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 -1/1 -1/2 0/1 -9/1 0/1 -17/2 0/1 1/1 -8/1 -1/1 0/1 1/0 -15/2 -1/1 -22/3 -1/1 -1/2 0/1 -7/1 0/1 -20/3 -2/1 0/1 -33/5 0/1 -13/2 -2/1 -3/2 -32/5 -1/1 0/1 1/0 -19/3 0/1 -6/1 -1/1 -23/4 -1/2 0/1 -17/3 0/1 -45/8 1/0 -28/5 -2/1 -1/1 1/0 -39/7 0/1 -11/2 -2/1 -1/1 -27/5 -2/3 -16/3 -1/2 -1/3 0/1 -21/4 0/1 2/1 -5/1 -2/1 0/1 -24/5 1/0 -19/4 2/1 1/0 -14/3 -3/1 -2/1 1/0 -23/5 -2/1 -32/7 -2/1 -1/1 1/0 -41/9 -2/1 -9/2 -2/1 0/1 -31/7 -12/7 -22/5 -2/1 -3/2 -1/1 -57/13 -4/3 -35/8 -2/1 -4/3 -48/11 -1/1 -61/14 -4/3 -1/1 -13/3 -4/3 -30/7 -1/1 -17/4 -1/1 -2/3 -21/5 0/1 -4/1 -2/1 -1/1 1/0 -23/6 -3/2 -4/3 -19/5 -4/3 -15/4 -1/1 -26/7 -1/1 -4/5 -3/4 -63/17 -2/3 -37/10 -2/3 -1/2 -48/13 -1/1 -59/16 -1/1 -2/3 -11/3 -2/3 -29/8 0/1 1/2 -18/5 1/0 -61/17 -2/1 -43/12 -3/1 -2/1 -25/7 -2/1 -57/16 -2/1 -4/3 -89/25 -10/9 -32/9 -1/1 0/1 1/0 -39/11 -2/1 -7/2 -1/1 0/1 -38/11 -3/1 -2/1 1/0 -31/9 -4/3 -24/7 1/0 -41/12 -4/1 1/0 -58/17 -3/1 -2/1 1/0 -17/5 -2/1 -61/18 -2/1 -1/1 -44/13 -1/1 0/1 1/0 -27/8 -2/1 0/1 -10/3 -2/1 -1/1 1/0 -33/10 -2/1 0/1 -23/7 -2/1 -59/18 -4/3 -1/1 -36/11 -1/1 -13/4 0/1 1/0 -16/5 -2/1 -1/1 1/0 -19/6 0/1 1/0 -22/7 -4/1 -3/1 1/0 -3/1 -2/1 -23/8 -2/1 1/0 -20/7 -2/1 -17/6 -2/1 -5/3 -14/5 -3/2 -4/3 -1/1 -53/19 0/1 -39/14 -2/1 0/1 -25/9 -2/1 -4/3 -61/22 -1/1 0/1 -36/13 -1/1 -11/4 -2/1 -1/1 -30/11 -2/1 -19/7 -2/1 -27/10 -2/1 -8/5 -89/33 -14/9 -62/23 -2/1 -3/2 -1/1 -35/13 -2/1 -43/16 -2/1 -1/1 -8/3 -2/1 -5/3 -3/2 -37/14 -3/2 -4/3 -66/25 -1/1 -29/11 -4/3 -50/19 -3/2 -4/3 -1/1 -121/46 -4/3 -1/1 -71/27 -4/3 -21/8 -2/1 -4/3 -55/21 -2/1 -8/5 -89/34 -2/1 -3/2 -123/47 -2/1 -34/13 -5/3 -8/5 -3/2 -13/5 -4/3 -31/12 -2/1 1/0 -18/7 -3/2 -59/23 -4/3 -100/39 -2/1 -4/3 -41/16 -3/2 -4/3 -23/9 -4/3 -28/11 -4/3 -5/4 -1/1 -5/2 -2/1 -4/3 -32/13 -4/3 -5/4 -1/1 -27/11 -2/1 -49/20 -6/5 -1/1 -22/9 -1/1 0/1 1/0 -61/25 -2/1 -100/41 -4/1 -2/1 -39/16 -4/1 -2/1 -17/7 -2/1 -29/12 -8/5 -3/2 -12/5 -3/2 -31/13 -2/1 -50/21 -2/1 -3/2 -1/1 -69/29 -2/1 -19/8 -2/1 -3/2 -26/11 -3/2 -7/5 -4/3 -59/25 -4/3 -33/14 -2/1 -4/3 -40/17 -2/1 -4/3 -7/3 -2/1 -30/13 -3/2 -23/10 -3/2 -16/11 -85/37 -10/7 -62/27 -3/2 -13/9 -10/7 -101/44 -3/2 -16/11 -39/17 -10/7 -16/7 -3/2 -7/5 -4/3 -41/18 -3/2 -10/7 -25/11 -10/7 -4/3 -59/26 -24/17 -7/5 -34/15 -7/5 -11/8 -4/3 -43/19 -4/3 -9/4 -10/7 -4/3 -29/13 -34/25 -20/9 -4/3 -31/14 -4/3 -21/16 -11/5 -14/11 -24/11 -1/1 -13/6 -5/4 -6/5 -28/13 -7/6 -8/7 -1/1 -15/7 -1/1 -17/8 -1/1 0/1 -2/1 -3/2 -4/3 -1/1 -17/9 -4/3 -15/8 -3/2 -28/15 -3/2 -7/5 -4/3 -13/7 -4/3 -24/13 -7/5 -11/6 -7/5 -4/3 -20/11 -4/3 -29/16 -4/3 -5/4 -9/5 -4/3 -43/24 -7/5 -4/3 -120/67 -4/3 -77/43 -4/3 -34/19 -3/2 -4/3 -1/1 -59/33 -4/3 -25/14 -4/3 -91/51 -6/5 -66/37 -1/1 -41/23 -2/1 -16/9 -7/5 -11/8 -4/3 -39/22 -42/31 -4/3 -62/35 -23/17 -50/37 -27/20 -23/13 -4/3 -30/17 -4/3 -7/4 -4/3 -17/13 -33/19 -22/17 -92/53 -40/31 -49/38 -9/7 -151/87 -130/101 -210/121 -9/7 -59/34 -9/7 -32/25 -26/15 -4/3 -13/10 -9/7 -45/26 -9/7 -19/11 -14/11 -69/40 -4/3 -14/11 -50/29 -9/7 -14/11 -5/4 -31/18 -4/3 -5/4 -12/7 -5/4 -29/17 -6/5 -75/44 -5/4 -121/71 -26/21 -46/27 -5/4 -16/13 -11/9 -17/10 -6/5 -1/1 -39/23 -4/3 -139/82 -5/4 -6/5 -100/59 -4/3 -6/5 -61/36 -6/5 -1/1 -83/49 -4/3 -22/13 -4/3 -5/4 -1/1 -27/16 -2/1 -4/3 -5/3 -4/3 -33/20 -4/3 -14/11 -61/37 -4/3 -28/17 -4/3 -9/7 -5/4 -23/14 -4/3 -13/10 -41/25 -4/3 -100/61 -4/3 -22/17 -59/36 -4/3 -9/7 -18/11 -9/7 -31/19 -24/19 -75/46 -5/4 -44/27 -4/3 -9/7 -5/4 -13/8 -14/11 -5/4 -60/37 -5/4 -47/29 -16/13 -34/21 -4/3 -5/4 -1/1 -89/55 0/1 -55/34 -4/3 -21/13 -4/3 -71/44 -9/7 -14/11 -50/31 -4/3 -9/7 -5/4 -29/18 -14/11 -5/4 -37/23 -4/3 -82/51 -4/3 -9/7 -5/4 -45/28 -9/7 -8/5 -9/7 -14/11 -5/4 -35/22 -14/11 -24/19 -97/61 -24/19 -62/39 -29/23 -34/27 -5/4 -151/95 -54/43 -240/151 -5/4 -89/56 -4/3 -5/4 -27/17 -24/19 -73/46 -63/50 -34/27 -119/75 -44/35 -46/29 -29/23 -34/27 -5/4 -19/12 -54/43 -5/4 -30/19 -5/4 -11/7 -36/29 -36/23 -21/17 -61/39 -16/13 -25/16 -16/13 -89/57 -70/57 -64/41 -27/22 -38/31 -11/9 -39/25 -16/13 -53/34 -38/31 -11/9 -120/77 -11/9 -67/43 -28/23 -14/9 -5/4 -16/13 -11/9 -59/38 -38/31 -11/9 -45/29 -11/9 -31/20 -28/23 -17/14 -17/11 -6/5 -37/24 -17/14 -6/5 -20/13 -6/5 -23/15 -6/5 -3/2 -4/3 -6/5 -22/15 -4/3 -9/7 -5/4 -41/28 -24/19 -5/4 -60/41 -5/4 -19/13 -16/13 -16/11 -6/5 -7/6 -1/1 -61/42 -8/7 -1/1 -45/31 -1/1 -29/20 -3/2 -4/3 -13/9 -6/5 -36/25 -1/1 -59/41 -4/3 -82/57 -9/7 -14/11 -5/4 -23/16 -5/4 -6/5 -10/7 -5/4 -6/5 -1/1 -37/26 -5/4 -6/5 -64/45 -3/2 -4/3 -1/1 -91/64 -14/11 -5/4 -27/19 -6/5 -44/31 -4/3 -9/7 -5/4 -105/74 -5/4 -61/43 -6/5 -17/12 -6/5 -1/1 -58/41 -2/1 -3/2 -1/1 -99/70 -4/3 -6/5 -140/99 -4/3 -6/5 -41/29 -4/3 -24/17 -5/4 -55/39 -16/13 -6/5 -31/22 -5/4 -6/5 -7/5 -6/5 -39/28 -4/3 -6/5 -32/23 -3/2 -4/3 -1/1 -121/87 -4/3 -210/151 -4/3 -89/64 -4/3 -5/4 -57/41 -4/3 -25/18 -4/3 -6/5 -68/49 -5/4 -11/9 -6/5 -43/31 -6/5 -61/44 -6/5 -1/1 -18/13 -1/1 -29/21 -10/7 -40/29 -4/3 -11/8 -4/3 -9/7 -59/43 -14/11 -48/35 -9/7 -85/62 -32/25 -14/11 -37/27 -14/11 -63/46 -14/11 -52/41 -89/65 -100/79 -26/19 -19/15 -24/19 -5/4 -15/11 -5/4 -34/25 -5/4 -31/25 -26/21 -19/14 -5/4 -16/13 -23/17 -16/13 -27/20 -16/13 -6/5 -31/23 -26/21 -4/3 -5/4 -11/9 -6/5 -29/22 -17/14 -40/33 -25/19 -40/33 -6/5 -21/16 -52/43 -6/5 -17/13 -6/5 -30/23 -6/5 -13/10 -6/5 -31/26 -61/47 -32/27 -48/37 -13/11 -83/64 -20/17 -7/6 -35/27 -6/5 -57/44 -6/5 -20/17 -22/17 -6/5 -7/6 -1/1 -53/41 -6/5 -31/24 -5/4 -6/5 -9/7 -6/5 -41/32 -6/5 -7/6 -32/25 -6/5 -7/6 -1/1 -23/18 -5/4 -6/5 -60/47 -6/5 -37/29 -6/5 -14/11 -6/5 -7/6 -1/1 -61/48 -4/3 -1/1 -47/37 -4/3 -33/26 -4/3 -6/5 -19/15 -6/5 -24/19 -5/4 -29/23 -38/31 -5/4 -6/5 -21/17 -6/5 -16/13 -19/16 -32/27 -13/11 -27/22 -6/5 -32/27 -38/31 -32/27 -45/38 -13/11 -49/40 -110/93 -13/11 -60/49 -13/11 -11/9 -20/17 -39/32 -6/5 -20/17 -28/23 -6/5 -19/16 -13/11 -45/37 -13/11 -17/14 -13/11 -20/17 -40/33 -20/17 -23/19 -20/17 -29/24 -34/29 -7/6 -6/5 -7/6 -31/26 -6/5 -7/6 -25/21 -6/5 -8/7 -19/16 -7/6 -8/7 -32/27 -7/6 -8/7 -1/1 -13/11 -8/7 -33/28 -6/5 -8/7 -20/17 -6/5 -8/7 -27/23 -8/7 -7/6 -6/5 -13/11 -22/19 -20/17 -27/23 -7/6 -15/13 -7/6 -38/33 -7/6 -50/43 -43/37 -23/20 -7/6 -22/19 -8/7 -7/6 -8/7 -1/1 -17/15 -8/7 -9/8 -6/5 -8/7 -10/9 -7/6 -8/7 -1/1 -11/10 -6/5 -1/1 -1/1 -8/7 0/1 -1/1 1/1 -8/9 10/9 -1/1 -8/9 -7/8 9/8 -8/9 -6/7 17/15 -8/9 8/7 -1/1 -8/9 -7/8 15/13 -7/8 22/19 -7/8 -27/31 -20/23 7/6 -13/15 -6/7 20/17 -8/9 -6/7 33/28 -8/9 -6/7 13/11 -8/9 32/27 -1/1 -8/9 -7/8 19/16 -8/9 -7/8 6/5 -7/8 23/19 -20/23 17/14 -20/23 -13/15 45/37 -13/15 28/23 -13/15 -19/22 -6/7 39/32 -20/23 -6/7 11/9 -20/23 27/22 -32/37 -6/7 16/13 -13/15 -32/37 -19/22 21/17 -6/7 5/4 -6/7 24/19 -5/6 19/15 -6/7 14/11 -1/1 -7/8 -6/7 23/18 -6/7 -5/6 32/25 -1/1 -7/8 -6/7 41/32 -7/8 -6/7 9/7 -6/7 31/24 -6/7 -5/6 22/17 -1/1 -7/8 -6/7 57/44 -20/23 -6/7 35/27 -6/7 48/37 -13/15 61/47 -32/37 13/10 -31/36 -6/7 30/23 -6/7 17/13 -6/7 21/16 -6/7 -52/61 4/3 -6/7 -11/13 -5/6 23/17 -16/19 19/14 -16/19 -5/6 15/11 -5/6 26/19 -5/6 -24/29 -19/23 63/46 -52/63 -14/17 37/27 -14/17 48/35 -9/11 59/43 -14/17 11/8 -9/11 -4/5 29/21 -10/13 18/13 -1/1 61/44 -1/1 -6/7 43/31 -6/7 25/18 -6/7 -4/5 57/41 -4/5 89/64 -5/6 -4/5 32/23 -1/1 -4/5 -3/4 39/28 -6/7 -4/5 7/5 -6/7 38/27 -1/1 -7/8 -6/7 31/22 -6/7 -5/6 24/17 -5/6 41/29 -4/5 58/41 -1/1 -3/4 -2/3 17/12 -1/1 -6/7 61/43 -6/7 44/31 -5/6 -9/11 -4/5 27/19 -6/7 10/7 -1/1 -6/7 -5/6 33/23 -6/7 23/16 -6/7 -5/6 59/41 -4/5 36/25 -1/1 13/9 -6/7 16/11 -1/1 -7/8 -6/7 19/13 -16/19 22/15 -5/6 -9/11 -4/5 3/2 -6/7 -4/5 23/15 -6/7 20/13 -6/7 17/11 -6/7 14/9 -11/13 -16/19 -5/6 53/34 -11/13 -38/45 39/25 -16/19 25/16 -16/19 61/39 -16/19 36/23 -21/25 11/7 -36/43 30/19 -5/6 19/12 -5/6 -54/65 27/17 -24/29 89/56 -5/6 -4/5 62/39 -5/6 -34/41 -29/35 35/22 -24/29 -14/17 43/27 -14/17 8/5 -5/6 -14/17 -9/11 37/23 -4/5 66/41 -5/6 29/18 -5/6 -14/17 50/31 -5/6 -9/11 -4/5 121/75 -4/5 71/44 -14/17 -9/11 21/13 -4/5 55/34 -4/5 89/55 0/1 123/76 -8/9 -6/7 34/21 -1/1 -5/6 -4/5 13/8 -5/6 -14/17 31/19 -24/29 18/11 -9/11 59/36 -9/11 -4/5 100/61 -22/27 -4/5 41/25 -4/5 23/14 -13/16 -4/5 28/17 -5/6 -9/11 -4/5 5/3 -4/5 32/19 -1/1 -4/5 -3/4 27/16 -4/5 -2/3 49/29 0/1 22/13 -1/1 -5/6 -4/5 61/36 -1/1 -6/7 100/59 -6/7 -4/5 39/23 -4/5 17/10 -1/1 -6/7 29/17 -6/7 12/7 -5/6 31/18 -5/6 -4/5 50/29 -5/6 -14/17 -9/11 69/40 -14/17 -4/5 19/11 -14/17 26/15 -9/11 -13/16 -4/5 59/34 -32/39 -9/11 33/19 -22/27 40/23 -22/27 -4/5 7/4 -17/21 -4/5 30/17 -4/5 23/13 -4/5 85/48 -4/5 -58/73 62/35 -27/34 -50/63 -23/29 101/57 -4/5 39/22 -4/5 -42/53 16/9 -4/5 -11/14 -7/9 41/23 -2/3 25/14 -4/5 59/33 -4/5 34/19 -1/1 -4/5 -3/4 43/24 -4/5 -7/9 9/5 -4/5 29/16 -5/6 -4/5 20/11 -4/5 31/17 -42/53 11/6 -4/5 -7/9 24/13 -7/9 13/7 -4/5 28/15 -4/5 -7/9 -3/4 15/8 -3/4 17/9 -4/5 2/1 -1/1 -4/5 -3/4 17/8 -1/1 0/1 15/7 -1/1 28/13 -1/1 -8/9 -7/8 13/6 -6/7 -5/6 24/11 -1/1 11/5 -14/17 20/9 -4/5 29/13 -34/43 9/4 -4/5 -10/13 43/19 -4/5 120/53 -4/5 77/34 -4/5 -15/19 34/15 -4/5 -11/14 -7/9 59/26 -7/9 -24/31 25/11 -4/5 -10/13 91/40 -4/5 -3/4 66/29 -3/4 41/18 -10/13 -3/4 16/7 -4/5 -7/9 -3/4 39/17 -10/13 62/27 -10/13 -13/17 -3/4 23/10 -16/21 -3/4 30/13 -3/4 7/3 -2/3 33/14 -4/5 -2/3 92/39 -1/1 -4/5 -3/4 151/64 -5/6 -4/5 210/89 -4/5 59/25 -4/5 26/11 -4/5 -7/9 -3/4 45/19 -3/4 19/8 -3/4 -2/3 69/29 -2/3 50/21 -1/1 -3/4 -2/3 31/13 -2/3 12/5 -3/4 29/12 -3/4 -8/11 75/31 -5/7 121/50 -5/7 -22/31 