INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -9/1 -8/1 -15/2 -22/3 -20/3 -6/1 -28/5 -27/5 -16/3 -21/4 -5/1 -24/5 -14/3 -9/2 -35/8 -48/11 -21/5 -4/1 -15/4 -26/7 -18/5 -25/7 -10/3 -3/1 -20/7 -25/9 -100/39 -5/2 -12/5 -20/9 -24/11 -15/7 -2/1 -15/8 -5/3 -18/11 -45/29 -3/2 -45/31 -10/7 -15/11 -5/4 -6/5 -15/13 -10/9 0/1 1/1 10/9 15/13 6/5 5/4 30/23 15/11 10/7 3/2 30/19 18/11 5/3 30/17 15/8 2/1 15/7 24/11 20/9 120/53 30/13 210/89 12/5 5/2 100/39 60/23 240/89 30/11 25/9 120/43 45/16 20/7 3/1 60/19 45/14 10/3 27/8 7/2 210/59 25/7 18/5 26/7 15/4 4/1 25/6 21/5 30/7 13/3 48/11 35/8 9/2 60/13 14/3 19/4 24/5 29/6 5/1 21/4 16/3 27/5 60/11 11/2 28/5 17/3 23/4 29/5 6/1 25/4 19/3 13/2 20/3 27/4 7/1 22/3 15/2 23/3 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/1 -9/1 -1/2 -17/2 0/1 1/5 -8/1 0/1 -15/2 -1/2 -22/3 -1/3 -7/1 -1/2 -20/3 0/1 -33/5 1/2 -13/2 -1/1 -2/3 -32/5 -2/5 -19/3 -1/4 -6/1 -1/3 -23/4 -2/9 -1/5 -17/3 -3/10 -45/8 -1/4 -28/5 -2/9 -39/7 -3/14 -11/2 -1/7 0/1 -27/5 1/0 -16/3 -2/5 -21/4 -1/4 -5/1 -1/4 -24/5 0/1 -19/4 -4/19 -1/5 -14/3 -1/7 -23/5 1/2 -32/7 0/1 -41/9 -3/8 -9/2 -1/4 -31/7 -1/4 -22/5 -3/13 -57/13 -3/14 -35/8 -1/4 -48/11 -2/9 -61/14 -2/9 -5/23 -13/3 -3/14 -30/7 -1/5 -17/4 -1/5 -4/21 -21/5 -1/6 -4/1 0/1 -23/6 -5/27 -2/11 -19/5 -1/6 -15/4 -1/6 -26/7 -3/19 -63/17 -5/32 -37/10 -4/25 -3/19 -48/13 -2/13 -59/16 -3/19 -2/13 -11/3 -3/20 -29/8 -1/7 0/1 -18/5 -1/7 -61/17 -17/124 -43/12 -9/67 -2/15 -25/7 -1/8 -57/16 -1/8 -89/25 -1/8 -32/9 0/1 -39/11 -1/10 -7/2 -1/5 0/1 -38/11 -5/31 -31/9 -1/6 -24/7 -2/13 -41/12 -1/7 -2/15 -58/17 -1/5 -17/5 -5/32 -61/18 -2/13 -1/7 -44/13 -2/13 -27/8 -3/20 -10/3 -1/7 -33/10 -3/22 -23/7 -1/8 -59/18 -1/7 -2/15 -36/11 -2/15 -13/4 -1/7 -2/15 -16/5 -2/17 -19/6 -1/11 0/1 -22/7 -1/5 -3/1 -1/8 -23/8 -1/9 -2/19 -20/7 0/1 -17/6 -1/7 0/1 -14/5 -3/25 -53/19 -11/94 -39/14 -3/26 -25/9 -1/8 -61/22 -3/25 -2/17 -36/13 -2/17 -11/4 -4/35 -1/9 -30/11 -1/9 -19/7 -7/64 -27/10 -3/28 -89/33 -3/28 -62/23 -1/9 -35/13 -3/28 -43/16 -13/123 -2/19 -8/3 -2/19 -37/14 -4/41 -3/31 -66/25 -1/11 -29/11 -1/10 -50/19 -1/11 -121/46 -1/9 0/1 -71/27 -1/12 -21/8 -1/10 -55/21 -1/10 -89/34 -6/65 -1/11 -123/47 -3/34 -34/13 -1/11 -13/5 -1/8 -31/12 -2/17 -1/9 -18/7 -1/9 -59/23 -23/212 -100/39 -4/37 -41/16 -7/65 -10/93 -23/9 -7/66 -28/11 -2/19 -5/2 -1/10 -32/13 -2/21 -27/11 -1/10 -49/20 -15/157 -2/21 -22/9 -5/53 -61/25 -25/268 -100/41 -4/43 -39/16 -5/54 -17/7 -3/34 -29/12 -1/11 0/1 -12/5 0/1 -31/13 -1/10 -50/21 -1/11 -69/29 -1/10 -19/8 -1/9 0/1 -26/11 -5/51 -59/25 -25/258 -33/14 -5/52 -40/17 -2/21 -7/3 -3/32 -30/13 -1/11 -23/10 -1/11 -10/111 -85/37 -7/78 -62/27 -1/11 -101/44 -13/145 -32/357 -39/17 -5/56 -16/7 -4/45 -41/18 -2/23 -3/35 -25/11 -3/34 -59/26 -1/11 -2/23 -34/15 -5/57 -43/19 -17/196 -9/4 -1/12 -29/13 -1/12 -20/9 0/1 -31/14 -1/11 -2/23 -11/5 -1/10 -24/11 -2/23 -13/6 -2/23 -3/35 -28/13 -6/71 -15/7 -1/12 -17/8 -5/61 -4/49 -2/1 -1/13 -17/9 -9/124 -15/8 -1/14 -28/15 -8/113 -13/7 -1/14 -24/13 -2/29 -11/6 -1/15 0/1 -20/11 -2/29 -29/16 -4/59 -1/15 -9/5 -1/14 -43/24 -15/217 -2/29 -120/67 -2/29 -77/43 -31/450 -34/19 -9/131 -59/33 -33/482 -25/14 -3/44 -91/51 -3/44 -66/37 -7/103 -41/23 -11/162 -16/9 -4/59 -39/22 -7/104 -62/35 -1/15 -23/13 -13/194 -30/17 -1/15 -7/4 -1/15 -4/61 -33/19 -1/16 -92/53 -2/31 -151/87 -1/16 -210/121 -1/15 -59/34 -1/15 -2/31 -26/15 -3/47 -45/26 -1/16 -19/11 -1/16 -69/40 -3/44 -50/29 -1/15 -31/18 -1/15 -2/31 -12/7 -2/31 -29/17 -1/16 -75/44 -1/16 -121/71 -21/338 -46/27 -3/49 -17/10 -1/15 0/1 -39/23 -3/46 -139/82 -9/139 -20/309 -100/59 -2/31 -61/36 -2/31 -3/47 -83/49 -5/78 -22/13 -1/15 -27/16 -5/78 -5/3 -1/16 -33/20 -7/114 -61/37 -37/604 -28/17 -8/131 -23/14 -2/33 -5/83 -41/25 -1/16 -100/61 -2/33 -59/36 -2/33 -1/17 -18/11 -1/17 -31/19 -1/16 -75/46 -1/16 -44/27 -6/97 -13/8 -3/49 -2/33 -60/37 -2/33 -47/29 -11/182 -34/21 -5/83 -89/55 -3/50 -55/34 -3/50 -21/13 -3/50 -71/44 -6/101 -13/219 -50/31 -1/17 -29/18 -1/17 0/1 -37/23 -1/18 -82/51 -1/15 -45/28 -1/16 -8/5 -2/33 -35/22 -5/84 -97/61 -9/152 -62/39 -1/17 -151/95 -5/84 -240/151 -6/101 -89/56 -6/101 -1/17 -27/17 -5/84 -73/46 -32/539 -13/219 -119/75 -75/1264 -46/29 -15/253 -19/12 -12/203 -1/17 -30/19 -1/17 -11/7 -7/120 -36/23 -4/69 -61/39 -39/674 -25/16 -3/52 -89/57 -3/52 -64/41 -8/139 -39/25 -3/52 -53/34 -13/227 -2/35 -120/77 -2/35 -67/43 -13/228 -14/9 -1/17 -59/38 -2/35 -3/53 -45/29 -1/18 -31/20 -1/17 -2/35 -17/11 -5/86 -37/24 -8/139 -5/87 -20/13 -2/35 -23/15 -5/88 -3/2 -1/18 -22/15 -3/55 -41/28 -15/277 -2/37 -60/41 -2/37 -19/13 -7/130 -16/11 -2/37 -61/42 -2/37 -1/19 -45/31 -3/56 -29/20 -4/75 -1/19 -13/9 -3/56 -36/25 -4/75 -59/41 -41/770 -82/57 -29/545 -23/16 -11/207 -6/113 -10/7 -1/19 -37/26 -17/325 -8/153 -64/45 -6/115 -91/64 -1/19 -8/153 -27/19 -7/134 -44/31 -16/307 -105/74 -5/96 -61/43 -43/826 -17/12 -4/77 -7/135 -58/41 -5/97 -99/70 -7/136 -140/99 -2/39 -41/29 -1/20 -24/17 -2/39 -55/39 -1/20 -31/22 -1/19 -6/115 -7/5 -3/58 -39/28 -5/98 -32/23 -8/157 -121/87 -53/1042 -210/151 -3/59 -89/64 -3/59 -34/669 -57/41 -7/138 -25/18 -1/20 -68/49 -4/77 -43/31 -9/176 -61/44 -2/39 -3/59 -18/13 -3/59 -29/21 -1/20 -40/29 -2/39 -11/8 -3/59 -4/79 -59/43 -43/852 -48/35 -6/119 -85/62 -13/258 -37/27 -15/298 -63/46 -1/20 -89/65 -1/20 -26/19 -9/179 -15/11 -1/20 -34/25 -13/261 -19/14 -8/161 -7/141 -23/17 -7/142 -27/20 -1/20 -31/23 -1/20 -4/3 -2/41 -29/22 -4/83 -1/21 -25/19 -3/62 -21/16 -5/104 -17/13 -13/272 -30/23 -1/21 -13/10 -1/21 -10/211 -61/47 -47/994 -48/37 -6/127 -83/64 -28/593 -11/233 -35/27 -5/106 -57/44 -5/106 -22/17 -1/21 -53/41 -3/64 -31/24 -1/21 -6/127 -9/7 -3/64 -41/32 -5/107 -2/43 -32/25 -8/171 -23/18 -13/279 -2/43 -60/47 -2/43 -37/29 -21/452 -14/11 -3/65 -61/48 -1/21 -2/43 -47/37 -1/22 -33/26 -5/108 -19/15 -7/152 -24/19 -4/87 -29/23 -1/22 -5/4 -1/22 -21/17 -1/22 -16/13 -2/45 -27/22 -5/112 -38/31 -11/247 -49/40 -31/697 -2/45 -60/49 -2/45 -11/9 -7/158 -39/32 -3/68 -28/23 -8/181 -45/37 -3/68 -17/14 -4/91 -1/23 -40/33 -4/91 -23/19 -3/68 -29/24 -4/91 -1/23 -6/5 -1/23 -31/26 -1/23 -6/139 -25/21 -5/116 -19/16 -4/93 -7/163 -32/27 -10/233 -13/11 -3/70 -33/28 -7/164 -20/17 -2/47 -27/23 -5/118 -7/6 -3/71 -4/95 -22/19 -9/215 -15/13 -1/24 -38/33 -17/409 -23/20 -10/241 -9/217 -8/7 -4/97 -17/15 -13/318 -9/8 -3/74 -10/9 -1/25 -11/10 -4/101 -7/177 -1/1 -1/28 0/1 0/1 1/1 1/30 10/9 1/27 9/8 3/80 17/15 13/344 8/7 4/105 15/13 1/26 22/19 9/233 7/6 4/103 3/77 20/17 2/51 33/28 7/178 13/11 3/76 32/27 10/253 19/16 7/177 4/101 6/5 1/25 23/19 3/74 17/14 1/25 4/99 45/37 3/74 28/23 8/197 39/32 3/74 11/9 7/172 27/22 5/122 16/13 2/49 21/17 1/24 5/4 1/24 24/19 4/95 19/15 7/166 14/11 3/71 23/18 2/47 13/305 32/25 8/187 41/32 2/47 5/117 9/7 3/70 31/24 6/139 1/23 22/17 1/23 57/44 5/116 35/27 5/116 48/37 6/139 61/47 47/1088 13/10 10/231 1/23 30/23 1/23 17/13 13/298 21/16 5/114 4/3 2/45 23/17 7/156 19/14 7/155 8/177 15/11 1/22 26/19 9/197 63/46 1/22 37/27 15/328 48/35 6/131 59/43 43/938 11/8 4/87 3/65 29/21 1/22 18/13 3/65 61/44 3/65 2/43 43/31 9/194 25/18 1/22 57/41 7/152 89/64 34/737 3/65 32/23 8/173 39/28 5/108 7/5 3/64 38/27 1/21 31/22 6/127 1/21 24/17 2/43 41/29 1/22 58/41 5/107 17/12 7/149 4/85 61/43 43/912 44/31 16/339 27/19 7/148 10/7 1/21 33/23 7/146 23/16 6/125 11/229 59/41 41/852 36/25 4/83 13/9 3/62 16/11 2/41 19/13 7/144 22/15 3/61 3/2 1/20 23/15 5/98 20/13 2/39 17/11 5/96 14/9 1/19 53/34 2/39 13/253 39/25 3/58 25/16 3/58 61/39 39/752 36/23 4/77 11/7 7/134 30/19 1/19 19/12 1/19 12/227 27/17 5/94 89/56 1/19 6/113 62/39 1/19 35/22 5/94 43/27 21/394 8/5 2/37 37/23 1/20 66/41 1/19 29/18 0/1 1/19 50/31 1/19 121/75 29/548 71/44 13/245 6/113 21/13 3/56 55/34 3/56 89/55 3/56 123/76 3/56 34/21 5/93 13/8 2/37 3/55 31/19 1/18 18/11 1/19 59/36 1/19 2/37 100/61 2/37 41/25 1/18 23/14 5/93 2/37 28/17 8/147 5/3 1/18 32/19 10/177 27/16 5/88 49/29 17/298 22/13 1/17 61/36 3/53 2/35 100/59 2/35 39/23 3/52 17/10 0/1 1/17 29/17 1/18 12/7 2/35 31/18 2/35 1/17 50/29 1/17 69/40 3/50 19/11 1/18 26/15 3/53 59/34 2/35 1/17 33/19 1/18 40/23 2/35 7/4 4/69 1/17 30/17 1/17 23/13 13/220 85/48 9/152 62/35 1/17 101/57 25/422 39/22 7/118 16/9 4/67 41/23 11/184 25/14 3/50 59/33 33/548 34/19 9/149 43/24 2/33 15/247 9/5 1/16 29/16 1/17 4/67 20/11 2/33 31/17 1/16 11/6 0/1 1/17 24/13 2/33 13/7 1/16 28/15 8/129 15/8 1/16 17/9 9/142 2/1 1/15 17/8 4/57 5/71 15/7 1/14 28/13 6/83 13/6 3/41 2/27 24/11 2/27 11/5 1/12 20/9 0/1 29/13 1/14 9/4 1/14 43/19 17/230 120/53 2/27 77/34 2/27 29/391 34/15 5/67 59/26 2/27 1/13 25/11 3/40 91/40 4/53 1/13 66/29 1/13 41/18 3/41 2/27 16/7 4/53 39/17 5/66 62/27 1/13 23/10 10/131 1/13 30/13 1/13 7/3 3/38 33/14 5/62 92/39 20/247 151/64 62/765 3/37 210/89 3/37 59/25 25/308 26/11 5/61 45/19 1/12 19/8 0/1 1/11 69/29 1/12 50/21 1/13 31/13 1/12 12/5 0/1 29/12 0/1 1/13 75/31 1/12 121/50 0/1 1/11 46/19 1/13 17/7 3/40 39/16 5/64 139/57 21/268 100/41 4/51 61/25 25/318 83/34 16/203 19/241 22/9 5/63 27/11 1/12 5/2 1/12 33/13 1/12 61/24 2/23 1/11 28/11 2/23 23/9 7/80 41/16 10/113 7/79 100/39 4/45 59/23 23/258 18/7 1/11 31/12 1/11 2/21 75/29 1/10 44/17 0/1 13/5 1/10 60/23 0/1 47/18 0/1 1/17 34/13 1/13 89/34 1/13 6/77 55/21 1/12 21/8 1/12 71/27 1/14 50/19 1/13 29/11 1/12 37/14 3/37 4/49 82/31 11/133 45/17 1/12 8/3 2/23 35/13 3/34 97/36 6/67 1/11 62/23 1/11 151/56 2/23 1/11 240/89 2/23 89/33 3/34 27/10 3/34 73/27 5/56 119/44 4/45 9/101 46/17 1/11 19/7 7/78 30/11 1/11 11/4 1/11 4/43 36/13 2/21 61/22 2/21 3/31 25/9 1/10 89/32 1/11 2/21 64/23 0/1 39/14 3/32 53/19 11/116 120/43 2/21 67/24 2/21 15/157 14/5 3/31 59/21 21/212 45/16 1/10 31/11 1/10 17/6 0/1 1/9 37/13 1/10 20/7 0/1 23/8 2/23 1/11 3/1 1/10 22/7 1/7 41/13 1/2 60/19 0/1 19/6 0/1 1/13 16/5 2/21 61/19 19/192 45/14 1/10 29/9 1/10 13/4 2/19 1/9 36/11 2/19 59/18 2/19 1/9 82/25 5/47 23/7 1/10 10/3 1/9 37/11 5/44 64/19 2/17 91/27 3/26 27/8 3/26 44/13 2/17 105/31 3/26 61/18 1/9 2/17 17/5 5/42 58/17 1/7 99/29 1/6 140/41 0/1 41/12 2/19 1/9 24/7 2/17 55/16 1/8 31/9 1/8 7/2 0/1 1/7 39/11 1/12 32/9 0/1 121/34 0/1 1/11 210/59 1/11 89/25 1/10 57/16 1/10 25/7 1/10 68/19 2/19 43/12 2/19 9/85 61/17 17/158 18/5 1/9 29/8 0/1 1/9 40/11 2/17 11/3 3/26 59/16 2/17 3/25 48/13 2/17 85/23 5/42 37/10 3/25 4/33 63/17 5/42 89/24 3/25 22/183 26/7 3/25 15/4 1/8 34/9 5/39 19/5 1/8 23/6 2/15 5/37 27/7 1/8 31/8 2/15 1/7 4/1 0/1 29/7 1/8 25/6 1/8 21/5 1/8 17/4 4/29 1/7 30/7 1/7 13/3 3/20 61/14 5/33 2/13 48/11 2/13 83/19 11/70 35/8 1/6 57/13 3/20 22/5 3/19 53/12 3/17 2/11 31/7 1/6 9/2 1/6 41/9 3/14 32/7 0/1 23/5 1/0 60/13 0/1 37/8 0/1 1/17 14/3 1/9 61/13 13/102 47/10 3/23 8/61 33/7 3/22 19/4 1/7 4/27 24/5 0/1 29/6 4/29 1/7 5/1 1/6 21/4 1/6 16/3 2/9 27/5 1/2 38/7 -1/1 49/9 -1/10 60/11 0/1 11/2 0/1 1/9 39/7 3/20 28/5 2/13 45/8 1/6 17/3 3/16 40/7 0/1 23/4 1/7 2/13 29/5 1/6 6/1 1/5 31/5 1/4 25/4 1/4 19/3 1/6 32/5 2/9 13/2 2/7 1/3 33/5 1/0 20/3 0/1 27/4 1/8 7/1 1/4 22/3 1/5 15/2 1/4 38/5 3/11 23/3 3/10 8/1 0/1 17/2 -1/3 0/1 9/1 1/4 10/1 1/3 11/1 1/4 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(121,1260,-46,-479) (-10/1,1/0) -> (-50/19,-121/46) Hyperbolic Matrix(119,1140,50,479) (-10/1,-9/1) -> (69/29,50/21) Hyperbolic Matrix(61,540,34,301) (-9/1,-17/2) -> (43/24,9/5) Hyperbolic Matrix(179,1500,50,419) (-17/2,-8/1) -> (68/19,43/12) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(299,2220,-186,-1381) (-15/2,-22/3) -> (-82/51,-45/28) Hyperbolic Matrix(59,420,42,299) (-22/3,-7/1) -> (7/5,38/27) Hyperbolic Matrix(61,420,-26,-179) (-7/1,-20/3) -> (-40/17,-7/3) Hyperbolic Matrix(299,1980,172,1139) (-20/3,-33/5) -> (33/19,40/23) Hyperbolic Matrix(301,1980,64,421) (-33/5,-13/2) -> (47/10,33/7) Hyperbolic Matrix(121,780,56,361) (-13/2,-32/5) -> (28/13,13/6) Hyperbolic Matrix(301,1920,66,421) (-32/5,-19/3) -> (41/9,32/7) Hyperbolic Matrix(239,1500,-134,-841) (-19/3,-6/1) -> (-66/37,-41/23) Hyperbolic Matrix(301,1740,-114,-659) (-6/1,-23/4) -> (-37/14,-66/25) Hyperbolic Matrix(179,1020,-116,-661) (-23/4,-17/3) -> (-17/11,-37/24) Hyperbolic Matrix(181,1020,96,541) (-17/3,-45/8) -> (15/8,17/9) Hyperbolic Matrix(299,1680,160,899) (-45/8,-28/5) -> (28/15,15/8) Hyperbolic Matrix(419,2340,118,659) (-28/5,-39/7) -> (39/11,32/9) Hyperbolic Matrix(539,3000,334,1859) (-39/7,-11/2) -> (71/44,21/13) Hyperbolic Matrix(299,1620,-122,-661) (-11/2,-27/5) -> (-27/11,-49/20) Hyperbolic Matrix(301,1620,212,1141) (-27/5,-16/3) -> (44/31,27/19) Hyperbolic Matrix(181,960,102,541) (-16/3,-21/4) -> (39/22,16/9) Hyperbolic Matrix(241,1260,92,481) (-21/4,-5/1) -> (55/21,21/8) Hyperbolic Matrix(299,1440,-212,-1021) (-5/1,-24/5) -> (-24/17,-55/39) Hyperbolic Matrix(301,1440,88,421) (-24/5,-19/4) -> (41/12,24/7) Hyperbolic