INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 96 Genus: 97 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -20/3 -6/1 -28/5 -16/3 -14/3 -60/13 -9/2 -22/5 -4/1 -15/4 -26/7 -18/5 -38/11 -27/8 -10/3 -54/17 -3/1 -30/11 -18/7 -12/5 -9/4 -24/11 -15/7 -2/1 -9/5 -18/11 -27/17 -54/35 -3/2 -18/13 -9/7 -6/5 -9/8 0/1 1/1 6/5 9/7 18/13 3/2 54/35 18/11 30/17 9/5 2/1 36/17 15/7 24/11 144/65 9/4 144/61 12/5 144/59 5/2 18/7 108/41 30/11 36/13 3/1 54/17 36/11 10/3 24/7 7/2 18/5 396/109 11/3 26/7 108/29 15/4 34/9 72/19 4/1 17/4 30/7 13/3 22/5 9/2 32/7 60/13 144/31 14/3 24/5 5/1 16/3 11/2 28/5 17/3 6/1 32/5 13/2 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 -1/2 1/0 -7/1 -1/1 -2/3 -20/3 -1/2 1/0 -13/2 -1/1 0/1 -6/1 -1/1 -23/4 -1/1 -2/3 -17/3 -2/3 -1/2 -28/5 -3/4 -1/2 -39/7 -2/3 -11/2 -1/2 0/1 -16/3 -1/2 1/0 -37/7 -1/1 0/1 -21/4 0/1 -5/1 -1/1 -2/3 -19/4 -1/2 0/1 -14/3 -1/1 0/1 -65/14 -1/1 0/1 -51/11 0/1 -37/8 -1/1 0/1 -60/13 -1/1 -23/5 -1/1 0/1 -32/7 -1/2 1/0 -9/2 -1/1 -22/5 -1/1 -1/2 -35/8 -1/1 -2/3 -13/3 -1/1 -2/3 -17/4 -8/15 -1/2 -4/1 -1/2 1/0 -19/5 -8/15 -1/2 -15/4 -2/5 -41/11 -4/11 -1/3 -26/7 -1/3 0/1 -37/10 -1/3 0/1 -11/3 -1/2 0/1 -18/5 0/1 -25/7 0/1 1/0 -57/16 0/1 -32/9 -1/2 1/0 -7/2 -1/1 0/1 -38/11 -1/1 -1/2 -31/9 -2/3 -3/5 -24/7 -1/2 -17/5 -1/2 -2/5 -44/13 -1/2 -3/8 -71/21 -2/5 -1/3 -27/8 -1/3 -37/11 -1/3 0/1 -47/14 -1/4 0/1 -10/3 -1/3 0/1 -13/4 0/1 1/1 -16/5 -1/2 1/0 -35/11 -1/1 0/1 -54/17 -1/1 -19/6 -2/3 -1/2 -3/1 0/1 -23/8 -1/1 0/1 -20/7 -1/2 1/0 -37/13 -1/1 0/1 -54/19 -1/1 -17/6 -1/2 0/1 -14/5 -1/3 0/1 -11/4 0/1 1/2 -41/15 0/1 1/1 -71/26 0/1 1/1 -30/11 1/1 -19/7 -4/1 1/0 -27/10 -1/1 -8/3 -1/2 1/0 -29/11 -2/1 -1/1 -50/19 -1/1 -3/4 -21/8 -2/3 -55/21 -12/23 -1/2 -34/13 -1/2 -3/7 -47/18 -1/2 -2/5 -60/23 -1/3 -13/5 -1/3 0/1 -18/7 0/1 -23/9 0/1 1/1 -28/11 1/2 1/0 -33/13 0/1 -5/2 -1/1 0/1 -22/9 -1/1 -1/2 -61/25 -1/2 -2/5 -39/16 0/1 -17/7 -2/3 -1/2 -12/5 0/1 -19/8 2/1 1/0 -26/11 -1/1 0/1 -59/25 -1/1 0/1 -33/14 0/1 -7/3 -1/1 0/1 -37/16 -1/1 0/1 -30/13 -1/1 -23/10 -1/3 0/1 -16/7 -1/2 1/0 -25/11 -1/2 0/1 -34/15 -1/2 -1/3 -9/4 0/1 -38/17 -1/1 1/0 -29/13 -2/1 -1/1 -20/9 -1/2 1/0 -51/23 0/1 -82/37 -1/1 0/1 -31/14 -1/1 0/1 -11/5 0/1 1/0 -35/16 -1/1 0/1 -24/11 -1/2 1/0 -13/6 -1/1 0/1 -15/7 0/1 -17/8 -1/2 0/1 -2/1 -1/1 0/1 -19/10 -1/2 0/1 -36/19 0/1 -17/9 0/1 1/0 -15/8 0/1 -43/23 -1/1 0/1 -28/15 -1/2 1/0 -13/7 -1/1 0/1 -37/20 -1/1 0/1 -24/13 -1/2 1/0 -11/6 -1/2 0/1 -31/17 -1/1 0/1 -144/79 -1/2 1/0 -113/62 -1/1 0/1 -82/45 -1/1 0/1 -51/28 0/1 -20/11 -1/2 1/0 -29/16 -1/1 -2/3 -9/5 0/1 -43/24 1/1 2/1 -34/19 1/1 1/0 -25/14 0/1 1/0 -16/9 -1/2 1/0 -23/13 0/1 1/1 -30/17 -1/1 -37/21 -1/1 0/1 -44/25 -1/2 1/0 -7/4 -1/1 0/1 -40/23 -1/2 1/0 -73/42 -1/1 0/1 -33/19 0/1 -59/34 -1/1 0/1 -144/83 -1/2 1/0 -85/49 -1/1 0/1 -26/15 -1/1 0/1 -45/26 -1/1 -19/11 -1/2 -2/5 -12/7 0/1 -17/10 -2/1 1/0 -39/23 0/1 -61/36 2/1 1/0 -144/85 1/0 -83/49 -4/1 1/0 -22/13 -1/1 1/0 -27/16 -1/1 -32/19 -1/2 1/0 -37/22 -1/1 0/1 -5/3 -1/1 0/1 -18/11 0/1 -31/19 0/1 1/3 -106/65 1/2 1/1 -75/46 0/1 -44/27 1/2 1/0 -101/62 0/1 1/1 -57/35 0/1 -13/8 0/1 1/1 -60/37 1/1 -47/29 2/1 1/0 -34/21 3/1 1/0 -21/13 -2/1 -71/44 -2/1 -1/1 -50/31 -3/2 -1/1 -79/49 -8/7 -1/1 -108/67 -1/1 -29/18 -1/1 -2/3 -8/5 -1/2 1/0 -35/22 -1/1 0/1 -27/17 -1/1 -73/46 -1/1 -2/3 -46/29 -1/1 -2/3 -19/12 -4/7 -1/2 -49/31 -3/7 -2/5 -30/19 -1/3 -71/45 -1/3 0/1 -41/26 -1/3 0/1 -11/7 -1/4 0/1 -36/23 0/1 -25/16 0/1 1/6 -14/9 0/1 1/1 -17/11 0/1 1/0 -54/35 -1/1 -37/24 -1/1 0/1 -57/37 0/1 -20/13 -1/2 1/0 -3/2 0/1 -19/13 -2/1 1/0 -54/37 -1/1 -35/24 -1/1 0/1 -16/11 -1/2 1/0 -13/9 -1/3 0/1 -36/25 0/1 -23/16 0/1 1/5 -10/7 0/1 1/1 -57/40 0/1 -47/33 0/1 1/2 -84/59 1/1 -37/26 0/1 1/1 -27/19 1/1 -71/50 1/1 2/1 -115/81 1/1 2/1 -44/31 3/2 1/0 -17/12 2/1 1/0 -41/29 3/1 4/1 -24/17 1/0 -31/22 -3/1 -2/1 -69/49 -2/1 -107/76 -2/1 -1/1 -38/27 -1/1 1/0 -7/5 -1/1 0/1 -18/13 0/1 -29/21 0/1 1/1 -69/50 0/1 -178/129 1/2 1/1 -287/208 2/3 1/1 -396/287 1/1 -109/79 0/1 1/1 -40/29 1/2 1/0 -51/37 0/1 -62/45 0/1 1/1 -11/8 0/1 1/0 -48/35 1/2 1/0 -37/27 0/1 1/1 -63/46 1/1 -26/19 0/1 1/1 -67/49 4/5 1/1 -108/79 1/1 -41/30 1/1 4/3 -15/11 2/1 -34/25 7/1 1/0 -53/39 22/1 1/0 -72/53 1/0 -19/14 -8/1 1/0 -4/3 -1/2 1/0 -17/13 -8/1 1/0 -30/23 -3/1 -13/10 -2/1 -1/1 -48/37 -3/2 1/0 -35/27 -2/1 -1/1 -92/71 -3/2 1/0 -57/44 -2/1 -22/17 -1/1 1/0 -31/24 -2/1 -1/1 -9/7 -1/1 -41/32 -1/1 0/1 -73/57 -1/1 0/1 -32/25 -1/2 1/0 -87/68 0/1 -55/43 0/1 1/0 -23/18 -1/1 0/1 -60/47 -1/1 -97/76 -1/2 0/1 -37/29 -1/1 0/1 -51/40 0/1 -65/51 -1/1 0/1 -144/113 -1/2 1/0 -79/62 -1/1 0/1 -14/11 -1/1 0/1 -19/15 0/1 1/0 -24/19 1/0 -5/4 -2/1 -1/1 -21/17 0/1 -37/30 -1/1 0/1 -16/13 -1/2 1/0 -11/9 0/1 1/0 -39/32 -2/1 -28/23 -3/2 1/0 -17/14 -2/1 1/0 -6/5 -1/1 -19/16 -1/2 0/1 -51/43 0/1 -32/27 -1/2 1/0 -13/11 -1/1 0/1 -33/28 0/1 -20/17 -1/2 1/0 -7/6 -2/1 -1/1 -8/7 -1/2 1/0 -9/8 -1/1 -1/1 -1/1 0/1 0/1 -1/2 1/0 1/1 -1/1 0/1 8/7 -1/2 1/0 7/6 -1/1 -2/3 20/17 -1/2 1/0 13/11 -1/1 0/1 6/5 -1/1 23/19 -1/1 -2/3 17/14 -2/3 -1/2 28/23 -3/4 -1/2 39/32 -2/3 11/9 -1/2 0/1 16/13 -1/2 1/0 37/30 -1/1 0/1 21/17 0/1 5/4 -1/1 -2/3 19/15 -1/2 0/1 14/11 -1/1 0/1 65/51 -1/1 0/1 51/40 0/1 37/29 -1/1 0/1 60/47 -1/1 23/18 -1/1 0/1 32/25 -1/2 1/0 9/7 -1/1 22/17 -1/1 -1/2 35/27 -1/1 -2/3 13/10 -1/1 -2/3 17/13 -8/15 -1/2 4/3 -1/2 1/0 19/14 -8/15 -1/2 15/11 -2/5 41/30 -4/11 -1/3 26/19 -1/3 0/1 37/27 -1/3 0/1 11/8 -1/2 0/1 18/13 0/1 25/18 0/1 1/0 57/41 0/1 32/23 -1/2 1/0 7/5 -1/1 0/1 38/27 -1/1 -1/2 31/22 -2/3 -3/5 24/17 -1/2 17/12 -1/2 -2/5 44/31 -1/2 -3/8 71/50 -2/5 -1/3 27/19 -1/3 37/26 -1/3 0/1 47/33 -1/4 0/1 10/7 -1/3 0/1 13/9 0/1 1/1 16/11 -1/2 1/0 35/24 -1/1 0/1 54/37 -1/1 19/13 -2/3 -1/2 3/2 0/1 23/15 -1/1 0/1 20/13 -1/2 1/0 37/24 -1/1 0/1 54/35 -1/1 17/11 -1/2 0/1 14/9 -1/3 0/1 11/7 0/1 1/2 41/26 0/1 1/1 71/45 0/1 1/1 30/19 1/1 19/12 -4/1 1/0 27/17 -1/1 8/5 -1/2 1/0 29/18 -2/1 -1/1 50/31 -1/1 -3/4 21/13 -2/3 55/34 -12/23 -1/2 34/21 -1/2 -3/7 47/29 -1/2 -2/5 60/37 -1/3 13/8 -1/3 0/1 18/11 0/1 23/14 0/1 1/1 28/17 1/2 1/0 33/20 0/1 5/3 -1/1 0/1 22/13 -1/1 -1/2 61/36 -1/2 -2/5 39/23 0/1 17/10 -2/3 -1/2 12/7 0/1 19/11 2/1 1/0 26/15 -1/1 0/1 59/34 -1/1 0/1 33/19 0/1 7/4 -1/1 0/1 37/21 -1/1 0/1 30/17 -1/1 23/13 -1/3 0/1 16/9 -1/2 1/0 25/14 -1/2 0/1 34/19 -1/2 -1/3 9/5 0/1 38/21 -1/1 1/0 29/16 -2/1 -1/1 20/11 -1/2 1/0 51/28 0/1 82/45 -1/1 0/1 31/17 -1/1 0/1 11/6 0/1 1/0 35/19 -1/1 0/1 24/13 -1/2 1/0 13/7 -1/1 0/1 15/8 0/1 17/9 -1/2 0/1 2/1 -1/1 0/1 19/9 -1/2 0/1 36/17 0/1 17/8 0/1 1/0 15/7 0/1 43/20 -1/1 0/1 28/13 -1/2 1/0 13/6 -1/1 0/1 37/17 -1/1 0/1 24/11 -1/2 1/0 11/5 -1/2 0/1 31/14 -1/1 0/1 144/65 -1/2 1/0 113/51 -1/1 0/1 82/37 -1/1 0/1 51/23 0/1 20/9 -1/2 1/0 29/13 -1/1 -2/3 9/4 0/1 43/19 1/1 2/1 34/15 1/1 1/0 25/11 0/1 1/0 16/7 -1/2 1/0 23/10 0/1 1/1 30/13 -1/1 37/16 -1/1 0/1 44/19 -1/2 1/0 7/3 -1/1 0/1 40/17 -1/2 1/0 73/31 -1/1 0/1 33/14 0/1 59/25 -1/1 0/1 144/61 -1/2 1/0 85/36 -1/1 0/1 26/11 -1/1 0/1 45/19 -1/1 19/8 -1/2 -2/5 12/5 0/1 17/7 -2/1 1/0 39/16 0/1 61/25 2/1 1/0 144/59 1/0 83/34 -4/1 1/0 22/9 -1/1 1/0 27/11 -1/1 32/13 -1/2 1/0 37/15 -1/1 0/1 5/2 -1/1 0/1 18/7 0/1 31/12 0/1 1/3 106/41 1/2 1/1 75/29 0/1 44/17 1/2 1/0 101/39 0/1 1/1 57/22 0/1 13/5 0/1 1/1 60/23 1/1 47/18 2/1 1/0 34/13 3/1 1/0 21/8 -2/1 71/27 -2/1 -1/1 50/19 -3/2 -1/1 79/30 -8/7 -1/1 108/41 -1/1 29/11 -1/1 -2/3 8/3 -1/2 1/0 35/13 -1/1 0/1 27/10 -1/1 73/27 -1/1 -2/3 46/17 -1/1 -2/3 19/7 -4/7 -1/2 49/18 -3/7 -2/5 30/11 -1/3 71/26 -1/3 0/1 41/15 -1/3 0/1 11/4 -1/4 0/1 36/13 0/1 25/9 0/1 1/6 14/5 0/1 1/1 17/6 0/1 1/0 54/19 -1/1 37/13 -1/1 0/1 57/20 0/1 20/7 -1/2 1/0 3/1 0/1 19/6 -2/1 1/0 54/17 -1/1 35/11 -1/1 0/1 16/5 -1/2 1/0 13/4 -1/3 0/1 36/11 0/1 23/7 0/1 1/5 10/3 0/1 1/1 57/17 0/1 47/14 0/1 1/2 84/25 1/1 37/11 0/1 1/1 27/8 1/1 71/21 1/1 2/1 115/34 1/1 2/1 44/13 3/2 1/0 17/5 2/1 1/0 41/12 3/1 4/1 24/7 1/0 31/9 -3/1 -2/1 69/20 -2/1 107/31 -2/1 -1/1 38/11 -1/1 1/0 7/2 -1/1 0/1 18/5 0/1 29/8 0/1 1/1 69/19 0/1 178/49 1/2 1/1 287/79 2/3 1/1 396/109 1/1 109/30 0/1 1/1 40/11 1/2 1/0 51/14 0/1 62/17 0/1 1/1 11/3 0/1 1/0 48/13 1/2 1/0 37/10 0/1 1/1 63/17 1/1 26/7 0/1 1/1 67/18 4/5 1/1 108/29 1/1 41/11 1/1 4/3 15/4 2/1 34/9 7/1 1/0 53/14 22/1 1/0 72/19 1/0 19/5 -8/1 1/0 4/1 -1/2 1/0 17/4 -8/1 1/0 30/7 -3/1 13/3 -2/1 -1/1 48/11 -3/2 1/0 35/8 -2/1 -1/1 92/21 -3/2 1/0 57/13 -2/1 22/5 -1/1 1/0 31/7 -2/1 -1/1 9/2 -1/1 41/9 -1/1 0/1 73/16 -1/1 0/1 32/7 -1/2 1/0 87/19 0/1 55/12 0/1 1/0 23/5 -1/1 0/1 60/13 -1/1 97/21 -1/2 0/1 37/8 -1/1 0/1 51/11 0/1 65/14 -1/1 0/1 144/31 -1/2 1/0 79/17 -1/1 0/1 14/3 -1/1 0/1 19/4 0/1 1/0 24/5 1/0 5/1 -2/1 -1/1 21/4 0/1 37/7 -1/1 0/1 16/3 -1/2 1/0 11/2 0/1 1/0 39/7 -2/1 28/5 -3/2 1/0 17/3 -2/1 1/0 6/1 -1/1 19/3 -1/2 0/1 51/8 0/1 32/5 -1/2 1/0 13/2 -1/1 0/1 33/5 0/1 20/3 -1/2 1/0 7/1 -2/1 -1/1 8/1 -1/2 1/0 9/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(35,288,-22,-181) (-8/1,1/0) -> (-8/5,-35/22) Hyperbolic Matrix(37,288,14,109) (-8/1,-7/1) -> (29/11,8/3) Hyperbolic Matrix(107,720,48,323) (-7/1,-20/3) -> (20/9,29/13) Hyperbolic Matrix(109,720,-38,-251) (-20/3,-13/2) -> (-23/8,-20/7) Hyperbolic Matrix(35,216,-6,-37) (-13/2,-6/1) -> (-6/1,-23/4) Parabolic Matrix(289,1656,-226,-1295) (-23/4,-17/3) -> (-55/43,-23/18) Hyperbolic Matrix(217,1224,64,361) (-17/3,-28/5) -> (44/13,17/5) Hyperbolic Matrix(683,3816,264,1475) (-28/5,-39/7) -> (75/29,44/17) Hyperbolic Matrix(505,2808,298,1657) (-39/7,-11/2) -> (61/36,39/23) Hyperbolic Matrix(107,576,60,323) (-11/2,-16/3) -> (16/9,25/14) Hyperbolic Matrix(217,1152,68,361) (-16/3,-37/7) -> (35/11,16/5) Hyperbolic Matrix(505,2664,396,2089) (-37/7,-21/4) -> (51/40,37/29) Hyperbolic Matrix(179,936,48,251) (-21/4,-5/1) -> (41/11,15/4) Hyperbolic