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 -8/1 -20/3 -6/1 -28/5 -16/3 -14/3 -60/13 -9/2 -22/5 -4/1 -15/4 -26/7 -18/5 -38/11 -27/8 -10/3 -54/17 -3/1 -30/11 -18/7 -12/5 -9/4 -24/11 -15/7 -2/1 -9/5 -18/11 -27/17 -54/35 -3/2 -18/13 -9/7 -6/5 -9/8 0/1 1/1 6/5 9/7 18/13 3/2 54/35 18/11 30/17 9/5 2/1 36/17 15/7 24/11 144/65 9/4 144/61 12/5 144/59 5/2 18/7 108/41 30/11 36/13 3/1 54/17 36/11 10/3 24/7 7/2 18/5 396/109 11/3 26/7 108/29 15/4 34/9 72/19 4/1 17/4 30/7 13/3 22/5 9/2 32/7 60/13 144/31 14/3 24/5 5/1 16/3 11/2 28/5 17/3 6/1 32/5 13/2 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 2/3 -7/1 1/0 -20/3 1/1 -13/2 1/6 -6/1 1/2 -23/4 15/26 -17/3 17/28 -28/5 7/11 -39/7 9/14 -11/2 7/10 -16/3 2/3 -37/7 3/4 -21/4 3/4 -5/1 1/0 -19/4 3/14 -14/3 1/3 2/5 -65/14 9/22 -51/11 1/2 -37/8 1/2 -60/13 1/3 -23/5 3/8 -32/7 4/9 -9/2 1/2 -22/5 4/7 3/5 -35/8 1/2 -13/3 7/12 -17/4 17/26 -4/1 1/1 -19/5 -1/8 -15/4 1/4 -41/11 5/16 -26/7 1/3 2/5 -37/10 1/2 -11/3 3/8 -18/5 1/2 -25/7 13/24 -57/16 11/20 -32/9 4/7 -7/2 1/2 -38/11 3/5 2/3 -31/9 5/8 -24/7 2/3 -17/5 17/24 -44/13 11/15 -71/21 3/4 -27/8 3/4 -37/11 3/4 -47/14 5/6 -10/3 4/5 1/1 -13/4 7/6 -16/5 2/1 -35/11 1/0 -54/17 1/0 -19/6 -5/2 -3/1 1/2 -23/8 15/22 -20/7 5/7 -37/13 3/4 -54/19 3/4 -17/6 17/22 -14/5 6/7 1/1 -11/4 7/6 -41/15 11/8 -71/26 3/2 -30/11 3/2 -19/7 9/4 -27/10 1/0 -8/3 0/1 -29/11 3/4 -50/19 1/1 2/1 -21/8 1/0 -55/21 -1/12 -34/13 0/1 1/5 -47/18 1/6 -60/23 1/3 -13/5 1/4 -18/7 1/2 -23/9 7/12 -28/11 3/5 -33/13 1/2 -5/2 1/2 -22/9 7/9 4/5 -61/25 45/56 -39/16 13/16 -17/7 17/20 -12/5 1/1 -19/8 13/10 -26/11 5/3 2/1 -59/25 17/8 -33/14 1/0 -7/3 1/0 -37/16 1/2 -30/13 1/2 -23/10 5/6 -16/7 0/1 -25/11 1/4 -34/15 0/1 1/3 -9/4 1/2 -38/17 2/3 1/1 -29/13 3/4 -20/9 1/1 -51/23 1/2 -82/37 7/11 2/3 -31/14 7/10 -11/5 1/0 -35/16 1/2 -24/11 2/3 -13/6 1/2 -15/7 5/6 -17/8 17/18 -2/1 0/1 1/1 -19/10 17/18 -36/19 1/1 -17/9 17/16 -15/8 5/4 -43/23 11/8 -28/15 1/1 -13/7 1/0 -37/20 3/2 -24/13 2/1 -11/6 1/2 -31/17 7/4 -144/79 2/1 -113/62 21/10 -82/45 2/1 7/3 -51/28 1/0 -20/11 1/1 -29/16 3/2 -9/5 1/0 -43/24 -1/2 -34/19 -1/1 0/1 -25/14 -1/2 -16/9 0/1 -23/13 5/4 -30/17 1/0 -37/21 1/0 -44/25 -1/1 -7/4 1/2 -40/23 2/3 -73/42 1/2 -33/19 1/2 -59/34 17/26 -144/83 2/3 -85/49 27/40 -26/15 2/3 5/7 -45/26 3/4 -19/11 13/16 -12/7 1/1 -17/10 17/14 -39/23 13/10 -61/36 45/34 -144/85 4/3 -83/49 59/44 -22/13 4/3 7/5 -27/16 3/2 -32/19 2/1 -37/22 3/2 -5/3 1/0 -18/11 1/0 -31/19 1/0 -106/65 -2/1 -1/1 -75/46 1/0 -44/27 -1/1 -101/62 -5/2 -57/35 -3/2 -13/8 -1/2 -60/37 -1/1 -47/29 -1/4 -34/21 -1/3 0/1 -21/13 1/2 -71/44 1/2 -50/31 2/3 1/1 -79/49 7/8 -108/67 1/1 -29/18 3/2 -8/5 0/1 -35/22 1/2 -27/17 1/2 -73/46 1/2 -46/29 5/9 4/7 -19/12 9/14 -49/31 17/24 -30/19 3/4 -71/45 3/4 -41/26 11/14 -11/7 7/8 -36/23 1/1 -25/16 19/18 -14/9 1/1 6/5 -17/11 17/12 -54/35 3/2 -37/24 3/2 -57/37 3/2 -20/13 5/3 -3/2 1/0 -19/13 5/12 -54/37 1/2 -35/24 1/2 -16/11 2/3 -13/9 7/8 -36/25 1/1 -23/16 15/14 -10/7 1/1 4/3 -57/40 11/8 -47/33 5/4 -84/59 7/5 -37/26 3/2 -27/19 3/2 -71/50 3/2 -115/81 31/20 -44/31 11/7 -17/12 17/10 -41/29 15/8 -24/17 2/1 -31/22 5/2 -69/49 5/2 -107/76 5/2 -38/27 2/1 3/1 -7/5 1/0 -18/13 1/0 -29/21 1/0 -69/50 1/0 -178/129 -4/1 -3/1 -287/208 -7/2 -396/287 -3/1 -109/79 1/0 -40/29 -4/1 -51/37 -5/2 -62/45 -2/1 -1/1 -11/8 -3/2 -48/35 0/1 -37/27 1/0 -63/46 1/0 -26/19 -2/1 -1/1 -67/49 -9/8 -108/79 -1/1 -41/30 -5/6 -15/11 -1/2 -34/25 -1/7 0/1 -53/39 -1/24 -72/53 0/1 -19/14 1/10 -4/3 1/1 -17/13 17/8 -30/23 5/2 -13/10 7/2 -48/37 4/1 -35/27 1/0 -92/71 1/1 -57/44 1/0 -22/17 3/1 4/1 -31/24 11/2 -9/7 1/0 -41/32 -9/2 -73/57 1/0 -32/25 -4/1 -87/68 -13/4 -55/43 -23/8 -23/18 -3/2 -60/47 -1/1 -97/76 1/2 -37/29 1/0 -51/40 1/0 -65/51 -9/4 -144/113 -2/1 -79/62 -11/6 -14/11 -2/1 -1/1 -19/15 -3/8 -24/19 0/1 -5/4 1/2 -21/17 3/2 -37/30 3/2 -16/13 2/1 -11/9 7/4 -39/32 9/4 -28/23 7/3 -17/14 17/6 -6/5 1/0 -19/16 -7/6 -51/43 -5/6 -32/27 -2/3 -13/11 -1/4 -33/28 1/4 -20/17 1/1 -7/6 1/2 -8/7 2/1 -9/8 1/0 -1/1 1/0 0/1 0/1 1/1 1/4 8/7 2/7 7/6 1/2 20/17 1/3 13/11 1/8 6/5 1/4 23/19 15/56 17/14 17/62 28/23 7/25 39/32 9/32 11/9 7/24 16/13 2/7 37/30 3/10 21/17 3/10 5/4 1/2 19/15 3/20 14/11 1/5 2/9 65/51 9/40 51/40 1/4 37/29 1/4 60/47 1/5 23/18 3/14 32/25 4/17 9/7 1/4 22/17 4/15 3/11 35/27 1/4 13/10 7/26 17/13 17/60 4/3 1/3 19/14 -1/6 15/11 1/6 41/30 5/26 26/19 1/5 2/9 37/27 1/4 11/8 3/14 18/13 1/4 25/18 13/50 57/41 11/42 32/23 4/15 7/5 1/4 38/27 3/11 2/7 31/22 5/18 24/17 2/7 17/12 17/58 44/31 11/37 71/50 3/10 27/19 3/10 37/26 3/10 47/33 5/16 10/7 4/13 1/3 13/9 7/20 16/11 2/5 35/24 1/2 54/37 1/2 19/13 5/8 3/2 1/4 23/15 15/52 20/13 5/17 37/24 3/10 54/35 3/10 17/11 17/56 14/9 6/19 1/3 11/7 7/20 41/26 11/30 71/45 3/8 30/19 3/8 19/12 9/22 27/17 1/2 8/5 0/1 29/18 3/10 50/31 1/3 2/5 21/13 1/2 55/34 -1/10 34/21 0/1 1/7 47/29 1/8 60/37 1/5 13/8 1/6 18/11 1/4 23/14 7/26 28/17 3/11 33/20 1/4 5/3 1/4 22/13 7/23 4/13 61/36 45/146 39/23 13/42 17/10 17/54 12/7 1/3 19/11 13/36 26/15 5/13 2/5 59/34 17/42 33/19 1/2 7/4 1/2 37/21 1/4 30/17 1/4 23/13 5/16 16/9 0/1 25/14 1/6 34/19 0/1 1/5 9/5 1/4 38/21 2/7 1/3 29/16 3/10 20/11 1/3 51/28 1/4 82/45 7/25 2/7 31/17 7/24 11/6 1/2 35/19 1/4 24/13 2/7 13/7 1/4 15/8 5/16 17/9 17/52 2/1 0/1 1/3 19/9 17/52 36/17 1/3 17/8 17/50 15/7 5/14 43/20 11/30 28/13 1/3 13/6 1/2 37/17 3/8 24/11 2/5 11/5 1/4 31/14 7/18 144/65 2/5 113/51 21/52 82/37 2/5 7/17 51/23 1/2 20/9 1/3 29/13 3/8 9/4 1/2 43/19 1/0 34/15 0/1 1/1 25/11 1/0 16/7 0/1 23/10 5/14 30/13 1/2 37/16 1/2 44/19 1/1 7/3 1/4 40/17 2/7 73/31 1/4 33/14 1/4 59/25 17/60 144/61 2/7 85/36 27/94 26/11 2/7 5/17 45/19 3/10 19/8 13/42 12/5 1/3 17/7 17/48 39/16 13/36 61/25 45/124 144/59 4/11 83/34 59/162 22/9 4/11 7/19 27/11 3/8 32/13 2/5 37/15 3/8 5/2 1/2 18/7 1/2 31/12 1/2 106/41 2/3 1/1 75/29 1/2 44/17 1/1 101/39 5/8 57/22 3/4 13/5 1/0 60/23 1/1 47/18 -1/2 34/13 -1/1 0/1 21/8 1/4 71/27 1/4 50/19 2/7 1/3 79/30 7/22 108/41 1/3 29/11 3/8 8/3 0/1 35/13 1/4 27/10 1/4 73/27 1/4 46/17 5/19 4/15 19/7 9/32 49/18 17/58 30/11 3/10 71/26 3/10 41/15 11/36 11/4 7/22 36/13 1/3 25/9 19/56 14/5 1/3 6/17 17/6 17/46 54/19 3/8 37/13 3/8 57/20 3/8 20/7 5/13 3/1 1/2 19/6 5/22 54/17 1/4 35/11 1/4 16/5 2/7 13/4 7/22 36/11 1/3 23/7 15/44 10/3 1/3 4/11 57/17 11/30 47/14 5/14 84/25 7/19 37/11 3/8 27/8 3/8 71/21 3/8 115/34 31/82 44/13 11/29 17/5 17/44 41/12 15/38 24/7 2/5 31/9 5/12 69/20 5/12 107/31 5/12 38/11 2/5 3/7 7/2 1/2 18/5 1/2 29/8 1/2 69/19 1/2 178/49 4/7 3/5 287/79 7/12 396/109 3/5 109/30 1/2 40/11 4/7 51/14 5/8 62/17 2/3 1/1 11/3 3/4 48/13 0/1 37/10 1/2 63/17 1/2 26/7 2/3 1/1 67/18 9/10 108/29 1/1 41/11 5/4 15/4 1/0 34/9 -1/5 0/1 53/14 -1/22 72/19 0/1 19/5 1/12 4/1 1/3 17/4 17/42 30/7 5/12 13/3 7/16 48/11 4/9 35/8 1/2 92/21 1/3 57/13 1/2 22/5 3/7 4/9 31/7 11/24 9/2 1/2 41/9 9/16 73/16 1/2 32/7 4/7 87/19 13/22 55/12 23/38 23/5 3/4 60/13 1/1 97/21 1/4 37/8 1/2 51/11 1/2 65/14 9/14 144/31 2/3 79/17 11/16 14/3 2/3 1/1 19/4 -3/2 24/5 0/1 5/1 1/4 21/4 3/8 37/7 3/8 16/3 2/5 11/2 7/18 39/7 9/22 28/5 7/17 17/3 17/40 6/1 1/2 19/3 7/8 51/8 5/4 32/5 2/1 13/2 -1/2 33/5 1/6 20/3 1/3 7/1 1/4 8/1 2/5 9/1 1/2 1/0 1/2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(35,288,-22,-181) (-8/1,1/0) -> (-8/5,-35/22) Hyperbolic Matrix(37,288,14,109) (-8/1,-7/1) -> (29/11,8/3) Hyperbolic Matrix(107,720,48,323) (-7/1,-20/3) -> (20/9,29/13) Hyperbolic