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: 120 Genus: 133 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -7/1 -20/3 -6/1 -16/3 -21/4 -26/5 -24/5 -14/3 -21/5 -4/1 -18/5 -7/2 -24/7 -42/13 -20/7 -14/5 -8/3 -21/8 -12/5 -7/3 -16/7 -2/1 -7/4 -12/7 -21/13 -14/9 -42/29 -7/5 -4/3 -21/16 -14/11 -21/17 -7/6 0/1 1/1 7/6 28/23 14/11 21/16 4/3 7/5 3/2 14/9 84/53 21/13 28/17 12/7 7/4 84/47 28/15 2/1 15/7 28/13 280/123 16/7 7/3 196/83 112/47 12/5 56/23 5/2 28/11 70/27 280/107 21/8 8/3 14/5 20/7 3/1 35/11 42/13 56/17 84/25 24/7 7/2 196/55 25/7 18/5 112/31 56/15 4/1 112/27 21/5 224/53 56/13 13/3 22/5 84/19 9/2 168/37 14/3 19/4 24/5 5/1 26/5 21/4 16/3 27/5 11/2 28/5 17/3 23/4 6/1 19/3 13/2 20/3 27/4 7/1 22/3 15/2 23/3 31/4 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 -11/1 1/1 -10/1 2/1 4/1 -9/1 -7/1 -17/2 1/0 -8/1 -2/1 -15/2 -1/2 -7/1 1/0 -20/3 -3/1 -13/2 1/0 -19/3 -3/1 -6/1 -2/1 0/1 -23/4 1/0 -17/3 -1/1 -28/5 -1/1 -11/2 -1/2 -16/3 0/1 -21/4 1/0 -26/5 -2/1 0/1 -5/1 1/1 -24/5 2/1 -19/4 1/0 -14/3 1/0 -37/8 1/0 -23/5 -5/1 -55/12 1/0 -32/7 -4/1 -9/2 -5/2 -22/5 -2/1 0/1 -13/3 -1/1 -30/7 0/1 2/1 -77/18 1/0 -47/11 5/1 -17/4 1/0 -38/9 -2/1 0/1 -21/5 1/0 -25/6 1/0 -4/1 1/0 -31/8 1/0 -58/15 -22/5 -4/1 -27/7 -11/3 -23/6 -7/2 -19/5 -3/1 -34/9 -8/3 -2/1 -49/13 -5/2 -15/4 -9/4 -26/7 -2/1 -12/7 -11/3 -1/1 -29/8 1/0 -47/13 -19/9 -18/5 -2/1 -8/5 -25/7 -5/3 -7/2 -1/1 -31/9 1/1 -86/25 0/1 2/1 -55/16 1/0 -24/7 -2/1 -41/12 -5/4 -17/5 -1/1 -27/8 1/0 -10/3 -2/3 0/1 -23/7 1/3 -36/11 1/1 -13/4 1/0 -42/13 -1/1 -29/9 -1/1 -16/5 0/1 -19/6 1/0 -3/1 -1/1 -20/7 1/0 -37/13 3/1 -17/6 1/0 -14/5 1/0 -39/14 1/0 -64/23 -12/1 -25/9 -9/1 -11/4 1/0 -30/11 -4/1 -18/5 -19/7 -3/1 -84/31 -3/1 -65/24 -47/16 -46/17 -20/7 -14/5 -27/10 -11/4 -8/3 -2/1 -29/11 -7/5 -79/30 -3/2 -50/19 -2/1 -4/3 -71/27 -11/9 -21/8 -1/1 -97/37 -1/3 -76/29 -1/1 -55/21 -1/1 -89/34 -1/2 -123/47 -1/3 -34/13 -2/1 0/1 -13/5 -1/1 -31/12 -3/2 -18/7 -2/1 -4/3 -59/23 -3/1 -41/16 1/0 -64/25 -4/3 -23/9 -1/1 -28/11 -1/1 -5/2 1/0 -27/11 -3/1 -49/20 -1/1 -22/9 -2/1 0/1 -17/7 -1/1 -29/12 1/0 -70/29 1/0 -41/17 -3/1 -53/22 -5/2 -65/27 -11/7 -77/32 -3/2 -12/5 -1/1 -31/13 -1/3 -50/21 0/1 2/3 -19/8 1/0 -26/11 -2/1 -4/3 -7/3 -1/1 -30/13 -2/1 0/1 -83/36 -5/6 -53/23 -3/5 -23/10 1/0 -39/17 -1/1 -55/24 -1/2 -16/7 0/1 -57/25 -1/1 -41/18 1/0 -107/47 -1/5 -66/29 0/1 2/1 -25/11 -1/1 -84/37 -1/1 -59/26 -3/4 -34/15 -2/3 0/1 -9/4 -1/4 -29/13 1/5 -20/9 1/2 -11/5 1/1 -46/21 -2/1 0/1 -35/16 1/1 -59/27 3/1 -24/11 2/1 -13/6 1/0 -28/13 1/0 -15/7 -7/1 -2/1 -2/1 0/1 -17/9 -1/1 -15/8 -7/6 -28/15 -1/1 -13/7 -1/1 -24/13 -2/3 -59/32 -3/4 -35/19 -1/2 -46/25 -2/1 0/1 -11/6 -1/2 -31/17 -3/7 -51/28 -5/12 -71/39 -5/13 -20/11 -1/3 -49/27 -1/4 -29/16 -1/6 -9/5 1/3 -25/14 1/0 -91/51 1/0 -66/37 -2/3 0/1 -173/97 -1/7 -280/157 0/1 -107/60 1/4 -41/23 -1/1 -98/55 1/0 -57/32 1/0 -16/9 0/1 -55/31 1/1 -94/53 0/1 2/1 -39/22 1/0 -23/13 -1/1 -7/4 1/0 -33/19 -3/1 -59/34 -1/2 -85/49 3/1 -196/113 1/0 -111/64 1/0 -26/15 -4/1 -2/1 -19/11 -1/1 -50/29 -2/5 0/1 -81/47 -1/7 -112/65 0/1 -31/18 1/2 -43/25 1/1 -55/32 1/0 -67/39 -1/1 -79/46 1/0 -12/7 1/0 -65/38 -11/4 -53/31 -5/3 -41/24 -3/2 -111/65 -1/1 -70/41 -1/1 -29/17 -1/1 -17/10 1/0 -56/33 -2/1 -39/23 -1/1 -22/13 -2/1 0/1 -49/29 1/0 -27/16 -3/2 -59/35 -1/3 -32/19 0/1 -5/3 -1/1 -28/17 1/0 -23/14 1/0 -41/25 -1/1 -59/36 -3/2 -77/47 1/0 -18/11 -4/1 -2/1 -31/19 -3/1 -44/27 -1/1 -101/62 -3/2 -57/35 -1/1 -70/43 -1/1 -13/8 1/0 -34/21 -2/1 0/1 -157/97 -1/3 -280/173 0/1 -123/76 1/2 -212/131 1/1 -89/55 1/1 -55/34 1/0 -131/81 1/1 -76/47 1/0 -21/13 1/0 -92/57 1/0 -71/44 -11/2 -50/31 -4/1 -2/1 -29/18 -7/2 -8/5 -2/1 -27/17 -11/7 -19/12 -3/2 -30/19 -18/13 -4/3 -11/7 -1/1 -36/23 -7/6 -97/62 -23/20 -61/39 -17/15 -86/55 -8/7 -10/9 -25/16 -9/8 -14/9 -1/1 -31/20 -7/8 -110/71 -6/7 -16/19 -79/51 -1/1 -48/31 -4/5 -17/11 -1/1 -54/35 -6/7 -4/5 -37/24 -3/4 -94/61 -2/3 0/1 -57/37 -1/1 -20/13 -1/1 -23/15 -3/5 -3/2 1/0 -22/15 -2/3 0/1 -19/13 -1/1 -54/37 -2/5 0/1 -89/61 -1/1 -124/85 -1/1 -35/24 -1/2 -16/11 0/1 -29/20 1/0 -42/29 1/0 -55/38 1/0 -13/9 -1/1 -36/25 -1/2 -59/41 -3/7 -23/16 -1/4 -56/39 0/1 -33/23 1/5 -10/7 0/1 2/1 -47/33 11/1 -84/59 1/0 -37/26 1/0 -27/19 -1/1 -17/12 1/0 -75/53 -1/1 -58/41 0/1 2/1 -41/29 -5/1 -106/75 -8/3 -2/1 -171/121 -9/5 -65/46 -1/2 -24/17 -2/1 -7/5 1/0 -32/23 -4/1 -57/41 -3/1 -196/141 -3/1 -139/100 -23/8 -82/59 -8/3 -2/1 -25/18 -5/2 -18/13 -8/3 -2/1 -65/47 -27/13 -112/81 -2/1 -47/34 -19/10 -29/21 -1/1 -40/29 -2/1 -11/8 1/0 -26/19 -12/5 -2/1 -41/30 -21/10 -56/41 -2/1 -15/11 -9/5 -34/25 -2/1 -8/5 -53/39 -1/1 -19/14 -3/2 -23/17 -7/5 -27/20 -11/8 -4/3 -1/1 -29/22 -1/4 -112/85 0/1 -83/63 1/7 -54/41 0/1 2/3 -25/19 -1/1 -46/35 0/1 2/1 -21/16 -1/1 -59/45 -1/3 -38/29 -2/1 0/1 -131/100 -1/2 -224/171 0/1 -93/71 1/1 -55/42 1/0 -17/13 -1/1 -47/36 -5/6 -30/23 -2/3 0/1 -43/33 -1/3 -56/43 0/1 -13/10 1/0 -22/17 -2/1 0/1 -53/41 1/1 -84/65 1/0 -31/24 1/0 -9/7 -5/3 -59/46 -19/14 -168/131 -4/3 -109/85 -33/25 -50/39 -4/3 -14/11 -41/32 -7/6 -32/25 -4/3 -55/43 -1/1 -23/18 -5/4 -14/11 -1/1 -33/26 -7/8 -19/15 -1/1 -43/34 -3/4 -24/19 -2/3 -53/42 -5/8 -29/23 -1/3 -5/4 -1/2 -31/25 -1/1 -26/21 -2/1 0/1 -47/38 -3/4 -68/55 1/0 -21/17 -1/1 -100/81 -1/2 -79/64 -1/2 -58/47 -2/1 0/1 -37/30 -1/2 -16/13 0/1 -27/22 1/0 -11/9 1/1 -28/23 1/0 -17/14 1/0 -23/19 -1/1 -29/24 -3/2 -6/5 -2/1 0/1 -19/16 -3/2 -32/27 -4/3 -13/11 -1/1 -20/17 -3/2 -27/23 -9/7 -7/6 -1/1 -22/19 -2/3 0/1 -15/13 1/1 -23/20 1/0 -54/47 -2/3 0/1 -31/27 1/1 -8/7 -2/1 -17/15 -1/1 -9/8 -7/6 -10/9 -4/5 -2/3 -11/10 -1/2 -1/1 -1/1 0/1 0/1 1/1 1/1 11/10 1/2 10/9 2/3 4/5 9/8 7/6 17/15 1/1 8/7 2/1 15/13 -1/1 7/6 1/1 20/17 3/2 13/11 1/1 19/16 3/2 6/5 0/1 2/1 23/19 1/1 17/14 1/0 28/23 1/0 11/9 -1/1 16/13 0/1 21/17 1/1 26/21 0/1 2/1 5/4 1/2 24/19 2/3 19/15 1/1 14/11 1/1 37/29 1/1 23/18 5/4 55/43 1/1 32/25 4/3 9/7 5/3 22/17 0/1 2/1 13/10 1/0 30/23 0/1 2/3 77/59 1/1 47/36 5/6 17/13 1/1 38/29 0/1 2/1 21/16 1/1 25/19 1/1 4/3 1/1 31/23 1/1 58/43 22/17 4/3 27/20 11/8 23/17 7/5 19/14 3/2 34/25 8/5 2/1 49/36 5/3 15/11 9/5 26/19 2/1 12/5 11/8 1/0 29/21 1/1 47/34 19/10 18/13 2/1 8/3 25/18 5/2 7/5 1/0 31/22 1/2 86/61 0/1 2/3 55/39 1/1 24/17 2/1 41/29 5/1 17/12 1/0 27/19 1/1 10/7 -2/1 0/1 23/16 1/4 36/25 1/2 13/9 1/1 42/29 1/0 29/20 1/0 16/11 0/1 19/13 1/1 3/2 1/0 20/13 1/1 37/24 3/4 17/11 1/1 14/9 1/1 39/25 1/1 64/41 12/11 25/16 9/8 11/7 1/1 30/19 4/3 18/13 19/12 3/2 84/53 3/2 65/41 47/31 46/29 20/13 14/9 27/17 11/7 8/5 2/1 29/18 7/2 79/49 3/1 50/31 2/1 4/1 71/44 11/2 21/13 1/0 97/60 -1/2 76/47 1/0 55/34 1/0 89/55 -1/1 123/76 -1/2 34/21 0/1 2/1 13/8 1/0 31/19 3/1 18/11 2/1 4/1 59/36 3/2 41/25 1/1 64/39 4/1 23/14 1/0 28/17 1/0 5/3 1/1 27/16 3/2 49/29 1/0 22/13 0/1 2/1 17/10 1/0 29/17 1/1 70/41 1/1 41/24 3/2 53/31 5/3 65/38 11/4 77/45 3/1 12/7 1/0 31/18 -1/2 50/29 0/1 2/5 19/11 1/1 26/15 2/1 4/1 7/4 1/0 30/17 0/1 2/1 83/47 -5/1 53/30 -3/2 23/13 1/1 39/22 1/0 55/31 -1/1 16/9 0/1 57/32 1/0 41/23 1/1 107/60 -1/4 66/37 0/1 2/3 25/14 1/0 84/47 1/0 59/33 -3/1 34/19 -2/1 0/1 9/5 -1/3 29/16 1/6 20/11 1/3 11/6 1/2 46/25 0/1 2/1 35/19 1/2 59/32 3/4 24/13 2/3 13/7 1/1 28/15 1/1 15/8 7/6 2/1 0/1 2/1 17/8 1/0 15/7 7/1 28/13 1/0 13/6 1/0 24/11 -2/1 59/27 -3/1 35/16 -1/1 46/21 0/1 2/1 11/5 -1/1 31/14 -3/4 51/23 -5/7 71/32 -5/8 20/9 -1/2 49/22 -1/3 29/13 -1/5 9/4 1/4 25/11 1/1 91/40 1/1 66/29 -2/1 0/1 173/76 -1/6 280/123 0/1 107/47 1/5 41/18 1/0 98/43 1/1 57/25 1/1 16/7 0/1 55/24 1/2 94/41 0/1 2/3 39/17 1/1 23/10 1/0 7/3 1/1 33/14 3/2 59/25 -1/1 85/36 3/4 196/83 1/1 111/47 1/1 26/11 4/3 2/1 19/8 1/0 50/21 -2/3 0/1 81/34 -1/6 112/47 0/1 31/13 1/3 43/18 1/2 55/23 1/1 67/28 1/0 79/33 1/1 12/5 1/1 65/27 11/7 53/22 5/2 41/17 3/1 111/46 1/0 70/29 1/0 29/12 1/0 17/7 1/1 56/23 2/1 39/16 1/0 22/9 0/1 2/1 49/20 1/1 27/11 3/1 59/24 -1/2 32/13 0/1 5/2 1/0 28/11 1/1 23/9 1/1 41/16 1/0 59/23 3/1 77/30 1/1 18/7 4/3 2/1 31/12 3/2 44/17 1/0 101/39 3/1 57/22 1/0 70/27 1/0 13/5 1/1 34/13 0/1 2/1 157/60 -1/2 280/107 0/1 123/47 1/3 212/81 1/2 89/34 1/2 55/21 1/1 131/50 1/2 76/29 1/1 21/8 1/1 92/35 1/1 71/27 11/9 50/19 4/3 2/1 29/11 7/5 8/3 2/1 27/10 11/4 19/7 3/1 30/11 18/5 4/1 11/4 1/0 36/13 7/1 97/35 23/3 61/22 17/2 86/31 8/1 10/1 25/9 9/1 14/5 1/0 31/11 -7/1 110/39 -6/1 -16/3 79/28 1/0 48/17 -4/1 17/6 1/0 54/19 -6/1 -4/1 37/13 -3/1 94/33 -2/1 0/1 57/20 1/0 20/7 1/0 23/8 -3/2 3/1 1/1 22/7 -2/1 0/1 19/6 1/0 54/17 -2/3 0/1 89/28 1/0 124/39 1/0 35/11 -1/1 16/5 0/1 29/9 1/1 42/13 1/1 55/17 1/1 13/4 1/0 36/11 -1/1 59/18 -3/4 23/7 -1/3 56/17 0/1 33/10 1/6 10/3 0/1 2/3 47/14 11/12 84/25 1/1 37/11 1/1 27/8 1/0 17/5 1/1 75/22 1/0 58/17 0/1 2/3 41/12 5/4 106/31 8/5 2/1 171/50 9/4 65/19 -1/1 24/7 2/1 7/2 1/1 32/9 4/3 57/16 3/2 196/55 3/2 139/39 23/15 82/23 8/5 2/1 25/7 5/3 18/5 8/5 2/1 65/18 27/14 112/31 2/1 47/13 19/9 29/8 1/0 40/11 2/1 11/3 1/1 26/7 12/7 2/1 41/11 21/11 56/15 2/1 15/4 9/4 34/9 2/1 8/3 53/14 1/0 19/5 3/1 23/6 7/2 27/7 11/3 4/1 1/0 29/7 -1/3 112/27 0/1 83/20 1/8 54/13 0/1 2/5 25/6 1/0 46/11 0/1 2/3 21/5 1/0 59/14 -1/2 38/9 0/1 2/1 131/31 -1/1 224/53 0/1 93/22 1/2 55/13 1/1 17/4 1/0 47/11 -5/1 30/7 -2/1 0/1 43/10 -1/2 56/13 0/1 13/3 1/1 22/5 0/1 2/1 53/12 1/2 84/19 1/1 31/7 1/1 9/2 5/2 59/13 19/5 168/37 4/1 109/24 33/8 50/11 4/1 14/3 41/9 7/1 32/7 4/1 55/12 1/0 23/5 5/1 14/3 1/0 33/7 -7/1 19/4 1/0 43/9 -3/1 24/5 -2/1 53/11 -5/3 29/6 -1/2 5/1 -1/1 31/6 1/0 26/5 0/1 2/1 47/9 -3/1 68/13 1/1 21/4 1/0 100/19 -1/1 79/15 -1/1 58/11 0/1 2/1 37/7 -1/1 16/3 0/1 27/5 1/1 11/2 1/2 28/5 1/1 17/3 1/1 23/4 1/0 29/5 3/1 6/1 0/1 2/1 19/3 3/1 32/5 4/1 13/2 1/0 20/3 3/1 27/4 9/2 7/1 1/0 22/3 -2/1 0/1 15/2 1/2 23/3 1/1 54/7 -2/1 0/1 31/4 1/2 8/1 2/1 17/2 1/0 9/1 7/1 10/1 -4/1 -2/1 11/1 -1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(57,728,22,281) (-11/1,1/0) -> (101/39,57/22) Hyperbolic Matrix(57,616,26,281) (-11/1,-10/1) -> (46/21,11/5) Hyperbolic Matrix(111,1064,70,671) (-10/1,-9/1) -> (65/41,46/29) Hyperbolic Matrix(111,952,26,223) (-9/1,-17/2) -> (17/4,47/11) Hyperbolic Matrix(113,952,40,337) (-17/2,-8/1) -> (48/17,17/6) Hyperbolic Matrix(169,1288,-66,-503) (-8/1,-15/2) -> (-41/16,-64/25) Hyperbolic Matrix(113,840,-30,-223) (-15/2,-7/1) -> (-49/13,-15/4) Hyperbolic Matrix(167,1120,-92,-617) (-7/1,-20/3) -> (-20/11,-49/27) Hyperbolic Matrix(111,728,34,223) (-20/3,-13/2) -> (13/4,36/11) Hyperbolic Matrix(167,1064,-132,-841) (-13/2,-19/3) -> (-19/15,-43/34) Hyperbolic Matrix(169,1064,98,617) (-19/3,-6/1) -> (50/29,19/11) Hyperbolic Matrix(279,1624,-106,-617) (-6/1,-23/4) -> (-79/30,-50/19) Hyperbolic Matrix(225,1288,98,561) (-23/4,-17/3) -> (39/17,23/10) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(169,896,-116,-615) (-16/3,-21/4) -> (-35/24,-16/11) Hyperbolic Matrix(505,2632,-118,-615) (-21/4,-26/5) -> (-30/7,-77/18) Hyperbolic Matrix(391,2016,-250,-1289) (-26/5,-5/1) -> (-61/39,-86/55) Hyperbolic Matrix(57,280,-34,-167) (-5/1,-24/5) -> (-32/19,-5/3) Hyperbolic Matrix(223,1064,-188,-897) (-24/5,-19/4) -> (-19/16,-32/27) Hyperbolic Matrix(167,784,-36,-169) (-19/4,-14/3) -> (-14/3,-37/8) Parabolic Matrix(279,1288,206,951) (-37/8,-23/5) -> (23/17,19/14) Hyperbolic Matrix(1343,6160,830,3807) (-23/5,-55/12) -> (55/34,89/55) Hyperbolic Matrix(783,3584,220,1007) (-55/12,-32/7) -> (32/9,57/16) Hyperbolic Matrix(503,2296,-356,-1625) (-32/7,-9/2) -> (-65/46,-24/17) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(391,1680,-300,-1289) (-13/3,-30/7) -> (-30/23,-43/33) Hyperbolic Matrix(2017,8624,-838,-3583) (-77/18,-47/11) -> (-65/27,-77/32) Hyperbolic Matrix(223,952,26,111) (-47/11,-17/4) -> (17/2,9/1) Hyperbolic Matrix(727,3080,-410,-1737) (-17/4,-38/9) -> (-94/53,-39/22) Hyperbolic Matrix(783,3304,-478,-2017) (-38/9,-21/5) -> (-77/47,-18/11) Hyperbolic Matrix(671,2800,-376,-1569) (-21/5,-25/6) -> (-25/14,-91/51) Hyperbolic Matrix(55,224,-14,-57) (-25/6,-4/1) -> (-4/1,-31/8) Parabolic Matrix(897,3472,116,449) (-31/8,-58/15) -> (54/7,31/4) Hyperbolic