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): 1800 Minimal number of generators: 301 Number of equivalence classes of cusps: 84 Genus: 109 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -4/5 -11/15 -52/75 -3/5 -74/125 -7/15 -9/20 -21/50 -2/5 -49/125 -19/50 -8/25 -3/10 -27/100 -67/250 -4/15 -53/200 -13/50 -6/25 -5/21 -11/50 -5/24 -1/5 -4/21 -9/50 -4/23 -13/75 -4/25 -3/19 -3/20 -7/50 -3/22 -2/15 -3/25 -2/17 -1/10 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 5/23 2/9 3/13 1/4 4/15 3/11 5/18 7/25 2/7 3/10 23/75 1/3 9/25 2/5 5/12 11/25 9/20 7/15 1/2 14/25 3/5 16/25 2/3 17/25 18/25 11/15 19/25 4/5 62/75 21/25 22/25 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/23 -9/10 0/1 -8/9 2/43 1/21 -7/8 1/21 2/41 -13/15 1/20 -6/7 0/1 1/21 -17/20 2/41 -11/13 2/41 1/20 -5/6 1/20 2/39 -14/17 0/1 1/19 -9/11 2/39 1/19 -13/16 0/1 1/19 -4/5 1/19 -15/19 2/37 1/18 -11/14 1/19 4/75 -18/23 3/56 2/37 -7/9 2/37 3/55 -31/40 4/73 -24/31 6/109 1/18 -17/22 1/18 2/35 -61/79 1/18 2/35 -105/136 0/1 1/17 -44/57 0/1 1/19 -27/35 1/18 -10/13 2/37 1/18 -23/30 2/37 -13/17 4/73 5/91 -3/4 1/18 2/35 -14/19 2/35 3/52 -25/34 7/121 4/69 -36/49 4/69 1/17 -11/15 1/17 -41/56 1/18 2/35 -30/41 2/35 1/17 -19/26 2/35 1/17 -8/11 2/35 1/17 -37/51 7/121 4/69 -29/40 4/69 -50/69 5/86 6/103 -21/29 5/86 6/103 -55/76 6/103 1/17 -34/47 5/86 6/103 -47/65 7/120 -13/18 10/171 1/17 -18/25 1/17 -5/7 1/17 4/67 -17/24 1/17 2/33 -29/41 1/17 2/33 -12/17 1/17 4/67 -31/44 3/50 2/33 -81/115 1/17 -50/71 3/50 2/33 -69/98 4/67 3/50 -88/125 3/50 -19/27 3/50 2/33 -7/10 2/33 -16/23 2/33 1/16 -25/36 3/49 4/65 -84/121 2/33 1/16 -59/85 3/49 -34/49 3/49 4/65 -43/62 6/97 1/16 -52/75 1/16 -9/13 2/33 1/16 -11/16 3/49 4/65 -13/19 6/97 1/16 -2/3 1/16 2/31 -13/20 2/31 -11/17 7/107 4/61 -9/14 8/121 1/15 -16/25 1/15 -7/11 1/15 6/89 -19/30 4/59 -31/49 1/15 4/59 -12/19 3/44 2/29 -29/46 7/102 2/29 -17/27 2/29 5/72 -39/62 2/29 1/14 -22/35 1/14 -5/8 1/15 2/29 -13/21 2/29 5/72 -34/55 3/43 -21/34 3/43 4/57 -8/13 2/29 1/14 -19/31 1/14 2/27 -30/49 0/1 1/13 -71/116 0/1 1/11 -41/67 0/1 1/19 -11/18 1/15 2/29 -25/41 2/29 7/101 -14/23 2/29 1/14 -3/5 1/14 -16/27 1/14 2/27 -45/76 2/27 1/13 -74/125 1/13 -29/49 0/1 1/13 -13/22 1/14 2/27 -23/39 2/27 1/13 -10/17 0/1 1/13 -17/29 1/14 6/83 -24/41 3/41 2/27 -55/94 5/68 2/27 -31/53 2/27 3/40 -7/12 1/14 2/27 -11/19 2/27 3/40 -26/45 1/13 -41/71 2/27 3/40 -15/26 2/27 1/13 -4/7 0/1 1/13 -17/30 2/27 -30/53 1/14 2/27 -43/76 2/27 1/13 -13/23 1/14 2/27 -9/16 4/53 1/13 -14/25 1/13 -5/9 1/13 2/25 -16/29 1/12 2/23 -43/78 1/12 2/23 -27/49 0/1 1/11 -11/20 0/1 -6/11 1/13 2/25 -13/24 1/13 2/25 -7/13 2/25 1/12 -8/15 1/12 -9/17 0/1 1/15 -1/2 0/1 1/12 -8/17 0/1 1/9 -7/15 1/12 -6/13 1/12 2/23 -5/11 2/23 1/11 -9/20 0/1 -13/29 2/25 1/12 -4/9 2/23 1/11 -11/25 1/11 -7/16 1/11 4/43 -17/39 1/11 2/21 -27/62 3/32 2/21 -10/23 2/21 1/10 -13/30 2/21 -3/7 0/1 1/11 -11/26 1/11 2/21 -8/19 3/32 2/21 -21/50 2/21 -13/31 2/21 5/52 -5/12 2/21 1/10 -22/53 3/32 2/21 -17/41 2/21 3/31 -12/29 6/61 1/10 -31/75 1/10 -19/46 1/10 6/59 -7/17 0/1 1/11 -9/22 2/21 1/10 -2/5 1/10 -11/28 1/10 2/19 -20/51 4/39 3/29 -49/125 3/29 -29/74 3/29 2/19 -9/23 1/10 2/19 -7/18 2/19 1/9 -33/85 1/8 -26/67 0/1 1/5 -19/49 0/1 1/11 -12/31 2/21 1/10 -29/75 1/10 -17/44 1/10 6/59 -5/13 1/10 2/19 -13/34 4/39 3/29 -8/21 5/48 2/19 -19/50 2/19 -11/29 2/19 7/66 -3/8 2/19 1/9 -13/35 1/10 -36/97 5/48 2/19 -23/62 1/10 2/19 -10/27 5/48 2/19 -7/19 2/19 3/28 -18/49 4/37 1/9 -47/128 2/19 3/28 -29/79 2/19 3/28 -11/30 4/37 -4/11 6/55 1/9 -9/25 1/9 -5/14 1/9 8/71 -11/31 6/53 5/44 -17/48 5/44 4/35 -6/17 4/35 7/61 -7/20 2/17 -8/23 2/17 1/8 -1/3 2/17 1/8 -8/25 1/8 -7/22 1/8 14/111 -6/19 1/8 6/47 -5/16 4/31 3/23 -4/13 1/8 2/15 -7/23 1/8 2/15 -3/10 2/15 -8/27 2/15 3/22 -5/17 4/29 1/7 -22/75 1/7 -17/58 1/7 2/13 -12/41 2/15 1/7 -7/24 2/15 1/7 -2/7 4/29 1/7 -7/25 1/7 -5/18 1/7 10/69 -23/83 8/55 31/213 -18/65 7/48 -31/112 7/48 6/41 -13/47 6/41 5/34 -34/123 6/41 5/34 -21/76 1/7 6/41 -8/29 6/41 5/34 -27/98 5/34 4/27 -19/69 6/41 5/34 -11/40 4/27 -14/51 4/27 7/47 -17/62 3/20 2/13 -3/11 1/7 2/13 -10/37 3/20 2/13 -27/100 2/13 -17/63 2/13 1/6 -7/26 1/7 2/13 -11/41 1/7 2/13 -26/97 7/46 2/13 -67/250 2/13 -41/153 2/13 9/58 -15/56 2/13 1/6 -4/15 1/7 -13/49 1/7 4/27 -22/83 25/169 4/27 -53/200 4/27 -31/117 4/27 39/263 -9/34 4/27 7/47 -5/19 3/20 2/13 -6/23 11/72 2/13 -13/50 2/13 -7/27 2/13 13/84 -1/4 2/13 1/6 -6/25 1/6 -5/21 1/6 10/59 -4/17 5/29 4/23 -7/30 2/11 -3/13 1/6 2/11 -8/35 1/6 -5/22 2/13 1/6 -17/75 1/6 -12/53 1/6 14/83 -7/31 1/6 6/35 -9/40 4/23 -2/9 3/17 2/11 -11/50 2/11 -9/41 2/11 13/71 -7/32 2/11 5/27 -5/23 2/11 3/16 -8/37 2/11 3/16 -27/125 3/16 -19/88 3/16 10/53 -11/51 4/21 1/5 -14/65 1/5 -3/14 4/21 1/5 -7/33 0/1 1/3 -11/52 0/1 1/6 -15/71 1/6 2/11 -4/19 1/6 2/11 -5/24 2/11 1/5 -1/5 1/5 -5/26 1/5 2/9 -4/21 3/14 2/9 -3/16 0/1 1/5 -5/27 3/14 2/9 -7/38 2/9 1/4 -9/49 0/1 1/3 -2/11 1/5 2/9 -9/50 2/9 -7/39 2/9 3/13 -5/28 2/9 1/4 -3/17 0/1 1/5 -4/23 2/9 1/4 -13/75 1/4 -9/52 0/1 1/4 -5/29 2/9 1/4 -11/64 0/1 1/5 -6/35 1/5 -1/6 2/9 1/4 -4/25 1/4 -3/19 1/4 6/23 -2/13 1/4 2/7 -3/20 2/7 -1/7 0/1 1/3 -7/50 0/1 -6/43 0/1 1/7 -5/36 0/1 1/5 -4/29 2/9 1/4 -3/22 2/9 1/4 -2/15 1/4 -1/8 2/7 1/3 -3/25 1/3 -2/17 1/3 4/11 -1/9 1/3 2/5 -1/10 0/1 0/1 0/1 1/1 1/10 0/1 1/9 -2/1 -1/1 1/8 -1/1 -2/3 2/15 -1/2 1/7 -1/1 0/1 3/20 -2/3 2/13 -2/3 -1/2 1/6 -1/2 -2/5 3/17 -1/3 0/1 2/11 -2/5 -1/3 3/16 -1/3 0/1 1/5 -1/3 4/19 -2/7 -1/4 3/14 -1/3 -4/13 5/23 -3/10 -2/7 2/9 -2/7 -3/11 9/40 -4/15 7/31 -6/23 -1/4 5/22 -1/4 -2/9 18/79 -1/4 -2/9 31/136 -1/5 0/1 13/57 -1/3 0/1 8/35 -1/4 3/13 -2/7 -1/4 7/30 -2/7 4/17 -4/15 -5/19 1/4 -1/4 -2/9 5/19 -2/9 -3/14 9/34 -7/33 -4/19 13/49 -4/19 -1/5 4/15 -1/5 15/56 -1/4 -2/9 11/41 -2/9 -1/5 7/26 -2/9 -1/5 3/11 -2/9 -1/5 14/51 -7/33 -4/19 11/40 -4/19 19/69 -5/24 -6/29 8/29 -5/24 -6/29 21/76 -6/29 -1/5 13/47 -5/24 -6/29 18/65 -7/34 5/18 -10/49 -1/5 7/25 -1/5 2/7 -1/5 -4/21 7/24 -1/5 -2/11 12/41 -1/5 -2/11 5/17 -1/5 -4/21 13/44 -3/16 -2/11 34/115 -1/5 21/71 -3/16 -2/11 29/98 -4/21 -3/16 37/125 -3/16 8/27 -3/16 -2/11 3/10 -2/11 7/23 -2/11 -1/6 11/36 -3/17 -4/23 37/121 -2/11 -1/6 26/85 -3/17 15/49 -3/17 -4/23 19/62 -6/35 -1/6 23/75 -1/6 4/13 -2/11 -1/6 5/16 -3/17 -4/23 6/19 -6/35 -1/6 1/3 -1/6 -2/13 7/20 -2/13 6/17 -7/47 -4/27 5/14 -8/55 -1/7 9/25 -1/7 4/11 -1/7 -6/43 11/30 -4/29 18/49 -1/7 -4/29 7/19 -3/22 -2/15 17/46 -7/52 -2/15 10/27 -2/15 -5/38 23/62 -2/15 -1/8 13/35 -1/8 3/8 -1/7 -2/15 8/21 -2/15 -5/38 21/55 -3/23 13/34 -3/23 -4/31 5/13 -2/15 -1/8 12/31 -1/8 -2/17 19/49 -1/9 0/1 45/116 -1/11 0/1 26/67 -1/3 0/1 7/18 -1/7 -2/15 16/41 -2/15 -7/53 9/23 -2/15 -1/8 2/5 -1/8 11/27 -1/8 -2/17 31/76 -2/17 -1/9 51/125 -1/9 20/49 -1/9 0/1 9/22 -1/8 -2/17 16/39 -2/17 -1/9 7/17 -1/9 0/1 12/29 -1/8 -6/49 17/41 -3/25 -2/17 39/94 -5/42 -2/17 22/53 -2/17 -3/26 5/12 -1/8 -2/17 8/19 -2/17 -3/26 19/45 -1/9 30/71 -2/17 -3/26 11/26 -2/17 -1/9 3/7 -1/9 0/1 13/30 -2/17 23/53 -1/8 -2/17 33/76 -2/17 -1/9 10/23 -1/8 -2/17 7/16 -4/35 -1/9 11/25 -1/9 4/9 -1/9 -2/19 13/29 -1/10 -2/21 35/78 -1/10 -2/21 22/49 -1/11 0/1 9/20 0/1 5/11 -1/9 -2/19 11/24 -1/9 -2/19 6/13 -2/19 -1/10 7/15 -1/10 8/17 -1/7 0/1 1/2 -1/10 0/1 9/17 -1/13 0/1 8/15 -1/10 7/13 -1/10 -2/21 6/11 -2/21 -1/11 11/20 0/1 16/29 -2/19 -1/10 5/9 -2/21 -1/11 14/25 -1/11 9/16 -1/11 -4/45 22/39 -1/11 -2/23 35/62 -3/34 -2/23 13/23 -2/23 -1/12 17/30 -2/23 4/7 -1/11 0/1 15/26 -1/11 -2/23 11/19 -3/34 -2/23 29/50 -2/23 18/31 -2/23 -5/58 7/12 -2/23 -1/12 31/53 -3/34 -2/23 24/41 -2/23 -3/35 17/29 -6/71 -1/12 44/75 -1/12 27/46 -1/12 -6/73 10/17 -1/11 0/1 13/22 -2/23 -1/12 3/5 -1/12 17/28 -1/12 -2/25 31/51 -4/49 -3/37 76/125 -3/37 45/74 -3/37 -2/25 14/23 -1/12 -2/25 11/18 -2/25 -1/13 52/85 -1/14 41/67 -1/17 0/1 30/49 -1/11 0/1 19/31 -2/23 -1/12 46/75 -1/12 27/44 -1/12 -6/73 8/13 -1/12 -2/25 21/34 -4/49 -3/37 13/21 -5/62 -2/25 31/50 -2/25 18/29 -2/25 -7/88 5/8 -2/25 -1/13 22/35 -1/12 61/97 -5/62 -2/25 39/62 -1/12 -2/25 17/27 -5/62 -2/25 12/19 -2/25 -3/38 31/49 -4/51 -1/13 81/128 -2/25 -3/38 50/79 -2/25 -3/38 19/30 -4/51 7/11 -6/77 -1/13 16/25 -1/13 9/14 -1/13 -8/105 20/31 -6/79 -5/66 31/48 -5/66 -4/53 11/17 -4/53 -7/93 13/20 -2/27 15/23 -2/27 -1/14 2/3 -2/27 -1/14 17/25 -1/14 15/22 -1/14 -14/197 13/19 -1/14 -6/85 11/16 -4/57 -3/43 9/13 -1/14 -2/29 16/23 -1/14 -2/29 7/10 -2/29 19/27 -2/29 -3/44 12/17 -4/59 -1/15 53/75 -1/15 41/58 -1/15 -2/31 29/41 -2/29 -1/15 17/24 -2/29 -1/15 5/7 -4/59 -1/15 18/25 -1/15 13/18 -1/15 -10/151 60/83 -8/121 -31/469 47/65 -7/106 81/112 -7/106 -6/91 34/47 -6/91 -5/76 89/123 -6/91 -5/76 55/76 -1/15 -6/91 21/29 -6/91 -5/76 71/98 -5/76 -4/61 50/69 -6/91 -5/76 29/40 -4/61 37/51 -4/61 -7/107 45/62 -3/46 -2/31 8/11 -1/15 -2/31 27/37 -3/46 -2/31 73/100 -2/31 46/63 -2/31 -1/16 19/26 -1/15 -2/31 30/41 -1/15 -2/31 71/97 -7/108 -2/31 183/250 -2/31 112/153 -2/31 -9/140 41/56 -2/31 -1/16 11/15 -1/15 36/49 -1/15 -4/61 61/83 -25/381 -4/61 147/200 -4/61 86/117 -4/61 -39/595 25/34 -4/61 -7/107 14/19 -3/46 -2/31 17/23 -11/170 -2/31 37/50 -2/31 20/27 -2/31 -13/202 3/4 -2/31 -1/16 19/25 -1/16 16/21 -1/16 -10/161 13/17 -5/81 -4/65 23/30 -2/33 10/13 -1/16 -2/33 27/35 -1/16 17/22 -2/31 -1/16 58/75 -1/16 41/53 -1/16 -14/225 24/31 -1/16 -6/97 31/40 -4/65 7/9 -3/49 -2/33 39/50 -2/33 32/41 -2/33 -13/215 25/32 -2/33 -5/83 18/23 -2/33 -3/50 29/37 -2/33 -3/50 98/125 -3/50 69/88 -3/50 -10/167 40/51 -4/67 -1/17 51/65 -1/17 11/14 -4/67 -1/17 26/33 -1/19 0/1 41/52 -1/16 0/1 56/71 -1/16 -2/33 15/19 -1/16 -2/33 19/24 -2/33 -1/17 4/5 -1/17 21/26 -1/17 -2/35 17/21 -3/52 -2/35 13/16 -1/17 0/1 22/27 -3/52 -2/35 31/38 -2/35 -1/18 40/49 -1/19 0/1 9/11 -1/17 -2/35 41/50 -2/35 32/39 -2/35 -3/53 23/28 -2/35 -1/18 14/17 -1/17 0/1 19/23 -2/35 -1/18 62/75 -1/18 43/52 -1/18 0/1 24/29 -2/35 -1/18 53/64 -1/17 0/1 29/35 -1/17 5/6 -2/35 -1/18 21/25 -1/18 16/19 -1/18 -6/109 11/13 -1/18 -2/37 17/20 -2/37 6/7 -1/19 0/1 43/50 0/1 37/43 -1/15 0/1 31/36 -1/17 0/1 25/29 -2/35 -1/18 19/22 -2/35 -1/18 13/15 -1/18 7/8 -2/37 -1/19 22/25 -1/19 15/17 -1/19 -4/77 8/9 -1/19 -2/39 9/10 0/1 1/1 -1/21 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(399,362,550,499) (-1/1,-9/10) -> (29/40,37/51) Hyperbolic Matrix(101,90,450,401) (-9/10,-8/9) -> (2/9,9/40) Hyperbolic Matrix(249,220,-850,-751) (-8/9,-7/8) -> (-17/58,-12/41) Hyperbolic Matrix(149,130,400,349) (-7/8,-13/15) -> (13/35,3/8) Hyperbolic Matrix(849,734,-1100,-951) (-13/15,-6/7) -> (-44/57,-27/35) Hyperbolic Matrix(199,170,350,299) (-6/7,-17/20) -> (17/30,4/7) Hyperbolic Matrix(151,128,650,551) (-17/20,-11/13) -> (3/13,7/30) Hyperbolic Matrix(251,212,-650,-549) (-11/13,-5/6) -> (-17/44,-5/13) Hyperbolic Matrix(599,494,-850,-701) (-5/6,-14/17) -> (-12/17,-31/44) Hyperbolic Matrix(501,412,-850,-699) (-14/17,-9/11) -> (-23/39,-10/17) Hyperbolic Matrix(349,284,-800,-651) (-9/11,-13/16) -> (-7/16,-17/39) Hyperbolic Matrix(649,526,-1050,-851) (-13/16,-4/5) -> (-34/55,-21/34) Hyperbolic Matrix(549,434,-950,-751) (-4/5,-15/19) -> (-11/19,-26/45) Hyperbolic Matrix(249,196,-700,-551) (-15/19,-11/14) -> (-5/14,-11/31) Hyperbolic Matrix(799,626,-1150,-901) (-11/14,-18/23) -> (-16/23,-25/36) Hyperbolic Matrix(701,548,-1150,-899) (-18/23,-7/9) -> (-25/41,-14/23) Hyperbolic Matrix(49,38,450,349) (-7/9,-31/40) -> (1/10,1/9) Hyperbolic Matrix(2899,2246,4000,3099) (-31/40,-24/31) -> (50/69,29/40) Hyperbolic Matrix(349,270,-1100,-851) (-24/31,-17/22) -> (-7/22,-6/19) Hyperbolic Matrix(3051,2356,6800,5251) (-17/22,-61/79) -> (13/29,35/78) Hyperbolic Matrix(5901,4556,19300,14901) (-61/79,-105/136) -> (11/36,37/121) Hyperbolic Matrix(1101,850,-7900,-6099) (-105/136,-44/57) -> (-6/43,-5/36) Hyperbolic Matrix(301,232,650,501) (-27/35,-10/13) -> (6/13,7/15) Hyperbolic Matrix(99,76,650,499) (-10/13,-23/30) -> (3/20,2/13) Hyperbolic Matrix(551,422,850,651) (-23/30,-13/17) -> (11/17,13/20) Hyperbolic Matrix(351,268,-850,-649) (-13/17,-3/4) -> (-19/46,-7/17) Hyperbolic Matrix(599,442,-950,-701) (-3/4,-14/19) -> (-12/19,-29/46) Hyperbolic Matrix(299,220,950,699) (-14/19,-25/34) -> (5/16,6/19) Hyperbolic Matrix(4499,3306,-7350,-5401) (-25/34,-36/49) -> (-30/49,-71/116) Hyperbolic Matrix(3401,2498,-4900,-3599) (-36/49,-11/15) -> (-59/85,-34/49) Hyperbolic Matrix(5001,3662,-7100,-5199) (-11/15,-41/56) -> (-31/44,-81/115) Hyperbolic Matrix(3599,2634,-6150,-4501) (-41/56,-30/41) -> (-24/41,-55/94) Hyperbolic Matrix(599,438,2050,1499) (-30/41,-19/26) -> (7/24,12/41) Hyperbolic Matrix(299,218,-550,-401) (-19/26,-8/11) -> (-6/11,-13/24) Hyperbolic Matrix(201,146,-1100,-799) (-8/11,-37/51) -> (-9/49,-2/11) Hyperbolic Matrix(499,362,550,399) (-37/51,-29/40) -> (9/10,1/1) Hyperbolic Matrix(3099,2246,4000,2899) (-29/40,-50/69) -> (24/31,31/40) Hyperbolic Matrix(1151,834,-5450,-3949) (-50/69,-21/29) -> (-15/71,-4/19) Hyperbolic Matrix(1901,1376,2350,1701) (-21/29,-55/76) -> (21/26,17/21) Hyperbolic Matrix(4301,3112,-7600,-5499) (-55/76,-34/47) -> (-30/53,-43/76) Hyperbolic Matrix(2951,2134,-7950,-5749) (-34/47,-47/65) -> (-13/35,-36/97) Hyperbolic Matrix(1049,758,-2700,-1951) (-47/65,-13/18) -> (-7/18,-33/85) Hyperbolic Matrix(649,468,900,649) (-13/18,-18/25) -> (18/25,13/18) Hyperbolic Matrix(251,180,350,251) (-18/25,-5/7) -> (5/7,18/25) Hyperbolic Matrix(149,106,350,249) (-5/7,-17/24) -> (11/26,3/7) Hyperbolic Matrix(551,390,2050,1451) (-17/24,-29/41) -> (11/41,7/26) Hyperbolic Matrix(99,70,-850,-601) (-29/41,-12/17) -> (-2/17,-1/9) Hyperbolic Matrix(13849,9754,-19950,-14051) (-81/115,-50/71) -> (-84/121,-59/85) Hyperbolic Matrix(8399,5914,10650,7499) (-50/71,-69/98) -> (41/52,56/71) Hyperbolic Matrix(11451,8062,13850,9751) (-69/98,-88/125) -> (62/75,43/52) Hyperbolic Matrix(4049,2850,4900,3449) (-88/125,-19/27) -> (19/23,62/75) Hyperbolic Matrix(151,106,500,351) (-19/27,-7/10) -> (3/10,7/23) Hyperbolic Matrix(149,104,500,349) (-7/10,-16/23) -> (8/27,3/10) Hyperbolic Matrix(4399,3054,19300,13399) (-25/36,-84/121) -> (18/79,31/136) Hyperbolic Matrix(3999,2774,4900,3399) (-34/49,-43/62) -> (31/38,40/49) Hyperbolic Matrix(11251,7802,14350,9951) (-43/62,-52/75) -> (98/125,69/88) Hyperbolic Matrix(3449,2390,4400,3049) (-52/75,-9/13) -> (29/37,98/125) Hyperbolic Matrix(249,172,650,449) (-9/13,-11/16) -> (13/34,5/13) Hyperbolic Matrix(251,172,950,651) (-11/16,-13/19) -> (5/19,9/34) Hyperbolic Matrix(249,170,-1100,-751) (-13/19,-2/3) -> (-12/53,-7/31) Hyperbolic Matrix(651,424,-1150,-749) (-2/3,-13/20) -> (-17/30,-30/53) Hyperbolic Matrix(651,422,850,551) (-13/20,-11/17) -> (13/17,23/30) Hyperbolic Matrix(149,96,-700,-451) (-11/17,-9/14) -> (-3/14,-7/33) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(351,224,550,351) (-16/25,-7/11) -> (7/11,16/25) Hyperbolic Matrix(249,158,550,349) (-7/11,-19/30) -> (9/20,5/11) Hyperbolic Matrix(1349,854,-2450,-1551) (-19/30,-31/49) -> (-27/49,-11/20) Hyperbolic Matrix(949,600,2450,1549) (-31/49,-12/19) -> (12/31,19/49) Hyperbolic Matrix(349,220,-1350,-851) (-29/46,-17/27) -> (-7/27,-1/4) Hyperbolic Matrix(1751,1102,3100,1951) (-17/27,-39/62) -> (35/62,13/23) Hyperbolic Matrix(2201,1384,-7950,-4999) (-39/62,-22/35) -> (-18/65,-31/112) Hyperbolic Matrix(51,32,400,251) (-22/35,-5/8) -> (1/8,2/15) Hyperbolic Matrix(151,94,-400,-249) (-5/8,-13/21) -> (-11/29,-3/8) Hyperbolic Matrix(2801,1732,-4850,-2999) (-13/21,-34/55) -> (-26/45,-41/71) Hyperbolic Matrix(201,124,650,401) (-21/34,-8/13) -> (4/13,5/16) Hyperbolic Matrix(101,62,-650,-399) (-8/13,-19/31) -> (-3/19,-2/13) Hyperbolic Matrix(901,552,2450,1501) (-19/31,-30/49) -> (18/49,7/19) Hyperbolic Matrix(4199,2570,-15850,-9701) (-71/116,-41/67) -> (-31/117,-9/34) Hyperbolic Matrix(749,458,-2700,-1651) (-41/67,-11/18) -> (-5/18,-23/83) Hyperbolic Matrix(449,274,-2050,-1251) (-11/18,-25/41) -> (-9/41,-7/32) Hyperbolic Matrix(149,90,-250,-151) (-14/23,-3/5) -> (-3/5,-16/27) Parabolic Matrix(1651,978,3800,2251) (-16/27,-45/76) -> (33/76,10/23) Hyperbolic Matrix(11401,6750,18750,11101) (-45/76,-74/125) -> (76/125,45/74) Hyperbolic Matrix(7599,4498,12500,7399) (-74/125,-29/49) -> (31/51,76/125) Hyperbolic Matrix(2701,1598,-4900,-2899) (-29/49,-13/22) -> (-43/78,-27/49) Hyperbolic Matrix(349,206,-1950,-1151) (-13/22,-23/39) -> (-7/39,-5/28) Hyperbolic Matrix(201,118,-850,-499) (-10/17,-17/29) -> (-5/21,-4/17) Hyperbolic Matrix(649,380,1450,849) (-17/29,-24/41) -> (4/9,13/29) Hyperbolic Matrix(4649,2720,-17350,-10151) (-55/94,-31/53) -> (-41/153,-15/56) Hyperbolic Matrix(1799,1052,-6500,-3801) (-31/53,-7/12) -> (-31/112,-13/47) Hyperbolic Matrix(251,146,-600,-349) (-7/12,-11/19) -> (-13/31,-5/12) Hyperbolic Matrix(4451,2570,6150,3551) (-41/71,-15/26) -> (55/76,21/29) Hyperbolic Matrix(101,58,350,201) (-15/26,-4/7) -> (2/7,7/24) Hyperbolic Matrix(299,170,350,199) (-4/7,-17/30) -> (17/20,6/7) Hyperbolic Matrix(1549,876,3800,2149) (-43/76,-13/23) -> (11/27,31/76) Hyperbolic Matrix(149,84,-800,-451) (-13/23,-9/16) -> (-3/16,-5/27) Hyperbolic Matrix(449,252,800,449) (-9/16,-14/25) -> (14/25,9/16) Hyperbolic Matrix(251,140,450,251) (-14/25,-5/9) -> (5/9,14/25) Hyperbolic Matrix(601,332,1450,801) (-5/9,-16/29) -> (12/29,17/41) Hyperbolic Matrix(1549,854,6800,3749) (-16/29,-43/78) -> (5/22,18/79) Hyperbolic Matrix(201,110,550,301) (-11/20,-6/11) -> (4/11,11/30) Hyperbolic Matrix(499,270,-1850,-1001) (-13/24,-7/13) -> (-17/63,-7/26) Hyperbolic Matrix(149,80,650,349) (-7/13,-8/15) -> (8/35,3/13) Hyperbolic Matrix(651,346,-2350,-1249) (-8/15,-9/17) -> (-23/83,-18/65) Hyperbolic Matrix(549,290,850,449) (-9/17,-1/2) -> (31/48,11/17) Hyperbolic