INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -8/1 -7/1 -19/3 -6/1 -17/3 -16/3 -5/1 -19/4 -13/3 -4/1 -11/3 -7/2 -17/5 -3/1 -14/5 -19/7 -8/3 -23/9 -17/7 -43/18 -7/3 -9/4 -11/5 -2/1 -1/1 -9/14 -8/13 -3/5 -6/11 -1/2 -4/9 -7/17 -3/8 -1/3 -2/7 -11/41 -1/4 -3/13 -4/19 -1/6 0/1 1/9 3/17 1/5 1/4 1/3 3/7 1/2 7/13 11/19 19/31 2/3 5/7 3/4 13/17 11/14 9/11 7/8 1/1 8/7 11/9 5/4 14/11 9/7 17/13 23/17 7/5 3/2 61/39 11/7 31/19 5/3 19/11 7/4 16/9 77/43 13/7 2/1 17/8 15/7 41/19 9/4 7/3 46/19 17/7 5/2 18/7 13/5 29/11 8/3 19/7 11/4 147/53 14/5 48/17 3/1 19/6 61/19 13/4 10/3 27/8 17/5 31/9 7/2 39/11 11/3 15/4 4/1 13/3 9/2 14/3 33/7 5/1 16/3 11/2 17/3 6/1 13/2 20/3 7/1 22/3 15/2 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -3/1 -8/1 -3/1 -1/1 -15/2 -2/1 -7/1 -2/1 -1/1 1/0 -20/3 -1/1 -1/3 -13/2 0/1 -19/3 -1/1 1/1 -6/1 1/0 -17/3 -4/1 -3/1 1/0 -28/5 -5/1 -3/1 -39/7 -3/1 -11/2 -4/1 -16/3 -3/1 -7/3 -5/1 -3/1 -1/1 -24/5 -3/1 -1/1 -19/4 -2/1 -14/3 -5/3 -1/1 -23/5 -1/1 0/1 1/0 -55/12 1/0 -32/7 1/0 -9/2 0/1 -22/5 1/1 3/1 -13/3 1/0 -30/7 -7/1 -5/1 -17/4 1/0 -21/5 -5/1 -3/1 -25/6 -10/3 -4/1 -3/1 -1/1 -19/5 -3/1 -2/1 1/0 -15/4 1/0 -41/11 1/0 -26/7 -3/1 -1/1 -11/3 -3/1 -1/1 -18/5 -1/1 1/1 -25/7 -1/1 0/1 1/0 -7/2 1/0 -31/9 -3/1 -2/1 1/0 -24/7 -5/1 -3/1 -41/12 1/0 -17/5 -3/1 -61/18 -2/1 -44/13 -3/1 -7/3 -27/8 -3/2 -10/3 -3/1 -1/1 -23/7 -3/1 -36/11 -2/1 -13/4 1/0 -16/5 -3/1 -1/1 -19/6 -2/1 -22/7 1/0 -3/1 -2/1 -1/1 1/0 -23/8 -2/1 -20/7 -3/1 -1/1 -17/6 -2/1 -14/5 -3/1 -1/1 -39/14 1/0 -25/9 -3/1 -11/4 1/0 -41/15 -2/1 -1/1 1/0 -30/11 -3/1 -1/1 -79/29 1/0 -49/18 -2/1 -68/25 -3/1 -1/1 -19/7 -3/1 -1/1 -27/10 -2/1 -8/3 -2/1 -37/14 -2/1 -29/11 -2/1 -1/1 1/0 -21/8 1/0 -55/21 -2/1 -1/1 1/0 -34/13 -3/1 -1/1 -13/5 -3/1 -1/1 -18/7 -5/3 -1/1 -41/16 -2/1 -64/25 -1/1 1/1 -23/9 -2/1 -1/1 1/0 -28/11 -3/1 -1/1 -5/2 -2/1 -27/11 -3/1 -1/1 -22/9 -3/1 -1/1 -17/7 -2/1 -29/12 -7/4 -12/5 -5/3 -1/1 -55/23 -1/1 -43/18 -3/2 -74/31 -7/5 -1/1 -31/13 -2/1 -3/2 -1/1 -50/21 -9/7 -1/1 -19/8 1/0 -45/19 -3/1 -2/1 1/0 -26/11 -2/1 -33/14 -2/1 -7/3 -1/1 -30/13 -3/1 -1/1 -23/10 -2/1 -16/7 -1/1 1/1 -25/11 -2/1 -1/1 1/0 -34/15 -3/1 -1/1 -9/4 -2/1 -29/13 -5/3 -1/1 -20/9 -5/3 -1/1 -11/5 -2/1 -3/2 -1/1 -13/6 0/1 -28/13 1/0 -15/7 -1/1 -17/8 1/0 -2/1 -3/1 -1/1 -1/1 -1/1 -2/3 -1/1 -1/3 -15/23 -1/1 -13/20 1/0 -11/17 -1/1 -2/3 -1/2 -20/31 -1/1 -3/5 -9/14 -1/2 -34/53 -1/1 -1/3 -25/39 -1/1 -1/2 0/1 -16/25 -1/1 1/1 -7/11 -1/1 -26/41 -1/2 -19/30 0/1 -31/49 -1/1 -2/3 -1/2 -43/68 -2/3 -12/19 -1/1 -3/5 -17/27 -1/2 -22/35 -1/1 -1/3 -5/8 -1/2 -28/45 -1/1 -1/3 -23/37 -1/1 -1/2 0/1 -18/29 -1/1 -3/5 -13/21 -1/1 -1/3 -34/55 -1/1 -1/3 -21/34 0/1 -8/13 -1/2 -27/44 -1/2 -19/31 -1/1 -1/3 -49/80 -1/2 -30/49 -1/1 -1/3 -11/18 0/1 -14/23 -1/1 -1/3 -17/28 -1/2 -3/5 -1/1 -1/2 0/1 -16/27 -1/1 -1/3 -13/22 0/1 -10/17 -1/1 -1/3 -27/46 -2/3 -44/75 -3/7 -1/3 -17/29 -1/3 -41/70 0/1 -24/41 -1/3 -1/5 -7/12 0/1 -18/31 -1/1 1/1 -11/19 -1/1 -1/3 -26/45 -1/1 -1/3 -41/71 0/1 -15/26 0/1 -34/59 -1/2 -19/33 -1/2 -1/3 0/1 -4/7 -1/1 -1/3 -17/30 0/1 -13/23 0/1 -9/16 1/0 -32/57 0/1 -23/41 -1/1 0/1 1/0 -37/66 -2/1 -14/25 -1/1 -3/5 -33/59 -1/1 -1/2 0/1 -19/34 -1/2 -5/9 -1/1 -1/3 -11/20 -1/4 -28/51 -1/3 -1/5 -17/31 -1/3 -1/4 0/1 -6/11 0/1 -13/24 1/0 -7/13 -1/1 -1/2 0/1 -15/28 -1/2 -8/15 -1/1 -1/3 -9/17 -1/3 -1/2 0/1 -8/17 1/5 1/3 -7/15 1/1 -6/13 -1/1 1/1 -5/11 -1/1 0/1 1/0 -9/20 -1/2 -13/29 -1/1 -1/3 -4/9 0/1 -15/34 2/5 -11/25 0/1 1/2 1/1 -7/16 1/2 -17/39 1/1 2/1 1/0 -10/23 1/1 3/1 -13/30 0/1 -29/67 0/1 1/1 1/0 -16/37 -1/1 1/1 -3/7 -1/1 1/1 -14/33 -1/1 1/1 -11/26 1/0 -8/19 -3/1 -1/1 -13/31 -1/1 -1/2 0/1 -31/74 0/1 -49/117 -1/1 -18/43 0/1 -5/12 -1/2 -17/41 -1/3 -12/29 -1/3 -1/5 -7/17 0/1 -9/22 0/1 -20/49 1/3 1/1 -11/27 1/3 1/1 -2/5 -1/1 1/1 -11/28 1/0 -20/51 1/3 1/1 -9/23 0/1 1/1 1/0 -7/18 0/1 -5/13 -1/1 1/1 -18/47 1/1 3/1 -31/81 1/0 -13/34 -2/1 -21/55 -2/1 -3/2 -1/1 -29/76 -5/4 -8/21 -1/1 -1/3 -19/50 -2/1 -11/29 -1/1 -1/2 0/1 -3/8 0/1 -13/35 0/1 1/1 1/0 -10/27 1/3 1/1 -7/19 1/1 -25/68 1/0 -18/49 1/1 3/1 -11/30 -2/1 -26/71 0/1 -15/41 0/1 1/1 1/0 -19/52 1/0 -4/11 -1/1 1/1 -13/36 1/2 -9/25 1/1 -14/39 1/0 -5/14 0/1 -6/17 -1/1 1/1 -7/20 1/0 -8/23 0/1 -1/3 -1/1 0/1 1/0 -7/22 1/0 -6/19 -1/1 1/1 -11/35 -1/1 1/1 -5/16 1/0 -4/13 -1/1 1/1 -11/36 0/1 -7/23 1/1 -10/33 1/1 3/1 -3/10 0/1 -8/27 -1/1 1/1 -13/44 1/0 -18/61 -1/1 1/1 -23/78 1/0 -5/17 -1/1 1/1 -12/41 1/3 1/1 -7/24 1/0 -2/7 1/0 -9/32 1/0 -7/25 -1/1 0/1 1/0 -19/68 -3/2 -12/43 -1/1 -3/5 -5/18 0/1 -3/11 -1/1 1/1 -10/37 1/3 1/1 -7/26 2/1 -18/67 5/1 7/1 -11/41 1/0 -4/15 -3/1 -1/1 -9/34 1/0 -5/19 -1/1 0/1 1/0 -1/4 1/0 -7/29 -1/1 0/1 1/0 -6/25 -1/1 1/1 -5/21 -1/1 1/1 -9/38 0/1 -4/17 -1/1 1/1 -3/13 1/0 -8/35 -7/1 -5/1 -5/22 -4/1 -7/31 -3/1 -2/9 -3/1 -1/1 -9/41 -1/1 -7/32 -2/1 -12/55 -5/3 -1/1 -17/78 -6/5 -5/23 -2/1 -1/1 1/0 -8/37 -7/5 -1/1 -3/14 0/1 -7/33 0/1 1/1 1/0 -11/52 1/0 -4/19 1/0 -5/24 1/0 -16/77 -3/1 -1/1 -11/53 -2/1 -1/1 1/0 -6/29 -3/1 -1/1 -1/5 -1/1 -3/16 1/0 -5/27 -2/1 -1/1 1/0 -7/38 -4/3 -2/11 -1/1 -1/3 -7/39 1/1 -5/28 1/0 -8/45 -1/1 1/1 -3/17 -1/1 0/1 1/0 -1/6 1/0 -3/19 -3/1 -1/1 -5/32 1/0 -2/13 -3/1 -1/1 -5/33 -5/3 -1/1 -3/20 -3/2 -4/27 -1/1 -1/3 -1/7 -2/1 -1/1 1/0 -2/15 -9/7 -1/1 -1/8 -1/2 -2/17 0/1 -1/9 -1/1 0/1 -1/1 1/1 1/9 0/1 2/17 -1/1 1/1 1/8 1/0 1/7 -1/1 1/6 -2/1 3/17 -1/1 5/28 -9/10 2/11 -1/1 -7/9 1/5 -1/1 -1/2 0/1 5/24 1/0 4/19 -3/1 -1/1 7/33 -1/1 3/14 -2/3 5/23 -1/1 -3/5 12/55 -1/1 -3/5 7/32 -1/2 2/9 -1/1 -1/3 3/13 -1/1 -1/3 1/4 0/1 5/19 -1/1 1/1 9/34 0/1 4/15 -1/1 1/1 7/26 0/1 3/11 -1/1 0/1 1/0 8/29 -1/1 1/1 5/18 0/1 12/43 0/1 19/68 1/2 7/25 1/1 9/32 1/0 2/7 -3/1 -1/1 5/17 -1/1 -1/2 0/1 13/44 -1/2 8/27 -1/2 3/10 0/1 7/23 0/1 4/13 -1/1 1/1 9/29 -1/1 0/1 1/0 5/16 1/0 1/3 -1/1 6/17 -1/1 -1/3 11/31 -1/1 -1/2 0/1 5/14 0/1 14/39 -5/13 -1/3 9/25 -1/3 -1/4 0/1 22/61 -1/3 -1/5 13/36 -1/4 4/11 0/1 3/8 1/0 5/13 -1/1 -1/2 0/1 17/44 -5/6 12/31 -1/1 -3/5 19/49 -1/1 -3/5 7/18 -1/2 2/5 -1/1 -1/3 9/22 0/1 16/39 -1/2 7/17 -1/3 19/46 -1/2 31/75 -1/2 -2/5 -1/3 12/29 -5/13 -1/3 17/41 -1/3 -2/7 -1/4 5/12 -1/4 3/7 0/1 7/16 1/2 18/41 1/3 1/1 11/25 1/3 1/1 4/9 -1/1 1/1 21/47 -1/1 1/1 17/38 1/0 13/29 0/1 1/1 1/0 9/20 1/0 14/31 0/1 19/42 2/3 5/11 -1/1 1/1 11/24 0/1 6/13 -1/1 1/1 7/15 -1/1 0/1 1/0 1/2 0/1 8/15 -1/1 1/1 7/13 -1/1 1/1 6/11 -1/1 1/1 29/53 0/1 1/1 1/0 23/42 1/0 17/31 -1/1 11/20 1/0 5/9 -1/1 0/1 1/0 4/7 -1/1 -1/3 19/33 -1/3 -1/5 15/26 0/1 11/19 0/1 7/12 1/2 24/41 1/2 17/29 1/2 2/3 1/1 10/17 1/1 3/1 3/5 -1/1 1/1 11/18 0/1 41/67 -1/1 30/49 -1/1 -1/3 19/31 0/1 46/75 -1/1 1/1 27/44 1/0 8/13 -1/1 1/1 21/34 1/0 34/55 -1/1 1/1 47/76 1/0 13/21 -1/1 0/1 1/0 18/29 -1/1 1/1 5/8 1/0 22/35 -3/1 -1/1 17/27 -1/1 12/19 -5/3 -1/1 7/11 -1/1 0/1 1/0 2/3 0/1 9/13 0/1 1/2 1/1 25/36 5/6 41/59 1/1 16/23 1/1 7/5 23/33 1/1 7/10 0/1 19/27 1/1 2/1 1/0 12/17 1/1 3/1 29/41 1/0 46/65 -7/1 -5/1 17/24 1/0 39/55 -2/1 -1/1 1/0 22/31 -1/1 1/1 27/38 1/0 5/7 -1/1 1/1 28/39 -1/1 1/1 23/32 0/1 18/25 -1/1 1/1 31/43 0/1 1/1 1/0 44/61 1/0 13/18 0/1 8/11 -1/1 1/1 27/37 -1/1 1/1 19/26 1/0 11/15 -1/1 0/1 1/0 25/34 2/1 14/19 -1/1 1/1 17/23 -1/1 1/1 3/4 1/0 13/17 0/1 23/30 0/1 10/13 1/3 1/1 27/35 0/1 1/1 1/0 17/22 0/1 7/9 1/1 25/32 1/2 43/55 1/2 2/3 1/1 61/78 6/7 18/23 1/1 5/3 47/60 1/0 29/37 1/1 2/1 1/0 11/14 1/0 26/33 -1/1 1/1 15/19 0/1 1/1 1/0 34/43 -1/1 1/1 53/67 1/1 19/24 1/0 4/5 -1/1 1/1 13/16 1/0 9/11 -1/1 1/1 23/28 1/0 14/17 -1/1 1/1 5/6 0/1 6/7 -1/1 1/1 13/15 -1/1 1/1 20/23 -1/1 1/1 7/8 0/1 15/17 1/1 8/9 -1/1 1/1 1/1 -1/1 0/1 1/0 10/9 -1/1 1/1 9/8 1/0 17/15 1/1 8/7 1/0 23/20 1/0 15/13 -1/1 7/6 0/1 20/17 1/3 1/1 13/11 -1/1 1/1 6/5 -1/1 1/1 17/14 0/1 11/9 -1/1 1/1 27/22 0/1 16/13 -1/1 1/1 5/4 1/0 29/23 -1/1 1/1 24/19 -1/1 1/1 19/15 -1/1 0/1 1/0 33/26 0/1 14/11 0/1 37/29 0/1 1/2 1/1 97/76 1/2 60/47 -1/1 1/1 23/18 0/1 32/25 -1/1 1/1 9/7 1/1 22/17 3/5 1/1 79/61 1/1 57/44 7/6 35/27 1/1 3/2 2/1 13/10 2/1 30/23 3/1 5/1 17/13 1/0 4/3 -1/1 1/1 27/20 1/0 23/17 -1/1 1/1 19/14 0/1 34/25 -1/1 1/1 15/11 0/1 1/1 1/0 26/19 1/0 37/27 -3/1 -1/1 48/35 -5/3 -1/1 11/8 -1/2 29/21 0/1 47/34 0/1 65/47 1/5 18/13 1/3 1/1 43/31 0/1 1/2 1/1 68/49 1/3 1/1 93/67 1/1 25/18 0/1 57/41 0/1 1/2 1/1 32/23 0/1 39/28 1/2 46/33 -1/1 1/1 7/5 1/1 31/22 0/1 86/61 1/1 3/1 55/39 0/1 1/1 1/0 24/17 1/1 3/1 41/29 1/0 17/12 1/0 27/19 0/1 1/2 1/1 37/26 2/3 10/7 1/1 3/1 3/2 1/0 14/9 -1/1 1/1 39/25 -1/1 64/41 1/0 25/16 1/0 61/39 -3/1 -1/1 36/23 -3/1 -1/1 47/30 -2/1 11/7 -2/1 -1/1 1/0 30/19 -7/5 -1/1 49/31 -1/1 19/12 -1/2 27/17 -1/1 1/1 8/5 -3/1 -1/1 45/28 -7/6 37/23 -1/1 29/18 -4/5 21/13 -1/1 -2/3 -1/2 97/60 -1/2 173/107 -1/1 76/47 -1/1 -3/5 55/34 -2/3 34/21 -1/2 47/29 -1/3 13/8 -1/2 44/27 -1/5 -1/7 31/19 0/1 80/49 1/11 1/9 49/30 0/1 116/71 1/5 1/3 67/41 1/5 1/3 18/11 1/3 1/1 5/3 -1/1 1/1 17/10 0/1 12/7 -1/1 1/1 31/18 0/1 19/11 1/0 45/26 -2/1 71/41 -1/1 26/15 -3/1 -1/1 33/19 -1/1 7/4 1/0 16/9 0/1 41/23 1/1 25/14 0/1 59/33 1/3 1/1 34/19 1/3 1/1 77/43 1/1 43/24 1/0 9/5 0/1 1/1 1/0 20/11 1/1 3/1 11/6 0/1 24/13 -1/1 1/1 13/7 -1/1 1/1 28/15 -1/1 1/1 15/8 1/0 2/1 -1/1 1/1 17/8 0/1 15/7 0/1 1/2 1/1 28/13 9/11 1/1 41/19 1/1 54/25 1/1 25/23 13/6 4/3 24/11 2/1 11/5 1/1 3/1 42/19 1/1 3/1 31/14 1/0 20/9 1/1 3/1 29/13 2/1 3/1 1/0 38/17 2/1 9/4 1/0 7/3 1/0 19/8 1/0 31/13 -5/1 43/18 -4/1 98/41 -5/1 -3/1 55/23 -5/1 -4/1 1/0 12/5 -5/1 -3/1 41/17 -3/1 -2/1 1/0 70/29 -3/1 -1/1 99/41 -3/1 -1/1 29/12 1/0 75/31 -3/1 -2/1 1/0 46/19 1/0 17/7 -3/1 56/23 -3/1 -13/5 39/16 -2/1 22/9 -3/1 -1/1 5/2 -2/1 23/9 -1/1 64/25 1/3 1/1 41/16 1/0 18/7 1/0 67/26 -2/1 49/19 -1/1 80/31 -3/1 -1/1 31/12 1/0 44/17 -3/1 -1/1 101/39 -3/1 -1/1 57/22 -2/1 13/5 -2/1 -1/1 1/0 21/8 -3/2 50/19 -13/11 -1/1 29/11 -1/1 66/25 -1/1 -15/17 37/14 -4/5 8/3 -1/1 -1/3 19/7 -1/1 0/1 1/0 87/32 1/0 68/25 -3/1 -1/1 185/68 -3/2 117/43 -1/1 166/61 -1/1 -3/5 49/18 0/1 79/29 -1/1 30/11 -3/1 -1/1 41/15 -1/1 11/4 0/1 36/13 -1/1 1/1 61/22 0/1 147/53 1/1 86/31 -1/1 1/1 25/9 0/1 1/1 1/0 39/14 0/1 14/5 -1/1 1/1 59/21 -1/1 1/1 45/16 1/0 31/11 -1/1 0/1 1/0 48/17 0/1 17/6 0/1 20/7 -3/1 -1/1 3/1 -1/1 1/1 19/6 1/0 16/5 -1/1 1/1 77/24 1/0 61/19 -1/1 1/1 106/33 -1/1 1/1 45/14 0/1 29/9 0/1 1/1 1/0 42/13 1/0 13/4 1/0 23/7 0/1 10/3 1/3 1/1 27/8 0/1 44/13 -1/1 1/1 61/18 0/1 139/41 1/3 1/1 78/23 1/3 1/1 17/5 0/1 1/2 1/1 24/7 5/7 1/1 55/16 7/8 31/9 1/1 38/11 1/1 13/11 7/2 2/1 39/11 1/0 32/9 1/1 3/1 25/7 1/1 68/19 1/1 3/1 43/12 2/1 61/17 2/1 3/1 1/0 18/5 1/1 3/1 47/13 1/1 3/1 76/21 1/1 3/1 29/8 1/0 11/3 1/1 2/1 1/0 37/10 2/1 63/17 1/1 3/1 26/7 1/1 3/1 15/4 5/2 4/1 1/0 17/4 -7/2 47/11 -3/1 -8/3 -5/2 30/7 -3/1 -7/3 13/3 -3/1 -1/1 48/11 -3/1 -1/1 35/8 1/0 22/5 -3/1 -1/1 9/2 -2/1 41/9 -2/1 32/7 -5/3 -1/1 87/19 -2/1 -1/1 1/0 55/12 1/0 78/17 -2/1 23/5 -1/1 14/3 -5/3 -1/1 47/10 -6/5 33/7 -1/1 52/11 -1/1 -9/11 19/4 -1/2 24/5 -1/1 1/1 5/1 -1/1 0/1 1/0 26/5 -1/1 1/1 21/4 0/1 16/3 -1/1 1/1 11/2 0/1 28/5 -1/1 1/1 17/3 -1/1 1/1 40/7 -1/1 1/1 23/4 1/0 6/1 -1/1 1/1 13/2 1/0 33/5 -1/1 0/1 1/0 20/3 -1/1 1/1 27/4 1/0 7/1 1/1 22/3 2/1 37/5 2/1 3/1 1/0 15/2 2/1 8/1 3/1 5/1 17/2 8/1 9/1 1/0 10/1 -5/1 -3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(9,88,32,313) (-9/1,1/0) -> (7/25,9/32) Hyperbolic Matrix(67,548,-28,-229) (-9/1,-8/1) -> (-12/5,-55/23) Hyperbolic Matrix(67,508,12,91) (-8/1,-15/2) -> (11/2,28/5) Hyperbolic Matrix(89,648,32,233) (-15/2,-7/1) -> (25/9,39/14) Hyperbolic Matrix(7,48,-48,-329) (-7/1,-20/3) -> (-4/27,-1/7) Hyperbolic Matrix(171,1132,-292,-1933) (-20/3,-13/2) -> (-41/70,-24/41) Hyperbolic Matrix(37,236,-156,-995) (-13/2,-19/3) -> (-5/21,-9/38) Hyperbolic Matrix(115,716,84,523) (-19/3,-6/1) -> (26/19,37/27) Hyperbolic Matrix(93,532,68,389) (-6/1,-17/3) -> (15/11,26/19) Hyperbolic Matrix(199,1120,-320,-1801) (-17/3,-28/5) -> (-28/45,-23/37) Hyperbolic Matrix(131,732,148,827) (-28/5,-39/7) -> (15/17,8/9) Hyperbolic Matrix(457,2536,264,1465) (-39/7,-11/2) -> (45/26,71/41) Hyperbolic Matrix(73,392,-192,-1031) (-11/2,-16/3) -> (-8/21,-19/50) Hyperbolic Matrix(37,196,84,445) (-16/3,-5/1) -> (11/25,4/9) Hyperbolic Matrix(31,152,-72,-353) (-5/1,-24/5) -> (-16/37,-3/7) Hyperbolic Matrix(169,808,32,153) (-24/5,-19/4) -> (21/4,16/3) Hyperbolic Matrix(195,916,-76,-357) (-19/4,-14/3) -> (-18/7,-41/16) Hyperbolic Matrix(343,1584,-144,-665) (-14/3,-23/5) -> (-31/13,-50/21) Hyperbolic