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): 2520 Minimal number of generators: 421 Number of equivalence classes of cusps: 84 Genus: 169 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -51/116 -49/116 -45/116 -111/290 -21/58 -17/58 -57/203 -81/290 -77/290 -15/58 -55/232 -27/116 -25/116 -5/26 -11/58 -5/28 -4/25 -4/27 -3/23 -1/11 -1/12 0/1 1/10 1/9 2/17 1/8 2/15 3/22 4/29 1/7 3/20 2/13 3/19 1/6 5/29 4/23 3/17 2/11 5/27 3/16 4/21 1/5 6/29 5/24 4/19 3/14 19/87 2/9 3/13 5/21 7/29 1/4 8/29 5/18 7/25 2/7 44/145 9/29 1/3 32/87 11/29 56/145 2/5 12/29 13/29 7/15 1/2 16/29 17/29 89/145 18/29 55/87 2/3 20/29 101/145 146/203 21/29 22/29 68/87 23/29 24/29 25/29 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -9/10 1/3 -8/9 1/0 -15/17 0/1 -7/8 1/1 -13/15 -2/5 -32/37 -1/4 -19/22 -1/11 -25/29 0/1 -6/7 1/6 -17/20 1/3 -28/33 1/4 -39/46 1/3 -11/13 0/1 -16/19 1/4 -5/6 1/3 -24/29 1/2 -19/23 4/7 -14/17 1/2 -9/11 0/1 -22/27 3/2 -13/16 -1/1 -17/21 0/1 -4/5 1/0 -23/29 0/1 -19/24 1/11 -15/19 0/1 -11/14 3/11 -40/51 7/20 -29/37 2/5 -47/60 1/3 -18/23 1/2 -43/55 6/13 -68/87 1/2 -25/32 3/5 -7/9 0/1 -24/31 1/4 -17/22 3/13 -10/13 1/2 -23/30 1/3 -13/17 2/5 -16/21 5/12 -35/46 3/7 -19/25 6/13 -22/29 1/2 -3/4 1/1 -17/23 0/1 -14/19 1/2 -25/34 7/13 -11/15 4/5 -30/41 3/2 -49/67 2/1 -19/26 -1/1 -46/63 -1/2 -27/37 0/1 -8/11 1/0 -21/29 0/1 -13/18 1/5 -44/61 1/4 -31/43 4/15 -18/25 1/2 -5/7 2/5 -22/31 1/2 -17/24 -1/1 -12/17 1/4 -19/27 0/1 -45/64 1/3 -71/101 2/1 -26/37 1/2 -7/10 1/3 -23/33 0/1 -62/89 7/22 -101/145 1/3 -39/56 1/3 -16/23 3/8 -9/13 4/9 -20/29 1/2 -11/16 5/9 -13/19 2/3 -2/3 1/2 -15/23 0/1 -13/20 1/1 -37/57 0/1 -24/37 1/4 -11/17 0/1 -9/14 5/9 -25/39 2/3 -16/25 3/4 -39/61 2/3 -23/36 5/7 -7/11 0/1 -26/41 1/2 -19/30 1/1 -50/79 3/2 -81/128 1/1 -31/49 0/1 -43/68 1/1 -55/87 1/1 -12/19 1/0 -17/27 0/1 -22/35 1/2 -27/43 -2/1 -5/8 1/3 -18/29 1/2 -13/21 6/11 -60/97 9/16 -47/76 5/9 -34/55 1/2 -21/34 5/9 -8/13 5/8 -43/70 7/11 -35/57 2/3 -62/101 33/50 -89/145 2/3 -27/44 13/19 -19/31 2/3 -30/49 9/14 -11/18 5/7 -47/77 2/3 -36/59 3/4 -25/41 4/5 -14/23 1/2 -17/28 1/1 -37/61 2/3 -20/33 3/4 -23/38 1/1 -3/5 0/1 -19/32 1/1 -16/27 3/4 -13/22 7/9 -36/61 3/4 -23/39 4/5 -33/56 1/1 -10/17 5/6 -17/29 1/1 -7/12 1/1 -39/67 2/1 -32/55 1/0 -25/43 6/1 -43/74 -3/1 -18/31 -1/2 -11/19 0/1 -26/45 -1/2 -15/26 1/3 -4/7 3/4 -21/37 2/1 -17/30 1/1 -13/23 0/1 -22/39 1/2 -9/16 1/1 -41/73 10/1 -32/57 1/0 -23/41 0/1 -37/66 -1/1 -14/25 1/2 -33/59 0/1 -19/34 -1/1 -5/9 0/1 -16/29 1/2 -11/20 3/5 -17/31 2/3 -6/11 1/2 -7/13 2/3 -8/15 5/4 -1/2 1/1 -8/17 1/0 -7/15 6/7 -13/28 1/1 -6/13 3/2 -11/24 -1/1 -16/35 1/0 -21/46 1/3 -5/11 2/3 -14/31 5/6 -9/20 1/1 -13/29 1/1 -4/9 5/4 -23/52 1/1 -19/43 18/13 -15/34 11/7 -26/59 3/2 -11/25 2/1 -51/116 2/1 -40/91 9/4 -29/66 3/1 -18/41 3/2 -25/57 2/1 -7/16 3/1 -17/39 0/1 -10/23 1/2 -13/30 1/1 -16/37 3/4 -3/7 4/3 -14/33 3/2 -25/59 2/1 -36/85 1/0 -11/26 1/1 -30/71 11/6 -49/116 2/1 -19/45 2/1 -8/19 1/0 -13/31 2/1 -18/43 13/6 -23/55 2/1 -51/122 3/1 -28/67 1/0 -5/12 3/1 -12/29 1/0 -7/17 -2/1 -23/56 -1/1 -39/95 -2/3 -16/39 1/0 -9/22 -1/3 -11/27 0/1 -13/32 1/1 -2/5 1/2 -13/33 0/1 -11/28 1/1 -9/23 2/1 -16/41 1/0 -23/59 0/1 -53/136 1/1 -30/77 1/2 -7/18 1/1 -26/67 -1/6 -45/116 0/1 -19/49 0/1 -12/31 1/4 -17/44 7/15 -56/145 1/2 -39/101 18/35 -22/57 1/2 -27/70 3/5 -5/13 2/3 -18/47 1/2 -49/128 1/1 -80/209 5/8 -111/290 2/3 -31/81 2/3 -13/34 7/9 -34/89 5/6 -89/233 4/5 -144/377 5/6 -55/144 1/1 -21/55 4/5 -29/76 11/13 -37/97 6/7 -8/21 7/8 -11/29 1/1 -3/8 1/1 -13/35 2/1 -23/62 9/5 -10/27 5/2 -7/19 2/1 -32/87 1/0 -25/68 -1/1 -18/49 1/2 -47/128 1/1 -29/79 0/1 -11/30 1/1 -4/11 1/0 -21/58 1/1 -17/47 6/5 -13/36 7/5 -22/61 3/2 -31/86 1/1 -9/25 2/1 -5/14 9/5 -11/31 2/1 -6/17 5/2 -7/20 3/1 -15/43 18/5 -8/23 1/0 -1/3 0/1 -7/22 -1/1 -6/19 1/2 -5/16 1/1 -9/29 1/1 -4/13 5/4 -11/36 13/9 -29/95 8/5 -18/59 3/2 -25/82 11/7 -7/23 2/1 -17/56 1/1 -44/145 3/2 -27/89 2/1 -10/33 3/2 -13/43 -2/1 -16/53 3/4 -3/10 1/1 -17/57 2/1 -31/104 1/1 -14/47 3/2 -11/37 2/1 -30/101 -3/2 -19/64 1/1 -8/27 5/4 -13/44 17/11 -5/17 2/1 -17/58 2/1 -12/41 9/4 -7/24 1/1 -16/55 1/0 -25/86 1/1 -9/31 2/1 -11/38 1/1 -2/7 5/2 -9/32 5/1 -25/89 4/1 -41/146 5/1 -57/203 5/1 -16/57 1/0 -7/25 4/1 -19/68 5/1 -50/179 29/6 -81/290 5/1 -31/111 26/5 -12/43 23/4 -17/61 6/1 -5/18 9/1 -8/29 1/0 -3/11 -4/1 -13/48 -3/1 -10/37 -5/2 -7/26 -1/1 -11/41 -2/1 -15/56 -1/1 -4/15 -3/4 -17/64 -1/3 -47/177 0/1 -77/290 0/1 -30/113 -1/2 -13/49 0/1 -9/34 -1/5 -5/19 0/1 -6/23 -1/2 -7/27 0/1 -15/58 0/1 -8/31 1/8 -1/4 1/1 -7/29 1/1 -6/25 7/6 -11/46 1/1 -5/21 4/3 -14/59 3/2 -23/97 2/1 -55/232 2/1 -32/135 1/0 -9/38 1/1 -4/17 1/0 -7/30 1/1 -17/73 12/13 -27/116 1/1 -10/43 11/10 -3/13 4/3 -8/35 7/4 -21/92 9/5 -13/57 2/1 -18/79 11/6 -5/22 3/1 -7/31 2/1 -2/9 5/2 -9/41 2/1 -7/32 3/1 -19/87 3/1 -12/55 1/0 -5/23 2/1 -13/60 3/1 -21/97 2/1 -8/37 1/0 -11/51 20/7 -25/116 3/1 -14/65 31/10 -3/14 11/3 -7/33 4/1 -18/85 31/6 -11/52 5/1 -4/19 1/0 -5/24 15/1 -6/29 1/0 -1/5 -2/1 -5/26 -1/1 -4/21 -1/4 -11/58 0/1 -7/37 0/1 -3/16 1/1 -11/59 0/1 -8/43 1/8 -5/27 0/1 -2/11 1/2 -5/28 1/1 -3/17 0/1 -4/23 3/4 -5/29 1/1 -1/6 1/1 -5/31 2/1 -4/25 1/0 -3/19 2/1 -2/13 5/2 -7/46 7/3 -5/33 8/3 -8/53 11/4 -11/73 0/1 -3/20 3/1 -4/27 1/0 -1/7 6/1 -4/29 1/0 -3/22 -15/1 -5/37 -8/1 -2/15 -9/2 -7/53 -8/3 -5/38 -3/1 -3/23 -2/1 -1/8 -1/1 -2/17 1/2 -1/9 0/1 -1/10 1/1 -1/11 0/1 -1/12 3/1 0/1 1/0 1/10 -1/1 1/9 0/1 2/17 -1/2 1/8 1/1 2/15 9/2 5/37 8/1 3/22 15/1 4/29 1/0 1/7 -6/1 3/20 -3/1 5/33 -8/3 7/46 -7/3 2/13 -5/2 3/19 -2/1 1/6 -1/1 5/29 -1/1 4/23 -3/4 3/17 0/1 2/11 -1/2 5/27 0/1 3/16 -1/1 4/21 1/4 1/5 2/1 6/29 1/0 5/24 -15/1 4/19 1/0 3/14 -11/3 11/51 -20/7 8/37 1/0 13/60 -3/1 5/23 -2/1 12/55 1/0 19/87 -3/1 7/32 -3/1 2/9 -5/2 7/31 -2/1 5/22 -3/1 3/13 -4/3 7/30 -1/1 4/17 1/0 5/21 -4/3 11/46 -1/1 6/25 -7/6 7/29 -1/1 1/4 -1/1 6/23 1/2 5/19 0/1 9/34 1/5 4/15 3/4 11/41 2/1 18/67 3/2 7/26 1/1 17/63 4/3 10/37 5/2 3/11 4/1 8/29 1/0 5/18 -9/1 17/61 -6/1 12/43 -23/4 7/25 -4/1 2/7 -5/2 9/31 -2/1 7/24 -1/1 5/17 -2/1 8/27 -5/4 19/64 -1/1 30/101 3/2 11/37 -2/1 3/10 -1/1 10/33 -3/2 27/89 -2/1 44/145 -3/2 17/56 -1/1 7/23 -2/1 4/13 -5/4 9/29 -1/1 5/16 -1/1 6/19 -1/2 1/3 0/1 8/23 1/0 7/20 -3/1 20/57 1/0 13/37 -4/1 6/17 -5/2 5/14 -9/5 14/39 -3/2 9/25 -2/1 22/61 -3/2 13/36 -7/5 4/11 1/0 15/41 -2/1 11/30 -1/1 29/79 0/1 47/128 -1/1 18/49 -1/2 25/68 1/1 32/87 1/0 7/19 -2/1 10/27 -5/2 13/35 -2/1 16/43 -19/12 3/8 -1/1 11/29 -1/1 8/21 -7/8 37/97 -6/7 29/76 -11/13 21/55 -4/5 13/34 -7/9 5/13 -2/3 27/70 -3/5 22/57 -1/2 39/101 -18/35 56/145 -1/2 17/44 -7/15 12/31 -1/4 19/49 0/1 7/18 -1/1 30/77 -1/2 23/59 0/1 16/41 1/0 9/23 -2/1 11/28 -1/1 24/61 1/0 13/33 0/1 15/38 -1/1 2/5 -1/2 13/32 -1/1 11/27 0/1 9/22 1/3 25/61 0/1 16/39 1/0 23/56 1/1 7/17 2/1 12/29 1/0 5/12 -3/1 28/67 1/0 23/55 -2/1 18/43 -13/6 31/74 -1/1 13/31 -2/1 8/19 1/0 19/45 -2/1 11/26 -1/1 3/7 -4/3 16/37 -3/4 13/30 -1/1 10/23 -1/2 17/39 0/1 7/16 -3/1 32/73 -17/8 25/57 -2/1 18/41 -3/2 29/66 -3/1 11/25 -2/1 26/59 -3/2 15/34 -11/7 4/9 -5/4 13/29 -1/1 9/20 -1/1 14/31 -5/6 5/11 -2/3 6/13 -3/2 7/15 -6/7 1/2 -1/1 9/17 0/1 8/15 -5/4 15/28 -1/1 7/13 -2/3 13/24 -7/9 19/35 -2/3 25/46 -1/1 6/11 -1/2 17/31 -2/3 11/20 -3/5 16/29 -1/2 5/9 0/1 29/52 -1/1 24/43 -3/8 19/34 1/1 33/59 0/1 14/25 -1/2 65/116 0/1 51/91 0/1 37/66 1/1 23/41 0/1 32/57 1/0 9/16 -1/1 22/39 -1/2 13/23 0/1 17/30 -1/1 21/37 -2/1 4/7 -3/4 19/33 0/1 34/59 -1/2 49/85 0/1 15/26 -1/3 41/71 0/1 67/116 0/1 26/45 1/2 11/19 0/1 18/31 1/2 25/43 -6/1 32/55 1/0 71/122 -1/1 39/67 -2/1 7/12 -1/1 17/29 -1/1 10/17 -5/6 33/56 -1/1 56/95 -3/4 23/39 -4/5 13/22 -7/9 16/27 -3/4 19/32 -1/1 3/5 0/1 20/33 -3/4 17/28 -1/1 14/23 -1/2 25/41 -4/5 36/59 -3/4 83/136 -5/7 47/77 -2/3 11/18 -5/7 41/67 -2/3 71/116 -2/3 30/49 -9/14 19/31 -2/3 27/44 -13/19 89/145 -2/3 62/101 -33/50 35/57 -2/3 43/70 -7/11 8/13 -5/8 29/47 -10/17 79/128 -11/19 129/209 -4/7 179/290 -4/7 50/81 -1/2 21/34 -5/9 55/89 -4/7 144/233 -9/16 233/377 -5/9 89/144 -5/9 34/55 -1/2 47/76 -5/9 60/97 -9/16 13/21 -6/11 18/29 -1/2 5/8 -1/3 22/35 -1/2 39/62 -1/5 17/27 0/1 12/19 1/0 55/87 -1/1 43/68 -1/1 31/49 0/1 81/128 -1/1 50/79 -3/2 19/30 -1/1 7/11 0/1 37/58 -1/1 30/47 -5/6 23/36 -5/7 39/61 -2/3 55/86 -1/1 16/25 -3/4 9/14 -5/9 20/31 -3/8 11/17 0/1 13/20 -1/1 28/43 -5/8 15/23 0/1 2/3 -1/2 15/22 -3/5 13/19 -2/3 11/16 -5/9 20/29 -1/2 9/13 -4/9 25/36 -7/17 66/95 -7/18 41/59 -2/5 57/82 -5/13 16/23 -3/8 39/56 -1/3 101/145 -1/3 62/89 -7/22 23/33 0/1 30/43 -7/18 37/53 -6/17 7/10 -1/3 40/57 -1/4 73/104 -1/5 33/47 -2/7 26/37 -1/2 71/101 -2/1 45/64 -1/3 19/27 0/1 31/44 1/3 12/17 -1/4 41/58 0/1 29/41 0/1 17/24 1/1 39/55 0/1 61/86 -1/1 22/31 -1/2 27/38 -1/1 5/7 -2/5 23/32 -1/3 64/89 -1/4 105/146 -1/3 146/203 -1/4 41/57 0/1 18/25 -1/2 49/68 -1/3 129/179 -6/17 209/290 -1/3 80/111 -5/16 31/43 -4/15 44/61 -1/4 13/18 -1/5 21/29 0/1 8/11 1/0 35/48 -1/1 27/37 0/1 19/26 1/1 30/41 -3/2 41/56 -1/1 11/15 -4/5 47/64 -3/5 130/177 -1/2 213/290 -2/3 83/113 -2/3 36/49 -5/8 25/34 -7/13 14/19 -1/2 17/23 0/1 20/27 -1/8 43/58 0/1 23/31 0/1 3/4 -1/1 22/29 -1/2 19/25 -6/13 35/46 -3/7 16/21 -5/12 45/59 -2/5 74/97 -1/2 177/232 -2/5 103/135 -2/5 29/38 -1/3 13/17 -2/5 23/30 -1/3 56/73 -15/44 89/116 -1/3 33/43 -8/25 10/13 -1/2 27/35 -2/7 71/92 -5/19 44/57 -1/4 61/79 -4/15 17/22 -3/13 24/31 -1/4 7/9 0/1 32/41 1/0 25/32 -3/5 68/87 -1/2 43/55 -6/13 18/23 -1/2 47/60 -1/3 76/97 -1/4 29/37 -2/5 40/51 -7/20 91/116 -1/3 51/65 -10/31 11/14 -3/11 26/33 -1/6 67/85 0/1 41/52 -1/5 15/19 0/1 19/24 -1/11 23/29 0/1 4/5 1/0 21/26 -1/1 17/21 0/1 47/58 0/1 30/37 1/6 13/16 1/1 48/59 1/0 35/43 -8/1 22/27 -3/2 9/11 0/1 23/28 -1/1 14/17 -1/2 19/23 -4/7 24/29 -1/2 5/6 -1/3 26/31 -5/14 21/25 -2/7 16/19 -1/4 11/13 0/1 39/46 -1/3 28/33 -1/4 45/53 -2/5 62/73 -5/18 17/20 -1/3 23/27 0/1 6/7 -1/6 25/29 0/1 19/22 1/11 32/37 1/4 13/15 2/5 46/53 3/2 33/38 1/1 20/23 1/0 7/8 -1/1 15/17 0/1 8/9 1/0 9/10 -1/3 10/11 -1/2 11/12 -1/3 1/1 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(173,156,-580,-523) (-1/1,-9/10) -> (-3/10,-17/57) Hyperbolic Matrix(405,362,1102,985) (-9/10,-8/9) -> (18/49,25/68) Hyperbolic Matrix(405,358,1508,1333) (-8/9,-15/17) -> (11/41,18/67) Hyperbolic Matrix(813,716,1450,1277) (-15/17,-7/8) -> (37/66,23/41) Hyperbolic Matrix(291,254,-464,-405) (-7/8,-13/15) -> (-27/43,-5/8) Hyperbolic Matrix(3017,2610,4292,3713) (-13/15,-32/37) -> (26/37,71/101) Hyperbolic Matrix(2377,2054,3422,2957) (-32/37,-19/22) -> (25/36,66/95) Hyperbolic Matrix(1101,950,1276,1101) (-19/22,-25/29) -> (25/29,19/22) Hyperbolic Matrix(349,300,406,349) (-25/29,-6/7) -> (6/7,25/29) Hyperbolic Matrix(117,100,-406,-347) (-6/7,-17/20) -> (-11/38,-2/7) Hyperbolic Matrix(1159,984,-1914,-1625) (-17/20,-28/33) -> (-20/33,-23/38) Hyperbolic Matrix(639,542,2668,2263) (-28/33,-39/46) -> (11/46,6/25) Hyperbolic Matrix(581,492,1508,1277) (-39/46,-11/13) -> (5/13,27/70) Hyperbolic Matrix(465,392,1102,929) (-11/13,-16/19) -> (8/19,19/45) Hyperbolic Matrix(233,196,-1102,-927) (-16/19,-5/6) -> (-11/52,-4/19) Hyperbolic Matrix(289,240,348,289) (-5/6,-24/29) -> (24/29,5/6) Hyperbolic Matrix(1103,912,1334,1103) (-24/29,-19/23) -> (19/23,24/29) Hyperbolic Matrix(521,430,1334,1101) (-19/23,-14/17) -> (16/41,9/23) Hyperbolic Matrix(405,332,-638,-523) (-14/17,-9/11) -> (-7/11,-26/41) Hyperbolic Matrix(289,236,638,521) (-9/11,-22/27) -> (14/31,5/11) Hyperbolic Matrix(1449,1180,-2494,-2031) (-22/27,-13/16) -> (-43/74,-18/31) Hyperbolic Matrix(175,142,-928,-753) (-13/16,-17/21) -> (-7/37,-3/16) Hyperbolic Matrix(1101,890,-1508,-1219) (-17/21,-4/5) -> (-46/63,-27/37) Hyperbolic Matrix(231,184,290,231) (-4/5,-23/29) -> (23/29,4/5) Hyperbolic Matrix(1103,874,1392,1103) (-23/29,-19/24) -> (19/24,23/29) Hyperbolic Matrix(291,230,1102,871) (-19/24,-15/19) -> (5/19,9/34) Hyperbolic Matrix(521,410,-812,-639) (-15/19,-11/14) -> (-9/14,-25/39) Hyperbolic Matrix(349,274,-1624,-1275) (-11/14,-40/51) -> (-14/65,-3/14) Hyperbolic Matrix(1219,956,2146,1683) (-40/51,-29/37) -> (21/37,4/7) Hyperbolic Matrix(3191,2500,-7772,-6089) (-29/37,-47/60) -> (-23/56,-39/95) Hyperbolic Matrix(1857,1454,2668,2089) (-47/60,-18/23) -> (16/23,39/56) Hyperbolic Matrix(463,362,1334,1043) (-18/23,-43/55) -> (1/3,8/23) Hyperbolic Matrix(7481,5848,9570,7481) (-43/55,-68/87) -> (68/87,43/55) Hyperbolic Matrix(4351,3400,5568,4351) (-68/87,-25/32) -> (25/32,68/87) Hyperbolic Matrix(1739,1358,-2378,-1857) (-25/32,-7/9) -> (-49/67,-19/26) Hyperbolic Matrix(697,540,1798,1393) (-7/9,-24/31) -> (12/31,19/49) Hyperbolic Matrix(755,584,1276,987) (-24/31,-17/22) -> (13/22,16/27) Hyperbolic Matrix(231,178,-754,-581) (-17/22,-10/13) -> (-4/13,-11/36) Hyperbolic Matrix(349,268,-754,-579) (-10/13,-23/30) -> (-13/28,-6/13) Hyperbolic Matrix(637,488,1740,1333) (-23/30,-13/17) -> (15/41,11/30) Hyperbolic Matrix(639,488,-986,-753) (-13/17,-16/21) -> (-24/37,-11/17) Hyperbolic Matrix(4001,3046,6322,4813) (-16/21,-35/46) -> (81/128,50/79) Hyperbolic Matrix(405,308,2668,2029) (-35/46,-19/25) -> (5/33,7/46) Hyperbolic Matrix(1101,836,1450,1101) (-19/25,-22/29) -> (22/29,19/25) Hyperbolic Matrix(175,132,232,175) (-22/29,-3/4) -> (3/4,22/29) Hyperbolic Matrix(581,430,-1566,-1159) (-3/4,-17/23) -> (-13/35,-23/62) Hyperbolic Matrix(753,556,1334,985) (-17/23,-14/19) -> (22/39,13/23) Hyperbolic Matrix(231,170,1102,811) (-14/19,-25/34) -> (5/24,4/19) Hyperbolic Matrix(871,640,-1972,-1449) (-25/34,-11/15) -> (-19/43,-15/34) Hyperbolic Matrix(407,298,-870,-637) (-11/15,-30/41) -> (-8/17,-7/15) Hyperbolic Matrix(175,128,1508,1103) (-30/41,-49/67) -> (1/9,2/17) Hyperbolic Matrix(871,636,2146,1567) (-19/26,-46/63) -> (2/5,13/32) Hyperbolic Matrix(639,466,-2146,-1565) (-27/37,-8/11) -> (-14/47,-11/37) Hyperbolic Matrix(463,336,638,463) (-8/11,-21/29) -> (21/29,8/11) Hyperbolic Matrix(755,546,1044,755) (-21/29,-13/18) -> (13/18,21/29) Hyperbolic Matrix(3479,2510,5626,4059) (-13/18,-44/61) -> (34/55,47/76) Hyperbolic