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): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/9 -7/9 -2/3 -5/9 -7/15 -4/9 -5/12 -7/18 -41/108 -29/81 -19/54 -1/3 -17/54 -49/162 -7/24 -5/18 -29/108 -43/162 -19/72 -7/27 -5/21 -17/72 -2/9 -23/108 -5/24 -28/135 -5/26 -4/21 -14/81 -1/6 -3/20 -4/27 -3/22 -2/15 -3/23 -7/54 -2/17 -1/9 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 2/13 3/19 4/25 1/6 4/23 3/17 2/11 5/27 3/16 4/21 1/5 4/19 3/14 2/9 3/13 5/21 1/4 5/18 7/25 2/7 8/27 1/3 10/27 7/18 2/5 11/27 5/12 4/9 7/15 1/2 5/9 16/27 17/27 52/81 2/3 19/27 20/27 7/9 107/135 22/27 67/81 23/27 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -3/8 -7/19 -8/9 -1/3 -7/8 -3/10 -5/17 -13/15 -5/18 -6/7 -6/23 -1/4 -11/13 -1/4 -16/19 -4/17 -7/30 -21/25 -13/56 -5/6 -2/9 -24/29 -14/65 -3/14 -19/23 -11/52 -14/17 -4/19 -5/24 -9/11 -9/44 -22/27 -1/5 -13/16 -1/5 -13/66 -17/21 -5/26 -4/5 -3/16 -2/11 -15/19 -7/40 -41/52 -7/41 -1/6 -26/33 -3/17 -11/14 -3/17 -1/6 -18/23 -11/64 -6/35 -7/9 -1/6 -24/31 -17/104 -8/49 -41/53 -41/252 -17/22 -11/68 -5/31 -27/35 -7/44 -10/13 -1/6 -4/25 -13/17 -5/32 -16/21 -3/19 -3/4 -3/20 -1/7 -14/19 -8/57 -7/50 -25/34 -5/36 -19/137 -36/49 -21/152 -4/29 -11/15 -3/22 -30/41 -3/22 -2/15 -19/26 -1/7 -3/22 -8/11 -3/22 -2/15 -21/29 -7/52 -13/18 -2/15 -18/25 -5/38 -8/61 -41/57 -7/54 -23/32 -5/39 -1/8 -5/7 -1/8 -17/24 -6/47 -12/17 -12/95 -1/8 -19/27 -1/8 -7/10 -1/8 -7/57 -30/43 -25/206 -4/33 -23/33 -7/58 -39/56 -19/158 -3/25 -16/23 -1/8 -2/17 -9/13 -1/8 -11/16 -3/25 -5/42 -13/19 -7/60 -15/22 -5/44 -1/9 -2/3 -1/9 -13/20 -1/9 -3/28 -11/17 -5/48 -20/31 -7/68 -4/39 -9/14 -1/9 -1/10 -34/53 -2/19 -1/10 -25/39 -1/10 -66/103 -11/104 -2/19 -41/64 -7/67 -5/48 -16/25 -1/10 0/1 -7/11 -7/68 -19/30 -6/59 -12/19 -12/119 -1/10 -17/27 -1/10 -5/8 -1/10 -5/51 -18/29 -9/94 -2/21 -31/50 -5/53 -3/32 -13/21 -1/10 -60/97 -17/178 -2/21 -47/76 -5/53 -3/32 -34/55 -1/10 -2/21 -21/34 -3/32 -1/11 -8/13 -1/10 0/1 -19/31 -7/72 -11/18 -2/21 -14/23 -2/21 -3/32 -31/51 -5/54 -48/79 -9/98 -10/109 -17/28 -1/11 -3/34 -3/5 -3/32 -16/27 -1/11 -13/22 -1/11 -13/144 -23/39 -7/78 -10/17 -5/56 -4/45 -17/29 -11/124 -24/41 -22/249 -3/34 -31/53 -31/352 -7/12 -2/23 -32/55 -3/34 -2/23 -25/43 -9/104 -18/31 -4/47 -1/12 -11/19 -1/12 -37/64 -5/53 -3/32 -26/45 -1/11 -15/26 -1/11 -3/34 -19/33 -3/34 -4/7 -2/23 -1/12 -13/23 -7/80 -22/39 -7/81 -31/55 -31/360 -9/16 -3/35 -7/82 -23/41 -1/12 -14/25 -4/47 -9/106 -5/9 -1/12 -16/29 -6/73 -11/134 -27/49 -17/208 -11/20 -1/12 -3/37 -28/51 -3/37 -17/31 -13/160 -6/11 -2/25 -3/38 -7/13 -1/12 -8/15 -1/13 -1/2 -1/13 -1/14 -9/19 -5/72 -8/17 -3/44 -4/59 -7/15 -1/14 -6/13 -1/14 0/1 -11/24 0/1 -5/11 -5/72 -14/31 -3/44 -4/59 -9/20 -5/73 -3/44 -4/9 -1/15 -15/34 -11/167 -5/76 -26/59 -4/61 -11/168 -11/25 -5/76 -7/16 -1/15 -3/46 -24/55 -3/46 -2/31 -17/39 -3/46 -27/62 -11/170 -13/201 -10/23 -2/31 -9/140 -23/53 -23/360 -13/30 -4/63 -3/7 -1/16 -17/40 -1/14 -1/15 -14/33 -1/15 -11/26 -1/15 -3/46 -19/45 -1/16 -27/64 -1/15 -1/16 -8/19 -1/14 0/1 -21/50 -11/164 -1/15 -34/81 -1/15 -13/31 -9/136 -18/43 -13/198 -4/61 -41/98 -11/168 -29/443 -23/55 -23/352 -5/12 -2/31 -22/53 -2/31 -5/78 -39/94 -5/78 -3/47 -56/135 -3/47 -17/41 -1/16 -12/29 -3/46 -2/31 -19/46 -5/78 -13/203 -26/63 -3/47 -7/17 -1/16 -23/56 -5/79 -11/174 -16/39 -5/79 -9/22 -9/143 -1/16 -11/27 -1/16 -2/5 -1/16 -2/33 -13/33 -1/18 -11/28 -1/17 -1/18 -20/51 -1/17 -9/23 -3/52 -7/18 0/1 -12/31 -1/16 0/1 -5/13 -1/16 -18/47 -12/191 -1/16 -31/81 -1/16 -13/34 -1/16 -11/177 -34/89 -20/323 -13/210 -55/144 -6/97 -21/55 -21/340 -29/76 -13/211 -17/276 -8/21 -3/49 -19/50 -7/115 -9/148 -30/79 -21/346 -2/33 -41/108 -2/33 -11/29 -7/116 -14/37 -1/16 -2/33 -3/8 -3/50 -1/17 -10/27 -1/17 -7/19 -7/120 -18/49 -13/224 -4/69 -29/79 -3/52 -11/30 -4/69 -15/41 -3/52 -4/11 -2/35 -1/18 -9/25 -5/88 -32/89 -4/71 -1/18 -23/64 -3/53 -7/124 -14/39 -5/89 -19/53 -19/340 -24/67 -22/395 -1/18 -29/81 -1/18 -5/14 -1/18 -3/55 -6/17 -1/20 0/1 -19/54 0/1 -13/37 -1/12 -7/20 -1/15 -1/16 -8/23 -1/16 -2/33 -1/3 -1/18 -6/19 -1/22 0/1 -17/54 0/1 -11/35 -1/12 -5/16 -1/17 -1/18 -9/29 -3/52 -4/13 -1/18 -4/73 -7/23 -1/20 -24/79 -6/107 -1/18 -41/135 -1/18 -17/56 -1/18 -7/127 -10/33 -3/55 -23/76 -11/203 -13/240 -36/119 -33/610 -2/37 -49/162 -2/37 -13/43 -11/204 -3/10 -3/56 -1/19 -8/27 -1/19 -5/17 -5/96 -12/41 -3/58 -2/39 -7/24 -2/39 -23/79 -1/20 -16/55 -3/58 -2/39 -9/31 -7/136 -2/7 -2/39 -1/20 -11/39 -3/62 -9/32 -1/21 -3/64 -16/57 -1/21 -23/82 -1/21 -1/22 -53/189 -1/22 -30/107 -1/22 0/1 -7/25 -1/20 -5/18 0/1 -8/29 -2/35 -1/18 -3/11 -3/56 -10/37 -2/39 -1/20 -17/63 -1/20 -7/26 -1/19 -3/58 -18/67 -3/58 -2/39 -29/108 -2/39 -11/41 -1/20 -4/15 -1/19 -17/64 -5/97 -7/136 -30/113 -23/448 -2/39 -43/162 -2/39 -13/49 -9/176 -9/34 -1/19 -1/20 -14/53 -3/58 -2/39 -19/72 -2/39 -24/91 -9/176 -16/313 -5/19 -1/20 -6/23 -6/119 -1/20 -7/27 -1/20 -1/4 -1/20 -1/21 -5/21 -1/18 -9/38 -1/19 -7/134 -13/55 -13/252 -17/72 -2/39 -4/17 -4/79 -1/20 -7/30 -2/41 -3/13 -1/20 -8/35 -5/102 -2/41 -13/57 -3/62 -5/22 -1/20 -3/61 -2/9 -1/21 -7/32 -3/64 -5/107 -12/55 -2/43 -1/22 -5/23 -5/108 -8/37 -3/64 -2/43 -3/14 -1/22 -1/23 -13/61 -1/24 -23/108 0/1 -10/47 -1/20 0/1 -7/33 -1/22 -11/52 -1/21 -5/106 -15/71 -3/64 -19/90 -2/43 -4/19 -4/87 -1/22 -5/24 -2/45 -11/53 -11/252 -28/135 -1/23 -17/82 -1/23 -15/346 -6/29 -3/70 -2/47 -1/5 -1/20 -5/26 -1/21 -5/106 -4/21 -1/21 -7/37 -3/64 -17/90 -2/43 -10/53 -2/43 -1/22 -3/16 -3/65 -1/22 -5/27 -1/22 -2/11 -1/22 -2/45 -5/28 -1/22 -1/23 -8/45 -1/23 -3/17 -1/24 -4/23 -2/45 -3/68 -9/52 -9/206 -1/23 -14/81 -1/23 -5/29 -5/116 -1/6 0/1 -4/25 -1/22 -4/89 -7/44 -5/113 -3/68 -3/19 -1/24 -2/13 -1/22 0/1 -3/20 -3/68 -1/23 -4/27 -1/23 -1/7 -1/24 -3/22 -3/71 -1/24 -2/15 -1/25 -3/23 -1/32 -7/54 0/1 -4/31 -1/12 0/1 -1/8 -1/22 -1/23 -2/17 -1/24 0/1 -1/9 -1/24 -1/10 -1/24 -1/25 -1/11 -1/20 0/1 -1/26 0/1 1/10 -1/27 -1/28 1/9 -1/28 1/8 -1/29 -1/30 2/15 -1/27 1/7 -1/28 2/13 -1/30 0/1 3/19 -1/28 4/25 -4/119 -1/30 1/6 0/1 5/29 -5/144 4/23 -3/88 -2/59 3/17 -1/28 2/11 -2/59 -1/30 5/27 -1/30 3/16 -1/30 -3/91 4/21 -1/31 1/5 -1/32 4/19 -1/30 -4/121 11/52 -5/154 -1/31 7/33 -1/30 3/14 -1/29 -1/30 5/23 -5/152 2/9 -1/31 7/31 -7/220 12/53 -3/94 -2/63 5/22 -3/95 -1/32 8/35 -2/63 -5/158 3/13 -1/32 4/17 -1/32 -4/129 5/21 -1/34 1/4 -1/31 -1/32 5/19 -1/32 9/34 -1/32 -1/33 13/49 -9/292 4/15 -1/33 11/41 -1/32 7/26 -3/98 -1/33 3/11 -3/100 8/29 -1/34 -2/69 5/18 0/1 7/25 -1/32 16/57 -1/31 9/32 -3/92 -1/31 2/7 -1/32 -2/65 7/24 -2/65 5/17 -5/164 8/27 -1/33 3/10 -1/33 -3/100 13/43 -11/368 10/33 -3/101 17/56 -7/237 -1/34 7/23 -1/32 4/13 -4/135 -1/34 5/16 -1/34 -1/35 6/19 -1/30 0/1 7/22 -1/31 -1/32 1/3 -1/34 7/20 -1/36 -1/37 6/17 -1/32 0/1 11/31 -1/36 5/14 -3/101 -1/34 19/53 -19/648 14/39 -5/171 37/103 -25/856 23/64 -7/240 -3/103 9/25 -5/172 4/11 -1/34 -2/69 11/30 -4/139 7/19 -7/244 10/27 -1/35 3/8 -1/35 -3/106 11/29 -7/248 19/50 -9/320 -7/249 8/21 -3/107 37/97 -31/1108 29/76 -17/608 -13/465 21/55 -21/752 13/34 -11/395 -1/36 5/13 -1/36 12/31 -1/36 0/1 7/18 0/1 9/23 -3/104 20/51 -1/35 31/79 -1/36 11/28 -1/34 -1/35 2/5 -2/71 -1/36 11/27 -1/36 9/22 -1/36 -9/325 16/39 -5/181 7/17 -1/36 12/29 -2/73 -3/110 17/41 -1/36 22/53 -5/182 -2/73 5/12 -2/73 23/55 -23/844 18/43 -4/147 -13/478 13/31 -9/332 8/19 -1/38 0/1 27/64 -1/36 -1/37 19/45 -1/36 11/26 -3/110 -1/37 14/33 -1/37 3/7 -1/36 10/23 -9/328 -2/73 17/39 -3/110 24/55 -2/73 -3/110 7/16 -3/110 -1/37 18/41 -14/513 -3/110 11/25 -5/184 4/9 -1/37 13/29 -3/112 22/49 -13/484 -4/149 9/20 -3/112 -5/187 23/51 -1/38 14/31 -4/149 -3/112 5/11 -5/188 6/13 -1/38 0/1 7/15 -1/38 1/2 -1/38 -1/39 10/19 -3/118 -8/315 9/17 -1/40 8/15 -1/39 7/13 -1/40 13/24 0/1 6/11 -3/118 -2/79 17/31 -13/516 11/20 -3/119 -1/40 5/9 -1/40 19/34 -1/40 -7/281 33/59 -23/924 14/25 -9/362 -4/161 9/16 -7/282 -3/121 31/55 -31/1252 22/39 -7/283 35/62 -11/445 -13/526 13/23 -7/284 30/53 -2/81 -3/122 17/30 -2/81 4/7 -1/40 -2/81 23/40 -5/203 -3/122 19/33 -3/122 15/26 -3/122 -1/41 26/45 -1/41 37/64 -3/124 -5/207 11/19 -1/40 29/50 -3/119 -1/40 47/81 -1/40 18/31 -1/40 -4/161 25/43 -9/364 57/98 -1/40 -1/41 32/55 -2/81 -3/122 7/12 -2/81 31/53 -31/1260 55/94 -53/2155 -3/122 79/135 -3/122 24/41 -3/122 -22/895 17/29 -11/448 27/46 -3/122 -1/41 37/63 -5/204 10/17 -4/163 -5/204 33/56 -7/286 -15/613 23/39 -7/286 13/22 -13/532 -1/41 16/27 -1/41 3/5 -3/124 20/33 -1/41 17/28 -3/122 -1/41 31/51 -5/206 14/23 -3/124 -2/83 11/18 -2/83 19/31 -7/292 8/13 -1/42 0/1 29/47 -1/40 50/81 -1/41 21/34 -1/41 -3/124 55/89 -3/124 89/144 -2/83 34/55 -2/83 -1/42 47/76 -3/124 -5/207 13/21 -1/42 31/50 -3/124 -5/207 49/79 -19/788 67/108 -2/83 18/29 -2/83 -9/374 23/37 -5/208 5/8 -5/209 -1/42 17/27 -1/42 12/19 -1/42 -12/505 31/49 -17/716 50/79 -22/927 -29/1222 19/30 -6/253 26/41 -1/42 -6/253 7/11 -7/296 16/25 -1/42 0/1 57/89 -7/296 41/64 -5/212 -7/297 25/39 -1/42 34/53 -1/42 -2/85 43/67 -3/128 52/81 -1/43 9/14 -1/42 -1/43 11/17 -5/212 35/54 -2/85 24/37 -2/85 -11/468 13/20 -3/128 -1/43 15/23 -1/44 2/3 -1/43 13/19 -7/304 37/54 -2/87 24/35 -2/87 -13/566 11/16 -5/218 -3/131 20/29 -3/130 -2/87 9/13 -1/44 16/23 -2/87 -1/44 55/79 -23/1004 94/135 -3/131 39/56 -3/131 -19/830 23/33 -7/306 53/76 -15/656 -19/831 83/119 -63/2756 113/162 -4/175 30/43 -4/175 -25/1094 7/10 -7/307 -1/44 19/27 -1/44 12/17 -1/44 -12/529 29/41 -1/44 17/24 -6/265 56/79 -26/1149 -31/1370 39/55 -39/1724 22/31 -17/752 -4/177 5/7 -1/44 28/39 -1/45 23/32 -1/44 -5/221 41/57 -7/310 59/82 -31/1374 -3/133 136/189 -3/133 77/107 -47/2084 18/25 -8/355 -5/222 13/18 -2/89 21/29 -7/312 8/11 -2/89 -3/134 27/37 -5/224 46/63 -1/45 19/26 -3/134 -1/45 49/67 -1/44 79/108 -2/89 30/41 -2/89 -3/134 11/15 -3/134 47/64 -11/492 -15/671 83/113 -43/1924 119/162 -4/179 36/49 -4/179 -21/940 25/34 -19/851 -5/224 39/53 -39/1748 53/72 -6/269 67/91 -19/852 14/19 -7/314 -8/359 17/23 -17/764 20/27 -1/45 3/4 -1/45 -3/136 16/21 -3/137 29/38 -1/45 -1/46 42/55 -2/91 -1/46 55/72 -2/91 13/17 -5/228 23/30 -4/183 10/13 -4/183 -1/46 27/35 -7/320 44/57 -5/229 17/22 -5/229 -11/504 7/9 -1/46 25/32 -9/415 -17/784 43/55 -43/1984 18/23 -6/277 -11/508 29/37 -9/416 11/14 -1/46 -3/139 48/61 -9/416 -4/185 85/108 -4/185 37/47 -7/324 26/33 -3/139 41/52 -1/46 -7/323 56/71 -14/647 -9/416 71/90 -4/185 15/19 -7/324 19/24 -2/93 42/53 -1/46 -2/93 107/135 -1/46 65/82 -1/46 -3/139 23/29 -5/232 4/5 -2/93 -3/140 21/26 -5/234 -1/47 17/21 -5/234 30/37 -7/328 -22/1031 73/90 -8/375 43/53 -43/2016 13/16 -13/610 -1/47 22/27 -1/47 9/11 -9/424 23/28 -1/47 -3/142 37/45 -5/236 14/17 -5/236 -4/189 19/23 -11/520 43/52 -25/1183 -3/142 67/81 -3/142 24/29 -3/142 -14/663 5/6 -2/95 21/25 -13/620 37/44 -3/143 -1/48 16/19 -7/334 -4/191 11/13 -1/48 17/20 -17/815 -1/48 23/27 -1/48 6/7 -1/48 -6/289 19/22 -13/628 -3/145 13/15 -5/242 20/23 -17/824 -2/97 47/54 -2/97 27/31 -23/1116 7/8 -5/243 -3/146 15/17 -5/244 8/9 -1/49 9/10 -7/345 -3/148 10/11 -2/99 -9/446 1/1 -1/52 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(271,248,-648,-593) (-1/1,-9/10) -> (-41/98,-23/55) Hyperbolic Matrix(593,530,1026,917) (-9/10,-8/9) -> (26/45,37/64) Hyperbolic Matrix(379,334,-918,-809) (-8/9,-7/8) -> (-19/46,-26/63) Hyperbolic Matrix(541,470,-1242,-1079) (-7/8,-13/15) -> (-17/39,-27/62) Hyperbolic