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): 2520 Minimal number of generators: 421 Number of equivalence classes of cusps: 84 Genus: 169 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 29/25 29/24 29/23 87/68 29/22 29/21 145/101 29/20 3/2 87/55 29/18 145/89 29/17 29/16 2/1 15/7 29/13 116/51 116/49 29/12 5/2 116/45 145/56 290/111 377/144 29/11 87/32 58/21 3/1 29/9 145/44 58/17 7/2 203/57 290/81 18/5 29/8 290/77 58/15 4/1 29/7 21/5 232/55 116/27 13/3 9/2 87/19 116/25 14/3 19/4 24/5 29/6 5/1 26/5 21/4 58/11 16/3 27/5 11/2 28/5 17/3 23/4 29/5 6/1 25/4 19/3 13/2 33/5 20/3 27/4 7/1 29/4 22/3 15/2 23/3 8/1 17/2 9/1 10/1 11/1 12/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -6/17 -9/1 -1/3 -17/2 -3/10 -8/1 -4/15 -15/2 -7/26 -37/5 -5/19 -22/3 -10/39 -29/4 -1/4 -7/1 -3/13 -20/3 -8/33 -33/5 -3/13 -46/7 -6/25 -13/2 -5/22 -19/3 -7/33 -6/1 -2/9 -29/5 -1/5 -23/4 -7/36 -17/3 -1/5 -11/2 -1/4 -27/5 -1/5 -16/3 -4/21 -21/4 -5/28 -5/1 -1/5 -29/6 -1/6 -24/5 -4/25 -19/4 -3/20 -14/3 -2/15 -51/11 1/3 -37/8 -1/4 -60/13 -8/39 -23/5 -3/17 -55/12 -1/6 -87/19 -1/6 -32/7 -4/25 -9/2 -1/6 -31/7 -1/7 -22/5 -2/13 -13/3 -1/7 -30/7 -2/7 -17/4 -1/6 -21/5 -1/7 -46/11 -2/15 -25/6 -1/6 -29/7 -1/7 -4/1 0/1 -23/6 -1/6 -19/5 -1/5 -34/9 -2/15 -15/4 -1/10 -41/11 -1/5 -67/18 -1/6 -26/7 -2/13 -63/17 -3/19 -37/10 -3/20 -11/3 -1/7 -29/8 -1/7 -18/5 -2/15 -61/17 -1/9 -43/12 -5/36 -25/7 -1/9 -7/2 -1/6 -31/9 -1/7 -24/7 -4/29 -17/5 -3/23 -27/8 -1/8 -64/19 -4/33 -101/30 -1/6 -37/11 -1/9 -10/3 -2/17 -33/10 -3/20 -89/27 -1/7 -145/44 -1/7 -56/17 -12/85 -23/7 -5/37 -13/4 -1/8 -29/9 -1/8 -16/5 -4/33 -19/6 -5/42 -3/1 -1/9 -23/8 -3/28 -20/7 -8/75 -57/20 -11/106 -37/13 -1/9 -17/6 -1/10 -14/5 -6/55 -39/14 -1/10 -25/9 -5/47 -61/22 -7/66 -36/13 -16/151 -11/4 -5/48 -41/15 -3/29 -30/11 -14/137 -79/29 -7/69 -128/47 -20/197 -49/18 -1/10 -68/25 -16/159 -87/32 -1/10 -19/7 -1/11 -27/10 -1/10 -35/13 -1/9 -43/16 -7/68 -8/3 -4/39 -29/11 -1/10 -21/8 -1/10 -97/37 -41/415 -76/29 -8/81 -55/21 -5/51 -34/13 -6/61 -13/5 -3/31 -70/27 -2/23 -57/22 -5/48 -101/39 -13/129 -145/56 -1/10 -44/17 -8/81 -31/12 -1/10 -49/19 -5/51 -18/7 -2/21 -77/30 -13/136 -59/23 -7/75 -41/16 -1/10 -23/9 -5/51 -28/11 -16/165 -61/24 -11/114 -33/13 -3/31 -38/15 -22/229 -5/2 -3/32 -32/13 -4/43 -27/11 -1/11 -22/9 -2/21 -61/25 -1/11 -39/16 -17/184 -56/23 -36/391 -17/7 -1/11 -29/12 -1/11 -12/5 -8/89 -67/28 -5/56 -55/23 -7/79 -43/18 -1/10 -74/31 -6/67 -31/13 -1/11 -19/8 -7/78 -45/19 -17/191 -26/11 -10/113 -7/3 -5/57 -37/16 -9/104 -30/13 -22/255 -23/10 -1/12 -39/17 -1/11 -16/7 -4/47 -73/32 -17/198 -57/25 -29/339 -41/18 -7/82 -66/29 -34/399 -25/11 -13/153 -59/26 -31/366 -34/15 -6/71 -9/4 -1/12 -29/13 -1/12 -20/9 -16/193 -31/14 -1/12 -11/5 -5/61 -13/6 -5/62 -15/7 -13/163 -2/1 -2/27 -17/9 -3/43 -15/8 -13/188 -28/15 -24/349 -13/7 -5/73 -24/13 -4/59 -35/19 -23/339 -46/25 -30/443 -11/6 -5/74 -31/17 -1/15 -20/11 -16/239 -29/16 -1/15 -9/5 -1/15 -52/29 -16/243 -43/24 -13/198 -34/19 -6/91 -59/33 -31/471 -25/14 -13/198 -116/65 -4/61 -91/51 -47/717 -66/37 -34/519 -41/23 -7/107 -57/32 -29/444 -16/9 -4/61 -39/22 -1/16 -23/13 -1/15 -30/17 -22/339 -37/21 -9/139 -7/4 -5/78 -33/19 -1/15 -59/34 -23/360 -85/49 -3/47 -26/15 -10/157 -71/41 -27/425 -116/67 -4/63 -45/26 -17/268 -19/11 -7/111 -31/18 -1/16 -43/25 -1/17 -55/32 -7/110 -122/71 -22/347 -67/39 -5/79 -12/7 -8/127 -29/17 -1/16 -17/10 -1/16 -56/33 -36/581 -95/56 -13/210 -39/23 -17/275 -22/13 -2/33 -27/16 -1/16 -32/19 -4/65 -5/3 -3/49 -33/20 -3/50 -28/17 -16/267 -23/14 -5/84 -41/25 -1/17 -59/36 -7/114 -136/83 -20/329 -77/47 -13/215 -18/11 -2/33 -67/41 -7/117 -116/71 -4/67 -49/30 -5/84 -31/19 -1/17 -44/27 -8/135 -145/89 -1/17 -101/62 -13/222 -57/35 -5/87 -70/43 -2/31 -13/8 -3/50 -47/29 -11/185 -128/79 -52/875 -209/129 -83/1397 -290/179 -6/101 -81/50 -31/522 -34/21 -6/101 -89/55 -1/17 -233/144 -21/356 -377/233 -1/17 -144/89 -4/69 -55/34 -5/84 -76/47 -8/135 -97/60 -41/692 -21/13 -1/17 -29/18 -1/17 -8/5 -4/69 -35/22 -1/18 -62/39 -2/35 -27/17 -1/17 -19/12 -1/16 -87/55 -1/17 -68/43 -16/273 -49/31 -1/17 -128/81 -20/343 -79/50 -7/120 -30/19 -14/241 -11/7 -5/87 -58/37 -2/35 -47/30 -21/368 -36/23 -16/281 -61/39 -7/123 -86/55 -38/669 -25/16 -5/88 -14/9 -6/107 -31/20 -1/18 -17/11 -1/17 -20/13 -8/141 -43/28 -11/196 -23/15 -3/53 -3/2 -1/18 -22/15 -2/35 -19/13 -5/93 -16/11 -4/75 -29/20 -1/19 -13/9 -1/19 -36/25 0/1 -95/66 -5/96 -59/41 -13/251 -82/57 -2/39 -23/16 -5/98 -56/39 -12/239 -145/101 -1/20 -89/62 -1/20 -33/23 -3/61 -43/30 -3/64 -53/37 -1/27 -10/7 -2/37 -57/40 -11/212 -104/73 -12/233 -47/33 -1/19 -37/26 -1/18 -101/71 -1/21 -64/45 -4/75 -27/19 -1/19 -44/31 -8/153 -17/12 -3/58 -58/41 -2/39 -41/29 -7/137 -24/17 -4/79 -55/39 -5/99 -86/61 -14/279 -31/22 -1/20 -38/27 -6/121 -7/5 -1/21 -32/23 -4/79 -89/64 -1/20 -146/105 -18/359 -203/146 -1/20 -57/41 -7/141 -25/18 -1/18 -68/49 -8/155 -179/129 -21/409 -290/209 -2/39 -111/80 -13/254 -43/31 -5/99 -61/44 -1/18 -18/13 -2/39 -29/21 -1/20 -11/8 -1/20 -48/35 -4/81 -37/27 -3/61 -26/19 -2/41 -41/30 -1/22 -56/41 -4/93 -15/11 -1/17 -64/47 -4/77 -177/130 -11/214 -290/213 -2/39 -113/83 -7/137 -49/36 -1/20 -34/25 -2/39 -19/14 -1/22 -23/17 -1/21 -27/20 -1/20 -58/43 -2/41 -31/23 -1/21 -4/3 0/1 -29/22 -1/20 -25/19 -1/21 -46/35 -2/39 -21/16 -1/20 -59/45 -3/67 -97/74 -1/30 -232/177 0/1 -135/103 -1/7 -38/29 -2/37 -17/13 -1/21 -30/23 -2/47 -73/56 -1/36 -116/89 0/1 -43/33 -1/11 -13/10 -1/20 -35/27 -1/23 -92/71 0/1 -57/44 -5/96 -79/61 -3/59 -22/17 -2/41 -31/24 -1/20 -9/7 -1/21 -41/32 -1/20 -32/25 -4/83 -87/68 -1/21 -55/43 -1/21 -23/18 -3/64 -60/47 -8/177 -97/76 -9/202 -37/29 -1/23 -51/40 -1/30 -116/91 0/1 -65/51 -1/9 -14/11 -2/39 -33/26 -3/62 -85/67 -1/21 -52/41 0/1 -19/15 -3/61 -24/19 -4/83 -29/23 -1/21 -5/4 -1/22 -26/21 -2/43 -21/17 -5/107 -58/47 -2/43 -37/30 -9/194 -16/13 -4/87 -59/48 -15/328 -43/35 -3/67 -27/22 -1/22 -11/9 -1/23 -28/23 -8/171 -17/14 -1/22 -23/19 -7/153 -29/24 -1/22 -6/5 -2/45 -31/26 -1/22 -25/21 -5/111 -19/16 -7/156 -13/11 -5/113 -46/39 -6/137 -33/28 -3/68 -53/45 -15/341 -73/62 -23/524 -20/17 -8/183 -27/23 -1/23 -7/6 -3/68 -29/25 -1/23 -22/19 -10/231 -37/32 -5/116 -15/13 -7/163 -53/46 -9/212 -38/33 -2/49 -23/20 -1/24 -8/7 -4/93 -17/15 -3/71 -9/8 -1/24 -10/9 -6/145 -11/10 -1/24 -12/11 -8/197 -1/1 -1/27 0/1 0/1 1/1 1/27 10/9 6/145 9/8 1/24 17/15 3/71 8/7 4/93 15/13 7/163 37/32 5/116 22/19 10/231 29/25 1/23 7/6 3/68 20/17 8/183 33/28 3/68 46/39 6/137 13/11 5/113 19/16 7/156 6/5 2/45 29/24 1/22 23/19 7/153 17/14 1/22 11/9 1/23 27/22 1/22 16/13 4/87 21/17 5/107 5/4 1/22 29/23 1/21 24/19 4/83 19/15 3/61 14/11 2/39 51/40 1/30 37/29 1/23 60/47 8/177 23/18 3/64 55/43 1/21 87/68 1/21 32/25 4/83 9/7 1/21 31/24 1/20 22/17 2/41 13/10 1/20 30/23 2/47 17/13 1/21 21/16 1/20 46/35 2/39 25/19 1/21 29/22 1/20 4/3 0/1 23/17 1/21 19/14 1/22 34/25 2/39 15/11 1/17 41/30 1/22 67/49 1/21 26/19 2/41 63/46 3/62 37/27 3/61 11/8 1/20 29/21 1/20 18/13 2/39 61/44 1/18 43/31 5/99 25/18 1/18 7/5 1/21 31/22 1/20 24/17 4/79 17/12 3/58 27/19 1/19 64/45 4/75 101/71 1/21 37/26 1/18 10/7 2/37 33/23 3/61 89/62 1/20 145/101 1/20 56/39 12/239 23/16 5/98 13/9 1/19 29/20 1/19 16/11 4/75 19/13 5/93 3/2 1/18 23/15 3/53 20/13 8/141 57/37 11/191 37/24 1/18 17/11 1/17 14/9 6/107 39/25 1/17 25/16 5/88 61/39 7/123 36/23 16/281 11/7 5/87 41/26 3/52 30/19 14/241 79/50 7/120 128/81 20/343 49/31 1/17 68/43 16/273 87/55 1/17 19/12 1/16 27/17 1/17 35/22 1/18 43/27 7/121 8/5 4/69 29/18 1/17 21/13 1/17 97/60 41/692 76/47 8/135 55/34 5/84 34/21 6/101 13/8 3/50 70/43 2/31 57/35 5/87 101/62 13/222 145/89 1/17 44/27 8/135 31/19 1/17 49/30 5/84 18/11 2/33 77/47 13/215 59/36 7/114 41/25 1/17 23/14 5/84 28/17 16/267 61/37 11/183 33/20 3/50 38/23 22/365 5/3 3/49 32/19 4/65 27/16 1/16 22/13 2/33 61/36 1/16 39/23 17/275 56/33 36/581 17/10 1/16 29/17 1/16 12/7 8/127 67/39 5/79 55/32 7/110 43/25 1/17 74/43 6/95 31/18 1/16 19/11 7/111 45/26 17/268 26/15 10/157 7/4 5/78 37/21 9/139 30/17 22/339 23/13 1/15 39/22 1/16 16/9 4/61 73/41 17/261 57/32 29/444 41/23 7/107 66/37 34/519 25/14 13/198 59/33 31/471 34/19 6/91 9/5 1/15 29/16 1/15 20/11 16/239 31/17 1/15 11/6 5/74 13/7 5/73 15/8 13/188 2/1 2/27 17/8 3/38 15/7 13/163 28/13 24/299 13/6 5/62 24/11 4/49 35/16 23/282 46/21 30/367 11/5 5/61 31/14 1/12 20/9 16/193 29/13 1/12 9/4 1/12 52/23 16/189 43/19 13/153 34/15 6/71 59/26 31/366 25/11 13/153 116/51 4/47 91/40 47/552 66/29 34/399 41/18 7/82 57/25 29/339 16/7 4/47 39/17 1/11 23/10 1/12 30/13 22/255 37/16 9/104 7/3 5/57 33/14 1/12 59/25 23/261 85/36 3/34 26/11 10/113 71/30 27/304 116/49 4/45 45/19 17/191 19/8 7/78 31/13 1/11 43/18 1/10 55/23 7/79 122/51 22/247 67/28 5/56 12/5 8/89 29/12 1/11 17/7 1/11 56/23 36/391 95/39 13/141 39/16 17/184 22/9 2/21 27/11 1/11 32/13 4/43 5/2 3/32 33/13 3/31 28/11 16/165 23/9 5/51 41/16 1/10 59/23 7/75 136/53 20/211 77/30 13/136 18/7 2/21 67/26 7/72 116/45 4/41 49/19 5/51 31/12 1/10 44/17 8/81 145/56 1/10 101/39 13/129 57/22 5/48 70/27 2/23 13/5 3/31 47/18 11/112 128/49 52/529 209/80 83/844 290/111 6/61 81/31 31/315 34/13 6/61 89/34 1/10 233/89 21/211 377/144 1/10 144/55 4/39 55/21 5/51 76/29 8/81 97/37 41/415 21/8 1/10 29/11 1/10 8/3 4/39 35/13 1/9 62/23 2/19 27/10 1/10 19/7 1/11 87/32 1/10 68/25 16/159 49/18 1/10 128/47 20/197 79/29 7/69 30/11 14/137 11/4 5/48 58/21 2/19 47/17 21/199 36/13 16/151 61/22 7/66 86/31 38/357 25/9 5/47 14/5 6/55 31/11 1/9 17/6 1/10 20/7 8/75 43/15 11/101 23/8 3/28 3/1 1/9 22/7 2/19 19/6 5/42 16/5 4/33 29/9 1/8 13/4 1/8 36/11 0/1 95/29 5/39 59/18 13/100 82/25 2/15 23/7 5/37 56/17 12/85 145/44 1/7 89/27 1/7 33/10 3/20 43/13 3/17 53/16 1/0 10/3 2/17 57/17 11/85 104/31 12/91 47/14 1/8 37/11 1/9 101/30 1/6 64/19 4/33 27/8 1/8 44/13 8/63 17/5 3/23 58/17 2/15 41/12 7/52 24/7 4/29 55/16 5/36 86/25 14/99 31/9 1/7 38/11 6/41 7/2 1/6 32/9 4/29 89/25 1/7 146/41 18/127 203/57 1/7 57/16 7/48 25/7 1/9 68/19 8/61 179/50 21/158 290/81 2/15 111/31 13/97 43/12 5/36 61/17 1/9 18/5 2/15 29/8 1/7 11/3 1/7 48/13 4/27 37/10 3/20 26/7 2/13 41/11 1/5 56/15 4/15 15/4 1/10 64/17 4/31 177/47 11/83 290/77 2/15 113/30 7/52 49/13 1/7 34/9 2/15 19/5 1/5 23/6 1/6 27/7 1/7 58/15 2/13 31/8 1/6 4/1 0/1 29/7 1/7 25/6 1/6 46/11 2/15 21/5 1/7 59/14 3/14 97/23 -1/3 232/55 0/1 135/32 1/20 38/9 2/17 17/4 1/6 30/7 2/7 73/17 -1/9 116/27 0/1 43/10 1/16 13/3 1/7 35/8 1/4 92/21 0/1 57/13 5/39 79/18 3/22 22/5 2/13 31/7 1/7 9/2 1/6 41/9 1/7 32/7 4/25 87/19 1/6 55/12 1/6 23/5 3/17 60/13 8/39 97/21 9/41 37/8 1/4 51/11 -1/3 116/25 0/1 65/14 1/18 14/3 2/15 33/7 3/19 85/18 1/6 52/11 0/1 19/4 3/20 24/5 4/25 29/6 1/6 5/1 1/5 26/5 2/11 21/4 5/28 58/11 2/11 37/7 9/49 16/3 4/21 59/11 15/77 43/8 3/14 27/5 1/5 11/2 1/4 28/5 8/45 17/3 1/5 23/4 7/36 29/5 1/5 6/1 2/9 31/5 1/5 25/4 5/24 19/3 7/33 13/2 5/22 46/7 6/25 33/5 3/13 53/8 15/64 73/11 23/97 20/3 8/33 27/4 1/4 7/1 3/13 29/4 1/4 22/3 10/39 37/5 5/19 15/2 7/26 53/7 9/31 38/5 2/5 23/3 1/3 8/1 4/15 17/2 3/10 9/1 1/3 10/1 6/17 11/1 1/3 12/1 8/19 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(57,580,-40,-407) (-10/1,1/0) -> (-10/7,-57/40) Hyperbolic Matrix(117,1102,74,697) (-10/1,-9/1) -> (49/31,68/43) Hyperbolic Matrix(175,1508,128,1103) (-9/1,-17/2) -> (41/30,67/49) Hyperbolic Matrix(173,1450,76,637) (-17/2,-8/1) -> (66/29,41/18) Hyperbolic Matrix(59,464,-22,-173) (-8/1,-15/2) -> (-43/16,-8/3) Hyperbolic Matrix(579,4292,172,1275) (-15/2,-37/5) -> (37/11,101/30) Hyperbolic Matrix(465,3422,142,1045) (-37/5,-22/3) -> (36/11,95/29) Hyperbolic Matrix(175,1276,24,175) (-22/3,-29/4) -> (29/4,22/3) Hyperbolic Matrix(57,406,8,57) (-29/4,-7/1) -> (7/1,29/4) Hyperbolic Matrix(59,406,-42,-289) (-7/1,-20/3) -> (-38/27,-7/5) Hyperbolic Matrix(289,1914,-114,-755) (-20/3,-33/5) -> (-33/13,-38/15) Hyperbolic Matrix(405,2668,308,2029) (-33/5,-46/7) -> (46/35,25/19) Hyperbolic Matrix(231,1508,142,927) (-46/7,-13/2) -> (13/8,70/43) Hyperbolic Matrix(173,1102,100,637) (-13/2,-19/3) -> (19/11,45/26) Hyperbolic Matrix(175,1102,-138,-869) (-19/3,-6/1) -> (-52/41,-19/15) Hyperbolic Matrix(59,348,10,59) (-6/1,-29/5) -> (29/5,6/1) Hyperbolic Matrix(231,1334,40,231) (-29/5,-23/4) -> (23/4,29/5) Hyperbolic Matrix(233,1334,142,813) (-23/4,-17/3) -> (41/25,23/14) Hyperbolic Matrix(115,638,-42,-233) (-17/3,-11/2) -> (-11/4,-41/15) Hyperbolic Matrix(117,638,64,349) (-11/2,-27/5) -> (31/17,11/6) Hyperbolic Matrix(463,2494,-194,-1045) (-27/5,-16/3) -> (-74/31,-31/13) Hyperbolic Matrix(175,928,-142,-753) (-16/3,-21/4) -> (-37/30,-16/13) Hyperbolic Matrix(289,1508,-78,-407) (-21/4,-5/1) -> (-63/17,-37/10) Hyperbolic Matrix(59,290,12,59) (-5/1,-29/6) -> (29/6,5/1) Hyperbolic Matrix(289,1392,60,289) (-29/6,-24/5) -> (24/5,29/6) Hyperbolic Matrix(231,1102,170,811) (-24/5,-19/4) -> (19/14,34/25) Hyperbolic Matrix(173,812,-62,-291) (-19/4,-14/3) -> (-14/5,-39/14) Hyperbolic Matrix(349,1624,-274,-1275) (-14/3,-51/11) -> (-65/51,-14/11) Hyperbolic Matrix(463,2146,200,927) (-51/11,-37/8) -> (37/16,7/3) Hyperbolic Matrix(1683,7772,-992,-4581) (-37/8,-60/13) -> (-56/33,-95/56) Hyperbolic Matrix(579,2668,176,811) (-60/13,-23/5) -> (23/7,56/17) Hyperbolic Matrix(291,1334,190,871) (-23/5,-55/12) -> (3/2,23/15) Hyperbolic Matrix(2089,9570,456,2089) (-55/12,-87/19) -> (87/19,55/12) Hyperbolic Matrix(1217,5568,266,1217) (-87/19,-32/7) -> (32/7,87/19) Hyperbolic Matrix(521,2378,-140,-639) (-32/7,-9/2) -> (-67/18,-26/7) Hyperbolic Matrix(405,1798,248,1101) (-9/2,-31/7) -> (31/19,49/30) Hyperbolic Matrix(289,1276,118,521) (-31/7,-22/5) -> (22/9,27/11) Hyperbolic Matrix(173,754,-120,-523) (-22/5,-13/3) -> (-13/9,-36/25) Hyperbolic Matrix(175,754,-94,-405) (-13/3,-30/7) -> (-28/15,-13/7) Hyperbolic Matrix(407,1740,258,1103) (-30/7,-17/4) -> (41/26,30/19) Hyperbolic Matrix(233,986,-82,-347) (-17/4,-21/5) -> (-37/13,-17/6) Hyperbolic Matrix(1509,6322,554,2321) (-21/5,-46/11) -> (128/47,79/29) Hyperbolic Matrix(639,2668,542,2263) (-46/11,-25/6) -> (33/28,46/39) Hyperbolic Matrix(349,1450,84,349) (-25/6,-29/7) -> (29/7,25/6) Hyperbolic Matrix(57,232,14,57) (-29/7,-4/1) -> (4/1,29/7) Hyperbolic Matrix(407,1566,-256,-985) (-4/1,-23/6) -> (-35/22,-62/39) Hyperbolic Matrix(349,1334,152,581) (-23/6,-19/5) -> (39/17,23/10) Hyperbolic Matrix(291,1102,230,871) (-19/5,-34/9) -> (24/19,19/15) Hyperbolic Matrix(523,1972,-292,-1101) (-34/9,-15/4) -> (-43/24,-34/19) Hyperbolic Matrix(233,870,-124,-463) (-15/4,-41/11) -> (-17/9,-15/8) Hyperbolic Matrix(405,1508,358,1333) (-41/11,-67/18) -> (9/8,17/15) Hyperbolic Matrix(579,2146,344,1275) (-26/7,-63/17) -> (5/3,32/19) Hyperbolic Matrix(581,2146,-408,-1507) (-37/10,-11/3) -> (-47/33,-37/26) Hyperbolic