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 -10/1 -8/1 -15/2 -22/3 -20/3 -32/5 -6/1 -28/5 -16/3 -5/1 -24/5 -14/3 -32/7 -30/7 -4/1 -15/4 -26/7 -18/5 -24/7 -10/3 -36/11 -20/7 -25/9 -36/13 -30/11 -8/3 -34/13 -44/17 -100/39 -5/2 -12/5 -16/7 -20/9 -15/7 -2/1 -28/15 -20/11 -30/17 -12/7 -100/59 -5/3 -30/19 -20/13 -10/7 -4/3 -5/4 -20/17 -10/9 0/1 1/1 10/9 20/17 5/4 4/3 10/7 3/2 20/13 30/19 5/3 100/59 12/7 30/17 20/11 28/15 2/1 15/7 20/9 120/53 16/7 40/17 160/67 12/5 80/33 5/2 100/39 80/31 44/17 8/3 30/11 25/9 120/43 20/7 3/1 10/3 200/59 24/7 7/2 18/5 40/11 11/3 160/43 15/4 34/9 4/1 80/19 30/7 13/3 520/119 40/9 9/2 32/7 14/3 80/17 24/5 5/1 16/3 38/7 11/2 28/5 17/3 40/7 6/1 19/3 32/5 13/2 20/3 7/1 80/11 22/3 15/2 38/5 8/1 17/2 26/3 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/2 -19/2 -1/3 -2/7 -9/1 -1/5 0/1 -17/2 -2/5 -1/3 -8/1 -1/3 -23/3 -1/3 0/1 -15/2 -1/4 -22/3 -1/6 -7/1 -1/3 -2/7 -20/3 -1/4 -13/2 -3/13 -2/9 -32/5 -2/9 -19/3 -6/29 -1/5 -25/4 -1/6 -6/1 -1/4 -17/3 -1/5 -6/31 -28/5 -3/16 -11/2 -2/11 -3/17 -16/3 0/1 -21/4 -1/5 0/1 -5/1 -1/6 -24/5 -1/7 -43/9 -1/9 0/1 -19/4 -2/13 -1/7 -71/15 -1/5 0/1 -52/11 -1/8 -33/7 -1/9 0/1 -14/3 -1/6 -23/5 -5/31 -4/25 -32/7 -2/13 -41/9 -2/13 -1/7 -9/2 -4/27 -1/7 -22/5 -5/36 -13/3 -5/37 -2/15 -43/10 -4/31 -5/39 -30/7 -1/8 -17/4 -1/7 -2/15 -4/1 -1/8 -23/6 -1/9 0/1 -42/11 -1/8 -19/5 -2/17 -1/9 -15/4 -1/8 -41/11 -3/25 -2/17 -67/18 -27/229 -2/17 -26/7 -7/60 -63/17 -11/95 -14/121 -37/10 -7/61 -4/35 -48/13 -4/35 -11/3 -6/53 -1/9 -18/5 -5/46 -61/17 -1/9 -2/19 -43/12 -9/83 -4/37 -25/7 -3/28 -32/9 -2/19 -39/11 -2/19 -3/29 -7/2 -1/9 -2/19 -38/11 -1/10 -31/9 -2/21 -1/11 -55/16 -1/10 -24/7 -1/9 -41/12 -1/9 -2/19 -17/5 -2/19 -7/67 -10/3 -1/10 -23/7 -4/41 -11/113 -59/18 -3/31 -32/331 -36/11 -5/52 -13/4 -2/21 -1/11 -16/5 -2/21 -19/6 -2/21 -1/11 -22/7 -1/10 -25/8 -3/32 -3/1 -1/11 -2/23 -20/7 -1/12 -37/13 -13/157 -12/145 -17/6 -7/85 -6/73 -14/5 -1/12 -53/19 -3/37 -8/99 -39/14 -2/25 -1/13 -25/9 -1/12 -61/22 -22/271 -3/37 -36/13 -5/62 -47/17 -7/87 -16/199 -58/21 -13/162 -11/4 -2/25 -5/63 -52/19 -1/12 -41/15 -2/25 -5/63 -30/11 -3/38 -19/7 -2/25 -1/13 -8/3 -1/13 -21/8 -1/13 -4/53 -34/13 -5/66 -81/31 -1/13 -4/53 -47/18 -4/53 -7/93 -13/5 -1/13 -2/27 -44/17 -7/94 -119/46 -9/121 -2/27 -75/29 -7/94 -31/12 -17/229 -2/27 -18/7 -5/68 -59/23 -3/41 -4/55 -100/39 -1/14 -41/16 -1/13 -2/27 -23/9 -8/109 -3/41 -28/11 -1/14 -33/13 -4/55 -5/69 -5/2 -1/14 -32/13 -4/57 -27/11 -5/71 -4/57 -22/9 -5/72 -61/25 -3/43 -2/29 -100/41 -5/72 -39/16 -3/43 -2/29 -17/7 -11/159 -2/29 -46/19 -15/218 -75/31 -11/160 -29/12 -12/175 -5/73 -99/41 -5/73 -18/263 -70/29 -3/44 -41/17 -2/29 -9/131 -53/22 -5/73 -8/117 -12/5 -3/44 -67/28 -2/29 -1/15 -55/23 -3/44 -43/18 -15/221 -4/59 -74/31 -13/192 -105/44 -5/74 -31/13 -6/89 -1/15 -19/8 -6/89 -1/15 -45/19 -7/104 -71/30 -8/119 -33/491 -26/11 -11/164 -7/3 -1/15 -6/91 -44/19 -3/46 -37/16 -1/15 -4/61 -30/13 -3/46 -23/10 -8/123 -5/77 -39/17 -9/139 -2/31 -16/7 -2/31 -41/18 -2/31 -3/47 -25/11 -5/78 -34/15 -11/172 -43/19 -3/47 -28/439 -52/23 -7/110 -9/4 -4/63 -5/79 -20/9 -1/16 -31/14 -14/225 -13/209 -42/19 -1/16 -11/5 -6/97 -5/81 -24/11 -3/49 -37/17 -8/131 -13/213 -13/6 -11/181 -2/33 -41/19 -2/33 -13/215 -28/13 -7/116 -43/20 -5/83 -28/465 -15/7 -3/50 -17/8 -11/185 -6/101 -2/1 -1/18 -19/10 -1/19 -18/343 -17/9 -6/115 -11/211 -15/8 -3/58 -43/23 -28/543 -5/97 -28/15 -7/136 -13/7 -2/39 -11/215 -37/20 -13/255 -8/157 -24/13 -3/59 -35/19 -7/138 -11/6 -5/99 -6/119 -20/11 -1/20 -29/16 -13/261 -12/241 -38/21 -1/20 -9/5 -5/101 -4/81 -52/29 -7/142 -43/24 -28/569 -3/61 -120/67 -3/61 -77/43 -3/61 -50/1017 -34/19 -11/224 -25/14 -5/102 -41/23 -3/61 -2/41 -16/9 -2/41 -39/22 -2/41 -9/185 -23/13 -5/103 -8/165 -30/17 -3/62 -37/21 -4/83 -1/21 -7/4 -6/125 -1/21 -40/23 -1/21 -33/19 -1/21 -28/589 -26/15 -11/232 -71/41 -33/697 -8/169 -45/26 -7/148 -19/11 -1/21 -6/127 -50/29 -5/106 -81/47 -1/21 -4/85 -31/18 -1/21 -6/127 -74/43 -13/276 -117/68 -41/871 -4/85 -160/93 -4/85 -43/25 -4/85 -15/319 -12/7 -3/64 -53/31 -8/171 -5/107 -41/24 -9/193 -2/43 -70/41 -3/64 -99/58 -18/385 -5/107 -29/17 -5/107 -12/257 -75/44 -11/236 -121/71 -13/279 -2/43 -46/27 -15/322 -63/37 -41/881 -2/43 -80/47 -2/43 -17/10 -2/43 -11/237 -39/23 -2/43 -3/65 -100/59 -5/108 -61/36 -2/43 -3/65 -22/13 -5/108 -5/3 -1/22 -38/23 -1/22 -33/20 -5/111 -4/89 -28/17 -1/22 -23/14 -3/67 -8/179 -41/25 -2/45 -1/23 -100/61 -1/22 -59/36 -4/89 -3/67 -18/11 -5/112 -49/30 -27/607 -2/45 -80/49 -2/45 -31/19 -2/45 -17/383 -75/46 -7/158 -119/73 -2/45 -9/203 -163/100 -2/45 -5/113 -44/27 -7/158 -13/8 -2/45 -1/23 -60/37 -3/68 -47/29 -7/159 -4/91 -81/50 -4/91 -1/23 -115/71 -3/68 -34/21 -5/114 -55/34 -3/68 -21/13 -4/91 -1/23 -8/5 -1/23 -19/12 -1/23 -2/47 -49/31 -1/23 -2/47 -30/19 -3/70 -71/45 -8/187 -5/117 -41/26 -5/117 -2/47 -11/7 -5/117 -2/47 -47/30 -16/377 -7/165 -83/53 -2/47 -7/165 -119/76 -2/47 -3/71 -36/23 -5/118 -61/39 -3/71 -22/521 -25/16 -1/24 -39/25 -1/23 -2/47 -53/34 -8/189 -3/71 -120/77 -3/71 -67/43 -3/71 -10/237 -14/9 -1/24 -17/11 -6/143 -7/167 -20/13 -1/24 -23/15 -8/193 -7/169 -3/2 -2/49 -1/25 -22/15 -1/26 -19/13 -1/25 -2/51 -16/11 -2/51 -29/20 -4/103 -5/129 -42/29 -1/26 -55/38 -1/26 -13/9 -1/25 -2/51 -10/7 -1/26 -27/19 -5/131 -4/105 -44/31 -7/184 -61/43 -34/895 -3/79 -200/141 -3/79 -139/98 -3/79 -80/2107 -78/55 -23/606 -17/12 -7/185 -2/53 -41/29 -2/53 -1/27 -65/46 -3/80 -24/17 -1/27 -55/39 -1/26 -31/22 -1/25 -2/51 -38/27 -1/26 -45/32 -1/26 -7/5 -2/53 -1/27 -39/28 -3/79 -2/53 -32/23 -2/53 -57/41 -19/505 -12/319 -25/18 -3/80 -93/67 -10/267 -7/187 -68/49 -3/80 -43/31 -4/107 -9/241 -61/44 -2/53 -1/27 -18/13 -5/134 -29/21 -16/431 -1/27 -40/29 -1/27 -11/8 -1/27 -6/163 -59/43 -1/27 0/1 -48/35 -4/109 -85/62 -3/82 -122/89 -3/82 -159/116 -1/27 -4/109 -37/27 -4/109 -7/191 -63/46 -14/383 -11/301 -89/65 -27/739 -8/219 -26/19 -7/192 -93/68 -41/1127 -2/55 -160/117 -2/55 -67/49 -2/55 -27/743 -41/30 -2/55 -3/83 -56/41 -3/83 -15/11 -1/28 -34/25 -3/82 -19/14 -1/27 -2/55 -4/3 -1/28 -21/16 -1/29 0/1 -80/61 0/1 -59/45 -1/27 0/1 -38/29 -1/28 -55/42 -1/28 -17/13 -2/57 -1/29 -30/23 -1/28 -43/33 -5/141 -4/113 -13/10 -2/57 -5/143 -48/37 -2/57 -83/64 -2/57 -1/29 -201/155 -2/57 -5/143 -520/401 -5/143 -319/246 -5/143 -8/229 -118/91 -3/86 -35/27 -3/86 -22/17 -5/144 -31/24 -14/405 -1/29 -40/31 -1/29 -9/7 -1/29 -4/117 -41/32 -1/29 -2/59 -32/25 -2/59 -55/43 -5/148 -23/18 -4/119 -5/149 -14/11 -1/30 -47/37 -1/33 0/1 -80/63 0/1 -33/26 -1/27 0/1 -52/41 -1/28 -71/56 -1/31 0/1 -19/15 -1/29 -2/59 -43/34 -1/27 0/1 -24/19 -1/29 -29/23 -8/235 -5/147 -5/4 -1/30 -21/17 -1/31 0/1 -16/13 0/1 -27/22 -1/29 0/1 -65/53 -1/30 -38/31 -1/30 -11/9 -3/91 -2/61 -39/32 -3/91 -2/61 -67/55 -2/61 -21/641 -28/23 -3/92 -17/14 -6/185 -1/31 -40/33 -1/31 -23/19 -1/31 -8/249 -6/5 -1/32 -31/26 -1/29 -2/59 -25/21 -1/30 -19/16 -1/31 -6/187 -51/43 -1/31 0/1 -32/27 -2/63 -13/11 -2/63 -3/95 -20/17 -1/32 -27/23 -4/129 -3/97 -7/6 -2/65 -1/33 -29/25 -1/39 0/1 -80/69 0/1 -51/44 -1/21 0/1 -22/19 -1/30 -37/32 -4/123 -1/31 -15/13 -1/32 -38/33 -1/32 -23/20 -1/33 0/1 -8/7 -1/33 -17/15 -1/33 -2/67 -26/23 -3/104 -9/8 -1/31 0/1 -19/17 -2/65 -1/33 -10/9 -1/34 -1/1 -1/37 0/1 0/1 0/1 1/1 0/1 1/39 10/9 1/36 19/17 1/35 2/69 9/8 0/1 1/33 17/15 2/71 1/35 8/7 1/35 23/20 0/1 1/35 15/13 1/34 22/19 1/32 7/6 1/35 2/69 20/17 1/34 13/11 3/101 2/67 32/27 2/67 19/16 6/199 1/33 25/21 1/32 6/5 1/34 17/14 1/33 6/197 28/23 3/98 11/9 2/65 3/97 16/13 0/1 21/17 0/1 1/33 5/4 1/32 24/19 1/31 43/34 0/1 1/29 19/15 2/63 1/31 71/56 0/1 1/33 52/41 1/30 33/26 0/1 1/29 14/11 1/32 23/18 5/159 4/127 32/25 2/63 41/32 2/63 1/31 9/7 4/125 1/31 22/17 5/154 13/10 5/153 2/61 43/33 4/121 5/151 30/23 1/30 17/13 1/31 2/61 4/3 1/30 23/17 0/1 1/29 42/31 1/30 19/14 2/59 1/29 15/11 1/30 41/30 3/89 2/59 67/49 27/797 2/59 26/19 7/206 63/46 11/323 14/411 37/27 7/205 4/117 48/35 4/117 11/8 6/175 1/29 18/13 5/144 61/44 1/29 2/57 43/31 9/259 4/115 25/18 3/86 32/23 2/57 39/28 2/57 3/85 7/5 1/29 2/57 38/27 1/28 31/22 2/55 1/27 55/39 1/28 24/17 1/29 41/29 1/29 2/57 17/12 2/57 7/199 10/7 1/28 23/16 4/111 11/305 59/41 3/83 32/885 36/25 5/138 13/9 2/55 1/27 16/11 2/55 19/13 2/55 1/27 22/15 1/28 25/17 3/82 3/2 1/27 2/53 20/13 1/26 37/24 13/337 12/311 17/11 7/181 6/155 14/9 1/26 53/34 3/77 8/205 39/25 2/51 1/25 25/16 1/26 61/39 22/565 3/77 36/23 5/128 47/30 7/179 16/409 58/37 13/332 11/7 2/51 5/127 52/33 1/26 41/26 2/51 5/127 30/19 3/76 19/12 2/51 1/25 8/5 1/25 21/13 1/25 4/99 34/21 5/124 81/50 1/25 4/99 47/29 4/99 7/173 13/8 1/25 2/49 44/27 7/172 119/73 9/221 2/49 75/46 7/172 31/19 17/417 2/49 18/11 5/122 59/36 3/73 4/97 100/61 1/24 41/25 1/25 2/49 23/14 8/195 3/73 28/17 1/24 33/20 4/97 5/121 5/3 1/24 32/19 4/95 27/16 5/119 4/95 22/13 5/118 61/36 3/71 2/47 100/59 5/118 39/23 3/71 2/47 17/10 11/259 2/47 46/27 15/352 75/44 11/258 29/17 12/281 5/117 99/58 5/117 18/421 70/41 3/70 41/24 2/47 9/211 53/31 5/117 8/187 12/7 3/70 67/39 2/47 1/23 55/32 3/70 43/25 15/349 4/93 74/43 13/302 105/61 5/116 31/18 6/139 1/23 19/11 6/139 1/23 45/26 7/162 71/41 8/185 33/763 26/15 11/254 7/4 1/23 6/137 44/25 3/68 37/21 1/23 4/91 30/17 3/68 23/13 8/181 5/113 39/22 9/203 2/45 16/9 2/45 41/23 2/45 3/67 25/14 5/112 34/19 11/246 43/24 3/67 28/625 52/29 7/156 9/5 4/89 5/111 20/11 1/22 31/17 14/307 13/285 42/23 1/22 11/6 6/131 5/109 24/13 3/65 37/20 8/173 13/281 13/7 11/237 2/43 41/22 2/43 13/279 28/15 7/150 43/23 5/107 28/599 15/8 3/64 17/9 11/233 6/127 2/1 1/20 19/9 1/19 18/341 17/8 6/113 11/207 15/7 3/56 43/20 28/521 5/93 28/13 7/130 13/6 2/37 11/203 37/17 13/239 8/147 24/11 3/55 35/16 7/128 11/5 5/91 6/109 20/9 1/18 29/13 13/233 12/215 38/17 1/18 9/4 5/89 4/71 52/23 7/124 43/19 28/495 3/53 120/53 3/53 77/34 3/53 50/883 34/15 11/194 25/11 5/88 41/18 3/53 2/35 16/7 2/35 39/17 2/35 9/157 23/10 5/87 8/139 30/13 3/52 37/16 4/69 1/17 7/3 6/103 1/17 40/17 1/17 33/14 1/17 28/475 26/11 11/186 71/30 33/557 8/135 45/19 7/118 19/8 1/17 6/101 50/21 5/84 81/34 1/17 4/67 31/13 1/17 6/101 74/31 13/218 117/49 41/687 4/67 160/67 4/67 43/18 4/67 15/251 12/5 3/50 53/22 8/133 5/83 41/17 9/149 2/33 70/29 3/50 99/41 18/299 5/83 29/12 5/83 12/199 75/31 11/182 121/50 13/215 2/33 46/19 15/248 63/26 41/677 2/33 80/33 2/33 17/7 2/33 11/181 39/16 2/33 3/49 100/41 5/82 61/25 2/33 3/49 22/9 5/82 5/2 1/16 38/15 1/16 33/13 5/79 4/63 28/11 1/16 23/9 3/47 8/125 41/16 2/31 1/15 100/39 1/16 59/23 4/63 3/47 18/7 5/78 49/19 27/419 2/31 80/31 2/31 31/12 2/31 17/263 75/29 7/108 119/46 2/31 9/139 163/63 2/31 5/77 44/17 7/108 13/5 2/31 1/15 60/23 3/46 