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: 96 Genus: 97 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -16/9 -5/3 -14/9 -13/9 -4/3 -11/9 -1/1 -8/9 -5/6 -7/9 -11/15 -2/3 -35/54 -17/27 -5/9 -1/2 -7/15 -11/24 -4/9 -5/12 -10/27 -13/36 -1/3 -17/54 -11/36 -3/10 -3/11 -29/108 -4/15 -1/4 -17/72 -3/13 -2/9 -3/14 -1/5 -3/16 -3/17 -1/6 -1/7 -5/36 -2/15 -1/8 -1/9 -1/10 0/1 1/9 1/8 1/7 2/13 1/6 3/17 2/11 3/16 1/5 3/14 2/9 3/13 4/17 1/4 4/15 3/11 5/18 2/7 4/13 1/3 6/17 4/11 10/27 7/18 2/5 5/12 4/9 11/24 1/2 5/9 4/7 11/18 17/27 2/3 13/18 11/15 7/9 4/5 5/6 8/9 1/1 11/9 19/15 4/3 13/9 14/9 5/3 26/15 16/9 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 -1/2 1/0 -13/7 -2/1 0/1 -24/13 1/0 -11/6 1/0 -20/11 1/0 -29/16 -3/1 -1/1 -67/37 -2/1 -12/7 -38/21 -1/1 -9/5 -2/1 -25/14 -1/1 -16/9 -1/1 -39/22 -1/1 -62/35 -1/2 -1/4 -23/13 -2/3 0/1 -7/4 -1/1 1/1 -33/19 -2/1 -4/3 -26/15 0/1 -71/41 0/1 2/1 -45/26 1/1 -64/37 1/0 -19/11 0/1 -12/7 1/0 -17/10 -1/1 -22/13 -3/2 1/0 -5/3 -1/1 -23/14 -1/1 -18/11 -1/2 1/0 -31/19 0/1 -13/8 -1/1 1/1 -34/21 -2/1 -89/55 -4/3 -6/5 -55/34 -1/1 -21/13 -2/1 -8/5 1/0 -27/17 -4/1 -2/1 -19/12 -1/1 -11/7 -2/1 -25/16 -9/7 -1/1 -14/9 -1/1 -17/11 -2/3 0/1 -3/2 -1/1 -19/13 -2/3 0/1 -35/24 -1/1 -1/3 -16/11 1/0 -13/9 -1/1 -36/25 -5/6 -23/16 -1/1 -7/9 -10/7 -3/4 -1/2 -17/12 -1/1 -7/5 -2/3 0/1 -18/13 -3/4 -1/2 -29/21 -2/3 -69/50 -1/1 -40/29 -1/2 -11/8 -1/1 -3/5 -37/27 -1/2 -26/19 -1/2 -3/8 -15/11 0/1 -34/25 -3/4 -1/2 -19/14 -1/1 -4/3 -1/2 1/0 -21/16 -1/1 -1/3 -17/13 0/1 -30/23 -1/2 1/0 -13/10 -1/1 -35/27 -1/2 -22/17 -1/2 -5/12 -9/7 -2/5 0/1 -14/11 -1/2 1/0 -33/26 -1/1 -19/15 0/1 -5/4 -1/1 -1/3 -21/17 -2/7 -16/13 -1/4 -11/9 0/1 -28/23 1/2 -45/37 0/1 -17/14 1/1 -6/5 -1/2 1/0 -13/11 -2/5 0/1 -7/6 0/1 -8/7 -1/2 -9/8 -1/3 -1/5 -1/1 0/1 -8/9 0/1 -7/8 1/5 1/3 -6/7 1/2 1/0 -17/20 1/1 3/1 -11/13 0/1 2/1 -5/6 0/1 -19/23 0/1 -14/17 3/8 1/2 -9/11 0/1 2/3 -22/27 1/1 -13/16 1/1 3/1 -30/37 -5/2 1/0 -47/58 -1/1 -17/21 0/1 -21/26 1/1 -25/31 0/1 2/1 -4/5 1/0 -15/19 -2/3 -11/14 -1/3 -7/9 0/1 -17/22 1/7 -27/35 0/1 -10/13 1/6 1/4 -13/17 2/7 -3/4 1/3 1/1 -17/23 0/1 2/1 -14/19 1/2 3/4 -11/15 0/1 2/1 -30/41 1/2 1/0 -19/26 1/1 -27/37 -2/1 0/1 -35/48 -1/1 1/1 -8/11 1/0 -13/18 0/1 -18/25 1/4 1/2 -5/7 0/1 2/3 -12/17 1/2 -19/27 1/1 -26/37 3/2 1/0 -7/10 1/1 -9/13 0/1 -11/16 1/1 3/1 -2/3 0/1 -13/20 1/3 3/7 -24/37 1/2 -35/54 1/2 -11/17 4/7 2/3 -9/14 1/1 -7/11 0/1 -19/30 0/1 -12/19 1/0 -17/27 0/1 -22/35 1/2 1/0 -5/8 1/3 1/1 -18/29 1/2 1/0 -31/50 1/3 -13/21 0/1 2/3 -34/55 3/4 5/6 -21/34 1/1 -29/47 0/1 2/1 -37/60 -1/1 1/1 -8/13 1/2 -11/18 1/1 -14/23 3/2 1/0 -3/5 0/1 2/1 -13/22 1/1 -10/17 1/4 1/2 -17/29 2/3 -7/12 1/1 -11/19 0/1 -15/26 1/1 -4/7 1/0 -17/30 0/1 -13/23 0/1 2/1 -9/16 -1/1 1/1 -5/9 0/1 -11/20 1/3 1/1 -6/11 1/2 1/0 -19/35 0/1 -32/59 1/4 -13/24 1/3 1/1 -7/13 0/1 2/3 -1/2 1/1 -7/15 2/1 -6/13 3/2 1/0 -17/37 2/1 -11/24 1/1 3/1 -16/35 1/0 -5/11 0/1 2/1 -4/9 1/0 -11/25 -2/1 0/1 -18/41 1/2 1/0 -25/57 0/1 2/1 -7/16 -1/1 1/1 -17/39 1/1 -10/23 1/2 1/0 -3/7 0/1 -8/19 1/0 -13/31 0/1 2/3 -5/12 1/1 -7/17 2/1 4/1 -37/90 1/0 -30/73 -9/2 1/0 -23/56 -1/1 1/1 -16/39 1/2 1/0 -9/22 1/1 -2/5 1/2 1/0 -7/18 1/1 -12/31 3/2 -5/13 2/1 -13/34 1/1 -8/21 3/2 1/0 -27/71 2/1 -19/50 3/1 -30/79 3/2 1/0 -41/108 1/1 3/1 -11/29 0/1 2/1 -14/37 3/2 1/0 -3/8 1/1 3/1 -13/35 0/1 2/1 -10/27 1/0 -27/73 -2/1 0/1 -17/46 1/1 -7/19 0/1 -11/30 1/0 -4/11 1/0 -13/36 1/1 -22/61 5/4 3/2 -9/25 2/1 -5/14 1/1 -6/17 3/2 7/4 -1/3 1/0 -6/19 -1/2 -1/4 -17/54 0/1 -11/35 0/1 -5/16 1/3 1/1 -9/29 2/1 -4/13 1/0 -11/36 -1/1 1/1 -18/59 1/2 1/0 -7/23 0/1 -3/10 1/1 -14/47 1/2 1/0 -11/37 0/1 2/3 -8/27 1/1 -13/44 1/1 3/1 -5/17 2/1 -7/24 1/1 -2/7 3/2 1/0 -5/18 1/0 -8/29 1/0 -3/11 0/1 -13/48 -1/1 1/1 -23/85 0/1 2/1 -10/37 -1/2 1/0 -7/26 1/1 -18/67 1/2 1/0 -29/108 -1/1 1/1 -40/149 1/0 -11/41 0/1 2/1 -4/15 1/2 1/0 -9/34 1/1 -14/53 3/4 5/6 -19/72 1/1 -5/19 4/3 2/1 -1/4 1/1 3/1 -5/21 2/1 -9/38 3/1 -13/55 14/5 20/7 -17/72 3/1 -4/17 7/2 -7/30 4/1 -3/13 4/1 6/1 -2/9 1/0 -5/23 -6/1 -4/1 -13/60 -5/1 -3/1 -8/37 1/0 -19/88 -7/1 -5/1 -11/51 -6/1 -4/1 -3/14 -3/1 -7/33 -3/1 -11/52 -3/1 -7/3 -15/71 -2/1 -19/90 -2/1 -4/19 -3/2 -1/5 0/1 -4/21 1/0 -7/37 -2/5 0/1 -3/16 1/3 1/1 -2/11 3/2 1/0 -3/17 2/1 8/3 -4/23 1/0 -1/6 1/0 -3/19 -2/1 -2/13 1/2 1/0 -1/7 0/1 2/1 -5/36 1/1 3/1 -4/29 1/0 -3/22 1/1 -5/37 2/1 -2/15 2/1 -1/8 3/1 5/1 -1/9 1/0 -1/10 -3/1 0/1 1/0 1/9 1/0 1/8 -5/1 -3/1 1/7 -2/1 2/13 -3/2 1/0 1/6 1/0 4/23 1/0 3/17 -2/1 2/11 -5/2 1/0 3/16 -3/1 -1/1 7/37 -2/1 4/21 -3/2 1/0 1/5 -2/1 0/1 4/19 -1/2 3/14 1/1 2/9 1/0 5/22 -5/1 8/35 1/0 3/13 -4/1 4/17 -7/2 1/4 -3/1 -1/1 5/19 -4/3 4/15 1/0 11/41 -2/1 7/26 -1/1 10/37 -1/2 1/0 13/48 -3/1 -1/1 3/11 -2/1 0/1 5/18 1/0 2/7 -5/2 1/0 5/17 -12/5 -2/1 8/27 -2/1 11/37 -2/1 3/10 -1/1 4/13 1/0 5/16 -3/1 -1/1 1/3 -2/1 0/1 7/20 -3/1 -1/1 13/37 -20/9 -2/1 19/54 -2/1 6/17 -7/4 -3/2 5/14 -1/1 4/11 1/0 11/30 1/0 7/19 -8/3 -2/1 10/27 -2/1 13/35 -2/1 3/8 -5/3 -1/1 11/29 -2/1 19/50 -1/1 8/21 -3/2 21/55 -6/5 13/34 -1/1 5/13 -2/1 -4/3 7/18 -1/1 2/5 -3/2 1/0 9/22 -5/3 7/17 -4/3 5/12 -1/1 8/19 -3/2 3/7 -2/1 -4/3 10/23 -3/2 -5/4 7/16 -9/7 -1/1 4/9 -1/1 9/20 -1/1 -3/5 5/11 0/1 16/35 1/0 11/24 -3/1 -1/1 6/13 -3/2 1/0 1/2 -1/1 7/13 0/1 20/37 1/0 13/24 -3/1 -1/1 19/35 -2/1 -4/3 6/11 -3/2 1/0 5/9 -1/1 14/25 -7/8 -5/6 9/16 -1/1 -7/9 13/23 -2/3 4/7 -1/2 11/19 0/1 2/1 7/12 -1/1 10/17 -1/2 -1/4 13/22 -1/1 3/5 0/1 11/18 -1/1 8/13 -1/2 21/34 -1/1 13/21 -1/2 44/71 -1/2 31/50 -1/3 49/79 0/1 67/108 -1/1 -1/3 18/29 -1/2 -1/4 5/8 -1/1 1/1 22/35 -1/2 1/0 17/27 -1/1 12/19 1/0 19/30 0/1 7/11 -2/1 0/1 23/36 -1/1 16/25 -1/2 9/14 -1/1 11/17 2/1 2/3 -1/1 13/19 -4/7 37/54 -1/2 24/35 -1/2 11/16 -1/1 -1/3 9/13 -2/3 0/1 25/36 -1/1 -1/3 16/23 -1/2 7/10 -1/1 26/37 -1/2 -1/4 19/27 0/1 12/17 -1/2 5/7 0/1 13/18 0/1 8/11 1/0 35/48 -1/1 -1/3 27/37 0/1 19/26 1/1 49/67 0/1 79/108 -1/1 1/1 30/41 1/2 1/0 11/15 1/0 25/34 -1/1 39/53 -6/5 53/72 -1/1 14/19 -3/4 -1/2 3/4 -1/1 1/1 13/17 -2/3 0/1 23/30 1/0 10/13 -3/2 1/0 7/9 -1/1 18/23 -3/4 -1/2 47/60 -1/1 -5/7 29/37 -8/11 -2/3 40/51 -1/2 11/14 -1/1 15/19 -2/5 0/1 4/5 -1/2 17/21 -1/1 30/37 -7/12 -1/2 13/16 -1/1 -1/3 9/11 0/1 14/17 -1/2 -3/8 19/23 -2/7 0/1 5/6 0/1 16/19 1/2 11/13 0/1 6/7 -1/2 1/0 7/8 -1/1 1/1 8/9 -1/1 1/1 -2/1 0/1 9/8 -1/1 1/1 8/7 1/0 15/13 0/1 7/6 0/1 13/11 0/1 19/16 1/1 3/1 44/37 1/0 25/21 1/0 6/5 1/2 1/0 17/14 1/1 11/9 1/0 27/22 -3/1 43/35 -2/1 -4/3 16/13 1/0 21/17 -2/1 -4/3 5/4 -1/1 1/1 24/19 -3/2 19/15 -1/1 52/41 -1/2 33/26 -1/3 47/37 0/1 14/11 -1/2 1/0 23/18 0/1 9/7 0/1 22/17 5/2 1/0 35/27 1/0 48/37 1/0 13/10 -1/1 17/13 0/1 2/1 21/16 1/1 3/1 4/3 1/0 27/20 -1/1 1/1 50/37 7/2 1/0 73/54 1/0 23/17 -4/1 19/14 -1/1 15/11 -2/1 0/1 26/19 3/2 1/0 37/27 1/0 11/8 -3/1 -1/1 40/29 -3/2 69/50 -1/1 29/21 -1/1 76/55 -5/4 47/34 -1/1 18/13 -3/2 1/0 25/18 -1/1 7/5 0/1 24/17 -3/2 17/12 -1/1 27/19 -2/5 0/1 10/7 -1/2 1/0 33/23 0/1 23/16 -1/1 1/1 13/9 1/0 29/20 -3/1 -1/1 16/11 1/0 35/24 -3/1 -1/1 19/13 -2/1 3/2 -1/1 20/13 -1/2 57/37 -2/1 0/1 37/24 -1/1 -1/3 17/11 0/1 14/9 0/1 39/25 0/1 25/16 -1/1 1/1 36/23 1/0 11/7 -2/1 0/1 30/19 -5/2 1/0 19/12 -1/1 27/17 -2/3 8/5 1/0 29/18 -1/1 21/13 -2/3 0/1 55/34 -1/1 34/21 -1/1 115/71 -2/3 -8/13 81/50 -1/1 128/79 -1/2 175/108 -1/1 -3/5 47/29 -2/3 13/8 -1/1 -1/3 44/27 0/1 31/19 0/1 2/3 18/11 -1/2 1/0 59/36 -1/1 41/25 -2/3 0/1 23/14 -1/1 28/17 -1/4 5/3 0/1 32/19 -1/2 91/54 0/1 59/35 0/1 2/11 27/16 1/3 1/1 22/13 1/2 1/0 61/36 -1/1 1/1 39/23 0/1 2/1 17/10 -1/1 63/37 0/1 46/27 0/1 29/17 0/1 2/5 12/7 1/0 31/18 1/0 19/11 -2/1 0/1 64/37 1/0 45/26 -3/1 116/67 1/0 187/108 -3/1 -1/1 71/41 -2/1 26/15 -1/1 59/34 -1/1 92/53 -5/4 125/72 -1/1 33/19 -2/3 7/4 -1/1 1/1 30/17 -3/4 -1/2 23/13 0/1 16/9 0/1 41/23 0/1 107/60 1/3 1/1 66/37 3/8 1/2 91/51 1/1 25/14 1/1 9/5 0/1 2/1 38/21 0/1 67/37 0/1 29/16 1/3 1/1 20/11 1/0 11/6 1/0 24/13 1/0 13/7 0/1 15/8 -1/1 1/1 2/1 -1/2 1/0 1/0 -1/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(109,204,-288,-539) (-2/1,-13/7) -> (-11/29,-14/37) Hyperbolic Matrix(395,732,252,467) (-13/7,-24/13) -> (36/23,11/7) Hyperbolic Matrix(37,68,216,397) (-24/13,-11/6) -> (1/6,4/23) Hyperbolic Matrix(145,264,396,721) (-11/6,-20/11) -> (4/11,11/30) Hyperbolic Matrix(575,1044,396,719) (-20/11,-29/16) -> (29/20,16/11) Hyperbolic Matrix(1943,3520,1152,2087) (-29/16,-67/37) -> (59/35,27/16) Hyperbolic Matrix(3673,6648,2268,4105) (-67/37,-38/21) -> (34/21,115/71) Hyperbolic Matrix(1621,2932,936,1693) (-38/21,-9/5) -> (71/41,26/15) Hyperbolic Matrix(107,192,180,323) (-9/5,-25/14) -> (13/22,3/5) Hyperbolic Matrix(575,1024,-324,-577) (-25/14,-16/9) -> (-16/9,-39/22) Parabolic Matrix(2305,4084,-2844,-5039) (-39/22,-62/35) -> (-30/37,-47/58) Hyperbolic Matrix(935,1656,-3456,-6121) (-62/35,-23/13) -> (-23/85,-10/37) Hyperbolic Matrix(107,188,-144,-253) (-23/13,-7/4) -> (-3/4,-17/23) Hyperbolic Matrix(179,312,144,251) (-7/4,-33/19) -> (21/17,5/4) Hyperbolic Matrix(1981,3436,-1224,-2123) (-33/19,-26/15) -> (-34/21,-89/55) Hyperbolic Matrix(1693,2932,936,1621) (-26/15,-71/41) -> (9/5,38/21) Hyperbolic Matrix(1511,2616,-1872,-3241) (-71/41,-45/26) -> (-21/26,-25/31) Hyperbolic Matrix(1729,2992,1332,2305) (-45/26,-64/37) -> (48/37,13/10) Hyperbolic Matrix(361,624,792,1369) (-64/37,-19/11) -> (5/11,16/35) Hyperbolic Matrix(109,188,-396,-683) (-19/11,-12/7) -> (-8/29,-3/11) Hyperbolic Matrix(145,248,-252,-431) (-12/7,-17/10) -> (-15/26,-4/7) Hyperbolic Matrix(469,796,-360,-611) (-17/10,-22/13) -> (-30/23,-13/10) Hyperbolic Matrix(251,424,-576,-973) (-22/13,-5/3) -> (-17/39,-10/23) Hyperbolic Matrix(107,176,-504,-829) (-5/3,-23/14) -> (-3/14,-7/33) Hyperbolic Matrix(685,1124,-504,-827) (-23/14,-18/11) -> (-34/25,-19/14) Hyperbolic Matrix(71,116,396,647) (-18/11,-31/19) -> (3/17,2/11) Hyperbolic Matrix(287,468,-972,-1585) (-31/19,-13/8) -> (-13/44,-5/17) Hyperbolic Matrix(37,60,-288,-467) (-13/8,-34/21) -> (-2/15,-1/8) Hyperbolic Matrix(937,1516,-3960,-6407) (-89/55,-55/34) -> (-9/38,-13/55) Hyperbolic Matrix(685,1108,468,757) (-55/34,-21/13) -> (19/13,3/2) Hyperbolic Matrix(181,292,-468,-755) (-21/13,-8/5) -> (-12/31,-5/13) Hyperbolic Matrix(143,228,180,287) (-8/5,-27/17) -> (15/19,4/5) Hyperbolic Matrix(613,972,432,685) (-27/17,-19/12) -> (17/12,27/19) Hyperbolic