Matrix(107,92,-378,-325) (-13/15,-6/7) -> (-2/7,-11/39) Hyperbolic Matrix(269,228,-702,-595) (-6/7,-11/13) -> (-5/13,-18/47) Hyperbolic Matrix(161,136,702,593) (-11/13,-16/19) -> (8/35,3/13) Hyperbolic Matrix(971,816,-2700,-2269) (-16/19,-21/25) -> (-9/25,-32/89) Hyperbolic Matrix(55,46,324,271) (-21/25,-5/6) -> (1/6,5/29) Hyperbolic Matrix(53,44,324,269) (-5/6,-24/29) -> (4/25,1/6) Hyperbolic Matrix(755,624,-2484,-2053) (-24/29,-19/23) -> (-7/23,-24/79) Hyperbolic Matrix(325,268,918,757) (-19/23,-14/17) -> (6/17,11/31) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(485,396,594,485) (-9/11,-22/27) -> (22/27,9/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(269,218,-1134,-919) (-13/16,-17/21) -> (-5/21,-9/38) Hyperbolic Matrix(107,86,-270,-217) (-17/21,-4/5) -> (-2/5,-13/33) Hyperbolic Matrix(377,298,-1026,-811) (-4/5,-15/19) -> (-7/19,-18/49) Hyperbolic Matrix(487,384,-1026,-809) (-15/19,-41/52) -> (-1/2,-9/19) Hyperbolic Matrix(1081,852,3564,2809) (-41/52,-26/33) -> (10/33,17/56) Hyperbolic Matrix(757,596,-1782,-1403) (-26/33,-11/14) -> (-17/40,-14/33) Hyperbolic Matrix(487,382,-756,-593) (-11/14,-18/23) -> (-20/31,-9/14) Hyperbolic Matrix(377,294,-486,-379) (-18/23,-7/9) -> (-7/9,-24/31) Parabolic Matrix(2375,1838,3348,2591) (-24/31,-41/53) -> (39/55,22/31) Hyperbolic Matrix(1999,1546,5238,4051) (-41/53,-17/22) -> (29/76,21/55) Hyperbolic Matrix(811,626,-1188,-917) (-17/22,-27/35) -> (-13/19,-15/22) Hyperbolic Matrix(109,84,702,541) (-27/35,-10/13) -> (2/13,3/19) Hyperbolic Matrix(269,206,-918,-703) (-10/13,-13/17) -> (-5/17,-12/41) Hyperbolic Matrix(215,164,-1134,-865) (-13/17,-16/21) -> (-4/21,-7/37) Hyperbolic Matrix(431,328,1134,863) (-16/21,-3/4) -> (19/50,8/21) Hyperbolic Matrix(431,318,-1026,-757) (-3/4,-14/19) -> (-8/19,-21/50) Hyperbolic Matrix(1403,1032,-3672,-2701) (-14/19,-25/34) -> (-13/34,-34/89) Hyperbolic Matrix(1189,874,2646,1945) (-25/34,-36/49) -> (22/49,9/20) Hyperbolic Matrix(2215,1626,-3456,-2537) (-36/49,-11/15) -> (-25/39,-66/103) Hyperbolic Matrix(377,276,810,593) (-11/15,-30/41) -> (6/13,7/15) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(107,78,-594,-433) (-19/26,-8/11) -> (-2/11,-5/28) Hyperbolic Matrix(215,156,594,431) (-8/11,-21/29) -> (9/25,4/11) Hyperbolic Matrix(271,196,972,703) (-21/29,-13/18) -> (5/18,7/25) Hyperbolic Matrix(269,194,972,701) (-13/18,-18/25) -> (8/29,5/18) Hyperbolic Matrix(3511,2526,-5778,-4157) (-18/25,-41/57) -> (-31/51,-48/79) Hyperbolic Matrix(431,310,1350,971) (-41/57,-23/32) -> (7/22,1/3) Hyperbolic Matrix(53,38,-378,-271) (-23/32,-5/7) -> (-1/7,-3/22) Hyperbolic Matrix(163,116,-378,-269) (-5/7,-17/24) -> (-13/30,-3/7) Hyperbolic Matrix(215,152,-918,-649) (-17/24,-12/17) -> (-4/17,-7/30) Hyperbolic Matrix(647,456,918,647) (-12/17,-19/27) -> (19/27,12/17) Hyperbolic Matrix(379,266,540,379) (-19/27,-7/10) -> (7/10,19/27) Hyperbolic Matrix(1943,1356,-4644,-3241) (-7/10,-30/43) -> (-18/43,-41/98) Hyperbolic Matrix(2539,1770,-4104,-2861) (-30/43,-23/33) -> (-13/21,-60/97) Hyperbolic Matrix(755,526,3564,2483) (-23/33,-39/56) -> (11/52,7/33) Hyperbolic Matrix(431,300,-2484,-1729) (-39/56,-16/23) -> (-4/23,-9/52) Hyperbolic Matrix(271,188,702,487) (-16/23,-9/13) -> (5/13,12/31) Hyperbolic Matrix(485,334,-864,-595) (-9/13,-11/16) -> (-9/16,-23/41) Hyperbolic Matrix(271,186,-864,-593) (-11/16,-13/19) -> (-11/35,-5/16) Hyperbolic Matrix(379,258,1350,919) (-15/22,-2/3) -> (16/57,9/32) Hyperbolic Matrix(593,386,-1080,-703) (-2/3,-13/20) -> (-11/20,-28/51) Hyperbolic Matrix(379,246,-1080,-701) (-13/20,-11/17) -> (-13/37,-7/20) Hyperbolic Matrix(161,104,918,593) (-11/17,-20/31) -> (4/23,3/17) Hyperbolic Matrix(2375,1524,-5724,-3673) (-9/14,-34/53) -> (-22/53,-39/94) Hyperbolic Matrix(1837,1178,4212,2701) (-34/53,-25/39) -> (17/39,24/55) Hyperbolic Matrix(3671,2352,-13824,-8857) (-66/103,-41/64) -> (-17/64,-30/113) Hyperbolic Matrix(431,276,-2700,-1729) (-41/64,-16/25) -> (-4/25,-7/44) Hyperbolic Matrix(163,104,594,379) (-16/25,-7/11) -> (3/11,8/29) Hyperbolic Matrix(271,172,-594,-377) (-7/11,-19/30) -> (-11/24,-5/11) Hyperbolic Matrix(215,136,-1026,-649) (-19/30,-12/19) -> (-4/19,-5/24) Hyperbolic Matrix(647,408,1026,647) (-12/19,-17/27) -> (17/27,12/19) Hyperbolic Matrix(271,170,432,271) (-17/27,-5/8) -> (5/8,17/27) Hyperbolic Matrix(647,402,-1566,-973) (-5/8,-18/29) -> (-12/29,-19/46) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(271,168,1134,703) (-31/50,-13/21) -> (5/21,1/4) Hyperbolic Matrix(4967,3072,-16416,-10153) (-60/97,-47/76) -> (-23/76,-36/119) Hyperbolic Matrix(1187,734,5238,3239) (-47/76,-34/55) -> (12/53,5/22) Hyperbolic Matrix(971,600,-3672,-2269) (-34/55,-21/34) -> (-9/34,-14/53) Hyperbolic Matrix(107,66,-702,-433) (-21/34,-8/13) -> (-2/13,-3/20) Hyperbolic Matrix(215,132,702,431) (-8/13,-19/31) -> (7/23,4/13) Hyperbolic Matrix(379,232,972,595) (-19/31,-11/18) -> (7/18,9/23) Hyperbolic Matrix(377,230,972,593) (-11/18,-14/23) -> (12/31,7/18) Hyperbolic Matrix(1243,756,2754,1675) (-14/23,-31/51) -> (23/51,14/31) Hyperbolic Matrix(1511,918,-7290,-4429) (-48/79,-17/28) -> (-17/82,-6/29) Hyperbolic Matrix(53,32,-270,-163) (-17/28,-3/5) -> (-1/5,-5/26) Hyperbolic Matrix(161,96,270,161) (-3/5,-16/27) -> (16/27,3/5) Hyperbolic Matrix(703,416,1188,703) (-16/27,-13/22) -> (13/22,16/27) Hyperbolic Matrix(593,350,-2106,-1243) (-13/22,-23/39) -> (-11/39,-9/32) Hyperbolic Matrix(431,254,-918,-541) (-23/39,-10/17) -> (-8/17,-7/15) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(973,570,2214,1297) (-17/29,-24/41) -> (18/41,11/25) Hyperbolic Matrix(2051,1200,-5724,-3349) (-24/41,-31/53) -> (-19/53,-24/67) Hyperbolic Matrix(541,316,1296,757) (-31/53,-7/12) -> (5/12,23/55) Hyperbolic Matrix(539,314,1296,755) (-7/12,-32/55) -> (22/53,5/12) Hyperbolic Matrix(55,32,-648,-377) (-32/55,-25/43) -> (-1/11,0/1) Hyperbolic Matrix(757,440,1674,973) (-25/43,-18/31) -> (14/31,5/11) Hyperbolic Matrix(269,156,-1026,-595) (-18/31,-11/19) -> (-5/19,-6/23) Hyperbolic Matrix(325,188,-2052,-1187) (-11/19,-37/64) -> (-7/44,-3/19) Hyperbolic Matrix(917,530,1026,593) (-37/64,-26/45) -> (8/9,9/10) Hyperbolic Matrix(433,250,-2430,-1403) (-26/45,-15/26) -> (-5/28,-8/45) Hyperbolic Matrix(701,404,-1782,-1027) (-15/26,-19/33) -> (-13/33,-11/28) Hyperbolic Matrix(379,218,-1782,-1025) (-19/33,-4/7) -> (-10/47,-7/33) Hyperbolic Matrix(109,62,-378,-215) (-4/7,-13/23) -> (-9/31,-2/7) Hyperbolic Matrix(163,92,-1242,-701) (-13/23,-22/39) -> (-2/15,-3/23) Hyperbolic Matrix(1511,852,4212,2375) (-22/39,-31/55) -> (19/53,14/39) Hyperbolic Matrix(703,396,-2970,-1673) (-31/55,-9/16) -> (-9/38,-13/55) Hyperbolic Matrix(917,514,2214,1241) (-23/41,-14/25) -> (12/29,17/41) Hyperbolic Matrix(269,150,-486,-271) (-14/25,-5/9) -> (-5/9,-16/29) Parabolic Matrix(3349,1846,5292,2917) (-16/29,-27/49) -> (31/49,50/79) Hyperbolic Matrix(701,386,2646,1457) (-27/49,-11/20) -> (9/34,13/49) Hyperbolic Matrix(1079,592,2754,1511) (-28/51,-17/31) -> (9/23,20/51) Hyperbolic Matrix(701,384,1674,917) (-17/31,-6/11) -> (18/43,13/31) Hyperbolic Matrix(217,118,-594,-323) (-6/11,-7/13) -> (-15/41,-4/11) Hyperbolic Matrix(217,116,810,433) (-7/13,-8/15) -> (4/15,11/41) Hyperbolic Matrix(377,200,-918,-487) (-8/15,-1/2) -> (-23/56,-16/39) Hyperbolic Matrix(541,256,-2052,-971) (-9/19,-8/17) -> (-24/91,-5/19) Hyperbolic Matrix(593,276,810,377) (-7/15,-6/13) -> (30/41,11/15) Hyperbolic Matrix(539,248,702,323) (-6/13,-11/24) -> (23/30,10/13) Hyperbolic Matrix(973,440,1674,757) (-5/11,-14/31) -> (18/31,25/43) Hyperbolic Matrix(377,170,-1080,-487) (-14/31,-9/20) -> (-7/20,-8/23) Hyperbolic Matrix(215,96,-486,-217) (-9/20,-4/9) -> (-4/9,-15/34) Parabolic Matrix(2699,1190,3672,1619) (-15/34,-26/59) -> (36/49,25/34) Hyperbolic Matrix(1457,642,1836,809) (-26/59,-11/25) -> (23/29,4/5) Hyperbolic Matrix(269,118,-864,-379) (-11/25,-7/16) -> (-5/16,-9/29) Hyperbolic Matrix(325,142,-1728,-755) (-7/16,-24/55) -> (-10/53,-3/16) Hyperbolic Matrix(2701,1178,4212,1837) (-24/55,-17/39) -> (25/39,34/53) Hyperbolic Matrix(271,118,-2106,-917) (-27/62,-10/23) -> (-4/31,-1/8) Hyperbolic Matrix(1943,844,2484,1079) (-10/23,-23/53) -> (43/55,18/23) Hyperbolic Matrix(595,258,-2862,-1241) (-23/53,-13/30) -> (-5/24,-11/53) Hyperbolic Matrix(541,230,-2538,-1079) (-3/7,-17/40) -> (-3/14,-13/61) Hyperbolic Matrix(269,114,-1404,-595) (-14/33,-11/26) -> (-5/26,-4/21) Hyperbolic Matrix(757,320,-2808,-1187) (-11/26,-19/45) -> (-17/63,-7/26) Hyperbolic Matrix(109,46,1026,433) (-19/45,-27/64) -> (1/10,1/9) Hyperbolic Matrix(2485,1048,-6912,-2915) (-27/64,-8/19) -> (-32/89,-23/64) Hyperbolic Matrix(1243,522,1674,703) (-21/50,-34/81) -> (20/27,3/4) Hyperbolic Matrix(1997,838,2700,1133) (-34/81,-13/31) -> (17/23,20/27) Hyperbolic Matrix(917,384,1674,701) (-13/31,-18/43) -> (6/11,17/31) Hyperbolic Matrix(757,316,1296,541) (-23/55,-5/12) -> (7/12,31/53) Hyperbolic Matrix(755,314,1296,539) (-5/12,-22/53) -> (32/55,7/12) Hyperbolic Matrix(6103,2532,9504,3943) (-39/94,-56/135) -> (52/81,9/14) Hyperbolic Matrix(7937,3292,12366,5129) (-56/135,-17/41) -> (43/67,52/81) Hyperbolic Matrix(1081,448,1566,649) (-17/41,-12/29) -> (20/29,9/13) Hyperbolic Matrix(2483,1024,3402,1403) (-26/63,-7/17) -> (27/37,46/63) Hyperbolic Matrix(1027,422,-4860,-1997) (-7/17,-23/56) -> (-11/52,-15/71) Hyperbolic Matrix(161,66,-1188,-487) (-16/39,-9/22) -> (-3/22,-2/15) Hyperbolic Matrix(485,198,1188,485) (-9/22,-11/27) -> (11/27,9/22) Hyperbolic Matrix(109,44,270,109) (-11/27,-2/5) -> (2/5,11/27) Hyperbolic Matrix(1621,636,-5778,-2267) (-11/28,-20/51) -> (-16/57,-23/82) Hyperbolic Matrix(811,318,1242,487) (-20/51,-9/23) -> (15/23,2/3) Hyperbolic Matrix(595,232,972,379) (-9/23,-7/18) -> (11/18,19/31) Hyperbolic Matrix(593,230,972,377) (-7/18,-12/31) -> (14/23,11/18) Hyperbolic Matrix(487,188,702,271) (-12/31,-5/13) -> (9/13,16/23) Hyperbolic Matrix(1567,600,1836,703) (-18/47,-31/81) -> (23/27,6/7) Hyperbolic Matrix(2159,826,2538,971) (-31/81,-13/34) -> (17/20,23/27) Hyperbolic Matrix(2267,866,-10746,-4105) (-34/89,-55/144) -> (-19/90,-4/19) Hyperbolic Matrix(2807,1072,-11880,-4537) (-55/144,-21/55) -> (-13/55,-17/72) Hyperbolic Matrix(4643,1772,5940,2267) (-21/55,-29/76) -> (25/32,43/55) Hyperbolic Matrix(1243,474,-4104,-1565) (-29/76,-8/21) -> (-10/33,-23/76) Hyperbolic Matrix(863,328,1134,431) (-8/21,-19/50) -> (3/4,16/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(53,20,-432,-163) (-14/37,-3/8) -> (-1/8,-2/17) Hyperbolic Matrix(161,60,432,161) (-3/8,-10/27) -> (10/27,3/8) Hyperbolic Matrix(379,140,1026,379) (-10/27,-7/19) -> (7/19,10/27) Hyperbolic Matrix(2375,872,5292,1943) (-18/49,-29/79) -> (13/29,22/49) Hyperbolic Matrix(1243,456,-4266,-1565) (-29/79,-11/30) -> (-7/24,-23/79) Hyperbolic Matrix(1567,574,2214,811) (-11/30,-15/41) -> (29/41,17/24) Hyperbolic Matrix(431,156,594,215) (-4/11,-9/25) -> (21/29,8/11) Hyperbolic Matrix(919,330,-3456,-1241) (-23/64,-14/39) -> (-4/15,-17/64) Hyperbolic Matrix(2375,852,4212,1511) (-14/39,-19/53) -> (31/55,22/39) Hyperbolic Matrix(7237,2592,12366,4429) (-24/67,-29/81) -> (79/135,24/41) Hyperbolic