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 0/1 1/37 -9/10 1/34 -17/19 1/33 2/65 -8/9 0/1 1/31 -15/17 2/67 1/33 -7/8 1/33 -20/23 0/1 1/33 -13/15 1/32 -19/22 1/30 -6/7 1/33 2/65 -17/20 1/32 -11/13 3/95 2/63 -27/32 2/63 -16/19 6/187 1/31 -21/25 1/30 -5/6 1/32 -14/17 1/31 6/185 -23/28 3/92 -9/11 2/61 3/91 -13/16 0/1 -17/21 0/1 1/31 -4/5 1/30 -19/24 1/29 -34/43 0/1 1/27 -15/19 2/59 1/29 -56/71 0/1 1/31 -41/52 1/28 -26/33 0/1 1/27 -11/14 1/30 -18/23 5/149 4/119 -25/32 2/59 -32/41 2/59 1/29 -7/9 4/117 1/29 -17/22 5/144 -10/13 5/143 2/57 -33/43 4/113 5/141 -23/30 1/28 -13/17 1/29 2/57 -3/4 1/28 -17/23 0/1 1/27 -31/42 1/28 -14/19 2/55 1/27 -11/15 1/28 -30/41 3/83 2/55 -49/67 27/743 2/55 -19/26 7/192 -46/63 11/301 14/383 -27/37 7/191 4/109 -35/48 4/109 -8/11 6/163 1/27 -13/18 5/134 -44/61 1/27 2/53 -31/43 9/241 4/107 -18/25 3/80 -23/32 2/53 -28/39 2/53 3/79 -5/7 1/27 2/53 -27/38 1/26 -22/31 2/51 1/25 -39/55 1/26 -17/24 1/27 -29/41 1/27 2/53 -12/17 2/53 7/185 -7/10 1/26 -16/23 4/103 11/283 -41/59 3/77 32/821 -25/36 5/128 -9/13 2/51 1/25 -11/16 2/51 -13/19 2/51 1/25 -15/22 1/26 -17/25 3/76 -2/3 1/25 2/49 -13/20 1/24 -24/37 13/311 12/287 -11/17 7/167 6/143 -9/14 1/24 -34/53 3/71 8/189 -25/39 2/47 1/23 -16/25 1/24 -39/61 22/521 3/71 -23/36 5/118 -30/47 7/165 16/377 -37/58 13/306 -7/11 2/47 5/117 -33/52 1/24 -26/41 2/47 5/117 -19/30 3/70 -12/19 2/47 1/23 -5/8 1/23 -13/21 1/23 4/91 -21/34 5/114 -50/81 1/23 4/91 -29/47 4/91 7/159 -8/13 1/23 2/45 -27/44 7/158 -73/119 9/203 2/45 -46/75 7/158 -19/31 17/383 2/45 -11/18 5/112 -36/59 3/67 4/89 -61/100 1/22 -25/41 1/23 2/45 -14/23 8/179 3/67 -17/28 1/22 -20/33 4/89 5/111 -3/5 1/22 -19/32 4/87 -16/27 5/109 4/87 -13/22 5/108 -36/61 3/65 2/43 -59/100 5/108 -23/39 3/65 2/43 -10/17 11/237 2/43 -27/46 15/322 -44/75 11/236 -17/29 12/257 5/107 -58/99 5/107 18/385 -41/70 3/64 -24/41 2/43 9/193 -31/53 5/107 8/171 -7/12 3/64 -39/67 2/43 1/21 -32/55 3/64 -25/43 15/319 4/85 -43/74 13/276 -61/105 5/106 -18/31 6/127 1/21 -11/19 6/127 1/21 -26/45 7/148 -41/71 8/169 33/697 -15/26 11/232 -4/7 1/21 6/125 -25/44 3/62 -21/37 1/21 4/83 -17/30 3/62 -13/23 8/165 5/103 -22/39 9/185 2/41 -9/16 2/41 -23/41 2/41 3/61 -14/25 5/102 -19/34 11/224 -24/43 3/61 28/569 -29/52 7/142 -5/9 4/81 5/101 -11/20 1/20 -17/31 14/279 13/259 -23/42 1/20 -6/11 6/119 5/99 -13/24 3/59 -20/37 8/157 13/255 -7/13 11/215 2/39 -22/41 2/39 13/253 -15/28 7/136 -23/43 5/97 28/543 -8/15 3/58 -9/17 11/211 6/115 -1/2 1/18 -9/19 1/17 18/305 -8/17 6/101 11/185 -7/15 3/50 -20/43 28/465 5/83 -13/28 7/116 -6/13 2/33 11/181 -17/37 13/213 8/131 -11/24 3/49 -16/35 7/114 -5/11 5/81 6/97 -9/20 1/16 -13/29 13/207 12/191 -17/38 1/16 -4/9 5/79 4/63 -23/52 7/110 -19/43 28/439 3/47 -53/120 3/47 -34/77 3/47 50/783 -15/34 11/172 -11/25 5/78 -18/41 3/47 2/31 -7/16 2/31 -17/39 2/31 9/139 -10/23 5/77 8/123 -13/30 3/46 -16/37 4/61 1/15 -3/7 6/91 1/15 -17/40 1/15 -14/33 1/15 28/419 -11/26 11/164 -30/71 33/491 8/119 -19/45 7/104 -8/19 1/15 6/89 -21/50 5/74 -34/81 1/15 4/59 -13/31 1/15 6/89 -31/74 13/192 -49/117 41/605 4/59 -67/160 4/59 -18/43 4/59 15/221 -5/12 3/44 -22/53 8/117 5/73 -17/41 9/131 2/29 -29/70 3/44 -41/99 18/263 5/73 -12/29 5/73 12/175 -31/75 11/160 -50/121 13/189 2/29 -19/46 15/218 -26/63 41/595 2/29 -33/80 2/29 -7/17 2/29 11/159 -16/39 2/29 3/43 -41/100 5/72 -25/61 2/29 3/43 -9/22 5/72 -2/5 1/14 -15/38 1/14 -13/33 5/69 4/55 -11/28 1/14 -9/23 3/41 8/109 -16/41 2/27 1/13 -39/100 1/14 -23/59 4/55 3/41 -7/18 5/68 -19/49 27/365 2/27 -31/80 2/27 -12/31 2/27 17/229 -29/75 7/94 -46/119 2/27 9/121 -63/163 2/27 5/67 -17/44 7/94 -5/13 2/27 1/13 -23/60 3/40 -18/47 7/93 4/53 -31/81 4/53 1/13 -44/115 3/40 -13/34 5/66 -21/55 3/40 -8/21 4/53 1/13 -3/8 1/13 -7/19 1/13 2/25 -18/49 1/13 2/25 -11/30 3/38 -26/71 8/101 5/63 -15/41 5/63 2/25 -4/11 5/63 2/25 -17/47 16/199 7/87 -30/83 2/25 7/87 -43/119 2/25 3/37 -13/36 5/62 -22/61 3/37 22/271 -9/25 1/12 -14/39 1/13 2/25 -19/53 8/99 3/37 -43/120 3/37 -24/67 3/37 10/123 -5/14 1/12 -6/17 6/73 7/85 -7/20 1/12 -8/23 8/95 7/83 -1/3 2/23 1/11 -7/22 1/10 -6/19 1/11 2/21 -5/16 2/21 -9/29 4/41 5/51 -13/42 1/10 -17/55 1/10 -4/13 1/11 2/21 -3/10 1/10 -8/27 5/49 4/39 -13/44 7/68 -18/61 34/329 3/29 -59/200 3/29 -41/139 3/29 80/773 -23/78 23/222 -5/17 7/67 2/19 -12/41 2/19 1/9 -19/65 3/28 -7/24 1/9 -16/55 1/10 -9/31 1/11 2/21 -11/38 1/10 -13/45 1/10 -2/7 2/19 1/9 -11/39 3/29 2/19 -9/32 2/19 -16/57 19/179 12/113 -7/25 3/28 -26/93 10/93 7/65 -19/68 3/28 -12/43 4/37 9/83 -17/61 2/19 1/9 -5/18 5/46 -8/29 16/145 1/9 -11/40 1/9 -3/11 1/9 6/53 -16/59 0/1 1/9 -13/48 4/35 -23/85 3/26 -33/122 3/26 -43/159 1/9 4/35 -10/37 4/35 7/61 -17/63 14/121 11/95 -24/89 27/233 8/69 -7/26 7/60 -25/93 41/349 2/17 -43/160 2/17 -18/67 2/17 27/229 -11/41 2/17 3/25 -15/56 3/25 -4/15 1/8 -9/34 3/26 -5/19 1/9 2/17 -1/4 1/8 -5/21 0/1 1/7 -19/80 0/1 -14/59 0/1 1/9 -9/38 1/8 -13/55 1/8 -4/17 2/15 1/7 -7/30 1/8 -10/43 5/39 4/31 -3/13 2/15 5/37 -11/48 2/15 -19/83 2/15 1/7 -46/201 2/15 5/37 -119/520 5/37 -73/319 5/37 8/59 -27/118 3/22 -8/35 3/22 -5/22 5/36 -7/31 14/99 1/7 -9/40 1/7 -2/9 1/7 4/27 -9/41 1/7 2/13 -7/32 2/13 -12/55 5/32 -5/23 4/25 5/31 -3/14 1/6 -10/47 0/1 1/3 -17/80 0/1 -7/33 0/1 1/9 -11/52 1/8 -15/71 0/1 1/5 -4/19 1/7 2/13 -9/43 0/1 1/9 -5/24 1/7 -6/29 8/53 5/33 -1/5 1/6 -4/21 0/1 1/5 -3/16 0/1 -5/27 0/1 1/7 -12/65 1/6 -7/38 1/6 -2/11 3/17 2/11 -7/39 3/17 2/11 -12/67 2/11 21/115 -5/28 3/16 -3/17 6/31 1/5 -7/40 1/5 -4/23 1/5 8/39 -1/6 1/4 -5/31 1/7 2/13 -4/25 1/6 -3/19 1/5 6/29 -8/51 0/1 1/5 -5/32 2/9 -2/13 2/9 3/13 -3/20 1/4 -4/27 4/15 3/11 -1/7 2/7 1/3 -4/29 -1/3 0/1 -11/80 0/1 -7/51 0/1 1/15 -3/22 1/6 -5/37 4/21 1/5 -2/15 1/4 -5/38 1/4 -3/23 0/1 1/3 -1/8 1/3 -2/17 1/3 2/5 -3/26 3/4 -1/9 0/1 1/5 -2/19 2/7 1/3 -1/10 1/2 0/1 -1/1 0/1 1/10 -1/4 2/19 -1/5 -2/11 1/9 -1/7 0/1 2/17 -2/9 -1/5 1/8 -1/5 3/23 -1/5 0/1 2/15 -1/6 3/22 -1/8 1/7 -1/5 -2/11 3/20 -1/6 2/13 -3/19 -2/13 5/32 -2/13 3/19 -6/41 -1/7 4/25 -1/8 1/6 -1/6 3/17 -1/7 -6/43 5/28 -3/22 2/11 -2/15 -3/23 3/16 0/1 4/21 -1/7 0/1 1/5 -1/8 5/24 -1/9 9/43 -1/11 0/1 4/19 -2/17 -1/9 15/71 -1/7 0/1 11/52 -1/10 7/33 -1/11 0/1 3/14 -1/8 5/23 -5/41 -4/33 7/32 -2/17 9/41 -2/17 -1/9 2/9 -4/35 -1/9 5/22 -5/46 3/13 -5/47 -2/19 10/43 -4/39 -5/49 7/30 -1/10 4/17 -1/9 -2/19 1/4 -1/10 6/23 -1/11 0/1 11/42 -1/10 5/19 -2/21 -1/11 4/15 -1/10 11/41 -3/31 -2/21 18/67 -27/283 -2/21 7/26 -7/74 17/63 -11/117 -14/149 10/37 -7/75 -4/43 13/48 -4/43 3/11 -6/65 -1/11 5/18 -5/56 17/61 -1/11 -2/23 12/43 -9/101 -4/45 7/25 -3/34 9/32 -2/23 11/39 -2/23 -3/35 2/7 -1/11 -2/23 11/38 -1/12 9/31 -2/25 -1/13 16/55 -1/12 7/24 -1/11 12/41 -1/11 -2/23 5/17 -2/23 -7/81 3/10 -1/12 7/23 -4/49 -11/135 18/59 -3/37 -32/395 11/36 -5/62 4/13 -2/25 -1/13 5/16 -2/25 6/19 -2/25 -1/13 7/22 -1/12 8/25 -3/38 1/3 -1/13 -2/27 7/20 -1/14 13/37 -13/183 -12/169 6/17 -7/99 -6/85 5/14 -1/14 19/53 -3/43 -8/115 14/39 -2/29 -1/15 9/25 -1/14 22/61 -22/315 -3/43 13/36 -5/72 17/47 -7/101 -16/231 21/58 -13/188 4/11 -2/29 -5/73 19/52 -1/14 15/41 -2/29 -5/73 11/30 -3/44 7/19 -2/29 -1/15 3/8 -1/15 8/21 -1/15 -4/61 13/34 -5/76 31/81 -1/15 -4/61 18/47 -4/61 -7/107 5/13 -1/15 -2/31 17/44 -7/108 46/119 -9/139 -2/31 29/75 -7/108 12/31 -17/263 -2/31 7/18 -5/78 23/59 -3/47 -4/63 39/100 -1/16 16/41 -1/15 -2/31 9/23 -8/125 -3/47 11/28 -1/16 13/33 -4/63 -5/79 2/5 -1/16 13/32 -4/65 11/27 -5/81 -4/65 9/22 -5/82 25/61 -3/49 -2/33 41/100 -5/82 16/39 -3/49 -2/33 7/17 -11/181 -2/33 19/46 -15/248 31/75 -11/182 12/29 -12/199 -5/83 41/99 -5/83 -18/299 29/70 -3/50 17/41 -2/33 -9/149 22/53 -5/83 -8/133 5/12 -3/50 28/67 -2/33 -1/17 23/55 -3/50 18/43 -15/251 -4/67 31/74 -13/218 44/105 -5/84 13/31 -6/101 -1/17 8/19 -6/101 -1/17 19/45 -7/118 30/71 -8/135 -33/557 11/26 -11/186 3/7 -1/17 -6/103 19/44 -3/52 16/37 -1/17 -4/69 13/30 -3/52 10/23 -8/139 -5/87 17/39 -9/157 -2/35 7/16 -2/35 18/41 -2/35 -3/53 11/25 -5/88 15/34 -11/194 19/43 -3/53 -28/495 23/52 -7/124 4/9 -4/71 -5/89 9/20 -1/18 14/31 -14/253 -13/235 19/42 -1/18 5/11 -6/109 -5/91 11/24 -3/55 17/37 -8/147 -13/239 6/13 -11/203 -2/37 19/41 -2/37 -13/241 13/28 -7/130 20/43 -5/93 -28/521 7/15 -3/56 8/17 -11/207 -6/113 1/2 -1/20 10/19 -1/21 -18/379 9/17 -6/127 -11/233 8/15 -3/64 23/43 -28/599 -5/107 15/28 -7/150 7/13 -2/43 -11/237 20/37 -13/281 -8/173 13/24 -3/65 19/35 -7/152 6/11 -5/109 -6/131 11/20 -1/22 16/29 -13/287 -12/265 21/38 -1/22 5/9 -5/111 -4/89 29/52 -7/156 24/43 -28/625 -3/67 67/120 -3/67 43/77 -3/67 -50/1117 19/34 -11/246 14/25 -5/112 23/41 -3/67 -2/45 9/16 -2/45 22/39 -2/45 -9/203 13/23 -5/113 -8/181 17/30 -3/68 21/37 -4/91 -1/23 4/7 -6/137 -1/23 23/40 -1/23 19/33 -1/23 -28/645 15/26 -11/254 41/71 -33/763 -8/185 26/45 -7/162 11/19 -1/23 -6/139 29/50 -5/116 47/81 -1/23 -4/93 18/31 -1/23 -6/139 43/74 -13/302 68/117 -41/953 -4/93 93/160 -4/93 25/43 -4/93 -15/349 7/12 -3/70 31/53 -8/187 -5/117 24/41 -9/211 -2/47 41/70 -3/70 58/99 -18/421 -5/117 17/29 -5/117 -12/281 44/75 -11/258 71/121 -13/305 -2/47 27/46 -15/352 37/63 -41/963 -2/47 47/80 -2/47 10/17 -2/47 -11/259 23/39 -2/47 -3/71 59/100 -5/118 36/61 -2/47 -3/71 13/22 -5/118 3/5 -1/24 23/38 -1/24 20/33 -5/121 -4/97 17/28 -1/24 14/23 -3/73 -8/195 25/41 -2/49 -1/25 61/100 -1/24 36/59 -4/97 -3/73 11/18 -5/122 30/49 -27/661 -2/49 49/80 -2/49 19/31 -2/49 -17/417 46/75 -7/172 73/119 -2/49 -9/221 100/163 -2/49 -5/123 27/44 -7/172 8/13 -2/49 -1/25 37/60 -3/74 29/47 -7/173 -4/99 50/81 -4/99 -1/25 71/115 -3/74 21/34 -5/124 34/55 -3/74 13/21 -4/99 -1/25 5/8 -1/25 12/19 -1/25 -2/51 31/49 -1/25 -2/51 19/30 -3/76 45/71 -8/203 -5/127 26/41 -5/127 -2/51 7/11 -5/127 -2/51 30/47 -16/409 -7/179 53/83 -2/51 -7/179 76/119 -2/51 -3/77 23/36 -5/128 39/61 -3/77 -22/565 16/25 -1/26 25/39 -1/25 -2/51 34/53 -8/205 -3/77 77/120 -3/77 43/67 -3/77 -10/257 9/14 -1/26 11/17 -6/155 -7/181 13/20 -1/26 15/23 -8/209 -7/183 2/3 -2/53 -1/27 15/22 -1/28 13/19 -1/27 -2/55 11/16 -2/55 20/29 -4/111 -5/139 29/42 -1/28 38/55 -1/28 9/13 -1/27 -2/55 7/10 -1/28 19/27 -5/141 -4/113 31/44 -7/198 43/61 -34/963 -3/85 141/200 -3/85 98/139 -3/85 -80/2267 55/78 -23/652 12/17 -7/199 -2/57 29/41 -2/57 -1/29 46/65 -3/86 17/24 -1/29 39/55 -1/28 22/31 -1/27 -2/55 27/38 -1/28 32/45 -1/28 5/7 -2/57 -1/29 28/39 -3/85 -2/57 23/32 -2/57 41/57 -19/543 -12/343 18/25 -3/86 67/93 -10/287 -7/201 49/68 -3/86 31/43 -4/115 -9/259 44/61 -2/57 -1/29 13/18 -5/144 21/29 -16/463 -1/29 29/40 -1/29 8/11 -1/29 -6/175 43/59 -1/29 0/1 35/48 -4/117 62/85 -3/88 89/122 -3/88 116/159 -1/29 -4/117 27/37 -4/117 -7/205 46/63 -14/411 -11/323 65/89 -27/793 -8/235 19/26 -7/206 68/93 -41/1209 -2/59 117/160 -2/59 49/67 -2/59 -27/797 30/41 -2/59 -3/89 41/56 -3/89 11/15 -1/30 25/34 -3/88 14/19 -1/29 -2/59 3/4 -1/30 16/21 -1/31 0/1 61/80 0/1 45/59 -1/29 0/1 29/38 -1/30 42/55 -1/30 13/17 -2/61 -1/31 23/30 -1/30 33/43 -5/151 -4/121 10/13 -2/61 -5/153 37/48 -2/61 64/83 -2/61 -1/31 155/201 -2/61 -5/153 401/520 -5/153 246/319 -5/153 -8/245 91/118 -3/92 27/35 -3/92 17/22 -5/154 24/31 -14/433 -1/31 31/40 -1/31 7/9 -1/31 -4/125 32/41 -1/31 -2/63 25/32 -2/63 43/55 -5/158 18/23 -4/127 -5/159 11/14 -1/32 37/47 -1/35 0/1 63/80 0/1 26/33 -1/29 0/1 41/52 -1/30 56/71 -1/33 0/1 15/19 -1/31 -2/63 34/43 -1/29 0/1 19/24 -1/31 23/29 -8/251 -5/157 4/5 -1/32 17/21 -1/33 0/1 13/16 0/1 22/27 -1/31 0/1 53/65 -1/32 31/38 -1/32 9/11 -3/97 -2/65 32/39 -3/97 -2/65 55/67 -2/65 -21/683 23/28 -3/98 14/17 -6/197 -1/33 33/40 -1/33 19/23 -1/33 -8/265 5/6 -1/34 26/31 -1/31 -2/63 21/25 -1/32 16/19 -1/33 -6/199 43/51 -1/33 0/1 27/32 -2/67 11/13 -2/67 -3/101 17/20 -1/34 23/27 -4/137 -3/103 6/7 -2/69 -1/35 25/29 -1/41 0/1 69/80 0/1 44/51 -1/23 0/1 19/22 -1/32 32/37 -4/131 -1/33 13/15 -1/34 33/38 -1/34 20/23 -1/35 0/1 7/8 -1/35 15/17 -1/35 -2/71 23/26 -3/110 8/9 -1/33 0/1 17/19 -2/69 -1/35 9/10 -1/36 1/1 -1/39 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(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(65,-2,-1072,33) Matrix(961,862,2320,2081) -> Matrix(269,-8,-4472,133) Matrix(1199,1072,1520,1359) -> Matrix(1,0,-64,1) Matrix(561,496,-2080,-1839) -> Matrix(275,-8,2372,-69) Matrix(41,36,320,281) -> Matrix(67,-2,-368,11) Matrix(39,34,320,279) -> Matrix(65,-2,-292,9) Matrix(359,312,-1520,-1321) -> Matrix(65,-2,488,-15) Matrix(599,518,-880,-761) -> Matrix(61,-2,1556,-51) Matrix(919,792,-1440,-1241) -> Matrix(73,-2,1716,-47) Matrix(521,444,-1360,-1159) -> Matrix(323,-10,4296,-133) Matrix(399,338,-1040,-881) -> Matrix(253,-8,3384,-107) Matrix(521,440,1280,1081) -> Matrix(65,-2,-1072,33) Matrix(759,640,-2800,-2361) -> Matrix(187,-6,1652,-53) Matrix(721,606,2000,1681) -> Matrix(121,-4,-1724,57) Matrix(1441,1208,-2480,-2079) -> Matrix(115,-4,2444,-85) Matrix(41,34,-240,-199) -> Matrix(63,-2,284,-9) Matrix(681,560,1120,921) -> Matrix(307,-10,-7460,243) Matrix(559,458,-880,-721) -> Matrix(123,-4,2860,-93) Matrix(199,162,-640,-521) -> Matrix(59,-2,620,-21) Matrix(439,356,640,519) -> Matrix(63,-2,-1732,55) Matrix(601,486,1040,841) -> Matrix(187,-6,-4332,139) Matrix(439,348,-960,-761) -> Matrix(293,-10,4776,-163) Matrix(1039,822,1920,1519) -> Matrix(229,-8,-4952,173) Matrix(959,758,3440,2719) -> Matrix(117,-4,-1316,45) Matrix(1359,1072,1520,1199) -> Matrix(1,0,-64,1) Matrix(1841,1452,4160,3281) -> Matrix(119,-4,-2112,71) Matrix(1601,1262,2640,2081) -> Matrix(113,-4,-2740,97) Matrix(239,188,-1120,-881) -> Matrix(1,0,-24,1) Matrix(199,156,560,439) -> Matrix(61,-2,-884,29) Matrix(719,562,-2560,-2001) -> Matrix(473,-16,4464,-151) Matrix(1839,1436,2560,1999) -> Matrix(235,-8,-6668,227) Matrix(2079,1622,3280,2559) -> Matrix(353,-12,-8972,305) Matrix(199,154,-880,-681) -> Matrix(289,-10,2052,-71) Matrix(521,402,-880,-679) -> Matrix(287,-10,6228,-217) Matrix(479,368,1040,799) -> Matrix(341,-12,-6280,221) Matrix(1361,1044,2400,1841) -> Matrix(451,-16,-10232,363) Matrix(679,520,1200,919) -> Matrix(53,-2,-1192,45) Matrix(119,90,-160,-121) -> Matrix(57,-2,1568,-55) Matrix(241,178,-1840,-1359) -> Matrix(1,0,-24,1) Matrix(759,560,-3200,-2361) -> Matrix(55,-2,468,-17) Matrix(519,382,-1360,-1001) -> Matrix(53,-2,716,-27) Matrix(959,702,-3280,-2401) -> Matrix(221,-8,2072,-75) Matrix(1761,1288,-3280,-2399) -> Matrix(881,-32,17152,-623) Matrix(1119,818,-4160,-3041) -> Matrix(769