47/18 7/107 4/61 81/31 4/61 1/15 115/44 3/46 34/13 5/76 55/21 3/46 21/8 4/61 1/15 8/3 1/15 19/7 1/15 2/29 49/18 1/15 2/29 30/11 3/44 71/26 8/117 5/73 41/15 5/73 2/29 11/4 5/73 2/29 47/17 16/231 7/101 83/30 2/29 7/101 119/43 2/29 3/43 36/13 5/72 61/22 3/43 22/315 25/9 1/14 39/14 1/15 2/29 53/19 8/115 3/43 120/43 3/43 67/24 3/43 10/143 14/5 1/14 17/6 6/85 7/99 20/7 1/14 23/8 8/111 7/97 3/1 2/27 1/13 22/7 1/12 19/6 1/13 2/25 16/5 2/25 29/9 4/49 5/61 42/13 1/12 55/17 1/12 13/4 1/13 2/25 10/3 1/12 27/8 5/59 4/47 44/13 7/82 61/18 34/397 3/35 200/59 3/35 139/41 3/35 80/933 78/23 23/268 17/5 7/81 2/23 41/12 2/23 1/11 65/19 3/34 24/7 1/11 55/16 1/12 31/9 1/13 2/25 38/11 1/12 45/13 1/12 7/2 2/23 1/11 39/11 3/35 2/23 32/9 2/23 57/16 19/217 12/137 25/7 3/34 93/26 10/113 7/79 68/19 3/34 43/12 4/45 9/101 61/17 2/23 1/11 18/5 5/56 29/8 16/177 1/11 40/11 1/11 11/3 1/11 6/65 59/16 0/1 1/11 48/13 4/43 85/23 3/32 122/33 3/32 159/43 1/11 4/43 37/10 4/43 7/75 63/17 14/149 11/117 89/24 27/287 8/85 26/7 7/74 93/25 41/431 2/21 160/43 2/21 67/18 2/21 27/283 41/11 2/21 3/31 56/15 3/31 15/4 1/10 34/9 3/32 19/5 1/11 2/21 4/1 1/10 21/5 0/1 1/9 80/19 0/1 59/14 0/1 1/11 38/9 1/10 55/13 1/10 17/4 2/19 1/9 30/7 1/10 43/10 5/49 4/39 13/3 2/19 5/47 48/11 2/19 83/19 2/19 1/9 201/46 2/19 5/47 520/119 5/47 319/73 5/47 8/75 118/27 3/28 35/8 3/28 22/5 5/46 31/7 14/127 1/9 40/9 1/9 9/2 1/9 4/35 41/9 1/9 2/17 32/7 2/17 55/12 5/42 23/5 4/33 5/41 14/3 1/8 47/10 0/1 1/5 80/17 0/1 33/7 0/1 1/11 52/11 1/10 71/15 0/1 1/7 19/4 1/9 2/17 43/9 0/1 1/11 24/5 1/9 29/6 8/69 5/43 5/1 1/8 21/4 0/1 1/7 16/3 0/1 27/5 0/1 1/9 65/12 1/8 38/7 1/8 11/2 3/23 2/15 39/7 3/23 2/15 67/12 2/15 21/157 28/5 3/22 17/3 6/43 1/7 40/7 1/7 23/4 1/7 8/55 6/1 1/6 31/5 1/9 2/17 25/4 1/8 19/3 1/7 6/41 51/8 0/1 1/7 32/5 2/13 13/2 2/13 3/19 20/3 1/6 27/4 4/23 3/17 7/1 2/11 1/5 29/4 -1/1 0/1 80/11 0/1 51/7 0/1 1/17 22/3 1/8 37/5 4/29 1/7 15/2 1/6 38/5 1/6 23/3 0/1 1/5 8/1 1/5 17/2 1/5 2/9 26/3 3/10 9/1 0/1 1/7 19/2 2/11 1/5 10/1 1/4 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,480,24,281) (-10/1,1/0) -> (70/41,41/24) Hyperbolic Matrix(239,2320,140,1359) (-10/1,-19/2) -> (99/58,70/41) Hyperbolic Matrix(161,1520,34,321) (-19/2,-9/1) -> (71/15,19/4) Hyperbolic Matrix(241,2080,-176,-1519) (-9/1,-17/2) -> (-63/46,-89/65) Hyperbolic Matrix(39,320,34,279) (-17/2,-8/1) -> (8/7,23/20) Hyperbolic Matrix(41,320,36,281) (-8/1,-23/3) -> (17/15,8/7) Hyperbolic Matrix(199,1520,-152,-1161) (-23/3,-15/2) -> (-55/42,-17/13) Hyperbolic Matrix(119,880,-38,-281) (-15/2,-22/3) -> (-22/7,-25/8) Hyperbolic Matrix(199,1440,-72,-521) (-22/3,-7/1) -> (-47/17,-58/21) Hyperbolic Matrix(201,1360,-124,-839) (-7/1,-20/3) -> (-60/37,-47/29) Hyperbolic Matrix(159,1040,-98,-641) (-20/3,-13/2) -> (-13/8,-60/37) Hyperbolic Matrix(199,1280,118,759) (-13/2,-32/5) -> (32/19,27/16) Hyperbolic Matrix(439,2800,-320,-2041) (-32/5,-19/3) -> (-59/43,-48/35) Hyperbolic Matrix(319,2000,204,1279) (-19/3,-25/4) -> (25/16,61/39) Hyperbolic Matrix(401,2480,-168,-1039) (-25/4,-6/1) -> (-74/31,-105/44) Hyperbolic Matrix(41,240,-34,-199) (-6/1,-17/3) -> (-23/19,-6/5) Hyperbolic Matrix(199,1120,78,439) (-17/3,-28/5) -> (28/11,23/9) Hyperbolic Matrix(159,880,-58,-321) (-28/5,-11/2) -> (-11/4,-52/19) Hyperbolic Matrix(119,640,-82,-441) (-11/2,-16/3) -> (-16/11,-29/20) Hyperbolic Matrix(121,640,38,201) (-16/3,-21/4) -> (19/6,16/5) Hyperbolic Matrix(199,1040,84,439) (-21/4,-5/1) -> (45/19,19/8) Hyperbolic Matrix(199,960,-108,-521) (-5/1,-24/5) -> (-24/13,-35/19) Hyperbolic Matrix(401,1920,184,881) (-24/5,-43/9) -> (37/17,24/11) Hyperbolic Matrix(721,3440,520,2481) (-43/9,-19/4) -> (61/44,43/31) Hyperbolic Matrix(321,1520,34,161) (-19/4,-71/15) -> (9/1,19/2) Hyperbolic Matrix(879,4160,490,2319) (-71/15,-52/11) -> (52/29,9/5) Hyperbolic Matrix(559,2640,220,1039) (-52/11,-33/7) -> (33/13,28/11) Hyperbolic Matrix(239,1120,-188,-881) (-33/7,-14/3) -> (-14/11,-47/37) Hyperbolic Matrix(121,560,78,361) (-14/3,-23/5) -> (17/11,14/9) Hyperbolic Matrix(559,2560,-402,-1841) (-23/5,-32/7) -> (-32/23,-57/41) Hyperbolic Matrix(561,2560,158,721) (-32/7,-41/9) -> (39/11,32/9) Hyperbolic Matrix(721,3280,264,1201) (-41/9,-9/2) -> (71/26,41/15) Hyperbolic Matrix(199,880,-154,-681) (-9/2,-22/5) -> (-22/17,-31/24) Hyperbolic Matrix(201,880,-82,-359) (-22/5,-13/3) -> (-27/11,-22/9) Hyperbolic Matrix(241,1040,130,561) (-13/3,-43/10) -> (37/20,13/7) Hyperbolic Matrix(559,2400,242,1039) (-43/10,-30/7) -> (30/13,37/16) Hyperbolic Matrix(281,1200,122,521) (-30/7,-17/4) -> (23/10,30/13) Hyperbolic Matrix(39,160,-10,-41) (-17/4,-4/1) -> (-4/1,-23/6) Parabolic Matrix(481,1840,-418,-1599) (-23/6,-42/11) -> (-38/33,-23/20) Hyperbolic Matrix(839,3200,-640,-2441) (-42/11,-19/5) -> (-59/45,-38/29) Hyperbolic Matrix(359,1360,-222,-841) (-19/5,-15/4) -> (-55/34,-21/13) Hyperbolic Matrix(879,3280,-622,-2321) (-15/4,-41/11) -> (-41/29,-65/46) Hyperbolic Matrix(881,3280,-408,-1519) (-41/11,-67/18) -> (-13/6,-41/19) Hyperbolic Matrix(1119,4160,-818,-3041) (-67/18,-26/7) -> (-26/19,-93/68) Hyperbolic Matrix(561,2080,-496,-1839) (-26/7,-63/17) -> (-17/15,-26/23) Hyperbolic Matrix(799,2960,518,1919) (-63/17,-37/10) -> (37/24,17/11) Hyperbolic Matrix(1559,5760,-1202,-4441) (-37/10,-48/13) -> (-48/37,-83/64) Hyperbolic Matrix(759,2800,-640,-2361) (-48/13,-11/3) -> (-51/43,-32/27) Hyperbolic Matrix(199,720,-144,-521) (-11/3,-18/5) -> (-18/13,-29/21) Hyperbolic Matrix(601,2160,234,841) (-18/5,-61/17) -> (59/23,18/7) Hyperbolic Matrix(959,3440,758,2719) (-61/17,-43/12) -> (43/34,19/15) Hyperbolic Matrix(961,3440,-402,-1439) (-43/12,-25/7) -> (-55/23,-43/18) Hyperbolic Matrix(719,2560,-562,-2001) (-25/7,-32/9) -> (-32/25,-55/43) Hyperbolic Matrix(721,2560,158,561) (-32/9,-39/11) -> (41/9,32/7) Hyperbolic Matrix(679,2400,260,919) (-39/11,-7/2) -> (47/18,81/31) Hyperbolic Matrix(439,1520,-266,-921) (-7/2,-38/11) -> (-38/23,-33/20) Hyperbolic Matrix(719,2480,394,1359) (-38/11,-31/9) -> (31/17,42/23) Hyperbolic Matrix(1441,4960,-604,-2079) (-31/9,-55/16) -> (-105/44,-31/13) Hyperbolic Matrix(1001,3440,268,921) (-55/16,-24/7) -> (56/15,15/4) Hyperbolic Matrix(959,3280,-702,-2401) (-24/7,-41/12) -> (-41/30,-56/41) Hyperbolic Matrix(399,1360,164,559) (-41/12,-17/5) -> (17/7,39/16) Hyperbolic Matrix(119,400,-36,-121) (-17/5,-10/3) -> (-10/3,-23/7) Parabolic Matrix(439,1440,-232,-761) (-23/7,-59/18) -> (-19/10,-17/9) Hyperbolic Matrix(1319,4320,476,1559) (-59/18,-36/11) -> (36/13,61/22) Hyperbolic Matrix(319,1040,196,639) (-36/11,-13/4) -> (13/8,44/27) Hyperbolic Matrix(199,640,-162,-521) (-13/4,-16/5) -> (-16/13,-27/22) Hyperbolic Matrix(201,640,38,121) (-16/5,-19/6) -> (21/4,16/3) Hyperbolic Matrix(559,1760,330,1039) (-19/6,-22/7) -> (22/13,61/36) Hyperbolic Matrix(359,1120,192,599) (-25/8,-3/1) -> (43/23,15/8) Hyperbolic Matrix(279,800,-98,-281) (-3/1,-20/7) -> (-20/7,-37/13) Parabolic Matrix(1041,2960,760,2161) (-37/13,-17/6) -> (63/46,37/27) Hyperbolic Matrix(199,560,156,439) (-17/6,-14/5) -> (14/11,23/18) Hyperbolic Matrix(601,1680,-386,-1079) (-14/5,-53/19) -> (-67/43,-14/9) Hyperbolic Matrix(1521,4240,890,2481) (-53/19,-39/14) -> (41/24,53/31) Hyperbolic Matrix(719,2000,316,879) (-39/14,-25/9) -> (25/11,41/18) Hyperbolic Matrix(721,2000,606,1681) (-25/9,-61/22) -> (19/16,25/21) Hyperbolic Matrix(1761,4880,520,1441) (-61/22,-36/13) -> (44/13,61/18) Hyperbolic Matrix(839,2320,-362,-1001) (-36/13,-47/17) -> (-7/3,-44/19) Hyperbolic Matrix(1159,3200,-1000,-2761) (-58/21,-11/4) -> (-51/44,-22/19) Hyperbolic Matrix(1199,3280,-556,-1521) (-52/19,-41/15) -> (-41/19,-28/13) Hyperbolic Matrix(1641,4480,-952,-2599) (-41/15,-30/11) -> (-50/29,-81/47) Hyperbolic Matrix(559,1520,-324,-881) (-30/11,-19/7) -> (-19/11,-50/29) Hyperbolic Matrix(119,320,74,199) (-19/7,-8/3) -> (8/5,21/13) Hyperbolic Matrix(121,320,76,201) (-8/3,-21/8) -> (19/12,8/5) Hyperbolic Matrix(519,1360,-382,-1001) (-21/8,-34/13) -> (-34/25,-19/14) Hyperbolic Matrix(2999,7840,-1760,-4601) (-34/13,-81/31) -> (-121/71,-46/27) Hyperbolic Matrix(919,2400,260,679) (-81/31,-47/18) -> (7/2,39/11) Hyperbolic Matrix(521,1360,-444,-1159) (-47/18,-13/5) -> (-27/23,-7/6) Hyperbolic Matrix(401,1040,278,721) (-13/5,-44/17) -> (36/25,13/9) Hyperbolic Matrix(3679,9520,-2350,-6081) (-44/17,-119/46) -> (-119/76,-36/23) Hyperbolic Matrix(6959,18000,2876,7439) (-119/46,-75/29) -> (75/31,121/50) Hyperbolic Matrix(2599,6720,1098,2839) (-75/29,-31/12) -> (71/30,45/19) Hyperbolic Matrix(559,1440,-342,-881) (-31/12,-18/7) -> (-18/11,-49/30) Hyperbolic Matrix(841,2160,234,601) (-18/7,-59/23) -> (61/17,18/5) Hyperbolic Matrix(4679,12000,1918,4919) (-59/23,-100/39) -> (100/41,61/25) Hyperbolic Matrix(3121,8000,1280,3281) (-100/39,-41/16) -> (39/16,100/41) Hyperbolic Matrix(719,1840,406,1039) (-41/16,-23/9) -> (23/13,39/22) Hyperbolic Matrix(439,1120,78,199) (-23/9,-28/11) -> (28/5,17/3) Hyperbolic Matrix(1039,2640,220,559) (-28/11,-33/13) -> (33/7,52/11) Hyperbolic Matrix(599,1520,-426,-1081) (-33/13,-5/2) -> (-45/32,-7/5) Hyperbolic Matrix(1201,2960,-876,-2159) (-5/2,-32/13) -> (-48/35,-85/62) Hyperbolic Matrix(521,1280,440,1081) (-32/13,-27/11) -> (13/11,32/27) Hyperbolic Matrix(721,1760,492,1201) (-22/9,-61/25) -> (19/13,22/15) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(3281,8000,1280,3121) (-100/41,-39/16) -> (41/16,100/39) Hyperbolic Matrix(559,1360,164,399) (-39/16,-17/7) -> (17/5,41/12) Hyperbolic Matrix(1519,3680,-892,-2161) (-17/7,-46/19) -> (-46/27,-63/37) Hyperbolic Matrix(3239,7840,-2000,-4841) (-46/19,-75/31) -> (-115/71,-34/21) Hyperbolic Matrix(959,2320,198,479) (-75/31,-29/12) -> (29/6,5/1) Hyperbolic Matrix(2319,5600,364,879) (-29/12,-99/41) -> (19/3,51/8) Hyperbolic Matrix(961,2320,862,2081) (-99/41,-70/29) -> (10/9,19/17) Hyperbolic Matrix(199,480,182,439) (-70/29,-41/17) -> (1/1,10/9) Hyperbolic Matrix(1759,4240,1128,2719) (-41/17,-53/22) -> (53/34,39/25) Hyperbolic Matrix(599,1440,-250,-601) (-53/22,-12/5) -> (-12/5,-67/28) Parabolic Matrix(1839,4400,568,1359) (-67/28,-55/23) -> (55/17,13/4) Hyperbolic Matrix(4959,11840,-2882,-6881) (-43/18,-74/31) -> (-74/43,-117/68) Hyperbolic Matrix(639,1520,-404,-961) (-31/13,-19/8) -> (-19/12,-49/31) Hyperbolic Matrix(439,1040,84,199) (-19/8,-45/19) -> (5/1,21/4) Hyperbolic Matrix(2839,6720,1098,2599) (-45/19,-71/30) -> (31/12,75/29) Hyperbolic Matrix(879,2080,-778,-1841) (-71/30,-26/11) -> (-26/23,-9/8) Hyperbolic Matrix(441,1040,-254,-599) (-26/11,-7/3) -> (-33/19,-26/15) Hyperbolic