INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -8/17 -7/16 -2/5 -5/14 -4/13 -1/4 -2/11 0/1 1/8 1/5 5/22 2/7 4/11 5/13 8/19 1/2 10/17 8/13 7/11 11/16 5/7 4/5 1/1 8/7 5/4 47/34 7/5 16/11 3/2 11/7 50/31 13/8 17/10 35/19 2/1 37/17 56/25 113/49 19/8 17/7 5/2 136/53 13/5 137/52 79/29 11/4 119/43 20/7 3/1 41/13 16/5 55/17 10/3 7/2 11/3 85/23 19/5 107/28 4/1 17/4 73/17 13/3 22/5 9/2 37/8 14/3 19/4 67/14 5/1 68/13 21/4 16/3 11/2 17/3 23/4 6/1 19/3 13/2 20/3 47/7 7/1 15/2 23/3 8/1 17/2 26/3 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/52 -8/17 1/49 -7/15 3/146 5/243 -13/28 5/242 -6/13 6/289 1/48 -11/24 1/48 -5/11 2/95 -14/31 4/189 5/236 -9/20 9/424 -13/29 1/47 13/610 -17/38 5/234 -4/9 3/140 2/93 -15/34 7/324 -26/59 3/139 -11/25 3/139 1/46 -18/41 11/508 6/277 -7/16 1/46 -24/55 17/780 8/367 -17/39 11/504 5/229 -10/23 1/46 4/183 -13/30 5/228 -3/7 3/136 1/45 -14/33 8/359 7/314 -25/59 5/224 19/851 -11/26 3/134 -19/45 1/45 3/134 -8/19 3/134 2/89 -13/31 2/89 -5/12 1/44 -17/41 6/265 -12/29 12/529 1/44 -7/17 1/44 7/307 -9/22 1/44 -11/27 3/131 5/218 -13/32 7/304 -2/5 1/43 -13/33 1/43 3/128 -11/28 5/212 -9/23 1/43 1/42 -7/18 7/296 -19/49 6/253 -12/31 12/505 1/42 -5/13 1/42 5/209 -18/47 9/374 2/83 -13/34 1/42 -34/89 1/42 2/83 -21/55 3/124 1/41 -8/21 0/1 1/42 -11/29 2/83 -3/8 3/124 -13/35 1/41 13/532 -23/62 7/286 -10/27 5/204 4/163 -17/46 11/448 -7/19 2/81 -18/49 4/161 1/40 -11/30 1/40 -26/71 1/41 -15/41 1/41 3/122 -19/52 3/122 -4/11 2/81 1/40 -13/36 7/284 -22/61 7/283 -9/25 3/121 7/282 -14/39 4/161 9/362 -5/14 1/40 -16/45 6/239 11/438 -11/31 1/40 3/119 -6/17 2/79 3/118 -7/20 1/40 -1/3 1/39 1/38 -6/19 0/1 1/38 -5/16 5/188 -9/29 5/187 3/112 -4/13 1/37 -15/49 11/405 5/184 -11/36 5/184 -7/23 1/37 3/110 -17/56 3/110 -27/89 11/402 13/475 -10/33 2/73 9/328 -13/43 4/145 -3/10 1/36 -17/57 1/38 1/37 -14/47 1/37 -11/37 1/37 3/110 -19/64 1/36 -8/27 0/1 1/38 -21/71 11/408 1/37 -13/44 9/332 -5/17 2/73 -12/41 3/110 2/73 -19/65 5/182 13/473 -7/24 1/36 -16/55 5/181 -9/31 9/325 1/36 -2/7 1/36 2/71 -7/25 0/1 -5/18 1/36 -18/65 12/433 1/36 -13/47 1/36 11/395 -34/123 20/717 13/466 -55/199 6/215 -21/76 21/752 -8/29 3/107 -11/40 7/248 -14/51 1/36 2/71 -3/11 3/106 1/35 -7/26 7/244 -18/67 13/452 4/139 -11/41 4/139 -4/15 2/69 1/34 -5/19 1/34 3/101 -6/23 0/1 1/32 -13/50 1/40 -7/27 1/37 1/36 -1/4 1/34 -6/25 0/1 1/30 -11/46 1/40 -5/21 1/35 1/34 -4/17 1/34 4/135 -3/13 3/100 1/33 -5/22 5/164 -7/31 2/65 -9/40 7/228 -2/9 2/65 1/32 -5/23 0/1 -3/14 3/100 -10/47 2/65 1/32 -7/33 1/33 3/98 -4/19 1/33 -9/43 1/33 1/32 -14/67 3/98 2/65 -19/91 2/65 -5/24 1/32 -6/29 6/193 1/32 -1/5 1/32 1/31 -4/21 4/129 1/32 -3/16 1/32 -5/27 1/32 3/95 -2/11 1/31 -7/39 3/92 5/153 -5/28 5/152 -3/17 1/30 1/29 -13/74 1/28 -10/57 0/1 1/32 -7/40 1/30 -4/23 4/121 1/30 -5/29 2/59 -1/6 1/32 -4/25 1/31 -3/19 3/91 1/30 -2/13 1/30 2/59 -5/33 1/30 1/29 -3/20 1/28 -1/7 0/1 -2/15 0/1 1/30 -3/23 3/88 1/29 -1/8 1/28 -2/17 1/27 -3/26 1/20 -4/35 0/1 1/40 -1/9 1/30 1/29 -1/10 1/28 0/1 0/1 1/26 1/9 1/25 1/24 2/17 0/1 1/26 1/8 1/24 1/7 1/23 1/22 2/13 1/25 1/6 1/24 2/11 0/1 1/22 5/27 3/64 1/21 3/16 1/24 4/21 4/89 1/22 1/5 0/1 5/24 5/116 4/19 3/68 2/45 7/33 1/22 1/21 3/14 1/24 2/9 2/45 1/22 5/22 1/22 8/35 1/22 8/175 3/13 1/22 3/65 4/17 1/21 1/4 1/20 4/15 1/22 4/87 11/41 5/106 1/21 7/26 1/22 3/11 1/23 1/22 5/18 5/108 2/7 1/21 7/24 7/144 19/65 2/41 12/41 3/62 2/41 17/58 3/62 5/17 3/61 1/20 8/27 2/41 5/102 19/64 11/224 11/37 4/81 3/10 1/20 4/13 1/20 4/79 5/16 1/18 6/19 0/1 1/14 1/3 1/21 1/20 5/14 1/20 9/25 1/20 1/19 13/36 9/176 4/11 1/19 19/52 1/20 15/41 1/19 1/18 11/30 1/20 7/19 3/58 1/19 3/8 3/56 11/29 1/18 1/17 19/50 1/18 27/71 1/21 1/20 8/21 1/18 2/35 21/55 3/49 1/16 34/89 1/15 13/34 1/16 5/13 0/1 7/18 1/20 16/41 1/21 25/64 1/24 9/23 3/64 1/21 2/5 1/20 2/39 7/17 2/39 5/12 5/96 8/19 1/19 11/26 11/208 3/7 1/19 3/56 13/30 11/204 10/23 3/55 27/62 7/128 17/39 7/127 1/18 7/16 1/20 4/9 4/73 1/18 5/11 1/18 1/17 6/13 0/1 1/22 7/15 1/21 1/20 8/17 3/58 4/77 1/2 1/18 7/13 1/16 1/15 6/11 0/1 1/20 17/31 2/37 28/51 6/109 1/18 11/20 1/16 5/9 3/55 1/18 19/34 19/340 33/59 7/125 27/482 14/25 5/89 37/66 25/444 23/41 7/124 3/53 9/16 5/88 13/23 2/35 4/7 1/18 2/35 11/19 4/69 7/12 7/120 10/17 1/17 13/22 13/220 3/5 1/17 3/50 11/18 7/116 19/31 9/148 7/115 27/44 1/16 35/57 7/115 5/82 8/13 3/49 37/60 31/504 29/47 17/276 13/211 21/34 21/340 13/21 11/177 1/16 5/8 1/16 17/27 1/16 5/79 46/73 13/202 2/31 75/119 9/139 7/108 29/46 3/46 41/65 7/106 1/15 12/19 0/1 1/16 31/49 1/15 5/74 50/79 1/15 19/30 1/16 7/11 0/1 16/25 2/37 1/18 9/14 3/52 20/31 1/17 31/48 1/16 11/17 1/18 1/17 2/3 2/33 1/16 11/16 1/16 20/29 1/16 20/319 9/13 1/16 9/143 16/23 5/79 7/10 1/16 12/17 2/31 3/46 29/41 3/47 5/78 17/24 1/16 22/31 5/78 2/31 5/7 2/31 23/32 23/352 18/25 4/61 13/198 31/43 5/76 1/15 44/61 1/15 13/18 9/136 8/11 0/1 1/14 27/37 1/16 1/15 46/63 0/1 1/14 19/26 1/16 11/15 3/46 1/15 14/19 1/15 3/4 1/16 10/13 9/140 2/31 17/22 3/46 41/53 3/46 1/15 24/31 2/31 3/46 7/9 3/46 1/15 18/23 14/215 3/46 47/60 47/720 29/37 10/153 11/14 5/76 4/5 1/15 13/16 3/44 48/59 5/74 4/59 35/43 4/59 22/27 13/192 4/59 53/65 23/339 19/280 31/38 11/162 9/11 3/44 5/73 23/28 1/14 60/73 3/46 4/61 37/45 1/15 9/134 14/17 4/59 3/44 19/23 2/29 24/29 7/102 2/29 5/6 5/72 6/7 0/1 1/14 13/15 1/15 1/14 7/8 1/14 1/1 1/14 1/13 10/9 3/38 8/101 9/8 1/12 8/7 1/13 15/13 1/13 3/38 22/19 3/38 2/25 7/6 1/12 20/17 6/73 1/12 13/11 0/1 6/5 3/38 2/25 23/19 8/99 17/14 13/160 11/9 3/37 1/12 5/4 1/12 19/15 1/12 7/83 52/41 7/83 33/26 23/272 47/37 16/189 14/11 9/106 4/47 9/7 7/82 3/35 31/24 31/360 22/17 7/81 35/27 11/127 13/150 13/10 7/80 30/23 2/23 3/34 17/13 2/23 4/3 1/12 2/23 23/17 5/57 3/34 19/14 3/34 15/11 3/34 1/11 26/19 1/11 63/46 17/184 37/27 3/32 5/53 11/8 1/12 29/21 3/37 1/12 47/34 1/12 65/47 1/12 11/131 18/13 1/12 4/47 43/31 1/12 1/11 25/18 9/104 57/41 1/12 1/11 32/23 2/23 3/34 7/5 2/23 38/27 29/330 8/91 69/49 19/216 49/557 31/22 31/352 55/39 53/601 3/34 79/56 3/34 24/17 3/34 22/249 41/29 3/34 7/79 17/12 11/124 27/19 3/34 1/11 37/26 5/56 47/33 3/34 1/11 10/7 4/45 5/56 33/23 7/78 15/167 23/16 7/78 13/9 13/144 1/11 16/11 1/11 19/13 1/11 19/208 3/2 3/32 20/13 1/11 17/11 3/34 1/11 31/20 5/54 45/29 7/75 3/32 14/9 3/32 2/21 11/7 2/21 30/19 5/52 8/83 79/50 1/10 49/31 3/31 1/10 19/12 7/72 46/29 1/11 73/46 13/136 100/63 2/21 1/10 27/17 5/52 3/31 8/5 0/1 1/10 29/18 1/12 50/31 1/11 71/44 7/76 21/13 1/11 3/32 55/34 3/32 89/55 2/21 34/21 2/21 1/10 81/50 5/52 47/29 3/32 5/53 13/8 1/10 57/35 1/11 9/98 101/62 23/248 44/27 10/107 3/32 31/19 3/32 5/53 49/30 19/200 67/41 2/21 18/11 2/21 9/94 23/14 5/52 5/3 5/51 1/10 17/10 1/10 29/17 1/10 29/289 12/7 1/10 12/119 31/18 17/168 81/47 23/227 15/148 50/29 22/217 29/286 19/11 6/59 45/26 9/88 26/15 1/10 6/59 7/4 7/68 16/9 0/1 1/10 57/32 7/68 41/23 5/48 7/67 25/14 1/10 59/33 1/10 1/9 93/52 5/48 34/19 1/10 2/19 43/24 3/28 52/29 1/9 9/5 1/10 1/9 11/6 5/48 35/19 2/19 59/32 27/256 24/13 2/19 11/104 13/7 3/28 1/9 15/8 1/8 17/9 1/10 1/9 2/1 1/9 13/6 7/60 37/17 2/17 61/28 33/280 24/11 2/17 13/110 11/5 5/42 3/25 20/9 3/26 2/17 29/13 2/17 38/17 2/17 5/42 47/21 5/42 3/25 56/25 3/25 9/4 1/8 25/11 2/17 16/7 2/17 1/8 55/24 23/192 94/41 3/25 39/17 3/25 19/158 101/44 13/108 62/27 24/199 7/58 23/10 7/58 53/23 15/124 19/157 83/36 63/520 113/49 4/33 30/13 4/33 25/206 7/3 7/57 1/8 19/8 1/8 31/13 1/8 31/247 12/5 1/8 12/95 29/12 1/8 46/19 8/63 15/118 17/7 6/47 56/23 26/203 31/242 39/16 39/304 61/25 37/288 23/179 22/9 17/132 4/31 5/2 1/8 28/11 1/7 23/9 1/8 5/39 41/16 7/54 59/23 31/238 3/23 136/53 3/23 77/30 47/360 18/7 8/61 5/38 31/12 19/144 13/5 2/15 34/13 16/119 7/52 89/34 17/126 55/21 5/37 13/96 21/8 7/52 92/35 8/59 3/22 71/27 5/37 13/96 192/73 77/568 8/59 121/46 51/376 50/19 11/81 79/30 49/360 108/41 62/455 3/22 137/52 3/22 29/11 3/22 13/95 8/3 2/15 3/22 27/10 5/36 73/27 7/50 15/107 46/17 1/7 19/7 3/22 1/7 49/18 1/8 79/29 2/15 109/40 7/52 30/11 2/15 3/22 41/15 5/37 3/22 93/34 11/80 52/19 5/36 6/43 11/4 3/22 47/17 11/80 15/109 83/30 43/312 119/43 4/29 155/56 85/616 36/13 4/29 21/152 25/9 19/137 5/36 39/14 39/280 53/19 6/43 120/43 6/43 31/222 67/24 19/136 14/5 7/50 8/57 17/6 17/120 20/7 1/7 23/8 23/160 3/1 1/7 3/20 22/7 15/98 2/13 41/13 2/13 19/6 13/84 16/5 3/19 29/9 1/7 1/6 42/13 2/13 1/6 55/17 2/13 68/21 20/129 9/58 13/4 5/32 23/7 4/25 33/10 3/20 10/3 4/25 1/6 37/11 4/25 27/8 7/44 44/13 5/31 105/31 5/31 1/6 166/49 4/25 1/6 61/18 9/56 17/5 5/31 11/68 7/2 1/6 25/7 9/53 17/100 118/33 97/570 8/47 211/59 8/47 93/26 79/464 68/19 23/135 43/12 43/252 190/53 7/41 147/41 7/41 139/814 104/29 55/322 48/281 61/17 20/117 18/5 6/35 11/64 47/13 4/23 29/8 9/52 11/3 1/6 3/17 48/13 9/52 4/23 85/23 4/23 122/33 4/23 23/132 37/10 7/40 26/7 3/17 67/18 1/4 108/29 6/37 1/6 41/11 1/6 7/41 56/15 14/81 9/52 127/34 59/340 71/19 4/23 15/4 7/40 19/5 2/11 42/11 1/6 2/11 107/28 1/6 172/45 1/6 4/23 65/17 1/6 3/17 23/6 5/28 27/7 13/73 5/28 4/1 2/11 3/16 21/5 5/26 1/5 17/4 5/26 30/7 7/36 22/113 103/24 39/200 73/17 8/41 43/10 43/220 13/3 13/66 1/5 22/5 1/5 31/7 1/5 31/154 9/2 9/44 23/5 1/5 3/14 37/8 5/24 51/11 1/5 3/14 14/3 5/24 4/19 33/7 3/14 5/23 19/4 11/52 43/9 25/117 3/14 67/14 3/14 91/19 3/14 53/247 24/5 3/14 14/65 29/6 7/32 5/1 2/9 26/5 8/35 11/48 47/9 29/126 3/13 68/13 3/13 21/4 13/56 37/7 3/13 1/4 16/3 7/30 4/17 43/8 9/38 27/5 3/13 1/4 11/2 1/4 17/3 17/69 1/4 23/4 1/4 29/5 1/4 29/115 6/1 1/4 6/23 19/3 13/48 3/11 13/2 5/18 20/3 17/60 2/7 47/7 2/7 74/11 2/7 63/220 27/4 23/80 7/1 5/17 3/10 15/2 5/16 23/3 7/22 1/3 8/1 1/3 17/2 7/20 26/3 5/14 14/39 9/1 7/19 3/8 10/1 2/5 9/22 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(1123,530,820,387) (-1/2,-8/17) -> (26/19,63/46) Hyperbolic Matrix(1931,906,714,335) (-8/17,-7/15) -> (73/27,46/17) Hyperbolic Matrix(1011,470,-3332,-1549) (-7/15,-13/28) -> (-17/56,-27/89) Hyperbolic Matrix(2109,976,806,373) (-13/28,-6/13) -> (34/13,89/34) Hyperbolic Matrix(497,228,-1794,-823) (-6/13,-11/24) -> (-5/18,-18/65) Hyperbolic Matrix(297,136,998,457) (-11/24,-5/11) -> (11/37,3/10) Hyperbolic Matrix(593,268,1082,489) (-5/11,-14/31) -> (6/11,17/31) Hyperbolic Matrix(293,132,-1374,-619) (-14/31,-9/20) -> (-3/14,-10/47) Hyperbolic Matrix(881,396,198,89) (-9/20,-13/29) -> (31/7,9/2) Hyperbolic Matrix(2543,1138,1562,699) (-13/29,-17/38) -> (13/8,57/35) Hyperbolic Matrix(1851,826,1172,523) (-17/38,-4/9) -> (30/19,79/50) Hyperbolic Matrix(675,298,-2512,-1109) (-4/9,-15/34) -> (-7/26,-18/67) Hyperbolic Matrix(1933,852,4440,1957) (-15/34,-26/59) -> (10/23,27/62) Hyperbolic Matrix(1353,596,-4538,-1999) (-26/59,-11/25) -> (-17/57,-14/47) Hyperbolic Matrix(387,170,1828,803) (-11/25,-18/41) -> (4/19,7/33) Hyperbolic Matrix(671,294,-1536,-673) (-18/41,-7/16) -> (-7/16,-24/55) Parabolic Matrix(4213,1838,1726,753) (-24/55,-17/39) -> (61/25,22/9) Hyperbolic