INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -17/37 -4/9 -3/7 -7/17 -3/8 -7/19 -11/31 -1/3 -9/29 -5/17 -2/7 -3/13 -1/5 -1/6 -1/7 -3/23 0/1 1/9 1/7 3/17 1/4 13/47 7/23 1/3 3/7 1/2 7/13 11/19 3/5 2/3 41/59 5/7 13/17 7/9 9/11 13/15 7/8 1/1 13/11 11/9 67/53 14/11 9/7 17/13 23/17 93/67 7/5 41/29 47/33 3/2 61/39 11/7 49/31 27/17 31/19 5/3 19/11 23/13 16/9 77/43 9/5 13/7 2/1 41/19 11/5 7/3 31/13 141/59 17/7 5/2 23/9 18/7 101/39 13/5 29/11 35/13 117/43 41/15 11/4 25/9 3/1 61/19 23/7 10/3 17/5 31/9 7/2 39/11 25/7 47/13 11/3 63/17 71/19 19/5 27/7 4/1 21/5 13/3 9/2 23/5 14/3 33/7 5/1 21/4 37/7 16/3 27/5 439/81 11/2 17/3 6/1 69/11 19/3 45/7 13/2 33/5 7/1 22/3 37/5 15/2 23/3 8/1 25/3 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/39 -8/17 0/1 1/33 -7/15 1/35 -13/28 1/34 -19/41 1/32 -6/13 1/35 2/69 -17/37 1/34 -11/24 3/101 2/67 -16/35 6/199 1/33 -5/11 1/34 -14/31 1/33 6/197 -9/20 2/65 3/97 -13/29 0/1 -4/9 1/32 -19/43 1/31 -15/34 2/63 1/31 -26/59 0/1 1/29 -11/25 1/32 -7/16 4/125 1/31 -17/39 5/154 -10/23 5/153 2/61 -13/30 1/31 2/61 -3/7 1/30 -17/40 0/1 1/29 -31/73 1/30 -14/33 2/59 1/29 -11/26 1/30 -30/71 3/89 2/59 -49/116 27/797 2/59 -19/45 7/206 -27/64 7/205 4/117 -35/83 4/117 -8/19 6/175 1/29 -13/31 5/144 -31/74 9/259 4/115 -18/43 3/86 -23/55 2/57 -5/12 1/29 2/57 -22/53 2/55 1/27 -17/41 1/29 -12/29 2/57 7/199 -7/17 1/28 -16/39 4/111 11/305 -9/22 2/55 1/27 -11/27 2/55 -2/5 1/27 2/53 -9/23 1/26 -16/41 1/26 -23/59 5/128 -30/77 7/179 16/409 -37/95 13/332 -7/18 2/51 5/127 -5/13 1/25 -8/21 1/25 2/49 -19/50 17/417 2/49 -11/29 5/122 -14/37 8/195 3/73 -3/8 1/24 -16/43 5/119 4/95 -13/35 5/118 -10/27 11/259 2/47 -27/73 15/352 -17/46 12/281 5/117 -24/65 2/47 9/211 -7/19 3/70 -32/87 3/70 -25/68 15/349 4/93 -43/117 13/302 -18/49 6/139 1/23 -11/30 6/139 1/23 -15/41 11/254 -4/11 1/23 6/137 -13/36 8/181 5/113 -9/25 2/45 -14/39 5/112 -5/14 4/89 5/111 -11/31 1/22 -17/48 14/307 13/285 -6/17 6/131 5/109 -13/37 3/65 -7/20 11/237 2/43 -15/43 7/150 -8/23 3/64 -1/3 1/20 -7/22 3/56 -13/41 7/130 -6/19 2/37 11/203 -11/35 3/55 -5/16 5/91 6/109 -9/29 1/18 -13/42 13/233 12/215 -4/13 5/89 4/71 -11/36 5/88 -7/23 2/35 -10/33 5/87 8/139 -3/10 6/103 1/17 -14/47 1/17 28/475 -11/37 11/186 -8/27 1/17 6/101 -13/44 1/17 6/101 -31/105 13/218 -49/166 41/687 4/67 -18/61 4/67 15/251 -5/17 3/50 -17/58 9/149 2/33 -12/41 5/83 12/199 -19/65 15/248 -26/89 41/677 2/33 -7/24 2/33 11/181 -9/31 5/82 -2/7 1/16 -9/32 3/47 8/125 -7/25 5/78 -19/68 27/419 2/31 -12/43 2/31 17/263 -5/18 2/31 1/15 -3/11 1/15 -4/15 5/73 2/29 -17/64 16/231 7/101 -13/49 5/72 -9/34 1/14 -5/19 1/14 -1/4 2/27 1/13 -5/21 2/25 -9/38 4/49 5/61 -4/17 1/13 2/25 -3/13 1/12 -8/35 5/59 4/47 -5/22 7/81 2/23 -7/31 1/11 -9/40 1/13 2/25 -2/9 2/23 1/11 -9/41 2/23 -7/32 3/34 -19/87 3/34 -12/55 4/45 9/101 -5/23 5/56 -8/37 16/177 1/11 -3/14 1/11 6/65 -13/61 4/43 -10/47 4/43 7/75 -7/33 7/74 -25/118 41/431 2/21 -18/85 2/21 27/283 -11/52 2/21 3/31 -4/19 1/10 -5/24 1/11 2/21 -1/5 1/10 -5/26 0/1 1/9 -14/73 0/1 1/11 -9/47 1/10 -4/21 2/19 1/9 -3/16 2/19 5/47 -8/43 3/28 -5/27 5/46 -7/38 14/127 1/9 -2/11 1/9 4/35 -3/17 1/8 -10/57 0/1 1/5 -7/40 0/1 1/11 -4/23 1/9 2/17 -5/29 1/9 -1/6 1/8 -3/19 0/1 -5/32 0/1 1/9 -2/13 3/23 2/15 -3/20 6/43 1/7 -4/27 1/7 8/55 -1/7 1/6 -3/22 1/7 6/41 -2/15 2/13 3/19 -3/23 1/6 -1/8 2/11 1/5 -4/33 -1/1 0/1 -7/58 0/1 1/17 -3/25 1/8 -2/17 1/6 -1/9 1/5 -1/10 0/1 1/7 0/1 0/1 1/1 1/10 -2/1 -1/1 1/9 -1/2 2/17 -1/3 -2/7 1/8 -1/5 0/1 2/15 -2/5 -1/3 3/22 -1/2 1/7 -1/3 4/27 -5/17 -2/7 3/20 -1/3 0/1 2/13 -1/4 3/19 -1/6 1/6 -1/3 -2/7 3/17 -1/4 2/11 -3/13 -2/9 7/38 -1/4 12/65 -2/9 -1/5 5/27 -2/9 3/16 -6/29 -1/5 4/21 -1/6 1/5 -1/4 3/14 -1/5 -6/31 8/37 -3/16 5/23 -3/16 2/9 -2/11 -3/17 3/13 0/1 7/30 -4/19 -1/5 4/17 -1/5 0/1 5/21 -5/26 1/4 -1/6 5/19 -1/7 9/34 -1/9 0/1 4/15 -2/13 -1/7 15/56 -1/5 0/1 11/41 -1/8 18/67 -1/8 7/26 -1/9 0/1 3/11 -1/6 8/29 -3/17 -4/23 13/47 -1/6 5/18 -5/31 -4/25 7/25 -2/13 9/32 -2/13 -1/7 2/7 -4/27 -1/7 5/17 -5/36 3/10 -5/37 -2/15 10/33 -4/31 -5/39 7/23 -1/8 18/59 -2/17 -1/9 29/95 -1/8 11/36 -4/35 -1/9 4/13 -1/7 -2/15 1/3 -1/8 6/17 -1/9 0/1 11/31 -1/8 5/14 -2/17 -1/9 4/11 -1/8 11/30 -3/25 -2/17 18/49 -27/229 -2/17 7/19 -7/60 17/46 -11/95 -14/121 27/73 -3/26 10/27 -7/61 -4/35 13/35 -4/35 3/8 -6/53 -1/9 5/13 -5/46 17/44 -1/9 -2/19 12/31 -9/83 -4/37 7/18 -3/28 9/23 -2/19 11/28 -2/19 -3/29 2/5 -1/9 -2/19 11/27 -1/10 9/22 -2/21 -1/11 16/39 -1/10 7/17 -1/9 12/29 -1/9 -2/19 17/41 -1/10 5/12 -2/19 -7/67 3/7 -1/10 7/16 -4/41 -11/113 18/41 -3/31 -32/331 11/25 -5/52 15/34 -15/157 -2/21 4/9 -2/21 -1/11 5/11 -2/21 6/13 -2/21 -1/11 7/15 -1/10 8/17 -3/32 1/2 -1/11 -2/23 7/13 -1/12 13/24 -13/157 -12/145 19/35 -19/230 6/11 -7/85 -6/73 17/31 -4/49 11/20 -10/123 -3/37 5/9 -1/12 19/34 -3/37 -8/99 33/59 -5/62 14/25 -2/25 -1/13 9/16 -1/12 31/55 -7/86 22/39 -22/271 -3/37 13/23 -5/62 17/30 -7/87 -16/199 21/37 -13/162 4/7 -2/25 -5/63 19/33 -1/12 15/26 -2/25 -5/63 11/19 -3/38 7/12 -2/25 -1/13 17/29 -1/12 27/46 -2/25 -5/63 37/63 -3/38 10/17 -4/51 -1/13 3/5 -1/13 11/18 -4/53 -7/93 30/49 -4/53 -7/93 19/31 -3/40 27/44 -1/13 -4/53 8/13 -1/13 -4/53 13/21 -5/66 31/50 -1/13 -4/53 49/79 -4/53 18/29 -4/53 -7/93 5/8 -1/13 -2/27 22/35 -8/107 -21/281 17/27 -7/94 46/73 -9/121 -2/27 29/46 -7/94 41/65 -29/390 12/19 -17/229 -2/27 7/11 -5/68 23/36 -3/41 -4/55 39/61 -1/14 16/25 -1/13 -2/27 9/14 -8/109 -3/41 20/31 -11/151 -4/55 11/17 -1/14 24/37 -3/41 -10/137 13/20 -4/55 -5/69 2/3 -1/14 13/19 -4/57 24/35 -16/229 -3/43 11/16 -5/71 -4/57 9/13 -5/72 25/36 -3/43 -2/29 41/59 -5/72 16/23 -3/43 -2/29 23/33 -3/43 7/10 -11/159 -2/29 19/27 -15/218 31/44 -11/160 43/61 -9/131 12/17 -12/175 -5/73 41/58 -5/73 -18/263 29/41 -3/44 46/65 -3/43 -2/29 17/24 -2/29 -9/131 22/31 -5/73 -8/117 5/7 -3/44 28/39 -2/29 -1/15 23/32 -3/44 18/25 -15/221 -4/59 31/43 -13/192 44/61 -5/74 13/18 -6/89 -1/15 8/11 -6/89 -1/15 27/37 -6/89 19/26 -7/104 30/41 -8/119 -33/491 11/15 -11/164 3/4 -1/15 -6/91 19/25 -3/46 16/21 -1/15 -4/61 13/17 -3/46 23/30 -8/123 -21/323 10/13 -8/123 -5/77 27/35 -3/46 17/22 -9/139 -2/31 7/9 -2/31 25/32 -16/249 -7/109 18/23 -2/31 -3/47 29/37 -5/78 11/14 -5/78 15/19 -11/172 19/24 -3/47 -28/439 42/53 -13/204 23/29 -7/110 4/5 -4/63 -5/79 9/11 -1/16 14/17 -14/225 -13/209 33/40 -11/177 -10/161 52/63 -1/16 19/23 -1/16 24/29 -9/145 -8/129 5/6 -6/97 -5/81 11/13 -3/49 17/20 -8/131 -13/213 6/7 -11/181 -2/33 19/22 -2/33 -13/215 13/15 -7/116 20/23 -5/83 -28/465 7/8 -3/50 15/17 -4/67 8/9 -11/185 -6/101 1/1 -1/18 10/9 -1/19 -18/343 9/8 -6/115 -11/211 8/7 -3/58 23/20 -28/543 -5/97 15/13 -7/136 7/6 -2/39 -11/215 27/23 -5/98 20/17 -13/255 -8/157 33/28 -14/275 -3/59 13/11 -3/59 19/16 -7/138 25/21 -15/296 6/5 -5/99 -6/119 11/9 -1/20 16/13 -13/261 -12/241 37/30 -10/201 -9/181 21/17 -1/20 26/21 -8/161 -7/141 5/4 -5/101 -4/81 34/27 -3/61 -2/41 29/23 -7/142 24/19 -28/569 -3/61 67/53 -3/61 43/34 -3/61 -50/1017 19/15 -11/224 33/26 -3/61 -8/163 14/11 -5/102 37/29 -5/102 60/47 -7/143 -16/327 23/18 -3/61 -2/41 9/7 -2/41 31/24 -7/144 22/17 -2/41 -9/185 79/61 -7/144 57/44 -12/247 -5/103 35/27 -3/62 13/10 -5/103 -8/165 30/23 -21/433 -8/165 17/13 -3/62 38/29 -33/683 -10/207 21/16 -4/83 -1/21 4/3 -6/125 -1/21 23/17 -1/21 42/31 -1/21 -62/1303 19/14 -1/21 -28/589 15/11 -11/232 41/30 -33/697 -8/169 67/49 -7/148 26/19 -7/148 11/8 -1/21 -6/127 29/21 -5/106 47/34 -1/21 -4/85 18/13 -1/21 -6/127 43/31 -13/276 68/49 -41/871 -4/85 93/67 -4/85 118/85 -4/85 -71/1509 25/18 -4/85 -15/319 7/5 -3/64 31/22 -8/171 -5/107 86/61 -5/107 -22/471 55/39 -7/150 24/17 -9/193 -2/43 65/46 -2/43 -3/65 41/29 -3/64 99/70 -8/171 -21/449 58/41 -18/385 -5/107 75/53 -2/43 17/12 -5/107 -12/257 61/43 -9/193 44/31 -11/236 115/81 -11/236 186/131 -9/193 -2/43 71/50 -13/279 -2/43 27/19 -15/322 37/26 -41/881 -2/43 47/33 -2/43 57/40 -2/43 -63/1355 10/7 -2/43 -11/237 33/23 -3/65 56/39 -1/22 23/16 -2/43 -3/65 59/41 -5/108 36/25 -2/43 -3/65 49/34 -14/303 -3/65 62/43 -1/22 13/9 -5/108 3/2 -1/22 23/15 -1/22 20/13 -5/111 -4/89 37/24 -10/223 -3/67 17/11 -1/22 65/42 -37/823 -4/89 48/31 -4/89 -11/245 31/20 -4/89 -11/245 14/9 -3/67 -8/179 39/25 -2/45 25/16 -2/45 -1/23 61/39 -1/22 36/23 -4/89 -3/67 47/30 -7/157 -2/45 11/7 -5/112 30/19 -27/607 -2/45 49/31 -2/45 68/43 -2/45 -61/1373 19/12 -2/45 -17/383 46/29 -7/158 73/46 -2/45 -9/203 100/63 -2/45 -5/113 27/17 -7/158 62/39 -52/1175 -5/113 35/22 -21/475 -8/181 8/5 -2/45 -1/23 37/23 -3/68 29/18 -7/159 -4/91 50/31 -4/91 -1/23 71/44 -3/68 21/13 -5/114 76/47 -1/23 -8/185 131/81 -1/24 55/34 -1/21 0/1 34/21 -3/68 13/8 -4/91 -1/23 44/27 -4/91 -1/23 31/19 -3/68 80/49 -10/227 -7/159 49/30 -7/159 -4/91 116/71 -4/91 -41/933 67/41 -5/114 18/11 -7/159 -4/91 5/3 -1/23 17/10 -1/23 -4/93 63/37 -3/70 46/27 -5/117 -2/47 75/44 -1/23 -2/47 29/17 -1/24 41/24 -3/70 12/7 -1/23 -2/47 31/18 -1/23 -2/47 19/11 -3/70 45/26 -8/187 -5/117 26/15 -5/117 -2/47 7/4 -5/117 -2/47 30/17 -16/377 -7/165 53/30 -2/47 -7/165 76/43 -2/47 -3/71 23/13 -5/118 62/35 -14/331 -31/733 39/22 -3/71 -22/521 55/31 -7/166 16/9 -1/24 41/23 -2/47 25/14 -1/23 -2/47 59/33 -5/118 34/19 -8/189 -3/71 77/43 -3/71 120/67 -3/71 -28/663 43/24 -3/71 -10/237 9/5 -1/24 20/11 -3/71 -10/237 51/28 -3/71 -4/95 31/17 -4/95 42/23 -9/214 11/6 -6/143 -7/167 13/7 -1/24 15/8 -8/193 -7/169 32/17 -19/459 -6/145 17/9 -9/218 2/1 -2/49 -1/25 15/7 -1/26 28/13 -1/25 -2/51 41/19 -1/26 13/6 -1/25 -2/51 24/11 -3/76 11/5 -2/51 20/9 -4/103 -5/129 49/22 -4/105 -3/79 29/13 -1/26 38/17 -1/26 47/21 -1/26 9/4 -1/25 -2/51 7/3 -1/26 19/8 -5/131 -4/105 50/21 -4/105 -27/709 81/34 -7/184 112/47 -4/105 -11/289 31/13 -7/184 74/31 -13/342 43/18 -34/895 -3/79 141/59 -3/79 98/41 -3/79 -80/2107 55/23 -23/606 12/5 -7/185 -2/53 41/17 -1/26 70/29 -2/53 -1/27 99/41 -1/26 29/12 -2/53 -1/27 46/19 -3/80 109/45 -1/26 63/26 -5/133 -8/213 17/7 -1/27 56/23 -1/27 0/1 39/16 -1/26 22/9 -1/25 -2/51 27/11 -1/26 32/13 -1/26 5/2 -2/53 -1/27 33/13 -5/132 61/24 -1/26 28/11 -3/79 -2/53 51/20 -4/105 -3/79 23/9 -2/53 41/16 -19/505 -12/319 100/39 -72/1915 -5/133 59/23 -23/612 18/7 -3/80 67/26 -10/267 -7/187 49/19 -3/80 31/12 -4/107 -9/241 75/29 -1/27 44/17 -2/53 -1/27 101/39 -3/80 57/22 -7/187 -4/107 13/5 -5/134 21/8 -16/431 -1/27 29/11 -1/27 37/14 -1/27 -28/757 8/3 -1/27 -6/163 43/16 -1/27 0/1 35/13 -4/109 62/23 -3/82 89/33 -3/82 116/43 -1/27 -4/109 27/10 -4/109 -7/191 46/17 -14/383 -11/301 65/24 -27/739 -8/219 19/7 -7/192 68/25 -41/1127 -2/55 117/43 -2/55 166/61 -2/55 -95/2613 49/18 -2/55 -27/743 30/11 -2/55 -3/83 41/15 -3/83 52/19 -1/27 0/1 63/23 -5/138 11/4 -1/28 36/13 -3/79 -2/53 61/22 -10/269 -1/27 147/53 -1/27 