Matrix(181,864,-128,-611) (-5/1,-19/4) -> (-17/12,-41/29) Hyperbolic Matrix(107,504,38,179) (-19/4,-14/3) -> (14/5,17/6) Hyperbolic Matrix(433,2016,-340,-1583) (-14/3,-65/14) -> (-79/62,-14/11) Hyperbolic Matrix(683,3168,318,1475) (-65/14,-51/11) -> (15/7,43/20) Hyperbolic Matrix(575,2664,466,2159) (-51/11,-37/8) -> (37/30,21/17) Hyperbolic Matrix(1153,5328,-810,-3743) (-37/8,-60/13) -> (-84/59,-37/26) Hyperbolic Matrix(469,2160,180,829) (-60/13,-23/5) -> (13/5,60/23) Hyperbolic Matrix(251,1152,-212,-973) (-23/5,-32/7) -> (-32/27,-13/11) Hyperbolic Matrix(253,1152,-150,-683) (-32/7,-9/2) -> (-27/16,-32/19) Hyperbolic Matrix(179,792,-106,-469) (-9/2,-22/5) -> (-22/13,-27/16) Hyperbolic Matrix(755,3312,-468,-2053) (-22/5,-35/8) -> (-71/44,-50/31) Hyperbolic Matrix(215,936,-116,-505) (-35/8,-13/3) -> (-13/7,-37/20) Hyperbolic Matrix(253,1080,-160,-683) (-13/3,-17/4) -> (-19/12,-49/31) Hyperbolic Matrix(35,144,26,107) (-17/4,-4/1) -> (4/3,19/14) Hyperbolic Matrix(37,144,28,109) (-4/1,-19/5) -> (17/13,4/3) Hyperbolic Matrix(325,1224,-124,-467) (-19/5,-15/4) -> (-21/8,-55/21) Hyperbolic Matrix(251,936,48,179) (-15/4,-41/11) -> (5/1,21/4) Hyperbolic Matrix(755,2808,-552,-2053) (-41/11,-26/7) -> (-26/19,-67/49) Hyperbolic Matrix(971,3600,-612,-2269) (-26/7,-37/10) -> (-73/46,-46/29) Hyperbolic Matrix(215,792,-98,-361) (-37/10,-11/3) -> (-11/5,-35/16) Hyperbolic Matrix(179,648,-50,-181) (-11/3,-18/5) -> (-18/5,-25/7) Parabolic Matrix(1151,4104,-808,-2881) (-25/7,-57/16) -> (-57/40,-47/33) Hyperbolic Matrix(1295,4608,-1012,-3601) (-57/16,-32/9) -> (-32/25,-87/68) Hyperbolic Matrix(143,504,-82,-289) (-32/9,-7/2) -> (-7/4,-40/23) Hyperbolic Matrix(395,1368,218,755) (-7/2,-38/11) -> (38/21,29/16) Hyperbolic Matrix(1295,4464,-794,-2737) (-38/11,-31/9) -> (-31/19,-106/65) Hyperbolic Matrix(251,864,52,179) (-31/9,-24/7) -> (24/5,5/1) Hyperbolic Matrix(253,864,-200,-683) (-24/7,-17/5) -> (-19/15,-24/19) Hyperbolic Matrix(361,1224,64,217) (-17/5,-44/13) -> (28/5,17/3) Hyperbolic Matrix(1405,4752,-798,-2699) (-44/13,-71/21) -> (-37/21,-44/25) Hyperbolic Matrix(1151,3888,426,1439) (-71/21,-27/8) -> (27/10,73/27) Hyperbolic Matrix(577,1944,214,721) (-27/8,-37/11) -> (35/13,27/10) Hyperbolic Matrix(1585,5328,-1242,-4175) (-37/11,-47/14) -> (-97/76,-37/29) Hyperbolic Matrix(901,3024,-654,-2195) (-47/14,-10/3) -> (-62/45,-11/8) Hyperbolic Matrix(109,360,-76,-251) (-10/3,-13/4) -> (-23/16,-10/7) Hyperbolic Matrix(179,576,78,251) (-13/4,-16/5) -> (16/7,23/10) Hyperbolic Matrix(361,1152,68,217) (-16/5,-35/11) -> (37/7,16/3) Hyperbolic Matrix(1223,3888,430,1367) (-35/11,-54/17) -> (54/19,37/13) Hyperbolic Matrix(613,1944,216,685) (-54/17,-19/6) -> (17/6,54/19) Hyperbolic Matrix(251,792,148,467) (-19/6,-3/1) -> (39/23,17/10) Hyperbolic Matrix(323,936,186,539) (-3/1,-23/8) -> (59/34,33/19) Hyperbolic Matrix(1441,4104,-1112,-3167) (-20/7,-37/13) -> (-35/27,-92/71) Hyperbolic Matrix(1367,3888,430,1223) (-37/13,-54/19) -> (54/17,35/11) Hyperbolic Matrix(685,1944,216,613) (-54/19,-17/6) -> (19/6,54/17) Hyperbolic Matrix(179,504,38,107) (-17/6,-14/5) -> (14/3,19/4) Hyperbolic Matrix(181,504,-116,-323) (-14/5,-11/4) -> (-25/16,-14/9) Hyperbolic Matrix(289,792,158,433) (-11/4,-41/15) -> (31/17,11/6) Hyperbolic Matrix(685,1872,-408,-1115) (-41/15,-71/26) -> (-37/22,-5/3) Hyperbolic Matrix(1187,3240,514,1403) (-71/26,-30/11) -> (30/13,37/16) Hyperbolic Matrix(397,1080,-304,-827) (-30/11,-19/7) -> (-17/13,-30/23) Hyperbolic Matrix(505,1368,-292,-791) (-19/7,-27/10) -> (-45/26,-19/11) Hyperbolic Matrix(107,288,-94,-253) (-27/10,-8/3) -> (-8/7,-9/8) Hyperbolic Matrix(109,288,14,37) (-8/3,-29/11) -> (7/1,8/1) Hyperbolic Matrix(2051,5400,-1272,-3349) (-29/11,-50/19) -> (-50/31,-79/49) Hyperbolic Matrix(1259,3312,-972,-2557) (-50/19,-21/8) -> (-57/44,-22/17) Hyperbolic Matrix(1403,3672,-1032,-2701) (-55/21,-34/13) -> (-34/25,-53/39) Hyperbolic Matrix(937,2448,524,1369) (-34/13,-47/18) -> (25/14,34/19) Hyperbolic Matrix(3311,8640,-2594,-6769) (-47/18,-60/23) -> (-60/47,-97/76) Hyperbolic Matrix(829,2160,180,469) (-60/23,-13/5) -> (23/5,60/13) Hyperbolic Matrix(251,648,-98,-253) (-13/5,-18/7) -> (-18/7,-23/9) Parabolic Matrix(395,1008,-212,-541) (-23/9,-28/11) -> (-28/15,-13/7) Hyperbolic Matrix(793,2016,142,361) (-28/11,-33/13) -> (39/7,28/5) Hyperbolic Matrix(541,1368,-384,-971) (-33/13,-5/2) -> (-31/22,-69/49) Hyperbolic Matrix(323,792,-250,-613) (-5/2,-22/9) -> (-22/17,-31/24) Hyperbolic Matrix(1297,3168,-766,-1871) (-22/9,-61/25) -> (-83/49,-22/13) Hyperbolic Matrix(1151,2808,944,2303) (-61/25,-39/16) -> (39/32,11/9) Hyperbolic Matrix(325,792,222,541) (-39/16,-17/7) -> (19/13,3/2) Hyperbolic Matrix(179,432,104,251) (-17/7,-12/5) -> (12/7,19/11) Hyperbolic Matrix(181,432,106,253) (-12/5,-19/8) -> (17/10,12/7) Hyperbolic Matrix(577,1368,-364,-863) (-19/8,-26/11) -> (-46/29,-19/12) Hyperbolic Matrix(1585,3744,-914,-2159) (-26/11,-59/25) -> (-85/49,-26/15) Hyperbolic Matrix(397,936,260,613) (-59/25,-33/14) -> (3/2,23/15) Hyperbolic Matrix(613,1440,-444,-1043) (-33/14,-7/3) -> (-29/21,-69/50) Hyperbolic Matrix(2053,4752,-1446,-3347) (-7/3,-37/16) -> (-71/50,-115/81) Hyperbolic Matrix(1403,3240,514,1187) (-37/16,-30/13) -> (30/11,71/26) Hyperbolic Matrix(937,2160,344,793) (-30/13,-23/10) -> (49/18,30/11) Hyperbolic Matrix(251,576,78,179) (-23/10,-16/7) -> (16/5,13/4) Hyperbolic Matrix(253,576,206,469) (-16/7,-25/11) -> (11/9,16/13) Hyperbolic Matrix(1079,2448,666,1511) (-25/11,-34/15) -> (34/21,47/29) Hyperbolic Matrix(287,648,-128,-289) (-34/15,-9/4) -> (-9/4,-38/17) Parabolic Matrix(613,1368,436,973) (-38/17,-29/13) -> (7/5,38/27) Hyperbolic Matrix(323,720,48,107) (-29/13,-20/9) -> (20/3,7/1) Hyperbolic Matrix(973,2160,-632,-1403) (-20/9,-51/23) -> (-57/37,-20/13) Hyperbolic Matrix(2339,5184,698,1547) (-51/23,-82/37) -> (10/3,57/17) Hyperbolic Matrix(5329,11808,-2924,-6479) (-82/37,-31/14) -> (-113/62,-82/45) Hyperbolic Matrix(359,792,228,503) (-31/14,-11/5) -> (11/7,41/26) Hyperbolic Matrix(1153,2520,264,577) (-35/16,-24/11) -> (48/11,35/8) Hyperbolic Matrix(431,936,-332,-721) (-24/11,-13/6) -> (-13/10,-48/37) Hyperbolic Matrix(433,936,-266,-575) (-13/6,-15/7) -> (-57/35,-13/8) Hyperbolic Matrix(541,1152,-456,-971) (-15/7,-17/8) -> (-19/16,-51/43) Hyperbolic Matrix(35,72,-18,-37) (-17/8,-2/1) -> (-2/1,-19/10) Parabolic Matrix(683,1296,322,611) (-19/10,-36/19) -> (36/17,17/8) Hyperbolic Matrix(685,1296,324,613) (-36/19,-17/9) -> (19/9,36/17) Hyperbolic Matrix(1223,2304,-956,-1801) (-17/9,-15/8) -> (-87/68,-55/43) Hyperbolic Matrix(1693,3168,1328,2485) (-15/8,-43/23) -> (65/51,51/40) Hyperbolic Matrix(1117,2088,482,901) (-43/23,-28/15) -> (44/19,7/3) Hyperbolic Matrix(1441,2664,390,721) (-37/20,-24/13) -> (48/13,37/10) Hyperbolic Matrix(431,792,-314,-577) (-24/13,-11/6) -> (-11/8,-48/35) Hyperbolic Matrix(433,792,158,289) (-11/6,-31/17) -> (41/15,11/4) Hyperbolic Matrix(11375,20736,5134,9359) (-31/17,-144/79) -> (144/65,113/51) Hyperbolic Matrix(11377,20736,5136,9361) (-144/79,-113/62) -> (31/14,144/65) Hyperbolic Matrix(4031,7344,1106,2015) (-82/45,-51/28) -> (51/14,62/17) Hyperbolic Matrix(3203,5832,-2472,-4501) (-51/28,-20/11) -> (-92/71,-57/44) Hyperbolic Matrix(397,720,338,613) (-20/11,-29/16) -> (7/6,20/17) Hyperbolic Matrix(359,648,-200,-361) (-29/16,-9/5) -> (-9/5,-43/24) Parabolic Matrix(1045,1872,302,541) (-43/24,-34/19) -> (38/11,7/2) Hyperbolic Matrix(1369,2448,524,937) (-34/19,-25/14) -> (47/18,34/13) Hyperbolic Matrix(323,576,60,107) (-25/14,-16/9) -> (16/3,11/2) Hyperbolic Matrix(325,576,224,397) (-16/9,-23/13) -> (13/9,16/11) Hyperbolic Matrix(611,1080,142,251) (-23/13,-30/17) -> (30/7,13/3) Hyperbolic Matrix(1837,3240,1164,2053) (-30/17,-37/21) -> (71/45,30/19) Hyperbolic Matrix(1187,2088,552,971) (-44/25,-7/4) -> (43/20,28/13) Hyperbolic Matrix(3023,5256,662,1151) (-40/23,-73/42) -> (73/16,32/7) Hyperbolic Matrix(4931,8568,-3502,-6085) (-73/42,-33/19) -> (-69/49,-107/76) Hyperbolic Matrix(1369,2376,208,361) (-33/19,-59/34) -> (13/2,33/5) Hyperbolic Matrix(11951,20736,5062,8783) (-59/34,-144/83) -> (144/61,85/36) Hyperbolic Matrix(11953,20736,5064,8785) (-144/83,-85/49) -> (59/25,144/61) Hyperbolic Matrix(1621,2808,-1184,-2051) (-26/15,-45/26) -> (-63/46,-26/19) Hyperbolic Matrix(251,432,104,179) (-19/11,-12/7) -> (12/5,17/7) Hyperbolic Matrix(253,432,106,181) (-12/7,-17/10) -> (19/8,12/5) Hyperbolic Matrix(467,792,148,251) (-17/10,-39/23) -> (3/1,19/6) Hyperbolic Matrix(1657,2808,298,505) (-39/23,-61/36) -> (11/2,39/7) Hyperbolic Matrix(12239,20736,5014,8495) (-61/36,-144/85) -> (144/59,83/34) Hyperbolic Matrix(12241,20736,5016,8497) (-144/85,-83/49) -> (61/25,144/59) Hyperbolic Matrix(2951,4968,812,1367) (-32/19,-37/22) -> (109/30,40/11) Hyperbolic Matrix(395,648,-242,-397) (-5/3,-18/11) -> (-18/11,-31/19) Parabolic Matrix(12673,20664,-9184,-14975) (-106/65,-75/46) -> (-69/50,-178/129) Hyperbolic Matrix(2341,3816,1922,3133) (-75/46,-44/27) -> (28/23,39/32) Hyperbolic Matrix(5833,9504,1724,2809) (-44/27,-101/62) -> (115/34,44/13) Hyperbolic Matrix(5437,8856,1172,1909) (-101/62,-57/35) -> (51/11,65/14) Hyperbolic Matrix(1331,2160,1042,1691) (-13/8,-60/37) -> (60/47,23/18) Hyperbolic Matrix(4175,6768,-2932,-4753) (-60/37,-47/29) -> (-47/33,-84/59) Hyperbolic Matrix(1511,2448,666,1079) (-47/29,-34/21) -> (34/15,25/11) Hyperbolic Matrix(757,1224,-556,-899) (-34/21,-21/13) -> (-15/11,-34/25) Hyperbolic Matrix(2989,4824,-1940,-3131) (-21/13,-71/44) -> (-37/24,-57/37) Hyperbolic Matrix(7235,11664,2746,4427) (-79/49,-108/67) -> (108/41,29/11) Hyperbolic Matrix(7237,11664,2748,4429) (-108/67,-29/18) -> (79/30,108/41) Hyperbolic