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): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/9 -7/9 -2/3 -5/9 -7/15 -4/9 -5/12 -7/18 -41/108 -29/81 -19/54 -1/3 -17/54 -49/162 -7/24 -5/18 -29/108 -43/162 -19/72 -7/27 -5/21 -17/72 -2/9 -23/108 -5/24 -28/135 -5/26 -4/21 -14/81 -1/6 -3/20 -4/27 -3/22 -2/15 -3/23 -7/54 -2/17 -1/9 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 2/13 3/19 4/25 1/6 4/23 3/17 2/11 5/27 3/16 4/21 1/5 4/19 3/14 2/9 3/13 5/21 1/4 5/18 7/25 2/7 8/27 1/3 10/27 7/18 2/5 11/27 5/12 4/9 7/15 1/2 5/9 16/27 17/27 52/81 2/3 19/27 20/27 7/9 107/135 22/27 67/81 23/27 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -3/1 1/0 -8/9 -1/1 -7/8 -1/1 1/0 -13/15 1/2 -6/7 4/1 1/0 -11/13 1/0 -16/19 -4/1 -15/4 -21/25 -25/8 -5/6 -2/1 -24/29 -2/1 -3/2 -19/23 1/0 -14/17 -2/1 -7/4 -9/11 -5/4 -22/27 -1/1 -13/16 -1/1 -5/6 -17/21 -1/2 -4/5 -1/2 0/1 -15/19 5/4 -41/52 1/1 3/2 -26/33 1/1 -11/14 1/1 1/0 -18/23 7/2 4/1 -7/9 1/0 -24/31 -13/2 -6/1 -41/53 1/0 -17/22 -11/2 -5/1 -27/35 -15/4 -10/13 -4/1 1/0 -13/17 -11/4 -16/21 -7/3 -3/4 -3/2 -1/1 -14/19 -4/5 -3/4 -25/34 -3/4 -11/15 -36/49 -15/22 -2/3 -11/15 -1/2 -30/41 -3/4 -2/3 -19/26 -3/5 -1/2 -8/11 -1/2 -2/5 -21/29 -3/16 -13/18 0/1 -18/25 0/1 1/2 -41/57 1/2 -23/32 1/3 1/2 -5/7 1/0 -17/24 2/1 -12/17 6/1 1/0 -19/27 1/0 -7/10 -5/1 1/0 -30/43 -9/2 -4/1 -23/33 -7/2 -39/56 -31/10 -3/1 -16/23 -8/3 -5/2 -9/13 1/0 -11/16 -3/1 -5/2 -13/19 -15/8 -15/22 -17/10 -5/3 -2/3 -1/1 -13/20 -1/3 -1/4 -11/17 1/4 -20/31 3/2 2/1 -9/14 -1/1 1/0 -34/53 -2/3 -1/2 -25/39 -1/2 -66/103 -1/10 0/1 -41/64 1/1 1/0 -16/25 -1/2 0/1 -7/11 1/0 -19/30 2/1 -12/19 4/1 1/0 -17/27 1/0 -5/8 -3/1 1/0 -18/29 -13/6 -2/1 -31/50 -13/7 -11/6 -13/21 -3/2 -60/97 -5/2 -2/1 -47/76 -5/3 -3/2 -34/55 -3/2 -10/7 -21/34 -5/4 -1/1 -8/13 0/1 1/0 -19/31 1/0 -11/18 -2/1 -14/23 -8/5 -3/2 -31/51 -3/2 -48/79 -2/1 -3/2 -17/28 -5/3 -3/2 -3/5 -5/4 -16/27 -1/1 -13/22 -1/1 -17/18 -23/39 -9/10 -10/17 -7/8 -6/7 -17/29 -19/24 -24/41 -22/29 -3/4 -31/53 -3/4 -7/12 -2/3 -32/55 -2/3 -1/2 -25/43 -5/8 -18/31 -6/11 -1/2 -11/19 -1/4 -37/64 1/1 1/0 -26/45 -1/1 -15/26 -3/5 -1/2 -19/33 -1/2 -4/7 0/1 1/0 -13/23 -1/4 -22/39 1/1 -31/55 1/0 -9/16 -1/1 -1/2 -23/41 1/0 -14/25 0/1 1/2 -5/9 1/0 -16/29 -2/1 -3/2 -27/49 -9/4 -11/20 -1/1 1/0 -28/51 -5/3 -17/31 -5/4 -6/11 -2/1 -3/2 -7/13 1/0 -8/15 -1/1 -1/2 -1/1 -1/2 -9/19 -3/4 -8/17 -2/1 1/0 -7/15 -1/2 -6/13 0/1 1/0 -11/24 0/1 -5/11 1/0 -14/31 -3/2 -10/7 -9/20 -9/7 -5/4 -4/9 -1/1 -15/34 -23/25 -11/12 -26/59 -10/11 -49/54 -11/25 -25/28 -7/16 -11/13 -5/6 -24/55 -5/6 -14/17 -17/39 -5/6 -27/62 -13/16 -17/21 -10/23 -4/5 -11/14 -23/53 -3/4 -13/30 -4/5 -3/7 -3/4 -17/40 -5/8 -3/5 -14/33 -3/5 -11/26 -3/5 -1/2 -19/45 -1/2 -27/64 -3/7 -5/12 -8/19 0/1 1/0 -21/50 -7/6 -1/1 -34/81 -1/1 -13/31 -7/8 -18/43 -5/6 -4/5 -41/98 -1/1 -3/4 -23/55 -3/4 -5/12 -2/3 -22/53 -2/3 -1/2 -39/94 -1/1 1/0 -56/135 -1/1 -17/41 -3/4 -12/29 -7/10 -2/3 -19/46 -5/8 -3/5 -26/63 -3/5 -7/17 -5/8 -23/56 -3/5 -13/22 -16/39 -3/5 -9/22 -5/9 -1/2 -11/27 -1/2 -2/5 -1/2 0/1 -13/33 -1/2 -11/28 -5/9 -1/2 -20/51 -3/7 -9/23 -1/4 -7/18 0/1 -12/31 1/2 2/3 -5/13 1/0 -18/47 10/1 1/0 -31/81 1/0 -13/34 -9/1 1/0 -34/89 -4/1 1/0 -55/144 -4/1 -21/55 1/0 -29/76 -5/1 -9/2 -8/21 -3/1 -19/50 -11/5 -13/6 -30/79 -37/18 -2/1 -41/108 -2/1 -11/29 -15/8 -14/37 -13/8 -8/5 -3/8 -5/4 -1/1 -10/27 -1/1 -7/19 -15/16 -18/49 -31/34 -10/11 -29/79 -65/72 -11/30 -8/9 -15/41 -7/8 -4/11 -6/7 -5/6 -9/25 -25/32 -32/89 -24/31 -65/84 -23/64 -27/35 -37/48 -14/39 -13/17 -19/53 -3/4 -24/67 -58/77 -3/4 -29/81 -3/4 -5/14 -3/4 -11/15 -6/17 -11/16 -2/3 -19/54 -2/3 -13/37 -21/32 -7/20 -7/11 -5/8 -8/23 -1/2 0/1 -1/3 -1/2 -6/19 -1/8 0/1 -17/54 0/1 -11/35 1/12 -5/16 1/3 1/2 -9/29 7/4 -4/13 -4/1 1/0 -7/23 1/0 -24/79 -2/1 -3/2 -41/135 -3/2 -17/56 -3/2 -1/1 -10/33 -1/1 -23/76 -3/1 -5/2 -36/119 -13/6 -2/1 -49/162 -2/1 -13/43 -7/4 -3/10 -5/4 -1/1 -8/27 -1/1 -5/17 -11/12 -12/41 -7/8 -6/7 -7/24 -6/7 -23/79 -57/68 -16/55 -5/6 -34/41 -9/31 -13/16 -2/7 -4/5 -3/4 -11/39 -13/18 -9/32 -5/7 -27/38 -16/57 -19/27 -23/82 -75/107 -7/10 -53/189 -7/10 -30/107 -7/10 -100/143 -7/25 -25/36 -5/18 -2/3 -8/29 -2/3 -9/14 -3/11 -5/8 -10/37 -4/7 -9/16 -17/63 -1/2 -7/26 -3/5 -1/2 -18/67 -3/4 -2/3 -29/108 -2/3 -11/41 -5/8 -4/15 -3/5 -17/64 -19/33 -23/40 -30/113 -63/110 -4/7 -43/162 -4/7 -13/49 -25/44 -9/34 -9/16 -5/9 -14/53 -2/3 -1/2 -19/72 -4/7 -24/91 -9/16 -14/25 -5/19 -11/20 -6/23 -12/23 -1/2 -7/27 -1/2 -1/4 -1/2 -1/3 -5/21 1/2 -9/38 1/1 3/2 -13/55 1/0 -17/72 0/1 -4/17 2/1 1/0 -7/30 -2/1 -3/13 1/0 -8/35 -9/4 -2/1 -13/57 -3/2 -5/22 -3/2 -1/1 -2/9 -1/1 -7/32 -1/1 -5/6 -12/55 -26/31 -5/6 -5/23 -3/4 -8/37 -13/16 -4/5 -3/14 -3/4 -5/7 -13/61 -11/16 -23/108 -2/3 -10/47 -2/3 -5/8 -7/33 -1/2 -11/52 -1/1 -9/10 -15/71 -3/4 -19/90 -4/5 -4/19 -4/5 -3/4 -5/24 -2/3 -11/53 -3/4 -28/135 -5/7 -17/82 -5/7 -7/10 -6/29 -7/10 -2/3 -1/5 -5/8 -5/26 -5/9 -1/2 -4/21 -5/9 -7/37 -15/28 -17/90 -8/15 -10/53 -6/11 -1/2 -3/16 -11/21 -1/2 -5/27 -1/2 -2/11 -1/2 -6/13 -5/28 -1/2 -1/3 -8/45 -3/7 -3/17 -5/12 -4/23 -4/11 -5/14 -9/52 -17/50 -1/3 -14/81 -1/3 -5/29 -9/28 -1/6 0/1 -4/25 -1/2 0/1 -7/44 1/1 1/0 -3/19 -1/4 -2/13 0/1 1/0 -3/20 -5/4 -1/1 -4/27 -1/1 -1/7 -3/4 -3/22 -3/5 -1/2 -2/15 -1/1 -3/23 -11/16 -7/54 -2/3 -4/31 -2/3 -17/26 -1/8 -5/8 -3/5 -2/17 -11/20 -6/11 -1/9 -1/2 -1/10 -3/8 -1/3 -1/11 1/0 0/1 -1/2 0/1 1/10 -1/1 -3/4 1/9 -1/2 1/8 -3/7 -5/12 2/15 -1/3 1/7 -3/8 2/13 -1/4 0/1 3/19 1/0 4/25 -1/2 0/1 1/6 0/1 5/29 -9/8 4/23 -5/6 -4/5 3/17 -5/8 2/11 -6/11 -1/2 5/27 -1/2 3/16 -1/2 -11/23 4/21 -5/11 1/5 -5/12 4/19 -3/8 -4/11 11/52 -9/26 -1/3 7/33 -1/2 3/14 -5/13 -3/8 5/23 -3/8 2/9 -1/3 7/31 -5/16 12/53 -3/10 -14/47 5/22 -1/3 -3/10 8/35 -2/7 -9/32 3/13 -1/4 4/17 -1/4 -2/9 5/21 -1/6 1/4 -1/1 -1/2 5/19 -11/24 9/34 -5/11 -9/20 13/49 -25/56 4/15 -3/7 11/41 -5/12 7/26 -1/2 -3/7 3/11 -5/12 8/29 -9/22 -2/5 5/18 -2/5 7/25 -25/64 16/57 -19/49 9/32 -27/70 -5/13 2/7 -3/8 -4/11 7/24 -6/17 5/17 -11/32 8/27 -1/3 3/10 -1/3 -5/16 13/43 -7/24 10/33 -1/3 17/56 -1/3 -3/10 7/23 -1/4 4/13 -4/15 -1/4 5/16 -1/6 -1/7 6/19 0/1 1/4 7/22 -1/1 -1/2 1/3 -1/2 7/20 -5/12 -7/17 6/17 -2/5 -11/28 11/31 -3/8 5/14 -11/29 -3/8 19/53 -3/8 14/39 -13/35 37/103 -83/224 23/64 -37/100 -27/73 9/25 -25/68 4/11 -5/14 -6/17 11/30 -8/23 7/19 -15/44 10/27 -1/3 3/8 -1/3 -5/16 11/29 -15/52 19/50 -13/46 -11/39 8/21 -3/11 37/97 -15/56 29/76 -9/34 -5/19 21/55 -1/4 13/34 -9/35 -1/4 5/13 -1/4 12/31 -2/11 -1/6 7/18 0/1 9/23 1/0 20/51 -3/5 31/79 -15/28 11/28 -1/2 -5/11 2/5 -1/2 0/1 11/27 -1/2 9/22 -1/2 -5/11 16/39 -3/7 7/17 -5/12 12/29 -2/5 -7/18 17/41 -3/8 22/53 -1/2 -2/5 5/12 -2/5 23/55 -3/8 18/43 -4/11 -5/14 13/31 -7/20 8/19 -1/4 0/1 27/64 -5/8 -3/5 19/45 -1/2 11/26 -1/2 -3/7 14/33 -3/7 3/7 -3/8 10/23 -11/30 -4/11 17/39 -5/14 24/55 -14/39 -5/14 7/16 -5/14 -11/31 18/41 -34/97 -7/20 11/25 -25/72 4/9 -1/3 13/29 -23/72 22/49 -31/98 -6/19 9/20 -5/16 -9/29 23/51 -3/10 14/31 -10/33 -3/10 5/11 -1/4 6/13 -1/4 0/1 7/15 -1/2 1/2 -1/2 -1/3 10/19 -5/16 -4/13 9/17 -5/16 8/15 -1/3 7/13 -1/4 13/24 0/1 6/11 -3/10 -2/7 17/31 -5/16 11/20 -1/3 -1/4 5/9 -1/4 19/34 -1/4 -1/5 33/59 1/0 14/25 -1/6 0/1 9/16 -1/2 -1/3 31/55 -1/4 22/39 -1/5 35/62 -1/7 -1/8 13/23 1/0 30/53 -6/11 -1/2 17/30 -2/5 4/7 -1/4 0/1 23/40 1/1 1/0 19/33 -1/2 15/26 -1/2 -3/7 26/45 -1/3 37/64 -1/4 -1/5 11/19 1/0 29/50 -7/13 -1/2 47/81 -1/2 18/31 -1/2 -6/13 25/43 -5/12 57/98 -1/3 -1/4 32/55 -1/2 -2/5 7/12 -2/5 31/53 -3/8 55/94 -47/125 -3/8 79/135 -3/8 24/41 -3/8 -22/59 17/29 -19/52 27/46 -9/25 -23/64 37/63 -5/14 10/17 -6/17 -7/20 33/56 -9/26 -1/3 23/39 -9/26 13/22 -17/50 -1/3 16/27 -1/3 3/5 -5/16 20/33 -5/17 17/28 -3/10 -5/17 31/51 -3/10 14/23 -3/10 -8/27 11/18 -2/7 19/31 -1/4 8/13 -1/4 0/1 29/47 -3/8 50/81 -1/3 21/34 -1/3 -5/16 55/89 -1/4 89/144 -4/13 34/55 -10/33 -3/10 47/76 -3/10 -5/17 13/21 -3/10 31/50 -11/38 -13/45 49/79 -39/136 67/108 -2/7 18/29 -2/7 -13/46 23/37 -1/4 5/8 -3/11 -1/4 17/27 -1/4 12/19 -1/4 -4/17 31/49 -9/40 50/79 -2/9 -3/14 19/30 -2/9 26/41 -1/4 -2/9 7/11 -1/4 16/25 -1/2 0/1 57/89 1/0 41/64 -1/4 -1/5 25/39 -1/2 34/53 -1/2 -2/5 43/67 -3/8 52/81 -1/3 9/14 -1/3 -1/4 11/17 -1/8 35/54 0/1 24/37 0/1 1/8 13/20 -1/1 1/0 15/23 -3/4 2/3 -1/3 13/19 -15/52 37/54 -2/7 24/35 -2/7 -25/88 11/16 -5/18 -3/11 20/29 -3/10 -2/7 9/13 -1/4 16/23 -5/18 -8/29 55/79 -47/172 94/135 -3/11 39/56 -3/11 -31/114 23/33 -7/26 53/76 -7/26 -11/41 83/119 -31/116 113/162 -4/15 30/43 -4/15 -9/34 7/10 -5/19 -1/4 19/27 -1/4 12/17 -1/4 -6/25 29/41 -1/4 17/24 -2/9 56/79 -2/9 -3/14 39/55 -1/4 22/31 -5/22 -2/9 5/7 -1/4 28/39 -1/5 23/32 -1/6 -1/7 41/57 -1/6 59/82 -1/6 -1/7 136/189 -1/7 77/107 -1/8 18/25 -1/6 0/1 13/18 0/1 21/29 3/4 8/11 -2/3 -1/2 27/37 -3/8 46/63 -1/3 19/26 -1/2 -3/7 49/67 -5/12 79/108 -2/5 30/41 -2/5 -3/8 11/15 -1/2 47/64 -5/12 -7/17 83/113 -29/72 119/162 -2/5 36/49 -2/5 -15/38 25/34 -11/29 -3/8 39/53 -3/8 53/72 -4/11 67/91 -3/8 14/19 -3/8 -4/11 17/23 -11/32 20/27 -1/3 3/4 -1/3 -3/10 16/21 -7/25 29/38 -5/18 -23/83 42/55 -2/7 -5/18 55/72 -8/29 13/17 -11/40 23/30 -4/15 10/13 -4/15 -1/4 27/35 -15/56 44/57 -13/49 17/22 -5/19 -11/42 7/9 -1/4 25/32 -5/21 -9/38 43/55 -1/4 18/23 -4/17 -7/30 29/37 -9/40 11/14 -1/4 -1/5 48/61 -9/40 -2/9 85/108 -2/9 37/47 -7/32 26/33 -1/5 41/52 -3/14 -1/5 56/71 -1/4 0/1 71/90 -2/9 15/19 -5/24 19/24 -2/11 42/53 -10/59 -1/6 107/135 -1/6 65/82 -1/6 -15/91 23/29 -5/32 4/5 -1/2 0/1 21/26 -1/2 -5/11 17/21 -1/2 30/37 -3/8 -4/11 73/90 -2/5 43/53 -3/8 13/16 -5/14 -1/3 22/27 -1/3 9/11 -5/16 23/28 -1/3 -3/10 37/45 -3/10 14/17 -7/24 -2/7 19/23 -1/4 43/52 -1/3 -3/10 67/81 -3/10 24/29 -3/10 -2/7 5/6 -2/7 21/25 -25/92 37/44 -27/100 -17/63 16/19 -15/56 -4/15 11/13 -1/4 17/20 -15/59 -1/4 23/27 -1/4 6/7 -1/4 -4/17 19/22 -7/34 -1/5 13/15 -1/6 20/23 -1/10 0/1 47/54 0/1 27/31 1/4 7/8 -1/3 -1/4 15/17 -1/4 8/9 -1/3 9/10 -3/11 -1/4 10/11 -2/7 -5/18 1/1 -1/4 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(271,248,-648,-593) (-1/1,-9/10) -> (-41/98,-23/55) Hyperbolic Matrix(593,530,1026,917) (-9/10,-8/9) -> (26/45,37/64) Hyperbolic Matrix(379,334,-918,-809) (-8/9,-7/8) -> (-19/46,-26/63) Hyperbolic Matrix(541,470,-1242,-1079) (-7/8,-13/15) -> (-17/39,-27/62) Hyperbolic Matrix(107,92,-378,-325) (-13/15,-6/7) -> (-2/7,-11/39) Hyperbolic Matrix(269,228,-702,-595) (-6/7,-11/13) -> (-5/13,-18/47) Hyperbolic Matrix(161,136,702,593) (-11/13,-16/19) -> (8/35,3/13) Hyperbolic Matrix(971,816,-2700,-2269) (-16/19,-21/25) -> (-9/25,-32/89) Hyperbolic Matrix(55,46,324,271) (-21/25,-5/6) -> (1/6,5/29) Hyperbolic Matrix(53,44,324,269) (-5/6,-24/29) -> (4/25,1/6) Hyperbolic Matrix(755,624,-2484,-2053) (-24/29,-19/23) -> (-7/23,-24/79) Hyperbolic Matrix(325,268,918,757) (-19/23,-14/17) -> (6/17,11/31) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(485,396,594,485) (-9/11,-22/27) -> (22/27,9/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(269,218,-1134,-919) (-13/16,-17/21) -> (-5/21,-9/38) Hyperbolic