INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 2304 Minimal number of generators: 385 Number of equivalence classes of cusps: 128 Genus: 129 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -13/28 -5/11 -4/9 -11/26 -7/17 -2/5 -3/8 -1/3 -2/7 -1/4 -3/13 -4/19 -1/6 -1/7 -2/17 0/1 1/9 2/13 3/17 1/5 1/4 7/23 1/3 4/11 3/7 1/2 11/19 7/11 2/3 5/7 13/17 4/5 7/8 1/1 8/7 13/11 11/9 5/4 17/13 121/89 7/5 3/2 11/7 46/29 37/23 13/8 5/3 19/11 16/9 9/5 13/7 2/1 17/8 41/19 11/5 31/14 25/11 7/3 19/8 17/7 5/2 43/17 28/11 151/59 18/7 13/5 76/29 51/19 35/13 11/4 31/11 89/31 26/9 3/1 19/6 16/5 61/19 23/7 10/3 27/8 17/5 31/9 7/2 47/13 11/3 19/5 4/1 21/5 17/4 81/19 13/3 61/14 22/5 49/11 9/2 41/9 23/5 37/8 14/3 33/7 19/4 24/5 5/1 21/4 16/3 27/5 38/7 11/2 28/5 17/3 23/4 6/1 25/4 19/3 13/2 20/3 7/1 22/3 15/2 53/7 23/3 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/2 -8/17 1/3 1/1 -7/15 2/5 -13/28 1/2 -6/13 4/7 3/5 -17/37 2/3 -11/24 1/2 -16/35 2/3 1/1 -5/11 1/1 -19/42 1/2 -14/31 -1/1 0/1 -23/51 0/1 -9/20 1/0 -13/29 0/1 -4/9 1/2 -15/34 7/12 -11/25 3/5 -18/41 2/3 9/13 -7/16 2/3 -17/39 1/1 -27/62 4/5 -37/85 4/5 -10/23 7/8 1/1 -13/30 7/6 -3/7 0/1 -14/33 1/3 2/5 -11/26 1/2 -19/45 3/5 -27/64 7/12 -35/83 2/3 -8/19 2/3 1/1 -13/31 3/5 -31/74 5/8 -18/43 2/3 -23/55 2/3 -5/12 3/4 -22/53 3/4 1/1 -17/41 3/4 -12/29 4/5 1/1 -19/46 6/7 -7/17 1/1 -23/56 6/5 -16/39 4/3 7/5 -9/22 1/0 -11/27 0/1 -2/5 1/3 1/1 -13/33 1/2 -11/28 3/4 -9/23 1/1 -25/64 2/3 -16/41 3/4 -7/18 7/8 -12/31 1/1 12/11 -17/44 6/5 -39/101 19/15 -22/57 4/3 -5/13 2/1 -23/60 5/2 -41/107 3/1 -18/47 -1/1 1/0 -13/34 2/1 -21/55 3/1 -8/21 -1/1 1/0 -11/29 -1/1 -14/37 -1/3 0/1 -3/8 0/1 -16/43 1/3 1/1 -13/35 1/3 -10/27 1/3 2/5 -7/19 1/2 -11/30 1/2 -15/41 1/1 -19/52 2/3 -4/11 4/5 1/1 -13/36 13/12 -9/25 4/3 -14/39 3/2 -19/53 5/3 -5/14 2/1 -11/31 1/0 -6/17 -2/1 -1/1 -7/20 -1/2 -8/23 0/1 -1/3 1/1 -7/22 0/1 -6/19 1/5 1/4 -5/16 3/8 -9/29 1/2 -4/13 3/5 1/1 -15/49 1/1 -11/36 2/3 -7/23 4/5 -10/33 10/11 1/1 -3/10 3/2 -14/47 1/1 3/1 -11/37 3/1 -19/64 1/0 -8/27 1/1 2/1 -5/17 1/0 -7/24 -3/2 -9/31 -1/3 -11/38 0/1 -2/7 0/1 -9/32 1/6 -7/25 1/3 -5/18 1/2 -18/65 1/2 7/13 -13/47 3/5 -8/29 1/3 1/1 -11/40 1/2 -14/51 1/3 2/5 -17/62 1/2 -3/11 2/3 -13/48 2/3 -23/85 11/15 -10/37 7/9 1/1 -17/63 1/1 -7/26 7/8 -4/15 1/1 4/3 -9/34 2/1 -14/53 1/1 5/3 -5/19 3/1 -6/23 -1/1 0/1 -7/27 1/0 -1/4 0/1 -5/21 2/5 -4/17 1/2 3/5 -7/30 1/2 -3/13 1/1 -11/48 5/4 -8/35 1/1 5/3 -5/22 1/0 -7/31 1/0 -9/40 1/0 -2/9 -1/1 0/1 -9/41 0/1 -7/32 0/1 -12/55 0/1 1/3 -5/23 1/1 -3/14 -1/2 -13/61 0/1 -10/47 -1/1 -2/3 -7/33 -1/3 -4/19 0/1 -9/43 1/5 -5/24 1/4 -1/5 0/1 -4/21 4/5 1/1 -3/16 3/2 -11/59 2/1 -8/43 2/1 -5/27 3/1 -2/11 -1/1 1/1 -5/28 -1/4 -8/45 0/1 1/9 -3/17 1/3 -7/40 2/3 -4/23 1/1 4/3 -1/6 0/1 -3/19 2/1 -2/13 0/1 1/3 -5/33 0/1 -3/20 1/4 -4/27 1/3 2/5 -5/34 1/2 -1/7 1/1 -3/22 1/0 -2/15 1/2 1/1 -3/23 0/1 -1/8 1/0 -2/17 0/1 -3/26 1/4 -1/9 0/1 -1/10 0/1 0/1 0/1 1/1 1/9 1/1 1/8 0/1 3/23 -1/1 2/15 0/1 1/3 3/22 0/1 1/7 0/1 2/13 0/1 3/19 1/3 1/6 1/2 3/17 0/1 8/45 2/7 1/3 5/28 0/1 7/39 3/7 2/11 1/1 1/0 5/27 0/1 3/16 1/2 1/5 1/1 4/19 -2/1 -1/1 3/14 -1/2 8/37 0/1 5/23 0/1 7/32 0/1 2/9 -1/1 0/1 5/22 0/1 8/35 1/3 2/5 3/13 2/3 7/30 7/6 11/47 5/3 4/17 1/1 3/1 5/21 -1/1 1/4 0/1 5/19 1/2 9/34 1/2 4/15 4/5 1/1 3/11 -1/1 5/18 1/6 12/43 0/1 19/68 0/1 7/25 0/1 9/32 1/4 2/7 1/3 1/1 7/24 1/2 5/17 3/5 13/44 2/3 21/71 2/3 8/27 2/3 11/37 2/3 14/47 2/3 1/1 3/10 3/4 7/23 1/1 11/36 11/10 4/13 1/1 4/3 9/29 1/1 14/45 1/1 2/1 5/16 2/1 1/3 0/1 6/17 -1/3 0/1 11/31 -1/1 5/14 -1/2 4/11 0/1 7/19 1/5 17/46 0/1 10/27 2/7 1/3 13/35 0/1 16/43 0/1 1/3 3/8 1/4 8/21 1/2 1/1 21/55 2/3 13/34 1/2 5/13 1/1 17/44 1/0 29/75 -4/1 12/31 -1/1 0/1 7/18 0/1 16/41 -1/1 1/1 25/64 1/0 9/23 0/1 11/28 0/1 13/33 -1/1 2/5 0/1 1/3 13/32 1/2 11/27 3/5 9/22 1/2 7/17 1/2 19/46 4/7 12/29 3/5 8/13 17/41 7/11 22/53 2/3 5/12 1/2 18/43 2/3 1/1 13/31 2/3 21/50 5/8 29/69 5/7 8/19 5/7 1/1 3/7 1/1 10/23 1/1 7/5 7/16 1/0 18/41 1/1 2/1 11/25 2/1 4/9 3/1 1/0 5/11 -2/1 11/24 0/1 17/37 -1/1 6/13 -1/1 0/1 7/15 1/1 1/2 0/1 9/17 1/1 8/15 1/3 2/5 15/28 1/4 7/13 1/2 6/11 0/1 1/3 5/9 3/5 19/34 7/10 14/25 5/7 1/1 9/16 2/3 22/39 2/3 1/1 13/23 2/3 4/7 4/5 1/1 11/19 1/1 18/31 1/1 18/17 7/12 7/6 10/17 1/1 7/5 33/56 3/2 23/39 11/7 13/22 2/1 16/27 5/3 2/1 3/5 2/1 14/23 -2/1 -1/1 25/41 1/1 11/18 1/0 19/31 -1/1 46/75 -1/1 0/1 73/119 0/1 27/44 -1/2 8/13 -1/1 1/1 21/34 2/1 55/89 1/0 34/55 1/1 1/0 81/131 2/1 47/76 2/1 13/21 3/1 5/8 1/0 12/19 -1/1 1/0 19/30 -5/2 7/11 -1/1 23/36 -1/2 39/61 0/1 16/25 -1/1 -2/3 25/39 0/1 34/53 -3/7 -1/3 9/14 -1/4 20/31 -1/1 1/1 11/17 0/1 2/3 0/1 13/19 0/1 11/16 0/1 20/29 -1/1 0/1 9/13 1/5 25/36 1/4 41/59 2/7 16/23 3/11 1/3 39/56 2/7 23/33 4/13 7/10 3/8 12/17 3/7 1/2 17/24 1/2 5/7 1/2 18/25 0/1 1/1 31/43 3/7 13/18 1/2 34/47 5/9 3/5 21/29 3/5 50/69 3/5 2/3 29/40 2/3 8/11 2/3 1/1 11/15 3/5 25/34 1/2 14/19 3/5 1/1 17/23 2/3 3/4 3/4 13/17 1/1 23/30 23/22 10/13 1/1 10/9 47/61 8/7 37/48 8/7 27/35 13/11 44/57 1/1 8/7 17/22 6/5 7/9 4/3 25/32 2/1 43/55 5/3 18/23 1/1 2/1 11/14 2/1 26/33 1/1 2/1 67/85 2/1 41/52 2/1 15/19 1/1 19/24 5/2 4/5 1/1 3/1 17/21 5/1 13/16 1/0 9/11 1/0 14/17 -3/1 1/0 5/6 -3/2 16/19 -1/2 11/13 0/1 28/33 -1/1 0/1 17/20 -1/2 6/7 -1/2 -1/3 19/22 -1/4 13/15 0/1 7/8 0/1 15/17 0/1 8/9 0/1 1/5 1/1 1/1 10/9 -2/1 -1/1 9/8 -1/2 8/7 0/1 23/20 1/10 15/13 0/1 7/6 1/4 20/17 2/5 3/7 13/11 0/1 32/27 0/1 1/3 19/16 0/1 6/5 1/3 2/5 11/9 1/2 27/22 13/24 16/13 1/2 5/9 37/30 1/2 21/17 3/5 5/4 2/3 29/23 2/3 24/19 3/5 2/3 67/53 2/3 43/34 11/16 19/15 5/7 52/41 5/7 1/1 33/26 3/4 14/11 3/4 51/40 3/4 37/29 7/9 23/18 3/4 32/25 9/11 1/1 9/7 4/5 31/24 6/7 22/17 15/17 1/1 35/27 17/19 13/10 13/14 17/13 1/1 21/16 21/20 4/3 1/1 4/3 19/14 2/1 53/39 2/1 87/64 1/0 121/89 1/1 34/25 1/1 2/1 49/36 2/1 15/11 1/1 26/19 2/1 11/8 1/0 51/37 2/1 40/29 7/3 3/1 69/50 5/2 29/21 3/1 76/55 11/3 4/1 47/34 4/1 18/13 1/1 1/0 43/31 3/1 25/18 5/2 7/5 1/0 24/17 -1/1 0/1 41/29 1/1 17/12 1/0 44/31 1/0 71/50 1/0 27/19 -5/1 10/7 -2/1 -1/1 33/23 -2/3 56/39 -1/2 23/16 0/1 82/57 -1/1 -2/3 59/41 0/1 36/25 -1/1 0/1 49/34 1/0 13/9 -1/1 16/11 -1/1 1/1 3/2 0/1 20/13 1/3 1/1 37/24 1/2 17/11 0/1 31/20 0/1 14/9 0/1 1/5 53/34 2/5 39/25 0/1 25/16 1/4 61/39 0/1 97/62 0/1 36/23 0/1 1/3 47/30 1/2 11/7 1/3 30/19 2/5 3/7 49/31 1/2 19/12 1/2 65/41 7/15 46/29 1/2 27/17 4/7 8/5 1/3 1/2 37/23 1/2 66/41 1/2 17/33 29/18 1/2 21/13 3/5 55/34 1/2 34/21 1/2 47/29 4/7 13/8 2/3 57/35 2/3 44/27 2/3 5/7 31/19 1/1 49/30 1/2 18/11 1/3 1/2 23/14 5/8 74/45 3/5 2/3 51/31 3/5 28/17 2/3 5/3 2/3 22/13 4/5 83/49 4/5 61/36 31/38 39/23 19/23 95/56 5/6 151/89 5/6 56/33 5/6 51/61 17/10 6/7 46/27 19/22 13/15 75/44 7/8 29/17 15/17 12/7 12/13 1/1 19/11 1/1 26/15 1/1 26/25 7/4 7/6 30/17 7/5 3/2 23/13 4/3 62/35 10/7 13/9 39/22 3/2 55/31 1/1 16/9 3/2 57/32 3/2 98/55 17/11 11/7 41/23 8/5 25/14 2/1 59/33 2/1 34/19 9/5 2/1 77/43 2/1 43/24 9/4 9/5 1/1 38/21 1/1 2/1 29/16 2/1 49/27 2/1 20/11 3/1 1/0 11/6 3/2 24/13 0/1 1/1 37/20 2/1 13/7 1/0 28/15 -1/1 0/1 15/8 1/2 17/9 1/1 2/1 -1/1 1/1 17/8 0/1 15/7 1/1 28/13 -1/1 0/1 41/19 0/1 13/6 1/2 37/17 1/3 61/28 1/2 24/11 1/2 11/5 0/1 42/19 0/1 1/1 31/14 0/1 51/23 1/3 20/9 1/2 1/1 9/4 1/2 34/15 4/5 1/1 25/11 2/3 66/29 3/4 41/18 3/4 57/25 11/15 73/32 3/4 16/7 7/9 4/5 7/3 1/1 26/11 17/15 8/7 45/19 8/7 64/27 57/49 7/6 83/35 41/35 19/8 6/5 69/29 13/11 119/50 43/36 50/21 6/5 23/19 31/13 16/13 74/31 5/4 117/49 49/39 43/18 5/4 55/23 9/7 12/5 1/1 4/3 41/17 15/11 70/29 1/1 7/5 99/41 4/3 29/12 11/8 46/19 3/2 63/26 3/2 17/7 3/2 39/16 2/1 61/25 5/3 22/9 1/1 3/2 5/2 3/2 43/17 2/1 38/15 2/1 15/7 33/13 7/3 28/11 1/1 3/1 51/20 3/2 23/9 2/1 87/34 5/2 151/59 3/1 64/25 3/1 1/0 105/41 1/1 41/16 2/1 59/23 3/1 18/7 2/1 49/19 4/1 80/31 1/1 3/1 31/12 5/2 44/17 2/1 3/1 101/39 2/1 57/22 1/0 13/5 3/1 34/13 3/1 1/0 55/21 8/1 131/50 1/0 76/29 1/0 21/8 1/0 50/19 3/1 5/1 29/11 1/0 8/3 1/1 2/1 51/19 3/1 43/16 1/0 78/29 1/2 1/1 35/13 2/1 62/23 2/1 89/33 13/5 27/10 7/2 46/17 3/1 5/1 65/24 1/0 19/7 3/1 11/4 1/0 25/9 -3/1 14/5 -2/1 -1/1 59/21 0/1 45/16 1/0 31/11 -1/1 17/6 1/2 20/7 1/1 3/1 43/15 7/1 66/23 21/1 1/0 89/31 1/0 23/8 1/0 26/9 1/0 3/1 0/1 25/8 2/5 22/7 1/2 7/13 41/13 3/5 19/6 2/3 16/5 5/7 1/1 61/19 2/3 45/14 3/4 29/9 7/9 13/4 7/8 23/7 1/1 33/10 21/20 10/3 1/1 7/6 57/17 21/17 47/14 5/4 37/11 4/3 64/19 1/1 2/1 27/8 4/3 71/21 4/3 186/55 4/3 7/5 301/89 7/5 115/34 3/2 44/13 1/1 7/5 61/18 5/4 139/41 4/3 78/23 4/3 7/5 17/5 1/1 75/22 3/2 58/17 4/3 41/12 3/2 24/7 7/5 3/2 31/9 3/2 7/2 2/1 39/11 1/1 32/9 5/3 2/1 57/16 7/4 25/7 2/1 118/33 1/1 1/0 211/59 1/1 93/26 3/2 68/19 1/1 5/3 43/12 2/1 18/5 9/5 2/1 47/13 2/1 76/21 2/1 43/21 29/8 17/8 11/3 3/1 59/16 2/1 48/13 2/1 3/1 85/23 2/1 37/10 1/0 63/17 2/1 26/7 7/3 3/1 15/4 7/2 79/21 4/1 64/17 3/1 5/1 49/13 11/3 34/9 4/1 5/1 19/5 1/0 23/6 1/0 4/1 1/0 25/6 1/0 46/11 -3/1 -1/1 21/5 -1/1 17/4 -2/1 81/19 -2/1 64/15 -4/3 -1/1 47/11 -5/3 77/18 -4/3 30/7 -6/5 -1/1 13/3 0/1 61/14 0/1 48/11 -1/1 0/1 35/8 1/0 22/5 -1/1 -1/3 31/7 -1/3 40/9 -1/9 0/1 49/11 0/1 58/13 0/1 1/13 9/2 1/2 50/11 0/1 1/1 41/9 1/1 32/7 -1/1 1/1 55/12 1/2 23/5 0/1 60/13 -1/3 -1/4 37/8 0/1 51/11 1/7 14/3 0/1 1/3 33/7 1/2 52/11 1/3 1/1 19/4 1/0 24/5 3/7 1/2 5/1 1/1 26/5 13/9 3/2 47/9 8/5 21/4 2/1 16/3 1/1 2/1 43/8 2/1 27/5 2/1 38/7 2/1 11/2 1/0 50/9 1/1 2/1 39/7 1/1 28/5 1/1 5/3 45/8 7/4 17/3 2/1 40/7 9/4 7/3 23/4 2/1 6/1 3/1 4/1 25/4 1/0 19/3 7/1 13/2 1/0 33/5 -11/1 53/8 1/0 20/3 -6/1 -5/1 7/1 -2/1 22/3 0/1 15/2 -1/2 53/7 0/1 38/5 0/1 1/5 23/3 1/1 8/1 -1/1 1/1 17/2 1/2 9/1 1/1 10/1 2/1 3/1 11/1 2/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(1253,592,908,429) (-1/2,-8/17) -> (40/29,69/50) Hyperbolic Matrix(2033,952,788,369) (-8/17,-7/15) -> (49/19,80/31) Hyperbolic Matrix(339,158,-1238,-577) (-7/15,-13/28) -> (-17/62,-3/11) Hyperbolic Matrix(225,104,556,257) (-13/28,-6/13) -> (2/5,13/32) Hyperbolic Matrix(335,154,1886,867) (-6/13,-17/37) -> (3/17,8/45) Hyperbolic Matrix(2881,1322,778,357) (-17/37,-11/24) -> (37/10,63/17) Hyperbolic Matrix(2763,1264,776,355) (-11/24,-16/35) -> (32/9,57/16) Hyperbolic Matrix(661,302,1438,657) (-16/35,-5/11) -> (17/37,6/13) Hyperbolic Matrix(1975,894,-5154,-2333) (-5/11,-19/42) -> (-23/60,-41/107) Hyperbolic Matrix(1641,742,878,397) (-19/42,-14/31) -> (28/15,15/8) Hyperbolic Matrix(873,394,986,445) (-14/31,-23/51) -> (15/17,8/9) Hyperbolic Matrix(3061,1380,1200,541) (-23/51,-9/20) -> (51/20,23/9) Hyperbolic Matrix(869,390,2070,929) (-9/20,-13/29) -> (13/31,21/50) Hyperbolic Matrix(1409,630,870,389) (-13/29,-4/9) -> (34/21,47/29) Hyperbolic Matrix(1825,806,754,333) (-4/9,-15/34) -> (29/12,46/19) Hyperbolic Matrix(753,332,-2792,-1231) (-15/34,-11/25) -> (-17/63,-7/26) Hyperbolic Matrix(323,142,-1822,-801) (-11/25,-18/41) -> (-8/45,-3/17) Hyperbolic Matrix(1495,656,964,423) (-18/41,-7/16) -> (31/20,14/9) Hyperbolic