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 -5/6 -7/9 -13/18 -2/3 -35/54 -11/18 -17/30 -5/9 -1/2 -17/36 -7/15 -11/24 -65/144 -4/9 -61/144 -5/12 -59/144 -7/18 -41/108 -11/30 -13/36 -1/3 -17/54 -11/36 -3/10 -7/24 -5/18 -109/396 -7/26 -29/108 -4/15 -9/34 -19/72 -1/4 -7/30 -5/22 -2/9 -7/32 -13/60 -31/144 -3/14 -5/24 -3/16 -5/28 -1/6 -5/32 -3/20 -1/8 -1/9 0/1 1/8 1/7 3/20 2/13 1/6 3/17 5/28 2/11 3/16 1/5 3/14 13/60 2/9 5/22 3/13 4/17 1/4 4/15 7/26 3/11 5/18 2/7 8/27 3/10 17/54 1/3 11/30 13/34 7/18 2/5 5/12 4/9 11/24 7/15 1/2 5/9 11/18 17/27 35/54 2/3 13/18 7/9 5/6 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/2 -7/8 2/3 -6/7 1/0 -17/20 1/1 -11/13 1/2 -5/6 1/2 -19/23 1/2 -14/17 11/16 -23/28 1/1 -32/39 3/4 -9/11 1/2 -13/16 2/3 -30/37 3/4 -17/21 5/6 -4/5 1/0 -15/19 5/2 -11/14 0/1 1/1 -51/65 1/6 -40/51 1/4 -29/37 1/2 -47/60 1/1 -18/23 1/0 -25/32 0/1 -7/9 1/2 -17/22 2/3 1/1 -27/35 1/2 -10/13 3/4 -13/17 9/10 -3/4 1/1 -14/19 7/8 -11/15 3/2 -30/41 3/4 -19/26 1/1 4/3 -27/37 3/2 -8/11 1/0 -13/18 1/0 -18/25 1/0 -41/57 -1/2 -23/32 0/1 -5/7 1/2 -27/38 0/1 1/1 -22/31 3/4 -17/24 1/1 -12/17 7/4 -31/44 3/1 -50/71 1/0 -19/27 1/0 -26/37 1/0 -33/47 -1/2 -7/10 0/1 1/1 -9/13 3/2 -11/16 2/1 -24/35 1/0 -37/54 1/0 -13/19 -3/2 -2/3 1/0 -15/23 1/2 -13/20 1/1 -24/37 1/0 -35/54 1/0 -11/17 -5/2 -9/14 -1/1 0/1 -7/11 1/2 -26/41 1/4 -45/71 1/2 -19/30 1/2 -12/19 5/4 -17/27 1/0 -5/8 0/1 -18/29 3/4 -31/50 1/1 2/1 -13/21 1/2 -34/55 11/12 -21/34 1/1 4/3 -29/47 3/2 -37/60 1/1 -8/13 1/0 -11/18 1/0 -14/23 1/0 -17/28 -1/1 -20/33 1/0 -3/5 -1/2 -13/22 -1/1 0/1 -36/61 -3/4 -23/39 -1/2 -10/17 -3/8 -7/12 0/1 -11/19 3/10 -15/26 0/1 1/1 -34/59 1/4 -19/33 1/2 -4/7 1/0 -21/37 1/2 -17/30 1/2 -13/23 1/2 -9/16 0/1 -14/25 1/0 -19/34 1/1 2/1 -5/9 1/0 -21/38 -1/1 0/1 -16/29 1/0 -11/20 -1/1 -28/51 -1/4 -45/82 -1/5 0/1 -17/31 1/2 -6/11 1/0 -19/35 -1/2 -13/24 0/1 -7/13 -1/2 -8/15 -1/4 -9/17 -1/14 -1/2 0/1 1/1 -9/19 -1/14 -17/36 0/1 -8/17 1/16 -7/15 1/6 -20/43 1/8 -13/28 1/5 -6/13 1/4 -17/37 1/2 -11/24 0/1 -5/11 1/2 -14/31 1/0 -65/144 0/1 -51/113 1/14 -37/82 0/1 1/7 -23/51 1/6 -9/20 1/3 -13/29 1/2 -4/9 1/2 -19/43 1/2 -15/34 2/3 1/1 -11/25 1/2 -7/16 0/1 -10/23 1/0 -13/30 1/0 -16/37 1/0 -19/44 -1/1 -3/7 1/2 -17/40 0/1 -31/73 1/2 -14/33 1/0 -25/59 -1/2 -61/144 0/1 -36/85 1/4 -11/26 0/1 1/1 -19/45 1/0 -8/19 -3/4 -5/12 0/1 -7/17 3/14 -16/39 1/4 -25/61 3/10 -59/144 1/3 -34/83 3/8 -9/22 0/1 1/3 -11/27 1/2 -13/32 0/1 -15/37 1/2 -2/5 1/4 -7/18 1/2 -12/31 7/12 -41/106 3/5 2/3 -29/75 1/2 -17/44 3/5 -39/101 9/14 -22/57 5/8 -5/13 1/2 -23/60 1/1 -18/47 3/4 -13/34 4/5 1/1 -8/21 1/0 -27/71 1/2 -19/50 2/3 1/1 -30/79 7/8 -41/108 1/1 -11/29 3/2 -3/8 0/1 -13/35 1/2 -10/27 1/2 -27/73 1/2 -17/46 3/5 2/3 -7/19 5/6 -18/49 1/0 -11/30 1/0 -26/71 1/0 -15/41 -1/2 -4/11 1/0 -13/36 0/1 -9/25 1/6 -5/14 0/1 1/3 -6/17 5/12 -19/54 1/2 -13/37 1/2 -20/57 5/8 -7/20 1/1 -1/3 1/2 -6/19 3/8 -17/54 1/2 -11/35 1/2 -5/16 2/3 -4/13 3/4 -11/36 1/1 -7/23 3/2 -3/10 0/1 1/1 -17/57 1/2 -14/47 1/4 -25/84 1/3 -11/37 1/2 -8/27 1/2 -21/71 1/2 -34/115 9/16 -13/44 3/5 -5/17 7/10 -12/41 3/4 -7/24 1/1 -9/31 3/2 -20/69 1/0 -31/107 1/2 -11/38 0/1 1/1 -2/7 1/0 -5/18 1/2 -8/29 5/8 -19/69 1/2 -49/178 3/5 2/3 -79/287 1/2 -109/396 3/5 -30/109 5/8 -11/40 2/3 -14/51 3/4 -17/62 2/3 5/7 -3/11 1/2 -13/48 2/3 -10/37 3/4 -17/63 3/4 -7/26 4/5 1/1 -18/67 11/12 -29/108 1/1 -11/41 3/2 -4/15 3/4 -9/34 8/9 1/1 -14/53 23/24 -19/72 1/1 -5/19 7/6 -1/4 1/1 -4/17 9/8 -7/30 3/2 -3/13 3/2 -11/48 2/1 -8/35 1/0 -21/92 -1/1 -13/57 1/2 -5/22 1/1 2/1 -7/31 3/2 -2/9 1/0 -9/41 -1/2 -16/73 1/0 -7/32 0/1 -19/87 -1/2 -12/55 1/8 -5/23 1/2 -13/60 1/1 -21/97 3/2 -8/37 1/0 -11/51 -1/2 -14/65 -1/4 -31/144 0/1 -17/79 1/6 -3/14 0/1 1/1 -4/19 5/8 -5/24 1/1 -1/5 1/2 -4/21 5/4 -7/37 3/2 -3/16 2/1 -2/11 1/0 -7/39 3/2 -5/28 1/1 -3/17 11/6 -1/6 1/0 -3/19 -1/6 -8/51 1/4 -5/32 0/1 -2/13 1/0 -5/33 1/2 -3/20 1/1 -1/7 1/2 -1/8 2/1 -1/9 1/0 0/1 1/0 1/8 -2/1 1/7 -1/2 3/20 -1/1 2/13 1/0 1/6 1/0 4/23 1/0 3/17 -11/6 5/28 -1/1 7/39 -3/2 2/11 1/0 3/16 -2/1 7/37 -3/2 4/21 -5/4 1/5 -1/2 4/19 -5/8 3/14 -1/1 0/1 14/65 1/4 11/51 1/2 8/37 1/0 13/60 -1/1 5/23 -1/2 7/32 0/1 2/9 1/0 5/22 -2/1 -1/1 8/35 1/0 3/13 -3/2 4/17 -9/8 1/4 -1/1 5/19 -7/6 4/15 -3/4 11/41 -3/2 7/26 -1/1 -4/5 10/37 -3/4 3/11 -1/2 5/18 -1/2 7/25 -1/2 16/57 -1/4 9/32 0/1 2/7 1/0 11/38 -1/1 0/1 9/31 -3/2 7/24 -1/1 5/17 -7/10 13/44 -3/5 21/71 -1/2 8/27 -1/2 11/37 -1/2 14/47 -1/4 3/10 -1/1 0/1 4/13 -3/4 5/16 -2/3 11/35 -1/2 17/54 -1/2 6/19 -3/8 1/3 -1/2 8/23 1/0 7/20 -1/1 13/37 -1/2 19/54 -1/2 6/17 -5/12 5/14 -1/3 0/1 4/11 1/0 15/41 1/2 26/71 1/0 11/30 1/0 7/19 -5/6 10/27 -1/2 3/8 0/1 11/29 -3/2 19/50 -1/1 -2/3 8/21 1/0 21/55 -11/10 13/34 -1/1 -4/5 18/47 -3/4 23/60 -1/1 5/13 -1/2 7/18 -1/2 9/23 -1/2 11/28 -1/3 13/33 -1/2 2/5 -1/4 9/22 -1/3 0/1 25/61 -3/10 16/39 -1/4 7/17 -3/14 5/12 0/1 8/19 3/4 11/26 -1/1 0/1 25/59 1/2 14/33 1/0 3/7 -1/2 16/37 1/0 13/30 1/0 10/23 1/0 7/16 0/1 11/25 -1/2 15/34 -1/1 -2/3 4/9 -1/2 17/38 -1/3 0/1 13/29 -1/2 9/20 -1/3 23/51 -1/6 37/82 -1/7 0/1 14/31 1/0 5/11 -1/2 16/35 -1/4 11/24 0/1 6/13 -1/4 7/15 -1/6 8/17 -1/16 1/2 -1/1 0/1 10/19 -1/16 19/36 0/1 9/17 1/14 8/15 1/4 23/43 1/6 15/28 1/3 7/13 1/2 20/37 1/0 13/24 0/1 6/11 1/0 17/31 -1/2 79/144 0/1 62/113 1/12 45/82 0/1 1/5 28/51 1/4 11/20 1/1 16/29 1/0 5/9 1/0 24/43 1/0 19/34 -2/1 -1/1 14/25 1/0 9/16 0/1 13/23 -1/2 17/30 -1/2 21/37 -1/2 25/44 -1/3 4/7 1/0 23/40 0/1 42/73 1/0 19/33 -1/2 34/59 -1/4 83/144 0/1 49/85 1/2 15/26 -1/1 0/1 26/45 -1/2 11/19 -3/10 7/12 0/1 10/17 3/8 23/39 1/2 36/61 3/4 85/144 1/1 49/83 3/2 13/22 0/1 1/1 16/27 1/0 19/32 0/1 22/37 1/0 3/5 1/2 11/18 1/0 19/31 -7/2 65/106 -3/1 -2/1 46/75 1/0 27/44 -3/1 62/101 -9/4 35/57 -5/2 8/13 1/0 37/60 -1/1 29/47 -3/2 21/34 -4/3 -1/1 13/21 -1/2 44/71 1/0 31/50 -2/1 -1/1 49/79 -7/6 67/108 -1/1 18/29 -3/4 5/8 0/1 22/35 1/0 17/27 1/0 46/73 1/0 29/46 -3/1 -2/1 12/19 -5/4 31/49 -1/2 19/30 -1/2 45/71 -1/2 26/41 -1/4 7/11 -1/2 23/36 0/1 16/25 1/4 9/14 0/1 1/1 11/17 5/2 35/54 1/0 24/37 1/0 37/57 -5/2 13/20 -1/1 2/3 1/0 13/19 3/2 37/54 1/0 24/35 1/0 11/16 -2/1 9/13 -3/2 25/36 -1/1 16/23 -3/4 7/10 -1/1 0/1 40/57 1/0 33/47 1/2 59/84 1/1 26/37 1/0 19/27 1/0 50/71 1/0 81/115 -9/2 31/44 -3/1 12/17 -7/4 29/41 -3/2 17/24 -1/1 22/31 -3/4 49/69 -1/2 76/107 1/0 27/38 -1/1 0/1 5/7 -1/2 13/18 1/0 21/29 -5/2 50/69 1/0 129/178 -3/1 -2/1 208/287 1/0 287/396 -3/1 79/109 -5/2 29/40 -2/1 37/51 -3/2 45/62 -2/1 -5/3 8/11 1/0 35/48 -2/1 27/37 -3/2 46/63 -3/2 19/26 -4/3 -1/1 49/67 -11/10 79/108 -1/1 30/41 -3/4 11/15 -3/2 25/34 -8/7 -1/1 39/53 -23/22 53/72 -1/1 14/19 -7/8 3/4 -1/1 13/17 -9/10 23/30 -3/4 10/13 -3/4 37/48 -2/3 27/35 -1/2 71/92 -1/3 44/57 1/0 17/22 -1/1 -2/3 24/31 -3/4 7/9 -1/2 32/41 -1/4 57/73 -1/2 25/32 0/1 68/87 -1/4 43/55 1/6 18/23 1/0 47/60 -1/1 76/97 -3/4 29/37 -1/2 40/51 -1/4 51/65 -1/6 113/144 0/1 62/79 1/4 11/14 -1/1 0/1 15/19 -5/2 19/24 -1/1 4/5 1/0 17/21 -5/6 30/37 -3/4 13/16 -2/3 9/11 -1/2 32/39 -3/4 23/28 -1/1 14/17 -11/16 5/6 -1/2 16/19 -1/8 43/51 1/2 27/32 0/1 11/13 -1/2 28/33 1/0 17/20 -1/1 6/7 1/0 7/8 -2/3 8/9 -1/2 