46/19 -5/7 -12/17 -7/10 17/7 -2/3 39/16 -2/3 -4/7 139/57 -2/3 100/41 -2/3 -4/7 61/25 -2/3 83/34 -4/7 -1/2 22/9 -1/1 -1/2 0/1 27/11 -2/3 5/2 -4/5 -2/3 33/13 -2/3 61/24 -4/3 -1/1 28/11 -1/1 -5/6 -4/5 23/9 -4/5 41/16 -4/5 -3/4 100/39 -4/5 -2/3 59/23 -4/5 18/7 -3/4 31/12 -2/3 -1/2 75/29 -1/1 44/17 -1/1 -5/6 -4/5 13/5 -4/5 60/23 -3/4 47/18 -3/4 -14/19 34/13 -3/4 -8/11 -5/7 89/34 -3/4 -2/3 55/21 -8/11 -2/3 21/8 -4/5 -2/3 71/27 -4/5 50/19 -1/1 -4/5 -3/4 29/11 -4/5 37/14 -4/5 -3/4 82/31 -13/17 -16/21 -3/4 45/17 -3/4 8/3 -3/4 -5/7 -2/3 35/13 -2/3 97/36 -4/5 -3/4 62/23 -1/1 -3/4 -2/3 151/56 -16/21 -3/4 240/89 -3/4 89/33 -14/19 27/10 -8/11 -2/3 73/27 -8/11 119/44 -8/11 -5/7 46/17 -5/7 -7/10 -2/3 19/7 -2/3 30/11 -2/3 11/4 -1/1 -2/3 36/13 -1/1 61/22 -1/1 0/1 25/9 -4/5 -2/3 89/32 -4/5 -3/4 64/23 -5/7 -7/10 -2/3 39/14 -2/3 0/1 53/19 0/1 120/43 -1/1 67/24 -1/1 -6/7 14/5 -1/1 -4/5 -3/4 59/21 -10/13 45/16 -3/4 31/11 -2/3 17/6 -5/7 -2/3 37/13 -2/3 20/7 -2/3 23/8 -2/3 -1/2 3/1 -2/3 22/7 -3/5 -4/7 -1/2 41/13 -8/15 60/19 -1/2 19/6 -1/2 0/1 16/5 -1/1 -2/3 -1/2 61/19 -4/7 45/14 -1/2 29/9 -2/5 13/4 -1/2 0/1 36/11 -1/1 59/18 -1/1 -4/5 82/25 -1/1 -3/4 -2/3 23/7 -2/3 10/3 -1/1 -2/3 -1/2 37/11 -2/3 64/19 -1/1 -1/2 0/1 91/27 -4/7 27/8 -2/3 0/1 44/13 -1/1 -1/2 0/1 105/31 -1/1 61/18 -1/1 -2/3 17/5 -2/3 58/17 -2/3 -3/5 -1/2 99/29 -2/3 140/41 -2/3 -4/7 41/12 -4/7 -1/2 24/7 -1/2 55/16 0/1 31/9 -4/5 7/2 -1/1 0/1 39/11 -2/3 32/9 -1/1 -1/2 0/1 121/34 -8/7 -1/1 210/59 -1/1 89/25 -10/11 57/16 -4/5 -2/3 25/7 -2/3 68/19 -1/1 -2/3 -1/2 43/12 -2/3 -3/5 61/17 -2/3 18/5 -1/2 29/8 -1/4 0/1 40/11 0/1 11/3 -2/1 59/16 -2/1 -1/1 48/13 -1/1 85/23 0/1 37/10 -2/1 1/0 63/17 -2/1 89/24 -2/1 -3/2 26/7 -3/2 -4/3 -1/1 15/4 -1/1 34/9 -1/1 -7/8 -6/7 19/5 -4/5 23/6 -4/5 -3/4 27/7 -4/5 31/8 -3/4 -8/11 4/1 -1/1 -2/3 -1/2 29/7 -2/5 25/6 0/1 21/5 0/1 17/4 -2/1 -1/1 30/7 -1/1 13/3 -4/5 61/14 -1/1 -4/5 48/11 -1/1 83/19 -4/5 35/8 -4/5 -2/3 57/13 -4/5 22/5 -1/1 -3/4 -2/3 53/12 -8/11 -5/7 31/7 -12/17 9/2 -2/3 0/1 41/9 -2/3 32/7 -1/1 -2/3 -1/2 23/5 -2/3 60/13 -2/3 37/8 -2/3 -5/8 14/3 -2/3 -3/5 -1/2 61/13 0/1 47/10 -2/3 -5/8 33/7 -4/7 19/4 -1/2 -2/5 24/5 -1/2 29/6 -1/2 0/1 5/1 -2/3 0/1 21/4 -2/5 0/1 16/3 0/1 1/1 1/0 27/5 -2/1 38/7 -3/2 -4/3 -1/1 49/9 -8/7 60/11 -1/1 11/2 -1/1 -2/3 39/7 0/1 28/5 -1/1 -2/3 -1/2 45/8 -1/2 17/3 0/1 40/7 0/1 23/4 0/1 1/0 29/5 0/1 6/1 -1/1 31/5 -4/5 25/4 -2/3 19/3 0/1 32/5 -1/1 -1/2 0/1 13/2 -3/4 -2/3 33/5 0/1 20/3 -2/3 0/1 27/4 -2/3 0/1 7/1 0/1 22/3 -1/1 0/1 1/0 15/2 -1/1 38/5 -1/1 -2/3 -1/2 23/3 -2/3 8/1 -1/1 -1/2 0/1 17/2 -1/3 0/1 9/1 0/1 10/1 -1/1 0/1 1/0 11/1 0/1 1/0 -1/1 0/1 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(5,4,-4,-3) Matrix(119,1140,50,479) -> Matrix(1,2,-2,-3) Matrix(61,540,34,301) -> Matrix(3,4,-4,-5) Matrix(179,1500,50,419) -> Matrix(1,2,-2,-3) Matrix(61,480,-38,-299) -> Matrix(5,14,-4,-11) Matrix(299,2220,-186,-1381) -> Matrix(13,4,-10,-3) Matrix(59,420,42,299) -> Matrix(5,6,-6,-7) Matrix(61,420,-26,-179) -> Matrix(3,2,-2,-1) Matrix(299,1980,172,1139) -> Matrix(13,22,-16,-27) Matrix(301,1980,64,421) -> Matrix(1,4,-2,-7) Matrix(121,780,56,361) -> Matrix(7,8,-8,-9) Matrix(301,1920,66,421) -> Matrix(1,2,-2,-3) Matrix(239,1500,-134,-841) -> Matrix(3,2,-2,-1) Matrix(301,1740,-114,-659) -> Matrix(5,4,-4,-3) Matrix(179,1020,-116,-661) -> Matrix(5,-6,-4,5) Matrix(181,1020,96,541) -> Matrix(3,4,-4,-5) Matrix(299,1680,160,899) -> Matrix(3,10,-4,-13) Matrix(419,2340,118,659) -> Matrix(1,2,-2,-3) Matrix(539,3000,334,1859) -> Matrix(5,-4,-6,5) Matrix(299,1620,-122,-661) -> Matrix(5,4,-4,-3) Matrix(301,1620,212,1141) -> Matrix(3,4,-4,-5) Matrix(181,960,102,541) -> Matrix(19,4,-24,-5) Matrix(241,1260,92,481) -> Matrix(3,-2,-4,3) Matrix(299,1440,-212,-1021) -> Matrix(5,-6,-4,5) Matrix(301,1440,88,421) -> Matrix(1,2,-2,-3) Matrix(241,1140,-152,-719) -> Matrix(5,44,-4,-35) Matrix(181,840,-142,-659) -> Matrix(7,20,-6,-17) Matrix(301,1380,118,541) -> Matrix(5,6,-6,-7) Matrix(421,1920,66,301) -> Matrix(1,2,-2,-3) Matrix(659,3000,382,1739) -> Matrix(5,-4,-6,5) Matrix(121,540,54,241) -> Matrix(3,10,-4,-13) Matrix(421,1860,-122,-539) -> Matrix(5,8,-2,-3) Matrix(301,1320,96,421) -> Matrix(7,10,-12,-17) Matrix(781,3420,562,2461) -> Matrix(7,8,-8,-9) Matrix(1319,5760,-962,-4201) -> Matrix(41,50,-32,-39) Matrix(1321,5760,358,1561) -> Matrix(1,2,-2,-3) Matrix(1379,6000,510,2219) -> Matrix(7,12,-10,-17) Matrix(181,780,42,181) -> Matrix(7,8,-8,-9) Matrix(239,1020,56,239) -> Matrix(5,4,-4,-3) Matrix(241,1020,142,601) -> Matrix(3,4,-4,-5) Matrix(359,1500,-230,-961) -> Matrix(27,16,-22,-13) Matrix(421,1620,-296,-1139) -> Matrix(3,2,-2,-1) Matrix(361,1380,220,841) -> Matrix(31,40,-38,-49) Matrix(301,1140,-174,-659) -> Matrix(41,50,-32,-39) Matrix(419,1560,-242,-901) -> Matrix(49,40,-38,-31) Matrix(1439,5340,-550,-2041) -> Matrix(17,12,-10,-7) Matrix(421,1560,146,541) -> Matrix(1,0,0,1) Matrix(1559,5760,-1202,-4441) -> Matrix(19,6,-16,-5) Matrix(1561,5760,358,1321) -> Matrix(1,2,-2,-3) Matrix(179,660,16,59) -> Matrix(3,2,-2,-1) Matrix(181,660,-82,-299) -> Matrix(13,4,-10,-3) Matrix(299,1080,116,419) -> Matrix(3,-2,-4,3) Matrix(601,2160,234,841) -> Matrix(3,10,-4,-13) Matrix(1021,3660,720,2581) -> Matrix(5,16,-6,-19) Matrix(721,2580,-268,-959) -> Matrix(3,8,-2,-5) Matrix(959,3420,740,2639) -> Matrix(19,32,-22,-37) Matrix(4499,16020,2780,9899) -> Matrix(9,10,-10,-11) Matrix(3659,13020,-2108,-7501) -> Matrix(49,40,-38,-31) Matrix(659,2340,118,419) -> Matrix(1,2,-2,-3) Matrix(661,2340,424,1501) -> Matrix(27,38,-32,-45) Matrix(121,420,104,361) -> Matrix(7,-6,-8,7) Matrix(419,1440,-332,-1141) -> Matrix(5,-6,-4,5) Matrix(421,1440,88,301) -> Matrix(1,2,-2,-3) Matrix(2461,8400,-1072,-3659) -> Matrix(3,-4,-2,3) Matrix(299,1020,158,539) -> Matrix(3,10,-4,-13) Matrix(1079,3660,778,2639) -> Matrix(7,8,-8,-9) Matrix(1081,3660,-744,-2519) -> Matrix(7,6,-6,-5) Matrix(479,1620,390,1319) -> Matrix(19,32,-22,-37) Matrix(179,600,-54,-181) -> Matrix(1,0,0,1) Matrix(419,1380,-310,-1021) -> Matrix(5,-6,-4,5) Matrix(1921,6300,-1134,-3719) -> Matrix(3,2,-2,-1) Matrix(1319,4320,476,1559) -> Matrix(3,4,-4,-5) Matrix(239,780,110,359) -> Matrix(5,6,-6,-7) Matrix(241,780,-148,-479) -> Matrix(5,14,-4,-11) Matrix(301,960,132,421) -> Matrix(3,10,-4,-13) Matrix(419,1320,-286,-901) -> Matrix(5,24,-4,-19) Matrix(421,1320,96,301) -> Matrix(3,10,-4,-13) Matrix(541,1560,146,421) -> Matrix(1,0,0,1) Matrix(481,1380,84,241) -> Matrix(1,2,0,1) Matrix(359,1020,-296,-841) -> Matrix(73,126,-62,-107) Matrix(361,1020,-212,-599) -> Matrix(17,28,-14,-23) Matrix(601,1680,-386,-1079) -> Matrix(17,28,-14,-23) Matrix(839,2340,602,1679) -> Matrix(5,6,-6,-7) Matrix(539,1500,-410,-1141) -> Matrix(29,52,-24,-43) Matrix(1081,3000,476,1321) -> Matrix(17,24,-22,-31) Matrix(1559,4320,476,1319) -> Matrix(3,4,-4,-5) Matrix(239,660,130,359) -> Matrix(3,10,-4,-13) Matrix(241,660,88,241) -> Matrix(3,4,-4,-5) Matrix(419,1140,154,419) -> Matrix(11,20,-16,-29) Matrix(421,1140,-332,-899) -> Matrix(17,28,-14,-23) Matrix(1801,4860,534,1441) -> Matrix(1,2,-4,-7) Matrix(5519,14880,-3472,-9361) -> Matrix(63,92,-50,-73) Matrix(2761,7440,-1202,-3239) -> Matrix(23,36,-16,-25) Matrix(179,480,22,59) -> Matrix(1,2,-4,-7) Matrix(181,480,-158,-419) -> Matrix(23,38,-20,-33) Matrix(3001,7920,-1682,-4439) -> Matrix(3,2,-2,-1) Matrix(1139,3000,478,1259) -> Matrix(5,6,-6,-7) Matrix(2099,5520,570,1499) -> Matrix(1,2,-2,-3) Matrix(1141,3000,936,2461) -> Matrix(19,32,-22,-37) Matrix(481,1260,92,241) -> Matrix(1,2,-4,-7) Matrix(779,2040,160,419) -> Matrix(1,2,-4,-7) Matrix(6121,16020,4402,11521) -> Matrix(13,22,-16,-27) Matrix(781,2040,-482,-1259) -> Matrix(17,28,-14,-23) Matrix(301,780,-208,-539) -> Matrix(3,2,-2,-1) Matrix(419,1080,116,299) -> Matrix(1,2,-4,-7) Matrix(841,2160,234,601) -> Matrix(7,10,-12,-17) Matrix(4679,12000,1918,4919) -> Matrix(7,10,-12,-17) Matrix(7021,18000,-4142,-10619) -> Matrix(3,2,-2,-1) Matrix(539,1380,398,1019) -> Matrix(47,68,-56,-81) Matrix(541,1380,118,301) -> Matrix(5,6,-6,-7) Matrix(119,300,-48,-121) -> Matrix(1,0,0,1) Matrix(1441,3540,-830,-2039) -> Matrix(13,4,-10,-3) Matrix(1201,2940,-980,-2399) -> Matrix(45,32,-38,-27) Matrix(2581,6300,-1794,-4379) -> Matrix(5,14,-4,-11) Matrix(4919,12000,1918,4679) -> Matrix(3,10,-4,-13) Matrix(6299,15360,-4454,-10861) -> Matrix(5,14,-4,-11) Matrix(419,1020,320,779) -> Matrix(29,64,-34,-75) Matrix(421,1020,-272,-659) -> Matrix(29,52,-24,-43) Matrix(299,720,174,419) -> Matrix(33,52,-40,-63) Matrix(301,720,176,421) -> Matrix(7,8,-8,-9) Matrix(1259,3000,478,1139) -> Matrix(5,6,-6,-7) Matrix(479,1140,50,119) -> Matrix(1,2,-2,-3) Matrix(1261,3000,984,2341) -> Matrix(19,32,-22,-37) Matrix(481,1140,-354,-839) -> Matrix(37,58,-30,-47) Matrix(1499,3540,838,1979) -> Matrix(17,24,-22,-31) Matrix(1679,3960,-1018,-2401) -> Matrix(23,32,-18,-25) Matrix(841,1980,714,1681) -> Matrix(9,10,-10,-11) Matrix(181,420,78,181) -> Matrix(7,12,-10,-17) Matrix(599,1380,260,599) -> Matrix(65,96,-86,-127) Matrix(2219,5100,600,1379) -> Matrix(7,10,2,3) Matrix(4079,9360,-2406,-5521) -> Matrix(43,62,-34,-49) Matrix(419,960,340,779) -> Matrix(121,172,-140,-199) Matrix(421,960,132,301) -> Matrix(7,10,-12,-17) Matrix(659,1500,-554,-1261) -> Matrix(33,46,-28,-39) Matrix(1321,3000,476,1081) -> Matrix(17,24,-22,-31) Matrix(1561,3540,900,2041) -> Matrix(7,8,-8,-9) Matrix(1801,4080,-1006,-2279) -> Matrix(23,32,-18,-25) Matrix(239,540,212,479) -> Matrix(37,52,-42,-59) Matrix(241,540,54,121) -> Matrix(7,10,-12,-17) Matrix(539,1200,296,659) -> Matrix(113,152,-142,-191) Matrix(541,1200,298,661) -> Matrix(79,104,-98,-129) Matrix(301,660,192,421) -> Matrix(89,110,-106,-131) Matrix(359,780,110,239) -> Matrix(5,6,-6,-7) Matrix(361,780,56,121) -> Matrix(7,8,-8,-9) Matrix(781,1680,642,1381) -> Matrix(97,110,-112,-127) Matrix(479,1020,394,839) -> Matrix(33,20,-38,-23) Matrix(481,1020,340,721) -> Matrix(5,6,-6,-7) Matrix(539,1020,158,299) -> Matrix(7,10,-12,-17) Matrix(541,1020,96,181) -> Matrix(3,4,-4,-5) Matrix(899,1680,160,299) -> Matrix(7,10,-12,-17) Matrix(419,780,354,659) -> Matrix(37,52,-42,-59) Matrix(421,780,292,541) -> Matrix(27,38,-32,-45) Matrix(359,660,130,239) -> Matrix(7,10,-12,-17) Matrix(361,660,-262,-479) -> Matrix(47,64,-36,-49) Matrix(959,1740,264,479) -> Matrix(3,4,-16,-21) Matrix(299,540,232,419) -> Matrix(9,10,-10,-11) Matrix(301,540,34,61) -> Matrix(3,4,-4,-5) Matrix(8039,14400,3550,6359) -> Matrix(65,88,-82,-111) Matrix(8041,14400,3552,6361) -> Matrix(31,40,-38,-49) Matrix(1979,3540,838,1499) -> Matrix(17,24,-22,-31) Matrix(1679,3000,1074,1919) -> Matrix(143,196,-170,-233) Matrix(1681,3000,404,721) -> Matrix(3,4,-10,-13) Matrix(539,960,370,659) -> Matrix(27,38,-32,-45) Matrix(541,960,102,181) -> Matrix(3,4,8,11) Matrix(4741,8400,-3352,-5939) -> Matrix(71,96,-54,-73) Matrix(4201,7440,-2642,-4679) -> Matrix(495,668,-392,-529) Matrix(781,1380,442,781) -> Matrix(233,312,-292,-391) Matrix(239,420,136,239) -> Matrix(103,136,-128,-169) Matrix(241,420,-206,-359) -> Matrix(39,50,-32,-41) Matrix(29039,50400,8158,14159) -> Matrix(171,220,-178,-229) Matrix(21781,37800,6120,10621) -> Matrix(81,104,-74,-95) Matrix(2041,3540,900,1561) -> Matrix(7,8,-8,-9) Matrix(1739,3000,382,659) -> Matrix(3,4,-10,-13) Matrix(661,1140,592,1021) -> Matrix(45,58,-52,-67) Matrix(1741,3000,1080,1861) -> Matrix(71,90,-86,-109) Matrix(419,720,174,299) -> Matrix(41,52,-56,-71) Matrix(421,720,176,301) -> Matrix(7,8,-8,-9) Matrix(2041,3480,634,1081) -> Matrix(3,4,-10,-13) Matrix(5879,10020,1830,3119) -> Matrix(37,46,-70,-87) Matrix(2641,4500,564,961) -> Matrix(21,26,-38,-47) Matrix(601,1020,142,241) -> Matrix(3,4,-4,-5) Matrix(7081,12000,4320,7321) -> Matrix(49,58,-60,-71) Matrix(2161,3660,284,481) -> Matrix(5,6,-6,-7) Matrix(959,1620,-782,-1321) -> Matrix(7,20,-6,-17) Matrix(179,300,-108,-181) -> Matrix(23,32,-18,-25) Matrix(3241,5340,-2330,-3839) -> Matrix(25,32,-18,-23) Matrix(839,1380,656,1079) -> Matrix(45,58,-52,-67) Matrix(841,1380,220,361) -> Matrix(31,40,-38,-49) Matrix(6001,9840,-4244,-6959) -> Matrix(25,32,-18,-23) Matrix(7321,12000,4320,7081) -> Matrix(45,58,-52,-67) Matrix(1319,2160,952,1559) -> Matrix(45,58,-52,-67) Matrix(661,1080,478,781) -> Matrix(17,22,-24,-31) Matrix(2281,3720,810,1321) -> Matrix(65,82,-88,-111) Matrix(4859,7920,-3424,-5581) -> Matrix(1,0,0,1) Matrix(2219,3600,850,1379) -> Matrix(89,112,-120,-151) Matrix(2221,3600,852,1381) -> Matrix(55,68,-72,-89) Matrix(3299,5340,-2410,-3901) -> Matrix(81,100,-64,-79) Matrix(4079,6600,1186,1919) -> Matrix(3,4,-4,-5) Matrix(779,1260,630,1019) -> Matrix(81,106,-94,-123) Matrix(1859,3000,334,539) -> Matrix(3,4,-10,-13) Matrix(781,1260,-706,-1139) -> Matrix(53,68,-46,-59) Matrix(1861,3000,1080,1741) -> Matrix(71,90,-86,-109) Matrix(1081,1740,-894,-1439) -> Matrix(59,72,-50,-61) Matrix(3059,4920,932,1499) -> Matrix(17,22,-24,-31) Matrix(1621,2580,-1168,-1859) -> Matrix(79,100,-64,-81) Matrix(3961,6300,906,1441) -> Matrix(41,52,-56,-71) Matrix(36239,57600,13438,21359) -> Matrix(185,232,-248,-311) Matrix(36241,57600,13440,21361) -> Matrix(55,68,-72,-89) Matrix(2039,3240,528,839) -> Matrix(41,52,-56,-71) Matrix(1739,2760,264,419) -> Matrix(19,24,-42,-53) Matrix(3781,6000,2912,4621) -> Matrix(537,676,-622,-783) Matrix(2761,4380,984,1561) -> Matrix(65,82,-88,-111) Matrix(721,1140,456,721) -> Matrix(431,540,-518,-649) Matrix(419,660,266,419) -> Matrix(289,360,-346,-431) Matrix(421,660,192,301) -> Matrix(89,110,-106,-131) Matrix(2761,4320,1918,3001) -> Matrix(55,68,-72,-89) Matrix(1919,3000,1074,1679) -> Matrix(159,196,-202,-249) Matrix(1921,3000,308,481) -> Matrix(83,102,-118,-145) Matrix(7379,11520,2190,3419) -> Matrix(31,38,-40,-49) Matrix(1501,2340,424,661) -> Matrix(31,38,-40,-49) Matrix(9239,14400,3310,5159) -> Matrix(85,104,-94,-115) Matrix(9241,14400,3312,5161) -> Matrix(23,28,-14,-17) Matrix(2819,4380,1042,1619) -> Matrix(83,102,-118,-145) Matrix(5759,8940,1700,2639) -> Matrix(49,60,-58,-71) Matrix(2399,3720,928,1439) -> Matrix(5,6,4,5) Matrix(779,1200,272,419) -> Matrix(33,40,-52,-63) Matrix(781,1200,274,421) -> Matrix(47,56,-68,-81) Matrix(1019,1560,744,1139) -> Matrix(109,128,-132,-155) Matrix(899,1320,694,1019) -> Matrix(45,58,-52,-67) Matrix(2459,3600,778,1139) -> Matrix(19,24,-42,-53) Matrix(2461,3600,780,1141) -> Matrix(45,56,-86,-107) Matrix(659,960,370,539) -> Matrix(31,38,-40,-49) Matrix(6901,10020,2852,4141) -> Matrix(57,62,-80,-87) Matrix(2399,3480,992,1439) -> Matrix(7,12,-10,-17) Matrix(541,780,292,421) -> Matrix(31,38,-40,-49) Matrix(3001,4320,1918,2761) -> Matrix(47,68,-56,-81) Matrix(3421,4920,1294,1861) -> Matrix(31,38,-40,-49) Matrix(419,600,-294,-421) -> Matrix(1,0,0,1) Matrix(8101,11520,2912,4141) -> Matrix(17,22,-24,-31) Matrix(3419,4860,2152,3059) -> Matrix(71,90,-86,-109) Matrix(1141,1620,212,301) -> Matrix(3,4,-4,-5) Matrix(6301,8940,2242,3181) -> Matrix(55,68,-72,-89) Matrix(2581,3660,720,1021) -> Matrix(13,16,-22,-27) Matrix(721,1020,340,481) -> Matrix(5,6,-6,-7) Matrix(1019,1440,806,1139) -> Matrix(9,10,-10,-11) Matrix(4681,6600,1788,2521) -> Matrix(7,8,-8,-9) Matrix(1321,1860,-1022,-1439) -> Matrix(1,0,0,1) Matrix(1679,2340,602,839) -> Matrix(5,6,-6,-7) Matrix(1681,2340,1380,1921) -> Matrix(45,58,-52,-67) Matrix(27179,37800,11518,16019) -> Matrix(17,24,-22,-31) Matrix(36241,50400,15360,21361) -> Matrix(31,40,-38,-49) Matrix(7681,10680,2072,2881) -> Matrix(1,2,-2,-3) Matrix(2461,3420,562,781) -> Matrix(7,8,-8,-9) Matrix(1081,1500,952,1321) -> Matrix(67,82,-76,-93) Matrix(2639,3660,778,1079) -> Matrix(7,8,-8,-9) Matrix(1559,2160,952,1319) -> Matrix(49,58,-60,-71) Matrix(781,1080,478,661) -> Matrix(13,22,-16,-27) Matrix(1261,1740,566,781) -> Matrix(65,88,-82,-111) Matrix(4021,5520,2492,3421) -> Matrix(71,90,-86,-109) Matrix(4199,5760,3236,4439) -> Matrix(81,106,-94,-123) Matrix(3721,5100,2102,2881) -> Matrix(369,470,-464,-591) Matrix(1139,1560,744,1019) -> Matrix(101,128,-116,-147) Matrix(7799,10680,2190,2999) -> Matrix(71,90,-86,-109) Matrix(659,900,-484,-661) -> Matrix(199,250,-160,-201) Matrix(1019,1380,398,539) -> Matrix(55,68,-72,-89) Matrix(2401,3240,890,1201) -> Matrix(7,8,-8,-9) Matrix(179,240,44,59) -> Matrix(13,16,-22,-27) Matrix(181,240,46,61) -> Matrix(13,16,-22,-27) Matrix(2279,3000,1002,1319) -> Matrix(155,188,-202,-245) Matrix(779,1020,320,419) -> Matrix(53,64,-82,-99) Matrix(781,1020,598,781) -> Matrix(529,636,-618,-743) Matrix(599,780,460,599) -> Matrix(311,372,-362,-433) Matrix(2819,3660,600,779) -> Matrix(27,32,-38,-45) Matrix(4439,5760,3236,4199) -> Matrix(89,106,-110,-131) Matrix(4859,6300,1804,2339) -> Matrix(27,32,-38,-45) Matrix(2639,3420,740,959) -> Matrix(27,32,-38,-45) Matrix(1019,1320,694,899) -> Matrix(49,58,-60,-71) Matrix(1021,1320,140,181) -> Matrix(5,6,-6,-7) Matrix(419,540,232,299) -> Matrix(9,10,-10,-11) Matrix(2341,3000,984,1261) -> Matrix(27,32,-38,-45) Matrix(1499,1920,1264,1619) -> Matrix(13,14,-14,-15) Matrix(1079,1380,656,839) -> Matrix(49,58,-60,-71) Matrix(2819,3600,610,779) -> Matrix(33,40,-52,-63) Matrix(2821,3600,612,781) -> Matrix(47,56,-68,-81) Matrix(3539,4500,1462,1859) -> Matrix(37,42,-52,-59) Matrix(2881,3660,662,841) -> Matrix(7,8,-8,-9) Matrix(1559,1980,1322,1679) -> Matrix(11,12,-12,-13) Matrix(1139,1440,806,1019) -> Matrix(9,10,-10,-11) Matrix(1621,2040,1002,1261) -> Matrix(31,38,-40,-49) Matrix(1019,1260,630,779) -> Matrix(89,106,-110,-131) Matrix(779,960,340,419) -> Matrix(145,172,-188,-223) Matrix(1319,1620,390,479) -> Matrix(27,32,-38,-45) Matrix(2939,3600,538,659) -> Matrix(115,136,-126,-149) Matrix(2941,3600,540,661) -> Matrix(105,124,-94,-111) Matrix(2461,3000,936,1141) -> Matrix(27,32,-38,-45) Matrix(1921,2340,1380,1681) -> Matrix(49,58,-60,-71) Matrix(1381,1680,642,781) -> Matrix(93,110,-104,-123) Matrix(839,1020,394,479) -> Matrix(17,20,-6,-7) Matrix(1139,1380,742,899) -> Matrix(155,182,-178,-209) Matrix(299,360,-250,-301) -> Matrix(167,196,-144,-169) Matrix(2519,3000,906,1079) -> Matrix(9,10,-10,-11) Matrix(1619,1920,1264,1499) -> Matrix(13,14,-14,-15) Matrix(659,780,354,419) -> Matrix(45,52,-58,-67) Matrix(2341,2760,866,1021) -> Matrix(27,32,-38,-45) Matrix(1019,1200,152,179) -> Matrix(7,8,-8,-9) Matrix(1021,1200,154,181) -> Matrix(7,8,-8,-9) Matrix(1139,1320,258,299) -> Matrix(63,74,-86,-101) Matrix(779,900,-676,-781) -> Matrix(419,490,-360,-421) Matrix(3179,3660,1302,1499) -> Matrix(43,50,-80,-93) Matrix(421,480,264,301) -> Matrix(49,58,-60,-71) Matrix(479,540,212,239) -> Matrix(45,52,-58,-67) Matrix(1021,1140,592,661) -> Matrix(49,58,-60,-71) Matrix(601,660,438,481) -> Matrix(49,58,-60,-71) Matrix(1,