Matrix(109,720,-38,-251) (-20/3,-13/2) -> (-23/8,-20/7) Hyperbolic Matrix(35,216,-6,-37) (-13/2,-6/1) -> (-6/1,-23/4) Parabolic Matrix(289,1656,-226,-1295) (-23/4,-17/3) -> (-55/43,-23/18) Hyperbolic Matrix(217,1224,64,361) (-17/3,-28/5) -> (44/13,17/5) Hyperbolic Matrix(683,3816,264,1475) (-28/5,-39/7) -> (75/29,44/17) Hyperbolic Matrix(505,2808,298,1657) (-39/7,-11/2) -> (61/36,39/23) Hyperbolic Matrix(107,576,60,323) (-11/2,-16/3) -> (16/9,25/14) Hyperbolic Matrix(217,1152,68,361) (-16/3,-37/7) -> (35/11,16/5) Hyperbolic Matrix(505,2664,396,2089) (-37/7,-21/4) -> (51/40,37/29) Hyperbolic Matrix(179,936,48,251) (-21/4,-5/1) -> (41/11,15/4) Hyperbolic Matrix(181,864,-128,-611) (-5/1,-19/4) -> (-17/12,-41/29) Hyperbolic Matrix(107,504,38,179) (-19/4,-14/3) -> (14/5,17/6) Hyperbolic Matrix(433,2016,-340,-1583) (-14/3,-65/14) -> (-79/62,-14/11) Hyperbolic Matrix(683,3168,318,1475) (-65/14,-51/11) -> (15/7,43/20) Hyperbolic Matrix(575,2664,466,2159) (-51/11,-37/8) -> (37/30,21/17) Hyperbolic Matrix(1153,5328,-810,-3743) (-37/8,-60/13) -> (-84/59,-37/26) Hyperbolic Matrix(469,2160,180,829) (-60/13,-23/5) -> (13/5,60/23) Hyperbolic Matrix(251,1152,-212,-973) (-23/5,-32/7) -> (-32/27,-13/11) Hyperbolic Matrix(253,1152,-150,-683) (-32/7,-9/2) -> (-27/16,-32/19) Hyperbolic Matrix(179,792,-106,-469) (-9/2,-22/5) -> (-22/13,-27/16) Hyperbolic Matrix(755,3312,-468,-2053) (-22/5,-35/8) -> (-71/44,-50/31) Hyperbolic Matrix(215,936,-116,-505) (-35/8,-13/3) -> (-13/7,-37/20) Hyperbolic Matrix(253,1080,-160,-683) (-13/3,-17/4) -> (-19/12,-49/31) Hyperbolic Matrix(35,144,26,107) (-17/4,-4/1) -> (4/3,19/14) Hyperbolic Matrix(37,144,28,109) (-4/1,-19/5) -> (17/13,4/3) Hyperbolic Matrix(325,1224,-124,-467) (-19/5,-15/4) -> (-21/8,-55/21) Hyperbolic Matrix(251,936,48,179) (-15/4,-41/11) -> (5/1,21/4) Hyperbolic Matrix(755,2808,-552,-2053) (-41/11,-26/7) -> (-26/19,-67/49) Hyperbolic Matrix(971,3600,-612,-2269) (-26/7,-37/10) -> (-73/46,-46/29) Hyperbolic Matrix(215,792,-98,-361) (-37/10,-11/3) -> (-11/5,-35/16) Hyperbolic Matrix(179,648,-50,-181) (-11/3,-18/5) -> (-18/5,-25/7) Parabolic Matrix(1151,4104,-808,-2881) (-25/7,-57/16) -> (-57/40,-47/33) Hyperbolic Matrix(1295,4608,-1012,-3601) (-57/16,-32/9) -> (-32/25,-87/68) Hyperbolic Matrix(143,504,-82,-289) (-32/9,-7/2) -> (-7/4,-40/23) Hyperbolic Matrix(395,1368,218,755) (-7/2,-38/11) -> (38/21,29/16) Hyperbolic Matrix(1295,4464,-794,-2737) (-38/11,-31/9) -> (-31/19,-106/65) Hyperbolic Matrix(251,864,52,179) (-31/9,-24/7) -> (24/5,5/1) Hyperbolic Matrix(253,864,-200,-683) (-24/7,-17/5) -> (-19/15,-24/19) Hyperbolic Matrix(361,1224,64,217) (-17/5,-44/13) -> (28/5,17/3) Hyperbolic Matrix(1405,4752,-798,-2699) (-44/13,-71/21) -> (-37/21,-44/25) Hyperbolic Matrix(1151,3888,426,1439) (-71/21,-27/8) -> (27/10,73/27) Hyperbolic Matrix(577,1944,214,721) (-27/8,-37/11) -> (35/13,27/10) Hyperbolic Matrix(1585,5328,-1242,-4175) (-37/11,-47/14) -> (-97/76,-37/29) Hyperbolic Matrix(901,3024,-654,-2195) (-47/14,-10/3) -> (-62/45,-11/8) Hyperbolic Matrix(109,360,-76,-251) (-10/3,-13/4) -> (-23/16,-10/7) Hyperbolic Matrix(179,576,78,251) (-13/4,-16/5) -> (16/7,23/10) Hyperbolic Matrix(361,1152,68,217) (-16/5,-35/11) -> (37/7,16/3) Hyperbolic Matrix(1223,3888,430,1367) (-35/11,-54/17) -> (54/19,37/13) Hyperbolic Matrix(613,1944,216,685) (-54/17,-19/6) -> (17/6,54/19) Hyperbolic Matrix(251,792,148,467) (-19/6,-3/1) -> (39/23,17/10) Hyperbolic Matrix(323,936,186,539) (-3/1,-23/8) -> (59/34,33/19) Hyperbolic Matrix(1441,4104,-1112,-3167) (-20/7,-37/13) -> (-35/27,-92/71) Hyperbolic Matrix(1367,3888,430,1223) (-37/13,-54/19) -> (54/17,35/11) Hyperbolic Matrix(685,1944,216,613) (-54/19,-17/6) -> (19/6,54/17) Hyperbolic Matrix(179,504,38,107) (-17/6,-14/5) -> (14/3,19/4) Hyperbolic Matrix(181,504,-116,-323) (-14/5,-11/4) -> (-25/16,-14/9) Hyperbolic Matrix(289,792,158,433) (-11/4,-41/15) -> (31/17,11/6) Hyperbolic Matrix(685,1872,-408,-1115) (-41/15,-71/26) -> (-37/22,-5/3) Hyperbolic Matrix(1187,3240,514,1403) (-71/26,-30/11) -> (30/13,37/16) Hyperbolic Matrix(397,1080,-304,-827) (-30/11,-19/7) -> (-17/13,-30/23) Hyperbolic Matrix(505,1368,-292,-791) (-19/7,-27/10) -> (-45/26,-19/11) Hyperbolic Matrix(107,288,-94,-253) (-27/10,-8/3) -> (-8/7,-9/8) Hyperbolic Matrix(109,288,14,37) (-8/3,-29/11) -> (7/1,8/1) Hyperbolic Matrix(2051,5400,-1272,-3349) (-29/11,-50/19) -> (-50/31,-79/49) Hyperbolic Matrix(1259,3312,-972,-2557) (-50/19,-21/8) -> (-57/44,-22/17) Hyperbolic Matrix(1403,3672,-1032,-2701) (-55/21,-34/13) -> (-34/25,-53/39) Hyperbolic Matrix(937,2448,524,1369) (-34/13,-47/18) -> (25/14,34/19) Hyperbolic Matrix(3311,8640,-2594,-6769) (-47/18,-60/23) -> (-60/47,-97/76) Hyperbolic Matrix(829,2160,180,469) (-60/23,-13/5) -> (23/5,60/13) Hyperbolic Matrix(251,648,-98,-253) (-13/5,-18/7) -> (-18/7,-23/9) Parabolic Matrix(395,1008,-212,-541) (-23/9,-28/11) -> (-28/15,-13/7) Hyperbolic Matrix(793,2016,142,361) (-28/11,-33/13) -> (39/7,28/5) Hyperbolic Matrix(541,1368,-384,-971) (-33/13,-5/2) -> (-31/22,-69/49) Hyperbolic Matrix(323,792,-250,-613) (-5/2,-22/9) -> (-22/17,-31/24) Hyperbolic Matrix(1297,3168,-766,-1871) (-22/9,-61/25) -> (-83/49,-22/13) Hyperbolic Matrix(1151,2808,944,2303) (-61/25,-39/16) -> (39/32,11/9) Hyperbolic Matrix(325,792,222,541) (-39/16,-17/7) -> (19/13,3/2) Hyperbolic Matrix(179,432,104,251) (-17/7,-12/5) -> (12/7,19/11) Hyperbolic Matrix(181,432,106,253) (-12/5,-19/8) -> (17/10,12/7) Hyperbolic Matrix(577,1368,-364,-863) (-19/8,-26/11) -> (-46/29,-19/12) Hyperbolic Matrix(1585,3744,-914,-2159) (-26/11,-59/25) -> (-85/49,-26/15) Hyperbolic Matrix(397,936,260,613) (-59/25,-33/14) -> (3/2,23/15) Hyperbolic Matrix(613,1440,-444,-1043) (-33/14,-7/3) -> (-29/21,-69/50) Hyperbolic Matrix(2053,4752,-1446,-3347) (-7/3,-37/16) -> (-71/50,-115/81) Hyperbolic Matrix(1403,3240,514,1187) (-37/16,-30/13) -> (30/11,71/26) Hyperbolic Matrix(937,2160,344,793) (-30/13,-23/10) -> (49/18,30/11) Hyperbolic Matrix(251,576,78,179) (-23/10,-16/7) -> (16/5,13/4) Hyperbolic Matrix(253,576,206,469) (-16/7,-25/11) -> (11/9,16/13) Hyperbolic Matrix(1079,2448,666,1511) (-25/11,-34/15) -> (34/21,47/29) Hyperbolic Matrix(287,648,-128,-289) (-34/15,-9/4) -> (-9/4,-38/17) Parabolic Matrix(613,1368,436,973) (-38/17,-29/13) -> (7/5,38/27) Hyperbolic Matrix(323,720,48,107) (-29/13,-20/9) -> (20/3,7/1) Hyperbolic Matrix(973,2160,-632,-1403) (-20/9,-51/23) -> (-57/37,-20/13) Hyperbolic Matrix(2339,5184,698,1547) (-51/23,-82/37) -> (10/3,57/17) Hyperbolic Matrix(5329,11808,-2924,-6479) (-82/37,-31/14) -> (-113/62,-82/45) Hyperbolic Matrix(359,792,228,503) (-31/14,-11/5) -> (11/7,41/26) Hyperbolic Matrix(1153,2520,264,577) (-35/16,-24/11) -> (48/11,35/8) Hyperbolic Matrix(431,936,-332,-721) (-24/11,-13/6) -> (-13/10,-48/37) Hyperbolic Matrix(433,936,-266,-575) (-13/6,-15/7) -> (-57/35,-13/8) Hyperbolic Matrix(541,1152,-456,-971) (-15/7,-17/8) -> (-19/16,-51/43) Hyperbolic Matrix(35,72,-18,-37) (-17/8,-2/1) -> (-2/1,-19/10) Parabolic Matrix(683,1296,322,611) (-19/10,-36/19) -> (36/17,17/8) Hyperbolic Matrix(685,1296,324,613) (-36/19,-17/9) -> (19/9,36/17) Hyperbolic Matrix(1223,2304,-956,-1801) (-17/9,-15/8) -> (-87/68,-55/43) Hyperbolic