Matrix(241,1140,-152,-719) (-19/4,-14/3) -> (-46/29,-19/12) Hyperbolic Matrix(181,840,-142,-659) (-14/3,-23/5) -> (-37/29,-14/11) Hyperbolic Matrix(301,1380,118,541) (-23/5,-32/7) -> (28/11,23/9) Hyperbolic Matrix(421,1920,66,301) (-32/7,-41/9) -> (19/3,32/5) Hyperbolic Matrix(659,3000,382,1739) (-41/9,-9/2) -> (69/40,19/11) Hyperbolic Matrix(121,540,54,241) (-9/2,-31/7) -> (29/13,9/4) Hyperbolic Matrix(421,1860,-122,-539) (-31/7,-22/5) -> (-38/11,-31/9) Hyperbolic Matrix(301,1320,96,421) (-22/5,-57/13) -> (3/1,22/7) Hyperbolic Matrix(781,3420,562,2461) (-57/13,-35/8) -> (25/18,57/41) Hyperbolic Matrix(1319,5760,-962,-4201) (-35/8,-48/11) -> (-48/35,-85/62) Hyperbolic Matrix(1321,5760,358,1561) (-48/11,-61/14) -> (59/16,48/13) Hyperbolic Matrix(1379,6000,510,2219) (-61/14,-13/3) -> (73/27,119/44) Hyperbolic Matrix(181,780,42,181) (-13/3,-30/7) -> (30/7,13/3) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(241,1020,142,601) (-17/4,-21/5) -> (39/23,17/10) Hyperbolic Matrix(359,1500,-230,-961) (-21/5,-4/1) -> (-64/41,-39/25) Hyperbolic Matrix(421,1620,-296,-1139) (-4/1,-23/6) -> (-37/26,-64/45) Hyperbolic Matrix(361,1380,220,841) (-23/6,-19/5) -> (41/25,23/14) Hyperbolic Matrix(301,1140,-174,-659) (-19/5,-15/4) -> (-45/26,-19/11) Hyperbolic Matrix(419,1560,-242,-901) (-15/4,-26/7) -> (-26/15,-45/26) Hyperbolic Matrix(1439,5340,-550,-2041) (-26/7,-63/17) -> (-123/47,-34/13) Hyperbolic Matrix(421,1560,146,541) (-63/17,-37/10) -> (23/8,3/1) Hyperbolic Matrix(1559,5760,-1202,-4441) (-37/10,-48/13) -> (-48/37,-83/64) Hyperbolic Matrix(1561,5760,358,1321) (-48/13,-59/16) -> (61/14,48/11) Hyperbolic Matrix(179,660,16,59) (-59/16,-11/3) -> (11/1,1/0) Hyperbolic Matrix(181,660,-82,-299) (-11/3,-29/8) -> (-31/14,-11/5) Hyperbolic Matrix(299,1080,116,419) (-29/8,-18/5) -> (18/7,31/12) Hyperbolic Matrix(601,2160,234,841) (-18/5,-61/17) -> (59/23,18/7) Hyperbolic Matrix(1021,3660,720,2581) (-61/17,-43/12) -> (17/12,61/43) Hyperbolic Matrix(721,2580,-268,-959) (-43/12,-25/7) -> (-35/13,-43/16) Hyperbolic Matrix(959,3420,740,2639) (-25/7,-57/16) -> (57/44,35/27) Hyperbolic Matrix(4499,16020,2780,9899) (-57/16,-89/25) -> (89/55,123/76) Hyperbolic Matrix(3659,13020,-2108,-7501) (-89/25,-32/9) -> (-92/53,-151/87) Hyperbolic Matrix(659,2340,118,419) (-32/9,-39/11) -> (39/7,28/5) Hyperbolic Matrix(661,2340,424,1501) (-39/11,-7/2) -> (53/34,39/25) Hyperbolic Matrix(121,420,104,361) (-7/2,-38/11) -> (22/19,7/6) Hyperbolic Matrix(419,1440,-332,-1141) (-31/9,-24/7) -> (-24/19,-29/23) Hyperbolic Matrix(421,1440,88,301) (-24/7,-41/12) -> (19/4,24/5) Hyperbolic Matrix(2461,8400,-1072,-3659) (-41/12,-58/17) -> (-62/27,-101/44) Hyperbolic Matrix(299,1020,158,539) (-58/17,-17/5) -> (17/9,2/1) Hyperbolic Matrix(1079,3660,778,2639) (-17/5,-61/18) -> (61/44,43/31) Hyperbolic Matrix(1081,3660,-744,-2519) (-61/18,-44/13) -> (-16/11,-61/42) Hyperbolic Matrix(479,1620,390,1319) (-44/13,-27/8) -> (27/22,16/13) Hyperbolic Matrix(179,600,-54,-181) (-27/8,-10/3) -> (-10/3,-33/10) Parabolic Matrix(419,1380,-310,-1021) (-33/10,-23/7) -> (-23/17,-27/20) Hyperbolic Matrix(1921,6300,-1134,-3719) (-23/7,-59/18) -> (-61/36,-83/49) Hyperbolic Matrix(1319,4320,476,1559) (-59/18,-36/11) -> (36/13,61/22) Hyperbolic Matrix(239,780,110,359) (-36/11,-13/4) -> (13/6,24/11) Hyperbolic Matrix(241,780,-148,-479) (-13/4,-16/5) -> (-44/27,-13/8) Hyperbolic Matrix(301,960,132,421) (-16/5,-19/6) -> (41/18,16/7) Hyperbolic Matrix(419,1320,-286,-901) (-19/6,-22/7) -> (-22/15,-41/28) Hyperbolic Matrix(421,1320,96,301) (-22/7,-3/1) -> (57/13,22/5) Hyperbolic Matrix(541,1560,146,421) (-3/1,-23/8) -> (37/10,63/17) Hyperbolic Matrix(481,1380,84,241) (-23/8,-20/7) -> (40/7,23/4) Hyperbolic Matrix(359,1020,-296,-841) (-20/7,-17/6) -> (-17/14,-40/33) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(601,1680,-386,-1079) (-14/5,-53/19) -> (-67/43,-14/9) Hyperbolic Matrix(839,2340,602,1679) (-53/19,-39/14) -> (39/28,7/5) Hyperbolic Matrix(539,1500,-410,-1141) (-39/14,-25/9) -> (-25/19,-21/16) Hyperbolic Matrix(1081,3000,476,1321) (-25/9,-61/22) -> (59/26,25/11) Hyperbolic Matrix(1559,4320,476,1319) (-61/22,-36/13) -> (36/11,59/18) Hyperbolic Matrix(239,660,130,359) (-36/13,-11/4) -> (11/6,24/13) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(421,1140,-332,-899) (-19/7,-27/10) -> (-33/26,-19/15) Hyperbolic Matrix(1801,4860,534,1441) (-27/10,-89/33) -> (91/27,27/8) Hyperbolic Matrix(5519,14880,-3472,-9361) (-89/33,-62/23) -> (-62/39,-151/95) Hyperbolic Matrix(2761,7440,-1202,-3239) (-62/23,-35/13) -> (-85/37,-62/27) Hyperbolic Matrix(179,480,22,59) (-43/16,-8/3) -> (8/1,17/2) Hyperbolic Matrix(181,480,-158,-419) (-8/3,-37/14) -> (-23/20,-8/7) Hyperbolic Matrix(3001,7920,-1682,-4439) (-66/25,-29/11) -> (-91/51,-66/37) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(2099,5520,570,1499) (-121/46,-71/27) -> (11/3,59/16) Hyperbolic Matrix(1141,3000,936,2461) (-71/27,-21/8) -> (39/32,11/9) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(779,2040,160,419) (-55/21,-89/34) -> (29/6,5/1) Hyperbolic Matrix(6121,16020,4402,11521) (-89/34,-123/47) -> (57/41,89/64) Hyperbolic Matrix(781,2040,-482,-1259) (-34/13,-13/5) -> (-47/29,-34/21) Hyperbolic Matrix(301,780,-208,-539) (-13/5,-31/12) -> (-29/20,-13/9) Hyperbolic Matrix(419,1080,116,299) (-31/12,-18/7) -> (18/5,29/8) Hyperbolic Matrix(841,2160,234,601) (-18/7,-59/23) -> (61/17,18/5) Hyperbolic Matrix(4679,12000,1918,4919) (-59/23,-100/39) -> (100/41,61/25) Hyperbolic Matrix(7021,18000,-4142,-10619) (-100/39,-41/16) -> (-139/82,-100/59) Hyperbolic Matrix(539,1380,398,1019) (-41/16,-23/9) -> (23/17,19/14) Hyperbolic Matrix(541,1380,118,301) (-23/9,-28/11) -> (32/7,23/5) Hyperbolic Matrix(119,300,-48,-121) (-28/11,-5/2) -> (-5/2,-32/13) Parabolic Matrix(1441,3540,-830,-2039) (-32/13,-27/11) -> (-33/19,-92/53) Hyperbolic Matrix(1201,2940,-980,-2399) (-49/20,-22/9) -> (-38/31,-49/40) Hyperbolic Matrix(2581,6300,-1794,-4379) (-22/9,-61/25) -> (-59/41,-82/57) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(6299,15360,-4454,-10861) (-100/41,-39/16) -> (-99/70,-140/99) Hyperbolic Matrix(419,1020,320,779) (-39/16,-17/7) -> (17/13,21/16) Hyperbolic Matrix(421,1020,-272,-659) (-17/7,-29/12) -> (-31/20,-17/11) Hyperbolic Matrix(299,720,174,419) (-29/12,-12/5) -> (12/7,31/18) Hyperbolic Matrix(301,720,176,421) (-12/5,-31/13) -> (29/17,12/7) Hyperbolic Matrix(1259,3000,478,1139) (-31/13,-50/21) -> (50/19,29/11) Hyperbolic Matrix(479,1140,50,119) (-50/21,-69/29) -> (9/1,10/1) Hyperbolic Matrix(1261,3000,984,2341) (-69/29,-19/8) -> (41/32,9/7) Hyperbolic Matrix(481,1140,-354,-839) (-19/8,-26/11) -> (-34/25,-19/14) Hyperbolic Matrix(1499,3540,838,1979) (-26/11,-59/25) -> (59/33,34/19) Hyperbolic Matrix(1679,3960,-1018,-2401) (-59/25,-33/14) -> (-33/20,-61/37) Hyperbolic Matrix(841,1980,714,1681) (-33/14,-40/17) -> (20/17,33/28) Hyperbolic Matrix(181,420,78,181) (-7/3,-30/13) -> (30/13,7/3) Hyperbolic Matrix(599,1380,260,599) (-30/13,-23/10) -> (23/10,30/13) Hyperbolic Matrix(2219,5100,600,1379) (-23/10,-85/37) -> (85/23,37/10) Hyperbolic Matrix(4079,9360,-2406,-5521) (-101/44,-39/17) -> (-39/23,-139/82) Hyperbolic Matrix(419,960,340,779) (-39/17,-16/7) -> (16/13,21/17) Hyperbolic Matrix(421,960,132,301) (-16/7,-41/18) -> (19/6,16/5) Hyperbolic Matrix(659,1500,-554,-1261) (-41/18,-25/11) -> (-25/21,-19/16) Hyperbolic Matrix(1321,3000,476,1081) (-25/11,-59/26) -> (61/22,25/9) Hyperbolic Matrix(1561,3540,900,2041) (-59/26,-34/15) -> (26/15,59/34) Hyperbolic Matrix(1801,4080,-1006,-2279) (-34/15,-43/19) -> (-77/43,-34/19) Hyperbolic Matrix(239,540,212,479) (-43/19,-9/4) -> (9/8,17/15) Hyperbolic Matrix(241,540,54,121) (-9/4,-29/13) -> (31/7,9/2) Hyperbolic Matrix(539,1200,296,659) (-29/13,-20/9) -> (20/11,31/17) Hyperbolic Matrix(541,1200,298,661) (-20/9,-31/14) -> (29/16,20/11) Hyperbolic Matrix(301,660,192,421) (-11/5,-24/11) -> (36/23,11/7) Hyperbolic Matrix(359,780,110,239) (-24/11,-13/6) -> (13/4,36/11) Hyperbolic Matrix(361,780,56,121) (-13/6,-28/13) -> (32/5,13/2) Hyperbolic Matrix(781,1680,642,1381) (-28/13,-15/7) -> (45/37,28/23) Hyperbolic Matrix(479,1020,394,839) (-15/7,-17/8) -> (17/14,45/37) Hyperbolic Matrix(481,1020,340,721) (-17/8,-2/1) -> (58/41,17/12) Hyperbolic Matrix(539,1020,158,299) (-2/1,-17/9) -> (17/5,58/17) Hyperbolic Matrix(541,1020,96,181) (-17/9,-15/8) -> (45/8,17/3) Hyperbolic Matrix(899,1680,160,299) (-15/8,-28/15) -> (28/5,45/8) Hyperbolic Matrix(419,780,354,659) (-28/15,-13/7) -> (13/11,32/27) Hyperbolic Matrix(421,780,292,541) (-13/7,-24/13) -> (36/25,13/9) Hyperbolic Matrix(359,660,130,239) (-24/13,-11/6) -> (11/4,36/13) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(959,1740,264,479) (-20/11,-29/16) -> (29/8,40/11) Hyperbolic Matrix(299,540,232,419) (-29/16,-9/5) -> (9/7,31/24) Hyperbolic Matrix(301,540,34,61) (-9/5,-43/24) -> (17/2,9/1) Hyperbolic Matrix(8039,14400,3550,6359) (-43/24,-120/67) -> (120/53,77/34) Hyperbolic Matrix(8041,14400,3552,6361) (-120/67,-77/43) -> (43/19,120/53) Hyperbolic Matrix(1979,3540,838,1499) (-34/19,-59/33) -> (59/25,26/11) Hyperbolic Matrix(1679,3000,1074,1919) (-59/33,-25/14) -> (25/16,61/39) Hyperbolic Matrix(1681,3000,404,721) (-25/14,-91/51) -> (29/7,25/6) Hyperbolic Matrix(539,960,370,659) (-41/23,-16/9) -> (16/11,19/13) Hyperbolic Matrix(541,960,102,181) (-16/9,-39/22) -> (21/4,16/3) Hyperbolic Matrix(4741,8400,-3352,-5939) (-39/22,-62/35) -> (-58/41,-99/70) Hyperbolic Matrix(4201,7440,-2642,-4679) (-62/35,-23/13) -> (-97/61,-62/39) Hyperbolic Matrix(781,1380,442,781) (-23/13,-30/17) -> (30/17,23/13) Hyperbolic Matrix(239,420,136,239) (-30/17,-7/4) -> (7/4,30/17) Hyperbolic Matrix(241,420,-206,-359) (-7/4,-33/19) -> (-27/23,-7/6) Hyperbolic Matrix(29039,50400,8158,14159) (-151/87,-210/121) -> (210/59,89/25) Hyperbolic Matrix(21781,37800,6120,10621) (-210/121,-59/34) -> (121/34,210/59) Hyperbolic Matrix(2041,3540,900,1561) (-59/34,-26/15) -> (34/15,59/26) Hyperbolic Matrix(1739,3000,382,659) (-19/11,-69/40) -> (9/2,41/9) Hyperbolic Matrix(661,1140,592,1021) (-69/40,-50/29) -> (10/9,9/8) Hyperbolic Matrix(1741,3000,1080,1861) (-50/29,-31/18) -> (29/18,50/31) Hyperbolic Matrix(419,720,174,299) (-31/18,-12/7) -> (12/5,29/12) Hyperbolic Matrix(421,720,176,301) (-12/7,-29/17) -> (31/13,12/5) Hyperbolic Matrix(2041,3480,634,1081) (-29/17,-75/44) -> (45/14,29/9) Hyperbolic Matrix(5879,10020,1830,3119) (-75/44,-121/71) -> (61/19,45/14) Hyperbolic Matrix(2641,4500,564,961) (-121/71,-46/27) -> (14/3,61/13) Hyperbolic Matrix(601,1020,142,241) (-17/10,-39/23) -> (21/5,17/4) Hyperbolic Matrix(7081,12000,4320,7321) (-100/59,-61/36) -> (59/36,100/61) Hyperbolic Matrix(2161,3660,284,481) (-83/49,-22/13) -> (38/5,23/3) Hyperbolic Matrix(959,1620,-782,-1321) (-22/13,-27/16) -> (-27/22,-38/31) Hyperbolic Matrix(179,300,-108,-181) (-27/16,-5/3) -> (-5/3,-33/20) Parabolic Matrix(3241,5340,-2330,-3839) (-61/37,-28/17) -> (-32/23,-121/87) Hyperbolic Matrix(839,1380,656,1079) (-28/17,-23/14) -> (23/18,32/25) Hyperbolic Matrix(841,1380,220,361) (-23/14,-41/25) -> (19/5,23/6) Hyperbolic Matrix(6001,9840,-4244,-6959) (-41/25,-100/61) -> (-140/99,-41/29) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(661,1080,478,781) (-18/11,-31/19) -> (29/21,18/13) Hyperbolic Matrix(2281,3720,810,1321) (-31/19,-75/46) -> (45/16,31/11) Hyperbolic Matrix(4859,7920,-3424,-5581) (-75/46,-44/27) -> (-44/31,-105/74) Hyperbolic Matrix(2219,3600,850,1379) (-13/8,-60/37) -> (60/23,47/18) Hyperbolic Matrix(2221,3600,852,1381) (-60/37,-47/29) -> (13/5,60/23) Hyperbolic Matrix(3299,5340,-2410,-3901) (-34/21,-89/55) -> (-89/65,-26/19) Hyperbolic Matrix(4079,6600,1186,1919) (-89/55,-55/34) -> (55/16,31/9) Hyperbolic Matrix(779,1260,630,1019) (-55/34,-21/13) -> (21/17,5/4) Hyperbolic Matrix(1859,3000,334,539) (-21/13,-71/44) -> (11/2,39/7) Hyperbolic Matrix(781,1260,-706,-1139) (-71/44,-50/31) -> (-10/9,-11/10) Hyperbolic Matrix(1861,3000,1080,1741) (-50/31,-29/18) -> (31/18,50/29) Hyperbolic Matrix(1081,1740,-894,-1439) (-29/18,-37/23) -> (-23/19,-29/24) Hyperbolic Matrix(3059,4920,932,1499) (-37/23,-82/51) -> (82/25,23/7) Hyperbolic Matrix(1621,2580,-1168,-1859) (-8/5,-35/22) -> (-25/18,-68/49) Hyperbolic Matrix(3961,6300,906,1441) (-35/22,-97/61) -> (83/19,35/8) Hyperbolic Matrix(36239,57600,13438,21359) (-151/95,-240/151) -> (240/89,89/33) Hyperbolic Matrix(36241,57600,13440,21361) (-240/151,-89/56) -> (151/56,240/89) Hyperbolic Matrix(2039,3240,528,839) (-89/56,-27/17) -> (27/7,31/8) Hyperbolic