Matrix(89,408,-368,-1687) (-23/5,-55/12) -> (-1/4,-7/29) Hyperbolic Matrix(257,1176,224,1025) (-55/12,-32/7) -> (8/7,23/20) Hyperbolic Matrix(147,668,-68,-309) (-32/7,-9/2) -> (-13/6,-28/13) Hyperbolic Matrix(35,156,-116,-517) (-9/2,-22/5) -> (-10/33,-3/10) Hyperbolic Matrix(155,676,-36,-157) (-22/5,-13/3) -> (-13/3,-30/7) Parabolic Matrix(123,524,196,835) (-30/7,-17/4) -> (5/8,22/35) Hyperbolic Matrix(37,156,-236,-995) (-17/4,-21/5) -> (-3/19,-5/32) Hyperbolic Matrix(125,524,276,1157) (-21/5,-25/6) -> (19/42,5/11) Hyperbolic Matrix(89,368,-408,-1687) (-25/6,-4/1) -> (-12/55,-17/78) Hyperbolic Matrix(43,164,156,595) (-4/1,-19/5) -> (3/11,8/29) Hyperbolic Matrix(275,1036,-116,-437) (-19/5,-15/4) -> (-19/8,-45/19) Hyperbolic Matrix(351,1312,248,927) (-15/4,-41/11) -> (41/29,17/12) Hyperbolic Matrix(883,3284,-324,-1205) (-41/11,-26/7) -> (-30/11,-79/29) Hyperbolic Matrix(193,712,-312,-1151) (-26/7,-11/3) -> (-13/21,-34/55) Hyperbolic Matrix(45,164,76,277) (-11/3,-18/5) -> (10/17,3/5) Hyperbolic Matrix(155,556,-356,-1277) (-18/5,-25/7) -> (-17/39,-10/23) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(395,1356,164,563) (-31/9,-24/7) -> (12/5,41/17) Hyperbolic Matrix(83,284,396,1355) (-24/7,-41/12) -> (5/24,4/19) Hyperbolic Matrix(431,1472,248,847) (-41/12,-17/5) -> (33/19,7/4) Hyperbolic Matrix(1037,3516,-2476,-8395) (-17/5,-61/18) -> (-31/74,-49/117) Hyperbolic Matrix(1441,4880,520,1761) (-61/18,-44/13) -> (36/13,61/22) Hyperbolic Matrix(521,1760,320,1081) (-44/13,-27/8) -> (13/8,44/27) Hyperbolic Matrix(253,852,68,229) (-27/8,-10/3) -> (26/7,15/4) Hyperbolic Matrix(35,116,-156,-517) (-10/3,-23/7) -> (-7/31,-2/9) Hyperbolic Matrix(563,1844,316,1035) (-23/7,-36/11) -> (16/9,41/23) Hyperbolic Matrix(159,520,440,1439) (-36/11,-13/4) -> (13/36,4/11) Hyperbolic Matrix(89,288,72,233) (-13/4,-16/5) -> (16/13,5/4) Hyperbolic Matrix(165,524,-404,-1283) (-16/5,-19/6) -> (-9/22,-20/49) Hyperbolic Matrix(577,1816,224,705) (-19/6,-22/7) -> (18/7,67/26) Hyperbolic Matrix(245,764,76,237) (-22/7,-3/1) -> (29/9,42/13) Hyperbolic Matrix(531,1532,148,427) (-3/1,-23/8) -> (43/12,61/17) Hyperbolic Matrix(385,1104,536,1537) (-23/8,-20/7) -> (28/39,23/32) Hyperbolic Matrix(87,248,-368,-1049) (-20/7,-17/6) -> (-9/38,-4/17) Hyperbolic Matrix(109,308,132,373) (-17/6,-14/5) -> (14/17,5/6) Hyperbolic Matrix(581,1620,940,2621) (-14/5,-39/14) -> (21/34,34/55) Hyperbolic Matrix(269,748,652,1813) (-39/14,-25/9) -> (7/17,19/46) Hyperbolic Matrix(113,312,-272,-751) (-25/9,-11/4) -> (-5/12,-17/41) Hyperbolic Matrix(345,944,-944,-2583) (-11/4,-41/15) -> (-15/41,-19/52) Hyperbolic Matrix(785,2144,-1224,-3343) (-41/15,-30/11) -> (-34/53,-25/39) Hyperbolic Matrix(905,2464,256,697) (-79/29,-49/18) -> (7/2,39/11) Hyperbolic Matrix(2743,7464,1696,4615) (-49/18,-68/25) -> (76/47,55/34) Hyperbolic Matrix(465,1264,536,1457) (-68/25,-19/7) -> (13/15,20/23) Hyperbolic Matrix(71,192,328,887) (-19/7,-27/10) -> (3/14,5/23) Hyperbolic Matrix(191,512,-72,-193) (-27/10,-8/3) -> (-8/3,-37/14) Parabolic Matrix(633,1672,488,1289) (-37/14,-29/11) -> (35/27,13/10) Hyperbolic Matrix(73,192,-392,-1031) (-29/11,-21/8) -> (-3/16,-5/27) Hyperbolic Matrix(371,972,-692,-1813) (-21/8,-55/21) -> (-7/13,-15/28) Hyperbolic Matrix(741,1940,940,2461) (-55/21,-34/13) -> (26/33,15/19) Hyperbolic Matrix(273,712,-472,-1231) (-34/13,-13/5) -> (-11/19,-26/45) Hyperbolic Matrix(125,324,76,197) (-13/5,-18/7) -> (18/11,5/3) Hyperbolic Matrix(1871,4792,768,1967) (-41/16,-64/25) -> (56/23,39/16) Hyperbolic Matrix(1591,4072,1128,2887) (-64/25,-23/9) -> (55/39,24/17) Hyperbolic Matrix(439,1120,-800,-2041) (-23/9,-28/11) -> (-28/51,-17/31) Hyperbolic Matrix(27,68,52,131) (-28/11,-5/2) -> (1/2,8/15) Hyperbolic Matrix(109,268,412,1013) (-5/2,-27/11) -> (5/19,9/34) Hyperbolic Matrix(165,404,-524,-1283) (-27/11,-22/9) -> (-6/19,-11/35) Hyperbolic Matrix(277,676,84,205) (-22/9,-17/7) -> (23/7,10/3) Hyperbolic Matrix(367,888,112,271) (-17/7,-29/12) -> (13/4,23/7) Hyperbolic Matrix(113,272,-312,-751) (-29/12,-12/5) -> (-4/11,-13/36) Hyperbolic Matrix(835,1996,1524,3643) (-55/23,-43/18) -> (23/42,17/31) Hyperbolic Matrix(1037,2476,-3516,-8395) (-43/18,-74/31) -> (-18/61,-23/78) Hyperbolic Matrix(1847,4408,432,1031) (-74/31,-31/13) -> (47/11,30/7) Hyperbolic Matrix(841,2000,320,761) (-50/21,-19/8) -> (21/8,50/19) Hyperbolic Matrix(673,1592,528,1249) (-45/19,-26/11) -> (14/11,37/29) Hyperbolic Matrix(559,1320,440,1039) (-26/11,-33/14) -> (33/26,14/11) Hyperbolic Matrix(563,1324,236,555) (-33/14,-7/3) -> (31/13,43/18) Hyperbolic Matrix(31,72,-152,-353) (-7/3,-30/13) -> (-6/29,-1/5) Hyperbolic Matrix(399,920,520,1199) (-30/13,-23/10) -> (23/30,10/13) Hyperbolic Matrix(155,356,-556,-1277) (-23/10,-16/7) -> (-12/43,-5/18) Hyperbolic Matrix(283,644,156,355) (-16/7,-25/11) -> (9/5,20/11) Hyperbolic Matrix(599,1360,440,999) (-25/11,-34/15) -> (34/25,15/11) Hyperbolic Matrix(189,428,412,933) (-34/15,-9/4) -> (11/24,6/13) Hyperbolic Matrix(163,364,356,795) (-9/4,-29/13) -> (5/11,11/24) Hyperbolic Matrix(359,800,-880,-1961) (-29/13,-20/9) -> (-20/49,-11/27) Hyperbolic Matrix(231,512,328,727) (-20/9,-11/5) -> (19/27,12/17) Hyperbolic Matrix(271,592,168,367) (-11/5,-13/6) -> (29/18,21/13) Hyperbolic Matrix(277,596,244,525) (-28/13,-15/7) -> (17/15,8/7) Hyperbolic Matrix(245,524,36,77) (-15/7,-17/8) -> (27/4,7/1) Hyperbolic Matrix(395,836,644,1363) (-17/8,-2/1) -> (46/75,27/44) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(811,532,468,307) (-2/3,-15/23) -> (71/41,26/15) Hyperbolic Matrix(577,376,2064,1345) (-15/23,-13/20) -> (19/68,7/25) Hyperbolic Matrix(913,592,-2392,-1551) (-13/20,-11/17) -> (-21/55,-29/76) Hyperbolic Matrix(563,364,116,75) (-11/17,-20/31) -> (24/5,5/1) Hyperbolic Matrix(1241,800,560,361) (-20/31,-9/14) -> (31/14,20/9) Hyperbolic Matrix(2231,1432,1008,647) (-9/14,-34/53) -> (42/19,31/14) Hyperbolic Matrix(1005,644,-2564,-1643) (-25/39,-16/25) -> (-20/51,-9/23) Hyperbolic Matrix(557,356,884,565) (-16/25,-7/11) -> (17/27,12/19) Hyperbolic Matrix(2301,1460,1420,901) (-7/11,-26/41) -> (34/21,47/29) Hyperbolic Matrix(1635,1036,-2836,-1797) (-26/41,-19/30) -> (-15/26,-34/59) Hyperbolic Matrix(2503,1584,-4464,-2825) (-19/30,-31/49) -> (-23/41,-37/66) Hyperbolic Matrix(1853,1172,868,549) (-31/49,-43/68) -> (17/8,15/7) Hyperbolic Matrix(5441,3440,1520,961) (-43/68,-12/19) -> (68/19,43/12) Hyperbolic Matrix(431,272,328,207) (-12/19,-17/27) -> (17/13,4/3) Hyperbolic Matrix(1405,884,1076,677) (-17/27,-22/35) -> (30/23,17/13) Hyperbolic Matrix(1401,880,320,201) (-22/35,-5/8) -> (35/8,22/5) Hyperbolic Matrix(1913,1192,528,329) (-5/8,-28/45) -> (76/21,29/8) Hyperbolic Matrix(1475,916,-2636,-1637) (-23/37,-18/29) -> (-14/25,-33/59) Hyperbolic Matrix(523,324,-1364,-845) (-18/29,-13/21) -> (-5/13,-18/47) Hyperbolic Matrix(2621,1620,940,581) (-34/55,-21/34) -> (39/14,14/5) Hyperbolic Matrix(311,192,1048,647) (-21/34,-8/13) -> (8/27,3/10) Hyperbolic Matrix(521,320,1760,1081) (-8/13,-27/44) -> (13/44,8/27) Hyperbolic Matrix(313,192,-2072,-1271) (-27/44,-19/31) -> (-5/33,-3/20) Hyperbolic Matrix(2475,1516,1964,1203) (-19/31,-49/80) -> (5/4,29/23) Hyperbolic Matrix(209,128,1752,1073) (-49/80,-30/49) -> (2/17,1/8) Hyperbolic Matrix(1543,944,1136,695) (-30/49,-11/18) -> (19/14,34/25) Hyperbolic Matrix(511,312,208,127) (-11/18,-14/23) -> (22/9,5/2) Hyperbolic Matrix(921,560,1120,681) (-14/23,-17/28) -> (23/28,14/17) Hyperbolic Matrix(409,248,912,553) (-17/28,-3/5) -> (13/29,9/20) Hyperbolic Matrix(883,524,396,235) (-3/5,-16/27) -> (20/9,29/13) Hyperbolic Matrix(1081,640,880,521) (-16/27,-13/22) -> (27/22,16/13) Hyperbolic Matrix(197,116,484,285) (-13/22,-10/17) -> (2/5,9/22) Hyperbolic Matrix(1069,628,1452,853) (-10/17,-27/46) -> (25/34,14/19) Hyperbolic Matrix(1643,964,196,115) (-27/46,-44/75) -> (8/1,17/2) Hyperbolic Matrix(5995,3516,2324,1363) (-44/75,-17/29) -> (49/19,80/31) Hyperbolic Matrix(3189,1868,5212,3053) (-17/29,-41/70) -> (11/18,41/67) Hyperbolic Matrix(1635,956,484,283) (-24/41,-7/12) -> (27/8,44/13) Hyperbolic Matrix(957,556,284,165) (-7/12,-18/31) -> (10/3,27/8) Hyperbolic Matrix(283,164,-1044,-605) (-18/31,-11/19) -> (-3/11,-10/37) Hyperbolic Matrix(187,108,1612,931) (-26/45,-41/71) -> (1/9,2/17) Hyperbolic Matrix(1705,984,376,217) (-41/71,-15/26) -> (9/2,41/9) Hyperbolic Matrix(5943,3424,2456,1415) (-34/59,-19/33) -> (75/31,46/19) Hyperbolic Matrix(285,164,-1604,-923) (-19/33,-4/7) -> (-8/45,-3/17) Hyperbolic Matrix(649,368,552,313) (-4/7,-17/30) -> (7/6,20/17) Hyperbolic Matrix(919,520,1200,679) (-17/30,-13/23) -> (13/17,23/30) Hyperbolic Matrix(277,156,364,205) (-13/23,-9/16) -> (3/4,13/17) Hyperbolic Matrix(1275,716,4564,2563) (-9/16,-32/57) -> (12/43,19/68) Hyperbolic Matrix(4561,2560,3280,1841) (-32/57,-23/41) -> (57/41,32/23) Hyperbolic Matrix(5281,2960,2000,1121) (-37/66,-14/25) -> (66/25,37/14) Hyperbolic Matrix(2175,1216,5264,2943) (-33/59,-19/34) -> (19/46,31/75) Hyperbolic Matrix(273,152,88,49) (-19/34,-5/9) -> (3/1,19/6) Hyperbolic Matrix(711,392,448,247) (-5/9,-11/20) -> (19/12,27/17) Hyperbolic Matrix(1777,976,264,145) (-11/20,-28/51) -> (20/3,27/4) Hyperbolic Matrix(971,532,-2652,-1453) (-17/31,-6/11) -> (-26/71,-15/41) Hyperbolic Matrix(435,236,964,523) (-6/11,-13/24) -> (9/20,14/31) Hyperbolic Matrix(89,48,432,233) (-13/24,-7/13) -> (1/5,5/24) Hyperbolic Matrix(1465,784,256,137) (-15/28,-8/15) -> (40/7,23/4) Hyperbolic Matrix(1531,812,428,227) (-8/15,-9/17) -> (25/7,68/19) Hyperbolic Matrix(929,488,672,353) (-9/17,-1/2) -> (47/34,65/47) Hyperbolic Matrix(993,472,608,289) (-1/2,-8/17) -> (80/49,49/30) Hyperbolic Matrix(1351,632,528,247) (-8/17,-7/15) -> (23/9,64/25) Hyperbolic Matrix(147,68,-668,-309) (-7/15,-6/13) -> (-2/9,-9/41) Hyperbolic Matrix(367,168,592,271) (-6/13,-5/11) -> (13/21,18/29) Hyperbolic Matrix(727,328,512,231) (-5/11,-9/20) -> (17/12,27/19) Hyperbolic Matrix(365,164,-1164,-523) (-9/20,-13/29) -> (-11/35,-5/16) Hyperbolic Matrix(795,356,364,163) (-13/29,-4/9) -> (24/11,11/5) Hyperbolic Matrix(933,412,428,189) (-4/9,-15/34) -> (13/6,24/11) Hyperbolic Matrix(999,440,1360,599) (-15/34,-11/25) -> (11/15,25/34) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(853,372,-3052,-1331) (-7/16,-17/39) -> (-7/25,-19/68) Hyperbolic Matrix(1199,520,920,399) (-10/23,-13/30) -> (13/10,30/23) Hyperbolic Matrix(2115,916,284,123) (-13/30,-29/67) -> (37/5,15/2) Hyperbolic Matrix(1479,640,-7120,-3081) (-29/67,-16/37) -> (-16/77,-11/53) Hyperbolic Matrix(489,208,1112,473) (-3/7,-14/33) -> (18/41,11/25) Hyperbolic Matrix(1039,440,1320,559) (-14/33,-11/26) -> (11/14,26/33) Hyperbolic Matrix(275,116,-1036,-437) (-11/26,-8/19) -> (-4/15,-9/34) Hyperbolic Matrix(343,144,-1584,-665) (-8/19,-13/31) -> (-5/23,-8/37) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(10115,4236,2204,923) (-49/117,-18/43) -> (78/17,23/5) Hyperbolic Matrix(67,28,-548,-229) (-18/43,-5/12) -> (-1/8,-2/17) Hyperbolic Matrix(1573,652,1228,509) (-17/41,-12/29) -> (32/25,9/7) Hyperbolic Matrix(271,112,888,367) (-12/29,-7/17) -> (7/23,4/13) Hyperbolic Matrix(205,84,676,277) (-7/17,-9/22) -> (3/10,7/23) Hyperbolic Matrix(875,356,204,83) (-11/27,-2/5) -> (30/7,13/3) Hyperbolic Matrix(131,52,68,27) (-2/5,-11/28) -> (15/8,2/1) Hyperbolic Matrix(3883,1524,1516,595) (-11/28,-20/51) -> (64/25,41/16) Hyperbolic Matrix(195,76,-916,-357) (-9/23,-7/18) -> (-3/14,-7/33) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(1233,472,128,49) (-18/47,-31/81) -> (9/1,10/1) Hyperbolic Matrix(1683,644,196,75) (-31/81,-13/34) -> (17/2,9/1) Hyperbolic Matrix(2461,940,1940,741) (-13/34,-21/55) -> (19/15,33/26) Hyperbolic Matrix(1553,592,968,369) (-29/76,-8/21) -> (8/5,45/28) Hyperbolic Matrix(453,172,-2452,-931) (-19/50,-11/29) -> (-5/27,-7/38) Hyperbolic Matrix(191,72,-512,-193) (-11/29,-3/8) -> (-3/8,-13/35) Parabolic Matrix(1079,400,1400,519) (-13/35,-10/27) -> (10/13,27/35) Hyperbolic Matrix(887,328,192,71) (-10/27,-7/19) -> (23/5,14/3) Hyperbolic Matrix(1457,536,1264,465) (-7/19,-25/68) -> (23/20,15/13) Hyperbolic Matrix(4615,1696,7464,2743) (-25/68,-18/49) -> (34/55,47/76) Hyperbolic Matrix(883,324,-3284,-1205) (-18/49,-11/30) -> (-7/26,-18/67) Hyperbolic