Matrix(193,84,1050,457) (-17/39,-10/23) -> (2/11,5/27) Hyperbolic Matrix(1815,788,1048,455) (-10/23,-13/30) -> (45/26,26/15) Hyperbolic Matrix(759,328,1238,535) (-13/30,-3/7) -> (19/31,27/44) Hyperbolic Matrix(749,318,-2532,-1075) (-3/7,-14/33) -> (-8/27,-21/71) Hyperbolic Matrix(2435,1032,-8808,-3733) (-14/33,-25/59) -> (-13/47,-34/123) Hyperbolic Matrix(2063,874,2528,1071) (-25/59,-11/26) -> (31/38,9/11) Hyperbolic Matrix(653,276,750,317) (-11/26,-19/45) -> (13/15,7/8) Hyperbolic Matrix(185,78,-1212,-511) (-19/45,-8/19) -> (-2/13,-5/33) Hyperbolic Matrix(371,156,654,275) (-8/19,-13/31) -> (13/23,4/7) Hyperbolic Matrix(463,194,1210,507) (-13/31,-5/12) -> (13/34,5/13) Hyperbolic Matrix(279,116,-926,-385) (-5/12,-17/41) -> (-13/43,-3/10) Hyperbolic Matrix(1197,496,1016,421) (-17/41,-12/29) -> (20/17,13/11) Hyperbolic Matrix(1103,456,462,191) (-12/29,-7/17) -> (31/13,12/5) Hyperbolic Matrix(459,188,730,299) (-7/17,-9/22) -> (5/8,17/27) Hyperbolic Matrix(1097,448,1550,633) (-9/22,-11/27) -> (29/41,17/24) Hyperbolic Matrix(457,186,-1914,-779) (-11/27,-13/32) -> (-11/46,-5/21) Hyperbolic Matrix(637,258,1632,661) (-13/32,-2/5) -> (16/41,25/64) Hyperbolic Matrix(1607,634,2228,879) (-2/5,-13/33) -> (31/43,44/61) Hyperbolic Matrix(625,246,-2406,-947) (-13/33,-11/28) -> (-13/50,-7/27) Hyperbolic Matrix(265,104,1246,489) (-11/28,-9/23) -> (7/33,3/14) Hyperbolic Matrix(267,104,706,275) (-9/23,-7/18) -> (3/8,11/29) Hyperbolic Matrix(2031,788,616,239) (-7/18,-19/49) -> (23/7,33/10) Hyperbolic Matrix(351,136,-2026,-785) (-19/49,-12/31) -> (-4/23,-5/29) Hyperbolic Matrix(1055,408,618,239) (-12/31,-5/13) -> (29/17,12/7) Hyperbolic Matrix(1049,402,-3588,-1375) (-5/13,-18/47) -> (-12/41,-19/65) Hyperbolic Matrix(439,168,1398,535) (-18/47,-13/34) -> (5/16,6/19) Hyperbolic Matrix(1921,734,6556,2505) (-13/34,-34/89) -> (12/41,17/58) Hyperbolic Matrix(1571,600,-7512,-2869) (-34/89,-21/55) -> (-9/43,-14/67) Hyperbolic Matrix(173,66,-1308,-499) (-21/55,-8/21) -> (-2/15,-3/23) Hyperbolic Matrix(611,232,956,363) (-8/21,-11/29) -> (7/11,16/25) Hyperbolic Matrix(607,230,958,363) (-11/29,-3/8) -> (19/30,7/11) Hyperbolic Matrix(257,96,174,65) (-3/8,-13/35) -> (19/13,3/2) Hyperbolic Matrix(6525,2422,2492,925) (-13/35,-23/62) -> (89/34,55/21) Hyperbolic Matrix(3521,1306,1286,477) (-23/62,-10/27) -> (52/19,11/4) Hyperbolic Matrix(941,348,-3426,-1267) (-10/27,-17/46) -> (-11/40,-14/51) Hyperbolic Matrix(1543,570,1968,727) (-17/46,-7/19) -> (29/37,11/14) Hyperbolic Matrix(1197,440,1450,533) (-7/19,-18/49) -> (14/17,19/23) Hyperbolic Matrix(425,156,-2046,-751) (-18/49,-11/30) -> (-5/24,-6/29) Hyperbolic Matrix(1447,530,172,63) (-11/30,-26/71) -> (8/1,17/2) Hyperbolic Matrix(1961,718,254,93) (-26/71,-15/41) -> (23/3,8/1) Hyperbolic Matrix(5787,2116,3662,1339) (-15/41,-19/52) -> (79/50,49/31) Hyperbolic Matrix(597,218,-3404,-1243) (-19/52,-4/11) -> (-10/57,-7/40) Hyperbolic Matrix(171,62,-764,-277) (-4/11,-13/36) -> (-9/40,-2/9) Hyperbolic Matrix(255,92,-2198,-793) (-13/36,-22/61) -> (-2/17,-3/26) Hyperbolic Matrix(2363,852,4224,1523) (-22/61,-9/25) -> (33/59,14/25) Hyperbolic Matrix(1431,514,2024,727) (-9/25,-14/39) -> (12/17,29/41) Hyperbolic Matrix(419,150,-1176,-421) (-14/39,-5/14) -> (-5/14,-16/45) Parabolic Matrix(5195,1846,3014,1071) (-16/45,-11/31) -> (81/47,50/29) Hyperbolic Matrix(1085,384,1506,533) (-11/31,-6/17) -> (18/25,31/43) Hyperbolic Matrix(1413,496,584,205) (-6/17,-7/20) -> (29/12,46/19) Hyperbolic Matrix(333,116,910,317) (-7/20,-1/3) -> (15/41,11/30) Hyperbolic Matrix(869,276,318,101) (-1/3,-6/19) -> (30/11,41/15) Hyperbolic Matrix(787,248,238,75) (-6/19,-5/16) -> (33/10,10/3) Hyperbolic Matrix(1413,440,1018,317) (-5/16,-9/29) -> (43/31,25/18) Hyperbolic Matrix(311,96,-1014,-313) (-9/29,-4/13) -> (-4/13,-15/49) Parabolic Matrix(2099,642,546,167) (-15/49,-11/36) -> (23/6,27/7) Hyperbolic Matrix(1867,570,1320,403) (-11/36,-7/23) -> (41/29,17/12) Hyperbolic Matrix(3879,1178,2170,659) (-7/23,-17/56) -> (25/14,59/33) Hyperbolic Matrix(389,118,-3412,-1035) (-27/89,-10/33) -> (-4/35,-1/9) Hyperbolic Matrix(2787,844,776,235) (-10/33,-13/43) -> (61/17,18/5) Hyperbolic Matrix(771,230,-4388,-1309) (-3/10,-17/57) -> (-3/17,-13/74) Hyperbolic Matrix(3307,984,5226,1555) (-14/47,-11/37) -> (31/49,50/79) Hyperbolic Matrix(4377,1300,3074,913) (-11/37,-19/64) -> (37/26,47/33) Hyperbolic Matrix(155,46,1304,387) (-19/64,-8/27) -> (2/17,1/8) Hyperbolic Matrix(1765,522,612,181) (-21/71,-13/44) -> (23/8,3/1) Hyperbolic Matrix(1301,384,1074,317) (-13/44,-5/17) -> (23/19,17/14) Hyperbolic Matrix(1529,448,686,201) (-5/17,-12/41) -> (20/9,29/13) Hyperbolic Matrix(3507,1024,1298,379) (-19/65,-7/24) -> (27/10,73/27) Hyperbolic Matrix(1141,332,3124,909) (-7/24,-16/55) -> (4/11,19/52) Hyperbolic Matrix(2209,642,5784,1681) (-16/55,-9/31) -> (21/55,34/89) Hyperbolic Matrix(683,198,990,287) (-9/31,-2/7) -> (20/29,9/13) Hyperbolic Matrix(827,232,524,147) (-2/7,-7/25) -> (11/7,30/19) Hyperbolic Matrix(675,188,298,83) (-7/25,-5/18) -> (9/4,25/11) Hyperbolic Matrix(2167,600,372,103) (-18/65,-13/47) -> (29/5,6/1) Hyperbolic Matrix(20297,5610,6270,1733) (-34/123,-55/199) -> (55/17,68/21) Hyperbolic Matrix(30669,8476,8210,2269) (-55/199,-21/76) -> (127/34,71/19) Hyperbolic Matrix(6415,1772,1792,495) (-21/76,-8/29) -> (68/19,43/12) Hyperbolic Matrix(1191,328,374,103) (-8/29,-11/40) -> (19/6,16/5) Hyperbolic Matrix(2755,756,594,163) (-14/51,-3/11) -> (51/11,14/3) Hyperbolic Matrix(221,60,372,101) (-3/11,-7/26) -> (13/22,3/5) Hyperbolic Matrix(3247,872,3988,1071) (-18/67,-11/41) -> (35/43,22/27) Hyperbolic Matrix(2141,574,884,237) (-11/41,-4/15) -> (46/19,17/7) Hyperbolic Matrix(587,156,222,59) (-4/15,-5/19) -> (29/11,8/3) Hyperbolic Matrix(1025,268,218,57) (-5/19,-6/23) -> (14/3,33/7) Hyperbolic Matrix(2557,666,1386,361) (-6/23,-13/50) -> (59/32,24/13) Hyperbolic Matrix(1017,262,656,169) (-7/27,-1/4) -> (31/20,45/29) Hyperbolic Matrix(1139,274,212,51) (-1/4,-6/25) -> (16/3,43/8) Hyperbolic Matrix(2629,630,1206,289) (-6/25,-11/46) -> (61/28,24/11) Hyperbolic Matrix(1201,284,850,201) (-5/21,-4/17) -> (24/17,41/29) Hyperbolic Matrix(563,132,354,83) (-4/17,-3/13) -> (27/17,8/5) Hyperbolic Matrix(209,48,492,113) (-3/13,-5/22) -> (11/26,3/7) Hyperbolic Matrix(1813,410,1048,237) (-5/22,-7/31) -> (19/11,45/26) Hyperbolic Matrix(977,220,3344,753) (-7/31,-9/40) -> (7/24,19/65) Hyperbolic Matrix(899,196,344,75) (-2/9,-5/23) -> (13/5,34/13) Hyperbolic Matrix(895,194,346,75) (-5/23,-3/14) -> (31/12,13/5) Hyperbolic Matrix(2539,540,1782,379) (-10/47,-7/33) -> (47/33,10/7) Hyperbolic Matrix(549,116,478,101) (-7/33,-4/19) -> (8/7,15/13) Hyperbolic Matrix(2597,544,2048,429) (-4/19,-9/43) -> (19/15,52/41) Hyperbolic Matrix(14471,3022,5186,1083) (-14/67,-19/91) -> (53/19,120/43) Hyperbolic Matrix(11125,2322,2592,541) (-19/91,-5/24) -> (103/24,73/17) Hyperbolic Matrix(1975,408,1428,295) (-6/29,-1/5) -> (65/47,18/13) Hyperbolic Matrix(871,168,534,103) (-1/5,-4/21) -> (44/27,31/19) Hyperbolic Matrix(467,88,398,75) (-4/21,-3/16) -> (7/6,20/17) Hyperbolic Matrix(729,136,134,25) (-3/16,-5/27) -> (27/5,11/2) Hyperbolic Matrix(131,24,-726,-133) (-5/27,-2/11) -> (-2/11,-7/39) Parabolic Matrix(4475,802,2762,495) (-7/39,-5/28) -> (81/50,47/29) Hyperbolic Matrix(1247,222,264,47) (-5/28,-3/17) -> (33/7,19/4) Hyperbolic Matrix(11137,1956,3012,529) (-13/74,-10/57) -> (122/33,37/10) Hyperbolic Matrix(3009,526,1310,229) (-7/40,-4/23) -> (62/27,23/10) Hyperbolic Matrix(1239,212,976,167) (-5/29,-1/6) -> (33/26,47/37) Hyperbolic Matrix(775,126,1224,199) (-1/6,-4/25) -> (50/79,19/30) Hyperbolic Matrix(1027,164,1672,267) (-4/25,-3/19) -> (35/57,8/13) Hyperbolic Matrix(191,30,834,131) (-3/19,-2/13) -> (8/35,3/13) Hyperbolic Matrix(955,144,126,19) (-5/33,-3/20) -> (15/2,23/3) Hyperbolic Matrix(1143,170,316,47) (-3/20,-1/7) -> (47/13,29/8) Hyperbolic Matrix(625,84,186,25) (-1/7,-2/15) -> (10/3,37/11) Hyperbolic Matrix(1801,234,1116,145) (-3/23,-1/8) -> (71/44,21/13) Hyperbolic Matrix(493,60,1290,157) (-1/8,-2/17) -> (34/89,13/34) Hyperbolic Matrix(2869,330,426,49) (-3/26,-4/35) -> (74/11,27/4) Hyperbolic Matrix(843,88,182,19) (-1/9,-1/10) -> (37/8,51/11) Hyperbolic Matrix(479,46,656,63) (-1/10,0/1) -> (46/63,19/26) Hyperbolic Matrix(345,-32,248,-23) (0/1,1/9) -> (57/41,32/23) Hyperbolic Matrix(2035,-234,774,-89) (1/9,2/17) -> (92/35,71/27) Hyperbolic Matrix(475,-64,334,-45) (1/8,1/7) -> (27/19,37/26) Hyperbolic Matrix(609,-92,470,-71) (1/7,2/13) -> (22/17,35/27) Hyperbolic Matrix(233,-38,92,-15) (2/13,1/6) -> (5/2,28/11) Hyperbolic Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(819,-152,2096,-389) (5/27,3/16) -> (25/64,9/23) Hyperbolic Matrix(1453,-276,816,-155) (3/16,4/21) -> (16/9,57/32) Hyperbolic Matrix(497,-96,906,-175) (4/21,1/5) -> (17/31,28/51) Hyperbolic Matrix(359,-74,1208,-249) (1/5,5/24) -> (19/64,11/37) Hyperbolic Matrix(1429,-300,624,-131) (5/24,4/19) -> (16/7,55/24) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(221,-50,968,-219) (2/9,5/22) -> (5/22,8/35) Parabolic Matrix(701,-164,218,-51) (3/13,4/17) -> (16/5,29/9) Hyperbolic Matrix(131,-32,86,-21) (4/17,1/4) -> (3/2,20/13) Hyperbolic Matrix(513,-136,298,-79) (1/4,4/15) -> (12/7,31/18) Hyperbolic Matrix(425,-114,384,-103) (4/15,11/41) -> (1/1,10/9) Hyperbolic Matrix(2255,-606,3576,-961) (11/41,7/26) -> (29/46,41/65) Hyperbolic Matrix(807,-218,596,-161) (7/26,3/11) -> (23/17,19/14) Hyperbolic Matrix(211,-58,382,-105) (3/11,5/18) -> (11/20,5/9) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(4555,-1332,5598,-1637) (19/65,12/41) -> (48/59,35/43) Hyperbolic Matrix(4843,-1420,7684,-2253) (17/58,5/17) -> (75/119,29/46) Hyperbolic Matrix(291,-86,626,-185) (5/17,8/27) -> (6/13,7/15) Hyperbolic Matrix(6455,-1916,2456,-729) (8/27,19/64) -> (21/8,92/35) Hyperbolic Matrix(497,-152,206,-63) (3/10,4/13) -> (12/5,29/12) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(123,-40,40,-13) (6/19,1/3) -> (3/1,22/7) Hyperbolic Matrix(439,-156,318,-113) (1/3,5/14) -> (11/8,29/21) Hyperbolic Matrix(1669,-600,1032,-371) (5/14,9/25) -> (21/13,55/34) Hyperbolic Matrix(3691,-1332,2142,-773) (9/25,13/36) -> (31/18,81/47) Hyperbolic Matrix(911,-330,1626,-589) (13/36,4/11) -> (14/25,37/66) Hyperbolic Matrix(6169,-2256,2688,-983) (19/52,15/41) -> (39/17,101/44) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(2543,-966,3288,-1249) (11/29,19/50) -> (17/22,41/53) Hyperbolic Matrix(4851,-1844,5948,-2261) (19/50,27/71) -> (53/65,31/38) Hyperbolic Matrix(2035,-774,234,-89) (27/71,8/21) -> (26/3,9/1) Hyperbolic Matrix(587,-224,1250,-477) (8/21,21/55) -> (7/15,8/17) Hyperbolic Matrix(351,-136,622,-241) (5/13,7/18) -> (9/16,13/23) Hyperbolic Matrix(1631,-636,2526,-985) (7/18,16/41) -> (20/31,31/48) Hyperbolic Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(497,-206,152,-63) (7/17,5/12) -> (13/4,23/7) Hyperbolic