Matrix(1693,3168,1328,2485) (-15/8,-43/23) -> (65/51,51/40) Hyperbolic Matrix(1117,2088,482,901) (-43/23,-28/15) -> (44/19,7/3) Hyperbolic Matrix(1441,2664,390,721) (-37/20,-24/13) -> (48/13,37/10) Hyperbolic Matrix(431,792,-314,-577) (-24/13,-11/6) -> (-11/8,-48/35) Hyperbolic Matrix(433,792,158,289) (-11/6,-31/17) -> (41/15,11/4) Hyperbolic Matrix(11375,20736,5134,9359) (-31/17,-144/79) -> (144/65,113/51) Hyperbolic Matrix(11377,20736,5136,9361) (-144/79,-113/62) -> (31/14,144/65) Hyperbolic Matrix(4031,7344,1106,2015) (-82/45,-51/28) -> (51/14,62/17) Hyperbolic Matrix(3203,5832,-2472,-4501) (-51/28,-20/11) -> (-92/71,-57/44) Hyperbolic Matrix(397,720,338,613) (-20/11,-29/16) -> (7/6,20/17) Hyperbolic Matrix(359,648,-200,-361) (-29/16,-9/5) -> (-9/5,-43/24) Parabolic Matrix(1045,1872,302,541) (-43/24,-34/19) -> (38/11,7/2) Hyperbolic Matrix(1369,2448,524,937) (-34/19,-25/14) -> (47/18,34/13) Hyperbolic Matrix(323,576,60,107) (-25/14,-16/9) -> (16/3,11/2) Hyperbolic Matrix(325,576,224,397) (-16/9,-23/13) -> (13/9,16/11) Hyperbolic Matrix(611,1080,142,251) (-23/13,-30/17) -> (30/7,13/3) Hyperbolic Matrix(1837,3240,1164,2053) (-30/17,-37/21) -> (71/45,30/19) Hyperbolic Matrix(1187,2088,552,971) (-44/25,-7/4) -> (43/20,28/13) Hyperbolic Matrix(3023,5256,662,1151) (-40/23,-73/42) -> (73/16,32/7) Hyperbolic Matrix(4931,8568,-3502,-6085) (-73/42,-33/19) -> (-69/49,-107/76) Hyperbolic Matrix(1369,2376,208,361) (-33/19,-59/34) -> (13/2,33/5) Hyperbolic Matrix(11951,20736,5062,8783) (-59/34,-144/83) -> (144/61,85/36) Hyperbolic Matrix(11953,20736,5064,8785) (-144/83,-85/49) -> (59/25,144/61) Hyperbolic Matrix(1621,2808,-1184,-2051) (-26/15,-45/26) -> (-63/46,-26/19) Hyperbolic Matrix(251,432,104,179) (-19/11,-12/7) -> (12/5,17/7) Hyperbolic Matrix(253,432,106,181) (-12/7,-17/10) -> (19/8,12/5) Hyperbolic Matrix(467,792,148,251) (-17/10,-39/23) -> (3/1,19/6) Hyperbolic Matrix(1657,2808,298,505) (-39/23,-61/36) -> (11/2,39/7) Hyperbolic Matrix(12239,20736,5014,8495) (-61/36,-144/85) -> (144/59,83/34) Hyperbolic Matrix(12241,20736,5016,8497) (-144/85,-83/49) -> (61/25,144/59) Hyperbolic Matrix(2951,4968,812,1367) (-32/19,-37/22) -> (109/30,40/11) Hyperbolic Matrix(395,648,-242,-397) (-5/3,-18/11) -> (-18/11,-31/19) Parabolic Matrix(12673,20664,-9184,-14975) (-106/65,-75/46) -> (-69/50,-178/129) Hyperbolic Matrix(2341,3816,1922,3133) (-75/46,-44/27) -> (28/23,39/32) Hyperbolic Matrix(5833,9504,1724,2809) (-44/27,-101/62) -> (115/34,44/13) Hyperbolic Matrix(5437,8856,1172,1909) (-101/62,-57/35) -> (51/11,65/14) Hyperbolic Matrix(1331,2160,1042,1691) (-13/8,-60/37) -> (60/47,23/18) Hyperbolic Matrix(4175,6768,-2932,-4753) (-60/37,-47/29) -> (-47/33,-84/59) Hyperbolic Matrix(1511,2448,666,1079) (-47/29,-34/21) -> (34/15,25/11) Hyperbolic Matrix(757,1224,-556,-899) (-34/21,-21/13) -> (-15/11,-34/25) Hyperbolic Matrix(2989,4824,-1940,-3131) (-21/13,-71/44) -> (-37/24,-57/37) Hyperbolic Matrix(7235,11664,2746,4427) (-79/49,-108/67) -> (108/41,29/11) Hyperbolic Matrix(7237,11664,2748,4429) (-108/67,-29/18) -> (79/30,108/41) Hyperbolic Matrix(179,288,156,251) (-29/18,-8/5) -> (8/7,7/6) Hyperbolic Matrix(1223,1944,860,1367) (-35/22,-27/17) -> (27/19,37/26) Hyperbolic Matrix(2449,3888,1724,2737) (-27/17,-73/46) -> (71/50,27/19) Hyperbolic Matrix(1367,2160,774,1223) (-49/31,-30/19) -> (30/17,23/13) Hyperbolic Matrix(2053,3240,1164,1837) (-30/19,-71/45) -> (37/21,30/17) Hyperbolic Matrix(3743,5904,-2922,-4609) (-71/45,-41/26) -> (-41/32,-73/57) Hyperbolic Matrix(503,792,228,359) (-41/26,-11/7) -> (11/5,31/14) Hyperbolic Matrix(827,1296,298,467) (-11/7,-36/23) -> (36/13,25/9) Hyperbolic Matrix(829,1296,300,469) (-36/23,-25/16) -> (11/4,36/13) Hyperbolic Matrix(325,504,256,397) (-14/9,-17/11) -> (19/15,14/11) Hyperbolic Matrix(1259,1944,862,1331) (-17/11,-54/35) -> (54/37,19/13) Hyperbolic Matrix(2521,3888,1728,2665) (-54/35,-37/24) -> (35/24,54/37) Hyperbolic Matrix(469,720,-398,-611) (-20/13,-3/2) -> (-33/28,-20/17) Hyperbolic Matrix(541,792,222,325) (-3/2,-19/13) -> (17/7,39/16) Hyperbolic Matrix(1331,1944,862,1259) (-19/13,-54/37) -> (54/35,17/11) Hyperbolic Matrix(2665,3888,1728,2521) (-54/37,-35/24) -> (37/24,54/35) Hyperbolic Matrix(791,1152,642,935) (-35/24,-16/11) -> (16/13,37/30) Hyperbolic Matrix(397,576,224,325) (-16/11,-13/9) -> (23/13,16/9) Hyperbolic Matrix(899,1296,274,395) (-13/9,-36/25) -> (36/11,23/7) Hyperbolic Matrix(901,1296,276,397) (-36/25,-23/16) -> (13/4,36/11) Hyperbolic Matrix(3637,5184,1996,2845) (-10/7,-57/40) -> (51/28,82/45) Hyperbolic Matrix(253,360,26,37) (-37/26,-27/19) -> (9/1,1/0) Hyperbolic Matrix(3853,5472,1040,1477) (-27/19,-71/50) -> (37/10,63/17) Hyperbolic Matrix(6695,9504,2586,3671) (-115/81,-44/31) -> (44/17,101/39) Hyperbolic Matrix(863,1224,710,1007) (-44/31,-17/12) -> (17/14,28/23) Hyperbolic Matrix(1223,1728,356,503) (-41/29,-24/17) -> (24/7,31/9) Hyperbolic Matrix(1225,1728,358,505) (-24/17,-31/22) -> (41/12,24/7) Hyperbolic Matrix(21277,29952,-15420,-21707) (-107/76,-38/27) -> (-178/129,-287/208) Hyperbolic Matrix(1331,1872,588,827) (-38/27,-7/5) -> (43/19,34/15) Hyperbolic Matrix(467,648,-338,-469) (-7/5,-18/13) -> (-18/13,-29/21) Parabolic Matrix(113651,156816,31282,43163) (-287/208,-396/287) -> (396/109,109/30) Hyperbolic Matrix(113653,156816,31284,43165) (-396/287,-109/79) -> (287/79,396/109) Hyperbolic Matrix(3601,4968,1462,2017) (-109/79,-40/29) -> (32/13,37/15) Hyperbolic Matrix(2663,3672,-2246,-3097) (-40/29,-51/37) -> (-51/43,-32/27) Hyperbolic Matrix(5329,7344,2404,3313) (-51/37,-62/45) -> (82/37,51/23) Hyperbolic Matrix(1943,2664,892,1223) (-48/35,-37/27) -> (37/17,24/11) Hyperbolic Matrix(3995,5472,1182,1619) (-37/27,-63/46) -> (27/8,71/21) Hyperbolic Matrix(8531,11664,2290,3131) (-67/49,-108/79) -> (108/29,41/11) Hyperbolic Matrix(8533,11664,2292,3133) (-108/79,-41/30) -> (67/18,108/29) Hyperbolic Matrix(685,936,554,757) (-41/30,-15/11) -> (21/17,5/4) Hyperbolic Matrix(3815,5184,1006,1367) (-53/39,-72/53) -> (72/19,19/5) Hyperbolic Matrix(3817,5184,1008,1369) (-72/53,-19/14) -> (53/14,72/19) Hyperbolic Matrix(107,144,26,35) (-19/14,-4/3) -> (4/1,17/4) Hyperbolic Matrix(109,144,28,37) (-4/3,-17/13) -> (19/5,4/1) Hyperbolic Matrix(829,1080,360,469) (-30/23,-13/10) -> (23/10,30/13) Hyperbolic Matrix(1943,2520,1054,1367) (-48/37,-35/27) -> (35/19,24/13) Hyperbolic Matrix(503,648,-392,-505) (-31/24,-9/7) -> (-9/7,-41/32) Parabolic Matrix(4105,5256,1744,2233) (-73/57,-32/25) -> (40/17,73/31) Hyperbolic Matrix(1691,2160,1042,1331) (-23/18,-60/47) -> (60/37,13/8) Hyperbolic Matrix(2089,2664,396,505) (-37/29,-51/40) -> (21/4,37/7) Hyperbolic Matrix(6947,8856,2682,3419) (-51/40,-65/51) -> (101/39,57/22) Hyperbolic Matrix(16271,20736,3502,4463) (-65/51,-144/113) -> (144/31,79/17) Hyperbolic Matrix(16273,20736,3504,4465) (-144/113,-79/62) -> (65/14,144/31) Hyperbolic Matrix(397,504,256,325) (-14/11,-19/15) -> (17/11,14/9) Hyperbolic Matrix(685,864,486,613) (-24/19,-5/4) -> (31/22,24/17) Hyperbolic Matrix(757,936,554,685) (-5/4,-21/17) -> (15/11,41/30) Hyperbolic Matrix(2159,2664,466,575) (-21/17,-37/30) -> (37/8,51/11) Hyperbolic Matrix(935,1152,642,791) (-37/30,-16/13) -> (16/11,35/24) Hyperbolic Matrix(469,576,206,253) (-16/13,-11/9) -> (25/11,16/7) Hyperbolic