86/31 -1/27 -16/433 25/9 -3/82 14/5 -1/27 -2/55 3/1 -1/28 16/5 -1/29 0/1 61/19 0/1 106/33 -1/25 0/1 45/14 -1/27 0/1 29/9 -1/28 71/22 -2/57 -1/29 42/13 -1/28 13/4 -2/57 -1/29 36/11 -1/27 -4/109 23/7 -1/28 56/17 -5/141 -14/395 89/27 -1/28 122/37 -4/113 -3/85 33/10 -5/141 -4/113 43/13 -3/85 10/3 -2/57 -5/143 47/14 -1/29 -2/59 84/25 -4/115 -1/29 37/11 -2/57 64/19 -2/57 -1/29 155/46 -2/57 -5/143 401/119 -5/143 246/73 -5/143 -8/229 91/27 -3/86 27/8 -3/86 17/5 -5/144 24/7 -14/405 -1/29 31/9 -1/29 38/11 -1/29 -22/639 7/2 -1/29 -4/117 39/11 -3/88 32/9 -1/29 -2/59 57/16 -5/147 -2/59 25/7 -2/59 43/12 -5/148 61/17 -17/504 140/39 -74/2195 -3/89 219/61 -3/89 79/22 -3/89 -40/1187 18/5 -4/119 -5/149 47/13 -1/30 76/21 -10/301 -9/271 29/8 -4/121 -3/91 11/3 -1/30 37/10 -1/33 0/1 63/17 0/1 89/24 -1/21 0/1 26/7 -1/27 0/1 41/11 -1/28 97/26 -8/231 -1/29 56/15 -1/31 0/1 71/19 -1/28 15/4 -1/29 -2/59 49/13 -1/28 34/9 -1/27 0/1 53/14 -7/199 -2/57 19/5 -1/29 23/6 -8/235 -5/147 27/7 -5/148 31/8 -2/59 -3/89 4/1 -1/30 25/6 -2/61 -9/275 21/5 -5/154 17/4 -1/31 0/1 47/11 -1/32 77/18 -1/30 30/7 -1/31 -4/125 13/3 0/1 22/5 -1/29 0/1 75/17 -1/30 53/12 -1/30 84/19 -1/29 0/1 31/7 -1/30 40/9 -5/149 -6/179 9/2 -3/91 -2/61 32/7 -3/91 -2/61 55/12 -2/61 -21/641 23/5 -3/92 60/13 -2/61 -5/153 97/21 -3/92 231/50 -2/61 -1/31 134/29 -2/61 -5/153 37/8 -3/92 14/3 -6/185 -1/31 33/7 -1/31 52/11 -1/31 -22/683 19/4 -1/31 -8/249 5/1 -1/32 26/5 -1/29 -2/59 21/4 -1/30 37/7 -3/92 16/3 -1/31 -6/187 59/11 -3/94 43/8 -1/31 0/1 27/5 -2/63 65/12 -1/31 -2/63 168/31 -2/63 -3/95 439/81 -3/95 271/50 -3/95 -4/127 103/19 -1/32 38/7 -1/32 11/2 -2/63 -3/95 17/3 -1/32 23/4 -4/129 -3/97 6/1 -2/65 -1/33 25/4 -1/39 0/1 69/11 0/1 113/18 -1/3 0/1 44/7 -1/21 0/1 19/3 -1/30 32/5 -4/123 -1/31 45/7 -3/94 13/2 -1/32 46/7 -1/33 0/1 33/5 -1/32 20/3 -1/33 0/1 47/7 -7/226 27/4 -2/65 -5/163 7/1 -1/33 22/3 -1/34 37/5 -1/34 15/2 -1/33 -2/67 23/3 -3/104 8/1 -1/31 0/1 25/3 -1/34 17/2 -2/65 -1/33 9/1 -1/34 19/2 -4/139 -1/35 10/1 -1/35 -2/71 1/0 -1/37 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(381,182,538,257) (-1/2,-8/17) -> (46/65,17/24) Hyperbolic Matrix(77,36,524,245) (-8/17,-7/15) -> (1/7,4/27) Hyperbolic Matrix(73,34,526,245) (-7/15,-13/28) -> (3/22,1/7) Hyperbolic Matrix(4473,2074,1046,485) (-13/28,-19/41) -> (47/11,77/18) Hyperbolic Matrix(1711,792,-4392,-2033) (-19/41,-6/13) -> (-30/77,-37/95) Hyperbolic Matrix(2521,1160,1480,681) (-6/13,-17/37) -> (63/37,46/27) Hyperbolic Matrix(2141,982,1258,577) (-17/37,-11/24) -> (17/10,63/37) Hyperbolic Matrix(961,440,1400,641) (-11/24,-16/35) -> (24/35,11/16) Hyperbolic Matrix(1327,606,2354,1075) (-16/35,-5/11) -> (31/55,22/39) Hyperbolic Matrix(75,34,-514,-233) (-5/11,-14/31) -> (-4/27,-1/7) Hyperbolic Matrix(1241,560,800,361) (-14/31,-9/20) -> (31/20,14/9) Hyperbolic Matrix(361,162,-1522,-683) (-9/20,-13/29) -> (-5/21,-9/38) Hyperbolic Matrix(795,356,364,163) (-13/29,-4/9) -> (24/11,11/5) Hyperbolic Matrix(2441,1080,1720,761) (-4/9,-19/43) -> (61/43,44/31) Hyperbolic Matrix(1861,822,1578,697) (-19/43,-15/34) -> (33/28,13/11) Hyperbolic Matrix(2863,1262,1858,819) (-15/34,-26/59) -> (20/13,37/24) Hyperbolic Matrix(427,188,-2428,-1069) (-26/59,-11/25) -> (-3/17,-10/57) Hyperbolic Matrix(355,156,644,283) (-11/25,-7/16) -> (11/20,5/9) Hyperbolic Matrix(353,154,-1914,-835) (-7/16,-17/39) -> (-5/27,-7/38) Hyperbolic Matrix(923,402,-2482,-1081) (-17/39,-10/23) -> (-16/43,-13/35) Hyperbolic Matrix(1199,520,920,399) (-10/23,-13/30) -> (13/10,30/23) Hyperbolic Matrix(209,90,-490,-211) (-13/30,-3/7) -> (-3/7,-17/40) Parabolic Matrix(2575,1094,346,147) (-17/40,-31/73) -> (37/5,15/2) Hyperbolic Matrix(1319,560,-6880,-2921) (-31/73,-14/33) -> (-14/73,-9/47) Hyperbolic Matrix(1665,706,974,413) (-14/33,-11/26) -> (41/24,12/7) Hyperbolic Matrix(4225,1786,1734,733) (-11/26,-30/71) -> (56/23,39/16) Hyperbolic Matrix(10183,4302,6578,2779) (-30/71,-49/116) -> (65/42,48/31) Hyperbolic Matrix(1937,818,-9138,-3859) (-49/116,-19/45) -> (-7/33,-25/118) Hyperbolic Matrix(1801,760,3320,1401) (-19/45,-27/64) -> (13/24,19/35) Hyperbolic Matrix(7123,3004,1316,555) (-27/64,-35/83) -> (27/5,65/12) Hyperbolic Matrix(7675,3236,2284,963) (-35/83,-8/19) -> (84/25,37/11) Hyperbolic Matrix(343,144,-1584,-665) (-8/19,-13/31) -> (-5/23,-8/37) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(3443,1442,-9362,-3921) (-31/74,-18/43) -> (-32/87,-25/68) Hyperbolic Matrix(3643,1524,1996,835) (-18/43,-23/55) -> (31/17,42/23) Hyperbolic Matrix(3435,1436,964,403) (-23/55,-5/12) -> (57/16,25/7) Hyperbolic Matrix(1917,796,2324,965) (-5/12,-22/53) -> (14/17,33/40) Hyperbolic Matrix(4305,1786,1574,653) (-22/53,-17/41) -> (41/15,52/19) Hyperbolic Matrix(1367,566,954,395) (-17/41,-12/29) -> (10/7,33/23) Hyperbolic Matrix(475,196,-1156,-477) (-12/29,-7/17) -> (-7/17,-16/39) Parabolic Matrix(679,278,1082,443) (-16/39,-9/22) -> (5/8,22/35) Hyperbolic Matrix(201,82,-1282,-523) (-9/22,-11/27) -> (-3/19,-5/32) Hyperbolic Matrix(875,356,204,83) (-11/27,-2/5) -> (30/7,13/3) Hyperbolic Matrix(199,78,722,283) (-2/5,-9/23) -> (3/11,8/29) Hyperbolic Matrix(1839,718,1442,563) (-9/23,-16/41) -> (14/11,37/29) Hyperbolic Matrix(5637,2198,2362,921) (-16/41,-23/59) -> (31/13,74/31) Hyperbolic Matrix(10157,3958,3082,1201) (-23/59,-30/77) -> (56/17,89/27) Hyperbolic Matrix(719,280,-5960,-2321) (-37/95,-7/18) -> (-7/58,-3/25) Hyperbolic Matrix(197,76,324,125) (-7/18,-5/13) -> (3/5,11/18) Hyperbolic Matrix(193,74,326,125) (-5/13,-8/21) -> (10/17,3/5) Hyperbolic Matrix(515,196,1164,443) (-8/21,-19/50) -> (15/34,4/9) Hyperbolic Matrix(901,342,-3222,-1223) (-19/50,-11/29) -> (-7/25,-19/68) Hyperbolic Matrix(1289,488,1672,633) (-11/29,-14/37) -> (10/13,27/35) Hyperbolic Matrix(1481,560,320,121) (-14/37,-3/8) -> (37/8,14/3) Hyperbolic Matrix(317,118,1722,641) (-3/8,-16/43) -> (2/11,7/38) Hyperbolic Matrix(1527,566,634,235) (-13/35,-10/27) -> (12/5,41/17) Hyperbolic Matrix(2411,892,-8252,-3053) (-10/27,-27/73) -> (-19/65,-26/89) Hyperbolic Matrix(2921,1080,760,281) (-27/73,-17/46) -> (23/6,27/7) Hyperbolic Matrix(65,24,696,257) (-17/46,-24/65) -> (0/1,1/10) Hyperbolic Matrix(2411,890,4310,1591) (-24/65,-7/19) -> (33/59,14/25) Hyperbolic Matrix(4811,1770,2150,791) (-7/19,-32/87) -> (38/17,47/21) Hyperbolic Matrix(7841,2882,-26562,-9763) (-25/68,-43/117) -> (-31/105,-49/166) Hyperbolic Matrix(9171,3370,3350,1231) (-43/117,-18/49) -> (52/19,63/23) Hyperbolic Matrix(1957,718,1202,441) (-18/49,-11/30) -> (13/8,44/27) Hyperbolic Matrix(1327,486,314,115) (-11/30,-15/41) -> (21/5,17/4) Hyperbolic Matrix(695,254,-2334,-853) (-15/41,-4/11) -> (-14/47,-11/37) Hyperbolic Matrix(1439,520,440,159) (-4/11,-13/36) -> (13/4,36/11) Hyperbolic Matrix(877,316,1124,405) (-13/36,-9/25) -> (7/9,25/32) Hyperbolic Matrix(1999,718,1122,403) (-9/25,-14/39) -> (16/9,41/23) Hyperbolic Matrix(2621,940,1620,581) (-14/39,-5/14) -> (55/34,34/21) Hyperbolic Matrix(681,242,-1922,-683) (-5/14,-11/31) -> (-11/31,-17/48) Parabolic Matrix(1793,634,806,285) (-17/48,-6/17) -> (20/9,49/22) Hyperbolic Matrix(1175,414,1666,587) (-6/17,-13/37) -> (43/61,12/17) Hyperbolic Matrix(2341,822,618,217) (-13/37,-7/20) -> (53/14,19/5) Hyperbolic Matrix(3135,1094,2026,707) (-7/20,-15/43) -> (17/11,65/42) Hyperbolic Matrix(2335,814,2946,1027) (-15/43,-8/23) -> (42/53,23/29) Hyperbolic Matrix(1411,490,550,191) (-8/23,-1/3) -> (59/23,18/7) Hyperbolic Matrix(1471,470,410,131) (-1/3,-7/22) -> (43/12,61/17) Hyperbolic Matrix(1523,484,236,75) (-7/22,-13/41) -> (45/7,13/2) Hyperbolic Matrix(6029,1910,3690,1169) (-13/41,-6/19) -> (116/71,67/41) Hyperbolic Matrix(1167,368,352,111) (-6/19,-11/35) -> (43/13,10/3) Hyperbolic Matrix(1571,492,1108,347) (-11/35,-5/16) -> (17/12,61/43) Hyperbolic Matrix(521,162,-1682,-523) (-5/16,-9/29) -> (-9/29,-13/42) Parabolic Matrix(1797,556,404,125) (-13/42,-4/13) -> (40/9,9/2) Hyperbolic Matrix(1439,440,520,159) (-4/13,-11/36) -> (11/4,36/13) Hyperbolic Matrix(1037,316,804,245) (-11/36,-7/23) -> (9/7,31/24) Hyperbolic Matrix(1609,488,1032,313) (-7/23,-10/33) -> (14/9,39/25) Hyperbolic Matrix(403,122,1318,399) (-10/33,-3/10) -> (11/36,4/13) Hyperbolic Matrix(1313,392,968,289) (-3/10,-14/47) -> (42/31,19/14) Hyperbolic Matrix(283,84,1196,355) (-11/37,-8/27) -> (4/17,5/21) Hyperbolic Matrix(1081,320,1760,521) (-8/27,-13/44) -> (27/44,8/13) Hyperbolic Matrix(11411,3370,4710,1391) (-13/44,-31/105) -> (109/45,63/26) Hyperbolic Matrix(21113,6232,15208,4489) (-49/166,-18/61) -> (118/85,25/18) Hyperbolic Matrix(1363,402,-6242,-1841) (-18/61,-5/17) -> (-19/87,-12/55) Hyperbolic Matrix(3847,1128,2152,631) (-5/17,-17/58) -> (25/14,59/33) Hyperbolic Matrix(621,182,58,17) (-17/58,-12/41) -> (10/1,1/0) Hyperbolic Matrix(1415,414,1186,347) (-12/41,-19/65) -> (25/21,6/5) Hyperbolic Matrix(5313,1552,3728,1089) (-26/89,-7/24) -> (57/40,10/7) Hyperbolic Matrix(563,164,1356,395) (-7/24,-9/31) -> (17/41,5/12) Hyperbolic Matrix(283,82,-1522,-441) (-9/31,-2/7) -> (-8/43,-5/27) Hyperbolic Matrix(277,78,1282,361) (-2/7,-9/32) -> (3/14,8/37) Hyperbolic Matrix(1445,406,1114,313) (-9/32,-7/25) -> (35/27,13/10) Hyperbolic Matrix(5441,1520,3440,961) (-19/68,-12/43) -> (68/43,19/12) Hyperbolic Matrix(1717,478,722,201) (-12/43,-5/18) -> (19/8,50/21) Hyperbolic Matrix(277,76,164,45) (-5/18,-3/11) -> (5/3,17/10) Hyperbolic Matrix(273,74,166,45) (-3/11,-4/15) -> (18/11,5/3) Hyperbolic Matrix(271,72,-2232,-593) (-4/15,-17/64) -> (-1/8,-4/33) Hyperbolic Matrix(2395,636,7844,2083) (-17/64,-13/49) -> (29/95,11/36) Hyperbolic Matrix(2287,606,434,115) (-13/49,-9/34) -> (21/4,37/7) Hyperbolic Matrix(1195,316,1524,403) (-9/34,-5/19) -> (29/37,11/14) Hyperbolic Matrix(595,156,164,43) (-5/19,-1/4) -> (29/8,11/3) Hyperbolic Matrix(159,38,682,163) (-1/4,-5/21) -> (3/13,7/30) Hyperbolic Matrix(997,236,1204,285) (-9/38,-4/17) -> (24/29,5/6) Hyperbolic Matrix(155,36,-676,-157) (-4/17,-3/13) -> (-3/13,-8/35) Parabolic Matrix(1401,320,880,201) (-8/35,-5/22) -> (35/22,8/5) Hyperbolic Matrix(723,164,1036,235) (-5/22,-7/31) -> (23/33,7/10) Hyperbolic Matrix(2633,594,1086,245) (-7/31,-9/40) -> (63/26,17/7) Hyperbolic Matrix(1085,244,876,197) (-9/40,-2/9) -> (26/21,5/4) Hyperbolic Matrix(1179,260,1900,419) (-2/9,-9/41) -> (49/79,18/29) Hyperbolic Matrix(767,168,872,191) (-9/41,-7/32) -> (7/8,15/17) Hyperbolic Matrix(7011,1532,1588,347) (-7/32,-19/87) -> (75/17,53/12) Hyperbolic Matrix(3477,758,922,201) (-12/55,-5/23) -> (49/13,34/9) Hyperbolic Matrix(1481,320,560,121) (-8/37,-3/14) -> (37/14,8/3) Hyperbolic