Matrix(531,232,428,187) (-7/16,-17/39) -> (21/17,5/4) Hyperbolic Matrix(1593,694,746,325) (-17/39,-27/62) -> (17/8,15/7) Hyperbolic Matrix(6059,2638,7862,3423) (-27/62,-37/85) -> (47/61,37/48) Hyperbolic Matrix(7435,3236,2764,1203) (-37/85,-10/23) -> (78/29,35/13) Hyperbolic Matrix(1059,460,320,139) (-10/23,-13/30) -> (33/10,10/3) Hyperbolic Matrix(739,320,1060,459) (-13/30,-3/7) -> (23/33,7/10) Hyperbolic Matrix(937,398,1462,621) (-3/7,-14/33) -> (16/25,25/39) Hyperbolic Matrix(835,354,-2814,-1193) (-14/33,-11/26) -> (-19/64,-8/27) Hyperbolic Matrix(1141,482,-3842,-1623) (-11/26,-19/45) -> (-11/37,-19/64) Hyperbolic Matrix(1763,744,936,395) (-19/45,-27/64) -> (15/8,17/9) Hyperbolic Matrix(10375,4376,6124,2583) (-27/64,-35/83) -> (83/49,61/36) Hyperbolic Matrix(1039,438,102,43) (-35/83,-8/19) -> (10/1,11/1) Hyperbolic Matrix(1139,478,722,303) (-8/19,-13/31) -> (11/7,30/19) Hyperbolic Matrix(2271,952,1448,607) (-13/31,-31/74) -> (47/30,11/7) Hyperbolic Matrix(2273,952,308,129) (-31/74,-18/43) -> (22/3,15/2) Hyperbolic Matrix(1343,562,4538,1899) (-18/43,-23/55) -> (21/71,8/27) Hyperbolic Matrix(3301,1380,720,301) (-23/55,-5/12) -> (55/12,23/5) Hyperbolic Matrix(2153,894,1746,725) (-5/12,-22/53) -> (16/13,37/30) Hyperbolic Matrix(4309,1788,6972,2893) (-22/53,-17/41) -> (55/89,34/55) Hyperbolic Matrix(1945,806,514,213) (-17/41,-12/29) -> (34/9,19/5) Hyperbolic Matrix(513,212,2248,929) (-12/29,-19/46) -> (5/22,8/35) Hyperbolic Matrix(713,294,-1734,-715) (-19/46,-7/17) -> (-7/17,-23/56) Parabolic Matrix(2851,1170,1830,751) (-23/56,-16/39) -> (14/9,53/34) Hyperbolic Matrix(713,292,608,249) (-16/39,-9/22) -> (7/6,20/17) Hyperbolic Matrix(813,332,2128,869) (-9/22,-11/27) -> (21/55,13/34) Hyperbolic Matrix(909,370,710,289) (-11/27,-2/5) -> (32/25,9/7) Hyperbolic Matrix(1881,742,398,157) (-2/5,-13/33) -> (33/7,52/11) Hyperbolic Matrix(691,272,1288,507) (-13/33,-11/28) -> (15/28,7/13) Hyperbolic Matrix(1779,698,1282,503) (-11/28,-9/23) -> (43/31,25/18) Hyperbolic Matrix(1085,424,2756,1077) (-9/23,-25/64) -> (11/28,13/33) Hyperbolic Matrix(4527,1768,3152,1231) (-25/64,-16/41) -> (56/39,23/16) Hyperbolic Matrix(493,192,588,229) (-16/41,-7/18) -> (5/6,16/19) Hyperbolic Matrix(685,266,394,153) (-7/18,-12/31) -> (26/15,7/4) Hyperbolic Matrix(393,152,-2252,-871) (-12/31,-17/44) -> (-7/40,-4/23) Hyperbolic Matrix(5571,2152,2348,907) (-17/44,-39/101) -> (83/35,19/8) Hyperbolic Matrix(11335,4376,4204,1623) (-39/101,-22/57) -> (62/23,89/33) Hyperbolic Matrix(685,264,96,37) (-22/57,-5/13) -> (7/1,22/3) Hyperbolic Matrix(99,38,-878,-337) (-5/13,-23/60) -> (-3/26,-1/9) Hyperbolic Matrix(4281,1640,1360,521) (-41/107,-18/47) -> (22/7,41/13) Hyperbolic Matrix(2821,1080,2040,781) (-18/47,-13/34) -> (47/34,18/13) Hyperbolic Matrix(1649,630,390,149) (-13/34,-21/55) -> (21/5,17/4) Hyperbolic Matrix(1263,482,-4562,-1741) (-21/55,-8/21) -> (-18/65,-13/47) Hyperbolic Matrix(1259,478,482,183) (-8/21,-11/29) -> (13/5,34/13) Hyperbolic Matrix(581,220,1640,621) (-11/29,-14/37) -> (6/17,11/31) Hyperbolic Matrix(1735,656,484,183) (-14/37,-3/8) -> (43/12,18/5) Hyperbolic Matrix(2393,892,668,249) (-3/8,-16/43) -> (68/19,43/12) Hyperbolic Matrix(1527,568,3632,1351) (-16/43,-13/35) -> (29/69,8/19) Hyperbolic Matrix(383,142,1238,459) (-13/35,-10/27) -> (4/13,9/29) Hyperbolic Matrix(477,176,664,245) (-10/27,-7/19) -> (5/7,18/25) Hyperbolic Matrix(473,174,666,245) (-7/19,-11/30) -> (17/24,5/7) Hyperbolic Matrix(475,174,-2274,-833) (-11/30,-15/41) -> (-9/43,-5/24) Hyperbolic Matrix(2461,900,3120,1141) (-15/41,-19/52) -> (41/52,15/19) Hyperbolic Matrix(471,172,2648,967) (-19/52,-4/11) -> (8/45,5/28) Hyperbolic Matrix(375,136,284,103) (-4/11,-13/36) -> (21/16,4/3) Hyperbolic Matrix(283,102,1218,439) (-13/36,-9/25) -> (3/13,7/30) Hyperbolic Matrix(1029,370,470,169) (-9/25,-14/39) -> (24/11,11/5) Hyperbolic Matrix(2993,1074,1686,605) (-14/39,-19/53) -> (55/31,16/9) Hyperbolic Matrix(95,34,746,267) (-19/53,-5/14) -> (1/8,3/23) Hyperbolic Matrix(651,232,188,67) (-5/14,-11/31) -> (31/9,7/2) Hyperbolic Matrix(1763,624,1116,395) (-11/31,-6/17) -> (30/19,49/31) Hyperbolic Matrix(833,292,368,129) (-6/17,-7/20) -> (9/4,34/15) Hyperbolic Matrix(1013,354,186,65) (-7/20,-8/23) -> (38/7,11/2) Hyperbolic Matrix(457,158,1102,381) (-8/23,-1/3) -> (17/41,22/53) Hyperbolic Matrix(1233,394,266,85) (-1/3,-7/22) -> (37/8,51/11) Hyperbolic Matrix(2023,642,438,139) (-7/22,-6/19) -> (60/13,37/8) Hyperbolic Matrix(613,192,348,109) (-6/19,-5/16) -> (7/4,30/17) Hyperbolic Matrix(959,298,782,243) (-5/16,-9/29) -> (11/9,27/22) Hyperbolic Matrix(1827,566,694,215) (-9/29,-4/13) -> (50/19,29/11) Hyperbolic Matrix(691,212,88,27) (-4/13,-15/49) -> (23/3,8/1) Hyperbolic Matrix(2941,900,2160,661) (-15/49,-11/36) -> (49/36,15/11) Hyperbolic Matrix(433,132,948,289) (-11/36,-7/23) -> (5/11,11/24) Hyperbolic Matrix(1119,340,260,79) (-7/23,-10/33) -> (30/7,13/3) Hyperbolic Matrix(859,260,1120,339) (-10/33,-3/10) -> (23/30,10/13) Hyperbolic Matrix(2395,714,426,127) (-3/10,-14/47) -> (28/5,45/8) Hyperbolic Matrix(2817,838,2222,661) (-14/47,-11/37) -> (19/15,52/41) Hyperbolic Matrix(597,176,424,125) (-8/27,-5/17) -> (7/5,24/17) Hyperbolic Matrix(593,174,426,125) (-5/17,-7/24) -> (25/18,7/5) Hyperbolic Matrix(1099,320,340,99) (-7/24,-9/31) -> (29/9,13/4) Hyperbolic Matrix(3211,930,1350,391) (-9/31,-11/38) -> (19/8,69/29) Hyperbolic Matrix(589,170,2110,609) (-11/38,-2/7) -> (12/43,19/68) Hyperbolic Matrix(419,118,1502,423) (-2/7,-9/32) -> (5/18,12/43) Hyperbolic Matrix(1417,398,502,141) (-9/32,-7/25) -> (31/11,17/6) Hyperbolic Matrix(415,116,1084,303) (-7/25,-5/18) -> (13/34,5/13) Hyperbolic Matrix(3073,852,1908,529) (-5/18,-18/65) -> (66/41,29/18) Hyperbolic Matrix(333,92,1408,389) (-13/47,-8/29) -> (4/17,5/21) Hyperbolic Matrix(1737,478,2402,661) (-8/29,-11/40) -> (13/18,34/47) Hyperbolic Matrix(415,114,-2814,-773) (-11/40,-14/51) -> (-4/27,-5/34) Hyperbolic Matrix(4715,1294,2066,567) (-14/51,-17/62) -> (73/32,16/7) Hyperbolic Matrix(81,22,578,157) (-3/11,-13/48) -> (3/22,1/7) Hyperbolic Matrix(8801,2382,2058,557) (-13/48,-23/85) -> (47/11,77/18) Hyperbolic Matrix(3291,890,1150,311) (-23/85,-10/37) -> (20/7,43/15) Hyperbolic Matrix(3207,866,574,155) (-10/37,-17/63) -> (39/7,28/5) Hyperbolic Matrix(573,154,986,265) (-7/26,-4/15) -> (18/31,7/12) Hyperbolic Matrix(489,130,410,109) (-4/15,-9/34) -> (19/16,6/5) Hyperbolic Matrix(2611,690,3750,991) (-9/34,-14/53) -> (16/23,39/56) Hyperbolic Matrix(2281,602,898,237) (-14/53,-5/19) -> (33/13,28/11) Hyperbolic Matrix(1055,276,1464,383) (-5/19,-6/23) -> (18/25,31/43) Hyperbolic Matrix(1055,274,566,147) (-6/23,-7/27) -> (13/7,28/15) Hyperbolic Matrix(1051,272,568,147) (-7/27,-1/4) -> (37/20,13/7) Hyperbolic Matrix(553,132,708,169) (-1/4,-5/21) -> (7/9,25/32) Hyperbolic Matrix(1649,390,630,149) (-5/21,-4/17) -> (34/13,55/21) Hyperbolic Matrix(469,110,550,129) (-4/17,-7/30) -> (17/20,6/7) Hyperbolic Matrix(233,54,-1014,-235) (-7/30,-3/13) -> (-3/13,-11/48) Parabolic Matrix(1947,446,3034,695) (-11/48,-8/35) -> (34/53,9/14) Hyperbolic Matrix(1709,390,390,89) (-8/35,-5/22) -> (35/8,22/5) Hyperbolic Matrix(389,88,1472,333) (-5/22,-7/31) -> (5/19,9/34) Hyperbolic Matrix(2633,594,1086,245) (-7/31,-9/40) -> (63/26,17/7) Hyperbolic Matrix(465,104,76,17) (-9/40,-2/9) -> (6/1,25/4) Hyperbolic Matrix(1925,424,1076,237) (-2/9,-9/41) -> (59/33,34/19) Hyperbolic Matrix(3379,740,1000,219) (-9/41,-7/32) -> (27/8,71/21) Hyperbolic Matrix(229,50,1690,369) (-7/32,-12/55) -> (2/15,3/22) Hyperbolic Matrix(3301,720,1380,301) (-12/55,-5/23) -> (55/23,12/5) Hyperbolic Matrix(535,116,844,183) (-5/23,-3/14) -> (19/30,7/11) Hyperbolic Matrix(2669,570,4350,929) (-3/14,-13/61) -> (73/119,27/44) Hyperbolic Matrix(2819,600,3660,779) (-13/61,-10/47) -> (10/13,47/61) Hyperbolic Matrix(687,146,1294,275) (-10/47,-7/33) -> (9/17,8/15) Hyperbolic Matrix(303,64,-1444,-305) (-7/33,-4/19) -> (-4/19,-9/43) Parabolic Matrix(1061,220,680,141) (-5/24,-1/5) -> (39/25,25/16) Hyperbolic Matrix(743,142,518,99) (-1/5,-4/21) -> (10/7,33/23) Hyperbolic Matrix(295,56,964,183) (-4/21,-3/16) -> (11/36,4/13) Hyperbolic Matrix(3543,662,958,179) (-3/16,-11/59) -> (85/23,37/10) Hyperbolic Matrix(4867,906,2874,535) (-11/59,-8/43) -> (22/13,83/49) Hyperbolic Matrix(3023,562,1178,219) (-8/43,-5/27) -> (59/23,18/7) Hyperbolic Matrix(295,54,366,67) (-5/27,-2/11) -> (4/5,17/21) Hyperbolic Matrix(659,118,1022,183) (-2/11,-5/28) -> (9/14,20/31) Hyperbolic Matrix(3433,612,948,169) (-5/28,-8/45) -> (76/21,29/8) Hyperbolic Matrix(365,64,2036,357) (-3/17,-7/40) -> (5/28,7/39) Hyperbolic Matrix(509,88,1232,213) (-4/23,-1/6) -> (19/46,12/29) Hyperbolic Matrix(643,102,498,79) (-1/6,-3/19) -> (9/7,31/24) Hyperbolic Matrix(1353,212,568,89) (-3/19,-2/13) -> (50/21,31/13) Hyperbolic Matrix(2193,334,1346,205) (-2/13,-5/33) -> (57/35,44/27) Hyperbolic Matrix(1059,160,920,139) (-5/33,-3/20) -> (23/20,15/13) Hyperbolic Matrix(565,84,1056,157) (-3/20,-4/27) -> (8/15,15/28) Hyperbolic Matrix(1685,246,774,113) (-5/34,-1/7) -> (37/17,61/28) Hyperbolic Matrix(905,124,416,57) (-1/7,-3/22) -> (13/6,37/17) Hyperbolic Matrix(417,56,484,65) (-3/22,-2/15) -> (6/7,19/22) Hyperbolic Matrix(1175,154,206,27) (-2/15,-3/23) -> (17/3,40/7) Hyperbolic Matrix(1171,152,208,27) (-3/23,-1/8) -> (45/8,17/3) Hyperbolic Matrix(1161,140,340,41) (-1/8,-2/17) -> (58/17,41/12) Hyperbolic Matrix(2783,324,816,95) (-2/17,-3/26) -> (75/22,58/17) Hyperbolic Matrix(335,34,266,27) (-1/9,-1/10) -> (5/4,29/23) Hyperbolic Matrix(529,50,730,69) (-1/10,0/1) -> (50/69,29/40) Hyperbolic Matrix(433,-46,706,-75) (0/1,1/9) -> (19/31,46/75) Hyperbolic Matrix(375,-46,106,-13) (1/9,1/8) -> (7/2,39/11) Hyperbolic Matrix(1219,-160,160,-21) (3/23,2/15) -> (38/5,23/3) Hyperbolic Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(1195,-186,726,-113) (2/13,3/19) -> (51/31,28/17) Hyperbolic Matrix(829,-132,672,-107) (3/19,1/6) -> (37/30,21/17) Hyperbolic Matrix(153,-26,206,-35) (1/6,3/17) -> (17/23,3/4) Hyperbolic Matrix(1017,-184,304,-55) (7/39,2/11) -> (10/3,57/17) Hyperbolic Matrix(1873,-346,406,-75) (2/11,5/27) -> (23/5,60/13) Hyperbolic Matrix(1113,-208,808,-151) (5/27,3/16) -> (11/8,51/37) Hyperbolic Matrix(707,-134,554,-105) (3/16,1/5) -> (37/29,23/18) Hyperbolic Matrix(545,-114,894,-187) (1/5,4/19) -> (14/23,25/41) Hyperbolic Matrix(545,-116,296,-63) (4/19,3/14) -> (11/6,24/13) Hyperbolic Matrix(493,-106,1186,-255) (3/14,8/37) -> (22/53,5/12) Hyperbolic Matrix(1873,-406,346,-75) (8/37,5/23) -> (27/5,38/7) Hyperbolic Matrix(2463,-538,1378,-301) (5/23,7/32) -> (25/14,59/33) Hyperbolic Matrix(2855,-626,2066,-453) (7/32,2/9) -> (76/55,47/34) Hyperbolic Matrix(539,-122,782,-177) (2/9,5/22) -> (11/16,20/29) Hyperbolic Matrix(1171,-268,3028,-693) (8/35,3/13) -> (29/75,12/31) Hyperbolic