Matrix(1739,2760,264,419) (-27/17,-73/46) -> (13/2,33/5) Hyperbolic Matrix(3781,6000,2912,4621) (-73/46,-119/75) -> (61/47,13/10) Hyperbolic Matrix(2761,4380,984,1561) (-119/75,-46/29) -> (14/5,59/21) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) Hyperbolic Matrix(421,660,192,301) (-11/7,-36/23) -> (24/11,11/5) Hyperbolic Matrix(2761,4320,1918,3001) (-36/23,-61/39) -> (59/41,36/25) Hyperbolic Matrix(1919,3000,1074,1679) (-61/39,-25/16) -> (25/14,59/33) Hyperbolic Matrix(1921,3000,308,481) (-25/16,-89/57) -> (31/5,25/4) Hyperbolic Matrix(7379,11520,2190,3419) (-89/57,-64/41) -> (64/19,91/27) Hyperbolic Matrix(1501,2340,424,661) (-39/25,-53/34) -> (7/2,39/11) Hyperbolic Matrix(9239,14400,3310,5159) (-53/34,-120/77) -> (120/43,67/24) Hyperbolic Matrix(9241,14400,3312,5161) (-120/77,-67/43) -> (53/19,120/43) Hyperbolic Matrix(2819,4380,1042,1619) (-14/9,-59/38) -> (119/44,46/17) Hyperbolic Matrix(5759,8940,1700,2639) (-59/38,-45/29) -> (105/31,61/18) Hyperbolic Matrix(2399,3720,928,1439) (-45/29,-31/20) -> (31/12,75/29) Hyperbolic Matrix(779,1200,272,419) (-37/24,-20/13) -> (20/7,23/8) Hyperbolic Matrix(781,1200,274,421) (-20/13,-23/15) -> (37/13,20/7) Hyperbolic Matrix(1019,1560,744,1139) (-23/15,-3/2) -> (63/46,37/27) Hyperbolic Matrix(899,1320,694,1019) (-3/2,-22/15) -> (22/17,57/44) Hyperbolic Matrix(2459,3600,778,1139) (-41/28,-60/41) -> (60/19,19/6) Hyperbolic Matrix(2461,3600,780,1141) (-60/41,-19/13) -> (41/13,60/19) Hyperbolic Matrix(659,960,370,539) (-19/13,-16/11) -> (16/9,41/23) Hyperbolic Matrix(6901,10020,2852,4141) (-61/42,-45/31) -> (75/31,121/50) Hyperbolic Matrix(2399,3480,992,1439) (-45/31,-29/20) -> (29/12,75/31) Hyperbolic Matrix(541,780,292,421) (-13/9,-36/25) -> (24/13,13/7) Hyperbolic Matrix(3001,4320,1918,2761) (-36/25,-59/41) -> (61/39,36/23) Hyperbolic Matrix(3421,4920,1294,1861) (-82/57,-23/16) -> (37/14,82/31) Hyperbolic Matrix(419,600,-294,-421) (-23/16,-10/7) -> (-10/7,-37/26) Parabolic Matrix(8101,11520,2912,4141) (-64/45,-91/64) -> (89/32,64/23) Hyperbolic Matrix(3419,4860,2152,3059) (-91/64,-27/19) -> (27/17,89/56) Hyperbolic Matrix(1141,1620,212,301) (-27/19,-44/31) -> (16/3,27/5) Hyperbolic Matrix(6301,8940,2242,3181) (-105/74,-61/43) -> (59/21,45/16) Hyperbolic Matrix(2581,3660,720,1021) (-61/43,-17/12) -> (43/12,61/17) Hyperbolic Matrix(721,1020,340,481) (-17/12,-58/41) -> (2/1,17/8) Hyperbolic Matrix(1019,1440,806,1139) (-41/29,-24/17) -> (24/19,19/15) Hyperbolic Matrix(4681,6600,1788,2521) (-55/39,-31/22) -> (89/34,55/21) Hyperbolic Matrix(1321,1860,-1022,-1439) (-31/22,-7/5) -> (-53/41,-31/24) Hyperbolic Matrix(1679,2340,602,839) (-7/5,-39/28) -> (39/14,53/19) Hyperbolic Matrix(1681,2340,1380,1921) (-39/28,-32/23) -> (28/23,39/32) Hyperbolic Matrix(27179,37800,11518,16019) (-121/87,-210/151) -> (210/89,59/25) Hyperbolic Matrix(36241,50400,15360,21361) (-210/151,-89/64) -> (151/64,210/89) Hyperbolic Matrix(7681,10680,2072,2881) (-89/64,-57/41) -> (63/17,89/24) Hyperbolic Matrix(2461,3420,562,781) (-57/41,-25/18) -> (35/8,57/13) Hyperbolic Matrix(1081,1500,952,1321) (-68/49,-43/31) -> (17/15,8/7) Hyperbolic Matrix(2639,3660,778,1079) (-43/31,-61/44) -> (61/18,17/5) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(781,1080,478,661) (-18/13,-29/21) -> (31/19,18/11) Hyperbolic Matrix(1261,1740,566,781) (-29/21,-40/29) -> (20/9,29/13) Hyperbolic Matrix(4021,5520,2492,3421) (-11/8,-59/43) -> (121/75,71/44) Hyperbolic Matrix(4199,5760,3236,4439) (-59/43,-48/35) -> (48/37,61/47) Hyperbolic Matrix(3721,5100,2102,2881) (-85/62,-37/27) -> (23/13,85/48) Hyperbolic Matrix(1139,1560,744,1019) (-37/27,-63/46) -> (3/2,23/15) Hyperbolic Matrix(7799,10680,2190,2999) (-63/46,-89/65) -> (89/25,57/16) Hyperbolic Matrix(659,900,-484,-661) (-26/19,-15/11) -> (-15/11,-34/25) Parabolic Matrix(1019,1380,398,539) (-19/14,-23/17) -> (23/9,41/16) Hyperbolic Matrix(2401,3240,890,1201) (-27/20,-31/23) -> (89/33,27/10) Hyperbolic Matrix(179,240,44,59) (-31/23,-4/3) -> (4/1,29/7) Hyperbolic Matrix(181,240,46,61) (-4/3,-29/22) -> (31/8,4/1) Hyperbolic Matrix(2279,3000,1002,1319) (-29/22,-25/19) -> (25/11,91/40) Hyperbolic Matrix(779,1020,320,419) (-21/16,-17/13) -> (17/7,39/16) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(599,780,460,599) (-30/23,-13/10) -> (13/10,30/23) Hyperbolic Matrix(2819,3660,600,779) (-13/10,-61/47) -> (61/13,47/10) Hyperbolic Matrix(4439,5760,3236,4199) (-61/47,-48/37) -> (48/35,59/43) Hyperbolic Matrix(4859,6300,1804,2339) (-83/64,-35/27) -> (35/13,97/36) Hyperbolic Matrix(2639,3420,740,959) (-35/27,-57/44) -> (57/16,25/7) Hyperbolic Matrix(1019,1320,694,899) (-57/44,-22/17) -> (22/15,3/2) Hyperbolic Matrix(1021,1320,140,181) (-22/17,-53/41) -> (7/1,22/3) Hyperbolic Matrix(419,540,232,299) (-31/24,-9/7) -> (9/5,29/16) Hyperbolic Matrix(2341,3000,984,1261) (-9/7,-41/32) -> (19/8,69/29) Hyperbolic Matrix(1499,1920,1264,1619) (-41/32,-32/25) -> (32/27,19/16) Hyperbolic Matrix(1079,1380,656,839) (-32/25,-23/18) -> (23/14,28/17) Hyperbolic Matrix(2819,3600,610,779) (-23/18,-60/47) -> (60/13,37/8) Hyperbolic Matrix(2821,3600,612,781) (-60/47,-37/29) -> (23/5,60/13) Hyperbolic Matrix(3539,4500,1462,1859) (-14/11,-61/48) -> (121/50,46/19) Hyperbolic Matrix(2881,3660,662,841) (-61/48,-47/37) -> (13/3,61/14) Hyperbolic Matrix(1559,1980,1322,1679) (-47/37,-33/26) -> (33/28,13/11) Hyperbolic Matrix(1139,1440,806,1019) (-19/15,-24/19) -> (24/17,41/29) Hyperbolic Matrix(1621,2040,1002,1261) (-29/23,-5/4) -> (55/34,89/55) Hyperbolic Matrix(1019,1260,630,779) (-5/4,-21/17) -> (21/13,55/34) Hyperbolic Matrix(779,960,340,419) (-21/17,-16/13) -> (16/7,39/17) Hyperbolic Matrix(1319,1620,390,479) (-16/13,-27/22) -> (27/8,44/13) Hyperbolic Matrix(2939,3600,538,659) (-49/40,-60/49) -> (60/11,11/2) Hyperbolic Matrix(2941,3600,540,661) (-60/49,-11/9) -> (49/9,60/11) Hyperbolic Matrix(2461,3000,936,1141) (-11/9,-39/32) -> (21/8,71/27) Hyperbolic Matrix(1921,2340,1380,1681) (-39/32,-28/23) -> (32/23,39/28) Hyperbolic Matrix(1381,1680,642,781) (-28/23,-45/37) -> (15/7,28/13) Hyperbolic Matrix(839,1020,394,479) (-45/37,-17/14) -> (17/8,15/7) Hyperbolic Matrix(1139,1380,742,899) (-40/33,-23/19) -> (23/15,20/13) Hyperbolic Matrix(299,360,-250,-301) (-29/24,-6/5) -> (-6/5,-31/26) Parabolic Matrix(2519,3000,906,1079) (-31/26,-25/21) -> (25/9,89/32) Hyperbolic Matrix(1619,1920,1264,1499) (-19/16,-32/27) -> (32/25,41/32) Hyperbolic Matrix(659,780,354,419) (-32/27,-13/11) -> (13/7,28/15) Hyperbolic Matrix(2341,2760,866,1021) (-13/11,-33/28) -> (27/10,73/27) Hyperbolic Matrix(1019,1200,152,179) (-33/28,-20/17) -> (20/3,27/4) Hyperbolic Matrix(1021,1200,154,181) (-20/17,-27/23) -> (33/5,20/3) Hyperbolic Matrix(1139,1320,258,299) (-7/6,-22/19) -> (22/5,53/12) Hyperbolic Matrix(779,900,-676,-781) (-22/19,-15/13) -> (-15/13,-38/33) Parabolic Matrix(3179,3660,1302,1499) (-38/33,-23/20) -> (83/34,22/9) Hyperbolic Matrix(421,480,264,301) (-8/7,-17/15) -> (43/27,8/5) Hyperbolic Matrix(479,540,212,239) (-17/15,-9/8) -> (9/4,43/19) Hyperbolic Matrix(1021,1140,592,661) (-9/8,-10/9) -> (50/29,69/40) Hyperbolic Matrix(601,660,438,481) (-11/10,-1/1) -> (59/43,11/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(1139,-1260,706,-781) (1/1,10/9) -> (50/31,121/75) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(1921,-2220,726,-839) (15/13,22/19) -> (82/31,45/17) Hyperbolic Matrix(359,-420,206,-241) (7/6,20/17) -> (40/23,7/4) Hyperbolic Matrix(1261,-1500,554,-659) (19/16,6/5) -> (66/29,41/18) Hyperbolic Matrix(1439,-1740,894,-1081) (6/5,23/19) -> (37/23,66/41) Hyperbolic Matrix(841,-1020,296,-359) (23/19,17/14) -> (17/6,37/13) Hyperbolic Matrix(1321,-1620,782,-959) (11/9,27/22) -> (27/16,49/29) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(659,-840,142,-181) (14/11,23/18) -> (37/8,14/3) Hyperbolic Matrix(1439,-1860,1022,-1321) (31/24,22/17) -> (38/27,31/22) Hyperbolic Matrix(4441,-5760,1202,-1559) (35/27,48/37) -> (48/13,85/23) Hyperbolic Matrix(1141,-1500,410,-539) (21/16,4/3) -> (64/23,39/14) Hyperbolic Matrix(1199,-1620,356,-481) (4/3,23/17) -> (37/11,64/19) Hyperbolic Matrix(839,-1140,354,-481) (19/14,15/11) -> (45/19,19/8) Hyperbolic Matrix(1141,-1560,482,-659) (15/11,26/19) -> (26/11,45/19) Hyperbolic Matrix(3901,-5340,2410,-3299) (26/19,63/46) -> (123/76,34/21) Hyperbolic Matrix(4201,-5760,962,-1319) (37/27,48/35) -> (48/11,83/19) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(1859,-2580,1168,-1621) (43/31,25/18) -> (35/22,43/27) Hyperbolic Matrix(9361,-13020,3968,-5519) (89/64,32/23) -> (92/39,151/64) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(5939,-8400,3352,-4741) (41/29,58/41) -> (62/35,101/57) Hyperbolic Matrix(2579,-3660,804,-1141) (61/43,44/31) -> (16/5,61/19) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(4379,-6300,1794,-2581) (23/16,59/41) -> (61/25,83/34) Hyperbolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(901,-1320,286,-419) (19/13,22/15) -> (22/7,41/13) Hyperbolic Matrix(661,-1020,116,-179) (20/13,17/11) -> (17/3,40/7) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(1079,-1680,386,-601) (14/9,53/34) -> (67/24,14/5) Hyperbolic Matrix(961,-1500,230,-359) (39/25,25/16) -> (25/6,21/5) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(4679,-7440,2642,-4201) (62/39,35/22) -> (85/48,62/35) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(4919,-7920,2162,-3481) (66/41,29/18) -> (91/40,66/29) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(10979,-18000,4502,-7381) (100/61,41/25) -> (139/57,100/41) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(2099,-3540,890,-1501) (32/19,27/16) -> (33/14,92/39) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(3719,-6300,1134,-1921) (22/13,61/36) -> (59/18,82/25) Hyperbolic Matrix(9061,-15360,2654,-4499) (100/59,39/23) -> (99/29,140/41) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(659,-1140,174,-301) (19/11,26/15) -> (34/9,19/5) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(5281,-9360,2166,-3839) (101/57,39/22) -> (39/16,139/57) Hyperbolic Matrix(841,-1500,134,-239) (41/23,25/14) -> (25/4,19/3) Hyperbolic Matrix(2279,-4080,1006,-1801) (34/19,43/24) -> (77/34,34/15) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(3659,-8400,1072,-2461) (39/17,62/27) -> (58/17,99/29) Hyperbolic Matrix(3239,-7440,1202,-2761) (62/27,23/10) -> (97/36,62/23) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(3839,-9840,1124,-2881) (41/16,100/39) -> (140/41,41/12) Hyperbolic Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(2041,-5340,550,-1439) (34/13,89/34) -> (89/24,26/7) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(959,-2580,268,-721) (8/3,35/13) -> (25/7,68/19) Hyperbolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(61,-360,10,-59) (29/5,6/1) -> (6/1,31/5) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(121,1260,-46,-479) -> Matrix(1,0,-10,1) Matrix(119,1140,50,479) -> Matrix(1,0,14,1) Matrix(61,540,34,301) -> Matrix(5,2,82,33) Matrix(179,1500,50,419) -> Matrix(1,-2,10,-19) Matrix(61,480,-38,-299) -> Matrix(3,2,-50,-33) Matrix(299,2220,-186,-1381) -> Matrix(5,2,-78,-31) Matrix(59,420,42,299) -> Matrix(7,2,150,43) Matrix(61,420,-26,-179) -> Matrix(7,2,-74,-21) Matrix(299,1980,172,1139) -> Matrix(5,-2,88,-35) Matrix(301,1980,64,421) -> Matrix(1,-2,8,-15) Matrix(121,780,56,361) -> Matrix(7,4,96,55) Matrix(301,1920,66,421) -> Matrix(5,2,22,9) Matrix(239,1500,-134,-841) -> Matrix(5,4,-74,-59) Matrix(301,1740,-114,-659) -> Matrix(7,2,-74,-21) Matrix(179,1020,-116,-661) -> Matrix(5,2,-88,-35) Matrix(181,1020,96,541) -> Matrix(23,6,364,95) Matrix(299,1680,160,899) -> Matrix(41,10,660,161) Matrix(419,2340,118,659) -> Matrix(9,2,94,21) Matrix(539,3000,334,1859) -> Matrix(29,6,546,113) Matrix(299,1620,-122,-661) -> Matrix(1,-2,-10,21) Matrix(301,1620,212,1141) -> Matrix(7,6,148,127) Matrix(181,960,102,541) -> Matrix(17,6,286,101) Matrix(241,1260,92,481) -> Matrix(1,0,16,1) Matrix(299,1440,-212,-1021) -> Matrix(9,2,-176,-39) Matrix(301,1440,88,421) -> Matrix(9,2,76,17) Matrix(241,1140,-152,-719) -> Matrix(41,8,-692,-135) Matrix(181,840,-142,-659) -> Matrix(17,2,-366,-43) Matrix(301,1380,118,541) -> Matrix(3,2,34,23) Matrix(421,1920,66,301) -> Matrix(5,2,22,9) Matrix(659,3000,382,1739) -> Matrix(5,2,82,33) Matrix(121,540,54,241) -> Matrix(1,0,18,1) Matrix(421,1860,-122,-539) -> Matrix(7,2,-46,-13) Matrix(301,1320,96,421) -> Matrix(9,2,76,17) Matrix(781,3420,562,2461) -> Matrix(7,2,150,43) Matrix(1319,5760,-962,-4201) -> Matrix(141,32,-2798,-635) Matrix(1321,5760,358,1561) -> Matrix(19,4,166,35) Matrix(1379,6000,510,2219) -> Matrix(11,2,126,23) Matrix(181,780,42,181) -> Matrix(29,6,198,41) Matrix(239,1020,56,239) -> Matrix(41,8,292,57) Matrix(241,1020,142,601) -> Matrix(21,4,362,69) Matrix(359,1500,-230,-961) -> Matrix(45,8,-782,-139) Matrix(421,1620,-296,-1139) -> Matrix(29,6,-556,-115) Matrix(361,1380,220,841) -> Matrix(1,0,24,1) Matrix(301,1140,-174,-659) -> Matrix(11,2,-182,-33) Matrix(419,1560,-242,-901) -> Matrix(37,6,-586,-95) Matrix(1439,5340,-550,-2041) -> Matrix(25,4,-294,-47) Matrix(421,1560,146,541) -> Matrix(13,2,162,25) Matrix(1559,5760,-1202,-4441) -> Matrix(257,40,-5442,-847) Matrix(1561,5760,358,1321) -> Matrix(27,4,182,27) Matrix(179,660,16,59) -> Matrix(13,2,32,5) Matrix(181,660,-82,-299) -> Matrix(13,2,-150,-23) Matrix(299,1080,116,419) -> Matrix(13,2,136,21) Matrix(601,2160,234,841) -> Matrix(57,8,634,89) Matrix(1021,3660,720,2581) -> Matrix(163,22,3460,467) Matrix(721,2580,-268,-959) -> Matrix(61,8,-572,-75) Matrix(959,3420,740,2639) -> Matrix(37,4,860,93) Matrix(4499,16020,2780,9899) -> Matrix(13,2,240,37) Matrix(3659,13020,-2108,-7501) -> Matrix(17,2,-264,-31) Matrix(659,2340,118,419) -> Matrix(17,2,110,13) Matrix(661,2340,424,1501) -> Matrix(23,2,448,39) Matrix(121,420,104,361) -> Matrix(23,4,592,103) Matrix(419,1440,-332,-1141) -> Matrix(37,6,-808,-131) Matrix(421,1440,88,301) -> Matrix(13,2,84,13) Matrix(2461,8400,-1072,-3659) -> Matrix(29,6,-324,-67) Matrix(299,1020,158,539) -> Matrix(11,2,170,31) Matrix(1079,3660,778,2639) -> Matrix(53,8,1146,173) Matrix(1081,3660,-744,-2519) -> Matrix(1,0,-12,1) Matrix(479,1620,390,1319) -> Matrix(25,4,606,97) Matrix(179,600,-54,-181) -> Matrix(41,6,-294,-43) Matrix(419,1380,-310,-1021) -> Matrix(73,10,-1482,-203) Matrix(1921,6300,-1134,-3719) -> Matrix(59,8,-922,-125) Matrix(1319,4320,476,1559) -> Matrix(59,8,612,83) Matrix(239,780,110,359) -> Matrix(31,4,426,55) Matrix(241,780,-148,-479) -> Matrix(31,4,-504,-65) Matrix(301,960,132,421) -> Matrix(19,2,256,27) Matrix(419,1320,-286,-901) -> Matrix(7,2,-130,-37) Matrix(421,1320,96,301) -> Matrix(13,2,84,13) Matrix(541,1560,146,421) -> Matrix(21,2,178,17) Matrix(481,1380,84,241) -> Matrix(1,0,16,1) Matrix(359,1020,-296,-841) -> Matrix(29,4,-660,-91) Matrix(361,1020,-212,-599) -> Matrix(1,0,-8,1) Matrix(601,1680,-386,-1079) -> Matrix(33,4,-586,-71) Matrix(839,2340,602,1679) -> Matrix(137,16,2954,345) Matrix(539,1500,-410,-1141) -> Matrix(19,2,-390,-41) Matrix(1081,3000,476,1321) -> Matrix(67,8,896,107) Matrix(1559,4320,476,1319) -> Matrix(67,8,628,75) Matrix(239,660,130,359) -> Matrix(35,4,586,67) Matrix(241,660,88,241) -> Matrix(71,8,772,87) Matrix(419,1140,154,419) -> Matrix(127,14,1406,155) Matrix(421,1140,-332,-899) -> Matrix(129,14,-2792,-303) Matrix(1801,4860,534,1441) -> Matrix(1,0,18,1) Matrix(5519,14880,-3472,-9361) -> Matrix(73,8,-1232,-135) Matrix(2761,7440,-1202,-3239) -> Matrix(35,4,-394,-45) Matrix(179,480,22,59) -> Matrix(19,2,66,7) Matrix(181,480,-158,-419) -> Matrix(59,6,-1426,-145) Matrix(3001,7920,-1682,-4439) -> Matrix(37,4,-546,-59) Matrix(1139,3000,478,1259) -> Matrix(21,2,262,25) Matrix(2099,5520,570,1499) -> Matrix(21,2,178,17) Matrix(1141,3000,936,2461) -> Matrix(17,2,416,49) Matrix(481,1260,92,241) -> Matrix(1,0,16,1) Matrix(779,2040,160,419) -> Matrix(21,2,136,13) Matrix(6121,16020,4402,11521) -> Matrix(179,16,3882,347) Matrix(781,2040,-482,-1259) -> Matrix(27,2,-446,-33) Matrix(301,780,-208,-539) -> Matrix(19,2,-352,-37) Matrix(419,1080,116,299) -> Matrix(17,2,144,17) Matrix(841,2160,234,601) -> Matrix(73,8,666,73) Matrix(4679,12000,1918,4919) -> Matrix(591,64,7526,815) Matrix(7021,18000,-4142,-10619) -> Matrix(463,50,-7158,-773) Matrix(539,1380,398,1019) -> Matrix(131,14,2910,311) Matrix(541,1380,118,301) -> Matrix(19,2,66,7) Matrix(119,300,-48,-121) -> Matrix(39,4,-400,-41) Matrix(1441,3540,-830,-2039) -> Matrix(41,4,-646,-63) Matrix(1201,2940,-980,-2399) -> Matrix(337,32,-7572,-719) Matrix(2581,6300,-1794,-4379) -> Matrix(663,62,-12458,-1165) Matrix(4919,12000,1918,4679) -> Matrix(687,64,7718,719) Matrix(6299,15360,-4454,-10861) -> Matrix(409,38,-7954,-739) Matrix(419,1020,320,779) -> Matrix(109,10,2496,229) Matrix(421,1020,-272,-659) -> Matrix(21,2,-368,-35) Matrix(299,720,174,419) -> Matrix(23,2,402,35) Matrix(301,720,176,421) -> Matrix(19,2,332,35) Matrix(1259,3000,478,1139) -> Matrix(21,2,262,25) Matrix(479,1140,50,119) -> Matrix(1,0,14,1) Matrix(1261,3000,984,2341) -> Matrix(23,2,540,47) Matrix(481,1140,-354,-839) -> Matrix(79,8,-1590,-161) Matrix(1499,3540,838,1979) -> Matrix(267,26,4426,431) Matrix(1679,3960,-1018,-2401) -> Matrix(373,36,-6082,-587) Matrix(841,1980,714,1681) -> Matrix(251,24,6390,611) Matrix(181,420,78,181) -> Matrix(65,6,834,77) Matrix(599,1380,260,599) -> Matrix(221,20,2884,261) Matrix(2219,5100,600,1379) -> Matrix(289,26,2412,217) Matrix(4079,9360,-2406,-5521) -> Matrix(313,28,-4818,-431) Matrix(419,960,340,779) -> Matrix(157,14,3824,341) Matrix(421,960,132,301) -> Matrix(23,2,264,23) Matrix(659,1500,-554,-1261) -> Matrix(21,2,-494,-47) Matrix(1321,3000,476,1081) -> Matrix(91,8,944,83) Matrix(1561,3540,900,2041) -> Matrix(45,4,776,69) Matrix(1801,4080,-1006,-2279) -> Matrix(321,28,-4666,-407) Matrix(239,540,212,479) -> Matrix(93,8,2476,213) Matrix(241,540,54,121) -> Matrix(1,0,18,1) Matrix(539,1200,296,659) -> Matrix(25,2,412,33) Matrix(541,1200,298,661) -> Matrix(21,2,346,33) Matrix(301,660,192,421) -> Matrix(67,6,1284,115) Matrix(359,780,110,239) -> Matrix(47,4,458,39) Matrix(361,780,56,121) -> Matrix(47,4,176,15) Matrix(781,1680,642,1381) -> Matrix(309,26,7618,641) Matrix(479,1020,394,839) -> Matrix(195,16,4814,395) Matrix(481,1020,340,721) -> Matrix(99,8,2116,171) Matrix(539,1020,158,299) -> Matrix(27,2,202,15) Matrix(541,1020,96,181) -> Matrix(83,6,484,35) Matrix(899,1680,160,299) -> Matrix(141,10,860,61) Matrix(419,780,354,659) -> Matrix(199,14,5046,355) Matrix(421,780,292,541) -> Matrix(143,10,2960,207) Matrix(359,660,130,239) -> Matrix(59,4,634,43) Matrix(361,660,-262,-479) -> Matrix(57,4,-1126,-79) Matrix(959,1740,264,479) -> Matrix(59,4,516,35) Matrix(299,540,232,419) -> Matrix(31,2,728,47) Matrix(301,540,34,61) -> Matrix(29,2,130,9) Matrix(8039,14400,3550,6359) -> Matrix(1275,88,17198,1187) Matrix(8041,14400,3552,6361) -> Matrix(1393,96,18820,1297) Matrix(1979,3540,838,1499) -> Matrix(379,26,4650,319) Matrix(1679,3000,1074,1919) -> Matrix(527,36,10174,695) Matrix(1681,3000,404,721) -> Matrix(59,4,516,35) Matrix(539,960,370,659) -> Matrix(89,6,1854,125) Matrix(541,960,102,181) -> Matrix(89,6,430,29) Matrix(4741,8400,-3352,-5939) -> Matrix(625,42,-12128,-815) Matrix(4201,7440,-2642,-4679) -> Matrix(59,4,-1018,-69) Matrix(781,1380,442,781) -> Matrix(389,26,6598,441) Matrix(239,420,136,239) -> Matrix(121,8,2072,137) Matrix(241,420,-206,-359) -> Matrix(123,8,-2906,-189) Matrix(29039,50400,8158,14159) -> Matrix(1,0,26,1) Matrix(21781,37800,6120,10621) -> Matrix(31,2,356,23) Matrix(2041,3540,900,1561) -> Matrix(61,4,808,53) Matrix(1739,3000,382,659) -> Matrix(29,2,130,9) Matrix(661,1140,592,1021) -> Matrix(89,6,2388,161) Matrix(1741,3000,1080,1861) -> Matrix(31,2,604,39) Matrix(419,720,174,299) -> Matrix(31,2,418,27) Matrix(421,720,176,301) -> Matrix(31,2,356,23) Matrix(2041,3480,634,1081) -> Matrix(127,8,1254,79) Matrix(5879,10020,1830,3119) -> Matrix(321,20,3226,201) Matrix(2641,4500,564,961) -> Matrix(65,4,536,33) Matrix(601,1020,142,241) -> Matrix(61,4,442,29) Matrix(7081,12000,4320,7321) -> Matrix(125,8,2328,149) Matrix(2161,3660,284,481) -> Matrix(63,4,236,15) Matrix(959,1620,-782,-1321) -> Matrix(311,20,-6982,-449) Matrix(179,300,-108,-181) -> Matrix(95,6,-1536,-97) Matrix(3241,5340,-2330,-3839) -> Matrix(785,48,-15422,-943) Matrix(839,1380,656,1079) -> Matrix(263,16,6164,375) Matrix(841,1380,220,361) -> Matrix(1,0,24,1) Matrix(6001,9840,-4244,-6959) -> Matrix(65,4,-1284,-79) Matrix(7321,12000,4320,7081) -> Matrix(133,8,2344,141) Matrix(1319,2160,952,1559) -> Matrix(133,8,2876,173) Matrix(661,1080,478,781) -> Matrix(31,2,666,43) Matrix(2281,3720,810,1321) -> Matrix(63,4,614,39) Matrix(4859,7920,-3424,-5581) -> Matrix(741,46,-14224,-883) Matrix(2219,3600,850,1379) -> Matrix(33,2,610,37) Matrix(2221,3600,852,1381) -> Matrix(33,2,148,9) Matrix(3299,5340,-2410,-3901) -> Matrix(367,22,-7290,-437) Matrix(4079,6600,1186,1919) -> Matrix(67,4,586,35) Matrix(779,1260,630,1019) -> Matrix(167,10,4058,243) Matrix(1859,3000,334,539) -> Matrix(101,6,690,41) Matrix(781,1260,-706,-1139) -> Matrix(169,10,-4242,-251) Matrix(1861,3000,1080,1741) -> Matrix(35,2,612,35) Matrix(1081,1740,-894,-1439) -> Matrix(69,4,-1570,-91) Matrix(3059,4920,932,1499) -> Matrix(35,2,332,19) Matrix(1621,2580,-1168,-1859) -> Matrix(101,6,-1936,-115) Matrix(3961,6300,906,1441) -> Matrix(269,16,1698,101) Matrix(36239,57600,13438,21359) -> Matrix(471,28,5366,319) Matrix(36241,57600,13440,21361) -> Matrix(67,4,720,43) Matrix(2039,3240,528,839) -> Matrix(67,4,452,27) Matrix(1739,2760,264,419) -> Matrix(101,6,84,5) Matrix(3781,6000,2912,4621) -> Matrix(1651,98,38192,2267) Matrix(2761,4380,984,1561) -> Matrix(607,36,6188,367) Matrix(721,1140,456,721) -> Matrix(407,24,7716,455) Matrix(419,660,266,419) -> Matrix(239,14,4558,267) Matrix(421,660,192,301) -> Matrix(103,6,1356,79) Matrix(2761,4320,1918,3001) -> Matrix(1105,64,22946,1329) Matrix(1919,3000,1074,1679) -> Matrix(623,36,10366,599) Matrix(1921,3000,308,481) -> Matrix(139,8,608,35) Matrix(7379,11520,2190,3419) -> Matrix(313,18,2730,157) Matrix(1501,2340,424,661) -> Matrix(35,2,472,27) Matrix(9239,14400,3310,5159) -> Matrix(979,56,10262,587) Matrix(9241,14400,3312,5161) -> Matrix(841,48,8848,505) Matrix(2819,4380,1042,1619) -> Matrix(103,6,1150,67) Matrix(5759,8940,1700,2639) -> Matrix(141,8,1216,69) Matrix(2399,3720,928,1439) -> Matrix(1,0,28,1) Matrix(779,1200,272,419) -> Matrix(35,2,472,27) Matrix(781,1200,274,421) -> Matrix(35,2,262,15) Matrix(1019,1560,744,1139) -> Matrix(179,10,3920,219) Matrix(899,1320,694,1019) -> Matrix(257,14,5966,325) Matrix(2459,3600,778,1139) -> Matrix(37,2,758,41) Matrix(2461,3600,780,1141) -> Matrix(37,2,-56,-3) Matrix(659,960,370,539) -> Matrix(113,6,1902,101) Matrix(6901,10020,2852,4141) -> Matrix(37,2,388,21) Matrix(2399,3480,992,1439) -> Matrix(75,4,956,51) Matrix(541,780,292,421) -> Matrix(187,10,3048,163) Matrix(3001,4320,1918,2761) -> Matrix(1201,64,23138,1233) Matrix(3421,4920,1294,1861) -> Matrix(489,26,5962,317) Matrix(419,600,-294,-421) -> Matrix(265,14,-5054,-267) Matrix(8101,11520,2912,4141) -> Matrix(115,6,1284,67) Matrix(3419,4860,2152,3059) -> Matrix(39,2,760,39) Matrix(1141,1620,212,301) -> Matrix(115,6,364,19) Matrix(6301,8940,2242,3181) -> Matrix(1421,74,14306,745) Matrix(2581,3660,720,1021) -> Matrix(423,22,3980,207) Matrix(721,1020,340,481) -> Matrix(155,8,2228,115) Matrix(1019,1440,806,1139) -> Matrix(193,10,4574,237) Matrix(4681,6600,1788,2521) -> Matrix(1,0,32,1) Matrix(1321,1860,-1022,-1439) -> Matrix(1,0,-2,1) Matrix(1679,2340,602,839) -> Matrix(313,16,3306,169) Matrix(1681,2340,1380,1921) -> Matrix(313,16,7688,393) Matrix(27179,37800,11518,16019) -> Matrix(4601,234,56726,2885) Matrix(36241,50400,15360,21361) -> Matrix(5665,288,69888,3553) Matrix(7681,10680,2072,2881) -> Matrix(709,36,5928,301) Matrix(2461,3420,562,781) -> Matrix(39,2,214,11) Matrix(1081,1500,952,1321) -> Matrix(155,8,4088,211) Matrix(2639,3660,778,1079) -> Matrix(157,8,1354,69) Matrix(1559,2160,952,1319) -> Matrix(157,8,2924,149) Matrix(781,1080,478,661) -> Matrix(39,2,682,35) Matrix(1261,1740,566,781) -> Matrix(39,2,526,27) Matrix(4021,5520,2492,3421) -> Matrix(673,34,12688,641) Matrix(4199,5760,3236,4439) -> Matrix(2141,108,49580,2501) Matrix(3721,5100,2102,2881) -> Matrix(1509,76,25514,1285) Matrix(1139,1560,744,1019) -> Matrix(199,10,3960,199) Matrix(7799,10680,2190,2999) -> Matrix(159,8,1570,79) Matrix(659,900,-484,-661) -> Matrix(439,22,-8800,-441) Matrix(1019,1380,398,539) -> Matrix(283,14,3214,159) Matrix(2401,3240,890,1201) -> Matrix(163,8,1854,91) Matrix(179,240,44,59) -> Matrix(41,2,348,17) Matrix(181,240,46,61) -> Matrix(41,2,266,13) Matrix(2279,3000,1002,1319) -> Matrix(1,0,34,1) Matrix(779,1020,320,419) -> Matrix(209,10,2696,129) Matrix(781,1020,598,781) -> Matrix(545,26,12514,597) Matrix(599,780,460,599) -> Matrix(421,20,9704,461) Matrix(2819,3660,600,779) -> Matrix(465,22,3572,169) Matrix(4439,5760,3236,4199) -> Matrix(2285,108,49868,2357) Matrix(4859,6300,1804,2339) -> Matrix(805,38,9088,429) Matrix(2639,3420,740,