,-28,6564,-239) Matrix(241,176,-2080,-1519) -> Matrix(219,-8,356,-13) Matrix(1041,760,2960,2161) -> Matrix(875,-32,-12332,451) Matrix(1319,962,-5760,-4201) -> Matrix(491,-18,3628,-133) Matrix(439,320,-2800,-2041) -> Matrix(163,-6,788,-29) Matrix(199,144,-720,-521) -> Matrix(269,-10,2448,-91) Matrix(1319,952,2160,1559) -> Matrix(267,-10,-6488,243) Matrix(721,520,3440,2481) -> Matrix(107,-4,-936,35) Matrix(2001,1442,-3440,-2479) -> Matrix(641,-24,13648,-511) Matrix(559,402,-2560,-1841) -> Matrix(425,-16,2736,-103) Matrix(1999,1436,2560,1839) -> Matrix(211,-8,-6620,251) Matrix(1481,1062,2400,1721) -> Matrix(263,-10,-6496,247) Matrix(599,426,-1520,-1081) -> Matrix(157,-6,2172,-83) Matrix(1121,796,2480,1761) -> Matrix(313,-12,-5660,217) Matrix(2881,2044,-4960,-3519) -> Matrix(99,-4,2104,-85) Matrix(2519,1786,3440,2439) -> Matrix(51,-2,-1504,59) Matrix(879,622,-3280,-2321) -> Matrix(213,-8,1784,-67) Matrix(801,566,1360,961) -> Matrix(213,-8,-5032,189) Matrix(279,196,-400,-281) -> Matrix(157,-6,4056,-155) Matrix(679,472,-1440,-1001) -> Matrix(565,-22,9528,-371) Matrix(2761,1918,4320,3001) -> Matrix(769,-30,-19712,769) Matrix(401,278,1040,721) -> Matrix(101,-4,-1540,61) Matrix(119,82,-640,-441) -> Matrix(51,-2,332,-13) Matrix(519,356,640,439) -> Matrix(51,-2,-1708,67) Matrix(721,492,1760,1201) -> Matrix(203,-8,-3324,131) Matrix(521,354,1120,761) -> Matrix(455,-18,-8468,335) Matrix(519,338,-800,-521) -> Matrix(337,-14,8064,-335) Matrix(799,518,2960,1919) -> Matrix(765,-32,-8152,341) Matrix(121,78,560,361) -> Matrix(47,-2,-352,15) Matrix(601,386,-1680,-1079) -> Matrix(143,-6,1740,-73) Matrix(1759,1128,4240,2719) -> Matrix(377,-16,-6244,265) Matrix(1121,718,2000,1281) -> Matrix(187,-8,-4184,179) Matrix(319,204,2000,1279) -> Matrix(95,-4,-736,31) Matrix(3439,2198,4880,3119) -> Matrix(851,-36,-24088,1019) Matrix(1319,842,-2320,-1481) -> Matrix(613,-26,12708,-539) Matrix(439,280,-3200,-2041) -> Matrix(47,-2,588,-25) Matrix(1759,1116,-3280,-2081) -> Matrix(377,-16,7328,-311) Matrix(1881,1192,-4480,-2839) -> Matrix(515,-22,7608,-325) Matrix(639,404,-1520,-961) -> Matrix(185,-8,2752,-119) Matrix(121,76,320,201) -> Matrix(139,-6,-2108,91) Matrix(119,74,320,199) -> Matrix(137,-6,-2032,89) Matrix(359,222,-1360,-841) -> Matrix(45,-2,428,-19) Matrix(3239,2000,-7840,-4841) -> Matrix(1137,-50,16532,-727) Matrix(1721,1062,2400,1481) -> Matrix(227,-10,-6424,283) Matrix(201,124,-1360,-839) -> Matrix(227,-10,840,-37) Matrix(319,196,1040,639) -> Matrix(91,-4,-1160,51) Matrix(3439,2110,-9520,-5841) -> Matrix(541,-24,6740,-299) Matrix(10561,6478,18000,11041) -> Matrix(179,-8,-4184,187) Matrix(3881,2380,6720,4121) -> Matrix(1579,-70,-36520,1619) Matrix(559,342,-1440,-881) -> Matrix(449,-20,6084,-271) Matrix(1559,952,2160,1319) -> Matrix(223,-10,-6400,287) Matrix(7081,4320,12000,7321) -> Matrix(401,-18,-9468,425) Matrix(4719,2878,8000,4879) -> Matrix(181,-8,-4276,189) Matrix(801,488,1840,1121) -> Matrix(359,-16,-6260,279) Matrix(921,560,1120,681) -> Matrix(223,-10,-7292,327) Matrix(2081,1262,2640,1601) -> Matrix(89,-4,-2692,121) Matrix(439,266,-1520,-921) -> Matrix(133,-6,1308,-59) Matrix(801,476,-2960,-1759) -> Matrix(349,-16,3032,-139) Matrix(199,118,1280,759) -> Matrix(43,-2,-236,11) Matrix(559,330,1760,1039) -> Matrix(173,-8,-2184,101) Matrix(7321,4320,12000,7081) -> Matrix(389,-18,-9444,437) Matrix(4879,2878,8000,4719) -> Matrix(173,-8,-4260,197) Matrix(961,566,1360,801) -> Matrix(173,-8,-4952,229) Matrix(1519,892,-3680,-2161) -> Matrix(1289,-60,18712,-871) Matrix(2999,1760,-7840,-4601) -> Matrix(1073,-50,14228,-663) Matrix(1841,1080,2320,1361) -> Matrix(429,-20,-13492,629) Matrix(4721,2766,5600,3281) -> Matrix(257,-12,-8588,401) Matrix(239,140,2320,1359) -> Matrix(171,-8,-748,35) Matrix(41,24,480,281) -> Matrix(43,-2,-236,11) Matrix(1521,890,4240,2481) -> Matrix(343,-16,-4952,231) Matrix(839,490,-1440,-841) -> Matrix(385,-18,8192,-383) Matrix(3041,1770,4400,2561) -> Matrix(85,-4,-2316,109) Matrix(4959,2882,-11840,-6881) -> Matrix(2209,-104,32604,-1535) Matrix(559,324,-1520,-881) -> Matrix(169,-8,2176,-103) Matrix(841,486,1040,601) -> Matrix(127,-6,-4212,199) Matrix(4121,2380,6720,3881) -> Matrix(1479,-70,-36320,1719) Matrix(239,138,-2080,-1201) -> Matrix(169,-8,148,-7) Matrix(441,254,-1040,-599) -> Matrix(463,-22,6924,-329) Matrix(3401,1932,-8800,-4999) -> Matrix(457,-22,6128,-295) Matrix(1841,1044,2400,1361) -> Matrix(331,-16,-9992,483) Matrix(919,520,1200,679) -> Matrix(41,-2,-1168,57) Matrix(719,406,1840,1039) -> Matrix(329,-16,-5120,249) Matrix(561,316,1280,721) -> Matrix(493,-24,-8648,421) Matrix(559,314,1280,719) -> Matrix(491,-24,-8572,419) Matrix(1281,718,2000,1121) -> Matrix(163,-8,-4136,203) Matrix(1681,940,2720,1521) -> Matrix(81,-4,-1964,97) Matrix(1801,1006,-4080,-2279) -> Matrix(1343,-66,21020,-1033) Matrix(1599,892,3440,1919) -> Matrix(1137,-56,-21136,1041) Matrix(879,490,4160,2319) -> Matrix(81,-4,-668,33) Matrix(439,242,-800,-441) -> Matrix(361,-18,7200,-359) Matrix(719,394,2480,1359) -> Matrix(239,-12,-2848,143) Matrix(1159,634,1680,919) -> Matrix(199,-10,-5552,279) Matrix(199,108,-960,-521) -> Matrix(197,-10,1320,-67) Matrix(1519,822,1920,1039) -> Matrix(157,-8,-4808,245) Matrix(241,130,1040,561) -> Matrix(235,-12,-2252,115) Matrix(1521,814,3440,1841) -> Matrix(1087,-56,-19236,991) Matrix(359,192,1120,599) -> Matrix(349,-18,-4440,229) Matrix(921,490,1280,681) -> Matrix(347,-18,-9928,515) Matrix(401,212,-1360,-719) -> Matrix(383,-20,3696,-193) Matrix(519,248,-1760,-841) -> Matrix(445,-26,4296,-251) Matrix(1001,470,1280,601) -> Matrix(235,-14,-7436,443) Matrix(1039,484,1200,559) -> Matrix(133,-8,-4472,269) Matrix(1919,892,3440,1599) -> Matrix(929,-56,-20720,1249) Matrix(401,186,-2240,-1039) -> Matrix(331,-20,1804,-109) Matrix(799,368,1040,479) -> Matrix(197,-12,-5992,365) Matrix(401,184,1920,881) -> Matrix(131,-8,-1228,75) Matrix(1079,492,1840,839) -> Matrix(487,-30,-11412,703) Matrix(359,162,-800,-361) -> Matrix(289,-18,4608,-287) Matrix(1241,556,1520,681) -> Matrix(159,-10,-5072,319) Matrix(1079,482,1520,679) -> Matrix(95,-6,-2644,167) Matrix(3281,1452,4160,1841) -> Matrix(63,-4,-2000,127) Matrix(1841,814,3440,1521) -> Matrix(879,-56,-18820,1199) Matrix(8041,3552,14400,6361) -> Matrix(3667,-234,-81912,5227) Matrix(8039,3550,14400,6359) -> Matrix(3665,-234,-81836,5225) Matrix(999,440,1360,599) -> Matrix(31,-2,-852,55) Matrix(719,316,2000,879) -> Matrix(125,-8,-1828,117) Matrix(721,316,1280,561) -> Matrix(373,-24,-8408,541) Matrix(719,314,1280,559) -> Matrix(371,-24,-8332,539) Matrix(1121,488,1840,801) -> Matrix(247,-16,-6036,391) Matrix(281,122,1200,521) -> Matrix(31,-2,-356,23) Matrix(559,242,2400,1039) -> Matrix(245,-16,-2404,157) Matrix(839,362,-2320,-1001) -> Matrix(397,-26,4932,-323) Matrix(921,392,1600,681) -> Matrix(511,-34,-11768,783) Matrix(919,390,1600,679) -> Matrix(509,-34,-11692,781) Matrix(1121,474,-4160,-1759) -> Matrix(715,-48,6152,-413) Matrix(2599,1098,6720,2839) -> Matrix(1041,-70,-16076,1081) Matrix(199,84,1040,439) -> Matrix(89,-6,-608,41) Matrix(1559,654,2000,839) -> Matrix(29,-2,-884,61) Matrix(401,168,-2480,-1039) -> Matrix(59,-4,428,-29) Matrix(14881,6232,25600,10721) -> Matrix(3305,-224,-76856,5209) Matrix(14879,6230,25600,10719) -> Matrix(3303,-224,-76780,5207) Matrix(961,402,-3440,-1439) -> Matrix(353,-24,3280,-223) Matrix(1319,548,-4720,-1961) -> Matrix(89,-6,816,-55) Matrix(2719,1128,4240,1759) -> Matrix(233,-16,-5956,409) Matrix(439,182,480,199) -> Matrix(29,-2,-1000,69) Matrix(2081,862,2320,961) -> Matrix(117,-8,-4168,285) Matrix(2039,844,2800,1159) -> Matrix(263,-18,-7700,527) Matrix(1001,414,1840,761) -> Matrix(437,-30,-9512,653) Matrix(6959,2876,18000,7439) -> Matrix(117,-8,-1828,125) Matrix(3761,1552,6400,2641) -> Matrix(1509,-104,-35476,2445) Matrix(3759,1550,6400,2639) -> Matrix(1507,-104,-35400,2443) Matrix(399,164,1360,559) -> Matrix(115,-8,-1308,91) Matrix(3121,1280,8000,3281) -> Matrix(115,-8,-1768,123) Matrix(4679,1918,12000,4919) -> Matrix(259,-18,-4072,283) Matrix(1201,492,1760,721) -> Matrix(115,-8,-3148,219) Matrix(201,82,-880,-359) -> Matrix(143,-10,1044,-73) Matrix(439,174,-1920,-761) -> Matrix(193,-14,1420,-103) Matrix(559,220,2640,1039) -> Matrix(55,-4,-536,39) Matrix(199,78,1120,439) -> Matrix(137,-10,-1000,73) Matrix(1039,406,1840,719) -> Matrix(217,-16,-4896,361) Matrix(3281,1280,8000,3121) -> Matrix(107,-8,-1752,131) Matrix(4919,1918,12000,4679) -> Matrix(247,-18,-4048,295) Matrix(601,234,2160,841) -> Matrix(137,-10,-1548,113) Matrix(3921,1520,6400,2481) -> Matrix(1189,-88,-29144,2157) Matrix(3919,1518,6400,2479) -> Matrix(1187,-88,-29068,2155) Matrix(2839,1098,6720,2599) -> Matrix(941,-70,-15876,1181) Matrix(12199,4716,19760,7639) -> Matrix(457,-34,-11304,841) Matrix(9759,3772,-42640,-16481) -> Matrix(107,-8,816,-61) Matrix(1239,478,1760,679) -> Matrix(187,-14,-5276,395) Matrix(679,260,2400,919) -> Matrix(133,-10,-1556,117) Matrix(12121,4638,19760,7561) -> Matrix(451,-34,-11076,835) Matrix(1199,458,2720,1039) -> Matrix(55,-4,-976,71) Matrix(201,76,320,121) -> Matrix(79,-6,-1988,151) Matrix(199,74,320,119) -> Matrix(77,-6,-1912,149) Matrix(1319,484,-3600,-1321) -> Matrix(229,-18,2888,-227) Matrix(721,264,3280,1201) -> Matrix(151,-12,-1296,103) Matrix(159,58,-880,-321) -> Matrix(51,-4,268,-21) Matrix(199,72,-1440,-521) -> Matrix(25,-2,-12,1) Matrix(4759,1720,-17600,-6361) -> Matrix(173,-14,1520,-123) Matrix(1319,476,4320,1559) -> Matrix(371,-30,-4588,371) Matrix(1681,606,2000,721) -> Matrix(49,-4,-1580,129) Matrix(879,316,2000,719) -> Matrix(101,-8,-1780,141) Matrix(2481,890,4240,1521) -> Matrix(199,-16,-4664,375) Matrix(9241,3312,14400,5161) -> Matrix(667,-54,-17132,1387) Matrix(9239,3310,14400,5159) -> Matrix(665,-54,-17056,1385) Matrix(439,156,560,199) -> Matrix(25,-2,-812,65) Matrix(279,98,-800,-281) -> Matrix(169,-14,2016,-167) Matrix(759,262,1040,359) -> Matrix(117,-10,-3428,293) Matrix(119,38,-880,-281) -> Matrix(21,-2,116,-11) Matrix(1039,330,1760,559) -> Matrix(85,-8,-2008,189) Matrix(121,38,640,201) -> Matrix(21,-2,-136,13) Matrix(761,236,1680,521) -> Matrix(101,-10,-1828,181) Matrix(2361,730,2720,841) -> Matrix(21,-2,-724,69) Matrix(1839,568,4400,1359) -> Matrix(43,-4,-720,67) Matrix(119,36,-400,-121) -> Matrix(61,-6,600,-59) Matrix(1081,320,1760,521) -> Matrix(137,-14,-3376,345) Matrix(1761,520,4880,1441) -> Matrix(349,-36,-5012,517) Matrix(28201,8320,40000,11801) -> Matrix(3307,-342,-93708,9691) Matrix(28199,8318,40000,11799) -> Matrix(3305,-342,-93632,9689) Matrix(559,164,1360,399) -> Matrix(75,-8,-1228,131) Matrix(2041,596,2880,841) -> Matrix(19,-2,-560,59) Matrix(2039,594,2880,839) -> Matrix(17,-2,-484,57) Matrix(399,116,-2480,-721) -> Matrix(1,0,-4,1) Matrix(841,244,1520,441) -> Matrix(61,-6,-1352,133) Matrix(2359,682,-8720,-2521) -> Matrix(97,-10,844,-87) Matrix(919,260,2400,679) -> Matrix(97,-10,-1484,153) Matrix(561,158,2560,721) -> Matrix(77,-8,-664,69) Matrix(599,168,1280,359) -> Matrix(169,-18,-3164,337) Matrix(5479,1532,6720,1879) -> Matrix(93,-10,-2948,317) Matrix(2719,758,3440,959) -> Matrix(37,-4,-1156,125) Matrix(841,234,2160,601) -> Matrix(93,-10,-1460,157) Matrix(1161,320,1600,441) -> Matrix(199,-22,-5780,639) Matrix(1159,318,1600,439) -> Matrix(197,-22,-5704,637) Matrix(1641,446,2800,761) -> Matrix(157,-18,-3672,421) Matrix(13199,3570,-57680,-15601) -> Matrix(103,-12,764,-89) Matrix(681,184,1040,281) -> Matrix(87,-10,-2288,263) Matrix(18721,5032,25600,6881) -> Matrix(1157,-136,-34140,4013) Matrix(18719,5030,25600,6879) -> Matrix(1155,-136,-34064,4011) Matrix(961,258,-5360,-1439) -> Matrix(101,-12,564,-67) Matrix(1001,268,3440,921) -> Matrix(17,-2,-212,25) Matrix(761,202,1360,361) -> Matrix(21,-2,-472,45) Matrix(39,10,-160,-41) -> Matrix(17,-2,128,-15) Matrix(4881,1160,6400,1521) -> Matrix(1,0,-36,1) Matrix(4879,1158,6400,1519) -> Matrix(1,0,-40,1) Matrix(3719,880,4560,1079) -> Matrix(15,-2,-472,63) Matrix(521,122,1200,281) -> Matrix(19,-2,-332,35) Matrix(1039,242,2400,559) -> Matrix(125,-16,-2164,277) Matrix(561,130,1040,241) -> Matrix(91,-12,-1964,259) Matrix(879,202,1040,239) -> Matrix(29,-4,-964,133) Matrix(208521,47720,270400,61881) -> Matrix(371,-50,-11360,1531) Matrix(208519,47718,270400,61879) -> Matrix(369,-50,-11284,1529) Matrix(1241,280,1600,361) -> Matrix(127,-18,-3944,559) Matrix(1239,278,1600,359) -> Matrix(125,-18,-3868,557) Matrix(1161,256,2000,441) -> Matrix(15,-2,-352,47) Matrix(721,158,2560,561) -> Matrix(53,-8,-616,93) Matrix(679,148,1280,279) -> Matrix(89,-14,-1888,297) Matrix(361,78,560,121) -> Matrix(11,-2,-280,51) Matrix(5041,1072,6400,1361) -> Matrix(1,0,-32,1) Matrix(5039,1070,6400,1359) -> Matrix(1,0,-44,1) Matrix(1039,220,2640,559) -> Matrix(31,-4,-488,63) Matrix(2319,490,4160,879) -> Matrix(25,-4,-556,89) Matrix(161,34,1520,321) -> Matrix(1,0,-12,1) Matrix(2481,520,3440,721) -> Matrix(27,-4,-776,115) Matrix(881,184,1920,401) -> Matrix(59,-8,-1084,147) Matrix(959,198,2320,479) -> Matrix(131,-20,-2168,331) Matrix(439,84,1040,199) -> Matrix(29,-6,-488,101) Matrix(201,38,640,121) -> Matrix(9,-2,-112,25) Matrix(4841,894,6720,1241) -> Matrix(63,-10,-1808,287) Matrix(3481,642,4560,841) -> Matrix(13,-2,-396,61) Matrix(839,154,1520,279) -> Matrix(61,-10,-1348,221) Matrix(439,78,1120,199) -> Matrix(53,-10,-832,157) Matrix(1321,232,1600,281) -> Matrix(71,-14,-2348,463) Matrix(1319,230,1600,279) -> Matrix(69,-14,-2272,461) Matrix(1279,204,2000,319) -> Matrix(23,-4,-592,103) Matrix(2319,364,5600,879) -> Matrix(55,-12,-912,199) Matrix(801,124,1040,161) -> Matrix(19,-4,-584,123) Matrix(119,18,-800,-121) -> Matrix(25,-6,96,-23) Matrix(5521,760,6400,881) -> Matrix(1,0,-20,1) Matrix(5519,758,6400,879) -> Matrix(1,0,-56,1) Matrix(641,86,1200,161) -> Matrix(35,-8,-748,171) Matrix(1879,248,2720,359) -> Matrix(7,-2,-192,55) Matrix(281,36,320,41) -> Matrix(7,-2,-248,71) Matrix(279,34,320,39) -> Matrix(5,-2,-172,69) Matrix(321,34,1520,161) -> Matrix(1,0,-12,1) Matrix(1359,140,2320,239) -> Matrix(19,-8,-444,187) Matrix(281,24,480,41) -> Matrix(7,-2,-164,47) Matrix(1519,-176,2080,-241) -> Matrix(29,8,-852,-235) Matrix(1161,-152,1520,-199) -> Matrix(11,2,-336,-61) Matrix(281