Matrix(107,86,-270,-217) (-17/21,-4/5) -> (-2/5,-13/33) Hyperbolic Matrix(377,298,-1026,-811) (-4/5,-15/19) -> (-7/19,-18/49) Hyperbolic Matrix(487,384,-1026,-809) (-15/19,-41/52) -> (-1/2,-9/19) Hyperbolic Matrix(1081,852,3564,2809) (-41/52,-26/33) -> (10/33,17/56) Hyperbolic Matrix(757,596,-1782,-1403) (-26/33,-11/14) -> (-17/40,-14/33) Hyperbolic Matrix(487,382,-756,-593) (-11/14,-18/23) -> (-20/31,-9/14) Hyperbolic Matrix(377,294,-486,-379) (-18/23,-7/9) -> (-7/9,-24/31) Parabolic Matrix(2375,1838,3348,2591) (-24/31,-41/53) -> (39/55,22/31) Hyperbolic Matrix(1999,1546,5238,4051) (-41/53,-17/22) -> (29/76,21/55) Hyperbolic Matrix(811,626,-1188,-917) (-17/22,-27/35) -> (-13/19,-15/22) Hyperbolic Matrix(109,84,702,541) (-27/35,-10/13) -> (2/13,3/19) Hyperbolic Matrix(269,206,-918,-703) (-10/13,-13/17) -> (-5/17,-12/41) Hyperbolic Matrix(215,164,-1134,-865) (-13/17,-16/21) -> (-4/21,-7/37) Hyperbolic Matrix(431,328,1134,863) (-16/21,-3/4) -> (19/50,8/21) Hyperbolic Matrix(431,318,-1026,-757) (-3/4,-14/19) -> (-8/19,-21/50) Hyperbolic Matrix(1403,1032,-3672,-2701) (-14/19,-25/34) -> (-13/34,-34/89) Hyperbolic Matrix(1189,874,2646,1945) (-25/34,-36/49) -> (22/49,9/20) Hyperbolic Matrix(2215,1626,-3456,-2537) (-36/49,-11/15) -> (-25/39,-66/103) Hyperbolic Matrix(377,276,810,593) (-11/15,-30/41) -> (6/13,7/15) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(107,78,-594,-433) (-19/26,-8/11) -> (-2/11,-5/28) Hyperbolic Matrix(215,156,594,431) (-8/11,-21/29) -> (9/25,4/11) Hyperbolic Matrix(271,196,972,703) (-21/29,-13/18) -> (5/18,7/25) Hyperbolic Matrix(269,194,972,701) (-13/18,-18/25) -> (8/29,5/18) Hyperbolic Matrix(3511,2526,-5778,-4157) (-18/25,-41/57) -> (-31/51,-48/79) Hyperbolic Matrix(431,310,1350,971) (-41/57,-23/32) -> (7/22,1/3) Hyperbolic Matrix(53,38,-378,-271) (-23/32,-5/7) -> (-1/7,-3/22) Hyperbolic Matrix(163,116,-378,-269) (-5/7,-17/24) -> (-13/30,-3/7) Hyperbolic Matrix(215,152,-918,-649) (-17/24,-12/17) -> (-4/17,-7/30) Hyperbolic Matrix(647,456,918,647) (-12/17,-19/27) -> (19/27,12/17) Hyperbolic Matrix(379,266,540,379) (-19/27,-7/10) -> (7/10,19/27) Hyperbolic Matrix(1943,1356,-4644,-3241) (-7/10,-30/43) -> (-18/43,-41/98) Hyperbolic Matrix(2539,1770,-4104,-2861) (-30/43,-23/33) -> (-13/21,-60/97) Hyperbolic Matrix(755,526,3564,2483) (-23/33,-39/56) -> (11/52,7/33) Hyperbolic Matrix(431,300,-2484,-1729) (-39/56,-16/23) -> (-4/23,-9/52) Hyperbolic Matrix(271,188,702,487) (-16/23,-9/13) -> (5/13,12/31) Hyperbolic Matrix(485,334,-864,-595) (-9/13,-11/16) -> (-9/16,-23/41) Hyperbolic Matrix(271,186,-864,-593) (-11/16,-13/19) -> (-11/35,-5/16) Hyperbolic Matrix(379,258,1350,919) (-15/22,-2/3) -> (16/57,9/32) Hyperbolic Matrix(593,386,-1080,-703) (-2/3,-13/20) -> (-11/20,-28/51) Hyperbolic Matrix(379,246,-1080,-701) (-13/20,-11/17) -> (-13/37,-7/20) Hyperbolic Matrix(161,104,918,593) (-11/17,-20/31) -> (4/23,3/17) Hyperbolic Matrix(2375,1524,-5724,-3673) (-9/14,-34/53) -> (-22/53,-39/94) Hyperbolic Matrix(1837,1178,4212,2701) (-34/53,-25/39) -> (17/39,24/55) Hyperbolic Matrix(3671,2352,-13824,-8857) (-66/103,-41/64) -> (-17/64,-30/113) Hyperbolic Matrix(431,276,-2700,-1729) (-41/64,-16/25) -> (-4/25,-7/44) Hyperbolic Matrix(163,104,594,379) (-16/25,-7/11) -> (3/11,8/29) Hyperbolic Matrix(271,172,-594,-377) (-7/11,-19/30) -> (-11/24,-5/11) Hyperbolic Matrix(215,136,-1026,-649) (-19/30,-12/19) -> (-4/19,-5/24) Hyperbolic Matrix(647,408,1026,647) (-12/19,-17/27) -> (17/27,12/19) Hyperbolic Matrix(271,170,432,271) (-17/27,-5/8) -> (5/8,17/27) Hyperbolic Matrix(647,402,-1566,-973) (-5/8,-18/29) -> (-12/29,-19/46) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(271,168,1134,703) (-31/50,-13/21) -> (5/21,1/4) Hyperbolic Matrix(4967,3072,-16416,-10153) (-60/97,-47/76) -> (-23/76,-36/119) Hyperbolic Matrix(1187,734,5238,3239) (-47/76,-34/55) -> (12/53,5/22) Hyperbolic Matrix(971,600,-3672,-2269) (-34/55,-21/34) -> (-9/34,-14/53) Hyperbolic Matrix(107,66,-702,-433) (-21/34,-8/13) -> (-2/13,-3/20) Hyperbolic Matrix(215,132,702,431) (-8/13,-19/31) -> (7/23,4/13) Hyperbolic Matrix(379,232,972,595) (-19/31,-11/18) -> (7/18,9/23) Hyperbolic Matrix(377,230,972,593) (-11/18,-14/23) -> (12/31,7/18) Hyperbolic Matrix(1243,756,2754,1675) (-14/23,-31/51) -> (23/51,14/31) Hyperbolic Matrix(1511,918,-7290,-4429) (-48/79,-17/28) -> (-17/82,-6/29) Hyperbolic Matrix(53,32,-270,-163) (-17/28,-3/5) -> (-1/5,-5/26) Hyperbolic Matrix(161,96,270,161) (-3/5,-16/27) -> (16/27,3/5) Hyperbolic Matrix(703,416,1188,703) (-16/27,-13/22) -> (13/22,16/27) Hyperbolic Matrix(593,350,-2106,-1243) (-13/22,-23/39) -> (-11/39,-9/32) Hyperbolic Matrix(431,254,-918,-541) (-23/39,-10/17) -> (-8/17,-7/15) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(973,570,2214,1297) (-17/29,-24/41) -> (18/41,11/25) Hyperbolic Matrix(2051,1200,-5724,-3349) (-24/41,-31/53) -> (-19/53,-24/67) Hyperbolic Matrix(541,316,1296,757) (-31/53,-7/12) -> (5/12,23/55) Hyperbolic Matrix(539,314,1296,755) (-7/12,-32/55) -> (22/53,5/12) Hyperbolic Matrix(55,32,-648,-377) (-32/55,-25/43) -> (-1/11,0/1) Hyperbolic Matrix(757,440,1674,973) (-25/43,-18/31) -> (14/31,5/11) Hyperbolic Matrix(269,156,-1026,-595) (-18/31,-11/19) -> (-5/19,-6/23) Hyperbolic Matrix(325,188,-2052,-1187) (-11/19,-37/64) -> (-7/44,-3/19) Hyperbolic Matrix(917,530,1026,593) (-37/64,-26/45) -> (8/9,9/10) Hyperbolic Matrix(433,250,-2430,-1403) (-26/45,-15/26) -> (-5/28,-8/45) Hyperbolic Matrix(701,404,-1782,-1027) (-15/26,-19/33) -> (-13/33,-11/28) Hyperbolic Matrix(379,218,-1782,-1025) (-19/33,-4/7) -> (-10/47,-7/33) Hyperbolic Matrix(109,62,-378,-215) (-4/7,-13/23) -> (-9/31,-2/7) Hyperbolic Matrix(163,92,-1242,-701) (-13/23,-22/39) -> (-2/15,-3/23) Hyperbolic Matrix(1511,852,4212,2375) (-22/39,-31/55) -> (19/53,14/39) Hyperbolic Matrix(703,396,-2970,-1673) (-31/55,-9/16) -> (-9/38,-13/55) Hyperbolic Matrix(917,514,2214,1241) (-23/41,-14/25) -> (12/29,17/41) Hyperbolic Matrix(269,150,-486,-271) (-14/25,-5/9) -> (-5/9,-16/29) Parabolic Matrix(3349,1846,5292,2917) (-16/29,-27/49) -> (31/49,50/79) Hyperbolic Matrix(701,386,2646,1457) (-27/49,-11/20) -> (9/34,13/49) Hyperbolic Matrix(1079,592,2754,1511) (-28/51,-17/31) -> (9/23,20/51) Hyperbolic Matrix(701,384,1674,917) (-17/31,-6/11) -> (18/43,13/31) Hyperbolic Matrix(217,118,-594,-323) (-6/11,-7/13) -> (-15/41,-4/11) Hyperbolic Matrix(217,116,810,433) (-7/13,-8/15) -> (4/15,11/41) Hyperbolic Matrix(377,200,-918,-487) (-8/15,-1/2) -> (-23/56,-16/39) Hyperbolic Matrix(541,256,-2052,-971) (-9/19,-8/17) -> (-24/91,-5/19) Hyperbolic Matrix(593,276,810,377) (-7/15,-6/13) -> (30/41,11/15) Hyperbolic Matrix(539,248,702,323) (-6/13,-11/24) -> (23/30,10/13) Hyperbolic Matrix(973,440,1674,757) (-5/11,-14/31) -> (18/31,25/43) Hyperbolic Matrix(377,170,-1080,-487) (-14/31,-9/20) -> (-7/20,-8/23) Hyperbolic Matrix(215,96,-486,-217) (-9/20,-4/9) -> (-4/9,-15/34) Parabolic Matrix(2699,1190,3672,1619) (-15/34,-26/59) -> (36/49,25/34) Hyperbolic Matrix(1457,642,1836,809) (-26/59,-11/25) -> (23/29,4/5) Hyperbolic Matrix(269,118,-864,-379) (-11/25,-7/16) -> (-5/16,-9/29) Hyperbolic Matrix(325,142,-1728,-755) (-7/16,-24/55) -> (-10/53,-3/16) Hyperbolic Matrix(2701,1178,4212,1837) (-24/55,-17/39) -> (25/39,34/53) Hyperbolic Matrix(271,118,-2106,-917) (-27/62,-10/23) -> (-4/31,-1/8) Hyperbolic Matrix(1943,844,2484,1079) (-10/23,-23/53) -> (43/55,18/23) Hyperbolic Matrix(595,258,-2862,-1241) (-23/53,-13/30) -> (-5/24,-11/53) Hyperbolic Matrix(541,230,-2538,-1079) (-3/7,-17/40) -> (-3/14,-13/61) Hyperbolic Matrix(269,114,-1404,-595) (-14/33,-11/26) -> (-5/26,-4/21) Hyperbolic Matrix(757,320,-2808,-1187) (-11/26,-19/45) -> (-17/63,-7/26) Hyperbolic Matrix(109,46,1026,433) (-19/45,-27/64) -> (1/10,1/9) Hyperbolic Matrix(2485,1048,-6912,-2915) (-27/64,-8/19) -> (-32/89,-23/64) Hyperbolic Matrix(1243,522,1674,703) (-21/50,-34/81) -> (20/27,3/4) Hyperbolic Matrix(1997,838,2700,1133) (-34/81,-13/31) -> (17/23,20/27) Hyperbolic Matrix(917,384,1674,701) (-13/31,-18/43) -> (6/11,17/31) Hyperbolic Matrix(757,316,1296,541) (-23/55,-5/12) -> (7/12,31/53) Hyperbolic Matrix(755,314,1296,539) (-5/12,-22/53) -> (32/55,7/12) Hyperbolic Matrix(6103,2532,9504,3943) (-39/94,-56/135) -> (52/81,9/14) Hyperbolic Matrix(7937,3292,12366,5129) (-56/135,-17/41) -> (43/67,52/81) Hyperbolic Matrix(1081,448,1566,649) (-17/41,-12/29) -> (20/29,9/13) Hyperbolic Matrix(2483,1024,3402,1403) (-26/63,-7/17) -> (27/37,46/63) Hyperbolic Matrix(1027,422,-4860,-1997) (-7/17,-23/56) -> (-11/52,-15/71) Hyperbolic Matrix(161,66,-1188,-487) (-16/39,-9/22) -> (-3/22,-2/15) Hyperbolic Matrix(485,198,1188,485) (-9/22,-11/27) -> (11/27,9/22) Hyperbolic Matrix(109,44,270,109) (-11/27,-2/5) -> (2/5,11/27) Hyperbolic Matrix(1621,636,-5778,-2267) (-11/28,-20/51) -> (-16/57,-23/82) Hyperbolic Matrix(811,318,1242,487) (-20/51,-9/23) -> (15/23,2/3) Hyperbolic Matrix(595,232,972,379) (-9/23,-7/18) -> (11/18,19/31) Hyperbolic Matrix(593,230,972,377) (-7/18,-12/31) -> (14/23,11/18) Hyperbolic Matrix(487,188,702,271) (-12/31,-5/13) -> (9/13,16/23) Hyperbolic Matrix(1567,600,1836,703) (-18/47,-31/81) -> (23/27,6/7) Hyperbolic Matrix(2159,826,2538,971) (-31/81,-13/34) -> (17/20,23/27) Hyperbolic Matrix(2267,866,-10746,-4105) (-34/89,-55/144) -> (-19/90,-4/19) Hyperbolic Matrix(2807,1072,-11880,-4537) (-55/144,-21/55) -> (-13/55,-17/72) Hyperbolic Matrix(4643,1772,5940,2267) (-21/55,-29/76) -> (25/32,43/55) Hyperbolic Matrix(1243,474,-4104,-1565) (-29/76,-8/21) -> (-10/33,-23/76) Hyperbolic Matrix(863,328,1134,431) (-8/21,-19/50) -> (3/4,16/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(53,20,-432,-163) (-14/37,-3/8) -> (-1/8,-2/17) Hyperbolic Matrix(161,60,432,161) (-3/8,-10/27) -> (10/27,3/8) Hyperbolic Matrix(379,140,1026,379) (-10/27,-7/19) -> (7/19,10/27) Hyperbolic Matrix(2375,872,5292,1943) (-18/49,-29/79) -> (13/29,22/49) Hyperbolic Matrix(1243,456,-4266,-1565) (-29/79,-11/30) -> (-7/24,-23/79) Hyperbolic Matrix(1567,574,2214,811) (-11/30,-15/41) -> (29/41,17/24) Hyperbolic Matrix(431,156,594,215) (-4/11,-9/25) -> (21/29,8/11) Hyperbolic Matrix(919,330,-3456,-1241) (-23/64,-14/39) -> (-4/15,-17/64) Hyperbolic Matrix(2375,852,4212,1511) (-14/39,-19/53) -> (31/55,22/39) Hyperbolic Matrix(7237,2592,12366,4429) (-24/67,-29/81) -> (79/135,24/41) Hyperbolic Matrix(5561,1990,9504,3401) (-29/81,-5/14) -> (55/94,79/135) Hyperbolic Matrix(163,58,-756,-269) (-5/14,-6/17) -> (-8/37,-3/14) Hyperbolic Matrix(1891,666,2916,1027) (-6/17,-19/54) -> (35/54,24/37) Hyperbolic Matrix(1889,664,2916,1025) (-19/54,-13/37) -> (11/17,35/54) Hyperbolic Matrix(755,262,1242,431) (-8/23,-1/3) -> (31/51,14/23) Hyperbolic Matrix(271,86,-1188,-377) (-1/3,-6/19) -> (-8/35,-13/57) Hyperbolic Matrix(1999,630,2916,919) (-6/19,-17/54) -> (37/54,24/35) Hyperbolic Matrix(1997,628,2916,917) (-17/54,-11/35) -> (13/19,37/54) Hyperbolic