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(107,94,-288,-253) (-1/1,-7/8) -> (-3/8,-13/35) Hyperbolic Matrix(179,156,288,251) (-7/8,-6/7) -> (18/29,5/8) Hyperbolic Matrix(397,338,720,613) (-6/7,-17/20) -> (11/20,16/29) Hyperbolic Matrix(469,398,-720,-611) (-17/20,-11/13) -> (-15/23,-13/20) Hyperbolic Matrix(179,150,-216,-181) (-11/13,-5/6) -> (-5/6,-19/23) Parabolic Matrix(361,298,-1656,-1367) (-19/23,-14/17) -> (-12/55,-5/23) Hyperbolic Matrix(863,710,1224,1007) (-14/17,-23/28) -> (31/44,12/17) Hyperbolic Matrix(2341,1922,3816,3133) (-23/28,-32/39) -> (46/75,27/44) Hyperbolic Matrix(1151,944,2808,2303) (-32/39,-9/11) -> (25/61,16/39) Hyperbolic Matrix(253,206,576,469) (-9/11,-13/16) -> (7/16,11/25) Hyperbolic Matrix(791,642,1152,935) (-13/16,-30/37) -> (24/35,11/16) Hyperbolic Matrix(575,466,2664,2159) (-30/37,-17/21) -> (11/51,8/37) Hyperbolic Matrix(685,554,936,757) (-17/21,-4/5) -> (30/41,11/15) Hyperbolic Matrix(253,200,-864,-683) (-4/5,-15/19) -> (-5/17,-12/41) Hyperbolic Matrix(325,256,504,397) (-15/19,-11/14) -> (9/14,11/17) Hyperbolic Matrix(433,340,-2016,-1583) (-11/14,-51/65) -> (-17/79,-3/14) Hyperbolic Matrix(1693,1328,3168,2485) (-51/65,-40/51) -> (8/15,23/43) Hyperbolic Matrix(505,396,2664,2089) (-40/51,-29/37) -> (7/37,4/21) Hyperbolic Matrix(1585,1242,-5328,-4175) (-29/37,-47/60) -> (-25/84,-11/37) Hyperbolic Matrix(1331,1042,2160,1691) (-47/60,-18/23) -> (8/13,37/60) Hyperbolic Matrix(179,140,-1152,-901) (-18/23,-25/32) -> (-5/32,-2/13) Hyperbolic Matrix(469,366,-1152,-899) (-25/32,-7/9) -> (-11/27,-13/32) Hyperbolic Matrix(323,250,-792,-613) (-7/9,-17/22) -> (-9/22,-11/27) Hyperbolic 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(397,304,-1080,-827) (-10/13,-13/17) -> (-7/19,-18/49) Hyperbolic Matrix(37,28,144,109) (-13/17,-3/4) -> (1/4,5/19) Hyperbolic Matrix(35,26,144,107) (-3/4,-14/19) -> (4/17,1/4) Hyperbolic Matrix(757,556,-1224,-899) (-14/19,-11/15) -> (-13/21,-34/55) Hyperbolic Matrix(757,554,936,685) (-11/15,-30/41) -> (4/5,17/21) 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(431,314,-792,-577) (-27/37,-8/11) -> (-6/11,-19/35) Hyperbolic Matrix(467,338,-648,-469) (-8/11,-13/18) -> (-13/18,-18/25) Parabolic Matrix(1223,880,-4104,-2953) (-18/25,-41/57) -> (-17/57,-14/47) Hyperbolic Matrix(1007,724,-4608,-3313) (-41/57,-23/32) -> (-7/32,-19/87) Hyperbolic Matrix(215,154,-504,-361) (-23/32,-5/7) -> (-3/7,-17/40) Hyperbolic Matrix(613,436,1368,973) (-5/7,-27/38) -> (17/38,13/29) Hyperbolic Matrix(1727,1226,-4464,-3169) (-27/38,-22/31) -> (-12/31,-41/106) Hyperbolic Matrix(685,486,864,613) (-22/31,-17/24) -> (19/24,4/5) Hyperbolic Matrix(181,128,-864,-611) (-17/24,-12/17) -> (-4/19,-5/24) Hyperbolic Matrix(1007,710,1224,863) (-12/17,-31/44) -> (23/28,14/17) Hyperbolic Matrix(2053,1446,-4752,-3347) (-31/44,-50/71) -> (-16/37,-19/44) Hyperbolic Matrix(2449,1724,3888,2737) (-50/71,-19/27) -> (17/27,46/73) Hyperbolic Matrix(1223,860,1944,1367) (-19/27,-26/37) -> (22/35,17/27) Hyperbolic Matrix(1153,810,-5328,-3743) (-26/37,-33/47) -> (-21/97,-8/37) Hyperbolic Matrix(829,582,-3024,-2123) (-33/47,-7/10) -> (-17/62,-3/11) 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(935,642,1152,791) (-11/16,-24/35) -> (30/37,13/16) Hyperbolic Matrix(2521,1728,3888,2665) (-24/35,-37/54) -> (35/54,24/37) Hyperbolic Matrix(1259,862,1944,1331) (-37/54,-13/19) -> (11/17,35/54) Hyperbolic Matrix(325,222,792,541) (-13/19,-2/3) -> (16/39,7/17) Hyperbolic Matrix(397,260,936,613) (-2/3,-15/23) -> (25/59,14/33) Hyperbolic Matrix(937,608,-4104,-2663) (-13/20,-24/37) -> (-8/35,-21/92) Hyperbolic Matrix(2665,1728,3888,2521) (-24/37,-35/54) -> (37/54,24/35) Hyperbolic Matrix(1331,862,1944,1259) (-35/54,-11/17) -> (13/19,37/54) 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(359,228,792,503) (-7/11,-26/41) -> (14/31,5/11) Hyperbolic Matrix(757,480,-1872,-1187) (-26/41,-45/71) -> (-15/37,-2/5) Hyperbolic Matrix(1837,1164,3240,2053) (-45/71,-19/30) -> (17/30,21/37) Hyperbolic Matrix(253,160,-1080,-683) (-19/30,-12/19) -> (-4/17,-7/30) Hyperbolic Matrix(577,364,-1368,-863) (-12/19,-17/27) -> (-19/45,-8/19) Hyperbolic Matrix(35,22,-288,-181) (-17/27,-5/8) -> (-1/8,-1/9) 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(755,468,-3312,-2053) (-31/50,-13/21) -> (-13/57,-5/22) Hyperbolic Matrix(971,600,-3672,-2269) (-34/55,-21/34) -> (-9/34,-14/53) Hyperbolic Matrix(1079,666,2448,1511) (-21/34,-29/47) -> (11/25,15/34) Hyperbolic Matrix(1871,1154,-8640,-5329) (-29/47,-37/60) -> (-13/60,-21/97) Hyperbolic Matrix(1691,1042,2160,1331) (-37/60,-8/13) -> (18/23,47/60) Hyperbolic Matrix(395,242,-648,-397) (-8/13,-11/18) -> (-11/18,-14/23) Parabolic Matrix(467,284,-1008,-613) (-14/23,-17/28) -> (-13/28,-6/13) Hyperbolic Matrix(1655,1004,2016,1223) (-17/28,-20/33) -> (32/39,23/28) Hyperbolic Matrix(397,240,-1368,-827) (-20/33,-3/5) -> (-9/31,-20/69) Hyperbolic Matrix(179,106,-792,-469) (-3/5,-13/22) -> (-5/22,-7/31) Hyperbolic Matrix(1297,766,-3168,-1871) (-13/22,-36/61) -> (-34/83,-9/22) Hyperbolic Matrix(505,298,2808,1657) (-36/61,-23/39) -> (7/39,2/11) Hyperbolic Matrix(251,148,792,467) (-23/39,-10/17) -> (6/19,1/3) Hyperbolic Matrix(181,106,432,253) (-10/17,-7/12) -> (5/12,8/19) 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(1585,914,-3744,-2159) (-15/26,-34/59) -> (-36/85,-11/26) Hyperbolic Matrix(323,186,936,539) (-34/59,-19/33) -> (1/3,8/23) Hyperbolic Matrix(397,228,-1440,-827) (-19/33,-4/7) -> (-8/29,-19/69) Hyperbolic Matrix(1405,798,-4752,-2699) (-4/7,-21/37) -> (-21/71,-34/115) Hyperbolic Matrix(2053,1164,3240,1837) (-21/37,-17/30) -> (19/30,45/71) Hyperbolic Matrix(1367,774,2160,1223) (-17/30,-13/23) -> (31/49,19/30) Hyperbolic Matrix(397,224,576,325) (-13/23,-9/16) -> (11/16,9/13) Hyperbolic Matrix(107,60,576,323) (-9/16,-14/25) -> (2/11,3/16) Hyperbolic Matrix(937,524,2448,1369) (-14/25,-19/34) -> (13/34,18/47) Hyperbolic Matrix(359,200,-648,-361) (-19/34,-5/9) -> (-5/9,-21/38) Parabolic Matrix(395,218,1368,755) (-21/38,-16/29) -> (2/7,11/38) Hyperbolic Matrix(613,338,720,397) (-16/29,-11/20) -> (17/20,6/7) Hyperbolic Matrix(757,416,-2160,-1187) (-11/20,-28/51) -> (-20/57,-7/20) Hyperbolic Matrix(3637,1996,5184,2845) (-28/51,-45/82) -> (7/10,40/57) Hyperbolic Matrix(5329,2924,-11808,-6479) (-45/82,-17/31) -> (-51/113,-37/82) Hyperbolic Matrix(289,158,792,433) (-17/31,-6/11) -> (4/11,15/41) Hyperbolic Matrix(1943,1054,2520,1367) (-19/35,-13/24) -> (37/48,27/35) Hyperbolic Matrix(215,116,-936,-505) (-13/24,-7/13) -> (-3/13,-11/48) Hyperbolic Matrix(361,194,-936,-503) (-7/13,-8/15) -> (-22/57,-5/13) Hyperbolic Matrix(181,96,-1152,-611) (-8/15,-9/17) -> (-3/19,-8/51) Hyperbolic Matrix(35,18,-72,-37) (-9/17,-1/2) -> (-1/2,-9/19) Parabolic Matrix(685,324,1296,613) (-9/19,-17/36) -> (19/36,9/17) Hyperbolic Matrix(683,322,1296,611) (-17/36,-8/17) -> (10/19,19/36) Hyperbolic Matrix(503,236,-2304,-1081) (-8/17,-7/15) -> (-19/87,-12/55) Hyperbolic Matrix(683,318,3168,1475) (-7/15,-20/43) -> (14/65,11/51) Hyperbolic Matrix(1187,552,2088,971) (-20/43,-13/28) -> (25/44,4/7) Hyperbolic