Matrix(749,354,950,449) (-1/2,-8/17) -> (26/33,41/52) Hyperbolic Matrix(951,446,-2450,-1149) (-8/17,-7/15) -> (-33/85,-26/67) Hyperbolic Matrix(501,232,650,301) (-7/15,-6/13) -> (10/13,27/35) Hyperbolic Matrix(149,68,-550,-251) (-6/13,-5/11) -> (-3/11,-10/37) Hyperbolic Matrix(349,158,550,249) (-5/11,-9/20) -> (19/30,7/11) Hyperbolic Matrix(899,404,-2450,-1101) (-9/20,-13/29) -> (-29/79,-11/30) Hyperbolic Matrix(849,380,1450,649) (-13/29,-4/9) -> (24/41,17/29) Hyperbolic Matrix(199,88,450,199) (-4/9,-11/25) -> (11/25,4/9) Hyperbolic Matrix(351,154,800,351) (-11/25,-7/16) -> (7/16,11/25) Hyperbolic Matrix(849,370,-3100,-1351) (-17/39,-27/62) -> (-17/62,-3/11) Hyperbolic Matrix(1149,500,3100,1349) (-27/62,-10/23) -> (10/27,23/62) Hyperbolic Matrix(401,174,-1150,-499) (-10/23,-13/30) -> (-7/20,-8/23) Hyperbolic Matrix(51,22,350,151) (-13/30,-3/7) -> (1/7,3/20) Hyperbolic Matrix(249,106,350,149) (-3/7,-11/26) -> (17/24,5/7) Hyperbolic Matrix(199,84,-950,-401) (-11/26,-8/19) -> (-4/19,-5/24) Hyperbolic Matrix(1451,610,2500,1051) (-8/19,-21/50) -> (29/50,18/31) Hyperbolic Matrix(1449,608,2500,1049) (-21/50,-13/31) -> (11/19,29/50) Hyperbolic Matrix(1651,686,-4450,-1849) (-5/12,-22/53) -> (-36/97,-23/62) Hyperbolic Matrix(1649,684,-6150,-2551) (-22/53,-17/41) -> (-11/41,-26/97) Hyperbolic Matrix(801,332,1450,601) (-17/41,-12/29) -> (16/29,5/9) Hyperbolic Matrix(1751,724,2300,951) (-12/29,-31/75) -> (19/25,16/21) Hyperbolic Matrix(1099,454,1450,599) (-31/75,-19/46) -> (3/4,19/25) Hyperbolic Matrix(151,62,-850,-349) (-7/17,-9/22) -> (-5/28,-3/17) Hyperbolic Matrix(99,40,-250,-101) (-9/22,-2/5) -> (-2/5,-11/28) Parabolic Matrix(2901,1138,-7900,-3099) (-11/28,-20/51) -> (-18/49,-47/128) Hyperbolic Matrix(5101,2000,12500,4901) (-20/51,-49/125) -> (51/125,20/49) Hyperbolic Matrix(7649,2998,18750,7349) (-49/125,-29/74) -> (31/76,51/125) Hyperbolic Matrix(7851,3076,10850,4251) (-29/74,-9/23) -> (89/123,55/76) Hyperbolic Matrix(251,98,-1150,-449) (-9/23,-7/18) -> (-7/32,-5/23) Hyperbolic Matrix(1949,756,-7350,-2851) (-26/67,-19/49) -> (-13/49,-22/83) Hyperbolic Matrix(1549,600,2450,949) (-19/49,-12/31) -> (12/19,31/49) Hyperbolic Matrix(1851,716,2200,851) (-12/31,-29/75) -> (21/25,16/19) Hyperbolic Matrix(1299,502,1550,599) (-29/75,-17/44) -> (5/6,21/25) Hyperbolic Matrix(449,172,650,249) (-5/13,-13/34) -> (11/16,9/13) Hyperbolic Matrix(199,76,-1050,-401) (-13/34,-8/21) -> (-4/21,-3/16) Hyperbolic Matrix(1551,590,2500,951) (-8/21,-19/50) -> (31/50,18/29) Hyperbolic Matrix(1549,588,2500,949) (-19/50,-11/29) -> (13/21,31/50) Hyperbolic Matrix(349,130,400,149) (-3/8,-13/35) -> (13/15,7/8) Hyperbolic Matrix(2201,816,2700,1001) (-23/62,-10/27) -> (22/27,31/38) Hyperbolic Matrix(249,92,-950,-351) (-10/27,-7/19) -> (-5/19,-6/23) Hyperbolic Matrix(1501,552,2450,901) (-7/19,-18/49) -> (30/49,19/31) Hyperbolic Matrix(4701,1726,5450,2001) (-47/128,-29/79) -> (25/29,19/22) Hyperbolic Matrix(301,110,550,201) (-11/30,-4/11) -> (6/11,11/20) Hyperbolic Matrix(199,72,550,199) (-4/11,-9/25) -> (9/25,4/11) Hyperbolic Matrix(251,90,700,251) (-9/25,-5/14) -> (5/14,9/25) Hyperbolic Matrix(1749,620,-6350,-2251) (-11/31,-17/48) -> (-27/98,-19/69) Hyperbolic Matrix(401,142,850,301) (-17/48,-6/17) -> (8/17,1/2) Hyperbolic Matrix(199,70,850,299) (-6/17,-7/20) -> (7/30,4/17) Hyperbolic Matrix(401,138,-1450,-499) (-8/23,-1/3) -> (-13/47,-34/123) Hyperbolic Matrix(1199,386,1550,499) (-1/3,-8/25) -> (58/75,41/53) Hyperbolic Matrix(1701,542,2200,701) (-8/25,-7/22) -> (17/22,58/75) Hyperbolic Matrix(699,220,950,299) (-6/19,-5/16) -> (25/34,14/19) Hyperbolic Matrix(401,124,650,201) (-5/16,-4/13) -> (8/13,21/34) Hyperbolic Matrix(249,76,-1150,-351) (-4/13,-7/23) -> (-5/23,-8/37) Hyperbolic Matrix(351,106,500,151) (-7/23,-3/10) -> (7/10,19/27) Hyperbolic Matrix(349,104,500,149) (-3/10,-8/27) -> (16/23,7/10) Hyperbolic Matrix(149,44,-850,-251) (-8/27,-5/17) -> (-3/17,-4/23) Hyperbolic Matrix(1499,440,1700,499) (-5/17,-22/75) -> (22/25,15/17) Hyperbolic Matrix(1801,528,2050,601) (-22/75,-17/58) -> (7/8,22/25) Hyperbolic Matrix(1499,438,2050,599) (-12/41,-7/24) -> (19/26,30/41) Hyperbolic Matrix(201,58,350,101) (-7/24,-2/7) -> (4/7,15/26) Hyperbolic Matrix(99,28,350,99) (-2/7,-7/25) -> (7/25,2/7) Hyperbolic Matrix(251,70,900,251) (-7/25,-5/18) -> (5/18,7/25) Hyperbolic Matrix(6599,1824,10850,2999) (-34/123,-21/76) -> (45/74,14/23) Hyperbolic Matrix(2599,718,6150,1699) (-21/76,-8/29) -> (30/71,11/26) Hyperbolic Matrix(3599,992,4350,1199) (-8/29,-27/98) -> (43/52,24/29) Hyperbolic Matrix(901,248,4000,1101) (-19/69,-11/40) -> (9/40,7/31) Hyperbolic Matrix(51,14,550,151) (-11/40,-14/51) -> (0/1,1/10) Hyperbolic Matrix(5999,1646,7650,2099) (-14/51,-17/62) -> (69/88,40/51) Hyperbolic Matrix(7301,1972,10000,2701) (-10/37,-27/100) -> (73/100,46/63) Hyperbolic Matrix(7299,1970,10000,2699) (-27/100,-17/63) -> (27/37,73/100) Hyperbolic Matrix(1451,390,2050,551) (-7/26,-11/41) -> (29/41,17/24) Hyperbolic Matrix(45751,12262,62500,16751) (-26/97,-67/250) -> (183/250,112/153) Hyperbolic Matrix(45749,12260,62500,16749) (-67/250,-41/153) -> (71/97,183/250) Hyperbolic Matrix(351,94,-2050,-549) (-15/56,-4/15) -> (-6/35,-1/6) Hyperbolic Matrix(851,226,-3950,-1049) (-4/15,-13/49) -> (-11/51,-14/65) Hyperbolic Matrix(29401,7792,40000,10601) (-22/83,-53/200) -> (147/200,86/117) Hyperbolic Matrix(29399,7790,40000,10599) (-53/200,-31/117) -> (61/83,147/200) Hyperbolic Matrix(651,172,950,251) (-9/34,-5/19) -> (13/19,11/16) Hyperbolic Matrix(1851,482,2500,651) (-6/23,-13/50) -> (37/50,20/27) Hyperbolic Matrix(1849,480,2500,649) (-13/50,-7/27) -> (17/23,37/50) Hyperbolic Matrix(851,206,1450,351) (-1/4,-6/25) -> (44/75,27/46) Hyperbolic Matrix(1349,322,2300,549) (-6/25,-5/21) -> (17/29,44/75) Hyperbolic Matrix(299,70,850,199) (-4/17,-7/30) -> (7/20,6/17) Hyperbolic Matrix(551,128,650,151) (-7/30,-3/13) -> (11/13,17/20) Hyperbolic Matrix(349,80,650,149) (-3/13,-8/35) -> (8/15,7/13) Hyperbolic Matrix(149,34,-1100,-251) (-8/35,-5/22) -> (-3/22,-2/15) Hyperbolic Matrix(1499,340,2200,499) (-5/22,-17/75) -> (17/25,15/22) Hyperbolic Matrix(1051,238,1550,351) (-17/75,-12/53) -> (2/3,17/25) Hyperbolic Matrix(1101,248,4000,901) (-7/31,-9/40) -> (11/40,19/69) Hyperbolic Matrix(401,90,450,101) (-9/40,-2/9) -> (8/9,9/10) Hyperbolic Matrix(1951,430,2500,551) (-2/9,-11/50) -> (39/50,32/41) Hyperbolic Matrix(1949,428,2500,549) (-11/50,-9/41) -> (7/9,39/50) Hyperbolic Matrix(1351,292,4400,951) (-8/37,-27/125) -> (23/75,4/13) Hyperbolic Matrix(4399,950,14350,3099) (-27/125,-19/88) -> (19/62,23/75) Hyperbolic Matrix(5551,1198,7650,1651) (-19/88,-11/51) -> (37/51,45/62) Hyperbolic Matrix(799,172,-4650,-1001) (-14/65,-3/14) -> (-11/64,-6/35) Hyperbolic Matrix(501,106,950,201) (-7/33,-11/52) -> (1/2,9/17) Hyperbolic Matrix(3151,666,10650,2251) (-11/52,-15/71) -> (21/71,29/98) Hyperbolic Matrix(49,10,-250,-51) (-5/24,-1/5) -> (-1/5,-5/26) Parabolic Matrix(649,124,2350,449) (-5/26,-4/21) -> (8/29,21/76) Hyperbolic Matrix(1699,314,2700,499) (-5/27,-7/38) -> (39/62,17/27) Hyperbolic Matrix(1501,276,4900,901) (-7/38,-9/49) -> (15/49,19/62) Hyperbolic Matrix(2051,370,2500,451) (-2/11,-9/50) -> (41/50,32/39) Hyperbolic Matrix(2049,368,2500,449) (-9/50,-7/39) -> (9/11,41/50) Hyperbolic Matrix(1451,252,4900,851) (-4/23,-13/75) -> (37/125,8/27) Hyperbolic Matrix(4099,710,13850,2399) (-13/75,-9/52) -> (29/98,37/125) Hyperbolic Matrix(3151,544,4350,751) (-9/52,-5/29) -> (21/29,71/98) Hyperbolic Matrix(2499,430,2900,499) (-5/29,-11/64) -> (31/36,25/29) Hyperbolic Matrix(951,154,1550,251) (-1/6,-4/25) -> (46/75,27/44) Hyperbolic Matrix(1349,214,2200,349) (-4/25,-3/19) -> (19/31,46/75) Hyperbolic Matrix(499,76,650,99) (-2/13,-3/20) -> (23/30,10/13) Hyperbolic Matrix(151,22,350,51) (-3/20,-1/7) -> (3/7,13/30) Hyperbolic Matrix(2151,302,2500,351) (-1/7,-7/50) -> (43/50,37/43) Hyperbolic Matrix(2149,300,2500,349) (-7/50,-6/43) -> (6/7,43/50) Hyperbolic Matrix(2401,332,2900,401) (-5/36,-4/29) -> (24/29,53/64) Hyperbolic Matrix(3449,474,5450,749) (-4/29,-3/22) -> (81/128,50/79) Hyperbolic Matrix(251,32,400,51) (-2/15,-1/8) -> (5/8,22/35) Hyperbolic Matrix(1449,176,2050,249) (-1/8,-3/25) -> (53/75,41/58) Hyperbolic Matrix(1201,142,1700,201) (-3/25,-2/17) -> (12/17,53/75) Hyperbolic Matrix(349,38,450,49) (-1/9,-1/10) -> (31/40,7/9) Hyperbolic Matrix(151,14,550,51) (-1/10,0/1) -> (14/51,11/40) Hyperbolic Matrix(601,-70,850,-99) (1/9,1/8) -> (41/58,29/41) Hyperbolic Matrix(251,-34,1100,-149) (2/15,1/7) -> (13/57,8/35) Hyperbolic Matrix(399,-62,650,-101) (2/13,1/6) -> (27/44,8/13) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(349,-62,850,-151) (3/17,2/11) -> (16/39,7/17) Hyperbolic