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): 1800 Minimal number of generators: 301 Number of equivalence classes of cusps: 84 Genus: 109 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -4/5 -11/15 -52/75 -3/5 -74/125 -7/15 -9/20 -21/50 -2/5 -49/125 -19/50 -8/25 -3/10 -27/100 -67/250 -4/15 -53/200 -13/50 -6/25 -5/21 -11/50 -5/24 -1/5 -4/21 -9/50 -4/23 -13/75 -4/25 -3/19 -3/20 -7/50 -3/22 -2/15 -3/25 -2/17 -1/10 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 5/23 2/9 3/13 1/4 4/15 3/11 5/18 7/25 2/7 3/10 23/75 1/3 9/25 2/5 5/12 11/25 9/20 7/15 1/2 14/25 3/5 16/25 2/3 17/25 18/25 11/15 19/25 4/5 62/75 21/25 22/25 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/2 -9/10 0/1 -8/9 2/5 3/7 -7/8 1/2 -13/15 3/5 -6/7 2/3 1/1 -17/20 2/3 -11/13 3/4 4/5 -5/6 1/0 -14/17 0/1 1/1 -9/11 0/1 1/4 -13/16 3/8 -4/5 1/2 -15/19 1/2 6/11 -11/14 5/8 -18/23 3/5 8/13 -7/9 2/3 3/4 -31/40 2/3 -24/31 1/2 3/5 -17/22 7/10 -61/79 2/3 7/10 -105/136 3/4 -44/57 2/3 9/13 -27/35 5/7 -10/13 3/4 7/9 -23/30 4/5 -13/17 4/5 5/6 -3/4 1/0 -14/19 1/3 1/2 -25/34 1/2 -36/49 0/1 1/3 -11/15 1/3 -41/56 1/2 -30/41 3/7 4/9 -19/26 1/2 -8/11 0/1 1/1 -37/51 0/1 1/2 -29/40 0/1 -50/69 1/5 1/4 -21/29 2/5 1/2 -55/76 1/2 -34/47 1/3 1/2 -47/65 1/3 -13/18 1/2 -18/25 1/2 -5/7 1/2 2/3 -17/24 1/2 -29/41 1/2 4/7 -12/17 3/5 2/3 -31/44 5/8 -81/115 7/11 -50/71 7/11 9/14 -69/98 21/32 -88/125 2/3 -19/27 2/3 3/4 -7/10 2/3 -16/23 0/1 1/1 -25/36 1/2 -84/121 1/2 1/1 -59/85 1/1 -34/49 2/3 1/1 -43/62 1/2 -52/75 2/3 -9/13 2/3 3/4 -11/16 5/6 -13/19 6/7 7/8 -2/3 1/1 1/0 -13/20 0/1 -11/17 0/1 1/0 -9/14 1/0 -16/25 0/1 -7/11 0/1 1/2 -19/30 0/1 -31/49 1/2 4/7 -12/19 1/1 1/0 -29/46 -1/2 -17/27 0/1 1/4 -39/62 1/2 -22/35 0/1 -5/8 1/2 -13/21 1/2 4/7 -34/55 1/2 -21/34 5/8 -8/13 1/2 1/1 -19/31 2/3 3/4 -30/49 2/3 1/1 -71/116 1/2 -41/67 2/3 3/4 -11/18 1/2 -25/41 2/3 11/16 -14/23 5/7 8/11 -3/5 1/1 -16/27 7/5 10/7 -45/76 3/2 -74/125 3/2 -29/49 3/2 26/17 -13/22 7/4 -23/39 2/1 5/2 -10/17 1/1 2/1 -17/29 2/1 5/2 -24/41 3/1 4/1 -55/94 1/0 -31/53 2/1 1/0 -7/12 1/0 -11/19 -4/1 1/0 -26/45 1/0 -41/71 -2/1 1/0 -15/26 1/0 -4/7 -1/1 0/1 -17/30 0/1 -30/53 -1/1 -1/2 -43/76 -1/2 -13/23 -1/2 0/1 -9/16 -1/4 -14/25 0/1 -5/9 0/1 1/4 -16/29 1/3 3/8 -43/78 7/16 -27/49 1/2 4/7 -11/20 0/1 -6/11 1/3 2/5 -13/24 1/2 -7/13 1/2 6/11 -8/15 2/3 -9/17 2/3 3/4 -1/2 1/0 -8/17 0/1 1/3 -7/15 1/3 -6/13 5/11 1/2 -5/11 1/2 2/3 -9/20 2/3 -13/29 1/2 2/3 -4/9 4/5 1/1 -11/25 1/1 -7/16 7/6 -17/39 4/3 3/2 -27/62 3/2 -10/23 4/3 7/5 -13/30 2/1 -3/7 2/1 1/0 -11/26 1/0 -8/19 5/1 1/0 -21/50 1/0 -13/31 -8/1 1/0 -5/12 1/0 -22/53 -1/1 1/0 -17/41 -2/1 1/0 -12/29 -5/4 -1/1 -31/75 -1/1 -19/46 -7/8 -7/17 -2/3 -1/2 -9/22 -1/2 -2/5 0/1 -11/28 1/2 -20/51 0/1 1/3 -49/125 1/3 -29/74 1/2 -9/23 0/1 1/2 -7/18 1/4 -33/85 1/3 -26/67 0/1 1/3 -19/49 2/9 1/4 -12/31 3/10 1/3 -29/75 1/3 -17/44 5/14 -5/13 0/1 1/2 -13/34 3/8 -8/21 3/7 1/2 -19/50 1/2 -11/29 1/2 4/7 -3/8 1/2 -13/35 3/5 -36/97 3/5 5/8 -23/62 5/8 -10/27 7/11 2/3 -7/19 1/2 2/3 -18/49 2/3 1/1 -47/128 1/2 -29/79 1/2 2/3 -11/30 2/3 -4/11 4/5 1/1 -9/25 1/1 -5/14 5/4 -11/31 3/2 8/5 -17/48 5/2 -6/17 1/1 2/1 -7/20 2/1 -8/23 4/1 5/1 -1/3 0/1 1/0 -8/25 0/1 -7/22 1/8 -6/19 1/4 1/3 -5/16 1/4 -4/13 1/2 1/1 -7/23 0/1 1/0 -3/10 0/1 -8/27 2/7 1/3 -5/17 4/9 1/2 -22/75 1/2 -17/58 1/2 -12/41 4/7 3/5 -7/24 1/2 -2/7 2/3 1/1 -7/25 1/1 -5/18 5/4 -23/83 4/3 3/2 -18/65 4/3 -31/112 3/2 -13/47 4/3 3/2 -34/123 16/11 19/13 -21/76 3/2 -8/29 3/2 5/3 -27/98 9/4 -19/69 0/1 1/0 -11/40 2/1 -14/51 1/1 2/1 -17/62 1/0 -3/11 2/1 1/0 -10/37 9/1 1/0 -27/100 1/0 -17/63 -10/1 1/0 -7/26 1/0 -11/41 0/1 1/0 -26/97 1/1 1/0 -67/250 1/0 -41/153 0/1 1/0 -15/56 1/0 -4/15 1/0 -13/49 0/1 1/0 -22/83 -3/1 -2/1 -53/200 -2/1 -31/117 -2/1 -3/2 -9/34 1/0 -5/19 -1/2 0/1 -6/23 -1/5 0/1 -13/50 0/1 -7/27 0/1 1/6 -1/4 1/0 -6/25 0/1 -5/21 0/1 1/6 -4/17 0/1 1/3 -7/30 0/1 -3/13 2/5 1/2 -8/35 2/3 -5/22 5/6 -17/75 1/1 -12/53 1/1 11/10 -7/31 4/3 3/2 -9/40 2/1 -2/9 -1/1 0/1 -11/50 0/1 -9/41 0/1 1/10 -7/32 1/4 -5/23 0/1 1/2 -8/37 1/4 1/3 -27/125 1/3 -19/88 3/8 -11/51 2/5 1/2 -14/65 1/2 -3/14 1/2 -7/33 0/1 1/2 -11/52 3/10 -15/71 4/11 3/8 -4/19 3/7 1/2 -5/24 1/2 -1/5 1/1 -5/26 1/0 -4/21 1/1 1/0 -3/16 -1/2 -5/27 0/1 1/0 -7/38 1/2 -9/49 0/1 1/0 -2/11 -1/1 0/1 -9/50 0/1 -7/39 0/1 1/8 -5/28 1/2 -3/17 2/5 1/2 -4/23 4/5 1/1 -13/75 1/1 -9/52 9/8 -5/29 3/2 2/1 -11/64 1/0 -6/35 1/0 -1/6 1/0 -4/25 0/1 -3/19 0/1 1/4 -2/13 1/3 1/2 -3/20 0/1 -1/7 0/1 1/0 -7/50 0/1 -6/43 0/1 1/7 -5/36 1/4 -4/29 1/4 1/3 -3/22 3/4 -2/15 0/1 -1/8 1/2 -3/25 1/1 -2/17 1/1 2/1 -1/9 0/1 1/0 -1/10 0/1 0/1 0/1 1/1 1/10 0/1 1/9 0/1 1/2 1/8 1/0 2/15 0/1 1/7 0/1 1/2 3/20 0/1 2/13 -1/1 1/0 1/6 1/2 3/17 -2/1 1/0 2/11 0/1 1/3 3/16 1/4 1/5 1/1 4/19 -3/1 1/0 3/14 1/0 5/23 0/1 1/0 2/9 0/1 1/3 9/40 2/3 7/31 3/4 4/5 5/22 5/4 18/79 5/3 7/4 31/136 7/4 13/57 2/1 1/0 8/35 2/1 3/13 -2/1 1/0 7/30 0/1 4/17 -1/1 0/1 1/4 1/2 5/19 0/1 1/4 9/34 1/2 13/49 0/1 1/2 4/15 1/2 15/56 1/2 11/41 0/1 1/2 7/26 1/2 3/11 1/2 2/3 14/51 2/3 1/1 11/40 2/3 19/69 0/1 1/2 8/29 5/7 3/4 21/76 3/4 13/47 3/4 4/5 18/65 4/5 5/18 5/6 7/25 1/1 2/7 1/1 2/1 7/24 1/0 12/41 3/1 4/1 5/17 -4/1 1/0 13/44 -3/2 34/115 -3/2 21/71 -4/3 -5/4 29/98 -11/10 37/125 -1/1 8/27 -1/1 -2/3 3/10 0/1 7/23 0/1 1/2 11/36 1/2 37/121 0/1 1/4 26/85 1/2 15/49 1/2 2/3 19/62 3/4 23/75 1/1 4/13 1/1 1/0 5/16 -1/2 6/19 -1/1 -1/2 1/3 0/1 1/2 7/20 2/3 6/17 2/3 1/1 5/14 5/6 9/25 1/1 4/11 1/1 4/3 11/30 2/1 18/49 1/1 2/1 7/19 2/1 1/0 17/46 3/2 10/27 2/1 7/3 23/62 5/2 13/35 3/1 