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): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 64 Genus: 113 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -51/16 0/1 1/1 17/15 17/14 17/13 17/12 3/2 17/11 17/10 17/9 2/1 17/8 136/61 34/15 136/57 12/5 17/7 5/2 85/33 34/13 68/25 17/6 3/1 102/31 17/5 7/2 68/19 18/5 11/3 374/101 34/9 4/1 17/4 30/7 13/3 136/31 22/5 102/23 9/2 14/3 136/29 24/5 34/7 5/1 68/13 16/3 11/2 28/5 17/3 6/1 19/3 32/5 13/2 20/3 34/5 7/1 8/1 17/2 26/3 9/1 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/28 -17/2 1/28 -8/1 1/28 3/83 -7/1 5/136 -20/3 1/27 7/188 -13/2 3/80 -19/3 3/80 -25/4 3/80 -6/1 2/53 1/26 -17/3 1/26 -28/5 1/26 9/233 -11/2 7/180 -16/3 1/26 1/25 -5/1 3/76 -24/5 1/25 7/174 -43/9 5/124 -19/4 5/124 -33/7 19/468 -47/10 7/172 -61/13 23/564 -14/3 2/49 1/24 -9/2 1/24 -40/9 1/26 1/25 -31/7 5/124 -22/5 3/74 2/49 -57/13 25/612 -35/8 19/464 -13/3 1/24 -43/10 1/24 -30/7 8/193 1/24 -17/4 1/24 -4/1 1/24 1/23 -15/4 7/160 -26/7 3/68 2/45 -63/17 3/68 -37/10 3/68 -11/3 5/112 -18/5 0/1 1/22 -25/7 1/24 -32/9 1/24 1/23 -7/2 3/68 -31/9 7/156 -24/7 5/111 1/22 -17/5 1/22 -10/3 1/22 2/43 -53/16 3/64 -43/13 3/64 -33/10 13/276 -56/17 9/190 1/21 -23/7 5/104 -36/11 1/21 1/20 -49/15 1/20 -13/4 1/20 -42/13 0/1 1/24 -29/9 1/24 -16/5 1/23 1/22 -51/16 1/22 -35/11 13/284 -19/6 5/108 -3/1 1/20 -20/7 3/61 1/20 -17/6 1/20 -14/5 1/20 2/39 -11/4 3/56 -30/11 0/1 1/16 -19/7 1/24 -46/17 0/1 1/22 -27/10 3/64 -8/3 1/20 1/19 -13/5 3/56 -44/17 3/55 1/18 -31/12 3/56 -18/7 0/1 1/18 -23/9 5/92 -28/11 1/18 3/53 -33/13 7/120 -5/2 1/20 -27/11 1/20 -22/9 2/37 1/18 -17/7 1/18 -12/5 1/18 1/17 -55/23 1/16 -43/18 1/16 -74/31 0/1 1/14 -31/13 1/20 -19/8 3/52 -26/11 2/33 1/16 -85/36 1/16 -59/25 1/16 -33/14 5/76 -40/17 1/14 1/13 -7/3 1/20 -30/13 0/1 1/16 -23/10 3/56 -16/7 1/18 1/17 -9/4 1/16 -38/17 1/16 2/31 -29/13 1/12 -78/35 0/1 1/22 -49/22 1/20 -20/9 1/17 1/16 -31/14 1/16 -11/5 1/12 -35/16 3/64 -59/27 1/20 -24/11 1/19 1/18 -13/6 1/16 -41/19 1/24 -28/13 1/18 1/17 -43/20 1/16 -15/7 1/16 -32/15 1/17 1/16 -17/8 1/16 -2/1 0/1 1/16 -17/9 1/16 -15/8 1/16 -28/15 1/15 1/14 -13/7 1/16 -24/13 1/14 1/13 -35/19 3/32 -11/6 1/20 -31/17 1/16 -20/11 1/16 1/15 -49/27 1/12 -78/43 0/1 1/10 -107/59 1/0 -136/75 0/1 -29/16 1/20 -67/37 7/120 -38/21 2/33 1/16 -9/5 1/16 -34/19 1/15 -25/14 3/44 -16/9 1/15 1/14 -23/13 3/40 -7/4 1/12 -47/27 1/20 -40/23 1/19 1/18 -33/19 5/84 -59/34 1/16 -26/15 1/16 2/31 -19/11 3/44 -69/40 11/156 -119/69 1/14 -50/29 1/14 2/27 -31/18 1/12 -136/79 0/1 -105/61 1/24 -74/43 0/1 1/18 -43/25 1/16 -55/32 1/16 -12/7 1/15 1/14 -17/10 1/14 -22/13 1/14 2/27 -27/16 1/12 -32/19 3/40 1/13 -37/22 1/12 -5/3 1/12 -18/11 0/1 1/14 -85/52 1/14 -67/41 15/208 -49/30 7/96 -31/19 3/40 -44/27 1/14 3/41 -13/8 3/40 -34/21 1/13 -21/13 5/64 -8/5 1/13 1/12 -27/17 3/32 -46/29 0/1 1/10 -65/41 3/32 -19/12 1/8 -68/43 0/1 -49/31 1/24 -30/19 0/1 1/16 -101/64 9/136 -71/45 3/44 -41/26 1/12 -11/7 3/40 -36/23 1/13 1/12 -25/16 1/12 -14/9 2/25 1/12 -17/11 1/12 -20/13 1/12 3/35 -3/2 1/12 -19/13 5/52 -16/11 1/10 1/9 -13/9 1/12 -36/25 1/12 1/11 -23/16 5/56 -102/71 1/11 -79/55 23/252 -56/39 1/11 9/98 -89/62 7/76 -33/23 13/140 -10/7 2/21 1/10 -17/12 1/10 -24/17 1/10 5/49 -31/22 7/68 -100/71 19/184 3/29 -69/49 29/280 -38/27 5/48 2/19 -7/5 3/28 -39/28 3/28 -32/23 1/9 1/8 -25/18 1/8 -68/49 0/1 -43/31 1/12 -18/13 0/1 1/10 -29/21 1/8 -98/71 1/12 2/23 -69/50 7/76 -40/29 3/31 1/10 -11/8 5/48 -37/27 3/28 -137/100 15/136 -374/273 1/9 -237/173 17/152 -100/73 1/9 1/8 -63/46 3/28 -26/19 2/19 3/28 -15/11 7/64 -34/25 1/9 -19/14 9/80 -4/3 1/9 1/8 -17/13 1/8 -30/23 1/8 8/63 -43/33 1/8 -13/10 1/8 -48/37 3/23 11/84 -83/64 21/160 -35/27 19/144 -57/44 25/188 -136/105 2/15 -79/61 31/232 -22/17 2/15 3/22 -53/41 7/52 -31/24 5/36 -102/79 1/7 -71/55 7/48 -40/31 1/7 1/6 -49/38 1/8 -9/7 1/8 -32/25 1/8 1/7 -23/18 3/20 -14/11 1/8 2/15 -75/59 25/188 -136/107 2/15 -61/48 23/172 -47/37 7/52 -80/63 17/126 5/37 -33/26 19/140 -85/67 3/22 -52/41 3/22 13/95 -19/15 5/36 -43/34 5/36 -67/53 39/280 -24/19 7/50 1/7 -29/23 17/120 -34/27 1/7 -5/4 3/20 -26/21 3/20 2/13 -47/38 11/72 -68/55 2/13 -21/17 5/32 -16/13 1/7 1/6 -11/9 7/44 -28/23 9/55 1/6 -17/14 1/6 -6/5 1/6 2/11 -25/21 3/16 -19/16 3/16 -51/43 3/16 -32/27 3/16 1/5 -13/11 3/16 -33/28 23/120 -53/45 17/88 -20/17 7/36 1/5 -27/23 19/96 -34/29 1/5 -7/6 5/24 -8/7 3/13 1/4 -17/15 1/4 -26/23 1/4 10/39 -9/8 1/4 -19/17 1/4 -10/9 2/7 3/10 -1/1 1/0 0/1 0/1 1/1 1/64 9/8 1/60 17/15 1/60 8/7 1/60 3/179 7/6 5/296 20/17 1/59 7/412 13/11 3/176 19/16 3/176 25/21 3/176 6/5 2/117 1/58 17/14 1/58 28/23 1/58 9/521 11/9 7/404 16/13 1/58 1/57 5/4 3/172 24/19 1/57 7/398 43/34 5/284 19/15 5/284 33/26 19/1076 47/37 7/396 61/48 23/1300 14/11 2/113 1/56 9/7 1/56 40/31 1/58 1/57 31/24 5/284 22/17 3/170 2/113 57/44 25/1412 35/27 19/1072 13/10 1/56 43/33 1/56 30/23 8/449 1/56 17/13 1/56 4/3 1/56 1/55 15/11 7/384 26/19 3/164 2/109 63/46 3/164 37/27 3/164 11/8 5/272 18/13 0/1 1/54 25/18 1/56 32/23 1/56 1/55 7/5 3/164 31/22 7/380 24/17 5/271 1/54 17/12 1/54 10/7 1/54 2/107 53/37 3/160 43/30 3/160 33/23 13/692 56/39 9/478 1/53 23/16 5/264 36/25 1/53 1/52 49/34 1/52 13/9 1/52 42/29 0/1 1/56 29/20 1/56 16/11 1/55 1/54 51/35 1/54 35/24 13/700 19/13 5/268 3/2 1/52 20/13 3/157 1/52 17/11 1/52 14/9 1/52 2/103 11/7 3/152 30/19 0/1 1/48 19/12 1/56 46/29 0/1 1/54 27/17 3/160 8/5 1/52 1/51 13/8 3/152 44/27 3/151 1/50 31/19 3/152 18/11 0/1 1/50 23/14 5/252 28/17 1/50 3/149 33/20 7/344 5/3 1/52 27/16 1/52 22/13 2/101 1/50 17/10 1/50 12/7 1/50 1/49 55/32 1/48 43/25 1/48 74/43 0/1 1/46 31/18 1/52 19/11 3/148 26/15 2/97 1/48 85/49 1/48 59/34 1/48 33/19 5/236 40/23 1/46 1/45 7/4 1/52 30/17 0/1 1/48 23/13 3/152 16/9 1/50 1/49 9/5 1/48 38/21 1/48 2/95 29/16 1/44 78/43 0/1 1/54 49/27 1/52 20/11 1/49 1/48 31/17 1/48 11/6 1/44 35/19 3/160 59/32 1/52 24/13 1/51 1/50 13/7 1/48 41/22 1/56 28/15 1/50 1/49 43/23 1/48 15/8 1/48 32/17 1/49 1/48 17/9 1/48 2/1 0/1 1/48 17/8 1/48 15/7 1/48 28/13 1/47 1/46 13/6 1/48 24/11 1/46 1/45 35/16 3/128 11/5 1/52 31/14 1/48 20/9 1/48 1/47 49/22 1/44 78/35 0/1 1/42 107/48 1/32 136/61 0/1 29/13 1/52 67/30 7/344 38/17 2/97 1/48 9/4 1/48 34/15 1/47 25/11 3/140 16/7 1/47 1/46 23/10 3/136 7/3 1/44 47/20 1/52 40/17 1/51 1/50 33/14 5/244 59/25 1/48 26/11 1/48 2/95 19/8 3/140 69/29 11/508 119/50 1/46 50/21 1/46 2/91 31/13 1/44 136/57 0/1 105/44 1/56 74/31 0/1 1/50 43/18 1/48 55/23 1/48 12/5 1/47 1/46 17/7 1/46 22/9 1/46 2/91 27/11 1/44 32/13 3/136 1/45 37/15 1/44 5/2 1/44 18/7 0/1 1/46 85/33 1/46 67/26 15/688 49/19 7/320 31/12 3/136 44/17 1/46 3/137 13/5 3/136 34/13 1/45 21/8 5/224 8/3 1/45 1/44 27/10 3/128 46/17 0/1 1/42 65/24 3/128 19/7 1/40 68/25 0/1 49/18 1/56 30/11 0/1 1/48 101/37 9/424 71/26 3/140 41/15 1/44 11/4 3/136 36/13 1/45 1/44 25/9 1/44 14/5 2/89 1/44 17/6 1/44 20/7 1/44 3/131 3/1 1/44 19/6 5/212 16/5 1/42 1/41 13/4 1/44 36/11 1/44 1/43 23/7 5/216 102/31 1/43 79/24 23/988 56/17 1/43 9/386 89/27 7/300 33/10 13/556 10/3 2/85 1/42 17/5 1/42 24/7 1/42 5/209 31/9 7/292 100/29 19/792 3/125 69/20 29/1208 38/11 5/208 2/83 7/2 3/124 39/11 3/124 32/9 1/41 1/40 25/7 1/40 68/19 0/1 43/12 1/44 18/5 0/1 1/42 29/8 1/40 98/27 1/44 2/87 69/19 7/300 40/11 3/127 1/42 11/3 5/208 37/10 3/124 137/37 15/616 374/101 1/41 237/64 17/696 100/27 1/41 1/40 63/17 3/124 26/7 2/83 3/124 15/4 7/288 34/9 1/41 19/5 9/368 4/1 1/41 1/40 17/4 1/40 30/7 1/40 8/319 43/10 1/40 13/3 1/40 48/11 3/119 11/436 83/19 21/832 35/8 19/752 57/13 25/988 136/31 2/79 79/18 31/1224 22/5 2/79 3/118 53/12 7/276 31/7 5/196 102/23 1/39 71/16 7/272 40/9 1/39 1/38 49/11 1/40 9/2 1/40 32/7 1/40 1/39 23/5 3/116 14/3 1/40 2/79 75/16 25/988 136/29 2/79 61/13 23/908 47/10 7/276 80/17 17/670 5/197 33/7 19/748 85/18 3/118 52/11 3/118 13/511 19/4 5/196 43/9 5/196 67/14 39/1528 24/5 7/274 1/39 29/6 17/664 34/7 1/39 5/1 3/116 26/5 3/116 2/77 47/9 11/424 68/13 