Matrix(2087,446,1474,315) (-3/14,-13/61) -> (75/53,17/12) Hyperbolic Matrix(967,206,5234,1115) (-13/61,-10/47) -> (12/65,5/27) Hyperbolic Matrix(865,184,456,97) (-10/47,-7/33) -> (17/9,2/1) Hyperbolic Matrix(23753,5032,8728,1849) (-25/118,-18/85) -> (166/61,49/18) Hyperbolic Matrix(10197,2158,6242,1321) (-18/85,-11/52) -> (49/30,116/71) Hyperbolic Matrix(3349,708,2332,493) (-11/52,-4/19) -> (56/39,23/16) Hyperbolic Matrix(963,202,758,159) (-4/19,-5/24) -> (33/26,14/11) Hyperbolic Matrix(49,10,-250,-51) (-5/24,-1/5) -> (-1/5,-5/26) Parabolic Matrix(6041,1160,1880,361) (-5/26,-14/73) -> (106/33,45/14) Hyperbolic Matrix(4599,880,1040,199) (-9/47,-4/21) -> (84/19,31/7) Hyperbolic Matrix(643,122,838,159) (-4/21,-3/16) -> (23/30,10/13) Hyperbolic Matrix(1081,202,198,37) (-3/16,-8/43) -> (38/7,11/2) Hyperbolic Matrix(1521,280,440,81) (-7/38,-2/11) -> (38/11,7/2) Hyperbolic Matrix(439,78,242,43) (-2/11,-3/17) -> (9/5,20/11) Hyperbolic Matrix(6113,1072,1648,289) (-10/57,-7/40) -> (89/24,26/7) Hyperbolic Matrix(1259,220,1940,339) (-7/40,-4/23) -> (24/37,13/20) Hyperbolic Matrix(3001,520,1160,201) (-4/23,-5/29) -> (75/29,44/17) Hyperbolic Matrix(1157,198,1642,281) (-5/29,-1/6) -> (31/44,43/61) Hyperbolic Matrix(523,84,716,115) (-1/6,-3/19) -> (27/37,19/26) Hyperbolic Matrix(993,154,806,125) (-5/32,-2/13) -> (16/13,37/30) Hyperbolic Matrix(517,78,802,121) (-2/13,-3/20) -> (9/14,20/31) Hyperbolic Matrix(1553,232,328,49) (-3/20,-4/27) -> (52/11,19/4) Hyperbolic Matrix(1483,204,836,115) (-1/7,-3/22) -> (39/22,55/31) Hyperbolic Matrix(925,124,276,37) (-3/22,-2/15) -> (10/3,47/14) Hyperbolic Matrix(785,104,1336,177) (-2/15,-3/23) -> (37/63,10/17) Hyperbolic Matrix(917,118,1562,201) (-3/23,-1/8) -> (27/46,37/63) Hyperbolic Matrix(6281,760,1000,121) (-4/33,-7/58) -> (113/18,44/7) Hyperbolic Matrix(1771,212,1228,147) (-3/25,-2/17) -> (62/43,13/9) Hyperbolic Matrix(317,36,44,5) (-2/17,-1/9) -> (7/1,22/3) Hyperbolic Matrix(313,34,46,5) (-1/9,-1/10) -> (27/4,7/1) Hyperbolic Matrix(305,24,216,17) (-1/10,0/1) -> (24/17,65/46) Hyperbolic Matrix(977,-102,182,-19) (1/10,1/9) -> (59/11,43/8) Hyperbolic Matrix(1147,-134,214,-25) (1/9,2/17) -> (16/3,59/11) Hyperbolic Matrix(357,-44,284,-35) (2/17,1/8) -> (5/4,34/27) Hyperbolic Matrix(1343,-176,496,-65) (1/8,2/15) -> (46/17,65/24) Hyperbolic Matrix(2643,-358,598,-81) (2/15,3/22) -> (53/12,84/19) Hyperbolic Matrix(1045,-156,556,-83) (4/27,3/20) -> (15/8,32/17) Hyperbolic Matrix(1009,-152,312,-47) (3/20,2/13) -> (42/13,13/4) Hyperbolic Matrix(243,-38,518,-81) (2/13,3/19) -> (7/15,8/17) Hyperbolic Matrix(449,-72,792,-127) (3/19,1/6) -> (17/30,21/37) Hyperbolic Matrix(715,-124,444,-77) (1/6,3/17) -> (37/23,29/18) Hyperbolic Matrix(543,-98,338,-61) (3/17,2/11) -> (8/5,37/23) Hyperbolic Matrix(7497,-1382,1622,-299) (7/38,12/65) -> (134/29,37/8) Hyperbolic Matrix(1721,-320,640,-119) (5/27,3/16) -> (43/16,35/13) Hyperbolic Matrix(2087,-394,874,-165) (3/16,4/21) -> (74/31,43/18) Hyperbolic Matrix(871,-168,1208,-233) (4/21,1/5) -> (31/43,44/61) Hyperbolic Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(821,-178,3058,-663) (8/37,5/23) -> (11/41,18/67) Hyperbolic Matrix(263,-58,458,-101) (5/23,2/9) -> (4/7,19/33) Hyperbolic Matrix(359,-82,162,-37) (2/9,3/13) -> (11/5,20/9) Hyperbolic Matrix(1913,-448,1328,-311) (7/30,4/17) -> (36/25,49/34) Hyperbolic Matrix(773,-186,1226,-295) (5/21,1/4) -> (29/46,41/65) Hyperbolic Matrix(413,-108,348,-91) (1/4,5/19) -> (13/11,19/16) Hyperbolic Matrix(2089,-552,632,-167) (5/19,9/34) -> (33/10,43/13) Hyperbolic Matrix(1929,-512,1232,-327) (9/34,4/15) -> (36/23,47/30) Hyperbolic Matrix(4733,-1266,3346,-895) (4/15,15/56) -> (99/70,58/41) Hyperbolic Matrix(9591,-2570,5930,-1589) (15/56,11/41) -> (131/81,55/34) Hyperbolic Matrix(3563,-958,4318,-1161) (18/67,7/26) -> (33/40,52/63) Hyperbolic Matrix(693,-188,188,-51) (7/26,3/11) -> (11/3,37/10) Hyperbolic Matrix(1253,-346,3386,-935) (8/29,13/47) -> (27/73,10/27) Hyperbolic Matrix(1285,-356,3476,-963) (13/47,5/18) -> (17/46,27/73) Hyperbolic Matrix(1439,-402,562,-157) (5/18,7/25) -> (23/9,41/16) Hyperbolic Matrix(2343,-658,3778,-1061) (7/25,9/32) -> (31/50,49/79) Hyperbolic Matrix(2903,-818,1778,-501) (9/32,2/7) -> (80/49,49/30) Hyperbolic Matrix(527,-154,154,-45) (2/7,5/17) -> (17/5,24/7) Hyperbolic Matrix(277,-82,402,-119) (5/17,3/10) -> (11/16,9/13) Hyperbolic Matrix(2089,-632,552,-167) (3/10,10/33) -> (34/9,53/14) Hyperbolic Matrix(645,-196,2116,-643) (10/33,7/23) -> (7/23,18/59) Parabolic Matrix(24455,-7464,17224,-5257) (18/59,29/95) -> (115/81,186/131) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(1181,-418,178,-63) (6/17,11/31) -> (33/5,20/3) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(1699,-622,702,-257) (4/11,11/30) -> (29/12,46/19) Hyperbolic Matrix(1111,-408,1288,-473) (11/30,18/49) -> (6/7,19/22) Hyperbolic Matrix(2223,-818,818,-301) (18/49,7/19) -> (19/7,68/25) Hyperbolic Matrix(1343,-496,176,-65) (7/19,17/46) -> (15/2,23/3) Hyperbolic Matrix(3239,-1202,962,-357) (10/27,13/35) -> (37/11,64/19) Hyperbolic Matrix(1721,-640,320,-119) (13/35,3/8) -> (43/8,27/5) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(2281,-880,1760,-679) (5/13,17/44) -> (57/44,35/27) Hyperbolic Matrix(1903,-736,1616,-625) (17/44,12/31) -> (20/17,33/28) Hyperbolic Matrix(1037,-402,1442,-559) (12/31,7/18) -> (23/32,18/25) Hyperbolic Matrix(1439,-562,402,-157) (7/18,9/23) -> (25/7,43/12) Hyperbolic Matrix(2041,-800,1120,-439) (9/23,11/28) -> (51/28,31/17) Hyperbolic Matrix(1663,-656,976,-385) (11/28,2/5) -> (46/27,75/44) Hyperbolic Matrix(655,-266,426,-173) (2/5,11/27) -> (23/15,20/13) Hyperbolic Matrix(1961,-800,880,-359) (11/27,9/22) -> (49/22,29/13) Hyperbolic Matrix(1475,-604,2044,-837) (9/22,16/39) -> (44/61,13/18) Hyperbolic Matrix(2239,-920,1560,-641) (16/39,7/17) -> (33/23,56/39) Hyperbolic Matrix(1699,-702,622,-257) (7/17,12/29) -> (30/11,41/15) Hyperbolic Matrix(1583,-656,736,-305) (12/29,17/41) -> (15/7,28/13) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(529,-232,472,-207) (7/16,18/41) -> (10/9,9/8) Hyperbolic Matrix(1917,-842,362,-159) (18/41,11/25) -> (37/7,16/3) Hyperbolic Matrix(3303,-1456,2416,-1065) (11/25,15/34) -> (41/30,67/49) Hyperbolic Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(439,-202,602,-277) (5/11,6/13) -> (8/11,27/37) Hyperbolic Matrix(1583,-736,656,-305) (6/13,7/15) -> (41/17,70/29) Hyperbolic Matrix(407,-194,514,-245) (8/17,1/2) -> (19/24,42/53) Hyperbolic Matrix(183,-98,338,-181) (1/2,7/13) -> (7/13,13/24) Parabolic Matrix(1217,-662,182,-99) (19/35,6/11) -> (20/3,47/7) Hyperbolic Matrix(413,-226,466,-255) (6/11,17/31) -> (15/17,8/9) Hyperbolic Matrix(2041,-1120,800,-439) (17/31,11/20) -> (51/20,23/9) Hyperbolic Matrix(693,-386,386,-215) (5/9,19/34) -> (43/24,9/5) Hyperbolic Matrix(2129,-1190,950,-531) (19/34,33/59) -> (47/21,9/4) Hyperbolic Matrix(1127,-632,872,-489) (14/25,9/16) -> (31/24,22/17) Hyperbolic Matrix(1613,-908,588,-331) (9/16,31/55) -> (63/23,11/4) Hyperbolic Matrix(2479,-1400,1560,-881) (22/39,13/23) -> (27/17,62/39) Hyperbolic Matrix(639,-362,842,-477) (13/23,17/30) -> (3/4,19/25) Hyperbolic Matrix(1761,-1000,280,-159) (21/37,4/7) -> (44/7,19/3) Hyperbolic Matrix(965,-556,1116,-643) (19/33,15/26) -> (19/22,13/15) Hyperbolic Matrix(1647,-952,1192,-689) (15/26,11/19) -> (29/21,47/34) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(1185,-694,934,-547) (7/12,17/29) -> (19/15,33/26) Hyperbolic Matrix(1663,-976,656,-385) (17/29,27/46) -> (5/2,33/13) Hyperbolic Matrix(2383,-1458,1538,-941) (11/18,30/49) -> (48/31,31/20) Hyperbolic Matrix(2903,-1778,818,-501) (30/49,19/31) -> (39/11,32/9) Hyperbolic Matrix(1933,-1186,546,-335) (19/31,27/44) -> (7/2,39/11) Hyperbolic Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(2841,-1760,2000,-1239) (13/21,31/50) -> (71/50,27/19) Hyperbolic Matrix(715,-444,124,-77) (18/29,5/8) -> (23/4,6/1) Hyperbolic Matrix(2479,-1560,1400,-881) (22/35,17/27) -> (23/13,62/35) Hyperbolic Matrix(3731,-2350,2110,-1329) (17/27,46/73) -> (76/43,23/13) Hyperbolic Matrix(5741,-3618,2258,-1423) (46/73,29/46) -> (61/24,28/11) Hyperbolic Matrix(2403,-1516,1276,-805) (41/65,12/19) -> (32/17,17/9) Hyperbolic Matrix(539,-342,342,-217) (12/19,7/11) -> (11/7,30/19) Hyperbolic Matrix(1929,-1232,512,-327) (7/11,23/36) -> (15/4,49/13) Hyperbolic Matrix(2269,-1450,1050,-671) (23/36,39/61) -> (41/19,13/6) Hyperbolic Matrix(2733,-1748,1268,-811) (39/61,16/25) -> (28/13,41/19) Hyperbolic Matrix(877,-562,1122,-719) (16/25,9/14) -> (25/32,18/23) Hyperbolic Matrix(2383,-1538,1458,-941) (20/31,11/17) -> (67/41,18/11) Hyperbolic Matrix(1651,-1070,1310,-849) (11/17,24/37) -> (34/27,29/23) Hyperbolic Matrix(655,-426,266,-173) (13/20,2/3) -> (32/13,5/2) Hyperbolic Matrix(1283,-876,476,-325) (2/3,13/19) -> (35/13,62/23) Hyperbolic Matrix(3727,-2554,2634,-1805) (13/19,24/35) -> (58/41,75/53) Hyperbolic Matrix(1913,-1328,448,-311) (9/13,25/36) -> (17/4,47/11) Hyperbolic Matrix(6207,-4312,4792,-3329) (25/36,41/59) -> (79/61,57/44) Hyperbolic Matrix(3115,-2166,2406,-1673) (41/59,16/23) -> (22/17,79/61) Hyperbolic Matrix(2239,-1560,920,-641) (16/23,23/33) -> (17/7,56/23) Hyperbolic Matrix(1269,-892,892,-627) (7/10,19/27) -> (27/19,37/26) Hyperbolic Matrix(2841,-2000,1760,-1239) (19/27,31/44) -> (71/44,21/13) Hyperbolic Matrix(5671,-4008,1688,-1193) (12/17,41/58) -> (47/14,84/25) Hyperbolic Matrix(4733,-3346,1266,-895) (41/58,29/41) -> (71/19,15/4) Hyperbolic Matrix(6911,-4890,1850,-1309) (29/41,46/65) -> (56/15,71/19) Hyperbolic Matrix(2153,-1526,1686,-1195) (17/24,22/31) -> (60/47,23/18) Hyperbolic Matrix(351,-250,490,-349) (22/31,5/7) -> (5/7,28/39) Parabolic Matrix(1979,-1422,302,-217) (28/39,23/32) -> (13/2,46/7) Hyperbolic Matrix(3999,-2882,2882,-2077) (18/25,31/43) -> (43/31,68/49) Hyperbolic Matrix(557,-404,324,-235) (13/18,8/11) -> (12/7,31/18) Hyperbolic Matrix(4621,-3380,1940,-1419) (19/26,30/41) -> (50/21,81/34) Hyperbolic Matrix(1063,-778,138,-101) (30/41,11/15) -> (23/3,8/1) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(3067,-2332,1932,-1469) (19/25,16/21) -> (100/63,27/17) Hyperbolic Matrix(907,-692,772,-589) (16/21,13/17) -> (27/23,20/17) Hyperbolic Matrix(929,-712,792,-607) (13/17,23/30) -> (7/6,27/23) Hyperbolic Matrix(2281,-1760,880,-679) (27/35,17/22) -> (57/22,13/5) Hyperbolic Matrix(1127,-872,632,-489) (17/22,7/9) -> (41/23,25/14) Hyperbolic Matrix(2153,-1686,1526,-1195) (18/23,29/37) -> (55/39,24/17) Hyperbolic Matrix(1185,-934,694,-547) (11/14,15/19) -> (29/17,41/24) Hyperbolic