3/8 1/0 8/21 -3/1 1/0 21/55 -3/1 13/34 -3/2 5/13 0/1 1/0 12/31 -1/1 -3/4 19/49 -1/2 -2/5 45/116 -1/2 26/67 -1/1 0/1 7/18 -1/2 16/41 0/1 1/3 9/23 0/1 1/0 2/5 0/1 11/27 0/1 1/4 31/76 1/4 51/125 1/3 20/49 0/1 1/3 9/22 1/4 16/39 0/1 1/7 7/17 1/4 2/7 12/29 1/3 5/14 17/41 2/5 1/2 39/94 1/2 22/53 1/3 1/2 5/12 1/2 8/19 1/2 5/9 19/45 1/1 30/71 1/2 1/1 11/26 1/2 3/7 1/2 2/3 13/30 2/3 23/53 8/11 3/4 33/76 3/4 10/23 7/9 4/5 7/16 7/8 11/25 1/1 4/9 1/1 4/3 13/29 2/1 1/0 35/78 1/0 22/49 1/1 2/1 9/20 2/1 5/11 2/1 1/0 11/24 1/0 6/13 -5/1 1/0 7/15 -1/1 8/17 -1/1 0/1 1/2 1/2 9/17 3/2 2/1 8/15 2/1 7/13 6/1 1/0 6/11 -2/1 -1/1 11/20 0/1 16/29 -3/2 -1/1 5/9 -1/2 0/1 14/25 0/1 9/16 1/6 22/39 0/1 1/5 35/62 1/2 13/23 0/1 1/4 17/30 0/1 4/7 0/1 1/3 15/26 1/2 11/19 4/9 1/2 29/50 1/2 18/31 1/2 9/17 7/12 1/2 31/53 1/2 2/3 24/41 4/7 3/5 17/29 5/8 2/3 44/75 2/3 27/46 7/10 10/17 2/3 1/1 13/22 7/10 3/5 1/1 17/28 11/8 31/51 28/19 3/2 76/125 3/2 45/74 3/2 14/23 8/5 5/3 11/18 1/0 52/85 2/1 41/67 3/2 2/1 30/49 1/1 2/1 19/31 3/2 2/1 46/75 2/1 27/44 5/2 8/13 1/1 1/0 21/34 5/2 13/21 4/1 1/0 31/50 1/0 18/29 -3/1 1/0 5/8 1/0 22/35 0/1 61/97 0/1 1/0 39/62 1/0 17/27 -1/2 0/1 12/19 1/2 1/1 31/49 4/1 1/0 81/128 -7/2 50/79 -3/2 -1/1 19/30 0/1 7/11 0/1 1/0 16/25 0/1 9/14 1/2 20/31 1/2 3/5 31/48 3/2 11/17 0/1 1/2 13/20 0/1 15/23 0/1 1/2 2/3 1/2 1/1 17/25 1/1 15/22 15/14 13/19 7/6 6/5 11/16 5/4 9/13 3/2 2/1 16/23 0/1 1/1 7/10 2/1 19/27 3/2 2/1 12/17 2/1 3/1 53/75 3/1 41/58 7/2 29/41 4/1 1/0 17/24 1/0 5/7 2/1 1/0 18/25 1/0 13/18 1/0 60/83 -2/1 -1/1 47/65 -1/1 81/112 1/0 34/47 -1/1 1/0 89/123 0/1 1/0 55/76 1/0 21/29 -2/1 1/0 71/98 -5/6 50/69 -1/2 -1/3 29/40 0/1 37/51 0/1 1/0 45/62 -1/2 8/11 0/1 1/1 27/37 8/1 1/0 73/100 1/0 46/63 -11/1 1/0 19/26 1/0 30/41 -4/1 -3/1 71/97 -2/1 1/0 183/250 1/0 112/153 -3/1 1/0 41/56 1/0 11/15 -1/1 36/49 -1/1 0/1 61/83 -1/2 0/1 147/200 0/1 86/117 0/1 1/1 25/34 1/0 14/19 -1/1 1/0 17/23 -1/4 0/1 37/50 0/1 20/27 0/1 1/7 3/4 1/2 19/25 1/1 16/21 1/1 11/10 13/17 5/4 4/3 23/30 4/3 10/13 7/5 3/2 27/35 5/3 17/22 7/4 58/75 2/1 41/53 2/1 9/4 24/31 3/1 1/0 31/40 2/1 7/9 3/2 2/1 39/50 2/1 32/41 2/1 19/9 25/32 9/4 18/23 8/3 3/1 29/37 2/1 1/0 98/125 2/1 69/88 5/2 40/51 2/1 3/1 51/65 3/1 11/14 5/2 26/33 3/1 4/1 41/52 15/4 56/71 13/3 9/2 15/19 6/1 1/0 19/24 1/0 4/5 1/0 21/26 1/0 17/21 0/1 1/0 13/16 -3/2 22/27 -1/3 0/1 31/38 -1/2 40/49 -1/1 0/1 9/11 -1/2 0/1 41/50 0/1 32/39 0/1 1/7 23/28 1/4 14/17 0/1 1/1 19/23 -1/2 0/1 62/75 0/1 43/52 1/10 24/29 1/4 1/3 53/64 1/4 29/35 1/3 5/6 1/2 21/25 1/1 16/19 1/1 7/6 11/13 4/3 3/2 17/20 2/1 6/7 1/1 2/1 43/50 2/1 37/43 2/1 13/6 31/36 5/2 25/29 2/1 1/0 19/22 1/0 13/15 3/1 7/8 1/0 22/25 1/0 15/17 -10/1 1/0 8/9 -3/1 -2/1 9/10 0/1 1/1 0/1 1/0 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(399,362,550,499) (-1/1,-9/10) -> (29/40,37/51) Hyperbolic Matrix(101,90,450,401) (-9/10,-8/9) -> (2/9,9/40) Hyperbolic Matrix(249,220,-850,-751) (-8/9,-7/8) -> (-17/58,-12/41) Hyperbolic Matrix(149,130,400,349) (-7/8,-13/15) -> (13/35,3/8) Hyperbolic Matrix(849,734,-1100,-951) (-13/15,-6/7) -> (-44/57,-27/35) Hyperbolic Matrix(199,170,350,299) (-6/7,-17/20) -> (17/30,4/7) Hyperbolic Matrix(151,128,650,551) (-17/20,-11/13) -> (3/13,7/30) Hyperbolic Matrix(251,212,-650,-549) (-11/13,-5/6) -> (-17/44,-5/13) Hyperbolic Matrix(599,494,-850,-701) (-5/6,-14/17) -> (-12/17,-31/44) Hyperbolic Matrix(501,412,-850,-699) (-14/17,-9/11) -> (-23/39,-10/17) Hyperbolic Matrix(349,284,-800,-651) (-9/11,-13/16) -> (-7/16,-17/39) Hyperbolic Matrix(649,526,-1050,-851) (-13/16,-4/5) -> (-34/55,-21/34) Hyperbolic Matrix(549,434,-950,-751) (-4/5,-15/19) -> (-11/19,-26/45) Hyperbolic Matrix(249,196,-700,-551) (-15/19,-11/14) -> (-5/14,-11/31) Hyperbolic Matrix(799,626,-1150,-901) (-11/14,-18/23) -> (-16/23,-25/36) Hyperbolic Matrix(701,548,-1150,-899) (-18/23,-7/9) -> (-25/41,-14/23) Hyperbolic Matrix(49,38,450,349) (-7/9,-31/40) -> (1/10,1/9) Hyperbolic Matrix(2899,2246,4000,3099) (-31/40,-24/31) -> (50/69,29/40) Hyperbolic Matrix(349,270,-1100,-851) (-24/31,-17/22) -> (-7/22,-6/19) Hyperbolic Matrix(3051,2356,6800,5251) (-17/22,-61/79) -> (13/29,35/78) Hyperbolic Matrix(5901,4556,19300,14901) (-61/79,-105/136) -> (11/36,37/121) Hyperbolic Matrix(1101,850,-7900,-6099) (-105/136,-44/57) -> (-6/43,-5/36) Hyperbolic Matrix(301,232,650,501) (-27/35,-10/13) -> (6/13,7/15) Hyperbolic Matrix(99,76,650,499) (-10/13,-23/30) -> (3/20,2/13) Hyperbolic Matrix(551,422,850,651) (-23/30,-13/17) -> (11/17,13/20) Hyperbolic Matrix(351,268,-850,-649) (-13/17,-3/4) -> (-19/46,-7/17) Hyperbolic Matrix(599,442,-950,-701) (-3/4,-14/19) -> (-12/19,-29/46) Hyperbolic Matrix(299,220,950,699) (-14/19,-25/34) -> (5/16,6/19) Hyperbolic Matrix(4499,3306,-7350,-5401) (-25/34,-36/49) -> (-30/49,-71/116) Hyperbolic Matrix(3401,2498,-4900,-3599) (-36/49,-11/15) -> (-59/85,-34/49) Hyperbolic Matrix(5001,3662,-7100,-5199) (-11/15,-41/56) -> (-31/44,-81/115) Hyperbolic Matrix(3599,2634,-6150,-4501) (-41/56,-30/41) -> (-24/41,-55/94) Hyperbolic Matrix(599,438,2050,1499) (-30/41,-19/26) -> (7/24,12/41) Hyperbolic Matrix(299,218,-550,-401) (-19/26,-8/11) -> (-6/11,-13/24) Hyperbolic Matrix(201,146,-1100,-799) (-8/11,-37/51) -> (-9/49,-2/11) Hyperbolic Matrix(499,362,550,399) (-37/51,-29/40) -> (9/10,1/1) Hyperbolic Matrix(3099,2246,4000,2899) (-29/40,-50/69) -> (24/31,31/40) Hyperbolic Matrix(1151,834,-5450,-3949) (-50/69,-21/29) -> (-15/71,-4/19) Hyperbolic