INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -15/2 -6/1 -21/4 -9/2 -21/5 -18/5 -3/1 -18/7 -12/5 -9/4 -15/7 -9/5 -81/52 -3/2 -27/20 -9/7 -27/23 -9/8 0/1 1/1 9/8 27/22 9/7 27/19 3/2 27/17 27/16 9/5 2/1 15/7 9/4 12/5 27/11 5/2 18/7 108/41 27/10 81/29 54/19 3/1 54/17 135/41 162/49 27/8 24/7 7/2 189/53 18/5 108/29 162/43 27/7 4/1 21/5 72/17 13/3 9/2 14/3 108/23 19/4 24/5 135/28 5/1 26/5 21/4 90/17 16/3 27/5 11/2 17/3 23/4 81/14 29/5 6/1 25/4 19/3 13/2 20/3 27/4 7/1 22/3 15/2 23/3 54/7 8/1 17/2 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 0/1 1/1 -9/1 0/1 -8/1 0/1 1/0 -15/2 -1/1 0/1 1/0 -7/1 -1/1 0/1 -13/2 -1/1 -1/2 -19/3 -1/2 -2/5 -25/4 -1/1 -1/2 -6/1 0/1 -29/5 -2/3 -1/2 -23/4 -1/2 -1/3 -17/3 -1/3 -2/7 -11/2 -1/6 0/1 -27/5 0/1 -16/3 0/1 1/5 -21/4 0/1 1/2 1/1 -5/1 -1/1 0/1 -19/4 -1/2 -3/7 -52/11 -1/2 0/1 -33/7 -2/5 -14/3 -1/2 0/1 -23/5 -1/4 0/1 -9/2 0/1 -31/7 0/1 1/0 -53/12 0/1 1/2 -22/5 0/1 1/1 -35/8 -3/1 1/0 -13/3 0/1 1/0 -17/4 -1/1 -3/4 -21/5 -2/3 -4/1 -1/2 0/1 -19/5 -1/2 -2/5 -34/9 -2/5 -1/3 -49/13 -2/5 -1/3 -15/4 -1/2 -2/5 -1/3 -41/11 -1/2 0/1 -26/7 -2/5 -1/3 -11/3 -1/3 0/1 -29/8 -3/8 -1/3 -18/5 -1/3 -25/7 -1/4 0/1 -57/16 -1/1 -1/2 0/1 -32/9 -2/5 -1/3 -7/2 -1/3 0/1 -24/7 0/1 -17/5 -2/5 -1/3 -27/8 -1/3 -10/3 -1/3 -2/7 -43/13 -5/17 -2/7 -33/10 -2/7 -3/11 -1/4 -56/17 -4/15 -1/4 -23/7 -2/7 -1/4 -13/4 -1/3 -1/4 -16/5 -2/7 -3/11 -19/6 -1/4 -5/21 -22/7 -2/9 -1/5 -3/1 0/1 -20/7 -2/5 -1/3 -17/6 -1/3 -5/16 -31/11 -3/10 -2/7 -14/5 -2/7 -1/4 -53/19 -1/3 0/1 -39/14 -1/3 -1/4 0/1 -103/37 -1/3 0/1 -64/23 -1/3 -2/7 -25/9 -1/4 0/1 -11/4 -2/7 -1/4 -30/11 -4/15 -19/7 -6/23 -1/4 -27/10 -1/4 -8/3 -1/4 -2/9 -29/11 -1/4 0/1 -50/19 -1/4 -2/9 -21/8 -1/4 -2/9 -1/5 -97/37 -7/31 -2/9 -76/29 -2/9 -5/23 -55/21 -2/9 -1/5 -34/13 -4/19 -1/5 -13/5 -1/6 0/1 -31/12 -1/3 -1/4 -18/7 -1/4 -23/9 -1/4 -2/9 -51/20 -3/13 -5/22 -2/9 -79/31 -9/40 -2/9 -28/11 -2/9 -5/23 -5/2 -1/4 -1/5 -27/11 -1/5 -22/9 -1/5 -2/11 -39/16 -1/5 -2/11 -1/6 -17/7 -1/5 0/1 -29/12 -1/6 -1/7 -41/17 -1/12 0/1 -53/22 -1/2 0/1 -12/5 0/1 -55/23 -1/5 0/1 -43/18 -1/2 0/1 -31/13 -2/7 -1/4 -19/8 -1/4 -1/5 -64/27 -3/13 -2/9 -45/19 -2/9 -26/11 -2/9 -1/5 -33/14 -2/9 -3/14 -1/5 -7/3 -1/5 0/1 -23/10 -1/5 -1/6 -39/17 0/1 -55/24 -1/4 0/1 -16/7 -1/3 0/1 -41/18 -1/4 -1/5 -25/11 -1/4 -2/9 -9/4 -1/5 -29/13 -3/16 -2/11 -49/22 -1/5 -1/6 -20/9 -1/5 -2/11 -51/23 -4/21 -31/14 -1/5 -3/16 -11/5 -2/11 -3/17 -13/6 -1/5 -1/6 -15/7 0/1 -2/1 -1/6 0/1 -19/10 -1/6 -3/19 -17/9 -2/13 -1/7 -15/8 -1/6 -1/7 0/1 -13/7 -1/6 -2/13 -24/13 0/1 -11/6 -1/6 -2/13 -31/17 -3/20 -4/27 -20/11 -2/13 -1/7 -9/5 -1/7 -34/19 -1/7 -4/29 -59/33 -1/7 -4/29 -25/14 -1/7 -3/22 -16/9 -1/7 0/1 -55/31 -1/7 -2/15 -39/22 -1/7 -2/15 -1/8 -62/35 -2/15 -1/8 -23/13 -1/8 0/1 -53/30 -1/10 0/1 -30/17 0/1 -7/4 -1/7 0/1 -40/23 -4/29 -3/22 -33/19 -2/15 -26/15 -2/15 -3/23 -45/26 -1/8 -64/37 -1/7 -2/15 -19/11 -1/8 0/1 -50/29 -2/15 -1/8 -81/47 -1/8 -31/18 -1/8 -1/9 -43/25 -1/11 0/1 -98/57 -1/9 0/1 -55/32 -1/10 0/1 -12/7 0/1 -53/31 -1/5 0/1 -94/55 -2/11 -1/6 -135/79 -1/6 -41/24 -1/6 -1/7 -29/17 -1/6 0/1 -46/27 -1/6 -2/13 -63/37 -2/13 -17/10 -1/6 -1/7 -56/33 -1/6 -2/13 -39/23 -2/13 -22/13 -4/27 -1/7 -27/16 -1/7 -5/3 -1/7 -2/15 -33/20 -2/15 -5/38 -3/23 -28/17 -2/15 -3/23 -51/31 -2/15 -23/14 -3/23 -1/8 -18/11 -1/8 -31/19 -1/8 0/1 -13/8 -1/7 -1/8 -47/29 -1/7 0/1 -81/50 -1/7 -34/21 -1/7 -2/15 -89/55 -3/22 -2/15 -144/89 -2/15 -55/34 -3/22 -2/15 -76/47 -1/7 -2/15 -21/13 -2/15 -50/31 -4/31 -1/8 -79/49 -6/47 -1/8 -108/67 -1/8 -29/18 -1/7 -1/8 -37/23 -2/15 -3/23 -8/5 -4/31 -1/8 -27/17 -1/8 -19/12 -1/8 -11/89 -49/31 -8/65 -7/57 -79/50 -1/8 -7/57 -30/19 -6/49 -41/26 -1/8 -5/41 -11/7 -4/33 -3/25 -25/16 -3/25 -5/42 -89/57 -5/42 -12/101 -64/41 -7/59 -2/17 -39/25 -2/17 -53/34 -13/110 -2/17 -67/43 -33/280 -2/17 -81/52 -2/17 -14/9 -2/17 -7/60 -17/11 -6/53 -1/9 -54/35 -1/9 -37/24 -1/9 -9/82 -20/13 -1/9 -2/19 -23/15 -1/10 0/1 -3/2 -1/8 -1/9 0/1 -19/13 -4/31 -1/8 -54/37 -1/8 -35/24 -1/8 -11/89 -16/11 -4/33 -3/25 -29/20 -3/25 -5/42 -13/9 -2/17 -7/60 -23/16 -3/26 -1/9 -79/55 -8/69 -3/26 -135/94 -3/26 -56/39 -3/26 -10/87 -33/23 -4/35 -76/53 -7/61 -4/35 -119/83 -31/271 -4/35 -162/113 -4/35 -43/30 -4/35 -13/114 -10/7 -6/53 -1/9 -27/19 -1/9 -17/12 -1/9 -9/82 -41/29 -6/55 -5/46 -24/17 -4/37 -79/56 -1/9 -3/28 -55/39 -1/9 -4/37 -31/22 -1/9 -3/28 -7/5 -1/9 -2/19 -39/28 -1/9 -2/19 -1/10 -32/23 -1/9 -2/19 -57/41 0/1 -82/59 -1/9 0/1 -189/136 -1/9 -107/77 -1/9 -2/19 -25/18 -1/9 -1/10 -18/13 -1/9 -29/21 -4/37 -3/28 -11/8 -3/28 -2/19 -37/27 -3/29 -4/39 -63/46 -1/10 -26/19 -2/19 -3/29 -67/49 -4/39 -1/10 -108/79 -1/10 -41/30 -1/9 -1/10 -15/11 -2/19 -64/47 -2/19 -3/29 -113/83 -8/77 -3/29 -162/119 -3/29 -49/36 -3/29 -1/10 -34/25 -2/19 -3/29 -53/39 -3/29 -4/39 -72/53 -4/39 -91/67 -4/39 -5/49 -19/14 -3/29 -1/10 -23/17 -6/59 -1/10 -27/20 -1/10 -4/3 -1/10 0/1 -21/16 -1/10 -1/11 0/1 -38/29 -1/7 0/1 -55/42 -1/8 0/1 -72/55 0/1 -17/13 -1/9 0/1 -30/23 -2/19 -13/10 -1/9 -1/10 -35/27 -4/39 -1/10 -57/44 -1/10 -1/11 0/1 -22/17 -1/9 -2/19 -9/7 -1/10 -32/25 -5/51 -4/41 -55/43 -4/41 -3/31 -23/18 -1/10 -3/31 -37/29 -10/103 -3/31 -14/11 -2/21 -3/32 -61/48 -6/65 -1/11 -108/85 -1/11 -47/37 -1/11 -2/23 -33/26 -1/10 -1/11 0/1 -52/41 -1/10 -2/21 -71/56 -1/10 -1/11 -90/71 0/1 -19/15 -1/10 0/1 -24/19 -2/21 -53/42 -9/94 -2/21 -135/107 -2/21 -82/65 -2/21 -17/179 -29/23 -2/21 -3/32 -5/4 -1/10 -1/11 -26/21 -2/21 -5/53 -21/17 -2/21 -37/30 -1/10 -1/11 -90/73 -2/21 -53/43 -2/21 -1/11 -16/13 -4/43 -1/11 -27/22 -1/11 -11/9 -1/11 -2/23 -28/23 -1/11 0/1 -45/37 0/1 -17/14 -1/10 -1/11 -23/19 -2/23 -1/12 -52/43 -4/47 -1/12 -81/67 -1/12 -29/24 -1/12 -1/13 -6/5 0/1 -25/21 -1/10 -2/21 -44/37 -1/11 0/1 -19/16 -1/9 -1/10 -13/11 -1/10 -2/21 -20/17 -6/65 -1/11 -27/23 -1/11 -7/6 -1/11 -2/23 -22/19 -1/11 0/1 -15/13 -2/23 -23/20 -3/35 -1/12 -54/47 -1/12 -31/27 -1/12 0/1 -8/7 -2/23 -1/12 -17/15 -1/11 0/1 -9/8 -1/12 -10/9 -2/25 -1/13 -11/10 -1/10 0/1 -1/1 -1/13 0/1 0/1 0/1 1/1 0/1 1/13 10/9 1/13 2/25 9/8 1/12 8/7 1/12 2/23 15/13 2/23 7/6 2/23 1/11 13/11 2/21 1/10 19/16 1/10 1/9 25/21 2/21 1/10 6/5 0/1 29/24 1/13 1/12 23/19 1/12 2/23 17/14 1/11 1/10 11/9 2/23 1/11 27/22 1/11 16/13 1/11 4/43 21/17 2/21 5/4 1/11 1/10 19/15 0/1 1/10 52/41 2/21 1/10 33/26 0/1 1/11 1/10 14/11 3/32 2/21 23/18 3/31 1/10 9/7 1/10 31/24 1/10 3/29 53/41 3/29 2/19 22/17 2/19 1/9 35/27 1/10 4/39 13/10 1/10 1/9 17/13 0/1 1/9 21/16 0/1 1/11 1/10 4/3 0/1 1/10 19/14 1/10 3/29 34/25 3/29 2/19 49/36 1/10 3/29 15/11 2/19 41/30 1/10 1/9 26/19 3/29 2/19 11/8 2/19 3/28 29/21 3/28 4/37 18/13 1/9 25/18 1/10 1/9 57/41 0/1 32/23 2/19 1/9 7/5 2/19 1/9 24/17 4/37 17/12 9/82 1/9 27/19 1/9 10/7 1/9 6/53 43/30 13/114 4/35 33/23 4/35 56/39 10/87 3/26 23/16 1/9 3/26 13/9 7/60 2/17 16/11 3/25 4/33 19/13 1/8 4/31 22/15 2/15 1/7 3/2 0/1 1/9 1/8 20/13 2/19 1/9 17/11 1/9 6/53 31/20 1/9 3/26 14/9 7/60 2/17 53/34 2/17 13/110 39/25 2/17 103/66 9/76 7/59 64/41 2/17 7/59 25/16 5/42 3/25 11/7 3/25 4/33 30/19 6/49 19/12 11/89 1/8 27/17 1/8 8/5 1/8 4/31 29/18 1/8 1/7 50/31 1/8 4/31 21/13 2/15 97/60 9/68 2/15 76/47 2/15 1/7 55/34 2/15 3/22 34/21 2/15 1/7 13/8 1/8 1/7 31/19 0/1 1/8 18/11 1/8 23/14 1/8 3/23 51/31 2/15 79/48 1/8 3/23 28/17 3/23 2/15 5/3 2/15 1/7 27/16 1/7 22/13 1/7 4/27 39/23 2/13 17/10 1/7 1/6 29/17 0/1 1/6 41/24 1/7 1/6 53/31 0/1 1/5 12/7 0/1 55/32 0/1 1/10 43/25 0/1 1/11 31/18 1/9 1/8 19/11 0/1 1/8 64/37 2/15 1/7 45/26 1/8 26/15 3/23 2/15 33/19 2/15 7/4 0/1 1/7 23/13 0/1 1/8 39/22 1/8 2/15 1/7 55/31 2/15 1/7 16/9 0/1 1/7 41/23 9/68 2/15 25/14 3/22 1/7 9/5 1/7 29/16 1/7 3/20 49/27 1/7 2/13 20/11 1/7 2/13 51/28 1/7 5/34 4/27 31/17 4/27 3/20 11/6 2/13 1/6 13/7 2/13 1/6 15/8 0/1 1/7 1/6 2/1 0/1 1/6 19/9 1/6 2/11 17/8 1/6 1/5 15/7 0/1 13/6 1/6 1/5 24/11 0/1 11/5 3/17 2/11 31/14 3/16 1/5 20/9 2/11 1/5 9/4 1/5 34/15 1/5 2/9 59/26 1/5 3/14 25/11 2/9 1/4 16/7 0/1 1/3 55/24 0/1 1/4 39/17 0/1 62/27 0/1 1/6 23/10 1/6 1/5 53/23 2/11 1/5 30/13 2/11 7/3 0/1 1/5 40/17 5/24 4/19 33/14 1/5 3/14 2/9 26/11 1/5 2/9 45/19 2/9 64/27 2/9 3/13 19/8 1/5 1/4 50/21 4/17 1/4 81/34 1/4 31/13 1/4 2/7 43/18 0/1 1/2 98/41 1/5 2/9 55/23 0/1 1/5 12/5 0/1 53/22 0/1 1/2 94/39 -1/8 0/1 135/56 0/1 41/17 0/1 1/12 29/12 1/7 1/6 46/19 1/6 2/11 63/26 1/6 17/7 0/1 1/5 56/23 1/6 2/11 39/16 1/6 2/11 1/5 22/9 2/11 1/5 27/11 1/5 5/2 1/5 1/4 33/13 2/9 28/11 5/23 2/9 51/20 2/9 5/22 3/13 23/9 2/9 1/4 18/7 1/4 31/12 1/4 1/3 13/5 0/1 1/6 47/18 4/21 1/5 81/31 1/5 34/13 1/5 4/19 89/34 1/5 3/14 144/55 2/9 55/21 1/5 2/9 76/29 5/23 2/9 21/8 1/5 2/9 1/4 50/19 2/9 1/4 79/30 5/21 1/4 108/41 1/4 29/11 0/1 1/4 37/14 1/5 1/4 8/3 2/9 1/4 27/10 1/4 19/7 1/4 6/23 49/18 1/4 5/19 79/29 9/34 4/15 30/11 4/15 41/15 1/4 2/7 11/4 1/4 2/7 25/9 0/1 1/4 89/32 1/4 3/11 64/23 2/7 1/3 39/14 0/1 1/4 1/3 53/19 0/1 1/3 67/24 1/5 1/4 81/29 1/4 14/5 1/4 2/7 17/6 5/16 1/3 54/19 1/3 37/13 1/3 10/29 20/7 1/3 2/5 23/8 1/3 1/2 3/1 0/1 19/6 5/21 1/4 54/17 1/4 35/11 1/4 10/39 16/5 3/11 2/7 29/9 0/1 1/4 13/4 1/4 1/3 23/7 1/4 2/7 79/24 1/5 1/4 135/41 1/4 56/17 1/4 4/15 33/10 1/4 3/11 2/7 76/23 7/25 2/7 119/36 17/60 2/7 162/49 2/7 43/13 2/7 5/17 10/3 2/7 1/3 27/8 1/3 17/5 1/3 2/5 41/12 1/3 1/2 24/7 0/1 79/23 0/1 1/0 55/16 0/1 1/6 31/9 0/1 1/4 7/2 0/1 1/3 39/11 0/1 32/9 1/3 2/5 57/16 0/1 1/2 1/1 82/23 -1/3 0/1 189/53 0/1 107/30 0/1 1/10 25/7 0/1 1/4 18/5 1/3 29/8 1/3 3/8 11/3 0/1 1/3 37/10 1/3 3/8 63/17 2/5 26/7 1/3 2/5 67/18 3/7 1/2 108/29 1/2 41/11 0/1 1/2 15/4 1/3 2/5 1/2 64/17 0/1 1/3 113/30 1/4 1/3 162/43 1/3 49/13 1/3 2/5 34/9 1/3 2/5 53/14 2/5 1/2 72/19 2/5 91/24 3/7 1/2 19/5 2/5 1/2 23/6 3/7 1/2 27/7 1/2 4/1 0/1 1/2 21/5 2/3 38/9 0/1 1/1 55/13 2/3 1/1 72/17 2/3 17/4 3/4 1/1 30/7 2/1 13/3 0/1 1/0 35/8 3/1 1/0 57/13 -2/1 22/5 -1/1 0/1 9/2 0/1 32/7 0/1 1/3 55/12 0/1 1/2 23/5 0/1 1/4 37/8 3/10 1/3 14/3 0/1 1/2 61/13 4/13 1/3 108/23 1/3 47/10 1/3 4/11 33/7 2/5 52/11 0/1 1/2 71/15 1/3 2/5 90/19 2/5 19/4 3/7 1/2 24/5 2/3 53/11 2/3 1/1 135/28 1/1 82/17 0/1 1/1 29/6 1/2 1/1 5/1 0/1 1/1 26/5 -1/1 0/1 21/4 -1/1 -1/2 0/1 37/7 -1/3 0/1 90/17 0/1 53/10 -1/4 0/1 16/3 -1/5 0/1 27/5 0/1 11/2 0/1 1/6 28/5 0/1 1/3 45/8 1/4 17/3 2/7 1/3 23/4 1/3 1/2 52/9 4/9 1/2 81/14 1/2 29/5 1/2 2/3 6/1 0/1 25/4 1/2 1/1 44/7 0/1 1/3 19/3 2/5 1/2 13/2 1/2 1/1 20/3 2/3 1/1 27/4 1/1 7/1 0/1 1/1 22/3 0/1 1/1 15/2 0/1 1/1 1/0 23/3 2/1 1/0 54/7 1/0 31/4 -1/1 1/0 8/1 0/1 1/0 17/2 -1/1 1/0 9/1 0/1 10/1 -1/1 0/1 11/1 0/1 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(55,648,-32,-377) (-10/1,1/0) -> (-98/57,-55/32) Hyperbolic Matrix(109,1026,46,433) (-10/1,-9/1) -> (45/19,64/27) Hyperbolic Matrix(109,918,-64,-539) (-9/1,-8/1) -> (-46/27,-63/37) Hyperbolic Matrix(163,1242,-92,-701) (-8/1,-15/2) -> (-39/22,-62/35) Hyperbolic Matrix(53,378,-38,-271) (-15/2,-7/1) -> (-7/5,-39/28) Hyperbolic Matrix(107,702,-66,-433) (-7/1,-13/2) -> (-13/8,-47/29) Hyperbolic Matrix(109,702,84,541) (-13/2,-19/3) -> (35/27,13/10) Hyperbolic Matrix(431,2700,-276,-1729) (-19/3,-25/4) -> (-25/16,-89/57) Hyperbolic Matrix(53,324,44,269) (-25/4,-6/1) -> (6/5,29/24) Hyperbolic Matrix(55,324,46,271) (-6/1,-29/5) -> (25/21,6/5) Hyperbolic Matrix(431,2484,-300,-1729) (-29/5,-23/4) -> (-23/16,-79/55) Hyperbolic