Matrix(253,400,-432,-683) (-19/12,-11/7) -> (-17/29,-7/12) Hyperbolic Matrix(179,280,-576,-901) (-11/7,-25/16) -> (-5/16,-9/29) Hyperbolic Matrix(469,732,-576,-899) (-25/16,-14/9) -> (-22/27,-13/16) Hyperbolic Matrix(323,500,-396,-613) (-14/9,-17/11) -> (-9/11,-22/27) Hyperbolic Matrix(289,444,-468,-719) (-17/11,-3/2) -> (-21/34,-29/47) Hyperbolic Matrix(757,1108,468,685) (-3/2,-19/13) -> (21/13,55/34) Hyperbolic Matrix(721,1052,-2664,-3887) (-19/13,-35/24) -> (-13/48,-23/85) Hyperbolic Matrix(577,840,792,1153) (-35/24,-16/11) -> (8/11,35/48) Hyperbolic Matrix(467,676,-324,-469) (-16/11,-13/9) -> (-13/9,-36/25) Parabolic Matrix(1045,1504,576,829) (-36/25,-23/16) -> (29/16,20/11) Hyperbolic Matrix(215,308,-252,-361) (-23/16,-10/7) -> (-6/7,-17/20) Hyperbolic Matrix(73,104,-252,-359) (-10/7,-17/12) -> (-7/24,-2/7) Hyperbolic Matrix(181,256,-432,-611) (-17/12,-7/5) -> (-13/31,-5/12) Hyperbolic Matrix(109,152,-180,-251) (-7/5,-18/13) -> (-14/23,-3/5) Hyperbolic Matrix(217,300,-468,-647) (-18/13,-29/21) -> (-7/15,-6/13) Hyperbolic Matrix(1837,2536,-2268,-3131) (-29/21,-69/50) -> (-47/58,-17/21) Hyperbolic Matrix(287,396,-2088,-2881) (-69/50,-40/29) -> (-4/29,-3/22) Hyperbolic Matrix(325,448,288,397) (-40/29,-11/8) -> (9/8,8/7) Hyperbolic Matrix(35,48,288,395) (-11/8,-37/27) -> (1/9,1/8) Hyperbolic Matrix(1259,1724,972,1331) (-37/27,-26/19) -> (22/17,35/27) Hyperbolic Matrix(325,444,396,541) (-26/19,-15/11) -> (9/11,14/17) Hyperbolic Matrix(467,636,-1296,-1765) (-15/11,-34/25) -> (-22/61,-9/25) Hyperbolic Matrix(251,340,-612,-829) (-19/14,-4/3) -> (-16/39,-9/22) Hyperbolic Matrix(325,428,-792,-1043) (-4/3,-21/16) -> (-23/56,-16/39) Hyperbolic Matrix(827,1084,576,755) (-21/16,-17/13) -> (33/23,23/16) Hyperbolic Matrix(395,516,-1296,-1693) (-17/13,-30/23) -> (-18/59,-7/23) Hyperbolic Matrix(37,48,-360,-467) (-13/10,-35/27) -> (-1/9,-1/10) Hyperbolic Matrix(1331,1724,972,1259) (-35/27,-22/17) -> (26/19,37/27) Hyperbolic Matrix(397,512,252,325) (-22/17,-9/7) -> (11/7,30/19) Hyperbolic Matrix(181,232,-252,-323) (-9/7,-14/11) -> (-18/25,-5/7) Hyperbolic Matrix(397,504,-1332,-1691) (-14/11,-33/26) -> (-3/10,-14/47) Hyperbolic Matrix(757,960,-936,-1187) (-33/26,-19/15) -> (-17/21,-21/26) Hyperbolic Matrix(35,44,-144,-181) (-19/15,-5/4) -> (-1/4,-5/21) Hyperbolic Matrix(251,312,144,179) (-5/4,-21/17) -> (33/19,7/4) Hyperbolic Matrix(107,132,612,755) (-21/17,-16/13) -> (4/23,3/17) Hyperbolic Matrix(395,484,-324,-397) (-16/13,-11/9) -> (-11/9,-28/23) Parabolic Matrix(1621,1972,-2988,-3635) (-28/23,-45/37) -> (-19/35,-32/59) Hyperbolic Matrix(181,220,-1332,-1619) (-45/37,-17/14) -> (-3/22,-5/37) Hyperbolic Matrix(73,88,180,217) (-17/14,-6/5) -> (2/5,9/22) Hyperbolic Matrix(253,300,-576,-683) (-6/5,-13/11) -> (-11/25,-18/41) Hyperbolic Matrix(251,296,396,467) (-13/11,-7/6) -> (19/30,7/11) Hyperbolic Matrix(143,164,-252,-289) (-7/6,-8/7) -> (-4/7,-17/30) Hyperbolic Matrix(397,448,288,325) (-8/7,-9/8) -> (11/8,40/29) Hyperbolic Matrix(107,120,288,323) (-9/8,-1/1) -> (13/35,3/8) Hyperbolic Matrix(107,96,360,323) (-1/1,-8/9) -> (8/27,11/37) Hyperbolic Matrix(469,412,288,253) (-8/9,-7/8) -> (13/8,44/27) Hyperbolic Matrix(179,156,288,251) (-7/8,-6/7) -> (18/29,5/8) Hyperbolic Matrix(613,520,468,397) (-17/20,-11/13) -> (17/13,21/16) Hyperbolic Matrix(109,92,-468,-395) (-11/13,-5/6) -> (-7/30,-3/13) Hyperbolic Matrix(251,208,216,179) (-5/6,-19/23) -> (15/13,7/6) Hyperbolic Matrix(1081,892,612,505) (-19/23,-14/17) -> (30/17,23/13) Hyperbolic Matrix(541,444,396,325) (-14/17,-9/11) -> (15/11,26/19) Hyperbolic Matrix(1331,1080,-3240,-2629) (-13/16,-30/37) -> (-30/73,-23/56) Hyperbolic Matrix(1295,1044,-4824,-3889) (-25/31,-4/5) -> (-40/149,-11/41) Hyperbolic Matrix(287,228,180,143) (-4/5,-15/19) -> (27/17,8/5) Hyperbolic Matrix(325,256,504,397) (-15/19,-11/14) -> (9/14,11/17) Hyperbolic Matrix(251,196,-324,-253) (-11/14,-7/9) -> (-7/9,-17/22) Parabolic Matrix(1259,972,-3312,-2557) (-17/22,-27/35) -> (-27/71,-19/50) Hyperbolic Matrix(431,332,-936,-721) (-27/35,-10/13) -> (-6/13,-17/37) Hyperbolic Matrix(73,56,-468,-359) (-10/13,-13/17) -> (-3/19,-2/13) Hyperbolic Matrix(37,28,144,109) (-13/17,-3/4) -> (1/4,5/19) Hyperbolic Matrix(683,504,828,611) (-17/23,-14/19) -> (14/17,19/23) Hyperbolic Matrix(757,556,-1224,-899) (-14/19,-11/15) -> (-13/21,-34/55) Hyperbolic Matrix(1295,948,-2952,-2161) (-11/15,-30/41) -> (-18/41,-25/57) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(1331,972,-3600,-2629) (-19/26,-27/37) -> (-27/73,-17/46) Hyperbolic Matrix(3131,2284,3996,2915) (-27/37,-35/48) -> (47/60,29/37) Hyperbolic Matrix(1153,840,792,577) (-35/48,-8/11) -> (16/11,35/24) Hyperbolic Matrix(287,208,396,287) (-8/11,-13/18) -> (13/18,8/11) Hyperbolic Matrix(827,596,648,467) (-13/18,-18/25) -> (14/11,23/18) Hyperbolic Matrix(107,76,252,179) (-5/7,-12/17) -> (8/19,3/7) Hyperbolic Matrix(613,432,972,685) (-12/17,-19/27) -> (17/27,12/19) Hyperbolic Matrix(1223,860,1944,1367) (-19/27,-26/37) -> (22/35,17/27) Hyperbolic Matrix(359,252,1332,935) (-26/37,-7/10) -> (7/26,10/37) Hyperbolic Matrix(109,76,-360,-251) (-7/10,-9/13) -> (-7/23,-3/10) Hyperbolic