Matrix(1273,-1006,1006,-795) (15/19,19/24) -> (43/34,19/15) Hyperbolic Matrix(357,-284,44,-35) (23/29,4/5) -> (8/1,25/3) Hyperbolic Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic Matrix(7363,-6078,1358,-1121) (52/63,19/23) -> (103/19,38/7) Hyperbolic Matrix(2015,-1666,306,-253) (19/23,24/29) -> (46/7,33/5) Hyperbolic Matrix(413,-348,108,-91) (5/6,11/13) -> (19/5,23/6) Hyperbolic Matrix(1903,-1616,736,-625) (11/13,17/20) -> (31/12,75/29) Hyperbolic Matrix(907,-772,692,-589) (17/20,6/7) -> (38/29,21/16) Hyperbolic Matrix(4153,-3608,2568,-2231) (13/15,20/23) -> (76/47,131/81) Hyperbolic Matrix(2011,-1750,470,-409) (20/23,7/8) -> (77/18,30/7) Hyperbolic Matrix(507,-452,212,-189) (8/9,1/1) -> (55/23,12/5) Hyperbolic Matrix(593,-648,248,-271) (1/1,10/9) -> (98/41,55/23) Hyperbolic Matrix(413,-466,226,-255) (9/8,8/7) -> (42/23,11/6) Hyperbolic Matrix(1583,-1818,1098,-1261) (8/7,23/20) -> (49/34,62/43) Hyperbolic Matrix(2081,-2398,558,-643) (23/20,15/13) -> (41/11,97/26) Hyperbolic Matrix(853,-986,186,-215) (15/13,7/6) -> (55/12,23/5) Hyperbolic Matrix(1809,-2152,712,-847) (19/16,25/21) -> (33/13,61/24) Hyperbolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(2077,-2564,644,-795) (37/30,21/17) -> (29/9,71/22) Hyperbolic Matrix(3057,-3782,662,-819) (21/17,26/21) -> (60/13,97/21) Hyperbolic Matrix(1591,-2008,248,-313) (29/23,24/19) -> (32/5,45/7) Hyperbolic Matrix(7351,-9290,2650,-3349) (24/19,67/53) -> (147/53,86/31) Hyperbolic Matrix(8231,-10408,2968,-3753) (67/53,43/34) -> (61/22,147/53) Hyperbolic Matrix(5079,-6482,3602,-4597) (37/29,60/47) -> (86/61,55/39) Hyperbolic Matrix(877,-1122,562,-719) (23/18,9/7) -> (39/25,25/16) Hyperbolic Matrix(885,-1156,676,-883) (30/23,17/13) -> (17/13,38/29) Parabolic Matrix(639,-842,362,-477) (21/16,4/3) -> (30/17,53/30) Hyperbolic Matrix(783,-1058,578,-781) (4/3,23/17) -> (23/17,42/31) Parabolic Matrix(1285,-1754,474,-647) (15/11,41/30) -> (65/24,19/7) Hyperbolic Matrix(4341,-5938,3058,-4183) (67/49,26/19) -> (44/31,115/81) Hyperbolic Matrix(439,-602,202,-277) (26/19,11/8) -> (13/6,24/11) Hyperbolic Matrix(1343,-1858,738,-1021) (47/34,18/13) -> (20/11,51/28) Hyperbolic Matrix(871,-1208,168,-233) (18/13,43/31) -> (5/1,26/5) Hyperbolic Matrix(12463,-17298,8978,-12461) (68/49,93/67) -> (93/67,118/85) Parabolic Matrix(1037,-1442,402,-559) (25/18,7/5) -> (49/19,31/12) Hyperbolic Matrix(1413,-1988,548,-771) (7/5,31/22) -> (67/26,49/19) Hyperbolic Matrix(5263,-7418,2938,-4141) (31/22,86/61) -> (120/67,43/24) Hyperbolic Matrix(4757,-6724,3364,-4755) (65/46,41/29) -> (41/29,99/70) Parabolic Matrix(36961,-52480,8000,-11359) (186/131,71/50) -> (231/50,134/29) Hyperbolic Matrix(3103,-4418,2178,-3101) (37/26,47/33) -> (47/33,57/40) Parabolic Matrix(3953,-5686,1526,-2195) (23/16,59/41) -> (101/39,57/22) Hyperbolic Matrix(4329,-6232,1672,-2407) (59/41,36/25) -> (44/17,101/39) Hyperbolic Matrix(277,-402,82,-119) (13/9,3/2) -> (27/8,17/5) Hyperbolic Matrix(587,-894,174,-265) (3/2,23/15) -> (91/27,27/8) Hyperbolic Matrix(787,-1214,94,-145) (37/24,17/11) -> (25/3,17/2) Hyperbolic Matrix(2715,-4244,1124,-1757) (25/16,61/39) -> (99/41,29/12) Hyperbolic Matrix(5007,-7834,2074,-3245) (61/39,36/23) -> (70/29,99/41) Hyperbolic Matrix(3039,-4802,1922,-3037) (30/19,49/31) -> (49/31,68/43) Parabolic Matrix(773,-1226,186,-295) (19/12,46/29) -> (4/1,25/6) Hyperbolic Matrix(1083,-1718,278,-441) (46/29,73/46) -> (31/8,4/1) Hyperbolic Matrix(12709,-20172,3772,-5987) (73/46,100/63) -> (64/19,155/46) Hyperbolic Matrix(3799,-6042,1482,-2357) (62/39,35/22) -> (41/16,100/39) Hyperbolic Matrix(2343,-3778,658,-1061) (29/18,50/31) -> (32/9,57/16) Hyperbolic Matrix(7439,-12002,3122,-5037) (50/31,71/44) -> (81/34,112/47) Hyperbolic Matrix(2293,-3706,826,-1335) (21/13,76/47) -> (86/31,25/9) Hyperbolic Matrix(2357,-3844,1444,-2355) (44/27,31/19) -> (31/19,80/49) Parabolic Matrix(1715,-2924,444,-757) (75/44,29/17) -> (27/7,31/8) Hyperbolic Matrix(837,-1444,484,-835) (31/18,19/11) -> (19/11,45/26) Parabolic Matrix(1493,-2586,586,-1015) (45/26,26/15) -> (28/11,51/20) Hyperbolic Matrix(263,-458,58,-101) (26/15,7/4) -> (9/2,32/7) Hyperbolic Matrix(449,-792,72,-127) (7/4,30/17) -> (6/1,25/4) Hyperbolic Matrix(4641,-8200,1720,-3039) (53/30,76/43) -> (116/43,27/10) Hyperbolic Matrix(3161,-5600,880,-1559) (62/35,39/22) -> (79/22,18/5) Hyperbolic Matrix(2407,-4274,994,-1765) (55/31,16/9) -> (46/19,109/45) Hyperbolic Matrix(2151,-3848,488,-873) (59/33,34/19) -> (22/5,75/17) Hyperbolic Matrix(6623,-11858,3698,-6621) (34/19,77/43) -> (77/43,120/67) Parabolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic Matrix(243,-518,38,-81) (2/1,15/7) -> (19/3,32/5) Hyperbolic Matrix(915,-2044,124,-277) (29/13,38/17) -> (22/3,37/5) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(5769,-13750,1750,-4171) (112/47,31/13) -> (89/27,122/37) Hyperbolic Matrix(8603,-20556,2396,-5725) (43/18,141/59) -> (219/61,79/22) Hyperbolic Matrix(17239,-41202,4802,-11477) (141/59,98/41) -> (140/39,219/61) Hyperbolic Matrix(605,-1476,116,-283) (39/16,22/9) -> (26/5,21/4) Hyperbolic Matrix(719,-1762,162,-397) (22/9,27/11) -> (31/7,40/9) Hyperbolic Matrix(1839,-4522,682,-1677) (27/11,32/13) -> (62/23,89/33) Hyperbolic Matrix(5599,-14360,1560,-4001) (100/39,59/23) -> (61/17,140/39) Hyperbolic Matrix(1589,-4092,492,-1267) (18/7,67/26) -> (71/22,42/13) Hyperbolic Matrix(639,-1682,242,-637) (21/8,29/11) -> (29/11,37/14) Parabolic Matrix(217,-582,22,-59) (8/3,43/16) -> (19/2,10/1) Hyperbolic Matrix(12031,-32450,3570,-9629) (89/33,116/43) -> (246/73,91/27) Hyperbolic Matrix(1253,-3386,346,-935) (27/10,46/17) -> (76/21,29/8) Hyperbolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(1181,-3218,258,-703) (49/18,30/11) -> (32/7,55/12) Hyperbolic Matrix(2493,-6908,668,-1851) (36/13,61/22) -> (97/26,56/15) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(2319,-7442,722,-2317) (16/5,61/19) -> (61/19,106/33) Parabolic Matrix(645,-2116,196,-643) (36/11,23/7) -> (23/7,56/17) Parabolic Matrix(4085,-13474,754,-2487) (122/37,33/10) -> (65/12,168/31) Hyperbolic Matrix(52443,-176716,9676,-32605) (155/46,401/119) -> (439/81,271/50) Hyperbolic Matrix(52039,-175362,9602,-32357) (401/119,246/73) -> (168/31,439/81) Hyperbolic Matrix(559,-1922,162,-557) (24/7,31/9) -> (31/9,38/11) Parabolic Matrix(1223,-4418,338,-1221) (18/5,47/13) -> (47/13,76/21) Parabolic Matrix(2143,-7938,578,-2141) (37/10,63/17) -> (63/17,89/24) Parabolic Matrix(821,-3058,178,-663) (26/7,41/11) -> (23/5,60/13) Hyperbolic Matrix(417,-1742,62,-259) (25/6,21/5) -> (47/7,27/4) Hyperbolic Matrix(10841,-50080,2000,-9239) (97/21,231/50) -> (271/50,103/19) Hyperbolic Matrix(463,-2178,98,-461) (14/3,33/7) -> (33/7,52/11) Parabolic Matrix(103,-578,18,-101) (11/2,17/3) -> (17/3,23/4) Parabolic Matrix(1519,-9522,242,-1517) (25/4,69/11) -> (69/11,113/18) Parabolic Matrix(37,-324,4,-35) (17/2,9/1) -> (9/1,19/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,76,1) Matrix(381,182,538,257) -> Matrix(69,-2,-1000,29) Matrix(77,36,524,245) -> Matrix(71,-2,-248,7) Matrix(73,34,526,245) -> Matrix(69,-2,-172,5) Matrix(4473,2074,1046,485) -> Matrix(1,0,-64,1) Matrix(1711,792,-4392,-2033) -> Matrix(77,-2,1964,-51) Matrix(2521,1160,1480,681) -> Matrix(275,-8,-6428,187) Matrix(2141,982,1258,577) -> Matrix(337,-10,-7852,233) Matrix(961,440,1400,641) -> Matrix(69,-2,-1000,29) Matrix(1327,606,2354,1075) -> Matrix(129,-4,-1580,49) Matrix(75,34,-514,-233) -> Matrix(67,-2,436,-13) Matrix(1241,560,800,361) -> Matrix(327,-10,-7292,223) Matrix(361,162,-1522,-683) -> Matrix(63,-2,788,-25) Matrix(795,356,364,163) -> Matrix(67,-2,-1708,51) Matrix(2441,1080,1720,761) -> Matrix(629,-20,-13492,429) Matrix(1861,822,1578,697) -> Matrix(245,-8,-4808,157) Matrix(2863,1262,1858,819) -> Matrix(121,-4,-2692,89) Matrix(427,188,-2428,-1069) -> Matrix(1,0,-24,1) Matrix(355,156,644,283) -> Matrix(65,-2,-812,25) Matrix(353,154,-1914,-835) -> Matrix(309,-10,2812,-91) Matrix(923,402,-2482,-1081) -> Matrix(307,-10,7276,-237) Matrix(1199,520,920,399) -> Matrix(57,-2,-1168,41) Matrix(209,90,-490,-211) -> Matrix(61,-2,1800,-59) Matrix(2575,1094,346,147) -> Matrix(59,-2,-1976,67) Matrix(1319,560,-6880,-2921) -> Matrix(59,-2,620,-21) Matrix(1665,706,974,413) -> Matrix(117,-4,-2720,93) Matrix(4225,1786,1734,733) -> Matrix(59,-2,-1504,51) Matrix(10183,4302,6578,2779) -> Matrix(1005,-34,-22376,757) Matrix(1937,818,-9138,-3859) -> Matrix(825,-28,8692,-295) Matrix(1801,760,3320,1401) -> Matrix(939,-32,-11356,387) Matrix(7123,3004,1316,555) -> Matrix(293,-10,-9288,317) Matrix(7675,3236,2284,963) -> Matrix(59,-2,-1740,59) Matrix(343,144,-1584,-665) -> Matrix(289,-10,3208,-111) Matrix(2271,952,1448,607) -> Matrix(287,-10,-6400,223) Matrix(3443,1442,-9362,-3921) -> Matrix(689,-24,16048,-559) Matrix(3643,1524,1996,835) -> Matrix(857,-30,-20368,713) Matrix(3435,1436,964,403) -> Matrix(227,-8,-6668,235) Matrix(1917,796,2324,965) -> Matrix(337,-12,-5420,193) Matrix(4305,1786,1574,653) -> Matrix(55,-2,-1512,55) Matrix(1367,566,954,395) -> Matrix(229,-8,-4952,173) Matrix(475,196,-1156,-477) -> Matrix(169,-6,4704,-167) Matrix(679,278,1082,443) -> Matrix(109,-4,-1444,53) Matrix(201,82,-1282,-523) -> Matrix(55,-2,468,-17) Matrix(875,356,204,83) -> Matrix(55,-2,-1732,63) Matrix(199,78,722,283) -> Matrix(51,-2,-280,11) Matrix(1839,718,1442,563) -> Matrix(203,-8,-4136,163) Matrix(5637,2198,2362,921) -> Matrix(923,-36,-24280,947) Matrix(10157,3958,3082,1201) -> Matrix(461,-18,-13036,509) Matrix(719,280,-5960,-2321) -> Matrix(51,-2,740,-29) Matrix(197,76,324,125) -> Matrix(151,-6,-1988,79) Matrix(193,74,326,125) -> Matrix(149,-6,-1912,77) Matrix(515,196,1164,443) -> Matrix(99,-4,-1064,43) Matrix(901,342,-3222,-1223) -> Matrix(489,-20,7604,-311) Matrix(1289,488,1672,633) -> Matrix(391,-16,-6036,247) Matrix(1481,560,320,121) -> Matrix(243,-10,-7460,307) Matrix(317,118,1722,641) -> Matrix(47,-2,-164,7) Matrix(1527,566,634,235) -> Matrix(189,-8,-5032,213) Matrix(2411,892,-8252,-3053) -> Matrix(1409,-60,23272,-991) Matrix(2921,1080,760,281) -> Matrix(469,-20,-13812,589) Matrix(65,24,696,257) -> Matrix(47,-2,-164,7) Matrix(2411,890,4310,1591) -> Matrix(375,-16,-4664,199) Matrix(4811,1770,2150,791) -> Matrix(93,-4,-2348,101) Matrix(7841,2882,-26562,-9763) -> Matrix(2417,-104,40508,-1743) Matrix(9171,3370,3350,1231) -> Matrix(139,-6,-3776,163) Matrix(1957,718,1202,441) -> Matrix(47,-2,-1104,47) Matrix(1327,486,314,115) -> Matrix(139,-6,-4332,187) Matrix(695,254,-2334,-853) -> Matrix(507,-22,8596,-373) Matrix(1439,520,440,159) -> Matrix(45,-2,-1192,53) Matrix(877,316,1124,405) -> Matrix(541,-24,-8408,373) Matrix(1999,718,1122,403) -> Matrix(179,-8,-4184,187) Matrix(2621,940,1620,581) -> Matrix(89,-4,-1980,89) Matrix(681,242,-1922,-683) -> Matrix(397,-18,8712,-395) Matrix(1793,634,806,285) -> Matrix(219,-10,-5672,259) Matrix(1175,414,1666,587) -> Matrix(653,-30,-9512,437) Matrix(2341,822,618,217) -> Matrix(173,-8,-4952,229) Matrix(3135,1094,2026,707) -> Matrix(643,-30,-14296,667) Matrix(2335,814,2946,1027) -> Matrix(1199,-56,-18820,879) Matrix(1411,490,550,191) -> Matrix(383,-18,-10192,479) Matrix(1471,470,410,131) -> Matrix(263,-14,-7796,415) Matrix(1523,484,236,75) -> Matrix(149,-8,-4712,253) Matrix(6029,1910,3690,1169) -> Matrix(705,-38,-16048,865) Matrix(1167,368,352,111) -> Matrix(221,-12,-6280,341) Matrix(1571,492,1108,347) -> Matrix(547,-30,-11724,643) Matrix(521,162,-1682,-523) -> Matrix(325,-18,5832,-323) Matrix(1797,556,404,125) -> Matrix(179,-10,-5352,299) Matrix(1439,440,520,159) -> Matrix(35,-2,-892,51) Matrix(1037,316,804,245) -> Matrix(421,-24,-8648,493) Matrix(1609,488,1032,313) -> Matrix(279,-16,-6260,359) Matrix(403,122,1318,399) -> Matrix(35,-2,-332,19) Matrix(1313,392,968,289) -> Matrix(579,-34,-12176,715) Matrix(283,84,1196,355) -> Matrix(101,-6,-488,29) Matrix(1081,320,1760,521) -> Matrix(33,-2,-412,25) Matrix(11411,3370,4710,1391) -> Matrix(369,-22,-9812,585) Matrix(21113,6232,15208,4489) -> Matrix(3753,-224,-79768,4761) Matrix(1363,402,-6242,-1841) -> Matrix(401,-24,4528,-271) Matrix(3847,1128,2152,631) -> Matrix(265,-16,-6244,377) Matrix(621,182,58,17) -> Matrix(33,-2,-1072,65) Matrix(1415,414,1186,347) -> Matrix(497,-30,-9824,593) Matrix(5313,1552,3728,1089) -> Matrix(1717,-104,-36932,2237) Matrix(563,164,1356,395) -> Matrix(131,-8,-1228,75) Matrix(283,82,-1522,-441) -> Matrix(163,-10,1516,-93) Matrix(277,78,1282,361) -> Matrix(157,-10,-832,53) Matrix(1445,406,1114,313) -> Matrix(249,-16,-5120,329) Matrix(5441,1520,3440,961) -> Matrix(1365,-88,-30728,1981) Matrix(1717,478,722,201) -> Matrix(215,-14,-5636,367) Matrix(277,76,164,45) -> Matrix(91,-6,-2108,139) Matrix(273,74,166,45) -> Matrix(89,-6,-2032,137) Matrix(271,72,-2232,-593) -> Matrix(29,-2,44,-3) Matrix(2395,636,7844,2083) -> Matrix(173,-12,-1456,101) Matrix(2287,606,434,115) -> Matrix(57,-4,-1724,121) Matrix(1195,316,1524,403) -> Matrix(117,-8,-1828,125) Matrix(595,156,164,43) -> Matrix(29,-2,-884,61) Matrix(159,38,682,163) -> Matrix(25,-2,-112,9) Matrix(997,236,1204,285) -> Matrix(121,-10,-1948,161) Matrix(155,36,-676,-157) -> Matrix(73,-6,864,-71) Matrix(1401,320,880,201) -> Matrix(165,-14,-3736,317) Matrix(723,164,1036,235) -> Matrix(91,-8,-1308,115) Matrix(2633,594,1086,245) -> Matrix(21,-2,-556,53) Matrix(1085,244,876,197) -> Matrix(73,-6,-1472,121) Matrix(1179,260,1900,419) -> Matrix(117,-10,-1556,133) Matrix(767,168,872,191) -> Matrix(205,-18,-3428,301) Matrix(7011,1532,1588,347) -> Matrix(113,-10,-3356,297) Matrix(3477,758,922,201) -> Matrix(45,-4,-1316,117) Matrix(1481,320,560,121) -> Matrix(243,-22,-6572,595) Matrix(2087,446,1474,315) -> Matrix(193,-18,-4128,385) Matrix(967,206,5234,1115) -> Matrix(107,-10,-460,43) Matrix(865,184,456,97) -> Matrix(107,-10,-2600,243) Matrix(23753,5032,8728,1849) -> Matrix(1429,-136,-39308,3741) Matrix(10197,2158,6242,1321) -> Matrix(271,-26,-6160,591) Matrix(3349,708,2332,493) -> Matrix(1,0,-32,1) Matrix(963,202,758,159) -> Matrix(25,-2,-512,41) Matrix(49,10,-250,-51) -> Matrix(21,-2,200,-19) Matrix(6041,1160,1880,361) -> Matrix(1,0,-36,1) Matrix(4599,880,1040,199) -> Matrix(19,-2,-560,59) Matrix(643,122,838,159) -> Matrix(23,-2,-356,31) Matrix(1081,202,198,37) -> Matrix(37,-4,-1156,125) Matrix(1521,280,440,81) -> Matrix(163,-18,-4736,523) Matrix(439,78,242,43) -> Matrix(15,-2,-352,47) Matrix(6113,1072,1648,289) -> Matrix(1,0,-32,1) Matrix(1259,220,1940,339) -> Matrix(39,-4,-536,55) Matrix(3001,520,1160,201) -> Matrix(35,-4,-936,107) Matrix(1157,198,1642,281) -> Matrix(171,-20,-2488,291) Matrix(523,84,716,115) -> Matrix(41,-6,-608,89) Matrix(993,154,806,125) -> Matrix(81,-10,-1628,201) Matrix(517,78,802,121) -> Matrix(73,-10,-1000,137) Matrix(1553,232,328,49) -> Matrix(99,-14,-3076,435) Matrix(1483,204,836,115) -> Matrix(31,-4,-736,95) Matrix(925,124,276,37) -> Matrix(27,-4,-776,115) Matrix(785,104,1336,177) -> Matrix(63,-10,-800,127) Matrix(917,118,1562,201) -> Matrix(45,-8,-568,101) Matrix(6281,760,1000,121) -> Matrix(1,0,-20,1) Matrix(1771,212,1228,147) -> Matrix(11,-2,-236,43) Matrix(317,36,44,5) -> Matrix(11,-2,-368,67) Matrix(313,34,46,5) -> Matrix(9,-2,-292,65) Matrix(305,24,216,17) -> Matrix(11,-2,-236,43) Matrix(977,-102,182,-19) -> Matrix(1,2,-32,-63) Matrix(1147,-134,214,-25) -> Matrix(11,4,-344,-125) Matrix(357,-44,284,-35) -> Matrix(15,4,-304,-81) Matrix(1343,-176,496,-65) -> Matrix(13,8,-356,-219) Matrix(2643,-358,598,-81) -> Matrix(5,2,-148,-59) Matrix(1045,-156,556,-83) -> Matrix(31,8,-748,-193) Matrix(1009,-152,312,-47) -> Matrix(7,2,-200,-57) Matrix(243,-38,518,-81) -> Matrix(11,2,-116,-21) Matrix(449,-72,792,-127) -> Matrix(1,-2,-12,25) Matrix(715,-124,444,-77) -> Matrix(37,10,-840,-227) Matrix(543,-98,338,-61) -> Matrix(35,8,-792,-181) Matrix(7497,-1382,1622,-299) -> Matrix(35,8,-1072,-245) Matrix(1721,-320,640,-119) -> Matrix(29,6,-788,-163) Matrix(2087,-394,874,-165) -> Matrix(83,16,-2184,-421) Matrix(871,-168,1208,-233) -> Matrix(29,4,-428,-59) Matrix(165,-34,34,-7) -> Matrix(9,2,-284,-63) Matrix(821,-178,3058,-663) -> Matrix(11,2,-72,-13) Matrix(263,-58,458,-101) -> Matrix(21,4,-268,-51) Matrix(359,-82,162,-37) -> Matrix(13,2,-332,-51) Matrix(1913,-448,1328,-311) -> Matrix(13,2,-280,-43) Matrix(773,-186,1226,-295) -> Matrix(89,16,-1196,-215) Matrix(413,-108,348,-91) -> Matrix(67,10,-1320,-197) Matrix(2089,-552,632,-167) -> Matrix(31,4,-876,-113) Matrix(1929,-512,1232,-327) -> Matrix(11,2,-248,-45) Matrix(4733,-1266,3346,-895) -> Matrix(61,8,-1304,-171) Matrix(9591,-2570,5930,-1589) -> Matrix(1,0,-16,1) Matrix(3563,-958,4318,-1161) -> Matrix(79,10,-1272,-161) Matrix(693,-188,188,-51) -> Matrix(1,0,-24,1) Matrix(1253,-346,3386,-935) -> Matrix(93,16,-808,-139) Matrix(1285,-356,3476,-963) -> Matrix(159,26,-1376,-225) Matrix(1439,-402,562,-157) -> Matrix(103,16,-2736,-425) Matrix(2343,-658,3778,-1061) -> Matrix(41,6,-540,-79) Matrix(2903,-818,1778,-501) -> Matrix(119,18,-2704,-409) Matrix(527,-154,154,-45) -> Matrix(71,10,-2052,-289) Matrix(277,-82,402,-119) -> Matrix(73,10,-1044,-143) Matrix(2089,-632,552,-167) -> Matrix(31,4,-876,-113) Matrix(645,-196,2116,-643) -> Matrix(47,6,-384,-49) Matrix(24455,-7464,17224,-5257) -> Matrix(171,20,-3668,-429) Matrix(31,-10,90,-29) -> Matrix(15,2,-128,-17) Matrix(1181,-418,178,-63) -> Matrix(1,0,-24,1) Matrix(1801,-640,560,-199) -> Matrix(17,2,-468,-55) Matrix(619,-222,382,-137) -> Matrix(19,2,-428,-45) Matrix(1699,-622,702,-257) -> Matrix(67,8,-1784,-213) Matrix(1111,-408,1288,-473) -> Matrix(271,32,-4480,-529) Matrix(2223,-818,818,-301) -> Matrix(239,28,-6564,-769) Matrix(1343,-496,176,-65) -> Matrix(69,8,-2372,-275) Matrix(3239,-1202,962,-357) -> Matrix(157,18,-4492,-515) Matrix(1721,-640,320,-119) -> Matrix(53,6,-1652,-187) Matrix(377,-144,144,-55) -> Matrix(91,10,-2448,-269) Matrix(2281,-880,1760,-679) -> Matrix(203,22,-4180,-453) Matrix(1903,-736,1616,-625) -> Matrix(183,20,-3596,-393) Matrix(1037,-402,1442,-559) -> Matrix(223,24,-3280,-353) Matrix(1439,-562,402,-157) -> Matrix(151,16,-4464,-473) Matrix(2041,-800,1120,-439) -> Matrix(173,18,-4104,-427) Matrix(1663,-656,976,-385) -> Matrix(77,8,-1800,-187) Matrix(655,-266,426,-173) -> Matrix(59,6,-1308,-133) Matrix(1961,-800,880,-359) -> Matrix(19,2,-504,-53) Matrix(1475,-604,2044,-837) -> Matrix(45,4,-664,-59) Matrix(2239,-920,1560,-641) -> Matrix(21,2,-452,-43) Matrix(1699,-702,622,-257) -> Matrix(75,8,-2072,-221) Matrix(1583,-656,736,-305) -> Matrix(1,0,-16,1) Matrix(85,-36,196,-83) -> Matrix(59,6,-600,-61) Matrix(529,-232,472,-207) -> Matrix(227,22,-4344,-421) Matrix(1917,-842,362,-159) -> Matrix(145,14,-4464,-431) Matrix(3303,-1456,2416,-1065) -> Matrix(563,54,-11896,-1141) Matrix(359,-162,82,-37) -> Matrix(21,2,-620,-59) Matrix(439,-202,602,-277) -> Matrix(45,4,-664,-59) Matrix(1583,-736,656,-305) -> Matrix(1,0,-16,1) Matrix(407,-194,514,-245) -> Matrix(239,22,-3748,-345) Matrix(183,-98,338,-181) -> Matrix(167,14,-2016,-169) Matrix(1217,-662,182,-99) -> Matrix(73,6,-2324,-191) Matrix(413,-226,466,-255) -> Matrix(293,24,-4920,-403) Matrix(2041,-1120,800,-439) -> Matrix(221,18,-5832,-475) Matrix(693,-386,386,-215) -> Matrix(73,6,-1740,-143) Matrix(2129,-1190,950,-531) -> Matrix(25,2,-588,-47) Matrix(1127,-632,872,-489) -> Matrix(199,16,-4092,-329) Matrix(1613,-908,588,-331) -> Matrix(73,6,-2032,-167) Matrix(2479,-1400,1560,-881) -> Matrix(569,46,-12852,-1039) Matrix(639,-362,842,-477) -> Matrix(323,26,-4932,-397) Matrix(1761,-1000,280,-159) -> Matrix(25,2,-588,-47) Matrix(965,-556,1116,-643) -> Matrix(199,16,-3296,-265) Matrix(1647,-952,1192,-689) -> Matrix(277,22,-5880,-467) Matrix(557,-324,404,-235) -> Matrix(103,8,-2176,-169) Matrix(1185,-694,934,-547) -> Matrix(179,14,-3644,-285) Matrix(1663,-976,656,-385) -> Matrix(101,8,-2664,-211) Matrix(2383,-1458,1538,-941) -> Matrix(211,16,-4708,-357) Matrix(2903,-1778,818,-501) -> Matrix(239,18,-7024,-529) Matrix(1933,-1186,546,-335) -> Matrix(1,0,-16,1) Matrix(619,-382,222,-137) -> Matrix(27,2,-716,-53) Matrix(2841,-1760,2000,-1239) -> Matrix(663,50,-14228,-1073) Matrix(715,-444,124,-77) -> Matrix(133,10,-4296,-323) Matrix(2479,-1560,1400,-881) -> Matrix(617,46,-14580,-1087) Matrix(3731,-2350,2110,-1329) -> Matrix(323,24,-7604,-565) Matrix(5741,-3618,2258,-1423) -> Matrix(161,12,-4280,-319) Matrix(2403,-1516,1276,-805) -> Matrix(861,64,-20812,-1547) Matrix(539,-342,342,-217) -> Matrix(271,20,-6084,-449) Matrix(1929,-1232,512,-327) -> Matrix(27,2,-824,-61) Matrix(2269,-1450,1050,-671) -> Matrix(27,2,-716,-53) Matrix(2733,-1748,1268,-811) -> Matrix(1,0,-12,1) Matrix(877,-562,1122,-719) -> Matrix(107,8,-1672,-125) Matrix(2383,-1538,1458,-941) -> Matrix(219,16,-4996,-365) Matrix(1651,-1070,1310,-849) -> Matrix(329,24,-6676,-487) Matrix(655,-426,266,-173) -> Matrix(83,6,-2172,-157) Matrix(1283,-876,476,-325) -> Matrix(227,16,-6200,-437) Matrix(3727,-2554,2634,-1805) -> Matrix(371,26,-7948,-557) Matrix(1913,-1328,448,-311) -> Matrix(29,2,-856,-59) Matrix(6207,-4312,4792,-3329) -> Matrix(661,46,-13608,-947) Matrix(3115,-2166,2406,-1673) -> Matrix(347,24,-7128,-493) Matrix(2239,-1560,920,-641) -> Matrix(29,2,-740,-51) Matrix(1269,-892,892,-627) -> Matrix(871,60,-18712,-1289) Matrix(2841,-2000,1760,-1239) -> Matrix(727,50,-16532,-1137) Matrix(5671,-4008,1688,-1193) -> Matrix(117,8,-3320,-227) Matrix(4733,-3346,1266,-895) -> Matrix(117,8,-3320,-227) Matrix(6911,-4890,1850,-1309) -> Matrix(29,2,-856,-59) Matrix(2153,-1526,1686,-1195) -> Matrix(349,24,-7140,-491) Matrix(351,-250,490,-349) -> Matrix(263,18,-3872,-265) Matrix(1979,-1422,302,-217) -> Matrix(29,2,-972,-67) Matrix(3999,-2882,2882,-2077) -> Matrix(1535,104,-32604,-2209) Matrix(557,-404,324,-235) -> Matrix(119,8,-2752,-185) Matrix(4621,-3380,1940,-1419) -> Matrix(1249,84,-32816,-2207) Matrix(1063,-778,138,-101) -> Matrix(119,8,-4180,-281) Matrix(345,-254,254,-187) -> Matrix(329,22,-6924,-463) Matrix(3067,-2332,1932,-1469) -> Matrix(335,22,-7568,-497) Matrix(907,-692,772,-589) -> Matrix(673,44,-13200,-863) Matrix(929,-712,792,-607) -> Matrix(707,46,-13848,-901) Matrix(2281,-1760,880,-679) -> Matrix(339,22,-9076,-589) Matrix(1127,-872,632,-489) -> Matrix(247,16,-5820,-377) Matrix(2153,-1686,1526,-1195) -> Matrix(373,24,-8004,-515) Matrix(1185,-934,694,-547) -> Matrix(219,14,-5084,-325) Matrix(1273,-1006,1006,-795) -> Matrix(1033,66,-21020,-1343) Matrix(357,-284,44,-35) -> Matrix(63,4,-2032,-129) Matrix(199,-162,242,-197) -> Matrix(287,18,-4608,-289) Matrix(7363,-6078,1358,-1121) -> Matrix(193,12,-6160,-383) Matrix(2015,-1666,306,-253) -> Matrix(129,8,-4112,-255) Matrix(413,-348,108,-91) -> Matrix(163,10,-4776,-293) Matrix(1903,-1616,736,-625) -> Matrix(327,20,-8780,-537) Matrix(907,-772,692,-589) -> Matrix(721,44,-14928,-911) Matrix(4153,-3608,2568,-2231) -> Matrix(199,12,-4660,-281) Matrix(2011,-1750,470,-409) -> Matrix(133,8,-4040,-243) Matrix(507,-452,212,-189) -> Matrix(337,20,-8880,-527) Matrix(593,-648,248,-271) -> Matrix(491,26,-12936,-685) Matrix(413,-466,226,-255) -> Matrix(461,24,-10968,-571) Matrix(1583,-1818,1098,-1261) -> Matrix(271,14,-5904,-305) Matrix(2081,-2398,558,-643) -> Matrix(233,12,-6660,-343) Matrix(853,-986,186,-215) -> Matrix(389,20,-11884,-611) Matrix(1809,-2152,712,-847) -> Matrix(197,10,-5260,-267) Matrix(199,-242,162,-197) -> Matrix(359,18,-7200,-361) Matrix(2077,-2564,644,-795) -> Matrix(161,8,-4488,-223) Matrix(3057,-3782,662,-819) -> Matrix(523,26,-16032,-797) Matrix(1591,-2008,248,-313) -> Matrix(325,16,-10136,-499) Matrix(7351,-9290,2650,-3349) -> Matrix(1545,76,-41776,-2055) Matrix(8231,-10408,2968,-3753) -> Matrix(1627,80,-43868,-2157) Matrix(5079,-6482,3602,-4597) -> Matrix(1511,74,-32364,-1585) Matrix(877,-1122,562,-719) -> Matrix(163,8,-3688,-181) Matrix(885,-1156,676,-883) -> Matrix(1115,54,-23064,-1117) Matrix(639,-842,362,-477) -> Matrix(539,26,-12708,-613) Matrix(783,-1058,578,-781) -> Matrix(1427,68,-29988,-1429) Matrix(1285,-1754,474,-647) -> Matrix(1013,48,-27752,-1315) Matrix(4341,-5938,3058,-4183) -> Matrix(2155,102,-46248,-2189) Matrix(439,-602,202,-277) -> Matrix(85,4,-2104,-99) Matrix(1343,-1858,738,-1021) -> Matrix(171,8,-4040,-189) Matrix(871,-1208,168,-233) -> Matrix(85,4,-2444,-115) Matrix(12463,-17298,8978,-12461) -> Matrix(9519,448,-202300,-9521) Matrix(1037,-1442,402,-559) -> Matrix(511,24,-13648,-641) Matrix(1413,-1988,548,-771) -> Matrix(127,6,-3408,-161) Matrix(5263,-7418,2938,-4141) -> Matrix(1583,74,-37500,-1753) Matrix(4757,-6724,3364,-4755) -> Matrix(383,18,-8192,-385) Matrix(36961,-52480,8000,-11359) -> Matrix(601,28,-18352,-855) Matrix(3103,-4418,2178,-3101) -> Matrix(4471,208,-96148,-4473) Matrix(3953,-5686,1526,-2195) -> Matrix(561,26,-14996,-695) Matrix(4329,-6232,1672,-2407) -> Matrix(87,4,-2284,-105) Matrix(277,-402,82,-119) -> Matrix(217,10,-6228,-287) Matrix(587,-894,174,-265) -> Matrix(311,14,-8908,-401) Matrix(787,-1214,94,-145) -> Matrix(89,4,-3004,-135) Matrix(2715,-4244,1124,-1757) -> Matrix(1,0,-4,1) Matrix(5007,-7834,2074,-3245) -> Matrix(45,2,-1148,-51) Matrix(3039,-4802,1922,-3037) -> Matrix(3959,176,-89100,-3961) Matrix(773,-1226,186,-295) -> Matrix(361,16,-10988,-487) Matrix(1083,-1718,278,-441) -> Matrix(271,12,-7972,-353) Matrix(12709,-20172,3772,-5987) -> Matrix(181,8,-5136,-227) Matrix(3799,-6042,1482,-2357) -> Matrix(2261,100,-60120,-2659) Matrix(2343,-3778,658,-1061) -> Matrix(137,6,-3996,-175) Matrix(7439,-12002,3122,-5037) -> Matrix(909,40,-23884,-1051) Matrix(2293,-3706,826,-1335) -> Matrix(183,8,-4964,-217) Matrix(2357,-3844,1444,-2355) -> Matrix(407,18,-9248,-409) Matrix(1715,-2924,444,-757) -> Matrix(187,8,-5540,-237) Matrix(837,-1444,484,-835) -> Matrix(419,18,-9800,-421) Matrix(1493,-2586,586,-1015) -> Matrix(93,4,-2488,-107) Matrix(263,-458,58,-101) -> Matrix(93,4,-2860,-123) Matrix(449,-792,72,-127) -> Matrix(47,2,-1716,-73) Matrix(4641,-8200,1720,-3039) -> Matrix(331,14,-9008,-381) Matrix(3161,-5600,880,-1559) -> Matrix(1277,54,-37908,-1603) Matrix(2407,-4274,994,-1765) -> Matrix(237,10,-6328,-267) Matrix(2151,-3848,488,-873) -> Matrix(189,8,-5552,-235) Matrix(6623,-11858,3698,-6621) -> Matrix(2555,108,-60492,-2557) Matrix(183,-338,98,-181) -> Matrix(335,14,-8064,-337) Matrix(243,-518,38,-81) -> Matrix(51,2,-1556,-61) Matrix(915,-2044,124,-277) -> Matrix(1,0,-8,1) Matrix(85,-196,36,-83) -> Matrix(155,6,-4056,-157) Matrix(5769,-13750,1750,-4171) -> Matrix(841,32,-23732,-903) Matrix(8603,-20556,2396,-5725) -> Matrix(5845,222,-173428,-6587) Matrix(17239,-41202,4802,-11477) -> Matrix(12167,462,-360928,-13705) Matrix(605,-1476,116,-283) -> Matrix(1,0,-4,1) Matrix(719,-1762,162,-397) -> Matrix(105,4,-3124,-119) Matrix(1839,-4522,682,-1677) -> Matrix(263,10,-7180,-273) Matrix(5599,-14360,1560,-4001) -> Matrix(4097,154,-121500,-4567) Matrix(1589,-4092,492,-1267) -> Matrix(107,4,-2916,-109) Matrix(639,-1682,242,-637) -> Matrix(1187,44,-32076,-1189) Matrix(217,-582,22,-59) -> Matrix(109,4,-3788,-139) Matrix(12031,-32450,3570,-9629) -> Matrix(329,12,-9404,-343) Matrix(1253,-3386,346,-935) -> Matrix(437,16,-13192,-483) Matrix(10063,-27378,3698,-10061) -> Matrix(7479,272,-205700,-7481) Matrix(1181,-3218,258,-703) -> Matrix(331,12,-10068,-365) Matrix(2493,-6908,668,-1851) -> Matrix(53,2,-1564,-59) Matrix(31,-90,10,-29) -> Matrix(55,2,-1568,-57) Matrix(2319,-7442,722,-2317) -> Matrix(1,0,4,1) Matrix(645,-2116,196,-643) -> Matrix(167,6,-4704,-169) Matrix(4085,-13474,754,-2487) -> Matrix(169,6,-5380,-191) Matrix(52443,-176716,9676,-32605) -> Matrix(743,26,-23576,-825) Matrix(52039,-175362,9602,-32357) -> Matrix(973,34,-30764,-1075) Matrix(559,-1922,162,-557) -> Matrix(1043,36,-30276,-1045) Matrix(1223,-4418,338,-1221) -> Matrix(419,14,-12600,-421) Matrix(2143,-7938,578,-2141) -> Matrix(1,0,12,1) Matrix(821,-3058,178,-663) -> Matrix(59,2,-1800,-61) Matrix(417,-1742,62,-259) -> Matrix(245,8,-7932,-259) Matrix(10841,-50080,2000,-9239) -> Matrix(307,10,-9732,-317) Matrix(463,-2178,98,-461) -> Matrix(867,28,-26908,-869) Matrix(103,-578,18,-101) -> Matrix(191,6,-6144,-193) Matrix(1519,-9522,242,-1517) -> Matrix(1,0,36,1) Matrix(37,-324,4,-35) -> Matrix(67,2,-2312,-69) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 96 Degree of the the map X: 192 Degree of the the map Y: 384 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/9 1/7 1/4 1/3 3/7 11/19 3/5 7/9 1/1 11/9 17/13 23/17 7/5 47/33 3/2 61/39 5/3 19/11 13/7 2/1 7/3 17/7 13/5 29/11 19/7 25/9 3/1 61/19 23/7 17/5 31/9 11/3 63/17 19/5 4/1 13/3 23/5 33/7 5/1 17/3 6/1 13/2 33/5 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 0/1 1/1 1/9 -1/2 1/8 -1/5 0/1 1/7 -1/3 3/20 -1/3 0/1 2/13 -1/4 1/6 -1/3 -2/7 1/5 -1/4 3/14 -1/5 -6/31 2/9 -2/11 -3/17 3/13 0/1 4/17 -1/5 0/1 1/4 -1/6 4/15 -2/13 -1/7 7/26 -1/9 0/1 3/11 -1/6 2/7 -4/27 -1/7 5/17 -5/36 3/10 -5/37 -2/15 7/23 -1/8 4/13 -1/7 -2/15 1/3 -1/8 6/17 -1/9 0/1 11/31 -1/8 5/14 -2/17 -1/9 4/11 -1/8 7/19 -7/60 10/27 -7/61 -4/35 13/35 -4/35 3/8 -6/53 -1/9 5/13 -5/46 2/5 -1/9 -2/19 3/7 -1/10 4/9 -2/21 -1/11 5/11 -2/21 6/13 -2/21 -1/11 1/2 -1/11 -2/23 5/9 -1/12 4/7 -2/25 -5/63 11/19 -3/38 7/12 -2/25 -1/13 3/5 -1/13 8/13 -1/13 -4/53 13/21 -5/66 5/8 -1/13 -2/27 7/11 -5/68 16/25 -1/13 -2/27 9/14 -8/109 -3/41 11/17 -1/14 13/20 -4/55 -5/69 2/3 -1/14 11/16 -5/71 -4/57 9/13 -5/72 16/23 -3/43 -2/29 7/10 -11/159 -2/29 19/27 -15/218 12/17 -12/175 -5/73 29/41 -3/44 17/24 -2/29 -9/131 5/7 -3/44 13/18 -6/89 -1/15 8/11 -6/89 -1/15 11/15 -11/164 3/4 -1/15 -6/91 13/17 -3/46 10/13 -8/123 -5/77 17/22 -9/139 -2/31 7/9 -2/31 18/23 -2/31 -3/47 11/14 -5/78 15/19 -11/172 4/5 -4/63 -5/79 1/1 -1/18 6/5 -5/99 -6/119 11/9 -1/20 16/13 -13/261 -12/241 21/17 -1/20 5/4 -5/101 -4/81 19/15 -11/224 14/11 -5/102 9/7 -2/41 22/17 -2/41 -9/185 13/10 -5/103 -8/165 17/13 -3/62 4/3 -6/125 -1/21 23/17 -1/21 19/14 -1/21 -28/589 15/11 -11/232 26/19 -7/148 11/8 -1/21 -6/127 29/21 -5/106 18/13 -1/21 -6/127 25/18 -4/85 -15/319 7/5 -3/64 31/22 -8/171 -5/107 24/17 -9/193 -2/43 41/29 -3/64 17/12 -5/107 -12/257 27/19 -15/322 37/26 -41/881 -2/43 47/33 -2/43 10/7 -2/43 -11/237 23/16 -2/43 -3/65 59/41 -5/108 36/25 -2/43 -3/65 13/9 -5/108 3/2 -1/22 20/13 -5/111 -4/89 17/11 -1/22 14/9 -3/67 -8/179 25/16 -2/45 -1/23 61/39 -1/22 36/23 -4/89 -3/67 11/7 -5/112 8/5 -2/45 -1/23 29/18 -7/159 -4/91 21/13 -5/114 34/21 -3/68 13/8 -4/91 -1/23 5/3 -1/23 12/7 -1/23 -2/47 19/11 -3/70 26/15 -5/117 -2/47 7/4 -5/117 -2/47 9/5 -1/24 11/6 -6/143 -7/167 13/7 -1/24 15/8 -8/193 -7/169 2/1 -2/49 -1/25 7/3 -1/26 12/5 -7/185 -2/53 29/12 -2/53 -1/27 17/7 -1/27 22/9 -1/25 -2/51 27/11 -1/26 32/13 -1/26 5/2 -2/53 -1/27 13/5 -5/134 21/8 -16/431 -1/27 29/11 -1/27 8/3 -1/27 -6/163 27/10 -4/109 -7/191 46/17 -14/383 -11/301 19/7 -7/192 30/11 -2/55 -3/83 11/4 -1/28 25/9 -3/82 14/5 -1/27 -2/55 3/1 -1/28 16/5 -1/29 0/1 61/19 0/1 45/14 -1/27 0/1 29/9 -1/28 42/13 -1/28 13/4 -2/57 -1/29 23/7 -1/28 10/3 -2/57 -5/143 27/8 -3/86 17/5 -5/144 24/7 -14/405 -1/29 31/9 -1/29 7/2 -1/29 -4/117 11/3 -1/30 37/10 -1/33 0/1 63/17 0/1 26/7 -1/27 0/1 41/11 -1/28 15/4 -1/29 -2/59 19/5 -1/29 4/1 -1/30 17/4 -1/31 0/1 13/3 0/1 22/5 -1/29 0/1 53/12 -1/30 31/7 -1/30 9/2 -3/91 -2/61 23/5 -3/92 14/3 -6/185 -1/31 33/7 -1/31 19/4 -1/31 -8/249 5/1 -1/32 11/2 -2/63 -3/95 17/3 -1/32 23/4 -4/129 -3/97 6/1 -2/65 -1/33 13/2 -1/32 33/5 -1/32 20/3 -1/33 0/1 7/1 -1/33 15/2 -1/33 -2/67 8/1 -1/31 0/1 9/1 -1/34 1/0 -1/37 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(182,-17,257,-24) (0/1,1/9) -> (29/41,17/24) Hyperbolic Matrix(340,-41,481,-58) (1/9,1/8) -> (12/17,29/41) Hyperbolic Matrix(125,-16,336,-43) (1/8,1/7) -> (13/35,3/8) Hyperbolic