Matrix(305,-128,722,-303) (5/12,8/19) -> (8/19,11/26) Parabolic Matrix(1885,-816,1356,-587) (3/7,13/30) -> (25/18,57/41) Hyperbolic Matrix(1091,-474,1770,-769) (13/30,10/23) -> (8/13,37/60) Hyperbolic Matrix(6169,-2688,2256,-983) (27/62,17/39) -> (41/15,93/34) Hyperbolic Matrix(1429,-624,300,-131) (17/39,7/16) -> (19/4,43/9) Hyperbolic Matrix(337,-148,526,-231) (7/16,4/9) -> (16/25,9/14) Hyperbolic Matrix(261,-118,334,-151) (4/9,5/11) -> (7/9,18/23) Hyperbolic Matrix(407,-186,186,-85) (5/11,6/13) -> (24/11,11/5) Hyperbolic Matrix(511,-244,622,-297) (8/17,1/2) -> (23/28,60/73) Hyperbolic Matrix(317,-170,386,-207) (1/2,7/13) -> (9/11,23/28) Hyperbolic Matrix(455,-246,246,-133) (7/13,6/11) -> (24/13,13/7) Hyperbolic Matrix(5577,-3064,1498,-823) (28/51,11/20) -> (67/18,108/29) Hyperbolic Matrix(2149,-1200,1524,-851) (5/9,19/34) -> (31/22,55/39) Hyperbolic Matrix(7897,-4416,4848,-2711) (19/34,33/59) -> (57/35,101/62) Hyperbolic Matrix(6505,-3648,2352,-1319) (37/66,23/41) -> (47/17,83/30) Hyperbolic Matrix(1453,-816,276,-155) (23/41,9/16) -> (21/4,37/7) Hyperbolic Matrix(205,-118,172,-99) (4/7,11/19) -> (13/11,6/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(341,-200,578,-339) (7/12,10/17) -> (10/17,13/22) Parabolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(7897,-4848,4416,-2711) (27/44,35/57) -> (59/33,93/52) Hyperbolic Matrix(7081,-4368,3072,-1895) (37/60,29/47) -> (53/23,83/36) Hyperbolic Matrix(3907,-2412,1602,-989) (29/47,21/34) -> (39/16,61/25) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(6063,-3820,4306,-2713) (17/27,46/73) -> (38/27,69/49) Hyperbolic Matrix(15867,-10000,4438,-2797) (46/73,75/119) -> (25/7,118/33) Hyperbolic Matrix(2583,-1630,496,-313) (41/65,12/19) -> (26/5,47/9) Hyperbolic Matrix(1389,-878,1688,-1067) (12/19,31/49) -> (37/45,14/17) Hyperbolic Matrix(1019,-656,1412,-909) (9/14,20/31) -> (44/61,13/18) Hyperbolic Matrix(3511,-2268,918,-593) (31/48,11/17) -> (65/17,23/6) Hyperbolic Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(353,-242,512,-351) (2/3,11/16) -> (11/16,20/29) Parabolic Matrix(893,-620,350,-243) (9/13,16/23) -> (28/11,23/9) Hyperbolic Matrix(287,-200,254,-177) (16/23,7/10) -> (9/8,8/7) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(2149,-1524,1200,-851) (17/24,22/31) -> (34/19,43/24) Hyperbolic Matrix(757,-538,916,-651) (22/31,5/7) -> (19/23,24/29) Hyperbolic Matrix(1257,-902,1604,-1151) (5/7,23/32) -> (47/60,29/37) Hyperbolic Matrix(345,-248,32,-23) (23/32,18/25) -> (10/1,1/0) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(999,-728,188,-137) (8/11,27/37) -> (37/7,16/3) Hyperbolic Matrix(5401,-3942,3402,-2483) (27/37,46/63) -> (100/63,27/17) Hyperbolic Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(623,-458,404,-297) (11/15,14/19) -> (20/13,17/11) Hyperbolic Matrix(807,-596,218,-161) (14/19,3/4) -> (37/10,26/7) Hyperbolic Matrix(153,-116,62,-47) (3/4,10/13) -> (22/9,5/2) Hyperbolic Matrix(609,-470,92,-71) (10/13,17/22) -> (13/2,20/3) Hyperbolic Matrix(3471,-2686,1552,-1201) (41/53,24/31) -> (38/17,47/21) Hyperbolic Matrix(1277,-990,396,-307) (24/31,7/9) -> (29/9,42/13) Hyperbolic Matrix(8297,-6498,3150,-2467) (18/23,47/60) -> (79/30,108/41) Hyperbolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(6255,-5086,1846,-1501) (13/16,48/59) -> (166/49,61/18) Hyperbolic Matrix(14397,-11738,5474,-4463) (22/27,53/65) -> (71/27,192/73) Hyperbolic Matrix(15411,-12668,4298,-3533) (60/73,37/45) -> (147/41,104/29) Hyperbolic Matrix(2717,-2252,1712,-1419) (24/29,5/6) -> (73/46,100/63) Hyperbolic Matrix(205,-172,118,-99) (5/6,6/7) -> (26/15,7/4) Hyperbolic Matrix(435,-376,376,-325) (6/7,13/15) -> (15/13,22/19) Hyperbolic Matrix(287,-254,200,-177) (7/8,1/1) -> (33/23,23/16) Hyperbolic Matrix(715,-796,256,-285) (10/9,9/8) -> (67/24,14/5) Hyperbolic Matrix(2251,-2608,826,-957) (22/19,7/6) -> (109/40,30/11) Hyperbolic Matrix(757,-916,538,-651) (6/5,23/19) -> (7/5,38/27) Hyperbolic Matrix(317,-386,170,-207) (17/14,11/9) -> (13/7,15/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(6261,-7942,2380,-3019) (52/41,33/26) -> (121/46,50/19) Hyperbolic Matrix(4519,-5742,1260,-1601) (47/37,14/11) -> (104/29,61/17) Hyperbolic Matrix(261,-334,118,-151) (14/11,9/7) -> (11/5,20/9) Hyperbolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(2543,-3288,966,-1249) (31/24,22/17) -> (50/19,79/30) Hyperbolic Matrix(799,-1036,118,-153) (35/27,13/10) -> (27/4,7/1) Hyperbolic Matrix(2203,-2872,1360,-1773) (13/10,30/23) -> (34/21,81/50) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(849,-1148,230,-311) (4/3,23/17) -> (11/3,48/13) Hyperbolic Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(4011,-5494,2848,-3901) (63/46,37/27) -> (69/49,31/22) Hyperbolic Matrix(1867,-2560,1048,-1437) (37/27,11/8) -> (57/32,41/23) Hyperbolic Matrix(3197,-4418,2312,-3195) (29/21,47/34) -> (47/34,65/47) Parabolic Matrix(1019,-1412,656,-909) (18/13,43/31) -> (45/29,14/9) Hyperbolic Matrix(857,-1194,384,-535) (32/23,7/5) -> (29/13,38/17) Hyperbolic Matrix(6967,-9826,2644,-3729) (55/39,79/56) -> (137/52,29/11) Hyperbolic Matrix(8377,-11820,3180,-4487) (79/56,24/17) -> (108/41,137/52) Hyperbolic Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(353,-512,242,-351) (13/9,16/11) -> (16/11,19/13) Parabolic Matrix(1631,-2526,636,-985) (17/11,31/20) -> (41/16,59/23) Hyperbolic Matrix(337,-526,148,-231) (14/9,11/7) -> (25/11,16/7) Hyperbolic Matrix(669,-1058,356,-563) (49/31,19/12) -> (15/8,17/9) Hyperbolic Matrix(2255,-3576,606,-961) (19/12,46/29) -> (26/7,67/18) Hyperbolic Matrix(5825,-9242,1628,-2583) (46/29,73/46) -> (93/26,68/19) Hyperbolic Matrix(3101,-5000,1922,-3099) (29/18,50/31) -> (50/31,71/44) Parabolic Matrix(3239,-5240,866,-1401) (55/34,89/55) -> (71/19,15/4) Hyperbolic Matrix(3465,-5608,1072,-1735) (89/55,34/21) -> (42/13,55/17) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(6901,-11244,1848,-3011) (101/62,44/27) -> (56/15,127/34) Hyperbolic Matrix(2009,-3282,636,-1039) (49/30,67/41) -> (41/13,19/6) Hyperbolic Matrix(1353,-2212,430,-703) (67/41,18/11) -> (22/7,41/13) Hyperbolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(341,-578,200,-339) (5/3,17/10) -> (17/10,29/17) Parabolic Matrix(1109,-1914,456,-787) (50/29,19/11) -> (17/7,56/23) Hyperbolic Matrix(351,-622,136,-241) (7/4,16/9) -> (18/7,31/12) Hyperbolic Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(7513,-13438,2692,-4815) (93/52,34/19) -> (120/43,67/24) Hyperbolic Matrix(1605,-2876,716,-1283) (43/24,52/29) -> (56/25,9/4) Hyperbolic Matrix(1643,-2948,734,-1317) (52/29,9/5) -> (47/21,56/25) Hyperbolic Matrix(211,-382,58,-105) (9/5,11/6) -> (29/8,11/3) Hyperbolic Matrix(1331,-2450,722,-1329) (11/6,35/19) -> (35/19,59/32) Parabolic Matrix(501,-958,148,-283) (17/9,2/1) -> (44/13,105/31) Hyperbolic Matrix(291,-626,86,-185) (2/1,13/6) -> (27/8,44/13) Hyperbolic Matrix(1259,-2738,578,-1257) (13/6,37/17) -> (37/17,61/28) Parabolic Matrix(2493,-5714,476,-1091) (55/24,94/41) -> (68/13,21/4) Hyperbolic Matrix(3083,-7070,590,-1353) (94/41,39/17) -> (47/9,68/13) Hyperbolic Matrix(3343,-7674,1032,-2369) (101/44,62/27) -> (68/21,13/4) Hyperbolic Matrix(12153,-28022,3398,-7835) (83/36,113/49) -> (211/59,93/26) Hyperbolic Matrix(8525,-19664,2384,-5499) (113/49,30/13) -> (118/33,211/59) Hyperbolic Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(305,-722,128,-303) (7/3,19/8) -> (19/8,31/13) Parabolic Matrix(2059,-5014,802,-1953) (56/23,39/16) -> (77/30,18/7) Hyperbolic Matrix(819,-2096,152,-389) (23/9,41/16) -> (43/8,27/5) Hyperbolic Matrix(12161,-31202,3392,-8703) (59/23,136/53) -> (190/53,147/41) Hyperbolic Matrix(7979,-20478,2226,-5713) (136/53,77/30) -> (43/12,190/53) Hyperbolic Matrix(1417,-3712,418,-1095) (55/21,21/8) -> (61/18,17/5) Hyperbolic Matrix(12971,-34116,4686,-12325) (192/73,121/46) -> (155/56,36/13) Hyperbolic Matrix(4583,-12482,1682,-4581) (49/18,79/29) -> (79/29,109/40) Parabolic Matrix(2977,-8146,694,-1899) (93/34,52/19) -> (30/7,103/24) Hyperbolic Matrix(10235,-28322,3698,-10233) (83/30,119/43) -> (119/43,155/56) Parabolic Matrix(387,-1072,100,-277) (36/13,25/9) -> (27/7,4/1) Hyperbolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(359,-1208,74,-249) (37/11,27/8) -> (29/6,5/1) Hyperbolic Matrix(8517,-28850,2228,-7547) (105/31,166/49) -> (172/45,65/17) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(363,-1312,70,-253) (18/5,47/13) -> (5/1,26/5) Hyperbolic Matrix(3911,-14450,1058,-3909) (48/13,85/23) -> (85/23,122/33) Parabolic Matrix(2903,-10812,606,-2257) (108/29,41/11) -> (91/19,24/5) Hyperbolic Matrix(5993,-22898,1568,-5991) (42/11,107/28) -> (107/28,172/45) Parabolic Matrix(221,-968,50,-219) (13/3,22/5) -> (22/5,31/7) Parabolic Matrix(1877,-8978,392,-1875) (43/9,67/14) -> (67/14,91/19) Parabolic Matrix(241,-1162,28,-135) (24/5,29/6) -> (17/2,26/3) Hyperbolic Matrix(185,-1058,32,-183) (17/3,23/4) -> (23/4,29/5) Parabolic Matrix(659,-4418,98,-657) (20/3,47/7) -> (47/7,74/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,52,1) Matrix(1123,530,820,387) -> Matrix(295,-6,3196,-65) Matrix(1931,906,714,335) -> Matrix(489,-10,3472,-71) Matrix(1011,470,-3332,-1549) -> Matrix(775,-16,28336,-585) Matrix(2109,976,806,373) -> Matrix(1255,-26,9316,-193) Matrix(497,228,-1794,-823) -> Matrix(287,-6,10380,-217) Matrix(297,136,998,457) -> Matrix(287,-6,5788,-121) Matrix(593,268,1082,489) -> Matrix(189,-4,3544,-75) Matrix(293,132,-1374,-619) -> Matrix(283,-6,9292,-197) Matrix(881,396,198,89) -> Matrix(847,-18,4188,-89) Matrix(2543,1138,1562,699) -> Matrix(187,-4,2104,-45) Matrix(1851,826,1172,523) -> Matrix(655,-14,6784,-145) Matrix(675,298,-2512,-1109) -> Matrix(649,-14,22576,-487) Matrix(1933,852,4440,1957) -> Matrix(1,0,-28,1) Matrix(1353,596,-4538,-1999) -> Matrix(185,-4,6984,-151) Matrix(387,170,1828,803) -> Matrix(185,-4,4024,-87) Matrix(671,294,-1536,-673) -> Matrix(645,-14,29624,-643) Matrix(4213,1838,1726,753) -> Matrix(3119,-68,24264,-529) Matrix(193,84,1050,457) -> Matrix(183,-4,4072,-89) Matrix(1815,788,1048,455) -> Matrix(93,-2,884,-19) Matrix(759,328,1238,535) -> Matrix(547,-12,8980,-197) Matrix(749,318,-2532,-1075) -> Matrix(359,-8,13328,-297) Matrix(2435,1032,-8808,-3733) -> Matrix(1613,-36,57844,-1291) Matrix(2063,874,2528,1071) -> Matrix(1433,-32,21092,-471) Matrix(653,276,750,317) -> Matrix(89,-2,1380,-31) Matrix(185,78,-1212,-511) -> Matrix(179,-4,5236,-117) Matrix(371,156,654,275) -> Matrix(179,-4,3088,-69) Matrix(463,194,1210,507) -> Matrix(89,-2,1380,-31) Matrix(279,116,-926,-385) -> Matrix(89,-2,3160,-71) Matrix(1197,496,1016,421) -> Matrix(265,-6,3136,-71) Matrix(1103,456,462,191) -> Matrix(1057,-24,8412,-191) Matrix(459,188,730,299) -> Matrix(87,-2,1436,-33) Matrix(1097