Matrix(451,-84,800,-149) (2/11,3/16) -> (9/16,22/39) Hyperbolic Matrix(401,-76,1050,-199) (3/16,1/5) -> (21/55,13/34) Hyperbolic Matrix(401,-84,950,-199) (1/5,4/19) -> (8/19,19/45) Hyperbolic Matrix(451,-96,700,-149) (4/19,3/14) -> (9/14,20/31) Hyperbolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(449,-98,1150,-251) (5/23,2/9) -> (16/41,9/23) Hyperbolic Matrix(751,-170,1100,-249) (7/31,5/22) -> (15/22,13/19) Hyperbolic Matrix(6799,-1550,7900,-1801) (31/136,13/57) -> (37/43,31/36) Hyperbolic Matrix(499,-118,850,-201) (4/17,1/4) -> (27/46,10/17) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(2851,-756,7350,-1949) (9/34,13/49) -> (19/49,45/116) Hyperbolic Matrix(1499,-398,4900,-1301) (13/49,4/15) -> (26/85,15/49) Hyperbolic Matrix(2099,-562,7100,-1901) (4/15,15/56) -> (13/44,34/115) Hyperbolic Matrix(2551,-684,6150,-1649) (15/56,11/41) -> (17/41,39/94) Hyperbolic Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(899,-246,1100,-301) (3/11,14/51) -> (40/49,9/11) Hyperbolic Matrix(4299,-1184,5450,-1501) (19/69,8/29) -> (56/71,15/19) Hyperbolic Matrix(3299,-912,7600,-2101) (21/76,13/47) -> (23/53,33/76) Hyperbolic Matrix(4999,-1384,7950,-2201) (13/47,18/65) -> (22/35,61/97) Hyperbolic Matrix(1651,-458,2700,-749) (18/65,5/18) -> (11/18,52/85) Hyperbolic Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(6101,-1804,19950,-5899) (34/115,21/71) -> (37/121,26/85) Hyperbolic Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(499,-174,1150,-401) (1/3,7/20) -> (13/30,23/53) Hyperbolic Matrix(551,-196,700,-249) (6/17,5/14) -> (11/14,26/33) Hyperbolic Matrix(1101,-404,2450,-899) (11/30,18/49) -> (22/49,9/20) Hyperbolic Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(5749,-2134,7950,-2951) (23/62,13/35) -> (47/65,81/112) Hyperbolic Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(2049,-782,4850,-1851) (8/21,21/55) -> (19/45,30/71) Hyperbolic Matrix(549,-212,650,-251) (5/13,12/31) -> (16/19,11/13) Hyperbolic Matrix(11651,-4520,15850,-6149) (45/116,26/67) -> (86/117,25/34) Hyperbolic Matrix(1951,-758,2700,-1049) (26/67,7/18) -> (13/18,60/83) Hyperbolic Matrix(1601,-624,2050,-799) (7/18,16/41) -> (32/41,25/32) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(2199,-898,4900,-2001) (20/49,9/22) -> (35/78,22/49) Hyperbolic Matrix(1601,-656,1950,-799) (9/22,16/39) -> (32/39,23/28) Hyperbolic Matrix(649,-268,850,-351) (7/17,12/29) -> (16/21,13/17) Hyperbolic Matrix(12701,-5270,17350,-7199) (39/94,22/53) -> (112/153,41/56) Hyperbolic Matrix(4701,-1952,6500,-2699) (22/53,5/12) -> (81/112,34/47) Hyperbolic Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(651,-284,800,-349) (10/23,7/16) -> (13/16,22/27) Hyperbolic Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(1699,-796,2350,-1101) (7/15,8/17) -> (60/83,47/65) Hyperbolic Matrix(1499,-796,2450,-1301) (9/17,8/15) -> (52/85,41/67) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(1551,-854,2450,-1349) (11/20,16/29) -> (50/79,19/30) Hyperbolic Matrix(2251,-1270,3100,-1749) (22/39,35/62) -> (45/62,8/11) Hyperbolic Matrix(749,-424,1150,-651) (13/23,17/30) -> (13/20,15/23) Hyperbolic Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(2799,-1636,4450,-2601) (7/12,31/53) -> (61/97,39/62) Hyperbolic Matrix(4501,-2634,6150,-3599) (31/53,24/41) -> (30/41,71/97) Hyperbolic Matrix(699,-412,850,-501) (10/17,13/22) -> (23/28,14/17) Hyperbolic Matrix(151,-90,250,-149) (13/22,3/5) -> (3/5,17/28) Parabolic Matrix(4999,-3038,7900,-4801) (17/28,31/51) -> (31/49,81/128) Hyperbolic Matrix(899,-548,1150,-701) (14/23,11/18) -> (25/32,18/23) Hyperbolic Matrix(5401,-3306,7350,-4499) (41/67,30/49) -> (36/49,61/83) Hyperbolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(4601,-2970,6350,-4099) (20/31,31/48) -> (71/98,50/69) Hyperbolic Matrix(1049,-688,1450,-951) (15/23,2/3) -> (34/47,89/123) Hyperbolic Matrix(901,-626,1150,-799) (9/13,16/23) -> (18/23,29/37) Hyperbolic Matrix(701,-494,850,-599) (19/27,12/17) -> (14/17,19/23) Hyperbolic Matrix(1699,-1244,2050,-1501) (41/56,11/15) -> (29/35,5/6) Hyperbolic Matrix(3099,-2276,3950,-2901) (11/15,36/49) -> (40/51,51/65) Hyperbolic Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(3851,-3022,4650,-3649) (51/65,11/14) -> (53/64,29/35) Hyperbolic Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-44,1) Matrix(399,362,550,499) -> Matrix(85,-4,-1296,61) Matrix(101,90,450,401) -> Matrix(87,-4,-326,15) Matrix(249,220,-850,-751) -> Matrix(1,0,-14,1) Matrix(149,130,400,349) -> Matrix(1,0,-28,1) Matrix(849,734,-1100,-951) -> Matrix(1,0,-2,1) Matrix(199,170,350,299) -> Matrix(1,0,-32,1) Matrix(151,128,650,551) -> Matrix(1,0,-24,1) Matrix(251,212,-650,-549) -> Matrix(81,-4,790,-39) Matrix(599,494,-850,-701) -> Matrix(77,-4,1290,-67) Matrix(501,412,-850,-699) -> Matrix(1,0,-6,1) Matrix(349,284,-800,-651) -> Matrix(77,-4,828,-43) Matrix(649,526,-1050,-851) -> Matrix(79,-4,1126,-57) Matrix(549,434,-950,-751) -> Matrix(75,-4,994,-53) Matrix(249,196,-700,-551) -> Matrix(77,-4,674,-35) Matrix(799,626,-1150,-901) -> Matrix(149,-8,2440,-131) Matrix(701,548,-1150,-899) -> Matrix(149,-8,2142,-115) Matrix(49,38,450,349) -> Matrix(73,-4,-18,1) Matrix(2899,2246,4000,3099) -> Matrix(437,-24,-6646,365) Matrix(349,270,-1100,-851) -> Matrix(217,-12,1718,-95) Matrix(3051,2356,6800,5251) -> Matrix(1,0,-28,1) Matrix(5901,4556,19300,14901) -> Matrix(71,-4,-408,23) Matrix(1101,850,-7900,-6099) -> Matrix(1,0,-12,1) Matrix(301,232,650,501) -> Matrix(1,0,-28,1) Matrix(99,76,650,499) -> Matrix(1,0,-20,1) Matrix(551,422,850,651) -> Matrix(147,-8,-1966,107) Matrix(351,268,-850,-649) -> Matrix(73,-4,712,-39) Matrix(599,442,-950,-701) -> Matrix(209,-12,3048,-175) Matrix(299,220,950,699) -> Matrix(277,-16,-1610,93) Matrix(4499,3306,-7350,-5401) -> Matrix(69,-4,880,-51) Matrix(3401,2498,-4900,-3599) -> Matrix(275,-16,4486,-261) Matrix(5001,3662,-7100,-5199) -> Matrix(69,-4,1156,-67) Matrix(3599,2634,-6150,-4501) -> Matrix(139,-8,1894,-109) Matrix(599,438,2050,1499) -> Matrix(69,-4,-362,21) Matrix(299,218,-550,-401) -> Matrix(69,-4,880,-51) Matrix(201,146,-1100,-799) -> Matrix(69,-4,328,-19) Matrix(499,362,550,399) -> Matrix(69,-4,-1328,77) Matrix(3099,2246,4000,2899) -> Matrix(413,-24,-6694,389) Matrix(1151,834,-5450,-3949) -> Matrix(69,-4,328,-19) Matrix(1901,1376,2350,1701) -> Matrix(137,-8,-2346,137) Matrix(4301,3112,-7600,-5499) -> Matrix(69,-4,880,-51) Matrix(2951,2134,-7950,-5749) -> Matrix(343,-20,3310,-193) Matrix(1049,758,-2700,-1951) -> Matrix(137,-8,1216,-71) Matrix(649,468,900,649) -> Matrix(341,-20,-5132,301) Matrix(251,180,350,251) -> Matrix(135,-8,-2008,119) Matrix(149,106,350,249) -> Matrix(67,-4,-586,35) Matrix(551,390,2050,1451) -> Matrix(67,-4,-318,19) Matrix(99,70,-850,-601) -> Matrix(1,0,-14,1) Matrix(13849,9754,-19950,-14051) -> Matrix(133,-8,2178,-131) Matrix(8399,5914,10650,7499) -> Matrix(67,-4,-1122,67) Matrix(11451,8062,13850,9751) -> Matrix(67,-4,-1256,75) Matrix(4049,2850,4900,3449) -> Matrix(133,-8,-2344,141) Matrix(151,106,500,351) -> Matrix(133,-8,-748,45) Matrix(149,104,500,349) -> Matrix(131,-8,-704,43) Matrix(4399,3054,19300,13399) -> Matrix(65,-4,-276,17) Matrix(3999,2774,4900,3399) -> Matrix(65,-4,-1186,73) Matrix(11251,7802,14350,9951) -> Matrix(451,-28,-7522,467) Matrix(3449,2390,4400,3049) -> Matrix(67,-4,-1122,67) Matrix(249,172,650,449) -> Matrix(1,0,-24,1) Matrix(251,172,950,651) -> Matrix(259,-16,-1214,75) Matrix(249,170,-1100,-751) -> Matrix(193,-12,1142,-71) Matrix(651,424,-1150,-749) -> Matrix(1,0,-2,1) Matrix(651,422,850,551) -> Matrix(123,-8,-2014,131) Matrix(149,96,-700,-451) -> Matrix(61,-4,290,-19) Matrix(449,288,700,449) -> Matrix(241,-16,-3148,209) Matrix(351,224,550,351) -> Matrix(179,-12,-2312,155) Matrix(249,158,550,349) -> Matrix(59,-4,-516,35) Matrix(1349,854,-2450,-1551) -> Matrix(59,-4,664,-45) Matrix(949,600,2450,1549) -> Matrix(59,-4,-516,35) Matrix(349,220,-1350,-851) -> Matrix(233,-16,1500,-103) Matrix(1751,1102,3100,1951) -> Matrix(115,-8,-1308,91) Matrix(2201,1384,-7950,-4999) -> Matrix(287,-20,1966,-137) Matrix(51,32,400,251) -> Matrix(1,0,-16,1) Matrix(151,94,-400,-249) -> Matrix(59,-4,546,-37) Matrix(2801,1732,-4850,-2999) -> Matrix(57,-4,784,-55) Matrix(201,124,650,401) -> Matrix(1,0,-20,1) Matrix(101,62,-650,-399) -> Matrix(57,-4,214,-15) Matrix(901,552,2450,1501) -> Matrix(53,-4,-384,29) Matrix(4199,2570,-15850,-9701) -> Matrix(37,-4,250,-27) Matrix(749,458,-2700,-1651) -> Matrix(121,-8,832,-55) Matrix(449,274,-2050,-1251) -> Matrix(175,-12,948,-65) Matrix(149,90,-250,-151) -> Matrix(57,-4,784,-55) Matrix(1651,978,3800,2251) -> Matrix(1,0,-22,1) Matrix(11401,6750,18750,11101) -> Matrix(107,-8,-1324,99) Matrix(7599,4498,12500