Matrix(179,288,156,251) (-29/18,-8/5) -> (8/7,7/6) Hyperbolic Matrix(1223,1944,860,1367) (-35/22,-27/17) -> (27/19,37/26) Hyperbolic Matrix(2449,3888,1724,2737) (-27/17,-73/46) -> (71/50,27/19) Hyperbolic Matrix(1367,2160,774,1223) (-49/31,-30/19) -> (30/17,23/13) Hyperbolic Matrix(2053,3240,1164,1837) (-30/19,-71/45) -> (37/21,30/17) Hyperbolic Matrix(3743,5904,-2922,-4609) (-71/45,-41/26) -> (-41/32,-73/57) Hyperbolic Matrix(503,792,228,359) (-41/26,-11/7) -> (11/5,31/14) Hyperbolic Matrix(827,1296,298,467) (-11/7,-36/23) -> (36/13,25/9) Hyperbolic Matrix(829,1296,300,469) (-36/23,-25/16) -> (11/4,36/13) Hyperbolic Matrix(325,504,256,397) (-14/9,-17/11) -> (19/15,14/11) Hyperbolic Matrix(1259,1944,862,1331) (-17/11,-54/35) -> (54/37,19/13) Hyperbolic Matrix(2521,3888,1728,2665) (-54/35,-37/24) -> (35/24,54/37) Hyperbolic Matrix(469,720,-398,-611) (-20/13,-3/2) -> (-33/28,-20/17) Hyperbolic Matrix(541,792,222,325) (-3/2,-19/13) -> (17/7,39/16) Hyperbolic Matrix(1331,1944,862,1259) (-19/13,-54/37) -> (54/35,17/11) Hyperbolic Matrix(2665,3888,1728,2521) (-54/37,-35/24) -> (37/24,54/35) Hyperbolic Matrix(791,1152,642,935) (-35/24,-16/11) -> (16/13,37/30) Hyperbolic Matrix(397,576,224,325) (-16/11,-13/9) -> (23/13,16/9) Hyperbolic Matrix(899,1296,274,395) (-13/9,-36/25) -> (36/11,23/7) Hyperbolic Matrix(901,1296,276,397) (-36/25,-23/16) -> (13/4,36/11) Hyperbolic Matrix(3637,5184,1996,2845) (-10/7,-57/40) -> (51/28,82/45) Hyperbolic Matrix(253,360,26,37) (-37/26,-27/19) -> (9/1,1/0) Hyperbolic Matrix(3853,5472,1040,1477) (-27/19,-71/50) -> (37/10,63/17) Hyperbolic Matrix(6695,9504,2586,3671) (-115/81,-44/31) -> (44/17,101/39) Hyperbolic Matrix(863,1224,710,1007) (-44/31,-17/12) -> (17/14,28/23) Hyperbolic Matrix(1223,1728,356,503) (-41/29,-24/17) -> (24/7,31/9) Hyperbolic Matrix(1225,1728,358,505) (-24/17,-31/22) -> (41/12,24/7) Hyperbolic Matrix(21277,29952,-15420,-21707) (-107/76,-38/27) -> (-178/129,-287/208) Hyperbolic Matrix(1331,1872,588,827) (-38/27,-7/5) -> (43/19,34/15) Hyperbolic Matrix(467,648,-338,-469) (-7/5,-18/13) -> (-18/13,-29/21) Parabolic Matrix(113651,156816,31282,43163) (-287/208,-396/287) -> (396/109,109/30) Hyperbolic Matrix(113653,156816,31284,43165) (-396/287,-109/79) -> (287/79,396/109) Hyperbolic Matrix(3601,4968,1462,2017) (-109/79,-40/29) -> (32/13,37/15) Hyperbolic Matrix(2663,3672,-2246,-3097) (-40/29,-51/37) -> (-51/43,-32/27) Hyperbolic Matrix(5329,7344,2404,3313) (-51/37,-62/45) -> (82/37,51/23) Hyperbolic Matrix(1943,2664,892,1223) (-48/35,-37/27) -> (37/17,24/11) Hyperbolic Matrix(3995,5472,1182,1619) (-37/27,-63/46) -> (27/8,71/21) Hyperbolic Matrix(8531,11664,2290,3131) (-67/49,-108/79) -> (108/29,41/11) Hyperbolic Matrix(8533,11664,2292,3133) (-108/79,-41/30) -> (67/18,108/29) Hyperbolic Matrix(685,936,554,757) (-41/30,-15/11) -> (21/17,5/4) Hyperbolic Matrix(3815,5184,1006,1367) (-53/39,-72/53) -> (72/19,19/5) Hyperbolic Matrix(3817,5184,1008,1369) (-72/53,-19/14) -> (53/14,72/19) Hyperbolic Matrix(107,144,26,35) (-19/14,-4/3) -> (4/1,17/4) Hyperbolic Matrix(109,144,28,37) (-4/3,-17/13) -> (19/5,4/1) Hyperbolic Matrix(829,1080,360,469) (-30/23,-13/10) -> (23/10,30/13) Hyperbolic Matrix(1943,2520,1054,1367) (-48/37,-35/27) -> (35/19,24/13) Hyperbolic Matrix(503,648,-392,-505) (-31/24,-9/7) -> (-9/7,-41/32) Parabolic Matrix(4105,5256,1744,2233) (-73/57,-32/25) -> (40/17,73/31) Hyperbolic Matrix(1691,2160,1042,1331) (-23/18,-60/47) -> (60/37,13/8) Hyperbolic Matrix(2089,2664,396,505) (-37/29,-51/40) -> (21/4,37/7) Hyperbolic Matrix(6947,8856,2682,3419) (-51/40,-65/51) -> (101/39,57/22) Hyperbolic Matrix(16271,20736,3502,4463) (-65/51,-144/113) -> (144/31,79/17) Hyperbolic Matrix(16273,20736,3504,4465) (-144/113,-79/62) -> (65/14,144/31) Hyperbolic Matrix(397,504,256,325) (-14/11,-19/15) -> (17/11,14/9) Hyperbolic Matrix(685,864,486,613) (-24/19,-5/4) -> (31/22,24/17) Hyperbolic Matrix(757,936,554,685) (-5/4,-21/17) -> (15/11,41/30) Hyperbolic Matrix(2159,2664,466,575) (-21/17,-37/30) -> (37/8,51/11) Hyperbolic Matrix(935,1152,642,791) (-37/30,-16/13) -> (16/11,35/24) Hyperbolic Matrix(469,576,206,253) (-16/13,-11/9) -> (25/11,16/7) Hyperbolic Matrix(2303,2808,944,1151) (-11/9,-39/32) -> (39/16,61/25) Hyperbolic Matrix(1655,2016,1004,1223) (-39/32,-28/23) -> (28/17,33/20) Hyperbolic Matrix(1007,1224,710,863) (-28/23,-17/14) -> (17/12,44/31) Hyperbolic Matrix(179,216,-150,-181) (-17/14,-6/5) -> (-6/5,-19/16) Parabolic Matrix(2015,2376,854,1007) (-13/11,-33/28) -> (33/14,59/25) Hyperbolic Matrix(613,720,338,397) (-20/17,-7/6) -> (29/16,20/11) Hyperbolic Matrix(251,288,156,179) (-7/6,-8/7) -> (8/5,29/18) Hyperbolic Matrix(323,360,96,107) (-9/8,-1/1) -> (37/11,27/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(253,-288,94,-107) (1/1,8/7) -> (8/3,35/13) Hyperbolic Matrix(611,-720,398,-469) (20/17,13/11) -> (23/15,20/13) Hyperbolic Matrix(181,-216,150,-179) (13/11,6/5) -> (6/5,23/19) Parabolic Matrix(1367,-1656,298,-361) (23/19,17/14) -> (55/12,23/5) Hyperbolic Matrix(683,-864,200,-253) (5/4,19/15) -> (17/5,41/12) Hyperbolic Matrix(1583,-2016,340,-433) (14/11,65/51) -> (79/17,14/3) Hyperbolic Matrix(4175,-5328,1242,-1585) (37/29,60/47) -> (84/25,37/11) Hyperbolic Matrix(901,-1152,140,-179) (23/18,32/25) -> (32/5,13/2) Hyperbolic Matrix(899,-1152,366,-469) (32/25,9/7) -> (27/11,32/13) Hyperbolic Matrix(613,-792,250,-323) (9/7,22/17) -> (22/9,27/11) Hyperbolic Matrix(2557,-3312,972,-1259) (22/17,35/27) -> (71/27,50/19) Hyperbolic Matrix(721,-936,332,-431) (35/27,13/10) -> (13/6,37/17) Hyperbolic Matrix(827,-1080,304,-397) (13/10,17/13) -> (19/7,49/18) Hyperbolic Matrix(899,-1224,556,-757) (19/14,15/11) -> (21/13,55/34) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(2629,-3600,972,-1331) (26/19,37/27) -> (73/27,46/17) Hyperbolic Matrix(577,-792,314,-431) (37/27,11/8) -> (11/6,35/19) Hyperbolic Matrix(469,-648,338,-467) (11/8,18/13) -> (18/13,25/18) Parabolic Matrix(2953,-4104,880,-1223) (25/18,57/41) -> (57/17,47/14) Hyperbolic Matrix(3313,-4608,724,-1007) (57/41,32/23) -> (32/7,87/19) Hyperbolic Matrix(361,-504,154,-215) (32/23,7/5) -> (7/3,40/17) Hyperbolic Matrix(3169,-4464,1226,-1727) (38/27,31/22) -> (31/12,106/41) Hyperbolic Matrix(611,-864,128,-181) (24/17,17/12) -> (19/4,24/5) Hyperbolic Matrix(3347,-4752,1446,-2053) (44/31,71/50) -> (37/16,44/19) Hyperbolic Matrix(3743,-5328,810,-1153) (37/26,47/33) -> (97/21,37/8) Hyperbolic Matrix(2123,-3024,582,-829) (47/33,10/7) -> (62/17,11/3) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(2663,-4104,608,-937) (20/13,37/24) -> (35/8,92/21) Hyperbolic Matrix(323,-504,116,-181) (14/9,11/7) -> (25/9,14/5) Hyperbolic Matrix(1187,-1872,480,-757) (41/26,71/45) -> (37/15,5/2) Hyperbolic Matrix(683,-1080,160,-253) (30/19,19/12) -> (17/4,30/7) Hyperbolic Matrix(863,-1368,364,-577) (19/12,27/17) -> (45/19,19/8) Hyperbolic Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(2053,-3312,468,-755) (50/31,21/13) -> (57/13,22/5) Hyperbolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(5329,-8640,1154,-1871) (47/29,60/37) -> (60/13,97/21) Hyperbolic Matrix(397,-648,242,-395) (13/8,18/11) -> (18/11,23/14) Parabolic Matrix(613,-1008,284,-467) (23/14,28/17) -> (28/13,13/6) Hyperbolic Matrix(827,-1368,240,-397) (33/20,5/3) -> (31/9,69/20) Hyperbolic Matrix(469,-792,106,-179) (5/3,22/13) -> (22/5,31/7) Hyperbolic Matrix(1871,-3168,766,-1297) (22/13,61/36) -> (83/34,22/9) Hyperbolic Matrix(791,-1368,292,-505) (19/11,26/15) -> (46/17,19/7) Hyperbolic Matrix(2159,-3744,914,-1585) (26/15,59/34) -> (85/36,26/11) Hyperbolic Matrix(827,-1440,228,-397) (33/19,7/4) -> (29/8,69/19) Hyperbolic Matrix(2699,-4752,798,-1405) (7/4,37/21) -> (71/21,115/34) Hyperbolic Matrix(361,-648,200,-359) (34/19,9/5) -> (9/5,38/21) Parabolic Matrix(1187,-2160,416,-757) (20/11,51/28) -> (57/20,20/7) Hyperbolic Matrix(6479,-11808,2924,-5329) (82/45,31/17) -> (113/51,82/37) Hyperbolic Matrix(505,-936,116,-215) (24/13,13/7) -> (13/3,48/11) Hyperbolic Matrix(503,-936,194,-361) (13/7,15/8) -> (57/22,13/5) Hyperbolic Matrix(611,-1152,96,-181) (15/8,17/9) -> (19/3,51/8) Hyperbolic Matrix(37,-72,18,-35) (17/9,2/1) -> (2/1,19/9) Parabolic Matrix(1081,-2304,236,-503) (17/8,15/7) -> (87/19,55/12) Hyperbolic Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(2629,-5832,600,-1331) (51/23,20/9) -> (92/21,57/13) Hyperbolic Matrix(289,-648,128,-287) (29/13,9/4) -> (9/4,43/19) Parabolic Matrix(3637,-8568,1054,-2483) (73/31,33/14) -> (69/20,107/31) Hyperbolic Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(253,-648,98,-251) (5/2,18/7) -> (18/7,31/12) Parabolic Matrix(7991,-20664,2200,-5689) (106/41,75/29) -> (69/19,178/49) Hyperbolic Matrix(2593,-6768,772,-2015) (60/23,47/18) -> (47/14,84/25) Hyperbolic Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(1835,-4824,644,-1693) (21/8,71/27) -> (37/13,57/20) Hyperbolic Matrix(2161,-5904,474,-1295) (71/26,41/15) -> (41/9,73/16) Hyperbolic Matrix(251,-720,38,-109) (20/7,3/1) -> (33/5,20/3) Hyperbolic Matrix(8675,-29952,2388,-8245) (107/31,38/11) -> (178/49,287/79) Hyperbolic Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(1009,-3672,158,-575) (40/11,51/14) -> (51/8,32/5) Hyperbolic