2/77 21/4 5/192 16/3 1/39 1/38 11/2 7/268 28/5 9/343 1/38 17/3 1/38 6/1 1/38 2/75 25/4 3/112 19/3 3/112 51/8 3/112 32/5 3/112 1/37 13/2 3/112 33/5 23/856 53/8 17/632 20/3 7/260 1/37 27/4 19/704 34/5 1/37 7/1 5/184 8/1 3/109 1/36 17/2 1/36 26/3 1/36 10/359 9/1 1/36 19/2 1/36 10/1 2/71 3/106 1/0 1/32 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(33,340,-10,-103) (-9/1,1/0) -> (-43/13,-33/10) Hyperbolic Matrix(203,1768,-86,-749) (-9/1,-17/2) -> (-85/36,-59/25) Hyperbolic Matrix(33,272,4,33) (-17/2,-8/1) -> (8/1,17/2) Hyperbolic Matrix(35,272,22,171) (-8/1,-7/1) -> (27/17,8/5) Hyperbolic Matrix(101,680,-86,-579) (-7/1,-20/3) -> (-20/17,-27/23) Hyperbolic Matrix(135,884,-104,-681) (-20/3,-13/2) -> (-13/10,-48/37) Hyperbolic Matrix(137,884,-42,-271) (-13/2,-19/3) -> (-49/15,-13/4) Hyperbolic Matrix(205,1292,162,1021) (-19/3,-25/4) -> (43/34,19/15) Hyperbolic Matrix(339,2108,142,883) (-25/4,-6/1) -> (74/31,43/18) Hyperbolic Matrix(35,204,6,35) (-6/1,-17/3) -> (17/3,6/1) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(171,952,104,579) (-28/5,-11/2) -> (23/14,28/17) Hyperbolic Matrix(101,544,44,237) (-11/2,-16/3) -> (16/7,23/10) Hyperbolic Matrix(103,544,-32,-169) (-16/3,-5/1) -> (-29/9,-16/5) Hyperbolic Matrix(169,816,-134,-647) (-5/1,-24/5) -> (-24/19,-29/23) Hyperbolic Matrix(511,2448,-234,-1121) (-24/5,-43/9) -> (-59/27,-24/11) Hyperbolic Matrix(271,1292,228,1087) (-43/9,-19/4) -> (19/16,25/21) Hyperbolic Matrix(273,1292,-86,-407) (-19/4,-33/7) -> (-35/11,-19/6) Hyperbolic Matrix(953,4488,-664,-3127) (-33/7,-47/10) -> (-89/62,-33/23) Hyperbolic Matrix(681,3196,290,1361) (-47/10,-61/13) -> (7/3,47/20) Hyperbolic Matrix(407,1904,-320,-1497) (-61/13,-14/3) -> (-14/11,-75/59) Hyperbolic Matrix(103,476,-66,-305) (-14/3,-9/2) -> (-25/16,-14/9) Hyperbolic Matrix(443,1972,-206,-917) (-9/2,-40/9) -> (-28/13,-43/20) Hyperbolic Matrix(919,4080,-712,-3161) (-40/9,-31/7) -> (-71/55,-40/31) Hyperbolic Matrix(647,2856,-408,-1801) (-31/7,-22/5) -> (-46/29,-65/41) Hyperbolic Matrix(681,2992,-526,-2311) (-22/5,-57/13) -> (-79/61,-22/17) Hyperbolic Matrix(543,2380,248,1087) (-57/13,-35/8) -> (35/16,11/5) Hyperbolic Matrix(203,884,-172,-749) (-35/8,-13/3) -> (-13/11,-33/28) Hyperbolic Matrix(679,2924,284,1223) (-13/3,-43/10) -> (43/18,55/23) Hyperbolic Matrix(443,1904,198,851) (-43/10,-30/7) -> (38/17,9/4) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(33,136,8,33) (-17/4,-4/1) -> (4/1,17/4) Hyperbolic Matrix(35,136,-26,-101) (-4/1,-15/4) -> (-19/14,-4/3) Hyperbolic Matrix(237,884,100,373) (-15/4,-26/7) -> (26/11,19/8) Hyperbolic Matrix(477,1768,92,341) (-26/7,-63/17) -> (5/1,26/5) Hyperbolic Matrix(679,2516,-404,-1497) (-63/17,-37/10) -> (-37/22,-5/3) Hyperbolic Matrix(203,748,92,339) (-37/10,-11/3) -> (11/5,31/14) Hyperbolic Matrix(169,612,-66,-239) (-11/3,-18/5) -> (-18/7,-23/9) Hyperbolic Matrix(341,1224,-246,-883) (-18/5,-25/7) -> (-43/31,-18/13) Hyperbolic Matrix(477,1700,172,613) (-25/7,-32/9) -> (36/13,25/9) Hyperbolic Matrix(307,1088,-182,-645) (-32/9,-7/2) -> (-27/16,-32/19) Hyperbolic Matrix(511,1768,-324,-1121) (-7/2,-31/9) -> (-71/45,-41/26) Hyperbolic Matrix(613,2108,376,1293) (-31/9,-24/7) -> (44/27,31/19) Hyperbolic Matrix(239,816,70,239) (-24/7,-17/5) -> (17/5,24/7) Hyperbolic Matrix(101,340,30,101) (-17/5,-10/3) -> (10/3,17/5) Hyperbolic Matrix(1395,4624,626,2075) (-10/3,-53/16) -> (49/22,78/35) Hyperbolic Matrix(883,2924,472,1563) (-53/16,-43/13) -> (43/23,15/8) Hyperbolic Matrix(1361,4488,-1072,-3535) (-33/10,-56/17) -> (-80/63,-33/26) Hyperbolic Matrix(1735,5712,-1208,-3977) (-56/17,-23/7) -> (-79/55,-56/39) Hyperbolic Matrix(477,1564,104,341) (-23/7,-36/11) -> (32/7,23/5) Hyperbolic Matrix(645,2108,-302,-987) (-36/11,-49/15) -> (-15/7,-32/15) Hyperbolic Matrix(715,2312,-578,-1869) (-13/4,-42/13) -> (-26/21,-47/38) Hyperbolic Matrix(1053,3400,284,917) (-42/13,-29/9) -> (63/17,26/7) Hyperbolic Matrix(1257,4012,266,849) (-16/5,-51/16) -> (85/18,52/11) Hyperbolic Matrix(2413,7684,1014,3229) (-51/16,-35/11) -> (69/29,119/50) Hyperbolic Matrix(409,1292,-258,-815) (-19/6,-3/1) -> (-65/41,-19/12) Hyperbolic Matrix(237,680,130,373) (-3/1,-20/7) -> (20/11,31/17) Hyperbolic Matrix(239,680,84,239) (-20/7,-17/6) -> (17/6,20/7) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(171,476,-134,-373) (-14/5,-11/4) -> (-23/18,-14/11) Hyperbolic Matrix(373,1020,-162,-443) (-11/4,-30/11) -> (-30/13,-23/10) Hyperbolic Matrix(749,2040,-474,-1291) (-30/11,-19/7) -> (-49/31,-30/19) Hyperbolic Matrix(1055,2856,-816,-2209) (-19/7,-46/17) -> (-22/17,-53/41) Hyperbolic Matrix(679,1836,402,1087) (-46/17,-27/10) -> (27/16,22/13) Hyperbolic Matrix(101,272,88,237) (-27/10,-8/3) -> (8/7,7/6) Hyperbolic Matrix(103,272,-64,-169) (-8/3,-13/5) -> (-21/13,-8/5) Hyperbolic Matrix(341,884,184,477) (-13/5,-44/17) -> (24/13,13/7) Hyperbolic Matrix(815,2108,578,1495) (-44/17,-31/12) -> (31/22,24/17) Hyperbolic Matrix(817,2108,-474,-1223) (-31/12,-18/7) -> (-50/29,-31/18) Hyperbolic Matrix(373,952,306,781) (-23/9,-28/11) -> (28/23,11/9) Hyperbolic Matrix(883,2244,508,1291) (-28/11,-33/13) -> (33/19,40/23) Hyperbolic Matrix(511,1292,-282,-713) (-33/13,-5/2) -> (-29/16,-67/37) Hyperbolic Matrix(443,1088,-318,-781) (-5/2,-27/11) -> (-7/5,-39/28) Hyperbolic Matrix(749,1836,472,1157) (-27/11,-22/9) -> (46/29,27/17) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(169,408,70,169) (-17/7,-12/5) -> (12/5,17/7) Hyperbolic Matrix(2075,4964,-1634,-3909) (-12/5,-55/23) -> (-47/37,-80/63) Hyperbolic Matrix(1223,2924,284,679) (-55/23,-43/18) -> (43/10,13/3) Hyperbolic Matrix(883,2108,142,339) (-43/18,-74/31) -> (6/1,25/4) Hyperbolic Matrix(4217,10064,-2450,-5847) (-74/31,-31/13) -> (-105/61,-74/43) Hyperbolic Matrix(885,2108,-542,-1291) (-31/13,-19/8) -> (-49/30,-31/19) Hyperbolic Matrix(373,884,100,237) (-19/8,-26/11) -> (26/7,15/4) Hyperbolic Matrix(1123,2652,130,307) (-26/11,-85/36) -> (17/2,26/3) Hyperbolic Matrix(1701,4012,-778,-1835) (-59/25,-33/14) -> (-35/16,-59/27) Hyperbolic Matrix(953,2244,578,1361) (-33/14,-40/17) -> (28/17,33/20) Hyperbolic Matrix(781,1836,-362,-851) (-40/17,-7/3) -> (-41/19,-28/13) Hyperbolic Matrix(205,476,-146,-339) (-7/3,-30/13) -> (-38/27,-7/5) Hyperbolic Matrix(237,544,44,101) (-23/10,-16/7) -> (16/3,11/2) Hyperbolic Matrix(239,544,-134,-305) (-16/7,-9/4) -> (-25/14,-16/9) Hyperbolic Matrix(851,1904,198,443) (-9/4,-38/17) -> (30/7,43/10) Hyperbolic Matrix(1767,3944,-1280,-2857) (-38/17,-29/13) -> (-29/21,-98/71) Hyperbolic Matrix(4759,10608,-2624,-5849) (-29/13,-78/35) -> (-78/43,-107/59) Hyperbolic Matrix(885,1972,92,205) (-78/35,-49/22) -> (19/2,10/1) Hyperbolic Matrix(1803,4012,-1390,-3093) (-49/22,-20/9) -> (-48/37,-83/64) Hyperbolic Matrix(307,680,200,443) (-20/9,-31/14) -> (3/2,20/13) Hyperbolic Matrix(339,748,92,203) (-31/14,-11/5) -> (11/3,37/10) Hyperbolic Matrix(1087,2380,248,543) (-11/5,-35/16) -> (35/8,57/13) Hyperbolic Matrix(407,884,250,543) (-24/11,-13/6) -> (13/8,44/27) Hyperbolic Matrix(1259,2720,268,579) (-13/6,-41/19) -> (61/13,47/10) Hyperbolic Matrix(1361,2924,950,2041) (-43/20,-15/7) -> (53/37,43/30) Hyperbolic Matrix(1021,2176,160,341) (-32/15,-17/8) -> (51/8,32/5) Hyperbolic Matrix(33,68,16,33) (-17/8,-2/1) -> (2/1,17/8) Hyperbolic Matrix(35,68,18,35) (-2/1,-17/9) -> (17/9,2/1) Hyperbolic Matrix(579,1088,-488,-917) (-17/9,-15/8) -> (-19/16,-51/43) Hyperbolic Matrix(1055,1972,-818,-1529) (-15/8,-28/15) -> (-40/31,-49/38) Hyperbolic Matrix(985,1836,-566,-1055) (-28/15,-13/7) -> (-47/27,-40/23) Hyperbolic Matrix(477,884,184,341) (-13/7,-24/13) -> (44/17,13/5) Hyperbolic Matrix(1327,2448,-1050,-1937) (-24/13,-35/19) -> (-67/53,-24/19) Hyperbolic Matrix(1293,2380,998,1837) (-35/19,-11/6) -> (57/44,35/27) Hyperbolic Matrix(409,748,298,545) (-11/6,-31/17) -> (37/27,11/8) Hyperbolic Matrix(373,680,130,237) (-31/17,-20/11) -> (20/7,3/1) Hyperbolic