INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/10 -17/20 -4/5 -3/4 -11/15 -7/10 -13/20 -23/36 -19/30 -3/5 -59/100 -7/12 -17/30 -11/20 -15/28 -1/2 -7/15 -9/20 -53/120 -7/16 -17/40 -67/160 -5/12 -33/80 -2/5 -39/100 -31/80 -3/8 -11/30 -43/120 -7/20 -3/10 -59/200 -7/24 -5/18 -11/40 -43/160 -4/15 -9/34 -1/4 -19/80 -7/30 -119/520 -9/40 -7/32 -3/14 -17/80 -5/24 -1/5 -3/16 -7/38 -5/28 -7/40 -1/6 -5/32 -3/20 -11/80 -3/22 -2/15 -5/38 -1/8 -3/26 -1/10 0/1 1/10 2/19 1/9 2/17 1/8 2/15 3/22 1/7 3/20 2/13 5/32 3/19 1/6 3/17 5/28 2/11 3/16 1/5 5/24 3/14 7/32 2/9 3/13 7/30 1/4 4/15 7/26 3/11 5/18 2/7 7/24 3/10 11/36 1/3 7/20 13/36 11/30 3/8 13/34 39/100 2/5 5/12 7/16 9/20 7/15 1/2 15/28 11/20 17/30 7/12 59/100 3/5 19/30 23/36 13/20 2/3 7/10 11/15 3/4 4/5 17/20 9/10 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/38 -9/10 1/34 -17/19 1/34 -8/9 5/168 -15/17 5/166 -7/8 1/33 -20/23 1/32 -13/15 3/98 -19/22 5/163 2/65 -6/7 1/32 -17/20 1/32 -11/13 9/286 -27/32 2/63 -16/19 1/32 -21/25 1/32 -5/6 2/63 1/31 -14/17 11/340 -23/28 5/154 -9/11 1/30 -13/16 2/61 -17/21 1/30 -4/5 1/30 -19/24 1/29 -34/43 1/28 -15/19 1/30 -56/71 7/208 -41/52 1/30 -26/33 5/148 -11/14 2/59 1/29 -18/23 5/148 -25/32 2/59 -32/41 23/676 -7/9 5/146 -17/22 1/29 6/173 -10/13 7/200 -33/43 5/142 -23/30 1/28 -13/17 3/86 -3/4 1/28 -17/23 1/26 -31/42 0/1 1/27 -14/19 1/28 -11/15 1/28 -30/41 19/524 -49/67 29/798 -19/26 2/55 5/137 -46/63 13/356 -27/37 3/82 -35/48 2/55 -8/11 5/136 -13/18 1/27 4/107 -44/61 3/80 -31/43 7/186 -18/25 3/80 -23/32 2/53 -28/39 17/448 -5/7 1/26 -27/38 1/27 2/53 -22/31 1/28 -39/55 1/28 -17/24 1/27 -29/41 17/454 -12/17 5/132 -7/10 1/26 -16/23 3/76 -41/59 1/26 -25/36 1/26 -9/13 5/126 -11/16 0/1 -13/19 1/26 -15/22 3/77 2/51 -17/25 1/26 -2/3 1/24 -13/20 1/24 -24/37 1/24 -11/17 5/118 -9/14 2/47 1/23 -34/53 15/344 -25/39 11/250 -16/25 1/22 -39/61 1/22 -23/36 1/22 -30/47 1/20 -37/58 0/1 1/17 -7/11 1/26 -33/52 3/74 -26/41 11/268 -19/30 1/24 -12/19 1/24 -5/8 1/23 -13/21 1/22 -21/34 1/23 2/45 -50/81 19/424 -29/47 1/22 -8/13 3/64 -27/44 1/20 -73/119 9/170 -46/75 1/18 -19/31 1/14 -11/18 0/1 1/25 -36/59 1/24 -61/100 1/24 -25/41 9/214 -14/23 5/116 -17/28 1/22 -20/33 1/24 -3/5 1/22 -19/32 0/1 -16/27 5/108 -13/22 1/21 2/41 -36/61 1/20 -59/100 1/20 -23/39 7/138 -10/17 1/16 -27/46 0/1 1/29 -44/75 1/26 -17/29 1/26 -58/99 1/24 -41/70 1/24 -24/41 7/164 -31/53 9/206 -7/12 1/22 -39/67 7/146 -32/55 1/20 -25/43 1/18 -43/74 0/1 1/25 -61/105 1/24 -18/31 1/24 -11/19 1/22 -26/45 1/22 -41/71 7/150 -15/26 2/43 1/21 -4/7 1/20 -25/44 1/22 -21/37 3/62 -17/30 1/20 -13/23 3/58 -22/39 5/88 -9/16 0/1 -23/41 5/118 -14/25 1/22 -19/34 2/43 1/21 -24/43 5/104 -29/52 1/20 -5/9 1/22 -11/20 1/20 -17/31 3/58 -23/42 0/1 1/19 -6/11 1/20 -13/24 1/19 -20/37 1/20 -7/13 1/14 -22/41 3/76 -15/28 1/22 -23/43 3/62 -8/15 1/20 -9/17 1/18 -1/2 0/1 1/19 -9/19 1/18 -8/17 1/20 -7/15 1/18 -20/43 3/52 -13/28 1/16 -6/13 1/24 -17/37 1/18 -11/24 1/19 -16/35 1/18 -5/11 1/18 -9/20 1/18 -13/29 1/18 -17/38 2/35 1/17 -4/9 1/16 -23/52 1/18 -19/43 5/86 -53/120 1/17 -34/77 9/152 -15/34 1/17 2/33 -11/25 1/16 -18/41 5/72 -7/16 0/1 -17/39 5/102 -10/23 3/56 -13/30 1/18 -16/37 3/52 -3/7 1/18 -17/40 1/17 -14/33 5/84 -11/26 1/17 2/33 -30/71 7/116 -19/45 1/16 -8/19 1/16 -21/50 1/16 -34/81 13/204 -13/31 1/14 -31/74 0/1 1/13 -49/117 1/6 -67/160 0/1 -18/43 1/20 -5/12 1/16 -22/53 9/136 -17/41 7/102 -29/70 1/14 -41/99 1/14 -12/29 1/12 -31/75 1/12 -50/121 7/76 -19/46 0/1 1/9 -26/63 -1/4 -33/80 0/1 -7/17 1/22 -16/39 7/128 -41/100 1/18 -25/61 1/18 -9/22 2/35 1/17 -2/5 1/16 -15/38 1/15 2/29 -13/33 1/14 -11/28 1/16 -9/23 5/74 -16/41 9/128 -39/100 1/14 -23/59 1/14 -7/18 0/1 1/13 -19/49 1/2 -31/80 0/1 -12/31 1/24 -29/75 1/20 -46/119 9/172 -63/163 5/94 -17/44 1/18 -5/13 3/50 -23/60 1/16 -18/47 1/16 -31/81 19/298 -44/115 5/78 -13/34 2/31 1/15 -21/55 1/16 -8/21 1/16 -3/8 1/15 -7/19 1/14 -18/49 5/72 -11/30 1/14 -26/71 11/152 -15/41 11/150 -4/11 1/12 -17/47 1/18 -30/83 3/52 -43/119 11/186 -13/36 1/16 -22/61 1/16 -9/25 1/16 -14/39 11/168 -19/53 15/226 -43/120 1/15 -24/67 19/284 -5/14 1/15 2/29 -6/17 5/72 -7/20 1/14 -8/23 7/96 -1/3 1/14 -7/22 2/25 3/37 -6/19 1/12 -5/16 0/1 -9/29 1/14 -13/42 0/1 1/13 -17/55 1/14 -4/13 5/64 -3/10 1/12 -8/27 11/128 -13/44 1/12 -18/61 1/12 -59/200 3/35 -41/139 5/58 -23/78 3/35 2/23 -5/17 5/58 -12/41 17/192 -19/65 5/56 -7/24 1/11 -16/55 1/10 -9/31 1/10 -11/38 2/23 1/11 -13/45 1/10 -2/7 1/12 -11/39 17/198 -9/32 2/23 -16/57 1/12 -7/25 3/34 -26/93 9/100 -19/68 1/12 -12/43 7/80 -17/61 3/34 -5/18 4/45 1/11 -8/29 13/144 -11/40 1/11 -3/11 5/54 -16/59 3/32 -13/48 2/21 -23/85 1/10 -33/122 2/23 1/11 -43/159 17/186 -10/37 3/32 -17/63 13/138 -24/89 11/116 -7/26 5/53 2/21 -25/93 39/410 -43/160 2/21 -18/67 29/304 -11/41 19/198 -15/56 3/31 -4/15 1/10 -9/34 1/11 2/21 -5/19 1/10 -1/4 1/10 -5/21 1/10 -19/80 2/19 -14/59 3/28 -9/38 2/19 1/9 -13/55 1/10 -4/17 3/28 -7/30 1/10 -10/43 5/48 -3/13 7/66 -11/48 4/37 -19/83 5/46 -46/201 19/172 -119/520 1/9 -73/319 19/170 -27/118 0/1 1/9 -8/35 3/28 -5/22 6/55 1/9 -7/31 17/154 -9/40 1/9 -2/9 5/44 -9/41 23/198 -7/32 2/17 -12/55 1/8 -5/23 5/42 -3/14 1/9 2/17 -10/47 7/60 -17/80 2/17 -7/33 5/42 -11/52 1/8 -15/71 7/58 -4/19 1/8 -9/43 1/10 -5/24 1/9 -6/29 1/8 -1/5 1/8 -4/21 1/8 -3/16 2/15 -5/27 7/50 -12/65 1/8 -7/38 2/15 1/7 -2/11 1/8 -7/39 25/182 -12/67 37/268 -5/28 5/36 -3/17 11/78 -7/40 1/7 -4/23 15/104 -1/6 1/7 2/13 -5/31 1/6 -4/25 1/6 -3/19 1/6 -8/51 1/8 -5/32 2/13 -2/13 9/56 -3/20 1/6 -4/27 19/112 -1/7 1/6 -4/29 13/72 -11/80 2/11 -7/51 23/126 -3/22 2/11 5/27 -5/37 5/26 -2/15 3/16 -5/38 2/11 1/5 -3/23 1/6 -1/8 1/5 -2/17 5/24 -3/26 1/5 2/9 -1/9 5/22 -2/19 1/4 -1/10 1/4 0/1 1/0 1/10 -1/4 2/19 -1/4 1/9 -5/22 2/17 -5/24 1/8 -1/5 3/23 -1/6 2/15 -3/16 3/22 -5/27 -2/11 1/7 -1/6 3/20 -1/6 2/13 -9/56 5/32 -2/13 3/19 -1/6 4/25 -1/6 1/6 -2/13 -1/7 3/17 -11/78 5/28 -5/36 2/11 -1/8 3/16 -2/15 4/21 -1/8 1/5 -1/8 5/24 -1/9 9/43 -1/10 4/19 -1/8 15/71 -7/58 11/52 -1/8 7/33 -5/42 3/14 -2/17 -1/9 5/23 -5/42 7/32 -2/17 9/41 -23/198 2/9 -5/44 5/22 -1/9 -6/55 3/13 -7/66 10/43 -5/48 7/30 -1/10 4/17 -3/28 1/4 -1/10 6/23 -1/12 11/42 -1/11 0/1 5/19 -1/10 4/15 -1/10 11/41 -19/198 18/67 -29/304 7/26 -2/21 -5/53 17/63 -13/138 10/37 -3/32 13/48 -2/21 3/11 -5/54 5/18 -1/11 -4/45 17/61 -3/34 12/43 -7/80 7/25 -3/34 9/32 -2/23 11/39 -17/198 2/7 -1/12 11/38 -1/11 -2/23 9/31 -1/10 16/55 -1/10 7/24 -1/11 12/41 -17/192 5/17 -5/58 3/10 -1/12 7/23 -3/38 18/59 -1/12 11/36 -1/12 4/13 -5/64 5/16 0/1 6/19 -1/12 7/22 -3/37 -2/25 8/25 -1/12 1/3 -1/14 7/20 -1/14 13/37 -1/14 6/17 -5/72 5/14 -2/29 -1/15 19/53 -15/226 14/39 -11/168 9/25 -1/16 22/61 -1/16 13/36 -1/16 17/47 -1/18 21/58 -1/21 0/1 4/11 -1/12 19/52 -3/40 15/41 -11/150 11/30 -1/14 7/19 -1/14 3/8 -1/15 8/21 -1/16 13/34 -1/15 -2/31 31/81 -19/298 18/47 -1/16 5/13 -3/50 17/44 -1/18 46/119 -9/172 29/75 -1/20 12/31 -1/24 7/18 -1/13 0/1 23/59 -1/14 39/100 -1/14 16/41 -9/128 9/23 -5/74 11/28 -1/16 13/33 -1/14 2/5 -1/16 13/32 0/1 11/27 -5/82 9/22 -1/17 -2/35 25/61 -1/18 41/100 -1/18 16/39 -7/128 7/17 -1/22 19/46 -1/9 0/1 31/75 -1/12 12/29 -1/12 41/99 -1/14 29/70 -1/14 17/41 -7/102 22/53 -9/136 5/12 -1/16 28/67 -7/120 23/55 -1/18 18/43 -1/20 31/74 -1/13 0/1 44/105 -1/14 13/31 -1/14 8/19 -1/16 19/45 -1/16 30/71 -7/116 11/26 -2/33 -1/17 3/7 -1/18 19/44 -1/16 16/37 -3/52 13/30 -1/18 10/23 -3/56 17/39 -5/102 7/16 0/1 18/41 -5/72 11/25 -1/16 15/34 -2/33 -1/17 19/43 -5/86 23/52 -1/18 4/9 -1/16 9/20 -1/18 14/31 -3/56 19/42 -1/19 0/1 5/11 -1/18 11/24 -1/19 17/37 -1/18 6/13 -1/24 19/41 -3/38 13/28 -1/16 20/43 -3/52 7/15 -1/18 8/17 -1/20 1/2 -1/19 0/1 10/19 -1/20 9/17 -1/18 8/15 -1/20 23/43 -3/62 15/28 -1/22 7/13 -1/14 20/37 -1/20 13/24 -1/19 19/35 -1/20 6/11 -1/20 11/20 -1/20 16/29 -1/20 21/38 -2/41 -1/21 5/9 -1/22 29/52 -1/20 24/43 -5/104 67/120 -1/21 43/77 -9/190 19/34 -1/21 -2/43 14/25 -1/22 23/41 -5/118 9/16 0/1 22/39 -5/88 13/23 -3/58 17/30 -1/20 21/37 -3/62 4/7 -1/20 23/40 -1/21 19/33 -5/106 15/26 -1/21 -2/43 41/71 -7/150 26/45 -1/22 11/19 -1/22 29/50 -1/22 47/81 -13/290 18/31 -1/24 43/74 -1/25 0/1 68/117 -1/32 93/160 0/1 25/43 -1/18 7/12 -1/22 31/53 -9/206 24/41 -7/164 41/70 -1/24 58/99 -1/24 17/29 -1/26 44/75 -1/26 71/121 -7/190 27/46 -1/29 0/1 37/63 -1/42 47/80 0/1 10/17 -1/16 23/39 -7/138 59/100 -1/20 36/61 -1/20 13/22 -2/41 -1/21 3/5 -1/22 23/38 -1/23 -2/47 20/33 -1/24 17/28 -1/22 14/23 -5/116 25/41 -9/214 61/100 -1/24 36/59 -1/24 11/18 -1/25 0/1 30/49 -1/36 49/80 0/1 19/31 -1/14 46/75 -1/18 73/119 -9/170 100/163 -5/96 27/44 -1/20 8/13 -3/64 37/60 -1/22 29/47 -1/22 50/81 -19/424 71/115 -5/112 21/34 -2/45 -1/23 34/55 -1/22 13/21 -1/22 5/8 -1/23 12/19 -1/24 31/49 -5/118 19/30 -1/24 45/71 -11/266 26/41 -11/268 7/11 -1/26 30/47 -1/20 53/83 -3/62 76/119 -11/232 23/36 -1/22 39/61 -1/22 16/25 -1/22 25/39 -11/250 34/53 -15/344 77/120 -1/23 43/67 -19/438 9/14 -1/23 -2/47 11/17 -5/118 13/20 -1/24 15/23 -7/170 2/3 -1/24 15/22 -2/51 -3/77 13/19 -1/26 11/16 0/1 20/29 -1/24 29/42 -1/25 0/1 38/55 -1/24 9/13 -5/126 7/10 -1/26 19/27 -11/290 31/44 -1/26 43/61 -1/26 141/200 -3/79 98/139 -5/132 55/78 -3/79 -2/53 12/17 -5/132 29/41 -17/454 46/65 -5/134 17/24 -1/27 39/55 -1/28 22/31 -1/28 27/38 -2/53 -1/27 32/45 -1/28 5/7 -1/26 28/39 -17/448 23/32 -2/53 41/57 -1/26 18/25 -3/80 67/93 -9/242 49/68 -1/26 31/43 -7/186 44/61 -3/80 13/18 -4/107 -1/27 21/29 -13/350 29/40 -1/27 8/11 -5/136 43/59 -3/82 35/48 -2/55 62/85 -1/28 89/122 -2/53 -1/27 116/159 -17/460 27/37 -3/82 46/63 -13/356 65/89 -11/302 19/26 -5/137 -2/55 68/93 -39/1072 117/160 -2/55 49/67 -29/798 30/41 -19/524 41/56 -3/83 11/15 -1/28 25/34 -1/27 -2/55 14/19 -1/28 3/4 -1/28 16/21 -1/28 61/80 -2/57 45/59 -3/86 29/38 -2/57 -1/29 42/55 -1/28 13/17 -3/86 23/30 -1/28 33/43 -5/142 10/13 -7/200 37/48 -4/115 64/83 -5/144 155/201 -19/550 401/520 -1/29 246/319 -19/552 91/118 -1/29 0/1 27/35 -3/86 17/22 -6/173 -1/29 24/31 -17/492 31/40 -1/29 7/9 -5/146 32/41 -23/676 25/32 -2/59 43/55 -1/30 18/23 -5/148 11/14 -1/29 -2/59 37/47 -7/206 63/80 -2/59 26/33 -5/148 41/52 -1/30 56/71 -7/208 15/19 -1/30 34/43 -1/28 19/24 -1/29 23/29 -1/30 4/5 -1/30 17/21 -1/30 13/16 -2/61 22/27 -7/216 53/65 -1/30 31/38 -2/61 -1/31 9/11 -1/30 32/39 -25/768 55/67 -37/1138 23/28 -5/154 14/17 -11/340 33/40 -1/31 19/23 -15/466 5/6 -1/31 -2/63 26/31 -1/32 21/25 -1/32 16/19 -1/32 43/51 -1/30 