -1/1 87/23 -1/1 -9/10 53/14 -1/1 -2/3 19/5 -1/1 -3/4 23/6 -1/1 -2/3 27/7 -3/4 -5/7 4/1 -2/3 0/1 25/6 -1/2 0/1 21/5 -1/1 0/1 17/4 -1/1 -2/3 13/3 -2/3 0/1 35/8 -1/1 -2/3 22/5 0/1 53/12 -1/1 -4/5 31/7 -1/1 -4/5 9/2 -2/3 -1/2 32/7 -2/3 -4/7 55/12 -6/11 -1/2 78/17 -1/2 23/5 -1/2 -2/5 37/8 -1/3 0/1 88/19 -2/5 0/1 51/11 -1/4 -1/5 14/3 0/1 33/7 -1/1 1/0 52/11 -1/1 19/4 -1/1 -2/3 43/9 -1/1 -3/4 110/23 -2/3 67/14 -1/1 -2/3 24/5 -2/3 -4/7 5/1 -1/2 0/1 26/5 0/1 21/4 -1/1 0/1 58/11 0/1 95/18 0/1 1/0 37/7 -1/1 1/0 53/10 -2/1 -1/1 16/3 -2/3 0/1 27/5 -1/3 -1/4 11/2 -1/2 0/1 28/5 -2/1 0/1 17/3 -1/2 -1/3 23/4 -1/5 0/1 52/9 0/1 29/5 0/1 1/2 6/1 0/1 19/3 -1/1 1/0 13/2 0/1 33/5 1/2 1/1 53/8 2/3 1/1 20/3 0/1 2/1 7/1 -1/1 1/0 22/3 -2/1 37/5 -3/2 -1/1 52/7 -1/1 15/2 -1/1 0/1 8/1 -2/1 0/1 17/2 -4/3 -1/1 26/3 -1/1 9/1 -1/1 -1/2 10/1 -2/1 11/1 -1/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(53,572,-24,-259) (-10/1,1/0) -> (-42/19,-53/24) Hyperbolic Matrix(53,520,16,157) (-10/1,-9/1) -> (43/13,10/3) Hyperbolic Matrix(105,884,-74,-623) (-9/1,-8/1) -> (-44/31,-61/43) Hyperbolic Matrix(53,416,20,157) (-8/1,-15/2) -> (37/14,8/3) Hyperbolic Matrix(51,364,-22,-157) (-15/2,-7/1) -> (-7/3,-37/16) Hyperbolic Matrix(53,364,38,261) (-7/1,-20/3) -> (32/23,7/5) Hyperbolic Matrix(103,676,-16,-105) (-20/3,-13/2) -> (-13/2,-32/5) Parabolic Matrix(415,2652,-228,-1457) (-32/5,-19/3) -> (-71/39,-20/11) Hyperbolic Matrix(157,988,58,365) (-19/3,-6/1) -> (46/17,19/7) Hyperbolic Matrix(155,884,-64,-365) (-6/1,-17/3) -> (-17/7,-46/19) Hyperbolic Matrix(157,884,-46,-259) (-17/3,-11/2) -> (-41/12,-17/5) Hyperbolic Matrix(155,832,-68,-365) (-11/2,-16/3) -> (-16/7,-41/18) Hyperbolic Matrix(727,3848,-570,-3017) (-16/3,-37/7) -> (-37/29,-88/69) Hyperbolic Matrix(987,5200,-622,-3277) (-37/7,-21/4) -> (-73/46,-119/75) Hyperbolic Matrix(209,1092,40,209) (-21/4,-26/5) -> (26/5,21/4) Hyperbolic Matrix(51,260,10,51) (-26/5,-5/1) -> (5/1,26/5) Hyperbolic Matrix(53,260,32,157) (-5/1,-24/5) -> (28/17,5/3) Hyperbolic Matrix(521,2496,-282,-1351) (-24/5,-43/9) -> (-61/33,-24/13) Hyperbolic Matrix(469,2236,142,677) (-43/9,-19/4) -> (33/10,43/13) Hyperbolic Matrix(155,728,-122,-573) (-19/4,-14/3) -> (-14/11,-33/26) Hyperbolic Matrix(313,1456,112,521) (-14/3,-51/11) -> (53/19,14/5) Hyperbolic Matrix(831,3848,-674,-3121) (-51/11,-37/8) -> (-37/30,-53/43) Hyperbolic Matrix(417,1924,158,729) (-37/8,-23/5) -> (29/11,37/14) Hyperbolic Matrix(103,468,-46,-209) (-23/5,-9/2) -> (-9/4,-29/13) Hyperbolic Matrix(363,1612,152,675) (-9/2,-31/7) -> (31/13,43/18) Hyperbolic Matrix(729,3224,400,1769) (-31/7,-53/12) -> (51/28,31/17) Hyperbolic Matrix(625,2756,354,1561) (-53/12,-22/5) -> (30/17,53/30) Hyperbolic Matrix(261,1144,-154,-675) (-22/5,-13/3) -> (-39/23,-22/13) Hyperbolic Matrix(207,884,-122,-521) (-13/3,-17/4) -> (-17/10,-39/23) Hyperbolic Matrix(209,884,74,313) (-17/4,-21/5) -> (31/11,17/6) Hyperbolic Matrix(573,2392,212,885) (-21/5,-25/6) -> (27/10,73/27) Hyperbolic Matrix(51,208,38,155) (-25/6,-4/1) -> (4/3,27/20) Hyperbolic Matrix(53,208,40,157) (-4/1,-27/7) -> (25/19,4/3) Hyperbolic Matrix(677,2600,420,1613) (-27/7,-23/6) -> (29/18,79/49) Hyperbolic Matrix(313,1196,218,833) (-23/6,-19/5) -> (33/23,23/16) Hyperbolic Matrix(1249,4732,-686,-2599) (-19/5,-53/14) -> (-51/28,-71/39) Hyperbolic Matrix(1663,6292,522,1975) (-53/14,-87/23) -> (35/11,51/16) Hyperbolic Matrix(1871,7072,-1376,-5201) (-87/23,-34/9) -> (-34/25,-121/89) Hyperbolic Matrix(675,2548,-262,-989) (-34/9,-15/4) -> (-67/26,-18/7) Hyperbolic Matrix(209,780,56,209) (-15/4,-26/7) -> (26/7,15/4) Hyperbolic Matrix(155,572,42,155) (-26/7,-11/3) -> (11/3,26/7) Hyperbolic Matrix(415,1508,-172,-625) (-11/3,-29/8) -> (-29/12,-41/17) Hyperbolic Matrix(259,936,158,571) (-29/8,-18/5) -> (18/11,23/14) Hyperbolic Matrix(363,1300,-160,-573) (-18/5,-25/7) -> (-25/11,-34/15) Hyperbolic Matrix(467,1664,-190,-677) (-25/7,-32/9) -> (-32/13,-27/11) Hyperbolic Matrix(103,364,88,311) (-32/9,-7/2) -> (7/6,20/17) Hyperbolic Matrix(467,1612,-166,-573) (-7/2,-31/9) -> (-31/11,-45/16) Hyperbolic Matrix(831,2860,-514,-1769) (-31/9,-24/7) -> (-76/47,-21/13) Hyperbolic Matrix(365,1248,198,677) (-24/7,-41/12) -> (11/6,24/13) Hyperbolic Matrix(415,1404,-154,-521) (-17/5,-27/8) -> (-27/10,-35/13) Hyperbolic Matrix(987,3328,632,2131) (-27/8,-64/19) -> (64/41,25/16) Hyperbolic Matrix(989,3328,-726,-2443) (-64/19,-37/11) -> (-15/11,-64/47) Hyperbolic Matrix(573,1924,-232,-779) (-37/11,-47/14) -> (-5/2,-37/15) Hyperbolic Matrix(311,1040,-218,-729) (-47/14,-10/3) -> (-10/7,-57/40) Hyperbolic Matrix(157,520,16,53) (-10/3,-43/13) -> (9/1,10/1) Hyperbolic Matrix(677,2236,142,469) (-43/13,-33/10) -> (19/4,43/9) Hyperbolic Matrix(363,1196,268,883) (-33/10,-23/7) -> (23/17,19/14) Hyperbolic Matrix(365,1196,-206,-675) (-23/7,-13/4) -> (-39/22,-23/13) Hyperbolic Matrix(259,832,-146,-469) (-13/4,-16/5) -> (-16/9,-39/22) Hyperbolic Matrix(521,1664,98,313) (-16/5,-51/16) -> (53/10,16/3) Hyperbolic Matrix(1975,6292,522,1663) (-51/16,-35/11) -> (87/23,53/14) Hyperbolic Matrix(623,1976,262,831) (-35/11,-19/6) -> (19/8,69/29) Hyperbolic Matrix(313,988,198,625) (-19/6,-3/1) -> (49/31,19/12) Hyperbolic Matrix(417,1196,-326,-935) (-3/1,-20/7) -> (-32/25,-55/43) Hyperbolic Matrix(675,1924,-274,-781) (-20/7,-37/13) -> (-37/15,-32/13) Hyperbolic Matrix(311,884,146,415) (-37/13,-17/6) -> (17/8,15/7) Hyperbolic Matrix(313,884,74,209) (-17/6,-31/11) -> (21/5,17/4) Hyperbolic Matrix(833,2340,-592,-1663) (-45/16,-14/5) -> (-38/27,-45/32) Hyperbolic Matrix(521,1456,112,313) (-14/5,-53/19) -> (51/11,14/3) Hyperbolic Matrix(2443,6812,-1772,-4941) (-53/19,-39/14) -> (-91/66,-51/37) Hyperbolic Matrix(2653,7384,-1924,-5355) (-39/14,-64/23) -> (-40/29,-91/66) Hyperbolic Matrix(1197,3328,842,2341) (-64/23,-25/9) -> (27/19,64/45) Hyperbolic Matrix(469,1300,-206,-571) (-25/9,-11/4) -> (-41/18,-25/11) Hyperbolic Matrix(571,1560,-362,-989) (-11/4,-30/11) -> (-30/19,-41/26) Hyperbolic Matrix(935,2548,-382,-1041) (-30/11,-49/18) -> (-49/20,-22/9) Hyperbolic Matrix(363,988,248,675) (-49/18,-19/7) -> (19/13,3/2) Hyperbolic Matrix(365,988,58,157) (-19/7,-46/17) -> (6/1,19/3) Hyperbolic Matrix(1923,5200,-1558,-4213) (-46/17,-73/27) -> (-21/17,-58/47) Hyperbolic Matrix(885,2392,212,573) (-73/27,-27/10) -> (25/6,21/5) Hyperbolic Matrix(155,416,-136,-365) (-35/13,-8/3) -> (-8/7,-17/15) Hyperbolic Matrix(157,416,20,53) (-8/3,-37/14) -> (15/2,8/1) Hyperbolic Matrix(729,1924,158,417) (-37/14,-29/11) -> (23/5,37/8) Hyperbolic Matrix(987,2600,730,1923) (-29/11,-79/30) -> (27/20,23/17) Hyperbolic Matrix(3951,10400,-2450,-6449) (-79/30,-50/19) -> (-50/31,-129/80) Hyperbolic Matrix(989,2600,574,1509) (-50/19,-21/8) -> (31/18,50/29) Hyperbolic Matrix(259,676,-100,-261) (-21/8,-13/5) -> (-13/5,-31/12) Parabolic Matrix(1249,3224,-886,-2287) (-31/12,-49/19) -> (-55/39,-31/22) Hyperbolic Matrix(3329,8580,-2340,-6031) (-49/19,-67/26) -> (-37/26,-101/71) Hyperbolic Matrix(365,936,264,677) (-18/7,-23/9) -> (29/21,18/13) Hyperbolic Matrix(937,2392,530,1353) (-23/9,-51/20) -> (53/30,23/13) Hyperbolic Matrix(5201,13260,2040,5201) (-51/20,-130/51) -> (130/51,51/20) Hyperbolic Matrix(8059,20540,3162,8059) (-130/51,-79/31) -> (79/31,130/51) Hyperbolic Matrix(1613,4108,470,1197) (-79/31,-28/11) -> (24/7,79/23) Hyperbolic Matrix(103,260,82,207) (-28/11,-5/2) -> (5/4,24/19) Hyperbolic Matrix(3225,7904,-1994,-4887) (-27/11,-49/20) -> (-55/34,-131/81) Hyperbolic Matrix(469,1144,-362,-883) (-22/9,-17/7) -> (-35/27,-22/17) Hyperbolic Matrix(623,1508,-516,-1249) (-46/19,-29/12) -> (-29/24,-6/5) Hyperbolic Matrix(1143,2756,-518,-1249) (-41/17,-53/22) -> (-53/24,-11/5) Hyperbolic Matrix(2289,5512,-1468,-3535) (-53/22,-12/5) -> (-92/59,-53/34) Hyperbolic Matrix(1977,4732,-1390,-3327) (-12/5,-55/23) -> (-101/71,-64/45) Hyperbolic Matrix(8527,20384,-4960,-11857) (-55/23,-98/41) -> (-98/57,-153/89) Hyperbolic Matrix(3743,8944,-2960,-7073) (-98/41,-43/18) -> (-43/34,-110/87) Hyperbolic Matrix(675,1612,152,363) (-43/18,-31/13) -> (31/7,9/2) Hyperbolic Matrix(1091,2600,676,1611) (-31/13,-50/21) -> (50/31,21/13) Hyperbolic Matrix(415,988,218,519) (-50/21,-69/29) -> (17/9,2/1) Hyperbolic Matrix(831,1976,262,623) (-69/29,-19/8) -> (19/6,35/11) Hyperbolic Matrix(417,988,176,417) (-19/8,-26/11) -> (26/11,19/8) Hyperbolic Matrix(155,364,66,155) (-26/11,-7/3) -> (7/3,26/11) Hyperbolic Matrix(833,1924,-720,-1663) (-37/16,-30/13) -> (-22/19,-37/32) Hyperbolic Matrix(1195,2756,924,2131) (-30/13,-53/23) -> (53/41,22/17) Hyperbolic Matrix(1039,2392,632,1455) (-53/23,-23/10) -> (23/14,51/31) Hyperbolic Matrix(521,1196,-362,-831) (-23/10,-16/7) -> (-36/25,-23/16) Hyperbolic Matrix(987,2236,-712,-1613) (-34/15,-9/4) -> (-61/44,-18/13) Hyperbolic Matrix(467,1040,-304,-677) (-29/13,-20/9) -> (-20/13,-23/15) Hyperbolic Matrix(937,2080,-796,-1767) (-20/9,-51/23) -> (-53/45,-20/17) Hyperbolic Matrix(1455,3224,1126,2495) (-51/23,-31/14) -> (31/24,53/41) Hyperbolic Matrix(1975,4368,-1082,-2393) (-31/14,-42/19) -> (-42/23,-73/40) Hyperbolic Matrix(571,1248,404,883) (-11/5,-24/11) -> (24/17,41/29) Hyperbolic Matrix(311,676,-144,-313) (-24/11,-13/6) -> (-13/6,-28/13) Parabolic Matrix(1039,2236,-822,-1769) (-28/13,-15/7) -> (-67/53,-24/19) Hyperbolic Matrix(415,884,146,311) (-15/7,-17/8) -> (17/6,37/13) Hyperbolic Matrix(469,988,272,573) (-17/8,-2/1) -> (50/29,69/40) Hyperbolic Matrix(519,988,218,415) (-2/1,-17/9) -> (69/29,50/21) Hyperbolic Matrix(469,884,304,573) (-17/9,-15/8) -> (37/24,17/11) Hyperbolic Matrix(363,676,-196,-365) (-15/8,-13/7) -> (-13/7,-37/20) Parabolic Matrix(3121,5772,-2530,-4679) (-37/20,-61/33) -> (-95/77,-37/30) Hyperbolic Matrix(311,572,56,103) (-24/13,-11/6) -> (11/2,28/5) Hyperbolic Matrix(313,572,-284,-519) (-11/6,-42/23) -> (-10/9,-11/10) Hyperbolic Matrix(5927,10816,2678,4887) (-73/40,-104/57) -> (104/47,31/14) Hyperbolic Matrix(5929,10816,2680,4889) (-104/57,-31/17) -> (73/33,104/47) Hyperbolic Matrix(1769,3224,400,729) (-31/17,-51/28) -> (53/12,31/7) Hyperbolic Matrix(259,468,-202,-365) (-20/11,-9/5) -> (-9/7,-32/25) Hyperbolic