,-38,880,-119) -> Matrix(15,2,-188,-25) Matrix(521,-72,1440,-199) -> Matrix(3,2,-44,-29) Matrix(839,-124,1360,-201) -> Matrix(57,10,-1408,-247) Matrix(641,-98,1040,-159) -> Matrix(51,8,-1256,-197) Matrix(2041,-320,2800,-439) -> Matrix(41,6,-1196,-175) Matrix(1039,-168,2480,-401) -> Matrix(37,4,-620,-67) Matrix(199,-34,240,-41) -> Matrix(13,2,-436,-67) Matrix(321,-58,880,-159) -> Matrix(29,4,-428,-59) Matrix(441,-82,640,-119) -> Matrix(17,2,-468,-55) Matrix(521,-108,960,-199) -> Matrix(87,10,-1888,-217) Matrix(881,-188,1120,-239) -> Matrix(1,0,-24,1) Matrix(1841,-402,2560,-559) -> Matrix(135,16,-3856,-457) Matrix(681,-154,880,-199) -> Matrix(91,10,-2812,-309) Matrix(359,-82,880,-201) -> Matrix(93,10,-1516,-163) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) Matrix(1599,-418,1840,-481) -> Matrix(1,0,-24,1) Matrix(2441,-640,3200,-839) -> Matrix(21,2,-620,-59) Matrix(841,-222,1360,-359) -> Matrix(23,2,-564,-49) Matrix(2321,-622,3280,-879) -> Matrix(83,8,-2376,-229) Matrix(1519,-408,3280,-881) -> Matrix(335,32,-6208,-593) Matrix(3041,-818,4160,-1119) -> Matrix(295,28,-8692,-825) Matrix(1839,-496,2080,-561) -> Matrix(85,8,-3092,-291) Matrix(4441,-1202,5760,-1559) -> Matrix(193,18,-5908,-551) Matrix(2361,-640,2800,-759) -> Matrix(65,6,-2156,-199) Matrix(521,-144,720,-199) -> Matrix(111,10,-3208,-289) Matrix(1439,-402,3440,-961) -> Matrix(271,24,-4528,-401) Matrix(2001,-562,2560,-719) -> Matrix(183,16,-5776,-505) Matrix(921,-266,1520,-439) -> Matrix(71,6,-1716,-145) Matrix(2079,-604,4960,-1441) -> Matrix(53,4,-888,-67) Matrix(2401,-702,3280,-959) -> Matrix(91,8,-2696,-237) Matrix(121,-36,400,-119) -> Matrix(71,6,-864,-73) Matrix(761,-232,1440,-439) -> Matrix(271,22,-5728,-465) Matrix(521,-162,640,-199) -> Matrix(25,2,-788,-63) Matrix(281,-98,800,-279) -> Matrix(195,14,-2744,-197) Matrix(1079,-386,1680,-601) -> Matrix(85,6,-2196,-155) Matrix(1001,-362,2320,-839) -> Matrix(375,26,-6476,-449) Matrix(2761,-1000,3200,-1159) -> Matrix(29,2,-740,-51) Matrix(1521,-556,3280,-1199) -> Matrix(231,16,-4288,-297) Matrix(2599,-952,4480,-1641) -> Matrix(321,22,-7456,-511) Matrix(881,-324,1520,-559) -> Matrix(119,8,-2752,-185) Matrix(1001,-382,1360,-519) -> Matrix(31,2,-884,-57) Matrix(4601,-1760,7840,-2999) -> Matrix(763,50,-17900,-1173) Matrix(1159,-444,1360,-521) -> Matrix(153,10,-5248,-343) Matrix(6081,-2350,9520,-3679) -> Matrix(371,24,-9476,-613) Matrix(881,-342,1440,-559) -> Matrix(311,20,-7604,-489) Matrix(1081,-426,1520,-599) -> Matrix(95,6,-2676,-169) Matrix(2159,-876,2960,-1201) -> Matrix(259,16,-7592,-469) Matrix(2161,-892,3680,-1519) -> Matrix(991,60,-23272,-1409) Matrix(4841,-2000,7840,-3239) -> Matrix(827,50,-20460,-1237) Matrix(601,-250,1440,-599) -> Matrix(299,18,-5000,-301) Matrix(6881,-2882,11840,-4959) -> Matrix(1743,104,-40508,-2417) Matrix(961,-404,1520,-639) -> Matrix(135,8,-3392,-201) Matrix(1841,-778,2080,-879) -> Matrix(135,8,-5012,-297) Matrix(599,-254,1040,-441) -> Matrix(373,22,-8596,-507) Matrix(5399,-2332,8800,-3801) -> Matrix(379,22,-9320,-541) Matrix(2279,-1006,4080,-1801) -> Matrix(1165,66,-26036,-1475) Matrix(361,-162,800,-359) -> Matrix(323,18,-5832,-325) Matrix(761,-348,960,-439) -> Matrix(183,10,-5728,-313) Matrix(959,-452,1360,-641) -> Matrix(377,20,-10688,-567) Matrix(1241,-648,1760,-919) -> Matrix(543,26,-15392,-737) Matrix(1839,-986,2240,-1201) -> Matrix(429,20,-13964,-651) Matrix(441,-242,800,-439) -> Matrix(395,18,-8712,-397) Matrix(1481,-842,2320,-1319) -> Matrix(591,26,-15116,-665) Matrix(3039,-1754,4160,-2401) -> Matrix(1109,48,-32600,-1411) Matrix(2079,-1208,2480,-1441) -> Matrix(93,4,-2860,-123) Matrix(2479,-1442,3440,-2001) -> Matrix(559,24,-16048,-689) Matrix(3401,-1988,4720,-2759) -> Matrix(139,6,-4008,-173) Matrix(679,-402,880,-521) -> Matrix(237,10,-7276,-307) Matrix(1481,-894,1920,-1159) -> Matrix(339,14,-10388,-429) Matrix(32881,-20172,42640,-26159) -> Matrix(197,8,-5984,-243) Matrix(2281,-1444,3600,-2279) -> Matrix(455,18,-11552,-457) Matrix(721,-458,880,-559) -> Matrix(101,4,-3308,-131) Matrix(1241,-792,1440,-919) -> Matrix(51,2,-1964,-77) Matrix(12841,-8200,17600,-11239) -> Matrix(359,14,-10488,-409) Matrix(521,-338,800,-519) -> Matrix(363,14,-9464,-365) Matrix(761,-518,880,-599) -> Matrix(55,2,-1788,-65) Matrix(281,-196,400,-279) -> Matrix(167,6,-4704,-169) Matrix(2081,-1476,2480,-1759) -> Matrix(1,0,-4,1) Matrix(6361,-4522,8720,-6199) -> Matrix(283,10,-8292,-293) Matrix(44481,-32450,57680,-42079) -> Matrix(353,12,-10796,-367) Matrix(4399,-3218,5360,-3921) -> Matrix(355,12,-11508,-389) Matrix(121,-90,160,-119) -> Matrix(59,2,-1800,-61) Matrix(681,-578,800,-679) -> Matrix(203,6,-6936,-205) 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 1/10 1/9 1/8 1/7 1/6 3/16 1/5 3/14 5/22 7/30 1/4 7/26 5/18 3/10 5/16 1/3 11/30 3/8 13/34 2/5 5/12 13/30 7/16 1/2 11/20 21/38 9/16 23/40 7/12 47/80 59/100 3/5 5/8 19/30 13/20 7/10 29/40 3/4 61/80 31/40 63/80 4/5 33/40 17/20 7/8 9/10 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 0/1 1/10 -1/4 1/9 -1/7 0/1 1/8 -1/5 3/23 -1/5 0/1 2/15 -1/6 1/7 -1/5 -2/11 1/6 -1/6 3/17 -1/7 -6/43 2/11 -2/15 -3/23 3/16 0/1 4/21 -1/7 0/1 1/5 -1/8 4/19 -2/17 -1/9 7/33 -1/11 0/1 3/14 -1/8 2/9 -4/35 -1/9 5/22 -5/46 3/13 -5/47 -2/19 7/30 -1/10 4/17 -1/9 -2/19 1/4 -1/10 6/23 -1/11 0/1 11/42 -1/10 5/19 -2/21 -1/11 4/15 -1/10 7/26 -7/74 10/37 -7/75 -4/43 13/48 -4/43 3/11 -6/65 -1/11 5/18 -5/56 2/7 -1/11 -2/23 3/10 -1/12 4/13 -2/25 -1/13 5/16 -2/25 6/19 -2/25 -1/13 1/3 -1/13 -2/27 5/14 -1/14 4/11 -2/29 -5/73 11/30 -3/44 7/19 -2/29 -1/15 3/8 -1/15 8/21 -1/15 -4/61 13/34 -5/76 5/13 -1/15 -2/31 7/18 -5/78 16/41 -1/15 -2/31 9/23 -8/125 -3/47 11/28 -1/16 13/33 -4/63 -5/79 2/5 -1/16 11/27 -5/81 -4/65 9/22 -5/82 16/39 -3/49 -2/33 7/17 -11/181 -2/33 19/46 -15/248 12/29 -12/199 -5/83 29/70 -3/50 17/41 -2/33 -9/149 5/12 -3/50 13/31 -6/101 -1/17 8/19 -6/101 -1/17 11/26 -11/186 3/7 -1/17 -6/103 13/30 -3/52 10/23 -8/139 -5/87 17/39 -9/157 -2/35 7/16 -2/35 18/41 -2/35 -3/53 11/25 -5/88 15/34 -11/194 4/9 -4/71 -5/89 1/2 -1/20 6/11 -5/109 -6/131 11/20 -1/22 16/29 -13/287 -12/265 21/38 -1/22 5/9 -5/111 -4/89 19/34 -11/246 14/25 -5/112 9/16 -2/45 22/39 -2/45 -9/203 13/23 -5/113 -8/181 17/30 -3/68 4/7 -6/137 -1/23 23/40 -1/23 19/33 -1/23 -28/645 15/26 -11/254 26/45 -7/162 11/19 -1/23 -6/139 29/50 -5/116 18/31 -1/23 -6/139 25/43 -4/93 -15/349 7/12 -3/70 31/53 -8/187 -5/117 24/41 -9/211 -2/47 41/70 -3/70 17/29 -5/117 -12/281 27/46 -15/352 37/63 -41/963 -2/47 47/80 -2/47 10/17 -2/47 -11/259 23/39 -2/47 -3/71 59/100 -5/118 36/61 -2/47 -3/71 13/22 -5/118 3/5 -1/24 20/33 -5/121 -4/97 17/28 -1/24 14/23 -3/73 -8/195 25/41 -2/49 -1/25 61/100 -1/24 36/59 -4/97 -3/73 11/18 -5/122 8/13 -2/49 -1/25 29/47 -7/173 -4/99 21/34 -5/124 34/55 -3/74 13/21 -4/99 -1/25 5/8 -1/25 12/19 -1/25 -2/51 19/30 -3/76 26/41 -5/127 -2/51 7/11 -5/127 -2/51 9/14 -1/26 11/17 -6/155 -7/181 13/20 -1/26 15/23 -8/209 -7/183 2/3 -2/53 -1/27 7/10 -1/28 12/17 -7/199 -2/57 29/41 -2/57 -1/29 17/24 -1/29 22/31 -1/27 -2/55 27/38 -1/28 32/45 -1/28 5/7 -2/57 -1/29 13/18 -5/144 21/29 -16/463 -1/29 29/40 -1/29 8/11 -1/29 -6/175 27/37 -4/117 -7/205 46/63 -14/411 -11/323 19/26 -7/206 30/41 -2/59 -3/89 11/15 -1/30 25/34 -3/88 14/19 -1/29 -2/59 3/4 -1/30 16/21 -1/31 0/1 61/80 0/1 45/59 -1/29 0/1 29/38 -1/30 42/55 -1/30 13/17 -2/61 -1/31 23/30 -1/30 10/13 -2/61 -5/153 27/35 -3/92 17/22 -5/154 24/31 -14/433 -1/31 31/40 -1/31 7/9 -1/31 -4/125 11/14 -1/32 37/47 -1/35 0/1 63/80 0/1 26/33 -1/29 0/1 41/52 -1/30 15/19 -1/31 -2/63 19/24 -1/31 4/5 -1/32 17/21 -1/33 0/1 13/16 0/1 22/27 -1/31 0/1 53/65 -1/32 31/38 -1/32 9/11 -3/97 -2/65 23/28 -3/98 14/17 -6/197 -1/33 33/40 -1/33 19/23 -1/33 -8/265 5/6 -1/34 11/13 -2/67 -3/101 17/20 -1/34 23/27 -4/137 -3/103 6/7 -2/69 -1/35 13/15 -1/34 33/38 -1/34 20/23 -1/35 0/1 7/8 -1/35 15/17 -1/35 -2/71 8/9 -1/33 0/1 9/10 -1/36 1/1 -1/39 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(199,-17,480,-41) (0/1,1/10) -> (29/70,17/41) Hyperbolic Matrix(381,-41,920,-99) (1/10,1/9) -> (12/29,29/70) Hyperbolic Matrix(141,-16,520,-59) (1/9,1/8) -> (13/48,3/11) Hyperbolic Matrix(379,-49,1400,-181) (1/8,3/23) -> (10/37,13/48) Hyperbolic Matrix(1161,-152,1520,-199) (3/23,2/15) -> (42/55,13/17) Hyperbolic Matrix(339,-47,440,-61) (2/15,1/7) -> (10/13,27/35) Hyperbolic Matrix(101,-16,120,-19) (1/7,1/6) -> (5/6,11/13) Hyperbolic Matrix(199,-34,240,-41) (1/6,3/17) -> (19/23,5/6) Hyperbolic Matrix(581,-104,1000,-179) (3/17,2/11) -> (18/31,25/43) Hyperbolic Matrix(539,-100,760,-141) (2/11,3/16) -> (17/24,22/31) Hyperbolic Matrix(821,-155,1160,-219) (3/16,4/21) -> (29/41,17/24) Hyperbolic Matrix(601,-115,1040,-199) (4/21,1/5) -> (26/45,11/19) Hyperbolic Matrix(299,-62,680,-141) (1/5,4/19) -> (18/41,11/25) Hyperbolic Matrix(1381,-292,2360,-499) (4/19,7/33) -> (31/53,24/41) Hyperbolic Matrix(881,-188,1120,-239) (7/33,3/14) -> (11/14,37/47) Hyperbolic Matrix(179,-39,280,-61) (3/14,2/9) -> (7/11,9/14) 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(341,-79,600,-139) (3/13,7/30) -> (17/30,4/7) Hyperbolic Matrix(679,-159,1200,-281) (7/30,4/17) -> (13/23,17/30) 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(901,-242,1560,-419) (4/15,7/26) -> (15/26,26/45) Hyperbolic Matrix(1899,-512,2600,-701) (7/26,10/37) -> (46/63,19/26) Hyperbolic Matrix(521,-144,720,-199) (3/11,5/18) -> (13/18,21/29) Hyperbolic Matrix(139,-39,360,-101) (5/18,2/7) -> (5/13,7/18) Hyperbolic Matrix(61,-18,200,-59) (2/7,3/10) -> (3/10,4/13) 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(259,-83,440,-141) (6/19,1/3) -> (10/17,23/39) Hyperbolic Matrix(181,-64,280,-99) (1/3,5/14) -> (9/14,11/17) Hyperbolic Matrix(219,-79,280,-101) (5/14,4/11) -> (7/9,11/14) Hyperbolic Matrix(859,-314,1480,-541) (4/11,11/30) -> (29/50,18/31) 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(1259,-482,2040,-781) (13/34,5/13) -> (29/47,21/34) Hyperbolic Matrix(1099,-428,1800,-701) (7/18,16/41) -> (36/59,11/18) Hyperbolic Matrix(801,-313,1840,-719) (16/41,9/23) -> (10/23,17/39) Hyperbolic Matrix(921,-361,1120,-439) (9/23,11/28) -> (23/28,14/17) Hyperbolic Matrix(2081,-819,2640,-1039) (11/28,13/33) -> (26/33,41/52) Hyperbolic Matrix(1081,-426,1520,-599) (13/33,2/5) -> (32/45,5/7) Hyperbolic Matrix(381,-155,440,-179) (2/5,11/27) -> (6/7,13/15) Hyperbolic Matrix(1299,-532,2200,-901) (9/22,16/39) -> (36/61,13/22) Hyperbolic Matrix(961,-395,1360,-559) (16/39,7/17) -> (12/17,29/41) Hyperbolic Matrix(2161,-892,3680,-1519) (7/17,19/46) -> (27/46,37/63) Hyperbolic Matrix(781,-323,1400,-579) (19/46,12/29) -> (5/9,19/34) Hyperbolic Matrix(1861,-772,2360,-979) (17/41,5/12) -> (41/52,15/19) Hyperbolic Matrix(821,-344,1000,-419) (5/12,13/31) -> (9/11,23/28) Hyperbolic Matrix(939,-394,1480,-621) (13/31,8/19) -> (26/41,7/11) Hyperbolic Matrix(1141,-482,1560,-659) (8/19,11/26) -> (19/26,30/41) Hyperbolic Matrix(599,-254,1040,-441) (11/26,3/7) -> (19/33,15/26) Hyperbolic Matrix(461,-199,600,-259) (3/7,13/30) -> (23/30,10/13) Hyperbolic Matrix(919,-399,1200,-521) (13/30,10/23) -> (13/17,23/30) Hyperbolic Matrix(561,-245,1280,-559) (17/39,7/16) -> (7/16,18/41) Parabolic Matrix(1681,-741,2720,-1199) (11/25,15/34) -> (21/34,34/55) Hyperbolic Matrix(821,-363,1400,-619) (15/34,4/9) -> (17/29,27/46) Hyperbolic Matrix(21,-10,40,-19) (4/9,1/2) -> (1/2,6/11) Parabolic Matrix(441,-242,800,-439) (6/11,11/20) -> (11/20,16/29) Parabolic Matrix(1241,-685,1520,-839) (16/29,21/38) -> (31/38,9/11) Hyperbolic Matrix(1079,-597,1520,-841) (21/38,5/9) -> (22/31,27/38) Hyperbolic Matrix(999,-559,1360,-761) (19/34,14/25) -> (11/15,25/34) Hyperbolic Matrix(539,-302,680,-381) (14/25,9/16) -> (19/24,4/5) Hyperbolic Matrix(981,-553,1240,-699) (9/16,22/39) -> (15/19,19/24) Hyperbolic 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(899,-523,1480,-861) (25/43,7/12) -> (17/28,14/23) Hyperbolic Matrix(1141,-667,1880,-1099) (7/12,31/53) -> (20/33,17/28) Hyperbolic Matrix(439,-257,480,-281) (24/41,41/70) -> (9/10,1/1) Hyperbolic Matrix(821,-481,920,-539) (41/70,17/29) -> (8/9,9/10) Hyperbolic Matrix(3761,-2209,6400,-3759) (37/63,47/80) -> (47/80,10/17) Parabolic Matrix(5979,-3527,9800,-5781) (23/39,59/100) -> (61/100,36/59) Hyperbolic Matrix(6221,-3671,10200,-6019) (59/100,36/61) -> (25/41,61/100) Hyperbolic Matrix(679,-402,880,-521) (13/22,3/5) -> (27/35,17/22) Hyperbolic Matrix(1859,-1126,2280,-1381) (3/5,20/33) -> (22/27,53/65) Hyperbolic Matrix(259,-159,360,-221) (11/18,8/13) -> (5/7,13/18) Hyperbolic Matrix(581,-358,680,-419) (8/13,29/47) -> (23/27,6/7) Hyperbolic Matrix(201,-125,320,-199) (13/21,5/8) -> (5/8,12/19) Parabolic Matrix(1141,-722,1800,-1139) (12/19,19/30) -> (19/30,26/41) Parabolic Matrix(521,-338,800,-519) (11/17,13/20) -> (13/20,15/23) Parabolic Matrix(759,-497,1040,-681) (15/23,2/3) -> (27/37,46/63) Hyperbolic Matrix(141,-98,200,-139) (2/3,7/10) -> (7/10,12/17) Parabolic Matrix(1979,-1407,2280,-1621) (27/38,32/45) -> (13/15,33/38) Hyperbolic Matrix(1161,-841,1600,-1159) (21/29,29/40) -> (29/40,8/11) Parabolic Matrix(461,-336,520,-379) (8/11,27/37) -> (15/17,8/9) Hyperbolic Matrix(419,-307,520,-381) (30/41,11/15) -> (4/5,17/21) Hyperbolic 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(3719,-2839,4560,-3481) (29/38,42/55) -> (53/65,31/38) Hyperbolic Matrix(1241,-961,1600,-1239) (24/31,31/40) -> (31/40,7/9) Parabolic Matrix(5041,-3969,6400,-5039) (37/47,63/80) -> (63/80,26/33) Parabolic Matrix(1321,-1089,1600,-1319) (14/17,33/40) -> (33/40,19/23) Parabolic Matrix(681,-578,800,-679) (11/13,17/20) -> (17/20,23/27) Parabolic