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): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -9/1 -8/1 -15/2 -22/3 -20/3 -6/1 -28/5 -27/5 -16/3 -21/4 -5/1 -24/5 -14/3 -9/2 -35/8 -48/11 -21/5 -4/1 -15/4 -26/7 -18/5 -25/7 -10/3 -3/1 -20/7 -25/9 -100/39 -5/2 -12/5 -20/9 -24/11 -15/7 -2/1 -15/8 -5/3 -18/11 -45/29 -3/2 -45/31 -10/7 -15/11 -5/4 -6/5 -15/13 -10/9 0/1 1/1 10/9 15/13 6/5 5/4 30/23 15/11 10/7 3/2 30/19 18/11 5/3 30/17 15/8 2/1 15/7 24/11 20/9 120/53 30/13 210/89 12/5 5/2 100/39 60/23 240/89 30/11 25/9 120/43 45/16 20/7 3/1 60/19 45/14 10/3 27/8 7/2 210/59 25/7 18/5 26/7 15/4 4/1 25/6 21/5 30/7 13/3 48/11 35/8 9/2 60/13 14/3 19/4 24/5 29/6 5/1 21/4 16/3 27/5 60/11 11/2 28/5 17/3 23/4 29/5 6/1 25/4 19/3 13/2 20/3 27/4 7/1 22/3 15/2 23/3 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 1/0 -9/1 -3/1 -17/2 -3/2 -8/1 0/1 -15/2 1/0 -22/3 -8/1 -6/1 -7/1 -3/1 -20/3 -2/1 -33/5 -1/1 -13/2 1/0 -32/5 0/1 -19/3 -1/1 -6/1 1/0 -23/4 1/0 -17/3 -3/1 -45/8 1/0 -28/5 -2/1 -39/7 -3/1 -11/2 -5/2 -27/5 -1/1 -16/3 0/1 -21/4 1/0 -5/1 1/0 -24/5 -2/1 -19/4 1/0 -14/3 -8/3 -2/1 -23/5 -9/5 -32/7 -4/3 -41/9 -1/1 -9/2 1/0 -31/7 -11/7 -22/5 -2/1 0/1 -57/13 -1/1 -35/8 -1/1 -48/11 0/1 -61/14 1/0 -13/3 -1/1 -30/7 1/0 -17/4 1/0 -21/5 -3/1 -4/1 -2/1 -23/6 1/0 -19/5 -1/1 -15/4 -1/1 -26/7 -2/1 0/1 -63/17 -1/1 -37/10 1/0 -48/13 0/1 -59/16 1/0 -11/3 -1/1 -29/8 -13/8 -18/5 -1/1 -61/17 -1/1 -43/12 -1/2 -25/7 1/0 -57/16 1/0 -89/25 9/1 -32/9 -4/1 -39/11 -3/1 -7/2 -3/2 -38/11 -2/3 0/1 -31/9 3/1 -24/7 -2/1 -41/12 -3/2 -58/17 -2/1 -8/5 -17/5 -1/1 -61/18 -3/2 -44/13 -10/7 -27/8 -3/2 -10/3 -1/1 -33/10 -1/2 -23/7 1/1 -59/18 1/0 -36/11 -2/1 -13/4 1/0 -16/5 0/1 -19/6 1/0 -22/7 -2/1 -4/3 -3/1 -1/1 -23/8 -1/2 -20/7 0/1 -17/6 1/0 -14/5 -2/3 0/1 -53/19 1/3 -39/14 1/0 -25/9 1/0 -61/22 1/0 -36/13 -2/1 -11/4 -3/2 -30/11 -1/1 -19/7 -1/1 -27/10 -3/4 -89/33 -21/31 -62/23 -2/3 -12/19 -35/13 -1/2 -43/16 -3/4 -8/3 0/1 -37/14 -3/4 -66/25 -3/4 -29/11 -7/11 -50/19 -1/2 -121/46 -1/2 -71/27 -3/7 -21/8 -1/2 -55/21 -1/2 -89/34 -7/20 -123/47 -1/3 -34/13 -2/7 0/1 -13/5 1/1 -31/12 -7/2 -18/7 -1/1 -59/23 -1/1 -100/39 -2/3 -41/16 -1/2 -23/9 -1/3 -28/11 2/1 -5/2 -1/1 -32/13 -4/7 -27/11 -1/3 -49/20 -1/6 -22/9 -2/1 0/1 -61/25 -1/1 -100/41 -2/3 -39/16 -1/2 -17/7 -1/1 -29/12 -5/12 -12/5 0/1 -31/13 5/3 -50/21 1/0 -69/29 -3/1 -19/8 1/0 -26/11 -2/1 0/1 -59/25 -1/1 -33/14 -1/2 -40/17 0/1 -7/3 -1/1 -30/13 -1/1 -23/10 -3/4 -85/37 -3/4 -62/27 -2/3 -4/7 -101/44 -1/2 -39/17 -1/1 -16/7 0/1 -41/18 -1/2 -25/11 -1/2 -59/26 -1/2 -34/15 -2/5 0/1 -43/19 1/1 -9/4 -1/2 -29/13 -3/13 -20/9 0/1 -31/14 3/8 -11/5 1/1 -24/11 0/1 -13/6 1/0 -28/13 -2/1 -15/7 -1/1 -17/8 -1/2 -2/1 -2/1 0/1 -17/9 1/1 -15/8 1/0 -28/15 -2/1 -13/7 -1/1 -24/13 0/1 -11/6 -1/2 -20/11 0/1 -29/16 3/10 -9/5 1/1 -43/24 -1/2 -120/67 0/1 -77/43 1/5 -34/19 0/1 2/3 -59/33 1/1 -25/14 1/1 -91/51 11/5 -66/37 1/0 -41/23 1/1 -16/9 0/1 -39/22 1/0 -62/35 4/3 2/1 -23/13 3/1 -30/17 1/0 -7/4 1/0 -33/19 1/1 -92/53 6/1 -151/87 19/1 -210/121 1/0 -59/34 1/0 -26/15 -2/1 0/1 -45/26 -1/1 -19/11 -1/1 -69/40 -3/2 -50/29 -1/1 -31/18 -5/8 -12/7 0/1 -29/17 5/7 -75/44 1/1 -121/71 1/1 -46/27 4/3 2/1 -17/10 1/0 -39/23 1/1 -139/82 1/0 -100/59 2/1 -61/36 1/0 -83/49 3/1 -22/13 -2/1 0/1 -27/16 1/2 -5/3 1/0 -33/20 -3/2 -61/37 -1/1 -28/17 -2/3 -23/14 1/2 -41/25 1/1 -100/61 2/1 -59/36 1/0 -18/11 1/0 -31/19 -7/5 -75/46 -1/1 -44/27 -2/3 -13/8 -1/2 -60/37 0/1 -47/29 1/7 -34/21 0/1 2/5 -89/55 7/13 -55/34 1/1 -21/13 1/1 -71/44 3/4 -50/31 1/1 -29/18 7/4 -37/23 3/1 -82/51 6/1 8/1 -45/28 1/0 -8/5 0/1 -35/22 1/1 -97/61 1/1 -62/39 12/7 2/1 -151/95 33/17 -240/151 2/1 -89/56 21/10 -27/17 3/1 -73/46 5/2 -119/75 3/1 -46/29 10/3 4/1 -19/12 1/0 -30/19 1/0 -11/7 -3/1 -36/23 -2/1 -61/39 -1/1 -25/16 -1/1 -89/57 -1/7 -64/41 0/1 -39/25 -1/1 -53/34 -1/4 -120/77 0/1 -67/43 1/5 -14/9 0/1 2/1 -59/38 1/0 -45/29 1/0 -31/20 -9/2 -17/11 -1/1 -37/24 1/0 -20/13 0/1 -23/15 1/1 -3/2 1/0 -22/15 -4/1 -2/1 -41/28 -5/2 -60/41 -2/1 -19/13 -1/1 -16/11 0/1 -61/42 1/0 -45/31 1/0 -29/20 -11/2 -13/9 -1/1 -36/25 -2/1 -59/41 -1/1 -82/57 -2/1 -4/3 -23/16 -1/2 -10/7 1/0 -37/26 -9/2 -64/45 -4/1 -91/64 -33/8 -27/19 -3/1 -44/31 -10/3 -105/74 -3/1 -61/43 -3/1 -17/12 1/0 -58/41 -8/3 -2/1 -99/70 1/0 -140/99 -2/1 -41/29 -3/1 -24/17 -2/1 -55/39 -3/2 -31/22 -3/4 -7/5 -3/1 -39/28 -3/2 -32/23 -4/3 -121/87 -1/1 -210/151 -1/1 -89/64 -9/10 -57/41 -1/1 -25/18 -1/1 -68/49 -2/1 -43/31 1/1 -61/44 1/0 -18/13 1/0 -29/21 -13/5 -40/29 -2/1 -11/8 1/0 -59/43 -1/1 -48/35 0/1 -85/62 -1/1 -37/27 -1/1 -63/46 1/0 -89/65 -9/1 -26/19 -2/1 0/1 -15/11 1/0 -34/25 -4/1 -2/1 -19/14 1/0 -23/17 -1/1 -27/20 -5/2 -31/23 -13/7 -4/3 -2/1 -29/22 -15/8 -25/19 -3/2 -21/16 -3/2 -17/13 -1/1 -30/23 -1/1 -13/10 1/0 -61/47 -1/1 -48/37 0/1 -83/64 1/0 -35/27 1/0 -57/44 1/0 -22/17 -2/1 0/1 -53/41 -5/1 -31/24 -11/4 -9/7 -1/1 -41/32 1/0 -32/25 -4/1 -23/18 -9/4 -60/47 -2/1 -37/29 -17/9 -14/11 -2/1 -8/5 -61/48 -3/2 -47/37 -7/5 -33/26 -3/2 -19/15 -1/1 -24/19 -2/1 -29/23 -17/11 -5/4 -1/1 -21/17 -1/1 -16/13 0/1 -27/22 1/0 -38/31 -12/5 -2/1 -49/40 -17/8 -60/49 -2/1 -11/9 -5/3 -39/32 -3/2 -28/23 -2/1 -45/37 -1/1 -17/14 -3/2 -40/33 -2/1 -23/19 -1/1 -29/24 -19/14 -6/5 -1/1 -31/26 -1/6 -25/21 1/0 -19/16 1/0 -32/27 0/1 -13/11 -1/1 -33/28 1/0 -20/17 -2/1 -27/23 -5/3 -7/6 -3/2 -22/19 -6/5 -8/7 -15/13 -1/1 -38/33 -8/9 -6/7 -23/20 -3/4 -8/7 0/1 -17/15 -3/1 -9/8 -3/2 -10/9 -1/1 -11/10 1/0 -1/1 -1/1 0/1 0/1 1/1 1/1 10/9 1/1 9/8 3/2 17/15 3/1 8/7 0/1 15/13 1/1 22/19 8/7 6/5 7/6 3/2 20/17 2/1 33/28 1/0 13/11 1/1 32/27 0/1 19/16 1/0 6/5 1/1 23/19 1/1 17/14 3/2 45/37 1/1 28/23 2/1 39/32 3/2 11/9 5/3 27/22 1/0 16/13 0/1 21/17 1/1 5/4 1/1 24/19 2/1 19/15 1/1 14/11 8/5 2/1 23/18 9/4 32/25 4/1 41/32 1/0 9/7 1/1 31/24 11/4 22/17 0/1 2/1 57/44 1/0 35/27 1/0 48/37 0/1 61/47 1/1 13/10 1/0 30/23 1/1 17/13 1/1 21/16 3/2 4/3 2/1 23/17 1/1 19/14 1/0 15/11 1/0 26/19 0/1 2/1 63/46 1/0 37/27 1/1 48/35 0/1 59/43 1/1 11/8 1/0 29/21 13/5 18/13 1/0 61/44 1/0 43/31 -1/1 25/18 1/1 57/41 1/1 89/64 9/10 32/23 4/3 39/28 3/2 7/5 3/1 38/27 -2/1 0/1 31/22 3/4 24/17 2/1 41/29 3/1 58/41 2/1 8/3 17/12 1/0 61/43 3/1 44/31 10/3 27/19 3/1 10/7 1/0 33/23 -1/1 23/16 1/2 59/41 1/1 36/25 2/1 13/9 1/1 16/11 0/1 19/13 1/1 22/15 2/1 4/1 3/2 1/0 23/15 -1/1 20/13 0/1 17/11 1/1 14/9 -2/1 0/1 53/34 1/4 39/25 1/1 25/16 1/1 61/39 1/1 36/23 2/1 11/7 3/1 30/19 1/0 19/12 1/0 27/17 -3/1 89/56 -21/10 62/39 -2/1 -12/7 35/22 -1/1 43/27 -3/1 8/5 0/1 37/23 -3/1 66/41 -3/1 29/18 -7/4 50/31 -1/1 121/75 -1/1 71/44 -3/4 21/13 -1/1 55/34 -1/1 89/55 -7/13 123/76 -1/2 34/21 -2/5 0/1 13/8 1/2 31/19 7/5 18/11 1/0 59/36 1/0 100/61 -2/1 41/25 -1/1 23/14 -1/2 28/17 2/3 5/3 1/0 32/19 -4/3 27/16 -1/2 49/29 -1/5 22/13 0/1 2/1 61/36 1/0 100/59 -2/1 39/23 -1/1 17/10 1/0 29/17 -5/7 12/7 0/1 31/18 5/8 50/29 1/1 69/40 3/2 19/11 1/1 26/15 0/1 2/1 59/34 1/0 33/19 -1/1 40/23 0/1 7/4 1/0 30/17 1/0 23/13 -3/1 85/48 -3/1 62/35 -2/1 -4/3 101/57 -1/1 39/22 1/0 16/9 0/1 41/23 -1/1 25/14 -1/1 59/33 -1/1 34/19 -2/3 0/1 43/24 1/2 9/5 -1/1 29/16 -3/10 20/11 0/1 31/17 3/11 11/6 1/2 24/13 0/1 13/7 1/1 28/15 2/1 15/8 1/0 17/9 -1/1 2/1 0/1 2/1 17/8 1/2 15/7 1/1 28/13 2/1 13/6 1/0 24/11 0/1 11/5 -1/1 20/9 0/1 29/13 3/13 9/4 1/2 43/19 -1/1 120/53 0/1 77/34 1/6 34/15 0/1 2/5 59/26 1/2 25/11 1/2 91/40 11/16 66/29 1/1 41/18 1/2 16/7 0/1 39/17 1/1 62/27 4/7 2/3 23/10 3/4 30/13 1/1 7/3 1/1 33/14 1/2 92/39 6/7 151/64 19/20 210/89 1/1 59/25 1/1 26/11 0/1 2/1 45/19 1/0 19/8 1/0 69/29 3/1 50/21 1/0 31/13 -5/3 12/5 0/1 29/12 5/12 75/31 1/2 121/50 1/2 46/19 4/7 2/3 17/7 1/1 39/16 1/2 139/57 1/1 100/41 2/3 61/25 1/1 83/34 3/4 22/9 0/1 2/1 27/11 1/3 5/2 1/1 33/13 3/1 61/24 1/0 28/11 -2/1 23/9 1/3 41/16 1/2 100/39 2/3 59/23 1/1 18/7 1/1 31/12 7/2 75/29 1/0 44/17 -2/1 13/5 -1/1 60/23 0/1 47/18 1/8 34/13 0/1 2/7 89/34 7/20 55/21 1/2 21/8 1/2 71/27 3/7 50/19 1/2 29/11 7/11 37/14 3/4 82/31 6/7 8/9 45/17 1/1 8/3 0/1 35/13 1/2 97/36 1/2 62/23 12/19 2/3 151/56 33/50 240/89 2/3 89/33 21/31 27/10 3/4 73/27 5/7 119/44 3/4 46/17 10/13 4/5 19/7 1/1 30/11 1/1 11/4 3/2 36/13 2/1 61/22 1/0 25/9 1/0 89/32 -1/6 64/23 0/1 39/14 1/0 53/19 -1/3 120/43 0/1 67/24 1/6 14/5 0/1 2/3 59/21 1/1 45/16 1/1 31/11 9/7 17/6 1/0 37/13 1/1 20/7 0/1 23/8 1/2 3/1 1/1 22/7 4/3 2/1 41/13 5/3 60/19 2/1 19/6 1/0 16/5 0/1 61/19 1/1 45/14 1/1 29/9 11/9 13/4 1/0 36/11 2/1 59/18 1/0 82/25 2/1 4/1 23/7 -1/1 10/3 1/1 37/11 9/7 64/19 4/3 91/27 33/25 27/8 3/2 44/13 10/7 105/31 3/2 61/18 3/2 17/5 1/1 58/17 8/5 2/1 99/29 1/1 140/41 2/1 41/12 3/2 24/7 2/1 55/16 3/1 31/9 -3/1 7/2 3/2 39/11 3/1 32/9 4/1 121/34 1/0 210/59 1/0 89/25 -9/1 57/16 1/0 25/7 1/0 68/19 2/1 43/12 1/2 61/17 1/1 18/5 1/1 29/8 13/8 40/11 2/1 11/3 1/1 59/16 1/0 48/13 0/1 85/23 1/0 37/10 1/0 63/17 1/1 89/24 9/8 26/7 0/1 2/1 15/4 1/1 34/9 4/3 2/1 19/5 1/1 23/6 1/0 27/7 5/3 31/8 13/6 4/1 2/1 29/7 15/7 25/6 3/1 21/5 3/1 17/4 1/0 30/7 1/0 13/3 1/1 61/14 1/0 48/11 0/1 83/19 1/1 35/8 1/1 57/13 1/1 22/5 0/1 2/1 53/12 5/4 31/7 11/7 9/2 1/0 41/9 1/1 32/7 4/3 23/5 9/5 60/13 2/1 37/8 17/8 14/3 2/1 8/3 61/13 3/1 47/10 7/2 33/7 3/1 19/4 1/0 24/5 2/1 29/6 17/6 5/1 1/0 21/4 1/0 16/3 0/1 27/5 1/1 38/7 12/7 2/1 49/9 17/9 60/11 2/1 11/2 5/2 39/7 3/1 28/5 2/1 45/8 1/0 17/3 3/1 40/7 2/1 23/4 1/0 29/5 19/5 6/1 1/0 31/5 -1/5 25/4 1/1 19/3 1/1 32/5 0/1 13/2 1/0 33/5 1/1 20/3 2/1 27/4 5/2 7/1 3/1 22/3 6/1 8/1 15/2 1/0 38/5 -8/1 -6/1 23/3 -3/1 8/1 0/1 17/2 3/2 9/1 3/1 10/1 1/0 11/1 1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(121,1260,-46,-479) (-10/1,1/0) -> (-50/19,-121/46) Hyperbolic Matrix(119,1140,50,479) (-10/1,-9/1) -> (69/29,50/21) Hyperbolic Matrix(61,540,34,301) (-9/1,-17/2) -> (43/24,9/5) Hyperbolic Matrix(179,1500,50,419) (-17/2,-8/1) -> (68/19,43/12) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(299,2220,-186,-1381) (-15/2,-22/3) -> (-82/51,-45/28) Hyperbolic Matrix(59,420,42,299) (-22/3,-7/1) -> (7/5,38/27) Hyperbolic Matrix(61,420,-26,-179) (-7/1,-20/3) -> (-40/17,-7/3) Hyperbolic Matrix(299,1980,172,1139) (-20/3,-33/5) -> (33/19,40/23) Hyperbolic Matrix(301,1980,64,421) (-33/5,-13/2) -> (47/10,33/7) Hyperbolic Matrix(121,780,56,361) (-13/2,-32/5) -> (28/13,13/6) Hyperbolic Matrix(301,1920,66,421) (-32/5,-19/3) -> (41/9,32/7) Hyperbolic Matrix(239,1500,-134,-841) (-19/3,-6/1) -> (-66/37,-41/23) Hyperbolic Matrix(301,1740,-114,-659) (-6/1,-23/4) -> (-37/14,-66/25) Hyperbolic Matrix(179,1020,-116,-661) (-23/4,-17/3) -> (-17/11,-37/24) Hyperbolic Matrix(181,1020,96,541) (-17/3,-45/8) -> (15/8,17/9) Hyperbolic Matrix(299,1680,160,899) (-45/8,-28/5) -> (28/15,15/8) Hyperbolic Matrix(419,2340,118,659) (-28/5,-39/7) -> (39/11,32/9) Hyperbolic Matrix(539,3000,334,1859) (-39/7,-11/2) -> (71/44,21/13) Hyperbolic Matrix(299,1620,-122,-661) (-11/2,-27/5) -> (-27/11,-49/20) Hyperbolic Matrix(301,1620,212,1141) (-27/5,-16/3) -> (44/31,27/19) Hyperbolic Matrix(181,960,102,541) (-16/3,-21/4) -> (39/22,16/9) Hyperbolic Matrix(241,1260,92,481) (-21/4,-5/1) -> (55/21,21/8) Hyperbolic Matrix(299,1440,-212,-1021) (-5/1,-24/5) -> (-24/17,-55/39) Hyperbolic Matrix(301,1440,88,421) (-24/5,-19/4) -> (41/12,24/7) Hyperbolic Matrix(241,1140,-152,-719) (-19/4,-14/3) -> (-46/29,-19/12) Hyperbolic Matrix(181,840,-142,-659) (-14/3,-23/5) -> (-37/29,-14/11) Hyperbolic Matrix(301,1380,118,541) (-23/5,-32/7) -> (28/11,23/9) Hyperbolic Matrix(421,1920,66,301) (-32/7,-41/9) -> (19/3,32/5) Hyperbolic Matrix(659,3000,382,1739) (-41/9,-9/2) -> (69/40,19/11) Hyperbolic Matrix(121,540,54,241) (-9/2,-31/7) -> (29/13,9/4) Hyperbolic Matrix(421,1860,-122,-539) (-31/7,-22/5) -> (-38/11,-31/9) Hyperbolic Matrix(301,1320,96,421) (-22/5,-57/13) -> (3/1,22/7) Hyperbolic Matrix(781,3420,562,2461) (-57/13,-35/8) -> (25/18,57/41) Hyperbolic Matrix(1319,5760,-962,-4201) (-35/8,-48/11) -> (-48/35,-85/62) Hyperbolic Matrix(1321,5760,358,1561) (-48/11,-61/14) -> (59/16,48/13) Hyperbolic Matrix(1379,6000,510,2219) (-61/14,-13/3) -> (73/27,119/44) Hyperbolic