Matrix(1623,6272,-1232,-4761) (-58/15,-27/7) -> (-83/63,-54/41) Hyperbolic Matrix(335,1288,58,223) (-27/7,-23/6) -> (23/4,29/5) Hyperbolic Matrix(337,1288,264,1009) (-23/6,-19/5) -> (37/29,23/18) Hyperbolic Matrix(281,1064,-192,-727) (-19/5,-34/9) -> (-22/15,-19/13) Hyperbolic Matrix(727,2744,430,1623) (-34/9,-49/13) -> (49/29,22/13) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(169,616,-138,-503) (-11/3,-29/8) -> (-27/22,-11/9) Hyperbolic Matrix(449,1624,248,897) (-29/8,-47/13) -> (9/5,29/16) Hyperbolic Matrix(559,2016,-404,-1457) (-47/13,-18/5) -> (-18/13,-65/47) Hyperbolic Matrix(281,1008,172,617) (-18/5,-25/7) -> (31/19,18/11) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(1399,4816,504,1735) (-31/9,-86/25) -> (86/31,25/9) Hyperbolic Matrix(3191,10976,-1840,-6329) (-86/25,-55/16) -> (-111/64,-26/15) Hyperbolic Matrix(897,3080,196,673) (-55/16,-24/7) -> (32/7,55/12) Hyperbolic Matrix(671,2296,-524,-1793) (-24/7,-41/12) -> (-41/32,-32/25) Hyperbolic Matrix(279,952,-148,-505) (-41/12,-17/5) -> (-17/9,-15/8) Hyperbolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(169,560,-118,-391) (-10/3,-23/7) -> (-33/23,-10/7) Hyperbolic Matrix(393,1288,-256,-839) (-23/7,-36/11) -> (-20/13,-23/15) Hyperbolic Matrix(223,728,34,111) (-36/11,-13/4) -> (13/2,20/3) Hyperbolic Matrix(449,1456,-276,-895) (-13/4,-42/13) -> (-70/43,-13/8) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(281,896,-228,-727) (-16/5,-19/6) -> (-37/30,-16/13) Hyperbolic Matrix(337,1064,-248,-783) (-19/6,-3/1) -> (-53/39,-19/14) Hyperbolic Matrix(449,1288,-312,-895) (-3/1,-20/7) -> (-36/25,-59/41) Hyperbolic Matrix(1905,5432,-1178,-3359) (-20/7,-37/13) -> (-131/81,-76/47) Hyperbolic Matrix(671,1904,-474,-1345) (-37/13,-17/6) -> (-17/12,-75/53) Hyperbolic Matrix(279,784,-100,-281) (-17/6,-14/5) -> (-14/5,-39/14) Parabolic Matrix(503,1400,60,167) (-39/14,-64/23) -> (8/1,17/2) Hyperbolic Matrix(785,2184,-684,-1903) (-64/23,-25/9) -> (-31/27,-8/7) Hyperbolic Matrix(223,616,-122,-337) (-25/9,-11/4) -> (-11/6,-31/17) Hyperbolic Matrix(225,616,164,449) (-11/4,-30/11) -> (26/19,11/8) Hyperbolic Matrix(391,1064,226,615) (-30/11,-19/7) -> (19/11,26/15) Hyperbolic Matrix(1735,4704,516,1399) (-19/7,-84/31) -> (84/25,37/11) Hyperbolic Matrix(3473,9408,1034,2801) (-84/31,-65/24) -> (47/14,84/25) Hyperbolic Matrix(393,1064,352,953) (-65/24,-46/17) -> (10/9,9/8) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(1063,2800,276,727) (-29/11,-79/30) -> (23/6,27/7) Hyperbolic Matrix(3641,9576,-2576,-6775) (-50/19,-71/27) -> (-41/29,-106/75) Hyperbolic Matrix(1343,3528,-512,-1345) (-71/27,-21/8) -> (-21/8,-97/37) Parabolic Matrix(4145,10864,1496,3921) (-97/37,-76/29) -> (36/13,97/35) Hyperbolic Matrix(2073,5432,-1346,-3527) (-76/29,-55/21) -> (-57/37,-20/13) Hyperbolic Matrix(2353,6160,1840,4817) (-55/21,-89/34) -> (23/18,55/43) Hyperbolic Matrix(5991,15680,-3488,-9129) (-89/34,-123/47) -> (-67/39,-79/46) Hyperbolic Matrix(3639,9520,-2248,-5881) (-123/47,-34/13) -> (-34/21,-157/97) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(1287,3304,-982,-2521) (-18/7,-59/23) -> (-59/45,-38/29) Hyperbolic Matrix(1791,4592,1048,2687) (-59/23,-41/16) -> (41/24,53/31) Hyperbolic Matrix(2407,6160,-1554,-3977) (-64/25,-23/9) -> (-79/51,-48/31) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(113,280,-90,-223) (-5/2,-27/11) -> (-29/23,-5/4) Hyperbolic Matrix(1119,2744,502,1231) (-27/11,-49/20) -> (49/22,29/13) Hyperbolic Matrix(1121,2744,824,2017) (-49/20,-22/9) -> (34/25,49/36) Hyperbolic Matrix(505,1232,-298,-727) (-22/9,-17/7) -> (-39/23,-22/13) Hyperbolic Matrix(393,952,116,281) (-17/7,-29/12) -> (27/8,17/5) Hyperbolic Matrix(1345,3248,928,2241) (-29/12,-70/29) -> (42/29,29/20) Hyperbolic Matrix(2855,6888,-1602,-3865) (-70/29,-41/17) -> (-41/23,-98/55) Hyperbolic Matrix(1905,4592,1162,2801) (-41/17,-53/22) -> (59/36,41/25) Hyperbolic Matrix(1791,4312,-1396,-3361) (-53/22,-65/27) -> (-9/7,-59/46) Hyperbolic Matrix(4143,9968,-2840,-6833) (-77/32,-12/5) -> (-124/85,-35/24) Hyperbolic Matrix(727,1736,-446,-1065) (-12/5,-31/13) -> (-31/19,-44/27) Hyperbolic Matrix(2351,5600,-1364,-3249) (-31/13,-50/21) -> (-50/29,-81/47) Hyperbolic Matrix(447,1064,376,895) (-50/21,-19/8) -> (19/16,6/5) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(2575,5936,534,1231) (-83/36,-53/23) -> (53/11,29/6) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(561,1288,98,225) (-23/10,-39/17) -> (17/3,23/4) Hyperbolic Matrix(1343,3080,-1026,-2353) (-39/17,-55/24) -> (-55/42,-17/13) Hyperbolic Matrix(783,1792,440,1007) (-55/24,-16/7) -> (16/9,57/32) Hyperbolic Matrix(785,1792,442,1009) (-16/7,-57/25) -> (55/31,16/9) Hyperbolic Matrix(3023,6888,-1770,-4033) (-57/25,-41/18) -> (-41/24,-111/65) Hyperbolic Matrix(4255,9688,1918,4367) (-41/18,-107/47) -> (51/23,71/32) Hyperbolic Matrix(8119,18480,-4552,-10361) (-107/47,-66/29) -> (-66/37,-173/97) Hyperbolic Matrix(1231,2800,-936,-2129) (-66/29,-25/11) -> (-25/19,-46/35) Hyperbolic Matrix(2071,4704,468,1063) (-25/11,-84/37) -> (84/19,31/7) Hyperbolic Matrix(4145,9408,938,2129) (-84/37,-59/26) -> (53/12,84/19) Hyperbolic Matrix(1679,3808,444,1007) (-59/26,-34/15) -> (34/9,53/14) Hyperbolic Matrix(727,1624,526,1175) (-9/4,-29/13) -> (29/21,47/34) Hyperbolic Matrix(503,1120,-428,-953) (-29/13,-20/9) -> (-20/17,-27/23) Hyperbolic Matrix(279,616,-178,-393) (-20/9,-11/5) -> (-11/7,-36/23) Hyperbolic Matrix(281,616,26,57) (-11/5,-46/21) -> (10/1,11/1) Hyperbolic Matrix(2967,6496,1304,2855) (-46/21,-35/16) -> (91/40,66/29) Hyperbolic Matrix(3023,6608,1178,2575) (-35/16,-59/27) -> (59/23,77/30) Hyperbolic Matrix(1231,2688,256,559) (-59/27,-24/11) -> (24/5,53/11) Hyperbolic Matrix(617,1344,-488,-1063) (-24/11,-13/6) -> (-43/34,-24/19) Hyperbolic Matrix(337,728,156,337) (-13/6,-28/13) -> (28/13,13/6) Hyperbolic Matrix(391,840,182,391) (-28/13,-15/7) -> (15/7,28/13) Hyperbolic Matrix(447,952,-316,-673) (-15/7,-2/1) -> (-58/41,-41/29) Hyperbolic Matrix(503,952,-326,-617) (-2/1,-17/9) -> (-17/11,-54/35) Hyperbolic Matrix(449,840,240,449) (-15/8,-28/15) -> (28/15,15/8) Hyperbolic Matrix(391,728,210,391) (-28/15,-13/7) -> (13/7,28/15) Hyperbolic Matrix(393,728,-332,-615) (-13/7,-24/13) -> (-32/27,-13/11) Hyperbolic Matrix(1791,3304,728,1343) (-24/13,-59/32) -> (59/24,32/13) Hyperbolic Matrix(1793,3304,426,785) (-59/32,-35/19) -> (21/5,59/14) Hyperbolic Matrix(1399,2576,334,615) (-35/19,-46/25) -> (46/11,21/5) Hyperbolic Matrix(335,616,304,559) (-46/25,-11/6) -> (11/10,10/9) Hyperbolic Matrix(953,1736,-768,-1399) (-31/17,-51/28) -> (-5/4,-31/25) Hyperbolic Matrix(5321,9688,2984,5433) (-51/28,-71/39) -> (41/23,107/60) Hyperbolic Matrix(4369,7952,1662,3025) (-71/39,-20/11) -> (92/35,71/27) Hyperbolic Matrix(1513,2744,896,1625) (-49/27,-29/16) -> (27/16,49/29) Hyperbolic Matrix(897,1624,248,449) (-29/16,-9/5) -> (47/13,29/8) Hyperbolic Matrix(281,504,-218,-391) (-9/5,-25/14) -> (-31/24,-9/7) Hyperbolic Matrix(3641,6496,1978,3529) (-91/51,-66/37) -> (46/25,35/19) Hyperbolic Matrix(43959,78400,19310,34439) (-173/97,-280/157) -> (280/123,107/47) Hyperbolic Matrix(43961,78400,19312,34441) (-280/157,-107/60) -> (173/76,280/123) Hyperbolic Matrix(7223,12880,2606,4647) (-107/60,-41/23) -> (97/35,61/22) Hyperbolic Matrix(5375,9576,2074,3695) (-98/55,-57/32) -> (57/22,70/27) Hyperbolic Matrix(1007,1792,440,783) (-57/32,-16/9) -> (16/7,55/24) Hyperbolic Matrix(1009,1792,442,785) (-16/9,-55/31) -> (57/25,16/7) Hyperbolic Matrix(5935,10528,-3852,-6833) (-55/31,-94/53) -> (-94/61,-57/37) Hyperbolic Matrix(727,1288,600,1063) (-39/22,-23/13) -> (23/19,17/14) Hyperbolic Matrix(223,392,-128,-225) (-23/13,-7/4) -> (-7/4,-33/19) Parabolic Matrix(1903,3304,580,1007) (-33/19,-59/34) -> (59/18,23/7) Hyperbolic Matrix(3809,6608,1550,2689) (-59/34,-85/49) -> (27/11,59/24) Hyperbolic Matrix(25311,43904,7102,12319) (-85/49,-196/113) -> (196/55,139/39) Hyperbolic Matrix(18985,32928,5328,9241) (-196/113,-111/64) -> (57/16,196/55) Hyperbolic Matrix(615,1064,226,391) (-26/15,-19/11) -> (19/7,30/11) Hyperbolic Matrix(617,1064,98,169) (-19/11,-50/29) -> (6/1,19/3) Hyperbolic Matrix(7279,12544,3054,5263) (-81/47,-112/65) -> (112/47,31/13) Hyperbolic Matrix(7281,12544,3056,5265) (-112/65,-31/18) -> (81/34,112/47) Hyperbolic Matrix(1791,3080,-1238,-2129) (-43/25,-55/32) -> (-55/38,-13/9) Hyperbolic Matrix(391,672,32,55) (-55/32,-67/39) -> (11/1,1/0) Hyperbolic Matrix(5153,8848,-4174,-7167) (-79/46,-12/7) -> (-100/81,-79/64) Hyperbolic Matrix(2913,4984,-2356,-4031) (-12/7,-65/38) -> (-47/38,-68/55) Hyperbolic Matrix(8513,14560,-6024,-10303) (-65/38,-53/31) -> (-171/121,-65/46) Hyperbolic Matrix(2687,4592,1048,1791) (-53/31,-41/24) -> (41/16,59/23) Hyperbolic Matrix(4985,8512,1542,2633) (-111/65,-70/41) -> (42/13,55/17) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(1847,3136,758,1287) (-17/10,-56/33) -> (56/23,39/16) Hyperbolic Matrix(1849,3136,760,1289) (-56/33,-39/23) -> (17/7,56/23) Hyperbolic Matrix(729,1232,100,169) (-22/13,-49/29) -> (7/1,22/3) Hyperbolic Matrix(895,1512,132,223) (-49/29,-27/16) -> (27/4,7/1) Hyperbolic Matrix(3919,6608,1660,2799) (-27/16,-59/35) -> (59/25,85/36) Hyperbolic Matrix(1961,3304,898,1513) (-59/35,-32/19) -> (24/11,59/27) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(785,1288,-682,-1119) (-23/14,-41/25) -> (-15/13,-23/20) Hyperbolic Matrix(2801,4592,1162,1905) (-41/25,-59/36) -> (53/22,41/17) Hyperbolic Matrix(4033,6608,2188,3585) (-59/36,-77/47) -> (35/19,59/32) Hyperbolic Matrix(617,1008,172,281) (-18/11,-31/19) -> (25/7,18/5) Hyperbolic Matrix(16465,26824,-10174,-16575) (-44/27,-101/62) -> (-123/76,-212/131) Hyperbolic Matrix(447,728,412,671) (-101/62,-57/35) -> (1/1,11/10) Hyperbolic Matrix(5881,9576,2580,4201) (-57/35,-70/43) -> (98/43,57/25) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(48439,78400,18510,29959) (-157/97,-280/173) -> (280/107,123/47) Hyperbolic Matrix(48441,78400,18512,29961) (-280/173,-123/76) -> (157/60,280/107) Hyperbolic Matrix(18479,29904,-12666,-20497) (-212/131,-89/55) -> (-89/61,-124/85) Hyperbolic Matrix(3807,6160,830,1343) (-89/55,-55/34) -> (55/12,23/5) Hyperbolic Matrix(7617,12320,-5816,-9407) (-55/34,-131/81) -> (-93/71,-55/42) Hyperbolic Matrix(2183,3528,-1352,-2185) (-76/47,-21/13) -> (-21/13,-92/57) Parabolic Matrix(4927,7952,2220,3583) (-92/57,-71/44) -> (71/32,20/9) Hyperbolic Matrix(3471,5600,-2708,-4369) (-71/44,-50/31) -> (-50/39,-41/32) Hyperbolic Matrix(1007,1624,-834,-1345) (-50/31,-29/18) -> (-29/24,-6/5) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(6943,10864,4294,6719) (-36/23,-97/62) -> (97/60,76/47) Hyperbolic Matrix(8233,12880,3616,5657) (-97/62,-61/39) -> (107/47,41/18) Hyperbolic Matrix(3081,4816,2186,3417) (-86/55,-25/16) -> (31/22,86/61) Hyperbolic Matrix(503,784,-324,-505) (-25/16,-14/9) -> (-14/9,-31/20) Parabolic Matrix(2855,4424,686,1063) (-31/20,-110/71) -> (54/13,25/6) Hyperbolic Matrix(8567,13272,1626,2519) (-110/71,-79/51) -> (79/15,58/11) Hyperbolic Matrix(615,952,542,839) (-48/31,-17/11) -> (17/15,8/7) Hyperbolic Matrix(1961,3024,618,953) (-54/35,-37/24) -> (19/6,54/17) Hyperbolic Matrix(8903,13720,-6796,-10473) (-37/24,-94/61) -> (-38/29,-131/100) Hyperbolic Matrix(841,1288,476,729) (-23/15,-3/2) -> (53/30,23/13) Hyperbolic Matrix(839,1232,190,279) (-3/2,-22/15) -> (22/5,53/12) Hyperbolic Matrix(2071,3024,728,1063) (-19/13,-54/37) -> (54/19,37/13) Hyperbolic Matrix(4145,6048,538,785) (-54/37,-89/61) -> (23/3,54/7) Hyperbolic Matrix(1119,1624,308,447) (-16/11,-29/20) -> (29/8,40/11) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(5879,8512,2436,3527) (-42/29,-55/38) -> (111/46,70/29) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(2183,3136,662,951) (-23/16,-56/39) -> (56/17,33/10) Hyperbolic Matrix(2185,3136,664,953) (-56/39,-33/23) -> (23/7,56/17) Hyperbolic Matrix(393,560,40,57) (-10/7,-47/33) -> (9/1,10/1) Hyperbolic