0,2,1) -> Matrix(15,16,-16,-17) Matrix(1139,-1260,706,-781) -> Matrix(77,68,-94,-83) Matrix(419,-480,158,-181) -> Matrix(43,38,-60,-53) Matrix(1921,-2220,726,-839) -> Matrix(197,172,-260,-227) Matrix(359,-420,206,-241) -> Matrix(59,50,-72,-61) Matrix(1261,-1500,554,-659) -> Matrix(53,46,-68,-59) Matrix(1439,-1740,894,-1081) -> Matrix(83,72,-98,-85) Matrix(841,-1020,296,-359) -> Matrix(145,126,-206,-179) Matrix(1321,-1620,782,-959) -> Matrix(23,20,-38,-33) Matrix(1141,-1440,332,-419) -> Matrix(7,6,-20,-17) Matrix(899,-1140,332,-421) -> Matrix(33,28,-46,-39) Matrix(659,-840,142,-181) -> Matrix(23,20,-38,-33) Matrix(1439,-1860,1022,-1321) -> Matrix(1,0,0,1) Matrix(4441,-5760,1202,-1559) -> Matrix(7,6,8,7) Matrix(1141,-1500,410,-539) -> Matrix(61,52,-88,-75) Matrix(1199,-1620,356,-481) -> Matrix(7,6,-20,-17) Matrix(839,-1140,354,-481) -> Matrix(69,58,-94,-79) Matrix(1141,-1560,482,-659) -> Matrix(111,92,-146,-121) Matrix(3901,-5340,2410,-3299) -> Matrix(121,100,-144,-119) Matrix(4201,-5760,962,-1319) -> Matrix(61,50,-72,-59) Matrix(479,-660,262,-361) -> Matrix(79,64,-100,-81) Matrix(1859,-2580,1168,-1621) -> Matrix(119,100,-144,-121) Matrix(9361,-13020,3968,-5519) -> Matrix(1,0,0,1) Matrix(1021,-1440,212,-299) -> Matrix(7,6,-20,-17) Matrix(5939,-8400,3352,-4741) -> Matrix(119,96,-150,-121) Matrix(2579,-3660,804,-1141) -> Matrix(17,14,-28,-23) Matrix(421,-600,294,-419) -> Matrix(1,0,0,1) Matrix(961,-1380,250,-359) -> Matrix(3,2,-2,-1) Matrix(4379,-6300,1794,-2581) -> Matrix(17,14,-28,-23) Matrix(539,-780,208,-301) -> Matrix(3,2,-2,-1) Matrix(901,-1320,286,-419) -> Matrix(29,24,-52,-43) Matrix(661,-1020,116,-179) -> Matrix(7,6,-20,-17) Matrix(659,-1020,272,-421) -> Matrix(61,52,-88,-75) Matrix(1079,-1680,386,-601) -> Matrix(33,28,-46,-39) Matrix(961,-1500,230,-359) -> Matrix(19,16,-6,-5) Matrix(719,-1140,152,-241) -> Matrix(53,44,-100,-83) Matrix(9361,-14880,3472,-5519) -> Matrix(111,92,-146,-121) Matrix(4679,-7440,2642,-4201) -> Matrix(807,668,-1016,-841) Matrix(299,-480,38,-61) -> Matrix(17,14,-28,-23) Matrix(4919,-7920,2162,-3481) -> Matrix(75,62,-98,-81) Matrix(1259,-2040,482,-781) -> Matrix(33,28,-46,-39) Matrix(479,-780,148,-241) -> Matrix(17,14,-28,-23) Matrix(10979,-18000,4502,-7381) -> Matrix(37,30,-58,-47) Matrix(181,-300,108,-179) -> Matrix(39,32,-50,-41) Matrix(2099,-3540,890,-1501) -> Matrix(1,0,0,1) Matrix(1739,-2940,320,-541) -> Matrix(9,8,-8,-7) Matrix(3719,-6300,1134,-1921) -> Matrix(3,2,-2,-1) Matrix(9061,-15360,2654,-4499) -> Matrix(17,14,-28,-23) Matrix(599,-1020,212,-361) -> Matrix(33,28,-46,-39) Matrix(659,-1140,174,-301) -> Matrix(61,50,-72,-59) Matrix(2281,-3960,898,-1559) -> Matrix(5,4,6,5) Matrix(5281,-9360,2166,-3839) -> Matrix(43,34,-62,-49) Matrix(841,-1500,134,-239) -> Matrix(3,2,-2,-1) Matrix(2279,-4080,1006,-1801) -> Matrix(39,32,-50,-41) Matrix(299,-660,82,-181) -> Matrix(5,4,6,5) Matrix(3659,-8400,1072,-2461) -> Matrix(5,4,-14,-11) Matrix(3239,-7440,1202,-2761) -> Matrix(47,36,-64,-49) Matrix(179,-420,26,-61) -> Matrix(3,2,-2,-1) Matrix(661,-1620,122,-299) -> Matrix(5,4,-4,-3) Matrix(121,-300,48,-119) -> Matrix(1,0,0,1) Matrix(2099,-5340,590,-1501) -> Matrix(5,4,-4,-3) Matrix(3839,-9840,1124,-2881) -> Matrix(11,8,-18,-13) Matrix(3061,-7920,904,-2339) -> Matrix(5,4,-4,-3) Matrix(2041,-5340,550,-1439) -> Matrix(17,12,-10,-7) Matrix(479,-1260,46,-121) -> Matrix(5,4,-4,-3) Matrix(659,-1740,114,-301) -> Matrix(5,4,-4,-3) Matrix(959,-2580,268,-721) -> Matrix(11,8,-18,-13) Matrix(181,-600,54,-179) -> Matrix(1,0,0,1) Matrix(539,-1860,122,-421) -> Matrix(13,8,-18,-11) Matrix(241,-900,64,-239) -> Matrix(9,10,-10,-11) Matrix(61,-360,10,-59) -> Matrix(3,4,-4,-5) Matrix(121,-900,16,-119) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 96 Degree of the the map X: 96 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 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 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: 64 Genus: 65 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -15/2 -6/1 -5/1 -24/5 -14/3 -4/1 -15/4 -18/5 -5/2 -12/5 -15/7 -2/1 -5/3 -15/11 -5/4 -10/9 0/1 1/1 5/4 15/11 10/7 3/2 30/19 5/3 30/17 2/1 15/7 20/9 12/5 5/2 100/39 60/23 30/11 20/7 3/1 10/3 7/2 18/5 11/3 15/4 4/1 21/5 17/4 30/7 9/2 60/13 14/3 24/5 5/1 21/4 27/5 60/11 11/2 17/3 6/1 20/3 27/4 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 0/1 -8/1 -1/1 0/1 1/0 -15/2 -1/1 -7/1 0/1 -6/1 -1/1 -17/3 0/1 -11/2 -2/1 -1/1 -27/5 -2/3 -16/3 -1/2 -1/3 0/1 -21/4 0/1 2/1 -5/1 -2/1 0/1 -24/5 1/0 -19/4 2/1 1/0 -14/3 -3/1 -2/1 1/0 -23/5 -2/1 -32/7 -2/1 -1/1 1/0 -9/2 -2/1 0/1 -4/1 -2/1 -1/1 1/0 -23/6 -3/2 -4/3 -19/5 -4/3 -15/4 -1/1 -26/7 -1/1 -4/5 -3/4 -11/3 -2/3 -18/5 1/0 -7/2 -1/1 0/1 -24/7 1/0 -41/12 -4/1 1/0 -58/17 -3/1 -2/1 1/0 -17/5 -2/1 -44/13 -1/1 0/1 1/0 -27/8 -2/1 0/1 -10/3 -2/1 -1/1 1/0 -3/1 -2/1 -20/7 -2/1 -17/6 -2/1 -5/3 -14/5 -3/2 -4/3 -1/1 -25/9 -2/1 -4/3 -36/13 -1/1 -11/4 -2/1 -1/1 -30/11 -2/1 -19/7 -2/1 -27/10 -2/1 -8/5 -35/13 -2/1 -8/3 -2/1 -5/3 -3/2 -29/11 -4/3 -50/19 -3/2 -4/3 -1/1 -21/8 -2/1 -4/3 -55/21 -2/1 -8/5 -34/13 -5/3 -8/5 -3/2 -13/5 -4/3 -18/7 -3/2 -41/16 -3/2 -4/3 -23/9 -4/3 -28/11 -4/3 -5/4 -1/1 -5/2 -2/1 -4/3 -27/11 -2/1 -49/20 -6/5 -1/1 -22/9 -1/1 0/1 1/0 -61/25 -2/1 -100/41 -4/1 -2/1 -39/16 -4/1 -2/1 -17/7 -2/1 -29/12 -8/5 -3/2 -12/5 -3/2 -31/13 -2/1 -50/21 -2/1 -3/2 -1/1 -69/29 -2/1 -19/8 -2/1 -3/2 -26/11 -3/2 -7/5 -4/3 -33/14 -2/1 -4/3 -7/3 -2/1 -30/13 -3/2 -23/10 -3/2 -16/11 -39/17 -10/7 -16/7 -3/2 -7/5 -4/3 -9/4 -10/7 -4/3 -20/9 -4/3 -11/5 -14/11 -24/11 -1/1 -13/6 -5/4 -6/5 -15/7 -1/1 -17/8 -1/1 0/1 -2/1 -3/2 -4/3 -1/1 -17/9 -4/3 -15/8 -3/2 -13/7 -4/3 -11/6 -7/5 -4/3 -20/11 -4/3 -9/5 -4/3 -7/4 -4/3 -17/13 -33/19 -22/17 -26/15 -4/3 -13/10 -9/7 -45/26 -9/7 -19/11 -14/11 -50/29 -9/7 -14/11 -5/4 -31/18 -4/3 -5/4 -12/7 -5/4 -29/17 -6/5 -46/27 -5/4 -16/13 -11/9 -17/10 -6/5 -1/1 -39/23 -4/3 -100/59 -4/3 -6/5 -61/36 -6/5 -1/1 -22/13 -4/3 -5/4 -1/1 -27/16 -2/1 -4/3 -5/3 -4/3 -28/17 -4/3 -9/7 -5/4 -23/14 -4/3 -13/10 -41/25 -4/3 -100/61 -4/3 -22/17 -59/36 -4/3 -9/7 -18/11 -9/7 -13/8 -14/11 -5/4 -60/37 -5/4 -47/29 -16/13 -34/21 -4/3 -5/4 -1/1 -21/13 -4/3 -50/31 -4/3 -9/7 -5/4 -29/18 -14/11 -5/4 -37/23 -4/3 -45/28 -9/7 -8/5 -9/7 -14/11 -5/4 -35/22 -14/11 -24/19 -27/17 -24/19 -46/29 -29/23 -34/27 -5/4 -19/12 -54/43 -5/4 -30/19 -5/4 -11/7 -36/29 -36/23 -21/17 -25/16 -16/13 -39/25 -16/13 -14/9 -5/4 -16/13 -11/9 -17/11 -6/5 -20/13 -6/5 -3/2 -4/3 -6/5 -10/7 -5/4 -6/5 -1/1 -27/19 -6/5 -44/31 -4/3 -9/7 -5/4 -17/12 -6/5 -1/1 -58/41 -2/1 -3/2 -1/1 -41/29 -4/3 -24/17 -5/4 -31/22 -5/4 -6/5 -7/5 -6/5 -18/13 -1/1 -29/21 -10/7 -40/29 -4/3 -11/8 -4/3 -9/7 -37/27 -14/11 -26/19 -19/15 -24/19 -5/4 -15/11 -5/4 -34/25 -5/4 -31/25 -26/21 -19/14 -5/4 -16/13 -23/17 -16/13 -4/3 -5/4 -11/9 -6/5 -21/16 -52/43 -6/5 -17/13 -6/5 -30/23 -6/5 -13/10 -6/5 -31/26 -9/7 -6/5 -32/25 -6/5 -7/6 -1/1 -23/18 -5/4 -6/5 -60/47 -6/5 -37/29 -6/5 -14/11 -6/5 -7/6 -1/1 -33/26 -4/3 -6/5 -19/15 -6/5 -24/19 -5/4 -5/4 -6/5 -21/17 -6/5 -16/13 -19/16 -32/27 -13/11 -27/22 -6/5 -32/27 -38/31 -32/27 -45/38 -13/11 -49/40 -110/93 -13/11 -60/49 -13/11 -11/9 -20/17 -28/23 -6/5 -19/16 -13/11 -17/14 -13/11 -20/17 -40/33 -20/17 -23/19 -20/17 -6/5 -7/6 -13/11 -8/7 -33/28 -6/5 -8/7 -20/17 -6/5 -8/7 -27/23 -8/7 -7/6 -6/5 -13/11 -15/13 -7/6 -23/20 -7/6 -22/19 -8/7 -7/6 -8/7 -1/1 -9/8 -6/5 -8/7 -10/9 -7/6 -8/7 -1/1 -1/1 -8/7 0/1 -1/1 1/1 -8/9 9/8 -8/9 -6/7 8/7 -1/1 -8/9 -7/8 15/13 -7/8 7/6 -13/15 -6/7 6/5 -7/8 17/14 -20/23 -13/15 11/9 -20/23 27/22 -32/37 -6/7 16/13 -13/15 -32/37 -19/22 21/17 -6/7 5/4 -6/7 24/19 -5/6 19/15 -6/7 14/11 -1/1 -7/8 -6/7 23/18 -6/7 -5/6 32/25 -1/1 -7/8 -6/7 9/7 -6/7 4/3 -6/7 -11/13 -5/6 23/17 -16/19 19/14 -16/19 -5/6 15/11 -5/6 26/19 -5/6 -24/29 -19/23 11/8 -9/11 -4/5 18/13 -1/1 7/5 -6/7 24/17 -5/6 41/29 -4/5 58/41 -1/1 -3/4 -2/3 17/12 -1/1 -6/7 44/31 -5/6 -9/11 -4/5 27/19 -6/7 10/7 -1/1 -6/7 -5/6 3/2 -6/7 -4/5 20/13 -6/7 17/11 -6/7 14/9 -11/13 -16/19 -5/6 25/16 -16/19 36/23 -21/25 11/7 -36/43 30/19 -5/6 19/12 -5/6 -54/65 27/17 -24/29 35/22 -24/29 -14/17 8/5 -5/6 -14/17 -9/11 29/18 -5/6 -14/17 50/31 -5/6 -9/11 -4/5 21/13 -4/5 55/34 -4/5 34/21 -1/1 -5/6 -4/5 13/8 -5/6 -14/17 18/11 -9/11 41/25 -4/5 23/14 -13/16 -4/5 28/17 -5/6 -9/11 -4/5 5/3 -4/5 27/16 -4/5 -2/3 49/29 0/1 22/13 -1/1 -5/6 -4/5 61/36 -1/1 -6/7 100/59 -6/7 -4/5 39/23 -4/5 17/10 -1/1 -6/7 29/17 -6/7 12/7 -5/6 31/18 -5/6 -4/5 50/29 -5/6 -14/17 -9/11 69/40 -14/17 -4/5 19/11 -14/17 26/15 -9/11 -13/16 -4/5 33/19 -22/27 7/4 -17/21 -4/5 30/17 -4/5 23/13 -4/5 39/22 -4/5 -42/53 16/9 -4/5 -11/14 -7/9 9/5 -4/5 20/11 -4/5 11/6 -4/5 -7/9 24/13 -7/9 13/7 -4/5 15/8 -3/4 17/9 -4/5 2/1 -1/1 -4/5 -3/4 17/8 -1/1 0/1 15/7 -1/1 13/6 -6/7 -5/6 11/5 -14/17 20/9 -4/5 9/4 -4/5 -10/13 7/3 -2/3 33/14 -4/5 -2/3 26/11 -4/5 -7/9 -3/4 45/19 -3/4 19/8 -3/4 -2/3 50/21 -1/1 -3/4 -2/3 31/13 -2/3 12/5 -3/4 29/12 -3/4 -8/11 46/19 -5/7 -12/17 -7/10 17/7 -2/3 39/16 -2/3 -4/7 100/41 -2/3 -4/7 61/25 -2/3 22/9 -1/1 -1/2 0/1 27/11 -2/3 5/2 -4/5 -2/3 28/11 -1/1 -5/6 -4/5 23/9 -4/5 41/16 -4/5 -3/4 100/39 -4/5 -2/3 59/23 -4/5 18/7 -3/4 13/5 -4/5 60/23 -3/4 47/18 -3/4 -14/19 34/13 -3/4 -8/11 -5/7 21/8 -4/5 -2/3 50/19 -1/1 -4/5 -3/4 29/11 -4/5 37/14 -4/5 -3/4 45/17 -3/4 8/3 -3/4 -5/7 -2/3 35/13 -2/3 27/10 -8/11 -2/3 46/17 -5/7 -7/10 -2/3 19/7 -2/3 30/11 -2/3 11/4 -1/1 -2/3 36/13 -1/1 25/9 -4/5 -2/3 39/14 -2/3 0/1 14/5 -1/1 -4/5 -3/4 17/6 -5/7 -2/3 20/7 -2/3 3/1 -2/3 10/3 -1/1 -2/3 -1/2 27/8 -2/3 0/1 44/13 -1/1 -1/2 0/1 17/5 -2/3 58/17 -2/3 -3/5 -1/2 41/12 -4/7 -1/2 24/7 -1/2 31/9 -4/5 7/2 -1/1 0/1 18/5 -1/2 29/8 -1/4 0/1 40/11 0/1 11/3 -2/1 37/10 -2/1 1/0 26/7 -3/2 -4/3 -1/1 15/4 -1/1 34/9 -1/1 -7/8 -6/7 19/5 -4/5 23/6 -4/5 -3/4 4/1 -1/1 -2/3 -1/2 21/5 0/1 17/4 -2/1 -1/1 30/7 -1/1 13/3 -4/5 9/2 -2/3 0/1 32/7 -1/1 -2/3 -1/2 23/5 -2/3 60/13 -2/3 37/8 -2/3 -5/8 14/3 -2/3 -3/5 -1/2 33/7 -4/7 19/4 -1/2 -2/5 24/5 -1/2 5/1 -2/3 0/1 21/4 -2/5 0/1 16/3 0/1 1/1 1/0 27/5 -2/1 38/7 -3/2 -4/3 -1/1 49/9 -8/7 60/11 -1/1 11/2 -1/1 -2/3 28/5 -1/1 -2/3 -1/2 17/3 0/1 40/7 0/1 23/4 0/1 1/0 6/1 -1/1 13/2 -3/4 -2/3 33/5 0/1 20/3 -2/3 0/1 27/4 -2/3 0/1 7/1 0/1 15/2 -1/1 23/3 -2/3 8/1 -1/1 -1/2 0/1 9/1 0/1 10/1 -1/1 0/1 1/0 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(19,240,-8,-101) (-9/1,1/0) -> (-69/29,-19/8) Hyperbolic Matrix(41,360,32,281) (-9/1,-8/1) -> (32/25,9/7) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(41,300,22,161) (-15/2,-7/1) -> (13/7,15/8) Hyperbolic Matrix(19,120,-16,-101) (-7/1,-6/1) -> (-6/5,-13/11) Hyperbolic Matrix(41,240,-34,-199) (-6/1,-17/3) -> (-23/19,-6/5) Hyperbolic Matrix(161,900,-100,-559) (-17/3,-11/2) -> (-29/18,-37/23) 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(139,720,50,259) (-21/4,-5/1) -> (25/9,39/14) Hyperbolic Matrix(161,780,58,281) (-5/1,-24/5) -> (36/13,25/9) 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(79,360,70,319) (-32/7,-9/2) -> (9/8,8/7) Hyperbolic Matrix(41,180,-18,-79) (-9/2,-4/1) -> (-16/7,-9/4) Hyperbolic Matrix(281,1080,198,761) (-4/1,-23/6) -> (17/12,44/31) 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(341,1260,-200,-739) (-26/7,-11/3) -> (-29/17,-46/27) Hyperbolic Matrix(199,720,-144,-521) (-11/3,-18/5) -> (-18/13,-29/21) Hyperbolic Matrix(101,360,62,221) (-18/5,-7/2) -> (13/8,18/11) Hyperbolic Matrix(139,480,-64,-221) (-7/2,-24/7) -> (-24/11,-13/6) Hyperbolic Matrix(421,1440,88,301) (-24/7,-41/12) -> (19/4,24/5) Hyperbolic Matrix(1301,4440,768,2621) (-41/12,-58/17) -> (22/13,61/36) Hyperbolic Matrix(299,1020,158,539) (-58/17,-17/5) -> (17/9,2/1) Hyperbolic Matrix(319,1080,236,799) (-17/5,-44/13) -> (4/3,23/17) Hyperbolic Matrix(479,1620,390,1319) (-44/13,-27/8) -> (27/22,16/13) Hyperbolic Matrix(161,540,48,161) (-27/8,-10/3) -> (10/3,27/8) Hyperbolic Matrix(19,60,6,19) (-10/3,-3/1) -> (3/1,10/3) Hyperbolic Matrix(41,120,14,41) (-3/1,-20/7) -> (20/7,3/1) 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(581,1620,-222,-619) (-14/5,-25/9) -> (-55/21,-34/13) Hyperbolic Matrix(281,780,58,161) (-25/9,-36/13) -> (24/5,5/1) 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(401,1080,238,641) (-27/10,-35/13) -> (5/3,27/16) Hyperbolic Matrix(379,1020,230,619) (-35/13,-8/3) -> (28/17,5/3) Hyperbolic Matrix(341,900,-280,-739) (-8/3,-29/11) -> (-11/9,-28/23) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(799,2100,304,799) (-50/19,-21/8) -> (21/8,50/19) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(781,2040,-482,-1259) (-34/13,-13/5) -> (-47/29,-34/21) Hyperbolic Matrix(139,360,100,259) (-13/5,-18/7) -> (18/13,7/5) Hyperbolic Matrix(701,1800,-428,-1099) (-18/7,-41/16) -> (-59/36,-18/11) 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(401,1020,252,641) (-28/11,-5/2) -> (35/22,8/5) Hyperbolic Matrix(439,1080,276,679) (-5/2,-27/11) -> (27/17,35/22) Hyperbolic Matrix(1201,2940,-980,-2399) (-49/20,-22/9) -> (-38/31,-49/40) Hyperbolic Matrix(1819,4440,1286,3139) (-22/9,-61/25) -> (41/29,58/41) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(3199,7800,1312,3199) (-100/41,-39/16) -> (39/16,100/41) Hyperbolic Matrix(641,1560,362,881) (-39/16,-17/7) -> (23/13,39/22) Hyperbolic Matrix(521,1260,-380,-919) (-17/7,-29/12) -> (-11/8,-37/27) 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(481,1140,-354,-839) (-19/8,-26/11) -> (-34/25,-19/14) Hyperbolic Matrix(941,2220,348,821) (-26/11,-33/14) -> (27/10,46/17) Hyperbolic Matrix(281,660,-238,-559) (-33/14,-7/3) -> (-13/11,-33/28) Hyperbolic Matrix(259,600,60,139) (-7/3,-30/13) -> (30/7,13/3) Hyperbolic Matrix(521,1200,122,281) (-30/13,-23/10) -> (17/4,30/7) Hyperbolic Matrix(679,1560,400,919) (-23/10,-39/17) -> (39/23,17/10) Hyperbolic Matrix(419,960,340,779) (-39/17,-16/7) -> (16/13,21/17) Hyperbolic Matrix(161,360,72,161) (-9/4,-20/9) -> (20/9,9/4) Hyperbolic Matrix(461,1020,-334,-739) (-20/9,-11/5) -> (-29/21,-40/29) Hyperbolic Matrix(301,660,192,421) (-11/5,-24/11) -> (36/23,11/7) Hyperbolic Matrix(139,300,120,259) (-13/6,-15/7) -> (15/13,7/6) Hyperbolic Matrix(619,1320,234,499) (-15/7,-17/8) -> (37/14,45/17) 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(319,600,42,79) (-17/9,-15/8) -> (15/2,23/3) Hyperbolic Matrix(161,300,22,41) (-15/8,-13/7) -> (7/1,15/2) Hyperbolic Matrix(259,480,-184,-341) (-13/7,-11/6) -> (-31/22,-7/5) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(101,180,-78,-139) (-9/5,-7/4) -> (-13/10,-9/7) Hyperbolic Matrix(241,420,-206,-359) (-7/4,-33/19) -> (-27/23,-7/6) Hyperbolic Matrix(761,1320,162,281) (-33/19,-26/15) -> (14/3,33/7) Hyperbolic Matrix(139,240,-128,-221) (-19/11,-50/29) -> (-10/9,-1/1) 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(601,1020,142,241) (-17/10,-39/23) -> (21/5,17/4) Hyperbolic Matrix(4601,7800,2714,4601) (-39/23,-100/59) -> (100/59,39/23) Hyperbolic Matrix(6019,10200,2348,3979) (-100/59,-61/36) -> (41/16,100/39) Hyperbolic Matrix(2621,4440,768,1301) (-61/36,-22/13) -> (58/17,41/12) Hyperbolic Matrix(959,1620,-782,-1321) (-22/13,-27/16) -> (-27/22,-38/31) Hyperbolic Matrix(641,1080,238,401) (-27/16,-5/3) -> (35/13,27/10) Hyperbolic Matrix(619,1020,230,379) (-5/3,-28/17) -> (8/3,35/13) 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(6221,10200,2550,4181) (-41/25,-100/61) -> (100/41,61/25) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(221,360,62,101) (-18/11,-13/8) -> (7/2,18/5) 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(1001,1620,-642,-1039) (-34/21,-21/13) -> (-39/25,-14/9) Hyperbolic Matrix(1301,2100,806,1301) (-21/13,-50/31) -> (50/31,21/13) Hyperbolic Matrix(1861,3000,1080,1741) (-50/31,-29/18) -> (31/18,50/29) Hyperbolic Matrix(821,1320,436,701) (-37/23,-45/28) -> (15/8,17/9) Hyperbolic Matrix(641,1020,252,401) (-8/5,-35/22) -> (5/2,28/11) Hyperbolic Matrix(679,1080,276,439) (-35/22,-27/17) -> (27/11,5/2) Hyperbolic Matrix(1399,2220,806,1279) (-27/17,-46/29) -> (26/15,33/19) 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(881,1380,256,401) (-11/7,-36/23) -> (24/7,31/9) Hyperbolic Matrix(499,780,396,619) (-36/23,-25/16) -> (5/4,24/19) Hyperbolic Matrix(461,720,372,581) (-25/16,-39/25) -> (21/17,5/4) Hyperbolic Matrix(619,960,-452,-701) (-14/9,-17/11) -> (-37/27,-26/19) Hyperbolic Matrix(739,1140,-610,-941) (-17/11,-20/13) -> (-40/33,-23/19) Hyperbolic Matrix(79,120,52,79) (-20/13,-3/2) -> (3/2,20/13) Hyperbolic Matrix(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(379,540,266,379) (-10/7,-27/19) -> (27/19,10/7) Hyperbolic Matrix(1141,1620,212,301) (-27/19,-44/31) -> (16/3,27/5) Hyperbolic Matrix(761,1080,198,281) (-44/31,-17/12) -> (23/6,4/1) Hyperbolic Matrix(721,1020,340,481) (-17/12,-58/41) -> (2/1,17/8) Hyperbolic Matrix(3139,4440,1286,1819) (-58/41,-41/29) -> (61/25,22/9) Hyperbolic Matrix(1019,1440,806,1139) (-41/29,-24/17) -> (24/19,19/15) Hyperbolic Matrix(979,1380,354,499) (-24/17,-31/22) -> (11/4,36/13) Hyperbolic Matrix(259,360,100,139) (-7/5,-18/13) -> (18/7,13/5) 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(799,1080,236,319) (-23/17,-4/3) -> (44/13,17/5) Hyperbolic Matrix(319,420,60,79) (-4/3,-21/16) -> (21/4,16/3) Hyperbolic Matrix(779,1020,320,419) (-21/16,-17/13) -> (17/7,39/16) Hyperbolic Matrix(919,1200,520,679) (-17/13,-30/23) -> (30/17,23/13) Hyperbolic Matrix(461,600,262,341) (-30/23,-13/10) -> (7/4,30/17) Hyperbolic Matrix(281,360,32,41) (-9/7,-32/25) -> (8/1,9/1) 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(1039,1320,440,559) (-14/11,-33/26) -> (33/14,26/11) Hyperbolic Matrix(1139,1440,806,1019) (-19/15,-24/19) -> (24/17,41/29) Hyperbolic Matrix(619,780,396,499) (-24/19,-5/4) -> (25/16,36/23) Hyperbolic Matrix(1019,1260,630,779) (-5/4,-21/17) -> (21/13,55/34) Hyperbolic Matrix(341,420,82,101) (-21/17,-16/13) -> (4/1,21/5) 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(641,780,-558,-679) (-28/23,-17/14) -> (-23/20,-8/7) 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(259,300,120,139) (-7/6,-15/13) -> (15/7,13/6) Hyperbolic Matrix(521,600,244,281) (-15/13,-23/20) -> (17/8,15/7) Hyperbolic Matrix(319,360,70,79) (-8/7,-9/8) -> (9/2,32/7) Hyperbolic Matrix(1021,1140,592,661) (-9/8,-10/9) -> (50/29,69/40) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(221,-240,128,-139) (1/1,9/8) -> (69/40,19/11) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(739,-900,280,-341) (17/14,11/9) -> (29/11,37/14) Hyperbolic Matrix(1321,-1620,782,-959) (11/9,27/22) -> (27/16,49/29) 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(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) 