,448,1550,633) -> Matrix(1,0,-28,1) Matrix(457,186,-1914,-779) -> Matrix(87,-2,3176,-73) Matrix(637,258,1632,661) -> Matrix(87,-2,1784,-41) Matrix(1607,634,2228,879) -> Matrix(343,-8,5188,-121) Matrix(625,246,-2406,-947) -> Matrix(85,-2,3188,-75) Matrix(265,104,1246,489) -> Matrix(85,-2,1828,-43) Matrix(267,104,706,275) -> Matrix(85,-2,1488,-35) Matrix(2031,788,616,239) -> Matrix(85,-2,468,-11) Matrix(351,136,-2026,-785) -> Matrix(337,-8,10068,-239) Matrix(1055,408,618,239) -> Matrix(1009,-24,10048,-239) Matrix(1049,402,-3588,-1375) -> Matrix(499,-12,18172,-437) Matrix(439,168,1398,535) -> Matrix(83,-2,1536,-37) Matrix(1921,734,6556,2505) -> Matrix(165,-4,3424,-83) Matrix(1571,600,-7512,-2869) -> Matrix(165,-4,5404,-131) Matrix(173,66,-1308,-499) -> Matrix(1,0,-12,1) Matrix(611,232,956,363) -> Matrix(83,-2,1536,-37) Matrix(607,230,958,363) -> Matrix(83,-2,1204,-29) Matrix(257,96,174,65) -> Matrix(247,-6,2676,-65) Matrix(6525,2422,2492,925) -> Matrix(2127,-52,15748,-385) Matrix(3521,1306,1286,477) -> Matrix(409,-10,2904,-71) Matrix(941,348,-3426,-1267) -> Matrix(245,-6,8616,-211) Matrix(1543,570,1968,727) -> Matrix(977,-24,14940,-367) Matrix(1197,440,1450,533) -> Matrix(323,-8,4724,-117) Matrix(425,156,-2046,-751) -> Matrix(79,-2,2568,-65) Matrix(1447,530,172,63) -> Matrix(247,-6,700,-17) Matrix(1961,718,254,93) -> Matrix(409,-10,1268,-31) Matrix(5787,2116,3662,1339) -> Matrix(325,-8,3372,-83) Matrix(597,218,-3404,-1243) -> Matrix(81,-2,2552,-63) Matrix(171,62,-764,-277) -> Matrix(1,0,-8,1) Matrix(255,92,-2198,-793) -> Matrix(81,-2,1904,-47) Matrix(2363,852,4224,1523) -> Matrix(1293,-32,23072,-571) Matrix(1431,514,2024,727) -> Matrix(241,-6,3816,-95) Matrix(419,150,-1176,-421) -> Matrix(401,-10,16000,-399) Matrix(5195,1846,3014,1071) -> Matrix(2705,-68,26692,-671) Matrix(1085,384,1506,533) -> Matrix(555,-14,8444,-213) Matrix(1413,496,584,205) -> Matrix(241,-6,1888,-47) Matrix(333,116,910,317) -> Matrix(1,0,-20,1) Matrix(869,276,318,101) -> Matrix(73,-2,548,-15) Matrix(787,248,238,75) -> Matrix(151,-4,944,-25) Matrix(1413,440,1018,317) -> Matrix(299,-8,3476,-93) Matrix(311,96,-1014,-313) -> Matrix(297,-8,10952,-295) Matrix(2099,642,546,167) -> Matrix(367,-10,2092,-57) Matrix(1867,570,1320,403) -> Matrix(881,-24,9948,-271) Matrix(3879,1178,2170,659) -> Matrix(147,-4,1360,-37) Matrix(389,118,-3412,-1035) -> Matrix(73,-2,2592,-71) Matrix(2787,844,776,235) -> Matrix(1165,-32,6808,-187) Matrix(771,230,-4388,-1309) -> Matrix(1,0,-8,1) Matrix(3307,984,5226,1555) -> Matrix(75,-2,1088,-29) Matrix(4377,1300,3074,913) -> Matrix(221,-6,2468,-67) Matrix(155,46,1304,387) -> Matrix(1,0,-12,1) Matrix(1765,522,612,181) -> Matrix(519,-14,3596,-97) Matrix(1301,384,1074,317) -> Matrix(515,-14,6364,-173) Matrix(1529,448,686,201) -> Matrix(1,0,-28,1) Matrix(3507,1024,1298,379) -> Matrix(581,-16,4176,-115) Matrix(1141,332,3124,909) -> Matrix(217,-6,4304,-119) Matrix(2209,642,5784,1681) -> Matrix(217,-6,3436,-95) Matrix(683,198,990,287) -> Matrix(649,-18,10348,-287) Matrix(827,232,524,147) -> Matrix(67,-2,704,-21) Matrix(675,188,298,83) -> Matrix(71,-2,604,-17) Matrix(2167,600,372,103) -> Matrix(649,-18,2560,-71) Matrix(20297,5610,6270,1733) -> Matrix(2867,-80,18528,-517) Matrix(30669,8476,8210,2269) -> Matrix(5231,-146,30132,-841) Matrix(6415,1772,1792,495) -> Matrix(2433,-68,14276,-399) Matrix(1191,328,374,103) -> Matrix(427,-12,2740,-77) Matrix(2755,756,594,163) -> Matrix(211,-6,1020,-29) Matrix(221,60,372,101) -> Matrix(211,-6,3552,-101) Matrix(3247,872,3988,1071) -> Matrix(1,0,-20,1) Matrix(2141,574,884,237) -> Matrix(763,-22,6000,-173) Matrix(587,156,222,59) -> Matrix(139,-4,1008,-29) Matrix(1025,268,218,57) -> Matrix(133,-4,632,-19) Matrix(2557,666,1386,361) -> Matrix(53,-2,504,-19) Matrix(1017,262,656,169) -> Matrix(141,-4,1516,-43) Matrix(1139,274,212,51) -> Matrix(127,-4,540,-17) Matrix(2629,630,1206,289) -> Matrix(47,-2,400,-17) Matrix(1201,284,850,201) -> Matrix(343,-10,3876,-113) Matrix(563,132,354,83) -> Matrix(135,-4,1384,-41) Matrix(209,48,492,113) -> Matrix(199,-6,3748,-113) Matrix(1813,410,1048,237) -> Matrix(523,-16,5132,-157) Matrix(977,220,3344,753) -> Matrix(1,0,-12,1) Matrix(899,196,344,75) -> Matrix(57,-2,428,-15) Matrix(895,194,346,75) -> Matrix(73,-2,548,-15) Matrix(2539,540,1782,379) -> Matrix(197,-6,2200,-67) Matrix(549,116,478,101) -> Matrix(1,0,-20,1) Matrix(2597,544,2048,429) -> Matrix(257,-8,3052,-95) Matrix(14471,3022,5186,1083) -> Matrix(2603,-80,18644,-573) Matrix(11125,2322,2592,541) -> Matrix(2791,-86,14312,-441) Matrix(1975,408,1428,295) -> Matrix(321,-10,3820,-119) Matrix(871,168,534,103) -> Matrix(67,-2,704,-21) Matrix(467,88,398,75) -> Matrix(63,-2,788,-25) Matrix(729,136,134,25) -> Matrix(191,-6,796,-25) Matrix(131,24,-726,-133) -> Matrix(125,-4,3844,-123) Matrix(4475,802,2762,495) -> Matrix(1,0,-20,1) Matrix(1247,222,264,47) -> Matrix(63,-2,284,-9) Matrix(11137,1956,3012,529) -> Matrix(105,-4,604,-23) Matrix(3009,526,1310,229) -> Matrix(127,-4,1048,-33) Matrix(1239,212,976,167) -> Matrix(169,-6,2000,-71) Matrix(775,126,1224,199) -> Matrix(1,0,-16,1) Matrix(1027,164,1672,267) -> Matrix(245,-8,4012,-131) Matrix(191,30,834,131) -> Matrix(181,-6,3952,-131) Matrix(955,144,126,19) -> Matrix(173,-6,548,-19) Matrix(1143,170,316,47) -> Matrix(121,-4,696,-23) Matrix(625,84,186,25) -> Matrix(119,-4,744,-25) Matrix(1801,234,1116,145) -> Matrix(175,-6,1896,-65) Matrix(493,60,1290,157) -> Matrix(1,0,-12,1) Matrix(2869,330,426,49) -> Matrix(17,-2,60,-7) Matrix(843,88,182,19) -> Matrix(117,-4,556,-19) Matrix(479,46,656,63) -> Matrix(1,0,-12,1) Matrix(345,-32,248,-23) -> Matrix(49,-2,564,-23) Matrix(2035,-234,774,-89) -> Matrix(205,-8,1512,-59) Matrix(475,-64,334,-45) -> Matrix(91,-4,1024,-45) Matrix(609,-92,470,-71) -> Matrix(57,-2,656,-23) Matrix(233,-38,92,-15) -> Matrix(49,-2,368,-15) Matrix(367,-66,228,-41) -> Matrix(1,0,-12,1) Matrix(819,-152,2096,-389) -> Matrix(1,0,0,1) Matrix(1453,-276,816,-155) -> Matrix(89,-4,868,-39) Matrix(497,-96,906,-175) -> Matrix(43,-2,796,-37) Matrix(359,-74,1208,-249) -> Matrix(95,-4,1924,-81) Matrix(1429,-300,624,-131) -> Matrix(181,-8,1516,-67) Matrix(355,-78,132,-29) -> Matrix(91,-4,660,-29) Matrix(221,-50,968,-219) -> Matrix(221,-10,4840,-219) Matrix(701,-164,218,-51) -> Matrix(87,-4,544,-25) Matrix(131,-32,86,-21) -> Matrix(43,-2,452,-21) Matrix(513,-136,298,-79) -> Matrix(177,-8,1748,-79) Matrix(425,-114,384,-103) -> Matrix(85,-4,1084,-51) Matrix(2255,-606,3576,-961) -> Matrix(41,-2,636,-31) Matrix(807,-218,596,-161) -> Matrix(41,-2,472,-23) Matrix(211,-58,382,-105) -> Matrix(43,-2,796,-37) Matrix(85,-24,294,-83) -> Matrix(85,-4,1764,-83) Matrix(4555,-1332,5598,-1637) -> Matrix(43,-2,624,-29) Matrix(4843,-1420,7684,-2253) -> Matrix(247,-12,3808,-185) Matrix(291,-86,626,-185) -> Matrix(41,-2,800,-39) Matrix(6455,-1916,2456,-729) -> Matrix(693,-34,5116,-251) Matrix(497,-152,206,-63) -> Matrix(161,-8,1268,-63) Matrix(701,-218,164,-51) -> Matrix(113,-6,584,-31) Matrix(123,-40,40,-13) -> Matrix(43,-2,280,-13) Matrix(439,-156,318,-113) -> Matrix(39,-2,488,-25) Matrix(1669,-600,1032,-371) -> Matrix(77,-4,828,-43) Matrix(3691,-1332,2142,-773) -> Matrix(745,-38,7352,-375) Matrix(911,-330,1626,-589) -> Matrix(271,-14,4820,-249) Matrix(6169,-2256,2688,-983) -> Matrix(307,-16,2552,-133) Matrix(1501,-552,552,-203) -> Matrix(1,0,-12,1) Matrix(355,-132,78,-29) -> Matrix(115,-6,556,-29) Matrix(2543,-966,3288,-1249) -> Matrix(33,-2,512,-31) Matrix(4851,-1844,5948,-2261) -> Matrix(61,-4,900,-59) Matrix(2035,-774,234,-89) -> Matrix(77,-4,212,-11) Matrix(587,-224,1250,-477) -> Matrix(33,-2,644,-39) Matrix(351,-136,622,-241) -> Matrix(45,-2,788,-35) Matrix(1631,-636,2526,-985) -> Matrix(1,0,-4,1) Matrix(233,-92,38,-15) -> Matrix(81,-4,304,-15) Matrix(153,-62,116,-47) -> Matrix(1,0,-8,1) Matrix(497,-206,152,-63) -> Matrix(193,-10,1216,-63) Matrix(305,-128,722,-303) -> Matrix(305,-16,5776,-303) Matrix(1885,-816,1356,-587) -> Matrix(75,-4,844,-45) Matrix(1091,-474,1770,-769) -> Matrix(331,-18,5388,-293) Matrix(6169,-2688,2256,-983) -> Matrix(291,-16,2128,-117) Matrix(1429,-624,300,-131) -> Matrix(69,-4,328,-19) Matrix(337,-148,526,-231) -> Matrix(37,-2,648,-35) Matrix(261,-118,334,-151) -> Matrix(33,-2,512,-31) Matrix(407,-186,186,-85) -> Matrix(31,-2,264,-17) Matrix(511,-244,622,-297) -> Matrix(1,0,-4,1) Matrix(317,-170,386,-207) -> Matrix(35,-2,508,-29) Matrix(455,-246,246,-133) -> Matrix(29,-2,276,-19) Matrix(5577,-3064,1498,-823) -> Matrix(1,0,-12,1) Matrix(2149,-1200,1524,-851) -> Matrix(789,-44,8948,-499) Matrix(7897,-4416,4848,-2711) -> Matrix(643,-36,6948,-389) Matrix(6505,-3648,2352,-1319) -> Matrix(1277,-72,9276,-523) Matrix(1453,-816,276,-155) -> Matrix(425,-24,1824,-103) Matrix(205,-118,172,-99) -> Matrix(69,-4,880,-51) Matrix(513,-298,136,-79) -> Matrix(241,-14,1360,-79) Matrix(341,-200,578,-339) -> Matrix(341,-20,5780,-339) Matrix(571,-348,402,-245) -> Matrix(101,-6,1128,-67) Matrix(2077,-1272,1272,-779) -> Matrix(395,-24,4164,-253) Matrix(7897,-4848,4416,-2711) -> Matrix(197,-12,1888,-115) Matrix(7081,-4368,3072,-1895) -> Matrix(2079,-128,17168,-1057) Matrix(3907,-2412,1602,-989) -> Matrix(1459,-90,11364,-701) Matrix(1669,-1032,600,-371) -> Matrix(581,-36,4180,-259) Matrix(367,-228,66,-41) -> Matrix(95,-6,396,-25) Matrix(6063,-3820,4306,-2713) -> Matrix(717,-46,8152,-523) Matrix(15867,-10000,4438,-2797) -> Matrix(1391,-90,8176,-529) Matrix(2583,-1630,496,-313) -> Matrix(117,-8,512,-35) Matrix(1389,-878,1688,-1067) -> Matrix(61,-4,900,-59) Matrix(1019,-656,1412,-909) -> Matrix(101,-6,1532,-91) Matrix(3511,-2268,918,-593) -> Matrix(37,-2,204,-11) Matrix(131,-86,32,-21) -> Matrix(67,-4,352,-21) Matrix(353,-242,512,-351) -> Matrix(353,-22,5632,-351) Matrix(893,-620,350,-243) -> Matrix(63,-4,520,-33) Matrix(287,-200,254,-177) -> Matrix(95,-6,1156,-73) Matrix(571,-402,348,-245) -> Matrix(187,-12,1948,-125) Matrix(2149,-1524,1200,-851) -> Matrix(125,-8,1172,-75) Matrix(757,-538,916,-651) -> Matrix(61,-4,900,-59) Matrix(1257,-902,1604,-1151) -> Matrix(553,-36,8464,-551) Matrix(345,-248,32,-23) -> Matrix(153,-10,352,-23) Matrix(439,-318,156,-113) -> Matrix(119,-8,848,-57) Matrix(999,-728,188,-137) -> Matrix(63,-4,268,-17) Matrix(5401,-3942,3402,-2483) -> Matrix(27,-2,284,-21) Matrix(1153,-844,250,-183) -> Matrix(91,-6,440,-29) Matrix(623,-458,404,-297) -> Matrix(1,0,-4,1) Matrix(807,-596,218,-161) -> Matrix(57,-4,328,-23) Matrix(153,-116,62,-47) -> Matrix(33,-2,248,-15) Matrix(609,-470,92,-71) -> Matrix(247,-16,880,-57) Matrix(3471,-2686,1552,-1201) -> Matrix(63,-4,520,-33) Matrix(1277,-990,396,-307) -> Matrix(61,-4,412,-27) Matrix(8297,-6498,3150,-2467) -> Matrix(2207,-144,16200,-1057) Matrix(121,-96,150,-119) -> Matrix(121,-8,1800,-119) Matrix(6255,