Matrix(1943,892,2664,1223) (-17/37,-11/24) -> (35/48,27/37) Hyperbolic Matrix(215,98,-792,-361) (-11/24,-5/11) -> (-3/11,-13/48) Hyperbolic Matrix(503,228,792,359) (-5/11,-14/31) -> (26/41,7/11) Hyperbolic Matrix(11377,5136,20736,9361) (-14/31,-65/144) -> (79/144,62/113) Hyperbolic Matrix(11375,5134,20736,9359) (-65/144,-51/113) -> (17/31,79/144) Hyperbolic Matrix(5329,2404,7344,3313) (-37/82,-23/51) -> (37/51,45/62) Hyperbolic Matrix(1331,600,-5832,-2629) (-23/51,-9/20) -> (-21/92,-13/57) Hyperbolic Matrix(107,48,720,323) (-9/20,-13/29) -> (1/7,3/20) Hyperbolic Matrix(287,128,-648,-289) (-13/29,-4/9) -> (-4/9,-19/43) Parabolic Matrix(1331,588,1872,827) (-19/43,-15/34) -> (27/38,5/7) Hyperbolic Matrix(1511,666,2448,1079) (-15/34,-11/25) -> (29/47,21/34) Hyperbolic Matrix(469,206,576,253) (-11/25,-7/16) -> (13/16,9/11) Hyperbolic Matrix(179,78,576,251) (-7/16,-10/23) -> (4/13,5/16) Hyperbolic Matrix(829,360,1080,469) (-10/23,-13/30) -> (23/30,10/13) Hyperbolic Matrix(1187,514,3240,1403) (-13/30,-16/37) -> (26/71,11/30) Hyperbolic Matrix(1117,482,2088,901) (-19/44,-3/7) -> (23/43,15/28) Hyperbolic Matrix(4105,1744,5256,2233) (-17/40,-31/73) -> (57/73,25/32) Hyperbolic Matrix(2483,1054,-8568,-3637) (-31/73,-14/33) -> (-20/69,-31/107) Hyperbolic Matrix(2015,854,2376,1007) (-14/33,-25/59) -> (11/13,28/33) Hyperbolic Matrix(11953,5064,20736,8785) (-25/59,-61/144) -> (83/144,49/85) Hyperbolic Matrix(11951,5062,20736,8783) (-61/144,-36/85) -> (34/59,83/144) Hyperbolic Matrix(757,320,-2808,-1187) (-11/26,-19/45) -> (-17/63,-7/26) Hyperbolic Matrix(253,106,432,181) (-8/19,-5/12) -> (7/12,10/17) Hyperbolic Matrix(251,104,432,179) (-5/12,-7/17) -> (11/19,7/12) Hyperbolic Matrix(541,222,792,325) (-7/17,-16/39) -> (2/3,13/19) Hyperbolic Matrix(2303,944,2808,1151) (-16/39,-25/61) -> (9/11,32/39) Hyperbolic Matrix(12241,5016,20736,8497) (-25/61,-59/144) -> (85/144,49/83) Hyperbolic Matrix(12239,5014,20736,8495) (-59/144,-34/83) -> (36/61,85/144) Hyperbolic Matrix(3601,1462,4968,2017) (-13/32,-15/37) -> (79/109,29/40) Hyperbolic Matrix(251,98,-648,-253) (-2/5,-7/18) -> (-7/18,-12/31) Parabolic Matrix(5689,2200,-20664,-7991) (-41/106,-29/75) -> (-19/69,-49/178) Hyperbolic Matrix(683,264,3816,1475) (-29/75,-17/44) -> (5/28,7/39) Hyperbolic Matrix(6695,2586,9504,3671) (-17/44,-39/101) -> (81/115,31/44) Hyperbolic Matrix(6947,2682,8856,3419) (-39/101,-22/57) -> (40/51,51/65) Hyperbolic Matrix(469,180,2160,829) (-5/13,-23/60) -> (13/60,5/23) Hyperbolic Matrix(2015,772,-6768,-2593) (-23/60,-18/47) -> (-14/47,-25/84) Hyperbolic Matrix(1369,524,2448,937) (-18/47,-13/34) -> (19/34,14/25) Hyperbolic Matrix(325,124,-1224,-467) (-13/34,-8/21) -> (-4/15,-9/34) Hyperbolic Matrix(1693,644,-4824,-1835) (-8/21,-27/71) -> (-13/37,-20/57) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(37,14,288,109) (-11/29,-3/8) -> (1/8,1/7) Hyperbolic Matrix(577,214,1944,721) (-13/35,-10/27) -> (8/27,11/37) Hyperbolic Matrix(1151,426,3888,1439) (-10/27,-27/73) -> (21/71,8/27) Hyperbolic Matrix(937,344,2160,793) (-18/49,-11/30) -> (13/30,10/23) Hyperbolic Matrix(1403,514,3240,1187) (-11/30,-26/71) -> (16/37,13/30) Hyperbolic Matrix(1295,474,-5904,-2161) (-26/71,-15/41) -> (-9/41,-16/73) Hyperbolic Matrix(433,158,792,289) (-15/41,-4/11) -> (6/11,17/31) Hyperbolic Matrix(829,300,1296,469) (-4/11,-13/36) -> (23/36,16/25) Hyperbolic Matrix(827,298,1296,467) (-13/36,-9/25) -> (7/11,23/36) Hyperbolic Matrix(107,38,504,179) (-5/14,-6/17) -> (4/19,3/14) Hyperbolic Matrix(613,216,1944,685) (-6/17,-19/54) -> (17/54,6/19) Hyperbolic Matrix(1223,430,3888,1367) (-19/54,-13/37) -> (11/35,17/54) Hyperbolic Matrix(109,38,-720,-251) (-7/20,-1/3) -> (-5/33,-3/20) Hyperbolic Matrix(467,148,792,251) (-1/3,-6/19) -> (10/17,23/39) Hyperbolic Matrix(685,216,1944,613) (-6/19,-17/54) -> (19/54,6/17) Hyperbolic Matrix(1367,430,3888,1223) (-17/54,-11/35) -> (13/37,19/54) Hyperbolic Matrix(217,68,1152,361) (-11/35,-5/16) -> (3/16,7/37) Hyperbolic Matrix(251,78,576,179) (-5/16,-4/13) -> (10/23,7/16) Hyperbolic Matrix(901,276,1296,397) (-4/13,-11/36) -> (25/36,16/23) Hyperbolic Matrix(899,274,1296,395) (-11/36,-7/23) -> (9/13,25/36) Hyperbolic Matrix(2339,698,5184,1547) (-3/10,-17/57) -> (23/51,37/82) Hyperbolic Matrix(323,96,360,107) (-11/37,-8/27) -> (8/9,1/1) Hyperbolic Matrix(3995,1182,5472,1619) (-8/27,-21/71) -> (27/37,46/63) Hyperbolic Matrix(5833,1724,9504,2809) (-34/115,-13/44) -> (27/44,62/101) Hyperbolic Matrix(217,64,1224,361) (-13/44,-5/17) -> (3/17,5/28) Hyperbolic Matrix(1225,358,1728,505) (-12/41,-7/24) -> (17/24,22/31) Hyperbolic Matrix(1223,356,1728,503) (-7/24,-9/31) -> (29/41,17/24) Hyperbolic Matrix(8245,2388,-29952,-8675) (-31/107,-11/38) -> (-49/178,-79/287) Hyperbolic Matrix(1045,302,1872,541) (-11/38,-2/7) -> (24/43,19/34) Hyperbolic Matrix(179,50,-648,-181) (-2/7,-5/18) -> (-5/18,-8/29) Parabolic Matrix(113653,31284,156816,43165) (-79/287,-109/396) -> (287/396,79/109) Hyperbolic Matrix(113651,31282,156816,43163) (-109/396,-30/109) -> (208/287,287/396) Hyperbolic Matrix(2951,812,4968,1367) (-30/109,-11/40) -> (19/32,22/37) Hyperbolic Matrix(575,158,-3672,-1009) (-11/40,-14/51) -> (-8/51,-5/32) Hyperbolic Matrix(4031,1106,7344,2015) (-14/51,-17/62) -> (45/82,28/51) Hyperbolic Matrix(1441,390,2664,721) (-13/48,-10/37) -> (20/37,13/24) Hyperbolic Matrix(3853,1040,5472,1477) (-10/37,-17/63) -> (19/27,50/71) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) 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(3815,1006,5184,1367) (-19/72,-5/19) -> (39/53,53/72) Hyperbolic Matrix(109,28,144,37) (-5/19,-1/4) -> (3/4,13/17) Hyperbolic Matrix(107,26,144,35) (-1/4,-4/17) -> (14/19,3/4) Hyperbolic Matrix(611,142,1080,251) (-7/30,-3/13) -> (13/23,17/30) Hyperbolic Matrix(1153,264,2520,577) (-11/48,-8/35) -> (16/35,11/24) Hyperbolic Matrix(143,32,-648,-145) (-7/31,-2/9) -> (-2/9,-9/41) Parabolic Matrix(3023,662,5256,1151) (-16/73,-7/32) -> (23/40,42/73) Hyperbolic Matrix(829,180,2160,469) (-5/23,-13/60) -> (23/60,5/13) Hyperbolic Matrix(2159,466,2664,575) (-8/37,-11/51) -> (17/21,30/37) Hyperbolic Matrix(5437,1172,8856,1909) (-11/51,-14/65) -> (62/101,35/57) Hyperbolic Matrix(16273,3504,20736,4465) (-14/65,-31/144) -> (113/144,62/79) Hyperbolic Matrix(16271,3502,20736,4463) (-31/144,-17/79) -> (51/65,113/144) Hyperbolic Matrix(179,38,504,107) (-3/14,-4/19) -> (6/17,5/14) Hyperbolic Matrix(251,52,864,179) (-5/24,-1/5) -> (9/31,7/24) 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(361,68,1152,217) (-7/37,-3/16) -> (5/16,11/35) Hyperbolic Matrix(323,60,576,107) (-3/16,-2/11) -> (14/25,9/16) Hyperbolic Matrix(1657,298,2808,505) (-2/11,-7/39) -> (23/39,36/61) Hyperbolic Matrix(793,142,2016,361) (-7/39,-5/28) -> (11/28,13/33) Hyperbolic Matrix(361,64,1224,217) (-5/28,-3/17) -> (5/17,13/44) Hyperbolic Matrix(35,6,-216,-37) (-3/17,-1/6) -> (-1/6,-3/19) Parabolic Matrix(1369,208,2376,361) (-2/13,-5/33) -> (19/33,34/59) Hyperbolic Matrix(323,48,720,107) (-3/20,-1/7) -> (13/29,9/20) Hyperbolic