Matrix(5561,1990,9504,3401) (-29/81,-5/14) -> (55/94,79/135) Hyperbolic Matrix(163,58,-756,-269) (-5/14,-6/17) -> (-8/37,-3/14) Hyperbolic Matrix(1891,666,2916,1027) (-6/17,-19/54) -> (35/54,24/37) Hyperbolic Matrix(1889,664,2916,1025) (-19/54,-13/37) -> (11/17,35/54) Hyperbolic Matrix(755,262,1242,431) (-8/23,-1/3) -> (31/51,14/23) Hyperbolic Matrix(271,86,-1188,-377) (-1/3,-6/19) -> (-8/35,-13/57) Hyperbolic Matrix(1999,630,2916,919) (-6/19,-17/54) -> (37/54,24/35) Hyperbolic Matrix(1997,628,2916,917) (-17/54,-11/35) -> (13/19,37/54) Hyperbolic Matrix(917,284,1566,485) (-9/29,-4/13) -> (24/41,17/29) Hyperbolic Matrix(431,132,702,215) (-4/13,-7/23) -> (19/31,8/13) Hyperbolic Matrix(8533,2592,10314,3133) (-24/79,-41/135) -> (67/81,24/29) Hyperbolic Matrix(9557,2902,11556,3509) (-41/135,-17/56) -> (43/52,67/81) Hyperbolic Matrix(2809,852,3564,1081) (-17/56,-10/33) -> (26/33,41/52) Hyperbolic Matrix(18307,5538,26244,7939) (-36/119,-49/162) -> (113/162,30/43) Hyperbolic Matrix(18305,5536,26244,7937) (-49/162,-13/43) -> (83/119,113/162) Hyperbolic Matrix(53,16,-540,-163) (-13/43,-3/10) -> (-1/10,-1/11) Hyperbolic Matrix(161,48,540,161) (-3/10,-8/27) -> (8/27,3/10) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(1403,410,2214,647) (-12/41,-7/24) -> (19/30,26/41) Hyperbolic Matrix(2755,802,-9828,-2861) (-23/79,-16/55) -> (-30/107,-7/25) Hyperbolic Matrix(757,220,3348,973) (-16/55,-9/31) -> (7/31,12/53) Hyperbolic Matrix(2377,668,3078,865) (-9/32,-16/57) -> (44/57,17/22) Hyperbolic Matrix(21059,5906,26568,7451) (-23/82,-53/189) -> (107/135,65/82) Hyperbolic Matrix(19387,5436,24462,6859) (-53/189,-30/107) -> (42/53,107/135) Hyperbolic Matrix(703,196,972,271) (-7/25,-5/18) -> (13/18,21/29) Hyperbolic Matrix(701,194,972,269) (-5/18,-8/29) -> (18/25,13/18) Hyperbolic Matrix(379,104,594,163) (-8/29,-3/11) -> (7/11,16/25) Hyperbolic Matrix(1999,540,3402,919) (-10/37,-17/63) -> (37/63,10/17) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) Hyperbolic Matrix(433,116,810,217) (-11/41,-4/15) -> (8/15,7/13) Hyperbolic Matrix(19279,5118,26244,6967) (-30/113,-43/162) -> (119/162,36/49) Hyperbolic Matrix(19277,5116,26244,6965) (-43/162,-13/49) -> (83/113,119/162) Hyperbolic Matrix(2053,544,3672,973) (-13/49,-9/34) -> (19/34,33/59) Hyperbolic Matrix(1621,428,-8586,-2267) (-14/53,-19/72) -> (-17/90,-10/53) Hyperbolic Matrix(8803,2322,10854,2863) (-19/72,-24/91) -> (30/37,73/90) Hyperbolic Matrix(1567,408,2700,703) (-6/23,-7/27) -> (47/81,18/31) Hyperbolic Matrix(971,250,1674,431) (-7/27,-1/4) -> (29/50,47/81) Hyperbolic Matrix(703,168,1134,271) (-1/4,-5/21) -> (13/21,31/50) Hyperbolic Matrix(5239,1236,6642,1567) (-17/72,-4/17) -> (56/71,71/90) Hyperbolic Matrix(379,88,702,163) (-7/30,-3/13) -> (7/13,13/24) Hyperbolic Matrix(593,136,702,161) (-3/13,-8/35) -> (16/19,11/13) Hyperbolic Matrix(2213,504,3078,701) (-13/57,-5/22) -> (23/32,41/57) Hyperbolic Matrix(107,24,-486,-109) (-5/22,-2/9) -> (-2/9,-7/32) Parabolic Matrix(3673,802,5940,1297) (-7/32,-12/55) -> (34/55,47/76) Hyperbolic Matrix(1405,306,2484,541) (-12/55,-5/23) -> (13/23,30/53) Hyperbolic Matrix(1025,222,1242,269) (-5/23,-8/37) -> (14/17,19/23) Hyperbolic Matrix(9181,1956,11664,2485) (-13/61,-23/108) -> (85/108,37/47) Hyperbolic Matrix(9179,1954,11664,2483) (-23/108,-10/47) -> (48/61,85/108) Hyperbolic Matrix(2483,526,3564,755) (-7/33,-11/52) -> (39/56,23/33) Hyperbolic Matrix(5075,1072,6642,1403) (-15/71,-19/90) -> (55/72,13/17) Hyperbolic Matrix(17603,3652,24462,5075) (-11/53,-28/135) -> (136/189,77/107) Hyperbolic Matrix(19117,3964,26568,5509) (-28/135,-17/82) -> (59/82,136/189) Hyperbolic Matrix(1027,212,1836,379) (-6/29,-1/5) -> (33/59,14/25) Hyperbolic Matrix(7991,1510,10854,2051) (-7/37,-17/90) -> (53/72,67/91) Hyperbolic Matrix(161,30,864,161) (-3/16,-5/27) -> (5/27,3/16) Hyperbolic Matrix(109,20,594,109) (-5/27,-2/11) -> (2/11,5/27) Hyperbolic Matrix(811,144,918,163) (-8/45,-3/17) -> (15/17,8/9) Hyperbolic Matrix(973,170,1242,217) (-3/17,-4/23) -> (18/23,29/37) Hyperbolic Matrix(8047,1392,11556,1999) (-9/52,-14/81) -> (94/135,39/56) Hyperbolic Matrix(7181,1240,10314,1781) (-14/81,-5/29) -> (55/79,94/135) Hyperbolic Matrix(271,46,324,55) (-5/29,-1/6) -> (5/6,21/25) Hyperbolic Matrix(269,44,324,53) (-1/6,-4/25) -> (24/29,5/6) Hyperbolic Matrix(541,84,702,109) (-3/19,-2/13) -> (10/13,27/35) Hyperbolic Matrix(1567,234,2538,379) (-3/20,-4/27) -> (50/81,21/34) Hyperbolic Matrix(1133,166,1836,269) (-4/27,-1/7) -> (29/47,50/81) Hyperbolic Matrix(2539,330,2916,379) (-3/23,-7/54) -> (47/54,27/31) Hyperbolic Matrix(2537,328,2916,377) (-7/54,-4/31) -> (20/23,47/54) Hyperbolic Matrix(755,88,918,107) (-2/17,-1/9) -> (37/45,14/17) Hyperbolic Matrix(433,46,1026,109) (-1/9,-1/10) -> (27/64,19/45) Hyperbolic Matrix(377,-32,648,-55) (0/1,1/10) -> (57/98,32/55) Hyperbolic Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(701,-92,1242,-163) (1/8,2/15) -> (22/39,35/62) Hyperbolic Matrix(271,-38,378,-53) (2/15,1/7) -> (5/7,28/39) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(1729,-300,2484,-431) (5/29,4/23) -> (16/23,55/79) Hyperbolic Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(865,-164,1134,-215) (3/16,4/21) -> (16/21,29/38) Hyperbolic Matrix(163,-32,270,-53) (4/21,1/5) -> (3/5,20/33) Hyperbolic Matrix(649,-136,1026,-215) (1/5,4/19) -> (12/19,31/49) Hyperbolic Matrix(539,-114,1026,-217) (4/19,11/52) -> (1/2,10/19) Hyperbolic Matrix(1025,-218,1782,-379) (7/33,3/14) -> (23/40,19/33) Hyperbolic Matrix(269,-58,756,-163) (3/14,5/23) -> (11/31,5/14) Hyperbolic Matrix(109,-24,486,-107) (5/23,2/9) -> (2/9,7/31) Parabolic Matrix(377,-86,1188,-271) (5/22,8/35) -> (6/19,7/22) Hyperbolic Matrix(649,-152,918,-215) (3/13,4/17) -> (12/17,29/41) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(2269,-600,3672,-971) (5/19,9/34) -> (21/34,55/89) Hyperbolic Matrix(1241,-330,3456,-919) (13/49,4/15) -> (14/39,37/103) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(703,-206,918,-269) (7/24,5/17) -> (13/17,23/30) Hyperbolic Matrix(2701,-816,4644,-1403) (3/10,13/43) -> (25/43,57/98) Hyperbolic Matrix(1565,-474,4104,-1243) (13/43,10/33) -> (8/21,37/97) Hyperbolic Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(379,-118,864,-269) (4/13,5/16) -> (7/16,18/41) Hyperbolic Matrix(593,-186,864,-271) (5/16,6/19) -> (24/35,11/16) Hyperbolic Matrix(487,-170,1080,-377) (1/3,7/20) -> (9/20,23/51) Hyperbolic Matrix(701,-246,1080,-379) (7/20,6/17) -> (24/37,13/20) Hyperbolic Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(10153,-3648,13824,-4967) (37/103,23/64) -> (47/64,83/113) Hyperbolic Matrix(2269,-816,2700,-971) (23/64,9/25) -> (21/25,37/44) Hyperbolic Matrix(323,-118,594,-217) (4/11,11/30) -> (13/24,6/11) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(11449,-4368,16416,-6263) (37/97,29/76) -> (53/76,83/119) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(1513,-620,2106,-863) (9/22,16/39) -> (28/39,23/32) Hyperbolic Matrix(487,-200,918,-377) (16/39,7/17) -> (9/17,8/15) Hyperbolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(3673,-1524,5724,-2375) (17/41,22/53) -> (34/53,43/67) Hyperbolic Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1727,-728,2052,-865) (8/19,27/64) -> (37/44,16/19) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(1081,-458,1782,-755) (11/26,14/33) -> (20/33,17/28) Hyperbolic Matrix(1403,-596,1782,-757) (14/33,3/7) -> (37/47,26/33) Hyperbolic Matrix(269,-116,378,-163) (3/7,10/23) -> (22/31,5/7) Hyperbolic Matrix(1079,-470,1242,-541) (10/23,17/39) -> (13/15,20/23) Hyperbolic Matrix(2267,-990,2970,-1297) (24/55,7/16) -> (29/38,42/55) Hyperbolic Matrix(217,-96,486,-215) (11/25,4/9) -> (4/9,13/29) Parabolic Matrix(377,-172,594,-271) (5/11,6/13) -> (26/41,7/11) Hyperbolic Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(1511,-796,2052,-1081) (10/19,9/17) -> (67/91,14/19) Hyperbolic Matrix(703,-386,1080,-593) (17/31,11/20) -> (13/20,15/23) Hyperbolic Matrix(271,-150,486,-269) (11/20,5/9) -> (5/9,19/34) Parabolic Matrix(595,-334,864,-485) (14/25,9/16) -> (11/16,20/29) Hyperbolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1835,-1036,2106,-1189) (35/62,13/23) -> (27/31,7/8) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1997,-1148,2538,-1459) (4/7,23/40) -> (11/14,48/61) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(4157,-2526,5778,-3511) (17/28,31/51) -> (41/57,59/82) Hyperbolic Matrix(8479,-5240,10746,-6641) (55/89,89/144) -> (71/90,15/19) Hyperbolic Matrix(9073,-5608,11880,-7343) (89/144,34/55) -> (42/55,55/72) Hyperbolic Matrix(2861,-1770,4104,-2539) (47/76,13/21) -> (23/33,53/76) Hyperbolic Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(3023,-1914,4266,-2701) (50/79,19/30) -> (17/24,56/79) Hyperbolic Matrix(2537,-1626,3456,-2215) (41/64,25/39) -> (11/15,47/64) Hyperbolic Matrix(593,-382,756,-487) (9/14,11/17) -> (29/37,11/14) Hyperbolic Matrix(917,-626,1188,-811) (2/3,13/19) -> (27/35,44/57) Hyperbolic Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(7073,-5014,9828,-6967) (56/79,39/55) -> (77/107,18/25) Hyperbolic Matrix(6965,-5126,8586,-6319) (39/53,53/72) -> (73/90,43/53) Hyperbolic Matrix(379,-294,486,-377) (17/22,7/9) -> (7/9,25/32) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-52,1) Matrix(271,248,-648,-593) -> Matrix(23,10,-352,-153) Matrix(593,530,1026,917) -> Matrix(17,6,-700,-247) Matrix(379,334,-918,-809) -> Matrix(45,14,-704,-219) Matrix(541,470,-1242,-1079) -> Matrix(57,16,-880,-247) Matrix(107,92,-378,-325) -> Matrix(15,4,-304,-81) Matrix(269,228,-702,-595) -> Matrix(25,6,-396,-95) Matrix(161,136,702,593) -> Matrix(25,6,-796,-191) Matrix(971,816,-2700,-2269) -> Matrix(103,24,-1824,-425) Matrix(55,46,324,271) -> Matrix(9,2,-248,-55) Matrix(53,44,324,269) -> Matrix(9,2,-284,-63) Matrix(755,624,-2484,-2053) -> Matrix(19,4,-328,-69) Matrix(325,268,918,757) -> Matrix(19,4,-632,-133) Matrix(161,132,-594,-487) -> Matrix(29,6,-556,-115) Matrix(485,396,594,485) -> Matrix(89,18,-4188,-847) Matrix(703,572,864,703) -> Matrix(131,26,-6152,-1221) Matrix(269,218,-1134,-919) -> Matrix(31,6,-584,-113) Matrix(107,86,-270,-217) -> Matrix(21,4,-352,-67) Matrix(377,298,-1026,-811) -> Matrix(79,14,-1360,-241) Matrix(487,384,-1026,-809) -> Matrix(35,6,-496,-85) Matrix(1081,852,3564,2809) -> Matrix(1,0,-28,1) Matrix(757,596,-1782,-1403) -> Matrix(23,4,-328,-57) Matrix(487,382,-756,-593) -> Matrix(11,2,-116,-21) Matrix(377,294,-486,-379) -> Matrix(83,14,-504,-85) Matrix(2375,1838,3348,2591) -> Matrix(417,68,-18440,-3007) Matrix(1999,1546,5238,4051) -> Matrix(357,58,-12772,-2075) Matrix(811,626,-1188,-917) -> Matrix(87,14,-752,-121) Matrix(109,84,702,541) -> Matrix(25,4,-744,-119) Matrix(269,206,-918,-703) -> Matrix(63,10,-1216,-193) Matrix(215,164,-1134,-865) -> Matrix(25,4,-544,-87) Matrix(431,328,1134,863) -> Matrix(77,12,-2740,-427) Matrix(431,318,-1026,-757) -> Matrix(57,8,-848,-119) Matrix(1403,1032,-3672,-2701) -> Matrix(259,36,-4180,-581) Matrix(1189,874,2646,1945) -> Matrix(231,32,-8612,-1193) Matrix(2215,1626,-3456,-2537) -> Matrix(15,2,-128,-17) Matrix(377,276,810,593) -> Matrix(15,2,-548,-73) Matrix(755,552,-2808,-2053) -> Matrix(1,0,-12,1) Matrix(107,78,-594,-433) -> Matrix(29,4,-660,-91) Matrix(215,156,594,431) -> Matrix(29,4,-1008,-139) Matrix(271,196,972,703) -> Matrix(15,2,-428,-57) Matrix(269,194,972,701) -> Matrix(15,2,-548,-73) Matrix(3511,2526,-5778,-4157) -> Matrix(169,22,-1836,-239) Matrix(431,310,1350,971) -> Matrix(31,4,-1000,-129) Matrix(53,38,-378,-271) -> Matrix(15,2,-368,-49) Matrix(163,116,-378,-269) -> Matrix(15,2,-248,-33) Matrix(215,152,-918,-649) -> Matrix(63,8,-1268,-161) Matrix(647,456,918,647) -> Matrix(191,24,-8412,-1057) Matrix(379,266,540,379) -> Matrix(113,14,-4964,-615) Matrix(1943,1356,-4644,-3241) -> Matrix(395,48,-6032,-733) Matrix(2539,1770,-4104,-2861) -> Matrix(149,18,-1548,-187) Matrix(755,526,3564,2483) -> Matrix(33,4,-1048,-127) Matrix(431,300,-2484,-1729) -> Matrix(67,8,-1516,-181) Matrix(271,188,702,487) -> Matrix(17,2,-604,-71) Matrix(485,334,-864,-595) -> Matrix(49,6,-580,-71) Matrix(271,186,-864,-593) -> Matrix(17,2,-264,-31) Matrix(379,258,1350,919) -> Matrix(17,2,-536,-63) Matrix(593,386,-1080,-703) -> Matrix(93,10,-1144,-123) Matrix(379,246,-1080,-701) -> Matrix(19,2,-276,-29) Matrix(161,104,918,593) -> Matrix(19,2,-580,-61) Matrix(2375,1524,-5724,-3673) -> Matrix(75,8,-1172,-125) Matrix(1837,1178,4212,2701) -> Matrix(37,4,-1360,-147) Matrix(3671,2352,-13824,-8857) -> Matrix(229,24,-4456,-467) Matrix(431,276,-2700,-1729) -> Matrix(39,4,-868,-89) Matrix(163,104,594,379) -> Matrix(19,2,-656,-69) Matrix(271,172,-594,-377) -> Matrix(59,6,-836,-85) Matrix(215,136,-1026,-649) -> Matrix(79,8,-1748,-177) Matrix(647,408,1026,647) -> Matrix(239,24,-10048,-1009) Matrix(271,170,432,271) -> Matrix(101,10,-4232,-419) Matrix(647,402,-1566,-973) -> Matrix(125,12,-1948,-187) Matrix(2051,1272,-5400,-3349) -> Matrix(253,24,-4164,-395) Matrix(271,168,1134,703) -> Matrix(21,2,-704,-67) Matrix(4967,3072,-16416,-10153) -> Matrix(337,32,-6224,-591) Matrix(1187,734,5238,3239) -> Matrix(43,4,-1344,-125) Matrix(971,600,-3672,-2269) -> Matrix(43,4,-828,-77) Matrix(107,66,-702,-433) -> Matrix(1,0,-12,1) Matrix(215,132,702,431) -> Matrix(41,4,-1384,-135) Matrix(379,232,972,595) -> Matrix(21,2,-704,-67) Matrix(377,230,972,593) -> Matrix(21,2,-788,-75) Matrix(1243,756,2754,1675) -> Matrix(65,6,-2416,-223) Matrix(1511,918,-7290,-4429) -> Matrix(131,12,-3024,-277) Matrix(53,32,-270,-163) -> Matrix(21,2,-452,-43) Matrix(161,96,270,161) -> Matrix(65,6,-2676,-247) Matrix(703,416,1188,703) -> Matrix(287,26,-11756,-1065) Matrix(593,350,-2106,-1243) -> Matrix(111,10,-2320,-209) Matrix(431,254,-918,-541) -> Matrix(89,8,-1324,-119) Matrix(593,348,-1566,-919) -> Matrix(67,6,-1128,-101) Matrix(973,570,2214,1297) -> Matrix(271,24,-9948,-881) Matrix(2051,1200,-5724,-3349) -> Matrix(499,44,-8948,-789) Matrix(541,316,1296,757) -> Matrix(137,12,-5012,-439) Matrix(539,314,1296,755) -> Matrix(47,4,-1704,-145) Matrix(55,32,-648,-377) -> Matrix(23,2,-564,-49) Matrix(757,440,1674,973) -> Matrix(93,8,-3476,-299) Matrix(269,156,-1026,-595) -> Matrix(25,2,-488,-39) Matrix(325,188,-2052,-1187) -> Matrix(1,0,-12,1) Matrix(917,530,1026,593) -> Matrix(65,6,-3196,-295) Matrix(433,250,-2430,-1403) -> Matrix(45,4,-1024,-91) Matrix(701,404,-1782,-1027) -> Matrix(23,2,-380,-33) Matrix(379,218,-1782,-1025) -> Matrix(23,2,-472,-41) Matrix(109,62,-378,-215) -> Matrix(1,0,-8,1) Matrix(163,92,-1242,-701) -> Matrix(23,2,-656,-57) Matrix(1511,852,4212,2375) -> Matrix(371,32,-12672,-1093) Matrix(703,396,-2970,-1673) -> Matrix(163,14,-3132,-269) Matrix(917,514,2214,1241) -> Matrix(71,6,-2568,-217) Matrix(269,150,-486,-271) -> Matrix(119,10,-1440,-121) Matrix(3349,1846,5292,2917) -> Matrix(831,68,-35012,-2865) Matrix(701,386,2646,1457) -> Matrix(25,2,-788,-63) Matrix(1079,592,2754,1511) -> Matrix(49,4,-1752,-143) Matrix(701,384,1674,917) -> Matrix(173,14,-6364,-515) Matrix(217,118,-594,-323) -> Matrix(51,4,-880,-69) Matrix(217,116,810,433) -> Matrix(1,0,-20,1) Matrix(377,200,-918,-487) -> Matrix(73,6,-1156,-95) Matrix(541,256,-2052,-971) -> Matrix(173,12,-3388,-235) Matrix(593,276,810,377) -> Matrix(31,2,-1380,-89) Matrix(539,248,702,323) -> Matrix(57,4,-2608,-183) Matrix(973,440,1674,757) -> Matrix(117,8,-4724,-323) Matrix(377,170,-1080,-487) -> Matrix(29,2,-508,-35) Matrix(215,96,-486,-217) -> Matrix(119,8,-1800,-121) Matrix(2699,1190,3672,1619) -> Matrix(609,40,-27268,-1791) Matrix(1457,642,1836,809) -> Matrix(153,10,-7084,-463) Matrix(269,118,-864,-379) -> Matrix(31,2,-512,-33) Matrix(325,142,-1728,-755) -> Matrix(123,8,-2660,-173) Matrix(2701,1178,4212,1837) -> Matrix(61,4,-2608,-171) Matrix(271,118,-2106,-917) -> Matrix(31,2,-512,-33) Matrix(1943,844,2484,1079) -> Matrix(499,32,-23032,-1477) Matrix(595,258,-2862,-1241) -> Matrix(157,10,-3564,-227) Matrix(541,230,-2538,-1079) -> Matrix(1,0,-8,1) Matrix(269,114,-1404,-595) -> Matrix(29,2,-624,-43) Matrix(757,320,-2808,-1187) -> Matrix(1,0,-4,1) Matrix(109,46,1026,433) -> Matrix(1,0,-12,1) Matrix(2485,1048,-6912,-2915) -> Matrix(57,4,-1012,-71) Matrix(1243,522,1674,703) -> Matrix(209,14,-9420,-631) Matrix(1997,838,2700,1133) -> Matrix(391,26,-17580,-1169) Matrix(917,384,1674,701) -> Matrix(213,14,-8444,-555) Matrix(757,316,1296,541) -> Matrix(185,12,-7508,-487) Matrix(755,314,1296,539) -> Matrix(63,4,-2536,-161) Matrix(6103,2532,9504,3943) -> Matrix(31,2,-1380,-89) Matrix(7937,3292,12366,5129) -> Matrix(157,10,-6704,-427) Matrix(1081,448,1566,649) -> Matrix(1,0,-28,1) Matrix(2483,1024,3402,1403) -> Matrix(251,16,-11248,-717) Matrix(1027,422,-4860,-1997) -> Matrix(221,14,-4720,-299) Matrix(161,66,-1188,-487) -> Matrix(95,6,-2296,-145) Matrix(485,198,1188,485) -> Matrix(287,18,-10348,-649) Matrix(109,44,270,109) -> Matrix(65,4,-2324,-143) Matrix(1621,636,-5778,-2267) -> Matrix(1,0,-4,1) Matrix(811,318,1242,487) -> Matrix(35,2,-1488,-85) Matrix(595,232,972,379) -> Matrix(37,2,-1536,-83) Matrix(593,230,972,377) -> Matrix(29,2,-1204,-83) Matrix(487,188,702,271) -> Matrix(33,2,-1436,-87) Matrix(1567,600,1836,703) -> Matrix(287,18,-13792,-865) Matrix(2159,826,2538,971) -> Matrix(449,28,-21536,-1343) Matrix(2267,866,-10746,-4105) -> Matrix(517,32,-11164,-691) Matrix(2807,1072,-11880,-4537) -> Matrix(647,40,-12568,-777) Matrix(4643,1772,5940,2267) -> Matrix(1103,68,-50884,-3137) Matrix(1243,474,-4104,-1565) -> Matrix(293,18,-5388,-331) Matrix(863,328,1134,431) -> Matrix(197,12,-8980,-547) Matrix(7237,2748,11664,4429) -> Matrix(989,60,-41060,-2491) Matrix(7235,2746,11664,4427) -> Matrix(859,52,-35632,-2157) Matrix(53,20,-432,-163) -> Matrix(33,2,-776,-47) Matrix(161,60,432,161) -> Matrix(101,6,-3552,-211) Matrix(379,140,1026,379) -> Matrix(239,14,-8348,-489) Matrix(2375,872,5292,1943) -> Matrix(1,0,-20,1) Matrix(1243,456,-4266,-1565) -> Matrix(35,2,-648,-37) Matrix(1567,574,2214,811) -> Matrix(381,22,-16816,-971) Matrix(431,156,594,215) -> Matrix(69,4,-3088,-179) Matrix(919,330,-3456,-1241) -> Matrix(249,14,-4820,-271) Matrix(2375,852,4212,1511) -> Matrix(571,32,-23072,-1293) Matrix(7237,2592,12366,4429) -> Matrix(1581,88,-64300,-3579) Matrix(5561,1990,9504,3401) -> Matrix(1119,62,-45500,-2521) Matrix(163,58,-756,-269) -> Matrix(37,2,-796,-43) Matrix(1891,666,2916,1027) -> Matrix(51,2,-2168,-85) Matrix(1889,664,2916,1025) -> Matrix(19,2,-808,-85) Matrix(755,262,1242,431) -> Matrix(67,4,-2764,-165) Matrix(271,86,-1188,-377) -> Matrix(39,2,-800,-41) Matrix(1999,630,2916,919) -> Matrix(57,2,-2480,-87) Matrix(1997,628,2916,917) -> Matrix(17,2,-740,-87) Matrix(917,284,1566,485) -> Matrix(177,10,-7204,-407) Matrix(431,132,702,215) -> Matrix(73,4,-3048,-167) Matrix(8533,2592,10314,3133) -> Matrix(573,32,-27128,-1515) Matrix(9557,2902,11556,3509) -> Matrix(831,46,-39328,-2177) Matrix(2809,852,3564,1081) -> Matrix(1,0,-28,1) Matrix(18307,5538,26244,7939) -> Matrix(3365,182,-147228,-7963) Matrix(18305,5536,26244,7937) -> Matrix(3147,170,-137672,-7437) Matrix(53,16,-540,-163) -> Matrix(37,2,-944,-51) Matrix(161,48,540,161) -> Matrix(113,6,-3748,-199) Matrix(271,80,918,271) -> Matrix(191,10,-6284,-329) Matrix(1403,410,2214,647) -> Matrix(309,16,-13036,-675) Matrix(2755,802,-9828,-2861) -> Matrix(39,2,-800,-41) Matrix(757,220,3348,973) -> Matrix(1,0,-12,1) Matrix(2377,668,3078,865) -> Matrix(89,4,-4072,-183) Matrix(21059,5906,26568,7451) -> Matrix(87,4,-4024,-185) Matrix(19387,5436,24462,6859) -> Matrix(43,2,-2000,-93) Matrix(703,196,972,271) -> Matrix(47,2,-2092,-89) Matrix(701,194,972,269) -> Matrix(31,2,-1380,-89) Matrix(379,104,594,163) -> Matrix(35,2,-1488,-85) Matrix(1999,540,3402,919) -> Matrix(115,6,-4696,-245) Matrix(8533,2292,11664,3133) -> Matrix(233,12,-10388,-535) Matrix(8531,2290,11664,3131) -> Matrix(79,4,-3496,-177) Matrix(433,116,810,217) -> Matrix(1,0,-20,1) Matrix(19279,5118,26244,6967) -> Matrix(2611,134,-116852,-5997) Matrix(19277,5116,26244,6965) -> Matrix(2381,122,-106540,-5459) Matrix(2053,544,3672,973) -> Matrix(159,8,-6380,-321) Matrix(1621,428,-8586,-2267) -> Matrix(155,8,-3352,-173) Matrix(8803,2322,10854,2863) -> Matrix(1681,86,-78792,-4031) Matrix(1567,408,2700,703) -> Matrix(199,10,-7980,-401) Matrix(971,250,1674,431) -> Matrix(81,4,-3220,-159) Matrix(703,168,1134,271) -> Matrix(37,2,-1536,-83) Matrix(5239,1236,6642,1567) -> Matrix(431,22,-19924,-1017) Matrix(379,88,702,163) -> Matrix(41,2,-1620,-79) Matrix(593,136,702,161) -> Matrix(121,6,-5788,-287) Matrix(2213,504,3078,701) -> Matrix(39,2,-1736,-89) Matrix(107,24,-486,-109) -> Matrix(83,4,-1764,-85) Matrix(3673,802,5940,1297) -> Matrix(1,0,-20,1) Matrix(1405,306,2484,541) -> Matrix(85,4,-3464,-163) Matrix(1025,222,1242,269) -> Matrix(41,2,-1948,-95) Matrix(9181,1956,11664,2485) -> Matrix(103,4,-4764,-185) Matrix(9179,1954,11664,2483) -> Matrix(71,4,-3284,-185) Matrix(2483,526,3564,755) -> Matrix(81,4,-3544,-175) Matrix(5075,1072,6642,1403) -> Matrix(343,16,-15628,-729) Matrix(17603,3652,24462,5075) -> Matrix(1837,80,-81448,-3547) Matrix(19117,3964,26568,5509) -> Matrix(1751,76,-77620,-3369) Matrix(1027,212,1836,379) -> Matrix(143,6,-5744,-241) Matrix(7991,1510,10854,2051) -> Matrix(1201,56,-53852,-2511) Matrix(161,30,864,161) -> Matrix(131,6,-3952,-181) Matrix(109,20,594,109) -> Matrix(89,4,-2648,-119) Matrix(811,144,918,163) -> Matrix(139,6,-6788,-293) Matrix(973,170,1242,217) -> Matrix(87,4,-4024,-185) Matrix(8047,1392,11556,1999) -> Matrix(1055,46,-46076,-2009) Matrix(7181,1240,10314,1781) -> Matrix(877,38,-38288,-1659) Matrix(271,46,324,55) -> Matrix(49,2,-2328,-95) Matrix(269,44,324,53) -> Matrix(41,2,-1948,-95) Matrix(541,84,702,109) -> Matrix(89,4,-4072,-183) Matrix(1567,234,2538,379) -> Matrix(137,6,-5640,-247) Matrix(1133,166,1836,269) -> Matrix(47,2,-1904,-81) Matrix(2539,330,2916,379) -> Matrix(87,2,-4220,-97) Matrix(2537,328,2916,377) -> Matrix(7,2,-340,-97) Matrix(755,88,918,107) -> Matrix(91,4,-4300,-189) Matrix(433,46,1026,109) -> Matrix(1,0,-12,1) Matrix(377,-32,648,-55) -> Matrix(55,2,-2228,-81) Matrix(539,-64,918,-109) -> Matrix(117,4,-4768,-163) Matrix(701,-92,1242,-163) -> Matrix(47,2,-1904,-81) Matrix(271,-38,378,-53) -> Matrix(55,2,-2448,-89) Matrix(433,-66,702,-107) -> Matrix(1,0,-12,1) Matrix(1729,-276,2700,-431) -> Matrix