Matrix(1123,2040,-954,-1733) (-20/11,-49/27) -> (-53/45,-20/17) Hyperbolic Matrix(2549,4624,1780,3229) (-49/27,-78/43) -> (10/7,53/37) Hyperbolic Matrix(10199,18496,4574,8295) (-107/59,-136/75) -> (136/61,29/13) Hyperbolic Matrix(10201,18496,4576,8297) (-136/75,-29/16) -> (107/48,136/61) Hyperbolic Matrix(3231,5848,1184,2143) (-67/37,-38/21) -> (30/11,101/37) Hyperbolic Matrix(1053,1904,808,1461) (-38/21,-9/5) -> (43/33,30/23) Hyperbolic Matrix(645,1156,284,509) (-9/5,-34/19) -> (34/15,25/11) Hyperbolic Matrix(647,1156,286,511) (-34/19,-25/14) -> (9/4,34/15) Hyperbolic Matrix(307,544,250,443) (-16/9,-23/13) -> (11/9,16/13) Hyperbolic Matrix(577,1020,-366,-647) (-23/13,-7/4) -> (-41/26,-11/7) Hyperbolic Matrix(1835,3196,1444,2515) (-7/4,-47/27) -> (47/37,61/48) Hyperbolic Matrix(2347,4080,646,1123) (-40/23,-33/19) -> (69/19,40/11) Hyperbolic Matrix(3095,5372,-2448,-4249) (-33/19,-59/34) -> (-43/34,-67/53) Hyperbolic Matrix(1019,1768,-902,-1565) (-59/34,-26/15) -> (-26/23,-9/8) Hyperbolic Matrix(511,884,374,647) (-26/15,-19/11) -> (15/11,26/19) Hyperbolic Matrix(2483,4284,-2108,-3637) (-19/11,-69/40) -> (-33/28,-53/45) Hyperbolic Matrix(4455,7684,3056,5271) (-69/40,-119/69) -> (51/35,35/24) Hyperbolic Matrix(3707,6392,1440,2483) (-119/69,-50/29) -> (18/7,85/33) Hyperbolic Matrix(10743,18496,4502,7751) (-31/18,-136/79) -> (136/57,105/44) Hyperbolic Matrix(10745,18496,4504,7753) (-136/79,-105/61) -> (31/13,136/57) Hyperbolic Matrix(1225,2108,1028,1769) (-74/43,-43/25) -> (25/21,6/5) Hyperbolic Matrix(1701,2924,1306,2245) (-43/25,-55/32) -> (13/10,43/33) Hyperbolic Matrix(2415,4148,-1682,-2889) (-55/32,-12/7) -> (-56/39,-89/62) Hyperbolic Matrix(239,408,140,239) (-12/7,-17/10) -> (17/10,12/7) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(1087,1836,402,679) (-22/13,-27/16) -> (27/10,46/17) Hyperbolic Matrix(2789,4692,-1980,-3331) (-32/19,-37/22) -> (-31/22,-100/71) Hyperbolic Matrix(373,612,-270,-443) (-5/3,-18/11) -> (-18/13,-29/21) Hyperbolic Matrix(3909,6392,1642,2685) (-18/11,-85/52) -> (119/50,50/21) Hyperbolic Matrix(5201,8500,1102,1801) (-85/52,-67/41) -> (33/7,85/18) Hyperbolic Matrix(4453,7276,-3434,-5611) (-67/41,-49/30) -> (-83/64,-35/27) Hyperbolic Matrix(1293,2108,376,613) (-31/19,-44/27) -> (24/7,31/9) Hyperbolic Matrix(543,884,250,407) (-44/27,-13/8) -> (13/6,24/11) Hyperbolic Matrix(713,1156,272,441) (-13/8,-34/21) -> (34/13,21/8) Hyperbolic Matrix(715,1156,274,443) (-34/21,-21/13) -> (13/5,34/13) Hyperbolic Matrix(171,272,22,35) (-8/5,-27/17) -> (7/1,8/1) Hyperbolic Matrix(1157,1836,472,749) (-27/17,-46/29) -> (22/9,27/11) Hyperbolic Matrix(2923,4624,1074,1699) (-19/12,-68/43) -> (68/25,49/18) Hyperbolic Matrix(2925,4624,1076,1701) (-68/43,-49/31) -> (19/7,68/25) Hyperbolic Matrix(3705,5848,1658,2617) (-30/19,-101/64) -> (67/30,38/17) Hyperbolic Matrix(8533,13464,-6228,-9827) (-101/64,-71/45) -> (-37/27,-137/100) Hyperbolic Matrix(781,1224,238,373) (-11/7,-36/23) -> (36/11,23/7) Hyperbolic Matrix(1087,1700,782,1223) (-36/23,-25/16) -> (25/18,32/23) Hyperbolic Matrix(307,476,198,307) (-14/9,-17/11) -> (17/11,14/9) Hyperbolic Matrix(441,680,286,441) (-17/11,-20/13) -> (20/13,17/11) Hyperbolic Matrix(443,680,200,307) (-20/13,-3/2) -> (31/14,20/9) Hyperbolic Matrix(509,748,-394,-579) (-3/2,-19/13) -> (-53/41,-31/24) Hyperbolic Matrix(885,1292,-698,-1019) (-19/13,-16/11) -> (-52/41,-19/15) Hyperbolic Matrix(375,544,-304,-441) (-16/11,-13/9) -> (-21/17,-16/13) Hyperbolic Matrix(613,884,-518,-747) (-13/9,-36/25) -> (-32/27,-13/11) Hyperbolic Matrix(851,1224,308,443) (-36/25,-23/16) -> (11/4,36/13) Hyperbolic Matrix(7241,10404,2200,3161) (-23/16,-102/71) -> (102/31,79/24) Hyperbolic Matrix(7243,10404,2202,3163) (-102/71,-79/55) -> (23/7,102/31) Hyperbolic Matrix(237,340,-214,-307) (-33/23,-10/7) -> (-10/9,-1/1) Hyperbolic Matrix(239,340,168,239) (-10/7,-17/12) -> (17/12,10/7) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(1495,2108,578,815) (-24/17,-31/22) -> (31/12,44/17) Hyperbolic Matrix(21727,30600,-15860,-22337) (-100/71,-69/49) -> (-237/173,-100/73) Hyperbolic Matrix(6665,9384,1836,2585) (-69/49,-38/27) -> (98/27,69/19) Hyperbolic Matrix(4249,5916,-3102,-4319) (-39/28,-32/23) -> (-100/73,-63/46) Hyperbolic Matrix(783,1088,172,239) (-32/23,-25/18) -> (9/2,32/7) Hyperbolic Matrix(3331,4624,930,1291) (-25/18,-68/49) -> (68/19,43/12) Hyperbolic Matrix(3333,4624,932,1293) (-68/49,-43/31) -> (25/7,68/19) Hyperbolic Matrix(6799,9384,1970,2719) (-98/71,-69/50) -> (69/20,38/11) Hyperbolic Matrix(2957,4080,1256,1733) (-69/50,-40/29) -> (40/17,33/14) Hyperbolic Matrix(543,748,98,135) (-40/29,-11/8) -> (11/2,28/5) Hyperbolic Matrix(545,748,298,409) (-11/8,-37/27) -> (31/17,11/6) Hyperbolic Matrix(102101,139876,27572,37773) (-137/100,-374/273) -> (374/101,237/64) Hyperbolic Matrix(102103,139876,27574,37775) (-374/273,-237/173) -> (137/37,374/101) Hyperbolic Matrix(2483,3400,1714,2347) (-63/46,-26/19) -> (42/29,29/20) Hyperbolic Matrix(647,884,374,511) (-26/19,-15/11) -> (19/11,26/15) Hyperbolic Matrix(849,1156,224,305) (-15/11,-34/25) -> (34/9,19/5) Hyperbolic Matrix(851,1156,226,307) (-34/25,-19/14) -> (15/4,34/9) Hyperbolic Matrix(103,136,78,103) (-4/3,-17/13) -> (17/13,4/3) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(1461,1904,808,1053) (-30/23,-43/33) -> (9/5,38/21) Hyperbolic Matrix(2245,2924,1306,1701) (-43/33,-13/10) -> (55/32,43/25) Hyperbolic Matrix(1837,2380,998,1293) (-35/27,-57/44) -> (11/6,35/19) Hyperbolic Matrix(14279,18496,3254,4215) (-57/44,-136/105) -> (136/31,79/18) Hyperbolic Matrix(14281,18496,3256,4217) (-136/105,-79/61) -> (57/13,136/31) Hyperbolic Matrix(8057,10404,1816,2345) (-31/24,-102/79) -> (102/23,71/16) Hyperbolic Matrix(8059,10404,1818,2347) (-102/79,-71/55) -> (31/7,102/23) Hyperbolic Matrix(475,612,52,67) (-49/38,-9/7) -> (9/1,19/2) Hyperbolic Matrix(849,1088,238,305) (-9/7,-32/25) -> (32/9,25/7) Hyperbolic Matrix(1223,1564,850,1087) (-32/25,-23/18) -> (23/16,36/25) Hyperbolic Matrix(14551,18496,3102,3943) (-75/59,-136/107) -> (136/29,61/13) Hyperbolic Matrix(14553,18496,3104,3945) (-136/107,-61/48) -> (75/16,136/29) Hyperbolic Matrix(2141,2720,1150,1461) (-61/48,-47/37) -> (13/7,41/22) Hyperbolic Matrix(6699,8500,2600,3299) (-33/26,-85/67) -> (85/33,67/26) Hyperbolic Matrix(3163,4012,2172,2755) (-85/67,-52/41) -> (16/11,51/35) Hyperbolic Matrix(1021,1292,162,205) (-19/15,-43/34) -> (25/4,19/3) Hyperbolic Matrix(917,1156,188,237) (-29/23,-34/27) -> (34/7,5/1) Hyperbolic Matrix(919,1156,190,239) (-34/27,-5/4) -> (29/6,34/7) Hyperbolic Matrix(1427,1768,1042,1291) (-5/4,-26/21) -> (26/19,63/46) Hyperbolic Matrix(3739,4624,714,883) (-47/38,-68/55) -> (68/13,21/4) Hyperbolic Matrix(3741,4624,716,885) (-68/55,-21/17) -> (47/9,68/13) Hyperbolic Matrix(443,544,250,307) (-16/13,-11/9) -> (23/13,16/9) Hyperbolic Matrix(613,748,168,205) (-11/9,-28/23) -> (40/11,11/3) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(169,204,140,169) (-17/14,-6/5) -> (6/5,17/14) Hyperbolic Matrix(1769,2108,1028,1225) (-6/5,-25/21) -> (43/25,74/43) Hyperbolic Matrix(1087,1292,228,271) (-25/21,-19/16) -> (19/4,43/9) Hyperbolic Matrix(1835,2176,974,1155) (-51/43,-32/27) -> (32/17,17/9) Hyperbolic Matrix(985,1156,144,169) (-27/23,-34/29) -> (34/5,7/1) Hyperbolic Matrix(987,1156,146,171) (-34/29,-7/6) -> (27/4,34/5) Hyperbolic Matrix(237,272,88,101) (-7/6,-8/7) -> (8/3,27/10) Hyperbolic Matrix(239,272,210,239) (-8/7,-17/15) -> (17/15,8/7) Hyperbolic Matrix(2345,2652,1352,1529) (-17/15,-26/23) -> (26/15,85/49) Hyperbolic Matrix(545,612,122,137) (-9/8,-19/17) -> (49/11,9/2) Hyperbolic Matrix(1767,1972,974,1087) (-19/17,-10/9) -> (78/43,49/27) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(307,-340,214,-237) (1/1,9/8) -> (43/30,33/23) Hyperbolic Matrix(1565,-1768,902,-1019) (9/8,17/15) -> (85/49,59/34) Hyperbolic