Matrix(175,638,48,175) (-11/3,-29/8) -> (29/8,11/3) Hyperbolic Matrix(289,1044,80,289) (-29/8,-18/5) -> (18/5,29/8) Hyperbolic Matrix(1567,5626,598,2147) (-18/5,-61/17) -> (55/21,76/29) Hyperbolic Matrix(1391,4988,582,2087) (-61/17,-43/12) -> (43/18,55/23) Hyperbolic Matrix(697,2494,-486,-1739) (-43/12,-25/7) -> (-33/23,-43/30) Hyperbolic Matrix(115,406,-66,-233) (-25/7,-7/2) -> (-7/4,-33/19) Hyperbolic Matrix(117,406,-100,-347) (-7/2,-31/9) -> (-27/23,-7/6) Hyperbolic Matrix(929,3190,-574,-1971) (-31/9,-24/7) -> (-34/21,-89/55) Hyperbolic Matrix(407,1392,-288,-985) (-24/7,-17/5) -> (-41/29,-24/17) Hyperbolic Matrix(291,986,-188,-637) (-17/5,-27/8) -> (-31/20,-17/11) Hyperbolic Matrix(637,2146,-534,-1799) (-27/8,-64/19) -> (-6/5,-31/26) Hyperbolic Matrix(2205,7424,586,1973) (-64/19,-101/30) -> (15/4,64/17) Hyperbolic Matrix(1275,4292,172,579) (-101/30,-37/11) -> (37/5,15/2) Hyperbolic Matrix(639,2146,-466,-1565) (-37/11,-10/3) -> (-48/35,-37/27) Hyperbolic Matrix(755,2494,-544,-1797) (-10/3,-33/10) -> (-25/18,-68/49) Hyperbolic Matrix(985,3248,158,521) (-33/10,-89/27) -> (31/5,25/4) Hyperbolic Matrix(7831,25810,2376,7831) (-89/27,-145/44) -> (145/44,89/27) Hyperbolic Matrix(4929,16240,1496,4929) (-145/44,-56/17) -> (56/17,145/44) Hyperbolic Matrix(811,2668,176,579) (-56/17,-23/7) -> (23/5,60/13) Hyperbolic Matrix(231,754,-178,-581) (-23/7,-13/4) -> (-13/10,-35/27) Hyperbolic Matrix(233,754,72,233) (-13/4,-29/9) -> (29/9,13/4) Hyperbolic Matrix(289,928,90,289) (-29/9,-16/5) -> (16/5,29/9) Hyperbolic Matrix(291,928,164,523) (-16/5,-19/6) -> (39/22,16/9) Hyperbolic Matrix(405,1276,-166,-523) (-19/6,-3/1) -> (-61/25,-39/16) Hyperbolic Matrix(463,1334,362,1043) (-3/1,-23/8) -> (23/18,55/43) Hyperbolic Matrix(465,1334,-404,-1159) (-23/8,-20/7) -> (-38/33,-23/20) Hyperbolic Matrix(3133,8932,-1912,-5451) (-20/7,-57/20) -> (-59/36,-136/83) Hyperbolic Matrix(2667,7598,814,2319) (-57/20,-37/13) -> (95/29,59/18) Hyperbolic Matrix(349,986,-246,-695) (-17/6,-14/5) -> (-44/31,-17/12) Hyperbolic Matrix(521,1450,-438,-1219) (-39/14,-25/9) -> (-25/21,-19/16) Hyperbolic Matrix(1275,3538,-502,-1393) (-25/9,-61/22) -> (-61/24,-33/13) Hyperbolic Matrix(1277,3538,754,2089) (-61/22,-36/13) -> (22/13,61/36) Hyperbolic Matrix(755,2088,-482,-1333) (-36/13,-11/4) -> (-47/30,-36/23) Hyperbolic Matrix(637,1740,488,1333) (-41/15,-30/11) -> (30/23,17/13) Hyperbolic Matrix(1277,3480,724,1973) (-30/11,-79/29) -> (37/21,30/17) Hyperbolic Matrix(2321,6322,554,1509) (-79/29,-128/47) -> (46/11,21/5) Hyperbolic Matrix(3365,9164,1406,3829) (-128/47,-49/18) -> (67/28,12/5) Hyperbolic Matrix(405,1102,362,985) (-49/18,-68/25) -> (10/9,9/8) Hyperbolic Matrix(4351,11832,1600,4351) (-68/25,-87/32) -> (87/32,68/25) Hyperbolic Matrix(1217,3306,448,1217) (-87/32,-19/7) -> (19/7,87/32) Hyperbolic Matrix(407,1102,236,639) (-19/7,-27/10) -> (31/18,19/11) Hyperbolic Matrix(581,1566,-430,-1159) (-27/10,-35/13) -> (-23/17,-27/20) Hyperbolic Matrix(927,2494,-604,-1625) (-35/13,-43/16) -> (-43/28,-23/15) Hyperbolic Matrix(175,464,66,175) (-8/3,-29/11) -> (29/11,8/3) Hyperbolic Matrix(463,1218,176,463) (-29/11,-21/8) -> (21/8,29/11) Hyperbolic Matrix(2145,5626,464,1217) (-21/8,-97/37) -> (97/21,37/8) Hyperbolic Matrix(2899,7598,1770,4639) (-97/37,-76/29) -> (18/11,77/47) Hyperbolic Matrix(2147,5626,598,1567) (-76/29,-55/21) -> (61/17,18/5) Hyperbolic Matrix(1219,3190,-864,-2261) (-55/21,-34/13) -> (-24/17,-55/39) Hyperbolic Matrix(289,754,-156,-407) (-34/13,-13/5) -> (-13/7,-24/13) Hyperbolic Matrix(581,1508,492,1277) (-13/5,-70/27) -> (46/39,13/11) Hyperbolic Matrix(3827,9918,-2686,-6961) (-70/27,-57/22) -> (-57/40,-104/73) Hyperbolic Matrix(3829,9918,2150,5569) (-57/22,-101/39) -> (73/41,57/32) Hyperbolic Matrix(11311,29290,4368,11311) (-101/39,-145/56) -> (145/56,101/39) Hyperbolic Matrix(4929,12760,1904,4929) (-145/56,-44/17) -> (44/17,145/56) Hyperbolic Matrix(987,2552,292,755) (-44/17,-31/12) -> (27/8,44/13) Hyperbolic Matrix(697,1798,540,1393) (-31/12,-49/19) -> (9/7,31/24) Hyperbolic Matrix(811,2088,-496,-1277) (-49/19,-18/7) -> (-18/11,-67/41) Hyperbolic Matrix(2959,7598,1830,4699) (-18/7,-77/30) -> (97/60,76/47) Hyperbolic Matrix(4001,10266,-3052,-7831) (-77/30,-59/23) -> (-59/45,-97/74) Hyperbolic Matrix(1855,4756,814,2087) (-59/23,-41/16) -> (41/18,57/25) Hyperbolic Matrix(521,1334,430,1101) (-41/16,-23/9) -> (23/19,17/14) Hyperbolic Matrix(523,1334,296,755) (-23/9,-28/11) -> (30/17,23/13) Hyperbolic Matrix(2669,6786,776,1973) (-28/11,-61/24) -> (55/16,86/25) Hyperbolic Matrix(871,2204,-756,-1913) (-38/15,-5/2) -> (-53/46,-38/33) Hyperbolic Matrix(871,2146,636,1567) (-5/2,-32/13) -> (26/19,63/46) Hyperbolic Matrix(1391,3422,-802,-1973) (-32/13,-27/11) -> (-85/49,-26/15) Hyperbolic Matrix(521,1276,118,289) (-27/11,-22/9) -> (22/5,31/7) Hyperbolic Matrix(1449,3538,926,2261) (-22/9,-61/25) -> (61/39,36/23) Hyperbolic Matrix(3191,7772,-2500,-6089) (-39/16,-56/23) -> (-60/47,-97/76) Hyperbolic Matrix(1335,3248,358,871) (-56/23,-17/7) -> (41/11,56/15) Hyperbolic Matrix(407,986,168,407) (-17/7,-29/12) -> (29/12,17/7) Hyperbolic Matrix(289,696,120,289) (-29/12,-12/5) -> (12/5,29/12) Hyperbolic Matrix(3829,9164,1406,3365) (-12/5,-67/28) -> (49/18,128/47) Hyperbolic Matrix(4291,10266,-3152,-7541) (-67/28,-55/23) -> (-113/83,-49/36) Hyperbolic Matrix(2087,4988,582,1391) (-55/23,-43/18) -> (43/12,61/17) Hyperbolic Matrix(2551,6090,-1118,-2669) (-43/18,-74/31) -> (-16/7,-73/32) Hyperbolic Matrix(463,1102,292,695) (-31/13,-19/8) -> (19/12,27/17) Hyperbolic Matrix(465,1102,392,929) (-19/8,-45/19) -> (13/11,19/16) Hyperbolic Matrix(1275,3016,-736,-1741) (-45/19,-26/11) -> (-26/15,-71/41) Hyperbolic Matrix(173,406,-124,-291) (-26/11,-7/3) -> (-7/5,-32/23) Hyperbolic Matrix(927,2146,200,463) (-7/3,-37/16) -> (37/8,51/11) Hyperbolic Matrix(1507,3480,954,2203) (-37/16,-30/13) -> (30/19,79/50) Hyperbolic Matrix(579,1334,352,811) (-30/13,-23/10) -> (23/14,28/17) Hyperbolic Matrix(581,1334,152,349) (-23/10,-39/17) -> (19/5,23/6) Hyperbolic Matrix(405,928,278,637) (-39/17,-16/7) -> (16/11,19/13) Hyperbolic Matrix(4349,9918,2670,6089) (-73/32,-57/25) -> (57/35,101/62) Hyperbolic Matrix(2087,4756,814,1855) (-57/25,-41/18) -> (41/16,59/23) Hyperbolic Matrix(637,1450,76,173) (-41/18,-66/29) -> (8/1,17/2) Hyperbolic Matrix(3365,7656,-1886,-4291) (-66/29,-25/11) -> (-91/51,-66/37) Hyperbolic Matrix(1277,2900,358,813) (-25/11,-59/26) -> (57/16,25/7) Hyperbolic Matrix(3247,7366,-2506,-5685) (-59/26,-34/15) -> (-92/71,-57/44) Hyperbolic Matrix(871,1972,-640,-1449) (-34/15,-9/4) -> (-49/36,-34/25) Hyperbolic Matrix(233,522,104,233) (-9/4,-29/13) -> (29/13,9/4) Hyperbolic Matrix(521,1160,234,521) (-29/13,-20/9) -> (20/9,29/13) Hyperbolic Matrix(811,1798,-576,-1277) (-20/9,-31/14) -> (-31/22,-38/27) Hyperbolic Matrix(289,638,236,521) (-31/14,-11/5) -> (11/9,27/22) Hyperbolic Matrix(347,754,-214,-465) (-11/5,-13/6) -> (-13/8,-47/29) Hyperbolic Matrix(349,754,-268,-579) (-13/6,-15/7) -> (-43/33,-13/10) Hyperbolic Matrix(407,870,-298,-637) (-15/7,-2/1) -> (-56/41,-15/11) Hyperbolic Matrix(521,986,214,405) (-2/1,-17/9) -> (17/7,56/23) Hyperbolic Matrix(1335,2494,-1024,-1913) (-15/8,-28/15) -> (-30/23,-73/56) Hyperbolic Matrix(2203,4060,-1700,-3133) (-24/13,-35/19) -> (-35/27,-92/71) Hyperbolic Matrix(7657,14094,-4726,-8699) (-35/19,-46/25) -> (-128/79,-209/129) Hyperbolic Matrix(347,638,-316,-581) (-46/25,-11/6) -> (-11/10,-12/11) Hyperbolic Matrix(349,638,64,117) (-11/6,-31/17) -> (27/5,11/2) Hyperbolic Matrix(637,1160,-542,-987) (-31/17,-20/11) -> (-20/17,-27/23) Hyperbolic Matrix(639,1160,352,639) (-20/11,-29/16) -> (29/16,20/11) Hyperbolic Matrix(289,522,160,289) (-29/16,-9/5) -> (9/5,29/16) Hyperbolic Matrix(2553,4582,-1486,-2667) (-9/5,-52/29) -> (-122/71,-67/39) Hyperbolic Matrix(4465,8004,1326,2377) (-52/29,-43/24) -> (101/30,64/19) Hyperbolic Matrix(3827,6844,-2660,-4757) (-34/19,-59/33) -> (-59/41,-82/57) Hyperbolic Matrix(1915,3422,812,1451) (-59/33,-25/14) -> (33/14,59/25) Hyperbolic Matrix(7539,13456,3314,5915) (-25/14,-116/65) -> (116/51,91/40) Hyperbolic Matrix(7541,13456,3316,5917) (-116/65,-91/51) -> (25/11,116/51) Hyperbolic Matrix(813,1450,716,1277) (-66/37,-41/23) -> (17/15,8/7) Hyperbolic Matrix(2669,4756,1628,2901) (-41/23,-57/32) -> (59/36,41/25) Hyperbolic Matrix(1043,1856,-848,-1509) (-57/32,-16/9) -> (-16/13,-59/48) Hyperbolic Matrix(523,928,164,291) (-16/9,-39/22) -> (19/6,16/5) Hyperbolic Matrix(753,1334,556,985) (-39/22,-23/13) -> (23/17,19/14) Hyperbolic Matrix(755,1334,296,523) (-23/13,-30/17) -> (28/11,23/9) Hyperbolic Matrix(1973,3480,724,1277) (-30/17,-37/21) -> (79/29,30/11) Hyperbolic Matrix(1219,2146,956,1683) (-37/21,-7/4) -> (51/40,37/29) Hyperbolic Matrix(1971,3422,868,1507) (-33/19,-59/34) -> (59/26,25/11) Hyperbolic Matrix(14443,25056,-8926,-15485) (-59/34,-85/49) -> (-89/55,-233/144) Hyperbolic Matrix(7771,13456,3282,5683) (-71/41,-116/67) -> (116/49,45/19) Hyperbolic Matrix(7773,13456,3284,5685) (-116/67,-45/26) -> (71/30,116/49) Hyperbolic Matrix(637,1102,100,173) (-45/26,-19/11) -> (19/3,13/2) Hyperbolic Matrix(639,1102,236,407) (-19/11,-31/18) -> (27/10,19/7) Hyperbolic Matrix(1449,2494,-1180,-2031) (-31/18,-43/25) -> (-43/35,-27/22) Hyperbolic Matrix(2901,4988,2092,3597) (-43/25,-55/32) -> (61/44,43/31) Hyperbolic Matrix(14615,25114,-10734,-18445) (-55/32,-122/71) -> (-64/47,-177/130) Hyperbolic Matrix(5335,9164,3376,5799) (-67/39,-12/7) -> (128/81,49/31) Hyperbolic Matrix(407,696,238,407) (-12/7,-29/17) -> (29/17,12/7) Hyperbolic Matrix(579,986,340,579) (-29/17,-17/10) -> (17/10,29/17) Hyperbolic Matrix(581,986,274,465) (-17/10,-56/33) -> (2/1,17/8) Hyperbolic Matrix(5915,10034,2256,3827) (-95/56,-39/23) -> (97/37,21/8) Hyperbolic Matrix(753,1276,-514,-871) (-39/23,-22/13) -> (-22/15,-19/13) Hyperbolic Matrix(755,1276,584,987) (-22/13,-27/16) -> (31/24,22/17) Hyperbolic Matrix(2203,3712,-1584,-2669) (-27/16,-32/19) -> (-32/23,-89/64) Hyperbolic Matrix(173,290,34,57) (-32/19,-5/3) -> (5/1,26/5) Hyperbolic Matrix(1159,1914,-984,-1625) (-5/3,-33/20) -> (-33/28,-53/45) Hyperbolic Matrix(2145,3538,-1372,-2263) (-33/20,-28/17) -> (-86/55,-25/16) Hyperbolic Matrix(811,1334,352,579) (-28/17,-23/14) -> (23/10,30/13) Hyperbolic Matrix(813,1334,142,233) (-23/14,-41/25) -> (17/3,23/4) Hyperbolic Matrix(2901,4756,1628,2669) (-41/25,-59/36) -> (57/32,41/23) Hyperbolic Matrix(12991,21286,-9912,-16241) (-136/83,-77/47) -> (-135/103,-38/29) Hyperbolic Matrix(4639,7598,1770,2899) (-77/47,-18/11) -> (76/29,97/37) Hyperbolic Matrix(8235,13456,3194,5219) (-67/41,-116/71) -> (116/45,49/19) Hyperbolic Matrix(8237,13456,3196,5221) (-116/71,-49/30) -> (67/26,116/45) Hyperbolic Matrix(1101,1798,248,405) (-49/30,-31/19) -> (31/7,9/2) Hyperbolic Matrix(1103,1798,392,639) (-31/19,-44/27) -> (14/5,31/11) Hyperbolic Matrix(7831,12760,4806,7831) (-44/27,-145/89) -> (145/89,44/27) Hyperbolic Matrix(17979,29290,11036,17979) (-145/89,-101/62) -> (101/62,145/89) Hyperbolic Matrix(5163,8410,962,1567) (-101/62,-57/35) -> (59/11,43/8) Hyperbolic Matrix(463,754,-428,-697) (-57/35,-70/43) -> (-12/11,-1/1) Hyperbolic Matrix(927,1508,142,231) (-70/43,-13/8) -> (13/2,46/7) Hyperbolic Matrix(6729,10904,-4724,-7655) (-47/29,-128/79) -> (-104/73,-47/33) Hyperbolic Matrix(51909,84100,19868,32189) (-209/129,-290/179) -> (290/111,81/31) Hyperbolic Matrix(51911,84100,19870,32191) (-290/179,-81/50) -> (209/80,290/111) Hyperbolic Matrix(4583,7424,-3186,-5161) (-81/50,-34/21) -> (-82/57,-23/16) Hyperbolic Matrix(42513,68788,11936,19313) (-233/144,-377/233) -> (203/57,57/16) Hyperbolic Matrix(52085,84274,14626,23665) (-377/233,-144/89) -> (146/41,203/57) Hyperbolic Matrix(8353,13514,3012,4873) (-144/89,-55/34) -> (61/22,86/31) Hyperbolic Matrix(3479,5626,2510,4059) (-55/34,-76/47) -> (18/13,61/44) Hyperbolic Matrix(4699,7598,1830,2959) (-76/47,-97/60) -> (77/30,18/7) Hyperbolic Matrix(6207,10034,2548,4119) (-97/60,-21/13) -> (95/39,39/16) Hyperbolic Matrix(755,1218,468,755) (-21/13,-29/18) -> (29/18,21/13) Hyperbolic Matrix(289,464,180,289) (-29/18,-8/5) -> (8/5,29/18) Hyperbolic Matrix(291,464,-254,-405) (-8/5,-35/22) -> (-23/20,-8/7) Hyperbolic Matrix(1277,2030,-948,-1507) (-62/39,-27/17) -> (-31/23,-4/3) Hyperbolic Matrix(695,1102,292,463) (-27/17,-19/12) -> (19/8,31/13) Hyperbolic Matrix(2089,3306,1320,2089) (-19/12,-87/55) -> (87/55,19/12) Hyperbolic Matrix(7481,11832,4730,7481) (-87/55,-68/43) -> (68/43,87/55) Hyperbolic Matrix(697,1102,74,117) (-68/43,-49/31) -> (9/1,10/1) Hyperbolic Matrix(5799,9164,3376,5335) (-49/31,-128/81) -> (12/7,67/39) Hyperbolic Matrix(4001,6322,3046,4813) (-128/81,-79/50) -> (21/16,46/35) Hyperbolic Matrix(2203,3480,954,1507) (-79/50,-30/19) -> (30/13,37/16) Hyperbolic Matrix(405,638,-332,-523) (-30/19,-11/7) -> (-11/9,-28/23) Hyperbolic Matrix(2145,3364,776,1217) (-11/7,-58/37) -> (58/21,47/17) Hyperbolic Matrix(2147,3364,778,1219) (-58/37,-47/30) -> (11/4,58/21) Hyperbolic Matrix(927,1450,296,463) (-36/23,-61/39) -> (3/1,22/7) Hyperbolic Matrix(8641,13514,3300,5161) (-61/39,-86/55) -> (144/55,55/21) Hyperbolic Matrix(521,812,-410,-639) (-25/16,-14/9) -> (-14/11,-33/26) Hyperbolic Matrix(1159,1798,448,695) (-14/9,-31/20) -> (31/12,44/17) Hyperbolic Matrix(639,986,-488,-753) (-17/11,-20/13) -> (-38/29,-17/13) Hyperbolic Matrix(1509,2320,-1282,-1971) (-20/13,-43/28) -> (-73/62,-20/17) Hyperbolic Matrix(871,1334,190,291) (-23/15,-3/2) -> (55/12,23/5) Hyperbolic Matrix(987,1450,356,523) (-3/2,-22/15) -> (36/13,61/22) Hyperbolic Matrix(637,928,278,405) (-19/13,-16/11) -> (16/7,39/17) Hyperbolic Matrix(639,928,440,639) (-16/11,-29/20) -> (29/20,16/11) Hyperbolic Matrix(521,754,360,521) (-29/20,-13/9) -> (13/9,29/20) Hyperbolic Matrix(2377,3422,2054,2957) (-36/25,-95/66) -> (37/32,22/19) Hyperbolic Matrix(5279,7598,3426,4931) (-95/66,-59/41) -> (57/37,37/24) Hyperbolic Matrix(1857,2668,1454,2089) (-23/16,-56/39) -> (60/47,23/18) Hyperbolic Matrix(11311,16240,7878,11311) (-56/39,-145/101) -> (145/101,56/39) Hyperbolic Matrix(17979,25810,12524,17979) (-145/101,-89/62) -> (89/62,145/101) Hyperbolic Matrix(4001,5742,848,1217) (-89/62,-33/23) -> (33/7,85/18) Hyperbolic Matrix(4291,6148,-3644,-5221) (-43/30,-53/37) -> (-53/45,-73/62) Hyperbolic Matrix(3769,5394,-2716,-3887) (-53/37,-10/7) -> (-68/49,-179/129) Hyperbolic Matrix(3017,4292,2610,3713) (-37/26,-101/71) -> (15/13,37/32) Hyperbolic Matrix(5627,8004,2488,3539) (-101/71,-64/45) -> (52/23,43/19) Hyperbolic