-5086,1846,-1501) -> Matrix(355,-24,2204,-149) Matrix(14397,-11738,5474,-4463) -> Matrix(3007,-204,22184,-1505) Matrix(15411,-12668,4298,-3533) -> Matrix(1147,-76,6716,-445) Matrix(2717,-2252,1712,-1419) -> Matrix(233,-16,2432,-167) Matrix(205,-172,118,-99) -> Matrix(85,-6,836,-59) Matrix(435,-376,376,-325) -> Matrix(31,-2,388,-25) Matrix(287,-254,200,-177) -> Matrix(119,-8,1324,-89) Matrix(715,-796,256,-285) -> Matrix(403,-32,2884,-229) Matrix(2251,-2608,826,-957) -> Matrix(151,-12,1120,-89) Matrix(757,-916,538,-651) -> Matrix(421,-34,4792,-387) Matrix(317,-386,170,-207) -> Matrix(123,-10,1144,-93) Matrix(121,-150,96,-119) -> Matrix(121,-10,1440,-119) Matrix(6261,-7942,2380,-3019) -> Matrix(1445,-122,10648,-899) Matrix(4519,-5742,1260,-1601) -> Matrix(2503,-212,14652,-1241) Matrix(261,-334,118,-151) -> Matrix(71,-6,580,-49) Matrix(613,-790,142,-183) -> Matrix(373,-32,1900,-163) Matrix(2543,-3288,966,-1249) -> Matrix(881,-76,6480,-559) Matrix(799,-1036,118,-153) -> Matrix(369,-32,1280,-111) Matrix(2203,-2872,1360,-1773) -> Matrix(45,-4,484,-43) Matrix(983,-1284,258,-337) -> Matrix(91,-8,512,-45) Matrix(849,-1148,230,-311) -> Matrix(159,-14,920,-81) Matrix(481,-654,114,-155) -> Matrix(21,-2,116,-11) Matrix(867,-1184,320,-437) -> Matrix(1,0,-4,1) Matrix(4011,-5494,2848,-3901) -> Matrix(561,-52,6376,-591) Matrix(1867,-2560,1048,-1437) -> Matrix(41,-4,400,-39) Matrix(3197,-4418,2312,-3195) -> Matrix(169,-14,2016,-167) Matrix(1019,-1412,656,-909) -> Matrix(117,-10,1252,-107) Matrix(857,-1194,384,-535) -> Matrix(47,-4,388,-33) Matrix(6967,-9826,2644,-3729) -> Matrix(2245,-198,16452,-1451) Matrix(8377,-11820,3180,-4487) -> Matrix(2855,-252,20948,-1849) Matrix(1575,-2258,422,-605) -> Matrix(379,-34,2196,-197) Matrix(421,-606,66,-95) -> Matrix(289,-26,1056,-95) Matrix(353,-512,242,-351) -> Matrix(353,-32,3872,-351) Matrix(1631,-2526,636,-985) -> Matrix(239,-22,1836,-169) Matrix(337,-526,148,-231) -> Matrix(85,-8,712,-67) Matrix(669,-1058,356,-563) -> Matrix(41,-4,400,-39) Matrix(2255,-3576,606,-961) -> Matrix(41,-4,236,-23) Matrix(5825,-9242,1628,-2583) -> Matrix(571,-54,3352,-317) Matrix(3101,-5000,1922,-3099) -> Matrix(89,-8,968,-87) Matrix(3239,-5240,866,-1401) -> Matrix(275,-26,1576,-149) Matrix(3465,-5608,1072,-1735) -> Matrix(1,0,-4,1) Matrix(1091,-1770,474,-769) -> Matrix(187,-18,1548,-149) Matrix(6901,-11244,1848,-3011) -> Matrix(515,-48,2972,-277) Matrix(2009,-3282,636,-1039) -> Matrix(673,-64,4364,-415) Matrix(1353,-2212,430,-703) -> Matrix(503,-48,3280,-313) Matrix(143,-236,20,-33) -> Matrix(103,-10,340,-33) Matrix(341,-578,200,-339) -> Matrix(341,-34,3400,-339) Matrix(1109,-1914,456,-787) -> Matrix(709,-72,5544,-563) Matrix(351,-622,136,-241) -> Matrix(75,-8,572,-61) Matrix(911,-1626,330,-589) -> Matrix(17,-2,128,-15) Matrix(7513,-13438,2692,-4815) -> Matrix(649,-68,4648,-487) Matrix(1605,-2876,716,-1283) -> Matrix(93,-10,772,-83) Matrix(1643,-2948,734,-1317) -> Matrix(15,-2,128,-17) Matrix(211,-382,58,-105) -> Matrix(21,-2,116,-11) Matrix(1331,-2450,722,-1329) -> Matrix(609,-64,5776,-607) Matrix(501,-958,148,-283) -> Matrix(59,-6,364,-37) Matrix(291,-626,86,-185) -> Matrix(121,-14,752,-87) Matrix(1259,-2738,578,-1257) -> Matrix(681,-80,5780,-679) Matrix(2493,-5714,476,-1091) -> Matrix(901,-108,3896,-467) Matrix(3083,-7070,590,-1353) -> Matrix(1199,-144,5204,-625) Matrix(3343,-7674,1032,-2369) -> Matrix(631,-76,4060,-489) Matrix(12153,-28022,3398,-7835) -> Matrix(6767,-820,39752,-4817) Matrix(8525,-19664,2384,-5499) -> Matrix(4849,-588,28492,-3455) Matrix(147,-340,16,-37) -> Matrix(115,-14,304,-37) Matrix(305,-722,128,-303) -> Matrix(305,-38,2432,-303) Matrix(2059,-5014,802,-1953) -> Matrix(921,-118,7048,-903) Matrix(819,-2096,152,-389) -> Matrix(63,-8,260,-33) Matrix(12161,-31202,3392,-8703) -> Matrix(4863,-634,28480,-3713) Matrix(7979,-20478,2226,-5713) -> Matrix(3509,-458,20556,-2683) Matrix(1417,-3712,418,-1095) -> Matrix(73,-10,460,-63) Matrix(12971,-34116,4686,-12325) -> Matrix(3511,-476,25440,-3449) Matrix(4583,-12482,1682,-4581) -> Matrix(121,-16,900,-119) Matrix(2977,-8146,694,-1899) -> Matrix(491,-68,2520,-349) Matrix(10235,-28322,3698,-10233) -> Matrix(3713,-512,26912,-3711) Matrix(387,-1072,100,-277) -> Matrix(217,-30,1208,-167) Matrix(1839,-5126,428,-1193) -> Matrix(1363,-190,6980,-973) Matrix(281,-800,98,-279) -> Matrix(281,-40,1960,-279) Matrix(359,-1208,74,-249) -> Matrix(87,-14,404,-65) Matrix(8517,-28850,2228,-7547) -> Matrix(49,-8,288,-47) Matrix(85,-294,24,-83) -> Matrix(85,-14,504,-83) Matrix(363,-1312,70,-253) -> Matrix(127,-22,560,-97) Matrix(3911,-14450,1058,-3909) -> Matrix(737,-128,4232,-735) Matrix(2903,-10812,606,-2257) -> Matrix(195,-32,908,-149) Matrix(5993,-22898,1568,-5991) -> Matrix(13,-2,72,-11) Matrix(221,-968,50,-219) -> Matrix(221,-44,1100,-219) Matrix(1877,-8978,392,-1875) -> Matrix(1093,-234,5096,-1091) Matrix(241,-1162,28,-135) -> Matrix(129,-28,364,-79) Matrix(185,-1058,32,-183) -> Matrix(185,-46,736,-183) Matrix(659,-4418,98,-657) -> Matrix(561,-160,1960,-559) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 Degree of the the map X: 162 Degree of the the map Y: 324 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 972 Minimal number of generators: 163 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -7/16 -2/5 -5/14 -1/4 0/1 1/8 1/5 5/22 2/7 8/19 1/2 10/17 11/16 5/7 4/5 1/1 5/4 47/34 7/5 79/56 16/11 3/2 11/7 50/31 13/8 17/10 2/1 19/8 5/2 13/5 46/17 79/29 11/4 20/7 3/1 41/13 10/3 7/2 107/28 4/1 17/4 22/5 9/2 37/8 19/4 67/14 5/1 21/4 11/2 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/52 -5/11 2/95 -9/20 9/424 -13/29 1/47 13/610 -4/9 3/140 2/93 -11/25 3/139 1/46 -7/16 1/46 -10/23 1/46 4/183 -3/7 3/136 1/45 -5/12 1/44 -2/5 1/43 -5/13 1/42 5/209 -3/8 3/124 -13/35 1/41 13/532 -10/27 5/204 4/163 -7/19 2/81 -4/11 2/81 1/40 -9/25 3/121 7/282 -5/14 1/40 -6/17 2/79 3/118 -1/3 1/39 1/38 -3/10 1/36 -5/17 2/73 -2/7 1/36 2/71 -7/25 0/1 -5/18 1/36 -3/11 3/106 1/35 -7/26 7/244 -11/41 4/139 -4/15 2/69 1/34 -5/19 1/34 3/101 -1/4 1/34 -4/17 1/34 4/135 -3/13 3/100 1/33 -5/22 5/164 -7/31 2/65 -2/9 2/65 1/32 -5/23 0/1 -3/14 3/100 -1/5 1/32 1/31 -1/6 1/32 -1/7 0/1 0/1 0/1 1/26 1/9 1/25 1/24 1/8 1/24 1/7 1/23 1/22 2/13 1/25 1/6 1/24 2/11 0/1 1/22 5/27 3/64 1/21 3/16 1/24 4/21 4/89 1/22 1/5 0/1 4/19 3/68 2/45 7/33 1/22 1/21 3/14 1/24 2/9 2/45 1/22 5/22 1/22 3/13 1/22 3/65 4/17 1/21 1/4 1/20 4/15 1/22 4/87 11/41 5/106 1/21 7/26 1/22 3/11 1/23 1/22 5/18 5/108 2/7 1/21 3/10 1/20 4/13 1/20 4/79 5/16 1/18 6/19 0/1 1/14 1/3 1/21 1/20 5/14 1/20 9/25 1/20 1/19 4/11 1/19 11/30 1/20 7/19 3/58 1/19 3/8 3/56 5/13 0/1 7/18 1/20 16/41 1/21 25/64 1/24 9/23 3/64 1/21 2/5 1/20 2/39 7/17 2/39 5/12 5/96 8/19 1/19 11/26 11/208 3/7 1/19 3/56 13/30 11/204 10/23 3/55 17/39 7/127 1/18 7/16 1/20 4/9 4/73 1/18 1/2 1/18 5/9 3/55 1/18 19/34 19/340 14/25 5/89 23/41 7/124 3/53 9/16 5/88 4/7 1/18 2/35 11/19 4/69 7/12 7/120 10/17 1/17 13/22 13/220 3/5 1/17 3/50 11/18 7/116 19/31 9/148 7/115 8/13 3/49 21/34 21/340 13/21 11/177 1/16 5/8 1/16 7/11 0/1 9/14 3/52 20/31 1/17 31/48 1/16 11/17 1/18 1/17 2/3 2/33 1/16 11/16 1/16 9/13 1/16 9/143 16/23 5/79 7/10 1/16 12/17 2/31 3/46 29/41 3/47 5/78 17/24 1/16 5/7 2/31 23/32 23/352 18/25 4/61 13/198 31/43 5/76 1/15 44/61 1/15 13/18 9/136 8/11 0/1 1/14 27/37 1/16 1/15 19/26 1/16 11/15 3/46 1/15 14/19 1/15 3/4 1/16 10/13 9/140 2/31 17/22 3/46 24/31 2/31 3/46 7/9 3/46 1/15 11/14 5/76 4/5 1/15 5/6 5/72 6/7 0/1 1/14 13/15 1/15 1/14 7/8 1/14 1/1 1/14 1/13 10/9 3/38 8/101 9/8 1/12 8/7 1/13 15/13 1/13 3/38 22/19 3/38 2/25 7/6 1/12 6/5 3/38 2/25 5/4 1/12 9/7 7/82 3/35 31/24 31/360 22/17 7/81 35/27 11/127 13/150 13/10 7/80 30/23 2/23 3/34 17/13 2/23 4/3 1/12 2/23 23/17 5/57 3/34 19/14 3/34 15/11 3/34 1/11 26/19 1/11 63/46 17/184 37/27 3/32 5/53 11/8 1/12 29/21 3/37 1/12 47/34 1/12 18/13 1/12 4/47 25/18 9/104 57/41 1/12 1/11 32/23 2/23 3/34 7/5 2/23 31/22 31/352 55/39 53/601 3/34 79/56 3/34 24/17 3/34 22/249 17/12 11/124 27/19 3/34 1/11 37/26 5/56 10/7 4/45 5/56 33/23 7/78 15/167 23/16 7/78 13/9 13/144 1/11 16/11 1/11 19/13 1/11 19/208 3/2 3/32 14/9 3/32 2/21 11/7 2/21 30/19 5/52 8/83 49/31 3/31 1/10 19/12 7/72 27/17 5/52 3/31 8/5 0/1 1/10 29/18 1/12 50/31 1/11 71/44 7/76 21/13 1/11 3/32 55/34 3/32 89/55 2/21 34/21 2/21 1/10 47/29 3/32 5/53 13/8 1/10 31/19 3/32 5/53 49/30 19/200 67/41 2/21 18/11 2/21 9/94 23/14 5/52 5/3 5/51 1/10 17/10 1/10 12/7 1/10 12/119 19/11 6/59 45/26 9/88 26/15 1/10 6/59 7/4 7/68 16/9 0/1 1/10 57/32 7/68 41/23 5/48 7/67 25/14 1/10 9/5 1/10 1/9 11/6 5/48 2/1 1/9 11/5 5/42 3/25 9/4 1/8 25/11 2/17 16/7 2/17 1/8 23/10 7/58 53/23 15/124 19/157 30/13 4/33 25/206 7/3 7/57 1/8 19/8 1/8 12/5 1/8 12/95 29/12 1/8 46/19 8/63 15/118 17/7 6/47 5/2 1/8 18/7 8/61 5/38 31/12 19/144 13/5 2/15 34/13 16/119 7/52 55/21 5/37 13/96 21/8 7/52 29/11 3/22 13/95 8/3 2/15 3/22 27/10 5/36 73/27 7/50 15/107 46/17 1/7 19/7 3/22 1/7 49/18 1/8 79/29 2/15 109/40 7/52 30/11 2/15 3/22 11/4 3/22 47/17 11/80 15/109 36/13 4/29 21/152 25/9 19/137 5/36 39/14 39/280 53/19 6/43 14/5 7/50 8/57 17/6 17/120 20/7 1/7 23/8 23/160 3/1 1/7 3/20 22/7 15/98 2/13 41/13 2/13 19/6 13/84 16/5 3/19 29/9 1/7 1/6 42/13 2/13 1/6 13/4 5/32 10/3 4/25 1/6 7/2 1/6 11/3 1/6 3/17 48/13 9/52 4/23 37/10 7/40 26/7 3/17 41/11 1/6 7/41 56/15 14/81 9/52 15/4 7/40 19/5 2/11 42/11 1/6 2/11 107/28 1/6 65/17 1/6 3/17 23/6 5/28 4/1 2/11 3/16 21/5 5/26 1/5 17/4 5/26 30/7 7/36 22/113 43/10 43/220 13/3 13/66 1/5 22/5 1/5 31/7 1/5 31/154 9/2 9/44 23/5 1/5 3/14 37/8 5/24 14/3 5/24 4/19 19/4 11/52 43/9 25/117 3/14 67/14 3/14 24/5 3/14 14/65 5/1 2/9 21/4 13/56 37/7 3/13 1/4 16/3 7/30 4/17 11/2 1/4 17/3 17/69 1/4 23/4 1/4 6/1 1/4 6/23 19/3 13/48 3/11 13/2 5/18 20/3 17/60 2/7 27/4 23/80 7/1 5/17 3/10 15/2 5/16 23/3 7/22 1/3 8/1 1/3 17/2 7/20 9/1 7/19 3/8 10/1 2/5 9/22 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(247,113,400,183) (-1/2,-5/11) -> (8/13,21/34) Hyperbolic Matrix(343,155,790,357) (-5/11,-9/20) -> (13/30,10/23) Hyperbolic Matrix(881,396,198,89) (-9/20,-13/29) -> (31/7,9/2) Hyperbolic Matrix(1807,809,784,351) (-13/29,-4/9) -> (53/23,30/13) Hyperbolic Matrix(143,63,774,341) (-4/9,-11/25) -> (2/11,5/27) Hyperbolic Matrix(335,147,-768,-337) (-11/25,-7/16) -> (-7/16,-10/23) Parabolic Matrix(141,61,668,289) (-10/23,-3/7) -> (4/19,7/33) Hyperbolic Matrix(141,59,184,77) (-3/7,-5/12) -> (3/4,10/13) Hyperbolic Matrix(229,95,94,39) (-5/12,-2/5) -> (17/7,5/2) Hyperbolic Matrix(307,119,178,69) (-2/5,-5/13) -> (12/7,19/11) Hyperbolic Matrix(45,17,172,65) (-5/13,-3/8) -> (1/4,4/15) Hyperbolic Matrix(257,96,174,65) (-3/8,-13/35) -> (19/13,3/2) Hyperbolic Matrix(2617,971,946,351) (-13/35,-10/27) -> (47/17,36/13) Hyperbolic Matrix(815,301,1454,537) (-10/27,-7/19) -> (14/25,23/41) Hyperbolic