27/32 -2/63 11/13 -9/286 17/20 -1/32 23/27 -19/610 6/7 -1/32 25/29 -13/422 69/80 -2/65 44/51 -23/748 19/22 -2/65 -5/163 32/37 -5/164 13/15 -3/98 33/38 -2/65 -1/33 20/23 -1/32 7/8 -1/33 15/17 -5/166 23/26 -1/33 -2/67 8/9 -5/168 17/19 -1/34 9/10 -1/34 1/1 -1/38 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(199,182,480,439) (-1/1,-9/10) -> (29/70,17/41) Hyperbolic Matrix(961,862,2320,2081) (-9/10,-17/19) -> (41/99,29/70) Hyperbolic Matrix(1199,1072,1520,1359) (-17/19,-8/9) -> (56/71,15/19) Hyperbolic Matrix(561,496,-2080,-1839) (-8/9,-15/17) -> (-17/63,-24/89) Hyperbolic Matrix(41,36,320,281) (-15/17,-7/8) -> (1/8,3/23) Hyperbolic Matrix(39,34,320,279) (-7/8,-20/23) -> (2/17,1/8) Hyperbolic Matrix(359,312,-1520,-1321) (-20/23,-13/15) -> (-13/55,-4/17) Hyperbolic Matrix(599,518,-880,-761) (-13/15,-19/22) -> (-15/22,-17/25) Hyperbolic Matrix(919,792,-1440,-1241) (-19/22,-6/7) -> (-30/47,-37/58) Hyperbolic Matrix(521,444,-1360,-1159) (-6/7,-17/20) -> (-23/60,-18/47) Hyperbolic Matrix(399,338,-1040,-881) (-17/20,-11/13) -> (-5/13,-23/60) Hyperbolic Matrix(521,440,1280,1081) (-11/13,-27/32) -> (13/32,11/27) Hyperbolic Matrix(759,640,-2800,-2361) (-27/32,-16/19) -> (-16/59,-13/48) Hyperbolic Matrix(721,606,2000,1681) (-16/19,-21/25) -> (9/25,22/61) Hyperbolic Matrix(1441,1208,-2480,-2079) (-21/25,-5/6) -> (-43/74,-61/105) Hyperbolic Matrix(41,34,-240,-199) (-5/6,-14/17) -> (-4/23,-1/6) Hyperbolic Matrix(681,560,1120,921) (-14/17,-23/28) -> (17/28,14/23) Hyperbolic Matrix(559,458,-880,-721) (-23/28,-9/11) -> (-7/11,-33/52) Hyperbolic Matrix(199,162,-640,-521) (-9/11,-13/16) -> (-5/16,-9/29) Hyperbolic Matrix(439,356,640,519) (-13/16,-17/21) -> (13/19,11/16) Hyperbolic Matrix(601,486,1040,841) (-17/21,-4/5) -> (26/45,11/19) Hyperbolic Matrix(439,348,-960,-761) (-4/5,-19/24) -> (-11/24,-16/35) Hyperbolic Matrix(1039,822,1920,1519) (-19/24,-34/43) -> (20/37,13/24) Hyperbolic Matrix(959,758,3440,2719) (-34/43,-15/19) -> (17/61,12/43) Hyperbolic Matrix(1359,1072,1520,1199) (-15/19,-56/71) -> (8/9,17/19) Hyperbolic Matrix(1841,1452,4160,3281) (-56/71,-41/52) -> (23/52,4/9) Hyperbolic Matrix(1601,1262,2640,2081) (-41/52,-26/33) -> (20/33,17/28) Hyperbolic Matrix(239,188,-1120,-881) (-26/33,-11/14) -> (-3/14,-10/47) Hyperbolic Matrix(199,156,560,439) (-11/14,-18/23) -> (6/17,5/14) Hyperbolic Matrix(719,562,-2560,-2001) (-18/23,-25/32) -> (-9/32,-16/57) Hyperbolic Matrix(1839,1436,2560,1999) (-25/32,-32/41) -> (28/39,23/32) Hyperbolic Matrix(2079,1622,3280,2559) (-32/41,-7/9) -> (45/71,26/41) Hyperbolic Matrix(199,154,-880,-681) (-7/9,-17/22) -> (-5/22,-7/31) Hyperbolic Matrix(521,402,-880,-679) (-17/22,-10/13) -> (-16/27,-13/22) Hyperbolic Matrix(479,368,1040,799) (-10/13,-33/43) -> (17/37,6/13) Hyperbolic Matrix(1361,1044,2400,1841) (-33/43,-23/30) -> (17/30,21/37) Hyperbolic Matrix(679,520,1200,919) (-23/30,-13/17) -> (13/23,17/30) Hyperbolic Matrix(119,90,-160,-121) (-13/17,-3/4) -> (-3/4,-17/23) Parabolic Matrix(241,178,-1840,-1359) (-17/23,-31/42) -> (-5/38,-3/23) Hyperbolic Matrix(759,560,-3200,-2361) (-31/42,-14/19) -> (-14/59,-9/38) Hyperbolic Matrix(519,382,-1360,-1001) (-14/19,-11/15) -> (-21/55,-8/21) Hyperbolic Matrix(959,702,-3280,-2401) (-11/15,-30/41) -> (-12/41,-19/65) Hyperbolic Matrix(1761,1288,-3280,-2399) (-30/41,-49/67) -> (-7/13,-22/41) Hyperbolic Matrix(1119,818,-4160,-3041) (-49/67,-19/26) -> (-7/26,-25/93) Hyperbolic Matrix(241,176,-2080,-1519) (-19/26,-46/63) -> (-2/17,-3/26) Hyperbolic Matrix(1041,760,2960,2161) (-46/63,-27/37) -> (13/37,6/17) Hyperbolic Matrix(1319,962,-5760,-4201) (-27/37,-35/48) -> (-11/48,-19/83) Hyperbolic Matrix(439,320,-2800,-2041) (-35/48,-8/11) -> (-8/51,-5/32) Hyperbolic Matrix(199,144,-720,-521) (-8/11,-13/18) -> (-5/18,-8/29) Hyperbolic Matrix(1319,952,2160,1559) (-13/18,-44/61) -> (36/59,11/18) Hyperbolic Matrix(721,520,3440,2481) (-44/61,-31/43) -> (9/43,4/19) Hyperbolic Matrix(2001,1442,-3440,-2479) (-31/43,-18/25) -> (-32/55,-25/43) Hyperbolic Matrix(559,402,-2560,-1841) (-18/25,-23/32) -> (-7/32,-12/55) Hyperbolic Matrix(1999,1436,2560,1839) (-23/32,-28/39) -> (32/41,25/32) Hyperbolic Matrix(1481,1062,2400,1721) (-28/39,-5/7) -> (29/47,50/81) Hyperbolic Matrix(599,426,-1520,-1081) (-5/7,-27/38) -> (-15/38,-13/33) Hyperbolic Matrix(1121,796,2480,1761) (-27/38,-22/31) -> (14/31,19/42) Hyperbolic Matrix(2881,2044,-4960,-3519) (-22/31,-39/55) -> (-61/105,-18/31) Hyperbolic Matrix(2519,1786,3440,2439) (-39/55,-17/24) -> (41/56,11/15) Hyperbolic Matrix(879,622,-3280,-2321) (-17/24,-29/41) -> (-11/41,-15/56) Hyperbolic Matrix(801,566,1360,961) (-29/41,-12/17) -> (10/17,23/39) Hyperbolic Matrix(279,196,-400,-281) (-12/17,-7/10) -> (-7/10,-16/23) Parabolic Matrix(679,472,-1440,-1001) (-16/23,-41/59) -> (-9/19,-8/17) Hyperbolic Matrix(2761,1918,4320,3001) (-41/59,-25/36) -> (23/36,39/61) Hyperbolic Matrix(401,278,1040,721) (-25/36,-9/13) -> (5/13,17/44) Hyperbolic Matrix(119,82,-640,-441) (-9/13,-11/16) -> (-3/16,-5/27) Hyperbolic Matrix(519,356,640,439) (-11/16,-13/19) -> (17/21,13/16) Hyperbolic Matrix(721,492,1760,1201) (-13/19,-15/22) -> (9/22,25/61) Hyperbolic Matrix(521,354,1120,761) (-17/25,-2/3) -> (20/43,7/15) Hyperbolic Matrix(519,338,-800,-521) (-2/3,-13/20) -> (-13/20,-24/37) Parabolic Matrix(799,518,2960,1919) (-24/37,-11/17) -> (17/63,10/37) Hyperbolic Matrix(121,78,560,361) (-11/17,-9/14) -> (3/14,5/23) Hyperbolic Matrix(601,386,-1680,-1079) (-9/14,-34/53) -> (-24/67,-5/14) Hyperbolic Matrix(1759,1128,4240,2719) (-34/53,-25/39) -> (17/41,22/53) Hyperbolic Matrix(1121,718,2000,1281) (-25/39,-16/25) -> (14/25,23/41) Hyperbolic Matrix(319,204,2000,1279) (-16/25,-39/61) -> (3/19,4/25) Hyperbolic Matrix(3439,2198,4880,3119) (-39/61,-23/36) -> (31/44,43/61) Hyperbolic Matrix(1319,842,-2320,-1481) (-23/36,-30/47) -> (-4/7,-25/44) Hyperbolic Matrix(439,280,-3200,-2041) (-37/58,-7/11) -> (-7/51,-3/22) Hyperbolic Matrix(1759,1116,-3280,-2081) (-33/52,-26/41) -> (-22/41,-15/28) Hyperbolic Matrix(1881,1192,-4480,-2839) (-26/41,-19/30) -> (-21/50,-34/81) Hyperbolic Matrix(639,404,-1520,-961) (-19/30,-12/19) -> (-8/19,-21/50) Hyperbolic Matrix(121,76,320,201) (-12/19,-5/8) -> (3/8,8/21) Hyperbolic Matrix(119,74,320,199) (-5/8,-13/21) -> (7/19,3/8) Hyperbolic Matrix(359,222,-1360,-841) (-13/21,-21/34) -> (-9/34,-5/19) Hyperbolic Matrix(3239,2000,-7840,-4841) (-21/34,-50/81) -> (-50/121,-19/46) Hyperbolic Matrix(1721,1062,2400,1481) (-50/81,-29/47) -> (5/7,28/39) Hyperbolic Matrix(201,124,-1360,-839) (-29/47,-8/13) -> (-4/27,-1/7) Hyperbolic Matrix(319,196,1040,639) (-8/13,-27/44) -> (11/36,4/13) Hyperbolic Matrix(3439,2110,-9520,-5841) (-27/44,-73/119) -> (-43/119,-13/36) Hyperbolic Matrix(10561,6478,18000,11041) (-73/119,-46/75) -> (44/75,71/121) Hyperbolic Matrix(3881,2380,6720,4121) (-46/75,-19/31) -> (41/71,26/45) Hyperbolic Matrix(559,342,-1440,-881) (-19/31,-11/18) -> (-7/18,-19/49) Hyperbolic Matrix(1559,952,2160,1319) (-11/18,-36/59) -> (44/61,13/18) Hyperbolic Matrix(7081,4320,12000,7321) (-36/59,-61/100) -> (59/100,36/61) Hyperbolic Matrix(4719,2878,8000,4879) (-61/100,-25/41) -> (23/39,59/100) Hyperbolic Matrix(801,488,1840,1121) (-25/41,-14/23) -> (10/23,17/39) Hyperbolic Matrix(921,560,1120,681) (-14/23,-17/28) -> (23/28,14/17) Hyperbolic Matrix(2081,1262,2640,1601) (-17/28,-20/33) -> (26/33,41/52) Hyperbolic Matrix(439,266,-1520,-921) (-20/33,-3/5) -> (-13/45,-2/7) Hyperbolic Matrix(801,476,-2960,-1759) (-3/5,-19/32) -> (-13/48,-23/85) Hyperbolic Matrix(199,118,1280,759) (-19/32,-16/27) -> (2/13,5/32) Hyperbolic Matrix(559,330,1760,1039) (-13/22,-36/61) -> (6/19,7/22) Hyperbolic Matrix(7321,4320,12000,7081) (-36/61,-59/100) -> (61/100,36/59) Hyperbolic Matrix(4879,2878,8000,4719) (-59/100,-23/39) -> (25/41,61/100) Hyperbolic Matrix(961,566,1360,801) (-23/39,-10/17) -> (12/17,29/41) Hyperbolic Matrix(1519,892,-3680,-2161) (-10/17,-27/46) -> (-19/46,-26/63) Hyperbolic Matrix(2999,1760,-7840,-4601) (-27/46,-44/75) -> (-44/115,-13/34) Hyperbolic Matrix(1841,1080,2320,1361) (-44/75,-17/29) -> (23/29,4/5) Hyperbolic Matrix(4721,2766,5600,3281) (-17/29,-58/99) -> (16/19,43/51) Hyperbolic Matrix(239,140,2320,1359) (-58/99,-41/70) -> (1/10,2/19) Hyperbolic Matrix(41,24,480,281) (-41/70,-24/41) -> (0/1,1/10) Hyperbolic Matrix(1521,890,4240,2481) (-24/41,-31/53) -> (19/53,14/39) Hyperbolic Matrix(839,490,-1440,-841) (-31/53,-7/12) -> (-7/12,-39/67) Parabolic Matrix(3041,1770,4400,2561) (-39/67,-32/55) -> (38/55,9/13) Hyperbolic Matrix(4959,2882,-11840,-6881) (-25/43,-43/74) -> (-31/74,-49/117) Hyperbolic Matrix(559,324,-1520,-881) (-18/31,-11/19) -> (-7/19,-18/49) Hyperbolic Matrix(841,486,1040,601) (-11/19,-26/45) -> (4/5,17/21) Hyperbolic Matrix(4121,2380,6720,3881) (-26/45,-41/71) -> (19/31,46/75) Hyperbolic Matrix(239,138,-2080,-1201) (-41/71,-15/26) -> (-3/26,-1/9) Hyperbolic Matrix(441,254,-1040,-599) (-15/26,-4/7) -> (-14/33,-11/26) Hyperbolic Matrix(3401,1932,-8800,-4999) (-25/44,-21/37) -> (-63/163,-17/44) Hyperbolic Matrix(1841,1044,2400,1361) (-21/37,-17/30) -> (23/30,33/43) Hyperbolic Matrix(919,520,1200,679) (-17/30,-13/23) -> (13/17,23/30) Hyperbolic Matrix(719,406,1840,1039) (-13/23,-22/39) -> (16/41,9/23) Hyperbolic Matrix(561,316,1280,721) (-22/39,-9/16) -> (7/16,18/41) Hyperbolic Matrix(559,314,1280,719) (-9/16,-23/41) -> (17/39,7/16) Hyperbolic Matrix(1281,718,2000,1121) (-23/41,-14/25) -> (16/25,25/39) Hyperbolic Matrix(1681,940,2720,1521) (-14/25,-19/34) -> (21/34,34/55) Hyperbolic Matrix(1801,1006,-4080,-2279) (-19/34,-24/43) -> (-34/77,-15/34) Hyperbolic Matrix(1599,892,3440,1919) (-24/43,-29/52) -> (13/28,20/43) Hyperbolic Matrix(879,490,4160,2319) (-29/52,-5/9) -> (15/71,11/52) Hyperbolic Matrix(439,242,-800,-441) (-5/9,-11/20) -> (-11/20,-17/31) Parabolic Matrix(719,394,2480,1359) (-17/31,-23/42) -> (11/38,9/31) Hyperbolic Matrix(1159,634,1680,919) (-23/42,-6/11) -> (20/29,29/42) Hyperbolic Matrix(199,108,-960,-521) (-6/11,-13/24) -> (-5/24,-6/29) Hyperbolic Matrix(1519,822,1920,1039) (-13/24,-20/37) -> (34/43,19/24) Hyperbolic Matrix(241,130,1040,561) (-20/37,-7/13) -> (3/13,10/43) Hyperbolic Matrix(1521,814,3440,1841) (-15/28,-23/43) -> (19/43,23/52) Hyperbolic Matrix(359,192,1120,599) (-23/43,-8/15) -> (8/25,1/3) Hyperbolic