Matrix(325,224,576,397) (-9/13,-11/16) -> (9/16,13/23) Hyperbolic Matrix(71,48,-108,-73) (-11/16,-2/3) -> (-2/3,-13/20) Parabolic Matrix(863,560,-3996,-2593) (-13/20,-24/37) -> (-8/37,-19/88) Hyperbolic Matrix(2665,1728,3888,2521) (-24/37,-35/54) -> (37/54,24/35) Hyperbolic Matrix(1007,652,-2448,-1585) (-35/54,-11/17) -> (-7/17,-37/90) Hyperbolic Matrix(397,256,504,325) (-11/17,-9/14) -> (11/14,15/19) Hyperbolic Matrix(181,116,-504,-323) (-9/14,-7/11) -> (-9/25,-5/14) Hyperbolic Matrix(467,296,396,251) (-7/11,-19/30) -> (7/6,13/11) Hyperbolic Matrix(253,160,-1080,-683) (-19/30,-12/19) -> (-4/17,-7/30) Hyperbolic Matrix(685,432,972,613) (-12/19,-17/27) -> (19/27,12/17) Hyperbolic Matrix(1367,860,1944,1223) (-17/27,-22/35) -> (26/37,19/27) Hyperbolic Matrix(541,340,288,181) (-22/35,-5/8) -> (15/8,2/1) Hyperbolic Matrix(251,156,288,179) (-5/8,-18/29) -> (6/7,7/8) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(613,380,-2844,-1763) (-31/50,-13/21) -> (-11/51,-3/14) Hyperbolic Matrix(971,600,-3672,-2269) (-34/55,-21/34) -> (-9/34,-14/53) Hyperbolic Matrix(791,488,2916,1799) (-29/47,-37/60) -> (13/48,3/11) Hyperbolic Matrix(2089,1288,-3852,-2375) (-37/60,-8/13) -> (-32/59,-13/24) Hyperbolic Matrix(287,176,468,287) (-8/13,-11/18) -> (11/18,8/13) Hyperbolic Matrix(899,548,648,395) (-11/18,-14/23) -> (18/13,25/18) Hyperbolic Matrix(323,192,180,107) (-3/5,-13/22) -> (25/14,9/5) Hyperbolic Matrix(217,128,612,361) (-13/22,-10/17) -> (6/17,5/14) Hyperbolic Matrix(791,464,612,359) (-10/17,-17/29) -> (9/7,22/17) Hyperbolic Matrix(179,104,432,251) (-7/12,-11/19) -> (7/17,5/12) Hyperbolic Matrix(505,292,-1368,-791) (-11/19,-15/26) -> (-17/46,-7/19) Hyperbolic Matrix(685,388,828,469) (-17/30,-13/23) -> (19/23,5/6) Hyperbolic Matrix(397,224,576,325) (-13/23,-9/16) -> (11/16,9/13) Hyperbolic Matrix(179,100,-324,-181) (-9/16,-5/9) -> (-5/9,-11/20) Parabolic Matrix(73,40,396,217) (-11/20,-6/11) -> (2/11,3/16) Hyperbolic Matrix(1007,548,792,431) (-6/11,-19/35) -> (47/37,14/11) Hyperbolic Matrix(289,156,-1332,-719) (-13/24,-7/13) -> (-5/23,-13/60) Hyperbolic Matrix(179,96,468,251) (-7/13,-1/2) -> (13/34,5/13) Hyperbolic Matrix(145,68,-612,-287) (-1/2,-7/15) -> (-5/21,-9/38) Hyperbolic Matrix(1943,892,2664,1223) (-17/37,-11/24) -> (35/48,27/37) Hyperbolic Matrix(935,428,1728,791) (-11/24,-16/35) -> (20/37,13/24) Hyperbolic Matrix(1369,624,792,361) (-16/35,-5/11) -> (19/11,64/37) Hyperbolic Matrix(143,64,-324,-145) (-5/11,-4/9) -> (-4/9,-11/25) Parabolic Matrix(1259,552,-5832,-2557) (-25/57,-7/16) -> (-19/88,-11/51) Hyperbolic Matrix(541,236,-2556,-1115) (-7/16,-17/39) -> (-7/33,-11/52) Hyperbolic Matrix(37,16,252,109) (-10/23,-3/7) -> (1/7,2/13) Hyperbolic Matrix(179,76,252,107) (-3/7,-8/19) -> (12/17,5/7) Hyperbolic Matrix(143,60,684,287) (-8/19,-13/31) -> (1/5,4/19) Hyperbolic Matrix(251,104,432,179) (-5/12,-7/17) -> (11/19,7/12) Hyperbolic Matrix(9829,4040,7272,2989) (-37/90,-30/73) -> (50/37,73/54) Hyperbolic Matrix(217,88,180,73) (-9/22,-2/5) -> (6/5,17/14) Hyperbolic Matrix(71,28,180,71) (-2/5,-7/18) -> (7/18,2/5) Hyperbolic Matrix(1043,404,648,251) (-7/18,-12/31) -> (8/5,29/18) Hyperbolic Matrix(251,96,468,179) (-5/13,-13/34) -> (1/2,7/13) Hyperbolic Matrix(325,124,-1224,-467) (-13/34,-8/21) -> (-4/15,-9/34) Hyperbolic Matrix(431,164,2268,863) (-8/21,-27/71) -> (7/37,4/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(253,96,-1800,-683) (-41/108,-11/29) -> (-1/7,-5/36) Hyperbolic Matrix(361,136,576,217) (-14/37,-3/8) -> (5/8,22/35) Hyperbolic Matrix(323,120,288,107) (-3/8,-13/35) -> (1/1,9/8) Hyperbolic Matrix(1079,400,-2916,-1081) (-13/35,-10/27) -> (-10/27,-27/73) Parabolic Matrix(109,40,-684,-251) (-7/19,-11/30) -> (-1/6,-3/19) Hyperbolic Matrix(721,264,396,145) (-11/30,-4/11) -> (20/11,11/6) Hyperbolic Matrix(829,300,1296,469) (-4/11,-13/36) -> (23/36,16/25) Hyperbolic Matrix(4247,1532,2592,935) (-13/36,-22/61) -> (18/11,59/36) Hyperbolic Matrix(361,128,612,217) (-5/14,-6/17) -> (10/17,13/22) Hyperbolic Matrix(35,12,-108,-37) (-6/17,-1/3) -> (-1/3,-6/19) Parabolic Matrix(685,216,1944,613) (-6/19,-17/54) -> (19/54,6/17) Hyperbolic Matrix(1475,464,-6984,-2197) (-17/54,-11/35) -> (-15/71,-19/90) Hyperbolic Matrix(217,68,1152,361) (-11/35,-5/16) -> (3/16,7/37) Hyperbolic Matrix(865,268,468,145) (-9/29,-4/13) -> (24/13,13/7) Hyperbolic Matrix(901,276,1296,397) (-4/13,-11/36) -> (25/36,16/23) Hyperbolic Matrix(4391,1340,2592,791) (-11/36,-18/59) -> (22/13,61/36) Hyperbolic Matrix(1115,332,2052,611) (-14/47,-11/37) -> (19/35,6/11) Hyperbolic Matrix(323,96,360,107) (-11/37,-8/27) -> (8/9,1/1) Hyperbolic Matrix(541,160,612,181) (-8/27,-13/44) -> (7/8,8/9) Hyperbolic Matrix(971,284,612,179) (-5/17,-7/24) -> (19/12,27/17) Hyperbolic Matrix(71,20,252,71) (-2/7,-5/18) -> (5/18,2/7) Hyperbolic Matrix(1115,308,648,179) (-5/18,-8/29) -> (12/7,31/18) Hyperbolic Matrix(1223,332,792,215) (-3/11,-13/48) -> (37/24,17/11) Hyperbolic Matrix(935,252,1332,359) (-10/37,-7/26) -> (7/10,26/37) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(40391,10844,23328,6263) (-29/108,-40/149) -> (116/67,187/108) Hyperbolic