Matrix(3939,-920,1460,-341) (7/30,11/47) -> (89/33,27/10) Hyperbolic Matrix(3841,-900,1020,-239) (11/47,4/17) -> (64/17,49/13) Hyperbolic Matrix(1063,-256,436,-105) (5/21,1/4) -> (39/16,61/25) Hyperbolic Matrix(809,-212,332,-87) (1/4,5/19) -> (17/7,39/16) Hyperbolic Matrix(475,-126,426,-113) (9/34,4/15) -> (10/9,9/8) Hyperbolic Matrix(567,-152,332,-89) (4/15,3/11) -> (29/17,12/7) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(5581,-1560,7080,-1979) (19/68,7/25) -> (67/85,41/52) Hyperbolic Matrix(891,-250,1030,-289) (7/25,9/32) -> (19/22,13/15) Hyperbolic Matrix(375,-106,46,-13) (9/32,2/7) -> (8/1,17/2) Hyperbolic Matrix(1347,-392,512,-149) (2/7,7/24) -> (21/8,50/19) Hyperbolic Matrix(417,-122,1022,-299) (7/24,5/17) -> (11/27,9/22) Hyperbolic Matrix(2317,-684,2964,-875) (5/17,13/44) -> (25/32,43/55) Hyperbolic Matrix(6901,-2040,11160,-3299) (13/44,21/71) -> (81/131,47/76) Hyperbolic Matrix(3239,-962,1202,-357) (8/27,11/37) -> (35/13,62/23) Hyperbolic Matrix(5133,-1528,8368,-2491) (11/37,14/47) -> (46/75,73/119) Hyperbolic Matrix(1017,-304,184,-55) (14/47,3/10) -> (11/2,50/9) Hyperbolic Matrix(323,-98,1058,-321) (3/10,7/23) -> (7/23,11/36) Parabolic Matrix(4441,-1380,2700,-839) (9/29,14/45) -> (74/45,51/31) Hyperbolic Matrix(4941,-1538,3158,-983) (14/45,5/16) -> (97/62,36/23) Hyperbolic Matrix(731,-230,410,-129) (5/16,1/3) -> (41/23,25/14) Hyperbolic Matrix(843,-296,356,-125) (1/3,6/17) -> (26/11,45/19) Hyperbolic Matrix(1949,-692,752,-267) (11/31,5/14) -> (57/22,13/5) Hyperbolic Matrix(485,-174,354,-127) (5/14,4/11) -> (26/19,11/8) Hyperbolic Matrix(659,-242,482,-177) (4/11,7/19) -> (15/11,26/19) Hyperbolic Matrix(1491,-550,2410,-889) (7/19,17/46) -> (47/76,13/21) Hyperbolic Matrix(2103,-778,1138,-421) (17/46,10/27) -> (24/13,37/20) Hyperbolic Matrix(3239,-1202,962,-357) (10/27,13/35) -> (37/11,64/19) Hyperbolic Matrix(5335,-1984,1444,-537) (13/35,16/43) -> (48/13,85/23) Hyperbolic Matrix(787,-294,174,-65) (16/43,3/8) -> (9/2,50/11) Hyperbolic Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(2129,-812,1172,-447) (8/21,21/55) -> (49/27,20/11) Hyperbolic Matrix(1949,-752,692,-267) (5/13,17/44) -> (45/16,31/11) Hyperbolic Matrix(12245,-4734,4674,-1807) (17/44,29/75) -> (55/21,131/50) Hyperbolic Matrix(691,-268,1168,-453) (12/31,7/18) -> (13/22,16/27) Hyperbolic Matrix(733,-286,346,-135) (7/18,16/41) -> (2/1,17/8) Hyperbolic Matrix(3969,-1550,950,-371) (16/41,25/64) -> (25/6,46/11) Hyperbolic Matrix(5393,-2108,3968,-1551) (25/64,9/23) -> (53/39,87/64) Hyperbolic Matrix(1895,-744,1164,-457) (9/23,11/28) -> (13/8,57/35) Hyperbolic Matrix(1419,-560,560,-221) (13/33,2/5) -> (38/15,33/13) Hyperbolic Matrix(3795,-1544,1664,-677) (13/32,11/27) -> (57/25,73/32) Hyperbolic Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(2887,-1192,4672,-1929) (7/17,19/46) -> (21/34,55/89) Hyperbolic Matrix(2587,-1072,3352,-1389) (12/29,17/41) -> (27/35,44/57) Hyperbolic Matrix(2453,-1026,1566,-655) (5/12,18/43) -> (36/23,47/30) Hyperbolic Matrix(1775,-744,804,-337) (18/43,13/31) -> (11/5,42/19) Hyperbolic Matrix(11661,-4900,4900,-2059) (21/50,29/69) -> (69/29,119/50) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(711,-310,250,-109) (10/23,7/16) -> (17/6,20/7) Hyperbolic Matrix(2585,-1134,1794,-787) (7/16,18/41) -> (36/25,49/34) Hyperbolic Matrix(1333,-586,1126,-495) (18/41,11/25) -> (13/11,32/27) Hyperbolic Matrix(957,-422,542,-239) (11/25,4/9) -> (30/17,23/13) Hyperbolic Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(1687,-774,534,-245) (11/24,17/37) -> (41/13,19/6) Hyperbolic Matrix(615,-286,286,-133) (6/13,7/15) -> (15/7,28/13) Hyperbolic Matrix(733,-346,286,-135) (7/15,1/2) -> (41/16,59/23) Hyperbolic Matrix(907,-474,354,-185) (1/2,9/17) -> (105/41,41/16) Hyperbolic Matrix(545,-296,116,-63) (7/13,6/11) -> (14/3,33/7) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(693,-386,386,-215) (5/9,19/34) -> (43/24,9/5) Hyperbolic Matrix(2463,-1378,538,-301) (19/34,14/25) -> (32/7,55/12) Hyperbolic Matrix(731,-410,230,-129) (14/25,9/16) -> (19/6,16/5) Hyperbolic Matrix(2455,-1384,1804,-1017) (9/16,22/39) -> (34/25,49/36) Hyperbolic Matrix(1073,-606,1266,-715) (22/39,13/23) -> (11/13,28/33) Hyperbolic Matrix(957,-542,422,-239) (13/23,4/7) -> (34/15,25/11) Hyperbolic Matrix(419,-242,722,-417) (4/7,11/19) -> (11/19,18/31) Parabolic Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(6457,-3804,3624,-2135) (10/17,33/56) -> (57/32,98/55) Hyperbolic Matrix(5889,-3472,3472,-2047) (33/56,23/39) -> (39/23,95/56) Hyperbolic Matrix(2037,-1202,2642,-1559) (23/39,13/22) -> (37/48,27/35) Hyperbolic Matrix(903,-536,716,-425) (16/27,3/5) -> (29/23,24/19) Hyperbolic Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(2757,-1682,2162,-1319) (25/41,11/18) -> (51/40,37/29) Hyperbolic Matrix(1265,-774,894,-547) (11/18,19/31) -> (41/29,17/12) Hyperbolic Matrix(1895,-1164,744,-457) (27/44,8/13) -> (28/11,51/20) Hyperbolic Matrix(1151,-710,890,-549) (8/13,21/34) -> (31/24,22/17) Hyperbolic Matrix(16833,-10408,4708,-2911) (34/55,81/131) -> (25/7,118/33) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(993,-628,808,-511) (12/19,19/30) -> (27/22,16/13) Hyperbolic Matrix(2453,-1566,1026,-655) (7/11,23/36) -> (43/18,55/23) Hyperbolic Matrix(4941,-3158,1538,-983) (23/36,39/61) -> (61/19,45/14) Hyperbolic Matrix(6477,-4142,4502,-2879) (39/61,16/25) -> (82/57,59/41) Hyperbolic Matrix(5995,-3844,3364,-2157) (25/39,34/53) -> (98/55,41/23) Hyperbolic Matrix(2261,-1460,1640,-1059) (20/31,11/17) -> (51/37,40/29) Hyperbolic Matrix(73,-48,108,-71) (11/17,2/3) -> (2/3,13/19) Parabolic Matrix(1209,-830,890,-611) (13/19,11/16) -> (19/14,53/39) Hyperbolic Matrix(1419,-980,320,-221) (20/29,9/13) -> (31/7,40/9) Hyperbolic Matrix(2585,-1794,1134,-787) (9/13,25/36) -> (41/18,57/25) Hyperbolic Matrix(4779,-3320,1700,-1181) (25/36,41/59) -> (59/21,45/16) Hyperbolic Matrix(6407,-4454,2654,-1845) (41/59,16/23) -> (70/29,99/41) Hyperbolic Matrix(3325,-2316,636,-443) (39/56,23/33) -> (47/9,21/4) Hyperbolic Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(1987,-1434,1254,-905) (31/43,13/18) -> (19/12,65/41) Hyperbolic Matrix(2855,-2066,626,-453) (34/47,21/29) -> (41/9,32/7) Hyperbolic Matrix(4279,-3100,940,-681) (21/29,50/69) -> (50/11,41/9) Hyperbolic Matrix(1113,-808,208,-151) (29/40,8/11) -> (16/3,43/8) Hyperbolic Matrix(485,-354,174,-127) (8/11,11/15) -> (25/9,14/5) Hyperbolic Matrix(2455,-1804,1384,-1017) (11/15,25/34) -> (39/22,55/31) Hyperbolic Matrix(1383,-1018,898,-661) (25/34,14/19) -> (20/13,37/24) Hyperbolic Matrix(1795,-1324,484,-357) (14/19,17/23) -> (63/17,26/7) Hyperbolic Matrix(443,-338,578,-441) (3/4,13/17) -> (13/17,23/30) Parabolic Matrix(3115,-2406,2166,-1673) (44/57,17/22) -> (23/16,82/57) Hyperbolic Matrix(1151,-890,710,-549) (17/22,7/9) -> (47/29,13/8) Hyperbolic Matrix(4681,-3660,1380,-1079) (43/55,18/23) -> (78/23,17/5) Hyperbolic Matrix(707,-554,134,-105) (18/23,11/14) -> (21/4,16/3) Hyperbolic Matrix(1075,-846,906,-713) (11/14,26/33) -> (32/27,19/16) Hyperbolic Matrix(18153,-14308,5368,-4231) (26/33,67/85) -> (71/21,186/55) Hyperbolic Matrix(1273,-1006,1006,-795) (15/19,19/24) -> (43/34,19/15) Hyperbolic Matrix(2075,-1644,804,-637) (19/24,4/5) -> (80/31,31/12) Hyperbolic Matrix(829,-672,132,-107) (17/21,13/16) -> (25/4,19/3) Hyperbolic Matrix(993,-808,628,-511) (13/16,9/11) -> (49/31,19/12) Hyperbolic Matrix(791,-650,230,-189) (9/11,14/17) -> (24/7,31/9) Hyperbolic Matrix(1333,-1126,586,-495) (16/19,11/13) -> (25/11,66/29) Hyperbolic Matrix(2239,-1902,1362,-1157) (28/33,17/20) -> (23/14,74/45) Hyperbolic Matrix(225,-196,256,-223) (13/15,7/8) -> (7/8,15/17) Parabolic Matrix(475,-426,126,-113) (8/9,1/1) -> (49/13,34/9) Hyperbolic Matrix(487,-534,114,-125) (1/1,10/9) -> (64/15,47/11) Hyperbolic Matrix(225,-256,196,-223) (9/8,8/7) -> (8/7,23/20) Parabolic Matrix(891,-1030,250,-289) (15/13,7/6) -> (57/16,25/7) Hyperbolic Matrix(1073,-1266,606,-715) (20/17,13/11) -> (23/13,62/35) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(3021,-3818,398,-503) (24/19,67/53) -> (53/7,38/5) Hyperbolic Matrix(2597,-3284,344,-435) (67/53,43/34) -> (15/2,53/7) Hyperbolic Matrix(5581,-7080,1560,-1979) (52/41,33/26) -> (93/26,68/19) Hyperbolic Matrix(2167,-2752,952,-1209) (33/26,14/11) -> (66/29,41/18) Hyperbolic Matrix(1293,-1648,448,-571) (14/11,51/40) -> (23/8,26/9) Hyperbolic Matrix(2317,-2964,684,-875) (23/18,32/25) -> (44/13,61/18) Hyperbolic Matrix(2587,-3352,1072,-1389) (22/17,35/27) -> (41/17,70/29) Hyperbolic Matrix(2037,-2642,1202,-1559) (35/27,13/10) -> (61/36,39/23) Hyperbolic Matrix(443,-578,338,-441) (13/10,17/13) -> (17/13,21/16) Parabolic Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(29499,-40102,8722,-11857) (87/64,121/89) -> (301/89,115/34) Hyperbolic Matrix(24079,-32740,7120,-9681) (121/89,34/25) -> (186/55,301/89) Hyperbolic Matrix(3453,-4766,1286,-1775) (69/50,29/21) -> (51/19,43/16) Hyperbolic Matrix(2973,-4108,1108,-1531) (29/21,76/55) -> (8/3,51/19) Hyperbolic Matrix(1283,-1778,578,-801) (18/13,43/31) -> (51/23,20/9) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(1563,-2216,596,-845) (17/12,44/31) -> (76/29,21/8) Hyperbolic Matrix(7861,-11160,3000,-4259) (44/31,71/50) -> (131/50,76/29) Hyperbolic Matrix(3743,-5316,1116,-1585) (71/50,27/19) -> (57/17,47/14) Hyperbolic Matrix(715,-1026,246,-353) (33/23,56/39) -> (26/9,3/1) Hyperbolic Matrix(4329,-6232,1672,-2407) (59/41,36/25) -> (44/17,101/39) Hyperbolic Matrix(1253,-1808,368,-531) (49/34,13/9) -> (17/5,75/22) Hyperbolic Matrix(539,-782,122,-177) (13/9,16/11) -> (22/5,31/7) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(1509,-2330,590,-911) (37/24,17/11) -> (23/9,87/34) Hyperbolic Matrix(1013,-1568,188,-291) (17/11,31/20) -> (43/8,27/5) Hyperbolic Matrix(727,-1134,234,-365) (53/34,39/25) -> (3/1,25/8) Hyperbolic Matrix(2715,-4244,1124,-1757) (25/16,61/39) -> (99/41,29/12) Hyperbolic Matrix(5685,-8894,1334,-2087) (61/39,97/62) -> (17/4,81/19) Hyperbolic Matrix(6427,-10192,2692,-4269) (65/41,46/29) -> (74/31,117/49) Hyperbolic Matrix(2157,-3424,904,-1435) (46/29,27/17) -> (31/13,74/31) Hyperbolic Matrix(1703,-2738,1058,-1701) (8/5,37/23) -> (37/23,66/41) Parabolic Matrix(1491,-2410,550,-889) (21/13,55/34) -> (65/24,19/7) Hyperbolic Matrix(2887,-4672,1192,-1929) (55/34,34/21) -> (46/19,63/26) Hyperbolic Matrix(433,-706,46,-75) (44/27,31/19) -> (9/1,10/1) Hyperbolic Matrix(593,-968,68,-111) (31/19,49/30) -> (17/2,9/1) Hyperbolic Matrix(545,-894,114,-187) (18/11,23/14) -> (19/4,24/5) Hyperbolic Matrix(691,-1168,268,-453) (5/3,22/13) -> (18/7,49/19) Hyperbolic Matrix(7031,-11928,2448,-4153) (95/56,151/89) -> (89/31,23/8) Hyperbolic Matrix(8811,-14950,3070,-5209) (151/89,56/33) -> (66/23,89/31) Hyperbolic