Matrix(921,490,1280,681) (-8/15,-9/17) -> (41/57,18/25) Hyperbolic Matrix(401,212,-1360,-719) (-9/17,-1/2) -> (-23/78,-5/17) Hyperbolic Matrix(519,248,-1760,-841) (-1/2,-9/19) -> (-41/139,-23/78) Hyperbolic Matrix(1001,470,1280,601) (-8/17,-7/15) -> (43/55,18/23) Hyperbolic Matrix(1039,484,1200,559) (-7/15,-20/43) -> (32/37,13/15) Hyperbolic Matrix(1919,892,3440,1599) (-20/43,-13/28) -> (29/52,24/43) Hyperbolic Matrix(401,186,-2240,-1039) (-13/28,-6/13) -> (-12/67,-5/28) Hyperbolic Matrix(799,368,1040,479) (-6/13,-17/37) -> (33/43,10/13) Hyperbolic Matrix(401,184,1920,881) (-17/37,-11/24) -> (5/24,9/43) Hyperbolic Matrix(1079,492,1840,839) (-16/35,-5/11) -> (17/29,44/75) Hyperbolic Matrix(359,162,-800,-361) (-5/11,-9/20) -> (-9/20,-13/29) Parabolic Matrix(1241,556,1520,681) (-13/29,-17/38) -> (31/38,9/11) Hyperbolic Matrix(1079,482,1520,679) (-17/38,-4/9) -> (22/31,27/38) Hyperbolic Matrix(3281,1452,4160,1841) (-4/9,-23/52) -> (41/52,56/71) Hyperbolic Matrix(1841,814,3440,1521) (-23/52,-19/43) -> (23/43,15/28) Hyperbolic Matrix(8041,3552,14400,6361) (-19/43,-53/120) -> (67/120,43/77) Hyperbolic Matrix(8039,3550,14400,6359) (-53/120,-34/77) -> (24/43,67/120) Hyperbolic Matrix(999,440,1360,599) (-15/34,-11/25) -> (11/15,25/34) Hyperbolic Matrix(719,316,2000,879) (-11/25,-18/41) -> (14/39,9/25) Hyperbolic Matrix(721,316,1280,561) (-18/41,-7/16) -> (9/16,22/39) Hyperbolic Matrix(719,314,1280,559) (-7/16,-17/39) -> (23/41,9/16) Hyperbolic Matrix(1121,488,1840,801) (-17/39,-10/23) -> (14/23,25/41) Hyperbolic Matrix(281,122,1200,521) (-10/23,-13/30) -> (7/30,4/17) Hyperbolic Matrix(559,242,2400,1039) (-13/30,-16/37) -> (10/43,7/30) Hyperbolic Matrix(839,362,-2320,-1001) (-16/37,-3/7) -> (-17/47,-30/83) Hyperbolic Matrix(921,392,1600,681) (-3/7,-17/40) -> (23/40,19/33) Hyperbolic Matrix(919,390,1600,679) (-17/40,-14/33) -> (4/7,23/40) Hyperbolic Matrix(1121,474,-4160,-1759) (-11/26,-30/71) -> (-24/89,-7/26) Hyperbolic Matrix(2599,1098,6720,2839) (-30/71,-19/45) -> (29/75,12/31) Hyperbolic Matrix(199,84,1040,439) (-19/45,-8/19) -> (4/21,1/5) Hyperbolic Matrix(1559,654,2000,839) (-34/81,-13/31) -> (7/9,32/41) Hyperbolic Matrix(401,168,-2480,-1039) (-13/31,-31/74) -> (-1/6,-5/31) Hyperbolic Matrix(14881,6232,25600,10721) (-49/117,-67/160) -> (93/160,25/43) Hyperbolic Matrix(14879,6230,25600,10719) (-67/160,-18/43) -> (68/117,93/160) Hyperbolic Matrix(961,402,-3440,-1439) (-18/43,-5/12) -> (-19/68,-12/43) Hyperbolic Matrix(1319,548,-4720,-1961) (-5/12,-22/53) -> (-26/93,-19/68) Hyperbolic Matrix(2719,1128,4240,1759) (-22/53,-17/41) -> (25/39,34/53) Hyperbolic Matrix(439,182,480,199) (-17/41,-29/70) -> (9/10,1/1) Hyperbolic Matrix(2081,862,2320,961) (-29/70,-41/99) -> (17/19,9/10) Hyperbolic Matrix(2039,844,2800,1159) (-41/99,-12/29) -> (8/11,43/59) Hyperbolic Matrix(1001,414,1840,761) (-12/29,-31/75) -> (19/35,6/11) Hyperbolic Matrix(6959,2876,18000,7439) (-31/75,-50/121) -> (46/119,29/75) Hyperbolic Matrix(3761,1552,6400,2641) (-26/63,-33/80) -> (47/80,10/17) Hyperbolic Matrix(3759,1550,6400,2639) (-33/80,-7/17) -> (37/63,47/80) Hyperbolic Matrix(399,164,1360,559) (-7/17,-16/39) -> (12/41,5/17) Hyperbolic Matrix(3121,1280,8000,3281) (-16/39,-41/100) -> (39/100,16/41) Hyperbolic Matrix(4679,1918,12000,4919) (-41/100,-25/61) -> (23/59,39/100) Hyperbolic Matrix(1201,492,1760,721) (-25/61,-9/22) -> (15/22,13/19) Hyperbolic Matrix(201,82,-880,-359) (-9/22,-2/5) -> (-8/35,-5/22) Hyperbolic Matrix(439,174,-1920,-761) (-2/5,-15/38) -> (-27/118,-8/35) Hyperbolic Matrix(559,220,2640,1039) (-13/33,-11/28) -> (11/52,7/33) Hyperbolic Matrix(199,78,1120,439) (-11/28,-9/23) -> (3/17,5/28) Hyperbolic Matrix(1039,406,1840,719) (-9/23,-16/41) -> (22/39,13/23) Hyperbolic Matrix(3281,1280,8000,3121) (-16/41,-39/100) -> (41/100,16/39) Hyperbolic Matrix(4919,1918,12000,4679) (-39/100,-23/59) -> (25/61,41/100) Hyperbolic Matrix(601,234,2160,841) (-23/59,-7/18) -> (5/18,17/61) Hyperbolic Matrix(3921,1520,6400,2481) (-19/49,-31/80) -> (49/80,19/31) Hyperbolic Matrix(3919,1518,6400,2479) (-31/80,-12/31) -> (30/49,49/80) Hyperbolic Matrix(2839,1098,6720,2599) (-12/31,-29/75) -> (19/45,30/71) Hyperbolic Matrix(12199,4716,19760,7639) (-29/75,-46/119) -> (50/81,71/115) Hyperbolic Matrix(9759,3772,-42640,-16481) (-46/119,-63/163) -> (-19/83,-46/201) Hyperbolic Matrix(1239,478,1760,679) (-17/44,-5/13) -> (19/27,31/44) Hyperbolic Matrix(679,260,2400,919) (-18/47,-31/81) -> (11/39,2/7) Hyperbolic Matrix(12121,4638,19760,7561) (-31/81,-44/115) -> (46/75,73/119) Hyperbolic Matrix(1199,458,2720,1039) (-13/34,-21/55) -> (11/25,15/34) Hyperbolic Matrix(201,76,320,121) (-8/21,-3/8) -> (5/8,12/19) Hyperbolic Matrix(199,74,320,119) (-3/8,-7/19) -> (13/21,5/8) Hyperbolic Matrix(1319,484,-3600,-1321) (-18/49,-11/30) -> (-11/30,-26/71) Parabolic Matrix(721,264,3280,1201) (-26/71,-15/41) -> (9/41,2/9) Hyperbolic Matrix(159,58,-880,-321) (-15/41,-4/11) -> (-2/11,-7/39) Hyperbolic Matrix(199,72,-1440,-521) (-4/11,-17/47) -> (-1/7,-4/29) Hyperbolic Matrix(4759,1720,-17600,-6361) (-30/83,-43/119) -> (-43/159,-10/37) Hyperbolic Matrix(1319,476,4320,1559) (-13/36,-22/61) -> (18/59,11/36) Hyperbolic Matrix(1681,606,2000,721) (-22/61,-9/25) -> (21/25,16/19) Hyperbolic Matrix(879,316,2000,719) (-9/25,-14/39) -> (18/41,11/25) Hyperbolic Matrix(2481,890,4240,1521) (-14/39,-19/53) -> (31/53,24/41) Hyperbolic Matrix(9241,3312,14400,5161) (-19/53,-43/120) -> (77/120,43/67) Hyperbolic Matrix(9239,3310,14400,5159) (-43/120,-24/67) -> (34/53,77/120) Hyperbolic Matrix(439,156,560,199) (-5/14,-6/17) -> (18/23,11/14) Hyperbolic Matrix(279,98,-800,-281) (-6/17,-7/20) -> (-7/20,-8/23) Parabolic Matrix(759,262,1040,359) (-8/23,-1/3) -> (27/37,46/63) Hyperbolic Matrix(119,38,-880,-281) (-1/3,-7/22) -> (-3/22,-5/37) Hyperbolic Matrix(1039,330,1760,559) (-7/22,-6/19) -> (36/61,13/22) Hyperbolic Matrix(121,38,640,201) (-6/19,-5/16) -> (3/16,4/21) Hyperbolic Matrix(761,236,1680,521) (-9/29,-13/42) -> (19/42,5/11) Hyperbolic Matrix(2361,730,2720,841) (-13/42,-17/55) -> (13/15,33/38) Hyperbolic Matrix(1839,568,4400,1359) (-17/55,-4/13) -> (28/67,23/55) Hyperbolic Matrix(119,36,-400,-121) (-4/13,-3/10) -> (-3/10,-8/27) Parabolic Matrix(1081,320,1760,521) (-8/27,-13/44) -> (27/44,8/13) Hyperbolic Matrix(1761,520,4880,1441) (-13/44,-18/61) -> (22/61,13/36) Hyperbolic Matrix(28201,8320,40000,11801) (-18/61,-59/200) -> (141/200,98/139) Hyperbolic Matrix(28199,8318,40000,11799) (-59/200,-41/139) -> (43/61,141/200) Hyperbolic Matrix(559,164,1360,399) (-5/17,-12/41) -> (16/39,7/17) Hyperbolic Matrix(2041,596,2880,841) (-19/65,-7/24) -> (17/24,39/55) Hyperbolic Matrix(2039,594,2880,839) (-7/24,-16/55) -> (46/65,17/24) Hyperbolic Matrix(399,116,-2480,-721) (-16/55,-9/31) -> (-5/31,-4/25) Hyperbolic Matrix(841,244,1520,441) (-9/31,-11/38) -> (21/38,5/9) Hyperbolic Matrix(2359,682,-8720,-2521) (-11/38,-13/45) -> (-23/85,-33/122) Hyperbolic Matrix(919,260,2400,679) (-2/7,-11/39) -> (31/81,18/47) Hyperbolic Matrix(561,158,2560,721) (-11/39,-9/32) -> (7/32,9/41) Hyperbolic Matrix(599,168,1280,359) (-16/57,-7/25) -> (7/15,8/17) Hyperbolic Matrix(5479,1532,6720,1879) (-7/25,-26/93) -> (22/27,53/65) Hyperbolic Matrix(2719,758,3440,959) (-12/43,-17/61) -> (15/19,34/43) Hyperbolic Matrix(841,234,2160,601) (-17/61,-5/18) -> (7/18,23/59) Hyperbolic Matrix(1161,320,1600,441) (-8/29,-11/40) -> (29/40,8/11) Hyperbolic Matrix(1159,318,1600,439) (-11/40,-3/11) -> (21/29,29/40) Hyperbolic Matrix(1641,446,2800,761) (-3/11,-16/59) -> (58/99,17/29) Hyperbolic Matrix(13199,3570,-57680,-15601) (-33/122,-43/159) -> (-73/319,-27/118) Hyperbolic Matrix(681,184,1040,281) (-10/37,-17/63) -> (15/23,2/3) Hyperbolic Matrix(18721,5032,25600,6881) (-25/93,-43/160) -> (117/160,49/67) Hyperbolic Matrix(18719,5030,25600,6879) (-43/160,-18/67) -> (68/93,117/160) Hyperbolic Matrix(961,258,-5360,-1439) (-18/67,-11/41) -> (-7/39,-12/67) Hyperbolic Matrix(1001,268,3440,921) (-15/56,-4/15) -> (16/55,7/24) Hyperbolic Matrix(761,202,1360,361) (-4/15,-9/34) -> (19/34,14/25) Hyperbolic Matrix(39,10,-160,-41) (-5/19,-1/4) -> (-1/4,-5/21) Parabolic Matrix(4881,1160,6400,1521) (-5/21,-19/80) -> (61/80,45/59) Hyperbolic Matrix(4879,1158,6400,1519) (-19/80,-14/59) -> (16/21,61/80) Hyperbolic Matrix(3719,880,4560,1079) (-9/38,-13/55) -> (53/65,31/38) Hyperbolic Matrix(521,122,1200,281) (-4/17,-7/30) -> (13/30,10/23) Hyperbolic Matrix(1039,242,2400,559) (-7/30,-10/43) -> (16/37,13/30) Hyperbolic Matrix(561,130,1040,241) (-10/43,-3/13) -> (7/13,20/37) Hyperbolic Matrix(879,202,1040,239) (-3/13,-11/48) -> (27/32,11/13) Hyperbolic Matrix(208521,47720,270400,61881) (-46/201,-119/520) -> (401/520,246/319) Hyperbolic Matrix(208519,47718,270400,61879) (-119/520,-73/319) -> (155/201,401/520) Hyperbolic Matrix(1241,280,1600,361) (-7/31,-9/40) -> (31/40,7/9) Hyperbolic Matrix(1239,278,1600,359) (-9/40,-2/9) -> (24/31,31/40) Hyperbolic Matrix(1161,256,2000,441) (-2/9,-9/41) -> (47/81,18/31) Hyperbolic Matrix(721,158,2560,561) (-9/41,-7/32) -> (9/32,11/39) Hyperbolic Matrix(679,148,1280,279) (-12/55,-5/23) -> (9/17,8/15) Hyperbolic Matrix(361,78,560,121) (-5/23,-3/14) -> (9/14,11/17) Hyperbolic Matrix(5041,1072,6400,1361) (-10/47,-17/80) -> (63/80,26/33) Hyperbolic Matrix(5039,1070,6400,1359) (-17/80,-7/33) -> (37/47,63/80) Hyperbolic Matrix(1039,220,2640,559) (-7/33,-11/52) -> (11/28,13/33) Hyperbolic Matrix(2319,490,4160,879) (-11/52,-15/71) -> (5/9,29/52) Hyperbolic Matrix(161,34,1520,321) (-15/71,-4/19) -> (2/19,1/9) Hyperbolic Matrix(2481,520,3440,721) (-4/19,-9/43) -> (31/43,44/61) Hyperbolic Matrix(881,184,1920,401) (-9/43,-5/24) -> (11/24,17/37) Hyperbolic Matrix(959,198,2320,479) (-6/29,-1/5) -> (31/75,12/29) Hyperbolic Matrix(439,84,1040,199) (-1/5,-4/21) -> (8/19,19/45) Hyperbolic Matrix(201,38,640,121) (-4/21,-3/16) -> (5/16,6/19) Hyperbolic Matrix(4841,894,6720,1241) (-5/27,-12/65) -> (18/25,67/93) Hyperbolic Matrix(3481,642,4560,841) (-12/65,-7/38) -> (29/38,42/55) Hyperbolic Matrix(839,154,1520,279) (-7/38,-2/11) -> (16/29,21/38) Hyperbolic Matrix(439,78,1120,199) (-5/28,-3/17) -> (9/23,11/28) Hyperbolic Matrix(1321,232,1600,281) (-3/17,-7/40) -> (33/40,19/23) Hyperbolic Matrix(1319,230,1600,279) (-7/40,-4/23) -> (14/17,33/40) Hyperbolic