Matrix(181,780,42,181) (-13/3,-30/7) -> (30/7,13/3) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(241,1020,142,601) (-17/4,-21/5) -> (39/23,17/10) Hyperbolic Matrix(359,1500,-230,-961) (-21/5,-4/1) -> (-64/41,-39/25) Hyperbolic Matrix(421,1620,-296,-1139) (-4/1,-23/6) -> (-37/26,-64/45) Hyperbolic Matrix(361,1380,220,841) (-23/6,-19/5) -> (41/25,23/14) Hyperbolic Matrix(301,1140,-174,-659) (-19/5,-15/4) -> (-45/26,-19/11) Hyperbolic Matrix(419,1560,-242,-901) (-15/4,-26/7) -> (-26/15,-45/26) Hyperbolic Matrix(1439,5340,-550,-2041) (-26/7,-63/17) -> (-123/47,-34/13) Hyperbolic Matrix(421,1560,146,541) (-63/17,-37/10) -> (23/8,3/1) Hyperbolic Matrix(1559,5760,-1202,-4441) (-37/10,-48/13) -> (-48/37,-83/64) Hyperbolic Matrix(1561,5760,358,1321) (-48/13,-59/16) -> (61/14,48/11) Hyperbolic Matrix(179,660,16,59) (-59/16,-11/3) -> (11/1,1/0) Hyperbolic Matrix(181,660,-82,-299) (-11/3,-29/8) -> (-31/14,-11/5) Hyperbolic Matrix(299,1080,116,419) (-29/8,-18/5) -> (18/7,31/12) Hyperbolic Matrix(601,2160,234,841) (-18/5,-61/17) -> (59/23,18/7) Hyperbolic Matrix(1021,3660,720,2581) (-61/17,-43/12) -> (17/12,61/43) Hyperbolic Matrix(721,2580,-268,-959) (-43/12,-25/7) -> (-35/13,-43/16) Hyperbolic Matrix(959,3420,740,2639) (-25/7,-57/16) -> (57/44,35/27) Hyperbolic Matrix(4499,16020,2780,9899) (-57/16,-89/25) -> (89/55,123/76) Hyperbolic Matrix(3659,13020,-2108,-7501) (-89/25,-32/9) -> (-92/53,-151/87) Hyperbolic Matrix(659,2340,118,419) (-32/9,-39/11) -> (39/7,28/5) Hyperbolic Matrix(661,2340,424,1501) (-39/11,-7/2) -> (53/34,39/25) Hyperbolic Matrix(121,420,104,361) (-7/2,-38/11) -> (22/19,7/6) Hyperbolic Matrix(419,1440,-332,-1141) (-31/9,-24/7) -> (-24/19,-29/23) Hyperbolic Matrix(421,1440,88,301) (-24/7,-41/12) -> (19/4,24/5) Hyperbolic Matrix(2461,8400,-1072,-3659) (-41/12,-58/17) -> (-62/27,-101/44) Hyperbolic Matrix(299,1020,158,539) (-58/17,-17/5) -> (17/9,2/1) Hyperbolic Matrix(1079,3660,778,2639) (-17/5,-61/18) -> (61/44,43/31) Hyperbolic Matrix(1081,3660,-744,-2519) (-61/18,-44/13) -> (-16/11,-61/42) Hyperbolic Matrix(479,1620,390,1319) (-44/13,-27/8) -> (27/22,16/13) Hyperbolic Matrix(179,600,-54,-181) (-27/8,-10/3) -> (-10/3,-33/10) Parabolic Matrix(419,1380,-310,-1021) (-33/10,-23/7) -> (-23/17,-27/20) Hyperbolic Matrix(1921,6300,-1134,-3719) (-23/7,-59/18) -> (-61/36,-83/49) Hyperbolic Matrix(1319,4320,476,1559) (-59/18,-36/11) -> (36/13,61/22) Hyperbolic Matrix(239,780,110,359) (-36/11,-13/4) -> (13/6,24/11) Hyperbolic Matrix(241,780,-148,-479) (-13/4,-16/5) -> (-44/27,-13/8) Hyperbolic Matrix(301,960,132,421) (-16/5,-19/6) -> (41/18,16/7) Hyperbolic Matrix(419,1320,-286,-901) (-19/6,-22/7) -> (-22/15,-41/28) Hyperbolic Matrix(421,1320,96,301) (-22/7,-3/1) -> (57/13,22/5) Hyperbolic Matrix(541,1560,146,421) (-3/1,-23/8) -> (37/10,63/17) Hyperbolic Matrix(481,1380,84,241) (-23/8,-20/7) -> (40/7,23/4) Hyperbolic Matrix(359,1020,-296,-841) (-20/7,-17/6) -> (-17/14,-40/33) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(601,1680,-386,-1079) (-14/5,-53/19) -> (-67/43,-14/9) Hyperbolic Matrix(839,2340,602,1679) (-53/19,-39/14) -> (39/28,7/5) Hyperbolic Matrix(539,1500,-410,-1141) (-39/14,-25/9) -> (-25/19,-21/16) Hyperbolic Matrix(1081,3000,476,1321) (-25/9,-61/22) -> (59/26,25/11) Hyperbolic Matrix(1559,4320,476,1319) (-61/22,-36/13) -> (36/11,59/18) Hyperbolic Matrix(239,660,130,359) (-36/13,-11/4) -> (11/6,24/13) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(421,1140,-332,-899) (-19/7,-27/10) -> (-33/26,-19/15) Hyperbolic Matrix(1801,4860,534,1441) (-27/10,-89/33) -> (91/27,27/8) Hyperbolic Matrix(5519,14880,-3472,-9361) (-89/33,-62/23) -> (-62/39,-151/95) Hyperbolic Matrix(2761,7440,-1202,-3239) (-62/23,-35/13) -> (-85/37,-62/27) Hyperbolic Matrix(179,480,22,59) (-43/16,-8/3) -> (8/1,17/2) Hyperbolic Matrix(181,480,-158,-419) (-8/3,-37/14) -> (-23/20,-8/7) Hyperbolic Matrix(3001,7920,-1682,-4439) (-66/25,-29/11) -> (-91/51,-66/37) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(2099,5520,570,1499) (-121/46,-71/27) -> (11/3,59/16) Hyperbolic Matrix(1141,3000,936,2461) (-71/27,-21/8) -> (39/32,11/9) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(779,2040,160,419) (-55/21,-89/34) -> (29/6,5/1) Hyperbolic Matrix(6121,16020,4402,11521) (-89/34,-123/47) -> (57/41,89/64) Hyperbolic Matrix(781,2040,-482,-1259) (-34/13,-13/5) -> (-47/29,-34/21) Hyperbolic Matrix(301,780,-208,-539) (-13/5,-31/12) -> (-29/20,-13/9) Hyperbolic Matrix(419,1080,116,299) (-31/12,-18/7) -> (18/5,29/8) Hyperbolic Matrix(841,2160,234,601) (-18/7,-59/23) -> (61/17,18/5) Hyperbolic Matrix(4679,12000,1918,4919) (-59/23,-100/39) -> (100/41,61/25) Hyperbolic Matrix(7021,18000,-4142,-10619) (-100/39,-41/16) -> (-139/82,-100/59) Hyperbolic Matrix(539,1380,398,1019) (-41/16,-23/9) -> (23/17,19/14) Hyperbolic Matrix(541,1380,118,301) (-23/9,-28/11) -> (32/7,23/5) Hyperbolic Matrix(119,300,-48,-121) (-28/11,-5/2) -> (-5/2,-32/13) Parabolic Matrix(1441,3540,-830,-2039) (-32/13,-27/11) -> (-33/19,-92/53) Hyperbolic Matrix(1201,2940,-980,-2399) (-49/20,-22/9) -> (-38/31,-49/40) Hyperbolic Matrix(2581,6300,-1794,-4379) (-22/9,-61/25) -> (-59/41,-82/57) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(6299,15360,-4454,-10861) (-100/41,-39/16) -> (-99/70,-140/99) Hyperbolic Matrix(419,1020,320,779) (-39/16,-17/7) -> (17/13,21/16) Hyperbolic Matrix(421,1020,-272,-659) (-17/7,-29/12) -> (-31/20,-17/11) Hyperbolic Matrix(299,720,174,419) (-29/12,-12/5) -> (12/7,31/18) Hyperbolic Matrix(301,720,176,421) (-12/5,-31/13) -> (29/17,12/7) Hyperbolic Matrix(1259,3000,478,1139) (-31/13,-50/21) -> (50/19,29/11) Hyperbolic Matrix(479,1140,50,119) (-50/21,-69/29) -> (9/1,10/1) Hyperbolic Matrix(1261,3000,984,2341) (-69/29,-19/8) -> (41/32,9/7) Hyperbolic Matrix(481,1140,-354,-839) (-19/8,-26/11) -> (-34/25,-19/14) Hyperbolic Matrix(1499,3540,838,1979) (-26/11,-59/25) -> (59/33,34/19) Hyperbolic Matrix(1679,3960,-1018,-2401) (-59/25,-33/14) -> (-33/20,-61/37) Hyperbolic Matrix(841,1980,714,1681) (-33/14,-40/17) -> (20/17,33/28) Hyperbolic Matrix(181,420,78,181) (-7/3,-30/13) -> (30/13,7/3) Hyperbolic Matrix(599,1380,260,599) (-30/13,-23/10) -> (23/10,30/13) Hyperbolic Matrix(2219,5100,600,1379) (-23/10,-85/37) -> (85/23,37/10) Hyperbolic Matrix(4079,9360,-2406,-5521) (-101/44,-39/17) -> (-39/23,-139/82) Hyperbolic Matrix(419,960,340,779) (-39/17,-16/7) -> (16/13,21/17) Hyperbolic Matrix(421,960,132,301) (-16/7,-41/18) -> (19/6,16/5) Hyperbolic Matrix(659,1500,-554,-1261) (-41/18,-25/11) -> (-25/21,-19/16) Hyperbolic Matrix(1321,3000,476,1081) (-25/11,-59/26) -> (61/22,25/9) Hyperbolic Matrix(1561,3540,900,2041) (-59/26,-34/15) -> (26/15,59/34) Hyperbolic Matrix(1801,4080,-1006,-2279) (-34/15,-43/19) -> (-77/43,-34/19) Hyperbolic Matrix(239,540,212,479) (-43/19,-9/4) -> (9/8,17/15) Hyperbolic Matrix(241,540,54,121) (-9/4,-29/13) -> (31/7,9/2) Hyperbolic Matrix(539,1200,296,659) (-29/13,-20/9) -> (20/11,31/17) Hyperbolic Matrix(541,1200,298,661) (-20/9,-31/14) -> (29/16,20/11) Hyperbolic Matrix(301,660,192,421) (-11/5,-24/11) -> (36/23,11/7) Hyperbolic Matrix(359,780,110,239) (-24/11,-13/6) -> (13/4,36/11) Hyperbolic Matrix(361,780,56,121) (-13/6,-28/13) -> (32/5,13/2) Hyperbolic Matrix(781,1680,642,1381) (-28/13,-15/7) -> (45/37,28/23) Hyperbolic Matrix(479,1020,394,839) (-15/7,-17/8) -> (17/14,45/37) Hyperbolic Matrix(481,1020,340,721) (-17/8,-2/1) -> (58/41,17/12) Hyperbolic Matrix(539,1020,158,299) (-2/1,-17/9) -> (17/5,58/17) Hyperbolic Matrix(541,1020,96,181) (-17/9,-15/8) -> (45/8,17/3) Hyperbolic Matrix(899,1680,160,299) (-15/8,-28/15) -> (28/5,45/8) Hyperbolic Matrix(419,780,354,659) (-28/15,-13/7) -> (13/11,32/27) Hyperbolic Matrix(421,780,292,541) (-13/7,-24/13) -> (36/25,13/9) Hyperbolic Matrix(359,660,130,239) (-24/13,-11/6) -> (11/4,36/13) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(959,1740,264,479) (-20/11,-29/16) -> (29/8,40/11) Hyperbolic Matrix(299,540,232,419) (-29/16,-9/5) -> (9/7,31/24) Hyperbolic Matrix(301,540,34,61) (-9/5,-43/24) -> (17/2,9/1) Hyperbolic Matrix(8039,14400,3550,6359) (-43/24,-120/67) -> (120/53,77/34) Hyperbolic Matrix(8041,14400,3552,6361) (-120/67,-77/43) -> (43/19,120/53) Hyperbolic Matrix(1979,3540,838,1499) (-34/19,-59/33) -> (59/25,26/11) Hyperbolic Matrix(1679,3000,1074,1919) (-59/33,-25/14) -> (25/16,61/39) Hyperbolic Matrix(1681,3000,404,721) (-25/14,-91/51) -> (29/7,25/6) Hyperbolic Matrix(539,960,370,659) (-41/23,-16/9) -> (16/11,19/13) Hyperbolic Matrix(541,960,102,181) (-16/9,-39/22) -> (21/4,16/3) Hyperbolic Matrix(4741,8400,-3352,-5939) (-39/22,-62/35) -> (-58/41,-99/70) Hyperbolic Matrix(4201,7440,-2642,-4679) (-62/35,-23/13) -> (-97/61,-62/39) Hyperbolic Matrix(781,1380,442,781) (-23/13,-30/17) -> (30/17,23/13) Hyperbolic Matrix(239,420,136,239) (-30/17,-7/4) -> (7/4,30/17) Hyperbolic Matrix(241,420,-206,-359) (-7/4,-33/19) -> (-27/23,-7/6) Hyperbolic Matrix(29039,50400,8158,14159) (-151/87,-210/121) -> (210/59,89/25) Hyperbolic Matrix(21781,37800,6120,10621) (-210/121,-59/34) -> (121/34,210/59) Hyperbolic Matrix(2041,3540,900,1561) (-59/34,-26/15) -> (34/15,59/26) Hyperbolic Matrix(1739,3000,382,659) (-19/11,-69/40) -> (9/2,41/9) Hyperbolic Matrix(661,1140,592,1021) (-69/40,-50/29) -> (10/9,9/8) Hyperbolic Matrix(1741,3000,1080,1861) (-50/29,-31/18) -> (29/18,50/31) Hyperbolic Matrix(419,720,174,299) (-31/18,-12/7) -> (12/5,29/12) Hyperbolic Matrix(421,720,176,301) (-12/7,-29/17) -> (31/13,12/5) Hyperbolic Matrix(2041,3480,634,1081) (-29/17,-75/44) -> (45/14,29/9) Hyperbolic Matrix(5879,10020,1830,3119) (-75/44,-121/71) -> (61/19,45/14) Hyperbolic Matrix(2641,4500,564,961) (-121/71,-46/27) -> (14/3,61/13) Hyperbolic Matrix(601,1020,142,241) (-17/10,-39/23) -> (21/5,17/4) Hyperbolic Matrix(7081,12000,4320,7321) (-100/59,-61/36) -> (59/36,100/61) Hyperbolic Matrix(2161,3660,284,481) (-83/49,-22/13) -> (38/5,23/3) Hyperbolic Matrix(959,1620,-782,-1321) (-22/13,-27/16) -> (-27/22,-38/31) Hyperbolic Matrix(179,300,-108,-181) (-27/16,-5/3) -> (-5/3,-33/20) Parabolic Matrix(3241,5340,-2330,-3839) (-61/37,-28/17) -> (-32/23,-121/87) Hyperbolic Matrix(839,1380,656,1079) (-28/17,-23/14) -> (23/18,32/25) Hyperbolic Matrix(841,1380,220,361) (-23/14,-41/25) -> (19/5,23/6) Hyperbolic Matrix(6001,9840,-4244,-6959) (-41/25,-100/61) -> (-140/99,-41/29) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(661,1080,478,781) (-18/11,-31/19) -> (29/21,18/13) Hyperbolic Matrix(2281,3720,810,1321) (-31/19,-75/46) -> (45/16,31/11) Hyperbolic Matrix(4859,7920,-3424,-5581) (-75/46,-44/27) -> (-44/31,-105/74) Hyperbolic Matrix(2219,3600,850,1379) (-13/8,-60/37) -> (60/23,47/18) Hyperbolic Matrix(2221,3600,852,1381) (-60/37,-47/29) -> (13/5,60/23) Hyperbolic Matrix(3299,5340,-2410,-3901) (-34/21,-89/55) -> (-89/65,-26/19) Hyperbolic Matrix(4079,6600,1186,1919) (-89/55,-55/34) -> (55/16,31/9) Hyperbolic Matrix(779,1260,630,1019) (-55/34,-21/13) -> (21/17,5/4) Hyperbolic Matrix(1859,3000,334,539) (-21/13,-71/44) -> (11/2,39/7) Hyperbolic Matrix(781,1260,-706,-1139) (-71/44,-50/31) -> (-10/9,-11/10) Hyperbolic Matrix(1861,3000,1080,1741) (-50/31,-29/18) -> (31/18,50/29) Hyperbolic Matrix(1081,1740,-894,-1439) (-29/18,-37/23) -> (-23/19,-29/24) Hyperbolic Matrix(3059,4920,932,1499) (-37/23,-82/51) -> (82/25,23/7) Hyperbolic Matrix(1621,2580,-1168,-1859) (-8/5,-35/22) -> (-25/18,-68/49) Hyperbolic Matrix(3961,6300,906,1441) (-35/22,-97/61) -> (83/19,35/8) Hyperbolic Matrix(36239,57600,13438,21359) (-151/95,-240/151) -> (240/89,89/33) Hyperbolic Matrix(36241,57600,13440,21361) (-240/151,-89/56) -> (151/56,240/89) Hyperbolic Matrix(2039,3240,528,839) (-89/56,-27/17) -> (27/7,31/8) Hyperbolic Matrix(1739,2760,264,419) (-27/17,-73/46) -> (13/2,33/5) Hyperbolic Matrix(3781,6000,2912,4621) (-73/46,-119/75) -> (61/47,13/10) Hyperbolic Matrix(2761,4380,984,1561) (-119/75,-46/29) -> (14/5,59/21) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) Hyperbolic Matrix(421,660,192,301) (-11/7,-36/23) -> (24/11,11/5) Hyperbolic