INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 64 Genus: 113 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 2/15 3/14 4/13 5/12 1/2 6/11 7/10 8/9 1/1 9/8 19/15 7/5 10/7 3/2 52/33 21/13 43/25 11/6 2/1 71/31 12/5 5/2 49/19 13/5 8/3 25/9 3/1 13/4 23/7 10/3 105/31 79/23 7/2 11/3 107/29 67/18 19/5 27/7 4/1 55/13 13/3 305/69 9/2 14/3 5/1 57/11 16/3 27/5 11/2 17/3 29/5 6/1 19/3 13/2 7/1 15/2 23/3 8/1 25/3 61/7 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -2/1 -1/1 -17/37 -1/1 -5/6 -11/24 -1/1 -2/3 -16/35 -1/1 -2/3 -5/11 -2/3 -9/20 -2/5 -1/3 -4/9 -1/1 0/1 -19/43 -1/1 -3/4 -15/34 -1/1 -2/3 -26/59 -1/1 -2/3 -37/84 -5/7 -2/3 -11/25 -2/3 -7/16 -1/1 -2/3 -31/71 -3/4 -2/3 -24/55 -2/3 -7/11 -17/39 -2/3 -27/62 -3/5 -4/7 -10/23 -3/5 -4/7 -3/7 -1/2 0/1 -11/26 -1/1 0/1 -8/19 -1/1 0/1 -13/31 0/1 -18/43 -1/1 0/1 -5/12 -1/1 -2/3 -7/17 -2/5 -23/56 -4/11 -1/3 -39/95 -7/20 -1/3 -16/39 -1/3 -4/13 -9/22 -1/3 0/1 -11/27 -1/2 0/1 -24/59 -1/3 0/1 -13/32 -1/3 0/1 -2/5 -1/1 0/1 -9/23 -2/5 -7/18 -1/3 -2/7 -19/49 0/1 -12/31 -1/3 0/1 -5/13 -1/4 0/1 -8/21 0/1 1/5 -19/50 0/1 1/1 -11/29 0/1 -14/37 0/1 1/1 -3/8 -1/1 0/1 -7/19 -1/2 -1/3 -25/68 -1/1 0/1 -18/49 -1/3 0/1 -11/30 -1/3 0/1 -4/11 -1/3 0/1 -9/25 -1/8 0/1 -5/14 0/1 1/5 -16/45 0/1 1/1 -27/76 0/1 1/1 -11/31 1/1 1/0 -6/17 -1/1 0/1 -7/20 0/1 1/1 -15/43 -1/2 0/1 -8/23 -1/1 0/1 -1/3 0/1 -7/22 -1/1 0/1 -13/41 0/1 1/0 -6/19 -1/3 0/1 -5/16 -1/1 0/1 -9/29 -1/2 -1/3 -22/71 -1/3 0/1 -13/42 -1/3 0/1 -4/13 -1/7 0/1 -11/36 0/1 1/19 -7/23 0/1 1/6 -3/10 0/1 1/1 -8/27 0/1 1/1 -29/98 1/1 2/1 -21/71 0/1 -13/44 0/1 1/1 -18/61 -1/1 0/1 -5/17 1/1 1/0 -2/7 -1/1 0/1 -7/25 0/1 -26/93 -2/5 -1/3 -19/68 -1/3 0/1 -12/43 -1/3 0/1 -5/18 -1/7 0/1 -8/29 0/1 1/11 -3/11 0/1 1/2 -7/26 0/1 1/1 -18/67 0/1 1/1 -11/41 0/1 -4/15 2/3 1/1 -9/34 1/1 2/1 -5/19 2/1 -1/4 -1/1 0/1 -6/25 0/1 1/1 -5/21 0/1 1/0 -4/17 0/1 1/1 -7/30 4/5 1/1 -24/103 1/1 18/17 -17/73 1/1 7/6 -10/43 1/1 4/3 -3/13 2/1 -2/9 -2/1 -1/1 -7/32 -1/1 0/1 -12/55 -1/1 0/1 -5/23 0/1 -8/37 0/1 1/1 -3/14 -1/1 0/1 -4/19 -1/1 0/1 -5/24 0/1 1/1 -1/5 0/1 1/0 -3/16 -4/1 -3/1 -11/59 -3/1 -5/2 -19/102 -3/1 -2/1 -8/43 -4/1 -3/1 -5/27 -2/1 -7/38 -7/3 -2/1 -16/87 -2/1 -13/7 -9/49 -2/1 -3/2 -2/11 -2/1 -1/1 -5/28 -1/1 -2/3 -3/17 -2/1 -10/57 -2/1 -5/3 -7/40 -2/1 -1/1 -11/63 -2/1 1/0 -4/23 -2/1 -1/1 -5/29 -3/2 -1/1 -6/35 -6/5 -1/1 -1/6 -1/1 0/1 -2/13 1/1 2/1 -1/7 -2/1 -3/22 -2/1 -1/1 -2/15 -2/1 -1/1 -5/38 -2/1 -1/1 -8/61 -4/3 -1/1 -3/23 -5/4 -1/1 -4/31 -12/11 -1/1 -1/8 -1/1 -2/3 0/1 -1/1 0/1 1/8 -1/1 -2/3 2/15 -1/2 1/7 -1/2 0/1 2/13 -1/1 0/1 1/6 -2/1 -1/1 3/17 -1/1 -5/6 2/11 -1/1 -2/3 3/16 -1/1 -2/3 7/37 -1/1 -3/4 4/21 -5/7 -2/3 5/26 -1/1 -2/3 1/5 -2/3 4/19 -5/9 -6/11 3/14 -1/2 5/23 -1/2 -4/9 7/32 -3/7 -2/5 2/9 -2/5 -1/3 7/31 0/1 5/22 -1/5 0/1 3/13 0/1 1/0 1/4 -1/1 0/1 5/19 -1/1 -3/4 9/34 -5/7 -2/3 4/15 -1/1 -2/3 7/26 -1/1 -2/3 10/37 -5/7 -2/3 13/48 -1/1 -2/3 3/11 -2/3 2/7 -1/1 -2/3 9/31 -3/4 -2/3 7/24 -2/3 -7/11 5/17 -2/3 13/44 -2/3 -3/5 8/27 -3/5 -4/7 3/10 -3/5 -4/7 16/53 -4/7 -5/9 13/43 -5/9 -11/20 10/33 -17/31 -6/11 17/56 -6/11 -7/13 7/23 -8/15 4/13 -1/2 9/29 -8/17 5/16 -4/9 -3/7 1/3 -1/2 0/1 4/11 -1/1 0/1 11/30 -1/1 0/1 18/49 -1/1 -4/5 25/68 -2/3 -3/5 7/19 0/1 17/46 -1/1 0/1 10/27 -1/1 -2/3 3/8 -1/1 0/1 5/13 0/1 7/18 -1/1 0/1 9/23 -1/1 1/0 2/5 -1/1 -2/3 9/22 -3/5 -4/7 7/17 -5/9 -1/2 5/12 -1/2 13/31 -1/2 -9/19 8/19 -6/13 -5/11 3/7 -2/5 19/44 -2/5 -1/3 16/37 -2/5 -1/3 29/67 -1/2 -2/5 13/30 -2/5 -1/3 10/23 -4/11 -1/3 17/39 -7/20 -1/3 7/16 -1/3 -4/13 11/25 -1/3 -1/4 15/34 -1/3 0/1 4/9 -1/3 0/1 13/29 0/1 9/20 -1/3 0/1 5/11 -1/2 0/1 16/35 -1/2 11/24 -1/3 0/1 6/13 -1/3 0/1 1/2 -1/1 0/1 7/13 -3/5 -1/2 6/11 -1/2 11/20 -5/11 -4/9 5/9 -2/5 4/7 -1/3 -2/7 11/19 0/1 7/12 -1/3 0/1 17/29 0/1 10/17 -2/5 -1/3 13/22 -1/3 0/1 29/49 -2/7 16/27 -1/3 -2/7 3/5 -1/4 0/1 5/8 0/1 1/5 22/35 0/1 1/3 17/27 1/3 1/2 12/19 0/1 1/1 7/11 0/1 9/14 0/1 1/1 11/17 -2/1 1/0 13/20 -6/5 -1/1 2/3 -1/1 0/1 11/16 -1/1 0/1 20/29 -1/1 -2/3 29/42 -5/7 -2/3 9/13 -2/3 7/10 -1/2 19/27 -4/9 12/17 -3/7 -2/5 5/7 -1/2 -1/3 23/32 -2/7 -3/11 18/25 -1/1 0/1 31/43 0/1 13/18 -1/3 0/1 8/11 -1/3 0/1 19/26 -1/3 0/1 11/15 0/1 36/49 -1/2 25/34 -3/7 -2/5 14/19 -4/11 -1/3 31/42 -1/3 -2/7 17/23 -1/4 0/1 3/4 -1/3 0/1 13/17 0/1 10/13 -1/5 -2/11 17/22 -1/7 0/1 41/53 0/1 24/31 -1/7 0/1 7/9 -1/8 0/1 4/5 0/1 1/5 21/26 2/5 3/7 17/21 2/3 13/16 0/1 1/1 35/43 0/1 22/27 0/1 1/1 9/11 1/1 1/0 14/17 -2/1 -1/1 33/40 -1/1 0/1 19/23 0/1 5/6 -1/1 0/1 21/25 0/1 16/19 -2/1 -1/1 27/32 -1/3 0/1 11/13 -1/1 -1/2 17/20 -1/3 0/1 6/7 0/1 1/1 25/29 0/1 19/22 -1/1 0/1 13/15 -1/2 0/1 20/23 -1/1 0/1 7/8 -1/1 0/1 15/17 -1/1 -1/2 8/9 -1/2 9/10 -1/3 0/1 1/1 0/1 10/9 0/1 1/1 9/8 1/0 8/7 -1/1 0/1 15/13 0/1 1/0 7/6 -1/3 0/1 13/11 -1/1 1/0 19/16 -1/1 -2/3 25/21 0/1 31/26 -1/1 0/1 6/5 -1/1 0/1 17/14 -1/1 -2/3 28/23 -1/2 11/9 -1/2 -1/3 27/22 -1/3 0/1 70/57 -1/3 0/1 43/35 0/1 59/48 -1/3 0/1 75/61 -1/2 -1/4 16/13 -1/3 0/1 37/30 -6/17 -1/3 21/17 -2/7 5/4 -1/7 0/1 19/15 0/1 33/26 0/1 1/45 14/11 0/1 1/19 9/7 0/1 1/6 31/24 0/1 1/5 22/17 0/1 1/5 13/10 2/7 1/3 4/3 0/1 1/1 35/26 0/1 1/1 31/23 0/1 27/20 -1/1 0/1 23/17 0/1 1/2 19/14 1/1 4/3 34/25 2/1 3/1 15/11 0/1 41/30 1/1 2/1 26/19 0/1 1/1 11/8 0/1 1/1 40/29 1/1 2/1 69/50 1/0 29/21 0/1 18/13 0/1 1/1 79/57 1/2 1/0 61/44 0/1 1/1 43/31 0/1 68/49 0/1 1/1 25/18 -1/1 0/1 32/23 3/5 2/3 7/5 1/1 1/0 17/12 2/1 3/1 10/7 1/0 23/16 -4/1 -3/1 36/25 -4/1 -3/1 13/9 -2/1 16/11 -1/1 0/1 19/13 -3/2 -1/1 22/15 -1/1 -2/3 3/2 -1/1 0/1 11/7 0/1 63/40 -1/1 -2/3 52/33 -1/2 93/59 -1/2 -2/5 41/26 -2/5 -1/3 30/19 -1/3 0/1 19/12 -1/3 0/1 46/29 -2/7 -3/11 27/17 -1/4 -1/5 62/39 -1/5 -2/11 35/22 -1/5 0/1 8/5 -1/7 0/1 21/13 0/1 34/21 0/1 1/29 13/8 0/1 1/11 5/3 0/1 1/2 32/19 1/2 59/35 4/7 27/16 2/3 1/1 49/29 2/3 22/13 0/1 1/1 17/10 1/1 2/1 46/27 1/1 2/1 29/17 0/1 41/24 0/1 1/3 12/7 0/1 1/1 43/25 1/2 1/0 74/43 0/1 1/1 31/18 0/1 1/1 19/11 0/1 83/48 2/3 1/1 64/37 8/9 1/1 45/26 1/1 2/1 26/15 -1/1 0/1 7/4 2/3 1/1 30/17 1/1 2/1 53/30 1/1 2/1 76/43 1/0 23/13 1/1 1/0 62/35 1/1 4/3 39/22 1/1 4/3 16/9 1/1 2/1 9/5 2/1 20/11 4/1 5/1 11/6 1/0 24/13 -6/1 -5/1 13/7 -3/1 1/0 15/8 -2/1 -1/1 2/1 -1/1 0/1 13/6 0/1 1/1 11/5 0/1 1/0 9/4 0/1 1/1 25/11 1/2 1/1 41/18 0/1 1/1 16/7 4/5 1/1 71/31 1/1 126/55 1/1 40/39 55/24 1/1 18/17 39/17 1/1 7/6 62/27 9/7 4/3 23/10 1/1 4/3 7/3 2/1 19/8 5/1 6/1 12/5 1/0 29/12 -9/1 -8/1 75/31 -8/1 121/50 -64/9 -7/1 46/19 -7/1 -6/1 17/7 -5/1 1/0 39/16 -13/3 -4/1 22/9 -4/1 -3/1 71/29 -19/6 -3/1 49/20 -3/1 -26/9 27/11 -2/1 5/2 -2/1 -1/1 28/11 -2/1 -1/1 23/9 -1/1 -1/2 41/16 -1/1 -4/5 18/7 -1/1 0/1 49/19 -1/2 1/0 80/31 -1/1 0/1 31/12 -1/1 0/1 13/5 0/1 21/8 0/1 1/1 71/27 2/3 50/19 1/1 6/5 79/30 1/1 2/1 108/41 5/3 2/1 29/11 2/1 1/0 37/14 1/0 8/3 -1/1 0/1 35/13 1/1 1/0 27/10 -2/1 -1/1 100/37 -12/11 -1/1 273/101 -1/1 173/64 -1/1 -18/19 73/27 -1/1 -3/4 46/17 -1/1 0/1 65/24 -1/1 0/1 84/31 -1/1 0/1 19/7 0/1 68/25 -3/1 -2/1 49/18 -4/3 -1/1 79/29 -1/2 0/1 30/11 -1/1 0/1 11/4 -1/1 0/1 25/9 0/1 39/14 0/1 1/3 14/5 0/1 1/1 3/1 0/1 1/0 16/5 3/1 4/1 13/4 1/0 36/11 -13/1 -12/1 59/18 -31/3 -10/1 23/7 -8/1 56/17 -7/1 -6/1 33/10 -6/1 -17/3 43/13 -11/2 -5/1 53/16 -5/1 -4/1 10/3 -4/1 -3/1 37/11 -3/1 -5/2 64/19 -3/1 -2/1 27/8 -4/1 -3/1 98/29 -7/3 -2/1 71/21 -3/1 -5/2 44/13 -3/1 -2/1 105/31 -5/2 1/0 166/49 -3/1 -2/1 61/18 -3/1 -2/1 17/5 -2/1 41/12 -3/1 -2/1 24/7 -7/3 -2/1 79/23 -2/1 134/39 -2/1 -33/17 55/16 -2/1 -13/7 31/9 -2/1 -3/2 38/11 -2/1 -1/1 45/13 -2/1 7/2 -2/1 -1/1 32/9 -4/3 -1/1 57/16 -4/3 -1/1 82/23 -6/5 -1/1 107/30 -16/15 -1/1 25/7 -1/1 1/0 68/19 -2/1 -1/1 43/12 -2/1 -1/1 18/5 -1/1 -2/3 11/3 -2/1 59/16 -2/1 -1/1 107/29 -3/2 1/0 155/42 -2/1 -1/1 48/13 -2/1 -1/1 85/23 -2/1 1/0 37/10 -2/1 -5/3 63/17 -5/4 -1/1 26/7 -2/1 -1/1 93/25 0/1 67/18 1/0 108/29 -3/1 -2/1 41/11 -2/1 1/0 15/4 -2/1 -1/1 49/13 -2/1 34/9 -2/1 -5/3 53/14 -1/1 0/1 19/5 -3/2 -1/1 23/6 -6/5 -1/1 27/7 -1/1 31/8 -1/1 -6/7 4/1 -1/1 0/1 29/7 -3/2 -1/1 25/6 -1/1 -2/3 21/5 0/1 38/9 -1/1 0/1 55/13 -1/2 1/0 72/17 -1/1 0/1 17/4 -1/1 0/1 13/3 -1/2 0/1 22/5 0/1 1/3 53/12 2/3 1/1 137/31 7/8 1/1 221/50 22/23 1/1 305/69 1/1 84/19 1/1 8/7 31/7 0/1 9/2 1/1 2/1 32/7 2/1 3/1 87/19 8/3 55/12 3/1 16/5 23/5 4/1 1/0 14/3 1/0 33/7 -8/1 1/0 19/4 -6/1 -5/1 5/1 -2/1 31/6 -2/1 -1/1 57/11 -3/2 1/0 26/5 -2/1 -1/1 21/4 -2/1 -5/3 58/11 -1/1 0/1 37/7 -3/2 -1/1 16/3 -2/1 -1/1 43/8 -3/2 70/13 -4/3 -1/1 27/5 -3/2 -1/1 11/2 -2/1 -1/1 28/5 -2/1 -1/1 45/8 -4/3 -1/1 17/3 -5/4 -1/1 23/4 -12/11 -1/1 29/5 -1/1 35/6 -1/1 -16/17 6/1 -1/1 -2/3 19/3 0/1 32/5 0/1 1/1 13/2 -1/1 0/1 7/1 0/1 1/0 22/3 1/1 2/1 15/2 1/0 38/5 -7/1 -6/1 23/3 -4/1 8/1 -2/1 -1/1 25/3 -2/1 -3/2 17/2 -2/1 -1/1 26/3 -2/1 -1/1 61/7 -3/2 1/0 35/4 -2/1 -1/1 9/1 -2/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(189,88,320,149) (-1/2,-6/13) -> (10/17,13/22) Hyperbolic Matrix(187,86,-1446,-665) (-6/13,-17/37) -> (-3/23,-4/31) Hyperbolic Matrix(375,172,-2008,-921) (-17/37,-11/24) -> (-3/16,-11/59) Hyperbolic Matrix(3137,1436,876,401) (-11/24,-16/35) -> (68/19,43/12) Hyperbolic Matrix(2253,1028,1624,741) (-16/35,-5/11) -> (43/31,68/49) Hyperbolic Matrix(309,140,64,29) (-5/11,-9/20) -> (19/4,5/1) Hyperbolic Matrix(557,250,430,193) (-9/20,-4/9) -> (22/17,13/10) Hyperbolic Matrix(303,134,-1766,-781) (-4/9,-19/43) -> (-5/29,-6/35) Hyperbolic Matrix(367,162,1946,859) (-19/43,-15/34) -> (3/16,7/37) Hyperbolic Matrix(1583,698,-3894,-1717) (-15/34,-26/59) -> (-24/59,-13/32) Hyperbolic Matrix(1521,670,5042,2221) (-26/59,-37/84) -> (3/10,16/53) Hyperbolic Matrix(3279,1444,2432,1071) (-37/84,-11/25) -> (31/23,27/20) Hyperbolic Matrix(305,134,-1154,-507) (-11/25,-7/16) -> (-9/34,-5/19) Hyperbolic Matrix(1387,606,3202,1399) (-7/16,-31/71) -> (29/67,13/30) Hyperbolic Matrix(1631,712,-8872,-3873) (-31/71,-24/55) -> (-16/87,-9/49) Hyperbolic