Matrix(3801,8800,-2332,-5399) (-44/19,-37/16) -> (-163/100,-44/27) Hyperbolic Matrix(1039,2400,242,559) (-37/16,-30/13) -> (30/7,43/10) Hyperbolic Matrix(521,1200,122,281) (-30/13,-23/10) -> (17/4,30/7) Hyperbolic Matrix(801,1840,488,1121) (-23/10,-39/17) -> (41/25,23/14) Hyperbolic Matrix(559,1280,314,719) (-39/17,-16/7) -> (16/9,41/23) Hyperbolic Matrix(561,1280,316,721) (-16/7,-41/18) -> (39/22,16/9) Hyperbolic Matrix(879,2000,316,719) (-41/18,-25/11) -> (25/9,39/14) Hyperbolic Matrix(1199,2720,458,1039) (-25/11,-34/15) -> (34/13,55/21) Hyperbolic Matrix(1801,4080,-1006,-2279) (-34/15,-43/19) -> (-77/43,-34/19) Hyperbolic Matrix(1521,3440,814,1841) (-43/19,-52/23) -> (28/15,43/23) Hyperbolic Matrix(1841,4160,1452,3281) (-52/23,-9/4) -> (71/56,52/41) Hyperbolic Matrix(359,800,-162,-361) (-9/4,-20/9) -> (-20/9,-31/14) Parabolic Matrix(1121,2480,796,1761) (-31/14,-42/19) -> (38/27,31/22) Hyperbolic Matrix(761,1680,236,521) (-42/19,-11/5) -> (29/9,42/13) Hyperbolic Matrix(439,960,-348,-761) (-11/5,-24/11) -> (-24/19,-29/23) Hyperbolic Matrix(881,1920,184,401) (-24/11,-37/17) -> (43/9,24/5) Hyperbolic Matrix(479,1040,368,799) (-37/17,-13/6) -> (13/10,43/33) Hyperbolic Matrix(1599,3440,892,1919) (-28/13,-43/20) -> (43/24,52/29) Hyperbolic Matrix(521,1120,354,761) (-43/20,-15/7) -> (25/17,3/2) Hyperbolic Matrix(599,1280,168,359) (-15/7,-17/8) -> (57/16,25/7) Hyperbolic Matrix(641,1360,-452,-959) (-17/8,-2/1) -> (-78/55,-17/12) Hyperbolic Matrix(919,1760,-648,-1241) (-2/1,-19/10) -> (-139/98,-78/55) Hyperbolic Matrix(679,1280,148,279) (-17/9,-15/8) -> (55/12,23/5) Hyperbolic Matrix(641,1200,86,161) (-15/8,-43/23) -> (37/5,15/2) Hyperbolic Matrix(1841,3440,814,1521) (-43/23,-28/15) -> (52/23,43/19) Hyperbolic Matrix(1201,2240,-986,-1839) (-28/15,-13/7) -> (-67/55,-28/23) Hyperbolic Matrix(561,1040,130,241) (-13/7,-37/20) -> (43/10,13/3) Hyperbolic Matrix(1039,1920,822,1519) (-37/20,-24/13) -> (24/19,43/34) Hyperbolic Matrix(1001,1840,414,761) (-35/19,-11/6) -> (29/12,75/31) Hyperbolic Matrix(439,800,-242,-441) (-11/6,-20/11) -> (-20/11,-29/16) Parabolic Matrix(839,1520,154,279) (-29/16,-38/21) -> (38/7,11/2) Hyperbolic Matrix(841,1520,244,441) (-38/21,-9/5) -> (31/9,38/11) Hyperbolic Matrix(2319,4160,490,879) (-9/5,-52/29) -> (52/11,71/15) Hyperbolic Matrix(1919,3440,892,1599) (-52/29,-43/24) -> (43/20,28/13) Hyperbolic Matrix(8039,14400,3550,6359) (-43/24,-120/67) -> (120/53,77/34) Hyperbolic Matrix(8041,14400,3552,6361) (-120/67,-77/43) -> (43/19,120/53) Hyperbolic Matrix(761,1360,202,361) (-34/19,-25/14) -> (15/4,34/9) Hyperbolic Matrix(1121,2000,718,1281) (-25/14,-41/23) -> (39/25,25/16) Hyperbolic Matrix(719,1280,314,559) (-41/23,-16/9) -> (16/7,39/17) Hyperbolic Matrix(721,1280,316,561) (-16/9,-39/22) -> (41/18,16/7) Hyperbolic Matrix(1039,1840,406,719) (-39/22,-23/13) -> (23/9,41/16) Hyperbolic Matrix(679,1200,520,919) (-23/13,-30/17) -> (30/23,17/13) Hyperbolic Matrix(1361,2400,1044,1841) (-30/17,-37/21) -> (43/33,30/23) Hyperbolic Matrix(1319,2320,-842,-1481) (-37/21,-7/4) -> (-47/30,-83/53) Hyperbolic Matrix(919,1600,390,679) (-7/4,-40/23) -> (40/17,33/14) Hyperbolic Matrix(921,1600,392,681) (-40/23,-33/19) -> (7/3,40/17) Hyperbolic Matrix(2401,4160,-1754,-3039) (-26/15,-71/41) -> (-89/65,-26/19) Hyperbolic Matrix(3881,6720,2380,4121) (-71/41,-45/26) -> (75/46,31/19) Hyperbolic Matrix(601,1040,486,841) (-45/26,-19/11) -> (21/17,5/4) Hyperbolic Matrix(1161,2000,256,441) (-81/47,-31/18) -> (9/2,41/9) Hyperbolic Matrix(1441,2480,-1208,-2079) (-31/18,-74/43) -> (-6/5,-31/26) Hyperbolic Matrix(14879,25600,6230,10719) (-117/68,-160/93) -> (160/67,43/18) Hyperbolic Matrix(14881,25600,6232,10721) (-160/93,-43/25) -> (117/49,160/67) Hyperbolic Matrix(2001,3440,-1442,-2479) (-43/25,-12/7) -> (-68/49,-43/31) Hyperbolic Matrix(2759,4720,-1988,-3401) (-12/7,-53/31) -> (-93/67,-68/49) Hyperbolic Matrix(2481,4240,890,1521) (-53/31,-41/24) -> (39/14,53/19) Hyperbolic Matrix(281,480,24,41) (-41/24,-70/41) -> (10/1,1/0) Hyperbolic Matrix(1359,2320,140,239) (-70/41,-99/58) -> (19/2,10/1) Hyperbolic Matrix(1641,2800,446,761) (-99/58,-29/17) -> (11/3,59/16) Hyperbolic Matrix(1079,1840,492,839) (-29/17,-75/44) -> (35/16,11/5) Hyperbolic Matrix(10561,18000,6478,11041) (-75/44,-121/71) -> (119/73,75/46) Hyperbolic Matrix(3759,6400,1550,2639) (-63/37,-80/47) -> (80/33,17/7) Hyperbolic Matrix(3761,6400,1552,2641) (-80/47,-17/10) -> (63/26,80/33) Hyperbolic Matrix(801,1360,566,961) (-17/10,-39/23) -> (41/29,17/12) Hyperbolic Matrix(4719,8000,2878,4879) (-39/23,-100/59) -> (100/61,41/25) Hyperbolic Matrix(7081,12000,4320,7321) (-100/59,-61/36) -> (59/36,100/61) Hyperbolic Matrix(1039,1760,330,559) (-61/36,-22/13) -> (22/7,19/6) Hyperbolic Matrix(521,880,-402,-679) (-22/13,-5/3) -> (-35/27,-22/17) Hyperbolic Matrix(1159,1920,-894,-1481) (-5/3,-38/23) -> (-118/91,-35/27) Hyperbolic Matrix(1601,2640,1262,2081) (-33/20,-28/17) -> (52/41,33/26) Hyperbolic Matrix(681,1120,560,921) (-28/17,-23/14) -> (17/14,28/23) Hyperbolic Matrix(1121,1840,488,801) (-23/14,-41/25) -> (39/17,23/10) Hyperbolic Matrix(4879,8000,2878,4719) (-41/25,-100/61) -> (100/59,39/23) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(3919,6400,1518,2479) (-49/30,-80/49) -> (80/31,31/12) Hyperbolic Matrix(3921,6400,1520,2481) (-80/49,-31/19) -> (49/19,80/31) Hyperbolic Matrix(4121,6720,2380,3881) (-31/19,-75/46) -> (45/26,71/41) Hyperbolic Matrix(12121,19760,4638,7561) (-75/46,-119/73) -> (81/31,115/44) Hyperbolic Matrix(26159,42640,-20172,-32881) (-119/73,-163/100) -> (-83/64,-201/155) Hyperbolic Matrix(1081,1760,320,521) (-44/27,-13/8) -> (27/8,44/13) Hyperbolic Matrix(1481,2400,1062,1721) (-47/29,-81/50) -> (39/28,7/5) Hyperbolic Matrix(12199,19760,4716,7639) (-81/50,-115/71) -> (75/29,119/46) Hyperbolic Matrix(1681,2720,940,1521) (-34/21,-55/34) -> (25/14,34/19) Hyperbolic Matrix(199,320,74,119) (-21/13,-8/5) -> (8/3,19/7) Hyperbolic Matrix(201,320,76,121) (-8/5,-19/12) -> (21/8,8/3) Hyperbolic Matrix(2279,3600,-1444,-2281) (-49/31,-30/19) -> (-30/19,-71/45) Parabolic Matrix(2079,3280,1622,2559) (-71/45,-41/26) -> (41/32,9/7) Hyperbolic Matrix(559,880,-458,-721) (-41/26,-11/7) -> (-11/9,-39/32) Hyperbolic Matrix(919,1440,-792,-1241) (-11/7,-47/30) -> (-7/6,-29/25) Hyperbolic Matrix(11239,17600,-8200,-12841) (-83/53,-119/76) -> (-159/116,-37/27) Hyperbolic Matrix(2761,4320,1918,3001) (-36/23,-61/39) -> (59/41,36/25) Hyperbolic Matrix(1279,2000,204,319) (-61/39,-25/16) -> (25/4,19/3) Hyperbolic Matrix(1281,2000,718,1121) (-25/16,-39/25) -> (41/23,25/14) Hyperbolic Matrix(2719,4240,1128,1759) (-39/25,-53/34) -> (53/22,41/17) Hyperbolic Matrix(9239,14400,3310,5159) (-53/34,-120/77) -> (120/43,67/24) Hyperbolic Matrix(9241,14400,3312,5161) (-120/77,-67/43) -> (53/19,120/43) Hyperbolic Matrix(361,560,78,121) (-14/9,-17/11) -> (23/5,14/3) Hyperbolic Matrix(519,800,-338,-521) (-17/11,-20/13) -> (-20/13,-23/15) Parabolic Matrix(681,1040,184,281) (-23/15,-3/2) -> (37/10,63/17) Hyperbolic Matrix(599,880,-518,-761) (-3/2,-22/15) -> (-22/19,-37/32) Hyperbolic Matrix(1201,1760,492,721) (-22/15,-19/13) -> (61/25,22/9) Hyperbolic Matrix(439,640,356,519) (-19/13,-16/11) -> (16/13,21/17) Hyperbolic Matrix(1159,1680,634,919) (-29/20,-42/29) -> (42/23,11/6) Hyperbolic Matrix(1879,2720,248,359) (-42/29,-55/38) -> (15/2,38/5) Hyperbolic Matrix(3041,4400,1770,2561) (-55/38,-13/9) -> (67/39,55/32) Hyperbolic Matrix(279,400,-196,-281) (-13/9,-10/7) -> (-10/7,-27/19) Parabolic Matrix(1239,1760,478,679) (-27/19,-44/31) -> (44/17,13/5) Hyperbolic Matrix(3439,4880,2198,3119) (-44/31,-61/43) -> (61/39,36/23) Hyperbolic Matrix(28199,40000,8318,11799) (-61/43,-200/141) -> (200/59,139/41) Hyperbolic Matrix(28201,40000,8320,11801) (-200/141,-139/98) -> (61/18,200/59) Hyperbolic Matrix(961,1360,566,801) (-17/12,-41/29) -> (39/23,17/10) Hyperbolic Matrix(2039,2880,594,839) (-65/46,-24/17) -> (24/7,55/16) Hyperbolic Matrix(2041,2880,596,841) (-24/17,-55/39) -> (65/19,24/7) Hyperbolic Matrix(1759,2480,-1476,-2081) (-55/39,-31/22) -> (-31/26,-25/21) Hyperbolic Matrix(1079,1520,482,679) (-31/22,-38/27) -> (38/17,9/4) Hyperbolic Matrix(6199,8720,-4522,-6361) (-38/27,-45/32) -> (-85/62,-122/89) Hyperbolic Matrix(1721,2400,1062,1481) (-7/5,-39/28) -> (81/50,47/29) Hyperbolic Matrix(1839,2560,1436,1999) (-39/28,-32/23) -> (32/25,41/32) Hyperbolic Matrix(921,1280,490,681) (-57/41,-25/18) -> (15/8,17/9) Hyperbolic Matrix(4841,6720,894,1241) (-25/18,-93/67) -> (27/5,65/12) Hyperbolic Matrix(2481,3440,520,721) (-43/31,-61/44) -> (19/4,43/9) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(1159,1600,318,439) (-29/21,-40/29) -> (40/11,11/3) Hyperbolic Matrix(1161,1600,320,441) (-40/29,-11/8) -> (29/8,40/11) Hyperbolic Matrix(2039,2800,844,1159) (-11/8,-59/43) -> (99/41,29/12) Hyperbolic Matrix(42079,57680,-32450,-44481) (-122/89,-159/116) -> (-319/246,-118/91) Hyperbolic Matrix(759,1040,262,359) (-37/27,-63/46) -> (23/8,3/1) Hyperbolic Matrix(18719,25600,5030,6879) (-93/68,-160/117) -> (160/43,67/18) Hyperbolic Matrix(18721,25600,5032,6881) (-160/117,-67/49) -> (93/25,160/43) Hyperbolic Matrix(3921,5360,-3218,-4399) (-67/49,-41/30) -> (-39/32,-67/55) Hyperbolic Matrix(2519,3440,1786,2439) (-56/41,-15/11) -> (55/39,24/17) Hyperbolic Matrix(999,1360,440,599) (-15/11,-34/25) -> (34/15,25/11) Hyperbolic Matrix(119,160,-90,-121) (-19/14,-4/3) -> (-4/3,-21/16) Parabolic Matrix(4879,6400,1158,1519) (-21/16,-80/61) -> (80/19,59/14) Hyperbolic Matrix(4881,6400,1160,1521) (-80/61,-59/45) -> (21/5,80/19) Hyperbolic Matrix(3481,4560,642,841) (-38/29,-55/42) -> (65/12,38/7) Hyperbolic Matrix(919,1200,520,679) (-17/13,-30/23) -> (30/17,23/13) Hyperbolic Matrix(1841,2400,1044,1361) (-30/23,-43/33) -> (37/21,30/17) Hyperbolic Matrix(799,1040,368,479) (-43/33,-13/10) -> (13/6,37/17) Hyperbolic Matrix(801,1040,124,161) (-13/10,-48/37) -> (32/5,13/2) Hyperbolic Matrix(208519,270400,47718,61879) (-201/155,-520/401) -> (520/119,319/73) Hyperbolic Matrix(208521,270400,47720,61881) (-520/401,-319/246) -> (201/46,520/119) Hyperbolic Matrix(1239,1600,278,359) (-31/24,-40/31) -> (40/9,9/2) Hyperbolic Matrix(1241,1600,280,361) (-40/31,-9/7) -> (31/7,40/9) Hyperbolic Matrix(1559,2000,654,839) (-9/7,-41/32) -> (81/34,31/13) Hyperbolic Matrix(1999,2560,1436,1839) (-41/32,-32/25) -> (32/23,39/28) Hyperbolic Matrix(1001,1280,470,601) (-55/43,-23/18) -> (17/8,15/7) Hyperbolic