(119,4,-5028,-169) Matrix(1729,-300,2484,-431) -> Matrix(235,8,-10252,-349) Matrix(433,-78,594,-107) -> Matrix(117,4,-5236,-179) Matrix(865,-164,1134,-215) -> Matrix(121,4,-5536,-183) Matrix(163,-32,270,-53) -> Matrix(61,2,-2532,-83) Matrix(649,-136,1026,-215) -> Matrix(239,8,-10068,-337) Matrix(539,-114,1026,-217) -> Matrix(123,4,-4828,-157) Matrix(1025,-218,1782,-379) -> Matrix(63,2,-2552,-81) Matrix(269,-58,756,-163) -> Matrix(61,2,-2044,-67) Matrix(109,-24,486,-107) -> Matrix(123,4,-3844,-125) Matrix(377,-86,1188,-271) -> Matrix(63,2,-2048,-65) Matrix(649,-152,918,-215) -> Matrix(255,8,-11252,-353) Matrix(919,-218,1134,-269) -> Matrix(199,6,-9320,-281) Matrix(595,-156,1026,-269) -> Matrix(65,2,-2568,-79) Matrix(2269,-600,3672,-971) -> Matrix(131,4,-5404,-165) Matrix(1241,-330,3456,-919) -> Matrix(457,14,-15636,-479) Matrix(2053,-552,2808,-755) -> Matrix(1,0,-12,1) Matrix(487,-132,594,-161) -> Matrix(197,6,-9292,-283) Matrix(2267,-636,5778,-1621) -> Matrix(1,0,-4,1) Matrix(325,-92,378,-107) -> Matrix(127,4,-6128,-193) Matrix(215,-62,378,-109) -> Matrix(1,0,-8,1) Matrix(703,-206,918,-269) -> Matrix(327,10,-14944,-457) Matrix(2701,-816,4644,-1403) -> Matrix(133,4,-5420,-163) Matrix(1565,-474,4104,-1243) -> Matrix(605,18,-21612,-643) Matrix(2053,-624,2484,-755) -> Matrix(139,4,-6568,-189) Matrix(379,-118,864,-269) -> Matrix(71,2,-2592,-73) Matrix(593,-186,864,-271) -> Matrix(73,2,-3176,-87) Matrix(487,-170,1080,-377) -> Matrix(69,2,-2588,-75) Matrix(701,-246,1080,-379) -> Matrix(75,2,-3188,-85) Matrix(3349,-1200,5724,-2051) -> Matrix(1499,44,-60948,-1789) Matrix(10153,-3648,13824,-4967) -> Matrix(2467,72,-110364,-3221) Matrix(2269,-816,2700,-971) -> Matrix(823,24,-39264,-1145) Matrix(323,-118,594,-217) -> Matrix(139,4,-5456,-157) Matrix(811,-298,1026,-377) -> Matrix(487,14,-22576,-649) Matrix(919,-348,1566,-593) -> Matrix(211,6,-8616,-245) Matrix(3349,-1272,5400,-2051) -> Matrix(853,24,-35364,-995) Matrix(11449,-4368,16416,-6263) -> Matrix(4577,128,-200208,-5599) Matrix(2701,-1032,3672,-1403) -> Matrix(1291,36,-57844,-1613) Matrix(595,-228,702,-269) -> Matrix(217,6,-10380,-287) Matrix(5779,-2268,7290,-2861) -> Matrix(67,2,-3116,-93) Matrix(217,-86,270,-107) -> Matrix(141,4,-6592,-187) Matrix(1513,-620,2106,-863) -> Matrix(145,4,-6344,-175) Matrix(487,-200,918,-377) -> Matrix(217,6,-8644,-239) Matrix(973,-402,1566,-647) -> Matrix(437,12,-18172,-499) Matrix(3673,-1524,5724,-2375) -> Matrix(291,8,-12404,-341) Matrix(593,-248,648,-271) -> Matrix(367,10,-18240,-497) Matrix(757,-318,1026,-431) -> Matrix(297,8,-13328,-359) Matrix(1727,-728,2052,-865) -> Matrix(145,4,-6924,-191) Matrix(1997,-844,2430,-1027) -> Matrix(221,6,-10424,-283) Matrix(1081,-458,1782,-755) -> Matrix(1,0,-4,1) Matrix(1403,-596,1782,-757) -> Matrix(151,4,-6984,-185) Matrix(269,-116,378,-163) -> Matrix(71,2,-3160,-89) Matrix(1079,-470,1242,-541) -> Matrix(585,16,-28336,-775) Matrix(2267,-990,2970,-1297) -> Matrix(147,4,-6652,-181) Matrix(217,-96,486,-215) -> Matrix(295,8,-10952,-297) Matrix(377,-172,594,-271) -> Matrix(227,6,-9572,-253) Matrix(541,-254,918,-431) -> Matrix(297,8,-12140,-327) Matrix(1511,-796,2052,-1081) -> Matrix(1261,32,-56548,-1435) Matrix(703,-386,1080,-593) -> Matrix(397,10,-16952,-427) Matrix(271,-150,486,-269) -> Matrix(399,10,-16000,-401) Matrix(595,-334,864,-485) -> Matrix(241,6,-10564,-263) Matrix(1403,-790,1728,-973) -> Matrix(1291,32,-60556,-1501) Matrix(1835,-1036,2106,-1189) -> Matrix(1295,32,-62848,-1553) Matrix(2267,-1284,2862,-1621) -> Matrix(325,8,-15072,-371) Matrix(1997,-1148,2538,-1459) -> Matrix(569,14,-26296,-647) Matrix(1135,-654,1404,-809) -> Matrix(83,2,-3860,-93) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,-4,1) Matrix(4427,-2560,6912,-3997) -> Matrix(167,4,-7056,-169) Matrix(3833,-2258,4860,-2863) -> Matrix(1389,34,-64180,-1571) Matrix(1027,-606,1188,-701) -> Matrix(1063,26,-51392,-1257) Matrix(4157,-2526,5778,-3511) -> Matrix(905,22,-40108,-975) Matrix(8479,-5240,10746,-6641) -> Matrix(1077,26,-49832,-1203) Matrix(9073,-5608,11880,-7343) -> Matrix(1,0,-4,1) Matrix(2861,-1770,4104,-2539) -> Matrix(749,18,-32748,-787) Matrix(379,-236,432,-269) -> Matrix(417,10,-20308,-487) Matrix(3023,-1914,4266,-2701) -> Matrix(3035,72,-134088,-3181) Matrix(2537,-1626,3456,-2215) -> Matrix(87,2,-3872,-89) Matrix(593,-382,756,-487) -> Matrix(83,2,-3860,-93) Matrix(917,-626,1188,-811) -> Matrix(607,14,-27792,-641) Matrix(487,-340,540,-377) -> Matrix(613,14,-30256,-691) Matrix(7073,-5014,9828,-6967) -> Matrix(5215,118,-231272,-5233) Matrix(6965,-5126,8586,-6319) -> Matrix(8517,190,-399268,-8907) Matrix(379,-294,486,-377) -> Matrix(643,14,-29624,-645) 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): 81 Degree of the the map X: 162 Degree of the the map Y: 324 ----------------------------------------------------------------------- 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): 972 Minimal number of generators: 163 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: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/9 -7/9 -2/3 -5/9 -4/9 -5/12 -41/108 -1/3 -29/108 -2/9 -1/6 -4/27 0/1 1/10 1/9 1/8 1/7 2/13 3/19 1/6 3/17 2/11 5/27 1/5 5/23 2/9 3/13 5/21 1/4 3/11 7/25 2/7 8/27 1/3 10/27 2/5 11/27 5/12 19/45 4/9 7/15 1/2 5/9 47/81 79/135 16/27 13/21 17/27 2/3 19/27 11/15 20/27 7/9 107/135 22/27 67/81 23/27 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -3/8 -7/19 -8/9 -1/3 -7/8 -3/10 -5/17 -6/7 -6/23 -1/4 -5/6 -2/9 -14/17 -4/19 -5/24 -9/11 -9/44 -22/27 -1/5 -13/16 -1/5 -13/66 -17/21 -5/26 -4/5 -3/16 -2/11 -15/19 -7/40 -11/14 -3/17 -1/6 -7/9 -1/6 -10/13 -1/6 -4/25 -13/17 -5/32 -3/4 -3/20 -1/7 -14/19 -8/57 -7/50 -11/15 -3/22 -30/41 -3/22 -2/15 -19/26 -1/7 -3/22 -8/11 -3/22 -2/15 -5/7 -1/8 -7/10 -1/8 -7/57 -9/13 -1/8 -11/16 -3/25 -5/42 -2/3 -1/9 -11/17 -5/48 -9/14 -1/9 -1/10 -7/11 -7/68 -5/8 -1/10 -5/51 -18/29 -9/94 -2/21 -31/50 -5/53 -3/32 -13/21 -1/10 -21/34 -3/32 -1/11 -8/13 -1/10 0/1 -3/5 -3/32 -16/27 -1/11 -13/22 -1/11 -13/144 -23/39 -7/78 -10/17 -5/56 -4/45 -17/29 -11/124 -7/12 -2/23 -11/19 -1/12 -37/64 -5/53 -3/32 -26/45 -1/11 -15/26 -1/11 -3/34 -4/7 -2/23 -1/12 -13/23 -7/80 -9/16 -3/35 -7/82 -5/9 -1/12 -6/11 -2/25 -3/38 -7/13 -1/12 -1/2 -1/13 -1/14 -5/11 -5/72 -4/9 -1/15 -3/7 -1/16 -8/19 -1/14 0/1 -21/50 -11/164 -1/15 -34/81 -1/15 -13/31 -9/136 -5/12 -2/31 -12/29 -3/46 -2/31 -19/46 -5/78 -13/203 -26/63 -3/47 -7/17 -1/16 -2/5 -1/16 -2/33 -11/28 -1/17 -1/18 -9/23 -3/52 -7/18 0/1 -5/13 -1/16 -8/21 -3/49 -19/50 -7/115 -9/148 -30/79 -21/346 -2/33 -41/108 -2/33 -11/29 -7/116 -14/37 -1/16 -2/33 -3/8 -3/50 -1/17 -10/27 -1/17 -7/19 -7/120 -18/49 -13/224 -4/69 -11/30 -4/69 -4/11 -2/35 -1/18 -9/25 -5/88 -5/14 -1/18 -3/55 -1/3 -1/18 -4/13 -1/18 -4/73 -7/23 -1/20 -3/10 -3/56 -1/19 -8/27 -1/19 -5/17 -5/96 -7/24 -2/39 -9/31 -7/136 -2/7 -2/39 -1/20 -9/32 -1/21 -3/64 -7/25 -1/20 -5/18 0/1 -3/11 -3/56 -10/37 -2/39 -1/20 -7/26 -1/19 -3/58 -18/67 -3/58 -2/39 -29/108 -2/39 -11/41 -1/20 -4/15 -1/19 -1/4 -1/20 -1/21 -3/13 -1/20 -2/9 -1/21 -1/5 -1/20 -2/11 -1/22 -2/45 -5/28 -1/22 -1/23 -8/45 -1/23 -3/17 -1/24 -1/6 0/1 -2/13 -1/22 0/1 -3/20 -3/68 -1/23 -4/27 -1/23 -1/7 -1/24 0/1 -1/26 0/1 1/10 -1/27 -1/28 1/9 -1/28 1/8 -1/29 -1/30 1/7 -1/28 2/13 -1/30 0/1 3/19 -1/28 4/25 -4/119 -1/30 1/6 0/1 4/23 -3/88 -2/59 3/17 -1/28 2/11 -2/59 -1/30 5/27 -1/30 3/16 -1/30 -3/91 1/5 -1/32 3/14 -1/29 -1/30 5/23 -5/152 2/9 -1/31 3/13 -1/32 4/17 -1/32 -4/129 5/21 -1/34 1/4 -1/31 -1/32 5/19 -1/32 4/15 -1/33 11/41 -1/32 7/26 -3/98 -1/33 3/11 -3/100 5/18 0/1 7/25 -1/32 16/57 -1/31 9/32 -3/92 -1/31 2/7 -1/32 -2/65 7/24 -2/65 5/17 -5/164 8/27 -1/33 3/10 -1/33 -3/100 10/33 -3/101 17/56 -7/237 -1/34 7/23 -1/32 4/13 -4/135 -1/34 1/3 -1/34 5/14 -3/101 -1/34 19/53 -19/648 14/39 -5/171 9/25 -5/172 4/11 -1/34 -2/69 11/30 -4/139 7/19 -7/244 10/27 -1/35 3/8 -1/35 -3/106 11/29 -7/248 19/50 -9/320 -7/249 8/21 -3/107 13/34 -11/395 -1/36 5/13 -1/36 7/18 0/1 9/23 -3/104 20/51 -1/35 31/79 -1/36 11/28 -1/34 -1/35 2/5 -2/71 -1/36 11/27 -1/36 9/22 -1/36 -9/325 7/17 -1/36 12/29 -2/73 -3/110 17/41 -1/36 5/12 -2/73 23/55 -23/844 18/43 -4/147 -13/478 13/31 -9/332 8/19 -1/38 0/1 27/64 -1/36 -1/37 19/45 -1/36 11/26 -3/110 -1/37 3/7 -1/36 7/16 -3/110 -1/37 11/25 -5/184 4/9 -1/37 5/11 -5/188 6/13 -1/38 0/1 7/15 -1/38 1/2 -1/38 -1/39 8/15 -1/39 7/13 -1/40 6/11 -3/118 -2/79 5/9 -1/40 9/16 -7/282 -3/121 31/55 -31/1252 22/39 -7/283 13/23 -7/284 30/53 -2/81 -3/122 17/30 -2/81 4/7 -1/40 -2/81 19/33 -3/122 15/26 -3/122 -1/41 26/45 -1/41 37/64 -3/124 -5/207 11/19 -1/40 29/50 -3/119 -1/40 47/81 -1/40 18/31 -1/40 -4/161 7/12 -2/81 31/53 -31/1260 55/94 -53/2155 -3/122 79/135 -3/122 24/41 -3/122 -22/895 17/29 -11/448 27/46 -3/122 -1/41 37/63 -5/204 10/17 -4/163 -5/204 33/56 -7/286 -15/613 23/39 -7/286 13/22 -13/532 -1/41 16/27 -1/41 3/5 -3/124 11/18 -2/83 19/31 -7/292 8/13 -1/42 0/1 29/47 -1/40 50/81 -1/41 21/34 -1/41 -3/124 34/55 -2/83 -1/42 47/76 -3/124 -5/207 13/21 -1/42 31/50 -3/124 -5/207 49/79 -19/788 67/108 -2/83 18/29 -2/83 -9/374 23/37 -5/208 5/8 -5/209 -1/42 17/27 -1/42 12/19 -1/42 -12/505 7/11 -7/296 16/25 -1/42 0/1 57/89 -7/296 41/64 -5/212 -7/297 25/39 -1/42 9/14 -1/42 -1/43 11/17 -5/212 2/3 -1/43 11/16 -5/218 -3/131 9/13 -1/44 16/23 -2/87 -1/44 23/33 -7/306 30/43 -4/175 -25/1094 7/10 -7/307 -1/44 19/27 -1/44 12/17 -1/44 -12/529 5/7 -1/44 13/18 -2/89 21/29 -7/312 8/11 -2/89 -3/134 27/37 -5/224 46/63 -1/45 19/26 -3/134 -1/45 49/67 -1/44 79/108 -2/89 30/41 -2/89 -3/134 11/15 -3/134 36/49 -4/179 -21/940 25/34 -19/851 -5/224 14/19 -7/314 -8/359 17/23 -17/764 20/27 -1/45 3/4 -1/45 -3/136 16/21 -3/137 13/17 -5/228 10/13 -4/183 -1/46 7/9 -1/46 11/14 -1/46 -3/139 26/33 -3/139 41/52 -1/46 -7/323 56/71 -14/647 -9/416 15/19 -7/324 19/24 -2/93 42/53 -1/46 -2/93 107/135 -1/46 65/82 -1/46 -3/139 23/29 -5/232 4/5 -2/93 -3/140 21/26 -5/234 -1/47 17/21 -5/234 30/37 -7/328 -22/1031 43/53 -43/2016 13/16 -13/610 -1/47 22/27 -1/47 9/11 -9/424 23/28 -1/47 -3/142 37/45 -5/236 14/17 -5/236 -4/189 19/23 -11/520 43/52 -25/1183 -3/142 67/81 -3/142 24/29 -3/142 -14/663 5/6 -2/95 11/13 -1/48 17/20 -17/815 -1/48 23/27 -1/48 6/7 -1/48 -6/289 19/22 -13/628 -3/145 13/15 -5/242 7/8 -5/243 -3/146 15/17 -5/244 8/9 -1/49 9/10 -7/345 -3/148 10/11 -2/99 -9/446 1/1 -1/52 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(460,417,567,514) (-1/1,-9/10) -> (30/37,43/53) Hyperbolic Matrix(593,530,1026,917) (-9/10,-8/9) -> (26/45,37/64) Hyperbolic Matrix(379,334,-918,-809) (-8/9,-7/8) -> (-19/46,-26/63) Hyperbolic Matrix(298,259,405,352) (-7/8,-6/7) -> (25/34,14/19) Hyperbolic Matrix(134,113,351,296) (-6/7,-5/6) -> (8/21,13/34) Hyperbolic Matrix(188,155,621,512) (-5/6,-14/17) -> (3/10,10/33) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(485,396,594,485) (-9/11,-22/27) -> (22/27,9/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(998,809,1431,1160) (-13/16,-17/21) -> (23/33,30/43) Hyperbolic Matrix(1052,851,1701,1376) (-17/21,-4/5) -> (47/76,13/21) Hyperbolic Matrix(377,298,-1026,-811) (-4/5,-15/19) -> (-7/19,-18/49) Hyperbolic Matrix(80,63,513,404) (-15/19,-11/14) -> (2/13,3/19) Hyperbolic