Matrix(579,-680,86,-101) (7/6,20/17) -> (20/3,27/4) Hyperbolic Matrix(749,-884,172,-203) (20/17,13/11) -> (13/3,48/11) Hyperbolic Matrix(747,-884,518,-613) (13/11,19/16) -> (49/34,13/9) Hyperbolic Matrix(441,-544,304,-375) (16/13,5/4) -> (29/20,16/11) Hyperbolic Matrix(647,-816,134,-169) (5/4,24/19) -> (24/5,29/6) Hyperbolic Matrix(1937,-2448,1050,-1327) (24/19,43/34) -> (59/32,24/13) Hyperbolic Matrix(1019,-1292,698,-885) (19/15,33/26) -> (35/24,19/13) Hyperbolic Matrix(3535,-4488,1072,-1361) (33/26,47/37) -> (89/27,33/10) Hyperbolic Matrix(1497,-1904,320,-407) (61/48,14/11) -> (14/3,75/16) Hyperbolic Matrix(373,-476,134,-171) (14/11,9/7) -> (25/9,14/5) Hyperbolic Matrix(1529,-1972,818,-1055) (9/7,40/31) -> (28/15,43/23) Hyperbolic Matrix(3161,-4080,712,-919) (40/31,31/24) -> (71/16,40/9) Hyperbolic Matrix(2209,-2856,816,-1055) (31/24,22/17) -> (46/17,65/24) Hyperbolic Matrix(2311,-2992,526,-681) (22/17,57/44) -> (79/18,22/5) Hyperbolic Matrix(681,-884,104,-135) (35/27,13/10) -> (13/2,33/5) Hyperbolic Matrix(101,-136,26,-35) (4/3,15/11) -> (19/5,4/1) Hyperbolic Matrix(1837,-2516,744,-1019) (63/46,37/27) -> (37/15,5/2) Hyperbolic Matrix(443,-612,270,-373) (11/8,18/13) -> (18/11,23/14) Hyperbolic Matrix(883,-1224,246,-341) (18/13,25/18) -> (43/12,18/5) Hyperbolic Matrix(781,-1088,318,-443) (32/23,7/5) -> (27/11,32/13) Hyperbolic Matrix(1257,-1768,460,-647) (7/5,31/22) -> (71/26,41/15) Hyperbolic Matrix(3127,-4488,664,-953) (33/23,56/39) -> (80/17,33/7) Hyperbolic Matrix(3977,-5712,1208,-1735) (56/39,23/16) -> (79/24,56/17) Hyperbolic Matrix(1463,-2108,778,-1121) (36/25,49/34) -> (15/8,32/17) Hyperbolic Matrix(1597,-2312,306,-443) (13/9,42/29) -> (26/5,47/9) Hyperbolic Matrix(883,-1292,326,-477) (19/13,3/2) -> (65/24,19/7) Hyperbolic Matrix(305,-476,66,-103) (14/9,11/7) -> (23/5,14/3) Hyperbolic Matrix(647,-1020,366,-577) (11/7,30/19) -> (30/17,23/13) Hyperbolic Matrix(1291,-2040,474,-749) (30/19,19/12) -> (49/18,30/11) Hyperbolic Matrix(1801,-2856,408,-647) (19/12,46/29) -> (22/5,53/12) Hyperbolic Matrix(169,-272,64,-103) (8/5,13/8) -> (21/8,8/3) Hyperbolic Matrix(1291,-2108,542,-885) (31/19,18/11) -> (50/21,31/13) Hyperbolic Matrix(781,-1292,350,-579) (33/20,5/3) -> (29/13,67/30) Hyperbolic Matrix(645,-1088,182,-307) (5/3,27/16) -> (7/2,39/11) Hyperbolic Matrix(2889,-4964,614,-1055) (12/7,55/32) -> (47/10,80/17) Hyperbolic Matrix(5847,-10064,2450,-4217) (74/43,31/18) -> (105/44,74/31) Hyperbolic Matrix(1223,-2108,474,-817) (31/18,19/11) -> (49/19,31/12) Hyperbolic Matrix(2311,-4012,1254,-2177) (59/34,33/19) -> (35/19,59/32) Hyperbolic Matrix(1055,-1836,566,-985) (40/23,7/4) -> (41/22,28/15) Hyperbolic Matrix(271,-476,78,-137) (7/4,30/17) -> (38/11,7/2) Hyperbolic Matrix(305,-544,134,-239) (16/9,9/5) -> (25/11,16/7) Hyperbolic Matrix(2177,-3944,600,-1087) (38/21,29/16) -> (29/8,98/27) Hyperbolic Matrix(5849,-10608,2624,-4759) (29/16,78/43) -> (78/35,107/48) Hyperbolic Matrix(2209,-4012,506,-919) (49/27,20/11) -> (48/11,83/19) Hyperbolic Matrix(509,-1088,80,-171) (17/8,15/7) -> (19/3,51/8) Hyperbolic Matrix(917,-1972,206,-443) (15/7,28/13) -> (40/9,49/11) Hyperbolic Matrix(851,-1836,362,-781) (28/13,13/6) -> (47/20,40/17) Hyperbolic Matrix(1121,-2448,234,-511) (24/11,35/16) -> (67/14,24/5) Hyperbolic Matrix(917,-2040,138,-307) (20/9,49/22) -> (53/8,20/3) Hyperbolic Matrix(443,-1020,162,-373) (23/10,7/3) -> (41/15,11/4) Hyperbolic Matrix(2277,-5372,476,-1123) (33/14,59/25) -> (43/9,67/14) Hyperbolic Matrix(749,-1768,86,-203) (59/25,26/11) -> (26/3,9/1) Hyperbolic Matrix(1801,-4284,272,-647) (19/8,69/29) -> (33/5,53/8) Hyperbolic Matrix(1733,-4148,526,-1259) (55/23,12/5) -> (56/17,89/27) Hyperbolic Matrix(1903,-4692,552,-1361) (32/13,37/15) -> (31/9,100/29) Hyperbolic Matrix(239,-612,66,-169) (5/2,18/7) -> (18/5,29/8) Hyperbolic Matrix(2823,-7276,646,-1665) (67/26,49/19) -> (83/19,35/8) Hyperbolic Matrix(4931,-13464,1332,-3637) (101/37,71/26) -> (37/10,137/37) Hyperbolic Matrix(239,-748,54,-169) (3/1,19/6) -> (53/12,31/7) Hyperbolic Matrix(407,-1292,86,-273) (19/6,16/5) -> (52/11,19/4) Hyperbolic Matrix(169,-544,32,-103) (16/5,13/4) -> (21/4,16/3) Hyperbolic Matrix(271,-884,42,-137) (13/4,36/11) -> (32/5,13/2) Hyperbolic Matrix(103,-340,10,-33) (33/10,10/3) -> (10/1,1/0) Hyperbolic Matrix(8873,-30600,2396,-8263) (100/29,69/20) -> (237/64,100/27) Hyperbolic Matrix(1667,-5916,450,-1597) (39/11,32/9) -> (100/27,63/17) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(33,340,-10,-103) -> Matrix(115,-4,2444,-85) Matrix(203,1768,-86,-749) -> Matrix(225,-8,3572,-127) Matrix(33,272,4,33) -> Matrix(167,-6,6040,-217) Matrix(35,272,22,171) -> Matrix(55,-2,2888,-105) Matrix(101,680,-86,-579) -> Matrix(377,-14,1912,-71) Matrix(135,884,-104,-681) -> Matrix(267,-10,2056,-77) Matrix(137,884,-42,-271) -> Matrix(53,-2,1140,-43) Matrix(205,1292,162,1021) -> Matrix(55,-2,3108,-113) Matrix(339,2108,142,883) -> Matrix(53,-2,2624,-99) Matrix(35,204,6,35) -> Matrix(105,-4,3964,-151) Matrix(169,952,30,169) -> Matrix(467,-18,17772,-685) Matrix(171,952,104,579) -> Matrix(155,-6,7776,-301) Matrix(101,544,44,237) -> Matrix(51,-2,2372,-93) Matrix(103,544,-32,-169) -> Matrix(51,-2,1148,-45) Matrix(169,816,-134,-647) -> Matrix(349,-14,2468,-99) Matrix(511,2448,-234,-1121) -> Matrix(149,-6,2856,-115) Matrix(271,1292,228,1087) -> Matrix(49,-2,2916,-119) Matrix(273,1292,-86,-407) -> Matrix(247,-10,5360,-217) Matrix(953,4488,-664,-3127) -> Matrix(689,-28,7456,-303) Matrix(681,3196,290,1361) -> Matrix(49,-2,2720,-111) Matrix(407,1904,-320,-1497) -> Matrix(97,-4,752,-31) Matrix(103,476,-66,-305) -> Matrix(1,0,-12,1) Matrix(443,1972,-206,-917) -> Matrix(1,0,-8,1) Matrix(919,4080,-712,-3161) -> Matrix(51,-2,332,-13) Matrix(647,2856,-408,-1801) -> Matrix(49,-2,564,-23) Matrix(681,2992,-526,-2311) -> Matrix(295,-12,2188,-89) Matrix(543,2380,248,1087) -> Matrix(49,-2,1936,-79) Matrix(203,884,-172,-749) -> Matrix(243,-10,1288,-53) Matrix(679,2924,284,1223) -> Matrix(145,-6,6936,-287) Matrix(443,1904,198,851) -> Matrix(145,-6,6936,-287) Matrix(239,1020,56,239) -> Matrix(385,-16,15376,-639) Matrix(33,136,8,33) -> Matrix(47,-2,1904,-81) Matrix(35,136,-26,-101) -> Matrix(47,-2,400,-17) Matrix(237,884,100,373) -> Matrix(91,-4,4300,-189) Matrix(477,1768,92,341) -> Matrix(1,0,16,1) Matrix(679,2516,-404,-1497) -> Matrix(45,-2,608,-27) Matrix(203,748,92,339) -> Matrix(45,-2,2228,-99) Matrix(169,612,-66,-239) -> Matrix(1,0,-4,1) Matrix(341,1224,-246,-883) -> Matrix(1,0,-12,1) Matrix(477,1700,172,613) -> Matrix(47,-2,2092,-89) Matrix(307,1088,-182,-645) -> Matrix(45,-2,608,-27) Matrix(511,1768,-324,-1121) -> Matrix(45,-2,608,-27) Matrix(613,2108,376,1293) -> Matrix(45,-2,2228,-99) Matrix(239,816,70,239) -> Matrix(221,-10,9260,-419) Matrix(101,340,30,101) -> Matrix(87,-4,3676,-169) Matrix(1395,4624,626,2075) -> Matrix(43,-2,1828,-85) Matrix(883,2924,472,1563) -> Matrix(43,-2,2000,-93) Matrix(1361,4488,-1072,-3535) -> Matrix(593,-28,4384,-207) Matrix(1735,5712,-1208,-3977) -> Matrix(379,-18,4148,-197) Matrix(477,1564,104,341) -> Matrix(41,-2,1620,-79) Matrix(645,2108,-302,-987) -> Matrix(1,0,-4,1) Matrix(715,2312,-578,-1869) -> Matrix(51,-2,332,-13) Matrix(1053,3400,284,917) -> Matrix(45,-2,1868,-83) Matrix(1257,4012,266,849) -> Matrix(355,-16,13956,-629) Matrix(2413,7684,1014,3229) -> Matrix(263,-12,12120,-553) Matrix(409,1292,-258,-815) -> Matrix(43,-2,452,-21) Matrix(237,680,130,373) -> Matrix(41,-2,1948,-95) Matrix(239,680,84,239) -> Matrix(121,-6,5304,-263) Matrix(169,476,60,169) -> Matrix(79,-4,3496,-177) Matrix(171,476,-134,-373) -> Matrix(1,0,-12,1) Matrix(373,1020,-162,-443) -> Matrix(1,0,0,1) Matrix(749,2040,-474,-1291) -> Matrix(1,0,0,1) Matrix(1055,2856,-816,-2209) -> Matrix(41,-2,308,-15) Matrix(679,1836,402,1087) -> Matrix(43,-2,2172,-101) Matrix(101,