Matrix(4813,6844,-3794,-5395) (-64/45,-27/19) -> (-85/67,-52/41) Hyperbolic Matrix(1797,2552,1102,1565) (-27/19,-44/31) -> (44/27,31/19) Hyperbolic Matrix(2377,3364,696,985) (-17/12,-58/41) -> (58/17,41/12) Hyperbolic Matrix(2379,3364,698,987) (-58/41,-41/29) -> (17/5,58/17) Hyperbolic Matrix(4813,6786,2920,4117) (-55/39,-86/61) -> (28/17,61/37) Hyperbolic Matrix(8641,12180,-6214,-8759) (-86/61,-31/22) -> (-89/64,-146/105) Hyperbolic Matrix(60609,84274,23150,32189) (-146/105,-203/146) -> (377/144,144/55) Hyperbolic Matrix(49475,68788,18898,26275) (-203/146,-57/41) -> (233/89,377/144) Hyperbolic Matrix(2087,2900,1168,1623) (-57/41,-25/18) -> (25/14,59/33) Hyperbolic Matrix(60609,84100,16928,23489) (-179/129,-290/209) -> (290/81,111/31) Hyperbolic Matrix(60611,84100,16930,23491) (-290/209,-111/80) -> (179/50,290/81) Hyperbolic Matrix(2843,3944,-2466,-3421) (-111/80,-43/31) -> (-15/13,-53/46) Hyperbolic Matrix(3597,4988,2092,2901) (-43/31,-61/44) -> (55/32,43/25) Hyperbolic Matrix(4059,5626,2510,3479) (-61/44,-18/13) -> (76/47,55/34) Hyperbolic Matrix(755,1044,546,755) (-18/13,-29/21) -> (29/21,18/13) Hyperbolic Matrix(463,638,336,463) (-29/21,-11/8) -> (11/8,29/21) Hyperbolic Matrix(465,638,-422,-579) (-11/8,-48/35) -> (-10/9,-11/10) Hyperbolic Matrix(1101,1508,-890,-1219) (-37/27,-26/19) -> (-26/21,-21/17) Hyperbolic Matrix(1739,2378,-1358,-1857) (-26/19,-41/30) -> (-41/32,-32/25) Hyperbolic Matrix(2377,3248,1400,1913) (-41/30,-56/41) -> (56/33,17/10) Hyperbolic Matrix(5451,7424,3832,5219) (-15/11,-64/47) -> (64/45,101/71) Hyperbolic Matrix(61769,84100,16400,22329) (-177/130,-290/213) -> (290/77,113/30) Hyperbolic Matrix(61771,84100,16402,22331) (-290/213,-113/83) -> (177/47,290/77) Hyperbolic Matrix(811,1102,170,231) (-34/25,-19/14) -> (19/4,24/5) Hyperbolic Matrix(985,1334,556,753) (-19/14,-23/17) -> (23/13,39/22) Hyperbolic Matrix(2493,3364,644,869) (-27/20,-58/43) -> (58/15,31/8) Hyperbolic Matrix(2495,3364,646,871) (-58/43,-31/23) -> (27/7,58/15) Hyperbolic Matrix(175,232,132,175) (-4/3,-29/22) -> (29/22,4/3) Hyperbolic Matrix(1101,1450,836,1101) (-29/22,-25/19) -> (25/19,29/22) Hyperbolic Matrix(2029,2668,308,405) (-25/19,-46/35) -> (46/7,33/5) Hyperbolic Matrix(4813,6322,3046,4001) (-46/35,-21/16) -> (79/50,128/81) Hyperbolic Matrix(4467,5858,1018,1335) (-21/16,-59/45) -> (57/13,79/18) Hyperbolic Matrix(41063,53824,9734,12759) (-97/74,-232/177) -> (232/55,135/32) Hyperbolic Matrix(41065,53824,9736,12761) (-232/177,-135/103) -> (97/23,232/55) Hyperbolic Matrix(755,986,134,175) (-17/13,-30/23) -> (28/5,17/3) Hyperbolic Matrix(10323,13456,2402,3131) (-73/56,-116/89) -> (116/27,43/10) Hyperbolic Matrix(10325,13456,2404,3133) (-116/89,-43/33) -> (73/17,116/27) Hyperbolic Matrix(4523,5858,1074,1391) (-57/44,-79/61) -> (21/5,59/14) Hyperbolic Matrix(1971,2552,268,347) (-79/61,-22/17) -> (22/3,37/5) Hyperbolic Matrix(987,1276,584,755) (-22/17,-31/24) -> (27/16,22/13) Hyperbolic Matrix(1393,1798,540,697) (-31/24,-9/7) -> (49/19,31/12) Hyperbolic Matrix(407,522,46,59) (-9/7,-41/32) -> (17/2,9/1) Hyperbolic Matrix(4351,5568,3400,4351) (-32/25,-87/68) -> (87/68,32/25) Hyperbolic Matrix(7481,9570,5848,7481) (-87/68,-55/43) -> (55/43,87/68) Hyperbolic Matrix(1043,1334,362,463) (-55/43,-23/18) -> (23/8,3/1) Hyperbolic Matrix(2089,2668,1454,1857) (-23/18,-60/47) -> (56/39,23/16) Hyperbolic Matrix(4409,5626,2728,3481) (-97/76,-37/29) -> (21/13,97/60) Hyperbolic Matrix(1683,2146,956,1219) (-37/29,-51/40) -> (7/4,37/21) Hyperbolic Matrix(10555,13456,2274,2899) (-51/40,-116/91) -> (116/25,65/14) Hyperbolic Matrix(10557,13456,2276,2901) (-116/91,-65/51) -> (51/11,116/25) Hyperbolic Matrix(4525,5742,1372,1741) (-33/26,-85/67) -> (89/27,33/10) Hyperbolic Matrix(871,1102,230,291) (-19/15,-24/19) -> (34/9,19/5) Hyperbolic Matrix(1103,1392,874,1103) (-24/19,-29/23) -> (29/23,24/19) Hyperbolic Matrix(231,290,184,231) (-29/23,-5/4) -> (5/4,29/23) Hyperbolic Matrix(233,290,94,117) (-5/4,-26/21) -> (32/13,5/2) Hyperbolic Matrix(2725,3364,516,637) (-21/17,-58/47) -> (58/11,37/7) Hyperbolic Matrix(2727,3364,518,639) (-58/47,-37/30) -> (21/4,58/11) Hyperbolic Matrix(6843,8410,2642,3247) (-59/48,-43/35) -> (101/39,57/22) Hyperbolic Matrix(521,638,236,289) (-27/22,-11/9) -> (11/5,31/14) Hyperbolic Matrix(811,986,190,231) (-28/23,-17/14) -> (17/4,30/7) Hyperbolic Matrix(1101,1334,430,521) (-17/14,-23/19) -> (23/9,41/16) Hyperbolic Matrix(1103,1334,912,1103) (-23/19,-29/24) -> (29/24,23/19) Hyperbolic Matrix(289,348,240,289) (-29/24,-6/5) -> (6/5,29/24) Hyperbolic Matrix(2727,3248,1900,2263) (-31/26,-25/21) -> (33/23,89/62) Hyperbolic Matrix(929,1102,392,465) (-19/16,-13/11) -> (45/19,19/8) Hyperbolic Matrix(1277,1508,492,581) (-13/11,-46/39) -> (70/27,13/5) Hyperbolic Matrix(2263,2668,542,639) (-46/39,-33/28) -> (25/6,46/11) Hyperbolic Matrix(349,406,300,349) (-7/6,-29/25) -> (29/25,7/6) Hyperbolic Matrix(1101,1276,950,1101) (-29/25,-22/19) -> (22/19,29/25) Hyperbolic Matrix(2205,2552,502,581) (-22/19,-37/32) -> (79/18,22/5) Hyperbolic Matrix(3713,4292,2610,3017) (-37/32,-15/13) -> (101/71,37/26) Hyperbolic Matrix(1277,1450,716,813) (-8/7,-17/15) -> (41/23,66/37) Hyperbolic Matrix(463,522,102,115) (-17/15,-9/8) -> (9/2,41/9) Hyperbolic Matrix(985,1102,362,405) (-9/8,-10/9) -> (68/25,49/18) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(523,-580,156,-173) (1/1,10/9) -> (10/3,57/17) Hyperbolic Matrix(405,-464,254,-291) (8/7,15/13) -> (43/27,8/5) Hyperbolic Matrix(347,-406,100,-117) (7/6,20/17) -> (38/11,7/2) Hyperbolic Matrix(1625,-1914,984,-1159) (20/17,33/28) -> (33/20,38/23) Hyperbolic Matrix(927,-1102,196,-233) (19/16,6/5) -> (52/11,19/4) Hyperbolic Matrix(523,-638,332,-405) (17/14,11/9) -> (11/7,41/26) Hyperbolic Matrix(2031,-2494,1180,-1449) (27/22,16/13) -> (74/43,31/18) Hyperbolic Matrix(753,-928,142,-175) (16/13,21/17) -> (37/7,16/3) Hyperbolic Matrix(1219,-1508,890,-1101) (21/17,5/4) -> (63/46,37/27) Hyperbolic Matrix(639,-812,410,-521) (19/15,14/11) -> (14/9,39/25) Hyperbolic Matrix(1275,-1624,274,-349) (14/11,51/40) -> (65/14,14/3) Hyperbolic Matrix(6089,-7772,2500,-3191) (37/29,60/47) -> (56/23,95/39) Hyperbolic Matrix(1857,-2378,1358,-1739) (32/25,9/7) -> (67/49,26/19) Hyperbolic Matrix(581,-754,178,-231) (22/17,13/10) -> (13/4,36/11) Hyperbolic Matrix(579,-754,268,-349) (13/10,30/23) -> (28/13,13/6) Hyperbolic Matrix(753,-986,488,-639) (17/13,21/16) -> (37/24,17/11) Hyperbolic Matrix(1159,-1566,430,-581) (4/3,23/17) -> (35/13,62/23) Hyperbolic Matrix(1449,-1972,640,-871) (34/25,15/11) -> (43/19,34/15) Hyperbolic Matrix(637,-870,298,-407) (15/11,41/30) -> (17/8,15/7) Hyperbolic Matrix(1565,-2146,466,-639) (37/27,11/8) -> (47/14,37/11) Hyperbolic Matrix(1797,-2494,544,-755) (43/31,25/18) -> (33/10,43/13) Hyperbolic Matrix(291,-406,124,-173) (25/18,7/5) -> (7/3,33/14) Hyperbolic Matrix(289,-406,42,-59) (7/5,31/22) -> (27/4,7/1) Hyperbolic Matrix(2261,-3190,864,-1219) (31/22,24/17) -> (34/13,89/34) Hyperbolic Matrix(985,-1392,288,-407) (24/17,17/12) -> (41/12,24/7) Hyperbolic Matrix(695,-986,246,-349) (17/12,27/19) -> (31/11,17/6) Hyperbolic Matrix(1509,-2146,244,-347) (27/19,64/45) -> (6/1,31/5) Hyperbolic Matrix(1507,-2146,408,-581) (37/26,10/7) -> (48/13,37/10) Hyperbolic Matrix(1739,-2494,486,-697) (10/7,33/23) -> (25/7,68/19) Hyperbolic Matrix(523,-754,120,-173) (23/16,13/9) -> (13/3,35/8) Hyperbolic Matrix(871,-1276,514,-753) (19/13,3/2) -> (61/36,39/23) Hyperbolic Matrix(869,-1334,114,-175) (23/15,20/13) -> (38/5,23/3) Hyperbolic Matrix(5799,-8932,2260,-3481) (20/13,57/37) -> (59/23,136/53) Hyperbolic Matrix(637,-986,188,-291) (17/11,14/9) -> (44/13,17/5) Hyperbolic Matrix(929,-1450,148,-231) (39/25,25/16) -> (25/4,19/3) Hyperbolic Matrix(2263,-3538,1372,-2145) (25/16,61/39) -> (61/37,33/20) Hyperbolic Matrix(1333,-2088,482,-755) (36/23,11/7) -> (47/17,36/13) Hyperbolic Matrix(985,-1566,256,-407) (27/17,35/22) -> (23/6,27/7) Hyperbolic Matrix(1567,-2494,546,-869) (35/22,43/27) -> (43/15,23/8) Hyperbolic Matrix(1971,-3190,574,-929) (55/34,34/21) -> (24/7,55/16) Hyperbolic Matrix(465,-754,214,-347) (34/21,13/8) -> (13/6,24/11) Hyperbolic Matrix(6091,-9918,1816,-2957) (70/43,57/35) -> (57/17,104/31) Hyperbolic Matrix(1277,-2088,496,-811) (49/30,18/11) -> (18/7,67/26) Hyperbolic Matrix(6265,-10266,1486,-2435) (77/47,59/36) -> (59/14,97/23) Hyperbolic Matrix(1333,-2204,176,-291) (38/23,5/3) -> (53/7,38/5) Hyperbolic Matrix(2031,-3422,860,-1449) (32/19,27/16) -> (85/36,26/11) Hyperbolic Matrix(4581,-7772,992,-1683) (39/23,56/33) -> (60/13,97/21) Hyperbolic Matrix(5975,-10266,1586,-2725) (67/39,55/32) -> (113/30,49/13) Hyperbolic Matrix(3539,-6090,1988,-3421) (43/25,74/43) -> (16/9,73/41) Hyperbolic Matrix(1741,-3016,736,-1275) (45/26,26/15) -> (26/11,71/30) Hyperbolic Matrix(233,-406,66,-115) (26/15,7/4) -> (7/2,32/9) Hyperbolic Matrix(4291,-7656,1886,-3365) (66/37,25/14) -> (91/40,66/29) Hyperbolic Matrix(4119,-7366,940,-1681) (59/33,34/19) -> (92/21,57/13) Hyperbolic Matrix(1101,-1972,292,-523) (34/19,9/5) -> (49/13,34/9) Hyperbolic Matrix(987,-1798,286,-521) (20/11,31/17) -> (31/9,38/11) Hyperbolic Matrix(407,-754,156,-289) (11/6,13/7) -> (13/5,47/18) Hyperbolic Matrix(405,-754,94,-175) (13/7,15/8) -> (43/10,13/3) Hyperbolic Matrix(463,-870,124,-233) (15/8,2/1) -> (56/15,15/4) Hyperbolic Matrix(1159,-2494,270,-581) (15/7,28/13) -> (30/7,73/17) Hyperbolic Matrix(1857,-4060,424,-927) (24/11,35/16) -> (35/8,92/21) Hyperbolic Matrix(6437,-14094,2464,-5395) (35/16,46/21) -> (128/49,209/80) Hyperbolic Matrix(291,-638,26,-57) (46/21,11/5) -> (11/1,12/1) Hyperbolic Matrix(523,-1160,78,-173) (31/14,20/9) -> (20/3,27/4) Hyperbolic Matrix(2029,-4582,848,-1915) (9/4,52/23) -> (122/51,67/28) Hyperbolic Matrix(3017,-6844,920,-2087) (34/15,59/26) -> (59/18,82/25) Hyperbolic Matrix(813,-1856,152,-347) (57/25,16/7) -> (16/3,59/11) Hyperbolic Matrix(10613,-25056,4054,-9571) (59/25,85/36) -> (89/34,233/89) Hyperbolic Matrix(1045,-2494,194,-463) (31/13,43/18) -> (43/8,27/5) Hyperbolic Matrix(10499,-25114,2788,-6669) (55/23,122/51) -> (64/17,177/47) Hyperbolic Matrix(523,-1276,166,-405) (39/16,22/9) -> (22/7,19/6) Hyperbolic Matrix(1509,-3712,424,-1043) (27/11,32/13) -> (32/9,89/25) Hyperbolic Matrix(755,-1914,114,-289) (5/2,33/13) -> (33/5,53/8) Hyperbolic Matrix(1393,-3538,502,-1275) (33/13,28/11) -> (86/31,25/9) Hyperbolic Matrix(8295,-21286,1966,-5045) (136/53,77/30) -> (135/32,38/9) Hyperbolic Matrix(291,-754,22,-57) (57/22,70/27) -> (12/1,1/0) Hyperbolic Matrix(4175,-10904,1244,-3249) (47/18,128/49) -> (104/31,47/14) Hyperbolic Matrix(2841,-7424,866,-2263) (81/31,34/13) -> (82/25,23/7) Hyperbolic Matrix(173,-464,22,-59) (8/3,35/13) -> (23/3,8/1) Hyperbolic Matrix(753,-2030,194,-523) (62/23,27/10) -> (31/8,4/1) Hyperbolic Matrix(233,-638,42,-115) (30/11,11/4) -> (11/2,28/5) Hyperbolic Matrix(291,-812,62,-173) (25/9,14/5) -> (14/3,33/7) Hyperbolic Matrix(347,-986,82,-233) (17/6,20/7) -> (38/9,17/4) Hyperbolic Matrix(811,-2320,122,-349) (20/7,43/15) -> (73/11,20/3) Hyperbolic Matrix(1857,-6148,280,-927) (43/13,53/16) -> (53/8,73/11) Hyperbolic Matrix(1625,-5394,454,-1507) (53/16,10/3) -> (68/19,179/50) Hyperbolic Matrix(2031,-6844,430,-1449) (64/19,27/8) -> (85/18,52/11) Hyperbolic Matrix(3539,-12180,994,-3421) (86/25,31/9) -> (89/25,146/41) Hyperbolic Matrix(1101,-3944,146,-523) (111/31,43/12) -> (15/2,53/7) Hyperbolic Matrix(173,-638,16,-59) (11/3,48/13) -> (10/1,11/1) Hyperbolic Matrix(407,-1508,78,-289) (37/10,26/7) -> (26/5,21/4) Hyperbolic Matrix(639,-2378,140,-521) (26/7,41/11) -> (41/9,32/7) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(57,580,-40,-407) -> Matrix(11,4,-212,-77) Matrix(117,1102,74,697) -> Matrix(31,10,530,171) Matrix(175,1508,128,1103) -> Matrix(13,4,276,85) Matrix(173,1450,76,637) -> Matrix(89,26,1044,305) Matrix(59,464,-22,-173) -> Matrix(1,0,-6,1) Matrix(579,4292,172,1275) -> Matrix(15,4,116,31) Matrix(465,3422,142,1045) -> Matrix(39,10,308,79) Matrix(175,1276,24,175) -> Matrix(79,20,312,79) Matrix(57,406,8,57) -> Matrix(25,6,104,25) Matrix(59,406,-42,-289) -> Matrix(9,2,-176,-39) Matrix(289,1914,-114,-755) -> Matrix(77,18,-800,-187) Matrix(405,2668,308,2029) -> Matrix(17,4,344,81) Matrix(231,1508,142,927) -> Matrix(17,4,276,65) Matrix(173,1102,100,637) -> Matrix(65,14,1026,221) Matrix(175,1102,-138,-869) -> Matrix(9,2,-194,-43) Matrix(59,348,10,59) -> Matrix(19,4,90,19) Matrix(231,1334,40,231) -> Matrix(71,14,360,71) Matrix(233,1334,142,813) -> Matrix(11,2,192,35) Matrix(115,638,-42,-233) -> Matrix(13,2,-124,-19) Matrix(117,638,64,349) -> Matrix(29,6,430,89) Matrix(463,2494,-194,-1045) -> Matrix(9,2,-104,-23) Matrix(175,928,-142,-753) -> Matrix(43,8,-930,-173) Matrix(289,1508,-78,-407) -> Matrix(23,4,-144,-25) Matrix(59,290,12,59) -> Matrix(11,2,60,11) Matrix(289,1392,60,289) -> Matrix(49,8,300,49) Matrix(231,1102,170,811) -> Matrix(13,2,266,41) Matrix(173,812,-62,-291) -> Matrix(27,4,-250,-37) Matrix(349,1624,-274,-1275) -> Matrix(1,0,-12,1) Matrix(463,2146,200,927) -> Matrix(1,-2,12,-23) Matrix(1683,7772,-992,-4581) -> Matrix(93,20,-1502,-323) Matrix(579,2668,176,811) -> Matrix(21,4,152,29) Matrix(291,1334,190,871) -> Matrix(35,6,624,107) Matrix(2089,9570,456,2089) -> Matrix(83,14,492,83) Matrix(1217,5568,266,1217) -> Matrix(49,8,300,49) Matrix(521,2378,-140,-639) -> Matrix(13,2,-72,-11) Matrix(405,1798,248,1101) -> Matrix(41,6,690,101) Matrix(289,1276,118,521) -> Matrix(27,4,290,43) Matrix(173,754,-120,-523) -> Matrix(13,2,-254,-39) Matrix(175,754,-94,-405) -> Matrix(19,2,-276,-29) Matrix(407,1740,258,1103) -> Matrix(21,4,362,69) Matrix(233,986,-82,-347) -> Matrix(13,2,-124,-19) Matrix(1509,6322,554,2321) -> Matrix(35,6,344,59) Matrix(639,2668,542,2263) -> Matrix(27,4,614,91) Matrix(349,1450,84,349) -> Matrix(13,2,84,13) Matrix(57,232,14,57) -> Matrix(1,0,14,1) Matrix(407,1566,-256,-985) -> Matrix(13,2,-228,-35) Matrix(349,1334,152,581) -> Matrix(11,2,126,23) Matrix(291,1102,230,871) -> Matrix(13,2,266,41) Matrix(523,1972,-292,-1101) -> Matrix(27,4,-412,-61) Matrix(233,870,-124,-463) -> Matrix(7,2,-102,-29) Matrix(405,1508,358,1333) -> Matrix(23,4,546,95) Matrix(579,2146,344,1275) -> Matrix(37,6,598,97) Matrix(581,2146,-408,-1507) -> Matrix(13,2,-254,-39) Matrix(175,638,48,175) -> Matrix(13,2,84,13) Matrix(289,1044,80,289) -> Matrix(29,4,210,29) Matrix(1567,5626,598,2147) -> Matrix(49,6,498,61) Matrix(1391,4988,582,2087) -> Matrix(29,4,326,45) Matrix(697,2494,-486,-1739) -> Matrix(15,2,-308,-41) Matrix(115