Matrix(917,284,1566,485) (-9/29,-4/13) -> (24/41,17/29) Hyperbolic Matrix(431,132,702,215) (-4/13,-7/23) -> (19/31,8/13) Hyperbolic Matrix(8533,2592,10314,3133) (-24/79,-41/135) -> (67/81,24/29) Hyperbolic Matrix(9557,2902,11556,3509) (-41/135,-17/56) -> (43/52,67/81) Hyperbolic Matrix(2809,852,3564,1081) (-17/56,-10/33) -> (26/33,41/52) Hyperbolic Matrix(18307,5538,26244,7939) (-36/119,-49/162) -> (113/162,30/43) Hyperbolic Matrix(18305,5536,26244,7937) (-49/162,-13/43) -> (83/119,113/162) Hyperbolic Matrix(53,16,-540,-163) (-13/43,-3/10) -> (-1/10,-1/11) Hyperbolic Matrix(161,48,540,161) (-3/10,-8/27) -> (8/27,3/10) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(1403,410,2214,647) (-12/41,-7/24) -> (19/30,26/41) Hyperbolic Matrix(2755,802,-9828,-2861) (-23/79,-16/55) -> (-30/107,-7/25) Hyperbolic Matrix(757,220,3348,973) (-16/55,-9/31) -> (7/31,12/53) Hyperbolic Matrix(2377,668,3078,865) (-9/32,-16/57) -> (44/57,17/22) Hyperbolic Matrix(21059,5906,26568,7451) (-23/82,-53/189) -> (107/135,65/82) Hyperbolic Matrix(19387,5436,24462,6859) (-53/189,-30/107) -> (42/53,107/135) Hyperbolic Matrix(703,196,972,271) (-7/25,-5/18) -> (13/18,21/29) Hyperbolic Matrix(701,194,972,269) (-5/18,-8/29) -> (18/25,13/18) Hyperbolic Matrix(379,104,594,163) (-8/29,-3/11) -> (7/11,16/25) Hyperbolic Matrix(1999,540,3402,919) (-10/37,-17/63) -> (37/63,10/17) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) Hyperbolic Matrix(433,116,810,217) (-11/41,-4/15) -> (8/15,7/13) Hyperbolic Matrix(19279,5118,26244,6967) (-30/113,-43/162) -> (119/162,36/49) Hyperbolic Matrix(19277,5116,26244,6965) (-43/162,-13/49) -> (83/113,119/162) Hyperbolic Matrix(2053,544,3672,973) (-13/49,-9/34) -> (19/34,33/59) Hyperbolic Matrix(1621,428,-8586,-2267) (-14/53,-19/72) -> (-17/90,-10/53) Hyperbolic Matrix(8803,2322,10854,2863) (-19/72,-24/91) -> (30/37,73/90) Hyperbolic Matrix(1567,408,2700,703) (-6/23,-7/27) -> (47/81,18/31) Hyperbolic Matrix(971,250,1674,431) (-7/27,-1/4) -> (29/50,47/81) Hyperbolic Matrix(703,168,1134,271) (-1/4,-5/21) -> (13/21,31/50) Hyperbolic Matrix(5239,1236,6642,1567) (-17/72,-4/17) -> (56/71,71/90) Hyperbolic Matrix(379,88,702,163) (-7/30,-3/13) -> (7/13,13/24) Hyperbolic Matrix(593,136,702,161) (-3/13,-8/35) -> (16/19,11/13) Hyperbolic Matrix(2213,504,3078,701) (-13/57,-5/22) -> (23/32,41/57) Hyperbolic Matrix(107,24,-486,-109) (-5/22,-2/9) -> (-2/9,-7/32) Parabolic Matrix(3673,802,5940,1297) (-7/32,-12/55) -> (34/55,47/76) Hyperbolic Matrix(1405,306,2484,541) (-12/55,-5/23) -> (13/23,30/53) Hyperbolic Matrix(1025,222,1242,269) (-5/23,-8/37) -> (14/17,19/23) Hyperbolic Matrix(9181,1956,11664,2485) (-13/61,-23/108) -> (85/108,37/47) Hyperbolic Matrix(9179,1954,11664,2483) (-23/108,-10/47) -> (48/61,85/108) Hyperbolic Matrix(2483,526,3564,755) (-7/33,-11/52) -> (39/56,23/33) Hyperbolic Matrix(5075,1072,6642,1403) (-15/71,-19/90) -> (55/72,13/17) Hyperbolic Matrix(17603,3652,24462,5075) (-11/53,-28/135) -> (136/189,77/107) Hyperbolic Matrix(19117,3964,26568,5509) (-28/135,-17/82) -> (59/82,136/189) Hyperbolic Matrix(1027,212,1836,379) (-6/29,-1/5) -> (33/59,14/25) Hyperbolic Matrix(7991,1510,10854,2051) (-7/37,-17/90) -> (53/72,67/91) Hyperbolic Matrix(161,30,864,161) (-3/16,-5/27) -> (5/27,3/16) Hyperbolic Matrix(109,20,594,109) (-5/27,-2/11) -> (2/11,5/27) Hyperbolic Matrix(811,144,918,163) (-8/45,-3/17) -> (15/17,8/9) Hyperbolic Matrix(973,170,1242,217) (-3/17,-4/23) -> (18/23,29/37) Hyperbolic Matrix(8047,1392,11556,1999) (-9/52,-14/81) -> (94/135,39/56) Hyperbolic Matrix(7181,1240,10314,1781) (-14/81,-5/29) -> (55/79,94/135) Hyperbolic Matrix(271,46,324,55) (-5/29,-1/6) -> (5/6,21/25) Hyperbolic Matrix(269,44,324,53) (-1/6,-4/25) -> (24/29,5/6) Hyperbolic Matrix(541,84,702,109) (-3/19,-2/13) -> (10/13,27/35) Hyperbolic Matrix(1567,234,2538,379) (-3/20,-4/27) -> (50/81,21/34) Hyperbolic Matrix(1133,166,1836,269) (-4/27,-1/7) -> (29/47,50/81) Hyperbolic Matrix(2539,330,2916,379) (-3/23,-7/54) -> (47/54,27/31) Hyperbolic Matrix(2537,328,2916,377) (-7/54,-4/31) -> (20/23,47/54) Hyperbolic Matrix(755,88,918,107) (-2/17,-1/9) -> (37/45,14/17) Hyperbolic Matrix(433,46,1026,109) (-1/9,-1/10) -> (27/64,19/45) Hyperbolic Matrix(377,-32,648,-55) (0/1,1/10) -> (57/98,32/55) Hyperbolic Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(701,-92,1242,-163) (1/8,2/15) -> (22/39,35/62) Hyperbolic Matrix(271,-38,378,-53) (2/15,1/7) -> (5/7,28/39) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(1729,-300,2484,-431) (5/29,4/23) -> (16/23,55/79) Hyperbolic Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(865,-164,1134,-215) (3/16,4/21) -> (16/21,29/38) Hyperbolic Matrix(163,-32,270,-53) (4/21,1/5) -> (3/5,20/33) Hyperbolic Matrix(649,-136,1026,-215) (1/5,4/19) -> (12/19,31/49) Hyperbolic Matrix(539,-114,1026,-217) (4/19,11/52) -> (1/2,10/19) Hyperbolic Matrix(1025,-218,1782,-379) (7/33,3/14) -> (23/40,19/33) Hyperbolic Matrix(269,-58,756,-163) (3/14,5/23) -> (11/31,5/14) Hyperbolic Matrix(109,-24,486,-107) (5/23,2/9) -> (2/9,7/31) Parabolic Matrix(377,-86,1188,-271) (5/22,8/35) -> (6/19,7/22) Hyperbolic Matrix(649,-152,918,-215) (3/13,4/17) -> (12/17,29/41) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(2269,-600,3672,-971) (5/19,9/34) -> (21/34,55/89) Hyperbolic Matrix(1241,-330,3456,-919) (13/49,4/15) -> (14/39,37/103) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(703,-206,918,-269) (7/24,5/17) -> (13/17,23/30) Hyperbolic Matrix(2701,-816,4644,-1403) (3/10,13/43) -> (25/43,57/98) Hyperbolic Matrix(1565,-474,4104,-1243) (13/43,10/33) -> (8/21,37/97) Hyperbolic Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(379,-118,864,-269) (4/13,5/16) -> (7/16,18/41) Hyperbolic Matrix(593,-186,864,-271) (5/16,6/19) -> (24/35,11/16) Hyperbolic Matrix(487,-170,1080,-377) (1/3,7/20) -> (9/20,23/51) Hyperbolic Matrix(701,-246,1080,-379) (7/20,6/17) -> (24/37,13/20) Hyperbolic Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(10153,-3648,13824,-4967) (37/103,23/64) -> (47/64,83/113) Hyperbolic Matrix(2269,-816,2700,-971) (23/64,9/25) -> (21/25,37/44) Hyperbolic Matrix(323,-118,594,-217) (4/11,11/30) -> (13/24,6/11) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(11449,-4368,16416,-6263) (37/97,29/76) -> (53/76,83/119) Hyperbolic Matrix(2701,-1032,3672,-1403) (21/55,13/34) -> (25/34,39/53) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(1513,-620,2106,-863) (9/22,16/39) -> (28/39,23/32) Hyperbolic Matrix(487,-200,918,-377) (16/39,7/17) -> (9/17,8/15) Hyperbolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(3673,-1524,5724,-2375) (17/41,22/53) -> (34/53,43/67) Hyperbolic Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1727,-728,2052,-865) (8/19,27/64) -> (37/44,16/19) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(1081,-458,1782,-755) (11/26,14/33) -> (20/33,17/28) Hyperbolic Matrix(1403,-596,1782,-757) (14/33,3/7) -> (37/47,26/33) Hyperbolic Matrix(269,-116,378,-163) (3/7,10/23) -> (22/31,5/7) Hyperbolic Matrix(1079,-470,1242,-541) (10/23,17/39) -> (13/15,20/23) Hyperbolic Matrix(2267,-990,2970,-1297) (24/55,7/16) -> (29/38,42/55) Hyperbolic Matrix(217,-96,486,-215) (11/25,4/9) -> (4/9,13/29) Parabolic Matrix(377,-172,594,-271) (5/11,6/13) -> (26/41,7/11) Hyperbolic Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(1511,-796,2052,-1081) (10/19,9/17) -> (67/91,14/19) Hyperbolic Matrix(703,-386,1080,-593) (17/31,11/20) -> (13/20,15/23) Hyperbolic Matrix(271,-150,486,-269) (11/20,5/9) -> (5/9,19/34) Parabolic Matrix(595,-334,864,-485) (14/25,9/16) -> (11/16,20/29) Hyperbolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1835,-1036,2106,-1189) (35/62,13/23) -> (27/31,7/8) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1997,-1148,2538,-1459) (4/7,23/40) -> (11/14,48/61) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(4157,-2526,5778,-3511) (17/28,31/51) -> (41/57,59/82) Hyperbolic Matrix(8479,-5240,10746,-6641) (55/89,89/144) -> (71/90,15/19) Hyperbolic Matrix(9073,-5608,11880,-7343) (89/144,34/55) -> (42/55,55/72) Hyperbolic Matrix(2861,-1770,4104,-2539) (47/76,13/21) -> (23/33,53/76) Hyperbolic Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(3023,-1914,4266,-2701) (50/79,19/30) -> (17/24,56/79) Hyperbolic Matrix(2537,-1626,3456,-2215) (41/64,25/39) -> (11/15,47/64) Hyperbolic Matrix(593,-382,756,-487) (9/14,11/17) -> (29/37,11/14) Hyperbolic Matrix(917,-626,1188,-811) (2/3,13/19) -> (27/35,44/57) Hyperbolic Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(7073,-5014,9828,-6967) (56/79,39/55) -> (77/107,18/25) Hyperbolic Matrix(6965,-5126,8586,-6319) (39/53,53/72) -> (73/90,43/53) Hyperbolic Matrix(379,-294,486,-377) (17/22,7/9) -> (7/9,25/32) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(271,248,-648,-593) -> Matrix(3,10,-4,-13) Matrix(593,530,1026,917) -> Matrix(1,2,-4,-7) Matrix(379,334,-918,-809) -> Matrix(5,2,-8,-3) Matrix(541,470,-1242,-1079) -> Matrix(13,-4,-16,5) Matrix(107,92,-378,-325) -> Matrix(3,-8,-4,11) Matrix(269,228,-702,-595) -> Matrix(1,6,0,1) Matrix(161,136,702,593) -> Matrix(1,6,-4,-23) Matrix(971,816,-2700,-2269) -> Matrix(31,100,-40,-129) Matrix(55,46,324,271) -> Matrix(1,2,0,1) Matrix(53,44,324,269) -> Matrix(1,2,-4,-7) Matrix(755,624,-2484,-2053) -> Matrix(1,0,0,1) Matrix(325,268,918,757) -> Matrix(3,8,-8,-21) Matrix(161,132,-594,-487) -> Matrix(7,10,-12,-17) Matrix(485,396,594,485) -> Matrix(9,10,-28,-31) Matrix(703,572,864,703) -> Matrix(11,10,-32,-29) Matrix(269,218,-1134,-919) -> Matrix(3,2,4,3) Matrix(107,86,-270,-217) -> Matrix(1,0,0,1) Matrix(377,298,-1026,-811) -> Matrix(11,-10,-12,11) Matrix(487,384,-1026,-809) -> Matrix(1,-2,0,1) Matrix(1081,852,3564,2809) -> Matrix(1,0,-4,1) Matrix(757,596,-1782,-1403) -> Matrix(5,-8,-8,13) Matrix(487,382,-756,-593) -> Matrix(1,-2,0,1) Matrix(377,294,-486,-379) -> Matrix(1,-10,0,1) Matrix(2375,1838,3348,2591) -> Matrix(1,4,-4,-15) Matrix(1999,1546,5238,4051) -> Matrix(1,10,-4,-39) Matrix(811,626,-1188,-917) -> Matrix(7,30,-4,-17) Matrix(109,84,702,541) -> Matrix(1,4,-4,-15) Matrix(269,206,-918,-703) -> Matrix(7,22,-8,-25) Matrix(215,164,-1134,-865) -> Matrix(13,32,-24,-59) Matrix(431,328,1134,863) -> Matrix(9,20,-32,-71) Matrix(431,318,-1026,-757) -> Matrix(5,4,-4,-3) Matrix(1403,1032,-3672,-2701) -> Matrix(21,16,-4,-3) Matrix(1189,874,2646,1945) -> Matrix(39,28,-124,-89) Matrix(2215,1626,-3456,-2537) -> Matrix(3,2,-8,-5) Matrix(377,276,810,593) -> Matrix(3,2,-8,-5) Matrix(755,552,-2808,-2053) -> Matrix(1,0,0,1) Matrix(107,78,-594,-433) -> Matrix(7,4,-16,-9) Matrix(215,156,594,431) -> Matrix(13,4,-36,-11) Matrix(271,196,972,703) -> Matrix(19,2,-48,-5) Matrix(269,194,972,701) -> Matrix(13,-2,-32,5) Matrix(3511,2526,-5778,-4157) -> Matrix(1,-2,0,1) Matrix(431,310,1350,971) -> Matrix(1,0,-4,1) Matrix(53,38,-378,-271) -> Matrix(3,-2,-