Matrix(215,79,596,219) (-7/19,-4/11) -> (9/25,4/11) Hyperbolic Matrix(973,351,1350,487) (-4/11,-9/25) -> (18/25,31/43) Hyperbolic Matrix(209,75,-588,-211) (-9/25,-5/14) -> (-5/14,-6/17) Parabolic Matrix(291,101,412,143) (-6/17,-1/3) -> (12/17,29/41) Hyperbolic Matrix(195,59,76,23) (-1/3,-3/10) -> (5/2,18/7) Hyperbolic Matrix(37,11,232,69) (-3/10,-5/17) -> (2/13,1/6) Hyperbolic Matrix(265,77,382,111) (-5/17,-2/7) -> (9/13,16/23) Hyperbolic Matrix(827,232,524,147) (-2/7,-7/25) -> (11/7,30/19) Hyperbolic Matrix(675,188,298,83) (-7/25,-5/18) -> (9/4,25/11) Hyperbolic Matrix(409,113,76,21) (-5/18,-3/11) -> (16/3,11/2) Hyperbolic Matrix(221,60,372,101) (-3/11,-7/26) -> (13/22,3/5) Hyperbolic Matrix(1441,387,3690,991) (-7/26,-11/41) -> (16/41,25/64) Hyperbolic Matrix(2141,574,884,237) (-11/41,-4/15) -> (46/19,17/7) Hyperbolic Matrix(587,156,222,59) (-4/15,-5/19) -> (29/11,8/3) Hyperbolic Matrix(35,9,-144,-37) (-5/19,-1/4) -> (-1/4,-4/17) Parabolic Matrix(563,132,354,83) (-4/17,-3/13) -> (27/17,8/5) Hyperbolic Matrix(209,48,492,113) (-3/13,-5/22) -> (11/26,3/7) Hyperbolic Matrix(1813,410,1048,237) (-5/22,-7/31) -> (19/11,45/26) Hyperbolic Matrix(1357,305,1882,423) (-7/31,-2/9) -> (31/43,44/61) Hyperbolic Matrix(899,196,344,75) (-2/9,-5/23) -> (13/5,34/13) Hyperbolic Matrix(895,194,346,75) (-5/23,-3/14) -> (31/12,13/5) Hyperbolic Matrix(377,79,272,57) (-3/14,-1/5) -> (18/13,25/18) Hyperbolic Matrix(99,17,64,11) (-1/5,-1/6) -> (3/2,14/9) Hyperbolic Matrix(31,5,130,21) (-1/6,-1/7) -> (4/17,1/4) Hyperbolic Matrix(91,11,124,15) (-1/7,0/1) -> (11/15,14/19) Hyperbolic Matrix(345,-32,248,-23) (0/1,1/9) -> (57/41,32/23) Hyperbolic Matrix(413,-47,290,-33) (1/9,1/8) -> (37/26,10/7) Hyperbolic Matrix(475,-64,334,-45) (1/8,1/7) -> (27/19,37/26) Hyperbolic Matrix(609,-92,470,-71) (1/7,2/13) -> (22/17,35/27) Hyperbolic Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(819,-152,2096,-389) (5/27,3/16) -> (25/64,9/23) Hyperbolic Matrix(1453,-276,816,-155) (3/16,4/21) -> (16/9,57/32) Hyperbolic Matrix(295,-57,678,-131) (4/21,1/5) -> (10/23,17/39) Hyperbolic Matrix(247,-51,402,-83) (1/5,4/19) -> (19/31,8/13) Hyperbolic Matrix(1849,-393,1068,-227) (7/33,3/14) -> (45/26,26/15) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(111,-25,484,-109) (2/9,5/22) -> (5/22,3/13) Parabolic Matrix(701,-164,218,-51) (3/13,4/17) -> (16/5,29/9) Hyperbolic Matrix(425,-114,384,-103) (4/15,11/41) -> (1/1,10/9) Hyperbolic Matrix(361,-97,1150,-309) (11/41,7/26) -> (5/16,6/19) Hyperbolic Matrix(807,-218,596,-161) (7/26,3/11) -> (23/17,19/14) Hyperbolic Matrix(149,-41,338,-93) (3/11,5/18) -> (7/16,4/9) Hyperbolic Matrix(189,-53,296,-83) (5/18,2/7) -> (7/11,9/14) Hyperbolic Matrix(105,-31,166,-49) (2/7,3/10) -> (5/8,7/11) Hyperbolic Matrix(497,-152,206,-63) (3/10,4/13) -> (12/5,29/12) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(123,-40,40,-13) (6/19,1/3) -> (3/1,22/7) Hyperbolic Matrix(439,-156,318,-113) (1/3,5/14) -> (11/8,29/21) Hyperbolic Matrix(1669,-600,1032,-371) (5/14,9/25) -> (21/13,55/34) Hyperbolic Matrix(337,-123,474,-173) (4/11,11/30) -> (17/24,5/7) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(97,-37,118,-45) (3/8,5/13) -> (4/5,5/6) Hyperbolic Matrix(215,-83,272,-105) (5/13,7/18) -> (11/14,4/5) Hyperbolic Matrix(1631,-636,2526,-985) (7/18,16/41) -> (20/31,31/48) Hyperbolic Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(211,-87,114,-47) (7/17,5/12) -> (11/6,2/1) Hyperbolic Matrix(305,-128,722,-303) (5/12,8/19) -> (8/19,11/26) Parabolic Matrix(1885,-816,1356,-587) (3/7,13/30) -> (25/18,57/41) Hyperbolic Matrix(1429,-624,300,-131) (17/39,7/16) -> (19/4,43/9) Hyperbolic Matrix(19,-9,36,-17) (4/9,1/2) -> (1/2,5/9) Parabolic Matrix(2149,-1200,1524,-851) (5/9,19/34) -> (31/22,55/39) Hyperbolic Matrix(745,-417,1038,-581) (19/34,14/25) -> (5/7,23/32) Hyperbolic Matrix(1453,-816,276,-155) (23/41,9/16) -> (21/4,37/7) Hyperbolic Matrix(189,-107,242,-137) (9/16,4/7) -> (7/9,11/14) Hyperbolic Matrix(223,-129,102,-59) (4/7,11/19) -> (2/1,11/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(341,-200,578,-339) (7/12,10/17) -> (10/17,13/22) Parabolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(1019,-656,1412,-909) (9/14,20/31) -> (44/61,13/18) Hyperbolic Matrix(3511,-2268,918,-593) (31/48,11/17) -> (65/17,23/6) Hyperbolic Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(177,-121,256,-175) (2/3,11/16) -> (11/16,9/13) Parabolic Matrix(287,-200,254,-177) (16/23,7/10) -> (9/8,8/7) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(2293,-1623,948,-671) (29/41,17/24) -> (29/12,46/19) Hyperbolic Matrix(345,-248,32,-23) (23/32,18/25) -> (10/1,1/0) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(999,-728,188,-137) (8/11,27/37) -> (37/7,16/3) Hyperbolic Matrix(1733,-1265,374,-273) (27/37,19/26) -> (37/8,14/3) Hyperbolic Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(807,-596,218,-161) (14/19,3/4) -> (37/10,26/7) Hyperbolic Matrix(609,-470,92,-71) (10/13,17/22) -> (13/2,20/3) Hyperbolic Matrix(503,-389,578,-447) (17/22,24/31) -> (13/15,7/8) Hyperbolic Matrix(1277,-990,396,-307) (24/31,7/9) -> (29/9,42/13) Hyperbolic Matrix(205,-172,118,-99) (5/6,6/7) -> (26/15,7/4) Hyperbolic Matrix(435,-376,376,-325) (6/7,13/15) -> (15/13,22/19) Hyperbolic Matrix(287,-254,200,-177) (7/8,1/1) -> (33/23,23/16) Hyperbolic Matrix(827,-927,306,-343) (10/9,9/8) -> (27/10,73/27) Hyperbolic Matrix(315,-361,226,-259) (8/7,15/13) -> (32/23,7/5) Hyperbolic Matrix(2251,-2608,826,-957) (22/19,7/6) -> (109/40,30/11) Hyperbolic Matrix(111,-131,50,-59) (7/6,6/5) -> (11/5,9/4) Hyperbolic Matrix(61,-75,48,-59) (6/5,5/4) -> (5/4,9/7) Parabolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(695,-899,494,-639) (31/24,22/17) -> (7/5,31/22) Hyperbolic Matrix(799,-1036,118,-153) (35/27,13/10) -> (27/4,7/1) Hyperbolic Matrix(927,-1207,586,-763) (13/10,30/23) -> (49/31,19/12) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(849,-1148,230,-311) (4/3,23/17) -> (11/3,48/13) Hyperbolic Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(3179,-4353,1140,-1561) (26/19,63/46) -> (39/14,53/19) Hyperbolic Matrix(2541,-3481,592,-811) (63/46,37/27) -> (30/7,43/10) Hyperbolic Matrix(1867,-2560,1048,-1437) (37/27,11/8) -> (57/32,41/23) Hyperbolic Matrix(1599,-2209,1156,-1597) (29/21,47/34) -> (47/34,18/13) Parabolic Matrix(4425,-6241,3136,-4423) (55/39,79/56) -> (79/56,24/17) Parabolic Matrix(705,-997,268,-379) (24/17,17/12) -> (21/8,29/11) Hyperbolic Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(353,-512,242,-351) (13/9,16/11) -> (16/11,19/13) Parabolic Matrix(337,-526,148,-231) (14/9,11/7) -> (25/11,16/7) Hyperbolic Matrix(2103,-3323,1298,-2051) (30/19,49/31) -> (34/21,47/29) Hyperbolic Matrix(491,-779,104,-165) (19/12,27/17) -> (14/3,19/4) Hyperbolic Matrix(3101,-5000,1922,-3099) (29/18,50/31) -> (50/31,71/44) Parabolic Matrix(2593,-4185,702,-1133) (71/44,21/13) -> (48/13,37/10) Hyperbolic Matrix(1207,-1953,144,-233) (55/34,89/55) -> (8/1,17/2) Hyperbolic Matrix(1433,-2319,186,-301) (89/55,34/21) -> (23/3,8/1) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(565,-921,246,-401) (13/8,31/19) -> (16/7,23/10) Hyperbolic Matrix(2009,-3282,636,-1039) (49/30,67/41) -> (41/13,19/6) Hyperbolic Matrix(1353,-2212,430,-703) (67/41,18/11) -> (22/7,41/13) Hyperbolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(171,-289,100,-169) (5/3,17/10) -> (17/10,12/7) Parabolic Matrix(351,-622,136,-241) (7/4,16/9) -> (18/7,31/12) Hyperbolic Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(475,-849,174,-311) (25/14,9/5) -> (30/11,11/4) Hyperbolic Matrix(125,-227,38,-69) (9/5,11/6) -> (13/4,10/3) Hyperbolic Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(153,-361,64,-151) (7/3,19/8) -> (19/8,12/5) Parabolic Matrix(993,-2599,358,-937) (34/13,55/21) -> (36/13,25/9) Hyperbolic Matrix(515,-1349,134,-351) (55/21,21/8) -> (23/6,4/1) Hyperbolic Matrix(1669,-4513,598,-1617) (73/27,46/17) -> (53/19,14/5) Hyperbolic Matrix(4583,-12482,1682,-4581) (49/18,79/29) -> (79/29,109/40) Parabolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(187,-541,28,-81) (23/8,3/1) -> (20/3,27/4) Hyperbolic Matrix(135,-431,26,-83) (19/6,16/5) -> (5/1,21/4) Hyperbolic Matrix(287,-929,38,-123) (42/13,13/4) -> (15/2,23/3) Hyperbolic Matrix(43,-147,12,-41) (10/3,7/2) -> (7/2,11/3) Parabolic Matrix(223,-829,46,-171) (26/7,41/11) -> (24/5,5/1) Hyperbolic Matrix(291,-1087,34,-127) (56/15,15/4) -> (17/2,9/1) Hyperbolic Matrix(2997,-11449,784,-2995) (42/11,107/28) -> (107/28,65/17) Parabolic Matrix(221,-968,50,-219) (13/3,22/5) -> (22/5,31/7) Parabolic Matrix(939,-4489,196,-937) (43/9,67/14) -> (67/14,24/5) Parabolic Matrix(93,-529,16,-91) (17/3,23/4) -> (23/4,6/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,52,1) Matrix(247,113,400,183) -> Matrix(239,-5,3872,-81) Matrix(343,155,790,357) -> Matrix(331,-7,6100,-129) Matrix(881,396,198,89) -> Matrix(847,-18,4188,-89) Matrix(1807,809,784,351) -> Matrix(1265,-27,10448,-223) Matrix(143,63,774,341) -> Matrix(139,-3,3012,-65) Matrix(335,147,-768,-337) -> Matrix(323,-7,14812,-321) Matrix(141,61,668,289) -> Matrix(137,-3,3060,-67) Matrix(141,59,184,77) -> Matrix(133,-3,2084,-47) Matrix(229,95,94,39) -> Matrix(221,-5,1724,-39) Matrix(307,119,178,69) -> Matrix(295,-7,2908,-69) Matrix(45,17,172,65) -> Matrix(41,-1,944,-23) Matrix(257,96,174,65) -> Matrix(247,-6,2676,-65) Matrix(2617,971,946,351) -> Matrix(1267,-31,9196,-225) Matrix(815,301,1454,537) -> Matrix(529,-13,9400,-231) Matrix(215,79,596,219) -> Matrix(121,-3,2380,-59) Matrix(973,351,1350,487) -> Matrix(445,-11,6756,-167) Matrix(209,75,-588,-211) -> Matrix(201,-5,8000,-199) Matrix(291,101,412,143) -> Matrix(41,-1,616,-15) Matrix(195,59,76,23) -> Matrix(109,-3,836,-23) Matrix(37,11,232,69) -> Matrix(37,-1,852,-23) Matrix(265,77,382,111) -> Matrix(253,-7,4012,-111) Matrix(827,232,524,147) -> Matrix(67,-2,704,-21) Matrix(675,188,298,83) -> Matrix(71,-2,604,-17) Matrix(409,113,76,21) -> Matrix(179,-5,752,-21) Matrix(221,60,372,101) -> Matrix(211,-6,3552,-101) Matrix(1441,387,3690,991) -> Matrix(35,-1,596,-17) Matrix(2141,574,884,237) -> Matrix(763,-22,6000,-173) Matrix(587,156,222,59) -> Matrix(139,-4,1008,-29) Matrix(35,9,-144,-37) -> Matrix(35,-1,1156,-33) Matrix(563,132,354,83) -> Matrix(135,-4,1384,-41) Matrix(209,48,492,113) -> Matrix(199,-6,3748,-113) Matrix(1813,410,1048,237) -> Matrix(523,-16,5132,-157) Matrix(1357,305,1882,423) -> Matrix(357,-11,5420,-167) Matrix(899,196,344,75) -> Matrix(57,-2,428,-15) Matrix(895,194,346,75) -> Matrix(73,-2,548,-15) Matrix(377,79,272,57) -> Matrix(97,-3,1132,-35) Matrix(99,17,64,11) -> Matrix(29,-1,320,-11) Matrix(31,5,130,21) -> Matrix(31,-1,652,-21) Matrix(91,11,124,15) -> Matrix(29,-1,436,-15) Matrix(345,-32,248,-23) -> Matrix(49,-