272,88,237) -> Matrix(41,-2,2440,-119) Matrix(103,272,-64,-169) -> Matrix(39,-2,488,-25) Matrix(341,884,184,477) -> Matrix(37,-2,1832,-99) Matrix(815,2108,578,1495) -> Matrix(35,-2,1908,-109) Matrix(817,2108,-474,-1223) -> Matrix(37,-2,500,-27) Matrix(373,952,306,781) -> Matrix(109,-6,6304,-347) Matrix(883,2244,508,1291) -> Matrix(35,-2,1628,-93) Matrix(511,1292,-282,-713) -> Matrix(1,0,0,1) Matrix(443,1088,-318,-781) -> Matrix(37,-2,352,-19) Matrix(749,1836,472,1157) -> Matrix(37,-2,1980,-107) Matrix(307,748,126,307) -> Matrix(73,-4,3340,-183) Matrix(169,408,70,169) -> Matrix(35,-2,1628,-93) Matrix(2075,4964,-1634,-3909) -> Matrix(199,-12,1476,-89) Matrix(1223,2924,284,679) -> Matrix(97,-6,3864,-239) Matrix(883,2108,142,339) -> Matrix(29,-2,1088,-75) Matrix(4217,10064,-2450,-5847) -> Matrix(1,0,4,1) Matrix(885,2108,-542,-1291) -> Matrix(37,-2,500,-27) Matrix(373,884,100,237) -> Matrix(67,-4,2764,-165) Matrix(1123,2652,130,307) -> Matrix(193,-12,6932,-431) Matrix(1701,4012,-778,-1835) -> Matrix(31,-2,636,-41) Matrix(953,2244,578,1361) -> Matrix(29,-2,1436,-99) Matrix(781,1836,-362,-851) -> Matrix(1,0,4,1) Matrix(205,476,-146,-339) -> Matrix(37,-2,352,-19) Matrix(237,544,44,101) -> Matrix(35,-2,1348,-77) Matrix(239,544,-134,-305) -> Matrix(35,-2,508,-29) Matrix(851,1904,198,443) -> Matrix(97,-6,3864,-239) Matrix(1767,3944,-1280,-2857) -> Matrix(1,0,-4,1) Matrix(4759,10608,-2624,-5849) -> Matrix(1,0,-12,1) Matrix(885,1972,92,205) -> Matrix(41,-2,1456,-71) Matrix(1803,4012,-1390,-3093) -> Matrix(139,-8,1060,-61) Matrix(307,680,200,443) -> Matrix(31,-2,1628,-105) Matrix(339,748,92,203) -> Matrix(29,-2,1204,-83) Matrix(1087,2380,248,543) -> Matrix(49,-2,1936,-79) Matrix(407,884,250,543) -> Matrix(35,-2,1768,-101) Matrix(1259,2720,268,579) -> Matrix(25,-2,988,-79) Matrix(1361,2924,950,2041) -> Matrix(29,-2,1552,-107) Matrix(1021,2176,160,341) -> Matrix(67,-4,2496,-149) Matrix(33,68,16,33) -> Matrix(1,0,32,1) Matrix(35,68,18,35) -> Matrix(1,0,32,1) Matrix(579,1088,-488,-917) -> Matrix(29,-2,160,-11) Matrix(1055,1972,-818,-1529) -> Matrix(1,0,-8,1) Matrix(985,1836,-566,-1055) -> Matrix(1,0,4,1) Matrix(477,884,184,341) -> Matrix(29,-2,1320,-91) Matrix(1327,2448,-1050,-1937) -> Matrix(77,-6,552,-43) Matrix(1293,2380,998,1837) -> Matrix(15,-2,848,-113) Matrix(409,748,298,545) -> Matrix(35,-2,1908,-109) Matrix(373,680,130,237) -> Matrix(33,-2,1436,-87) Matrix(1123,2040,-954,-1733) -> Matrix(89,-6,460,-31) Matrix(2549,4624,1780,3229) -> Matrix(21,-2,1124,-107) Matrix(10199,18496,4574,8295) -> Matrix(1,0,52,1) Matrix(10201,18496,4576,8297) -> Matrix(1,0,12,1) Matrix(3231,5848,1184,2143) -> Matrix(33,-2,1568,-95) Matrix(1053,1904,808,1461) -> Matrix(95,-6,5336,-337) Matrix(645,1156,284,509) -> Matrix(61,-4,2852,-187) Matrix(647,1156,286,511) -> Matrix(59,-4,2788,-189) Matrix(307,544,250,443) -> Matrix(29,-2,1668,-115) Matrix(577,1020,-366,-647) -> Matrix(1,0,0,1) Matrix(1835,3196,1444,2515) -> Matrix(47,-2,2656,-113) Matrix(2347,4080,646,1123) -> Matrix(35,-2,1488,-85) Matrix(3095,5372,-2448,-4249) -> Matrix(261,-16,1876,-115) Matrix(1019,1768,-902,-1565) -> Matrix(129,-8,500,-31) Matrix(511,884,374,647) -> Matrix(61,-4,3340,-219) Matrix(2483,4284,-2108,-3637) -> Matrix(229,-16,1188,-83) Matrix(4455,7684,3056,5271) -> Matrix(169,-12,9112,-647) Matrix(3707,6392,1440,2483) -> Matrix(27,-2,1256,-93) Matrix(10743,18496,4502,7751) -> Matrix(1,0,44,1) Matrix(10745,18496,4504,7753) -> Matrix(1,0,20,1) Matrix(1225,2108,1028,1769) -> Matrix(35,-2,2048,-117) Matrix(1701,2924,1306,2245) -> Matrix(95,-6,5336,-337) Matrix(2415,4148,-1682,-2889) -> Matrix(121,-8,1316,-87) Matrix(239,408,140,239) -> Matrix(29,-2,1436,-99) Matrix(441,748,260,441) -> Matrix(55,-4,2764,-201) Matrix(1087,1836,402,679) -> Matrix(27,-2,1148,-85) Matrix(2789,4692,-1980,-3331) -> Matrix(127,-10,1232,-97) Matrix(373,612,-270,-443) -> Matrix(1,0,-4,1) Matrix(3909,6392,1642,2685) -> Matrix(29,-2,1320,-91) Matrix(5201,8500,1102,1801) -> Matrix(445,-32,17508,-1259) Matrix(4453,7276,-3434,-5611) -> Matrix(387,-28,2944,-213) Matrix(1293,2108,376,613) -> Matrix(29,-2,1204,-83) Matrix(543,884,250,407) -> Matrix(27,-2,1256,-93) Matrix(713,1156,272,441) -> Matrix(105,-8,4712,-359) Matrix(715,1156,274,443) -> Matrix(103,-8,4648,-361) Matrix(171,272,22,35) -> Matrix(23,-2,840,-73) Matrix(1157,1836,472,749) -> Matrix(21,-2,956,-91) Matrix(2923,4624,1074,1699) -> Matrix(1,0,48,1) Matrix(2925,4624,1076,1701) -> Matrix(1,0,16,1) Matrix(3705,5848,1658,2617) -> Matrix(31,-2,1504,-97) Matrix(8533,13464,-6228,-9827) -> Matrix(89,-6,816,-55) Matrix(781,1224,238,373) -> Matrix(25,-2,1088,-87) Matrix(1087,1700,782,1223) -> Matrix(25,-2,1388,-111) Matrix(307,476,198,307) -> Matrix(49,-4,2536,-207) Matrix(441,680,286,441) -> Matrix(71,-6,3704,-313) Matrix(443,680,200,307) -> Matrix(23,-2,1116,-97) Matrix(509,748,-394,-579) -> Matrix(43,-4,312,-29) Matrix(885,1292,-698,-1019) -> Matrix(103,-10,752,-73) Matrix(375,544,-304,-441) -> Matrix(19,-2,124,-13) Matrix(613,884,-518,-747) -> Matrix(21,-2,116,-11) Matrix(851,1224,308,443) -> Matrix(23,-2,1024,-89) Matrix(7241,10404,2200,3161) -> Matrix(309,-28,13276,-1203) Matrix(7243,10404,2202,3163) -> Matrix(307,-28,13212,-1205) Matrix(237,340,-214,-307) -> Matrix(43,-4,140,-13) Matrix(239,340,168,239) -> Matrix(41,-4,2204,-215) Matrix(577,816,408,577) -> Matrix(99,-10,5356,-541) Matrix(1495,2108,578,815) -> Matrix(19,-2,884,-93) Matrix(21727,30600,-15860,-22337) -> Matrix(213,-22,1888,-195) Matrix(6665,9384,1836,2585) -> Matrix(77,-8,3340,-347) Matrix(4249,5916,-3102,-4319) -> Matrix(1,0,0,1) Matrix(783,1088,172,239) -> Matrix(17,-2,672,-79) Matrix(3331,4624,930,1291) -> Matrix(1,0,36,1) Matrix(3333,4624,932,1293) -> Matrix(1,0,28,1) Matrix(6799,9384,1970,2719) -> Matrix(91,-8,3788,-333) Matrix(2957,4080,1256,1733) -> Matrix(21,-2,1040,-99) Matrix(543,748,98,135) -> Matrix(59,-6,2252,-229) Matrix(545,748,298,409) -> Matrix(19,-2,884,-93) Matrix(102101,139876,27572,37773) -> Matrix(289,-32,11840,-1311) Matrix(102103,139876,27574,37775) -> Matrix(287,-32,11776,-1313) Matrix(2483,3400,1714,2347) -> Matrix(19,-2,1036,-109) Matrix(647,884,374,511) -> Matrix(37,-4,1804,-195) Matrix(849,1156,224,305) -> Matrix(145,-16,5936,-655) Matrix(851,1156,226,307) -> Matrix(143,-16,5872,-657) Matrix(103,136,78,103) -> Matrix(17,-2,944,-111) Matrix(781,1020,598,781) -> Matrix(127,-16,7120,-897) Matrix(1461,1904,808,1053) -> Matrix(47,-6,2264,-289) Matrix(2245,2924,1306,1701) -> Matrix(47,-6,2264,-289) Matrix(1837,2380,998,1293) -> Matrix(15,-2,848,-113) Matrix(14279,18496,3254,4215) -> Matrix(841,-112,33212,-4423) Matrix(14281,18496,3256,4217) -> Matrix(839,-112,33148,-4425) Matrix(8057,10404,1816,2345) -> Matrix(85,-12,3308,-467) Matrix(8059,10404,1818,2347) -> Matrix(83,-12,3244,-469) Matrix(475,612,52,67) -> Matrix(17,-2,604,-71) Matrix(849,1088,238,305) -> Matrix(15,-2,608,-81) Matrix(1223,1564,850,1087) -> Matrix(15,-2,788,-105) Matrix(14551,18496,3102,3943) -> Matrix(721,-96,28472,-3791) Matrix(14553,18496,3104,3945) -> Matrix(719,-96,28408,-3793) Matrix(2141,2720,1150,1461) -> Matrix(15,-2,668,-89) Matrix(6699,8500,2600,3299) -> Matrix(235,-32,10788,-1469) Matrix(3163,4012,2172,2755) -> Matrix(117,-16,6340,-867) Matrix(1021,1292,162,205) -> Matrix(15,-2,548,-73) Matrix(917,1156,188,237) -> Matrix(141,-20,5492,-779) Matrix(919,1156,190,239) -> Matrix(139,-20,5428,-781) Matrix(1427,1768,1042,1291) -> Matrix(1,0,48,1) Matrix(3739,4624,714,883) -> Matrix(209,-32,8040,-1231) Matrix(3741,4624,716,885) -> Matrix(207,-32,7976,-1233) Matrix(443,544,250,307) -> Matrix(13,-2,644,-99) Matrix(613,748,168,205) -> Matrix(37,-6,1548,-251) Matrix(783,952,644,783) -> Matrix(109,-18,6316,-1043) Matrix(169,204,140,169) -> Matrix(23,-4,1340,-233) Matrix(1769,2108,1028,1225) -> Matrix(11,-2,512,-93) Matrix(