4,3) Matrix(163,116,-378,-269) -> Matrix(3,-2,-4,3) Matrix(215,152,-918,-649) -> Matrix(1,-4,0,1) Matrix(647,456,918,647) -> Matrix(1,-12,-4,49) Matrix(379,266,540,379) -> Matrix(1,10,-4,-39) Matrix(1943,1356,-4644,-3241) -> Matrix(3,16,-4,-21) Matrix(2539,1770,-4104,-2861) -> Matrix(1,2,0,1) Matrix(755,526,3564,2483) -> Matrix(1,4,-4,-15) Matrix(431,300,-2484,-1729) -> Matrix(7,20,-20,-57) Matrix(271,188,702,487) -> Matrix(1,2,-4,-7) Matrix(485,334,-864,-595) -> Matrix(1,2,0,1) Matrix(271,186,-864,-593) -> Matrix(1,2,4,9) Matrix(379,258,1350,919) -> Matrix(31,50,-80,-129) Matrix(593,386,-1080,-703) -> Matrix(7,2,-4,-1) Matrix(379,246,-1080,-701) -> Matrix(13,2,-20,-3) Matrix(161,104,918,593) -> Matrix(3,-2,-4,3) Matrix(2375,1524,-5724,-3673) -> Matrix(1,0,0,1) Matrix(1837,1178,4212,2701) -> Matrix(13,4,-36,-11) Matrix(3671,2352,-13824,-8857) -> Matrix(23,-4,-40,7) Matrix(431,276,-2700,-1729) -> Matrix(1,0,0,1) Matrix(163,104,594,379) -> Matrix(5,-2,-12,5) Matrix(271,172,-594,-377) -> Matrix(1,-2,0,1) Matrix(215,136,-1026,-649) -> Matrix(3,-8,-4,11) Matrix(647,408,1026,647) -> Matrix(1,-8,-4,33) Matrix(271,170,432,271) -> Matrix(1,6,-4,-23) Matrix(647,402,-1566,-973) -> Matrix(5,12,-8,-19) Matrix(2051,1272,-5400,-3349) -> Matrix(25,48,-12,-23) Matrix(271,168,1134,703) -> Matrix(1,2,-8,-15) Matrix(4967,3072,-16416,-10153) -> Matrix(9,16,-4,-7) Matrix(1187,734,5238,3239) -> Matrix(7,12,-24,-41) Matrix(971,600,-3672,-2269) -> Matrix(11,16,-20,-29) Matrix(107,66,-702,-433) -> Matrix(1,0,0,1) Matrix(215,132,702,431) -> Matrix(1,4,-4,-15) Matrix(379,232,972,595) -> Matrix(1,2,0,1) Matrix(377,230,972,593) -> Matrix(1,2,-8,-15) Matrix(1243,756,2754,1675) -> Matrix(5,6,-16,-19) Matrix(1511,918,-7290,-4429) -> Matrix(11,20,-16,-29) Matrix(53,32,-270,-163) -> Matrix(7,10,-12,-17) Matrix(161,96,270,161) -> Matrix(9,10,-28,-31) Matrix(703,416,1188,703) -> Matrix(35,34,-104,-101) Matrix(593,350,-2106,-1243) -> Matrix(63,58,-88,-81) Matrix(431,254,-918,-541) -> Matrix(9,8,-8,-7) Matrix(593,348,-1566,-919) -> Matrix(27,22,-16,-13) Matrix(973,570,2214,1297) -> Matrix(67,52,-192,-149) Matrix(2051,1200,-5724,-3349) -> Matrix(145,108,-192,-143) Matrix(541,316,1296,757) -> Matrix(17,12,-44,-31) Matrix(539,314,1296,755) -> Matrix(7,4,-16,-9) Matrix(55,32,-648,-377) -> Matrix(3,2,-8,-5) Matrix(757,440,1674,973) -> Matrix(13,8,-44,-27) Matrix(269,156,-1026,-595) -> Matrix(13,6,-24,-11) Matrix(325,188,-2052,-1187) -> Matrix(1,0,0,1) Matrix(917,530,1026,593) -> Matrix(1,2,-4,-7) Matrix(433,250,-2430,-1403) -> Matrix(7,4,-16,-9) Matrix(701,404,-1782,-1027) -> Matrix(5,2,-8,-3) Matrix(379,218,-1782,-1025) -> Matrix(5,2,-8,-3) Matrix(109,62,-378,-215) -> Matrix(3,4,-4,-5) Matrix(163,92,-1242,-701) -> Matrix(3,-2,-4,3) Matrix(1511,852,4212,2375) -> Matrix(3,-16,-8,43) Matrix(703,396,-2970,-1673) -> Matrix(1,2,0,1) Matrix(917,514,2214,1241) -> Matrix(3,2,-8,-5) Matrix(269,150,-486,-271) -> Matrix(1,-2,0,1) Matrix(3349,1846,5292,2917) -> Matrix(1,0,-4,1) Matrix(701,386,2646,1457) -> Matrix(9,14,-20,-31) Matrix(1079,592,2754,1511) -> Matrix(3,4,-4,-5) Matrix(701,384,1674,917) -> Matrix(3,2,-8,-5) Matrix(217,118,-594,-323) -> Matrix(7,8,-8,-9) Matrix(217,116,810,433) -> Matrix(5,8,-12,-19) Matrix(377,200,-918,-487) -> Matrix(7,10,-12,-17) Matrix(541,256,-2052,-971) -> Matrix(9,4,-16,-7) Matrix(593,276,810,377) -> Matrix(3,2,-8,-5) Matrix(539,248,702,323) -> Matrix(1,4,-4,-15) Matrix(973,440,1674,757) -> Matrix(5,8,-12,-19) Matrix(377,170,-1080,-487) -> Matrix(7,10,-12,-17) Matrix(215,96,-486,-217) -> Matrix(15,16,-16,-17) Matrix(2699,1190,3672,1619) -> Matrix(57,52,-148,-135) Matrix(1457,642,1836,809) -> Matrix(11,10,-76,-69) Matrix(269,118,-864,-379) -> Matrix(7,6,8,7) Matrix(325,142,-1728,-755) -> Matrix(53,44,-100,-83) Matrix(2701,1178,4212,1837) -> Matrix(5,4,-4,-3) Matrix(271,118,-2106,-917) -> Matrix(57,46,-88,-71) Matrix(1943,844,2484,1079) -> Matrix(21,16,-88,-67) Matrix(595,258,-2862,-1241) -> Matrix(23,18,-32,-25) Matrix(541,230,-2538,-1079) -> Matrix(25,16,-36,-23) Matrix(269,114,-1404,-595) -> Matrix(5,2,-8,-3) Matrix(757,320,-2808,-1187) -> Matrix(1,0,0,1) Matrix(109,46,1026,433) -> Matrix(9,4,-16,-7) Matrix(2485,1048,-6912,-2915) -> Matrix(65,24,-84,-31) Matrix(1243,522,1674,703) -> Matrix(9,10,-28,-31) Matrix(1997,838,2700,1133) -> Matrix(19,18,-56,-53) Matrix(917,384,1674,701) -> Matrix(3,2,-8,-5) Matrix(757,316,1296,541) -> Matrix(17,12,-44,-31) Matrix(755,314,1296,539) -> Matrix(7,4,-16,-9) Matrix(6103,2532,9504,3943) -> Matrix(1,2,-4,-7) Matrix(7937,3292,12366,5129) -> Matrix(7,6,-20,-17) Matrix(1081,448,1566,649) -> Matrix(11,8,-40,-29) Matrix(2483,1024,3402,1403) -> Matrix(7,4,-16,-9) Matrix(1027,422,-4860,-1997) -> Matrix(23,14,-28,-17) Matrix(161,66,-1188,-487) -> Matrix(3,2,-8,-5) Matrix(485,198,1188,485) -> Matrix(19,10,-40,-21) Matrix(109,44,270,109) -> Matrix(1,0,0,1) Matrix(1621,636,-5778,-2267) -> Matrix(87,40,-124,-57) Matrix(811,318,1242,487) -> Matrix(5,2,-8,-3) Matrix(595,232,972,379) -> Matrix(9,2,-32,-7) Matrix(593,230,972,377) -> Matrix(7,-2,-24,7) Matrix(487,188,702,271) -> Matrix(1,2,-4,-7) Matrix(1567,600,1836,703) -> Matrix(1,-14,-4,57) Matrix(2159,826,2538,971) -> Matrix(1,24,-4,-95) Matrix(2267,866,-10746,-4105) -> Matrix(3,16,-4,-21) Matrix(2807,1072,-11880,-4537) -> Matrix(1,4,0,1) Matrix(4643,1772,5940,2267) -> Matrix(1,0,-4,1) Matrix(1243,474,-4104,-1565) -> Matrix(1,2,0,1) Matrix(863,328,1134,431) -> Matrix(9,20,-32,-71) Matrix(7237,2748,11664,4429) -> Matrix(49,100,-172,-351) Matrix(7235,2746,11664,4427) -> Matrix(55,108,-192,-377) Matrix(53,20,-432,-163) -> Matrix(7,10,-12,-17) Matrix(161,60,432,161) -> Matrix(9,10,-28,-31) Matrix(379,140,1026,379) -> Matrix(31,30,-92,-89) Matrix(2375,872,5292,1943) -> Matrix(137,124,-432,-391) Matrix(1243,456,-4266,-1565) -> Matrix(105,94,-124,-111) Matrix(1567,574,2214,811) -> Matrix(25,22,-108,-95) Matrix(431,156,594,215) -> Matrix(5,4,-4,-3) Matrix(919,330,-3456,-1241) -> Matrix(107,82,-184,-141) Matrix(2375,852,4212,1511) -> Matrix(21,16,-88,-67) Matrix(7237,2592,12366,4429) -> Matrix(319,240,-852,-641) Matrix(5561,1990,9504,3401) -> Matrix(233,174,-620,-463) Matrix(163,58,-756,-269) -> Matrix(25,18,-32,-23) Matrix(1891,666,2916,1027) -> Matrix(3,2,40,27) Matrix(1889,664,2916,1025) -> Matrix(3,2,-56,-37) Matrix(755,262,1242,431) -> Matrix(13,8,-44,-27) Matrix(271,86,-1188,-377) -> Matrix(7,2,-4,-1) Matrix(1999,630,2916,919) -> Matrix(41,2,-144,-7) Matrix(1997,628,2916,917) -> Matrix(39,-2,-136,7) Matrix(917,284,1566,485) -> Matrix(3,-10,-8,27) Matrix(431,132,702,215) -> Matrix(1,4,-4,-15) Matrix(8533,2592,10314,3133) -> Matrix(7,12,-24,-41) Matrix(9557,2902,11556,3509) -> Matrix(5,6,-16,-19) Matrix(2809,852,3564,1081) -> Matrix(1,0,-4,1) Matrix(18307,5538,26244,7939) -> Matrix(33,70,-124,-263) Matrix(18305,5536,26244,7937) -> Matrix(47,90,-176,-337) Matrix(53,16,-540,-163) -> Matrix(1,2,-4,-7) Matrix(161,48,540,161) -> Matrix(9,10,-28,-31) Matrix(271,80,918,271) -> Matrix(23,22,-68,-65) Matrix(1403,410,2214,647) -> Matrix(9,8,-44,-39) Matrix(2755,802,-9828,-2861) -> Matrix(313,262,-448,-375) Matrix(757,220,3348,973) -> Matrix(39,32,-128,-105) Matrix(2377,668,3078,865) -> Matrix(113,80,-428,-303) Matrix(21059,5906,26568,7451) -> Matrix(257,180,-1552,-1087) Matrix(19387,5436,24462,6859) -> Matrix(243,170,-1448,-1013) Matrix(703,196,972,271) -> Matrix(3,2,16,11) Matrix(701,194,972,269) -> Matrix(3,2,-32,-21) Matrix(379,104,594,163) -> Matrix(3,2,-20,-13) Matrix(1999,540,3402,919) -> Matrix(47,26,-132,-73) Matrix(8533,2292,11664,3133) -> Matrix(17,12,-44,-31) Matrix(8531,2290,11664,3131) -> Matrix(31,20,-76,-49) Matrix(433,116,810,217) -> Matrix(13,8,-44,-27) Matrix(19279,5118,26244,6967) -> Matrix(325,186,-816,-467) Matrix(19277,5116,26244,6965) -> Matrix(291,166,-724,-413) Matrix(2053,544,3672,973) -> Matrix(7,4,-44,-25) Matrix(1621,428,-8586,-2267) -> Matrix(9,4,-16,-7) Matrix(8803,2322,10854,2863) -> Matrix(11,6,-24,-13) Matrix(1567,408,2700,703) -> Matrix(35,18,-72,-37) Matrix(971,250,1674,431) -> Matrix(17,8,-32,-15) Matrix(703,168,1134,271) -> Matrix(7,-2,-24,7) Matrix(5239,1236,6642,1567) -> Matrix(1,-2,-4,9) Matrix(379,88,702,163) -> Matrix(1,2,-4,-7) Matrix(593,136,702,161) -> Matrix(1,6,-4,-23) Matrix(2213,504,3078,701) -> Matrix(1,2,-8,-15) Matrix(107,24,-486,-109) -> Matrix(7,8,-8,-9) Matrix(3673,802,5940,1297) -> Matrix(33,28,-112,-95) Matrix(1405,306,2484,541) -> Matrix(5,4,-4,-3) Matrix(1025,222,1242,269) -> Matrix(3,2,-8,-5) Matrix(9181,1956,11664,2485) -> Matrix(53,36,-240,-163) Matrix(9179,1954,11664,2483) -> Matrix(43,28,-192,-125) Matrix(2483,526,3564,755) -> Matrix(1,4,-4,-15) Matrix(5075,1072,6642,1403) -> Matrix(23,20,-84,-73) Matrix(17603,3652,24462,5075) -> Matrix(11,8,-84,-61) Matrix(19117,3964,26568,5509) -> Matrix(17,12,-112,-79) Matrix(1027,212,1836,379) -> Matrix(3,2,-8,-5) Matrix(7991,1510,10854,2051) -> Matrix(67,36,-188,-101) Matrix(161,30,864,161) -> Matrix(43,22,-88,-45) Matrix(109,20,594,109) -> Matrix(25,12,-48,-23) Matrix(811,144,918,163) -> Matrix(5,2,-8,-3) Matrix(973,170,1242,217) -> Matrix(21,8,-92,-35) Matrix(8047,1392,11556,1999) -> Matrix(243,82,-892,-301) Matrix(7181,1240,10314,1781) -> Matrix(225,74,-824,-271) Matrix(271,46,324,55) -> Matrix(9,2,-32,-7) Matrix(269,44,324,53) -> Matrix(1,2,-4,-7) Matrix(541,84,702,109) -> Matrix(1,4,-4,-15) Matrix(1567,234,2538,379) -> Matrix(9,10,-28,-31) Matrix(1133,166,1836,269) -> Matrix(7,6,-20,-17) Matrix(2539,330,2916,379) -> Matrix(3,2,28,19) Matrix(2537,328,2916,377) -> Matrix(3,2,-56,-37) Matrix(755,88,918,107) -> Matrix(37,20,-124,-67) Matrix(433,46,1026,109) -> Matrix(9,4,-16,-7) Matrix(377,-32,648,-55) -> Matrix(3,2,-8,-5) Matrix(539,-64,918,-109) -> Matrix(53,24,-148,-67) Matrix(701,-92,1242,-163) -> Matrix(5,2,-28,-11) Matrix(271,-38,378,-53) -> Matrix(5,2,-28,-11) Matrix(433,-66,702,-107) -> Matrix(1,0,0,1) Matrix(1729,-276,2700,-431) -> Matrix(1,0,0,1) Matrix(1729,-300,2484,-431) -> Matrix(23,20,-84,-73) Matrix(433,-78,594,-107) -> Matrix(7,4,-16,-9) Matrix(865,-164,1134,-215) -> Matrix(69,32,-248,-115) Matrix(163,-32,270,-53) -> Matrix(23,10,-76,-33) Matrix(649,-136,1026,-215) -> Matrix(21,8,-92,-35) Matrix(539,-114,1026,-217) -> Matrix(23,8,-72,-25) Matrix(1025,-218,1782,-379) -> Matrix(5,2,-8,-3) Matrix(269,-58,756,-163) -> Matrix(49,18,-128,-47) Matrix(109,-24,486,-107) -> Matrix(23,8,-72,-25) Matrix(377,-86,1188,-271) -> Matrix(7,2,-4,-1) Matrix(649,-152,918,-215) -> Matrix(15,4,-64,-17) Matrix(919,-218,1134,-269) -> Matrix(11,2,-28,-5) Matrix(595,-156,1026,-269) -> Matrix(13,6,-24,-11) Matrix(2269,-600,3672,-971) -> Matrix(35,16,-116,-53) Matrix(1241,-330,3456,-919) -> Matrix(187,82,-504,-221) Matrix(2053,-552,2808,-755) -> Matrix(1,0,0,1) Matrix(487,-132,594,-161) -> Matrix(23,10,-76,-33) Matrix(2267,-636