Matrix(2901,2092,4988,3597) (-44/61,-31/43) -> (25/43,32/55) Hyperbolic Matrix(755,544,-2494,-1797) (-31/43,-18/25) -> (-10/33,-13/43) Hyperbolic Matrix(173,124,-406,-291) (-18/25,-5/7) -> (-3/7,-14/33) Hyperbolic Matrix(59,42,-406,-289) (-5/7,-22/31) -> (-4/27,-1/7) Hyperbolic Matrix(1219,864,-3190,-2261) (-22/31,-17/24) -> (-13/34,-34/89) Hyperbolic Matrix(407,288,-1392,-985) (-17/24,-12/17) -> (-12/41,-7/24) Hyperbolic Matrix(349,246,-986,-695) (-12/17,-19/27) -> (-11/31,-6/17) Hyperbolic Matrix(347,244,-2146,-1509) (-19/27,-45/64) -> (-1/6,-5/31) Hyperbolic Matrix(5451,3832,7424,5219) (-45/64,-71/101) -> (11/15,47/64) Hyperbolic Matrix(3713,2610,4292,3017) (-71/101,-26/37) -> (32/37,13/15) Hyperbolic Matrix(581,408,-2146,-1507) (-26/37,-7/10) -> (-13/48,-10/37) Hyperbolic Matrix(697,486,-2494,-1739) (-7/10,-23/33) -> (-7/25,-19/68) Hyperbolic Matrix(2727,1900,3248,2263) (-23/33,-62/89) -> (26/31,21/25) Hyperbolic Matrix(17979,12524,25810,17979) (-62/89,-101/145) -> (101/145,62/89) Hyperbolic Matrix(11311,7878,16240,11311) (-101/145,-39/56) -> (39/56,101/145) Hyperbolic Matrix(2089,1454,2668,1857) (-39/56,-16/23) -> (18/23,47/60) Hyperbolic Matrix(173,120,-754,-523) (-16/23,-9/13) -> (-3/13,-8/35) Hyperbolic Matrix(521,360,754,521) (-9/13,-20/29) -> (20/29,9/13) Hyperbolic Matrix(639,440,928,639) (-20/29,-11/16) -> (11/16,20/29) Hyperbolic Matrix(405,278,928,637) (-11/16,-13/19) -> (17/39,7/16) Hyperbolic Matrix(753,514,-1276,-871) (-13/19,-2/3) -> (-36/61,-23/39) Hyperbolic Matrix(291,190,1334,871) (-2/3,-15/23) -> (5/23,12/55) Hyperbolic Matrix(175,114,-1334,-869) (-15/23,-13/20) -> (-5/38,-3/23) Hyperbolic Matrix(3481,2260,-8932,-5799) (-13/20,-37/57) -> (-23/59,-53/136) Hyperbolic Matrix(5279,3426,7598,4931) (-37/57,-24/37) -> (66/95,41/59) Hyperbolic Matrix(291,188,-986,-637) (-11/17,-9/14) -> (-13/44,-5/17) Hyperbolic Matrix(231,148,-1450,-929) (-25/39,-16/25) -> (-4/25,-3/19) Hyperbolic Matrix(2145,1372,-3538,-2263) (-16/25,-39/61) -> (-37/61,-20/33) Hyperbolic Matrix(1449,926,3538,2261) (-39/61,-23/36) -> (9/22,25/61) Hyperbolic Matrix(755,482,-2088,-1333) (-23/36,-7/11) -> (-17/47,-13/36) Hyperbolic Matrix(407,258,1740,1103) (-26/41,-19/30) -> (7/30,4/17) Hyperbolic Matrix(1507,954,3480,2203) (-19/30,-50/79) -> (16/37,13/30) Hyperbolic Matrix(4813,3046,6322,4001) (-50/79,-81/128) -> (35/46,16/21) Hyperbolic Matrix(5335,3376,9164,5799) (-81/128,-31/49) -> (39/67,7/12) Hyperbolic Matrix(117,74,1102,697) (-31/49,-43/68) -> (1/10,1/9) Hyperbolic Matrix(7481,4730,11832,7481) (-43/68,-55/87) -> (55/87,43/68) Hyperbolic Matrix(2089,1320,3306,2089) (-55/87,-12/19) -> (12/19,55/87) Hyperbolic Matrix(463,292,1102,695) (-12/19,-17/27) -> (13/31,8/19) Hyperbolic Matrix(407,256,-1566,-985) (-17/27,-22/35) -> (-6/23,-7/27) Hyperbolic Matrix(869,546,-2494,-1567) (-22/35,-27/43) -> (-15/43,-8/23) Hyperbolic Matrix(289,180,464,289) (-5/8,-18/29) -> (18/29,5/8) Hyperbolic Matrix(755,468,1218,755) (-18/29,-13/21) -> (13/21,18/29) Hyperbolic Matrix(4409,2728,5626,3481) (-13/21,-60/97) -> (76/97,29/37) Hyperbolic Matrix(2959,1830,7598,4699) (-60/97,-47/76) -> (7/18,30/77) Hyperbolic Matrix(4059,2510,5626,3479) (-47/76,-34/55) -> (44/61,13/18) Hyperbolic Matrix(929,574,-3190,-1971) (-34/55,-21/34) -> (-7/24,-16/55) Hyperbolic Matrix(347,214,-754,-465) (-21/34,-8/13) -> (-6/13,-11/24) Hyperbolic Matrix(231,142,1508,927) (-8/13,-43/70) -> (7/46,2/13) Hyperbolic Matrix(2957,1816,-9918,-6091) (-43/70,-35/57) -> (-17/57,-31/104) Hyperbolic Matrix(4349,2670,9918,6089) (-35/57,-62/101) -> (32/73,25/57) Hyperbolic Matrix(17979,11036,29290,17979) (-62/101,-89/145) -> (89/145,62/101) Hyperbolic Matrix(7831,4806,12760,7831) (-89/145,-27/44) -> (27/44,89/145) Hyperbolic Matrix(1797,1102,2552,1565) (-27/44,-19/31) -> (19/27,31/44) Hyperbolic Matrix(405,248,1798,1101) (-19/31,-30/49) -> (2/9,7/31) Hyperbolic Matrix(811,496,-2088,-1277) (-30/49,-11/18) -> (-7/18,-26/67) Hyperbolic Matrix(2899,1770,7598,4639) (-11/18,-47/77) -> (37/97,29/76) Hyperbolic Matrix(2435,1486,-10266,-6265) (-47/77,-36/59) -> (-14/59,-23/97) Hyperbolic Matrix(2669,1628,4756,2901) (-36/59,-25/41) -> (23/41,32/57) Hyperbolic Matrix(233,142,1334,813) (-25/41,-14/23) -> (4/23,3/17) Hyperbolic Matrix(579,352,1334,811) (-14/23,-17/28) -> (13/30,10/23) Hyperbolic Matrix(4813,2920,6786,4117) (-17/28,-37/61) -> (39/55,61/86) Hyperbolic Matrix(291,176,-2204,-1333) (-23/38,-3/5) -> (-7/53,-5/38) Hyperbolic Matrix(579,344,2146,1275) (-3/5,-19/32) -> (7/26,17/63) Hyperbolic Matrix(1449,860,-3422,-2031) (-19/32,-16/27) -> (-36/85,-11/26) Hyperbolic Matrix(987,584,1276,755) (-16/27,-13/22) -> (17/22,24/31) Hyperbolic Matrix(1277,754,3538,2089) (-13/22,-36/61) -> (22/61,13/36) Hyperbolic Matrix(1683,992,-7772,-4581) (-23/39,-33/56) -> (-13/60,-21/97) Hyperbolic Matrix(2377,1400,3248,1913) (-33/56,-10/17) -> (30/41,41/56) Hyperbolic Matrix(579,340,986,579) (-10/17,-17/29) -> (17/29,10/17) Hyperbolic Matrix(407,238,696,407) (-17/29,-7/12) -> (7/12,17/29) Hyperbolic Matrix(5799,3376,9164,5335) (-7/12,-39/67) -> (31/49,81/128) Hyperbolic Matrix(2725,1586,-10266,-5975) (-39/67,-32/55) -> (-30/113,-13/49) Hyperbolic Matrix(3597,2092,4988,2901) (-32/55,-25/43) -> (31/43,44/61) Hyperbolic Matrix(3421,1988,-6090,-3539) (-25/43,-43/74) -> (-9/16,-41/73) Hyperbolic Matrix(407,236,1102,639) (-18/31,-11/19) -> (7/19,10/27) Hyperbolic Matrix(173,100,1102,637) (-11/19,-26/45) -> (2/13,3/19) Hyperbolic Matrix(1275,736,-3016,-1741) (-26/45,-15/26) -> (-11/26,-30/71) Hyperbolic Matrix(115,66,-406,-233) (-15/26,-4/7) -> (-2/7,-9/32) Hyperbolic Matrix(1683,956,2146,1219) (-4/7,-21/37) -> (29/37,40/51) Hyperbolic Matrix(1277,724,3480,1973) (-21/37,-17/30) -> (11/30,29/79) Hyperbolic Matrix(523,296,1334,755) (-17/30,-13/23) -> (9/23,11/28) Hyperbolic Matrix(985,556,1334,753) (-13/23,-22/39) -> (14/19,17/23) Hyperbolic Matrix(291,164,928,523) (-22/39,-9/16) -> (5/16,6/19) Hyperbolic Matrix(3829,2150,9918,5569) (-41/73,-32/57) -> (22/57,39/101) Hyperbolic Matrix(2901,1628,4756,2669) (-32/57,-23/41) -> (25/41,36/59) Hyperbolic Matrix(1277,716,1450,813) (-23/41,-37/66) -> (7/8,15/17) Hyperbolic Matrix(3365,1886,-7656,-4291) (-37/66,-14/25) -> (-40/91,-29/66) Hyperbolic Matrix(2087,1168,2900,1623) (-14/25,-33/59) -> (41/57,18/25) Hyperbolic Matrix(1681,940,-7366,-4119) (-33/59,-19/34) -> (-21/92,-13/57) Hyperbolic Matrix(523,292,-1972,-1101) (-19/34,-5/9) -> (-13/49,-9/34) Hyperbolic Matrix(289,160,522,289) (-5/9,-16/29) -> (16/29,5/9) Hyperbolic Matrix(639,352,1160,639) (-16/29,-11/20) -> (11/20,16/29) Hyperbolic Matrix(521,286,-1798,-987) (-11/20,-17/31) -> (-9/31,-11/38) Hyperbolic Matrix(117,64,638,349) (-17/31,-6/11) -> (2/11,5/27) Hyperbolic Matrix(289,156,-754,-407) (-6/11,-7/13) -> (-5/13,-18/47) Hyperbolic Matrix(175,94,-754,-405) (-7/13,-8/15) -> (-10/43,-3/13) Hyperbolic Matrix(233,124,-870,-463) (-8/15,-1/2) -> (-15/56,-4/15) Hyperbolic Matrix(581,274,986,465) (-1/2,-8/17) -> (10/17,33/56) Hyperbolic Matrix(581,270,-2494,-1159) (-7/15,-13/28) -> (-7/30,-17/73) Hyperbolic Matrix(927,424,-4060,-1857) (-11/24,-16/35) -> (-8/35,-21/92) Hyperbolic Matrix(5395,2464,-14094,-6437) (-16/35,-21/46) -> (-49/128,-80/209) Hyperbolic Matrix(57,26,-638,-291) (-21/46,-5/11) -> (-1/11,-1/12) Hyperbolic Matrix(521,236,638,289) (-5/11,-14/31) -> (22/27,9/11) Hyperbolic Matrix(173,78,-1160,-523) (-14/31,-9/20) -> (-3/20,-4/27) Hyperbolic Matrix(521,234,1160,521) (-9/20,-13/29) -> (13/29,9/20) Hyperbolic Matrix(233,104,522,233) (-13/29,-4/9) -> (4/9,13/29) Hyperbolic Matrix(1915,848,-4582,-2029) (-4/9,-23/52) -> (-51/122,-28/67) Hyperbolic Matrix(5627,2488,8004,3539) (-23/52,-19/43) -> (71/101,45/64) Hyperbolic Matrix(2087,920,-6844,-3017) (-15/34,-26/59) -> (-18/59,-25/82) Hyperbolic Matrix(1971,868,3422,1507) (-26/59,-11/25) -> (19/33,34/59) Hyperbolic Matrix(7541,3316,13456,5917) (-11/25,-51/116) -> (65/116,51/91) Hyperbolic Matrix(7539,3314,13456,5915) (-51/116,-40/91) -> (14/25,65/116) Hyperbolic Matrix(173,76,1450,637) (-29/66,-18/41) -> (2/17,1/8) Hyperbolic Matrix(1855,814,4756,2087) (-18/41,-25/57) -> (23/59,16/41) Hyperbolic Matrix(347,152,-1856,-813) (-25/57,-7/16) -> (-3/16,-11/59) Hyperbolic Matrix(637,278,928,405) (-7/16,-17/39) -> (13/19,11/16) Hyperbolic Matrix(349,152,1334,581) (-17/39,-10/23) -> (6/23,5/19) Hyperbolic Matrix(811,352,1334,579) (-10/23,-13/30) -> (17/28,14/23) Hyperbolic Matrix(2203,954,3480,1507) (-13/30,-16/37) -> (50/79,19/30) Hyperbolic Matrix(463,200,2146,927) (-16/37,-3/7) -> (11/51,8/37) Hyperbolic Matrix(1915,812,3422,1451) (-14/33,-25/59) -> (33/59,14/25) Hyperbolic Matrix(9571,4054,-25056,-10613) (-25/59,-36/85) -> (-34/89,-89/233) Hyperbolic Matrix(7773,3284,13456,5685) (-30/71,-49/116) -> (67/116,26/45) Hyperbolic Matrix(7771,3282,13456,5683) (-49/116,-19/45) -> (41/71,67/116) Hyperbolic Matrix(929,392,1102,465) (-19/45,-8/19) -> (16/19,11/13) Hyperbolic Matrix(695,292,1102,463) (-8/19,-13/31) -> (17/27,12/19) Hyperbolic Matrix(463,194,-2494,-1045) (-13/31,-18/43) -> (-8/43,-5/27) Hyperbolic Matrix(1391,582,4988,2087) (-18/43,-23/55) -> (17/61,12/43) Hyperbolic Matrix(6669,2788,-25114,-10499) (-23/55,-51/122) -> (-17/64,-47/177) Hyperbolic Matrix(3365,1406,9164,3829) (-28/67,-5/12) -> (47/128,18/49) Hyperbolic Matrix(289,120,696,289) (-5/12,-12/29) -> (12/29,5/12) Hyperbolic Matrix(407,168,986,407) (-12/29,-7/17) -> (7/17,12/29) Hyperbolic Matrix(521,214,986,405) (-7/17,-23/56) -> (1/2,9/17) Hyperbolic Matrix(6207,2548,10034,4119) (-39/95,-16/39) -> (60/97,13/21) Hyperbolic Matrix(405,166,-1276,-523) (-16/39,-9/22) -> (-7/22,-6/19) Hyperbolic Matrix(289,118,1276,521) (-9/22,-11/27) -> (7/31,5/22) Hyperbolic Matrix(1043,424,-3712,-1509) (-11/27,-13/32) -> (-9/32,-25/89) Hyperbolic Matrix(233,94,290,117) (-13/32,-2/5) -> (4/5,21/26) Hyperbolic Matrix(289,114,-1914,-755) (-2/5,-13/33) -> (-5/33,-8/53) Hyperbolic Matrix(1275,502,-3538,-1393) (-13/33,-11/28) -> (-31/86,-9/25) Hyperbolic Matrix(755,296,1334,523) (-11/28,-9/23) -> (13/23,17/30) Hyperbolic Matrix(1101,430,1334,521) (-9/23,-16/41) -> (14/17,19/23) Hyperbolic Matrix(2087,814,4756,1855) (-16/41,-23/59) -> (25/57,18/41) Hyperbolic Matrix(5045,1966,-21286,-8295) (-53/136,-30/77) -> (-32/135,-9/38) Hyperbolic Matrix(4699,1830,7598,2959) (-30/77,-7/18) -> (47/76,60/97) Hyperbolic Matrix(8237,3196,13456,5221) (-26/67,-45/116) -> (71/116,30/49) Hyperbolic Matrix(8235,3194,13456,5219) (-45/116,-19/49) -> (41/67,71/116) Hyperbolic Matrix(1393,540,1798,697) (-19/49,-12/31) -> (24/31,7/9) Hyperbolic Matrix(1159,448,1798,695) (-12/31,-17/44) -> (9/14,20/31) Hyperbolic Matrix(4929,1904,12760,4929) (-17/44,-56/145) -> (56/145,17/44) Hyperbolic Matrix(11311,4368,29290,11311) (-56/145,-39/101) -> (39/101,56/145) Hyperbolic Matrix(6843,2642,8410,3247) (-39/101,-22/57) -> (48/59,35/43) Hyperbolic Matrix(57,22,-754,-291) (-22/57,-27/70) -> (-1/12,0/1) Hyperbolic Matrix(1277,492,1508,581) (-27/70,-5/13) -> (11/13,39/46) Hyperbolic Matrix(3249,1244,-10904,-4175) (-18/47,-49/128) -> (-31/104,-14/47) Hyperbolic Matrix(51911,19870,84100,32191) (-80/209,-111/290) -> (179/290,50/81) Hyperbolic Matrix(51909,19868,84100,32189) (-111/290,-31/81) -> (129/209,179/290) Hyperbolic Matrix(2263,866,-7424,-2841) (-31/81,-13/34) -> (-25/82,-7/23) Hyperbolic Matrix(49475,18898,68788,26275) (-89/233,-144/377) -> (146/203,41/57) Hyperbolic Matrix(60609,23150,84274,32189) (-144/377,-55/144) -> (105/146,146/203) Hyperbolic Matrix(8641,3300,13514,5161) (-55/144,-21/55) -> (39/61,55/86) Hyperbolic Matrix(1567,598,5626,2147) (-21/55,-29/76) -> (5/18,17/61) Hyperbolic Matrix(4639,1770,7598,2899) (-29/76,-37/97) -> (47/77,11/18) Hyperbolic Matrix(5915,2256,10034,3827) (-37/97,-8/21) -> (56/95,23/39) Hyperbolic Matrix(463,176,1218,463) (-8/21,-11/29) -> (11/29,8/21) Hyperbolic Matrix(175,66,464,175) (-11/29,-3/8) -> (3/8,11/29) Hyperbolic Matrix(59,22,-464,-173) (-3/8,-13/35) -> (-3/23,-1/8) Hyperbolic Matrix(523,194,-2030,-753) (-23/62,-10/27) -> (-8/31,-1/4) Hyperbolic Matrix(639,236,1102,407) (-10/27,-7/19) -> (11/19,18/31) Hyperbolic Matrix(1217,448,3306,1217) (-7/19,-32/87) -> (32/87,7/19) Hyperbolic Matrix(4351,1600,11832,4351) (-32/87,-25/68) -> (25/68,32/87) Hyperbolic Matrix(985,362,1102,405) (-25/68,-18/49) -> (8/9,9/10) Hyperbolic Matrix(3829,1406,9164,3365) (-18/49,-47/128) -> (5/12,28/67) Hyperbolic Matrix(1509,554,6322,2321) (-47/128,-29/79) -> (5/21,11/46) Hyperbolic Matrix(1973,724,3480,1277) (-29/79,-11/30) -> (17/30,21/37) Hyperbolic Matrix(115,42,-638,-233) (-11/30,-4/11) -> (-2/11,-5/28) Hyperbolic Matrix(2147,778,3364,1219) (-4/11,-21/58) -> (37/58,30/47) Hyperbolic Matrix(2145,776,3364,1217) (-21/58,-17/47) -> (7/11,37/58) Hyperbolic Matrix(987,356,1450,523) (-13/36,-22/61) -> (2/3,15/22) Hyperbolic Matrix(8353,3012,13514,4873) (-22/61,-31/86) -> (89/144,34/55) Hyperbolic Matrix(173,62,-812,-291) (-9/25,-5/14) -> (-3/14,-7/33) Hyperbolic Matrix(1103,392,1798,639) (-5/14,-11/31) -> (19/31,27/44) Hyperbolic Matrix(233,82,-986,-347) (-6/17,-7/20) -> (-9/38,-4/17) Hyperbolic Matrix(349,122,-2320,-811) (-7/20,-15/43) -> (-11/73,-3/20) Hyperbolic Matrix(1043,362,1334,463) (-8/23,-1/3) -> (43/55,18/23) Hyperbolic Matrix(927,296,1450,463) (-1/3,-7/22) -> (23/36,39/61) Hyperbolic Matrix(523,164,928,291) (-6/19,-5/16) -> (9/16,22/39) Hyperbolic Matrix(289,90,928,289) (-5/16,-9/29) -> (9/29,5/16) Hyperbolic Matrix(233,72,754,233) (-9/29,-4/13) -> (4/13,9/29) Hyperbolic Matrix(465,142,3422,1045) (-11/36,-29/95) -> (5/37,3/22) Hyperbolic Matrix(2667,814,7598,2319) (-29/95,-18/59) -> (20/57,13/37) Hyperbolic Matrix(579,176,2668,811) (-7/23,-17/56) -> (13/60,5/23) Hyperbolic Matrix(4929,1496,16240,4929) (-17/56,-44/145) -> (44/145,17/56) Hyperbolic