Matrix(2293,1000,360,157) (-24/55,-17/39) -> (19/3,32/5) Hyperbolic Matrix(2291,998,1926,839) (-17/39,-27/62) -> (19/16,25/21) Hyperbolic Matrix(239,104,-1804,-785) (-27/62,-10/23) -> (-2/15,-5/38) Hyperbolic Matrix(181,78,58,25) (-10/23,-3/7) -> (3/1,16/5) Hyperbolic Matrix(61,26,-298,-127) (-3/7,-11/26) -> (-5/24,-1/5) Hyperbolic Matrix(885,374,646,273) (-11/26,-8/19) -> (26/19,11/8) Hyperbolic Matrix(643,270,-1698,-713) (-8/19,-13/31) -> (-11/29,-14/37) Hyperbolic Matrix(587,246,-2694,-1129) (-13/31,-18/43) -> (-12/55,-5/23) Hyperbolic Matrix(1869,782,1054,441) (-18/43,-5/12) -> (39/22,16/9) Hyperbolic Matrix(407,168,172,71) (-5/12,-7/17) -> (7/3,19/8) Hyperbolic Matrix(1845,758,3118,1281) (-7/17,-23/56) -> (13/22,29/49) Hyperbolic Matrix(7443,3056,2248,923) (-23/56,-39/95) -> (43/13,53/16) Hyperbolic Matrix(2943,1208,-12632,-5185) (-39/95,-16/39) -> (-24/103,-17/73) Hyperbolic Matrix(2073,850,578,237) (-16/39,-9/22) -> (43/12,18/5) Hyperbolic Matrix(1035,422,802,327) (-9/22,-11/27) -> (9/7,31/24) Hyperbolic Matrix(5335,2172,1432,583) (-11/27,-24/59) -> (108/29,41/11) Hyperbolic Matrix(1089,442,170,69) (-13/32,-2/5) -> (32/5,13/2) Hyperbolic Matrix(505,198,278,109) (-2/5,-9/23) -> (9/5,20/11) Hyperbolic Matrix(169,66,-950,-371) (-9/23,-7/18) -> (-5/28,-3/17) Hyperbolic Matrix(999,388,224,87) (-7/18,-19/49) -> (31/7,9/2) Hyperbolic Matrix(1223,474,-4554,-1765) (-19/49,-12/31) -> (-18/67,-11/41) Hyperbolic Matrix(57,22,386,149) (-12/31,-5/13) -> (1/7,2/13) Hyperbolic Matrix(167,64,-608,-233) (-5/13,-8/21) -> (-8/29,-3/11) Hyperbolic Matrix(657,250,770,293) (-8/21,-19/50) -> (17/20,6/7) Hyperbolic Matrix(1427,542,-4826,-1833) (-19/50,-11/29) -> (-21/71,-13/44) Hyperbolic Matrix(275,104,1256,475) (-14/37,-3/8) -> (7/32,2/9) Hyperbolic Matrix(379,140,268,99) (-3/8,-7/19) -> (7/5,17/12) Hyperbolic Matrix(3551,1306,1074,395) (-7/19,-25/68) -> (33/10,43/13) Hyperbolic Matrix(2797,1028,536,197) (-25/68,-18/49) -> (26/5,21/4) Hyperbolic Matrix(1291,474,-4622,-1697) (-18/49,-11/30) -> (-19/68,-12/43) Hyperbolic Matrix(1021,374,374,137) (-11/30,-4/11) -> (30/11,11/4) Hyperbolic Matrix(693,250,158,57) (-4/11,-9/25) -> (13/3,22/5) Hyperbolic Matrix(373,134,-1222,-439) (-9/25,-5/14) -> (-11/36,-7/23) Hyperbolic Matrix(2269,808,688,245) (-5/14,-16/45) -> (56/17,33/10) Hyperbolic Matrix(2741,974,318,113) (-16/45,-27/76) -> (17/2,26/3) Hyperbolic Matrix(1425,506,-7646,-2715) (-27/76,-11/31) -> (-11/59,-19/102) Hyperbolic Matrix(843,298,314,111) (-11/31,-6/17) -> (8/3,35/13) Hyperbolic Matrix(525,184,836,293) (-6/17,-7/20) -> (5/8,22/35) Hyperbolic Matrix(3291,1150,890,311) (-7/20,-15/43) -> (85/23,37/10) Hyperbolic Matrix(1355,472,3132,1091) (-15/43,-8/23) -> (16/37,29/67) Hyperbolic Matrix(53,18,50,17) (-8/23,-1/3) -> (1/1,10/9) Hyperbolic Matrix(49,16,52,17) (-1/3,-7/22) -> (9/10,1/1) Hyperbolic Matrix(1247,396,148,47) (-7/22,-13/41) -> (25/3,17/2) Hyperbolic Matrix(4979,1578,1890,599) (-13/41,-6/19) -> (108/41,29/11) Hyperbolic Matrix(793,250,498,157) (-6/19,-5/16) -> (35/22,8/5) Hyperbolic Matrix(643,200,344,107) (-5/16,-9/29) -> (13/7,15/8) Hyperbolic Matrix(445,138,-3402,-1055) (-9/29,-22/71) -> (-8/61,-3/23) Hyperbolic Matrix(2021,626,4678,1449) (-22/71,-13/42) -> (19/44,16/37) Hyperbolic Matrix(641,198,2114,653) (-13/42,-4/13) -> (10/33,17/56) Hyperbolic Matrix(933,286,734,225) (-4/13,-11/36) -> (33/26,14/11) Hyperbolic Matrix(145,44,636,193) (-7/23,-3/10) -> (5/22,3/13) Hyperbolic Matrix(337,100,920,273) (-3/10,-8/27) -> (4/11,11/30) Hyperbolic Matrix(919,272,-7004,-2073) (-8/27,-29/98) -> (-5/38,-8/61) Hyperbolic Matrix(5551,1642,3526,1043) (-29/98,-21/71) -> (11/7,63/40) Hyperbolic Matrix(481,142,2510,741) (-13/44,-18/61) -> (4/21,5/26) Hyperbolic Matrix(963,284,3184,939) (-18/61,-5/17) -> (13/43,10/33) Hyperbolic Matrix(239,70,338,99) (-5/17,-2/7) -> (12/17,5/7) Hyperbolic Matrix(235,66,-1086,-305) (-2/7,-7/25) -> (-5/23,-8/37) Hyperbolic Matrix(9299,2600,2500,699) (-7/25,-26/93) -> (26/7,93/25) Hyperbolic Matrix(2311,646,-12410,-3469) (-26/93,-19/68) -> (-19/102,-8/43) Hyperbolic Matrix(2073,578,850,237) (-12/43,-5/18) -> (39/16,22/9) Hyperbolic Matrix(989,274,610,169) (-5/18,-8/29) -> (34/21,13/8) Hyperbolic Matrix(325,88,48,13) (-3/11,-7/26) -> (13/2,7/1) Hyperbolic Matrix(4001,1076,2324,625) (-7/26,-18/67) -> (74/43,31/18) Hyperbolic Matrix(187,50,834,223) (-11/41,-4/15) -> (2/9,7/31) Hyperbolic Matrix(1159,308,508,135) (-4/15,-9/34) -> (41/18,16/7) Hyperbolic Matrix(229,60,416,109) (-5/19,-1/4) -> (11/20,5/9) Hyperbolic Matrix(805,194,1166,281) (-1/4,-6/25) -> (20/29,29/42) Hyperbolic Matrix(359,86,-2058,-493) (-6/25,-5/21) -> (-11/63,-4/23) Hyperbolic Matrix(623,148,804,191) (-5/21,-4/17) -> (24/31,7/9) Hyperbolic Matrix(1019,238,578,135) (-4/17,-7/30) -> (7/4,30/17) Hyperbolic Matrix(9445,2202,4122,961) (-7/30,-24/103) -> (126/55,55/24) Hyperbolic Matrix(1727,402,5718,1331) (-17/73,-10/43) -> (16/53,13/43) Hyperbolic Matrix(2393,556,1416,329) (-10/43,-3/13) -> (49/29,22/13) Hyperbolic Matrix(131,30,310,71) (-3/13,-2/9) -> (8/19,3/7) Hyperbolic Matrix(1087,238,306,67) (-2/9,-7/32) -> (7/2,32/9) Hyperbolic Matrix(4265,932,1652,361) (-7/32,-12/55) -> (80/31,31/12) Hyperbolic Matrix(781,168,172,37) (-8/37,-3/14) -> (9/2,32/7) Hyperbolic Matrix(473,100,648,137) (-3/14,-4/19) -> (8/11,19/26) Hyperbolic Matrix(1077,226,386,81) (-4/19,-5/24) -> (39/14,14/5) Hyperbolic Matrix(41,8,128,25) (-1/5,-3/16) -> (5/16,1/3) Hyperbolic Matrix(1335,248,1588,295) (-8/43,-5/27) -> (21/25,16/19) Hyperbolic Matrix(1125,208,1628,301) (-5/27,-7/38) -> (29/42,9/13) Hyperbolic Matrix(9877,1818,2874,529) (-7/38,-16/87) -> (134/39,55/16) Hyperbolic Matrix(667,122,82,15) (-9/49,-2/11) -> (8/1,25/3) Hyperbolic Matrix(955,172,372,67) (-2/11,-5/28) -> (41/16,18/7) Hyperbolic Matrix(1527,268,1772,311) (-3/17,-10/57) -> (6/7,25/29) Hyperbolic Matrix(3421,600,1032,181) (-10/57,-7/40) -> (53/16,10/3) Hyperbolic Matrix(6303,1102,3998,699) (-7/40,-11/63) -> (93/59,41/26) Hyperbolic Matrix(1315,228,248,43) (-4/23,-5/29) -> (37/7,16/3) Hyperbolic Matrix(1109,190,286,49) (-6/35,-1/6) -> (31/8,4/1) Hyperbolic Matrix(281,44,364,57) (-1/6,-2/13) -> (10/13,17/22) Hyperbolic Matrix(41,6,198,29) (-2/13,-1/7) -> (1/5,4/19) Hyperbolic Matrix(1183,162,314,43) (-1/7,-3/22) -> (15/4,49/13) Hyperbolic Matrix(1455,196,824,111) (-3/22,-2/15) -> (30/17,53/30) Hyperbolic Matrix(1133,146,194,25) (-4/31,-1/8) -> (35/6,6/1) Hyperbolic Matrix(193,22,114,13) (-1/8,0/1) -> (22/13,17/10) Hyperbolic Matrix(93,-10,214,-23) (0/1,1/8) -> (13/30,10/23) Hyperbolic Matrix(663,-86,902,-117) (1/8,2/15) -> (36/49,25/34) Hyperbolic Matrix(299,-42,178,-25) (2/15,1/7) -> (5/3,32/19) Hyperbolic Matrix(263,-42,382,-61) (2/13,1/6) -> (11/16,20/29) Hyperbolic Matrix(493,-86,86,-15) (1/6,3/17) -> (17/3,23/4) Hyperbolic Matrix(577,-104,172,-31) (3/17,2/11) -> (10/3,37/11) Hyperbolic Matrix(229,-42,518,-95) (2/11,3/16) -> (15/34,4/9) Hyperbolic Matrix(5117,-970,1514,-287) (7/37,4/21) -> (98/29,71/21) Hyperbolic Matrix(285,-56,56,-11) (5/26,1/5) -> (5/1,31/6) Hyperbolic Matrix(815,-172,308,-65) (4/19,3/14) -> (37/14,8/3) Hyperbolic Matrix(1257,-272,476,-103) (3/14,5/23) -> (29/11,37/14) Hyperbolic Matrix(1257,-274,1702,-371) (5/23,7/32) -> (31/42,17/23) Hyperbolic Matrix(2549,-578,1054,-239) (7/31,5/22) -> (29/12,75/31) Hyperbolic Matrix(137,-32,304,-71) (3/13,1/4) -> (9/20,5/11) Hyperbolic Matrix(513,-134,134,-35) (1/4,5/19) -> (19/5,23/6) Hyperbolic Matrix(887,-234,1050,-277) (5/19,9/34) -> (27/32,11/13) Hyperbolic Matrix(2687,-712,1936,-513) (9/34,4/15) -> (68/49,25/18) Hyperbolic Matrix(321,-86,698,-187) (4/15,7/26) -> (11/24,6/13) Hyperbolic Matrix(2463,-664,1072,-289) (7/26,10/37) -> (62/27,23/10) Hyperbolic Matrix(8107,-2194,3078,-833) (10/37,13/48) -> (79/30,108/41) Hyperbolic Matrix(1177,-320,320,-87) (13/48,3/11) -> (11/3,59/16) Hyperbolic Matrix(239,-66,134,-37) (3/11,2/7) -> (16/9,9/5) Hyperbolic Matrix(711,-206,818,-237) (2/7,9/31) -> (13/15,20/23) Hyperbolic Matrix(2449,-712,712,-207) (9/31,7/24) -> (55/16,31/9) Hyperbolic Matrix(1393,-408,816,-239) (7/24,5/17) -> (29/17,41/24) Hyperbolic Matrix(1785,-526,526,-155) (5/17,13/44) -> (61/18,17/5) Hyperbolic Matrix(3673,-1086,2310,-683) (13/44,8/27) -> (62/39,35/22) Hyperbolic Matrix(577,-172,104,-31) (8/27,3/10) -> (11/2,28/5) Hyperbolic Matrix(2973,-904,1720,-523) (17/56,7/23) -> (19/11,83/48) Hyperbolic Matrix(209,-64,676,-207) (7/23,4/13) -> (4/13,9/29) Parabolic Matrix(881,-274,1090,-339) (9/29,5/16) -> (21/26,17/21) Hyperbolic Matrix(75,-26,26,-9) (1/3,4/11) -> (14/5,3/1) Hyperbolic Matrix(5371,-1972,2040,-749) (11/30,18/49) -> (50/19,79/30) Hyperbolic Matrix(4973,-1828,944,-347) (18/49,25/68) -> (21/4,58/11) Hyperbolic Matrix(4525,-1664,2684,-987) (25/68,7/19) -> (59/35,27/16) Hyperbolic Matrix(2209,-816,2856,-1055) (7/19,17/46) -> (17/22,41/53) Hyperbolic Matrix(1093,-404,744,-275) (17/46,10/27) -> (22/15,3/2) Hyperbolic Matrix(421,-156,224,-83) (10/27,3/8) -> (15/8,2/1) Hyperbolic Matrix(173,-66,270,-103) (3/8,5/13) -> (7/11,9/14) Hyperbolic Matrix(637,-246,246,-95) (5/13,7/18) -> (31/12,13/5) Hyperbolic Matrix(1393,-544,612,-239) (7/18,9/23) -> (25/11,41/18) Hyperbolic Matrix(463,-182,318,-125) (9/23,2/5) -> (16/11,19/13) Hyperbolic Matrix(797,-324,460,-187) (2/5,9/22) -> (45/26,26/15) Hyperbolic Matrix(531,-218,626,-257) (9/22,7/17) -> (11/13,17/20) Hyperbolic Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic Matrix(1939,-814,1222,-513) (13/31,8/19) -> (46/29,27/17) Hyperbolic Matrix(641,-276,72,-31) (3/7,19/44) -> (35/4,9/1) Hyperbolic Matrix(2463,-1072,664,-289) (10/23,17/39) -> (63/17,26/7) Hyperbolic Matrix(2769,-1208,1208,-527) (17/39,7/16) -> (55/24,39/17) Hyperbolic