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 -9/10 -13/15 -5/6 -4/5 -11/15 -18/25 -7/10 -2/3 -11/18 -3/5 -8/15 -1/2 -7/15 -11/24 -9/20 -53/120 -89/210 -5/12 -2/5 -39/100 -23/60 -89/240 -9/25 -43/120 -16/45 -7/20 -1/3 -19/60 -14/45 -3/10 -8/27 -59/210 -7/25 -5/18 -7/26 -4/15 -1/4 -6/25 -5/21 -11/48 -2/9 -13/60 -3/14 -5/24 -6/29 -1/5 -4/21 -3/16 -5/27 -11/60 -5/28 -5/29 -1/6 -4/25 -3/20 -4/27 -3/22 -2/15 -3/23 -1/8 -1/9 -1/10 -1/11 0/1 1/10 1/9 2/17 1/8 2/15 3/22 1/7 3/20 2/13 3/19 1/6 4/23 3/17 5/28 2/11 5/27 3/16 4/21 1/5 5/24 4/19 3/14 2/9 11/48 3/13 7/30 5/21 1/4 4/15 7/26 5/18 7/25 2/7 3/10 1/3 7/20 9/25 11/30 39/100 2/5 5/12 13/30 9/20 11/24 7/15 1/2 8/15 17/30 3/5 11/18 19/30 29/45 2/3 31/45 7/10 18/25 11/15 23/30 4/5 5/6 13/15 9/10 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 -1/1 -8/9 1/0 -15/17 1/2 -7/8 2/1 -13/15 1/0 -19/22 -11/1 -6/7 -4/1 -3/1 -17/20 -2/1 -28/33 -3/2 -11/13 -1/2 -27/32 -4/1 -16/19 -7/3 -2/1 -5/6 -1/1 -19/23 1/0 -14/17 1/1 2/1 -37/45 1/0 -23/28 -2/1 -32/39 -3/2 -9/11 -1/2 -22/27 1/2 -13/16 0/1 -17/21 3/2 -4/5 1/0 -19/24 -4/1 -15/19 -13/4 -11/14 -3/1 -18/23 -2/1 -9/5 -25/32 -2/1 -32/41 -4/3 -9/7 -7/9 1/0 -24/31 -2/1 -5/3 -17/22 -1/1 -44/57 -7/4 -27/35 -3/2 -37/48 -2/1 -47/61 -3/2 -10/13 -4/3 -1/1 -23/30 -1/1 -13/17 -3/4 -16/21 -1/2 -3/4 0/1 -17/23 7/2 -14/19 5/1 6/1 -11/15 1/0 -19/26 -11/1 -46/63 -17/2 -27/37 -15/2 -35/48 -6/1 -43/59 1/0 -8/11 -6/1 -5/1 -21/29 -29/8 -13/18 -3/1 -44/61 -3/1 -14/5 -31/43 -11/4 -18/25 -5/2 -41/57 -5/2 -64/89 -3/1 -2/1 -23/32 -2/1 -28/39 -9/4 -5/7 -3/2 -27/38 -3/1 -22/31 -2/1 -1/1 -17/24 -2/1 -29/41 -13/8 -41/58 -11/7 -12/17 -2/1 -1/1 -43/61 -3/2 -31/44 -10/7 -19/27 -3/2 -7/10 -1/1 -23/33 -3/4 -16/23 -2/3 -3/5 -41/59 -1/2 -25/36 0/1 -9/13 -1/4 -11/16 0/1 -13/19 -1/6 -15/22 1/3 -2/3 1/0 -15/23 -9/4 -13/20 -2/1 -11/17 -3/2 -9/14 -1/1 -34/53 -2/1 -17/9 -25/39 -7/4 -16/25 -3/2 -39/61 -3/2 -23/36 -4/3 -7/11 -5/4 -19/30 -1/1 -12/19 -1/1 -6/7 -17/27 -3/4 -56/89 -21/31 -2/3 -39/62 -7/11 -22/35 -1/2 -27/43 -3/4 -5/8 0/1 -23/37 -1/2 -41/66 -1/3 -18/29 0/1 1/1 -31/50 -1/1 -75/121 -1/2 -44/71 -1/3 0/1 -13/21 -1/2 -34/55 -1/4 -55/89 -7/34 -76/123 -3/16 -21/34 -1/7 -8/13 0/1 1/5 -19/31 7/12 -11/18 1/1 -36/59 1/1 2/1 -61/100 4/3 -25/41 5/4 -14/23 5/3 2/1 -17/28 2/1 -3/5 1/0 -19/32 -4/1 -16/27 1/0 -29/49 -17/4 -13/22 -3/1 -36/61 -3/1 -2/1 -59/100 -4/1 -23/39 -7/2 -10/17 -3/1 -14/5 -17/29 -29/12 -7/12 -2/1 -18/31 -2/1 -1/1 -29/50 -5/3 -40/69 -3/2 -11/19 -7/4 -15/26 -1/1 -34/59 -10/9 -1/1 -19/33 1/0 -23/40 -2/1 -4/7 -4/3 -1/1 -17/30 -1/1 -13/23 -9/10 -48/85 -7/8 -35/62 -11/13 -57/101 -7/8 -22/39 -5/6 -9/16 -2/3 -23/41 -9/14 -14/25 -1/2 -33/59 -1/2 -19/34 -1/3 -24/43 0/1 1/1 -5/9 -1/2 -16/29 -1/5 0/1 -11/20 0/1 -17/31 3/14 -6/11 2/3 1/1 -13/24 2/1 -7/13 5/2 -15/28 6/1 -8/15 1/0 -9/17 1/0 -1/2 -1/1 -8/17 2/1 3/1 -7/15 1/0 -13/28 -8/1 -6/13 -5/1 -4/1 -11/24 -2/1 -5/11 -5/2 -9/20 -2/1 -13/29 -29/16 -4/9 -3/2 -19/43 -11/8 -53/120 -4/3 -34/77 -4/3 -17/13 -15/34 -1/1 -26/59 -1/1 -2/3 -11/25 -3/2 -40/91 -4/3 -17/13 -29/66 -1/1 -18/41 -15/11 -4/3 -7/16 -6/5 -17/39 -9/8 -27/62 -19/17 -10/23 -14/13 -1/1 -13/30 -1/1 -3/7 -3/4 -14/33 -1/2 -39/92 -2/3 -64/151 -2/3 -3/5 -89/210 -3/5 -25/59 -1/2 -11/26 -3/5 -19/45 -1/2 -8/19 -3/7 -2/5 -29/69 -5/14 -21/50 -1/3 -13/31 -5/18 -5/12 0/1 -12/29 0/1 1/3 -31/75 1/2 -50/121 0/1 1/1 -19/46 1/1 -7/17 1/2 -16/39 1/0 -57/139 3/2 -41/100 2/1 -25/61 1/0 -34/83 4/1 5/1 -9/22 -1/1 -11/27 1/2 -2/5 1/0 -13/33 -7/2 -24/61 -34/11 -3/1 -11/28 -8/3 -9/23 -3/2 -16/41 -4/1 -3/1 -39/100 -2/1 -23/59 1/0 -7/18 -3/1 -12/31 -3/1 -2/1 -29/75 1/0 -17/44 -2/1 -5/13 -9/4 -23/60 -2/1 -18/47 -2/1 -37/19 -13/34 -13/7 -34/89 -2/1 -9/5 -21/55 -11/6 -8/21 -7/4 -27/71 -27/16 -19/50 -5/3 -11/29 -29/18 -14/37 -17/11 -20/13 -31/82 -35/23 -17/45 -3/2 -3/8 -4/3 -13/35 -5/4 -36/97 -38/31 -11/9 -23/62 -23/19 -56/151 -107/89 -6/5 -89/240 -6/5 -33/89 -67/56 -10/27 -7/6 -27/73 -11/10 -44/119 -8/7 -1/1 -17/46 -1/1 -7/19 -13/12 -11/30 -1/1 -4/11 -1/1 -6/7 -13/36 -2/3 -22/61 -2/1 -1/1 -9/25 -3/4 -32/89 -13/19 -2/3 -23/64 -2/3 -14/39 -3/4 -19/53 -15/22 -43/120 -2/3 -24/67 -2/3 -19/29 -5/14 -3/5 -21/59 -1/2 -16/45 -1/2 -11/31 -9/20 -6/17 -1/3 -2/7 -13/37 -1/4 -7/20 0/1 -8/23 2/3 1/1 -1/3 1/0 -7/22 -7/3 -13/41 -25/12 -19/60 -2/1 -6/19 -2/1 -13/7 -5/16 -8/5 -19/61 -3/2 -14/45 -3/2 -9/29 -29/20 -4/13 -4/3 -9/7 -11/36 -6/5 -18/59 -2/1 -1/1 -25/82 -1/1 -7/23 -5/4 -3/10 -1/1 -11/37 -9/10 -19/64 -20/23 -27/91 -55/64 -8/27 -5/6 -13/44 -4/5 -31/105 -3/4 -18/61 -1/1 -2/3 -5/17 -3/4 -17/58 -11/15 -29/99 -3/4 -41/140 -2/3 -12/41 -8/11 -5/7 -7/24 -2/3 -16/55 -5/8 -9/31 -13/22 -2/7 -1/3 0/1 -11/39 1/2 -9/32 2/3 -34/121 16/17 1/1 -59/210 1/1 -25/89 13/12 -16/57 3/2 -7/25 1/0 -19/68 0/1 -12/43 0/1 1/1 -17/61 1/0 -5/18 -1/1 -8/29 -1/1 0/1 -11/40 0/1 -3/11 1/0 -16/59 1/1 2/1 -13/48 2/1 -23/85 1/0 -10/37 1/1 4/3 -17/63 1/0 -24/89 1/1 2/1 -7/26 3/1 -4/15 1/0 -9/34 -5/1 -5/19 -7/2 -6/23 -2/1 -1/1 -7/27 -5/2 -8/31 -2/1 -13/7 -1/4 -2/1 -7/29 -29/22 -6/25 -5/4 -5/21 -7/6 -4/17 -14/13 -1/1 -7/30 -1/1 -3/13 -9/10 -14/61 -1/1 -6/7 -11/48 -6/7 -19/83 -3/4 -8/35 -5/6 -13/57 -5/6 -5/22 -7/9 -12/53 -17/23 -14/19 -7/31 -17/24 -2/9 -1/2 -9/41 -1/4 -7/32 -2/5 -5/23 -1/6 -13/60 0/1 -8/37 0/1 1/7 -3/14 1/1 -13/61 1/0 -10/47 -3/1 -2/1 -7/33 1/0 -4/19 -1/1 -2/3 -5/24 0/1 -6/29 0/1 1/1 -1/5 1/0 -4/21 -3/2 -3/16 0/1 -5/27 1/0 -7/38 -7/3 -9/49 -17/8 -11/60 -2/1 -2/11 -2/1 -5/3 -7/39 -3/2 -5/28 -8/5 -8/45 -3/2 -3/17 -3/2 -7/40 -4/3 -4/23 -9/7 -14/11 -5/29 -29/24 -1/6 -1/1 -5/31 -21/26 -4/25 -3/4 -3/19 -5/8 -5/32 -4/7 -2/13 -1/1 0/1 -5/33 -1/2 -3/20 0/1 -4/27 1/0 -1/7 -1/2 -3/22 1/1 -2/15 1/0 -5/38 -3/1 -3/23 1/0 -1/8 -2/1 -2/17 -3/1 -2/1 -1/9 -3/2 -1/10 -1/1 -1/11 -1/2 0/1 -1/1 0/1 1/10 -1/1 1/9 -3/4 2/17 -2/3 -3/5 1/8 -2/3 2/15 -1/2 3/22 -1/3 1/7 1/0 3/20 0/1 5/33 1/0 2/13 -1/1 0/1 5/32 -4/1 3/19 -5/2 1/6 -1/1 4/23 -14/17 -9/11 3/17 -3/4 8/45 -3/4 5/28 -8/11 7/39 -3/4 2/11 -5/7 -2/3 5/27 -1/2 3/16 0/1 4/21 -3/4 1/5 -1/2 5/24 0/1 4/19 -2/1 -1/1 3/14 -1/3 5/23 1/4 7/32 2/1 9/41 1/2 2/9 1/0 7/31 -17/10 5/22 -7/5 13/57 -5/4 8/35 -5/4 11/48 -6/5 14/61 -6/5 -1/1 3/13 -9/8 7/30 -1/1 4/17 -1/1 -14/15 5/21 -7/8 1/4 -2/3 6/23 -1/1 -2/3 5/19 -7/12 4/15 -1/2 7/26 -3/7 17/63 -1/2 10/37 -4/11 -1/3 13/48 -2/5 16/59 -2/5 -1/3 3/11 -1/2 8/29 -1/1 0/1 5/18 -1/1 17/61 -1/2 12/43 -1/3 0/1 7/25 -1/2 16/57 -3/8 