,406,-66,-233) -> Matrix(17,2,-264,-31) Matrix(117,406,-100,-347) -> Matrix(15,2,-338,-45) Matrix(929,3190,-574,-1971) -> Matrix(71,10,-1200,-169) Matrix(407,1392,-288,-985) -> Matrix(59,8,-1158,-157) Matrix(291,986,-188,-637) -> Matrix(15,2,-278,-37) Matrix(637,2146,-534,-1799) -> Matrix(17,2,-366,-43) Matrix(2205,7424,586,1973) -> Matrix(1,0,16,1) Matrix(1275,4292,172,579) -> Matrix(31,4,116,15) Matrix(639,2146,-466,-1565) -> Matrix(15,2,-308,-41) Matrix(755,2494,-544,-1797) -> Matrix(13,2,-254,-39) Matrix(985,3248,158,521) -> Matrix(55,8,268,39) Matrix(7831,25810,2376,7831) -> Matrix(209,30,1456,209) Matrix(4929,16240,1496,4929) -> Matrix(169,24,1190,169) Matrix(811,2668,176,579) -> Matrix(29,4,152,21) Matrix(231,754,-178,-581) -> Matrix(15,2,-308,-41) Matrix(233,754,72,233) -> Matrix(47,6,368,47) Matrix(289,928,90,289) -> Matrix(65,8,528,65) Matrix(291,928,164,523) -> Matrix(67,8,1030,123) Matrix(405,1276,-166,-523) -> Matrix(37,4,-398,-43) Matrix(463,1334,362,1043) -> Matrix(55,6,1164,127) Matrix(465,1334,-404,-1159) -> Matrix(19,2,-428,-45) Matrix(3133,8932,-1912,-5451) -> Matrix(115,12,-1888,-197) Matrix(2667,7598,814,2319) -> Matrix(59,6,462,47) Matrix(349,986,-246,-695) -> Matrix(17,2,-332,-39) Matrix(521,1450,-438,-1219) -> Matrix(93,10,-2074,-223) Matrix(1275,3538,-502,-1393) -> Matrix(319,34,-3312,-353) Matrix(1277,3538,754,2089) -> Matrix(283,30,4594,487) Matrix(755,2088,-482,-1333) -> Matrix(303,32,-5312,-561) Matrix(637,1740,488,1333) -> Matrix(39,4,848,87) Matrix(1277,3480,724,1973) -> Matrix(393,40,6062,617) Matrix(2321,6322,554,1509) -> Matrix(59,6,344,35) Matrix(3365,9164,1406,3829) -> Matrix(355,36,3974,403) Matrix(405,1102,362,985) -> Matrix(99,10,2366,239) Matrix(4351,11832,1600,4351) -> Matrix(319,32,3180,319) Matrix(1217,3306,448,1217) -> Matrix(21,2,220,21) Matrix(407,1102,236,639) -> Matrix(59,6,934,95) Matrix(581,1566,-430,-1159) -> Matrix(19,2,-390,-41) Matrix(927,2494,-604,-1625) -> Matrix(21,2,-368,-35) Matrix(175,464,66,175) -> Matrix(79,8,780,79) Matrix(463,1218,176,463) -> Matrix(221,22,2220,221) Matrix(2145,5626,464,1217) -> Matrix(101,10,414,41) Matrix(2899,7598,1770,4639) -> Matrix(223,22,3720,367) Matrix(2147,5626,598,1567) -> Matrix(61,6,498,49) Matrix(1219,3190,-864,-2261) -> Matrix(101,10,-2010,-199) Matrix(289,754,-156,-407) -> Matrix(143,14,-2094,-205) Matrix(581,1508,492,1277) -> Matrix(43,4,978,91) Matrix(3827,9918,-2686,-6961) -> Matrix(17,2,-332,-39) Matrix(3829,9918,2150,5569) -> Matrix(217,22,3324,337) Matrix(11311,29290,4368,11311) -> Matrix(259,26,2580,259) Matrix(4929,12760,1904,4929) -> Matrix(161,16,1620,161) Matrix(987,2552,292,755) -> Matrix(1,0,18,1) Matrix(697,1798,540,1393) -> Matrix(61,6,1230,121) Matrix(811,2088,-496,-1277) -> Matrix(83,8,-1380,-133) Matrix(2959,7598,1830,4699) -> Matrix(227,22,3828,371) Matrix(4001,10266,-3052,-7831) -> Matrix(21,2,-494,-47) Matrix(1855,4756,814,2087) -> Matrix(47,4,552,47) Matrix(521,1334,430,1101) -> Matrix(19,2,408,43) Matrix(523,1334,296,755) -> Matrix(143,14,2196,215) Matrix(2669,6786,776,1973) -> Matrix(269,26,1914,185) Matrix(871,2204,-756,-1913) -> Matrix(125,12,-2948,-283) Matrix(871,2146,636,1567) -> Matrix(65,6,1354,125) Matrix(1391,3422,-802,-1973) -> Matrix(239,22,-3748,-345) Matrix(521,1276,118,289) -> Matrix(43,4,290,27) Matrix(1449,3538,926,2261) -> Matrix(323,30,5674,527) Matrix(3191,7772,-2500,-6089) -> Matrix(217,20,-4850,-447) Matrix(1335,3248,358,871) -> Matrix(87,8,424,39) Matrix(407,986,168,407) -> Matrix(241,22,2640,241) Matrix(289,696,120,289) -> Matrix(177,16,1958,177) Matrix(3829,9164,1406,3365) -> Matrix(403,36,3974,355) Matrix(4291,10266,-3152,-7541) -> Matrix(157,14,-3084,-275) Matrix(2087,4988,582,1391) -> Matrix(45,4,326,29) Matrix(2551,6090,-1118,-2669) -> Matrix(157,14,-1828,-163) Matrix(463,1102,292,695) -> Matrix(67,6,1150,103) Matrix(465,1102,392,929) -> Matrix(157,14,3510,313) Matrix(1275,3016,-736,-1741) -> Matrix(451,40,-7092,-629) Matrix(173,406,-124,-291) -> Matrix(23,2,-426,-37) Matrix(927,2146,200,463) -> Matrix(23,2,-12,-1) Matrix(1507,3480,954,2203) -> Matrix(463,40,7952,687) Matrix(579,1334,352,811) -> Matrix(163,14,2736,235) Matrix(581,1334,152,349) -> Matrix(23,2,126,11) Matrix(405,928,278,637) -> Matrix(93,8,1732,149) Matrix(4349,9918,2670,6089) -> Matrix(257,22,4404,377) Matrix(2087,4756,814,1855) -> Matrix(47,4,552,47) Matrix(637,1450,76,173) -> Matrix(305,26,1044,89) Matrix(3365,7656,-1886,-4291) -> Matrix(1597,136,-24366,-2075) Matrix(1277,2900,358,813) -> Matrix(47,4,270,23) Matrix(3247,7366,-2506,-5685) -> Matrix(71,6,-1290,-109) Matrix(871,1972,-640,-1449) -> Matrix(47,4,-952,-81) Matrix(233,522,104,233) -> Matrix(167,14,1992,167) Matrix(521,1160,234,521) -> Matrix(385,32,4632,385) Matrix(811,1798,-576,-1277) -> Matrix(121,10,-2408,-199) Matrix(289,638,236,521) -> Matrix(73,6,1618,133) Matrix(347,754,-214,-465) -> Matrix(173,14,-2904,-235) Matrix(349,754,-268,-579) -> Matrix(25,2,-438,-35) Matrix(407,870,-298,-637) -> Matrix(25,2,-588,-47) Matrix(521,986,214,405) -> Matrix(315,22,3422,239) Matrix(1335,2494,-1024,-1913) -> Matrix(29,2,-856,-59) Matrix(2203,4060,-1700,-3133) -> Matrix(59,4,-1018,-69) Matrix(7657,14094,-4726,-8699) -> Matrix(2863,194,-48184,-3265) Matrix(347,638,-316,-581) -> Matrix(207,14,-5042,-341) Matrix(349,638,64,117) -> Matrix(89,6,430,29) Matrix(637,1160,-542,-987) -> Matrix(119,8,-2752,-185) Matrix(639,1160,352,639) -> Matrix(479,32,7170,479) Matrix(289,522,160,289) -> Matrix(211,14,3180,211) Matrix(2553,4582,-1486,-2667) -> Matrix(515,34,-8134,-537) Matrix(4465,8004,1326,2377) -> Matrix(61,4,564,37) Matrix(3827,6844,-2660,-4757) -> Matrix(425,28,-8242,-543) Matrix(1915,3422,812,1451) -> Matrix(335,22,3822,251) Matrix(7539,13456,3314,5915) -> Matrix(3659,240,42978,2819) Matrix(7541,13456,3316,5917) -> Matrix(3661,240,43032,2821) Matrix(813,1450,716,1277) -> Matrix(397,26,9360,613) Matrix(2669,4756,1628,2901) -> Matrix(61,4,930,61) Matrix(1043,1856,-848,-1509) -> Matrix(123,8,-2660,-173) Matrix(523,928,164,291) -> Matrix(123,8,1030,67) Matrix(753,1334,556,985) -> Matrix(31,2,666,43) Matrix(755,1334,296,523) -> Matrix(215,14,2196,143) Matrix(1973,3480,724,1277) -> Matrix(617,40,6062,393) Matrix(1219,2146,956,1683) -> Matrix(31,2,852,55) Matrix(1971,3422,868,1507) -> Matrix(343,22,4038,259) Matrix(14443,25056,-8926,-15485) -> Matrix(627,40,-10612,-677) Matrix(7771,13456,3282,5683) -> Matrix(2771,176,31158,1979) Matrix(7773,13456,3284,5685) -> Matrix(2773,176,31212,1981) Matrix(637,1102,100,173) -> Matrix(221,14,1026,65) Matrix(639,1102,236,407) -> Matrix(95,6,934,59) Matrix(1449,2494,-1180,-2031) -> Matrix(31,2,-698,-45) Matrix(2901,4988,2092,3597) -> Matrix(63,4,1244,79) Matrix(14615,25114,-10734,-18445) -> Matrix(473,30,-9192,-583) Matrix(5335,9164,3376,5799) -> Matrix(569,36,9752,617) Matrix(407,696,238,407) -> Matrix(255,16,4064,255) Matrix(579,986,340,579) -> Matrix(353,22,5664,353) Matrix(581,986,274,465) -> Matrix(355,22,4502,279) Matrix(5915,10034,2256,3827) -> Matrix(1777,110,17980,1113) Matrix(753,1276,-514,-871) -> Matrix(65,4,-1154,-71) Matrix(755,1276,584,987) -> Matrix(65,4,1316,81) Matrix(2203,3712,-1584,-2669) -> Matrix(129,8,-2564,-159) Matrix(173,290,34,57) -> Matrix(33,2,214,13) Matrix(1159,1914,-984,-1625) -> Matrix(299,18,-6794,-409) Matrix(2145,3538,-1372,-2263) -> Matrix(565,34,-9954,-599) Matrix(811,1334,352,579) -> Matrix(235,14,2736,163) Matrix(813,1334,142,233) -> Matrix(35,2,192,11) Matrix(2901,4756,1628,2669) -> Matrix(61,4,930,61) Matrix(12991,21286,-9912,-16241) -> Matrix(33,2,-446,-27) Matrix(4639,7598,1770,2899) -> Matrix(367,22,3720,223) Matrix(8235,13456,3194,5219) -> Matrix(803,48,8214,491) Matrix(8237,13456,3196,5221) -> Matrix(805,48,8268,493) Matrix(1101,1798,248,405) -> Matrix(101,6,690,41) Matrix(1103,1798,392,639) -> Matrix(33,2,280,17) Matrix(7831,12760,4806,7831) -> Matrix(271,16,4590,271) Matrix(17979,29290,11036,17979) -> Matrix(443,26,7548,443) Matrix(5163,8410,962,1567) -> Matrix(171,10,872,51) Matrix(463,754,-428,-697) -> Matrix(35,2,-858,-49) Matrix(927,1508,142,231) -> Matrix(65,4,276,17) Matrix(6729,10904,-4724,-7655) -> Matrix(269,16,-5296,-315) Matrix(51909,84100,19868,32189) -> Matrix(11513,684,117032,6953) Matrix(51911,84100,19870,32191) -> Matrix(11515,684,117086,6955) Matrix(4583,7424,-3186,-5161) -> Matrix(539,32,-10460,-621) Matrix(42513,68788,11936,19313) -> Matrix(475,28,3308,195) Matrix(52085,84274,14626,23665) -> Matrix(375,22,2642,155) Matrix(8353,13514,3012,4873) -> Matrix(301,18,2826,169) Matrix(3479,5626,2510,4059) -> Matrix(101,6,1902,113) Matrix(4699,7598,1830,2959) -> Matrix(371,22,3828,227) Matrix(6207,10034,2548,4119) -> Matrix(1857,110,20140,1193) Matrix(755,1218,468,755) -> Matrix(373,22,6324,373) Matrix(289,464,180,289) -> Matrix(137,8,2346,137) Matrix(291,464,-254,-405) -> Matrix(1,0,-6,1) Matrix(1277,2030,-948,-1507) -> Matrix(35,2,-718,-41) Matrix(695,1102,292,463) -> Matrix(103,6,1150,67) Matrix(2089,3306,1320,2089) -> Matrix(33,2,544,33) Matrix(7481,11832,4730,7481) -> Matrix(545,32,9282,545) Matrix(697,1102,74,117) -> Matrix(171,10,530,31) Matrix(5799,9164,3376,5335) -> Matrix(617,36,9752,569) Matrix(4001,6322,3046,4813) -> Matrix(103,6,2180,127) Matrix(2203,3480,954,1507) -> Matrix(687,40,7952,463) Matrix(405,638,-332,-523) -> Matrix(35,2,-718,-41) Matrix(2145,3364,776,1217) -> Matrix(909,52,8618,493) Matrix(2147,3364,778,1219) -> Matrix(911,52,8672,495) Matrix(927,1450,296,463) -> Matrix(35,2,192,11) Matrix(8641,13514,3300,5161) -> Matrix(317,18,3258,185) Matrix(521,812,-410,-639) -> Matrix(71,4,-1438,-81) Matrix(1159,1798,448,695) -> Matrix(37,2,388,21) Matrix(639,986,-488,-753) -> Matrix(35,2,-718,-41) Matrix(1509,2320,-1282,-1971) -> Matrix(283,16,-6456,-365) Matrix(871,1334,190,291) -> Matrix(107,6,624,35) Matrix(987,1450,356,523) -> Matrix(43,2,408,19) Matrix(637,928,278,405) -> Matrix(149,8,1732,93) Matrix(639,928,440,639) -> Matrix(151,8,2850,151) Matrix(521,754,360,521) -> Matrix(115,6,2204,115) Matrix(2377,3422,2054,2957) -> Matrix(191,10,4412,231) Matrix(5279,7598,3426,4931) -> Matrix(115,6,1974,103) Matrix(1857,2668,1454,2089) -> Matrix(79,4,1718,87) Matrix(11311,16240,7878,11311) -> Matrix(479,24,9560,479) Matrix(17979,25810,12524,17979) -> Matrix(601,30,12040,601) Matrix(4001,5742,848,1217) -> Matrix(121,6,746,37) Matrix(4291,6148,-3644,-5221) -> Matrix(93,4,-2116,-91) Matrix(3769,5394,-2716,-3887) -> Matrix(33,2,-644,-39) Matrix(3017,4292,2610,3713) -> Matrix(77,4,1790,93) Matrix(5627,8004,2488,3539) -> Matrix(71,4,834,47) Matrix(4813,6844,-3794,-5395) -> Matrix(75,4,-1594,-85) Matrix(1797,2552,1102,1565) -> Matrix(1,0,36,1) Matrix(2377,3364,696,985) -> Matrix(389,20,2898,149) Matrix(2379,3364,698,987) -> Matrix(391,20,2952,151) Matrix(4813,6786,2920,4117) -> Matrix(517,26,8610,433) Matrix(8641,12180,-6214,-8759) -> Matrix(81,4,-1600,-79) Matrix(60609,84274,23150,32189) -> Matrix(439,22,4370,219) Matrix(49475,68788,18898,26275) -> Matrix(561,28,5630,281) Matrix(2087,2900,1168,1623) -> Matrix(85,4,1296,61) Matrix(60609,84100,16928,23489) -> Matrix(1325,68,9918,509) Matrix(60611,84100,16930,23491) -> Matrix(1327,68,9972,511) Matrix(2843,3944,-2466,-3421) -> Matrix(157,8,-3670,-187) Matrix(3597,4988,2092,2901) -> Matrix(79,4,1244,63) Matrix(4059,5626,2510,3479) -> Matrix(113,6,1902,101) Matrix(755,1044,546,755) -> Matrix(79,4,1560,79) Matrix(463,638,336,463) -> Matrix(41,2,840,41) Matrix(465,638,-422,-579) -> Matrix(39,2,-956,-49) Matrix(1101,1508,-890,-1219) -> Matrix(83,4,-1764,-85) Matrix(1739,2378,-1358,-1857) -> Matrix(43,2,-882,-41) Matrix(2377,3248,1400,1913) -> Matrix(177,8,2854,129) Matrix(5451,7424,3832,5219) -> Matrix(1,0,38,1) Matrix(61769,84100,16400,22329) -> Matrix(701,36,5238,269) Matrix(61771,84100,16402,22331) -> Matrix(703,36,5292,271) Matrix(811,1102,170,231) -> Matrix(41,2,266,13) Matrix(985,1334,556,753) -> Matrix(43,2,666,31) Matrix(2493,3364,644,869) -> Matrix(81,4,506,25) Matrix(2495,3364,646,871) -> Matrix(83,4,560,27) Matrix(175,232,132,175) -> Matrix(1,0,40,1) Matrix(1101,1450,836,1101) -> Matrix(41,2,840,41) Matrix(2029,2668,308,405) -> Matrix(81,4,344,17) Matrix(4813,6322,3046,4001) -> Matrix(127,6,2180,103) Matrix(4467,5858,1018,1335) -> Matrix(43,2,322,15) Matrix(41063,53824,9734,12759) -> Matrix(1,0,50,1) Matrix(41065,53824,9736,12761) -> Matrix(1,0,4,1) Matrix(755,986,134,175) -> Matrix(43,2,236,11) Matrix(10323,13456,2402,3131) -> Matrix(1,0,52,1) Matrix(10325,13456,2404,3133) -> Matrix(1,0,2,1) Matrix(4523,5858,1074,1391) -> Matrix(39,2,214,11) Matrix(1971,2552,268,347) -> Matrix(159,8,616,31) Matrix(987,1276,584,755) -> Matrix(81,4,1316,65) Matrix(1393,1798,540,697) -> Matrix(121,6,1230,61) Matrix(407,522,46,59) -> Matrix(43,2,150,7) Matrix(4351,5568,3400,4351) -> Matrix(167,8,3486,167) Matrix(7481,9570,5848,7481) -> Matrix(295,14,6216,295) Matrix(1043,1334,362,463) -> Matrix(127,6,1164,55) Matrix(2089,2668,1454,1857) -> Matrix(87,4,1718,79) Matrix(4409,5626,2728,3481) -> Matrix(229,10,3870,169) Matrix(1683,2146,956,1219) -> Matrix(55,2,852,31) Matrix(10555,13456,2274,2899) -> Matrix(1,0,48,1) Matrix(10557,13456,2276,2901) -> Matrix(1,0,6,1) Matrix(4525,5742,1372,1741) -> Matrix(125,6,854,41) Matrix(871,1102,230,291) -> Matrix(41,2,266,13) Matrix(1103,1392,874,1103) -> Matrix(167,8,3486,167) Matrix(231,290,184,231) -> Matrix(43,2,924,43) Matrix(233,290,94,117) -> Matrix(41,2,430,21) Matrix(2725,3364,516,637) -> Matrix(601,28,3284,153) Matrix(2727,3364,518,639) -> Matrix(603,28,3338,155) Matrix(6843,8410,2642,3247) -> Matrix(219,10,2168,99) Matrix(521,638,236,289) -> Matrix(133,6,1618,73) Matrix(811,986,190,231) -> Matrix(43,2,236,11) Matrix(1101,1334,430,521) -> Matrix(43,2,408,19) Matrix(1103,1334,912,1103) -> Matrix(307,14,6732,307) Matrix(289,348,240,289) -> Matrix(89,4,1980,89) Matrix(2727,3248,1900,2263) -> Matrix(177,8,3562,161) Matrix(929,1102,392,465) -> Matrix(313,14,3510,157) Matrix(1277,1508,492,581) -> Matrix(91,4,978,43) Matrix(2263,2668,542,639) -> Matrix(91,4,614,27) Matrix(349,406,300,349) -> Matrix(137,6,3128,137) Matrix(1101,1276,950,1101) -> Matrix(461,20,10626,461) Matrix(2205,2552,502,581) -> Matrix(185,8,1318,57) Matrix(3713,4292,2610,3017) -> Matrix(93,4,1790,77) Matrix(1277,1450,716,813) -> Matrix(613,26,9360,397) Matrix(463,522,102,115) -> Matrix(47,2,258,11) Matrix(985,1102,362,405) -> Matrix(239,10,2366,99) Matrix(1,0,2,1) -> Matrix(1,0,54,1) Matrix(523,-580,156,-173) -> Matrix(97,-4,