Matrix(1901,1376,2350,1701) (-21/29,-55/76) -> (21/26,17/21) Hyperbolic Matrix(4301,3112,-7600,-5499) (-55/76,-34/47) -> (-30/53,-43/76) Hyperbolic Matrix(2951,2134,-7950,-5749) (-34/47,-47/65) -> (-13/35,-36/97) Hyperbolic Matrix(1049,758,-2700,-1951) (-47/65,-13/18) -> (-7/18,-33/85) Hyperbolic Matrix(649,468,900,649) (-13/18,-18/25) -> (18/25,13/18) Hyperbolic Matrix(251,180,350,251) (-18/25,-5/7) -> (5/7,18/25) Hyperbolic Matrix(149,106,350,249) (-5/7,-17/24) -> (11/26,3/7) Hyperbolic Matrix(551,390,2050,1451) (-17/24,-29/41) -> (11/41,7/26) Hyperbolic Matrix(99,70,-850,-601) (-29/41,-12/17) -> (-2/17,-1/9) Hyperbolic Matrix(13849,9754,-19950,-14051) (-81/115,-50/71) -> (-84/121,-59/85) Hyperbolic Matrix(8399,5914,10650,7499) (-50/71,-69/98) -> (41/52,56/71) Hyperbolic Matrix(11451,8062,13850,9751) (-69/98,-88/125) -> (62/75,43/52) Hyperbolic Matrix(4049,2850,4900,3449) (-88/125,-19/27) -> (19/23,62/75) Hyperbolic Matrix(151,106,500,351) (-19/27,-7/10) -> (3/10,7/23) Hyperbolic Matrix(149,104,500,349) (-7/10,-16/23) -> (8/27,3/10) Hyperbolic Matrix(4399,3054,19300,13399) (-25/36,-84/121) -> (18/79,31/136) Hyperbolic Matrix(3999,2774,4900,3399) (-34/49,-43/62) -> (31/38,40/49) Hyperbolic Matrix(11251,7802,14350,9951) (-43/62,-52/75) -> (98/125,69/88) Hyperbolic Matrix(3449,2390,4400,3049) (-52/75,-9/13) -> (29/37,98/125) Hyperbolic Matrix(249,172,650,449) (-9/13,-11/16) -> (13/34,5/13) Hyperbolic Matrix(251,172,950,651) (-11/16,-13/19) -> (5/19,9/34) Hyperbolic Matrix(249,170,-1100,-751) (-13/19,-2/3) -> (-12/53,-7/31) Hyperbolic Matrix(651,424,-1150,-749) (-2/3,-13/20) -> (-17/30,-30/53) Hyperbolic Matrix(651,422,850,551) (-13/20,-11/17) -> (13/17,23/30) Hyperbolic Matrix(149,96,-700,-451) (-11/17,-9/14) -> (-3/14,-7/33) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(351,224,550,351) (-16/25,-7/11) -> (7/11,16/25) Hyperbolic Matrix(249,158,550,349) (-7/11,-19/30) -> (9/20,5/11) Hyperbolic Matrix(1349,854,-2450,-1551) (-19/30,-31/49) -> (-27/49,-11/20) Hyperbolic Matrix(949,600,2450,1549) (-31/49,-12/19) -> (12/31,19/49) Hyperbolic Matrix(349,220,-1350,-851) (-29/46,-17/27) -> (-7/27,-1/4) Hyperbolic Matrix(1751,1102,3100,1951) (-17/27,-39/62) -> (35/62,13/23) Hyperbolic Matrix(2201,1384,-7950,-4999) (-39/62,-22/35) -> (-18/65,-31/112) Hyperbolic Matrix(51,32,400,251) (-22/35,-5/8) -> (1/8,2/15) Hyperbolic Matrix(151,94,-400,-249) (-5/8,-13/21) -> (-11/29,-3/8) Hyperbolic Matrix(2801,1732,-4850,-2999) (-13/21,-34/55) -> (-26/45,-41/71) Hyperbolic Matrix(201,124,650,401) (-21/34,-8/13) -> (4/13,5/16) Hyperbolic Matrix(101,62,-650,-399) (-8/13,-19/31) -> (-3/19,-2/13) Hyperbolic Matrix(901,552,2450,1501) (-19/31,-30/49) -> (18/49,7/19) Hyperbolic Matrix(4199,2570,-15850,-9701) (-71/116,-41/67) -> (-31/117,-9/34) Hyperbolic Matrix(749,458,-2700,-1651) (-41/67,-11/18) -> (-5/18,-23/83) Hyperbolic Matrix(449,274,-2050,-1251) (-11/18,-25/41) -> (-9/41,-7/32) Hyperbolic Matrix(149,90,-250,-151) (-14/23,-3/5) -> (-3/5,-16/27) Parabolic Matrix(1651,978,3800,2251) (-16/27,-45/76) -> (33/76,10/23) Hyperbolic Matrix(11401,6750,18750,11101) (-45/76,-74/125) -> (76/125,45/74) Hyperbolic Matrix(7599,4498,12500,7399) (-74/125,-29/49) -> (31/51,76/125) Hyperbolic Matrix(2701,1598,-4900,-2899) (-29/49,-13/22) -> (-43/78,-27/49) Hyperbolic Matrix(349,206,-1950,-1151) (-13/22,-23/39) -> (-7/39,-5/28) Hyperbolic Matrix(201,118,-850,-499) (-10/17,-17/29) -> (-5/21,-4/17) Hyperbolic Matrix(649,380,1450,849) (-17/29,-24/41) -> (4/9,13/29) Hyperbolic Matrix(4649,2720,-17350,-10151) (-55/94,-31/53) -> (-41/153,-15/56) Hyperbolic Matrix(1799,1052,-6500,-3801) (-31/53,-7/12) -> (-31/112,-13/47) Hyperbolic Matrix(251,146,-600,-349) (-7/12,-11/19) -> (-13/31,-5/12) Hyperbolic Matrix(4451,2570,6150,3551) (-41/71,-15/26) -> (55/76,21/29) Hyperbolic Matrix(101,58,350,201) (-15/26,-4/7) -> (2/7,7/24) Hyperbolic Matrix(299,170,350,199) (-4/7,-17/30) -> (17/20,6/7) Hyperbolic Matrix(1549,876,3800,2149) (-43/76,-13/23) -> (11/27,31/76) Hyperbolic Matrix(149,84,-800,-451) (-13/23,-9/16) -> (-3/16,-5/27) Hyperbolic Matrix(449,252,800,449) (-9/16,-14/25) -> (14/25,9/16) Hyperbolic Matrix(251,140,450,251) (-14/25,-5/9) -> (5/9,14/25) Hyperbolic Matrix(601,332,1450,801) (-5/9,-16/29) -> (12/29,17/41) Hyperbolic Matrix(1549,854,6800,3749) (-16/29,-43/78) -> (5/22,18/79) Hyperbolic Matrix(201,110,550,301) (-11/20,-6/11) -> (4/11,11/30) Hyperbolic Matrix(499,270,-1850,-1001) (-13/24,-7/13) -> (-17/63,-7/26) Hyperbolic Matrix(149,80,650,349) (-7/13,-8/15) -> (8/35,3/13) Hyperbolic Matrix(651,346,-2350,-1249) (-8/15,-9/17) -> (-23/83,-18/65) Hyperbolic Matrix(549,290,850,449) (-9/17,-1/2) -> (31/48,11/17) Hyperbolic Matrix(749,354,950,449) (-1/2,-8/17) -> (26/33,41/52) Hyperbolic Matrix(951,446,-2450,-1149) (-8/17,-7/15) -> (-33/85,-26/67) Hyperbolic Matrix(501,232,650,301) (-7/15,-6/13) -> (10/13,27/35) Hyperbolic Matrix(149,68,-550,-251) (-6/13,-5/11) -> (-3/11,-10/37) Hyperbolic Matrix(349,158,550,249) (-5/11,-9/20) -> (19/30,7/11) Hyperbolic Matrix(899,404,-2450,-1101) (-9/20,-13/29) -> (-29/79,-11/30) Hyperbolic Matrix(849,380,1450,649) (-13/29,-4/9) -> (24/41,17/29) Hyperbolic Matrix(199,88,450,199) (-4/9,-11/25) -> (11/25,4/9) Hyperbolic Matrix(351,154,800,351) (-11/25,-7/16) -> (7/16,11/25) Hyperbolic Matrix(849,370,-3100,-1351) (-17/39,-27/62) -> (-17/62,-3/11) Hyperbolic Matrix(1149,500,3100,1349) (-27/62,-10/23) -> (10/27,23/62) Hyperbolic