Matrix(727,1300,-524,-937) (-9/5,-25/14) -> (-25/18,-43/31) Hyperbolic Matrix(467,832,-380,-677) (-25/14,-16/9) -> (-16/13,-27/22) Hyperbolic Matrix(1353,2392,530,937) (-23/13,-53/30) -> (51/20,23/9) Hyperbolic Matrix(1561,2756,354,625) (-53/30,-30/17) -> (22/5,53/12) Hyperbolic Matrix(207,364,-178,-313) (-30/17,-7/4) -> (-7/6,-22/19) Hyperbolic Matrix(209,364,120,209) (-7/4,-26/15) -> (26/15,7/4) Hyperbolic Matrix(571,988,330,571) (-26/15,-19/11) -> (19/11,26/15) Hyperbolic Matrix(1145,1976,784,1353) (-19/11,-69/40) -> (35/24,19/13) Hyperbolic Matrix(573,988,272,469) (-69/40,-50/29) -> (2/1,17/8) Hyperbolic Matrix(1509,2600,574,989) (-50/29,-31/18) -> (21/8,50/19) Hyperbolic Matrix(937,1612,726,1249) (-31/18,-43/25) -> (9/7,31/24) Hyperbolic Matrix(6865,11804,-5564,-9567) (-43/25,-98/57) -> (-58/47,-95/77) Hyperbolic Matrix(25167,43264,10526,18095) (-153/89,-208/121) -> (208/87,55/23) Hyperbolic Matrix(25169,43264,10528,18097) (-208/121,-55/32) -> (153/64,208/87) Hyperbolic Matrix(2391,4108,-1756,-3017) (-55/32,-12/7) -> (-64/47,-49/36) Hyperbolic Matrix(883,1508,-640,-1093) (-12/7,-29/17) -> (-29/21,-40/29) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(1507,2548,-954,-1613) (-22/13,-27/16) -> (-79/50,-30/19) Hyperbolic Matrix(987,1664,-710,-1197) (-27/16,-5/3) -> (-57/41,-25/18) Hyperbolic Matrix(157,260,32,53) (-5/3,-28/17) -> (24/5,5/1) Hyperbolic Matrix(5875,9672,2242,3691) (-28/17,-79/48) -> (131/50,76/29) Hyperbolic Matrix(12481,20540,7584,12481) (-79/48,-130/79) -> (130/79,79/48) Hyperbolic Matrix(8059,13260,4898,8059) (-130/79,-51/31) -> (51/31,130/79) Hyperbolic Matrix(1455,2392,632,1039) (-51/31,-23/14) -> (23/10,53/23) Hyperbolic Matrix(571,936,158,259) (-23/14,-18/11) -> (18/5,29/8) Hyperbolic Matrix(415,676,-256,-417) (-18/11,-13/8) -> (-13/8,-34/21) Parabolic Matrix(2185,3536,-1606,-2599) (-34/21,-55/34) -> (-49/36,-34/25) Hyperbolic Matrix(5981,9672,2348,3797) (-131/81,-76/47) -> (28/11,79/31) Hyperbolic Matrix(1611,2600,676,1091) (-21/13,-50/31) -> (50/21,31/13) Hyperbolic Matrix(26831,43264,10190,16431) (-129/80,-208/129) -> (208/79,79/30) Hyperbolic Matrix(26833,43264,10192,16433) (-208/129,-79/49) -> (129/49,208/79) Hyperbolic Matrix(1613,2600,420,677) (-79/49,-29/18) -> (23/6,27/7) Hyperbolic Matrix(1195,1924,936,1507) (-29/18,-37/23) -> (37/29,23/18) Hyperbolic Matrix(259,416,226,363) (-37/23,-8/5) -> (8/7,15/13) Hyperbolic Matrix(883,1404,-622,-989) (-8/5,-27/17) -> (-27/19,-44/31) Hyperbolic Matrix(1507,2392,1146,1819) (-27/17,-73/46) -> (21/16,25/19) Hyperbolic Matrix(10193,16172,-8062,-12791) (-119/75,-46/29) -> (-110/87,-67/53) Hyperbolic Matrix(623,988,524,831) (-46/29,-19/12) -> (19/16,6/5) Hyperbolic Matrix(625,988,198,313) (-19/12,-49/31) -> (3/1,19/6) Hyperbolic Matrix(5199,8216,-3686,-5825) (-49/31,-79/50) -> (-79/56,-55/39) Hyperbolic Matrix(1715,2704,626,987) (-41/26,-52/33) -> (52/19,11/4) Hyperbolic Matrix(1717,2704,628,989) (-52/33,-11/7) -> (41/15,52/19) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(2131,3328,632,987) (-25/16,-64/41) -> (64/19,27/8) Hyperbolic Matrix(3899,6084,-2500,-3901) (-64/41,-39/25) -> (-39/25,-92/59) Parabolic Matrix(935,1456,734,1143) (-53/34,-14/9) -> (14/11,51/40) Hyperbolic Matrix(1039,1612,-738,-1145) (-14/9,-31/20) -> (-31/22,-38/27) Hyperbolic Matrix(571,884,436,675) (-31/20,-17/11) -> (17/13,21/16) Hyperbolic Matrix(573,884,304,469) (-17/11,-37/24) -> (15/8,17/9) Hyperbolic Matrix(1925,2964,-1384,-2131) (-37/24,-20/13) -> (-32/23,-89/64) Hyperbolic Matrix(1561,2392,340,521) (-23/15,-26/17) -> (78/17,23/5) Hyperbolic Matrix(1091,1664,238,363) (-26/17,-3/2) -> (55/12,78/17) Hyperbolic Matrix(675,988,248,363) (-3/2,-19/13) -> (19/7,49/18) Hyperbolic Matrix(1353,1976,784,1145) (-19/13,-35/24) -> (69/40,19/11) Hyperbolic Matrix(4317,6292,3176,4629) (-35/24,-51/35) -> (53/39,87/64) Hyperbolic Matrix(3641,5304,786,1145) (-51/35,-16/11) -> (88/19,51/11) Hyperbolic Matrix(467,676,-324,-469) (-16/11,-13/9) -> (-13/9,-36/25) Parabolic Matrix(833,1196,218,313) (-23/16,-33/23) -> (19/5,23/6) Hyperbolic Matrix(1559,2236,1232,1767) (-33/23,-43/30) -> (43/34,19/15) Hyperbolic Matrix(363,520,326,467) (-43/30,-10/7) -> (10/9,9/8) Hyperbolic Matrix(7591,10816,2262,3223) (-57/40,-104/73) -> (104/31,47/14) Hyperbolic Matrix(7593,10816,2264,3225) (-104/73,-47/33) -> (57/17,104/31) Hyperbolic Matrix(4419,6292,-3178,-4525) (-47/33,-37/26) -> (-89/64,-57/41) Hyperbolic Matrix(2341,3328,842,1197) (-64/45,-27/19) -> (25/9,64/23) Hyperbolic Matrix(1613,2288,184,261) (-61/43,-78/55) -> (26/3,9/1) Hyperbolic Matrix(1247,1768,146,207) (-78/55,-17/12) -> (17/2,26/3) Hyperbolic Matrix(625,884,-514,-727) (-17/12,-24/17) -> (-28/23,-17/14) Hyperbolic Matrix(2911,4108,1768,2495) (-24/17,-79/56) -> (79/48,28/17) Hyperbolic Matrix(1923,2704,554,779) (-45/32,-52/37) -> (52/15,7/2) Hyperbolic Matrix(1925,2704,556,781) (-52/37,-7/5) -> (45/13,52/15) Hyperbolic Matrix(261,364,38,53) (-7/5,-32/23) -> (20/3,7/1) Hyperbolic Matrix(7799,10816,2174,3015) (-43/31,-104/75) -> (104/29,61/17) Hyperbolic Matrix(7801,10816,2176,3017) (-104/75,-61/44) -> (43/12,104/29) Hyperbolic Matrix(677,936,264,365) (-18/13,-29/21) -> (23/9,18/7) Hyperbolic Matrix(415,572,-378,-521) (-51/37,-11/8) -> (-11/10,-1/1) Hyperbolic Matrix(417,572,304,417) (-11/8,-26/19) -> (26/19,11/8) Hyperbolic Matrix(571,780,418,571) (-26/19,-15/11) -> (15/11,26/19) Hyperbolic Matrix(31823,43264,8414,11439) (-121/89,-208/153) -> (208/55,87/23) Hyperbolic Matrix(31825,43264,8416,11441) (-208/153,-87/64) -> (121/32,208/55) Hyperbolic Matrix(4629,6292,3176,4317) (-87/64,-53/39) -> (51/35,35/24) Hyperbolic Matrix(2029,2756,-1722,-2339) (-53/39,-19/14) -> (-33/28,-53/45) Hyperbolic Matrix(883,1196,268,363) (-19/14,-23/17) -> (23/7,33/10) Hyperbolic Matrix(1923,2600,730,987) (-23/17,-27/20) -> (79/30,29/11) Hyperbolic Matrix(155,208,38,51) (-27/20,-4/3) -> (4/1,25/6) Hyperbolic Matrix(157,208,40,53) (-4/3,-25/19) -> (27/7,4/1) Hyperbolic Matrix(1819,2392,1146,1507) (-25/19,-21/16) -> (73/46,27/17) Hyperbolic Matrix(675,884,436,571) (-21/16,-17/13) -> (17/11,31/20) Hyperbolic Matrix(519,676,-400,-521) (-17/13,-13/10) -> (-13/10,-35/27) Parabolic Matrix(2131,2756,924,1195) (-22/17,-53/41) -> (53/23,30/13) Hyperbolic Matrix(2495,3224,1126,1455) (-53/41,-31/24) -> (31/14,51/23) Hyperbolic Matrix(1249,1612,726,937) (-31/24,-9/7) -> (43/25,31/18) Hyperbolic Matrix(1301,1664,448,573) (-55/43,-78/61) -> (26/9,3/1) Hyperbolic Matrix(1871,2392,650,831) (-78/61,-23/18) -> (23/8,26/9) Hyperbolic Matrix(1507,1924,936,1195) (-23/18,-37/29) -> (37/23,29/18) Hyperbolic Matrix(4159,5304,1304,1663) (-88/69,-51/40) -> (51/16,16/5) Hyperbolic Matrix(1143,1456,734,935) (-51/40,-14/11) -> (14/9,53/34) Hyperbolic Matrix(2131,2704,450,571) (-33/26,-52/41) -> (52/11,19/4) Hyperbolic Matrix(2133,2704,452,573) (-52/41,-19/15) -> (33/7,52/11) Hyperbolic Matrix(1767,2236,1232,1559) (-19/15,-43/34) -> (43/30,33/23) Hyperbolic Matrix(207,260,82,103) (-24/19,-5/4) -> (5/2,28/11) Hyperbolic Matrix(209,260,168,209) (-5/4,-26/21) -> (26/21,5/4) Hyperbolic Matrix(883,1092,714,883) (-26/21,-21/17) -> (21/17,26/21) Hyperbolic Matrix(1351,1664,928,1143) (-53/43,-16/13) -> (16/11,51/35) Hyperbolic Matrix(469,572,214,261) (-11/9,-28/23) -> (24/11,11/5) Hyperbolic Matrix(2235,2704,386,467) (-23/19,-52/43) -> (52/9,29/5) Hyperbolic Matrix(2237,2704,388,469) (-52/43,-29/24) -> (23/4,52/9) Hyperbolic Matrix(831,988,524,623) (-6/5,-19/16) -> (19/12,46/29) Hyperbolic Matrix(571,676,-484,-573) (-19/16,-13/11) -> (-13/11,-33/28) Parabolic Matrix(311,364,88,103) (-20/17,-7/6) -> (7/2,32/9) Hyperbolic Matrix(2339,2704,314,363) (-37/32,-52/45) -> (52/7,15/2) Hyperbolic Matrix(2341,2704,316,365) (-52/45,-15/13) -> (37/5,52/7) Hyperbolic Matrix(363,416,226,259) (-15/13,-8/7) -> (8/5,37/23) Hyperbolic Matrix(1561,1768,460,521) (-17/15,-26/23) -> (78/23,17/5) Hyperbolic Matrix(2027,2288,598,675) (-26/23,-9/8) -> (61/18,78/23) Hyperbolic Matrix(467,520,326,363) (-9/8,-10/9) -> (10/7,43/30) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(519,-572,284,-313) (1/1,10/9) -> (42/23,53/29) Hyperbolic Matrix(779,-884,230,-261) (9/8,8/7) -> (44/13,61/18) Hyperbolic Matrix(313,-364,178,-207) (15/13,7/6) -> (7/4,37/21) Hyperbolic Matrix(573,-676,484,-571) (20/17,13/11) -> (13/11,32/27) Parabolic Matrix(2237,-2652,1008,-1195) (32/27,19/16) -> (71/32,20/9) Hyperbolic Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(3121,-3848,674,-831) (16/13,37/30) -> (37/8,88/19) Hyperbolic Matrix(4213,-5200,1558,-1923) (37/30,21/17) -> (73/27,119/44) Hyperbolic Matrix(1975,-2496,906,-1145) (24/19,43/34) -> (61/28,24/11) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(3017,-3848,570,-727) (51/40,37/29) -> (37/7,53/10) Hyperbolic Matrix(365,-468,202,-259) (23/18,9/7) -> (9/5,29/16) Hyperbolic Matrix(883,-1144,362,-469) (22/17,13/10) -> (39/16,22/9) Hyperbolic Matrix(677,-884,278,-363) (13/10,17/13) -> (17/7,39/16) Hyperbolic Matrix(3483,-4732,1570,-2133) (19/14,53/39) -> (51/23,71/32) Hyperbolic Matrix(5201,-7072,1376,-1871) (87/64,34/25) -> (34/9,121/32) Hyperbolic Matrix(1873,-2548,1146,-1559) (34/25,15/11) -> (67/41,18/11) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1197,-1664,710,-987) (25/18,32/23) -> (32/19,27/16) Hyperbolic Matrix(1145,-1612,738,-1039) (7/5,31/22) -> (31/20,45/29) Hyperbolic Matrix(2029,-2860,774,-1091) (31/22,24/17) -> (76/29,21/8) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2339,-3328,622,-885) (64/45,37/26) -> (15/4,64/17) Hyperbolic Matrix(1351,-1924,804,-1145) (37/26,47/33) -> (5/3,37/22) Hyperbolic Matrix(729,-1040,218,-311) (47/33,10/7) -> (10/3,57/17) Hyperbolic Matrix(831,-1196,362,-521) (23/16,13/9) -> (39/17,23/10) Hyperbolic Matrix(573,-832,250,-363) (13/9,16/11) -> (16/7,39/17) Hyperbolic Matrix(779,-1196,170,-261) (3/2,20/13) -> (32/7,55/12) Hyperbolic Matrix(1249,-1924,742,-1143) (20/13,37/24) -> (37/22,32/19) Hyperbolic Matrix(1507,-2340,436,-677) (45/29,14/9) -> (38/11,45/13) Hyperbolic Matrix(4369,-6812,1200,-1871) (53/34,39/25) -> (91/25,51/14) Hyperbolic