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