Matrix(401,174,-1150,-499) (-10/23,-13/30) -> (-7/20,-8/23) Hyperbolic Matrix(51,22,350,151) (-13/30,-3/7) -> (1/7,3/20) Hyperbolic Matrix(249,106,350,149) (-3/7,-11/26) -> (17/24,5/7) Hyperbolic Matrix(199,84,-950,-401) (-11/26,-8/19) -> (-4/19,-5/24) Hyperbolic Matrix(1451,610,2500,1051) (-8/19,-21/50) -> (29/50,18/31) Hyperbolic Matrix(1449,608,2500,1049) (-21/50,-13/31) -> (11/19,29/50) Hyperbolic Matrix(1651,686,-4450,-1849) (-5/12,-22/53) -> (-36/97,-23/62) Hyperbolic Matrix(1649,684,-6150,-2551) (-22/53,-17/41) -> (-11/41,-26/97) Hyperbolic Matrix(801,332,1450,601) (-17/41,-12/29) -> (16/29,5/9) Hyperbolic Matrix(1751,724,2300,951) (-12/29,-31/75) -> (19/25,16/21) Hyperbolic Matrix(1099,454,1450,599) (-31/75,-19/46) -> (3/4,19/25) Hyperbolic Matrix(151,62,-850,-349) (-7/17,-9/22) -> (-5/28,-3/17) Hyperbolic Matrix(99,40,-250,-101) (-9/22,-2/5) -> (-2/5,-11/28) Parabolic Matrix(2901,1138,-7900,-3099) (-11/28,-20/51) -> (-18/49,-47/128) Hyperbolic Matrix(5101,2000,12500,4901) (-20/51,-49/125) -> (51/125,20/49) Hyperbolic Matrix(7649,2998,18750,7349) (-49/125,-29/74) -> (31/76,51/125) Hyperbolic Matrix(7851,3076,10850,4251) (-29/74,-9/23) -> (89/123,55/76) Hyperbolic Matrix(251,98,-1150,-449) (-9/23,-7/18) -> (-7/32,-5/23) Hyperbolic Matrix(1949,756,-7350,-2851) (-26/67,-19/49) -> (-13/49,-22/83) Hyperbolic Matrix(1549,600,2450,949) (-19/49,-12/31) -> (12/19,31/49) Hyperbolic Matrix(1851,716,2200,851) (-12/31,-29/75) -> (21/25,16/19) Hyperbolic Matrix(1299,502,1550,599) (-29/75,-17/44) -> (5/6,21/25) Hyperbolic Matrix(449,172,650,249) (-5/13,-13/34) -> (11/16,9/13) Hyperbolic Matrix(199,76,-1050,-401) (-13/34,-8/21) -> (-4/21,-3/16) Hyperbolic Matrix(1551,590,2500,951) (-8/21,-19/50) -> (31/50,18/29) Hyperbolic Matrix(1549,588,2500,949) (-19/50,-11/29) -> (13/21,31/50) Hyperbolic Matrix(349,130,400,149) (-3/8,-13/35) -> (13/15,7/8) Hyperbolic Matrix(2201,816,2700,1001) (-23/62,-10/27) -> (22/27,31/38) Hyperbolic Matrix(249,92,-950,-351) (-10/27,-7/19) -> (-5/19,-6/23) Hyperbolic Matrix(1501,552,2450,901) (-7/19,-18/49) -> (30/49,19/31) Hyperbolic Matrix(4701,1726,5450,2001) (-47/128,-29/79) -> (25/29,19/22) Hyperbolic Matrix(301,110,550,201) (-11/30,-4/11) -> (6/11,11/20) Hyperbolic Matrix(199,72,550,199) (-4/11,-9/25) -> (9/25,4/11) Hyperbolic Matrix(251,90,700,251) (-9/25,-5/14) -> (5/14,9/25) Hyperbolic Matrix(1749,620,-6350,-2251) (-11/31,-17/48) -> (-27/98,-19/69) Hyperbolic Matrix(401,142,850,301) (-17/48,-6/17) -> (8/17,1/2) Hyperbolic Matrix(199,70,850,299) (-6/17,-7/20) -> (7/30,4/17) Hyperbolic Matrix(401,138,-1450,-499) (-8/23,-1/3) -> (-13/47,-34/123) Hyperbolic Matrix(1199,386,1550,499) (-1/3,-8/25) -> (58/75,41/53) Hyperbolic Matrix(1701,542,2200,701) (-8/25,-7/22) -> (17/22,58/75) Hyperbolic Matrix(699,220,950,299) (-6/19,-5/16) -> (25/34,14/19) Hyperbolic Matrix(401,124,650,201) (-5/16,-4/13) -> (8/13,21/34) Hyperbolic Matrix(249,76,-1150,-351) (-4/13,-7/23) -> (-5/23,-8/37) Hyperbolic Matrix(351,106,500,151) (-7/23,-3/10) -> (7/10,19/27) Hyperbolic Matrix(349,104,500,149) (-3/10,-8/27) -> (16/23,7/10) Hyperbolic Matrix(149,44,-850,-251) (-8/27,-5/17) -> (-3/17,-4/23) Hyperbolic Matrix(1499,440,1700,499) (-5/17,-22/75) -> (22/25,15/17) Hyperbolic Matrix(1801,528,2050,601) (-22/75,-17/58) -> (7/8,22/25) Hyperbolic Matrix(1499,438,2050,599) (-12/41,-7/24) -> (19/26,30/41) Hyperbolic Matrix(201,58,350,101) (-7/24,-2/7) -> (4/7,15/26) Hyperbolic Matrix(99,28,350,99) (-2/7,-7/25) -> (7/25,2/7) Hyperbolic Matrix(251,70,900,251) (-7/25,-5/18) -> (5/18,7/25) Hyperbolic Matrix(6599,1824,10850,2999) (-34/123,-21/76) -> (45/74,14/23) Hyperbolic Matrix(2599,718,6150,1699) (-21/76,-8/29) -> (30/71,11/26) Hyperbolic Matrix(3599,992,4350,1199) (-8/29,-27/98) -> (43/52,24/29) Hyperbolic Matrix(901,248,4000,1101) (-19/69,-11/40) -> (9/40,7/31) Hyperbolic Matrix(51,14,550,151) (-11/40,-14/51) -> (0/1,1/10) Hyperbolic Matrix(5999,1646,7650,2099) (-14/51,-17/62) -> (69/88,40/51) Hyperbolic Matrix(7301,1972,10000,2701) (-10/37,-27/100) -> (73/100,46/63) Hyperbolic Matrix(7299,1970,10000,2699) (-27/100,-17/63) -> (27/37,73/100) Hyperbolic Matrix(1451,390,2050,551) (-7/26,-11/41) -> (29/41,17/24) Hyperbolic Matrix(45751,12262,62500,16751) (-26/97,-67/250) -> (183/250,112/153) Hyperbolic Matrix(45749,12260,62500,16749) (-67/250,-41/153) -> (71/97,183/250) Hyperbolic Matrix(351,94,-2050,-549) (-15/56,-4/15) -> (-6/35,-1/6) Hyperbolic Matrix(851,226,-3950,-1049) (-4/15,-13/49) -> (-11/51,-14/65) Hyperbolic Matrix(29401,7792,40000,10601) (-22/83,-53/200) -> (147/200,86/117) Hyperbolic Matrix(29399,7790,40000,10599) (-53/200,-31/117) -> (61/83,147/200) Hyperbolic Matrix(651,172,950,251) (-9/34,-5/19) -> (13/19,11/16) Hyperbolic Matrix(1851,482,2500,651) (-6/23,-13/50) -> (37/50,20/27) Hyperbolic Matrix(1849,480,2500,649) (-13/50,-7/27) -> (17/23,37/50) Hyperbolic Matrix(851,206,1450,351) (-1/4,-6/25) -> (44/75,27/46) Hyperbolic Matrix(1349,322,2300,549) (-6/25,-5/21) -> (17/29,44/75) Hyperbolic Matrix(299,70,850,199) (-4/17,-7/30) -> (7/20,6/17) Hyperbolic Matrix(551,128,650,151) (-7/30,-3/13) -> (11/13,17/20) Hyperbolic Matrix(349,80,650,149) (-3/13,-8/35) -> (8/15,7/13) Hyperbolic Matrix(149,34,-1100,-251) (-8/35,-5/22) -> (-3/22,-2/15) Hyperbolic Matrix(1499,340,2200,499) (-5/22,-17/75) -> (17/25,15/22) Hyperbolic Matrix(1051,238,1550,351) (-17/75,-12/53) -> (2/3,17/25) Hyperbolic Matrix(1101,248,4000,901) (-7/31,-9/40) -> (11/40,19/69) Hyperbolic