Matrix(1279,204,2000,319) (-4/25,-3/19) -> (39/61,16/25) Hyperbolic Matrix(2319,364,5600,879) (-3/19,-8/51) -> (12/29,41/99) Hyperbolic Matrix(801,124,1040,161) (-5/32,-2/13) -> (10/13,37/48) Hyperbolic Matrix(119,18,-800,-121) (-2/13,-3/20) -> (-3/20,-4/27) Parabolic Matrix(5521,760,6400,881) (-4/29,-11/80) -> (69/80,44/51) Hyperbolic Matrix(5519,758,6400,879) (-11/80,-7/51) -> (25/29,69/80) Hyperbolic Matrix(641,86,1200,161) (-5/37,-2/15) -> (8/15,23/43) Hyperbolic Matrix(1879,248,2720,359) (-2/15,-5/38) -> (29/42,38/55) Hyperbolic Matrix(281,36,320,41) (-3/23,-1/8) -> (7/8,15/17) Hyperbolic Matrix(279,34,320,39) (-1/8,-2/17) -> (20/23,7/8) Hyperbolic Matrix(321,34,1520,161) (-1/9,-2/19) -> (4/19,15/71) Hyperbolic Matrix(1359,140,2320,239) (-2/19,-1/10) -> (41/70,58/99) Hyperbolic Matrix(281,24,480,41) (-1/10,0/1) -> (24/41,41/70) Hyperbolic Matrix(1519,-176,2080,-241) (1/9,2/17) -> (46/63,65/89) Hyperbolic Matrix(1161,-152,1520,-199) (3/23,2/15) -> (42/55,13/17) Hyperbolic Matrix(281,-38,880,-119) (2/15,3/22) -> (7/22,8/25) Hyperbolic Matrix(521,-72,1440,-199) (3/22,1/7) -> (17/47,21/58) Hyperbolic Matrix(839,-124,1360,-201) (1/7,3/20) -> (37/60,29/47) Hyperbolic Matrix(641,-98,1040,-159) (3/20,2/13) -> (8/13,37/60) Hyperbolic Matrix(2041,-320,2800,-439) (5/32,3/19) -> (43/59,35/48) Hyperbolic Matrix(1039,-168,2480,-401) (4/25,1/6) -> (31/74,44/105) Hyperbolic Matrix(199,-34,240,-41) (1/6,3/17) -> (19/23,5/6) Hyperbolic Matrix(321,-58,880,-159) (5/28,2/11) -> (4/11,19/52) Hyperbolic Matrix(441,-82,640,-119) (2/11,3/16) -> (11/16,20/29) Hyperbolic Matrix(521,-108,960,-199) (1/5,5/24) -> (13/24,19/35) Hyperbolic Matrix(881,-188,1120,-239) (7/33,3/14) -> (11/14,37/47) Hyperbolic Matrix(1841,-402,2560,-559) (5/23,7/32) -> (23/32,41/57) Hyperbolic Matrix(681,-154,880,-199) (2/9,5/22) -> (17/22,24/31) Hyperbolic Matrix(359,-82,880,-201) (5/22,3/13) -> (11/27,9/22) Hyperbolic Matrix(41,-10,160,-39) (4/17,1/4) -> (1/4,6/23) Parabolic Matrix(1599,-418,1840,-481) (6/23,11/42) -> (33/38,20/23) Hyperbolic Matrix(2441,-640,3200,-839) (11/42,5/19) -> (45/59,29/38) Hyperbolic Matrix(841,-222,1360,-359) (5/19,4/15) -> (34/55,13/21) Hyperbolic Matrix(2321,-622,3280,-879) (4/15,11/41) -> (29/41,46/65) Hyperbolic Matrix(1519,-408,3280,-881) (11/41,18/67) -> (6/13,19/41) Hyperbolic Matrix(3041,-818,4160,-1119) (18/67,7/26) -> (19/26,68/93) Hyperbolic Matrix(1839,-496,2080,-561) (7/26,17/63) -> (15/17,23/26) Hyperbolic Matrix(4441,-1202,5760,-1559) (10/37,13/48) -> (37/48,64/83) Hyperbolic Matrix(2361,-640,2800,-759) (13/48,3/11) -> (43/51,27/32) Hyperbolic Matrix(521,-144,720,-199) (3/11,5/18) -> (13/18,21/29) Hyperbolic Matrix(1439,-402,3440,-961) (12/43,7/25) -> (23/55,18/43) Hyperbolic Matrix(2001,-562,2560,-719) (7/25,9/32) -> (25/32,43/55) Hyperbolic Matrix(921,-266,1520,-439) (2/7,11/38) -> (23/38,20/33) Hyperbolic Matrix(2079,-604,4960,-1441) (9/31,16/55) -> (44/105,13/31) Hyperbolic Matrix(2401,-702,3280,-959) (7/24,12/41) -> (30/41,41/56) Hyperbolic Matrix(121,-36,400,-119) (5/17,3/10) -> (3/10,7/23) Parabolic Matrix(761,-232,1440,-439) (7/23,18/59) -> (10/19,9/17) Hyperbolic Matrix(521,-162,640,-199) (4/13,5/16) -> (13/16,22/27) Hyperbolic Matrix(281,-98,800,-279) (1/3,7/20) -> (7/20,13/37) Parabolic Matrix(1079,-386,1680,-601) (5/14,19/53) -> (43/67,9/14) Hyperbolic Matrix(1001,-362,2320,-839) (13/36,17/47) -> (3/7,19/44) Hyperbolic Matrix(2761,-1000,3200,-1159) (21/58,4/11) -> (44/51,19/22) Hyperbolic Matrix(1521,-556,3280,-1199) (19/52,15/41) -> (19/41,13/28) Hyperbolic Matrix(2599,-952,4480,-1641) (15/41,11/30) -> (29/50,47/81) Hyperbolic Matrix(881,-324,1520,-559) (11/30,7/19) -> (11/19,29/50) Hyperbolic Matrix(1001,-382,1360,-519) (8/21,13/34) -> (25/34,14/19) Hyperbolic Matrix(4601,-1760,7840,-2999) (13/34,31/81) -> (71/121,27/46) Hyperbolic Matrix(1159,-444,1360,-521) (18/47,5/13) -> (23/27,6/7) Hyperbolic Matrix(6081,-2350,9520,-3679) (17/44,46/119) -> (76/119,23/36) Hyperbolic Matrix(881,-342,1440,-559) (12/31,7/18) -> (11/18,30/49) Hyperbolic Matrix(1081,-426,1520,-599) (13/33,2/5) -> (32/45,5/7) Hyperbolic Matrix(2159,-876,2960,-1201) (2/5,13/32) -> (35/48,62/85) Hyperbolic Matrix(2161,-892,3680,-1519) (7/17,19/46) -> (27/46,37/63) Hyperbolic Matrix(4841,-2000,7840,-3239) (19/46,31/75) -> (71/115,21/34) Hyperbolic Matrix(601,-250,1440,-599) (22/53,5/12) -> (5/12,28/67) Parabolic Matrix(6881,-2882,11840,-4959) (18/43,31/74) -> (43/74,68/117) Hyperbolic Matrix(961,-404,1520,-639) (13/31,8/19) -> (12/19,31/49) Hyperbolic Matrix(1841,-778,2080,-879) (30/71,11/26) -> (23/26,8/9) Hyperbolic Matrix(599,-254,1040,-441) (11/26,3/7) -> (19/33,15/26) Hyperbolic Matrix(5399,-2332,8800,-3801) (19/44,16/37) -> (100/163,27/44) Hyperbolic Matrix(2279,-1006,4080,-1801) (15/34,19/43) -> (43/77,19/34) Hyperbolic Matrix(361,-162,800,-359) (4/9,9/20) -> (9/20,14/31) Parabolic Matrix(761,-348,960,-439) (5/11,11/24) -> (19/24,23/29) Hyperbolic Matrix(959,-452,1360,-641) (8/17,1/2) -> (55/78,12/17) Hyperbolic Matrix(1241,-648,1760,-919) (1/2,10/19) -> (98/139,55/78) Hyperbolic Matrix(1839,-986,2240,-1201) (15/28,7/13) -> (55/67,23/28) Hyperbolic Matrix(441,-242,800,-439) (6/11,11/20) -> (11/20,16/29) Parabolic Matrix(1481,-842,2320,-1319) (21/37,4/7) -> (30/47,53/83) Hyperbolic Matrix(3039,-1754,4160,-2401) (15/26,41/71) -> (65/89,19/26) Hyperbolic Matrix(2079,-1208,2480,-1441) (18/31,43/74) -> (5/6,26/31) Hyperbolic Matrix(2479,-1442,3440,-2001) (25/43,7/12) -> (49/68,31/43) Hyperbolic Matrix(3401,-1988,4720,-2759) (7/12,31/53) -> (67/93,49/68) Hyperbolic Matrix(679,-402,880,-521) (13/22,3/5) -> (27/35,17/22) Hyperbolic Matrix(1481,-894,1920,-1159) (3/5,23/38) -> (91/118,27/35) Hyperbolic Matrix(32881,-20172,42640,-26159) (73/119,100/163) -> (64/83,155/201) Hyperbolic Matrix(2281,-1444,3600,-2279) (31/49,19/30) -> (19/30,45/71) Parabolic Matrix(721,-458,880,-559) (26/41,7/11) -> (9/11,32/39) Hyperbolic Matrix(1241,-792,1440,-919) (7/11,30/47) -> (6/7,25/29) Hyperbolic Matrix(12841,-8200,17600,-11239) (53/83,76/119) -> (116/159,27/37) Hyperbolic Matrix(521,-338,800,-519) (11/17,13/20) -> (13/20,15/23) Parabolic Matrix(761,-518,880,-599) (2/3,15/22) -> (19/22,32/37) Hyperbolic Matrix(281,-196,400,-279) (9/13,7/10) -> (7/10,19/27) Parabolic Matrix(2081,-1476,2480,-1759) (39/55,22/31) -> (26/31,21/25) Hyperbolic Matrix(6361,-4522,8720,-6199) (27/38,32/45) -> (62/85,89/122) Hyperbolic Matrix(44481,-32450,57680,-42079) (89/122,116/159) -> (246/319,91/118) Hyperbolic Matrix(4399,-3218,5360,-3921) (49/67,30/41) -> (32/39,55/67) Hyperbolic Matrix(121,-90,160,-119) (14/19,3/4) -> (3/4,16/21) Parabolic Matrix(681,-578,800,-679) (11/13,17/20) -> (17/20,23/27) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-76,1) Matrix(199,182,480,439) -> Matrix(69,-2,-1000,29) Matrix(961,862,2320,2081) -> Matrix(203,-6,-2808,83) Matrix(1199,1072,1520,1359) -> Matrix(203,-6,-6056,179) Matrix(561,496,-2080,-1839) -> Matrix(401,-12,4244,-127) Matrix(41,36,320,281) -> Matrix(199,-6,-1028,31) Matrix(39,34,320,279) -> Matrix(197,-6,-952,29) Matrix(359,312,-1520,-1321) -> Matrix(131,-4,1212,-37) Matrix(599,518,-880,-761) -> Matrix(131,-4,3308,-101) Matrix(919,792,-1440,-1241) -> Matrix(65,-2,1268,-39) Matrix(521,444,-1360,-1159) -> Matrix(257,-8,4080,-127) Matrix(399,338,-1040,-881) -> Matrix(191,-6,3088,-97) Matrix(521,440,1280,1081) -> Matrix(63,-2,-976,31) Matrix(759,640,-2800,-2361) -> Matrix(125,-4,1344,-43) Matrix(721,606,2000,1681) -> Matrix(63,-2,-976,31) Matrix(1441,1208,-2480,-2079) -> Matrix(63,-2,1544,-49) Matrix(41,34,-240,-199) -> Matrix(125,-4,844,-27) Matrix(681,560,1120,921) -> Matrix(185,-6,-4224,137) Matrix(559,458,-880,-721) -> Matrix(61,-2,1556,-51) Matrix(199,162,-640,-521) -> Matrix(61,-2,824,-27) Matrix(439,356,640,519) -> Matrix(61,-2,-1616,53) Matrix(601,486,1040,841) -> Matrix(1,0,-52,1) Matrix(439,348,-960,-761) -> Matrix(59,-2,1092,-37) Matrix(1039,822,1920,1519) -> Matrix(1,0,-48,1) Matrix(959,758,3440,2719) -> Matrix(63,-2,-724,23) Matrix(1359,1072,1520,1199) -> Matrix(179,-6,-6056,203) Matrix(1841,1452,4160,3281) -> Matrix(119,-4,-2112,71) Matrix(1601,1262,2640,2081) -> Matrix(59,-2,-1268,43) Matrix(239,188,-1120,-881) -> Matrix(117,-4,1024,-35) Matrix(199,156,560,439) -> Matrix(1,0,-44,1) Matrix(719,562,-2560,-2001) -> Matrix(237,-8,2696,-91) Matrix(1839,1436,2560,1999) -> Matrix(471,-16,-12452,423) Matrix(2079,1622,3280,2559) -> Matrix(411,-14,-9952,339) Matrix(199,154,-880,-681) -> Matrix(347,-12,3152,-109) Matrix(521,402,-880,-679) -> Matrix(115,-4,2444,-85) Matrix(479,368,1040,799) -> Matrix(57,-2,-1168,41) Matrix(1361,1044,2400,1841) -> Matrix(113,-4,-2288,81) Matrix(679,520,1200,919) -> Matrix(1,0,-48,1) Matrix(119,90,-160,-121) -> Matrix(57,-2,1568,-55) Matrix(241,178,-1840,-1359) -> Matrix(53,-2,292,-11) Matrix(759,560,-3200,-2361) -> Matrix(53,-2,504,-19) Matrix(519,382,-1360,-1001) -> Matrix(1,0,-12,1) Matrix(959,702,-3280,-2401) -> Matrix(387,-14,4340,-157) Matrix(1761,1288,-3280,-2399) -> Matrix(55,-2,1568,-57) Matrix(1119,818,-4160,-3041) -> Matrix(549,-20,5792,-211) Matrix(241,176,-2080,-1519) -> Matrix(329,-12,1508,-55) Matrix(1041,760,2960,2161) -> Matrix(383,-14,-5444,199) Matrix(1319,962,-5760,-4201) -> Matrix(53,-2,504,-19) Matrix(439,320,-2800,-2041) -> Matrix(109,-4,736,-27) Matrix(199,144,-720,-521) -> Matrix(215,-8,2392,-89) Matrix(1319,952,2160,1559) -> Matrix(107,-4,-2648,99) Matrix(721,520,3440,2481) -> Matrix(53,-2,-344,13) Matrix(2001,1442,-3440,-2479) -> Matrix(53,-2,1140,-43) Matrix(559,402,-2560,-1841) -> Matrix(213,-8,1784,-67) Matrix(1999,1436,2560,1839) -> Matrix(423,-16,-12452,471) Matrix(1481,1062,2400,1721) -> Matrix(157,-6,-3480,133) Matrix(599,426,-1520,-1081) -> Matrix(1,0,-12,1) Matrix(1121,796,2480,1761) -> Matrix(53,-2,-980,37) Matrix(2881,2044,-4960,-3519) -> Matrix(1,0,-4,1) Matrix(2519,1786,3440,2439) -> Matrix(111,-4,-3080,111) Matrix(879,622,-3280,-2321) -> Matrix(375,-14,3884,-145) Matrix(801,566,1360,961) -> Matrix(53,-2,-980,37) Matrix(279,196,-400,-281) -> Matrix(105,-4,2704,-103) Matrix(679,472,-1440,-1001) -> Matrix(51,-2,944,-37) Matrix(2761,1918,4320,3001) -> Matrix(51,-2,-1096,43) Matrix(401,278,1040,721) -> Matrix(51,-2,-892,35) Matrix(119,82,-640,-441) -> Matrix(49,-2