Matrix(2303,2808,944,1151) (-11/9,-39/32) -> (39/16,61/25) Hyperbolic Matrix(1655,2016,1004,1223) (-39/32,-28/23) -> (28/17,33/20) Hyperbolic Matrix(1007,1224,710,863) (-28/23,-17/14) -> (17/12,44/31) Hyperbolic Matrix(179,216,-150,-181) (-17/14,-6/5) -> (-6/5,-19/16) Parabolic Matrix(2015,2376,854,1007) (-13/11,-33/28) -> (33/14,59/25) Hyperbolic Matrix(613,720,338,397) (-20/17,-7/6) -> (29/16,20/11) Hyperbolic Matrix(251,288,156,179) (-7/6,-8/7) -> (8/5,29/18) Hyperbolic Matrix(323,360,96,107) (-9/8,-1/1) -> (37/11,27/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(253,-288,94,-107) (1/1,8/7) -> (8/3,35/13) Hyperbolic Matrix(611,-720,398,-469) (20/17,13/11) -> (23/15,20/13) Hyperbolic Matrix(181,-216,150,-179) (13/11,6/5) -> (6/5,23/19) Parabolic Matrix(1367,-1656,298,-361) (23/19,17/14) -> (55/12,23/5) Hyperbolic Matrix(683,-864,200,-253) (5/4,19/15) -> (17/5,41/12) Hyperbolic Matrix(1583,-2016,340,-433) (14/11,65/51) -> (79/17,14/3) Hyperbolic Matrix(4175,-5328,1242,-1585) (37/29,60/47) -> (84/25,37/11) Hyperbolic Matrix(901,-1152,140,-179) (23/18,32/25) -> (32/5,13/2) Hyperbolic Matrix(899,-1152,366,-469) (32/25,9/7) -> (27/11,32/13) Hyperbolic Matrix(613,-792,250,-323) (9/7,22/17) -> (22/9,27/11) Hyperbolic Matrix(2557,-3312,972,-1259) (22/17,35/27) -> (71/27,50/19) Hyperbolic Matrix(721,-936,332,-431) (35/27,13/10) -> (13/6,37/17) Hyperbolic Matrix(827,-1080,304,-397) (13/10,17/13) -> (19/7,49/18) Hyperbolic Matrix(899,-1224,556,-757) (19/14,15/11) -> (21/13,55/34) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(2629,-3600,972,-1331) (26/19,37/27) -> (73/27,46/17) Hyperbolic Matrix(577,-792,314,-431) (37/27,11/8) -> (11/6,35/19) Hyperbolic Matrix(469,-648,338,-467) (11/8,18/13) -> (18/13,25/18) Parabolic Matrix(2953,-4104,880,-1223) (25/18,57/41) -> (57/17,47/14) Hyperbolic Matrix(3313,-4608,724,-1007) (57/41,32/23) -> (32/7,87/19) Hyperbolic Matrix(361,-504,154,-215) (32/23,7/5) -> (7/3,40/17) Hyperbolic Matrix(3169,-4464,1226,-1727) (38/27,31/22) -> (31/12,106/41) Hyperbolic Matrix(611,-864,128,-181) (24/17,17/12) -> (19/4,24/5) Hyperbolic Matrix(3347,-4752,1446,-2053) (44/31,71/50) -> (37/16,44/19) Hyperbolic Matrix(3743,-5328,810,-1153) (37/26,47/33) -> (97/21,37/8) Hyperbolic Matrix(2123,-3024,582,-829) (47/33,10/7) -> (62/17,11/3) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(2663,-4104,608,-937) (20/13,37/24) -> (35/8,92/21) Hyperbolic Matrix(323,-504,116,-181) (14/9,11/7) -> (25/9,14/5) Hyperbolic Matrix(1187,-1872,480,-757) (41/26,71/45) -> (37/15,5/2) Hyperbolic Matrix(683,-1080,160,-253) (30/19,19/12) -> (17/4,30/7) Hyperbolic Matrix(863,-1368,364,-577) (19/12,27/17) -> (45/19,19/8) Hyperbolic Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(2053,-3312,468,-755) (50/31,21/13) -> (57/13,22/5) Hyperbolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(5329,-8640,1154,-1871) (47/29,60/37) -> (60/13,97/21) Hyperbolic Matrix(397,-648,242,-395) (13/8,18/11) -> (18/11,23/14) Parabolic Matrix(613,-1008,284,-467) (23/14,28/17) -> (28/13,13/6) Hyperbolic Matrix(827,-1368,240,-397) (33/20,5/3) -> (31/9,69/20) Hyperbolic Matrix(469,-792,106,-179) (5/3,22/13) -> (22/5,31/7) Hyperbolic Matrix(1871,-3168,766,-1297) (22/13,61/36) -> (83/34,22/9) Hyperbolic Matrix(791,-1368,292,-505) (19/11,26/15) -> (46/17,19/7) Hyperbolic Matrix(2159,-3744,914,-1585) (26/15,59/34) -> (85/36,26/11) Hyperbolic Matrix(827,-1440,228,-397) (33/19,7/4) -> (29/8,69/19) Hyperbolic Matrix(2699,-4752,798,-1405) (7/4,37/21) -> (71/21,115/34) Hyperbolic Matrix(361,-648,200,-359) (34/19,9/5) -> (9/5,38/21) Parabolic Matrix(1187,-2160,416,-757) (20/11,51/28) -> (57/20,20/7) Hyperbolic Matrix(6479,-11808,2924,-5329) (82/45,31/17) -> (113/51,82/37) Hyperbolic Matrix(505,-936,116,-215) (24/13,13/7) -> (13/3,48/11) Hyperbolic Matrix(503,-936,194,-361) (13/7,15/8) -> (57/22,13/5) Hyperbolic Matrix(611,-1152,96,-181) (15/8,17/9) -> (19/3,51/8) Hyperbolic Matrix(37,-72,18,-35) (17/9,2/1) -> (2/1,19/9) Parabolic Matrix(1081,-2304,236,-503) (17/8,15/7) -> (87/19,55/12) Hyperbolic Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(2629,-5832,600,-1331) (51/23,20/9) -> (92/21,57/13) Hyperbolic Matrix(289,-648,128,-287) (29/13,9/4) -> (9/4,43/19) Parabolic Matrix(3637,-8568,1054,-2483) (73/31,33/14) -> (69/20,107/31) Hyperbolic Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(253,-648,98,-251) (5/2,18/7) -> (18/7,31/12) Parabolic Matrix(7991,-20664,2200,-5689) (106/41,75/29) -> (69/19,178/49) Hyperbolic Matrix(2593,-6768,772,-2015) (60/23,47/18) -> (47/14,84/25) Hyperbolic Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(1835,-4824,644,-1693) (21/8,71/27) -> (37/13,57/20) Hyperbolic Matrix(2161,-5904,474,-1295) (71/26,41/15) -> (41/9,73/16) Hyperbolic Matrix(251,-720,38,-109) (20/7,3/1) -> (33/5,20/3) Hyperbolic Matrix(8675,-29952,2388,-8245) (107/31,38/11) -> (178/49,287/79) Hyperbolic Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(1009,-3672,158,-575) (40/11,51/14) -> (51/8,32/5) Hyperbolic Matrix(145,-648,32,-143) (31/7,9/2) -> (9/2,41/9) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(35,288,-22,-181) -> Matrix(3,-2,8,-5) Matrix(37,288,14,109) -> Matrix(3,-2,8,-5) Matrix(107,720,48,323) -> Matrix(3,-2,8,-5) Matrix(109,720,-38,-251) -> Matrix(3,2,4,3) Matrix(35,216,-6,-37) -> Matrix(9,-4,16,-7) Matrix(289,1656,-226,-1295) -> Matrix(31,-18,-12,7) Matrix(217,1224,64,361) -> Matrix(55,-34,144,-89) Matrix(683,3816,264,1475) -> Matrix(25,-16,36,-23) Matrix(505,2808,298,1657) -> Matrix(95,-62,308,-201) Matrix(107,576,60,323) -> Matrix(3,-2,8,-5) Matrix(217,1152,68,361) -> Matrix(11,-8,40,-29) Matrix(505,2664,396,2089) -> Matrix(13,-10,56,-43) Matrix(179,936,48,251) -> Matrix(5,-4,4,-3) Matrix(181,864,-128,-611) -> Matrix(15,-2,8,-1) Matrix(107,504,38,179) -> Matrix(13,-4,36,-11) Matrix(433,2016,-340,-1583) -> Matrix(11,-4,-8,3) Matrix(683,3168,318,1475) -> Matrix(33,-14,92,-39) Matrix(575,2664,466,2159) -> Matrix(23,-10,76,-33) Matrix(1153,5328,-810,-3743) -> Matrix(5,-4,4,-3) Matrix(469,2160,180,829) -> Matrix(5,-2,8,-3) Matrix(251,1152,-212,-973) -> Matrix(5,-2,-12,5) Matrix(253,1152,-150,-683) -> Matrix(31,-14,20,-9) Matrix(179,792,-106,-469) -> Matrix(29,-16,20,-11) Matrix(755,3312,-468,-2053) -> Matrix(3,-2,8,-5) Matrix(215,936,-116,-505) -> Matrix(17,-10,12,-7) Matrix(253,1080,-160,-683) -> Matrix(25,-16,36,-23) Matrix(35,144,26,107) -> Matrix(3,-2,8,-5) Matrix(37,144,28,109) -> Matrix(1,-2,4,-7) Matrix(325,1224,-124,-467) -> Matrix(1,0,-4,1) Matrix(251,936,48,179) -> Matrix(13,-4,36,-11) Matrix(755,2808,-552,-2053) -> Matrix(11,-4,-8,3) Matrix(971,3600,-612,-2269) -> Matrix(13,-6,24,-11) Matrix(215,792,-98,-361) -> Matrix(5,-2,8,-3) Matrix(179,648,-50,-181) -> Matrix(17,-8,32,-15) Matrix(1151,4104,-808,-2881) -> Matrix(41,-22,28,-15) Matrix(1295,4608,-1012,-3601) -> Matrix(57,-32,-16,9) Matrix(143,504,-82,-289) -> Matrix(3,-2,8,-5) Matrix(395,1368,218,755) -> Matrix(13,-8,44,-27) Matrix(1295,4464,-794,-2737) -> Matrix(13,-8,-8,5) Matrix(251,864,52,179) -> Matrix(3,-2,20,-13) Matrix(253,864,-200,-683) -> Matrix(3,-2,-16,11) Matrix(361,1224,64,217) -> Matrix(47,-34,112,-81) Matrix(1405,4752,-798,-2699) -> Matrix(19,-14,-4,3) Matrix(1151,3888,426,1439) -> Matrix(43,-32,168,-125) Matrix(577,1944,214,721) -