Matrix(161,918,104,593) (-23/4,-17/3) -> (17/11,31/20) Hyperbolic Matrix(107,594,-78,-433) (-17/3,-11/2) -> (-11/8,-37/27) Hyperbolic Matrix(109,594,20,109) (-11/2,-27/5) -> (27/5,11/2) Hyperbolic Matrix(161,864,30,161) (-27/5,-16/3) -> (16/3,27/5) Hyperbolic Matrix(215,1134,-164,-865) (-16/3,-21/4) -> (-21/16,-38/29) Hyperbolic Matrix(53,270,-32,-163) (-21/4,-5/1) -> (-5/3,-33/20) Hyperbolic Matrix(215,1026,-136,-649) (-5/1,-19/4) -> (-19/12,-49/31) Hyperbolic Matrix(217,1026,-114,-539) (-19/4,-52/11) -> (-2/1,-19/10) Hyperbolic Matrix(755,3564,526,2483) (-52/11,-33/7) -> (33/23,56/39) Hyperbolic Matrix(379,1782,-218,-1025) (-33/7,-14/3) -> (-40/23,-33/19) Hyperbolic Matrix(163,756,-58,-269) (-14/3,-23/5) -> (-31/11,-14/5) Hyperbolic Matrix(107,486,-24,-109) (-23/5,-9/2) -> (-9/2,-31/7) Parabolic Matrix(757,3348,220,973) (-31/7,-53/12) -> (55/16,31/9) Hyperbolic Matrix(1187,5238,734,3239) (-53/12,-22/5) -> (76/47,55/34) Hyperbolic Matrix(271,1188,-86,-377) (-22/5,-35/8) -> (-19/6,-22/7) Hyperbolic Matrix(161,702,136,593) (-35/8,-13/3) -> (13/11,19/16) Hyperbolic Matrix(215,918,-152,-649) (-13/3,-17/4) -> (-17/12,-41/29) Hyperbolic Matrix(269,1134,-218,-919) (-17/4,-21/5) -> (-21/17,-37/30) Hyperbolic Matrix(271,1134,168,703) (-21/5,-4/1) -> (50/31,21/13) Hyperbolic Matrix(269,1026,-156,-595) (-4/1,-19/5) -> (-19/11,-50/29) Hyperbolic Matrix(971,3672,-600,-2269) (-19/5,-34/9) -> (-34/21,-89/55) Hyperbolic Matrix(701,2646,386,1457) (-34/9,-49/13) -> (49/27,20/11) Hyperbolic Matrix(919,3456,-330,-1241) (-49/13,-15/4) -> (-39/14,-103/37) Hyperbolic Matrix(217,810,116,433) (-15/4,-41/11) -> (13/7,15/8) Hyperbolic Matrix(755,2808,-552,-2053) (-41/11,-26/7) -> (-26/19,-67/49) Hyperbolic Matrix(161,594,-132,-487) (-26/7,-11/3) -> (-11/9,-28/23) Hyperbolic Matrix(163,594,104,379) (-11/3,-29/8) -> (25/16,11/7) Hyperbolic Matrix(269,972,194,701) (-29/8,-18/5) -> (18/13,25/18) Hyperbolic Matrix(271,972,196,703) (-18/5,-25/7) -> (29/21,18/13) Hyperbolic Matrix(1621,5778,-636,-2267) (-25/7,-57/16) -> (-51/20,-79/31) Hyperbolic Matrix(379,1350,258,919) (-57/16,-32/9) -> (22/15,3/2) Hyperbolic Matrix(107,378,-92,-325) (-32/9,-7/2) -> (-7/6,-22/19) Hyperbolic Matrix(109,378,-62,-215) (-7/2,-24/7) -> (-30/17,-7/4) Hyperbolic Matrix(269,918,-206,-703) (-24/7,-17/5) -> (-17/13,-30/23) Hyperbolic Matrix(271,918,80,271) (-17/5,-27/8) -> (27/8,17/5) Hyperbolic Matrix(161,540,48,161) (-27/8,-10/3) -> (10/3,27/8) Hyperbolic Matrix(1403,4644,-816,-2701) (-10/3,-43/13) -> (-43/25,-98/57) Hyperbolic Matrix(1243,4104,-474,-1565) (-43/13,-33/10) -> (-21/8,-97/37) Hyperbolic Matrix(1081,3564,852,2809) (-33/10,-56/17) -> (52/41,33/26) Hyperbolic Matrix(755,2484,-624,-2053) (-56/17,-23/7) -> (-23/19,-52/43) Hyperbolic Matrix(215,702,132,431) (-23/7,-13/4) -> (13/8,31/19) Hyperbolic Matrix(269,864,-118,-379) (-13/4,-16/5) -> (-16/7,-41/18) Hyperbolic Matrix(271,864,-186,-593) (-16/5,-19/6) -> (-35/24,-16/11) Hyperbolic Matrix(431,1350,310,971) (-22/7,-3/1) -> (57/41,32/23) Hyperbolic Matrix(377,1080,-170,-487) (-3/1,-20/7) -> (-20/9,-51/23) Hyperbolic Matrix(379,1080,-246,-701) (-20/7,-17/6) -> (-37/24,-20/13) Hyperbolic Matrix(325,918,268,757) (-17/6,-31/11) -> (23/19,17/14) Hyperbolic Matrix(2051,5724,-1200,-3349) (-14/5,-53/19) -> (-53/31,-94/55) Hyperbolic Matrix(1511,4212,852,2375) (-53/19,-39/14) -> (39/22,55/31) Hyperbolic Matrix(4967,13824,-3648,-10153) (-103/37,-64/23) -> (-64/47,-113/83) Hyperbolic Matrix(971,2700,-816,-2269) (-64/23,-25/9) -> (-25/21,-44/37) Hyperbolic Matrix(215,594,156,431) (-25/9,-11/4) -> (11/8,29/21) Hyperbolic Matrix(217,594,-118,-323) (-11/4,-30/11) -> (-24/13,-11/6) Hyperbolic Matrix(377,1026,-298,-811) (-30/11,-19/7) -> (-19/15,-24/19) Hyperbolic Matrix(379,1026,140,379) (-19/7,-27/10) -> (27/10,19/7) Hyperbolic Matrix(161,432,60,161) (-27/10,-8/3) -> (8/3,27/10) Hyperbolic Matrix(593,1566,-348,-919) (-8/3,-29/11) -> (-29/17,-46/27) Hyperbolic Matrix(2051,5400,-1272,-3349) (-29/11,-50/19) -> (-50/31,-79/49) Hyperbolic Matrix(431,1134,328,863) (-50/19,-21/8) -> (21/16,4/3) Hyperbolic Matrix(6263,16416,-4368,-11449) (-97/37,-76/29) -> (-76/53,-119/83) Hyperbolic Matrix(1999,5238,1546,4051) (-76/29,-55/21) -> (53/41,22/17) Hyperbolic Matrix(1403,3672,-1032,-2701) (-55/21,-34/13) -> (-34/25,-53/39) Hyperbolic Matrix(269,702,-228,-595) (-34/13,-13/5) -> (-13/11,-20/17) Hyperbolic Matrix(271,702,188,487) (-13/5,-31/12) -> (23/16,13/9) Hyperbolic Matrix(377,972,230,593) (-31/12,-18/7) -> (18/11,23/14) Hyperbolic Matrix(379,972,232,595) (-18/7,-23/9) -> (31/19,18/11) Hyperbolic Matrix(1079,2754,592,1511) (-23/9,-51/20) -> (51/28,31/17) Hyperbolic Matrix(2861,7290,-2268,-5779) (-79/31,-28/11) -> (-82/65,-29/23) Hyperbolic Matrix(107,270,-86,-217) (-28/11,-5/2) -> (-5/4,-26/21) Hyperbolic Matrix(109,270,44,109) (-5/2,-27/11) -> (27/11,5/2) Hyperbolic Matrix(485,1188,198,485) (-27/11,-22/9) -> (22/9,27/11) Hyperbolic Matrix(863,2106,-620,-1513) (-22/9,-39/16) -> (-39/28,-32/23) Hyperbolic Matrix(377,918,-200,-487) (-39/16,-17/7) -> (-17/9,-15/8) Hyperbolic Matrix(647,1566,-402,-973) (-17/7,-29/12) -> (-29/18,-37/23) Hyperbolic Matrix(917,2214,514,1241) (-29/12,-41/17) -> (41/23,25/14) Hyperbolic Matrix(2375,5724,-1524,-3673) (-41/17,-53/22) -> (-53/34,-67/43) Hyperbolic Matrix(539,1296,314,755) (-53/22,-12/5) -> (12/7,55/32) Hyperbolic Matrix(541,1296,316,757) (-12/5,-55/23) -> (53/31,12/7) Hyperbolic Matrix(271,648,-248,-593) (-55/23,-43/18) -> (-11/10,-1/1) Hyperbolic Matrix(701,1674,384,917) (-43/18,-31/13) -> (31/17,11/6) Hyperbolic Matrix(431,1026,-318,-757) (-31/13,-19/8) -> (-19/14,-23/17) Hyperbolic Matrix(865,2052,-728,-1727) (-19/8,-64/27) -> (-44/37,-19/16) Hyperbolic Matrix(433,1026,46,109) (-64/27,-45/19) -> (9/1,10/1) Hyperbolic Matrix(1027,2430,-844,-1997) (-45/19,-26/11) -> (-28/23,-45/37) Hyperbolic Matrix(755,1782,-458,-1081) (-26/11,-33/14) -> (-33/20,-28/17) Hyperbolic Matrix(757,1782,-596,-1403) (-33/14,-7/3) -> (-47/37,-33/26) Hyperbolic Matrix(163,378,-116,-269) (-7/3,-23/10) -> (-31/22,-7/5) Hyperbolic Matrix(541,1242,-470,-1079) (-23/10,-39/17) -> (-15/13,-23/20) Hyperbolic Matrix(1837,4212,1178,2701) (-39/17,-55/24) -> (53/34,39/25) Hyperbolic Matrix(1297,2970,-990,-2267) (-55/24,-16/7) -> (-38/29,-55/42) Hyperbolic Matrix(973,2214,570,1297) (-41/18,-25/11) -> (29/17,41/24) Hyperbolic Matrix(215,486,-96,-217) (-25/11,-9/4) -> (-9/4,-29/13) Parabolic Matrix(2375,5292,872,1943) (-29/13,-49/22) -> (49/18,79/29) Hyperbolic Matrix(1189,2646,874,1945) (-49/22,-20/9) -> (34/25,49/36) Hyperbolic Matrix(1243,2754,756,1675) (-51/23,-31/14) -> (23/14,51/31) Hyperbolic Matrix(757,1674,440,973) (-31/14,-11/5) -> (43/25,31/18) Hyperbolic Matrix(271,594,-172,-377) (-11/5,-13/6) -> (-41/26,-11/7) Hyperbolic Matrix(377,810,276,593) (-13/6,-15/7) -> (15/11,41/30) Hyperbolic Matrix(431,918,-254,-541) (-15/7,-2/1) -> (-56/33,-39/23) Hyperbolic Matrix(1081,2052,-796,-1511) (-19/10,-17/9) -> (-91/67,-19/14) Hyperbolic Matrix(433,810,116,217) (-15/8,-13/7) -> (41/11,15/4) Hyperbolic Matrix(379,702,88,163) (-13/7,-24/13) -> (30/7,13/3) Hyperbolic Matrix(917,1674,384,701) (-11/6,-31/17) -> (31/13,43/18) Hyperbolic Matrix(593,1080,-386,-703) (-31/17,-20/11) -> (-20/13,-23/15) Hyperbolic Matrix(269,486,-150,-271) (-20/11,-9/5) -> (-9/5,-34/19) Parabolic Matrix(2053,3672,544,973) (-34/19,-59/33) -> (49/13,34/9) Hyperbolic Matrix(1027,1836,212,379) (-59/33,-25/14) -> (29/6,5/1) Hyperbolic Matrix(485,864,-334,-595) (-25/14,-16/9) -> (-16/11,-29/20) Hyperbolic Matrix(973,1728,-790,-1403) (-16/9,-55/31) -> (-53/43,-16/13) Hyperbolic Matrix(2375,4212,852,1511) (-55/31,-39/22) -> (39/14,53/19) Hyperbolic Matrix(1189,2106,-1036,-1835) (-62/35,-23/13) -> (-31/27,-8/7) Hyperbolic Matrix(1405,2484,306,541) (-23/13,-53/30) -> (55/12,23/5) Hyperbolic Matrix(1621,2862,-1284,-2267) (-53/30,-30/17) -> (-24/19,-53/42) Hyperbolic Matrix(1459,2538,-1148,-1997) (-7/4,-40/23) -> (-14/11,-61/48) Hyperbolic Matrix(809,1404,-654,-1135) (-33/19,-26/15) -> (-26/21,-21/17) Hyperbolic Matrix(1621,2808,-1184,-2051) (-26/15,-45/26) -> (-63/46,-26/19) Hyperbolic Matrix(593,1026,530,917) (-45/26,-64/37) -> (10/9,9/8) Hyperbolic Matrix(3997,6912,-2560,-4427) (-64/37,-19/11) -> (-89/57,-64/41) Hyperbolic Matrix(971,1674,250,431) (-50/29,-81/47) -> (27/7,4/1) Hyperbolic Matrix(1567,2700,408,703) (-81/47,-31/18) -> (23/6,27/7) Hyperbolic Matrix(973,1674,440,757) (-31/18,-43/25) -> (11/5,31/14) Hyperbolic Matrix(755,1296,314,539) (-55/32,-12/7) -> (12/5,53/22) Hyperbolic Matrix(757,1296,316,541) (-12/7,-53/31) -> (55/23,12/5) Hyperbolic Matrix(5561,9504,1990,3401) (-94/55,-135/79) -> (81/29,14/5) Hyperbolic Matrix(7237,12366,2592,4429) (-135/79,-41/24) -> (67/24,81/29) Hyperbolic Matrix(917,1566,284,485) (-41/24,-29/17) -> (29/9,13/4) Hyperbolic Matrix(1999,3402,540,919) (-63/37,-17/10) -> (37/10,63/17) Hyperbolic Matrix(2863,4860,-2258,-3833) (-17/10,-56/33) -> (-52/41,-71/56) Hyperbolic Matrix(701,1188,-606,-1027) (-39/23,-22/13) -> (-22/19,-15/13) Hyperbolic Matrix(703,1188,416,703) (-22/13,-27/16) -> (27/16,22/13) Hyperbolic Matrix(161,270,96,161) (-27/16,-5/3) -> (5/3,27/16) Hyperbolic Matrix(3511,5778,-2526,-4157) (-28/17,-51/31) -> (-57/41,-82/59) Hyperbolic Matrix(755,1242,262,431) (-51/31,-23/14) -> (23/8,3/1) Hyperbolic Matrix(593,972,230,377) (-23/14,-18/11) -> (18/7,31/12) Hyperbolic Matrix(595,972,232,379) (-18/11,-31/19) -> (23/9,18/7) Hyperbolic Matrix(431,702,132,215) (-31/19,-13/8) -> (13/4,23/7) Hyperbolic Matrix(1133,1836,166,269) (-47/29,-81/50) -> (27/4,7/1) Hyperbolic Matrix(1567,2538,234,379) (-81/50,-34/21) -> (20/3,27/4) Hyperbolic Matrix(6641,10746,-5240,-8479) (-89/55,-144/89) -> (-90/71,-19/15) Hyperbolic Matrix(7343,11880,-5608,-9073) (-144/89,-55/34) -> (-55/42,-72/55) Hyperbolic Matrix(3673,5940,802,1297) (-55/34,-76/47) -> (32/7,55/12) Hyperbolic Matrix(2539,4104,-1770,-2861) (-76/47,-21/13) -> (-33/23,-76/53) Hyperbolic Matrix(703,1134,168,271) (-21/13,-50/31) -> (4/1,21/5) Hyperbolic Matrix(7235,11664,2746,4427) (-79/49,-108/67) -> (108/41,29/11) Hyperbolic Matrix(7237,11664,2748,4429) (-108/67,-29/18) -> (79/30,108/41) Hyperbolic Matrix(269,432,-236,-379) (-37/23,-8/5) -> (-8/7,-17/15) Hyperbolic Matrix(271,432,170,271) (-8/5,-27/17) -> (27/17,8/5) Hyperbolic Matrix(647,1026,408,647) (-27/17,-19/12) -> (19/12,27/17) Hyperbolic Matrix(3349,5292,1846,2917) (-49/31,-79/50) -> (29/16,49/27) Hyperbolic Matrix(2701,4266,-1914,-3023) (-79/50,-30/19) -> (-24/17,-79/56) Hyperbolic Matrix(1403,2214,410,647) (-30/19,-41/26) -> (41/12,24/7) Hyperbolic Matrix(379,594,104,163) (-11/7,-25/16) -> (29/8,11/3) Hyperbolic Matrix(2215,3456,-1626,-2537) (-64/41,-39/25) -> (-15/11,-64/47) Hyperbolic Matrix(2701,4212,1178,1837) (-39/25,-53/34) -> (55/24,39/17) Hyperbolic Matrix(7937,12366,3292,5129) (-67/43,-81/52) -> (135/56,41/17) Hyperbolic Matrix(6103,9504,2532,3943) (-81/52,-14/9) -> (94/39,135/56) Hyperbolic Matrix(487,756,-382,-593) (-14/9,-17/11) -> (-37/29,-14/11) Hyperbolic Matrix(1889,2916,664,1025) (-17/11,-54/35) -> (54/19,37/13) Hyperbolic