Matrix(7831,2376,25810,7831) (-44/145,-27/89) -> (27/89,44/145) Hyperbolic Matrix(4525,1372,5742,1741) (-27/89,-10/33) -> (26/33,67/85) Hyperbolic Matrix(927,280,-6148,-1857) (-13/43,-16/53) -> (-8/53,-11/73) Hyperbolic Matrix(1507,454,-5394,-1625) (-16/53,-3/10) -> (-19/68,-50/179) Hyperbolic Matrix(579,172,4292,1275) (-11/37,-30/101) -> (2/15,5/37) Hyperbolic Matrix(4465,1326,8004,2377) (-30/101,-19/64) -> (29/52,24/43) Hyperbolic Matrix(1449,430,-6844,-2031) (-19/64,-8/27) -> (-18/85,-11/52) Hyperbolic Matrix(987,292,2552,755) (-8/27,-13/44) -> (17/44,12/31) Hyperbolic Matrix(2379,698,3364,987) (-5/17,-17/58) -> (41/58,29/41) Hyperbolic Matrix(2377,696,3364,985) (-17/58,-12/41) -> (12/17,41/58) Hyperbolic Matrix(2669,776,6786,1973) (-16/55,-25/86) -> (11/28,24/61) Hyperbolic Matrix(3421,994,-12180,-3539) (-25/86,-9/31) -> (-25/89,-41/146) Hyperbolic Matrix(52085,14626,84274,23665) (-41/146,-57/203) -> (233/377,89/144) Hyperbolic Matrix(42513,11936,68788,19313) (-57/203,-16/57) -> (144/233,233/377) Hyperbolic Matrix(1277,358,2900,813) (-16/57,-7/25) -> (11/25,26/59) Hyperbolic Matrix(60611,16930,84100,23491) (-50/179,-81/290) -> (209/290,80/111) Hyperbolic Matrix(60609,16928,84100,23489) (-81/290,-31/111) -> (129/179,209/290) Hyperbolic Matrix(523,146,-3944,-1101) (-31/111,-12/43) -> (-2/15,-7/53) Hyperbolic Matrix(2087,582,4988,1391) (-12/43,-17/61) -> (23/55,18/43) Hyperbolic Matrix(2147,598,5626,1567) (-17/61,-5/18) -> (29/76,21/55) Hyperbolic Matrix(289,80,1044,289) (-5/18,-8/29) -> (8/29,5/18) Hyperbolic Matrix(175,48,638,175) (-8/29,-3/11) -> (3/11,8/29) Hyperbolic Matrix(59,16,-638,-173) (-3/11,-13/48) -> (-1/10,-1/11) Hyperbolic Matrix(289,78,-1508,-407) (-10/37,-7/26) -> (-5/26,-4/21) Hyperbolic Matrix(521,140,-2378,-639) (-7/26,-11/41) -> (-9/41,-7/32) Hyperbolic Matrix(1335,358,3248,871) (-11/41,-15/56) -> (23/56,7/17) Hyperbolic Matrix(2205,586,7424,1973) (-4/15,-17/64) -> (19/64,30/101) Hyperbolic Matrix(61771,16402,84100,22331) (-47/177,-77/290) -> (213/290,83/113) Hyperbolic Matrix(61769,16400,84100,22329) (-77/290,-30/113) -> (130/177,213/290) Hyperbolic Matrix(871,230,1102,291) (-9/34,-5/19) -> (15/19,19/24) Hyperbolic Matrix(581,152,1334,349) (-5/19,-6/23) -> (10/23,17/39) Hyperbolic Matrix(2495,646,3364,871) (-7/27,-15/58) -> (43/58,23/31) Hyperbolic Matrix(2493,644,3364,869) (-15/58,-8/31) -> (20/27,43/58) Hyperbolic Matrix(57,14,232,57) (-1/4,-7/29) -> (7/29,1/4) Hyperbolic Matrix(349,84,1450,349) (-7/29,-6/25) -> (6/25,7/29) Hyperbolic Matrix(2263,542,2668,639) (-6/25,-11/46) -> (39/46,28/33) Hyperbolic Matrix(2321,554,6322,1509) (-11/46,-5/21) -> (29/79,47/128) Hyperbolic Matrix(4523,1074,5858,1391) (-5/21,-14/59) -> (44/57,61/79) Hyperbolic Matrix(41065,9736,53824,12761) (-23/97,-55/232) -> (177/232,103/135) Hyperbolic Matrix(41063,9734,53824,12759) (-55/232,-32/135) -> (74/97,177/232) Hyperbolic Matrix(811,190,986,231) (-4/17,-7/30) -> (23/28,14/17) Hyperbolic Matrix(10325,2404,13456,3133) (-17/73,-27/116) -> (89/116,33/43) Hyperbolic Matrix(10323,2402,13456,3131) (-27/116,-10/43) -> (56/73,89/116) Hyperbolic Matrix(4467,1018,5858,1335) (-13/57,-18/79) -> (16/21,45/59) Hyperbolic Matrix(2205,502,2552,581) (-18/79,-5/22) -> (19/22,32/37) Hyperbolic Matrix(521,118,1276,289) (-5/22,-7/31) -> (11/27,9/22) Hyperbolic Matrix(1101,248,1798,405) (-7/31,-2/9) -> (30/49,19/31) Hyperbolic Matrix(463,102,522,115) (-2/9,-9/41) -> (15/17,8/9) Hyperbolic Matrix(1217,266,5568,1217) (-7/32,-19/87) -> (19/87,7/32) Hyperbolic Matrix(2089,456,9570,2089) (-19/87,-12/55) -> (12/55,19/87) Hyperbolic Matrix(871,190,1334,291) (-12/55,-5/23) -> (15/23,2/3) Hyperbolic Matrix(811,176,2668,579) (-5/23,-13/60) -> (17/56,7/23) Hyperbolic Matrix(2145,464,5626,1217) (-21/97,-8/37) -> (8/21,37/97) Hyperbolic Matrix(927,200,2146,463) (-8/37,-11/51) -> (3/7,16/37) Hyperbolic Matrix(10557,2276,13456,2901) (-11/51,-25/116) -> (91/116,51/65) Hyperbolic Matrix(10555,2274,13456,2899) (-25/116,-14/65) -> (40/51,91/116) Hyperbolic Matrix(4001,848,5742,1217) (-7/33,-18/85) -> (62/89,23/33) Hyperbolic Matrix(811,170,1102,231) (-4/19,-5/24) -> (25/34,14/19) Hyperbolic Matrix(289,60,1392,289) (-5/24,-6/29) -> (6/29,5/24) Hyperbolic Matrix(59,12,290,59) (-6/29,-1/5) -> (1/5,6/29) Hyperbolic Matrix(173,34,290,57) (-1/5,-5/26) -> (19/32,3/5) Hyperbolic Matrix(2727,518,3364,639) (-4/21,-11/58) -> (47/58,30/37) Hyperbolic Matrix(2725,516,3364,637) (-11/58,-7/37) -> (17/21,47/58) Hyperbolic Matrix(5163,962,8410,1567) (-11/59,-8/43) -> (62/101,35/57) Hyperbolic Matrix(349,64,638,117) (-5/27,-2/11) -> (6/11,17/31) Hyperbolic Matrix(755,134,986,175) (-5/28,-3/17) -> (13/17,23/30) Hyperbolic Matrix(813,142,1334,233) (-3/17,-4/23) -> (14/23,25/41) Hyperbolic Matrix(231,40,1334,231) (-4/23,-5/29) -> (5/29,4/23) Hyperbolic Matrix(59,10,348,59) (-5/29,-1/6) -> (1/6,5/29) Hyperbolic Matrix(985,158,3248,521) (-5/31,-4/25) -> (10/33,27/89) Hyperbolic Matrix(637,100,1102,173) (-3/19,-2/13) -> (26/45,11/19) Hyperbolic Matrix(927,142,1508,231) (-2/13,-7/46) -> (43/70,8/13) Hyperbolic Matrix(2029,308,2668,405) (-7/46,-5/33) -> (19/25,35/46) Hyperbolic Matrix(57,8,406,57) (-1/7,-4/29) -> (4/29,1/7) Hyperbolic Matrix(175,24,1276,175) (-4/29,-3/22) -> (3/22,4/29) Hyperbolic Matrix(1971,268,2552,347) (-3/22,-5/37) -> (61/79,17/22) Hyperbolic Matrix(1275,172,4292,579) (-5/37,-2/15) -> (30/101,11/37) Hyperbolic Matrix(637,76,1450,173) (-1/8,-2/17) -> (18/41,29/66) Hyperbolic Matrix(407,46,522,59) (-2/17,-1/9) -> (7/9,32/41) Hyperbolic Matrix(697,74,1102,117) (-1/9,-1/10) -> (43/68,31/49) Hyperbolic Matrix(407,-40,580,-57) (0/1,1/10) -> (7/10,40/57) Hyperbolic Matrix(173,-22,464,-59) (1/8,2/15) -> (16/43,3/8) Hyperbolic Matrix(289,-42,406,-59) (1/7,3/20) -> (27/38,5/7) Hyperbolic Matrix(755,-114,1914,-289) (3/20,5/33) -> (13/33,15/38) Hyperbolic Matrix(869,-138,1102,-175) (3/19,1/6) -> (41/52,15/19) Hyperbolic Matrix(233,-42,638,-115) (3/17,2/11) -> (4/11,15/41) Hyperbolic Matrix(1045,-194,2494,-463) (5/27,3/16) -> (31/74,13/31) Hyperbolic Matrix(753,-142,928,-175) (3/16,4/21) -> (30/37,13/16) Hyperbolic Matrix(407,-78,1508,-289) (4/21,1/5) -> (17/63,10/37) Hyperbolic Matrix(291,-62,812,-173) (4/19,3/14) -> (5/14,14/39) Hyperbolic Matrix(1275,-274,1624,-349) (3/14,11/51) -> (51/65,11/14) Hyperbolic Matrix(4581,-992,7772,-1683) (8/37,13/60) -> (33/56,56/95) Hyperbolic Matrix(639,-140,2378,-521) (7/32,2/9) -> (18/67,7/26) Hyperbolic Matrix(523,-120,754,-173) (5/22,3/13) -> (9/13,25/36) Hyperbolic Matrix(405,-94,754,-175) (3/13,7/30) -> (15/28,7/13) Hyperbolic Matrix(347,-82,986,-233) (4/17,5/21) -> (13/37,6/17) Hyperbolic Matrix(985,-256,1566,-407) (1/4,6/23) -> (22/35,39/62) Hyperbolic Matrix(1101,-292,1972,-523) (9/34,4/15) -> (24/43,19/34) Hyperbolic Matrix(463,-124,870,-233) (4/15,11/41) -> (9/17,8/15) Hyperbolic Matrix(1507,-408,2146,-581) (10/37,3/11) -> (33/47,26/37) Hyperbolic Matrix(1739,-486,2494,-697) (12/43,7/25) -> (23/33,30/43) Hyperbolic Matrix(233,-66,406,-115) (7/25,2/7) -> (4/7,19/33) Hyperbolic Matrix(347,-100,406,-117) (2/7,9/31) -> (23/27,6/7) Hyperbolic Matrix(1971,-574,3190,-929) (9/31,7/24) -> (21/34,55/89) Hyperbolic Matrix(985,-288,1392,-407) (7/24,5/17) -> (29/41,17/24) Hyperbolic Matrix(637,-188,986,-291) (5/17,8/27) -> (20/31,11/17) Hyperbolic Matrix(1799,-534,2146,-637) (8/27,19/64) -> (5/6,26/31) Hyperbolic Matrix(1565,-466,2146,-639) (11/37,3/10) -> (35/48,27/37) Hyperbolic Matrix(1797,-544,2494,-755) (3/10,10/33) -> (18/25,49/68) Hyperbolic Matrix(581,-178,754,-231) (7/23,4/13) -> (10/13,27/35) Hyperbolic Matrix(523,-166,1276,-405) (6/19,1/3) -> (25/61,16/39) Hyperbolic Matrix(1159,-404,1334,-465) (8/23,7/20) -> (33/38,20/23) Hyperbolic Matrix(5451,-1912,8932,-3133) (7/20,20/57) -> (36/59,83/136) Hyperbolic Matrix(695,-246,986,-349) (6/17,5/14) -> (31/44,12/17) Hyperbolic Matrix(1219,-438,1450,-521) (14/39,9/25) -> (21/25,16/19) Hyperbolic Matrix(1393,-502,3538,-1275) (9/25,22/61) -> (24/61,13/33) Hyperbolic Matrix(1333,-482,2088,-755) (13/36,4/11) -> (30/47,23/36) Hyperbolic Matrix(1159,-430,1566,-581) (10/27,13/35) -> (17/23,20/27) Hyperbolic Matrix(1625,-604,2494,-927) (13/35,16/43) -> (28/43,15/23) Hyperbolic Matrix(2261,-864,3190,-1219) (21/55,13/34) -> (17/24,39/55) Hyperbolic Matrix(407,-156,754,-289) (13/34,5/13) -> (7/13,13/24) Hyperbolic Matrix(6961,-2686,9918,-3827) (27/70,22/57) -> (40/57,73/104) Hyperbolic Matrix(1277,-496,2088,-811) (19/49,7/18) -> (11/18,41/67) Hyperbolic Matrix(7831,-3052,10266,-4001) (30/77,23/59) -> (45/59,74/97) Hyperbolic Matrix(1913,-756,2204,-871) (15/38,2/5) -> (46/53,33/38) Hyperbolic Matrix(1973,-802,3422,-1391) (13/32,11/27) -> (49/85,15/26) Hyperbolic Matrix(6089,-2500,7772,-3191) (16/39,23/56) -> (47/60,76/97) Hyperbolic Matrix(7541,-3152,10266,-4291) (28/67,23/55) -> (83/113,36/49) Hyperbolic Matrix(2669,-1118,6090,-2551) (18/43,31/74) -> (7/16,32/73) Hyperbolic Matrix(1741,-736,3016,-1275) (19/45,11/26) -> (15/26,41/71) Hyperbolic Matrix(291,-124,406,-173) (11/26,3/7) -> (5/7,23/32) Hyperbolic Matrix(4291,-1886,7656,-3365) (29/66,11/25) -> (51/91,37/66) Hyperbolic Matrix(5685,-2506,7366,-3247) (26/59,15/34) -> (71/92,44/57) Hyperbolic Matrix(1449,-640,1972,-871) (15/34,4/9) -> (36/49,25/34) Hyperbolic Matrix(1277,-576,1798,-811) (9/20,14/31) -> (22/31,27/38) Hyperbolic Matrix(465,-214,754,-347) (5/11,6/13) -> (8/13,29/47) Hyperbolic Matrix(579,-268,754,-349) (6/13,7/15) -> (33/43,10/13) Hyperbolic Matrix(637,-298,870,-407) (7/15,1/2) -> (41/56,11/15) Hyperbolic Matrix(1913,-1024,2494,-1335) (8/15,15/28) -> (23/30,56/73) Hyperbolic Matrix(3133,-1700,4060,-2203) (13/24,19/35) -> (27/35,71/92) Hyperbolic Matrix(8699,-4726,14094,-7657) (19/35,25/46) -> (79/128,129/209) Hyperbolic Matrix(581,-316,638,-347) (25/46,6/11) -> (10/11,11/12) Hyperbolic Matrix(987,-542,1160,-637) (17/31,11/20) -> (17/20,23/27) Hyperbolic Matrix(2667,-1486,4582,-2553) (5/9,29/52) -> (71/122,39/67) Hyperbolic Matrix(4757,-2660,6844,-3827) (19/34,33/59) -> (41/59,57/82) Hyperbolic Matrix(1509,-848,1856,-1043) (32/57,9/16) -> (13/16,48/59) Hyperbolic Matrix(15485,-8926,25056,-14443) (34/59,49/85) -> (55/89,144/233) Hyperbolic Matrix(2031,-1180,2494,-1449) (18/31,25/43) -> (35/43,22/27) Hyperbolic Matrix(18445,-10734,25114,-14615) (32/55,71/122) -> (47/64,130/177) Hyperbolic Matrix(871,-514,1276,-753) (23/39,13/22) -> (15/22,13/19) Hyperbolic Matrix(2669,-1584,3712,-2203) (16/27,19/32) -> (23/32,64/89) Hyperbolic Matrix(1625,-984,1914,-1159) (3/5,20/33) -> (28/33,45/53) Hyperbolic Matrix(2263,-1372,3538,-2145) (20/33,17/28) -> (55/86,16/25) Hyperbolic Matrix(16241,-9912,21286,-12991) (83/136,47/77) -> (103/135,29/38) Hyperbolic Matrix(697,-428,754,-463) (35/57,43/70) -> (11/12,1/1) Hyperbolic Matrix(7655,-4724,10904,-6729) (29/47,79/128) -> (73/104,33/47) Hyperbolic Matrix(5161,-3186,7424,-4583) (50/81,21/34) -> (57/82,16/23) Hyperbolic Matrix(405,-254,464,-291) (5/8,22/35) -> (20/23,7/8) Hyperbolic Matrix(1507,-948,2030,-1277) (39/62,17/27) -> (23/31,3/4) Hyperbolic Matrix(523,-332,638,-405) (19/30,7/11) -> (9/11,23/28) Hyperbolic Matrix(639,-410,812,-521) (16/25,9/14) -> (11/14,26/33) Hyperbolic Matrix(753,-488,986,-639) (11/17,13/20) -> (29/38,13/17) Hyperbolic Matrix(1971,-1282,2320,-1509) (13/20,28/43) -> (62/73,17/20) Hyperbolic Matrix(5221,-3644,6148,-4291) (30/43,37/53) -> (45/53,62/73) Hyperbolic Matrix(3887,-2716,5394,-3769) (37/53,7/10) -> (49/68,129/179) Hyperbolic Matrix(5395,-3794,6844,-4813) (45/64,19/27) -> (67/85,41/52) Hyperbolic Matrix(8759,-6214,12180,-8641) (61/86,22/31) -> (64/89,105/146) Hyperbolic Matrix(3421,-2466,3944,-2843) (80/111,31/43) -> (13/15,46/53) Hyperbolic Matrix(579,-422,638,-465) (8/11,35/48) -> (9/10,10/11) Hyperbolic Matrix(1219,-890,1508,-1101) (27/37,19/26) -> (21/26,17/21) Hyperbolic