Matrix(439,560,156,199) (-23/18,-14/11) -> (14/5,17/6) Hyperbolic Matrix(5039,6400,1070,1359) (-47/37,-80/63) -> (80/17,33/7) Hyperbolic Matrix(5041,6400,1072,1361) (-80/63,-33/26) -> (47/10,80/17) Hyperbolic Matrix(2081,2640,1262,1601) (-33/26,-52/41) -> (28/17,33/20) Hyperbolic Matrix(3281,4160,1452,1841) (-52/41,-71/56) -> (9/4,52/23) Hyperbolic Matrix(1199,1520,1072,1359) (-71/56,-19/15) -> (19/17,9/8) Hyperbolic Matrix(2719,3440,758,959) (-19/15,-43/34) -> (43/12,61/17) Hyperbolic Matrix(1519,1920,822,1039) (-43/34,-24/19) -> (24/13,37/20) Hyperbolic Matrix(1841,2320,1080,1361) (-29/23,-5/4) -> (75/44,29/17) Hyperbolic Matrix(841,1040,486,601) (-5/4,-21/17) -> (19/11,45/26) Hyperbolic Matrix(519,640,356,439) (-21/17,-16/13) -> (16/11,19/13) Hyperbolic Matrix(5479,6720,1532,1879) (-27/22,-65/53) -> (25/7,93/26) Hyperbolic Matrix(3719,4560,880,1079) (-65/53,-38/31) -> (38/9,55/13) Hyperbolic Matrix(1241,1520,556,681) (-38/31,-11/9) -> (29/13,38/17) Hyperbolic Matrix(921,1120,560,681) (-28/23,-17/14) -> (23/14,28/17) Hyperbolic Matrix(1319,1600,230,279) (-17/14,-40/33) -> (40/7,23/4) Hyperbolic Matrix(1321,1600,232,281) (-40/33,-23/19) -> (17/3,40/7) Hyperbolic Matrix(1681,2000,606,721) (-25/21,-19/16) -> (61/22,25/9) Hyperbolic Matrix(4721,5600,2766,3281) (-19/16,-51/43) -> (29/17,99/58) Hyperbolic Matrix(879,1040,202,239) (-32/27,-13/11) -> (13/3,48/11) Hyperbolic Matrix(679,800,-578,-681) (-13/11,-20/17) -> (-20/17,-27/23) Parabolic Matrix(5519,6400,758,879) (-29/25,-80/69) -> (80/11,51/7) Hyperbolic Matrix(5521,6400,760,881) (-80/69,-51/44) -> (29/4,80/11) Hyperbolic Matrix(1039,1200,484,559) (-37/32,-15/13) -> (15/7,43/20) Hyperbolic Matrix(2361,2720,730,841) (-15/13,-38/33) -> (42/13,55/17) Hyperbolic Matrix(279,320,34,39) (-23/20,-8/7) -> (8/1,17/2) Hyperbolic Matrix(281,320,36,41) (-8/7,-17/15) -> (23/3,8/1) Hyperbolic Matrix(1359,1520,1072,1199) (-9/8,-19/17) -> (19/15,71/56) Hyperbolic Matrix(2081,2320,862,961) (-19/17,-10/9) -> (70/29,99/41) Hyperbolic Matrix(439,480,182,199) (-10/9,-1/1) -> (41/17,70/29) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(1839,-2080,496,-561) (9/8,17/15) -> (63/17,89/24) Hyperbolic Matrix(1321,-1520,312,-359) (23/20,15/13) -> (55/13,17/4) Hyperbolic Matrix(761,-880,518,-599) (15/13,22/19) -> (22/15,25/17) Hyperbolic Matrix(1241,-1440,792,-919) (22/19,7/6) -> (47/30,58/37) Hyperbolic Matrix(1159,-1360,444,-521) (7/6,20/17) -> (60/23,47/18) Hyperbolic Matrix(881,-1040,338,-399) (20/17,13/11) -> (13/5,60/23) Hyperbolic Matrix(2361,-2800,640,-759) (32/27,19/16) -> (59/16,48/13) Hyperbolic Matrix(2079,-2480,1208,-1441) (25/21,6/5) -> (74/43,105/61) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(721,-880,458,-559) (28/23,11/9) -> (11/7,52/33) Hyperbolic Matrix(521,-640,162,-199) (11/9,16/13) -> (16/5,29/9) Hyperbolic Matrix(761,-960,348,-439) (5/4,24/19) -> (24/11,35/16) Hyperbolic Matrix(881,-1120,188,-239) (33/26,14/11) -> (14/3,47/10) Hyperbolic Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(681,-880,154,-199) (9/7,22/17) -> (22/5,31/7) Hyperbolic Matrix(679,-880,402,-521) (22/17,13/10) -> (27/16,22/13) Hyperbolic Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(1359,-1840,178,-241) (23/17,42/31) -> (38/5,23/3) Hyperbolic Matrix(2361,-3200,560,-759) (42/31,19/14) -> (59/14,38/9) Hyperbolic Matrix(1001,-1360,382,-519) (19/14,15/11) -> (55/21,21/8) Hyperbolic Matrix(2401,-3280,702,-959) (15/11,41/30) -> (41/12,65/19) Hyperbolic Matrix(2399,-3280,1288,-1761) (41/30,67/49) -> (13/7,41/22) Hyperbolic Matrix(3041,-4160,818,-1119) (67/49,26/19) -> (26/7,93/25) Hyperbolic Matrix(1519,-2080,176,-241) (26/19,63/46) -> (17/2,26/3) Hyperbolic Matrix(4201,-5760,962,-1319) (37/27,48/35) -> (48/11,83/19) Hyperbolic Matrix(2041,-2800,320,-439) (48/35,11/8) -> (51/8,32/5) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(2479,-3440,1442,-2001) (43/31,25/18) -> (55/32,43/25) Hyperbolic Matrix(1841,-2560,402,-559) (25/18,32/23) -> (32/7,55/12) Hyperbolic Matrix(1081,-1520,426,-599) (7/5,38/27) -> (38/15,33/13) Hyperbolic Matrix(3519,-4960,2044,-2881) (31/22,55/39) -> (105/61,31/18) Hyperbolic Matrix(2321,-3280,622,-879) (24/17,41/29) -> (41/11,56/15) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(1001,-1440,472,-679) (23/16,59/41) -> (19/9,17/8) Hyperbolic Matrix(441,-640,82,-119) (13/9,16/11) -> (16/3,27/5) Hyperbolic Matrix(521,-800,338,-519) (3/2,20/13) -> (20/13,37/24) Parabolic Matrix(1079,-1680,386,-601) (14/9,53/34) -> (67/24,14/5) Hyperbolic Matrix(1481,-2320,842,-1319) (36/23,47/30) -> (7/4,44/25) Hyperbolic Matrix(2041,-3200,280,-439) (58/37,11/7) -> (51/7,22/3) Hyperbolic Matrix(2081,-3280,1116,-1759) (52/33,41/26) -> (41/22,28/15) Hyperbolic Matrix(2839,-4480,1192,-1881) (41/26,30/19) -> (50/21,81/34) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(4841,-7840,2000,-3239) (34/21,81/50) -> (121/50,46/19) Hyperbolic Matrix(839,-1360,124,-201) (47/29,13/8) -> (27/4,7/1) Hyperbolic Matrix(5841,-9520,2110,-3439) (44/27,119/73) -> (119/43,36/13) Hyperbolic Matrix(881,-1440,342,-559) (31/19,18/11) -> (18/7,49/19) Hyperbolic Matrix(921,-1520,266,-439) (33/20,5/3) -> (45/13,7/2) Hyperbolic Matrix(1759,-2960,476,-801) (5/3,32/19) -> (48/13,85/23) Hyperbolic Matrix(2161,-3680,892,-1519) (17/10,46/27) -> (46/19,63/26) Hyperbolic Matrix(4601,-7840,1760,-2999) (46/27,75/44) -> (115/44,34/13) Hyperbolic Matrix(841,-1440,490,-839) (53/31,12/7) -> (12/7,67/39) Parabolic Matrix(6881,-11840,2882,-4959) (43/25,74/43) -> (74/31,117/49) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(1201,-2080,138,-239) (71/41,26/15) -> (26/3,9/1) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(4999,-8800,1932,-3401) (44/25,37/21) -> (163/63,44/17) Hyperbolic Matrix(2279,-4080,1006,-1801) (34/19,43/24) -> (77/34,34/15) Hyperbolic Matrix(441,-800,242,-439) (9/5,20/11) -> (20/11,31/17) Parabolic Matrix(521,-960,108,-199) (11/6,24/13) -> (24/5,29/6) Hyperbolic Matrix(719,-1360,212,-401) (17/9,2/1) -> (78/23,17/5) Hyperbolic Matrix(841,-1760,248,-519) (2/1,19/9) -> (139/41,78/23) Hyperbolic Matrix(1039,-2240,186,-401) (28/13,13/6) -> (67/12,28/5) Hyperbolic Matrix(361,-800,162,-359) (11/5,20/9) -> (20/9,29/13) Parabolic Matrix(1001,-2320,362,-839) (37/16,7/3) -> (47/17,83/30) Hyperbolic Matrix(1759,-4160,474,-1121) (26/11,71/30) -> (89/24,26/7) Hyperbolic Matrix(1039,-2480,168,-401) (31/13,74/31) -> (6/1,31/5) Hyperbolic Matrix(1439,-3440,402,-961) (43/18,12/5) -> (68/19,43/12) Hyperbolic Matrix(1961,-4720,548,-1319) (12/5,53/22) -> (93/26,68/19) Hyperbolic Matrix(359,-880,82,-201) (22/9,5/2) -> (35/8,22/5) Hyperbolic Matrix(761,-1920,174,-439) (5/2,38/15) -> (118/27,35/8) Hyperbolic Matrix(16481,-42640,3772,-9759) (119/46,163/63) -> (83/19,201/46) Hyperbolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(321,-880,58,-159) (41/15,11/4) -> (11/2,39/7) Hyperbolic Matrix(521,-1440,72,-199) (11/4,47/17) -> (7/1,29/4) Hyperbolic Matrix(6361,-17600,1720,-4759) (83/30,119/43) -> (159/43,37/10) Hyperbolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(281,-880,38,-119) (3/1,22/7) -> (22/3,37/5) Hyperbolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(721,-2480,116,-399) (55/16,31/9) -> (31/5,25/4) Hyperbolic Matrix(2521,-8720,682,-2359) (38/11,45/13) -> (85/23,122/33) Hyperbolic Matrix(15601,-57680,3570,-13199) (122/33,159/43) -> (319/73,118/27) Hyperbolic Matrix(1439,-5360,258,-961) (67/18,41/11) -> (39/7,67/12) Hyperbolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(121,-800,18,-119) (13/2,20/3) -> (20/3,27/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,480,24,281) -> Matrix(7,2,164,47) Matrix(239,2320,140,1359) -> Matrix(19,8,444,187) Matrix(161,1520,34,321) -> Matrix(1,0,12,1) Matrix(241,2080,-176,-1519) -> Matrix(13,8,-356,-219) Matrix(39,320,34,279) -> Matrix(5,2,172,69) Matrix(41,320,36,281) -> Matrix(7,2,248,71) Matrix(199,1520,-152,-1161) -> Matrix(7,2,-200,-57) Matrix(119,880,-38,-281) -> Matrix(11,2,-116,-21) Matrix(199,1440,-72,-521) -> Matrix(1,-2,-12,25) Matrix(201,1360,-124,-839) -> Matrix(37,10,-840,-227) Matrix(159,1040,-98,-641) -> Matrix(35,8,-792,-181) Matrix(199,1280,118,759) -> Matrix(7,2,164,47) Matrix(439,2800,-320,-2041) -> Matrix(29,6,-788,-163) Matrix(319,2000,204,1279) -> Matrix(23,4,592,103) Matrix(401,2480,-168,-1039) -> Matrix(29,4,-428,-59) Matrix(41,240,-34,-199) -> Matrix(9,2,-284,-63) Matrix(199,1120,78,439) -> Matrix(53,10,832,157) Matrix(159,880,-58,-321) -> Matrix(21,4,-268,-51) Matrix(119,640,-82,-441) -> Matrix(13,2,-332,-51) Matrix(121,640,38,201) -> Matrix(9,2,112,25) Matrix(199,1040,84,439) -> Matrix(29,6,488,101) Matrix(199,960,-108,-521) -> Matrix(67,10,-1320,-197) Matrix(401,1920,184,881) -> Matrix(59,8,1084,147) Matrix(721,3440,520,2481) -> Matrix(27,4,776,115) Matrix(321,1520,34,161) -> Matrix(1,0,12,1) Matrix(879,4160,490,2319) -> Matrix(25,4,556,89) Matrix(559,2640,220,1039) -> Matrix(31,4,488,63) Matrix(239,1120,-188,-881) -> Matrix(1,0,-24,1) Matrix(121,560,78,361) -> Matrix(11,2,280,51) Matrix(559,2560,-402,-1841) -> Matrix(103,16,-2736,-425) Matrix(561,2560,158,721) -> Matrix(53,8,616,93) Matrix(721,3280,264,1201) -> Matrix(79,12,1152,175) Matrix(199,880,-154,-681) -> Matrix(71,10,-2052,-289) Matrix(201,880,-82,-359) -> Matrix(73,10,-1044,-143) Matrix(241,1040,130,561) -> Matrix(91,12,1964,259) Matrix(559,2400,242,1039) -> Matrix(125,16,2164,277) Matrix(281,1200,122,521) -> Matrix(19,2,332,35) Matrix(39,160,-10,-41) -> Matrix(15,2,-128,-17) Matrix(481,1840,-418,-1599) -> Matrix(1,0,-24,1) Matrix(839,3200,-640,-2441) -> Matrix(17,2,-468,-55) Matrix(359,1360,-222,-841) -> Matrix(19,2,-428,-45) Matrix(879,3280,-622,-2321) -> Matrix(67,8,-1784,-213) Matrix(881,3280,-408,-1519) -> Matrix(271,32,-4480,-529) Matrix(1119,4160,-818,-3041) -> Matrix(239,28,-6564,-769) Matrix(561,2080,-496,-1839) -> Matrix(69,8,-2372,-275) Matrix(799,2960,518,1919) -> Matrix(277,32,7176,829) Matrix(1559,5760,-1202,-4441) -> Matrix(157,18,-4492,-515) Matrix(759,2800,-640,-2361) -> Matrix(53,6,-1652,-187) Matrix(199,720,-144,-521) -> Matrix(91,10,-2448,-269) Matrix(601,2160,234,841) -> Matrix(93,10,1460,157) Matrix(959,3440,758,2719) -> Matrix(37,4,1156,125) Matrix(961,3440,-402,-1439) -> Matrix(223,24,-3280,-353) Matrix(719,2560,-562,-2001) -> Matrix(151,16,-4464,-473) Matrix(721,2560,158,561) -> Matrix(77,8,664,69) Matrix(679,2400,260,919) -> Matrix(97,10,1484,153) Matrix(439,1520,-266,-921) -> Matrix(59,6,-1308,-133) Matrix(719,2480