Matrix(4731,-7384,1300,-2029) (39/25,64/41) -> (40/11,91/25) Hyperbolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(1613,-2548,954,-1507) (30/19,49/31) -> (49/29,22/13) Hyperbolic Matrix(3277,-5200,622,-987) (46/29,73/46) -> (21/4,58/11) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(6449,-10400,2450,-3951) (79/49,50/31) -> (50/19,129/49) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(1975,-3224,574,-937) (31/19,49/30) -> (55/16,31/9) Hyperbolic Matrix(5251,-8580,1560,-2549) (49/30,67/41) -> (37/11,101/30) Hyperbolic Matrix(4679,-7904,1786,-3017) (27/16,49/29) -> (55/21,131/50) Hyperbolic Matrix(675,-1144,154,-261) (22/13,17/10) -> (35/8,22/5) Hyperbolic Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(1613,-2756,882,-1507) (41/24,53/31) -> (53/29,11/6) Hyperbolic Matrix(3223,-5512,1156,-1977) (53/31,12/7) -> (92/33,53/19) Hyperbolic Matrix(2755,-4732,818,-1405) (12/7,55/32) -> (101/30,64/19) Hyperbolic Matrix(11857,-20384,4960,-8527) (55/32,98/57) -> (98/41,153/64) Hyperbolic Matrix(5201,-8944,1088,-1871) (98/57,43/25) -> (43/9,110/23) Hyperbolic Matrix(1091,-1924,148,-261) (37/21,30/17) -> (22/3,37/5) Hyperbolic Matrix(675,-1196,206,-365) (23/13,16/9) -> (36/11,23/7) Hyperbolic Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(573,-1040,200,-363) (29/16,20/11) -> (20/7,23/8) Hyperbolic Matrix(1143,-2080,172,-313) (20/11,51/28) -> (53/8,20/3) Hyperbolic Matrix(2393,-4368,1082,-1975) (31/17,42/23) -> (42/19,73/33) Hyperbolic Matrix(365,-676,196,-363) (24/13,13/7) -> (13/7,28/15) Parabolic Matrix(1197,-2236,250,-467) (28/15,15/8) -> (67/14,24/5) Hyperbolic Matrix(313,-676,144,-311) (15/7,13/6) -> (13/6,37/17) Parabolic Matrix(2651,-5772,502,-1093) (37/17,61/28) -> (95/18,37/7) Hyperbolic Matrix(259,-572,24,-53) (11/5,42/19) -> (10/1,11/1) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(157,-364,22,-51) (30/13,7/3) -> (7/1,22/3) Hyperbolic Matrix(4939,-11804,936,-2237) (43/18,98/41) -> (58/11,95/18) Hyperbolic Matrix(1717,-4108,456,-1091) (55/23,12/5) -> (64/17,49/13) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(261,-676,100,-259) (18/7,13/5) -> (13/5,34/13) Parabolic Matrix(1351,-3536,358,-937) (34/13,55/21) -> (49/13,34/9) Hyperbolic Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(5979,-16172,1250,-3381) (119/44,46/17) -> (110/23,67/14) Hyperbolic Matrix(3017,-8216,878,-2391) (49/18,79/29) -> (79/23,55/16) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(2185,-6084,784,-2183) (64/23,39/14) -> (39/14,92/33) Parabolic Matrix(573,-1612,166,-467) (14/5,31/11) -> (31/9,38/11) Hyperbolic Matrix(1039,-2964,292,-833) (37/13,20/7) -> (32/9,89/25) Hyperbolic Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(1873,-6292,526,-1767) (47/14,37/11) -> (89/25,57/16) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(157,-572,14,-51) (51/14,11/3) -> (11/1,1/0) Hyperbolic Matrix(727,-2756,110,-417) (53/14,19/5) -> (33/5,53/8) Hyperbolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(53,572,-24,-259) -> Matrix(1,-2,0,1) Matrix(53,520,16,157) -> Matrix(1,0,0,1) Matrix(105,884,-74,-623) -> Matrix(7,6,-6,-5) Matrix(53,416,20,157) -> Matrix(1,0,0,1) Matrix(51,364,-22,-157) -> Matrix(3,2,-2,-1) Matrix(53,364,38,261) -> Matrix(1,2,-2,-3) Matrix(103,676,-16,-105) -> Matrix(1,0,2,1) Matrix(415,2652,-228,-1457) -> Matrix(3,8,-2,-5) Matrix(157,988,58,365) -> Matrix(1,0,0,1) Matrix(155,884,-64,-365) -> Matrix(1,-2,0,1) Matrix(157,884,-46,-259) -> Matrix(1,0,0,1) Matrix(155,832,-68,-365) -> Matrix(1,0,0,1) Matrix(727,3848,-570,-3017) -> Matrix(5,4,-4,-3) Matrix(987,5200,-622,-3277) -> Matrix(1,-2,0,1) Matrix(209,1092,40,209) -> Matrix(1,0,0,1) Matrix(51,260,10,51) -> Matrix(1,0,-2,1) Matrix(53,260,32,157) -> Matrix(3,4,-4,-5) Matrix(521,2496,-282,-1351) -> Matrix(11,24,-6,-13) Matrix(469,2236,142,677) -> Matrix(1,2,-2,-3) Matrix(155,728,-122,-573) -> Matrix(5,4,-4,-3) Matrix(313,1456,112,521) -> Matrix(1,0,0,1) Matrix(831,3848,-674,-3121) -> Matrix(3,-4,-2,3) Matrix(417,1924,158,729) -> Matrix(1,0,-2,1) Matrix(103,468,-46,-209) -> Matrix(1,-2,0,1) Matrix(363,1612,152,675) -> Matrix(3,4,-4,-5) Matrix(729,3224,400,1769) -> Matrix(3,-2,-4,3) Matrix(625,2756,354,1561) -> Matrix(1,2,-2,-3) Matrix(261,1144,-154,-675) -> Matrix(3,8,-2,-5) Matrix(207,884,-122,-521) -> Matrix(3,8,-2,-5) Matrix(209,884,74,313) -> Matrix(1,0,0,1) Matrix(573,2392,212,885) -> Matrix(1,0,-2,1) Matrix(51,208,38,155) -> Matrix(3,10,-4,-13) Matrix(53,208,40,157) -> Matrix(3,10,-4,-13) Matrix(677,2600,420,1613) -> Matrix(5,6,-6,-7) Matrix(313,1196,218,833) -> Matrix(5,6,-6,-7) Matrix(1249,4732,-686,-2599) -> Matrix(23,28,-14,-17) Matrix(1663,6292,522,1975) -> Matrix(5,6,-6,-7) Matrix(1871,7072,-1376,-5201) -> Matrix(3,-10,-2,7) Matrix(675,2548,-262,-989) -> Matrix(1,2,-2,-3) Matrix(209,780,56,209) -> Matrix(11,12,-12,-13) Matrix(155,572,42,155) -> Matrix(7,6,-6,-5) Matrix(415,1508,-172,-625) -> Matrix(5,4,-4,-3) Matrix(259,936,158,571) -> Matrix(1,2,-2,-3) Matrix(363,1300,-160,-573) -> Matrix(5,2,2,1) Matrix(467,1664,-190,-677) -> Matrix(15,4,-4,-1) Matrix(103,364,88,311) -> Matrix(13,-4,-16,5) Matrix(467,1612,-166,-573) -> Matrix(1,2,-2,-3) Matrix(831,2860,-514,-1769) -> Matrix(3,2,-2,-1) Matrix(365,1248,198,677) -> Matrix(7,-2,-10,3) Matrix(415,1404,-154,-521) -> Matrix(1,0,0,1) Matrix(987,3328,632,2131) -> Matrix(3,4,-4,-5) Matrix(989,3328,-726,-2443) -> Matrix(3,-16,-2,11) Matrix(573,1924,-232,-779) -> Matrix(1,-6,0,1) Matrix(311,1040,-218,-729) -> Matrix(3,8,-2,-5) Matrix(157,520,16,53) -> Matrix(1,0,0,1) Matrix(677,2236,142,469) -> Matrix(1,2,-2,-3) Matrix(363,1196,268,883) -> Matrix(3,10,-4,-13) Matrix(365,1196,-206,-675) -> Matrix(3,2,-2,-1) Matrix(259,832,-146,-469) -> Matrix(3,2,-2,-1) Matrix(521,1664,98,313) -> Matrix(1,2,-2,-3) Matrix(1975,6292,522,1663) -> Matrix(5,6,-6,-7) Matrix(623,1976,262,831) -> Matrix(1,2,-2,-3) Matrix(313,988,198,625) -> Matrix(3,-2,-4,3) Matrix(417,1196,-326,-935) -> Matrix(9,8,-8,-7) Matrix(675,1924,-274,-781) -> Matrix(11,6,-2,-1) Matrix(311,884,146,415) -> Matrix(1,2,-2,-3) Matrix(313,884,74,209) -> Matrix(1,0,0,1) Matrix(833,2340,-592,-1663) -> Matrix(7,2,-4,-1) Matrix(521,1456,112,313) -> Matrix(1,0,0,1) Matrix(2443,6812,-1772,-4941) -> Matrix(15,2,-8,-1) Matrix(2653,7384,-1924,-5355) -> Matrix(5,-2,-2,1) Matrix(1197,3328,842,2341) -> Matrix(5,-4,-6,5) Matrix(469,1300,-206,-571) -> Matrix(1,0,0,1) Matrix(571,1560,-362,-989) -> Matrix(3,8,-2,-5) Matrix(935,2548,-382,-1041) -> Matrix(5,8,-2,-3) Matrix(363,988,248,675) -> Matrix(3,4,-4,-5) Matrix(365,988,58,157) -> Matrix(1,0,0,1) Matrix(1923,5200,-1558,-4213) -> Matrix(3,-4,-2,3) Matrix(885,2392,212,573) -> Matrix(1,0,-2,1) Matrix(155,416,-136,-365) -> Matrix(5,14,-4,-11) Matrix(157,416,20,53) -> Matrix(1,0,0,1) Matrix(729,1924,158,417) -> Matrix(1,0,-2,1) Matrix(987,2600,730,1923) -> Matrix(3,10,-4,-13) Matrix(3951,10400,-2450,-6449) -> Matrix(3,8,-2,-5) Matrix(989,2600,574,1509) -> Matrix(3,4,-4,-5) Matrix(259,676,-100,-261) -> Matrix(1,0,0,1) Matrix(1249,3224,-886,-2287) -> Matrix(3,2,-2,-1) Matrix(3329,8580,-2340,-6031) -> Matrix(11,18,-8,-13) Matrix(365,936,264,677) -> Matrix(3,4,-4,-5) Matrix(937,2392,530,1353) -> Matrix(5,6,-6,-7) Matrix(5201,13260,2040,5201) -> Matrix(15,16,-16,-17) Matrix(8059,20540,3162,8059) -> Matrix(23,22,-22,-21) Matrix(1613,4108,470,1197) -> Matrix(3,2,-2,-1) Matrix(103,260,82,207) -> Matrix(3,4,-4,-5) Matrix(3225,7904,-1994,-4887) -> Matrix(7,20,-6,-17) Matrix(469,1144,-362,-883) -> Matrix(21,46,-16,-35) Matrix(623,1508,-516,-1249) -> Matrix(3,2,-2,-1) Matrix(1143,2756,-518,-1249) -> Matrix(5,8,-2,-3) Matrix(2289,5512,-1468,-3535) -> Matrix(3,2,-2,-1) Matrix(1977,4732,-1390,-3327) -> Matrix(11,18,-8,-13) Matrix(8527,20384,-4960,-11857) -> Matrix(5,8,-2,-3) Matrix(3743,8944,-2960,-7073) -> Matrix(11,18,-8,-13) Matrix(675,1612,152,363) -> Matrix(3,4,-4,-5) Matrix(1091,2600,676,1611) -> Matrix(3,4,-4,-5) Matrix(415,988,218,519) -> Matrix(3,4,-4,-5) Matrix(831,1976,262,623) -> Matrix(1,2,-2,-3) Matrix(417,988,176,417) -> Matrix(3,4,-4,-5) Matrix(155,364,66,155) -> Matrix(1,2,-2,-3) Matrix(833,1924,-720,-1663) -> Matrix(13,4,-10,-3) Matrix(1195,2756,924,2131) -> Matrix(13,-4,-16,5) Matrix(1039,2392,632,1455) -> Matrix(3,10,-4,-13) Matrix(521,1196,-362,-831) -> Matrix(3,2,-2,-1) Matrix(987,2236,-712,-1613) -> Matrix(3,-16,-2,11) Matrix(467,1040,-304,-677) -> Matrix(3,20,-2,-13) Matrix(937,2080,-796,-1767) -> Matrix(37,152,-28,-115) Matrix(1455,3224,1126,2495) -> Matrix(31,102,-38,-125) Matrix(1975,4368,-1082,-2393) -> Matrix(37,106,-22,-63) Matrix(571,1248,404,883) -> Matrix(1,4,-2,-7) Matrix(311,676,-144,-313) -> Matrix(11,24,-6,-13) Matrix(1039,2236,-822,-1769) -> Matrix(11,18,-8,-13) Matrix(415,884,146,311) -> Matrix(1,2,-2,-3) Matrix(469,988,272,573) -> Matrix(3,4,-4,-5) Matrix(519,988,218,415) -> Matrix(3,4,-4,-5) Matrix(469,884,304,573) -> Matrix(3,-2,-4,3) Matrix(363,676,-196,-365) -> Matrix(15,32,-8,-17) Matrix(3121,5772,-2530,-4679) -> Matrix(27,50,-20,-37) Matrix(311,572,56,103) -> Matrix(1,2,-6,-11) Matrix(313,572,-284,-519) -> Matrix(5,8,-2,-3) Matrix(5927,10816,2678,4887) -> Matrix(159,266,-266,-445) Matrix(5929,10816,2680,4889) -> Matrix(129,214,-214,-355) Matrix(1769,3224,400,729) -> Matrix(1,2,-4,-7) Matrix(259,468,-202,-365) -> Matrix(17,28,-14,-23) Matrix(727,1300,-524,-937) -> Matrix(13,18,-8,-11) Matrix(467,832,-380,-677) -> Matrix(1,0,0,1) Matrix(1353,2392,530,937) -> Matrix(5,6,-6,-7) Matrix(1561,2756,354,625) -> Matrix(1,2,-2,-3) Matrix(207,364,-178,-313) -> Matrix(5,14,-4,-11) Matrix(209,364,120,209) -> Matrix(7,12,-10,-17) Matrix(571,988,330,571) -> Matrix(5,6,-6,-7) Matrix(1145,1976,784,1353) -> Matrix(5,6,-6,-7) Matrix(573,988,272,469) -> Matrix(3,4,-4,-5) Matrix(1509,2600,574,989) -> Matrix(3,4,-4,-5) Matrix(937,1612,726,1249) -> Matrix(13,22,-16,-27) Matrix(6865,11804,-5564,-9567) -> Matrix(3,2,-2,-1) Matrix(25167,43264,10526,18095) -> Matrix(9,20,-14,-31) Matrix(25169,43264,10528,18097) -> Matrix(19,36,-28,-53) Matrix(2391,4108,-1756,-3017) -> Matrix(35,54,-24,-37) Matrix