Matrix(1393,-612,544,-239) (7/16,11/25) -> (23/9,41/16) Hyperbolic Matrix(685,-302,778,-343) (11/25,15/34) -> (7/8,15/17) Hyperbolic Matrix(1291,-578,306,-137) (4/9,13/29) -> (21/5,38/9) Hyperbolic Matrix(1337,-600,1620,-727) (13/29,9/20) -> (33/40,19/23) Hyperbolic Matrix(3827,-1748,2428,-1109) (5/11,16/35) -> (52/33,93/59) Hyperbolic Matrix(3453,-1580,2192,-1003) (16/35,11/24) -> (63/40,52/33) Hyperbolic Matrix(557,-258,326,-151) (6/13,1/2) -> (41/24,12/7) Hyperbolic Matrix(421,-224,156,-83) (1/2,7/13) -> (35/13,27/10) Hyperbolic Matrix(485,-262,398,-215) (7/13,6/11) -> (28/23,11/9) Hyperbolic Matrix(747,-410,614,-337) (6/11,11/20) -> (17/14,28/23) Hyperbolic Matrix(239,-134,66,-37) (5/9,4/7) -> (18/5,11/3) Hyperbolic Matrix(281,-162,366,-211) (4/7,11/19) -> (13/17,10/13) Hyperbolic Matrix(817,-474,474,-275) (11/19,7/12) -> (31/18,19/11) Hyperbolic Matrix(1393,-816,408,-239) (7/12,17/29) -> (17/5,41/12) Hyperbolic Matrix(1265,-742,878,-515) (17/29,10/17) -> (36/25,13/9) Hyperbolic Matrix(4591,-2718,3738,-2213) (29/49,16/27) -> (70/57,43/35) Hyperbolic Matrix(299,-178,42,-25) (16/27,3/5) -> (7/1,22/3) Hyperbolic Matrix(105,-64,64,-39) (3/5,5/8) -> (13/8,5/3) Hyperbolic Matrix(3673,-2310,1086,-683) (22/35,17/27) -> (71/21,44/13) Hyperbolic Matrix(1565,-986,646,-407) (17/27,12/19) -> (46/19,17/7) Hyperbolic Matrix(749,-474,542,-343) (12/19,7/11) -> (29/21,18/13) Hyperbolic Matrix(785,-506,166,-107) (9/14,11/17) -> (33/7,19/4) Hyperbolic Matrix(2413,-1566,886,-575) (11/17,13/20) -> (49/18,79/29) Hyperbolic Matrix(431,-282,350,-229) (13/20,2/3) -> (16/13,37/30) Hyperbolic Matrix(463,-318,182,-125) (2/3,11/16) -> (5/2,28/11) Hyperbolic Matrix(281,-196,400,-279) (9/13,7/10) -> (7/10,19/27) Parabolic Matrix(1735,-1222,1018,-717) (19/27,12/17) -> (46/27,29/17) Hyperbolic Matrix(2275,-1634,614,-441) (5/7,23/32) -> (37/10,63/17) Hyperbolic Matrix(653,-470,810,-583) (23/32,18/25) -> (4/5,21/26) Hyperbolic Matrix(2687,-1936,712,-513) (18/25,31/43) -> (49/13,34/9) Hyperbolic Matrix(3397,-2450,2450,-1767) (31/43,13/18) -> (61/44,43/31) Hyperbolic Matrix(749,-542,474,-343) (13/18,8/11) -> (30/19,19/12) Hyperbolic Matrix(569,-416,688,-503) (19/26,11/15) -> (19/23,5/6) Hyperbolic Matrix(3371,-2476,2000,-1469) (11/15,36/49) -> (32/19,59/35) Hyperbolic Matrix(1057,-778,1254,-923) (25/34,14/19) -> (16/19,27/32) Hyperbolic Matrix(4265,-3146,2466,-1819) (14/19,31/42) -> (83/48,64/37) Hyperbolic Matrix(489,-362,566,-419) (17/23,3/4) -> (19/22,13/15) Hyperbolic Matrix(193,-146,78,-59) (3/4,13/17) -> (27/11,5/2) Hyperbolic Matrix(5041,-3900,1860,-1439) (41/53,24/31) -> (84/31,19/7) Hyperbolic Matrix(171,-134,134,-105) (7/9,4/5) -> (14/11,9/7) Hyperbolic Matrix(1577,-1280,600,-487) (17/21,13/16) -> (21/8,71/27) Hyperbolic Matrix(3225,-2624,2624,-2135) (13/16,35/43) -> (43/35,59/48) Hyperbolic Matrix(2849,-2320,824,-671) (35/43,22/27) -> (38/11,45/13) Hyperbolic Matrix(1703,-1390,506,-413) (22/27,9/11) -> (37/11,64/19) Hyperbolic Matrix(485,-398,262,-215) (9/11,14/17) -> (24/13,13/7) Hyperbolic Matrix(4249,-3504,1192,-983) (14/17,33/40) -> (57/16,82/23) Hyperbolic Matrix(925,-776,776,-651) (5/6,21/25) -> (25/21,31/26) Hyperbolic Matrix(1697,-1464,1260,-1087) (25/29,19/22) -> (35/26,31/23) Hyperbolic Matrix(1181,-1030,962,-839) (20/23,7/8) -> (27/22,70/57) Hyperbolic Matrix(1499,-1324,848,-749) (15/17,8/9) -> (76/43,23/13) Hyperbolic Matrix(1237,-1108,700,-627) (8/9,9/10) -> (53/30,76/43) Hyperbolic Matrix(947,-1060,176,-197) (10/9,9/8) -> (43/8,70/13) Hyperbolic Matrix(429,-488,80,-91) (9/8,8/7) -> (16/3,43/8) Hyperbolic Matrix(711,-818,206,-237) (8/7,15/13) -> (31/9,38/11) Hyperbolic Matrix(489,-566,362,-419) (15/13,7/6) -> (27/20,23/17) Hyperbolic Matrix(531,-626,218,-257) (7/6,13/11) -> (17/7,39/16) Hyperbolic Matrix(887,-1050,234,-277) (13/11,19/16) -> (53/14,19/5) Hyperbolic Matrix(4621,-5512,1364,-1627) (31/26,6/5) -> (166/49,61/18) Hyperbolic Matrix(569,-688,416,-503) (6/5,17/14) -> (41/30,26/19) Hyperbolic Matrix(779,-954,138,-169) (11/9,27/22) -> (45/8,17/3) Hyperbolic Matrix(5063,-6224,580,-713) (59/48,75/61) -> (61/7,35/4) Hyperbolic Matrix(2379,-2926,274,-337) (75/61,16/13) -> (26/3,61/7) Hyperbolic Matrix(4307,-5316,1780,-2197) (37/30,21/17) -> (75/31,121/50) Hyperbolic Matrix(1095,-1354,334,-413) (21/17,5/4) -> (59/18,23/7) Hyperbolic Matrix(571,-722,450,-569) (5/4,19/15) -> (19/15,33/26) Parabolic Matrix(2209,-2856,816,-1055) (31/24,22/17) -> (46/17,65/24) Hyperbolic Matrix(281,-366,162,-211) (13/10,4/3) -> (26/15,7/4) Hyperbolic Matrix(1713,-2300,464,-623) (4/3,35/26) -> (155/42,48/13) Hyperbolic Matrix(1257,-1702,274,-371) (23/17,19/14) -> (55/12,23/5) Hyperbolic Matrix(1801,-2448,476,-647) (19/14,34/25) -> (34/9,53/14) Hyperbolic Matrix(663,-902,86,-117) (34/25,15/11) -> (23/3,8/1) Hyperbolic Matrix(905,-1236,216,-295) (15/11,41/30) -> (25/6,21/5) Hyperbolic Matrix(1529,-2108,272,-375) (11/8,40/29) -> (28/5,45/8) Hyperbolic Matrix(7343,-10132,1972,-2721) (40/29,69/50) -> (67/18,108/29) Hyperbolic Matrix(6057,-8360,1628,-2247) (69/50,29/21) -> (93/25,67/18) Hyperbolic Matrix(2223,-3080,428,-593) (18/13,79/57) -> (57/11,26/5) Hyperbolic Matrix(4275,-5926,826,-1145) (79/57,61/44) -> (31/6,57/11) Hyperbolic Matrix(2005,-2788,612,-851) (25/18,32/23) -> (36/11,59/18) Hyperbolic Matrix(1207,-1682,526,-733) (32/23,7/5) -> (39/17,62/27) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(1937,-2788,544,-783) (23/16,36/25) -> (32/9,57/16) Hyperbolic Matrix(263,-382,42,-61) (13/9,16/11) -> (6/1,19/3) Hyperbolic Matrix(1351,-1980,552,-809) (19/13,22/15) -> (22/9,71/29) Hyperbolic Matrix(173,-270,66,-103) (3/2,11/7) -> (13/5,21/8) Hyperbolic Matrix(2177,-3434,646,-1019) (41/26,30/19) -> (64/19,27/8) Hyperbolic Matrix(1801,-2856,408,-647) (19/12,46/29) -> (22/5,53/12) Hyperbolic Matrix(2429,-3860,460,-731) (27/17,62/39) -> (58/11,37/7) Hyperbolic Matrix(547,-882,338,-545) (8/5,21/13) -> (21/13,34/21) Parabolic Matrix(923,-1558,266,-449) (27/16,49/29) -> (45/13,7/2) Hyperbolic Matrix(1673,-2848,944,-1607) (17/10,46/27) -> (62/35,39/22) Hyperbolic Matrix(2151,-3698,1250,-2149) (12/7,43/25) -> (43/25,74/43) Parabolic Matrix(3599,-6228,1332,-2305) (64/37,45/26) -> (27/10,100/37) Hyperbolic Matrix(1067,-1890,258,-457) (23/13,62/35) -> (4/1,29/7) Hyperbolic Matrix(265,-484,144,-263) (20/11,11/6) -> (11/6,24/13) Parabolic Matrix(185,-394,54,-115) (2/1,13/6) -> (41/12,24/7) Hyperbolic Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(137,-304,32,-71) (11/5,9/4) -> (17/4,13/3) Hyperbolic Matrix(229,-518,42,-95) (9/4,25/11) -> (27/5,11/2) Hyperbolic Matrix(4403,-10082,1922,-4401) (16/7,71/31) -> (71/31,126/55) Parabolic Matrix(93,-214,10,-23) (23/10,7/3) -> (9/1,1/0) Hyperbolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(6133,-14844,1720,-4163) (121/50,46/19) -> (82/23,107/30) Hyperbolic Matrix(6477,-15860,2396,-5867) (71/29,49/20) -> (173/64,73/27) Hyperbolic Matrix(2345,-5748,512,-1255) (49/20,27/11) -> (87/19,55/12) Hyperbolic Matrix(1217,-3102,450,-1147) (28/11,23/9) -> (73/27,46/17) Hyperbolic Matrix(1863,-4802,722,-1861) (18/7,49/19) -> (49/19,80/31) Parabolic Matrix(2857,-7514,646,-1699) (71/27,50/19) -> (84/19,31/7) Hyperbolic Matrix(19769,-53432,4472,-12087) (100/37,273/101) -> (305/69,84/19) Hyperbolic Matrix(41841,-113098,9466,-25587) (273/101,173/64) -> (221/50,305/69) Hyperbolic Matrix(2255,-6108,532,-1441) (65/24,84/31) -> (72/17,17/4) Hyperbolic Matrix(841,-2286,110,-299) (19/7,68/25) -> (38/5,23/3) Hyperbolic Matrix(2439,-6638,722,-1965) (68/25,49/18) -> (27/8,98/29) Hyperbolic Matrix(2327,-6342,630,-1717) (79/29,30/11) -> (48/13,85/23) Hyperbolic Matrix(451,-1250,162,-449) (11/4,25/9) -> (25/9,39/14) Parabolic Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(1703,-5608,372,-1225) (23/7,56/17) -> (32/7,87/19) Hyperbolic Matrix(6511,-22050,1922,-6509) (44/13,105/31) -> (105/31,166/49) Parabolic Matrix(3635,-12482,1058,-3633) (24/7,79/23) -> (79/23,134/39) Parabolic Matrix(5657,-20184,1280,-4567) (107/30,25/7) -> (137/31,221/50) Hyperbolic Matrix(1003,-3586,186,-665) (25/7,68/19) -> (70/13,27/5) Hyperbolic Matrix(6207,-22898,1682,-6205) (59/16,107/29) -> (107/29,155/42) Parabolic Matrix(379,-1458,98,-377) (23/6,27/7) -> (27/7,31/8) Parabolic Matrix(1193,-4962,270,-1123) (29/7,25/6) -> (53/12,137/31) Hyperbolic Matrix(1431,-6050,338,-1429) (38/9,55/13) -> (55/13,72/17) Parabolic Matrix(169,-784,36,-167) (23/5,14/3) -> (14/3,33/7) Parabolic