Matrix(1857,-1358,2378,-1739) (19/26,30/41) -> (32/41,25/32) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(173,156,-580,-523) -> Matrix(7,-2,4,-1) Matrix(405,362,1102,985) -> Matrix(1,0,-2,1) Matrix(405,358,1508,1333) -> Matrix(3,-2,2,-1) Matrix(813,716,1450,1277) -> Matrix(1,0,0,1) Matrix(291,254,-464,-405) -> Matrix(1,0,2,1) Matrix(3017,2610,4292,3713) -> Matrix(1,0,2,1) Matrix(2377,2054,3422,2957) -> Matrix(15,2,-38,-5) Matrix(1101,950,1276,1101) -> Matrix(1,0,22,1) Matrix(349,300,406,349) -> Matrix(1,0,-12,1) Matrix(117,100,-406,-347) -> Matrix(7,-2,4,-1) Matrix(1159,984,-1914,-1625) -> Matrix(5,-2,8,-3) Matrix(639,542,2668,2263) -> Matrix(17,-6,-14,5) Matrix(581,492,1508,1277) -> Matrix(3,-2,-4,3) Matrix(465,392,1102,929) -> Matrix(9,-2,-4,1) Matrix(233,196,-1102,-927) -> Matrix(23,-6,4,-1) Matrix(289,240,348,289) -> Matrix(5,-2,-12,5) Matrix(1103,912,1334,1103) -> Matrix(15,-8,-28,15) Matrix(521,430,1334,1101) -> Matrix(3,-2,2,-1) Matrix(405,332,-638,-523) -> Matrix(1,0,0,1) Matrix(289,236,638,521) -> Matrix(3,-2,-4,3) Matrix(1449,1180,-2494,-2031) -> Matrix(1,-2,0,1) Matrix(175,142,-928,-753) -> Matrix(1,0,2,1) Matrix(1101,890,-1508,-1219) -> Matrix(1,0,-2,1) Matrix(231,184,290,231) -> Matrix(1,0,0,1) Matrix(1103,874,1392,1103) -> Matrix(1,0,-22,1) Matrix(291,230,1102,871) -> Matrix(1,0,-6,1) Matrix(521,410,-812,-639) -> Matrix(9,-2,14,-3) Matrix(349,274,-1624,-1275) -> Matrix(33,-10,10,-3) Matrix(1219,956,2146,1683) -> Matrix(11,-4,-8,3) Matrix(3191,2500,-7772,-6089) -> Matrix(1,0,-4,1) Matrix(1857,1454,2668,2089) -> Matrix(11,-4,-30,11) Matrix(463,362,1334,1043) -> Matrix(13,-6,-2,1) Matrix(7481,5848,9570,7481) -> Matrix(25,-12,-52,25) Matrix(4351,3400,5568,4351) -> Matrix(11,-6,-20,11) Matrix(1739,1358,-2378,-1857) -> Matrix(3,-2,2,-1) Matrix(697,540,1798,1393) -> Matrix(1,0,-8,1) Matrix(755,584,1276,987) -> Matrix(11,-2,-16,3) Matrix(231,178,-754,-581) -> Matrix(13,-4,10,-3) Matrix(349,268,-754,-579) -> Matrix(7,-2,4,-1) Matrix(637,488,1740,1333) -> Matrix(11,-4,-8,3) Matrix(639,488,-986,-753) -> Matrix(5,-2,8,-3) Matrix(4001,3046,6322,4813) -> Matrix(9,-4,-2,1) Matrix(405,308,2668,2029) -> Matrix(49,-22,-20,9) Matrix(1101,836,1450,1101) -> Matrix(25,-12,-52,25) Matrix(175,132,232,175) -> Matrix(3,-2,-4,3) Matrix(581,430,-1566,-1159) -> Matrix(11,-2,6,-1) Matrix(753,556,1334,985) -> Matrix(1,0,-4,1) Matrix(231,170,1102,811) -> Matrix(17,-8,-2,1) Matrix(871,640,-1972,-1449) -> Matrix(17,-10,12,-7) Matrix(407,298,-870,-637) -> Matrix(1,-2,2,-3) Matrix(175,128,1508,1103) -> Matrix(1,-2,0,1) Matrix(871,636,2146,1567) -> Matrix(1,0,0,1) Matrix(639,466,-2146,-1565) -> Matrix(3,-2,2,-1) Matrix(463,336,638,463) -> Matrix(1,0,0,1) Matrix(755,546,1044,755) -> Matrix(1,0,-10,1) Matrix(3479,2510,5626,4059) -> Matrix(15,-4,-26,7) Matrix(2901,2092,4988,3597) -> Matrix(9,-2,-4,1) Matrix(755,544,-2494,-1797) -> Matrix(7,-2,4,-1) Matrix(173,124,-406,-291) -> Matrix(7,-2,4,-1) Matrix(59,42,-406,-289) -> Matrix(7,-4,2,-1) Matrix(1219,864,-3190,-2261) -> Matrix(3,-4,4,-5) Matrix(407,288,-1392,-985) -> Matrix(1,2,0,1) Matrix(349,246,-986,-695) -> Matrix(3,-2,2,-1) Matrix(347,244,-2146,-1509) -> Matrix(7,-2,4,-1) Matrix(5451,3832,7424,5219) -> Matrix(3,-2,-4,3) Matrix(3713,2610,4292,3017) -> Matrix(1,0,2,1) Matrix(581,408,-2146,-1507) -> Matrix(9,-2,-4,1) Matrix(697,486,-2494,-1739) -> Matrix(7,-4,2,-1) Matrix(2727,1900,3248,2263) -> Matrix(7,-2,-24,7) Matrix(17979,12524,25810,17979) -> Matrix(43,-14,-132,43) Matrix(11311,7878,16240,11311) -> Matrix(35,-12,-102,35) Matrix(2089,1454,2668,1857) -> Matrix(11,-4,-30,11) Matrix(173,120,-754,-523) -> Matrix(19,-8,12,-5) Matrix(521,360,754,521) -> Matrix(17,-8,-36,17) Matrix(639,440,928,639) -> Matrix(19,-10,-36,19) Matrix(405,278,928,637) -> Matrix(3,-2,2,-1) Matrix(753,514,-1276,-871) -> Matrix(1,-2,2,-3) Matrix(291,190,1334,871) -> Matrix(5,-2,-2,1) Matrix(175,114,-1334,-869) -> Matrix(5,-2,-2,1) Matrix(3481,2260,-8932,-5799) -> Matrix(1,0,0,1) Matrix(5279,3426,7598,4931) -> Matrix(1,-2,-2,5) Matrix(291,188,-986,-637) -> Matrix(7,-2,4,-1) Matrix(231,148,-1450,-929) -> Matrix(5,-4,4,-3) Matrix(2145,1372,-3538,-2263) -> Matrix(1,0,0,1) Matrix(1449,926,3538,2261) -> Matrix(3,-2,2,-1) Matrix(755,482,-2088,-1333) -> Matrix(7,-6,6,-5) Matrix(407,258,1740,1103) -> Matrix(1,0,-2,1) Matrix(1507,954,3480,2203) -> Matrix(1,0,-2,1) Matrix(4813,3046,6322,4001) -> Matrix(1,-4,-2,9) Matrix(5335,3376,9164,5799) -> Matrix(1,-2,0,1) Matrix(117,74,1102,697) -> Matrix(1,0,-2,1) Matrix(7481,4730,11832,7481) -> Matrix(5,-4,-6,5) Matrix(2089,1320,3306,2089) -> Matrix(1,-2,0,1) Matrix(463,292,1102,695) -> Matrix(1,-2,0,1) Matrix(407,256,-1566,-985) -> Matrix(1,0,-4,1) Matrix(869,546,-2494,-1567) -> Matrix(7,-4,2,-1) Matrix(289,180,464,289) -> Matrix(5,-2,-12,5) Matrix(755,468,1218,755) -> Matrix(23,-12,-44,23) Matrix(4409,2728,5626,3481) -> Matrix(7,-4,-12,7) Matrix(2959,1830,7598,4699) -> Matrix(7,-4,2,-1) Matrix(4059,2510,5626,3479) -> Matrix(7,-4,-26,15) Matrix(929,574,-3190,-1971) -> Matrix(11,-6,2,-1) Matrix(347,214,-754,-465) -> Matrix(7,-4,2,-1) Matrix(231,142,1508,927) -> Matrix(1,0,-2,1) Matrix(2957,1816,-9918,-6091) -> Matrix(19,-12,8,-5) Matrix(4349,2670,9918,6089) -> Matrix(49,-32,-26,17) Matrix(17979,11036,29290,17979) -> Matrix(199,-132,-300,199) Matrix(7831,4806,12760,7831) -> Matrix(77,-52,-114,77) Matrix(1797,1102,2552,1565) -> Matrix(3,-2,-10,7) Matrix(405,248,1798,1101) -> Matrix(13,-8,-8,5) Matrix(811,496,-2088,-1277) -> Matrix(3,-2,-4,3) Matrix(2899,1770,7598,4639) -> Matrix(9,-8,-10,9) Matrix(2435,1486,-10266,-6265) -> Matrix(17,-12,10,-7) Matrix(2669,1628,4756,2901) -> Matrix(5,-4,4,-3) Matrix(233,142,1334,813) -> Matrix(5,-4,-6,5) Matrix(579,352,1334,811) -> Matrix(3,-2,-4,3) Matrix(4813,2920,6786,4117) -> Matrix(3,-2,-4,3) Matrix(291,176,-2204,-1333) -> Matrix(11,-8,-4,3) Matrix(579,344,2146,1275) -> Matrix(5,-4,4,-3) Matrix(1449,860,-3422,-2031) -> Matrix(5,-4,4,-3) Matrix(987,584,1276,755) -> Matrix(3,-2,-16,11) Matrix(1277,754,3538,2089) -> Matrix(1,0,-2,1) Matrix(1683,992,-7772,-4581) -> Matrix(13,-10,4,-3) Matrix(2377,1400,3248,1913) -> Matrix(3,-2,-4,3) Matrix(579,340,986,579) -> Matrix(11,-10,-12,11) Matrix(407,238,696,407) -> Matrix(3,-4,-2,3) Matrix(5799,3376,9164,5335) -> Matrix(1,-2,0,1) Matrix(2725,1586,-10266,-5975) -> Matrix(1,-2,-2,5) Matrix(3597,2092,4988,2901) -> Matrix(1,-2,-4,9) Matrix(3421,1988,-6090,-3539) -> Matrix(1,4,0,1) Matrix(407,236,1102,639) -> Matrix(1,-2,0,1) Matrix(173,100,1102,637) -> Matrix(1,-2,0,1) Matrix(1275,736,-3016,-1741) -> Matrix(7,-2,4,-1) Matrix(115,66,-406,-233) -> Matrix(7,-4,2,-1) Matrix(1683,956,2146,1219) -> Matrix(3,-4,-8,11) Matrix(1277,724,3480,1973) -> Matrix(1,-2,0,1) Matrix(523,296,1334,755) -> Matrix(1,-2,0,1) Matrix(985,556,1334,753) -> Matrix(1,0,-4,1) Matrix(291,164,928,523) -> Matrix(3,-2,-4,3) Matrix(3829,2150,9918,5569) -> Matrix(1,8,-2,-15) Matrix(2901,1628,4756,2669) -> Matrix(3,4,-4,-5) Matrix(1277,716,1450,813) -> Matrix(1,0,0,1) Matrix(3365,1886,-7656,-4291) -> Matrix(5,2,2,1) Matrix(2087,1168,2900,1623) -> Matrix(1,0,-4,1) Matrix(1681,940,-7366,-4119) -> Matrix(7,-2,4,-1) Matrix(523,292,-1972,-1101) -> Matrix(1,0,-4,1) Matrix(289,160,522,289) -> Matrix(1,0,-4,1) Matrix(639,352,1160,639) -> Matrix(11,-6,-20,11) Matrix(521,286,-1798,-987) -> Matrix(7,-4,2,-1) Matrix(117,64,638,349) -> Matrix(3,-2,-4,3) Matrix(289,156,-754,-407) -> Matrix(1,0,0,1) Matrix(175,94,-754,-405) -> Matrix(7,-6,6,-5) Matrix(233,124,-870,-463) -> Matrix(1,-2,0,1) Matrix(581,274,986,465) -> Matrix(5,-4,-6,5) Matrix(581,270,-2494,-1159) -> Matrix(5,-6,6,-7) Matrix(927,424,-4060,-1857) -> Matrix(7,-2,4,-1) Matrix(5395,2464,-14094,-6437) -> Matrix(5,-2,8,-3) Matrix(57,26,-638,-291) -> Matrix(3,-2,2,-1) Matrix(521,236,638,289) -> Matrix(3,-2,-4,3) Matrix(173,78,-1160,-523) -> Matrix(19,-16,6,-5) Matrix(521,234,1160,521) -> Matrix(17,-16,-18,17) Matrix(233,104,522,233) -> Matrix(9,-10,-8,9) Matrix(1915,848,-4582,-2029) -> Matrix(11,-14,4,-5) Matrix(5627,2488,8004,3539) -> Matrix(3,-4,-8,11) Matrix(2087,920,-6844,-3017) -> Matrix(1,0,0,1) Matrix(1971,868,3422,1507) -> Matrix(1,-2,0,1) Matrix(7541,3316,13456,5917) -> Matrix(1,-2,8,-15) Matrix(7539,3314,13456,5915) -> Matrix(1,-2,-6,13) Matrix(173,76,1450,637) -> Matrix(1,-2,0,1) Matrix(1855,814,4756,2087) -> Matrix(1,-2,2,-3) Matrix(347,152,-1856,-813) -> Matrix(1,-2,0,1) Matrix(637,278,928,405) -> Matrix(1,2,-2,-3) Matrix(349,152,1334,581) -> Matrix(1,0,0,1) Matrix(811,352,1334,579) -> Matrix(3,-2,-4,3) Matrix(2203,954,3480,1507) -> Matrix(1,0,-2,1) Matrix(463,200,2146,927) -> Matrix(11,-8,-4,3) Matrix(1915,812,3422,1451) -> Matrix(1,-2,0,1) Matrix(9571,4054,-25056,-10613) -> Matrix(5,-6,6,-7) Matrix(7773,3284,13456,5685) -> Matrix(1,-2,8,-15) Matrix(7771,3282,13456,5683) -> Matrix(1,-2,-10,21) Matrix(929,392,1102,465) -> Matrix(1,-2,-4,9) Matrix(695,292,1102,463) -> Matrix(1,-2,0,1) Matrix(463,194,-2494,-1045) -> Matrix(1,-2,2,-3) Matrix(1391,582,4988,2087) -> Matrix(13,-32,-2,5) Matrix(6669,2788,-25114,-10499) -> Matrix(1,-2,-4,9) Matrix(3365,1406,9164,3829) -> Matrix(1,-2,-2,5) Matrix(289,120,696,289) -> Matrix(1,-6,0,1) Matrix(407,168,986,407) -> Matrix(1,4,0,1) Matrix(521,214,986,405) -> Matrix(1,2,-2,-3) Matrix(6207,2548,10034,4119) -> Matrix(9,4,-16,-7) Matrix(405,166,-1276,-523) -> Matrix(1,0,2,1) Matrix(289,118,1276,521) -> Matrix(3,2,-2,-1) Matrix(1043,424,-3712,-1509) -> Matrix(1,4,0,1) Matrix(233,94,290,117) -> Matrix(1,0,-2,1) Matrix(289,114,-1914,-755) -> Matrix(5,-8,2,-3) Matrix(1275,502,-3538,-1393) -> Matrix(3,-2,2,-1) Matrix(755,296,1334,523) -> Matrix(1,-2,0,1) Matrix(1101,430,1334,521) -> Matrix(1,2,-2,-3) Matrix(2087,814,4756,1855) -> Matrix(3,2,-2,-1) Matrix(5045,1966,-21286,-8295) -> Matrix(3,-2,2,-1) Matrix(4699,1830,7598,2959) -> Matrix(1,4,-2,-7) Matrix(8237,3196,13456,5221) -> Matrix(21,2,-32,-3) Matrix(8235,3194,13456,5219) -> Matrix(31,-2,-46,3) Matrix(1393,540,1798,697) -> Matrix(1,0,-8,1) Matrix(1159,448,1798,695) -> Matrix(5,-2,-12,5) Matrix(4929,1904,12760,4929) -> Matrix(29,-14,-60,29) Matrix(11311,4368,29290,11311) -> Matrix(71,-36,-140,71) Matrix(6843,2642,8410,3247) -> Matrix(19,-10,2,-1) Matrix(57,22,-754,-291) -> Matrix(11,-6,2,-1) Matrix(1277,492,1508,581) -> Matrix(3,-2,-4,3) Matrix(3249,1244,-10904,-4175) -> Matrix(5,-4,4,-3) Matrix(51911,19870,84100,32191) -> Matrix(35,-22,-62,39) Matrix(51909,19868,84100,32189) -> Matrix(85,-58,-148,101) Matrix(2263,866,-7424,-2841) -> Matrix(17,-12,10,-7) Matrix(49475,18898,68788,26275) -> Matrix(5,-4,-26,21) Matrix(60609,23150,84274,32189) -> Matrix(7,-6,-22,19) Matrix(8641,3300,13514,5161) -> Matrix(7,-6,-8,7) Matrix(1567,598,5626,2147) -> Matrix(41,-34,-6,5) Matrix(4639,1770,7598,2899) -> Matrix(9,-8,-10,9) Matrix(5915,2256,10034,3827) -> Matrix(11,-10,-12,11) Matrix(463,176,1218,463) -> Matrix(15,-14,-16,15) Matrix(175,66,464,175) -> Matrix(7,-8,-6,7) Matrix(59,22,-464,-173) -> Matrix(3,-4,-2,3) Matrix(523,194,-2030,-753) -> Matrix(1,-2,6,-11) Matrix(639,236,1102,407) -> Matrix(1,-2,0,1) Matrix(1217,448,3306,1217) -> Matrix(1,-4,0,1) Matrix(4351,1600,11832,4351) -> Matrix(1,2,0,1) Matrix(985,362,1102,405) -> Matrix(1,0,-2,1) Matrix(3829,1406,9164,3365) -> Matrix(5,-2,-2,1) Matrix(1509,554,6322,2321) -> Matrix(3,-4,-2,3) Matrix(1973,724,3480,1277) -> Matrix(1,-2,0,1) Matrix(115,42,-638,-233) -> Matrix(1,-2,2,-3) Matrix(2147,778,3364,1219) -> Matrix(5,-4,-6,5) Matrix(2145,776,3364,1217) -> Matrix(5,-6,-4,5) Matrix(987,356,1450,523) -> Matrix(1,-2,0,1) Matrix(8353,3012,13514,4873) -> Matrix(9,-14,-16,25) Matrix(173,62,-812,-291) -> Matrix(9,-14,2,-3) Matrix(1103,392,1798,639) -> Matrix(3,-8,-4,11) Matrix(233,82,-986,-347) -> Matrix(3,-8,2,-5) Matrix(349,122,-2320,-811) -> Matrix(5,-18,2,-7) Matrix(1043,362,1334,463) -> Matrix(1,-6,-2,13) Matrix(927,296,1450,463) -> Matrix(3,-2,-4,3) Matrix(523,164,928,291) -> Matrix(3,-2,-4,3) Matrix(289,90,928,289) -> Matrix(9,-8,-10,9) Matrix(233,72,754,233) -> Matrix(9,-10,-8,9) Matrix(465,142,3422,1045) -> Matrix(21,-32,2,-3) Matrix(2667,814,7598,2319) -> Matrix(3,-4,-2,3) Matrix(579,176,2668,811) -> Matrix(1,-4,0,1) Matrix(4929,1496,16240,4929) -> Matrix(5,-6,-4,5) Matrix(7831,2376,25810,7831) -> Matrix(7,-12,-4,7) Matrix(4525,1372,5742,1741) -> Matrix(1,-2,-4,9) Matrix(927,280,-6148,-1857) -> Matrix(1,2,0,1) Matrix(1507,454,-5394,-1625) -> Matrix(9,-14,2,-3) Matrix(579,172,4292,1275) -> Matrix(1,6,0,1) Matrix(4465,1326,8004,2377) -> Matrix(1,0,-2,1) Matrix(1449,430,-6844,-2031) -> Matrix(11,-6,2,-1) Matrix(987,292,2552,755) -> Matrix(3,-4,-8,11) Matrix(2379,698,3364,987) -> Matrix(1,-2,6,-11) Matrix(2377,696,3364,985) -> Matrix(1,-2,-8,17) Matrix(2669,776,6786,1973) -> Matrix(1,-2,0,1) Matrix(3421,994,-12180,-3539) -> Matrix(9,-14,2,-3) Matrix(52085,14626,84274,23665) -> Matrix(1,0,-2,1) Matrix(42513,11936,68788,19313) -> Matrix(9,-50,-16,89) Matrix(1277,358,2900,813) -> Matrix(3,-10,-2,7) Matrix(60611,16930,84100,23491) -> Matrix(11,-54,-34,167) Matrix(60609,16928,84100,23489) -> Matrix(11,-56,-32,163) Matrix(523,146,-3944,-1101) -> Matrix(7,-38,-2,11) Matrix(2087,582,4988,1391) -> Matrix(5,-32,-2,13) Matrix(2147,598,5626,1567) -> Matrix(5,-34,-6,41) Matrix(289,80,1044,289) -> Matrix(1,-18,0,1) Matrix(175,48,638,175) -> Matrix(1,8,0,1) Matrix(59,16,-638,-173) -> Matrix(1,4,0,1) Matrix(289,78,-1508,-407) -> Matrix(1,2,-2,-3) Matrix(521,140,-2378,-639) -> Matrix(1,4,0,1) Matrix(1335,358,3248,871) -> Matrix(3,4,2,3) Matrix(2205,586,7424,1973) -> Matrix(1,0,2,1) Matrix(61771,16402,84100,22331) -> Matrix(9,2,-14,-3) Matrix(61769,16400,84100,22329) -> Matrix(5,2,-8,-3) Matrix(871,230,1102,291) -> Matrix(1,0,-6,1) Matrix(581,152,1334,349) -> Matrix(1,0,0,1) Matrix(2495,646,3364,871) -> Matrix(1,0,10,1) Matrix(2493,644,3364,869) -> Matrix(1,0,-16,1) Matrix(57,14,232,57) -> Matrix(1,0,-2,1) Matrix(349,84,1450,349) -> Matrix(13,-14,-12,13) Matrix(2263,542,2668,639) -> Matrix(5,-6,-14,17) Matrix(2321,554,6322,1509) -> Matrix(3,-4,-2,3) Matrix(4523,1074,5858,1391) -> Matrix(5,-8,-18,29) Matrix(41065,9736,53824,12761) -> Matrix(11,-20,-28,51) Matrix(41063,9734,53824,12759) -> Matrix(1,-4,-2,9) Matrix(811,190,986,231) -> Matrix(1,0,-2,1) Matrix(10325,2404,13456,3133) -> Matrix(21,-20,-64,61) Matrix(10323,2402,13456,3131) -> Matrix(25,-26,-74,77) Matrix(4467,1018,5858,1335) -> Matrix(7,-12,-18,31) Matrix(2205,502,2552,581) -> Matrix(1,-2,10,-19) Matrix(521,118,1276,289) -> Matrix(1,-2,2,-3) Matrix(1101,248,1798,405) -> Matrix(5,-8,-8,13) Matrix(463,102,522,115) -> Matrix(1,-2,-2,5) Matrix(1217,266,5568,1217) -> Matrix(5,-12,-2,5) Matrix(2089,456,9570,2089) -> Matrix(1,-6,0,1) Matrix(871,190,1334,291) -> Matrix(1,-2,-2,5) Matrix(811,176,2668,579) -> Matrix(1,-4,0,1) Matrix(2145,464,5626,1217) -> Matrix(7,-20,-8,23) Matrix(927,200,2146,463) -> Matrix(3,-8,-4,11) Matrix(10557,2276,13456,2901) -> Matrix(17,-50,-52,153) Matrix(10555,2274,13456,2899) -> Matrix(17,-52,-50,153) Matrix(4001,848,5742,1217) -> Matrix(1,-4,-4,17) Matrix(811,170,1102,231) -> Matrix(1,-8,-2,17) Matrix(289,60,1392,289) -> Matrix(1,-30,0,1) Matrix(59,12,290,59) -> Matrix(1,4,0,1) Matrix(173,34,290,57) -> Matrix(1,2,-2,-3) Matrix(2727,518,3364,639) -> Matrix(1,0,10,1) Matrix(2725,516,3364,637) -> Matrix(1,0,-12,1) Matrix(5163,962,8410,1567) -> Matrix(17,2,-26,-3) Matrix(349,64,638,117) -> Matrix(3,-2,-4,3) Matrix(755,134,986,175) -> Matrix(1,-2,-2,5) Matrix(813,142,1334,233) -> Matrix(5,-4,-6,5) Matrix(231,40,1334,231) -> Matrix(7,-6,-8,7) Matrix(59,10,348,59) -> Matrix(3,-4,-2,3) Matrix(985,158,3248,521) -> Matrix(3,-4,-2,3) Matrix(637,100,1102,173) -> Matrix(1,-2,0,1) Matrix(927,142,1508,231) -> Matrix(1,0,-2,1) Matrix(2029,308,2668,405) -> Matrix(9,-22,-20,49) Matrix(57