> Matrix(13,-10,56,-43) Matrix(1585,5328,-1242,-4175) -> Matrix(5,-4,4,-3) Matrix(901,3024,-654,-2195) -> Matrix(3,-2,-4,3) Matrix(109,360,-76,-251) -> Matrix(9,-8,8,-7) Matrix(179,576,78,251) -> Matrix(1,-2,4,-7) Matrix(361,1152,68,217) -> Matrix(3,-8,8,-21) Matrix(1223,3888,430,1367) -> Matrix(3,-32,8,-85) Matrix(613,1944,216,685) -> Matrix(3,16,8,43) Matrix(251,792,148,467) -> Matrix(5,4,16,13) Matrix(323,936,186,539) -> Matrix(7,-4,16,-9) Matrix(1441,4104,-1112,-3167) -> Matrix(3,-2,-4,3) Matrix(1367,3888,430,1223) -> Matrix(43,-32,168,-125) Matrix(685,1944,216,613) -> Matrix(21,-16,88,-67) Matrix(179,504,38,107) -> Matrix(5,-4,4,-3) Matrix(181,504,-116,-323) -> Matrix(13,-12,12,-11) Matrix(289,792,158,433) -> Matrix(5,-6,16,-19) Matrix(685,1872,-408,-1115) -> Matrix(13,-18,8,-11) Matrix(1187,3240,514,1403) -> Matrix(3,-4,4,-5) Matrix(397,1080,-304,-827) -> Matrix(9,-16,4,-7) Matrix(505,1368,-292,-791) -> Matrix(3,-10,4,-13) Matrix(107,288,-94,-253) -> Matrix(1,2,0,1) Matrix(109,288,14,37) -> Matrix(3,-2,8,-5) Matrix(2051,5400,-1272,-3349) -> Matrix(3,-4,4,-5) Matrix(1259,3312,-972,-2557) -> Matrix(1,2,0,1) Matrix(1403,3672,-1032,-2701) -> Matrix(1,0,-12,1) Matrix(937,2448,524,1369) -> Matrix(1,0,0,1) Matrix(3311,8640,-2594,-6769) -> Matrix(1,0,-4,1) Matrix(829,2160,180,469) -> Matrix(5,-2,8,-3) Matrix(251,648,-98,-253) -> Matrix(9,-4,16,-7) Matrix(395,1008,-212,-541) -> Matrix(17,-10,12,-7) Matrix(793,2016,142,361) -> Matrix(31,-20,76,-49) Matrix(541,1368,-384,-971) -> Matrix(19,-12,8,-5) Matrix(323,792,-250,-613) -> Matrix(21,-16,4,-3) Matrix(1297,3168,-766,-1871) -> Matrix(71,-56,52,-41) Matrix(1151,2808,944,2303) -> Matrix(77,-62,272,-219) Matrix(325,792,222,541) -> Matrix(5,-4,4,-3) Matrix(179,432,104,251) -> Matrix(11,-10,32,-29) Matrix(181,432,106,253) -> Matrix(9,-10,28,-31) Matrix(577,1368,-364,-863) -> Matrix(7,-10,12,-17) Matrix(1585,3744,-914,-2159) -> Matrix(11,-20,16,-29) Matrix(397,936,260,613) -> Matrix(1,-4,4,-15) Matrix(613,1440,-444,-1043) -> Matrix(1,-6,0,1) Matrix(2053,4752,-1446,-3347) -> Matrix(31,-14,20,-9) Matrix(1403,3240,514,1187) -> Matrix(11,-4,36,-13) Matrix(937,2160,344,793) -> Matrix(13,-8,44,-27) Matrix(251,576,78,179) -> Matrix(1,-2,4,-7) Matrix(253,576,206,469) -> Matrix(1,-2,4,-7) Matrix(1079,2448,666,1511) -> Matrix(1,0,4,1) Matrix(287,648,-128,-289) -> Matrix(5,-2,8,-3) Matrix(613,1368,436,973) -> Matrix(11,-8,40,-29) Matrix(323,720,48,107) -> Matrix(3,-2,8,-5) Matrix(973,2160,-632,-1403) -> Matrix(7,-2,4,-1) Matrix(2339,5184,698,1547) -> Matrix(41,-26,112,-71) Matrix(5329,11808,-2924,-6479) -> Matrix(43,-28,20,-13) Matrix(359,792,228,503) -> Matrix(7,-6,20,-17) Matrix(1153,2520,264,577) -> Matrix(11,-6,24,-13) Matrix(431,936,-332,-721) -> Matrix(13,-10,4,-3) Matrix(433,936,-266,-575) -> Matrix(3,-2,-4,3) Matrix(541,1152,-456,-971) -> Matrix(11,-10,-12,11) Matrix(35,72,-18,-37) -> Matrix(1,0,0,1) Matrix(683,1296,322,611) -> Matrix(35,-34,104,-101) Matrix(685,1296,324,613) -> Matrix(33,-34,100,-103) Matrix(1223,2304,-956,-1801) -> Matrix(25,-28,-8,9) Matrix(1693,3168,1328,2485) -> Matrix(11,-14,48,-61) Matrix(1117,2088,482,901) -> Matrix(3,-4,4,-5) Matrix(1441,2664,390,721) -> Matrix(1,-2,4,-7) Matrix(431,792,-314,-577) -> Matrix(1,-2,0,1) Matrix(433,792,158,289) -> Matrix(5,-6,16,-19) Matrix(11375,20736,5134,9359) -> Matrix(29,-56,72,-139) Matrix(11377,20736,5136,9361) -> Matrix(27,-56,68,-141) Matrix(4031,7344,1106,2015) -> Matrix(5,-12,8,-19) Matrix(3203,5832,-2472,-4501) -> Matrix(1,0,0,1) Matrix(397,720,338,613) -> Matrix(1,-2,4,-7) Matrix(359,648,-200,-361) -> Matrix(1,-2,0,1) Matrix(1045,1872,302,541) -> Matrix(5,2,12,5) Matrix(1369,2448,524,937) -> Matrix(1,0,0,1) Matrix(323,576,60,107) -> Matrix(3,-2,8,-5) Matrix(325,576,224,397) -> Matrix(3,-2,8,-5) Matrix(611,1080,142,251) -> Matrix(5,-8,12,-19) Matrix(1837,3240,1164,2053) -> Matrix(3,4,8,11) Matrix(1187,2088,552,971) -> Matrix(3,4,8,11) Matrix(3023,5256,662,1151) -> Matrix(5,-2,8,-3) Matrix(4931,8568,-3502,-6085) -> Matrix(19,-12,8,-5) Matrix(1369,2376,208,361) -> Matrix(3,-2,20,-13) Matrix(11951,20736,5062,8783) -> Matrix(133,-88,464,-307) Matrix(11953,20736,5064,8785) -> Matrix(131,-88,460,-309) Matrix(1621,2808,-1184,-2051) -> Matrix(11,-8,-4,3) Matrix(251,432,104,179) -> Matrix(11,-10,32,-29) Matrix(253,432,106,181) -> Matrix(9,-10,28,-31) Matrix(467,792,148,251) -> Matrix(3,-4,16,-21) Matrix(1657,2808,298,505) -> Matrix(47,-62,116,-153) Matrix(12239,20736,5014,8495) -> Matrix(313,-416,860,-1143) Matrix(12241,20736,5016,8497) -> Matrix(311,-416,856,-1145) Matrix(2951,4968,812,1367) -> Matrix(7,-10,12,-17) Matrix(395,648,-242,-397) -> Matrix(1,-4,0,1) Matrix(12673,20664,-9184,-14975) -> Matrix(1,-2,0,1) Matrix(2341,3816,1922,3133) -> Matrix(9,16,32,57) Matrix(5833,9504,1724,2809) -> Matrix(3,-8,8,-21) Matrix(5437,8856,1172,1909) -> Matrix(5,8,8,13) Matrix(1331,2160,1042,1691) -> Matrix(1,2,4,9) Matrix(4175,6768,-2932,-4753) -> Matrix(11,4,8,3) Matrix(1511,2448,666,1079) -> Matrix(1,0,4,1) Matrix(757,1224,-556,-899) -> Matrix(1,0,-4,1) Matrix(2989,4824,-1940,-3131) -> Matrix(19,-8,12,-5) Matrix(7235,11664,2746,4427) -> Matrix(11,-10,32,-29) Matrix(7237,11664,2748,4429) -> Matrix(9,-10,28,-31) Matrix(179,288,156,251) -> Matrix(1,-2,4,-7) Matrix(1223,1944,860,1367) -> Matrix(23,-10,76,-33) Matrix(2449,3888,1724,2737) -> Matrix(61,-32,204,-107) Matrix(1367,2160,774,1223) -> Matrix(11,-8,40,-29) Matrix(2053,3240,1164,1837) -> Matrix(5,-4,24,-19) Matrix(3743,5904,-2922,-4609) -> Matrix(11,-8,-4,3) Matrix(503,792,228,359) -> Matrix(7,-6,20,-17) Matrix(827,1296,298,467) -> Matrix(27,-26,80,-77) Matrix(829,1296,300,469) -> Matrix(25,-26,76,-79) Matrix(325,504,256,397) -> Matrix(3,-4,16,-21) Matrix(1259,1944,862,1331) -> Matrix(11,-16,20,-29) Matrix(2521,3888,1728,2665) -> Matrix(21,-32,44,-67) Matrix(469,720,-398,-611) -> Matrix(1,-2,4,-7) Matrix(541,792,222,325) -> Matrix(13,-4,36,-11) Matrix(1331,1944,862,1259) -> Matrix(35,-16,116,-53) Matrix(2665,3888,1728,2521) -> Matrix(61,-32,204,-107) Matrix(791,1152,642,935) -> Matrix(13,-8,44,-27) Matrix(397,576,224,325) -> Matrix(3,-2,8,-5) Matrix(899,1296,274,395) -> Matrix(23,-22,68,-65) Matrix(901,1296,276,397) -> Matrix(21,-22,64,-67) Matrix(3637,5184,1996,2845) -> Matrix(19,-26,68,-93) Matrix(253,360,26,37) -> Matrix(3,-4,4,-5) Matrix(3853,5472,1040,1477) -> Matrix(9,-14,20,-31) Matrix(6695,9504,2586,3671) -> Matrix(5,-8,12,-19) Matrix(863,1224,710,1007) -> Matrix(21,-34,76,-123) Matrix(1223,1728,356,503) -> Matrix(21,-40,52,-99) Matrix(1225,1728,358,505) -> Matrix(19,-40,48,-101) Matrix(21277,29952,-15420,-21707) -> Matrix(1,-6,0,1) Matrix(1331,1872,588,827) -> Matrix(1,-2,0,1) Matrix(467,648,-338,-469) -> Matrix(1,-8,0,1) Matrix(113651,156816,31282,43163) -> Matrix(5,18,8,29) Matrix(113653,156816,31284,43165) -> Matrix(7,18,12,31) Matrix(3601,4968,1462,2017) -> Matrix(3,10,8,27) Matrix(2663,3672,-2246,-3097) -> Matrix(3,10,-4,-13) Matrix(5329,7344,2404,3313) -> Matrix(5,12,12,29) Matrix(1943,2664,892,1223) -> Matrix(3,-2,8,-5) Matrix(3995,5472,1182,1619) -> Matrix(3,-14,8,-37) Matrix(8531,11664,2290,3131) -> Matrix(13,14,12,13) Matrix(8533,11664,2292,3133) -> Matrix(15,14,16,15) Matrix(685,936,554,757) -> Matrix(5,4,16,13) Matrix(3815,