Matrix(145,-648,32,-143) (31/7,9/2) -> (9/2,41/9) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(35,288,-22,-181) -> Matrix(1,0,0,1) Matrix(37,288,14,109) -> Matrix(1,0,0,1) Matrix(107,720,48,323) -> Matrix(1,0,0,1) Matrix(109,720,-38,-251) -> Matrix(1,0,0,1) Matrix(35,216,-6,-37) -> Matrix(1,2,-2,-3) Matrix(289,1656,-226,-1295) -> Matrix(3,2,-2,-1) Matrix(217,1224,64,361) -> Matrix(1,0,2,1) Matrix(683,3816,264,1475) -> Matrix(3,2,4,3) Matrix(505,2808,298,1657) -> Matrix(3,2,-8,-5) Matrix(107,576,60,323) -> Matrix(1,0,0,1) Matrix(217,1152,68,361) -> Matrix(1,0,0,1) Matrix(505,2664,396,2089) -> Matrix(1,0,0,1) Matrix(179,936,48,251) -> Matrix(1,2,0,1) Matrix(181,864,-128,-611) -> Matrix(5,2,2,1) Matrix(107,504,38,179) -> Matrix(1,0,2,1) Matrix(433,2016,-340,-1583) -> Matrix(1,0,0,1) Matrix(683,3168,318,1475) -> Matrix(1,0,0,1) Matrix(575,2664,466,2159) -> Matrix(1,0,0,1) Matrix(1153,5328,-810,-3743) -> Matrix(1,0,2,1) Matrix(469,2160,180,829) -> Matrix(1,0,2,1) Matrix(251,1152,-212,-973) -> Matrix(1,0,0,1) Matrix(253,1152,-150,-683) -> Matrix(1,0,0,1) Matrix(179,792,-106,-469) -> Matrix(3,2,-2,-1) Matrix(755,3312,-468,-2053) -> Matrix(5,4,-4,-3) Matrix(215,936,-116,-505) -> Matrix(3,2,-2,-1) Matrix(253,1080,-160,-683) -> Matrix(7,4,-16,-9) Matrix(35,144,26,107) -> Matrix(1,0,0,1) Matrix(37,144,28,109) -> Matrix(1,0,0,1) Matrix(325,1224,-124,-467) -> Matrix(9,4,-16,-7) Matrix(251,936,48,179) -> Matrix(5,2,-8,-3) Matrix(755,2808,-552,-2053) -> Matrix(1,0,4,1) Matrix(971,3600,-612,-2269) -> Matrix(5,2,-8,-3) Matrix(215,792,-98,-361) -> Matrix(1,0,2,1) Matrix(179,648,-50,-181) -> Matrix(1,0,2,1) Matrix(1151,4104,-808,-2881) -> Matrix(1,0,2,1) Matrix(1295,4608,-1012,-3601) -> Matrix(1,0,0,1) Matrix(143,504,-82,-289) -> Matrix(1,0,0,1) Matrix(395,1368,218,755) -> Matrix(3,2,-2,-1) Matrix(1295,4464,-794,-2737) -> Matrix(3,2,4,3) Matrix(251,864,52,179) -> Matrix(7,4,-2,-1) Matrix(253,864,-200,-683) -> Matrix(5,2,2,1) Matrix(361,1224,64,217) -> Matrix(1,0,2,1) Matrix(1405,4752,-798,-2699) -> Matrix(5,2,-8,-3) Matrix(1151,3888,426,1439) -> Matrix(11,4,-14,-5) Matrix(577,1944,214,721) -> Matrix(1,0,2,1) Matrix(1585,5328,-1242,-4175) -> Matrix(1,0,2,1) Matrix(901,3024,-654,-2195) -> Matrix(1,0,4,1) Matrix(109,360,-76,-251) -> Matrix(1,0,4,1) Matrix(179,576,78,251) -> Matrix(1,0,0,1) Matrix(361,1152,68,217) -> Matrix(1,0,0,1) Matrix(1223,3888,430,1367) -> Matrix(1,0,0,1) Matrix(613,1944,216,685) -> Matrix(3,2,-2,-1) Matrix(251,792,148,467) -> Matrix(1,0,0,1) Matrix(323,936,186,539) -> Matrix(1,0,0,1) Matrix(1441,4104,-1112,-3167) -> Matrix(3,2,-2,-1) Matrix(1367,3888,430,1223) -> Matrix(1,0,0,1) Matrix(685,1944,216,613) -> Matrix(3,2,-2,-1) Matrix(179,504,38,107) -> Matrix(1,0,2,1) Matrix(181,504,-116,-323) -> Matrix(1,0,4,1) Matrix(289,792,158,433) -> Matrix(1,0,-2,1) Matrix(685,1872,-408,-1115) -> Matrix(1,0,-2,1) Matrix(1187,3240,514,1403) -> Matrix(1,0,-2,1) Matrix(397,1080,-304,-827) -> Matrix(1,-4,0,1) Matrix(505,1368,-292,-791) -> Matrix(1,2,-2,-3) Matrix(107,288,-94,-253) -> Matrix(1,0,0,1) Matrix(109,288,14,37) -> Matrix(1,0,0,1) Matrix(2051,5400,-1272,-3349) -> Matrix(7,6,-6,-5) Matrix(1259,3312,-972,-2557) -> Matrix(5,4,-4,-3) Matrix(1403,3672,-1032,-2701) -> Matrix(21,10,2,1) Matrix(937,2448,524,1369) -> Matrix(5,2,-8,-3) Matrix(3311,8640,-2594,-6769) -> Matrix(5,2,-8,-3) Matrix(829,2160,180,469) -> Matrix(1,0,2,1) Matrix(251,648,-98,-253) -> Matrix(1,0,4,1) Matrix(395,1008,-212,-541) -> Matrix(1,0,-2,1) Matrix(793,2016,142,361) -> Matrix(1,-2,0,1) Matrix(541,1368,-384,-971) -> Matrix(1,-2,0,1) Matrix(323,792,-250,-613) -> Matrix(3,2,-2,-1) Matrix(1297,3168,-766,-1871) -> Matrix(3,2,-2,-1) Matrix(1151,2808,944,2303) -> Matrix(5,2,-8,-3) Matrix(325,792,222,541) -> Matrix(1,0,0,1) Matrix(179,432,104,251) -> Matrix(1,0,2,1) Matrix(181,432,106,253) -> Matrix(1,0,-2,1) Matrix(577,1368,-364,-863) -> Matrix(1,2,-2,-3) Matrix(1585,3744,-914,-2159) -> Matrix(1,0,0,1) Matrix(397,936,260,613) -> Matrix(1,0,0,1) Matrix(613,1440,-444,-1043) -> Matrix(1,0,2,1) Matrix(2053,4752,-1446,-3347) -> Matrix(1,2,0,1) Matrix(1403,3240,514,1187) -> Matrix(1,0,-2,1) Matrix(937,2160,344,793) -> Matrix(3,2,-8,-5) Matrix(251,576,78,179) -> Matrix(1,0,0,1) Matrix(253,576,206,469) -> Matrix(1,0,0,1) Matrix(1079,2448,666,1511) -> Matrix(3,2,-8,-5) Matrix(287,648,-128,-289) -> Matrix(1,0,2,1) Matrix(613,1368,436,973) -> Matrix(1,2,-2,-3) Matrix(323,720,48,107) -> Matrix(1,0,0,1) Matrix(973,2160,-632,-1403) -> Matrix(1,0,0,1) Matrix(2339,5184,698,1547) -> Matrix(1,0,2,1) Matrix(5329,11808,-2924,-6479) -> Matrix(1,0,0,1) Matrix(359,792,228,503) -> Matrix(1,0,2,1) Matrix(1153,2520,264,577) -> Matrix(3,2,-2,-1) Matrix(431,936,-332,-721) -> Matrix(3,2,-2,-1) Matrix(433,936,-266,-575) -> Matrix(1,0,2,1) Matrix(541,1152,-456,-971) -> Matrix(1,0,0,1) Matrix(35,72,-18,-37) -> Matrix(1,0,0,1) Matrix(683,1296,322,611) -> Matrix(1,0,2,1) Matrix(685,1296,324,613) -> Matrix(1,0,-2,1) Matrix(1223,2304,-956,-1801) -> Matrix(1,0,0,1) Matrix(1693,3168,1328,2485) -> Matrix(1,0,0,1) Matrix(1117,2088,482,901) -> Matrix(1,0,0,1) Matrix(1441,2664,390,721) -> Matrix(1,0,2,1) Matrix(431,792,-314,-577) -> Matrix(1,0,2,1) Matrix(433,792,158,289) -> Matrix(1,0,-2,1) Matrix(11375,20736,5134,9359) -> Matrix(1,0,0,1) Matrix(11377,20736,5136,9361) -> Matrix(1,0,0,1) Matrix(4031,7344,1106,2015) -> Matrix(1,0,2,1) Matrix(3203,5832,-2472,-4501) -> Matrix(3,2,-2,-1) Matrix(397,720,338,613) -> Matrix(1,0,0,1) Matrix(359,648,-200,-361) -> Matrix(1,0,2,1) Matrix(1045,1872,302,541) -> Matrix(1,-2,0,1) Matrix(1369,2448,524,937) -> Matrix(1,2,0,1) Matrix(323,576,60,107) -> Matrix(1,0,0,1) Matrix(325,576,224,397) -> Matrix(1,0,0,1) Matrix(611,1080,142,251) -> Matrix(1,-2,0,1) Matrix(1837,3240,1164,2053) -> Matrix(1,0,2,1) Matrix(1187,2088,552,971) -> Matrix(1,0,0,1) Matrix(3023,5256,662,1151) -> Matrix(1,0,0,1) Matrix(4931,8568,-3502,-6085) -> Matrix(3,2,-2,-1) Matrix(1369,2376,208,361) -> Matrix(1,0,0,1) Matrix(11951,20736,5062,8783) -> Matrix(1,0,0,1) Matrix(11953,20736,5064,8785) -> Matrix(1,0,0,1) Matrix(1621,2808,-1184,-2051) -> Matrix(1,0,2,1) Matrix(251,432,104,179) -> Matrix(1,0,2,1) Matrix(253,432,106,181) -> Matrix(1,0,-2,1) Matrix(467,792,148,251) -> Matrix(1,0,0,1) Matrix(1657,2808,298,505) -> Matrix(1,-2,0,1) Matrix(12239,20736,5014,8495) -> Matrix(1,-6,0,1) Matrix(12241,20736,5016,8497) -> Matrix(1,6,0,1) Matrix(2951,4968,812,1367) -> Matrix(1,0,2,1) Matrix(395,648,-242,-397) -> Matrix(1,0,4,1) Matrix(12673,20664,-9184,-14975) -> Matrix(1,0,0,1) Matrix(2341,3816,1922,3133) -> Matrix(3,-2,-4,3) Matrix(5833,9504,1724,2809) -> Matrix(3,-2,2,-1) Matrix(5437,8856,1172,1909) -> Matrix(1,0,-2,1) Matrix(1331,2160,1042,1691) -> Matrix(1,0,-2,1) Matrix(4175,6768,-2932,-4753) -> Matrix(1,-2,2,-3) Matrix(1511,2448,666,1079) -> Matrix(1,-2,0,1) Matrix(757,1224,-556,-899) -> Matrix(1,4,0,1) Matrix(2989,4824,-1940,-3131) -> Matrix(1,2,-2,-3) Matrix(7235,11664,2746,4427) -> Matrix(9,10,-10,-11) Matrix(7237,11664,2748,4429) -> Matrix(11,10,-10,-9) Matrix(179,288,156,251) -> Matrix(1,0,0,1) Matrix(1223,1944,860,1367) -> Matrix(1,0,-2,1) Matrix(2449,3888,1724,2737) -> Matrix(5,4,-14,-11) Matrix(1367,2160,774,1223) -> Matrix(5,2,-8,-3) Matrix(2053,3240,1164,1837) -> Matrix(1,0,2,1) Matrix(3743,5904,-2922,-4609) -> Matrix(1,0,2,1) Matrix(503,792,228,359) -> Matrix(1,0,2,1) Matrix(827,1296,298,467) -> Matrix(1,0,10,1) Matrix(829,1296,300,469) -> Matrix(1,0,-10,1) Matrix(325,504,256,397) -> Matrix(1,0,-2,1) Matrix(1259,1944,862,1331) -> Matrix(1,2,-2,-3) Matrix(2521,3888,1728,2665) -> Matrix(1,0,0,1) Matrix(469,720,-398,-611) -> Matrix(1,0,0,1) Matrix(541,792,222,325) -> Matrix(1,0,0,1) Matrix(1331,1944,862,1259) -> Matrix(1,2,-2,-3) Matrix(2665,3888,1728,2521) -> Matrix(1,0,0,1) Matrix(791,1152,642,935) -> Matrix(1,0,0,1) Matrix(397,576,224,325) -> Matrix(1,0,0,1) Matrix(899,1296,274,395) -> Matrix(1,0,8,1) Matrix(901,1296,276,397) -> Matrix(1,0,-8,1) Matrix(3637,5184,1996,2845) -> Matrix(1,0,-2,1) Matrix(253,360,26,37) -> Matrix(1,0,-2,1) Matrix(3853,5472,1040,1477) -> Matrix(1,-2,2,-3) Matrix(6695,9504,2586,3671) -> Matrix(1,-2,2,-3) Matrix(863,1224,710,1007) -> Matrix(1,0,-2,1) Matrix(1223,1728,356,503) -> Matrix(1,-6,0,1) Matrix(1225,1728,358,505) -> Matrix(1,6,0,1) Matrix(21277,29952,-15420,-21707) -> Matrix(1,0,2,1) Matrix(1331,1872,588,827) -> Matrix(1,2,0,1) Matrix(467,648,-338,-469) -> Matrix(1,0,2,1) Matrix(113651,156816,31282,43163) -> Matrix(3,-2,2,-1) Matrix(113653,156816,31284,43165) -> Matrix(1,-2,2,-3) Matrix(3601,4968,1462,2017) -> Matrix(1,0,-2,1) Matrix(2663,3672,-2246,-3097) -> Matrix(1,0,-2,1) Matrix(5329,7344,2404,3313) -> Matrix(1,0,-2,1) Matrix(1943,2664,892,1223) -> Matrix(1,0,-2,1) Matrix(3995,5472,1182,1619) -> Matrix(3,-2,2,-1) Matrix(8531,11664,2290,3131) -> Matrix(9,-8,8,-7) Matrix(8533,11664,2292,3133) -> Matrix(7,-8,8,-9) Matrix(685,936,554,757) -> Matrix(1,-2,0,1) Matrix(3815,5184,1006,1367) -> Matrix(1,-30,0,1) Matrix(3817,5184,1008,1369) -> Matrix(1,30,0,1) Matrix(107,144,26,35) -> Matrix(1,0,0,1) Matrix(109,144,28,37) -> Matrix(1,0,0,1) Matrix(829,1080,360,469) -> Matrix(1,2,0,1) Matrix(1943,2520,1054,1367) -> Matrix(1,2,-2,-3) Matrix(503,648,-392,-505) -> Matrix(1,2,-2,-3) Matrix(4105,5256,1744,2233) -> Matrix(1,0,0,1) Matrix(1691,2160,1042,1331) -> Matrix(1,0,-2,1) Matrix(2089,2664,396,505) -> Matrix(1,0,0,1) Matrix(6947,8856,2682,3419) -> Matrix(1,0,2,1) Matrix(16271,20736,3502,4463) -> Matrix(1,0,0,1) Matrix(16273,20736,3504,4465) -> Matrix(1,0,0,1) Matrix(397,504,256,325) -> Matrix(1,0,-2,1) Matrix(685,864,486,613) -> Matrix(1,4,-2,-7) Matrix(757,936,554,685) -> Matrix(3,2,-8,-5) Matrix(2159,2664,466,575) -> Matrix(1,0,0,1) Matrix(935,1152,642,791) -> Matrix(1,0,0,1) Matrix(469,576,206,253) -> Matrix(1,0,0,1) Matrix(2303,2808,944,1151) -> Matrix(1,2,0,1) Matrix(1655,2016,1004,1223) -> Matrix(1,2,0,1) Matrix(1007,1224,710,863) -> Matrix(1,0,-2,1) Matrix(179,216,-150,-181) -> Matrix(1,2,-2,-3) Matrix(2015,2376,854,1007