Matrix(291,-1682,50,-289) (23/4,29/5) -> (29/5,35/6) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,0,1) Matrix(189,88,320,149) -> Matrix(1,0,-2,1) Matrix(187,86,-1446,-665) -> Matrix(11,10,-10,-9) Matrix(375,172,-2008,-921) -> Matrix(13,10,-4,-3) Matrix(3137,1436,876,401) -> Matrix(5,4,-4,-3) Matrix(2253,1028,1624,741) -> Matrix(3,2,4,3) Matrix(309,140,64,29) -> Matrix(7,4,-2,-1) Matrix(557,250,430,193) -> Matrix(1,0,6,1) Matrix(303,134,-1766,-781) -> Matrix(7,6,-6,-5) Matrix(367,162,1946,859) -> Matrix(1,0,0,1) Matrix(1583,698,-3894,-1717) -> Matrix(3,2,-8,-5) Matrix(1521,670,5042,2221) -> Matrix(19,14,-34,-25) Matrix(3279,1444,2432,1071) -> Matrix(3,2,4,3) Matrix(305,134,-1154,-507) -> Matrix(1,0,2,1) Matrix(1387,606,3202,1399) -> Matrix(5,4,-14,-11) Matrix(1631,712,-8872,-3873) -> Matrix(17,12,-10,-7) Matrix(2293,1000,360,157) -> Matrix(3,2,-8,-5) Matrix(2291,998,1926,839) -> Matrix(3,2,-8,-5) Matrix(239,104,-1804,-785) -> Matrix(17,10,-12,-7) Matrix(181,78,58,25) -> Matrix(1,0,2,1) Matrix(61,26,-298,-127) -> Matrix(1,0,2,1) Matrix(885,374,646,273) -> Matrix(1,0,2,1) Matrix(643,270,-1698,-713) -> Matrix(1,0,2,1) Matrix(587,246,-2694,-1129) -> Matrix(1,0,0,1) Matrix(1869,782,1054,441) -> Matrix(1,2,0,1) Matrix(407,168,172,71) -> Matrix(9,4,2,1) Matrix(1845,758,3118,1281) -> Matrix(11,4,-36,-13) Matrix(7443,3056,2248,923) -> Matrix(67,24,-14,-5) Matrix(2943,1208,-12632,-5185) -> Matrix(41,14,38,13) Matrix(2073,850,578,237) -> Matrix(7,2,-4,-1) Matrix(1035,422,802,327) -> Matrix(1,0,8,1) Matrix(5335,2172,1432,583) -> Matrix(3,2,-2,-1) Matrix(1089,442,170,69) -> Matrix(1,0,2,1) Matrix(505,198,278,109) -> Matrix(9,4,2,1) Matrix(169,66,-950,-371) -> Matrix(1,0,2,1) Matrix(999,388,224,87) -> Matrix(1,0,4,1) Matrix(1223,474,-4554,-1765) -> Matrix(1,0,4,1) Matrix(57,22,386,149) -> Matrix(1,0,2,1) Matrix(167,64,-608,-233) -> Matrix(1,0,6,1) Matrix(657,250,770,293) -> Matrix(1,0,-4,1) Matrix(1427,542,-4826,-1833) -> Matrix(1,0,0,1) Matrix(275,104,1256,475) -> Matrix(1,-2,-2,5) Matrix(379,140,268,99) -> Matrix(5,2,2,1) Matrix(3551,1306,1074,395) -> Matrix(23,6,-4,-1) Matrix(2797,1028,536,197) -> Matrix(7,2,-4,-1) Matrix(1291,474,-4622,-1697) -> Matrix(1,0,0,1) Matrix(1021,374,374,137) -> Matrix(1,0,2,1) Matrix(693,250,158,57) -> Matrix(1,0,6,1) Matrix(373,134,-1222,-439) -> Matrix(1,0,14,1) Matrix(2269,808,688,245) -> Matrix(13,-6,-2,1) Matrix(2741,974,318,113) -> Matrix(1,-2,0,1) Matrix(1425,506,-7646,-2715) -> Matrix(5,-2,-2,1) Matrix(843,298,314,111) -> Matrix(1,0,0,1) Matrix(525,184,836,293) -> Matrix(1,0,4,1) Matrix(3291,1150,890,311) -> Matrix(3,2,-2,-1) Matrix(1355,472,3132,1091) -> Matrix(3,2,-8,-5) Matrix(53,18,50,17) -> Matrix(1,0,2,1) Matrix(49,16,52,17) -> Matrix(1,0,-2,1) Matrix(1247,396,148,47) -> Matrix(3,2,-2,-1) Matrix(4979,1578,1890,599) -> Matrix(1,2,0,1) Matrix(793,250,498,157) -> Matrix(1,0,-4,1) Matrix(643,200,344,107) -> Matrix(3,2,-2,-1) Matrix(445,138,-3402,-1055) -> Matrix(13,4,-10,-3) Matrix(2021,626,4678,1449) -> Matrix(7,2,-18,-5) Matrix(641,198,2114,653) -> Matrix(25,6,-46,-11) Matrix(933,286,734,225) -> Matrix(1,0,26,1) Matrix(145,44,636,193) -> Matrix(1,0,-6,1) Matrix(337,100,920,273) -> Matrix(1,0,-2,1) Matrix(919,272,-7004,-2073) -> Matrix(3,-4,-2,3) Matrix(5551,1642,3526,1043) -> Matrix(1,0,-2,1) Matrix(481,142,2510,741) -> Matrix(3,-2,-4,3) Matrix(963,284,3184,939) -> Matrix(11,-6,-20,11) Matrix(239,70,338,99) -> Matrix(1,-2,-2,5) Matrix(235,66,-1086,-305) -> Matrix(1,0,2,1) Matrix(9299,2600,2500,699) -> Matrix(1,0,2,1) Matrix(2311,646,-12410,-3469) -> Matrix(3,2,-2,-1) Matrix(2073,578,850,237) -> Matrix(15,4,-4,-1) Matrix(989,274,610,169) -> Matrix(1,0,18,1) Matrix(325,88,48,13) -> Matrix(1,0,-2,1) Matrix(4001,1076,2324,625) -> Matrix(1,0,0,1) Matrix(187,50,834,223) -> Matrix(1,0,-4,1) Matrix(1159,308,508,135) -> Matrix(1,-2,2,-3) Matrix(229,60,416,109) -> Matrix(1,-4,-2,9) Matrix(805,194,1166,281) -> Matrix(3,-2,-4,3) Matrix(359,86,-2058,-493) -> Matrix(1,-2,0,1) Matrix(623,148,804,191) -> Matrix(1,0,-8,1) Matrix(1019,238,578,135) -> Matrix(3,-2,2,-1) Matrix(9445,2202,4122,961) -> Matrix(23,-22,22,-21) Matrix(1727,402,5718,1331) -> Matrix(19,-24,-34,43) Matrix(2393,556,1416,329) -> Matrix(3,-4,4,-5) Matrix(131,30,310,71) -> Matrix(1,-4,-2,9) Matrix(1087,238,306,67) -> Matrix(3,2,-2,-1) Matrix(4265,932,1652,361) -> Matrix(1,0,0,1) Matrix(781,168,172,37) -> Matrix(1,2,0,1) Matrix(473,100,648,137) -> Matrix(1,0,-2,1) Matrix(1077,226,386,81) -> Matrix(1,0,2,1) Matrix(41,8,128,25) -> Matrix(1,0,-2,1) Matrix(1335,248,1588,295) -> Matrix(1,2,0,1) Matrix(1125,208,1628,301) -> Matrix(1,4,-2,-7) Matrix(9877,1818,2874,529) -> Matrix(19,40,-10,-21) Matrix(667,122,82,15) -> Matrix(1,0,0,1) Matrix(955,172,372,67) -> Matrix(1,2,-2,-3) Matrix(1527,268,1772,311) -> Matrix(1,2,-2,-3) Matrix(3421,600,1032,181) -> Matrix(9,14,-2,-3) Matrix(6303,1102,3998,699) -> Matrix(1,0,-2,1) Matrix(1315,228,248,43) -> Matrix(1,0,0,1) Matrix(1109,190,286,49) -> Matrix(5,6,-6,-7) Matrix(281,44,364,57) -> Matrix(1,0,-6,1) Matrix(41,6,198,29) -> Matrix(1,4,-2,-7) Matrix(1183,162,314,43) -> Matrix(1,0,0,1) Matrix(1455,196,824,111) -> Matrix(3,4,2,3) Matrix(1133,146,194,25) -> Matrix(13,14,-14,-15) Matrix(193,22,114,13) -> Matrix(1,0,2,1) Matrix(93,-10,214,-23) -> Matrix(5,4,-14,-11) Matrix(663,-86,902,-117) -> Matrix(7,4,-16,-9) Matrix(299,-42,178,-25) -> Matrix(1,0,4,1) Matrix(263,-42,382,-61) -> Matrix(1,2,-2,-3) Matrix(493,-86,86,-15) -> Matrix(11,10,-10,-9) Matrix(577,-104,172,-31) -> Matrix(13,10,-4,-3) Matrix(229,-42,518,-95) -> Matrix(3,2,-8,-5) Matrix(5117,-970,1514,-287) -> Matrix(7,4,-2,-1) Matrix(285,-56,56,-11) -> Matrix(5,4,-4,-3) Matrix(815,-172,308,-65) -> Matrix(11,6,-2,-1) Matrix(1257,-272,476,-103) -> Matrix(13,6,2,1) Matrix(1257,-274,1702,-371) -> Matrix(9,4,-34,-15) Matrix(2549,-578,1054,-239) -> Matrix(31,8,-4,-1) Matrix(137,-32,304,-71) -> Matrix(1,0,-2,1) Matrix(513,-134,134,-35) -> Matrix(7,6,-6,-5) Matrix(887,-234,1050,-277) -> Matrix(3,2,-2,-1) Matrix(2687,-712,1936,-513) -> Matrix(3,2,4,3) Matrix(321,-86,698,-187) -> Matrix(3,2,-8,-5) Matrix(2463,-664,1072,-289) -> Matrix(1,2,0,1) Matrix(8107,-2194,3078,-833) -> Matrix(1,0,2,1) Matrix(1177,-320,320,-87) -> Matrix(5,4,-4,-3) Matrix(239,-66,134,-37) -> Matrix(1,0,2,1) Matrix(711,-206,818,-237) -> Matrix(3,2,-2,-1) Matrix(2449,-712,712,-207) -> Matrix(17,12,-10,-7) Matrix(1393,-408,816,-239) -> Matrix(3,2,-2,-1) Matrix(1785,-526,526,-155) -> Matrix(19,12,-8,-5) Matrix(3673,-1086,2310,-683) -> Matrix(3,2,-20,-13) Matrix(577,-172,104,-31) -> Matrix(17,10,-12,-7) Matrix(2973,-904,1720,-523) -> Matrix(15,8,28,15) Matrix(209,-64,676,-207) -> Matrix(31,16,-64,-33) Matrix(881,-274,1090,-339) -> Matrix(13,6,28,13) Matrix(75,-26,26,-9) -> Matrix(1,0,2,1) Matrix(5371,-1972,2040,-749) -> Matrix(1,2,0,1) Matrix(4973,-1828,944,-347) -> Matrix(5,4,-4,-3) Matrix(4525,-1664,2684,-987) -> Matrix(7,4,12,7) Matrix(2209,-816,2856,-1055) -> Matrix(1,0,-6,1) Matrix(1093,-404,744,-275) -> Matrix(1,0,0,1) Matrix(421,-156,224,-83) -> Matrix(3,2,-2,-1) Matrix(173,-66,270,-103) -> Matrix(1,0,2,1) Matrix(637,-246,246,-95) -> Matrix(1,0,0,1) Matrix(1393,-544,612,-239) -> Matrix(1,0,2,1) Matrix(463,-182,318,-125) -> Matrix(3,2,-2,-1) Matrix(797,-324,460,-187) -> Matrix(3,2,-2,-1) Matrix(531,-218,626,-257) -> Matrix(7,4,-16,-9) Matrix(241,-100,576,-239) -> Matrix(27,14,-56,-29) Matrix(1939,-814,1222,-513) -> Matrix(17,8,-66,-31) Matrix(641,-276,72,-31) -> Matrix(1,0,2,1) Matrix(2463,-1072,664,-289) -> Matrix(5,2,-8,-3) Matrix(2769,-1208,1208,-527) -> Matrix(41,14,38,13) Matrix(1393,-612,544,-239) -> Matrix(1,0,2,1) Matrix(685,-302,778,-343) -> Matrix(1,0,2,1) Matrix(1291,-578,306,-137) -> Matrix(1,0,2,1) Matrix(1337,-600,1620,-727) -> Matrix(1,0,2,1) Matrix(3827,-1748,2428,-1109) -> Matrix(3,2,-8,-5) Matrix(3453,-1580,2192,-1003) -> Matrix(5,2,-8,-3) Matrix(557,-258,326,-151) -> Matrix(1,0,4,1) Matrix(421,-224,156,-83) -> Matrix(3,2,-2,-1) Matrix(485,-262,398,-215) -> Matrix(7,4,-16,-9) Matrix(747,-410,614,-337) -> Matrix(13,6,-24,-11) Matrix(239,-134,66,-37) -> Matrix(1,0,2,1) Matrix(281,-162,366,-211) -> Matrix(1,0,-2,1) Matrix(817,-474,474,-275) -> Matrix(1,0,4,1) Matrix(1393,-816,408,-239) -> Matrix(3,2,-2,-1) Matrix(1265,-742,878,-515) -> Matrix(3,2,-2,-1) Matrix(4591,-2718,3738,-2213) -> Matrix(7,2,-18,-5) Matrix(299,-178,42,-25) -> Matrix(1,0,4,1) Matrix(105,-64,64,-39) -> Matrix(1,0,6,1) Matrix(3673,-2310,1086,-683) -> Matrix(9,-2,-4,1) Matrix(1565,-986,646,-407) -> Matrix(13,-6,-2,1) Matrix(749,-474,542,-343) -> Matrix(1,0,0,1) Matrix(785,-506,166,-107) -> Matrix(1,-6,0,1) Matrix(2413,-1566,886,-575) -> Matrix(1,2,-2,-3) Matrix(431,-282,350,-229) -> Matrix(1,0,-2,1) Matrix(463,-318,182,-125) -> Matrix(3,2,-2,-1) Matrix(281,-196,400,-279) -> Matrix(11,6,-24,-13) Matrix(1735,-1222,1018,-717) -> Matrix(9,4,2,1) Matrix(2275,-1634,614,-441) -> Matrix(13,4,-10,-3) Matrix(653,-470,810,-583) -> Matrix(1,0,6,1) Matrix(2687,-1936,712,-513) -> Matrix(7,2,-4,-1) Matrix(3397,-2450,2450,-1767) -> Matrix(1,0,4,1) Matrix(749,-542,474,-343) -> Matrix(1,0,0,1) Matrix(569,-416,688,-503) -> Matrix(1,0,2,1) Matrix(3371,-2476,2000,-1469) -> Matrix(7,4,12,7) Matrix(1057,-778,1254,-923) -> Matrix(5,2,-8,-3) Matrix(4265,-3146,2466,-1819) -> Matrix(13,4,16,5) Matrix(489,-362,566,-419) -> Matrix(1,0,2,1) Matrix(193,-146,78,-59) -> Matrix(7,2,-4,-1) Matrix(5041,-3900,1860,-1439) -> Matrix(1,0,6,1) Matrix(171,-134,134,-105) -> Matrix(1,0,14,1) Matrix(1577,-1280,600,-487) -> Matrix(1,0,0,1) Matrix(3225,-2624,2624,-2135) -> Matrix(1,0,-4,1) Matrix(2849,-2320,824,-671) -> Matrix(1,-2,0,1) Matrix(1703,-1390,506,-413) -> Matrix(5,-2,-2,1) Matrix(485,-398,262,-215) -> Matrix(1,-4,0,1) Matrix(4249,-3504,1192,-983) -> Matrix(5,4,-4,-3) Matrix(925,-776,776,-651) -> Matrix(1,0,0,1) Matrix(1697,-1464,1260,-1087) -> Matrix(1,0,2,1) Matrix(1181,-1030,962,-839) -> Matrix(1,0,-2,1) Matrix(1499,-1324,848,-749) -> Matrix(1,0,2,1) Matrix(1237,-1108,700,-627) -> Matrix(5,2,2,1) Matrix(947,-1060,176,-197) -> Matrix(3,-4,-2,3) Matrix(429,-488,80,-91) -> Matrix(3,2,-2,-1) Matrix(711,-818,206,-237) -> Matrix(3,2,-2,-1) Matrix(489,-566,362,-419) -> Matrix(1,0,2,1) Matrix(531,-626,218,-257) -> Matrix(1,-4,0,1) Matrix(887,-1050,234,-277) -> Matrix(3,2,-2,-1) Matrix(4621,-5512,1364,-1627) -> Matrix(1,-2,0,1) Matrix(569,-688,416,-503) -> Matrix(1,0,2,1) Matrix(779,-954,138,-169) -> Matrix(13,4,-10,-3) Matrix(5063,-6224,580,-713) -> Matrix(7,2,-4,-1) Matrix(2379,-2926,274,-337) -> Matrix(7,2,-4,-1) Matrix(4307,-5316,1780,-2197) -> Matrix(73,22,-10,-3) Matrix(1095,-1354,334,-413) -> Matrix(39,10,-4,-1) Matrix(571,-722,450,-569) -> Matrix(1,0,52,1) Matrix(2209,-2856,816,-1055) -> Matrix(1,0,-6,1) Matrix(281,-366,162,-211) -> Matrix(1,0,-2,1) Matrix(1713,-2300,464,-623) -> Matrix(1,-2,0,1) Matrix(1257,-1702,274,-371) -> Matrix(7,-4,2,-1) Matrix(1801,-2448,476,-647) -> Matrix(3,-4,-2,3) Matrix(663,-902,86,-117) -> Matrix(1,-4,0,1) Matrix(905,-1236