25/89 -13/38 9/32 -2/7 11/39 -1/4 2/7 0/1 1/1 11/38 -7/1 9/31 -13/4 7/24 -2/1 12/41 -5/3 -8/5 17/58 -11/7 5/17 -3/2 18/61 -2/1 -1/1 13/44 -4/3 8/27 -5/4 3/10 -1/1 10/33 -9/10 7/23 -5/6 18/59 -1/1 -2/3 11/36 -6/7 4/13 -9/11 -4/5 5/16 -8/11 6/19 -13/19 -2/3 7/22 -7/11 1/3 -1/2 8/23 -1/3 -2/7 7/20 0/1 6/17 2/3 1/1 5/14 -3/1 19/53 -15/8 14/39 -3/2 9/25 -3/2 22/61 -1/1 -2/3 13/36 -2/1 4/11 -6/5 -1/1 11/30 -1/1 7/19 -13/14 10/27 -7/8 33/89 -67/78 23/62 -23/27 13/35 -5/6 16/43 -9/11 -4/5 3/8 -4/5 14/37 -20/27 -17/23 25/66 -11/15 11/29 -29/40 19/50 -5/7 46/121 -5/7 -32/45 27/71 -27/38 8/21 -7/10 21/55 -11/16 34/89 -9/13 -2/3 47/123 -11/16 13/34 -13/19 5/13 -9/14 12/31 -2/3 -3/5 7/18 -3/5 23/59 -1/2 39/100 -2/3 16/41 -3/5 -4/7 9/23 -3/4 11/28 -8/13 2/5 -1/2 13/32 -4/11 11/27 -1/4 20/49 -1/7 0/1 9/22 -1/1 25/61 -1/2 41/100 -2/5 16/39 -1/2 7/17 -1/4 12/29 -1/5 0/1 5/12 0/1 13/31 5/8 21/50 1/1 29/69 5/4 8/19 2/1 3/1 11/26 -3/1 25/59 1/0 14/33 1/0 17/40 -2/1 3/7 -3/2 13/30 -1/1 10/23 -1/1 -14/15 37/85 -11/12 27/62 -19/21 44/101 -1/1 -10/11 17/39 -9/10 7/16 -6/7 18/41 -4/5 -15/19 11/25 -3/4 26/59 -2/1 -1/1 15/34 -1/1 19/43 -11/14 4/9 -3/4 13/29 -29/42 9/20 -2/3 14/31 -2/3 -7/11 5/11 -5/8 11/24 -2/3 6/13 -4/7 -5/9 13/28 -8/15 7/15 -1/2 8/17 -3/7 -2/5 1/2 -1/1 9/17 -1/2 8/15 -1/2 15/28 -6/13 7/13 -5/12 13/24 -2/5 6/11 -1/3 -2/7 11/20 0/1 16/29 0/1 1/3 5/9 1/0 24/43 -1/3 0/1 67/120 0/1 43/77 1/4 19/34 1/1 33/59 1/0 14/25 1/0 51/91 -23/6 37/66 -3/1 23/41 -9/4 9/16 -2/1 22/39 -5/4 35/62 -11/9 13/23 -9/8 17/30 -1/1 4/7 -1/1 -4/5 19/33 -1/2 53/92 -4/3 87/151 -19/18 121/210 -1/1 34/59 -1/1 -10/11 15/26 -1/1 26/45 -3/4 11/19 -7/10 40/69 -3/4 29/50 -5/7 18/31 -1/1 -2/3 7/12 -2/3 17/29 -29/46 44/75 -5/8 71/121 -5/8 27/46 -23/37 10/17 -14/23 -3/5 23/39 -7/12 82/139 -3/5 -10/17 59/100 -4/7 36/61 -2/3 -3/5 49/83 -7/12 13/22 -3/5 16/27 -1/2 3/5 -1/2 20/33 -1/2 37/61 -1/2 17/28 -2/5 14/23 -2/5 -5/13 25/41 -5/14 61/100 -4/11 36/59 -2/5 -1/3 11/18 -1/3 19/31 -7/26 46/75 -1/4 27/44 -4/17 8/13 -1/7 0/1 37/60 0/1 29/47 1/16 21/34 1/5 55/89 7/20 34/55 1/2 13/21 1/0 44/71 0/1 1/1 31/50 -1/1 18/29 -1/3 