,7399) -> Matrix(49,-4,-600,49) Matrix(2701,1598,-4900,-2899) -> Matrix(1,0,-2,1) Matrix(349,206,-1950,-1151) -> Matrix(55,-4,234,-17) Matrix(201,118,-850,-499) -> Matrix(57,-4,328,-23) Matrix(649,380,1450,849) -> Matrix(55,-4,-536,39) Matrix(4649,2720,-17350,-10151) -> Matrix(163,-12,1046,-77) Matrix(1799,1052,-6500,-3801) -> Matrix(105,-8,722,-55) Matrix(251,146,-600,-349) -> Matrix(55,-4,564,-41) Matrix(4451,2570,6150,3551) -> Matrix(105,-8,-1588,121) Matrix(101,58,350,201) -> Matrix(53,-4,-278,21) Matrix(299,170,350,199) -> Matrix(1,0,-32,1) Matrix(1549,876,3800,2149) -> Matrix(1,0,-22,1) Matrix(149,84,-800,-451) -> Matrix(53,-4,252,-19) Matrix(449,252,800,449) -> Matrix(105,-8,-1168,89) Matrix(251,140,450,251) -> Matrix(51,-4,-548,43) Matrix(601,332,1450,801) -> Matrix(49,-4,-404,33) Matrix(1549,854,6800,3749) -> Matrix(1,0,-16,1) Matrix(201,110,550,301) -> Matrix(53,-4,-384,29) Matrix(499,270,-1850,-1001) -> Matrix(1,0,-6,1) Matrix(149,80,650,349) -> Matrix(1,0,-16,1) Matrix(651,346,-2350,-1249) -> Matrix(89,-8,612,-55) Matrix(549,290,850,449) -> Matrix(53,-4,-702,53) Matrix(749,354,950,449) -> Matrix(1,0,-28,1) Matrix(951,446,-2450,-1149) -> Matrix(1,0,-4,1) Matrix(501,232,650,301) -> Matrix(1,0,-28,1) Matrix(149,68,-550,-251) -> Matrix(45,-4,304,-27) Matrix(349,158,550,249) -> Matrix(43,-4,-548,51) Matrix(899,404,-2450,-1101) -> Matrix(51,-4,472,-37) Matrix(849,380,1450,649) -> Matrix(47,-4,-552,47) Matrix(199,88,450,199) -> Matrix(45,-4,-416,37) Matrix(351,154,800,351) -> Matrix(87,-8,-772,71) Matrix(849,370,-3100,-1351) -> Matrix(1,0,-4,1) Matrix(1149,500,3100,1349) -> Matrix(85,-8,-648,61) Matrix(401,174,-1150,-499) -> Matrix(1,0,-2,1) Matrix(51,22,350,151) -> Matrix(1,0,-12,1) Matrix(249,106,350,149) -> Matrix(43,-4,-634,59) Matrix(199,84,-950,-401) -> Matrix(43,-4,226,-21) Matrix(1451,610,2500,1051) -> Matrix(169,-16,-1954,185) Matrix(1449,608,2500,1049) -> Matrix(167,-16,-1910,183) Matrix(1651,686,-4450,-1849) -> Matrix(41,-4,400,-39) Matrix(1649,684,-6150,-2551) -> Matrix(83,-8,550,-53) Matrix(801,332,1450,601) -> Matrix(41,-4,-420,41) Matrix(1751,724,2300,951) -> Matrix(161,-16,-2586,257) Matrix(1099,454,1450,599) -> Matrix(79,-8,-1254,127) Matrix(151,62,-850,-349) -> Matrix(1,0,-6,1) Matrix(99,40,-250,-101) -> Matrix(41,-4,400,-39) Matrix(2901,1138,-7900,-3099) -> Matrix(77,-8,722,-75) Matrix(5101,2000,12500,4901) -> Matrix(39,-4,-380,39) Matrix(7649,2998,18750,7349) -> Matrix(77,-8,-664,69) Matrix(7851,3076,10850,4251) -> Matrix(155,-16,-2354,243) Matrix(251,98,-1150,-449) -> Matrix(77,-8,414,-43) Matrix(1949,756,-7350,-2851) -> Matrix(45,-4,304,-27) Matrix(1549,600,2450,949) -> Matrix(43,-4,-548,51) Matrix(1851,716,2200,851) -> Matrix(81,-8,-1468,145) Matrix(1299,502,1550,599) -> Matrix(79,-8,-1412,143) Matrix(449,172,650,249) -> Matrix(1,0,-24,1) Matrix(199,76,-1050,-401) -> Matrix(39,-4,166,-17) Matrix(1551,590,2500,951) -> Matrix(229,-24,-2872,301) Matrix(1549,588,2500,949) -> Matrix(227,-24,-2828,299) Matrix(349,130,400,149) -> Matrix(1,0,-28,1) Matrix(2201,816,2700,1001) -> Matrix(39,-4,-692,71) Matrix(249,92,-950,-351) -> Matrix(113,-12,744,-79) Matrix(1501,552,2450,901) -> Matrix(37,-4,-416,45) Matrix(4701,1726,5450,2001) -> Matrix(37,-4,-638,69) Matrix(301,110,550,201) -> Matrix(37,-4,-416,45) Matrix(199,72,550,199) -> Matrix(109,-12,-772,85) Matrix(251,90,700,251) -> Matrix(143,-16,-992,111) Matrix(1749,620,-6350,-2251) -> Matrix(1,0,-2,1) Matrix(401,142,850,301) -> Matrix(35,-4,-306,35) Matrix(199,70,850,299) -> Matrix(69,-8,-250,29) Matrix(401,138,-1450,-499) -> Matrix(37,-4,250,-27) Matrix(1199,386,1550,499) -> Matrix(129,-16,-2072,257) Matrix(1701,542,2200,701) -> Matrix(127,-16,-2024,255) Matrix(699,220,950,299) -> Matrix(125,-16,-1914,245) Matrix(401,124,650,201) -> Matrix(1,0,-20,1) Matrix(249,76,-1150,-351) -> Matrix(61,-8,328,-43) Matrix(351,106,500,151) -> Matrix(61,-8,-892,117) Matrix(349,104,500,149) -> Matrix(59,-8,-848,115) Matrix(149,44,-850,-251) -> Matrix(29,-4,138,-19) Matrix(1499,440,1700,499) -> Matrix(57,-8,-1090,153) Matrix(1801,528,2050,601) -> Matrix(27,-4,-506,75) Matrix(1499,438,2050,599) -> Matrix(29,-4,-442,61) Matrix(201,58,350,101) -> Matrix(29,-4,-326,45) Matrix(99,28,350,99) -> Matrix(57,-8,-292,41) Matrix(251,70,900,251) -> Matrix(139,-20,-688,99) Matrix(6599,1824,10850,2999) -> Matrix(109,-16,-1342,197) Matrix(2599,718,6150,1699) -> Matrix(55,-8,-488,71) Matrix(3599,992,4350,1199) -> Matrix(27,-4,-452,67) Matrix(901,248,4000,1101) -> Matrix(163,-24,-618,91) Matrix(51,14,550,151) -> Matrix(27,-4,-20,3) Matrix(5999,1646,7650,2099) -> Matrix(161,-24,-2690,401) Matrix(7301,1972,10000,2701) -> Matrix(53,-8,-828,125) Matrix(7299,1970,10000,2699) -> Matrix(51,-8,-784,123) Matrix(1451,390,2050,551) -> Matrix(27,-4,-398,59) Matrix(45751,12262,62500,16751) -> Matrix(209,-32,-3246,497) Matrix(45749,12260,62500,16749) -> Matrix(207,-32,-3202,495) Matrix(351,94,-2050,-549) -> Matrix(1,0,-2,1) Matrix(851,226,-3950,-1049) -> Matrix(55,-8,282,-41) Matrix(29401,7792,40000,10601) -> Matrix(1729,-256,-26374,3905) Matrix(29399,7790,40000,10599) -> Matrix(1727,-256,-26330,3903) Matrix(651,172,950,251) -> Matrix(107,-16,-1518,227) Matrix(1851,482,2500,651) -> Matrix(313,-48,-4858,745) Matrix(1849,480,2500,649) -> Matrix(311,-48,-4814,743) Matrix(851,206,1450,351) -> Matrix(49,-8,-594,97) Matrix(1349,322,2300,549) -> Matrix(95,-16,-1134,191) Matrix(299,70,850,199) -> Matrix(45,-8,-298,53) Matrix(551,128,650,151) -> Matrix(1,0,-24,1) Matrix(349,80,650,149) -> Matrix(1,0,-16,1) Matrix(149,34,-1100,-251) -> Matrix(1,0,-2,1) Matrix(1499,340,2200,499) -> Matrix(97,-16,-1364,225) Matrix(1051,238,1550,351) -> Matrix(95,-16,-1324,223) Matrix(1101,248,4000,901) -> Matrix(139,-24,-666,115) Matrix(401,90,450,101) -> Matrix(23,-4,-454,79) Matrix(1951,430,2500,551) -> Matrix(177,-32,-2926,529) Matrix(1949,428,2500,549) -> Matrix(175,-32,-2882,527) Matrix(1351,292,4400,951) -> Matrix(21,-4,-110,21) Matrix(4399,950,14350,3099) -> Matrix(149,-28,-878,165) Matrix(5551,1198,7650,1651) -> Matrix(127,-24,-1942,367) Matrix(799,172,-4650,-1001) -> Matrix(21,-4,100,-19) Matrix(501,106,950,201) -> Matrix(1,0,-16,1) Matrix(3151,666,10650,2251) -> Matrix(21,-4,-110,21) Matrix(49,10,-250,-51) -> Matrix(21,-4,100,-19) Matrix(649,124,2350,449) -> Matrix(39,-8,-190,39) Matrix(1699,314,2700,499) -> Matrix(17,-4,-208,49) Matrix(1501,276,4900,901) -> Matrix(15,-4,-86,23) Matrix(2051,370,2500,451) -> Matrix(37,-8,-652,141) Matrix(2049,368,2500,449) -> Matrix(35,-8,-608,139) Matrix(1451,252,4900,851) -> Matrix(35,-8,-188,43) Matrix(4099,710,13850,2399) -> Matrix(13,-4,-68,21) Matrix(3151,544,4350,751) -> Matrix(21,-4,-320,61) Matrix(2499,430,2900,499) -> Matrix(1,0,-22,1) Matrix(951,154,1550,251) -> Matrix(33,-8,-400,97) Matrix(1349,214,2200,349) -> Matrix(31,-8,-368,95) Matrix(499,76,650,99) -> Matrix(1,0,-20,1) Matrix(151,22,350,51) -> Matrix(1,0,-12,1) Matrix(2151,302,2500,351) -> Matrix(1,0,-18,1) Matrix(2149,300,2500,349) -> Matrix(1,0,-26,1) Matrix(2401,332,2900,401) -> Matrix(1,0,-22,1) Matrix(3449,474,5450,749) -> Matrix(19,-4,-242,51) Matrix(251,32,400,51) -> Matrix(1,0,-16,1) Matrix(1449,176,2050,249) -> Matrix(13,-4,-198,61) Matrix(1201,142,1700,201) -> Matrix(23,-8,-342,119) Matrix(349,38,450,49) -> Matrix(9,-4,-146,65) Matrix(151,14,550,51) -> Matrix(11,-4,-52,19) Matrix(601,-70,850,-99) -> Matrix(1,0,-14,1) Matrix(251,-34,1100,-149) -> Matrix(1,0,-2,1) Matrix(399,-62,650,-101) -> Matrix(7,4,-86,-49) Matrix(251,-44,850,-149) -> Matrix(11,4,-58,-21) Matrix(349,-62,850,-151) -> Matrix(1,0,-6,1) Matrix(451,-84,800,-149) -> Matrix(11,4,-124,-45) Matrix(401,-76,1050,-199) -> Matrix(9,4,-70,-31) Matrix(401,-84,950,-199) -> Matrix(13,4,-114,-35) Matrix(451,-96,700,-149) -> Matrix(11,4,-146,-53) Matrix(351,-76,1150,-249) -> Matrix(27,8,-152,-45) Matrix(449,-98,1150,-251) -> Matrix(27,8,-206,-61) Matrix(751,-170,1100,-249) -> Matrix(47,12,-662,-169) Matrix(6799,-1550,7900,-1801) -> Matrix(1,0,-12,1) Matrix(499,-118,850,-201) -> Matrix(15,4,-184,-49) Matrix(351,-92,950,-249) -> Matrix(55,12,-408,-89) Matrix(2851,-756,7350,-1949) -> Matrix(19,4,-176,-37) Matrix(1499,-398,4900,-1301) -> Matrix(77,16,-438,-91) Matrix(2099,-562,7100,-1901) -> Matrix(19,4,-100,-21) Matrix(2551,-684,6150,-1649) -> Matrix(37,8,-310,-67) Matrix(251,-68,550,-149) -> Matrix(19,4,-176,-37) Matrix(899,-246,1100,-301) -> Matrix(19,4,-328,-69) Matrix(4299,-1184,5450,-1501) -> Matrix(19,4,-328,-69) Matrix(3299,-912,7600,-2101) -> Matrix(19,4,-176,-37) Matrix(4999,-1384,7950,-2201) -> Matrix(97,20,-1198,-247) Matrix(1651,-458,2700,-749) -> Matrix(39,8,-512,-105) Matrix(751,-220,850,-249) -