Matrix(1045,-1774,334,-567) (56/33,17/10) -> (25/8,22/7) Hyperbolic Matrix(1021,-1738,178,-303) (17/10,46/27) -> (40/7,23/4) Hyperbolic Matrix(4593,-7828,1708,-2911) (46/27,75/44) -> (43/16,78/29) Hyperbolic Matrix(5879,-10022,2462,-4197) (75/44,29/17) -> (117/49,43/18) Hyperbolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(2295,-4066,346,-613) (62/35,39/22) -> (53/8,20/3) Hyperbolic Matrix(1317,-2344,604,-1075) (16/9,57/32) -> (61/28,24/11) Hyperbolic Matrix(2451,-4388,968,-1733) (34/19,77/43) -> (43/17,38/15) Hyperbolic Matrix(1247,-2234,494,-885) (77/43,43/24) -> (5/2,43/17) Hyperbolic Matrix(1069,-1932,192,-347) (9/5,38/21) -> (50/9,39/7) Hyperbolic Matrix(2049,-3710,470,-851) (38/21,29/16) -> (61/14,48/11) Hyperbolic Matrix(1855,-3366,426,-773) (29/16,49/27) -> (13/3,61/14) Hyperbolic Matrix(435,-824,104,-197) (17/9,2/1) -> (46/11,21/5) Hyperbolic Matrix(3289,-7090,970,-2091) (28/13,41/19) -> (139/41,78/23) Hyperbolic Matrix(1993,-4308,588,-1271) (41/19,13/6) -> (61/18,139/41) Hyperbolic Matrix(1793,-3966,486,-1075) (42/19,31/14) -> (59/16,48/13) Hyperbolic Matrix(1511,-3350,410,-909) (31/14,51/23) -> (11/3,59/16) Hyperbolic Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(1763,-4178,338,-801) (45/19,64/27) -> (26/5,47/9) Hyperbolic Matrix(3471,-8230,1210,-2869) (64/27,83/35) -> (43/15,66/23) Hyperbolic Matrix(3089,-7352,692,-1647) (119/50,50/21) -> (58/13,9/2) Hyperbolic Matrix(493,-1186,106,-255) (12/5,41/17) -> (51/11,14/3) Hyperbolic Matrix(2545,-6214,994,-2427) (61/25,22/9) -> (64/25,105/41) Hyperbolic Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(12661,-32400,3540,-9059) (87/34,151/59) -> (211/59,93/26) Hyperbolic Matrix(12237,-31322,3422,-8759) (151/59,64/25) -> (118/33,211/59) Hyperbolic Matrix(1171,-3028,268,-693) (31/12,44/17) -> (48/11,35/8) Hyperbolic Matrix(2323,-6018,618,-1601) (101/39,57/22) -> (15/4,79/21) Hyperbolic Matrix(843,-2278,178,-481) (27/10,46/17) -> (52/11,19/4) Hyperbolic Matrix(3011,-8150,890,-2409) (46/17,65/24) -> (115/34,44/13) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(1749,-4910,410,-1151) (14/5,59/21) -> (81/19,64/15) Hyperbolic Matrix(1611,-5168,428,-1373) (16/5,61/19) -> (79/21,64/17) Hyperbolic Matrix(939,-3022,142,-457) (45/14,29/9) -> (33/5,53/8) Hyperbolic Matrix(323,-1058,98,-321) (13/4,23/7) -> (23/7,33/10) Parabolic Matrix(165,-554,14,-47) (47/14,37/11) -> (11/1,1/0) Hyperbolic Matrix(1703,-5738,398,-1341) (64/19,27/8) -> (77/18,30/7) Hyperbolic Matrix(1223,-4418,338,-1221) (18/5,47/13) -> (47/13,76/21) Parabolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(1079,-4802,242,-1077) (40/9,49/11) -> (49/11,58/13) Parabolic Matrix(51,-250,10,-49) (24/5,5/1) -> (5/1,26/5) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(1253,592,908,429) -> Matrix(1,2,0,1) Matrix(2033,952,788,369) -> Matrix(3,-2,2,-1) Matrix(339,158,-1238,-577) -> Matrix(9,-4,16,-7) Matrix(225,104,556,257) -> Matrix(7,-4,16,-9) Matrix(335,154,1886,867) -> Matrix(3,-2,14,-9) Matrix(2881,1322,778,357) -> Matrix(7,-4,2,-1) Matrix(2763,1264,776,355) -> Matrix(17,-12,10,-7) Matrix(661,302,1438,657) -> Matrix(3,-2,-4,3) Matrix(1975,894,-5154,-2333) -> Matrix(1,2,0,1) Matrix(1641,742,878,397) -> Matrix(1,0,0,1) Matrix(873,394,986,445) -> Matrix(1,0,6,1) Matrix(3061,1380,1200,541) -> Matrix(3,-2,2,-1) Matrix(869,390,2070,929) -> Matrix(5,-2,8,-3) Matrix(1409,630,870,389) -> Matrix(9,-4,16,-7) Matrix(1825,806,754,333) -> Matrix(29,-16,20,-11) Matrix(753,332,-2792,-1231) -> Matrix(23,-14,28,-17) Matrix(323,142,-1822,-801) -> Matrix(3,-2,14,-9) Matrix(1495,656,964,423) -> Matrix(3,-2,2,-1) Matrix(531,232,428,187) -> Matrix(11,-8,18,-13) Matrix(1593,694,746,325) -> Matrix(5,-4,4,-3) Matrix(6059,2638,7862,3423) -> Matrix(13,-12,12,-11) Matrix(7435,3236,2764,1203) -> Matrix(7,-6,6,-5) Matrix(1059,460,320,139) -> Matrix(15,-14,14,-13) Matrix(739,320,1060,459) -> Matrix(3,-4,10,-13) Matrix(937,398,1462,621) -> Matrix(1,0,-4,1) Matrix(835,354,-2814,-1193) -> Matrix(1,0,-2,1) Matrix(1141,482,-3842,-1623) -> Matrix(11,-6,2,-1) Matrix(1763,744,936,395) -> Matrix(7,-4,2,-1) Matrix(10375,4376,6124,2583) -> Matrix(47,-30,58,-37) Matrix(1039,438,102,43) -> Matrix(7,-4,2,-1) Matrix(1139,478,722,303) -> Matrix(7,-4,16,-9) Matrix(2271,952,1448,607) -> Matrix(3,-2,14,-9) Matrix(2273,952,308,129) -> Matrix(3,-2,2,-1) Matrix(1343,562,4538,1899) -> Matrix(1,0,0,1) Matrix(3301,1380,720,301) -> Matrix(3,-2,2,-1) Matrix(2153,894,1746,725) -> Matrix(19,-14,34,-25) Matrix(4309,1788,6972,2893) -> Matrix(5,-4,4,-3) Matrix(1945,806,514,213) -> Matrix(21,-16,4,-3) Matrix(513,212,2248,929) -> Matrix(7,-6,20,-17) Matrix(713,294,-1734,-715) -> Matrix(13,-12,12,-11) Matrix(2851,1170,1830,751) -> Matrix(3,-4,10,-13) Matrix(713,292,608,249) -> Matrix(1,-2,4,-7) Matrix(813,332,2128,869) -> Matrix(1,-2,2,-3) Matrix(909,370,710,289) -> Matrix(3,-4,4,-5) Matrix(1881,742,398,157) -> Matrix(1,0,0,1) Matrix(691,272,1288,507) -> Matrix(3,-2,8,-5) Matrix(1779,698,1282,503) -> Matrix(7,-4,2,-1) Matrix(1085,424,2756,1077) -> Matrix(3,-2,-4,3) Matrix(4527,1768,3152,1231) -> Matrix(3,-2,-10,7) Matrix(493,192,588,229) -> Matrix(5,-4,-6,5) Matrix(685,266,394,153) -> Matrix(15,-14,14,-13) Matrix(393,152,-2252,-871) -> Matrix(7,-8,8,-9) Matrix(5571,2152,2348,907) -> Matrix(59,-72,50,-61) Matrix(11335,4376,4204,1623) -> Matrix(23,-30,10,-13) Matrix(685,264,96,37) -> Matrix(3,-4,-2,3) Matrix(99,38,-878,-337) -> Matrix(1,-2,2,-3) Matrix(4281,1640,1360,521) -> Matrix(1,-6,2,-11) Matrix(2821,1080,2040,781) -> Matrix(1,2,0,1) Matrix(1649,630,390,149) -> Matrix(1,-4,0,1) Matrix(1263,482,-4562,-1741) -> Matrix(1,-6,2,-11) Matrix(1259,478,482,183) -> Matrix(1,4,0,1) Matrix(581,220,1640,621) -> Matrix(1,0,0,1) Matrix(1735,656,484,183) -> Matrix(3,-2,2,-1) Matrix(2393,892,668,249) -> Matrix(7,-2,4,-1) Matrix(1527,568,3632,1351) -> Matrix(1,-2,2,-3) Matrix(383,142,1238,459) -> Matrix(7,-2,4,-1) Matrix(477,176,664,245) -> Matrix(5,-2,8,-3) Matrix(473,174,666,245) -> Matrix(7,-4,16,-9) Matrix(475,174,-2274,-833) -> Matrix(3,-2,14,-9) Matrix(2461,900,3120,1141) -> Matrix(5,-4,4,-3) Matrix(471,172,2648,967) -> Matrix(3,-2,8,-5) Matrix(375,136,284,103) -> Matrix(9,-8,8,-7) Matrix(283,102,1218,439) -> Matrix(5,-6,6,-7) Matrix(1029,370,470,169) -> Matrix(3,-4,4,-5) Matrix(2993,1074,1686,605) -> Matrix(11,-18,8,-13) Matrix(95,34,746,267) -> Matrix(1,-2,2,-3) Matrix(651,232,188,67) -> Matrix(3,-8,2,-5) Matrix(1763,624,1116,395) -> Matrix(1,4,2,9) Matrix(833,292,368,129) -> Matrix(3,2,4,3) Matrix(1013,354,186,65) -> Matrix(5,2,2,1) Matrix(457,158,1102,381) -> Matrix(9,-2,14,-3) Matrix(1233,394,266,85) -> Matrix(1,0,6,1) Matrix(2023,642,438,139) -> Matrix(1,0,-8,1) Matrix(613,192,348,109) -> Matrix(13,-4,10,-3) Matrix(959,298,782,243) -> Matrix(17,-8,32,-15) Matrix(1827,566,694,215) -> Matrix(11,-6,2,-1) Matrix(691,212,88,27) -> Matrix(3,-2,2,-1) Matrix(2941,900,2160,661) -> Matrix(5,-4,4,-3) Matrix(433,132,948,289) -> Matrix(3,-2,-4,3) Matrix(1119,340,260,79) -> Matrix(5,-4,-6,5) Matrix(859,260,1120,339) -> Matrix(21,-20,20,-19) Matrix(2395,714,426,127) -> Matrix(3,-8,2,-5) Matrix(2817,838,2222,661) -> Matrix(3,-4,4,-5) Matrix(597,176,424,125) -> Matrix(1,-2,0,1) Matrix(593,174,426,125) -> Matrix(1,4,0,1) Matrix(1099,320,340,99) -> Matrix(5,4,6,5) Matrix(3211,930,1350,391) -> Matrix(5,6,4,5) Matrix(589,170,2110,609) -> Matrix(1,0,4,1) Matrix(419,118,1502,423) -> Matrix(1,0,0,1) Matrix(1417,398,502,141) -> Matrix(1,0,-4,1) Matrix(415,116,1084,303) -> Matrix(5,-2,8,-3) Matrix(3073,852,1908,529) -> Matrix(21,-10,40,-19) Matrix(333,92,1408,389) -> Matrix(3,-2,2,-1) Matrix(1737,478,2402,661) -> Matrix(9,-4,16,-7) Matrix(415,114,-2814,-773) -> Matrix(1,0,0,1) Matrix(4715,1294,2066,567) -> Matrix(23,-10,30,-13) Matrix(81,22,578,157) -> Matrix(3,-2,2,-1) Matrix(8801,2382,2058,557) -> Matrix(25,-18,-18,13) Matrix(3291,890,1150,311) -> Matrix(13,-10,4,-3) Matrix(3207,866,574,155) -> Matrix(7,-6,6,-5) Matrix(573,154,986,265) -> Matrix(15,-14,14,-13) Matrix(489,130,410,109) -> Matrix(1,-2,4,-7) Matrix(2611,690,3750,991) -> Matrix(3,-4,10,-13) Matrix(2281,602,898,237) -> Matrix(5,-8,2,-3) Matrix(1055,276,1464,383) -> Matrix(1,0,2,1) Matrix(1055,274,566,147) -> Matrix(1,0,0,1) Matrix(1051,272,568,147) -> Matrix(1,2,0,1) Matrix(553,132,708,169) -> Matrix(7,-2,4,-1) Matrix(1649,390,630,149) -> Matrix(11,-6,2,-1) Matrix(469,110,550,129) -> Matrix(3,-2,-4,3) Matrix(233,54,-1014,-235) -> Matrix(7,-6,6,-5) Matrix(1947,446,3034,695) -> Matrix(3,-4,-8,11) Matrix(1709,390,390,89) -> Matrix(1,-2,0,1) Matrix(389,88,1472,333) -> Matrix(1,-4,2,-7) Matrix(2633,594,1086,245) -> Matrix(3,4,2,3) Matrix(465,104,76,17) -> Matrix(1,4,0,1) Matrix(1925,424,1076,237) -> Matrix(7,-2,4,-1) Matrix(3379,740,1000,219) -> Matrix(5,-4,4,-3) Matrix(229,50,1690,369) -> Matrix(1,0,0,1) Matrix(3301,720,1380,301) -> Matrix(13,-4,10,-3) Matrix(535,116,844,183) -> Matrix(1,-2,0,1) Matrix(2669,570,4350,929) -> Matrix(1,0,0,1) Matrix(2819,600,3660,779) -> Matrix(7,8,6,7) Matrix(687,146,1294,275) -> Matrix(1,0,4,1) Matrix(303,64,-1444,-305) -> Matrix(1,0,8,1) Matrix(1061,220,680,141) -> Matrix(1,0,0,1) Matrix(743,142,518,99) -> Matrix(3,-2,-4,3) Matrix(295,56,964,183) -> Matrix(9,-8,8,-7) Matrix(3543,662,958,179) -> Matrix(5,-8,2,-3) Matrix(4867,906,2874,535) -> Matrix(13,-22,16,-27) Matrix(3023,562,1178,219) -> Matrix(1,0,0,1) Matrix(295,54,366,67) -> Matrix(1,2,0,1) Matrix(659,118,1022,183) -> Matrix(1,0,0,1) Matrix(3433,612,948,169) -> Matrix(25,2,12,1) Matrix(365,64,2036,357) -> Matrix(3,-2,8,-5) Matrix(509,88,1232,213) -> Matrix(1,-4,2,-7) Matrix(643,102,498,79) -> Matrix(5,-6,6,-7) Matrix(1353,212,568,89) -> Matrix(5,6,4,5) Matrix(2193,334,1346,205) -> Matrix(1,-2,2,-3) Matrix(1059,160,920,139) -> Matrix(1,0,6,1) Matrix(565,84,1056,157) -> Matrix(1,0,0,1) Matrix(1685,246,774,113) -> Matrix(3,-2,8,-5) Matrix(905,124,416,57) -> Matrix(1,0,2,1) Matrix(417,56,484,65) -> Matrix(1,0,-4,1) Matrix(1175,154,206,27) -> Matrix(5,2,2,1) Matrix(1171,152,208,27) -> Matrix(7,-2,4,-1) Matrix(1161,140,340,41) -> Matrix(3,4,2,3) Matrix(2783,324,816,95) -> Matrix(13,-4,10,-3) Matrix(335,34,266,27) -> Matrix(1,-2,2,-3) Matrix(529,50,730,69) -> Matrix(5,-2,8,-3) Matrix(433,-46,706,-75) -> Matrix(1,0,-2,1) Matrix(375,-46,106,-13) -> Matrix(3,-2,2,-1) Matrix(1219,-160,160,-21) -> Matrix(1,0,2,1) Matrix(261,-38,158,-23) -> Matrix(1,-2,2,-3) Matrix(1195,-186,726,-113) -> Matrix(9,-2,14,-3) Matrix(829,-132,672,-107) -> Matrix(9,-4,16,-7) Matrix(153,-26,206,-35) -> Matrix(1,-2,2,-3) Matrix(1017,-184,304,-55) -> Matrix(7,-6,6,-5) Matrix(1873,-346,406,-75) -> Matrix(1,0,-4,1) Matrix(1113,-208,808,-151) -> Matrix(3,-2,2,-1) Matrix(707,-134,554,-105) -> Matrix(11,-4,14,-5