,8,406,57) -> Matrix(1,-12,0,1) Matrix(175,24,1276,175) -> Matrix(1,30,0,1) Matrix(1971,268,2552,347) -> Matrix(1,12,-4,-47) Matrix(1275,172,4292,579) -> Matrix(1,6,0,1) Matrix(637,76,1450,173) -> Matrix(1,-2,0,1) Matrix(407,46,522,59) -> Matrix(1,0,-2,1) Matrix(697,74,1102,117) -> Matrix(1,0,-2,1) Matrix(407,-40,580,-57) -> Matrix(1,2,-4,-7) Matrix(173,-22,464,-59) -> Matrix(3,-4,-2,3) Matrix(289,-42,406,-59) -> Matrix(1,4,-2,-7) Matrix(755,-114,1914,-289) -> Matrix(3,8,-2,-5) Matrix(869,-138,1102,-175) -> Matrix(1,2,-6,-11) Matrix(233,-42,638,-115) -> Matrix(3,2,-2,-1) Matrix(1045,-194,2494,-463) -> Matrix(3,2,-2,-1) Matrix(753,-142,928,-175) -> Matrix(1,0,2,1) Matrix(407,-78,1508,-289) -> Matrix(3,-2,2,-1) Matrix(291,-62,812,-173) -> Matrix(3,14,-2,-9) Matrix(1275,-274,1624,-349) -> Matrix(3,10,-10,-33) Matrix(4581,-992,7772,-1683) -> Matrix(3,10,-4,-13) Matrix(639,-140,2378,-521) -> Matrix(1,4,0,1) Matrix(523,-120,754,-173) -> Matrix(5,8,-12,-19) Matrix(405,-94,754,-175) -> Matrix(5,6,-6,-7) Matrix(347,-82,986,-233) -> Matrix(5,8,-2,-3) Matrix(985,-256,1566,-407) -> Matrix(1,0,-4,1) Matrix(1101,-292,1972,-523) -> Matrix(1,0,-4,1) Matrix(463,-124,870,-233) -> Matrix(1,-2,0,1) Matrix(1507,-408,2146,-581) -> Matrix(1,-2,-4,9) Matrix(1739,-486,2494,-697) -> Matrix(1,4,-2,-7) Matrix(233,-66,406,-115) -> Matrix(1,4,-2,-7) Matrix(347,-100,406,-117) -> Matrix(1,2,-4,-7) Matrix(1971,-574,3190,-929) -> Matrix(1,6,-2,-11) Matrix(985,-288,1392,-407) -> Matrix(1,2,0,1) Matrix(637,-188,986,-291) -> Matrix(1,2,-4,-7) Matrix(1799,-534,2146,-637) -> Matrix(1,0,-2,1) Matrix(1565,-466,2146,-639) -> Matrix(1,2,-2,-3) Matrix(1797,-544,2494,-755) -> Matrix(1,2,-4,-7) Matrix(581,-178,754,-231) -> Matrix(3,4,-10,-13) Matrix(523,-166,1276,-405) -> Matrix(1,0,2,1) Matrix(1159,-404,1334,-465) -> Matrix(1,4,0,1) Matrix(5451,-1912,8932,-3133) -> Matrix(3,4,-4,-5) Matrix(695,-246,986,-349) -> Matrix(1,2,-2,-3) Matrix(1219,-438,1450,-521) -> Matrix(3,4,-10,-13) Matrix(1393,-502,3538,-1275) -> Matrix(1,2,-2,-3) Matrix(1333,-482,2088,-755) -> Matrix(5,6,-6,-7) Matrix(1159,-430,1566,-581) -> Matrix(1,2,-6,-11) Matrix(1625,-604,2494,-927) -> Matrix(1,2,-4,-7) Matrix(2261,-864,3190,-1219) -> Matrix(5,4,-4,-3) Matrix(407,-156,754,-289) -> Matrix(1,0,0,1) Matrix(6961,-2686,9918,-3827) -> Matrix(7,4,-30,-17) Matrix(1277,-496,2088,-811) -> Matrix(3,-2,-4,3) Matrix(7831,-3052,10266,-4001) -> Matrix(3,2,-8,-5) Matrix(1913,-756,2204,-871) -> Matrix(1,2,0,1) Matrix(1973,-802,3422,-1391) -> Matrix(1,0,-2,1) Matrix(6089,-2500,7772,-3191) -> Matrix(1,0,-4,1) Matrix(7541,-3152,10266,-4291) -> Matrix(5,12,-8,-19) Matrix(2669,-1118,6090,-2551) -> Matrix(5,8,-2,-3) Matrix(1741,-736,3016,-1275) -> Matrix(1,2,-4,-7) Matrix(291,-124,406,-173) -> Matrix(1,2,-4,-7) Matrix(4291,-1886,7656,-3365) -> Matrix(1,2,2,5) Matrix(5685,-2506,7366,-3247) -> Matrix(3,4,-10,-13) Matrix(1449,-640,1972,-871) -> Matrix(7,10,-12,-17) Matrix(1277,-576,1798,-811) -> Matrix(5,4,-4,-3) Matrix(465,-214,754,-347) -> Matrix(1,4,-2,-7) Matrix(579,-268,754,-349) -> Matrix(1,2,-4,-7) Matrix(637,-298,870,-407) -> Matrix(3,2,-2,-1) Matrix(1913,-1024,2494,-1335) -> Matrix(11,10,-32,-29) Matrix(3133,-1700,4060,-2203) -> Matrix(11,8,-40,-29) Matrix(8699,-4726,14094,-7657) -> Matrix(29,18,-50,-31) Matrix(581,-316,638,-347) -> Matrix(3,2,-8,-5) Matrix(987,-542,1160,-637) -> Matrix(3,2,-14,-9) Matrix(2667,-1486,4582,-2553) -> Matrix(3,2,-2,-1) Matrix(4757,-2660,6844,-3827) -> Matrix(3,2,-8,-5) Matrix(1509,-848,1856,-1043) -> Matrix(1,2,0,1) Matrix(15485,-8926,25056,-14443) -> Matrix(17,4,-30,-7) Matrix(2031,-1180,2494,-1449) -> Matrix(1,-2,0,1) Matrix(18445,-10734,25114,-14615) -> Matrix(1,4,-2,-7) Matrix(871,-514,1276,-753) -> Matrix(3,2,-2,-1) Matrix(2669,-1584,3712,-2203) -> Matrix(3,2,-8,-5) Matrix(1625,-984,1914,-1159) -> Matrix(3,2,-8,-5) Matrix(2263,-1372,3538,-2145) -> Matrix(1,0,0,1) Matrix(16241,-9912,21286,-12991) -> Matrix(17,12,-44,-31) Matrix(697,-428,754,-463) -> Matrix(3,2,-20,-13) Matrix(7655,-4724,10904,-6729) -> Matrix(7,4,-16,-9) Matrix(5161,-3186,7424,-4583) -> Matrix(17,10,-46,-27) Matrix(405,-254,464,-291) -> Matrix(1,0,2,1) Matrix(1507,-948,2030,-1277) -> Matrix(1,0,4,1) Matrix(523,-332,638,-405) -> Matrix(1,0,0,1) Matrix(639,-410,812,-521) -> Matrix(3,2,-14,-9) Matrix(753,-488,986,-639) -> Matrix(3,2,-8,-5) Matrix(1971,-1282,2320,-1509) -> Matrix(1,0,-2,1) Matrix(5221,-3644,6148,-4291) -> Matrix(11,4,-36,-13) Matrix(3887,-2716,5394,-3769) -> Matrix(1,0,0,1) Matrix(5395,-3794,6844,-4813) -> Matrix(1,0,-2,1) Matrix(8759,-6214,12180,-8641) -> Matrix(1,0,-2,1) Matrix(3421,-2466,3944,-2843) -> Matrix(7,2,10,3) Matrix(579,-422,638,-465) -> Matrix(1,0,-2,1) Matrix(1219,-890,1508,-1101) -> Matrix(1,0,-2,1) Matrix(1857,-1358,2378,-1739) -> Matrix(1,2,-2,-3) 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): 140 Degree of the the map X: 140 Degree of the the map Y: 420 ----------------------------------------------------------------------- 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): 1260 Minimal number of generators: 211 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: 56 Genus: 78 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/10 1/9 2/17 1/8 2/15 4/29 1/7 2/13 1/6 5/29 4/23 2/11 1/5 6/29 4/19 3/14 19/87 2/9 3/13 6/25 7/29 1/4 3/11 8/29 2/7 8/27 44/145 9/29 1/3 32/87 11/29 8/21 56/145 2/5 12/29 5/12 13/29 1/2 16/29 17/29 18/29 55/87 2/3 20/29 146/203 21/29 43/58 22/29 89/116 68/87 23/29 24/29 25/29 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -8/9 1/0 -15/17 0/1 -7/8 1/1 -13/15 -2/5 -19/22 -1/11 -25/29 0/1 -6/7 1/6 -5/6 1/3 -14/17 1/2 -9/11 0/1 -4/5 1/0 -23/29 0/1 -19/24 1/11 -15/19 0/1 -11/14 3/11 -29/37 2/5 -18/23 1/2 -25/32 3/5 -7/9 0/1 -24/31 1/4 -17/22 3/13 -10/13 1/2 -23/30 1/3 -13/17 2/5 -16/21 5/12 -3/4 1/1 -17/23 0/1 -14/19 1/2 -11/15 4/5 -8/11 1/0 -21/29 0/1 -13/18 1/5 -18/25 1/2 -5/7 2/5 -12/17 1/4 -19/27 0/1 -26/37 1/2 -7/10 1/3 -16/23 3/8 -9/13 4/9 -2/3 1/2 -15/23 0/1 -13/20 1/1 -24/37 1/4 -11/17 0/1 -9/14 5/9 -25/39 2/3 -16/25 3/4 -7/11 0/1 -26/41 1/2 -19/30 1/1 -50/79 3/2 -31/49 0/1 -43/68 1/1 -55/87 1/1 -12/19 1/0 -17/27 0/1 -22/35 1/2 -5/8 1/3 -8/13 5/8 -11/18 5/7 -36/59 3/4 -25/41 4/5 -14/23 1/2 -17/28 1/1 -3/5 0/1 -10/17 5/6 -17/29 1/1 -7/12 1/1 -4/7 3/4 -9/16 1/1 -32/57 1/0 -23/41 0/1 -37/66 -1/1 -14/25 1/2 -19/34 -1/1 -5/9 0/1 -6/11 1/2 -7/13 2/3 -8/15 5/4 -1/2 1/1 -5/11 2/3 -9/20 1/1 -13/29 1/1 -4/9 5/4 -7/16 3/1 -10/23 1/2 -13/30 1/1 -16/37 3/4 -3/7 4/3 -14/33 3/2 -25/59 2/1 -11/26 1/1 -8/19 1/0 -13/31 2/1 -18/43 13/6 -5/12 3/1 -2/5 1/2 -7/18 1/1 -12/31 1/4 -17/44 7/15 -22/57 1/2 -5/13 2/3 -13/34 7/9 -21/55 4/5 -8/21 7/8 -11/29 1/1 -3/8 1/1 -13/35 2/1 -23/62 9/5 -10/27 5/2 -7/19 2/1 -18/49 1/2 -11/30 1/1 -4/11 1/0 -5/14 9/5 -11/31 2/1 -6/17 5/2 -7/20 3/1 -1/3 0/1 -5/16 1/1 -9/29 1/1 -4/13 5/4 -7/23 2/1 -17/56 1/1 -10/33 3/2 -3/10 1/1 -2/7 5/2 -3/11 -4/1 -13/48 -3/1 -10/37 -5/2 -7/26 -1/1 -11/41 -2/1 -4/15 -3/4 -13/49 0/1 -9/34 -1/5 -5/19 0/1 -1/4 1/1 -7/29 1/1 -6/25 7/6 -5/21 4/3 -4/17 1/0 -7/30 1/1 -10/43 11/10 -3/13 4/3 -2/9 5/2 -9/41 2/1 -7/32 3/1 -19/87 3/1 -12/55 1/0 -5/23 2/1 -8/37 1/0 -11/51 20/7 -3/14 11/3 -4/19 1/0 -1/5 -2/1 -3/16 1/1 -2/11 1/2 -5/28 1/1 -3/17 0/1 -4/23 3/4 -5/29 1/1 -1/6 1/1 -2/13 5/2 -1/7 6/1 -2/15 -9/2 -3/23 -2/1 -1/8 -1/1 -1/9 0/1 -1/10 1/1 0/1 1/0 1/10 -1/1 1/9 0/1 2/17 -1/2 1/8 1/1 2/15 9/2 3/22 15/1 4/29 1/0 1/7 -6/1 2/13 -5/2 1/6 -1/1 5/29 -1/1 4/23 -3/4 3/17 0/1 2/11 -1/2 3/16 -1/1 1/5 2/1 6/29 1/0 5/24 -15/1 4/19 1/0 3/14 -11/3 11/51 -20/7 8/37 1/0 13/60 -3/1 5/23 -2/1 12/55 1/0 19/87 -3/1 7/32 -3/1 2/9 -5/2 3/13 -4/3 7/30 -1/1 4/17 1/0 5/21 -4/3 6/25 -7/6 7/29 -1/1 1/4 -1/1 6/23 1/2 5/19 0/1 9/34 1/5 4/15 3/4 11/41 2/1 18/67 3/2 7/26 1/1 10/37 5/2 3/11 4/1 8/29 1/0 5/18 -9/1 2/7 -5/2 5/17 -2/1 8/27 -5/4 3/10 -1/1 10/33 -3/2 27/89 -2/1 44/145 -3/2 17/56 -1/1 7/23 -2/1 4/13 -5/4 9/29 -1/1 5/16 -1/1 6/19 -1/2 1/3 0/1 7/20 -3/1 13/37 -4/1 6/17 -5/2 5/14 -9/5 4/11 1/0 15/41 -2/1 11/30 -1/1 18/49 -1/2 25/68 1/1 32/87 1/0 7/19 -2/1 10/27 -5/2 13/35 -2/1 16/43 -19/12 3/8 -1/1 11/29 -1/1 8/21 -7/8 21/55 -4/5 13/34 -7/9 5/13 -2/3 22/57 -1/2 39/101 -18/35 56/145 -1/2 17/44 -7/15 12/31 -1/4 19/49 0/1 7/18 -1/1 2/5 -1/2 7/17 2/1 12/29 1/0 5/12 -3/1 18/43 -13/6 13/31 -2/1 8/19 1/0 19/45 -2/1 11/26 -1/1 3/7 -4/3 16/37 -3/4 13/30 -1/1 10/23 -1/2 7/16 -3/1 4/9 -5/4 13/29 -1/1 9/20 -1/1 14/31 -5/6 5/11 -2/3 6/13 -3/2 7/15 -6/7 1/2 -1/1 8/15 -5/4 15/28 -1/1 7/13 -2/3 6/11 -1/2 11/20 -3/5 16/29 -1/2 5/9 0/1 29/52 -1/1 24/43 -3/8 19/34 1/1 33/59 0/1 14/25 -1/2 37/66 1/1 23/41 0/1 32/57 1/0 9/16 -1/1 22/39 -1/2 13/23 0/1 4/7 -3/4 11/19 0/1 18/31 1/2 25/43 -6/1 7/12 -1/1 17/29 -1/1 10/17 -5/6 13/22 -7/9 16/27 -3/4 19/32 -1/1 3/5 0/1 20/33 -3/4 17/28 -1/1 14/23 -1/2 25/41 -4/5 36/59 -3/4 47/77 -2/3 11/18 -5/7 19/31 -2/3 27/44 -13/19 89/145 -2/3 62/101 -33/50 35/57 -2/3 8/13 -5/8 13/21 -6/11 18/29 -1/2 5/8 -1/3 22/35 -1/2 39/62 -1/5 17/27 0/1 12/19 1/0 55/87 -1/1 43/68 -1/1 31/49 0/1 50/79 -3/2 19/30 -1/1 7/11 0/1 16/25 -3/4 9/14 -5/9 20/31 -3/8 11/17 0/1 13/20 -1/1 28/43 -5/8 15/23 0/1 2/3 -1/2 11/16 -5/9 20/29 -1/2 9/13 -4/9 16/23 -3/8 39/56 -1/3 101/145 -1/3 62/89 -7/22 23/33 0/1 7/10 -1/3 40/57 -1/4 33/47 -2/7 26/37 -1/2 45/64 -1/3 19/27 0/1 31/44 1/3 12/17 -1/4 17/24 1/1 39/55 0/1 61/86 -1/1 22/31 -1/2 5/7 -2/5 23/32 -1/3 64/89 -1/4 105/146 -1/3 146/203 -1/4 41/57 0/1 18/25 -1/2 13/18 -1/5 21/29 0/1 8/11 1/0 11/15 -4/5 14/19 -1/2 17/23 0/1 20/27 -1/8 43/58 0/1 23/31 0/1 3/4 -1/1 22/29 -1/2 19/25 -6/13 16/21 -5/12 29/38 -1/3 13/17 -2/5 23/30 -1/3 56/73 -15/44 89/116 -1/3 33/43 -8/25 10/13 -1/2 17/22 -3/13 24/31 -1/4 7/9 0/1 25/32 -3/5 68/87 -1/2 43/55 -6/13 18/23 -1/2 29/37 -2/5 11/14 -3/11 26/33 -1/6 15/19 0/1 19/24 -1/11 23/29 0/1 4/5 1/0 9/11 0/1 23/28 -1/1 14/17 -1/2 19/23 -4/7 24/29 -1/2 5/6 -1/3 16/19 -1/4 11/13 0/1 6/7 -1/6 25/29 0/1 19/22 1/11 13/15 2/5 7/8 -1/1 15/17 0/1 8/9 1/0 1/1 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(117,106,-319,-289) (-1/1,-8/9) -> (-18/49,-11/30) Hyperbolic Matrix(405,358,1508,1333) (-8/9,-15/17) -> (11/41,18/67) Hyperbolic Matrix(813,716,1450,1277) (-15/17,-7/8) -> (37/66,23/41) Hyperbolic Matrix(523,454,-667,-579) (-7/8,-13/15) -> (-11/14,-29/37) Hyperbolic Matrix(231,200,-1073,-929) (-13/15,-19/22) -> (-11/51,-3/14) Hyperbolic Matrix(1101,950,1276,1101) (-19/22,-25/29) -> (25/29,19/22) Hyperbolic Matrix(349,300,406,349) (-25/29,-6/7) -> (6/7,25/29) Hyperbolic Matrix(115,98,203,173) (-6/7,-5/6) -> (13/23,4/7) Hyperbolic Matrix(407,336,493,407) (-5/6,-14/17) -> (14/17,19/23) Hyperbolic Matrix(405,332,-638,-523) (-14/17,-9/11) -> (-7/11,-26/41) Hyperbolic Matrix(57,46,-145,-117) (-9/11,-4/5) -> (-2/5,-7/18) Hyperbolic Matrix(231,184,290,231) (-4/5,-23/29) -> (23/29,4/5) Hyperbolic Matrix(1103,874,1392,1103) (-23/29,-19/24) -> (19/24,23/29) Hyperbolic Matrix(291,230,1102,871) (-19/24,-15/19) -> (5/19,9/34) Hyperbolic Matrix(521,410,-812,-639) (-15/19,-11/14) -> (-9/14,-25/39) Hyperbolic Matrix(929,728,-1479,-1159) (-29/37,-18/23) -> (-22/35,-5/8) Hyperbolic Matrix(1565,1224,2001,1565) (-18/23,-25/32) -> (43/55,18/23) Hyperbolic Matrix(233,182,-667,-521) (-25/32,-7/9) -> (-7/20,-1/3) Hyperbolic Matrix(697,540,1798,1393) (-7/9,-24/31) -> (12/31,19/49) Hyperbolic Matrix(755,584,1276,987) (-24/31,-17/22) -> (13/22,16/27) Hyperbolic Matrix(57,44,-377,-291) (-17/22,-10/13) -> (-2/13,-1/7) Hyperbolic Matrix(695,534,1131,869) (-10/13,-23/30) -> (35/57,8/13) Hyperbolic Matrix(637,488,1740,1333) (-23/30,-13/17) -> (15/41,11/30) Hyperbolic Matrix(639,488,-986,-753) (-13/17,-16/21) -> (-24/37,-11/17) Hyperbolic Matrix(463,352,609,463) (-16/21,-3/4) -> (19/25,16/21) Hyperbolic Matrix(581,430,-1566,-1159) (-3/4,-17/23) -> (-13/35,-23/62) Hyperbolic Matrix(753,556,1334,985) (-17/23,-14/19) -> (22/39,13/23) Hyperbolic Matrix(117,86,-551,-405) (-14/19,-11/15) -> (-3/14,-4/19) Hyperbolic Matrix(115,84,-319,-233) (-11/15,-8/11) -> (-4/11,-5/14) Hyperbolic Matrix(463,336,638,463) (-8/11,-21/29) -> (21/29,8/11) Hyperbolic Matrix(755,546,1044,755) (-21/29,-13/18) -> (13/18,21/29) Hyperbolic Matrix(463,334,-725,-523) (-13/18,-18/25) -> (-16/25,-7/11) Hyperbolic Matrix(173,124,-406,-291) (-18/25,-5/7) -> (-3/7,-14/33) Hyperbolic Matrix(291,206,493,349) (-5/7,-12/17) -> (10/17,13/22) Hyperbolic Matrix(349,246,-986,-695) (-12/17,-19/27) -> (-11/31,-6/17) Hyperbolic Matrix(697,490,3219,2263) (-19/27,-26/37) -> (8/37,13/60) Hyperbolic Matrix(581,408,-2146,-1507) (-26/37,-7/10) -> (-13/48,-10/37) Hyperbolic Matrix(175,122,667,465) (-7/10,-16/23) -> (6/23,5/19) Hyperbolic Matrix(291,202,-667,-463) (-16/23,-9/13) -> (-7/16,-10/23) Hyperbolic Matrix(59,40,87,59) (-9/13,-2/3) -> (2/3,11/16) Hyperbolic Matrix(291,190,1334,871) (-2/3,-15/23) -> (5/23,12/55) Hyperbolic Matrix(695,452,1247,811) (-15/23,-13/20) -> (5/9,29/52) Hyperbolic Matrix(2147,1394,-3393,-2203) (-13/20,-24/37) -> (-50/79,-31/49) Hyperbolic Matrix(523,338,899,581) (-11/17,-9/14) -> (25/43,7/12) Hyperbolic Matrix(465,298,-1537,-985) (-25/39,-16/25) -> (-10/33,-3/10) Hyperbolic Matrix(407,258,1740,1103) (-26/41,-19/30) -> (7/30,4/17) Hyperbolic Matrix(1507,954,3480,2203) (-19/30,-50/79) -> (16/37,13/30) Hyperbolic Matrix(117,74,1102,697) (-31/49,-43/68) -> (1/10,1/9) Hyperbolic Matrix(7481,4730,11832,7481) (-43/68,-55/87) -> (55/87,43/68) Hyperbolic Matrix(2089,1320,3306,2089) (-55/87,-12/19) -> (12/19,55/87) Hyperbolic Matrix(463,292,1102,695) (-12/19,-17/27) -> (13/31,8/19) Hyperbolic Matrix(1797,1130,2581,1623) (-17/27,-22/35) -> (16/23,39/56) Hyperbolic Matrix(233,144,377,233) (-5/8,-8/13) -> (8/13,13/21) Hyperbolic Matrix(173,106,377,231) (-8/13,-11/18) -> (5/11,6/13) Hyperbolic Matrix(2667,1628,3799,2319) (-11/18,-36/59) -> (40/57,33/47) Hyperbolic