Matrix(6607,9408,4168,5935) (-47/33,-84/59) -> (84/53,65/41) Hyperbolic Matrix(3305,4704,2086,2969) (-84/59,-37/26) -> (19/12,84/53) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(4591,6496,870,1231) (-75/53,-58/41) -> (58/11,37/7) Hyperbolic Matrix(14225,20104,-11094,-15679) (-106/75,-171/121) -> (-109/85,-50/39) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(2577,3584,2014,2801) (-32/23,-57/41) -> (55/43,32/25) Hyperbolic Matrix(23687,32928,10030,13943) (-57/41,-196/141) -> (196/83,111/47) Hyperbolic Matrix(31585,43904,13376,18593) (-196/141,-139/100) -> (85/36,196/83) Hyperbolic Matrix(2297,3192,444,617) (-82/59,-25/18) -> (31/6,26/5) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(617,840,-534,-727) (-15/11,-34/25) -> (-22/19,-15/13) Hyperbolic Matrix(2801,3808,1566,2129) (-34/25,-53/39) -> (59/33,34/19) Hyperbolic Matrix(785,1064,166,225) (-19/14,-23/17) -> (33/7,19/4) Hyperbolic Matrix(2073,2800,1286,1737) (-23/17,-27/20) -> (29/18,79/49) Hyperbolic Matrix(167,224,-126,-169) (-27/20,-4/3) -> (-4/3,-29/22) Parabolic Matrix(9519,12544,2294,3023) (-29/22,-112/85) -> (112/27,83/20) Hyperbolic Matrix(9521,12544,2296,3025) (-112/85,-83/63) -> (29/7,112/27) Hyperbolic Matrix(3361,4424,1192,1569) (-54/41,-25/19) -> (31/11,110/39) Hyperbolic Matrix(1961,2576,896,1177) (-46/35,-21/16) -> (35/16,46/21) Hyperbolic Matrix(2519,3304,1152,1511) (-21/16,-59/45) -> (59/27,35/16) Hyperbolic Matrix(38303,50176,9062,11871) (-131/100,-224/171) -> (224/53,93/22) Hyperbolic Matrix(38305,50176,9064,11873) (-224/171,-93/71) -> (131/31,224/53) Hyperbolic Matrix(729,952,644,841) (-17/13,-47/36) -> (9/8,17/15) Hyperbolic Matrix(2017,2632,-1630,-2127) (-47/36,-30/23) -> (-26/21,-47/38) Hyperbolic Matrix(2407,3136,558,727) (-43/33,-56/43) -> (56/13,13/3) Hyperbolic Matrix(2409,3136,560,729) (-56/43,-13/10) -> (43/10,56/13) Hyperbolic Matrix(561,728,346,449) (-13/10,-22/17) -> (34/21,13/8) Hyperbolic Matrix(953,1232,304,393) (-22/17,-53/41) -> (3/1,22/7) Hyperbolic Matrix(7279,9408,4072,5263) (-53/41,-84/65) -> (84/47,59/33) Hyperbolic Matrix(3641,4704,2038,2633) (-84/65,-31/24) -> (25/14,84/47) Hyperbolic Matrix(22007,28224,4846,6215) (-59/46,-168/131) -> (168/37,109/24) Hyperbolic Matrix(22009,28224,4848,6217) (-168/131,-109/85) -> (59/13,168/37) Hyperbolic Matrix(2407,3080,1706,2183) (-32/25,-55/43) -> (55/39,24/17) Hyperbolic Matrix(4817,6160,1840,2353) (-55/43,-23/18) -> (89/34,55/21) Hyperbolic Matrix(615,784,-484,-617) (-23/18,-14/11) -> (-14/11,-33/26) Parabolic Matrix(839,1064,220,279) (-33/26,-19/15) -> (19/5,23/6) Hyperbolic Matrix(2129,2688,1154,1457) (-24/19,-53/42) -> (59/32,24/13) Hyperbolic Matrix(4705,5936,2664,3361) (-53/42,-29/23) -> (83/47,53/30) Hyperbolic Matrix(2575,3192,722,895) (-31/25,-26/21) -> (82/23,25/7) Hyperbolic Matrix(2855,3528,-2312,-2857) (-68/55,-21/17) -> (-21/17,-100/81) Parabolic Matrix(10753,13272,3812,4705) (-79/64,-58/47) -> (110/39,79/28) Hyperbolic Matrix(5265,6496,1544,1905) (-58/47,-37/30) -> (75/22,58/17) Hyperbolic Matrix(729,896,502,617) (-16/13,-27/22) -> (29/20,16/11) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(1063,1288,600,727) (-17/14,-23/19) -> (23/13,39/22) Hyperbolic Matrix(1065,1288,788,953) (-23/19,-29/24) -> (27/20,23/17) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(617,728,428,505) (-13/11,-20/17) -> (36/25,13/9) Hyperbolic Matrix(1289,1512,526,617) (-27/23,-7/6) -> (49/20,27/11) Hyperbolic Matrix(1063,1232,434,503) (-7/6,-22/19) -> (22/9,49/20) Hyperbolic Matrix(5263,6048,1656,1903) (-23/20,-54/47) -> (54/17,89/28) Hyperbolic Matrix(3023,3472,2242,2575) (-54/47,-31/27) -> (31/23,58/43) Hyperbolic Matrix(1233,1400,790,897) (-8/7,-17/15) -> (39/25,64/41) Hyperbolic Matrix(841,952,644,729) (-17/15,-9/8) -> (47/36,17/13) Hyperbolic Matrix(503,560,150,167) (-9/8,-10/9) -> (10/3,47/14) Hyperbolic Matrix(559,616,304,335) (-10/9,-11/10) -> (11/6,46/25) Hyperbolic Matrix(617,672,258,281) (-11/10,-1/1) -> (55/23,67/28) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(1119,-1288,682,-785) (8/7,15/13) -> (41/25,64/39) Hyperbolic Matrix(727,-840,534,-617) (15/13,7/6) -> (49/36,15/11) Hyperbolic Matrix(953,-1120,428,-503) (7/6,20/17) -> (20/9,49/22) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(1345,-1624,834,-1007) (6/5,23/19) -> (79/49,50/31) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(727,-896,228,-281) (16/13,21/17) -> (35/11,16/5) Hyperbolic Matrix(2127,-2632,1630,-2017) (21/17,26/21) -> (30/23,77/59) Hyperbolic Matrix(1625,-2016,586,-727) (26/21,5/4) -> (61/22,86/31) Hyperbolic Matrix(223,-280,90,-113) (5/4,24/19) -> (32/13,5/2) Hyperbolic Matrix(841,-1064,132,-167) (24/19,19/15) -> (19/3,32/5) Hyperbolic Matrix(617,-784,484,-615) (19/15,14/11) -> (14/11,37/29) Parabolic Matrix(1793,-2296,524,-671) (32/25,9/7) -> (65/19,24/7) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(1289,-1680,300,-391) (13/10,30/23) -> (30/7,43/10) Hyperbolic Matrix(6607,-8624,3862,-5041) (77/59,47/36) -> (65/38,77/45) Hyperbolic Matrix(2353,-3080,1026,-1343) (17/13,38/29) -> (94/41,39/17) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2129,-2800,936,-1231) (21/16,25/19) -> (25/11,91/40) Hyperbolic Matrix(169,-224,126,-167) (25/19,4/3) -> (4/3,31/23) Parabolic Matrix(4649,-6272,1120,-1511) (58/43,27/20) -> (83/20,54/13) Hyperbolic Matrix(783,-1064,248,-337) (19/14,34/25) -> (22/7,19/6) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(1625,-2296,356,-503) (24/17,41/29) -> (41/9,32/7) Hyperbolic Matrix(673,-952,316,-447) (41/29,17/12) -> (17/8,15/7) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(1007,-1456,388,-561) (13/9,42/29) -> (70/27,13/5) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(839,-1288,256,-393) (3/2,20/13) -> (36/11,59/18) Hyperbolic Matrix(3527,-5432,1346,-2073) (20/13,37/24) -> (131/50,76/29) Hyperbolic Matrix(1233,-1904,362,-559) (37/24,17/11) -> (17/5,75/22) Hyperbolic Matrix(505,-784,324,-503) (17/11,14/9) -> (14/9,39/25) Parabolic Matrix(1399,-2184,180,-281) (64/41,25/16) -> (31/4,8/1) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(5935,-9576,1736,-2801) (50/31,71/44) -> (41/12,106/31) Hyperbolic Matrix(2185,-3528,1352,-2183) (71/44,21/13) -> (21/13,97/60) Parabolic Matrix(3359,-5432,1178,-1905) (76/47,55/34) -> (57/20,20/7) Hyperbolic Matrix(9689,-15680,4048,-6551) (89/55,123/76) -> (67/28,79/33) Hyperbolic Matrix(5881,-9520,2248,-3639) (123/76,34/21) -> (34/13,157/60) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(2017,-3304,478,-783) (18/11,59/36) -> (59/14,38/9) Hyperbolic Matrix(3753,-6160,1330,-2183) (64/39,23/14) -> (79/28,48/17) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(4033,-6888,1770,-3023) (70/41,41/24) -> (41/18,98/43) Hyperbolic Matrix(2521,-4312,556,-951) (53/31,65/38) -> (9/2,59/13) Hyperbolic Matrix(5825,-9968,1832,-3135) (77/45,12/7) -> (124/39,35/11) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(1737,-3080,410,-727) (39/22,55/31) -> (55/13,17/4) Hyperbolic Matrix(3865,-6888,1602,-2855) (57/32,41/23) -> (41/17,111/46) Hyperbolic Matrix(10361,-18480,4552,-8119) (107/60,66/37) -> (66/29,173/76) Hyperbolic Matrix(1569,-2800,376,-671) (66/37,25/14) -> (25/6,46/11) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(337,-616,122,-223) (20/11,11/6) -> (11/4,36/13) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(505,-952,148,-279) (15/8,2/1) -> (58/17,41/12) Hyperbolic Matrix(449,-952,158,-335) (2/1,17/8) -> (17/6,54/19) Hyperbolic Matrix(335,-728,52,-113) (13/6,24/11) -> (32/5,13/2) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(4593,-10528,1612,-3695) (55/24,94/41) -> (94/33,57/20) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1289,-3080,398,-951) (43/18,55/23) -> (55/17,13/4) Hyperbolic Matrix(3695,-8848,702,-1681) (79/33,12/5) -> (100/19,79/15) Hyperbolic Matrix(2071,-4984,396,-953) (12/5,65/27) -> (47/9,68/13) Hyperbolic Matrix(6047,-14560,1768,-4257) (65/27,53/22) -> (171/50,65/19) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(10359,-26824,3958,-10249) (44/17,101/39) -> (123/47,212/81) Hyperbolic Matrix(11425,-29904,3594,-9407) (212/81,89/34) -> (89/28,124/39) Hyperbolic Matrix(4703,-12320,1112,-2913) (55/21,131/50) -> (93/22,55/13) Hyperbolic Matrix(1345,-3528,512,-1343) (76/29,21/8) -> (21/8,92/35) Parabolic Matrix(2129,-5600,468,-1231) (71/27,50/19) -> (50/11,41/9) Hyperbolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(281,-784,100,-279) (25/9,14/5) -> (14/5,31/11) Parabolic Matrix(4817,-13720,1140,-3247) (37/13,94/33) -> (38/9,131/31) Hyperbolic Matrix(5879,-20104,1294,-4425) (106/31,171/50) -> (109/24,50/11) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(57,-224,14,-55) (27/7,4/1) -> (4/1,29/7) Parabolic Matrix(615,-2632,118,-505) (47/11,30/7) -> (26/5,47/9) Hyperbolic Matrix(169,-784,36,-167) (23/5,14/3) -> (14/3,33/7) Parabolic Matrix(673,-3528,128,-671) (68/13,21/4) -> (21/4,100/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(57,728,22,281) -> Matrix(1,2,0,1) Matrix(57,616,26,281) -> Matrix(1,-2,0,1) Matrix(111,1064,70,671) -> Matrix(3,-26,2,-17) Matrix(111,952,26,223) -> Matrix(1,2,0,1) Matrix(113,952,40,337) -> Matrix(1,-2,0,1) Matrix(169,1288,-66,-503) -> Matrix(3,2,-2,-1) Matrix(113,840,-30,-223) -> Matrix(5,-2,-2,1) Matrix(167,1120,-92,-617) -> Matrix(1,4,-4,-15) Matrix(111,728,34,223) -> Matrix(1,2,0,1) Matrix(167,1064,-132,-841) -> Matrix(3,10,-4,-13) Matrix(169,1064,98,617) -> Matrix(1,2,2,5) Matrix(279,1624,-106,-617) -> Matrix(3,2,-2,-1) Matrix(225,1288,98,561) -> Matrix(1,2,0,1) Matrix(169,952,30,169) -> Matrix(5,6,4,5) Matrix(111,616,20,111) -> Matrix(3,2,4,3) Matrix(113,616,-82,-447) -> Matrix(3,2,-2,-1) Matrix(169,896,-116,-615) -> Matrix(1,0,-2,1) Matrix(505,2632,-118,-615) -> Matrix(1,2,0,1) Matrix(391,2016,-250,-1289) -> Matrix(9,8,-8,-7) Matrix(57,280,-34,-167) -> Matrix(1,-2,0,1) Matrix(223,1064,-188,-897) -> Matrix(3,-10,-2,7) Matrix(167,784,-36,-169) -> Matrix(1,-12,0,1) Matrix(279,1288,206,951) -> Matrix(3,22,2,15) Matrix(1343,6160,830,3807) -> Matrix(1,4,0,1) Matrix(783,3584,220,1007) -> Matrix(3,16,2,11) Matrix(503,2296,-356,-1625) -> Matrix(1,2,0,1) Matrix(113,504,-50,-223) -> Matrix(1,2,-2,-3) Matrix(167,728,64,279) -> Matrix(1,2,0,1) Matrix(391,1680,-300,-1289) -> Matrix(1,0,-2,1) Matrix(2017,8624,-838,-3583) -> Matrix(3,-4,-2,3) Matrix(223,952,26,111) -> Matrix(1,2,0,1) Matrix(727,3080,-410,-1737) -> Matrix(1,2,0,1) Matrix(783,3304,-478,-2017) -> Matrix(1,-2,0,1) Matrix(671,2800,-376,-1569) -> Matrix(1,0,0,1) Matrix(55,224,-14,-57) -> Matrix(1,-4,0,1) Matrix(897,3472,116,449) -> Matrix(1,4,2,9) Matrix(1623,6272,-1232,-4761) -> Matrix(1,4,4,17) Matrix(335,1288,58,223) -> Matrix(3,10,2,7) Matrix(337,1288,264,1009) -> Matrix(7,22,6,19) Matrix(281,1064,-192,-727) -> Matrix(1,2,0,1) Matrix(727,2744,430,1623) -> Matrix(1,2,2,5) Matrix(391,1456,-286,-1065) -> Matrix(13,24,-6,-11) Matrix(167,616,106,391) -> Matrix(5,6,4,5) Matrix(169,616,-138,-503) -> Matrix(1,2,0,1) Matrix(449,1624,248,897) -> Matrix(1,2,6,13) Matrix(559,2016,-404,-1457) -> Matrix(9,16,-4,-7) Matrix(281,1008,172,617) -> Matrix(3,4,2,3) Matrix(111,392,-32,-113) -> Matrix(1,2,-2,-3) Matrix(1399,4816,504,1735) -> Matrix(1,8,0,1) Matrix(3191,10976,-1840,-6329) -> Matrix(1,-4,0,1) Matrix(897,3080,196,673) -> Matrix(1,6,0,1) Matrix(671,2296,-524,-1793) -> Matrix(3,2,-2,-1) Matrix(279,952,-148,-505) -> Matrix(3,2,-2,-1) Matrix(281,952,116,393) -> Matrix(1,2,0,1) Matrix(449,1512,-166,-559) -> Matrix(11,14,-4,-5) Matrix(169,560,-118,-391) -> Matrix(1,0,2,1) Matrix(393,1288,-256,-839) -> Matrix(3,-2,-4,3) Matrix(223,728,34,111) -> Matrix(1,2,0,1) Matrix(449,1456,-276,-895) -> Matrix(1,0,0,1) Matrix(1007,3248,590,1903) -> Matrix(1,0,2,1) Matrix(279,896,52,167) -> Matrix(1,0,2,1) Matrix(281,896,-228,-727) -> Matrix(1,0,-2,1) Matrix(337,1064,-248,-783) -> Matrix(3,2,-2,-1) Matrix(449,1288,-312,-895) -> Matrix(1,-2,-2