752,-31) Matrix(405,-464,254,-291) -> Matrix(1,0,-6,1) Matrix(347,-406,100,-117) -> Matrix(45,-2,338,-15) Matrix(1625,-1914,984,-1159) -> Matrix(409,-18,6794,-299) Matrix(927,-1102,196,-233) -> Matrix(45,-2,248,-11) Matrix(523,-638,332,-405) -> Matrix(41,-2,718,-35) Matrix(2031,-2494,1180,-1449) -> Matrix(45,-2,698,-31) Matrix(753,-928,142,-175) -> Matrix(173,-8,930,-43) Matrix(1219,-1508,890,-1101) -> Matrix(85,-4,1764,-83) Matrix(639,-812,410,-521) -> Matrix(81,-4,1438,-71) Matrix(1275,-1624,274,-349) -> Matrix(1,0,-12,1) Matrix(6089,-7772,2500,-3191) -> Matrix(447,-20,4850,-217) Matrix(1857,-2378,1358,-1739) -> Matrix(41,-2,882,-43) Matrix(581,-754,178,-231) -> Matrix(41,-2,308,-15) Matrix(579,-754,268,-349) -> Matrix(35,-2,438,-25) Matrix(753,-986,488,-639) -> Matrix(41,-2,718,-35) Matrix(1159,-1566,430,-581) -> Matrix(41,-2,390,-19) Matrix(1449,-1972,640,-871) -> Matrix(81,-4,952,-47) Matrix(637,-870,298,-407) -> Matrix(47,-2,588,-25) Matrix(1565,-2146,466,-639) -> Matrix(41,-2,308,-15) Matrix(1797,-2494,544,-755) -> Matrix(39,-2,254,-13) Matrix(291,-406,124,-173) -> Matrix(37,-2,426,-23) Matrix(289,-406,42,-59) -> Matrix(39,-2,176,-9) Matrix(2261,-3190,864,-1219) -> Matrix(199,-10,2010,-101) Matrix(985,-1392,288,-407) -> Matrix(157,-8,1158,-59) Matrix(695,-986,246,-349) -> Matrix(39,-2,332,-17) Matrix(1509,-2146,244,-347) -> Matrix(37,-2,204,-11) Matrix(1507,-2146,408,-581) -> Matrix(39,-2,254,-13) Matrix(1739,-2494,486,-697) -> Matrix(41,-2,308,-15) Matrix(523,-754,120,-173) -> Matrix(39,-2,254,-13) Matrix(871,-1276,514,-753) -> Matrix(71,-4,1154,-65) Matrix(869,-1334,114,-175) -> Matrix(35,-2,158,-9) Matrix(5799,-8932,2260,-3481) -> Matrix(209,-12,2212,-127) Matrix(637,-986,188,-291) -> Matrix(37,-2,278,-15) Matrix(929,-1450,148,-231) -> Matrix(177,-10,832,-47) Matrix(2263,-3538,1372,-2145) -> Matrix(599,-34,9954,-565) Matrix(1333,-2088,482,-755) -> Matrix(561,-32,5312,-303) Matrix(985,-1566,256,-407) -> Matrix(35,-2,228,-13) Matrix(1567,-2494,546,-869) -> Matrix(33,-2,314,-19) Matrix(1971,-3190,574,-929) -> Matrix(169,-10,1200,-71) Matrix(465,-754,214,-347) -> Matrix(235,-14,2904,-173) Matrix(6091,-9918,1816,-2957) -> Matrix(37,-2,278,-15) Matrix(1277,-2088,496,-811) -> Matrix(133,-8,1380,-83) Matrix(6265,-10266,1486,-2435) -> Matrix(33,-2,116,-7) Matrix(1333,-2204,176,-291) -> Matrix(199,-12,680,-41) Matrix(2031,-3422,860,-1449) -> Matrix(355,-22,4018,-249) Matrix(4581,-7772,992,-1683) -> Matrix(323,-20,1502,-93) Matrix(5975,-10266,1586,-2725) -> Matrix(221,-14,1626,-103) Matrix(3539,-6090,1988,-3421) -> Matrix(221,-14,3394,-215) Matrix(1741,-3016,736,-1275) -> Matrix(629,-40,7092,-451) Matrix(233,-406,66,-115) -> Matrix(31,-2,264,-17) Matrix(4291,-7656,1886,-3365) -> Matrix(2075,-136,24366,-1597) Matrix(4119,-7366,940,-1681) -> Matrix(91,-6,804,-53) Matrix(1101,-1972,292,-523) -> Matrix(61,-4,412,-27) Matrix(987,-1798,286,-521) -> Matrix(149,-10,1058,-71) Matrix(407,-754,156,-289) -> Matrix(205,-14,2094,-143) Matrix(405,-754,94,-175) -> Matrix(29,-2,276,-19) Matrix(463,-870,124,-233) -> Matrix(29,-2,102,-7) Matrix(1159,-2494,270,-581) -> Matrix(25,-2,-62,5) Matrix(1857,-4060,424,-927) -> Matrix(49,-4,478,-39) Matrix(6437,-14094,2464,-5395) -> Matrix(2375,-194,24154,-1973) Matrix(291,-638,26,-57) -> Matrix(171,-14,452,-37) Matrix(523,-1160,78,-173) -> Matrix(97,-8,376,-31) Matrix(2029,-4582,848,-1915) -> Matrix(403,-34,4516,-381) Matrix(3017,-6844,920,-2087) -> Matrix(331,-28,2518,-213) Matrix(813,-1856,152,-347) -> Matrix(93,-8,500,-43) Matrix(10613,-25056,4054,-9571) -> Matrix(453,-40,4564,-403) Matrix(1045,-2494,194,-463) -> Matrix(23,-2,104,-9) Matrix(10499,-25114,2788,-6669) -> Matrix(337,-30,2550,-227) Matrix(523,-1276,166,-405) -> Matrix(43,-4,398,-37) Matrix(1509,-3712,424,-1043) -> Matrix(87,-8,620,-57) Matrix(755,-1914,114,-289) -> Matrix(187,-18,800,-77) Matrix(1393,-3538,502,-1275) -> Matrix(353,-34,3312,-319) Matrix(8295,-21286,1966,-5045) -> Matrix(21,-2,284,-27) Matrix(291,-754,22,-57) -> Matrix(19,-2,48,-5) Matrix(4175,-10904,1244,-3249) -> Matrix(163,-16,1192,-117) Matrix(2841,-7424,866,-2263) -> Matrix(325,-32,2468,-243) Matrix(173,-464,22,-59) -> Matrix(1,0,-6,1) Matrix(753,-2030,194,-523) -> Matrix(19,-2,124,-13) Matrix(233,-638,42,-115) -> Matrix(19,-2,124,-13) Matrix(291,-812,62,-173) -> Matrix(37,-4,250,-27) Matrix(347,-986,82,-233) -> Matrix(19,-2,124,-13) Matrix(811,-2320,122,-349) -> Matrix(149,-16,624,-67) Matrix(1857,-6148,280,-927) -> Matrix(15,-4,64,-17) Matrix(1625,-5394,454,-1507) -> Matrix(21,-2,158,-15) Matrix(2031,-6844,430,-1449) -> Matrix(33,-4,190,-23) Matrix(3539,-12180,994,-3421) -> Matrix(27,-4,196,-29) Matrix(1101,-3944,146,-523) -> Matrix(59,-8,214,-29) Matrix(173,-638,16,-59) -> Matrix(15,-2,38,-5) Matrix(407,-1508,78,-289) -> Matrix(25,-4,144,-23) Matrix(639,-2378,140,-521) -> Matrix(11,-2,72,-13) 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): 210 Degree of the the map X: 210 Degree of the the map Y: 420 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 1260 Minimal number of generators: 211 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: 56 Genus: 78 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 29/13 116/51 116/49 29/12 116/45 145/56 290/111 29/11 87/32 58/21 3/1 29/9 145/44 58/17 203/57 290/81 18/5 29/8 290/77 58/15 4/1 29/7 232/55 116/27 87/19 116/25 14/3 24/5 29/6 5/1 26/5 21/4 58/11 16/3 28/5 29/5 6/1 25/4 19/3 13/2 20/3 27/4 7/1 29/4 22/3 15/2 23/3 8/1 17/2 9/1 10/1 11/1 12/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/27 10/9 6/145 9/8 1/24 17/15 3/71 8/7 4/93 15/13 7/163 37/32 5/116 22/19 10/231 29/25 1/23 7/6 3/68 20/17 8/183 33/28 3/68 46/39 6/137 13/11 5/113 19/16 7/156 6/5 2/45 29/24 1/22 23/19 7/153 17/14 1/22 11/9 1/23 27/22 1/22 16/13 4/87 21/17 5/107 5/4 1/22 29/23 1/21 24/19 4/83 19/15 3/61 14/11 2/39 51/40 1/30 37/29 1/23 60/47 8/177 23/18 3/64 55/43 1/21 87/68 1/21 32/25 4/83 9/7 1/21 31/24 1/20 22/17 2/41 13/10 1/20 30/23 2/47 17/13 1/21 21/16 1/20 46/35 2/39 25/19 1/21 29/22 1/20 4/3 0/1 23/17 1/21 19/14 1/22 34/25 2/39 15/11 1/17 41/30 1/22 67/49 1/21 26/19 2/41 63/46 3/62 37/27 3/61 11/8 1/20 29/21 1/20 18/13 2/39 61/44 1/18 43/31 5/99 25/18 1/18 7/5 1/21 31/22 1/20 24/17 4/79 17/12 3/58 27/19 1/19 64/45 4/75 101/71 1/21 37/26 1/18 10/7 2/37 33/23 3/61 89/62 1/20 145/101 1/20 56/39 12/239 23/16 5/98 13/9 1/19 29/20 1/19 16/11 4/75 19/13 5/93 3/2 1/18 23/15 3/53 20/13 8/141 57/37 11/191 37/24 1/18 17/11 1/17 14/9 6/107 39/25 1/17 25/16 5/88 61/39 7/123 36/23 16/281 11/7 5/87 41/26 3/52 30/19 14/241 79/50 7/120 128/81 20/343 49/31 1/17 68/43 16/273 87/55 1/17 19/12 1/16 27/17 1/17 35/22 1/18 43/27 7/121 8/5 4/69 29/18 1/17 21/13 1/17 97/60 41/692 76/47 8/135 55/34 5/84 34/21 6/101 13/8 3/50 70/43 2/31 57/35 5/87 101/62 13/222 145/89 1/17 44/27 8/135 31/19 1/17 49/30 5/84 18/11 2/33 77/47 13/215 59/36 7/114 41/25 1/17 23/14 5/84 28/17 16/267 61/37 11/183 33/20 3/50 38/23 22/365 5/3 3/49 32/19 4/65 27/16 1/16 22/13 2/33 61/36 1/16 39/23 17/275 56/33 36/581 17/10 1/16 29/17 1/16 12/7 8/127 67/39 5/79 55/32 7/110 43/25 1/17 74/43 6/95 31/18 1/16 19/11 7/111 45/26 17/268 26/15 10/157 7/4 5/78 37/21 9/139 30/17 22/339 23/13 1/15 39/22 1/16 16/9 4/61 73/41 17/261 57/32 29/444 41/23 7/107 66/37 34/519 25/14 13/198 59/33 31/471 34/19 6/91 9/5 1/15 29/16 1/15 20/11 16/239 31/17 1/15 11/6 5/74 13/7 5/73 15/8 13/188 2/1 2/27 17/8 3/38 15/7 13/163 28/13 24/299 13/6 5/62 24/11 4/49 35/16 23/282 46/21 30/367 11/5 5/61 31/14 1/12 20/9 16/193 29/13 1/12 9/4 1/12 52/23 16/189 43/19 13/153 34/15 6/71 59/26 31/366 25/11 13/153 116/51 4/47 91/40 47/552 66/29 34/399 41/18 7/82 57/25 29/339 16/7 4/47 39/17 1/11 23/10 1/12 30/13 22/255 37/16 9/104 7/3 5/57 33/14 1/12 59/25 23/261 85/36 3/34 26/11 10/113 71/30 27/304 116/49 4/45 45/19 17/191 19/8 7/78 31/13 1/11 43/18 1/10 55/23 7/79 122/51 22/247 67/28 5/56 12/5 8/89 29/12 1/11 17/7 1/11 56/23 36/391 95/39 13/141 39/16 17/184 22/9 2/21 27/11 1/11 32/13 4/43 5/2 3/32 33/13 3/31 28/11 16/165 23/9 5/51 41/16 1/10 59/23 7/75 136/53 20/211 77/30 13/136 18/7 2/21 67/26 7/72 116/45 4/41 49/19 5/51 31/12 1/10 44/17 8/81 145/56 1/10 101/39 13/129 57/22 5/48 70/27 2/23 13/5 3/31 47/18 11/112 128/49 52/529 209/80 83/844 290/111 6/61 81/31 31/315 34/13 6/61 89/34 1/10 233/89 21/211 377/144 1/10 144/55 4/39 55/21 5/51 76/29 8/81 97/37 41/415 21/8 1/10 29/11 1/10 8/3 4/39 35/13 1/9 62/23 2/19 27/10 1/10 19/7 1/11 87/32 1/10 68/25 16/159 49/18 1/10 128/47 20/197 79/29 7/69 30/11 14/137 11/4 5/48 58/21 2/19 47/17 21/199 36/13 16/151 61/22 7/66 86/31 38/357 25/9 5/47 14/5 6/55 31/11 1/9 17/6 1/10 20/7 8/75 43/15 11/101 23/8 3/28 3/1 1/9 22/7 2/19 19/6 5/42 16/5 4/33 29/9 1/8 13/4 1/8 36/11 0/1 95/29 5/39 59/18 13/100 82/25 2/15 23/7 5/37 56/17 12/85 145/44 1/7 89/27 1/7 33/10 3/20 43/13 3/17 53/16 1/0 10/3 2/17 57/17 11/85 104/31 12/91 47/14 1/8 37/11 1/9 101/30 1/6 64/19 4/33 27/8 1/8 44/13 8/63 17/5 3/23 58/17 2/15 41/12 7/52 24/7 4/29 55/16 5/36 86/25 14/99 31/9 1/7 38/11 6/41 7/2 1/6 32/9 4/29 89/25 1/7 146/41 18/127 203/57 1/7 57/16 7/48 25/7 1/9 68/19 8/61 179/50 21/158 290/81 2/15 111/31 13/97 43/12 5/36 61/17 1/9 18/5 2/15 29/8 1/7 11/3 1/7 48/13 4/27 37/10 3/20 26/7 2/13 41/11 1/5 56/15 4/15 15/4 1/10 64/17 4/31 177/47 11/83 290/77 2/15 113/30 7/52 49/13 1/7 34/9 2/15 19/5 1/5 23/6 1/6 27/7 1/7 58/15 2/13 31/8 1/6 4/1 0/1 29/7 1/7 25/6 1/6 46/11 2/15 21/5 1/7 59/14 3/14 97/23 -1/3 232/55 0/1 135/32 1/20 38/9 2/17 17/4 1/6 30/7 2/7 73/17 -1/9 116/27 0/1 43/10 1/16 13/3 1/7 35/8 1/4 92/21 0/1 57/13 5/39 79/18 3/22 22/5 2/13 31/7 1/7 9/2 1/6 41/9 1/7 32/7 4/25 87/19 1/6 55/12 1/6 23/5 3/17 60/13 8/39 97/21 9/41 37/8 1/4 51/11 -1/3 116/25 0/1 65/14 1/18 14/3 2/15 33/7 3/19 85/18 1/6 52/11 0/1 19/4 3/20 24/5 4/25 29/6 1/6 5/1 1/5 26/5 2/11 21/4 5/28 58/11 2/11 37/7 9/49 16/3 4/21 59/11 15/77 43/8 3/14 27/5 1/5 11/2 1/4 28/5 8/45 17/3 1/5 23/4 7/36 29/5 1/5 6/1 2/9 31/5 1/5 25/4 5/24 19/3 7/33 13/2 5/22 46/7 6/25 33/5 3/13 53/8 15/64 73/11 23/97 20/3 8/33 27/4 1/4 7/1 3/13 29/4 1/4 22/3 10/39 37/5 5/19 15/2 7/26 53/7 9/31 38/5 2/5 23/3 1/3 8/1 4/15 17/2 3/10 9/1 1/3 10/1 6/17 11/1 1/3 12/1 8/19 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(523,-580,156,-173) (1/1,10/9) -> (10/3,57/17) Hyperbolic Matrix(985,-1102,623,-697) (10/9,9/8) -> (49/31,68/43) Hyperbolic Matrix(1333,-1508,975,-1103) (9/8,17/15) -> (41/30,67/49) Hyperbolic Matrix(1277,-1450,561,-637) (17/15,8/7) -> (66/29,41/18) Hyperbolic Matrix(405,-464,254,-291) (8/7,15/13) -> (43/27,8/5) Hyperbolic Matrix(3713,-4292,1103,-1275) (15/13,37/32) -> (37/11,101/30) Hyperbolic Matrix(2957,-3422,903,-1045) (37/32,22/19) -> (36/11,95/29) Hyperbolic Matrix(1101,-1276,151,-175) (22/19,29/25) -> (29/4,22/3) Hyperbolic Matrix(349,-406,49,-57) (29/25,7/6) -> (7/1,29/4) Hyperbolic Matrix(347,-406,100,-117) (7/6,20/17) -> (38/11,7/2) Hyperbolic Matrix(1625,-1914,984,-1159) (20/17,33/28) -> (33/20,38/23) Hyperbolic Matrix(2263,-2668,1721,-2029) (33/28,46/39) -> (46/35,25/19) Hyperbolic Matrix(1277,-1508,785,-927) (46/39,13/11) -> (13/8,70/43) Hyperbolic Matrix(929,-1102,537,-637) (13/11,19/16) -> (19/11,45/26) Hyperbolic Matrix(927,-1102,196,-233) (19/16,6/5) -> (52/11,19/4) Hyperbolic Matrix(289,-348,49,-59) (6/5,29/24) -> (29/5,6/1) Hyperbolic Matrix(1103,-1334,191,-231) (29/24,23/19) -> (23/4,29/5) Hyperbolic Matrix(1101,-1334,671,-813) (23/19,17/14) -> (41/25,23/14) Hyperbolic Matrix(523,-638,332,-405) (17/14,11/9) -> (11/7,41/26) Hyperbolic Matrix(521,-638,285,-349) (11/9,27/22) -> (31/17,11/6) Hyperbolic Matrix(2031,-2494,1180,-1449) (27/22,16/13) -> (74/43,31/18) Hyperbolic Matrix(753,-928,142,-175) (16/13,21/17) -> (37/7,16/3) Hyperbolic Matrix(1219,-1508,890,-1101) (21/17,5/4) -> (63/46,37/27) Hyperbolic Matrix(231,-290,47,-59) (5/4,29/23) -> (29/6,5/1) Hyperbolic Matrix(1103,-1392,229,-289) (29/23,24/19) -> (24/5,29/6) Hyperbolic Matrix(871,-1102,641,-811) (24/19,19/15) -> (19/14,34/25) Hyperbolic Matrix(639,-812,410,-521) (19/15,14/11) -> (14/9,39/25) Hyperbolic Matrix(1275,-1624,274,-349) (14/11,51/40) -> (65/14,14/3) Hyperbolic Matrix(1683,-2146,727,-927) (51/40,37/29) -> (37/16,7/3) Hyperbolic Matrix(6089,-7772,2500,-3191) (37/29,60/47) -> (56/23,95/39) Hyperbolic Matrix(2089,-2668,635,-811) (60/47,23/18) -> (23/7,56/17) Hyperbolic Matrix(1043,-1334,681,-871) (23/18,55/43) -> (3/2,23/15) Hyperbolic Matrix(7481,-9570,1633,-2089) (55/43,87/68) -> (87/19,55/12) Hyperbolic Matrix(4351,-5568,951,-1217) (87/68,32/25) -> (32/7,87/19) Hyperbolic Matrix(1857,-2378,1358,-1739) (32/25,9/7) -> (67/49,26/19) Hyperbolic Matrix(1393,-1798,853,-1101) (9/7,31/24) -> (31/19,49/30) Hyperbolic Matrix(987,-1276,403,-521) (31/24,22/17) -> (22/9,27/11) Hyperbolic Matrix(581,-754,178,-231) (22/17,13/10) -> (13/4,36/11) Hyperbolic Matrix(579,-754,268,-349) (13/10,30/23) -> (28/13,13/6) Hyperbolic Matrix(1333,-1740,845,-1103) (30/23,17/13) -> (41/26,30/19) Hyperbolic Matrix(753,-986,488,-639) (17/13,21/16) -> (37/24,17/11) Hyperbolic Matrix(4813,-6322,1767,-2321) (21/16,46/35) -> (128/47,79/29) Hyperbolic Matrix(1101,-1450,265,-349) (25/19,29/22) -> (29/7,25/6) Hyperbolic Matrix(175,-232,43,-57) (29/22,4/3) -> (4/1,29/7) Hyperbolic Matrix(1159,-1566,430,-581) (4/3,23/17) -> (35/13,62/23) Hyperbolic Matrix(985,-1334,429,-581) (23/17,19/14) -> (39/17,23/10) Hyperbolic Matrix(1449,-1972,640,-871) (34/25,15/11) -> (43/19,34/15) Hyperbolic Matrix(637,-870,298,-407) (15/11,41/30) -> (17/8,15/7) Hyperbolic Matrix(1567,-2146,931,-1275) (26/19,63/46) -> (5/3,32/19) Hyperbolic Matrix(1565,-2146,466,-639) (37/27,11/8) -> (47/14,37/11) Hyperbolic Matrix(463,-638,127,-175) (11/8,29/21) -> (29/8,11/3) Hyperbolic Matrix(755,-1044,209,-289) (29/21,18/13) -> (18/5,29/8) Hyperbolic Matrix(4059,-5626,1549,-2147) (18/13,61/44) -> (55/21,76/29) Hyperbolic Matrix(3597,-4988,1505,-2087) (61/44,43/31) -> (43/18,55/23) Hyperbolic Matrix(1797,-2494,544,-755) (43/31,25/18) -> (33/10,43/13) Hyperbolic Matrix(291,-406,124,-173) (25/18,7/5) -> (7/3,33/14) Hyperbolic Matrix(289,-406,42,-59) (7/5,31/22) -> (27/4,7/1) Hyperbolic Matrix(2261,-3190,864,-1219) (31/22,24/17) -> (34/13,89/34) Hyperbolic Matrix(985,-1392,288,-407) (24/17,17/12) -> (41/12,24/7) Hyperbolic Matrix(695,-986,246,-349) (17/12,27/19) -> (31/11,17/6) Hyperbolic Matrix(1509,-2146,244,-347) (27/19,64/45) -> (6/1,31/5) Hyperbolic Matrix(5219,-7424,1387,-1973) (64/45,101/71) -> (15/4,64/17) Hyperbolic