(883,1508,-640,-1093) -> Matrix(1,0,0,1) Matrix(519,884,-428,-729) -> Matrix(19,34,-14,-25) Matrix(1507,2548,-954,-1613) -> Matrix(11,18,-8,-13) Matrix(987,1664,-710,-1197) -> Matrix(1,0,0,1) Matrix(157,260,32,53) -> Matrix(3,4,-4,-5) Matrix(5875,9672,2242,3691) -> Matrix(5,8,-12,-19) Matrix(12481,20540,7584,12481) -> Matrix(127,192,-170,-257) Matrix(8059,13260,4898,8059) -> Matrix(101,150,-134,-199) Matrix(1455,2392,632,1039) -> Matrix(7,10,-12,-17) Matrix(571,936,158,259) -> Matrix(1,2,-2,-3) Matrix(415,676,-256,-417) -> Matrix(1,0,0,1) Matrix(2185,3536,-1606,-2599) -> Matrix(23,36,-16,-25) Matrix(5981,9672,2348,3797) -> Matrix(1,0,0,1) Matrix(1611,2600,676,1091) -> Matrix(3,4,-4,-5) Matrix(26831,43264,10190,16431) -> Matrix(5,8,-12,-19) Matrix(26833,43264,10192,16433) -> Matrix(15,22,-28,-41) Matrix(1613,2600,420,677) -> Matrix(5,6,-6,-7) Matrix(1195,1924,936,1507) -> Matrix(5,6,-6,-7) Matrix(259,416,226,363) -> Matrix(13,22,-16,-27) Matrix(883,1404,-622,-989) -> Matrix(3,2,-2,-1) Matrix(1507,2392,1146,1819) -> Matrix(11,26,-14,-33) Matrix(10193,16172,-8062,-12791) -> Matrix(5,14,-4,-11) Matrix(623,988,524,831) -> Matrix(11,26,-14,-33) Matrix(625,988,198,313) -> Matrix(1,2,-4,-7) Matrix(5199,8216,-3686,-5825) -> Matrix(23,36,-16,-25) Matrix(1715,2704,626,987) -> Matrix(5,8,-12,-19) Matrix(1717,2704,628,989) -> Matrix(7,10,-12,-17) Matrix(365,572,-298,-467) -> Matrix(11,18,-8,-13) Matrix(2131,3328,632,987) -> Matrix(3,4,-4,-5) Matrix(3899,6084,-2500,-3901) -> Matrix(1,0,0,1) Matrix(935,1456,734,1143) -> Matrix(5,6,-6,-7) Matrix(1039,1612,-738,-1145) -> Matrix(1,0,0,1) Matrix(571,884,436,675) -> Matrix(3,10,-4,-13) Matrix(573,884,304,469) -> Matrix(1,2,-4,-7) Matrix(1925,2964,-1384,-2131) -> Matrix(1,0,0,1) Matrix(1561,2392,340,521) -> Matrix(17,26,-36,-55) Matrix(1091,1664,238,363) -> Matrix(15,22,-28,-41) Matrix(675,988,248,363) -> Matrix(3,4,-4,-5) Matrix(1353,1976,784,1145) -> Matrix(5,6,-6,-7) Matrix(4317,6292,3176,4629) -> Matrix(23,10,-30,-13) Matrix(3641,5304,786,1145) -> Matrix(1,2,-4,-7) Matrix(467,676,-324,-469) -> Matrix(1,0,0,1) Matrix(833,1196,218,313) -> Matrix(5,6,-6,-7) Matrix(1559,2236,1232,1767) -> Matrix(5,6,-6,-7) Matrix(363,520,326,467) -> Matrix(7,8,-8,-9) Matrix(7591,10816,2262,3223) -> Matrix(29,44,-60,-91) Matrix(7593,10816,2264,3225) -> Matrix(35,52,-68,-101) Matrix(4419,6292,-3178,-4525) -> Matrix(37,54,-24,-35) Matrix(2341,3328,842,1197) -> Matrix(3,4,-10,-13) Matrix(1613,2288,184,261) -> Matrix(7,8,-8,-9) Matrix(1247,1768,146,207) -> Matrix(3,2,-2,-1) Matrix(625,884,-514,-727) -> Matrix(11,18,-8,-13) Matrix(2911,4108,1768,2495) -> Matrix(19,30,-26,-41) Matrix(1923,2704,554,779) -> Matrix(5,8,-12,-19) Matrix(1925,2704,556,781) -> Matrix(7,10,-12,-17) Matrix(261,364,38,53) -> Matrix(1,2,-2,-3) Matrix(7799,10816,2174,3015) -> Matrix(29,44,-2,-3) Matrix(7801,10816,2176,3017) -> Matrix(31,46,2,3) Matrix(677,936,264,365) -> Matrix(3,4,-4,-5) Matrix(415,572,-378,-521) -> Matrix(11,18,-8,-13) Matrix(417,572,304,417) -> Matrix(31,48,-42,-65) Matrix(571,780,418,571) -> Matrix(77,114,-102,-151) Matrix(31823,43264,8414,11439) -> Matrix(155,224,-164,-237) Matrix(31825,43264,8416,11441) -> Matrix(115,166,-106,-153) Matrix(4629,6292,3176,4317) -> Matrix(7,10,2,3) Matrix(2029,2756,-1722,-2339) -> Matrix(379,542,-286,-409) Matrix(883,1196,268,363) -> Matrix(7,10,-12,-17) Matrix(1923,2600,730,987) -> Matrix(7,10,-12,-17) Matrix(155,208,38,51) -> Matrix(7,10,-12,-17) Matrix(157,208,40,53) -> Matrix(7,10,-12,-17) Matrix(1819,2392,1146,1507) -> Matrix(19,26,-30,-41) Matrix(675,884,436,571) -> Matrix(7,10,-12,-17) Matrix(519,676,-400,-521) -> Matrix(119,160,-90,-121) Matrix(2131,2756,924,1195) -> Matrix(3,4,-16,-21) Matrix(2495,3224,1126,1455) -> Matrix(79,102,-134,-173) Matrix(1249,1612,726,937) -> Matrix(17,22,-24,-31) Matrix(1301,1664,448,573) -> Matrix(11,12,-12,-13) Matrix(1871,2392,650,831) -> Matrix(5,4,-4,-3) Matrix(1507,1924,936,1195) -> Matrix(5,6,-6,-7) Matrix(4159,5304,1304,1663) -> Matrix(5,6,-6,-7) Matrix(1143,1456,734,935) -> Matrix(5,6,-6,-7) Matrix(2131,2704,450,571) -> Matrix(7,8,-8,-9) Matrix(2133,2704,452,573) -> Matrix(1,2,-2,-3) Matrix(1767,2236,1232,1559) -> Matrix(5,6,-6,-7) Matrix(207,260,82,103) -> Matrix(3,4,-4,-5) Matrix(209,260,168,209) -> Matrix(17,24,-22,-31) Matrix(883,1092,714,883) -> Matrix(7,8,-8,-9) Matrix(1351,1664,928,1143) -> Matrix(5,6,-6,-7) Matrix(469,572,214,261) -> Matrix(19,26,-30,-41) Matrix(2235,2704,386,467) -> Matrix(3,4,20,27) Matrix(2237,2704,388,469) -> Matrix(3,4,-22,-29) Matrix(831,988,524,623) -> Matrix(19,26,-30,-41) Matrix(571,676,-484,-573) -> Matrix(239,320,-180,-241) Matrix(311,364,88,103) -> Matrix(3,4,-16,-21) Matrix(2339,2704,314,363) -> Matrix(17,22,-24,-31) Matrix(2341,2704,316,365) -> Matrix(25,32,-18,-23) Matrix(363,416,226,259) -> Matrix(17,22,-24,-31) Matrix(1561,1768,460,521) -> Matrix(19,24,-42,-53) Matrix(2027,2288,598,675) -> Matrix(21,26,-38,-47) Matrix(467,520,326,363) -> Matrix(7,8,-8,-9) Matrix(1,0,2,1) -> Matrix(9,10,-10,-11) Matrix(519,-572,284,-313) -> Matrix(13,8,-18,-11) Matrix(779,-884,230,-261) -> Matrix(17,14,-28,-23) Matrix(313,-364,178,-207) -> Matrix(17,14,-28,-23) Matrix(573,-676,484,-571) -> Matrix(399,320,-500,-401) Matrix(2237,-2652,1008,-1195) -> Matrix(211,168,-368,-293) Matrix(729,-884,428,-519) -> Matrix(43,34,-62,-49) Matrix(727,-884,514,-625) -> Matrix(23,18,-32,-25) Matrix(677,-832,380,-467) -> Matrix(1,0,0,1) Matrix(3121,-3848,674,-831) -> Matrix(5,4,-14,-11) Matrix(4213,-5200,1558,-1923) -> Matrix(5,4,-14,-11) Matrix(1975,-2496,906,-1145) -> Matrix(37,30,-58,-47) Matrix(573,-728,122,-155) -> Matrix(5,4,-4,-3) Matrix(3017,-3848,570,-727) -> Matrix(5,4,-4,-3) Matrix(365,-468,202,-259) -> Matrix(33,28,-46,-39) Matrix(883,-1144,362,-469) -> Matrix(57,46,-88,-71) Matrix(677,-884,278,-363) -> Matrix(43,34,-62,-49) Matrix(3483,-4732,1570,-2133) -> Matrix(211,162,-366,-281) Matrix(5201,-7072,1376,-1871) -> Matrix(13,10,-30,-23) Matrix(1873,-2548,1146,-1559) -> Matrix(47,36,-64,-49) Matrix(1093,-1508,640,-883) -> Matrix(1,0,0,1) Matrix(937,-1300,524,-727) -> Matrix(25,18,-32,-23) Matrix(1197,-1664,710,-987) -> Matrix(1,0,0,1) Matrix(1145,-1612,738,-1039) -> Matrix(1,0,0,1) Matrix(2029,-2860,774,-1091) -> Matrix(3,2,-2,-1) Matrix(989,-1404,622,-883) -> Matrix(3,2,-2,-1) Matrix(2339,-3328,622,-885) -> Matrix(41,32,-50,-39) Matrix(1351,-1924,804,-1145) -> Matrix(71,54,-96,-73) Matrix(729,-1040,218,-311) -> Matrix(11,8,-18,-13) Matrix(831,-1196,362,-521) -> Matrix(3,2,-2,-1) Matrix(573,-832,250,-363) -> Matrix(3,2,-2,-1) Matrix(779,-1196,170,-261) -> Matrix(19,14,-34,-25) Matrix(1249,-1924,742,-1143) -> Matrix(1,0,0,1) Matrix(1507,-2340,436,-677) -> Matrix(11,8,-18,-13) Matrix(4369,-6812,1200,-1871) -> Matrix(7,6,-6,-5) Matrix(4731,-7384,1300,-2029) -> Matrix(7,6,-6,-5) Matrix(831,-1300,466,-729) -> Matrix(25,18,-32,-23) Matrix(989,-1560,362,-571) -> Matrix(11,8,-18,-13) Matrix(1613,-2548,954,-1507) -> Matrix(23,18,-32,-25) Matrix(3277,-5200,622,-987) -> Matrix(3,2,-8,-5) Matrix(261,-416,32,-51) -> Matrix(5,4,-4,-3) Matrix(6449,-10400,2450,-3951) -> Matrix(11,8,-18,-13) Matrix(417,-676,256,-415) -> Matrix(1,0,0,1) Matrix(1975,-3224,574,-937) -> Matrix(3,2,-2,-1) Matrix(5251,-8580,1560,-2549) -> Matrix(5,4,-14,-11) Matrix(4679,-7904,1786,-3017) -> Matrix(27,20,-50,-37) Matrix(675,-1144,154,-261) -> Matrix(11,8,-18,-13) Matrix(885,-1508,152,-259) -> Matrix(3,2,4,3) Matrix(1613,-2756,882,-1507) -> Matrix(69,50,-98,-71) Matrix(3223,-5512,1156,-1977) -> Matrix(3,2,16,11) Matrix(2755,-4732,818,-1405) -> Matrix(3,2,-2,-1) Matrix(11857,-20384,4960,-8527) -> Matrix(13,8,-18,-11) Matrix(5201,-8944,1088,-1871) -> Matrix(1,0,0,1) Matrix(1091,-1924,148,-261) -> Matrix(5,4,-4,-3) Matrix(675,-1196,206,-365) -> Matrix(3,2,-2,-1) Matrix(1249,-2236,348,-623) -> Matrix(21,16,-4,-3) Matrix(573,-1040,200,-363) -> Matrix(17,12,-10,-7) Matrix(1143,-2080,172,-313) -> Matrix(11,8,4,3) Matrix(2393,-4368,1082,-1975) -> Matrix(149,106,-246,-175) Matrix(365,-676,196,-363) -> Matrix(47,32,-72,-49) Matrix(1197,-2236,250,-467) -> Matrix(13,8,-18,-11) Matrix(313,-676,144,-311) -> Matrix(35,24,-54,-37) Matrix(2651,-5772,502,-1093) -> Matrix(3,2,-14,-9) Matrix(259,-572,24,-53) -> Matrix(3,2,-8,-5) Matrix(209,-468,46,-103) -> Matrix(3,2,-8,-5) Matrix(573,-1300,160,-363) -> Matrix(5,2,2,1) Matrix(365,-832,68,-155) -> Matrix(1,0,0,1) Matrix(157,-364,22,-51) -> Matrix(3,2,-2,-1) Matrix(4939,-11804,936,-2237) -> Matrix(3,2,4,3) Matrix(1717,-4108,456,-1091) -> Matrix(1,2,-2,-3) Matrix(625,-1508,172,-415) -> Matrix(5,4,-4,-3) Matrix(365,-884,64,-155) -> Matrix(3,2,-8,-5) Matrix(1041,-2548,382,-935) -> Matrix(13,8,-18,-11) Matrix(677,-1664,190,-467) -> Matrix(7,4,12,7) Matrix(261,-676,100,-259) -> Matrix(1,0,0,1) Matrix(1351,-3536,358,-937) -> Matrix(1,2,-2,-3) Matrix(521,-1404,154,-415) -> Matrix(1,0,0,1) Matrix(5979,-16172,1250,-3381) -> Matrix(5,2,-8,-3) Matrix(3017,-8216,878,-2391) -> Matrix(1,2,-2,-3) Matrix(207,-572,38,-105) -> Matrix(1,0,0,1) Matrix(2185,-6084,784,-2183) -> Matrix(1,0,10,1) Matrix(573,-1612,166,-467) -> Matrix(1,2,-2,-3) Matrix(1039,-2964,292,-833) -> Matrix(1,2,2,5) Matrix(209,-676,64,-207) -> Matrix(1,0,0,1) Matrix(1873,-6292,526,-1767) -> Matrix(5,2,12,5) Matrix(259,-884,46,-157) -> Matrix(1,0,0,1) Matrix(157,-572,14,-51) -> Matrix(1,2,-2,-3) Matrix(727,-2756,110,-417) -> Matrix(5,4,6,5) Matrix(157,-676,36,-155) -> Matrix(1,0,0,1) Matrix(105,-676,16,-103) -> Matrix(1,0,2,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 84 Degree of the the map X: 84 Degree of the the map Y: 336 ----------------------------------------------------------------------- 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): 1008 Minimal number of generators: 169 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: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 13/11 13/10 13/9 3/2 39/25 13/8 13/7 2/1 13/6 26/11 12/5 5/2 130/51 13/5 52/19 39/14 3/1 13/4 10/3 104/31 7/2 104/29 18/5 11/3 26/7 4/1 13/3 22/5 9/2 78/17 14/3 52/11 24/5 5/1 26/5 16/3 