1087,1292,228,271) -> Matrix(9,-2,356,-79) Matrix(1835,2176,974,1155) -> Matrix(21,-4,1024,-195) Matrix(985,1156,144,169) -> Matrix(121,-24,4472,-887) Matrix(987,1156,146,171) -> Matrix(119,-24,4408,-889) Matrix(237,272,88,101) -> Matrix(9,-2,392,-87) Matrix(239,272,210,239) -> Matrix(25,-6,1496,-359) Matrix(2345,2652,1352,1529) -> Matrix(47,-12,2260,-577) Matrix(545,612,122,137) -> Matrix(7,-2,284,-81) Matrix(1767,1972,974,1087) -> Matrix(7,-2,368,-105) Matrix(1,0,2,1) -> Matrix(1,0,64,1) Matrix(307,-340,214,-237) -> Matrix(243,-4,12940,-213) Matrix(1565,-1768,902,-1019) -> Matrix(481,-8,23028,-383) Matrix(579,-680,86,-101) -> Matrix(825,-14,30584,-519) Matrix(749,-884,172,-203) -> Matrix(587,-10,23304,-397) Matrix(747,-884,518,-613) -> Matrix(117,-2,6260,-107) Matrix(441,-544,304,-375) -> Matrix(115,-2,6268,-109) Matrix(647,-816,134,-169) -> Matrix(797,-14,31140,-547) Matrix(1937,-2448,1050,-1327) -> Matrix(341,-6,17448,-307) Matrix(1019,-1292,698,-885) -> Matrix(567,-10,30448,-537) Matrix(3535,-4488,1072,-1361) -> Matrix(1585,-28,67872,-1199) Matrix(1497,-1904,320,-407) -> Matrix(225,-4,8944,-159) Matrix(373,-476,134,-171) -> Matrix(1,0,-12,1) Matrix(1529,-1972,818,-1055) -> Matrix(1,0,-8,1) Matrix(3161,-4080,712,-919) -> Matrix(115,-2,4428,-77) Matrix(2209,-2856,816,-1055) -> Matrix(113,-2,4916,-87) Matrix(2311,-2992,526,-681) -> Matrix(679,-12,26764,-473) Matrix(681,-884,104,-135) -> Matrix(563,-10,21000,-373) Matrix(101,-136,26,-35) -> Matrix(111,-2,4496,-81) Matrix(1837,-2516,744,-1019) -> Matrix(109,-2,4960,-91) Matrix(443,-612,270,-373) -> Matrix(1,0,-4,1) Matrix(883,-1224,246,-341) -> Matrix(1,0,-12,1) Matrix(781,-1088,318,-443) -> Matrix(109,-2,4960,-91) Matrix(1257,-1768,460,-647) -> Matrix(109,-2,4960,-91) Matrix(3127,-4488,664,-953) -> Matrix(1489,-28,58656,-1103) Matrix(3977,-5712,1208,-1735) -> Matrix(955,-18,41012,-773) Matrix(1463,-2108,778,-1121) -> Matrix(1,0,-4,1) Matrix(1597,-2312,306,-443) -> Matrix(115,-2,4428,-77) Matrix(883,-1292,326,-477) -> Matrix(107,-2,4548,-85) Matrix(305,-476,66,-103) -> Matrix(1,0,-12,1) Matrix(647,-1020,366,-577) -> Matrix(1,0,0,1) Matrix(1291,-2040,474,-749) -> Matrix(1,0,0,1) Matrix(1801,-2856,408,-647) -> Matrix(105,-2,4148,-79) Matrix(169,-272,64,-103) -> Matrix(103,-2,4584,-89) Matrix(1291,-2108,542,-885) -> Matrix(101,-2,4596,-91) Matrix(781,-1292,350,-579) -> Matrix(1,0,0,1) Matrix(645,-1088,182,-307) -> Matrix(101,-2,4192,-83) Matrix(2889,-4964,614,-1055) -> Matrix(583,-12,22980,-473) Matrix(5847,-10064,2450,-4217) -> Matrix(1,0,4,1) Matrix(1223,-2108,474,-817) -> Matrix(101,-2,4596,-91) Matrix(2311,-4012,1254,-2177) -> Matrix(95,-2,4988,-105) Matrix(1055,-1836,566,-985) -> Matrix(1,0,4,1) Matrix(271,-476,78,-137) -> Matrix(101,-2,4192,-83) Matrix(305,-544,134,-239) -> Matrix(99,-2,4604,-93) Matrix(2177,-3944,600,-1087) -> Matrix(1,0,-4,1) Matrix(5849,-10608,2624,-4759) -> Matrix(1,0,-12,1) Matrix(2209,-4012,506,-919) -> Matrix(395,-8,15652,-317) Matrix(509,-1088,80,-171) -> Matrix(93,-2,3488,-75) Matrix(917,-1972,206,-443) -> Matrix(1,0,-8,1) Matrix(851,-1836,362,-781) -> Matrix(1,0,4,1) Matrix(1121,-2448,234,-511) -> Matrix(269,-6,10536,-235) Matrix(917,-2040,138,-307) -> Matrix(281,-6,10444,-223) Matrix(443,-1020,162,-373) -> Matrix(1,0,0,1) Matrix(2277,-5372,476,-1123) -> Matrix(773,-16,30292,-627) Matrix(749,-1768,86,-203) -> Matrix(385,-8,13812,-287) Matrix(1801,-4284,272,-647) -> Matrix(741,-16,27556,-595) Matrix(1733,-4148,526,-1259) -> Matrix(377,-8,16164,-343) Matrix(1903,-4692,552,-1361) -> Matrix(447,-10,18640,-417) Matrix(239,-612,66,-169) -> Matrix(1,0,-4,1) Matrix(2823,-7276,646,-1665) -> Matrix(1283,-28,50816,-1109) Matrix(4931,-13464,1332,-3637) -> Matrix(281,-6,11568,-247) Matrix(239,-748,54,-169) -> Matrix(171,-4,6712,-157) Matrix(407,-1292,86,-273) -> Matrix(423,-10,16624,-393) Matrix(169,-544,32,-103) -> Matrix(83,-2,3196,-77) Matrix(271,-884,42,-137) -> Matrix(85,-2,3188,-75) Matrix(103,-340,10,-33) -> Matrix(171,-4,6028,-141) Matrix(8873,-30600,2396,-8263) -> Matrix(917,-22,37472,-899) Matrix(1667,-5916,450,-1597) -> Matrix(1,0,0,1) 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): 72 Degree of the the map X: 144 Degree of the the map Y: 288 ----------------------------------------------------------------------- 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): 432 Minimal number of generators: 73 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: 32 Genus: 21 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 17/8 34/15 12/5 17/7 34/13 17/6 3/1 17/5 34/9 4/1 17/4 136/31 102/23 14/3 85/18 34/7 5/1 16/3 11/2 17/3 6/1 19/3 13/2 34/5 7/1 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 0/1 0/1 1/1 1/64 9/8 1/60 17/15 1/60 8/7 1/60 3/179 7/6 5/296 20/17 1/59 7/412 13/11 3/176 19/16 3/176 25/21 3/176 6/5 2/117 1/58 17/14 1/58 11/9 7/404 5/4 3/172 24/19 1/57 7/398 43/34 5/284 19/15 5/284 33/26 19/1076 14/11 2/113 1/56 9/7 1/56 22/17 3/170 2/113 35/27 19/1072 13/10 1/56 17/13 1/56 4/3 1/56 1/55 15/11 7/384 11/8 5/272 18/13 0/1 1/54 7/5 3/164 17/12 1/54 10/7 1/54 2/107 43/30 3/160 33/23 13/692 56/39 9/478 1/53 23/16 5/264 13/9 1/52 3/2 1/52 17/11 1/52 14/9 1/52 2/103 11/7 3/152 19/12 1/56 8/5 1/52 1/51 13/8 3/152 18/11 0/1 1/50 5/3 1/52 17/10 1/50 12/7 1/50 1/49 43/25 1/48 74/43 0/1 1/46 31/18 1/52 19/11 3/148 7/4 1/52 16/9 1/50 1/49 9/5 1/48 11/6 1/44 13/7 1/48 15/8 1/48 17/9 1/48 2/1 0/1 1/48 17/8 1/48 15/7 1/48 13/6 1/48 11/5 1/52 9/4 1/48 34/15 1/47 25/11 3/140 16/7 1/47 1/46 7/3 1/44 26/11 1/48 2/95 19/8 3/140 31/13 1/44 12/5 1/47 1/46 17/7 1/46 5/2 1/44 18/7 0/1 1/46 85/33 1/46 67/26 15/688 49/19 7/320 31/12 3/136 13/5 3/136 34/13 1/45 21/8 5/224 8/3 1/45 1/44 27/10 3/128 19/7 1/40 11/4 3/136 25/9 1/44 14/5 2/89 1/44 17/6 1/44 3/1 1/44 19/6 5/212 16/5 1/42 1/41 13/4 1/44 23/7 5/216 33/10 13/556 10/3 2/85 1/42 17/5 1/42 7/2 3/124 18/5 0/1 1/42 29/8 1/40 11/3 5/208 15/4 7/288 34/9 1/41 19/5 9/368 4/1 1/41 1/40 17/4 1/40 13/3 1/40 48/11 3/119 11/436 35/8 19/752 57/13 25/988 136/31 2/79 79/18 31/1224 22/5 2/79 3/118 31/7 5/196 102/23 1/39 71/16 7/272 40/9 1/39 1/38 9/2 1/40 23/5 3/116 14/3 1/40 2/79 33/7 19/748 85/18 3/118 52/11 3/118 13/511 19/4 5/196 43/9 5/196 24/5 7/274 1/39 29/6 17/664 34/7 1/39 5/1 3/116 16/3 1/39 1/38 11/2 7/268 17/3 1/38 6/1 1/38 2/75 25/4 3/112 19/3 3/112 13/2 3/112 33/5 23/856 20/3 7/260 1/37 27/4 19/704 34/5 1/37 7/1 5/184 8/1 3/109 1/36 17/2 1/36 9/1 1/36 10/1 2/71 3/106 1/0 1/32 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(307,-340,214,-237) (1/1,9/8) -> (43/30,33/23) Hyperbolic Matrix(271,-306,31,-35) (9/8,17/15) -> (17/2,9/1) Hyperbolic Matrix(239,-272,29,-33) (17/15,8/7) -> (8/1,17/2) Hyperbolic Matrix(205,-238,87,-101) (8/7,7/6) -> (7/3,26/11) Hyperbolic Matrix(579,-680,86,-101) (7/6,20/17) -> (20/3,27/4) Hyperbolic Matrix(749,-884,172,-203) (20/17,13/11) -> (13/3,48/11) Hyperbolic Matrix(373,-442,173,-205) (13/11,19/16) -> (15/7,13/6) Hyperbolic Matrix(1087,-1292,859,-1021) (19/16,25/21) -> (43/34,19/15) Hyperbolic Matrix(885,-1054,199,-237) (25/21,6/5) -> (40/9,9/2) Hyperbolic Matrix(169,-204,29,-35) (6/5,17/14) -> (17/3,6/1) Hyperbolic Matrix(307,-374,55,-67) (17/14,11/9) -> (11/2,17/3) Hyperbolic Matrix(305,-374,84,-103) (11/9,5/4) -> (29/8,11/3) Hyperbolic Matrix(647,-816,134,-169) (5/4,24/19) -> (24/5,29/6) Hyperbolic Matrix(511,-646,53,-67) (24/19,43/34) -> (9/1,10/1) Hyperbolic Matrix(2279,-2890,884,-1121) (19/15,33/26) -> (67/26,49/19) Hyperbolic Matrix(1633,-2074,374,-475) (33/26,14/11) -> (48/11,35/8) Hyperbolic Matrix(373,-476,134,-171) (14/11,9/7) -> (25/9,14/5) Hyperbolic Matrix(815,-1054,474,-613) (9/7,22/17) -> (12/7,43/25) Hyperbolic Matrix(2073,-2686,1444,-1871) (22/17,35/27) -> (33/23,56/39) Hyperbolic Matrix(681,-884,104,-135) (35/27,13/10) -> (13/2,33/5) Hyperbolic