) Matrix(545,-114,894,-187) -> Matrix(1,0,0,1) Matrix(545,-116,296,-63) -> Matrix(1,2,0,1) Matrix(493,-106,1186,-255) -> Matrix(3,2,4,3) Matrix(1873,-406,346,-75) -> Matrix(7,-2,4,-1) Matrix(2463,-538,1378,-301) -> Matrix(7,-2,4,-1) Matrix(2855,-626,2066,-453) -> Matrix(7,-4,2,-1) Matrix(539,-122,782,-177) -> Matrix(1,0,0,1) Matrix(1171,-268,3028,-693) -> Matrix(5,-2,-2,1) Matrix(3939,-920,1460,-341) -> Matrix(11,-14,4,-5) Matrix(3841,-900,1020,-239) -> Matrix(1,2,0,1) Matrix(1063,-256,436,-105) -> Matrix(3,-2,2,-1) Matrix(809,-212,332,-87) -> Matrix(7,-2,4,-1) Matrix(475,-126,426,-113) -> Matrix(3,-2,-4,3) Matrix(567,-152,332,-89) -> Matrix(7,-8,8,-9) Matrix(517,-142,142,-39) -> Matrix(5,2,2,1) Matrix(5581,-1560,7080,-1979) -> Matrix(7,-2,4,-1) Matrix(891,-250,1030,-289) -> Matrix(1,0,-8,1) Matrix(375,-106,46,-13) -> Matrix(1,0,-2,1) Matrix(1347,-392,512,-149) -> Matrix(7,-4,2,-1) Matrix(417,-122,1022,-299) -> Matrix(1,0,0,1) Matrix(2317,-684,2964,-875) -> Matrix(5,-4,4,-3) Matrix(6901,-2040,11160,-3299) -> Matrix(7,-4,2,-1) Matrix(3239,-962,1202,-357) -> Matrix(7,-4,2,-1) Matrix(5133,-1528,8368,-2491) -> Matrix(3,-2,-4,3) Matrix(1017,-304,184,-55) -> Matrix(5,-4,4,-3) Matrix(323,-98,1058,-321) -> Matrix(15,-14,14,-13) Matrix(4441,-1380,2700,-839) -> Matrix(1,-4,2,-7) Matrix(4941,-1538,3158,-983) -> Matrix(1,-2,4,-7) Matrix(731,-230,410,-129) -> Matrix(3,-8,2,-5) Matrix(843,-296,356,-125) -> Matrix(7,8,6,7) Matrix(1949,-692,752,-267) -> Matrix(5,2,2,1) Matrix(485,-174,354,-127) -> Matrix(5,2,2,1) Matrix(659,-242,482,-177) -> Matrix(11,-2,6,-1) Matrix(1491,-550,2410,-889) -> Matrix(7,-2,4,-1) Matrix(2103,-778,1138,-421) -> Matrix(7,-2,4,-1) Matrix(3239,-1202,962,-357) -> Matrix(13,-4,10,-3) Matrix(5335,-1984,1444,-537) -> Matrix(3,-2,2,-1) Matrix(787,-294,174,-65) -> Matrix(1,0,-2,1) Matrix(217,-82,262,-99) -> Matrix(5,-2,-2,1) Matrix(2129,-812,1172,-447) -> Matrix(7,-4,2,-1) Matrix(1949,-752,692,-267) -> Matrix(1,-2,0,1) Matrix(12245,-4734,4674,-1807) -> Matrix(1,12,0,1) Matrix(691,-268,1168,-453) -> Matrix(3,-2,2,-1) Matrix(733,-286,346,-135) -> Matrix(1,0,0,1) Matrix(3969,-1550,950,-371) -> Matrix(1,-2,0,1) Matrix(5393,-2108,3968,-1551) -> Matrix(1,2,0,1) Matrix(1895,-744,1164,-457) -> Matrix(1,-2,2,-3) Matrix(1419,-560,560,-221) -> Matrix(9,2,4,1) Matrix(3795,-1544,1664,-677) -> Matrix(37,-20,50,-27) Matrix(809,-332,212,-87) -> Matrix(7,-4,2,-1) Matrix(2887,-1192,4672,-1929) -> Matrix(11,-6,2,-1) Matrix(2587,-1072,3352,-1389) -> Matrix(27,-16,22,-13) Matrix(2453,-1026,1566,-655) -> Matrix(3,-2,8,-5) Matrix(1775,-744,804,-337) -> Matrix(3,-2,2,-1) Matrix(11661,-4900,4900,-2059) -> Matrix(81,-56,68,-47) Matrix(127,-54,294,-125) -> Matrix(7,-6,6,-5) Matrix(711,-310,250,-109) -> Matrix(1,-2,2,-3) Matrix(2585,-1134,1794,-787) -> Matrix(1,-2,0,1) Matrix(1333,-586,1126,-495) -> Matrix(1,-2,4,-7) Matrix(957,-422,542,-239) -> Matrix(3,-2,2,-1) Matrix(331,-148,208,-93) -> Matrix(1,-2,2,-3) Matrix(1687,-774,534,-245) -> Matrix(1,-2,2,-3) Matrix(615,-286,286,-133) -> Matrix(1,0,0,1) Matrix(733,-346,286,-135) -> Matrix(1,2,0,1) Matrix(907,-474,354,-185) -> Matrix(3,-2,2,-1) Matrix(545,-296,116,-63) -> Matrix(1,0,0,1) Matrix(387,-212,272,-149) -> Matrix(5,-2,-2,1) Matrix(693,-386,386,-215) -> Matrix(7,-4,2,-1) Matrix(2463,-1378,538,-301) -> Matrix(3,-2,-4,3) Matrix(731,-410,230,-129) -> Matrix(1,0,0,1) Matrix(2455,-1384,1804,-1017) -> Matrix(5,-4,4,-3) Matrix(1073,-606,1266,-715) -> Matrix(3,-2,-4,3) Matrix(957,-542,422,-239) -> Matrix(1,0,0,1) Matrix(419,-242,722,-417) -> Matrix(23,-22,22,-21) Matrix(567,-332,152,-89) -> Matrix(11,-14,4,-5) Matrix(6457,-3804,3624,-2135) -> Matrix(37,-54,24,-35) Matrix(5889,-3472,3472,-2047) -> Matrix(73,-112,88,-135) Matrix(2037,-1202,2642,-1559) -> Matrix(23,-38,20,-33) Matrix(903,-536,716,-425) -> Matrix(3,-4,4,-5) Matrix(261,-158,38,-23) -> Matrix(1,-4,0,1) Matrix(2757,-1682,2162,-1319) -> Matrix(3,-10,4,-13) Matrix(1265,-774,894,-547) -> Matrix(1,2,0,1) Matrix(1895,-1164,744,-457) -> Matrix(1,2,0,1) Matrix(1151,-710,890,-549) -> Matrix(7,-8,8,-9) Matrix(16833,-10408,4708,-2911) -> Matrix(1,0,0,1) Matrix(777,-482,482,-299) -> Matrix(1,-6,2,-11) Matrix(331,-208,148,-93) -> Matrix(1,0,2,1) Matrix(993,-628,808,-511) -> Matrix(1,-4,2,-7) Matrix(2453,-1566,1026,-655) -> Matrix(23,14,18,11) Matrix(4941,-3158,1538,-983) -> Matrix(7,2,10,3) Matrix(6477,-4142,4502,-2879) -> Matrix(1,0,0,1) Matrix(5995,-3844,3364,-2157) -> Matrix(13,8,8,5) Matrix(2261,-1460,1640,-1059) -> Matrix(5,2,2,1) Matrix(73,-48,108,-71) -> Matrix(1,0,4,1) Matrix(1209,-830,890,-611) -> Matrix(7,-2,4,-1) Matrix(1419,-980,320,-221) -> Matrix(1,0,-8,1) Matrix(2585,-1794,1134,-787) -> Matrix(29,-8,40,-11) Matrix(4779,-3320,1700,-1181) -> Matrix(7,-2,4,-1) Matrix(6407,-4454,2654,-1845) -> Matrix(37,-10,26,-7) Matrix(3325,-2316,636,-443) -> Matrix(41,-12,24,-7) Matrix(387,-272,212,-149) -> Matrix(1,0,-2,1) Matrix(1265,-894,774,-547) -> Matrix(5,-2,8,-3) Matrix(1987,-1434,1254,-905) -> Matrix(7,-4,16,-9) Matrix(2855,-2066,626,-453) -> Matrix(7,-4,2,-1) Matrix(4279,-3100,940,-681) -> Matrix(3,-2,8,-5) Matrix(1113,-808,208,-151) -> Matrix(5,-4,4,-3) Matrix(485,-354,174,-127) -> Matrix(1,0,-2,1) Matrix(2455,-1804,1384,-1017) -> Matrix(17,-10,12,-7) Matrix(1383,-1018,898,-661) -> Matrix(3,-2,8,-5) Matrix(1795,-1324,484,-357) -> Matrix(19,-12,8,-5) Matrix(443,-338,578,-441) -> Matrix(27,-26,26,-25) Matrix(3115,-2406,2166,-1673) -> Matrix(5,-6,-4,5) Matrix(1151,-890,710,-549) -> Matrix(13,-16,22,-27) Matrix(4681,-3660,1380,-1079) -> Matrix(11,-18,8,-13) Matrix(707,-554,134,-105) -> Matrix(1,0,0,1) Matrix(1075,-846,906,-713) -> Matrix(1,-2,4,-7) Matrix(18153,-14308,5368,-4231) -> Matrix(11,-18,8,-13) Matrix(1273,-1006,1006,-795) -> Matrix(7,-12,10,-17) Matrix(2075,-1644,804,-637) -> Matrix(1,0,0,1) Matrix(829,-672,132,-107) -> Matrix(1,2,0,1) Matrix(993,-808,628,-511) -> Matrix(1,-2,2,-3) Matrix(791,-650,230,-189) -> Matrix(3,16,2,11) Matrix(1333,-1126,586,-495) -> Matrix(7,2,10,3) Matrix(2239,-1902,1362,-1157) -> Matrix(1,-2,2,-3) Matrix(225,-196,256,-223) -> Matrix(1,0,14,1) Matrix(475,-426,126,-113) -> Matrix(15,-4,4,-1) Matrix(487,-534,114,-125) -> Matrix(3,2,-2,-1) Matrix(225,-256,196,-223) -> Matrix(1,0,12,1) Matrix(891,-1030,250,-289) -> Matrix(15,-2,8,-1) Matrix(1073,-1266,606,-715) -> Matrix(5,-4,4,-3) Matrix(217,-262,82,-99) -> Matrix(1,0,-2,1) Matrix(3021,-3818,398,-503) -> Matrix(3,-2,20,-13) Matrix(2597,-3284,344,-435) -> Matrix(3,-2,-22,15) Matrix(5581,-7080,1560,-1979) -> Matrix(17,-12,10,-7) Matrix(2167,-2752,952,-1209) -> Matrix(1,0,0,1) Matrix(1293,-1648,448,-571) -> Matrix(3,-2,-4,3) Matrix(2317,-2964,684,-875) -> Matrix(9,-8,8,-7) Matrix(2587,-3352,1072,-1389) -> Matrix(59,-52,42,-37) Matrix(2037,-2642,1202,-1559) -> Matrix(95,-86,116,-105) Matrix(443,-578,338,-441) -> Matrix(35,-34,34,-33) Matrix(153,-206,26,-35) -> Matrix(5,-8,2,-3) Matrix(29499,-40102,8722,-11857) -> Matrix(3,4,2,3) Matrix(24079,-32740,7120,-9681) -> Matrix(11,-18,8,-13) Matrix(3453,-4766,1286,-1775) -> Matrix(7,-18,2,-5) Matrix(2973,-4108,1108,-1531) -> Matrix(5,-18,2,-7) Matrix(1283,-1778,578,-801) -> Matrix(1,-2,2,-3) Matrix(1591,-2248,448,-633) -> Matrix(3,-2,2,-1) Matrix(1563,-2216,596,-845) -> Matrix(1,2,0,1) Matrix(7861,-11160,3000,-4259) -> Matrix(1,26,0,1) Matrix(3743,-5316,1116,-1585) -> Matrix(5,46,4,37) Matrix(715,-1026,246,-353) -> Matrix(3,2,-2,-1) Matrix(4329,-6232,1672,-2407) -> Matrix(5,2,2,1) Matrix(1253,-1808,368,-531) -> Matrix(3,4,2,3) Matrix(539,-782,122,-177) -> Matrix(1,0,-2,1) Matrix(73,-108,48,-71) -> Matrix(1,0,2,1) Matrix(1509,-2330,590,-911) -> Matrix(1,2,0,1) Matrix(1013,-1568,188,-291) -> Matrix(7,-2,4,-1) Matrix(727,-1134,234,-365) -> Matrix(1,0,0,1) Matrix(2715,-4244,1124,-1757) -> Matrix(5,-4,4,-3) Matrix(5685,-8894,1334,-2087) -> Matrix(5,-2,-2,1) Matrix(6427,-10192,2692,-4269) -> Matrix(173,-84,138,-67) Matrix(2157,-3424,904,-1435) -> Matrix(67,-36,54,-29) Matrix(1703,-2738,1058,-1701) -> Matrix(37,-18,72,-35) Matrix(1491,-2410,550,-889) -> Matrix(11,-6,2,-1) Matrix(2887,-4672,1192,-1929) -> Matrix(29,-16,20,-11) Matrix(433,-706,46,-75) -> Matrix(5,-4,4,-3) Matrix(593,-968,68,-111) -> Matrix(1,0,0,1) Matrix(545,-894,114,-187) -> Matrix(3,-2,8,-5) Matrix(691,-1168,268,-453) -> Matrix(13,-10,4,-3) Matrix(7031,-11928,2448,-4153) -> Matrix(137,-114,-6,5) Matrix(8811,-14950,3070,-5209) -> Matrix(187,-156,6,-5) Matrix(1045,-1774,334,-567) -> Matrix(19,-16,44,-37) Matrix(1021,-1738,178,-303) -> Matrix(19,-16,6,-5) Matrix(4593,-7828,1708,-2911) -> Matrix(7,-6,-8,7) Matrix(5879,-10022,2462,-4197) -> Matrix(307,-268,244,-213) Matrix(419,-722,242,-417) -> Matrix(39,-38,38,-37) Matrix(2295,-4066,346,-613) -> Matrix(19,-28,-2,3) Matrix(1317,-2344,604,-1075) -> Matrix(1,-2,4,-7) Matrix(2451,-4388,968,-1733) -> Matrix(25,-48,12,-23) Matrix(1247,-2234,494,-885) -> Matrix(11,-24,6,-13) Matrix(1069,-1932,192,-347) -> Matrix(1,0,0,1) Matrix(2049,-3710,470,-851) -> Matrix(1,-2,0,1) Matrix(1855,-3366,426,-773) -> Matrix(1,-2,-2,5) Matrix(435,-824,104,-197) -> Matrix(1,-2,0,1) Matrix(3289,-7090,970,-2091) -> Matrix(11,4,8,3) Matrix(1993,-4308,588,-1271) -> Matrix(13,-4,10,-3) Matrix(1793,-3966,486,-1075) -> Matrix(1,2,0,1) Matrix(1511,-3350,410,-909) -> Matrix(3,-2,2,-1) Matrix(127,-294,54,-125) -> Matrix(13,-12,12,-11) Matrix(1763,-4178,338,-801) -> Matrix(69,-80,44,-51) Matrix(3471,-8230,1210,-2869) -> Matrix(77,-90,6,-7) Matrix(3089,-7352,692,-1647) -> Matrix(5,-6,46,-55) Matrix(493,-1186,106,-255) -> Matrix(3,-4,10,-13) Matrix(2545,-6214,994,-2427) -> Matrix(5,-8,2,-3) Matrix(417,-1022,122,-299) -> Matrix(11,-18,8,-13) Matrix(12661,-32400,3540,-9059) -> Matrix(5,-14,4,-11) Matrix(12237,-31322,3422,-8759) -> Matrix(1,-2,0,1) Matrix(1171,-3028,268,-693) -> Matrix(1,-2,-2,5) Matrix(2323,-6018,618,-1601) -> Matrix(7,-18,2,-5) Matrix(843,-2278,178,-481) -> Matrix(1,-4,2,-7) Matrix(3011,-8150,890,-2409) -> Matrix(3,-8,2,-5) Matrix(177,-484,64,-175) -> Matrix(1,-6,0,1) Matrix(1749,-4910,410,-1151) -> Matrix(3,2,-2,-1) Matrix(1611,-5168,428,-1373) -> Matrix(13,-10,4,-3) Matrix(939,-3022,142,-457) -> Matrix(35,-26,-4,3) Matrix(323,-1058,98,-321) -> Matrix(29,-28,28,-27) Matrix(165,-554,14,-47) -> Matrix(11,-14,4,-5) Matrix(1703,-5738,398,-1341) -> Matrix(7,-8,-6,7) Matrix(1223,-4418,338,-1221) -> Matrix(53,-104,26,-51) Matrix(49,-192,12,-47) -> Matrix(1,-4,0,1) Matrix(1079,-4802,242,-1077) -> Matrix(1,0,22,1) Matrix(51,-250,10,-49) -> Matrix(5,-4,4,-3) Matrix(105,-676,16,-103) -> Matrix(1,-18,0,1) 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 -1/1 0/1 1 1 0/1 (0/1,1/1) 0 30 1/9 1/1 1 3 1/8 0/1 1 10 2/15 (0/1,1/3) 0 30 1/7 0/1 1 15 2/13 0/1 2 2 3/19 1/3 1 15 1/6 1/2 1 30 3/17 0/1 3 3 