,368,-15) Matrix(519,356,640,439) -> Matrix(53,-2,-1616,61) Matrix(721,492,1760,1201) -> Matrix(103,-4,-1828,71) Matrix(521,354,1120,761) -> Matrix(51,-2,-892,35) Matrix(519,338,-800,-521) -> Matrix(145,-6,3456,-143) Matrix(799,518,2960,1919) -> Matrix(333,-14,-3544,149) Matrix(121,78,560,361) -> Matrix(1,0,-32,1) Matrix(601,386,-1680,-1079) -> Matrix(93,-4,1372,-59) Matrix(1759,1128,4240,2719) -> Matrix(137,-6,-2032,89) Matrix(1121,718,2000,1281) -> Matrix(45,-2,-1012,45) Matrix(319,204,2000,1279) -> Matrix(45,-2,-292,13) Matrix(3439,2198,4880,3119) -> Matrix(45,-2,-1192,53) Matrix(1319,842,-2320,-1481) -> Matrix(1,0,0,1) Matrix(439,280,-3200,-2041) -> Matrix(29,-2,160,-11) Matrix(1759,1116,-3280,-2081) -> Matrix(49,-2,1152,-47) Matrix(1881,1192,-4480,-2839) -> Matrix(145,-6,2296,-95) Matrix(639,404,-1520,-961) -> Matrix(47,-2,776,-33) Matrix(121,76,320,201) -> Matrix(47,-2,-728,31) Matrix(119,74,320,199) -> Matrix(45,-2,-652,29) Matrix(359,222,-1360,-841) -> Matrix(1,0,-12,1) Matrix(3239,2000,-7840,-4841) -> Matrix(45,-2,428,-19) Matrix(1721,1062,2400,1481) -> Matrix(133,-6,-3480,157) Matrix(201,124,-1360,-839) -> Matrix(177,-8,1040,-47) Matrix(319,196,1040,639) -> Matrix(41,-2,-512,25) Matrix(3439,2110,-9520,-5841) -> Matrix(39,-2,644,-33) Matrix(10561,6478,18000,11041) -> Matrix(37,-2,-980,53) Matrix(3881,2380,6720,4121) -> Matrix(35,-2,-752,43) Matrix(559,342,-1440,-881) -> Matrix(1,0,-12,1) Matrix(1559,952,2160,1319) -> Matrix(99,-4,-2648,107) Matrix(7081,4320,12000,7321) -> Matrix(241,-10,-4844,201) Matrix(4719,2878,8000,4879) -> Matrix(191,-8,-3796,159) Matrix(801,488,1840,1121) -> Matrix(47,-2,-916,39) Matrix(921,560,1120,681) -> Matrix(137,-6,-4224,185) Matrix(2081,1262,2640,1601) -> Matrix(43,-2,-1268,59) Matrix(439,266,-1520,-921) -> Matrix(1,0,-12,1) Matrix(801,476,-2960,-1759) -> Matrix(43,-2,452,-21) Matrix(199,118,1280,759) -> Matrix(45,-2,-292,13) Matrix(559,330,1760,1039) -> Matrix(81,-4,-992,49) Matrix(7321,4320,12000,7081) -> Matrix(201,-10,-4844,241) Matrix(4879,2878,8000,4719) -> Matrix(159,-8,-3796,191) Matrix(961,566,1360,801) -> Matrix(37,-2,-980,53) Matrix(1519,892,-3680,-2161) -> Matrix(1,0,-20,1) Matrix(2999,1760,-7840,-4601) -> Matrix(57,-2,884,-31) Matrix(1841,1080,2320,1361) -> Matrix(51,-2,-1504,59) Matrix(4721,2766,5600,3281) -> Matrix(1,0,-56,1) Matrix(239,140,2320,1359) -> Matrix(145,-6,-604,25) Matrix(41,24,480,281) -> Matrix(47,-2,-164,7) Matrix(1521,890,4240,2481) -> Matrix(139,-6,-2108,91) Matrix(839,490,-1440,-841) -> Matrix(45,-2,968,-43) Matrix(3041,1770,4400,2561) -> Matrix(41,-2,-1004,49) Matrix(4959,2882,-11840,-6881) -> Matrix(1,0,-12,1) Matrix(559,324,-1520,-881) -> Matrix(43,-2,624,-29) Matrix(841,486,1040,601) -> Matrix(1,0,-52,1) Matrix(4121,2380,6720,3881) -> Matrix(43,-2,-752,35) Matrix(239,138,-2080,-1201) -> Matrix(85,-4,404,-19) Matrix(441,254,-1040,-599) -> Matrix(85,-4,1424,-67) Matrix(3401,1932,-8800,-4999) -> Matrix(43,-2,796,-37) Matrix(1841,1044,2400,1361) -> Matrix(81,-4,-2288,113) Matrix(919,520,1200,679) -> Matrix(1,0,-48,1) Matrix(719,406,1840,1039) -> Matrix(37,-2,-536,29) Matrix(561,316,1280,721) -> Matrix(1,0,-32,1) Matrix(559,314,1280,719) -> Matrix(1,0,-44,1) Matrix(1281,718,2000,1121) -> Matrix(45,-2,-1012,45) Matrix(1681,940,2720,1521) -> Matrix(1,0,-44,1) Matrix(1801,1006,-4080,-2279) -> Matrix(85,-4,1424,-67) Matrix(1599,892,3440,1919) -> Matrix(41,-2,-676,33) Matrix(879,490,4160,2319) -> Matrix(81,-4,-668,33) Matrix(439,242,-800,-441) -> Matrix(41,-2,800,-39) Matrix(719,394,2480,1359) -> Matrix(39,-2,-448,23) Matrix(1159,634,1680,919) -> Matrix(1,0,-44,1) Matrix(199,108,-960,-521) -> Matrix(39,-2,332,-17) Matrix(1519,822,1920,1039) -> Matrix(1,0,-48,1) Matrix(241,130,1040,561) -> Matrix(35,-2,-332,19) Matrix(1521,814,3440,1841) -> Matrix(43,-2,-752,35) Matrix(359,192,1120,599) -> Matrix(41,-2,-512,25) Matrix(921,490,1280,681) -> Matrix(37,-2,-980,53) Matrix(401,212,-1360,-719) -> Matrix(41,-2,472,-23) Matrix(519,248,-1760,-841) -> Matrix(41,-2,472,-23) Matrix(1001,470,1280,601) -> Matrix(35,-2,-1032,59) Matrix(1039,484,1200,559) -> Matrix(33,-2,-1072,65) Matrix(1919,892,3440,1599) -> Matrix(33,-2,-676,41) Matrix(401,186,-2240,-1039) -> Matrix(59,-4,428,-29) Matrix(799,368,1040,479) -> Matrix(41,-2,-1168,57) Matrix(401,184,1920,881) -> Matrix(1,0,-28,1) Matrix(1079,492,1840,839) -> Matrix(1,0,-44,1) Matrix(359,162,-800,-361) -> Matrix(37,-2,648,-35) Matrix(1241,556,1520,681) -> Matrix(1,0,-48,1) Matrix(1079,482,1520,679) -> Matrix(1,0,-44,1) Matrix(3281,1452,4160,1841) -> Matrix(71,-4,-2112,119) Matrix(1841,814,3440,1521) -> Matrix(35,-2,-752,43) Matrix(8041,3552,14400,6361) -> Matrix(239,-14,-5036,295) Matrix(8039,3550,14400,6359) -> Matrix(237,-14,-4960,293) Matrix(999,440,1360,599) -> Matrix(1,0,-44,1) Matrix(719,316,2000,879) -> Matrix(31,-2,-480,31) Matrix(721,316,1280,561) -> Matrix(1,0,-32,1) Matrix(719,314,1280,559) -> Matrix(1,0,-44,1) Matrix(1121,488,1840,801) -> Matrix(39,-2,-916,47) Matrix(281,122,1200,521) -> Matrix(1,0,-28,1) Matrix(559,242,2400,1039) -> Matrix(71,-4,-692,39) Matrix(839,362,-2320,-1001) -> Matrix(1,0,0,1) Matrix(921,392,1600,681) -> Matrix(103,-6,-2180,127) Matrix(919,390,1600,679) -> Matrix(101,-6,-2104,125) Matrix(1121,474,-4160,-1759) -> Matrix(131,-8,1392,-85) Matrix(2599,1098,6720,2839) -> Matrix(33,-2,-676,41) Matrix(199,84,1040,439) -> Matrix(1,0,-24,1) Matrix(1559,654,2000,839) -> Matrix(61,-4,-1784,117) Matrix(401,168,-2480,-1039) -> Matrix(27,-2,176,-13) Matrix(14881,6232,25600,10721) -> Matrix(1,0,-24,1) Matrix(14879,6230,25600,10719) -> Matrix(1,0,-52,1) Matrix(961,402,-3440,-1439) -> Matrix(33,-2,380,-23) Matrix(1319,548,-4720,-1961) -> Matrix(1,0,-4,1) Matrix(2719,1128,4240,1759) -> Matrix(89,-6,-2032,137) Matrix(439,182,480,199) -> Matrix(29,-2,-1000,69) Matrix(2081,862,2320,961) -> Matrix(83,-6,-2808,203) Matrix(2039,844,2800,1159) -> Matrix(53,-4,-1444,109) Matrix(1001,414,1840,761) -> Matrix(1,0,-32,1) Matrix(6959,2876,18000,7439) -> Matrix(23,-2,-448,39) Matrix(3761,1552,6400,2641) -> Matrix(1,0,-12,1) Matrix(3759,1550,6400,2639) -> Matrix(1,0,-64,1) Matrix(399,164,1360,559) -> Matrix(39,-2,-448,23) Matrix(3121,1280,8000,3281) -> Matrix(145,-8,-2048,113) Matrix(4679,1918,12000,4919) -> Matrix(179,-10,-2488,139) Matrix(1201,492,1760,721) -> Matrix(71,-4,-1828,103) Matrix(201,82,-880,-359) -> Matrix(67,-4,620,-37) Matrix(439,174,-1920,-761) -> Matrix(29,-2,276,-19) Matrix(559,220,2640,1039) -> Matrix(33,-2,-280,17) Matrix(199,78,1120,439) -> Matrix(91,-6,-652,43) Matrix(1039,406,1840,719) -> Matrix(29,-2,-536,37) Matrix(3281,1280,8000,3121) -> Matrix(113,-8,-2048,145) Matrix(4919,1918,12000,4679) -> Matrix(139,-10,-2488,179) Matrix(601,234,2160,841) -> Matrix(53,-4,-596,45) Matrix(3921,1520,6400,2481) -> Matrix(1,0,-16,1) Matrix(3919,1518,6400,2479) -> Matrix(1,0,-60,1) Matrix(2839,1098,6720,2599) -> Matrix(41,-2,-676,33) Matrix(12199,4716,19760,7639) -> Matrix(155,-8,-3468,179) Matrix(9759,3772,-42640,-16481) -> Matrix(189,-10,1720,-91) Matrix(1239,478,1760,679) -> Matrix(37,-2,-980,53) Matrix(679,260,2400,919) -> Matrix(95,-6,-1124,71) Matrix(12121,4638,19760,7561) -> Matrix(125,-8,-2328,149) Matrix(1199,458,2720,1039) -> Matrix(1,0,-32,1) Matrix(201,76,320,121) -> Matrix(31,-2,-728,47) Matrix(199,74,320,119) -> Matrix(29,-2,-652,45) Matrix(1319,484,-3600,-1321) -> Matrix(113,-8,1568,-111) Matrix(721,264,3280,1201) -> Matrix(193,-14,-1668,121) Matrix(159,58,-880,-321) -> Matrix(25,-2,188,-15) Matrix(199,72,-1440,-521) -> Matrix(37,-2,204,-11) Matrix(4759,1720,-17600,-6361) -> Matrix(103,-6,1116,-65) Matrix(1319,476,4320,1559) -> Matrix(33,-2,-412,25) Matrix(1681,606,2000,721) -> Matrix(31,-2,-976,63) Matrix(879,316,2000,719) -> Matrix(31,-2,-480,31) Matrix(2481,890,4240,1521) -> Matrix(91,-6,-2108,139) Matrix(9241,3312,14400,5161) -> Matrix(511,-34,-11768,783) Matrix(9239,3310,14400,5159) -> Matrix(509,-34,-11692,781) Matrix(439,156,560,199) -> Matrix(1,0,-44,1) Matrix(279,98,-800,-281) -> Matrix(85,-6,1176,-83) Matrix(759,262,1040,359) -> Matrix(53,-4,-1444,109) Matrix(119,38,-880,-281) -> Matrix(51,-4,268,-21) Matrix(1039,330,1760,559) -> Matrix(49,-4,-992,81) Matrix(121,38,640,201) -> Matrix(23,-2,-172,15) Matrix(761,236,1680,521) -> Matrix(1,0,-32,1) Matrix(2361,730,2720,841) -> Matrix(25,-2,-812,65) Matrix(1839,568,4400,1359) -> Matrix(27,-2,-472,35) Matrix(119,36,-400,-121) -> Matrix(49,-4,576,-47) Matrix(1081,320,1760,521) -> Matrix(23,-2,-448,39) Matrix(1761,520,4880,1441) -> Matrix(23,-2,-356,31) Matrix(28201,8320,40000,11801) -> Matrix(211,-18,-5568,475) Matrix(28199,8318,40000,11799) -> Matrix(209,-18,-5492,473) Matrix(559,164,1360,399) -> Matrix(23,-2,-448,39) Matrix(2041,596,2880,841) -> Matrix(67,-6,-1820,163) Matrix(2039,594,2880,839) -> Matrix(65,-6,-1744,161) Matrix(399,116,-2480,-721) -> Matrix(19,-2,124,-13) Matrix(841,244,1520,441) -> Matrix(1,0,-32,1) Matrix(2359,682,-8720,-2521) -> Matrix(1,0,0,1) Matrix(919,260,2400,679) -> Matrix(71,-6,-1124,95) Matrix(561,158,2560,721) -> Matrix(185,-16,-1584,137) Matrix(599,168,1280,359) -> Matrix(23,-2,-448,39) Matrix(5479,1532,6720,1879) -> Matrix(23,-2,-724,63) Matrix(2719,758,3440,959) -> Matrix(23,-2,-724,63) Matrix(841,234,2160,601) -> Matrix(45,-4,-596,53) Matrix(1161,320,1600,441) -> Matrix(199,-18,-5384,487) Matrix(1159,318,1600,439) -> Matrix(197,-18,-5308,485) Matrix(1641,446,2800,761) -> Matrix(43,-4,-1064,99) Matrix(13199,3570,-57680,-15601) -> Matrix(23,-2,196,-17) Matrix(681,184,1040,281) -> Matrix(43,-4,-1064,99) Matrix(18721,5032,25600,6881) -> Matrix(1429,-136,-39308,3741) Matrix(18719,5030,25600,6879) -> Matrix(1427,-136,-39232,3739) Matrix(961,258,-5360,-1439) -> Matrix(439,-42,3188,-305) Matrix(1001,268,3440,921) -> Matrix(41,-4,-420,41) Matrix(761,202,1360,361) -> Matrix(1,0,-32,1) Matrix(39,10,-160,-41) -> Matrix(21,-2,200,-19) Matrix(4881,1160,6400,1521) -> Matrix(77,-8,-2204,229) Matrix(4879,1158,6400,1519) -> Matrix(75,-8,-2128,227) Matrix(3719,880,4560,1079) -> Matrix(1,0,-40,1) Matrix(521,122,1200,281) -> Matrix(1,0,-28,1) Matrix(1039,242,2400,559) -> Matrix(39,-4,-692,71) Matrix(561,130,1040,241) -> Matrix(19,-2,-332,35) Matrix(879,202,1040,239) -> Matrix(93,-10,-2948,317) Matrix(208521,47720