,394,1359) -> Matrix(119,12,2608,263) Matrix(1441,4960,-604,-2079) -> Matrix(45,4,-664,-59) Matrix(1001,3440,268,921) -> Matrix(21,2,220,21) Matrix(959,3280,-702,-2401) -> Matrix(75,8,-2072,-221) Matrix(399,1360,164,559) -> Matrix(75,8,1228,131) Matrix(119,400,-36,-121) -> Matrix(59,6,-600,-61) Matrix(439,1440,-232,-761) -> Matrix(227,22,-4344,-421) Matrix(1319,4320,476,1559) -> Matrix(311,30,4468,431) Matrix(319,1040,196,639) -> Matrix(43,4,1064,99) Matrix(199,640,-162,-521) -> Matrix(21,2,-620,-59) Matrix(201,640,38,121) -> Matrix(21,2,136,13) Matrix(559,1760,330,1039) -> Matrix(85,8,2008,189) Matrix(359,1120,192,599) -> Matrix(193,18,4128,385) Matrix(279,800,-98,-281) -> Matrix(167,14,-2016,-169) Matrix(1041,2960,760,2161) -> Matrix(387,32,11356,939) Matrix(199,560,156,439) -> Matrix(25,2,812,65) Matrix(601,1680,-386,-1079) -> Matrix(73,6,-1740,-143) Matrix(1521,4240,890,2481) -> Matrix(199,16,4664,375) Matrix(719,2000,316,879) -> Matrix(101,8,1780,141) Matrix(721,2000,606,1681) -> Matrix(49,4,1580,129) Matrix(1761,4880,520,1441) -> Matrix(445,36,5204,421) Matrix(839,2320,-362,-1001) -> Matrix(323,26,-4932,-397) Matrix(1159,3200,-1000,-2761) -> Matrix(25,2,-588,-47) Matrix(1199,3280,-556,-1521) -> Matrix(199,16,-3296,-265) Matrix(1641,4480,-952,-2599) -> Matrix(277,22,-5880,-467) Matrix(559,1520,-324,-881) -> Matrix(103,8,-2176,-169) Matrix(119,320,74,199) -> Matrix(77,6,1912,149) Matrix(121,320,76,201) -> Matrix(79,6,1988,151) Matrix(519,1360,-382,-1001) -> Matrix(27,2,-716,-53) Matrix(2999,7840,-1760,-4601) -> Matrix(663,50,-14228,-1073) Matrix(919,2400,260,679) -> Matrix(133,10,1556,117) Matrix(521,1360,-444,-1159) -> Matrix(133,10,-4296,-323) Matrix(401,1040,278,721) -> Matrix(53,4,1444,109) Matrix(3679,9520,-2350,-6081) -> Matrix(323,24,-7604,-565) Matrix(6959,18000,2876,7439) -> Matrix(109,8,1812,133) Matrix(2599,6720,1098,2839) -> Matrix(941,70,15876,1181) Matrix(559,1440,-342,-881) -> Matrix(271,20,-6084,-449) Matrix(841,2160,234,601) -> Matrix(137,10,1548,113) Matrix(4679,12000,1918,4919) -> Matrix(247,18,4048,295) Matrix(3121,8000,1280,3281) -> Matrix(107,8,1752,131) Matrix(719,1840,406,1039) -> Matrix(217,16,4896,361) Matrix(439,1120,78,199) -> Matrix(137,10,1000,73) Matrix(1039,2640,220,559) -> Matrix(55,4,536,39) Matrix(599,1520,-426,-1081) -> Matrix(83,6,-2172,-157) Matrix(1201,2960,-876,-2159) -> Matrix(227,16,-6200,-437) Matrix(521,1280,440,1081) -> Matrix(29,2,1000,69) Matrix(721,1760,492,1201) -> Matrix(115,8,3148,219) Matrix(4919,12000,1918,4679) -> Matrix(259,18,4072,283) Matrix(3281,8000,1280,3121) -> Matrix(115,8,1768,123) Matrix(559,1360,164,399) -> Matrix(115,8,1308,91) Matrix(1519,3680,-892,-2161) -> Matrix(871,60,-18712,-1289) Matrix(3239,7840,-2000,-4841) -> Matrix(727,50,-16532,-1137) Matrix(959,2320,198,479) -> Matrix(291,20,2488,171) Matrix(2319,5600,364,879) -> Matrix(175,12,1152,79) Matrix(961,2320,862,2081) -> Matrix(117,8,4168,285) Matrix(199,480,182,439) -> Matrix(29,2,1000,69) Matrix(1759,4240,1128,2719) -> Matrix(233,16,5956,409) Matrix(599,1440,-250,-601) -> Matrix(263,18,-3872,-265) Matrix(1839,4400,568,1359) -> Matrix(59,4,752,51) Matrix(4959,11840,-2882,-6881) -> Matrix(1535,104,-32604,-2209) Matrix(639,1520,-404,-961) -> Matrix(119,8,-2752,-185) Matrix(439,1040,84,199) -> Matrix(89,6,608,41) Matrix(2839,6720,1098,2599) -> Matrix(1041,70,16076,1081) Matrix(879,2080,-778,-1841) -> Matrix(119,8,-4180,-281) Matrix(441,1040,-254,-599) -> Matrix(329,22,-6924,-463) Matrix(3801,8800,-2332,-5399) -> Matrix(335,22,-7568,-497) Matrix(1039,2400,242,559) -> Matrix(245,16,2404,157) Matrix(521,1200,122,281) -> Matrix(31,2,356,23) Matrix(801,1840,488,1121) -> Matrix(247,16,6036,391) Matrix(559,1280,314,719) -> Matrix(371,24,8332,539) Matrix(561,1280,316,721) -> Matrix(373,24,8408,541) Matrix(879,2000,316,719) -> Matrix(125,8,1828,117) Matrix(1199,2720,458,1039) -> Matrix(63,4,992,63) Matrix(1801,4080,-1006,-2279) -> Matrix(1033,66,-21020,-1343) Matrix(1521,3440,814,1841) -> Matrix(879,56,18820,1199) Matrix(1841,4160,1452,3281) -> Matrix(63,4,2000,127) Matrix(359,800,-162,-361) -> Matrix(287,18,-4608,-289) Matrix(1121,2480,796,1761) -> Matrix(193,12,5420,337) Matrix(761,1680,236,521) -> Matrix(161,10,1948,121) Matrix(439,960,-348,-761) -> Matrix(163,10,-4776,-293) Matrix(881,1920,184,401) -> Matrix(131,8,1228,75) Matrix(479,1040,368,799) -> Matrix(197,12,5992,365) Matrix(1599,3440,892,1919) -> Matrix(929,56,20720,1249) Matrix(521,1120,354,761) -> Matrix(299,18,8156,491) Matrix(599,1280,168,359) -> Matrix(301,18,3428,205) Matrix(641,1360,-452,-959) -> Matrix(337,20,-8880,-527) Matrix(919,1760,-648,-1241) -> Matrix(491,26,-12936,-685) Matrix(679,1280,148,279) -> Matrix(269,14,2248,117) Matrix(641,1200,86,161) -> Matrix(155,8,988,51) Matrix(1841,3440,814,1521) -> Matrix(1087,56,19236,991) Matrix(1201,2240,-986,-1839) -> Matrix(389,20,-11884,-611) Matrix(561,1040,130,241) -> Matrix(235,12,2252,115) Matrix(1039,1920,822,1519) -> Matrix(157,8,4808,245) Matrix(1001,1840,414,761) -> Matrix(593,30,9824,497) Matrix(439,800,-242,-441) -> Matrix(359,18,-7200,-361) Matrix(839,1520,154,279) -> Matrix(201,10,1628,81) Matrix(841,1520,244,441) -> Matrix(121,6,1472,73) Matrix(2319,4160,490,879) -> Matrix(81,4,668,33) Matrix(1919,3440,892,1599) -> Matrix(1137,56,21136,1041) Matrix(8039,14400,3550,6359) -> Matrix(4757,234,84020,4133) Matrix(8041,14400,3552,6361) -> Matrix(4759,234,84096,4135) Matrix(761,1360,202,361) -> Matrix(41,2,512,25) Matrix(1121,2000,718,1281) -> Matrix(163,8,4136,203) Matrix(719,1280,314,559) -> Matrix(491,24,8572,419) Matrix(721,1280,316,561) -> Matrix(493,24,8648,421) Matrix(1039,1840,406,719) -> Matrix(329,16,5120,249) Matrix(679,1200,520,919) -> Matrix(41,2,1168,57) Matrix(1361,2400,1044,1841) -> Matrix(331,16,9992,483) Matrix(1319,2320,-842,-1481) -> Matrix(539,26,-12708,-613) Matrix(919,1600,390,679) -> Matrix(713,34,12100,577) Matrix(921,1600,392,681) -> Matrix(715,34,12176,579) Matrix(2401,4160,-1754,-3039) -> Matrix(1013,48,-27752,-1315) Matrix(3881,6720,2380,4121) -> Matrix(1479,70,36320,1719) Matrix(601,1040,486,841) -> Matrix(127,6,4212,199) Matrix(1161,2000,256,441) -> Matrix(43,2,408,19) Matrix(1441,2480,-1208,-2079) -> Matrix(85,4,-2444,-115) Matrix(14879,25600,6230,10719) -> Matrix(4759,224,79692,3751) Matrix(14881,25600,6232,10721) -> Matrix(4761,224,79768,3753) Matrix(2001,3440,-1442,-2479) -> Matrix(511,24,-13648,-641) Matrix(2759,4720,-1988,-3401) -> Matrix(127,6,-3408,-161) Matrix(2481,4240,890,1521) -> Matrix(343,16,4952,231) Matrix(281,480,24,41) -> Matrix(43,2,236,11) Matrix(1359,2320,140,239) -> Matrix(171,8,748,35) Matrix(1641,2800,446,761) -> Matrix(385,18,4128,193) Matrix(1079,1840,492,839) -> Matrix(643,30,11724,547) Matrix(10561,18000,6478,11041) -> Matrix(171,8,4168,195) Matrix(3759,6400,1550,2639) -> Matrix(2235,104,36856,1715) Matrix(3761,6400,1552,2641) -> Matrix(2237,104,36932,1717) Matrix(801,1360,566,961) -> Matrix(173,8,4952,229) Matrix(4719,8000,2878,4879) -> Matrix(173,8,4260,197) Matrix(7081,12000,4320,7321) -> Matrix(389,18,9444,437) Matrix(1039,1760,330,559) -> Matrix(173,8,2184,101) Matrix(521,880,-402,-679) -> Matrix(217,10,-6228,-287) Matrix(1159,1920,-894,-1481) -> Matrix(311,14,-8908,-401) Matrix(1601,2640,1262,2081) -> Matrix(89,4,2692,121) Matrix(681,1120,560,921) -> Matrix(223,10,7292,327) Matrix(1121,1840,488,801) -> Matrix(359,16,6260,279) Matrix(4879,8000,2878,4719) -> Matrix(181,8,4276,189) Matrix(7321,12000,4320,7081) -> Matrix(401,18,9468,425) Matrix(1319,2160,952,1559) -> Matrix(223,10,6400,287) Matrix(3919,6400,1518,2479) -> Matrix(1979,88,30652,1363) Matrix(3921,6400,1520,2481) -> Matrix(1981,88,30728,1365) Matrix(4121,6720,2380,3881) -> Matrix(1579,70,36520,1619) Matrix(12121,19760,4638,7561) -> Matrix(767,34,11708,519) Matrix(26159,42640,-20172,-32881) -> Matrix(181,8,-5136,-227) Matrix(1081,1760,320,521) -> Matrix(317,14,3736,165) Matrix(1481,2400,1062,1721) -> Matrix(227,10,6424,283) Matrix(12199,19760,4716,7639) -> Matrix(773,34,11936,525) Matrix(1681,2720,940,1521) -> Matrix(89,4,1980,89) Matrix(199,320,74,119) -> Matrix(137,6,2032,89) Matrix(201,320,76,121) -> Matrix(139,6,2108,91) Matrix(2279,3600,-1444,-2281) -> Matrix(419,18,-9800,-421) Matrix(2079,3280,1622,2559) -> Matrix(281,12,8828,377) Matrix(559,880,-458,-721) -> Matrix(93,4,-2860,-123) Matrix(919,1440,-792,-1241) -> Matrix(47,2,-1716,-73) Matrix(11239,17600,-8200,-12841) -> Matrix(331,14,-9008,-381) Matrix(2761,4320,1918,3001) -> Matrix(709,30,19592,829) Matrix(1279,2000,204,319) -> Matrix(95,4,736,31) Matrix(1281,2000,718,1121) -> Matrix(187,8,4184,179) Matrix(2719,4240,1128,1759) -> Matrix(377,16,6244,265) Matrix(9239,14400,3310,5159) -> Matrix(1277,54,18280,773) Matrix(9241,14400,3312,5161) -> Matrix(1279,54,18356,775) Matrix(361,560,78,121) -> Matrix(47,2,352,15) Matrix(519,800,-338,-521) -> Matrix(335,14,-8064,-337) Matrix(681,1040,184,281) -> Matrix(243,10,2600,107) Matrix(599,880,-518,-761) -> Matrix(51,2,-1556,-61) Matrix(1201,1760,492,721) -> Matrix(203,8,3324,131) Matrix(439,640,356,519) -> Matrix(51,2,1708,67) Matrix(1159,1680,634,919) -> Matrix(259,10,5672,219) Matrix(1879,2720,248,359) -> Matrix(51,2,280,11) Matrix(3041,4400,1770,2561) -> Matrix(101,4,2348,93) Matrix(279,400,-196,-281) -> Matrix(155,6,-4056,-157) Matrix(1239,1760,478,679) -> Matrix(367,14,5636,215) Matrix(3439,4880,2198,3119) -> Matrix(947,36,24280,923) Matrix(28199,40000,8318,11799) -> Matrix(9005,342,105032,3989) Matrix(28201,40000,8320,11801) -> Matrix(9007,342,105108,3991) Matrix(961,1360,566,801) -> Matrix(213,8,5032,189) Matrix(2039,2880,594,839) -> Matrix(53,2,556,21) Matrix(2041,2880,596,841) -> Matrix(55,2,632,23) Matrix(1759,2480,-1476,-2081) -> Matrix(1,0,-4,1) Matrix(1079,1520,482,679) -> Matrix(155,6,2764,107) Matrix(6199,8720,-4522,-6361) -> Matrix(263,10,-7180,-273) Matrix(1721,2400,1062,1481) -> Matrix(263,10,6496,247) Matrix(1839,2560,1436,1999) -> Matrix(211,8,6620,251) Matrix(921,1280,490,681) -> Matrix(479,18,10192,383) Matrix(4841,6720,894,1241) -> Matrix(267,10,2216,83) Matrix(2481,3440,520,721) -> Matrix(107,4,936,35) Matrix(1559,2160,952,1319) -> Matrix(267,10,6488,243) Matrix(1159,1600,318,439) -> Matrix(593,22,6496,241) Matrix(1161,1600,320,441) -> Matrix(595,22,6572,243) Matrix(2039,2800,844,1159) -> Matrix(491,18,8156,299) Matrix(42079,57680,-32450,-44481) -> Matrix(329,12,-9404,-343) Matrix(759,1040,262,359) -> Matrix(273