2,564,-23) Matrix(413,-47,290,-33) -> Matrix(29,-1,320,-11) Matrix(475,-64,334,-45) -> Matrix(91,-4,1024,-45) Matrix(609,-92,470,-71) -> Matrix(57,-2,656,-23) Matrix(367,-66,228,-41) -> Matrix(1,0,-12,1) Matrix(819,-152,2096,-389) -> Matrix(1,0,0,1) Matrix(1453,-276,816,-155) -> Matrix(89,-4,868,-39) Matrix(295,-57,678,-131) -> Matrix(65,-3,1192,-55) Matrix(247,-51,402,-83) -> Matrix(71,-3,1160,-49) Matrix(1849,-393,1068,-227) -> Matrix(111,-5,1088,-49) Matrix(355,-78,132,-29) -> Matrix(91,-4,660,-29) Matrix(111,-25,484,-109) -> Matrix(111,-5,2420,-109) Matrix(701,-164,218,-51) -> Matrix(87,-4,544,-25) Matrix(425,-114,384,-103) -> Matrix(85,-4,1084,-51) Matrix(361,-97,1150,-309) -> Matrix(21,-1,400,-19) Matrix(807,-218,596,-161) -> Matrix(41,-2,472,-23) Matrix(149,-41,338,-93) -> Matrix(65,-3,1192,-55) Matrix(189,-53,296,-83) -> Matrix(21,-1,400,-19) Matrix(105,-31,166,-49) -> Matrix(21,-1,316,-15) Matrix(497,-152,206,-63) -> Matrix(161,-8,1268,-63) Matrix(701,-218,164,-51) -> Matrix(113,-6,584,-31) Matrix(123,-40,40,-13) -> Matrix(43,-2,280,-13) Matrix(439,-156,318,-113) -> Matrix(39,-2,488,-25) Matrix(1669,-600,1032,-371) -> Matrix(77,-4,828,-43) Matrix(337,-123,474,-173) -> Matrix(21,-1,316,-15) Matrix(1501,-552,552,-203) -> Matrix(1,0,-12,1) Matrix(355,-132,78,-29) -> Matrix(115,-6,556,-29) Matrix(97,-37,118,-45) -> Matrix(17,-1,256,-15) Matrix(215,-83,272,-105) -> Matrix(25,-1,376,-15) Matrix(1631,-636,2526,-985) -> Matrix(1,0,-4,1) Matrix(233,-92,38,-15) -> Matrix(81,-4,304,-15) Matrix(153,-62,116,-47) -> Matrix(1,0,-8,1) Matrix(211,-87,114,-47) -> Matrix(97,-5,912,-47) Matrix(305,-128,722,-303) -> Matrix(305,-16,5776,-303) Matrix(1885,-816,1356,-587) -> Matrix(75,-4,844,-45) Matrix(1429,-624,300,-131) -> Matrix(69,-4,328,-19) Matrix(19,-9,36,-17) -> Matrix(19,-1,324,-17) Matrix(2149,-1200,1524,-851) -> Matrix(789,-44,8948,-499) Matrix(745,-417,1038,-581) -> Matrix(303,-17,4652,-261) Matrix(1453,-816,276,-155) -> Matrix(425,-24,1824,-103) Matrix(189,-107,242,-137) -> Matrix(87,-5,1340,-77) Matrix(223,-129,102,-59) -> Matrix(121,-7,1020,-59) Matrix(513,-298,136,-79) -> Matrix(241,-14,1360,-79) Matrix(341,-200,578,-339) -> Matrix(341,-20,5780,-339) Matrix(571,-348,402,-245) -> Matrix(101,-6,1128,-67) Matrix(2077,-1272,1272,-779) -> Matrix(395,-24,4164,-253) Matrix(1669,-1032,600,-371) -> Matrix(581,-36,4180,-259) Matrix(367,-228,66,-41) -> Matrix(95,-6,396,-25) Matrix(1019,-656,1412,-909) -> Matrix(101,-6,1532,-91) Matrix(3511,-2268,918,-593) -> Matrix(37,-2,204,-11) Matrix(131,-86,32,-21) -> Matrix(67,-4,352,-21) Matrix(177,-121,256,-175) -> Matrix(177,-11,2816,-175) Matrix(287,-200,254,-177) -> Matrix(95,-6,1156,-73) Matrix(571,-402,348,-245) -> Matrix(187,-12,1948,-125) Matrix(2293,-1623,948,-671) -> Matrix(81,-5,632,-39) Matrix(345,-248,32,-23) -> Matrix(153,-10,352,-23) Matrix(439,-318,156,-113) -> Matrix(119,-8,848,-57) Matrix(999,-728,188,-137) -> Matrix(63,-4,268,-17) Matrix(1733,-1265,374,-273) -> Matrix(11,-1,56,-5) Matrix(1153,-844,250,-183) -> Matrix(91,-6,440,-29) Matrix(807,-596,218,-161) -> Matrix(57,-4,328,-23) Matrix(609,-470,92,-71) -> Matrix(247,-16,880,-57) Matrix(503,-389,578,-447) -> Matrix(15,-1,256,-17) Matrix(1277,-990,396,-307) -> Matrix(61,-4,412,-27) Matrix(205,-172,118,-99) -> Matrix(85,-6,836,-59) Matrix(435,-376,376,-325) -> Matrix(31,-2,388,-25) Matrix(287,-254,200,-177) -> Matrix(119,-8,1324,-89) Matrix(827,-927,306,-343) -> Matrix(137,-11,984,-79) Matrix(315,-361,226,-259) -> Matrix(37,-3,432,-35) Matrix(2251,-2608,826,-957) -> Matrix(151,-12,1120,-89) Matrix(111,-131,50,-59) -> Matrix(11,-1,100,-9) Matrix(61,-75,48,-59) -> Matrix(61,-5,720,-59) Matrix(613,-790,142,-183) -> Matrix(373,-32,1900,-163) Matrix(695,-899,494,-639) -> Matrix(359,-31,4088,-353) Matrix(799,-1036,118,-153) -> Matrix(369,-32,1280,-111) Matrix(927,-1207,586,-763) -> Matrix(79,-7,824,-73) Matrix(983,-1284,258,-337) -> Matrix(91,-8,512,-45) Matrix(849,-1148,230,-311) -> Matrix(159,-14,920,-81) Matrix(481,-654,114,-155) -> Matrix(21,-2,116,-11) Matrix(867,-1184,320,-437) -> Matrix(1,0,-4,1) Matrix(3179,-4353,1140,-1561) -> Matrix(511,-47,3664,-337) Matrix(2541,-3481,592,-811) -> Matrix(333,-31,1708,-159) Matrix(1867,-2560,1048,-1437) -> Matrix(41,-4,400,-39) Matrix(1599,-2209,1156,-1597) -> Matrix(85,-7,1008,-83) Matrix(4425,-6241,3136,-4423) -> Matrix(2551,-225,28900,-2549) Matrix(705,-997,268,-379) -> Matrix(305,-27,2248,-199) Matrix(1575,-2258,422,-605) -> Matrix(379,-34,2196,-197) Matrix(421,-606,66,-95) -> Matrix(289,-26,1056,-95) Matrix(353,-512,242,-351) -> Matrix(353,-32,3872,-351) Matrix(337,-526,148,-231) -> Matrix(85,-8,712,-67) Matrix(2103,-3323,1298,-2051) -> Matrix(11,-1,100,-9) Matrix(491,-779,104,-165) -> Matrix(53,-5,244,-23) Matrix(3101,-5000,1922,-3099) -> Matrix(89,-8,968,-87) Matrix(2593,-4185,702,-1133) -> Matrix(227,-21,1308,-121) Matrix(1207,-1953,144,-233) -> Matrix(179,-17,516,-49) Matrix(1433,-2319,186,-301) -> Matrix(157,-15,492,-47) Matrix(1091,-1770,474,-769) -> Matrix(187,-18,1548,-149) Matrix(565,-921,246,-401) -> Matrix(117,-11,968,-91) Matrix(2009,-3282,636,-1039) -> Matrix(673,-64,4364,-415) Matrix(1353,-2212,430,-703) -> Matrix(503,-48,3280,-313) Matrix(143,-236,20,-33) -> Matrix(103,-10,340,-33) Matrix(171,-289,100,-169) -> Matrix(171,-17,1700,-169) Matrix(351,-622,136,-241) -> Matrix(75,-8,572,-61) Matrix(911,-1626,330,-589) -> Matrix(17,-2,128,-15) Matrix(475,-849,174,-311) -> Matrix(47,-5,348,-37) Matrix(125,-227,38,-69) -> Matrix(49,-5,304,-31) Matrix(147,-340,16,-37) -> Matrix(115,-14,304,-37) Matrix(153,-361,64,-151) -> Matrix(153,-19,1216,-151) Matrix(993,-2599,358,-937) -> Matrix(393,-53,2840,-383) Matrix(515,-1349,134,-351) -> Matrix(81,-11,464,-63) Matrix(1669,-4513,598,-1617) -> Matrix(349,-49,2500,-351) Matrix(4583,-12482,1682,-4581) -> Matrix(121,-16,900,-119) Matrix(281,-800,98,-279) -> Matrix(281,-40,1960,-279) Matrix(187,-541,28,-81) -> Matrix(159,-23,560,-81) Matrix(135,-431,26,-83) -> Matrix(83,-13,364,-57) Matrix(287,-929,38,-123) -> Matrix(97,-15,304,-47) Matrix(43,-147,12,-41) -> Matrix(43,-7,252,-41) Matrix(223,-829,46,-171) -> Matrix(39,-7,184,-33) Matrix(291,-1087,34,-127) -> Matrix(121,-21,340,-59) Matrix(2997,-11449,784,-2995) -> Matrix(7,-1,36,-5) Matrix(221,-968,50,-219) -> Matrix(221,-44,1100,-219) Matrix(939,-4489,196,-937) -> Matrix(547,-117,2548,-545) Matrix(93,-529,16,-91) -> Matrix(93,-23,368,-91) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 26 1 0/1 (0/1,1/26) 0 27 1/6 1/24 1 27 2/11 (0/1,1/22) 0 27 1/5 0/1 2 9 3/14 1/24 1 27 2/9 (2/45,1/22) 0 27 5/22 1/22 5 1 1/4 1/20 1 27 2/7 1/21 2 3 3/10 1/20 1 27 1/3 (1/21,1/20) 0 27 4/11 1/19 2 9 11/30 1/20 1 27 7/19 (3/58,1/19) 0 27 3/8 3/56 1 27 5/13 0/1 4 3 7/18 1/20 1 27 9/23 (3/64,1/21) 0 27 2/5 (1/20,2/39) 0 27 7/17 2/39 2 9 5/12 5/96 1 27 8/19 1/19 8 1 3/7 (1/19,3/56) 0 27 7/16 1/20 1 27 4/9 (4/73,1/18) 0 27 1/2 1/18 1 9 5/9 (3/55,1/18) 0 27 9/16 5/88 1 27 4/7 (1/18,2/35) 0 27 11/19 4/69 2 9 7/12 7/120 1 27 10/17 1/17 10 1 3/5 (1/17,3/50) 0 27 11/18 7/116 1 27 19/31 (9/148,7/115) 0 27 8/13 3/49 2 9 5/8 1/16 1 27 7/11 0/1 2 3 9/14 3/52 1 27 11/17 (1/18,1/17) 0 27 2/3 (2/33,1/16) 0 27 11/16 1/16 11 1 7/10 1/16 1 27 12/17 (2/31,3/46) 0 27 5/7 2/31 2 9 13/18 9/136 1 27 8/11 (0/1,1/14) 0 27 19/26 1/16 1 3 11/15 (3/46,1/15) 0 27 3/4 1/16 1 27 4/5 1/15 4 3 5/6 5/72 1 27 1/1 (1/14,1/13) 0 27 8/7 1/13 2 9 7/6 1/12 1 27 6/5 (3/38,2/25) 0 27 5/4 1/12 5 3 9/7 (7/82,3/35) 0 27 31/24 31/360 1 27 22/17 7/81 2 9 13/10 7/80 1 27 30/23 (2/23,3/34) 0 27 17/13 2/23 2 9 4/3 (1/12,2/23) 0 27 15/11 (3/34,1/11) 0 27 26/19 1/11 8 3 37/27 (3/32,5/53) 0 27 11/8 1/12 1 27 47/34 1/12 7 1 18/13 (1/12,4/47) 0 27 7/5 2/23 2 9 31/22 31/352 1 27 79/56 3/34 25 1 24/17 (3/34,22/249) 0 27 17/12 11/124 1 27 27/19 (3/34,1/11) 0 27 37/26 5/56 1 3 10/7 (4/45,5/56) 0 27 23/16 7/78 1 9 13/9 (13/144,1/11) 0 27 16/11 1/11 16 1 3/2 3/32 1 27 11/7 2/21 2 3 19/12 7/72 1 27 8/5 (0/1,1/10) 0 27 29/18 1/12 1 27 50/31 1/11 4 1 21/13 (1/11,3/32) 0 27 34/21 (2/21,1/10) 0 27 13/8 1/10 1 9 31/19 (3/32,5/53) 0 27 49/30 19/200 1 27 67/41 2/21 14 1 18/11 (2/21,9/94) 0 27 23/14 5/52 1 27 5/3 (5/51,1/10) 0 27 17/10 1/10 17 1 7/4 7/68 1 27 16/9 (0/1,1/10) 0 27 41/23 (5/48,7/67) 0 27 25/14 1/10 1 9 9/5 (1/10,1/9) 0 27 11/6 5/48 1 27 2/1 1/9 2 9 11/5 (5/42,3/25) 0 27 9/4 1/8 1 27 16/7 (2/17,1/8) 0 27 23/10 7/58 1 9 7/3 (7/57,1/8) 0 27 19/8 1/8 19 1 5/2 1/8 1 27 13/5 2/15 4 3 21/8 7/52 1 27 8/3 (2/15,3/22) 0 27 27/10 5/36 1 27 46/17 1/7 8 3 19/7 (3/22,1/7) 0 27 49/18 1/8 1 27 79/29 2/15 2 1 30/11 (2/15,3/22) 0 27 11/4 3/22 1 9 14/5 (7/50,8/57) 0 27 17/6 17/120 1 27 20/7 1/7 20 1 3/1 (1/7,3/20) 0 27 16/5 3/19 2 9 13/4 5/32 1 27 10/3 (4/25,1/6) 0 27 7/2 1/6 7 3 11/3 (1/6,3/17) 0 27 26/7 3/17 2 9 41/11 (1/6,7/41) 0 27 56/15 (14/81,9/52) 0 27 15/4 7/40 1 27 19/5 2/11 2 9 42/11 (1/6,2/11) 0 27 107/28 1/6 1 1 23/6 5/28 1 27 4/1 (2/11,3/16) 0 27 21/5 (5/26,1/5) 0 27 17/4 5/26 1 9 30/7 (7/36,22/113) 0 27 13/3 (13/66,1/5) 0 27 22/5 1/5 22 1 9/2 9/44 1 27 23/5 (1/5,3/14) 0 27 37/8 5/24 1 3 14/3 (5/24,4/19) 0 27 19/4 11/52 1 27 67/14 3/14 13 1 24/5 (3/14,14/65) 0 27 5/1 2/9 2 9 11/2 1/4 1 27 23/4 1/4 23 1 6/1 (1/4,6/23) 0 27 19/3 (13/48,3/11) 0 27 13/2 5/18 1 9 7/1 (5/17,3/10) 0 27 15/2 5/16 1 27 8/1 1/3 8 3 9/1 (7/19,3/8) 0 27 10/1 (2/5,9/22) 0 27 1/0 1/0 1 27 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(69,-11,94,-15) (0/1,1/6) -> (11/15,3/4) Glide Reflection Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(341,-63,92,-17) (2/11,1/5) -> (11/3,26/7) Glide Reflection Matrix(289,-61,90,-19) (1/5,3/14) -> (16/5,13/4) Glide Reflection Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(89,-20,396,-89) (2/9,5/22) -> (2/9,5/22) Reflection Matrix(21,-5,88,-21) (5/22,1/4) -> (5/22,1/4) Reflection Matrix(65,-17,42,-11) (1/4,2/7) -> (3/2,11/7) Glide Reflection Matrix(105,-31,166,-49) (2/7,3/10) -> (5/8,7/11) Hyperbolic Matrix(187,-57,82,-25) (3/10,1/3) -> (9/4,16/7) Glide Reflection Matrix(219,-79,158,-57) (1/3,4/11) -> (18/13,7/5) Glide Reflection Matrix(317,-116,276,-101) (4/11,11/30) -> (8/7,7/6) Glide Reflection Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(97,-37,118,-45) (3/8,5/13) -> (4/5,5/6) Hyperbolic Matrix(507,-196,194,-75) (5/13,7/18) -> (13/5,21/8) Glide Reflection Matrix(601,-235,156,-61) (7/18,9/23) -> (23/6,4/1) Glide Reflection Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(211,-87,114,-47) (7/17,5/12) -> (11/6,2/1) Hyperbolic Matrix(191,-80,456,-191) (5/12,8/19) -> (5/12,8/19) Reflection Matrix(113,-48,266,-113) (8/19,3/7) -> (8/19,3/7) Reflection Matrix(357,-155,76,-33) (3/7,7/16) -> (14/3,19/4) Glide Reflection Matrix(299,-132,188,-83) (7/16,4/9) -> (19/12,8/5) Glide Reflection