5/28 0/1 1 10 2/11 (1/1,1/0) 0 30 5/27 0/1 1 15 3/16 1/2 1 30 1/5 1/1 1 5 4/19 (-2/1,-1/1) 0 30 3/14 -1/2 1 30 8/37 0/1 6 2 5/23 0/1 1 15 7/32 0/1 1 10 2/9 (-1/1,0/1) 0 30 5/22 0/1 1 10 3/13 2/3 1 15 4/17 0 10 1/4 0/1 1 6 5/19 1/2 3 5 4/15 (4/5,1/1) 0 30 3/11 -1/1 1 15 5/18 1/6 1 30 7/25 0/1 1 15 9/32 1/4 1 30 2/7 0 10 7/24 1/2 1 30 5/17 3/5 1 15 13/44 2/3 1 10 8/27 2/3 2 6 11/37 2/3 1 5 14/47 (2/3,1/1) 0 30 3/10 3/4 1 30 7/23 1/1 7 1 4/13 (1/1,4/3) 0 30 5/16 2/1 1 10 1/3 0/1 1 15 6/17 (-1/3,0/1) 0 30 5/14 -1/2 1 30 4/11 0/1 4 2 7/19 1/5 1 15 17/46 0/1 1 10 10/27 (2/7,1/3) 0 30 13/35 0/1 1 5 16/43 (0/1,1/3) 0 30 3/8 1/4 1 30 8/21 (1/2,1/1) 0 30 5/13 1/1 2 5 17/44 1/0 1 30 12/31 (-1/1,0/1) 0 30 7/18 0/1 1 6 16/41 0 10 25/64 1/0 1 30 9/23 0/1 1 15 11/28 0/1 1 10 2/5 (0/1,1/3) 0 30 11/27 3/5 1 15 9/22 1/2 1 30 7/17 1/2 3 5 12/29 (3/5,8/13) 0 30 17/41 7/11 1 15 5/12 1/2 1 30 18/43 (2/3,1/1) 0 30 13/31 2/3 1 15 8/19 0 10 3/7 1/1 3 3 10/23 0 10 7/16 1/0 1 30 18/41 (1/1,2/1) 0 30 11/25 2/1 1 5 4/9 (3/1,1/0) 0 30 5/11 -2/1 1 15 6/13 (-1/1,0/1) 0 30 7/15 1/1 1 15 1/2 0/1 1 10 8/15 (1/3,2/5) 0 30 7/13 1/2 1 3 6/11 (0/1,1/3) 0 30 5/9 3/5 1 15 19/34 7/10 1 30 14/25 0 10 9/16 2/3 1 6 22/39 (2/3,1/1) 0 30 13/23 2/3 1 5 4/7 (4/5,1/1) 0 30 11/19 1/1 11 1 7/12 7/6 1 30 10/17 0 10 33/56 3/2 1 30 23/39 11/7 1 15 13/22 2/1 1 6 16/27 (5/3,2/1) 0 30 3/5 2/1 1 15 14/23 (-2/1,-1/1) 0 30 25/41 1/1 1 5 11/18 1/0 1 30 19/31 -1/1 1 3 46/75 (-1/1,0/1) 0 30 27/44 -1/2 1 30 8/13 0 10 21/34 2/1 1 6 34/55 (1/1,1/0) 0 30 47/76 2/1 1 10 13/21 3/1 1 15 5/8 1/0 1 30 12/19 (-1/1,1/0) 0 30 7/11 -1/1 2 5 23/36 -1/2 1 30 39/61 0/1 1 3 16/25 (-1/1,-2/3) 0 30 9/14 -1/4 1 30 11/17 0/1 1 15 2/3 0/1 2 6 13/19 0/1 1 15 11/16 0/1 1 10 20/29 (-1/1,0/1) 0 30 9/13 1/5 1 15 25/36 1/4 1 30 41/59 2/7 1 3 16/23 0 10 7/10 3/8 1 30 12/17 (3/7,1/2) 0 30 5/7 1/2 3 5 13/18 1/2 1 30 21/29 3/5 1 3 29/40 2/3 1 10 8/11 (2/3,1/1) 0 30 11/15 3/5 1 15 25/34 1/2 1 30 14/19 0 10 17/23 2/3 3 3 3/4 3/4 1 30 13/17 1/1 13 1 10/13 (1/1,10/9) 0 30 37/48 8/7 1 6 27/35 13/11 1 15 44/57 (1/1,8/7) 0 30 17/22 6/5 1 10 7/9 4/3 1 15 18/23 (1/1,2/1) 0 30 11/14 2/1 1 6 26/33 (1/1,2/1) 0 30 15/19 1/1 1 15 19/24 5/2 1 30 4/5 0 10 13/16 1/0 1 30 9/11 1/0 7 3 14/17 (-3/1,1/0) 0 30 5/6 -3/2 1 30 11/13 0/1 1 5 6/7 (-1/2,-1/3) 0 30 13/15 0/1 1 15 7/8 0/1 7 2 8/9 (0/1,1/5) 0 30 1/1 1/1 1 15 9/8 -1/2 1 30 8/7 0/1 6 2 15/13 0/1 1 15 7/6 1/4 1 30 13/11 0/1 1 5 6/5 (1/3,2/5) 0 30 11/9 1/2 7 3 16/13 (1/2,5/9) 0 30 5/4 2/3 1 10 24/19 (3/5,2/3) 0 30 67/53 2/3 7 1 43/34 11/16 1 30 19/15 5/7 1 15 33/26 3/4 1 30 14/11 3/4 2 6 51/40 3/4 1 30 37/29 7/9 1 5 23/18 3/4 1 30 9/7 4/5 1 15 22/17 0 10 35/27 17/19 1 15 13/10 13/14 1 30 17/13 1/1 17 1 4/3 (1/1,4/3) 0 30 19/14 2/1 1 10 53/39 2/1 1 15 87/64 1/0 1 30 121/89 1/1 1 1 34/25 (1/1,2/1) 0 30 15/11 1/1 1 15 26/19 2/1 4 2 11/8 1/0 1 30 40/29 0 10 29/21 3/1 2 3 18/13 (1/1,1/0) 0 30 7/5 1/0 3 5 17/12 1/0 1 30 44/31 1/0 12 2 71/50 1/0 1 30 27/19 -5/1 1 15 10/7 (-2/1,-1/1) 0 30 23/16 0/1 1 10 82/57 (-1/1,-2/3) 0 30 59/41 0/1 1 3 36/25 (-1/1,0/1) 0 30 49/34 1/0 1 30 13/9 -1/1 1 15 16/11 0 10 3/2 0/1 1 6 20/13 0 10 37/24 1/2 1 30 17/11 0/1 1 15 14/9 (0/1,1/5) 0 30 25/16 1/4 1 30 61/39 0/1 1 3 36/23 (0/1,1/3) 0 30 11/7 1/3 1 5 19/12 1/2 1 30 46/29 1/2 12 2 27/17 4/7 1 15 8/5 (1/3,1/2) 0 30 37/23 1/2 9 1 29/18 1/2 1 30 21/13 3/5 1 15 55/34 1/2 1 30 34/21 1/2 2 6 13/8 2/3 1 10 44/27 (2/3,5/7) 0 30 31/19 1/1 2 3 18/11 (1/3,1/2) 0 30 23/14 5/8 1 30 51/31 3/5 1 15 28/17 2/3 2 2 5/3 2/3 1 15 22/13 4/5 2 6 61/36 31/38 1 30 39/23 19/23 1 15 95/56 5/6 1 30 151/89 5/6 27 1 56/33 (5/6,51/61) 0 30 17/10 6/7 1 10 46/27 (19/22,13/15) 0 30 75/44 7/8 1 30 29/17 15/17 1 15 12/7 (12/13,1/1) 0 30 19/11 1/1 19 1 7/4 7/6 1 30 23/13 4/3 1 5 39/22 3/2 1 30 16/9 3/2 2 6 57/32 3/2 1 30 41/23 8/5 1 15 25/14 2/1 1 10 34/19 (9/5,2/1) 0 30 77/43 2/1 9 1 43/24 9/4 1 30 9/5 1/1 1 15 38/21 (1/1,2/1) 0 30 29/16 2/1 1 2 20/11 (3/1,1/0) 0 30 11/6 3/2 1 30 24/13 (0/1,1/1) 0 30 13/7 1/0 1 3 15/8 1/2 1 30 2/1 0 10 15/7 1/1 1 15 28/13 (-1/1,0/1) 0 30 41/19 0/1 3 1 13/6 1/2 1 30 11/5 0/1 1 15 42/19 (0/1,1/1) 0 30 31/14 0/1 1 2 20/9 (1/2,1/1) 0 30 9/4 1/2 1 30 25/11 2/3 1 5 41/18 3/4 1 30 57/25 11/15 1 15 16/7 (7/9,4/5) 0 30 7/3 1/1 6 3 26/11 (17/15,8/7) 0 30 45/19 8/7 1 15 64/27 (57/49,7/6) 0 30 19/8 6/5 1 10 31/13 16/13 1 15 74/31 5/4 12 2 43/18 5/4 1 30 12/5 (1/1,4/3) 0 30 41/17 15/11 1 15 70/29 0 10 99/41 4/3 1 3 29/12 11/8 1 30 17/7 3/2 3 5 39/16 2/1 1 6 22/9 (1/1,3/2) 0 30 5/2 3/2 1 30 28/11 0 10 23/9 2/1 1 15 87/34 5/2 1 30 151/59 3/1 2 1 64/25 (3/1,1/0) 0 30 41/16 2/1 1 10 18/7 2/1 2 6 49/19 4/1 1 15 31/12 5/2 1 30 44/17 (2/1,3/1) 0 30 13/5 3/1 1 5 21/8 1/0 1 30 29/11 1/0 7 3 8/3 (1/1,2/1) 0 30 43/16 1/0 1 30 35/13 2/1 1 5 62/23 2/1 2 6 27/10 7/2 1 30 46/17 0 10 65/24 1/0 1 30 19/7 3/1 1 15 11/4 1/0 3 2 25/9 -3/1 1 15 14/5 (-2/1,-1/1) 0 30 17/6 1/2 1 30 20/7 0 10 23/8 1/0 1 30 3/1 0/1 1 15 22/7 (1/2,7/13) 0 30 19/6 2/3 1 6 16/5 0 10 13/4 7/8 1 30 23/7 1/1 14 1 10/3 (1/1,7/6) 0 30 47/14 5/4 1 30 37/11 4/3 1 5 64/19 (1/1,2/1) 0 30 27/8 4/3 1 6 44/13 0 10 17/5 1/1 1 15 41/12 3/2 1 30 24/7 (7/5,3/2) 0 30 7/2 2/1 1 10 32/9 (5/3,2/1) 0 30 25/7 2/1 1 15 18/5 (9/5,2/1) 0 30 47/13 2/1 13 1 29/8 17/8 1 30 11/3 3/1 1 15 48/13 (2/1,3/1) 0 30 37/10 1/0 1 30 26/7 0 10 15/4 7/2 1 30 19/5 1/0 3 5 23/6 1/0 1 30 4/1 1/0 2 6 17/4 -2/1 1 10 13/3 0/1 1 15 22/5 0 10 31/7 -1/3 1 15 40/9 (-1/9,0/1) 0 30 49/11 0/1 11 1 9/2 1/2 1 30 32/7 0 10 23/5 0/1 1 15 37/8 0/1 7 2 14/3 (0/1,1/3) 0 30 33/7 1/2 1 3 19/4 1/0 1 30 24/5 (3/7,1/2) 0 30 5/1 1/1 2 5 26/5 (13/9,3/2) 0 30 21/4 2/1 1 6 16/3 (1/1,2/1) 0 30 27/5 2/1 1 15 11/2 1/0 1 30 28/5 0 10 17/3 2/1 3 3 23/4 2/1 1 10 6/1 (3/1,4/1) 0 30 19/3 7/1 1 15 13/2 1/0 9 2 33/5 -11/1 1 15 20/3 (-6/1,-5/1) 0 30 7/1 -2/1 1 15 15/2 -1/2 1 30 8/1 0 10 9/1 1/1 2 3 10/1 (2/1,3/1) 0 30 1/0 1/0 1 30 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(433,-46,706,-75) (0/1,1/9) -> (19/31,46/75) Hyperbolic Matrix(429,-50,592,-69) (1/9,1/8) -> (21/29,29/40) Glide Reflection Matrix(267,-34,212,-27) (1/8,2/15) -> (5/4,24/19) Glide Reflection Matrix(157,-22,264,-37) (2/15,1/7) -> (16/27,3/5) Glide Reflection Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(1195,-186,726,-113) (2/13,3/19) -> (51/31,28/17) Hyperbolic Matrix(881,-140,258,-41) (3/19,1/6) -> (17/5,41/12) Glide Reflection Matrix(153,-26,206,-35) (1/6,3/17) -> (17/23,3/4) Hyperbolic Matrix(867,-154,152,-27) (3/17,5/28) -> (17/3,23/4) Glide Reflection Matrix(1475,-264,866,-155) (5/28,2/11) -> (17/10,46/27) Glide Reflection Matrix(305,-56,354,-65) (2/11,5/27) -> (6/7,13/15) Glide Reflection Matrix(355,-66,1264,-235) (5/27,3/16) -> (7/25,9/32) Glide Reflection Matrix(707,-134,554,-105) (3/16,1/5) -> (37/29,23/18) Hyperbolic Matrix(545,-114,894,-187) (1/5,4/19) -> (14/23,25/41) Hyperbolic Matrix(545,-116,296,-63) (4/19,3/14) -> (11/6,24/13) Hyperbolic Matrix(445,-96,394,-85) (3/14,8/37) -> (9/8,8/7) Glide Reflection Matrix(739,-160,642,-139) (8/37,5/23) -> (8/7,15/13) Glide Reflection Matrix(541,-118,1380,-301) (5/23,7/32) -> (9/23,11/28) Glide Reflection Matrix(1525,-334,936,-205) (7/32,2/9) -> (13/8,44/27) Glide Reflection Matrix(539,-122,782,-177) (2/9,5/22) -> (11/16,20/29) Hyperbolic Matrix(929,-212,390,-89) (5/22,3/13) -> (19/8,31/13) Glide Reflection Matrix(439,-102,340,-79) (3/13,4/17) -> (9/7,22/17) Glide Reflection Matrix(389,-92,630,-149) (4/17,1/4) -> (8/13,21/34) Glide Reflection Matrix(809,-212,332,-87) (1/4,5/19) -> (17/7,39/16) Hyperbolic Matrix(333,-88,806,-213) (5/19,4/15) -> (7/17,12/29) Glide Reflection Matrix(567,-152,332,-89) (4/15,3/11) -> (29/17,12/7) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(423,-118,656,-183) (5/18,7/25) -> (9/14,11/17) Glide Reflection Matrix(1357,-382,984,-277) (9/32,2/7) -> (11/8,40/29) Glide Reflection Matrix(187,-54,232,-67) (2/7,7/24) -> (4/5,13/16) Glide Reflection Matrix(417,-122,1022,-299) (7/24,5/17) -> (11/27,9/22) Hyperbolic Matrix(325,-96,694,-205) (5/17,13/44) -> (7/15,1/2) Glide Reflection Matrix(1899,-562,740,-219) (13/44,8/27) -> (41/16,18/7) Glide Reflection Matrix(3239,-962,1202,-357) (8/27,11/37) -> (35/13,62/23) Hyperbolic Matrix(1203,-358,3236,-963) (11/37,14/47) -> (13/35,16/43) Glide Reflection Matrix(2219,-662,600,-179) (14/47,3/10) -> (48/13,37/10) Glide Reflection Matrix(139,-42,460,-139) (3/10,7/23) -> (3/10,7/23) Reflection Matrix(183,-56,598,-183) (7/23,4/13) -> (7/23,4/13) Reflection Matrix(459,-142,320,-99) (4/13,5/16) -> (10/7,23/16) Glide Reflection Matrix(731,-230,410,-129) (5/16,1/3) -> (41/23,25/14) Hyperbolic Matrix(843,-296,356,-125) (1/3,6/17) -> (26/11,45/19) Hyperbolic Matrix(621,-220,398,-141) (6/17,5/14) -> (14/9,25/16) Glide Reflection Matrix(485,-174,354,-127) (5/14,4/11) -> (26/19,11/8) Hyperbolic Matrix(659,-242,482,-177) (4/11,7/19) -> (15/11,26/19) Hyperbolic Matrix(1491,-550,2410,-889) (7/19,17/46) -> (47/76,13/21) Hyperbolic Matrix(395,-146,744,-275) (17/46,10/27) -> (1/2,8/15) Glide Reflection Matrix(3239,-1202,962,-357) (10/27,13/35) -> (37/11,64/19) Hyperbolic Matrix(1529,-570,2492,-929) (16/43,3/8) -> (46/75,27/44) Glide Reflection Matrix(217,-82,262,-99) (3/8,8/21) -> (14/17,5/6) Hyperbolic Matrix(303,-116,478,-183) (8/21,5/13) -> (12/19,7/11) Glide Reflection Matrix(607,-234,952,-367) (5/13,17/44) -> (7/11,23/36) Glide Reflection Matrix(1861,-720,778,-301) (17/44,12/31) -> (43/18,12/5) Glide Reflection Matrix(691,-268,1168,-453) (12/31,7/18) -> (13/22,16/27) Hyperbolic Matrix(1899,-740,562,-219) (7/18,16/41) -> (27/8,44/13) Glide Reflection Matrix(5609,-2190,2072,-809) (16/41,25/64) -> (46/17,65/24) Glide Reflection Matrix(5393,-2108,3968,-1551) (25/64,9/23) -> (53/39,87/64) Hyperbolic Matrix(1077,-424,602,-237) (11/28,2/5) -> (25/14,34/19) Glide Reflection Matrix(257,-104,42,-17) (2/5,11/27) -> (6/1,19/3) Glide Reflection Matrix(809,-332,212,-87) (9/22,7/17) -> (19/5,23/6) Hyperbolic Matrix(2587,-1072,3352,-1389) (12/29,17/41) -> (27/35,44/57) Hyperbolic Matrix(381,-158,340,-141) (17/41,5/12) -> (1/1,9/8) Glide Reflection Matrix(1861,-778,720,-301) (5/12,18/43) -> (31/12,44/17) Glide Reflection Matrix(1775,-744,804,-337) (18/43,13/31) -> (11/5,42/19) Hyperbolic Matrix(929,-390,212,-89) (13/31,8/19) -> (13/3,22/5) Glide Reflection Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(711,-310,250,-109) (10/23,7/16) -> (17/6,20/7) Hyperbolic Matrix(2585,-1134,1794,-787) (7/16,18/41) -> (36/25,49/34) Hyperbolic Matrix(1083,-476,1918,-843) (18/41,11/25) -> (22/39,13/23) Glide Reflection Matrix(249,-110,292,-129) (11/25,4/9) -> (11/13,6/7) Glide Reflection Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(289,-132,370,-169) (5/11,6/13) -> (7/9,18/23) Glide Reflection