Matrix(1891,2916,666,1027) (-54/35,-37/24) -> (17/6,54/19) Hyperbolic Matrix(811,1242,318,487) (-23/15,-3/2) -> (51/20,23/9) Hyperbolic Matrix(811,1188,-626,-917) (-3/2,-19/13) -> (-35/27,-57/44) Hyperbolic Matrix(1997,2916,628,917) (-19/13,-54/37) -> (54/17,35/11) Hyperbolic Matrix(1999,2916,630,919) (-54/37,-35/24) -> (19/6,54/17) Hyperbolic Matrix(1081,1566,448,649) (-29/20,-13/9) -> (41/17,29/12) Hyperbolic Matrix(487,702,188,271) (-13/9,-23/16) -> (31/12,13/5) Hyperbolic Matrix(7181,10314,1240,1781) (-79/55,-135/94) -> (81/14,29/5) Hyperbolic Matrix(8047,11556,1392,1999) (-135/94,-56/39) -> (52/9,81/14) Hyperbolic Matrix(2483,3564,526,755) (-56/39,-33/23) -> (33/7,52/11) Hyperbolic Matrix(18305,26244,5536,7937) (-119/83,-162/113) -> (162/49,43/13) Hyperbolic Matrix(18307,26244,5538,7939) (-162/113,-43/30) -> (119/36,162/49) Hyperbolic Matrix(377,540,-340,-487) (-43/30,-10/7) -> (-10/9,-11/10) Hyperbolic Matrix(379,540,266,379) (-10/7,-27/19) -> (27/19,10/7) Hyperbolic Matrix(647,918,456,647) (-27/19,-17/12) -> (17/12,27/19) Hyperbolic Matrix(1567,2214,574,811) (-41/29,-24/17) -> (30/11,41/15) Hyperbolic Matrix(6967,9828,-5014,-7073) (-79/56,-55/39) -> (-107/77,-25/18) Hyperbolic Matrix(2375,3348,1838,2591) (-55/39,-31/22) -> (31/24,53/41) Hyperbolic Matrix(2213,3078,504,701) (-32/23,-57/41) -> (57/13,22/5) Hyperbolic Matrix(19117,26568,3964,5509) (-82/59,-189/136) -> (135/28,82/17) Hyperbolic Matrix(17603,24462,3652,5075) (-189/136,-107/77) -> (53/11,135/28) Hyperbolic Matrix(701,972,194,269) (-25/18,-18/13) -> (18/5,29/8) Hyperbolic Matrix(703,972,196,271) (-18/13,-29/21) -> (25/7,18/5) Hyperbolic Matrix(431,594,156,215) (-29/21,-11/8) -> (11/4,25/9) Hyperbolic Matrix(2483,3402,1024,1403) (-37/27,-63/46) -> (63/26,17/7) Hyperbolic Matrix(8531,11664,2290,3131) (-67/49,-108/79) -> (108/29,41/11) Hyperbolic Matrix(8533,11664,2292,3133) (-108/79,-41/30) -> (67/18,108/29) Hyperbolic Matrix(593,810,276,377) (-41/30,-15/11) -> (15/7,13/6) Hyperbolic Matrix(19277,26244,5116,6965) (-113/83,-162/119) -> (162/43,49/13) Hyperbolic Matrix(19279,26244,5118,6967) (-162/119,-49/36) -> (113/30,162/43) Hyperbolic Matrix(2699,3672,1190,1619) (-49/36,-34/25) -> (34/15,59/26) Hyperbolic Matrix(6319,8586,-5126,-6965) (-53/39,-72/53) -> (-90/73,-53/43) Hyperbolic Matrix(7991,10854,1510,2051) (-72/53,-91/67) -> (37/7,90/17) Hyperbolic Matrix(1997,2700,838,1133) (-23/17,-27/20) -> (81/34,31/13) Hyperbolic Matrix(1243,1674,522,703) (-27/20,-4/3) -> (50/21,81/34) Hyperbolic Matrix(863,1134,328,431) (-4/3,-21/16) -> (21/8,50/19) Hyperbolic Matrix(5075,6642,1072,1403) (-72/55,-17/13) -> (71/15,90/19) Hyperbolic Matrix(539,702,248,323) (-30/23,-13/10) -> (13/6,24/11) Hyperbolic Matrix(541,702,84,109) (-13/10,-35/27) -> (19/3,13/2) Hyperbolic Matrix(2377,3078,668,865) (-57/44,-22/17) -> (32/9,57/16) Hyperbolic Matrix(377,486,-294,-379) (-22/17,-9/7) -> (-9/7,-32/25) Parabolic Matrix(4643,5940,1772,2267) (-32/25,-55/43) -> (55/21,76/29) Hyperbolic Matrix(1943,2484,844,1079) (-55/43,-23/18) -> (23/10,53/23) Hyperbolic Matrix(973,1242,170,217) (-23/18,-37/29) -> (17/3,23/4) Hyperbolic Matrix(9179,11664,1954,2483) (-61/48,-108/85) -> (108/23,47/10) Hyperbolic Matrix(9181,11664,1956,2485) (-108/85,-47/37) -> (61/13,108/23) Hyperbolic Matrix(2809,3564,852,1081) (-33/26,-52/41) -> (56/17,33/10) Hyperbolic Matrix(5239,6642,1236,1567) (-71/56,-90/71) -> (72/17,17/4) Hyperbolic Matrix(19387,24462,5436,6859) (-53/42,-135/107) -> (189/53,107/30) Hyperbolic Matrix(21059,26568,5906,7451) (-135/107,-82/65) -> (82/23,189/53) Hyperbolic Matrix(1457,1836,642,809) (-29/23,-5/4) -> (59/26,25/11) Hyperbolic Matrix(8803,10854,2322,2863) (-37/30,-90/73) -> (72/19,91/24) Hyperbolic Matrix(703,864,572,703) (-16/13,-27/22) -> (27/22,16/13) Hyperbolic Matrix(485,594,396,485) (-27/22,-11/9) -> (11/9,27/22) Hyperbolic Matrix(755,918,88,107) (-45/37,-17/14) -> (17/2,9/1) Hyperbolic Matrix(1025,1242,222,269) (-17/14,-23/19) -> (23/5,37/8) Hyperbolic Matrix(9557,11556,2902,3509) (-52/43,-81/67) -> (135/41,56/17) Hyperbolic Matrix(8533,10314,2592,3133) (-81/67,-29/24) -> (79/24,135/41) Hyperbolic Matrix(269,324,44,53) (-29/24,-6/5) -> (6/1,25/4) Hyperbolic Matrix(271,324,46,55) (-6/5,-25/21) -> (29/5,6/1) Hyperbolic Matrix(593,702,136,161) (-19/16,-13/11) -> (13/3,35/8) Hyperbolic Matrix(2159,2538,826,971) (-20/17,-27/23) -> (81/31,34/13) Hyperbolic Matrix(1567,1836,600,703) (-27/23,-7/6) -> (47/18,81/31) Hyperbolic Matrix(2537,2916,328,377) (-23/20,-54/47) -> (54/7,31/4) Hyperbolic Matrix(2539,2916,330,379) (-54/47,-31/27) -> (23/3,54/7) Hyperbolic Matrix(811,918,144,163) (-17/15,-9/8) -> (45/8,17/3) Hyperbolic Matrix(917,1026,530,593) (-9/8,-10/9) -> (64/37,45/26) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(593,-648,248,-271) (1/1,10/9) -> (98/41,55/23) Hyperbolic Matrix(809,-918,334,-379) (9/8,8/7) -> (46/19,63/26) Hyperbolic Matrix(1079,-1242,470,-541) (8/7,15/13) -> (39/17,62/27) Hyperbolic Matrix(325,-378,92,-107) (15/13,7/6) -> (7/2,39/11) Hyperbolic Matrix(595,-702,228,-269) (7/6,13/11) -> (13/5,47/18) Hyperbolic Matrix(2269,-2700,816,-971) (19/16,25/21) -> (25/9,89/32) Hyperbolic Matrix(2053,-2484,624,-755) (29/24,23/19) -> (23/7,79/24) Hyperbolic Matrix(487,-594,132,-161) (17/14,11/9) -> (11/3,37/10) Hyperbolic Matrix(919,-1134,218,-269) (16/13,21/17) -> (21/5,38/9) Hyperbolic Matrix(217,-270,86,-107) (21/17,5/4) -> (5/2,33/13) Hyperbolic Matrix(811,-1026,298,-377) (5/4,19/15) -> (19/7,49/18) Hyperbolic Matrix(809,-1026,384,-487) (19/15,52/41) -> (2/1,19/9) Hyperbolic Matrix(1403,-1782,596,-757) (33/26,14/11) -> (40/17,33/14) Hyperbolic Matrix(593,-756,382,-487) (14/11,23/18) -> (31/20,14/9) Hyperbolic Matrix(379,-486,294,-377) (23/18,9/7) -> (9/7,31/24) Parabolic Matrix(917,-1188,626,-811) (22/17,35/27) -> (19/13,22/15) Hyperbolic Matrix(703,-918,206,-269) (13/10,17/13) -> (17/5,41/12) Hyperbolic Matrix(865,-1134,164,-215) (17/13,21/16) -> (21/4,37/7) Hyperbolic Matrix(757,-1026,318,-431) (4/3,19/14) -> (19/8,50/21) Hyperbolic Matrix(2701,-3672,1032,-1403) (19/14,34/25) -> (34/13,89/34) Hyperbolic Matrix(2537,-3456,1626,-2215) (49/36,15/11) -> (39/25,103/66) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(433,-594,78,-107) (26/19,11/8) -> (11/2,28/5) Hyperbolic Matrix(4157,-5778,2526,-3511) (25/18,57/41) -> (51/31,79/48) Hyperbolic Matrix(271,-378,38,-53) (32/23,7/5) -> (7/1,22/3) Hyperbolic Matrix(269,-378,116,-163) (7/5,24/17) -> (30/13,7/3) Hyperbolic Matrix(649,-918,152,-215) (24/17,17/12) -> (17/4,30/7) Hyperbolic Matrix(3241,-4644,1356,-1943) (10/7,43/30) -> (43/18,98/41) Hyperbolic Matrix(2861,-4104,1770,-2539) (43/30,33/23) -> (21/13,97/60) Hyperbolic Matrix(1729,-2484,300,-431) (56/39,23/16) -> (23/4,52/9) Hyperbolic Matrix(595,-864,334,-485) (13/9,16/11) -> (16/9,41/23) Hyperbolic Matrix(593,-864,186,-271) (16/11,19/13) -> (35/11,16/5) Hyperbolic Matrix(703,-1080,386,-593) (3/2,20/13) -> (20/11,51/28) Hyperbolic Matrix(701,-1080,246,-379) (20/13,17/11) -> (37/13,20/7) Hyperbolic Matrix(3673,-5724,1524,-2375) (14/9,53/34) -> (53/22,94/39) Hyperbolic Matrix(8857,-13824,2352,-3671) (103/66,64/41) -> (64/17,113/30) Hyperbolic Matrix(1729,-2700,276,-431) (64/41,25/16) -> (25/4,44/7) Hyperbolic Matrix(377,-594,172,-271) (11/7,30/19) -> (24/11,11/5) Hyperbolic Matrix(649,-1026,136,-215) (30/19,19/12) -> (19/4,24/5) Hyperbolic Matrix(973,-1566,402,-647) (8/5,29/18) -> (29/12,46/19) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(10153,-16416,3072,-4967) (97/60,76/47) -> (76/23,119/36) Hyperbolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(433,-702,66,-107) (34/21,13/8) -> (13/2,20/3) Hyperbolic Matrix(4429,-7290,918,-1511) (79/48,28/17) -> (82/17,29/6) Hyperbolic Matrix(163,-270,32,-53) (28/17,5/3) -> (5/1,26/5) Hyperbolic Matrix(1243,-2106,350,-593) (22/13,39/23) -> (39/11,32/9) Hyperbolic Matrix(541,-918,254,-431) (39/23,17/10) -> (17/8,15/7) Hyperbolic Matrix(919,-1566,348,-593) (17/10,29/17) -> (29/11,37/14) Hyperbolic Matrix(3349,-5724,1200,-2051) (41/24,53/31) -> (53/19,67/24) Hyperbolic Matrix(377,-648,32,-55) (55/32,43/25) -> (11/1,1/0) Hyperbolic Matrix(595,-1026,156,-269) (31/18,19/11) -> (19/5,23/6) Hyperbolic Matrix(1187,-2052,188,-325) (19/11,64/37) -> (44/7,19/3) Hyperbolic Matrix(1403,-2430,250,-433) (45/26,26/15) -> (28/5,45/8) Hyperbolic Matrix(1027,-1782,404,-701) (26/15,33/19) -> (33/13,28/11) Hyperbolic Matrix(1025,-1782,218,-379) (33/19,7/4) -> (47/10,33/7) Hyperbolic Matrix(215,-378,62,-109) (7/4,23/13) -> (31/9,7/2) Hyperbolic Matrix(701,-1242,92,-163) (23/13,39/22) -> (15/2,23/3) Hyperbolic Matrix(1673,-2970,396,-703) (55/31,16/9) -> (38/9,55/13) Hyperbolic Matrix(271,-486,150,-269) (25/14,9/5) -> (9/5,29/16) Parabolic Matrix(323,-594,118,-217) (11/6,13/7) -> (41/15,11/4) Hyperbolic Matrix(487,-918,200,-377) (15/8,2/1) -> (56/23,39/16) Hyperbolic Matrix(971,-2052,256,-541) (19/9,17/8) -> (91/24,19/5) Hyperbolic Matrix(487,-1080,170,-377) (31/14,20/9) -> (20/7,23/8) Hyperbolic Matrix(217,-486,96,-215) (20/9,9/4) -> (9/4,34/15) Parabolic Matrix(379,-864,118,-269) (25/11,16/7) -> (16/5,29/9) Hyperbolic Matrix(755,-1728,142,-325) (16/7,55/24) -> (53/10,16/3) Hyperbolic Matrix(917,-2106,118,-271) (62/27,23/10) -> (31/4,8/1) Hyperbolic Matrix(1241,-2862,258,-595) (53/23,30/13) -> (24/5,53/11) Hyperbolic Matrix(1079,-2538,230,-541) (7/3,40/17) -> (14/3,61/13) Hyperbolic Matrix(595,-1404,114,-269) (33/14,26/11) -> (26/5,21/4) Hyperbolic Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(2915,-6912,1048,-2485) (64/27,19/8) -> (89/32,64/23) Hyperbolic Matrix(1997,-4860,422,-1027) (17/7,56/23) -> (52/11,71/15) Hyperbolic Matrix(487,-1188,66,-161) (39/16,22/9) -> (22/3,15/2) Hyperbolic Matrix(2267,-5778,636,-1621) (28/11,51/20) -> (57/16,82/23) Hyperbolic Matrix(4105,-10746,866,-2267) (89/34,144/55) -> (90/19,19/4) Hyperbolic Matrix(4537,-11880,1072,-2807) (144/55,55/21) -> (55/13,72/17) Hyperbolic Matrix(1565,-4104,474,-1243) (76/29,21/8) -> (33/10,76/23) Hyperbolic Matrix(163,-432,20,-53) (37/14,8/3) -> (8/1,17/2) Hyperbolic Matrix(1565,-4266,456,-1243) (79/29,30/11) -> (24/7,79/23) Hyperbolic Matrix(1241,-3456,330,-919) (64/23,39/14) -> (15/4,64/17) Hyperbolic Matrix(269,-756,58,-163) (14/5,17/6) -> (37/8,14/3) Hyperbolic Matrix(377,-1188,86,-271) (3/1,19/6) -> (35/8,57/13) Hyperbolic Matrix(163,-540,16,-53) (43/13,10/3) -> (10/1,11/1) Hyperbolic Matrix(2861,-9828,802,-2755) (79/23,55/16) -> (107/30,25/7) Hyperbolic Matrix(2267,-8586,428,-1621) (53/14,72/19) -> (90/17,53/10) Hyperbolic