Matrix(109,14,288,37) (-1/7,-1/8) -> (3/8,11/29) Hyperbolic Matrix(253,26,360,37) (-1/9,0/1) -> (26/37,19/27) Hyperbolic Matrix(181,-22,288,-35) (0/1,1/8) -> (5/8,22/35) Hyperbolic Matrix(251,-38,720,-109) (3/20,2/13) -> (8/23,7/20) Hyperbolic Matrix(37,-6,216,-35) (2/13,1/6) -> (1/6,4/23) Parabolic Matrix(1295,-226,1656,-289) (4/23,3/17) -> (43/55,18/23) Hyperbolic Matrix(611,-128,864,-181) (1/5,4/19) -> (12/17,29/41) Hyperbolic Matrix(1583,-340,2016,-433) (3/14,14/65) -> (62/79,11/14) Hyperbolic Matrix(3743,-810,5328,-1153) (8/37,13/60) -> (59/84,26/37) Hyperbolic Matrix(973,-212,1152,-251) (5/23,7/32) -> (27/32,11/13) Hyperbolic Matrix(683,-150,1152,-253) (7/32,2/9) -> (16/27,19/32) Hyperbolic Matrix(469,-106,792,-179) (2/9,5/22) -> (13/22,16/27) Hyperbolic 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(683,-160,1080,-253) (3/13,4/17) -> (12/19,31/49) 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(2269,-612,3600,-971) (7/26,10/37) -> (46/73,29/46) Hyperbolic Matrix(361,-98,792,-215) (10/37,3/11) -> (5/11,16/35) Hyperbolic Matrix(181,-50,648,-179) (3/11,5/18) -> (5/18,7/25) Parabolic Matrix(2881,-808,4104,-1151) (7/25,16/57) -> (40/57,33/47) Hyperbolic Matrix(3601,-1012,4608,-1295) (16/57,9/32) -> (25/32,68/87) Hyperbolic Matrix(289,-82,504,-143) (9/32,2/7) -> (4/7,23/40) Hyperbolic Matrix(2737,-794,4464,-1295) (11/38,9/31) -> (19/31,65/106) Hyperbolic Matrix(683,-200,864,-253) (7/24,5/17) -> (15/19,19/24) Hyperbolic Matrix(2699,-798,4752,-1405) (13/44,21/71) -> (21/37,25/44) Hyperbolic Matrix(4175,-1242,5328,-1585) (11/37,14/47) -> (76/97,29/37) Hyperbolic Matrix(2195,-654,3024,-901) (14/47,3/10) -> (45/62,8/11) Hyperbolic Matrix(251,-76,360,-109) (3/10,4/13) -> (16/23,7/10) Hyperbolic Matrix(3167,-1112,4104,-1441) (7/20,13/37) -> (27/35,71/92) Hyperbolic Matrix(323,-116,504,-181) (5/14,4/11) -> (16/25,9/14) Hyperbolic Matrix(1115,-408,1872,-685) (15/41,26/71) -> (22/37,3/5) Hyperbolic Matrix(827,-304,1080,-397) (11/30,7/19) -> (13/17,23/30) Hyperbolic Matrix(791,-292,1368,-505) (7/19,10/27) -> (26/45,11/19) Hyperbolic Matrix(253,-94,288,-107) (10/27,3/8) -> (7/8,8/9) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(2557,-972,3312,-1259) (19/50,8/21) -> (44/57,17/22) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(6769,-2594,8640,-3311) (18/47,23/60) -> (47/60,76/97) Hyperbolic Matrix(253,-98,648,-251) (5/13,7/18) -> (7/18,9/23) Parabolic Matrix(541,-212,1008,-395) (9/23,11/28) -> (15/28,7/13) Hyperbolic Matrix(971,-384,1368,-541) (13/33,2/5) -> (22/31,49/69) Hyperbolic Matrix(613,-250,792,-323) (2/5,9/22) -> (17/22,24/31) Hyperbolic Matrix(1871,-766,3168,-1297) (9/22,25/61) -> (49/83,13/22) Hyperbolic Matrix(863,-364,1368,-577) (8/19,11/26) -> (29/46,12/19) Hyperbolic Matrix(2159,-914,3744,-1585) (11/26,25/59) -> (49/85,15/26) Hyperbolic Matrix(1043,-444,1440,-613) (14/33,3/7) -> (21/29,50/69) Hyperbolic Matrix(3347,-1446,4752,-2053) (3/7,16/37) -> (50/71,81/115) Hyperbolic Matrix(289,-128,648,-287) (15/34,4/9) -> (4/9,17/38) Parabolic Matrix(1403,-632,2160,-973) (9/20,23/51) -> (37/57,13/20) Hyperbolic Matrix(6479,-2924,11808,-5329) (37/82,14/31) -> (62/113,45/82) Hyperbolic Matrix(721,-332,936,-431) (11/24,6/13) -> (10/13,37/48) Hyperbolic Matrix(575,-266,936,-433) (6/13,7/15) -> (35/57,8/13) Hyperbolic Matrix(971,-456,1152,-541) (7/15,8/17) -> (16/19,43/51) Hyperbolic Matrix(37,-18,72,-35) (8/17,1/2) -> (1/2,10/19) Parabolic Matrix(1801,-956,2304,-1223) (9/17,8/15) -> (68/87,43/55) Hyperbolic Matrix(577,-314,792,-431) (13/24,6/11) -> (8/11,35/48) Hyperbolic Matrix(4501,-2472,5832,-3203) (28/51,11/20) -> (71/92,44/57) Hyperbolic Matrix(361,-200,648,-359) (16/29,5/9) -> (5/9,24/43) Parabolic Matrix(6085,-3502,8568,-4931) (42/73,19/33) -> (49/69,76/107) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(397,-242,648,-395) (3/5,11/18) -> (11/18,19/31) Parabolic Matrix(14975,-9184,20664,-12673) (65/106,46/75) -> (50/69,129/178) Hyperbolic Matrix(4753,-2932,6768,-4175) (37/60,29/47) -> (33/47,59/84) Hyperbolic Matrix(899,-556,1224,-757) (21/34,13/21) -> (11/15,25/34) Hyperbolic Matrix(3131,-1940,4824,-2989) (13/21,44/71) -> (24/37,37/57) Hyperbolic Matrix(4609,-2922,5904,-3743) (45/71,26/41) -> (32/41,57/73) Hyperbolic Matrix(611,-398,720,-469) (13/20,2/3) -> (28/33,17/20) Hyperbolic Matrix(21707,-15420,29952,-21277) (76/107,27/38) -> (129/178,208/287) Hyperbolic Matrix(469,-338,648,-467) (5/7,13/18) -> (13/18,21/29) Parabolic Matrix(3097,-2246,3672,-2663) (29/40,37/51) -> (43/51,27/32) Hyperbolic Matrix(505,-392,648,-503) (24/31,7/9) -> (7/9,32/41) Parabolic Matrix(181,-150,216,-179) (14/17,5/6) -> (5/6,16/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(107,94,-288,-253) -> Matrix(3,-2,8,-5) Matrix(179,156,288,251) -> Matrix(3,-2,-4,3) Matrix(397,338,720,613) -> Matrix(1,0,0,1) Matrix(469,398,-720,-611) -> Matrix(1,0,0,1) Matrix(179,150,-216,-181) -> Matrix(5,-2,8,-3) Matrix(361,298,-1656,-1367) -> Matrix(3,-2,8,-5) Matrix(863,710,1224,1007) -> Matrix(11,-8,-4,3) Matrix(2341,1922,3816,3133) -> Matrix(11,-8,-4,3) Matrix(1151,944,2808,2303) -> Matrix(5,-4,-16,13) Matrix(253,206,576,469) -> Matrix(3,-2,-4,3) Matrix(791,642,1152,935) -> Matrix(11,-8,-4,3) Matrix(575,466,2664,2159) -> Matrix(5,-4,4,-3) Matrix(685,554,936,757) -> Matrix(3,-2,-4,3) Matrix(253,200,-864,-683) -> Matrix(3,-4,4,-5) Matrix(325,256,504,397) -> Matrix(1,0,0,1) Matrix(433,340,-2016,-1583) -> Matrix(1,0,0,1) Matrix(1693,1328,3168,2485) -> Matrix(1,0,0,1) Matrix(505,396,2664,2089) -> Matrix(11,-4,-8,3) Matrix(1585,1242,-5328,-4175) -> Matrix(3,-2,8,-5) Matrix(1331,1042,2160,1691) -> Matrix(1,-2,0,1) Matrix(179,140,-1152,-901) -> Matrix(1,0,0,1) Matrix(469,366,-1152,-899) -> Matrix(1,0,0,1) Matrix(323,250,-792,-613) -> Matrix(3,-2,8,-5) Matrix(1259,972,-3312,-2557) -> Matrix(1,0,0,1) Matrix(431,332,-936,-721) -> Matrix(3,-2,8,-5) Matrix(397,304,-1080,-827) -> Matrix(5,-4,4,-3) Matrix(37,28,144,109) -> Matrix(3,-2,-4,3) Matrix(35,26,144,107) -> Matrix(1,-2,0,1) Matrix(757,556,-1224,-899) -> Matrix(3,-4,4,-5) Matrix(757,554,936,685) -> Matrix(3,-2,-4,3) Matrix(755,552,-2808,-2053) -> Matrix(7,-8,8,-9) Matrix(1331,972,-3600,-2629) -> Matrix(7,-10,12,-17) Matrix(431,314,-792,-577) -> Matrix(1,-2,0,1) Matrix(467,338,-648,-469) -> Matrix(1,-2,0,1) Matrix(1223,880,-4104,-2953) -> Matrix(1,0,4,1) Matrix(1007,724,-4608,-3313) -> Matrix(1,0,0,1) Matrix(215,154,-504,-361) -> Matrix(1,0,0,1) Matrix(613,436,1368,973) -> Matrix(1,0,-4,1) Matrix(1727,1226,-4464,-3169) -> Matrix(5,-2,8,-3) Matrix(685,486,864,613) -> Matrix(3,-2,-4,3) Matrix(181,128,-864,-611) -> Matrix(3,-4,4,-5) Matrix(1007,710,1224,863) -> Matrix(3,-8,-4,11) Matrix(2053,1446,-4752,-3347) -> Matrix(1,-4,0,1) Matrix(2449,1724,3888,2737) -> Matrix(1,-8,0,1) Matrix(1223,860,1944,1367) -> Matrix(1,2,0,1) Matrix(1153,810,-5328,-3743) -> Matrix(1,2,0,1) Matrix(829,582,-3024,-2123) -> Matrix(3,2,4,3) Matrix(109,76,-360,-251) -> Matrix(1,0,0,1) Matrix(325,224,576,397) -> Matrix(1,-2,0,1) Matrix(935,642,1152,791) -> Matrix(3,-8,-4,11