Matrix(615,-286,286,-133) (6/13,7/15) -> (15/7,28/13) Hyperbolic Matrix(507,-272,274,-147) (8/15,7/13) -> (24/13,13/7) Glide Reflection Matrix(545,-296,116,-63) (7/13,6/11) -> (14/3,33/7) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(693,-386,386,-215) (5/9,19/34) -> (43/24,9/5) Hyperbolic Matrix(1077,-602,424,-237) (19/34,14/25) -> (5/2,28/11) Glide Reflection Matrix(731,-410,230,-129) (14/25,9/16) -> (19/6,16/5) Hyperbolic Matrix(845,-476,1074,-605) (9/16,22/39) -> (11/14,26/33) Glide Reflection Matrix(229,-130,192,-109) (13/23,4/7) -> (13/11,6/5) Glide Reflection Matrix(153,-88,266,-153) (4/7,11/19) -> (4/7,11/19) Reflection Matrix(265,-154,456,-265) (11/19,7/12) -> (11/19,7/12) Reflection Matrix(567,-332,152,-89) (7/12,10/17) -> (26/7,15/4) Hyperbolic Matrix(1511,-890,528,-311) (10/17,33/56) -> (20/7,23/8) Glide Reflection Matrix(5889,-3472,3472,-2047) (33/56,23/39) -> (39/23,95/56) Hyperbolic Matrix(2037,-1202,2642,-1559) (23/39,13/22) -> (37/48,27/35) Hyperbolic Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(2757,-1682,2162,-1319) (25/41,11/18) -> (51/40,37/29) Hyperbolic Matrix(781,-478,1080,-661) (11/18,19/31) -> (13/18,21/29) Glide Reflection Matrix(1525,-936,334,-205) (27/44,8/13) -> (9/2,32/7) Glide Reflection Matrix(2893,-1788,1186,-733) (21/34,34/55) -> (39/16,22/9) Glide Reflection Matrix(7119,-4402,2780,-1719) (34/55,47/76) -> (64/25,41/16) Glide Reflection Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(331,-208,148,-93) (5/8,12/19) -> (20/9,9/4) Hyperbolic Matrix(3001,-1918,4320,-2761) (23/36,39/61) -> (25/36,41/59) Glide Reflection Matrix(6477,-4142,4502,-2879) (39/61,16/25) -> (82/57,59/41) Hyperbolic Matrix(621,-398,220,-141) (16/25,9/14) -> (14/5,17/6) Glide Reflection Matrix(73,-48,108,-71) (11/17,2/3) -> (2/3,13/19) Parabolic Matrix(1209,-830,890,-611) (13/19,11/16) -> (19/14,53/39) Hyperbolic Matrix(1419,-980,320,-221) (20/29,9/13) -> (31/7,40/9) Hyperbolic Matrix(2585,-1794,1134,-787) (9/13,25/36) -> (41/18,57/25) Hyperbolic Matrix(6407,-4454,2654,-1845) (41/59,16/23) -> (70/29,99/41) Hyperbolic Matrix(459,-320,142,-99) (16/23,7/10) -> (16/5,13/4) Glide Reflection Matrix(387,-272,212,-149) (7/10,12/17) -> (20/11,11/6) Hyperbolic Matrix(245,-174,176,-125) (12/17,5/7) -> (18/13,7/5) Glide Reflection Matrix(245,-176,174,-125) (5/7,13/18) -> (7/5,17/12) Glide Reflection Matrix(1357,-984,382,-277) (29/40,8/11) -> (7/2,32/9) Glide Reflection Matrix(485,-354,174,-127) (8/11,11/15) -> (25/9,14/5) Hyperbolic Matrix(1141,-838,900,-661) (11/15,25/34) -> (19/15,33/26) Glide Reflection Matrix(1383,-1018,898,-661) (25/34,14/19) -> (20/13,37/24) Hyperbolic Matrix(967,-714,172,-127) (14/19,17/23) -> (28/5,17/3) Glide Reflection Matrix(103,-78,136,-103) (3/4,13/17) -> (3/4,13/17) Reflection Matrix(339,-260,442,-339) (13/17,10/13) -> (13/17,10/13) Reflection Matrix(3423,-2638,1016,-783) (10/13,37/48) -> (64/19,27/8) Glide Reflection Matrix(3115,-2406,2166,-1673) (44/57,17/22) -> (23/16,82/57) Hyperbolic Matrix(439,-340,102,-79) (17/22,7/9) -> (17/4,13/3) Glide Reflection Matrix(707,-554,134,-105) (18/23,11/14) -> (21/4,16/3) Hyperbolic Matrix(1141,-900,838,-661) (26/33,15/19) -> (34/25,15/11) Glide Reflection Matrix(1273,-1006,1006,-795) (15/19,19/24) -> (43/34,19/15) Hyperbolic Matrix(267,-212,34,-27) (19/24,4/5) -> (15/2,8/1) Glide Reflection Matrix(695,-566,264,-215) (13/16,9/11) -> (21/8,29/11) Glide Reflection Matrix(363,-298,296,-243) (9/11,14/17) -> (11/9,16/13) Glide Reflection Matrix(229,-192,130,-109) (5/6,11/13) -> (7/4,23/13) Glide Reflection Matrix(739,-642,160,-139) (13/15,7/8) -> (23/5,37/8) Glide Reflection Matrix(445,-394,96,-85) (7/8,8/9) -> (37/8,14/3) Glide Reflection Matrix(381,-340,158,-141) (8/9,1/1) -> (12/5,41/17) Glide Reflection Matrix(305,-354,56,-65) (15/13,7/6) -> (27/5,11/2) Glide Reflection Matrix(249,-292,110,-129) (7/6,13/11) -> (9/4,25/11) Glide Reflection Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(187,-232,54,-67) (16/13,5/4) -> (24/7,7/2) Glide Reflection Matrix(2545,-3216,2014,-2545) (24/19,67/53) -> (24/19,67/53) Reflection Matrix(4557,-5762,3604,-4557) (67/53,43/34) -> (67/53,43/34) Reflection Matrix(845,-1074,476,-605) (33/26,14/11) -> (39/22,16/9) Glide Reflection Matrix(1267,-1614,712,-907) (14/11,51/40) -> (16/9,57/32) Glide Reflection Matrix(289,-370,132,-169) (23/18,9/7) -> (13/6,11/5) Glide Reflection Matrix(2587,-3352,1072,-1389) (22/17,35/27) -> (41/17,70/29) Hyperbolic Matrix(2037,-2642,1202,-1559) (35/27,13/10) -> (61/36,39/23) Hyperbolic Matrix(339,-442,260,-339) (13/10,17/13) -> (13/10,17/13) Reflection Matrix(103,-136,78,-103) (17/13,4/3) -> (17/13,4/3) Reflection Matrix(153,-206,26,-35) (4/3,19/14) -> (23/4,6/1) Hyperbolic Matrix(15487,-21054,11392,-15487) (87/64,121/89) -> (87/64,121/89) Reflection Matrix(6051,-8228,4450,-6051) (121/89,34/25) -> (121/89,34/25) Reflection Matrix(429,-592,50,-69) (40/29,29/21) -> (8/1,9/1) Glide Reflection Matrix(781,-1080,478,-661) (29/21,18/13) -> (31/19,18/11) Glide Reflection Matrix(1141,-1618,720,-1021) (17/12,44/31) -> (19/12,46/29) Glide Reflection Matrix(5033,-7146,2108,-2993) (44/31,71/50) -> (74/31,43/18) Glide Reflection Matrix(2875,-4084,1686,-2395) (71/50,27/19) -> (75/44,29/17) Glide Reflection Matrix(3001,-4320,1918,-2761) (59/41,36/25) -> (61/39,36/23) Glide Reflection Matrix(1941,-2798,1180,-1701) (49/34,13/9) -> (23/14,51/31) Glide Reflection Matrix(539,-782,122,-177) (13/9,16/11) -> (22/5,31/7) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(1509,-2330,590,-911) (37/24,17/11) -> (23/9,87/34) Hyperbolic Matrix(423,-656,118,-183) (17/11,14/9) -> (25/7,18/5) Glide Reflection Matrix(2715,-4244,1124,-1757) (25/16,61/39) -> (99/41,29/12) Hyperbolic Matrix(607,-952,234,-367) (36/23,11/7) -> (44/17,13/5) Glide Reflection Matrix(303,-478,116,-183) (11/7,19/12) -> (13/5,21/8) Glide Reflection Matrix(2157,-3424,904,-1435) (46/29,27/17) -> (31/13,74/31) Hyperbolic Matrix(369,-592,230,-369) (8/5,37/23) -> (8/5,37/23) Reflection Matrix(1333,-2146,828,-1333) (37/23,29/18) -> (37/23,29/18) Reflection Matrix(1491,-2410,550,-889) (21/13,55/34) -> (65/24,19/7) Hyperbolic Matrix(619,-1002,160,-259) (55/34,34/21) -> (23/6,4/1) Glide Reflection Matrix(389,-630,92,-149) (34/21,13/8) -> (4/1,17/4) Glide Reflection Matrix(433,-706,46,-75) (44/27,31/19) -> (9/1,10/1) Hyperbolic Matrix(545,-894,114,-187) (18/11,23/14) -> (19/4,24/5) Hyperbolic Matrix(691,-1168,268,-453) (5/3,22/13) -> (18/7,49/19) Hyperbolic Matrix(2583,-4376,958,-1623) (22/13,61/36) -> (62/23,27/10) Glide Reflection Matrix(16911,-28690,9968,-16911) (95/56,151/89) -> (95/56,151/89) Reflection Matrix(9967,-16912,5874,-9967) (151/89,56/33) -> (151/89,56/33) Reflection Matrix(1267,-2152,534,-907) (56/33,17/10) -> (64/27,19/8) Glide Reflection Matrix(1709,-2912,510,-869) (46/27,75/44) -> (10/3,47/14) Glide Reflection Matrix(265,-456,154,-265) (12/7,19/11) -> (12/7,19/11) Reflection Matrix(153,-266,88,-153) (19/11,7/4) -> (19/11,7/4) Reflection Matrix(1083,-1918,476,-843) (23/13,39/22) -> (25/11,41/18) Glide Reflection Matrix(625,-1114,216,-385) (57/32,41/23) -> (23/8,3/1) Glide Reflection Matrix(2925,-5236,1634,-2925) (34/19,77/43) -> (34/19,77/43) Reflection Matrix(3697,-6622,2064,-3697) (77/43,43/24) -> (77/43,43/24) Reflection Matrix(471,-850,128,-231) (9/5,38/21) -> (11/3,48/13) Glide Reflection Matrix(1323,-2396,598,-1083) (38/21,29/16) -> (42/19,31/14) Glide Reflection Matrix(661,-1200,298,-541) (29/16,20/11) -> (31/14,20/9) Glide Reflection Matrix(397,-742,84,-157) (13/7,15/8) -> (33/7,19/4) Glide Reflection Matrix(395,-744,146,-275) (15/8,2/1) -> (27/10,46/17) Glide Reflection Matrix(325,-694,96,-205) (2/1,15/7) -> (44/13,17/5) Glide Reflection Matrix(1065,-2296,494,-1065) (28/13,41/19) -> (28/13,41/19) Reflection Matrix(493,-1066,228,-493) (41/19,13/6) -> (41/19,13/6) Reflection Matrix(731,-1668,110,-251) (57/25,16/7) -> (33/5,20/3) Glide Reflection Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(499,-1182,160,-379) (45/19,64/27) -> (3/1,22/7) Glide Reflection Matrix(333,-806,88,-213) (29/12,17/7) -> (15/4,19/5) Glide Reflection Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(541,-1380,118,-301) (28/11,23/9) -> (32/7,23/5) Glide Reflection Matrix(10267,-26274,4012,-10267) (87/34,151/59) -> (87/34,151/59) Reflection Matrix(7551,-19328,2950,-7551) (151/59,64/25) -> (151/59,64/25) Reflection Matrix(369,-952,50,-129) (49/19,31/12) -> (7/1,15/2) Glide Reflection Matrix(163,-438,16,-43) (8/3,43/16) -> (10/1,1/0) Glide Reflection Matrix(1203,-3236,358,-963) (43/16,35/13) -> (47/14,37/11) Glide Reflection Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(303,-956,58,-183) (22/7,19/6) -> (26/5,21/4) Glide Reflection Matrix(183,-598,56,-183) (13/4,23/7) -> (13/4,23/7) Reflection Matrix(139,-460,42,-139) (23/7,10/3) -> (23/7,10/3) Reflection Matrix(355,-1264,66,-235) (32/9,25/7) -> (16/3,27/5) Glide Reflection Matrix(469,-1692,130,-469) (18/5,47/13) -> (18/5,47/13) Reflection Matrix(753,-2726,208,-753) (47/13,29/8) -> (47/13,29/8) Reflection Matrix(357,-1322,64,-237) (37/10,26/7) -> (11/2,28/5) Glide Reflection Matrix(881,-3920,198,-881) (40/9,49/11) -> (40/9,49/11) Reflection Matrix(197,-882,44,-197) (49/11,9/2) -> (49/11,9/2) Reflection Matrix(51,-250,10,-49) (24/5,5/1) -> (5/1,26/5) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(433,-46,706,-75) -> Matrix(1,0,-2,1) 0/1 Matrix(429,-50,592,-69) -> Matrix(1,2,2,3) Matrix(267,-34,212,-27) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(157,-22,264,-37) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(261,-38,158,-23) -> Matrix(1,-2,2,-3) 1/1 Matrix(1195,-186,726,-113) -> Matrix(9,-2,14,-3) Matrix(881,-140,258,-41) -> Matrix(11,-4,8,-3) Matrix(153,-26,206,-35) -> Matrix(1,-2,2,-3) 1/1 Matrix(867,-154,152,-27) -> Matrix(9,-2,4,-1) Matrix(1475,-264,866,-155) -> Matrix(19,-6,22,-7) Matrix(305,-56,354,-65) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(355,-66,1264,-235) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(707,-134,554,-105) -> Matrix(11,-4,14,-5) Matrix(545,-114,894,-187) -> Matrix(1,0,0,1) Matrix(545,-116,296,-63) -> Matrix(1,2,0,1) 1/0 Matrix(445,-96,394,-85) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(739,-160,642,-139) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(541,-118,1380,-301) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1525,-334,936,-205) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(539,-122,782,-177) -> Matrix(1,0,0,1) Matrix(929,-212,390,-89) -> Matrix(17,-6,14,-5) Matrix(439,-102,340,-79) -> Matrix(7,-6,8,-7) *** -> (3/4,1/1) Matrix(389,-92,630,-149) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(809,-212,332,-87) -> Matrix(7,-2,4,-1) Matrix(333,-88,806,-213) -> Matrix(7,-4,12,-7) *** -> (1/2,2/3) Matrix(567,-152,332,-89) -> Matrix(7,-8,8,-9) 