,5778,-1621) -> Matrix(103,40,-188,-73) Matrix(325,-92,378,-107) -> Matrix(21,8,-92,-35) Matrix(215,-62,378,-109) -> Matrix(11,4,-36,-13) Matrix(703,-206,918,-269) -> Matrix(63,22,-232,-81) Matrix(2701,-816,4644,-1403) -> Matrix(13,4,-36,-11) Matrix(1565,-474,4104,-1243) -> Matrix(9,2,-32,-7) Matrix(2053,-624,2484,-755) -> Matrix(1,0,0,1) Matrix(379,-118,864,-269) -> Matrix(31,6,-88,-17) Matrix(593,-186,864,-271) -> Matrix(17,2,-60,-7) Matrix(487,-170,1080,-377) -> Matrix(23,10,-76,-33) Matrix(701,-246,1080,-379) -> Matrix(5,2,12,5) Matrix(3349,-1200,5724,-2051) -> Matrix(289,108,-768,-287) Matrix(10153,-3648,13824,-4967) -> Matrix(335,124,-824,-305) Matrix(2269,-816,2700,-971) -> Matrix(271,100,-1000,-369) Matrix(323,-118,594,-217) -> Matrix(23,8,-72,-25) Matrix(811,-298,1026,-377) -> Matrix(29,10,-148,-51) Matrix(919,-348,1566,-593) -> Matrix(75,22,-208,-61) Matrix(3349,-1272,5400,-2051) -> Matrix(169,48,-588,-167) Matrix(11449,-4368,16416,-6263) -> Matrix(241,64,-900,-239) Matrix(2701,-1032,3672,-1403) -> Matrix(61,16,-164,-43) Matrix(595,-228,702,-269) -> Matrix(25,6,-96,-23) Matrix(5779,-2268,7290,-2861) -> Matrix(19,10,-116,-61) Matrix(217,-86,270,-107) -> Matrix(1,0,0,1) Matrix(1513,-620,2106,-863) -> Matrix(9,4,-52,-23) Matrix(487,-200,918,-377) -> Matrix(23,10,-76,-33) Matrix(973,-402,1566,-647) -> Matrix(29,12,-104,-43) Matrix(3673,-1524,5724,-2375) -> Matrix(1,0,0,1) Matrix(593,-248,648,-271) -> Matrix(27,10,-100,-37) Matrix(757,-318,1026,-431) -> Matrix(13,4,-36,-11) Matrix(1727,-728,2052,-865) -> Matrix(1,4,-4,-15) Matrix(1997,-844,2430,-1027) -> Matrix(23,10,-76,-33) Matrix(1081,-458,1782,-755) -> Matrix(11,4,-36,-13) Matrix(1403,-596,1782,-757) -> Matrix(19,8,-88,-37) Matrix(269,-116,378,-163) -> Matrix(5,2,-28,-11) Matrix(1079,-470,1242,-541) -> Matrix(11,4,-80,-29) Matrix(2267,-990,2970,-1297) -> Matrix(167,60,-604,-217) Matrix(217,-96,486,-215) -> Matrix(47,16,-144,-49) Matrix(377,-172,594,-271) -> Matrix(7,2,-32,-9) Matrix(541,-254,918,-431) -> Matrix(25,8,-72,-23) Matrix(1511,-796,2052,-1081) -> Matrix(25,8,-72,-23) Matrix(703,-386,1080,-593) -> Matrix(7,2,-4,-1) Matrix(271,-150,486,-269) -> Matrix(7,2,-32,-9) Matrix(595,-334,864,-485) -> Matrix(9,2,-32,-7) Matrix(1403,-790,1728,-973) -> Matrix(13,4,-36,-11) Matrix(1835,-1036,2106,-1189) -> Matrix(1,0,4,1) Matrix(2267,-1284,2862,-1621) -> Matrix(9,4,-52,-23) Matrix(1997,-1148,2538,-1459) -> Matrix(1,-2,-4,9) Matrix(1135,-654,1404,-809) -> Matrix(3,2,-8,-5) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(4427,-2560,6912,-3997) -> Matrix(1,0,0,1) Matrix(3833,-2258,4860,-2863) -> Matrix(17,6,-88,-31) Matrix(1027,-606,1188,-701) -> Matrix(29,10,-148,-51) Matrix(4157,-2526,5778,-3511) -> Matrix(7,2,-32,-9) Matrix(8479,-5240,10746,-6641) -> Matrix(19,6,-92,-29) Matrix(9073,-5608,11880,-7343) -> Matrix(145,44,-524,-159) Matrix(2861,-1770,4104,-2539) -> Matrix(9,2,-32,-7) Matrix(379,-236,432,-269) -> Matrix(7,2,-32,-9) Matrix(3023,-1914,4266,-2701) -> Matrix(1,0,0,1) Matrix(2537,-1626,3456,-2215) -> Matrix(3,2,-8,-5) Matrix(593,-382,756,-487) -> Matrix(7,2,-32,-9) Matrix(917,-626,1188,-811) -> Matrix(103,30,-388,-113) Matrix(487,-340,540,-377) -> Matrix(7,2,-32,-9) Matrix(7073,-5014,9828,-6967) -> Matrix(9,2,-68,-15) Matrix(6965,-5126,8586,-6319) -> Matrix(49,18,-128,-47) Matrix(379,-294,486,-377) -> Matrix(39,10,-160,-41) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 Degree of the the map X: 162 Degree of the the map Y: 324 ----------------------------------------------------------------------- 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): 972 Minimal number of generators: 163 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: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/9 -7/9 -2/3 -5/9 -4/9 -5/12 -41/108 -1/3 -29/108 -2/9 -1/6 -4/27 0/1 1/10 1/9 1/8 1/7 2/13 3/19 1/6 3/17 2/11 5/27 1/5 5/23 2/9 3/13 5/21 1/4 3/11 7/25 2/7 8/27 1/3 10/27 2/5 11/27 5/12 19/45 4/9 7/15 1/2 5/9 47/81 79/135 16/27 13/21 17/27 2/3 19/27 11/15 20/27 7/9 107/135 22/27 67/81 23/27 8/9 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -9/10 -3/1 1/0 -8/9 -1/1 -7/8 -1/1 1/0 -6/7 4/1 1/0 -5/6 -2/1 -14/17 -2/1 -7/4 -9/11 -5/4 -22/27 -1/1 -13/16 -1/1 -5/6 -17/21 -1/2 -4/5 -1/2 0/1 -15/19 5/4 -11/14 1/1 1/0 -7/9 1/0 -10/13 -4/1 1/0 -13/17 -11/4 -3/4 -3/2 -1/1 -14/19 -4/5 -3/4 -11/15 -1/2 -30/41 -3/4 -2/3 -19/26 -3/5 -1/2 -8/11 -1/2 -2/5 -5/7 1/0 -7/10 -5/1 1/0 -9/13 1/0 -11/16 -3/1 -5/2 -2/3 -1/1 -11/17 1/4 -9/14 -1/1 1/0 -7/11 1/0 -5/8 -3/1 1/0 -18/29 -13/6 -2/1 -31/50 -13/7 -11/6 -13/21 -3/2 -21/34 -5/4 -1/1 -8/13 0/1 1/0 -3/5 -5/4 -16/27 -1/1 -13/22 -1/1 -17/18 -23/39 -9/10 -10/17 -7/8 -6/7 -17/29 -19/24 -7/12 -2/3 -11/19 -1/4 -37/64 1/1 1/0 -26/45 -1/1 -15/26 -3/5 -1/2 -4/7 0/1 1/0 -13/23 -1/4 -9/16 -1/1 -1/2 -5/9 1/0 -6/11 -2/1 -3/2 -7/13 1/0 -1/2 -1/1 -1/2 -5/11 1/0 -4/9 -1/1 -3/7 -3/4 -8/19 0/1 1/0 -21/50 -7/6 -1/1 -34/81 -1/1 -13/31 -7/8 -5/12 -2/3 -12/29 -7/10 -2/3 -19/46 -5/8 -3/5 -26/63 -3/5 -7/17 -5/8 -2/5 -1/2 0/1 -11/28 -5/9 -1/2 -9/23 -1/4 -7/18 0/1 -5/13 1/0 -8/21 -3/1 -19/50 -11/5 -13/6 -30/79 -37/18 -2/1 -41/108 -2/1 -11/29 -15/8 -14/37 -13/8 -8/5 -3/8 -5/4 -1/1 -10/27 -1/1 -7/19 -15/16 -18/49 -31/34 -10/11 -11/30 -8/9 -4/11 -6/7 -5/6 -9/25 -25/32 -5/14 -3/4 -11/15 -1/3 -1/2 -4/13 -4/1 1/0 -7/23 1/0 -3/10 -5/4 -1/1 -8/27 -1/1 -5/17 -11/12 -7/24 -6/7 -9/31 -13/16 -2/7 -4/5 -3/4 -9/32 -5/7 -27/38 -7/25 -25/36 -5/18 -2/3 -3/11 -5/8 -10/37 -4/7 -9/16 -7/26 -3/5 -1/2 -18/67 -3/4 -2/3 -29/108 -2/3 -11/41 -5/8 -4/15 -3/5 -1/4 -1/2 -1/3 -3/13 1/0 -2/9 -1/1 -1/5 -5/8 -2/11 -1/2 -6/13 -5/28 -1/2 -1/3 -8/45 -3/7 -3/17 -5/12 -1/6 0/1 -2/13 0/1 1/0 -3/20 -5/4 -1/1 -4/27 -1/1 -1/7 -3/4 0/1 -1/2 0/1 1/10 -1/1 -3/4 1/9 -1/2 1/8 -3/7 -5/12 1/7 -3/8 2/13 -1/4 0/1 3/19 1/0 4/25 -1/2 0/1 1/6 0/1 4/23 -5/6 -4/5 3/17 -5/8 2/11 -6/11 -1/2 5/27 -1/2 3/16 -1/2 -11/23 1/5 -5/12 3/14 -5/13 -3/8 5/23 -3/8 2/9 -1/3 3/13 -1/4 4/17 -1/4 -2/9 5/21 -1/6 1/4 -1/1 -1/2 5/19 -11/24 4/15 -3/7 11/41 -5/12 7/26 -1/2 -3/7 3/11 -5/12 5/18 -2/5 7/25 -25/64 16/57 -19/49 9/32 -27/70 -5/13 2/7 -3/8 -4/11 7/24 -6/17 5/17 -11/32 8/27 -1/3 3/10 -1/3 -5/16 10/33 -1/3 17/56 -1/3 -3/10 7/23 -1/4 4/13 -4/15 -1/4 1/3 -1/2 5/14 -11/29 -3/8 19/53 -3/8 14/39 -13/35 9/25 -25/68 4/11 -5/14 -6/17 11/30 -8/23 7/19 -15/44 10/27 -1/3 3/8 -1/3 -5/16 11/29 -15/52 19/50 -13/46 -11/39 8/21 -3/11 13/34 -9/35 -1/4 5/13 -1/4 7/18 0/1 9/23 1/0 20/51 -3/5 31/79 -15/28 11/28 -1/2 -5/11 2/5 -1/2 0/1 11/27 -1/2 9/22 -1/2 -5/11 7/17 -5/12 12/29 -2/5 -7/18 17/41 -3/8 5/12 -2/5 23/55 -3/8 18/43 -4/11 -5/14 13/31 -7/20 8/19 -1/4 0/1 27/64 -5/8 -3/5 19/45 -1/2 11/26 -1/2 -3/7 3/7 -3/8 7/16 -5/14 -11/31 11/25 -25/72 4/9 -1/3 5/11 -1/4 6/13 -1/4 0/1 7/15 -1/2 1/2 -1/2 -1/3 8/15 -1/3 7/13 -1/4 6/11 -3/10 -2/7 5/9 -1/4 9/16 -1/2 -1/3 31/55 -1/4 22/39 -1/5 13/23 1/0 30/53 -6/11 -1/2 17/30 -2/5 4/7 -1/4 0/1 19/33 -1/2 15/26 -1/2 -3/7 26/45 -1/3 37/64 -1/4 -1/5 11/19 1/0 29/50 -7/13 -1/2 47/81 -1/2 18/31 -1/2 -6/13 7/12 -2/5 31/53 -3/8 55/94 -47/125 -3/8 79/135 -3/8 24/41 -3/8 -22/59 17/29 -19/52 27/46 -9/25 -23/64 37/63 -5/14 10/17 -6/17 -7/20 33/56 -9/26 -1/3 23/39 -9/26 13/22 -17/50 -1/3 16/27 -1/3 3/5 -5/16 11/18 -2/7 19/31 -1/4 8/13 -1/4 0/1 29/47 -3/8 50/81 -1/3 21/34 -1/3 -5/16 34/55 -10/33 -3/10 47/76 -3/10 -5/17 13/21 -3/10 31/50 -11/38 -13/45 49/79 -39/136 67/108 -2/7 18/29 -2/7 -13/46 23/37 -1/4 5/8 -3/11 -1/4 17/27 -1/4 12/19 -1/4 -4/17 7/11 -1/4 16/25 -1/2 0/1 57/89 1/0 41/64 -1/4 -1/5 25/39 -1/2 9/14 -1/3 -1/4 11/17 -1/8 2/3 -1/3 11/16 -5/18 -3/11 9/13 -1/4 16/23 -5/18 -8/29 23/33 -7/26 30/43 -4/15 -9/34 7/10 -5/19 -1/4 19/27 -1/4 12/17 -1/4 -6/25 5/7 -1/4 13/18 0/1 21/29 3/4 8/11 -2/3 -1/2 27/37 -3/8 46/63 -1/3 19/26 -1/2 -3/7 49/67 -5/12 79/108 -2/5 30/41 -2/5 -3/8 11/15 -1/2 36/49 -2/5 -15/38 25/34 -11/29 -3/8 14/19 -3/8 -4/11 17/23 -11/32 20/27 -1/3 3/4 -1/3 -3/10 16/21 -7/25 13/17 -11/40 10/13 -4/15 -1/4 7/9 -1/4 11/14 -1/4 -1/5 26/33 -1/5 41/52 -3/14 -1/5 56/71 -1/4 0/1 15/19 -5/24 19/24 -2/11 42/53 -10/59 -1/6 107/135 -1/6 65/82 -1/6 -15/91 23/29 -5/32 4/5 -1/2 0/1 21/26 -1/2 -5/11 17/21 -1/2 30/37 -3/8 -4/11 43/53 -3/8 13/16 -5/14 -1/3 22/27 -1/3 9/11 -5/16 23/28 -1/3 -3/10 37/45 -3/10 14/17 -7/24 -2/7 19/23 -1/4 43/52 -1/3 -3/10 67/81 -3/10 24/29 -3/10 -2/7 5/6 -2/7 11/13 -1/4 17/20 -15/59 -1/4 23/27 -1/4 6/7 -1/4 -4/17 19/22 -7/34 -1/5 13/15 -1/6 7/8 -1/3 -1/4 15/17 -1/4 8/9 -1/3 9/10 -3/11 -1/4 10/11 -2/7 -5/18 1/1 -1/4 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(460,417,567,514) (-1/1,-9/10) -> (30/37,43/53) Hyperbolic Matrix(593,530,1026,917) (-9/10,-8/9) -> (26/45,37/64) Hyperbolic Matrix(379,334,-918,-809) (-8/9,-7/8) -> (-19/46,-26/63) Hyperbolic Matrix(298,259,405,352) (-7/8,-6/7) -> (25/34,14/19) Hyperbolic Matrix(134,113,351,296) (-6/7,-5/6) -> (8/21,13/34) Hyperbolic Matrix(188,155,621,512) (-5/6,-14/17) -> (3/10,10/33) Hyperbolic Matrix(161,132,-594,-487) (-14/17,-9/11) -> (-3/11,-10/37) Hyperbolic Matrix(485,396,594,485) (-9/11,-22/27) -> (22/27,9/11) Hyperbolic Matrix(703,572,864,703) (-22/27,-13/16) -> (13/16,22/27) Hyperbolic Matrix(998,809,1431,1160) (-13/16,-17/21) -> (23/33,30/43) Hyperbolic Matrix(1052,851,1701,1376) (-17/21,-4/5) -> (47/76,13/21) Hyperbolic Matrix(377,298,-1026,-811) (-4/5,-15/19) -> (-7/19,-18/49) Hyperbolic Matrix(80,63,513,404) (-15/19,-11/14) -> (2/13,3/19) Hyperbolic Matrix(188,147,-243,-190) (-11/14,-7/9) -> (-7/9,-10/13) Parabolic Matrix(296,227,-459,-352) (-10/13,-13/17) -> (-11/17,-9/14) Hyperbolic Matrix(80,61,459,350) (-13/17,-3/4) -> (4/23,3/17) Hyperbolic Matrix(431,318,-1026,-757) (-3/4,-14/19) -> (-8/19,-21/50) Hyperbolic Matrix(352,259,405,298) (-14/19,-11/15) -> (13/15,7/8) Hyperbolic Matrix(377,276,810,593) (-11/15,-30/41) -> (6/13,7/15) Hyperbolic Matrix(755,552,-2808,-2053) (-30/41,-19/26) -> (-7/26,-18/67) Hyperbolic Matrix(107,78,-594,-433) (-19/26,-8/11) -> (-2/11,-5/28) Hyperbolic Matrix(82,59,189,136) (-8/11,-5/7) -> (3/7,7/16) Hyperbolic Matrix(134,95,189,134) (-5/7,-7/10) -> (12/17,5/7) Hyperbolic Matrix(82,57,351,244) (-7/10,-9/13) -> (3/13,4/17) Hyperbolic Matrix(190,131,-351,-242) (-9/13,-11/16) -> (-6/11,-7/13) Hyperbolic Matrix(188,129,-513,-352) (-11/16,-2/3) -> (-11/30,-4/11) Hyperbolic Matrix(134,87,-459,-298) (-2/3,-11/17) -> (-5/17,-7/24) Hyperbolic Matrix(136,87,297,190) (-9/14,-7/11) -> (5/11,6/13) Hyperbolic Matrix(188,119,297,188) (-7/11,-5/8) -> (12/19,7/11) Hyperbolic Matrix(647,402,-1566,-973) (-5/8,-18/29) -> (-12/29,-19/46) Hyperbolic Matrix(2051,1272,-5400,-3349) (-18/29,-31/50) -> (-19/50,-30/79) Hyperbolic Matrix(271,168,1134,703) (-31/50,-13/21) -> (5/21,1/4) Hyperbolic Matrix(730,451,1269,784) (-13/21,-21/34) -> (4/7,19/33) Hyperbolic Matrix(107,66,-702,-433) (-21/34,-8/13) -> (-2/13,-3/20) Hyperbolic Matrix(28,17,135,82) (-8/13,-3/5) -> (1/5,3/14) Hyperbolic