Matrix(109,-486,24,-107) (22/5,9/2) -> (9/2,32/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(55,648,-32,-377) -> Matrix(1,0,-10,1) Matrix(109,1026,46,433) -> Matrix(1,2,4,9) Matrix(109,918,-64,-539) -> Matrix(1,-2,-6,13) Matrix(163,1242,-92,-701) -> Matrix(1,2,-8,-15) Matrix(53,378,-38,-271) -> Matrix(1,2,-10,-19) Matrix(107,702,-66,-433) -> Matrix(1,0,-6,1) Matrix(109,702,84,541) -> Matrix(3,2,28,19) Matrix(431,2700,-276,-1729) -> Matrix(1,-2,-8,17) Matrix(53,324,44,269) -> Matrix(1,0,14,1) Matrix(55,324,46,271) -> Matrix(1,0,12,1) Matrix(431,2484,-300,-1729) -> Matrix(7,2,-60,-17) Matrix(161,918,104,593) -> Matrix(11,4,96,35) Matrix(107,594,-78,-433) -> Matrix(9,2,-86,-19) Matrix(109,594,20,109) -> Matrix(1,0,12,1) Matrix(161,864,30,161) -> Matrix(1,0,-10,1) Matrix(215,1134,-164,-865) -> Matrix(1,0,-12,1) Matrix(53,270,-32,-163) -> Matrix(1,2,-8,-15) Matrix(215,1026,-136,-649) -> Matrix(15,8,-122,-65) Matrix(217,1026,-114,-539) -> Matrix(1,0,-4,1) Matrix(755,3564,526,2483) -> Matrix(23,10,200,87) Matrix(379,1782,-218,-1025) -> Matrix(11,4,-80,-29) Matrix(163,756,-58,-269) -> Matrix(5,2,-18,-7) Matrix(107,486,-24,-109) -> Matrix(1,0,4,1) Matrix(757,3348,220,973) -> Matrix(1,0,4,1) Matrix(1187,5238,734,3239) -> Matrix(1,-2,8,-15) Matrix(271,1188,-86,-377) -> Matrix(1,-2,-4,9) Matrix(161,702,136,593) -> Matrix(1,2,10,21) Matrix(215,918,-152,-649) -> Matrix(5,6,-46,-55) Matrix(269,1134,-218,-919) -> Matrix(5,4,-54,-43) Matrix(271,1134,168,703) -> Matrix(7,4,54,31) Matrix(269,1026,-156,-595) -> Matrix(5,2,-38,-15) Matrix(971,3672,-600,-2269) -> Matrix(11,4,-80,-29) Matrix(701,2646,386,1457) -> Matrix(11,4,74,27) Matrix(919,3456,-330,-1241) -> Matrix(5,2,-18,-7) Matrix(217,810,116,433) -> Matrix(5,2,32,13) Matrix(755,2808,-552,-2053) -> Matrix(9,4,-88,-39) Matrix(161,594,-132,-487) -> Matrix(5,2,-58,-23) Matrix(163,594,104,379) -> Matrix(9,4,74,33) Matrix(269,972,194,701) -> Matrix(5,2,42,17) Matrix(271,972,196,703) -> Matrix(13,4,120,37) Matrix(1621,5778,-636,-2267) -> Matrix(1,-2,-4,9) Matrix(379,1350,258,919) -> Matrix(1,0,10,1) Matrix(107,378,-92,-325) -> Matrix(5,2,-58,-23) Matrix(109,378,-62,-215) -> Matrix(1,0,-4,1) Matrix(269,918,-206,-703) -> Matrix(5,2,-48,-19) Matrix(271,918,80,271) -> Matrix(11,4,30,11) Matrix(161,540,48,161) -> Matrix(13,4,42,13) Matrix(1403,4644,-816,-2701) -> Matrix(7,2,-60,-17) Matrix(1243,4104,-474,-1565) -> Matrix(15,4,-64,-17) Matrix(1081,3564,852,2809) -> Matrix(7,2,66,19) Matrix(755,2484,-624,-2053) -> Matrix(1,0,-8,1) Matrix(215,702,132,431) -> Matrix(7,2,52,15) Matrix(269,864,-118,-379) -> Matrix(7,2,-32,-9) Matrix(271,864,-186,-593) -> Matrix(23,6,-188,-49) Matrix(431,1350,310,971) -> Matrix(1,0,14,1) Matrix(377,1080,-170,-487) -> Matrix(11,4,-58,-21) Matrix(379,1080,-246,-701) -> Matrix(11,4,-102,-37) Matrix(325,918,268,757) -> Matrix(13,4,146,45) Matrix(2051,5724,-1200,-3349) -> Matrix(1,0,-2,1) Matrix(1511,4212,852,2375) -> Matrix(7,2,52,15) Matrix(4967,13824,-3648,-10153) -> Matrix(27,8,-260,-77) Matrix(971,2700,-816,-2269) -> Matrix(7,2,-74,-21) Matrix(215,594,156,431) -> Matrix(13,4,120,37) Matrix(217,594,-118,-323) -> Matrix(15,4,-94,-25) Matrix(377,1026,-298,-811) -> Matrix(23,6,-234,-61) Matrix(379,1026,140,379) -> Matrix(47,12,184,47) Matrix(161,432,60,161) -> Matrix(17,4,72,17) Matrix(593,1566,-348,-919) -> Matrix(1,0,-2,1) Matrix(2051,5400,-1272,-3349) -> Matrix(25,6,-196,-47) Matrix(431,1134,328,863) -> Matrix(9,2,94,21) Matrix(6263,16416,-4368,-11449) -> Matrix(155,34,-1354,-297) Matrix(1999,5238,1546,4051) -> Matrix(37,8,356,77) Matrix(1403,3672,-1032,-2701) -> Matrix(47,10,-456,-97) Matrix(269,702,-228,-595) -> Matrix(11,2,-116,-21) Matrix(271,702,188,487) -> Matrix(5,2,42,17) Matrix(377,972,230,593) -> Matrix(15,4,116,31) Matrix(379,972,232,595) -> Matrix(9,2,76,17) Matrix(1079,2754,592,1511) -> Matrix(43,10,288,67) Matrix(2861,7290,-2268,-5779) -> Matrix(107,24,-1128,-253) Matrix(107,270,-86,-217) -> Matrix(1,0,-6,1) Matrix(109,270,44,109) -> Matrix(9,2,40,9) Matrix(485,1188,198,485) -> Matrix(21,4,110,21) Matrix(863,2106,-620,-1513) -> Matrix(1,0,-4,1) Matrix(377,918,-200,-487) -> Matrix(11,2,-72,-13) Matrix(647,1566,-402,-973) -> Matrix(13,2,-98,-15) Matrix(917,2214,514,1241) -> Matrix(15,2,112,15) Matrix(2375,5724,-1524,-3673) -> Matrix(9,-2,-76,17) Matrix(539,1296,314,755) -> Matrix(1,0,12,1) Matrix(541,1296,316,757) -> Matrix(1,0,10,1) Matrix(271,648,-248,-593) -> Matrix(1,0,-8,1) Matrix(701,1674,384,917) -> Matrix(5,2,32,13) Matrix(431,1026,-318,-757) -> Matrix(17,4,-166,-39) Matrix(865,2052,-728,-1727) -> Matrix(9,2,-86,-19) Matrix(433,1026,46,109) -> Matrix(9,2,4,1) Matrix(1027,2430,-844,-1997) -> Matrix(9,2,-104,-23) Matrix(755,1782,-458,-1081) -> Matrix(17,4,-132,-31) Matrix(757,1782,-596,-1403) -> Matrix(9,2,-104,-23) Matrix(163,378,-116,-269) -> Matrix(9,2,-86,-19) Matrix(541,1242,-470,-1079) -> Matrix(13,2,-150,-23) Matrix(1837,4212,1178,2701) -> Matrix(21,2,178,17) Matrix(1297,2970,-990,-2267) -> Matrix(1,0,-4,1) Matrix(973,2214,570,1297) -> Matrix(9,2,58,13) Matrix(215,486,-96,-217) -> Matrix(19,4,-100,-21) Matrix(2375,5292,872,1943) -> Matrix(35,6,134,23) Matrix(1189,2646,874,1945) -> Matrix(23,4,224,39) Matrix(1243,2754,756,1675) -> Matrix(53,10,408,77) Matrix(757,1674,440,973) -> Matrix(11,2,104,19) Matrix(271,594,-172,-377) -> Matrix(35,6,-286,-49) Matrix(377,810,276,593) -> Matrix(11,2,104,19) Matrix(431,918,-254,-541) -> Matrix(11,2,-72,-13) Matrix(1081,2052,-796,-1511) -> Matrix(37,6,-364,-59) Matrix(433,810,116,217) -> Matrix(13,2,32,5) Matrix(379,702,88,163) -> Matrix(13,2,6,1) Matrix(917,1674,384,701) -> Matrix(13,2,32,5) Matrix(593,1080,-386,-703) -> Matrix(27,4,-250,-37) Matrix(269,486,-150,-271) -> Matrix(41,6,-294,-43) Matrix(2053,3672,544,973) -> Matrix(15,2,52,7) Matrix(1027,1836,212,379) -> Matrix(29,4,36,5) Matrix(485,864,-334,-595) -> Matrix(31,4,-256,-33) Matrix(973,1728,-790,-1403) -> Matrix(29,4,-312,-43) Matrix(2375,4212,852,1511) -> Matrix(15,2,52,7) Matrix(1189,2106,-1036,-1835) -> Matrix(1,0,-4,1) Matrix(1405,2484,306,541) -> Matrix(1,0,12,1) Matrix(1621,2862,-1284,-2267) -> Matrix(11,2,-116,-21) Matrix(1459,2538,-1148,-1997) -> Matrix(43,6,-466,-65) Matrix(809,1404,-654,-1135) -> Matrix(29,4,-312,-43) Matrix(1621,2808,-1184,-2051) -> Matrix(1,0,-2,1) Matrix(593,1026,530,917) -> Matrix(1,0,20,1) Matrix(3997,6912,-2560,-4427) -> Matrix(91,12,-766,-101) Matrix(971,1674,250,431) -> Matrix(15,2,22,3) Matrix(1567,2700,408,703) -> Matrix(33,4,74,9) Matrix(973,1674,440,757) -> Matrix(19,2,104,11) Matrix(755,1296,314,539) -> Matrix(1,0,12,1) Matrix(757,1296,316,541) -> Matrix(1,0,10,1) Matrix(5561,9504,1990,3401) -> Matrix(23,4,86,15) Matrix(7237,12366,2592,4429) -> Matrix(13,2,58,9) Matrix(917,1566,284,485) -> Matrix(1,0,10,1) Matrix(1999,3402,540,919) -> Matrix(27,4,74,11) Matrix(2863,4860,-2258,-3833) -> Matrix(1,0,-4,1) Matrix(701,1188,-606,-1027) -> Matrix(27,4,-304,-45) Matrix(703,1188,416,703) -> Matrix(55,8,378,55) Matrix(161,270,96,161) -> Matrix(29,4,210,29) Matrix(3511,5778,-2526,-4157) -> Matrix(15,2,-158,-21) Matrix(755,1242,262,431) -> Matrix(15,2,22,3) Matrix(593,972,230,377) -> Matrix(31,4,116,15) Matrix(595,972,232,379) -> Matrix(17,2,76,9) Matrix(431,702,132,215) -> Matrix(15,2,52,7) Matrix(1133,1836,166,269) -> Matrix(1,0,8,1) Matrix(1567,2538,234,379) -> Matrix(29,4,36,5) Matrix(6641,10746,-5240,-8479) -> Matrix(15,2,-128,-17) Matrix(7343,11880,-5608,-9073) -> Matrix(15,2,-98,-13) Matrix(3673,5940,802,1297) -> Matrix(15,2,52,7) Matrix(2539,4104,-1770,-2861) -> Matrix(77,10,-670,-87) Matrix(703,1134,168,271) -> Matrix(31,4,54,7) Matrix(7235,11664,2746,4427) -> Matrix(47,6,180,23) Matrix(7237,11664,2748,4429) -> Matrix(33,4,140,17) Matrix(269,432,-236,-379) -> Matrix(15,2,-188,-25) Matrix(271,432,170,271) -> Matrix(63,8,496,63) Matrix(647,1026,408,647) -> Matrix(177,22,1424,177) Matrix(3349,5292,1846,2917) -> Matrix(179,22,1196,147) Matrix(2701,4266,-1914,-3023) -> Matrix(179,22,-1668,-205) Matrix(1403,2214,410,647) -> Matrix(49,6,106,13) Matrix(379,594,104,163) -> Matrix(33,4,74,9) Matrix(2215,3456,-1626,-2537) -> Matrix(169,20,-1614,-191) Matrix(2701,4212,1178,1837) -> Matrix(17,2,178,21) Matrix(7937,12366,3292,5129) -> Matrix(17,2,484,57) Matrix(6103,9504,2532,3943) -> Matrix(17,2,-196,-23) Matrix(487,756,-382,-593) -> Matrix(69,8,-716,-83) Matrix(1889,2916,664,1025) -> Matrix(143,16,420,47) Matrix(1891,2916,666,1027) -> Matrix(127,14,390,43) Matrix(811,1242,318,487) -> Matrix(21,2,94,9) Matrix(811,1188,-626,-917) -> Matrix(1,0,-2,1) Matrix(1997,2916,628,917) -> Matrix(111,14,436,55) Matrix(1999,2916,630,919) -> Matrix(129,16,524,65) Matrix(1081,1566,448,649) -> Matrix(17,2,144,17) Matrix(487,702,188,271) -> Matrix(17,2,42,5) Matrix(7181,10314,1240,1781) -> Matrix(121,14,216,25) Matrix(8047,11556,1392,1999) -> Matrix(191,22,408,47) Matrix(2483,3564,526,755) -> Matrix(87,10,200,23) Matrix(18305,26244,5536,7937) -> Matrix(717,82,2492,285) Matrix(18307,26244,5538,7939) -> Matrix(823,94,2898,331) Matrix(377,540,-340,-487) -> Matrix(35,4,-464,-53) Matrix(379,540,266,379) -> Matrix(107,12,954,107) Matrix(647,918,456,647) -> Matrix(163,18,1476,163) Matrix(1567,2214,574,811) -> Matrix(147,16,542,59) Matrix(6967,9828,-5014,-7073) -> Matrix(19,2,-162,-17) Matrix(2375,3348,1838,2591) -> Matrix(93,10,902,97) Matrix(2213,3078,504,701) -> Matrix(19,2,-10,-1) Matrix(19117,26568,3964,5509) -> Matrix(1,0,10,1) Matrix(17603,24462,3652,5075) -> Matrix(37,4,46,5) Matrix(701,972,194,269) -> Matrix(17,2,42,5) Matrix(703,972,196,271) -> Matrix(37,4,120,13) Matrix(431,594,156,215) -> Matrix(37,4,120,13) Matrix(2483,3402,1024,1403) -> Matrix(39,4,224,23) Matrix(8531,11664,2290,3131) -> Matrix(39,4,68,7) Matrix(8533,11664,2292,3133) -> Matrix(21,2,52,5) Matrix(593,810,276,377) -> Matrix(19,2,104,11) Matrix(19277,26244,5116,6965) -> Matrix(135,14,376,39) Matrix(19279,26244,5118,6967) -> Matrix(39,4,146,15) Matrix(2699,3672,1190,1619) -> Matrix(77,8,356,37) Matrix(6319,8586,-5126,-6965) -> Matrix(97,10,-1038,-107) Matrix(7991,10854,1510,2051) -> Matrix(39,4,-166,-17) Matrix(1997,2700,838,1133) -> Matrix(79,8,306,31) Matrix(1243,1674,522,703) -> Matrix(41,4,174,17) Matrix(863,1134,328,431) -> Matrix(21,2,94,9) Matrix(5075,6642,1072,1403) -> Matrix(17,2,42,5) Matrix(539,702,248,323) -> Matrix(19,2,104,11) Matrix(541,702,84,109) -> Matrix(19,2,28,3) Matrix(2377,3078,668,865) -> Matrix(1,0,12,1) Matrix(377,486,-294,-379) -> Matrix(59,6,-600,-61) Matrix(4643,5940,1772,2267) -> Matrix(103,10,484,47) Matrix(1943,2484,844,1079) -> Matrix(21,2,136,13) Matrix(973,1242,170,217) -> Matrix(41,4,92,9) Matrix(9179,11664,1954,2483) -> Matrix(109,10,316,29) Matrix(9181,11664,1956,2485) -> Matrix(67,6,212,19) Matrix(2809,3564,852,1081) -> Matrix(19,2,66,7) Matrix(5239,6642,1236,1567) -> Matrix(23,2,34,3) Matrix(19387,24462,5436,6859) -> Matrix(21,2,304,29) Matrix(21059,26568,5906,7451) -> Matrix(21,2,-242,-23) Matrix(1457,1836,642,809) -> Matrix(43,4,204,19) Matrix(8803,10854,2322,2863) -> Matrix(41,4,92,9) Matrix(703,864,572,703) -> Matrix(87,8,946,87) Matrix(485,594,396,485) -> Matrix(45,4,506,45) Matrix(755,918,88,107) -> Matrix(1,0,10,1) Matrix(1025,1242,222,269) -> Matrix(23,2,80,7) Matrix(9557,11556,2902,3509) -> Matrix(95,8,368,31) Matrix(8533,10314,2592,3133) -> Matrix(25,2,112,9) Matrix(269,324,44,53) -> Matrix(1,0,14,1) Matrix(271,324,46,55) -> Matrix(1,0,12,1) Matrix(593,702,136,161) -> Matrix(21,2,10,1) Matrix(2159,2538,826,971) -> Matrix(109,10,534,49) Matrix(1567,1836,600,703) -> Matrix(67,6,346,31) Matrix(2537,2916,328,377) -> Matrix(47,4,-12,-1) Matrix(2539,2916,330,379) -> Matrix(25,2,12,1) Matrix(811,918,144,163) -> Matrix(23,2,80,7) Matrix(917,1026,530,593) -> Matrix(1,0,20,1) Matrix(1,0,2,1) -> Matrix(1,0,26,1) Matrix(593,-648,248,-271) -> Matrix(1,0,-8,1) Matrix(809,-918,334,-379) -> Matrix(1,0,-6,1) Matrix(1079,-1242,470,-541) -> Matrix(23,-2,150,-13) Matrix(325,-378,92,-107) -> Matrix(23,-2,58,-5) Matrix(595,-702,228,-269) -> Matrix(21,-2,116,-11) Matrix(2269,-2700,816,-971) -> Matrix(21,-2,74,-7) Matrix(2053,-2484,624,-755) -> Matrix(1,0,-8,1) Matrix(487,-594,132,-161) -> Matrix(23,-2,58,-5) Matrix(919,-1134,218,-269) -> Matrix(43,-4,54,-5) Matrix(217,-270,86,-107) -> Matrix(1,0,-6,1) Matrix(811,-1026,298,-377) -> Matrix(61,-6,234,-23) Matrix(809,-1026,384,-487) -> Matrix(21,-2,116,-11) Matrix(1403,-1782,596,-757) -> Matrix(23,-2,104,-9) Matrix(593,-756,382,-487) -> Matrix(83,-8,716,-69) Matrix(379,-486,294,-377) -> Matrix(61,-6,600,-59) Matrix(917,-1188,626,-811) -> Matrix(1,0,-2,1) Matrix(703,-918,206,-269) -> Matrix(19,-2,48,-5) Matrix(865,-1134,164,-215) -> Matrix(1,0,-12,1) Matrix(757,-1026,318,-431) -> Matrix(39,-4,166,-17) Matrix(2701,-3672,1032,-1403) -> Matrix(97,-10,456,-47) Matrix(2537,-3456,1626,-2215) -> Matrix(191,-20,1614,-169) Matrix(2053,-2808,552,-755) -> Matrix(39,-4,88,-9) Matrix(433,-594,78,-107) -> Matrix(19,-2,86,-9) Matrix(4157,-5778,2526,-3511) -> Matrix(21,-2,158,-15) Matrix(271,-378,38,-53) -> Matrix(19,-2,10,-1) Matrix(269,-378,116,-163) -> Matrix(19,-2,86,-9) Matrix(649,-918,152,-215) -> Matrix(55,-6,46,-5) Matrix(3241,-4644,1356,-1943) -> Matrix(35,-4,184,-21) Matrix(2861,-4104,1770,-2539) -> Matrix(87,-10,670,-77) Matrix(1729,-2484,300,-431) -> Matrix(17,-2,60,-7) Matrix(595,-864,334,-485) -> Matrix(33,-4,256,-31) Matrix(593,-864,186,-271) -> Matrix(49,-6,188,-23) Matrix(703,-1080,386,-593) -> Matrix(37,-4,250,-27) Matrix(701,-1080,246,-379) -> Matrix(37,-4,102,-11) Matrix(3673,-5724,1524,-2375) -> Matrix(17,-2,-76,9) Matrix(8857,-13824,2352,-3671) -> Matrix(17,-2,-8,1) Matrix(1729,-2700,276,-431) -> Matrix(17,-2,-8,1) Matrix(377,-594,172,-271) -> Matrix(49,-6,286,-35) Matrix(649,-1026,136,-215) -> Matrix(65,-8,122,-15) Matrix(973,-1566,402,-647) -> Matrix(15,-2,98,-13) Matrix(3349,-5400,1272,-2051) -> Matrix(47,-6,196,-25) Matrix(10153,-16416,3072,-4967) -> Matrix(119,-16,424,-57) Matrix(2269,-3672,600,-971) -> Matrix(29,-4,80,-11) Matrix(433,-702,66,-107) -> Matrix(1,0,-6,1) Matrix(4429,-7290,918,-1511) -> Matrix(15,-2,38,-5) Matrix(163,-270,32,-53) -> Matrix(15,-2,8,-1) Matrix(1243,-2106,350,-593) -> Matrix(13,-2,46,-7) Matrix(541,-918,254,-431) -> Matrix(13,-2,72,-11) Matrix(919,-1566,348,-593) -> Matrix(1,0,-2,1) Matrix(3349,-5724,1200,-2051) -> Matrix(1,0,-2,1) Matrix(377,-648,32,-55) -> Matrix(1,0,-10,1) Matrix(595,-1026,156,-269) -> Matrix(15,-2,38,-5) Matrix(1187,-2052,188,-325) -> Matrix(15,-2,38,-5) Matrix(1403,-2430,250,-433) -> Matrix(15,-2,68,-9) Matrix(1027,-1782,404,-701) -> Matrix(29,-4,138,-19) Matrix(1025,-1782,218,-379) -> Matrix(29,-4,80,-11) Matrix(215,-378,62,-109) -> Matrix(1,0,-4,1) Matrix(701,-1242,92,-163) -> Matrix(15,-2,8,-1) Matrix(1673,-2970,396,-703) -> Matrix(1,0,-6,1) Matrix(271,-486,150,-269) -> Matrix(43,-6,294,-41) Matrix(323,-594,118,-217) -> Matrix(25,-4,94,-15) Matrix(487,-918,200,-377) -> Matrix(13,-2,72,-11) Matrix(971,-2052,256,-541) -> Matrix(23,-4,52,-9) Matrix(487,-1080,170,-377) -> Matrix(21,-4,58,-11) Matrix(217,-486,96,-215) -> Matrix(21,-4,100,-19) Matrix(379,-864,118,-269) -> Matrix(9,-2,32,-7) Matrix(755,-1728,142,-325) -> Matrix(1,0,-8,1) Matrix(917,-2106,118,-271) -> Matrix(1,0,-6,1) Matrix(1241,-2862,258,-595) -> Matrix(1,0,-4,1) Matrix(1079,-2538,230,-541) -> Matrix(19,-4,62,-13) Matrix(595,-1404,114,-269) -> Matrix(9,-2,-4,1) Matrix(1187,-2808,320,-757) -> Matrix(1,0,-2,1) Matrix(2915,-6912,1048,-2485) -> Matrix(17,-4,64,-15) Matrix(1997,-4860,422,-1027) -> Matrix(11,-2,28,-5) Matrix(487,-1188,66,-161) -> Matrix(11,-2,6,-1) Matrix(2267,-5778,636,-1621) -> Matrix(9,-2,-4,1) Matrix(4105,-10746,866,-2267) -> Matrix(37,-8,88,-19) Matrix(4537,-11880,1072,-2807) -> Matrix(19,-4,24,-5) Matrix(1565,-4104,474,-1243) -> Matrix(17,-4,64,-15) Matrix(163,-432,20,-53) -> Matrix(9,-2,-4,1) Matrix(1565,-4266,456,-1243) -> Matrix(15,-4,34,-9) Matrix(1241,-3456,330,-919) -> Matrix(7,-2,18,-5) Matrix(269,-756,58,-163) -> Matrix(7,-2,18,-5) Matrix(377,-1188,86,-271) -> Matrix(9,-2,-4,1) Matrix(163,-540,16,-53) -> Matrix(7,-2,-10,3) Matrix(2861,-9828,802,-2755) -> Matrix(1,0,4,1) Matrix(2267,-8586,428,-1621) -> Matrix(5,-2,-22,9) Matrix(109,-486,24,-107) -> Matrix(1,0,4,1) 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): 88 Degree of the the map X: 88 Degree of the the map Y: 324 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 972 Minimal number of generators: 163 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -6/1 -21/4 -9/2 -3/1 -12/5 -9/4 -9/5 -3/2 -9/7 -27/23 0/1 1/1 9/8 27/22 9/7 27/19 3/2 27/17 27/16 9/5 2/1 9/4 81/34 12/5 135/56 27/11 5/2 108/41 27/10 3/1 27/8 7/2 108/29 15/4 27/7 4/1 13/3 9/2 19/4 135/28 29/6 5/1 21/4 27/5 11/2 45/8 23/4 81/14 6/1 13/2 27/4 7/1 15/2 8/1 17/2 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 0/1 1/1 -9/1 0/1 -8/1 0/1 1/0 -7/1 -1/1 0/1 -6/1 0/1 -17/3 -1/3 -2/7 -11/2 -1/6 0/1 -27/5 0/1 -16/3 0/1 1/5 -21/4 0/1 1/2 1/1 -5/1 -1/1 0/1 -19/4 -1/2 -3/7 -14/3 -1/2 0/1 -9/2 0/1 -13/3 0/1 1/0 -17/4 -1/1 -3/4 -4/1 -1/2 0/1 -19/5 -1/2 -2/5 -15/4 -1/2 -2/5 -1/3 -41/11 -1/2 0/1 -26/7 -2/5 -1/3 -11/3 -1/3 0/1 -7/2 -1/3 0/1 -10/3 -1/3 -2/7 -13/4 -1/3 -1/4 -16/5 -2/7 -3/11 -3/1 0/1 -17/6 -1/3 -5/16 -14/5 -2/7 -1/4 -11/4 -2/7 -1/4 -8/3 -1/4 -2/9 -29/11 -1/4 0/1 -50/19 -1/4 -2/9 -21/8 -1/4 -2/9 -1/5 -34/13 -4/19 -1/5 -13/5 -1/6 0/1 -5/2 -1/4 -1/5 -27/11 -1/5 -22/9 -1/5 -2/11 -39/16 -1/5 -2/11 -1/6 -17/7 -1/5 0/1 -29/12 -1/6 -1/7 -12/5 0/1 -19/8 -1/4 -1/5 -64/27 -3/13 -2/9 -45/19 -2/9 -26/11 -2/9 -1/5 -7/3 -1/5 0/1 -23/10 -1/5 -1/6 -16/7 -1/3 0/1 -9/4 -1/5 -11/5 -2/11 -3/17 -13/6 -1/5 -1/6 -2/1 -1/6 0/1 -11/6 -1/6 -2/13 -9/5 -1/7 -7/4 -1/7 0/1 -19/11 -1/8 0/1 -50/29 -2/15 -1/8 -81/47 -1/8 -31/18 -1/8 -1/9 -12/7 0/1 -29/17 -1/6 0/1 -46/27 -1/6 -2/13 -63/37 -2/13 -17/10 -1/6 -1/7 -5/3 -1/7 -2/15 -28/17 -2/15 -3/23 -23/14 -3/23 -1/8 -18/11 -1/8 -13/8 -1/7 -1/8 -21/13 -2/15 -50/31 -4/31 -1/8 -79/49 -6/47 -1/8 -108/67 -1/8 -29/18 -1/7 -1/8 -37/23 -2/15 -3/23 -8/5 -4/31 -1/8 -27/17 -1/8 -19/12 -1/8 -11/89 -49/31 -8/65 -7/57 -30/19 -6/49 -11/7 -4/33 -3/25 -25/16 -3/25 -5/42 -14/9 -2/17 -7/60 -3/2 -1/8 -1/9 0/1 -13/9 -2/17 -7/60 -23/16 -3/26 -1/9 -10/7 -6/53 -1/9 -27/19 -1/9 -17/12 -1/9 -9/82 -24/17 -4/37 -31/22 -1/9 -3/28 -7/5 -1/9 -2/19 -32/23 -1/9 -2/19 -25/18 -1/9 -1/10 -18/13 -1/9 -11/8 -3/28 -2/19 -37/27 -3/29 -4/39 -26/19 -2/19 -3/29 -67/49 -4/39 -1/10 -108/79 -1/10 -41/30 -1/9 -1/10 -15/11 -2/19 -4/3 -1/10 0/1 -13/10 -1/9 -1/10 -9/7 -1/10 -5/4 -1/10 -1/11 -11/9 -1/11 -2/23 -28/23 -1/11 0/1 -45/37 0/1 -17/14 -1/10 -1/11 -6/5 0/1 -13/11 -1/10 -2/21 -20/17 -6/65 -1/11 -27/23 -1/11 -7/6 -1/11 -2/23 -1/1 -1/13 0/1 0/1 0/1 1/1 0/1 1/13 10/9 1/13 2/25 9/8 1/12 8/7 1/12 2/23 7/6 2/23 1/11 13/11 2/21 1/10 19/16 1/10 1/9 25/21 2/21 1/10 6/5 0/1 23/19 1/12 2/23 17/14 1/11 1/10 11/9 2/23 1/11 27/22 1/11 16/13 1/11 4/43 5/4 1/11 1/10 14/11 3/32 2/21 23/18 3/31 1/10 9/7 1/10 13/10 1/10 1/9 17/13 0/1 1/9 21/16 0/1 1/11 1/10 4/3 0/1 1/10 19/14 1/10 3/29 15/11 2/19 41/30 1/10 1/9 26/19 3/29 2/19 11/8 2/19 3/28 18/13 1/9 25/18 1/10 1/9 57/41 0/1 32/23 2/19 1/9 7/5 2/19 1/9 24/17 4/37 17/12 9/82 1/9 27/19 1/9 10/7 1/9 6/53 33/23 4/35 56/39 10/87 3/26 23/16 1/9 3/26 13/9 7/60 2/17 3/2 0/1 1/9 1/8 14/9 7/60 2/17 53/34 2/17 13/110 39/25 2/17 25/16 5/42 3/25 11/7 3/25 4/33 30/19 6/49 19/12 11/89 1/8 27/17 1/8 8/5 1/8 4/31 29/18 1/8 1/7 50/31 1/8 4/31 21/13 2/15 34/21 2/15 1/7 13/8 1/8 1/7 18/11 1/8 23/14 1/8 3/23 51/31 2/15 79/48 1/8 3/23 28/17 3/23 2/15 5/3 2/15 1/7 27/16 1/7 22/13 1/7 4/27 17/10 1/7 1/6 29/17 0/1 1/6 41/24 1/7 1/6 12/7 0/1 55/32 0/1 1/10 43/25 0/1 1/11 31/18 1/9 1/8 19/11 0/1 1/8 64/37 2/15 1/7 45/26 1/8 26/15 3/23 2/15 7/4 0/1 1/7 16/9 0/1 1/7 25/14 3/22 1/7 9/5 1/7 11/6 2/13 1/6 13/7 2/13 1/6 15/8 0/1 1/7 1/6 2/1 0/1 1/6 15/7 0/1 13/6 1/6 1/5 11/5 3/17 2/11 9/4 1/5 16/7 0/1 1/3 55/24 0/1 1/4 39/17 0/1 23/10 1/6 1/5 53/23 2/11 1/5 30/13 2/11 7/3 0/1 1/5 33/14 1/5 3/14 2/9 26/11 1/5 2/9 45/19 2/9 64/27 2/9 3/13 19/8 1/5 1/4 50/21 4/17 1/4 81/34 1/4 31/13 1/4 2/7 12/5 0/1 53/22 0/1 1/2 94/39 -1/8 0/1 135/56 0/1 41/17 0/1 1/12 29/12 1/7 1/6 46/19 1/6 2/11 63/26 1/6 17/7 0/1 1/5 56/23 1/6 2/11 39/16 1/6 2/11 1/5 22/9 2/11 1/5 27/11 1/5 5/2 1/5 1/4 18/7 1/4 31/12 1/4 1/3 13/5 0/1 1/6 47/18 4/21 1/5 81/31 1/5 34/13 1/5 4/19 55/21 1/5 2/9 76/29 5/23 2/9 21/8 1/5 2/9 1/4 50/19 2/9 1/4 79/30 5/21 1/4 108/41 1/4 29/11 0/1 1/4 37/14 1/5 1/4 8/3 2/9 1/4 27/10 1/4 19/7 1/4 6/23 11/4 1/4 2/7 25/9 0/1 1/4 89/32 1/4 3/11 64/23 2/7 1/3 39/14 0/1 1/4 1/3 14/5 1/4 2/7 17/6 5/16 1/3 3/1 0/1 16/5 3/11 2/7 13/4 1/4 1/3 23/7 1/4 2/7 33/10 1/4 3/11 2/7 43/13 2/7 5/17 10/3 2/7 1/3 27/8 1/3 17/5 1/3 2/5 7/2 0/1 1/3 18/5 1/3 29/8 1/3 3/8 11/3 0/1 1/3 37/10 1/3 3/8 63/17 2/5 26/7 1/3 2/5 67/18 3/7 1/2 108/29 1/2 41/11 0/1 1/2 15/4 1/3 2/5 1/2 49/13 1/3 2/5 34/9 1/3 2/5 19/5 2/5 1/2 23/6 3/7 1/2 27/7 1/2 4/1 0/1 1/2 21/5 2/3 17/4 3/4 1/1 13/3 0/1 1/0 9/2 0/1 14/3 0/1 1/2 33/7 2/5 52/11 0/1 1/2 71/15 1/3 2/5 19/4 3/7 1/2 24/5 2/3 53/11 2/3 1/1 135/28 1/1 82/17 0/1 1/1 29/6 1/2 1/1 5/1 0/1 1/1 26/5 -1/1 0/1 21/4 -1/1 -1/2 0/1 37/7 -1/3 0/1 53/10 -1/4 0/1 16/3 -1/5 0/1 27/5 0/1 11/2 0/1 1/6 28/5 0/1 1/3 45/8 1/4 17/3 2/7 1/3 23/4 1/3 1/2 52/9 4/9 1/2 81/14 1/2 29/5 1/2 2/3 6/1 0/1 13/2 1/2 1/1 20/3 2/3 1/1 27/4 1/1 7/1 0/1 1/1 22/3 0/1 1/1 15/2 0/1 1/1 1/0 8/1 0/1 1/0 17/2 -1/1 1/0 9/1 0/1 10/1 -1/1 0/1 11/1 0/1 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(53,567,10,107) (-10/1,1/0) -> (37/7,53/10) Hyperbolic Matrix(109,1026,46,433) (-10/1,-9/1) -> (45/19,64/27) Hyperbolic Matrix(109,918,-64,-539) (-9/1,-8/1) -> (-46/27,-63/37) Hyperbolic Matrix(53,405,14,107) (-8/1,-7/1) -> (34/9,19/5) Hyperbolic Matrix(55,351,34,217) (-7/1,-6/1) -> (21/13,34/21) Hyperbolic Matrix(109,621,76,433) (-6/1,-17/3) -> (10/7,33/23) Hyperbolic Matrix(107,594,-78,-433) (-17/3,-11/2) -> (-11/8,-37/27) Hyperbolic Matrix(109,594,20,109) (-11/2,-27/5) -> (27/5,11/2) Hyperbolic Matrix(161,864,30,161) (-27/5,-16/3) -> (16/3,27/5) Hyperbolic Matrix(271,1431,82,433) (-16/3,-21/4) -> (33/10,43/13) Hyperbolic Matrix(325,1701,124,649) (-21/4,-5/1) -> (76/29,21/8) Hyperbolic Matrix(215,1026,-136,-649) (-5/1,-19/4) -> (-19/12,-49/31) Hyperbolic Matrix(109,513,92,433) (-19/4,-14/3) -> (13/11,19/16) Hyperbolic Matrix(53,243,-12,-55) (-14/3,-9/2) -> (-9/2,-13/3) Parabolic Matrix(107,459,-38,-163) (-13/3,-17/4) -> (-17/6,-14/5) Hyperbolic Matrix(109,459,90,379) (-17/4,-4/1) -> (23/19,17/14) Hyperbolic Matrix(269,1026,-156,-595) (-4/1,-19/5) -> (-19/11,-50/29) Hyperbolic Matrix(107,405,14,53) (-19/5,-15/4) -> (15/2,8/1) Hyperbolic Matrix(217,810,116,433) (-15/4,-41/11) -> (13/7,15/8) Hyperbolic