Matrix(281,-245,320,-279) (20/23,7/8) -> (7/8,15/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-38,1) Matrix(199,-17,480,-41) -> Matrix(11,2,-182,-33) Matrix(381,-41,920,-99) -> Matrix(23,5,-382,-83) Matrix(141,-16,520,-59) -> Matrix(1,1,-12,-11) Matrix(379,-49,1400,-181) -> Matrix(39,7,-418,-75) Matrix(1161,-152,1520,-199) -> Matrix(11,2,-336,-61) Matrix(339,-47,440,-61) -> Matrix(3,1,-94,-31) Matrix(101,-16,120,-19) -> Matrix(7,1,-232,-33) Matrix(199,-34,240,-41) -> Matrix(13,2,-436,-67) Matrix(581,-104,1000,-179) -> Matrix(67,9,-1556,-209) Matrix(539,-100,760,-141) -> Matrix(7,1,-204,-29) Matrix(821,-155,1160,-219) -> Matrix(5,1,-146,-29) Matrix(601,-115,1040,-199) -> Matrix(41,6,-950,-139) Matrix(299,-62,680,-141) -> Matrix(61,7,-1072,-123) Matrix(1381,-292,2360,-499) -> Matrix(47,5,-1100,-117) Matrix(881,-188,1120,-239) -> Matrix(1,0,-24,1) Matrix(179,-39,280,-61) -> Matrix(25,3,-642,-77) Matrix(681,-154,880,-199) -> Matrix(91,10,-2812,-309) Matrix(359,-82,880,-201) -> Matrix(93,10,-1516,-163) Matrix(341,-79,600,-139) -> Matrix(67,7,-1522,-159) Matrix(679,-159,1200,-281) -> Matrix(23,2,-518,-45) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) Matrix(1599,-418,1840,-481) -> Matrix(1,0,-24,1) Matrix(2441,-640,3200,-839) -> Matrix(21,2,-620,-59) Matrix(841,-222,1360,-359) -> Matrix(23,2,-564,-49) Matrix(901,-242,1560,-419) -> Matrix(157,15,-3632,-347) Matrix(1899,-512,2600,-701) -> Matrix(223,21,-6552,-617) Matrix(521,-144,720,-199) -> Matrix(111,10,-3208,-289) Matrix(139,-39,360,-101) -> Matrix(57,5,-878,-77) Matrix(61,-18,200,-59) -> Matrix(35,3,-432,-37) Matrix(521,-162,640,-199) -> Matrix(25,2,-788,-63) Matrix(519,-163,640,-201) -> Matrix(25,2,-838,-67) Matrix(259,-83,440,-141) -> Matrix(89,7,-2098,-165) Matrix(181,-64,280,-99) -> Matrix(71,5,-1832,-129) Matrix(219,-79,280,-101) -> Matrix(43,3,-1362,-95) Matrix(859,-314,1480,-541) -> Matrix(101,7,-2352,-163) Matrix(881,-324,1520,-559) -> Matrix(119,8,-2752,-185) Matrix(121,-45,320,-119) -> Matrix(89,6,-1350,-91) Matrix(1001,-382,1360,-519) -> Matrix(31,2,-884,-57) Matrix(1259,-482,2040,-781) -> Matrix(229,15,-5664,-371) Matrix(1099,-428,1800,-701) -> Matrix(79,5,-1912,-121) Matrix(801,-313,1840,-719) -> Matrix(249,16,-4342,-279) Matrix(921,-361,1120,-439) -> Matrix(157,10,-5134,-327) Matrix(2081,-819,2640,-1039) -> Matrix(63,4,-1906,-121) Matrix(1081,-426,1520,-599) -> Matrix(95,6,-2676,-169) Matrix(381,-155,440,-179) -> Matrix(49,3,-1650,-101) Matrix(1299,-532,2200,-901) -> Matrix(81,5,-1928,-119) Matrix(961,-395,1360,-559) -> Matrix(131,8,-3750,-229) Matrix(2161,-892,3680,-1519) -> Matrix(991,60,-23272,-1409) Matrix(781,-323,1400,-579) -> Matrix(381,23,-8498,-513) Matrix(1861,-772,2360,-979) -> Matrix(83,5,-2540,-153) Matrix(821,-344,1000,-419) -> Matrix(151,9,-4916,-293) Matrix(939,-394,1480,-621) -> Matrix(117,7,-2992,-179) Matrix(1141,-482,1560,-659) -> Matrix(253,15,-7472,-443) Matrix(599,-254,1040,-441) -> Matrix(373,22,-8596,-507) Matrix(461,-199,600,-259) -> Matrix(121,7,-3682,-213) Matrix(919,-399,1200,-521) -> Matrix(35,2,-998,-57) Matrix(561,-245,1280,-559) -> Matrix(419,24,-7350,-421) Matrix(1681,-741,2720,-1199) -> Matrix(71,4,-1722,-97) Matrix(821,-363,1400,-619) -> Matrix(407,23,-9538,-539) Matrix(21,-10,40,-19) -> Matrix(19,1,-400,-21) Matrix(441,-242,800,-439) -> Matrix(395,18,-8712,-397) Matrix(1241,-685,1520,-839) -> Matrix(221,10,-7050,-319) Matrix(1079,-597,1520,-841) -> Matrix(133,6,-3702,-167) Matrix(999,-559,1360,-761) -> Matrix(45,2,-1238,-55) Matrix(539,-302,680,-381) -> Matrix(157,7,-4912,-219) Matrix(981,-553,1240,-699) -> Matrix(113,5,-3458,-153) Matrix(1121,-633,1840,-1039) -> Matrix(361,16,-8822,-391) Matrix(921,-529,1600,-919) -> Matrix(781,34,-17986,-783) Matrix(899,-523,1480,-861) -> Matrix(303,13,-7342,-315) Matrix(1141,-667,1880,-1099) -> Matrix(163,7,-3982,-171) Matrix(439,-257,480,-281) -> Matrix(47,2,-1622,-69) Matrix(821,-481,920,-539) -> Matrix(117,5,-4142,-177) Matrix(3761,-2209,6400,-3759) -> Matrix(2443,104,-57434,-2445) Matrix(5979,-3527,9800,-5781) -> Matrix(401,17,-9742,-413) Matrix(6221,-3671,10200,-6019) -> Matrix(165,7,-4078,-173) Matrix(679,-402,880,-521) -> Matrix(237,10,-7276,-307) Matrix(1859,-1126,2280,-1381) -> Matrix(121,5,-3848,-159) Matrix(259,-159,360,-221) -> Matrix(123,5,-3518,-143) Matrix(581,-358,680,-419) -> Matrix(123,5,-4256,-173) Matrix(201,-125,320,-199) -> Matrix(149,6,-3750,-151) Matrix(1141,-722,1800,-1139) -> Matrix(227,9,-5776,-229) Matrix(521,-338,800,-519) -> Matrix(363,14,-9464,-365) Matrix(759,-497,1040,-681) -> Matrix(263,10,-7706,-293) Matrix(141,-98,200,-139) -> Matrix(83,3,-2352,-85) Matrix(1979,-1407,2280,-1621) -> Matrix(29,1,-958,-33) Matrix(1161,-841,1600,-1159) -> Matrix(637,22,-18502,-639) Matrix(461,-336,520,-379) -> Matrix(29,1,-1132,-39) Matrix(419,-307,520,-381) -> Matrix(89,3,-2878,-97) Matrix(121,-90,160,-119) -> Matrix(59,2,-1800,-61) Matrix(4881,-3721,6400,-4879) -> Matrix(1,0,2,1) Matrix(3719,-2839,4560,-3481) -> Matrix(61,2,-1922,-63) Matrix(1241,-961,1600,-1239) -> Matrix(557,18,-17298,-559) Matrix(5041,-3969,6400,-5039) -> Matrix(1,0,6,1) Matrix(1321,-1089,1600,-1319) -> Matrix(461,14,-15246,-463) Matrix(681,-578,800,-679) -> Matrix(203,6,-6936,-205) Matrix(281,-245,320,-279) -> Matrix(69,2,-2450,-71) 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 (-1/1,0/1) 0 40 1/10 -1/4 2 4 1/9 (-1/7,0/1) 0 40 1/8 -1/5 2 5 3/23 (-1/5,0/1) 0 40 2/15 -1/6 4 8 1/7 (-1/5,-2/11) 0 40 3/20 -1/6 6 2 1/6 -1/6 2 20 7/40 -1/7 14 1 3/17 (-1/7,-6/43) 0 40 2/11 (-2/15,-3/23) 0 40 3/16 0/1 2 5 4/21 (-1/7,0/1) 0 40 1/5 -1/8 2 8 4/19 (-2/17,-1/9) 0 40 7/33 (-1/11,0/1) 0 40 17/80 0/1 6 1 3/14 -1/8 2 20 2/9 (-4/35,-1/9) 0 40 9/40 -1/9 18 1 5/22 -5/46 2 20 3/13 (-5/47,-2/19) 0 40 7/30 -1/10 6 4 4/17 (-1/9,-2/19) 0 40 1/4 -1/10 2 10 6/23 (-1/11,0/1) 0 40 17/65 -1/10 4 8 11/42 -1/10 2 20 21/80 -2/21 2 1 5/19 (-2/21,-1/11) 0 40 4/15 -1/10 2 8 7/26 -7/74 2 20 10/37 (-7/75,-4/43) 0 40 13/48 -4/43 2 5 3/11 (-6/65,-1/11) 0 40 11/40 -1/11 22 1 5/18 -5/56 2 20 2/7 (-1/11,-2/23) 0 40 3/10 -1/12 6 4 4/13 (-2/25,-1/13) 0 40 13/42 -1/12 2 20 9/29 (-5/61,-4/49) 0 40 5/16 -2/25 2 5 6/19 (-2/25,-1/13) 0 40 1/3 (-1/13,-2/27) 0 40 7/20 -1/14 14 2 5/14 -1/14 2 20 4/11 (-2/29,-5/73) 0 40 11/30 -3/44 2 4 7/19 (-2/29,-1/15) 0 40 3/8 -1/15 6 5 8/21 (-1/15,-4/61) 0 40 21/55 -3/46 2 8 13/34 -5/76 2 20 23/60 -3/46 6 2 5/13 (-1/15,-2/31) 0 40 7/18 -5/78 2 20 39/100 -1/16 2 2 16/41 (-1/15,-2/31) 0 40 9/23 (-8/125,-3/47) 0 40 11/28 -1/16 2 10 13/33 (-4/63,-5/79) 0 40 15/38 -1/16 2 20 2/5 -1/16 4 8 11/27 (-5/81,-4/65) 0 40 9/22 -5/82 2 20 41/100 -5/82 2 2 16/39 (-3/49,-2/33) 0 40 7/17 (-11/181,-2/33) 0 40 33/80 -2/33 26 1 19/46 -15/248 2 20 12/29 (-12/199,-5/83) 0 40 29/70 -3/50 2 4 17/41 (-2/33,-9/149) 0 40 22/53 (-5/83,-8/133) 0 40 5/12 -3/50 2 10 18/43 (-15/251,-4/67) 0 40 13/31 (-6/101,-1/17) 0 40 21/50 -5/84 2 4 8/19 (-6/101,-1/17) 0 40 19/45 -7/118 2 8 11/26 -11/186 2 20 17/40 -1/17 34 1 3/7 (-1/17,-6/103) 0 40 13/30 -3/52 6 4 10/23 (-8/139,-5/87) 0 40 17/39 (-9/157,-2/35) 0 40 7/16 -2/35 6 5 18/41 (-2/35,-3/53) 0 40 11/25 -5/88 2 8 15/34 -11/194 2 20 4/9 (-4/71,-5/89) 0 40 17/38 -1/18 2 20 9/20 -1/18 18 2 1/2 -1/20 2 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(199,-17,480,-41) (0/1,1/10) -> (29/70,17/41) Hyperbolic Matrix(381,-41,920,-99) (1/10,1/9) -> (12/29,29/70) Hyperbolic Matrix(141,-16,520,-59) (1/9,1/8) -> (13/48,3/11) Hyperbolic Matrix(379,-49,1400,-181) (1/8,3/23) -> (10/37,13/48) Hyperbolic Matrix(481,-63,1840,-241) (3/23,2/15) -> (6/23,17/65) Glide Reflection Matrix(179,-24,440,-59) (2/15,1/7) -> (2/5,11/27) Glide Reflection