,270400,61881) -> Matrix(343,-38,-9956,1103) Matrix(208519,47718,270400,61879) -> Matrix(341,-38,-9880,1101) Matrix(1241,280,1600,361) -> Matrix(199,-22,-5780,639) Matrix(1239,278,1600,359) -> Matrix(197,-22,-5704,637) Matrix(1161,256,2000,441) -> Matrix(35,-4,-796,91) Matrix(721,158,2560,561) -> Matrix(137,-16,-1584,185) Matrix(679,148,1280,279) -> Matrix(17,-2,-348,41) Matrix(361,78,560,121) -> Matrix(1,0,-32,1) Matrix(5041,1072,6400,1361) -> Matrix(205,-24,-6056,709) Matrix(5039,1070,6400,1359) -> Matrix(203,-24,-5980,707) Matrix(1039,220,2640,559) -> Matrix(17,-2,-280,33) Matrix(2319,490,4160,879) -> Matrix(33,-4,-668,81) Matrix(161,34,1520,321) -> Matrix(49,-6,-204,25) Matrix(2481,520,3440,721) -> Matrix(13,-2,-344,53) Matrix(881,184,1920,401) -> Matrix(1,0,-28,1) Matrix(959,198,2320,479) -> Matrix(17,-2,-212,25) Matrix(439,84,1040,199) -> Matrix(1,0,-24,1) Matrix(201,38,640,121) -> Matrix(15,-2,-172,23) Matrix(4841,894,6720,1241) -> Matrix(13,-2,-344,53) Matrix(3481,642,4560,841) -> Matrix(1,0,-36,1) Matrix(839,154,1520,279) -> Matrix(1,0,-28,1) Matrix(439,78,1120,199) -> Matrix(43,-6,-652,91) Matrix(1321,232,1600,281) -> Matrix(183,-26,-5680,807) Matrix(1319,230,1600,279) -> Matrix(181,-26,-5604,805) Matrix(1279,204,2000,319) -> Matrix(13,-2,-292,45) Matrix(2319,364,5600,879) -> Matrix(1,0,-20,1) Matrix(801,124,1040,161) -> Matrix(63,-10,-1808,287) Matrix(119,18,-800,-121) -> Matrix(85,-14,504,-83) Matrix(5521,760,6400,881) -> Matrix(397,-72,-12908,2341) Matrix(5519,758,6400,879) -> Matrix(395,-72,-12832,2339) Matrix(641,86,1200,161) -> Matrix(11,-2,-236,43) Matrix(1879,248,2720,359) -> Matrix(11,-2,-280,51) Matrix(281,36,320,41) -> Matrix(31,-6,-1028,199) Matrix(279,34,320,39) -> Matrix(29,-6,-952,197) Matrix(321,34,1520,161) -> Matrix(25,-6,-204,49) Matrix(1359,140,2320,239) -> Matrix(25,-6,-604,145) Matrix(281,24,480,41) -> Matrix(7,-2,-164,47) Matrix(1519,-176,2080,-241) -> Matrix(55,12,-1508,-329) Matrix(1161,-152,1520,-199) -> Matrix(21,4,-604,-115) Matrix(281,-38,880,-119) -> Matrix(21,4,-268,-51) Matrix(521,-72,1440,-199) -> Matrix(11,2,-204,-37) Matrix(839,-124,1360,-201) -> Matrix(47,8,-1040,-177) Matrix(641,-98,1040,-159) -> Matrix(37,6,-808,-131) Matrix(2041,-320,2800,-439) -> Matrix(27,4,-736,-109) Matrix(1039,-168,2480,-401) -> Matrix(13,2,-176,-27) Matrix(199,-34,240,-41) -> Matrix(27,4,-844,-125) Matrix(321,-58,880,-159) -> Matrix(15,2,-188,-25) Matrix(441,-82,640,-119) -> Matrix(15,2,-368,-49) Matrix(521,-108,960,-199) -> Matrix(17,2,-332,-39) Matrix(881,-188,1120,-239) -> Matrix(35,4,-1024,-117) Matrix(1841,-402,2560,-559) -> Matrix(67,8,-1784,-213) Matrix(681,-154,880,-199) -> Matrix(109,12,-3152,-347) Matrix(359,-82,880,-201) -> Matrix(37,4,-620,-67) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) Matrix(1599,-418,1840,-481) -> Matrix(23,2,-748,-65) Matrix(2441,-640,3200,-839) -> Matrix(23,2,-656,-57) Matrix(841,-222,1360,-359) -> Matrix(1,0,-12,1) Matrix(2321,-622,3280,-879) -> Matrix(145,14,-3884,-375) Matrix(1519,-408,3280,-881) -> Matrix(21,2,-200,-19) Matrix(3041,-818,4160,-1119) -> Matrix(211,20,-5792,-549) Matrix(1839,-496,2080,-561) -> Matrix(127,12,-4244,-401) Matrix(4441,-1202,5760,-1559) -> Matrix(23,2,-656,-57) Matrix(2361,-640,2800,-759) -> Matrix(43,4,-1344,-125) Matrix(521,-144,720,-199) -> Matrix(89,8,-2392,-215) Matrix(1439,-402,3440,-961) -> Matrix(23,2,-380,-33) Matrix(2001,-562,2560,-719) -> Matrix(91,8,-2696,-237) Matrix(921,-266,1520,-439) -> Matrix(1,0,-12,1) Matrix(2079,-604,4960,-1441) -> Matrix(1,0,-4,1) Matrix(2401,-702,3280,-959) -> Matrix(157,14,-4340,-387) Matrix(121,-36,400,-119) -> Matrix(47,4,-576,-49) Matrix(761,-232,1440,-439) -> Matrix(25,2,-488,-39) Matrix(521,-162,640,-199) -> Matrix(27,2,-824,-61) Matrix(281,-98,800,-279) -> Matrix(83,6,-1176,-85) Matrix(1079,-386,1680,-601) -> Matrix(59,4,-1372,-93) Matrix(1001,-362,2320,-839) -> Matrix(1,0,0,1) Matrix(2761,-1000,3200,-1159) -> Matrix(47,2,-1528,-65) Matrix(1521,-556,3280,-1199) -> Matrix(27,2,-392,-29) Matrix(2599,-952,4480,-1641) -> Matrix(83,6,-1840,-133) Matrix(881,-324,1520,-559) -> Matrix(29,2,-624,-43) Matrix(1001,-382,1360,-519) -> Matrix(1,0,-12,1) Matrix(4601,-1760,7840,-2999) -> Matrix(31,2,-884,-57) Matrix(1159,-444,1360,-521) -> Matrix(127,8,-4080,-257) Matrix(6081,-2350,9520,-3679) -> Matrix(37,2,-796,-43) Matrix(881,-342,1440,-559) -> Matrix(1,0,-12,1) Matrix(1081,-426,1520,-599) -> Matrix(1,0,-12,1) Matrix(2159,-876,2960,-1201) -> Matrix(33,2,-908,-55) Matrix(2161,-892,3680,-1519) -> Matrix(1,0,-20,1) Matrix(4841,-2000,7840,-3239) -> Matrix(19,2,-428,-45) Matrix(601,-250,1440,-599) -> Matrix(31,2,-512,-33) Matrix(6881,-2882,11840,-4959) -> Matrix(1,0,-12,1) Matrix(961,-404,1520,-639) -> Matrix(33,2,-776,-47) Matrix(1841,-778,2080,-879) -> Matrix(67,4,-2228,-133) Matrix(599,-254,1040,-441) -> Matrix(67,4,-1424,-85) Matrix(5399,-2332,8800,-3801) -> Matrix(33,2,-644,-39) Matrix(2279,-1006,4080,-1801) -> Matrix(67,4,-1424,-85) Matrix(361,-162,800,-359) -> Matrix(35,2,-648,-37) Matrix(761,-348,960,-439) -> Matrix(37,2,-1092,-59) Matrix(959,-452,1360,-641) -> Matrix(35,2,-928,-53) Matrix(1241,-648,1760,-919) -> Matrix(35,2,-928,-53) Matrix(1839,-986,2240,-1201) -> Matrix(93,4,-2860,-123) Matrix(441,-242,800,-439) -> Matrix(39,2,-800,-41) Matrix(1481,-842,2320,-1319) -> Matrix(1,0,0,1) Matrix(3039,-1754,4160,-2401) -> Matrix(173,8,-4736,-219) Matrix(2079,-1208,2480,-1441) -> Matrix(49,2,-1544,-63) Matrix(2479,-1442,3440,-2001) -> Matrix(43,2,-1140,-53) Matrix(3401,-1988,4720,-2759) -> Matrix(1,0,-4,1) Matrix(679,-402,880,-521) -> Matrix(85,4,-2444,-115) Matrix(1481,-894,1920,-1159) -> Matrix(47,2,-1340,-57) Matrix(32881,-20172,42640,-26159) -> Matrix(191,10,-5520,-289) Matrix(2281,-1444,3600,-2279) -> Matrix(191,8,-4608,-193) Matrix(721,-458,880,-559) -> Matrix(51,2,-1556,-61) Matrix(1241,-792,1440,-919) -> Matrix(39,2,-1268,-65) Matrix(12841,-8200,17600,-11239) -> Matrix(125,6,-3396,-163) Matrix(521,-338,800,-519) -> Matrix(143,6,-3456,-145) Matrix(761,-518,880,-599) -> Matrix(101,4,-3308,-131) Matrix(281,-196,400,-279) -> Matrix(103,4,-2704,-105) Matrix(2081,-1476,2480,-1759) -> Matrix(57,2,-1796,-63) Matrix(6361,-4522,8720,-6199) -> Matrix(1,0,0,1) Matrix(44481,-32450,57680,-42079) -> Matrix(53,2,-1564,-59) Matrix(4399,-3218,5360,-3921) -> Matrix(1157,42,-35564,-1291) Matrix(121,-90,160,-119) -> Matrix(55,2,-1568,-57) Matrix(681,-578,800,-679) -> Matrix(447,14,-14336,-449) 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): 96 Degree of the the map X: 192 Degree of the the map Y: 384 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/9 1/8 1/7 3/20 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 1/4 4/15 5/18 3/10 5/16 1/3 7/20 3/8 2/5 41/100 5/12 7/16 9/20 7/15 1/2 8/15 9/16 23/40 93/160 7/12 3/5 5/8 19/30 7/10 29/40 117/160 11/15 3/4 61/80 31/40 4/5 33/40 7/8 9/10 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/9 -5/22 1/8 -1/5 1/7 -1/6 3/20 -1/6 2/13 -9/56 1/6 -2/13 -1/7 3/17 -11/78 2/11 -1/8 3/16 -2/15 1/5 -1/8 5/24 -1/9 4/19 -1/8 3/14 -2/17 -1/9 5/23 -5/42 7/32 -2/17 2/9 -5/44 3/13 -7/66 4/17 -3/28 1/4 -1/10 6/23 -1/12 11/42 -1/11 0/1 5/19 -1/10 4/15 -1/10 3/11 -5/54 5/18 -1/11 -4/45 12/43 -7/80 7/25 -3/34 2/7 -1/12 5/17 -5/58 3/10 -1/12 7/23 -3/38 4/13 -5/64 5/16 0/1 6/19 -1/12 1/3 -1/14 7/20 -1/14 6/17 -5/72 5/14 -2/29 -1/15 4/11 -1/12 15/41 -11/150 11/30 -1/14 7/19 -1/14 3/8 -1/15 8/21 -1/16 13/34 -1/15 -2/31 5/13 -3/50 12/31 -1/24 7/18 -1/13 0/1 2/5 -1/16 9/22 -1/17 -2/35 25/61 -1/18 41/100 -1/18 16/39 -7/128 7/17 -1/22 12/29 -1/12 17/41 -7/102 22/53 -9/136 5/12 -1/16 23/55 -1/18 18/43 -1/20 13/31 -1/14 8/19 -1/16 11/26 -2/33 -1/17 3/7 -1/18 7/16 0/1 18/41 -5/72 11/25 -1/16 15/34 -2/33 -1/17 4/9 -1/16 9/20 -1/18 5/11 -1/18 6/13 -1/24 13/28 -1/16 7/15 -1/18 8/17 -1/20 1/2 -1/19 0/1 9/17 -1/18 8/15 -1/20 15/28 -1/22 7/13 -1/14 6/11 -1/20 11/20 -1/20 5/9 -1/22 24/43 -5/104 19/34 -1/21 -2/43 14/25 -1/22 23/41 -5/118 9/16 0/1 22/39 -5/88 13/23 -3/58 4/7 -1/20 23/40 -1/21 19/33 -5/106 15/26 -1/21 -2/43 11/19 -1/22 29/50 -1/22 18/31 -1/24 43/74 -1/25 0/1 68/117 -1/32 93/160 0/1 25/43 -1/18 7/12 -1/22 31/53 -9/206 24/41 -7/164 17/29 -1/26 10/17 -1/16 3/5 -1/22 14/23 -5/116 25/41 -9/214 61/100 -1/24 36/59 -1/24 11/18 -1/25 0/1 8/13 -3/64 21/34 -2/45 -1/23 34/55 -1/22 13/21 -1/22 5/8 -1/23 12/19 -1/24 31/49 -5/118 19/30 -1/24 45/71 -11/266 26/41 -11/268 7/11 -1/26 16/25 -1/22 25/39 -11/250 34/53 -15/344 9/14 -1/23 -2/47 11/17 -5/118 13/20 -1/24 2/3 -1/24 15/22 -2/51 -3/77 13/19 -1/26 11/16 0/1 20/29 -1/24 9/13 -5/126 7/10 -1/26 19/27 -11/290 12/17 -5/132 29/41 -17/454 17/24 -1/27 5/7 -1/26 23/32 -2/53 41/57 -1/26 18/25 -3/80 49/68 -1/26 31/43 -7/186 44/61 -3/80 13/18 -4/107 -1/27 21/29 -13/350 29/40 -1/27 8/11 -5/136 19/26 -5/137 -2/55 68/93 -39/1072 117/160 -2/55 49/67 -29/798 30/41 -19/524 11/15 -1/28 25/34 -1/27 -2/55 14/19 -1/28 3/4 -1/28 16/21 -1/28 61/80 -2/57 45/59 -3/86 29/38 -2/57 -1/29 13/17 -3/86 10/13 -7/200 17/22 -6/173 -1/29 24/31 -17/492 31/40 -1/29 7/9 -5/146 25/32 -2/59 18/23 -5/148 11/14 -1/29 -2/59 15/19 -1/30 4/5 -1/30 17/21 -1/30 13/16 -2/61 22/27 -7/216 9/11 -1/30 14/17 -11/340 33/40 -1/31 19/23 -15/466 5/6 -1/31 -2/63 11/13 -9/286 17/20 -1/32 6/7 -1/32 13/15 -3/98 20/23 -1/32 7/8 -1/33 8/9 -5/168 9/10 -1/34 1/1 -1/38 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(279,-26,440,-41) (0/1,1/9) -> (45/71,26/41) Hyperbolic Matrix(79,-9,360,-41) (1/9,1/8) -> (7/32,2/9) Hyperbolic Matrix(201,-28,280,-39) (1/8,1/7) -> (5/7,23/32) Hyperbolic Matrix(239,-35,280,-41) (1/7,3/20) -> (17/20,6/7) Hyperbolic Matrix(441,-67,520,-79) (3/20,2/13) -> (11/13,17/20) Hyperbolic Matrix(199,-31,520,-81) (2/13,1/6) -> (13/34,5/13) Hyperbolic Matrix(199,-34,240,-41) (1/6,3/17) -> (19/23,5/6) Hyperbolic Matrix(399,-71,680,-121) (3/17,2/11) -> (17/29,10/17) Hyperbolic Matrix(441,-82,640,-119) (2/11,3/16) -> (11/16,20/29) Hyperbolic Matrix(41,-8,200,-39) (3/16,1/5) -> (1/5,5/24) Parabolic Matrix(521,-109,760,-159) (5/24,4/19) -> (13/19,11/16) Hyperbolic Matrix(439,-93,760,-161) (4/19,3/14) -> (15/26,11/19) Hyperbolic Matrix(199,-43,560,-121) (3/14,5/23) -> (6/17,5/14) Hyperbolic Matrix(1841,-402,2560,-559) (5/23,7/32) -> (23/32,41/57) Hyperbolic