Matrix(179,48,936,251) (-11/41,-4/15) -> (4/21,1/5) Hyperbolic Matrix(3817,1008,5184,1369) (-14/53,-19/72) -> (53/72,14/19) Hyperbolic Matrix(1259,332,-5328,-1405) (-19/72,-5/19) -> (-13/55,-17/72) Hyperbolic Matrix(109,28,144,37) (-5/19,-1/4) -> (3/4,13/17) Hyperbolic Matrix(8749,2064,5040,1189) (-17/72,-4/17) -> (92/53,125/72) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(1367,296,2988,647) (-13/60,-8/37) -> (16/35,11/24) Hyperbolic Matrix(5543,1172,3060,647) (-11/52,-15/71) -> (67/37,29/16) Hyperbolic Matrix(4609,972,2736,577) (-19/90,-4/19) -> (32/19,91/54) Hyperbolic Matrix(253,52,180,37) (-4/19,-1/5) -> (7/5,24/17) Hyperbolic Matrix(251,48,936,179) (-1/5,-4/21) -> (4/15,11/41) Hyperbolic Matrix(2089,396,2664,505) (-4/21,-7/37) -> (29/37,40/51) Hyperbolic Matrix(467,88,1332,251) (-7/37,-3/16) -> (7/20,13/37) Hyperbolic Matrix(323,60,576,107) (-3/16,-2/11) -> (14/25,9/16) Hyperbolic Matrix(647,116,396,71) (-2/11,-3/17) -> (31/19,18/11) Hyperbolic Matrix(755,132,612,107) (-3/17,-4/23) -> (16/13,21/17) Hyperbolic Matrix(397,68,216,37) (-4/23,-1/6) -> (11/6,24/13) Hyperbolic Matrix(109,16,252,37) (-2/13,-1/7) -> (3/7,10/23) Hyperbolic Matrix(9683,1340,5976,827) (-5/36,-4/29) -> (128/79,175/108) Hyperbolic Matrix(2411,324,1332,179) (-5/37,-2/15) -> (38/21,67/37) Hyperbolic Matrix(395,48,288,35) (-1/8,-1/9) -> (37/27,11/8) Hyperbolic Matrix(685,64,396,37) (-1/10,0/1) -> (64/37,45/26) Hyperbolic Matrix(467,-48,360,-37) (0/1,1/9) -> (35/27,48/37) Hyperbolic Matrix(467,-60,288,-37) (1/8,1/7) -> (47/29,13/8) Hyperbolic Matrix(359,-56,468,-73) (2/13,1/6) -> (23/30,10/13) Hyperbolic Matrix(829,-176,504,-107) (4/19,3/14) -> (23/14,28/17) Hyperbolic Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(2053,-468,3312,-755) (5/22,8/35) -> (44/71,31/50) Hyperbolic Matrix(505,-116,936,-215) (8/35,3/13) -> (7/13,20/37) Hyperbolic Matrix(395,-92,468,-109) (3/13,4/17) -> (16/19,11/13) Hyperbolic Matrix(181,-44,144,-35) (4/17,1/4) -> (5/4,24/19) Hyperbolic Matrix(467,-124,1224,-325) (5/19,4/15) -> (8/21,21/55) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(7127,-1928,3996,-1081) (10/37,13/48) -> (107/60,66/37) Hyperbolic Matrix(683,-188,396,-109) (3/11,5/18) -> (31/18,19/11) Hyperbolic Matrix(359,-104,252,-73) (2/7,5/17) -> (27/19,10/7) Hyperbolic Matrix(1585,-468,972,-287) (5/17,8/27) -> (44/27,31/19) Hyperbolic Matrix(1691,-504,1332,-397) (11/37,3/10) -> (33/26,47/37) Hyperbolic Matrix(251,-76,360,-109) (3/10,4/13) -> (16/23,7/10) Hyperbolic Matrix(901,-280,576,-179) (4/13,5/16) -> (25/16,36/23) Hyperbolic Matrix(37,-12,108,-35) (5/16,1/3) -> (1/3,7/20) Parabolic Matrix(6553,-2304,3888,-1367) (13/37,19/54) -> (91/54,59/35) Hyperbolic Matrix(323,-116,504,-181) (5/14,4/11) -> (16/25,9/14) Hyperbolic Matrix(827,-304,1080,-397) (11/30,7/19) -> (13/17,23/30) Hyperbolic Matrix(1657,-612,972,-359) (7/19,10/27) -> (46/27,29/17) Hyperbolic Matrix(3311,-1228,1944,-721) (10/27,13/35) -> (63/37,46/27) Hyperbolic Matrix(539,-204,288,-109) (3/8,11/29) -> (13/7,15/8) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(2231,-848,2844,-1081) (19/50,8/21) -> (40/51,11/14) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(755,-292,468,-181) (5/13,7/18) -> (29/18,21/13) Hyperbolic Matrix(829,-340,612,-251) (9/22,7/17) -> (23/17,19/14) Hyperbolic Matrix(611,-256,432,-181) (5/12,8/19) -> (24/17,17/12) Hyperbolic Matrix(973,-424,576,-251) (10/23,7/16) -> (27/16,22/13) Hyperbolic Matrix(145,-64,324,-143) (7/16,4/9) -> (4/9,9/20) Parabolic Matrix(469,-212,396,-179) (9/20,5/11) -> (13/11,19/16) Hyperbolic Matrix(1043,-480,1332,-613) (11/24,6/13) -> (18/23,47/60) Hyperbolic Matrix(647,-300,468,-217) (6/13,1/2) -> (47/34,18/13) Hyperbolic Matrix(2663,-1444,1728,-937) (13/24,19/35) -> (57/37,37/24) Hyperbolic Matrix(181,-100,324,-179) (6/11,5/9) -> (5/9,14/25) Parabolic Matrix(289,-164,252,-143) (13/23,4/7) -> (8/7,15/13) Hyperbolic Matrix(431,-248,252,-145) (4/7,11/19) -> (29/17,12/7) Hyperbolic Matrix(683,-400,432,-253) (7/12,10/17) -> (30/19,19/12) Hyperbolic Matrix(251,-152,180,-109) (3/5,11/18) -> (25/18,7/5) Hyperbolic Matrix(719,-444,468,-289) (8/13,21/34) -> (3/2,20/13) Hyperbolic Matrix(899,-556,1224,-757) (21/34,13/21) -> (11/15,25/34) Hyperbolic Matrix(2699,-1672,2268,-1405) (13/21,44/71) -> (44/37,25/21) Hyperbolic Matrix(18901,-11724,11664,-7235) (49/79,67/108) -> (175/108,47/29) Hyperbolic Matrix(575,-364,684,-433) (12/19,19/30) -> (5/6,16/19) Hyperbolic Matrix(2125,-1356,1296,-827) (7/11,23/36) -> (59/36,41/25) Hyperbolic Matrix(73,-48,108,-71) (11/17,2/3) -> (2/3,13/19) Parabolic Matrix(2629,-1800,1944,-1331) (13/19,37/54) -> (73/54,23/17) Hyperbolic Matrix(1369,-940,1152,-791) (24/35,11/16) -> (19/16,44/37) Hyperbolic Matrix(2197,-1524,1296,-899) (9/13,25/36) -> (61/36,39/23) Hyperbolic Matrix(323,-232,252,-181) (5/7,13/18) -> (23/18,9/7) Hyperbolic Matrix(2267,-1656,1332,-973) (27/37,19/26) -> (17/10,63/37) Hyperbolic Matrix(20197,-14772,11664,-8531) (49/67,79/108) -> (187/108,71/41) Hyperbolic