Matrix(161,96,270,161) (-3/5,-16/27) -> (16/27,3/5) Hyperbolic Matrix(703,416,1188,703) (-16/27,-13/22) -> (13/22,16/27) Hyperbolic Matrix(1646,971,2241,1322) (-13/22,-23/39) -> (11/15,36/49) Hyperbolic Matrix(2024,1193,3159,1862) (-23/39,-10/17) -> (41/64,25/39) Hyperbolic Matrix(593,348,-1566,-919) (-10/17,-17/29) -> (-11/29,-14/37) Hyperbolic Matrix(514,301,1431,838) (-17/29,-7/12) -> (14/39,9/25) Hyperbolic Matrix(136,79,513,298) (-7/12,-11/19) -> (5/19,4/15) Hyperbolic Matrix(2024,1171,2565,1484) (-11/19,-37/64) -> (56/71,15/19) Hyperbolic Matrix(917,530,1026,593) (-37/64,-26/45) -> (8/9,9/10) Hyperbolic Matrix(433,250,-2430,-1403) (-26/45,-15/26) -> (-5/28,-8/45) Hyperbolic Matrix(784,451,1269,730) (-15/26,-4/7) -> (21/34,34/55) Hyperbolic Matrix(109,62,-378,-215) (-4/7,-13/23) -> (-9/31,-2/7) Hyperbolic Matrix(622,351,1485,838) (-13/23,-9/16) -> (18/43,13/31) Hyperbolic Matrix(134,75,-243,-136) (-9/16,-5/9) -> (-5/9,-6/11) Parabolic Matrix(190,101,459,244) (-7/13,-1/2) -> (12/29,17/41) Hyperbolic Matrix(190,87,297,136) (-1/2,-5/11) -> (7/11,16/25) Hyperbolic Matrix(82,37,-297,-134) (-5/11,-4/9) -> (-5/18,-3/11) Hyperbolic Matrix(136,59,189,82) (-4/9,-3/7) -> (5/7,13/18) Hyperbolic Matrix(26,11,189,80) (-3/7,-8/19) -> (1/8,1/7) Hyperbolic Matrix(1243,522,1674,703) (-21/50,-34/81) -> (20/27,3/4) Hyperbolic Matrix(1997,838,2700,1133) (-34/81,-13/31) -> (17/23,20/27) Hyperbolic Matrix(838,351,1485,622) (-13/31,-5/12) -> (22/39,13/23) Hyperbolic Matrix(244,101,459,190) (-5/12,-12/29) -> (1/2,8/15) Hyperbolic Matrix(2483,1024,3402,1403) (-26/63,-7/17) -> (27/37,46/63) Hyperbolic Matrix(188,77,459,188) (-7/17,-2/5) -> (9/22,7/17) Hyperbolic Matrix(1486,585,2403,946) (-2/5,-11/28) -> (34/55,47/76) Hyperbolic Matrix(1054,413,1863,730) (-11/28,-9/23) -> (13/23,30/53) Hyperbolic Matrix(595,232,972,379) (-9/23,-7/18) -> (11/18,19/31) Hyperbolic Matrix(80,31,-351,-136) (-7/18,-5/13) -> (-3/13,-2/9) Hyperbolic Matrix(296,113,351,134) (-5/13,-8/21) -> (5/6,11/13) Hyperbolic Matrix(863,328,1134,431) (-8/21,-19/50) -> (3/4,16/21) Hyperbolic Matrix(7237,2748,11664,4429) (-30/79,-41/108) -> (67/108,18/29) Hyperbolic Matrix(7235,2746,11664,4427) (-41/108,-11/29) -> (49/79,67/108) Hyperbolic Matrix(512,193,1215,458) (-14/37,-3/8) -> (8/19,27/64) Hyperbolic Matrix(161,60,432,161) (-3/8,-10/27) -> (10/27,3/8) Hyperbolic Matrix(379,140,1026,379) (-10/27,-7/19) -> (7/19,10/27) Hyperbolic Matrix(1054,387,3753,1378) (-18/49,-11/30) -> (16/57,9/32) Hyperbolic Matrix(431,156,594,215) (-4/11,-9/25) -> (21/29,8/11) Hyperbolic Matrix(838,301,1431,514) (-9/25,-5/14) -> (24/41,17/29) Hyperbolic Matrix(26,9,-81,-28) (-5/14,-1/3) -> (-1/3,-4/13) Parabolic Matrix(431,132,702,215) (-4/13,-7/23) -> (19/31,8/13) Hyperbolic Matrix(512,155,621,188) (-7/23,-3/10) -> (14/17,19/23) Hyperbolic Matrix(161,48,540,161) (-3/10,-8/27) -> (8/27,3/10) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(836,243,2133,620) (-7/24,-9/31) -> (9/23,20/51) Hyperbolic Matrix(1052,297,1431,404) (-2/7,-9/32) -> (36/49,25/34) Hyperbolic Matrix(836,235,1053,296) (-9/32,-7/25) -> (23/29,4/5) Hyperbolic Matrix(703,196,972,271) (-7/25,-5/18) -> (13/18,21/29) Hyperbolic Matrix(26,7,297,80) (-10/37,-7/26) -> (0/1,1/10) Hyperbolic Matrix(8533,2292,11664,3133) (-18/67,-29/108) -> (79/108,30/41) Hyperbolic Matrix(8531,2290,11664,3131) (-29/108,-11/41) -> (49/67,79/108) Hyperbolic Matrix(433,116,810,217) (-11/41,-4/15) -> (8/15,7/13) Hyperbolic Matrix(298,79,513,136) (-4/15,-1/4) -> (18/31,7/12) Hyperbolic Matrix(244,57,351,82) (-1/4,-3/13) -> (9/13,16/23) Hyperbolic Matrix(82,17,135,28) (-2/9,-1/5) -> (3/5,11/18) Hyperbolic Matrix(26,5,135,26) (-1/5,-2/11) -> (3/16,1/5) Hyperbolic Matrix(811,144,918,163) (-8/45,-3/17) -> (15/17,8/9) Hyperbolic Matrix(350,61,459,80) (-3/17,-1/6) -> (16/21,13/17) Hyperbolic Matrix(404,63,513,80) (-1/6,-2/13) -> (11/14,26/33) Hyperbolic Matrix(1567,234,2538,379) (-3/20,-4/27) -> (50/81,21/34) Hyperbolic Matrix(1133,166,1836,269) (-4/27,-1/7) -> (29/47,50/81) Hyperbolic Matrix(80,11,189,26) (-1/7,0/1) -> (11/26,3/7) Hyperbolic Matrix(460,-47,783,-80) (1/10,1/9) -> (37/63,10/17) Hyperbolic Matrix(539,-64,918,-109) (1/9,1/8) -> (27/46,37/63) Hyperbolic Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(1729,-276,2700,-431) (3/19,4/25) -> (16/25,57/89) Hyperbolic Matrix(352,-57,1161,-188) (4/25,1/6) -> (10/33,17/56) Hyperbolic Matrix(298,-51,783,-134) (1/6,4/23) -> (19/50,8/21) Hyperbolic Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(136,-25,729,-134) (2/11,5/27) -> (5/27,3/16) Parabolic Matrix(190,-41,621,-134) (3/14,5/23) -> (7/23,4/13) Hyperbolic Matrix(242,-53,621,-136) (5/23,2/9) -> (7/18,9/23) Hyperbolic Matrix(136,-31,351,-80) (2/9,3/13) -> (5/13,7/18) Hyperbolic Matrix(919,-218,1134,-269) (4/17,5/21) -> (17/21,30/37) Hyperbolic Matrix(595,-156,1026,-269) (1/4,5/19) -> (11/19,29/50) Hyperbolic Matrix(460,-123,1107,-296) (4/15,11/41) -> (17/41,5/12) Hyperbolic Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(134,-37,297,-82) (3/11,5/18) -> (4/9,5/11) Hyperbolic Matrix(298,-83,675,-188) (5/18,7/25) -> (11/25,4/9) Hyperbolic Matrix(2267,-636,5778,-1621) (7/25,16/57) -> (20/51,31/79) Hyperbolic Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(298,-87,459,-134) (7/24,5/17) -> (11/17,2/3) Hyperbolic Matrix(2053,-624,2484,-755) (17/56,7/23) -> (19/23,43/52) Hyperbolic Matrix(28,-9,81,-26) (4/13,1/3) -> (1/3,5/14) Parabolic Matrix(3349,-1200,5724,-2051) (5/14,19/53) -> (31/53,55/94) Hyperbolic Matrix(1162,-417,2781,-998) (19/53,14/39) -> (5/12,23/55) Hyperbolic Matrix(296,-107,675,-244) (9/25,4/11) -> (7/16,11/25) Hyperbolic Matrix(352,-129,513,-188) (4/11,11/30) -> (2/3,11/16) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(595,-228,702,-269) (13/34,5/13) -> (11/13,17/20) Hyperbolic Matrix(5779,-2268,7290,-2861) (31/79,11/28) -> (65/82,23/29) Hyperbolic Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(298,-121,729,-296) (2/5,11/27) -> (11/27,9/22) Parabolic Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(593,-248,648,-271) (23/55,18/43) -> (10/11,1/1) Hyperbolic Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(2998,-1265,3645,-1538) (27/64,19/45) -> (37/45,14/17) Hyperbolic Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(541,-254,918,-431) (7/15,1/2) -> (33/56,23/39) Hyperbolic Matrix(242,-131,351,-190) (7/13,6/11) -> (11/16,9/13) Hyperbolic Matrix(136,-75,243,-134) (6/11,5/9) -> (5/9,9/16) Parabolic Matrix(1403,-790,1728,-973) (9/16,31/55) -> (43/53,13/16) Hyperbolic Matrix(1594,-899,2727,-1538) (31/55,22/39) -> (7/12,31/53) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(1135,-654,1404,-809) (19/33,15/26) -> (21/26,17/21) Hyperbolic Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(4427,-2560,6912,-3997) (37/64,11/19) -> (57/89,41/64) Hyperbolic Matrix(3808,-2209,6561,-3806) (29/50,47/81) -> (47/81,18/31) Parabolic Matrix(10666,-6241,18225,-10664) (55/94,79/135) -> (79/135,24/41) Parabolic Matrix(3833,-2258,4860,-2863) (10/17,33/56) -> (41/52,56/71) Hyperbolic Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(1486,-921,2133,-1322) (13/21,31/50) -> (16/23,23/33) Hyperbolic Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(460,-289,729,-458) (5/8,17/27) -> (17/27,12/19) Parabolic Matrix(1324,-849,1809,-1160) (25/39,9/14) -> (30/41,11/15) Hyperbolic Matrix(352,-227,459,-296) (9/14,11/17) -> (13/17,10/13) Hyperbolic Matrix(487,-340,540,-377) (30/43,7/10) -> (9/10,10/11) Hyperbolic Matrix(514,-361,729,-512) (7/10,19/27) -> (19/27,12/17) Parabolic Matrix(190,-147,243,-188) (10/13,7/9) -> (7/9,11/14) Parabolic Matrix(1052,-829,1269,-1000) (26/33,41/52) -> (24/29,5/6) Hyperbolic Matrix(14446,-11449,18225,-14444) (42/53,107/135) -> (107/135,65/82) Parabolic Matrix(5428,-4489,6561,-5426) (43/52,67/81) -> (67/81,24/29) Parabolic Matrix(622,-529,729,-620) (17/20,23/27) -> (23/27,6/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(460,417,567,514) -> Matrix(3,5,-8,-13) Matrix(593,530,1026,917) -> Matrix(1,2,-4,-7) Matrix(379,334,-918,-809) -> Matrix(5,2,-8,-3) Matrix(298,259,405,352) -> Matrix(3,-1,-8,3) Matrix(134,113,351,296) -> Matrix(1,5,-4,-19) Matrix(188,155,621,512) -> Matrix(1,3,-4,-11) Matrix(161,132,-594,-487) -> Matrix(7,10,-12,-17) Matrix(485,396,594,485) -> Matrix(9,10,-28,-31) Matrix(703,572,864,703) -> Matrix(11,10,-32,-29) Matrix(998,809,1431,1160) -> Matrix(15,11,-56,-41) Matrix(1052,851,1701,1376) -> Matrix(7,5,-24,-17) Matrix(377,298,-1026,-811) -> Matrix(11,-10,-12,11) Matrix(80,63,513,404) -> Matrix(1,-1,-4,5) Matrix(188,147,-243,-190) -> Matrix(1,-5,0,1) Matrix(296,227,-459,-352) -> Matrix(1,3,0,1) Matrix(80,61,459,350) -> Matrix(3,7,-4,-9) Matrix(431,318,-1026,-757) -> Matrix(5,4,-4,-3) Matrix(352,259,405,298) -> Matrix(1,1,-8,-7) Matrix(377,276,810,593) -> Matrix(3,2,-8,-5) Matrix(755,552,-2808,-2053) -> Matrix(1,0,0,1) Matrix(107,78,-594,-433) -> Matrix(7,4,-16,-9) Matrix(82,59,189,136) -> Matrix(3,-1,-8,3) Matrix(134,95,189,134) -> Matrix(1,-1,-4,5) Matrix(82,57,351,244) -> Matrix(1,3,-4,-11) Matrix(190,131,-351,-242) -> Matrix(1,1,0,1) Matrix(188,129,-513,-352) -> Matrix(7,15,-8,-17) Matrix(134,87,-459,-298) -> Matrix(7,1,-8,-1) Matrix(136,87,297,190) -> Matrix(1,1,-4,-3) Matrix(188,119,297,188) -> Matrix(1,-1,-4,5) Matrix(647,402,-1566,-973) -> Matrix(5,12,-8,-19) Matrix(2051,1272,-5400,-3349) -> Matrix(25,48,-12,-23) Matrix(271,168,1134,703) -> Matrix(1,2,-8,-15) Matrix(730,451,1269,784) -> Matrix(1,1,0,1) Matrix(107,66,-702,-433) -> Matrix(1,0,0,1) Matrix(28,17,135,82) -> Matrix(3,5,-8,-13) Matrix(161,96,270,161) -> Matrix(9,10,-28,-31) Matrix(703,416,1188,703) -> Matrix(35,34,-104,-101) Matrix(1646,971,2241,1322) -> Matrix(21,19,-52,-47) Matrix(2024,1193,3159,1862) -> Matrix(1,1,-12,-11) Matrix(593,348,-1566,-919) -> Matrix(27,22,-16,-13) Matrix(514,301,1431,838) -> Matrix(43,33,-116,-89) Matrix(136,79,513,298) -> Matrix(9,5,-20,-11) Matrix(2024,1171,2565,1484) -> Matrix(1,-1,-4,5) Matrix(917,530,1026,593) -> Matrix(1,2,-4,-7) Matrix(433,250,-2430,-1403) -> Matrix(7,4,-16,-9) Matrix(784,451,1269,730) -> Matrix(5,1,-16,-3) Matrix(109,62,-378,-215) -> Matrix(3,4,-4,-5) Matrix(622,351,1485,838) -> Matrix(3,-1,-8,3) Matrix(134,75,-243,-136) -> Matrix(1,-1,0,1) Matrix(190,101,459,244) -> Matrix(3,5,-8,-13) Matrix(190,87,297,136) -> Matrix(1,1,-4,-3) Matrix(82,37,-297,-134) -> Matrix(5,7,-8,-11) Matrix(136,59,189,82) -> Matrix(1,1,-8,-7) Matrix(26,11,189,80) -> Matrix(5,3,-12,-7) Matrix(1243,522,1674,703) -> Matrix(9,10,-28,-31) Matrix(1997,838,2700,1133) -> Matrix(19,18,-56,-53) Matrix(838,351,1485,622) -> Matrix(1,1,-8,-7) Matrix(244,101,459,190) -> Matrix(7,5,-24,-17) Matrix(2483,1024,3402,1403) -> Matrix(7,4,-16,-9) Matrix(188,77,459,188) -> Matrix(9,5,-20,-11) Matrix(1486,585,2403,946) -> Matrix(7,5,-24,-17) Matrix(1054,413,1863,730) -> Matrix(3,1,-4,-1) Matrix(595,232,972,379) -> Matrix(9,2,-32,-7) Matrix(80,31,-351,-136) -> Matrix(1,-1,0,1) Matrix(296,113,351,134) -> Matrix(1,5,-4,-19) Matrix(863,328,1134,431) -> Matrix(9,20,-32,-71) Matrix(7237,2748,11664,4429) -> Matrix(49,100,-172,-351) Matrix(7235,2746,11664,4427) -> Matrix(55,108,-192,-377) Matrix(512,193,1215,458) -> Matrix(1,1,0,1) Matrix(161,60,432,161) -> Matrix(9,10,-28,-31) Matrix(379,140,1026,379) -> Matrix(31,30,-92,-89) Matrix(1054,387,3753,1378) -> Matrix(127,115,-328,-297) Matrix(431,156,594,215) -> Matrix(5,4,-4,-3) Matrix(838,301,1431,514) -> Matrix(43,33,-116,-89) Matrix(26,9,-81,-28) -> Matrix(1,1,-4,-3) Matrix(431,132,702,215) -> Matrix(1,4,-4,-15) Matrix(512,155,621,188) -> Matrix(1,3,-4,-11) Matrix(161,48,540,161) -> Matrix(9,10,-28,-31) Matrix(271,80,918,271) -> Matrix(23,22,-68,-65) Matrix(836,243,2133,620) -> Matrix(11,9,-16,-13) Matrix(1052,297,1431,404) -> Matrix(29,21,-76,-55) Matrix(836,235,1053,296) -> Matrix(7,5,-52,-37) Matrix(703,196,972,271) -> Matrix(3,2,16,11) Matrix(26,7,297,80) -> Matrix(5,3,-12,-7) Matrix(8533,2292,11664,3133) -> Matrix(17,12,-44,-31) Matrix(8531,2290,11664,3131) -> Matrix(31,20,-76,-49) Matrix(433,116,810,217) -> Matrix(13,8,-44,-27) Matrix(298,79,513,136) -> Matrix(9,5,-20,-11) Matrix(244,57,351,82) -> Matrix(1,3,-4,-11) Matrix(82,17,135,28) -> Matrix(7,5,-24,-17) Matrix(26,5,135,26) -> Matrix(9,5,-20,-11) Matrix(811,144,918,163) -> Matrix(5,2,-8,-3) Matrix(350,61,459,80) -> Matrix(19,7,-68,-25) Matrix(404,63,513,80) -> Matrix(1,-1,-4,5) Matrix(1567,234,2538,379) -> Matrix(9,10,-28,-31) Matrix(1133,166,1836,269) -> Matrix(7,6,-20,-17) Matrix(80,11,189,26) -> Matrix(5,3,-12,-7) Matrix(460,-47,783,-80) -> Matrix(17,11,-48,-31) Matrix(539,-64,918,-109) -> Matrix(53,24,-148,-67) Matrix(433,-66,702,-107) -> Matrix(1,0,0,1) Matrix(1729,-276,2700,-431) -> Matrix(1,0,0,1) Matrix(352,-57,1161,-188) -> Matrix(5,1,-16,-3) Matrix(298,-51,783,-134) -> Matrix(1,3,-4,-11) Matrix(433,-78,594,-107) -> Matrix(7,4,-16,-9) Matrix(136,-25,729,-134) -> Matrix(33,17,-68,-35) Matrix(190,-41,621,-134) -> Matrix(19,7,-68,-25) Matrix(242,-53,621,-136) -> Matrix(3,1,8,3) Matrix(136,-31,351,-80) -> Matrix(3,1,-16,-5) Matrix(919,-218,1134,-269) -> Matrix(11,2,-28,-5) Matrix(595,-156,1026,-269) -> Matrix(13,6,-24,-11) Matrix(460,-123,1107,-296) -> Matrix(3,1,-4,-1) Matrix(2053,-552,2808,-755) -> Matrix(1,0,0,1) Matrix(487,-132,594,-161) -> Matrix(23,10,-76,-33) Matrix(134,-37,297,-82) -> Matrix(17,7,-56,-23) Matrix(298,-83,675,-188) -> Matrix(63,25,-184,-73) Matrix(2267,-636,5778,-1621) -> Matrix(103,40,-188,-73) Matrix(325,-92,378,-107) -> Matrix(21,8,-92,-35) Matrix(215,-62,378,-109) -> Matrix(11,4,-36,-13) Matrix(298,-87,459,-134) -> Matrix(3,1,8,3) Matrix(2053,-624,2484,-755) -> Matrix(1,0,0,1) Matrix(28,-9,81,-26) -> Matrix(1,1,-4,-3) Matrix(3349,-1200,5724,-2051) -> Matrix(289,108,-768,-287) Matrix(1162,-417,2781,-998) -> Matrix(121,45,-320,-119) Matrix(296,-107,675,-244) -> Matrix(69,25,-196,-71) Matrix(352,-129,513,-188) -> Matrix(43,15,-152,-53) Matrix(811,-298,1026,-377) -> Matrix(29,10,-148,-51) Matrix(919,-348,1566,-593) -> Matrix(75,22,-208,-61) Matrix(3349,-1272,5400,-2051) -> Matrix(169,48,-588,-167) Matrix(595,-228,702,-269) -> Matrix(25,6,-96,-23) Matrix(5779,-2268,7290,-2861) -> Matrix(19,10,-116,-61) Matrix(217,-86,270,-107) -> Matrix(1,0,0,1) Matrix(298,-121,729,-296) -> Matrix(9,5,-20,-11) Matrix(973,-402,1566,-647) -> Matrix(29,12,-104,-43) Matrix(593,-248,648,-271) -> Matrix(27,10,-100,-37) Matrix(757,-318,1026,-431) -> Matrix(13,4,-36,-11) Matrix(2998,-1265,3645,-1538) -> Matrix(19,11,-64,-37) Matrix(1997,-844,2430,-1027) -> Matrix(23,10,-76,-33) Matrix(541,-254,918,-431) -> Matrix(25,8,-72,-23) Matrix(242,-131,351,-190) -> Matrix(5,1,-16,-3) Matrix(136,-75,243,-134) -> Matrix(3,1,-16,-5) Matrix(1403,-790,1728,-973) -> Matrix(13,4,-36,-11) Matrix(1594,-899,2727,-1538) -> Matrix(23,5,-60,-13) Matrix(2267,-1284,2862,-1621) -> Matrix(9,4,-52,-23) Matrix(1135,-654,1404,-809) -> Matrix(3,2,-8,-5) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(4427,-2560,6912,-3997) -> Matrix(1,0,0,1) Matrix(3808,-2209,6561,-3806) -> Matrix(25,13,-52,-27) Matrix(10666,-6241,18225,-10664) -> Matrix(551,207,-1472,-553) Matrix(3833,-2258,4860,-2863) -> Matrix(17,6,-88,-31) Matrix(1027,-606,1188,-701) -> Matrix(29,10,-148,-51) Matrix(1486,-921,2133,-1322) -> Matrix(79,23,-292,-85) Matrix(379,-236,432,-269) -> Matrix(7,2,-32,-9) Matrix(460,-289,729,-458) -> Matrix(27,7,-112,-29) Matrix(1324,-849,1809,-1160) -> Matrix(1,1,-4,-3) Matrix(352,-227,459,-296) -> Matrix(13,3,-48,-11) Matrix(487,-340,540,-377) -> Matrix(7,2,-32,-9) Matrix(514,-361,729,-512) -> Matrix(43,11,-176,-45) Matrix(190,-147,243,-188) -> Matrix(19,5,-80,-21) Matrix(1052,-829,1269,-1000) -> Matrix(13,3,-48,-11) Matrix(14446,-11449,18225,-14444) -> Matrix(149,25,-900,-151) Matrix(5428,-4489,6561,-5426) -> Matrix(29,9,-100,-31) Matrix(622,-529,729,-620) -> Matrix(75,19,-304,-77) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 81 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/2,0/1) 0 27 1/7 -3/8 1 27 2/13 (-1/4,0/1) 0 27 1/6 0/1 2 9 3/17 -5/8 1 27 2/11 (-6/11,-1/2) 0 27 5/27 -1/2 17 1 1/5 -5/12 1 27 2/9 -1/3 4 3 3/13 -1/4 1 27 1/4 (-1/1,-1/2) 0 27 4/15 -3/7 2 9 11/41 -5/12 1 27 7/26 (-1/2,-3/7) 0 27 3/11 -5/12 1 27 5/18 -2/5 8 3 7/25 -25/64 1 27 9/32 (-27/70,-5/13) 0 27 2/7 (-3/8,-4/11) 0 27 7/24 -6/17 2 9 5/17 -11/32 1 27 8/27 -1/3 16 1 3/10 (-1/3,-5/16) 0 27 7/23 -1/4 1 27 4/13 (-4/15,-1/4) 0 27 1/3 -1/2 1 9 5/14 (-11/29,-3/8) 0 27 9/25 -25/68 1 27 4/11 (-5/14,-6/17) 0 27 11/30 -8/23 2 9 7/19 -15/44 1 27 10/27 -1/3 20 1 3/8 (-1/3,-5/16) 0 27 11/29 -15/52 1 27 19/50 (-13/46,-11/39) 0 27 8/21 -3/11 2 9 5/13 -1/4 1 27 7/18 0/1 4 3 9/23 1/0 1 27 11/28 (-1/2,-5/11) 0 27 2/5 (-1/2,0/1) 0 27 11/27 -1/2 5 1 7/17 -5/12 1 27 12/29 (-2/5,-7/18) 0 27 5/12 -2/5 2 9 13/31 -7/20 1 27 8/19 (-1/4,0/1) 0 27 19/45 -1/2 7 3 11/26 (-1/2,-3/7) 0 27 3/7 -3/8 1 27 4/9 -1/3 8 3 5/11 -1/4 1 27 1/2 (-1/2,-1/3) 0 27 8/15 -1/3 2 9 7/13 -1/4 1 27 6/11 (-3/10,-2/7) 0 27 5/9 -1/4 1 3 9/16 (-1/2,-1/3) 0 27 31/55 -1/4 1 27 22/39 -1/5 2 9 13/23 1/0 1 27 30/53 (-6/11,-1/2) 0 27 17/30 -2/5 2 9 4/7 (-1/4,0/1) 0 27 15/26 (-1/2,-3/7) 0 27 26/45 -1/3 2 3 37/64 (-1/4,-1/5) 0 27 11/19 1/0 1 27 47/81 -1/2 13 1 18/31 (-1/2,-6/13) 0 27 7/12 -2/5 2 9 31/53 -3/8 1 27 79/135 -3/8 23 1 24/41 (-3/8,-22/59) 0 27 17/29 -19/52 1 27 27/46 (-9/25,-23/64) 0 27 37/63 -5/14 7 3 10/17 (-6/17,-7/20) 0 27 23/39 -9/26 1 9 13/22 (-17/50,-1/3) 0 27 16/27 -1/3 22 1 3/5 -5/16 1 27 11/18 -2/7 4 3 19/31 -1/4 1 27 8/13 (-1/4,0/1) 0 27 29/47 -3/8 1 27 50/81 -1/3 8 1 21/34 (-1/3,-5/16) 0 27 34/55 (-10/33,-3/10) 0 27 13/21 -3/10 1 9 31/50 (-11/38,-13/45) 0 27 49/79 -39/136 1 27 67/108 -2/7 26 1 18/29 (-2/7,-13/46) 0 27 23/37 -1/4 1 27 5/8 (-3/11,-1/4) 0 27 17/27 -1/4 7 1 7/11 -1/4 1 27 16/25 (-1/2,0/1) 0 27 41/64 (-1/4,-1/5) 0 27 25/39 -1/2 1 9 9/14 (-1/3,-1/4) 0 27 11/17 -1/8 1 27 2/3 -1/3 2 9 11/16 (-5/18,-3/11) 0 27 9/13 -1/4 1 27 16/23 (-5/18,-8/29) 0 27 23/33 -7/26 1 9 7/10 (-5/19,-1/4) 0 27 19/27 -1/4 11 1 5/7 -1/4 1 27 13/18 0/1 8 3 21/29 3/4 1 27 8/11 (-2/3,-1/2) 0 27 27/37 -3/8 1 27 46/63 -1/3 2 3 19/26 (-1/2,-3/7) 0 27 49/67 -5/12 1 27 79/108 -2/5 4 1 30/41 (-2/5,-3/8) 0 27 11/15 -1/2 1 9 14/19 (-3/8,-4/11) 0 27 17/23 -11/32 1 27 20/27 -1/3 14 1 3/4 (-1/3,-3/10) 0 27 16/21 -7/25 2 9 13/17 -11/40 1 27 10/13 (-4/15,-1/4) 0 27 7/9 -1/4 5 3 11/14 (-1/4,-1/5) 0 27 26/33 -1/5 2 9 41/52 (-3/14,-1/5) 0 27 56/71 (-1/4,0/1) 0 27 15/19 -5/24 1 27 19/24 -2/11 2 9 42/53 (-10/59,-1/6) 0 27 107/135 -1/6 25 1 23/29 -5/32 1 27 4/5 (-1/2,0/1) 0 27 21/26 (-1/2,-5/11) 0 27 17/21 -1/2 1 9 30/37 (-3/8,-4/11) 0 27 13/16 (-5/14,-1/3) 0 27 22/27 -1/3 10 1 9/11 -5/16 1 27 23/28 (-1/3,-3/10) 0 27 37/45 -3/10 7 3 14/17 (-7/24,-2/7) 0 27 19/23 -1/4 1 27 67/81 -3/10 1 1 24/29 (-3/10,-2/7) 0 27 5/6 -2/7 2 9 11/13 -1/4 1 27 23/27 -1/4 19 1 6/7 (-1/4,-4/17) 0 27 19/22 (-7/34,-1/5) 0 27 13/15 -1/6 1 9 7/8 (-1/3,-1/4) 0 27 15/17 -1/4 1 27 8/9 -1/3 2 3 9/10 (-3/11,-1/4) 0 27 10/11 (-2/7,-5/18) 0 27 1/1 -1/4 1 27 1/0 0/1 2 1 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(80,-11,189,-26) (0/1,1/7) -> (11/26,3/7) Glide Reflection Matrix(433,-66,702,-107) (1/7,2/13) -> (8/13,29/47) Hyperbolic Matrix(404,-63,513,-80) (2/13,1/6) -> (11/14,26/33) Glide Reflection Matrix(350,-61,459,-80) (1/6,3/17) -> (16/21,13/17) Glide Reflection Matrix(433,-78,594,-107) (3/17,2/11) -> (8/11,27/37) Hyperbolic Matrix(109,-20,594,-109) (2/11,5/27) -> (2/11,5/27) Reflection Matrix(26,-5,135,-26) (5/27,1/5) -> (5/27,1/5) Reflection Matrix(82,-17,135,-28) (1/5,2/9) -> (3/5,11/18) Glide Reflection Matrix(136,-31,351,-80) (2/9,3/13) -> (5/13,7/18) Hyperbolic Matrix(244,-57,351,-82) (3/13,1/4) -> (9/13,16/23) Glide Reflection Matrix(298,-79,513,-136) (1/4,4/15) -> (18/31,7/12) Glide Reflection Matrix(433,-116,810,-217) (4/15,11/41) -> (8/15,7/13) Glide Reflection Matrix(2053,-552,2808,-755) (11/41,7/26) -> (19/26,49/67) Hyperbolic Matrix(487,-132,594,-161) (7/26,3/11) -> (9/11,23/28) Hyperbolic Matrix(134,-37,297,-82) (3/11,5/18) -> (4/9,5/11) Hyperbolic Matrix(703,-196,972,-271) (5/18,7/25) -> (13/18,21/29) Glide Reflection Matrix(836,-235,1053,-296) (7/25,9/32) -> (23/29,4/5) Glide Reflection Matrix(325,-92,378,-107) (9/32,2/7) -> (6/7,19/22) Hyperbolic Matrix(215,-62,378,-109) (2/7,7/24) -> (17/30,4/7) Hyperbolic Matrix(298,-87,459,-134) (7/24,5/17) -> (11/17,2/3) Hyperbolic Matrix(271,-80,918,-271) (5/17,8/27) -> (5/17,8/27) Reflection Matrix(161,-48,540,-161) (8/27,3/10) -> (8/27,3/10) Reflection Matrix(512,-155,621,-188) (3/10,7/23) -> (14/17,19/23) Glide Reflection Matrix(431,-132,702,-215) (7/23,4/13) -> (19/31,8/13) Glide Reflection Matrix(28,-9,81,-26) (4/13,1/3) -> (1/3,5/14) Parabolic Matrix(838,-301,1431,-514) (5/14,9/25) -> (24/41,17/29) Glide Reflection Matrix(431,-156,594,-215) (9/25,4/11) -> (21/29,8/11) Glide Reflection Matrix(352,-129,513,-188) (4/11,11/30) -> (2/3,11/16) Hyperbolic Matrix(811,-298,1026,-377) (11/30,7/19) -> (15/19,19/24) Hyperbolic Matrix(379,-140,1026,-379) (7/19,10/27) -> (7/19,10/27) Reflection Matrix(161,-60,432,-161) (10/27,3/8) -> (10/27,3/8) Reflection Matrix(919,-348,1566,-593) (3/8,11/29) -> (17/29,27/46) Hyperbolic Matrix(3349,-1272,5400,-2051) (11/29,19/50) -> (31/50,49/79) Hyperbolic Matrix(863,-328,1134,-431) (19/50,8/21) -> (3/4,16/21) Glide Reflection Matrix(296,-113,351,-134) (8/21,5/13) -> (5/6,11/13) Glide Reflection Matrix(595,-232,972,-379) (7/18,9/23) -> (11/18,19/31) Glide Reflection Matrix(1054,-413,1863,-730) (9/23,11/28) -> (13/23,30/53) Glide Reflection Matrix(217,-86,270,-107) (11/28,2/5) -> (4/5,21/26) Hyperbolic