Matrix(2761,4320,1918,3001) (-36/23,-61/39) -> (59/41,36/25) Hyperbolic Matrix(1919,3000,1074,1679) (-61/39,-25/16) -> (25/14,59/33) Hyperbolic Matrix(1921,3000,308,481) (-25/16,-89/57) -> (31/5,25/4) Hyperbolic Matrix(7379,11520,2190,3419) (-89/57,-64/41) -> (64/19,91/27) Hyperbolic Matrix(1501,2340,424,661) (-39/25,-53/34) -> (7/2,39/11) Hyperbolic Matrix(9239,14400,3310,5159) (-53/34,-120/77) -> (120/43,67/24) Hyperbolic Matrix(9241,14400,3312,5161) (-120/77,-67/43) -> (53/19,120/43) Hyperbolic Matrix(2819,4380,1042,1619) (-14/9,-59/38) -> (119/44,46/17) Hyperbolic Matrix(5759,8940,1700,2639) (-59/38,-45/29) -> (105/31,61/18) Hyperbolic Matrix(2399,3720,928,1439) (-45/29,-31/20) -> (31/12,75/29) Hyperbolic Matrix(779,1200,272,419) (-37/24,-20/13) -> (20/7,23/8) Hyperbolic Matrix(781,1200,274,421) (-20/13,-23/15) -> (37/13,20/7) Hyperbolic Matrix(1019,1560,744,1139) (-23/15,-3/2) -> (63/46,37/27) Hyperbolic Matrix(899,1320,694,1019) (-3/2,-22/15) -> (22/17,57/44) Hyperbolic Matrix(2459,3600,778,1139) (-41/28,-60/41) -> (60/19,19/6) Hyperbolic Matrix(2461,3600,780,1141) (-60/41,-19/13) -> (41/13,60/19) Hyperbolic Matrix(659,960,370,539) (-19/13,-16/11) -> (16/9,41/23) Hyperbolic Matrix(6901,10020,2852,4141) (-61/42,-45/31) -> (75/31,121/50) Hyperbolic Matrix(2399,3480,992,1439) (-45/31,-29/20) -> (29/12,75/31) Hyperbolic Matrix(541,780,292,421) (-13/9,-36/25) -> (24/13,13/7) Hyperbolic Matrix(3001,4320,1918,2761) (-36/25,-59/41) -> (61/39,36/23) Hyperbolic Matrix(3421,4920,1294,1861) (-82/57,-23/16) -> (37/14,82/31) Hyperbolic Matrix(419,600,-294,-421) (-23/16,-10/7) -> (-10/7,-37/26) Parabolic Matrix(8101,11520,2912,4141) (-64/45,-91/64) -> (89/32,64/23) Hyperbolic Matrix(3419,4860,2152,3059) (-91/64,-27/19) -> (27/17,89/56) Hyperbolic Matrix(1141,1620,212,301) (-27/19,-44/31) -> (16/3,27/5) Hyperbolic Matrix(6301,8940,2242,3181) (-105/74,-61/43) -> (59/21,45/16) Hyperbolic Matrix(2581,3660,720,1021) (-61/43,-17/12) -> (43/12,61/17) Hyperbolic Matrix(721,1020,340,481) (-17/12,-58/41) -> (2/1,17/8) Hyperbolic Matrix(1019,1440,806,1139) (-41/29,-24/17) -> (24/19,19/15) Hyperbolic Matrix(4681,6600,1788,2521) (-55/39,-31/22) -> (89/34,55/21) Hyperbolic Matrix(1321,1860,-1022,-1439) (-31/22,-7/5) -> (-53/41,-31/24) Hyperbolic Matrix(1679,2340,602,839) (-7/5,-39/28) -> (39/14,53/19) Hyperbolic Matrix(1681,2340,1380,1921) (-39/28,-32/23) -> (28/23,39/32) Hyperbolic Matrix(27179,37800,11518,16019) (-121/87,-210/151) -> (210/89,59/25) Hyperbolic Matrix(36241,50400,15360,21361) (-210/151,-89/64) -> (151/64,210/89) Hyperbolic Matrix(7681,10680,2072,2881) (-89/64,-57/41) -> (63/17,89/24) Hyperbolic Matrix(2461,3420,562,781) (-57/41,-25/18) -> (35/8,57/13) Hyperbolic Matrix(1081,1500,952,1321) (-68/49,-43/31) -> (17/15,8/7) Hyperbolic Matrix(2639,3660,778,1079) (-43/31,-61/44) -> (61/18,17/5) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(781,1080,478,661) (-18/13,-29/21) -> (31/19,18/11) Hyperbolic Matrix(1261,1740,566,781) (-29/21,-40/29) -> (20/9,29/13) Hyperbolic Matrix(4021,5520,2492,3421) (-11/8,-59/43) -> (121/75,71/44) Hyperbolic Matrix(4199,5760,3236,4439) (-59/43,-48/35) -> (48/37,61/47) Hyperbolic Matrix(3721,5100,2102,2881) (-85/62,-37/27) -> (23/13,85/48) Hyperbolic Matrix(1139,1560,744,1019) (-37/27,-63/46) -> (3/2,23/15) Hyperbolic Matrix(7799,10680,2190,2999) (-63/46,-89/65) -> (89/25,57/16) Hyperbolic Matrix(659,900,-484,-661) (-26/19,-15/11) -> (-15/11,-34/25) Parabolic Matrix(1019,1380,398,539) (-19/14,-23/17) -> (23/9,41/16) Hyperbolic Matrix(2401,3240,890,1201) (-27/20,-31/23) -> (89/33,27/10) Hyperbolic Matrix(179,240,44,59) (-31/23,-4/3) -> (4/1,29/7) Hyperbolic Matrix(181,240,46,61) (-4/3,-29/22) -> (31/8,4/1) Hyperbolic Matrix(2279,3000,1002,1319) (-29/22,-25/19) -> (25/11,91/40) Hyperbolic Matrix(779,1020,320,419) (-21/16,-17/13) -> (17/7,39/16) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(599,780,460,599) (-30/23,-13/10) -> (13/10,30/23) Hyperbolic Matrix(2819,3660,600,779) (-13/10,-61/47) -> (61/13,47/10) Hyperbolic Matrix(4439,5760,3236,4199) (-61/47,-48/37) -> (48/35,59/43) Hyperbolic Matrix(4859,6300,1804,2339) (-83/64,-35/27) -> (35/13,97/36) Hyperbolic Matrix(2639,3420,740,959) (-35/27,-57/44) -> (57/16,25/7) Hyperbolic Matrix(1019,1320,694,899) (-57/44,-22/17) -> (22/15,3/2) Hyperbolic Matrix(1021,1320,140,181) (-22/17,-53/41) -> (7/1,22/3) Hyperbolic Matrix(419,540,232,299) (-31/24,-9/7) -> (9/5,29/16) Hyperbolic Matrix(2341,3000,984,1261) (-9/7,-41/32) -> (19/8,69/29) Hyperbolic Matrix(1499,1920,1264,1619) (-41/32,-32/25) -> (32/27,19/16) Hyperbolic Matrix(1079,1380,656,839) (-32/25,-23/18) -> (23/14,28/17) Hyperbolic Matrix(2819,3600,610,779) (-23/18,-60/47) -> (60/13,37/8) Hyperbolic Matrix(2821,3600,612,781) (-60/47,-37/29) -> (23/5,60/13) Hyperbolic Matrix(3539,4500,1462,1859) (-14/11,-61/48) -> (121/50,46/19) Hyperbolic Matrix(2881,3660,662,841) (-61/48,-47/37) -> (13/3,61/14) Hyperbolic Matrix(1559,1980,1322,1679) (-47/37,-33/26) -> (33/28,13/11) Hyperbolic Matrix(1139,1440,806,1019) (-19/15,-24/19) -> (24/17,41/29) Hyperbolic Matrix(1621,2040,1002,1261) (-29/23,-5/4) -> (55/34,89/55) Hyperbolic Matrix(1019,1260,630,779) (-5/4,-21/17) -> (21/13,55/34) Hyperbolic Matrix(779,960,340,419) (-21/17,-16/13) -> (16/7,39/17) Hyperbolic Matrix(1319,1620,390,479) (-16/13,-27/22) -> (27/8,44/13) Hyperbolic Matrix(2939,3600,538,659) (-49/40,-60/49) -> (60/11,11/2) Hyperbolic Matrix(2941,3600,540,661) (-60/49,-11/9) -> (49/9,60/11) Hyperbolic Matrix(2461,3000,936,1141) (-11/9,-39/32) -> (21/8,71/27) Hyperbolic Matrix(1921,2340,1380,1681) (-39/32,-28/23) -> (32/23,39/28) Hyperbolic Matrix(1381,1680,642,781) (-28/23,-45/37) -> (15/7,28/13) Hyperbolic Matrix(839,1020,394,479) (-45/37,-17/14) -> (17/8,15/7) Hyperbolic Matrix(1139,1380,742,899) (-40/33,-23/19) -> (23/15,20/13) Hyperbolic Matrix(299,360,-250,-301) (-29/24,-6/5) -> (-6/5,-31/26) Parabolic Matrix(2519,3000,906,1079) (-31/26,-25/21) -> (25/9,89/32) Hyperbolic Matrix(1619,1920,1264,1499) (-19/16,-32/27) -> (32/25,41/32) Hyperbolic Matrix(659,780,354,419) (-32/27,-13/11) -> (13/7,28/15) Hyperbolic Matrix(2341,2760,866,1021) (-13/11,-33/28) -> (27/10,73/27) Hyperbolic Matrix(1019,1200,152,179) (-33/28,-20/17) -> (20/3,27/4) Hyperbolic Matrix(1021,1200,154,181) (-20/17,-27/23) -> (33/5,20/3) Hyperbolic Matrix(1139,1320,258,299) (-7/6,-22/19) -> (22/5,53/12) Hyperbolic Matrix(779,900,-676,-781) (-22/19,-15/13) -> (-15/13,-38/33) Parabolic Matrix(3179,3660,1302,1499) (-38/33,-23/20) -> (83/34,22/9) Hyperbolic Matrix(421,480,264,301) (-8/7,-17/15) -> (43/27,8/5) Hyperbolic Matrix(479,540,212,239) (-17/15,-9/8) -> (9/4,43/19) Hyperbolic Matrix(1021,1140,592,661) (-9/8,-10/9) -> (50/29,69/40) Hyperbolic Matrix(601,660,438,481) (-11/10,-1/1) -> (59/43,11/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(1139,-1260,706,-781) (1/1,10/9) -> (50/31,121/75) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(1921,-2220,726,-839) (15/13,22/19) -> (82/31,45/17) Hyperbolic Matrix(359,-420,206,-241) (7/6,20/17) -> (40/23,7/4) Hyperbolic Matrix(1261,-1500,554,-659) (19/16,6/5) -> (66/29,41/18) Hyperbolic Matrix(1439,-1740,894,-1081) (6/5,23/19) -> (37/23,66/41) Hyperbolic Matrix(841,-1020,296,-359) (23/19,17/14) -> (17/6,37/13) Hyperbolic Matrix(1321,-1620,782,-959) (11/9,27/22) -> (27/16,49/29) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(659,-840,142,-181) (14/11,23/18) -> (37/8,14/3) Hyperbolic Matrix(1439,-1860,1022,-1321) (31/24,22/17) -> (38/27,31/22) Hyperbolic Matrix(4441,-5760,1202,-1559) (35/27,48/37) -> (48/13,85/23) Hyperbolic Matrix(1141,-1500,410,-539) (21/16,4/3) -> (64/23,39/14) Hyperbolic Matrix(1199,-1620,356,-481) (4/3,23/17) -> (37/11,64/19) Hyperbolic Matrix(839,-1140,354,-481) (19/14,15/11) -> (45/19,19/8) Hyperbolic Matrix(1141,-1560,482,-659) (15/11,26/19) -> (26/11,45/19) Hyperbolic Matrix(3901,-5340,2410,-3299) (26/19,63/46) -> (123/76,34/21) Hyperbolic Matrix(4201,-5760,962,-1319) (37/27,48/35) -> (48/11,83/19) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(1859,-2580,1168,-1621) (43/31,25/18) -> (35/22,43/27) Hyperbolic Matrix(9361,-13020,3968,-5519) (89/64,32/23) -> (92/39,151/64) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(5939,-8400,3352,-4741) (41/29,58/41) -> (62/35,101/57) Hyperbolic Matrix(2579,-3660,804,-1141) (61/43,44/31) -> (16/5,61/19) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(4379,-6300,1794,-2581) (23/16,59/41) -> (61/25,83/34) Hyperbolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(901,-1320,286,-419) (19/13,22/15) -> (22/7,41/13) Hyperbolic Matrix(661,-1020,116,-179) (20/13,17/11) -> (17/3,40/7) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(1079,-1680,386,-601) (14/9,53/34) -> (67/24,14/5) Hyperbolic Matrix(961,-1500,230,-359) (39/25,25/16) -> (25/6,21/5) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(4679,-7440,2642,-4201) (62/39,35/22) -> (85/48,62/35) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(4919,-7920,2162,-3481) (66/41,29/18) -> (91/40,66/29) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(10979,-18000,4502,-7381) (100/61,41/25) -> (139/57,100/41) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(2099,-3540,890,-1501) (32/19,27/16) -> (33/14,92/39) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(3719,-6300,1134,-1921) (22/13,61/36) -> (59/18,82/25) Hyperbolic Matrix(9061,-15360,2654,-4499) (100/59,39/23) -> (99/29,140/41) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(659,-1140,174,-301) (19/11,26/15) -> (34/9,19/5) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(5281,-9360,2166,-3839) (101/57,39/22) -> (39/16,139/57) Hyperbolic Matrix(841,-1500,134,-239) (41/23,25/14) -> (25/4,19/3) Hyperbolic Matrix(2279,-4080,1006,-1801) (34/19,43/24) -> (77/34,34/15) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(3659,-8400,1072,-2461) (39/17,62/27) -> (58/17,99/29) Hyperbolic Matrix(3239,-7440,1202,-2761) (62/27,23/10) -> (97/36,62/23) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(3839,-9840,1124,-2881) (41/16,100/39) -> (140/41,41/12) Hyperbolic Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(2041,-5340,550,-1439) (34/13,89/34) -> (89/24,26/7) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(959,-2580,268,-721) (8/3,35/13) -> (25/7,68/19) Hyperbolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(61,-360,10,-59) (29/5,6/1) -> (6/1,31/5) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(121,1260,-46,-479) -> Matrix(1,-2,-2,5) Matrix(119,1140,50,479) -> Matrix(1,6,0,1) Matrix(61,540,34,301) -> Matrix(1,2,0,1) Matrix(179,1500,50,419) -> Matrix(1,2,0,1) Matrix(61,480,-38,-299) -> Matrix(1,0,0,1) Matrix(299,2220,-186,-1381) -> Matrix(1,14,0,1) Matrix(59,420,42,299) -> Matrix(1,6,0,1) Matrix(61,420,-26,-179) -> Matrix(1,2,0,1) Matrix(299,1980,172,1139) -> Matrix(1,2,-2,-3) Matrix(301,1980,64,421) -> Matrix(7,10,2,3) Matrix(121,780,56,361) -> Matrix(1,2,0,1) Matrix(301,1920,66,421) -> Matrix(3,4,2,3) Matrix(239,1500,-134,-841) -> Matrix(1,2,0,1) Matrix(301,1740,-114,-659) -> Matrix(3,10,-4,-13) Matrix(179,1020,-116,-661) -> Matrix(1,2,0,1) Matrix(181,1020,96,541) -> Matrix(1,2,0,1) Matrix(299,1680,160,899) -> Matrix(1,4,0,1) Matrix(419,2340,118,659) -> Matrix(1,6,0,1) Matrix(539,3000,334,1859) -> Matrix(1,4,-2,-7) Matrix(299,1620,-122,-661) -> Matrix(1,2,-4,-7) Matrix(301,1620,212,1141) -> Matrix(7,10,2,3) Matrix(181,960,102,541) -> Matrix(1,0,0,1) Matrix(241,1260,92,481) -> Matrix(1,2,2,5) Matrix(299,1440,-212,-1021) -> Matrix(3,8,-2,-5) Matrix(301,1440,88,421) -> Matrix(3,4,2,3) Matrix(241,1140,-152,-719) -> Matrix(1,6,0,1) Matrix(181,840,-142,-659) -> Matrix(7,16,-4,-9) Matrix(301,1380,118,541) -> Matrix(1,2,-2,-3) Matrix(421,1920,66,301) -> Matrix(3,4,2,3) Matrix(659,3000,382,1739) -> Matrix(3,4,2,3) Matrix(121,540,54,241) -> Matrix(1,2,2,5) Matrix(421,1860,-122,-539) -> Matrix(1,2,-2,-3) Matrix(301,1320,96,421) -> Matrix(3,4,2,3) Matrix(781,3420,562,2461) -> Matrix(1,2,0,1) Matrix(1319,5760,-962,-4201) -> Matrix(1,0,0,1) Matrix(1321,5760,358,1561) -> Matrix(1,0,0,1) Matrix(1379,6000,510,2219) -> Matrix(3,8,4,11) Matrix(181,780,42,181) -> Matrix(1,2,0,1) Matrix(239,1020,56,239) -> Matrix(1,6,0,1) Matrix(241,1020,142,601) -> Matrix(1,2,0,1) Matrix(359,1500,-230,-961) -> Matrix(1,2,0,1) Matrix(421,1620,-296,-1139) -> Matrix(9,14,-2,-3) Matrix(361,1380,220,841) -> Matrix(1,2,-2,-3) Matrix(301,1140,-174,-659) -> Matrix(1,2,-2,-3) Matrix(419,1560,-242,-901) -> Matrix(1,0,0,1) Matrix(1439,5340,-550,-2041) -> Matrix(1,2,-4,-7) Matrix(421,1560,146,541) -> Matrix(1,0,2,1) Matrix(1559,5760,-1202,-4441) -> Matrix(1,0,0,1) Matrix(1561,5760,358,1321) -> Matrix(1,0,0,1) Matrix(179,660,16,59) -> Matrix(1,2,0,1) Matrix(181,660,-82,-299) -> Matrix(1,2,0,1) Matrix(299,1080,116,419) -> Matrix(3,4,2,3) Matrix(601,2160,234,841) -> Matrix(1,0,2,1) Matrix(1021,3660,720,2581) -> Matrix(5,2,2,1) Matrix(721,2580,-268,-959) -> Matrix(1,2,-2,-3) Matrix(959,3420,740,2639) -> Matrix(1,2,0,1) Matrix(4499,16020,2780,9899) -> Matrix(1,-2,-2,5) Matrix(3659,13020,-2108,-7501) -> Matrix(1,10,0,1) Matrix(659,2340,118,419) -> Matrix(1,6,0,1) Matrix(661,2340,424,1501) -> Matrix(1,2,2,5) Matrix(121,420,104,361) -> Matrix(5,6,4,5) Matrix(419,1440,-332,-1141) -> Matrix(3,8,-2,-5) Matrix(421,1440,88,301) -> Matrix(3,4,2,3) Matrix(2461,8400,-1072,-3659) -> Matrix(3,4,-4,-5) Matrix(299,1020,158,539) -> Matrix(1,2,-2,-3) Matrix(1079,3660,778,2639) -> Matrix(1,2,-2,-3) Matrix(1081,3660,-744,-2519) -> Matrix(7,10,2,3) Matrix(479,1620,390,1319) -> Matrix(7,10,2,3) Matrix(179,600,-54,-181) -> Matrix(3,4,-4,-5) Matrix(419,1380,-310,-1021) -> Matrix(1,-2,0,1) Matrix(1921,6300,-1134,-3719) -> Matrix(1,2,0,1) Matrix(1319,4320,476,1559) -> Matrix(1,4,0,1) Matrix(239,780,110,359) -> Matrix(1,2,0,1) Matrix(241,780,-148,-479) -> Matrix(1,2,-2,-3) Matrix(301,960,132,421) -> Matrix(1,0,2,1) Matrix(419,1320,-286,-901) -> Matrix(5,8,-2,-3) Matrix(421,1320,96,301) -> Matrix(3,4,2,3) Matrix(541,1560,146,421) -> Matrix(1,0,2,1) Matrix(481,1380,84,241) -> Matrix(5,2,2,1) Matrix(359,1020,-296,-841) -> Matrix(3,2,-2,-1) Matrix(361,1020,-212,-599) -> Matrix(1,2,0,1) Matrix(601,1680,-386,-1079) -> Matrix(1,0,2,1) Matrix(839,2340,602,1679) -> Matrix(3,-2,2,-1) Matrix(539,1500,-410,-1141) -> Matrix(3,2,-2,-1) Matrix(1081,3000,476,1321) -> Matrix(1,0,2,1) Matrix(1559,4320,476,1319) -> Matrix(1,4,0,1) Matrix(239,660,130,359) -> Matrix(1,2,0,1) Matrix(241,660,88,241) -> Matrix(5,6,4,5) Matrix(419,1140,154,419) -> Matrix(11,10,12,11) Matrix(421,1140,-332,-899) -> Matrix(7,6,-6,-5) Matrix(1801,4860,534,1441) -> Matrix(25,18,18,13) Matrix(5519,14880,-3472,-9361) -> Matrix(37,24,20,13) Matrix(2761,7440,-1202,-3239) -> Matrix(13,8,-18,-11) Matrix(179,480,22,59) -> Matrix(1,0,2,1) Matrix(181,480,-158,-419) -> Matrix(1,0,0,1) Matrix(3001,7920,-1682,-4439) -> Matrix(11,8,4,3) Matrix(1139,3000,478,1259) -> Matrix(7,4,-2,-1) Matrix(2099,5520,570,1499) -> Matrix(9,4,2,1) Matrix(1141,3000,936,2461) -> Matrix(11,4,8,3) Matrix(481,1260,92,241) -> Matrix(5,2,2,1) Matrix(779,2040,160,419) -> Matrix(9,4,2,1) Matrix(6121,16020,4402,11521) -> Matrix(7,2,10,3) Matrix(781,2040,-482,-1259) -> Matrix(1,0,6,1) Matrix(301,780,-208,-539) -> Matrix(1,-2,0,1) Matrix(419,1080,116,299) -> Matrix(3,4,2,3) Matrix(841,2160,234,601) -> Matrix(1,0,2,1) Matrix(4679,12000,1918,4919) -> Matrix(5,4,6,5) Matrix(7021,18000,-4142,-10619) -> Matrix(1,0,2,1) Matrix(539,1380,398,1019) -> Matrix(5,2,2,1) Matrix(541,1380,118,301) -> Matrix(3,-2,2,-1) Matrix(119,300,-48,-121) -> Matrix(1,2,-2,-3) Matrix(1441,3540,-830,-2039) -> Matrix(5,2,2,1) Matrix(1201,2940,-980,-2399) -> Matrix(5,-2,-2,1) Matrix(2581,6300,-1794,-4379) -> Matrix(3,2,-2,-1) Matrix(4919,12000,1918,4679) -> Matrix(5,4,6,5) Matrix(6299,15360,-4454,-10861) -> Matrix(7,4,-2,-1) Matrix(419,1020,320,779) -> Matrix(1,2,0,1) Matrix(421,1020,-272,-659) -> Matrix(3,2,-2,-1) Matrix(299,720,174,419) -> Matrix(1,0,4,1) Matrix(301,720,176,421) -> Matrix(1,0,-2,1) Matrix(1259,3000,478,1139) -> Matrix(1,-4,2,-7) Matrix(479,1140,50,119) -> Matrix(1,6,0,1) Matrix(1261,3000,984,2341) -> Matrix(1,4,0,1) Matrix(481,1140,-354,-839) -> Matrix(1,-2,0,1) Matrix(1499,3540,838,1979) -> Matrix(1,2,-2,-3) Matrix(1679,3960,-1018,-2401) -> Matrix(5,4,-4,-3) Matrix(841,1980,714,1681) -> Matrix(5,2,2,1) Matrix(181,420,78,181) -> Matrix(1,2,0,1) Matrix(599,1380,260,599) -> Matrix(7,6,8,7) Matrix(2219,5100,600,1379) -> Matrix(3,2,4,3) Matrix(4079,9360,-2406,-5521) -> Matrix(1,0,2,1) Matrix(419,960,340,779) -> Matrix(1,0,2,1) Matrix(421,960,132,301) -> Matrix(1,0,2,1) Matrix(659,1500,-554,-1261) -> Matrix(3,2,-2,-1) Matrix(1321,3000,476,1081) -> Matrix(1,0,2,1) Matrix(1561,3540,900,2041) -> Matrix(5,2,2,1) Matrix(1801,4080,-1006,-2279) -> Matrix(1,0,4,1) Matrix(239,540,212,479) -> Matrix(1,2,0,1) Matrix(241,540,54,121) -> Matrix(5,2,2,1) Matrix(539,1200,296,659) -> Matrix(1,0,8,1) Matrix(541,1200,298,661) -> Matrix(1,0,-6,1) Matrix(301,660,192,421) -> Matrix(1,2,0,1) Matrix(359,780,110,239) -> Matrix(1,2,0,1) Matrix(361,780,56,121) -> Matrix(1,2,0,1) Matrix(781,1680,642,1381) -> Matrix(3,4,2,3) Matrix(479,1020,394,839) -> Matrix(1,2,0,1) Matrix(481,1020,340,721) -> Matrix(5,2,2,1) Matrix(539,1020,158,299) -> Matrix(3,-2,2,-1) Matrix(541,1020,96,181) -> Matrix(1,2,0,1) Matrix(899,1680,160,299) -> Matrix(1,4,0,1) Matrix(419,780,354,659) -> Matrix(1,2,0,1) Matrix(421,780,292,541) -> Matrix(1,2,0,1) Matrix(359,660,130,239) -> Matrix(1,2,0,1) Matrix(361,660,-262,-479) -> Matrix(3,2,-2,-1) Matrix(959,1740,264,479) -> Matrix(11,-2,6,-1) Matrix(299,540,232,419) -> Matrix(3,-2,2,-1) Matrix(301,540,34,61) -> Matrix(1,2,0,1) Matrix(8039,14400,3550,6359) -> Matrix(1,0,8,1) Matrix(8041,14400,3552,6361) -> Matrix(1,0,-6,1) Matrix(1979,3540,838,1499) -> Matrix(3,-2,2,-1) Matrix(1679,3000,1074,1919) -> Matrix(1,0,0,1) Matrix(1681,3000,404,721) -> Matrix(5,-8,2,-3) Matrix(539,960,370,659) -> Matrix(1,0,0,1) Matrix(541,960,102,181) -> Matrix(1,0,0,1) Matrix(4741,8400,-3352,-5939) -> Matrix(1,-4,0,1) Matrix(4201,7440,-2642,-4679) -> Matrix(3,-8,2,-5) Matrix(781,1380,442,781) -> Matrix(1,-6,0,1) Matrix(239,420,136,239) -> Matrix(1,2,0,1) Matrix(241,420,-206,-359) -> Matrix(3,2,-2,-1) Matrix(29039,50400,8158,14159) -> Matrix(1,-28,0,1) Matrix(21781,37800,6120,10621) -> Matrix(1,24,0,1) Matrix(2041,3540,900,1561) -> Matrix(1,2,2,5) Matrix(1739,3000,382,659) -> Matrix(3,4,2,3) Matrix(661,1140,592,1021) -> Matrix(5,6,4,5) Matrix(1741,3000,1080,1861) -> Matrix(5,4,-4,-3) Matrix(419,720,174,299) -> Matrix(1,0,4,1) Matrix(421,720,176,301) -> Matrix(1,0,-2,1) Matrix(2041,3480,634,1081) -> Matrix(9,-8,8,-7) Matrix(5879,10020,1830,3119) -> Matrix(13,-14,14,-15) Matrix(2641,4500,564,961) -> Matrix(11,-14,4,-5) Matrix(601,1020,142,241) -> Matrix(1,2,0,1) Matrix(7081,12000,4320,7321) -> Matrix(1,-4,0,1) Matrix(2161,3660,284,481) -> Matrix(1,-6,0,1) Matrix(959,1620,-782,-1321) -> Matrix(5,-2,-2,1) Matrix(179,300,-108,-181) -> Matrix(1,-2,0,1) Matrix(3241,5340,-2330,-3839) -> Matrix(7,6,-6,-5) Matrix(839,1380,656,1079) -> Matrix(5,2,2,1) Matrix(841,1380,220,361) -> Matrix(3,-2,2,-1) Matrix(6001,9840,-4244,-6959) -> Matrix(1,-4,0,1) Matrix(7321,12000,4320,7081) -> Matrix(1,-4,0,1) Matrix(1319,2160,952,1559) -> Matrix(1,0,0,1) Matrix(661,1080,478,781) -> Matrix(1,4,0,1) Matrix(2281,3720,810,1321) -> Matrix(7,8,6,7) Matrix(4859,7920,-3424,-5581) -> Matrix(19,16,-6,-5) Matrix(2219,3600,850,1379) -> Matrix(1,0,10,1) Matrix(2221,3600,852,1381) -> Matrix(1,0,-8,1) Matrix(3299,5340,-2410,-3901) -> Matrix(5,-2,-2,1) Matrix(4079,6600,1186,1919) -> Matrix(7,-4,2,-1) Matrix(779,1260,630,1019) -> Matrix(3,-2,2,-1) Matrix(1859,3000,334,539) -> Matrix(7,-4,2,-1) Matrix(781,1260,-706,-1139) -> Matrix(3,-2,-4,3) Matrix(1861,3000,1080,1741) -> Matrix(3,-4,4,-5) Matrix(1081,1740,-894,-1439) -> Matrix(3,-10,-2,7) Matrix(3059,4920,932,1499) -> Matrix(1,-4,0,1) Matrix(1621,2580,-1168,-1859) -> Matrix(1,-2,0,1) Matrix(3961,6300,906,1441) -> Matrix(1,-2,2,-3) Matrix(36239,57600,13438,21359) -> Matrix(55,-108,82,-161) Matrix(36241,57600,13440,21361) -> Matrix(53,-108,80,-163) Matrix(2039,3240,528,839) -> Matrix(7,-16,4,-9) Matrix(1739,2760,264,419) -> Matrix(3,-8,2,-5) Matrix(3781,6000,2912,4621) -> Matrix(3,-8,2,-5) Matrix(2761,4380,984,1561) -> Matrix(3,-10,4,-13) Matrix(721,1140,456,721) -> Matrix(1,-10,0,1) Matrix(419,660,266,419) -> Matrix(1,6,0,1) Matrix(421,660,192,301) -> Matrix(1,2,0,1) Matrix(2761,4320,1918,3001) -> Matrix(3,4,2,3) Matrix(1919,3000,1074,1679) -> Matrix(1,0,0,1) Matrix(1921,3000,308,481) -> Matrix(1,0,2,1) Matrix(7379,11520,2190,3419) -> Matrix(5,-4,4,-3) Matrix(1501,2340,424,661) -> Matrix(5,2,2,1) Matrix(9239,14400,3310,5159) -> Matrix(1,0,10,1) Matrix(9241,14400,3312,5161) -> Matrix(1,0,-8,1) Matrix(2819,4380,1042,1619) -> Matrix(3,-10,4,-13) Matrix(5759,8940,1700,2639) -> Matrix(3,-26,2,-17) Matrix(2399,3720,928,1439) -> Matrix(1,8,0,1) Matrix(779,1200,272,419) -> Matrix(1,0,2,1) Matrix(781,1200,274,421) -> Matrix(1,0,0,1) Matrix(1019,1560,744,1139) -> Matrix(1,0,0,1) Matrix(899,1320,694,1019) -> Matrix(1,4,0,1) Matrix(2459,3600,778,1139) -> Matrix(5,12,2,5) Matrix(2461,3600,780,1141) -> Matrix(7,12,4,7) Matrix(659,960,370,539) -> Matrix(1,0,0,1) Matrix(6901,10020,2852,4141) -> Matrix(1,-14,2,-27) Matrix(2399,3480,992,1439) -> Matrix(1,8,2,17) Matrix(541,780,292,421) -> Matrix(1,2,0,1) Matrix(3001,4320,1918,2761) -> Matrix(3,4,2,3) Matrix(3421,4920,1294,1861) -> Matrix(5,4,6,5) Matrix(419,600,-294,-421) -> Matrix(1,-4,0,1) Matrix(8101,11520,2912,4141) -> Matrix(1,4,2,9) Matrix(3419,4860,2152,3059) -> Matrix(5,18,-2,-7) Matrix(1141,1620,212,301) -> Matrix(3,10,2,7) Matrix(6301,8940,2242,3181) -> Matrix(9,26,10,29) Matrix(2581,3660,720,1021) -> Matrix(1,2,2,5) Matrix(721,1020,340,481) -> Matrix(1,2,2,5) Matrix(1019,1440,806,1139) -> Matrix(1,4,0,1) Matrix(4681,6600,1788,2521) -> Matrix(3,4,8,11) Matrix(1321,1860,-1022,-1439) -> Matrix(1,-2,0,1) Matrix(1679,2340,602,839) -> Matrix(1,2,-2,-3) Matrix(1681,2340,1380,1921) -> Matrix(5,6,4,5) Matrix(27179,37800,11518,16019) -> Matrix(23,24,22,23) Matrix(36241,50400,15360,21361) -> Matrix(29,28,30,29) Matrix(7681,10680,2072,2881) -> Matrix(1,0,2,1) Matrix(2461,3420,562,781) -> Matrix(1,2,0,1) Matrix(1081,1500,952,1321) -> Matrix(1,2,0,1) Matrix(2639,3660,778,1079) -> Matrix(3,-2,2,-1) Matrix(1559,2160,952,1319) -> Matrix(1,0,0,1) Matrix(781,1080,478,661) -> Matrix(1,4,0,1) Matrix(1261,1740,566,781) -> Matrix(1,2,6,13) Matrix(4021,5520,2492,3421) -> Matrix(3,4,-4,-5) Matrix(4199,5760,3236,4439) -> Matrix(1,0,2,1) Matrix(3721,5100,2102,2881) -> Matrix(1,-2,0,1) Matrix(1139,1560,744,1019) -> Matrix(1,0,0,1) Matrix(7799,10680,2190,2999) -> Matrix(1,0,0,1) Matrix(659,900,-484,-661) -> Matrix(1,-2,0,1) Matrix(1019,1380,398,539) -> Matrix(1,2,2,5) Matrix(2401,3240,890,1201) -> Matrix(7,16,10,23) Matrix(179,240,44,59) -> Matrix(1,4,0,1) Matrix(181,240,46,61) -> Matrix(3,4,2,3) Matrix(2279,3000,1002,1319) -> Matrix(5,8,8,13) Matrix(779,1020,320,419) -> Matrix(1,2,0,1) Matrix(781,1020,598,781) -> Matrix(5,6,4,5) Matrix(599,780,460,599) -> Matrix(1,2,0,1) Matrix(2819,3660,600,779) -> Matrix(7,10,2,3) Matrix(4439,5760,3236,4199) -> Matrix(1,0,2,1) Matrix(4859,6300,1804,2339) -> Matrix(1,-2,2,-3) Matrix(2639,3420,740,959) -> Matrix(1,2,0,1) Matrix(1019,1320,694,899) -> Matrix(1,4,0,1) Matrix(1021,1320,140,181) -> Matrix(1,8,0,1) Matrix(419,540,232,299) -> Matrix(1,2,-2,-3) Matrix(2341,3000,984,1261) -> Matrix(1,4,0,1) Matrix(1499,1920,1264,1619) -> Matrix(1,4,0,1) Matrix(1079,1380,656,839) -> Matrix(1,2,2,5) Matrix(2819,3600,610,779) -> Matrix(25,52,12,25) Matrix(2821,3600,612,781) -> Matrix(27,52,14,27) Matrix(3539,4500,1462,1859) -> Matrix(9,14,16,25) Matrix(2881,3660,662,841) -> Matrix(7,10,2,3) Matrix(1559,1980,1322,1679) -> Matrix(7,10,2,3) Matrix(1139,1440,806,1019) -> Matrix(1,4,0,1) Matrix(1621,2040,1002,1261) -> Matrix(3,4,-4,-5) Matrix(1019,1260,630,779) -> Matrix(1,2,-2,-3) Matrix(779,960,340,419) -> Matrix(1,0,2,1) Matrix(1319,1620,390,479) -> Matrix(3,10,2,7) Matrix(2939,3600,538,659) -> Matrix(21,44,10,21) Matrix(2941,3600,540,661) -> Matrix(23,44,12,23) Matrix(2461,3000,936,1141) -> Matrix(3,4,8,11) Matrix(1921,2340,1380,1681) -> Matrix(5,6,4,5) Matrix(1381,1680,642,781) -> Matrix(3,4,2,3) Matrix(839,1020,394,479) -> Matrix(1,2,0,1) Matrix(1139,1380,742,899) -> Matrix(1,2,-2,-3) Matrix(299,360,-250,-301) -> Matrix(3,4,-4,-5) Matrix(2519,3000,906,1079) -> Matrix(1,0,0,1) Matrix(1619,1920,1264,1499) -> Matrix(1,4,0,1) Matrix(659,780,354,419) -> Matrix(1,2,0,1) Matrix(2341,2760,866,1021) -> Matrix(3,8,4,11) Matrix(1019,1200,152,179) -> Matrix(5,12,2,5) Matrix(1021,1200,154,181) -> Matrix(7,12,4,7) Matrix(1139,1320,258,299) -> Matrix(7,8,6,7) Matrix(779,900,-676,-781) -> Matrix(13,14,-14,-15) Matrix(3179,3660,1302,1499) -> Matrix(7,6,8,7) Matrix(421,480,264,301) -> Matrix(1,0,0,1) Matrix(479,540,212,239) -> Matrix(1,2,0,1) Matrix(1021,1140,592,661) -> Matrix(5,6,4,5) Matrix(601,660,438,481) -> Matrix(1,2,0,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(1139,-1260,706,-781) -> Matrix(3,-2,-4,3) Matrix(419,-480,158,-181) -> Matrix(1,0,0,1) Matrix(1921,-2220,726,-839) -> Matrix(13,-14,14,-15) Matrix(359,-420,206,-241) -> Matrix(1,-2,2,-3) Matrix(1261,-1500,554,-659) -> Matrix(1,-2,2,-3) Matrix(1439,-1740,894,-1081) -> Matrix(7,-10,-2,3) Matrix(841,-1020,296,-359) -> Matrix(1,-2,2,-3) Matrix(1321,-1620,782,-959) -> Matrix(1,-2,-2,5) Matrix(1141,-1440,332,-419) -> Matrix(5,-8,2,-3) Matrix(899,-1140,332,-421) -> Matrix(5,-6,6,-7) Matrix(659,-840,142,-181) -> Matrix(9,-16,4,-7) Matrix(1439,-1860,1022,-1321) -> Matrix(1,-2,0,1) Matrix(4441,-5760,1202,-1559) -> Matrix(1,0,0,1) Matrix(1141,-1500,410,-539) -> Matrix(1,-2,2,-3) Matrix(1199,-1620,356,-481) -> Matrix(5,-14,4,-11) Matrix(839,-1140,354,-481) -> Matrix(1,-2,0,1) Matrix(1141,-1560,482,-659) -> Matrix(1,0,0,1) Matrix(3901,-5340,2410,-3299) -> Matrix(1,-2,-2,5) Matrix(4201,-5760,962,-1319) -> Matrix(1,0,0,1) Matrix(479,-660,262,-361) -> Matrix(1,-2,2,-3) Matrix(1859,-2580,1168,-1621) -> Matrix(1,-2,0,1) Matrix(9361,-13020,3968,-5519) -> Matrix(9,-10,10,-11) Matrix(1021,-1440,212,-299) -> Matrix(5,-8,2,-3) Matrix(5939,-8400,3352,-4741) -> Matrix(1,-4,0,1) Matrix(2579,-3660,804,-1141) -> Matrix(3,-10,4,-13) Matrix(421,-600,294,-419) -> Matrix(1,-4,0,1) Matrix(961,-1380,250,-359) -> Matrix(3,-2,2,-1) Matrix(4379,-6300,1794,-2581) -> Matrix(1,-2,2,-3) Matrix(539,-780,208,-301) -> Matrix(1,-2,0,1) Matrix(901,-1320,286,-419) -> Matrix(3,-8,2,-5) Matrix(661,-1020,116,-179) -> Matrix(1,2,0,1) Matrix(659,-1020,272,-421) -> Matrix(1,-2,2,-3) Matrix(1079,-1680,386,-601) -> Matrix(1,0,2,1) Matrix(961,-1500,230,-359) -> Matrix(1,2,0,1) Matrix(719,-1140,152,-241) -> Matrix(1,6,0,1) Matrix(9361,-14880,3472,-5519) -> Matrix(13,24,20,37) Matrix(4679,-7440,2642,-4201) -> Matrix(5,8,-2,-3) Matrix(299,-480,38,-61) -> Matrix(1,0,0,1) Matrix(4919,-7920,2162,-3481) -> Matrix(3,8,4,11) Matrix(1259,-2040,482,-781) -> Matrix(1,0,6,1) Matrix(479,-780,148,-241) -> Matrix(3,-2,2,-1) Matrix(10979,-18000,4502,-7381) -> Matrix(1,0,2,1) Matrix(181,-300,108,-179) -> Matrix(1,-2,0,1) Matrix(2099,-3540,890,-1501) -> Matrix(3,2,4,3) Matrix(1739,-2940,320,-541) -> Matrix(7,-2,4,-1) Matrix(3719,-6300,1134,-1921) -> Matrix(1,2,0,1) Matrix(9061,-15360,2654,-4499) -> Matrix(3,4,2,3) Matrix(599,-1020,212,-361) -> Matrix(1,2,0,1) Matrix(659,-1140,174,-301) -> Matrix(3,-2,2,-1) Matrix(2281,-3960,898,-1559) -> Matrix(1,4,0,1) Matrix(5281,-9360,2166,-3839) -> Matrix(1,0,2,1) Matrix(841,-1500,134,-239) -> Matrix(1,2,0,1) Matrix(2279,-4080,1006,-1801) -> Matrix(1,0,4,1) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) Matrix(3659,-8400,1072,-2461) -> Matrix(5,-4,4,-3) Matrix(3239,-7440,1202,-2761) -> Matrix(11,-8,18,-13) Matrix(179,-420,26,-61) -> Matrix(1,2,0,1) Matrix(661,-1620,122,-299) -> Matrix(7,-2,4,-1) Matrix(121,-300,48,-119) -> Matrix(3,-2,2,-1) Matrix(2099,-5340,590,-1501) -> Matrix(1,6,0,1) Matrix(3839,-9840,1124,-2881) -> Matrix(5,-4,4,-3) Matrix(3061,-7920,904,-2339) -> Matrix(3,16,2,11) Matrix(2041,-5340,550,-1439) -> Matrix(7,-2,4,-1) Matrix(479,-1260,46,-121) -> Matrix(5,-2,-2,1) Matrix(659,-1740,114,-301) -> Matrix(13,-10,4,-3) Matrix(959,-2580,268,-721) -> Matrix(3,-2,2,-1) Matrix(181,-600,54,-179) -> Matrix(5,-4,4,-3) Matrix(539,-1860,122,-421) -> Matrix(3,-2,2,-1) Matrix(241,-900,64,-239) -> Matrix(3,-2,2,-1) Matrix(61,-360,10,-59) -> Matrix(1,-4,0,1) Matrix(121,-900,16,-119) -> Matrix(1,-14,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 128 Degree of the the map X: 128 Degree of the the map Y: 384 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 1152 Minimal number of generators: 193 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: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 10/9 15/13 20/17 6/5 5/4 4/3 15/11 25/18 10/7 3/2 5/3 12/7 20/11 15/8 2/1 15/7 24/11 20/9 120/53 30/13 12/5 100/41 5/2 100/39 18/7 60/23 8/3 240/89 30/11 120/43 45/16 20/7 3/1 60/19 16/5 45/14 36/11 10/3 24/7 210/59 25/7 18/5 48/13 26/7 15/4 4/1 25/6 21/5 30/7 48/11 9/2 60/13 14/3 24/5 5/1 21/4 16/3 27/5 60/11 28/5 40/7 29/5 6/1 25/4 19/3 32/5 13/2 20/3 27/4 7/1 22/3 15/2 23/3 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/1 10/9 1/1 9/8 3/2 17/15 3/1 8/7 0/1 15/13 1/1 22/19 8/7 6/5 7/6 3/2 20/17 2/1 33/28 1/0 13/11 1/1 32/27 0/1 19/16 1/0 6/5 1/1 23/19 1/1 17/14 3/2 45/37 1/1 28/23 2/1 39/32 3/2 11/9 5/3 27/22 1/0 16/13 0/1 21/17 1/1 5/4 1/1 24/19 2/1 19/15 1/1 14/11 8/5 2/1 23/18 9/4 32/25 4/1 41/32 1/0 9/7 1/1 31/24 11/4 22/17 0/1 2/1 57/44 1/0 35/27 1/0 48/37 0/1 61/47 1/1 13/10 1/0 30/23 1/1 17/13 1/1 21/16 3/2 4/3 2/1 23/17 1/1 19/14 1/0 15/11 1/0 26/19 0/1 2/1 63/46 1/0 37/27 1/1 48/35 0/1 59/43 1/1 11/8 1/0 29/21 13/5 18/13 1/0 61/44 1/0 43/31 -1/1 25/18 1/1 57/41 1/1 89/64 9/10 32/23 4/3 39/28 3/2 7/5 3/1 38/27 -2/1 0/1 31/22 3/4 24/17 2/1 41/29 3/1 58/41 2/1 8/3 17/12 1/0 61/43 3/1 44/31 10/3 27/19 3/1 10/7 1/0 33/23 -1/1 23/16 1/2 59/41 1/1 36/25 2/1 13/9 1/1 16/11 0/1 19/13 1/1 22/15 2/1 4/1 3/2 1/0 23/15 -1/1 20/13 0/1 17/11 1/1 14/9 -2/1 0/1 53/34 1/4 39/25 1/1 25/16 1/1 61/39 1/1 36/23 2/1 11/7 3/1 30/19 1/0 19/12 1/0 27/17 -3/1 89/56 -21/10 62/39 -2/1 -12/7 35/22 -1/1 43/27 -3/1 8/5 0/1 37/23 -3/1 66/41 -3/1 29/18 -7/4 50/31 -1/1 121/75 -1/1 71/44 -3/4 21/13 -1/1 55/34 -1/1 89/55 -7/13 123/76 -1/2 34/21 -2/5 0/1 13/8 1/2 31/19 7/5 18/11 1/0 59/36 1/0 100/61 -2/1 41/25 -1/1 23/14 -1/2 28/17 2/3 5/3 1/0 32/19 -4/3 27/16 -1/2 49/29 -1/5 22/13 0/1 2/1 61/36 1/0 100/59 -2/1 39/23 -1/1 17/10 1/0 29/17 -5/7 12/7 0/1 31/18 5/8 50/29 1/1 69/40 3/2 19/11 1/1 26/15 0/1 2/1 59/34 1/0 33/19 -1/1 40/23 0/1 7/4 1/0 30/17 1/0 23/13 -3/1 85/48 -3/1 62/35 -2/1 -4/3 101/57 -1/1 39/22 1/0 16/9 0/1 41/23 -1/1 25/14 -1/1 59/33 -1/1 34/19 -2/3 0/1 43/24 1/2 9/5 -1/1 29/16 -3/10 20/11 0/1 31/17 3/11 11/6 1/2 24/13 0/1 13/7 1/1 28/15 2/1 15/8 1/0 17/9 -1/1 2/1 0/1 2/1 17/8 1/2 15/7 1/1 28/13 2/1 13/6 1/0 24/11 0/1 11/5 -1/1 20/9 0/1 29/13 3/13 9/4 1/2 43/19 -1/1 120/53 0/1 77/34 1/6 34/15 0/1 2/5 59/26 1/2 25/11 1/2 91/40 11/16 66/29 1/1 41/18 1/2 16/7 0/1 39/17 1/1 62/27 4/7 2/3 23/10 3/4 30/13 1/1 7/3 1/1 33/14 1/2 92/39 6/7 151/64 19/20 210/89 1/1 59/25 1/1 26/11 0/1 2/1 45/19 1/0 19/8 1/0 69/29 3/1 50/21 1/0 31/13 -5/3 12/5 0/1 29/12 5/12 75/31 1/2 121/50 1/2 46/19 4/7 2/3 17/7 1/1 39/16 1/2 139/57 1/1 100/41 2/3 61/25 1/1 83/34 3/4 22/9 0/1 2/1 27/11 1/3 5/2 1/1 33/13 3/1 61/24 1/0 28/11 -2/1 23/9 1/3 41/16 1/2 100/39 2/3 59/23 1/1 18/7 1/1 31/12 7/2 75/29 1/0 44/17 -2/1 13/5 -1/1 60/23 0/1 47/18 1/8 34/13 0/1 2/7 89/34 7/20 55/21 1/2 21/8 1/2 71/27 3/7 50/19 1/2 29/11 7/11 37/14 3/4 82/31 6/7 8/9 45/17 1/1 8/3 0/1 35/13 1/2 97/36 1/2 62/23 12/19 2/3 151/56 33/50 240/89 2/3 89/33 21/31 27/10 3/4 73/27 5/7 119/44 3/4 46/17 10/13 4/5 19/7 1/1 30/11 1/1 11/4 3/2 36/13 2/1 61/22 1/0 25/9 1/0 89/32 -1/6 64/23 0/1 39/14 1/0 53/19 -1/3 120/43 0/1 67/24 1/6 14/5 0/1 2/3 59/21 1/1 45/16 1/1 31/11 9/7 17/6 1/0 37/13 1/1 20/7 0/1 23/8 1/2 3/1 1/1 22/7 4/3 2/1 41/13 5/3 60/19 2/1 19/6 1/0 16/5 0/1 61/19 1/1 45/14 1/1 29/9 11/9 13/4 1/0 36/11 2/1 59/18 1/0 82/25 2/1 4/1 23/7 -1/1 10/3 1/1 37/11 9/7 64/19 4/3 91/27 33/25 27/8 3/2 44/13 10/7 105/31 3/2 61/18 3/2 17/5 1/1 58/17 8/5 2/1 99/29 1/1 140/41 2/1 41/12 3/2 24/7 2/1 55/16 3/1 31/9 -3/1 7/2 3/2 39/11 3/1 32/9 4/1 121/34 1/0 210/59 1/0 89/25 -9/1 57/16 1/0 25/7 1/0 68/19 2/1 43/12 1/2 61/17 1/1 18/5 1/1 29/8 13/8 40/11 2/1 11/3 1/1 59/16 1/0 48/13 0/1 85/23 1/0 37/10 1/0 63/17 1/1 89/24 9/8 26/7 0/1 2/1 15/4 1/1 34/9 4/3 2/1 19/5 1/1 23/6 1/0 27/7 5/3 31/8 13/6 4/1 2/1 29/7 15/7 25/6 3/1 21/5 3/1 17/4 1/0 30/7 1/0 13/3 1/1 61/14 1/0 48/11 0/1 83/19 1/1 35/8 1/1 57/13 1/1 22/5 0/1 2/1 53/12 5/4 31/7 11/7 9/2 1/0 41/9 1/1 32/7 4/3 23/5 9/5 60/13 2/1 37/8 17/8 14/3 2/1 8/3 61/13 3/1 47/10 7/2 33/7 3/1 19/4 1/0 24/5 2/1 29/6 17/6 5/1 1/0 21/4 1/0 16/3 0/1 27/5 1/1 38/7 12/7 2/1 49/9 17/9 60/11 2/1 11/2 5/2 39/7 3/1 28/5 2/1 45/8 1/0 17/3 3/1 40/7 2/1 23/4 1/0 29/5 19/5 6/1 1/0 31/5 -1/5 25/4 1/1 19/3 1/1 32/5 0/1 13/2 1/0 33/5 1/1 20/3 2/1 27/4 5/2 7/1 3/1 22/3 6/1 8/1 15/2 1/0 38/5 -8/1 -6/1 23/3 -3/1 8/1 0/1 17/2 3/2 9/1 3/1 10/1 1/0 11/1 1/1 1/0 1/0 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(1139,-1260,706,-781) (1/1,10/9) -> (50/31,121/75) Hyperbolic Matrix(1021,-1140,429,-479) (10/9,9/8) -> (69/29,50/21) Hyperbolic Matrix(479,-540,267,-301) (9/8,17/15) -> (43/24,9/5) Hyperbolic Matrix(1321,-1500,369,-419) (17/15,8/7) -> (68/19,43/12) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(1921,-2220,726,-839) (15/13,22/19) -> (82/31,45/17) Hyperbolic Matrix(361,-420,257,-299) (22/19,7/6) -> (7/5,38/27) Hyperbolic Matrix(359,-420,206,-241) (7/6,20/17) -> (40/23,7/4) Hyperbolic Matrix(1681,-1980,967,-1139) (20/17,33/28) -> (33/19,40/23) Hyperbolic Matrix(1679,-1980,357,-421) (33/28,13/11) -> (47/10,33/7) Hyperbolic Matrix(659,-780,305,-361) (13/11,32/27) -> (28/13,13/6) Hyperbolic Matrix(1619,-1920,355,-421) (32/27,19/16) -> (41/9,32/7) Hyperbolic Matrix(1261,-1500,554,-659) (19/16,6/5) -> (66/29,41/18) Hyperbolic Matrix(1439,-1740,894,-1081) (6/5,23/19) -> (37/23,66/41) Hyperbolic Matrix(841,-1020,296,-359) (23/19,17/14) -> (17/6,37/13) Hyperbolic Matrix(839,-1020,445,-541) (17/14,45/37) -> (15/8,17/9) Hyperbolic Matrix(1381,-1680,739,-899) (45/37,28/23) -> (28/15,15/8) Hyperbolic Matrix(1921,-2340,541,-659) (28/23,39/32) -> (39/11,32/9) Hyperbolic Matrix(2461,-3000,1525,-1859) (39/32,11/9) -> (71/44,21/13) Hyperbolic Matrix(1321,-1620,782,-959) (11/9,27/22) -> (27/16,49/29) Hyperbolic Matrix(1319,-1620,929,-1141) (27/22,16/13) -> (44/31,27/19) Hyperbolic Matrix(779,-960,439,-541) (16/13,21/17) -> (39/22,16/9) Hyperbolic Matrix(1019,-1260,389,-481) (21/17,5/4) -> (55/21,21/8) Hyperbolic Matrix(1141,-1440,332,-419) (5/4,24/19) -> (24/7,55/16) Hyperbolic Matrix(1139,-1440,333,-421) (24/19,19/15) -> (41/12,24/7) Hyperbolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(659,-840,142,-181) (14/11,23/18) -> (37/8,14/3) Hyperbolic Matrix(1079,-1380,423,-541) (23/18,32/25) -> (28/11,23/9) Hyperbolic Matrix(1499,-1920,235,-301) (32/25,41/32) -> (19/3,32/5) Hyperbolic Matrix(2341,-3000,1357,-1739) (41/32,9/7) -> (69/40,19/11) Hyperbolic Matrix(419,-540,187,-241) (9/7,31/24) -> (29/13,9/4) Hyperbolic Matrix(1439,-1860,1022,-1321) (31/24,22/17) -> (38/27,31/22) Hyperbolic Matrix(1019,-1320,325,-421) (22/17,57/44) -> (3/1,22/7) Hyperbolic Matrix(2639,-3420,1899,-2461) (57/44,35/27) -> (25/18,57/41) Hyperbolic Matrix(4441,-5760,1202,-1559) (35/27,48/37) -> (48/13,85/23) Hyperbolic Matrix(4439,-5760,1203,-1561) (48/37,61/47) -> (59/16,48/13) Hyperbolic