Matrix(755,2808,-552,-2053) (-41/11,-26/7) -> (-26/19,-67/49) Hyperbolic Matrix(161,594,-132,-487) (-26/7,-11/3) -> (-11/9,-28/23) Hyperbolic Matrix(53,189,30,107) (-11/3,-7/2) -> (7/4,16/9) Hyperbolic Matrix(55,189,16,55) (-7/2,-10/3) -> (17/5,7/2) Hyperbolic Matrix(107,351,82,269) (-10/3,-13/4) -> (13/10,17/13) Hyperbolic Matrix(109,351,-50,-161) (-13/4,-16/5) -> (-11/5,-13/6) Hyperbolic Matrix(161,513,-102,-325) (-16/5,-3/1) -> (-30/19,-11/7) Hyperbolic Matrix(161,459,-114,-325) (-3/1,-17/6) -> (-17/12,-24/17) Hyperbolic Matrix(107,297,58,161) (-14/5,-11/4) -> (11/6,13/7) Hyperbolic Matrix(109,297,40,109) (-11/4,-8/3) -> (19/7,11/4) Hyperbolic Matrix(593,1566,-348,-919) (-8/3,-29/11) -> (-29/17,-46/27) Hyperbolic Matrix(2051,5400,-1272,-3349) (-29/11,-50/19) -> (-50/31,-79/49) Hyperbolic Matrix(431,1134,328,863) (-50/19,-21/8) -> (21/16,4/3) Hyperbolic Matrix(485,1269,206,539) (-21/8,-34/13) -> (7/3,33/14) Hyperbolic Matrix(269,702,-228,-595) (-34/13,-13/5) -> (-13/11,-20/17) Hyperbolic Matrix(53,135,42,107) (-13/5,-5/2) -> (5/4,14/11) Hyperbolic Matrix(109,270,44,109) (-5/2,-27/11) -> (27/11,5/2) Hyperbolic Matrix(485,1188,198,485) (-27/11,-22/9) -> (22/9,27/11) Hyperbolic Matrix(919,2241,244,595) (-22/9,-39/16) -> (15/4,49/13) Hyperbolic Matrix(1297,3159,466,1135) (-39/16,-17/7) -> (64/23,39/14) Hyperbolic Matrix(647,1566,-402,-973) (-17/7,-29/12) -> (-29/18,-37/23) Hyperbolic Matrix(593,1431,380,917) (-29/12,-12/5) -> (39/25,25/16) Hyperbolic Matrix(215,513,158,377) (-12/5,-19/8) -> (19/14,15/11) Hyperbolic Matrix(1081,2565,228,541) (-19/8,-64/27) -> (71/15,19/4) Hyperbolic Matrix(433,1026,46,109) (-64/27,-45/19) -> (9/1,10/1) Hyperbolic Matrix(1027,2430,-844,-1997) (-45/19,-26/11) -> (-28/23,-45/37) Hyperbolic Matrix(539,1269,206,485) (-26/11,-7/3) -> (34/13,55/21) Hyperbolic Matrix(163,378,-116,-269) (-7/3,-23/10) -> (-31/22,-7/5) Hyperbolic Matrix(647,1485,376,863) (-23/10,-16/7) -> (43/25,31/18) Hyperbolic Matrix(107,243,-48,-109) (-16/7,-9/4) -> (-9/4,-11/5) Parabolic Matrix(215,459,126,269) (-13/6,-2/1) -> (29/17,41/24) Hyperbolic Matrix(161,297,58,107) (-2/1,-11/6) -> (11/4,25/9) Hyperbolic Matrix(163,297,-118,-215) (-11/6,-9/5) -> (-18/13,-11/8) Hyperbolic Matrix(107,189,30,53) (-9/5,-7/4) -> (7/2,18/5) Hyperbolic Matrix(109,189,94,163) (-7/4,-19/11) -> (8/7,7/6) Hyperbolic Matrix(971,1674,250,431) (-50/29,-81/47) -> (27/7,4/1) Hyperbolic Matrix(1567,2700,408,703) (-81/47,-31/18) -> (23/6,27/7) Hyperbolic Matrix(863,1485,376,647) (-31/18,-12/7) -> (39/17,23/10) Hyperbolic Matrix(269,459,126,215) (-12/7,-29/17) -> (2/1,15/7) Hyperbolic Matrix(1999,3402,540,919) (-63/37,-17/10) -> (37/10,63/17) Hyperbolic Matrix(271,459,160,271) (-17/10,-5/3) -> (22/13,17/10) Hyperbolic Matrix(1457,2403,556,917) (-5/3,-28/17) -> (55/21,76/29) Hyperbolic Matrix(1133,1863,492,809) (-28/17,-23/14) -> (23/10,53/23) Hyperbolic Matrix(593,972,230,377) (-23/14,-18/11) -> (18/7,31/12) Hyperbolic Matrix(215,351,-166,-271) (-18/11,-13/8) -> (-13/10,-9/7) Hyperbolic Matrix(217,351,34,55) (-13/8,-21/13) -> (6/1,13/2) Hyperbolic Matrix(703,1134,168,271) (-21/13,-50/31) -> (4/1,21/5) Hyperbolic Matrix(7235,11664,2746,4427) (-79/49,-108/67) -> (108/41,29/11) Hyperbolic Matrix(7237,11664,2748,4429) (-108/67,-29/18) -> (79/30,108/41) Hyperbolic Matrix(757,1215,438,703) (-37/23,-8/5) -> (19/11,64/37) Hyperbolic Matrix(271,432,170,271) (-8/5,-27/17) -> (27/17,8/5) Hyperbolic Matrix(647,1026,408,647) (-27/17,-19/12) -> (19/12,27/17) Hyperbolic Matrix(2375,3753,1708,2699) (-49/31,-30/19) -> (57/41,32/23) Hyperbolic Matrix(379,594,104,163) (-11/7,-25/16) -> (29/8,11/3) Hyperbolic Matrix(917,1431,380,593) (-25/16,-14/9) -> (41/17,29/12) Hyperbolic Matrix(53,81,-36,-55) (-14/9,-3/2) -> (-3/2,-13/9) Parabolic Matrix(487,702,188,271) (-13/9,-23/16) -> (31/12,13/5) Hyperbolic Matrix(433,621,76,109) (-23/16,-10/7) -> (17/3,23/4) Hyperbolic Matrix(379,540,266,379) (-10/7,-27/19) -> (27/19,10/7) Hyperbolic Matrix(647,918,456,647) (-27/19,-17/12) -> (17/12,27/19) Hyperbolic Matrix(1513,2133,920,1297) (-24/17,-31/22) -> (23/14,51/31) Hyperbolic Matrix(1027,1431,272,379) (-7/5,-32/23) -> (49/13,34/9) Hyperbolic Matrix(757,1053,156,217) (-32/23,-25/18) -> (29/6,5/1) Hyperbolic Matrix(701,972,194,269) (-25/18,-18/13) -> (18/5,29/8) Hyperbolic Matrix(217,297,198,271) (-37/27,-26/19) -> (1/1,10/9) Hyperbolic Matrix(8531,11664,2290,3131) (-67/49,-108/79) -> (108/29,41/11) Hyperbolic Matrix(8533,11664,2292,3133) (-108/79,-41/30) -> (67/18,108/29) Hyperbolic Matrix(593,810,276,377) (-41/30,-15/11) -> (15/7,13/6) Hyperbolic Matrix(377,513,158,215) (-15/11,-4/3) -> (31/13,12/5) Hyperbolic Matrix(269,351,82,107) (-4/3,-13/10) -> (13/4,23/7) Hyperbolic Matrix(107,135,42,53) (-9/7,-5/4) -> (5/2,18/7) Hyperbolic Matrix(109,135,88,109) (-5/4,-11/9) -> (16/13,5/4) Hyperbolic Matrix(755,918,88,107) (-45/37,-17/14) -> (17/2,9/1) Hyperbolic Matrix(379,459,90,109) (-17/14,-6/5) -> (21/5,17/4) Hyperbolic Matrix(433,513,92,109) (-6/5,-13/11) -> (14/3,33/7) Hyperbolic Matrix(2159,2538,826,971) (-20/17,-27/23) -> (81/31,34/13) Hyperbolic Matrix(1567,1836,600,703) (-27/23,-7/6) -> (47/18,81/31) Hyperbolic Matrix(163,189,94,109) (-7/6,-1/1) -> (26/15,7/4) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(703,-783,290,-323) (10/9,9/8) -> (63/26,17/7) Hyperbolic Matrix(809,-918,334,-379) (9/8,8/7) -> (46/19,63/26) Hyperbolic Matrix(595,-702,228,-269) (7/6,13/11) -> (13/5,47/18) Hyperbolic Matrix(2269,-2700,816,-971) (19/16,25/21) -> (25/9,89/32) Hyperbolic Matrix(973,-1161,678,-809) (25/21,6/5) -> (33/23,56/39) Hyperbolic Matrix(649,-783,402,-485) (6/5,23/19) -> (50/31,21/13) Hyperbolic Matrix(487,-594,132,-161) (17/14,11/9) -> (11/3,37/10) Hyperbolic Matrix(595,-729,484,-593) (11/9,27/22) -> (27/22,16/13) Parabolic Matrix(487,-621,338,-431) (14/11,23/18) -> (23/16,13/9) Hyperbolic Matrix(485,-621,296,-379) (23/18,9/7) -> (18/11,23/14) Hyperbolic Matrix(271,-351,166,-215) (9/7,13/10) -> (13/8,18/11) Hyperbolic Matrix(865,-1134,164,-215) (17/13,21/16) -> (21/4,37/7) Hyperbolic Matrix(757,-1026,318,-431) (4/3,19/14) -> (19/8,50/21) Hyperbolic Matrix(811,-1107,474,-647) (15/11,41/30) -> (41/24,12/7) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(433,-594,78,-107) (26/19,11/8) -> (11/2,28/5) Hyperbolic Matrix(215,-297,118,-163) (11/8,18/13) -> (9/5,11/6) Hyperbolic Matrix(487,-675,272,-377) (18/13,25/18) -> (25/14,9/5) Hyperbolic Matrix(4157,-5778,2526,-3511) (25/18,57/41) -> (51/31,79/48) Hyperbolic Matrix(271,-378,38,-53) (32/23,7/5) -> (7/1,22/3) Hyperbolic Matrix(269,-378,116,-163) (7/5,24/17) -> (30/13,7/3) Hyperbolic Matrix(325,-459,114,-161) (24/17,17/12) -> (17/6,3/1) Hyperbolic Matrix(1729,-2484,300,-431) (56/39,23/16) -> (23/4,52/9) Hyperbolic Matrix(55,-81,36,-53) (13/9,3/2) -> (3/2,14/9) Parabolic Matrix(3673,-5724,1524,-2375) (14/9,53/34) -> (53/22,94/39) Hyperbolic Matrix(1783,-2781,1038,-1619) (53/34,39/25) -> (12/7,55/32) Hyperbolic Matrix(431,-675,242,-379) (25/16,11/7) -> (16/9,25/14) Hyperbolic Matrix(325,-513,102,-161) (11/7,30/19) -> (3/1,16/5) Hyperbolic Matrix(649,-1026,136,-215) (30/19,19/12) -> (19/4,24/5) Hyperbolic Matrix(973,-1566,402,-647) (8/5,29/18) -> (29/12,46/19) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(433,-702,66,-107) (34/21,13/8) -> (13/2,20/3) Hyperbolic Matrix(4429,-7290,918,-1511) (79/48,28/17) -> (82/17,29/6) Hyperbolic Matrix(163,-270,32,-53) (28/17,5/3) -> (5/1,26/5) Hyperbolic Matrix(433,-729,256,-431) (5/3,27/16) -> (27/16,22/13) Parabolic Matrix(919,-1566,348,-593) (17/10,29/17) -> (29/11,37/14) Hyperbolic Matrix(377,-648,32,-55) (55/32,43/25) -> (11/1,1/0) Hyperbolic Matrix(595,-1026,156,-269) (31/18,19/11) -> (19/5,23/6) Hyperbolic Matrix(2107,-3645,374,-647) (64/37,45/26) -> (45/8,17/3) Hyperbolic Matrix(1403,-2430,250,-433) (45/26,26/15) -> (28/5,45/8) Hyperbolic Matrix(487,-918,200,-377) (15/8,2/1) -> (56/23,39/16) Hyperbolic Matrix(161,-351,50,-109) (13/6,11/5) -> (16/5,13/4) Hyperbolic Matrix(109,-243,48,-107) (11/5,9/4) -> (9/4,16/7) Parabolic Matrix(755,-1728,142,-325) (16/7,55/24) -> (53/10,16/3) Hyperbolic Matrix(1189,-2727,494,-1133) (55/24,39/17) -> (12/5,53/22) Hyperbolic Matrix(1241,-2862,258,-595) (53/23,30/13) -> (24/5,53/11) Hyperbolic Matrix(595,-1404,114,-269) (33/14,26/11) -> (26/5,21/4) Hyperbolic Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(2915,-6912,1048,-2485) (64/27,19/8) -> (89/32,64/23) Hyperbolic Matrix(2755,-6561,1156,-2753) (50/21,81/34) -> (81/34,31/13) Parabolic Matrix(7561,-18225,3136,-7559) (94/39,135/56) -> (135/56,41/17) Parabolic Matrix(1997,-4860,422,-1027) (17/7,56/23) -> (52/11,71/15) Hyperbolic Matrix(487,-1188,66,-161) (39/16,22/9) -> (22/3,15/2) Hyperbolic Matrix(811,-2133,246,-647) (21/8,50/19) -> (23/7,33/10) Hyperbolic Matrix(163,-432,20,-53) (37/14,8/3) -> (8/1,17/2) Hyperbolic Matrix(271,-729,100,-269) (8/3,27/10) -> (27/10,19/7) Parabolic Matrix(649,-1809,174,-485) (39/14,14/5) -> (41/11,15/4) Hyperbolic Matrix(163,-459,38,-107) (14/5,17/6) -> (17/4,13/3) Hyperbolic Matrix(163,-540,16,-53) (43/13,10/3) -> (10/1,11/1) Hyperbolic Matrix(217,-729,64,-215) (10/3,27/8) -> (27/8,17/5) Parabolic Matrix(55,-243,12,-53) (13/3,9/2) -> (9/2,14/3) Parabolic Matrix(269,-1269,46,-217) (33/7,52/11) -> (29/5,6/1) Hyperbolic Matrix(3781,-18225,784,-3779) (53/11,135/28) -> (135/28,82/17) Parabolic Matrix(1135,-6561,196,-1133) (52/9,81/14) -> (81/14,29/5) Parabolic