Matrix(401,90,450,101) (-9/40,-2/9) -> (8/9,9/10) Hyperbolic Matrix(1951,430,2500,551) (-2/9,-11/50) -> (39/50,32/41) Hyperbolic Matrix(1949,428,2500,549) (-11/50,-9/41) -> (7/9,39/50) Hyperbolic Matrix(1351,292,4400,951) (-8/37,-27/125) -> (23/75,4/13) Hyperbolic Matrix(4399,950,14350,3099) (-27/125,-19/88) -> (19/62,23/75) Hyperbolic Matrix(5551,1198,7650,1651) (-19/88,-11/51) -> (37/51,45/62) Hyperbolic Matrix(799,172,-4650,-1001) (-14/65,-3/14) -> (-11/64,-6/35) Hyperbolic Matrix(501,106,950,201) (-7/33,-11/52) -> (1/2,9/17) Hyperbolic Matrix(3151,666,10650,2251) (-11/52,-15/71) -> (21/71,29/98) Hyperbolic Matrix(49,10,-250,-51) (-5/24,-1/5) -> (-1/5,-5/26) Parabolic Matrix(649,124,2350,449) (-5/26,-4/21) -> (8/29,21/76) Hyperbolic Matrix(1699,314,2700,499) (-5/27,-7/38) -> (39/62,17/27) Hyperbolic Matrix(1501,276,4900,901) (-7/38,-9/49) -> (15/49,19/62) Hyperbolic Matrix(2051,370,2500,451) (-2/11,-9/50) -> (41/50,32/39) Hyperbolic Matrix(2049,368,2500,449) (-9/50,-7/39) -> (9/11,41/50) Hyperbolic Matrix(1451,252,4900,851) (-4/23,-13/75) -> (37/125,8/27) Hyperbolic Matrix(4099,710,13850,2399) (-13/75,-9/52) -> (29/98,37/125) Hyperbolic Matrix(3151,544,4350,751) (-9/52,-5/29) -> (21/29,71/98) Hyperbolic Matrix(2499,430,2900,499) (-5/29,-11/64) -> (31/36,25/29) Hyperbolic Matrix(951,154,1550,251) (-1/6,-4/25) -> (46/75,27/44) Hyperbolic Matrix(1349,214,2200,349) (-4/25,-3/19) -> (19/31,46/75) Hyperbolic Matrix(499,76,650,99) (-2/13,-3/20) -> (23/30,10/13) Hyperbolic Matrix(151,22,350,51) (-3/20,-1/7) -> (3/7,13/30) Hyperbolic Matrix(2151,302,2500,351) (-1/7,-7/50) -> (43/50,37/43) Hyperbolic Matrix(2149,300,2500,349) (-7/50,-6/43) -> (6/7,43/50) Hyperbolic Matrix(2401,332,2900,401) (-5/36,-4/29) -> (24/29,53/64) Hyperbolic Matrix(3449,474,5450,749) (-4/29,-3/22) -> (81/128,50/79) Hyperbolic Matrix(251,32,400,51) (-2/15,-1/8) -> (5/8,22/35) Hyperbolic Matrix(1449,176,2050,249) (-1/8,-3/25) -> (53/75,41/58) Hyperbolic Matrix(1201,142,1700,201) (-3/25,-2/17) -> (12/17,53/75) Hyperbolic Matrix(349,38,450,49) (-1/9,-1/10) -> (31/40,7/9) Hyperbolic Matrix(151,14,550,51) (-1/10,0/1) -> (14/51,11/40) Hyperbolic Matrix(601,-70,850,-99) (1/9,1/8) -> (41/58,29/41) Hyperbolic Matrix(251,-34,1100,-149) (2/15,1/7) -> (13/57,8/35) Hyperbolic Matrix(399,-62,650,-101) (2/13,1/6) -> (27/44,8/13) Hyperbolic Matrix(251,-44,850,-149) (1/6,3/17) -> (5/17,13/44) Hyperbolic Matrix(349,-62,850,-151) (3/17,2/11) -> (16/39,7/17) Hyperbolic Matrix(451,-84,800,-149) (2/11,3/16) -> (9/16,22/39) Hyperbolic Matrix(401,-76,1050,-199) (3/16,1/5) -> (21/55,13/34) Hyperbolic Matrix(401,-84,950,-199) (1/5,4/19) -> (8/19,19/45) Hyperbolic Matrix(451,-96,700,-149) (4/19,3/14) -> (9/14,20/31) Hyperbolic Matrix(351,-76,1150,-249) (3/14,5/23) -> (7/23,11/36) Hyperbolic Matrix(449,-98,1150,-251) (5/23,2/9) -> (16/41,9/23) Hyperbolic Matrix(751,-170,1100,-249) (7/31,5/22) -> (15/22,13/19) Hyperbolic Matrix(6799,-1550,7900,-1801) (31/136,13/57) -> (37/43,31/36) Hyperbolic Matrix(499,-118,850,-201) (4/17,1/4) -> (27/46,10/17) Hyperbolic Matrix(351,-92,950,-249) (1/4,5/19) -> (7/19,17/46) Hyperbolic Matrix(2851,-756,7350,-1949) (9/34,13/49) -> (19/49,45/116) Hyperbolic Matrix(1499,-398,4900,-1301) (13/49,4/15) -> (26/85,15/49) Hyperbolic Matrix(2099,-562,7100,-1901) (4/15,15/56) -> (13/44,34/115) Hyperbolic Matrix(2551,-684,6150,-1649) (15/56,11/41) -> (17/41,39/94) Hyperbolic Matrix(251,-68,550,-149) (7/26,3/11) -> (5/11,11/24) Hyperbolic Matrix(899,-246,1100,-301) (3/11,14/51) -> (40/49,9/11) Hyperbolic Matrix(4299,-1184,5450,-1501) (19/69,8/29) -> (56/71,15/19) Hyperbolic Matrix(3299,-912,7600,-2101) (21/76,13/47) -> (23/53,33/76) Hyperbolic Matrix(4999,-1384,7950,-2201) (13/47,18/65) -> (22/35,61/97) Hyperbolic Matrix(1651,-458,2700,-749) (18/65,5/18) -> (11/18,52/85) Hyperbolic Matrix(751,-220,850,-249) (12/41,5/17) -> (15/17,8/9) Hyperbolic Matrix(6101,-1804,19950,-5899) (34/115,21/71) -> (37/121,26/85) Hyperbolic Matrix(851,-270,1100,-349) (6/19,1/3) -> (41/53,24/31) Hyperbolic Matrix(499,-174,1150,-401) (1/3,7/20) -> (13/30,23/53) Hyperbolic Matrix(551,-196,700,-249) (6/17,5/14) -> (11/14,26/33) Hyperbolic Matrix(1101,-404,2450,-899) (11/30,18/49) -> (22/49,9/20) Hyperbolic Matrix(1001,-370,1350,-499) (17/46,10/27) -> (20/27,3/4) Hyperbolic Matrix(5749,-2134,7950,-2951) (23/62,13/35) -> (47/65,81/112) Hyperbolic Matrix(249,-94,400,-151) (3/8,8/21) -> (18/29,5/8) Hyperbolic Matrix(2049,-782,4850,-1851) (8/21,21/55) -> (19/45,30/71) Hyperbolic Matrix(549,-212,650,-251) (5/13,12/31) -> (16/19,11/13) Hyperbolic Matrix(11651,-4520,15850,-6149) (45/116,26/67) -> (86/117,25/34) Hyperbolic Matrix(1951,-758,2700,-1049) (26/67,7/18) -> (13/18,60/83) Hyperbolic Matrix(1601,-624,2050,-799) (7/18,16/41) -> (32/41,25/32) Hyperbolic Matrix(101,-40,250,-99) (9/23,2/5) -> (2/5,11/27) Parabolic Matrix(2199,-898,4900,-2001) (20/49,9/22) -> (35/78,22/49) Hyperbolic Matrix(1601,-656,1950,-799) (9/22,16/39) -> (32/39,23/28) Hyperbolic Matrix(649,-268,850,-351) (7/17,12/29) -> (16/21,13/17) Hyperbolic Matrix(12701,-5270,17350,-7199) (39/94,22/53) -> (112/153,41/56) Hyperbolic Matrix(4701,-1952,6500,-2699) (22/53,5/12) -> (81/112,34/47) Hyperbolic Matrix(349,-146,600,-251) (5/12,8/19) -> (18/31,7/12) Hyperbolic Matrix(651,-284,800,-349) (10/23,7/16) -> (13/16,22/27) Hyperbolic Matrix(1351,-620,1850,-849) (11/24,6/13) -> (46/63,19/26) Hyperbolic