Matrix(3017,-4292,407,-579) (101/71,37/26) -> (37/5,15/2) Hyperbolic Matrix(1507,-2146,408,-581) (37/26,10/7) -> (48/13,37/10) Hyperbolic Matrix(1739,-2494,486,-697) (10/7,33/23) -> (25/7,68/19) Hyperbolic Matrix(2263,-3248,363,-521) (33/23,89/62) -> (31/5,25/4) Hyperbolic Matrix(17979,-25810,5455,-7831) (89/62,145/101) -> (145/44,89/27) Hyperbolic Matrix(11311,-16240,3433,-4929) (145/101,56/39) -> (56/17,145/44) Hyperbolic Matrix(1857,-2668,403,-579) (56/39,23/16) -> (23/5,60/13) Hyperbolic Matrix(523,-754,120,-173) (23/16,13/9) -> (13/3,35/8) Hyperbolic Matrix(521,-754,161,-233) (13/9,29/20) -> (29/9,13/4) Hyperbolic Matrix(639,-928,199,-289) (29/20,16/11) -> (16/5,29/9) Hyperbolic Matrix(637,-928,359,-523) (16/11,19/13) -> (39/22,16/9) Hyperbolic Matrix(871,-1276,514,-753) (19/13,3/2) -> (61/36,39/23) Hyperbolic Matrix(869,-1334,114,-175) (23/15,20/13) -> (38/5,23/3) Hyperbolic Matrix(5799,-8932,2260,-3481) (20/13,57/37) -> (59/23,136/53) Hyperbolic Matrix(4931,-7598,1505,-2319) (57/37,37/24) -> (95/29,59/18) Hyperbolic Matrix(637,-986,188,-291) (17/11,14/9) -> (44/13,17/5) Hyperbolic Matrix(929,-1450,148,-231) (39/25,25/16) -> (25/4,19/3) Hyperbolic Matrix(2263,-3538,1372,-2145) (25/16,61/39) -> (61/37,33/20) Hyperbolic Matrix(2261,-3538,1335,-2089) (61/39,36/23) -> (22/13,61/36) Hyperbolic Matrix(1333,-2088,482,-755) (36/23,11/7) -> (47/17,36/13) Hyperbolic Matrix(2203,-3480,1249,-1973) (30/19,79/50) -> (37/21,30/17) Hyperbolic Matrix(4001,-6322,955,-1509) (79/50,128/81) -> (46/11,21/5) Hyperbolic Matrix(5799,-9164,2423,-3829) (128/81,49/31) -> (67/28,12/5) Hyperbolic Matrix(7481,-11832,2751,-4351) (68/43,87/55) -> (87/32,68/25) Hyperbolic Matrix(2089,-3306,769,-1217) (87/55,19/12) -> (19/7,87/32) Hyperbolic Matrix(695,-1102,403,-639) (19/12,27/17) -> (31/18,19/11) Hyperbolic Matrix(985,-1566,256,-407) (27/17,35/22) -> (23/6,27/7) Hyperbolic Matrix(1567,-2494,546,-869) (35/22,43/27) -> (43/15,23/8) Hyperbolic Matrix(289,-464,109,-175) (8/5,29/18) -> (29/11,8/3) Hyperbolic Matrix(755,-1218,287,-463) (29/18,21/13) -> (21/8,29/11) Hyperbolic Matrix(3481,-5626,753,-1217) (21/13,97/60) -> (97/21,37/8) Hyperbolic Matrix(4699,-7598,2869,-4639) (97/60,76/47) -> (18/11,77/47) Hyperbolic Matrix(3479,-5626,969,-1567) (76/47,55/34) -> (61/17,18/5) Hyperbolic Matrix(1971,-3190,574,-929) (55/34,34/21) -> (24/7,55/16) Hyperbolic Matrix(465,-754,214,-347) (34/21,13/8) -> (13/6,24/11) Hyperbolic Matrix(6091,-9918,1816,-2957) (70/43,57/35) -> (57/17,104/31) Hyperbolic Matrix(6089,-9918,3419,-5569) (57/35,101/62) -> (73/41,57/32) Hyperbolic Matrix(17979,-29290,6943,-11311) (101/62,145/89) -> (145/56,101/39) Hyperbolic Matrix(7831,-12760,3025,-4929) (145/89,44/27) -> (44/17,145/56) Hyperbolic Matrix(1565,-2552,463,-755) (44/27,31/19) -> (27/8,44/13) Hyperbolic Matrix(1277,-2088,496,-811) (49/30,18/11) -> (18/7,67/26) Hyperbolic Matrix(6265,-10266,1486,-2435) (77/47,59/36) -> (59/14,97/23) Hyperbolic Matrix(2901,-4756,1273,-2087) (59/36,41/25) -> (41/18,57/25) Hyperbolic Matrix(811,-1334,459,-755) (23/14,28/17) -> (30/17,23/13) Hyperbolic Matrix(4117,-6786,1197,-1973) (28/17,61/37) -> (55/16,86/25) Hyperbolic Matrix(1333,-2204,176,-291) (38/23,5/3) -> (53/7,38/5) Hyperbolic Matrix(2031,-3422,860,-1449) (32/19,27/16) -> (85/36,26/11) Hyperbolic Matrix(755,-1276,171,-289) (27/16,22/13) -> (22/5,31/7) Hyperbolic Matrix(4581,-7772,992,-1683) (39/23,56/33) -> (60/13,97/21) Hyperbolic Matrix(1913,-3248,513,-871) (56/33,17/10) -> (41/11,56/15) Hyperbolic Matrix(579,-986,239,-407) (17/10,29/17) -> (29/12,17/7) Hyperbolic Matrix(407,-696,169,-289) (29/17,12/7) -> (12/5,29/12) Hyperbolic Matrix(5335,-9164,1959,-3365) (12/7,67/39) -> (49/18,128/47) Hyperbolic Matrix(5975,-10266,1586,-2725) (67/39,55/32) -> (113/30,49/13) Hyperbolic Matrix(2901,-4988,809,-1391) (55/32,43/25) -> (43/12,61/17) Hyperbolic Matrix(3539,-6090,1988,-3421) (43/25,74/43) -> (16/9,73/41) Hyperbolic Matrix(1741,-3016,736,-1275) (45/26,26/15) -> (26/11,71/30) Hyperbolic Matrix(233,-406,66,-115) (26/15,7/4) -> (7/2,32/9) Hyperbolic Matrix(1219,-2146,263,-463) (7/4,37/21) -> (37/8,51/11) Hyperbolic Matrix(753,-1334,197,-349) (23/13,39/22) -> (19/5,23/6) Hyperbolic Matrix(2669,-4756,1041,-1855) (57/32,41/23) -> (41/16,59/23) Hyperbolic Matrix(813,-1450,97,-173) (41/23,66/37) -> (8/1,17/2) Hyperbolic Matrix(4291,-7656,1886,-3365) (66/37,25/14) -> (91/40,66/29) Hyperbolic Matrix(1623,-2900,455,-813) (25/14,59/33) -> (57/16,25/7) Hyperbolic Matrix(4119,-7366,940,-1681) (59/33,34/19) -> (92/21,57/13) Hyperbolic Matrix(1101,-1972,292,-523) (34/19,9/5) -> (49/13,34/9) Hyperbolic Matrix(289,-522,129,-233) (9/5,29/16) -> (29/13,9/4) Hyperbolic Matrix(639,-1160,287,-521) (29/16,20/11) -> (20/9,29/13) Hyperbolic Matrix(987,-1798,286,-521) (20/11,31/17) -> (31/9,38/11) Hyperbolic Matrix(407,-754,156,-289) (11/6,13/7) -> (13/5,47/18) Hyperbolic Matrix(405,-754,94,-175) (13/7,15/8) -> (43/10,13/3) Hyperbolic Matrix(463,-870,124,-233) (15/8,2/1) -> (56/15,15/4) Hyperbolic Matrix(465,-986,191,-405) (2/1,17/8) -> (17/7,56/23) Hyperbolic Matrix(1159,-2494,270,-581) (15/7,28/13) -> (30/7,73/17) Hyperbolic Matrix(1857,-4060,424,-927) (24/11,35/16) -> (35/8,92/21) Hyperbolic Matrix(6437,-14094,2464,-5395) (35/16,46/21) -> (128/49,209/80) Hyperbolic Matrix(291,-638,26,-57) (46/21,11/5) -> (11/1,12/1) Hyperbolic Matrix(289,-638,53,-117) (11/5,31/14) -> (27/5,11/2) Hyperbolic Matrix(523,-1160,78,-173) (31/14,20/9) -> (20/3,27/4) Hyperbolic Matrix(2029,-4582,848,-1915) (9/4,52/23) -> (122/51,67/28) Hyperbolic Matrix(3539,-8004,1051,-2377) (52/23,43/19) -> (101/30,64/19) Hyperbolic Matrix(3017,-6844,920,-2087) (34/15,59/26) -> (59/18,82/25) Hyperbolic Matrix(1507,-3422,639,-1451) (59/26,25/11) -> (33/14,59/25) Hyperbolic Matrix(5917,-13456,2601,-5915) (25/11,116/51) -> (116/51,91/40) Parabolic Matrix(813,-1856,152,-347) (57/25,16/7) -> (16/3,59/11) Hyperbolic Matrix(405,-928,127,-291) (16/7,39/17) -> (19/6,16/5) Hyperbolic Matrix(579,-1334,227,-523) (23/10,30/13) -> (28/11,23/9) Hyperbolic Matrix(1507,-3480,553,-1277) (30/13,37/16) -> (79/29,30/11) Hyperbolic Matrix(10613,-25056,4054,-9571) (59/25,85/36) -> (89/34,233/89) Hyperbolic Matrix(5685,-13456,2401,-5683) (71/30,116/49) -> (116/49,45/19) Parabolic Matrix(465,-1102,73,-173) (45/19,19/8) -> (19/3,13/2) Hyperbolic Matrix(463,-1102,171,-407) (19/8,31/13) -> (27/10,19/7) Hyperbolic Matrix(1045,-2494,194,-463) (31/13,43/18) -> (43/8,27/5) Hyperbolic Matrix(10499,-25114,2788,-6669) (55/23,122/51) -> (64/17,177/47) Hyperbolic Matrix(4119,-10034,1571,-3827) (95/39,39/16) -> (97/37,21/8) Hyperbolic Matrix(523,-1276,166,-405) (39/16,22/9) -> (22/7,19/6) Hyperbolic Matrix(1509,-3712,424,-1043) (27/11,32/13) -> (32/9,89/25) Hyperbolic Matrix(117,-290,23,-57) (32/13,5/2) -> (5/1,26/5) Hyperbolic Matrix(755,-1914,114,-289) (5/2,33/13) -> (33/5,53/8) Hyperbolic Matrix(1393,-3538,502,-1275) (33/13,28/11) -> (86/31,25/9) Hyperbolic Matrix(521,-1334,91,-233) (23/9,41/16) -> (17/3,23/4) Hyperbolic Matrix(8295,-21286,1966,-5045) (136/53,77/30) -> (135/32,38/9) Hyperbolic Matrix(2959,-7598,1129,-2899) (77/30,18/7) -> (76/29,97/37) Hyperbolic Matrix(5221,-13456,2025,-5219) (67/26,116/45) -> (116/45,49/19) Parabolic Matrix(697,-1798,157,-405) (49/19,31/12) -> (31/7,9/2) Hyperbolic Matrix(695,-1798,247,-639) (31/12,44/17) -> (14/5,31/11) Hyperbolic Matrix(3247,-8410,605,-1567) (101/39,57/22) -> (59/11,43/8) Hyperbolic Matrix(291,-754,22,-57) (57/22,70/27) -> (12/1,1/0) Hyperbolic Matrix(581,-1508,89,-231) (70/27,13/5) -> (13/2,46/7) Hyperbolic Matrix(4175,-10904,1244,-3249) (47/18,128/49) -> (104/31,47/14) Hyperbolic Matrix(32191,-84100,12321,-32189) (209/80,290/111) -> (290/111,81/31) Parabolic Matrix(2841,-7424,866,-2263) (81/31,34/13) -> (82/25,23/7) Hyperbolic Matrix(26275,-68788,7377,-19313) (233/89,377/144) -> (203/57,57/16) Hyperbolic Matrix(32189,-84274,9039,-23665) (377/144,144/55) -> (146/41,203/57) Hyperbolic Matrix(5161,-13514,1861,-4873) (144/55,55/21) -> (61/22,86/31) Hyperbolic Matrix(173,-464,22,-59) (8/3,35/13) -> (23/3,8/1) Hyperbolic Matrix(753,-2030,194,-523) (62/23,27/10) -> (31/8,4/1) Hyperbolic Matrix(405,-1102,43,-117) (68/25,49/18) -> (9/1,10/1) Hyperbolic Matrix(233,-638,42,-115) (30/11,11/4) -> (11/2,28/5) Hyperbolic Matrix(1219,-3364,441,-1217) (11/4,58/21) -> (58/21,47/17) Parabolic Matrix(523,-1450,167,-463) (36/13,61/22) -> (3/1,22/7) Hyperbolic Matrix(291,-812,62,-173) (25/9,14/5) -> (14/3,33/7) Hyperbolic Matrix(347,-986,82,-233) (17/6,20/7) -> (38/9,17/4) Hyperbolic Matrix(811,-2320,122,-349) (20/7,43/15) -> (73/11,20/3) Hyperbolic Matrix(463,-1334,101,-291) (23/8,3/1) -> (55/12,23/5) Hyperbolic Matrix(1741,-5742,369,-1217) (89/27,33/10) -> (33/7,85/18) Hyperbolic Matrix(1857,-6148,280,-927) (43/13,53/16) -> (53/8,73/11) Hyperbolic Matrix(1625,-5394,454,-1507) (53/16,10/3) -> (68/19,179/50) Hyperbolic Matrix(2031,-6844,430,-1449) (64/19,27/8) -> (85/18,52/11) Hyperbolic Matrix(987,-3364,289,-985) (17/5,58/17) -> (58/17,41/12) Parabolic Matrix(3539,-12180,994,-3421) (86/25,31/9) -> (89/25,146/41) Hyperbolic Matrix(23491,-84100,6561,-23489) (179/50,290/81) -> (290/81,111/31) Parabolic Matrix(1101,-3944,146,-523) (111/31,43/12) -> (15/2,53/7) Hyperbolic Matrix(173,-638,16,-59) (11/3,48/13) -> (10/1,11/1) Hyperbolic Matrix(407,-1508,78,-289) (37/10,26/7) -> (26/5,21/4) Hyperbolic Matrix(639,-2378,140,-521) (26/7,41/11) -> (41/9,32/7) Hyperbolic Matrix(22331,-84100,5929,-22329) (177/47,290/77) -> (290/77,113/30) Parabolic Matrix(291,-1102,61,-231) (34/9,19/5) -> (19/4,24/5) Hyperbolic Matrix(871,-3364,225,-869) (27/7,58/15) -> (58/15,31/8) Parabolic Matrix(639,-2668,97,-405) (25/6,46/11) -> (46/7,33/5) Hyperbolic Matrix(1391,-5858,317,-1335) (21/5,59/14) -> (57/13,79/18) Hyperbolic Matrix(12761,-53824,3025,-12759) (97/23,232/55) -> (232/55,135/32) Parabolic Matrix(231,-986,41,-175) (17/4,30/7) -> (28/5,17/3) Hyperbolic Matrix(3133,-13456,729,-3131) (73/17,116/27) -> (116/27,43/10) Parabolic Matrix(581,-2552,79,-347) (79/18,22/5) -> (22/3,37/5) Hyperbolic Matrix(115,-522,13,-59) (9/2,41/9) -> (17/2,9/1) Hyperbolic Matrix(2901,-13456,625,-2899) (51/11,116/25) -> (116/25,65/14) Parabolic Matrix(639,-3364,121,-637) (21/4,58/11) -> (58/11,37/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,27,1) Matrix(523,-580,156,-173) -> Matrix(97,-4,752,-31) Matrix(985,-1102,623,-697) -> Matrix(239,-10,4087,-171) Matrix(1333,-1508,975,-1103) -> Matrix(95,-4,2019,-85) Matrix(1277,-1450,561,-637) -> Matrix(613,-26,7191,-305) Matrix(405,-464,254,-291) -> Matrix(1,0,-6,1) Matrix(3713,-4292,1103,-1275) -> Matrix(93,-4,721,-31) Matrix(2957,-3422,903,-1045) -> Matrix(231,-10,1825,-79) Matrix(1101,-1276,151,-175) -> Matrix(461,-20,1821,-79) Matrix(349,-406,49,-57) -> Matrix(137,-6,571,-25) Matrix(347,-406,100,-117) -> Matrix(45,-2,338,-15) Matrix(1625,-1914,984,-1159) -> Matrix(409,-18,6794,-299) Matrix(2263,-2668,1721,-2029) -> Matrix(91,-4,1843,-81) Matrix(1277,-1508,785,-927) -> Matrix(91,-4,1479,-65) Matrix(929,-1102,537,-637) -> Matrix(313,-14,4941,-221) Matrix(927,-1102,196,-233) -> Matrix(45,-2,248,-11) Matrix(289,-348,49,-59) -> Matrix(89,-4,423,-19) Matrix(1103,-1334,191,-231) -> Matrix(307,-14,1557,-71) Matrix(1101,-1334,671,-813) -> Matrix(43,-2,753,-35) Matrix(523,-638,332,-405) -> Matrix(41,-2,718,-35) Matrix(521,-638,285,-349) -> Matrix(133,-6,1973,-89) Matrix(2031,-2494,1180,-1449) -> Matrix(45,-2,698,-31) Matrix(753,-928,142,-175) -> Matrix(173,-8,930,-43) Matrix(1219,-1508,890,-1101) -> Matrix(85,-4,1764,-83) Matrix(231,-290,47,-59) -> Matrix(43,-2,237,-11) Matrix(1103,-1392,229,-289) -> Matrix(167,-8,1023,-49) Matrix(871,-1102,641,-811) -> Matrix(41,-2,841,-41) Matrix(639,-812,410,-521) -> Matrix(81,-4,1438,-71) Matrix(1275,-1624,274,-349) -> Matrix(1,0,-12,1) Matrix(1683,-2146,727,-927) -> Matrix(55,-2,633,-23) Matrix(6089,-7772,2500,-3191) -> Matrix(447,-20,4850,-217) Matrix(2089,-2668,635,-811) -> Matrix(87,-4,631,-29) Matrix(1043,-1334,681,-871) -> Matrix(127,-6,2265,-107) Matrix(7481,-9570,1633,-2089) -> Matrix(295,-14,1749,-83) Matrix(4351,-5568,951,-1217) -> Matrix(167,-8,1023,-49) Matrix(1857,-2378,1358,-1739) -> Matrix(41,-2,882,-43) Matrix(1393,-1798,853,-1101) -> Matrix(121,-6,2037,-101) Matrix(987,-1276,403,-521) -> Matrix(81,-4,871,-43) Matrix(581,-754,178,-231) -> Matrix(41,-2,308,-15) Matrix(579,-754,268,-349) -> Matrix(35,-2,438,-25) Matrix(1333,-1740,845,-1103) -> Matrix(87,-4,1501,-69) Matrix(753,-986,488,-639) -> Matrix(41,-2,718,-35) Matrix(4813,-6322,1767,-2321) -> Matrix(127,-6,1249,-59) Matrix(1101,-1450,265,-349) -> Matrix(41,-2,267,-13) Matrix(175,-232,43,-57) -> Matrix(1,0,-13,1) Matrix(1159,-1566,430,-581) -> Matrix(41,-2,390,-19) Matrix(985,-1334,429,-581) -> Matrix(43,-2,495,-23) Matrix(1449,-1972,640,-871) -> Matrix(81,-4,952,-47) Matrix(637,-870,298,-407) -> Matrix(47,-2,588,-25) Matrix(1567,-2146,931,-1275) -> Matrix(125,-6,2021,-97) Matrix(1565,-2146,466,-639) -> Matrix(41,-2,308,-15) Matrix(463,-638,127,-175) -> Matrix(41,-2,267,-13) Matrix(755,-1044,209,-289) -> Matrix(79,-4,573,-29) Matrix(4059,-5626,1549,-2147) -> Matrix(113,-6,1149,-61) Matrix(3597,-4988,1505,-2087) -> Matrix(79,-4,889,-45) Matrix(1797,-2494,544,-755) -> Matrix(39,-2,254,-13) Matrix(291,-406,124,-173) -> Matrix(37,-2,426,-23) Matrix(289,-406,42,-59) -> Matrix(39,-2,176,-9) Matrix(2261,-3190,864,-1219) -> Matrix(199,-10,2010,-101) Matrix(985,-1392,288,-407) -> Matrix(157,-8,1158,-59) Matrix(695,-986,246,-349) -> Matrix(39,-2,332,-17) Matrix(1509,-2146,244,-347) -> Matrix(37,-2,204,-11) Matrix(5219,-7424,1387,-1973) -> Matrix(1,0,-11,1) Matrix(3017,-4292,407,-579) -> Matrix(77,-4,289,-15) Matrix(1507,-2146,408,-581) -> Matrix(39,-2,254,-13) Matrix(1739,-2494,486,-697) -> Matrix(41,-2,308,-15) Matrix(2263,-3248,363,-521) -> Matrix(161,-8,785,-39) Matrix(17979,-25810,5455,-7831) -> Matrix(601,-30,4187,-209) Matrix(11311,-16240,3433,-4929) -> Matrix(479,-24,3373,-169) Matrix(1857,-2668,403,-579) -> Matrix(79,-4,415,-21) Matrix(523,-754,120,-173) -> Matrix(39,-2,254,-13) Matrix(521,-754,161,-233) -> Matrix(115,-6,901,-47) Matrix(639,-928,199,-289) -> Matrix(151,-8,1227,-65) Matrix(637,-928,359,-523) -> Matrix(149,-8,2291,-123) Matrix(871,-1276,514,-753) -> Matrix(71,-4,1154,-65) Matrix(869,-1334,114,-175) -> Matrix(35,-2,158,-9) Matrix(5799,-8932,2260,-3481) -> Matrix(209,-12,2212,-127) Matrix(4931,-7598,1505,-2319) -> Matrix(103,-6,807,-47) Matrix(637