Matrix(1769,648,3912,1433) (-11/30,-26/71) -> (14/31,19/42) Hyperbolic Matrix(505,184,376,137) (-19/52,-4/11) -> (4/3,27/20) Hyperbolic Matrix(877,316,1124,405) (-13/36,-9/25) -> (7/9,25/32) Hyperbolic Matrix(1813,652,748,269) (-9/25,-14/39) -> (46/19,17/7) Hyperbolic Matrix(2621,940,1620,581) (-14/39,-5/14) -> (55/34,34/21) Hyperbolic Matrix(373,132,308,109) (-5/14,-6/17) -> (6/5,17/14) Hyperbolic Matrix(125,44,-804,-283) (-6/17,-7/20) -> (-5/32,-2/13) Hyperbolic Matrix(1537,536,1104,385) (-7/20,-8/23) -> (32/23,39/28) Hyperbolic Matrix(857,296,304,105) (-8/23,-1/3) -> (31/11,48/17) Hyperbolic Matrix(765,244,116,37) (-1/3,-7/22) -> (13/2,33/5) Hyperbolic Matrix(997,316,1404,445) (-7/22,-6/19) -> (22/31,27/38) Hyperbolic Matrix(233,72,288,89) (-5/16,-4/13) -> (4/5,13/16) Hyperbolic Matrix(1439,440,520,159) (-4/13,-11/36) -> (11/4,36/13) Hyperbolic Matrix(1729,528,632,193) (-11/36,-7/23) -> (41/15,11/4) Hyperbolic Matrix(1609,488,1032,313) (-7/23,-10/33) -> (14/9,39/25) Hyperbolic Matrix(229,68,852,253) (-3/10,-8/27) -> (4/15,7/26) Hyperbolic Matrix(1081,320,1760,521) (-8/27,-13/44) -> (27/44,8/13) Hyperbolic Matrix(1761,520,4880,1441) (-13/44,-18/61) -> (22/61,13/36) Hyperbolic Matrix(1927,568,4312,1271) (-23/78,-5/17) -> (21/47,17/38) Hyperbolic Matrix(847,248,1472,431) (-5/17,-12/41) -> (4/7,19/33) Hyperbolic Matrix(1355,396,284,83) (-12/41,-7/24) -> (19/4,24/5) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(669,188,1612,453) (-9/32,-7/25) -> (17/41,5/12) Hyperbolic Matrix(3997,1116,1164,325) (-19/68,-12/43) -> (24/7,55/16) Hyperbolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(549,148,1532,413) (-10/37,-7/26) -> (5/14,14/39) Hyperbolic Matrix(3829,1028,5412,1453) (-18/67,-11/41) -> (29/41,46/65) Hyperbolic Matrix(927,248,1312,351) (-11/41,-4/15) -> (12/17,29/41) Hyperbolic Matrix(1195,316,1524,403) (-9/34,-5/19) -> (29/37,11/14) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(2687,648,792,191) (-7/29,-6/25) -> (78/23,17/5) Hyperbolic Matrix(1157,276,524,125) (-6/25,-5/21) -> (11/5,42/19) Hyperbolic Matrix(155,36,-676,-157) (-4/17,-3/13) -> (-3/13,-8/35) Parabolic Matrix(1035,236,364,83) (-8/35,-5/22) -> (17/6,20/7) Hyperbolic Matrix(723,164,1036,235) (-5/22,-7/31) -> (23/33,7/10) Hyperbolic Matrix(767,168,872,191) (-9/41,-7/32) -> (7/8,15/17) Hyperbolic Matrix(1025,224,1176,257) (-7/32,-12/55) -> (20/23,7/8) Hyperbolic Matrix(4757,1036,6084,1325) (-17/78,-5/23) -> (43/55,61/78) Hyperbolic Matrix(1481,320,560,121) (-8/37,-3/14) -> (37/14,8/3) Hyperbolic Matrix(2589,548,3652,773) (-7/33,-11/52) -> (17/24,39/55) Hyperbolic Matrix(3803,804,2436,515) (-11/52,-4/19) -> (64/41,25/16) Hyperbolic Matrix(709,148,1212,253) (-4/19,-5/24) -> (7/12,24/41) Hyperbolic Matrix(6313,1312,1968,409) (-5/24,-16/77) -> (16/5,77/24) Hyperbolic Matrix(1159,240,2120,439) (-11/53,-6/29) -> (6/11,29/53) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(1521,280,440,81) (-7/38,-2/11) -> (38/11,7/2) Hyperbolic Matrix(1417,256,1024,185) (-2/11,-7/39) -> (65/47,18/13) Hyperbolic Matrix(827,148,732,131) (-7/39,-5/28) -> (9/8,17/15) Hyperbolic Matrix(1459,260,780,139) (-5/28,-8/45) -> (28/15,15/8) Hyperbolic Matrix(389,68,532,93) (-3/17,-1/6) -> (19/26,11/15) Hyperbolic Matrix(523,84,716,115) (-1/6,-3/19) -> (27/37,19/26) Hyperbolic Matrix(1465,224,896,137) (-2/13,-5/33) -> (67/41,18/11) Hyperbolic Matrix(1553,232,328,49) (-3/20,-4/27) -> (52/11,19/4) Hyperbolic Matrix(233,32,648,89) (-1/7,-2/15) -> (14/39,9/25) Hyperbolic Matrix(91,12,508,67) (-2/15,-1/8) -> (5/28,2/11) Hyperbolic Matrix(317,36,44,5) (-2/17,-1/9) -> (7/1,22/3) Hyperbolic Matrix(313,32,88,9) (-1/9,0/1) -> (32/9,25/7) Hyperbolic Matrix(329,-32,72,-7) (0/1,1/9) -> (41/9,32/7) Hyperbolic Matrix(213,-28,388,-51) (1/8,1/7) -> (17/31,11/20) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(1801,-320,1120,-199) (3/17,5/28) -> (45/28,37/23) Hyperbolic Matrix(237,-44,404,-75) (2/11,1/5) -> (17/29,10/17) Hyperbolic Matrix(2343,-496,496,-105) (4/19,7/33) -> (33/7,52/11) Hyperbolic Matrix(2013,-428,428,-91) (7/33,3/14) -> (47/10,33/7) Hyperbolic Matrix(1247,-272,2792,-609) (5/23,12/55) -> (4/9,21/47) Hyperbolic Matrix(6961,-1520,2560,-559) (12/55,7/32) -> (87/32,68/25) Hyperbolic Matrix(329,-72,32,-7) (7/32,2/9) -> (10/1,1/0) Hyperbolic Matrix(195,-44,164,-37) (2/9,3/13) -> (13/11,6/5) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(1929,-512,1232,-327) (9/34,4/15) -> (36/23,47/30) Hyperbolic Matrix(693,-188,188,-51) (7/26,3/11) -> (11/3,37/10) Hyperbolic Matrix(751,-208,408,-113) (8/29,5/18) -> (11/6,24/13) Hyperbolic Matrix(1595,-444,564,-157) (5/18,12/43) -> (48/17,17/6) Hyperbolic Matrix(1591,-448,2248,-633) (9/32,2/7) -> (46/65,17/24) Hyperbolic Matrix(587,-172,372,-109) (2/7,5/17) -> (11/7,30/19) Hyperbolic Matrix(2317,-684,2964,-875) (5/17,13/44) -> (25/32,43/55) Hyperbolic Matrix(1009,-312,152,-47) (4/13,9/29) -> (33/5,20/3) Hyperbolic Matrix(1801,-560,640,-199) (9/29,5/16) -> (45/16,31/11) Hyperbolic Matrix(791,-248,488,-153) (5/16,1/3) -> (47/29,13/8) Hyperbolic Matrix(355,-124,564,-197) (1/3,6/17) -> (22/35,17/27) Hyperbolic Matrix(1595,-564,444,-157) (6/17,11/31) -> (61/17,18/5) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(3675,-1324,1324,-477) (9/25,22/61) -> (86/31,25/9) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(2281,-880,1760,-679) (5/13,17/44) -> (57/44,35/27) Hyperbolic Matrix(2453,-948,1788,-691) (17/44,12/31) -> (48/35,11/8) Hyperbolic Matrix(2075,-804,1644,-637) (12/31,19/49) -> (29/23,24/19) Hyperbolic Matrix(1413,-548,1988,-771) (19/49,7/18) -> (27/38,5/7) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(1475,-604,2044,-837) (9/22,16/39) -> (44/61,13/18) Hyperbolic Matrix(2609,-1072,1672,-687) (16/39,7/17) -> (39/25,64/41) Hyperbolic Matrix(4923,-2036,1076,-445) (31/75,12/29) -> (32/7,87/19) Hyperbolic Matrix(1583,-656,736,-305) (12/29,17/41) -> (15/7,28/13) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(529,-232,472,-207) (7/16,18/41) -> (10/9,9/8) Hyperbolic Matrix(1769,-792,3232,-1447) (17/38,13/29) -> (29/53,23/42) Hyperbolic Matrix(1583,-736,656,-305) (6/13,7/15) -> (41/17,70/29) Hyperbolic Matrix(489,-232,352,-167) (7/15,1/2) -> (25/18,57/41) Hyperbolic Matrix(1693,-908,468,-251) (8/15,7/13) -> (47/13,76/21) Hyperbolic Matrix(751,-408,208,-113) (7/13,6/11) -> (18/5,47/13) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(2359,-1360,1320,-761) (19/33,15/26) -> (25/14,59/33) Hyperbolic Matrix(1647,-952,1192,-689) (15/26,11/19) -> (29/21,47/34) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(2547,-1492,3532,-2069) (24/41,17/29) -> (31/43,44/61) Hyperbolic Matrix(3425,-2096,2456,-1503) (41/67,30/49) -> (46/33,7/5) Hyperbolic Matrix(2357,-1444,3844,-2355) (30/49,19/31) -> (19/31,46/75) Parabolic Matrix(791,-488,248,-153) (8/13,21/34) -> (19/6,16/5) Hyperbolic Matrix(3633,-2248,2248,-1391) (47/76,13/21) -> (21/13,97/60) Hyperbolic Matrix(715,-444,124,-77) (18/29,5/8) -> (23/4,6/1) Hyperbolic Matrix(587,-372,172,-109) (12/19,7/11) -> (17/5,24/7) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1913,-1328,448,-311) (9/13,25/36) -> (17/4,47/11) Hyperbolic Matrix(6207,-4312,4792,-3329) (25/36,41/59) -> (79/61,57/44) Hyperbolic Matrix(2595,-1804,1204,-837) (41/59,16/23) -> (28/13,41/19) Hyperbolic Matrix(2239,-1560,920,-641) (16/23,23/33) -> (17/7,56/23) Hyperbolic Matrix(1269,-892,892,-627) (7/10,19/27) -> (27/19,37/26) Hyperbolic Matrix(6435,-4564,4564,-3237) (39/55,22/31) -> (86/61,55/39) Hyperbolic Matrix(3425,-2456,2096,-1503) (5/7,28/39) -> (116/71,67/41) Hyperbolic Matrix(489,-352,232,-167) (23/32,18/25) -> (2/1,17/8) Hyperbolic Matrix(1837,-1324,2324,-1675) (18/25,31/43) -> (15/19,34/43) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(1919,-1400,440,-321) (8/11,27/37) -> (13/3,48/11) Hyperbolic Matrix(1795,-1324,484,-357) (14/19,17/23) -> (63/17,26/7) Hyperbolic Matrix(713,-528,528,-391) (17/23,3/4) -> (27/20,23/17) Hyperbolic Matrix(2281,-1760,880,-679) (27/35,17/22) -> (57/22,13/5) Hyperbolic Matrix(1127,-872,632,-489) (17/22,7/9) -> (41/23,25/14) Hyperbolic Matrix(4511,-3528,2088,-1633) (61/78,18/23) -> (54/25,13/6) Hyperbolic Matrix(3657,-2864,2624,-2055) (18/23,47/60) -> (39/28,46/33) Hyperbolic Matrix(5809,-4552,4552,-3567) (47/60,29/37) -> (37/29,97/76) Hyperbolic Matrix(12083,-9556,4356,-3445) (34/43,53/67) -> (147/53,86/31) Hyperbolic Matrix(10651,-8428,6588,-5213) (53/67,19/24) -> (97/60,173/107) Hyperbolic Matrix(2075,-1644,804,-637) (19/24,4/5) -> (80/31,31/12) Hyperbolic Matrix(397,-324,484,-395) (13/16,9/11) -> (9/11,23/28) Parabolic Matrix(195,-164,44,-37) (5/6,6/7) -> (22/5,9/2) Hyperbolic Matrix(923,-796,516,-445) (6/7,13/15) -> (59/33,34/19) Hyperbolic Matrix(507,-452,212,-189) (8/9,1/1) -> (55/23,12/5) Hyperbolic Matrix(593,-648,248,-271) (1/1,10/9) -> (98/41,55/23) Hyperbolic Matrix(1111,-1288,408,-473) (15/13,7/6) -> (49/18,79/29) Hyperbolic Matrix(1157,-1364,844,-995) (20/17,13/11) -> (37/27,48/35) Hyperbolic Matrix(397,-484,324,-395) (17/14,11/9) -> (11/9,27/22) Parabolic Matrix(1837,-2324,1324,-1675) (24/19,19/15) -> (43/31,68/49) Hyperbolic Matrix(13863,-17696,5096,-6505) (97/76,60/47) -> (68/25,185/68) Hyperbolic Matrix(4391,-5608,2688,-3433) (60/47,23/18) -> (49/30,116/71) Hyperbolic Matrix(2317,-2964,684,-875) (23/18,32/25) -> (44/13,61/18) Hyperbolic Matrix(907,-1172,332,-429) (9/7,22/17) -> (30/11,41/15) Hyperbolic Matrix(3991,-5168,1848,-2393) (22/17,79/61) -> (41/19,54/25) Hyperbolic Matrix(1511,-2048,408,-553) (23/17,19/14) -> (37/10,63/17) Hyperbolic Matrix(871,-1208,168,-233) (18/13,43/31) -> (5/1,26/5) Hyperbolic Matrix(13569,-18832,8392,-11647) (68/49,93/67) -> (173/107,76/47) Hyperbolic Matrix(6733,-9348,2428,-3371) (93/67,25/18) -> (61/22,147/53) Hyperbolic Matrix(1413,-1988,548,-771) (7/5,31/22) -> (67/26,49/19) Hyperbolic Matrix(6641,-9360,2440,-3439) (31/22,86/61) -> (166/61,49/18) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(693,-988,148,-211) (37/26,10/7) -> (14/3,47/10) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(2715,-4244,1124,-1757) (25/16,61/39) -> (99/41,29/12) Hyperbolic Matrix(4039,-6320,1560,-2441) (61/39,36/23) -> (44/17,101/39) Hyperbolic Matrix(1767,-2792,512,-809) (30/19,49/31) -> (31/9,38/11) Hyperbolic Matrix(2077,-3284,604,-955) (49/31,19/12) -> (55/16,31/9) Hyperbolic Matrix(355,-564,124,-197) (27/17,8/5) -> (20/7,3/1) Hyperbolic Matrix(2357,-3844,1444,-2355) (44/27,31/19) -> (31/19,80/49) Parabolic Matrix(237,-404,44,-75) (17/10,12/7) -> (16/3,11/2) Hyperbolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(1755,-3044,644,-1117) (26/15,33/19) -> (79/29,30/11) Hyperbolic Matrix(9361,-16760,3440,-6159) (34/19,77/43) -> (117/43,166/61) Hyperbolic Matrix(10763,-19276,3956,-7085) (77/43,43/24) -> (185/68,117/43) Hyperbolic Matrix(2363,-4236,516,-925) (43/24,9/5) -> (87/19,55/12) Hyperbolic Matrix(213,-388,28,-51) (20/11,11/6) -> (15/2,8/1) Hyperbolic Matrix(365,-676,196,-363) (24/13,13/7) -> (13/7,28/15) Parabolic Matrix(915,-2044,124,-277) (29/13,38/17) -> (22/3,37/5) Hyperbolic Matrix(1247,-2792,272,-609) (38/17,9/4) -> (55/12,78/17) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(3753,-8968,1168,-2791) (43/18,98/41) -> (106/33,45/14) Hyperbolic Matrix(7229,-17452,2132,-5147) (70/29,99/41) -> (139/41,78/23) Hyperbolic Matrix(2925,-7076,1076,-2603) (29/12,75/31) -> (19/7,87/32) Hyperbolic Matrix(605,-1476,116,-283) (39/16,22/9) -> (26/5,21/4) Hyperbolic Matrix(763,-1956,236,-605) (41/16,18/7) -> (42/13,13/4) Hyperbolic Matrix(1171,-3028,268,-693) (31/12,44/17) -> (48/11,35/8) Hyperbolic Matrix(5437,-14084,1604,-4155) (101/39,57/22) -> (61/18,139/41) Hyperbolic Matrix(1277,-3364,484,-1275) (50/19,29/11) -> (29/11,66/25) Parabolic Matrix(2531,-7108,788,-2213) (14/5,59/21) -> (61/19,106/33) Hyperbolic