Matrix(1699,-796,2350,-1101) (7/15,8/17) -> (60/83,47/65) Hyperbolic Matrix(1499,-796,2450,-1301) (9/17,8/15) -> (52/85,41/67) Hyperbolic Matrix(401,-218,550,-299) (7/13,6/11) -> (8/11,27/37) Hyperbolic Matrix(1551,-854,2450,-1349) (11/20,16/29) -> (50/79,19/30) Hyperbolic Matrix(2251,-1270,3100,-1749) (22/39,35/62) -> (45/62,8/11) Hyperbolic Matrix(749,-424,1150,-651) (13/23,17/30) -> (13/20,15/23) Hyperbolic Matrix(751,-434,950,-549) (15/26,11/19) -> (15/19,19/24) Hyperbolic Matrix(2799,-1636,4450,-2601) (7/12,31/53) -> (61/97,39/62) Hyperbolic Matrix(4501,-2634,6150,-3599) (31/53,24/41) -> (30/41,71/97) Hyperbolic Matrix(699,-412,850,-501) (10/17,13/22) -> (23/28,14/17) Hyperbolic Matrix(151,-90,250,-149) (13/22,3/5) -> (3/5,17/28) Parabolic Matrix(4999,-3038,7900,-4801) (17/28,31/51) -> (31/49,81/128) Hyperbolic Matrix(899,-548,1150,-701) (14/23,11/18) -> (25/32,18/23) Hyperbolic Matrix(5401,-3306,7350,-4499) (41/67,30/49) -> (36/49,61/83) Hyperbolic Matrix(851,-526,1050,-649) (21/34,13/21) -> (17/21,13/16) Hyperbolic Matrix(701,-442,950,-599) (17/27,12/19) -> (14/19,17/23) Hyperbolic Matrix(4601,-2970,6350,-4099) (20/31,31/48) -> (71/98,50/69) Hyperbolic Matrix(1049,-688,1450,-951) (15/23,2/3) -> (34/47,89/123) Hyperbolic Matrix(901,-626,1150,-799) (9/13,16/23) -> (18/23,29/37) Hyperbolic Matrix(701,-494,850,-599) (19/27,12/17) -> (14/17,19/23) Hyperbolic Matrix(1699,-1244,2050,-1501) (41/56,11/15) -> (29/35,5/6) Hyperbolic Matrix(3099,-2276,3950,-2901) (11/15,36/49) -> (40/51,51/65) Hyperbolic Matrix(951,-734,1100,-849) (27/35,17/22) -> (19/22,13/15) Hyperbolic Matrix(3851,-3022,4650,-3649) (51/65,11/14) -> (53/64,29/35) Hyperbolic Matrix(201,-160,250,-199) (19/24,4/5) -> (4/5,21/26) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(399,362,550,499) -> Matrix(1,0,-2,1) Matrix(101,90,450,401) -> Matrix(5,-2,8,-3) Matrix(249,220,-850,-751) -> Matrix(13,-6,24,-11) Matrix(149,130,400,349) -> Matrix(11,-6,2,-1) Matrix(849,734,-1100,-951) -> Matrix(25,-16,36,-23) Matrix(199,170,350,299) -> Matrix(3,-2,8,-5) Matrix(151,128,650,551) -> Matrix(3,-2,-4,3) Matrix(251,212,-650,-549) -> Matrix(5,-4,14,-11) Matrix(599,494,-850,-701) -> Matrix(5,-2,8,-3) Matrix(501,412,-850,-699) -> Matrix(3,-2,2,-1) Matrix(349,284,-800,-651) -> Matrix(13,-4,10,-3) Matrix(649,526,-1050,-851) -> Matrix(9,-4,16,-7) Matrix(549,434,-950,-751) -> Matrix(3,-2,2,-1) Matrix(249,196,-700,-551) -> Matrix(17,-10,12,-7) Matrix(799,626,-1150,-901) -> Matrix(13,-8,18,-11) Matrix(701,548,-1150,-899) -> Matrix(25,-16,36,-23) Matrix(49,38,450,349) -> Matrix(3,-2,2,-1) Matrix(2899,2246,4000,3099) -> Matrix(3,-2,-4,3) Matrix(349,270,-1100,-851) -> Matrix(3,-2,14,-9) Matrix(3051,2356,6800,5251) -> Matrix(17,-12,10,-7) Matrix(5901,4556,19300,14901) -> Matrix(3,-2,2,-1) Matrix(1101,850,-7900,-6099) -> Matrix(3,-2,8,-5) Matrix(301,232,650,501) -> Matrix(11,-8,-4,3) Matrix(99,76,650,499) -> Matrix(5,-4,4,-3) Matrix(551,422,850,651) -> Matrix(5,-4,4,-3) Matrix(351,268,-850,-649) -> Matrix(7,-6,-8,7) Matrix(599,442,-950,-701) -> Matrix(1,0,-2,1) Matrix(299,220,950,699) -> Matrix(1,0,-4,1) Matrix(4499,3306,-7350,-5401) -> Matrix(5,-2,8,-3) Matrix(3401,2498,-4900,-3599) -> Matrix(5,-2,8,-3) Matrix(5001,3662,-7100,-5199) -> Matrix(29,-12,46,-19) Matrix(3599,2634,-6150,-4501) -> Matrix(1,0,-2,1) Matrix(599,438,2050,1499) -> Matrix(1,0,-2,1) Matrix(299,218,-550,-401) -> Matrix(3,-2,8,-5) Matrix(201,146,-1100,-799) -> Matrix(1,0,-2,1) Matrix(499,362,550,399) -> Matrix(1,0,-2,1) Matrix(3099,2246,4000,2899) -> Matrix(7,-2,4,-1) Matrix(1151,834,-5450,-3949) -> Matrix(7,-2,18,-5) Matrix(1901,1376,2350,1701) -> Matrix(5,-2,-2,1) Matrix(4301,3112,-7600,-5499) -> Matrix(1,0,-4,1) Matrix(2951,2134,-7950,-5749) -> Matrix(9,-2,14,-3) Matrix(1049,758,-2700,-1951) -> Matrix(5,-2,18,-7) Matrix(649,468,900,649) -> Matrix(9,-4,-2,1) Matrix(251,180,350,251) -> Matrix(7,-4,2,-1) Matrix(149,106,350,249) -> Matrix(1,0,0,1) Matrix(551,390,2050,1451) -> Matrix(7,-4,16,-9) Matrix(99,70,-850,-601) -> Matrix(7,-4,2,-1) Matrix(13849,9754,-19950,-14051) -> Matrix(25,-16,36,-23) Matrix(8399,5914,10650,7499) -> Matrix(83,-54,20,-13) Matrix(11451,8062,13850,9751) -> Matrix(3,-2,62,-41) Matrix(4049,2850,4900,3449) -> Matrix(3,-2,-10,7) Matrix(151,106,500,351) -> Matrix(3,-2,2,-1) Matrix(149,104,500,349) -> Matrix(3,-2,-4,3) Matrix(4399,3054,19300,13399) -> Matrix(17,-12,10,-7) Matrix(3999,2774,4900,3399) -> Matrix(3,-2,-4,3) Matrix(11251,7802,14350,9951) -> Matrix(19,-12,8,-5) Matrix(3449,2390,4400,3049) -> Matrix(5,-4,4,-3) Matrix(249,172,650,449) -> Matrix(3,-2,-4,3) Matrix(251,172,950,651) -> Matrix(7,-6,20,-17) Matrix(249,170,-1100,-751) -> Matrix(11,-10,10,-9) Matrix(651,424,-1150,-749) -> Matrix(1,0,-2,1) Matrix(651,422,850,551) -> Matrix(5,-4,4,-3) Matrix(149,96,-700,-451) -> Matrix(1,0,2,1) Matrix(449,288,700,449) -> Matrix(1,0,2,1) Matrix(351,224,550,351) -> Matrix(1,0,-2,1) Matrix(249,158,550,349) -> Matrix(3,-2,2,-1) Matrix(1349,854,-2450,-1551) -> Matrix(1,0,0,1) Matrix(949,600,2450,1549) -> Matrix(3,-2,-4,3) Matrix(349,220,-1350,-851) -> Matrix(1,0,2,1) Matrix(1751,1102,3100,1951) -> Matrix(1,0,0,1) Matrix(2201,1384,-7950,-4999) -> Matrix(5,-4,4,-3) Matrix(51,32,400,251) -> Matrix(1,0,-2,1) Matrix(151,94,-400,-249) -> Matrix(1,0,0,1) Matrix(2801,1732,-4850,-2999) -> Matrix(3,-2,2,-1) Matrix(201,124,650,401) -> Matrix(3,-2,2,-1) Matrix(101,62,-650,-399) -> Matrix(3