11/2 52/9 6/1 13/2 20/3 7/1 8/1 26/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/1 -1/2 -20/3 -2/5 0/1 -13/2 0/1 -6/1 0/1 -17/3 1/1 1/0 -11/2 0/1 1/0 -16/3 -2/1 0/1 -5/1 0/1 1/0 -19/4 -2/1 -1/1 -14/3 0/1 -9/2 -2/1 1/0 -22/5 0/1 -13/3 -2/1 0/1 -4/1 -2/1 0/1 -11/3 -1/1 -3/4 -29/8 -2/3 -3/5 -18/5 -2/3 -25/7 -3/8 -1/3 -32/9 -2/11 0/1 -7/2 0/1 1/0 -31/9 -2/1 -1/1 -24/7 -2/3 0/1 -41/12 0/1 1/0 -17/5 1/1 1/0 -27/8 0/1 1/0 -37/11 -1/1 1/0 -10/3 -2/1 -13/4 -2/1 0/1 -16/5 -2/1 0/1 -3/1 -2/1 -1/1 -17/6 -1/1 -2/3 -14/5 0/1 -39/14 0/1 -64/23 0/1 2/7 -25/9 1/2 1/1 -11/4 0/1 1/0 -30/11 -2/1 -19/7 -1/1 1/0 -27/10 0/1 1/0 -35/13 1/1 1/0 -8/3 -2/1 0/1 -13/5 -2/1 0/1 -18/7 0/1 -23/9 -2/1 -3/2 -51/20 -8/7 -1/1 -28/11 -2/3 0/1 -5/2 0/1 1/0 -27/11 -13/4 -3/1 -22/9 -2/1 -17/7 -1/1 1/0 -46/19 -2/1 -29/12 -2/1 -5/3 -41/17 -1/1 1/0 -53/22 -2/1 -1/1 -12/5 -2/1 0/1 -7/3 -1/1 1/0 -30/13 0/1 -53/23 5/1 1/0 -23/10 -2/1 -1/1 -16/7 -2/1 0/1 -41/18 0/1 1/0 -25/11 1/2 1/1 -34/15 4/1 -9/4 -4/1 1/0 -29/13 0/1 1/0 -20/9 -6/1 -4/1 -51/23 -25/7 -7/2 -31/14 -16/5 -3/1 -42/19 -8/3 -11/5 -3/1 -5/2 -24/11 -12/5 -2/1 -13/6 -2/1 -2/1 -2/1 -13/7 -2/1 -24/13 -2/1 -20/11 -11/6 -2/1 -7/4 -31/17 -5/3 -18/11 -20/11 -2/1 -8/5 -9/5 -11/7 -3/2 -25/14 -3/2 -10/7 -16/9 -2/1 -4/3 -23/13 -3/2 -4/3 -7/4 -2/1 -3/2 -26/15 -3/2 -19/11 -3/2 -1/1 -12/7 -2/1 -4/3 -29/17 -2/1 1/0 -17/10 -2/1 -5/3 -22/13 -8/5 -27/16 -3/2 -4/3 -5/3 -3/2 -4/3 -28/17 -2/1 -8/5 -79/48 -32/21 -3/2 -130/79 -3/2 -51/31 -3/2 -25/17 -23/14 -7/5 -4/3 -18/11 -4/3 -13/8 -2/1 -4/3 -8/5 -2/1 -4/3 -19/12 -2/1 -5/3 -49/31 -5/3 -8/5 -79/50 -3/2 -10/7 -30/19 -2/1 -41/26 -8/5 -3/2 -52/33 -3/2 -11/7 -3/2 -1/1 -25/16 -3/2 -4/3 -64/41 -2/1 -4/3 -39/25 -2/1 -4/3 -14/9 -2/1 -3/2 -3/2 -4/3 -16/11 -2/1 -4/3 -13/9 -2/1 -4/3 -10/7 -2/1 -57/40 -26/17 -3/2 -104/73 -3/2 -47/33 -3/2 -22/15 -37/26 -10/7 -7/5 -27/19 -3/2 -1/1 -17/12 -2/1 -1/1 -24/17 -2/1 -8/5 -7/5 -3/2 -1/1 -32/23 -2/1 -8/5 -57/41 -3/2 -4/3 -25/18 -3/2 -4/3 -43/31 -17/11 -3/2 -104/75 -3/2 -61/44 -3/2 -28/19 -18/13 -4/3 -29/21 -2/1 1/0 -40/29 -2/1 -4/3 -51/37 -7/4 -5/3 -11/8 -8/5 -3/2 -26/19 -3/2 -15/11 -3/2 -19/13 -4/3 -10/7 -4/3 -13/10 -4/3 -22/17 -4/3 -9/7 -9/7 -5/4 -32/25 -4/3 -6/5 -55/43 -10/9 -1/1 -78/61 -1/1 -23/18 -2/1 -1/1 -14/11 -4/3 -33/26 -6/5 -1/1 -52/41 -1/1 -19/15 -3/2 -1/1 -24/19 -4/3 -6/5 -5/4 -3/2 -4/3 -26/21 -4/3 -21/17 -4/3 -1/1 -16/13 -2/1 -4/3 -27/22 -3/2 -10/7 -11/9 -3/2 -7/5 -28/23 -2/1 -4/3 -17/14 -7/5 -4/3 -23/19 -19/14 -4/3 -52/43 -4/3 -29/24 -4/3 -9/7 -6/5 -4/3 -13/11 -4/3 -20/17 -4/3 -70/53 -7/6 -4/3 -13/10 -8/7 -4/3 -14/11 -17/15 -19/15 -5/4 -26/23 -5/4 -9/8 -5/4 -6/5 -1/1 -5/4 -1/1 0/1 -1/1 1/1 -1/1 -5/6 7/6 -13/16 -4/5 20/17 -70/87 -4/5 13/11 -4/5 6/5 -4/5 17/14 -4/5 -7/9 11/9 -7/9 -3/4 16/13 -4/5 -2/3 5/4 -4/5 -3/4 19/15 -1/1 -3/4 14/11 -4/5 9/7 -5/6 -9/11 22/17 -4/5 13/10 -4/5 4/3 -4/5 -10/13 11/8 -3/4 -8/11 29/21 -2/3 -1/2 18/13 -4/5 25/18 -4/5 -3/4 32/23 -8/11 -2/3 7/5 -1/1 -3/4 31/22 -1/1 -2/3 24/17 -8/11 -2/3 41/29 -1/1 -3/4 17/12 -1/1 -2/3 27/19 -1/1 -3/4 37/26 -7/9 -10/13 10/7 -2/3 13/9 -4/5 -2/3 16/11 -4/5 -2/3 3/2 -4/5 -3/4 17/11 -5/7 -7/10 14/9 -2/3 39/25 -4/5 -2/3 64/41 -4/5 -2/3 25/16 -4/5 -3/4 11/7 -1/1 -3/4 30/19 -2/3 19/12 -5/7 -2/3 27/17 -1/1 -1/2 35/22 -1/1 0/1 8/5 -4/5 -2/3 13/8 -4/5 -2/3 18/11 -4/5 23/14 -4/5 -7/9 51/31 -25/33 -3/4 28/17 -8/11 -2/3 5/3 -4/5 -3/4 27/16 -4/5 -3/4 22/13 -8/11 17/10 -5/7 -2/3 46/27 -2/3 29/17 -2/3 -1/2 41/24 -3/4 -8/11 53/31 -5/7 -7/10 12/7 -4/5 -2/3 7/4 -3/4 -2/3 30/17 -2/3 53/30 -2/1 -1/1 23/13 -4/5 -3/4 16/9 -4/5 -2/3 41/23 -7/9 -3/4 25/14 -10/13 -3/4 34/19 -10/13 9/5 -3/4 -11/15 29/16 -18/25 -5/7 20/11 -8/11 -2/3 51/28 -18/25 -5/7 31/17 -18/25 -5/7 42/23 -22/31 11/6 -7/10 -2/3 24/13 -20/29 -2/3 13/7 -2/3 2/1 -2/3 13/6 -2/3 24/11 -2/3 -12/19 11/5 -5/8 -3/5 31/14 -3/5 -16/27 20/9 -4/7 -6/11 9/4 -4/7 -1/2 25/11 -1/3 -1/4 16/7 -2/3 0/1 23/10 -1/1 -2/3 7/3 -1/1 -1/2 26/11 -1/1 19/8 -1/1 -2/3 12/5 -2/3 0/1 29/12 -5/7 -2/3 17/7 -1/1 -1/2 22/9 -2/3 27/11 -3/5 -13/22 5/2 -1/2 0/1 28/11 -2/1 0/1 79/31 -11/10 -1/1 130/51 -1/1 51/20 -1/1 -8/9 23/9 -3/4 -2/3 18/7 0/1 13/5 -2/3 0/1 8/3 -2/3 0/1 19/7 -1/1 -1/2 49/18 -1/2 0/1 79/29 -1/1 -7/8 30/11 -2/3 41/15 -3/5 -1/2 52/19 -1/2 11/4 -1/2 0/1 25/9 -1/3 -1/4 64/23 -2/11 0/1 39/14 0/1 14/5 0/1 3/1 -1/1 -2/3 16/5 -2/3 0/1 13/4 -2/3 0/1 10/3 -2/3 57/17 -10/19 -1/2 104/31 -1/2 47/14 -1/2 -6/13 37/11 -1/1 -1/2 27/8 -1/2 0/1 17/5 -1/2 -1/3 24/7 -2/1 0/1 7/2 -1/2 0/1 32/9 0/1 2/7 57/16 1/2 4/7 25/7 1/1 3/2 43/12 6/1 1/0 104/29 1/0 61/17 -9/1 1/0 18/5 -2/1 29/8 -3/1 -2/1 40/11 -2/1 -4/3 51/14 -2/1 -1/1 11/3 -3/2 -1/1 26/7 -1/1 15/4 -1/1 -6/7 4/1 -2/3 0/1 13/3 -2/3 0/1 22/5 0/1 9/2 -2/3 -1/2 32/7 -2/3 -4/7 55/12 -6/11 -1/2 78/17 -1/2 23/5 -1/2 -2/5 14/3 0/1 33/7 -1/1 1/0 52/11 -1/1 19/4 -1/1 -2/3 24/5 -2/3 -4/7 5/1 -1/2 0/1 26/5 0/1 21/4 -1/1 0/1 16/3 -2/3 0/1 27/5 -1/3 -1/4 11/2 -1/2 0/1 28/5 -2/1 0/1 17/3 -1/2 -1/3 23/4 -1/5 0/1 52/9 0/1 29/5 0/1 1/2 6/1 0/1 13/2 0/1 20/3 0/1 2/1 7/1 -1/1 1/0 8/1 -2/1 0/1 17/2 -4/3 -1/1 26/3 -1/1 9/1 -1/1 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(27,208,-10,-77) (-7/1,1/0) -> (-19/7,-27/10) Hyperbolic Matrix(53,364,38,261) (-7/1,-20/3) -> (32/23,7/5) Hyperbolic Matrix(79,520,12,79) (-20/3,-13/2) -> (13/2,20/3) Hyperbolic Matrix(25,156,4,25) (-13/2,-6/1) -> (6/1,13/2) Hyperbolic Matrix(155,884,-64,-365) (-6/1,-17/3) -> (-17/7,-46/19) Hyperbolic Matrix(157,884,-46,-259) (-17/3,-11/2) -> (-41/12,-17/5) Hyperbolic Matrix(155,832,-68,-365) (-11/2,-16/3) -> (-16/7,-41/18) Hyperbolic Matrix(79,416,-64,-337) (-16/3,-5/1) -> (-21/17,-16/13) Hyperbolic Matrix(131,624,-38,-181) (-5/1,-19/4) -> (-7/2,-31/9) Hyperbolic Matrix(155,728,-122,-573) (-19/4,-14/3) -> (-14/11,-33/26) Hyperbolic Matrix(79,364,-28,-129) (-14/3,-9/2) -> (-17/6,-14/5) Hyperbolic Matrix(129,572,76,337) (-9/2,-22/5) -> (22/13,17/10) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(25,104,6,25) (-13/3,-4/1) -> (4/1,13/3) Hyperbolic Matrix(27,104,-20,-77) (-4/1,-11/3) -> (-15/11,-4/3) Hyperbolic Matrix(415,1508,-172,-625) (-11/3,-29/8) -> (-29/12,-41/17) Hyperbolic Matrix(259,936,158,571) (-29/8,-18/5) -> (18/11,23/14) Hyperbolic Matrix(363,1300,-160,-573) (-18/5,-25/7) -> (-25/11,-34/15) Hyperbolic Matrix(599,2132,-270,-961) (-25/7,-32/9) -> (-20/9,-51/23) Hyperbolic Matrix(103,364,88,311) (-32/9,-7/2) -> (7/6,20/17) Hyperbolic Matrix(287,988,174,599) (-31/9,-24/7) -> (28/17,5/3) Hyperbolic Matrix(365,1248,198,677) (-24/7,-41/12) -> (11/6,24/13) Hyperbolic Matrix(415,1404,-154,-521) (-17/5,-27/8) -> (-27/10,-35/13) Hyperbolic Matrix(911,3068,-378,-1273) (-27/8,-37/11) -> (-41/17,-53/22) Hyperbolic Matrix(495,1664,-224,-753) (-37/11,-10/3) -> (-42/19,-11/5) Hyperbolic Matrix(79,260,24,79) (-10/3,-13/4) -> (13/4,10/3) Hyperbolic Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(131,416,74,235) (-16/5,-3/1) -> (23/13,16/9) Hyperbolic Matrix(183,520,-82,-233) (-3/1,-17/6) -> (-9/4,-29/13) Hyperbolic Matrix(391,1092,140,391) (-14/5,-39/14) -> (39/14,14/5) Hyperbolic Matrix(1793,4992,644,1793) (-39/14,-64/23) -> (64/23,39/14) Hyperbolic Matrix(1327,3692,776,2159) (-64/23,-25/9) -> (53/31,12/7) Hyperbolic Matrix(469,1300,-206,-571) (-25/9,-11/4) -> (-41/18,-25/11) Hyperbolic Matrix(571,1560,-362,-989) (-11/4,-30/11) -> (-30/19,-41/26) Hyperbolic Matrix(287,780,-124,-337) (-30/11,-19/7) -> (-7/3,-30/13) Hyperbolic Matrix(155,416,-136,-365) (-35/13,-8/3) -> (-8/7,-17/15) Hyperbolic Matrix(79,208,30,79) (-8/3,-13/5) -> (13/5,8/3) Hyperbolic Matrix(181,468,70,181) (-13/5,-18/7) -> (18/7,13/5) Hyperbolic Matrix(365,936,264,677) (-18/7,-23/9) -> (29/21,18/13) Hyperbolic Matrix(937,2392,530,1353) (-23/9,-51/20) -> (53/30,23/13) Hyperbolic Matrix(1429,3640,-868,-2211) (-51/20,-28/11) -> (-28/17,-79/48) Hyperbolic Matrix(389,988,276,701) (-28/11,-5/2) -> (31/22,24/17) Hyperbolic Matrix(443,1092,-200,-493) (-5/2,-27/11) -> (-51/23,-31/14) Hyperbolic Matrix(807,1976,-350,-857) (-27/11,-22/9) -> (-30/13,-53/23) Hyperbolic Matrix(235,572,182,443) (-22/9,-17/7) -> (9/7,22/17) Hyperbolic Matrix(623,1508,-516,-1249) (-46/19,-29/12) -> (-29/24,-6/5) Hyperbolic Matrix(1533,3692,982,2365) (-53/22,-12/5) -> (64/41,25/16) Hyperbolic Matrix(131,312,-76,-181) (-12/5,-7/3) -> (-19/11,-12/7) Hyperbolic Matrix(1039,2392,632,1455) (-53/23,-23/10) -> (23/14,51/31) Hyperbolic Matrix(181,416,124,285) (-23/10,-16/7) -> (16/11,3/2) Hyperbolic Matrix(987,2236,-712,-1613) (-34/15,-9/4) -> (-61/44,-18/13) Hyperbolic Matrix(911,2028,-712,-1585) (-29/13,-20/9) -> (-32/25,-55/43) Hyperbolic Matrix(1223,2704,-858,-1897) (-31/14,-42/19) -> (-10/7,-57/40) Hyperbolic Matrix(571,1248,404,883) (-11/5,-24/11) -> (24/17,41/29) Hyperbolic Matrix(287,624,132,287) (-24/11,-13/6) -> (13/6,24/11) Hyperbolic Matrix(25,52,12,25) (-13/6,-2/1) -> (2/1,13/6) Hyperbolic Matrix(27,52,14,27) (-2/1,-13/7) -> (13/7,2/1) Hyperbolic Matrix(337,624,182,337) (-13/7,-24/13) -> (24/13,13/7) Hyperbolic Matrix(311,572,56,103) (-24/13,-11/6) -> (11/2,28/5) Hyperbolic Matrix(911,1664,-640,-1169) (-11/6,-31/17) -> (-47/33,-37/26) Hyperbolic Matrix(1171,2132,-842,-1533) (-31/17,-20/11) -> (-32/23,-57/41) Hyperbolic Matrix(259,468,-202,-365) (-20/11,-9/5) -> (-9/7,-32/25) Hyperbolic Matrix(727,1300,-524,-937) (-9/5,-25/14) -> (-25/18,-43/31) Hyperbolic Matrix(467,832,-380,-677) (-25/14,-16/9) -> (-16/13,-27/22) Hyperbolic Matrix(235,416,74,131) (-16/9,-23/13) -> (3/1,16/5) Hyperbolic Matrix(443,780,-280,-493) (-23/13,-7/4) -> (-19/12,-49/31) Hyperbolic Matrix(389,676,164,285) (-7/4,-26/15) -> (26/11,19/8) Hyperbolic Matrix(391,676,166,287) (-26/15,-19/11) -> (7/3,26/11) Hyperbolic Matrix(883,1508,-640,-1093) (-12/7,-29/17) -> (-29/21,-40/29) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(337,572,76,129) (-17/10,-22/13) -> (22/5,9/2) Hyperbolic Matrix(1507,2548,-954,-1613) (-22/13,-27/16) -> (-79/50,-30/19) Hyperbolic Matrix(987,1664,-710,-1197) (-27/16,-5/3) -> (-57/41,-25/18) Hyperbolic Matrix(157,260,32,53) (-5/3,-28/17) -> (24/5,5/1) Hyperbolic Matrix(10269,16900,4028,6629) (-79/48,-130/79) -> (130/51,51/20) Hyperbolic