,5) Matrix(1905,5432,-1178,-3359) -> Matrix(1,-2,0,1) Matrix(671,1904,-474,-1345) -> Matrix(1,-4,0,1) Matrix(279,784,-100,-281) -> Matrix(1,-16,0,1) Matrix(503,1400,60,167) -> Matrix(1,14,0,1) Matrix(785,2184,-684,-1903) -> Matrix(1,10,0,1) Matrix(223,616,-122,-337) -> Matrix(1,6,-2,-11) Matrix(225,616,164,449) -> Matrix(1,6,0,1) Matrix(391,1064,226,615) -> Matrix(3,10,2,7) Matrix(1735,4704,516,1399) -> Matrix(13,40,12,37) Matrix(3473,9408,1034,2801) -> Matrix(27,80,28,83) Matrix(393,1064,352,953) -> Matrix(9,26,10,29) Matrix(167,448,104,279) -> Matrix(5,12,2,5) Matrix(169,448,106,281) -> Matrix(7,12,4,7) Matrix(1063,2800,276,727) -> Matrix(13,16,4,5) Matrix(3641,9576,-2576,-6775) -> Matrix(11,14,-4,-5) Matrix(1343,3528,-512,-1345) -> Matrix(5,6,-6,-7) Matrix(4145,10864,1496,3921) -> Matrix(1,8,0,1) Matrix(2073,5432,-1346,-3527) -> Matrix(1,2,-2,-3) Matrix(2353,6160,1840,4817) -> Matrix(3,4,2,3) Matrix(5991,15680,-3488,-9129) -> Matrix(1,0,2,1) Matrix(3639,9520,-2248,-5881) -> Matrix(1,0,0,1) Matrix(279,728,64,167) -> Matrix(1,2,0,1) Matrix(671,1736,-390,-1009) -> Matrix(1,2,0,1) Matrix(391,1008,282,727) -> Matrix(1,4,0,1) Matrix(1287,3304,-982,-2521) -> Matrix(1,2,-2,-3) Matrix(1791,4592,1048,2687) -> Matrix(3,4,2,3) Matrix(2407,6160,-1554,-3977) -> Matrix(7,8,-8,-9) Matrix(505,1288,198,505) -> Matrix(5,6,4,5) Matrix(111,280,44,111) -> Matrix(1,2,0,1) Matrix(113,280,-90,-223) -> Matrix(1,2,-2,-3) Matrix(1119,2744,502,1231) -> Matrix(1,2,-4,-7) Matrix(1121,2744,824,2017) -> Matrix(3,-2,2,-1) Matrix(505,1232,-298,-727) -> Matrix(1,0,0,1) Matrix(393,952,116,281) -> Matrix(1,2,0,1) Matrix(1345,3248,928,2241) -> Matrix(1,0,0,1) Matrix(2855,6888,-1602,-3865) -> Matrix(1,2,0,1) Matrix(1905,4592,1162,2801) -> Matrix(1,4,0,1) Matrix(1791,4312,-1396,-3361) -> Matrix(11,18,-8,-13) Matrix(4143,9968,-2840,-6833) -> Matrix(3,4,-4,-5) Matrix(727,1736,-446,-1065) -> Matrix(3,2,-2,-1) Matrix(2351,5600,-1364,-3249) -> Matrix(1,0,-4,1) Matrix(447,1064,376,895) -> Matrix(3,-2,2,-1) Matrix(449,1064,284,673) -> Matrix(3,10,2,7) Matrix(167,392,-72,-169) -> Matrix(1,2,-2,-3) Matrix(4759,10976,-3424,-7897) -> Matrix(5,8,-2,-3) Matrix(2575,5936,534,1231) -> Matrix(5,4,-4,-3) Matrix(559,1288,194,447) -> Matrix(3,2,-2,-1) Matrix(561,1288,98,225) -> Matrix(1,2,0,1) Matrix(1343,3080,-1026,-2353) -> Matrix(3,2,-2,-1) Matrix(783,1792,440,1007) -> Matrix(1,0,2,1) Matrix(785,1792,442,1009) -> Matrix(1,0,0,1) Matrix(3023,6888,-1770,-4033) -> Matrix(3,2,-2,-1) Matrix(4255,9688,1918,4367) -> Matrix(5,2,-8,-3) Matrix(8119,18480,-4552,-10361) -> Matrix(1,0,-2,1) Matrix(1231,2800,-936,-2129) -> Matrix(1,0,0,1) Matrix(2071,4704,468,1063) -> Matrix(3,4,2,3) Matrix(4145,9408,938,2129) -> Matrix(5,4,6,5) Matrix(1679,3808,444,1007) -> Matrix(11,8,4,3) Matrix(727,1624,526,1175) -> Matrix(11,-2,6,-1) Matrix(503,1120,-428,-953) -> Matrix(11,-4,-8,3) Matrix(279,616,-178,-393) -> Matrix(5,-6,-4,5) Matrix(281,616,26,57) -> Matrix(1,-2,0,1) Matrix(2967,6496,1304,2855) -> Matrix(1,0,0,1) Matrix(3023,6608,1178,2575) -> Matrix(1,0,0,1) Matrix(1231,2688,256,559) -> Matrix(3,-4,-2,3) Matrix(617,1344,-488,-1063) -> Matrix(3,-8,-4,11) Matrix(337,728,156,337) -> Matrix(1,-10,0,1) Matrix(391,840,182,391) -> Matrix(1,14,0,1) Matrix(447,952,-316,-673) -> Matrix(1,2,0,1) Matrix(503,952,-326,-617) -> Matrix(5,6,-6,-7) Matrix(449,840,240,449) -> Matrix(13,14,12,13) Matrix(391,728,210,391) -> Matrix(11,10,12,11) Matrix(393,728,-332,-615) -> Matrix(7,6,-6,-5) Matrix(1791,3304,728,1343) -> Matrix(3,2,-2,-1) Matrix(1793,3304,426,785) -> Matrix(3,2,-2,-1) Matrix(1399,2576,334,615) -> Matrix(1,0,2,1) Matrix(335,616,304,559) -> Matrix(3,2,4,3) Matrix(953,1736,-768,-1399) -> Matrix(5,2,2,1) Matrix(5321,9688,2984,5433) -> Matrix(5,2,-8,-3) Matrix(4369,7952,1662,3025) -> Matrix(23,8,20,7) Matrix(1513,2744,896,1625) -> Matrix(9,2,4,1) Matrix(897,1624,248,449) -> Matrix(13,2,6,1) Matrix(281,504,-218,-391) -> Matrix(1,-2,0,1) Matrix(3641,6496,1978,3529) -> Matrix(1,0,2,1) Matrix(43959,78400,19310,34439) -> Matrix(1,0,12,1) Matrix(43961,78400,19312,34441) -> Matrix(1,0,-10,1) Matrix(7223,12880,2606,4647) -> Matrix(15,-8,2,-1) Matrix(5375,9576,2074,3695) -> Matrix(1,2,0,1) Matrix(1007,1792,440,783) -> Matrix(1,0,2,1) Matrix(1009,1792,442,785) -> Matrix(1,0,0,1) Matrix(5935,10528,-3852,-6833) -> Matrix(1,0,-2,1) Matrix(727,1288,600,1063) -> Matrix(1,2,0,1) Matrix(223,392,-128,-225) -> Matrix(1,-2,0,1) Matrix(1903,3304,580,1007) -> Matrix(1,2,-2,-3) Matrix(3809,6608,1550,2689) -> Matrix(1,0,0,1) Matrix(25311,43904,7102,12319) -> Matrix(3,-32,2,-21) Matrix(18985,32928,5328,9241) -> Matrix(3,28,2,19) Matrix(615,1064,226,391) -> Matrix(7,10,2,3) Matrix(617,1064,98,169) -> Matrix(5,2,2,1) Matrix(7279,12544,3054,5263) -> Matrix(1,0,10,1) Matrix(7281,12544,3056,5265) -> Matrix(1,0,-8,1) Matrix(1791,3080,-1238,-2129) -> Matrix(1,-2,0,1) Matrix(391,672,32,55) -> Matrix(1,0,0,1) Matrix(5153,8848,-4174,-7167) -> Matrix(1,0,-2,1) Matrix(2913,4984,-2356,-4031) -> Matrix(1,2,0,1) Matrix(8513,14560,-6024,-10303) -> Matrix(3,8,-2,-5) Matrix(2687,4592,1048,1791) -> Matrix(3,4,2,3) Matrix(4985,8512,1542,2633) -> Matrix(3,4,2,3) Matrix(1903,3248,590,1007) -> Matrix(1,0,2,1) Matrix(559,952,394,671) -> Matrix(1,2,0,1) Matrix(1847,3136,758,1287) -> Matrix(1,4,0,1) Matrix(1849,3136,760,1289) -> Matrix(3,4,2,3) Matrix(729,1232,100,169) -> Matrix(1,0,0,1) Matrix(895,1512,132,223) -> Matrix(1,6,0,1) Matrix(3919,6608,1660,2799) -> Matrix(1,0,2,1) Matrix(1961,3304,898,1513) -> Matrix(3,2,-2,-1) Matrix(169,280,102,169) -> Matrix(1,2,0,1) Matrix(783,1288,476,783) -> Matrix(1,6,0,1) Matrix(785,1288,-682,-1119) -> Matrix(1,2,0,1) Matrix(2801,4592,1162,1905) -> Matrix(1,4,0,1) Matrix(4033,6608,2188,3585) -> Matrix(1,0,2,1) Matrix(617,1008,172,281) -> Matrix(3,4,2,3) Matrix(16465,26824,-10174,-16575) -> Matrix(1,2,0,1) Matrix(447,728,412,671) -> Matrix(1,2,0,1) Matrix(5881,9576,2580,4201) -> Matrix(1,2,0,1) Matrix(449,728,346,561) -> Matrix(1,2,0,1) Matrix(48439,78400,18510,29959) -> Matrix(1,0,6,1) Matrix(48441,78400,18512,29961) -> Matrix(1,0,-4,1) Matrix(18479,29904,-12666,-20497) -> Matrix(1,0,-2,1) Matrix(3807,6160,830,1343) -> Matrix(1,4,0,1) Matrix(7617,12320,-5816,-9407) -> Matrix(1,0,0,1) Matrix(2183,3528,-1352,-2185) -> Matrix(1,-6,0,1) Matrix(4927,7952,2220,3583) -> Matrix(1,8,-2,-15) Matrix(3471,5600,-2708,-4369) -> Matrix(5,24,-4,-19) Matrix(1007,1624,-834,-1345) -> Matrix(1,2,0,1) Matrix(279,448,104,167) -> Matrix(5,12,2,5) Matrix(281,448,106,169) -> Matrix(7,12,4,7) Matrix(953,1512,-670,-1063) -> Matrix(9,14,-2,-3) Matrix(673,1064,284,449) -> Matrix(7,10,2,3) Matrix(391,616,106,167) -> Matrix(5,6,4,5) Matrix(6943,10864,4294,6719) -> Matrix(7,8,6,7) Matrix(8233,12880,3616,5657) -> Matrix(7,8,20,23) Matrix(3081,4816,2186,3417) -> Matrix(7,8,6,7) Matrix(503,784,-324,-505) -> Matrix(15,16,-16,-17) Matrix(2855,4424,686,1063) -> Matrix(7,6,8,7) Matrix(8567,13272,1626,2519) -> Matrix(7,6,-6,-5) Matrix(615,952,542,839) -> Matrix(3,2,4,3) Matrix(1961,3024,618,953) -> Matrix(5,4,-4,-3) Matrix(8903,13720,-6796,-10473) -> Matrix(3,2,-2,-1) Matrix(841,1288,476,729) -> Matrix(3,2,-2,-1) Matrix(839,1232,190,279) -> Matrix(1,0,2,1) Matrix(2071,3024,728,1063) -> Matrix(7,4,-2,-1) Matrix(4145,6048,538,785) -> Matrix(1,0,2,1) Matrix(1119,1624,308,447) -> Matrix(1,2,0,1) Matrix(2241,3248,928,1345) -> Matrix(1,0,0,1) Matrix(5879,8512,2436,3527) -> Matrix(1,4,0,1) Matrix(505,728,428,617) -> Matrix(1,2,0,1) Matrix(2297,3304,974,1401) -> Matrix(5,2,2,1) Matrix(2183,3136,662,951) -> Matrix(1,0,10,1) Matrix(2185,3136,664,953) -> Matrix(1,0,-8,1) Matrix(393,560,40,57) -> Matrix(1,-4,0,1) Matrix(6607,9408,4168,5935) -> Matrix(3,-80,2,-53) Matrix(3305,4704,2086,2969) -> Matrix(3,40,2,27) Matrix(671,952,394,559) -> Matrix(1,2,0,1) Matrix(4591,6496,870,1231) -> Matrix(1,0,0,1) Matrix(14225,20104,-11094,-15679) -> Matrix(13,30,-10,-23) Matrix(279,392,-200,-281) -> Matrix(1,-2,0,1) Matrix(2577,3584,2014,2801) -> Matrix(5,16,4,13) Matrix(23687,32928,10030,13943) -> Matrix(9,28,8,25) Matrix(31585,43904,13376,18593) -> Matrix(11,32,12,35) Matrix(2297,3192,444,617) -> Matrix(1,2,2,5) Matrix(727,1008,282,391) -> Matrix(1,4,0,1) Matrix(9071,12544,2510,3471) -> Matrix(45,92,22,45) Matrix(9073,12544,2512,3473) -> Matrix(47,92,24,47) Matrix(1175,1624,526,727) -> Matrix(1,2,-6,-11) Matrix(1177,1624,366,505) -> Matrix(1,2,0,1) Matrix(449,616,164,225) -> Matrix(1,6,0,1) Matrix(2295,3136,614,839) -> Matrix(29,60,14,29) Matrix(2297,3136,616,841) -> Matrix(31,60,16,31) Matrix(617,840,-534,-727) -> Matrix(1,2,-4,-7) Matrix(2801,3808,1566,2129) -> Matrix(5,8,-2,-3) Matrix(785,1064,166,225) -> Matrix(9,14,-2,-3) Matrix(2073,2800,1286,1737) -> Matrix(11,16,2,3) Matrix(167,224,-126,-169) -> Matrix(3,4,-4,-5) Matrix(9519,12544,2294,3023) -> Matrix(1,0,12,1) Matrix(9521,12544,2296,3025) -> Matrix(1,0,-10,1) Matrix(3361,4424,1192,1569) -> Matrix(1,-6,0,1) Matrix(1961,2576,896,1177) -> Matrix(1,0,0,1) Matrix(2519,3304,1152,1511) -> Matrix(3,2,-2,-1) Matrix(38303,50176,9062,11871) -> Matrix(1,0,4,1) Matrix(38305,50176,9064,11873) -> Matrix(1,0,-2,1) Matrix(729,952,644,841) -> Matrix(1,2,0,1) Matrix(2017,2632,-1630,-2127) -> Matrix(3,2,-2,-1) Matrix(2407,3136,558,727) -> Matrix(1,0,4,1) Matrix(2409,3136,560,729) -> Matrix(1,0,-2,1) Matrix(561,728,346,449) -> Matrix(1,2,0,1) Matrix(953,1232,304,393) -> Matrix(1,0,0,1) Matrix(7279,9408,4072,5263) -> Matrix(1,-4,0,1) Matrix(3641,4704,2038,2633) -> Matrix(1,4,0,1) Matrix(22007,28224,4846,6215) -> Matrix(155,208,38,51) Matrix(22009,28224,4848,6217) -> Matrix(157,208,40,53) Matrix(2407,3080,1706,2183) -> Matrix(5,6,4,5) Matrix(4817,6160,1840,2353) -> Matrix(3,4,2,3) Matrix(615,784,-484,-617) -> Matrix(11,12,-12,-13) Matrix(839,1064,220,279) -> Matrix(17,14,6,5) Matrix(2129,2688,1154,1457) -> Matrix(7,4,12,7) Matrix(4705,5936,2664,3361) -> Matrix(7,4,-2,-1) Matrix(2575,3192,722,895) -> Matrix(3,-2,2,-1) Matrix(2855,3528,-2312,-2857) -> Matrix(1,2,-2,-3) Matrix(10753,13272,3812,4705) -> Matrix(11,6,-2,-1) Matrix(5265,6496,1544,1905) -> Matrix(1,0,2,1) Matrix(729,896,502,617) -> Matrix(1,0,0,1) Matrix(505,616,414,505) -> Matrix(1,-2,0,1) Matrix(783,952,644,783) -> Matrix(1,6,0,1) Matrix(1063,1288,600,727) -> Matrix(1,2,0,1) Matrix(1065,1288,788,953) -> Matrix(3,10,2,7) Matrix(895,1064,376,447) -> Matrix(1,2,-2,-3) Matrix(617,728,428,505) -> Matrix(1,2,0,1) Matrix(1289,1512,526,617) -> Matrix(5,6,4,5) Matrix(1063,1232,434,503) -> Matrix(1,0,2,1) Matrix(5263,6048,1656,1903) -> Matrix(1,0,0,1) Matrix(3023,3472,2242,2575) -> Matrix(5,-4,4,-3) Matrix(1233,1400,790,897) -> Matrix(13,14,12,13) Matrix(841,952,644,729) -> Matrix(1,2,0,1) Matrix(503,560,150,167) -> Matrix(5,4,6,5) Matrix(559,616,304,335) -> Matrix(3,2,4,3) Matrix(617,672,258,281) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(1119,-1288,682,-785) -> Matrix(1,2,0,1) Matrix(727,-840,534,-617) -> Matrix(7,-2,4,-1) Matrix(953,-1120,428,-503) -> Matrix(3,-4,-8,11) Matrix(897,-1064,188,-223) -> Matrix(7,-10,-2,3) Matrix(1345,-1624,834,-1007) -> Matrix(1,2,0,1) Matrix(503,-616,138,-169) -> Matrix(1,2,0,1) Matrix(727,-896,228,-281) -> Matrix(1,0,-2,1) Matrix(2127,-2632,1630,-2017) -> Matrix(1,-2,2,-3) Matrix(1625,-2016,586,-727) -> Matrix(1,8,0,1) Matrix(223,-280,90,-113) -> Matrix(3,-2,2,-1) Matrix(841,-1064,132,-167) -> Matrix(13,-10,4,-3) Matrix(617,-784,484,-615) -> Matrix(13,-12,12,-11) Matrix(1793,-2296,524,-671) -> Matrix(1,-2,2,-3) Matrix(391,-504,218,-281) -> Matrix(1,-2,0,1) Matrix(1289,-1680,300,-391) -> Matrix(1,0,-2,1) Matrix(6607,-8624,3862,-5041) -> Matrix(7,-4,2,-1) Matrix(2353,-3080,1026,-1343) -> Matrix(1,-2,2,-3) Matrix(2521,-3304,982,-1287) -> Matrix(3,-2,2,-1) Matrix(2129,-2800,936,-1231) -> Matrix(1,0,0,1) Matrix(169,-224,126,-167) -> Matrix(5,-4,4,-3) Matrix(4649,-6272,1120,-1511) -> Matrix(3,-4,16,-21) Matrix(783,-1064,248,-337) -> Matrix(1,-2,2,-3) Matrix(1065,-1456,286,-391) -> Matrix(11,-24,6,-13) Matrix(447,-616,82,-113) -> Matrix(1,-2,2,-3) Matrix(1457,-2016,404,-559) -> Matrix(7,-16,4,-9) Matrix(281,-392,200,-279) -> Matrix(1,-2,0,1) Matrix(7785,-10976,3296,-4647) -> Matrix(5,-4,4,-3) Matrix(1625,-2296,356,-503) -> Matrix(1,2,0,1) Matrix(673,-952,316,-447) -> Matrix(1,2,0,1) Matrix(1063,-1512,670,-953) -> Matrix(3,-14,2,-9) Matrix(391,-560,118,-169) -> Matrix(1,0,2,1) Matrix(895,-1288,312,-449) -> Matrix(5,-2,-2,1) Matrix(1007,-1456,388,-561) -> Matrix(1,0,0,1) Matrix(615,-896,116,-169) -> Matrix(1,0,-2,1) Matrix(727,-1064,192,-281) -> Matrix(1,2,0,1) Matrix(839,-1288,256,-393) -> Matrix(3,-2,-4,3) Matrix(3527,-5432,1346,-2073) -> Matrix(3,-2,2,-1) Matrix(1233,-1904,362,-559) -> Matrix(5,-4,4,-3) Matrix(505,-784,324,-503) -> Matrix(17,-16,16,-15) Matrix(1399,-2184,180,-281) -> Matrix(9,-10,10,-11) Matrix(393,-616,178,-279) -> Matrix(5,-6,-4,5) Matrix(5935,-9576,1736,-2801) -> Matrix(3,-14,2,-9) Matrix(2185,-3528,1352,-2183) -> Matrix(1,-6,0,1) Matrix(3359,-5432,1178,-1905) -> Matrix(1,-2,0,1) Matrix(9689,-15680,4048,-6551) -> Matrix(1,0,2,1) Matrix(5881,-9520,2248,-3639) -> Matrix(1,0,0,1) Matrix(1065,-1736,446,-727) -> Matrix(1,-2,2,-3) Matrix(2017,-3304,478,-783) -> Matrix(1,-2,0,1) Matrix(3753,-6160,1330,-2183) -> Matrix(1,-8,0,1) Matrix(167,-280,34,-57) -> Matrix(1,-2,0,1) Matrix(727,-1232,298,-505) -> Matrix(1,0,0,1) Matrix(4033,-6888,1770,-3023) -> Matrix(1,-2,2,-3) Matrix(2521,-4312,556,-951) -> Matrix(7,-18,2,-5) Matrix(5825,-9968,1832,-3135) -> Matrix(1,-4,0,1) Matrix(1009,-1736,390,-671) -> Matrix(1,2,0,1) Matrix(3249,-5600,1364,-2351) -> Matrix(1,0,-4,1) Matrix(225,-392,128,-223) -> Matrix(1,-2,0,1) Matrix(6217,-10976,1744,-3079) -> Matrix(3,-8,2,-5) Matrix(1737,-3080,410,-727) -> Matrix(1,2,0,1) Matrix(3865,-6888,1602,-2855) -> Matrix(1,2,0,1) Matrix(10361,-18480,4552,-8119) -> Matrix(1,0,-2,1) Matrix(1569,-2800,376,-671) -> Matrix(1,0,0,1) Matrix(617,-1120,92,-167) -> Matrix(15,-4,4,-1) Matrix(337,-616,122,-223) -> Matrix(11,-6,2,-1) Matrix(727,-1344,152,-281) -> Matrix(11,-8,-4,3) Matrix(505,-952,148,-279) -> Matrix(1,-2,2,-3) Matrix(449,-952,158,-335) -> Matrix(1,-6,0,1) Matrix(335,-728,52,-113) -> Matrix(1,6,0,1) Matrix(783,-1736,152,-337) -> Matrix(3,2,4,3) Matrix(223,-504,50,-113) -> Matrix(3,-2,2,-1) Matrix(4593,-10528,1612,-3695) -> Matrix(1,0,-2,1) Matrix(169,-392,72,-167) -> Matrix(3,-2,2,-1) Matrix(1289,-3080,398,-951) -> Matrix(3,-2,2,-1) Matrix(3695,-8848,702,-1681) -> Matrix(1,0,-2,1) Matrix(2071,-4984,396,-953) -> Matrix(1,-2,2,-3) Matrix(6047,-14560,1768,-4257) -> Matrix(5,-8,2,-3) Matrix(503,-1288,66,-169) -> Matrix(1,-2,2,-3) Matrix(10359,-26824,3958,-10249) -> Matrix(1,-2,2,-3) Matrix(11425,-29904,3594,-9407) -> Matrix(1,0,-2,1) Matrix(4703,-12320,1112,-2913) -> Matrix(1,0,0,1) Matrix(1345,-3528,512,-1343) -> Matrix(7,-6,6,-5) Matrix(2129,-5600,468,-1231) -> Matrix(19,-24,4,-5) Matrix(617,-1624,106,-279) -> Matrix(1,-2,2,-3) Matrix(559,-1512,166,-449) -> Matrix(5,-14,4,-11) Matrix(281,-784,100,-279) -> Matrix(1,-16,0,1) Matrix(4817,-13720,1140,-3247) -> Matrix(1,2,0,1) Matrix(5879,-20104,1294,-4425) -> Matrix(17,-30,4,-7) Matrix(113,-392,32,-111) -> Matrix(3,-2,2,-1) Matrix(223,-840,30,-113) -> Matrix(1,-2,-2,5) Matrix(57,-224,14,-55) -> Matrix(1,-4,0,1) Matrix(615,-2632,118,-505) -> Matrix(1,2,0,1) Matrix(169,-784,36,-167) -> Matrix(1,-12,0,1) Matrix(673,-3528,128,-671) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 128 Degree of the the map X: 128 Degree of the the map Y: 384 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 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: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 8/7 7/6 14/11 21/16 4/3 7/5 14/9 8/5 21/13 12/7 7/4 16/9 2/1 28/13 20/9 280/123 16/7 7/3 112/47 12/5 56/23 28/11 70/27 280/107 21/8 8/3 14/5 3/1 35/11 16/5 42/13 56/17 84/25 24/7 7/2 196/55 18/5 112/31 56/15 4/1 112/27 21/5 224/53 56/13 84/19 168/37 32/7 14/3 24/5 5/1 26/5 21/4 16/3 28/5 6/1 19/3 32/5 13/2 20/3 27/4 7/1 22/3 15/2 23/3 31/4 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/1 11/10 1/2 10/9 2/3 4/5 9/8 7/6 17/15 1/1 8/7 2/1 15/13 -1/1 7/6 1/1 20/17 3/2 13/11 1/1 19/16 3/2 6/5 0/1 2/1 23/19 1/1 17/14 1/0 28/23 1/0 11/9 -1/1 16/13 0/1 21/17 1/1 26/21 0/1 2/1 5/4 1/2 24/19 2/3 19/15 1/1 14/11 1/1 37/29 1/1 23/18 5/4 55/43 1/1 32/25 4/3 9/7 5/3 22/17 0/1 2/1 13/10 1/0 30/23 0/1 2/3 77/59 1/1 47/36 5/6 17/13 1/1 38/29 0/1 2/1 21/16 1/1 25/19 1/1 4/3 1/1 31/23 1/1 58/43 22/17 4/3 27/20 11/8 23/17 7/5 19/14 3/2 34/25 8/5 2/1 49/36 5/3 15/11 9/5 26/19 2/1 12/5 11/8 1/0 29/21 1/1 47/34 19/10 18/13 2/1 8/3 25/18 5/2 7/5 1/0 31/22 1/2 86/61 0/1 2/3 55/39 1/1 24/17 2/1 41/29 5/1 17/12 1/0 27/19 1/1 10/7 -2/1 0/1 23/16 1/4 36/25 1/2 13/9 1/1 42/29 1/0 29/20 1/0 16/11 0/1 19/13 1/1 3/2 1/0 20/13 1/1 37/24 3/4 17/11 1/1 14/9 1/1 39/25 1/1 64/41 12/11 25/16 9/8 11/7 1/1 30/19 4/3 18/13 19/12 3/2 84/53 3/2 65/41 47/31 46/29 20/13 14/9 27/17 11/7 8/5 2/1 29/18 7/2 79/49 3/1 50/31 2/1 4/1 71/44 11/2 21/13 1/0 97/60 -1/2 76/47 1/0 55/34 1/0 89/55 -1/1 123/76 -1/2 34/21 0/1 2/1 13/8 1/0 31/19 3/1 18/11 2/1 4/1 59/36 3/2 41/25 1/1 64/39 4/1 23/14 1/0 28/17 1/0 5/3 1/1 27/16 3/2 49/29 1/0 22/13 0/1 2/1 17/10 1/0 29/17 1/1 70/41 1/1 41/24 3/2 53/31 5/3 65/38 11/4 77/45 3/1 12/7 1/0 31/18 -1/2 50/29 0/1 2/5 19/11 1/1 26/15 2/1 4/1 7/4 1/0 30/17 0/1 2/1 83/47 -5/1 53/30 -3/2 23/13 1/1 39/22 1/0 55/31 -1/1 16/9 0/1 57/32 1/0 41/23 1/1 107/60 -1/4 66/37 0/1 2/3 25/14 1/0 84/47 1/0 59/33 -3/1 34/19 -2/1 0/1 9/5 -1/3 29/16 1/6 20/11 1/3 11/6 1/2 46/25 0/1 2/1 35/19 1/2 59/32 3/4 24/13 2/3 13/7 1/1 28/15 1/1 15/8 7/6 2/1 0/1 2/1 17/8 1/0 15/7 7/1 28/13 1/0 13/6 1/0 24/11 -2/1 59/27 -3/1 35/16 -1/1 46/21 0/1 2/1 11/5 -1/1 31/14 -3/4 51/23 -5/7 71/32 -5/8 20/9 -1/2 49/22 -1/3 29/13 -1/5 9/4 1/4 25/11 1/1 91/40 1/1 66/29 -2/1 0/1 173/76 -1/6 280/123 0/1 107/47 1/5 41/18 1/0 98/43 1/1 57/25 1/1 16/7 0/1 55/24 1/2 94/41 0/1 2/3 39/17 1/1 23/10 1/0 7/3 1/1 33/14 3/2 59/25 -1/1 85/36 3/4 196/83 1/1 111/47 1/1 26/11 4/3 2/1 19/8 1/0 50/21 -2/3 0/1 81/34 -1/6 112/47 0/1 31/13 1/3 43/18 1/2 55/23 1/1 67/28 1/0 79/33 1/1 12/5 1/1 65/27 11/7 53/22 5/2 41/17 3/1 111/46 1/0 70/29 1/0 29/12 1/0 17/7 1/1 56/23 2/1 39/16 1/0 22/9 0/1 2/1 49/20 1/1 27/11 3/1 59/24 -1/2 32/13 0/1 5/2 1/0 28/11 1/1 23/9 1/1 41/16 1/0 59/23 3/1 77/30 1/1 18/7 4/3 2/1 31/12 3/2 44/17 1/0 101/39 3/1 57/22 1/0 70/27 1/0 13/5 1/1 34/13 0/1 2/1 157/60 -1/2 280/107 0/1 123/47 1/3 212/81 1/2 89/34 1/2 55/21 1/1 131/50 1/2 76/29 1/1 21/8 1/1 92/35 1/1 71/27 11/9 50/19 4/3 2/1 29/11 7/5 8/3 2/1 27/10 11/4 19/7 3/1 30/11 18/5 4/1 11/4 1/0 36/13 7/1 97/35 23/3 61/22 17/2 86/31 8/1 10/1 25/9 9/1 14/5 1/0 31/11 -7/1 110/39 -6/1 -16/3 79/28 1/0 48/17 -4/1 17/6 1/0 54/19 -6/1 -4/1 37/13 -3/1 94/33 -2/1 0/1 57/20 1/0 20/7 1/0 23/8 -3/2 3/1 1/1 22/7 -2/1 0/1 19/6 1/0 54/17 -2/3 0/1 89/28 1/0 124/39 1/0 35/11 -1/1 16/5 0/1 29/9 1/1 42/13 1/1 55/17 1/1 13/4 1/0 36/11 -1/1 59/18 -3/4 23/7 -1/3 56/17 0/1 33/10 1/6 10/3 0/1 2/3 47/14 11/12 84/25 1/1 37/11 1/1 27/8 1/0 17/5 1/1 75/22 1/0 58/17 0/1 2/3 41/12 5/4 106/31 8/5 2/1 171/50 9/4 65/19 -1/1 24/7 2/1 7/2 1/1 32/9 4/3 57/16 3/2 196/55 3/2 139/39 23/15 82/23 8/5 2/1 25/7 5/3 18/5 8/5 2/1 65/18 27/14 112/31 2/1 47/13 19/9 29/8 1/0 40/11 2/1 11/3 1/1 26/7 12/7 2/1 41/11 21/11 56/15 2/1 15/4 9/4 34/9 2/1 8/3 53/14 1/0 19/5 3/1 23/6 7/2 27/7 11/3 4/1 1/0 29/7 -1/3 112/27 0/1 83/20 1/8 54/13 0/1 2/5 25/6 1/0 46/11 0/1 2/3 21/5 1/0 59/14 -1/2 38/9 0/1 2/1 131/31 -1/1 224/53 0/1 93/22 1/2 55/13 1/1 17/4 1/0 47/11 -5/1 30/7 -2/1 0/1 43/10 -1/2 56/13 0/1 13/3 1/1 22/5 0/1 2/1 53/12 1/2 84/19 1/1 31/7 1/1 9/2 5/2 59/13 19/5 168/37 4/1 109/24 33/8 50/11 4/1 14/3 41/9 7/1 32/7 4/1 55/12 1/0 23/5 5/1 14/3 1/0 33/7 -7/1 19/4 1/0 43/9 -3/1 24/5 -2/1 53/11 -5/3 29/6 -1/2 5/1 -1/1 31/6 1/0 26/5 0/1 2/1 47/9 -3/1 68/13 1/1 21/4 1/0 100/19 -1/1 79/15 -1/1 58/11 0/1 2/1 37/7 -1/1 16/3 0/1 27/5 1/1 11/2 1/2 28/5 1/1 17/3 1/1 23/4 1/0 29/5 3/1 6/1 0/1 2/1 19/3 3/1 32/5 4/1 13/2 1/0 20/3 3/1 27/4 9/2 7/1 1/0 22/3 -2/1 0/1 15/2 1/2 23/3 1/1 54/7 -2/1 0/1 31/4 1/2 8/1 2/1 17/2 1/0 9/1 7/1 10/1 -4/1 -2/1 11/1 -1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(671,-728,259,-281) (1/1,11/10) -> (101/39,57/22) Hyperbolic Matrix(559,-616,255,-281) (11/10,10/9) -> (46/21,11/5) Hyperbolic Matrix(953,-1064,601,-671) (10/9,9/8) -> (65/41,46/29) Hyperbolic Matrix(841,-952,197,-223) (9/8,17/15) -> (17/4,47/11) Hyperbolic Matrix(839,-952,297,-337) (17/15,8/7) -> (48/17,17/6) Hyperbolic Matrix(1119,-1288,682,-785) (8/7,15/13) -> (41/25,64/39) Hyperbolic Matrix(727,-840,534,-617) (15/13,7/6) -> (49/36,15/11) Hyperbolic Matrix(953,-1120,428,-503) (7/6,20/17) -> (20/9,49/22) Hyperbolic Matrix(617,-728,189,-223) (20/17,13/11) -> (13/4,36/11) Hyperbolic Matrix(897,-1064,188,-223) (13/11,19/16) -> (19/4,43/9) Hyperbolic Matrix(895,-1064,519,-617) (19/16,6/5) -> (50/29,19/11) Hyperbolic Matrix(1345,-1624,834,-1007) (6/5,23/19) -> (79/49,50/31) Hyperbolic Matrix(1063,-1288,463,-561) (23/19,17/14) -> (39/17,23/10) Hyperbolic Matrix(783,-952,139,-169) (17/14,28/23) -> (28/5,17/3) Hyperbolic Matrix(505,-616,91,-111) (28/23,11/9) -> (11/2,28/5) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(727,-896,228,-281) (16/13,21/17) -> (35/11,16/5) Hyperbolic Matrix(2127,-2632,1630,-2017) (21/17,26/21) -> (30/23,77/59) Hyperbolic Matrix(1625,-2016,586,-727) (26/21,5/4) -> (61/22,86/31) Hyperbolic Matrix(223,-280,90,-113) (5/4,24/19) -> (32/13,5/2) Hyperbolic Matrix(841,-1064,132,-167) (24/19,19/15) -> (19/3,32/5) Hyperbolic Matrix(617,-784,484,-615) (19/15,14/11) -> (14/11,37/29) Parabolic Matrix(1009,-1288,745,-951) (37/29,23/18) -> (23/17,19/14) Hyperbolic Matrix(4817,-6160,2977,-3807) (23/18,55/43) -> (55/34,89/55) Hyperbolic Matrix(2801,-3584,787,-1007) (55/43,32/25) -> (32/9,57/16) Hyperbolic Matrix(1793,-2296,524,-671) (32/25,9/7) -> (65/19,24/7) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(561,-728,215,-279) (22/17,13/10) -> (13/5,34/13) Hyperbolic Matrix(1289,-1680,300,-391) (13/10,30/23) -> (30/7,43/10) Hyperbolic Matrix(6607,-8624,3862,-5041) (77/59,47/36) -> (65/38,77/45) Hyperbolic Matrix(729,-952,85,-111) (47/36,17/13) -> (17/2,9/1) Hyperbolic Matrix(2353,-3080,1026,-1343) (17/13,38/29) -> (94/41,39/17) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2129,-2800,936,-1231) (21/16,25/19) -> (25/11,91/40) Hyperbolic Matrix(169,-224,126,-167) (25/19,4/3) -> (4/3,31/23) Parabolic Matrix(2575,-3472,333,-449) (31/23,58/43) -> (54/7,31/4) Hyperbolic Matrix(4649,-6272,1120,-1511) (58/43,27/20) -> (83/20,54/13) Hyperbolic Matrix(953,-1288,165,-223) (27/20,23/17) -> (23/4,29/5) Hyperbolic Matrix(783,-1064,248,-337) (19/14,34/25) -> (22/7,19/6) Hyperbolic Matrix(2017,-2744,1193,-1623) (34/25,49/36) -> (49/29,22/13) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(449,-616,285,-391) (26/19,11/8) -> (11/7,30/19) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1175,-1624,649,-897) (29/21,47/34) -> (9/5,29/16) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(727,-1008,445,-617) (18/13,25/18) -> (31/19,18/11) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(3417,-4816,1231,-1735) (31/22,86/61) -> (86/31,25/9) Hyperbolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(2183,-3080,477,-673) (55/39,24/17) -> (32/7,55/12) Hyperbolic Matrix(1625,-2296,356,-503) (24/17,41/29) -> (41/9,32/7) Hyperbolic Matrix(673,-952,316,-447) (41/29,17/12) -> (17/8,15/7) Hyperbolic Matrix(671,-952,277,-393) (17/12,27/19) -> (29/12,17/7) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(391,-560,118,-169) (10/7,23/16) -> (33/10,10/3) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(505,-728,77,-111) (36/25,13/9) -> (13/2,20/3) Hyperbolic