Matrix(2669,1628,4756,2901) (-36/59,-25/41) -> (23/41,32/57) Hyperbolic Matrix(233,142,1334,813) (-25/41,-14/23) -> (4/23,3/17) Hyperbolic Matrix(579,352,1334,811) (-14/23,-17/28) -> (13/30,10/23) Hyperbolic Matrix(697,422,1247,755) (-17/28,-3/5) -> (19/34,33/59) Hyperbolic Matrix(349,206,493,291) (-3/5,-10/17) -> (12/17,17/24) Hyperbolic Matrix(579,340,986,579) (-10/17,-17/29) -> (17/29,10/17) Hyperbolic Matrix(407,238,696,407) (-17/29,-7/12) -> (7/12,17/29) Hyperbolic Matrix(59,34,203,117) (-7/12,-4/7) -> (2/7,5/17) Hyperbolic Matrix(173,98,203,115) (-4/7,-9/16) -> (11/13,6/7) Hyperbolic Matrix(637,358,-1653,-929) (-9/16,-32/57) -> (-22/57,-5/13) Hyperbolic Matrix(2901,1628,4756,2669) (-32/57,-23/41) -> (25/41,36/59) Hyperbolic Matrix(1277,716,1450,813) (-23/41,-37/66) -> (7/8,15/17) Hyperbolic Matrix(521,292,-2175,-1219) (-37/66,-14/25) -> (-6/25,-5/21) Hyperbolic Matrix(755,422,1247,697) (-14/25,-19/34) -> (3/5,20/33) Hyperbolic Matrix(523,292,-1972,-1101) (-19/34,-5/9) -> (-13/49,-9/34) Hyperbolic Matrix(175,96,319,175) (-5/9,-6/11) -> (6/11,11/20) Hyperbolic Matrix(59,32,-319,-173) (-6/11,-7/13) -> (-3/16,-2/11) Hyperbolic Matrix(175,94,-754,-405) (-7/13,-8/15) -> (-10/43,-3/13) Hyperbolic Matrix(231,122,-551,-291) (-8/15,-1/2) -> (-13/31,-18/43) Hyperbolic Matrix(231,106,377,173) (-1/2,-5/11) -> (11/18,19/31) Hyperbolic Matrix(349,158,899,407) (-5/11,-9/20) -> (19/49,7/18) Hyperbolic Matrix(521,234,1160,521) (-9/20,-13/29) -> (13/29,9/20) Hyperbolic Matrix(233,104,522,233) (-13/29,-4/9) -> (4/9,13/29) Hyperbolic Matrix(59,26,-261,-115) (-4/9,-7/16) -> (-3/13,-2/9) Hyperbolic Matrix(811,352,1334,579) (-10/23,-13/30) -> (17/28,14/23) Hyperbolic Matrix(2203,954,3480,1507) (-13/30,-16/37) -> (50/79,19/30) Hyperbolic Matrix(463,200,2146,927) (-16/37,-3/7) -> (11/51,8/37) Hyperbolic Matrix(1915,812,3422,1451) (-14/33,-25/59) -> (33/59,14/25) Hyperbolic Matrix(3887,1646,5481,2321) (-25/59,-11/26) -> (39/55,61/86) Hyperbolic Matrix(175,74,551,233) (-11/26,-8/19) -> (6/19,1/3) Hyperbolic Matrix(695,292,1102,463) (-8/19,-13/31) -> (17/27,12/19) Hyperbolic Matrix(521,218,-1943,-813) (-18/43,-5/12) -> (-11/41,-4/15) Hyperbolic Matrix(59,24,145,59) (-5/12,-2/5) -> (2/5,7/17) Hyperbolic Matrix(407,158,899,349) (-7/18,-12/31) -> (14/31,5/11) Hyperbolic Matrix(1159,448,1798,695) (-12/31,-17/44) -> (9/14,20/31) Hyperbolic Matrix(3191,1232,8265,3191) (-17/44,-22/57) -> (22/57,39/101) Hyperbolic Matrix(115,44,-609,-233) (-5/13,-13/34) -> (-1/5,-3/16) Hyperbolic Matrix(811,310,1363,521) (-13/34,-21/55) -> (19/32,3/5) Hyperbolic Matrix(697,266,-2581,-985) (-21/55,-8/21) -> (-10/37,-7/26) Hyperbolic Matrix(463,176,1218,463) (-8/21,-11/29) -> (11/29,8/21) Hyperbolic Matrix(175,66,464,175) (-11/29,-3/8) -> (3/8,11/29) Hyperbolic Matrix(59,22,-464,-173) (-3/8,-13/35) -> (-3/23,-1/8) Hyperbolic Matrix(4465,1656,6409,2377) (-23/62,-10/27) -> (62/89,23/33) Hyperbolic Matrix(639,236,1102,407) (-10/27,-7/19) -> (11/19,18/31) Hyperbolic Matrix(1567,576,4263,1567) (-7/19,-18/49) -> (18/49,25/68) Hyperbolic Matrix(115,42,-638,-233) (-11/30,-4/11) -> (-2/11,-5/28) Hyperbolic Matrix(1103,392,1798,639) (-5/14,-11/31) -> (19/31,27/44) Hyperbolic Matrix(57,20,493,173) (-6/17,-7/20) -> (1/9,2/17) Hyperbolic Matrix(233,74,551,175) (-1/3,-5/16) -> (19/45,11/26) Hyperbolic Matrix(289,90,928,289) (-5/16,-9/29) -> (9/29,5/16) Hyperbolic Matrix(233,72,754,233) (-9/29,-4/13) -> (4/13,9/29) Hyperbolic Matrix(59,18,-377,-115) (-4/13,-7/23) -> (-1/6,-2/13) Hyperbolic Matrix(579,176,2668,811) (-7/23,-17/56) -> (13/60,5/23) Hyperbolic Matrix(1451,440,4785,1451) (-17/56,-10/33) -> (10/33,27/89) Hyperbolic Matrix(117,34,203,59) (-3/10,-2/7) -> (4/7,11/19) Hyperbolic Matrix(57,16,203,57) (-2/7,-3/11) -> (5/18,2/7) Hyperbolic Matrix(1045,284,1711,465) (-3/11,-13/48) -> (47/77,11/18) Hyperbolic Matrix(521,140,-2378,-639) (-7/26,-11/41) -> (-9/41,-7/32) Hyperbolic Matrix(1567,416,2407,639) (-4/15,-13/49) -> (13/20,28/43) Hyperbolic Matrix(871,230,1102,291) (-9/34,-5/19) -> (15/19,19/24) Hyperbolic Matrix(465,122,667,175) (-5/19,-1/4) -> (23/33,7/10) Hyperbolic Matrix(57,14,232,57) (-1/4,-7/29) -> (7/29,1/4) Hyperbolic Matrix(349,84,1450,349) (-7/29,-6/25) -> (6/25,7/29) Hyperbolic Matrix(59,14,493,117) (-5/21,-4/17) -> (2/17,1/8) Hyperbolic Matrix(811,190,986,231) (-4/17,-7/30) -> (23/28,14/17) Hyperbolic Matrix(3365,784,5481,1277) (-7/30,-10/43) -> (62/101,35/57) Hyperbolic Matrix(463,102,522,115) (-2/9,-9/41) -> (15/17,8/9) Hyperbolic Matrix(1217,266,5568,1217) (-7/32,-19/87) -> (19/87,7/32) Hyperbolic Matrix(2089,456,9570,2089) (-19/87,-12/55) -> (12/55,19/87) Hyperbolic Matrix(871,190,1334,291) (-12/55,-5/23) -> (15/23,2/3) Hyperbolic Matrix(2263,490,3219,697) (-5/23,-8/37) -> (26/37,45/64) Hyperbolic Matrix(927,200,2146,463) (-8/37,-11/51) -> (3/7,16/37) Hyperbolic Matrix(115,24,551,115) (-4/19,-1/5) -> (5/24,4/19) Hyperbolic Matrix(755,134,986,175) (-5/28,-3/17) -> (13/17,23/30) Hyperbolic Matrix(813,142,1334,233) (-3/17,-4/23) -> (14/23,25/41) Hyperbolic Matrix(231,40,1334,231) (-4/23,-5/29) -> (5/29,4/23) Hyperbolic Matrix(59,10,348,59) (-5/29,-1/6) -> (1/6,5/29) Hyperbolic Matrix(59,8,435,59) (-1/7,-2/15) -> (2/15,3/22) Hyperbolic Matrix(987,130,1769,233) (-2/15,-3/23) -> (29/52,24/43) Hyperbolic Matrix(173,20,493,57) (-1/8,-1/9) -> (7/20,13/37) Hyperbolic Matrix(697,74,1102,117) (-1/9,-1/10) -> (43/68,31/49) Hyperbolic Matrix(407,36,667,59) (-1/10,0/1) -> (36/59,47/77) Hyperbolic Matrix(407,-40,580,-57) (0/1,1/10) -> (7/10,40/57) Hyperbolic Matrix(173,-22,464,-59) (1/8,2/15) -> (16/43,3/8) Hyperbolic Matrix(117,-16,841,-115) (3/22,4/29) -> (4/29,1/7) Parabolic Matrix(291,-44,377,-57) (1/7,2/13) -> (10/13,17/22) Hyperbolic Matrix(115,-18,377,-59) (2/13,1/6) -> (7/23,4/13) Hyperbolic Matrix(233,-42,638,-115) (3/17,2/11) -> (4/11,15/41) Hyperbolic Matrix(173,-32,319,-59) (2/11,3/16) -> (7/13,6/11) Hyperbolic Matrix(233,-44,609,-115) (3/16,1/5) -> (13/34,5/13) Hyperbolic Matrix(175,-36,841,-173) (1/5,6/29) -> (6/29,5/24) Parabolic Matrix(405,-86,551,-117) (4/19,3/14) -> (11/15,14/19) Hyperbolic Matrix(929,-200,1073,-231) (3/14,11/51) -> (19/22,13/15) Hyperbolic Matrix(639,-140,2378,-521) (7/32,2/9) -> (18/67,7/26) Hyperbolic Matrix(115,-26,261,-59) (2/9,3/13) -> (7/16,4/9) Hyperbolic Matrix(405,-94,754,-175) (3/13,7/30) -> (15/28,7/13) Hyperbolic Matrix(347,-82,986,-233) (4/17,5/21) -> (13/37,6/17) Hyperbolic Matrix(1219,-292,2175,-521) (5/21,6/25) -> (14/25,37/66) Hyperbolic Matrix(985,-256,1566,-407) (1/4,6/23) -> (22/35,39/62) Hyperbolic Matrix(1101,-292,1972,-523) (9/34,4/15) -> (24/43,19/34) Hyperbolic Matrix(813,-218,1943,-521) (4/15,11/41) -> (5/12,18/43) Hyperbolic Matrix(985,-266,2581,-697) (7/26,10/37) -> (8/21,21/55) Hyperbolic Matrix(1507,-408,2146,-581) (10/37,3/11) -> (33/47,26/37) Hyperbolic Matrix(233,-64,841,-231) (3/11,8/29) -> (8/29,5/18) Parabolic Matrix(637,-188,986,-291) (5/17,8/27) -> (20/31,11/17) Hyperbolic Matrix(289,-86,783,-233) (8/27,3/10) -> (7/19,10/27) Hyperbolic Matrix(755,-228,957,-289) (3/10,10/33) -> (26/33,15/19) Hyperbolic Matrix(6381,-1936,21025,-6379) (27/89,44/145) -> (44/145,17/56) Parabolic Matrix(2957,-898,4205,-1277) (17/56,7/23) -> (45/64,19/27) Hyperbolic Matrix(465,-146,551,-173) (5/16,6/19) -> (16/19,11/13) Hyperbolic Matrix(521,-182,667,-233) (1/3,7/20) -> (7/9,25/32) Hyperbolic Matrix(695,-246,986,-349) (6/17,5/14) -> (31/44,12/17) Hyperbolic Matrix(233,-84,319,-115) (5/14,4/11) -> (8/11,11/15) Hyperbolic Matrix(289,-106,319,-117) (11/30,18/49) -> (8/9,1/1) Hyperbolic Matrix(2785,-1024,7569,-2783) (25/68,32/87) -> (32/87,7/19) Parabolic Matrix(1159,-430,1566,-581) (10/27,13/35) -> (17/23,20/27) Hyperbolic Matrix(1625,-604,2494,-927) (13/35,16/43) -> (28/43,15/23) Hyperbolic Matrix(2261,-864,3190,-1219) (21/55,13/34) -> (17/24,39/55) Hyperbolic Matrix(929,-358,1653,-637) (5/13,22/57) -> (32/57,9/16) Hyperbolic Matrix(8121,-3136,21025,-8119) (39/101,56/145) -> (56/145,17/44) Parabolic Matrix(1567,-606,2697,-1043) (17/44,12/31) -> (18/31,25/43) Hyperbolic Matrix(117,-46,145,-57) (7/18,2/5) -> (4/5,9/11) Hyperbolic Matrix(349,-144,841,-347) (7/17,12/29) -> (12/29,5/12) Parabolic Matrix(291,-122,551,-231) (18/43,13/31) -> (1/2,8/15) Hyperbolic Matrix(1161,-490,2059,-869) (8/19,19/45) -> (9/16,22/39) Hyperbolic Matrix(291,-124,406,-173) (11/26,3/7) -> (5/7,23/32) Hyperbolic Matrix(463,-202,667,-291) (10/23,7/16) -> (9/13,16/23) Hyperbolic Matrix(697,-314,899,-405) (9/20,14/31) -> (24/31,7/9) Hyperbolic Matrix(579,-268,754,-349) (6/13,7/15) -> (33/43,10/13) Hyperbolic Matrix(347,-164,493,-233) (7/15,1/2) -> (19/27,31/44) Hyperbolic Matrix(1913,-1024,2494,-1335) (8/15,15/28) -> (23/30,56/73) Hyperbolic Matrix(465,-256,841,-463) (11/20,16/29) -> (16/29,5/9) Parabolic Matrix(2669,-1584,3712,-2203) (16/27,19/32) -> (23/32,64/89) Hyperbolic Matrix(1857,-1126,2581,-1565) (20/33,17/28) -> (41/57,18/25) Hyperbolic Matrix(8701,-5340,11339,-6959) (27/44,89/145) -> (89/116,33/43) Hyperbolic Matrix(17109,-10502,22301,-13689) (89/145,62/101) -> (56/73,89/116) Hyperbolic Matrix(523,-324,841,-521) (13/21,18/29) -> (18/29,5/8) Parabolic Matrix(1159,-728,1479,-929) (5/8,22/35) -> (18/23,29/37) Hyperbolic Matrix(1507,-948,2030,-1277) (39/62,17/27) -> (23/31,3/4) Hyperbolic Matrix(3075,-1946,4031,-2551) (31/49,50/79) -> (16/21,29/38) Hyperbolic Matrix(523,-332,638,-405) (19/30,7/11) -> (9/11,23/28) Hyperbolic Matrix(523,-334,725,-463) (7/11,16/25) -> (18/25,13/18) Hyperbolic Matrix(639,-410,812,-521) (16/25,9/14) -> (11/14,26/33) Hyperbolic Matrix(753,-488,986,-639) (11/17,13/20) -> (29/38,13/17) Hyperbolic Matrix(581,-400,841,-579) (11/16,20/29) -> (20/29,9/13) Parabolic Matrix(5743,-4000,7743,-5393) (39/56,101/145) -> (43/58,23/31) Hyperbolic Matrix(6727,-4686,9077,-6323) (101/145,62/89) -> (20/27,43/58) Hyperbolic Matrix(8759,-6214,12180,-8641) (61/86,22/31) -> (64/89,105/146) Hyperbolic Matrix(695,-494,899,-639) (22/31,5/7) -> (17/22,24/31) Hyperbolic Matrix(29639,-21316,41209,-29637) (105/146,146/203) -> (146/203,41/57) Parabolic Matrix(463,-342,551,-407) (14/19,17/23) -> (5/6,16/19) Hyperbolic Matrix(639,-484,841,-637) (3/4,22/29) -> (22/29,19/25) Parabolic Matrix(5917,-4624,7569,-5915) (25/32,68/87) -> (68/87,43/55) Parabolic Matrix(579,-454,667,-523) (29/37,11/14) -> (13/15,7/8) Hyperbolic Matrix(697,-576,841,-695) (19/23,24/29) -> (24/29,5/6) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(117,106,-319,-289) -> Matrix(1,-1,2,-1) Matrix(405,358,1508,1333) -> Matrix(3,-2,2,-1) Matrix(813,716,1450,1277) -> Matrix(1,0,0,1) Matrix(523,454,-667,-579) -> Matrix(1,1,2,3) Matrix(231,200,-1073,-929) -> Matrix(13,3,4,1) Matrix(1101,950,1276,1101) -> Matrix(1,0,22,1) Matrix(349,300,406,349) -> Matrix(1,0,-12,1) Matrix(115,98,203,173) -> Matrix(3,-1,-2,1) Matrix(407,336,493,407) -> Matrix(5,-3,-8,5) Matrix(405,332,-638,-523) -> Matrix(1,0,0,1) Matrix(57,46,-145,-117) -> Matrix(1,-1,2,-1) Matrix(231,184,290,231) -> Matrix(1,0,0,1) Matrix(1103,874,1392,1103) -> Matrix(1,0,-22,1) Matrix(291,230,1102,871) -> Matrix(1,0,-6,1) Matrix(521,410,-812,-639) -> Matrix(9,-2,14,-3) Matrix(929,728,-1479,-1159) -> Matrix(3,-1,4,-1) Matrix(1565,1224,2001,1565) -> Matrix(7,-3,-16,7) Matrix(233,182,-667,-521) -> Matrix(5,-3,2,-1) Matrix(697,540,1798,1393) -> Matrix(1,0,-8,1) Matrix(755,584,1276,987) -> Matrix(11,-2,-16,3) Matrix(57,44,-377,-291) -> Matrix(11,-3,4,-1) Matrix(695,534,1131,869) -> Matrix(11,-3,-18,5) Matrix(637,488,1740,1333) -> Matrix(11,-4,-8,3) Matrix(639,488,-986,-753) -> Matrix(5,-2,8,-3) Matrix(463,352,609,463) -> Matrix(11,-5,-24,11) Matrix(581,430,-1566,-1159) -> Matrix(11,-2,6,-1) Matrix(753,556,1334,985) -> Matrix(1,0,-4,1) Matrix(117,86,-551,-405) -> Matrix(9,-5,2,-1) Matrix(115,84,-319,-233) -> Matrix(1,1,0,1) Matrix(463,336,638,463) -> Matrix(1,0,0,1) Matrix(755,546,1044,755) -> Matrix(1,0,-10,1) Matrix(463,334,-725,-523) -> Matrix(5,-1,6,-1) Matrix(173,124,-406,-291) -> Matrix(7,-2,4,-1) Matrix(291,206,493,349) -> Matrix(1,1,-2,-1) Matrix(349,246,-986,-695) -> Matrix(3,-2,2,-1) Matrix(697,490,3219,2263) -> Matrix(7,-3,-2,1) Matrix(581,408,-2146,-1507) -> Matrix(9,-2,-4,1) Matrix(175,122,667,465) -> Matrix(3,-1,-2,1) Matrix(291,202,-667,-463) -> Matrix(3,-1,-2,1) Matrix(59,40,87,59) -> Matrix(1,-1,0,1) Matrix(291,190,1334,871) -> Matrix(5,-2,-2,1) Matrix(695,452,1247,811) -> Matrix(1,-1,0,1) Matrix(2147,1394,-3393,-2203) -> Matrix(1,-1,2,-1) Matrix(523,338,899,581) -> Matrix(3,-1,-2,1) Matrix(465,298,-1537,-985) -> Matrix(5,-3,2,-1) Matrix(407,258,1740,1103) -> Matrix(1,0,-2,1) Matrix(1507,954,3480,2203) -> Matrix(1,0,-2,1) Matrix(117,74,1102,697) -> Matrix(1,0,-2,1) Matrix(7481,4730,11832,7481) -> Matrix(5,-4,-6,5) Matrix(2089,1320,3306,2089) -> Matrix(1,-2,0,1) Matrix(463,292,1102,695) -> Matrix(1,-2,0,1) Matrix(1797,1130,2581,1623) -> Matrix(5,-1,-14,3) Matrix(233,144,377,233) -> Matrix(9,-5,-16,9) Matrix(173,106,377,231) -> Matrix(1,-1,2,-1) Matrix(2667,1628,3799,2319) -> Matrix(1,-1,0,1) Matrix(2669,1628,4756,2901) -> Matrix(5,-4,4,-3) Matrix(233,142,1334,813) -> Matrix(5,-4,-6,5) Matrix(579,352,1334,811) -> Matrix(3,-2,-4,3) Matrix(697,422,1247,755) -> Matrix(1,-1,2,-1) Matrix(349,206,493,291) -> Matrix(1,-1,2,-1) Matrix(579,340,986,579) -> Matrix(11,-10,-12,11) Matrix(407,238,696,407) -> Matrix(3,-4,-2,3) Matrix(59,34,203,117) -> Matrix(3,-1,-2,1) Matrix(173,98,203,115) -> Matrix(1,-1,-2,3) Matrix(637,358,-1653,-929) -> Matrix(1,-3,2,-5) Matrix(2901,1628,4756,2669) -> Matrix(3,4,-4,-5) Matrix(1277,716,1450,813) -> Matrix(1,0,0,1) Matrix(521,292,-2175,-1219) -> Matrix(5,1,4,1) Matrix(755,422,1247,697) -> Matrix(1,1,-2,-1) Matrix(523,292,-1972,-1101) -> Matrix(1,0,-4,1) Matrix(175,96,319,175) -> Matrix(5,-3,-8,5) Matrix(59,32,-319,-173) -> Matrix(1,-