Matrix(4621,-6000,1709,-2219) (61/47,13/10) -> (73/27,119/44) Hyperbolic Matrix(599,-780,139,-181) (13/10,30/23) -> (30/7,13/3) Hyperbolic Matrix(781,-1020,183,-239) (30/23,17/13) -> (17/4,30/7) Hyperbolic Matrix(779,-1020,459,-601) (17/13,21/16) -> (39/23,17/10) Hyperbolic Matrix(1141,-1500,410,-539) (21/16,4/3) -> (64/23,39/14) Hyperbolic Matrix(1199,-1620,356,-481) (4/3,23/17) -> (37/11,64/19) Hyperbolic Matrix(1019,-1380,621,-841) (23/17,19/14) -> (41/25,23/14) Hyperbolic Matrix(839,-1140,354,-481) (19/14,15/11) -> (45/19,19/8) Hyperbolic Matrix(1141,-1560,482,-659) (15/11,26/19) -> (26/11,45/19) Hyperbolic Matrix(3901,-5340,2410,-3299) (26/19,63/46) -> (123/76,34/21) Hyperbolic Matrix(1139,-1560,395,-541) (63/46,37/27) -> (23/8,3/1) Hyperbolic Matrix(4201,-5760,962,-1319) (37/27,48/35) -> (48/11,83/19) Hyperbolic Matrix(4199,-5760,963,-1321) (48/35,59/43) -> (61/14,48/11) Hyperbolic Matrix(481,-660,43,-59) (59/43,11/8) -> (11/1,1/0) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(781,-1080,303,-419) (29/21,18/13) -> (18/7,31/12) Hyperbolic Matrix(1559,-2160,607,-841) (18/13,61/44) -> (59/23,18/7) Hyperbolic Matrix(2639,-3660,1861,-2581) (61/44,43/31) -> (17/12,61/43) Hyperbolic Matrix(1859,-2580,1168,-1621) (43/31,25/18) -> (35/22,43/27) Hyperbolic Matrix(11521,-16020,7119,-9899) (57/41,89/64) -> (89/55,123/76) Hyperbolic Matrix(9361,-13020,3968,-5519) (89/64,32/23) -> (92/39,151/64) Hyperbolic Matrix(1681,-2340,301,-419) (32/23,39/28) -> (39/7,28/5) Hyperbolic Matrix(1679,-2340,1077,-1501) (39/28,7/5) -> (53/34,39/25) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(1019,-1440,213,-301) (24/17,41/29) -> (19/4,24/5) Hyperbolic Matrix(5939,-8400,3352,-4741) (41/29,58/41) -> (62/35,101/57) Hyperbolic Matrix(721,-1020,381,-539) (58/41,17/12) -> (17/9,2/1) Hyperbolic Matrix(2579,-3660,804,-1141) (61/43,44/31) -> (16/5,61/19) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(4379,-6300,1794,-2581) (23/16,59/41) -> (61/25,83/34) Hyperbolic Matrix(3001,-4320,1083,-1559) (59/41,36/25) -> (36/13,61/22) Hyperbolic Matrix(541,-780,249,-359) (36/25,13/9) -> (13/6,24/11) Hyperbolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(659,-960,289,-421) (16/11,19/13) -> (41/18,16/7) Hyperbolic Matrix(901,-1320,286,-419) (19/13,22/15) -> (22/7,41/13) Hyperbolic Matrix(899,-1320,205,-301) (22/15,3/2) -> (57/13,22/5) Hyperbolic Matrix(1019,-1560,275,-421) (3/2,23/15) -> (37/10,63/17) Hyperbolic Matrix(899,-1380,157,-241) (23/15,20/13) -> (40/7,23/4) Hyperbolic Matrix(661,-1020,116,-179) (20/13,17/11) -> (17/3,40/7) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(1079,-1680,386,-601) (14/9,53/34) -> (67/24,14/5) Hyperbolic Matrix(961,-1500,230,-359) (39/25,25/16) -> (25/6,21/5) Hyperbolic Matrix(1919,-3000,845,-1321) (25/16,61/39) -> (59/26,25/11) Hyperbolic Matrix(2761,-4320,843,-1319) (61/39,36/23) -> (36/11,59/18) Hyperbolic Matrix(421,-660,229,-359) (36/23,11/7) -> (11/6,24/13) Hyperbolic Matrix(419,-660,153,-241) (11/7,30/19) -> (30/11,11/4) Hyperbolic Matrix(721,-1140,265,-419) (30/19,19/12) -> (19/7,30/11) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(3059,-4860,907,-1441) (27/17,89/56) -> (91/27,27/8) Hyperbolic Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(4679,-7440,2642,-4201) (62/39,35/22) -> (85/48,62/35) Hyperbolic Matrix(301,-480,37,-59) (43/27,8/5) -> (8/1,17/2) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(4919,-7920,2162,-3481) (66/41,29/18) -> (91/40,66/29) Hyperbolic Matrix(1861,-3000,781,-1259) (29/18,50/31) -> (50/21,31/13) Hyperbolic Matrix(3421,-5520,929,-1499) (121/75,71/44) -> (11/3,59/16) Hyperbolic Matrix(779,-1260,149,-241) (21/13,55/34) -> (5/1,21/4) Hyperbolic Matrix(1261,-2040,259,-419) (55/34,89/55) -> (29/6,5/1) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(661,-1080,183,-299) (31/19,18/11) -> (18/5,29/8) Hyperbolic Matrix(1319,-2160,367,-601) (18/11,59/36) -> (61/17,18/5) Hyperbolic Matrix(7321,-12000,3001,-4919) (59/36,100/61) -> (100/41,61/25) Hyperbolic Matrix(10979,-18000,4502,-7381) (100/61,41/25) -> (139/57,100/41) Hyperbolic Matrix(839,-1380,183,-301) (23/14,28/17) -> (32/7,23/5) Hyperbolic Matrix(181,-300,108,-179) (28/17,5/3) -> (5/3,32/19) Parabolic Matrix(2099,-3540,890,-1501) (32/19,27/16) -> (33/14,92/39) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(3719,-6300,1134,-1921) (22/13,61/36) -> (59/18,82/25) Hyperbolic Matrix(7081,-12000,2761,-4679) (61/36,100/59) -> (100/39,59/23) Hyperbolic Matrix(9061,-15360,2654,-4499) (100/59,39/23) -> (99/29,140/41) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(421,-720,245,-419) (29/17,12/7) -> (12/7,31/18) Parabolic Matrix(1741,-3000,661,-1139) (31/18,50/29) -> (50/19,29/11) Hyperbolic Matrix(661,-1140,69,-119) (50/29,69/40) -> (9/1,10/1) Hyperbolic Matrix(659,-1140,174,-301) (19/11,26/15) -> (34/9,19/5) Hyperbolic Matrix(2041,-3540,1141,-1979) (26/15,59/34) -> (59/33,34/19) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(239,-420,103,-181) (7/4,30/17) -> (30/13,7/3) Hyperbolic Matrix(781,-1380,339,-599) (30/17,23/13) -> (23/10,30/13) Hyperbolic Matrix(2881,-5100,779,-1379) (23/13,85/48) -> (85/23,37/10) Hyperbolic Matrix(5281,-9360,2166,-3839) (101/57,39/22) -> (39/16,139/57) Hyperbolic Matrix(539,-960,169,-301) (16/9,41/23) -> (19/6,16/5) Hyperbolic Matrix(841,-1500,134,-239) (41/23,25/14) -> (25/4,19/3) Hyperbolic Matrix(1679,-3000,605,-1081) (25/14,59/33) -> (61/22,25/9) Hyperbolic Matrix(2279,-4080,1006,-1801) (34/19,43/24) -> (77/34,34/15) Hyperbolic Matrix(299,-540,67,-121) (9/5,29/16) -> (31/7,9/2) Hyperbolic Matrix(661,-1200,363,-659) (29/16,20/11) -> (20/11,31/17) Parabolic Matrix(421,-780,129,-239) (24/13,13/7) -> (13/4,36/11) Hyperbolic Matrix(419,-780,65,-121) (13/7,28/15) -> (32/5,13/2) Hyperbolic Matrix(481,-1020,141,-299) (2/1,17/8) -> (17/5,58/17) Hyperbolic Matrix(479,-1020,85,-181) (17/8,15/7) -> (45/8,17/3) Hyperbolic Matrix(781,-1680,139,-299) (15/7,28/13) -> (28/5,45/8) Hyperbolic Matrix(301,-660,109,-239) (24/11,11/5) -> (11/4,36/13) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(781,-1740,215,-479) (20/9,29/13) -> (29/8,40/11) Hyperbolic Matrix(239,-540,27,-61) (9/4,43/19) -> (17/2,9/1) Hyperbolic Matrix(6361,-14400,2809,-6359) (43/19,120/53) -> (120/53,77/34) Parabolic Matrix(1561,-3540,661,-1499) (34/15,59/26) -> (59/25,26/11) Hyperbolic Matrix(1319,-3000,317,-721) (25/11,91/40) -> (29/7,25/6) Hyperbolic Matrix(419,-960,79,-181) (16/7,39/17) -> (21/4,16/3) Hyperbolic Matrix(3659,-8400,1072,-2461) (39/17,62/27) -> (58/17,99/29) Hyperbolic Matrix(3239,-7440,1202,-2761) (62/27,23/10) -> (97/36,62/23) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(21361,-50400,6001,-14159) (151/64,210/89) -> (210/59,89/25) Hyperbolic Matrix(16019,-37800,4501,-10621) (210/89,59/25) -> (121/34,210/59) Hyperbolic Matrix(1261,-3000,277,-659) (19/8,69/29) -> (9/2,41/9) Hyperbolic Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(1439,-3480,447,-1081) (29/12,75/31) -> (45/14,29/9) Hyperbolic Matrix(4141,-10020,1289,-3119) (75/31,121/50) -> (61/19,45/14) Hyperbolic Matrix(1859,-4500,397,-961) (121/50,46/19) -> (14/3,61/13) Hyperbolic Matrix(419,-1020,99,-241) (17/7,39/16) -> (21/5,17/4) Hyperbolic Matrix(1499,-3660,197,-481) (83/34,22/9) -> (38/5,23/3) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(539,-1380,141,-361) (23/9,41/16) -> (19/5,23/6) Hyperbolic Matrix(3839,-9840,1124,-2881) (41/16,100/39) -> (140/41,41/12) Hyperbolic Matrix(1439,-3720,511,-1321) (31/12,75/29) -> (45/16,31/11) Hyperbolic Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(1381,-3600,529,-1379) (13/5,60/23) -> (60/23,47/18) Parabolic Matrix(2041,-5340,550,-1439) (34/13,89/34) -> (89/24,26/7) Hyperbolic Matrix(2521,-6600,733,-1919) (89/34,55/21) -> (55/16,31/9) Hyperbolic Matrix(1141,-3000,205,-539) (21/8,71/27) -> (11/2,39/7) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(1861,-4920,567,-1499) (37/14,82/31) -> (82/25,23/7) Hyperbolic Matrix(959,-2580,268,-721) (8/3,35/13) -> (25/7,68/19) Hyperbolic Matrix(2339,-6300,535,-1441) (35/13,97/36) -> (83/19,35/8) Hyperbolic Matrix(21361,-57600,7921,-21359) (151/56,240/89) -> (240/89,89/33) Parabolic Matrix(1201,-3240,311,-839) (89/33,27/10) -> (27/7,31/8) Hyperbolic Matrix(1021,-2760,155,-419) (27/10,73/27) -> (13/2,33/5) Hyperbolic Matrix(1619,-4380,577,-1561) (119/44,46/17) -> (14/5,59/21) Hyperbolic Matrix(1079,-3000,173,-481) (25/9,89/32) -> (31/5,25/4) Hyperbolic Matrix(4141,-11520,1229,-3419) (89/32,64/23) -> (64/19,91/27) Hyperbolic Matrix(839,-2340,237,-661) (39/14,53/19) -> (7/2,39/11) Hyperbolic Matrix(5161,-14400,1849,-5159) (53/19,120/43) -> (120/43,67/24) Parabolic Matrix(3181,-8940,939,-2639) (59/21,45/16) -> (105/31,61/18) Hyperbolic Matrix(421,-1200,147,-419) (37/13,20/7) -> (20/7,23/8) Parabolic Matrix(1141,-3600,361,-1139) (41/13,60/19) -> (60/19,19/6) Parabolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(479,-1620,89,-301) (27/8,44/13) -> (16/3,27/5) Hyperbolic Matrix(1079,-3660,301,-1021) (61/18,17/5) -> (43/12,61/17) Hyperbolic Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(2999,-10680,809,-2881) (89/25,57/16) -> (63/17,89/24) Hyperbolic Matrix(959,-3420,219,-781) (57/16,25/7) -> (35/8,57/13) Hyperbolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(61,-240,15,-59) (31/8,4/1) -> (4/1,29/7) Parabolic Matrix(841,-3660,179,-779) (13/3,61/14) -> (61/13,47/10) Hyperbolic Matrix(299,-1320,41,-181) (22/5,53/12) -> (7/1,22/3) Hyperbolic Matrix(781,-3600,169,-779) (23/5,60/13) -> (60/13,37/8) Parabolic Matrix(661,-3600,121,-659) (49/9,60/11) -> (60/11,11/2) Parabolic Matrix(61,-360,10,-59) (29/5,6/1) -> (6/1,31/5) Parabolic Matrix(181,-1200,27,-179) (33/5,20/3) -> (20/3,27/4) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(1139,-1260,706,-781) -> Matrix(3,-2,-4,3) Matrix(1021,-1140,429,-479) -> Matrix(5,-6,1,-1) Matrix(479,-540,267,-301) -> Matrix(1,-2,1,-1) Matrix(1321,-1500,369,-419) -> Matrix(1,-2,1,-1) Matrix(419,-480,158,-181) -> Matrix(1,0,0,1) Matrix(1921,-2220,726,-839) -> Matrix(13,-14,14,-15) Matrix(361,-420,257,-299) -> Matrix(5,-6,1,-1) Matrix(359,-420,206,-241) -> Matrix(1,-2,2,-3) Matrix(1681,-1980,967,-1139) -> Matrix(1,-2,-1,3) Matrix(1679,-1980,357,-421) -> Matrix(3,-10,1,-3) Matrix(659,-780,305,-361) -> Matrix(1,-2,1,-1) Matrix(1619,-1920,355,-421) -> Matrix(1,-4,1,-3) Matrix(1261,-1500,554,-659) -> Matrix(1,-2,2,-3) Matrix(1439,-1740,894,-1081) -> Matrix(7,-10,-2,3) Matrix(841,-1020,296,-359) -> Matrix(1,-2,2,-3) Matrix(839,-1020,445,-541) -> Matrix(1,-2,1,-1) Matrix(1381,-1680,739,-899) -> Matrix(3,-4,1,-1) Matrix(1921,-2340,541,-659) -> Matrix(5,-6,1,-1) Matrix(2461,-3000,1525,-1859) -> Matrix(3,-4,-5,7) Matrix(1321,-1620,782,-959) -> Matrix(1,-2,-2,5) Matrix(1319,-1620,929,-1141) -> Matrix(3,-10,1,-3) Matrix(779,-960,439,-541) -> Matrix(1,0,-1,1) Matrix(1019,-1260,389,-481) -> Matrix(1,-2,3,-5) Matrix(1141,-1440,332,-419) -> Matrix(5,-8,2,-3) Matrix(1139,-1440,333,-421) -> Matrix(1,-4,1,-3) Matrix(899,-1140,332,-421) -> Matrix(5,-6,6,-7) Matrix(659,-840,142,-181) -> Matrix(9,-16,4,-7) Matrix(1079,-1380,423,-541) -> Matrix(1,-2,-1,3) Matrix(1499,-1920,235,-301) -> Matrix(1,-4,1,-3) Matrix(2341,-3000,1357,-1739) -> Matrix(1,-4,1,-3) Matrix(419,-540,187,-241) -> Matrix(1,-2,3,-5) Matrix(1439,-1860,1022,-1321) -> Matrix(1,-2,0,1) Matrix(1019,-1320,325,-421) -> Matrix(1,-4,1,-3) Matrix(2639,-3420,1899,-2461) -> Matrix(1,-2,1,-1) Matrix(4441,-5760,1202,-1559) -> Matrix(1,0,0,1) Matrix(4439,-5760,1203,-1561) -> Matrix(1,0,-1,1) Matrix(4621,-6000,1709,-2219) -> Matrix(5,-8,7,-11) Matrix(599,-780,139,-181) -> Matrix(1,-2,1,-1) Matrix(781,-1020,183,-239) -> Matrix(5,-6,1,-1) Matrix(779,-1020,459,-601) -> Matrix(1,-2,1,-1) Matrix(1141,-1500,410,-539) -> Matrix(1,-2,2,-3) Matrix(1199,-1620,356,-481) -> Matrix(5,-14,4,-11) Matrix(1019,-1380,621,-841) -> Matrix(1,-2,-1,3) Matrix(839,-1140,354,-481) -> Matrix(1,-2,0,1) Matrix(1141,-1560,482,-659) -> Matrix(1,0,0,1) Matrix(3901,-5340,2410,-3299) -> Matrix(1,-2,-2,5) Matrix(1139,-1560,395,-541) -> Matrix(1,0,1,1) Matrix(4201,-5760,962,-1319) -> Matrix(1,0,0,1) Matrix(4199,-5760,963,-1321) -> Matrix(1,0,-1,1) Matrix(481,-660,43,-59) -> Matrix(1,-2,1,-1) Matrix(479,-660,262,-361) -> Matrix(1,-2,2,-3) Matrix(781,-1080,303,-419) -> Matrix(1,-4,1,-3) Matrix(1559,-2160,607,-841) -> Matrix(1,0,1,1) Matrix(2639,-3660,1861,-2581) -> Matrix(3,2,1,1) Matrix(1859,-2580,1168,-1621) -> Matrix(1,-2,0,1) Matrix(11521,-16020,7119,-9899) -> Matrix(3,-2,-7,5) Matrix(9361,-13020,3968,-5519) -> Matrix(9,-10,10,-11) Matrix(1681,-2340,301,-419) -> Matrix(5,-6,1,-1) Matrix(1679,-2340,1077,-1501) -> Matrix(1,-2,3,-5) Matrix(1021,-1440,212,-299) -> Matrix(5,-8,2,-3) Matrix(1019,-1440,213,-301) -> Matrix(1,-4,1,-3) Matrix(5939,-8400,3352,-4741) -> Matrix(1,-4,0,1) Matrix(721,-1020,381,-539) -> Matrix(1,-2,-1,3) Matrix(2579,-3660,804,-1141) -> Matrix(3,-10,4,-13) Matrix(421,-600,294,-419) -> Matrix(1,-4,0,1) Matrix(961,-1380,250,-359) -> Matrix(3,-2,2,-1) Matrix(4379,-6300,1794,-2581) -> Matrix(1,-2,2,-3) Matrix(3001,-4320,1083,-1559) -> Matrix(3,-4,1,-1) Matrix(541,-780,249,-359) -> Matrix(1,-2,1,-1) Matrix(539,-780,208,-301) -> Matrix(1,-2,0,1) Matrix(659,-960,289,-421) -> Matrix(1,0,1,1) Matrix(901,-1320,286,-419) -> Matrix(3,-8,2,-5) Matrix(899,-1320,205,-301) -> Matrix(1,-4,1,-3) Matrix(1019,-1560,275,-421) -> Matrix(1,0,1,1) Matrix(899,-1380,157,-241) -> Matrix(3,2,1,1) Matrix(661,-1020,116,-179) -> Matrix(1,2,0,1) Matrix(659,-1020,272,-421) -> Matrix(1,-2,2,-3) Matrix(1079,-1680,386,-601) -> Matrix(1,0,2,1) Matrix(961,-1500,230,-359) -> Matrix(1,2,0,1) Matrix(1919,-3000,845,-1321) -> Matrix(1,0,1,1) Matrix(2761,-4320,843,-1319) -> Matrix(3,-4,1,-1) Matrix(421,-660,229,-359) -> Matrix(1,-2,1,-1) Matrix(419,-660,153,-241) -> Matrix(1,-6,1,-5) Matrix(721,-1140,265,-419) -> Matrix(1,10,1,11) Matrix(719,-1140,152,-241) -> Matrix(1,6,0,1) Matrix(3059,-4860,907,-1441) -> Matrix(7,18,5,13) Matrix(9361,-14880,3472,-5519) -> Matrix(13,24,20,37) Matrix(4679,-7440,2642,-4201) -> Matrix(5,8,-2,-3) Matrix(301,-480,37,-59) -> Matrix(1,0,1,1) Matrix(299,-480,38,-61) -> Matrix(1,0,0,1) Matrix(4919,-7920,2162,-3481) -> Matrix(3,8,4,11) Matrix(1861,-3000,781,-1259) -> Matrix(3,4,-1,-1) Matrix(3421,-5520,929,-1499) -> Matrix(5,4,1,1) Matrix(779,-1260,149,-241) -> Matrix(3,2,1,1) Matrix(1261,-2040,259,-419) -> Matrix(5,4,1,1) Matrix(1259,-2040,482,-781) -> Matrix(1,0,6,1) Matrix(479,-780,148,-241) -> Matrix(3,-2,2,-1) Matrix(661,-1080,183,-299) -> Matrix(1,-4,1,-3) Matrix(1319,-2160,367,-601) -> Matrix(1,0,1,1) Matrix(7321,-12000,3001,-4919) -> Matrix(1,4,1,5) Matrix(10979,-18000,4502,-7381) -> Matrix(1,0,2,1) Matrix(839,-1380,183,-301) -> Matrix(5,-2,3,-1) Matrix(181,-300,108,-179) -> Matrix(1,-2,0,1) Matrix(2099,-3540,890,-1501) -> Matrix(3,2,4,3) Matrix(1739,-2940,320,-541) -> Matrix(7,-2,4,-1) Matrix(3719,-6300,1134,-1921) -> Matrix(1,2,0,1) Matrix(7081,-12000,2761,-4679) -> Matrix(1,4,1,5) Matrix(9061,-15360,2654,-4499) -> Matrix(3,4,2,3) Matrix(599,-1020,212,-361) -> Matrix(1,2,0,1) Matrix(421,-720,245,-419) -> Matrix(1,0,3,1) Matrix(1741,-3000,661,-1139) -> Matrix(5,-4,9,-7) Matrix(661,-1140,69,-119) -> Matrix(5,-6,1,-1) Matrix(659,-1140,174,-301) -> Matrix(3,-2,2,-1) Matrix(2041,-3540,1141,-1979) -> Matrix(1,-2,-1,3) Matrix(2281,-3960,898,-1559) -> Matrix(1,4,0,1) Matrix(239,-420,103,-181) -> Matrix(1,-2,1,-1) Matrix(781,-1380,339,-599) -> Matrix(1,6,1,7) Matrix(2881,-5100,779,-1379) -> Matrix(1,2,1,3) Matrix(5281,-9360,2166,-3839) -> Matrix(1,0,2,1) Matrix(539,-960,169,-301) -> Matrix(1,0,1,1) Matrix(841,-1500,134,-239) -> Matrix(1,2,0,1) Matrix(1679,-3000,605,-1081) -> Matrix(1,0,1,1) Matrix(2279,-4080,1006,-1801) -> Matrix(1,0,4,1) Matrix(299,-540,67,-121) -> Matrix(3,2,1,1) Matrix(661,-1200,363,-659) -> Matrix(1,0,7,1) Matrix(421,-780,129,-239) -> Matrix(1,-2,1,-1) Matrix(419,-780,65,-121) -> Matrix(1,-2,1,-1) Matrix(481,-1020,141,-299) -> Matrix(5,-2,3,-1) Matrix(479,-1020,85,-181) -> Matrix(1,-2,1,-1) Matrix(781,-1680,139,-299) -> Matrix(3,-4,1,-1) Matrix(301,-660,109,-239) -> Matrix(1,-2,1,-1) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) Matrix(781,-1740,215,-479) -> Matrix(13,-2,7,-1) Matrix(239,-540,27,-61) -> Matrix(1,-2,1,-1) Matrix(6361,-14400,2809,-6359) -> Matrix(1,0,7,1) Matrix(1561,-3540,661,-1499) -> Matrix(5,-2,3,-1) Matrix(1319,-3000,317,-721) -> Matrix(13,-8,5,-3) Matrix(419,-960,79,-181) -> Matrix(1,0,-1,1) Matrix(3659,-8400,1072,-2461) -> Matrix(5,-4,4,-3) Matrix(3239,-7440,1202,-2761) -> Matrix(11,-8,18,-13) Matrix(179,-420,26,-61) -> Matrix(1,2,0,1) Matrix(21361,-50400,6001,-14159) -> Matrix(29,-28,-1,1) Matrix(16019,-37800,4501,-10621) -> Matrix(23,-24,1,-1) Matrix(1261,-3000,277,-659) -> Matrix(1,-4,1,-3) Matrix(301,-720,125,-299) -> Matrix(1,0,3,1) Matrix(1439,-3480,447,-1081) -> Matrix(17,-8,15,-7) Matrix(4141,-10020,1289,-3119) -> Matrix(27,-14,29,-15) Matrix(1859,-4500,397,-961) -> Matrix(25,-14,9,-5) Matrix(419,-1020,99,-241) -> Matrix(1,-2,1,-1) Matrix(1499,-3660,197,-481) -> Matrix(7,-6,-1,1) Matrix(661,-1620,122,-299) -> Matrix(7,-2,4,-1) Matrix(121,-300,48,-119) -> Matrix(3,-2,2,-1) Matrix(2099,-5340,590,-1501) -> Matrix(1,6,0,1) Matrix(539,-1380,141,-361) -> Matrix(5,-2,3,-1) Matrix(3839,-9840,1124,-2881) -> Matrix(5,-4,4,-3) Matrix(1439,-3720,511,-1321) -> Matrix(1,-8,1,-7) Matrix(3061,-7920,904,-2339) -> Matrix(3,16,2,11) Matrix(1381,-3600,529,-1379) -> Matrix(1,0,9,1) Matrix(2041,-5340,550,-1439) -> Matrix(7,-2,4,-1) Matrix(2521,-6600,733,-1919) -> Matrix(11,-4,3,-1) Matrix(1141,-3000,205,-539) -> Matrix(11,-4,3,-1) Matrix(479,-1260,46,-121) -> Matrix(5,-2,-2,1) Matrix(659,-1740,114,-301) -> Matrix(13,-10,4,-3) Matrix(1861,-4920,567,-1499) -> Matrix(5,-4,-1,1) Matrix(959,-2580,268,-721) -> Matrix(3,-2,2,-1) Matrix(2339,-6300,535,-1441) -> Matrix(3,-2,5,-3) Matrix(21361,-57600,7921,-21359) -> Matrix(163,-108,243,-161) Matrix(1201,-3240,311,-839) -> Matrix(23,-16,13,-9) Matrix(1021,-2760,155,-419) -> Matrix(11,-8,7,-5) Matrix(1619,-4380,577,-1561) -> Matrix(13,-10,17,-13) Matrix(1079,-3000,173,-481) -> Matrix(1,0,1,1) Matrix(4141,-11520,1229,-3419) -> Matrix(9,-4,7,-3) Matrix(839,-2340,237,-661) -> Matrix(3,2,1,1) Matrix(5161,-14400,1849,-5159) -> Matrix(1,0,9,1) Matrix(3181,-8940,939,-2639) -> Matrix(29,-26,19,-17) Matrix(421,-1200,147,-419) -> Matrix(1,0,1,1) Matrix(1141,-3600,361,-1139) -> Matrix(7,-12,3,-5) Matrix(181,-600,54,-179) -> Matrix(5,-4,4,-3) Matrix(479,-1620,89,-301) -> Matrix(7,-10,5,-7) Matrix(1079,-3660,301,-1021) -> Matrix(1,-2,3,-5) Matrix(539,-1860,122,-421) -> Matrix(3,-2,2,-1) Matrix(2999,-10680,809,-2881) -> Matrix(1,0,1,1) Matrix(959,-3420,219,-781) -> Matrix(1,-2,1,-1) Matrix(241,-900,64,-239) -> Matrix(3,-2,2,-1) Matrix(61,-240,15,-59) -> Matrix(3,-4,1,-1) Matrix(841,-3660,179,-779) -> Matrix(3,-10,1,-3) Matrix(299,-1320,41,-181) -> Matrix(7,-8,1,-1) Matrix(781,-3600,169,-779) -> Matrix(27,-52,13,-25) Matrix(661,-3600,121,-659) -> Matrix(23,-44,11,-21) Matrix(61,-360,10,-59) -> Matrix(1,-4,0,1) Matrix(181,-1200,27,-179) -> Matrix(7,-12,3,-5) Matrix(121,-900,16,-119) -> Matrix(1,-14,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 128 ----------------------------------------------------------------------- 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 0/1 1 1 2/1 (0/1,2/1) 0 15 17/8 1/2 1 30 15/7 1/1 1 2 28/13 2/1 1 15 13/6 1/0 1 30 24/11 0/1 1 5 11/5 -1/1 1 30 20/9 0/1 7 3 29/13 3/13 1 30 9/4 1/2 1 10 43/19 -1/1 1 30 120/53 0/1 7 1 34/15 (0/1,2/5) 0 15 59/26 1/2 1 30 25/11 1/2 1 6 41/18 1/2 1 30 16/7 0/1 1 15 39/17 1/1 1 10 62/27 (4/7,2/3) 0 15 23/10 3/4 1 30 30/13 1/1 4 1 7/3 1/1 1 30 33/14 1/2 1 10 59/25 1/1 1 30 26/11 (0/1,2/1) 0 15 19/8 1/0 1 30 69/29 3/1 1 10 50/21 1/0 6 3 31/13 -5/3 1 30 12/5 0/1 3 5 29/12 5/12 1 30 17/7 1/1 1 30 39/16 1/2 1 10 100/41 2/3 1 3 61/25 1/1 1 30 22/9 (0/1,2/1) 0 15 27/11 1/3 1 10 5/2 1/1 1 6 33/13 3/1 1 10 61/24 1/0 1 30 28/11 -2/1 1 15 23/9 1/3 1 30 41/16 1/2 1 30 100/39 2/3 1 3 59/23 1/1 1 30 18/7 1/1 2 5 31/12 7/2 1 30 13/5 -1/1 1 30 60/23 0/1 9 1 34/13 (0/1,2/7) 0 15 89/34 7/20 1 30 55/21 1/2 1 6 21/8 1/2 1 10 71/27 3/7 1 30 50/19 1/2 6 3 29/11 7/11 1 30 37/14 3/4 1 30 8/3 0/1 1 15 35/13 1/2 1 6 97/36 1/2 1 30 62/23 (12/19,2/3) 0 15 240/89 2/3 27 1 89/33 21/31 1 30 27/10 3/4 1 10 19/7 1/1 1 30 30/11 1/1 8 1 11/4 3/2 1 30 36/13 2/1 1 5 61/22 1/0 1 30 25/9 1/0 1 6 39/14 1/0 1 10 53/19 -1/3 1 30 120/43 0/1 9 1 14/5 (0/1,2/3) 0 15 59/21 1/1 1 30 45/16 1/1 11 2 31/11 9/7 1 30 17/6 1/0 1 30 20/7 0/1 1 3 23/8 1/2 1 30 3/1 1/1 1 10 22/7 (4/3,2/1) 0 15 60/19 2/1 3 1 19/6 1/0 1 30 16/5 0/1 1 15 45/14 1/1 11 2 29/9 11/9 1 30 13/4 1/0 1 30 36/11 2/1 1 5 59/18 1/0 1 30 82/25 (2/1,4/1) 0 15 23/7 -1/1 1 30 10/3 1/1 2 3 37/11 9/7 1 30 27/8 3/2 1 10 44/13 10/7 1 15 105/31 3/2 11 2 61/18 3/2 1 30 17/5 1/1 1 30 58/17 (8/5,2/1) 0 15 99/29 1/1 1 10 140/41 2/1 1 3 41/12 3/2 1 30 24/7 2/1 3 5 31/9 -3/1 1 30 7/2 3/2 1 30 39/11 3/1 1 10 32/9 4/1 1 15 121/34 1/0 1 30 210/59 1/0 26 1 89/25 -9/1 1 30 57/16 1/0 1 10 25/7 1/0 1 6 68/19 2/1 1 15 43/12 1/2 1 30 61/17 1/1 1 30 18/5 1/1 2 5 29/8 13/8 1 30 40/11 2/1 7 3 11/3 1/1 1 30 59/16 1/0 1 30 48/13 0/1 1 5 37/10 1/0 1 30 63/17 1/1 1 10 89/24 9/8 1 30 26/7 (0/1,2/1) 0 15 15/4 1/1 1 2 34/9 (4/3,2/1) 0 15 19/5 1/1 1 30 23/6 1/0 1 30 27/7 5/3 1 10 31/8 13/6 1 30 4/1 2/1 1 15 29/7 15/7 1 30 25/6 3/1 1 6 21/5 3/1 1 10 17/4 1/0 1 30 30/7 1/0 2 1 13/3 1/1 1 30 61/14 1/0 1 30 48/11 0/1 1 5 83/19 1/1 1 30 35/8 1/1 1 6 57/13 1/1 1 10 22/5 (0/1,2/1) 0 15 53/12 5/4 1 30 31/7 11/7 1 30 9/2 1/0 1 10 41/9 1/1 1 30 32/7 4/3 1 15 23/5 9/5 1 30 60/13 2/1 13 1 14/3 (2/1,8/3) 0 15 61/13 3/1 1 30 47/10 7/2 1 30 33/7 3/1 1 10 19/4 1/0 1 30 24/5 2/1 3 5 29/6 17/6 1 30 5/1 1/0 1 6 21/4 1/0 1 10 16/3 0/1 1 15 27/5 1/1 1 10 38/7 (12/7,2/1) 0 15 60/11 2/1 11 1 11/2 5/2 1 30 39/7 3/1 1 10 28/5 2/1 1 15 45/8 1/0 1 2 17/3 3/1 1 30 40/7 2/1 1 3 23/4 1/0 1 30 29/5 19/5 1 30 6/1 1/0 2 5 31/5 -1/5 1 30 25/4 1/1 1 6 19/3 1/1 1 30 32/5 0/1 1 15 13/2 1/0 1 30 33/5 1/1 1 10 20/3 2/1 3 3 27/4 5/2 1 10 7/1 3/1 1 30 22/3 (6/1,8/1) 0 15 15/2 1/0 7 2 38/5 (-8/1,-6/1) 0 15 23/3 -3/1 1 30 8/1 0/1 1 15 17/2 3/2 1 30 9/1 3/1 1 10 10/1 1/0 6 3 11/1 1/1 1 30 1/0 1/0 1 30 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(481,-1020,141,-299) (2/1,17/8) -> (17/5,58/17) Hyperbolic Matrix(479,-1020,85,-181) (17/8,15/7) -> (45/8,17/3) Hyperbolic Matrix(781,-1680,139,-299) (15/7,28/13) -> (28/5,45/8) Hyperbolic Matrix(361,-780,56,-121) (28/13,13/6) -> (32/5,13/2) Glide Reflection Matrix(359,-780,110,-239) (13/6,24/11) -> (13/4,36/11) Glide Reflection Matrix(301,-660,109,-239) (24/11,11/5) -> (11/4,36/13) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(781,-1740,215,-479) (20/9,29/13) -> (29/8,40/11) Hyperbolic Matrix(241,-540,54,-121) (29/13,9/4) -> (31/7,9/2) Glide Reflection Matrix(239,-540,27,-61) (9/4,43/19) -> (17/2,9/1) Hyperbolic Matrix(4559,-10320,2014,-4559) (43/19,120/53) -> (43/19,120/53) Reflection Matrix(1801,-4080,795,-1801) (120/53,34/15) -> (120/53,34/15) Reflection Matrix(1561,-3540,661,-1499) (34/15,59/26) -> (59/25,26/11) Hyperbolic Matrix(1321,-3000,476,-1081) (59/26,25/11) -> (61/22,25/9) Glide Reflection Matrix(659,-1500,105,-239) (25/11,41/18) -> (25/4,19/3) Glide Reflection Matrix(421,-960,132,-301) (41/18,16/7) -> (19/6,16/5) Glide Reflection Matrix(419,-960,79,-181) (16/7,39/17) -> (21/4,16/3) Hyperbolic Matrix(3659,-8400,1072,-2461) (39/17,62/27) -> (58/17,99/29) Hyperbolic Matrix(3239,-7440,1202,-2761) (62/27,23/10) -> (97/36,62/23) Hyperbolic Matrix(599,-1380,260,-599) (23/10,30/13) -> (23/10,30/13) Reflection Matrix(181,-420,78,-181) (30/13,7/3) -> (30/13,7/3) Reflection Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(1679,-3960,661,-1559) (33/14,59/25) -> (33/13,61/24) Glide