) Matrix(2521,1728,3888,2665) -> Matrix(1,-10,0,1) Matrix(1259,862,1944,1331) -> Matrix(1,4,0,1) Matrix(325,222,792,541) -> Matrix(1,0,-4,1) Matrix(397,260,936,613) -> Matrix(1,0,0,1) Matrix(937,608,-4104,-2663) -> Matrix(1,-2,0,1) Matrix(2665,1728,3888,2521) -> Matrix(1,-10,0,1) Matrix(1331,862,1944,1259) -> Matrix(1,4,0,1) Matrix(397,256,504,325) -> Matrix(1,0,0,1) Matrix(181,116,-504,-323) -> Matrix(1,0,4,1) Matrix(359,228,792,503) -> Matrix(1,0,-4,1) Matrix(757,480,-1872,-1187) -> Matrix(1,0,0,1) Matrix(1837,1164,3240,2053) -> Matrix(1,0,-4,1) Matrix(253,160,-1080,-683) -> Matrix(5,-4,4,-3) Matrix(577,364,-1368,-863) -> Matrix(1,-2,0,1) Matrix(35,22,-288,-181) -> Matrix(1,2,0,1) Matrix(251,156,288,179) -> Matrix(3,-2,-4,3) Matrix(2051,1272,-5400,-3349) -> Matrix(3,-4,4,-5) Matrix(755,468,-3312,-2053) -> Matrix(1,0,0,1) Matrix(971,600,-3672,-2269) -> Matrix(11,-12,12,-13) Matrix(1079,666,2448,1511) -> Matrix(1,-2,0,1) Matrix(1871,1154,-8640,-5329) -> Matrix(1,0,0,1) Matrix(1691,1042,2160,1331) -> Matrix(1,-2,0,1) Matrix(395,242,-648,-397) -> Matrix(1,-4,0,1) Matrix(467,284,-1008,-613) -> Matrix(1,2,4,9) Matrix(1655,1004,2016,1223) -> Matrix(3,4,-4,-5) Matrix(397,240,-1368,-827) -> Matrix(1,2,0,1) Matrix(179,106,-792,-469) -> Matrix(1,2,0,1) Matrix(1297,766,-3168,-1871) -> Matrix(1,0,4,1) Matrix(505,298,2808,1657) -> Matrix(5,4,-4,-3) Matrix(251,148,792,467) -> Matrix(1,0,0,1) Matrix(181,106,432,253) -> Matrix(1,0,4,1) Matrix(179,104,432,251) -> Matrix(1,0,-8,1) Matrix(505,292,-1368,-791) -> Matrix(5,-2,8,-3) Matrix(1585,914,-3744,-2159) -> Matrix(1,0,0,1) Matrix(323,186,936,539) -> Matrix(1,0,-4,1) Matrix(397,228,-1440,-827) -> Matrix(5,-2,8,-3) Matrix(1405,798,-4752,-2699) -> Matrix(9,-4,16,-7) Matrix(2053,1164,3240,1837) -> Matrix(1,0,-4,1) Matrix(1367,774,2160,1223) -> Matrix(3,-2,-4,3) Matrix(397,224,576,325) -> Matrix(1,-2,0,1) Matrix(107,60,576,323) -> Matrix(1,-2,0,1) Matrix(937,524,2448,1369) -> Matrix(3,-2,-4,3) Matrix(359,200,-648,-361) -> Matrix(1,-2,0,1) Matrix(395,218,1368,755) -> Matrix(1,0,0,1) Matrix(613,338,720,397) -> Matrix(1,0,0,1) Matrix(757,416,-2160,-1187) -> Matrix(3,2,4,3) Matrix(3637,1996,5184,2845) -> Matrix(1,0,4,1) Matrix(5329,2924,-11808,-6479) -> Matrix(1,0,12,1) Matrix(289,158,792,433) -> Matrix(1,0,0,1) Matrix(1943,1054,2520,1367) -> Matrix(5,2,-8,-3) Matrix(215,116,-936,-505) -> Matrix(1,2,0,1) Matrix(361,194,-936,-503) -> Matrix(3,2,4,3) Matrix(181,96,-1152,-611) -> Matrix(1,0,8,1) Matrix(35,18,-72,-37) -> Matrix(1,0,0,1) Matrix(685,324,1296,613) -> Matrix(1,0,28,1) Matrix(683,322,1296,611) -> Matrix(1,0,-32,1) Matrix(503,236,-2304,-1081) -> Matrix(1,0,-8,1) Matrix(683,318,3168,1475) -> Matrix(1,0,-4,1) Matrix(1187,552,2088,971) -> Matrix(1,0,-8,1) Matrix(1943,892,2664,1223) -> Matrix(1,-2,0,1) Matrix(215,98,-792,-361) -> Matrix(5,-2,8,-3) Matrix(503,228,792,359) -> Matrix(1,0,-4,1) Matrix(11377,5136,20736,9361) -> Matrix(1,0,12,1) Matrix(11375,5134,20736,9359) -> Matrix(1,0,-16,1) Matrix(5329,2404,7344,3313) -> Matrix(9,-2,-4,1) Matrix(1331,600,-5832,-2629) -> Matrix(1,0,-4,1) Matrix(107,48,720,323) -> Matrix(1,0,-4,1) Matrix(287,128,-648,-289) -> Matrix(5,-2,8,-3) Matrix(1331,588,1872,827) -> Matrix(3,-2,-4,3) Matrix(1511,666,2448,1079) -> Matrix(1,-2,0,1) Matrix(469,206,576,253) -> Matrix(3,-2,-4,3) Matrix(179,78,576,251) -> Matrix(3,-2,-4,3) Matrix(829,360,1080,469) -> Matrix(3,-2,-4,3) Matrix(1187,514,3240,1403) -> Matrix(1,0,0,1) Matrix(1117,482,2088,901) -> Matrix(1,0,4,1) Matrix(4105,1744,5256,2233) -> Matrix(1,0,-4,1) Matrix(2483,1054,-8568,-3637) -> Matrix(1,0,0,1) Matrix(2015,854,2376,1007) -> Matrix(1,0,0,1) Matrix(11953,5064,20736,8785) -> Matrix(1,0,4,1) Matrix(11951,5062,20736,8783) -> Matrix(1,0,-8,1) Matrix(757,320,-2808,-1187) -> Matrix(3,-4,4,-5) Matrix(253,106,432,181) -> Matrix(1,0,4,1) Matrix(251,104,432,179) -> Matrix(1,0,-8,1) Matrix(541,222,792,325) -> Matrix(1,0,-4,1) Matrix(2303,944,2808,1151) -> Matrix(13,-4,-16,5) Matrix(12241,5016,20736,8497) -> Matrix(19,-6,16,-5) Matrix(12239,5014,20736,8495) -> Matrix(17,-6,20,-7) Matrix(3601,1462,4968,2017) -> Matrix(9,-2,-4,1) Matrix(251,98,-648,-253) -> Matrix(9,-4,16,-7) Matrix(5689,2200,-20664,-7991) -> Matrix(1,0,0,1) Matrix(683,264,3816,1475) -> Matrix(13,-8,-8,5) Matrix(6695,2586,9504,3671) -> Matrix(29,-18,-8,5) Matrix(6947,2682,8856,3419) -> Matrix(3,-2,-4,3) Matrix(469,180,2160,829) -> Matrix(3,-2,-4,3) Matrix(2015,772,-6768,-2593) -> Matrix(3,-2,8,-5) Matrix(1369,524,2448,937) -> Matrix(3,-2,-4,3) Matrix(325,124,-1224,-467) -> Matrix(3,-4,4,-5) Matrix(1693,644,-4824,-1835) -> Matrix(5,-2,8,-3) Matrix(7237,2748,11664,4429) -> Matrix(11,-10,-12,11) Matrix(7235,2746,11664,4427) -> Matrix(9,-10,-8,9) Matrix(37,14,288,109) -> Matrix(1,-2,0,1) Matrix(577,214,1944,721) -> Matrix(5,-2,-12,5) Matrix(1151,426,3888,1439) -> Matrix(15,-8,-28,15) Matrix(937,344,2160,793) -> Matrix(1,-2,0,1) Matrix(1403,514,3240,1187) -> Matrix(1,0,0,1) Matrix(1295,474,-5904,-2161) -> Matrix(1,0,0,1) Matrix(433,158,792,289) -> Matrix(1,0,0,1) Matrix(829,300,1296,469) -> Matrix(1,0,4,1) Matrix(827,298,1296,467) -> Matrix(1,0,-8,1) Matrix(107,38,504,179) -> Matrix(1,0,-4,1) Matrix(613,216,1944,685) -> Matrix(9,-4,-20,9) Matrix(1223,430,3888,1367) -> Matrix(19,-10,-36,19) Matrix(109,38,-720,-251) -> Matrix(1,0,0,1) Matrix(467,148,792,251) -> Matrix(1,0,0,1) Matrix(685,216,1944,613) -> Matrix(9,-4,-20,9) Matrix(1367,430,3888,1223) -> Matrix(19,-10,-36,19) Matrix(217,68,1152,361) -> Matrix(13,-8,-8,5) Matrix(251,78,576,179) -> Matrix(3,-2,-4,3) Matrix(901,276,1296,397) -> Matrix(7,-6,-8,7) Matrix(899,274,1296,395) -> Matrix(5,-6,-4,5) Matrix(2339,698,5184,1547) -> Matrix(1,0,-8,1) Matrix(323,96,360,107) -> Matrix(1,0,-4,1) Matrix(3995,1182,5472,1619) -> Matrix(25,-14,-16,9) Matrix(5833,1724,9504,2809) -> Matrix(31,-18,-12,7) Matrix(217,64,1224,361) -> Matrix(13,-8,-8,5) Matrix(1225,358,1728,505) -> Matrix(7,-6,-8,7) Matrix(1223,356,1728,503) -> Matrix(5,-6,-4,5) Matrix(8245,2388,-29952,-8675) -> Matrix(5,-2,8,-3) Matrix(1045,302,1872,541) -> Matrix(1,-2,0,1) Matrix(179,50,-648,-181) -> Matrix(5,-2,8,-3) Matrix(113653,31284,156816,43165) -> Matrix(31,-18,-12,7) Matrix(113651,31282,156816,43163) -> Matrix(29,-18,-8,5) Matrix(2951,812,4968,1367) -> Matrix(3,-2,8,-5) Matrix(575,158,-3672,-1009) -> Matrix(3,-2,8,-5) Matrix(4031,1106,7344,2015) -> Matrix(3,-2,8,-5) Matrix(1441,390,2664,721) -> Matrix(3,-2,-4,3) Matrix(3853,1040,5472,1477) -> Matrix(19,-14,-4,3) Matrix(8533,2292,11664,3133) -> Matrix(15,-14,-16,15) Matrix(8531,2290,11664,3131) -> Matrix(13,-14,-12,13) Matrix(179,48,936,251) -> Matrix(1,-2,0,1) Matrix(3817,1008,5184,1369) -> Matrix(31,-30,-32,31) Matrix(3815,1006,5184,1367) -> Matrix(29,-30,-28,29) Matrix(109,28,144,37) -> Matrix(3,-2,-4,3) Matrix(107,26,144,35) -> Matrix(1,-2,0,1) Matrix(611,142,1080,251) -> Matrix(1,-2,0,1) Matrix(1153,264,2520,577) -> Matrix(1,-2,-4,9) Matrix(143,32,-648,-145) -> Matrix(1,-2,0,1) Matrix(3023,662,5256,1151) -> Matrix(1,0,0,1) Matrix(829,180