Matrix(19,-9,36,-17) (4/9,1/2) -> (1/2,5/9) Parabolic Matrix(537,-301,380,-213) (5/9,9/16) -> (24/17,17/12) Glide Reflection Matrix(275,-156,104,-59) (9/16,4/7) -> (21/8,8/3) Glide Reflection Matrix(223,-129,102,-59) (4/7,11/19) -> (2/1,11/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(239,-140,408,-239) (7/12,10/17) -> (7/12,10/17) Reflection Matrix(101,-60,170,-101) (10/17,3/5) -> (10/17,3/5) Reflection Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(535,-328,168,-103) (19/31,8/13) -> (3/1,16/5) Glide Reflection Matrix(183,-113,34,-21) (8/13,5/8) -> (5/1,11/2) Glide Reflection Matrix(363,-232,230,-147) (7/11,9/14) -> (11/7,19/12) Glide Reflection Matrix(641,-413,492,-317) (9/14,11/17) -> (13/10,30/23) Glide Reflection Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(65,-44,96,-65) (2/3,11/16) -> (2/3,11/16) Reflection Matrix(111,-77,160,-111) (11/16,7/10) -> (11/16,7/10) Reflection Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(143,-101,126,-89) (12/17,5/7) -> (1/1,8/7) Glide Reflection Matrix(487,-351,376,-271) (5/7,13/18) -> (22/17,13/10) Glide Reflection Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(1109,-809,780,-569) (8/11,19/26) -> (27/19,37/26) Glide Reflection Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(77,-59,30,-23) (3/4,4/5) -> (5/2,13/5) Glide Reflection Matrix(103,-87,58,-49) (5/6,1/1) -> (7/4,16/9) Glide Reflection Matrix(111,-131,50,-59) (7/6,6/5) -> (11/5,9/4) Hyperbolic Matrix(61,-75,48,-59) (6/5,5/4) -> (5/4,9/7) Parabolic Matrix(247,-319,24,-31) (9/7,31/24) -> (10/1,1/0) Glide Reflection Matrix(695,-899,494,-639) (31/24,22/17) -> (7/5,31/22) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(333,-451,206,-279) (4/3,15/11) -> (21/13,34/21) Glide Reflection Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(387,-530,46,-63) (26/19,37/27) -> (8/1,9/1) Glide Reflection Matrix(853,-1171,228,-313) (37/27,11/8) -> (56/15,15/4) Glide Reflection Matrix(375,-517,272,-375) (11/8,47/34) -> (11/8,47/34) Reflection Matrix(1223,-1692,884,-1223) (47/34,18/13) -> (47/34,18/13) Reflection Matrix(1737,-2449,1232,-1737) (31/22,79/56) -> (31/22,79/56) Reflection Matrix(2687,-3792,1904,-2687) (79/56,24/17) -> (79/56,24/17) Reflection Matrix(623,-888,134,-191) (37/26,10/7) -> (37/8,14/3) Glide Reflection Matrix(831,-1193,466,-669) (10/7,23/16) -> (41/23,25/14) Glide Reflection Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(287,-416,198,-287) (13/9,16/11) -> (13/9,16/11) Reflection Matrix(65,-96,44,-65) (16/11,3/2) -> (16/11,3/2) Reflection Matrix(1799,-2900,1116,-1799) (29/18,50/31) -> (29/18,50/31) Reflection Matrix(1301,-2100,806,-1301) (50/31,21/13) -> (50/31,21/13) Reflection Matrix(525,-851,124,-201) (34/21,13/8) -> (21/5,17/4) Glide Reflection Matrix(565,-921,246,-401) (13/8,31/19) -> (16/7,23/10) Hyperbolic Matrix(4019,-6566,2460,-4019) (49/30,67/41) -> (49/30,67/41) Reflection Matrix(1475,-2412,902,-1475) (67/41,18/11) -> (67/41,18/11) Reflection Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(101,-170,60,-101) (5/3,17/10) -> (5/3,17/10) Reflection Matrix(69,-119,40,-69) (17/10,7/4) -> (17/10,7/4) Reflection Matrix(1447,-2577,388,-691) (16/9,41/23) -> (41/11,56/15) Glide Reflection Matrix(475,-849,174,-311) (25/14,9/5) -> (30/11,11/4) Hyperbolic Matrix(125,-227,38,-69) (9/5,11/6) -> (13/4,10/3) Hyperbolic Matrix(351,-809,82,-189) (23/10,7/3) -> (17/4,30/7) Glide Reflection Matrix(113,-266,48,-113) (7/3,19/8) -> (7/3,19/8) Reflection Matrix(39,-95,16,-39) (19/8,5/2) -> (19/8,5/2) Reflection Matrix(335,-906,44,-119) (27/10,46/17) -> (15/2,8/1) Glide Reflection Matrix(2843,-7742,1044,-2843) (49/18,79/29) -> (49/18,79/29) Reflection Matrix(1739,-4740,638,-1739) (79/29,30/11) -> (79/29,30/11) Reflection Matrix(93,-259,14,-39) (11/4,14/5) -> (13/2,7/1) Glide Reflection Matrix(239,-680,84,-239) (17/6,20/7) -> (17/6,20/7) Reflection Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(43,-147,12,-41) (10/3,7/2) -> (7/2,11/3) Parabolic Matrix(223,-829,46,-171) (26/7,41/11) -> (24/5,5/1) Hyperbolic Matrix(2353,-8988,616,-2353) (42/11,107/28) -> (42/11,107/28) Reflection Matrix(643,-2461,168,-643) (107/28,23/6) -> (107/28,23/6) Reflection Matrix(97,-417,10,-43) (30/7,13/3) -> (9/1,10/1) Glide Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(267,-1273,56,-267) (19/4,67/14) -> (19/4,67/14) Reflection Matrix(671,-3216,140,-671) (67/14,24/5) -> (67/14,24/5) Reflection Matrix(45,-253,8,-45) (11/2,23/4) -> (11/2,23/4) Reflection Matrix(47,-276,8,-47) (23/4,6/1) -> (23/4,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,52,-1) (-1/1,0/1) -> (0/1,1/26) Matrix(69,-11,94,-15) -> Matrix(23,-1,344,-15) Matrix(367,-66,228,-41) -> Matrix(1,0,-12,1) 0/1 Matrix(341,-63,92,-17) -> Matrix(65,-3,368,-17) Matrix(289,-61,90,-19) -> Matrix(67,-3,424,-19) Matrix(355,-78,132,-29) -> Matrix(91,-4,660,-29) Matrix(89,-20,396,-89) -> Matrix(89,-4,1980,-89) (2/9,5/22) -> (2/45,1/22) Matrix(21,-5,88,-21) -> Matrix(21,-1,440,-21) (5/22,1/4) -> (1/22,1/20) Matrix(65,-17,42,-11) -> Matrix(23,-1,252,-11) Matrix(105,-31,166,-49) -> Matrix(21,-1,316,-15) Matrix(187,-57,82,-25) -> Matrix(61,-3,508,-25) Matrix(219,-79,158,-57) -> Matrix(59,-3,688,-35) Matrix(317,-116,276,-101) -> Matrix(1,0,32,-1) *** -> (0/1,1/16) Matrix(1501,-552,552,-203) -> Matrix(1,0,-12,1) 0/1 Matrix(355,-132,78,-29) -> Matrix(115,-6,556,-29) Matrix(97,-37,118,-45) -> Matrix(17,-1,256,-15) 1/16 Matrix(507,-196,194,-75) -> Matrix(47,-2,352,-15) Matrix(601,-235,156,-61) -> Matrix(65,-3,368,-17) Matrix(233,-92,38,-15) -> Matrix(81,-4,304,-15) Matrix(153,-62,116,-47) -> Matrix(1,0,-8,1) 0/1 Matrix(211,-87,114,-47) -> Matrix(97,-5,912,-47) Matrix(191,-80,456,-191) -> Matrix(191,-10,3648,-191) (5/12,8/19) -> (5/96,1/19) Matrix(113,-48,266,-113) -> Matrix(113,-6,2128,-113) (8/19,3/7) -> (1/19,3/56) Matrix(357,-155,76,-33) -> Matrix(129,-7,608,-33) Matrix(299,-132,188,-83) -> Matrix(73,-4,748,-41) Matrix(19,-9,36,-17) -> Matrix(19,-1,324,-17) 1/18 Matrix(537,-301,380,-213) -> Matrix(231,-13,2612,-147) Matrix(275,-156,104,-59) -> Matrix(69,-4,500,-29) Matrix(223,-129,102,-59) -> Matrix(121,-7,1020,-59) Matrix(513,-298,136,-79) -> Matrix(241,-14,1360,-79) Matrix(239,-140,408,-239) -> Matrix(239,-14,4080,-239) (7/12,10/17) -> (7/120,1/17) Matrix(101,-60,170,-101) -> Matrix(101,-6,1700,-101) (10/17,3/5) -> (1/17,3/50) Matrix(571,-348,402,-245) -> Matrix(101,-6,1128,-67) Matrix(2077,-1272,1272,-779) -> Matrix(395,-24,4164,-253) Matrix(535,-328,168,-103) -> Matrix(197,-12,1264,-77) Matrix(183,-113,34,-21) -> Matrix(81,-5,340,-21) Matrix(363,-232,230,-147) -> Matrix(37,-2,388,-21) Matrix(641,-413,492,-317) -> Matrix(15,-1,164,-11) Matrix(131,-86,32,-21) -> Matrix(67,-4,352,-21) Matrix(65,-44,96,-65) -> Matrix(65,-4,1056,-65) (2/3,11/16) -> (2/33,1/16) Matrix(111,-77,160,-111) -> Matrix(111,-7,1760,-111) (11/16,7/10) -> (1/16,7/110) Matrix(571,-402,348,-245) -> Matrix(187,-12,1948,-125) Matrix(143,-101,126,-89) -> Matrix(15,-1,164,-11) Matrix(487,-351,376,-271) -> Matrix(167,-11,1928,-127) Matrix(439,-318,156,-113) -> Matrix(119,-8,848,-57) Matrix(1109,-809,780,-569) -> Matrix(11,-1,120,-11) *** -> (1/12,1/10) Matrix(1153,-844,250,-183) -> Matrix(91,-6,440,-29) Matrix(77,-59,30,-23) -> Matrix(47,-3,360,-23) Matrix(103,-87,58,-49) -> Matrix(13,-1,116,-9) Matrix(111,-131,50,-59) -> Matrix(11,-1,100,-9) 1/10 Matrix(61,-75,48,-59) -> Matrix(61,-5,720,-59) 1/12 Matrix(247,-319,24,-31) -> Matrix(151,-13,360,-31) Matrix(695,-899,494,-639) -> Matrix(359,-31,4088,-353) Matrix(983,-1284,258,-337) -> Matrix(91,-8,512,-45) Matrix(333,-451,206,-279) -> Matrix(57,-5,604,-53) Matrix(867,-1184,320,-437) -> Matrix(1,0,-4,1) 0/1 Matrix(387,-530,46,-63) -> Matrix(65,-6,184,-17) Matrix(853,-1171,228,-313) -> Matrix(29,-3,164,-17) Matrix(375,-517,272,-375) -> Matrix(11,-1,120,-11) (11/8,47/34) -> (1/12,1/10) Matrix(1223,-1692,884,-1223) -> Matrix(95,-8,1128,-95) (47/34,18/13) -> (1/12,4/47) Matrix(1737,-2449,1232,-1737) -> Matrix(1055,-93,11968,-1055) (31/22,79/56) -> (31/352,3/34) Matrix(2687,-3792,1904,-2687) -> Matrix(1495,-132,16932,-1495) (79/56,24/17) -> (3/34,22/249) Matrix(623,-888,134,-191) -> Matrix(1,0,16,-1) *** -> (0/1,1/8) Matrix(831,-1193,466,-669) -> Matrix(167,-15,1592,-143) Matrix(421,-606,66,-95) -> Matrix(289,-26,1056,-95) Matrix(287,-416,198,-287) -> Matrix(287,-26,3168,-287) (13/9,16/11) -> (13/144,1/11) Matrix(65,-96,44,-65) -> Matrix(65,-6,704,-65) (16/11,3/2) -> (1/11,3/32) Matrix(1799,-2900,1116,-1799) -> Matrix(23,-2,264,-23) (29/18,50/31) -> (1/12,1/11) Matrix(1301,-2100,806,-1301) -> Matrix(65,-6,704,-65) (50/31,21/13) -> (1/11,3/32) Matrix(525,-851,124,-201) -> Matrix(95,-9,496,-47) Matrix(565,-921,246,-401) -> Matrix(117,-11,968,-91) Matrix(4019,-6566,2460,-4019) -> Matrix(799,-76,8400,-799) (49/30,67/41) -> (19/200,2/21) Matrix(1475,-2412,902,-1475) -> Matrix(377,-36,3948,-377) (67/41,18/11) -> (2/21,9/94) Matrix(143,-236,20,-33) -> Matrix(103,-10,340,-33) Matrix(101,-170,60,-101) -> Matrix(101,-10,1020,-101) (5/3,17/10) -> (5/51,1/10) Matrix(69,-119,40,-69) -> Matrix(69,-7,680,-69) (17/10,7/4) -> (1/10,7/68) Matrix(1447,-2577,388,-691) -> Matrix(69,-7,404,-41) Matrix(475,-849,174,-311) -> Matrix(47,-5,348,-37) Matrix(125,-227,38,-69) -> Matrix(49,-5,304,-31) Matrix(351,-809,82,-189) -> Matrix(223,-27,1148,-139) Matrix(113,-266,48,-113) -> Matrix(113,-14,912,-113) (7/3,19/8) -> (7/57,1/8) Matrix(39,-95,16,-39) -> Matrix(39,-5,304,-39) (19/8,5/2) -> (1/8,5/38) Matrix(335,-906,44,-119) -> Matrix(71,-10,220,-31) Matrix(2843,-7742,1044,-2843) -> Matrix(31,-4,240,-31) (49/18,79/29) -> (1/8,2/15) Matrix(1739,-4740,638,-1739) -> Matrix(89,-12,660,-89) (79/29,30/11) -> (2/15,3/22) Matrix(93,-259,14,-39) -> Matrix(79,-11,280,-39) Matrix(239,-680,84,-239) -> Matrix(239,-34,1680,-239) (17/6,20/7) -> (17/120,1/7) Matrix(41,-120,14,-41) -> Matrix(41,-6,280,-41) (20/7,3/1) -> (1/7,3/20) Matrix(43,-147,12,-41) -> Matrix(43,-7,252,-41) 1/6 Matrix(223,-829,46,-171) -> Matrix(39,-7,184,-33) Matrix(2353,-8988,616,-2353) -> Matrix(23,-4,132,-23) (42/11,107/28) -> (1/6,2/11) Matrix(643,-2461,168,-643) -> Matrix(29,-5,168,-29) (107/28,23/6) -> (1/6,5/28) Matrix(97,-417,10,-43) -> Matrix(87,-17,220,-43) Matrix(131,-572,30,-131) -> Matrix(131,-26,660,-131) (13/3,22/5) -> (13/66,1/5) Matrix(89,-396,20,-89) -> Matrix(89,-18,440,-89) (22/5,9/2) -> (1/5,9/44) Matrix(267,-1273,56,-267) -> Matrix(155,-33,728,-155) (19/4,67/14) -> (11/52,3/14) Matrix(671,-3216,140,-671) -> Matrix(391,-84,1820,-391) (67/14,24/5) -> (3/14,14/65) Matrix(45,-253,8,-45) -> Matrix(45,-11,184,-45) (11/2,23/4) -> (11/46,1/4) Matrix(47,-276,8,-47) -> Matrix(47,-12,184,-47) (23/4,6/1) -> (1/4,6/23) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.