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(919,-1260,380,-521) (26/19,11/8) -> (29/12,46/19) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(341,-480,184,-259) (7/5,24/17) -> (24/13,13/7) 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(1039,-1620,642,-1001) (14/9,25/16) -> (55/34,34/21) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(559,-900,100,-161) (8/5,29/18) -> (11/2,28/5) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(1099,-1800,428,-701) (18/11,41/25) -> (59/23,18/7) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(739,-1260,200,-341) (17/10,29/17) -> (11/3,37/10) Hyperbolic Matrix(659,-1140,174,-301) (19/11,26/15) -> (34/9,19/5) Hyperbolic Matrix(379,-660,58,-101) (33/19,7/4) -> (13/2,33/5) Hyperbolic Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(221,-480,64,-139) (13/6,11/5) -> (31/9,7/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(101,-240,8,-19) (19/8,50/21) -> (10/1,1/0) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(619,-1620,222,-581) (34/13,21/8) -> (39/14,14/5) Hyperbolic Matrix(341,-960,92,-259) (14/5,17/6) -> (37/10,26/7) Hyperbolic Matrix(401,-1140,70,-199) (17/6,20/7) -> (40/7,23/4) Hyperbolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic Matrix(139,-780,18,-101) (28/5,17/3) -> (23/3,8/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(19,240,-8,-101) -> Matrix(5,2,-3,-1) Matrix(41,360,32,281) -> Matrix(1,-6,-1,7) Matrix(61,480,-38,-299) -> Matrix(5,14,-4,-11) Matrix(41,300,22,161) -> Matrix(7,4,-9,-5) Matrix(19,120,-16,-101) -> Matrix(1,8,-1,-7) Matrix(41,240,-34,-199) -> Matrix(27,20,-23,-17) Matrix(161,900,-100,-559) -> Matrix(9,4,-7,-3) Matrix(299,1620,-122,-661) -> Matrix(5,4,-4,-3) Matrix(301,1620,212,1141) -> Matrix(3,4,-4,-5) Matrix(181,960,102,541) -> Matrix(19,4,-24,-5) Matrix(139,720,50,259) -> Matrix(1,-2,-1,3) Matrix(161,780,58,281) -> Matrix(1,-2,-1,3) Matrix(301,1440,88,421) -> Matrix(1,2,-2,-3) Matrix(241,1140,-152,-719) -> Matrix(5,44,-4,-35) Matrix(181,840,-142,-659) -> Matrix(7,20,-6,-17) Matrix(301,1380,118,541) -> Matrix(5,6,-6,-7) Matrix(79,360,70,319) -> Matrix(1,-6,-1,7) Matrix(41,180,-18,-79) -> Matrix(7,10,-5,-7) Matrix(281,1080,198,761) -> Matrix(9,14,-11,-17) Matrix(361,1380,220,841) -> Matrix(31,40,-38,-49) Matrix(301,1140,-174,-659) -> Matrix(41,50,-32,-39) Matrix(419,1560,-242,-901) -> Matrix(49,40,-38,-31) Matrix(341,1260,-200,-739) -> Matrix(9,4,-7,-3) Matrix(199,720,-144,-521) -> Matrix(1,4,-1,-3) Matrix(101,360,62,221) -> Matrix(9,14,-11,-17) Matrix(139,480,-64,-221) -> Matrix(1,6,-1,-5) Matrix(421,1440,88,301) -> Matrix(1,2,-2,-3) Matrix(1301,4440,768,2621) -> Matrix(1,-2,-1,3) Matrix(299,1020,158,539) -> Matrix(3,10,-4,-13) Matrix(319,1080,236,799) -> Matrix(11,6,-13,-7) Matrix(479,1620,390,1319) -> Matrix(19,32,-22,-37) Matrix(161,540,48,161) -> Matrix(1,0,-1,1) Matrix(19,60,6,19) -> Matrix(1,0,-1,1) Matrix(41,120,14,41) -> Matrix(5,8,-7,-11) Matrix(359,1020,-296,-841) -> Matrix(73,126,-62,-107) Matrix(361,1020,-212,-599) -> Matrix(17,28,-14,-23) Matrix(581,1620,-222,-619) -> Matrix(1,4,-1,-3) Matrix(281,780,58,161) -> Matrix(1,2,-3,-5) Matrix(239,660,130,359) -> Matrix(3,10,-4,-13) Matrix(241,660,88,241) -> Matrix(3,4,-4,-5) Matrix(419,1140,154,419) -> Matrix(11,20,-16,-29) Matrix(421,1140,-332,-899) -> Matrix(17,28,-14,-23) Matrix(401,1080,238,641) -> Matrix(9,14,-11,-17) Matrix(379,1020,230,619) -> Matrix(17,30,-21,-37) Matrix(341,900,-280,-739) -> Matrix(1,8,-1,-7) Matrix(1139,3000,478,1259) -> Matrix(5,6,-6,-7) Matrix(799,2100,304,799) -> Matrix(5,8,-7,-11) Matrix(481,1260,92,241) -> Matrix(1,2,-4,-7) Matrix(781,2040,-482,-1259) -> Matrix(17,28,-14,-23) Matrix(139,360,100,259) -> Matrix(9,14,-11,-17) Matrix(701,1800,-428,-1099) -> Matrix(35,48,-27,-37) Matrix(539,1380,398,1019) -> Matrix(47,68,-56,-81) Matrix(541,1380,118,301) -> Matrix(5,6,-6,-7) Matrix(401,1020,252,641) -> Matrix(29,34,-35,-41) Matrix(439,1080,276,679) -> Matrix(29,34,-35,-41) Matrix(1201,2940,-980,-2399) -> Matrix(45,32,-38,-27) Matrix(1819,4440,1286,3139) -> Matrix(1,-2,-1,3) Matrix(4919,12000,1918,4679) -> Matrix(3,10,-4,-13) Matrix(3199,7800,1312,3199) -> Matrix(3,8,-5,-13) Matrix(641,1560,362,881) -> Matrix(23,50,-29,-63) Matrix(521,1260,-380,-919) -> Matrix(37,60,-29,-47) Matrix(299,720,174,419) -> Matrix(33,52,-40,-63) Matrix(301,720,176,421) -> Matrix(7,8,-8,-9) Matrix(1259,3000,478,1139) -> Matrix(5,6,-6,-7) Matrix(479,1140,50,119) -> Matrix(1,2,-2,-3) Matrix(481,1140,-354,-839) -> Matrix(37,58,-30,-47) Matrix(941,2220,348,821) -> Matrix(11,14,-15,-19) Matrix(281,660,-238,-559) -> Matrix(15,22,-13,-19) Matrix(259,600,60,139) -> Matrix(9,14,-11,-17) Matrix(521,1200,122,281) -> Matrix(15,22,-13,-19) Matrix(679,1560,400,919) -> Matrix(1,2,-3,-5) Matrix(419,960,340,779) -> Matrix(121,172,-140,-199) Matrix(161,360,72,161) -> Matrix(29,40,-37,-51) Matrix(461,1020,-334,-739) -> Matrix(37,48,-27,-35) Matrix(301,660,192,421) -> Matrix(89,110,-106,-131) Matrix(139,300,120,259) -> Matrix(41,48,-47,-55) Matrix(619,1320,234,499) -> Matrix(7,4,-9,-5) Matrix(481,1020,340,721) -> Matrix(5,6,-6,-7) Matrix(539,1020,158,299) -> Matrix(7,10,-12,-17) Matrix(319,600,42,79) -> Matrix(1,2,-3,-5) Matrix(161,300,22,41) -> Matrix(3,4,-1,-1) Matrix(259,480,-184,-341) -> Matrix(15,22,-13,-19) Matrix(361,660,-262,-479) -> Matrix(47,64,-36,-49) Matrix(199,360,110,199) -> Matrix(5,8,-7,-11) Matrix(101,180,-78,-139) -> Matrix(15,22,-13,-19) Matrix(241,420,-206,-359) -> Matrix(39,50,-32,-41) Matrix(761,1320,162,281) -> Matrix(11,14,-15,-19) Matrix(139,240,-128,-221) -> Matrix(21,26,-17,-21) Matrix(1741,3000,1080,1861) -> Matrix(71,90,-86,-109) Matrix(419,720,174,299) -> Matrix(41,52,-56,-71) Matrix(421,720,176,301) -> Matrix(7,8,-8,-9) Matrix(601,1020,142,241) -> Matrix(3,4,-4,-5) Matrix(4601,7800,2714,4601) -> Matrix(19,24,-23,-29) Matrix(6019,10200,2348,3979) -> Matrix(11,14,-15,-19) Matrix(2621,4440,768,1301) -> Matrix(1,2,-3,-5) Matrix(959,1620,-782,-1321) -> Matrix(7,20,-6,-17) Matrix(641,1080,238,401) -> Matrix(11,14,-15,-19) Matrix(619,1020,230,379) -> Matrix(23,30,-33,-43) Matrix(839,1380,656,1079) -> Matrix(45,58,-52,-67) Matrix(841,1380,220,361) -> Matrix(31,40,-38,-49) Matrix(6221,10200,2550,4181) -> Matrix(11,14,-15,-19) Matrix(7321,12000,4320,7081) -> Matrix(45,58,-52,-67) Matrix(221,360,62,101) -> Matrix(11,14,-15,-19) Matrix(2219,3600,850,1379) -> Matrix(89,112,-120,-151) Matrix(2221,3600,852,1381) -> Matrix(55,68,-72,-89) Matrix(1001,1620,-642,-1039) -> Matrix(31,36,-25,-29) Matrix(1301,2100,806,1301) -> Matrix(43,56,-53,-69) Matrix(1861,3000,1080,1741) -> Matrix(71,90,-86,-109) Matrix(821,1320,436,701) -> Matrix(19,24,-23,-29) Matrix(641,1020,252,401) -> Matrix(27,34,-31,-39) Matrix(679,1080,276,439) -> Matrix(27,34,-31,-39) Matrix(1399,2220,806,1279) -> Matrix(259,326,-317,-399) Matrix(721,1140,456,721) -> Matrix(431,540,-518,-649) Matrix(419,660,266,419) -> Matrix(289,360,-346,-431) Matrix(881,1380,256,401) -> Matrix(13,16,-9,-11) Matrix(499,780,396,619) -> Matrix(167,206,-197,-243) Matrix(461,720,372,581) -> Matrix(301,370,-349,-429) Matrix(619,960,-452,-701) -> Matrix(151,184,-119,-145) Matrix(739,1140,-610,-941) -> Matrix(215,262,-183,-223) Matrix(79,120,52,79) -> Matrix(19,24,-23,-29) Matrix(41,60,28,41) -> Matrix(19,24,-23,-29) Matrix(379,540,266,379) -> Matrix(19,24,-23,-29) Matrix(1141,1620,212,301) -> Matrix(3,4,-4,-5) Matrix(761,1080,198,281) -> Matrix(11,14,-15,-19) Matrix(721,1020,340,481) -> Matrix(5,6,-6,-7) Matrix(3139,4440,1286,1819) -> Matrix(1,2,-3,-5) Matrix(1019,1440,806,1139) -> Matrix(9,10,-10,-11) Matrix(979,1380,354,499) -> Matrix(3,4,-7,-9) Matrix(259,360,100,139) -> Matrix(11,14,-15,-19) Matrix(659,900,-484,-661) -> Matrix(199,250,-160,-201) Matrix(1019,1380,398,539) -> Matrix(55,68,-72,-89) Matrix(799,1080,236,319) -> Matrix(5,6,-1,-1) Matrix(319,420,60,79) -> Matrix(5,6,9,11) Matrix(779,1020,320,419) -> Matrix(53,64,-82,-99) Matrix(919,1200,520,679) -> Matrix(371,446,-465,-559) Matrix(461,600,262,341) -> Matrix(189,226,-235,-281) Matrix(281,360,32,41) -> Matrix(5,6,-11,-13) Matrix(1079,1380,656,839) -> Matrix(49,58,-60,-71) Matrix(2819,3600,610,779) -> Matrix(33,40,-52,-63) Matrix(2821,3600,612,781) -> Matrix(47,56,-68,-81) Matrix(1039,1320,440,559) -> Matrix(11,14,-15,-19) Matrix(1139,1440,806,1019) -> Matrix(9,10,-10,-11) Matrix(619,780,396,499) -> Matrix(169,206,-201,-245) Matrix(1019,1260,630,779) -> Matrix(89,106,-110,-131) Matrix(341,420,82,101) -> Matrix(5,6,-21,-25) Matrix(1319,1620,390,479) -> Matrix(27,32,-38,-45) Matrix(2939,3600,538,659) -> Matrix(115,136,-126,-149) Matrix(2941,3600,540,661) -> Matrix(105,124,-94,-111) Matrix(641,780,-558,-679) -> Matrix(123,146,-107,-127) Matrix(1019,1200,152,179) -> Matrix(7,8,-8,-9) Matrix(1021,1200,154,181) -> Matrix(7,8,-8,-9) Matrix(259,300,120,139) -> Matrix(41,48,-47,-55) Matrix(521,600,244,281) -> Matrix(19,22,-13,-15) Matrix(319,360,70,79) -> Matrix(5,6,-11,-13) Matrix(1021,1140,592,661) -> Matrix(49,58,-60,-71) Matrix(1,0,2,1) -> Matrix(15,16,-16,-17) Matrix(221,-240,128,-139) -> Matrix(31,26,-37,-31) Matrix(419,-480,158,-181) -> Matrix(43,38,-60,-53) Matrix(101,-120,16,-19) -> Matrix(9,8,-17,-15) Matrix(199,-240,34,-41) -> Matrix(23,20,-15,-13) Matrix(739,-900,280,-341) -> Matrix(9,8,-17,-15) Matrix(1321,-1620,782,-959) -> Matrix(23,20,-38,-33) Matrix(899,-1140,332,-421) -> Matrix(33,28,-46,-39) Matrix(659,-840,142,-181) -> Matrix(23,20,-38,-33) Matrix(139,-180,78,-101) -> Matrix(25,22,-33,-29) Matrix(839,-1140,354,-481) -> Matrix(69,58,-94,-79) Matrix(1141,-1560,482,-659) -> Matrix(111,92,-146,-121) Matrix(919,-1260,380,-521) -> Matrix(73,60,-101,-83) Matrix(521,-720,144,-199) -> Matrix(5,4,-9,-7) Matrix(341,-480,184,-259) -> Matrix(25,22,-33,-29) Matrix(661,-1020,116,-179) -> Matrix(7,6,-20,-17) Matrix(659,-1020,272,-421) -> Matrix(61,52,-88,-75) Matrix(1039,-1620,642,-1001) -> Matrix(43,36,-49,-41) Matrix(719,-1140,152,-241) -> Matrix(53,44,-100,-83) Matrix(559,-900,100,-161) -> Matrix(5,4,1,1) Matrix(1259,-2040,482,-781) -> Matrix(33,28,-46,-39) Matrix(1099,-1800,428,-701) -> Matrix(59,48,-75,-61) Matrix(1739,-2940,320,-541) -> Matrix(9,8,-8,-7) Matrix(739,-1260,200,-341) -> Matrix(5,4,1,1) Matrix(659,-1140,174,-301) -> Matrix(61,50,-72,-59) Matrix(379,-660,58,-101) -> Matrix(27,22,-43,-35) Matrix(559,-1020,154,-281) -> Matrix(5,4,-29,-23) Matrix(221,-480,64,-139) -> Matrix(7,6,-13,-11) Matrix(299,-660,82,-181) -> Matrix(5,4,6,5) Matrix(79,-180,18,-41) -> Matrix(13,10,-17,-13) Matrix(179,-420,26,-61) -> Matrix(3,2,-2,-1) Matrix(101,-240,8,-19) -> Matrix(3,2,1,1) Matrix(661,-1620,122,-299) -> Matrix(5,4,-4,-3) Matrix(619,-1620,222,-581) -> Matrix(5,4,-9,-7) Matrix(341,-960,92,-259) -> Matrix(11,8,-7,-5) Matrix(401,-1140,70,-199) -> Matrix(3,2,7,5) Matrix(241,-900,64,-239) -> Matrix(9,10,-10,-11) Matrix(139,-780,18,-101) -> Matrix(3,2,-5,-3) 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): 96 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 8 1 1/1 -8/9 1 30 9/8 (-8/9,-6/7) 0 10 8/7 0 15 15/13 -7/8 5 2 7/6 (-13/15,-6/7) 0 30 6/5 -7/8 2 5 17/14 (-20/23,-13/15) 0 30 11/9 -20/23 1 30 27/22 (-32/37,-6/7) 0 10 16/13 0 15 21/17 -6/7 1 10 5/4 -6/7 3 6 24/19 -5/6 2 5 19/15 -6/7 1 30 14/11 0 15 23/18 (-6/7,-5/6) 0 30 32/25 0 15 9/7 -6/7 1 10 4/3 0 15 23/17 -16/19 1 30 19/14 (-16/19,-5/6) 0 30 15/11 -5/6 5 2 26/19 0 15 11/8 (-9/11,-4/5) 0 30 18/13 -1/1 2 5 7/5 -6/7 1 30 24/17 -5/6 2 5 41/29 -4/5 1 30 58/41 0 15 17/12 (-1/1,-6/7) 0 30 44/31 0 15 27/19 -6/7 1 10 10/7 (-6/7,-4/5) 0 3 3/2 (-6/7,-4/5) 0 10 20/13 -6/7 4 3 17/11 -6/7 1 30 14/9 0 15 25/16 -16/19 3 6 36/23 -21/25 2 5 11/7 -36/43 1 30 30/19 -5/6 18 1 19/12 (-5/6,-54/65) 0 30 27/17 -24/29 1 10 35/22 0 6 8/5 0 15 29/18 (-5/6,-14/17) 0 30 50/31 (-14/17,-4/5) 0 3 21/13 -4/5 1 10 55/34 -4/5 3 6 34/21 0 15 13/8 (-5/6,-14/17) 0 30 18/11 -9/11 2 5 41/25 -4/5 1 30 23/14 (-13/16,-4/5) 0 30 28/17 0 15 5/3 -4/5 1 6 27/16 (-4/5,-2/3) 0 10 49/29 0/1 1 30 22/13 0 15 61/36 (-1/1,-6/7) 0 30 100/59 (-6/7,-4/5) 0 3 39/23 -4/5 1 10 17/10 (-1/1,-6/7) 0 30 29/17 -6/7 1 30 12/7 -5/6 2 5 31/18 (-5/6,-4/5) 0 30 50/29 (-14/17,-4/5) 0 3 69/40 (-14/17,-4/5) 0 10 19/11 -14/17 1 30 26/15 0 15 33/19 -22/27 1 10 7/4 (-17/21,-4/5) 0 30 30/17 -4/5 14 1 23/13 -4/5 1 30 39/22 (-4/5,-42/53) 0 10 16/9 0 15 9/5 -4/5 1 10 20/11 -4/5 8 3 11/6 (-4/5,-7/9) 0 30 24/13 -7/9 2 5 13/7 -4/5 1 30 15/8 -3/4 1 2 17/9 -4/5 1 30 2/1 0 15 17/8 (-1/1,0/1) 0 30 15/7 -1/1 5 2 13/6 (-6/7,-5/6) 0 30 11/5 -14/17 1 30 20/9 -4/5 8 3 9/4 (-4/5,-10/13) 0 10 7/3 -2/3 1 30 33/14 (-4/5,-2/3) 0 10 26/11 0 15 45/19 -3/4 5 2 19/8 (-3/4,-2/3) 0 30 50/21 (-4/5,-2/3) 0 3 31/13 -2/3 1 30 12/5 -3/4 2 5 29/12 (-3/4,-8/11) 0 30 46/19 0 15 17/7 -2/3 1 30 39/16 (-2/3,-4/7) 0 10 100/41 (-2/3,-4/7) 0 3 61/25 -2/3 1 30 22/9 0 15 27/11 -2/3 1 10 5/2 0 6 28/11 0 15 23/9 -4/5 1 30 41/16 (-4/5,-3/4) 0 30 100/39 (-4/5,-2/3) 0 3 59/23 -4/5 1 30 18/7 -3/4 2 5 13/5 -4/5 1 30 60/23 -3/4 6 1 47/18 (-3/4,-14/19) 0 30 34/13 0 15 21/8 (-4/5,-2/3) 0 10 50/19 (-4/5,-2/3) 0 3 29/11 -4/5 1 30 37/14 (-4/5,-3/4) 0 30 45/17 -3/4 5 2 8/3 0 15 35/13 -2/3 1 6 27/10 (-8/11,-2/3) 0 10 46/17 0 15 19/7 -2/3 1 30 30/11 -2/3 2 1 11/4 (-1/1,-2/3) 0 30 36/13 -1/1 2 5 25/9 0 6 39/14 (-2/3,0/1) 0 10 14/5 0 15 17/6 (-5/7,-2/3) 0 30 20/7 -2/3 4 3 3/1 -2/3 1 10 10/3 (-2/3,0/1) 0 3 27/8 (-2/3,0/1) 0 10 44/13 0 15 17/5 -2/3 1 30 58/17 0 15 41/12 (-4/7,-1/2) 0 30 24/7 -1/2 2 5 31/9 -4/5 1 30 7/2 (-1/1,0/1) 0 30 18/5 -1/2 2 5 29/8 (-1/4,0/1) 0 30 40/11 0/1 8 3 11/3 -2/1 1 30 37/10 (-2/1,1/0) 0 30 26/7 0 15 15/4 -1/1 5 2 34/9 0 15 19/5 -4/5 1 30 23/6 (-4/5,-3/4) 0 30 4/1 0 15 21/5 0/1 1 10 17/4 (-2/1,-1/1) 0 30 30/7 -1/1 6 1 13/3 -4/5 1 30 9/2 (-2/3,0/1) 0 10 32/7 0 15 23/5 -2/3 1 30 60/13 -2/3 4 1 37/8 (-2/3,-5/8) 0 30 14/3 0 15 33/7 -4/7 1 10 19/4 (-1/2,-2/5) 0 30 24/5 -1/2 2 5 5/1 0 6 21/4 (-2/5,0/1) 0 10 16/3 0 15 27/5 -2/1 1 10 38/7 0 15 49/9 -8/7 1 30 60/11 -1/1 10 1 11/2 (-1/1,-2/3) 0 30 28/5 0 15 17/3 0/1 1 30 40/7 0/1 4 3 23/4 (0/1,1/0) 0 30 6/1 -1/1 2 5 13/2 (-3/4,-2/3) 0 30 33/5 0/1 1 10 20/3 (-2/3,0/1) 0 3 27/4 (-2/3,0/1) 0 10 7/1 0/1 1 30 15/2 -1/1 1 2 23/3 -2/3 1 30 8/1 0 15 9/1 0/1 1 10 10/1 (-2/1,0/1) 0 3 1/0 (-1/1,0/1) 0 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(221,-240,128,-139) (1/1,9/8) -> (69/40,19/11) Hyperbolic Matrix(319,-360,70,-79) (9/8,8/7) -> (9/2,32/7) Glide Reflection Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(259,-300,120,-139) (15/13,7/6) -> (15/7,13/6) Glide Reflection Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(739,-900,280,-341) (17/14,11/9) -> (29/11,37/14) Hyperbolic Matrix(1321,-1620,782,-959) (11/9,27/22) -> (27/16,49/29) Hyperbolic Matrix(1319,-1620,390,-479) (27/22,16/13) -> (27/8,44/13) Glide Reflection Matrix(341,-420,82,-101) (16/13,21/17) -> (4/1,21/5) Glide Reflection Matrix(1019,-1260,630,-779) (21/17,5/4) -> (21/13,55/34) Glide Reflection Matrix(619,-780,396,-499) (5/4,24/19) -> (25/16,36/23) Glide Reflection Matrix(1139,-1440,806,-1019) (24/19,19/15) -> (24/17,41/29) Glide Reflection 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,-1380,656,-839) (23/18,32/25) -> (23/14,28/17) Glide Reflection Matrix(281,-360,32,-41) (32/25,9/7) -> (8/1,9/1) Glide Reflection Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(799,-1080,236,-319) (4/3,23/17) -> (44/13,17/5) Glide Reflection Matrix(1019,-1380,398,-539) (23/17,19/14) -> (23/9,41/16) Glide Reflection 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(919,-1260,380,-521) (26/19,11/8) -> (29/12,46/19) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(259,-360,100,-139) (18/13,7/5) -> (18/7,13/5) Glide Reflection Matrix(341,-480,184,-259) (7/5,24/17) -> (24/13,13/7) Hyperbolic Matrix(3139,-4440,1286,-1819) (41/29,58/41) -> (61/25,22/9) Glide Reflection Matrix(721,-1020,340,-481) (58/41,17/12) -> (2/1,17/8) Glide Reflection Matrix(761,-1080,198,-281) (17/12,44/31) -> (23/6,4/1) Glide Reflection Matrix(1141,-1620,212,-301) (44/31,27/19) -> (16/3,27/5) Glide Reflection Matrix(379,-540,266,-379) (27/19,10/7) -> (27/19,10/7) Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(79,-120,52,-79) (3/2,20/13) -> (3/2,20/13) Reflection 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(1039,-1620,642,-1001) (14/9,25/16) -> (55/34,34/21) Hyperbolic Matrix(881,-1380,256,-401) (36/23,11/7) -> (24/7,31/9) Glide Reflection Matrix(419,-660,266,-419) (11/7,30/19) -> (11/7,30/19) Reflection Matrix(721,-1140,456,-721) (30/19,19/12) -> (30/19,19/12) Reflection Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(679,-1080,276,-439) (27/17,35/22) -> (27/11,5/2) Glide Reflection Matrix(641,-1020,252,-401) (35/22,8/5) -> (5/2,28/11) Glide Reflection Matrix(559,-900,100,-161) (8/5,29/18) -> (11/2,28/5) Hyperbolic Matrix(1861,-3000,1080,-1741) (29/18,50/31) -> (31/18,50/29) Glide Reflection Matrix(1301,-2100,806,-1301) (50/31,21/13) -> (50/31,21/13) Reflection Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(221,-360,62,-101) (13/8,18/11) -> (7/2,18/5) Glide Reflection Matrix(1099,-1800,428,-701) (18/11,41/25) -> (59/23,18/7) Hyperbolic Matrix(841,-1380,220,-361) (41/25,23/14) -> (19/5,23/6) Glide Reflection Matrix(619,-1020,230,-379) (28/17,5/3) -> (8/3,35/13) Glide Reflection Matrix(641,-1080,238,-401) (5/3,27/16) -> (35/13,27/10) Glide Reflection Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(2621,-4440,768,-1301) (22/13,61/36) -> (58/17,41/12) Glide Reflection Matrix(6019,-10200,2348,-3979) (61/36,100/59) -> (41/16,100/39) Glide Reflection Matrix(4601,-7800,2714,-4601) (100/59,39/23) -> (100/59,39/23) Reflection Matrix(601,-1020,142,-241) (39/23,17/10) -> (21/5,17/4) Glide Reflection Matrix(739,-1260,200,-341) (17/10,29/17) -> (11/3,37/10) Hyperbolic Matrix(421,-720,176,-301) (29/17,12/7) -> (31/13,12/5) Glide Reflection Matrix(419,-720,174,-299) (12/7,31/18) -> (12/5,29/12) Glide Reflection Matrix(4001,-6900,2320,-4001) (50/29,69/40) -> (50/29,69/40) Reflection Matrix(659,-1140,174,-301) (19/11,26/15) -> (34/9,19/5) Hyperbolic Matrix(761,-1320,162,-281) (26/15,33/19) -> (14/3,33/7) Glide Reflection Matrix(379,-660,58,-101) (33/19,7/4) -> (13/2,33/5) Hyperbolic Matrix(239,-420,136,-239) (7/4,30/17) -> (7/4,30/17) Reflection Matrix(781,-1380,442,-781) (30/17,23/13) -> (30/17,23/13) Reflection Matrix(881,-1560,362,-641) (23/13,39/22) -> (17/7,39/16) Glide Reflection Matrix(541,-960,102,-181) (39/22,16/9) -> (21/4,16/3) Glide Reflection Matrix(199,-360,110,-199) (9/5,20/11) -> (9/5,20/11) Reflection Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(359,-660,130,-239) (11/6,24/13) -> (11/4,36/13) Glide