,2160,469) -> Matrix(3,-2,-4,3) Matrix(2159,466,2664,575) -> Matrix(3,4,-4,-5) Matrix(5437,1172,8856,1909) -> Matrix(1,-2,0,1) Matrix(16273,3504,20736,4465) -> Matrix(1,0,8,1) Matrix(16271,3502,20736,4463) -> Matrix(1,0,-12,1) Matrix(179,38,504,107) -> Matrix(1,0,-4,1) Matrix(251,52,864,179) -> Matrix(1,-2,0,1) Matrix(251,48,936,179) -> Matrix(1,-2,0,1) Matrix(2089,396,2664,505) -> Matrix(3,-4,-8,11) Matrix(361,68,1152,217) -> Matrix(5,-8,-8,13) Matrix(323,60,576,107) -> Matrix(1,-2,0,1) Matrix(1657,298,2808,505) -> Matrix(3,-4,4,-5) Matrix(793,142,2016,361) -> Matrix(3,-4,-8,11) Matrix(361,64,1224,217) -> Matrix(5,-8,-8,13) Matrix(35,6,-216,-37) -> Matrix(1,-2,0,1) Matrix(1369,208,2376,361) -> Matrix(1,0,-4,1) Matrix(323,48,720,107) -> Matrix(1,0,-4,1) Matrix(109,14,288,37) -> Matrix(1,-2,0,1) Matrix(253,26,360,37) -> Matrix(1,0,0,1) Matrix(181,-22,288,-35) -> Matrix(1,2,0,1) Matrix(251,-38,720,-109) -> Matrix(1,0,0,1) Matrix(37,-6,216,-35) -> Matrix(1,-2,0,1) Matrix(1295,-226,1656,-289) -> Matrix(1,2,0,1) Matrix(611,-128,864,-181) -> Matrix(5,4,-4,-3) Matrix(1583,-340,2016,-433) -> Matrix(1,0,0,1) Matrix(3743,-810,5328,-1153) -> Matrix(1,2,0,1) Matrix(973,-212,1152,-251) -> Matrix(1,0,0,1) Matrix(683,-150,1152,-253) -> Matrix(1,0,0,1) Matrix(469,-106,792,-179) -> Matrix(1,2,0,1) Matrix(2053,-468,3312,-755) -> Matrix(1,0,0,1) Matrix(505,-116,936,-215) -> Matrix(1,2,0,1) Matrix(683,-160,1080,-253) -> Matrix(3,4,-4,-5) Matrix(467,-124,1224,-325) -> Matrix(5,4,-4,-3) Matrix(2053,-552,2808,-755) -> Matrix(9,8,-8,-7) Matrix(2269,-612,3600,-971) -> Matrix(13,10,-4,-3) Matrix(361,-98,792,-215) -> Matrix(3,2,-8,-5) Matrix(181,-50,648,-179) -> Matrix(3,2,-8,-5) Matrix(2881,-808,4104,-1151) -> Matrix(1,0,4,1) Matrix(3601,-1012,4608,-1295) -> Matrix(1,0,0,1) Matrix(289,-82,504,-143) -> Matrix(1,0,0,1) Matrix(2737,-794,4464,-1295) -> Matrix(1,-2,0,1) Matrix(683,-200,864,-253) -> Matrix(5,4,-4,-3) Matrix(2699,-798,4752,-1405) -> Matrix(7,4,-16,-9) Matrix(4175,-1242,5328,-1585) -> Matrix(5,2,-8,-3) Matrix(2195,-654,3024,-901) -> Matrix(7,2,-4,-1) Matrix(251,-76,360,-109) -> Matrix(1,0,0,1) Matrix(3167,-1112,4104,-1441) -> Matrix(3,2,-8,-5) Matrix(323,-116,504,-181) -> Matrix(1,0,4,1) Matrix(1115,-408,1872,-685) -> Matrix(1,0,0,1) Matrix(827,-304,1080,-397) -> Matrix(3,4,-4,-5) Matrix(791,-292,1368,-505) -> Matrix(3,2,-8,-5) Matrix(253,-94,288,-107) -> Matrix(5,2,-8,-3) Matrix(3349,-1272,5400,-2051) -> Matrix(5,4,-4,-3) Matrix(2557,-972,3312,-1259) -> Matrix(1,0,0,1) Matrix(2701,-1032,3672,-1403) -> Matrix(13,12,-12,-11) Matrix(6769,-2594,8640,-3311) -> Matrix(1,0,0,1) Matrix(253,-98,648,-251) -> Matrix(7,4,-16,-9) Matrix(541,-212,1008,-395) -> Matrix(5,2,12,5) Matrix(971,-384,1368,-541) -> Matrix(5,2,-8,-3) Matrix(613,-250,792,-323) -> Matrix(5,2,-8,-3) Matrix(1871,-766,3168,-1297) -> Matrix(1,0,4,1) Matrix(863,-364,1368,-577) -> Matrix(1,-2,0,1) Matrix(2159,-914,3744,-1585) -> Matrix(1,0,0,1) Matrix(1043,-444,1440,-613) -> Matrix(1,-2,0,1) Matrix(3347,-1446,4752,-2053) -> Matrix(1,-4,0,1) Matrix(289,-128,648,-287) -> Matrix(3,2,-8,-5) Matrix(1403,-632,2160,-973) -> Matrix(7,2,-4,-1) Matrix(6479,-2924,11808,-5329) -> Matrix(1,0,12,1) Matrix(721,-332,936,-431) -> Matrix(5,2,-8,-3) Matrix(575,-266,936,-433) -> Matrix(7,2,-4,-1) Matrix(971,-456,1152,-541) -> Matrix(1,0,8,1) Matrix(37,-18,72,-35) -> Matrix(1,0,0,1) Matrix(1801,-956,2304,-1223) -> Matrix(1,0,-8,1) Matrix(577,-314,792,-431) -> Matrix(1,-2,0,1) Matrix(4501,-2472,5832,-3203) -> Matrix(1,0,-4,1) Matrix(361,-200,648,-359) -> Matrix(1,-2,0,1) Matrix(6085,-3502,8568,-4931) -> Matrix(1,0,0,1) Matrix(2051,-1184,2808,-1621) -> Matrix(5,4,-4,-3) Matrix(397,-242,648,-395) -> Matrix(1,-4,0,1) Matrix(14975,-9184,20664,-12673) -> Matrix(1,0,0,1) Matrix(4753,-2932,6768,-4175) -> Matrix(1,2,0,1) Matrix(899,-556,1224,-757) -> Matrix(5,4,-4,-3) Matrix(3131,-1940,4824,-2989) -> Matrix(1,-2,0,1) Matrix(4609,-2922,5904,-3743) -> Matrix(1,0,0,1) Matrix(611,-398,720,-469) -> Matrix(1,0,0,1) Matrix(21707,-15420,29952,-21277) -> Matrix(1,-2,0,1) Matrix(469,-338,648,-467) -> Matrix(1,-2,0,1) Matrix(3097,-2246,3672,-2663) -> Matrix(1,2,0,1) Matrix(505,-392,648,-503) -> Matrix(3,2,-8,-5) Matrix(181,-150,216,-179) -> Matrix(3,2,-8,-5) 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): 48 Degree of the the map X: 96 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 1/8 1/7 2/13 1/6 2/11 3/16 1/5 3/14 2/9 4/17 1/4 4/15 5/18 8/27 3/10 5/16 1/3 19/54 3/8 7/18 5/12 4/9 11/24 1/2 13/24 5/9 7/12 67/108 23/36 2/3 25/36 79/108 11/15 53/72 3/4 7/9 5/6 8/9 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/8 -2/1 1/7 -1/2 2/13 1/0 1/6 1/0 2/11 1/0 3/16 -2/1 7/37 -3/2 4/21 -5/4 1/5 -1/2 3/14 -1/1 0/1 2/9 1/0 5/22 -2/1 -1/1 8/35 1/0 3/13 -3/2 4/17 -9/8 1/4 -1/1 5/19 -7/6 4/15 -3/4 11/41 -3/2 7/26 -1/1 -4/5 10/37 -3/4 3/11 -1/2 5/18 -1/2 2/7 1/0 5/17 -7/10 8/27 -1/2 11/37 -1/2 3/10 -1/1 0/1 4/13 -3/4 5/16 -2/3 1/3 -1/2 7/20 -1/1 13/37 -1/2 19/54 -1/2 6/17 -5/12 5/14 -1/3 0/1 4/11 1/0 11/30 1/0 7/19 -5/6 10/27 -1/2 3/8 0/1 11/29 -3/2 19/50 -1/1 -2/3 8/21 1/0 21/55 -11/10 13/34 -1/1 -4/5 5/13 -1/2 7/18 -1/2 2/5 -1/4 7/17 -3/14 5/12 0/1 8/19 3/4 3/7 -1/2 10/23 1/0 7/16 0/1 4/9 -1/2 9/20 -1/3 5/11 -1/2 16/35 -1/4 11/24 0/1 6/13 -1/4 1/2 -1/1 0/1 7/13 1/2 20/37 1/0 13/24 0/1 6/11 1/0 5/9 1/0 14/25 1/0 9/16 0/1 13/23 -1/2 4/7 1/0 11/19 -3/10 7/12 0/1 10/17 3/8 13/22 0/1 1/1 3/5 1/2 11/18 1/0 8/13 1/0 21/34 -4/3 -1/1 13/21 -1/2 44/71 1/0 31/50 -2/1 -1/1 49/79 -7/6 67/108 -1/1 18/29 -3/4 5/8 0/1 22/35 1/0 17/27 1/0 12/19 -5/4 7/11 -1/2 23/36 0/1 16/25 1/4 9/14 0/1 1/1 11/17 5/2 2/3 1/0 13/19 3/2 37/54 1/0 24/35 1/0 11/16 -2/1 9/13 -3/2 25/36 -1/1 16/23 -3/4 7/10 -1/1 0/1 26/37 1/0 19/27 1/0 12/17 -7/4 5/7 -1/2 13/18 1/0 8/11 1/0 35/48 -2/1 27/37 -3/2 19/26 -4/3 -1/1 49/67 -11/10 79/108 -1/1 30/41 -3/4 11/15 -3/2 25/34 -8/7 -1/1 39/53 -23/22 53/72 -1/1 14/19 -7/8 3/4 -1/1 13/17 -9/10 23/30 -3/4 10/13 -3/4 7/9 -1/2 18/23 1/0 47/60 -1/1 29/37 -1/2 40/51 -1/4 11/14 -1/1 0/1 15/19 -5/2 4/5 1/0 17/21 -5/6 30/37 -3/4 13/16 -2/3 9/11 -1/2 14/17 -11/16 5/6 -1/2 16/19 -1/8 11/13 -1/2 6/7 1/0 7/8 -2/3 8/9 -1/2 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(181,-22,288,-35) (0/1,1/8) -> (5/8,22/35) Hyperbolic Matrix(179,-23,288,-37) (1/8,1/7) -> (18/29,5/8) Hyperbolic Matrix(143,-21,252,-37) (1/7,2/13) -> (13/23,4/7) Hyperbolic Matrix(359,-56,468,-73) (2/13,1/6) -> (23/30,10/13) Hyperbolic Matrix(145,-26,396,-71) (1/6,2/11) -> (4/11,11/30) Hyperbolic Matrix(179,-33,396,-73) (2/11,3/16) -> (9/20,5/11) Hyperbolic Matrix(791,-149,1152,-217) (3/16,7/37) -> (24/35,11/16) Hyperbolic Matrix(1405,-267,2268,-431) (7/37,4/21) -> (13/21,44/71) Hyperbolic Matrix(685,-131,936,-179) (4/21,1/5) -> (30/41,11/15) Hyperbolic Matrix(107,-22,180,-37) (1/5,3/14) -> (13/22,3/5) 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(37,-9,144,-35) (4/17,1/4) -> (1/4,5/19) Parabolic Matrix(467,-124,1224,-325) (5/19,4/15) -> (8/21,21/55) Hyperbolic