Matrix(201,-46,520,-119) (2/9,3/13) -> (5/13,12/31) Hyperbolic Matrix(159,-37,520,-121) (3/13,4/17) -> (7/23,4/13) Hyperbolic Matrix(41,-10,160,-39) (4/17,1/4) -> (1/4,6/23) Parabolic Matrix(401,-105,760,-199) (6/23,11/42) -> (1/2,9/17) Hyperbolic Matrix(2441,-640,3200,-839) (11/42,5/19) -> (45/59,29/38) Hyperbolic Matrix(841,-222,1360,-359) (5/19,4/15) -> (34/55,13/21) Hyperbolic Matrix(281,-76,440,-119) (4/15,3/11) -> (7/11,16/25) Hyperbolic Matrix(521,-144,720,-199) (3/11,5/18) -> (13/18,21/29) Hyperbolic Matrix(681,-190,1000,-279) (5/18,12/43) -> (2/3,15/22) Hyperbolic Matrix(1439,-402,3440,-961) (12/43,7/25) -> (23/55,18/43) Hyperbolic Matrix(241,-68,280,-79) (7/25,2/7) -> (6/7,13/15) Hyperbolic Matrix(159,-46,280,-81) (2/7,5/17) -> (13/23,4/7) Hyperbolic Matrix(121,-36,400,-119) (5/17,3/10) -> (3/10,7/23) Parabolic Matrix(521,-162,640,-199) (4/13,5/16) -> (13/16,22/27) Hyperbolic Matrix(519,-163,640,-201) (5/16,6/19) -> (17/21,13/16) Hyperbolic Matrix(721,-230,1000,-319) (6/19,1/3) -> (31/43,44/61) Hyperbolic Matrix(79,-27,120,-41) (1/3,7/20) -> (13/20,2/3) Hyperbolic Matrix(441,-155,680,-239) (7/20,6/17) -> (11/17,13/20) Hyperbolic Matrix(321,-116,440,-159) (5/14,4/11) -> (8/11,19/26) Hyperbolic Matrix(961,-351,1640,-599) (4/11,15/41) -> (24/41,17/29) Hyperbolic Matrix(399,-146,440,-161) (15/41,11/30) -> (9/10,1/1) Hyperbolic Matrix(881,-324,1520,-559) (11/30,7/19) -> (11/19,29/50) Hyperbolic Matrix(121,-45,320,-119) (7/19,3/8) -> (3/8,8/21) Parabolic Matrix(1001,-382,1360,-519) (8/21,13/34) -> (25/34,14/19) Hyperbolic Matrix(959,-372,1240,-481) (12/31,7/18) -> (17/22,24/31) Hyperbolic Matrix(81,-32,200,-79) (7/18,2/5) -> (2/5,9/22) Parabolic Matrix(1761,-721,2440,-999) (9/22,25/61) -> (44/61,13/18) Hyperbolic Matrix(7321,-3001,12000,-4919) (25/61,41/100) -> (61/100,36/59) Hyperbolic Matrix(4879,-2001,8000,-3281) (41/100,16/39) -> (25/41,61/100) Hyperbolic Matrix(961,-395,1360,-559) (16/39,7/17) -> (12/17,29/41) Hyperbolic Matrix(559,-231,680,-281) (7/17,12/29) -> (9/11,14/17) Hyperbolic Matrix(1041,-431,1640,-679) (12/29,17/41) -> (26/41,7/11) Hyperbolic Matrix(3599,-1493,4920,-2041) (17/41,22/53) -> (49/67,30/41) Hyperbolic Matrix(879,-365,1640,-681) (22/53,5/12) -> (15/28,7/13) Hyperbolic Matrix(921,-385,1720,-719) (5/12,23/55) -> (8/15,15/28) Hyperbolic Matrix(959,-402,1720,-721) (18/43,13/31) -> (5/9,24/43) Hyperbolic Matrix(961,-404,1520,-639) (13/31,8/19) -> (12/19,31/49) Hyperbolic Matrix(599,-253,760,-321) (8/19,11/26) -> (11/14,15/19) Hyperbolic Matrix(599,-254,1040,-441) (11/26,3/7) -> (19/33,15/26) Hyperbolic Matrix(199,-86,280,-121) (3/7,7/16) -> (17/24,5/7) Hyperbolic Matrix(1161,-509,1640,-719) (7/16,18/41) -> (29/41,17/24) Hyperbolic Matrix(1281,-563,2000,-879) (18/41,11/25) -> (16/25,25/39) Hyperbolic Matrix(1681,-741,2720,-1199) (11/25,15/34) -> (21/34,34/55) Hyperbolic Matrix(999,-442,1720,-761) (15/34,4/9) -> (18/31,43/74) Hyperbolic Matrix(199,-89,360,-161) (4/9,9/20) -> (11/20,5/9) Hyperbolic Matrix(241,-109,440,-199) (9/20,5/11) -> (6/11,11/20) Hyperbolic Matrix(359,-164,440,-201) (5/11,6/13) -> (22/27,9/11) Hyperbolic Matrix(959,-445,1640,-761) (6/13,13/28) -> (7/12,31/53) Hyperbolic Matrix(1239,-577,1720,-801) (13/28,7/15) -> (18/25,49/68) Hyperbolic Matrix(921,-431,1280,-599) (7/15,8/17) -> (41/57,18/25) Hyperbolic Matrix(519,-245,680,-321) (8/17,1/2) -> (29/38,13/17) Hyperbolic Matrix(521,-277,600,-319) (9/17,8/15) -> (13/15,20/23) Hyperbolic Matrix(359,-194,520,-281) (7/13,6/11) -> (20/29,9/13) Hyperbolic Matrix(4161,-2324,7160,-3999) (24/43,19/34) -> (43/74,68/117) Hyperbolic Matrix(999,-559,1360,-761) (19/34,14/25) -> (11/15,25/34) Hyperbolic Matrix(1201,-673,1640,-919) (14/25,23/41) -> (30/41,11/15) Hyperbolic Matrix(721,-405,1280,-719) (23/41,9/16) -> (9/16,22/39) Parabolic Matrix(1121,-633,1840,-1039) (22/39,13/23) -> (14/23,25/41) Hyperbolic Matrix(921,-529,1600,-919) (4/7,23/40) -> (23/40,19/33) Parabolic Matrix(679,-394,760,-441) (29/50,18/31) -> (8/9,9/10) Hyperbolic Matrix(14881,-8649,25600,-14879) (68/117,93/160) -> (93/160,25/43) Parabolic Matrix(2479,-1442,3440,-2001) (25/43,7/12) -> (49/68,31/43) Hyperbolic Matrix(2719,-1591,4240,-2481) (31/53,24/41) -> (25/39,34/53) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(1119,-683,1640,-1001) (36/59,11/18) -> (15/22,13/19) Hyperbolic Matrix(401,-246,520,-319) (11/18,8/13) -> (10/13,17/22) Hyperbolic Matrix(439,-271,520,-321) (8/13,21/34) -> (5/6,11/13) Hyperbolic Matrix(201,-125,320,-199) (13/21,5/8) -> (5/8,12/19) Parabolic Matrix(2281,-1444,3600,-2279) (31/49,19/30) -> (19/30,45/71) Parabolic Matrix(1959,-1258,2680,-1721) (34/53,9/14) -> (19/26,68/93) Hyperbolic Matrix(439,-283,560,-361) (9/14,11/17) -> (18/23,11/14) Hyperbolic Matrix(281,-196,400,-279) (9/13,7/10) -> (7/10,19/27) Parabolic Matrix(521,-367,680,-479) (19/27,12/17) -> (13/17,10/13) Hyperbolic Matrix(1161,-841,1600,-1159) (21/29,29/40) -> (29/40,8/11) Parabolic Matrix(18721,-13689,25600,-18719) (68/93,117/160) -> (117/160,49/67) Parabolic Matrix(121,-90,160,-119) (14/19,3/4) -> (3/4,16/21) Parabolic Matrix(4881,-3721,6400,-4879) (16/21,61/80) -> (61/80,45/59) Parabolic Matrix(1241,-961,1600,-1239) (24/31,31/40) -> (31/40,7/9) Parabolic Matrix(319,-249,360,-281) (7/9,25/32) -> (7/8,8/9) Hyperbolic Matrix(801,-626,920,-719) (25/32,18/23) -> (20/23,7/8) Hyperbolic Matrix(161,-128,200,-159) (15/19,4/5) -> (4/5,17/21) Parabolic Matrix(1321,-1089,1600,-1319) (14/17,33/40) -> (33/40,19/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-38,1) Matrix(279,-26,440,-41) -> Matrix(11,3,-268,-73) Matrix(79,-9,360,-41) -> Matrix(23,5,-198,-43) Matrix(201,-28,280,-39) -> Matrix(17,3,-448,-79) Matrix(239,-35,280,-41) -> Matrix(29,5,-934,-161) Matrix(441,-67,520,-79) -> Matrix(55,9,-1754,-287) Matrix(199,-31,520,-81) -> Matrix(19,3,-298,-47) Matrix(199,-34,240,-41) -> Matrix(27,4,-844,-125) Matrix(399,-71,680,-121) -> Matrix(7,1,-190,-27) Matrix(441,-82,640,-119) -> Matrix(15,2,-368,-49) Matrix(41,-8,200,-39) -> Matrix(23,3,-192,-25) Matrix(521,-109,760,-159) -> Matrix(9,1,-226,-25) Matrix(439,-93,760,-161) -> Matrix(25,3,-542,-65) Matrix(199,-43,560,-121) -> Matrix(1,0,-6,1) Matrix(1841,-402,2560,-559) -> Matrix(67,8,-1784,-213) Matrix(201,-46,520,-119) -> Matrix(9,1,-172,-19) Matrix(159,-37,520,-121) -> Matrix(29,3,-358,-37) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) Matrix(401,-105,760,-199) -> Matrix(11,1,-210,-19) Matrix(2441,-640,3200,-839) -> Matrix(23,2,-656,-57) Matrix(841,-222,1360,-359) -> Matrix(1,0,-12,1) Matrix(281,-76,440,-119) -> Matrix(11,1,-232,-21) Matrix(521,-144,720,-199) -> Matrix(89,8,-2392,-215) Matrix(681,-190,1000,-279) -> Matrix(57,5,-1448,-127) Matrix(1439,-402,3440,-961) -> Matrix(23,2,-380,-33) Matrix(241,-68,280,-79) -> Matrix(35,3,-1132,-97) Matrix(159,-46,280,-81) -> Matrix(11,1,-232,-21) Matrix(121,-36,400,-119) -> Matrix(47,4,-576,-49) Matrix(521,-162,640,-199) -> Matrix(27,2,-824,-61) Matrix(519,-163,640,-201) -> Matrix(23,2,-702,-61) Matrix(721,-230,1000,-319) -> Matrix(63,5,-1676,-133) Matrix(79,-27,120,-41) -> Matrix(13,1,-326,-25) Matrix(441,-155,680,-239) -> Matrix(71,5,-1690,-119) Matrix(321,-116,440,-159) -> Matrix(17,1,-460,-27) Matrix(961,-351,1640,-599) -> Matrix(13,1,-326,-25) Matrix(399,-146,440,-161) -> Matrix(41,3,-1408,-103) Matrix(881,-324,1520,-559) -> Matrix(29,2,-624,-43) Matrix(121,-45,320,-119) -> Matrix(29,2,-450,-31) Matrix(1001,-382,1360,-519) -> Matrix(1,0,-12,1) Matrix(959,-372,1240,-481) -> Matrix(7,1,-204,-29) Matrix(81,-32,200,-79) -> Matrix(15,1,-256,-17) Matrix(1761,-721,2440,-999) -> Matrix(123,7,-3286,-187) Matrix(7321,-3001,12000,-4919) -> Matrix(179,10,-4314,-241) Matrix(4879,-2001,8000,-3281) -> Matrix(145,8,-3462,-191) Matrix(961,-395,1360,-559) -> Matrix(39,2,-1034,-53) Matrix(559,-231,680,-281) -> Matrix(11,1,-342,-31) Matrix(1041,-431,1640,-679) -> Matrix(13,1,-326,-25) Matrix(3599,-1493,4920,-2041) -> Matrix(163,11,-4490,-303) Matrix(879,-365,1640,-681) -> Matrix(15,1,-346,-23) Matrix(921,-385,1720,-719) -> Matrix(17,1,-358,-21) Matrix(959,-402,1720,-721) -> Matrix(15,1,-316,-21) Matrix(961,-404,1520,-639) -> Matrix(33,2,-776,-47) Matrix(599,-253,760,-321) -> Matrix(49,3,-1454,-89) Matrix(599,-254,1040,-441) -> Matrix(67,4,-1424,-85) Matrix(199,-86,280,-121) -> Matrix(17,1,-460,-27) Matrix(1161,-509,1640,-719) -> Matrix(11,1,-298,-27) Matrix(1281,-563,2000,-879) -> Matrix(31,2,-698,-45) Matrix(1681,-741,2720,-1199) -> Matrix(1,0,-6,1) Matrix(999,-442,1720,-761) -> Matrix(17,1,-392,-23) Matrix(199,-89,360,-161) -> Matrix(17,1,-358,-21) Matrix(241,-109,440,-199) -> Matrix(19,1,-362,-19) Matrix(359,-164,440,-201) -> Matrix(17,1,-528,-31) Matrix(959,-445,1640,-761) -> Matrix(15,1,-346,-23) Matrix(1239,-577,1720,-801) -> Matrix(15,1,-406,-27) Matrix(921,-431,1280,-599) -> Matrix(39,2,-1034,-53) Matrix(519,-245,680,-321) -> Matrix(17,1,-494,-29) Matrix(521,-277,600,-319) -> Matrix(17,1,-562,-33) Matrix(359,-194,520,-281) -> Matrix(19,1,-476,-25) Matrix(4161,-2324,7160,-3999) -> Matrix(21,1,-568,-27) Matrix(999,-559,1360,-761) -> Matrix(1,0,-6,1) Matrix(1201,-673,1640,-919) -> Matrix(67,3,-1854,-83) Matrix(721,-405,1280,-719) -> Matrix(1,0,6,1) Matrix(1121,-633,1840,-1039) -> Matrix(37,2,-870,-47) Matrix(921,-529,1600,-919) -> Matrix(125,6,-2646,-127) Matrix(679,-394,760,-441) -> Matrix(67,3,-2256,-101) Matrix(14881,-8649,25600,-14879) -> Matrix(1,0,14,1) Matrix(2479,-1442,3440,-2001) -> Matrix(43,2,-1140,-53) Matrix(2719,-1591,4240,-2481) -> Matrix(139,6,-3174,-137) Matrix(121,-72,200,-119) -> Matrix(21,1,-484,-23) Matrix(1119,-683,1640,-1001) -> Matrix(73,3,-1874,-77) Matrix(401,-246,520,-319) -> Matrix(19,1,-552,-29) Matrix(439,-271,520,-321) -> Matrix(67,3,-2122,-95) Matrix(201,-125,320,-199) -> Matrix(45,2,-1058,-47) Matrix(2281,-1444,3600,-2279) -> Matrix(191,8,-4608,-193) Matrix(1959,-1258,2680,-1721) -> Matrix(209,9,-5736,-247) Matrix(439,-283,560,-361) -> Matrix(1,0,-6,1) Matrix(281,-196,400,-279) -> Matrix(103,4,-2704,-105) Matrix(521,-367,680,-479) -> Matrix(27,1,-730,-27) Matrix(1161,-841,1600,-1159) -> Matrix(485,18,-13122,-487) Matrix(18721,-13689,25600,-18719) -> Matrix(3739,136,-102850,-3741) Matrix(121,-90,160,-119) -> Matrix(55,2,-1568,-57) Matrix(4881,-3721,6400,-4879) -> Matrix(227,8,-6498,-229) Matrix(1241,-961,1600,-1239) -> Matrix(637,22,-18502,-639) Matrix(319,-249,360,-281) -> Matrix(147,5,-4910,-167) Matrix(801,-626,920,-719) -> Matrix(207,7,-6772,-229) Matrix(161,-128,200,-159) -> Matrix(89,3,-2700,-91) Matrix(1321,-1089,1600,-1319) -> Matrix(805,26,-24986,-807) 