Matrix(109,-729,16,-107) (20/3,27/4) -> (27/4,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(53,567,10,107) -> Matrix(1,0,-4,1) Matrix(109,1026,46,433) -> Matrix(1,2,4,9) Matrix(109,918,-64,-539) -> Matrix(1,-2,-6,13) Matrix(53,405,14,107) -> Matrix(1,2,2,5) Matrix(55,351,34,217) -> Matrix(3,2,22,15) Matrix(109,621,76,433) -> Matrix(11,4,96,35) Matrix(107,594,-78,-433) -> Matrix(9,2,-86,-19) Matrix(109,594,20,109) -> Matrix(1,0,12,1) Matrix(161,864,30,161) -> Matrix(1,0,-10,1) Matrix(271,1431,82,433) -> Matrix(5,-2,18,-7) Matrix(325,1701,124,649) -> Matrix(3,-2,14,-9) Matrix(215,1026,-136,-649) -> Matrix(15,8,-122,-65) Matrix(109,513,92,433) -> Matrix(5,2,52,21) Matrix(53,243,-12,-55) -> Matrix(1,0,2,1) Matrix(107,459,-38,-163) -> Matrix(1,2,-4,-7) Matrix(109,459,90,379) -> Matrix(3,2,34,23) Matrix(269,1026,-156,-595) -> Matrix(5,2,-38,-15) Matrix(107,405,14,53) -> Matrix(5,2,2,1) Matrix(217,810,116,433) -> Matrix(5,2,32,13) Matrix(755,2808,-552,-2053) -> Matrix(9,4,-88,-39) Matrix(161,594,-132,-487) -> Matrix(5,2,-58,-23) Matrix(53,189,30,107) -> Matrix(1,0,10,1) Matrix(55,189,16,55) -> Matrix(1,0,6,1) Matrix(107,351,82,269) -> Matrix(7,2,66,19) Matrix(109,351,-50,-161) -> Matrix(1,0,-2,1) Matrix(161,513,-102,-325) -> Matrix(23,6,-188,-49) Matrix(161,459,-114,-325) -> Matrix(11,4,-102,-37) Matrix(107,297,58,161) -> Matrix(1,0,10,1) Matrix(109,297,40,109) -> Matrix(15,4,56,15) Matrix(593,1566,-348,-919) -> Matrix(1,0,-2,1) Matrix(2051,5400,-1272,-3349) -> Matrix(25,6,-196,-47) Matrix(431,1134,328,863) -> Matrix(9,2,94,21) Matrix(485,1269,206,539) -> Matrix(19,4,90,19) Matrix(269,702,-228,-595) -> Matrix(11,2,-116,-21) Matrix(53,135,42,107) -> Matrix(9,2,94,21) Matrix(109,270,44,109) -> Matrix(9,2,40,9) Matrix(485,1188,198,485) -> Matrix(21,4,110,21) Matrix(919,2241,244,595) -> Matrix(1,0,8,1) Matrix(1297,3159,466,1135) -> Matrix(11,2,38,7) Matrix(647,1566,-402,-973) -> Matrix(13,2,-98,-15) Matrix(593,1431,380,917) -> Matrix(17,2,144,17) Matrix(215,513,158,377) -> Matrix(7,2,66,19) Matrix(1081,2565,228,541) -> Matrix(17,4,38,9) Matrix(433,1026,46,109) -> Matrix(9,2,4,1) Matrix(1027,2430,-844,-1997) -> Matrix(9,2,-104,-23) Matrix(539,1269,206,485) -> Matrix(19,4,90,19) Matrix(163,378,-116,-269) -> Matrix(9,2,-86,-19) Matrix(647,1485,376,863) -> Matrix(1,0,14,1) Matrix(107,243,-48,-109) -> Matrix(9,2,-50,-11) Matrix(215,459,126,269) -> Matrix(1,0,12,1) Matrix(161,297,58,107) -> Matrix(1,0,10,1) Matrix(163,297,-118,-215) -> Matrix(27,4,-250,-37) Matrix(107,189,30,53) -> Matrix(1,0,10,1) Matrix(109,189,94,163) -> Matrix(15,2,172,23) Matrix(971,1674,250,431) -> Matrix(15,2,22,3) Matrix(1567,2700,408,703) -> Matrix(33,4,74,9) Matrix(863,1485,376,647) -> Matrix(1,0,14,1) Matrix(269,459,126,215) -> Matrix(1,0,12,1) Matrix(1999,3402,540,919) -> Matrix(27,4,74,11) Matrix(271,459,160,271) -> Matrix(13,2,84,13) Matrix(1457,2403,556,917) -> Matrix(61,8,282,37) Matrix(1133,1863,492,809) -> Matrix(31,4,178,23) Matrix(593,972,230,377) -> Matrix(31,4,116,15) Matrix(215,351,-166,-271) -> Matrix(1,0,-2,1) Matrix(217,351,34,55) -> Matrix(15,2,22,3) Matrix(703,1134,168,271) -> Matrix(31,4,54,7) Matrix(7235,11664,2746,4427) -> Matrix(47,6,180,23) Matrix(7237,11664,2748,4429) -> Matrix(33,4,140,17) Matrix(757,1215,438,703) -> Matrix(31,4,240,31) Matrix(271,432,170,271) -> Matrix(63,8,496,63) Matrix(647,1026,408,647) -> Matrix(177,22,1424,177) Matrix(2375,3753,1708,2699) -> Matrix(49,6,498,61) Matrix(379,594,104,163) -> Matrix(33,4,74,9) Matrix(917,1431,380,593) -> Matrix(17,2,144,17) Matrix(53,81,-36,-55) -> Matrix(1,0,0,1) Matrix(487,702,188,271) -> Matrix(17,2,42,5) Matrix(433,621,76,109) -> Matrix(35,4,96,11) Matrix(379,540,266,379) -> Matrix(107,12,954,107) Matrix(647,918,456,647) -> Matrix(163,18,1476,163) Matrix(1513,2133,920,1297) -> Matrix(93,10,716,77) Matrix(1027,1431,272,379) -> Matrix(1,0,12,1) Matrix(757,1053,156,217) -> Matrix(19,2,28,3) Matrix(701,972,194,269) -> Matrix(17,2,42,5) Matrix(217,297,198,271) -> Matrix(19,2,218,23) Matrix(8531,11664,2290,3131) -> Matrix(39,4,68,7) Matrix(8533,11664,2292,3133) -> Matrix(21,2,52,5) Matrix(593,810,276,377) -> Matrix(19,2,104,11) Matrix(377,513,158,215) -> Matrix(19,2,66,7) Matrix(269,351,82,107) -> Matrix(19,2,66,7) Matrix(107,135,42,53) -> Matrix(21,2,94,9) Matrix(109,135,88,109) -> Matrix(21,2,220,21) Matrix(755,918,88,107) -> Matrix(1,0,10,1) Matrix(379,459,90,109) -> Matrix(23,2,34,3) Matrix(433,513,92,109) -> Matrix(21,2,52,5) Matrix(2159,2538,826,971) -> Matrix(109,10,534,49) Matrix(1567,1836,600,703) -> Matrix(67,6,346,31) Matrix(163,189,94,109) -> Matrix(23,2,172,15) Matrix(1,0,2,1) -> Matrix(1,0,26,1) Matrix(703,-783,290,-323) -> Matrix(25,-2,138,-11) Matrix(809,-918,334,-379) -> Matrix(1,0,-6,1) Matrix(595,-702,228,-269) -> Matrix(21,-2,116,-11) Matrix(2269,-2700,816,-971) -> Matrix(21,-2,74,-7) Matrix(973,-1161,678,-809) -> Matrix(37,-4,324,-35) Matrix(649,-783,402,-485) -> Matrix(25,-2,188,-15) Matrix(487,-594,132,-161) -> Matrix(23,-2,58,-5) Matrix(595,-729,484,-593) -> Matrix(67,-6,726,-65) Matrix(487,-621,338,-431) -> Matrix(83,-8,716,-69) Matrix(485,-621,296,-379) -> Matrix(61,-6,478,-47) Matrix(271,-351,166,-215) -> Matrix(1,0,-2,1) Matrix(865,-1134,164,-215) -> Matrix(1,0,-12,1) Matrix(757,-1026,318,-431) -> Matrix(39,-4,166,-17) Matrix(811,-1107,474,-647) -> Matrix(19,-2,124,-13) Matrix(2053,-2808,552,-755) -> Matrix(39,-4,88,-9) Matrix(433,-594,78,-107) -> Matrix(19,-2,86,-9) Matrix(215,-297,118,-163) -> Matrix(37,-4,250,-27) Matrix(487,-675,272,-377) -> Matrix(17,-2,128,-15) Matrix(4157,-5778,2526,-3511) -> Matrix(21,-2,158,-15) Matrix(271,-378,38,-53) -> Matrix(19,-2,10,-1) Matrix(269,-378,116,-163) -> Matrix(19,-2,86,-9) Matrix(325,-459,114,-161) -> Matrix(37,-4,102,-11) Matrix(1729,-2484,300,-431) -> Matrix(17,-2,60,-7) Matrix(55,-81,36,-53) -> Matrix(1,0,0,1) Matrix(3673,-5724,1524,-2375) -> Matrix(17,-2,-76,9) Matrix(1783,-2781,1038,-1619) -> Matrix(17,-2,60,-7) Matrix(431,-675,242,-379) -> Matrix(33,-4,256,-31) Matrix(325,-513,102,-161) -> Matrix(49,-6,188,-23) Matrix(649,-1026,136,-215) -> Matrix(65,-8,122,-15) Matrix(973,-1566,402,-647) -> Matrix(15,-2,98,-13) Matrix(3349,-5400,1272,-2051) -> Matrix(47,-6,196,-25) Matrix(433,-702,66,-107) -> Matrix(1,0,-6,1) Matrix(4429,-7290,918,-1511) -> Matrix(15,-2,38,-5) Matrix(163,-270,32,-53) -> Matrix(15,-2,8,-1) Matrix(433,-729,256,-431) -> Matrix(43,-6,294,-41) Matrix(919,-1566,348,-593) -> Matrix(1,0,-2,1) Matrix(377,-648,32,-55) -> Matrix(1,0,-10,1) Matrix(595,-1026,156,-269) -> Matrix(15,-2,38,-5) Matrix(2107,-3645,374,-647) -> Matrix(1,0,-4,1) Matrix(1403,-2430,250,-433) -> Matrix(15,-2,68,-9) Matrix(487,-918,200,-377) -> Matrix(13,-2,72,-11) Matrix(161,-351,50,-109) -> Matrix(1,0,-2,1) Matrix(109,-243,48,-107) -> Matrix(11,-2,50,-9) Matrix(755,-1728,142,-325) -> Matrix(1,0,-8,1) Matrix(1189,-2727,494,-1133) -> Matrix(1,0,-2,1) Matrix(1241,-2862,258,-595) -> Matrix(1,0,-4,1) Matrix(595,-1404,114,-269) -> Matrix(9,-2,-4,1) Matrix(1187,-2808,320,-757) -> Matrix(1,0,-2,1) Matrix(2915,-6912,1048,-2485) -> Matrix(17,-4,64,-15) Matrix(2755,-6561,1156,-2753) -> Matrix(25,-6,96,-23) Matrix(7561,-18225,3136,-7559) -> Matrix(1,0,20,1) Matrix(1997,-4860,422,-1027) -> Matrix(11,-2,28,-5) Matrix(487,-1188,66,-161) -> Matrix(11,-2,6,-1) Matrix(811,-2133,246,-647) -> Matrix(17,-4,64,-15) Matrix(163,-432,20,-53) -> Matrix(9,-2,-4,1) Matrix(271,-729,100,-269) -> Matrix(33,-8,128,-31) Matrix(649,-1809,174,-485) -> Matrix(7,-2,18,-5) Matrix(163,-459,38,-107) -> Matrix(7,-2,4,-1) Matrix(163,-540,16,-53) -> Matrix(7,-2,-10,3) Matrix(217,-729,64,-215) -> Matrix(13,-4,36,-11) Matrix(55,-243,12,-53) -> Matrix(1,0,2,1) Matrix(269,-1269,46,-217) -> Matrix(5,-2,8,-3) Matrix(3781,-18225,784,-3779) -> Matrix(3,-2,2,-1) Matrix(1135,-6561,196,-1133) -> Matrix(13,-6,24,-11) Matrix(109,-729,16,-107) -> Matrix(3,-2,2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 44 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 13 1 1/1 (0/1,1/13) 0 27 7/6 (2/23,1/11) 0 27 13/11 (2/21,1/10) 0 27 6/5 0/1 1 9 17/14 (1/11,1/10) 0 27 11/9 (2/23,1/11) 0 27 27/22 1/11 6 1 5/4 (1/11,1/10) 0 27 9/7 1/10 3 3 13/10 (1/10,1/9) 0 27 4/3 (0/1,1/10) 0 27 15/11 2/19 1 9 41/30 (1/10,1/9) 0 27 26/19 (3/29,2/19) 0 27 11/8 (2/19,3/28) 0 27 18/13 1/9 3 3 25/18 (1/10,1/9) 0 27 32/23 (2/19,1/9) 0 27 7/5 (2/19,1/9) 0 27 24/17 4/37 1 9 17/12 (9/82,1/9) 0 27 27/19 1/9 15 1 10/7 (1/9,6/53) 0 27 23/16 (1/9,3/26) 0 27 13/9 (7/60,2/17) 0 27 3/2 0 9 14/9 (7/60,2/17) 0 27 25/16 (5/42,3/25) 0 27 11/7 (3/25,4/33) 0 27 30/19 6/49 1 9 19/12 (11/89,1/8) 0 27 27/17 1/8 15 1 8/5 (1/8,4/31) 0 27 29/18 (1/8,1/7) 0 27 50/31 (1/8,4/31) 0 27 21/13 2/15 1 9 13/8 (1/8,1/7) 0 27 18/11 1/8 3 3 23/14 (1/8,3/23) 0 27 28/17 (3/23,2/15) 0 27 5/3 (2/15,1/7) 0 27 27/16 1/7 6 1 17/10 (1/7,1/6) 0 27 29/17 (0/1,1/6) 0 27 12/7 0/1 1 9 31/18 (1/9,1/8) 0 27 19/11 (0/1,1/8) 0 27 45/26 1/8 2 3 26/15 (3/23,2/15) 0 27 7/4 (0/1,1/7) 0 27 9/5 1/7 3 3 11/6 (2/13,1/6) 0 27 2/1 (0/1,1/6) 0 27 15/7 0/1 1 9 13/6 (1/6,1/5) 0 27 11/5 (3/17,2/11) 0 27 9/4 1/5 2 3 16/7 (0/1,1/3) 0 27 55/24 (0/1,1/4) 0 27 39/17 0/1 1 9 23/10 (1/6,1/5) 0 27 53/23 (2/11,1/5) 0 27 30/13 2/11 1 9 7/3 (0/1,1/5) 0 27 26/11 (1/5,2/9) 0 27 45/19 2/9 1 3 64/27 (2/9,3/13) 0 27 19/8 (1/5,1/4) 0 27 81/34 1/4 6 1 31/13 (1/4,2/7) 0 27 12/5 0/1 1 9 53/22 (0/1,1/2) 0 27 135/56 0/1 20 1 41/17 (0/1,1/12) 0 27 29/12 (1/7,1/6) 0 27 46/19 (1/6,2/11) 0 27 63/26 1/6 2 3 17/7 (0/1,1/5) 0 27 39/16 0 9 22/9 (2/11,1/5) 0 27 27/11 1/5 3 1 5/2 (1/5,1/4) 0 27 18/7 1/4 3 3 31/12 (1/4,1/3) 0 27 13/5 (0/1,1/6) 0 27 47/18 (4/21,1/5) 0 27 81/31 1/5 8 1 34/13 (1/5,4/19) 0 27 55/21 (1/5,2/9) 0 27 21/8 0 9 50/19 (2/9,1/4) 0 27 79/30 (5/21,1/4) 0 27 108/41 1/4 5 1 29/11 (0/1,1/4) 0 27 37/14 (1/5,1/4) 0 27 8/3 (2/9,1/4) 0 27 27/10 1/4 8 1 11/4 (1/4,2/7) 0 27 25/9 (0/1,1/4) 0 27 64/23 (2/7,1/3) 0 27 39/14 0 9 14/5 (1/4,2/7) 0 27 17/6 (5/16,1/3) 0 27 3/1 0/1 1 9 16/5 (3/11,2/7) 0 27 13/4 (1/4,1/3) 0 27 23/7 (1/4,2/7) 0 27 33/10 0 9 10/3 (2/7,1/3) 0 27 27/8 1/3 4 1 7/2 (0/1,1/3) 0 27 18/5 1/3 3 3 29/8 (1/3,3/8) 0 27 11/3 (0/1,1/3) 0 27 37/10 (1/3,3/8) 0 27 63/17 2/5 1 3 26/7 (1/3,2/5) 0 27 67/18 (3/7,1/2) 0 27 108/29 1/2 3 1 41/11 (0/1,1/2) 0 27 15/4 0 9 19/5 (2/5,1/2) 0 27 23/6 (3/7,1/2) 0 27 27/7 1/2 3 1 4/1 (0/1,1/2) 0 27 21/5 2/3 1 9 17/4 (3/4,1/1) 0 27 13/3 (0/1,1/0) 0 27 9/2 0/1 2 3 14/3 (0/1,1/2) 0 27 33/7 2/5 1 9 52/11 (0/1,1/2) 0 27 71/15 (1/3,2/5) 0 27 19/4 (3/7,1/2) 0 27 24/5 2/3 1 9 53/11 (2/3,1/1) 0 27 135/28 1/1 2 1 29/6 (1/2,1/1) 0 27 5/1 (0/1,1/1) 0 27 26/5 (-1/1,0/1) 0 27 21/4 0 9 37/7 (-1/3,0/1) 0 27 16/3 (-1/5,0/1) 0 27 27/5 0/1 11 1 11/2 (0/1,1/6) 0 27 28/5 (0/1,1/3) 0 27 45/8 1/4 2 3 17/3 (2/7,1/3) 0 27 23/4 (1/3,1/2) 0 27 81/14 1/2 6 1 29/5 (1/2,2/3) 0 27 6/1 0/1 1 9 13/2 (1/2,1/1) 0 27 27/4 1/1 2 1 7/1 (0/1,1/1) 0 27 22/3 (0/1,1/1) 0 27 15/2 0 9 8/1 (0/1,1/0) 0 27 17/2 (-1/1,1/0) 0 27 9/1 0/1 1 3 10/1 (-1/1,0/1) 0 27 11/1 (0/1,1/1) 0 27 1/0 (0/1,1/0) 0 27 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(163,-189,94,-109) (1/1,7/6) -> (26/15,7/4) Glide Reflection Matrix(595,-702,228,-269) (7/6,13/11) -> (13/5,47/18) Hyperbolic Matrix(433,-513,92,-109) (13/11,6/5) -> (14/3,33/7) Glide Reflection Matrix(379,-459,90,-109) (6/5,17/14) -> (21/5,17/4) Glide Reflection Matrix(487,-594,132,-161) (17/14,11/9) -> (11/3,37/10) Hyperbolic Matrix(485,-594,396,-485) (11/9,27/22) -> (11/9,27/22) Reflection Matrix(109,-135,88,-109) (27/22,5/4) -> (27/22,5/4) Reflection Matrix(107,-135,42,-53) (5/4,9/7) -> (5/2,18/7) Glide Reflection Matrix(271,-351,166,-215) (9/7,13/10) -> (13/8,18/11) Hyperbolic Matrix(269,-351,82,-107) (13/10,4/3) -> (13/4,23/7) Glide Reflection Matrix(377,-513,158,-215) (4/3,15/11) -> (31/13,12/5) Glide Reflection Matrix(593,-810,276,-377) (15/11,41/30) -> (15/7,13/6) Glide Reflection Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(433,-594,78,-107) (26/19,11/8) -> (11/2,28/5) Hyperbolic Matrix(215,-297,118,-163) (11/8,18/13) -> (9/5,11/6) Hyperbolic Matrix(701,-972,194,-269) (18/13,25/18) -> (18/5,29/8) Glide Reflection Matrix(757,-1053,156,-217) (25/18,32/23) -> (29/6,5/1) Glide Reflection Matrix(271,-378,38,-53) (32/23,7/5) -> (7/1,22/3) Hyperbolic Matrix(269,-378,116,-163) (7/5,24/17) -> (30/13,7/3) Hyperbolic Matrix(325,-459,114,-161) (24/17,17/12) -> (17/6,3/1) Hyperbolic Matrix(647,-918,456,-647) (17/12,27/19) -> (17/12,27/19) Reflection Matrix(379,-540,266,-379) (27/19,10/7) -> (27/19,10/7) Reflection Matrix(433,-621,76,-109) (10/7,23/16) -> (17/3,23/4) Glide Reflection Matrix(487,-702,188,-271) (23/16,13/9) -> (31/12,13/5) Glide Reflection Matrix(55,-81,36,-53) (13/9,3/2) -> (3/2,14/9) Parabolic