5184,1006,1367) -> Matrix(1,0,36,1) Matrix(3817,5184,1008,1369) -> Matrix(1,0,-32,1) Matrix(107,144,26,35) -> Matrix(3,-2,8,-5) Matrix(109,144,28,37) -> Matrix(1,-2,4,-7) Matrix(829,1080,360,469) -> Matrix(3,-8,8,-21) Matrix(1943,2520,1054,1367) -> Matrix(1,-6,4,-23) Matrix(503,648,-392,-505) -> Matrix(1,-10,0,1) Matrix(4105,5256,1744,2233) -> Matrix(1,2,4,9) Matrix(1691,2160,1042,1331) -> Matrix(1,2,4,9) Matrix(2089,2664,396,505) -> Matrix(3,10,8,27) Matrix(6947,8856,2682,3419) -> Matrix(3,8,4,11) Matrix(16271,20736,3502,4463) -> Matrix(19,40,28,59) Matrix(16273,20736,3504,4465) -> Matrix(21,40,32,61) Matrix(397,504,256,325) -> Matrix(5,4,16,13) Matrix(685,864,486,613) -> Matrix(9,-2,32,-7) Matrix(757,936,554,685) -> Matrix(3,-4,16,-21) Matrix(2159,2664,466,575) -> Matrix(7,-10,12,-17) Matrix(935,1152,642,791) -> Matrix(5,-8,12,-19) Matrix(469,576,206,253) -> Matrix(1,-2,4,-7) Matrix(2303,2808,944,1151) -> Matrix(29,-62,80,-171) Matrix(1655,2016,1004,1223) -> Matrix(9,-20,32,-71) Matrix(1007,1224,710,863) -> Matrix(13,-34,44,-115) Matrix(179,216,-150,-181) -> Matrix(1,-4,0,1) Matrix(2015,2376,854,1007) -> Matrix(9,-2,32,-7) Matrix(613,720,338,397) -> Matrix(1,-2,4,-7) Matrix(251,288,156,179) -> Matrix(1,-2,4,-7) Matrix(323,360,96,107) -> Matrix(3,4,8,11) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(253,-288,94,-107) -> Matrix(7,-2,32,-9) Matrix(611,-720,398,-469) -> Matrix(1,-2,4,-7) Matrix(181,-216,150,-179) -> Matrix(17,-4,64,-15) Matrix(1367,-1656,298,-361) -> Matrix(67,-18,108,-29) Matrix(683,-864,200,-253) -> Matrix(19,-2,48,-5) Matrix(1583,-2016,340,-433) -> Matrix(19,-4,24,-5) Matrix(4175,-5328,1242,-1585) -> Matrix(13,-4,36,-11) Matrix(901,-1152,140,-179) -> Matrix(9,-2,-4,1) Matrix(899,-1152,366,-469) -> Matrix(59,-14,156,-37) Matrix(613,-792,250,-323) -> Matrix(61,-16,164,-43) Matrix(2557,-3312,972,-1259) -> Matrix(7,-2,32,-9) Matrix(721,-936,332,-431) -> Matrix(37,-10,100,-27) Matrix(827,-1080,304,-397) -> Matrix(57,-16,196,-55) Matrix(899,-1224,556,-757) -> Matrix(1,0,-4,1) Matrix(2053,-2808,552,-755) -> Matrix(19,-4,24,-5) Matrix(2629,-3600,972,-1331) -> Matrix(25,-6,96,-23) Matrix(577,-792,314,-431) -> Matrix(9,-2,32,-7) Matrix(469,-648,338,-467) -> Matrix(33,-8,128,-31) Matrix(2953,-4104,880,-1223) -> Matrix(85,-22,228,-59) Matrix(3313,-4608,724,-1007) -> Matrix(121,-32,208,-55) Matrix(361,-504,154,-215) -> Matrix(7,-2,32,-9) Matrix(3169,-4464,1226,-1727) -> Matrix(29,-8,40,-11) Matrix(611,-864,128,-181) -> Matrix(7,-2,-24,7) Matrix(3347,-4752,1446,-2053) -> Matrix(47,-14,84,-25) Matrix(3743,-5328,810,-1153) -> Matrix(13,-4,36,-11) Matrix(2123,-3024,582,-829) -> Matrix(7,-2,4,-1) Matrix(251,-360,76,-109) -> Matrix(25,-8,72,-23) Matrix(2663,-4104,608,-937) -> Matrix(7,-2,4,-1) Matrix(323,-504,116,-181) -> Matrix(37,-12,108,-35) Matrix(1187,-1872,480,-757) -> Matrix(49,-18,128,-47) Matrix(683,-1080,160,-253) -> Matrix(41,-16,100,-39) Matrix(863,-1368,364,-577) -> Matrix(23,-10,76,-33) Matrix(181,-288,22,-35) -> Matrix(3,-2,8,-5) Matrix(3349,-5400,1272,-2051) -> Matrix(11,-4,36,-13) Matrix(2053,-3312,468,-755) -> Matrix(3,-2,8,-5) Matrix(2269,-3672,600,-971) -> Matrix(1,0,-12,1) Matrix(5329,-8640,1154,-1871) -> Matrix(1,0,-4,1) Matrix(397,-648,242,-395) -> Matrix(17,-4,64,-15) Matrix(613,-1008,284,-467) -> Matrix(37,-10,100,-27) Matrix(827,-1368,240,-397) -> Matrix(43,-12,104,-29) Matrix(469,-792,106,-179) -> Matrix(53,-16,116,-35) Matrix(1871,-3168,766,-1297) -> Matrix(183,-56,500,-153) Matrix(791,-1368,292,-505) -> Matrix(27,-10,100,-37) Matrix(2159,-3744,914,-1585) -> Matrix(51,-20,176,-69) Matrix(827,-1440,228,-397) -> Matrix(13,-6,24,-11) Matrix(2699,-4752,798,-1405) -> Matrix(59,-14,156,-37) Matrix(361,-648,200,-359) -> Matrix(9,-2,32,-7) Matrix(1187,-2160,416,-757) -> Matrix(11,-2,28,-5) Matrix(6479,-11808,2924,-5329) -> Matrix(99,-28,244,-69) Matrix(505,-936,116,-215) -> Matrix(33,-10,76,-23) Matrix(503,-936,194,-361) -> Matrix(7,-2,4,-1) Matrix(611,-1152,96,-181) -> Matrix(31,-10,28,-9) Matrix(37,-72,18,-35) -> Matrix(1,0,0,1) Matrix(1081,-2304,236,-503) -> Matrix(81,-28,136,-47) Matrix(361,-792,98,-215) -> Matrix(5,-2,8,-3) Matrix(2629,-5832,600,-1331) -> Matrix(1,0,0,1) Matrix(289,-648,128,-287) -> Matrix(5,-2,8,-3) Matrix(3637,-8568,1054,-2483) -> Matrix(43,-12,104,-29) Matrix(1187,-2808,320,-757) -> Matrix(27,-8,44,-13) Matrix(253,-648,98,-251) -> Matrix(9,-4,16,-7) Matrix(7991,-20664,2200,-5689) -> Matrix(5,-2,8,-3) Matrix(2593,-6768,772,-2015) -> Matrix(3,4,8,11) Matrix(467,-1224,124,-325) -> Matrix(1,0,-4,1) Matrix(1835,-4824,644,-1693) -> Matrix(35,-8,92,-21) Matrix(2161,-5904,474,-1295) -> Matrix(27,-8,44,-13) Matrix(251,-720,38,-109) -> Matrix(5,-2,28,-11) Matrix(8675,-29952,2388,-8245) -> Matrix(13,-6,24,-11) Matrix(181,-648,50,-179) -> Matrix(17,-8,32,-15) Matrix(1009,-3672,158,-575) -> Matrix(17,-10,12,-7) Matrix(145,-648,32,-143) -> Matrix(21,-10,40,-19) Matrix(37,-216,6,-35) -> Matrix(9,-4,16,-7) 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: 40 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 6/5 9/7 4/3 3/2 12/7 9/5 24/13 2/1 24/11 9/4 12/5 18/7 108/41 8/3 27/10 36/13 3/1 54/17 16/5 36/11 10/3 18/5 108/29 15/4 72/19 4/1 9/2 14/3 5/1 21/4 16/3 11/2 17/3 6/1 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/4 8/7 2/7 7/6 1/2 13/11 1/8 6/5 1/4 11/9 7/24 16/13 2/7 37/30 3/10 21/17 3/10 5/4 1/2 14/11 1/5 2/9 9/7 1/4 22/17 4/15 3/11 35/27 1/4 13/10 7/26 17/13 17/60 4/3 1/3 19/14 -1/6 15/11 1/6 41/30 5/26 26/19 1/5 2/9 37/27 1/4 11/8 3/14 18/13 1/4 7/5 1/4 17/12 17/58 27/19 3/10 37/26 3/10 10/7 4/13 1/3 13/9 7/20 16/11 2/5 3/2 1/4 20/13 5/17 37/24 3/10 54/35 3/10 17/11 17/56 14/9 6/19 1/3 11/7 7/20 30/19 3/8 19/12 9/22 27/17 1/2 8/5 0/1 29/18 3/10 50/31 1/3 2/5 21/13 1/2 55/34 -1/10 34/21 0/1 1/7 13/8 1/6 18/11 1/4 5/3 1/4 17/10 17/54 12/7 1/3 19/11 13/36 7/4 1/2 23/13 5/16 16/9 0/1 9/5 1/4 20/11 1/3 11/6 1/2 35/19 1/4 24/13 2/7 13/7 1/4 2/1 0/1 1/3 13/6 1/2 37/17 3/8 24/11 2/5 11/5 1/4 9/4 1/2 25/11 1/0 16/7 0/1 23/10 5/14 7/3 1/4 19/8 13/42 12/5 1/3 17/7 17/48 22/9 4/11 7/19 5/2 1/2 18/7 1/2 13/5 1/0 34/13 -1/1 0/1 21/8 1/4 71/27 1/4 50/19 2/7 1/3 79/30 7/22 108/41 1/3 29/11 3/8 8/3 0/1 35/13 1/4 27/10 1/4 19/7 9/32 11/4 7/22 36/13 1/3 25/9 19/56 14/5 1/3 6/17 17/6 17/46 3/1 1/2 19/6 5/22 54/17 1/4 35/11 1/4 16/5 2/7 13/4 7/22 36/11 1/3 23/7 15/44 10/3 1/3 4/11 37/11 3/8 27/8 3/8 17/5 17/44 7/2 1/2 18/5 1/2 11/3 3/4 48/13 0/1 37/10 1/2 26/7 2/3 1/1 67/18 9/10 108/29 1/1 41/11 5/4 15/4 1/0 34/9 -1/5 0/1 53/14 -1/22 72/19 0/1 19/5 1/12 4/1 1/3 17/4 17/42 30/7 5/12 13/3 7/16 9/2 1/2 23/5 3/4 60/13 1/1 37/8 1/2 51/11 1/2 14/3 2/3 1/1 19/4 -3/2 5/1 1/4 21/4 3/8 37/7 3/8 16/3 2/5 11/2 7/18 17/3 17/40 6/1 1/2 19/3 7/8 13/2 -1/2 7/1 1/4 8/1 2/5 9/1 1/2 1/0 1/2 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(253,-288,94,-107) (1/1,8/7) -> (8/3,35/13) Hyperbolic Matrix(251,-288,95,-109) (8/7,7/6) -> (29/11,8/3) Hyperbolic Matrix(215,-252,93,-109) (7/6,13/11) -> (23/10,7/3) Hyperbolic Matrix(395,-468,92,-109) (13/11,6/5) -> (30/7,13/3) Hyperbolic Matrix(325,-396,206,-251) (6/5,11/9) -> (11/7,30/19) Hyperbolic Matrix(323,-396,177,-217) (11/9,16/13) -> (20/11,11/6) Hyperbolic Matrix(935,-1152,293,-361) (16/13,37/30) -> (35/11,16/5) Hyperbolic