,10,3740,137) Matrix(18719,25600,5030,6879) -> Matrix(3739,136,39232,1427) Matrix(18721,25600,5032,6881) -> Matrix(3741,136,39308,1429) Matrix(3921,5360,-3218,-4399) -> Matrix(331,12,-10068,-365) Matrix(2519,3440,1786,2439) -> Matrix(55,2,1512,55) Matrix(999,1360,440,599) -> Matrix(51,2,892,35) Matrix(119,160,-90,-121) -> Matrix(55,2,-1568,-57) Matrix(4879,6400,1158,1519) -> Matrix(1,0,40,1) Matrix(4881,6400,1160,1521) -> Matrix(1,0,36,1) Matrix(3481,4560,642,841) -> Matrix(57,2,484,17) Matrix(919,1200,520,679) -> Matrix(53,2,1192,45) Matrix(1841,2400,1044,1361) -> Matrix(451,16,10232,363) Matrix(799,1040,368,479) -> Matrix(341,12,6280,221) Matrix(801,1040,124,161) -> Matrix(115,4,776,27) Matrix(208519,270400,47718,61879) -> Matrix(1429,50,13404,469) Matrix(208521,270400,47720,61881) -> Matrix(1431,50,13480,471) Matrix(1239,1600,278,359) -> Matrix(521,18,4660,161) Matrix(1241,1600,280,361) -> Matrix(523,18,4736,163) Matrix(1559,2000,654,839) -> Matrix(57,2,940,33) Matrix(1999,2560,1436,1839) -> Matrix(235,8,6668,227) Matrix(1001,1280,470,601) -> Matrix(415,14,7796,263) Matrix(439,560,156,199) -> Matrix(61,2,884,29) Matrix(5039,6400,1070,1359) -> Matrix(1,0,44,1) Matrix(5041,6400,1072,1361) -> Matrix(1,0,32,1) Matrix(2081,2640,1262,1601) -> Matrix(113,4,2740,97) Matrix(3281,4160,1452,1841) -> Matrix(119,4,2112,71) Matrix(1199,1520,1072,1359) -> Matrix(1,0,64,1) Matrix(2719,3440,758,959) -> Matrix(117,4,1316,45) Matrix(1519,1920,822,1039) -> Matrix(229,8,4952,173) Matrix(1841,2320,1080,1361) -> Matrix(589,20,13812,469) Matrix(841,1040,486,601) -> Matrix(187,6,4332,139) Matrix(519,640,356,439) -> Matrix(63,2,1732,55) Matrix(5479,6720,1532,1879) -> Matrix(297,10,3356,113) Matrix(3719,4560,880,1079) -> Matrix(59,2,560,19) Matrix(1241,1520,556,681) -> Matrix(299,10,5352,179) Matrix(921,1120,560,681) -> Matrix(307,10,7460,243) Matrix(1319,1600,230,279) -> Matrix(433,14,3000,97) Matrix(1321,1600,232,281) -> Matrix(435,14,3076,99) Matrix(1681,2000,606,721) -> Matrix(121,4,1724,57) Matrix(4721,5600,2766,3281) -> Matrix(377,12,8828,281) Matrix(879,1040,202,239) -> Matrix(125,4,1156,37) Matrix(679,800,-578,-681) -> Matrix(191,6,-6144,-193) Matrix(5519,6400,758,879) -> Matrix(1,0,56,1) Matrix(5521,6400,760,881) -> Matrix(1,0,20,1) Matrix(1039,1200,484,559) -> Matrix(253,8,4712,149) Matrix(2361,2720,730,841) -> Matrix(65,2,812,25) Matrix(279,320,34,39) -> Matrix(65,2,292,9) Matrix(281,320,36,41) -> Matrix(67,2,368,11) Matrix(1359,1520,1072,1199) -> Matrix(1,0,64,1) Matrix(2081,2320,862,961) -> Matrix(269,8,4472,133) Matrix(439,480,182,199) -> Matrix(65,2,1072,33) Matrix(1,0,2,1) -> Matrix(1,0,76,1) Matrix(1839,-2080,496,-561) -> Matrix(291,-8,3092,-85) Matrix(1321,-1520,312,-359) -> Matrix(69,-2,656,-19) Matrix(761,-880,518,-599) -> Matrix(65,-2,1788,-55) Matrix(1241,-1440,792,-919) -> Matrix(77,-2,1964,-51) Matrix(1159,-1360,444,-521) -> Matrix(343,-10,5248,-153) Matrix(881,-1040,338,-399) -> Matrix(269,-8,4136,-123) Matrix(2361,-2800,640,-759) -> Matrix(199,-6,2156,-65) Matrix(2079,-2480,1208,-1441) -> Matrix(123,-4,2860,-93) Matrix(199,-240,34,-41) -> Matrix(67,-2,436,-13) Matrix(721,-880,458,-559) -> Matrix(131,-4,3308,-101) Matrix(521,-640,162,-199) -> Matrix(63,-2,788,-25) Matrix(761,-960,348,-439) -> Matrix(313,-10,5728,-183) Matrix(881,-1120,188,-239) -> Matrix(1,0,-24,1) Matrix(2001,-2560,562,-719) -> Matrix(505,-16,5776,-183) Matrix(681,-880,154,-199) -> Matrix(309,-10,2812,-91) Matrix(679,-880,402,-521) -> Matrix(307,-10,7276,-237) Matrix(121,-160,90,-119) -> Matrix(61,-2,1800,-59) Matrix(1359,-1840,178,-241) -> Matrix(1,0,-24,1) Matrix(2361,-3200,560,-759) -> Matrix(59,-2,620,-21) Matrix(1001,-1360,382,-519) -> Matrix(57,-2,884,-31) Matrix(2401,-3280,702,-959) -> Matrix(237,-8,2696,-91) Matrix(2399,-3280,1288,-1761) -> Matrix(945,-32,20288,-687) Matrix(3041,-4160,818,-1119) -> Matrix(825,-28,8692,-295) Matrix(1519,-2080,176,-241) -> Matrix(235,-8,852,-29) Matrix(4201,-5760,962,-1319) -> Matrix(527,-18,4948,-169) Matrix(2041,-2800,320,-439) -> Matrix(175,-6,1196,-41) Matrix(521,-720,144,-199) -> Matrix(289,-10,3208,-111) Matrix(2479,-3440,1442,-2001) -> Matrix(689,-24,16048,-559) Matrix(1841,-2560,402,-559) -> Matrix(457,-16,3856,-135) Matrix(1081,-1520,426,-599) -> Matrix(169,-6,2676,-95) Matrix(3519,-4960,2044,-2881) -> Matrix(107,-4,2488,-93) Matrix(2321,-3280,622,-879) -> Matrix(229,-8,2376,-83) Matrix(281,-400,196,-279) -> Matrix(169,-6,4704,-167) Matrix(1001,-1440,472,-679) -> Matrix(609,-22,11488,-415) Matrix(441,-640,82,-119) -> Matrix(55,-2,468,-17) Matrix(521,-800,338,-519) -> Matrix(365,-14,9464,-363) Matrix(1079,-1680,386,-601) -> Matrix(155,-6,2196,-85) Matrix(1481,-2320,842,-1319) -> Matrix(665,-26,15116,-591) Matrix(2041,-3200,280,-439) -> Matrix(51,-2,740,-29) Matrix(2081,-3280,1116,-1759) -> Matrix(409,-16,8768,-343) Matrix(2839,-4480,1192,-1881) -> Matrix(559,-22,9376,-369) Matrix(961,-1520,404,-639) -> Matrix(201,-8,3392,-135) Matrix(841,-1360,222,-359) -> Matrix(49,-2,564,-23) Matrix(4841,-7840,2000,-3239) -> Matrix(1237,-50,20460,-827) Matrix(839,-1360,124,-201) -> Matrix(247,-10,1408,-57) Matrix(5841,-9520,2110,-3439) -> Matrix(589,-24,8516,-347) Matrix(881,-1440,342,-559) -> Matrix(489,-20,7604,-311) Matrix(921,-1520,266,-439) -> Matrix(145,-6,1716,-71) Matrix(1759,-2960,476,-801) -> Matrix(381,-16,4072,-171) Matrix(2161,-3680,892,-1519) -> Matrix(1409,-60,23272,-991) Matrix(4601,-7840,1760,-2999) -> Matrix(1173,-50,17900,-763) Matrix(841,-1440,490,-839) -> Matrix(421,-18,9800,-419) Matrix(6881,-11840,2882,-4959) -> Matrix(2417,-104,40508,-1743) Matrix(881,-1520,324,-559) -> Matrix(185,-8,2752,-119) Matrix(1201,-2080,138,-239) -> Matrix(185,-8,532,-23) Matrix(599,-1040,254,-441) -> Matrix(507,-22,8596,-373) Matrix(4999,-8800,1932,-3401) -> Matrix(501,-22,7720,-339) Matrix(2279,-4080,1006,-1801) -> Matrix(1475,-66,26036,-1165) Matrix(441,-800,242,-439) -> Matrix(397,-18,8712,-395) Matrix(521,-960,108,-199) -> Matrix(217,-10,1888,-87) Matrix(719,-1360,212,-401) -> Matrix(423,-20,4928,-233) Matrix(841,-1760,248,-519) -> Matrix(497,-26,5792,-303) Matrix(1039,-2240,186,-401) -> Matrix(371,-20,2764,-149) Matrix(361,-800,162,-359) -> Matrix(325,-18,5832,-323) Matrix(1001,-2320,362,-839) -> Matrix(449,-26,6476,-375) Matrix(1759,-4160,474,-1121) -> Matrix(811,-48,8600,-509) Matrix(1039,-2480,168,-401) -> Matrix(67,-4,620,-37) Matrix(1439,-3440,402,-961) -> Matrix(401,-24,4528,-271) Matrix(1961,-4720,548,-1319) -> Matrix(101,-6,1128,-67) Matrix(359,-880,82,-201) -> Matrix(163,-10,1516,-93) Matrix(761,-1920,174,-439) -> Matrix(221,-14,2068,-131) Matrix(16481,-42640,3772,-9759) -> Matrix(123,-8,1184,-77) Matrix(1321,-3600,484,-1319) -> Matrix(265,-18,3872,-263) Matrix(321,-880,58,-159) -> Matrix(59,-4,428,-29) Matrix(521,-1440,72,-199) -> Matrix(29,-2,44,-3) Matrix(6361,-17600,1720,-4759) -> Matrix(201,-14,2168,-151) Matrix(281,-800,98,-279) -> Matrix(197,-14,2744,-195) Matrix(281,-880,38,-119) -> Matrix(25,-2,188,-15) Matrix(121,-400,36,-119) -> Matrix(73,-6,864,-71) Matrix(721,-2480,116,-399) -> Matrix(1,0,-4,1) Matrix(2521,-8720,682,-2359) -> Matrix(117,-10,1252,-107) Matrix(15601,-57680,3570,-13199) -> Matrix(127,-12,1196,-113) Matrix(1439,-5360,258,-961) -> Matrix(125,-12,948,-91) Matrix(41,-160,10,-39) -> Matrix(21,-2,200,-19) Matrix(121,-800,18,-119) -> Matrix(37,-6,216,-35) 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 10/9 8/7 5/4 4/3 10/7 30/19 8/5 16/9 2/1 20/9 30/13 40/17 12/5 80/33 5/2 100/39 8/3 30/11 20/7 3/1 10/3 24/7 18/5 40/11 26/7 34/9 4/1 80/19 30/7 22/5 40/9 14/3 80/17 24/5 5/1 16/3 28/5 40/7 6/1 20/3 7/1 15/2 38/5 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 0/1 1/39 10/9 1/36 9/8 0/1 1/33 8/7 1/35 23/20 0/1 1/35 15/13 1/34 7/6 1/35 2/69 6/5 1/34 17/14 1/33 6/197 11/9 2/65 3/97 16/13 0/1 21/17 0/1 1/33 5/4 1/32 19/15 2/63 1/31 33/26 0/1 1/29 14/11 1/32 9/7 4/125 1/31 22/17 5/154 13/10 5/153 2/61 30/23 1/30 17/13 1/31 2/61 4/3 1/30 23/17 0/1 1/29 42/31 1/30 19/14 2/59 1/29 15/11 1/30 26/19 7/206 37/27 7/205 4/117 48/35 4/117 11/8 6/175 1/29 18/13 5/144 7/5 1/29 2/57 10/7 1/28 13/9 2/55 1/27 16/11 2/55 19/13 2/55 1/27 3/2 1/27 2/53 14/9 1/26 11/7 2/51 5/127 30/19 3/76 19/12 2/51 1/25 8/5 1/25 21/13 1/25 4/99 34/21 5/124 13/8 1/25 2/49 18/11 5/122 41/25 1/25 2/49 23/14 8/195 3/73 28/17 1/24 33/20 4/97 5/121 5/3 1/24 27/16 5/119 4/95 22/13 5/118 39/23 3/71 2/47 17/10 11/259 2/47 46/27 15/352 29/17 12/281 5/117 70/41 3/70 41/24 2/47 9/211 12/7 3/70 31/18 6/139 1/23 19/11 6/139 1/23 26/15 11/254 7/4 1/23 6/137 30/17 3/68 23/13 8/181 5/113 39/22 9/203 2/45 16/9 2/45 41/23 2/45 3/67 25/14 5/112 34/19 11/246 9/5 4/89 5/111 2/1 1/20 11/5 5/91 6/109 20/9 1/18 29/13 13/233 12/215 38/17 1/18 9/4 5/89 4/71 34/15 11/194 25/11 5/88 16/7 2/35 39/17 2/35 9/157 23/10 5/87 8/139 30/13 3/52 7/3 6/103 1/17 40/17 1/17 33/14 1/17 28/475 26/11 11/186 45/19 7/118 19/8 1/17 6/101 50/21 5/84 31/13 1/17 6/101 43/18 4/67 15/251 12/5 3/50 53/22 8/133 5/83 41/17 9/149 2/33 70/29 3/50 29/12 5/83 12/199 46/19 15/248 63/26 41/677 2/33 80/33 2/33 17/7 2/33 11/181 39/16 2/33 3/49 100/41 5/82 61/25 2/33 3/49 22/9 5/82 5/2 1/16 33/13 5/79 4/63 28/11 1/16 23/9 3/47 8/125 41/16 2/31 1/15 100/39 1/16 59/23 4/63 3/47 18/7 5/78 13/5 2/31 1/15 47/18 7/107 4/61 34/13 5/76 55/21 3/46 21/8 4/61 1/15 8/3 1/15 19/7 1/15 2/29 30/11 3/44 41/15 5/73 2/29 11/4 5/73 2/29 14/5 1/14 17/6 6/85 7/99 20/7 1/14 23/8 8/111 7/97 3/1 2/27 1/13 10/3 1/12 17/5 7/81 2/23 41/12 2/23 1/11 24/7 1/11 31/9 1/13 2/25 38/11 1/12 45/13 1/12 7/2 2/23 1/11 18/5 5/56 29/8 16/177 1/11 40/11 1/11 11/3 1/11 6/65 37/10 4/43 7/75 63/17 14/149 11/117 26/7 7/74 41/11 2/21 3/31 15/4 1/10 34/9 3/32 19/5 1/11 2/21 4/1 1/10 21/5 0/1 1/9 80/19 0/1 59/14 0/1 1/11 38/9 1/10 55/13 1/10 17/4 2/19 1/9 30/7 1/10 13/3 2/19 5/47 35/8 3/28 22/5 5/46 31/7 14/127 1/9 40/9 1/9 9/2 1/9 4/35 14/3 1/8 47/10 0/1 1/5 80/17 0/1 33/7 0/1 1/11 52/11 1/10 19/4 1/9 2/17 24/5 1/9 5/1 1/8 21/4 0/1 1/7 16/3 0/1 27/5 0/1 1/9 65/12 1/8 38/7 1/8 11/2 3/23 2/15 28/5 3/22 17/3 6/43 1/7 40/7 1/7 23/4 1/7 8/55 6/1 1/6 13/2 2/13 3/19 20/3 1/6 27/4 4/23 3/17 7/1 2/11 1/5 15/2 1/6 38/5 1/6 23/3 0/1 1/5 8/1 1/5 17/2 1/5 2/9 9/1 0/1 1/7 10/1 1/4 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(439,-480,257,-281) (1/1,10/9) -> (70/41,41/24) Hyperbolic Matrix(821,-920,481,-539) (10/9,9/8) -> (29/17,70/41) Hyperbolic Matrix(461,-520,336,-379) (9/8,8/7) -> (48/35,11/8) Hyperbolic