Matrix(917,-1431,380,-593) (14/9,25/16) -> (41/17,29/12) Glide Reflection Matrix(379,-594,104,-163) (25/16,11/7) -> (29/8,11/3) Glide Reflection Matrix(325,-513,102,-161) (11/7,30/19) -> (3/1,16/5) Hyperbolic Matrix(649,-1026,136,-215) (30/19,19/12) -> (19/4,24/5) Hyperbolic Matrix(647,-1026,408,-647) (19/12,27/17) -> (19/12,27/17) Reflection Matrix(271,-432,170,-271) (27/17,8/5) -> (27/17,8/5) Reflection Matrix(973,-1566,402,-647) (8/5,29/18) -> (29/12,46/19) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(703,-1134,168,-271) (50/31,21/13) -> (4/1,21/5) Glide Reflection Matrix(217,-351,34,-55) (21/13,13/8) -> (6/1,13/2) Glide Reflection Matrix(593,-972,230,-377) (18/11,23/14) -> (18/7,31/12) Glide Reflection Matrix(1133,-1863,492,-809) (23/14,28/17) -> (23/10,53/23) Glide Reflection Matrix(163,-270,32,-53) (28/17,5/3) -> (5/1,26/5) Hyperbolic Matrix(161,-270,96,-161) (5/3,27/16) -> (5/3,27/16) Reflection Matrix(271,-459,160,-271) (27/16,17/10) -> (27/16,17/10) Reflection Matrix(919,-1566,348,-593) (17/10,29/17) -> (29/11,37/14) Hyperbolic Matrix(269,-459,126,-215) (29/17,12/7) -> (2/1,15/7) Glide Reflection Matrix(863,-1485,376,-647) (12/7,31/18) -> (39/17,23/10) Glide Reflection Matrix(595,-1026,156,-269) (31/18,19/11) -> (19/5,23/6) Hyperbolic Matrix(1889,-3267,780,-1349) (19/11,45/26) -> (46/19,63/26) Glide Reflection Matrix(1403,-2430,250,-433) (45/26,26/15) -> (28/5,45/8) Hyperbolic Matrix(107,-189,30,-53) (7/4,9/5) -> (7/2,18/5) Glide Reflection Matrix(161,-297,58,-107) (11/6,2/1) -> (11/4,25/9) Glide Reflection Matrix(161,-351,50,-109) (13/6,11/5) -> (16/5,13/4) Hyperbolic Matrix(109,-243,48,-107) (11/5,9/4) -> (9/4,16/7) Parabolic Matrix(271,-621,24,-55) (16/7,55/24) -> (11/1,1/0) Glide Reflection Matrix(1189,-2727,494,-1133) (55/24,39/17) -> (12/5,53/22) Hyperbolic Matrix(1241,-2862,258,-595) (53/23,30/13) -> (24/5,53/11) Hyperbolic Matrix(539,-1269,206,-485) (7/3,26/11) -> (34/13,55/21) Glide Reflection Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(433,-1026,46,-109) (45/19,64/27) -> (9/1,10/1) Glide Reflection Matrix(1081,-2565,228,-541) (64/27,19/8) -> (71/15,19/4) Glide Reflection Matrix(647,-1539,272,-647) (19/8,81/34) -> (19/8,81/34) Reflection Matrix(2107,-5022,884,-2107) (81/34,31/13) -> (81/34,31/13) Reflection Matrix(2969,-7155,1232,-2969) (53/22,135/56) -> (53/22,135/56) Reflection Matrix(4591,-11070,1904,-4591) (135/56,41/17) -> (135/56,41/17) Reflection Matrix(757,-1836,134,-325) (63/26,17/7) -> (45/8,17/3) Glide Reflection Matrix(1297,-3159,466,-1135) (17/7,39/16) -> (64/23,39/14) Glide Reflection Matrix(487,-1188,66,-161) (39/16,22/9) -> (22/3,15/2) Hyperbolic Matrix(485,-1188,198,-485) (22/9,27/11) -> (22/9,27/11) Reflection Matrix(109,-270,44,-109) (27/11,5/2) -> (27/11,5/2) Reflection Matrix(2915,-7614,1116,-2915) (47/18,81/31) -> (47/18,81/31) Reflection Matrix(2107,-5508,806,-2107) (81/31,34/13) -> (81/31,34/13) Reflection Matrix(649,-1701,124,-325) (55/21,21/8) -> (26/5,21/4) Glide Reflection Matrix(811,-2133,246,-647) (21/8,50/19) -> (23/7,33/10) Hyperbolic Matrix(6479,-17064,2460,-6479) (79/30,108/41) -> (79/30,108/41) Reflection Matrix(2377,-6264,902,-2377) (108/41,29/11) -> (108/41,29/11) Reflection Matrix(163,-432,20,-53) (37/14,8/3) -> (8/1,17/2) Hyperbolic Matrix(161,-432,60,-161) (8/3,27/10) -> (8/3,27/10) Reflection Matrix(109,-297,40,-109) (27/10,11/4) -> (27/10,11/4) Reflection Matrix(1835,-5103,388,-1079) (25/9,64/23) -> (52/11,71/15) Glide Reflection Matrix(649,-1809,174,-485) (39/14,14/5) -> (41/11,15/4) Hyperbolic Matrix(163,-459,38,-107) (14/5,17/6) -> (17/4,13/3) Hyperbolic Matrix(433,-1431,82,-271) (33/10,10/3) -> (21/4,37/7) Glide Reflection Matrix(161,-540,48,-161) (10/3,27/8) -> (10/3,27/8) Reflection Matrix(55,-189,16,-55) (27/8,7/2) -> (27/8,7/2) Reflection Matrix(379,-1404,44,-163) (37/10,63/17) -> (17/2,9/1) Glide Reflection Matrix(3887,-14472,1044,-3887) (67/18,108/29) -> (67/18,108/29) Reflection Matrix(2377,-8856,638,-2377) (108/29,41/11) -> (108/29,41/11) Reflection Matrix(107,-405,14,-53) (15/4,19/5) -> (15/2,8/1) Glide Reflection Matrix(323,-1242,84,-323) (23/6,27/7) -> (23/6,27/7) Reflection Matrix(55,-216,14,-55) (27/7,4/1) -> (27/7,4/1) Reflection Matrix(55,-243,12,-53) (13/3,9/2) -> (9/2,14/3) Parabolic Matrix(269,-1269,46,-217) (33/7,52/11) -> (29/5,6/1) Hyperbolic Matrix(2969,-14310,616,-2969) (53/11,135/28) -> (53/11,135/28) Reflection Matrix(811,-3915,168,-811) (135/28,29/6) -> (135/28,29/6) Reflection Matrix(107,-567,10,-53) (37/7,16/3) -> (10/1,11/1) Glide Reflection Matrix(161,-864,30,-161) (16/3,27/5) -> (16/3,27/5) Reflection Matrix(109,-594,20,-109) (27/5,11/2) -> (27/5,11/2) Reflection Matrix(323,-1863,56,-323) (23/4,81/14) -> (23/4,81/14) Reflection Matrix(811,-4698,140,-811) (81/14,29/5) -> (81/14,29/5) Reflection Matrix(53,-351,8,-53) (13/2,27/4) -> (13/2,27/4) Reflection Matrix(55,-378,8,-55) (27/4,7/1) -> (27/4,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,26,-1) (0/1,1/1) -> (0/1,1/13) Matrix(163,-189,94,-109) -> Matrix(23,-2,172,-15) Matrix(595,-702,228,-269) -> Matrix(21,-2,116,-11) Matrix(433,-513,92,-109) -> Matrix(21,-2,52,-5) Matrix(379,-459,90,-109) -> Matrix(23,-2,34,-3) Matrix(487,-594,132,-161) -> Matrix(23,-2,58,-5) Matrix(485,-594,396,-485) -> Matrix(45,-4,506,-45) (11/9,27/22) -> (2/23,1/11) Matrix(109,-135,88,-109) -> Matrix(21,-2,220,-21) (27/22,5/4) -> (1/11,1/10) Matrix(107,-135,42,-53) -> Matrix(21,-2,94,-9) Matrix(271,-351,166,-215) -> Matrix(1,0,-2,1) 0/1 Matrix(269,-351,82,-107) -> Matrix(19,-2,66,-7) Matrix(377,-513,158,-215) -> Matrix(19,-2,66,-7) Matrix(593,-810,276,-377) -> Matrix(19,-2,104,-11) Matrix(2053,-2808,552,-755) -> Matrix(39,-4,88,-9) Matrix(433,-594,78,-107) -> Matrix(19,-2,86,-9) Matrix(215,-297,118,-163) -> Matrix(37,-4,250,-27) Matrix(701,-972,194,-269) -> Matrix(17,-2,42,-5) Matrix(757,-1053,156,-217) -> Matrix(19,-2,28,-3) Matrix(271,-378,38,-53) -> Matrix(19,-2,10,-1) Matrix(269,-378,116,-163) -> Matrix(19,-2,86,-9) Matrix(325,-459,114,-161) -> Matrix(37,-4,102,-11) Matrix(647,-918,456,-647) -> Matrix(163,-18,1476,-163) (17/12,27/19) -> (9/82,1/9) Matrix(379,-540,266,-379) -> Matrix(107,-12,954,-107) (27/19,10/7) -> (1/9,6/53) Matrix(433,-621,76,-109) -> Matrix(35,-4,96,-11) Matrix(487,-702,188,-271) -> Matrix(17,-2,42,-5) Matrix(55,-81,36,-53) -> Matrix(1,0,0,1) Matrix(917,-1431,380,-593) -> Matrix(17,-2,144,-17) *** -> (1/9,1/8) Matrix(379,-594,104,-163) -> Matrix(33,-4,74,-9) Matrix(325,-513,102,-161) -> Matrix(49,-6,188,-23) Matrix(649,-1026,136,-215) -> Matrix(65,-8,122,-15) Matrix(647,-1026,408,-647) -> Matrix(177,-22,1424,-177) (19/12,27/17) -> (11/89,1/8) Matrix(271,-432,170,-271) -> Matrix(63,-8,496,-63) (27/17,8/5) -> (1/8,4/31) Matrix(973,-1566,402,-647) -> Matrix(15,-2,98,-13) 1/7 Matrix(3349,-5400,1272,-2051) -> Matrix(47,-6,196,-25) Matrix(703,-1134,168,-271) -> Matrix(31,-4,54,-7) Matrix(217,-351,34,-55) -> Matrix(15,-2,22,-3) Matrix(593,-972,230,-377) -> Matrix(31,-4,116,-15) Matrix(1133,-1863,492,-809) -> Matrix(31,-4,178,-23) Matrix(163,-270,32,-53) -> Matrix(15,-2,8,-1) Matrix(161,-270,96,-161) -> Matrix(29,-4,210,-29) (5/3,27/16) -> (2/15,1/7) Matrix(271,-459,160,-271) -> Matrix(13,-2,84,-13) (27/16,17/10) -> (1/7,1/6) Matrix(919,-1566,348,-593) -> Matrix(1,0,-2,1) 0/1 Matrix(269,-459,126,-215) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(863,-1485,376,-647) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(595,-1026,156,-269) -> Matrix(15,-2,38,-5) Matrix(1889,-3267,780,-1349) -> Matrix(15,-2,82,-11) Matrix(1403,-2430,250,-433) -> Matrix(15,-2,68,-9) Matrix(107,-189,30,-53) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(161,-297,58,-107) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(161,-351,50,-109) -> Matrix(1,0,-2,1) 0/1 Matrix(109,-243,48,-107) -> Matrix(11,-2,50,-9) 1/5 Matrix(271,-621,24,-55) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1189,-2727,494,-1133) -> Matrix(1,0,-2,1) 0/1 Matrix(1241,-2862,258,-595) -> Matrix(1,0,-4,1) 0/1 Matrix(539,-1269,206,-485) -> Matrix(19,-4,90,-19) *** -> (1/5,2/9) Matrix(1187,-2808,320,-757) -> Matrix(1,0,-2,1) 0/1 Matrix(433,-1026,46,-109) -> Matrix(9,-2,4,-1) Matrix(1081,-2565,228,-541) -> Matrix(17,-4,38,-9) Matrix(647,-1539,272,-647) -> Matrix(9,-2,40,-9) (19/8,81/34) -> (1/5,1/4) Matrix(2107,-5022,884,-2107) -> Matrix(15,-4,56,-15) (81/34,31/13) -> (1/4,2/7) Matrix(2969,-7155,1232,-2969) -> Matrix(1,0,4,-1) (53/22,135/56) -> (0/1,1/2) Matrix(4591,-11070,1904,-4591) -> Matrix(1,0,24,-1) (135/56,41/17) -> (0/1,1/12) Matrix(757,-1836,134,-325) -> Matrix(11,-2,38,-7) Matrix(1297,-3159,466,-1135) -> Matrix(11,-2,38,-7) Matrix(487,-1188,66,-161) -> Matrix(11,-2,6,-1) Matrix(485,-1188,198,-485) -> Matrix(21,-4,110,-21) (22/9,27/11) -> (2/11,1/5) Matrix(109,-270,44,-109) -> Matrix(9,-2,40,-9) (27/11,5/2) -> (1/5,1/4) Matrix(2915,-7614,1116,-2915) -> Matrix(41,-8,210,-41) (47/18,81/31) -> (4/21,1/5) Matrix(2107,-5508,806,-2107) -> Matrix(39,-8,190,-39) (81/31,34/13) -> (1/5,4/19) Matrix(649,-1701,124,-325) -> Matrix(9,-2,-14,3) Matrix(811,-2133,246,-647) -> Matrix(17,-4,64,-15) 1/4 Matrix(6479,-17064,2460,-6479) -> Matrix(41,-10,168,-41) (79/30,108/41) -> (5/21,1/4) Matrix(2377,-6264,902,-2377) -> Matrix(1,0,8,-1) (108/41,29/11) -> (0/1,1/4) Matrix(163,-432,20,-53) -> Matrix(9,-2,-4,1) Matrix(161,-432,60,-161) -> Matrix(17,-4,72,-17) (8/3,27/10) -> (2/9,1/4) Matrix(109,-297,40,-109) -> Matrix(15,-4,56,-15) (27/10,11/4) -> (1/4,2/7) Matrix(1835,-5103,388,-1079) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(649,-1809,174,-485) -> Matrix(7,-2,18,-5) 1/3 Matrix(163,-459,38,-107) -> Matrix(7,-2,4,-1) Matrix(433,-1431,82,-271) -> Matrix(7,-2,-18,5) Matrix(161,-540,48,-161) -> Matrix(13,-4,42,-13) (10/3,27/8) -> (2/7,1/3) Matrix(55,-189,16,-55) -> Matrix(1,0,6,-1) (27/8,7/2) -> (0/1,1/3) Matrix(379,-1404,44,-163) -> Matrix(5,-2,-8,3) Matrix(3887,-14472,1044,-3887) -> Matrix(13,-6,28,-13) (67/18,108/29) -> (3/7,1/2) Matrix(2377,-8856,638,-2377) -> Matrix(1,0,4,-1) (108/29,41/11) -> (0/1,1/2) Matrix(107,-405,14,-53) -> Matrix(5,-2,2,-1) Matrix(323,-1242,84,-323) -> Matrix(13,-6,28,-13) (23/6,27/7) -> (3/7,1/2) Matrix(55,-216,14,-55) -> Matrix(1,0,4,-1) (27/7,4/1) -> (0/1,1/2) Matrix(55,-243,12,-53) -> Matrix(1,0,2,1) 0/1 Matrix(269,-1269,46,-217) -> Matrix(5,-2,8,-3) 1/2 Matrix(2969,-14310,616,-2969) -> Matrix(5,-4,6,-5) (53/11,135/28) -> (2/3,1/1) Matrix(811,-3915,168,-811) -> Matrix(3,-2,4,-3) (135/28,29/6) -> (1/2,1/1) Matrix(107,-567,10,-53) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(161,-864,30,-161) -> Matrix(-1,0,10,1) (16/3,27/5) -> (-1/5,0/1) Matrix(109,-594,20,-109) -> Matrix(1,0,12,-1) (27/5,11/2) -> (0/1,1/6) Matrix(323,-1863,56,-323) -> Matrix(5,-2,12,-5) (23/4,81/14) -> (1/3,1/2) Matrix(811,-4698,140,-811) -> Matrix(7,-4,12,-7) (81/14,29/5) -> (1/2,2/3) Matrix(53,-351,8,-53) -> Matrix(3,-2,4,-3) (13/2,27/4) -> (1/2,1/1) Matrix(55,-378,8,-55) -> Matrix(1,0,2,-1) (27/4,7/1) -> (0/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.