Matrix(1837,-2268,699,-863) (37/30,21/17) -> (21/8,71/27) Hyperbolic Matrix(757,-936,203,-251) (21/17,5/4) -> (41/11,15/4) Hyperbolic Matrix(143,-180,58,-73) (5/4,14/11) -> (22/9,5/2) Hyperbolic Matrix(253,-324,196,-251) (14/11,9/7) -> (9/7,22/17) Parabolic Matrix(2557,-3312,972,-1259) (22/17,35/27) -> (71/27,50/19) Hyperbolic Matrix(721,-936,332,-431) (35/27,13/10) -> (13/6,37/17) Hyperbolic Matrix(359,-468,56,-73) (13/10,17/13) -> (19/3,13/2) Hyperbolic Matrix(109,-144,81,-107) (17/13,4/3) -> (4/3,19/14) Parabolic Matrix(899,-1224,556,-757) (19/14,15/11) -> (21/13,55/34) Hyperbolic Matrix(685,-936,131,-179) (15/11,41/30) -> (5/1,21/4) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(973,-1332,683,-935) (26/19,37/27) -> (37/26,10/7) Hyperbolic Matrix(577,-792,314,-431) (37/27,11/8) -> (11/6,35/19) Hyperbolic Matrix(287,-396,79,-109) (11/8,18/13) -> (18/5,11/3) Hyperbolic Matrix(181,-252,51,-71) (18/13,7/5) -> (7/2,18/5) Hyperbolic Matrix(179,-252,103,-145) (7/5,17/12) -> (19/11,7/4) Hyperbolic Matrix(685,-972,253,-359) (17/12,27/19) -> (27/10,19/7) Hyperbolic Matrix(1367,-1944,507,-721) (27/19,37/26) -> (35/13,27/10) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(397,-576,173,-251) (13/9,16/11) -> (16/7,23/10) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(865,-1332,163,-251) (20/13,37/24) -> (37/7,16/3) Hyperbolic Matrix(2521,-3888,793,-1223) (37/24,54/35) -> (54/17,35/11) Hyperbolic Matrix(1259,-1944,397,-613) (54/35,17/11) -> (19/6,54/17) Hyperbolic Matrix(325,-504,69,-107) (17/11,14/9) -> (14/3,19/4) Hyperbolic Matrix(323,-504,116,-181) (14/9,11/7) -> (25/9,14/5) Hyperbolic Matrix(683,-1080,160,-253) (30/19,19/12) -> (17/4,30/7) Hyperbolic Matrix(613,-972,181,-287) (19/12,27/17) -> (27/8,17/5) Hyperbolic Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(179,-288,23,-37) (8/5,29/18) -> (7/1,8/1) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(1763,-2844,380,-613) (50/31,21/13) -> (51/11,14/3) Hyperbolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(289,-468,155,-251) (34/21,13/8) -> (13/7,2/1) Hyperbolic Matrix(287,-468,111,-181) (13/8,18/11) -> (18/7,13/5) Hyperbolic Matrix(109,-180,43,-71) (18/11,5/3) -> (5/2,18/7) Hyperbolic Matrix(107,-180,22,-37) (5/3,17/10) -> (19/4,5/1) Hyperbolic Matrix(253,-432,147,-251) (17/10,12/7) -> (12/7,19/11) Parabolic Matrix(143,-252,21,-37) (7/4,23/13) -> (13/2,7/1) Hyperbolic Matrix(325,-576,101,-179) (23/13,16/9) -> (16/5,13/4) Hyperbolic Matrix(181,-324,100,-179) (16/9,9/5) -> (9/5,20/11) Parabolic Matrix(1621,-2988,351,-647) (35/19,24/13) -> (60/13,37/8) Hyperbolic Matrix(719,-1332,156,-289) (24/13,13/7) -> (23/5,60/13) Hyperbolic Matrix(217,-468,83,-179) (2/1,13/6) -> (13/5,34/13) Hyperbolic Matrix(1223,-2664,331,-721) (37/17,24/11) -> (48/13,37/10) Hyperbolic Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(145,-324,64,-143) (11/5,9/4) -> (9/4,25/11) Parabolic Matrix(253,-576,47,-107) (25/11,16/7) -> (16/3,11/2) Hyperbolic Matrix(107,-252,31,-73) (7/3,19/8) -> (17/5,7/2) Hyperbolic Matrix(181,-432,75,-179) (19/8,12/5) -> (12/5,17/7) Parabolic Matrix(251,-612,89,-217) (17/7,22/9) -> (14/5,17/6) Hyperbolic Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(4429,-11664,1681,-4427) (79/30,108/41) -> (108/41,29/11) Parabolic Matrix(145,-396,26,-71) (19/7,11/4) -> (11/2,17/3) Hyperbolic Matrix(469,-1296,169,-467) (11/4,36/13) -> (36/13,25/9) Parabolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(397,-1296,121,-395) (13/4,36/11) -> (36/11,23/7) Parabolic Matrix(397,-1332,107,-359) (10/3,37/11) -> (37/10,26/7) Hyperbolic Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) Hyperbolic Matrix(3133,-11664,841,-3131) (67/18,108/29) -> (108/29,41/11) Parabolic Matrix(1369,-5184,361,-1367) (53/14,72/19) -> (72/19,19/5) Parabolic Matrix(37,-144,9,-35) (19/5,4/1) -> (4/1,17/4) Parabolic Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(575,-2664,109,-505) (37/8,51/11) -> (21/4,37/7) Hyperbolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,2,1) Matrix(253,-288,94,-107) -> Matrix(7,-2,32,-9) Matrix(251,-288,95,-109) -> Matrix(7,-2,18,-5) Matrix(215,-252,93,-109) -> Matrix(3,-1,10,-3) Matrix(395,-468,92,-109) -> Matrix(17,-3,40,-7) Matrix(325,-396,206,-251) -> Matrix(25,-7,68,-19) Matrix(323,-396,177,-217) -> Matrix(17,-5,58,-17) Matrix(935,-1152,293,-361) -> Matrix(27,-8,98,-29) Matrix(1837,-2268,699,-863) -> Matrix(3,-1,22,-7) Matrix(757,-936,203,-251) -> Matrix(13,-4,10,-3) Matrix(143,-180,58,-73) -> Matrix(1,-1,4,-3) Matrix(253,-324,196,-251) -> Matrix(21,-5,80,-19) Matrix(2557,-3312,972,-1259) -> Matrix(7,-2,32,-9) Matrix(721,-936,332,-431) -> Matrix(37,-10,100,-27) Matrix(359,-468,56,-73) -> Matrix(11,-3,4,-1) Matrix(109,-144,81,-107) -> Matrix(7,-2,18,-5) Matrix(899,-1224,556,-757) -> Matrix(1,0,-4,1) Matrix(685,-936,131,-179) -> Matrix(21,-4,58,-11) Matrix(2053,-2808,552,-755) -> Matrix(19,-4,24,-5) Matrix(973,-1332,683,-935) -> Matrix(31,-7,102,-23) Matrix(577,-792,314,-431) -> Matrix(9,-2,32,-7) Matrix(287,-396,79,-109) -> Matrix(13,-3,22,-5) Matrix(181,-252,51,-71) -> Matrix(19,-5,42,-11) Matrix(179,-252,103,-145) -> Matrix(11,-3,26,-7) Matrix(685,-972,253,-359) -> Matrix(37,-11,138,-41) Matrix(1367,-1944,507,-721) -> Matrix(33,-10,142,-43) Matrix(251,-360,76,-109) -> Matrix(25,-8,72,-23) Matrix(397,-576,173,-251) -> Matrix(5,-2,18,-7) Matrix(73,-108,48,-71) -> Matrix(5,-1,16,-3) Matrix(865,-1332,163,-251) -> Matrix(71,-21,186,-55) Matrix(2521,-3888,793,-1223) -> Matrix(107,-32,418,-125) Matrix(1259,-1944,397,-613) -> Matrix(53,-16,222,-67) Matrix(325,-504,69,-107) -> Matrix(13,-4,10,-3) Matrix(323,-504,116,-181) -> Matrix(37,-12,108,-35) Matrix(683,-1080,160,-253) -> Matrix(41,-16,100,-39) Matrix(613,-972,181,-287) -> Matrix(25,-11,66,-29) Matrix(181,-288,22,-35) -> Matrix(3,-2,8,-5) Matrix(179,-288,23,-37) -> Matrix(7,-2,18,-5) Matrix(3349,-5400,1272,-2051) -> Matrix(11,-4,36,-13) Matrix(1763,-2844,380,-613) -> Matrix(7,-3,12,-5) Matrix(2269,-3672,600,-971) -> Matrix(1,0,-12,1) Matrix(289,-468,155,-251) -> Matrix(7,-1,22,-3) Matrix(287,-468,111,-181) -> Matrix(5,-1,6,-1) Matrix(109,-180,43,-71) -> Matrix(11,-3,26,-7) Matrix(107,-180,22,-37) -> Matrix(3,-1,16,-5) Matrix(253,-432,147,-251) -> Matrix(31,-10,90,-29) Matrix(143,-252,21,-37) -> Matrix(3,-1,10,-3) Matrix(325,-576,101,-179) -> Matrix(5,-2,18,-7) Matrix(181,-324,100,-179) -> Matrix(5,-1,16,-3) Matrix(1621,-2988,351,-647) -> Matrix(3,-1,10,-3) Matrix(719,-1332,156,-289) -> Matrix(17,-5,24,-7) Matrix(217,-468,83,-179) -> Matrix(3,-1,-2,1) Matrix(1223,-2664,331,-721) -> Matrix(5,-2,18,-7) Matrix(361,-792,98,-215) -> Matrix(5,-2,8,-3) Matrix(145,-324,64,-143) -> Matrix(3,-1,4,-1) Matrix(253,-576,47,-107) -> Matrix(7,-2,18,-5) Matrix(107,-252,31,-73) -> Matrix(11,-3,26,-7) Matrix(181,-432,75,-179) -> Matrix(31,-10,90,-29) Matrix(251,-612,89,-217) -> Matrix(47,-17,130,-47) Matrix(467,-1224,124,-325) -> Matrix(1,0,-4,1) Matrix(4429,-11664,1681,-4427) -> Matrix(31,-10,90,-29) Matrix(145,-396,26,-71) -> Matrix(23,-7,56,-17) Matrix(469,-1296,169,-467) -> Matrix(79,-26,234,-77) Matrix(37,-108,12,-35) -> Matrix(3,-1,4,-1) Matrix(397,-1296,121,-395) -> Matrix(67,-22,198,-65) Matrix(397,-1332,107,-359) -> Matrix(19,-7,30,-11) Matrix(107,-360,11,-37) -> Matrix(11,-4,14,-5) Matrix(3133,-11664,841,-3131) -> Matrix(15,-14,14,-13) Matrix(1369,-5184,361,-1367) -> Matrix(1,0,34,1) Matrix(37,-144,9,-35) -> Matrix(7,-2,18,-5) Matrix(73,-324,16,-71) -> Matrix(11,-5,20,-9) Matrix(575,-2664,109,-505) -> Matrix(17,-10,46,-27) Matrix(37,-216,6,-35) -> Matrix(9,-4,16,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 