Matrix(261,-38,680,-99) (1/7,3/20) -> (23/60,5/13) Hyperbolic Matrix(19,-3,120,-19) (3/20,1/6) -> (3/20,1/6) Reflection 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(419,-75,1000,-179) (3/17,2/11) -> (18/43,13/31) Glide Reflection Matrix(199,-37,640,-119) (2/11,3/16) -> (9/29,5/16) Glide Reflection Matrix(201,-38,640,-121) (3/16,4/21) -> (5/16,6/19) Glide Reflection Matrix(439,-84,1040,-199) (4/21,1/5) -> (8/19,19/45) Glide Reflection Matrix(299,-62,680,-141) (1/5,4/19) -> (18/41,11/25) Hyperbolic Matrix(979,-207,2360,-499) (4/19,7/33) -> (17/41,22/53) Glide Reflection Matrix(1121,-238,5280,-1121) (7/33,17/80) -> (7/33,17/80) Reflection Matrix(239,-51,1120,-239) (17/80,3/14) -> (17/80,3/14) Reflection Matrix(101,-22,280,-61) (3/14,2/9) -> (5/14,4/11) Glide Reflection Matrix(161,-36,720,-161) (2/9,9/40) -> (2/9,9/40) Reflection Matrix(199,-45,880,-199) (9/40,5/22) -> (9/40,5/22) Reflection Matrix(359,-82,880,-201) (5/22,3/13) -> (11/27,9/22) Hyperbolic Matrix(259,-60,600,-139) (3/13,7/30) -> (3/7,13/30) Glide Reflection Matrix(521,-122,1200,-281) (7/30,4/17) -> (13/30,10/23) Glide Reflection Matrix(41,-10,160,-39) (4/17,1/4) -> (1/4,6/23) Parabolic Matrix(1059,-277,2680,-701) (17/65,11/42) -> (15/38,2/5) Hyperbolic 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(659,-177,1560,-419) (4/15,7/26) -> (19/45,11/26) Glide Reflection Matrix(701,-189,2600,-701) (7/26,27/100) -> (7/26,27/100) Reflection Matrix(359,-97,1040,-281) (17/63,10/37) -> (1/3,8/23) Hyperbolic 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(139,-39,360,-101) (5/18,2/7) -> (5/13,7/18) Hyperbolic Matrix(61,-18,200,-59) (2/7,3/10) -> (3/10,4/13) Parabolic Matrix(741,-229,1880,-581) (4/13,13/42) -> (13/33,15/38) Glide Reflection Matrix(661,-205,1480,-459) (13/42,9/29) -> (4/9,17/38) Hyperbolic Matrix(181,-58,440,-141) (6/19,1/3) -> (16/39,7/17) Glide Reflection Matrix(181,-63,520,-181) (9/26,7/20) -> (9/26,7/20) Reflection Matrix(99,-35,280,-99) (7/20,5/14) -> (7/20,5/14) Reflection Matrix(621,-227,1480,-541) (4/11,11/30) -> (13/31,21/50) 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(781,-299,2040,-781) (13/34,23/60) -> (13/34,23/60) Reflection Matrix(701,-273,1800,-701) (7/18,39/100) -> (7/18,39/100) Reflection Matrix(3281,-1280,8000,-3121) (39/100,16/41) -> (41/100,16/39) Glide Reflection Matrix(801,-313,1840,-719) (16/41,9/23) -> (10/23,17/39) Hyperbolic Matrix(619,-243,1480,-581) (9/23,11/28) -> (5/12,18/43) Hyperbolic Matrix(781,-307,1880,-739) (11/28,13/33) -> (22/53,5/12) Hyperbolic Matrix(901,-369,2200,-901) (9/22,41/100) -> (9/22,41/100) Reflection Matrix(1121,-462,2720,-1121) (7/17,33/80) -> (7/17,33/80) Reflection Matrix(1519,-627,3680,-1519) (33/80,19/46) -> (33/80,19/46) Reflection Matrix(619,-256,1400,-579) (19/46,12/29) -> (15/34,4/9) 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(341,-153,760,-341) (17/38,9/20) -> (17/38,9/20) Reflection Matrix(19,-9,40,-19) (9/20,1/2) -> (9/20,1/2) 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(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(199,-17,480,-41) -> Matrix(11,2,-182,-33) Matrix(381,-41,920,-99) -> Matrix(23,5,-382,-83) Matrix(141,-16,520,-59) -> Matrix(1,1,-12,-11) Matrix(379,-49,1400,-181) -> Matrix(39,7,-418,-75) Matrix(481,-63,1840,-241) -> Matrix(-1,0,16,1) *** -> (-1/8,0/1) Matrix(179,-24,440,-59) -> Matrix(19,3,-310,-49) Matrix(261,-38,680,-99) -> Matrix(27,5,-416,-77) Matrix(19,-3,120,-19) -> Matrix(7,1,-48,-7) (3/20,1/6) -> (-1/6,-1/8) Matrix(41,-7,240,-41) -> Matrix(13,2,-84,-13) (1/6,7/40) -> (-1/6,-1/7) Matrix(239,-42,1360,-239) -> Matrix(85,12,-602,-85) (7/40,3/17) -> (-1/7,-6/43) Matrix(419,-75,1000,-179) -> Matrix(67,9,-1124,-151) Matrix(199,-37,640,-119) -> Matrix(17,2,-212,-25) Matrix(201,-38,640,-121) -> Matrix(13,2,-162,-25) Matrix(439,-84,1040,-199) -> Matrix(41,6,-690,-101) Matrix(299,-62,680,-141) -> Matrix(61,7,-1072,-123) Matrix(979,-207,2360,-499) -> Matrix(47,5,-780,-83) Matrix(1121,-238,5280,-1121) -> Matrix(-1,0,22,1) (7/33,17/80) -> (-1/11,0/1) Matrix(239,-51,1120,-239) -> Matrix(-1,0,16,1) (17/80,3/14) -> (-1/8,0/1) Matrix(101,-22,280,-61) -> Matrix(25,3,-358,-43) Matrix(161,-36,720,-161) -> Matrix(71,8,-630,-71) (2/9,9/40) -> (-4/35,-1/9) Matrix(199,-45,880,-199) -> Matrix(91,10,-828,-91) (9/40,5/22) -> (-1/9,-5/46) Matrix(359,-82,880,-201) -> Matrix(93,10,-1516,-163) Matrix(259,-60,600,-139) -> Matrix(67,7,-1158,-121) Matrix(521,-122,1200,-281) -> Matrix(23,2,-402,-35) Matrix(41,-10,160,-39) -> Matrix(19,2,-200,-21) -1/10 Matrix(1059,-277,2680,-701) -> Matrix(51,5,-806,-79) Matrix(881,-231,3360,-881) -> Matrix(41,4,-420,-41) (11/42,21/80) -> (-1/10,-2/21) Matrix(799,-210,3040,-799) -> Matrix(43,4,-462,-43) (21/80,5/19) -> (-2/21,-1/11) Matrix(519,-137,1360,-359) -> Matrix(23,2,-356,-31) Matrix(659,-177,1560,-419) -> Matrix(157,15,-2648,-253) Matrix(701,-189,2600,-701) -> Matrix(223,21,-2368,-223) (7/26,27/100) -> (-7/74,-3/32) Matrix(359,-97,1040,-281) -> Matrix(107,10,-1466,-137) Matrix(241,-66,880,-241) -> Matrix(131,12,-1430,-131) (3/11,11/40) -> (-6/65,-1/11) Matrix(199,-55,720,-199) -> Matrix(111,10,-1232,-111) (11/40,5/18) -> (-1/11,-5/56) Matrix(139,-39,360,-101) -> Matrix(57,5,-878,-77) Matrix(61,-18,200,-59) -> Matrix(35,3,-432,-37) -1/12 Matrix(741,-229,1880,-581) -> Matrix(35,3,-548,-47) Matrix(661,-205,1480,-459) -> Matrix(109,9,-1950,-161) Matrix(181,-58,440,-141) -> Matrix(89,7,-1462,-115) Matrix(181,-63,520,-181) -> Matrix(125,9,-1736,-125) (9/26,7/20) -> (-9/124,-1/14) Matrix(99,-35,280,-99) -> Matrix(71,5,-1008,-71) (7/20,5/14) -> (-1/14,-5/72) Matrix(621,-227,1480,-541) -> Matrix(101,7,-1688,-117) Matrix(639,-235,1520,-559) -> Matrix(119,8,-2008,-135) Matrix(121,-45,320,-119) -> Matrix(89,6,-1350,-91) -1/15 Matrix(1199,-458,2720,-1039) -> Matrix(63,4,-1118,-71) Matrix(781,-299,2040,-781) -> Matrix(229,15,-3496,-229) (13/34,23/60) -> (-5/76,-3/46) Matrix(701,-273,1800,-701) -> Matrix(79,5,-1248,-79) (7/18,39/100) -> (-5/78,-1/16) Matrix(3281,-1280,8000,-3121) -> Matrix(123,8,-2014,-131) Matrix(801,-313,1840,-719) -> Matrix(249,16,-4342,-279) Matrix(619,-243,1480,-581) -> Matrix(205,13,-3422,-217) Matrix(781,-307,1880,-739) -> Matrix(109,7,-1822,-117) Matrix(901,-369,2200,-901) -> Matrix(81,5,-1312,-81) (9/22,41/100) -> (-1/16,-5/82) Matrix(1121,-462,2720,-1121) -> Matrix(725,44,-11946,-725) (7/17,33/80) -> (-11/181,-2/33) Matrix(1519,-627,3680,-1519) -> Matrix(991,60,-16368,-991) (33/80,19/46) -> (-2/33,-15/248) Matrix(619,-256,1400,-579) -> Matrix(381,23,-6742,-407) Matrix(441,-187,1040,-441) -> Matrix(373,22,-6324,-373) (11/26,17/40) -> (-11/186,-1/17) Matrix(239,-102,560,-239) -> Matrix(205,12,-3502,-205) (17/40,3/7) -> (-1/17,-6/103) Matrix(561,-245,1280,-559) -> Matrix(419,24,-7350,-421) -2/35 Matrix(341,-153,760,-341) -> Matrix(305,17,-5472,-305) (17/38,9/20) -> (-17/304,-1/18) Matrix(19,-9,40,-19) -> Matrix(19,1,-360,-19) (9/20,1/2) -> (-1/18,-1/20) Matrix(-1,1,0,1) -> Matrix(-1,0,40,1) (1/2,1/0) -> (-1/20,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.