) -> Matrix(1,0,0,1) Matrix(613,720,338,397) -> Matrix(1,0,0,1) Matrix(251,288,156,179) -> Matrix(1,0,0,1) Matrix(323,360,96,107) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(253,-288,94,-107) -> Matrix(1,0,0,1) Matrix(611,-720,398,-469) -> Matrix(1,0,0,1) Matrix(181,-216,150,-179) -> Matrix(1,2,-2,-3) Matrix(1367,-1656,298,-361) -> Matrix(3,2,-2,-1) Matrix(683,-864,200,-253) -> Matrix(5,2,2,1) Matrix(1583,-2016,340,-433) -> Matrix(1,0,0,1) Matrix(4175,-5328,1242,-1585) -> Matrix(1,0,2,1) Matrix(901,-1152,140,-179) -> Matrix(1,0,0,1) Matrix(899,-1152,366,-469) -> Matrix(1,0,0,1) Matrix(613,-792,250,-323) -> Matrix(3,2,-2,-1) Matrix(2557,-3312,972,-1259) -> Matrix(5,4,-4,-3) Matrix(721,-936,332,-431) -> Matrix(3,2,-2,-1) Matrix(827,-1080,304,-397) -> Matrix(7,4,-16,-9) Matrix(899,-1224,556,-757) -> Matrix(9,4,-16,-7) Matrix(2053,-2808,552,-755) -> Matrix(1,0,4,1) Matrix(2629,-3600,972,-1331) -> Matrix(5,2,-8,-3) Matrix(577,-792,314,-431) -> Matrix(1,0,2,1) Matrix(469,-648,338,-467) -> Matrix(1,0,2,1) Matrix(2953,-4104,880,-1223) -> Matrix(1,0,2,1) Matrix(3313,-4608,724,-1007) -> Matrix(1,0,0,1) Matrix(361,-504,154,-215) -> Matrix(1,0,0,1) Matrix(3169,-4464,1226,-1727) -> Matrix(3,2,4,3) Matrix(611,-864,128,-181) -> Matrix(5,2,2,1) Matrix(3347,-4752,1446,-2053) -> Matrix(5,2,-8,-3) Matrix(3743,-5328,810,-1153) -> Matrix(1,0,2,1) Matrix(2123,-3024,582,-829) -> Matrix(1,0,4,1) Matrix(251,-360,76,-109) -> Matrix(1,0,4,1) Matrix(2663,-4104,608,-937) -> Matrix(3,2,-2,-1) Matrix(323,-504,116,-181) -> Matrix(1,0,4,1) Matrix(1187,-1872,480,-757) -> Matrix(1,0,-2,1) Matrix(683,-1080,160,-253) -> Matrix(1,-4,0,1) Matrix(863,-1368,364,-577) -> Matrix(1,2,-2,-3) Matrix(181,-288,22,-35) -> Matrix(1,0,0,1) Matrix(3349,-5400,1272,-2051) -> Matrix(7,6,-6,-5) Matrix(2053,-3312,468,-755) -> Matrix(5,4,-4,-3) Matrix(2269,-3672,600,-971) -> Matrix(21,10,2,1) Matrix(5329,-8640,1154,-1871) -> Matrix(5,2,-8,-3) Matrix(397,-648,242,-395) -> Matrix(1,0,4,1) Matrix(613,-1008,284,-467) -> Matrix(1,0,-2,1) Matrix(827,-1368,240,-397) -> Matrix(1,-2,0,1) Matrix(469,-792,106,-179) -> Matrix(3,2,-2,-1) Matrix(1871,-3168,766,-1297) -> Matrix(3,2,-2,-1) Matrix(791,-1368,292,-505) -> Matrix(1,2,-2,-3) Matrix(2159,-3744,914,-1585) -> Matrix(1,0,0,1) Matrix(827,-1440,228,-397) -> Matrix(1,0,2,1) Matrix(2699,-4752,798,-1405) -> Matrix(1,2,0,1) Matrix(361,-648,200,-359) -> Matrix(1,0,2,1) Matrix(1187,-2160,416,-757) -> Matrix(1,0,0,1) Matrix(6479,-11808,2924,-5329) -> Matrix(1,0,0,1) Matrix(505,-936,116,-215) -> Matrix(3,2,-2,-1) Matrix(503,-936,194,-361) -> Matrix(1,0,2,1) Matrix(611,-1152,96,-181) -> Matrix(1,0,0,1) Matrix(37,-72,18,-35) -> Matrix(1,0,0,1) Matrix(1081,-2304,236,-503) -> Matrix(1,0,0,1) Matrix(361,-792,98,-215) -> Matrix(1,0,2,1) Matrix(2629,-5832,600,-1331) -> Matrix(3,2,-2,-1) Matrix(289,-648,128,-287) -> Matrix(1,0,2,1) Matrix(3637,-8568,1054,-2483) -> Matrix(3,2,-2,-1) Matrix(1187,-2808,320,-757) -> Matrix(1,0,2,1) Matrix(253,-648,98,-251) -> Matrix(1,0,4,1) Matrix(7991,-20664,2200,-5689) -> Matrix(1,0,0,1) Matrix(2593,-6768,772,-2015) -> Matrix(1,-2,2,-3) Matrix(467,-1224,124,-325) -> Matrix(1,4,0,1) Matrix(1835,-4824,644,-1693) -> Matrix(1,2,-2,-3) Matrix(2161,-5904,474,-1295) -> Matrix(1,0,2,1) Matrix(251,-720,38,-109) -> Matrix(1,0,0,1) Matrix(8675,-29952,2388,-8245) -> Matrix(1,0,2,1) Matrix(181,-648,50,-179) -> Matrix(1,0,2,1) Matrix(1009,-3672,158,-575) -> Matrix(1,0,-2,1) Matrix(145,-648,32,-143) -> Matrix(1,2,-2,-3) Matrix(37,-216,6,-35) -> Matrix(1,2,-2,-3) 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): 48 Degree of the the map X: 48 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: 64 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 6/5 9/7 4/3 18/13 3/2 18/11 12/7 9/5 2/1 36/17 24/11 144/65 20/9 9/4 144/61 12/5 144/59 18/7 60/23 108/41 8/3 27/10 30/11 36/13 54/19 3/1 54/17 16/5 36/11 10/3 44/13 24/7 18/5 396/109 26/7 108/29 15/4 34/9 72/19 4/1 30/7 48/11 22/5 9/2 32/7 60/13 144/31 14/3 24/5 5/1 21/4 16/3 11/2 28/5 17/3 6/1 32/5 13/2 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/2 1/0 1/1 -1/1 0/1 8/7 -1/2 1/0 7/6 -1/1 -2/3 20/17 -1/2 1/0 13/11 -1/1 0/1 6/5 -1/1 23/19 -1/1 -2/3 17/14 -2/3 -1/2 28/23 -3/4 -1/2 39/32 -2/3 11/9 -1/2 0/1 16/13 -1/2 1/0 37/30 -1/1 0/1 21/17 0/1 5/4 -1/1 -2/3 19/15 -1/2 0/1 14/11 -1/1 0/1 65/51 -1/1 0/1 51/40 0/1 37/29 -1/1 0/1 60/47 -1/1 23/18 -1/1 0/1 32/25 -1/2 1/0 9/7 -1/1 22/17 -1/1 -1/2 35/27 -1/1 -2/3 13/10 -1/1 -2/3 17/13 -8/15 -1/2 4/3 -1/2 1/0 19/14 -8/15 -1/2 15/11 -2/5 41/30 -4/11 -1/3 26/19 -1/3 0/1 37/27 -1/3 0/1 11/8 -1/2 0/1 18/13 0/1 25/18 0/1 1/0 57/41 0/1 32/23 -1/2 1/0 7/5 -1/1 0/1 38/27 -1/1 -1/2 31/22 -2/3 -3/5 24/17 -1/2 17/12 -1/2 -2/5 44/31 -1/2 -3/8 71/50 -2/5 -1/3 27/19 -1/3 37/26 -1/3 0/1 47/33 -1/4 0/1 10/7 -1/3 0/1 13/9 0/1 1/1 16/11 -1/2 1/0 35/24 -1/1 0/1 54/37 -1/1 19/13 -2/3 -1/2 3/2 0/1 23/15 -1/1 0/1 20/13 -1/2 1/0 37/24 -1/1 0/1 54/35 -1/1 17/11 -1/2 0/1 14/9 -1/3 0/1 11/7 0/1 1/2 41/26 0/1 1/1 71/45 0/1 1/1 30/19 1/1 19/12 -4/1 1/0 27/17 -1/1 8/5 -1/2 1/0 29/18 -2/1 -1/1 50/31 -1/1 -3/4 21/13 -2/3 55/34 -12/23 -1/2 34/21 -1/2 -3/7 47/29 -1/2 -2/5 60/37 -1/3 13/8 -1/3 0/1 18/11 0/1 23/14 0/1 1/1 28/17 1/2 1/0 33/20 0/1 5/3 -1/1 0/1 22/13 -1/1 -1/2 61/36 -1/2 -2/5 39/23 0/1 17/10 -2/3 -1/2 12/7 0/1 19/11 2/1 1/0 26/15 -1/1 0/1 59/34 -1/1 0/1 33/19 0/1 7/4 -1/1 0/1 37/21 -1/1 0/1 30/17 -1/1 23/13 -1/3 0/1 16/9 -1/2 1/0 25/14 -1/2 0/1 34/19 -1/2 -1/3 9/5 0/1 38/21 -1/1 1/0 29/16 -2/1 -1/1 20/11 -1/2 1/0 51/28 0/1 82/45 -1/1 0/1 31/17 -1/1 0/1 11/6 0/1 1/0 35/19 -1/1 0/1 24/13 -1/2 1/0 13/7 -1/1 0/1 15/8 0/1 17/9 -1/2 0/1 2/1 -1/1 0/1 19/9 -1/2 0/1 36/17 0/1 17/8 0/1 1/0 15/7 0/1 43/20 -1/1 0/1 28/13 -1/2 1/0 13/6 -1/1 0/1 37/17 -1/1 0/1 24/11 -1/2 1/0 11/5 -1/2 0/1 31/14 -1/1 0/1 144/65 -1/2 1/0 113/51 -1/1 0/1 82/37 -1/1 0/1 51/23 0/1 20/9 -1/2 1/0 29/13 -1/1 -2/3 9/4 0/1 43/19 1/1 2/1 34/15 1/1 1/0 25/11 0/1 1/0 16/7 -1/2 1/0 23/10 0/1 1/1 30/13 -1/1 37/16 -1/1 0/1 44/19 -1/2 1/0 7/3 -1/1 0/1 40/17 -1/2 1/0 73/31 -1/1 0/1 33/14 0/1 59/25 -1/1 0/1 144/61 -1/2 1/0 85/36 -1/1 0/1 26/11 -1/1 0/1 45/19 -1/1 19/8 -1/2 -2/5 12/5 0/1 17/7 -2/1 1/0 39/16 0/1 61/25 2/1 1/0 144/59 1/0 83/34 -4/1 1/0 22/9 -1/1 1/0 27/11 -1/1 32/13 -1/2 1/0 37/15 -1/1 0/1 5/2 -1/1 0/1 18/7 0/1 31/12 0/1 1/3 106/41 1/2 1/1 75/29 0/1 44/17 1/2 1/0 101/39 0/1 1/1 57/22 0/1 13/5 0/1 1/1 60/23 1/1 47/18 2/1 1/0 34/13 3/1 1/0 21/8 -2/1 71/27 -2/1 -1/1 50/19 -3/2 -1/1 79/30 -8/7 -1/1 108/41 -1/1 29/11 -1/1 -2/3 8/3 -1/2 1/0 35/13 -1/1 0/1 27/10 -1/1 73/27 -1/1 -2/3 46/17 -1/1 -2/3 19/7 -4/7 -1/2 49/18 -3/7 -2/5 30/11 -1/3 71/26 -1/3 0/1 41/15 -1/3 0/1 11/4 -1/4 0/1 36/13 0/1 25/9 0/1 1/6 14/5 0/1 1/1 17/6 0/1 1/0 54/19 -1/1 37/13 -1/1 0/1 57/20 0/1 20/7 -1/2 1/0 3/1 0/1 19/6 -2/1 1/0 54/17 -1/1 35/11 -1/1 0/1 16/5 -1/2 1/0 13/4 -1/3 0/1 36/11 0/1 23/7 0/1 1/5 10/3 0/1 1/1 57/17 0/1 47/14 0/1 1/2 84/25 1/1 37/11 0/1 1/1 27/8 1/1 71/21 1/1 2/1 115/34 1/1 2/1 44/13 3/2 1/0 17/5 2/1 1/0 41/12 3/1 4/1 24/7 1/0 31/9 -3/1 -2/1 69/20 -2/1 107/31 -2/1 -1/1 38/11 -1/1 1/0 7/2 -1/1 0/1 18/5 0/1 29/8 0/1 1/1 69/19 0/1 178/49 1/2 1/1 287/79 2/3 1/1 396/109 1/1 109/30 0/1 1/1 40/11 1/2 1/0 51/14 0/1 62/17 0/1 1/1 11/3 0/1 1/0 48/13 1/2 1/0 37/10 0/1 1/1 63/17 1/1 26/7 0/1 1/1 67/18 4/5 1/1 108/29 1/1 41/11 1/1 4/3 15/4 2/1 34/9 7/1 1/0 53/14 22/1 1/0 72/19 1/0 19/5 -8/1 1/0 4/1 -1/2 1/0 17/4 -8/1 1/0 30/7 -3/1 13/3 -2/1 -1/1 48/11 -3/2 1/0 35/8 -2/1 -1/1 92/21 -3/2 1/0 57/13 -2/1 22/5 -1/1 1/0 31/7 -2/1 -1/1 9/2 -1/1 41/9 -1/1 0/1 73/16 -1/1 0/1 32/7 -1/2 1/0 87/19 0/1 55/12 0/1 1/0 23/5 -1/1 0/1 60/13 -1/1 97/21 -1/2 0/1 37/8 -1/1 0/1 51/11 0/1 65/14 -1/1 0/1 144/31 -1/2 1/0 79/17 -1/1 0/1 14/3 -1/1 0/1 19/4 0/1 1/0 24/5 1/0 5/1 -2/1 -1/1 21/4 0/1 37/7 -1/1 0/1 16/3 -1/2 1/0 11/2 0/1 1/0 39/7 -2/1 28/5 -3/2 1/0 17/3 -2/1 1/0 6/1 -1/1 19/3 -1/2 0/1 51/8 0/1 32/5 -1/2 1/0 13/2 -1/1 0/1 33/5 0/1 20/3 -1/2 1/0 7/1 -2/1 -1/1 8/1 -1/2 1/0 9/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(253,-288,94,-107) (1/1,8/7) -> (8/3,35/13) Hyperbolic Matrix(251,-288,95,-109) (8/7,7/6) -> (29/11,8/3) Hyperbolic Matrix(613,-720,275,-323) (7/6,20/17) -> (20/9,29/13) Hyperbolic Matrix(611,-720,398,-469) (20/17,13/11) -> (23/15,20/13) Hyperbolic Matrix(181,-216,150,-179) (13/11,6/5) -> (6/5,23/19) Parabolic Matrix(1367,-1656,298,-361) (23/19,17/14) -> (55/12,23/5) Hyperbolic Matrix(1007,-1224,297,-361) (17/14,28/23) -> (44/13,17/5) Hyperbolic Matrix(3133,-3816,1211,-1475) (28/23,39/32) -> (75/29,44/17) Hyperbolic Matrix(2303,-2808,1359,-1657) (39/32,11/9) -> (61/36,39/23) Hyperbolic Matrix(469,-576,263,-323) (11/9,16/13) -> (16/9,25/14) Hyperbolic Matrix(935,-1152,293,-361) (16/13,37/30) -> (35/11,16/5) Hyperbolic Matrix(2159,-2664,1693,-2089) (37/30,21/17) -> (51/40,37/29) Hyperbolic Matrix(757,-936,203,-251) (21/17,5/4) -> (41/11,15/4) Hyperbolic Matrix(683,-864,200,-253) (5/4,19/15) -> (17/5,41/12) Hyperbolic Matrix(397,-504,141,-179) (19/15,14/11) -> (14/5,17/6) Hyperbolic Matrix(1583,-2016,340,-433) (14/11,65/51) -> (79/17,14/3) Hyperbolic Matrix(2485,-3168,1157,-1475) (65/51,51/40) -> (15/7,43/20) Hyperbolic Matrix(4175,-5328,1242,-1585) (37/29,60/47) -> (84/25,37/11) Hyperbolic Matrix(1691,-2160,649,-829) (60/47,23/18) -> (13/5,60/23) Hyperbolic Matrix(901,-1152,140,-179) (23/18,32/25) -> (32/5,13/2) Hyperbolic Matrix(899,-1152,366,-469) (32/25,9/7) -> (27/11,32/13) Hyperbolic Matrix(613,-792,250,-323) (9/7,22/17) -> (22/9,27/11) Hyperbolic Matrix(2557,-3312,972,-1259) (22/17,35/27) -> (71/27,50/19) Hyperbolic Matrix(721,-936,332,-431) (35/27,13/10) -> (13/6,37/17) Hyperbolic