Matrix(2593,-7288,808,-2271) (59/21,45/16) -> (77/24,61/19) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(205,-1156,36,-203) (28/5,17/3) -> (17/3,40/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(9,88,32,313) -> Matrix(1,4,0,1) Matrix(67,548,-28,-229) -> Matrix(3,8,-2,-5) Matrix(67,508,12,91) -> Matrix(1,2,0,1) Matrix(89,648,32,233) -> Matrix(1,2,0,1) Matrix(7,48,-48,-329) -> Matrix(1,0,0,1) Matrix(171,1132,-292,-1933) -> Matrix(1,0,-2,1) Matrix(37,236,-156,-995) -> Matrix(1,0,0,1) Matrix(115,716,84,523) -> Matrix(1,-2,0,1) Matrix(93,532,68,389) -> Matrix(1,4,0,1) Matrix(199,1120,-320,-1801) -> Matrix(1,4,-2,-7) Matrix(131,732,148,827) -> Matrix(1,4,0,1) Matrix(457,2536,264,1465) -> Matrix(1,2,0,1) Matrix(73,392,-192,-1031) -> Matrix(1,2,0,1) Matrix(37,196,84,445) -> Matrix(1,2,2,5) Matrix(31,152,-72,-353) -> Matrix(1,2,0,1) Matrix(169,808,32,153) -> Matrix(1,2,0,1) Matrix(195,916,-76,-357) -> Matrix(1,0,0,1) Matrix(343,1584,-144,-665) -> Matrix(3,2,-2,-1) Matrix(89,408,-368,-1687) -> Matrix(1,0,0,1) Matrix(257,1176,224,1025) -> Matrix(1,0,0,1) Matrix(147,668,-68,-309) -> Matrix(1,0,0,1) Matrix(35,156,-116,-517) -> Matrix(1,0,0,1) Matrix(155,676,-36,-157) -> Matrix(1,-8,0,1) Matrix(123,524,196,835) -> Matrix(1,4,0,1) Matrix(37,156,-236,-995) -> Matrix(1,2,0,1) Matrix(125,524,276,1157) -> Matrix(1,4,0,1) Matrix(89,368,-408,-1687) -> Matrix(3,8,-2,-5) Matrix(43,164,156,595) -> Matrix(1,2,0,1) Matrix(275,1036,-116,-437) -> Matrix(1,0,0,1) Matrix(351,1312,248,927) -> Matrix(1,2,0,1) Matrix(883,3284,-324,-1205) -> Matrix(1,0,0,1) Matrix(193,712,-312,-1151) -> Matrix(1,2,-2,-3) Matrix(45,164,76,277) -> Matrix(1,2,0,1) Matrix(155,556,-356,-1277) -> Matrix(1,2,0,1) Matrix(111,392,-32,-113) -> Matrix(1,-2,0,1) Matrix(395,1356,164,563) -> Matrix(1,0,0,1) Matrix(83,284,396,1355) -> Matrix(1,2,0,1) Matrix(431,1472,248,847) -> Matrix(1,2,0,1) Matrix(1037,3516,-2476,-8395) -> Matrix(1,2,0,1) Matrix(1441,4880,520,1761) -> Matrix(1,2,2,5) Matrix(521,1760,320,1081) -> Matrix(1,2,-4,-7) Matrix(253,852,68,229) -> Matrix(1,4,0,1) Matrix(35,116,-156,-517) -> Matrix(1,0,0,1) Matrix(563,1844,316,1035) -> Matrix(1,2,2,5) Matrix(159,520,440,1439) -> Matrix(1,2,-4,-7) Matrix(89,288,72,233) -> Matrix(1,2,0,1) Matrix(165,524,-404,-1283) -> Matrix(1,2,2,5) Matrix(577,1816,224,705) -> Matrix(1,0,0,1) Matrix(245,764,76,237) -> Matrix(1,2,0,1) Matrix(531,1532,148,427) -> Matrix(1,4,0,1) Matrix(385,1104,536,1537) -> Matrix(1,2,0,1) Matrix(87,248,-368,-1049) -> Matrix(1,2,0,1) Matrix(109,308,132,373) -> Matrix(1,2,0,1) Matrix(581,1620,940,2621) -> Matrix(1,2,0,1) Matrix(269,748,652,1813) -> Matrix(1,2,-2,-3) Matrix(113,312,-272,-751) -> Matrix(1,2,-2,-3) Matrix(345,944,-944,-2583) -> Matrix(1,2,0,1) Matrix(785,2144,-1224,-3343) -> Matrix(1,2,-2,-3) Matrix(905,2464,256,697) -> Matrix(1,4,0,1) Matrix(2743,7464,1696,4615) -> Matrix(1,4,-2,-7) Matrix(465,1264,536,1457) -> Matrix(1,2,0,1) Matrix(71,192,328,887) -> Matrix(1,4,-2,-7) Matrix(191,512,-72,-193) -> Matrix(3,8,-2,-5) Matrix(633,1672,488,1289) -> Matrix(3,4,2,3) Matrix(73,192,-392,-1031) -> Matrix(1,0,0,1) Matrix(371,972,-692,-1813) -> Matrix(1,2,-2,-3) Matrix(741,1940,940,2461) -> Matrix(1,2,0,1) Matrix(273,712,-472,-1231) -> Matrix(1,2,-2,-3) Matrix(125,324,76,197) -> Matrix(1,2,0,1) Matrix(1871,4792,768,1967) -> Matrix(5,8,-2,-3) Matrix(1591,4072,1128,2887) -> Matrix(1,2,0,1) Matrix(439,1120,-800,-2041) -> Matrix(1,2,-4,-7) Matrix(27,68,52,131) -> Matrix(1,2,0,1) Matrix(109,268,412,1013) -> Matrix(1,2,0,1) Matrix(165,404,-524,-1283) -> Matrix(1,2,0,1) Matrix(277,676,84,205) -> Matrix(1,2,2,5) Matrix(367,888,112,271) -> Matrix(1,2,-4,-7) Matrix(113,272,-312,-751) -> Matrix(1,2,-2,-3) Matrix(835,1996,1524,3643) -> Matrix(1,2,-2,-3) Matrix(1037,2476,-3516,-8395) -> Matrix(3,4,2,3) Matrix(1847,4408,432,1031) -> Matrix(11,14,-4,-5) Matrix(841,2000,320,761) -> Matrix(3,2,-2,-1) Matrix(673,1592,528,1249) -> Matrix(1,2,2,5) Matrix(559,1320,440,1039) -> Matrix(1,2,-4,-7) Matrix(563,1324,236,555) -> Matrix(9,14,-2,-3) Matrix(31,72,-152,-353) -> Matrix(1,0,0,1) Matrix(399,920,520,1199) -> Matrix(1,2,2,5) Matrix(155,356,-556,-1277) -> Matrix(1,2,-2,-3) Matrix(283,644,156,355) -> Matrix(1,2,0,1) Matrix(599,1360,440,999) -> Matrix(1,2,0,1) Matrix(189,428,412,933) -> Matrix(1,2,0,1) Matrix(163,364,356,795) -> Matrix(1,2,-2,-3) Matrix(359,800,-880,-1961) -> Matrix(1,2,0,1) Matrix(231,512,328,727) -> Matrix(3,4,2,3) Matrix(271,592,168,367) -> Matrix(3,4,-4,-5) Matrix(277,596,244,525) -> Matrix(1,2,0,1) Matrix(245,524,36,77) -> Matrix(1,2,0,1) Matrix(395,836,644,1363) -> Matrix(1,2,0,1) Matrix(3,4,-4,-5) -> Matrix(1,2,-2,-3) Matrix(811,532,468,307) -> Matrix(3,2,-2,-1) Matrix(577,376,2064,1345) -> Matrix(1,0,2,1) Matrix(913,592,-2392,-1551) -> Matrix(5,4,-4,-3) Matrix(563,364,116,75) -> Matrix(3,2,-2,-1) Matrix(1241,800,560,361) -> Matrix(1,0,2,1) Matrix(2231,1432,1008,647) -> Matrix(5,2,2,1) Matrix(1005,644,-2564,-1643) -> Matrix(1,0,2,1) Matrix(557,356,884,565) -> Matrix(3,2,-2,-1) Matrix(2301,1460,1420,901) -> Matrix(3,2,-8,-5) Matrix(1635,1036,-2836,-1797) -> Matrix(1,0,0,1) Matrix(2503,1584,-4464,-2825) -> Matrix(3,2,-2,-1) Matrix(1853,1172,868,549) -> Matrix(3,2,4,3) Matrix(5441,3440,1520,961) -> Matrix(1,0,2,1) Matrix(431,272,328,207) -> Matrix(3,2,-2,-1) Matrix(1405,884,1076,677) -> Matrix(9,4,2,1) Matrix(1401,880,320,201) -> Matrix(3,2,-2,-1) Matrix(1913,1192,528,329) -> Matrix(5,2,2,1) Matrix(1475,916,-2636,-1637) -> Matrix(1,0,0,1) Matrix(523,324,-1364,-845) -> Matrix(1,0,2,1) Matrix(2621,1620,940,581) -> Matrix(1,0,2,1) Matrix(311,192,1048,647) -> Matrix(1,0,0,1) Matrix(521,320,1760,1081) -> Matrix(5,2,-8,-3) Matrix(313,192,-2072,-1271) -> Matrix(7,2,-4,-1) Matrix(2475,1516,1964,1203) -> Matrix(1,0,2,1) Matrix(209,128,1752,1073) -> Matrix(1,0,2,1) Matrix(1543,944,1136,695) -> Matrix(1,0,2,1) Matrix(511,312,208,127) -> Matrix(3,2,-2,-1) Matrix(921,560,1120,681) -> Matrix(1,0,2,1) Matrix(409,248,912,553) -> Matrix(1,0,2,1) Matrix(883,524,396,235) -> Matrix(5,2,2,1) Matrix(1081,640,880,521) -> Matrix(1,0,2,1) Matrix(197,116,484,285) -> Matrix(1,0,0,1) Matrix(1069,628,1452,853) -> Matrix(1,0,2,1) Matrix(1643,964,196,115) -> Matrix(13,6,2,1) Matrix(5995,3516,2324,1363) -> Matrix(1,0,2,1) Matrix(3189,1868,5212,3053) -> Matrix(1,0,2,1) Matrix(1635,956,484,283) -> Matrix(1,0,4,1) Matrix(957,556,284,165) -> Matrix(1,0,2,1) Matrix(283,164,-1044,-605) -> Matrix(1,0,2,1) Matrix(187,108,1612,931) -> Matrix(1,0,2,1) Matrix(1705,984,376,217) -> Matrix(3,2,-2,-1) Matrix(5943,3424,2456,1415) -> Matrix(3,2,-2,-1) Matrix(285,164,-1604,-923) -> Matrix(1,0,2,1) Matrix(649,368,552,313) -> Matrix(1,0,4,1) Matrix(919,520,1200,679) -> Matrix(1,0,8,1) Matrix(277,156,364,205) -> Matrix(1,0,0,1) Matrix(1275,716,4564,2563) -> Matrix(1,0,2,1) Matrix(4561,2560,3280,1841) -> Matrix(1,0,2,1) Matrix(5281,2960,2000,1121) -> Matrix(5,6,-6,-7) Matrix(2175,1216,5264,2943) -> Matrix(3,2,-8,-5) Matrix(273,152,88,49) -> Matrix(1,0,2,1) Matrix(711,392,448,247) -> Matrix(1,0,2,1) Matrix(1777,976,264,145) -> Matrix(1,0,4,1) Matrix(971,532,-2652,-1453) -> Matrix(1,0,4,1) Matrix(435,236,964,523) -> Matrix(1,0,0,1) Matrix(89,48,432,233) -> Matrix(1,0,0,1) Matrix(1465,784,256,137) -> Matrix(1,0,2,1) Matrix(1531,812,428,227) -> Matrix(5,2,2,1) Matrix(929,488,672,353) -> Matrix(1,0,8,1) Matrix(993,472,608,289) -> Matrix(1,0,6,1) Matrix(1351,632,528,247) -> Matrix(1,0,-2,1) Matrix(147,68,-668,-309) -> Matrix(1,-2,0,1) Matrix(367,168,592,271) -> Matrix(1,0,0,1) Matrix(727,328,512,231) -> Matrix(1,0,2,1) Matrix(365,164,-1164,-523) -> Matrix(1,0,2,1) Matrix(795,356,364,163) -> Matrix(5,2,2,1) Matrix(933,412,428,189) -> Matrix(7,-2,4,-1) Matrix(999,440,1360,599) -> Matrix(1,0,-2,1) Matrix(355,156,644,283) -> Matrix(1,0,-2,1) Matrix(853,372,-3052,-1331) -> Matrix(1,-2,0,1) Matrix(1199,520,920,399) -> Matrix(1,2,0,1) Matrix(2115,916,284,123) -> Matrix(1,2,0,1) Matrix(1479,640,-7120,-3081) -> Matrix(1,-2,0,1) Matrix(489,208,1112,473) -> Matrix(1,0,2,1) Matrix(1039,440,1320,559) -> Matrix(1,0,0,1) Matrix(275,116,-1036,-437) -> Matrix(1,0,0,1) Matrix(343,144,-1584,-665) -> Matrix(3,2,-2,-1) Matrix(2271,952,1448,607) -> Matrix(3,2,-2,-1) Matrix(10115,4236,2204,923) -> Matrix(3,2,-2,-1) Matrix(67,28,-548,-229) -> Matrix(1,0,0,1) Matrix(1573,652,1228,509) -> Matrix(1,0,4,1) Matrix(271,112,888,367) -> Matrix(1,0,4,1) Matrix(205,84,676,277) -> Matrix(1,0,-4,1) Matrix(875,356,204,83) -> Matrix(5,-2,-2,1) Matrix(131,52,68,27) -> Matrix(1,0,0,1) Matrix(3883,1524,1516,595) -> Matrix(1,0,0,1) Matrix(195,76,-916,-357) -> Matrix(1,0,0,1) Matrix(197,76,324,125) -> Matrix(1,0,0,1) Matrix(1233,472,128,49) -> Matrix(1,-6,0,1) Matrix(1683,644,196,75) -> Matrix(1,10,0,1) Matrix(2461,940,1940,741) -> Matrix(1,2,-2,-3) Matrix(1553,592,968,369) -> Matrix(3,2,-2,-1) Matrix(453,172,-2452,-931) -> Matrix(3,2,-2,-1) Matrix(191,72,-512,-193) -> Matrix(1,0,2,1) Matrix(1079,400,1400,519) -> Matrix(1,0,0,1) Matrix(887,328,192,71) -> Matrix(1,-2,0,1) Matrix(1457,536,1264,465) -> Matrix(1,-2,0,1) Matrix(4615,1696,7464,2743) -> Matrix(1,-2,0,1) Matrix(883,324,-3284,-1205) -> Matrix(1,4,0,1) Matrix(1769,648,3912,1433) -> Matrix(1,0,2,1) Matrix(505,184,376,137) -> Matrix(1,0,0,1) Matrix(877,316,1124,405) -> Matrix(1,0,0,1) Matrix(1813,652,748,269) -> Matrix(1,-4,0,1) Matrix(2621,940,1620,581) -> Matrix(1,2,-2,-3) Matrix(373,132,308,109) -> Matrix(1,0,0,1) Matrix(125,44,-804,-283) -> Matrix(1,-2,0,1) Matrix(1537,536,1104,385) -> Matrix(1,0,2,1) Matrix(857,296,304,105) -> Matrix(1,0,0,1) Matrix(765,244,116,37) -> Matrix(1,0,0,1) Matrix(997,316,1404,445) -> Matrix(1,0,0,1) Matrix(233,72,288,89) -> Matrix(1,0,0,1) Matrix(1439,440,520,159) -> Matrix(1,0,0,1) Matrix(1729,528,632,193) -> Matrix(1,0,-2,1) Matrix(1609,488,1032,313) -> Matrix(1,-2,0,1) Matrix(229,68,852,253) -> Matrix(1,0,0,1) Matrix(1081,320,1760,521) -> Matrix(1,0,0,1) Matrix(1761,520,4880,1441) -> Matrix(1,0,-4,1) Matrix(1927,568,4312,1271) -> Matrix(1,0,0,1) Matrix(847,248,1472,431) -> Matrix(1,0,-4,1) Matrix(1355,396,284,83) -> Matrix(1,0,-2,1) Matrix(111,32,-392,-113) -> Matrix(1,-2,0,1) Matrix(669,188,1612,453) -> Matrix(1,2,-4,-7) Matrix(3997,1116,1164,325) -> Matrix(5,4,6,5) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(549,148,1532,413) -> Matrix(1,-2,-2,5) Matrix(3829,1028,5412,1453) -> Matrix(1,-12,0,1) Matrix(927,248,1312,351) -> Matrix(1,4,0,1) Matrix(1195,316,1524,403) -> Matrix(1,2,0,1) Matrix(595,156,164,43) -> Matrix(1,2,0,1) Matrix(2687,648,792,191) -> Matrix(1,0,2,1) Matrix(1157,276,524,125) -> Matrix(1,2,0,1) Matrix(155,36,-676,-157) -> Matrix(1,-6,0,1) Matrix(1035,236,364,83) -> Matrix(1,4,0,1) Matrix(723,164,1036,235) -> Matrix(1,4,0,1) Matrix(767,168,872,191) -> Matrix(1,2,0,1) Matrix(1025,224,1176,257) -> Matrix(1,2,-2,-3) Matrix(4757,1036,6084,1325) -> Matrix(1,0,2,1) Matrix(1481,320,560,121) -> Matrix(3,4,-4,-5) Matrix(2589,548,3652,773) -> Matrix(1,-2,0,1) Matrix(3803,804,2436,515) -> Matrix(1,-2,0,1) Matrix(709,148,1212,253) -> Matrix(1,2,2,5) Matrix(6313,1312,1968,409) -> Matrix(1,2,0,1) Matrix(1159,240,2120,439) -> Matrix(1,2,0,1) Matrix(591,112,248,47) -> Matrix(1,-4,0,1) Matrix(1521,280,440,81) -> Matrix(5,6,4,5) Matrix(1417,256,1024,185) -> Matrix(1,0,4,1) Matrix(827,148,732,131) -> Matrix(1,0,0,1) Matrix(1459,260,780,139) -> Matrix(1,0,0,1) Matrix(389,68,532,93) -> Matrix(1,0,0,1) Matrix(523,84,716,115) -> Matrix(1,2,0,1) Matrix(1465,224,896,137) -> Matrix(1,2,2,5) Matrix(1553,232,328,49) -> Matrix(3,4,-4,-5) Matrix(233,32,648,89) -> Matrix(1,2,-4,-7) Matrix(91,12,508,67) -> Matrix(7,8,-8,-9) Matrix(317,36,44,5) -> Matrix(1,2,0,1) Matrix(313,32,88,9) -> Matrix(1,2,0,1) Matrix(329,-32,72,-7) -> Matrix(3,2,-2,-1) Matrix(213,-28,388,-51) -> Matrix(1,0,0,1) Matrix(173,-28,68,-11) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(5,6,-6,-7) Matrix(1801,-320,1120,-199) -> Matrix(17,16,-16,-15) Matrix(237,-44,404,-75) -> Matrix(3,2,4,3) Matrix(2343,-496,496,-105) -> Matrix(5,6,-6,-7) Matrix(2013,-428,428,-91) -> Matrix(9,8,-8,-7) Matrix(1247,-272,2792,-609) -> Matrix(3,2,-2,-1) Matrix(6961,-1520,2560,-559) -> Matrix(7,4,-2,-1) Matrix(329,-72,32,-7) -> Matrix(7,4,-2,-1) Matrix(195,-44,164,-37) -> Matrix(1,0,2,1) Matrix(33,-8,128,-31) -> Matrix(1,0,2,1) Matrix(1929,-512,1232,-327) -> Matrix(1,-2,0,1) Matrix(693,-188,188,-51) -> Matrix(1,2,0,1) Matrix(751,-208,408,-113) -> Matrix(1,0,0,1) Matrix(1595,-444,564,-157) -> Matrix(1,0,0,1) Matrix(1591,-448,2248,-633) -> Matrix(1,-4,0,1) Matrix(587,-172,372,-109) -> Matrix(3,2,-2,-1) Matrix(2317,-684,2964,-875) -> Matrix(3,2,4,3) Matrix(1009,-312,152,-47) -> Matrix(1,0,0,1) Matrix(1801,-560,640,-199) -> Matrix(1,0,0,1) Matrix(791,-248,488,-153) -> Matrix(1,0,-2,1) Matrix(355,-124,564,-197) -> Matrix(3,2,-2,-1) Matrix(1595,-564,444,-157) -> Matrix(5,2,2,1) Matrix(1801,-640,560,-199) -> Matrix(1,0,2,1) Matrix(3675,-1324,1324,-477) -> Matrix(1,0,4,1) Matrix(205,-76,116,-43) -> Matrix(1,0,0,1) Matrix(377,-144,144,-55) -> Matrix(3,2,-2,-1) Matrix(2281,-880,1760,-679) -> Matrix(1,2,0,1) Matrix(2453,-948,1788,-691) -> Matrix(5,4,-4,-3) Matrix(2075,-804,1644,-637) -> Matrix(3,2,-2,-1) Matrix(1413,-548,1988,-771) -> Matrix(3,2,-2,-1) Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) Matrix(1475,-604,2044,-837) -> Matrix(1,0,2,1) Matrix(2609,-1072,1672,-687) -> Matrix(1,0,2,1) Matrix(4923,-2036,1076,-445) -> Matrix(1,0,2,1) Matrix(1583,-656,736,-305) -> Matrix(7,2,10,3) Matrix(85,-36,196,-83) -> Matrix(1,0,6,1) Matrix(529,-232,472,-207) -> Matrix(1,0,-2,1) Matrix(1769,-792,3232,-1447) -> Matrix(1,0,0,1) Matrix(1583,-736,656,-305) -> Matrix(1,-2,0,1) Matrix(489,-232,352,-167) -> Matrix(1,0,2,1) Matrix(1693,-908,468,-251) -> Matrix(1,2,0,1) Matrix(751,-408,208,-113) -> Matrix(1,2,0,1) Matrix(205,-116,76,-43) -> Matrix(1,0,0,1) Matrix(2359,-1360,1320,-761) -> Matrix(1,0,6,1) Matrix(1647,-952,1192,-689) -> Matrix(1,0,12,1) Matrix(557,-324,404,-235) -> Matrix(1,0,-4,1) Matrix(2547,-1492,3532,-2069) -> Matrix(3,-2,2,-1) Matrix(3425,-2096,2456,-1503) -> Matrix(1,0,2,1) Matrix(2357,-1444,3844,-2355) -> Matrix(1,0,2,1) Matrix(791,-488,248,-153) -> Matrix(1,0,0,1) Matrix(3633,-2248,2248,-1391) -> Matrix(1,2,-2,-3) Matrix(715,-444,124,-77) -> Matrix(1,0,0,1) Matrix(587,-372,172,-109) -> Matrix(1,0,2,1) Matrix(49,-32,72,-47) -> Matrix(1,0,2,1) Matrix(1913,-1328,448,-311) -> Matrix(11,-8,-4,3) Matrix(6207,-4312,4792,-3329) -> Matrix(13,-12,12,-11) Matrix(2595,-1804,1204,-837) -> Matrix(7,-8,8,-9) Matrix(2239,-1560,920,-641) -> Matrix(1,-4,0,1) Matrix(1269,-892,892,-627) -> Matrix(1,-2,2,-3) Matrix(6435,-4564,4564,-3237) -> Matrix(1,2,0,1) Matrix(3425,-2456,2096,-1503) -> Matrix(1,0,4,1) Matrix(489,-352,232,-167) -> Matrix(1,0,0,1) Matrix(1837,-1324,2324,-1675) -> Matrix(1,0,0,1) Matrix(557,-404,324,-235) -> Matrix(1,0,0,1) Matrix(1919,-1400,440,-321) -> Matrix(1,-2,0,1) Matrix(1795,-1324,484,-357) -> Matrix(1,2,0,1) Matrix(713,-528,528,-391) -> Matrix(1,0,0,1) Matrix(2281,-1760,880,-679) -> Matrix(1,-2,0,1) Matrix(1127,-872,632,-489) -> Matrix(1,0,0,1) Matrix(4511,-3528,2088,-1633) -> Matrix(11,-10,10,-9) Matrix(3657,-2864,2624,-2055) -> Matrix(1,-2,2,-3) Matrix(5809,-4552,4552,-3567) -> Matrix(1,-2,2,-3) Matrix(12083,-9556,4356,-3445) -> Matrix(1,0,0,1) Matrix(10651,-8428,6588,-5213) -> Matrix(1,0,-2,1) Matrix(2075,-1644,804,-637) -> Matrix(1,-2,0,1) Matrix(397,-324,484,-395) -> Matrix(1,0,0,1) Matrix(195,-164,44,-37) -> Matrix(1,-2,0,1) Matrix(923,-796,516,-445) -> Matrix(1,0,2,1) Matrix(507,-452,212,-189) -> Matrix(1,-4,0,1) Matrix(593,-648,248,-271) -> Matrix(1,-4,0,1) Matrix(1111,-1288,408,-473) -> Matrix(1,0,0,1) Matrix(1157,-1364,844,-995) -> Matrix(1,-2,0,1) Matrix(397,-484,324,-395) -> Matrix(1,0,0,1) Matrix(1837,-2324,1324,-1675) -> Matrix(1,0,2,1) Matrix(13863,-17696,5096,-6505) -> Matrix(1,-2,0,1) Matrix(4391,-5608,2688,-3433) -> Matrix(1,0,4,1) Matrix(2317,-2964,684,-875) -> Matrix(1,0,0,1) Matrix(907,-1172,332,-429) -> Matrix(1,0,-2,1) Matrix(3991,-5168,1848,-2393) -> Matrix(15,-14,14,-13) Matrix(1511,-2048,408,-553) -> Matrix(1,2,0,1) Matrix(871,-1208,168,-233) -> Matrix(1,0,-2,1) Matrix(13569,-18832,8392,-11647) -> Matrix(3,-2,-4,3) Matrix(6733,-9348,2428,-3371) -> Matrix(1,0,0,1) Matrix(1413,-1988,548,-771) -> Matrix(1,-2,0,1) Matrix(6641,-9360,2440,-3439) -> Matrix(1,0,-2,1) Matrix(1591,-2248,448,-633) -> Matrix(1,0,0,1) Matrix(693,-988,148,-211) -> Matrix(3,-4,-2,3) Matrix(49,-72,32,-47) -> Matrix(1,-2,0,1) Matrix(2715,-4244,1124,-1757) -> Matrix(1,0,0,1) Matrix(4039,-6320,1560,-2441) -> Matrix(1,0,0,1) Matrix(1767,-2792,512,-809) -> Matrix(9,10,8,9) Matrix(2077,-3284,604,-955) -> Matrix(9,8,10,9) Matrix(355,-564,124,-197) -> Matrix(1,0,0,1) Matrix(2357,-3844,1444,-2355) -> Matrix(1,0,16,1) Matrix(237,-404,44,-75) -> Matrix(1,0,0,1) Matrix(837,-1444,484,-835) -> Matrix(1,-2,0,1) Matrix(1755,-3044,644,-1117) -> Matrix(1,0,0,1) Matrix(9361,-16760,3440,-6159) -> Matrix(3,-2,-4,3) Matrix(10763,-19276,3956,-7085) -> Matrix(3,-4,-2,3) Matrix(2363,-4236,516,-925) -> Matrix(1,-2,0,1) Matrix(213,-388,28,-51) -> Matrix(1,2,0,1) Matrix(365,-676,196,-363) -> Matrix(1,0,0,1) Matrix(915,-2044,124,-277) -> Matrix(1,0,0,1) Matrix(1247,-2792,272,-609) -> Matrix(1,-4,0,1) Matrix(85,-196,36,-83) -> Matrix(1,-8,0,1) Matrix(3753,-8968,1168,-2791) -> Matrix(1,4,0,1) Matrix(7229,-17452,2132,-5147) -> Matrix(1,2,2,5) Matrix(2925,-7076,1076,-2603) -> Matrix(1,2,0,1) Matrix(605,-1476,116,-283) -> Matrix(1,2,0,1) Matrix(763,-1956,236,-605) -> Matrix(1,0,0,1) Matrix(1171,-3028,268,-693) -> Matrix(1,0,0,1) Matrix(5437,-14084,1604,-4155) -> Matrix(1,2,2,5) Matrix(1277,-3364,484,-1275) -> Matrix(13,14,-14,-15) Matrix(2531,-7108,788,-2213) -> Matrix(1,0,0,1) Matrix(2593,-7288,808,-2271) -> Matrix(1,0,0,1) Matrix(33,-128,8,-31) -> Matrix(1,-6,0,1) Matrix(205,-1156,36,-203) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 64 Degree of the the map Y: 384 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 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: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -4/9 -3/7 -7/17 -3/8 -1/3 -2/7 -1/5 -1/6 -1/7 0/1 1/7 3/17 1/4 1/3 3/7 1/2 7/13 3/5 2/3 5/7 9/11 13/15 7/8 1/1 11/9 14/11 9/7 23/17 7/5 3/2 61/39 31/19 5/3 19/11 16/9 9/5 13/7 2/1 41/19 11/5 7/3 17/7 5/2 18/7 13/5 29/11 8/3 117/43 11/4 147/53 3/1 61/19 23/7 10/3 17/5 31/9 7/2 39/11 11/3 15/4 4/1 13/3 9/2 23/5 14/3 33/7 5/1 21/4 16/3 11/2 17/3 6/1 13/2 7/1 22/3 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 -1/2 0/1 -7/15 1/1 -6/13 -1/1 1/1 -5/11 -1/1 0/1 1/0 -9/20 -1/2 -13/29 -1/1 -1/3 -4/9 0/1 -11/25 0/1 1/2 1/1 -7/16 1/2 -10/23 1/1 3/1 -3/7 -1/1 1/1 -14/33 -1/1 1/1 -11/26 1/0 -8/19 -3/1 -1/1 -13/31 -1/1 -1/2 0/1 -31/74 0/1 -18/43 0/1 -5/12 -1/2 -12/29 -1/3 -1/5 -7/17 0/1 -9/22 0/1 -11/27 1/3 1/1 -2/5 -1/1 1/1 -9/23 0/1 1/1 1/0 -7/18 0/1 -5/13 -1/1 1/1 -8/21 -1/1 -1/3 -19/50 -2/1 -11/29 -1/1 -1/2 0/1 -3/8 0/1 -13/35 0/1 1/1 1/0 -10/27 1/3 1/1 -7/19 1/1 -25/68 1/0 -18/49 1/1 3/1 -11/30 -2/1 -4/11 -1/1 1/1 -9/25 1/1 -14/39 1/0 -5/14 0/1 -6/17 -1/1 1/1 -7/20 1/0 -8/23 0/1 -1/3 -1/1 0/1 1/0 -7/22 1/0 -6/19 -1/1 1/1 -5/16 1/0 -4/13 -1/1 1/1 -11/36 0/1 -7/23 1/1 -10/33 1/1 3/1 -3/10 0/1 -8/27 -1/1 1/1 -13/44 1/0 -18/61 -1/1 1/1 -5/17 -1/1 1/1 -7/24 1/0 -2/7 1/0 -9/32 1/0 -7/25 -1/1 0/1 1/0 -5/18 0/1 -3/11 -1/1 1/1 -4/15 -3/1 -1/1 -9/34 1/0 -5/19 -1/1 0/1 1/0 -1/4 1/0 -5/21 -1/1 1/1 -9/38 0/1 -4/17 -1/1 1/1 -3/13 1/0 -5/22 -4/1 -7/31 -3/1 -2/9 -3/1 -1/1 -9/41 -1/1 -7/32 -2/1 -12/55 -5/3 -1/1 -5/23 -2/1 -1/1 1/0 -8/37 -7/5 -1/1 -3/14 0/1 -7/33 0/1 1/1 1/0 -4/19 1/0 -5/24 1/0 -1/5 -1/1 -3/16 1/0 -5/27 -2/1 -1/1 1/0 -7/38 -4/3 -2/11 -1/1 -1/3 -3/17 -1/1 0/1 1/0 -1/6 1/0 -3/19 -3/1 -1/1 -5/32 1/0 -2/13 -3/1 -1/1 -1/7 -2/1 -1/1 1/0 -1/8 -1/2 -2/17 0/1 -1/9 -1/1 0/1 -1/1 1/1 1/8 1/0 1/7 -1/1 1/6 -2/1 3/17 -1/1 2/11 -1/1 -7/9 1/5 -1/1 -1/2 0/1 3/14 -2/3 5/23 -1/1 -3/5 2/9 -1/1 -1/3 3/13 -1/1 -1/3 1/4 0/1 5/19 -1/1 1/1 9/34 0/1 4/15 -1/1 1/1 7/26 0/1 3/11 -1/1 0/1 1/0 8/29 -1/1 1/1 5/18 0/1 7/25 1/1 9/32 1/0 2/7 -3/1 -1/1 3/10 0/1 7/23 0/1 4/13 -1/1 1/1 1/3 -1/1 6/17 -1/1 -1/3 11/31 -1/1 -1/2 0/1 5/14 0/1 4/11 0/1 3/8 1/0 5/13 -1/1 -1/2 0/1 12/31 -1/1 -3/5 7/18 -1/2 2/5 -1/1 -1/3 5/12 -1/4 3/7 0/1 7/16 1/2 18/41 1/3 1/1 11/25 1/3 1/1 4/9 -1/1 1/1 5/11 -1/1 1/1 6/13 -1/1 1/1 1/2 0/1 7/13 -1/1 1/1 6/11 -1/1 1/1 17/31 -1/1 11/20 1/0 5/9 -1/1 0/1 1/0 4/7 -1/1 -1/3 19/33 -1/3 -1/5 15/26 0/1 11/19 0/1 7/12 1/2 17/29 1/2 2/3 1/1 10/17 1/1 3/1 3/5 -1/1 1/1 11/18 0/1 19/31 0/1 27/44 1/0 8/13 -1/1 1/1 13/21 -1/1 0/1 1/0 18/29 -1/1 1/1 5/8 1/0 12/19 -5/3 -1/1 7/11 -1/1 0/1 1/0 2/3 0/1 9/13 0/1 1/2 1/1 25/36 5/6 41/59 1/1 16/23 1/1 7/5 7/10 0/1 19/27 1/1 2/1 1/0 12/17 1/1 3/1 17/24 1/0 22/31 -1/1 1/1 5/7 -1/1 1/1 28/39 -1/1 1/1 23/32 0/1 18/25 -1/1 1/1 13/18 0/1 8/11 -1/1 1/1 27/37 -1/1 1/1 19/26 1/0 11/15 -1/1 0/1 1/0 3/4 1/0 7/9 1/1 25/32 1/2 18/23 1/1 5/3 29/37 1/1 2/1 1/0 11/14 1/0 15/19 0/1 1/1 1/0 4/5 -1/1 1/1 9/11 -1/1 1/1 14/17 -1/1 1/1 5/6 0/1 6/7 -1/1 1/1 13/15 -1/1 1/1 20/23 -1/1 1/1 7/8 0/1 15/17 1/1 8/9 -1/1 1/1 1/1 -1/1 0/1 1/0 10/9 -1/1 1/1 9/8 1/0 8/7 1/0 23/20 1/0 15/13 -1/1 7/6 0/1 6/5 -1/1 1/1 11/9 -1/1 1/1 16/13 -1/1 1/1 5/4 1/0 24/19 -1/1 1/1 19/15 -1/1 0/1 1/0 33/26 0/1 14/11 0/1 37/29 0/1 1/2 1/1 60/47 -1/1 1/1 23/18 0/1 9/7 1/1 22/17 3/5 1/1 35/27 1/1 3/2 2/1 13/10 2/1 4/3 -1/1 1/1 23/17 -1/1 1/1 19/14 0/1 15/11 0/1 1/1 1/0 26/19 1/0 11/8 -1/2 29/21 0/1 18/13 1/3 1/1 43/31 0/1 1/2 1/1 68/49 1/3 1/1 93/67 1/1 25/18 0/1 7/5 1/1 31/22 0/1 86/61 1/1 3/1 55/39 0/1 1/1 1/0 24/17 1/1 3/1 41/29 1/0 17/12 1/0 27/19 0/1 1/2 1/1 37/26 2/3 10/7 1/1 3/1 3/2 1/0 14/9 -1/1 1/1 39/25 -1/1 25/16 1/0 61/39 -3/1 -1/1 36/23 -3/1 -1/1 47/30 -2/1 11/7 -2/1 -1/1 1/0 8/5 -3/1 -1/1 37/23 -1/1 29/18 -4/5 21/13 -1/1 -2/3 -1/2 76/47 -1/1 -3/5 55/34 -2/3 34/21 -1/2 13/8 -1/2 44/27 -1/5 -1/7 31/19 0/1 80/49 1/11 1/9 49/30 0/1 18/11 1/3 1/1 5/3 -1/1 1/1 17/10 0/1 12/7 -1/1 1/1 31/18 0/1 19/11 1/0 45/26 -2/1 26/15 -3/1 -1/1 7/4 1/0 16/9 0/1 25/14 0/1 59/33 1/3 1/1 34/19 1/3 1/1 9/5 0/1 1/1 1/0 20/11 1/1 3/1 11/6 0/1 13/7 -1/1 1/1 15/8 1/0 2/1 -1/1 1/1 15/7 0/1 1/2 1/1 28/13 9/11 1/1 41/19 1/1 13/6 4/3 24/11 2/1 11/5 1/1 3/1 20/9 1/1 3/1 9/4 1/0 7/3 1/0 19/8 1/0 31/13 -5/1 43/18 -4/1 98/41 -5/1 -3/1 55/23 -5/1 -4/1 1/0 12/5 -5/1 -3/1 41/17 -3/1 -2/1 1/0 29/12 1/0 46/19 1/0 17/7 -3/1 5/2 -2/1 23/9 -1/1 41/16 1/0 18/7 1/0 67/26 -2/1 49/19 -1/1 31/12 1/0 44/17 -3/1 -1/1 101/39 -3/1 -1/1 57/22 -2/1 13/5 -2/1 -1/1 1/0 21/8 -3/2 29/11 -1/1 37/14 -4/5 8/3 -1/1 -1/3 19/7 -1/1 0/1 1/0 68/25 -3/1 -1/1 117/43 -1/1 166/61 -1/1 -3/5 49/18 0/1 30/11 -3/1 -1/1 41/15 -1/1 11/4 0/1 36/13 -1/1 1/1 61/22 0/1 147/53 1/1 86/31 -1/1 1/1 25/9 0/1 1/1 1/0 14/5 -1/1 1/1 3/1 -1/1 1/1 16/5 -1/1 1/1 61/19 -1/1 1/1 106/33 -1/1 1/1 45/14 0/1 29/9 0/1 1/1 1/0 42/13 1/0 13/4 1/0 23/7 0/1 10/3 1/3 1/1 17/5 0/1 1/2 1/1 24/7 5/7 1/1 31/9 1/1 38/11 1/1 13/11 7/2 2/1 39/11 1/0 32/9 1/1 3/1 25/7 1/1 18/5 1/1 3/1 47/13 1/1 3/1 29/8 1/0 11/3 1/1 2/1 1/0 37/10 2/1 63/17 1/1 3/1 26/7 1/1 3/1 15/4 5/2 4/1 1/0 17/4 -7/2 47/11 -3/1 -8/3 -5/2 30/7 -3/1 -7/3 13/3 -3/1 -1/1 22/5 -3/1 -1/1 9/2 -2/1 32/7 -5/3 -1/1 55/12 1/0 23/5 -1/1 14/3 -5/3 -1/1 33/7 -1/1 52/11 -1/1 -9/11 19/4 -1/2 5/1 -1/1 0/1 1/0 21/4 0/1 16/3 -1/1 1/1 11/2 0/1 17/3 -1/1 1/1 23/4 1/0 6/1 -1/1 1/1 13/2 1/0 33/5 -1/1 0/1 1/0 20/3 -1/1 1/1 7/1 1/1 22/3 2/1 15/2 2/1 8/1 3/1 5/1 9/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(149,70,530,249) (-1/2,-7/15) -> (7/25,9/32) Hyperbolic Matrix(147,68,-668,-309) (-7/15,-6/13) -> (-2/9,-9/41) Hyperbolic Matrix(367,168,592,271) (-6/13,-5/11) -> (13/21,18/29) Hyperbolic Matrix(727,328,512,231) (-5/11,-9/20) -> (17/12,27/19) Hyperbolic Matrix(361,162,-1522,-683) (-9/20,-13/29) -> (-5/21,-9/38) Hyperbolic Matrix(795,356,364,163) (-13/29,-4/9) -> (24/11,11/5) Hyperbolic Matrix(785,346,574,253) (-4/9,-11/25) -> (15/11,26/19) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(565,246,-1486,-647) (-7/16,-10/23) -> (-8/21,-19/50) Hyperbolic Matrix(281,122,638,277) (-10/23,-3/7) -> (11/25,4/9) Hyperbolic Matrix(489,208,1112,473) (-3/7,-14/33) -> (18/41,11/25) Hyperbolic Matrix(1109,470,210,89) (-14/33,-11/26) -> (21/4,16/3) Hyperbolic Matrix(275,116,-1036,-437) (-11/26,-8/19) -> (-4/15,-9/34) Hyperbolic Matrix(343,144,-1584,-665) (-8/19,-13/31) -> (-5/23,-8/37) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(1581,662,1378,577) (-31/74,-18/43) -> (8/7,23/20) Hyperbolic Matrix(67,28,-548,-229) (-18/43,-5/12) -> (-1/8,-2/17) Hyperbolic Matrix(207,86,-686,-285) (-5/12,-12/29) -> (-10/33,-3/10) Hyperbolic Matrix(271,112,888,367) (-12/29,-7/17) -> (7/23,4/13) Hyperbolic