72 ----------------------------------------------------------------------- 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 2 1 2/1 (0/1,1/3) 0 18 13/6 1/2 1 36 24/11 2/5 2 3 11/5 1/4 1 36 9/4 1/2 1 4 25/11 1/0 1 36 16/7 0/1 2 9 23/10 5/14 1 36 7/3 1/4 1 36 19/8 13/42 1 36 12/5 1/3 10 3 17/7 17/48 1 36 5/2 1/2 1 36 18/7 1/2 4 2 13/5 1/0 1 36 34/13 (-1/1,0/1) 0 18 21/8 1/4 1 12 50/19 (2/7,1/3) 0 18 108/41 1/3 10 1 29/11 3/8 1 36 8/3 0/1 2 9 27/10 1/4 7 4 19/7 9/32 1 36 11/4 7/22 1 36 36/13 1/3 26 1 14/5 (1/3,6/17) 0 18 17/6 17/46 1 36 3/1 1/2 1 12 19/6 5/22 1 36 54/17 1/4 16 2 35/11 1/4 1 36 16/5 2/7 2 9 13/4 7/22 1 36 36/11 1/3 22 1 10/3 (1/3,4/11) 0 18 37/11 3/8 1 36 27/8 3/8 7 4 17/5 17/44 1 36 7/2 1/2 1 36 18/5 1/2 8 2 11/3 3/4 1 36 48/13 0/1 2 3 37/10 1/2 1 36 26/7 (2/3,1/1) 0 18 108/29 1/1 14 1 41/11 5/4 1 36 15/4 1/0 1 12 34/9 (-1/5,0/1) 0 18 72/19 0/1 34 1 19/5 1/12 1 36 4/1 1/3 2 9 17/4 17/42 1 36 13/3 7/16 1 36 9/2 1/2 5 4 23/5 3/4 1 36 60/13 1/1 2 3 37/8 1/2 1 36 51/11 1/2 1 12 14/3 (2/3,1/1) 0 18 19/4 -3/2 1 36 5/1 1/4 1 36 21/4 3/8 1 12 37/7 3/8 1 36 16/3 2/5 2 9 11/2 7/18 1 36 17/3 17/40 1 36 6/1 1/2 4 6 19/3 7/8 1 36 13/2 -1/2 1 36 7/1 1/4 1 36 8/1 2/5 2 9 9/1 1/2 7 4 1/0 1/2 1 36 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(217,-468,83,-179) (2/1,13/6) -> (13/5,34/13) Hyperbolic Matrix(613,-1332,133,-289) (13/6,24/11) -> (23/5,60/13) Glide Reflection Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(145,-324,64,-143) (11/5,9/4) -> (9/4,25/11) Parabolic Matrix(253,-576,47,-107) (25/11,16/7) -> (16/3,11/2) Hyperbolic Matrix(251,-576,78,-179) (16/7,23/10) -> (16/5,13/4) Glide Reflection Matrix(109,-252,16,-37) (23/10,7/3) -> (13/2,7/1) Glide Reflection Matrix(107,-252,31,-73) (7/3,19/8) -> (17/5,7/2) Hyperbolic Matrix(181,-432,75,-179) (19/8,12/5) -> (12/5,17/7) Parabolic Matrix(73,-180,15,-37) (17/7,5/2) -> (19/4,5/1) Glide Reflection Matrix(71,-180,28,-71) (5/2,18/7) -> (5/2,18/7) Reflection Matrix(181,-468,70,-181) (18/7,13/5) -> (18/7,13/5) Reflection Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(1081,-2844,233,-613) (21/8,50/19) -> (51/11,14/3) Glide Reflection Matrix(2051,-5400,779,-2051) (50/19,108/41) -> (50/19,108/41) Reflection Matrix(2377,-6264,902,-2377) (108/41,29/11) -> (108/41,29/11) Reflection Matrix(109,-288,14,-37) (29/11,8/3) -> (7/1,8/1) Glide Reflection Matrix(107,-288,13,-35) (8/3,27/10) -> (8/1,9/1) Glide Reflection Matrix(359,-972,106,-287) (27/10,19/7) -> (27/8,17/5) Glide Reflection Matrix(145,-396,26,-71) (19/7,11/4) -> (11/2,17/3) Hyperbolic Matrix(287,-792,104,-287) (11/4,36/13) -> (11/4,36/13) Reflection Matrix(181,-504,65,-181) (36/13,14/5) -> (36/13,14/5) Reflection Matrix(179,-504,38,-107) (14/5,17/6) -> (14/3,19/4) Glide Reflection Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(647,-2052,204,-647) (19/6,54/17) -> (19/6,54/17) Reflection Matrix(1189,-3780,374,-1189) (54/17,35/11) -> (54/17,35/11) Reflection Matrix(361,-1152,68,-217) (35/11,16/5) -> (37/7,16/3) Glide Reflection Matrix(287,-936,88,-287) (13/4,36/11) -> (13/4,36/11) Reflection Matrix(109,-360,33,-109) (36/11,10/3) -> (36/11,10/3) Reflection Matrix(397,-1332,107,-359) (10/3,37/11) -> (37/10,26/7) Hyperbolic Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) Hyperbolic Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(1081,-3996,234,-865) (48/13,37/10) -> (60/13,37/8) Glide Reflection Matrix(755,-2808,203,-755) (26/7,108/29) -> (26/7,108/29) Reflection Matrix(2377,-8856,638,-2377) (108/29,41/11) -> (108/29,41/11) Reflection Matrix(251,-936,48,-179) (41/11,15/4) -> (5/1,21/4) Glide Reflection Matrix(647,-2448,171,-647) (34/9,72/19) -> (34/9,72/19) Reflection Matrix(721,-2736,190,-721) (72/19,19/5) -> (72/19,19/5) Reflection Matrix(37,-144,9,-35) (19/5,4/1) -> (4/1,17/4) Parabolic Matrix(109,-468,17,-73) (17/4,13/3) -> (19/3,13/2) Glide Reflection Matrix(73,-324,16,-71) (13/3,9/2) -> (9/2,23/5) Parabolic Matrix(575,-2664,109,-505) (37/8,51/11) -> (21/4,37/7) Hyperbolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,4,-1) (0/1,1/0) -> (0/1,1/2) Matrix(1,0,1,-1) -> Matrix(1,0,6,-1) (0/1,2/1) -> (0/1,1/3) Matrix(217,-468,83,-179) -> Matrix(3,-1,-2,1) Matrix(613,-1332,133,-289) -> Matrix(13,-5,18,-7) Matrix(361,-792,98,-215) -> Matrix(5,-2,8,-3) 1/2 Matrix(145,-324,64,-143) -> Matrix(3,-1,4,-1) 1/2 Matrix(253,-576,47,-107) -> Matrix(7,-2,18,-5) 1/3 Matrix(251,-576,78,-179) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(109,-252,16,-37) -> Matrix(3,-1,8,-3) *** -> (1/4,1/2) Matrix(107,-252,31,-73) -> Matrix(11,-3,26,-7) Matrix(181,-432,75,-179) -> Matrix(31,-10,90,-29) 1/3 Matrix(73,-180,15,-37) -> Matrix(3,-1,14,-5) Matrix(71,-180,28,-71) -> Matrix(7,-3,16,-7) (5/2,18/7) -> (3/8,1/2) Matrix(181,-468,70,-181) -> Matrix(-1,1,0,1) (18/7,13/5) -> (1/2,1/0) Matrix(467,-1224,124,-325) -> Matrix(1,0,-4,1) 0/1 Matrix(1081,-2844,233,-613) -> Matrix(11,-3,18,-5) Matrix(2051,-5400,779,-2051) -> Matrix(13,-4,42,-13) (50/19,108/41) -> (2/7,1/3) Matrix(2377,-6264,902,-2377) -> Matrix(17,-6,48,-17) (108/41,29/11) -> (1/3,3/8) Matrix(109,-288,14,-37) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(107,-288,13,-35) -> Matrix(9,-2,22,-5) Matrix(359,-972,106,-287) -> Matrix(41,-11,108,-29) Matrix(145,-396,26,-71) -> Matrix(23,-7,56,-17) Matrix(287,-792,104,-287) -> Matrix(43,-14,132,-43) (11/4,36/13) -> (7/22,1/3) Matrix(181,-504,65,-181) -> Matrix(35,-12,102,-35) (36/13,14/5) -> (1/3,6/17) Matrix(179,-504,38,-107) -> Matrix(11,-4,8,-3) Matrix(37,-108,12,-35) -> Matrix(3,-1,4,-1) 1/2 Matrix(647,-2052,204,-647) -> Matrix(21,-5,88,-21) (19/6,54/17) -> (5/22,1/4) Matrix(1189,-3780,374,-1189) -> Matrix(43,-11,168,-43) (54/17,35/11) -> (1/4,11/42) Matrix(361,-1152,68,-217) -> Matrix(29,-8,76,-21) Matrix(287,-936,88,-287) -> Matrix(43,-14,132,-43) (13/4,36/11) -> (7/22,1/3) Matrix(109,-360,33,-109) -> Matrix(23,-8,66,-23) (36/11,10/3) -> (1/3,4/11) Matrix(397,-1332,107,-359) -> Matrix(19,-7,30,-11) Matrix(107,-360,11,-37) -> Matrix(11,-4,14,-5) Matrix(71,-252,20,-71) -> Matrix(11,-5,24,-11) (7/2,18/5) -> (5/12,1/2) Matrix(109,-396,30,-109) -> Matrix(5,-3,8,-5) (18/5,11/3) -> (1/2,3/4) Matrix(1081,-3996,234,-865) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(755,-2808,203,-755) -> Matrix(5,-4,6,-5) (26/7,108/29) -> (2/3,1/1) Matrix(2377,-8856,638,-2377) -> Matrix(9,-10,8,-9) (108/29,41/11) -> (1/1,5/4) Matrix(251,-936,48,-179) -> Matrix(3,-4,8,-11) Matrix(647,-2448,171,-647) -> Matrix(-1,0,10,1) (34/9,72/19) -> (-1/5,0/1) Matrix(721,-2736,190,-721) -> Matrix(1,0,24,-1) (72/19,19/5) -> (0/1,1/12) Matrix(37,-144,9,-35) -> Matrix(7,-2,18,-5) 1/3 Matrix(109,-468,17,-73) -> Matrix(7,-3,2,-1) Matrix(73,-324,16,-71) -> Matrix(11,-5,20,-9) 1/2 Matrix(575,-2664,109,-505) -> Matrix(17,-10,46,-27) Matrix(37,-216,6,-35) -> Matrix(9,-4,16,-7) 1/2 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.