1/1 Matrix(517,-142,142,-39) -> Matrix(5,2,2,1) Matrix(423,-118,656,-183) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1357,-382,984,-277) -> Matrix(9,-2,4,-1) Matrix(187,-54,232,-67) -> Matrix(5,-2,2,-1) Matrix(417,-122,1022,-299) -> Matrix(1,0,0,1) Matrix(325,-96,694,-205) -> Matrix(3,-2,-2,1) Matrix(1899,-562,740,-219) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(3239,-962,1202,-357) -> Matrix(7,-4,2,-1) Matrix(1203,-358,3236,-963) -> Matrix(3,-2,10,-7) Matrix(2219,-662,600,-179) -> Matrix(11,-8,4,-3) Matrix(139,-42,460,-139) -> Matrix(7,-6,8,-7) (3/10,7/23) -> (3/4,1/1) Matrix(183,-56,598,-183) -> Matrix(7,-8,6,-7) (7/23,4/13) -> (1/1,4/3) Matrix(459,-142,320,-99) -> Matrix(1,-2,-2,3) Matrix(731,-230,410,-129) -> Matrix(3,-8,2,-5) 2/1 Matrix(843,-296,356,-125) -> Matrix(7,8,6,7) Matrix(621,-220,398,-141) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(485,-174,354,-127) -> Matrix(5,2,2,1) Matrix(659,-242,482,-177) -> Matrix(11,-2,6,-1) Matrix(1491,-550,2410,-889) -> Matrix(7,-2,4,-1) Matrix(395,-146,744,-275) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(3239,-1202,962,-357) -> Matrix(13,-4,10,-3) Matrix(1529,-570,2492,-929) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(217,-82,262,-99) -> Matrix(5,-2,-2,1) Matrix(303,-116,478,-183) -> Matrix(3,-2,-2,1) Matrix(607,-234,952,-367) -> Matrix(1,-2,-2,3) Matrix(1861,-720,778,-301) -> Matrix(5,4,4,3) Matrix(691,-268,1168,-453) -> Matrix(3,-2,2,-1) 1/1 Matrix(1899,-740,562,-219) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(5609,-2190,2072,-809) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(5393,-2108,3968,-1551) -> Matrix(1,2,0,1) 1/0 Matrix(1077,-424,602,-237) -> Matrix(3,2,2,1) Matrix(257,-104,42,-17) -> Matrix(9,-4,2,-1) Matrix(809,-332,212,-87) -> Matrix(7,-4,2,-1) Matrix(2587,-1072,3352,-1389) -> Matrix(27,-16,22,-13) Matrix(381,-158,340,-141) -> Matrix(3,-2,-8,5) Matrix(1861,-778,720,-301) -> Matrix(11,-8,4,-3) Matrix(1775,-744,804,-337) -> Matrix(3,-2,2,-1) 1/1 Matrix(929,-390,212,-89) -> Matrix(3,-2,-2,1) Matrix(127,-54,294,-125) -> Matrix(7,-6,6,-5) 1/1 Matrix(711,-310,250,-109) -> Matrix(1,-2,2,-3) 1/1 Matrix(2585,-1134,1794,-787) -> Matrix(1,-2,0,1) 1/0 Matrix(1083,-476,1918,-843) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(249,-110,292,-129) -> Matrix(1,-2,-2,3) Matrix(331,-148,208,-93) -> Matrix(1,-2,2,-3) 1/1 Matrix(289,-132,370,-169) -> Matrix(3,2,2,1) Matrix(615,-286,286,-133) -> Matrix(1,0,0,1) Matrix(507,-272,274,-147) -> Matrix(5,-2,2,-1) Matrix(545,-296,116,-63) -> Matrix(1,0,0,1) Matrix(387,-212,272,-149) -> Matrix(5,-2,-2,1) Matrix(693,-386,386,-215) -> Matrix(7,-4,2,-1) Matrix(1077,-602,424,-237) -> Matrix(11,-8,4,-3) Matrix(731,-410,230,-129) -> Matrix(1,0,0,1) Matrix(845,-476,1074,-605) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(229,-130,192,-109) -> Matrix(3,-2,10,-7) Matrix(153,-88,266,-153) -> Matrix(9,-8,10,-9) (4/7,11/19) -> (4/5,1/1) Matrix(265,-154,456,-265) -> Matrix(13,-14,12,-13) (11/19,7/12) -> (1/1,7/6) Matrix(567,-332,152,-89) -> Matrix(11,-14,4,-5) Matrix(1511,-890,528,-311) -> Matrix(7,-10,2,-3) Matrix(5889,-3472,3472,-2047) -> Matrix(73,-112,88,-135) Matrix(2037,-1202,2642,-1559) -> Matrix(23,-38,20,-33) Matrix(261,-158,38,-23) -> Matrix(1,-4,0,1) 1/0 Matrix(2757,-1682,2162,-1319) -> Matrix(3,-10,4,-13) Matrix(781,-478,1080,-661) -> Matrix(1,4,2,7) Matrix(1525,-936,334,-205) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(2893,-1788,1186,-733) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(7119,-4402,2780,-1719) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(777,-482,482,-299) -> Matrix(1,-6,2,-11) Matrix(331,-208,148,-93) -> Matrix(1,0,2,1) 0/1 Matrix(3001,-1918,4320,-2761) -> Matrix(5,2,18,7) Matrix(6477,-4142,4502,-2879) -> Matrix(1,0,0,1) Matrix(621,-398,220,-141) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(73,-48,108,-71) -> Matrix(1,0,4,1) 0/1 Matrix(1209,-830,890,-611) -> Matrix(7,-2,4,-1) Matrix(1419,-980,320,-221) -> Matrix(1,0,-8,1) 0/1 Matrix(2585,-1794,1134,-787) -> Matrix(29,-8,40,-11) Matrix(6407,-4454,2654,-1845) -> Matrix(37,-10,26,-7) Matrix(459,-320,142,-99) -> Matrix(13,-4,16,-5) Matrix(387,-272,212,-149) -> Matrix(1,0,-2,1) 0/1 Matrix(245,-174,176,-125) -> Matrix(9,-4,2,-1) Matrix(245,-176,174,-125) -> Matrix(3,-2,-2,1) Matrix(1357,-984,382,-277) -> Matrix(13,-8,8,-5) Matrix(485,-354,174,-127) -> Matrix(1,0,-2,1) 0/1 Matrix(1141,-838,900,-661) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(1383,-1018,898,-661) -> Matrix(3,-2,8,-5) 1/2 Matrix(967,-714,172,-127) -> Matrix(13,-8,8,-5) Matrix(103,-78,136,-103) -> Matrix(7,-6,8,-7) (3/4,13/17) -> (3/4,1/1) Matrix(339,-260,442,-339) -> Matrix(19,-20,18,-19) (13/17,10/13) -> (1/1,10/9) Matrix(3423,-2638,1016,-783) -> Matrix(11,-12,10,-11) *** -> (1/1,6/5) Matrix(3115,-2406,2166,-1673) -> Matrix(5,-6,-4,5) Matrix(439,-340,102,-79) -> Matrix(3,-4,-4,5) Matrix(707,-554,134,-105) -> Matrix(1,0,0,1) Matrix(1141,-900,838,-661) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1273,-1006,1006,-795) -> Matrix(7,-12,10,-17) Matrix(267,-212,34,-27) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(695,-566,264,-215) -> Matrix(-1,6,0,1) *** -> (3/1,1/0) Matrix(363,-298,296,-243) -> Matrix(1,8,2,15) Matrix(229,-192,130,-109) -> Matrix(5,4,4,3) Matrix(739,-642,160,-139) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(445,-394,96,-85) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(381,-340,158,-141) -> Matrix(19,-4,14,-3) Matrix(305,-354,56,-65) -> Matrix(9,-2,4,-1) Matrix(249,-292,110,-129) -> Matrix(7,-2,10,-3) Matrix(217,-262,82,-99) -> Matrix(1,0,-2,1) 0/1 Matrix(187,-232,54,-67) -> Matrix(13,-8,8,-5) Matrix(2545,-3216,2014,-2545) -> Matrix(19,-12,30,-19) (24/19,67/53) -> (3/5,2/3) Matrix(4557,-5762,3604,-4557) -> Matrix(65,-44,96,-65) (67/53,43/34) -> (2/3,11/16) Matrix(845,-1074,476,-605) -> Matrix(25,-18,18,-13) Matrix(1267,-1614,712,-907) -> Matrix(23,-18,14,-11) Matrix(289,-370,132,-169) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(2587,-3352,1072,-1389) -> Matrix(59,-52,42,-37) Matrix(2037,-2642,1202,-1559) -> Matrix(95,-86,116,-105) Matrix(339,-442,260,-339) -> Matrix(27,-26,28,-27) (13/10,17/13) -> (13/14,1/1) Matrix(103,-136,78,-103) -> Matrix(7,-8,6,-7) (17/13,4/3) -> (1/1,4/3) Matrix(153,-206,26,-35) -> Matrix(5,-8,2,-3) 2/1 Matrix(15487,-21054,11392,-15487) -> Matrix(-1,2,0,1) (87/64,121/89) -> (1/1,1/0) Matrix(6051,-8228,4450,-6051) -> Matrix(3,-4,2,-3) (121/89,34/25) -> (1/1,2/1) Matrix(429,-592,50,-69) -> Matrix(1,-2,2,-5) Matrix(781,-1080,478,-661) -> Matrix(1,-2,2,-5) Matrix(1141,-1618,720,-1021) -> Matrix(1,-2,2,-5) Matrix(5033,-7146,2108,-2993) -> Matrix(5,74,4,59) Matrix(2875,-4084,1686,-2395) -> Matrix(7,50,8,57) Matrix(3001,-4320,1918,-2761) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1941,-2798,1180,-1701) -> Matrix(5,2,8,3) Matrix(539,-782,122,-177) -> Matrix(1,0,-2,1) 0/1 Matrix(73,-108,48,-71) -> Matrix(1,0,2,1) 0/1 Matrix(1509,-2330,590,-911) -> Matrix(1,2,0,1) 1/0 Matrix(423,-656,118,-183) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(2715,-4244,1124,-1757) -> Matrix(5,-4,4,-3) 1/1 Matrix(607,-952,234,-367) -> Matrix(9,-2,4,-1) Matrix(303,-478,116,-183) -> Matrix(9,-4,2,-1) Matrix(2157,-3424,904,-1435) -> Matrix(67,-36,54,-29) Matrix(369,-592,230,-369) -> Matrix(5,-2,12,-5) (8/5,37/23) -> (1/3,1/2) Matrix(1333,-2146,828,-1333) -> Matrix(31,-16,60,-31) (37/23,29/18) -> (1/2,8/15) Matrix(1491,-2410,550,-889) -> Matrix(11,-6,2,-1) Matrix(619,-1002,160,-259) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(389,-630,92,-149) -> Matrix(7,-4,-2,1) Matrix(433,-706,46,-75) -> Matrix(5,-4,4,-3) 1/1 Matrix(545,-894,114,-187) -> Matrix(3,-2,8,-5) 1/2 Matrix(691,-1168,268,-453) -> Matrix(13,-10,4,-3) Matrix(2583,-4376,958,-1623) -> Matrix(37,-30,16,-13) Matrix(16911,-28690,9968,-16911) -> Matrix(1009,-840,1212,-1009) (95/56,151/89) -> (84/101,5/6) Matrix(9967,-16912,5874,-9967) -> Matrix(611,-510,732,-611) (151/89,56/33) -> (5/6,51/61) Matrix(1267,-2152,534,-907) -> Matrix(85,-72,72,-61) Matrix(1709,-2912,510,-869) -> Matrix(83,-72,68,-59) Matrix(265,-456,154,-265) -> Matrix(25,-24,26,-25) (12/7,19/11) -> (12/13,1/1) Matrix(153,-266,88,-153) -> Matrix(13,-14,12,-13) (19/11,7/4) -> (1/1,7/6) Matrix(1083,-1918,476,-843) -> Matrix(13,-18,18,-25) Matrix(625,-1114,216,-385) -> Matrix(5,-8,-2,3) Matrix(2925,-5236,1634,-2925) -> Matrix(19,-36,10,-19) (34/19,77/43) -> (9/5,2/1) Matrix(3697,-6622,2064,-3697) -> Matrix(17,-36,8,-17) (77/43,43/24) -> (2/1,9/4) Matrix(471,-850,128,-231) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1323,-2396,598,-1083) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(661,-1200,298,-541) -> Matrix(1,-2,2,-5) Matrix(397,-742,84,-157) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(395,-744,146,-275) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(325,-694,96,-205) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1065,-2296,494,-1065) -> Matrix(-1,0,2,1) (28/13,41/19) -> (-1/1,0/1) Matrix(493,-1066,228,-493) -> Matrix(1,0,4,-1) (41/19,13/6) -> (0/1,1/2) Matrix(731,-1668,110,-251) -> Matrix(29,-22,-4,3) Matrix(127,-294,54,-125) -> Matrix(13,-12,12,-11) 1/1 Matrix(499,-1182,160,-379) -> Matrix(7,-8,20,-23) Matrix(333,-806,88,-213) -> Matrix(11,-16,2,-3) Matrix(417,-1022,122,-299) -> Matrix(11,-18,8,-13) 3/2 Matrix(541,-1380,118,-301) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(10267,-26274,4012,-10267) -> Matrix(11,-30,4,-11) (87/34,151/59) -> (5/2,3/1) Matrix(7551,-19328,2950,-7551) -> Matrix(-1,6,0,1) (151/59,64/25) -> (3/1,1/0) Matrix(369,-952,50,-129) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(163,-438,16,-43) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1203,-3236,358,-963) -> Matrix(5,-6,4,-5) *** -> (1/1,3/2) Matrix(177,-484,64,-175) -> Matrix(1,-6,0,1) 1/0 Matrix(303,-956,58,-183) -> Matrix(13,-8,8,-5) Matrix(183,-598,56,-183) -> Matrix(15,-14,16,-15) (13/4,23/7) -> (7/8,1/1) Matrix(139,-460,42,-139) -> Matrix(13,-14,12,-13) (23/7,10/3) -> (1/1,7/6) Matrix(355,-1264,66,-235) -> Matrix(7,-12,4,-7) *** -> (3/2,2/1) Matrix(469,-1692,130,-469) -> Matrix(19,-36,10,-19) (18/5,47/13) -> (9/5,2/1) Matrix(753,-2726,208,-753) -> Matrix(33,-68,16,-33) (47/13,29/8) -> (2/1,17/8) Matrix(357,-1322,64,-237) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(881,-3920,198,-881) -> Matrix(-1,0,18,1) (40/9,49/11) -> (-1/9,0/1) Matrix(197,-882,44,-197) -> Matrix(1,0,4,-1) (49/11,9/2) -> (0/1,1/2) Matrix(51,-250,10,-49) -> Matrix(5,-4,4,-3) 1/1 Matrix(105,-676,16,-103) -> Matrix(1,-18,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.