,216,-295) -> Matrix(1,0,-2,1) Matrix(1529,-2108,272,-375) -> Matrix(3,-4,-2,3) Matrix(7343,-10132,1972,-2721) -> Matrix(1,-4,0,1) Matrix(6057,-8360,1628,-2247) -> Matrix(1,0,0,1) Matrix(2223,-3080,428,-593) -> Matrix(1,-2,0,1) Matrix(4275,-5926,826,-1145) -> Matrix(1,-2,0,1) Matrix(2005,-2788,612,-851) -> Matrix(21,-10,-2,1) Matrix(1207,-1682,526,-733) -> Matrix(7,-6,6,-5) Matrix(281,-400,196,-279) -> Matrix(1,-6,0,1) Matrix(1937,-2788,544,-783) -> Matrix(3,8,-2,-5) Matrix(263,-382,42,-61) -> Matrix(1,2,-2,-3) Matrix(1351,-1980,552,-809) -> Matrix(13,10,-4,-3) Matrix(173,-270,66,-103) -> Matrix(1,0,2,1) Matrix(2177,-3434,646,-1019) -> Matrix(3,2,-2,-1) Matrix(1801,-2856,408,-647) -> Matrix(7,2,10,3) Matrix(2429,-3860,460,-731) -> Matrix(11,2,-6,-1) Matrix(547,-882,338,-545) -> Matrix(1,0,36,1) Matrix(923,-1558,266,-449) -> Matrix(1,0,-2,1) Matrix(1673,-2848,944,-1607) -> Matrix(3,-2,2,-1) Matrix(2151,-3698,1250,-2149) -> Matrix(1,0,0,1) Matrix(3599,-6228,1332,-2305) -> Matrix(3,-4,-2,3) Matrix(1067,-1890,258,-457) -> Matrix(3,-4,-2,3) Matrix(265,-484,144,-263) -> Matrix(1,-10,0,1) Matrix(185,-394,54,-115) -> Matrix(5,-2,-2,1) Matrix(321,-698,86,-187) -> Matrix(1,-2,0,1) Matrix(137,-304,32,-71) -> Matrix(1,0,-2,1) Matrix(229,-518,42,-95) -> Matrix(1,-2,0,1) Matrix(4403,-10082,1922,-4401) -> Matrix(45,-44,44,-43) Matrix(93,-214,10,-23) -> Matrix(3,-4,-2,3) Matrix(241,-576,100,-239) -> Matrix(1,-14,0,1) Matrix(6133,-14844,1720,-4163) -> Matrix(7,48,-6,-41) Matrix(6477,-15860,2396,-5867) -> Matrix(9,28,-10,-31) Matrix(2345,-5748,512,-1255) -> Matrix(11,30,4,11) Matrix(1217,-3102,450,-1147) -> Matrix(1,2,-2,-3) Matrix(1863,-4802,722,-1861) -> Matrix(1,0,0,1) Matrix(2857,-7514,646,-1699) -> Matrix(3,-2,2,-1) Matrix(19769,-53432,4472,-12087) -> Matrix(19,20,18,19) Matrix(41841,-113098,9466,-25587) -> Matrix(41,40,42,41) Matrix(2255,-6108,532,-1441) -> Matrix(1,0,0,1) Matrix(841,-2286,110,-299) -> Matrix(1,-4,0,1) Matrix(2439,-6638,722,-1965) -> Matrix(5,8,-2,-3) Matrix(2327,-6342,630,-1717) -> Matrix(3,2,-2,-1) Matrix(451,-1250,162,-449) -> Matrix(1,0,4,1) Matrix(209,-676,64,-207) -> Matrix(1,-16,0,1) Matrix(1703,-5608,372,-1225) -> Matrix(5,32,2,13) Matrix(6511,-22050,1922,-6509) -> Matrix(1,0,0,1) Matrix(3635,-12482,1058,-3633) -> Matrix(39,80,-20,-41) Matrix(5657,-20184,1280,-4567) -> Matrix(7,6,8,7) Matrix(1003,-3586,186,-665) -> Matrix(3,2,-2,-1) Matrix(6207,-22898,1682,-6205) -> Matrix(1,0,0,1) Matrix(379,-1458,98,-377) -> Matrix(11,12,-12,-13) Matrix(1193,-4962,270,-1123) -> Matrix(5,4,6,5) Matrix(1431,-6050,338,-1429) -> Matrix(1,0,0,1) Matrix(169,-784,36,-167) -> Matrix(1,-12,0,1) Matrix(291,-1682,50,-289) -> Matrix(27,28,-28,-29) Matrix(121,-900,16,-119) -> Matrix(1,-8,0,1) 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): 72 Degree of the the map X: 72 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): 864 Minimal number of generators: 145 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: 48 Genus: 49 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/1 9/8 75/61 19/15 79/57 7/5 10/7 21/13 43/25 11/6 2/1 71/31 12/5 49/19 13/5 273/101 25/9 3/1 13/4 23/7 105/31 17/5 79/23 11/3 107/29 67/18 19/5 27/7 4/1 55/13 13/3 9/2 23/5 14/3 5/1 27/5 11/2 17/3 29/5 6/1 7/1 15/2 23/3 8/1 17/2 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/8 -1/1 -2/3 2/15 -1/2 1/7 -1/2 0/1 1/6 -2/1 -1/1 3/17 -1/1 -5/6 2/11 -1/1 -2/3 3/16 -1/1 -2/3 4/21 -5/7 -2/3 1/5 -2/3 3/14 -1/2 5/23 -1/2 -4/9 2/9 -2/5 -1/3 3/13 0/1 1/0 1/4 -1/1 0/1 5/19 -1/1 -3/4 9/34 -5/7 -2/3 4/15 -1/1 -2/3 7/26 -1/1 -2/3 10/37 -5/7 -2/3 13/48 -1/1 -2/3 3/11 -2/3 2/7 -1/1 -2/3 9/31 -3/4 -2/3 7/24 -2/3 -7/11 5/17 -2/3 13/44 -2/3 -3/5 8/27 -3/5 -4/7 3/10 -3/5 -4/7 10/33 -17/31 -6/11 7/23 -8/15 4/13 -1/2 1/3 -1/2 0/1 4/11 -1/1 0/1 7/19 0/1 17/46 -1/1 0/1 10/27 -1/1 -2/3 3/8 -1/1 0/1 5/13 0/1 7/18 -1/1 0/1 9/23 -1/1 1/0 2/5 -1/1 -2/3 9/22 -3/5 -4/7 7/17 -5/9 -1/2 5/12 -1/2 3/7 -2/5 16/37 -2/5 -1/3 13/30 -2/5 -1/3 10/23 -4/11 -1/3 17/39 -7/20 -1/3 7/16 -1/3 -4/13 11/25 -1/3 -1/4 15/34 -1/3 0/1 4/9 -1/3 0/1 13/29 0/1 9/20 -1/3 0/1 5/11 -1/2 0/1 16/35 -1/2 11/24 -1/3 0/1 6/13 -1/3 0/1 1/2 -1/1 0/1 7/13 -3/5 -1/2 6/11 -1/2 5/9 -2/5 4/7 -1/3 -2/7 11/19 0/1 7/12 -1/3 0/1 17/29 0/1 10/17 -2/5 -1/3 3/5 -1/4 0/1 5/8 0/1 1/5 17/27 1/3 1/2 12/19 0/1 1/1 7/11 0/1 9/14 0/1 1/1 11/17 -2/1 1/0 13/20 -6/5 -1/1 2/3 -1/1 0/1 11/16 -1/1 0/1 9/13 -2/3 7/10 -1/2 5/7 -1/2 -1/3 23/32 -2/7 -3/11 18/25 -1/1 0/1 31/43 0/1 13/18 -1/3 0/1 8/11 -1/3 0/1 11/15 0/1 36/49 -1/2 25/34 -3/7 -2/5 14/19 -4/11 -1/3 17/23 -1/4 0/1 3/4 -1/3 0/1 13/17 0/1 10/13 -1/5 -2/11 7/9 -1/8 0/1 4/5 0/1 1/5 17/21 2/3 13/16 0/1 1/1 35/43 0/1 22/27 0/1 1/1 9/11 1/1 1/0 14/17 -2/1 -1/1 5/6 -1/1 0/1 16/19 -2/1 -1/1 27/32 -1/3 0/1 11/13 -1/1 -1/2 6/7 0/1 1/1 19/22 -1/1 0/1 13/15 -1/2 0/1 20/23 -1/1 0/1 7/8 -1/1 0/1 15/17 -1/1 -1/2 8/9 -1/2 1/1 0/1 9/8 1/0 8/7 -1/1 0/1 15/13 0/1 1/0 7/6 -1/3 0/1 13/11 -1/1 1/0 19/16 -1/1 -2/3 6/5 -1/1 0/1 17/14 -1/1 -2/3 11/9 -1/2 -1/3 27/22 -1/3 0/1 43/35 0/1 59/48 -1/3 0/1 75/61 -1/2 -1/4 16/13 -1/3 0/1 37/30 -6/17 -1/3 21/17 -2/7 5/4 -1/7 0/1 19/15 0/1 14/11 0/1 1/19 9/7 0/1 1/6 13/10 2/7 1/3 4/3 0/1 1/1 27/20 -1/1 0/1 23/17 0/1 1/2 19/14 1/1 4/3 34/25 2/1 3/1 15/11 0/1 11/8 0/1 1/1 40/29 1/1 2/1 69/50 1/0 29/21 0/1 18/13 0/1 1/1 79/57 1/2 1/0 61/44 0/1 1/1 43/31 0/1 25/18 -1/1 0/1 32/23 3/5 2/3 7/5 1/1 1/0 10/7 1/0 13/9 -2/1 16/11 -1/1 0/1 19/13 -3/2 -1/1 22/15 -1/1 -2/3 3/2 -1/1 0/1 11/7 0/1 52/33 -1/2 41/26 -2/5 -1/3 30/19 -1/3 0/1 19/12 -1/3 0/1 27/17 -1/4 -1/5 8/5 -1/7 0/1 21/13 0/1 13/8 0/1 1/11 5/3 0/1 1/2 17/10 1/1 2/1 29/17 0/1 41/24 0/1 1/3 12/7 0/1 1/1 43/25 1/2 1/0 31/18 0/1 1/1 19/11 0/1 64/37 8/9 1/1 45/26 1/1 2/1 26/15 -1/1 0/1 7/4 2/3 1/1 23/13 1/1 1/0 16/9 1/1 2/1 9/5 2/1 11/6 1/0 13/7 -3/1 1/0 2/1 -1/1 0/1 13/6 0/1 1/1 11/5 0/1 1/0 9/4 0/1 1/1 25/11 1/2 1/1 16/7 4/5 1/1 71/31 1/1 55/24 1/1 18/17 39/17 1/1 7/6 62/27 9/7 4/3 23/10 1/1 4/3 7/3 2/1 12/5 1/0 17/7 -5/1 1/0 22/9 -4/1 -3/1 71/29 -19/6 -3/1 49/20 -3/1 -26/9 27/11 -2/1 5/2 -2/1 -1/1 28/11 -2/1 -1/1 23/9 -1/1 -1/2 18/7 -1/1 0/1 49/19 -1/2 1/0 31/12 -1/1 0/1 13/5 0/1 21/8 0/1 1/1 71/27 2/3 50/19 1/1 6/5 29/11 2/1 1/0 8/3 -1/1 0/1 27/10 -2/1 -1/1 100/37 -12/11 -1/1 273/101 -1/1 173/64 -1/1 -18/19 73/27 -1/1 -3/4 46/17 -1/1 0/1 19/7 0/1 11/4 -1/1 0/1 25/9 0/1 14/5 0/1 1/1 3/1 0/1 1/0 13/4 1/0 23/7 -8/1 33/10 -6/1 -17/3 10/3 -4/1 -3/1 37/11 -3/1 -5/2 64/19 -3/1 -2/1 27/8 -4/1 -3/1 44/13 -3/1 -2/1 105/31 -5/2 1/0 61/18 -3/1 -2/1 17/5 -2/1 41/12 -3/1 -2/1 24/7 -7/3 -2/1 79/23 -2/1 55/16 -2/1 -13/7 31/9 -2/1 -3/2 38/11 -2/1 -1/1 7/2 -2/1 -1/1 25/7 -1/1 1/0 18/5 -1/1 -2/3 11/3 -2/1 59/16 -2/1 -1/1 107/29 -3/2 1/0 48/13 -2/1 -1/1 37/10 -2/1 -5/3 63/17 -5/4 -1/1 26/7 -2/1 -1/1 67/18 1/0 41/11 -2/1 1/0 15/4 -2/1 -1/1 34/9 -2/1 -5/3 53/14 -1/1 0/1 19/5 -3/2 -1/1 23/6 -6/5 -1/1 27/7 -1/1 4/1 -1/1 0/1 21/5 0/1 38/9 -1/1 0/1 55/13 -1/2 1/0 17/4 -1/1 0/1 13/3 -1/2 0/1 9/2 1/1 2/1 23/5 4/1 1/0 14/3 1/0 5/1 -2/1 21/4 -2/1 -5/3 16/3 -2/1 -1/1 43/8 -3/2 27/5 -3/2 -1/1 11/2 -2/1 -1/1 28/5 -2/1 -1/1 45/8 -4/3 -1/1 17/3 -5/4 -1/1 23/4 -12/11 -1/1 29/5 -1/1 6/1 -1/1 -2/3 7/1 0/1 1/0 15/2 1/0 23/3 -4/1 8/1 -2/1 -1/1 17/2 -2/1 -1/1 9/1 -2/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(93,-10,214,-23) (0/1,1/8) -> (13/30,10/23) Hyperbolic Matrix(663,-86,902,-117) (1/8,2/15) -> (36/49,25/34) Hyperbolic Matrix(210,-29,29,-4) (2/15,1/7) -> (7/1,15/2) Hyperbolic Matrix(88,-13,149,-22) (1/7,1/6) -> (10/17,3/5) Hyperbolic Matrix(493,-86,86,-15) (1/6,3/17) -> (17/3,23/4) Hyperbolic Matrix(577,-104,172,-31) (3/17,2/11) -> (10/3,37/11) Hyperbolic Matrix(229,-42,518,-95) (2/11,3/16) -> (15/34,4/9) Hyperbolic Matrix(228,-43,859,-162) (3/16,4/21) -> (9/34,4/15) Hyperbolic Matrix(1028,-197,741,-142) (4/21,1/5) -> (43/31,25/18) Hyperbolic Matrix(140,-29,29,-6) (1/5,3/14) -> (14/3,5/1) Hyperbolic Matrix(644,-139,139,-30) (3/14,5/23) -> (23/5,14/3) Hyperbolic Matrix(306,-67,475,-104) (5/23,2/9) -> (9/14,11/17) Hyperbolic Matrix(250,-57,193,-44) (2/9,3/13) -> (9/7,13/10) Hyperbolic Matrix(137,-32,304,-71) (3/13,1/4) -> (9/20,5/11) Hyperbolic Matrix(513,-134,134,-35) (1/4,5/19) -> (19/5,23/6) Hyperbolic Matrix(887,-234,1050,-277) (5/19,9/34) -> (27/32,11/13) Hyperbolic Matrix(321,-86,698,-187) (4/15,7/26) -> (11/24,6/13) Hyperbolic Matrix(2463,-664,1072,-289) (7/26,10/37) -> (62/27,23/10) Hyperbolic Matrix(1444,-391,1071,-290) (10/37,13/48) -> (4/3,27/20) Hyperbolic Matrix(1177,-320,320,-87) (13/48,3/11) -> (11/3,59/16) Hyperbolic Matrix(239,-66,134,-37) (3/11,2/7) -> (16/9,9/5) Hyperbolic Matrix(711,-206,818,-237) (2/7,9/31) -> (13/15,20/23) Hyperbolic Matrix(2449,-712,712,-207) (9/31,7/24) -> (55/16,31/9) Hyperbolic Matrix(1393,-408,816,-239) (7/24,5/17) -> (29/17,41/24) Hyperbolic Matrix(1785,-526,526,-155) (5/17,13/44) -> (61/18,17/5) Hyperbolic Matrix(998,-295,839,-248) (13/44,8/27) -> (19/16,6/5) Hyperbolic Matrix(577,-172,104,-31) (8/27,3/10) -> (11/2,28/5) Hyperbolic Matrix(1306,-395,939,-284) (3/10,10/33) -> (25/18,32/23) Hyperbolic Matrix(808,-245,653,-198) (10/33,7/23) -> (21/17,5/4) Hyperbolic Matrix(598,-183,183,-56) (7/23,4/13) -> (13/4,23/7) Hyperbolic Matrix(78,-25,25,-8) (4/13,1/3) -> (3/1,13/4) Hyperbolic Matrix(75,-26,26,-9) (1/3,4/11) -> (14/5,3/1) Hyperbolic Matrix(374,-137,273,-100) (4/11,7/19) -> (15/11,11/8) Hyperbolic Matrix(1042,-385,249,-92) (7/19,17/46) -> (4/1,21/5) Hyperbolic Matrix(1093,-404,744,-275) (17/46,10/27) -> (22/15,3/2) Hyperbolic Matrix(298,-111,247,-92) (10/27,3/8) -> (6/5,17/14) Hyperbolic Matrix(173,-66,270,-103) (3/8,5/13) -> (7/11,9/14) Hyperbolic Matrix(637,-246,246,-95) (5/13,7/18) -> (31/12,13/5) Hyperbolic Matrix(782,-305,441,-172) (7/18,9/23) -> (23/13,16/9) Hyperbolic