Matrix(188,147,-243,-190) (-11/14,-7/9) -> (-7/9,-10/13) Parabolic Matrix(296,227,-459,-352) (-10/13,-13/17) -> (-11/17,-9/14) Hyperbolic Matrix(80,61,459,350) (-13/17,-3/4) -> (4/23,3/17) Hyperbolic Matrix(431,318,-1026,-757) (-3/4,-14/19) -> (-8/19,-21/50) Hyperbolic Matrix(352,259,405,298) (-14/19,-11/15) -> (13/15,7/8) Hyperbolic Matrix(377,276,810,593) (-11/15,-30/41) -> (6/13,7/15) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(107,78,-594,-433) (-19/26,-8/11) -> (-2/11,-5/28) Hyperbolic Matrix(82,59,189,136) (-8/11,-5/7) -> (3/7,7/16) Hyperbolic Matrix(134,95,189,134) (-5/7,-7/10) -> (12/17,5/7) Hyperbolic Matrix(82,57,351,244) (-7/10,-9/13) -> (3/13,4/17) Hyperbolic Matrix(190,131,-351,-242) (-9/13,-11/16) -> (-6/11,-7/13) Hyperbolic Matrix(188,129,-513,-352) (-11/16,-2/3) -> (-11/30,-4/11) Hyperbolic Matrix(134,87,-459,-298) (-2/3,-11/17) -> (-5/17,-7/24) Hyperbolic Matrix(136,87,297,190) (-9/14,-7/11) -> (5/11,6/13) Hyperbolic Matrix(188,119,297,188) (-7/11,-5/8) -> (12/19,7/11) Hyperbolic Matrix(647,402,-1566,-973) (-5/8,-18/29) -> (-12/29,-19/46) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(271,168,1134,703) (-31/50,-13/21) -> (5/21,1/4) Hyperbolic Matrix(730,451,1269,784) (-13/21,-21/34) -> (4/7,19/33) Hyperbolic Matrix(107,66,-702,-433) (-21/34,-8/13) -> (-2/13,-3/20) Hyperbolic Matrix(28,17,135,82) (-8/13,-3/5) -> (1/5,3/14) Hyperbolic Matrix(161,96,270,161) (-3/5,-16/27) -> (16/27,3/5) Hyperbolic Matrix(703,416,1188,703) (-16/27,-13/22) -> (13/22,16/27) Hyperbolic Matrix(1646,971,2241,1322) (-13/22,-23/39) -> (11/15,36/49) Hyperbolic Matrix(2024,1193,3159,1862) (-23/39,-10/17) -> (41/64,25/39) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(514,301,1431,838) (-17/29,-7/12) -> (14/39,9/25) Hyperbolic Matrix(136,79,513,298) (-7/12,-11/19) -> (5/19,4/15) Hyperbolic Matrix(2024,1171,2565,1484) (-11/19,-37/64) -> (56/71,15/19) Hyperbolic Matrix(917,530,1026,593) (-37/64,-26/45) -> (8/9,9/10) Hyperbolic Matrix(433,250,-2430,-1403) (-26/45,-15/26) -> (-5/28,-8/45) Hyperbolic Matrix(784,451,1269,730) (-15/26,-4/7) -> (21/34,34/55) Hyperbolic Matrix(109,62,-378,-215) (-4/7,-13/23) -> (-9/31,-2/7) Hyperbolic Matrix(622,351,1485,838) (-13/23,-9/16) -> (18/43,13/31) Hyperbolic Matrix(134,75,-243,-136) (-9/16,-5/9) -> (-5/9,-6/11) Parabolic Matrix(190,101,459,244) (-7/13,-1/2) -> (12/29,17/41) Hyperbolic Matrix(190,87,297,136) (-1/2,-5/11) -> (7/11,16/25) Hyperbolic Matrix(82,37,-297,-134) (-5/11,-4/9) -> (-5/18,-3/11) Hyperbolic Matrix(136,59,189,82) (-4/9,-3/7) -> (5/7,13/18) Hyperbolic Matrix(26,11,189,80) (-3/7,-8/19) -> (1/8,1/7) Hyperbolic Matrix(1243,522,1674,703) (-21/50,-34/81) -> (20/27,3/4) Hyperbolic Matrix(1997,838,2700,1133) (-34/81,-13/31) -> (17/23,20/27) Hyperbolic Matrix(838,351,1485,622) (-13/31,-5/12) -> (22/39,13/23) Hyperbolic Matrix(244,101,459,190) (-5/12,-12/29) -> (1/2,8/15) Hyperbolic Matrix(2483,1024,3402,1403) (-26/63,-7/17) -> (27/37,46/63) Hyperbolic Matrix(188,77,459,188) (-7/17,-2/5) -> (9/22,7/17) Hyperbolic Matrix(1486,585,2403,946) (-2/5,-11/28) -> (34/55,47/76) Hyperbolic Matrix(1054,413,1863,730) (-11/28,-9/23) -> (13/23,30/53) Hyperbolic Matrix(595,232,972,379) (-9/23,-7/18) -> (11/18,19/31) Hyperbolic Matrix(80,31,-351,-136) (-7/18,-5/13) -> (-3/13,-2/9) Hyperbolic Matrix(296,113,351,134) (-5/13,-8/21) -> (5/6,11/13) Hyperbolic Matrix(863,328,1134,431) (-8/21,-19/50) -> (3/4,16/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(512,193,1215,458) (-14/37,-3/8) -> (8/19,27/64) Hyperbolic Matrix(161,60,432,161) (-3/8,-10/27) -> (10/27,3/8) Hyperbolic Matrix(379,140,1026,379) (-10/27,-7/19) -> (7/19,10/27) Hyperbolic Matrix(1054,387,3753,1378) (-18/49,-11/30) -> (16/57,9/32) Hyperbolic Matrix(431,156,594,215) (-4/11,-9/25) -> (21/29,8/11) Hyperbolic Matrix(838,301,1431,514) (-9/25,-5/14) -> (24/41,17/29) Hyperbolic Matrix(26,9,-81,-28) (-5/14,-1/3) -> (-1/3,-4/13) Parabolic Matrix(431,132,702,215) (-4/13,-7/23) -> (19/31,8/13) Hyperbolic Matrix(512,155,621,188) (-7/23,-3/10) -> (14/17,19/23) Hyperbolic Matrix(161,48,540,161) (-3/10,-8/27) -> (8/27,3/10) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(836,243,2133,620) (-7/24,-9/31) -> (9/23,20/51) Hyperbolic Matrix(1052,297,1431,404) (-2/7,-9/32) -> (36/49,25/34) Hyperbolic Matrix(836,235,1053,296) (-9/32,-7/25) -> (23/29,4/5) Hyperbolic Matrix(703,196,972,271) (-7/25,-5/18) -> (13/18,21/29) Hyperbolic Matrix(26,7,297,80) (-10/37,-7/26) -> (0/1,1/10) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) Hyperbolic Matrix(433,116,810,217) (-11/41,-4/15) -> (8/15,7/13) Hyperbolic Matrix(298,79,513,136) (-4/15,-1/4) -> (18/31,7/12) Hyperbolic Matrix(244,57,351,82) (-1/4,-3/13) -> (9/13,16/23) Hyperbolic Matrix(82,17,135,28) (-2/9,-1/5) -> (3/5,11/18) Hyperbolic Matrix(26,5,135,26) (-1/5,-2/11) -> (3/16,1/5) Hyperbolic Matrix(811,144,918,163) (-8/45,-3/17) -> (15/17,8/9) Hyperbolic Matrix(350,61,459,80) (-3/17,-1/6) -> (16/21,13/17) Hyperbolic Matrix(404,63,513,80) (-1/6,-2/13) -> (11/14,26/33) Hyperbolic Matrix(1567,234,2538,379) (-3/20,-4/27) -> (50/81,21/34) Hyperbolic Matrix(1133,166,1836,269) (-4/27,-1/7) -> (29/47,50/81) Hyperbolic Matrix(80,11,189,26) (-1/7,0/1) -> (11/26,3/7) Hyperbolic Matrix(460,-47,783,-80) (1/10,1/9) -> (37/63,10/17) Hyperbolic Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(352,-57,1161,-188) (4/25,1/6) -> (10/33,17/56) Hyperbolic Matrix(298,-51,783,-134) (1/6,4/23) -> (19/50,8/21) Hyperbolic Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(136,-25,729,-134) (2/11,5/27) -> (5/27,3/16) Parabolic Matrix(190,-41,621,-134) (3/14,5/23) -> (7/23,4/13) Hyperbolic Matrix(242,-53,621,-136) (5/23,2/9) -> (7/18,9/23) Hyperbolic Matrix(136,-31,351,-80) (2/9,3/13) -> (5/13,7/18) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(460,-123,1107,-296) (4/15,11/41) -> (17/41,5/12) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(134,-37,297,-82) (3/11,5/18) -> (4/9,5/11) Hyperbolic Matrix(298,-83,675,-188) (5/18,7/25) -> (11/25,4/9) Hyperbolic Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(298,-87,459,-134) (7/24,5/17) -> (11/17,2/3) Hyperbolic Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(28,-9,81,-26) (4/13,1/3) -> (1/3,5/14) Parabolic Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(1162,-417,2781,-998) (19/53,14/39) -> (5/12,23/55) Hyperbolic Matrix(296,-107,675,-244) (9/25,4/11) -> (7/16,11/25) Hyperbolic Matrix(352,-129,513,-188) (4/11,11/30) -> (2/3,11/16) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(298,-121,729,-296) (2/5,11/27) -> (11/27,9/22) Parabolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(2998,-1265,3645,-1538) (27/64,19/45) -> (37/45,14/17) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(242,-131,351,-190) (7/13,6/11) -> (11/16,9/13) Hyperbolic Matrix(136,-75,243,-134) (6/11,5/9) -> (5/9,9/16) Parabolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1594,-899,2727,-1538) (31/55,22/39) -> (7/12,31/53) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(3808,-2209,6561,-3806) (29/50,47/81) -> (47/81,18/31) Parabolic Matrix(10666,-6241,18225,-10664) (55/94,79/135) -> (79/135,24/41) Parabolic Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(1486,-921,2133,-1322) (13/21,31/50) -> (16/23,23/33) Hyperbolic Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(460,-289,729,-458) (5/8,17/27) -> (17/27,12/19) Parabolic Matrix(1324,-849,1809,-1160) (25/39,9/14) -> (30/41,11/15) Hyperbolic Matrix(352,-227,459,-296) (9/14,11/17) -> (13/17,10/13) Hyperbolic Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(514,-361,729,-512) (7/10,19/27) -> (19/27,12/17) Parabolic Matrix(190,-147,243,-188) (10/13,7/9) -> (7/9,11/14) Parabolic Matrix(1052,-829,1269,-1000) (26/33,41/52) -> (24/29,5/6) Hyperbolic Matrix(14446,-11449,18225,-14444) (42/53,107/135) -> (107/135,65/82) Parabolic Matrix(5428,-4489,6561,-5426) (43/52,67/81) -> (67/81,24/29) Parabolic Matrix(622,-529,729,-620) (17/20,23/27) -> (23/27,6/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-52,1) Matrix(460,417,567,514) -> Matrix(43,17,-2016,-797) Matrix(593,530,1026,917) -> Matrix(17,6,-700,-247) Matrix(379,334,-918,-809) -> Matrix(45,14,-704,-219) Matrix(298,259,405,352) -> Matrix(39,11,-1748,-493) Matrix(134,113,351,296) -> Matrix(21,5,-752,-179) Matrix(188,155,621,512) -> Matrix(33,7,-1108,-235) Matrix(161,132,-594,-487) -> Matrix(29,6,-556,-115) Matrix(485,396,594,485) -> Matrix(89,18,-4188,-847) Matrix(703,572,864,703) -> Matrix(131,26,-6152,-1221) Matrix(998,809,1431,1160) -> Matrix(139,27,-6080,-1181) Matrix(1052,851,1701,1376) -> Matrix(47,9,-1948,-373) Matrix(377,298,-1026,-811) -> Matrix(79,14,-1360,-241) Matrix(80,63,513,404) -> Matrix(17,3,-516,-91) Matrix(188,147,-243,-190) -> Matrix(41,7,-252,-43) Matrix(296,227,-459,-352) -> Matrix(31,5,-304,-49) Matrix(80,61,459,350) -> Matrix(19,3,-564,-89) Matrix(431,318,-1026,-757) -> Matrix(57,8,-848,-119) Matrix(352,259,405,298) -> Matrix(79,11,-3828,-533) Matrix(377,276,810,593) -> Matrix(15,2,-548,-73) Matrix(755,552,-2808,-2053) -> Matrix(1,0,-12,1) Matrix(107,78,-594,-433) -> Matrix(29,4,-660,-91) Matrix(82,59,189,136) -> Matrix(23,3,-836,-109) Matrix(134,95,189,134) -> Matrix(39,5,-1724,-221) Matrix(82,57,351,244) -> Matrix(25,3,-792,-95) Matrix(190,131,-351,-242) -> Matrix(9,1,-100,-11) Matrix(188,129,-513,-352) -> Matrix(59,7,-1020,-121) Matrix(134,87,-459,-298) -> Matrix(47,5,-912,-97) Matrix(136,87,297,190) -> Matrix(9,1,-352,-39) Matrix(188,119,297,188) -> Matrix(69,7,-2908,-295) Matrix(647,402,-1566,-973) -> Matrix(125,12,-1948,-187) Matrix(2051,1272,-5400,-3349) -> Matrix(253,24,-4164,-395) Matrix(271,168,1134,703) -> Matrix(21,2,-704,-67) Matrix(730,451,1269,784) -> Matrix(53,5,-2152,-203) Matrix(107,66,-702,-433) -> Matrix(1,0,-12,1) Matrix(28,17,135,82) -> Matrix(11,1,-320,-29) Matrix(161,96,270,161) -> Matrix(65,6,-2676,-247) Matrix(703,416,1188,703) -> Matrix(287,26,-11756,-1065) Matrix(1646,971,2241,1322) -> Matrix(345,31,-15436,-1387) Matrix(2024,1193,3159,1862) -> Matrix(167,15,-7092,-637) Matrix(593,348,-1566,-919) -> Matrix(67,6,-1128,-101) Matrix(514,301,1431,838) -> Matrix(147,13,-5032,-445) Matrix(136,79,513,298) -> Matrix(35,3,-1132,-97) Matrix(2024,1171,2565,1484) -> Matrix(29,3,-1344,-139) Matrix(917,530,1026,593) -> Matrix(65,6,-3196,-295) Matrix(433,250,-2430,-1403) -> Matrix(45,4,-1024,-91) Matrix(784,451,1269,730) -> Matrix(57,5,-2360,-207) Matrix(109,62,-378,-215) -> Matrix(1,0,-8,1) Matrix(622,351,1485,838) -> Matrix(127,11,-4676,-405) Matrix(134,75,-243,-136) -> Matrix(59,5,-720,-61) Matrix(190,101,459,244) -> Matrix(11,1,-408,-37) Matrix(190,87,297,136) -> Matrix(13,1,-560,-43) Matrix(82,37,-297,-134) -> Matrix(15,1,-256,-17) Matrix(136,59,189,82) -> Matrix(47,3,-2084,-133) Matrix(26,11,189,80) -> Matrix(15,1,-436,-29) Matrix(1243,522,1674,703) -> Matrix(209,14,-9420,-631) Matrix(1997,838,2700,1133) -> Matrix(391,26,-17580,-1169) Matrix(838,351,1485,622) -> Matrix(167,11,-6756,-445) Matrix(244,101,459,190) -> Matrix(15,1,-616,-41) Matrix(2483,1024,3402,1403) -> Matrix(251,16,-11248,-717) Matrix(188,77,459,188) -> Matrix(111,7,-4012,-253) Matrix(1486,585,2403,946) -> Matrix(19,1,-780,-41) Matrix(1054,413,1863,730) -> Matrix(15,1,-616,-41) Matrix(595,232,972,379) -> Matrix(37,2,-1536,-83) Matrix(80,31,-351,-136) -> Matrix(15,1,-316,-21) Matrix(296,113,351,134) -> Matrix(81,5,-3872,-239) Matrix(863,328,1134,431) -> Matrix(197,12,-8980,-547) Matrix(7237,2748,11664,4429) -> Matrix(989,60,-41060,-2491) Matrix(7235,2746,11664,4427) -> Matrix(859,52,-35632,-2157) Matrix(512,193,1215,458) -> Matrix(17,1,-596,-35) Matrix(161,60,432,161) -> Matrix(101,6,-3552,-211) Matrix(379,140,1026,379) -> Matrix(239,14,-8348,-489) Matrix(1054,387,3753,1378) -> Matrix(17,1,-596,-35) Matrix(431,156,594,215) -> Matrix(69,4,-3088,-179) Matrix(838,301,1431,514) -> Matrix(231,13,-9400,-529) Matrix(26,9,-81,-28) -> Matrix(17,1,-324,-19) Matrix(431,132,702,215) -> Matrix(73,4,-3048,-167) Matrix(512,155,621,188) -> Matrix(129,7,-6100,-331) Matrix(161,48,540,161) -> Matrix(113,6,-3748,-199) Matrix(271,80,918,271) -> Matrix(191,10,-6284,-329) Matrix(836,243,2133,620) -> Matrix(19,1,-704,-37) Matrix(1052,297,1431,404) -> Matrix(185,9,-8284,-403) Matrix(836,235,1053,296) -> Matrix(65,3,-3012,-139) Matrix(703,196,972,271) -> Matrix(47,2,-2092,-89) Matrix(26,7,297,80) -> Matrix(19,1,-552,-29) Matrix(8533,2292,11664,3133) -> Matrix(233,12,-10388,-535) Matrix(8531,2290,11664,3131) -> Matrix(79,4,-3496,-177) Matrix(433,116,810,217) -> Matrix(1,0,-20,1) Matrix(298,79,513,136) -> Matrix(59,3,-2380,-121) Matrix(244,57,351,82) -> Matrix(61,3,-2664,-131) Matrix(82,17,135,28) -> Matrix(23,1,-944,-41) Matrix(26,5,135,26) -> Matrix(21,1,-652,-31) Matrix(811,144,918,163) -> Matrix(139,6,-6788,-293) Matrix(350,61,459,80) -> Matrix(67,3,-3060,-137) Matrix(404,63,513,80) -> Matrix(65,3,-3012,-139) Matrix(1567,234,2538,379) -> Matrix(137,6,-5640,-247) Matrix(1133,166,1836,269) -> Matrix(47,2,-1904,-81) Matrix(80,11,189,26) -> Matrix(23,1,-852,-37) Matrix(460,-47,783,-80) -> Matrix(23,1,-944,-41) Matrix(539,-64,918,-109) -> Matrix(117,4,-4768,-163) Matrix(433,-66,702,-107) -> Matrix(1,0,-12,1) Matrix(1729,-276,2700,-431) -> Matrix(119,4,-5028,-169) Matrix(352,-57,1161,-188) -> Matrix(91,3,-3064,-101) Matrix(298,-51,783,-134) -> Matrix(85,3,-3032,-107) Matrix(433,-78,594,-107) -> Matrix(117,4,-5236,-179) Matrix(136,-25,729,-134) -> Matrix(149,5,-4500,-151) Matrix(190,-41,621,-134) -> Matrix(91,3,-3064,-101) Matrix(242,-53,621,-136) -> Matrix(31,1,-1024,-33) Matrix(136,-31,351,-80) -> Matrix(31,1,-1148,-37) Matrix(919,-218,1134,-269) -> Matrix(199,6,-9320,-281) Matrix(595,-156,1026,-269) -> Matrix(65,2,-2568,-79) Matrix(460,-123,1107,-296) -> Matrix(31,1,-1148,-37) Matrix(2053,-552,2808,-755) -> Matrix(1,0,-12,1) Matrix(487,-132,594,-161) -> Matrix(197,6,-9292,-283) Matrix(134,-37,297,-82) -> Matrix(35,1,-1296,-37) Matrix(298,-83,675,-188) -> Matrix(27,1,-1000,-37) Matrix(2267,-636,5778,-1621) -> Matrix(1,0,-4,1) Matrix(325,-92,378,-107) -> Matrix(127,4,-6128,-193) Matrix(215,-62,378,-109) -> Matrix(1,0,-8,1) Matrix(298,-87,459,-134) -> Matrix(163,5,-6944,-213) Matrix(2053,-624,2484,-755) -> Matrix(139,4,-6568,-189) Matrix(28,-9,81,-26) -> Matrix(33,1,-1156,-35) Matrix(3349,-1200,5724,-2051) -> Matrix(1499,44,-60948,-1789) Matrix(1162,-417,2781,-998) -> Matrix(581,17,-21292,-623) Matrix(296,-107,675,-244) -> Matrix(173,5,-6332,-183) Matrix(352,-129,513,-188) -> Matrix(243,7,-10588,-305) Matrix(811,-298,1026,-377) -> Matrix(487,14,-22576,-649) Matrix(919,-348,1566,-593) -> Matrix(211,6,-8616,-245) Matrix(3349,-1272,5400,-2051) -> Matrix(853,24,-35364,-995) Matrix(595,-228,702,-269) -> Matrix(217,6,-10380,-287) Matrix(5779,-2268,7290,-2861) -> Matrix(67,2,-3116,-93) Matrix(217,-86,270,-107) -> Matrix(141,4,-6592,-187) Matrix(298,-121,729,-296) -> Matrix(395,11,-14256,-397) Matrix(973,-402,1566,-647) -> Matrix(437,12,-18172,-499) Matrix(593,-248,648,-271) -> Matrix(367,10,-18240,-497) Matrix(757,-318,1026,-431) -> Matrix(297,8,-13328,-359) Matrix(2998,-1265,3645,-1538) -> Matrix(41,1,-1928,-47) Matrix(1997,-844,2430,-1027) -> Matrix(221,6,-10424,-283) Matrix(541,-254,918,-431) -> Matrix(297,8,-12140,-327) Matrix(242,-131,351,-190) -> Matrix(41,1,-1764,-43) Matrix(136,-75,243,-134) -> Matrix(199,5,-8000,-201) Matrix(1403,-790,1728,-973) -> Matrix(1291,32,-60556,-1501) Matrix(1594,-899,2727,-1538) -> Matrix(1253,31,-50888,-1259) Matrix(2267,-1284,2862,-1621) -> Matrix(325,8,-15072,-371) Matrix(1135,-654,1404,-809) -> Matrix(83,2,-3860,-93) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,-4,1) Matrix(4427,-2560,6912,-3997) -> Matrix(167,4,-7056,-169) Matrix(3808,-2209,6561,-3806) -> Matrix(279,7,-11200,-281) Matrix(10666,-6241,18225,-10664) -> Matrix(9149,225,-372100,-9151) Matrix(3833,-2258,4860,-2863) -> Matrix(1389,34,-64180,-1571) Matrix(1027,-606,1188,-701) -> Matrix(1063,26,-51392,-1257) Matrix(1486,-921,2133,-1322) -> Matrix(455,11,-19896,-481) Matrix(379,-236,432,-269) -> Matrix(417,10,-20308,-487) Matrix(460,-289,729,-458) -> Matrix(713,17,-29988,-715) Matrix(1324,-849,1809,-1160) -> Matrix(213,5,-9500,-223) Matrix(352,-227,459,-296) -> Matrix(211,5,-9664,-229) Matrix(487,-340,540,-377) -> Matrix(613,14,-30256,-691) Matrix(514,-361,729,-512) -> Matrix(835,19,-36784,-837) Matrix(190,-147,243,-188) -> Matrix(321,7,-14812,-323) Matrix(1052,-829,1269,-1000) -> Matrix(325,7,-15368,-331) Matrix(14446,-11449,18225,-14444) -> Matrix(45,1,-2116,-47) Matrix(5428,-4489,6561,-5426) -> Matrix(5537,117,-262132,-5539) Matrix(622,-529,729,-620) -> Matrix(1103,23,-52992,-1105) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 ----------------------------------------------------------------------- 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 (-1/26,0/1) 0 27 1/7 -1/28 1 27 2/13 (-1/30,0/1) 0 27 1/6 0/1 2 9 3/17 -1/28 1 27 2/11 (-2/59,-1/30) 0 27 5/27 -1/30 5 1 1/5 -1/32 1 27 2/9 -1/31 2 3 3/13 -1/32 1 27 1/4 (-1/31,-1/32) 0 27 4/15 -1/33 2 9 11/41 -1/32 1 27 7/26 (-3/98,-1/33) 0 27 3/11 -3/100 1 27 5/18 0/1 4 3 7/25 -1/32 1 27 9/32 (-3/92,-1/31) 0 27 2/7 (-1/32,-2/65) 0 27 7/24 -2/65 2 9 5/17 -5/164 1 27 8/27 -1/33 8 1 3/10 (-1/33,-3/100) 0 27 7/23 -1/32 1 27 4/13 (-4/135,-1/34) 0 27 1/3 -1/34 1 9 5/14 (-3/101,-1/34) 0 27 9/25 -5/172 1 27 4/11 (-1/34,-2/69) 0 27 11/30 -4/139 2 9 7/19 -7/244 1 27 10/27 -1/35 10 1 3/8 (-1/35,-3/106) 0 27 11/29 -7/248 1 27 19/50 (-9/320,-7/249) 0 27 8/21 -3/107 2 9 5/13 -1/36 1 27 7/18 0/1 2 3 9/23 -3/104 1 27 11/28 (-1/34,-1/35) 0 27 2/5 (-2/71,-1/36) 0 27 11/27 -1/36 11 1 7/17 -1/36 1 27 12/29 (-2/73,-3/110) 0 27 5/12 -2/73 2 9 13/31 -9/332 1 27 8/19 (-1/38,0/1) 0 27 19/45 -1/36 1 3 11/26 (-3/110,-1/37) 0 27 3/7 -1/36 1 27 4/9 -1/37 4 3 5/11 -5/188 1 27 1/2 (-1/38,-1/39) 0 27 8/15 -1/39 2 9 7/13 -1/40 1 27 6/11 (-3/118,-2/79) 0 27 5/9 -1/40 5 3 9/16 (-7/282,-3/121) 0 27 31/55 -31/1252 1 27 22/39 -7/283 2 9 13/23 -7/284 1 27 30/53 (-2/81,-3/122) 0 27 17/30 -2/81 2 9 4/7 (-1/40,-2/81) 0 27 15/26 (-3/122,-1/41) 0 27 26/45 -1/41 8 3 37/64 (-3/124,-5/207) 0 27 11/19 -1/40 1 27 47/81 -1/40 7 1 18/31 (-1/40,-4/161) 0 27 7/12 -2/81 2 9 31/53 -31/1260 1 27 79/135 -3/122 25 1 24/41 (-3/122,-22/895) 0 27 17/29 -11/448 1 27 27/46 (-3/122,-1/41) 0 27 37/63 -5/204 1 3 10/17 (-4/163,-5/204) 0 27 23/39 -7/286 1 9 13/22 (-13/532,-1/41) 0 27 16/27 -1/41 16 1 3/5 -3/124 1 27 11/18 -2/83 2 3 19/31 -7/292 1 27 8/13 (-1/42,0/1) 0 27 29/47 -1/40 1 27 50/81 -1/41 4 1 21/34 (-1/41,-3/124) 0 27 34/55 (-2/83,-1/42) 0 27 13/21 -1/42 1 9 31/50 (-3/124,-5/207) 0 27 49/79 -19/788 1 27 67/108 -2/83 14 1 18/29 (-2/83,-9/374) 0 27 23/37 -5/208 1 27 5/8 (-5/209,-1/42) 0 27 17/27 -1/42 17 1 7/11 -7/296 1 27 16/25 (-1/42,0/1) 0 27 41/64 (-5/212,-7/297) 0 27 25/39 -1/42 1 9 9/14 (-1/42,-1/43) 0 27 11/17 -5/212 1 27 2/3 -1/43 2 9 11/16 (-5/218,-3/131) 0 27 9/13 -1/44 1 27 16/23 (-2/87,-1/44) 0 27 23/33 -7/306 1 9 7/10 (-7/307,-1/44) 0 27 19/27 -1/44 19 1 5/7 -1/44 1 27 13/18 -2/89 4 3 21/29 -7/312 1 27 8/11 (-2/89,-3/134) 0 27 27/37 -5/224 1 27 46/63 -1/45 8 3 19/26 (-3/134,-1/45) 0 27 49/67 -1/44 1 27 79/108 -2/89 2 1 30/41 (-2/89,-3/134) 0 27 11/15 -3/134 1 9 14/19 (-7/314,-8/359) 0 27 17/23 -17/764 1 27 20/27 -1/45 20 1 3/4 (-1/45,-3/136) 0 27 16/21 -3/137 2 9 13/17 -5/228 1 27 10/13 (-4/183,-1/46) 0 27 7/9 -1/46 7 3 11/14 (-1/46,-3/139) 0 27 26/33 -3/139 2 9 41/52 (-1/46,-7/323) 0 27 56/71 (-14/647,-9/416) 0 27 15/19 -7/324 1 27 19/24 -2/93 2 9 42/53 (-1/46,-2/93) 0 27 107/135 -1/46 1 1 23/29 -5/232 1 27 4/5 (-2/93,-3/140) 0 27 21/26 (-5/234,-1/47) 0 27 17/21 -5/234 1 9 30/37 (-7/328,-22/1031) 0 27 13/16 (-13/610,-1/47) 0 27 22/27 -1/47 22 1 9/11 -9/424 1 27 23/28 (-1/47,-3/142) 0 27 37/45 -5/236 1 3 14/17 (-5/236,-4/189) 0 27 19/23 -11/520 1 27 67/81 -3/142 13 1 24/29 (-3/142,-14/663) 0 27 5/6 -2/95 2 9 11/13 -1/48 1 27 23/27 -1/48 23 1 6/7 (-1/48,-6/289) 0 27 19/22 (-13/628,-3/145) 0 27 13/15 -5/242 1 9 7/8 (-5/243,-3/146) 0 27 15/17 -5/244 1 27 8/9 -1/49 8 3 9/10 (-7/345,-3/148) 0 27 10/11 (-2/99,-9/446) 0 27 1/1 -1/52 1 27 1/0 0/1 26 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(80,-11,189,-26) (0/1,1/7) -> (11/26,3/7) Glide Reflection Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(404,-63,513,-80) (2/13,1/6) -> (11/14,26/33) Glide Reflection Matrix(350,-61,459,-80) (1/6,3/17) -> (16/21,13/17) Glide Reflection Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(109,-20,594,-109) (2/11,5/27) -> (2/11,5/27) Reflection Matrix(26,-5,135,-26) (5/27,1/5) -> (5/27,1/5) Reflection Matrix(82,-17,135,-28) (1/5,2/9) -> (3/5,11/18) Glide Reflection Matrix(136,-31,351,-80) (2/9,3/13) -> (5/13,7/18) Hyperbolic Matrix(244,-57,351,-82) (3/13,1/4) -> (9/13,16/23) Glide Reflection Matrix(298,-79,513,-136) (1/4,4/15) -> (18/31,7/12) Glide Reflection Matrix(433,-116,810,-217) (4/15,11/41) -> (8/15,7/13) Glide Reflection Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(134,-37,297,-82) (3/11,5/18) -> (4/9,5/11) Hyperbolic Matrix(703,-196,972,-271) (5/18,7/25) -> (13/18,21/29) Glide Reflection Matrix(836,-235,1053,-296) (7/25,9/32) -> (23/29,4/5) Glide Reflection Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(298,-87,459,-134) (7/24,5/17) -> (11/17,2/3) Hyperbolic Matrix(271,-80,918,-271) (5/17,8/27) -> (5/17,8/27) Reflection Matrix(161,-48,540,-161) (8/27,3/10) -> (8/27,3/10) Reflection Matrix(512,-155,621,-188) (3/10,7/23) -> (14/17,19/23) Glide Reflection Matrix(431,-132,702,-215) (7/23,4/13) -> (19/31,8/13) Glide Reflection Matrix(28,-9,81,-26) (4/13,1/3) -> (1/3,5/14) Parabolic Matrix(838,-301,1431,-514) (5/14,9/25) -> (24/41,17/29) Glide Reflection Matrix(431,-156,594,-215) (9/25,4/11) -> (21/29,8/11) Glide Reflection Matrix(352,-129,513,-188) (4/11,11/30) -> (2/3,11/16) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(379,-140,1026,-379) (7/19,10/27) -> (7/19,10/27) Reflection Matrix(161,-60,432,-161) (10/27,3/8) -> (10/27,3/8) Reflection Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(863,-328,1134,-431) (19/50,8/21) -> (3/4,16/21) Glide Reflection Matrix(296,-113,351,-134) (8/21,5/13) -> (5/6,11/13) Glide Reflection