> Matrix(1,0,-14,1) Matrix(6101,-1804,19950,-5899) -> Matrix(43,8,-242,-45) Matrix(851,-270,1100,-349) -> Matrix(71,12,-1142,-193) Matrix(499,-174,1150,-401) -> Matrix(1,0,-2,1) Matrix(551,-196,700,-249) -> Matrix(27,4,-466,-69) Matrix(1101,-404,2450,-899) -> Matrix(29,4,-312,-43) Matrix(1001,-370,1350,-499) -> Matrix(119,16,-1852,-249) Matrix(5749,-2134,7950,-2951) -> Matrix(153,20,-2318,-303) Matrix(249,-94,400,-151) -> Matrix(29,4,-370,-51) Matrix(2049,-782,4850,-1851) -> Matrix(31,4,-256,-33) Matrix(549,-212,650,-251) -> Matrix(31,4,-566,-73) Matrix(11651,-4520,15850,-6149) -> Matrix(51,4,-778,-61) Matrix(1951,-758,2700,-1049) -> Matrix(55,8,-832,-121) Matrix(1601,-624,2050,-799) -> Matrix(89,12,-1476,-199) Matrix(101,-40,250,-99) -> Matrix(31,4,-256,-33) Matrix(2199,-898,4900,-2001) -> Matrix(1,0,-2,1) Matrix(1601,-656,1950,-799) -> Matrix(33,4,-586,-71) Matrix(649,-268,850,-351) -> Matrix(31,4,-504,-65) Matrix(12701,-5270,17350,-7199) -> Matrix(101,12,-1574,-187) Matrix(4701,-1952,6500,-2699) -> Matrix(71,8,-1074,-121) Matrix(349,-146,600,-251) -> Matrix(33,4,-388,-47) Matrix(651,-284,800,-349) -> Matrix(35,4,-604,-69) Matrix(1351,-620,1850,-849) -> Matrix(1,0,-6,1) Matrix(1699,-796,2350,-1101) -> Matrix(87,8,-1316,-121) Matrix(1499,-796,2450,-1301) -> Matrix(1,0,-4,1) Matrix(401,-218,550,-299) -> Matrix(43,4,-656,-61) Matrix(1551,-854,2450,-1349) -> Matrix(37,4,-472,-51) Matrix(2251,-1270,3100,-1749) -> Matrix(1,0,-4,1) Matrix(749,-424,1150,-651) -> Matrix(1,0,-2,1) Matrix(751,-434,950,-549) -> Matrix(45,4,-754,-67) Matrix(2799,-1636,4450,-2601) -> Matrix(47,4,-576,-49) Matrix(4501,-2634,6150,-3599) -> Matrix(93,8,-1430,-123) Matrix(699,-412,850,-501) -> Matrix(1,0,-6,1) Matrix(151,-90,250,-149) -> Matrix(47,4,-576,-49) Matrix(4999,-3038,7900,-4801) -> Matrix(99,8,-1250,-101) Matrix(899,-548,1150,-701) -> Matrix(99,8,-1646,-133) Matrix(5401,-3306,7350,-4499) -> Matrix(43,4,-656,-61) Matrix(851,-526,1050,-649) -> Matrix(49,4,-870,-71) Matrix(701,-442,950,-599) -> Matrix(151,12,-2328,-185) Matrix(4601,-2970,6350,-4099) -> Matrix(1,0,-2,1) Matrix(1049,-688,1450,-951) -> Matrix(51,4,-778,-61) Matrix(901,-626,1150,-799) -> Matrix(115,8,-1912,-133) Matrix(701,-494,850,-599) -> Matrix(59,4,-1018,-69) Matrix(1699,-1244,2050,-1501) -> Matrix(1,0,-2,1) Matrix(3099,-2276,3950,-2901) -> Matrix(121,8,-2042,-135) Matrix(951,-734,1100,-849) -> Matrix(1,0,-2,1) Matrix(3851,-3022,4650,-3649) -> Matrix(67,4,-1156,-69) Matrix(201,-160,250,-199) -> Matrix(67,4,-1156,-69) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 50 Degree of the the map X: 100 Degree of the the map Y: 300 ----------------------------------------------------------------------- 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): 900 Minimal number of generators: 151 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: 48 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 5/23 5/22 1/4 4/15 5/18 7/25 7/24 3/10 23/75 1/3 7/20 9/25 8/21 2/5 51/125 5/12 11/25 9/20 1/2 8/15 11/20 29/50 3/5 31/50 17/25 7/10 73/100 183/250 11/15 147/200 37/50 19/25 39/50 4/5 41/50 62/75 21/25 43/50 22/25 9/10 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/10 0/1 1/9 -2/1 -1/1 1/8 -1/1 -2/3 2/15 -1/2 1/7 -1/1 0/1 3/20 -2/3 2/13 -2/3 -1/2 1/6 -1/2 -2/5 3/17 -1/3 0/1 2/11 -2/5 -1/3 3/16 -1/3 0/1 1/5 -1/3 4/19 -2/7 -1/4 3/14 -1/3 -4/13 5/23 -3/10 -2/7 2/9 -2/7 -3/11 9/40 -4/15 7/31 -6/23 -1/4 5/22 -1/4 -2/9 18/79 -1/4 -2/9 31/136 -1/5 0/1 13/57 -1/3 0/1 8/35 -1/4 3/13 -2/7 -1/4 7/30 -2/7 4/17 -4/15 -5/19 1/4 -1/4 -2/9 5/19 -2/9 -3/14 9/34 -7/33 -4/19 13/49 -4/19 -1/5 4/15 -1/5 15/56 -1/4 -2/9 11/41 -2/9 -1/5 7/26 -2/9 -1/5 3/11 -2/9 -1/5 14/51 -7/33 -4/19 11/40 -4/19 19/69 -5/24 -6/29 8/29 -5/24 -6/29 21/76 -6/29 -1/5 13/47 -5/24 -6/29 18/65 -7/34 5/18 -10/49 -1/5 7/25 -1/5 2/7 -1/5 -4/21 7/24 -1/5 -2/11 12/41 -1/5 -2/11 5/17 -1/5 -4/21 13/44 -3/16 -2/11 34/115 -1/5 21/71 -3/16 -2/11 29/98 -4/21 -3/16 37/125 -3/16 8/27 -3/16 -2/11 3/10 -2/11 7/23 -2/11 -1/6 11/36 -3/17 -4/23 37/121 -2/11 -1/6 26/85 -3/17 15/49 -3/17 -4/23 19/62 -6/35 -1/6 23/75 -1/6 4/13 -2/11 -1/6 5/16 -3/17 -4/23 6/19 -6/35 -1/6 1/3 -1/6 -2/13 7/20 -2/13 6/17 -7/47 -4/27 5/14 -8/55 -1/7 9/25 -1/7 4/11 -1/7 -6/43 11/30 -4/29 18/49 -1/7 -4/29 7/19 -3/22 -2/15 17/46 -7/52 -2/15 10/27 -2/15 -5/38 23/62 -2/15 -1/8 13/35 -1/8 3/8 -1/7 -2/15 8/21 -2/15 -5/38 21/55 -3/23 13/34 -3/23 -4/31 5/13 -2/15 -1/8 12/31 -1/8 -2/17 19/49 -1/9 0/1 45/116 -1/11 0/1 26/67 -1/3 0/1 7/18 -1/7 -2/15 16/41 -2/15 -7/53 9/23 -2/15 -1/8 2/5 -1/8 11/27 -1/8 -2/17 31/76 -2/17 -1/9 51/125 -1/9 20/49 -1/9 0/1 9/22 -1/8 -2/17 16/39 -2/17 -1/9 7/17 -1/9 0/1 12/29 -1/8 -6/49 17/41 -3/25 -2/17 39/94 -5/42 -2/17 22/53 -2/17 -3/26 5/12 -1/8 -2/17 8/19 -2/17 -3/26 19/45 -1/9 30/71 -2/17 -3/26 11/26 -2/17 -1/9 3/7 -1/9 0/1 13/30 -2/17 23/53 -1/8 -2/17 33/76 -2/17 -1/9 10/23 -1/8 -2/17 7/16 -4/35 -1/9 11/25 -1/9 4/9 -1/9 -2/19 13/29 -1/10 -2/21 35/78 -1/10 -2/21 22/49 -1/11 0/1 9/20 0/1 5/11 -1/9 -2/19 11/24 -1/9 -2/19 6/13 -2/19 -1/10 7/15 -1/10 8/17 -1/7 0/1 1/2 -1/10 0/1 9/17 -1/13 0/1 8/15 -1/10 7/13 -1/10 -2/21 6/11 -2/21 -1/11 11/20 0/1 16/29 -2/19 -1/10 5/9 -2/21 -1/11 14/25 -1/11 9/16 -1/11 -4/45 22/39 -1/11 -2/23 35/62 -3/34 -2/23 13/23 -2/23 -1/12 17/30 -2/23 4/7 -1/11 0/1 15/26 -1/11 -2/23 11/19 -3/34 -2/23 29/50 -2/23 18/31 -2/23 -5/58 7/12 -2/23 -1/12 31/53 -3/34 -2/23 24/41 -2/23 -3/35 17/29 -6/71 -1/12 44/75 -1/12 27/46 -1/12 -6/73 10/17 -1/11 0/1 13/22 -2/23 -1/12 3/5 -1/12 17/28 -1/12 -2/25 31/51 -4/49 -3/37 76/125 -3/37 45/74 -3/37 -2/25 14/23 -1/12 -2/25 11/18 -2/25 -1/13 52/85 -1/14 41/67 -1/17 0/1 30/49 -1/11 0/1 19/31 -2/23 -1/12 46/75 -1/12 27/44 -1/12 -6/73 8/13 -1/12 -2/25 21/34 -4/49 -3/37 13/21 -5/62 -2/25 31/50 -2/25 18/29 -2/25 -7/88 5/8 -2/25 -1/13 22/35 -1/12 61/97 -5/62 -2/25 39/62 -1/12 -2/25 17/27 -5/62 -2/25 12/19 -2/25 -3/38 31/49 -4/51 -1/13 81/128 -2/25 -3/38 50/79 -2/25 -3/38 19/30 -4/51 7/11 -6/77 -1/13 16/25 -1/13 9/14 -1/13 -8/105 20/31 -6/79 -5/66 31/48 -5/66 -4/53 11/17 -4/53 -7/93 13/20 -2/27 15/23 -2/27 -1/14 2/3 -2/27 -1/14 17/25 -1/14 15/22 -1/14 -14/197 13/19 -1/14 -6/85 11/16 -4/57 -3/43 9/13 -1/14 -2/29 16/23 -1/14 -2/29 7/10 -2/29 19/27 -2/29 -3/44 12/17 -4/59 -1/15 53/75 -1/15 41/58 -1/15 -2/31 29/41 -2/29 -1/15 17/24 -2/29 -1/15 5/7 -4/59 -1/15 18/25 -1/15 13/18 -1/15 -10/151 60/83 -8/121 -31/469 47/65 -7/106 81/112 -7/106 -6/91 34/47 -6/91 -5/76 89/123 -6/91 -5/76 55/76 -1/15 -6/91 21/29 -6/91 -5/76 71/98 -5/76 -4/61 50/69 -6/91 -5/76 29/40 -4/61 37/51 -4/61 -7/107 45/62 -3/46 -2/31 8/11 -1/15 -2/31 27/37 -3/46 -2/31 73/100 -2/31 46/63 -2/31 -1/16 19/26 -1/15 -2/31 30/41 -1/15 -2/31 71/97 -7/108 -2/31 183/250 -2/31 112/153 -2/31 -9/140 41/56 -2/31 -1/16 11/15 -1/15 36/49 -1/15 -4/61 61/83 -25/381 -4/61 147/200 -4/61 86/117 -4/61 -39/595 25/34 -4/61 -7/107 14/19 -3/46 -2/31 17/23 -11/170 -2/31 37/50 -2/31 20/27 -2/31 -13/202 3/4 -2/31 -1/16 19/25 -1/16 16/21 -1/16 -10/161 13/17 -5/81 -4/65 23/30 -2/33 10/13 -1/16 -2/33 27/35 -1/16 17/22 -2/31 -1/16 58/75 -1/16 41/53 -1/16 -14/225 24/31 -1/16 -6/97 31/40 -4/65 7/9 -3/49 -2/33 39/50 -2/33 32/41 -2/33 -13/215 25/32 -2/33 -5/83 18/23 -2/33 -3/50 29/37 -2/33 -3/50 98/125 -3/50 69/88 -3/50 -10/167 40/51 -4/67 -1/17 51/65 -1/17 11/14 -4/67 -1/17 26/33 -1/19 0/1 41/52 -1/16 0/1 56/71 -1/16 -2/33 15/19 -1/16 -2/33 19/24 -2/33 -1/17 4/5 -1/17 21/26 -1/17 -2/35 17/21 -3/52 -2/35 13/16 -1/17 0/1 22/27 -3/52 -2/35 31/38 -2/35 -1/18 40/49 -1/19 0/1 9/11 -1/17 -2/35 41/50 -2/35 32/39 -2/35 -3/53 23/28 -2/35 -1/18 14/17 -1/17 0/1 19/23 -2/35 -1/18 62/75 -1/18 43/52 -1/18 0/1 24/29 -2/35 -1/18 53/64 -1/17 0/1 29/35 -1/17 5/6 -2/35 -1/18 21/25 -1/18 16/19 -1/18 -6/109 11/13 -1/18 -2/37 17/20 -2/37 6/7 -1/19 0/1 43/50 0/1 37/43 -1/15 0/1 31/36 -1/17 0/1 25/29 -2/35 -1/18 19/22 -2/35 -1/18 13/15 -1/18 7/8 -2/37 -1/19 22/25 -1/19 15/17 -1/19 -4/77 8/9 -1/19 -2/39 9/10 0/1 1/1 -1/21 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(399,-37,550,-51) (0/1,1/10) -> (29/40,37/51) Hyperbolic Matrix(101,-11,450,-49) (1/10,1/9) -> (2/9,9/40) Hyperbolic Matrix(601,-70,850,-99) (1/9,1/8) -> (41/58,29/41) Hyperbolic Matrix(149,-19,400,-51) (1/8,2/15) -> (13/35,3/8) Hyperbolic Matrix(251,-34,1100,-149) (2/15,1/7) -> (13/57,8/35) Hyperbolic Matrix(199,-29,350,-51) (1/7,3/20) -> (17/30,4/7) Hyperbolic Matrix(151,-23,650,-99) (3/20,2/13) -> (3/13,7/30) Hyperbolic Matrix(399,-62,650,-101) (2/13,1/6) -> (27/44,8/13) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(349,-62,850,-151) (3/17,2/11) -> (16/39,7/17) Hyperbolic Matrix(451,-84,800,-149) (2/11,3/16) -> (9/16,22/39) Hyperbolic