Matrix(339,-442,79,-103) (13/10,17/13) -> (17/4,13/3) Hyperbolic Matrix(103,-136,25,-33) (17/13,4/3) -> (4/1,17/4) Hyperbolic Matrix(101,-136,26,-35) (4/3,15/11) -> (19/5,4/1) Hyperbolic Matrix(273,-374,173,-237) (15/11,11/8) -> (11/7,19/12) Hyperbolic Matrix(271,-374,50,-69) (11/8,18/13) -> (16/3,11/2) Hyperbolic Matrix(171,-238,97,-135) (18/13,7/5) -> (7/4,16/9) Hyperbolic Matrix(169,-238,49,-69) (7/5,17/12) -> (17/5,7/2) Hyperbolic Matrix(239,-340,71,-101) (17/12,10/7) -> (10/3,17/5) Hyperbolic Matrix(1021,-1462,213,-305) (10/7,43/30) -> (43/9,24/5) Hyperbolic Matrix(3433,-4930,782,-1123) (56/39,23/16) -> (79/18,22/5) Hyperbolic Matrix(307,-442,141,-203) (23/16,13/9) -> (13/6,11/5) Hyperbolic Matrix(305,-442,118,-171) (13/9,3/2) -> (31/12,13/5) Hyperbolic Matrix(67,-102,23,-35) (3/2,17/11) -> (17/6,3/1) Hyperbolic Matrix(307,-476,109,-169) (17/11,14/9) -> (14/5,17/6) Hyperbolic Matrix(305,-476,66,-103) (14/9,11/7) -> (23/5,14/3) Hyperbolic Matrix(407,-646,172,-273) (19/12,8/5) -> (26/11,19/8) Hyperbolic Matrix(169,-272,64,-103) (8/5,13/8) -> (21/8,8/3) Hyperbolic Matrix(271,-442,84,-137) (13/8,18/11) -> (16/5,13/4) Hyperbolic Matrix(103,-170,20,-33) (18/11,5/3) -> (5/1,16/3) Hyperbolic Matrix(101,-170,41,-69) (5/3,17/10) -> (17/7,5/2) Hyperbolic Matrix(239,-408,99,-169) (17/10,12/7) -> (12/5,17/7) Hyperbolic Matrix(1225,-2108,197,-339) (43/25,74/43) -> (6/1,25/4) Hyperbolic Matrix(3773,-6494,850,-1463) (74/43,31/18) -> (71/16,40/9) Hyperbolic Matrix(1223,-2108,474,-817) (31/18,19/11) -> (49/19,31/12) Hyperbolic Matrix(373,-646,138,-239) (19/11,7/4) -> (27/10,19/7) Hyperbolic Matrix(305,-544,134,-239) (16/9,9/5) -> (25/11,16/7) Hyperbolic Matrix(205,-374,74,-135) (9/5,11/6) -> (11/4,25/9) Hyperbolic Matrix(239,-442,73,-135) (11/6,13/7) -> (13/4,23/7) Hyperbolic Matrix(237,-442,37,-69) (13/7,15/8) -> (19/3,13/2) Hyperbolic Matrix(271,-510,127,-239) (15/8,17/9) -> (17/8,15/7) Hyperbolic Matrix(35,-68,17,-33) (17/9,2/1) -> (2/1,17/8) Parabolic Matrix(137,-306,30,-67) (11/5,9/4) -> (9/2,23/5) Hyperbolic Matrix(511,-1156,225,-509) (9/4,34/15) -> (34/15,25/11) Parabolic Matrix(103,-238,29,-67) (16/7,7/3) -> (7/2,18/5) Hyperbolic Matrix(271,-646,86,-205) (19/8,31/13) -> (3/1,19/6) Hyperbolic Matrix(441,-1054,100,-239) (31/13,12/5) -> (22/5,31/7) Hyperbolic Matrix(239,-612,66,-169) (5/2,18/7) -> (18/5,29/8) Hyperbolic Matrix(2311,-5950,489,-1259) (18/7,85/33) -> (85/18,52/11) Hyperbolic Matrix(3299,-8500,699,-1801) (85/33,67/26) -> (33/7,85/18) Hyperbolic Matrix(443,-1156,169,-441) (13/5,34/13) -> (34/13,21/8) Parabolic Matrix(101,-272,13,-35) (8/3,27/10) -> (7/1,8/1) Hyperbolic Matrix(137,-374,37,-101) (19/7,11/4) -> (11/3,15/4) Hyperbolic Matrix(407,-1292,86,-273) (19/6,16/5) -> (52/11,19/4) Hyperbolic Matrix(815,-2686,186,-613) (23/7,33/10) -> (35/8,57/13) Hyperbolic Matrix(103,-340,10,-33) (33/10,10/3) -> (10/1,1/0) Hyperbolic Matrix(307,-1156,81,-305) (15/4,34/9) -> (34/9,19/5) Parabolic Matrix(4217,-18496,961,-4215) (57/13,136/31) -> (136/31,79/18) Parabolic Matrix(2347,-10404,529,-2345) (31/7,102/23) -> (102/23,71/16) Parabolic Matrix(239,-1122,36,-169) (14/3,33/7) -> (33/5,20/3) Hyperbolic Matrix(271,-1292,43,-205) (19/4,43/9) -> (25/4,19/3) Hyperbolic Matrix(239,-1156,49,-237) (29/6,34/7) -> (34/7,5/1) Parabolic Matrix(171,-1156,25,-169) (27/4,34/5) -> (34/5,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,32,1) Matrix(307,-340,214,-237) -> Matrix(243,-4,12940,-213) Matrix(271,-306,31,-35) -> Matrix(421,-7,15096,-251) Matrix(239,-272,29,-33) -> Matrix(359,-6,12984,-217) Matrix(205,-238,87,-101) -> Matrix(59,-1,2892,-49) Matrix(579,-680,86,-101) -> Matrix(825,-14,30584,-519) Matrix(749,-884,172,-203) -> Matrix(587,-10,23304,-397) Matrix(373,-442,173,-205) -> Matrix(59,-1,2656,-45) Matrix(1087,-1292,859,-1021) -> Matrix(119,-2,6724,-113) Matrix(885,-1054,199,-237) -> Matrix(59,-1,2184,-37) Matrix(169,-204,29,-35) -> Matrix(233,-4,8796,-151) Matrix(307,-374,55,-67) -> Matrix(405,-7,15448,-267) Matrix(305,-374,84,-103) -> Matrix(57,-1,2452,-43) Matrix(647,-816,134,-169) -> Matrix(797,-14,31140,-547) Matrix(511,-646,53,-67) -> Matrix(625,-11,22216,-391) Matrix(2279,-2890,884,-1121) -> Matrix(737,-13,33732,-595) Matrix(1633,-2074,374,-475) -> Matrix(1075,-19,42604,-753) Matrix(373,-476,134,-171) -> Matrix(1,0,-12,1) Matrix(815,-1054,474,-613) -> Matrix(57,-1,2680,-47) Matrix(2073,-2686,1444,-1871) -> Matrix(847,-15,45004,-797) Matrix(681,-884,104,-135) -> Matrix(563,-10,21000,-373) Matrix(339,-442,79,-103) -> Matrix(393,-7,15664,-279) Matrix(103,-136,25,-33) -> Matrix(111,-2,4496,-81) Matrix(101,-136,26,-35) -> Matrix(111,-2,4496,-81) Matrix(273,-374,173,-237) -> Matrix(55,-1,2696,-49) Matrix(271,-374,50,-69) -> Matrix(53,-1,2068,-39) Matrix(171,-238,97,-135) -> Matrix(55,-1,2696,-49) Matrix(169,-238,49,-69) -> Matrix(163,-3,6792,-125) Matrix(239,-340,71,-101) -> Matrix(215,-4,9084,-169) Matrix(1021,-1462,213,-305) -> Matrix(695,-13,27212,-509) Matrix(3433,-4930,782,-1123) -> Matrix(1115,-21,44016,-829) Matrix(307,-442,141,-203) -> Matrix(53,-1,2492,-47) Matrix(305,-442,118,-171) -> Matrix(55,-1,2476,-45) Matrix(67,-102,23,-35) -> Matrix(53,-1,2280,-43) Matrix(307,-476,109,-169) -> Matrix(207,-4,9160,-177) Matrix(305,-476,66,-103) -> Matrix(1,0,-12,1) Matrix(407,-646,172,-273) -> Matrix(53,-1,2492,-47) Matrix(169,-272,64,-103) -> Matrix(103,-2,4584,-89) Matrix(271,-442,84,-137) -> Matrix(51,-1,2092,-41) Matrix(103,-170,20,-33) -> Matrix(49,-1,1912,-39) Matrix(101,-170,41,-69) -> Matrix(51,-1,2296,-45) Matrix(239,-408,99,-169) -> Matrix(99,-2,4604,-93) Matrix(1225,-2108,197,-339) -> Matrix(93,-2,3488,-75) Matrix(3773,-6494,850,-1463) -> Matrix(45,-1,1756,-39) Matrix(1223,-2108,474,-817) -> Matrix(101,-2,4596,-91) Matrix(373,-646,138,-239) -> Matrix(49,-1,2108,-43) Matrix(305,-544,134,-239) -> Matrix(99,-2,4604,-93) Matrix(205,-374,74,-135) -> Matrix(47,-1,2116,-45) Matrix(239,-442,73,-135) -> Matrix(49,-1,2108,-43) Matrix(237,-442,37,-69) -> Matrix(51,-1,1888,-37) Matrix(271,-510,127,-239) -> Matrix(49,-1,2304,-47) Matrix(35,-68,17,-33) -> Matrix(1,0,0,1) Matrix(137,-306,30,-67) -> Matrix(49,-1,1912,-39) Matrix(511,-1156,225,-509) -> Matrix(189,-4,8836,-187) Matrix(103,-238,29,-67) -> Matrix(47,-1,1928,-41) Matrix(271,-646,86,-205) -> Matrix(45,-1,1936,-43) Matrix(441,-1054,100,-239) -> Matrix(49,-1,1912,-39) Matrix(239,-612,66,-169) -> Matrix(1,0,-4,1) Matrix(2311,-5950,489,-1259) -> Matrix(601,-13,23624,-511) Matrix(3299,-8500,699,-1801) -> Matrix(1469,-32,57796,-1259) Matrix(443,-1156,169,-441) -> Matrix(361,-8,16200,-359) Matrix(101,-272,13,-35) -> Matrix(87,-2,3176,-73) Matrix(137,-374,37,-101) -> Matrix(47,-1,1928,-41) Matrix(407,-1292,86,-273) -> Matrix(423,-10,16624,-393) Matrix(815,-2686,186,-613) -> Matrix(643,-15,25420,-593) Matrix(103,-340,10,-33) -> Matrix(171,-4,6028,-141) Matrix(307,-1156,81,-305) -> Matrix(657,-16,26896,-655) Matrix(4217,-18496,961,-4215) -> Matrix(4425,-112,174748,-4423) Matrix(2347,-10404,529,-2345) -> Matrix(469,-12,18252,-467) Matrix(239,-1122,36,-169) -> Matrix(513,-13,19060,-483) Matrix(271,-1292,43,-205) -> Matrix(79,-2,2884,-73) Matrix(239,-1156,49,-237) -> Matrix(781,-20,30420,-779) Matrix(171,-1156,25,-169) -> Matrix(889,-24,32856,-887) 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): 36 ----------------------------------------------------------------------- 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 32 1 2/1 (0/1,1/48) 0 17 17/8 1/48 1 2 15/7 1/48 1 34 13/6 1/48 1 34 11/5 1/52 1 34 9/4 1/48 1 34 34/15 1/47 4 1 16/7 (1/47,1/46) 0 17 7/3 1/44 1 34 19/8 3/140 1 34 31/13 1/44 1 34 12/5 (1/47,1/46) 0 17 17/7 1/46 3 2 5/2 1/44 1 34 18/7 (0/1,1/46) 0 17 13/5 3/136 1 34 34/13 1/45 8 1 8/3 (1/45,1/44) 0 17 27/10 3/128 1 34 19/7 1/40 1 34 11/4 3/136 1 34 14/5 (2/89,1/44) 0 17 17/6 1/44 5 2 