Reflection Matrix(161,-300,22,-41) (13/7,15/8) -> (7/1,15/2) Glide Reflection Matrix(319,-600,42,-79) (15/8,17/9) -> (15/2,23/3) Glide Reflection Matrix(539,-1020,158,-299) (17/9,2/1) -> (17/5,58/17) Glide Reflection Matrix(619,-1320,234,-499) (17/8,15/7) -> (37/14,45/17) Glide Reflection Matrix(221,-480,64,-139) (13/6,11/5) -> (31/9,7/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(161,-360,72,-161) (20/9,9/4) -> (20/9,9/4) Reflection Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(941,-2220,348,-821) (33/14,26/11) -> (27/10,46/17) Glide Reflection Matrix(101,-240,8,-19) (19/8,50/21) -> (10/1,1/0) Hyperbolic Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(3199,-7800,1312,-3199) (39/16,100/41) -> (39/16,100/41) Reflection Matrix(4919,-12000,1918,-4679) (100/41,61/25) -> (100/39,59/23) Glide Reflection Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(541,-1380,118,-301) (28/11,23/9) -> (32/7,23/5) Glide Reflection Matrix(599,-1560,230,-599) (13/5,60/23) -> (13/5,60/23) Reflection Matrix(2161,-5640,828,-2161) (60/23,47/18) -> (60/23,47/18) Reflection Matrix(619,-1620,222,-581) (34/13,21/8) -> (39/14,14/5) Hyperbolic Matrix(799,-2100,304,-799) (21/8,50/19) -> (21/8,50/19) 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(281,-780,58,-161) (36/13,25/9) -> (24/5,5/1) Glide Reflection Matrix(259,-720,50,-139) (25/9,39/14) -> (5/1,21/4) Glide Reflection Matrix(341,-960,92,-259) (14/5,17/6) -> (37/10,26/7) Hyperbolic Matrix(401,-1140,70,-199) (17/6,20/7) -> (40/7,23/4) Hyperbolic Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(161,-540,48,-161) (10/3,27/8) -> (10/3,27/8) Reflection Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) Parabolic 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(599,-2760,130,-599) (23/5,60/13) -> (23/5,60/13) Reflection Matrix(961,-4440,208,-961) (60/13,37/8) -> (60/13,37/8) Reflection Matrix(1079,-5880,198,-1079) (49/9,60/11) -> (49/9,60/11) Reflection Matrix(241,-1320,44,-241) (60/11,11/2) -> (60/11,11/2) Reflection Matrix(139,-780,18,-101) (28/5,17/3) -> (23/3,8/1) Hyperbolic Matrix(199,-1320,30,-199) (33/5,20/3) -> (33/5,20/3) Reflection Matrix(161,-1080,24,-161) (20/3,27/4) -> (20/3,27/4) Reflection Matrix(19,-180,2,-19) (9/1,10/1) -> (9/1,10/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(17,16,-18,-17) (0/1,1/1) -> (-1/1,-8/9) Matrix(221,-240,128,-139) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(319,-360,70,-79) -> Matrix(7,6,-15,-13) Matrix(419,-480,158,-181) -> Matrix(43,38,-60,-53) Matrix(259,-300,120,-139) -> Matrix(55,48,-63,-55) *** -> (-8/9,-6/7) Matrix(101,-120,16,-19) -> Matrix(9,8,-17,-15) Matrix(199,-240,34,-41) -> Matrix(23,20,-15,-13) Matrix(739,-900,280,-341) -> Matrix(9,8,-17,-15) Matrix(1321,-1620,782,-959) -> Matrix(23,20,-38,-33) Matrix(1319,-1620,390,-479) -> Matrix(37,32,-52,-45) Matrix(341,-420,82,-101) -> Matrix(7,6,-29,-25) Matrix(1019,-1260,630,-779) -> Matrix(123,106,-152,-131) Matrix(619,-780,396,-499) -> Matrix(243,206,-289,-245) Matrix(1139,-1440,806,-1019) -> Matrix(11,10,-12,-11) *** -> (-1/1,-5/6) Matrix(899,-1140,332,-421) -> Matrix(33,28,-46,-39) Matrix(659,-840,142,-181) -> Matrix(23,20,-38,-33) Matrix(1079,-1380,656,-839) -> Matrix(67,58,-82,-71) Matrix(281,-360,32,-41) -> Matrix(7,6,-15,-13) Matrix(139,-180,78,-101) -> Matrix(25,22,-33,-29) Matrix(799,-1080,236,-319) -> Matrix(7,6,-1,-1) Matrix(1019,-1380,398,-539) -> Matrix(81,68,-106,-89) Matrix(839,-1140,354,-481) -> Matrix(69,58,-94,-79) Matrix(1141,-1560,482,-659) -> Matrix(111,92,-146,-121) Matrix(919,-1260,380,-521) -> Matrix(73,60,-101,-83) Matrix(521,-720,144,-199) -> Matrix(5,4,-9,-7) -2/3 Matrix(259,-360,100,-139) -> Matrix(17,14,-23,-19) Matrix(341,-480,184,-259) -> Matrix(25,22,-33,-29) Matrix(3139,-4440,1286,-1819) -> Matrix(3,2,-7,-5) Matrix(721,-1020,340,-481) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(761,-1080,198,-281) -> Matrix(17,14,-23,-19) Matrix(1141,-1620,212,-301) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(379,-540,266,-379) -> Matrix(29,24,-35,-29) (27/19,10/7) -> (-6/7,-4/5) Matrix(41,-60,28,-41) -> Matrix(29,24,-35,-29) (10/7,3/2) -> (-6/7,-4/5) Matrix(79,-120,52,-79) -> Matrix(29,24,-35,-29) (3/2,20/13) -> (-6/7,-4/5) Matrix(661,-1020,116,-179) -> Matrix(7,6,-20,-17) Matrix(659,-1020,272,-421) -> Matrix(61,52,-88,-75) Matrix(1039,-1620,642,-1001) -> Matrix(43,36,-49,-41) -6/7 Matrix(881,-1380,256,-401) -> Matrix(19,16,-13,-11) Matrix(419,-660,266,-419) -> Matrix(431,360,-516,-431) (11/7,30/19) -> (-36/43,-5/6) Matrix(721,-1140,456,-721) -> Matrix(649,540,-780,-649) (30/19,19/12) -> (-5/6,-54/65) Matrix(719,-1140,152,-241) -> Matrix(53,44,-100,-83) Matrix(679,-1080,276,-439) -> Matrix(41,34,-47,-39) Matrix(641,-1020,252,-401) -> Matrix(41,34,-47,-39) Matrix(559,-900,100,-161) -> Matrix(5,4,1,1) Matrix(1861,-3000,1080,-1741) -> Matrix(109,90,-132,-109) *** -> (-5/6,-9/11) Matrix(1301,-2100,806,-1301) -> Matrix(69,56,-85,-69) (50/31,21/13) -> (-14/17,-4/5) Matrix(1259,-2040,482,-781) -> Matrix(33,28,-46,-39) Matrix(221,-360,62,-101) -> Matrix(17,14,-23,-19) Matrix(1099,-1800,428,-701) -> Matrix(59,48,-75,-61) -4/5 Matrix(841,-1380,220,-361) -> Matrix(49,40,-60,-49) *** -> (-5/6,-4/5) Matrix(619,-1020,230,-379) -> Matrix(37,30,-53,-43) Matrix(641,-1080,238,-401) -> Matrix(17,14,-23,-19) Matrix(1739,-2940,320,-541) -> Matrix(9,8,-8,-7) -1/1 Matrix(2621,-4440,768,-1301) -> Matrix(3,2,-7,-5) Matrix(6019,-10200,2348,-3979) -> Matrix(17,14,-23,-19) Matrix(4601,-7800,2714,-4601) -> Matrix(29,24,-35,-29) (100/59,39/23) -> (-6/7,-4/5) Matrix(601,-1020,142,-241) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(739,-1260,200,-341) -> Matrix(5,4,1,1) Matrix(421,-720,176,-301) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(419,-720,174,-299) -> Matrix(63,52,-86,-71) Matrix(4001,-6900,2320,-4001) -> Matrix(69,56,-85,-69) (50/29,69/40) -> (-14/17,-4/5) Matrix(659,-1140,174,-301) -> Matrix(61,50,-72,-59) -5/6 Matrix(761,-1320,162,-281) -> Matrix(17,14,-23,-19) Matrix(379,-660,58,-101) -> Matrix(27,22,-43,-35) Matrix(239,-420,136,-239) -> Matrix(169,136,-210,-169) (7/4,30/17) -> (-17/21,-4/5) Matrix(781,-1380,442,-781) -> Matrix(391,312,-490,-391) (30/17,23/13) -> (-4/5,-39/49) Matrix(881,-1560,362,-641) -> Matrix(63,50,-97,-77) Matrix(541,-960,102,-181) -> Matrix(5,4,14,11) Matrix(199,-360,110,-199) -> Matrix(11,8,-15,-11) (9/5,20/11) -> (-4/5,-2/3) Matrix(559,-1020,154,-281) -> Matrix(5,4,-29,-23) Matrix(359,-660,130,-239) -> Matrix(13,10,-22,-17) Matrix(161,-300,22,-41) -> Matrix(5,4,-1,-1) Matrix(319,-600,42,-79) -> Matrix(3,2,-7,-5) Matrix(539,-1020,158,-299) -> Matrix(13,10,-22,-17) Matrix(619,-1320,234,-499) -> Matrix(1,4,-1,-5) Matrix(221,-480,64,-139) -> Matrix(7,6,-13,-11) Matrix(299,-660,82,-181) -> Matrix(5,4,6,5) Matrix(161,-360,72,-161) -> Matrix(51,40,-65,-51) (20/9,9/4) -> (-4/5,-10/13) Matrix(79,-180,18,-41) -> Matrix(13,10,-17,-13) (-1/1,-3/4).(-4/5,-2/3) Matrix(179,-420,26,-61) -> Matrix(3,2,-2,-1) -1/1 Matrix(941,-2220,348,-821) -> Matrix(17,14,-23,-19) Matrix(101,-240,8,-19) -> Matrix(3,2,1,1) Matrix(1259,-3000,478,-1139) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(3199,-7800,1312,-3199) -> Matrix(13,8,-21,-13) (39/16,100/41) -> (-2/3,-4/7) Matrix(4919,-12000,1918,-4679) -> Matrix(17,10,-22,-13) Matrix(661,-1620,122,-299) -> Matrix(5,4,-4,-3) -1/1 Matrix(541,-1380,118,-301) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(599,-1560,230,-599) -> Matrix(31,24,-40,-31) (13/5,60/23) -> (-4/5,-3/4) Matrix(2161,-5640,828,-2161) -> Matrix(113,84,-152,-113) (60/23,47/18) -> (-3/4,-14/19) Matrix(619,-1620,222,-581) -> Matrix(5,4,-9,-7) -2/3 Matrix(799,-2100,304,-799) -> Matrix(11,8,-15,-11) (21/8,50/19) -> (-4/5,-2/3) Matrix(419,-1140,154,-419) -> Matrix(29,20,-42,-29) (19/7,30/11) -> (-5/7,-2/3) Matrix(241,-660,88,-241) -> Matrix(5,4,-6,-5) (30/11,11/4) -> (-1/1,-2/3) Matrix(281,-780,58,-161) -> Matrix(3,2,-7,-5) Matrix(259,-720,50,-139) -> Matrix(3,2,-7,-5) Matrix(341,-960,92,-259) -> Matrix(11,8,-7,-5) Matrix(401,-1140,70,-199) -> Matrix(3,2,7,5) Matrix(41,-120,14,-41) -> Matrix(11,8,-15,-11) (20/7,3/1) -> (-4/5,-2/3) Matrix(19,-60,6,-19) -> Matrix(-1,0,3,1) (3/1,10/3) -> (-2/3,0/1) Matrix(161,-540,48,-161) -> Matrix(-1,0,3,1) (10/3,27/8) -> (-2/3,0/1) Matrix(421,-1440,88,-301) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(241,-900,64,-239) -> Matrix(9,10,-10,-11) -1/1 Matrix(239,-1020,56,-239) -> Matrix(3,4,-2,-3) (17/4,30/7) -> (-2/1,-1/1) Matrix(181,-780,42,-181) -> Matrix(9,8,-10,-9) (30/7,13/3) -> (-1/1,-4/5) Matrix(599,-2760,130,-599) -> Matrix(17,12,-24,-17) (23/5,60/13) -> (-3/4,-2/3) Matrix(961,-4440,208,-961) -> Matrix(31,20,-48,-31) (60/13,37/8) -> (-2/3,-5/8) Matrix(1079,-5880,198,-1079) -> Matrix(15,16,-14,-15) (49/9,60/11) -> (-8/7,-1/1) Matrix(241,-1320,44,-241) -> Matrix(5,4,-6,-5) (60/11,11/2) -> (-1/1,-2/3) Matrix(139,-780,18,-101) -> Matrix(3,2,-5,-3) (-1/1,-1/2).(-2/3,0/1) Matrix(199,-1320,30,-199) -> Matrix(-1,0,3,1) (33/5,20/3) -> (-2/3,0/1) Matrix(161,-1080,24,-161) -> Matrix(-1,0,3,1) (20/3,27/4) -> (-2/3,0/1) Matrix(19,-180,2,-19) -> Matrix(-1,0,1,1) (9/1,10/1) -> (-2/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.