,-2,8,-5) Matrix(901,552,2450,1501) -> Matrix(5,-4,4,-3) Matrix(4199,2570,-15850,-9701) -> Matrix(1,0,-2,1) Matrix(749,458,-2700,-1651) -> Matrix(7,-6,6,-5) Matrix(449,274,-2050,-1251) -> Matrix(3,-2,14,-9) Matrix(149,90,-250,-151) -> Matrix(7,-6,6,-5) Matrix(1651,978,3800,2251) -> Matrix(29,-42,38,-55) Matrix(11401,6750,18750,11101) -> Matrix(157,-234,104,-155) Matrix(7599,4498,12500,7399) -> Matrix(107,-162,72,-109) Matrix(2701,1598,-4900,-2899) -> Matrix(9,-14,20,-31) Matrix(349,206,-1950,-1151) -> Matrix(1,-2,6,-11) Matrix(201,118,-850,-499) -> Matrix(1,-2,4,-7) Matrix(649,380,1450,849) -> Matrix(3,-8,2,-5) Matrix(4649,2720,-17350,-10151) -> Matrix(1,-2,0,1) Matrix(1799,1052,-6500,-3801) -> Matrix(3,-2,2,-1) Matrix(251,146,-600,-349) -> Matrix(1,-4,0,1) Matrix(4451,2570,6150,3551) -> Matrix(1,0,0,1) Matrix(101,58,350,201) -> Matrix(1,2,0,1) Matrix(299,170,350,199) -> Matrix(1,2,0,1) Matrix(1549,876,3800,2149) -> Matrix(1,0,6,1) Matrix(149,84,-800,-451) -> Matrix(1,0,2,1) Matrix(449,252,800,449) -> Matrix(1,0,10,1) Matrix(251,140,450,251) -> Matrix(1,0,-6,1) Matrix(601,332,1450,801) -> Matrix(7,-2,18,-5) Matrix(1549,854,6800,3749) -> Matrix(19,-8,12,-5) Matrix(201,110,550,301) -> Matrix(7,-2,4,-1) Matrix(499,270,-1850,-1001) -> Matrix(9,-4,-2,1) Matrix(149,80,650,349) -> Matrix(7,-4,2,-1) Matrix(651,346,-2350,-1249) -> Matrix(7,-6,6,-5) Matrix(549,290,850,449) -> Matrix(3,-2,2,-1) Matrix(749,354,950,449) -> Matrix(15,-4,4,-1) Matrix(951,446,-2450,-1149) -> Matrix(1,0,0,1) Matrix(501,232,650,301) -> Matrix(19,-8,12,-5) Matrix(149,68,-550,-251) -> Matrix(7,-4,2,-1) Matrix(349,158,550,249) -> Matrix(3,-2,2,-1) Matrix(899,404,-2450,-1101) -> Matrix(1,0,0,1) Matrix(849,380,1450,649) -> Matrix(11,-8,18,-13) Matrix(199,88,450,199) -> Matrix(9,-8,8,-7) Matrix(351,154,800,351) -> Matrix(13,-14,14,-15) Matrix(849,370,-3100,-1351) -> Matrix(1,-2,2,-3) Matrix(1149,500,3100,1349) -> Matrix(11,-14,4,-5) Matrix(401,174,-1150,-499) -> Matrix(5,-8,2,-3) Matrix(51,22,350,151) -> Matrix(1,-2,2,-3) Matrix(249,106,350,149) -> Matrix(1,0,0,1) Matrix(199,84,-950,-401) -> Matrix(1,-2,2,-3) Matrix(1451,610,2500,1051) -> Matrix(1,-14,2,-27) Matrix(1449,608,2500,1049) -> Matrix(1,12,2,25) Matrix(1651,686,-4450,-1849) -> Matrix(5,8,8,13) Matrix(1649,684,-6150,-2551) -> Matrix(1,2,0,1) Matrix(801,332,1450,601) -> Matrix(1,2,-2,-3) Matrix(1751,724,2300,951) -> Matrix(15,16,14,15) Matrix(1099,454,1450,599) -> Matrix(9,8,10,9) Matrix(151,62,-850,-349) -> Matrix(1,0,4,1) Matrix(99,40,-250,-101) -> Matrix(1,0,4,1) Matrix(2901,1138,-7900,-3099) -> Matrix(5,-2,8,-3) Matrix(5101,2000,12500,4901) -> Matrix(1,0,0,1) Matrix(7649,2998,18750,7349) -> Matrix(5,-2,18,-7) Matrix(7851,3076,10850,4251) -> Matrix(1,0,-2,1) Matrix(251,98,-1150,-449) -> Matrix(1,0,0,1) Matrix(1949,756,-7350,-2851) -> Matrix(9,-2,-4,1) Matrix(1549,600,2450,949) -> Matrix(7,-2,4,-1) Matrix(1851,716,2200,851) -> Matrix(31,-10,28,-9) Matrix(1299,502,1550,599) -> Matrix(17,-6,20,-7) Matrix(449,172,650,249) -> Matrix(7,-2,4,-1) Matrix(199,76,-1050,-401) -> Matrix(5,-2,-2,1) Matrix(1551,590,2500,951) -> Matrix(13,-6,-2,1) Matrix(1549,588,2500,949) -> Matrix(15,-8,2,-1) Matrix(349,130,400,149) -> Matrix(11,-6,2,-1) Matrix(2201,816,2700,1001) -> Matrix(3,-2,2,-1) Matrix(249,92,-950,-351) -> Matrix(3,-2,-4,3) Matrix(1501,552,2450,901) -> Matrix(5,-4,4,-3) Matrix(4701,1726,5450,2001) -> Matrix(7,-4,2,-1) Matrix(301,110,550,201) -> Matrix(3,-2,-4,3) Matrix(199,72,550,199) -> Matrix(9,-8,8,-7) Matrix(251,90,700,251) -> Matrix(9,-10,10,-11) Matrix(1749,620,-6350,-2251) -> Matrix(5,-8,2,-3) Matrix(401,142,850,301) -> Matrix(1,-2,0,1) Matrix(199,70,850,299) -> Matrix(1,-2,0,1) Matrix(401,138,-1450,-499) -> Matrix(3,4,2,3) Matrix(1199,386,1550,499) -> Matrix(9,2,4,1) Matrix(1701,542,2200,701) -> Matrix(23,-2,12,-1) Matrix(699,220,950,299) -> Matrix(1,0,-4,1) Matrix(401,124,650,201) -> Matrix(3,-2,2,-1) Matrix(249,76,-1150,-351) -> Matrix(1,0,2,1) Matrix(351,106,500,151) -> Matrix(3,-2,2,-1) Matrix(349,104,500,149) -> Matrix(7,-2,4,-1) Matrix(149,44,-850,-251) -> Matrix(5,-2,8,-3) Matrix(1499,440,1700,499) -> Matrix(29,-14,-2,1) Matrix(1801,528,2050,601) -> Matrix(35,-18,2,-1) Matrix(1499,438,2050,599) -> Matrix(1,0,-2,1) Matrix(201,58,350,101) -> Matrix(3,-2,8,-5) Matrix(99,28,350,99) -> Matrix(5,-4,4,-3) Matrix(251,70,900,251) -> Matrix(9,-10,10,-11) Matrix(6599,1824,10850,2999) -> Matrix(49,-72,32,-47) Matrix(2599,718,6150,1699) -> Matrix(1,-2,4,-7) Matrix(3599,992,4350,1199) -> Matrix(1,-2,6,-11) Matrix(901,248,4000,1101) -> Matrix(3,-4,4,-5) Matrix(51,14,550,151) -> Matrix(1,-2,2,-3) Matrix(5999,1646,7650,2099) -> Matrix(5,-8,2,-3) Matrix(7301,1972,10000,2701) -> Matrix(1,-20,0,1) Matrix(7299,1970,10000,2699) -> Matrix(1,18,0,1) Matrix(1451,390,2050,551) -> Matrix(1,4,0,1) Matrix(45751,12262,62500,16751) -> Matrix(1,-4,0,1) Matrix(45749,12260,62500,16749) -> Matrix(1,-2,0,1) Matrix(351,94,-2050,-549) -> Matrix(1,0,0,1) Matrix(851,226,-3950,-1049) -> Matrix(1,2,2,5) Matrix(29401,7792,40000,10601) -> Matrix(1,2,2,5) Matrix(29399,7790,40000,10599) -> Matrix(1,2,-4,-7) Matrix(651,172,950,251) -> Matrix(5,6,4,5) Matrix(1851,482,2500,651) -> Matrix(1,0,12,1) Matrix(1849,480,2500,649) -> Matrix(1,0,-10,1) Matrix(851,206,1450,351) -> Matrix(7,2,10,3) Matrix(1349,322,2300,549) -> Matrix(17,-2,26,-3) Matrix(299,70,850,199) -> Matrix(5,-2,8,-3) Matrix(551,128,650,151) -> Matrix(7,-2,4,-1) Matrix(349,80,650,149) -> Matrix(7,-4,2,-1) Matrix(149,34,-1100,-251) -> Matrix(3,-2,2,-1) Matrix(1499,340,2200,499) -> Matrix(21,-20,20,-19) Matrix(1051,238,1550,351) -> Matrix(11,-12,12,-13) Matrix(1101,248,4000,901) -> Matrix(3,-4,4,-5) Matrix(401,90,450,101) -> Matrix(1,-2,0,1) Matrix(1951,430,2500,551) -> Matrix(21,2,10,1) Matrix(1949,428,2500,549) -> Matrix(23,-2,12,-1) Matrix(1351,292,4400,951) -> Matrix(7,-2,4,-1) Matrix(4399,950,14350,3099) -> Matrix(17,-6,20,-7) Matrix(5551,1198,7650,1651) -> Matrix(5,-2,-2,1) Matrix(799,172,-4650,-1001) -> Matrix(3,-2,2,-1) Matrix(501,106,950,201) -> Matrix(7,-2,4,-1) Matrix(3151,666,10650,2251) -> Matrix(23,-8,-20,7) Matrix(49,10,-250,-51) -> Matrix(3,-2,2,-1) Matrix(649,124,2350,449) -> Matrix(3,2,4,3) Matrix(1699,314,2700,499) -> Matrix(1,0,-2,1) Matrix(1501,276,4900,901) -> Matrix(1,-2,2,-3) Matrix(2051,370,2500,451) -> Matrix(1,0,8,1) Matrix(2049,368,2500,449) -> Matrix(1,0,-10,1) Matrix(1451,252,4900,851) -> Matrix(7,-6,-8,7) Matrix(4099,710,13850,2399) -> Matrix(19,-20,-18,19) Matrix(3151,544,4350,751) -> Matrix(3,-4,-2,3) Matrix(2499,430,2900,499) -> Matrix(5,-8,2,-3) Matrix(951,154,1550,251) -> Matrix(5,2,2,1) Matrix(1349,214,2200,349) -> Matrix(11,-2,6,-1) Matrix(499,76,650,99) -> Matrix(5,-4,4,-3) Matrix(151,22,350,51) -> Matrix(1,-2,2,-3) Matrix(2151,302,2500,351) -> Matrix(13,2,6,1) Matrix(2149,300,2500,349) -> Matrix(15,-2,8,-1) Matrix(2401,332,2900,401) -> Matrix(1,0,0,1) Matrix(3449,474,5450,749) -> Matrix(5,-2,-2,1) Matrix(251,32,400,51) -> Matrix(1,0,-2,1) Matrix(1449,176,2050,249) -> Matrix(13,-10,4,-3) Matrix(1201,142,1700,201) -> Matrix(5,-8,2,-3) Matrix(349,38,450,49) -> Matrix(3,-2,2,-1) Matrix(151,14,550,51) -> Matrix(1,-2,2,-3) Matrix(601,-70,850,-99) -> Matrix(7,-4,2,-1) Matrix(251,-34,1100,-149) -> Matrix(3,-2,2,-1) Matrix(399,-62,650,-101) -> Matrix(1,2,0,1) Matrix(251,-44,850,-149) -> Matrix(1,-2,0,1) Matrix(349,-62,850,-151) -> Matrix(1,0,4,1) Matrix(451,-84,800,-149) -> Matrix(1,0,2,1) Matrix(401,-76,1050,-199) -> Matrix(5,-2,-2,1) Matrix(401,-84,950,-199) -> Matrix(1,-2,2,-3) Matrix(451,-96,700,-149) -> Matrix(1,0,2,1) Matrix(351,-76,1150,-249) -> Matrix(1,0,2,1) Matrix(449,-98,1150,-251) -> Matrix(1,0,0,1) Matrix(751,-170,1100,-249) -> Matrix(11,-10,10,-9) Matrix(6799,-1550,7900,-1801) -> Matrix(13,-24,6,-11) Matrix(499,-118,850,-201) -> Matrix(3,2,4,3) Matrix(351,-92,950,-249) -> Matrix(7,-2,4,-1) Matrix(2851,-756,7350,-1949) -> Matrix(5,-2,-12,5) Matrix(1499,-398,4900,-1301) -> Matrix(5,-2,8,-3) Matrix(2099,-562,7100,-1901) -> Matrix(1,-2,0,1) Matrix(2551,-684,6150,-1649) -> Matrix(3,-2,8,-5) Matrix(251,-68,550,-149) -> Matrix(7,-4,2,-1) Matrix(899,-246,1100,-301) -> Matrix(3,-2,-4,3) Matrix(4299,-1184,5450,-1501) -> Matrix(11,-6,2,-1) Matrix(3299,-912,7600,-2101) -> Matrix(47,-36,64,-49) Matrix(4999,-1384,7950,-2201) -> Matrix(5,-4,4,-3) Matrix(1651,-458,2700,-749) -> Matrix(7,-6,6,-5) Matrix(751,-220,850,-249) -> Matrix(1,-6,0,1) Matrix(6101,-1804,19950,-5899) -> Matrix(3,4,8,11) Matrix(851,-270,1100,-349) -> Matrix(5,2,2,1) Matrix(499,-174,1150,-401) -> Matrix(13,-8,18,-11) Matrix(551,-196,700,-249) -> Matrix(13,-10,4,-3) Matrix(1101,-404,2450,-899) -> Matrix(1,0,0,1) Matrix(1001,-370,1350,-499) -> Matrix(1,-2,4,-7) Matrix(5749,-2134,7950,-2951) -> Matrix(1,-2,-2,5) Matrix(249,-94,400,-151) -> Matrix(1,0,0,1) Matrix(2049,-782,4850,-1851) -> Matrix(1,2,2,5) Matrix(549,-212,650,-251) -> Matrix(3,4,2,3) Matrix(11651,-4520,15850,-6149) -> Matrix(1,0,2,1) Matrix(1951,-758,2700,-1049) -> Matrix(3,2,-2,-1) Matrix(1601,-624,2050,-799) -> Matrix(13,2,6,1) Matrix(101,-40,250,-99) -> Matrix(1,0,4,1) Matrix(2199,-898,4900,-2001) -> Matrix(7,-2,4,-1) Matrix(1601,-656,1950,-799) -> Matrix(1,0,0,1) Matrix(649,-268,850,-351) -> Matrix(19,-6,16,-5) Matrix(12701,-5270,17350,-7199) -> Matrix(9,-4,-2,1) Matrix(4701,-1952,6500,-2699) -> Matrix(5,-2,-2,1) Matrix(349,-146,600,-251) -> Matrix(9,-4,16,-7) Matrix(651,-284,800,-349) -> Matrix(5,-4,-6,5) Matrix(1351,-620,1850,-849) -> Matrix(1,-6,0,1) Matrix(1699,-796,2350,-1101) -> Matrix(3,2,-2,-1) Matrix(1499,-796,2450,-1301) -> Matrix(1,0,0,1) Matrix(401,-218,550,-299) -> Matrix(1,2,0,1) Matrix(1551,-854,2450,-1349) -> Matrix(1,0,0,1) Matrix(2251,-1270,3100,-1749) -> Matrix(1,0,-4,1) Matrix(749,-424,1150,-651) -> Matrix(1,0,-2,1) Matrix(751,-434,950,-549) -> Matrix(3,-2,2,-1) Matrix(2799,-1636,4450,-2601) -> Matrix(3,-2,2,-1) Matrix(4501,-2634,6150,-3599) -> Matrix(1,0,-2,1) Matrix(699,-412,850,-501) -> Matrix(3,-2,2,-1) Matrix(151,-90,250,-149) -> Matrix(7,-6,6,-5) Matrix(4999,-3038,7900,-4801) -> Matrix(11,-16,-2,3) Matrix(899,-548,1150,-701) -> Matrix(9,-16,4,-7) Matrix(5401,-3306,7350,-4499) -> Matrix(1,-2,0,1) Matrix(851,-526,1050,-649) -> Matrix(1,-4,0,1) Matrix(701,-442,950,-599) -> Matrix(1,0,-2,1) Matrix(4601,-2970,6350,-4099) -> Matrix(3,-2,-4,3) Matrix(1049,-688,1450,-951) -> Matrix(1,0,-2,1) Matrix(901,-626,1150,-799) -> Matrix(5,-8,2,-3) Matrix(701,-494,850,-599) -> Matrix(1,-2,0,1) Matrix(1699,-1244,2050,-1501) -> Matrix(1,2,2,5) Matrix(3099,-2276,3950,-2901) -> Matrix(5,2,2,1) Matrix(951,-734,1100,-849) -> Matrix(9,-16,4,-7) Matrix(3851,-3022,4650,-3649) -> Matrix(1,-2,2,-3) Matrix(201,-160,250,-199) -> Matrix(1,-4,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 100 Degree of the the map X: 100 Degree of the the map Y: 300 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.