3/1 1/44 1 34 19/6 5/212 1 34 16/5 (1/42,1/41) 0 17 13/4 1/44 1 34 23/7 5/216 1 34 33/10 13/556 1 34 10/3 (2/85,1/42) 0 17 17/5 1/42 7 2 7/2 3/124 1 34 18/5 (0/1,1/42) 0 17 11/3 5/208 1 34 15/4 7/288 1 34 34/9 1/41 16 1 4/1 (1/41,1/40) 0 17 17/4 1/40 9 2 13/3 1/40 1 34 35/8 19/752 1 34 57/13 25/988 1 34 136/31 2/79 28 1 22/5 (2/79,3/118) 0 17 31/7 5/196 1 34 102/23 1/39 12 1 40/9 (1/39,1/38) 0 17 9/2 1/40 1 34 23/5 3/116 1 34 14/3 (1/40,2/79) 0 17 33/7 19/748 1 34 85/18 3/118 15 2 52/11 (3/118,13/511) 0 17 19/4 5/196 1 34 43/9 5/196 1 34 24/5 (7/274,1/39) 0 17 34/7 1/39 20 1 5/1 3/116 1 34 16/3 (1/39,1/38) 0 17 11/2 7/268 1 34 17/3 1/38 11 2 6/1 (1/38,2/75) 0 17 25/4 3/112 1 34 19/3 3/112 1 34 13/2 3/112 1 34 33/5 23/856 1 34 20/3 (7/260,1/37) 0 17 34/5 1/37 24 1 7/1 5/184 1 34 8/1 (3/109,1/36) 0 17 17/2 1/36 13 2 9/1 1/36 1 34 10/1 (2/71,3/106) 0 17 1/0 1/32 1 34 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(33,-68,16,-33) (2/1,17/8) -> (2/1,17/8) Reflection Matrix(239,-510,112,-239) (17/8,15/7) -> (17/8,15/7) Reflection Matrix(205,-442,32,-69) (15/7,13/6) -> (19/3,13/2) Glide Reflection Matrix(203,-442,62,-135) (13/6,11/5) -> (13/4,23/7) Glide Reflection Matrix(137,-306,30,-67) (11/5,9/4) -> (9/2,23/5) Hyperbolic Matrix(271,-612,120,-271) (9/4,34/15) -> (9/4,34/15) Reflection Matrix(239,-544,105,-239) (34/15,16/7) -> (34/15,16/7) Reflection Matrix(103,-238,29,-67) (16/7,7/3) -> (7/2,18/5) Hyperbolic Matrix(273,-646,101,-239) (7/3,19/8) -> (27/10,19/7) Glide Reflection Matrix(271,-646,86,-205) (19/8,31/13) -> (3/1,19/6) Hyperbolic Matrix(441,-1054,100,-239) (31/13,12/5) -> (22/5,31/7) Hyperbolic Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(67,-170,13,-33) (5/2,18/7) -> (5/1,16/3) Glide Reflection Matrix(171,-442,53,-137) (18/7,13/5) -> (16/5,13/4) Glide Reflection Matrix(339,-884,130,-339) (13/5,34/13) -> (13/5,34/13) Reflection Matrix(103,-272,39,-103) (34/13,8/3) -> (34/13,8/3) Reflection Matrix(101,-272,13,-35) (8/3,27/10) -> (7/1,8/1) Hyperbolic Matrix(137,-374,37,-101) (19/7,11/4) -> (11/3,15/4) Hyperbolic Matrix(171,-476,37,-103) (11/4,14/5) -> (23/5,14/3) Glide Reflection Matrix(169,-476,60,-169) (14/5,17/6) -> (14/5,17/6) Reflection Matrix(35,-102,12,-35) (17/6,3/1) -> (17/6,3/1) Reflection Matrix(407,-1292,86,-273) (19/6,16/5) -> (52/11,19/4) Hyperbolic Matrix(815,-2686,186,-613) (23/7,33/10) -> (35/8,57/13) Hyperbolic Matrix(103,-340,10,-33) (33/10,10/3) -> (10/1,1/0) Hyperbolic Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(103,-374,19,-69) (18/5,11/3) -> (16/3,11/2) Glide Reflection Matrix(271,-1020,72,-271) (15/4,34/9) -> (15/4,34/9) Reflection Matrix(35,-136,9,-35) (34/9,4/1) -> (34/9,4/1) Reflection Matrix(33,-136,8,-33) (4/1,17/4) -> (4/1,17/4) Reflection Matrix(103,-442,24,-103) (17/4,13/3) -> (17/4,13/3) Reflection Matrix(203,-884,31,-135) (13/3,35/8) -> (13/2,33/5) Glide Reflection Matrix(3535,-15504,806,-3535) (57/13,136/31) -> (57/13,136/31) Reflection Matrix(681,-2992,155,-681) (136/31,22/5) -> (136/31,22/5) Reflection Matrix(1427,-6324,322,-1427) (31/7,102/23) -> (31/7,102/23) Reflection Matrix(919,-4080,207,-919) (102/23,40/9) -> (102/23,40/9) Reflection Matrix(237,-1054,38,-169) (40/9,9/2) -> (6/1,25/4) Glide Reflection Matrix(239,-1122,36,-169) (14/3,33/7) -> (33/5,20/3) Hyperbolic Matrix(1189,-5610,252,-1189) (33/7,85/18) -> (33/7,85/18) Reflection Matrix(1871,-8840,396,-1871) (85/18,52/11) -> (85/18,52/11) Reflection Matrix(271,-1292,43,-205) (19/4,43/9) -> (25/4,19/3) Hyperbolic Matrix(135,-646,14,-67) (43/9,24/5) -> (9/1,10/1) Glide Reflection Matrix(169,-816,35,-169) (24/5,34/7) -> (24/5,34/7) Reflection Matrix(69,-340,14,-69) (34/7,5/1) -> (34/7,5/1) Reflection Matrix(67,-374,12,-67) (11/2,17/3) -> (11/2,17/3) Reflection Matrix(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection Matrix(101,-680,15,-101) (20/3,34/5) -> (20/3,34/5) Reflection Matrix(69,-476,10,-69) (34/5,7/1) -> (34/5,7/1) Reflection Matrix(33,-272,4,-33) (8/1,17/2) -> (8/1,17/2) Reflection Matrix(35,-306,4,-35) (17/2,9/1) -> (17/2,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,64,-1) (0/1,1/0) -> (0/1,1/32) Matrix(1,0,1,-1) -> Matrix(1,0,96,-1) (0/1,2/1) -> (0/1,1/48) Matrix(33,-68,16,-33) -> Matrix(1,0,96,-1) (2/1,17/8) -> (0/1,1/48) Matrix(239,-510,112,-239) -> Matrix(47,-1,2208,-47) (17/8,15/7) -> (1/48,1/46) Matrix(205,-442,32,-69) -> Matrix(45,-1,1664,-37) Matrix(203,-442,62,-135) -> Matrix(47,-1,2020,-43) Matrix(137,-306,30,-67) -> Matrix(49,-1,1912,-39) Matrix(271,-612,120,-271) -> Matrix(95,-2,4512,-95) (9/4,34/15) -> (1/48,1/47) Matrix(239,-544,105,-239) -> Matrix(93,-2,4324,-93) (34/15,16/7) -> (1/47,1/46) Matrix(103,-238,29,-67) -> Matrix(47,-1,1928,-41) Matrix(273,-646,101,-239) -> Matrix(47,-1,2020,-43) Matrix(271,-646,86,-205) -> Matrix(45,-1,1936,-43) 1/44 Matrix(441,-1054,100,-239) -> Matrix(49,-1,1912,-39) Matrix(169,-408,70,-169) -> Matrix(93,-2,4324,-93) (12/5,17/7) -> (1/47,1/46) Matrix(69,-170,28,-69) -> Matrix(45,-1,2024,-45) (17/7,5/2) -> (1/46,1/44) Matrix(67,-170,13,-33) -> Matrix(47,-1,1832,-39) Matrix(171,-442,53,-137) -> Matrix(45,-1,1844,-41) Matrix(339,-884,130,-339) -> Matrix(271,-6,12240,-271) (13/5,34/13) -> (3/136,1/45) Matrix(103,-272,39,-103) -> Matrix(89,-2,3960,-89) (34/13,8/3) -> (1/45,1/44) Matrix(101,-272,13,-35) -> Matrix(87,-2,3176,-73) Matrix(137,-374,37,-101) -> Matrix(47,-1,1928,-41) Matrix(171,-476,37,-103) -> Matrix(1,0,84,-1) *** -> (0/1,1/42) Matrix(169,-476,60,-169) -> Matrix(177,-4,7832,-177) (14/5,17/6) -> (2/89,1/44) Matrix(35,-102,12,-35) -> Matrix(43,-1,1848,-43) (17/6,3/1) -> (1/44,1/42) Matrix(407,-1292,86,-273) -> Matrix(423,-10,16624,-393) Matrix(815,-2686,186,-613) -> Matrix(643,-15,25420,-593) Matrix(103,-340,10,-33) -> Matrix(171,-4,6028,-141) Matrix(101,-340,30,-101) -> Matrix(169,-4,7140,-169) (10/3,17/5) -> (2/85,1/42) Matrix(69,-238,20,-69) -> Matrix(125,-3,5208,-125) (17/5,7/2) -> (1/42,3/124) Matrix(103,-374,19,-69) -> Matrix(43,-1,1676,-39) Matrix(271,-1020,72,-271) -> Matrix(575,-14,23616,-575) (15/4,34/9) -> (7/288,1/41) Matrix(35,-136,9,-35) -> Matrix(81,-2,3280,-81) (34/9,4/1) -> (1/41,1/40) Matrix(33,-136,8,-33) -> Matrix(81,-2,3280,-81) (4/1,17/4) -> (1/41,1/40) Matrix(103,-442,24,-103) -> Matrix(279,-7,11120,-279) (17/4,13/3) -> (1/40,7/278) Matrix(203,-884,31,-135) -> Matrix(397,-10,14808,-373) Matrix(3535,-15504,806,-3535) -> Matrix(3951,-100,156104,-3951) (57/13,136/31) -> (25/988,2/79) Matrix(681,-2992,155,-681) -> Matrix(473,-12,18644,-473) (136/31,22/5) -> (2/79,3/118) Matrix(1427,-6324,322,-1427) -> Matrix(391,-10,15288,-391) (31/7,102/23) -> (5/196,1/39) Matrix(919,-4080,207,-919) -> Matrix(77,-2,2964,-77) (102/23,40/9) -> (1/39,1/38) Matrix(237,-1054,38,-169) -> Matrix(37,-1,1368,-37) *** -> (1/38,1/36) Matrix(239,-1122,36,-169) -> Matrix(513,-13,19060,-483) Matrix(1189,-5610,252,-1189) -> Matrix(2243,-57,88264,-2243) (33/7,85/18) -> (19/748,3/118) Matrix(1871,-8840,396,-1871) -> Matrix(3067,-78,120596,-3067) (85/18,52/11) -> (3/118,13/511) Matrix(271,-1292,43,-205) -> Matrix(79,-2,2884,-73) Matrix(135,-646,14,-67) -> Matrix(431,-11,15320,-391) Matrix(169,-816,35,-169) -> Matrix(547,-14,21372,-547) (24/5,34/7) -> (7/274,1/39) Matrix(69,-340,14,-69) -> Matrix(233,-6,9048,-233) (34/7,5/1) -> (1/39,3/116) Matrix(67,-374,12,-67) -> Matrix(267,-7,10184,-267) (11/2,17/3) -> (7/268,1/38) Matrix(35,-204,6,-35) -> Matrix(151,-4,5700,-151) (17/3,6/1) -> (1/38,2/75) Matrix(101,-680,15,-101) -> Matrix(519,-14,19240,-519) (20/3,34/5) -> (7/260,1/37) Matrix(69,-476,10,-69) -> Matrix(369,-10,13616,-369) (34/5,7/1) -> (1/37,5/184) Matrix(33,-272,4,-33) -> Matrix(217,-6,7848,-217) (8/1,17/2) -> (3/109,1/36) Matrix(35,-306,4,-35) -> Matrix(251,-7,9000,-251) (17/2,9/1) -> (1/36,7/250) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.