1,4,-3) Matrix(175,94,-754,-405) -> Matrix(7,-6,6,-5) Matrix(231,122,-551,-291) -> Matrix(5,-3,2,-1) Matrix(231,106,377,173) -> Matrix(1,1,-2,-1) Matrix(349,158,899,407) -> Matrix(1,-1,2,-1) Matrix(521,234,1160,521) -> Matrix(17,-16,-18,17) Matrix(233,104,522,233) -> Matrix(9,-10,-8,9) Matrix(59,26,-261,-115) -> Matrix(3,-5,2,-3) Matrix(811,352,1334,579) -> Matrix(3,-2,-4,3) Matrix(2203,954,3480,1507) -> Matrix(1,0,-2,1) Matrix(463,200,2146,927) -> Matrix(11,-8,-4,3) Matrix(1915,812,3422,1451) -> Matrix(1,-2,0,1) Matrix(3887,1646,5481,2321) -> Matrix(1,-1,-2,3) Matrix(175,74,551,233) -> Matrix(1,-1,-2,3) Matrix(695,292,1102,463) -> Matrix(1,-2,0,1) Matrix(521,218,-1943,-813) -> Matrix(3,-7,-2,5) Matrix(59,24,145,59) -> Matrix(1,-1,0,1) Matrix(407,158,899,349) -> Matrix(1,1,-2,-1) Matrix(1159,448,1798,695) -> Matrix(5,-2,-12,5) Matrix(3191,1232,8265,3191) -> Matrix(21,-11,-40,21) Matrix(115,44,-609,-233) -> Matrix(1,-1,4,-3) Matrix(811,310,1363,521) -> Matrix(9,-7,-14,11) Matrix(697,266,-2581,-985) -> Matrix(11,-9,-6,5) Matrix(463,176,1218,463) -> Matrix(15,-14,-16,15) Matrix(175,66,464,175) -> Matrix(7,-8,-6,7) Matrix(59,22,-464,-173) -> Matrix(3,-4,-2,3) Matrix(4465,1656,6409,2377) -> Matrix(5,-9,-16,29) Matrix(639,236,1102,407) -> Matrix(1,-2,0,1) Matrix(1567,576,4263,1567) -> Matrix(1,-1,0,1) Matrix(115,42,-638,-233) -> Matrix(1,-2,2,-3) Matrix(1103,392,1798,639) -> Matrix(3,-8,-4,11) Matrix(57,20,493,173) -> Matrix(1,-3,0,1) Matrix(233,74,551,175) -> Matrix(3,-1,-2,1) Matrix(289,90,928,289) -> Matrix(9,-8,-10,9) Matrix(233,72,754,233) -> Matrix(9,-10,-8,9) Matrix(59,18,-377,-115) -> Matrix(3,-5,2,-3) Matrix(579,176,2668,811) -> Matrix(1,-4,0,1) Matrix(1451,440,4785,1451) -> Matrix(1,-3,0,1) Matrix(117,34,203,59) -> Matrix(1,-1,-2,3) Matrix(57,16,203,57) -> Matrix(1,-5,0,1) Matrix(1045,284,1711,465) -> Matrix(3,7,-4,-9) Matrix(521,140,-2378,-639) -> Matrix(1,4,0,1) Matrix(1567,416,2407,639) -> Matrix(3,1,-4,-1) Matrix(871,230,1102,291) -> Matrix(1,0,-6,1) Matrix(465,122,667,175) -> Matrix(1,-1,-2,3) Matrix(57,14,232,57) -> Matrix(1,0,-2,1) Matrix(349,84,1450,349) -> Matrix(13,-14,-12,13) Matrix(59,14,493,117) -> Matrix(1,-1,-2,3) Matrix(811,190,986,231) -> Matrix(1,0,-2,1) Matrix(3365,784,5481,1277) -> Matrix(13,-11,-20,17) Matrix(463,102,522,115) -> Matrix(1,-2,-2,5) Matrix(1217,266,5568,1217) -> Matrix(5,-12,-2,5) Matrix(2089,456,9570,2089) -> Matrix(1,-6,0,1) Matrix(871,190,1334,291) -> Matrix(1,-2,-2,5) Matrix(2263,490,3219,697) -> Matrix(1,-3,-2,7) Matrix(927,200,2146,463) -> Matrix(3,-8,-4,11) Matrix(115,24,551,115) -> Matrix(1,-13,0,1) Matrix(755,134,986,175) -> Matrix(1,-2,-2,5) Matrix(813,142,1334,233) -> Matrix(5,-4,-6,5) Matrix(231,40,1334,231) -> Matrix(7,-6,-8,7) Matrix(59,10,348,59) -> Matrix(3,-4,-2,3) Matrix(59,8,435,59) -> Matrix(1,9,0,1) Matrix(987,130,1769,233) -> Matrix(1,3,-2,-5) Matrix(173,20,493,57) -> Matrix(1,-3,0,1) Matrix(697,74,1102,117) -> Matrix(1,0,-2,1) Matrix(407,36,667,59) -> Matrix(3,-5,-4,7) Matrix(407,-40,580,-57) -> Matrix(1,2,-4,-7) Matrix(173,-22,464,-59) -> Matrix(3,-4,-2,3) Matrix(117,-16,841,-115) -> Matrix(1,-21,0,1) Matrix(291,-44,377,-57) -> Matrix(1,3,-4,-11) Matrix(115,-18,377,-59) -> Matrix(3,5,-2,-3) Matrix(233,-42,638,-115) -> Matrix(3,2,-2,-1) Matrix(173,-32,319,-59) -> Matrix(3,1,-4,-1) Matrix(233,-44,609,-115) -> Matrix(3,1,-4,-1) Matrix(175,-36,841,-173) -> Matrix(1,-17,0,1) Matrix(405,-86,551,-117) -> Matrix(1,5,-2,-9) Matrix(929,-200,1073,-231) -> Matrix(1,3,4,13) Matrix(639,-140,2378,-521) -> Matrix(1,4,0,1) Matrix(115,-26,261,-59) -> Matrix(3,5,-2,-3) Matrix(405,-94,754,-175) -> Matrix(5,6,-6,-7) Matrix(347,-82,986,-233) -> Matrix(5,8,-2,-3) Matrix(1219,-292,2175,-521) -> Matrix(1,1,4,5) Matrix(985,-256,1566,-407) -> Matrix(1,0,-4,1) Matrix(1101,-292,1972,-523) -> Matrix(1,0,-4,1) Matrix(813,-218,1943,-521) -> Matrix(5,-7,-2,3) Matrix(985,-266,2581,-697) -> Matrix(5,-9,-6,11) Matrix(1507,-408,2146,-581) -> Matrix(1,-2,-4,9) Matrix(233,-64,841,-231) -> Matrix(1,-13,0,1) Matrix(637,-188,986,-291) -> Matrix(1,2,-4,-7) Matrix(289,-86,783,-233) -> Matrix(3,5,-2,-3) Matrix(755,-228,957,-289) -> Matrix(1,1,-4,-3) Matrix(6381,-1936,21025,-6379) -> Matrix(5,9,-4,-7) Matrix(2957,-898,4205,-1277) -> Matrix(1,1,-2,-1) Matrix(465,-146,551,-173) -> Matrix(1,1,-6,-5) Matrix(521,-182,667,-233) -> Matrix(1,3,-2,-5) Matrix(695,-246,986,-349) -> Matrix(1,2,-2,-3) Matrix(233,-84,319,-115) -> Matrix(1,1,0,1) Matrix(289,-106,319,-117) -> Matrix(1,1,-2,-1) Matrix(2785,-1024,7569,-2783) -> Matrix(1,-3,0,1) Matrix(1159,-430,1566,-581) -> Matrix(1,2,-6,-11) Matrix(1625,-604,2494,-927) -> Matrix(1,2,-4,-7) Matrix(2261,-864,3190,-1219) -> Matrix(5,4,-4,-3) Matrix(929,-358,1653,-637) -> Matrix(5,3,-2,-1) Matrix(8121,-3136,21025,-8119) -> Matrix(49,25,-100,-51) Matrix(1567,-606,2697,-1043) -> Matrix(3,1,2,1) Matrix(117,-46,145,-57) -> Matrix(1,1,-2,-1) Matrix(349,-144,841,-347) -> Matrix(1,-5,0,1) Matrix(291,-122,551,-231) -> Matrix(1,3,-2,-5) Matrix(1161,-490,2059,-869) -> Matrix(1,3,-2,-5) Matrix(291,-124,406,-173) -> Matrix(1,2,-4,-7) Matrix(463,-202,667,-291) -> Matrix(1,-1,-2,3) Matrix(697,-314,899,-405) -> Matrix(1,1,-10,-9) Matrix(579,-268,754,-349) -> Matrix(1,2,-4,-7) Matrix(347,-164,493,-233) -> Matrix(1,1,-4,-3) Matrix(1913,-1024,2494,-1335) -> Matrix(11,10,-32,-29) Matrix(465,-256,841,-463) -> Matrix(5,3,-12,-7) Matrix(2669,-1584,3712,-2203) -> Matrix(3,2,-8,-5) Matrix(1857,-1126,2581,-1565) -> Matrix(1,1,-6,-5) Matrix(8701,-5340,11339,-6959) -> Matrix(43,29,-132,-89) Matrix(17109,-10502,22301,-13689) -> Matrix(95,63,-282,-187) Matrix(523,-324,841,-521) -> Matrix(13,7,-28,-15) Matrix(1159,-728,1479,-929) -> Matrix(1,1,-4,-3) Matrix(1507,-948,2030,-1277) -> Matrix(1,0,4,1) Matrix(3075,-1946,4031,-2551) -> Matrix(1,-1,-2,3) Matrix(523,-332,638,-405) -> Matrix(1,0,0,1) Matrix(523,-334,725,-463) -> Matrix(1,1,-6,-5) Matrix(639,-410,812,-521) -> Matrix(3,2,-14,-9) Matrix(753,-488,986,-639) -> Matrix(3,2,-8,-5) Matrix(581,-400,841,-579) -> Matrix(17,9,-36,-19) Matrix(5743,-4000,7743,-5393) -> Matrix(3,1,32,11) Matrix(6727,-4686,9077,-6323) -> Matrix(3,1,-46,-15) Matrix(8759,-6214,12180,-8641) -> Matrix(1,0,-2,1) Matrix(695,-494,899,-639) -> Matrix(1,1,-6,-5) Matrix(29639,-21316,41209,-29637) -> Matrix(3,1,-16,-5) Matrix(463,-342,551,-407) -> Matrix(3,1,-10,-3) Matrix(639,-484,841,-637) -> Matrix(13,7,-28,-15) Matrix(5917,-4624,7569,-5915) -> Matrix(17,9,-36,-19) Matrix(579,-454,667,-523) -> Matrix(3,1,2,1) Matrix(697,-576,841,-695) -> Matrix(9,5,-20,-11) 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): 140 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 1/0 1 29 1/10 -1/1 1 29 1/9 0/1 1 29 1/8 1/1 1 29 2/15 9/2 1 29 4/29 1/0 21 1 1/7 -6/1 1 29 2/13 -5/2 1 29 1/6 -1/1 1 29 5/29 -1/1 5 1 4/23 -3/4 1 29 3/17 0/1 1 29 2/11 -1/2 1 29 3/16 -1/1 1 29 1/5 2/1 1 29 6/29 1/0 17 1 4/19 1/0 1 29 3/14 -11/3 1 29 11/51 -20/7 1 29 8/37 1/0 1 29 5/23 -2/1 1 29 12/55 1/0 1 29 19/87 -3/1 1 1 7/32 -3/1 1 29 2/9 -5/2 1 29 3/13 -4/3 1 29 7/30 -1/1 1 29 4/17 1/0 1 29 5/21 -4/3 1 29 6/25 -7/6 1 29 7/29 -1/1 7 1 1/4 -1/1 1 29 5/19 0/1 1 29 9/34 1/5 1 29 4/15 3/4 1 29 11/41 2/1 1 29 18/67 3/2 1 29 7/26 1/1 1 29 10/37 5/2 1 29 3/11 4/1 1 29 8/29 1/0 13 1 2/7 -5/2 1 29 3/10 -1/1 1 29 10/33 -3/2 1 29 44/145 -3/2 1 1 17/56 -1/1 1 29 7/23 -2/1 1 29 4/13 -5/4 1 29 9/29 -1/1 9 1 5/16 -1/1 1 29 1/3 0/1 1 29 7/20 -3/1 1 29 13/37 -4/1 1 29 6/17 -5/2 1 29 5/14 -9/5 1 29 4/11 1/0 1 29 15/41 -2/1 1 29 11/30 -1/1 1 29 18/49 -1/2 1 29 32/87 1/0 3 1 7/19 -2/1 1 29 10/27 -5/2 1 29 13/35 -2/1 1 29 16/43 -19/12 1 29 3/8 -1/1 1 29 11/29 -1/1 11 1 8/21 -7/8 1 29 21/55 -4/5 1 29 13/34 -7/9 1 29 5/13 -2/3 1 29 22/57 -1/2 1 29 56/145 -1/2 25 1 17/44 -7/15 1 29 12/31 -1/4 1 29 7/18 -1/1 1 29 2/5 -1/2 1 29 12/29 1/0 5 1 5/12 -3/1 1 29 18/43 -13/6 1 29 13/31 -2/1 1 29 8/19 1/0 1 29 19/45 -2/1 1 29 11/26 -1/1 1 29 3/7 -4/3 1 29 16/37 -3/4 1 29 13/30 -1/1 1 29 10/23 -1/2 1 29 7/16 -3/1 1 29 4/9 -5/4 1 29 13/29 -1/1 13 1 9/20 -1/1 1 29 14/31 -5/6 1 29 5/11 -2/3 1 29 1/2 -1/1 1 29 8/15 -5/4 1 29 15/28 -1/1 1 29 7/13 -2/3 1 29 6/11 -1/2 1 29 16/29 -1/2 3 1 5/9 0/1 1 29 24/43 -3/8 1 29 19/34 1/1 1 29 14/25 -1/2 1 29 37/66 1/1 1 29 23/41 0/1 1 29 32/57 1/0 1 29 9/16 -1/1 1 29 4/7 -3/4 1 29 11/19 0/1 1 29 18/31 1/2 1 29 7/12 -1/1 1 29 17/29 -1/1 7 1 10/17 -5/6 1 29 3/5 0/1 1 29 20/33 -3/4 1 29 17/28 -1/1 1 29 14/23 -1/2 1 29 25/41 -4/5 1 29 36/59 -3/4 1 29 11/18 -5/7 1 29 19/31 -2/3 1 29 27/44 -13/19 1 29 8/13 -5/8 1 29 18/29 -1/2 7 1 5/8 -1/3 1 29 22/35 -1/2 1 29 17/27 0/1 1 29 12/19 1/0 1 29 55/87 -1/1 3 1 43/68 -1/1 1 29 31/49 0/1 1 29 50/79 -3/2 1 29 19/30 -1/1 1 29 7/11 0/1 1 29 16/25 -3/4 1 29 9/14 -5/9 1 29 20/31 -3/8 1 29 11/17 0/1 1 29 13/20 -1/1 1 29 28/43 -5/8 1 29 15/23 0/1 1 29 2/3 -1/2 1 29 20/29 -1/2 9 1 9/13 -4/9 1 29 16/23 -3/8 1 29 39/56 -1/3 1 29 23/33 0/1 1 29 7/10 -1/3 1 29 40/57 -1/4 1 29 33/47 -2/7 1 29 26/37 -1/2 1 29 45/64 -1/3 1 29 19/27 0/1 1 29 31/44 1/3 1 29 12/17 -1/4 1 29 17/24 1/1 1 29 39/55 0/1 1 29 22/31 -1/2 1 29 5/7 -2/5 1 29 23/32 -1/3 1 29 64/89 -1/4 1 29 146/203 -1/4 1 1 41/57 0/1 1 29 18/25 -1/2 1 29 13/18 -1/5 1 29 21/29 0/1 5 1 8/11 1/0 1 29 11/15 -4/5 1 29 14/19 -1/2 1 29 17/23 0/1 1 29 20/27 -1/8 1 29 43/58 0/1 13 1 23/31 0/1 1 29 3/4 -1/1 1 29 22/29 -1/2 7 1 16/21 -5/12 1 29 29/38 -1/3 1 29 13/17 -2/5 1 29 23/30 -1/3 1 29 56/73 -15/44 1 29 89/116 -1/3 23 1 33/43 -8/25 1 29 10/13 -1/2 1 29 17/22 -3/13 1 29 24/31 -1/4 1 29 7/9 0/1 1 29 25/32 -3/5 1 29 68/87 -1/2 9 1 18/23 -1/2 1 29 29/37 -2/5 1 29 11/14 -3/11 1 29 26/33 -1/6 1 29 15/19 0/1 1 29 19/24 -1/11 1 29 23/29 0/1 11 1 4/5 1/0 1 29 9/11 0/1 1 29 23/28 -1/1 1 29 14/17 -1/2 1 29 24/29 -1/2 5 1 5/6 -1/3 1 29 16/19 -1/4 1 29 11/13 0/1 1 29 6/7 -1/6 1 29 25/29 0/1 17 1 19/22 1/11 1 29 13/15 2/5 1 29 7/8 -1/1 1 29 15/17 0/1 1 29 8/9 1/0 1 29 1/1 0/1 1 29 1/0 0/1 1 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(407,-40,580,-57) (0/1,1/10) -> (7/10,40/57) Hyperbolic Matrix(697,-74,1102,-117) (1/10,1/9) -> (43/68,31/49) Glide Reflection Matrix(173,-20,493,-57) (1/9,1/8) -> (7/20,13/37) Glide Reflection Matrix(173,-22,464,-59) (1/8,2/15) -> (16/43,3/8) Hyperbolic Matrix(59,-8,435,-59) (2/15,4/29) -> (2/15,4/29) Reflection Matrix(57,-8,406,-57) (4/29,1/7) -> (4/29,1/7) Reflection Matrix(291,-44,377,-57) (1/7,2/13) -> (10/13,17/22) Hyperbolic Matrix(115,-18,377,-59) (2/13,1/6) -> (7/23,4/13) Hyperbolic Matrix(59,-10,348,-59) (1/6,5/29) -> (1/6,5/29) Reflection Matrix(231,-40,1334,-231) (5/29,4/23) -> (5/29,4/23) Reflection Matrix(813,-142,1334,-233) (4/23,3/17) -> (14/23,25/41) Glide Reflection Matrix(233,-42,638,-115) (3/17,2/11) -> (4/11,15/41) Hyperbolic Matrix(173,-32,319,-59) (2/11,3/16) -> (7/13,6/11) Hyperbolic Matrix(233,-44,609,-115) (3/16,1/5) -> (13/34,5/13) Hyperbolic Matrix(59,-12,290,-59) (1/5,6/29) -> (1/5,6/29) Reflection Matrix(115,-24,551,-115) (6/29,4/19) -> (6/29,4/19) Reflection Matrix(405,-86,551,-117) (4/19,3/14) -> (11/15,14/19) Hyperbolic Matrix(929,-200,1073,-231) (3/14,11/51) -> (19/22,13/15) Hyperbolic Matrix(927,-200,2146,-463) (11/51,8/37) -> (3/7,16/37) Glide Reflection Matrix(2263,-490,3219,-697) (8/37,5/23) -> (26/37,45/64) Glide Reflection Matrix(871,-190,1334,-291) (5/23,12/55) -> (15/23,2/3) Glide Reflection Matrix(2089,-456,9570,-2089) (12/55,19/87) -> (12/55,19/87) Reflection Matrix(1217,-266,5568,-1217) (19/87,7/32) -> (19/87,7/32) Reflection Matrix(639,-140,2378,-521) (7/32,2/9) -> (18/67,7/26) Hyperbolic Matrix(115,-26,261,-59) (2/9,3/13) -> (7/16,4/9) Hyperbolic Matrix(405,-94,754,-175) (3/13,7/30) -> (15/28,7/13) Hyperbolic Matrix(811,-190,986,-231) (7/30,4/17) -> (23/28,14/17) Glide Reflection Matrix(347,-82,986,-233) (4/17,5/21) -> (13/37,6/17) Hyperbolic Matrix(1219,-292,2175,-521) (5/21,6/25) -> (14/25,37/66) Hyperbolic Matrix(349,-84,1450,-349) (6/25,7/29) -> (6/25,7/29) Reflection Matrix(57,-14,232,-57) (7/29,1/4) -> (7/29,1/4) Reflection Matrix(465,-122,667,-175) (1/4,5/19) -> (23/33,7/10) Glide Reflection Matrix(871,-230,1102,-291) (5/19,9/34) -> (15/19,19/24) Glide Reflection Matrix(1101,-292,1972,-523) (9/34,4/15) -> (24/43,19/34) Hyperbolic Matrix(813,-218,1943,-521) (4/15,11/41) -> (5/12,18/43) Hyperbolic Matrix(1333,-358,1508,-405) (11/41,18/67) -> (15/17,8/9) Glide Reflection Matrix(985,-266,2581,-697) (7/26,10/37) -> (8/21,21/55) Hyperbolic Matrix(1507,-408,2146,-581) (10/37,3/11) -> (33/47,26/37) Hyperbolic Matrix(175,-48,638,-175) (3/11,8/29) -> (3/11,8/29) Reflection Matrix(57,-16,203,-57) (8/29,2/7) -> (8/29,2/7) Reflection Matrix(117,-34,203,-59) (2/7,3/10) -> (4/7,11/19) Glide Reflection Matrix(755,-228,957,-289) (3/10,10/33) -> (26/33,15/19) Hyperbolic Matrix(1451,-440,4785,-1451) (10/33,44/145) -> (10/33,44/145) Reflection Matrix(4929,-1496,16240,-4929) (44/145,17/56) -> (44/145,17/56) Reflection Matrix(2957,-898,4205,-1277) (17/56,7/23) -> (45/64,19/27) Hyperbolic Matrix(233,-72,754,-233) (4/13,9/29) -> (4/13,9/29) Reflection Matrix(289,-90,928,-289) (9/29,5/16) -> (9/29,5/16) Reflection Matrix(233,-74,551,-175) (5/16,1/3) -> (19/45,11/26) Glide Reflection Matrix(521,-182,667,-233) (1/3,7/20) -> (7/9,25/32) Hyperbolic Matrix(695,-246,986,-349) (6/17,5/14) -> (31/44,12/17) Hyperbolic Matrix(233,-84,319,-115) (5/14,4/11) -> (8/11,11/15) Hyperbolic Matrix(1333,-488,1740,-637) (15/41,11/30) -> (13/17,23/30) Glide Reflection Matrix(289,-106,319,-117) (11/30,18/49) -> (8/9,1/1) Hyperbolic Matrix(1567,-576,4263,-1567) (18/49,32/87) -> (18/49,32/87) Reflection Matrix(1217,-448,3306,-1217) (32/87,7/19) -> (32/87,7/19) Reflection Matrix(639,-236,1102,-407) (7/19,10/27) -> (11/19,18/31) Glide Reflection Matrix(1159,-430,1566,-581) (10/27,13/35) -> (17/23,20/27) Hyperbolic