Matrix(827,-1080,304,-397) (13/10,17/13) -> (19/7,49/18) Hyperbolic Matrix(109,-144,81,-107) (17/13,4/3) -> (4/3,19/14) Parabolic Matrix(899,-1224,556,-757) (19/14,15/11) -> (21/13,55/34) Hyperbolic Matrix(685,-936,131,-179) (15/11,41/30) -> (5/1,21/4) Hyperbolic Matrix(2053,-2808,552,-755) (41/30,26/19) -> (26/7,67/18) Hyperbolic Matrix(2629,-3600,972,-1331) (26/19,37/27) -> (73/27,46/17) Hyperbolic Matrix(577,-792,314,-431) (37/27,11/8) -> (11/6,35/19) Hyperbolic Matrix(469,-648,338,-467) (11/8,18/13) -> (18/13,25/18) Parabolic Matrix(2953,-4104,880,-1223) (25/18,57/41) -> (57/17,47/14) Hyperbolic Matrix(3313,-4608,724,-1007) (57/41,32/23) -> (32/7,87/19) Hyperbolic Matrix(361,-504,154,-215) (32/23,7/5) -> (7/3,40/17) Hyperbolic Matrix(973,-1368,537,-755) (7/5,38/27) -> (38/21,29/16) Hyperbolic Matrix(3169,-4464,1226,-1727) (38/27,31/22) -> (31/12,106/41) Hyperbolic Matrix(613,-864,127,-179) (31/22,24/17) -> (24/5,5/1) Hyperbolic Matrix(611,-864,128,-181) (24/17,17/12) -> (19/4,24/5) Hyperbolic Matrix(863,-1224,153,-217) (17/12,44/31) -> (28/5,17/3) Hyperbolic Matrix(3347,-4752,1446,-2053) (44/31,71/50) -> (37/16,44/19) Hyperbolic Matrix(2737,-3888,1013,-1439) (71/50,27/19) -> (27/10,73/27) Hyperbolic Matrix(1367,-1944,507,-721) (27/19,37/26) -> (35/13,27/10) Hyperbolic Matrix(3743,-5328,810,-1153) (37/26,47/33) -> (97/21,37/8) Hyperbolic Matrix(2123,-3024,582,-829) (47/33,10/7) -> (62/17,11/3) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(397,-576,173,-251) (13/9,16/11) -> (16/7,23/10) Hyperbolic Matrix(791,-1152,149,-217) (16/11,35/24) -> (37/7,16/3) Hyperbolic Matrix(2665,-3888,937,-1367) (35/24,54/37) -> (54/19,37/13) Hyperbolic Matrix(1331,-1944,469,-685) (54/37,19/13) -> (17/6,54/19) Hyperbolic Matrix(541,-792,319,-467) (19/13,3/2) -> (39/23,17/10) Hyperbolic Matrix(613,-936,353,-539) (3/2,23/15) -> (59/34,33/19) Hyperbolic Matrix(2663,-4104,608,-937) (20/13,37/24) -> (35/8,92/21) Hyperbolic Matrix(2521,-3888,793,-1223) (37/24,54/35) -> (54/17,35/11) Hyperbolic Matrix(1259,-1944,397,-613) (54/35,17/11) -> (19/6,54/17) Hyperbolic Matrix(325,-504,69,-107) (17/11,14/9) -> (14/3,19/4) Hyperbolic Matrix(323,-504,116,-181) (14/9,11/7) -> (25/9,14/5) Hyperbolic Matrix(503,-792,275,-433) (11/7,41/26) -> (31/17,11/6) Hyperbolic Matrix(1187,-1872,480,-757) (41/26,71/45) -> (37/15,5/2) Hyperbolic Matrix(2053,-3240,889,-1403) (71/45,30/19) -> (30/13,37/16) Hyperbolic Matrix(683,-1080,160,-253) (30/19,19/12) -> (17/4,30/7) Hyperbolic Matrix(863,-1368,364,-577) (19/12,27/17) -> (45/19,19/8) Hyperbolic Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(179,-288,23,-37) (8/5,29/18) -> (7/1,8/1) Hyperbolic Matrix(3349,-5400,1272,-2051) (29/18,50/31) -> (50/19,79/30) Hyperbolic Matrix(2053,-3312,468,-755) (50/31,21/13) -> (57/13,22/5) Hyperbolic Matrix(2269,-3672,600,-971) (55/34,34/21) -> (34/9,53/14) Hyperbolic Matrix(1511,-2448,845,-1369) (34/21,47/29) -> (25/14,34/19) Hyperbolic Matrix(5329,-8640,1154,-1871) (47/29,60/37) -> (60/13,97/21) Hyperbolic Matrix(1331,-2160,289,-469) (60/37,13/8) -> (23/5,60/13) Hyperbolic Matrix(397,-648,242,-395) (13/8,18/11) -> (18/11,23/14) Parabolic Matrix(613,-1008,284,-467) (23/14,28/17) -> (28/13,13/6) Hyperbolic Matrix(1223,-2016,219,-361) (28/17,33/20) -> (39/7,28/5) Hyperbolic Matrix(827,-1368,240,-397) (33/20,5/3) -> (31/9,69/20) Hyperbolic Matrix(469,-792,106,-179) (5/3,22/13) -> (22/5,31/7) Hyperbolic Matrix(1871,-3168,766,-1297) (22/13,61/36) -> (83/34,22/9) Hyperbolic Matrix(253,-432,147,-251) (17/10,12/7) -> (12/7,19/11) Parabolic Matrix(791,-1368,292,-505) (19/11,26/15) -> (46/17,19/7) Hyperbolic Matrix(2159,-3744,914,-1585) (26/15,59/34) -> (85/36,26/11) Hyperbolic Matrix(827,-1440,228,-397) (33/19,7/4) -> (29/8,69/19) Hyperbolic Matrix(2699,-4752,798,-1405) (7/4,37/21) -> (71/21,115/34) Hyperbolic Matrix(1837,-3240,673,-1187) (37/21,30/17) -> (30/11,71/26) Hyperbolic Matrix(1223,-2160,449,-793) (30/17,23/13) -> (49/18,30/11) Hyperbolic Matrix(325,-576,101,-179) (23/13,16/9) -> (16/5,13/4) Hyperbolic Matrix(361,-648,200,-359) (34/19,9/5) -> (9/5,38/21) Parabolic Matrix(397,-720,59,-107) (29/16,20/11) -> (20/3,7/1) Hyperbolic Matrix(1187,-2160,416,-757) (20/11,51/28) -> (57/20,20/7) Hyperbolic Matrix(2845,-5184,849,-1547) (51/28,82/45) -> (10/3,57/17) Hyperbolic Matrix(6479,-11808,2924,-5329) (82/45,31/17) -> (113/51,82/37) Hyperbolic Matrix(1367,-2520,313,-577) (35/19,24/13) -> (48/11,35/8) Hyperbolic Matrix(505,-936,116,-215) (24/13,13/7) -> (13/3,48/11) Hyperbolic Matrix(503,-936,194,-361) (13/7,15/8) -> (57/22,13/5) Hyperbolic Matrix(611,-1152,96,-181) (15/8,17/9) -> (19/3,51/8) Hyperbolic Matrix(37,-72,18,-35) (17/9,2/1) -> (2/1,19/9) Parabolic Matrix(613,-1296,289,-611) (19/9,36/17) -> (36/17,17/8) Parabolic Matrix(1081,-2304,236,-503) (17/8,15/7) -> (87/19,55/12) Hyperbolic Matrix(971,-2088,419,-901) (43/20,28/13) -> (44/19,7/3) Hyperbolic Matrix(1223,-2664,331,-721) (37/17,24/11) -> (48/13,37/10) Hyperbolic Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(359,-792,131,-289) (11/5,31/14) -> (41/15,11/4) Hyperbolic Matrix(9361,-20736,4225,-9359) (31/14,144/65) -> (144/65,113/51) Parabolic Matrix(3313,-7344,909,-2015) (82/37,51/23) -> (51/14,62/17) Hyperbolic Matrix(2629,-5832,600,-1331) (51/23,20/9) -> (92/21,57/13) Hyperbolic Matrix(289,-648,128,-287) (29/13,9/4) -> (9/4,43/19) Parabolic Matrix(827,-1872,239,-541) (43/19,34/15) -> (38/11,7/2) Hyperbolic Matrix(1079,-2448,413,-937) (34/15,25/11) -> (47/18,34/13) Hyperbolic Matrix(253,-576,47,-107) (25/11,16/7) -> (16/3,11/2) Hyperbolic Matrix(469,-1080,109,-251) (23/10,30/13) -> (30/7,13/3) Hyperbolic Matrix(2233,-5256,489,-1151) (40/17,73/31) -> (73/16,32/7) Hyperbolic Matrix(3637,-8568,1054,-2483) (73/31,33/14) -> (69/20,107/31) Hyperbolic Matrix(1007,-2376,153,-361) (33/14,59/25) -> (13/2,33/5) Hyperbolic Matrix(8785,-20736,3721,-8783) (59/25,144/61) -> (144/61,85/36) Parabolic Matrix(1187,-2808,320,-757) (26/11,45/19) -> (63/17,26/7) Hyperbolic Matrix(181,-432,75,-179) (19/8,12/5) -> (12/5,17/7) Parabolic Matrix(325,-792,103,-251) (17/7,39/16) -> (3/1,19/6) Hyperbolic Matrix(1151,-2808,207,-505) (39/16,61/25) -> (11/2,39/7) Hyperbolic Matrix(8497,-20736,3481,-8495) (61/25,144/59) -> (144/59,83/34) Parabolic Matrix(2017,-4968,555,-1367) (32/13,37/15) -> (109/30,40/11) Hyperbolic Matrix(253,-648,98,-251) (5/2,18/7) -> (18/7,31/12) Parabolic Matrix(7991,-20664,2200,-5689) (106/41,75/29) -> (69/19,178/49) Hyperbolic Matrix(3671,-9504,1085,-2809) (44/17,101/39) -> (115/34,44/13) Hyperbolic Matrix(3419,-8856,737,-1909) (101/39,57/22) -> (51/11,65/14) Hyperbolic Matrix(2593,-6768,772,-2015) (60/23,47/18) -> (47/14,84/25) Hyperbolic Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(1835,-4824,644,-1693) (21/8,71/27) -> (37/13,57/20) Hyperbolic Matrix(4429,-11664,1681,-4427) (79/30,108/41) -> (108/41,29/11) Parabolic Matrix(2161,-5904,474,-1295) (71/26,41/15) -> (41/9,73/16) Hyperbolic Matrix(469,-1296,169,-467) (11/4,36/13) -> (36/13,25/9) Parabolic Matrix(251,-720,38,-109) (20/7,3/1) -> (33/5,20/3) Hyperbolic Matrix(397,-1296,121,-395) (13/4,36/11) -> (36/11,23/7) Parabolic Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) Hyperbolic Matrix(1619,-5472,437,-1477) (27/8,71/21) -> (37/10,63/17) Hyperbolic Matrix(505,-1728,147,-503) (41/12,24/7) -> (24/7,31/9) Parabolic Matrix(8675,-29952,2388,-8245) (107/31,38/11) -> (178/49,287/79) Hyperbolic Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(43165,-156816,11881,-43163) (287/79,396/109) -> (396/109,109/30) Parabolic Matrix(1009,-3672,158,-575) (40/11,51/14) -> (51/8,32/5) Hyperbolic Matrix(3133,-11664,841,-3131) (67/18,108/29) -> (108/29,41/11) Parabolic Matrix(1369,-5184,361,-1367) (53/14,72/19) -> (72/19,19/5) Parabolic Matrix(37,-144,9,-35) (19/5,4/1) -> (4/1,17/4) Parabolic Matrix(145,-648,32,-143) (31/7,9/2) -> (9/2,41/9) Parabolic Matrix(575,-2664,109,-505) (37/8,51/11) -> (21/4,37/7) Hyperbolic Matrix(4465,-20736,961,-4463) (65/14,144/31) -> (144/31,79/17) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,0,1) Matrix(253,-288,94,-107) -> Matrix(1,0,0,1) Matrix(251,-288,95,-109) -> Matrix(1,0,0,1) Matrix(613,-720,275,-323) -> Matrix(1,0,0,1) Matrix(611,-720,398,-469) -> Matrix(1,0,0,1) Matrix(181,-216,150,-179) -> Matrix(1,2,-2,-3) Matrix(1367,-1656,298,-361) -> Matrix(3,2,-2,-1) Matrix(1007,-1224,297,-361) -> Matrix(1,0,2,1) Matrix(3133,-3816,1211,-1475) -> Matrix(3,2,4,3) Matrix(2303,-2808,1359,-1657) -> Matrix(3,2,-8,-5) Matrix(469,-576,263,-323) -> Matrix(1,0,0,1) Matrix(935,-1152,293,-361) -> Matrix(1,0,0,1) Matrix(2159,-2664,1693,-2089) -> Matrix(1,0,0,1) Matrix(757,-936,203,-251) -> Matrix(1,2,0,1) Matrix(683,-864,200,-253) -> Matrix(5,2,2,1) Matrix(397,-504,141,-179) -> Matrix(1,0,2,1) Matrix(1583,-2016,340,-433) -> Matrix(1,0,0,1) Matrix(2485,-3168,1157,-1475) -> Matrix(1,0,0,1) Matrix(4175,-5328,1242,-1585) -> Matrix(1,0,2,1) Matrix(1691,-2160,649,-829) -> Matrix(1,0,2,1) Matrix(901,-1152,140,-179) -> Matrix(1,0,0,1) Matrix(899,-1152,366,-469) -> Matrix(1,0,0,1) Matrix(613,-792,250,-323) -> Matrix(3,2,-2,-1) Matrix(2557,-3312,972,-1259) -> Matrix(5,4,-4,-3) Matrix(721,-936,332,-431) -> Matrix(3,2,-2,-1) Matrix(827,-1080,304,-397) -> Matrix(7,4,-16,-9) Matrix(109,-144,81,-107) -> Matrix(1,0,0,1) Matrix(899,-1224,556,-757) -> Matrix(9,4,-16,-7) Matrix(685,-936,131,-179) -> Matrix(5,2,-8,-3) Matrix(2053,-2808,552,-755) -> Matrix(1,0,4,1) Matrix(2629,-3600,972,-1331) -> Matrix(5,2,-8,-3) Matrix(577,-792,314,-431) -> Matrix(1,0,2,1) Matrix(469,-648,338,-467) -> Matrix(1