Matrix(109,-44,270,-109) (2/5,11/27) -> (2/5,11/27) Reflection Matrix(188,-77,459,-188) (11/27,7/17) -> (11/27,7/17) Reflection Matrix(973,-402,1566,-647) (7/17,12/29) -> (18/29,23/37) Hyperbolic Matrix(244,-101,459,-190) (12/29,5/12) -> (1/2,8/15) Glide Reflection Matrix(838,-351,1485,-622) (5/12,13/31) -> (22/39,13/23) Glide Reflection Matrix(757,-318,1026,-431) (13/31,8/19) -> (14/19,17/23) Hyperbolic Matrix(1918,-809,3267,-1378) (8/19,19/45) -> (27/46,37/63) Glide Reflection Matrix(1997,-844,2430,-1027) (19/45,11/26) -> (23/28,37/45) Hyperbolic Matrix(136,-59,189,-82) (3/7,4/9) -> (5/7,13/18) Glide Reflection Matrix(190,-87,297,-136) (5/11,1/2) -> (7/11,16/25) Glide Reflection Matrix(242,-131,351,-190) (7/13,6/11) -> (11/16,9/13) Hyperbolic Matrix(136,-75,243,-134) (6/11,5/9) -> (5/9,9/16) Parabolic Matrix(566,-319,621,-350) (9/16,31/55) -> (10/11,1/1) Glide Reflection Matrix(1594,-899,2727,-1538) (31/55,22/39) -> (7/12,31/53) Hyperbolic Matrix(2267,-1284,2862,-1621) (30/53,17/30) -> (19/24,42/53) Hyperbolic Matrix(784,-451,1269,-730) (4/7,15/26) -> (21/34,34/55) Glide Reflection Matrix(2051,-1184,2808,-1621) (15/26,26/45) -> (46/63,19/26) Hyperbolic Matrix(917,-530,1026,-593) (26/45,37/64) -> (8/9,9/10) Glide Reflection Matrix(2024,-1171,2565,-1484) (37/64,11/19) -> (56/71,15/19) Glide Reflection Matrix(892,-517,1539,-892) (11/19,47/81) -> (11/19,47/81) Reflection Matrix(2915,-1692,5022,-2915) (47/81,18/31) -> (47/81,18/31) Reflection Matrix(4186,-2449,7155,-4186) (31/53,79/135) -> (31/53,79/135) Reflection Matrix(6479,-3792,11070,-6479) (79/135,24/41) -> (79/135,24/41) Reflection Matrix(1511,-888,1836,-1079) (37/63,10/17) -> (37/45,14/17) Glide Reflection Matrix(2024,-1193,3159,-1862) (10/17,23/39) -> (41/64,25/39) Glide Reflection Matrix(1027,-606,1188,-701) (23/39,13/22) -> (19/22,13/15) Hyperbolic Matrix(703,-416,1188,-703) (13/22,16/27) -> (13/22,16/27) Reflection Matrix(161,-96,270,-161) (16/27,3/5) -> (16/27,3/5) Reflection Matrix(4699,-2900,7614,-4699) (29/47,50/81) -> (29/47,50/81) Reflection Matrix(3401,-2100,5508,-3401) (50/81,21/34) -> (50/81,21/34) Reflection Matrix(1376,-851,1701,-1052) (34/55,13/21) -> (21/26,17/21) Glide Reflection Matrix(1486,-921,2133,-1322) (13/21,31/50) -> (16/23,23/33) Hyperbolic Matrix(10585,-6566,17064,-10585) (49/79,67/108) -> (49/79,67/108) Reflection Matrix(3887,-2412,6264,-3887) (67/108,18/29) -> (67/108,18/29) Reflection Matrix(379,-236,432,-269) (23/37,5/8) -> (7/8,15/17) Hyperbolic Matrix(271,-170,432,-271) (5/8,17/27) -> (5/8,17/27) Reflection Matrix(188,-119,297,-188) (17/27,7/11) -> (17/27,7/11) Reflection Matrix(4024,-2577,5103,-3268) (16/25,41/64) -> (41/52,56/71) Glide Reflection Matrix(1324,-849,1809,-1160) (25/39,9/14) -> (30/41,11/15) Hyperbolic Matrix(352,-227,459,-296) (9/14,11/17) -> (13/17,10/13) Hyperbolic Matrix(1160,-809,1431,-998) (23/33,7/10) -> (17/21,30/37) Glide Reflection Matrix(379,-266,540,-379) (7/10,19/27) -> (7/10,19/27) Reflection Matrix(134,-95,189,-134) (19/27,5/7) -> (19/27,5/7) Reflection Matrix(1241,-906,1404,-1025) (27/37,46/63) -> (15/17,8/9) Glide Reflection Matrix(10585,-7742,14472,-10585) (49/67,79/108) -> (49/67,79/108) Reflection Matrix(6479,-4740,8856,-6479) (79/108,30/41) -> (79/108,30/41) Reflection Matrix(352,-259,405,-298) (11/15,14/19) -> (13/15,7/8) Glide Reflection Matrix(919,-680,1242,-919) (17/23,20/27) -> (17/23,20/27) Reflection Matrix(161,-120,216,-161) (20/27,3/4) -> (20/27,3/4) Reflection Matrix(190,-147,243,-188) (10/13,7/9) -> (7/9,11/14) Parabolic Matrix(1052,-829,1269,-1000) (26/33,41/52) -> (24/29,5/6) Hyperbolic Matrix(11341,-8988,14310,-11341) (42/53,107/135) -> (42/53,107/135) Reflection Matrix(3104,-2461,3915,-3104) (107/135,23/29) -> (107/135,23/29) Reflection Matrix(514,-417,567,-460) (30/37,13/16) -> (9/10,10/11) Glide Reflection Matrix(703,-572,864,-703) (13/16,22/27) -> (13/16,22/27) Reflection Matrix(485,-396,594,-485) (22/27,9/11) -> (22/27,9/11) Reflection Matrix(1540,-1273,1863,-1540) (19/23,67/81) -> (19/23,67/81) Reflection Matrix(3887,-3216,4698,-3887) (67/81,24/29) -> (67/81,24/29) Reflection Matrix(298,-253,351,-298) (11/13,23/27) -> (11/13,23/27) Reflection Matrix(323,-276,378,-323) (23/27,6/7) -> (23/27,6/7) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,4,1) (0/1,1/0) -> (-1/2,0/1) Matrix(80,-11,189,-26) -> Matrix(7,3,-16,-7) *** -> (-1/2,-3/8) Matrix(433,-66,702,-107) -> Matrix(1,0,0,1) Matrix(404,-63,513,-80) -> Matrix(5,1,-24,-5) *** -> (-1/4,-1/6) Matrix(350,-61,459,-80) -> Matrix(9,7,-32,-25) Matrix(433,-78,594,-107) -> Matrix(7,4,-16,-9) -1/2 Matrix(109,-20,594,-109) -> Matrix(23,12,-44,-23) (2/11,5/27) -> (-6/11,-1/2) Matrix(26,-5,135,-26) -> Matrix(11,5,-24,-11) (5/27,1/5) -> (-1/2,-5/12) Matrix(82,-17,135,-28) -> Matrix(13,5,-44,-17) Matrix(136,-31,351,-80) -> Matrix(3,1,-16,-5) -1/4 Matrix(244,-57,351,-82) -> Matrix(11,3,-40,-11) *** -> (-3/10,-1/4) Matrix(298,-79,513,-136) -> Matrix(11,5,-24,-11) *** -> (-1/2,-5/12) Matrix(433,-116,810,-217) -> Matrix(19,8,-64,-27) Matrix(2053,-552,2808,-755) -> Matrix(1,0,0,1) Matrix(487,-132,594,-161) -> Matrix(23,10,-76,-33) Matrix(134,-37,297,-82) -> Matrix(17,7,-56,-23) Matrix(703,-196,972,-271) -> Matrix(5,2,28,11) Matrix(836,-235,1053,-296) -> Matrix(13,5,-96,-37) Matrix(325,-92,378,-107) -> Matrix(21,8,-92,-35) Matrix(215,-62,378,-109) -> Matrix(11,4,-36,-13) -1/3 Matrix(298,-87,459,-134) -> Matrix(3,1,8,3) Matrix(271,-80,918,-271) -> Matrix(65,22,-192,-65) (5/17,8/27) -> (-11/32,-1/3) Matrix(161,-48,540,-161) -> Matrix(31,10,-96,-31) (8/27,3/10) -> (-1/3,-5/16) Matrix(512,-155,621,-188) -> Matrix(11,3,-40,-11) *** -> (-3/10,-1/4) Matrix(431,-132,702,-215) -> Matrix(15,4,-56,-15) *** -> (-2/7,-1/4) Matrix(28,-9,81,-26) -> Matrix(1,1,-4,-3) -1/2 Matrix(838,-301,1431,-514) -> Matrix(89,33,-240,-89) *** -> (-3/8,-11/30) Matrix(431,-156,594,-215) -> Matrix(11,4,-8,-3) Matrix(352,-129,513,-188) -> Matrix(43,15,-152,-53) Matrix(811,-298,1026,-377) -> Matrix(29,10,-148,-51) Matrix(379,-140,1026,-379) -> Matrix(89,30,-264,-89) (7/19,10/27) -> (-15/44,-1/3) Matrix(161,-60,432,-161) -> Matrix(31,10,-96,-31) (10/27,3/8) -> (-1/3,-5/16) Matrix(919,-348,1566,-593) -> Matrix(75,22,-208,-61) Matrix(3349,-1272,5400,-2051) -> Matrix(169,48,-588,-167) -2/7 Matrix(863,-328,1134,-431) -> Matrix(71,20,-252,-71) *** -> (-2/7,-5/18) Matrix(296,-113,351,-134) -> Matrix(19,5,-72,-19) *** -> (-5/18,-1/4) Matrix(595,-232,972,-379) -> Matrix(1,-2,-4,7) Matrix(1054,-413,1863,-730) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(217,-86,270,-107) -> Matrix(1,0,0,1) Matrix(109,-44,270,-109) -> Matrix(-1,0,4,1) (2/5,11/27) -> (-1/2,0/1) Matrix(188,-77,459,-188) -> Matrix(11,5,-24,-11) (11/27,7/17) -> (-1/2,-5/12) Matrix(973,-402,1566,-647) -> Matrix(29,12,-104,-43) Matrix(244,-101,459,-190) -> Matrix(13,5,-44,-17) Matrix(838,-351,1485,-622) -> Matrix(3,1,-20,-7) Matrix(757,-318,1026,-431) -> Matrix(13,4,-36,-11) -1/3 Matrix(1918,-809,3267,-1378) -> Matrix(13,9,-36,-25) Matrix(1997,-844,2430,-1027) -> Matrix(23,10,-76,-33) Matrix(136,-59,189,-82) -> Matrix(3,1,-20,-7) Matrix(190,-87,297,-136) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(242,-131,351,-190) -> Matrix(5,1,-16,-3) -1/4 Matrix(136,-75,243,-134) -> Matrix(3,1,-16,-5) -1/4 Matrix(566,-319,621,-350) -> Matrix(11,3,-40,-11) *** -> (-3/10,-1/4) Matrix(1594,-899,2727,-1538) -> Matrix(23,5,-60,-13) Matrix(2267,-1284,2862,-1621) -> Matrix(9,4,-52,-23) Matrix(784,-451,1269,-730) -> Matrix(1,-1,-4,3) Matrix(2051,-1184,2808,-1621) -> Matrix(1,0,0,1) Matrix(917,-530,1026,-593) -> Matrix(7,2,-24,-7) *** -> (-1/3,-1/4) Matrix(2024,-1171,2565,-1484) -> Matrix(5,1,-24,-5) *** -> (-1/4,-1/6) Matrix(892,-517,1539,-892) -> Matrix(1,1,0,-1) (11/19,47/81) -> (-1/2,1/0) Matrix(2915,-1692,5022,-2915) -> Matrix(25,12,-52,-25) (47/81,18/31) -> (-1/2,-6/13) Matrix(4186,-2449,7155,-4186) -> Matrix(199,75,-528,-199) (31/53,79/135) -> (-25/66,-3/8) Matrix(6479,-3792,11070,-6479) -> Matrix(353,132,-944,-353) (79/135,24/41) -> (-3/8,-22/59) Matrix(1511,-888,1836,-1079) -> Matrix(79,28,-268,-95) Matrix(2024,-1193,3159,-1862) -> Matrix(3,1,-32,-11) Matrix(1027,-606,1188,-701) -> Matrix(29,10,-148,-51) Matrix(703,-416,1188,-703) -> Matrix(101,34,-300,-101) (13/22,16/27) -> (-17/50,-1/3) Matrix(161,-96,270,-161) -> Matrix(31,10,-96,-31) (16/27,3/5) -> (-1/3,-5/16) Matrix(4699,-2900,7614,-4699) -> Matrix(17,6,-48,-17) (29/47,50/81) -> (-3/8,-1/3) Matrix(3401,-2100,5508,-3401) -> Matrix(31,10,-96,-31) (50/81,21/34) -> (-1/3,-5/16) Matrix(1376,-851,1701,-1052) -> Matrix(17,5,-44,-13) Matrix(1486,-921,2133,-1322) -> Matrix(79,23,-292,-85) Matrix(10585,-6566,17064,-10585) -> Matrix(545,156,-1904,-545) (49/79,67/108) -> (-39/136,-2/7) Matrix(3887,-2412,6264,-3887) -> Matrix(183,52,-644,-183) (67/108,18/29) -> (-2/7,-13/46) Matrix(379,-236,432,-269) -> Matrix(7,2,-32,-9) -1/4 Matrix(271,-170,432,-271) -> Matrix(23,6,-88,-23) (5/8,17/27) -> (-3/11,-1/4) Matrix(188,-119,297,-188) -> Matrix(5,1,-24,-5) (17/27,7/11) -> (-1/4,-1/6) Matrix(4024,-2577,5103,-3268) -> Matrix(5,1,-24,-5) *** -> (-1/4,-1/6) Matrix(1324,-849,1809,-1160) -> Matrix(1,1,-4,-3) -1/2 Matrix(352,-227,459,-296) -> Matrix(13,3,-48,-11) -1/4 Matrix(1160,-809,1431,-998) -> Matrix(41,11,-108,-29) Matrix(379,-266,540,-379) -> Matrix(39,10,-152,-39) (7/10,19/27) -> (-5/19,-1/4) Matrix(134,-95,189,-134) -> Matrix(5,1,-24,-5) (19/27,5/7) -> (-1/4,-1/6) Matrix(1241,-906,1404,-1025) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(10585,-7742,14472,-10585) -> Matrix(49,20,-120,-49) (49/67,79/108) -> (-5/12,-2/5) Matrix(6479,-4740,8856,-6479) -> Matrix(31,12,-80,-31) (79/108,30/41) -> (-2/5,-3/8) Matrix(352,-259,405,-298) -> Matrix(3,1,-20,-7) Matrix(919,-680,1242,-919) -> Matrix(65,22,-192,-65) (17/23,20/27) -> (-11/32,-1/3) Matrix(161,-120,216,-161) -> Matrix(19,6,-60,-19) (20/27,3/4) -> (-1/3,-3/10) Matrix(190,-147,243,-188) -> Matrix(19,5,-80,-21) -1/4 Matrix(1052,-829,1269,-1000) -> Matrix(13,3,-48,-11) -1/4 Matrix(11341,-8988,14310,-11341) -> Matrix(119,20,-708,-119) (42/53,107/135) -> (-10/59,-1/6) Matrix(3104,-2461,3915,-3104) -> Matrix(31,5,-192,-31) (107/135,23/29) -> (-1/6,-5/32) Matrix(514,-417,567,-460) -> Matrix(13,5,-44,-17) Matrix(703,-572,864,-703) -> Matrix(29,10,-84,-29) (13/16,22/27) -> (-5/14,-1/3) Matrix(485,-396,594,-485) -> Matrix(31,10,-96,-31) (22/27,9/11) -> (-1/3,-5/16) Matrix(1540,-1273,1863,-1540) -> Matrix(11,3,-40,-11) (19/23,67/81) -> (-3/10,-1/4) Matrix(3887,-3216,4698,-3887) -> Matrix(41,12,-140,-41) (67/81,24/29) -> (-3/10,-2/7) Matrix(298,-253,351,-298) -> Matrix(43,11,-168,-43) (11/13,23/27) -> (-11/42,-1/4) Matrix(323,-276,378,-323) -> Matrix(33,8,-136,-33) (23/27,6/7) -> (-1/4,-4/17) Matrix(-1,2,0,1) -> Matrix(-1,0,8,1) (1/1,1/0) -> (-1/4,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.