959) -> Matrix(85,4,956,45) Matrix(1019,1320,694,899) -> Matrix(297,14,6046,285) Matrix(1021,1320,140,181) -> Matrix(43,2,236,11) Matrix(419,540,232,299) -> Matrix(43,2,752,35) Matrix(2341,3000,984,1261) -> Matrix(43,2,580,27) Matrix(1499,1920,1264,1619) -> Matrix(127,6,3196,151) Matrix(1079,1380,656,839) -> Matrix(343,16,6324,295) Matrix(2819,3600,610,779) -> Matrix(43,2,1010,47) Matrix(2821,3600,612,781) -> Matrix(43,2,-452,-21) Matrix(3539,4500,1462,1859) -> Matrix(43,2,494,23) Matrix(2881,3660,662,841) -> Matrix(173,8,1146,53) Matrix(1559,1980,1322,1679) -> Matrix(85,4,2146,101) Matrix(1139,1440,806,1019) -> Matrix(217,10,4622,213) Matrix(1621,2040,1002,1261) -> Matrix(305,14,5686,261) Matrix(1019,1260,630,779) -> Matrix(223,10,4170,187) Matrix(779,960,340,419) -> Matrix(313,14,4136,185) Matrix(1319,1620,390,479) -> Matrix(89,4,734,33) Matrix(2939,3600,538,659) -> Matrix(45,2,1102,49) Matrix(2941,3600,540,661) -> Matrix(45,2,-608,-27) Matrix(2461,3000,936,1141) -> Matrix(45,2,472,21) Matrix(1921,2340,1380,1681) -> Matrix(361,16,7784,345) Matrix(1381,1680,642,781) -> Matrix(589,26,8178,361) Matrix(839,1020,394,479) -> Matrix(363,16,5150,227) Matrix(1139,1380,742,899) -> Matrix(319,14,6266,275) Matrix(299,360,-250,-301) -> Matrix(229,10,-5290,-231) Matrix(2519,3000,906,1079) -> Matrix(93,4,1046,45) Matrix(1619,1920,1264,1499) -> Matrix(139,6,3220,139) Matrix(659,780,354,419) -> Matrix(327,14,5302,227) Matrix(2341,2760,866,1021) -> Matrix(515,22,5782,247) Matrix(1019,1200,152,179) -> Matrix(47,2,540,23) Matrix(1021,1200,154,181) -> Matrix(47,2,-118,-5) Matrix(1139,1320,258,299) -> Matrix(143,6,834,35) Matrix(779,900,-676,-781) -> Matrix(623,26,-14976,-625) Matrix(3179,3660,1302,1499) -> Matrix(1107,46,14030,583) Matrix(421,480,264,301) -> Matrix(243,10,4544,187) Matrix(479,540,212,239) -> Matrix(197,8,2684,109) Matrix(1021,1140,592,661) -> Matrix(149,6,2508,101) Matrix(601,660,438,481) -> Matrix(405,16,8834,349) Matrix(1,0,2,1) -> Matrix(1,0,58,1) Matrix(1139,-1260,706,-781) -> Matrix(271,-10,5122,-189) Matrix(419,-480,158,-181) -> Matrix(157,-6,1858,-71) Matrix(1921,-2220,726,-839) -> Matrix(519,-20,6254,-241) Matrix(359,-420,206,-241) -> Matrix(205,-8,3562,-139) Matrix(1261,-1500,554,-659) -> Matrix(51,-2,638,-25) Matrix(1439,-1740,894,-1081) -> Matrix(99,-4,1906,-77) Matrix(841,-1020,296,-359) -> Matrix(99,-4,916,-37) Matrix(1321,-1620,782,-959) -> Matrix(489,-20,8582,-351) Matrix(1141,-1440,332,-419) -> Matrix(143,-6,1168,-49) Matrix(899,-1140,332,-421) -> Matrix(331,-14,3712,-157) Matrix(659,-840,142,-181) -> Matrix(47,-2,494,-21) Matrix(1439,-1860,1022,-1321) -> Matrix(1,0,-2,1) Matrix(4441,-5760,1202,-1559) -> Matrix(927,-40,7810,-337) Matrix(1141,-1500,410,-539) -> Matrix(45,-2,518,-23) Matrix(1199,-1620,356,-481) -> Matrix(179,-8,1544,-69) Matrix(839,-1140,354,-481) -> Matrix(177,-8,2102,-95) Matrix(1141,-1560,482,-659) -> Matrix(307,-14,3706,-169) Matrix(3901,-5340,2410,-3299) -> Matrix(481,-22,8986,-411) Matrix(4201,-5760,962,-1319) -> Matrix(699,-32,4478,-205) Matrix(479,-660,262,-361) -> Matrix(87,-4,1414,-65) Matrix(1859,-2580,1168,-1621) -> Matrix(127,-6,2392,-113) Matrix(9361,-13020,3968,-5519) -> Matrix(1819,-84,22456,-1037) Matrix(1021,-1440,212,-299) -> Matrix(43,-2,280,-13) Matrix(5939,-8400,3352,-4741) -> Matrix(899,-42,15176,-709) Matrix(2579,-3660,804,-1141) -> Matrix(551,-26,5616,-265) Matrix(421,-600,294,-419) -> Matrix(295,-14,6174,-293) Matrix(961,-1380,250,-359) -> Matrix(167,-8,1190,-57) Matrix(4379,-6300,1794,-2581) -> Matrix(1289,-62,16362,-787) Matrix(539,-780,208,-301) -> Matrix(41,-2,472,-23) Matrix(901,-1320,286,-419) -> Matrix(41,-2,226,-11) Matrix(661,-1020,116,-179) -> Matrix(39,-2,176,-9) Matrix(659,-1020,272,-421) -> Matrix(39,-2,488,-25) Matrix(1079,-1680,386,-601) -> Matrix(79,-4,810,-41) Matrix(961,-1500,230,-359) -> Matrix(155,-8,1182,-61) Matrix(719,-1140,152,-241) -> Matrix(151,-8,1076,-57) Matrix(9361,-14880,3472,-5519) -> Matrix(151,-8,1680,-89) Matrix(4679,-7440,2642,-4201) -> Matrix(77,-4,1290,-67) Matrix(299,-480,38,-61) -> Matrix(37,-2,130,-7) Matrix(4919,-7920,2162,-3481) -> Matrix(75,-4,994,-53) Matrix(1259,-2040,482,-781) -> Matrix(37,-2,574,-31) Matrix(479,-780,148,-241) -> Matrix(73,-4,712,-39) Matrix(10979,-18000,4502,-7381) -> Matrix(849,-46,10834,-587) Matrix(181,-300,108,-179) -> Matrix(109,-6,1944,-107) Matrix(2099,-3540,890,-1501) -> Matrix(529,-30,6542,-371) Matrix(1739,-2940,320,-541) -> Matrix(35,-2,-52,3) Matrix(3719,-6300,1134,-1921) -> Matrix(141,-8,1322,-75) Matrix(9061,-15360,2654,-4499) -> Matrix(35,-2,158,-9) Matrix(599,-1020,212,-361) -> Matrix(1,0,-8,1) Matrix(659,-1140,174,-301) -> Matrix(37,-2,278,-15) Matrix(2281,-3960,898,-1559) -> Matrix(1,0,-6,1) Matrix(5281,-9360,2166,-3839) -> Matrix(1147,-68,14658,-869) Matrix(841,-1500,134,-239) -> Matrix(67,-4,218,-13) Matrix(2279,-4080,1006,-1801) -> Matrix(463,-28,6234,-377) Matrix(299,-660,82,-181) -> Matrix(27,-2,230,-17) Matrix(3659,-8400,1072,-2461) -> Matrix(79,-6,540,-41) Matrix(3239,-7440,1202,-2761) -> Matrix(53,-4,570,-43) Matrix(179,-420,26,-61) -> Matrix(25,-2,138,-11) Matrix(661,-1620,122,-299) -> Matrix(25,-2,38,-3) Matrix(121,-300,48,-119) -> Matrix(49,-4,576,-47) Matrix(2099,-5340,590,-1501) -> Matrix(23,-2,242,-21) Matrix(3839,-9840,1124,-2881) -> Matrix(45,-4,484,-43) Matrix(3061,-7920,904,-2339) -> Matrix(23,-2,196,-17) Matrix(2041,-5340,550,-1439) -> Matrix(55,-4,454,-33) Matrix(479,-1260,46,-121) -> Matrix(1,0,-10,1) Matrix(659,-1740,114,-301) -> Matrix(25,-2,138,-11) Matrix(959,-2580,268,-721) -> Matrix(91,-8,876,-77) Matrix(181,-600,54,-179) -> Matrix(55,-6,486,-53) Matrix(539,-1860,122,-421) -> Matrix(17,-2,94,-11) Matrix(241,-900,64,-239) -> Matrix(65,-8,512,-63) Matrix(61,-360,10,-59) -> Matrix(11,-2,50,-9) Matrix(121,-900,16,-119) -> Matrix(17,-4,64,-15) 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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 192 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): 1152 Minimal number of generators: 193 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: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -39/7 -5/1 -14/3 -9/2 -4/1 -18/5 -25/7 -10/3 -3/1 -25/9 -5/2 -12/5 -20/9 -15/7 -2/1 -5/3 -27/17 -45/29 -3/2 -45/31 -10/7 -15/11 -5/4 -6/5 -15/13 -10/9 0/1 1/1 10/9 15/13 6/5 5/4 30/23 15/11 10/7 3/2 30/19 5/3 30/17 9/5 15/8 2/1 15/7 20/9 30/13 12/5 5/2 30/11 25/9 3/1 45/14 29/9 10/3 7/2 210/59 25/7 18/5 11/3 15/4 4/1 30/7 13/3 9/2 14/3 5/1 27/5 11/2 39/7 17/3 6/1 19/3 13/2 7/1 15/2 23/3 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 0/1 -15/2 -1/2 -7/1 -1/2 -6/1 -1/3 -17/3 -3/10 -28/5 -2/9 -39/7 -3/14 -11/2 -1/7 0/1 -5/1 -1/4 -19/4 -4/19 -1/5 -14/3 -1/7 -23/5 1/2 -32/7 0/1 -41/9 -3/8 -9/2 -1/4 -13/3 -3/14 -30/7 -1/5 -17/4 -1/5 -4/21 -4/1 0/1 -19/5 -1/6 -15/4 -1/6 -11/3 -3/20 -29/8 -1/7 0/1 -18/5 -1/7 -61/17 -17/124 -43/12 -9/67 -2/15 -25/7 -1/8 -32/9 0/1 -7/2 -1/5 0/1 -31/9 -1/6 -24/7 -2/13 -17/5 -5/32 -27/8 -3/20 -10/3 -1/7 -33/10 -3/22 -23/7 -1/8 -13/4 -1/7 -2/15 -3/1 -1/8 -17/6 -1/7 0/1 -14/5 -3/25 -25/9 -1/8 -61/22 -3/25 -2/17 -36/13 -2/17 -11/4 -4/35 -1/9 -30/11 -1/9 -19/7 -7/64 -27/10 -3/28 -89/33 -3/28 -62/23 -1/9 -35/13 -3/28 -8/3 -2/19 -37/14 -4/41 -3/31 -29/11 -1/10 -21/8 -1/10 -13/5 -1/8 -31/12 -2/17 -1/9 -18/7 -1/9 -59/23 -23/212 -41/16 -7/65 -10/93 -23/9 -7/66 -28/11 -2/19 -5/2 -1/10 -22/9 -5/53 -39/16 -5/54 -17/7 -3/34 -29/12 -1/11 0/1 -12/5 0/1 -7/3 -3/32 -30/13 -1/11 -23/10 -1/11 -10/111 -62/27 -1/11 -39/17 -5/56 -16/7 -4/45 -25/11 -3/34 -59/26 -1/11 -2/23 -34/15 -5/57 -9/4 -1/12 -29/13 -1/12 -20/9 0/1 -31/14 -1/11 -2/23 -11/5 -1/10 -13/6 -2/23 -3/35 -15/7 -1/12 -17/8 -5/61 -4/49 -2/1 -1/13 -17/9 -9/124 -15/8 -1/14 -13/7 -1/14 -11/6 -1/15 0/1 -20/11 -2/29 -29/16 -4/59 -1/15 -9/5 -1/14 -16/9 -4/59 -23/13 -13/194 -30/17 -1/15 -7/4 -1/15 -4/61 -33/19 -1/16 -59/34 -1/15 -2/31 -26/15 -3/47 -19/11 -1/16 -69/40 -3/44 -50/29 -1/15 -31/18 -1/15 -2/31 -12/7 -2/31 -5/3 -1/16 -18/11 -1/17 -31/19 -1/16 -75/46 -1/16 -44/27 -6/97 -13/8 -3/49 -2/33 -34/21 -5/83 -89/55 -3/50 -55/34 -3/50 -21/13 -3/50 -71/44 -6/101 -13/219 -50/31 -1/17 -29/18 -1/17 0/1 -37/23 -1/18 -45/28 -1/16 -8/5 -2/33 -35/22 -5/84 -62/39 -1/17 -151/95 -5/84 -240/151 -6/101 -89/56 -6/101 -1/17 -27/17 -5/84 -46/29 -15/253 -19/12 -12/203 -1/17 -30/19 -1/17 -11/7 -7/120 -14/9 -1/17 -45/29 -1/18 -31/20 -1/17 -2/35 -17/11 -5/86 -3/2 -1/18 -16/11 -2/37 -45/31 -3/56 -29/20 -4/75 -1/19 -13/9 -3/56 -23/16 -11/207 -6/113 -10/7 -1/19 -37/26 -17/325 -8/153 -27/19 -7/134 -44/31 -16/307 -105/74 -5/96 -61/43 -43/826 -17/12 -4/77 -7/135 -58/41 -5/97 -41/29 -1/20 -24/17 -2/39 -7/5 -3/58 -18/13 -3/59 -29/21 -1/20 -40/29 -2/39 -11/8 -3/59 -4/79 -15/11 -1/20 -19/14 -8/161 -7/141 -23/17 -7/142 -27/20 -1/20 -31/23 -1/20 -4/3 -2/41 -21/16 -5/104 -17/13 -13/272 -30/23 -1/21 -13/10 -1/21 -10/211 -35/27 -5/106 -22/17 -1/21 -31/24 -1/21 -6/127 -9/7 -3/64 -14/11 -3/65 -33/26 -5/108 -19/15 -7/152 -24/19 -4/87 -29/23 -1/22 -5/4 -1/22 -21/17 -1/22 -16/13 -2/45 -11/9 -7/158 -17/14 -4/91 -1/23 -23/19 -3/68 -29/24 -4/91 -1/23 -6/5 -1/23 -19/16 -4/93 -7/163 -13/11 -3/70 -7/6 -3/71 -4/95 -15/13 -1/24 -23/20 -10/241 -9/217 -8/7 -4/97 -9/8 -3/74 -10/9 -1/25 -11/10 -4/101 -7/177 -1/1 -1/28 0/1 0/1 1/1 1/30 10/9 1/27 9/8 3/80 8/7 4/105 15/13 1/26 7/6 4/103 3/77 13/11 3/76 6/5 1/25 17/14 1/25 4/99 11/9 7/172 5/4 1/24 24/19 4/95 19/15 7/166 14/11 3/71 9/7 3/70 22/17 1/23 35/27 5/116 13/10 10/231 1/23 30/23 1/23 17/13 13/298 21/16 5/114 4/3 2/45 15/11 1/22 26/19 9/197 37/27 15/328 11/8 4/87 3/65 7/5 3/64 17/12 7/149 4/85 61/43 43/912 44/31 16/339 27/19 7/148 10/7 1/21 33/23 7/146 23/16 6/125 11/229 13/9 3/62 16/11 2/41 3/2 1/20 17/11 5/96 14/9 1/19 39/25 3/58 25/16 3/58 11/7 7/134 30/19 1/19 19/12 1/19 12/227 27/17 5/94 8/5 2/37 37/23 1/20 29/18 0/1 1/19 50/31 1/19 71/44 13/245 6/113 21/13 3/56 55/34 3/56 89/55 3/56 34/21 5/93 13/8 2/37 3/55 5/3 1/18 17/10 0/1 1/17 29/17 1/18 12/7 2/35 31/18 2/35 1/17 50/29 1/17 69/40 3/50 19/11 1/18 26/15 3/53 59/34 2/35 1/17 33/19 1/18 7/4 4/69 1/17 30/17 1/17 23/13 13/220 16/9 4/67 9/5 1/16 29/16 1/17 4/67 20/11 2/33 11/6 0/1 1/17 24/13 2/33 13/7 1/16 15/8 1/16 2/1 1/15 15/7 1/14 28/13 6/83 13/6 3/41 2/27 11/5 1/12 20/9 0/1 9/4 1/14 34/15 5/67 59/26 2/27 1/13 25/11 3/40 16/7 4/53 39/17 5/66 23/10 10/131 1/13 30/13 1/13 7/3 3/38 19/8 0/1 1/11 50/21 1/13 31/13 1/12 12/5 0/1 29/12 0/1 1/13 75/31 1/12 46/19 1/13 17/7 3/40 39/16 5/64 22/9 5/63 27/11 1/12 5/2 1/12 33/13 1/12 61/24 2/23 1/11 28/11 2/23 23/9 7/80 41/16 10/113 7/79 100/39 4/45 59/23 23/258 18/7 1/11 31/12 1/11 2/21 75/29 1/10 44/17 0/1 13/5 1/10 21/8 1/12 50/19 1/13 29/11 1/12 37/14 3/37 4/49 45/17 1/12 8/3 2/23 35/13 3/34 27/10 3/34 46/17 1/11 19/7 7/78 30/11 1/11 11/4 1/11 4/43 36/13 2/21 61/22 2/21 3/31 25/9 1/10 14/5 3/31 3/1 1/10 16/5 2/21 61/19 19/192 45/14 1/10 29/9 1/10 13/4 2/19 1/9 36/11 2/19 59/18 2/19 1/9 23/7 1/10 10/3 1/9 37/11 5/44 64/19 2/17 91/27 3/26 27/8 3/26 17/5 5/42 24/7 2/17 55/16 1/8 31/9 1/8 7/2 0/1 1/7 39/11 1/12 32/9 0/1 121/34 0/1 1/11 210/59 1/11 89/25 1/10 57/16 1/10 25/7 1/10 43/12 2/19 9/85 61/17 17/158 18/5 1/9 29/8 0/1 1/9 40/11 2/17 11/3 3/26 15/4 1/8 19/5 1/8 4/1 0/1 17/4 4/29 1/7 30/7 1/7 13/3 3/20 9/2 1/6 41/9 3/14 32/7 0/1 23/5 1/0 14/3 1/9 5/1 1/6 16/3 2/9 27/5 1/2 11/2 0/1 1/9 39/7 3/20 28/5 2/13 45/8 1/6 17/3 3/16 6/1 1/5 19/3 1/6 32/5 2/9 13/2 2/7 1/3 7/1 1/4 15/2 1/4 23/3 3/10 8/1 0/1 9/1 1/4 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(31,270,-24,-209) (-8/1,1/0) -> (-22/17,-31/24) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(29,210,4,29) (-15/2,-7/1) -> (7/1,15/2) Hyperbolic Matrix(31,210,-22,-149) (-7/1,-6/1) -> (-24/17,-7/5) Hyperbolic Matrix(89,510,26,149) (-6/1,-17/3) -> (17/5,24/7) Hyperbolic Matrix(91,510,-48,-269) (-17/3,-28/5) -> (-2/1,-17/9) Hyperbolic Matrix(419,2340,118,659) (-28/5,-39/7) -> (39/11,32/9) Hyperbolic Matrix(539,3000,334,1859) (-39/7,-11/2) -> (71/44,21/13) Hyperbolic Matrix(29,150,-6,-31) (-11/2,-5/1) -> (-5/1,-19/4) Parabolic Matrix(241,1140,-152,-719) (-19/4,-14/3) -> (-46/29,-19/12) Hyperbolic Matrix(149,690,84,389) (-14/3,-23/5) -> (23/13,16/9) Hyperbolic Matrix(301,1380,118,541) (-23/5,-32/7) -> (28/11,23/9) Hyperbolic Matrix(421,1920,66,301) (-32/7,-41/9) -> (19/3,32/5) Hyperbolic Matrix(659,3000,382,1739) (-41/9,-9/2) -> (69/40,19/11) Hyperbolic Matrix(89,390,34,149) (-9/2,-13/3) -> (13/5,21/8) Hyperbolic