Matrix(1007,-1456,388,-561) (13/9,42/29) -> (70/27,13/5) Hyperbolic Matrix(2241,-3248,1313,-1903) (42/29,29/20) -> (29/17,70/41) Hyperbolic Matrix(617,-896,115,-167) (29/20,16/11) -> (16/3,27/5) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(839,-1288,256,-393) (3/2,20/13) -> (36/11,59/18) Hyperbolic Matrix(3527,-5432,1346,-2073) (20/13,37/24) -> (131/50,76/29) Hyperbolic Matrix(1233,-1904,362,-559) (37/24,17/11) -> (17/5,75/22) Hyperbolic Matrix(505,-784,324,-503) (17/11,14/9) -> (14/9,39/25) Parabolic Matrix(897,-1400,107,-167) (39/25,64/41) -> (8/1,17/2) Hyperbolic Matrix(1399,-2184,180,-281) (64/41,25/16) -> (31/4,8/1) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(673,-1064,389,-615) (30/19,19/12) -> (19/11,26/15) Hyperbolic Matrix(2969,-4704,883,-1399) (19/12,84/53) -> (84/25,37/11) Hyperbolic Matrix(5935,-9408,1767,-2801) (84/53,65/41) -> (47/14,84/25) Hyperbolic Matrix(281,-448,175,-279) (27/17,8/5) -> (8/5,29/18) Parabolic Matrix(1737,-2800,451,-727) (29/18,79/49) -> (23/6,27/7) Hyperbolic Matrix(5935,-9576,1736,-2801) (50/31,71/44) -> (41/12,106/31) Hyperbolic Matrix(2185,-3528,1352,-2183) (71/44,21/13) -> (21/13,97/60) Parabolic Matrix(6719,-10864,2425,-3921) (97/60,76/47) -> (36/13,97/35) Hyperbolic Matrix(3359,-5432,1178,-1905) (76/47,55/34) -> (57/20,20/7) Hyperbolic Matrix(9689,-15680,4048,-6551) (89/55,123/76) -> (67/28,79/33) Hyperbolic Matrix(5881,-9520,2248,-3639) (123/76,34/21) -> (34/13,157/60) Hyperbolic Matrix(449,-728,103,-167) (34/21,13/8) -> (13/3,22/5) Hyperbolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(2017,-3304,478,-783) (18/11,59/36) -> (59/14,38/9) Hyperbolic Matrix(2801,-4592,1639,-2687) (59/36,41/25) -> (41/24,53/31) Hyperbolic Matrix(3753,-6160,1330,-2183) (64/39,23/14) -> (79/28,48/17) Hyperbolic Matrix(783,-1288,307,-505) (23/14,28/17) -> (28/11,23/9) Hyperbolic Matrix(169,-280,67,-111) (28/17,5/3) -> (5/2,28/11) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(1625,-2744,729,-1231) (27/16,49/29) -> (49/22,29/13) Hyperbolic Matrix(727,-1232,298,-505) (22/13,17/10) -> (39/16,22/9) Hyperbolic Matrix(559,-952,165,-281) (17/10,29/17) -> (27/8,17/5) Hyperbolic Matrix(4033,-6888,1770,-3023) (70/41,41/24) -> (41/18,98/43) Hyperbolic Matrix(2521,-4312,556,-951) (53/31,65/38) -> (9/2,59/13) Hyperbolic Matrix(5825,-9968,1832,-3135) (77/45,12/7) -> (124/39,35/11) Hyperbolic Matrix(1009,-1736,390,-671) (12/7,31/18) -> (31/12,44/17) Hyperbolic Matrix(3249,-5600,1364,-2351) (31/18,50/29) -> (50/21,81/34) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(3361,-5936,697,-1231) (83/47,53/30) -> (53/11,29/6) Hyperbolic Matrix(729,-1288,253,-447) (53/30,23/13) -> (23/8,3/1) Hyperbolic Matrix(727,-1288,127,-225) (23/13,39/22) -> (17/3,23/4) Hyperbolic Matrix(1737,-3080,410,-727) (39/22,55/31) -> (55/13,17/4) Hyperbolic Matrix(1009,-1792,567,-1007) (55/31,16/9) -> (16/9,57/32) Parabolic Matrix(3865,-6888,1602,-2855) (57/32,41/23) -> (41/17,111/46) Hyperbolic Matrix(5433,-9688,2449,-4367) (41/23,107/60) -> (51/23,71/32) Hyperbolic Matrix(10361,-18480,4552,-8119) (107/60,66/37) -> (66/29,173/76) Hyperbolic Matrix(1569,-2800,376,-671) (66/37,25/14) -> (25/6,46/11) Hyperbolic Matrix(2633,-4704,595,-1063) (25/14,84/47) -> (84/19,31/7) Hyperbolic Matrix(5263,-9408,1191,-2129) (84/47,59/33) -> (53/12,84/19) Hyperbolic Matrix(2129,-3808,563,-1007) (59/33,34/19) -> (34/9,53/14) Hyperbolic Matrix(617,-1120,92,-167) (29/16,20/11) -> (20/3,27/4) Hyperbolic Matrix(337,-616,122,-223) (20/11,11/6) -> (11/4,36/13) Hyperbolic Matrix(335,-616,31,-57) (11/6,46/25) -> (10/1,11/1) Hyperbolic Matrix(3529,-6496,1551,-2855) (46/25,35/19) -> (91/40,66/29) Hyperbolic Matrix(3585,-6608,1397,-2575) (35/19,59/32) -> (59/23,77/30) Hyperbolic Matrix(1457,-2688,303,-559) (59/32,24/13) -> (24/5,53/11) Hyperbolic Matrix(727,-1344,152,-281) (24/13,13/7) -> (43/9,24/5) Hyperbolic Matrix(391,-728,181,-337) (13/7,28/15) -> (28/13,13/6) Hyperbolic Matrix(449,-840,209,-391) (28/15,15/8) -> (15/7,28/13) Hyperbolic Matrix(505,-952,148,-279) (15/8,2/1) -> (58/17,41/12) Hyperbolic Matrix(449,-952,158,-335) (2/1,17/8) -> (17/6,54/19) Hyperbolic Matrix(335,-728,52,-113) (13/6,24/11) -> (32/5,13/2) Hyperbolic Matrix(1513,-3304,615,-1343) (24/11,59/27) -> (59/24,32/13) Hyperbolic Matrix(1511,-3304,359,-785) (59/27,35/16) -> (21/5,59/14) Hyperbolic Matrix(1177,-2576,281,-615) (35/16,46/21) -> (46/11,21/5) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(3583,-7952,1363,-3025) (71/32,20/9) -> (92/35,71/27) Hyperbolic Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(34441,-78400,15129,-34439) (173/76,280/123) -> (280/123,107/47) Parabolic Matrix(5657,-12880,2041,-4647) (107/47,41/18) -> (97/35,61/22) Hyperbolic Matrix(4201,-9576,1621,-3695) (98/43,57/25) -> (57/22,70/27) Hyperbolic Matrix(785,-1792,343,-783) (57/25,16/7) -> (16/7,55/24) Parabolic Matrix(4593,-10528,1612,-3695) (55/24,94/41) -> (94/33,57/20) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2799,-6608,1139,-2689) (59/25,85/36) -> (27/11,59/24) Hyperbolic Matrix(18593,-43904,5217,-12319) (85/36,196/83) -> (196/55,139/39) Hyperbolic Matrix(13943,-32928,3913,-9241) (196/83,111/47) -> (57/16,196/55) Hyperbolic Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(5265,-12544,2209,-5263) (81/34,112/47) -> (112/47,31/13) Parabolic Matrix(1289,-3080,398,-951) (43/18,55/23) -> (55/17,13/4) Hyperbolic Matrix(281,-672,23,-55) (55/23,67/28) -> (11/1,1/0) Hyperbolic Matrix(3695,-8848,702,-1681) (79/33,12/5) -> (100/19,79/15) Hyperbolic Matrix(2071,-4984,396,-953) (12/5,65/27) -> (47/9,68/13) Hyperbolic Matrix(6047,-14560,1768,-4257) (65/27,53/22) -> (171/50,65/19) Hyperbolic Matrix(1905,-4592,743,-1791) (53/22,41/17) -> (41/16,59/23) Hyperbolic Matrix(3527,-8512,1091,-2633) (111/46,70/29) -> (42/13,55/17) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(1289,-3136,529,-1287) (17/7,56/23) -> (56/23,39/16) Parabolic Matrix(503,-1232,69,-169) (22/9,49/20) -> (7/1,22/3) Hyperbolic Matrix(617,-1512,91,-223) (49/20,27/11) -> (27/4,7/1) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(10359,-26824,3958,-10249) (44/17,101/39) -> (123/47,212/81) Hyperbolic Matrix(29961,-78400,11449,-29959) (157/60,280/107) -> (280/107,123/47) Parabolic Matrix(11425,-29904,3594,-9407) (212/81,89/34) -> (89/28,124/39) Hyperbolic Matrix(2353,-6160,513,-1343) (89/34,55/21) -> (55/12,23/5) Hyperbolic Matrix(4703,-12320,1112,-2913) (55/21,131/50) -> (93/22,55/13) Hyperbolic Matrix(1345,-3528,512,-1343) (76/29,21/8) -> (21/8,92/35) Parabolic Matrix(2129,-5600,468,-1231) (71/27,50/19) -> (50/11,41/9) Hyperbolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(169,-448,63,-167) (29/11,8/3) -> (8/3,27/10) Parabolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(281,-784,100,-279) (25/9,14/5) -> (14/5,31/11) Parabolic Matrix(1569,-4424,377,-1063) (31/11,110/39) -> (54/13,25/6) Hyperbolic Matrix(4705,-13272,893,-2519) (110/39,79/28) -> (79/15,58/11) Hyperbolic Matrix(1063,-3024,335,-953) (54/19,37/13) -> (19/6,54/17) Hyperbolic Matrix(4817,-13720,1140,-3247) (37/13,94/33) -> (38/9,131/31) Hyperbolic Matrix(393,-1232,89,-279) (3/1,22/7) -> (22/5,53/12) Hyperbolic Matrix(1903,-6048,247,-785) (54/17,89/28) -> (23/3,54/7) Hyperbolic Matrix(505,-1624,139,-447) (16/5,29/9) -> (29/8,40/11) Hyperbolic Matrix(953,-3136,289,-951) (23/7,56/17) -> (56/17,33/10) Parabolic Matrix(167,-560,17,-57) (10/3,47/14) -> (9/1,10/1) Hyperbolic Matrix(1905,-6496,361,-1231) (75/22,58/17) -> (58/11,37/7) Hyperbolic Matrix(5879,-20104,1294,-4425) (106/31,171/50) -> (109/24,50/11) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(895,-3192,173,-617) (82/23,25/7) -> (31/6,26/5) Hyperbolic Matrix(3473,-12544,961,-3471) (65/18,112/31) -> (112/31,47/13) Parabolic Matrix(841,-3136,225,-839) (41/11,56/15) -> (56/15,15/4) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(279,-1064,59,-225) (19/5,23/6) -> (33/7,19/4) Hyperbolic Matrix(57,-224,14,-55) (27/7,4/1) -> (4/1,29/7) Parabolic Matrix(3025,-12544,729,-3023) (29/7,112/27) -> (112/27,83/20) Parabolic Matrix(11873,-50176,2809,-11871) (131/31,224/53) -> (224/53,93/22) Parabolic Matrix(615,-2632,118,-505) (47/11,30/7) -> (26/5,47/9) Hyperbolic Matrix(729,-3136,169,-727) (43/10,56/13) -> (56/13,13/3) Parabolic Matrix(6217,-28224,1369,-6215) (59/13,168/37) -> (168/37,109/24) Parabolic Matrix(169,-784,36,-167) (23/5,14/3) -> (14/3,33/7) Parabolic Matrix(673,-3528,128,-671) (68/13,21/4) -> (21/4,100/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(671,-728,259,-281) -> Matrix(1,-2,1,-1) Matrix(559,-616,255,-281) -> Matrix(3,-2,-1,1) Matrix(953,-1064,601,-671) -> Matrix(29,-26,19,-17) Matrix(841,-952,197,-223) -> Matrix(1,-2,1,-1) Matrix(839,-952,297,-337) -> Matrix(3,-2,-1,1) Matrix(1119,-1288,682,-785) -> Matrix(1,2,0,1) Matrix(727,-840,534,-617) -> Matrix(7,-2,4,-1) Matrix(953,-1120,428,-503) -> Matrix(3,-4,-8,11) Matrix(617,-728,189,-223) -> Matrix(1,-2,1,-1) Matrix(897,-1064,188,-223) -> Matrix(7,-10,-2,3) Matrix(895,-1064,519,-617) -> Matrix(1,-2,3,-5) Matrix(1345,-1624,834,-1007) -> Matrix(1,2,0,1) Matrix(1063,-1288,463,-561) -> Matrix(1,-2,1,-1) Matrix(783,-952,139,-169) -> Matrix(1,-6,1,-5) Matrix(505,-616,91,-111) -> Matrix(1,2,1,3) Matrix(503,-616,138,-169) -> Matrix(1,2,0,1) Matrix(727,-896,228,-281) -> Matrix(1,0,-2,1) Matrix(2127,-2632,1630,-2017) -> Matrix(1,-2,2,-3) Matrix(1625,-2016,586,-727) -> Matrix(1,8,0,1) Matrix(223,-280,90,-113) -> Matrix(3,-2,2,-1) Matrix(841,-1064,132,-167) -> Matrix(13,-10,4,-3) Matrix(617,-784,484,-615) -> Matrix(13,-12,12,-11) Matrix(1009,-1288,745,-951) -> Matrix(19,-22,13,-15) Matrix(4817,-6160,2977,-3807) -> Matrix(3,-4,1,-1) Matrix(2801,-3584,787,-1007) -> Matrix(13,-16,9,-11) Matrix(1793,-2296,524,-671) -> Matrix(1,-2,2,-3) Matrix(391,-504,218,-281) -> Matrix(1,-2,0,1) Matrix(561,-728,215,-279) -> Matrix(1,-2,1,-1) Matrix(1289,-1680,300,-391) -> Matrix(1,0,-2,1) Matrix(6607,-8624,3862,-5041) -> Matrix(7,-4,2,-1) Matrix(729,-952,85,-111) -> Matrix(1,-2,1,-1) Matrix(2353,-3080,1026,-1343) -> Matrix(1,-2,2,-3) Matrix(2521,-3304,982,-1287) -> Matrix(3,-2,2,-1) Matrix(2129,-2800,936,-1231) -> Matrix(1,0,0,1) Matrix(169,-224,126,-167) -> Matrix(5,-4,4,-3) Matrix(2575,-3472,333,-449) -> Matrix(3,-4,7,-9) Matrix(4649,-6272,1120,-1511) -> Matrix(3,-4,16,-21) Matrix(953,-1288,165,-223) -> Matrix(7,-10,5,-7) Matrix(783,-1064,248,-337) -> Matrix(1,-2,2,-3) Matrix(2017,-2744,1193,-1623) -> Matrix(1,-2,3,-5) Matrix(1065,-1456,286,-391) -> Matrix(11,-24,6,-13) Matrix(449,-616,285,-391) -> Matrix(1,-6,1,-5) Matrix(447,-616,82,-113) -> Matrix(1,-2,2,-3) Matrix(1175,-1624,649,-897) -> Matrix(1,-2,7,-13) Matrix(1457,-2016,404,-559) -> Matrix(7,-16,4,-9) Matrix(727,-1008,445,-617) -> Matrix(1,-4,1,-3) Matrix(281,-392,200,-279) -> Matrix(1,-2,0,1) Matrix(3417,-4816,1231,-1735) -> Matrix(7,-8,1,-1) Matrix(7785,-10976,3296,-4647) -> Matrix(5,-4,4,-3) Matrix(2183,-3080,477,-673) -> Matrix(5,-6,1,-1) Matrix(1625,-2296,356,-503) -> Matrix(1,2,0,1) Matrix(673,-952,316,-447) -> Matrix(1,2,0,1) Matrix(671,-952,277,-393) -> Matrix(1,-2,1,-1) Matrix(1063,-1512,670,-953) -> Matrix(3,-14,2,-9) Matrix(391,-560,118,-169) -> Matrix(1,0,2,1) Matrix(895,-1288,312,-449) -> Matrix(5,-2,-2,1) Matrix(505,-728,77,-111) -> Matrix(1,-2,1,-1) Matrix(1007,-1456,388,-561) -> Matrix(1,0,0,1) Matrix(2241,-3248,1313,-1903) -> Matrix(1,0,1,1) Matrix(617,-896,115,-167) -> Matrix(1,0,1,1) Matrix(615,-896,116,-169) -> Matrix(1,0,-2,1) Matrix(727,-1064,192,-281) -> Matrix(1,2,0,1) Matrix(839,-1288,256,-393) -> Matrix(3,-2,-4,3) Matrix(3527,-5432,1346,-2073) -> Matrix(3,-2,2,-1) Matrix(1233,-1904,362,-559) -> Matrix(5,-4,4,-3) Matrix(505,-784,324,-503) -> Matrix(17,-16,16,-15) Matrix(897,-1400,107,-167) -> Matrix(13,-14,1,-1) Matrix(1399,-2184,180,-281) -> Matrix(9,-10,10,-11) Matrix(393,-616,178,-279) -> Matrix(5,-6,-4,5) Matrix(673,-1064,389,-615) -> Matrix(7,-10,5,-7) Matrix(2969,-4704,883,-1399) -> Matrix(27,-40,25,-37) Matrix(5935,-9408,1767,-2801) -> Matrix(53,-80,55,-83) Matrix(281,-448,175,-279) -> Matrix(7,-12,3,-5) Matrix(1737,-2800,451,-727) -> Matrix(3,-16,1,-5) Matrix(5935,-9576,1736,-2801) -> Matrix(3,-14,2,-9) Matrix(2185,-3528,1352,-2183) -> Matrix(1,-6,0,1) Matrix(6719,-10864,2425,-3921) -> Matrix(7,-8,1,-1) Matrix(3359,-5432,1178,-1905) -> Matrix(1,-2,0,1) Matrix(9689,-15680,4048,-6551) -> Matrix(1,0,2,1) Matrix(5881,-9520,2248,-3639) -> Matrix(1,0,0,1) Matrix(449,-728,103,-167) -> Matrix(1,-2,1,-1) Matrix(1065,-1736,446,-727) -> Matrix(1,-2,2,-3) Matrix(2017,-3304,478,-783) -> Matrix(1,-2,0,1) Matrix(2801,-4592,1639,-2687) -> Matrix(1,-4,1,-3) Matrix(3753,-6160,1330,-2183) -> Matrix(1,-8,0,1) Matrix(783,-1288,307,-505) -> Matrix(1,-6,1,-5) Matrix(169,-280,67,-111) -> Matrix(1,-2,1,-1) Matrix(167,-280,34,-57) -> Matrix(1,-2,0,1) Matrix(1625,-2744,729,-1231) -> Matrix(1,-2,-3,7) Matrix(727,-1232,298,-505) -> Matrix(1,0,0,1) Matrix(559,-952,165,-281) -> Matrix(1,-2,1,-1) Matrix(4033,-6888,1770,-3023) -> Matrix(1,-2,2,-3) Matrix(2521,-4312,556,-951) -> Matrix(7,-18,2,-5) Matrix(5825,-9968,1832,-3135) -> Matrix(1,-4,0,1) Matrix(1009,-1736,390,-671) -> Matrix(1,2,0,1) Matrix(3249,-5600,1364,-2351) -> Matrix(1,0,-4,1) Matrix(225,-392,128,-223) -> Matrix(1,-2,0,1) Matrix(6217,-10976,1744,-3079) -> Matrix(3,-8,2,-5) Matrix(3361,-5936,697,-1231) -> Matrix(1,4,-1,-3) Matrix(729,-1288,253,-447) -> Matrix(1,2,-1,-1) Matrix(727,-1288,127,-225) -> Matrix(1,-2,1,-1) Matrix(1737,-3080,410,-727) -> Matrix(1,2,0,1) Matrix(1009,-1792,567,-1007) -> Matrix(1,0,1,1) Matrix(3865,-6888,1602,-2855) -> Matrix(1,2,0,1) Matrix(5433,-9688,2449,-4367) -> Matrix(3,2,-5,-3) Matrix(10361,-18480,4552,-8119) -> Matrix(1,0,-2,1) Matrix(1569,-2800,376,-671) -> Matrix(1,0,0,1) Matrix(2633,-4704,595,-1063) -> Matrix(1,-4,1,-3) Matrix(5263,-9408,1191,-2129) -> Matrix(1,4,1,5) Matrix(2129,-3808,563,-1007) -> Matrix(3,8,1,3) Matrix(617,-1120,92,-167) -> Matrix(15,-4,4,-1) Matrix(337,-616,122,-223) -> Matrix(11,-6,2,-1) Matrix(335,-616,31,-57) -> Matrix(3,-2,-1,1) Matrix(3529,-6496,1551,-2855) -> Matrix(1,0,-1,1) Matrix(3585,-6608,1397,-2575) -> Matrix(1,0,-1,1) Matrix(1457,-2688,303,-559) -> Matrix(7,-4,-5,3) Matrix(727,-1344,152,-281) -> Matrix(11,-8,-4,3) Matrix(391,-728,181,-337) -> Matrix(11,-10,-1,1) Matrix(449,-840,209,-391) -> Matrix(13,-14,1,-1) Matrix(505,-952,148,-279) -> Matrix(1,-2,2,-3) Matrix(449,-952,158,-335) -> Matrix(1,-6,0,1) Matrix(335,-728,52,-113) -> Matrix(1,6,0,1) Matrix(1513,-3304,615,-1343) -> Matrix(1,2,-1,-1) Matrix(1511,-3304,359,-785) -> Matrix(1,2,-1,-1) Matrix(1177,-2576,281,-615) -> Matrix(1,0,1,1) Matrix(783,-1736,152,-337) -> Matrix(3,2,4,3) Matrix(3583,-7952,1363,-3025) -> Matrix(15,8,13,7) Matrix(727,-1624,201,-449) -> Matrix(11,2,5,1) Matrix(223,-504,50,-113) -> Matrix(3,-2,2,-1) Matrix(34441,-78400,15129,-34439) -> Matrix(1,0,11,1) Matrix(5657,-12880,2041,-4647) -> Matrix(23,-8,3,-1) Matrix(4201,-9576,1621,-3695) -> Matrix(1,-2,1,-1) Matrix(785,-1792,343,-783) -> Matrix(1,0,1,1) Matrix(4593,-10528,1612,-3695) -> Matrix(1,0,-2,1) Matrix(169,-392,72,-167) -> Matrix(3,-2,2,-1) Matrix(1401,-3304,427,-1007) -> Matrix(1,-2,-1,3) Matrix(2799,-6608,1139,-2689) -> Matrix(1,0,-1,1) Matrix(18593,-43904,5217,-12319) -> Matrix(35,-32,23,-21) Matrix(13943,-32928,3913,-9241) -> Matrix(25,-28,17,-19) Matrix(449,-1064,165,-391) -> Matrix(3,-10,1,-3) Matrix(447,-1064,71,-169) -> Matrix(3,2,1,1) Matrix(5265,-12544,2209,-5263) -> Matrix(1,0,9,1) Matrix(1289,-3080,398,-951) -> Matrix(3,-2,2,-1) Matrix(281,-672,23,-55) -> Matrix(1,0,-1,1) Matrix(3695,-8848,702,-1681) -> Matrix(1,0,-2,1) Matrix(2071,-4984,396,-953) -> Matrix(1,-2,2,-3) Matrix(6047,-14560,1768,-4257) -> Matrix(5,-8,2,-3) Matrix(1905,-4592,743,-1791) -> Matrix(1,-4,1,-3) Matrix(3527,-8512,1091,-2633) -> Matrix(1,-4,1,-3) Matrix(1345,-3248,417,-1007) -> Matrix(1,0,1,1) Matrix(1289,-3136,529,-1287) -> Matrix(3,-4,1,-1) Matrix(503,-1232,69,-169) -> Matrix(1,0,-1,1) Matrix(617,-1512,91,-223) -> Matrix(5,-6,1,-1) Matrix(503,-1288,66,-169) -> Matrix(1,-2,2,-3) Matrix(391,-1008,109,-281) -> Matrix(1,-4,1,-3) Matrix(10359,-26824,3958,-10249) -> Matrix(1,-2,2,-3) Matrix(29961,-78400,11449,-29959) -> Matrix(1,0,5,1) Matrix(11425,-29904,3594,-9407) -> Matrix(1,0,-2,1) Matrix(2353,-6160,513,-1343) -> Matrix(3,-4,1,-1) Matrix(4703,-12320,1112,-2913) -> Matrix(1,0,0,1) Matrix(1345,-3528,512,-1343) -> Matrix(7,-6,6,-5) Matrix(2129,-5600,468,-1231) -> Matrix(19,-24,4,-5) Matrix(617,-1624,106,-279) -> Matrix(1,-2,2,-3) Matrix(169,-448,63,-167) -> Matrix(7,-12,3,-5) Matrix(559,-1512,166,-449) -> Matrix(5,-14,4,-11) Matrix(225,-616,61,-167) -> Matrix(1,-6,1,-5) Matrix(281,-784,100,-279) -> Matrix(1,-16,0,1) Matrix(1569,-4424,377,-1063) -> Matrix(1,6,1,7) Matrix(4705,-13272,893,-2519) -> Matrix(1,6,-1,-5) Matrix(1063,-3024,335,-953) -> Matrix(1,4,-1,-3) Matrix(4817,-13720,1140,-3247) -> Matrix(1,2,0,1) Matrix(393,-1232,89,-279) -> Matrix(1,0,1,1) Matrix(1903,-6048,247,-785) -> Matrix(1,0,1,1) Matrix(505,-1624,139,-447) -> Matrix(1,-2,1,-1) Matrix(953,-3136,289,-951) -> Matrix(1,0,9,1) Matrix(167,-560,17,-57) -> Matrix(5,-4,-1,1) Matrix(1905,-6496,361,-1231) -> Matrix(1,0,-1,1) Matrix(5879,-20104,1294,-4425) -> Matrix(17,-30,4,-7) Matrix(113,-392,32,-111) -> Matrix(3,-2,2,-1) Matrix(895,-3192,173,-617) -> Matrix(1,-2,3,-5) Matrix(3473,-12544,961,-3471) -> Matrix(47,-92,23,-45) Matrix(841,-3136,225,-839) -> Matrix(31,-60,15,-29) Matrix(223,-840,30,-113) -> Matrix(1,-2,-2,5) Matrix(279,-1064,59,-225) -> Matrix(5,-14,-1,3) Matrix(57,-224,14,-55) -> Matrix(1,-4,0,1) Matrix(3025,-12544,729,-3023) -> Matrix(1,0,11,1) Matrix(11873,-50176,2809,-11871) -> Matrix(1,0,3,1) Matrix(615,-2632,118,-505) -> Matrix(1,2,0,1) Matrix(729,-3136,169,-727) -> Matrix(1,0,3,1) Matrix(6217,-28224,1369,-6215) -> Matrix(53,-208,13,-51) Matrix(169,-784,36,-167) -> Matrix(1,-12,0,1) Matrix(673,-3528,128,-671) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 128 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 1 1 2/1 (0/1,2/1) 0 14 15/7 7/1 1 28 28/13 1/0 12 1 13/6 1/0 1 28 24/11 -2/1 3 7 59/27 -3/1 1 28 35/16 -1/1 1 4 46/21 (0/1,2/1) 0 14 11/5 -1/1 1 28 20/9 -1/2 2 7 29/13 -1/5 1 28 9/4 1/4 1 28 25/11 1/1 1 28 66/29 (-2/1,0/1) 0 14 280/123 0/1 11 1 107/47 1/5 1 28 41/18 1/0 1 28 57/25 1/1 1 28 16/7 0/1 1 7 55/24 1/2 1 28 39/17 1/1 1 28 23/10 1/0 1 28 7/3 1/1 1 4 33/14 3/2 1 28 59/25 -1/1 1 28 85/36 3/4 1 28 26/11 (4/3,2/1) 0 14 19/8 1/0 1 28 50/21 (-2/3,0/1) 0 14 112/47 0/1 9 1 31/13 1/3 1 28 12/5 1/1 2 7 65/27 11/7 1 28 53/22 5/2 1 28 41/17 3/1 1 28 111/46 1/0 1 28 70/29 1/0 2 2 29/12 1/0 1 28 17/7 1/1 1 28 56/23 2/1 1 1 22/9 (0/1,2/1) 0 14 49/20 1/1 3 4 27/11 3/1 1 28 5/2 1/0 1 28 28/11 1/1 2 1 23/9 1/1 1 28 41/16 1/0 1 28 59/23 3/1 1 28 18/7 (4/3,2/1) 0 14 31/12 3/2 1 28 44/17 1/0 2 7 101/39 3/1 1 28 57/22 1/0 1 28 13/5 1/1 1 28 34/13 (0/1,2/1) 0 14 280/107 0/1 5 1 123/47 1/3 1 28 212/81 1/2 2 7 89/34 1/2 1 28 55/21 1/1 1 28 76/29 1/1 2 7 21/8 1/1 3 4 92/35 1/1 2 7 71/27 11/9 1 28 50/19 (4/3,2/1) 0 14 29/11 7/5 1 28 8/3 2/1 3 7 27/10 11/4 1 28 19/7 3/1 1 28 30/11 (18/5,4/1) 0 14 11/4 1/0 1 28 36/13 7/1 2 7 97/35 23/3 1 28 61/22 17/2 1 28 25/9 9/1 1 28 14/5 1/0 8 2 31/11 -7/1 1 28 48/17 -4/1 1 7 17/6 1/0 1 28 37/13 -3/1 1 28 57/20 1/0 1 28 20/7 1/0 2 7 3/1 1/1 1 28 19/6 1/0 1 28 16/5 0/1 3 7 29/9 1/1 1 28 42/13 1/1 2 2 55/17 1/1 1 28 13/4 1/0 1 28 36/11 -1/1 2 7 59/18 -3/4 1 28 23/7 -1/3 1 28 56/17 0/1 9 1 10/3 (0/1,2/3) 0 14 47/14 11/12 1 28 84/25 1/1 20 1 37/11 1/1 1 28 27/8 1/0 1 28 17/5 1/1 1 28 75/22 1/0 1 28 58/17 (0/1,2/3) 0 14 41/12 5/4 1 28 24/7 2/1 1 7 7/2 1/1 1 4 32/9 4/3 1 7 57/16 3/2 1 28 196/55 3/2 10 1 139/39 23/15 1 28 82/23 (8/5,2/1) 0 14 25/7 5/3 1 28 18/5 (8/5,2/1) 0 14 112/31 2/1 23 1 47/13 19/9 1 28 29/8 1/0 1 28 11/3 1/1 1 28 26/7 (12/7,2/1) 0 14 56/15 2/1 15 1 15/4 9/4 1 28 34/9 (2/1,8/3) 0 14 53/14 1/0 1 28 19/5 3/1 1 28 23/6 7/2 1 28 27/7 11/3 1 28 4/1 1/0 2 7 29/7 -1/3 1 28 112/27 0/1 11 1 54/13 (0/1,2/5) 0 14 25/6 1/0 1 28 46/11 (0/1,2/3) 0 14 21/5 1/0 1 4 59/14 -1/2 1 28 38/9 (0/1,2/1) 0 14 224/53 0/1 3 1 93/22 1/2 1 28 55/13 1/1 1 28 17/4 1/0 1 28 47/11 -5/1 1 28 30/7 (-2/1,0/1) 0 14 56/13 0/1 3 1 13/3 1/1 1 28 22/5 (0/1,2/1) 0 14 53/12 1/2 1 28 84/19 1/1 4 1 31/7 1/1 1 28 9/2 5/2 1 28 59/13 19/5 1 28 168/37 4/1 13 1 50/11 (4/1,14/3) 0 14 41/9 7/1 1 28 32/7 4/1 1 7 55/12 1/0 1 28 23/5 5/1 1 28 14/3 1/0 6 2 33/7 -7/1 1 28 19/4 1/0 1 28 24/5 -2/1 3 7 53/11 -5/3 1 28 29/6 -1/2 1 28 5/1 -1/1 1 28 31/6 1/0 1 28 26/5 (0/1,2/1) 0 14 47/9 -3/1 1 28 68/13 1/1 2 7 21/4 1/0 1 4 100/19 -1/1 2 7 79/15 -1/1 1 28 58/11 (0/1,2/1) 0 14 37/7 -1/1 1 28 16/3 0/1 3 7 27/5 1/1 1 28 11/2 1/2 1 28 28/5 1/1 4 1 17/3 1/1 1 28 23/4 1/0 1 28 29/5 3/1 1 28 6/1 (0/1,2/1) 0 14 19/3 3/1 1 28 32/5 4/1 3 7 13/2 1/0 1 28 20/3 3/1 2 7 27/4 9/2 1 28 7/1 1/0 3 4 22/3 (-2/1,0/1) 0 14 15/2 1/2 1 28 23/3 1/1 1 28 54/7 (-2/1,0/1) 0 14 31/4 1/2 1 28 8/1 2/1 1 7 17/2 1/0 1 28 9/1 7/1 1 28 10/1 (-4/1,-2/1) 0 14 11/1 -1/1 1 28 1/0 1/0 1 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(447,-952,131,-279) (2/1,15/7) -> (58/17,41/12) Glide Reflection Matrix(391,-840,182,-391) (15/7,28/13) -> (15/7,28/13) Reflection Matrix(337,-728,156,-337) (28/13,13/6) -> (28/13,13/6) Reflection Matrix(335,-728,52,-113) (13/6,24/11) -> (32/5,13/2) Hyperbolic Matrix(1231,-2688,256,-559) (24/11,59/27) -> (24/5,53/11) Glide Reflection Matrix(1511,-3304,359,-785) (59/27,35/16) -> (21/5,59/14) Hyperbolic Matrix(1177,-2576,281,-615) (35/16,46/21) -> (46/11,21/5) Hyperbolic Matrix(281,-616,26,-57) (46/21,11/5) -> (10/1,11/1) Glide Reflection Matrix(279,-616,101,-223) (11/5,20/9) -> (11/4,36/13) Glide Reflection Matrix(503,-1120,75,-167) (20/9,29/13) -> (20/3,27/4) Glide Reflection Matrix(727,-1624,201,-449) (29/13,9/4) -> (47/13,29/8) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1231,-2800,295,-671) (25/11,66/29) -> (25/6,46/11) Glide Reflection Matrix(8119,-18480,3567,-8119) (66/29,280/123) -> (66/29,280/123) Reflection Matrix(26321,-59920,11562,-26321) (280/123,107/47) -> (280/123,107/47) Reflection Matrix(5657,-12880,2041,-4647) (107/47,41/18) -> (97/35,61/22) Hyperbolic Matrix(3023,-6888,1253,-2855) (41/18,57/25) -> (41/17,111/46) Glide Reflection Matrix(785,-1792,343,-783) (57/25,16/7) -> (16/7,55/24) Parabolic Matrix(1343,-3080,317,-727) (55/24,39/17) -> (55/13,17/4) Glide Reflection Matrix(561,-1288,98,-225) (39/17,23/10) -> (17/3,23/4) Glide Reflection Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1401,-3304,427,-1007) (33/14,59/25) -> (59/18,23/7) Hyperbolic Matrix(2633,-6216,546,-1289) (59/25,85/36) -> (53/11,29/6) Glide Reflection Matrix(4481,-10584,1257,-2969) (85/36,26/11) -> (139/39,82/23) Glide Reflection Matrix(449,-1064,165,-391) (26/11,19/8) -> (19/7,30/11) Hyperbolic Matrix(447,-1064,71,-169) (19/8,50/21) -> (6/1,19/3) Hyperbolic Matrix(2351,-5600,987,-2351) (50/21,112/47) -> (50/21,112/47) Reflection Matrix(2913,-6944,1222,-2913) (112/47,31/13) -> (112/47,31/13) Reflection Matrix(727,-1736,281,-671) (31/13,12/5) -> (31/12,44/17) Glide Reflection Matrix(2071,-4984,396,-953) (12/5,65/27) -> (47/9,68/13) Hyperbolic Matrix(1791,-4312,395,-951) (65/27,53/22) -> (9/2,59/13) Glide Reflection Matrix(1905,-4592,743,-1791) (53/22,41/17) -> (41/16,59/23) Hyperbolic Matrix(3527,-8512,1091,-2633) (111/46,70/29) -> (42/13,55/17) Hyperbolic Matrix(1345,-3248,417,-1007) (70/29,29/12) -> (29/9,42/13) Hyperbolic Matrix(393,-952,116,-281) (29/12,17/7) -> (27/8,17/5) Glide Reflection Matrix(783,-1904,322,-783) (17/7,56/23) -> (17/7,56/23) Reflection Matrix(505,-1232,207,-505) (56/23,22/9) -> (56/23,22/9) Reflection Matrix(503,-1232,69,-169) (22/9,49/20) -> (7/1,22/3) Hyperbolic