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): 96 ----------------------------------------------------------------------- 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 40 1/9 -5/22 1 40 1/8 -1/5 6 5 1/7 -1/6 1 40 3/20 -1/6 14 2 2/13 -9/56 1 40 1/6 (-2/13,-1/7) 0 20 7/40 -1/7 26 1 3/17 -11/78 1 40 2/11 -1/8 1 40 3/16 -2/15 2 5 1/5 -1/8 3 8 5/24 -1/9 2 5 4/19 -1/8 1 40 3/14 (-2/17,-1/9) 0 20 5/23 -5/42 1 40 7/32 -2/17 6 5 2/9 -5/44 1 40 3/13 -7/66 1 40 4/17 -3/28 1 40 1/4 -1/10 2 10 6/23 -1/12 1 40 11/42 (-1/11,0/1) 0 20 21/80 0/1 2 1 5/19 -1/10 1 40 4/15 -1/10 3 8 3/11 -5/54 1 40 11/40 -1/11 18 1 5/18 (-1/11,-4/45) 0 20 12/43 -7/80 1 40 7/25 -3/34 1 8 16/57 -1/12 1 40 9/32 -2/23 6 5 2/7 -1/12 1 40 5/17 -5/58 1 40 3/10 -1/12 4 4 7/23 -3/38 1 40 4/13 -5/64 1 40 5/16 0/1 2 5 6/19 -1/12 1 40 7/22 (-3/37,-2/25) 0 20 1/3 -1/14 1 40 7/20 -1/14 6 2 6/17 -5/72 1 40 5/14 (-2/29,-1/15) 0 20 43/120 -1/15 34 1 19/53 -15/226 1 40 14/39 -11/168 1 40 9/25 -1/16 3 8 4/11 -1/12 1 40 15/41 -11/150 1 40 11/30 -1/14 8 4 7/19 -1/14 1 40 3/8 -1/15 2 5 8/21 -1/16 1 40 21/55 -1/16 3 8 13/34 (-1/15,-2/31) 0 20 5/13 -3/50 1 40 12/31 -1/24 1 40 31/80 0/1 22 1 7/18 (-1/13,0/1) 0 20 2/5 -1/16 1 8 9/22 (-1/17,-2/35) 0 20 25/61 -1/18 1 40 41/100 -1/18 18 2 16/39 -7/128 1 40 7/17 -1/22 1 40 12/29 -1/12 1 40 17/41 -7/102 1 40 22/53 -9/136 1 40 5/12 -1/16 2 10 23/55 -1/18 1 8 18/43 -1/20 1 40 13/31 -1/14 1 40 34/81 -13/204 1 40 21/50 -1/16 8 4 8/19 -1/16 1 40 11/26 (-2/33,-1/17) 0 20 17/40 -1/17 6 1 3/7 -1/18 1 40 10/23 -3/56 1 40 17/39 -5/102 1 40 7/16 0/1 6 5 18/41 -5/72 1 40 11/25 -1/16 3 8 15/34 (-2/33,-1/17) 0 20 53/120 -1/17 14 1 19/43 -5/86 1 40 4/9 -1/16 1 40 9/20 -1/18 2 2 5/11 -1/18 1 40 11/24 -1/19 2 5 6/13 -1/24 1 40 13/28 -1/16 2 10 7/15 -1/18 1 8 8/17 -1/20 1 40 1/2 (-1/19,0/1) 0 20 1/0 0/1 38 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(319,-34,760,-81) (0/1,1/9) -> (13/31,34/81) Hyperbolic Matrix(79,-9,360,-41) (1/9,1/8) -> (7/32,2/9) Hyperbolic Matrix(79,-11,280,-39) (1/8,1/7) -> (9/32,2/7) Glide Reflection Matrix(41,-6,280,-41) (1/7,3/20) -> (1/7,3/20) Reflection Matrix(79,-12,520,-79) (3/20,2/13) -> (3/20,2/13) Reflection Matrix(199,-31,520,-81) (2/13,1/6) -> (13/34,5/13) Hyperbolic Matrix(41,-7,240,-41) (1/6,7/40) -> (1/6,7/40) Reflection Matrix(239,-42,1360,-239) (7/40,3/17) -> (7/40,3/17) Reflection Matrix(281,-50,680,-121) (3/17,2/11) -> (7/17,12/29) Glide Reflection Matrix(201,-37,440,-81) (2/11,3/16) -> (5/11,11/24) Glide Reflection Matrix(41,-8,200,-39) (3/16,1/5) -> (1/5,5/24) Parabolic Matrix(239,-50,760,-159) (5/24,4/19) -> (5/16,6/19) Glide Reflection Matrix(321,-68,760,-161) (4/19,3/14) -> (8/19,11/26) Glide Reflection Matrix(199,-43,560,-121) (3/14,5/23) -> (6/17,5/14) Hyperbolic Matrix(719,-157,2560,-559) (5/23,7/32) -> (16/57,9/32) Glide Reflection Matrix(201,-46,520,-119) (2/9,3/13) -> (5/13,12/31) Hyperbolic Matrix(159,-37,520,-121) (3/13,4/17) -> (7/23,4/13) Hyperbolic Matrix(41,-10,160,-39) (4/17,1/4) -> (1/4,6/23) Parabolic Matrix(359,-94,760,-199) (6/23,11/42) -> (8/17,1/2) Glide Reflection Matrix(881,-231,3360,-881) (11/42,21/80) -> (11/42,21/80) Reflection Matrix(799,-210,3040,-799) (21/80,5/19) -> (21/80,5/19) Reflection Matrix(519,-137,1360,-359) (5/19,4/15) -> (8/21,21/55) Glide Reflection Matrix(159,-43,440,-119) (4/15,3/11) -> (9/25,4/11) Glide Reflection Matrix(241,-66,880,-241) (3/11,11/40) -> (3/11,11/40) Reflection Matrix(199,-55,720,-199) (11/40,5/18) -> (11/40,5/18) Reflection Matrix(319,-89,1000,-279) (5/18,12/43) -> (7/22,1/3) Glide Reflection Matrix(1439,-402,3440,-961) (12/43,7/25) -> (23/55,18/43) Hyperbolic Matrix(599,-168,1280,-359) (7/25,16/57) -> (7/15,8/17) Glide Reflection Matrix(121,-35,280,-81) (2/7,5/17) -> (3/7,10/23) Glide Reflection Matrix(121,-36,400,-119) (5/17,3/10) -> (3/10,7/23) Parabolic Matrix(239,-74,520,-161) (4/13,5/16) -> (11/24,6/13) Hyperbolic Matrix(721,-229,1760,-559) (6/19,7/22) -> (9/22,25/61) Hyperbolic Matrix(41,-14,120,-41) (1/3,7/20) -> (1/3,7/20) Reflection Matrix(239,-84,680,-239) (7/20,6/17) -> (7/20,6/17) Reflection Matrix(601,-215,1680,-601) (5/14,43/120) -> (5/14,43/120) Reflection Matrix(4559,-1634,12720,-4559) (43/120,19/53) -> (43/120,19/53) Reflection Matrix(1759,-631,4240,-1521) (19/53,14/39) -> (17/41,22/53) Hyperbolic Matrix(879,-316,2000,-719) (14/39,9/25) -> (18/41,11/25) Glide Reflection Matrix(679,-248,1640,-599) (4/11,15/41) -> (12/29,17/41) Glide Reflection Matrix(1881,-689,4480,-1641) (15/41,11/30) -> (34/81,21/50) Glide Reflection Matrix(639,-235,1520,-559) (11/30,7/19) -> (21/50,8/19) Glide Reflection Matrix(121,-45,320,-119) (7/19,3/8) -> (3/8,8/21) Parabolic Matrix(1199,-458,2720,-1039) (21/55,13/34) -> (11/25,15/34) Glide Reflection Matrix(1921,-744,4960,-1921) (12/31,31/80) -> (12/31,31/80) Reflection Matrix(559,-217,1440,-559) (31/80,7/18) -> (31/80,7/18) Reflection Matrix(81,-32,200,-79) (7/18,2/5) -> (2/5,9/22) Parabolic Matrix(5001,-2050,12200,-5001) (25/61,41/100) -> (25/61,41/100) Reflection Matrix(3199,-1312,7800,-3199) (41/100,16/39) -> (41/100,16/39) Reflection Matrix(679,-279,1560,-641) (16/39,7/17) -> (10/23,17/39) Hyperbolic Matrix(761,-316,1640,-681) (22/53,5/12) -> (6/13,13/28) Glide Reflection Matrix(799,-334,1720,-719) (5/12,23/55) -> (13/28,7/15) Glide Reflection Matrix(761,-319,1720,-721) (18/43,13/31) -> (19/43,4/9) Glide Reflection Matrix(441,-187,1040,-441) (11/26,17/40) -> (11/26,17/40) Reflection Matrix(239,-102,560,-239) (17/40,3/7) -> (17/40,3/7) Reflection Matrix(561,-245,1280,-559) (17/39,7/16) -> (7/16,18/41) Parabolic Matrix(1801,-795,4080,-1801) (15/34,53/120) -> (15/34,53/120) Reflection Matrix(4559,-2014,10320,-4559) (53/120,19/43) -> (53/120,19/43) Reflection Matrix(161,-72,360,-161) (4/9,9/20) -> (4/9,9/20) Reflection Matrix(199,-90,440,-199) (9/20,5/11) -> (9/20,5/11) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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(319,-34,760,-81) -> Matrix(13,3,-204,-47) Matrix(79,-9,360,-41) -> Matrix(23,5,-198,-43) Matrix(79,-11,280,-39) -> Matrix(17,3,-198,-35) Matrix(41,-6,280,-41) -> Matrix(29,5,-168,-29) (1/7,3/20) -> (-5/28,-1/6) Matrix(79,-12,520,-79) -> Matrix(55,9,-336,-55) (3/20,2/13) -> (-1/6,-9/56) Matrix(199,-31,520,-81) -> Matrix(19,3,-298,-47) Matrix(41,-7,240,-41) -> Matrix(27,4,-182,-27) (1/6,7/40) -> (-2/13,-1/7) Matrix(239,-42,1360,-239) -> Matrix(155,22,-1092,-155) (7/40,3/17) -> (-1/7,-11/78) Matrix(281,-50,680,-121) -> Matrix(7,1,-76,-11) Matrix(201,-37,440,-81) -> Matrix(7,1,-118,-17) Matrix(41,-8,200,-39) -> Matrix(23,3,-192,-25) -1/8 Matrix(239,-50,760,-159) -> Matrix(9,1,-116,-13) Matrix(321,-68,760,-161) -> Matrix(25,3,-408,-49) Matrix(199,-43,560,-121) -> Matrix(1,0,-6,1) 0/1 Matrix(719,-157,2560,-559) -> Matrix(67,8,-762,-91) Matrix(201,-46,520,-119) -> Matrix(9,1,-172,-19) Matrix(159,-37,520,-121) -> Matrix(29,3,-358,-37) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) -1/10 Matrix(359,-94,760,-199) -> Matrix(11,1,-208,-19) Matrix(881,-231,3360,-881) -> Matrix(-1,0,22,1) (11/42,21/80) -> (-1/11,0/1) Matrix(799,-210,3040,-799) -> Matrix(-1,0,20,1) (21/80,5/19) -> (-1/10,0/1) Matrix(519,-137,1360,-359) -> Matrix(-1,0,26,1) *** -> (-1/13,0/1) Matrix(159,-43,440,-119) -> Matrix(11,1,-186,-17) Matrix(241,-66,880,-241) -> Matrix(109,10,-1188,-109) (3/11,11/40) -> (-5/54,-1/11) Matrix(199,-55,720,-199) -> Matrix(89,8,-990,-89) (11/40,5/18) -> (-1/11,-4/45) Matrix(319,-89,1000,-279) -> Matrix(57,5,-718,-63) Matrix(1439,-402,3440,-961) -> Matrix(23,2,-380,-33) Matrix(599,-168,1280,-359) -> Matrix(23,2,-448,-39) Matrix(121,-35,280,-81) -> Matrix(11,1,-186,-17) Matrix(121,-36,400,-119) -> Matrix(47,4,-576,-49) -1/12 Matrix(239,-74,520,-161) -> Matrix(13,1,-248,-19) Matrix(721,-229,1760,-559) -> Matrix(49,4,-870,-71) Matrix(41,-14,120,-41) -> Matrix(13,1,-168,-13) (1/3,7/20) -> (-1/12,-1/14) Matrix(239,-84,680,-239) -> Matrix(71,5,-1008,-71) (7/20,6/17) -> (-1/14,-5/72) Matrix(601,-215,1680,-601) -> Matrix(59,4,-870,-59) (5/14,43/120) -> (-2/29,-1/15) Matrix(4559,-1634,12720,-4559) -> Matrix(451,30,-6780,-451) (43/120,19/53) -> (-1/15,-15/226) Matrix(1759,-631,4240,-1521) -> Matrix(91,6,-1350,-89) -1/15 Matrix(879,-316,2000,-719) -> Matrix(31,2,-480,-31) *** -> (-1/15,-1/16) Matrix(679,-248,1640,-599) -> Matrix(13,1,-168,-13) *** -> (-1/12,-1/14) Matrix(1881,-689,4480,-1641) -> Matrix(83,6,-1314,-95) Matrix(639,-235,1520,-559) -> Matrix(29,2,-478,-33) Matrix(121,-45,320,-119) -> Matrix(29,2,-450,-31) -1/15 Matrix(1199,-458,2720,-1039) -> Matrix(-1,0,32,1) *** -> (-1/16,0/1) Matrix(1921,-744,4960,-1921) -> Matrix(-1,0,48,1) (12/31,31/80) -> (-1/24,0/1) Matrix(559,-217,1440,-559) -> Matrix(-1,0,26,1) (31/80,7/18) -> (-1/13,0/1) Matrix(81,-32,200,-79) -> Matrix(15,1,-256,-17) -1/16 Matrix(5001,-2050,12200,-5001) -> Matrix(197,11,-3528,-197) (25/61,41/100) -> (-11/196,-1/18) Matrix(3199,-1312,7800,-3199) -> Matrix(127,7,-2304,-127) (41/100,16/39) -> (-1/18,-7/128) Matrix(679,-279,1560,-641) -> Matrix(19,1,-362,-19) (-1/18,-1/20).(-1/19,0/1) Matrix(761,-316,1640,-681) -> Matrix(15,1,-224,-15) *** -> (-1/14,-1/16) Matrix(799,-334,1720,-719) -> Matrix(17,1,-288,-17) *** -> (-1/16,-1/18) Matrix(761,-319,1720,-721) -> Matrix(15,1,-254,-17) Matrix(441,-187,1040,-441) -> Matrix(67,4,-1122,-67) (11/26,17/40) -> (-2/33,-1/17) Matrix(239,-102,560,-239) -> Matrix(35,2,-612,-35) (17/40,3/7) -> (-1/17,-1/18) Matrix(561,-245,1280,-559) -> Matrix(1,0,6,1) 0/1 Matrix(1801,-795,4080,-1801) -> Matrix(67,4,-1122,-67) (15/34,53/120) -> (-2/33,-1/17) Matrix(4559,-2014,10320,-4559) -> Matrix(171,10,-2924,-171) (53/120,19/43) -> (-1/17,-5/86) Matrix(161,-72,360,-161) -> Matrix(17,1,-288,-17) (4/9,9/20) -> (-1/16,-1/18) Matrix(199,-90,440,-199) -> Matrix(19,1,-360,-19) (9/20,5/11) -> (-1/18,-1/20) Matrix(-1,1,0,1) -> Matrix(-1,0,38,1) (1/2,1/0) -> (-1/19,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.