Matrix(1625,-604,2494,-927) (13/35,16/43) -> (28/43,15/23) Hyperbolic Matrix(175,-66,464,-175) (3/8,11/29) -> (3/8,11/29) Reflection Matrix(463,-176,1218,-463) (11/29,8/21) -> (11/29,8/21) Reflection Matrix(2261,-864,3190,-1219) (21/55,13/34) -> (17/24,39/55) Hyperbolic Matrix(929,-358,1653,-637) (5/13,22/57) -> (32/57,9/16) Hyperbolic Matrix(3191,-1232,8265,-3191) (22/57,56/145) -> (22/57,56/145) Reflection Matrix(4929,-1904,12760,-4929) (56/145,17/44) -> (56/145,17/44) Reflection Matrix(1159,-448,1798,-695) (17/44,12/31) -> (9/14,20/31) Glide Reflection Matrix(407,-158,899,-349) (12/31,7/18) -> (14/31,5/11) Glide Reflection Matrix(117,-46,145,-57) (7/18,2/5) -> (4/5,9/11) Hyperbolic Matrix(59,-24,145,-59) (2/5,12/29) -> (2/5,12/29) Reflection Matrix(289,-120,696,-289) (12/29,5/12) -> (12/29,5/12) Reflection Matrix(291,-122,551,-231) (18/43,13/31) -> (1/2,8/15) Hyperbolic Matrix(695,-292,1102,-463) (13/31,8/19) -> (17/27,12/19) Glide Reflection Matrix(929,-392,1102,-465) (8/19,19/45) -> (16/19,11/13) Glide Reflection Matrix(291,-124,406,-173) (11/26,3/7) -> (5/7,23/32) Hyperbolic Matrix(2203,-954,3480,-1507) (16/37,13/30) -> (50/79,19/30) Glide Reflection Matrix(811,-352,1334,-579) (13/30,10/23) -> (17/28,14/23) Glide Reflection Matrix(463,-202,667,-291) (10/23,7/16) -> (9/13,16/23) Hyperbolic Matrix(233,-104,522,-233) (4/9,13/29) -> (4/9,13/29) Reflection Matrix(521,-234,1160,-521) (13/29,9/20) -> (13/29,9/20) Reflection Matrix(697,-314,899,-405) (9/20,14/31) -> (24/31,7/9) Hyperbolic Matrix(231,-106,377,-173) (5/11,1/2) -> (11/18,19/31) Glide Reflection Matrix(1913,-1024,2494,-1335) (8/15,15/28) -> (23/30,56/73) Hyperbolic Matrix(175,-96,319,-175) (6/11,16/29) -> (6/11,16/29) Reflection Matrix(289,-160,522,-289) (16/29,5/9) -> (16/29,5/9) Reflection Matrix(811,-452,1247,-695) (5/9,24/43) -> (13/20,28/43) Glide Reflection Matrix(755,-422,1247,-697) (19/34,14/25) -> (3/5,20/33) Glide Reflection Matrix(1277,-716,1450,-813) (37/66,23/41) -> (7/8,15/17) Glide Reflection Matrix(2901,-1628,4756,-2669) (23/41,32/57) -> (25/41,36/59) Glide Reflection Matrix(173,-98,203,-115) (9/16,4/7) -> (11/13,6/7) Glide Reflection Matrix(581,-338,899,-523) (18/31,7/12) -> (20/31,11/17) Glide Reflection Matrix(407,-238,696,-407) (7/12,17/29) -> (7/12,17/29) Reflection Matrix(579,-340,986,-579) (17/29,10/17) -> (17/29,10/17) Reflection Matrix(349,-206,493,-291) (10/17,3/5) -> (12/17,17/24) Glide Reflection Matrix(1857,-1126,2581,-1565) (20/33,17/28) -> (41/57,18/25) Hyperbolic Matrix(2667,-1628,3799,-2319) (36/59,11/18) -> (40/57,33/47) Glide Reflection Matrix(1797,-1102,2552,-1565) (19/31,27/44) -> (19/27,31/44) Glide Reflection Matrix(869,-534,1131,-695) (27/44,8/13) -> (33/43,10/13) Glide Reflection Matrix(233,-144,377,-233) (8/13,18/29) -> (8/13,18/29) Reflection Matrix(289,-180,464,-289) (18/29,5/8) -> (18/29,5/8) Reflection Matrix(1159,-728,1479,-929) (5/8,22/35) -> (18/23,29/37) Hyperbolic Matrix(1797,-1130,2581,-1623) (22/35,17/27) -> (16/23,39/56) Glide Reflection Matrix(2089,-1320,3306,-2089) (12/19,55/87) -> (12/19,55/87) Reflection Matrix(7481,-4730,11832,-7481) (55/87,43/68) -> (55/87,43/68) Reflection Matrix(3075,-1946,4031,-2551) (31/49,50/79) -> (16/21,29/38) Hyperbolic Matrix(523,-332,638,-405) (19/30,7/11) -> (9/11,23/28) Hyperbolic Matrix(523,-334,725,-463) (7/11,16/25) -> (18/25,13/18) Hyperbolic Matrix(639,-410,812,-521) (16/25,9/14) -> (11/14,26/33) Hyperbolic Matrix(753,-488,986,-639) (11/17,13/20) -> (29/38,13/17) Hyperbolic Matrix(59,-40,87,-59) (2/3,20/29) -> (2/3,20/29) Reflection Matrix(521,-360,754,-521) (20/29,9/13) -> (20/29,9/13) Reflection Matrix(927,-646,1247,-869) (39/56,23/33) -> (23/31,3/4) Glide Reflection Matrix(4233,-3002,5887,-4175) (39/55,22/31) -> (23/32,64/89) Glide Reflection Matrix(695,-494,899,-639) (22/31,5/7) -> (17/22,24/31) Hyperbolic Matrix(12993,-9344,18067,-12993) (64/89,146/203) -> (64/89,146/203) Reflection Matrix(16645,-11972,23142,-16645) (146/203,41/57) -> (146/203,41/57) Reflection Matrix(755,-546,1044,-755) (13/18,21/29) -> (13/18,21/29) Reflection Matrix(463,-336,638,-463) (21/29,8/11) -> (21/29,8/11) Reflection Matrix(463,-342,551,-407) (14/19,17/23) -> (5/6,16/19) Hyperbolic Matrix(2321,-1720,3132,-2321) (20/27,43/58) -> (20/27,43/58) Reflection Matrix(2667,-1978,3596,-2667) (43/58,23/31) -> (43/58,23/31) Reflection Matrix(175,-132,232,-175) (3/4,22/29) -> (3/4,22/29) Reflection Matrix(463,-352,609,-463) (22/29,16/21) -> (22/29,16/21) Reflection Matrix(12993,-9968,16936,-12993) (56/73,89/116) -> (56/73,89/116) Reflection Matrix(7655,-5874,9976,-7655) (89/116,33/43) -> (89/116,33/43) Reflection Matrix(4351,-3400,5568,-4351) (25/32,68/87) -> (25/32,68/87) Reflection Matrix(1565,-1224,2001,-1565) (68/87,18/23) -> (68/87,18/23) Reflection Matrix(579,-454,667,-523) (29/37,11/14) -> (13/15,7/8) Hyperbolic Matrix(1103,-874,1392,-1103) (19/24,23/29) -> (19/24,23/29) Reflection Matrix(231,-184,290,-231) (23/29,4/5) -> (23/29,4/5) Reflection Matrix(407,-336,493,-407) (14/17,24/29) -> (14/17,24/29) Reflection Matrix(289,-240,348,-289) (24/29,5/6) -> (24/29,5/6) Reflection Matrix(349,-300,406,-349) (6/7,25/29) -> (6/7,25/29) Reflection Matrix(1101,-950,1276,-1101) (25/29,19/22) -> (25/29,19/22) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(407,-40,580,-57) -> Matrix(1,2,-4,-7) Matrix(697,-74,1102,-117) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(173,-20,493,-57) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(173,-22,464,-59) -> Matrix(3,-4,-2,3) Matrix(59,-8,435,-59) -> Matrix(-1,9,0,1) (2/15,4/29) -> (9/2,1/0) Matrix(57,-8,406,-57) -> Matrix(1,12,0,-1) (4/29,1/7) -> (-6/1,1/0) Matrix(291,-44,377,-57) -> Matrix(1,3,-4,-11) Matrix(115,-18,377,-59) -> Matrix(3,5,-2,-3) (-2/1,-1/1).(-3/2,1/0) Matrix(59,-10,348,-59) -> Matrix(3,4,-2,-3) (1/6,5/29) -> (-2/1,-1/1) Matrix(231,-40,1334,-231) -> Matrix(7,6,-8,-7) (5/29,4/23) -> (-1/1,-3/4) Matrix(813,-142,1334,-233) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(233,-42,638,-115) -> Matrix(3,2,-2,-1) -1/1 Matrix(173,-32,319,-59) -> Matrix(3,1,-4,-1) -1/2 Matrix(233,-44,609,-115) -> Matrix(3,1,-4,-1) -1/2 Matrix(59,-12,290,-59) -> Matrix(-1,4,0,1) (1/5,6/29) -> (2/1,1/0) Matrix(115,-24,551,-115) -> Matrix(1,13,0,-1) (6/29,4/19) -> (-13/2,1/0) Matrix(405,-86,551,-117) -> Matrix(1,5,-2,-9) Matrix(929,-200,1073,-231) -> Matrix(1,3,4,13) Matrix(927,-200,2146,-463) -> Matrix(3,8,-4,-11) Matrix(2263,-490,3219,-697) -> Matrix(1,3,-2,-7) Matrix(871,-190,1334,-291) -> Matrix(1,2,-2,-5) Matrix(2089,-456,9570,-2089) -> Matrix(1,6,0,-1) (12/55,19/87) -> (-3/1,1/0) Matrix(1217,-266,5568,-1217) -> Matrix(5,12,-2,-5) (19/87,7/32) -> (-3/1,-2/1) Matrix(639,-140,2378,-521) -> Matrix(1,4,0,1) 1/0 Matrix(115,-26,261,-59) -> Matrix(3,5,-2,-3) (-2/1,-1/1).(-3/2,1/0) Matrix(405,-94,754,-175) -> Matrix(5,6,-6,-7) -1/1 Matrix(811,-190,986,-231) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(347,-82,986,-233) -> Matrix(5,8,-2,-3) -2/1 Matrix(1219,-292,2175,-521) -> Matrix(1,1,4,5) Matrix(349,-84,1450,-349) -> Matrix(13,14,-12,-13) (6/25,7/29) -> (-7/6,-1/1) Matrix(57,-14,232,-57) -> Matrix(-1,0,2,1) (7/29,1/4) -> (-1/1,0/1) Matrix(465,-122,667,-175) -> Matrix(1,1,-2,-3) Matrix(871,-230,1102,-291) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(1101,-292,1972,-523) -> Matrix(1,0,-4,1) 0/1 Matrix(813,-218,1943,-521) -> Matrix(5,-7,-2,3) Matrix(1333,-358,1508,-405) -> Matrix(1,-2,-2,3) Matrix(985,-266,2581,-697) -> Matrix(5,-9,-6,11) Matrix(1507,-408,2146,-581) -> Matrix(1,-2,-4,9) Matrix(175,-48,638,-175) -> Matrix(-1,8,0,1) (3/11,8/29) -> (4/1,1/0) Matrix(57,-16,203,-57) -> Matrix(1,5,0,-1) (8/29,2/7) -> (-5/2,1/0) Matrix(117,-34,203,-59) -> Matrix(1,1,-2,-3) Matrix(755,-228,957,-289) -> Matrix(1,1,-4,-3) -1/2 Matrix(1451,-440,4785,-1451) -> Matrix(1,3,0,-1) (10/33,44/145) -> (-3/2,1/0) Matrix(4929,-1496,16240,-4929) -> Matrix(5,6,-4,-5) (44/145,17/56) -> (-3/2,-1/1) Matrix(2957,-898,4205,-1277) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(233,-72,754,-233) -> Matrix(9,10,-8,-9) (4/13,9/29) -> (-5/4,-1/1) Matrix(289,-90,928,-289) -> Matrix(9,8,-10,-9) (9/29,5/16) -> (-1/1,-4/5) Matrix(233,-74,551,-175) -> Matrix(3,1,-2,-1) Matrix(521,-182,667,-233) -> Matrix(1,3,-2,-5) Matrix(695,-246,986,-349) -> Matrix(1,2,-2,-3) -1/1 Matrix(233,-84,319,-115) -> Matrix(1,1,0,1) 1/0 Matrix(1333,-488,1740,-637) -> Matrix(3,4,-8,-11) Matrix(289,-106,319,-117) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(1567,-576,4263,-1567) -> Matrix(1,1,0,-1) (18/49,32/87) -> (-1/2,1/0) Matrix(1217,-448,3306,-1217) -> Matrix(1,4,0,-1) (32/87,7/19) -> (-2/1,1/0) Matrix(639,-236,1102,-407) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1159,-430,1566,-581) -> Matrix(1,2,-6,-11) Matrix(1625,-604,2494,-927) -> Matrix(1,2,-4,-7) Matrix(175,-66,464,-175) -> Matrix(7,8,-6,-7) (3/8,11/29) -> (-4/3,-1/1) Matrix(463,-176,1218,-463) -> Matrix(15,14,-16,-15) (11/29,8/21) -> (-1/1,-7/8) Matrix(2261,-864,3190,-1219) -> Matrix(5,4,-4,-3) -1/1 Matrix(929,-358,1653,-637) -> Matrix(5,3,-2,-1) Matrix(3191,-1232,8265,-3191) -> Matrix(21,11,-40,-21) (22/57,56/145) -> (-11/20,-1/2) Matrix(4929,-1904,12760,-4929) -> Matrix(29,14,-60,-29) (56/145,17/44) -> (-1/2,-7/15) Matrix(1159,-448,1798,-695) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(407,-158,899,-349) -> Matrix(1,-1,-2,1) Matrix(117,-46,145,-57) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(59,-24,145,-59) -> Matrix(1,1,0,-1) (2/5,12/29) -> (-1/2,1/0) Matrix(289,-120,696,-289) -> Matrix(1,6,0,-1) (12/29,5/12) -> (-3/1,1/0) Matrix(291,-122,551,-231) -> Matrix(1,3,-2,-5) Matrix(695,-292,1102,-463) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(929,-392,1102,-465) -> Matrix(1,2,-4,-9) Matrix(291,-124,406,-173) -> Matrix(1,2,-4,-7) Matrix(2203,-954,3480,-1507) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(811,-352,1334,-579) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(463,-202,667,-291) -> Matrix(1,-1,-2,3) Matrix(233,-104,522,-233) -> Matrix(9,10,-8,-9) (4/9,13/29) -> (-5/4,-1/1) Matrix(521,-234,1160,-521) -> Matrix(17,16,-18,-17) (13/29,9/20) -> (-1/1,-8/9) Matrix(697,-314,899,-405) -> Matrix(1,1,-10,-9) Matrix(231,-106,377,-173) -> Matrix(1,-1,-2,1) Matrix(1913,-1024,2494,-1335) -> Matrix(11,10,-32,-29) Matrix(175,-96,319,-175) -> Matrix(5,3,-8,-5) (6/11,16/29) -> (-3/4,-1/2) Matrix(289,-160,522,-289) -> Matrix(-1,0,4,1) (16/29,5/9) -> (-1/2,0/1) Matrix(811,-452,1247,-695) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(755,-422,1247,-697) -> Matrix(1,-1,-2,1) Matrix(1277,-716,1450,-813) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2901,-1628,4756,-2669) -> Matrix(3,-4,-4,5) Matrix(173,-98,203,-115) -> Matrix(1,1,-2,-3) Matrix(581,-338,899,-523) -> Matrix(1,1,-2,-3) Matrix(407,-238,696,-407) -> Matrix(3,4,-2,-3) (7/12,17/29) -> (-2/1,-1/1) Matrix(579,-340,986,-579) -> Matrix(11,10,-12,-11) (17/29,10/17) -> (-1/1,-5/6) Matrix(349,-206,493,-291) -> Matrix(1,1,2,1) Matrix(1857,-1126,2581,-1565) -> Matrix(1,1,-6,-5) Matrix(2667,-1628,3799,-2319) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(1797,-1102,2552,-1565) -> Matrix(3,2,-10,-7) Matrix(869,-534,1131,-695) -> Matrix(5,3,-18,-11) Matrix(233,-144,377,-233) -> Matrix(9,5,-16,-9) (8/13,18/29) -> (-5/8,-1/2) Matrix(289,-180,464,-289) -> Matrix(5,2,-12,-5) (18/29,5/8) -> (-1/2,-1/3) Matrix(1159,-728,1479,-929) -> Matrix(1,1,-4,-3) -1/2 Matrix(1797,-1130,2581,-1623) -> Matrix(5,1,-14,-3) Matrix(2089,-1320,3306,-2089) -> Matrix(1,2,0,-1) (12/19,55/87) -> (-1/1,1/0) Matrix(7481,-4730,11832,-7481) -> Matrix(5,4,-6,-5) (55/87,43/68) -> (-1/1,-2/3) Matrix(3075,-1946,4031,-2551) -> Matrix(1,-1,-2,3) Matrix(523,-332,638,-405) -> Matrix(1,0,0,1) Matrix(523,-334,725,-463) -> Matrix(1,1,-6,-5) Matrix(639,-410,812,-521) -> Matrix(3,2,-14,-9) Matrix(753,-488,986,-639) -> Matrix(3,2,-8,-5) -1/2 Matrix(59,-40,87,-59) -> Matrix(1,1,0,-1) (2/3,20/29) -> (-1/2,1/0) Matrix(521,-360,754,-521) -> Matrix(17,8,-36,-17) (20/29,9/13) -> (-1/2,-4/9) Matrix(927,-646,1247,-869) -> Matrix(3,1,-2,-1) Matrix(4233,-3002,5887,-4175) -> Matrix(1,1,-2,-3) Matrix(695,-494,899,-639) -> Matrix(1,1,-6,-5) Matrix(12993,-9344,18067,-12993) -> Matrix(3,1,-8,-3) (64/89,146/203) -> (-1/2,-1/4) Matrix(16645,-11972,23142,-16645) -> Matrix(-1,0,8,1) (146/203,41/57) -> (-1/4,0/1) Matrix(755,-546,1044,-755) -> Matrix(-1,0,10,1) (13/18,21/29) -> (-1/5,0/1) Matrix(463,-336,638,-463) -> Matrix(1,0,0,-1) (21/29,8/11) -> (0/1,1/0) Matrix(463,-342,551,-407) -> Matrix(3,1,-10,-3) (-1/2,-1/4).(-1/3,0/1) Matrix(2321,-1720,3132,-2321) -> Matrix(-1,0,16,1) (20/27,43/58) -> (-1/8,0/1) Matrix(2667,-1978,3596,-2667) -> Matrix(1,0,10,-1) (43/58,23/31) -> (0/1,1/5) Matrix(175,-132,232,-175) -> Matrix(3,2,-4,-3) (3/4,22/29) -> (-1/1,-1/2) Matrix(463,-352,609,-463) -> Matrix(11,5,-24,-11) (22/29,16/21) -> (-1/2,-5/12) Matrix(12993,-9968,16936,-12993) -> Matrix(89,30,-264,-89) (56/73,89/116) -> (-15/44,-1/3) Matrix(7655,-5874,9976,-7655) -> Matrix(49,16,-150,-49) (89/116,33/43) -> (-1/3,-8/25) Matrix(4351,-3400,5568,-4351) -> Matrix(11,6,-20,-11) (25/32,68/87) -> (-3/5,-1/2) Matrix(1565,-1224,2001,-1565) -> Matrix(7,3,-16,-7) (68/87,18/23) -> (-1/2,-3/8) Matrix(579,-454,667,-523) -> Matrix(3,1,2,1) Matrix(1103,-874,1392,-1103) -> Matrix(-1,0,22,1) (19/24,23/29) -> (-1/11,0/1) Matrix(231,-184,290,-231) -> Matrix(1,0,0,-1) (23/29,4/5) -> (0/1,1/0) Matrix(407,-336,493,-407) -> Matrix(5,3,-8,-5) (14/17,24/29) -> (-3/4,-1/2) Matrix(289,-240,348,-289) -> Matrix(5,2,-12,-5) (24/29,5/6) -> (-1/2,-1/3) Matrix(349,-300,406,-349) -> Matrix(-1,0,12,1) (6/7,25/29) -> (-1/6,0/1) Matrix(1101,-950,1276,-1101) -> Matrix(1,0,22,-1) (25/29,19/22) -> (0/1,1/11) Matrix(-1,2,0,1) -> Matrix(-1,0,2,1) (1/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.