Matrix(401,-76,1050,-199) (3/16,1/5) -> (21/55,13/34) Hyperbolic Matrix(401,-84,950,-199) (1/5,4/19) -> (8/19,19/45) Hyperbolic Matrix(451,-96,700,-149) (4/19,3/14) -> (9/14,20/31) Hyperbolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(449,-98,1150,-251) (5/23,2/9) -> (16/41,9/23) Hyperbolic Matrix(2899,-653,4000,-901) (9/40,7/31) -> (50/69,29/40) Hyperbolic Matrix(751,-170,1100,-249) (7/31,5/22) -> (15/22,13/19) Hyperbolic Matrix(3051,-695,6800,-1549) (5/22,18/79) -> (13/29,35/78) Hyperbolic Matrix(5901,-1345,19300,-4399) (18/79,31/136) -> (11/36,37/121) Hyperbolic Matrix(6799,-1550,7900,-1801) (31/136,13/57) -> (37/43,31/36) Hyperbolic Matrix(301,-69,650,-149) (8/35,3/13) -> (6/13,7/15) Hyperbolic Matrix(551,-129,850,-199) (7/30,4/17) -> (11/17,13/20) Hyperbolic Matrix(499,-118,850,-201) (4/17,1/4) -> (27/46,10/17) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(299,-79,950,-251) (5/19,9/34) -> (5/16,6/19) Hyperbolic Matrix(2851,-756,7350,-1949) (9/34,13/49) -> (19/49,45/116) Hyperbolic Matrix(1499,-398,4900,-1301) (13/49,4/15) -> (26/85,15/49) Hyperbolic Matrix(2099,-562,7100,-1901) (4/15,15/56) -> (13/44,34/115) Hyperbolic Matrix(2551,-684,6150,-1649) (15/56,11/41) -> (17/41,39/94) Hyperbolic Matrix(599,-161,2050,-551) (11/41,7/26) -> (7/24,12/41) Hyperbolic Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(899,-246,1100,-301) (3/11,14/51) -> (40/49,9/11) Hyperbolic Matrix(499,-137,550,-151) (14/51,11/40) -> (9/10,1/1) Hyperbolic Matrix(3099,-853,4000,-1101) (11/40,19/69) -> (24/31,31/40) Hyperbolic Matrix(4299,-1184,5450,-1501) (19/69,8/29) -> (56/71,15/19) Hyperbolic Matrix(1901,-525,2350,-649) (8/29,21/76) -> (21/26,17/21) Hyperbolic Matrix(3299,-912,7600,-2101) (21/76,13/47) -> (23/53,33/76) Hyperbolic Matrix(4999,-1384,7950,-2201) (13/47,18/65) -> (22/35,61/97) Hyperbolic Matrix(1651,-458,2700,-749) (18/65,5/18) -> (11/18,52/85) Hyperbolic Matrix(649,-181,900,-251) (5/18,7/25) -> (18/25,13/18) Hyperbolic Matrix(251,-71,350,-99) (7/25,2/7) -> (5/7,18/25) Hyperbolic Matrix(149,-43,350,-101) (2/7,7/24) -> (11/26,3/7) Hyperbolic Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(6101,-1804,19950,-5899) (34/115,21/71) -> (37/121,26/85) Hyperbolic Matrix(8399,-2485,10650,-3151) (21/71,29/98) -> (41/52,56/71) Hyperbolic Matrix(11451,-3389,13850,-4099) (29/98,37/125) -> (62/75,43/52) Hyperbolic Matrix(4049,-1199,4900,-1451) (37/125,8/27) -> (19/23,62/75) Hyperbolic Matrix(151,-45,500,-149) (8/27,3/10) -> (3/10,7/23) Parabolic Matrix(3999,-1225,4900,-1501) (15/49,19/62) -> (31/38,40/49) Hyperbolic Matrix(11251,-3449,14350,-4399) (19/62,23/75) -> (98/125,69/88) Hyperbolic Matrix(3449,-1059,4400,-1351) (23/75,4/13) -> (29/37,98/125) Hyperbolic Matrix(249,-77,650,-201) (4/13,5/16) -> (13/34,5/13) Hyperbolic Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(499,-174,1150,-401) (1/3,7/20) -> (13/30,23/53) Hyperbolic Matrix(651,-229,850,-299) (7/20,6/17) -> (13/17,23/30) Hyperbolic Matrix(551,-196,700,-249) (6/17,5/14) -> (11/14,26/33) Hyperbolic Matrix(449,-161,700,-251) (5/14,9/25) -> (16/25,9/14) Hyperbolic Matrix(351,-127,550,-199) (9/25,4/11) -> (7/11,16/25) Hyperbolic Matrix(249,-91,550,-201) (4/11,11/30) -> (9/20,5/11) Hyperbolic Matrix(1101,-404,2450,-899) (11/30,18/49) -> (22/49,9/20) Hyperbolic Matrix(949,-349,2450,-901) (18/49,7/19) -> (12/31,19/49) Hyperbolic Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(1751,-649,3100,-1149) (10/27,23/62) -> (35/62,13/23) Hyperbolic Matrix(5749,-2134,7950,-2951) (23/62,13/35) -> (47/65,81/112) Hyperbolic Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(2049,-782,4850,-1851) (8/21,21/55) -> (19/45,30/71) Hyperbolic Matrix(549,-212,650,-251) (5/13,12/31) -> (16/19,11/13) Hyperbolic Matrix(11651,-4520,15850,-6149) (45/116,26/67) -> (86/117,25/34) Hyperbolic Matrix(1951,-758,2700,-1049) (26/67,7/18) -> (13/18,60/83) Hyperbolic Matrix(1601,-624,2050,-799) (7/18,16/41) -> (32/41,25/32) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(1651,-673,3800,-1549) (11/27,31/76) -> (33/76,10/23) Hyperbolic Matrix(11401,-4651,18750,-7649) (31/76,51/125) -> (76/125,45/74) Hyperbolic Matrix(7599,-3101,12500,-5101) (51/125,20/49) -> (31/51,76/125) Hyperbolic Matrix(2199,-898,4900,-2001) (20/49,9/22) -> (35/78,22/49) Hyperbolic Matrix(1601,-656,1950,-799) (9/22,16/39) -> (32/39,23/28) Hyperbolic Matrix(649,-268,850,-351) (7/17,12/29) -> (16/21,13/17) Hyperbolic Matrix(649,-269,1450,-601) (12/29,17/41) -> (4/9,13/29) Hyperbolic Matrix(12701,-5270,17350,-7199) (39/94,22/53) -> (112/153,41/56) Hyperbolic Matrix(4701,-1952,6500,-2699) (22/53,5/12) -> (81/112,34/47) Hyperbolic Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(4451,-1881,6150,-2599) (30/71,11/26) -> (55/76,21/29) Hyperbolic Matrix(299,-129,350,-151) (3/7,13/30) -> (17/20,6/7) Hyperbolic Matrix(651,-284,800,-349) (10/23,7/16) -> (13/16,22/27) Hyperbolic Matrix(449,-197,800,-351) (7/16,11/25) -> (14/25,9/16) Hyperbolic Matrix(251,-111,450,-199) (11/25,4/9) -> (5/9,14/25) Hyperbolic Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(1699,-796,2350,-1101) (7/15,8/17) -> (60/83,47/65) Hyperbolic Matrix(549,-259,850,-401) (8/17,1/2) -> (31/48,11/17) Hyperbolic Matrix(749,-395,950,-501) (1/2,9/17) -> (26/33,41/52) Hyperbolic Matrix(1499,-796,2450,-1301) (9/17,8/15) -> (52/85,41/67) Hyperbolic Matrix(501,-269,650,-349) (8/15,7/13) -> (10/13,27/35) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(349,-191,550,-301) (6/11,11/20) -> (19/30,7/11) Hyperbolic Matrix(1551,-854,2450,-1349) (11/20,16/29) -> (50/79,19/30) Hyperbolic Matrix(849,-469,1450,-801) (16/29,5/9) -> (24/41,17/29) Hyperbolic Matrix(2251,-1270,3100,-1749) (22/39,35/62) -> (45/62,8/11) Hyperbolic Matrix(749,-424,1150,-651) (13/23,17/30) -> (13/20,15/23) Hyperbolic Matrix(249,-143,350,-201) (4/7,15/26) -> (17/24,5/7) Hyperbolic Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(1451,-841,2500,-1449) (11/19,29/50) -> (29/50,18/31) Parabolic Matrix(2799,-1636,4450,-2601) (7/12,31/53) -> (61/97,39/62) Hyperbolic Matrix(4501,-2634,6150,-3599) (31/53,24/41) -> (30/41,71/97) Hyperbolic Matrix(1751,-1027,2300,-1349) (17/29,44/75) -> (19/25,16/21) Hyperbolic Matrix(1099,-645,1450,-851) (44/75,27/46) -> (3/4,19/25) Hyperbolic Matrix(699,-412,850,-501) (10/17,13/22) -> (23/28,14/17) Hyperbolic Matrix(151,-90,250,-149) (13/22,3/5) -> (3/5,17/28) Parabolic Matrix(4999,-3038,7900,-4801) (17/28,31/51) -> (31/49,81/128) Hyperbolic Matrix(7851,-4775,10850,-6599) (45/74,14/23) -> (89/123,55/76) Hyperbolic Matrix(899,-548,1150,-701) (14/23,11/18) -> (25/32,18/23) Hyperbolic Matrix(5401,-3306,7350,-4499) (41/67,30/49) -> (36/49,61/83) Hyperbolic Matrix(1549,-949,2450,-1501) (30/49,19/31) -> (12/19,31/49) Hyperbolic Matrix(1851,-1135,2200,-1349) (19/31,46/75) -> (21/25,16/19) Hyperbolic Matrix(1299,-797,1550,-951) (46/75,27/44) -> (5/6,21/25) Hyperbolic Matrix(449,-277,650,-401) (8/13,21/34) -> (11/16,9/13) Hyperbolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(1551,-961,2500,-1549) (13/21,31/50) -> (31/50,18/29) Parabolic Matrix(349,-219,400,-251) (5/8,22/35) -> (13/15,7/8) Hyperbolic Matrix(2201,-1385,2700,-1699) (39/62,17/27) -> (22/27,31/38) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(4701,-2975,5450,-3449) (81/128,50/79) -> (25/29,19/22) Hyperbolic Matrix(4601,-2970,6350,-4099) (20/31,31/48) -> (71/98,50/69) Hyperbolic Matrix(1049,-688,1450,-951) (15/23,2/3) -> (34/47,89/123) Hyperbolic Matrix(1199,-813,1550,-1051) (2/3,17/25) -> (58/75,41/53) Hyperbolic Matrix(1701,-1159,2200,-1499) (17/25,15/22) -> (17/22,58/75) Hyperbolic Matrix(699,-479,950,-651) (13/19,11/16) -> (25/34,14/19) Hyperbolic Matrix(901,-626,1150,-799) (9/13,16/23) -> (18/23,29/37) Hyperbolic Matrix(351,-245,500,-349) (16/23,7/10) -> (7/10,19/27) Parabolic Matrix(701,-494,850,-599) (19/27,12/17) -> (14/17,19/23) Hyperbolic Matrix(1499,-1059,1700,-1201) (12/17,53/75) -> (22/25,15/17) Hyperbolic Matrix(1801,-1273,2050,-1449) (53/75,41/58) -> (7/8,22/25) Hyperbolic Matrix(1499,-1061,2050,-1451) (29/41,17/24) -> (19/26,30/41) Hyperbolic Matrix(3599,-2607,4350,-3151) (21/29,71/98) -> (43/52,24/29) Hyperbolic Matrix(5999,-4353,7650,-5551) (37/51,45/62) -> (69/88,40/51) Hyperbolic Matrix(7301,-5329,10000,-7299) (27/37,73/100) -> (73/100,46/63) Parabolic Matrix(45751,-33489,62500,-45749) (71/97,183/250) -> (183/250,112/153) Parabolic Matrix(1699,-1244,2050,-1501) (41/56,11/15) -> (29/35,5/6) Hyperbolic Matrix(3099,-2276,3950,-2901) (11/15,36/49) -> (40/51,51/65) Hyperbolic Matrix(29401,-21609,40000,-29399) (61/83,147/200) -> (147/200,86/117) Parabolic Matrix(1851,-1369,2500,-1849) (17/23,37/50) -> (37/50,20/27) Parabolic