Matrix(595,-232,972,-379) (7/18,9/23) -> (11/18,19/31) Glide Reflection Matrix(1054,-413,1863,-730) (9/23,11/28) -> (13/23,30/53) Glide Reflection Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(109,-44,270,-109) (2/5,11/27) -> (2/5,11/27) Reflection Matrix(188,-77,459,-188) (11/27,7/17) -> (11/27,7/17) Reflection Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(244,-101,459,-190) (12/29,5/12) -> (1/2,8/15) Glide Reflection Matrix(838,-351,1485,-622) (5/12,13/31) -> (22/39,13/23) Glide Reflection Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1918,-809,3267,-1378) (8/19,19/45) -> (27/46,37/63) Glide Reflection Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(136,-59,189,-82) (3/7,4/9) -> (5/7,13/18) Glide Reflection Matrix(190,-87,297,-136) (5/11,1/2) -> (7/11,16/25) Glide Reflection Matrix(242,-131,351,-190) (7/13,6/11) -> (11/16,9/13) Hyperbolic Matrix(136,-75,243,-134) (6/11,5/9) -> (5/9,9/16) Parabolic Matrix(566,-319,621,-350) (9/16,31/55) -> (10/11,1/1) Glide Reflection Matrix(1594,-899,2727,-1538) (31/55,22/39) -> (7/12,31/53) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(784,-451,1269,-730) (4/7,15/26) -> (21/34,34/55) Glide Reflection Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(917,-530,1026,-593) (26/45,37/64) -> (8/9,9/10) Glide Reflection Matrix(2024,-1171,2565,-1484) (37/64,11/19) -> (56/71,15/19) Glide Reflection Matrix(892,-517,1539,-892) (11/19,47/81) -> (11/19,47/81) Reflection Matrix(2915,-1692,5022,-2915) (47/81,18/31) -> (47/81,18/31) Reflection Matrix(4186,-2449,7155,-4186) (31/53,79/135) -> (31/53,79/135) Reflection Matrix(6479,-3792,11070,-6479) (79/135,24/41) -> (79/135,24/41) Reflection Matrix(1511,-888,1836,-1079) (37/63,10/17) -> (37/45,14/17) Glide Reflection Matrix(2024,-1193,3159,-1862) (10/17,23/39) -> (41/64,25/39) Glide Reflection Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(703,-416,1188,-703) (13/22,16/27) -> (13/22,16/27) Reflection Matrix(161,-96,270,-161) (16/27,3/5) -> (16/27,3/5) Reflection Matrix(4699,-2900,7614,-4699) (29/47,50/81) -> (29/47,50/81) Reflection Matrix(3401,-2100,5508,-3401) (50/81,21/34) -> (50/81,21/34) Reflection Matrix(1376,-851,1701,-1052) (34/55,13/21) -> (21/26,17/21) Glide Reflection Matrix(1486,-921,2133,-1322) (13/21,31/50) -> (16/23,23/33) Hyperbolic Matrix(10585,-6566,17064,-10585) (49/79,67/108) -> (49/79,67/108) Reflection Matrix(3887,-2412,6264,-3887) (67/108,18/29) -> (67/108,18/29) Reflection Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(271,-170,432,-271) (5/8,17/27) -> (5/8,17/27) Reflection Matrix(188,-119,297,-188) (17/27,7/11) -> (17/27,7/11) Reflection Matrix(4024,-2577,5103,-3268) (16/25,41/64) -> (41/52,56/71) Glide Reflection Matrix(1324,-849,1809,-1160) (25/39,9/14) -> (30/41,11/15) Hyperbolic Matrix(352,-227,459,-296) (9/14,11/17) -> (13/17,10/13) Hyperbolic Matrix(1160,-809,1431,-998) (23/33,7/10) -> (17/21,30/37) Glide Reflection Matrix(379,-266,540,-379) (7/10,19/27) -> (7/10,19/27) Reflection Matrix(134,-95,189,-134) (19/27,5/7) -> (19/27,5/7) Reflection Matrix(1241,-906,1404,-1025) (27/37,46/63) -> (15/17,8/9) Glide Reflection Matrix(10585,-7742,14472,-10585) (49/67,79/108) -> (49/67,79/108) Reflection Matrix(6479,-4740,8856,-6479) (79/108,30/41) -> (79/108,30/41) Reflection Matrix(352,-259,405,-298) (11/15,14/19) -> (13/15,7/8) Glide Reflection Matrix(919,-680,1242,-919) (17/23,20/27) -> (17/23,20/27) Reflection Matrix(161,-120,216,-161) (20/27,3/4) -> (20/27,3/4) Reflection Matrix(190,-147,243,-188) (10/13,7/9) -> (7/9,11/14) Parabolic Matrix(1052,-829,1269,-1000) (26/33,41/52) -> (24/29,5/6) Hyperbolic Matrix(11341,-8988,14310,-11341) (42/53,107/135) -> (42/53,107/135) Reflection Matrix(3104,-2461,3915,-3104) (107/135,23/29) -> (107/135,23/29) Reflection Matrix(514,-417,567,-460) (30/37,13/16) -> (9/10,10/11) Glide Reflection Matrix(703,-572,864,-703) (13/16,22/27) -> (13/16,22/27) Reflection Matrix(485,-396,594,-485) (22/27,9/11) -> (22/27,9/11) Reflection Matrix(1540,-1273,1863,-1540) (19/23,67/81) -> (19/23,67/81) Reflection Matrix(3887,-3216,4698,-3887) (67/81,24/29) -> (67/81,24/29) Reflection Matrix(298,-253,351,-298) (11/13,23/27) -> (11/13,23/27) Reflection Matrix(323,-276,378,-323) (23/27,6/7) -> (23/27,6/7) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,52,1) (0/1,1/0) -> (-1/26,0/1) Matrix(80,-11,189,-26) -> Matrix(29,1,-1072,-37) Matrix(433,-66,702,-107) -> Matrix(1,0,-12,1) 0/1 Matrix(404,-63,513,-80) -> Matrix(91,3,-4216,-139) Matrix(350,-61,459,-80) -> Matrix(89,3,-4064,-137) Matrix(433,-78,594,-107) -> Matrix(117,4,-5236,-179) Matrix(109,-20,594,-109) -> Matrix(119,4,-3540,-119) (2/11,5/27) -> (-2/59,-1/30) Matrix(26,-5,135,-26) -> Matrix(31,1,-960,-31) (5/27,1/5) -> (-1/30,-1/32) Matrix(82,-17,135,-28) -> Matrix(29,1,-1188,-41) Matrix(136,-31,351,-80) -> Matrix(31,1,-1148,-37) Matrix(244,-57,351,-82) -> Matrix(95,3,-4148,-131) Matrix(298,-79,513,-136) -> Matrix(97,3,-3912,-121) Matrix(433,-116,810,-217) -> Matrix(-1,0,72,1) *** -> (-1/36,0/1) Matrix(2053,-552,2808,-755) -> Matrix(1,0,-12,1) 0/1 Matrix(487,-132,594,-161) -> Matrix(197,6,-9292,-283) Matrix(134,-37,297,-82) -> Matrix(35,1,-1296,-37) -1/36 Matrix(703,-196,972,-271) -> Matrix(57,2,-2536,-89) Matrix(836,-235,1053,-296) -> Matrix(91,3,-4216,-139) Matrix(325,-92,378,-107) -> Matrix(127,4,-6128,-193) Matrix(215,-62,378,-109) -> Matrix(1,0,-8,1) 0/1 Matrix(298,-87,459,-134) -> Matrix(163,5,-6944,-213) Matrix(271,-80,918,-271) -> Matrix(329,10,-10824,-329) (5/17,8/27) -> (-5/164,-1/33) Matrix(161,-48,540,-161) -> Matrix(199,6,-6600,-199) (8/27,3/10) -> (-1/33,-3/100) Matrix(512,-155,621,-188) -> Matrix(235,7,-11112,-331) Matrix(431,-132,702,-215) -> Matrix(135,4,-5636,-167) Matrix(28,-9,81,-26) -> Matrix(33,1,-1156,-35) -1/34 Matrix(838,-301,1431,-514) -> Matrix(445,13,-18108,-529) Matrix(431,-156,594,-215) -> Matrix(139,4,-6220,-179) Matrix(352,-129,513,-188) -> Matrix(243,7,-10588,-305) Matrix(811,-298,1026,-377) -> Matrix(487,14,-22576,-649) Matrix(379,-140,1026,-379) -> Matrix(489,14,-17080,-489) (7/19,10/27) -> (-7/244,-1/35) Matrix(161,-60,432,-161) -> Matrix(211,6,-7420,-211) (10/27,3/8) -> (-1/35,-3/106) Matrix(919,-348,1566,-593) -> Matrix(211,6,-8616,-245) Matrix(3349,-1272,5400,-2051) -> Matrix(853,24,-35364,-995) Matrix(863,-328,1134,-431) -> Matrix(427,12,-19464,-547) Matrix(296,-113,351,-134) -> Matrix(179,5,-8556,-239) Matrix(595,-232,972,-379) -> Matrix(67,2,-2780,-83) Matrix(1054,-413,1863,-730) -> Matrix(37,1,-1516,-41) Matrix(217,-86,270,-107) -> Matrix(141,4,-6592,-187) Matrix(109,-44,270,-109) -> Matrix(143,4,-5112,-143) (2/5,11/27) -> (-2/71,-1/36) Matrix(188,-77,459,-188) -> Matrix(253,7,-9144,-253) (11/27,7/17) -> (-1/36,-7/254) Matrix(973,-402,1566,-647) -> Matrix(437,12,-18172,-499) Matrix(244,-101,459,-190) -> Matrix(37,1,-1516,-41) Matrix(838,-351,1485,-622) -> Matrix(405,11,-16384,-445) Matrix(757,-318,1026,-431) -> Matrix(297,8,-13328,-359) Matrix(1918,-809,3267,-1378) -> Matrix(41,1,-1680,-41) *** -> (-1/40,-1/42) Matrix(1997,-844,2430,-1027) -> Matrix(221,6,-10424,-283) Matrix(136,-59,189,-82) -> Matrix(109,3,-4832,-133) Matrix(190,-87,297,-136) -> Matrix(39,1,-1676,-43) Matrix(242,-131,351,-190) -> Matrix(41,1,-1764,-43) -1/42 Matrix(136,-75,243,-134) -> Matrix(199,5,-8000,-201) -1/40 Matrix(566,-319,621,-350) -> Matrix(525,13,-26048,-645) Matrix(1594,-899,2727,-1538) -> Matrix(1253,31,-50888,-1259) Matrix(2267,-1284,2862,-1621) -> Matrix(325,8,-15072,-371) Matrix(784,-451,1269,-730) -> Matrix(203,5,-8404,-207) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,-4,1) 0/1 Matrix(917,-530,1026,-593) -> Matrix(247,6,-12144,-295) Matrix(2024,-1171,2565,-1484) -> Matrix(127,3,-5884,-139) Matrix(892,-517,1539,-892) -> Matrix(41,1,-1680,-41) (11/19,47/81) -> (-1/40,-1/42) Matrix(2915,-1692,5022,-2915) -> Matrix(321,8,-12880,-321) (47/81,18/31) -> (-1/40,-4/161) Matrix(4186,-2449,7155,-4186) -> Matrix(3781,93,-153720,-3781) (31/53,79/135) -> (-31/1260,-3/122) Matrix(6479,-3792,11070,-6479) -> Matrix(5369,132,-218380,-5369) (79/135,24/41) -> (-3/122,-22/895) Matrix(1511,-888,1836,-1079) -> Matrix(-1,0,88,1) *** -> (-1/44,0/1) Matrix(2024,-1193,3159,-1862) -> Matrix(613,15,-26032,-637) Matrix(1027,-606,1188,-701) -> Matrix(1063,26,-51392,-1257) Matrix(703,-416,1188,-703) -> Matrix(1065,26,-43624,-1065) (13/22,16/27) -> (-13/532,-1/41) Matrix(161,-96,270,-161) -> Matrix(247,6,-10168,-247) (16/27,3/5) -> (-1/41,-3/124) Matrix(4699,-2900,7614,-4699) -> Matrix(81,2,-3280,-81) (29/47,50/81) -> (-1/40,-1/41) Matrix(3401,-2100,5508,-3401) -> Matrix(247,6,-10168,-247) (50/81,21/34) -> (-1/41,-3/124) Matrix(1376,-851,1701,-1052) -> Matrix(373,9,-17448,-421) Matrix(1486,-921,2133,-1322) -> Matrix(455,11,-19896,-481) Matrix(10585,-6566,17064,-10585) -> Matrix(3153,76,-130808,-3153) (49/79,67/108) -> (-19/788,-2/83) Matrix(3887,-2412,6264,-3887) -> Matrix(1495,36,-62084,-1495) (67/108,18/29) -> (-2/83,-9/374) Matrix(379,-236,432,-269) -> Matrix(417,10,-20308,-487) Matrix(271,-170,432,-271) -> Matrix(419,10,-17556,-419) (5/8,17/27) -> (-5/209,-1/42) Matrix(188,-119,297,-188) -> Matrix(295,7,-12432,-295) (17/27,7/11) -> (-1/42,-7/296) Matrix(4024,-2577,5103,-3268) -> Matrix(295,7,-13612,-323) Matrix(1324,-849,1809,-1160) -> Matrix(213,5,-9500,-223) Matrix(352,-227,459,-296) -> Matrix(211,5,-9664,-229) Matrix(1160,-809,1431,-998) -> Matrix(1181,27,-55332,-1265) Matrix(379,-266,540,-379) -> Matrix(615,14,-27016,-615) (7/10,19/27) -> (-7/307,-1/44) Matrix(134,-95,189,-134) -> Matrix(221,5,-9768,-221) (19/27,5/7) -> (-1/44,-5/222) Matrix(1241,-906,1404,-1025) -> Matrix(449,10,-21956,-489) Matrix(10585,-7742,14472,-10585) -> Matrix(177,4,-7832,-177) (49/67,79/108) -> (-1/44,-2/89) Matrix(6479,-4740,8856,-6479) -> Matrix(535,12,-23852,-535) (79/108,30/41) -> (-2/89,-3/134) Matrix(352,-259,405,-298) -> Matrix(493,11,-23888,-533) Matrix(919,-680,1242,-919) -> Matrix(1529,34,-68760,-1529) (17/23,20/27) -> (-17/764,-1/45) Matrix(161,-120,216,-161) -> Matrix(271,6,-12240,-271) (20/27,3/4) -> (-1/45,-3/136) Matrix(190,-147,243,-188) -> Matrix(321,7,-14812,-323) -1/46 Matrix(1052,-829,1269,-1000) -> Matrix(325,7,-15368,-331) Matrix(11341,-8988,14310,-11341) -> Matrix(185,4,-8556,-185) (42/53,107/135) -> (-1/46,-2/93) Matrix(3104,-2461,3915,-3104) -> Matrix(231,5,-10672,-231) (107/135,23/29) -> (-1/46,-5/232) Matrix(514,-417,567,-460) -> Matrix(797,17,-39428,-841) Matrix(703,-572,864,-703) -> Matrix(1221,26,-57340,-1221) (13/16,22/27) -> (-13/610,-1/47) Matrix(485,-396,594,-485) -> Matrix(847,18,-39856,-847) (22/27,9/11) -> (-1/47,-9/424) Matrix(1540,-1273,1863,-1540) -> Matrix(1561,33,-73840,-1561) (19/23,67/81) -> (-11/520,-3/142) Matrix(3887,-3216,4698,-3887) -> Matrix(3977,84,-188292,-3977) (67/81,24/29) -> (-3/142,-14/663) Matrix(298,-253,351,-298) -> Matrix(527,11,-25248,-527) (11/13,23/27) -> (-11/526,-1/48) Matrix(323,-276,378,-323) -> Matrix(577,12,-27744,-577) (23/27,6/7) -> (-1/48,-6/289) Matrix(-1,2,0,1) -> Matrix(-1,0,104,1) (1/1,1/0) -> (-1/52,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.