,-986,188,-291) -> Matrix(37,-2,278,-15) Matrix(929,-1450,148,-231) -> Matrix(177,-10,832,-47) Matrix(2263,-3538,1372,-2145) -> Matrix(599,-34,9954,-565) Matrix(2261,-3538,1335,-2089) -> Matrix(527,-30,8555,-487) Matrix(1333,-2088,482,-755) -> Matrix(561,-32,5312,-303) Matrix(2203,-3480,1249,-1973) -> Matrix(687,-40,10597,-617) Matrix(4001,-6322,955,-1509) -> Matrix(103,-6,601,-35) Matrix(5799,-9164,2423,-3829) -> Matrix(617,-36,6907,-403) Matrix(7481,-11832,2751,-4351) -> Matrix(545,-32,5433,-319) Matrix(2089,-3306,769,-1217) -> Matrix(33,-2,347,-21) Matrix(695,-1102,403,-639) -> Matrix(103,-6,1631,-95) Matrix(985,-1566,256,-407) -> Matrix(35,-2,228,-13) Matrix(1567,-2494,546,-869) -> Matrix(33,-2,314,-19) Matrix(289,-464,109,-175) -> Matrix(137,-8,1353,-79) Matrix(755,-1218,287,-463) -> Matrix(373,-22,3747,-221) Matrix(3481,-5626,753,-1217) -> Matrix(169,-10,693,-41) Matrix(4699,-7598,2869,-4639) -> Matrix(371,-22,6189,-367) Matrix(3479,-5626,969,-1567) -> Matrix(101,-6,825,-49) Matrix(1971,-3190,574,-929) -> Matrix(169,-10,1200,-71) Matrix(465,-754,214,-347) -> Matrix(235,-14,2904,-173) Matrix(6091,-9918,1816,-2957) -> Matrix(37,-2,278,-15) Matrix(6089,-9918,3419,-5569) -> Matrix(377,-22,5775,-337) Matrix(17979,-29290,6943,-11311) -> Matrix(443,-26,4413,-259) Matrix(7831,-12760,3025,-4929) -> Matrix(271,-16,2727,-161) Matrix(1565,-2552,463,-755) -> Matrix(1,0,-9,1) Matrix(1277,-2088,496,-811) -> Matrix(133,-8,1380,-83) Matrix(6265,-10266,1486,-2435) -> Matrix(33,-2,116,-7) Matrix(2901,-4756,1273,-2087) -> Matrix(61,-4,717,-47) Matrix(811,-1334,459,-755) -> Matrix(235,-14,3609,-215) Matrix(4117,-6786,1197,-1973) -> Matrix(433,-26,3081,-185) Matrix(1333,-2204,176,-291) -> Matrix(199,-12,680,-41) Matrix(2031,-3422,860,-1449) -> Matrix(355,-22,4018,-249) Matrix(755,-1276,171,-289) -> Matrix(65,-4,439,-27) Matrix(4581,-7772,992,-1683) -> Matrix(323,-20,1502,-93) Matrix(1913,-3248,513,-871) -> Matrix(129,-8,629,-39) Matrix(579,-986,239,-407) -> Matrix(353,-22,3867,-241) Matrix(407,-696,169,-289) -> Matrix(255,-16,2821,-177) Matrix(5335,-9164,1959,-3365) -> Matrix(569,-36,5611,-355) Matrix(5975,-10266,1586,-2725) -> Matrix(221,-14,1626,-103) Matrix(2901,-4988,809,-1391) -> Matrix(63,-4,457,-29) Matrix(3539,-6090,1988,-3421) -> Matrix(221,-14,3394,-215) Matrix(1741,-3016,736,-1275) -> Matrix(629,-40,7092,-451) Matrix(233,-406,66,-115) -> Matrix(31,-2,264,-17) Matrix(1219,-2146,263,-463) -> Matrix(31,-2,-15,1) Matrix(753,-1334,197,-349) -> Matrix(31,-2,171,-11) Matrix(2669,-4756,1041,-1855) -> Matrix(61,-4,717,-47) Matrix(813,-1450,97,-173) -> Matrix(397,-26,1359,-89) Matrix(4291,-7656,1886,-3365) -> Matrix(2075,-136,24366,-1597) Matrix(1623,-2900,455,-813) -> Matrix(61,-4,351,-23) Matrix(4119,-7366,940,-1681) -> Matrix(91,-6,804,-53) Matrix(1101,-1972,292,-523) -> Matrix(61,-4,412,-27) Matrix(289,-522,129,-233) -> Matrix(211,-14,2517,-167) Matrix(639,-1160,287,-521) -> Matrix(479,-32,5763,-385) Matrix(987,-1798,286,-521) -> Matrix(149,-10,1058,-71) Matrix(407,-754,156,-289) -> Matrix(205,-14,2094,-143) Matrix(405,-754,94,-175) -> Matrix(29,-2,276,-19) Matrix(463,-870,124,-233) -> Matrix(29,-2,102,-7) Matrix(465,-986,191,-405) -> Matrix(279,-22,3031,-239) Matrix(1159,-2494,270,-581) -> Matrix(25,-2,-62,5) Matrix(1857,-4060,424,-927) -> Matrix(49,-4,478,-39) Matrix(6437,-14094,2464,-5395) -> Matrix(2375,-194,24154,-1973) Matrix(291,-638,26,-57) -> Matrix(171,-14,452,-37) Matrix(289,-638,53,-117) -> Matrix(73,-6,353,-29) Matrix(523,-1160,78,-173) -> Matrix(97,-8,376,-31) Matrix(2029,-4582,848,-1915) -> Matrix(403,-34,4516,-381) Matrix(3539,-8004,1051,-2377) -> Matrix(47,-4,435,-37) Matrix(3017,-6844,920,-2087) -> Matrix(331,-28,2518,-213) Matrix(1507,-3422,639,-1451) -> Matrix(259,-22,2955,-251) Matrix(5917,-13456,2601,-5915) -> Matrix(2821,-240,33135,-2819) Matrix(813,-1856,152,-347) -> Matrix(93,-8,500,-43) Matrix(405,-928,127,-291) -> Matrix(93,-8,779,-67) Matrix(579,-1334,227,-523) -> Matrix(163,-14,1665,-143) Matrix(1507,-3480,553,-1277) -> Matrix(463,-40,4549,-393) Matrix(10613,-25056,4054,-9571) -> Matrix(453,-40,4564,-403) Matrix(5685,-13456,2401,-5683) -> Matrix(1981,-176,22275,-1979) Matrix(465,-1102,73,-173) -> Matrix(157,-14,729,-65) Matrix(463,-1102,171,-407) -> Matrix(67,-6,659,-59) Matrix(1045,-2494,194,-463) -> Matrix(23,-2,104,-9) Matrix(10499,-25114,2788,-6669) -> Matrix(337,-30,2550,-227) Matrix(4119,-10034,1571,-3827) -> Matrix(1193,-110,12071,-1113) Matrix(523,-1276,166,-405) -> Matrix(43,-4,398,-37) Matrix(1509,-3712,424,-1043) -> Matrix(87,-8,620,-57) Matrix(117,-290,23,-57) -> Matrix(21,-2,137,-13) Matrix(755,-1914,114,-289) -> Matrix(187,-18,800,-77) Matrix(1393,-3538,502,-1275) -> Matrix(353,-34,3312,-319) Matrix(521,-1334,91,-233) -> Matrix(19,-2,105,-11) Matrix(8295,-21286,1966,-5045) -> Matrix(21,-2,284,-27) Matrix(2959,-7598,1129,-2899) -> Matrix(227,-22,2301,-223) Matrix(5221,-13456,2025,-5219) -> Matrix(493,-48,5043,-491) Matrix(697,-1798,157,-405) -> Matrix(61,-6,417,-41) Matrix(695,-1798,247,-639) -> Matrix(21,-2,179,-17) Matrix(3247,-8410,605,-1567) -> Matrix(99,-10,505,-51) Matrix(291,-754,22,-57) -> Matrix(19,-2,48,-5) Matrix(581,-1508,89,-231) -> Matrix(43,-4,183,-17) Matrix(4175,-10904,1244,-3249) -> Matrix(163,-16,1192,-117) Matrix(32191,-84100,12321,-32189) -> Matrix(6955,-684,70699,-6953) Matrix(2841,-7424,866,-2263) -> Matrix(325,-32,2468,-243) Matrix(26275,-68788,7377,-19313) -> Matrix(281,-28,1957,-195) Matrix(32189,-84274,9039,-23665) -> Matrix(219,-22,1543,-155) Matrix(5161,-13514,1861,-4873) -> Matrix(185,-18,1737,-169) Matrix(173,-464,22,-59) -> Matrix(1,0,-6,1) Matrix(753,-2030,194,-523) -> Matrix(19,-2,124,-13) Matrix(405,-1102,43,-117) -> Matrix(99,-10,307,-31) Matrix(233,-638,42,-115) -> Matrix(19,-2,124,-13) Matrix(1219,-3364,441,-1217) -> Matrix(495,-52,4693,-493) Matrix(523,-1450,167,-463) -> Matrix(19,-2,105,-11) Matrix(291,-812,62,-173) -> Matrix(37,-4,250,-27) Matrix(347,-986,82,-233) -> Matrix(19,-2,124,-13) Matrix(811,-2320,122,-349) -> Matrix(149,-16,624,-67) Matrix(463,-1334,101,-291) -> Matrix(55,-6,321,-35) Matrix(1741,-5742,369,-1217) -> Matrix(41,-6,253,-37) Matrix(1857,-6148,280,-927) -> Matrix(15,-4,64,-17) Matrix(1625,-5394,454,-1507) -> Matrix(21,-2,158,-15) Matrix(2031,-6844,430,-1449) -> Matrix(33,-4,190,-23) Matrix(987,-3364,289,-985) -> Matrix(151,-20,1125,-149) Matrix(3539,-12180,994,-3421) -> Matrix(27,-4,196,-29) Matrix(23491,-84100,6561,-23489) -> Matrix(511,-68,3825,-509) Matrix(1101,-3944,146,-523) -> Matrix(59,-8,214,-29) Matrix(173,-638,16,-59) -> Matrix(15,-2,38,-5) Matrix(407,-1508,78,-289) -> Matrix(25,-4,144,-23) Matrix(639,-2378,140,-521) -> Matrix(11,-2,72,-13) Matrix(22331,-84100,5929,-22329) -> Matrix(271,-36,2025,-269) Matrix(291,-1102,61,-231) -> Matrix(13,-2,85,-13) Matrix(871,-3364,225,-869) -> Matrix(27,-4,169,-25) Matrix(639,-2668,97,-405) -> Matrix(27,-4,115,-17) Matrix(1391,-5858,317,-1335) -> Matrix(11,-2,83,-15) Matrix(12761,-53824,3025,-12759) -> Matrix(1,0,23,1) Matrix(231,-986,41,-175) -> Matrix(11,-2,61,-11) Matrix(3133,-13456,729,-3131) -> Matrix(1,0,25,1) Matrix(581,-2552,79,-347) -> Matrix(57,-8,221,-31) Matrix(115,-522,13,-59) -> Matrix(11,-2,39,-7) Matrix(2901,-13456,625,-2899) -> Matrix(1,0,21,1) Matrix(639,-3364,121,-637) -> Matrix(155,-28,847,-153) 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): 210 ----------------------------------------------------------------------- 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 27 1 2/1 2/27 1 29 15/7 13/163 1 29 13/6 5/62 1 29 11/5 5/61 1 29 31/14 1/12 1 29 20/9 16/193 1 29 29/13 1/12 23 1 9/4 1/12 1 29 34/15 6/71 1 29 59/26 31/366 1 29 25/11 13/153 1 29 116/51 4/47 15 1 66/29 34/399 1 29 41/18 7/82 1 29 57/25 29/339 1 29 16/7 4/47 1 29 39/17 1/11 1 29 23/10 1/12 1 29 30/13 22/255 1 29 37/16 9/104 1 29 7/3 5/57 1 29 26/11 10/113 1 29 116/49 4/45 11 1 45/19 17/191 1 29 19/8 7/78 1 29 31/13 1/11 1 29 43/18 1/10 1 29 55/23 7/79 1 29 67/28 5/56 1 29 12/5 8/89 1 29 29/12 1/11 19 1 17/7 1/11 1 29 56/23 36/391 1 29 39/16 17/184 1 29 22/9 2/21 1 29 27/11 1/11 1 29 32/13 4/43 1 29 5/2 3/32 1 29 33/13 3/31 1 29 28/11 16/165 1 29 23/9 5/51 1 29 41/16 1/10 1 29 59/23 7/75 1 29 77/30 13/136 1 29 18/7 2/21 1 29 116/45 4/41 3 1 49/19 5/51 1 29 31/12 1/10 1 29 44/17 8/81 1 29 145/56 1/10 21 1 101/39 13/129 1 29 57/22 5/48 1 29 70/27 2/23 1 29 13/5 3/31 1 29 47/18 11/112 1 29 128/49 52/529 1 29 290/111 6/61 19 1 81/31 31/315 1 29 34/13 6/61 1 29 55/21 5/51 1 29 76/29 8/81 1 29 97/37 41/415 1 29 21/8 1/10 1 29 29/11 1/10 15 1 8/3 4/39 1 29 35/13 1/9 1 29 27/10 1/10 1 29 19/7 1/11 1 29 87/32 1/10 17 1 68/25 16/159 1 29 49/18 1/10 1 29 128/47 20/197 1 29 79/29 7/69 1 29 30/11 14/137 1 29 11/4 5/48 1 29 58/21 2/19 13 1 36/13 16/151 1 29 61/22 7/66 1 29 86/31 38/357 1 29 25/9 5/47 1 29 14/5 6/55 1 29 17/6 1/10 1 29 20/7 8/75 1 29 23/8 3/28 1 29 3/1 1/9 1 29 22/7 2/19 1 29 19/6 5/42 1 29 16/5 4/33 1 29 29/9 1/8 7 1 13/4 1/8 1 29 23/7 5/37 1 29 56/17 12/85 1 29 145/44 1/7 27 1 89/27 1/7 1 29 33/10 3/20 1 29 10/3 2/17 1 29 37/11 1/9 1 29 101/30 1/6 1 29 64/19 4/33 1 29 27/8 1/8 1 29 44/13 8/63 1 29 17/5 3/23 1 29 58/17 2/15 5 1 24/7 4/29 1 29 55/16 5/36 1 29 86/25 14/99 1 29 31/9 1/7 1 29 7/2 1/6 1 29 32/9 4/29 1 29 89/25 1/7 1 29 146/41 18/127 1 29 203/57 1/7 25 1 57/16 7/48 1 29 25/7 1/9 1 29 68/19 8/61 1 29 290/81 2/15 17 1 111/31 13/97 1 29 43/12 5/36 1 29 61/17 1/9 1 29 18/5 2/15 1 29 29/8 1/7 3 1 11/3 1/7 1 29 48/13 4/27 1 29 37/10 3/20 1 29 26/7 2/13 1 29 41/11 1/5 1 29 56/15 4/15 1 29 15/4 1/10 1 29 64/17 4/31 1 29 290/77 2/15 9 1 113/30 7/52 1 29 49/13 1/7 1 29 34/9 2/15 1 29 19/5 1/5 1 29 23/6 1/6 1 29 27/7 1/7 1 29 58/15 2/13 1 1 4/1 0/1 1 29 29/7 1/7 1 1 25/6 1/6 1 29 46/11 2/15 1 29 21/5 1/7 1 29 59/14 3/14 1 29 97/23 -1/3 1 29 232/55 0/1 23 1 38/9 2/17 1 29 17/4 1/6 1 29 30/7 2/7 1 29 116/27 0/1 25 1 43/10 1/16 1 29 13/3 1/7 1 29 35/8 1/4 1 29 92/21 0/1 1 29 57/13 5/39 1 29 79/18 3/22 1 29 22/5 2/13 1 29 31/7 1/7 1 29 9/2 1/6 1 29 41/9 1/7 1 29 32/7 4/25 1 29 87/19 1/6 11 1 55/12 1/6 1 29 23/5 3/17 1 29 60/13 8/39 1 29 97/21 9/41 1 29 37/8 1/4 1 29 51/11 -1/3 1 29 116/25 0/1 21 1 14/3 2/15 1 29 33/7 3/19 1 29 19/4 3/20 1 29 24/5 4/25 1 29 29/6 1/6 5 1 5/1 1/5 1 29 26/5 2/11 1 29 21/4 5/28 1 29 58/11 2/11 7 1 16/3 4/21 1 29 59/11 15/77 1 29 43/8 3/14 1 29 27/5 1/5 1 29 11/2 1/4 1 29 28/5 8/45 1 29 17/3 1/5 1 29 23/4 7/36 1 29 29/5 1/5 9 1 6/1 2/9 1 29 31/5 1/5 1 29 25/4 5/24 1 29 19/3 7/33 1 29 13/2 5/22 1 29 46/7 6/25 1 29 33/5 3/13 1 29 53/8 15/64 1 29 20/3 8/33 1 29 27/4 1/4 1 29 7/1 3/13 1 29 29/4 1/4 13 1 22/3 10/39 1 29 37/5 5/19 1 29 15/2 7/26 1 29 53/7 9/31 1 29 38/5 2/5 1 29 23/3 1/3 1 29 8/1 4/15 1 29 17/2 3/10 1 29 9/1 1/3 1 29 10/1 6/17 1 29 11/1 1/3 1 29 12/1 8/19 1 29 1/0 1/0 1 29 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(407,-870,109,-233) (2/1,15/7) -> (56/15,15/4) Glide Reflection Matrix(349,-754,81,-175) (15/7,13/6) -> (43/10,13/3) Glide Reflection Matrix(347,-754,133,-289) (13/6,11/5) -> (13/5,47/18) Glide Reflection Matrix(289,-638,53,-117) (11/5,31/14) -> (27/5,11/2) Hyperbolic Matrix(523,-1160,78,-173) (31/14,20/9) -> (20/3,27/4) Hyperbolic Matrix(521,-1160,234,-521) (20/9,29/13) -> (20/9,29/13) Reflection Matrix(233,-522,104,-233) (29/13,9/4) -> (29/13,9/4) Reflection Matrix(871,-1972,231,-523) (9/4,34/15) -> (49/13,34/9) Glide Reflection Matrix(3247,-7366,741,-1681) (34/15,59/26) -> (92/21,57/13) Glide Reflection Matrix(1277,-2900,358,-813) (59/26,25/11) -> (57/16,25/7) Glide Reflection Matrix(2551,-5800,1122,-2551) (25/11,116/51) -> (25/11,116/51) Reflection Matrix(3365,-7656,1479,-3365) (116/51,66/29) -> (116/51,66/29) Reflection Matrix(637,-1450,76,-173) (66/29,41/18) -> (8/1,17/2) Glide Reflection Matrix(2087,-4756,814,-1855) (41/18,57/25) -> (41/16,59/23) Glide Reflection Matrix(813,-1856,152,-347) (57/25,16/7) -> (16/3,59/11) Hyperbolic Matrix(405,-928,127,-291) (16/7,39/17) -> (19/6,16/5) Hyperbolic Matrix(581,-1334,152,-349) (39/17,23/10) -> (19/5,23/6) Glide Reflection Matrix(579,-1334,227,-523) (23/10,30/13) -> (28/11,23/9) Hyperbolic Matrix(1507,-3480,553,-1277) (30/13,37/16) -> (79/29,30/11) Hyperbolic Matrix(927,-2146,200,-463) (37/16,7/3) -> (37/8,51/11) Glide Reflection Matrix(173,-406,49,-115) (7/3,26/11) -> (7/2,32/9) Glide Reflection Matrix(1275,-3016,539,-1275) (26/11,116/49) -> (26/11,116/49) Reflection Matrix(4409,-10440,1862,-4409) (116/49,45/19) -> (116/49,45/19) Reflection Matrix(465,-1102,73,-173) (45/19,19/8) -> (19/3,13/2) Hyperbolic Matrix(463,-1102,171,-407) (19/8,31/13) -> (27/10,19/7) Hyperbolic Matrix(1045,-2494,194,-463) (31/13,43/18) -> (43/8,27/5) Hyperbolic Matrix(2087,-4988,582,-1391) (43/18,55/23) -> (43/12,61/17) Glide Reflection Matrix(4291,-10266,1139,-2725) (55/23,67/28) -> (113/30,49/13) Glide Reflection Matrix(3829,-9164,1406,-3365) (67/28,12/5) -> (49/18,128/47) Glide Reflection Matrix(289,-696,120,-289) (12/5,29/12) -> (12/5,29/12) Reflection Matrix(407,-986,168,-407) (29/12,17/7) -> (29/12,17/7) Reflection Matrix(1335,-3248,358,-871) (17/7,56/23) -> (41/11,56/15) Glide Reflection Matrix(3191,-7772,691,-1683) (56/23,39/16) -> (60/13,97/21) Glide Reflection Matrix(523,-1276,166,-405) (39/16,22/9) -> (22/7,19/6) Hyperbolic Matrix(521,-1276,118,-289) (22/9,27/11) -> (22/5,31/7) Glide Reflection Matrix(1509,-3712,424,-1043) (27/11,32/13) -> (32/9,89/25) Hyperbolic Matrix(117,-290,23,-57) (32/13,5/2) -> (5/1,26/5) Hyperbolic Matrix(755,-1914,114,-289) (5/2,33/13) -> (33/5,53/8) Hyperbolic Matrix(1393,-3538,502,-1275) (33/13,28/11) -> (86/31,25/9) Hyperbolic Matrix(521,-1334,91,-233) (23/9,41/16) -> (17/3,23/4) Hyperbolic Matrix(4001,-10266,949,-2435) (59/23,77/30) -> (59/14,97/23) Glide Reflection Matrix(2959,-7598,1129,-2899) (77/30,18/7) -> (76/29,97/37) Hyperbolic Matrix(811,-2088,315,-811) (18/7,116/45) -> (18/7,116/45) Reflection Matrix(4409,-11368,1710,-4409) (116/45,49/19) -> (116/45,49/19) Reflection Matrix(697,-1798,157,-405) (49/19,31/12) -> (31/7,9/2) Hyperbolic Matrix(987,-2552,292,-755) (31/12,44/17) -> (27/8,44/13) Glide Reflection Matrix(4929,-12760,1904,-4929) (44/17,145/56) -> (44/17,145/56) Reflection Matrix(11311,-29290,4368,-11311) (145/56,101/39) -> (145/56,101/39) Reflection Matrix(3247,-8410,605,-1567) (101/39,57/22) -> (59/11,43/8) Hyperbolic Matrix(291,-754,22,-57) (57/22,70/27) -> (12/1,1/0) Hyperbolic Matrix(581,-1508,89,-231) (70/27,13/5) -> (13/2,46/7) Hyperbolic