Matrix(551,-423,650,-499) (23/30,10/13) -> (11/13,17/20) Hyperbolic Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(401,-311,450,-349) (31/40,7/9) -> (8/9,9/10) Hyperbolic Matrix(1951,-1521,2500,-1949) (7/9,39/50) -> (39/50,32/41) Parabolic Matrix(3851,-3022,4650,-3649) (51/65,11/14) -> (53/64,29/35) Hyperbolic Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic Matrix(2051,-1681,2500,-2049) (9/11,41/50) -> (41/50,32/39) Parabolic Matrix(2499,-2069,2900,-2401) (24/29,53/64) -> (31/36,25/29) Hyperbolic Matrix(2151,-1849,2500,-2149) (6/7,43/50) -> (43/50,37/43) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-22,1) Matrix(399,-37,550,-51) -> Matrix(3,4,-46,-61) Matrix(101,-11,450,-49) -> Matrix(1,4,-4,-15) Matrix(601,-70,850,-99) -> Matrix(1,0,-14,1) Matrix(149,-19,400,-51) -> Matrix(1,0,-6,1) Matrix(251,-34,1100,-149) -> Matrix(1,0,-2,1) Matrix(199,-29,350,-51) -> Matrix(1,0,-10,1) Matrix(151,-23,650,-99) -> Matrix(1,0,-2,1) Matrix(399,-62,650,-101) -> Matrix(7,4,-86,-49) Matrix(251,-44,850,-149) -> Matrix(11,4,-58,-21) Matrix(349,-62,850,-151) -> Matrix(1,0,-6,1) Matrix(451,-84,800,-149) -> Matrix(11,4,-124,-45) Matrix(401,-76,1050,-199) -> Matrix(9,4,-70,-31) Matrix(401,-84,950,-199) -> Matrix(13,4,-114,-35) Matrix(451,-96,700,-149) -> Matrix(11,4,-146,-53) Matrix(351,-76,1150,-249) -> Matrix(27,8,-152,-45) Matrix(449,-98,1150,-251) -> Matrix(27,8,-206,-61) Matrix(2899,-653,4000,-901) -> Matrix(91,24,-1384,-365) Matrix(751,-170,1100,-249) -> Matrix(47,12,-662,-169) Matrix(3051,-695,6800,-1549) -> Matrix(1,0,-6,1) Matrix(5901,-1345,19300,-4399) -> Matrix(17,4,-98,-23) Matrix(6799,-1550,7900,-1801) -> Matrix(1,0,-12,1) Matrix(301,-69,650,-149) -> Matrix(1,0,-6,1) Matrix(551,-129,850,-199) -> Matrix(29,8,-388,-107) Matrix(499,-118,850,-201) -> Matrix(15,4,-184,-49) Matrix(351,-92,950,-249) -> Matrix(55,12,-408,-89) Matrix(299,-79,950,-251) -> Matrix(75,16,-436,-93) Matrix(2851,-756,7350,-1949) -> Matrix(19,4,-176,-37) Matrix(1499,-398,4900,-1301) -> Matrix(77,16,-438,-91) Matrix(2099,-562,7100,-1901) -> Matrix(19,4,-100,-21) Matrix(2551,-684,6150,-1649) -> Matrix(37,8,-310,-67) Matrix(599,-161,2050,-551) -> Matrix(19,4,-100,-21) Matrix(251,-68,550,-149) -> Matrix(19,4,-176,-37) Matrix(899,-246,1100,-301) -> Matrix(19,4,-328,-69) Matrix(499,-137,550,-151) -> Matrix(19,4,-366,-77) Matrix(3099,-853,4000,-1101) -> Matrix(115,24,-1864,-389) Matrix(4299,-1184,5450,-1501) -> Matrix(19,4,-328,-69) Matrix(1901,-525,2350,-649) -> Matrix(39,8,-668,-137) Matrix(3299,-912,7600,-2101) -> Matrix(19,4,-176,-37) Matrix(4999,-1384,7950,-2201) -> Matrix(97,20,-1198,-247) Matrix(1651,-458,2700,-749) -> Matrix(39,8,-512,-105) Matrix(649,-181,900,-251) -> Matrix(99,20,-1490,-301) Matrix(251,-71,350,-99) -> Matrix(41,8,-610,-119) Matrix(149,-43,350,-101) -> Matrix(21,4,-184,-35) Matrix(751,-220,850,-249) -> Matrix(1,0,-14,1) Matrix(6101,-1804,19950,-5899) -> Matrix(43,8,-242,-45) Matrix(8399,-2485,10650,-3151) -> Matrix(21,4,-352,-67) Matrix(11451,-3389,13850,-4099) -> Matrix(21,4,-394,-75) Matrix(4049,-1199,4900,-1451) -> Matrix(43,8,-758,-141) Matrix(151,-45,500,-149) -> Matrix(43,8,-242,-45) Matrix(3999,-1225,4900,-1501) -> Matrix(23,4,-420,-73) Matrix(11251,-3449,14350,-4399) -> Matrix(165,28,-2752,-467) Matrix(3449,-1059,4400,-1351) -> Matrix(21,4,-352,-67) Matrix(249,-77,650,-201) -> Matrix(1,0,-2,1) Matrix(851,-270,1100,-349) -> Matrix(71,12,-1142,-193) Matrix(499,-174,1150,-401) -> Matrix(1,0,-2,1) Matrix(651,-229,850,-299) -> Matrix(53,8,-868,-131) Matrix(551,-196,700,-249) -> Matrix(27,4,-466,-69) Matrix(449,-161,700,-251) -> Matrix(111,16,-1450,-209) Matrix(351,-127,550,-199) -> Matrix(85,12,-1098,-155) Matrix(249,-91,550,-201) -> Matrix(29,4,-254,-35) Matrix(1101,-404,2450,-899) -> Matrix(29,4,-312,-43) Matrix(949,-349,2450,-901) -> Matrix(29,4,-254,-35) Matrix(1001,-370,1350,-499) -> Matrix(119,16,-1852,-249) Matrix(1751,-649,3100,-1149) -> Matrix(61,8,-694,-91) Matrix(5749,-2134,7950,-2951) -> Matrix(153,20,-2318,-303) Matrix(249,-94,400,-151) -> Matrix(29,4,-370,-51) Matrix(2049,-782,4850,-1851) -> Matrix(31,4,-256,-33) Matrix(549,-212,650,-251) -> Matrix(31,4,-566,-73) Matrix(11651,-4520,15850,-6149) -> Matrix(51,4,-778,-61) Matrix(1951,-758,2700,-1049) -> Matrix(55,8,-832,-121) Matrix(1601,-624,2050,-799) -> Matrix(89,12,-1476,-199) Matrix(101,-40,250,-99) -> Matrix(31,4,-256,-33) Matrix(1651,-673,3800,-1549) -> Matrix(1,0,0,1) Matrix(11401,-4651,18750,-7649) -> Matrix(69,8,-854,-99) Matrix(7599,-3101,12500,-5101) -> Matrix(39,4,-478,-49) Matrix(2199,-898,4900,-2001) -> Matrix(1,0,-2,1) Matrix(1601,-656,1950,-799) -> Matrix(33,4,-586,-71) Matrix(649,-268,850,-351) -> Matrix(31,4,-504,-65) Matrix(649,-269,1450,-601) -> Matrix(33,4,-322,-39) Matrix(12701,-5270,17350,-7199) -> Matrix(101,12,-1574,-187) Matrix(4701,-1952,6500,-2699) -> Matrix(71,8,-1074,-121) Matrix(349,-146,600,-251) -> Matrix(33,4,-388,-47) Matrix(4451,-1881,6150,-2599) -> Matrix(71,8,-1074,-121) Matrix(299,-129,350,-151) -> Matrix(1,0,-10,1) Matrix(651,-284,800,-349) -> Matrix(35,4,-604,-69) Matrix(449,-197,800,-351) -> Matrix(71,8,-790,-89) Matrix(251,-111,450,-199) -> Matrix(37,4,-398,-43) Matrix(1351,-620,1850,-849) -> Matrix(1,0,-6,1) Matrix(1699,-796,2350,-1101) -> Matrix(87,8,-1316,-121) Matrix(549,-259,850,-401) -> Matrix(35,4,-464,-53) Matrix(749,-395,950,-501) -> Matrix(1,0,-6,1) Matrix(1499,-796,2450,-1301) -> Matrix(1,0,-4,1) Matrix(501,-269,650,-349) -> Matrix(1,0,-6,1) Matrix(401,-218,550,-299) -> Matrix(43,4,-656,-61) Matrix(349,-191,550,-301) -> Matrix(45,4,-574,-51) Matrix(1551,-854,2450,-1349) -> Matrix(37,4,-472,-51) Matrix(849,-469,1450,-801) -> Matrix(41,4,-482,-47) Matrix(2251,-1270,3100,-1749) -> Matrix(1,0,-4,1) Matrix(749,-424,1150,-651) -> Matrix(1,0,-2,1) Matrix(249,-143,350,-201) -> Matrix(45,4,-664,-59) Matrix(751,-434,950,-549) -> Matrix(45,4,-754,-67) Matrix(1451,-841,2500,-1449) -> Matrix(183,16,-2116,-185) Matrix(2799,-1636,4450,-2601) -> Matrix(47,4,-576,-49) Matrix(4501,-2634,6150,-3599) -> Matrix(93,8,-1430,-123) Matrix(1751,-1027,2300,-1349) -> Matrix(191,16,-3068,-257) Matrix(1099,-645,1450,-851) -> Matrix(97,8,-1540,-127) Matrix(699,-412,850,-501) -> Matrix(1,0,-6,1) Matrix(151,-90,250,-149) -> Matrix(47,4,-576,-49) Matrix(4999,-3038,7900,-4801) -> Matrix(99,8,-1250,-101) Matrix(7851,-4775,10850,-6599) -> Matrix(197,16,-2992,-243) Matrix(899,-548,1150,-701) -> Matrix(99,8,-1646,-133) Matrix(5401,-3306,7350,-4499) -> Matrix(43,4,-656,-61) Matrix(1549,-949,2450,-1501) -> Matrix(45,4,-574,-51) Matrix(1851,-1135,2200,-1349) -> Matrix(95,8,-1722,-145) Matrix(1299,-797,1550,-951) -> Matrix(97,8,-1734,-143) Matrix(449,-277,650,-401) -> Matrix(1,0,-2,1) Matrix(851,-526,1050,-649) -> Matrix(49,4,-870,-71) Matrix(1551,-961,2500,-1549) -> Matrix(299,24,-3750,-301) Matrix(349,-219,400,-251) -> Matrix(1,0,-6,1) Matrix(2201,-1385,2700,-1699) -> Matrix(49,4,-870,-71) Matrix(701,-442,950,-599) -> Matrix(151,12,-2328,-185) Matrix(4701,-2975,5450,-3449) -> Matrix(51,4,-880,-69) Matrix(4601,-2970,6350,-4099) -> Matrix(1,0,-2,1) Matrix(1049,-688,1450,-951) -> Matrix(51,4,-778,-61) Matrix(1199,-813,1550,-1051) -> Matrix(223,16,-3582,-257) Matrix(1701,-1159,2200,-1499) -> Matrix(225,16,-3586,-255) Matrix(699,-479,950,-651) -> Matrix(227,16,-3476,-245) Matrix(901,-626,1150,-799) -> Matrix(115,8,-1912,-133) Matrix(351,-245,500,-349) -> Matrix(115,8,-1682,-117) Matrix(701,-494,850,-599) -> Matrix(59,4,-1018,-69) Matrix(1499,-1059,1700,-1201) -> Matrix(119,8,-2276,-153) Matrix(1801,-1273,2050,-1449) -> Matrix(61,4,-1144,-75) Matrix(1499,-1061,2050,-1451) -> Matrix(59,4,-900,-61) Matrix(3599,-2607,4350,-3151) -> Matrix(61,4,-1022,-67) Matrix(5999,-4353,7650,-5551) -> Matrix(367,24,-6132,-401) Matrix(7301,-5329,10000,-7299) -> Matrix(123,8,-1922,-125) Matrix(45751,-33489,62500,-45749) -> Matrix(495,32,-7688,-497) Matrix(1699,-1244,2050,-1501) -> Matrix(1,0,-2,1) Matrix(3099,-2276,3950,-2901) -> Matrix(121,8,-2042,-135) Matrix(29401,-21609,40000,-29399) -> Matrix(3903,256,-59536,-3905) Matrix(1851,-1369,2500,-1849) -> Matrix(743,48,-11532,-745) Matrix(551,-423,650,-499) -> Matrix(1,0,-2,1) Matrix(951,-734,1100,-849) -> Matrix(1,0,-2,1) Matrix(401,-311,450,-349) -> Matrix(65,4,-1284,-79) Matrix(1951,-1521,2500,-1949) -> Matrix(527,32,-8712,-529) Matrix(3851,-3022,4650,-3649) -> Matrix(67,4,-1156,-69) Matrix(201,-160,250,-199) -> Matrix(67,4,-1156,-69) Matrix(2051,-1681,2500,-2049) -> Matrix(139,8,-2450,-141) Matrix(2499,-2069,2900,-2401) -> Matrix(1,0,0,1) Matrix(2151,-1849,2500,-2149) -> Matrix(1,0,4,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 25 Imminent integer overflow caused the modular group computation to abort.