Matrix(10271,16900,4030,6631) (-130/79,-51/31) -> (79/31,130/51) Hyperbolic Matrix(2625,4316,964,1585) (-51/31,-23/14) -> (49/18,79/29) Hyperbolic Matrix(571,936,158,259) (-23/14,-18/11) -> (18/5,29/8) Hyperbolic Matrix(287,468,176,287) (-18/11,-13/8) -> (13/8,18/11) Hyperbolic Matrix(129,208,80,129) (-13/8,-8/5) -> (8/5,13/8) Hyperbolic Matrix(131,208,-114,-181) (-8/5,-19/12) -> (-7/6,-8/7) Hyperbolic Matrix(2731,4316,1070,1691) (-49/31,-79/50) -> (51/20,23/9) Hyperbolic Matrix(1715,2704,626,987) (-41/26,-52/33) -> (52/19,11/4) Hyperbolic Matrix(1717,2704,628,989) (-52/33,-11/7) -> (41/15,52/19) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(2731,4264,750,1171) (-25/16,-64/41) -> (40/11,51/14) Hyperbolic Matrix(3199,4992,2050,3199) (-64/41,-39/25) -> (39/25,64/41) Hyperbolic Matrix(701,1092,450,701) (-39/25,-14/9) -> (14/9,39/25) Hyperbolic Matrix(235,364,-184,-285) (-14/9,-3/2) -> (-23/18,-14/11) Hyperbolic Matrix(285,416,124,181) (-3/2,-16/11) -> (16/7,23/10) Hyperbolic Matrix(287,416,198,287) (-16/11,-13/9) -> (13/9,16/11) Hyperbolic Matrix(181,260,126,181) (-13/9,-10/7) -> (10/7,13/9) Hyperbolic Matrix(7591,10816,2262,3223) (-57/40,-104/73) -> (104/31,47/14) Hyperbolic Matrix(7593,10816,2264,3225) (-104/73,-47/33) -> (57/17,104/31) Hyperbolic Matrix(1535,2184,-1114,-1585) (-37/26,-27/19) -> (-51/37,-11/8) Hyperbolic Matrix(183,260,-164,-233) (-27/19,-17/12) -> (-9/8,-1/1) Hyperbolic Matrix(625,884,-514,-727) (-17/12,-24/17) -> (-28/23,-17/14) Hyperbolic Matrix(443,624,-350,-493) (-24/17,-7/5) -> (-19/15,-24/19) Hyperbolic Matrix(261,364,38,53) (-7/5,-32/23) -> (20/3,7/1) Hyperbolic Matrix(7799,10816,2174,3015) (-43/31,-104/75) -> (104/29,61/17) Hyperbolic Matrix(7801,10816,2176,3017) (-104/75,-61/44) -> (43/12,104/29) Hyperbolic Matrix(677,936,264,365) (-18/13,-29/21) -> (23/9,18/7) Hyperbolic Matrix(3093,4264,1112,1533) (-40/29,-51/37) -> (25/9,64/23) Hyperbolic Matrix(493,676,132,181) (-11/8,-26/19) -> (26/7,15/4) Hyperbolic Matrix(495,676,134,183) (-26/19,-15/11) -> (11/3,26/7) Hyperbolic Matrix(79,104,60,79) (-4/3,-13/10) -> (13/10,4/3) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(443,572,182,235) (-22/17,-9/7) -> (17/7,22/9) Hyperbolic Matrix(4757,6084,1036,1325) (-55/43,-78/61) -> (78/17,23/5) Hyperbolic Matrix(4759,6084,1038,1327) (-78/61,-23/18) -> (55/12,78/17) Hyperbolic Matrix(2131,2704,450,571) (-33/26,-52/41) -> (52/11,19/4) Hyperbolic Matrix(2133,2704,452,573) (-52/41,-19/15) -> (33/7,52/11) Hyperbolic Matrix(207,260,82,103) (-24/19,-5/4) -> (5/2,28/11) Hyperbolic Matrix(545,676,104,129) (-5/4,-26/21) -> (26/5,21/4) Hyperbolic Matrix(547,676,106,131) (-26/21,-21/17) -> (5/1,26/5) Hyperbolic Matrix(469,572,214,261) (-11/9,-28/23) -> (24/11,11/5) Hyperbolic Matrix(2235,2704,386,467) (-23/19,-52/43) -> (52/9,29/5) Hyperbolic Matrix(2237,2704,388,469) (-52/43,-29/24) -> (23/4,52/9) Hyperbolic Matrix(131,156,110,131) (-6/5,-13/11) -> (13/11,6/5) Hyperbolic Matrix(441,520,374,441) (-13/11,-20/17) -> (20/17,13/11) Hyperbolic Matrix(311,364,88,103) (-20/17,-7/6) -> (7/2,32/9) Hyperbolic Matrix(597,676,68,77) (-17/15,-26/23) -> (26/3,9/1) Hyperbolic Matrix(599,676,70,79) (-26/23,-9/8) -> (17/2,26/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(181,-208,114,-131) (1/1,7/6) -> (19/12,27/17) Hyperbolic Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(337,-416,64,-79) (16/13,5/4) -> (21/4,16/3) Hyperbolic Matrix(493,-624,350,-443) (5/4,19/15) -> (7/5,31/22) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(285,-364,184,-235) (14/11,9/7) -> (17/11,14/9) Hyperbolic Matrix(77,-104,20,-27) (4/3,11/8) -> (15/4,4/1) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1533,-2132,842,-1171) (25/18,32/23) -> (20/11,51/28) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2157,-3068,1262,-1795) (27/19,37/26) -> (41/24,53/31) Hyperbolic Matrix(1169,-1664,640,-911) (37/26,10/7) -> (42/23,11/6) Hyperbolic Matrix(337,-520,186,-287) (3/2,17/11) -> (9/5,29/16) Hyperbolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(493,-780,280,-443) (30/19,19/12) -> (7/4,30/17) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(2211,-3640,868,-1429) (51/31,28/17) -> (28/11,79/31) Hyperbolic Matrix(649,-1092,356,-599) (5/3,27/16) -> (51/28,31/17) Hyperbolic Matrix(1169,-1976,662,-1119) (27/16,22/13) -> (30/17,53/30) Hyperbolic Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(181,-312,76,-131) (12/7,7/4) -> (19/8,12/5) Hyperbolic Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(1117,-2028,244,-443) (29/16,20/11) -> (32/7,55/12) Hyperbolic Matrix(1481,-2704,442,-807) (31/17,42/23) -> (10/3,57/17) Hyperbolic Matrix(753,-1664,224,-495) (11/5,31/14) -> (47/14,37/11) Hyperbolic Matrix(961,-2132,270,-599) (31/14,20/9) -> (32/9,57/16) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(337,-780,124,-287) (23/10,7/3) -> (19/7,49/18) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(649,-2184,178,-599) (37/11,27/8) -> (51/14,11/3) Hyperbolic Matrix(77,-260,8,-27) (27/8,17/5) -> (9/1,1/0) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(181,-624,38,-131) (24/7,7/2) -> (19/4,24/5) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(27,208,-10,-77) -> Matrix(1,0,1,1) Matrix(53,364,38,261) -> Matrix(1,2,-2,-3) Matrix(79,520,12,79) -> Matrix(1,0,3,1) Matrix(25,156,4,25) -> Matrix(1,0,1,1) Matrix(155,884,-64,-365) -> Matrix(1,-2,0,1) Matrix(157,884,-46,-259) -> Matrix(1,0,0,1) Matrix(155,832,-68,-365) -> Matrix(1,0,0,1) Matrix(79,416,-64,-337) -> Matrix(1,4,-1,-3) Matrix(131,624,-38,-181) -> Matrix(1,2,-1,-1) Matrix(155,728,-122,-573) -> Matrix(5,4,-4,-3) Matrix(79,364,-28,-129) -> Matrix(1,0,-1,1) Matrix(129,572,76,337) -> Matrix(5,8,-7,-11) Matrix(131,572,30,131) -> Matrix(1,0,-1,1) Matrix(25,104,6,25) -> Matrix(1,0,-1,1) Matrix(27,104,-20,-77) -> Matrix(7,10,-5,-7) Matrix(415,1508,-172,-625) -> Matrix(5,4,-4,-3) Matrix(259,936,158,571) -> Matrix(1,2,-2,-3) Matrix(363,1300,-160,-573) -> Matrix(5,2,2,1) Matrix(599,2132,-270,-961) -> Matrix(19,4,-5,-1) Matrix(103,364,88,311) -> Matrix(13,-4,-16,5) Matrix(287,988,174,599) -> Matrix(1,-2,-1,3) Matrix(365,1248,198,677) -> Matrix(7,-2,-10,3) Matrix(415,1404,-154,-521) -> Matrix(1,0,0,1) Matrix(911,3068,-378,-1273) -> Matrix(1,2,-1,-1) Matrix(495,1664,-224,-753) -> Matrix(3,-2,-1,1) Matrix(79,260,24,79) -> Matrix(1,0,-1,1) Matrix(129,416,40,129) -> Matrix(1,0,-1,1) Matrix(131,416,74,235) -> Matrix(1,-2,-1,3) Matrix(183,520,-82,-233) -> Matrix(1,2,-1,-1) Matrix(391,1092,140,391) -> Matrix(1,0,1,1) Matrix(1793,4992,644,1793) -> Matrix(1,0,-9,1) Matrix(1327,3692,776,2159) -> Matrix(9,-2,-13,3) Matrix(469,1300,-206,-571) -> Matrix(1,0,0,1) Matrix(571,1560,-362,-989) -> Matrix(3,8,-2,-5) Matrix(287,780,-124,-337) -> Matrix(1,2,-1,-1) Matrix(155,416,-136,-365) -> Matrix(5,14,-4,-11) Matrix(79,208,30,79) -> Matrix(1,0,-1,1) Matrix(181,468,70,181) -> Matrix(1,0,-1,1) Matrix(365,936,264,677) -> Matrix(3,4,-4,-5) Matrix(937,2392,530,1353) -> Matrix(5,6,-6,-7) Matrix(1429,3640,-868,-2211) -> Matrix(11,8,-7,-5) Matrix(389,988,276,701) -> Matrix(1,-2,-1,3) Matrix(443,1092,-200,-493) -> Matrix(3,16,-1,-5) Matrix(807,1976,-350,-857) -> Matrix(1,2,1,3) Matrix(235,572,182,443) -> Matrix(9,14,-11,-17) Matrix(623,1508,-516,-1249) -> Matrix(3,2,-2,-1) Matrix(1533,3692,982,2365) -> Matrix(1,-2,-1,3) Matrix(131,312,-76,-181) -> Matrix(1,4,-1,-3) Matrix(1039,2392,632,1455) -> Matrix(3,10,-4,-13) Matrix(181,416,124,285) -> Matrix(1,-2,-1,3) Matrix(987,2236,-712,-1613) -> Matrix(3,-16,-2,11) Matrix(911,2028,-712,-1585) -> Matrix(1,10,-1,-9) Matrix(1223,2704,-858,-1897) -> Matrix(11,30,-7,-19) Matrix(571,1248,404,883) -> Matrix(1,4,-2,-7) Matrix(287,624,132,287) -> Matrix(11,24,-17,-37) Matrix(25,52,12,25) -> Matrix(1,0,-1,1) Matrix(27,52,14,27) -> Matrix(5,8,-7,-11) Matrix(337,624,182,337) -> Matrix(21,40,-31,-59) Matrix(311,572,56,103) -> Matrix(1,2,-6,-11) Matrix(911,1664,-640,-1169) -> Matrix(33,56,-23,-39) Matrix(1171,2132,-842,-1533) -> Matrix(21,34,-13,-21) Matrix(259,468,-202,-365) -> Matrix(17,28,-14,-23) Matrix(727,1300,-524,-937) -> Matrix(13,18,-8,-11) Matrix(467,832,-380,-677) -> Matrix(1,0,0,1) Matrix(235,416,74,131) -> Matrix(1,2,-3,-5) Matrix(443,780,-280,-493) -> Matrix(1,4,-1,-3) Matrix(389,676,164,285) -> Matrix(5,8,-7,-11) Matrix(391,676,166,287) -> Matrix(1,2,-3,-5) Matrix(883,1508,-640,-1093) -> Matrix(1,0,0,1) Matrix(519,884,-428,-729) -> Matrix(19,34,-14,-25) Matrix(337,572,76,129) -> Matrix(5,8,-7,-11) Matrix(1507,2548,-954,-1613) -> Matrix(11,18,-8,-13) Matrix(987,1664,-710,-1197) -> Matrix(1,0,0,1) Matrix(157,260,32,53) -> Matrix(3,4,-4,-5) Matrix(10269,16900,4028,6629) -> Matrix(37,56,-39,-59) Matrix(10271,16900,4030,6631) -> Matrix(39,58,-37,-55) Matrix(2625,4316,964,1585) -> Matrix(3,4,-1,-1) Matrix(571,936,158,259) -> Matrix(1,2,-2,-3) Matrix(287,468,176,287) -> Matrix(5,8,-7,-11) Matrix(129,208,80,129) -> Matrix(5,8,-7,-11) Matrix(131,208,-114,-181) -> Matrix(1,6,-1,-5) Matrix(2731,4316,1070,1691) -> Matrix(9,14,-11,-17) Matrix(1715,2704,626,987) -> Matrix(5,8,-12,-19) Matrix(1717,2704,628,989) -> Matrix(7,10,-12,-17) Matrix(365,572,-298,-467) -> Matrix(11,18,-8,-13) Matrix(2731,4264,750,1171) -> Matrix(7,10,-5,-7) Matrix(3199,4992,2050,3199) -> Matrix(5,8,-7,-11) Matrix(701,1092,450,701) -> Matrix(5,8,-7,-11) Matrix(235,364,-184,-285) -> Matrix(7,10,-5,-7) Matrix(285,416,124,181) -> Matrix(1,2,-3,-5) Matrix(287,416,198,287) -> Matrix(5,8,-7,-11) Matrix(181,260,126,181) -> Matrix(5,8,-7,-11) Matrix(7591,10816,2262,3223) -> Matrix(29,44,-60,-91) Matrix(7593,10816,2264,3225) -> Matrix(35,52,-68,-101) Matrix(1535,2184,-1114,-1585) -> Matrix(19,26,-11,-15) Matrix(183,260,-164,-233) -> Matrix(11,16,-9,-13) Matrix(625,884,-514,-727) -> Matrix(11,18,-8,-13) Matrix(443,624,-350,-493) -> Matrix(7,10,-5,-7) Matrix(261,364,38,53) -> Matrix(1,2,-2,-3) Matrix(7799,10816,2174,3015) -> Matrix(29,44,-2,-3) Matrix(7801,10816,2176,3017) -> Matrix(31,46,2,3) Matrix(677,936,264,365) -> Matrix(3,4,-4,-5) Matrix(3093,4264,1112,1533) -> Matrix(1,2,-7,-13) Matrix(493,676