Matrix(463,-182,318,-125) (9/23,2/5) -> (16/11,19/13) Hyperbolic Matrix(797,-324,460,-187) (2/5,9/22) -> (45/26,26/15) Hyperbolic Matrix(578,-237,917,-376) (9/22,7/17) -> (17/27,12/19) Hyperbolic Matrix(408,-169,169,-70) (7/17,5/12) -> (12/5,17/7) Hyperbolic Matrix(168,-71,71,-30) (5/12,3/7) -> (7/3,12/5) Hyperbolic Matrix(1780,-769,1449,-626) (3/7,16/37) -> (27/22,43/35) Hyperbolic Matrix(950,-411,1091,-472) (16/37,13/30) -> (20/23,7/8) Hyperbolic Matrix(2463,-1072,664,-289) (10/23,17/39) -> (63/17,26/7) Hyperbolic Matrix(2769,-1208,1208,-527) (17/39,7/16) -> (55/24,39/17) Hyperbolic Matrix(850,-373,237,-104) (7/16,11/25) -> (25/7,18/5) Hyperbolic Matrix(685,-302,778,-343) (11/25,15/34) -> (7/8,15/17) Hyperbolic Matrix(1291,-578,306,-137) (4/9,13/29) -> (21/5,38/9) Hyperbolic Matrix(1714,-769,633,-284) (13/29,9/20) -> (46/17,19/7) Hyperbolic Matrix(2172,-991,583,-266) (5/11,16/35) -> (67/18,41/11) Hyperbolic Matrix(3056,-1399,2215,-1014) (16/35,11/24) -> (40/29,69/50) Hyperbolic Matrix(557,-258,326,-151) (6/13,1/2) -> (41/24,12/7) Hyperbolic Matrix(200,-107,243,-130) (1/2,7/13) -> (9/11,14/17) Hyperbolic Matrix(286,-155,155,-84) (7/13,6/11) -> (11/6,13/7) Hyperbolic Matrix(198,-109,109,-60) (6/11,5/9) -> (9/5,11/6) Hyperbolic Matrix(239,-134,66,-37) (5/9,4/7) -> (18/5,11/3) Hyperbolic Matrix(281,-162,366,-211) (4/7,11/19) -> (13/17,10/13) Hyperbolic Matrix(817,-474,474,-275) (11/19,7/12) -> (31/18,19/11) Hyperbolic Matrix(1393,-816,408,-239) (7/12,17/29) -> (17/5,41/12) Hyperbolic Matrix(472,-277,685,-402) (17/29,10/17) -> (11/16,9/13) Hyperbolic Matrix(105,-64,64,-39) (3/5,5/8) -> (13/8,5/3) Hyperbolic Matrix(250,-157,293,-184) (5/8,17/27) -> (11/13,6/7) Hyperbolic Matrix(749,-474,542,-343) (12/19,7/11) -> (29/21,18/13) Hyperbolic Matrix(578,-375,783,-508) (11/17,13/20) -> (14/19,17/23) Hyperbolic Matrix(431,-282,350,-229) (13/20,2/3) -> (16/13,37/30) Hyperbolic Matrix(463,-318,182,-125) (2/3,11/16) -> (5/2,28/11) Hyperbolic Matrix(260,-181,181,-126) (9/13,7/10) -> (10/7,13/9) Hyperbolic Matrix(140,-99,99,-70) (7/10,5/7) -> (7/5,10/7) Hyperbolic Matrix(2275,-1634,614,-441) (5/7,23/32) -> (37/10,63/17) Hyperbolic Matrix(1306,-939,395,-284) (23/32,18/25) -> (33/10,10/3) Hyperbolic Matrix(1028,-741,197,-142) (18/25,31/43) -> (5/1,21/4) Hyperbolic Matrix(3397,-2450,2450,-1767) (31/43,13/18) -> (61/44,43/31) Hyperbolic Matrix(749,-542,474,-343) (13/18,8/11) -> (30/19,19/12) Hyperbolic Matrix(374,-273,137,-100) (8/11,11/15) -> (19/7,11/4) Hyperbolic Matrix(1352,-993,177,-130) (11/15,36/49) -> (15/2,23/3) Hyperbolic Matrix(1057,-778,1254,-923) (25/34,14/19) -> (16/19,27/32) Hyperbolic Matrix(489,-362,566,-419) (17/23,3/4) -> (19/22,13/15) Hyperbolic Matrix(193,-146,78,-59) (3/4,13/17) -> (27/11,5/2) Hyperbolic Matrix(250,-193,57,-44) (10/13,7/9) -> (13/3,9/2) Hyperbolic Matrix(171,-134,134,-105) (7/9,4/5) -> (14/11,9/7) Hyperbolic Matrix(808,-653,245,-198) (4/5,17/21) -> (23/7,33/10) Hyperbolic Matrix(1577,-1280,600,-487) (17/21,13/16) -> (21/8,71/27) Hyperbolic Matrix(3225,-2624,2624,-2135) (13/16,35/43) -> (43/35,59/48) Hyperbolic Matrix(974,-793,113,-92) (35/43,22/27) -> (17/2,9/1) Hyperbolic Matrix(1703,-1390,506,-413) (22/27,9/11) -> (37/11,64/19) Hyperbolic Matrix(298,-247,111,-92) (14/17,5/6) -> (8/3,27/10) Hyperbolic Matrix(998,-839,295,-248) (5/6,16/19) -> (27/8,44/13) Hyperbolic Matrix(1150,-991,311,-268) (6/7,19/22) -> (48/13,37/10) Hyperbolic Matrix(974,-861,181,-160) (15/17,8/9) -> (43/8,27/5) Hyperbolic Matrix(18,-17,17,-16) (8/9,1/1) -> (1/1,9/8) Parabolic Matrix(429,-488,80,-91) (9/8,8/7) -> (16/3,43/8) Hyperbolic Matrix(711,-818,206,-237) (8/7,15/13) -> (31/9,38/11) Hyperbolic Matrix(489,-566,362,-419) (15/13,7/6) -> (27/20,23/17) Hyperbolic Matrix(250,-293,157,-184) (7/6,13/11) -> (27/17,8/5) Hyperbolic Matrix(887,-1050,234,-277) (13/11,19/16) -> (53/14,19/5) Hyperbolic Matrix(200,-243,107,-130) (17/14,11/9) -> (13/7,2/1) Hyperbolic Matrix(779,-954,138,-169) (11/9,27/22) -> (45/8,17/3) Hyperbolic Matrix(4576,-5625,3721,-4574) (59/48,75/61) -> (75/61,16/13) Parabolic Matrix(1658,-2047,959,-1184) (37/30,21/17) -> (19/11,64/37) Hyperbolic Matrix(286,-361,225,-284) (5/4,19/15) -> (19/15,14/11) Parabolic Matrix(281,-366,162,-211) (13/10,4/3) -> (26/15,7/4) Hyperbolic Matrix(1256,-1701,477,-646) (23/17,19/14) -> (50/19,29/11) Hyperbolic Matrix(1801,-2448,476,-647) (19/14,34/25) -> (34/9,53/14) Hyperbolic Matrix(663,-902,86,-117) (34/25,15/11) -> (23/3,8/1) Hyperbolic Matrix(1529,-2108,272,-375) (11/8,40/29) -> (28/5,45/8) Hyperbolic Matrix(1642,-2267,1043,-1440) (69/50,29/21) -> (11/7,52/33) Hyperbolic Matrix(4504,-6241,3249,-4502) (18/13,79/57) -> (79/57,61/44) Parabolic Matrix(1207,-1682,526,-733) (32/23,7/5) -> (39/17,62/27) Hyperbolic Matrix(472,-685,277,-402) (13/9,16/11) -> (17/10,29/17) Hyperbolic Matrix(1351,-1980,552,-809) (19/13,22/15) -> (22/9,71/29) Hyperbolic Matrix(173,-270,66,-103) (3/2,11/7) -> (13/5,21/8) Hyperbolic Matrix(2600,-4099,699,-1102) (52/33,41/26) -> (26/7,67/18) Hyperbolic Matrix(2177,-3434,646,-1019) (41/26,30/19) -> (64/19,27/8) Hyperbolic Matrix(578,-917,237,-376) (19/12,27/17) -> (17/7,22/9) Hyperbolic Matrix(274,-441,169,-272) (8/5,21/13) -> (21/13,13/8) Parabolic Matrix(88,-149,13,-22) (5/3,17/10) -> (6/1,7/1) Hyperbolic Matrix(1076,-1849,625,-1074) (12/7,43/25) -> (43/25,31/18) Parabolic Matrix(3599,-6228,1332,-2305) (64/37,45/26) -> (27/10,100/37) Hyperbolic Matrix(308,-543,135,-238) (7/4,23/13) -> (25/11,16/7) Hyperbolic Matrix(185,-394,54,-115) (2/1,13/6) -> (41/12,24/7) Hyperbolic Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(137,-304,32,-71) (11/5,9/4) -> (17/4,13/3) Hyperbolic Matrix(229,-518,42,-95) (9/4,25/11) -> (27/5,11/2) Hyperbolic Matrix(2202,-5041,961,-2200) (16/7,71/31) -> (71/31,55/24) Parabolic Matrix(93,-214,10,-23) (23/10,7/3) -> (9/1,1/0) Hyperbolic Matrix(6477,-15860,2396,-5867) (71/29,49/20) -> (173/64,73/27) Hyperbolic Matrix(1970,-4829,749,-1836) (49/20,27/11) -> (71/27,50/19) Hyperbolic Matrix(1217,-3102,450,-1147) (28/11,23/9) -> (73/27,46/17) Hyperbolic Matrix(238,-611,67,-172) (23/9,18/7) -> (7/2,25/7) Hyperbolic Matrix(932,-2401,361,-930) (18/7,49/19) -> (49/19,31/12) Parabolic Matrix(168,-445,37,-98) (29/11,8/3) -> (9/2,23/5) Hyperbolic Matrix(27574,-74529,10201,-27572) (100/37,273/101) -> (273/101,173/64) Parabolic Matrix(226,-625,81,-224) (11/4,25/9) -> (25/9,14/5) Parabolic Matrix(3256,-11025,961,-3254) (44/13,105/31) -> (105/31,61/18) Parabolic Matrix(1818,-6241,529,-1816) (24/7,79/23) -> (79/23,55/16) Parabolic Matrix(122,-423,15,-52) (38/11,7/2) -> (8/1,17/2) Hyperbolic Matrix(3104,-11449,841,-3102) (59/16,107/29) -> (107/29,48/13) Parabolic Matrix(228,-859,43,-162) (15/4,34/9) -> (21/4,16/3) Hyperbolic Matrix(190,-729,49,-188) (23/6,27/7) -> (27/7,4/1) Parabolic Matrix(716,-3025,169,-714) (38/9,55/13) -> (55/13,17/4) Parabolic Matrix(146,-841,25,-144) (23/4,29/5) -> (29/5,6/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,0,1) Matrix(93,-10,214,-23) -> Matrix(5,4,-14,-11) Matrix(663,-86,902,-117) -> Matrix(7,4,-16,-9) Matrix(210,-29,29,-4) -> Matrix(1,0,2,1) Matrix(88,-13,149,-22) -> Matrix(1,0,-2,1) Matrix(493,-86,86,-15) -> Matrix(11,10,-10,-9) Matrix(577,-104,172,-31) -> Matrix(13,10,-4,-3) Matrix(229,-42,518,-95) -> Matrix(3,2,-8,-5) Matrix(228,-43,859,-162) -> Matrix(1,0,0,1) Matrix(1028,-197,741,-142) -> Matrix(3,2,4,3) Matrix(140,-29,29,-6) -> Matrix(7,4,-2,-1) Matrix(644,-139,139,-30) -> Matrix(17,8,2,1) Matrix(306,-67,475,-104) -> Matrix(5,2,2,1) Matrix(250,-57,193,-44) -> Matrix(1,0,6,1) Matrix(137,-32,304,-71) -> Matrix(1,0,-2,1) Matrix(513,-134,134,-35) -> Matrix(7,6,-6,-5) Matrix(887,-234,1050,-277) -> Matrix(3,2,-2,-1) Matrix(321,-86,698,-187) -> Matrix(3,2,-8,-5) Matrix(2463,-664,1072,-289) -> Matrix(1,2,0,1) Matrix(1444,-391,1071,-290) -> Matrix(3,2,4,3) Matrix(1177,-320,320,-87) -> Matrix(5,4,-4,-3) Matrix(239,-66,134,-37) -> Matrix(1,0,2,1) Matrix(711,-206,818,-237) -> Matrix(3,2,-2,-1) Matrix(2449,-712,712,-207) -> Matrix(17,12,-10,-7) Matrix(1393,-408,816,-239) -> Matrix(3,2,-2,-1) Matrix(1785,-526,526,-155) -> Matrix(19,12,-8,-5) Matrix(998,-295,839,-248) -> Matrix(3,2,-8,-5) Matrix(577,-172,104,-31) -> Matrix(17,10,-12,-7) Matrix(1306,-395,939,-284) -> Matrix(11,6,20,11) Matrix(808,-245,653,-198) -> Matrix(11,6,-46,-25) Matrix(598,-183,183,-56) -> Matrix(31,16,-2,-1) Matrix(78,-25,25,-8) -> Matrix(1,0,2,1) Matrix(75,-26,26,-9) -> Matrix(1,0,2,1) Matrix(374,-137,273,-100) -> Matrix(1,0,2,1) Matrix(1042,-385,249,-92) -> Matrix(1,0,0,1) Matrix(1093,-404,744,-275) -> Matrix(1,0,0,1) Matrix(298,-111,247,-92) -> Matrix(1,0,0,1) Matrix(173,-66,270,-103) -> Matrix(1,0,2,1) Matrix(637,-246,246,-95) -> Matrix(1,0,0,1) Matrix(782,-305,441,-172) -> Matrix(1,2,0,1) Matrix(463,-182,318,-125) -> Matrix(3,2,-2,-1) Matrix(797,-324,460,-187) -> Matrix(3,2,-2,-1) Matrix(578,-237,917,-376) -> Matrix(7,4,12,7) Matrix(408,-169,169,-70) -> Matrix(19,10,-2,-1) Matrix(168,-71,71,-30) -> Matrix(9,4,2,1) Matrix(1780,-769,1449,-626) -> Matrix(5,2,-18,-7) Matrix(950,-411,1091,-472) -> Matrix(5,2,-8,-3) Matrix(2463,-1072,664,-289) -> Matrix(5,2,-8,-3) Matrix(2769,-1208,1208,-527) -> Matrix(41,14,38,13) Matrix(850,-373,237,-104) -> Matrix(7,2,-4,-1) Matrix(685,-302,778,-343) -> Matrix(1,0,2,1) Matrix(1291,-578,306,-137) -> Matrix(1,0,2,1) Matrix(1714,-769,633,-284) -> Matrix(1,0,2,1) Matrix(2172,-991,583,-266) -> Matrix(3,2,-2,-1) Matrix(3056,-1399,2215,-1014) -> Matrix(5,2,2,1) Matrix(557,-258,326,-151) -> Matrix(1,0,4,1) Matrix(200,-107,243,-130) -> Matrix(3,2,-2,-1) Matrix(286,-155,155,-84) -> Matrix(11,6,-2,-1) Matrix(198,-109,109,-60) -> Matrix(9,4,2,1) Matrix(239,-134,66,-37) -> Matrix(1,0,2,1) Matrix(281,-162,366,-211) -> Matrix(1,0,-2,1) Matrix(817,-474,474,-275) -> Matrix(1,0,4,1) Matrix(1393,-816,408,-239) -> Matrix(3,2,-2,-1) Matrix(472,-277,685,-402) -> Matrix(5,2,-8,-3) Matrix(105,-64,64,-39) -> Matrix(1,0,6,1) Matrix(250,-157,293,-184) -> Matrix(1,0,-4,1) Matrix(749,-474,542,-343) -> Matrix(1,0,0,1) Matrix(578,-375,783,-508) -> Matrix(1,2,-4,-7) Matrix(431,-282,350,-229) -> Matrix(1,0,-2,1) Matrix(463,-318,182,-125) -> Matrix(3,2,-2,-1) Matrix(260,-181,181,-126) -> Matrix(7,4,-2,-1) Matrix(140,-99,99,-70) -> Matrix(5,2,2,1) Matrix(2275,-1634,614,-441) -> Matrix(13,4,-10,-3) Matrix(1306,-939,395,-284) -> Matrix(23,6,-4,-1) Matrix(1028,-741,197,-142) -> Matrix(7,2,-4,-1) Matrix(3397,-2450,2450,-1767) -> Matrix(1,0,4,1) Matrix(749,-542,474,-343) -> Matrix(1,0,0,1) Matrix(374,-273,137,-100) -> Matrix(1,0,2,1) Matrix(1352,-993,177,-130) -> Matrix(7,4,-2,-1) Matrix(1057,-778,1254,-923) -> Matrix(5,2,-8,-3) Matrix(489,-362,566,-419) -> Matrix(1,0,2,1) Matrix(193,-146,78,-59) -> Matrix(7,2,-4,-1) Matrix(250,-193,57,-44) -> Matrix(1,0,6,1) Matrix(171,-134,134,-105) -> Matrix(1,0,14,1) Matrix(808,-653,245,-198) -> Matrix(13,-6,-2,1) Matrix(1577,-1280,600,-487) -> Matrix(1,0,0,1) Matrix(3225,-2624,2624,-2135) -> Matrix(1,0,-4,1) Matrix(974,-793,113,-92) -> Matrix(1,-2,0,1) Matrix(1703,-1390,506,-413) -> Matrix(5,-2,-2,1) Matrix(298,-247,111,-92) -> Matrix(1,0,0,1) Matrix(998,-839,295,-248) -> Matrix(1,-2,0,1) Matrix(1150,-991,311,-268) -> Matrix(3,2,-2,-1) Matrix(974,-861,181,-160) -> Matrix(5,4,-4,-3) Matrix(18,-17,17,-16) -> Matrix(1,0,2,1) Matrix(429,-488,80,-91) -> Matrix(3,2,-2,-1) Matrix(711,-818,206,-237) -> Matrix(3,2,-2,-1) Matrix(489,-566,362,-419) -> Matrix(1,0,2,1) Matrix(250,-293,157,-184) -> Matrix(1,0,-4,1) Matrix(887,-1050,234,-277) -> Matrix(3,2,-2,-1) Matrix(200,-243,107,-130) -> Matrix(3,2,-2,-1) Matrix(779,-954,138,-169) -> Matrix(13,4,-10,-3) Matrix(4576,-5625,3721,-4574) -> Matrix(1,0,0,1) Matrix(1658,-2047,959,-1184) -> Matrix(7,2,10,3) Matrix(286,-361,225,-284) -> Matrix(1,0,26,1) Matrix(281,-366,162,-211) -> Matrix(1,0,-2,1) Matrix(1256,-1701,477,-646) -> Matrix(3,-2,2,-1) Matrix(1801,-2448,476,-647) -> Matrix(3,-4,-2,3) Matrix(663,-902,86,-117) -> Matrix(1,-4,0,1) Matrix(1529,-2108,272,-375) -> Matrix(3,-4,-2,3) Matrix(1642,-2267,1043,-1440) -> Matrix(1,0,-2,1) Matrix(4504,-6241,3249,-4502) -> Matrix(1,0,0,1) Matrix(1207,-1682,526,-733) -> Matrix(7,-6,6,-5) Matrix(472,-685,277,-402) -> Matrix(1,2,0,1) Matrix(1351,-1980,552,-809) -> Matrix(13,10,-4,-3) Matrix(173,-270,66,-103) -> Matrix(1,0,2,1) Matrix(2600,-4099,699,-1102) -> Matrix(1,0,2,1) Matrix(2177,-3434,646,-1019) -> Matrix(3,2,-2,-1) Matrix(578,-917,237,-376) -> Matrix(15,4,-4,-1) Matrix(274,-441,169,-272) -> Matrix(1,0,18,1) Matrix(88,-149,13,-22) -> Matrix(1,0,-2,1) Matrix(1076,-1849,625,-1074) -> Matrix(1,0,0,1) Matrix(3599,-6228,1332,-2305) -> Matrix(3,-4,-2,3) Matrix(308,-543,135,-238) -> Matrix(1,-2,2,-3) Matrix(185,-394,54,-115) -> Matrix(5,-2,-2,1) Matrix(321,-698,86,-187) -> Matrix(1,-2,0,1) Matrix(137,-304,32,-71) -> Matrix(1,0,-2,1) Matrix(229,-518,42,-95) -> Matrix(1,-2,0,1) Matrix(2202,-5041,961,-2200) -> Matrix(23,-22,22,-21) Matrix(93,-214,10,-23) -> Matrix(3,-4,-2,3) Matrix(6477,-15860,2396,-5867) -> Matrix(9,28,-10,-31) Matrix(1970,-4829,749,-1836) -> Matrix(3,8,4,11) Matrix(1217,-3102,450,-1147) -> Matrix(1,2,-2,-3) Matrix(238,-611,67,-172) -> Matrix(3,2,-2,-1) Matrix(932,-2401,361,-930) -> Matrix(1,0,0,1) Matrix(168,-445,37,-98) -> Matrix(1,2,0,1) Matrix(27574,-74529,10201,-27572) -> Matrix(29,30,-30,-31) Matrix(226,-625,81,-224) -> Matrix(1,0,2,1) Matrix(3256,-11025,961,-3254) -> Matrix(1,0,0,1) Matrix(1818,-6241,529,-1816) -> Matrix(19,40,-10,-21) Matrix(122,-423,15,-52) -> Matrix(1,0,0,1) Matrix(3104,-11449,841,-3102) -> Matrix(1,0,0,1) Matrix(228,-859,43,-162) -> Matrix(1,0,0,1) Matrix(190,-729,49,-188) -> Matrix(5,6,-6,-7) Matrix(716,-3025,169,-714) -> Matrix(1,0,0,1) Matrix(146,-841,25,-144) -> Matrix(13,14,-14,-15) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 36 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (-1/1,0/1) 0 1 1/1 0/1 2 17 9/8 1/0 1 2 8/7 (-1/1,0/1) 0 34 15/13 (0/1,1/0) 0 17 7/6 (-1/3,0/1) 0 34 13/11 (-1/1,1/0) 0 17 19/16 (-1/1,-2/3) 0 34 6/5 (-1/1,0/1) 0 34 17/14 (-1/1,-2/3) 0 34 11/9 (-1/2,-1/3) 0 17 27/22 (-1/3,0/1) 0 34 43/35 0/1 2 17 75/61 (-1/3,0/1) 0 1 16/13 (-1/3,0/1) 0 34 21/17 -2/7 2 17 5/4 (-1/7,0/1) 0 34 19/15 0/1 26 1 9/7 (0/1,1/6) 0 17 13/10 (2/7,1/3) 0 34 4/3 (0/1,1/1) 0 34 27/20 (-1/1,0/1) 0 34 23/17 (0/1,1/2) 0 17 19/14 (1/1,4/3) 0 34 34/25 (2/1,3/1) 0 34 15/11 0/1 2 17 11/8 (0/1,1/1) 0 34 18/13 (0/1,1/1) 0 34 79/57 (0/1,1/1) 0 1 43/31 0/1 2 17 25/18 (-1/1,0/1) 0 34 32/23 (3/5,2/3) 0 34 7/5 (1/1,1/0) 0 17 10/7 1/0 3 2 13/9 -2/1 2 17 16/11 (-1/1,0/1) 0 34 3/2 (-1/1,0/1) 0 34 11/7 0/1 2 17 52/33 -1/2 2 2 41/26 (-2/5,-1/3) 0 34 30/19 (-1/3,0/1) 0 34 19/12 (-1/3,0/1) 0 34 27/17 (-1/4,-1/5) 0 17 8/5 (-1/7,0/1) 0 34 21/13 0/1 18 1 5/3 (0/1,1/2) 0 17 17/10 (1/1,2/1) 0 34 29/17 0/1 2 17 12/7 (0/1,1/1) 0 34 43/25 (0/1,1/1) 0 1 19/11 0/1 2 17 26/15 (-1/1,0/1) 0 34 7/4 (2/3,1/1) 0 34 9/5 2/1 2 17 11/6 1/0 5 2 13/7 (-3/1,1/0) 0 17 2/1 (-1/1,0/1) 0 34 13/6 (0/1,1/1) 0 34 11/5 (0/1,1/0) 0 17 9/4 (0/1,1/1) 0 34 25/11 (1/2,1/1) 0 17 16/7 (4/5,1/1) 0 34 71/31 1/1 22 1 39/17 (1/1,7/6) 0 17 23/10 (1/1,4/3) 0 34 7/3 2/1 2 17 12/5 1/0 7 2 17/7 (-5/1,1/0) 0 17 22/9 (-4/1,-3/1) 0 34 49/20 (-3/1,-26/9) 0 34 27/11 -2/1 2 17 5/2 (-2/1,-1/1) 0 34 28/11 (-2/1,-1/1) 0 34 23/9 (-1/1,-1/2) 0 17 18/7 (-1/1,0/1) 0 34 49/19 (-1/1,0/1) 0 1 13/5 0/1 2 17 21/8 (0/1,1/1) 0 34 71/27 2/3 2 17 50/19 (1/1,6/5) 0 34 29/11 (2/1,1/0) 0 17 8/3 (-1/1,0/1) 0 34 27/10 (-2/1,-1/1) 0 34 100/37 (-12/11,-1/1) 0 34 273/101 -1/1 30 1 73/27 (-1/1,-3/4) 0 17 46/17 (-1/1,0/1) 0 34 19/7 0/1 2 17 11/4 (-1/1,0/1) 0 34 25/9 0/1 2 1 3/1 (0/1,1/0) 0 17 13/4 1/0 8 2 23/7 -8/1 2 17 33/10 (-6/1,-17/3) 0 34 10/3 (-4/1,-3/1) 0 34 27/8 (-4/1,-3/1) 0 34 44/13 (-3/1,-2/1) 0 34 105/31 (-3/1,-2/1) 0 1 17/5 -2/1 2 17 41/12 (-3/1,-2/1) 0 34 24/7 (-7/3,-2/1) 0 34 79/23 -2/1 10 1 31/9 (-2/1,-3/2) 0 17 38/11 (-2/1,-1/1) 0 34 7/2 (-2/1,-1/1) 0 34 25/7 (-1/1,1/0) 0 17 18/5 (-1/1,-2/3) 0 34 11/3 -2/1 2 17 107/29 (-2/1,-1/1) 0 1 48/13 (-2/1,-1/1) 0 34 37/10 (-2/1,-5/3) 0 34 63/17 (-5/4,-1/1) 0 17 26/7 (-2/1,-1/1) 0 34 67/18 1/0 2 2 41/11 (-2/1,1/0) 0 17 15/4 (-2/1,-1/1) 0 34 34/9 (-2/1,-5/3) 0 34 53/14 (-1/1,0/1) 0 34 19/5 (-3/2,-1/1) 0 17 27/7 -1/1 6 1 4/1 (-1/1,0/1) 0 34 21/5 0/1 2 17 55/13 (-1/1,0/1) 0 1 17/4 (-1/1,0/1) 0 34 13/3 (-1/2,0/1) 0 17 9/2 (1/1,2/1) 0 34 23/5 (4/1,1/0) 0 17 14/3 1/0 6 2 5/1 -2/1 2 17 21/4 (-2/1,-5/3) 0 34 16/3 (-2/1,-1/1) 0 34 43/8 -3/2 1 2 27/5 (-3/2,-1/1) 0 17 11/2 (-2/1,-1/1) 0 34 28/5 (-2/1,-1/1) 0 34 45/8 (-4/3,-1/1) 0 34 17/3 (-5/4,-1/1) 0 17 29/5 -1/1 14 1 6/1 (-1/1,-2/3) 0 34 7/1 (0/1,1/0) 0 17 15/2 1/0 4 2 23/3 -4/1 2 17 8/1 (-2/1,-1/1) 0 34 17/2 (-2/1,-1/1) 0 34 9/1 -2/1 2 17 1/0 (-1/1,0/1) 0 34 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(17,-18,16,-17) (1/1,9/8) -> (1/1,9/8) Reflection Matrix(429,-488,80,-91) (9/8,8/7) -> (16/3,43/8) Hyperbolic Matrix(711,-818,206,-237) (8/7,15/13) -> (31/9,38/11) Hyperbolic Matrix(489,-566,362,-419) (15/13,7/6) -> (27/20,23/17) Hyperbolic Matrix(250,-293,157,-184) (7/6,13/11) -> (27/17,8/5) Hyperbolic Matrix(887,-1050,234,-277) (13/11,19/16) -> (53/14,19/5) Hyperbolic Matrix(839,-998,248,-295) (19/16,6/5) -> (27/8,44/13) Glide Reflection Matrix(247,-298,92,-111) (6/5,17/14) -> (8/3,27/10) Glide Reflection Matrix(200,-243,107,-130) (17/14,11/9) -> (13/7,2/1) Hyperbolic Matrix(779,-954,138,-169) (11/9,27/22) -> (45/8,17/3) Hyperbolic Matrix(793,-974,92,-113) (27/22,43/35) -> (17/2,9/1) Glide Reflection Matrix(2624,-3225,2135,-2624) (43/35,75/61) -> (43/35,75/61) Reflection Matrix(1951,-2400,1586,-1951) (75/61,16/13) -> (75/61,16/13) Reflection Matrix(1280,-1577,487,-600) (16/13,21/17) -> (21/8,71/27) Glide Reflection Matrix(653,-808,198,-245) (21/17,5/4) -> (23/7,33/10) Glide Reflection Matrix(151,-190,120,-151) (5/4,19/15) -> (5/4,19/15) Reflection Matrix(134,-171,105,-134) (19/15,9/7) -> (19/15,9/7) Reflection Matrix(193,-250,44,-57) (9/7,13/10) -> (13/3,9/2) Glide Reflection Matrix(281,-366,162,-211) (13/10,4/3) -> (26/15,7/4) Hyperbolic Matrix(1071,-1444,290,-391) (4/3,27/20) -> (48/13,37/10) Glide Reflection Matrix(1256,-1701,477,-646) (23/17,19/14) -> (50/19,29/11) Hyperbolic Matrix(1801,-2448,476,-647) (19/14,34/25) -> (34/9,53/14) Hyperbolic Matrix(663,-902,86,-117) (34/25,15/11) -> (23/3,8/1) Hyperbolic Matrix(273,-374,100,-137) (15/11,11/8) -> (19/7,11/4) Glide Reflection Matrix(542,-749,343,-474) (11/8,18/13) -> (30/19,19/12) Glide Reflection Matrix(2053,-2844,1482,-2053) (18/13,79/57) -> (18/13,79/57) Reflection Matrix(2450,-3397,1767,-2450) (79/57,43/31) -> (79/57,43/31) Reflection Matrix(741,-1028,142,-197) (43/31,25/18) -> (5/1,21/4) Glide Reflection Matrix(939,-1306,284,-395) (25/18,32/23) -> (33/10,10/3) Glide Reflection Matrix(1634,-2275,441,-614) (32/23,7/5) -> (37/10,63/17) Glide Reflection Matrix(99,-140,70,-99) (7/5,10/7) -> (7/5,10/7) Reflection Matrix(181,-260,126,-181) (10/7,13/9) -> (10/7,13/9) Reflection Matrix(472,-685,277,-402) (13/9,16/11) -> (17/10,29/17) Hyperbolic Matrix(318,-463,125,-182) (16/11,3/2) -> (5/2,28/11) Glide Reflection Matrix(173,-270,66,-103) (3/2,11/7) -> (13/5,21/8) Hyperbolic Matrix(727,-1144,462,-727) (11/7,52/33) -> (11/7,52/33) Reflection Matrix(2600,-4099,699,-1102) (52/33,41/26) -> (26/7,67/18) Hyperbolic Matrix(1702,-2685,303,-478) (41/26,30/19) -> (28/5,45/8) Glide Reflection Matrix(578,-917,237,-376) (19/12,27/17) -> (17/7,22/9) Hyperbolic