Matrix(205,84,676,277) (-7/17,-9/22) -> (3/10,7/23) Hyperbolic Matrix(201,82,-1282,-523) (-9/22,-11/27) -> (-3/19,-5/32) Hyperbolic Matrix(875,356,204,83) (-11/27,-2/5) -> (30/7,13/3) Hyperbolic Matrix(199,78,722,283) (-2/5,-9/23) -> (3/11,8/29) Hyperbolic Matrix(195,76,-916,-357) (-9/23,-7/18) -> (-3/14,-7/33) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(193,74,326,125) (-5/13,-8/21) -> (10/17,3/5) Hyperbolic Matrix(453,172,-2452,-931) (-19/50,-11/29) -> (-5/27,-7/38) Hyperbolic Matrix(191,72,-512,-193) (-11/29,-3/8) -> (-3/8,-13/35) Parabolic Matrix(1527,566,634,235) (-13/35,-10/27) -> (12/5,41/17) Hyperbolic Matrix(887,328,192,71) (-10/27,-7/19) -> (23/5,14/3) Hyperbolic Matrix(1457,536,1264,465) (-7/19,-25/68) -> (23/20,15/13) Hyperbolic Matrix(5437,1998,1962,721) (-25/68,-18/49) -> (36/13,61/22) Hyperbolic Matrix(1957,718,1202,441) (-18/49,-11/30) -> (13/8,44/27) Hyperbolic Matrix(945,346,254,93) (-11/30,-4/11) -> (26/7,15/4) Hyperbolic Matrix(127,46,-566,-205) (-4/11,-9/25) -> (-7/31,-2/9) Hyperbolic Matrix(1813,652,748,269) (-9/25,-14/39) -> (46/19,17/7) Hyperbolic Matrix(2621,940,1620,581) (-14/39,-5/14) -> (55/34,34/21) Hyperbolic Matrix(309,110,250,89) (-5/14,-6/17) -> (16/13,5/4) Hyperbolic Matrix(125,44,-804,-283) (-6/17,-7/20) -> (-5/32,-2/13) Hyperbolic Matrix(1901,662,738,257) (-7/20,-8/23) -> (18/7,67/26) Hyperbolic Matrix(793,274,246,85) (-8/23,-1/3) -> (29/9,42/13) Hyperbolic Matrix(765,244,116,37) (-1/3,-7/22) -> (13/2,33/5) Hyperbolic Matrix(1053,334,1466,465) (-7/22,-6/19) -> (28/39,23/32) Hyperbolic Matrix(235,74,-994,-313) (-6/19,-5/16) -> (-9/38,-4/17) Hyperbolic Matrix(289,90,350,109) (-5/16,-4/13) -> (14/17,5/6) Hyperbolic Matrix(1439,440,520,159) (-4/13,-11/36) -> (11/4,36/13) Hyperbolic Matrix(1729,528,632,193) (-11/36,-7/23) -> (41/15,11/4) Hyperbolic Matrix(1609,488,1032,313) (-7/23,-10/33) -> (14/9,39/25) Hyperbolic Matrix(229,68,852,253) (-3/10,-8/27) -> (4/15,7/26) Hyperbolic Matrix(1081,320,1760,521) (-8/27,-13/44) -> (27/44,8/13) Hyperbolic Matrix(6699,1978,4142,1223) (-13/44,-18/61) -> (76/47,55/34) Hyperbolic Matrix(1133,334,1306,385) (-18/61,-5/17) -> (13/15,20/23) Hyperbolic Matrix(171,50,790,231) (-5/17,-7/24) -> (3/14,5/23) Hyperbolic Matrix(111,32,-392,-113) (-7/24,-2/7) -> (-2/7,-9/32) Parabolic Matrix(1445,406,1114,313) (-9/32,-7/25) -> (35/27,13/10) Hyperbolic Matrix(165,46,-886,-247) (-7/25,-5/18) -> (-3/16,-5/27) Hyperbolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(273,74,166,45) (-3/11,-4/15) -> (18/11,5/3) Hyperbolic Matrix(1195,316,1524,403) (-9/34,-5/19) -> (29/37,11/14) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(209,50,790,189) (-1/4,-5/21) -> (5/19,9/34) Hyperbolic Matrix(521,122,158,37) (-4/17,-3/13) -> (23/7,10/3) Hyperbolic Matrix(675,154,206,47) (-3/13,-5/22) -> (13/4,23/7) Hyperbolic Matrix(929,210,1190,269) (-5/22,-7/31) -> (7/9,25/32) Hyperbolic Matrix(767,168,872,191) (-9/41,-7/32) -> (7/8,15/17) Hyperbolic Matrix(1025,224,1176,257) (-7/32,-12/55) -> (20/23,7/8) Hyperbolic Matrix(3275,714,766,167) (-12/55,-5/23) -> (47/11,30/7) Hyperbolic Matrix(1481,320,560,121) (-8/37,-3/14) -> (37/14,8/3) Hyperbolic Matrix(1165,246,914,193) (-7/33,-4/19) -> (14/11,37/29) Hyperbolic Matrix(963,202,758,159) (-4/19,-5/24) -> (33/26,14/11) Hyperbolic Matrix(959,198,402,83) (-5/24,-1/5) -> (31/13,43/18) Hyperbolic Matrix(591,112,248,47) (-1/5,-3/16) -> (19/8,31/13) Hyperbolic Matrix(1521,280,440,81) (-7/38,-2/11) -> (38/11,7/2) Hyperbolic Matrix(439,78,242,43) (-2/11,-3/17) -> (9/5,20/11) Hyperbolic Matrix(389,68,532,93) (-3/17,-1/6) -> (19/26,11/15) Hyperbolic Matrix(523,84,716,115) (-1/6,-3/19) -> (27/37,19/26) Hyperbolic Matrix(331,50,470,71) (-2/13,-1/7) -> (19/27,12/17) Hyperbolic Matrix(371,50,230,31) (-1/7,-1/8) -> (29/18,21/13) Hyperbolic Matrix(317,36,44,5) (-2/17,-1/9) -> (7/1,22/3) Hyperbolic Matrix(313,32,88,9) (-1/9,0/1) -> (32/9,25/7) Hyperbolic Matrix(253,-26,146,-15) (0/1,1/8) -> (45/26,26/15) Hyperbolic Matrix(213,-28,388,-51) (1/8,1/7) -> (17/31,11/20) Hyperbolic Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(543,-98,338,-61) (3/17,2/11) -> (8/5,37/23) Hyperbolic Matrix(237,-44,404,-75) (2/11,1/5) -> (17/29,10/17) Hyperbolic Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(263,-58,458,-101) (5/23,2/9) -> (4/7,19/33) Hyperbolic Matrix(359,-82,162,-37) (2/9,3/13) -> (11/5,20/9) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(1929,-512,1232,-327) (9/34,4/15) -> (36/23,47/30) Hyperbolic Matrix(693,-188,188,-51) (7/26,3/11) -> (11/3,37/10) Hyperbolic Matrix(471,-130,250,-69) (8/29,5/18) -> (15/8,2/1) Hyperbolic Matrix(1439,-402,562,-157) (5/18,7/25) -> (23/9,41/16) Hyperbolic Matrix(2903,-818,1778,-501) (9/32,2/7) -> (80/49,49/30) Hyperbolic Matrix(155,-46,246,-73) (2/7,3/10) -> (5/8,12/19) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(1181,-418,178,-63) (6/17,11/31) -> (33/5,20/3) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(491,-190,230,-89) (5/13,12/31) -> (2/1,15/7) Hyperbolic Matrix(1037,-402,1442,-559) (12/31,7/18) -> (23/32,18/25) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(113,-46,86,-35) (2/5,5/12) -> (13/10,4/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(529,-232,472,-207) (7/16,18/41) -> (10/9,9/8) Hyperbolic Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(439,-202,602,-277) (5/11,6/13) -> (8/11,27/37) Hyperbolic Matrix(491,-230,190,-89) (6/13,1/2) -> (31/12,44/17) Hyperbolic Matrix(471,-250,130,-69) (1/2,7/13) -> (47/13,29/8) Hyperbolic Matrix(751,-408,208,-113) (7/13,6/11) -> (18/5,47/13) Hyperbolic Matrix(413,-226,466,-255) (6/11,17/31) -> (15/17,8/9) Hyperbolic Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(2359,-1360,1320,-761) (19/33,15/26) -> (25/14,59/33) Hyperbolic Matrix(253,-146,26,-15) (15/26,11/19) -> (9/1,1/0) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(1185,-694,934,-547) (7/12,17/29) -> (19/15,33/26) Hyperbolic Matrix(1265,-774,894,-547) (11/18,19/31) -> (41/29,17/12) Hyperbolic Matrix(1933,-1186,546,-335) (19/31,27/44) -> (7/2,39/11) Hyperbolic Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(715,-444,124,-77) (18/29,5/8) -> (23/4,6/1) Hyperbolic Matrix(587,-372,172,-109) (12/19,7/11) -> (17/5,24/7) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(1913,-1328,448,-311) (9/13,25/36) -> (17/4,47/11) Hyperbolic Matrix(2243,-1558,1038,-721) (25/36,41/59) -> (41/19,13/6) Hyperbolic Matrix(2595,-1804,1204,-837) (41/59,16/23) -> (28/13,41/19) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(1269,-892,892,-627) (7/10,19/27) -> (27/19,37/26) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(2153,-1526,1686,-1195) (17/24,22/31) -> (60/47,23/18) Hyperbolic Matrix(351,-250,490,-349) (22/31,5/7) -> (5/7,28/39) Parabolic Matrix(557,-402,442,-319) (18/25,13/18) -> (5/4,24/19) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(113,-86,46,-35) (3/4,7/9) -> (17/7,5/2) Hyperbolic Matrix(2153,-1686,1526,-1195) (18/23,29/37) -> (55/39,24/17) Hyperbolic Matrix(469,-370,90,-71) (11/14,15/19) -> (5/1,21/4) Hyperbolic Matrix(557,-442,402,-319) (15/19,4/5) -> (18/13,43/31) Hyperbolic Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic Matrix(195,-164,44,-37) (5/6,6/7) -> (22/5,9/2) Hyperbolic Matrix(923,-796,516,-445) (6/7,13/15) -> (59/33,34/19) Hyperbolic Matrix(507,-452,212,-189) (8/9,1/1) -> (55/23,12/5) Hyperbolic Matrix(593,-648,248,-271) (1/1,10/9) -> (98/41,55/23) Hyperbolic Matrix(281,-318,38,-43) (9/8,8/7) -> (22/3,15/2) Hyperbolic Matrix(853,-986,186,-215) (15/13,7/6) -> (55/12,23/5) Hyperbolic Matrix(165,-194,74,-87) (7/6,6/5) -> (20/9,9/4) Hyperbolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(1837,-2324,1324,-1675) (24/19,19/15) -> (43/31,68/49) Hyperbolic Matrix(5079,-6482,3602,-4597) (37/29,60/47) -> (86/61,55/39) Hyperbolic Matrix(877,-1122,562,-719) (23/18,9/7) -> (39/25,25/16) Hyperbolic Matrix(907,-1172,332,-429) (9/7,22/17) -> (30/11,41/15) Hyperbolic Matrix(1011,-1310,470,-609) (22/17,35/27) -> (15/7,28/13) Hyperbolic Matrix(631,-850,170,-229) (4/3,23/17) -> (63/17,26/7) Hyperbolic Matrix(1511,-2048,408,-553) (23/17,19/14) -> (37/10,63/17) Hyperbolic Matrix(439,-602,202,-277) (26/19,11/8) -> (13/6,24/11) Hyperbolic Matrix(285,-394,34,-47) (29/21,18/13) -> (8/1,9/1) Hyperbolic Matrix(12965,-17994,4674,-6487) (68/49,93/67) -> (147/53,86/31) Hyperbolic Matrix(6733,-9348,2428,-3371) (93/67,25/18) -> (61/22,147/53) Hyperbolic Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1413,-1988,548,-771) (7/5,31/22) -> (67/26,49/19) Hyperbolic Matrix(6641,-9360,2440,-3439) (31/22,86/61) -> (166/61,49/18) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(1485,-2114,314,-447) (37/26,10/7) -> (52/11,19/4) Hyperbolic Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(3839,-6002,1482,-2317) (25/16,61/39) -> (101/39,57/22) Hyperbolic Matrix(4039,-6320,1560,-2441) (61/39,36/23) -> (44/17,101/39) Hyperbolic Matrix(155,-246,46,-73) (11/7,8/5) -> (10/3,17/5) Hyperbolic Matrix(2293,-3706,826,-1335) (21/13,76/47) -> (86/31,25/9) Hyperbolic Matrix(2357,-3844,1444,-2355) (44/27,31/19) -> (31/19,80/49) Parabolic Matrix(237,-404,44,-75) (17/10,12/7) -> (16/3,11/2) Hyperbolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(263,-458,58,-101) (26/15,7/4) -> (9/2,32/7) Hyperbolic Matrix(905,-1614,374,-667) (16/9,25/14) -> (29/12,46/19) Hyperbolic Matrix(701,-1258,258,-463) (34/19,9/5) -> (19/7,68/25) Hyperbolic Matrix(213,-388,28,-51) (20/11,11/6) -> (15/2,8/1) Hyperbolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(3753,-8968,1168,-2791) (43/18,98/41) -> (106/33,45/14) Hyperbolic Matrix(1125,-2714,434,-1047) (41/17,29/12) -> (57/22,13/5) Hyperbolic Matrix(763,-1956,236,-605) (41/16,18/7) -> (42/13,13/4) Hyperbolic Matrix(639,-1682,242,-637) (21/8,29/11) -> (29/11,37/14) Parabolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(1181,-3218,258,-703) (49/18,30/11) -> (32/7,55/12) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(2319,-7442,722,-2317) (16/5,61/19) -> (61/19,106/33) Parabolic Matrix(559,-1922,162,-557) (24/7,31/9) -> (31/9,38/11) Parabolic Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(463,-2178,98,-461) (14/3,33/7) -> (33/7,52/11) Parabolic Matrix(103,-578,18,-101) (11/2,17/3) -> (17/3,23/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(0,-1,1,2) Matrix(149,70,530,249) -> Matrix(2,-1,1,0) Matrix(147,68,-668,-309) -> Matrix(1,-2,0,1) Matrix(367,168,592,271) -> Matrix(1,0,0,1) Matrix(727,328,512,231) -> Matrix(1,0,2,1) Matrix(361,162,-1522,-683) -> Matrix(2,1,-1,0) Matrix(795,356,364,163) -> Matrix(5,2,2,1) Matrix(785,346,574,253) -> Matrix(2,-1,1,0) Matrix(355,156,644,283) -> Matrix(1,0,-2,1) Matrix(565,246,-1486,-647) -> Matrix(0,-1,1,0) Matrix(281,122,638,277) -> Matrix(0,1,-1,2) Matrix(489,208,1112,473) -> Matrix(1,0,2,1) Matrix(1109,470,210,89) -> Matrix(0,-1,1,0) Matrix(275,116,-1036,-437) -> Matrix(1,0,0,1) Matrix(343,144,-1584,-665) -> Matrix(3,2,-2,-1) Matrix(2271,952,1448,607) -> Matrix(3,2,-2,-1) Matrix(1581,662,1378,577) -> Matrix(2,1,-1,0) Matrix(67,28,-548,-229) -> Matrix(1,0,0,1) Matrix(207,86,-686,-285) -> Matrix(2,1,-1,0) Matrix(271,112,888,367) -> Matrix(1,0,4,1) Matrix(205,84,676,277) -> Matrix(1,0,-4,1) Matrix(201,82,-1282,-523) -> Matrix(0,-1,1,0) Matrix(875,356,204,83) -> Matrix(5,-2,-2,1) Matrix(199,78,722,283) -> Matrix(0,-1,1,0) Matrix(195,76,-916,-357) -> Matrix(1,0,0,1) Matrix(197,76,324,125) -> Matrix(1,0,0,1) Matrix(193,74,326,125) -> Matrix(0,-1,1,0) Matrix(453,172,-2452,-931) -> Matrix(3,2,-2,-1) Matrix(191,72,-512,-193) -> Matrix(1,0,2,1) Matrix(1527,566,634,235) -> Matrix(2,1,-1,0) Matrix(887,328,192,71) -> Matrix(1,-2,0,1) Matrix(1457,536,1264,465) -> Matrix(1,-2,0,1) Matrix(5437,1998,1962,721) -> Matrix(0,1,-1,2) Matrix(1957,718,1202,441) -> Matrix(0,-1,1,4) Matrix(945,346,254,93) -> Matrix(2,-1,1,0) Matrix(127,46,-566,-205) -> Matrix(2,1,-1,0) Matrix(1813,652,748,269) -> Matrix(1,-4,0,1) Matrix(2621,940,1620,581) -> Matrix(1,2,-2,-3) Matrix(309,110,250,89) -> Matrix(0,-1,1,0) Matrix(125,44,-804,-283) -> Matrix(1,-2,0,1) Matrix(1901,662,738,257) -> Matrix(2,1,-1,0) Matrix(793,274,246