Reflection Matrix(481,-1140,127,-301) (26/11,19/8) -> (34/9,19/5) Glide Reflection Matrix(1261,-3000,277,-659) (19/8,69/29) -> (9/2,41/9) Hyperbolic Matrix(479,-1140,50,-119) (69/29,50/21) -> (9/1,10/1) Glide Reflection Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(421,-1020,149,-361) (29/12,17/7) -> (31/11,17/6) Glide Reflection Matrix(419,-1020,99,-241) (17/7,39/16) -> (21/5,17/4) Hyperbolic Matrix(6299,-15360,1845,-4499) (39/16,100/41) -> (99/29,140/41) Glide Reflection Matrix(4919,-12000,1918,-4679) (100/41,61/25) -> (100/39,59/23) Glide Reflection Matrix(2581,-6300,787,-1921) (61/25,22/9) -> (59/18,82/25) Glide Reflection Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(541,-1380,118,-301) (28/11,23/9) -> (32/7,23/5) Glide Reflection Matrix(539,-1380,141,-361) (23/9,41/16) -> (19/5,23/6) Hyperbolic Matrix(3839,-9840,1124,-2881) (41/16,100/39) -> (140/41,41/12) Hyperbolic Matrix(841,-2160,234,-601) (59/23,18/7) -> (61/17,18/5) Glide Reflection Matrix(419,-1080,116,-299) (18/7,31/12) -> (18/5,29/8) Glide Reflection Matrix(301,-780,93,-241) (31/12,13/5) -> (29/9,13/4) Glide Reflection Matrix(599,-1560,230,-599) (13/5,60/23) -> (13/5,60/23) Reflection Matrix(781,-2040,299,-781) (60/23,34/13) -> (60/23,34/13) Reflection Matrix(2041,-5340,550,-1439) (34/13,89/34) -> (89/24,26/7) Hyperbolic Matrix(779,-2040,160,-419) (89/34,55/21) -> (29/6,5/1) Glide Reflection Matrix(481,-1260,92,-241) (55/21,21/8) -> (5/1,21/4) Glide Reflection Matrix(1141,-3000,205,-539) (21/8,71/27) -> (11/2,39/7) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(181,-480,23,-61) (37/14,8/3) -> (23/3,8/1) Glide Reflection Matrix(959,-2580,268,-721) (8/3,35/13) -> (25/7,68/19) Hyperbolic Matrix(2339,-6300,535,-1441) (35/13,97/36) -> (83/19,35/8) Hyperbolic Matrix(5519,-14880,2047,-5519) (62/23,240/89) -> (62/23,240/89) Reflection Matrix(15841,-42720,5874,-15841) (240/89,89/33) -> (240/89,89/33) Reflection Matrix(1201,-3240,311,-839) (89/33,27/10) -> (27/7,31/8) Hyperbolic Matrix(421,-1140,89,-241) (27/10,19/7) -> (33/7,19/4) Glide Reflection Matrix(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(1559,-4320,476,-1319) (36/13,61/22) -> (36/11,59/18) Glide Reflection Matrix(539,-1500,129,-359) (25/9,39/14) -> (25/6,21/5) Glide Reflection Matrix(839,-2340,237,-661) (39/14,53/19) -> (7/2,39/11) Hyperbolic Matrix(4559,-12720,1634,-4559) (53/19,120/43) -> (53/19,120/43) Reflection Matrix(601,-1680,215,-601) (120/43,14/5) -> (120/43,14/5) Reflection Matrix(599,-1680,128,-359) (14/5,59/21) -> (14/3,61/13) Glide Reflection Matrix(3181,-8940,939,-2639) (59/21,45/16) -> (105/31,61/18) Hyperbolic Matrix(959,-2700,298,-839) (45/16,31/11) -> (45/14,29/9) Glide Reflection Matrix(359,-1020,63,-179) (17/6,20/7) -> (17/3,40/7) Glide Reflection Matrix(481,-1380,84,-241) (20/7,23/8) -> (40/7,23/4) Glide Reflection Matrix(541,-1560,146,-421) (23/8,3/1) -> (37/10,63/17) Glide Reflection Matrix(421,-1320,96,-301) (3/1,22/7) -> (57/13,22/5) Glide Reflection Matrix(419,-1320,133,-419) (22/7,60/19) -> (22/7,60/19) Reflection Matrix(721,-2280,228,-721) (60/19,19/6) -> (60/19,19/6) Reflection Matrix(1141,-3660,337,-1081) (16/5,45/14) -> (44/13,105/31) Glide Reflection Matrix(841,-2760,110,-361) (82/25,23/7) -> (38/5,23/3) Glide Reflection Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(481,-1620,125,-421) (37/11,27/8) -> (23/6,27/7) Glide Reflection Matrix(479,-1620,89,-301) (27/8,44/13) -> (16/3,27/5) Hyperbolic Matrix(1079,-3660,301,-1021) (61/18,17/5) -> (43/12,61/17) Hyperbolic Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection Matrix(419,-1440,87,-299) (24/7,31/9) -> (24/5,29/6) Glide Reflection Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(659,-2340,118,-419) (39/11,32/9) -> (39/7,28/5) Glide Reflection Matrix(14279,-50820,4012,-14279) (121/34,210/59) -> (121/34,210/59) Reflection Matrix(10501,-37380,2950,-10501) (210/59,89/25) -> (210/59,89/25) Reflection Matrix(2999,-10680,809,-2881) (89/25,57/16) -> (63/17,89/24) Hyperbolic Matrix(959,-3420,219,-781) (57/16,25/7) -> (35/8,57/13) Hyperbolic Matrix(419,-1500,50,-179) (68/19,43/12) -> (8/1,17/2) Glide Reflection Matrix(179,-660,16,-59) (11/3,59/16) -> (11/1,1/0) Glide Reflection Matrix(1561,-5760,358,-1321) (59/16,48/13) -> (61/14,48/11) Glide Reflection Matrix(1559,-5760,357,-1319) (48/13,37/10) -> (48/11,83/19) Glide Reflection Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(61,-240,15,-59) (31/8,4/1) -> (4/1,29/7) Parabolic Matrix(361,-1500,58,-241) (29/7,25/6) -> (31/5,25/4) Glide Reflection Matrix(239,-1020,56,-239) (17/4,30/7) -> (17/4,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(841,-3660,179,-779) (13/3,61/14) -> (61/13,47/10) Hyperbolic Matrix(299,-1320,41,-181) (22/5,53/12) -> (7/1,22/3) Hyperbolic Matrix(421,-1920,66,-301) (41/9,32/7) -> (19/3,32/5) Glide Reflection Matrix(599,-2760,130,-599) (23/5,60/13) -> (23/5,60/13) Reflection Matrix(181,-840,39,-181) (60/13,14/3) -> (60/13,14/3) Reflection Matrix(421,-1980,64,-301) (47/10,33/7) -> (13/2,33/5) Glide Reflection Matrix(419,-2280,77,-419) (38/7,60/11) -> (38/7,60/11) Reflection Matrix(241,-1320,44,-241) (60/11,11/2) -> (60/11,11/2) Reflection Matrix(61,-360,10,-59) (29/5,6/1) -> (6/1,31/5) Parabolic Matrix(181,-1200,27,-179) (33/5,20/3) -> (20/3,27/4) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(481,-1020,141,-299) -> Matrix(5,-2,3,-1) Matrix(479,-1020,85,-181) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(781,-1680,139,-299) -> Matrix(3,-4,1,-1) 2/1 Matrix(361,-780,56,-121) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(359,-780,110,-239) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(301,-660,109,-239) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) 1/0 Matrix(781,-1740,215,-479) -> Matrix(13,-2,7,-1) Matrix(241,-540,54,-121) -> Matrix(5,-2,2,-1) Matrix(239,-540,27,-61) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(4559,-10320,2014,-4559) -> Matrix(-1,0,2,1) (43/19,120/53) -> (-1/1,0/1) Matrix(1801,-4080,795,-1801) -> Matrix(1,0,5,-1) (120/53,34/15) -> (0/1,2/5) Matrix(1561,-3540,661,-1499) -> Matrix(5,-2,3,-1) Matrix(1321,-3000,476,-1081) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(659,-1500,105,-239) -> Matrix(3,-2,1,-1) Matrix(421,-960,132,-301) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(419,-960,79,-181) -> Matrix(1,0,-1,1) 0/1 Matrix(3659,-8400,1072,-2461) -> Matrix(5,-4,4,-3) 1/1 Matrix(3239,-7440,1202,-2761) -> Matrix(11,-8,18,-13) 2/3 Matrix(599,-1380,260,-599) -> Matrix(7,-6,8,-7) (23/10,30/13) -> (3/4,1/1) Matrix(181,-420,78,-181) -> Matrix(-1,2,0,1) (30/13,7/3) -> (1/1,1/0) Matrix(179,-420,26,-61) -> Matrix(1,2,0,1) 1/0 Matrix(1679,-3960,661,-1559) -> Matrix(5,-4,1,-1) Matrix(481,-1140,127,-301) -> Matrix(1,2,1,1) Matrix(1261,-3000,277,-659) -> Matrix(1,-4,1,-3) 2/1 Matrix(479,-1140,50,-119) -> Matrix(-1,6,0,1) *** -> (3/1,1/0) Matrix(1259,-3000,478,-1139) -> Matrix(1,4,2,7) Matrix(301,-720,125,-299) -> Matrix(1,0,3,1) 0/1 Matrix(421,-1020,149,-361) -> Matrix(3,-2,1,-1) Matrix(419,-1020,99,-241) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(6299,-15360,1845,-4499) -> Matrix(7,-4,5,-3) Matrix(4919,-12000,1918,-4679) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(2581,-6300,787,-1921) -> Matrix(3,-2,1,-1) Matrix(661,-1620,122,-299) -> Matrix(7,-2,4,-1) Matrix(121,-300,48,-119) -> Matrix(3,-2,2,-1) 1/1 Matrix(2099,-5340,590,-1501) -> Matrix(1,6,0,1) 1/0 Matrix(541,-1380,118,-301) -> Matrix(3,2,2,1) Matrix(539,-1380,141,-361) -> Matrix(5,-2,3,-1) Matrix(3839,-9840,1124,-2881) -> Matrix(5,-4,4,-3) 1/1 Matrix(841,-2160,234,-601) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(419,-1080,116,-299) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(301,-780,93,-241) -> Matrix(1,2,1,1) Matrix(599,-1560,230,-599) -> Matrix(-1,0,2,1) (13/5,60/23) -> (-1/1,0/1) Matrix(781,-2040,299,-781) -> Matrix(1,0,7,-1) (60/23,34/13) -> (0/1,2/7) Matrix(2041,-5340,550,-1439) -> Matrix(7,-2,4,-1) Matrix(779,-2040,160,-419) -> Matrix(9,-4,2,-1) Matrix(481,-1260,92,-241) -> Matrix(5,-2,2,-1) Matrix(1141,-3000,205,-539) -> Matrix(11,-4,3,-1) Matrix(479,-1260,46,-121) -> Matrix(5,-2,-2,1) Matrix(659,-1740,114,-301) -> Matrix(13,-10,4,-3) Matrix(181,-480,23,-61) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(959,-2580,268,-721) -> Matrix(3,-2,2,-1) 1/1 Matrix(2339,-6300,535,-1441) -> Matrix(3,-2,5,-3) (0/1,2/3).(1/2,1/1) Matrix(5519,-14880,2047,-5519) -> Matrix(37,-24,57,-37) (62/23,240/89) -> (12/19,2/3) Matrix(15841,-42720,5874,-15841) -> Matrix(125,-84,186,-125) (240/89,89/33) -> (2/3,21/31) Matrix(1201,-3240,311,-839) -> Matrix(23,-16,13,-9) Matrix(421,-1140,89,-241) -> Matrix(7,-6,1,-1) Matrix(419,-1140,154,-419) -> Matrix(11,-10,12,-11) (19/7,30/11) -> (5/6,1/1) Matrix(241,-660,88,-241) -> Matrix(5,-6,4,-5) (30/11,11/4) -> (1/1,3/2) Matrix(1559,-4320,476,-1319) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(539,-1500,129,-359) -> Matrix(3,-2,1,-1) Matrix(839,-2340,237,-661) -> Matrix(3,2,1,1) Matrix(4559,-12720,1634,-4559) -> Matrix(-1,0,6,1) (53/19,120/43) -> (-1/3,0/1) Matrix(601,-1680,215,-601) -> Matrix(1,0,3,-1) (120/43,14/5) -> (0/1,2/3) Matrix(599,-1680,128,-359) -> Matrix(11,-8,4,-3) Matrix(3181,-8940,939,-2639) -> Matrix(29,-26,19,-17) Matrix(959,-2700,298,-839) -> Matrix(9,-10,8,-9) *** -> (1/1,5/4) Matrix(359,-1020,63,-179) -> Matrix(3,-2,1,-1) Matrix(481,-1380,84,-241) -> Matrix(5,-2,2,-1) Matrix(541,-1560,146,-421) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(421,-1320,96,-301) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(419,-1320,133,-419) -> Matrix(5,-8,3,-5) (22/7,60/19) -> (4/3,2/1) Matrix(721,-2280,228,-721) -> Matrix(-1,4,0,1) (60/19,19/6) -> (2/1,1/0) Matrix(1141,-3660,337,-1081) -> Matrix(13,-10,9,-7) Matrix(841,-2760,110,-361) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(181,-600,54,-179) -> Matrix(5,-4,4,-3) 1/1 Matrix(481,-1620,125,-421) -> Matrix(11,-14,7,-9) Matrix(479,-1620,89,-301) -> Matrix(7,-10,5,-7) (1/1,3/2).(4/3,2/1) Matrix(1079,-3660,301,-1021) -> Matrix(1,-2,3,-5) Matrix(421,-1440,88,-301) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(419,-1440,87,-299) -> Matrix(3,-8,1,-3) *** -> (2/1,4/1) Matrix(539,-1860,122,-421) -> Matrix(3,-2,2,-1) 1/1 Matrix(659,-2340,118,-419) -> Matrix(-1,6,0,1) *** -> (3/1,1/0) Matrix(14279,-50820,4012,-14279) -> Matrix(-1,34,0,1) (121/34,210/59) -> (17/1,1/0) Matrix(10501,-37380,2950,-10501) -> Matrix(1,18,0,-1) (210/59,89/25) -> (-9/1,1/0) Matrix(2999,-10680,809,-2881) -> Matrix(1,0,1,1) 0/1 Matrix(959,-3420,219,-781) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(419,-1500,50,-179) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(179,-660,16,-59) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1561,-5760,358,-1321) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1559,-5760,357,-1319) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(241,-900,64,-239) -> Matrix(3,-2,2,-1) 1/1 Matrix(61,-240,15,-59) -> Matrix(3,-4,1,-1) 2/1 Matrix(361,-1500,58,-241) -> Matrix(1,-2,2,-5) Matrix(239,-1020,56,-239) -> Matrix(-1,6,0,1) (17/4,30/7) -> (3/1,1/0) Matrix(181,-780,42,-181) -> Matrix(-1,2,0,1) (30/7,13/3) -> (1/1,1/0) Matrix(841,-3660,179,-779) -> Matrix(3,-10,1,-3) (2/1,4/1).(3/1,1/0) Matrix(299,-1320,41,-181) -> Matrix(7,-8,1,-1) Matrix(421,-1920,66,-301) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(599,-2760,130,-599) -> Matrix(19,-36,10,-19) (23/5,60/13) -> (9/5,2/1) Matrix(181,-840,39,-181) -> Matrix(7,-16,3,-7) (60/13,14/3) -> (2/1,8/3) Matrix(421,-1980,64,-301) -> Matrix(3,-10,2,-7) Matrix(419,-2280,77,-419) -> Matrix(13,-24,7,-13) (38/7,60/11) -> (12/7,2/1) Matrix(241,-1320,44,-241) -> Matrix(9,-20,4,-9) (60/11,11/2) -> (2/1,5/2) Matrix(61,-360,10,-59) -> Matrix(1,-4,0,1) 1/0 Matrix(181,-1200,27,-179) -> Matrix(7,-12,3,-5) 2/1 Matrix(121,-900,16,-119) -> Matrix(1,-14,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.