,0,2,1) Matrix(2953,-4104,880,-1223) -> Matrix(1,0,2,1) Matrix(3313,-4608,724,-1007) -> Matrix(1,0,0,1) Matrix(361,-504,154,-215) -> Matrix(1,0,0,1) Matrix(973,-1368,537,-755) -> Matrix(3,2,-2,-1) Matrix(3169,-4464,1226,-1727) -> Matrix(3,2,4,3) Matrix(613,-864,127,-179) -> Matrix(7,4,-2,-1) Matrix(611,-864,128,-181) -> Matrix(5,2,2,1) Matrix(863,-1224,153,-217) -> Matrix(1,0,2,1) Matrix(3347,-4752,1446,-2053) -> Matrix(5,2,-8,-3) Matrix(2737,-3888,1013,-1439) -> Matrix(11,4,-14,-5) Matrix(1367,-1944,507,-721) -> Matrix(1,0,2,1) Matrix(3743,-5328,810,-1153) -> Matrix(1,0,2,1) Matrix(2123,-3024,582,-829) -> Matrix(1,0,4,1) Matrix(251,-360,76,-109) -> Matrix(1,0,4,1) Matrix(397,-576,173,-251) -> Matrix(1,0,0,1) Matrix(791,-1152,149,-217) -> Matrix(1,0,0,1) Matrix(2665,-3888,937,-1367) -> Matrix(1,0,0,1) Matrix(1331,-1944,469,-685) -> Matrix(3,2,-2,-1) Matrix(541,-792,319,-467) -> Matrix(1,0,0,1) Matrix(613,-936,353,-539) -> Matrix(1,0,0,1) Matrix(2663,-4104,608,-937) -> Matrix(3,2,-2,-1) Matrix(2521,-3888,793,-1223) -> Matrix(1,0,0,1) Matrix(1259,-1944,397,-613) -> Matrix(3,2,-2,-1) Matrix(325,-504,69,-107) -> Matrix(1,0,2,1) Matrix(323,-504,116,-181) -> Matrix(1,0,4,1) Matrix(503,-792,275,-433) -> Matrix(1,0,-2,1) Matrix(1187,-1872,480,-757) -> Matrix(1,0,-2,1) Matrix(2053,-3240,889,-1403) -> Matrix(1,0,-2,1) Matrix(683,-1080,160,-253) -> Matrix(1,-4,0,1) Matrix(863,-1368,364,-577) -> Matrix(1,2,-2,-3) Matrix(181,-288,22,-35) -> Matrix(1,0,0,1) Matrix(179,-288,23,-37) -> Matrix(1,0,0,1) Matrix(3349,-5400,1272,-2051) -> Matrix(7,6,-6,-5) Matrix(2053,-3312,468,-755) -> Matrix(5,4,-4,-3) Matrix(2269,-3672,600,-971) -> Matrix(21,10,2,1) Matrix(1511,-2448,845,-1369) -> Matrix(5,2,-8,-3) Matrix(5329,-8640,1154,-1871) -> Matrix(5,2,-8,-3) Matrix(1331,-2160,289,-469) -> Matrix(1,0,2,1) Matrix(397,-648,242,-395) -> Matrix(1,0,4,1) Matrix(613,-1008,284,-467) -> Matrix(1,0,-2,1) Matrix(1223,-2016,219,-361) -> Matrix(1,-2,0,1) Matrix(827,-1368,240,-397) -> Matrix(1,-2,0,1) Matrix(469,-792,106,-179) -> Matrix(3,2,-2,-1) Matrix(1871,-3168,766,-1297) -> Matrix(3,2,-2,-1) Matrix(253,-432,147,-251) -> Matrix(1,0,2,1) Matrix(791,-1368,292,-505) -> Matrix(1,2,-2,-3) Matrix(2159,-3744,914,-1585) -> Matrix(1,0,0,1) Matrix(827,-1440,228,-397) -> Matrix(1,0,2,1) Matrix(2699,-4752,798,-1405) -> Matrix(1,2,0,1) Matrix(1837,-3240,673,-1187) -> Matrix(1,0,-2,1) Matrix(1223,-2160,449,-793) -> Matrix(3,2,-8,-5) Matrix(325,-576,101,-179) -> Matrix(1,0,0,1) Matrix(361,-648,200,-359) -> Matrix(1,0,2,1) Matrix(397,-720,59,-107) -> Matrix(1,0,0,1) Matrix(1187,-2160,416,-757) -> Matrix(1,0,0,1) Matrix(2845,-5184,849,-1547) -> Matrix(1,0,2,1) Matrix(6479,-11808,2924,-5329) -> Matrix(1,0,0,1) Matrix(1367,-2520,313,-577) -> Matrix(3,2,-2,-1) Matrix(505,-936,116,-215) -> Matrix(3,2,-2,-1) Matrix(503,-936,194,-361) -> Matrix(1,0,2,1) Matrix(611,-1152,96,-181) -> Matrix(1,0,0,1) Matrix(37,-72,18,-35) -> Matrix(1,0,0,1) Matrix(613,-1296,289,-611) -> Matrix(1,0,2,1) Matrix(1081,-2304,236,-503) -> Matrix(1,0,0,1) Matrix(971,-2088,419,-901) -> Matrix(1,0,0,1) Matrix(1223,-2664,331,-721) -> Matrix(1,0,2,1) Matrix(361,-792,98,-215) -> Matrix(1,0,2,1) Matrix(359,-792,131,-289) -> Matrix(1,0,-2,1) Matrix(9361,-20736,4225,-9359) -> Matrix(1,0,0,1) Matrix(3313,-7344,909,-2015) -> Matrix(1,0,2,1) Matrix(2629,-5832,600,-1331) -> Matrix(3,2,-2,-1) Matrix(289,-648,128,-287) -> Matrix(1,0,2,1) Matrix(827,-1872,239,-541) -> Matrix(1,-2,0,1) Matrix(1079,-2448,413,-937) -> Matrix(1,2,0,1) Matrix(253,-576,47,-107) -> Matrix(1,0,0,1) Matrix(469,-1080,109,-251) -> Matrix(1,-2,0,1) Matrix(2233,-5256,489,-1151) -> Matrix(1,0,0,1) Matrix(3637,-8568,1054,-2483) -> Matrix(3,2,-2,-1) Matrix(1007,-2376,153,-361) -> Matrix(1,0,0,1) Matrix(8785,-20736,3721,-8783) -> Matrix(1,0,0,1) Matrix(1187,-2808,320,-757) -> Matrix(1,0,2,1) Matrix(181,-432,75,-179) -> Matrix(1,0,2,1) Matrix(325,-792,103,-251) -> Matrix(1,0,0,1) Matrix(1151,-2808,207,-505) -> Matrix(1,-2,0,1) Matrix(8497,-20736,3481,-8495) -> Matrix(1,-6,0,1) Matrix(2017,-4968,555,-1367) -> Matrix(1,0,2,1) Matrix(253,-648,98,-251) -> Matrix(1,0,4,1) Matrix(7991,-20664,2200,-5689) -> Matrix(1,0,0,1) Matrix(3671,-9504,1085,-2809) -> Matrix(3,-2,2,-1) Matrix(3419,-8856,737,-1909) -> Matrix(1,0,-2,1) Matrix(2593,-6768,772,-2015) -> Matrix(1,-2,2,-3) Matrix(467,-1224,124,-325) -> Matrix(1,4,0,1) Matrix(1835,-4824,644,-1693) -> Matrix(1,2,-2,-3) Matrix(4429,-11664,1681,-4427) -> Matrix(9,10,-10,-11) Matrix(2161,-5904,474,-1295) -> Matrix(1,0,2,1) Matrix(469,-1296,169,-467) -> Matrix(1,0,10,1) Matrix(251,-720,38,-109) -> Matrix(1,0,0,1) Matrix(397,-1296,121,-395) -> Matrix(1,0,8,1) Matrix(107,-360,11,-37) -> Matrix(1,0,-2,1) Matrix(1619,-5472,437,-1477) -> Matrix(1,-2,2,-3) Matrix(505,-1728,147,-503) -> Matrix(1,-6,0,1) Matrix(8675,-29952,2388,-8245) -> Matrix(1,0,2,1) Matrix(181,-648,50,-179) -> Matrix(1,0,2,1) Matrix(43165,-156816,11881,-43163) -> Matrix(3,-2,2,-1) Matrix(1009,-3672,158,-575) -> Matrix(1,0,-2,1) Matrix(3133,-11664,841,-3131) -> Matrix(9,-8,8,-7) Matrix(1369,-5184,361,-1367) -> Matrix(1,-30,0,1) Matrix(37,-144,9,-35) -> Matrix(1,0,0,1) Matrix(145,-648,32,-143) -> Matrix(1,2,-2,-3) Matrix(575,-2664,109,-505) -> Matrix(1,0,0,1) Matrix(4465,-20736,961,-4463) -> Matrix(1,0,0,1) Matrix(37,-216,6,-35) -> Matrix(1,2,-2,-3) 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): 24 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 1 2/1 (-1/1,0/1) 0 18 36/17 0/1 2 1 17/8 (0/1,1/0) 0 36 15/7 0/1 1 12 13/6 (-1/1,0/1) 0 36 24/11 0 3 11/5 (-1/2,0/1) 0 36 31/14 (-1/1,0/1) 0 36 144/65 (-1/1,0/1) 0 1 82/37 (-1/1,0/1) 0 18 51/23 0/1 1 12 20/9 0 9 29/13 (-1/1,-2/3) 0 36 9/4 0/1 1 4 43/19 (1/1,2/1) 0 36 34/15 (1/1,1/0) 0 18 25/11 (0/1,1/0) 0 36 16/7 0 9 23/10 (0/1,1/1) 0 36 30/13 -1/1 2 6 37/16 (-1/1,0/1) 0 36 7/3 (-1/1,0/1) 0 36 33/14 0/1 1 12 59/25 (-1/1,0/1) 0 36 144/61 (-1/1,0/1) 0 1 26/11 (-1/1,0/1) 0 18 19/8 (-1/2,-2/5) 0 36 12/5 0/1 2 3 17/7 (-2/1,1/0) 0 36 39/16 0/1 1 12 61/25 (2/1,1/0) 0 36 144/59 1/0 6 1 22/9 (-1/1,1/0) 0 18 5/2 (-1/1,0/1) 0 36 18/7 0/1 4 2 31/12 (0/1,1/3) 0 36 75/29 0/1 1 12 44/17 0 9 101/39 (0/1,1/1) 0 36 57/22 0/1 1 12 13/5 (0/1,1/1) 0 36 60/23 1/1 2 3 47/18 (2/1,1/0) 0 36 34/13 (3/1,1/0) 0 18 21/8 -2/1 1 12 50/19 (-3/2,-1/1) 0 18 108/41 -1/1 10 1 29/11 (-1/1,-2/3) 0 36 8/3 0 9 27/10 -1/1 2 4 46/17 (-1/1,-2/3) 0 18 19/7 (-4/7,-1/2) 0 36 30/11 -1/3 2 6 71/26 (-1/3,0/1) 0 36 41/15 (-1/3,0/1) 0 36 11/4 (-1/4,0/1) 0 36 36/13 0/1 10 1 14/5 (0/1,1/1) 0 18 17/6 (0/1,1/0) 0 36 54/19 -1/1 2 2 37/13 (-1/1,0/1) 0 36 20/7 0 9 3/1 0/1 1 12 19/6 (-2/1,1/0) 0 36 54/17 -1/1 2 2 35/11 (-1/1,0/1) 0 36 16/5 0 9 13/4 (-1/3,0/1) 0 36 36/11 0/1 8 1 10/3 (0/1,1/1) 0 18 47/14 (0/1,1/2) 0 36 37/11 (0/1,1/1) 0 36 27/8 1/1 2 4 71/21 (1/1,2/1) 0 36 115/34 (1/1,2/1) 0 36 44/13 0 9 17/5 (2/1,1/0) 0 36 24/7 1/0 6 3 31/9 (-3/1,-2/1) 0 36 69/20 -2/1 1 12 38/11 (-1/1,1/0) 0 18 7/2 (-1/1,0/1) 0 36 18/5 0/1 2 2 29/8 (0/1,1/1) 0 36 69/19 0/1 1 12 178/49 (1/2,1/1) 0 18 396/109 1/1 2 1 109/30 (0/1,1/1) 0 36 40/11 0 9 51/14 0/1 1 12 62/17 (0/1,1/1) 0 18 11/3 (0/1,1/0) 0 36 48/13 0 3 37/10 (0/1,1/1) 0 36 63/17 1/1 2 4 26/7 (0/1,1/1) 0 18 108/29 1/1 8 1 41/11 (1/1,4/3) 0 36 15/4 2/1 1 12 34/9 (7/1,1/0) 0 18 72/19 1/0 30 1 19/5 (-8/1,1/0) 0 36 4/1 0 9 17/4 (-8/1,1/0) 0 36 30/7 -3/1 2 6 13/3 (-2/1,-1/1) 0 36 48/11 0 3 35/8 (-2/1,-1/1) 0 36 92/21 0 9 57/13 -2/1 1 12 22/5 (-1/1,1/0) 0 18 31/7 (-2/1,-1/1) 0 36 9/2 -1/1 1 4 41/9 (-1/1,0/1) 0 36 73/16 (-1/1,0/1) 0 36 32/7 0 9 23/5 (-1/1,0/1) 0 36 60/13 -1/1 2 3 97/21 (-1/2,0/1) 0 36 37/8 (-1/1,0/1) 0 36 51/11 0/1 1 12 65/14 (-1/1,0/1) 0 36 144/31 (-1/1,0/1) 0 1 14/3 (-1/1,0/1) 0 18 19/4 (0/1,1/0) 0 36 24/5 1/0 6 3 5/1 (-2/1,-1/1) 0 36 21/4 0/1 1 12 37/7 (-1/1,0/1) 0 36 16/3 0 9 11/2 (0/1,1/0) 0 36 39/7 -2/1 1 12 28/5 0 9 17/3 (-2/1,1/0) 0 36 6/1 -1/1 2 6 19/3 (-1/2,0/1) 0 36 51/8 0/1 1 12 32/5 0 9 13/2 (-1/1,0/1) 0 36 33/5 0/1 1 12 20/3 0 9 7/1 (-2/1,-1/1) 0 36 8/1 0 9 9/1 -1/1 2 4 1/0 (-1/1,0/1) 0 36 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(35,-72,17,-35) (2/1,36/17) -> (2/1,36/17) Reflection Matrix(577,-1224,272,-577) (36/17,17/8) -> (36/17,17/8) Reflection Matrix(541,-1152,85,-181) (17/8,15/7) -> (19/3,51/8) Glide Reflection Matrix(433,-936,167,-361) (15/7,13/6) -> (57/22,13/5) Glide Reflection Matrix(431,-936,99,-215) (13/6,24/11) -> (13/3,48/11) Glide Reflection Matrix(361,-792,98,-215) (24/11,11/5) -> (11/3,48/13) Hyperbolic Matrix(359,-792,131,-289) (11/5,31/14) -> (41/15,11/4) Hyperbolic Matrix(4031,-8928,1820,-4031) (31/14,144/65) -> (31/14,144/65) Reflection Matrix(5329,-11808,2405,-5329) (144/65,82/37) -> (144/65,82/37) Reflection Matrix(3313,-7344,909,-2015) (82/37,51/23) -> (51/14,62/17) Hyperbolic Matrix(2629,-5832,600,-1331) (51/23,20/9) -> (92/21,57/13) Hyperbolic Matrix(323,-720,48,-107) (20/9,29/13) -> (20/3,7/1) Glide Reflection Matrix(289,-648,128,-287) (29/13,9/4) -> (9/4,43/19) Parabolic Matrix(827,-1872,239,-541) (43/19,34/15) -> (38/11,7/2) Hyperbolic Matrix(1079,-2448,413,-937) (34/15,25/11) -> (47/18,34/13) Hyperbolic Matrix(253,-576,47,-107) (25/11,16/7) -> (16/3,11/2) Hyperbolic Matrix(251,-576,78,-179) (16/7,23/10) -> (16/5,13/4) Glide Reflection Matrix(469,-1080,109,-251) (23/10,30/13) -> (30/7,13/3) Hyperbolic Matrix(1403,-3240,514,-1187) (30/13,37/16) -> (30/11,71/26) Glide Reflection Matrix(2053,-4752,607,-1405) (37/16,7/3) -> (71/21,115/34) Glide Reflection Matrix(613,-1440,169,-397) (7/3,33/14) -> (29/8,69/19) Glide Reflection Matrix(1007,-2376,153,-361) (33/14,59/25) -> (13/2,33/5) Hyperbolic