Matrix(755,-1972,67,-175) (47/18,128/49) -> (11/1,12/1) Glide Reflection Matrix(14209,-37120,5439,-14209) (128/49,290/111) -> (128/49,290/111) Reflection Matrix(17981,-46980,6882,-17981) (290/111,81/31) -> (290/111,81/31) Reflection Matrix(3307,-8642,755,-1973) (81/31,34/13) -> (35/8,92/21) Glide Reflection Matrix(1219,-3190,355,-929) (34/13,55/21) -> (24/7,55/16) Glide Reflection Matrix(2147,-5626,598,-1567) (55/21,76/29) -> (61/17,18/5) Glide Reflection Matrix(2145,-5626,464,-1217) (97/37,21/8) -> (97/21,37/8) Glide Reflection Matrix(463,-1218,176,-463) (21/8,29/11) -> (21/8,29/11) Reflection Matrix(175,-464,66,-175) (29/11,8/3) -> (29/11,8/3) Reflection Matrix(173,-464,22,-59) (8/3,35/13) -> (23/3,8/1) Hyperbolic Matrix(581,-1566,151,-407) (35/13,27/10) -> (23/6,27/7) Glide Reflection Matrix(1217,-3306,448,-1217) (19/7,87/32) -> (19/7,87/32) Reflection Matrix(4351,-11832,1600,-4351) (87/32,68/25) -> (87/32,68/25) Reflection Matrix(405,-1102,43,-117) (68/25,49/18) -> (9/1,10/1) Hyperbolic Matrix(2321,-6322,554,-1509) (128/47,79/29) -> (46/11,21/5) Glide Reflection Matrix(233,-638,42,-115) (30/11,11/4) -> (11/2,28/5) Hyperbolic Matrix(463,-1276,168,-463) (11/4,58/21) -> (11/4,58/21) Reflection Matrix(755,-2088,273,-755) (58/21,36/13) -> (58/21,36/13) Reflection Matrix(523,-1450,167,-463) (36/13,61/22) -> (3/1,22/7) Hyperbolic Matrix(3597,-9976,1046,-2901) (61/22,86/31) -> (55/16,86/25) Glide Reflection Matrix(291,-812,62,-173) (25/9,14/5) -> (14/3,33/7) Hyperbolic Matrix(349,-986,103,-291) (14/5,17/6) -> (44/13,17/5) Glide Reflection Matrix(347,-986,82,-233) (17/6,20/7) -> (38/9,17/4) Hyperbolic Matrix(465,-1334,61,-175) (20/7,23/8) -> (38/5,23/3) Glide Reflection Matrix(463,-1334,101,-291) (23/8,3/1) -> (55/12,23/5) Hyperbolic Matrix(289,-928,90,-289) (16/5,29/9) -> (16/5,29/9) Reflection Matrix(233,-754,72,-233) (29/9,13/4) -> (29/9,13/4) Reflection Matrix(231,-754,53,-173) (13/4,23/7) -> (13/3,35/8) Glide Reflection Matrix(811,-2668,176,-579) (23/7,56/17) -> (23/5,60/13) Glide Reflection Matrix(4929,-16240,1496,-4929) (56/17,145/44) -> (56/17,145/44) Reflection Matrix(7831,-25810,2376,-7831) (145/44,89/27) -> (145/44,89/27) Reflection Matrix(985,-3248,158,-521) (89/27,33/10) -> (31/5,25/4) Glide Reflection Matrix(755,-2494,211,-697) (33/10,10/3) -> (25/7,68/19) Glide Reflection Matrix(639,-2146,173,-581) (10/3,37/11) -> (48/13,37/10) Glide Reflection Matrix(1275,-4292,172,-579) (37/11,101/30) -> (37/5,15/2) Glide Reflection Matrix(2205,-7424,586,-1973) (101/30,64/19) -> (15/4,64/17) Glide Reflection Matrix(637,-2146,103,-347) (64/19,27/8) -> (6/1,31/5) Glide Reflection Matrix(579,-1972,170,-579) (17/5,58/17) -> (17/5,58/17) Reflection Matrix(407,-1392,119,-407) (58/17,24/7) -> (58/17,24/7) Reflection Matrix(3539,-12180,994,-3421) (86/25,31/9) -> (89/25,146/41) Hyperbolic Matrix(117,-406,17,-59) (31/9,7/2) -> (27/4,7/1) Glide Reflection Matrix(16645,-59276,4674,-16645) (146/41,203/57) -> (146/41,203/57) Reflection Matrix(6497,-23142,1824,-6497) (203/57,57/16) -> (203/57,57/16) Reflection Matrix(5509,-19720,1539,-5509) (68/19,290/81) -> (68/19,290/81) Reflection Matrix(17981,-64380,5022,-17981) (290/81,111/31) -> (290/81,111/31) Reflection Matrix(1101,-3944,146,-523) (111/31,43/12) -> (15/2,53/7) Hyperbolic Matrix(289,-1044,80,-289) (18/5,29/8) -> (18/5,29/8) Reflection Matrix(175,-638,48,-175) (29/8,11/3) -> (29/8,11/3) Reflection Matrix(173,-638,16,-59) (11/3,48/13) -> (10/1,11/1) Hyperbolic Matrix(407,-1508,78,-289) (37/10,26/7) -> (26/5,21/4) Hyperbolic Matrix(639,-2378,140,-521) (26/7,41/11) -> (41/9,32/7) Hyperbolic Matrix(4929,-18560,1309,-4929) (64/17,290/77) -> (64/17,290/77) Reflection Matrix(17401,-65540,4620,-17401) (290/77,113/30) -> (290/77,113/30) Reflection Matrix(291,-1102,61,-231) (34/9,19/5) -> (19/4,24/5) Hyperbolic Matrix(811,-3132,210,-811) (27/7,58/15) -> (27/7,58/15) Reflection Matrix(59,-232,15,-59) (58/15,4/1) -> (58/15,4/1) Reflection Matrix(57,-232,14,-57) (4/1,29/7) -> (4/1,29/7) Reflection Matrix(349,-1450,84,-349) (29/7,25/6) -> (29/7,25/6) Reflection Matrix(639,-2668,97,-405) (25/6,46/11) -> (46/7,33/5) Hyperbolic Matrix(1391,-5858,317,-1335) (21/5,59/14) -> (57/13,79/18) Hyperbolic Matrix(10671,-45008,2530,-10671) (97/23,232/55) -> (97/23,232/55) Reflection Matrix(2089,-8816,495,-2089) (232/55,38/9) -> (232/55,38/9) Reflection Matrix(231,-986,41,-175) (17/4,30/7) -> (28/5,17/3) Hyperbolic Matrix(811,-3480,189,-811) (30/7,116/27) -> (30/7,116/27) Reflection Matrix(2321,-9976,540,-2321) (116/27,43/10) -> (116/27,43/10) Reflection Matrix(581,-2552,79,-347) (79/18,22/5) -> (22/3,37/5) Hyperbolic Matrix(115,-522,13,-59) (9/2,41/9) -> (17/2,9/1) Hyperbolic Matrix(1217,-5568,266,-1217) (32/7,87/19) -> (32/7,87/19) Reflection Matrix(2089,-9570,456,-2089) (87/19,55/12) -> (87/19,55/12) Reflection Matrix(2551,-11832,550,-2551) (51/11,116/25) -> (51/11,116/25) Reflection Matrix(349,-1624,75,-349) (116/25,14/3) -> (116/25,14/3) Reflection Matrix(233,-1102,37,-175) (33/7,19/4) -> (25/4,19/3) Glide Reflection Matrix(289,-1392,60,-289) (24/5,29/6) -> (24/5,29/6) Reflection Matrix(59,-290,12,-59) (29/6,5/1) -> (29/6,5/1) Reflection Matrix(463,-2436,88,-463) (21/4,58/11) -> (21/4,58/11) Reflection Matrix(175,-928,33,-175) (58/11,16/3) -> (58/11,16/3) Reflection Matrix(231,-1334,40,-231) (23/4,29/5) -> (23/4,29/5) Reflection Matrix(59,-348,10,-59) (29/5,6/1) -> (29/5,6/1) Reflection Matrix(463,-3074,61,-405) (53/8,20/3) -> (53/7,38/5) Glide Reflection Matrix(57,-406,8,-57) (7/1,29/4) -> (7/1,29/4) Reflection Matrix(175,-1276,24,-175) (29/4,22/3) -> (29/4,22/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,27,-1) (0/1,2/1) -> (0/1,2/27) Matrix(407,-870,109,-233) -> Matrix(25,-2,87,-7) Matrix(349,-754,81,-175) -> Matrix(25,-2,237,-19) Matrix(347,-754,133,-289) -> Matrix(173,-14,1767,-143) Matrix(289,-638,53,-117) -> Matrix(73,-6,353,-29) Matrix(523,-1160,78,-173) -> Matrix(97,-8,376,-31) Matrix(521,-1160,234,-521) -> Matrix(385,-32,4632,-385) (20/9,29/13) -> (16/193,1/12) Matrix(233,-522,104,-233) -> Matrix(167,-14,1992,-167) (29/13,9/4) -> (1/12,7/83) Matrix(871,-1972,231,-523) -> Matrix(47,-4,317,-27) Matrix(3247,-7366,741,-1681) -> Matrix(71,-6,627,-53) Matrix(1277,-2900,358,-813) -> Matrix(47,-4,270,-23) Matrix(2551,-5800,1122,-2551) -> Matrix(1223,-104,14382,-1223) (25/11,116/51) -> (13/153,4/47) Matrix(3365,-7656,1479,-3365) -> Matrix(1597,-136,18753,-1597) (116/51,66/29) -> (4/47,34/399) Matrix(637,-1450,76,-173) -> Matrix(305,-26,1044,-89) Matrix(2087,-4756,814,-1855) -> Matrix(47,-4,552,-47) *** -> (1/12,2/23) Matrix(813,-1856,152,-347) -> Matrix(93,-8,500,-43) Matrix(405,-928,127,-291) -> Matrix(93,-8,779,-67) Matrix(581,-1334,152,-349) -> Matrix(23,-2,126,-11) Matrix(579,-1334,227,-523) -> Matrix(163,-14,1665,-143) Matrix(1507,-3480,553,-1277) -> Matrix(463,-40,4549,-393) Matrix(927,-2146,200,-463) -> Matrix(23,-2,-12,1) Matrix(173,-406,49,-115) -> Matrix(23,-2,195,-17) Matrix(1275,-3016,539,-1275) -> Matrix(451,-40,5085,-451) (26/11,116/49) -> (10/113,4/45) Matrix(4409,-10440,1862,-4409) -> Matrix(1529,-136,17190,-1529) (116/49,45/19) -> (4/45,17/191) Matrix(465,-1102,73,-173) -> Matrix(157,-14,729,-65) Matrix(463,-1102,171,-407) -> Matrix(67,-6,659,-59) Matrix(1045,-2494,194,-463) -> Matrix(23,-2,104,-9) Matrix(2087,-4988,582,-1391) -> Matrix(45,-4,326,-29) Matrix(4291,-10266,1139,-2725) -> Matrix(157,-14,1155,-103) Matrix(3829,-9164,1406,-3365) -> Matrix(403,-36,3974,-355) Matrix(289,-696,120,-289) -> Matrix(177,-16,1958,-177) (12/5,29/12) -> (8/89,1/11) Matrix(407,-986,168,-407) -> Matrix(241,-22,2640,-241) (29/12,17/7) -> (1/11,11/120) Matrix(1335,-3248,358,-871) -> Matrix(87,-8,424,-39) Matrix(3191,-7772,691,-1683) -> Matrix(217,-20,1009,-93) Matrix(523,-1276,166,-405) -> Matrix(43,-4,398,-37) Matrix(521,-1276,118,-289) -> Matrix(43,-4,290,-27) Matrix(1509,-3712,424,-1043) -> Matrix(87,-8,620,-57) Matrix(117,-290,23,-57) -> Matrix(21,-2,137,-13) Matrix(755,-1914,114,-289) -> Matrix(187,-18,800,-77) Matrix(1393,-3538,502,-1275) -> Matrix(353,-34,3312,-319) Matrix(521,-1334,91,-233) -> Matrix(19,-2,105,-11) Matrix(4001,-10266,949,-2435) -> Matrix(21,-2,73,-7) Matrix(2959,-7598,1129,-2899) -> Matrix(227,-22,2301,-223) Matrix(811,-2088,315,-811) -> Matrix(83,-8,861,-83) (18/7,116/45) -> (2/21,4/41) Matrix(4409,-11368,1710,-4409) -> Matrix(409,-40,4182,-409) (116/45,49/19) -> (4/41,5/51) Matrix(697,-1798,157,-405) -> Matrix(61,-6,417,-41) Matrix(987,-2552,292,-755) -> Matrix(1,0,18,-1) *** -> (0/1,1/9) Matrix(4929,-12760,1904,-4929) -> Matrix(161,-16,1620,-161) (44/17,145/56) -> (8/81,1/10) Matrix(11311,-29290,4368,-11311) -> Matrix(259,-26,2580,-259) (145/56,101/39) -> (1/10,13/129) Matrix(3247,-8410,605,-1567) -> Matrix(99,-10,505,-51) Matrix(291,-754,22,-57) -> Matrix(19,-2,48,-5) Matrix(581,-1508,89,-231) -> Matrix(43,-4,183,-17) Matrix(755,-1972,67,-175) -> Matrix(285,-28,743,-73) Matrix(14209,-37120,5439,-14209) -> Matrix(3173,-312,32269,-3173) (128/49,290/111) -> (52/529,6/61) Matrix(17981,-46980,6882,-17981) -> Matrix(3781,-372,38430,-3781) (290/111,81/31) -> (6/61,31/315) Matrix(3307,-8642,755,-1973) -> Matrix(61,-6,559,-55) Matrix(1219,-3190,355,-929) -> Matrix(101,-10,717,-71) Matrix(2147,-5626,598,-1567) -> Matrix(61,-6,498,-49) Matrix(2145,-5626,464,-1217) -> Matrix(101,-10,414,-41) Matrix(463,-1218,176,-463) -> Matrix(221,-22,2220,-221) (21/8,29/11) -> (11/111,1/10) Matrix(175,-464,66,-175) -> Matrix(79,-8,780,-79) (29/11,8/3) -> (1/10,4/39) Matrix(173,-464,22,-59) -> Matrix(1,0,-6,1) 0/1 Matrix(581,-1566,151,-407) -> Matrix(19,-2,123,-13) Matrix(1217,-3306,448,-1217) -> Matrix(21,-2,220,-21) (19/7,87/32) -> (1/11,1/10) Matrix(4351,-11832,1600,-4351) -> Matrix(319,-32,3180,-319) (87/32,68/25) -> (1/10,16/159) Matrix(405,-1102,43,-117) -> Matrix(99,-10,307,-31) Matrix(2321,-6322,554,-1509) -> Matrix(59,-6,344,-35) Matrix(233,-638,42,-115) -> Matrix(19,-2,124,-13) Matrix(463,-1276,168,-463) -> Matrix(191,-20,1824,-191) (11/4,58/21) -> (5/48,2/19) Matrix(755,-2088,273,-755) -> Matrix(303,-32,2869,-303) (58/21,36/13) -> (2/19,16/151) Matrix(523,-1450,167,-463) -> Matrix(19,-2,105,-11) Matrix(3597,-9976,1046,-2901) -> Matrix(301,-32,2154,-229) Matrix(291,-812,62,-173) -> Matrix(37,-4,250,-27) Matrix(349,-986,103,-291) -> Matrix(17,-2,127,-15) Matrix(347,-986,82,-233) -> Matrix(19,-2,124,-13) Matrix(465,-1334,61,-175) -> Matrix(19,-2,85,-9) Matrix(463,-1334,101,-291) -> Matrix(55,-6,321,-35) Matrix(289,-928,90,-289) -> Matrix(65,-8,528,-65) (16/5,29/9) -> (4/33,1/8) Matrix(233,-754,72,-233) -> Matrix(47,-6,368,-47) (29/9,13/4) -> (1/8,3/23) Matrix(231,-754,53,-173) -> Matrix(15,-2,97,-13) Matrix(811,-2668,176,-579) -> Matrix(29,-4,152,-21) Matrix(4929,-16240,1496,-4929) -> Matrix(169,-24,1190,-169) (56/17,145/44) -> (12/85,1/7) Matrix(7831,-25810,2376,-7831) -> Matrix(209,-30,1456,-209) (145/44,89/27) -> (1/7,15/104) Matrix(985,-3248,158,-521) -> Matrix(55,-8,268,-39) Matrix(755,-2494,211,-697) -> Matrix(13,-2,97,-15) Matrix(639,-2146,173,-581) -> Matrix(15,-2,97,-13) Matrix(1275,-4292,172,-579) -> Matrix(31,-4,116,-15) Matrix(2205,-7424,586,-1973) -> Matrix(1,0,16,-1) *** -> (0/1,1/8) Matrix(637,-2146,103,-347) -> Matrix(17,-2,93,-11) Matrix(579,-1972,170,-579) -> Matrix(91,-12,690,-91) (17/5,58/17) -> (3/23,2/15) Matrix(407,-1392,119,-407) -> Matrix(59,-8,435,-59) (58/17,24/7) -> (2/15,4/29) Matrix(3539,-12180,994,-3421) -> Matrix(27,-4,196,-29) 1/7 Matrix(117,-406,17,-59) -> Matrix(15,-2,67,-9) Matrix(16645,-59276,4674,-16645) -> Matrix(253,-36,1778,-253) (146/41,203/57) -> (18/127,1/7) Matrix(6497,-23142,1824,-6497) -> Matrix(97,-14,672,-97) (203/57,57/16) -> (1/7,7/48) Matrix(5509,-19720,1539,-5509) -> Matrix(121,-16,915,-121) (68/19,290/81) -> (8/61,2/15) Matrix(17981,-64380,5022,-17981) -> Matrix(389,-52,2910,-389) (290/81,111/31) -> (2/15,13/97) Matrix(1101,-3944,146,-523) -> Matrix(59,-8,214,-29) Matrix(289,-1044,80,-289) -> Matrix(29,-4,210,-29) (18/5,29/8) -> (2/15,1/7) Matrix(175,-638,48,-175) -> Matrix(13,-2,84,-13) (29/8,11/3) -> (1/7,1/6) Matrix(173,-638,16,-59) -> Matrix(15,-2,38,-5) Matrix(407,-1508,78,-289) -> Matrix(25,-4,144,-23) 1/6 Matrix(639,-2378,140,-521) -> Matrix(11,-2,72,-13) 1/6 Matrix(4929,-18560,1309,-4929) -> Matrix(61,-8,465,-61) (64/17,290/77) -> (4/31,2/15) Matrix(17401,-65540,4620,-17401) -> Matrix(209,-28,1560,-209) (290/77,113/30) -> (2/15,7/52) Matrix(291,-1102,61,-231) -> Matrix(13,-2,85,-13) (0/1,2/13).(1/7,1/6) Matrix(811,-3132,210,-811) -> Matrix(27,-4,182,-27) (27/7,58/15) -> (1/7,2/13) Matrix(59,-232,15,-59) -> Matrix(1,0,13,-1) (58/15,4/1) -> (0/1,2/13) Matrix(57,-232,14,-57) -> Matrix(1,0,14,-1) (4/1,29/7) -> (0/1,1/7) Matrix(349,-1450,84,-349) -> Matrix(13,-2,84,-13) (29/7,25/6) -> (1/7,1/6) Matrix(639,-2668,97,-405) -> Matrix(27,-4,115,-17) Matrix(1391,-5858,317,-1335) -> Matrix(11,-2,83,-15) Matrix(10671,-45008,2530,-10671) -> Matrix(-1,0,6,1) (97/23,232/55) -> (-1/3,0/1) Matrix(2089,-8816,495,-2089) -> Matrix(1,0,17,-1) (232/55,38/9) -> (0/1,2/17) Matrix(231,-986,41,-175) -> Matrix(11,-2,61,-11) (0/1,2/11).(1/6,1/5) Matrix(811,-3480,189,-811) -> Matrix(1,0,7,-1) (30/7,116/27) -> (0/1,2/7) Matrix(2321,-9976,540,-2321) -> Matrix(1,0,32,-1) (116/27,43/10) -> (0/1,1/16) Matrix(581,-2552,79,-347) -> Matrix(57,-8,221,-31) Matrix(115,-522,13,-59) -> Matrix(11,-2,39,-7) Matrix(1217,-5568,266,-1217) -> Matrix(49,-8,300,-49) (32/7,87/19) -> (4/25,1/6) Matrix(2089,-9570,456,-2089) -> Matrix(83,-14,492,-83) (87/19,55/12) -> (1/6,7/41) Matrix(2551,-11832,550,-2551) -> Matrix(-1,0,6,1) (51/11,116/25) -> (-1/3,0/1) Matrix(349,-1624,75,-349) -> Matrix(1,0,15,-1) (116/25,14/3) -> (0/1,2/15) Matrix(233,-1102,37,-175) -> Matrix(11,-2,49,-9) Matrix(289,-1392,60,-289) -> Matrix(49,-8,300,-49) (24/5,29/6) -> (4/25,1/6) Matrix(59,-290,12,-59) -> Matrix(11,-2,60,-11) (29/6,5/1) -> (1/6,1/5) Matrix(463,-2436,88,-463) -> Matrix(111,-20,616,-111) (21/4,58/11) -> (5/28,2/11) Matrix(175,-928,33,-175) -> Matrix(43,-8,231,-43) (58/11,16/3) -> (2/11,4/21) Matrix(231,-1334,40,-231) -> Matrix(71,-14,360,-71) (23/4,29/5) -> (7/36,1/5) Matrix(59,-348,10,-59) -> Matrix(19,-4,90,-19) (29/5,6/1) -> (1/5,2/9) Matrix(463,-3074,61,-405) -> Matrix(25,-6,79,-19) Matrix(57,-406,8,-57) -> Matrix(25,-6,104,-25) (7/1,29/4) -> (3/13,1/4) Matrix(175,-1276,24,-175) -> Matrix(79,-20,312,-79) (29/4,22/3) -> (1/4,10/39) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.