Matrix(757,-203,936,-251) (4/15,11/41) -> (4/5,17/21) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(397,-107,1332,-359) (7/26,10/37) -> (11/37,3/10) Hyperbolic Matrix(361,-98,792,-215) (10/37,3/11) -> (5/11,16/35) Hyperbolic Matrix(287,-79,396,-109) (3/11,5/18) -> (13/18,8/11) Hyperbolic Matrix(181,-51,252,-71) (5/18,2/7) -> (5/7,13/18) Hyperbolic Matrix(107,-31,252,-73) (2/7,5/17) -> (8/19,3/7) Hyperbolic Matrix(613,-181,972,-287) (5/17,8/27) -> (17/27,12/19) Hyperbolic Matrix(1223,-363,1944,-577) (8/27,11/37) -> (22/35,17/27) Hyperbolic Matrix(251,-76,360,-109) (3/10,4/13) -> (16/23,7/10) Hyperbolic Matrix(325,-101,576,-179) (4/13,5/16) -> (9/16,13/23) Hyperbolic Matrix(37,-12,108,-35) (5/16,1/3) -> (1/3,7/20) Parabolic Matrix(1081,-379,1332,-467) (7/20,13/37) -> (30/37,13/16) Hyperbolic Matrix(2665,-937,3888,-1367) (13/37,19/54) -> (37/54,24/35) Hyperbolic Matrix(1331,-469,1944,-685) (19/54,6/17) -> (13/19,37/54) Hyperbolic Matrix(397,-141,504,-179) (6/17,5/14) -> (11/14,15/19) 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(685,-253,972,-359) (7/19,10/27) -> (19/27,12/17) Hyperbolic Matrix(253,-94,288,-107) (10/27,3/8) -> (7/8,8/9) Hyperbolic Matrix(251,-95,288,-109) (3/8,11/29) -> (6/7,7/8) 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(217,-83,468,-179) (13/34,5/13) -> (6/13,1/2) Hyperbolic Matrix(287,-111,468,-181) (5/13,7/18) -> (11/18,8/13) Hyperbolic Matrix(109,-43,180,-71) (7/18,2/5) -> (3/5,11/18) Hyperbolic Matrix(143,-58,180,-73) (2/5,7/17) -> (15/19,4/5) Hyperbolic Matrix(181,-75,432,-179) (7/17,5/12) -> (5/12,8/19) Parabolic Matrix(215,-93,252,-109) (3/7,10/23) -> (11/13,6/7) Hyperbolic Matrix(397,-173,576,-251) (10/23,7/16) -> (11/16,9/13) Hyperbolic Matrix(145,-64,324,-143) (7/16,4/9) -> (4/9,9/20) Parabolic Matrix(2341,-1071,2988,-1367) (16/35,11/24) -> (47/60,29/37) Hyperbolic Matrix(1043,-480,1332,-613) (11/24,6/13) -> (18/23,47/60) Hyperbolic Matrix(289,-155,468,-251) (1/2,7/13) -> (8/13,21/34) Hyperbolic Matrix(1943,-1051,2664,-1441) (20/37,13/24) -> (35/48,27/37) Hyperbolic Matrix(577,-314,792,-431) (13/24,6/11) -> (8/11,35/48) Hyperbolic Matrix(181,-100,324,-179) (6/11,5/9) -> (5/9,14/25) Parabolic Matrix(469,-263,576,-323) (14/25,9/16) -> (13/16,9/11) Hyperbolic Matrix(179,-103,252,-145) (4/7,11/19) -> (12/17,5/7) Hyperbolic Matrix(253,-147,432,-251) (11/19,7/12) -> (7/12,10/17) Parabolic Matrix(395,-233,612,-361) (10/17,13/22) -> (9/14,11/17) Hyperbolic Matrix(899,-556,1224,-757) (21/34,13/21) -> (11/15,25/34) Hyperbolic Matrix(7237,-4489,11664,-7235) (49/79,67/108) -> (67/108,18/29) Parabolic Matrix(325,-206,396,-251) (12/19,7/11) -> (9/11,14/17) Hyperbolic Matrix(829,-529,1296,-827) (7/11,23/36) -> (23/36,16/25) Parabolic Matrix(73,-48,108,-71) (11/17,2/3) -> (2/3,13/19) Parabolic Matrix(901,-625,1296,-899) (9/13,25/36) -> (25/36,16/23) Parabolic Matrix(973,-683,1332,-935) (7/10,26/37) -> (27/37,19/26) Hyperbolic Matrix(323,-227,360,-253) (26/37,19/27) -> (8/9,1/1) Hyperbolic Matrix(8533,-6241,11664,-8531) (49/67,79/108) -> (79/108,30/41) Parabolic Matrix(3817,-2809,5184,-3815) (39/53,53/72) -> (53/72,14/19) Parabolic Matrix(109,-81,144,-107) (14/19,3/4) -> (3/4,13/17) Parabolic Matrix(253,-196,324,-251) (10/13,7/9) -> (7/9,18/23) Parabolic Matrix(2159,-1693,2664,-2089) (29/37,40/51) -> (17/21,30/37) Hyperbolic Matrix(181,-150,216,-179) (14/17,5/6) -> (5/6,16/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-2,1) Matrix(181,-22,288,-35) -> Matrix(1,2,0,1) Matrix(179,-23,288,-37) -> Matrix(1,2,-2,-3) Matrix(143,-21,252,-37) -> Matrix(1,1,-2,-1) Matrix(359,-56,468,-73) -> Matrix(3,1,-4,-1) Matrix(145,-26,396,-71) -> Matrix(1,1,0,1) Matrix(179,-33,396,-73) -> Matrix(1,1,-2,-1) Matrix(791,-149,1152,-217) -> Matrix(5,8,-2,-3) Matrix(1405,-267,2268,-431) -> Matrix(1,1,2,3) Matrix(685,-131,936,-179) -> Matrix(1,2,-2,-3) Matrix(107,-22,180,-37) -> Matrix(1,1,0,1) Matrix(73,-16,324,-71) -> Matrix(1,-1,0,1) Matrix(2053,-468,3312,-755) -> Matrix(1,0,0,1) Matrix(505,-116,936,-215) -> Matrix(1,2,0,1) Matrix(395,-92,468,-109) -> Matrix(1,1,0,1) Matrix(37,-9,144,-35) -> Matrix(1,2,-2,-3) Matrix(467,-124,1224,-325) -> Matrix(5,4,-4,-3) Matrix(757,-203,936,-251) -> Matrix(1,2,-2,-3) Matrix(2053,-552,2808,-755) -> Matrix(9,8,-8,-7) Matrix(397,-107,1332,-359) -> Matrix(1,1,-6,-5) Matrix(361,-98,792,-215) -> Matrix(3,2,-8,-5) Matrix(287,-79,396,-109) -> Matrix(5,3,-2,-1) Matrix(181,-51,252,-71) -> Matrix(1,1,-2,-1) Matrix(107,-31,252,-73) -> Matrix(1,1,-2,-1) Matrix(613,-181,972,-287) -> Matrix(5,3,-2,-1) Matrix(1223,-363,1944,-577) -> Matrix(5,2,2,1) Matrix(251,-76,360,-109) -> Matrix(1,0,0,1) Matrix(325,-101,576,-179) -> Matrix(3,2,-2,-1) Matrix(37,-12,108,-35) -> Matrix(1,1,-4,-3) Matrix(1081,-379,1332,-467) -> Matrix(7,5,-10,-7) Matrix(2665,-937,3888,-1367) -> Matrix(19,10,-2,-1) Matrix(1331,-469,1944,-685) -> Matrix(9,4,2,1) Matrix(397,-141,504,-179) -> Matrix(1,0,2,1) Matrix(323,-116,504,-181) -> Matrix(1,0,4,1) Matrix(827,-304,1080,-397) -> Matrix(3,4,-4,-5) Matrix(685,-253,972,-359) -> Matrix(5,3,-2,-1) Matrix(253,-94,288,-107) -> Matrix(5,2,-8,-3) Matrix(251,-95,288,-109) -> Matrix(1,2,-2,-3) Matrix(3349,-1272,5400,-2051) -> Matrix(5,4,-4,-3) Matrix(2231,-848,2844,-1081) -> Matrix(1,1,-4,-3) Matrix(2701,-1032,3672,-1403) -> Matrix(13,12,-12,-11) Matrix(217,-83,468,-179) -> Matrix(1,1,-6,-5) Matrix(287,-111,468,-181) -> Matrix(5,3,-2,-1) Matrix(109,-43,180,-71) -> Matrix(3,1,2,1) Matrix(143,-58,180,-73) -> Matrix(3,1,-4,-1) Matrix(181,-75,432,-179) -> Matrix(1,0,6,1) Matrix(215,-93,252,-109) -> Matrix(1,1,-2,-1) Matrix(397,-173,576,-251) -> Matrix(3,2,-2,-1) Matrix(145,-64,324,-143) -> Matrix(1,1,-4,-3) Matrix(2341,-1071,2988,-1367) -> Matrix(5,1,-6,-1) Matrix(1043,-480,1332,-613) -> Matrix(3,1,-4,-1) Matrix(289,-155,468,-251) -> Matrix(3,-1,-2,1) Matrix(1943,-1051,2664,-1441) -> Matrix(3,2,-2,-1) Matrix(577,-314,792,-431) -> Matrix(1,-2,0,1) Matrix(181,-100,324,-179) -> Matrix(1,-1,0,1) Matrix(469,-263,576,-323) -> Matrix(1,2,-2,-3) Matrix(179,-103,252,-145) -> Matrix(1,1,-2,-1) Matrix(253,-147,432,-251) -> Matrix(1,0,6,1) Matrix(395,-233,612,-361) -> Matrix(1,-1,2,-1) Matrix(899,-556,1224,-757) -> Matrix(5,4,-4,-3) Matrix(7237,-4489,11664,-7235) -> Matrix(9,10,-10,-11) Matrix(325,-206,396,-251) -> Matrix(3,1,-4,-1) Matrix(829,-529,1296,-827) -> Matrix(1,0,6,1) Matrix(73,-48,108,-71) -> Matrix(1,-1,0,1) Matrix(901,-625,1296,-899) -> Matrix(5,6,-6,-7) Matrix(973,-683,1332,-935) -> Matrix(3,-1,-2,1) Matrix(323,-227,360,-253) -> Matrix(1,0,-2,1) Matrix(8533,-6241,11664,-8531) -> Matrix(13,14,-14,-15) Matrix(3817,-2809,5184,-3815) -> Matrix(29,30,-30,-31) Matrix(109,-81,144,-107) -> Matrix(1,2,-2,-3) Matrix(253,-196,324,-251) -> Matrix(1,1,-4,-3) Matrix(2159,-1693,2664,-2089) -> Matrix(11,4,-14,-5) Matrix(181,-150,216,-179) -> Matrix(3,2,-8,-5) 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): 48 ----------------------------------------------------------------------- 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 1/0 1 36 1/8 -2/1 2 9 1/7 -1/2 