Matrix(209,-336,130,-209) (8/5,21/13) -> (8/5,21/13) Reflection Matrix(64,-105,39,-64) (21/13,5/3) -> (21/13,5/3) Reflection Matrix(88,-149,13,-22) (5/3,17/10) -> (6/1,7/1) Hyperbolic Matrix(816,-1393,239,-408) (29/17,12/7) -> (17/5,41/12) Glide Reflection Matrix(601,-1032,350,-601) (12/7,43/25) -> (12/7,43/25) Reflection Matrix(474,-817,275,-474) (43/25,19/11) -> (43/25,19/11) Reflection Matrix(460,-797,187,-324) (19/11,26/15) -> (27/11,5/2) Glide Reflection Matrix(134,-239,37,-66) (7/4,9/5) -> (18/5,11/3) Glide Reflection Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(155,-286,84,-155) (11/6,13/7) -> (11/6,13/7) Reflection Matrix(185,-394,54,-115) (2/1,13/6) -> (41/12,24/7) Hyperbolic Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(137,-304,32,-71) (11/5,9/4) -> (17/4,13/3) Hyperbolic Matrix(229,-518,42,-95) (9/4,25/11) -> (27/5,11/2) Hyperbolic Matrix(373,-850,104,-237) (25/11,16/7) -> (25/7,18/5) Glide Reflection Matrix(993,-2272,434,-993) (16/7,71/31) -> (16/7,71/31) Reflection Matrix(1208,-2769,527,-1208) (71/31,39/17) -> (71/31,39/17) Reflection Matrix(1072,-2463,289,-664) (39/17,23/10) -> (63/17,26/7) Glide Reflection Matrix(93,-214,10,-23) (23/10,7/3) -> (9/1,1/0) Hyperbolic Matrix(71,-168,30,-71) (7/3,12/5) -> (7/3,12/5) Reflection Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(1440,-3523,533,-1304) (22/9,49/20) -> (27/10,100/37) Glide Reflection Matrix(1970,-4829,749,-1836) (49/20,27/11) -> (71/27,50/19) Hyperbolic Matrix(1217,-3102,450,-1147) (28/11,23/9) -> (73/27,46/17) Hyperbolic Matrix(238,-611,67,-172) (23/9,18/7) -> (7/2,25/7) Hyperbolic Matrix(685,-1764,266,-685) (18/7,49/19) -> (18/7,49/19) Reflection Matrix(246,-637,95,-246) (49/19,13/5) -> (49/19,13/5) Reflection Matrix(168,-445,37,-98) (29/11,8/3) -> (9/2,23/5) Hyperbolic Matrix(20201,-54600,7474,-20201) (100/37,273/101) -> (100/37,273/101) Reflection Matrix(7372,-19929,2727,-7372) (273/101,73/27) -> (273/101,73/27) Reflection Matrix(385,-1042,92,-249) (46/17,19/7) -> (4/1,21/5) Glide Reflection Matrix(199,-550,72,-199) (11/4,25/9) -> (11/4,25/9) Reflection Matrix(26,-75,9,-26) (25/9,3/1) -> (25/9,3/1) Reflection Matrix(25,-78,8,-25) (3/1,13/4) -> (3/1,13/4) Reflection Matrix(183,-598,56,-183) (13/4,23/7) -> (13/4,23/7) Reflection Matrix(172,-577,31,-104) (10/3,27/8) -> (11/2,28/5) Glide Reflection Matrix(2729,-9240,806,-2729) (44/13,105/31) -> (44/13,105/31) Reflection Matrix(526,-1785,155,-526) (105/31,17/5) -> (105/31,17/5) Reflection Matrix(1105,-3792,322,-1105) (24/7,79/23) -> (24/7,79/23) Reflection Matrix(712,-2449,207,-712) (79/23,31/9) -> (79/23,31/9) Reflection Matrix(122,-423,15,-52) (38/11,7/2) -> (8/1,17/2) Hyperbolic Matrix(320,-1177,87,-320) (11/3,107/29) -> (11/3,107/29) Reflection Matrix(2783,-10272,754,-2783) (107/29,48/13) -> (107/29,48/13) Reflection Matrix(1475,-5494,396,-1475) (67/18,41/11) -> (67/18,41/11) Reflection Matrix(228,-859,43,-162) (15/4,34/9) -> (21/4,16/3) Hyperbolic Matrix(134,-513,35,-134) (19/5,27/7) -> (19/5,27/7) Reflection Matrix(55,-216,14,-55) (27/7,4/1) -> (27/7,4/1) Reflection Matrix(274,-1155,65,-274) (21/5,55/13) -> (21/5,55/13) Reflection Matrix(441,-1870,104,-441) (55/13,17/4) -> (55/13,17/4) Reflection Matrix(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(431,-2322,80,-431) (43/8,27/5) -> (43/8,27/5) Reflection Matrix(86,-493,15,-86) (17/3,29/5) -> (17/3,29/5) Reflection Matrix(59,-348,10,-59) (29/5,6/1) -> (29/5,6/1) Reflection Matrix(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(91,-690,12,-91) (15/2,23/3) -> (15/2,23/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(17,-18,16,-17) -> Matrix(1,0,0,-1) (1/1,9/8) -> (0/1,1/0) Matrix(429,-488,80,-91) -> Matrix(3,2,-2,-1) -1/1 Matrix(711,-818,206,-237) -> Matrix(3,2,-2,-1) -1/1 Matrix(489,-566,362,-419) -> Matrix(1,0,2,1) 0/1 Matrix(250,-293,157,-184) -> Matrix(1,0,-4,1) 0/1 Matrix(887,-1050,234,-277) -> Matrix(3,2,-2,-1) -1/1 Matrix(839,-998,248,-295) -> Matrix(5,2,-2,-1) Matrix(247,-298,92,-111) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(200,-243,107,-130) -> Matrix(3,2,-2,-1) -1/1 Matrix(779,-954,138,-169) -> Matrix(13,4,-10,-3) Matrix(793,-974,92,-113) -> Matrix(5,2,-2,-1) Matrix(2624,-3225,2135,-2624) -> Matrix(-1,0,6,1) (43/35,75/61) -> (-1/3,0/1) Matrix(1951,-2400,1586,-1951) -> Matrix(-1,0,6,1) (75/61,16/13) -> (-1/3,0/1) Matrix(1280,-1577,487,-600) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(653,-808,198,-245) -> Matrix(25,6,-4,-1) Matrix(151,-190,120,-151) -> Matrix(-1,0,14,1) (5/4,19/15) -> (-1/7,0/1) Matrix(134,-171,105,-134) -> Matrix(1,0,12,-1) (19/15,9/7) -> (0/1,1/6) Matrix(193,-250,44,-57) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(281,-366,162,-211) -> Matrix(1,0,-2,1) 0/1 Matrix(1071,-1444,290,-391) -> Matrix(3,-2,-2,1) Matrix(1256,-1701,477,-646) -> Matrix(3,-2,2,-1) 1/1 Matrix(1801,-2448,476,-647) -> Matrix(3,-4,-2,3) Matrix(663,-902,86,-117) -> Matrix(1,-4,0,1) 1/0 Matrix(273,-374,100,-137) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(542,-749,343,-474) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(2053,-2844,1482,-2053) -> Matrix(1,0,2,-1) (18/13,79/57) -> (0/1,1/1) Matrix(2450,-3397,1767,-2450) -> Matrix(1,0,2,-1) (79/57,43/31) -> (0/1,1/1) Matrix(741,-1028,142,-197) -> Matrix(3,-2,-2,1) Matrix(939,-1306,284,-395) -> Matrix(11,-6,-2,1) Matrix(1634,-2275,441,-614) -> Matrix(5,-4,-4,3) Matrix(99,-140,70,-99) -> Matrix(-1,2,0,1) (7/5,10/7) -> (1/1,1/0) Matrix(181,-260,126,-181) -> Matrix(1,4,0,-1) (10/7,13/9) -> (-2/1,1/0) Matrix(472,-685,277,-402) -> Matrix(1,2,0,1) 1/0 Matrix(318,-463,125,-182) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(173,-270,66,-103) -> Matrix(1,0,2,1) 0/1 Matrix(727,-1144,462,-727) -> Matrix(-1,0,4,1) (11/7,52/33) -> (-1/2,0/1) Matrix(2600,-4099,699,-1102) -> Matrix(1,0,2,1) 0/1 Matrix(1702,-2685,303,-478) -> Matrix(11,4,-8,-3) Matrix(578,-917,237,-376) -> Matrix(15,4,-4,-1) Matrix(209,-336,130,-209) -> Matrix(-1,0,14,1) (8/5,21/13) -> (-1/7,0/1) Matrix(64,-105,39,-64) -> Matrix(1,0,4,-1) (21/13,5/3) -> (0/1,1/2) Matrix(88,-149,13,-22) -> Matrix(1,0,-2,1) 0/1 Matrix(816,-1393,239,-408) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(601,-1032,350,-601) -> Matrix(1,0,2,-1) (12/7,43/25) -> (0/1,1/1) Matrix(474,-817,275,-474) -> Matrix(1,0,2,-1) (43/25,19/11) -> (0/1,1/1) Matrix(460,-797,187,-324) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(134,-239,37,-66) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(109,-198,60,-109) -> Matrix(-1,4,0,1) (9/5,11/6) -> (2/1,1/0) Matrix(155,-286,84,-155) -> Matrix(1,6,0,-1) (11/6,13/7) -> (-3/1,1/0) Matrix(185,-394,54,-115) -> Matrix(5,-2,-2,1) Matrix(321,-698,86,-187) -> Matrix(1,-2,0,1) 1/0 Matrix(137,-304,32,-71) -> Matrix(1,0,-2,1) 0/1 Matrix(229,-518,42,-95) -> Matrix(1,-2,0,1) 1/0 Matrix(373,-850,104,-237) -> Matrix(3,-2,-2,1) Matrix(993,-2272,434,-993) -> Matrix(9,-8,10,-9) (16/7,71/31) -> (4/5,1/1) Matrix(1208,-2769,527,-1208) -> Matrix(13,-14,12,-13) (71/31,39/17) -> (1/1,7/6) Matrix(1072,-2463,289,-664) -> Matrix(1,-2,-2,3) Matrix(93,-214,10,-23) -> Matrix(3,-4,-2,3) Matrix(71,-168,30,-71) -> Matrix(-1,4,0,1) (7/3,12/5) -> (2/1,1/0) Matrix(169,-408,70,-169) -> Matrix(1,10,0,-1) (12/5,17/7) -> (-5/1,1/0) Matrix(1440,-3523,533,-1304) -> Matrix(3,10,-2,-7) Matrix(1970,-4829,749,-1836) -> Matrix(3,8,4,11) Matrix(1217,-3102,450,-1147) -> Matrix(1,2,-2,-3) -1/1 Matrix(238,-611,67,-172) -> Matrix(3,2,-2,-1) -1/1 Matrix(685,-1764,266,-685) -> Matrix(-1,0,2,1) (18/7,49/19) -> (-1/1,0/1) Matrix(246,-637,95,-246) -> Matrix(-1,0,2,1) (49/19,13/5) -> (-1/1,0/1) Matrix(168,-445,37,-98) -> Matrix(1,2,0,1) 1/0 Matrix(20201,-54600,7474,-20201) -> Matrix(23,24,-22,-23) (100/37,273/101) -> (-12/11,-1/1) Matrix(7372,-19929,2727,-7372) -> Matrix(7,6,-8,-7) (273/101,73/27) -> (-1/1,-3/4) Matrix(385,-1042,92,-249) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(199,-550,72,-199) -> Matrix(-1,0,2,1) (11/4,25/9) -> (-1/1,0/1) Matrix(26,-75,9,-26) -> Matrix(1,0,0,-1) (25/9,3/1) -> (0/1,1/0) Matrix(25,-78,8,-25) -> Matrix(1,0,0,-1) (3/1,13/4) -> (0/1,1/0) Matrix(183,-598,56,-183) -> Matrix(1,16,0,-1) (13/4,23/7) -> (-8/1,1/0) Matrix(172,-577,31,-104) -> Matrix(3,10,-2,-7) Matrix(2729,-9240,806,-2729) -> Matrix(5,12,-2,-5) (44/13,105/31) -> (-3/1,-2/1) Matrix(526,-1785,155,-526) -> Matrix(5,12,-2,-5) (105/31,17/5) -> (-3/1,-2/1) Matrix(1105,-3792,322,-1105) -> Matrix(13,28,-6,-13) (24/7,79/23) -> (-7/3,-2/1) Matrix(712,-2449,207,-712) -> Matrix(7,12,-4,-7) (79/23,31/9) -> (-2/1,-3/2) Matrix(122,-423,15,-52) -> Matrix(1,0,0,1) Matrix(320,-1177,87,-320) -> Matrix(3,4,-2,-3) (11/3,107/29) -> (-2/1,-1/1) Matrix(2783,-10272,754,-2783) -> Matrix(3,4,-2,-3) (107/29,48/13) -> (-2/1,-1/1) Matrix(1475,-5494,396,-1475) -> Matrix(1,4,0,-1) (67/18,41/11) -> (-2/1,1/0) Matrix(228,-859,43,-162) -> Matrix(1,0,0,1) Matrix(134,-513,35,-134) -> Matrix(5,6,-4,-5) (19/5,27/7) -> (-3/2,-1/1) Matrix(55,-216,14,-55) -> Matrix(-1,0,2,1) (27/7,4/1) -> (-1/1,0/1) Matrix(274,-1155,65,-274) -> Matrix(-1,0,2,1) (21/5,55/13) -> (-1/1,0/1) Matrix(441,-1870,104,-441) -> Matrix(-1,0,2,1) (55/13,17/4) -> (-1/1,0/1) Matrix(139,-644,30,-139) -> Matrix(-1,8,0,1) (23/5,14/3) -> (4/1,1/0) Matrix(29,-140,6,-29) -> Matrix(1,4,0,-1) (14/3,5/1) -> (-2/1,1/0) Matrix(431,-2322,80,-431) -> Matrix(5,6,-4,-5) (43/8,27/5) -> (-3/2,-1/1) Matrix(86,-493,15,-86) -> Matrix(9,10,-8,-9) (17/3,29/5) -> (-5/4,-1/1) Matrix(59,-348,10,-59) -> Matrix(5,4,-6,-5) (29/5,6/1) -> (-1/1,-2/3) Matrix(29,-210,4,-29) -> Matrix(1,0,0,-1) (7/1,15/2) -> (0/1,1/0) Matrix(91,-690,12,-91) -> Matrix(1,8,0,-1) (15/2,23/3) -> (-4/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.