Matrix(181,780,42,181) (-13/3,-30/7) -> (30/7,13/3) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(149,630,92,389) (-17/4,-4/1) -> (34/21,13/8) Hyperbolic Matrix(149,570,86,329) (-4/1,-19/5) -> (19/11,26/15) Hyperbolic Matrix(151,570,40,151) (-19/5,-15/4) -> (15/4,19/5) Hyperbolic Matrix(89,330,24,89) (-15/4,-11/3) -> (11/3,15/4) Hyperbolic Matrix(181,660,-82,-299) (-11/3,-29/8) -> (-31/14,-11/5) Hyperbolic Matrix(299,1080,116,419) (-29/8,-18/5) -> (18/7,31/12) Hyperbolic Matrix(601,2160,234,841) (-18/5,-61/17) -> (59/23,18/7) Hyperbolic Matrix(1021,3660,720,2581) (-61/17,-43/12) -> (17/12,61/43) Hyperbolic Matrix(511,1830,394,1411) (-43/12,-25/7) -> (35/27,13/10) Hyperbolic Matrix(749,2670,-278,-991) (-25/7,-32/9) -> (-62/23,-35/13) Hyperbolic Matrix(331,1170,-144,-509) (-32/9,-7/2) -> (-23/10,-62/27) Hyperbolic Matrix(391,1350,148,511) (-7/2,-31/9) -> (29/11,37/14) Hyperbolic Matrix(419,1440,-332,-1141) (-31/9,-24/7) -> (-24/19,-29/23) Hyperbolic Matrix(149,510,26,89) (-24/7,-17/5) -> (17/3,6/1) Hyperbolic Matrix(151,510,98,331) (-17/5,-27/8) -> (3/2,17/11) Hyperbolic Matrix(179,600,-54,-181) (-27/8,-10/3) -> (-10/3,-33/10) Parabolic Matrix(419,1380,-310,-1021) (-33/10,-23/7) -> (-23/17,-27/20) Hyperbolic Matrix(211,690,-174,-569) (-23/7,-13/4) -> (-17/14,-23/19) Hyperbolic Matrix(29,90,-10,-31) (-13/4,-3/1) -> (-3/1,-17/6) Parabolic Matrix(329,930,-202,-571) (-17/6,-14/5) -> (-44/27,-13/8) Hyperbolic Matrix(269,750,118,329) (-14/5,-25/9) -> (25/11,16/7) Hyperbolic Matrix(1081,3000,476,1321) (-25/9,-61/22) -> (59/26,25/11) Hyperbolic Matrix(1559,4320,476,1319) (-61/22,-36/13) -> (36/11,59/18) Hyperbolic Matrix(239,660,130,359) (-36/13,-11/4) -> (11/6,24/13) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(421,1140,-332,-899) (-19/7,-27/10) -> (-33/26,-19/15) Hyperbolic Matrix(1801,4860,534,1441) (-27/10,-89/33) -> (91/27,27/8) Hyperbolic Matrix(5519,14880,-3472,-9361) (-89/33,-62/23) -> (-62/39,-151/95) Hyperbolic Matrix(391,1050,302,811) (-35/13,-8/3) -> (22/17,35/27) Hyperbolic Matrix(181,480,-158,-419) (-8/3,-37/14) -> (-23/20,-8/7) Hyperbolic Matrix(511,1350,148,391) (-37/14,-29/11) -> (31/9,7/2) Hyperbolic Matrix(331,870,-148,-389) (-29/11,-21/8) -> (-9/4,-29/13) Hyperbolic Matrix(149,390,34,89) (-21/8,-13/5) -> (13/3,9/2) Hyperbolic Matrix(301,780,-208,-539) (-13/5,-31/12) -> (-29/20,-13/9) Hyperbolic Matrix(419,1080,116,299) (-31/12,-18/7) -> (18/5,29/8) Hyperbolic Matrix(841,2160,234,601) (-18/7,-59/23) -> (61/17,18/5) Hyperbolic Matrix(269,690,-246,-631) (-59/23,-41/16) -> (-11/10,-1/1) Hyperbolic Matrix(691,1770,504,1291) (-41/16,-23/9) -> (37/27,11/8) Hyperbolic Matrix(541,1380,118,301) (-23/9,-28/11) -> (32/7,23/5) Hyperbolic Matrix(509,1290,-320,-811) (-28/11,-5/2) -> (-35/22,-62/39) Hyperbolic Matrix(331,810,-208,-509) (-5/2,-22/9) -> (-8/5,-35/22) Hyperbolic Matrix(209,510,184,449) (-22/9,-39/16) -> (9/8,8/7) Hyperbolic Matrix(419,1020,320,779) (-39/16,-17/7) -> (17/13,21/16) Hyperbolic Matrix(421,1020,-272,-659) (-17/7,-29/12) -> (-31/20,-17/11) Hyperbolic Matrix(299,720,174,419) (-29/12,-12/5) -> (12/7,31/18) Hyperbolic Matrix(89,210,-64,-151) (-12/5,-7/3) -> (-7/5,-18/13) Hyperbolic Matrix(181,420,78,181) (-7/3,-30/13) -> (30/13,7/3) Hyperbolic Matrix(599,1380,260,599) (-30/13,-23/10) -> (23/10,30/13) Hyperbolic Matrix(1529,3510,274,629) (-62/27,-39/17) -> (39/7,28/5) Hyperbolic Matrix(511,1170,328,751) (-39/17,-16/7) -> (14/9,39/25) Hyperbolic Matrix(329,750,118,269) (-16/7,-25/11) -> (25/9,14/5) Hyperbolic Matrix(1321,3000,476,1081) (-25/11,-59/26) -> (61/22,25/9) Hyperbolic Matrix(1561,3540,900,2041) (-59/26,-34/15) -> (26/15,59/34) Hyperbolic Matrix(331,750,252,571) (-34/15,-9/4) -> (21/16,4/3) Hyperbolic Matrix(929,2070,390,869) (-29/13,-20/9) -> (50/21,31/13) Hyperbolic Matrix(541,1200,298,661) (-20/9,-31/14) -> (29/16,20/11) Hyperbolic Matrix(151,330,124,271) (-11/5,-13/6) -> (17/14,11/9) Hyperbolic Matrix(209,450,-98,-211) (-13/6,-15/7) -> (-15/7,-17/8) Parabolic Matrix(269,570,42,89) (-17/8,-2/1) -> (32/5,13/2) Hyperbolic Matrix(541,1020,96,181) (-17/9,-15/8) -> (45/8,17/3) Hyperbolic Matrix(209,390,112,209) (-15/8,-13/7) -> (13/7,15/8) Hyperbolic Matrix(211,390,-178,-329) (-13/7,-11/6) -> (-19/16,-13/11) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(959,1740,264,479) (-20/11,-29/16) -> (29/8,40/11) Hyperbolic Matrix(149,270,16,29) (-29/16,-9/5) -> (9/1,1/0) Hyperbolic Matrix(151,270,118,211) (-9/5,-16/9) -> (14/11,9/7) Hyperbolic Matrix(389,690,84,149) (-16/9,-23/13) -> (23/5,14/3) Hyperbolic Matrix(781,1380,442,781) (-23/13,-30/17) -> (30/17,23/13) Hyperbolic Matrix(239,420,136,239) (-30/17,-7/4) -> (7/4,30/17) Hyperbolic Matrix(569,990,396,689) (-7/4,-33/19) -> (33/23,23/16) Hyperbolic Matrix(2609,4530,-1642,-2851) (-33/19,-59/34) -> (-89/56,-27/17) Hyperbolic Matrix(2041,3540,900,1561) (-59/34,-26/15) -> (34/15,59/26) Hyperbolic Matrix(329,570,86,149) (-26/15,-19/11) -> (19/5,4/1) Hyperbolic Matrix(1739,3000,382,659) (-19/11,-69/40) -> (9/2,41/9) Hyperbolic Matrix(661,1140,592,1021) (-69/40,-50/29) -> (10/9,9/8) Hyperbolic Matrix(1741,3000,1080,1861) (-50/29,-31/18) -> (29/18,50/31) Hyperbolic Matrix(419,720,174,299) (-31/18,-12/7) -> (12/5,29/12) Hyperbolic Matrix(89,150,-54,-91) (-12/7,-5/3) -> (-5/3,-18/11) Parabolic Matrix(569,930,238,389) (-18/11,-31/19) -> (31/13,12/5) Hyperbolic Matrix(2189,3570,680,1109) (-31/19,-75/46) -> (45/14,29/9) Hyperbolic Matrix(4859,7920,-3424,-5581) (-75/46,-44/27) -> (-44/31,-105/74) Hyperbolic Matrix(389,630,92,149) (-13/8,-34/21) -> (4/1,17/4) Hyperbolic Matrix(871,1410,-648,-1049) (-34/21,-89/55) -> (-31/23,-4/3) Hyperbolic Matrix(4079,6600,1186,1919) (-89/55,-55/34) -> (55/16,31/9) Hyperbolic Matrix(1651,2670,1058,1711) (-55/34,-21/13) -> (39/25,25/16) Hyperbolic Matrix(1859,3000,334,539) (-21/13,-71/44) -> (11/2,39/7) Hyperbolic Matrix(781,1260,-706,-1139) (-71/44,-50/31) -> (-10/9,-11/10) Hyperbolic Matrix(1861,3000,1080,1741) (-50/31,-29/18) -> (31/18,50/29) Hyperbolic Matrix(1081,1740,-894,-1439) (-29/18,-37/23) -> (-23/19,-29/24) Hyperbolic Matrix(989,1590,130,209) (-37/23,-45/28) -> (15/2,23/3) Hyperbolic Matrix(33389,53070,9380,14909) (-151/95,-240/151) -> (210/59,89/25) Hyperbolic Matrix(30031,47730,8438,13411) (-240/151,-89/56) -> (121/34,210/59) Hyperbolic Matrix(1531,2430,1078,1711) (-27/17,-46/29) -> (44/31,27/19) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) Hyperbolic Matrix(211,330,-172,-269) (-11/7,-14/9) -> (-16/13,-11/9) Hyperbolic Matrix(1951,3030,754,1171) (-14/9,-45/29) -> (75/29,44/17) Hyperbolic Matrix(2399,3720,928,1439) (-45/29,-31/20) -> (31/12,75/29) Hyperbolic Matrix(331,510,98,151) (-17/11,-3/2) -> (27/8,17/5) Hyperbolic Matrix(391,570,-308,-449) (-3/2,-16/11) -> (-14/11,-33/26) Hyperbolic Matrix(2251,3270,930,1351) (-16/11,-45/31) -> (75/31,46/19) Hyperbolic Matrix(2399,3480,992,1439) (-45/31,-29/20) -> (29/12,75/31) Hyperbolic Matrix(271,390,230,331) (-13/9,-23/16) -> (7/6,13/11) Hyperbolic Matrix(419,600,-294,-421) (-23/16,-10/7) -> (-10/7,-37/26) Parabolic Matrix(991,1410,570,811) (-37/26,-27/19) -> (33/19,7/4) Hyperbolic Matrix(1141,1620,212,301) (-27/19,-44/31) -> (16/3,27/5) Hyperbolic Matrix(6449,9150,2008,2849) (-105/74,-61/43) -> (61/19,45/14) Hyperbolic Matrix(2581,3660,720,1021) (-61/43,-17/12) -> (43/12,61/17) Hyperbolic Matrix(869,1230,402,569) (-17/12,-58/41) -> (28/13,13/6) Hyperbolic Matrix(2609,3690,572,809) (-58/41,-41/29) -> (41/9,32/7) Hyperbolic Matrix(1019,1440,806,1139) (-41/29,-24/17) -> (24/19,19/15) Hyperbolic Matrix(629,870,368,509) (-18/13,-29/21) -> (29/17,12/7) Hyperbolic Matrix(1891,2610,718,991) (-29/21,-40/29) -> (50/19,29/11) Hyperbolic Matrix(329,450,-242,-331) (-11/8,-15/11) -> (-15/11,-19/14) Parabolic Matrix(1019,1380,398,539) (-19/14,-23/17) -> (23/9,41/16) Hyperbolic Matrix(3091,4170,868,1171) (-27/20,-31/23) -> (89/25,57/16) Hyperbolic Matrix(571,750,252,331) (-4/3,-21/16) -> (9/4,34/15) Hyperbolic Matrix(779,1020,320,419) (-21/16,-17/13) -> (17/7,39/16) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(599,780,460,599) (-30/23,-13/10) -> (13/10,30/23) Hyperbolic Matrix(1411,1830,394,511) (-13/10,-35/27) -> (25/7,43/12) Hyperbolic Matrix(811,1050,302,391) (-35/27,-22/17) -> (8/3,35/13) Hyperbolic Matrix(419,540,232,299) (-31/24,-9/7) -> (9/5,29/16) Hyperbolic Matrix(211,270,118,151) (-9/7,-14/11) -> (16/9,9/5) Hyperbolic Matrix(451,570,72,91) (-19/15,-24/19) -> (6/1,19/3) Hyperbolic Matrix(1621,2040,1002,1261) (-29/23,-5/4) -> (55/34,89/55) Hyperbolic Matrix(1019,1260,630,779) (-5/4,-21/17) -> (21/13,55/34) Hyperbolic Matrix(779,960,340,419) (-21/17,-16/13) -> (16/7,39/17) Hyperbolic Matrix(271,330,124,151) (-11/9,-17/14) -> (13/6,11/5) Hyperbolic Matrix(1169,1410,422,509) (-29/24,-6/5) -> (36/13,61/22) Hyperbolic Matrix(631,750,228,271) (-6/5,-19/16) -> (11/4,36/13) Hyperbolic Matrix(331,390,230,271) (-13/11,-7/6) -> (23/16,13/9) Hyperbolic Matrix(389,450,-338,-391) (-7/6,-15/13) -> (-15/13,-23/20) Parabolic Matrix(449,510,184,209) (-8/7,-9/8) -> (39/16,22/9) Hyperbolic Matrix(1021,1140,592,661) (-9/8,-10/9) -> (50/29,69/40) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(631,-690,246,-269) (1/1,10/9) -> (100/39,59/23) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(751,-870,284,-329) (15/13,7/6) -> (37/14,45/17) Hyperbolic Matrix(329,-390,178,-211) (13/11,6/5) -> (24/13,13/7) Hyperbolic Matrix(569,-690,174,-211) (6/5,17/14) -> (13/4,36/11) Hyperbolic Matrix(269,-330,172,-211) (11/9,5/4) -> (25/16,11/7) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(209,-270,24,-31) (9/7,22/17) -> (8/1,9/1) Hyperbolic Matrix(331,-450,242,-329) (4/3,15/11) -> (15/11,26/19) Parabolic Matrix(2431,-3330,722,-989) (26/19,37/27) -> (37/11,64/19) Hyperbolic Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(149,-210,22,-31) (7/5,17/12) -> (13/2,7/1) Hyperbolic Matrix(2579,-3660,804,-1141) (61/43,44/31) -> (16/5,61/19) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(389,-570,144,-211) (16/11,3/2) -> (27/10,46/17) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(511,-810,94,-149) (19/12,27/17) -> (27/5,11/2) Hyperbolic Matrix(509,-810,208,-331) (27/17,8/5) -> (22/9,27/11) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(1771,-2850,540,-869) (37/23,29/18) -> (59/18,23/7) Hyperbolic Matrix(5671,-9150,2212,-3569) (50/31,71/44) -> (41/16,100/39) Hyperbolic Matrix(5431,-8790,1612,-2609) (89/55,34/21) -> (64/19,91/27) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(511,-870,158,-269) (17/10,29/17) -> (29/9,13/4) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(509,-930,214,-391) (20/11,11/6) -> (19/8,50/21) Hyperbolic Matrix(269,-510,48,-91) (15/8,2/1) -> (28/5,45/8) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(389,-870,148,-331) (20/9,9/4) -> (21/8,50/19) Hyperbolic