Matrix(1115,-816,936,-685) (30/41,11/15) -> (25/21,6/5) Hyperbolic Matrix(9001,-6624,5184,-3815) (39/53,53/72) -> (125/72,33/19) Hyperbolic Matrix(253,-188,144,-107) (14/19,3/4) -> (7/4,30/17) Hyperbolic Matrix(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) Parabolic Matrix(1187,-960,936,-757) (4/5,17/21) -> (19/15,52/41) Hyperbolic Matrix(4753,-3852,2664,-2159) (17/21,30/37) -> (66/37,91/51) Hyperbolic Matrix(1799,-1460,1332,-1081) (30/37,13/16) -> (27/20,50/37) Hyperbolic Matrix(899,-732,576,-469) (13/16,9/11) -> (39/25,25/16) Hyperbolic Matrix(361,-308,252,-215) (11/13,6/7) -> (10/7,33/23) Hyperbolic Matrix(397,-484,324,-395) (17/14,11/9) -> (11/9,27/22) Parabolic Matrix(5365,-6588,3312,-4067) (27/22,43/35) -> (115/71,81/50) Hyperbolic Matrix(1441,-1772,936,-1151) (43/35,16/13) -> (20/13,57/37) Hyperbolic Matrix(1691,-2140,1224,-1549) (24/19,19/15) -> (29/21,76/55) Hyperbolic Matrix(4861,-6168,2808,-3563) (52/41,33/26) -> (45/26,116/67) Hyperbolic Matrix(611,-796,360,-469) (13/10,17/13) -> (39/23,17/10) Hyperbolic Matrix(145,-192,108,-143) (21/16,4/3) -> (4/3,27/20) Parabolic Matrix(827,-1124,504,-685) (19/14,15/11) -> (41/25,23/14) Hyperbolic Matrix(8749,-12072,5400,-7451) (40/29,69/50) -> (81/50,128/79) Hyperbolic Matrix(5075,-7004,2844,-3925) (69/50,29/21) -> (91/51,25/14) Hyperbolic Matrix(6373,-8808,3672,-5075) (76/55,47/34) -> (59/34,92/53) Hyperbolic Matrix(469,-676,324,-467) (23/16,13/9) -> (13/9,29/20) Parabolic Matrix(2375,-3468,1332,-1945) (35/24,19/13) -> (41/23,107/60) Hyperbolic Matrix(505,-784,324,-503) (17/11,14/9) -> (14/9,39/25) Parabolic Matrix(2123,-3436,1224,-1981) (55/34,34/21) -> (26/15,59/34) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(577,-1024,324,-575) (23/13,16/9) -> (16/9,41/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,0,1) Matrix(109,204,-288,-539) -> Matrix(1,2,0,1) Matrix(395,732,252,467) -> Matrix(1,0,0,1) Matrix(37,68,216,397) -> Matrix(1,-4,0,1) Matrix(145,264,396,721) -> Matrix(1,0,0,1) Matrix(575,1044,396,719) -> Matrix(1,0,0,1) Matrix(1943,3520,1152,2087) -> Matrix(1,2,2,5) Matrix(3673,6648,2268,4105) -> Matrix(3,4,-4,-5) Matrix(1621,2932,936,1693) -> Matrix(1,0,0,1) Matrix(107,192,180,323) -> Matrix(1,2,-2,-3) Matrix(575,1024,-324,-577) -> Matrix(3,4,-4,-5) Matrix(2305,4084,-2844,-5039) -> Matrix(3,2,-2,-1) Matrix(935,1656,-3456,-6121) -> Matrix(1,0,2,1) Matrix(107,188,-144,-253) -> Matrix(1,0,2,1) Matrix(179,312,144,251) -> Matrix(1,0,0,1) Matrix(1981,3436,-1224,-2123) -> Matrix(3,2,-2,-1) Matrix(1693,2932,936,1621) -> Matrix(1,0,0,1) Matrix(1511,2616,-1872,-3241) -> Matrix(1,0,0,1) Matrix(1729,2992,1332,2305) -> Matrix(1,-2,0,1) Matrix(361,624,792,1369) -> Matrix(1,0,0,1) Matrix(109,188,-396,-683) -> Matrix(1,0,0,1) Matrix(145,248,-252,-431) -> Matrix(1,2,0,1) Matrix(469,796,-360,-611) -> Matrix(1,2,-2,-3) Matrix(251,424,-576,-973) -> Matrix(1,2,0,1) Matrix(107,176,-504,-829) -> Matrix(1,-2,0,1) Matrix(685,1124,-504,-827) -> Matrix(1,2,-2,-3) Matrix(71,116,396,647) -> Matrix(1,-2,0,1) Matrix(287,468,-972,-1585) -> Matrix(1,2,0,1) Matrix(37,60,-288,-467) -> Matrix(1,4,0,1) Matrix(937,1516,-3960,-6407) -> Matrix(5,2,2,1) Matrix(685,1108,468,757) -> Matrix(1,0,0,1) Matrix(181,292,-468,-755) -> Matrix(3,4,2,3) Matrix(143,228,180,287) -> Matrix(1,2,-2,-3) Matrix(613,972,432,685) -> Matrix(1,2,-2,-3) Matrix(253,400,-432,-683) -> Matrix(1,0,2,1) Matrix(179,280,-576,-901) -> Matrix(3,4,2,3) Matrix(469,732,-576,-899) -> Matrix(5,6,4,5) Matrix(323,500,-396,-613) -> Matrix(3,2,4,3) Matrix(289,444,-468,-719) -> Matrix(1,0,2,1) Matrix(757,1108,468,685) -> Matrix(1,0,0,1) Matrix(721,1052,-2664,-3887) -> Matrix(1,0,2,1) Matrix(577,840,792,1153) -> Matrix(1,0,0,1) Matrix(467,676,-324,-469) -> Matrix(5,6,-6,-7) Matrix(1045,1504,576,829) -> Matrix(5,4,6,5) Matrix(215,308,-252,-361) -> Matrix(3,2,4,3) Matrix(73,104,-252,-359) -> Matrix(1,0,2,1) Matrix(181,256,-432,-611) -> Matrix(3,2,4,3) Matrix(109,152,-180,-251) -> Matrix(1,0,2,1) Matrix(217,300,-468,-647) -> Matrix(1,0,2,1) Matrix(1837,2536,-2268,-3131) -> Matrix(3,2,-2,-1) Matrix(287,396,-2088,-2881) -> Matrix(1,0,2,1) Matrix(325,448,288,397) -> Matrix(3,2,-2,-1) Matrix(35,48,288,395) -> Matrix(11,6,-2,-1) Matrix(1259,1724,972,1331) -> Matrix(9,4,2,1) Matrix(325,444,396,541) -> Matrix(1,0,0,1) Matrix(467,636,-1296,-1765) -> Matrix(1,2,0,1) Matrix(251,340,-612,-829) -> Matrix(1,0,2,1) Matrix(325,428,-792,-1043) -> Matrix(1,0,2,1) Matrix(827,1084,576,755) -> Matrix(1,0,2,1) Matrix(395,516,-1296,-1693) -> Matrix(1,0,2,1) Matrix(37,48,-360,-467) -> Matrix(7,4,-2,-1) Matrix(1331,1724,972,1259) -> Matrix(9,4,2,1) Matrix(397,512,252,325) -> Matrix(1,0,2,1) Matrix(181,232,-252,-323) -> Matrix(1,0,4,1) Matrix(397,504,-1332,-1691) -> Matrix(1,0,2,1) Matrix(757,960,-936,-1187) -> Matrix(1,0,2,1) Matrix(35,44,-144,-181) -> Matrix(5,2,2,1) Matrix(251,312,144,179) -> Matrix(1,0,2,1) Matrix(107,132,612,755) -> Matrix(15,4,-4,-1) Matrix(395,484,-324,-397) -> Matrix(1,0,6,1) Matrix(1621,1972,-2988,-3635) -> Matrix(1,0,2,1) Matrix(181,220,-1332,-1619) -> Matrix(3,-2,2,-1) Matrix(73,88,180,217) -> Matrix(3,2,-2,-1) Matrix(253,300,-576,-683) -> Matrix(1,0,2,1) Matrix(251,296,396,467) -> Matrix(1,0,2,1) Matrix(143,164,-252,-289) -> Matrix(1,0,2,1) Matrix(397,448,288,325) -> Matrix(7,2,-4,-1) Matrix(107,120,288,323) -> Matrix(11,2,-6,-1) Matrix(107,96,360,323) -> Matrix(7,2,-4,-1) Matrix(469,412,288,253) -> Matrix(1,0,-6,1) Matrix(179,156,288,251) -> Matrix(1,0,-4,1) Matrix(613,520,468,397) -> Matrix(1,0,0,1) Matrix(109,92,-468,-395) -> Matrix(1,4,0,1) Matrix(251,208,216,179) -> Matrix(1,0,-4,1) Matrix(1081,892,612,505) -> Matrix(1,0,-4,1) Matrix(541,444,396,325) -> Matrix(1,0,-2,1) Matrix(1331,1080,-3240,-2629) -> Matrix(1,-2,0,1) Matrix(1295,1044,-4824,-3889) -> Matrix(1,0,0,1) Matrix(287,228,180,143) -> Matrix(1,0,0,1) Matrix(325,256,504,397) -> Matrix(1,0,2,1) Matrix(251,196,-324,-253) -> Matrix(1,0,10,1) Matrix(1259,972,-3312,-2557) -> Matrix(11,-2,6,-1) Matrix(431,332,-936,-721) -> Matrix(11,-2,6,-1) Matrix(73,56,-468,-359) -> Matrix(1,0,-4,1) Matrix(37,28,144,109) -> Matrix(5,-2,-2,1) Matrix(683,504,828,611) -> Matrix(1,0,-4,1) Matrix(757,556,-1224,-899) -> Matrix(1,-2,2,-3) Matrix(1295,948,-2952,-2161) -> Matrix(1,0,0,1) Matrix(755,552,-2808,-2053) -> Matrix(1,0,0,1) Matrix(1331,972,-3600,-2629) -> Matrix(1,0,0,1) Matrix(3131,2284,3996,2915) -> Matrix(3,-2,-4,3) Matrix(1153,840,792,577) -> Matrix(1,-2,0,1) Matrix(287,208,396,287) -> Matrix(1,0,0,1) Matrix(827,596,648,467) -> Matrix(1,0,-4,1) Matrix(107,76,252,179) -> Matrix(1,-2,0,1) Matrix(613,432,972,685) -> Matrix(1,0,-2,1) Matrix(1223,860,1944,1367) -> Matrix(1,-2,0,1) Matrix(359,252,1332,935) -> Matrix(1,-2,0,1) Matrix(109,76,-360,-251) -> Matrix(1,0,0,1) Matrix(325,224,576,397) -> Matrix(3,-2,-4,3) Matrix(71,48,-108,-73) -> Matrix(1,0,2,1) Matrix(863,560,-3996,-2593) -> Matrix(17,-8,-2,1) Matrix(2665,1728,3888,2521) -> Matrix(17,-8,-36,17) Matrix(1007,652,-2448,-1585) -> Matrix(11,-6,2,-1) Matrix(397,256,504,325) -> Matrix(3,-2,-4,3) Matrix(181,116,-504,-323) -> Matrix(3,-2,2,-1) Matrix(467,296,396,251) -> Matrix(1,0,0,1) Matrix(253,160,-1080,-683) -> Matrix(7,-4,2,-1) Matrix(685,432,972,613) -> Matrix(1,0,-2,1) Matrix(1367,860,1944,1223) -> Matrix(1,0,-4,1) Matrix(541,340,288,181) -> Matrix(1,0,-2,1) Matrix(251,156,288,179) -> Matrix(1,0,-2,1) Matrix(2051,1272,-5400,-3349) -> Matrix(3,-2,2,-1) Matrix(613,380,-2844,-1763) -> Matrix(9,-4,-2,1) Matrix(971,600,-3672,-2269) -> Matrix(1,0,0,1) Matrix(791,488,2916,1799) -> Matrix(1,-2,0,1) Matrix(2089,1288,-3852,-2375) -> Matrix(1,0,2,1) Matrix(287,176,468,287) -> Matrix(3,-2,-4,3) Matrix(899,548,648,395) -> Matrix(3,-4,-2,3) Matrix(323,192,180,107) -> Matrix(1,0,0,1) Matrix(217,128,612,361) -> Matrix(1,-2,0,1) Matrix(791,464,612,359) -> Matrix(3,-2,2,-1) Matrix(179,104,432,251) -> Matrix(3,-4,-2,3) Matrix(505,292,-1368,-791) -> Matrix(1,0,0,1) Matrix(685,388,828,469) -> Matrix(1,0,-4,1) Matrix(397,224,576,325) -> Matrix(1,0,-2,1) Matrix(179,100,-324,-181) -> Matrix(1,0,2,1) Matrix(73,40,396,217) -> Matrix(5,-2,-2,1) Matrix(1007,548,792,431) -> Matrix(1,0,-2,1) Matrix(289,156,-1332,-719) -> Matrix(9,-4,-2,1) Matrix(179,96,468,251) -> Matrix(1,-2,0,1) Matrix(145,68,-612,-287) -> Matrix(5,-8,2,-3) Matrix(1943,892,2664,1223) -> Matrix(1,-2,-2,5) Matrix(935,428,1728,791) -> Matrix(1,-4,0,1) Matrix(1369,624,792,361) -> Matrix(1,-2,0,1) Matrix(143,64,-324,-145) -> Matrix(1,-2,0,1) Matrix(1259,552,-5832,-2557) -> Matrix(1,-6,0,1) Matrix(541,236,-2556,-1115) -> Matrix(5,-2,-2,1) Matrix(37,16,252,109) -> Matrix(1,-2,0,1) Matrix(179,76,252,107) -> Matrix(1,0,-2,1) Matrix(143,60,684,287) -> Matrix(1,0,-2,1) Matrix(251,104,432,179) -> Matrix(1,-2,0,1) Matrix(9829,4040,7272,2989) -> Matrix(1,8,0,1) Matrix(217,88,180,73) -> Matrix(1,0,0,1) Matrix(71,28,180,71) -> Matrix(1,-2,0,1) Matrix(1043,404,648,251) -> Matrix(3,-4,-2,3) Matrix(251,96,468,179) -> Matrix(1,-2,0,1) Matrix(325,124,-1224,-467) -> Matrix(1,-2,2,-3) Matrix(431,164,2268,863) -> Matrix(3,-4,-2,3) Matrix(7237,2748,11664,4429) -> Matrix(1,-2,-2,5) Matrix(253,96,-1800,-683) -> Matrix(1,0,0,1) Matrix(361,136,576,217) -> Matrix(1,-2,0,1) Matrix(323,120,288,107) -> Matrix(1,-2,0,1) Matrix(1079,400,-2916,-1081) -> Matrix(1,-2,0,1) Matrix(109,40,-684,-251) -> Matrix(1,-2,0,1) Matrix(721,264,396,145) -> Matrix(1,0,0,1) Matrix(829,300,1296,469) -> Matrix(1,0,-2,1) Matrix(4247,1532,2592,935) -> Matrix(3,-4,-2,3) Matrix(361,128,612,217) -> Matrix(1,-2,0,1) Matrix(35,12,-108,-37) -> Matrix(1,-2,0,1) Matrix(685,216,1944,613) -> Matrix(11,2,-6,-1) Matrix(1475,464,-6984,-2197) -> Matrix(21,-2,-10,1) Matrix(217,68,1152,361) -> Matrix(5,-2,-2,1) Matrix(865,268,468,145) -> Matrix(1,-2,0,1) Matrix(901,276,1296,397) -> Matrix(1,0,-2,1) Matrix(4391,1340,2592,791) -> Matrix(1,0,0,1) Matrix(1115,332,2052,611) -> Matrix(1,-2,0,1) Matrix(323,96,360,107) -> Matrix(1,0,-2,1) Matrix(541,160,612,181) -> Matrix(1,-2,0,1) Matrix(971,284,612,179) -> Matrix(1,0,-2,1) Matrix(71,20,252,71) -> Matrix(1,-4,0,1) Matrix(1115,308,648,179) -> Matrix(1,2,0,1) Matrix(1223,332,792,215) -> Matrix(1,0,-2,1) Matrix(935,252,1332,359) -> Matrix(