Matrix(617,-1512,91,-223) (49/20,27/11) -> (27/4,7/1) Hyperbolic Matrix(113,-280,23,-57) (27/11,5/2) -> (29/6,5/1) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(505,-1288,198,-505) (28/11,23/9) -> (28/11,23/9) Reflection Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(1287,-3304,305,-783) (59/23,18/7) -> (59/14,38/9) Glide Reflection Matrix(391,-1008,109,-281) (18/7,31/12) -> (25/7,18/5) Hyperbolic Matrix(10359,-26824,3958,-10249) (44/17,101/39) -> (123/47,212/81) Hyperbolic Matrix(281,-728,22,-57) (101/39,57/22) -> (11/1,1/0) Glide Reflection Matrix(561,-1456,173,-449) (57/22,13/5) -> (55/17,13/4) Glide Reflection Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(3639,-9520,1391,-3639) (34/13,280/107) -> (34/13,280/107) Reflection Matrix(26321,-68880,10058,-26321) (280/107,123/47) -> (280/107,123/47) Reflection Matrix(9799,-25648,1861,-4871) (212/81,89/34) -> (100/19,79/15) Glide Reflection Matrix(2353,-6160,513,-1343) (89/34,55/21) -> (55/12,23/5) Hyperbolic Matrix(2073,-5432,727,-1905) (55/21,76/29) -> (57/20,20/7) Glide Reflection Matrix(1345,-3528,512,-1343) (76/29,21/8) -> (21/8,92/35) Parabolic Matrix(4367,-11480,1576,-4143) (92/35,71/27) -> (36/13,97/35) Glide Reflection Matrix(2129,-5600,468,-1231) (71/27,50/19) -> (50/11,41/9) Hyperbolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(169,-448,63,-167) (29/11,8/3) -> (8/3,27/10) Parabolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(225,-616,61,-167) (30/11,11/4) -> (11/3,26/7) Hyperbolic Matrix(727,-2016,141,-391) (61/22,25/9) -> (5/1,31/6) Glide Reflection Matrix(281,-784,100,-279) (25/9,14/5) -> (14/5,31/11) Parabolic Matrix(615,-1736,79,-223) (31/11,48/17) -> (31/4,8/1) Glide Reflection Matrix(337,-952,40,-113) (48/17,17/6) -> (8/1,17/2) Glide Reflection Matrix(671,-1904,197,-559) (17/6,37/13) -> (17/5,75/22) Glide Reflection Matrix(2575,-7336,609,-1735) (37/13,57/20) -> (93/22,55/13) Glide Reflection Matrix(449,-1288,137,-393) (20/7,3/1) -> (36/11,59/18) Glide Reflection Matrix(337,-1064,89,-281) (3/1,19/6) -> (53/14,19/5) Glide Reflection Matrix(281,-896,53,-169) (19/6,16/5) -> (37/7,16/3) Glide Reflection Matrix(279,-896,52,-167) (16/5,29/9) -> (16/3,27/5) Glide Reflection Matrix(223,-728,34,-111) (13/4,36/11) -> (13/2,20/3) Glide Reflection Matrix(783,-2576,238,-783) (23/7,56/17) -> (23/7,56/17) Reflection Matrix(169,-560,51,-169) (56/17,10/3) -> (56/17,10/3) Reflection Matrix(167,-560,17,-57) (10/3,47/14) -> (9/1,10/1) Hyperbolic Matrix(2351,-7896,700,-2351) (47/14,84/25) -> (47/14,84/25) Reflection Matrix(1849,-6216,550,-1849) (84/25,37/11) -> (84/25,37/11) Reflection Matrix(1905,-6496,361,-1231) (75/22,58/17) -> (58/11,37/7) Hyperbolic Matrix(671,-2296,147,-503) (41/12,24/7) -> (41/9,32/7) Glide Reflection Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(1007,-3584,220,-783) (32/9,57/16) -> (32/7,55/12) Glide Reflection Matrix(6271,-22344,1760,-6271) (57/16,196/55) -> (57/16,196/55) Reflection Matrix(15289,-54488,4290,-15289) (196/55,139/39) -> (196/55,139/39) Reflection Matrix(895,-3192,173,-617) (82/23,25/7) -> (31/6,26/5) Hyperbolic Matrix(559,-2016,155,-559) (18/5,112/31) -> (18/5,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(169,-616,31,-113) (29/8,11/3) -> (27/5,11/2) Glide Reflection Matrix(391,-1456,105,-391) (26/7,56/15) -> (26/7,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(785,-2968,178,-673) (34/9,53/14) -> (22/5,53/12) Glide Reflection Matrix(279,-1064,59,-225) (19/5,23/6) -> (33/7,19/4) Hyperbolic Matrix(335,-1288,58,-223) (23/6,27/7) -> (23/4,29/5) Glide Reflection Matrix(57,-224,14,-55) (27/7,4/1) -> (4/1,29/7) Parabolic Matrix(1567,-6496,378,-1567) (29/7,112/27) -> (29/7,112/27) Reflection Matrix(1457,-6048,351,-1457) (112/27,54/13) -> (112/27,54/13) Reflection Matrix(727,-3024,94,-391) (54/13,25/6) -> (54/7,31/4) Glide Reflection Matrix(2015,-8512,477,-2015) (38/9,224/53) -> (38/9,224/53) Reflection Matrix(9857,-41664,2332,-9857) (224/53,93/22) -> (224/53,93/22) Reflection Matrix(223,-952,26,-111) (17/4,47/11) -> (17/2,9/1) Glide Reflection Matrix(615,-2632,118,-505) (47/11,30/7) -> (26/5,47/9) Hyperbolic Matrix(391,-1680,91,-391) (30/7,56/13) -> (30/7,56/13) Reflection Matrix(337,-1456,78,-337) (56/13,13/3) -> (56/13,13/3) Reflection Matrix(2015,-8904,456,-2015) (53/12,84/19) -> (53/12,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(4367,-19824,962,-4367) (59/13,168/37) -> (59/13,168/37) Reflection Matrix(1849,-8400,407,-1849) (168/37,50/11) -> (168/37,50/11) Reflection Matrix(169,-784,36,-167) (23/5,14/3) -> (14/3,33/7) Parabolic Matrix(223,-1064,35,-167) (19/4,24/5) -> (19/3,32/5) Glide Reflection Matrix(673,-3528,128,-671) (68/13,21/4) -> (21/4,100/19) Parabolic Matrix(1063,-5600,138,-727) (79/15,58/11) -> (23/3,54/7) Glide Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(447,-952,131,-279) -> Matrix(1,-2,1,-3) Matrix(391,-840,182,-391) -> Matrix(-1,14,0,1) (15/7,28/13) -> (7/1,1/0) Matrix(337,-728,156,-337) -> Matrix(1,10,0,-1) (28/13,13/6) -> (-5/1,1/0) Matrix(335,-728,52,-113) -> Matrix(1,6,0,1) 1/0 Matrix(1231,-2688,256,-559) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(1511,-3304,359,-785) -> Matrix(1,2,-1,-1) (-2/1,0/1).(-1/1,1/0) Matrix(1177,-2576,281,-615) -> Matrix(1,0,1,1) 0/1 Matrix(281,-616,26,-57) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(279,-616,101,-223) -> Matrix(5,6,1,1) Matrix(503,-1120,75,-167) -> Matrix(11,4,3,1) Matrix(727,-1624,201,-449) -> Matrix(11,2,5,1) Matrix(223,-504,50,-113) -> Matrix(3,-2,2,-1) 1/1 Matrix(1231,-2800,295,-671) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(8119,-18480,3567,-8119) -> Matrix(-1,0,1,1) (66/29,280/123) -> (-2/1,0/1) Matrix(26321,-59920,11562,-26321) -> Matrix(1,0,10,-1) (280/123,107/47) -> (0/1,1/5) Matrix(5657,-12880,2041,-4647) -> Matrix(23,-8,3,-1) Matrix(3023,-6888,1253,-2855) -> Matrix(3,-2,1,-1) Matrix(785,-1792,343,-783) -> Matrix(1,0,1,1) 0/1 Matrix(1343,-3080,317,-727) -> Matrix(3,-2,1,-1) Matrix(561,-1288,98,-225) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(169,-392,72,-167) -> Matrix(3,-2,2,-1) 1/1 Matrix(1401,-3304,427,-1007) -> Matrix(1,-2,-1,3) Matrix(2633,-6216,546,-1289) -> Matrix(3,-2,-2,1) Matrix(4481,-10584,1257,-2969) -> Matrix(11,-14,7,-9) Matrix(449,-1064,165,-391) -> Matrix(3,-10,1,-3) (2/1,4/1).(3/1,1/0) Matrix(447,-1064,71,-169) -> Matrix(3,2,1,1) Matrix(2351,-5600,987,-2351) -> Matrix(-1,0,3,1) (50/21,112/47) -> (-2/3,0/1) Matrix(2913,-6944,1222,-2913) -> Matrix(1,0,6,-1) (112/47,31/13) -> (0/1,1/3) Matrix(727,-1736,281,-671) -> Matrix(3,-2,1,-1) Matrix(2071,-4984,396,-953) -> Matrix(1,-2,2,-3) 1/1 Matrix(1791,-4312,395,-951) -> Matrix(11,-18,3,-5) Matrix(1905,-4592,743,-1791) -> Matrix(1,-4,1,-3) 2/1 Matrix(3527,-8512,1091,-2633) -> Matrix(1,-4,1,-3) 2/1 Matrix(1345,-3248,417,-1007) -> Matrix(1,0,1,1) 0/1 Matrix(393,-952,116,-281) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(783,-1904,322,-783) -> Matrix(3,-4,2,-3) (17/7,56/23) -> (1/1,2/1) Matrix(505,-1232,207,-505) -> Matrix(1,0,1,-1) (56/23,22/9) -> (0/1,2/1) Matrix(503,-1232,69,-169) -> Matrix(1,0,-1,1) 0/1 Matrix(617,-1512,91,-223) -> Matrix(5,-6,1,-1) Matrix(113,-280,23,-57) -> Matrix(1,-2,-1,1) Matrix(111,-280,44,-111) -> Matrix(-1,2,0,1) (5/2,28/11) -> (1/1,1/0) Matrix(505,-1288,198,-505) -> Matrix(5,-6,4,-5) (28/11,23/9) -> (1/1,3/2) Matrix(503,-1288,66,-169) -> Matrix(1,-2,2,-3) 1/1 Matrix(1287,-3304,305,-783) -> Matrix(1,-2,-1,1) Matrix(391,-1008,109,-281) -> Matrix(1,-4,1,-3) 2/1 Matrix(10359,-26824,3958,-10249) -> Matrix(1,-2,2,-3) 1/1 Matrix(281,-728,22,-57) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(561,-1456,173,-449) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(279,-728,64,-167) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(3639,-9520,1391,-3639) -> Matrix(1,0,1,-1) (34/13,280/107) -> (0/1,2/1) Matrix(26321,-68880,10058,-26321) -> Matrix(1,0,6,-1) (280/107,123/47) -> (0/1,1/3) Matrix(9799,-25648,1861,-4871) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(2353,-6160,513,-1343) -> Matrix(3,-4,1,-1) 2/1 Matrix(2073,-5432,727,-1905) -> Matrix(1,-2,-1,1) Matrix(1345,-3528,512,-1343) -> Matrix(7,-6,6,-5) 1/1 Matrix(4367,-11480,1576,-4143) -> Matrix(43,-50,6,-7) Matrix(2129,-5600,468,-1231) -> Matrix(19,-24,4,-5) Matrix(617,-1624,106,-279) -> Matrix(1,-2,2,-3) 1/1 Matrix(169,-448,63,-167) -> Matrix(7,-12,3,-5) 2/1 Matrix(559,-1512,166,-449) -> Matrix(5,-14,4,-11) Matrix(225,-616,61,-167) -> Matrix(1,-6,1,-5) Matrix(727,-2016,141,-391) -> Matrix(1,-8,1,-9) Matrix(281,-784,100,-279) -> Matrix(1,-16,0,1) 1/0 Matrix(615,-1736,79,-223) -> Matrix(1,6,1,5) Matrix(337,-952,40,-113) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(671,-1904,197,-559) -> Matrix(1,4,1,3) Matrix(2575,-7336,609,-1735) -> Matrix(1,2,1,1) Matrix(449,-1288,137,-393) -> Matrix(1,2,-1,-3) Matrix(337,-1064,89,-281) -> Matrix(3,-2,1,-1) Matrix(281,-896,53,-169) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(279,-896,52,-167) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(223,-728,34,-111) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(783,-2576,238,-783) -> Matrix(-1,0,6,1) (23/7,56/17) -> (-1/3,0/1) Matrix(169,-560,51,-169) -> Matrix(1,0,3,-1) (56/17,10/3) -> (0/1,2/3) Matrix(167,-560,17,-57) -> Matrix(5,-4,-1,1) Matrix(2351,-7896,700,-2351) -> Matrix(23,-22,24,-23) (47/14,84/25) -> (11/12,1/1) Matrix(1849,-6216,550,-1849) -> Matrix(17,-18,16,-17) (84/25,37/11) -> (1/1,9/8) Matrix(1905,-6496,361,-1231) -> Matrix(1,0,-1,1) 0/1 Matrix(671,-2296,147,-503) -> Matrix(3,-2,1,-1) Matrix(113,-392,32,-111) -> Matrix(3,-2,2,-1) 1/1 Matrix(1007,-3584,220,-783) -> Matrix(11,-16,2,-3) Matrix(6271,-22344,1760,-6271) -> Matrix(29,-42,20,-29) (57/16,196/55) -> (7/5,3/2) Matrix(15289,-54488,4290,-15289) -> Matrix(91,-138,60,-91) (196/55,139/39) -> (3/2,23/15) Matrix(895,-3192,173,-617) -> Matrix(1,-2,3,-5) Matrix(559,-2016,155,-559) -> Matrix(9,-16,5,-9) (18/5,112/31) -> (8/5,2/1) Matrix(2913,-10528,806,-2913) -> Matrix(37,-76,18,-37) (112/31,47/13) -> (2/1,19/9) Matrix(169,-616,31,-113) -> Matrix(1,-2,1,-3) Matrix(391,-1456,105,-391) -> Matrix(13,-24,7,-13) (26/7,56/15) -> (12/7,2/1) Matrix(449,-1680,120,-449) -> Matrix(17,-36,8,-17) (56/15,15/4) -> (2/1,9/4) Matrix(223,-840,30,-113) -> Matrix(1,-2,-2,5) Matrix(785,-2968,178,-673) -> Matrix(1,-2,2,-5) Matrix(279,-1064,59,-225) -> Matrix(5,-14,-1,3) Matrix(335,-1288,58,-223) -> Matrix(3,-10,2,-7) Matrix(57,-224,14,-55) -> Matrix(1,-4,0,1) 1/0 Matrix(1567,-6496,378,-1567) -> Matrix(-1,0,6,1) (29/7,112/27) -> (-1/3,0/1) Matrix(1457,-6048,351,-1457) -> Matrix(1,0,5,-1) (112/27,54/13) -> (0/1,2/5) Matrix(727,-3024,94,-391) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(2015,-8512,477,-2015) -> Matrix(1,0,1,-1) (38/9,224/53) -> (0/1,2/1) Matrix(9857,-41664,2332,-9857) -> Matrix(1,0,4,-1) (224/53,93/22) -> (0/1,1/2) Matrix(223,-952,26,-111) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(615,-2632,118,-505) -> Matrix(1,2,0,1) 1/0 Matrix(391,-1680,91,-391) -> Matrix(-1,0,1,1) (30/7,56/13) -> (-2/1,0/1) Matrix(337,-1456,78,-337) -> Matrix(1,0,2,-1) (56/13,13/3) -> (0/1,1/1) Matrix(2015,-8904,456,-2015) -> Matrix(3,-2,4,-3) (53/12,84/19) -> (1/2,1/1) Matrix(1177,-5208,266,-1177) -> Matrix(5,-6,4,-5) (84/19,31/7) -> (1/1,3/2) Matrix(4367,-19824,962,-4367) -> Matrix(39,-152,10,-39) (59/13,168/37) -> (19/5,4/1) Matrix(1849,-8400,407,-1849) -> Matrix(13,-56,3,-13) (168/37,50/11) -> (4/1,14/3) Matrix(169,-784,36,-167) -> Matrix(1,-12,0,1) 1/0 Matrix(223,-1064,35,-167) -> Matrix(3,10,1,3) Matrix(673,-3528,128,-671) -> Matrix(1,-2,0,1) 1/0 Matrix(1063,-5600,138,-727) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(111,-616,20,-111) -> Matrix(3,-2,4,-3) (11/2,28/5) -> (1/2,1/1) Matrix(169,-952,30,-169) -> Matrix(5,-6,4,-5) (28/5,17/3) -> (1/1,3/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.