Matrix(1219,-1400,889,-1021) (8/7,23/20) -> (37/27,48/35) Hyperbolic Matrix(1321,-1520,312,-359) (23/20,15/13) -> (55/13,17/4) Hyperbolic Matrix(379,-440,87,-101) (15/13,7/6) -> (13/3,35/8) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(821,-1000,344,-419) (17/14,11/9) -> (31/13,43/18) Hyperbolic Matrix(619,-760,180,-221) (11/9,16/13) -> (24/7,31/9) Hyperbolic Matrix(941,-1160,275,-339) (16/13,21/17) -> (41/12,24/7) Hyperbolic Matrix(841,-1040,355,-439) (21/17,5/4) -> (45/19,19/8) Hyperbolic Matrix(539,-680,302,-381) (5/4,19/15) -> (41/23,25/14) Hyperbolic Matrix(1861,-2360,772,-979) (19/15,33/26) -> (53/22,41/17) Hyperbolic Matrix(881,-1120,188,-239) (33/26,14/11) -> (14/3,47/10) Hyperbolic Matrix(219,-280,79,-101) (14/11,9/7) -> (11/4,14/5) Hyperbolic Matrix(681,-880,154,-199) (9/7,22/17) -> (22/5,31/7) Hyperbolic Matrix(679,-880,402,-521) (22/17,13/10) -> (27/16,22/13) Hyperbolic Matrix(461,-600,199,-259) (13/10,30/23) -> (30/13,7/3) Hyperbolic Matrix(919,-1200,399,-521) (30/23,17/13) -> (23/10,30/13) Hyperbolic Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(1359,-1840,178,-241) (23/17,42/31) -> (38/5,23/3) Hyperbolic Matrix(2361,-3200,560,-759) (42/31,19/14) -> (59/14,38/9) Hyperbolic Matrix(1001,-1360,382,-519) (19/14,15/11) -> (55/21,21/8) Hyperbolic Matrix(1141,-1560,482,-659) (15/11,26/19) -> (26/11,45/19) Hyperbolic Matrix(1899,-2600,512,-701) (26/19,37/27) -> (63/17,26/7) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(259,-360,159,-221) (18/13,7/5) -> (13/8,18/11) Hyperbolic Matrix(141,-200,98,-139) (7/5,10/7) -> (10/7,13/9) Parabolic Matrix(441,-640,82,-119) (13/9,16/11) -> (16/3,27/5) Hyperbolic Matrix(439,-640,83,-121) (16/11,19/13) -> (21/4,16/3) Hyperbolic Matrix(299,-440,123,-181) (19/13,3/2) -> (17/7,39/16) Hyperbolic Matrix(181,-280,64,-99) (3/2,14/9) -> (14/5,17/6) Hyperbolic Matrix(179,-280,39,-61) (14/9,11/7) -> (9/2,14/3) Hyperbolic Matrix(939,-1480,394,-621) (11/7,30/19) -> (50/21,31/13) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(201,-320,125,-199) (19/12,8/5) -> (8/5,21/13) Parabolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(1099,-1800,428,-701) (18/11,41/25) -> (59/23,18/7) Hyperbolic Matrix(1121,-1840,633,-1039) (41/25,23/14) -> (23/13,39/22) Hyperbolic Matrix(681,-1120,121,-199) (23/14,28/17) -> (28/5,17/3) Hyperbolic Matrix(1601,-2640,339,-559) (28/17,33/20) -> (33/7,52/11) Hyperbolic Matrix(921,-1520,266,-439) (33/20,5/3) -> (45/13,7/2) Hyperbolic Matrix(261,-440,35,-59) (5/3,27/16) -> (7/1,15/2) Hyperbolic Matrix(1299,-2200,532,-901) (22/13,39/23) -> (61/25,22/9) Hyperbolic Matrix(801,-1360,235,-399) (39/23,17/10) -> (17/5,41/12) Hyperbolic Matrix(2161,-3680,892,-1519) (17/10,46/27) -> (46/19,63/26) Hyperbolic Matrix(821,-1400,363,-619) (46/27,29/17) -> (9/4,34/15) Hyperbolic Matrix(1381,-2360,292,-499) (41/24,12/7) -> (52/11,19/4) Hyperbolic Matrix(581,-1000,104,-179) (12/7,31/18) -> (11/2,28/5) Hyperbolic Matrix(859,-1480,314,-541) (31/18,19/11) -> (41/15,11/4) Hyperbolic Matrix(901,-1560,242,-419) (19/11,26/15) -> (26/7,41/11) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(341,-600,79,-139) (7/4,30/17) -> (30/7,13/3) Hyperbolic Matrix(679,-1200,159,-281) (30/17,23/13) -> (17/4,30/7) Hyperbolic Matrix(721,-1280,405,-719) (39/22,16/9) -> (16/9,41/23) Parabolic Matrix(1521,-2720,581,-1039) (25/14,34/19) -> (34/13,55/21) Hyperbolic Matrix(781,-1400,323,-579) (34/19,9/5) -> (29/12,46/19) Hyperbolic Matrix(21,-40,10,-19) (9/5,2/1) -> (2/1,11/5) Parabolic Matrix(361,-800,162,-359) (11/5,20/9) -> (20/9,29/13) Parabolic Matrix(681,-1520,125,-279) (29/13,38/17) -> (38/7,11/2) Hyperbolic Matrix(679,-1520,197,-441) (38/17,9/4) -> (31/9,38/11) Hyperbolic Matrix(599,-1360,159,-361) (34/15,25/11) -> (15/4,34/9) Hyperbolic Matrix(299,-680,62,-141) (25/11,16/7) -> (24/5,5/1) Hyperbolic Matrix(541,-1240,113,-259) (16/7,39/17) -> (19/4,24/5) Hyperbolic Matrix(801,-1840,313,-719) (39/17,23/10) -> (23/9,41/16) Hyperbolic Matrix(681,-1600,289,-679) (7/3,40/17) -> (40/17,33/14) Parabolic Matrix(619,-1480,243,-581) (43/18,12/5) -> (28/11,23/9) Hyperbolic Matrix(781,-1880,307,-739) (12/5,53/22) -> (33/13,28/11) Hyperbolic Matrix(199,-480,17,-41) (41/17,70/29) -> (10/1,1/0) Hyperbolic Matrix(381,-920,41,-99) (70/29,29/12) -> (9/1,10/1) Hyperbolic Matrix(2641,-6400,1089,-2639) (63/26,80/33) -> (80/33,17/7) Parabolic Matrix(4019,-9800,1567,-3821) (39/16,100/41) -> (100/39,59/23) Hyperbolic Matrix(4181,-10200,1631,-3979) (100/41,61/25) -> (41/16,100/39) Hyperbolic Matrix(359,-880,82,-201) (22/9,5/2) -> (35/8,22/5) Hyperbolic Matrix(899,-2280,166,-421) (5/2,33/13) -> (27/5,65/12) Hyperbolic Matrix(139,-360,39,-101) (18/7,13/5) -> (7/2,18/5) Hyperbolic Matrix(261,-680,38,-99) (13/5,47/18) -> (27/4,7/1) Hyperbolic Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(661,-1800,242,-659) (19/7,30/11) -> (30/11,41/15) Parabolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(359,-1040,97,-281) (23/8,3/1) -> (37/10,63/17) Hyperbolic Matrix(61,-200,18,-59) (3/1,10/3) -> (10/3,17/5) Parabolic Matrix(659,-2280,87,-301) (38/11,45/13) -> (15/2,38/5) Hyperbolic Matrix(441,-1600,121,-439) (29/8,40/11) -> (40/11,11/3) Parabolic Matrix(141,-520,16,-59) (11/3,37/10) -> (17/2,9/1) Hyperbolic Matrix(139,-520,27,-101) (41/11,15/4) -> (5/1,21/4) Hyperbolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(1521,-6400,361,-1519) (21/5,80/19) -> (80/19,59/14) Parabolic Matrix(1079,-4560,199,-841) (38/9,55/13) -> (65/12,38/7) Hyperbolic Matrix(361,-1600,81,-359) (31/7,40/9) -> (40/9,9/2) Parabolic Matrix(1361,-6400,289,-1359) (47/10,80/17) -> (80/17,33/7) Parabolic Matrix(281,-1600,49,-279) (17/3,40/7) -> (40/7,23/4) Parabolic Matrix(121,-800,18,-119) (13/2,20/3) -> (20/3,27/4) Parabolic Matrix(41,-320,5,-39) (23/3,8/1) -> (8/1,17/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,38,1) Matrix(439,-480,257,-281) -> Matrix(69,-2,1622,-47) Matrix(821,-920,481,-539) -> Matrix(177,-5,4142,-117) Matrix(461,-520,336,-379) -> Matrix(39,-1,1132,-29) Matrix(1219,-1400,889,-1021) -> Matrix(241,-7,7058,-205) Matrix(1321,-1520,312,-359) -> Matrix(69,-2,656,-19) Matrix(379,-440,87,-101) -> Matrix(37,-1,334,-9) Matrix(101,-120,16,-19) -> Matrix(33,-1,232,-7) Matrix(199,-240,34,-41) -> Matrix(67,-2,436,-13) Matrix(821,-1000,344,-419) -> Matrix(293,-9,4916,-151) Matrix(619,-760,180,-221) -> Matrix(33,-1,364,-11) Matrix(941,-1160,275,-339) -> Matrix(35,-1,386,-11) Matrix(841,-1040,355,-439) -> Matrix(199,-6,3350,-101) Matrix(539,-680,302,-381) -> Matrix(219,-7,4912,-157) Matrix(1861,-2360,772,-979) -> Matrix(153,-5,2540,-83) Matrix(881,-1120,188,-239) -> Matrix(1,0,-24,1) Matrix(219,-280,79,-101) -> Matrix(95,-3,1362,-43) Matrix(681,-880,154,-199) -> Matrix(309,-10,2812,-91) Matrix(679,-880,402,-521) -> Matrix(307,-10,7276,-237) Matrix(461,-600,199,-259) -> Matrix(213,-7,3682,-121) Matrix(919,-1200,399,-521) -> Matrix(57,-2,998,-35) Matrix(121,-160,90,-119) -> Matrix(61,-2,1800,-59) Matrix(1359,-1840,178,-241) -> Matrix(1,0,-24,1) Matrix(2361,-3200,560,-759) -> Matrix(59,-2,620,-21) Matrix(1001,-1360,382,-519) -> Matrix(57,-2,884,-31) Matrix(1141,-1560,482,-659) -> Matrix(443,-15,7472,-253) Matrix(1899,-2600,512,-701) -> Matrix(617,-21,6552,-223) Matrix(521,-720,144,-199) -> Matrix(289,-10,3208,-111) Matrix(259,-360,159,-221) -> Matrix(143,-5,3518,-123) Matrix(141,-200,98,-139) -> Matrix(85,-3,2352,-83) Matrix(441,-640,82,-119) -> Matrix(55,-2,468,-17) Matrix(439,-640,83,-121) -> Matrix(55,-2,358,-13) Matrix(299,-440,123,-181) -> Matrix(191,-7,3138,-115) Matrix(181,-280,64,-99) -> Matrix(129,-5,1832,-71) Matrix(179,-280,39,-61) -> Matrix(77,-3,642,-25) Matrix(939,-1480,394,-621) -> Matrix(179,-7,2992,-117) Matrix(961,-1520,404,-639) -> Matrix(201,-8,3392,-135) Matrix(201,-320,125,-199) -> Matrix(151,-6,3750,-149) Matrix(841,-1360,222,-359) -> Matrix(49,-2,564,-23) Matrix(1259,-2040,482,-781) -> Matrix(371,-15,5664,-229) Matrix(1099,-1800,428,-701) -> Matrix(121,-5,1912,-79) Matrix(1121,-1840,633,-1039) -> Matrix(391,-16,8822,-361) Matrix(681,-1120,121,-199) -> Matrix(243,-10,1774,-73) Matrix(1601,-2640,339,-559) -> Matrix(97,-4,946,-39) Matrix(921,-1520,266,-439) -> Matrix(145,-6,1716,-71) Matrix(261,-440,35,-59) -> Matrix(71,-3,450,-19) Matrix(1299,-2200,532,-901) -> Matrix(119,-5,1928,-81) Matrix(801,-1360,235,-399) -> Matrix(189,-8,2150,-91) Matrix(2161,-3680,892,-1519) -> Matrix(1409,-60,23272,-991) Matrix(821,-1400,363,-619) -> Matrix(539,-23,9538,-407) Matrix(1381,-2360,292,-499) -> Matrix(117,-5,1100,-47) Matrix(581,-1000,104,-179) -> Matrix(209,-9,1556,-67) Matrix(859,-1480,314,-541) -> Matrix(163,-7,2352,-101) Matrix(901,-1560,242,-419) -> Matrix(347,-15,3632,-157) Matrix(599,-1040,254,-441) -> Matrix(507,-22,8596,-373) Matrix(341,-600,79,-139) -> Matrix(159,-7,1522,-67) Matrix(679,-1200,159,-281) -> Matrix(45,-2,518,-23) Matrix(721,-1280,405,-719) -> Matrix(541,-24,12150,-539) Matrix(1521,-2720,581,-1039) -> Matrix(89,-4,1402,-63) Matrix(781,-1400,323,-579) -> Matrix(513,-23,8498,-381) Matrix(21,-40,10,-19) -> Matrix(21,-1,400,-19) Matrix(361,-800,162,-359) -> Matrix(325,-18,5832,-323) Matrix(681,-1520,125,-279) -> Matrix(179,-10,1450,-81) Matrix(679,-1520,197,-441) -> Matrix(107,-6,1302,-73) Matrix(599,-1360,159,-361) -> Matrix(35,-2,438,-25) Matrix(299,-680,62,-141) -> Matrix(123,-7,1072,-61) Matrix(541,-1240,113,-259) -> Matrix(87,-5,818,-47) Matrix(801,-1840,313,-719) -> Matrix(279,-16,4342,-249) Matrix(681,-1600,289,-679) -> Matrix(579,-34,9826,-577) Matrix(619,-1480,243,-581) -> Matrix(217,-13,3422,-205) Matrix(781,-1880,307,-739) -> Matrix(117,-7,1822,-109) Matrix(199,-480,17,-41) -> Matrix(33,-2,182,-11) Matrix(381,-920,41,-99) -> Matrix(83,-5,382,-23) Matrix(2641,-6400,1089,-2639) -> Matrix(1717,-104,28314,-1715) Matrix(4019,-9800,1567,-3821) -> Matrix(279,-17,4382,-267) Matrix(4181,-10200,1631,-3979) -> Matrix(115,-7,1758,-107) Matrix(359,-880,82,-201) -> Matrix(163,-10,1516,-93) Matrix(899,-2280,166,-421) -> Matrix(79,-5,648,-41) Matrix(139,-360,39,-101) -> Matrix(77,-5,878,-57) Matrix(261,-680,38,-99) -> Matrix(77,-5,416,-27) Matrix(121,-320,45,-119) -> Matrix(91,-6,1350,-89) Matrix(661,-1800,242,-659) -> Matrix(133,-9,1936,-131) Matrix(281,-800,98,-279) -> Matrix(197,-14,2744,-195) Matrix(359,-1040,97,-281) -> Matrix(137,-10,1466,-107) Matrix(61,-200,18,-59) -> Matrix(37,-3,432,-35) Matrix(659,-2280,87,-301) -> Matrix(11,-1,78,-7) Matrix(441,-1600,121,-439) -> Matrix(243,-22,2662,-241) Matrix(141,-520,16,-59) -> Matrix(11,-1,12,-1) Matrix(139,-520,27,-101) -> Matrix(31,-3,238,-23) Matrix(41,-160,10,-39) -> Matrix(21,-2,200,-19) Matrix(1521,-6400,361,-1519) -> Matrix(1,0,2,1) Matrix(1079,-4560,199,-841) -> Matrix(19,-2,162,-17) Matrix(361,-1600,81,-359) -> Matrix(163,-18,1458,-161) Matrix(1361,-6400,289,-1359) -> Matrix(1,0,6,1) Matrix(281,-1600,49,-279) -> Matrix(99,-14,686,-97) Matrix(121,-800,18,-119) -> Matrix(37,-6,216,-35) Matrix(41,-320,5,-39) -> Matrix(11,-2,50,-9) 