Matrix(330,-49,889,-132) (1/7,3/20) -> (10/27,13/35) Hyperbolic Matrix(1009,-152,312,-47) (3/20,2/13) -> (42/13,13/4) Hyperbolic Matrix(292,-47,87,-14) (2/13,1/6) -> (10/3,27/8) Hyperbolic Matrix(85,-16,16,-3) (1/6,1/5) -> (5/1,11/2) Hyperbolic Matrix(165,-34,34,-7) (1/5,3/14) -> (19/4,5/1) Hyperbolic Matrix(477,-104,344,-75) (3/14,2/9) -> (18/13,25/18) Hyperbolic Matrix(439,-100,180,-41) (2/9,3/13) -> (17/7,22/9) Hyperbolic Matrix(666,-155,275,-64) (3/13,4/17) -> (29/12,17/7) Hyperbolic Matrix(486,-115,355,-84) (4/17,1/4) -> (26/19,11/8) Hyperbolic Matrix(237,-62,302,-79) (1/4,4/15) -> (18/23,11/14) Hyperbolic Matrix(1089,-292,772,-207) (4/15,7/26) -> (31/22,24/17) Hyperbolic Matrix(693,-188,188,-51) (7/26,3/11) -> (11/3,37/10) Hyperbolic Matrix(140,-39,79,-22) (3/11,2/7) -> (7/4,9/5) Hyperbolic Matrix(527,-154,154,-45) (2/7,5/17) -> (17/5,24/7) Hyperbolic Matrix(277,-82,402,-119) (5/17,3/10) -> (11/16,9/13) Hyperbolic Matrix(262,-79,199,-60) (3/10,7/23) -> (17/13,4/3) Hyperbolic Matrix(520,-159,399,-122) (7/23,4/13) -> (13/10,17/13) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(1181,-418,178,-63) (6/17,11/31) -> (33/5,20/3) Hyperbolic Matrix(1801,-640,560,-199) (11/31,5/14) -> (45/14,29/9) Hyperbolic Matrix(619,-222,382,-137) (5/14,4/11) -> (34/21,13/8) Hyperbolic Matrix(659,-242,482,-177) (4/11,7/19) -> (15/11,26/19) Hyperbolic Matrix(1387,-512,512,-189) (7/19,10/27) -> (46/17,19/7) Hyperbolic Matrix(377,-144,144,-55) (3/8,5/13) -> (13/5,21/8) Hyperbolic Matrix(100,-39,159,-62) (5/13,2/5) -> (5/8,7/11) Hyperbolic Matrix(43,-18,98,-41) (2/5,3/7) -> (3/7,4/9) Parabolic Matrix(359,-162,82,-37) (4/9,5/11) -> (13/3,22/5) Hyperbolic Matrix(356,-163,83,-38) (5/11,6/13) -> (17/4,13/3) Hyperbolic Matrix(176,-83,123,-58) (6/13,1/2) -> (10/7,23/16) Hyperbolic Matrix(117,-64,64,-35) (1/2,5/9) -> (9/5,11/6) Hyperbolic Matrix(140,-79,39,-22) (5/9,4/7) -> (7/2,11/3) Hyperbolic Matrix(545,-314,394,-227) (4/7,11/19) -> (29/21,18/13) Hyperbolic Matrix(557,-324,404,-235) (11/19,7/12) -> (11/8,29/21) Hyperbolic Matrix(76,-45,125,-74) (7/12,3/5) -> (3/5,8/13) Parabolic Matrix(619,-382,222,-137) (8/13,13/21) -> (25/9,14/5) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(671,-428,428,-273) (7/11,16/25) -> (36/23,11/7) Hyperbolic Matrix(488,-313,633,-406) (16/25,9/14) -> (10/13,17/22) Hyperbolic Matrix(560,-361,121,-78) (9/14,11/17) -> (23/5,14/3) Hyperbolic Matrix(1262,-819,339,-220) (11/17,13/20) -> (26/7,41/11) Hyperbolic Matrix(655,-426,266,-173) (13/20,2/3) -> (32/13,5/2) Hyperbolic Matrix(226,-155,35,-24) (2/3,11/16) -> (6/1,13/2) Hyperbolic Matrix(767,-532,532,-369) (9/13,16/23) -> (36/25,13/9) Hyperbolic Matrix(566,-395,235,-164) (16/23,7/10) -> (12/5,29/12) Hyperbolic Matrix(1269,-892,892,-627) (7/10,19/27) -> (27/19,37/26) Hyperbolic Matrix(458,-323,363,-256) (19/27,12/17) -> (5/4,19/15) Hyperbolic Matrix(1089,-772,292,-207) (17/24,5/7) -> (41/11,15/4) Hyperbolic Matrix(477,-344,104,-75) (5/7,13/18) -> (9/2,23/5) Hyperbolic Matrix(545,-394,314,-227) (13/18,8/11) -> (26/15,7/4) Hyperbolic Matrix(659,-482,242,-177) (8/11,11/15) -> (19/7,30/11) Hyperbolic Matrix(345,-254,254,-187) (11/15,3/4) -> (19/14,15/11) Hyperbolic Matrix(262,-199,79,-60) (3/4,13/17) -> (23/7,10/3) Hyperbolic Matrix(520,-399,159,-122) (13/17,10/13) -> (13/4,23/7) Hyperbolic Matrix(316,-245,405,-314) (17/22,7/9) -> (7/9,18/23) Parabolic Matrix(940,-741,581,-458) (11/14,15/19) -> (21/13,34/21) Hyperbolic Matrix(458,-363,323,-256) (15/19,4/5) -> (17/12,27/19) Hyperbolic Matrix(11,-10,10,-9) (4/5,1/1) -> (1/1,6/5) Parabolic Matrix(199,-242,162,-197) (6/5,11/9) -> (11/9,16/13) Parabolic Matrix(556,-685,125,-154) (16/13,21/17) -> (31/7,9/2) Hyperbolic Matrix(482,-597,197,-244) (21/17,5/4) -> (22/9,27/11) Hyperbolic Matrix(440,-559,159,-202) (19/15,14/11) -> (11/4,25/9) Hyperbolic Matrix(237,-302,62,-79) (14/11,9/7) -> (19/5,4/1) Hyperbolic Matrix(428,-553,113,-146) (9/7,22/17) -> (15/4,19/5) Hyperbolic Matrix(488,-633,313,-406) (22/17,13/10) -> (14/9,25/16) Hyperbolic Matrix(392,-529,289,-390) (4/3,23/17) -> (23/17,19/14) Parabolic Matrix(376,-523,243,-338) (25/18,7/5) -> (17/11,14/9) Hyperbolic Matrix(474,-667,307,-432) (7/5,31/22) -> (20/13,17/11) Hyperbolic Matrix(182,-257,17,-24) (24/17,41/29) -> (9/1,1/0) Hyperbolic Matrix(340,-481,41,-58) (41/29,17/12) -> (8/1,9/1) Hyperbolic Matrix(1552,-2209,1089,-1550) (37/26,47/33) -> (47/33,10/7) Parabolic Matrix(2452,-3527,1567,-2254) (23/16,59/41) -> (61/39,36/23) Hyperbolic Matrix(2550,-3671,1631,-2348) (59/41,36/25) -> (25/16,61/39) Hyperbolic Matrix(277,-402,82,-119) (13/9,3/2) -> (27/8,17/5) Hyperbolic Matrix(733,-1126,166,-255) (3/2,20/13) -> (22/5,53/12) Hyperbolic Matrix(100,-159,39,-62) (11/7,8/5) -> (5/2,13/5) Hyperbolic Matrix(223,-358,38,-61) (8/5,29/18) -> (23/4,6/1) Hyperbolic Matrix(76,-125,45,-74) (13/8,5/3) -> (5/3,12/7) Parabolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic Matrix(262,-497,97,-184) (15/8,2/1) -> (27/10,46/17) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(572,-1407,87,-214) (27/11,32/13) -> (13/2,33/5) Hyperbolic Matrix(320,-841,121,-318) (21/8,29/11) -> (29/11,8/3) Parabolic Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(112,-307,27,-74) (30/11,11/4) -> (4/1,17/4) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(1160,-3721,361,-1158) (16/5,61/19) -> (61/19,45/14) Parabolic Matrix(880,-2839,199,-642) (29/9,42/13) -> (53/12,31/7) Hyperbolic Matrix(280,-961,81,-278) (24/7,31/9) -> (31/9,7/2) Parabolic Matrix(1072,-3969,289,-1070) (37/10,63/17) -> (63/17,26/7) Parabolic Matrix(232,-1089,49,-230) (14/3,33/7) -> (33/7,19/4) Parabolic Matrix(103,-578,18,-101) (11/2,17/3) -> (17/3,23/4) Parabolic Matrix(36,-245,5,-34) (20/3,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,38,1) Matrix(182,-17,257,-24) -> Matrix(7,2,-102,-29) Matrix(340,-41,481,-58) -> Matrix(13,5,-190,-73) Matrix(125,-16,336,-43) -> Matrix(1,-1,-8,9) Matrix(330,-49,889,-132) -> Matrix(25,7,-218,-61) Matrix(1009,-152,312,-47) -> Matrix(7,2,-200,-57) Matrix(292,-47,87,-14) -> Matrix(1,1,-30,-29) Matrix(85,-16,16,-3) -> Matrix(5,1,-156,-31) Matrix(165,-34,34,-7) -> Matrix(9,2,-284,-63) Matrix(477,-104,344,-75) -> Matrix(49,9,-1040,-191) Matrix(439,-100,180,-41) -> Matrix(5,1,-136,-27) Matrix(666,-155,275,-64) -> Matrix(3,1,-82,-27) Matrix(486,-115,355,-84) -> Matrix(29,6,-614,-127) Matrix(237,-62,302,-79) -> Matrix(47,7,-732,-109) Matrix(1089,-292,772,-207) -> Matrix(37,5,-792,-107) Matrix(693,-188,188,-51) -> Matrix(1,0,-24,1) Matrix(140,-39,79,-22) -> Matrix(19,3,-450,-71) Matrix(527,-154,154,-45) -> Matrix(71,10,-2052,-289) Matrix(277,-82,402,-119) -> Matrix(73,10,-1044,-143) Matrix(262,-79,199,-60) -> Matrix(53,7,-1098,-145) Matrix(520,-159,399,-122) -> Matrix(19,2,-390,-41) Matrix(31,-10,90,-29) -> Matrix(15,2,-128,-17) Matrix(1181,-418,178,-63) -> Matrix(1,0,-24,1) Matrix(1801,-640,560,-199) -> Matrix(17,2,-468,-55) Matrix(619,-222,382,-137) -> Matrix(19,2,-428,-45) Matrix(659,-242,482,-177) -> Matrix(127,15,-2684,-317) Matrix(1387,-512,512,-189) -> Matrix(181,21,-4956,-575) Matrix(377,-144,144,-55) -> Matrix(91,10,-2448,-269) Matrix(100,-39,159,-62) -> Matrix(47,5,-630,-67) Matrix(43,-18,98,-41) -> Matrix(29,3,-300,-31) Matrix(359,-162,82,-37) -> Matrix(21,2,-620,-59) Matrix(356,-163,83,-38) -> Matrix(21,2,-662,-63) Matrix(176,-83,123,-58) -> Matrix(75,7,-1618,-151) Matrix(117,-64,64,-35) -> Matrix(61,5,-1452,-119) Matrix(140,-79,39,-22) -> Matrix(37,3,-1098,-89) Matrix(545,-314,394,-227) -> Matrix(87,7,-1852,-149) Matrix(557,-324,404,-235) -> Matrix(103,8,-2176,-169) Matrix(76,-45,125,-74) -> Matrix(77,6,-1014,-79) Matrix(619,-382,222,-137) -> Matrix(27,2,-716,-53) Matrix(777,-482,482,-299) -> Matrix(199,15,-4524,-341) Matrix(671,-428,428,-273) -> Matrix(69,5,-1532,-111) Matrix(488,-313,633,-406) -> Matrix(217,16,-3350,-247) Matrix(560,-361,121,-78) -> Matrix(137,10,-4206,-307) Matrix(1262,-819,339,-220) -> Matrix(55,4,-1554,-113) Matrix(655,-426,266,-173) -> Matrix(83,6,-2172,-157) Matrix(226,-155,35,-24) -> Matrix(43,3,-1362,-95) Matrix(767,-532,532,-369) -> Matrix(71,5,-1548,-109) Matrix(566,-395,235,-164) -> Matrix(115,8,-3062,-213) Matrix(1269,-892,892,-627) -> Matrix(871,60,-18712,-1289) Matrix(458,-323,363,-256) -> Matrix(335,23,-6802,-467) Matrix(1089,-772,292,-207) -> Matrix(73,5,-2088,-143) Matrix(477,-344,104,-75) -> Matrix(133,9,-4064,-275) Matrix(545,-394,314,-227) -> Matrix(103,7,-2428,-165) Matrix(659,-482,242,-177) -> Matrix(223,15,-6140,-413) Matrix(345,-254,254,-187) -> Matrix(329,22,-6924,-463) Matrix(262,-199,79,-60) -> Matrix(107,7,-3042,-199) Matrix(520,-399,159,-122) -> Matrix(31,2,-822,-53) Matrix(316,-245,405,-314) -> Matrix(371,24,-5766,-373) Matrix(940,-741,581,-458) -> Matrix(63,4,-1402,-89) Matrix(458,-363,323,-256) -> Matrix(361,23,-7738,-493) Matrix(11,-10,10,-9) -> Matrix(17,1,-324,-19) Matrix(199,-242,162,-197) -> Matrix(359,18,-7200,-361) Matrix(556,-685,125,-154) -> Matrix(201,10,-6010,-299) Matrix(482,-597,197,-244) -> Matrix(121,6,-3126,-155) Matrix(440,-559,159,-202) -> Matrix(41,2,-1046,-51) Matrix(237,-302,62,-79) -> Matrix(143,7,-4188,-205) Matrix(428,-553,113,-146) -> Matrix(103,5,-2946,-143) Matrix(488,-633,313,-406) -> Matrix(329,16,-7382,-359) Matrix(392,-529,289,-390) -> Matrix(713,34,-14994,-715) Matrix(376,-523,243,-338) -> Matrix(277,13,-6158,-289) Matrix(474,-667,307,-432) -> Matrix(149,7,-3342,-157) Matrix(182,-257,17,-24) -> Matrix(43,2,-1398,-65) Matrix(340,-481,41,-58) -> Matrix(107,5,-3574,-167) Matrix(1552,-2209,1089,-1550) -> Matrix(2235,104,-48074,-2237) Matrix(2452,-3527,1567,-2254) -> Matrix(367,17,-8182,-379) Matrix(2550,-3671,1631,-2348) -> Matrix(151,7,-3430,-159) Matrix(277,-402,82,-119) -> Matrix(217,10,-6228,-287) Matrix(733,-1126,166,-255) -> Matrix(111,5,-3308,-149) Matrix(100,-159,39,-62) -> Matrix(113,5,-3006,-133) Matrix(223,-358,38,-61) -> Matrix(113,5,-3684,-163) Matrix(76,-125,45,-74) -> Matrix(137,6,-3174,-139) Matrix(419,-722,242,-417) -> Matrix(209,9,-4900,-211) Matrix(183,-338,98,-181) -> Matrix(335,14,-8064,-337) Matrix(262,-497,97,-184) -> Matrix(243,10,-6634,-273) Matrix(43,-98,18,-41) -> Matrix(77,3,-2028,-79) Matrix(572,-1407,87,-214) -> Matrix(27,1,-838,-31) Matrix(320,-841,121,-318) -> Matrix(593,22,-16038,-595) Matrix(125,-336,16,-43) -> Matrix(27,1,-1000,-37) Matrix(112,-307,27,-74) -> Matrix(83,3,-2518,-91) Matrix(31,-90,10,-29) -> Matrix(55,2,-1568,-57) Matrix(1160,-3721,361,-1158) -> Matrix(1,0,2,1) Matrix(880,-2839,199,-642) -> Matrix(57,2,-1682,-59) Matrix(280,-961,81,-278) -> Matrix(521,18,-15138,-523) Matrix(1072,-3969,289,-1070) -> Matrix(1,0,6,1) Matrix(232,-1089,49,-230) -> Matrix(433,14,-13454,-435) Matrix(103,-578,18,-101) -> Matrix(191,6,-6144,-193) Matrix(36,-245,5,-34) -> Matrix(65,2,-2178,-67) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 