Matrix(509,-1170,144,-331) (39/17,23/10) -> (7/2,39/11) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(991,-2670,278,-749) (35/13,27/10) -> (57/16,25/7) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(31,270,-24,-209) -> Matrix(5,1,-106,-21) Matrix(61,480,-38,-299) -> Matrix(3,2,-50,-33) Matrix(29,210,4,29) -> Matrix(3,1,14,5) Matrix(31,210,-22,-149) -> Matrix(5,1,-96,-19) Matrix(89,510,26,149) -> Matrix(5,1,44,9) Matrix(91,510,-48,-269) -> Matrix(13,3,-178,-41) Matrix(419,2340,118,659) -> Matrix(9,2,94,21) Matrix(539,3000,334,1859) -> Matrix(29,6,546,113) Matrix(29,150,-6,-31) -> Matrix(3,1,-16,-5) Matrix(241,1140,-152,-719) -> Matrix(41,8,-692,-135) Matrix(149,690,84,389) -> Matrix(11,1,186,17) Matrix(301,1380,118,541) -> Matrix(3,2,34,23) Matrix(421,1920,66,301) -> Matrix(5,2,22,9) Matrix(659,3000,382,1739) -> Matrix(5,2,82,33) Matrix(89,390,34,149) -> Matrix(5,1,64,13) Matrix(181,780,42,181) -> Matrix(29,6,198,41) Matrix(239,1020,56,239) -> Matrix(41,8,292,57) Matrix(149,630,92,389) -> Matrix(27,5,502,93) Matrix(149,570,86,329) -> Matrix(17,3,300,53) Matrix(151,570,40,151) -> Matrix(29,5,226,39) Matrix(89,330,24,89) -> Matrix(19,3,158,25) Matrix(181,660,-82,-299) -> Matrix(13,2,-150,-23) Matrix(299,1080,116,419) -> Matrix(13,2,136,21) Matrix(601,2160,234,841) -> Matrix(57,8,634,89) Matrix(1021,3660,720,2581) -> Matrix(163,22,3460,467) Matrix(511,1830,394,1411) -> Matrix(83,11,1924,255) Matrix(749,2670,-278,-991) -> Matrix(11,1,-100,-9) Matrix(331,1170,-144,-509) -> Matrix(15,1,-166,-11) Matrix(391,1350,148,511) -> Matrix(19,3,234,37) Matrix(419,1440,-332,-1141) -> Matrix(37,6,-808,-131) Matrix(149,510,26,89) -> Matrix(7,1,48,7) Matrix(151,510,98,331) -> Matrix(33,5,640,97) Matrix(179,600,-54,-181) -> Matrix(41,6,-294,-43) Matrix(419,1380,-310,-1021) -> Matrix(73,10,-1482,-203) Matrix(211,690,-174,-569) -> Matrix(53,7,-1204,-159) Matrix(29,90,-10,-31) -> Matrix(7,1,-64,-9) Matrix(329,930,-202,-571) -> Matrix(23,3,-376,-49) Matrix(269,750,118,329) -> Matrix(43,5,576,67) Matrix(1081,3000,476,1321) -> Matrix(67,8,896,107) Matrix(1559,4320,476,1319) -> Matrix(67,8,628,75) Matrix(239,660,130,359) -> Matrix(35,4,586,67) Matrix(241,660,88,241) -> Matrix(71,8,772,87) Matrix(419,1140,154,419) -> Matrix(127,14,1406,155) Matrix(421,1140,-332,-899) -> Matrix(129,14,-2792,-303) Matrix(1801,4860,534,1441) -> Matrix(1,0,18,1) Matrix(5519,14880,-3472,-9361) -> Matrix(73,8,-1232,-135) Matrix(391,1050,302,811) -> Matrix(67,7,1560,163) Matrix(181,480,-158,-419) -> Matrix(59,6,-1426,-145) Matrix(511,1350,148,391) -> Matrix(31,3,258,25) Matrix(331,870,-148,-389) -> Matrix(11,1,-122,-11) Matrix(149,390,34,89) -> Matrix(11,1,76,7) Matrix(301,780,-208,-539) -> Matrix(19,2,-352,-37) Matrix(419,1080,116,299) -> Matrix(17,2,144,17) Matrix(841,2160,234,601) -> Matrix(73,8,666,73) Matrix(269,690,-246,-631) -> Matrix(83,9,-2112,-229) Matrix(691,1770,504,1291) -> Matrix(177,19,3866,415) Matrix(541,1380,118,301) -> Matrix(19,2,66,7) Matrix(509,1290,-320,-811) -> Matrix(105,11,-1766,-185) Matrix(331,810,-208,-509) -> Matrix(95,9,-1594,-151) Matrix(209,510,184,449) -> Matrix(75,7,1982,185) Matrix(419,1020,320,779) -> Matrix(109,10,2496,229) Matrix(421,1020,-272,-659) -> Matrix(21,2,-368,-35) Matrix(299,720,174,419) -> Matrix(23,2,402,35) Matrix(89,210,-64,-151) -> Matrix(31,3,-610,-59) Matrix(181,420,78,181) -> Matrix(65,6,834,77) Matrix(599,1380,260,599) -> Matrix(221,20,2884,261) Matrix(1529,3510,274,629) -> Matrix(145,13,948,85) Matrix(511,1170,328,751) -> Matrix(79,7,1546,137) Matrix(329,750,118,269) -> Matrix(57,5,604,53) Matrix(1321,3000,476,1081) -> Matrix(91,8,944,83) Matrix(1561,3540,900,2041) -> Matrix(45,4,776,69) Matrix(331,750,252,571) -> Matrix(103,9,2346,205) Matrix(929,2070,390,869) -> Matrix(13,1,168,13) Matrix(541,1200,298,661) -> Matrix(21,2,346,33) Matrix(151,330,124,271) -> Matrix(57,5,1402,123) Matrix(209,450,-98,-211) -> Matrix(83,7,-1008,-85) Matrix(269,570,42,89) -> Matrix(37,3,160,13) Matrix(541,1020,96,181) -> Matrix(83,6,484,35) Matrix(209,390,112,209) -> Matrix(99,7,1598,113) Matrix(211,390,-178,-329) -> Matrix(101,7,-2352,-163) Matrix(361,660,-262,-479) -> Matrix(57,4,-1126,-79) Matrix(959,1740,264,479) -> Matrix(59,4,516,35) Matrix(149,270,16,29) -> Matrix(15,1,74,5) Matrix(151,270,118,211) -> Matrix(73,5,1708,117) Matrix(389,690,84,149) -> Matrix(15,1,194,13) Matrix(781,1380,442,781) -> Matrix(389,26,6598,441) Matrix(239,420,136,239) -> Matrix(121,8,2072,137) Matrix(569,990,396,689) -> Matrix(201,13,4190,271) Matrix(2609,4530,-1642,-2851) -> Matrix(171,11,-2876,-185) Matrix(2041,3540,900,1561) -> Matrix(61,4,808,53) Matrix(329,570,86,149) -> Matrix(47,3,360,23) Matrix(1739,3000,382,659) -> Matrix(29,2,130,9) Matrix(661,1140,592,1021) -> Matrix(89,6,2388,161) Matrix(1741,3000,1080,1861) -> Matrix(31,2,604,39) Matrix(419,720,174,299) -> Matrix(31,2,418,27) Matrix(89,150,-54,-91) -> Matrix(47,3,-768,-49) Matrix(569,930,238,389) -> Matrix(17,1,220,13) Matrix(2189,3570,680,1109) -> Matrix(79,5,774,49) Matrix(4859,7920,-3424,-5581) -> Matrix(741,46,-14224,-883) Matrix(389,630,92,149) -> Matrix(83,5,614,37) Matrix(871,1410,-648,-1049) -> Matrix(183,11,-3710,-223) Matrix(4079,6600,1186,1919) -> Matrix(67,4,586,35) Matrix(1651,2670,1058,1711) -> Matrix(151,9,2936,175) Matrix(1859,3000,334,539) -> Matrix(101,6,690,41) Matrix(781,1260,-706,-1139) -> Matrix(169,10,-4242,-251) Matrix(1861,3000,1080,1741) -> Matrix(35,2,612,35) Matrix(1081,1740,-894,-1439) -> Matrix(69,4,-1570,-91) Matrix(989,1590,130,209) -> Matrix(15,1,44,3) Matrix(33389,53070,9380,14909) -> Matrix(185,11,1934,115) Matrix(30031,47730,8438,13411) -> Matrix(17,1,288,17) Matrix(1531,2430,1078,1711) -> Matrix(623,37,13184,783) Matrix(721,1140,456,721) -> Matrix(407,24,7716,455) Matrix(419,660,266,419) -> Matrix(239,14,4558,267) Matrix(211,330,-172,-269) -> Matrix(121,7,-2714,-157) Matrix(1951,3030,754,1171) -> Matrix(17,1,152,9) Matrix(2399,3720,928,1439) -> Matrix(1,0,28,1) Matrix(331,510,98,151) -> Matrix(87,5,748,43) Matrix(391,570,-308,-449) -> Matrix(131,7,-2826,-151) Matrix(2251,3270,930,1351) -> Matrix(19,1,284,15) Matrix(2399,3480,992,1439) -> Matrix(75,4,956,51) Matrix(271,390,230,331) -> Matrix(169,9,4300,229) Matrix(419,600,-294,-421) -> Matrix(265,14,-5054,-267) Matrix(991,1410,570,811) -> Matrix(287,15,5032,263) Matrix(1141,1620,212,301) -> Matrix(115,6,364,19) Matrix(6449,9150,2008,2849) -> Matrix(1325,69,13346,695) Matrix(2581,3660,720,1021) -> Matrix(423,22,3980,207) Matrix(869,1230,402,569) -> Matrix(251,13,3456,179) Matrix(2609,3690,572,809) -> Matrix(97,5,446,23) Matrix(1019,1440,806,1139) -> Matrix(193,10,4574,237) Matrix(629,870,368,509) -> Matrix(99,5,1762,89) Matrix(1891,2610,718,991) -> Matrix(19,1,208,11) Matrix(329,450,-242,-331) -> Matrix(219,11,-4400,-221) Matrix(1019,1380,398,539) -> Matrix(283,14,3214,159) Matrix(3091,4170,868,1171) -> Matrix(61,3,630,31) Matrix(571,750,252,331) -> Matrix(187,9,2514,121) Matrix(779,1020,320,419) -> Matrix(209,10,2696,129) Matrix(781,1020,598,781) -> Matrix(545,26,12514,597) Matrix(599,780,460,599) -> Matrix(421,20,9704,461) Matrix(1411,1830,394,511) -> Matrix(233,11,2224,105) Matrix(811,1050,302,391) -> Matrix(149,7,1724,81) Matrix(419,540,232,299) -> Matrix(43,2,752,35) Matrix(211,270,118,151) -> Matrix(107,5,1776,83) Matrix(451,570,72,91) -> Matrix(65,3,238,11) Matrix(1621,2040,1002,1261) -> Matrix(305,14,5686,261) Matrix(1019,1260,630,779) -> Matrix(223,10,4170,187) Matrix(779,960,340,419) -> Matrix(313,14,4136,185) Matrix(271,330,124,151) -> Matrix(113,5,1514,67) Matrix(1169,1410,422,509) -> Matrix(251,11,2624,115) Matrix(631,750,228,271) -> Matrix(209,9,2206,95) Matrix(331,390,230,271) -> Matrix(211,9,4384,187) Matrix(389,450,-338,-391) -> Matrix(311,13,-7488,-313) Matrix(449,510,184,209) -> Matrix(171,7,2174,89) Matrix(1021,1140,592,661) -> Matrix(149,6,2508,101) Matrix(1,0,2,1) -> Matrix(1,0,58,1) Matrix(631,-690,246,-269) -> Matrix(247,-9,2772,-101) Matrix(419,-480,158,-181) -> Matrix(157,-6,1858,-71) Matrix(751,-870,284,-329) -> Matrix(181,-7,2198,-85) Matrix(329,-390,178,-211) -> Matrix(177,-7,2908,-115) Matrix(569,-690,174,-211) -> Matrix(173,-7,1656,-67) Matrix(269,-330,172,-211) -> Matrix(171,-7,3298,-135) Matrix(1141,-1440,332,-419) -> Matrix(143,-6,1168,-49) Matrix(899,-1140,332,-421) -> Matrix(331,-14,3712,-157) Matrix(209,-270,24,-31) -> Matrix(23,-1,162,-7) Matrix(331,-450,242,-329) -> Matrix(243,-11,5324,-241) Matrix(2431,-3330,722,-989) -> Matrix(547,-25,4748,-217) Matrix(151,-210,64,-89) -> Matrix(65,-3,802,-37) Matrix(149,-210,22,-31) -> Matrix(21,-1,148,-7) Matrix(2579,-3660,804,-1141) -> Matrix(551,-26,5616,-265) Matrix(421,-600,294,-419) -> Matrix(295,-14,6174,-293) Matrix(539,-780,208,-301) -> Matrix(41,-2,472,-23) Matrix(389,-570,144,-211) -> Matrix(143,-7,1614,-79) Matrix(659,-1020,272,-421) -> Matrix(39,-2,488,-25) Matrix(511,-810,94,-149) -> Matrix(19,-1,-56,3) Matrix(509,-810,208,-331) -> Matrix(169,-9,2122,-113) Matrix(299,-480,38,-61) -> Matrix(37,-2,130,-7) Matrix(1771,-2850,540,-869) -> Matrix(21,-1,190,-9) Matrix(5671,-9150,2212,-3569) -> Matrix(585,-31,6586,-349) Matrix(5431,-8790,1612,-2609) -> Matrix(167,-9,1466,-79) Matrix(91,-150,54,-89) -> Matrix(55,-3,972,-53) Matrix(511,-870,158,-269) -> Matrix(19,-1,172,-9) Matrix(2281,-3960,898,-1559) -> Matrix(1,0,-6,1) Matrix(509,-930,214,-391) -> Matrix(17,-1,188,-11) Matrix(269,-510,48,-91) -> Matrix(47,-3,298,-19) Matrix(211,-450,98,-209) -> Matrix(99,-7,1372,-97) Matrix(299,-660,82,-181) -> Matrix(27,-2,230,-17) Matrix(389,-870,148,-331) -> Matrix(13,-1,170,-13) Matrix(509,-1170,144,-331) -> Matrix(13,-1,222,-17) Matrix(121,-300,48,-119) -> Matrix(49,-4,576,-47) Matrix(2099,-5340,590,-1501) -> Matrix(23,-2,242,-21) Matrix(991,-2670,278,-749) -> Matrix(11,-1,144,-13) Matrix(31,-90,10,-29) -> Matrix(11,-1,100,-9) Matrix(181,-600,54,-179) -> Matrix(55,-6,486,-53) Matrix(31,-150,6,-29) -> Matrix(7,-1,36,-5) 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): 192 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 29 1 1/1 1/30 1 30 10/9 1/27 9 3 9/8 3/80 2 10 8/7 4/105 1 15 15/13 1/26 13 2 7/6 (4/103,3/77) 0 30 13/11 3/76 1 30 6/5 1/25 5 5 17/14 (1/25,4/99) 0 30 11/9 7/172 1 30 5/4 1/24 4 6 24/19 4/95 1 5 19/15 7/166 1 30 14/11 3/71 1 15 9/7 3/70 1 10 22/17 1/23 1 15 35/27 5/116 3 6 13/10 (10/231,1/23) 0 30 30/23 1/23 23 1 17/13 13/298 1 30 21/16 5/114 2 10 4/3 2/45 1 15 15/11 1/22 11 2 26/19 9/197 1 15 37/27 15/328 1 30 11/8 (4/87,3/65) 0 30 7/5 3/64 1 30 17/12 (7/149,4/85) 0 30 61/43 43/912 1 30 44/31 16/339 1 15 27/19 7/148 1 10 10/7 1/21 7 3 33/23 7/146 1 10 23/16 (6/125,11/229) 0 30 13/9 3/62 1 30 16/11 2/41 1 15 3/2 1/20 2 10 17/11 5/96 1 30 14/9 1/19 1 15 39/25 3/58 1 10 25/16 3/58 4 6 11/7 7/134 1 30 30/19 1/19 19 1 19/12 (1/19,12/227) 0 30 27/17 5/94 1 10 8/5 2/37 1 15 37/23 1/20 1 30 29/18 (0/1,1/19) 0 30 50/31 1/19 9 3 71/44 (13/245,6/113) 0 30 21/13 3/56 1 10 55/34 3/56 4 6 89/55 3/56 1 30 34/21 5/93 1 15 13/8 (2/37,3/55) 0 30 5/3 1/18 3 6 17/10 (0/1,1/17) 0 30 29/17 1/18 1 30 12/7 2/35 1 5 31/18 (2/35,1/17) 0 30 50/29 1/17 9 3 69/40 3/50 2 10 19/11 1/18 1 30 26/15 3/53 1 15 59/34 (2/35,1/17) 0 30 33/19 1/18 1 10 7/4 (4/69,1/17) 0 30 30/17 1/17 17 1 23/13 13/220 1 30 16/9 4/67 1 15 9/5 1/16 1 10 29/16 (1/17,4/67) 0 30 20/11 2/33 1 3 11/6 (0/1,1/17) 0 30 24/13 2/33 5 5 13/7 1/16 1 30 15/8 1/16 8 2 2/1 1/15 1 15 15/7 1/14 7 2 28/13 6/83 1 15 13/6 (3/41,2/27) 0 30 11/5 1/12 1 30 20/9 0/1 1 3 9/4 1/14 2 10 34/15 5/67 1 15 59/26 (2/27,1/13) 0 30 25/11 3/40 1 6 16/7 4/53 1 15 39/17 5/66 1 10 23/10 (10/131,1/13) 0 30 30/13 1/13 13 1 7/3 3/38 1 30 19/8 (0/1,1/11) 0 30 50/21 1/13 1 3 31/13 1/12 1 30 12/5 0/1 1 5 29/12 (0/1,1/13) 0 30 75/31 1/12 1 2 46/19 1/13 1 15 17/7 3/40 1 30 39/16 5/64 2 10 22/9 5/63 1 15 27/11 1/12 1 10 5/2 1/12 2 6 33/13 1/12 1 10 61/24 (2/23,1/11) 0 30 28/11 2/23 1 15 23/9 7/80 1 30 41/16 (10/113,7/79) 0 30 100/39 4/45 9 3 59/23 23/258 1 30 18/7 1/11 5 5 31/12 (1/11,2/21) 0 30 75/29 1/10 1 2 44/17 0/1 1 15 13/5 1/10 1 30 21/8 1/12 2 10 50/19 1/13 1 3 29/11 1/12 1 30 37/14 (3/37,4/49) 0 30 45/17 1/12 13 2 8/3 2/23 1 15 35/13 3/34 3 6 27/10 3/34 2 10 46/17 1/11 1 15 19/7 7/78 1 30 30/11 1/11 11 1 11/4 (1/11,4/43) 0 30 36/13 2/21 5 5 61/22 (2/21,3/31) 0 30 25/9 1/10 1 6 14/5 3/31 1 15 3/1 1/10 1 10 16/5 2/21 1 15 61/19 19/192 1 30 45/14 1/10 14 2 29/9 1/10 1 30 13/4 (2/19,1/9) 0 30 36/11 2/19 5 5 59/18 (2/19,1/9) 0 30 23/7 1/10 1 30 10/3 1/9 3 3 37/11 5/44 1 30 64/19 2/17 1 15 91/27 3/26 1 30 27/8 3/26 2 10 17/5 5/42 1 30 24/7 2/17 1 5 55/16 1/8 4 6 31/9 1/8 1 30 7/2 (0/1,1/7) 0 30 39/11 1/12 1 10 32/9 0/1 1 15 121/34 (0/1,1/11) 0 30 210/59 1/11 1 1 89/25 1/10 1 30 57/16 1/10 2 10 25/7 1/10 3 6 43/12 (2/19,9/85) 0 30 61/17 17/158 1 30 18/5 1/9 5 5 29/8 (0/1,1/9) 0 30 40/11 2/17 1 3 11/3 3/26 1 30 15/4 1/8 4 2 19/5 1/8 1 30 4/1 0/1 1 15 17/4 (4/29,1/7) 0 30 30/7 1/7 7 1 13/3 3/20 1 30 9/2 1/6 2 10 41/9 3/14 1 30 32/7 0/1 1 15 23/5 1/0 1 30 14/3 1/9 1 15 5/1 1/6 1 6 16/3 2/9 1 15 27/5 1/2 1 10 11/2 (0/1,1/9) 0 30 39/7 3/20 1 10 28/5 2/13 1 15 45/8 1/6 8 2 17/3 3/16 1 30 6/1 1/5 1 5 19/3 1/6 1 30 32/5 2/9 1 15 13/2 (2/7,1/3) 0 30 7/1 1/4 1 30 15/2 1/4 2 2 23/3 3/10 1 30 8/1 0/1 1 15 9/1 1/4 1 10 1/0 (0/1,1/1) 0 30 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(631,-690,246,-269) (1/1,10/9) -> (100/39,59/23) Hyperbolic Matrix(1021,-1140,592,-661) (10/9,9/8) -> (50/29,69/40) Glide Reflection Matrix(449,-510,184,-209) (9/8,8/7) -> (39/16,22/9) Glide Reflection Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(751,-870,284,-329) (15/13,7/6) -> (37/14,45/17) Hyperbolic Matrix(331,-390,230,-271) (7/6,13/11) -> (23/16,13/9) Glide Reflection Matrix(329,-390,178,-211) (13/11,6/5) -> (24/13,13/7) Hyperbolic Matrix(569,-690,174,-211) (6/5,17/14) -> (13/4,36/11) Hyperbolic Matrix(271,-330,124,-151) (17/14,11/9) -> (13/6,11/5) Glide Reflection Matrix(269,-330,172,-211) (11/9,5/4) -> (25/16,11/7) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(451,-570,72,-91) (24/19,19/15) -> (6/1,19/3) Glide Reflection Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(211,-270,118,-151) (14/11,9/7) -> (16/9,9/5) Glide Reflection Matrix(209,-270,24,-31) (9/7,22/17) -> (8/1,9/1) Hyperbolic