,132,181) -> Matrix(17,26,-19,-29) Matrix(495,676,134,183) -> Matrix(19,28,-17,-25) Matrix(79,104,60,79) -> Matrix(29,40,-37,-51) Matrix(441,572,340,441) -> Matrix(91,120,-113,-149) Matrix(443,572,182,235) -> Matrix(11,14,-15,-19) Matrix(4757,6084,1036,1325) -> Matrix(11,12,-23,-25) Matrix(4759,6084,1038,1327) -> Matrix(5,4,-9,-7) Matrix(2131,2704,450,571) -> Matrix(7,8,-8,-9) Matrix(2133,2704,452,573) -> Matrix(1,2,-2,-3) Matrix(207,260,82,103) -> Matrix(3,4,-4,-5) Matrix(545,676,104,129) -> Matrix(3,4,-1,-1) Matrix(547,676,106,131) -> Matrix(3,4,-7,-9) Matrix(469,572,214,261) -> Matrix(19,26,-30,-41) Matrix(2235,2704,386,467) -> Matrix(3,4,20,27) Matrix(2237,2704,388,469) -> Matrix(3,4,-22,-29) Matrix(131,156,110,131) -> Matrix(29,40,-37,-51) Matrix(441,520,374,441) -> Matrix(211,280,-263,-349) Matrix(311,364,88,103) -> Matrix(3,4,-16,-21) Matrix(597,676,68,77) -> Matrix(19,24,-23,-29) Matrix(599,676,70,79) -> Matrix(21,26,-17,-21) Matrix(1,0,2,1) -> Matrix(9,10,-10,-11) Matrix(181,-208,114,-131) -> Matrix(7,6,-13,-11) Matrix(729,-884,428,-519) -> Matrix(43,34,-62,-49) Matrix(727,-884,514,-625) -> Matrix(23,18,-32,-25) Matrix(677,-832,380,-467) -> Matrix(1,0,0,1) Matrix(337,-416,64,-79) -> Matrix(5,4,-9,-7) Matrix(493,-624,350,-443) -> Matrix(13,10,-17,-13) Matrix(573,-728,122,-155) -> Matrix(5,4,-4,-3) Matrix(285,-364,184,-235) -> Matrix(13,10,-17,-13) Matrix(77,-104,20,-27) -> Matrix(13,10,-17,-13) Matrix(1093,-1508,640,-883) -> Matrix(1,0,0,1) Matrix(937,-1300,524,-727) -> Matrix(25,18,-32,-23) Matrix(1533,-2132,842,-1171) -> Matrix(47,34,-65,-47) Matrix(989,-1404,622,-883) -> Matrix(3,2,-2,-1) Matrix(2157,-3068,1262,-1795) -> Matrix(33,26,-47,-37) Matrix(1169,-1664,640,-911) -> Matrix(73,56,-103,-79) Matrix(337,-520,186,-287) -> Matrix(47,34,-65,-47) Matrix(831,-1300,466,-729) -> Matrix(25,18,-32,-23) Matrix(989,-1560,362,-571) -> Matrix(11,8,-18,-13) Matrix(493,-780,280,-443) -> Matrix(5,4,-9,-7) Matrix(261,-416,32,-51) -> Matrix(5,4,-4,-3) Matrix(2211,-3640,868,-1429) -> Matrix(11,8,-7,-5) Matrix(649,-1092,356,-599) -> Matrix(47,34,-65,-47) Matrix(1169,-1976,662,-1119) -> Matrix(3,2,1,1) Matrix(885,-1508,152,-259) -> Matrix(3,2,4,3) Matrix(181,-312,76,-131) -> Matrix(5,4,-9,-7) Matrix(1249,-2236,348,-623) -> Matrix(21,16,-4,-3) Matrix(1117,-2028,244,-443) -> Matrix(17,12,-27,-19) Matrix(1481,-2704,442,-807) -> Matrix(45,32,-83,-59) Matrix(753,-1664,224,-495) -> Matrix(3,2,-11,-7) Matrix(961,-2132,270,-599) -> Matrix(7,4,19,11) Matrix(209,-468,46,-103) -> Matrix(3,2,-8,-5) Matrix(573,-1300,160,-363) -> Matrix(5,2,2,1) Matrix(365,-832,68,-155) -> Matrix(1,0,0,1) Matrix(337,-780,124,-287) -> Matrix(3,2,-5,-3) Matrix(625,-1508,172,-415) -> Matrix(5,4,-4,-3) Matrix(365,-884,64,-155) -> Matrix(3,2,-8,-5) Matrix(1041,-2548,382,-935) -> Matrix(13,8,-18,-11) Matrix(677,-1664,190,-467) -> Matrix(7,4,12,7) Matrix(77,-208,10,-27) -> Matrix(1,0,1,1) Matrix(207,-572,38,-105) -> Matrix(1,0,0,1) Matrix(129,-364,28,-79) -> Matrix(1,0,-1,1) Matrix(649,-2184,178,-599) -> Matrix(5,2,-3,-1) Matrix(77,-260,8,-27) -> Matrix(1,0,1,1) Matrix(259,-884,46,-157) -> Matrix(1,0,0,1) Matrix(181,-624,38,-131) -> Matrix(3,2,-5,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 84 ----------------------------------------------------------------------- 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 5 1 1/1 (-1/1,-5/6) 0 26 7/6 (-13/16,-4/5) 0 26 20/17 (-70/87,-4/5) 0 13 13/11 -4/5 10 2 6/5 -4/5 1 13 17/14 (-4/5,-7/9) 0 26 11/9 (-7/9,-3/4) 0 26 16/13 (-4/5,-2/3) 0 13 5/4 (-4/5,-3/4) 0 26 19/15 (-1/1,-3/4) 0 26 14/11 -4/5 1 13 9/7 (-5/6,-9/11) 0 26 22/17 -4/5 1 13 13/10 -4/5 5 2 4/3 (-4/5,-10/13) 0 13 11/8 (-3/4,-8/11) 0 26 29/21 (-2/3,-1/2) 0 26 18/13 -4/5 1 13 25/18 (-4/5,-3/4) 0 26 32/23 (-8/11,-2/3) 0 13 7/5 (-1/1,-3/4) 0 26 31/22 (-1/1,-2/3) 0 26 24/17 (-8/11,-2/3) 0 13 41/29 (-1/1,-3/4) 0 26 17/12 (-1/1,-2/3) 0 26 27/19 (-1/1,-3/4) 0 26 37/26 (-7/9,-10/13) 0 26 10/7 -2/3 1 13 13/9 (-4/5,-2/3) 0 2 16/11 (-4/5,-2/3) 0 13 3/2 (-4/5,-3/4) 0 26 17/11 (-5/7,-7/10) 0 26 14/9 -2/3 1 13 39/25 (-4/5,-2/3) 0 2 64/41 (-4/5,-2/3) 0 13 25/16 (-4/5,-3/4) 0 26 11/7 (-1/1,-3/4) 0 26 30/19 -2/3 1 13 19/12 (-5/7,-2/3) 0 26 27/17 (-1/1,-1/2) 0 26 35/22 (-1/1,0/1) 0 26 8/5 (-4/5,-2/3) 0 13 13/8 (-4/5,-2/3) 0 2 18/11 -4/5 1 13 23/14 (-4/5,-7/9) 0 26 51/31 (-25/33,-3/4) 0 26 28/17 (-8/11,-2/3) 0 13 5/3 (-4/5,-3/4) 0 26 27/16 (-4/5,-3/4) 0 26 22/13 -8/11 1 13 17/10 (-5/7,-2/3) 0 26 46/27 -2/3 1 13 29/17 (-2/3,-1/2) 0 26 41/24 (-3/4,-8/11) 0 26 53/31 (-5/7,-7/10) 0 26 12/7 (-4/5,-2/3) 0 13 7/4 (-3/4,-2/3) 0 26 30/17 -2/3 1 13 53/30 (-2/1,-1/1) 0 26 23/13 (-4/5,-3/4) 0 26 16/9 (-4/5,-2/3) 0 13 41/23 (-7/9,-3/4) 0 26 25/14 (-10/13,-3/4) 0 26 34/19 -10/13 1 13 9/5 (-3/4,-11/15) 0 26 29/16 (-18/25,-5/7) 0 26 20/11 (-8/11,-2/3) 0 13 51/28 (-18/25,-5/7) 0 26 31/17 (-18/25,-5/7) 0 26 42/23 -22/31 1 13 11/6 (-7/10,-2/3) 0 26 24/13 (-20/29,-2/3) 0 13 13/7 -2/3 4 2 2/1 -2/3 1 13 13/6 -2/3 3 2 24/11 (-2/3,-12/19) 0 13 11/5 (-5/8,-3/5) 0 26 31/14 (-3/5,-16/27) 0 26 20/9 (-4/7,-6/11) 0 13 9/4 (-4/7,-1/2) 0 26 25/11 (-1/3,-1/4) 0 26 16/7 (-2/3,0/1) 0 13 23/10 (-1/1,-2/3) 0 26 7/3 (-1/1,-1/2) 0 26 26/11 -1/1 1 1 19/8 (-1/1,-2/3) 0 26 12/5 (-2/3,0/1) 0 13 29/12 (-5/7,-2/3) 0 26 17/7 (-1/1,-1/2) 0 26 22/9 -2/3 1 13 27/11 (-3/5,-13/22) 0 26 5/2 (-1/2,0/1) 0 26 28/11 (-2/1,0/1) 0 13 79/31 (-11/10,-1/1) 0 26 130/51 -1/1 19 1 51/20 (-1/1,-8/9) 0 26 23/9 (-3/4,-2/3) 0 26 18/7 0/1 1 13 13/5 (-2/3,0/1) 0 2 8/3 (-2/3,0/1) 0 13 19/7 (-1/1,-1/2) 0 26 49/18 (-1/2,0/1) 0 26 79/29 (-1/1,-7/8) 0 26 30/11 -2/3 1 13 41/15 (-3/5,-1/2) 0 26 52/19 -1/2 3 1 11/4 (-1/2,0/1) 0 26 25/9 (-1/3,-1/4) 0 26 64/23 (-2/11,0/1) 0 13 39/14 0/1 5 2 14/5 0/1 1 13 3/1 (-1/1,-2/3) 0 26 16/5 (-2/3,0/1) 0 13 13/4 (-2/3,0/1) 0 2 10/3 -2/3 1 13 57/17 (-10/19,-1/2) 0 26 104/31 -1/2 16 1 47/14 (-1/2,-6/13) 0 26 37/11 (-1/1,-1/2) 0 26 27/8 (-1/2,0/1) 0 26 17/5 (-1/2,-1/3) 0 26 24/7 (-2/1,0/1) 0 13 7/2 (-1/2,0/1) 0 26 32/9 (0/1,2/7) 0 13 57/16 (1/2,4/7) 0 26 25/7 (1/1,3/2) 0 26 43/12 (6/1,1/0) 0 26 104/29 1/0 15 1 61/17 (-9/1,1/0) 0 26 18/5 -2/1 1 13 29/8 (-3/1,-2/1) 0 26 40/11 (-2/1,-4/3) 0 13 51/14 (-2/1,-1/1) 0 26 11/3 (-3/2,-1/1) 0 26 26/7 -1/1 9 1 15/4 (-1/1,-6/7) 0 26 4/1 (-2/3,0/1) 0 13 13/3 (-2/3,0/1) 0 2 22/5 0/1 1 13 9/2 (-2/3,-1/2) 0 26 32/7 (-2/3,-4/7) 0 13 55/12 (-6/11,-1/2) 0 26 78/17 -1/2 8 1 23/5 (-1/2,-2/5) 0 26 14/3 0/1 1 13 33/7 (-1/1,1/0) 0 26 52/11 -1/1 3 1 19/4 (-1/1,-2/3) 0 26 24/5 (-2/3,-4/7) 0 13 5/1 (-1/2,0/1) 0 26 26/5 0/1 1 1 21/4 (-1/1,0/1) 0 26 16/3 (-2/3,0/1) 0 13 27/5 (-1/3,-1/4) 0 26 11/2 (-1/2,0/1) 0 26 28/5 (-2/1,0/1) 0 13 17/3 (-1/2,-1/3) 0 26 23/4 (-1/5,0/1) 0 26 52/9 0/1 7 1 29/5 (0/1,1/2) 0 26 6/1 0/1 1 13 13/2 0/1 1 2 20/3 (0/1,2/1) 0 13 7/1 (-1/1,1/0) 0 26 8/1 (-2/1,0/1) 0 13 17/2 (-4/3,-1/1) 0 26 26/3 -1/1 5 1 9/1 (-1/1,-1/2) 0 26 1/0 (-1/1,0/1) 0 26 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(181,-208,114,-131) (1/1,7/6) -> (19/12,27/17) Hyperbolic Matrix(311,-364,88,-103) (7/6,20/17) -> (7/2,32/9) Glide Reflection Matrix(441,-520,374,-441) (20/17,13/11) -> (20/17,13/11) Reflection Matrix(131,-156,110,-131) (13/11,6/5) -> (13/11,6/5) Reflection Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(337,-416,64,-79) (16/13,5/4) -> (21/4,16/3) Hyperbolic Matrix(493,-624,350,-443) (5/4,19/15) -> (7/5,31/22) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(285,-364,184,-235) (14/11,9/7) -> (17/11,14/9) Hyperbolic Matrix(443,-572,182,-235) (9/7,22/17) -> (17/7,22/9) Glide Reflection Matrix(441,-572,340,-441) (22/17,13/10) -> (22/17,13/10) Reflection Matrix(79,-104,60,-79) (13/10,4/3) -> (13/10,4/3) Reflection Matrix(77,-104,20,-27) (4/3,11/8) -> (15/4,4/1) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(677,-936,264,-365) (29/21,18/13) -> (23/9,18/7) Glide Reflection Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1533,-2132,842,-1171) (25/18,32/23) -> (20/11,51/28) Hyperbolic Matrix(261,-364,38,-53) (32/23,7/5) -> (20/3,7/1) Glide Reflection Matrix(701,-988,276,-389) (31/22,24/17) -> (5/2,28/11) Glide Reflection Matrix(883,-1248,404,-571) (24/17,41/29) -> (24/11,11/5) Glide Reflection Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2157,-3068,1262,-1795) (27/19,37/26) -> (41/24,53/31) Hyperbolic Matrix(1169,-1664,640,-911) (37/26,10/7) -> (42/23,11/6) Hyperbolic Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) Reflection Matrix(287,-416,198,-287) (13/9,16/11) -> (13/9,16/11) Reflection Matrix(285,-416,124,-181) (16/11,3/2) -> (16/7,23/10) Glide Reflection Matrix(337,-520,186,-287) (3/2,17/11) -> (9/5,29/16) Hyperbolic Matrix(701,-1092,450,-701) (14/9,39/25) -> (14/9,39/25) Reflection Matrix(3199,-4992,2050,-3199) (39/25,64/41) -> (39/25,64/41) Reflection Matrix(2731,-4264,750,-1171) (64/41,25/16) -> (40/11,51/14) Glide Reflection Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(493,-780,280,-443) (30/19,19/12) -> (7/4,30/17) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(129,-208,80,-129) (8/5,13/8) -> (8/5,13/8) Reflection Matrix(287,-468,176,-287) (13/8,18/11) -> (13/8,18/11) Reflection Matrix(571,-936,158,-259) (18/11,23/14) -> (18/5,29/8) Glide Reflection Matrix(2625,-4316,964,-1585) (23/14,51/31) -> (49/18,79/29) Glide Reflection Matrix(2211,-3640,868,-1429) (51/31,28/17) -> (28/11,79/31) Hyperbolic Matrix(157,-260,32,-53) (28/17,5/3) -> (24/5,5/1) Glide Reflection Matrix(649,-1092,356,-599) (5/3,27/16) -> (51/28,31/17) Hyperbolic Matrix(1169,-1976,662,-1119) (27/16,22/13) -> (30/17,53/30) Hyperbolic Matrix(337,-572,76,-129) (22/13,17/10) -> (22/5,9/2) Glide Reflection Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(2159,-3692,776,-1327) (53/31,12/7) -> (25/9,64/23) Glide Reflection Matrix(181,-312,76,-131) (12/7,7/4) -> (19/8,12/5) Hyperbolic Matrix(1353,-2392,530,-937) (53/30,23/13) -> (51/20,23/9) Glide Reflection Matrix(235,-416,74,-131) (23/13,16/9) -> (3/1,16/5) Glide Reflection Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(1117,-2028,244,-443) (29/16,20/11) -> (32/7,55/12) Hyperbolic