1,0,-2,1) Matrix(8533,2292,11664,3133) -> Matrix(1,0,0,1) Matrix(40391,10844,23328,6263) -> Matrix(1,-2,0,1) Matrix(179,48,936,251) -> Matrix(1,-2,0,1) Matrix(3817,1008,5184,1369) -> Matrix(7,-6,-8,7) Matrix(1259,332,-5328,-1405) -> Matrix(23,-26,8,-9) Matrix(109,28,144,37) -> Matrix(1,-2,0,1) Matrix(8749,2064,5040,1189) -> Matrix(7,-22,-6,19) Matrix(71,16,-324,-73) -> Matrix(1,-10,0,1) Matrix(1367,296,2988,647) -> Matrix(1,2,0,1) Matrix(5543,1172,3060,647) -> Matrix(1,2,4,9) Matrix(4609,972,2736,577) -> Matrix(1,2,-4,-7) Matrix(253,52,180,37) -> Matrix(1,0,0,1) Matrix(251,48,936,179) -> Matrix(1,-2,0,1) Matrix(2089,396,2664,505) -> Matrix(1,2,-2,-3) Matrix(467,88,1332,251) -> Matrix(5,-2,-2,1) Matrix(323,60,576,107) -> Matrix(5,-4,-6,5) Matrix(647,116,396,71) -> Matrix(1,-2,0,1) Matrix(755,132,612,107) -> Matrix(1,-4,0,1) Matrix(397,68,216,37) -> Matrix(1,-4,0,1) Matrix(109,16,252,37) -> Matrix(3,-4,-2,3) Matrix(9683,1340,5976,827) -> Matrix(1,0,-2,1) Matrix(2411,324,1332,179) -> Matrix(1,-2,0,1) Matrix(395,48,288,35) -> Matrix(1,-6,0,1) Matrix(685,64,396,37) -> Matrix(1,0,0,1) Matrix(467,-48,360,-37) -> Matrix(1,-2,0,1) Matrix(467,-60,288,-37) -> Matrix(1,4,-2,-7) Matrix(359,-56,468,-73) -> Matrix(1,0,0,1) Matrix(829,-176,504,-107) -> Matrix(1,0,-2,1) Matrix(73,-16,324,-71) -> Matrix(1,-6,0,1) Matrix(2053,-468,3312,-755) -> Matrix(1,4,-2,-7) Matrix(505,-116,936,-215) -> Matrix(1,4,0,1) Matrix(395,-92,468,-109) -> Matrix(1,4,0,1) Matrix(181,-44,144,-35) -> Matrix(1,2,0,1) Matrix(467,-124,1224,-325) -> Matrix(3,2,-2,-1) Matrix(2053,-552,2808,-755) -> Matrix(1,2,0,1) Matrix(7127,-1928,3996,-1081) -> Matrix(1,2,2,5) Matrix(683,-188,396,-109) -> Matrix(1,0,0,1) Matrix(359,-104,252,-73) -> Matrix(1,2,0,1) Matrix(1585,-468,972,-287) -> Matrix(1,2,4,9) Matrix(1691,-504,1332,-397) -> Matrix(1,2,-4,-7) Matrix(251,-76,360,-109) -> Matrix(1,2,-2,-3) Matrix(901,-280,576,-179) -> Matrix(1,2,0,1) Matrix(37,-12,108,-35) -> Matrix(1,0,0,1) Matrix(6553,-2304,3888,-1367) -> Matrix(1,2,10,21) Matrix(323,-116,504,-181) -> Matrix(1,2,-2,-3) Matrix(827,-304,1080,-397) -> Matrix(1,2,0,1) Matrix(1657,-612,972,-359) -> Matrix(1,2,4,9) Matrix(3311,-1228,1944,-721) -> Matrix(1,2,-8,-15) Matrix(539,-204,288,-109) -> Matrix(1,2,-2,-3) Matrix(3349,-1272,5400,-2051) -> Matrix(1,2,-4,-7) Matrix(2231,-848,2844,-1081) -> Matrix(3,4,-4,-5) Matrix(2701,-1032,3672,-1403) -> Matrix(1,0,0,1) Matrix(755,-292,468,-181) -> Matrix(3,4,-4,-5) Matrix(829,-340,612,-251) -> Matrix(5,8,-2,-3) Matrix(611,-256,432,-181) -> Matrix(1,0,0,1) Matrix(973,-424,576,-251) -> Matrix(3,4,2,3) Matrix(145,-64,324,-143) -> Matrix(5,6,-6,-7) Matrix(469,-212,396,-179) -> Matrix(1,0,2,1) Matrix(1043,-480,1332,-613) -> Matrix(3,4,-4,-5) Matrix(647,-300,468,-217) -> Matrix(1,0,0,1) Matrix(2663,-1444,1728,-937) -> Matrix(1,2,-2,-3) Matrix(181,-100,324,-179) -> Matrix(7,8,-8,-9) Matrix(289,-164,252,-143) -> Matrix(3,2,-2,-1) Matrix(431,-248,252,-145) -> Matrix(1,0,2,1) Matrix(683,-400,432,-253) -> Matrix(3,2,-2,-1) Matrix(251,-152,180,-109) -> Matrix(1,0,0,1) Matrix(719,-444,468,-289) -> Matrix(1,0,0,1) Matrix(899,-556,1224,-757) -> Matrix(3,2,-2,-1) Matrix(2699,-1672,2268,-1405) -> Matrix(1,0,2,1) Matrix(18901,-11724,11664,-7235) -> Matrix(5,2,-8,-3) Matrix(575,-364,684,-433) -> Matrix(1,0,2,1) Matrix(2125,-1356,1296,-827) -> Matrix(1,2,-2,-3) Matrix(73,-48,108,-71) -> Matrix(1,2,-2,-3) Matrix(2629,-1800,1944,-1331) -> Matrix(15,8,-2,-1) Matrix(1369,-940,1152,-791) -> Matrix(5,2,2,1) Matrix(2197,-1524,1296,-899) -> Matrix(1,0,2,1) Matrix(323,-232,252,-181) -> Matrix(1,0,2,1) Matrix(2267,-1656,1332,-973) -> Matrix(1,0,-2,1) Matrix(20197,-14772,11664,-8531) -> Matrix(1,-2,0,1) Matrix(1115,-816,936,-685) -> Matrix(1,0,0,1) Matrix(9001,-6624,5184,-3815) -> Matrix(7,8,-8,-9) Matrix(253,-188,144,-107) -> Matrix(1,0,0,1) Matrix(253,-196,324,-251) -> Matrix(3,4,-4,-5) Matrix(1187,-960,936,-757) -> Matrix(1,0,0,1) Matrix(4753,-3852,2664,-2159) -> Matrix(3,2,4,3) Matrix(1799,-1460,1332,-1081) -> Matrix(1,0,2,1) Matrix(899,-732,576,-469) -> Matrix(1,0,2,1) Matrix(361,-308,252,-215) -> Matrix(1,0,0,1) Matrix(397,-484,324,-395) -> Matrix(1,-4,0,1) Matrix(5365,-6588,3312,-4067) -> Matrix(1,4,-2,-7) Matrix(1441,-1772,936,-1151) -> Matrix(1,2,-2,-3) Matrix(1691,-2140,1224,-1549) -> Matrix(3,2,-2,-1) Matrix(4861,-6168,2808,-3563) -> Matrix(3,2,-2,-1) Matrix(611,-796,360,-469) -> Matrix(1,0,0,1) Matrix(145,-192,108,-143) -> Matrix(1,-2,0,1) Matrix(827,-1124,504,-685) -> Matrix(1,2,-2,-3) Matrix(8749,-12072,5400,-7451) -> Matrix(3,4,-4,-5) Matrix(5075,-7004,2844,-3925) -> Matrix(1,2,0,1) Matrix(6373,-8808,3672,-5075) -> Matrix(1,0,0,1) Matrix(469,-676,324,-467) -> Matrix(1,-2,0,1) Matrix(2375,-3468,1332,-1945) -> Matrix(1,2,2,5) Matrix(505,-784,324,-503) -> Matrix(1,0,2,1) Matrix(2123,-3436,1224,-1981) -> Matrix(3,2,-2,-1) Matrix(181,-300,108,-179) -> Matrix(1,0,2,1) Matrix(577,-1024,324,-575) -> Matrix(1,0,4,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 60 Degree of the the map X: 60 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.