,85) -> Matrix(0,-1,1,0) Matrix(765,244,116,37) -> Matrix(1,0,0,1) Matrix(1053,334,1466,465) -> Matrix(0,-1,1,0) Matrix(235,74,-994,-313) -> Matrix(0,-1,1,0) Matrix(289,90,350,109) -> Matrix(0,-1,1,0) Matrix(1439,440,520,159) -> Matrix(1,0,0,1) Matrix(1729,528,632,193) -> Matrix(1,0,-2,1) Matrix(1609,488,1032,313) -> Matrix(1,-2,0,1) Matrix(229,68,852,253) -> Matrix(1,0,0,1) Matrix(1081,320,1760,521) -> Matrix(1,0,0,1) Matrix(6699,1978,4142,1223) -> Matrix(2,-1,-3,2) Matrix(1133,334,1306,385) -> Matrix(0,-1,1,0) Matrix(171,50,790,231) -> Matrix(2,-1,-3,2) Matrix(111,32,-392,-113) -> Matrix(1,-2,0,1) Matrix(1445,406,1114,313) -> Matrix(2,3,1,2) Matrix(165,46,-886,-247) -> Matrix(2,1,-1,0) Matrix(277,76,164,45) -> Matrix(1,0,0,1) Matrix(273,74,166,45) -> Matrix(0,-1,1,0) Matrix(1195,316,1524,403) -> Matrix(1,2,0,1) Matrix(595,156,164,43) -> Matrix(1,2,0,1) Matrix(209,50,790,189) -> Matrix(0,-1,1,0) Matrix(521,122,158,37) -> Matrix(0,1,-1,2) Matrix(675,154,206,47) -> Matrix(0,-1,1,4) Matrix(929,210,1190,269) -> Matrix(0,-1,1,2) Matrix(767,168,872,191) -> Matrix(1,2,0,1) Matrix(1025,224,1176,257) -> Matrix(1,2,-2,-3) Matrix(3275,714,766,167) -> Matrix(8,11,-3,-4) Matrix(1481,320,560,121) -> Matrix(3,4,-4,-5) Matrix(1165,246,914,193) -> Matrix(0,1,-1,2) Matrix(963,202,758,159) -> Matrix(0,-1,1,4) Matrix(959,198,402,83) -> Matrix(4,9,-1,-2) Matrix(591,112,248,47) -> Matrix(1,-4,0,1) Matrix(1521,280,440,81) -> Matrix(5,6,4,5) Matrix(439,78,242,43) -> Matrix(0,-1,1,0) Matrix(389,68,532,93) -> Matrix(1,0,0,1) Matrix(523,84,716,115) -> Matrix(1,2,0,1) Matrix(331,50,470,71) -> Matrix(2,3,1,2) Matrix(371,50,230,31) -> Matrix(2,3,-3,-4) Matrix(317,36,44,5) -> Matrix(1,2,0,1) Matrix(313,32,88,9) -> Matrix(1,2,0,1) Matrix(253,-26,146,-15) -> Matrix(2,1,-1,0) Matrix(213,-28,388,-51) -> Matrix(1,0,0,1) Matrix(173,-28,68,-11) -> Matrix(1,0,0,1) Matrix(715,-124,444,-77) -> Matrix(5,6,-6,-7) Matrix(543,-98,338,-61) -> Matrix(6,5,-5,-4) Matrix(237,-44,404,-75) -> Matrix(3,2,4,3) Matrix(165,-34,34,-7) -> Matrix(2,1,-1,0) Matrix(263,-58,458,-101) -> Matrix(2,1,-5,-2) Matrix(359,-82,162,-37) -> Matrix(0,-1,1,0) Matrix(33,-8,128,-31) -> Matrix(1,0,2,1) Matrix(1929,-512,1232,-327) -> Matrix(1,-2,0,1) Matrix(693,-188,188,-51) -> Matrix(1,2,0,1) Matrix(471,-130,250,-69) -> Matrix(0,-1,1,0) Matrix(1439,-402,562,-157) -> Matrix(0,-1,1,0) Matrix(2903,-818,1778,-501) -> Matrix(0,1,-1,8) Matrix(155,-46,246,-73) -> Matrix(2,1,-1,0) Matrix(31,-10,90,-29) -> Matrix(0,-1,1,2) Matrix(1181,-418,178,-63) -> Matrix(2,1,-1,0) Matrix(1801,-640,560,-199) -> Matrix(1,0,2,1) Matrix(619,-222,382,-137) -> Matrix(2,1,-5,-2) Matrix(205,-76,116,-43) -> Matrix(1,0,0,1) Matrix(377,-144,144,-55) -> Matrix(3,2,-2,-1) Matrix(491,-190,230,-89) -> Matrix(2,1,3,2) Matrix(1037,-402,1442,-559) -> Matrix(2,1,3,2) Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) Matrix(113,-46,86,-35) -> Matrix(2,1,-1,0) Matrix(85,-36,196,-83) -> Matrix(1,0,6,1) Matrix(529,-232,472,-207) -> Matrix(1,0,-2,1) Matrix(359,-162,82,-37) -> Matrix(2,1,-1,0) Matrix(439,-202,602,-277) -> Matrix(0,-1,1,0) Matrix(491,-230,190,-89) -> Matrix(2,1,-1,0) Matrix(471,-250,130,-69) -> Matrix(2,-1,1,0) Matrix(751,-408,208,-113) -> Matrix(1,2,0,1) Matrix(413,-226,466,-255) -> Matrix(0,-1,1,0) Matrix(205,-116,76,-43) -> Matrix(1,0,0,1) Matrix(2359,-1360,1320,-761) -> Matrix(1,0,6,1) Matrix(253,-146,26,-15) -> Matrix(6,1,-1,0) Matrix(557,-324,404,-235) -> Matrix(1,0,-4,1) Matrix(1185,-694,934,-547) -> Matrix(2,-1,-3,2) Matrix(1265,-774,894,-547) -> Matrix(0,-1,1,0) Matrix(1933,-1186,546,-335) -> Matrix(2,-1,1,0) Matrix(619,-382,222,-137) -> Matrix(0,-1,1,0) Matrix(715,-444,124,-77) -> Matrix(1,0,0,1) Matrix(587,-372,172,-109) -> Matrix(1,0,2,1) Matrix(49,-32,72,-47) -> Matrix(1,0,2,1) Matrix(1913,-1328,448,-311) -> Matrix(11,-8,-4,3) Matrix(2243,-1558,1038,-721) -> Matrix(10,-9,9,-8) Matrix(2595,-1804,1204,-837) -> Matrix(7,-8,8,-9) Matrix(755,-526,966,-673) -> Matrix(0,1,-1,2) Matrix(1269,-892,892,-627) -> Matrix(1,-2,2,-3) Matrix(1265,-894,774,-547) -> Matrix(0,1,-1,4) Matrix(2153,-1526,1686,-1195) -> Matrix(0,-1,1,0) Matrix(351,-250,490,-349) -> Matrix(0,-1,1,0) Matrix(557,-402,442,-319) -> Matrix(0,-1,1,0) Matrix(557,-404,324,-235) -> Matrix(1,0,0,1) Matrix(345,-254,254,-187) -> Matrix(0,-1,1,0) Matrix(113,-86,46,-35) -> Matrix(2,1,-1,0) Matrix(2153,-1686,1526,-1195) -> Matrix(0,1,-1,2) Matrix(469,-370,90,-71) -> Matrix(0,-1,1,0) Matrix(557,-442,402,-319) -> Matrix(0,1,-1,2) Matrix(199,-162,242,-197) -> Matrix(0,-1,1,0) Matrix(195,-164,44,-37) -> Matrix(1,-2,0,1) Matrix(923,-796,516,-445) -> Matrix(1,0,2,1) Matrix(507,-452,212,-189) -> Matrix(1,-4,0,1) Matrix(593,-648,248,-271) -> Matrix(1,-4,0,1) Matrix(281,-318,38,-43) -> Matrix(2,-1,1,0) Matrix(853,-986,186,-215) -> Matrix(2,1,-1,0) Matrix(165,-194,74,-87) -> Matrix(2,-1,1,0) Matrix(199,-242,162,-197) -> Matrix(0,-1,1,0) Matrix(1837,-2324,1324,-1675) -> Matrix(1,0,2,1) Matrix(5079,-6482,3602,-4597) -> Matrix(2,-1,1,0) Matrix(877,-1122,562,-719) -> Matrix(0,-1,1,0) Matrix(907,-1172,332,-429) -> Matrix(1,0,-2,1) Matrix(1011,-1310,470,-609) -> Matrix(2,-3,3,-4) Matrix(631,-850,170,-229) -> Matrix(2,-1,1,0) Matrix(1511,-2048,408,-553) -> Matrix(1,2,0,1) Matrix(439,-602,202,-277) -> Matrix(2,3,1,2) Matrix(285,-394,34,-47) -> Matrix(6,-1,1,0) Matrix(12965,-17994,4674,-6487) -> Matrix(2,-1,1,0) Matrix(6733,-9348,2428,-3371) -> Matrix(1,0,0,1) Matrix(1037,-1442,402,-559) -> Matrix(0,-1,1,0) Matrix(1413,-1988,548,-771) -> Matrix(1,-2,0,1) Matrix(6641,-9360,2440,-3439) -> Matrix(1,0,-2,1) Matrix(1591,-2248,448,-633) -> Matrix(1,0,0,1) Matrix(1485,-2114,314,-447) -> Matrix(4,-3,-5,4) Matrix(49,-72,32,-47) -> Matrix(1,-2,0,1) Matrix(3839,-6002,1482,-2317) -> Matrix(2,5,-1,-2) Matrix(4039,-6320,1560,-2441) -> Matrix(1,0,0,1) Matrix(155,-246,46,-73) -> Matrix(0,-1,1,0) Matrix(2293,-3706,826,-1335) -> Matrix(2,1,3,2) Matrix(2357,-3844,1444,-2355) -> Matrix(1,0,16,1) Matrix(237,-404,44,-75) -> Matrix(1,0,0,1) Matrix(837,-1444,484,-835) -> Matrix(1,-2,0,1) Matrix(263,-458,58,-101) -> Matrix(2,1,-1,0) Matrix(905,-1614,374,-667) -> Matrix(2,1,-1,0) Matrix(701,-1258,258,-463) -> Matrix(0,-1,1,0) Matrix(213,-388,28,-51) -> Matrix(1,2,0,1) Matrix(183,-338,98,-181) -> Matrix(0,-1,1,0) Matrix(85,-196,36,-83) -> Matrix(1,-8,0,1) Matrix(3753,-8968,1168,-2791) -> Matrix(1,4,0,1) Matrix(1125,-2714,434,-1047) -> Matrix(2,5,-1,-2) Matrix(763,-1956,236,-605) -> Matrix(1,0,0,1) Matrix(639,-1682,242,-637) -> Matrix(6,7,-7,-8) Matrix(10063,-27378,3698,-10061) -> Matrix(2,3,-3,-4) Matrix(1181,-3218,258,-703) -> Matrix(2,1,-1,0) Matrix(31,-90,10,-29) -> Matrix(0,-1,1,0) Matrix(2319,-7442,722,-2317) -> Matrix(0,-1,1,0) Matrix(559,-1922,162,-557) -> Matrix(10,-9,9,-8) Matrix(175,-626,26,-93) -> Matrix(0,1,-1,2) Matrix(33,-128,8,-31) -> Matrix(1,-6,0,1) Matrix(463,-2178,98,-461) -> Matrix(6,7,-7,-8) Matrix(103,-578,18,-101) -> Matrix(0,-1,1,0) 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): 64 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 -1/1 1 2 0/1 (-1/1,1/1) 0 20 1/8 1/0 1 20 1/7 -1/1 1 10 1/6 -2/1 1 20 3/17 -1/1 11 2 2/11 (-1/1,-7/9) 0 20 1/5 0 10 3/14 -2/3 1 20 2/9 (-1/1,-1/3) 0 20 3/13 (-1/1,-1/3).(-1/2,0/1) 0 10 1/4 0/1 1 4 5/19 (-1/1,1/1).(0/1,1/0) 0 10 4/15 (-1/1,1/1) 0 20 3/11 0 10 5/18 0/1 1 20 7/25 1/1 1 10 2/7 (-3/1,-1/1) 0 20 3/10 0/1 1 20 4/13 (-1/1,1/1) 0 20 1/3 -1/1 1 10 6/17 (-1/1,-1/3) 0 20 11/31 0 10 5/14 0/1 1 20 4/11 0/1 3 4 3/8 1/0 1 20 5/13 0 10 12/31 (-1/1,-3/5) 0 20 7/18 -1/2 1 4 2/5 (-1/1,-1/3) 0 20 5/12 -1/4 1 20 3/7 0/1 3 2 7/16 1/2 1 20 4/9 (-1/1,1/1) 0 20 5/11 (-1/1,1/1).(0/1,1/0) 0 10 6/13 (-1/1,1/1) 0 20 1/2 0/1 1 20 7/13 (-1/1,1/1).(0/1,1/0) 0 2 6/11 (-1/1,1/1) 0 20 5/9 0 10 4/7 (-1/1,-1/3) 0 20 15/26 0/1 1 20 11/19 0/1 8 2 7/12 1/2 1 20 3/5 (-1/1,1/1).(0/1,1/0) 0 10 8/13 (-1/1,1/1) 0 20 13/21 0 10 5/8 1/0 1 20 12/19 (-5/3,-1/1) 0 20 7/11 0 10 2/3 0/1 1 4 9/13 0 10 25/36 5/6 1 20 41/59 1/1 17 2 16/23 (1/1,7/5) 0 20 7/10 0/1 1 20 12/17 (1/1,3/1) 0 20 17/24 1/0 1 20 22/31 (-1/1,1/1) 0 20 5/7 (-1/1,1/1).(0/1,1/0) 0 10 23/32 0/1 1 4 18/25 (-1/1,1/1) 0 20 13/18 0/1 1 20 8/11 (-1/1,1/1) 0 20 11/15 0 10 3/4 1/0 1 20 7/9 1/1 1 10 18/23 (1/1,5/3) 0 20 11/14 1/0 1 4 15/19 0 10 4/5 (-1/1,1/1) 0 20 9/11 (-1/1,1/1).(0/1,1/0) 0 2 5/6 0/1 1 20 6/7 (-1/1,1/1) 0 20 13/15 (-1/1,1/1).(0/1,1/0) 0 10 7/8 0/1 1 4 8/9 (-1/1,1/1) 0 20 1/1 0 10 9/8 1/0 1 20 8/7 1/0 1 4 15/13 -1/1 1 10 7/6 0/1 1 20 6/5 (-1/1,1/1) 0 20 11/9 (-1/1,1/1).(0/1,1/0) 0 2 5/4 1/0 1 20 24/19 (-1/1,1/1) 0 20 19/15 0 10 14/11 0/1 3 4 23/18 0/1 1 20 9/7 1/1 1 10 22/17 (3/5,1/1) 0 20 13/10 2/1 1 20 4/3 (-1/1,1/1) 0 20 23/17 (-1/1,1/1).(0/1,1/0) 0 2 19/14 0/1 1 20 15/11 0 10 11/8 -1/2 1 20 29/21 0/1 8 2 18/13 (1/3,1/1) 0 20 43/31 0 10 68/49 (1/3,1/1) 0 20 93/67 1/1 1 2 25/18 0/1 1 20 7/5 1/1 1 10 31/22 0/1 1 20 24/17 (1/1,3/1) 0 20 17/12 1/0 1 20 10/7 (1/1,3/1) 0 20 3/2 1/0 1 4 14/9 (-1/1,1/1) 0 20 25/16 1/0 1 20 61/39 (-3/1,-1/1).(-2/1,1/0) 0 2 36/23 (-3/1,-1/1) 0 20 11/7 0 10 8/5 (-3/1,-1/1) 0 20 21/13 0 10 34/21 -1/2 3 4 13/8 -1/2 1 20 5/3 (-1/1,1/1).(0/1,1/0) 0 10 12/7 (-1/1,1/1) 0 20 31/18 0/1 1 20 19/11 1/0 1 2 45/26 -2/1 1 20 26/15 (-3/1,-1/1) 0 20 7/4 1/0 1 20 16/9 0/1 3 4 25/14 0/1 1 20 34/19 (1/3,1/1) 0 20 9/5 0 10 11/6 0/1 1 20 13/7 (-1/1,1/1).(0/1,1/0) 0 2 2/1 (-1/1,1/1) 0 20 15/7 0 10 13/6 4/3 1 20 11/5 (1/1,3/1).(2/1,1/0) 0 10 20/9 (1/1,3/1) 0 20 9/4 1/0 1 20 7/3 1/0 4 2 19/8 1/0 1 20 12/5 (-5/1,-3/1) 0 20 29/12 1/0 1 20 17/7 -3/1 1 10 5/2 -2/1 1 20 23/9 -1/1 1 10 41/16 1/0 1 20 18/7 1/0 1 4 49/19 -1/1 1 10 31/12 1/0 1 20 44/17 (-3/1,-1/1) 0 20 13/5 0 10 21/8 -3/2 1 20 29/11 -1/1 7 2 8/3 (-1/1,-1/3) 0 20 19/7 0 10 68/25 (-3/1,-1/1) 0 20 117/43 -1/1 3 2 49/18 0/1 1 20 30/11 (-3/1,-1/1) 0 20 11/4 0/1 1 4 25/9 0 10 14/5 (-1/1,1/1) 0 20 3/1 (-1/1,1/1).(0/1,1/0) 0 10 16/5 (-1/1,1/1) 0 20 61/19 (-1/1,1/1).(0/1,1/0) 0 2 45/14 0/1 1 20 29/9 0 10 13/4 1/0 1 20 10/3 (1/3,1/1) 0 20 17/5 0 10 24/7 (5/7,1/1) 0 20 31/9 1/1 9 2 7/2 2/1 1 20 25/7 1/1 1 10 18/5 (1/1,3/1) 0 20 11/3 0 10 15/4 5/2 1 20 4/1 1/0 3 4 17/4 -7/2 1 20 13/3 (-3/1,-1/1).(-2/1,1/0) 0 10 22/5 (-3/1,-1/1) 0 20 9/2 -2/1 1 20 14/3 (-5/3,-1/1) 0 20 33/7 -1/1 7 2 19/4 -1/2 1 20 5/1 0 10 11/2 0/1 1 20 17/3 (-1/1,1/1).(0/1,1/0) 0 2 6/1 (-1/1,1/1) 0 20 13/2 1/0 1 4 20/3 (-1/1,1/1) 0 20 7/1 1/1 1 10 8/1 (3/1,5/1) 0 20 9/1 1/0 8 2 1/0 1/0 1 20 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(253,-26,146,-15) (0/1,1/8) -> (45/26,26/15) Hyperbolic Matrix(249,-32,70,-9) (1/8,1/7) -> (7/2,25/7) Glide Reflection Matrix(173,-28,68,-11) (1/7,1/6) -> (5/2,23/9) Hyperbolic Matrix(35,-6,204,-35) (1/6,3/17) -> (1/6,3/17) Reflection Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(271,-50,168,-31) (2/11,1/5) -> (8/5,21/13) Glide Reflection Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(231,-50,328,-71) (3/14,2/9) -> (7/10,12/17) Glide Reflection Matrix(359,-82,162,-37) (2/9,3/13) -> (11/5,20/9) Hyperbolic Matrix(33,-8,128,-31) (3/13,1/4) -> (1/4,5/19) Parabolic Matrix(189,-50,412,-109) (5/19,4/15) -> (5/11,6/13) Glide Reflection Matrix(253,-68,346,-93) (4/15,3/11) -> (8/11,11/15) Glide Reflection Matrix(283,-78,156,-43) (3/11,5/18) -> (9/5,11/6) Glide Reflection Matrix(1439,-402,562,-157) (5/18,7/25) -> (23/9,41/16) Hyperbolic Matrix(249,-70,32,-9) (7/25,2/7) -> (7/1,8/1) Glide Reflection Matrix(155,-46,246,-73) (2/7,3/10) -> (5/8,12/19) Hyperbolic Matrix(367,-112,154,-47) (3/10,4/13) -> (19/8,12/5) Glide Reflection Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(265,-94,296,-105) (6/17,11/31) -> (8/9,1/1) Glide Reflection Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(205,-76,116,-43) (4/11,3/8) -> (7/4,16/9) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(491,-190,230,-89) (5/13,12/31) -> (2/1,15/7) Hyperbolic Matrix(1037,-402,1442,-559) (12/31,7/18) -> (23/32,18/25) Hyperbolic Matrix(173,-68,28,-11) (7/18,2/5) -> (6/1,13/2) Hyperbolic Matrix(113,-46,86,-35) (2/5,5/12) -> (13/10,4/3) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(277,-122,84,-37) (7/16,4/9) -> (13/4,10/3) Glide Reflection Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(491,-230,190,-89) (6/13,1/2) -> (31/12,44/17) Hyperbolic