Matrix(811,-1050,302,-391) (22/17,35/27) -> (8/3,35/13) Glide Reflection Matrix(1411,-1830,394,-511) (35/27,13/10) -> (25/7,43/12) Glide Reflection Matrix(599,-780,460,-599) (13/10,30/23) -> (13/10,30/23) Reflection Matrix(781,-1020,598,-781) (30/23,17/13) -> (30/23,17/13) Reflection Matrix(779,-1020,320,-419) (17/13,21/16) -> (17/7,39/16) Glide Reflection Matrix(571,-750,252,-331) (21/16,4/3) -> (9/4,34/15) Glide Reflection Matrix(331,-450,242,-329) (4/3,15/11) -> (15/11,26/19) Parabolic Matrix(2431,-3330,722,-989) (26/19,37/27) -> (37/11,64/19) Hyperbolic Matrix(1291,-1770,504,-691) (37/27,11/8) -> (23/9,41/16) Glide Reflection Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(149,-210,22,-31) (7/5,17/12) -> (13/2,7/1) Hyperbolic Matrix(2581,-3660,720,-1021) (17/12,61/43) -> (43/12,61/17) Glide Reflection Matrix(2579,-3660,804,-1141) (61/43,44/31) -> (16/5,61/19) Hyperbolic Matrix(1141,-1620,212,-301) (44/31,27/19) -> (16/3,27/5) Glide Reflection Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(689,-990,396,-569) (33/23,23/16) -> (33/19,7/4) Glide Reflection Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(389,-570,144,-211) (16/11,3/2) -> (27/10,46/17) Hyperbolic Matrix(331,-510,98,-151) (3/2,17/11) -> (27/8,17/5) Glide Reflection Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(751,-1170,328,-511) (14/9,39/25) -> (16/7,39/17) Glide Reflection Matrix(1711,-2670,1058,-1651) (39/25,25/16) -> (21/13,55/34) Glide Reflection Matrix(419,-660,266,-419) (11/7,30/19) -> (11/7,30/19) Reflection Matrix(721,-1140,456,-721) (30/19,19/12) -> (30/19,19/12) Reflection Matrix(511,-810,94,-149) (19/12,27/17) -> (27/5,11/2) Hyperbolic Matrix(509,-810,208,-331) (27/17,8/5) -> (22/9,27/11) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(1771,-2850,540,-869) (37/23,29/18) -> (59/18,23/7) Hyperbolic Matrix(1861,-3000,1080,-1741) (29/18,50/31) -> (31/18,50/29) Glide Reflection Matrix(5671,-9150,2212,-3569) (50/31,71/44) -> (41/16,100/39) Hyperbolic Matrix(1859,-3000,334,-539) (71/44,21/13) -> (11/2,39/7) Glide Reflection Matrix(4079,-6600,1186,-1919) (55/34,89/55) -> (55/16,31/9) Glide Reflection Matrix(5431,-8790,1612,-2609) (89/55,34/21) -> (64/19,91/27) Hyperbolic Matrix(389,-630,92,-149) (34/21,13/8) -> (4/1,17/4) Glide Reflection Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(511,-870,158,-269) (17/10,29/17) -> (29/9,13/4) Hyperbolic Matrix(421,-720,176,-301) (29/17,12/7) -> (31/13,12/5) Glide Reflection Matrix(419,-720,174,-299) (12/7,31/18) -> (12/5,29/12) Glide Reflection Matrix(1739,-3000,382,-659) (69/40,19/11) -> (9/2,41/9) Glide Reflection Matrix(329,-570,86,-149) (19/11,26/15) -> (19/5,4/1) Glide Reflection Matrix(2041,-3540,900,-1561) (26/15,59/34) -> (34/15,59/26) Glide Reflection Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(239,-420,136,-239) (7/4,30/17) -> (7/4,30/17) Reflection Matrix(781,-1380,442,-781) (30/17,23/13) -> (30/17,23/13) Reflection Matrix(389,-690,84,-149) (23/13,16/9) -> (23/5,14/3) Glide Reflection Matrix(149,-270,16,-29) (9/5,29/16) -> (9/1,1/0) Glide Reflection Matrix(959,-1740,264,-479) (29/16,20/11) -> (29/8,40/11) Glide Reflection Matrix(509,-930,214,-391) (20/11,11/6) -> (19/8,50/21) Hyperbolic Matrix(359,-660,130,-239) (11/6,24/13) -> (11/4,36/13) Glide Reflection Matrix(209,-390,112,-209) (13/7,15/8) -> (13/7,15/8) Reflection Matrix(269,-510,48,-91) (15/8,2/1) -> (28/5,45/8) Hyperbolic Matrix(211,-450,98,-209) (2/1,15/7) -> (15/7,28/13) Parabolic Matrix(361,-780,56,-121) (28/13,13/6) -> (32/5,13/2) Glide Reflection Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(389,-870,148,-331) (20/9,9/4) -> (21/8,50/19) Hyperbolic Matrix(1321,-3000,476,-1081) (59/26,25/11) -> (61/22,25/9) Glide Reflection Matrix(329,-750,118,-269) (25/11,16/7) -> (25/9,14/5) Glide Reflection Matrix(509,-1170,144,-331) (39/17,23/10) -> (7/2,39/11) Hyperbolic Matrix(599,-1380,260,-599) (23/10,30/13) -> (23/10,30/13) Reflection Matrix(181,-420,78,-181) (30/13,7/3) -> (30/13,7/3) Reflection Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(1861,-4500,720,-1741) (29/12,75/31) -> (31/12,75/29) Glide Reflection Matrix(2789,-6750,1078,-2609) (75/31,46/19) -> (75/29,44/17) Glide Reflection Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(541,-1380,118,-301) (28/11,23/9) -> (32/7,23/5) Glide Reflection Matrix(841,-2160,234,-601) (59/23,18/7) -> (61/17,18/5) Glide Reflection Matrix(419,-1080,116,-299) (18/7,31/12) -> (18/5,29/8) Glide Reflection Matrix(149,-390,34,-89) (13/5,21/8) -> (13/3,9/2) Glide Reflection Matrix(511,-1350,148,-391) (29/11,37/14) -> (31/9,7/2) Glide Reflection Matrix(991,-2670,278,-749) (35/13,27/10) -> (57/16,25/7) Hyperbolic Matrix(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(1559,-4320,476,-1319) (36/13,61/22) -> (36/11,59/18) Glide Reflection Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(1709,-5490,532,-1709) (61/19,45/14) -> (61/19,45/14) Reflection Matrix(811,-2610,252,-811) (45/14,29/9) -> (45/14,29/9) Reflection Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(2251,-7590,632,-2131) (91/27,27/8) -> (89/25,57/16) Glide Reflection Matrix(149,-510,26,-89) (17/5,24/7) -> (17/3,6/1) Glide Reflection Matrix(659,-2340,118,-419) (39/11,32/9) -> (39/7,28/5) Glide Reflection Matrix(14279,-50820,4012,-14279) (121/34,210/59) -> (121/34,210/59) Reflection Matrix(10501,-37380,2950,-10501) (210/59,89/25) -> (210/59,89/25) Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) Reflection Matrix(151,-570,40,-151) (15/4,19/5) -> (15/4,19/5) Reflection Matrix(239,-1020,56,-239) (17/4,30/7) -> (17/4,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(421,-1920,66,-301) (41/9,32/7) -> (19/3,32/5) Glide Reflection Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic Matrix(271,-1530,48,-271) (45/8,17/3) -> (45/8,17/3) Reflection Matrix(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(91,-690,12,-91) (15/2,23/3) -> (15/2,23/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(1,0,2,-1) -> Matrix(1,0,60,-1) (0/1,1/1) -> (0/1,1/30) Matrix(631,-690,246,-269) -> Matrix(247,-9,2772,-101) Matrix(1021,-1140,592,-661) -> Matrix(161,-6,2710,-101) Matrix(449,-510,184,-209) -> Matrix(185,-7,2352,-89) Matrix(419,-480,158,-181) -> Matrix(157,-6,1858,-71) Matrix(751,-870,284,-329) -> Matrix(181,-7,2198,-85) Matrix(331,-390,230,-271) -> Matrix(229,-9,4758,-187) Matrix(329,-390,178,-211) -> Matrix(177,-7,2908,-115) Matrix(569,-690,174,-211) -> Matrix(173,-7,1656,-67) Matrix(271,-330,124,-151) -> Matrix(123,-5,1648,-67) Matrix(269,-330,172,-211) -> Matrix(171,-7,3298,-135) Matrix(1141,-1440,332,-419) -> Matrix(143,-6,1168,-49) Matrix(451,-570,72,-91) -> Matrix(71,-3,260,-11) Matrix(899,-1140,332,-421) -> Matrix(331,-14,3712,-157) Matrix(211,-270,118,-151) -> Matrix(117,-5,1942,-83) Matrix(209,-270,24,-31) -> Matrix(23,-1,162,-7) Matrix(811,-1050,302,-391) -> Matrix(163,-7,1886,-81) Matrix(1411,-1830,394,-511) -> Matrix(255,-11,2434,-105) Matrix(599,-780,460,-599) -> Matrix(461,-20,10626,-461) (13/10,30/23) -> (10/231,1/23) Matrix(781,-1020,598,-781) -> Matrix(597,-26,13708,-597) (30/23,17/13) -> (1/23,13/298) Matrix(779,-1020,320,-419) -> Matrix(229,-10,2954,-129) Matrix(571,-750,252,-331) -> Matrix(205,-9,2756,-121) Matrix(331,-450,242,-329) -> Matrix(243,-11,5324,-241) 1/22 Matrix(2431,-3330,722,-989) -> Matrix(547,-25,4748,-217) Matrix(1291,-1770,504,-691) -> Matrix(415,-19,4696,-215) Matrix(151,-210,64,-89) -> Matrix(65,-3,802,-37) Matrix(149,-210,22,-31) -> Matrix(21,-1,148,-7) Matrix(2581,-3660,720,-1021) -> Matrix(467,-22,4394,-207) Matrix(2579,-3660,804,-1141) -> Matrix(551,-26,5616,-265) Matrix(1141,-1620,212,-301) -> Matrix(127,-6,402,-19) Matrix(421,-600,294,-419) -> Matrix(295,-14,6174,-293) 1/21 Matrix(689,-990,396,-569) -> Matrix(271,-13,4732,-227) Matrix(539,-780,208,-301) -> Matrix(41,-2,472,-23) Matrix(389,-570,144,-211) -> Matrix(143,-7,1614,-79) Matrix(331,-510,98,-151) -> Matrix(97,-5,834,-43) Matrix(659,-1020,272,-421) -> Matrix(39,-2,488,-25) Matrix(751,-1170,328,-511) -> Matrix(137,-7,1820,-93) Matrix(1711,-2670,1058,-1651) -> Matrix(175,-9,3286,-169) Matrix(419,-660,266,-419) -> Matrix(267,-14,5092,-267) (11/7,30/19) -> (7/134,1/19) Matrix(721,-1140,456,-721) -> Matrix(455,-24,8626,-455) (30/19,19/12) -> (1/19,12/227) Matrix(511,-810,94,-149) -> Matrix(19,-1,-56,3) Matrix(509,-810,208,-331) -> Matrix(169,-9,2122,-113) Matrix(299,-480,38,-61) -> Matrix(37,-2,130,-7) Matrix(1771,-2850,540,-869) -> Matrix(21,-1,190,-9) Matrix(1861,-3000,1080,-1741) -> Matrix(39,-2,682,-35) Matrix(5671,-9150,2212,-3569) -> Matrix(585,-31,6586,-349) Matrix(1859,-3000,334,-539) -> Matrix(113,-6,772,-41) Matrix(4079,-6600,1186,-1919) -> Matrix(75,-4,656,-35) Matrix(5431,-8790,1612,-2609) -> Matrix(167,-9,1466,-79) Matrix(389,-630,92,-149) -> Matrix(93,-5,688,-37) Matrix(91,-150,54,-89) -> Matrix(55,-3,972,-53) 1/18 Matrix(511,-870,158,-269) -> Matrix(19,-1,172,-9) Matrix(421,-720,176,-301) -> Matrix(35,-2,402,-23) Matrix(419,-720,174,-299) -> Matrix(35,-2,472,-27) Matrix(1739,-3000,382,-659) -> Matrix(33,-2,148,-9) Matrix(329,-570,86,-149) -> Matrix(53,-3,406,-23) Matrix(2041,-3540,900,-1561) -> Matrix(69,-4,914,-53) Matrix(2281,-3960,898,-1559) -> Matrix(1,0,-6,1) 0/1 Matrix(239,-420,136,-239) -> Matrix(137,-8,2346,-137) (7/4,30/17) -> (4/69,1/17) Matrix(781,-1380,442,-781) -> Matrix(441,-26,7480,-441) (30/17,23/13) -> (1/17,13/220) Matrix(389,-690,84,-149) -> Matrix(17,-1,220,-13) Matrix(149,-270,16,-29) -> Matrix(17,-1,84,-5) Matrix(959,-1740,264,-479) -> Matrix(67,-4,586,-35) Matrix(509,-930,214,-391) -> Matrix(17,-1,188,-11) Matrix(359,-660,130,-239) -> Matrix(67,-4,720,-43) Matrix(209,-390,112,-209) -> Matrix(113,-7,1824,-113) (13/7,15/8) -> (7/114,1/16) Matrix(269,-510,48,-91) -> Matrix(47,-3,298,-19) Matrix(211,-450,98,-209) -> Matrix(99,-7,1372,-97) 1/14 Matrix(361,-780,56,-121) -> Matrix(55,-4,206,-15) Matrix(299,-660,82,-181) -> Matrix(27,-2,230,-17) Matrix(389,-870,148,-331) -> Matrix(13,-1,170,-13) (0/1,1/13).(1/14,1/12) Matrix(1321,-3000,476,-1081) -> Matrix(107,-8,1110,-83) Matrix(329,-750,118,-269) -> Matrix(67,-5,710,-53) Matrix(509,-1170,144,-331) -> Matrix(13,-1,222,-17) Matrix(599,-1380,260,-599) -> Matrix(261,-20,3406,-261) (23/10,30/13) -> (10/131,1/13) Matrix(181,-420,78,-181) -> Matrix(77,-6,988,-77) (30/13,7/3) -> (1/13,3/38) Matrix(1259,-3000,478,-1139) -> Matrix(25,-2,312,-25) *** -> (1/13,1/12) Matrix(1861,-4500,720,-1741) -> Matrix(25,-2,262,-21) Matrix(2789,-6750,1078,-2609) -> Matrix(13,-1,142,-11) Matrix(121,-300,48,-119) -> Matrix(49,-4,576,-47) 1/12 Matrix(2099,-5340,590,-1501) -> Matrix(23,-2,242,-21) 1/11 Matrix(541,-1380,118,-301) -> Matrix(23,-2,80,-7) Matrix(841,-2160,234,-601) -> Matrix(89,-8,812,-73) Matrix(419,-1080,116,-299) -> Matrix(21,-2,178,-17) Matrix(149,-390,34,-89) -> Matrix(13,-1,90,-7) Matrix(511,-1350,148,-391) -> Matrix(37,-3,308,-25) Matrix(991,-2670,278,-749) -> Matrix(11,-1,144,-13) 1/12 Matrix(419,-1140,154,-419) -> Matrix(155,-14,1716,-155) (19/7,30/11) -> (7/78,1/11) Matrix(241,-660,88,-241) -> Matrix(87,-8,946,-87) (30/11,11/4) -> (1/11,4/43) Matrix(1559,-4320,476,-1319) -> Matrix(83,-8,778,-75) Matrix(31,-90,10,-29) -> Matrix(11,-1,100,-9) 1/10 Matrix(1709,-5490,532,-1709) -> Matrix(191,-19,1920,-191) (61/19,45/14) -> (19/192,1/10) Matrix(811,-2610,252,-811) -> Matrix(89,-9,880,-89) (45/14,29/9) -> (1/10,9/88) Matrix(181,-600,54,-179) -> Matrix(55,-6,486,-53) 1/9 Matrix(2251,-7590,632,-2131) -> Matrix(9,-1,116,-13) Matrix(149,-510,26,-89) -> Matrix(9,-1,62,-7) Matrix(659,-2340,118,-419) -> Matrix(21,-2,136,-13) Matrix(14279,-50820,4012,-14279) -> Matrix(1,0,22,-1) (121/34,210/59) -> (0/1,1/11) Matrix(10501,-37380,2950,-10501) -> Matrix(21,-2,220,-21) (210/59,89/25) -> (1/11,1/10) Matrix(89,-330,24,-89) -> Matrix(25,-3,208,-25) (11/3,15/4) -> (3/26,1/8) Matrix(151,-570,40,-151) -> Matrix(39,-5,304,-39) (15/4,19/5) -> (1/8,5/38) Matrix(239,-1020,56,-239) -> Matrix(57,-8,406,-57) (17/4,30/7) -> (4/29,1/7) Matrix(181,-780,42,-181) -> Matrix(41,-6,280,-41) (30/7,13/3) -> (1/7,3/20) Matrix(421,-1920,66,-301) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(31,-150,6,-29) -> Matrix(7,-1,36,-5) 1/6 Matrix(271,-1530,48,-271) -> Matrix(17,-3,96,-17) (45/8,17/3) -> (1/6,3/16) Matrix(29,-210,4,-29) -> Matrix(5,-1,24,-5) (7/1,15/2) -> (1/6,1/4) Matrix(91,-690,12,-91) -> Matrix(11,-3,40,-11) (15/2,23/3) -> (1/4,3/10) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.