Matrix(7199,-16992,3050,-7199) (59/25,144/61) -> (59/25,144/61) Reflection Matrix(1585,-3744,671,-1585) (144/61,26/11) -> (144/61,26/11) Reflection Matrix(577,-1368,213,-505) (26/11,19/8) -> (46/17,19/7) Glide Reflection Matrix(181,-432,75,-179) (19/8,12/5) -> (12/5,17/7) Parabolic Matrix(325,-792,103,-251) (17/7,39/16) -> (3/1,19/6) Hyperbolic Matrix(1151,-2808,207,-505) (39/16,61/25) -> (11/2,39/7) Hyperbolic Matrix(7199,-17568,2950,-7199) (61/25,144/59) -> (61/25,144/59) Reflection Matrix(1297,-3168,531,-1297) (144/59,22/9) -> (144/59,22/9) Reflection Matrix(323,-792,73,-179) (22/9,5/2) -> (22/5,31/7) Glide Reflection Matrix(253,-648,98,-251) (5/2,18/7) -> (18/7,31/12) Parabolic Matrix(1727,-4464,501,-1295) (31/12,75/29) -> (31/9,69/20) Glide Reflection Matrix(1475,-3816,264,-683) (75/29,44/17) -> (39/7,28/5) Glide Reflection Matrix(3671,-9504,1085,-2809) (44/17,101/39) -> (115/34,44/13) Hyperbolic Matrix(3419,-8856,737,-1909) (101/39,57/22) -> (51/11,65/14) Hyperbolic Matrix(829,-2160,180,-469) (13/5,60/23) -> (23/5,60/13) Glide Reflection Matrix(3311,-8640,717,-1871) (60/23,47/18) -> (60/13,97/21) Glide Reflection Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(1259,-3312,287,-755) (21/8,50/19) -> (57/13,22/5) Glide Reflection Matrix(2051,-5400,779,-2051) (50/19,108/41) -> (50/19,108/41) Reflection Matrix(2377,-6264,902,-2377) (108/41,29/11) -> (108/41,29/11) Reflection Matrix(109,-288,14,-37) (29/11,8/3) -> (7/1,8/1) Glide Reflection Matrix(107,-288,13,-35) (8/3,27/10) -> (8/1,9/1) Glide Reflection Matrix(1331,-3600,359,-971) (27/10,46/17) -> (63/17,26/7) Glide Reflection Matrix(397,-1080,93,-253) (19/7,30/11) -> (17/4,30/7) Glide Reflection Matrix(2161,-5904,474,-1295) (71/26,41/15) -> (41/9,73/16) Hyperbolic Matrix(287,-792,104,-287) (11/4,36/13) -> (11/4,36/13) Reflection Matrix(181,-504,65,-181) (36/13,14/5) -> (36/13,14/5) Reflection Matrix(179,-504,38,-107) (14/5,17/6) -> (14/3,19/4) Glide Reflection Matrix(685,-1944,216,-613) (17/6,54/19) -> (19/6,54/17) Glide Reflection Matrix(1367,-3888,430,-1223) (54/19,37/13) -> (54/17,35/11) Glide Reflection Matrix(1441,-4104,329,-937) (37/13,20/7) -> (35/8,92/21) Glide Reflection Matrix(251,-720,38,-109) (20/7,3/1) -> (33/5,20/3) Hyperbolic Matrix(361,-1152,68,-217) (35/11,16/5) -> (37/7,16/3) Glide Reflection Matrix(287,-936,88,-287) (13/4,36/11) -> (13/4,36/11) Reflection Matrix(109,-360,33,-109) (36/11,10/3) -> (36/11,10/3) Reflection Matrix(901,-3024,247,-829) (10/3,47/14) -> (62/17,11/3) Glide Reflection Matrix(1585,-5328,343,-1153) (47/14,37/11) -> (97/21,37/8) Glide Reflection Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) Hyperbolic Matrix(1619,-5472,437,-1477) (27/8,71/21) -> (37/10,63/17) Hyperbolic Matrix(361,-1224,64,-217) (44/13,17/5) -> (28/5,17/3) Glide Reflection Matrix(253,-864,53,-181) (17/5,24/7) -> (19/4,24/5) Glide Reflection Matrix(251,-864,52,-179) (24/7,31/9) -> (24/5,5/1) Glide Reflection Matrix(4319,-14904,1189,-4103) (69/20,38/11) -> (69/19,178/49) Glide Reflection Matrix(181,-648,50,-179) (7/2,18/5) -> (18/5,29/8) Parabolic Matrix(19403,-70488,5341,-19403) (178/49,396/109) -> (178/49,396/109) Reflection Matrix(23761,-86328,6540,-23761) (396/109,109/30) -> (396/109,109/30) Reflection Matrix(1763,-6408,386,-1403) (109/30,40/11) -> (73/16,32/7) Glide Reflection Matrix(1009,-3672,158,-575) (40/11,51/14) -> (51/8,32/5) Hyperbolic Matrix(935,-3456,214,-791) (48/13,37/10) -> (48/11,35/8) Glide Reflection Matrix(755,-2808,203,-755) (26/7,108/29) -> (26/7,108/29) Reflection Matrix(2377,-8856,638,-2377) (108/29,41/11) -> (108/29,41/11) Reflection Matrix(251,-936,48,-179) (41/11,15/4) -> (5/1,21/4) Glide Reflection Matrix(647,-2448,171,-647) (34/9,72/19) -> (34/9,72/19) Reflection Matrix(721,-2736,190,-721) (72/19,19/5) -> (72/19,19/5) Reflection Matrix(37,-144,9,-35) (19/5,4/1) -> (4/1,17/4) Parabolic Matrix(145,-648,32,-143) (31/7,9/2) -> (9/2,41/9) Parabolic Matrix(251,-1152,39,-179) (32/7,23/5) -> (32/5,13/2) Glide Reflection Matrix(575,-2664,109,-505) (37/8,51/11) -> (21/4,37/7) Hyperbolic Matrix(4031,-18720,868,-4031) (65/14,144/31) -> (65/14,144/31) Reflection Matrix(433,-2016,93,-433) (144/31,14/3) -> (144/31,14/3) Reflection Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(-1,0,2,1) (0/1,2/1) -> (-1/1,0/1) Matrix(35,-72,17,-35) -> Matrix(-1,0,2,1) (2/1,36/17) -> (-1/1,0/1) Matrix(577,-1224,272,-577) -> Matrix(1,0,0,-1) (36/17,17/8) -> (0/1,1/0) Matrix(541,-1152,85,-181) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(433,-936,167,-361) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(431,-936,99,-215) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(361,-792,98,-215) -> Matrix(1,0,2,1) 0/1 Matrix(359,-792,131,-289) -> Matrix(1,0,-2,1) 0/1 Matrix(4031,-8928,1820,-4031) -> Matrix(-1,0,2,1) (31/14,144/65) -> (-1/1,0/1) Matrix(5329,-11808,2405,-5329) -> Matrix(-1,0,2,1) (144/65,82/37) -> (-1/1,0/1) Matrix(3313,-7344,909,-2015) -> Matrix(1,0,2,1) 0/1 Matrix(2629,-5832,600,-1331) -> Matrix(3,2,-2,-1) -1/1 Matrix(323,-720,48,-107) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(289,-648,128,-287) -> Matrix(1,0,2,1) 0/1 Matrix(827,-1872,239,-541) -> Matrix(1,-2,0,1) 1/0 Matrix(1079,-2448,413,-937) -> Matrix(1,2,0,1) 1/0 Matrix(253,-576,47,-107) -> Matrix(1,0,0,1) Matrix(251,-576,78,-179) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(469,-1080,109,-251) -> Matrix(1,-2,0,1) 1/0 Matrix(1403,-3240,514,-1187) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(2053,-4752,607,-1405) -> Matrix(3,2,2,1) Matrix(613,-1440,169,-397) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1007,-2376,153,-361) -> Matrix(1,0,0,1) Matrix(7199,-16992,3050,-7199) -> Matrix(-1,0,2,1) (59/25,144/61) -> (-1/1,0/1) Matrix(1585,-3744,671,-1585) -> Matrix(-1,0,2,1) (144/61,26/11) -> (-1/1,0/1) Matrix(577,-1368,213,-505) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(181,-432,75,-179) -> Matrix(1,0,2,1) 0/1 Matrix(325,-792,103,-251) -> Matrix(1,0,0,1) Matrix(1151,-2808,207,-505) -> Matrix(1,-2,0,1) 1/0 Matrix(7199,-17568,2950,-7199) -> Matrix(-1,4,0,1) (61/25,144/59) -> (2/1,1/0) Matrix(1297,-3168,531,-1297) -> Matrix(1,2,0,-1) (144/59,22/9) -> (-1/1,1/0) Matrix(323,-792,73,-179) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(253,-648,98,-251) -> Matrix(1,0,4,1) 0/1 Matrix(1727,-4464,501,-1295) -> Matrix(3,-2,-2,1) Matrix(1475,-3816,264,-683) -> Matrix(3,-2,-2,1) Matrix(3671,-9504,1085,-2809) -> Matrix(3,-2,2,-1) 1/1 Matrix(3419,-8856,737,-1909) -> Matrix(1,0,-2,1) 0/1 Matrix(829,-2160,180,-469) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(3311,-8640,717,-1871) -> Matrix(1,-2,-2,3) Matrix(467,-1224,124,-325) -> Matrix(1,4,0,1) 1/0 Matrix(1259,-3312,287,-755) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(2051,-5400,779,-2051) -> Matrix(5,6,-4,-5) (50/19,108/41) -> (-3/2,-1/1) Matrix(2377,-6264,902,-2377) -> Matrix(5,4,-6,-5) (108/41,29/11) -> (-1/1,-2/3) Matrix(109,-288,14,-37) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(107,-288,13,-35) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1331,-3600,359,-971) -> Matrix(3,2,2,1) Matrix(397,-1080,93,-253) -> Matrix(9,4,-2,-1) Matrix(2161,-5904,474,-1295) -> Matrix(1,0,2,1) 0/1 Matrix(287,-792,104,-287) -> Matrix(-1,0,8,1) (11/4,36/13) -> (-1/4,0/1) Matrix(181,-504,65,-181) -> Matrix(1,0,2,-1) (36/13,14/5) -> (0/1,1/1) Matrix(179,-504,38,-107) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(685,-1944,216,-613) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1367,-3888,430,-1223) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1441,-4104,329,-937) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(251,-720,38,-109) -> Matrix(1,0,0,1) Matrix(361,-1152,68,-217) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(287,-936,88,-287) -> Matrix(-1,0,6,1) (13/4,36/11) -> (-1/3,0/1) Matrix(109,-360,33,-109) -> Matrix(1,0,2,-1) (36/11,10/3) -> (0/1,1/1) Matrix(901,-3024,247,-829) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1585,-5328,343,-1153) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(107,-360,11,-37) -> Matrix(1,0,-2,1) 0/1 Matrix(1619,-5472,437,-1477) -> Matrix(1,-2,2,-3) 1/1 Matrix(361,-1224,64,-217) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(253,-864,53,-181) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(251,-864,52,-179) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(4319,-14904,1189,-4103) -> Matrix(1,2,2,3) Matrix(181,-648,50,-179) -> Matrix(1,0,2,1) 0/1 Matrix(19403,-70488,5341,-19403) -> Matrix(3,-2,4,-3) (178/49,396/109) -> (1/2,1/1) Matrix(23761,-86328,6540,-23761) -> Matrix(1,0,2,-1) (396/109,109/30) -> (0/1,1/1) Matrix(1763,-6408,386,-1403) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1009,-3672,158,-575) -> Matrix(1,0,-2,1) 0/1 Matrix(935,-3456,214,-791) -> Matrix(3,-2,-2,1) Matrix(755,-2808,203,-755) -> Matrix(1,0,2,-1) (26/7,108/29) -> (0/1,1/1) Matrix(2377,-8856,638,-2377) -> Matrix(7,-8,6,-7) (108/29,41/11) -> (1/1,4/3) Matrix(251,-936,48,-179) -> Matrix(1,-2,-2,3) Matrix(647,-2448,171,-647) -> Matrix(-1,14,0,1) (34/9,72/19) -> (7/1,1/0) Matrix(721,-2736,190,-721) -> Matrix(1,16,0,-1) (72/19,19/5) -> (-8/1,1/0) Matrix(37,-144,9,-35) -> Matrix(1,0,0,1) Matrix(145,-648,32,-143) -> Matrix(1,2,-2,-3) -1/1 Matrix(251,-1152,39,-179) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(575,-2664,109,-505) -> Matrix(1,0,0,1) Matrix(4031,-18720,868,-4031) -> Matrix(-1,0,2,1) (65/14,144/31) -> (-1/1,0/1) Matrix(433,-2016,93,-433) -> Matrix(-1,0,2,1) (144/31,14/3) -> (-1/1,0/1) Matrix(37,-216,6,-35) -> Matrix(1,2,-2,-3) -1/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.