Matrix(1481,-2704,442,-807) (31/17,42/23) -> (10/3,57/17) Hyperbolic Matrix(311,-572,56,-103) (11/6,24/13) -> (11/2,28/5) Glide Reflection Matrix(337,-624,182,-337) (24/13,13/7) -> (24/13,13/7) Reflection Matrix(27,-52,14,-27) (13/7,2/1) -> (13/7,2/1) Reflection Matrix(25,-52,12,-25) (2/1,13/6) -> (2/1,13/6) Reflection Matrix(287,-624,132,-287) (13/6,24/11) -> (13/6,24/11) Reflection Matrix(753,-1664,224,-495) (11/5,31/14) -> (47/14,37/11) Hyperbolic Matrix(961,-2132,270,-599) (31/14,20/9) -> (32/9,57/16) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(337,-780,124,-287) (23/10,7/3) -> (19/7,49/18) Hyperbolic Matrix(155,-364,66,-155) (7/3,26/11) -> (7/3,26/11) Reflection Matrix(417,-988,176,-417) (26/11,19/8) -> (26/11,19/8) Reflection Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(8059,-20540,3162,-8059) (79/31,130/51) -> (79/31,130/51) Reflection Matrix(5201,-13260,2040,-5201) (130/51,51/20) -> (130/51,51/20) Reflection Matrix(181,-468,70,-181) (18/7,13/5) -> (18/7,13/5) Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(1559,-4264,570,-1559) (41/15,52/19) -> (41/15,52/19) Reflection Matrix(417,-1144,152,-417) (52/19,11/4) -> (52/19,11/4) Reflection Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1793,-4992,644,-1793) (64/23,39/14) -> (64/23,39/14) Reflection Matrix(391,-1092,140,-391) (39/14,14/5) -> (39/14,14/5) Reflection Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(129,-416,40,-129) (16/5,13/4) -> (16/5,13/4) Reflection Matrix(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(3535,-11856,1054,-3535) (57/17,104/31) -> (57/17,104/31) Reflection Matrix(2913,-9776,868,-2913) (104/31,47/14) -> (104/31,47/14) Reflection Matrix(649,-2184,178,-599) (37/11,27/8) -> (51/14,11/3) Hyperbolic Matrix(77,-260,8,-27) (27/8,17/5) -> (9/1,1/0) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(181,-624,38,-131) (24/7,7/2) -> (19/4,24/5) Hyperbolic Matrix(2495,-8944,696,-2495) (43/12,104/29) -> (43/12,104/29) Reflection Matrix(3537,-12688,986,-3537) (104/29,61/17) -> (104/29,61/17) Reflection Matrix(155,-572,42,-155) (11/3,26/7) -> (11/3,26/7) Reflection Matrix(209,-780,56,-209) (26/7,15/4) -> (26/7,15/4) Reflection Matrix(25,-104,6,-25) (4/1,13/3) -> (4/1,13/3) Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(1871,-8580,408,-1871) (55/12,78/17) -> (55/12,78/17) Reflection Matrix(781,-3588,170,-781) (78/17,23/5) -> (78/17,23/5) Reflection Matrix(727,-3432,154,-727) (33/7,52/11) -> (33/7,52/11) Reflection Matrix(417,-1976,88,-417) (52/11,19/4) -> (52/11,19/4) Reflection Matrix(51,-260,10,-51) (5/1,26/5) -> (5/1,26/5) Reflection Matrix(209,-1092,40,-209) (26/5,21/4) -> (26/5,21/4) Reflection Matrix(415,-2392,72,-415) (23/4,52/9) -> (23/4,52/9) Reflection Matrix(521,-3016,90,-521) (52/9,29/5) -> (52/9,29/5) Reflection Matrix(25,-156,4,-25) (6/1,13/2) -> (6/1,13/2) Reflection Matrix(79,-520,12,-79) (13/2,20/3) -> (13/2,20/3) Reflection Matrix(103,-884,12,-103) (17/2,26/3) -> (17/2,26/3) Reflection Matrix(53,-468,6,-53) (26/3,9/1) -> (26/3,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(11,10,-12,-11) (0/1,1/1) -> (-1/1,-5/6) Matrix(181,-208,114,-131) -> Matrix(7,6,-13,-11) Matrix(311,-364,88,-103) -> Matrix(5,4,-26,-21) Matrix(441,-520,374,-441) -> Matrix(349,280,-435,-349) (20/17,13/11) -> (-70/87,-4/5) Matrix(131,-156,110,-131) -> Matrix(51,40,-65,-51) (13/11,6/5) -> (-4/5,-10/13) Matrix(729,-884,428,-519) -> Matrix(43,34,-62,-49) Matrix(727,-884,514,-625) -> Matrix(23,18,-32,-25) -3/4 Matrix(677,-832,380,-467) -> Matrix(1,0,0,1) Matrix(337,-416,64,-79) -> Matrix(5,4,-9,-7) -2/3 Matrix(493,-624,350,-443) -> Matrix(13,10,-17,-13) (-1/1,-3/4).(-4/5,-2/3) Matrix(573,-728,122,-155) -> Matrix(5,4,-4,-3) -1/1 Matrix(285,-364,184,-235) -> Matrix(13,10,-17,-13) (-1/1,-3/4).(-4/5,-2/3) Matrix(443,-572,182,-235) -> Matrix(17,14,-23,-19) Matrix(441,-572,340,-441) -> Matrix(149,120,-185,-149) (22/17,13/10) -> (-30/37,-4/5) Matrix(79,-104,60,-79) -> Matrix(51,40,-65,-51) (13/10,4/3) -> (-4/5,-10/13) Matrix(77,-104,20,-27) -> Matrix(13,10,-17,-13) (-1/1,-3/4).(-4/5,-2/3) Matrix(1093,-1508,640,-883) -> Matrix(1,0,0,1) Matrix(677,-936,264,-365) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(937,-1300,524,-727) -> Matrix(25,18,-32,-23) -3/4 Matrix(1533,-2132,842,-1171) -> Matrix(47,34,-65,-47) (-3/4,-5/7).(-8/11,-2/3) Matrix(261,-364,38,-53) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(701,-988,276,-389) -> Matrix(3,2,-7,-5) Matrix(883,-1248,404,-571) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(989,-1404,622,-883) -> Matrix(3,2,-2,-1) -1/1 Matrix(2157,-3068,1262,-1795) -> Matrix(33,26,-47,-37) Matrix(1169,-1664,640,-911) -> Matrix(73,56,-103,-79) Matrix(181,-260,126,-181) -> Matrix(11,8,-15,-11) (10/7,13/9) -> (-4/5,-2/3) Matrix(287,-416,198,-287) -> Matrix(11,8,-15,-11) (13/9,16/11) -> (-4/5,-2/3) Matrix(285,-416,124,-181) -> Matrix(3,2,-7,-5) Matrix(337,-520,186,-287) -> Matrix(47,34,-65,-47) (-3/4,-5/7).(-8/11,-2/3) Matrix(701,-1092,450,-701) -> Matrix(11,8,-15,-11) (14/9,39/25) -> (-4/5,-2/3) Matrix(3199,-4992,2050,-3199) -> Matrix(11,8,-15,-11) (39/25,64/41) -> (-4/5,-2/3) Matrix(2731,-4264,750,-1171) -> Matrix(13,10,-9,-7) Matrix(831,-1300,466,-729) -> Matrix(25,18,-32,-23) -3/4 Matrix(989,-1560,362,-571) -> Matrix(11,8,-18,-13) -2/3 Matrix(493,-780,280,-443) -> Matrix(5,4,-9,-7) -2/3 Matrix(261,-416,32,-51) -> Matrix(5,4,-4,-3) -1/1 Matrix(129,-208,80,-129) -> Matrix(11,8,-15,-11) (8/5,13/8) -> (-4/5,-2/3) Matrix(287,-468,176,-287) -> Matrix(11,8,-15,-11) (13/8,18/11) -> (-4/5,-2/3) Matrix(571,-936,158,-259) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(2625,-4316,964,-1585) -> Matrix(5,4,-1,-1) Matrix(2211,-3640,868,-1429) -> Matrix(11,8,-7,-5) Matrix(157,-260,32,-53) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(649,-1092,356,-599) -> Matrix(47,34,-65,-47) (-3/4,-5/7).(-8/11,-2/3) Matrix(1169,-1976,662,-1119) -> Matrix(3,2,1,1) Matrix(337,-572,76,-129) -> Matrix(11,8,-15,-11) *** -> (-4/5,-2/3) Matrix(885,-1508,152,-259) -> Matrix(3,2,4,3) Matrix(2159,-3692,776,-1327) -> Matrix(3,2,-19,-13) Matrix(181,-312,76,-131) -> Matrix(5,4,-9,-7) -2/3 Matrix(1353,-2392,530,-937) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(235,-416,74,-131) -> Matrix(3,2,-7,-5) Matrix(1249,-2236,348,-623) -> Matrix(21,16,-4,-3) Matrix(1117,-2028,244,-443) -> Matrix(17,12,-27,-19) -2/3 Matrix(1481,-2704,442,-807) -> Matrix(45,32,-83,-59) Matrix(311,-572,56,-103) -> Matrix(3,2,-16,-11) Matrix(337,-624,182,-337) -> Matrix(59,40,-87,-59) (24/13,13/7) -> (-20/29,-2/3) Matrix(27,-52,14,-27) -> Matrix(11,8,-15,-11) (13/7,2/1) -> (-4/5,-2/3) Matrix(25,-52,12,-25) -> Matrix(-1,0,3,1) (2/1,13/6) -> (-2/3,0/1) Matrix(287,-624,132,-287) -> Matrix(37,24,-57,-37) (13/6,24/11) -> (-2/3,-12/19) Matrix(753,-1664,224,-495) -> Matrix(3,2,-11,-7) Matrix(961,-2132,270,-599) -> Matrix(7,4,19,11) Matrix(209,-468,46,-103) -> Matrix(3,2,-8,-5) -1/2 Matrix(573,-1300,160,-363) -> Matrix(5,2,2,1) Matrix(365,-832,68,-155) -> Matrix(1,0,0,1) Matrix(337,-780,124,-287) -> Matrix(3,2,-5,-3) (-1/1,-1/2).(-2/3,0/1) Matrix(155,-364,66,-155) -> Matrix(3,2,-4,-3) (7/3,26/11) -> (-1/1,-1/2) Matrix(417,-988,176,-417) -> Matrix(5,4,-6,-5) (26/11,19/8) -> (-1/1,-2/3) Matrix(625,-1508,172,-415) -> Matrix(5,4,-4,-3) -1/1 Matrix(365,-884,64,-155) -> Matrix(3,2,-8,-5) -1/2 Matrix(1041,-2548,382,-935) -> Matrix(13,8,-18,-11) -2/3 Matrix(677,-1664,190,-467) -> Matrix(7,4,12,7) Matrix(8059,-20540,3162,-8059) -> Matrix(21,22,-20,-21) (79/31,130/51) -> (-11/10,-1/1) Matrix(5201,-13260,2040,-5201) -> Matrix(17,16,-18,-17) (130/51,51/20) -> (-1/1,-8/9) Matrix(181,-468,70,-181) -> Matrix(-1,0,3,1) (18/7,13/5) -> (-2/3,0/1) Matrix(79,-208,30,-79) -> Matrix(-1,0,3,1) (13/5,8/3) -> (-2/3,0/1) Matrix(77,-208,10,-27) -> Matrix(1,0,1,1) 0/1 Matrix(1559,-4264,570,-1559) -> Matrix(11,6,-20,-11) (41/15,52/19) -> (-3/5,-1/2) Matrix(417,-1144,152,-417) -> Matrix(-1,0,4,1) (52/19,11/4) -> (-1/2,0/1) Matrix(207,-572,38,-105) -> Matrix(1,0,0,1) Matrix(1793,-4992,644,-1793) -> Matrix(-1,0,11,1) (64/23,39/14) -> (-2/11,0/1) Matrix(391,-1092,140,-391) -> Matrix(-1,0,1,1) (39/14,14/5) -> (-2/1,0/1) Matrix(129,-364,28,-79) -> Matrix(1,0,-1,1) 0/1 Matrix(129,-416,40,-129) -> Matrix(-1,0,3,1) (16/5,13/4) -> (-2/3,0/1) Matrix(79,-260,24,-79) -> Matrix(-1,0,3,1) (13/4,10/3) -> (-2/3,0/1) Matrix(3535,-11856,1054,-3535) -> Matrix(39,20,-76,-39) (57/17,104/31) -> (-10/19,-1/2) Matrix(2913,-9776,868,-2913) -> Matrix(25,12,-52,-25) (104/31,47/14) -> (-1/2,-6/13) Matrix(649,-2184,178,-599) -> Matrix(5,2,-3,-1) Matrix(77,-260,8,-27) -> Matrix(1,0,1,1) 0/1 Matrix(259,-884,46,-157) -> Matrix(1,0,0,1) Matrix(181,-624,38,-131) -> Matrix(3,2,-5,-3) (-1/1,-1/2).(-2/3,0/1) Matrix(2495,-8944,696,-2495) -> Matrix(-1,12,0,1) (43/12,104/29) -> (6/1,1/0) Matrix(3537,-12688,986,-3537) -> Matrix(1,18,0,-1) (104/29,61/17) -> (-9/1,1/0) Matrix(155,-572,42,-155) -> Matrix(5,6,-4,-5) (11/3,26/7) -> (-3/2,-1/1) Matrix(209,-780,56,-209) -> Matrix(13,12,-14,-13) (26/7,15/4) -> (-1/1,-6/7) Matrix(25,-104,6,-25) -> Matrix(-1,0,3,1) (4/1,13/3) -> (-2/3,0/1) Matrix(131,-572,30,-131) -> Matrix(-1,0,3,1) (13/3,22/5) -> (-2/3,0/1) Matrix(1871,-8580,408,-1871) -> Matrix(23,12,-44,-23) (55/12,78/17) -> (-6/11,-1/2) Matrix(781,-3588,170,-781) -> Matrix(9,4,-20,-9) (78/17,23/5) -> (-1/2,-2/5) Matrix(727,-3432,154,-727) -> Matrix(1,2,0,-1) (33/7,52/11) -> (-1/1,1/0) Matrix(417,-1976,88,-417) -> Matrix(5,4,-6,-5) (52/11,19/4) -> (-1/1,-2/3) Matrix(51,-260,10,-51) -> Matrix(-1,0,4,1) (5/1,26/5) -> (-1/2,0/1) Matrix(209,-1092,40,-209) -> Matrix(-1,0,2,1) (26/5,21/4) -> (-1/1,0/1) Matrix(415,-2392,72,-415) -> Matrix(-1,0,10,1) (23/4,52/9) -> (-1/5,0/1) Matrix(521,-3016,90,-521) -> Matrix(1,0,4,-1) (52/9,29/5) -> (0/1,1/2) Matrix(25,-156,4,-25) -> Matrix(-1,0,1,1) (6/1,13/2) -> (-2/1,0/1) Matrix(79,-520,12,-79) -> Matrix(1,0,1,-1) (13/2,20/3) -> (0/1,2/1) Matrix(103,-884,12,-103) -> Matrix(7,8,-6,-7) (17/2,26/3) -> (-4/3,-1/1) Matrix(53,-468,6,-53) -> Matrix(3,2,-4,-3) (26/3,9/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.