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 0/1 38 1 2/1 1/20 2 20 20/9 1/18 18 2 38/17 1/18 2 20 9/4 (5/89,4/71) 0 40 34/15 11/194 2 20 25/11 5/88 2 8 16/7 2/35 6 5 39/17 (2/35,9/157) 0 40 23/10 (5/87,8/139) 0 40 30/13 3/52 6 4 7/3 (6/103,1/17) 0 40 40/17 1/17 34 1 26/11 11/186 2 20 19/8 (1/17,6/101) 0 40 31/13 (1/17,6/101) 0 40 12/5 3/50 2 10 41/17 (9/149,2/33) 0 40 70/29 3/50 2 4 29/12 (5/83,12/199) 0 40 46/19 15/248 2 20 80/33 2/33 26 1 17/7 (2/33,11/181) 0 40 39/16 (2/33,3/49) 0 40 100/41 5/82 2 2 22/9 5/82 2 20 5/2 1/16 4 8 33/13 (5/79,4/63) 0 40 28/11 1/16 2 10 23/9 (3/47,8/125) 0 40 41/16 (2/31,1/15) 0 40 100/39 1/16 2 2 18/7 5/78 2 20 13/5 (2/31,1/15) 0 40 34/13 5/76 2 20 21/8 (4/61,1/15) 0 40 8/3 1/15 6 5 19/7 (1/15,2/29) 0 40 30/11 3/44 2 4 41/15 (5/73,2/29) 0 40 11/4 (5/73,2/29) 0 40 14/5 1/14 2 20 20/7 1/14 14 2 3/1 (2/27,1/13) 0 40 10/3 1/12 6 4 17/5 (7/81,2/23) 0 40 41/12 (2/23,1/11) 0 40 24/7 1/11 2 5 7/2 (2/23,1/11) 0 40 18/5 5/56 2 20 40/11 1/11 22 1 11/3 (1/11,6/65) 0 40 37/10 (4/43,7/75) 0 40 26/7 7/74 2 20 41/11 (2/21,3/31) 0 40 15/4 1/10 2 8 34/9 3/32 2 20 19/5 (1/11,2/21) 0 40 4/1 1/10 2 10 21/5 (0/1,1/9) 0 40 80/19 0/1 2 1 38/9 1/10 2 20 17/4 (2/19,1/9) 0 40 30/7 1/10 6 4 13/3 (2/19,5/47) 0 40 35/8 3/28 4 8 22/5 5/46 2 20 40/9 1/9 18 1 9/2 (1/9,4/35) 0 40 14/3 1/8 2 20 80/17 0/1 6 1 33/7 (0/1,1/11) 0 40 52/11 1/10 2 10 19/4 (1/9,2/17) 0 40 24/5 1/9 6 5 5/1 1/8 2 8 21/4 (0/1,1/7) 0 40 16/3 0/1 2 5 27/5 (0/1,1/9) 0 40 65/12 1/8 4 8 38/7 1/8 2 20 11/2 (3/23,2/15) 0 40 28/5 3/22 2 10 17/3 (6/43,1/7) 0 40 40/7 1/7 14 1 6/1 1/6 2 20 20/3 1/6 6 2 7/1 (2/11,1/5) 0 40 15/2 1/6 4 8 38/5 1/6 2 20 23/3 (0/1,1/5) 0 40 8/1 1/5 2 5 17/2 (1/5,2/9) 0 40 9/1 (0/1,1/7) 0 40 10/1 1/4 2 4 1/0 (0/1,1/1) 0 40 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(19,-40,9,-19) (2/1,20/9) -> (2/1,20/9) Reflection Matrix(341,-760,153,-341) (20/9,38/17) -> (20/9,38/17) Reflection Matrix(339,-760,62,-139) (38/17,9/4) -> (38/7,11/2) Glide Reflection Matrix(619,-1400,256,-579) (9/4,34/15) -> (29/12,46/19) Glide Reflection Matrix(599,-1360,159,-361) (34/15,25/11) -> (15/4,34/9) Hyperbolic Matrix(299,-680,62,-141) (25/11,16/7) -> (24/5,5/1) Hyperbolic Matrix(541,-1240,113,-259) (16/7,39/17) -> (19/4,24/5) Hyperbolic Matrix(801,-1840,313,-719) (39/17,23/10) -> (23/9,41/16) Hyperbolic Matrix(521,-1200,122,-281) (23/10,30/13) -> (17/4,30/7) Glide Reflection Matrix(259,-600,60,-139) (30/13,7/3) -> (30/7,13/3) Glide Reflection Matrix(239,-560,102,-239) (7/3,40/17) -> (7/3,40/17) Reflection Matrix(441,-1040,187,-441) (40/17,26/11) -> (40/17,26/11) Reflection Matrix(659,-1560,177,-419) (26/11,19/8) -> (26/7,41/11) Glide Reflection Matrix(621,-1480,227,-541) (19/8,31/13) -> (41/15,11/4) Glide Reflection Matrix(419,-1000,75,-179) (31/13,12/5) -> (11/2,28/5) Glide Reflection Matrix(979,-2360,207,-499) (12/5,41/17) -> (52/11,19/4) Glide Reflection Matrix(199,-480,17,-41) (41/17,70/29) -> (10/1,1/0) Hyperbolic Matrix(381,-920,41,-99) (70/29,29/12) -> (9/1,10/1) Hyperbolic Matrix(1519,-3680,627,-1519) (46/19,80/33) -> (46/19,80/33) Reflection Matrix(1121,-2720,462,-1121) (80/33,17/7) -> (80/33,17/7) Reflection Matrix(559,-1360,164,-399) (17/7,39/16) -> (17/5,41/12) Glide Reflection Matrix(3281,-8000,1280,-3121) (39/16,100/41) -> (41/16,100/39) Glide Reflection Matrix(901,-2200,369,-901) (100/41,22/9) -> (100/41,22/9) Reflection Matrix(359,-880,82,-201) (22/9,5/2) -> (35/8,22/5) Hyperbolic Matrix(899,-2280,166,-421) (5/2,33/13) -> (27/5,65/12) Hyperbolic Matrix(1039,-2640,220,-559) (33/13,28/11) -> (33/7,52/11) Glide Reflection Matrix(439,-1120,78,-199) (28/11,23/9) -> (28/5,17/3) Glide Reflection Matrix(701,-1800,273,-701) (100/39,18/7) -> (100/39,18/7) Reflection Matrix(139,-360,39,-101) (18/7,13/5) -> (7/2,18/5) Hyperbolic Matrix(261,-680,38,-99) (13/5,47/18) -> (27/4,7/1) Hyperbolic Matrix(781,-2040,299,-781) (60/23,34/13) -> (60/23,34/13) Reflection Matrix(519,-1360,137,-359) (34/13,21/8) -> (34/9,19/5) Glide Reflection Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(661,-1800,242,-659) (19/7,30/11) -> (30/11,41/15) Parabolic Matrix(101,-280,22,-61) (11/4,14/5) -> (9/2,14/3) Glide Reflection Matrix(99,-280,35,-99) (14/5,20/7) -> (14/5,20/7) Reflection Matrix(181,-520,63,-181) (20/7,26/9) -> (20/7,26/9) Reflection Matrix(359,-1040,97,-281) (23/8,3/1) -> (37/10,63/17) Hyperbolic Matrix(61,-200,18,-59) (3/1,10/3) -> (10/3,17/5) Parabolic Matrix(339,-1160,64,-219) (41/12,24/7) -> (21/4,16/3) Glide Reflection Matrix(221,-760,41,-141) (24/7,7/2) -> (16/3,27/5) Glide Reflection Matrix(199,-720,55,-199) (18/5,40/11) -> (18/5,40/11) Reflection Matrix(241,-880,66,-241) (40/11,11/3) -> (40/11,11/3) Reflection Matrix(141,-520,16,-59) (11/3,37/10) -> (17/2,9/1) Hyperbolic Matrix(701,-2600,189,-701) (100/27,26/7) -> (100/27,26/7) Reflection Matrix(139,-520,27,-101) (41/11,15/4) -> (5/1,21/4) Hyperbolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(799,-3360,190,-799) (21/5,80/19) -> (21/5,80/19) Reflection Matrix(721,-3040,171,-721) (80/19,38/9) -> (80/19,38/9) Reflection Matrix(359,-1520,47,-199) (38/9,17/4) -> (38/5,23/3) Glide Reflection Matrix(101,-440,14,-61) (13/3,35/8) -> (7/1,15/2) Glide Reflection Matrix(199,-880,45,-199) (22/5,40/9) -> (22/5,40/9) Reflection Matrix(161,-720,36,-161) (40/9,9/2) -> (40/9,9/2) Reflection Matrix(239,-1120,51,-239) (14/3,80/17) -> (14/3,80/17) Reflection Matrix(1121,-5280,238,-1121) (80/17,33/7) -> (80/17,33/7) Reflection Matrix(561,-3040,74,-401) (65/12,38/7) -> (15/2,38/5) Glide Reflection Matrix(239,-1360,42,-239) (17/3,40/7) -> (17/3,40/7) Reflection Matrix(41,-240,7,-41) (40/7,6/1) -> (40/7,6/1) Reflection Matrix(19,-120,3,-19) (6/1,20/3) -> (6/1,20/3) Reflection Matrix(101,-680,15,-101) (20/3,34/5) -> (20/3,34/5) Reflection Matrix(41,-320,5,-39) (23/3,8/1) -> (8/1,17/2) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(1,0,1,-1) -> Matrix(1,0,40,-1) (0/1,2/1) -> (0/1,1/20) Matrix(19,-40,9,-19) -> Matrix(19,-1,360,-19) (2/1,20/9) -> (1/20,1/18) Matrix(341,-760,153,-341) -> Matrix(305,-17,5472,-305) (20/9,38/17) -> (1/18,17/304) Matrix(339,-760,62,-139) -> Matrix(125,-7,982,-55) Matrix(619,-1400,256,-579) -> Matrix(407,-23,6742,-381) Matrix(599,-1360,159,-361) -> Matrix(35,-2,438,-25) Matrix(299,-680,62,-141) -> Matrix(123,-7,1072,-61) Matrix(541,-1240,113,-259) -> Matrix(87,-5,818,-47) Matrix(801,-1840,313,-719) -> Matrix(279,-16,4342,-249) Matrix(521,-1200,122,-281) -> Matrix(35,-2,402,-23) Matrix(259,-600,60,-139) -> Matrix(121,-7,1158,-67) Matrix(239,-560,102,-239) -> Matrix(205,-12,3502,-205) (7/3,40/17) -> (6/103,1/17) Matrix(441,-1040,187,-441) -> Matrix(373,-22,6324,-373) (40/17,26/11) -> (1/17,11/186) Matrix(659,-1560,177,-419) -> Matrix(253,-15,2648,-157) Matrix(621,-1480,227,-541) -> Matrix(117,-7,1688,-101) Matrix(419,-1000,75,-179) -> Matrix(151,-9,1124,-67) Matrix(979,-2360,207,-499) -> Matrix(83,-5,780,-47) Matrix(199,-480,17,-41) -> Matrix(33,-2,182,-11) Matrix(381,-920,41,-99) -> Matrix(83,-5,382,-23) Matrix(1519,-3680,627,-1519) -> Matrix(991,-60,16368,-991) (46/19,80/33) -> (15/248,2/33) Matrix(1121,-2720,462,-1121) -> Matrix(725,-44,11946,-725) (80/33,17/7) -> (2/33,11/181) Matrix(559,-1360,164,-399) -> Matrix(131,-8,1490,-91) Matrix(3281,-8000,1280,-3121) -> Matrix(131,-8,2014,-123) Matrix(901,-2200,369,-901) -> Matrix(81,-5,1312,-81) (100/41,22/9) -> (5/82,1/16) Matrix(359,-880,82,-201) -> Matrix(163,-10,1516,-93) Matrix(899,-2280,166,-421) -> Matrix(79,-5,648,-41) Matrix(1039,-2640,220,-559) -> Matrix(63,-4,614,-39) Matrix(439,-1120,78,-199) -> Matrix(157,-10,1146,-73) Matrix(701,-1800,273,-701) -> Matrix(79,-5,1248,-79) (100/39,18/7) -> (1/16,5/78) Matrix(139,-360,39,-101) -> Matrix(77,-5,878,-57) Matrix(261,-680,38,-99) -> Matrix(77,-5,416,-27) Matrix(781,-2040,299,-781) -> Matrix(229,-15,3496,-229) (60/23,34/13) -> (3/46,5/76) Matrix(519,-1360,137,-359) -> Matrix(31,-2,356,-23) Matrix(121,-320,45,-119) -> Matrix(91,-6,1350,-89) 1/15 Matrix(661,-1800,242,-659) -> Matrix(133,-9,1936,-131) 3/44 Matrix(101,-280,22,-61) -> Matrix(43,-3,358,-25) Matrix(99,-280,35,-99) -> Matrix(71,-5,1008,-71) (14/5,20/7) -> (5/72,1/14) Matrix(181,-520,63,-181) -> Matrix(125,-9,1736,-125) (20/7,26/9) -> (1/14,9/124) Matrix(359,-1040,97,-281) -> Matrix(137,-10,1466,-107) Matrix(61,-200,18,-59) -> Matrix(37,-3,432,-35) 1/12 Matrix(339,-1160,64,-219) -> Matrix(11,-1,54,-5) Matrix(221,-760,41,-141) -> Matrix(11,-1,76,-7) Matrix(199,-720,55,-199) -> Matrix(111,-10,1232,-111) (18/5,40/11) -> (5/56,1/11) Matrix(241,-880,66,-241) -> Matrix(131,-12,1430,-131) (40/11,11/3) -> (1/11,6/65) Matrix(141,-520,16,-59) -> Matrix(11,-1,12,-1) Matrix(701,-2600,189,-701) -> Matrix(223,-21,2368,-223) (100/27,26/7) -> (3/32,7/74) Matrix(139,-520,27,-101) -> Matrix(31,-3,238,-23) Matrix(41,-160,10,-39) -> Matrix(21,-2,200,-19) 1/10 Matrix(799,-3360,190,-799) -> Matrix(1,0,18,-1) (21/5,80/19) -> (0/1,1/9) Matrix(721,-3040,171,-721) -> Matrix(1,0,20,-1) (80/19,38/9) -> (0/1,1/10) Matrix(359,-1520,47,-199) -> Matrix(19,-2,104,-11) Matrix(101,-440,14,-61) -> Matrix(9,-1,26,-3) Matrix(199,-880,45,-199) -> Matrix(91,-10,828,-91) (22/5,40/9) -> (5/46,1/9) Matrix(161,-720,36,-161) -> Matrix(71,-8,630,-71) (40/9,9/2) -> (1/9,4/35) Matrix(239,-1120,51,-239) -> Matrix(1,0,16,-1) (14/3,80/17) -> (0/1,1/8) Matrix(1121,-5280,238,-1121) -> Matrix(1,0,22,-1) (80/17,33/7) -> (0/1,1/11) Matrix(561,-3040,74,-401) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(239,-1360,42,-239) -> Matrix(85,-12,602,-85) (17/3,40/7) -> (6/43,1/7) Matrix(41,-240,7,-41) -> Matrix(13,-2,84,-13) (40/7,6/1) -> (1/7,1/6) Matrix(19,-120,3,-19) -> Matrix(7,-1,48,-7) (6/1,20/3) -> (1/8,1/6) Matrix(101,-680,15,-101) -> Matrix(29,-5,168,-29) (20/3,34/5) -> (1/6,5/28) Matrix(41,-320,5,-39) -> Matrix(11,-2,50,-9) 1/5 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.