1 36 2/13 1/0 1 36 1/6 1/0 2 6 2/11 1/0 1 36 3/16 -2/1 2 9 7/37 -3/2 1 36 4/21 -5/4 1 12 1/5 -1/2 1 36 3/14 (-1/1,0/1) 0 18 2/9 1/0 1 4 5/22 (-2/1,-1/1) 0 18 8/35 1/0 1 36 3/13 -3/2 1 36 4/17 -9/8 1 36 1/4 -1/1 2 9 5/19 -7/6 1 36 4/15 -3/4 1 12 11/41 -3/2 1 36 29/108 -1/1 14 1 7/26 (-1/1,-4/5) 0 18 10/37 -3/4 1 36 3/11 -1/2 1 36 5/18 -1/2 2 2 2/7 1/0 1 36 5/17 -7/10 1 36 8/27 -1/2 5 4 11/37 -1/2 1 36 3/10 (-1/1,0/1) 0 18 11/36 -1/1 6 1 4/13 -3/4 1 36 5/16 -2/3 2 9 1/3 -1/2 1 12 7/20 -1/1 2 9 13/37 -1/2 1 36 19/54 -1/2 14 2 6/17 -5/12 1 36 5/14 (-1/3,0/1) 0 18 13/36 0/1 6 1 4/11 1/0 1 36 11/30 1/0 2 6 18/49 1/0 1 36 7/19 -5/6 1 36 10/27 -1/2 5 4 13/35 -1/2 1 36 3/8 0/1 2 9 11/29 -3/2 1 36 41/108 -1/1 10 1 19/50 (-1/1,-2/3) 0 18 27/71 -1/2 1 36 8/21 1/0 1 12 21/55 -11/10 1 36 55/144 -1/1 30 1 13/34 (-1/1,-4/5) 0 18 5/13 -1/2 1 36 7/18 -1/2 4 2 2/5 -1/4 1 36 9/22 (-1/3,0/1) 0 18 7/17 -3/14 1 36 5/12 0/1 6 3 8/19 3/4 1 36 3/7 -1/2 1 36 10/23 1/0 1 36 7/16 0/1 2 9 4/9 -1/2 1 4 9/20 -1/3 2 9 5/11 -1/2 1 36 16/35 -1/4 1 36 11/24 0/1 2 3 17/37 -1/2 1 36 6/13 -1/4 1 36 1/2 (-1/1,0/1) 0 18 1/0 0/1 2 1 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(107,-13,288,-35) (0/1,1/8) -> (13/35,3/8) Glide Reflection Matrix(109,-14,288,-37) (1/8,1/7) -> (3/8,11/29) Glide Reflection Matrix(109,-16,252,-37) (1/7,2/13) -> (3/7,10/23) Glide Reflection Matrix(251,-40,684,-109) (2/13,1/6) -> (11/30,18/49) Hyperbolic Matrix(145,-26,396,-71) (1/6,2/11) -> (4/11,11/30) Hyperbolic Matrix(179,-33,396,-73) (2/11,3/16) -> (9/20,5/11) Hyperbolic Matrix(467,-88,1332,-251) (3/16,7/37) -> (7/20,13/37) Glide Reflection Matrix(863,-164,2268,-431) (7/37,4/21) -> (27/71,8/21) Glide Reflection Matrix(251,-48,936,-179) (4/21,1/5) -> (4/15,11/41) Glide Reflection Matrix(73,-15,180,-37) (1/5,3/14) -> (2/5,9/22) Glide Reflection Matrix(73,-16,324,-71) (3/14,2/9) -> (2/9,5/22) Parabolic Matrix(1259,-287,3312,-755) (5/22,8/35) -> (19/50,27/71) Glide Reflection Matrix(431,-99,936,-215) (8/35,3/13) -> (17/37,6/13) Glide Reflection Matrix(397,-93,1080,-253) (3/13,4/17) -> (18/49,7/19) Glide Reflection Matrix(37,-9,144,-35) (4/17,1/4) -> (1/4,5/19) Parabolic Matrix(467,-124,1224,-325) (5/19,4/15) -> (8/21,21/55) Hyperbolic Matrix(2377,-638,8856,-2377) (11/41,29/108) -> (11/41,29/108) Reflection Matrix(755,-203,2808,-755) (29/108,7/26) -> (29/108,7/26) Reflection Matrix(397,-107,1332,-359) (7/26,10/37) -> (11/37,3/10) Hyperbolic Matrix(361,-98,792,-215) (10/37,3/11) -> (5/11,16/35) Hyperbolic Matrix(109,-30,396,-109) (3/11,5/18) -> (3/11,5/18) Reflection Matrix(71,-20,252,-71) (5/18,2/7) -> (5/18,2/7) Reflection Matrix(107,-31,252,-73) (2/7,5/17) -> (8/19,3/7) Hyperbolic Matrix(359,-106,972,-287) (5/17,8/27) -> (7/19,10/27) Glide Reflection Matrix(721,-214,1944,-577) (8/27,11/37) -> (10/27,13/35) Glide Reflection Matrix(109,-33,360,-109) (3/10,11/36) -> (3/10,11/36) Reflection Matrix(287,-88,936,-287) (11/36,4/13) -> (11/36,4/13) Reflection Matrix(251,-78,576,-179) (4/13,5/16) -> (10/23,7/16) Glide Reflection Matrix(37,-12,108,-35) (5/16,1/3) -> (1/3,7/20) Parabolic Matrix(1405,-494,3996,-1405) (13/37,19/54) -> (13/37,19/54) Reflection Matrix(647,-228,1836,-647) (19/54,6/17) -> (19/54,6/17) Reflection Matrix(251,-89,612,-217) (6/17,5/14) -> (9/22,7/17) Hyperbolic Matrix(181,-65,504,-181) (5/14,13/36) -> (5/14,13/36) Reflection Matrix(287,-104,792,-287) (13/36,4/11) -> (13/36,4/11) Reflection Matrix(2377,-902,6264,-2377) (11/29,41/108) -> (11/29,41/108) Reflection Matrix(2051,-779,5400,-2051) (41/108,19/50) -> (41/108,19/50) Reflection Matrix(6049,-2310,15840,-6049) (21/55,55/144) -> (21/55,55/144) Reflection Matrix(1871,-715,4896,-1871) (55/144,13/34) -> (55/144,13/34) Reflection Matrix(217,-83,468,-179) (13/34,5/13) -> (6/13,1/2) Hyperbolic Matrix(181,-70,468,-181) (5/13,7/18) -> (5/13,7/18) Reflection Matrix(71,-28,180,-71) (7/18,2/5) -> (7/18,2/5) Reflection Matrix(181,-75,432,-179) (7/17,5/12) -> (5/12,8/19) Parabolic Matrix(145,-64,324,-143) (7/16,4/9) -> (4/9,9/20) Parabolic Matrix(793,-363,1728,-791) (16/35,11/24) -> (11/24,17/37) Parabolic Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(107,-13,288,-35) -> Matrix(1,2,-2,-5) Matrix(109,-14,288,-37) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(109,-16,252,-37) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(251,-40,684,-109) -> Matrix(1,-1,0,1) 1/0 Matrix(145,-26,396,-71) -> Matrix(1,1,0,1) 1/0 Matrix(179,-33,396,-73) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(467,-88,1332,-251) -> Matrix(3,5,-4,-7) Matrix(863,-164,2268,-431) -> Matrix(1,1,-4,-5) Matrix(251,-48,936,-179) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(73,-15,180,-37) -> Matrix(1,1,-2,-3) Matrix(73,-16,324,-71) -> Matrix(1,-1,0,1) 1/0 Matrix(1259,-287,3312,-755) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(431,-99,936,-215) -> Matrix(1,2,-2,-5) Matrix(397,-93,1080,-253) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(37,-9,144,-35) -> Matrix(1,2,-2,-3) -1/1 Matrix(467,-124,1224,-325) -> Matrix(5,4,-4,-3) -1/1 Matrix(2377,-638,8856,-2377) -> Matrix(5,6,-4,-5) (11/41,29/108) -> (-3/2,-1/1) Matrix(755,-203,2808,-755) -> Matrix(9,8,-10,-9) (29/108,7/26) -> (-1/1,-4/5) Matrix(397,-107,1332,-359) -> Matrix(1,1,-6,-5) Matrix(361,-98,792,-215) -> Matrix(3,2,-8,-5) -1/2 Matrix(109,-30,396,-109) -> Matrix(5,3,-8,-5) (3/11,5/18) -> (-3/4,-1/2) Matrix(71,-20,252,-71) -> Matrix(1,1,0,-1) (5/18,2/7) -> (-1/2,1/0) Matrix(107,-31,252,-73) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(359,-106,972,-287) -> Matrix(5,3,-8,-5) *** -> (-3/4,-1/2) Matrix(721,-214,1944,-577) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(109,-33,360,-109) -> Matrix(-1,0,2,1) (3/10,11/36) -> (-1/1,0/1) Matrix(287,-88,936,-287) -> Matrix(7,6,-8,-7) (11/36,4/13) -> (-1/1,-3/4) Matrix(251,-78,576,-179) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(37,-12,108,-35) -> Matrix(1,1,-4,-3) -1/2 Matrix(1405,-494,3996,-1405) -> Matrix(17,9,-32,-17) (13/37,19/54) -> (-9/16,-1/2) Matrix(647,-228,1836,-647) -> Matrix(11,5,-24,-11) (19/54,6/17) -> (-1/2,-5/12) Matrix(251,-89,612,-217) -> Matrix(3,1,-10,-3) (-1/2,-1/4).(-1/3,0/1) Matrix(181,-65,504,-181) -> Matrix(-1,0,6,1) (5/14,13/36) -> (-1/3,0/1) Matrix(287,-104,792,-287) -> Matrix(1,0,0,-1) (13/36,4/11) -> (0/1,1/0) Matrix(2377,-902,6264,-2377) -> Matrix(5,6,-4,-5) (11/29,41/108) -> (-3/2,-1/1) Matrix(2051,-779,5400,-2051) -> Matrix(5,4,-6,-5) (41/108,19/50) -> (-1/1,-2/3) Matrix(6049,-2310,15840,-6049) -> Matrix(21,22,-20,-21) (21/55,55/144) -> (-11/10,-1/1) Matrix(1871,-715,4896,-1871) -> Matrix(9,8,-10,-9) (55/144,13/34) -> (-1/1,-4/5) Matrix(217,-83,468,-179) -> Matrix(1,1,-6,-5) Matrix(181,-70,468,-181) -> Matrix(5,3,-8,-5) (5/13,7/18) -> (-3/4,-1/2) Matrix(71,-28,180,-71) -> Matrix(3,1,-8,-3) (7/18,2/5) -> (-1/2,-1/4) Matrix(181,-75,432,-179) -> Matrix(1,0,6,1) 0/1 Matrix(145,-64,324,-143) -> Matrix(1,1,-4,-3) -1/2 Matrix(793,-363,1728,-791) -> Matrix(1,0,2,1) 0/1 Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.