Matrix(27,-14,52,-27) (1/2,7/13) -> (1/2,7/13) Reflection Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(283,-156,78,-43) (6/11,5/9) -> (18/5,11/3) Glide Reflection Matrix(205,-116,76,-43) (5/9,4/7) -> (8/3,19/7) Hyperbolic Matrix(431,-248,610,-351) (4/7,15/26) -> (12/17,17/24) Glide Reflection Matrix(253,-146,26,-15) (15/26,11/19) -> (9/1,1/0) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(125,-74,76,-45) (7/12,3/5) -> (13/8,5/3) Glide Reflection Matrix(125,-76,74,-45) (3/5,8/13) -> (5/3,12/7) Glide Reflection Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(271,-168,50,-31) (13/21,5/8) -> (5/1,11/2) Glide Reflection Matrix(587,-372,172,-109) (12/19,7/11) -> (17/5,24/7) Hyperbolic Matrix(49,-32,72,-47) (7/11,2/3) -> (2/3,9/13) Parabolic Matrix(709,-492,330,-229) (9/13,25/36) -> (15/7,13/6) Glide Reflection Matrix(2951,-2050,4248,-2951) (25/36,41/59) -> (25/36,41/59) Reflection Matrix(1887,-1312,2714,-1887) (41/59,16/23) -> (41/59,16/23) Reflection Matrix(519,-362,400,-279) (16/23,7/10) -> (22/17,13/10) Glide Reflection Matrix(1591,-1128,890,-631) (17/24,22/31) -> (25/14,34/19) Glide Reflection Matrix(445,-316,514,-365) (22/31,5/7) -> (6/7,13/15) Glide Reflection Matrix(465,-334,536,-385) (5/7,23/32) -> (13/15,7/8) Glide Reflection Matrix(557,-402,442,-319) (18/25,13/18) -> (5/4,24/19) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(113,-86,46,-35) (3/4,7/9) -> (17/7,5/2) Hyperbolic Matrix(405,-316,314,-245) (7/9,18/23) -> (9/7,22/17) Glide Reflection Matrix(673,-528,246,-193) (18/23,11/14) -> (30/11,11/4) Glide Reflection Matrix(559,-440,202,-159) (11/14,15/19) -> (11/4,25/9) Glide Reflection Matrix(557,-442,402,-319) (15/19,4/5) -> (18/13,43/31) Hyperbolic Matrix(89,-72,110,-89) (4/5,9/11) -> (4/5,9/11) Reflection Matrix(109,-90,132,-109) (9/11,5/6) -> (9/11,5/6) Reflection Matrix(195,-164,44,-37) (5/6,6/7) -> (22/5,9/2) Hyperbolic Matrix(277,-244,42,-37) (7/8,8/9) -> (13/2,20/3) Glide Reflection Matrix(245,-274,76,-85) (1/1,9/8) -> (29/9,13/4) Glide Reflection Matrix(431,-490,168,-191) (9/8,8/7) -> (41/16,18/7) Glide Reflection Matrix(577,-662,224,-257) (8/7,15/13) -> (18/7,49/19) Glide Reflection Matrix(445,-514,316,-365) (15/13,7/6) -> (7/5,31/22) Glide Reflection Matrix(165,-194,74,-87) (7/6,6/5) -> (20/9,9/4) Hyperbolic Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(89,-110,72,-89) (11/9,5/4) -> (11/9,5/4) Reflection Matrix(1837,-2324,1324,-1675) (24/19,19/15) -> (43/31,68/49) Hyperbolic Matrix(741,-940,458,-581) (19/15,14/11) -> (21/13,34/21) Glide Reflection Matrix(563,-718,316,-403) (14/11,23/18) -> (16/9,25/14) Glide Reflection Matrix(509,-652,210,-269) (23/18,9/7) -> (29/12,17/7) Glide Reflection Matrix(137,-184,102,-137) (4/3,23/17) -> (4/3,23/17) Reflection Matrix(645,-874,476,-645) (23/17,19/14) -> (23/17,19/14) Reflection Matrix(253,-346,68,-93) (15/11,11/8) -> (11/3,15/4) Glide Reflection Matrix(285,-394,34,-47) (29/21,18/13) -> (8/1,9/1) Hyperbolic Matrix(9113,-12648,6566,-9113) (68/49,93/67) -> (68/49,93/67) Reflection Matrix(3349,-4650,2412,-3349) (93/67,25/18) -> (93/67,25/18) Reflection Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1493,-2106,548,-773) (31/22,24/17) -> (49/18,30/11) Glide Reflection Matrix(431,-610,248,-351) (24/17,17/12) -> (26/15,7/4) Glide Reflection Matrix(231,-328,50,-71) (17/12,10/7) -> (9/2,14/3) Glide Reflection Matrix(49,-72,32,-47) (10/7,3/2) -> (3/2,14/9) Parabolic Matrix(453,-706,188,-293) (14/9,25/16) -> (12/5,29/12) Glide Reflection Matrix(1951,-3050,1248,-1951) (25/16,61/39) -> (25/16,61/39) Reflection Matrix(2807,-4392,1794,-2807) (61/39,36/23) -> (61/39,36/23) Reflection Matrix(607,-952,234,-367) (36/23,11/7) -> (44/17,13/5) Glide Reflection Matrix(155,-246,46,-73) (11/7,8/5) -> (10/3,17/5) Hyperbolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(701,-1258,258,-463) (34/19,9/5) -> (19/7,68/25) Hyperbolic Matrix(155,-286,84,-155) (11/6,13/7) -> (11/6,13/7) Reflection Matrix(27,-52,14,-27) (13/7,2/1) -> (13/7,2/1) Reflection Matrix(163,-356,38,-83) (13/6,11/5) -> (17/4,13/3) Glide Reflection Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(463,-1218,176,-463) (21/8,29/11) -> (21/8,29/11) Reflection Matrix(175,-464,66,-175) (29/11,8/3) -> (29/11,8/3) Reflection Matrix(5849,-15912,2150,-5849) (68/25,117/43) -> (68/25,117/43) Reflection Matrix(4213,-11466,1548,-4213) (117/43,49/18) -> (117/43,49/18) Reflection Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(609,-1952,190,-609) (16/5,61/19) -> (16/5,61/19) Reflection Matrix(1709,-5490,532,-1709) (61/19,45/14) -> (61/19,45/14) Reflection Matrix(433,-1488,126,-433) (24/7,31/9) -> (24/7,31/9) Reflection Matrix(125,-434,36,-125) (31/9,7/2) -> (31/9,7/2) Reflection Matrix(175,-626,26,-93) (25/7,18/5) -> (20/3,7/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(197,-924,42,-197) (14/3,33/7) -> (14/3,33/7) Reflection Matrix(265,-1254,56,-265) (33/7,19/4) -> (33/7,19/4) Reflection Matrix(67,-374,12,-67) (11/2,17/3) -> (11/2,17/3) Reflection Matrix(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Matrix(-1,0,2,1) -> Matrix(0,1,1,0) (-1/1,0/1) -> (-1/1,1/1) Matrix(253,-26,146,-15) -> Matrix(2,1,-1,0) -1/1 Matrix(249,-32,70,-9) -> Matrix(2,1,1,0) Matrix(173,-28,68,-11) -> Matrix(1,0,0,1) Matrix(35,-6,204,-35) -> Matrix(3,4,-2,-3) (1/6,3/17) -> (-2/1,-1/1) Matrix(67,-12,374,-67) -> Matrix(8,7,-9,-8) (3/17,2/11) -> (-1/1,-7/9) Matrix(271,-50,168,-31) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(165,-34,34,-7) -> Matrix(2,1,-1,0) -1/1 Matrix(231,-50,328,-71) -> Matrix(3,2,2,1) Matrix(359,-82,162,-37) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(33,-8,128,-31) -> Matrix(1,0,2,1) 0/1 Matrix(189,-50,412,-109) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(253,-68,346,-93) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(283,-78,156,-43) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1439,-402,562,-157) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(249,-70,32,-9) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(155,-46,246,-73) -> Matrix(2,1,-1,0) -1/1 Matrix(367,-112,154,-47) -> Matrix(-4,1,1,0) Matrix(31,-10,90,-29) -> Matrix(0,-1,1,2) -1/1 Matrix(265,-94,296,-105) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1801,-640,560,-199) -> Matrix(1,0,2,1) 0/1 Matrix(619,-222,382,-137) -> Matrix(2,1,-5,-2) (-1/1,-1/3).(-1/2,0/1) Matrix(205,-76,116,-43) -> Matrix(1,0,0,1) Matrix(377,-144,144,-55) -> Matrix(3,2,-2,-1) -1/1 Matrix(491,-190,230,-89) -> Matrix(2,1,3,2) Matrix(1037,-402,1442,-559) -> Matrix(2,1,3,2) Matrix(173,-68,28,-11) -> Matrix(1,0,2,1) 0/1 Matrix(113,-46,86,-35) -> Matrix(2,1,-1,0) -1/1 Matrix(85,-36,196,-83) -> Matrix(1,0,6,1) 0/1 Matrix(277,-122,84,-37) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(359,-162,82,-37) -> Matrix(2,1,-1,0) -1/1 Matrix(491,-230,190,-89) -> Matrix(2,1,-1,0) -1/1 Matrix(27,-14,52,-27) -> Matrix(1,0,0,-1) (1/2,7/13) -> (0/1,1/0) Matrix(155,-84,286,-155) -> Matrix(0,1,1,0) (7/13,6/11) -> (-1/1,1/1) Matrix(283,-156,78,-43) -> Matrix(2,1,1,0) Matrix(205,-116,76,-43) -> Matrix(1,0,0,1) Matrix(431,-248,610,-351) -> Matrix(4,1,1,0) Matrix(253,-146,26,-15) -> Matrix(6,1,-1,0) Matrix(557,-324,404,-235) -> Matrix(1,0,-4,1) 0/1 Matrix(125,-74,76,-45) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(125,-76,74,-45) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(619,-382,222,-137) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(271,-168,50,-31) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(587,-372,172,-109) -> Matrix(1,0,2,1) 0/1 Matrix(49,-32,72,-47) -> Matrix(1,0,2,1) 0/1 Matrix(709,-492,330,-229) -> Matrix(2,-1,3,-2) *** -> (1/3,1/1) Matrix(2951,-2050,4248,-2951) -> Matrix(11,-10,12,-11) (25/36,41/59) -> (5/6,1/1) Matrix(1887,-1312,2714,-1887) -> Matrix(6,-7,5,-6) (41/59,16/23) -> (1/1,7/5) Matrix(519,-362,400,-279) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1591,-1128,890,-631) -> Matrix(0,1,1,2) Matrix(445,-316,514,-365) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(465,-334,536,-385) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(557,-402,442,-319) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(557,-404,324,-235) -> Matrix(1,0,0,1) Matrix(345,-254,254,-187) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(113,-86,46,-35) -> Matrix(2,1,-1,0) -1/1 Matrix(405,-316,314,-245) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(673,-528,246,-193) -> Matrix(0,1,1,-2) Matrix(559,-440,202,-159) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(557,-442,402,-319) -> Matrix(0,1,-1,2) 1/1 Matrix(89,-72,110,-89) -> Matrix(0,1,1,0) (4/5,9/11) -> (-1/1,1/1) Matrix(109,-90,132,-109) -> Matrix(1,0,0,-1) (9/11,5/6) -> (0/1,1/0) Matrix(195,-164,44,-37) -> Matrix(1,-2,0,1) 1/0 Matrix(277,-244,42,-37) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(245,-274,76,-85) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(431,-490,168,-191) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(577,-662,224,-257) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(445,-514,316,-365) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(165,-194,74,-87) -> Matrix(2,-1,1,0) 1/1 Matrix(109,-132,90,-109) -> Matrix(0,1,1,0) (6/5,11/9) -> (-1/1,1/1) Matrix(89,-110,72,-89) -> Matrix(1,0,0,-1) (11/9,5/4) -> (0/1,1/0) Matrix(1837,-2324,1324,-1675) -> Matrix(1,0,2,1) 0/1 Matrix(741,-940,458,-581) -> Matrix(2,1,-3,-2) *** -> (-1/1,-1/3) Matrix(563,-718,316,-403) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(509,-652,210,-269) -> Matrix(-4,1,1,0) Matrix(137,-184,102,-137) -> Matrix(0,1,1,0) (4/3,23/17) -> (-1/1,1/1) Matrix(645,-874,476,-645) -> Matrix(1,0,0,-1) (23/17,19/14) -> (0/1,1/0) Matrix(253,-346,68,-93) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(285,-394,34,-47) -> Matrix(6,-1,1,0) Matrix(9113,-12648,6566,-9113) -> Matrix(2,-1,3,-2) (68/49,93/67) -> (1/3,1/1) Matrix(3349,-4650,2412,-3349) -> Matrix(1,0,2,-1) (93/67,25/18) -> (0/1,1/1) Matrix(1037,-1442,402,-559) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(1493,-2106,548,-773) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(431,-610,248,-351) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(231,-328,50,-71) -> Matrix(-2,1,1,0) Matrix(49,-72,32,-47) -> Matrix(1,-2,0,1) 1/0 Matrix(453,-706,188,-293) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(1951,-3050,1248,-1951) -> Matrix(1,4,0,-1) (25/16,61/39) -> (-2/1,1/0) Matrix(2807,-4392,1794,-2807) -> Matrix(2,3,-1,-2) (61/39,36/23) -> (-3/1,-1/1) Matrix(607,-952,234,-367) -> Matrix(2,3,-1,-2) *** -> (-3/1,-1/1) Matrix(155,-246,46,-73) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(837,-1444,484,-835) -> Matrix(1,-2,0,1) 1/0 Matrix(701,-1258,258,-463) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(155,-286,84,-155) -> Matrix(1,0,0,-1) (11/6,13/7) -> (0/1,1/0) Matrix(27,-52,14,-27) -> Matrix(0,1,1,0) (13/7,2/1) -> (-1/1,1/1) Matrix(163,-356,38,-83) -> Matrix(2,-5,-1,2) Matrix(85,-196,36,-83) -> Matrix(1,-8,0,1) 1/0 Matrix(463,-1218,176,-463) -> Matrix(5,6,-4,-5) (21/8,29/11) -> (-3/2,-1/1) Matrix(175,-464,66,-175) -> Matrix(2,1,-3,-2) (29/11,8/3) -> (-1/1,-1/3) Matrix(5849,-15912,2150,-5849) -> Matrix(2,3,-1,-2) (68/25,117/43) -> (-3/1,-1/1) Matrix(4213,-11466,1548,-4213) -> Matrix(-1,0,2,1) (117/43,49/18) -> (-1/1,0/1) Matrix(31,-90,10,-29) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(609,-1952,190,-609) -> Matrix(0,1,1,0) (16/5,61/19) -> (-1/1,1/1) Matrix(1709,-5490,532,-1709) -> Matrix(1,0,0,-1) (61/19,45/14) -> (0/1,1/0) Matrix(433,-1488,126,-433) -> Matrix(6,-5,7,-6) (24/7,31/9) -> (5/7,1/1) Matrix(125,-434,36,-125) -> Matrix(3,-4,2,-3) (31/9,7/2) -> (1/1,2/1) Matrix(175,-626,26,-93) -> Matrix(0,1,-1,2) 1/1 Matrix(33,-128,8,-31) -> Matrix(1,-6,0,1) 1/0 Matrix(197,-924,42,-197) -> Matrix(4,5,-3,-4) (14/3,33/7) -> (-5/3,-1/1) Matrix(265,-1254,56,-265) -> Matrix(3,2,-4,-3) (33/7,19/4) -> (-1/1,-1/2) Matrix(67,-374,12,-67) -> Matrix(1,0,0,-1) (11/2,17/3) -> (0/1,1/0) Matrix(35,-204,6,-35) -> Matrix(0,1,1,0) (17/3,6/1) -> (-1/1,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.