96 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 38 1 1/1 -1/18 2 20 11/9 -1/20 18 2 21/17 -1/20 2 20 5/4 (-5/101,-4/81) 0 40 19/15 -11/224 2 20 14/11 -5/102 2 8 9/7 -2/41 6 5 22/17 (-2/41,-9/185) 0 40 13/10 (-5/103,-8/165) 0 40 17/13 -3/62 6 4 4/3 (-6/125,-1/21) 0 40 23/17 -1/21 34 1 15/11 -11/232 2 20 11/8 (-1/21,-6/127) 0 40 18/13 (-1/21,-6/127) 0 40 7/5 -3/64 2 10 24/17 (-9/193,-2/43) 0 40 41/29 -3/64 2 4 17/12 (-5/107,-12/257) 0 40 27/19 -15/322 2 20 47/33 -2/43 26 1 10/7 (-2/43,-11/237) 0 40 23/16 (-2/43,-3/65) 0 40 59/41 -5/108 2 2 13/9 -5/108 2 20 3/2 -1/22 4 8 20/13 (-5/111,-4/89) 0 40 17/11 -1/22 2 10 14/9 (-3/67,-8/179) 0 40 25/16 (-2/45,-1/23) 0 40 61/39 -1/22 2 2 11/7 -5/112 2 20 8/5 (-2/45,-1/23) 0 40 21/13 -5/114 2 20 13/8 (-4/91,-1/23) 0 40 5/3 -1/23 6 5 12/7 (-1/23,-2/47) 0 40 19/11 -3/70 2 4 26/15 (-5/117,-2/47) 0 40 7/4 (-5/117,-2/47) 0 40 9/5 -1/24 2 20 13/7 -1/24 14 2 2/1 (-2/49,-1/25) 0 40 7/3 -1/26 6 4 12/5 (-7/185,-2/53) 0 40 29/12 (-2/53,-1/27) 0 40 17/7 -1/27 2 5 5/2 (-2/53,-1/27) 0 40 13/5 -5/134 2 20 29/11 -1/27 22 1 8/3 (-1/27,-6/163) 0 40 27/10 (-4/109,-7/191) 0 40 19/7 -7/192 2 20 30/11 (-2/55,-3/83) 0 40 11/4 -1/28 2 8 25/9 -3/82 2 20 14/5 (-1/27,-2/55) 0 40 3/1 -1/28 2 10 16/5 (-1/29,0/1) 0 40 61/19 0/1 2 1 29/9 -1/28 2 20 13/4 (-2/57,-1/29) 0 40 23/7 -1/28 6 4 10/3 (-2/57,-5/143) 0 40 27/8 -3/86 4 8 17/5 -5/144 2 20 31/9 -1/29 18 1 7/2 (-1/29,-4/117) 0 40 11/3 -1/30 2 20 63/17 0/1 6 1 26/7 (-1/27,0/1) 0 40 41/11 -1/28 2 10 15/4 (-1/29,-2/59) 0 40 19/5 -1/29 6 5 4/1 -1/30 2 8 17/4 (-1/31,0/1) 0 40 13/3 0/1 2 5 22/5 (-1/29,0/1) 0 40 53/12 -1/30 4 8 31/7 -1/30 2 20 9/2 (-3/91,-2/61) 0 40 23/5 -3/92 2 10 14/3 (-6/185,-1/31) 0 40 33/7 -1/31 14 1 5/1 -1/32 2 20 17/3 -1/32 6 2 6/1 (-2/65,-1/33) 0 40 13/2 -1/32 4 8 33/5 -1/32 2 20 20/3 (-1/33,0/1) 0 40 7/1 -1/33 2 5 15/2 (-1/33,-2/67) 0 40 8/1 (-1/31,0/1) 0 40 9/1 -1/34 2 4 1/0 (-1/37,0/1) 0 40 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(10,-11,9,-10) (1/1,11/9) -> (1/1,11/9) Reflection Matrix(188,-231,153,-188) (11/9,21/17) -> (11/9,21/17) Reflection Matrix(277,-344,62,-77) (21/17,5/4) -> (31/7,9/2) Glide Reflection Matrix(363,-458,256,-323) (5/4,19/15) -> (17/12,27/19) Glide Reflection Matrix(440,-559,159,-202) (19/15,14/11) -> (11/4,25/9) Hyperbolic Matrix(237,-302,62,-79) (14/11,9/7) -> (19/5,4/1) Hyperbolic Matrix(428,-553,113,-146) (9/7,22/17) -> (15/4,19/5) Hyperbolic Matrix(488,-633,313,-406) (22/17,13/10) -> (14/9,25/16) Hyperbolic Matrix(399,-520,122,-159) (13/10,17/13) -> (13/4,23/7) Glide Reflection Matrix(199,-262,60,-79) (17/13,4/3) -> (23/7,10/3) Glide Reflection Matrix(137,-184,102,-137) (4/3,23/17) -> (4/3,23/17) Reflection Matrix(254,-345,187,-254) (23/17,15/11) -> (23/17,15/11) Reflection Matrix(482,-659,177,-242) (15/11,11/8) -> (19/7,30/11) Glide Reflection Matrix(394,-545,227,-314) (11/8,18/13) -> (26/15,7/4) Glide Reflection Matrix(344,-477,75,-104) (18/13,7/5) -> (9/2,23/5) Glide Reflection Matrix(772,-1089,207,-292) (7/5,24/17) -> (41/11,15/4) Glide Reflection Matrix(182,-257,17,-24) (24/17,41/29) -> (9/1,1/0) Hyperbolic Matrix(340,-481,41,-58) (41/29,17/12) -> (8/1,9/1) Hyperbolic Matrix(892,-1269,627,-892) (27/19,47/33) -> (27/19,47/33) Reflection Matrix(659,-940,462,-659) (47/33,10/7) -> (47/33,10/7) Reflection Matrix(395,-566,164,-235) (10/7,23/16) -> (12/5,29/12) Glide Reflection Matrix(2001,-2878,1280,-1841) (23/16,59/41) -> (25/16,61/39) Glide Reflection Matrix(532,-767,369,-532) (59/41,13/9) -> (59/41,13/9) Reflection Matrix(277,-402,82,-119) (13/9,3/2) -> (27/8,17/5) Hyperbolic Matrix(733,-1126,166,-255) (3/2,20/13) -> (22/5,53/12) Hyperbolic Matrix(819,-1262,220,-339) (20/13,17/11) -> (26/7,41/11) Glide Reflection Matrix(361,-560,78,-121) (17/11,14/9) -> (23/5,14/3) Glide Reflection Matrix(428,-671,273,-428) (61/39,11/7) -> (61/39,11/7) Reflection Matrix(100,-159,39,-62) (11/7,8/5) -> (5/2,13/5) Hyperbolic Matrix(223,-358,38,-61) (8/5,29/18) -> (23/4,6/1) Hyperbolic Matrix(482,-777,299,-482) (37/23,21/13) -> (37/23,21/13) Reflection Matrix(382,-619,137,-222) (21/13,13/8) -> (25/9,14/5) Glide Reflection Matrix(76,-125,45,-74) (13/8,5/3) -> (5/3,12/7) Parabolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(79,-140,22,-39) (7/4,9/5) -> (7/2,11/3) Glide Reflection Matrix(64,-117,35,-64) (9/5,13/7) -> (9/5,13/7) Reflection Matrix(118,-221,63,-118) (13/7,17/9) -> (13/7,17/9) Reflection Matrix(262,-497,97,-184) (15/8,2/1) -> (27/10,46/17) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(275,-666,64,-155) (29/12,17/7) -> (17/4,13/3) Glide Reflection Matrix(180,-439,41,-100) (17/7,5/2) -> (13/3,22/5) Glide Reflection Matrix(144,-377,55,-144) (13/5,29/11) -> (13/5,29/11) Reflection Matrix(175,-464,66,-175) (29/11,8/3) -> (29/11,8/3) Reflection Matrix(125,-336,16,-43) (8/3,27/10) -> (15/2,8/1) Hyperbolic Matrix(512,-1387,189,-512) (73/27,19/7) -> (73/27,19/7) Reflection Matrix(112,-307,27,-74) (30/11,11/4) -> (4/1,17/4) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(609,-1952,190,-609) (16/5,61/19) -> (16/5,61/19) Reflection Matrix(550,-1769,171,-550) (61/19,29/9) -> (61/19,29/9) Reflection Matrix(312,-1009,47,-152) (29/9,13/4) -> (33/5,20/3) Glide Reflection Matrix(87,-292,14,-47) (10/3,27/8) -> (6/1,13/2) Glide Reflection Matrix(154,-527,45,-154) (17/5,31/9) -> (17/5,31/9) Reflection Matrix(125,-434,36,-125) (31/9,7/2) -> (31/9,7/2) Reflection Matrix(188,-693,51,-188) (11/3,63/17) -> (11/3,63/17) Reflection Matrix(883,-3276,238,-883) (63/17,26/7) -> (63/17,26/7) Reflection Matrix(487,-2152,74,-327) (53/12,31/7) -> (13/2,33/5) Glide Reflection Matrix(197,-924,42,-197) (14/3,33/7) -> (14/3,33/7) Reflection Matrix(34,-165,7,-34) (33/7,5/1) -> (33/7,5/1) Reflection Matrix(16,-85,3,-16) (5/1,17/3) -> (5/1,17/3) Reflection Matrix(86,-493,15,-86) (17/3,29/5) -> (17/3,29/5) Reflection Matrix(36,-245,5,-34) (20/3,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,74,1) (-1/1,1/0) -> (-1/37,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,36,1) (-1/1,1/1) -> (-1/18,0/1) Matrix(10,-11,9,-10) -> Matrix(19,1,-360,-19) (1/1,11/9) -> (-1/18,-1/20) Matrix(188,-231,153,-188) -> Matrix(341,17,-6840,-341) (11/9,21/17) -> (-1/20,-17/342) Matrix(277,-344,62,-77) -> Matrix(141,7,-4250,-211) Matrix(363,-458,256,-323) -> Matrix(467,23,-10010,-493) Matrix(440,-559,159,-202) -> Matrix(41,2,-1046,-51) Matrix(237,-302,62,-79) -> Matrix(143,7,-4188,-205) Matrix(428,-553,113,-146) -> Matrix(103,5,-2946,-143) Matrix(488,-633,313,-406) -> Matrix(329,16,-7382,-359) Matrix(399,-520,122,-159) -> Matrix(41,2,-1086,-53) Matrix(199,-262,60,-79) -> Matrix(145,7,-4122,-199) Matrix(137,-184,102,-137) -> Matrix(251,12,-5250,-251) (4/3,23/17) -> (-6/125,-1/21) Matrix(254,-345,187,-254) -> Matrix(463,22,-9744,-463) (23/17,15/11) -> (-1/21,-11/232) Matrix(482,-659,177,-242) -> Matrix(317,15,-8728,-413) Matrix(394,-545,227,-314) -> Matrix(149,7,-3512,-165) Matrix(344,-477,75,-104) -> Matrix(191,9,-5836,-275) Matrix(772,-1089,207,-292) -> Matrix(107,5,-3060,-143) Matrix(182,-257,17,-24) -> Matrix(43,2,-1398,-65) Matrix(340,-481,41,-58) -> Matrix(107,5,-3574,-167) Matrix(892,-1269,627,-892) -> Matrix(1289,60,-27692,-1289) (27/19,47/33) -> (-15/322,-2/43) Matrix(659,-940,462,-659) -> Matrix(947,44,-20382,-947) (47/33,10/7) -> (-2/43,-11/237) Matrix(395,-566,164,-235) -> Matrix(173,8,-4606,-213) Matrix(2001,-2878,1280,-1841) -> Matrix(173,8,-3914,-181) Matrix(532,-767,369,-532) -> Matrix(109,5,-2376,-109) (59/41,13/9) -> (-5/108,-1/22) Matrix(277,-402,82,-119) -> Matrix(217,10,-6228,-287) Matrix(733,-1126,166,-255) -> Matrix(111,5,-3308,-149) Matrix(819,-1262,220,-339) -> Matrix(89,4,-2514,-113) Matrix(361,-560,78,-121) -> Matrix(223,10,-6846,-307) Matrix(428,-671,273,-428) -> Matrix(111,5,-2464,-111) (61/39,11/7) -> (-1/22,-5/112) Matrix(100,-159,39,-62) -> Matrix(113,5,-3006,-133) Matrix(223,-358,38,-61) -> Matrix(113,5,-3684,-163) Matrix(482,-777,299,-482) -> Matrix(341,15,-7752,-341) (37/23,21/13) -> (-3/68,-5/114) Matrix(382,-619,137,-222) -> Matrix(45,2,-1192,-53) Matrix(76,-125,45,-74) -> Matrix(137,6,-3174,-139) -1/23 Matrix(419,-722,242,-417) -> Matrix(209,9,-4900,-211) -3/70 Matrix(79,-140,22,-39) -> Matrix(71,3,-2106,-89) Matrix(64,-117,35,-64) -> Matrix(119,5,-2832,-119) (9/5,13/7) -> (-5/118,-1/24) Matrix(118,-221,63,-118) -> Matrix(217,9,-5232,-217) (13/7,17/9) -> (-1/24,-9/218) Matrix(262,-497,97,-184) -> Matrix(243,10,-6634,-273) Matrix(43,-98,18,-41) -> Matrix(77,3,-2028,-79) -1/26 Matrix(275,-666,64,-155) -> Matrix(27,1,-890,-33) Matrix(180,-439,41,-100) -> Matrix(27,1,-836,-31) Matrix(144,-377,55,-144) -> Matrix(269,10,-7236,-269) (13/5,29/11) -> (-5/134,-1/27) Matrix(175,-464,66,-175) -> Matrix(325,12,-8802,-325) (29/11,8/3) -> (-1/27,-6/163) Matrix(125,-336,16,-43) -> Matrix(27,1,-1000,-37) Matrix(512,-1387,189,-512) -> Matrix(575,21,-15744,-575) (73/27,19/7) -> (-3/82,-7/192) Matrix(112,-307,27,-74) -> Matrix(83,3,-2518,-91) Matrix(31,-90,10,-29) -> Matrix(55,2,-1568,-57) -1/28 Matrix(609,-1952,190,-609) -> Matrix(-1,0,58,1) (16/5,61/19) -> (-1/29,0/1) Matrix(550,-1769,171,-550) -> Matrix(-1,0,56,1) (61/19,29/9) -> (-1/28,0/1) Matrix(312,-1009,47,-152) -> Matrix(57,2,-1852,-65) Matrix(87,-292,14,-47) -> Matrix(29,1,-1014,-35) Matrix(154,-527,45,-154) -> Matrix(289,10,-8352,-289) (17/5,31/9) -> (-5/144,-1/29) Matrix(125,-434,36,-125) -> Matrix(233,8,-6786,-233) (31/9,7/2) -> (-1/29,-4/117) Matrix(188,-693,51,-188) -> Matrix(-1,0,60,1) (11/3,63/17) -> (-1/30,0/1) Matrix(883,-3276,238,-883) -> Matrix(-1,0,54,1) (63/17,26/7) -> (-1/27,0/1) Matrix(487,-2152,74,-327) -> Matrix(-1,0,62,1) *** -> (-1/31,0/1) Matrix(197,-924,42,-197) -> Matrix(371,12,-11470,-371) (14/3,33/7) -> (-6/185,-1/31) Matrix(34,-165,7,-34) -> Matrix(63,2,-1984,-63) (33/7,5/1) -> (-1/31,-1/32) Matrix(16,-85,3,-16) -> Matrix(31,1,-960,-31) (5/1,17/3) -> (-1/30,-1/32) Matrix(86,-493,15,-86) -> Matrix(161,5,-5184,-161) (17/3,29/5) -> (-1/32,-5/162) Matrix(36,-245,5,-34) -> Matrix(65,2,-2178,-67) -1/33 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.