0/1 23/37 1/0 51/82 1/1 28/45 1/0 5/8 0/1 22/35 1/0 61/97 -7/2 39/62 -7/3 95/151 -37/18 151/240 -2/1 56/89 -2/1 -21/11 17/27 -3/2 46/73 -2/1 -5/3 75/119 -3/2 29/46 -7/5 12/19 -6/5 -1/1 19/30 -1/1 7/11 -5/6 23/36 -4/5 39/61 -3/4 16/25 -3/4 57/89 -51/70 41/64 -18/25 25/39 -7/10 34/53 -17/25 -2/3 77/120 -2/3 43/67 -17/26 9/14 -1/1 38/59 -1/1 -2/3 29/45 -3/4 20/31 -5/7 -2/3 11/17 -3/4 24/37 -16/23 -9/13 13/20 -2/3 15/23 -9/14 2/3 -1/2 15/22 -1/5 28/41 -1/15 0/1 41/60 0/1 13/19 1/4 11/16 0/1 42/61 -1/1 -2/3 31/45 -1/2 20/29 -1/1 0/1 9/13 1/2 25/36 0/1 41/59 1/0 57/82 3/1 16/23 -3/1 -2/1 7/10 -1/1 26/37 -9/11 -4/5 45/64 -4/5 64/91 -33/41 -4/5 19/27 -3/4 31/44 -10/13 74/105 -3/4 43/61 -3/4 12/17 -1/1 -2/3 41/58 -11/15 70/99 -3/4 99/140 -8/11 29/41 -13/18 17/24 -2/3 39/55 -1/2 22/31 -1/1 -2/3 5/7 -3/4 28/39 -9/14 23/32 -2/3 87/121 -5/8 151/210 -3/5 64/89 -2/3 -3/5 41/57 -5/8 18/25 -5/8 49/68 -2/3 31/43 -11/18 44/61 -14/23 -3/5 13/18 -3/5 21/29 -29/50 29/40 -4/7 8/11 -5/9 -6/11 43/59 -1/2 35/48 -6/11 62/85 -1/2 27/37 -15/28 46/63 -17/32 65/89 -73/138 19/26 -11/21 11/15 -1/2 25/34 -11/23 14/19 -6/13 -5/11 17/23 -7/16 20/27 -5/12 23/31 -15/38 3/4 0/1 22/29 0/1 1/5 19/25 1/0 16/21 1/0 13/17 -3/2 23/30 -1/1 10/13 -1/1 -4/5 47/61 -3/4 37/48 -2/3 64/83 -1/1 0/1 27/35 -3/4 44/57 -7/10 17/22 -1/1 41/53 -7/10 24/31 -5/7 -2/3 7/9 -1/2 32/41 -9/11 -4/5 25/32 -2/3 18/23 -9/13 -2/3 47/60 -2/3 29/37 -17/26 11/14 -3/5 48/61 -2/3 -3/5 37/47 -7/12 26/33 -5/8 15/19 -13/22 19/24 -4/7 23/29 -29/52 4/5 -1/2 17/21 -3/8 13/16 0/1 22/27 -1/4 31/38 -1/5 40/49 -1/11 0/1 49/60 0/1 9/11 1/0 32/39 -3/4 23/28 -2/3 37/45 -1/2 14/17 -2/5 -1/3 33/40 0/1 19/23 -1/2 24/29 -1/5 0/1 5/6 -1/1 26/31 -9/13 -2/3 21/25 -1/2 16/19 -2/3 -7/11 27/32 -4/7 11/13 1/0 28/33 -3/4 17/20 -2/3 23/27 -5/8 6/7 -3/5 -4/7 19/22 -11/21 13/15 -1/2 33/38 -15/31 20/23 -10/21 -9/19 7/8 -2/5 15/17 -1/4 8/9 -1/2 9/10 -1/1 10/11 -2/3 -3/5 1/1 -1/2 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(781,706,-1260,-1139) (-1/1,-9/10) -> (-31/50,-75/121) Hyperbolic Matrix(661,592,1140,1021) (-9/10,-8/9) -> (40/69,29/50) Hyperbolic Matrix(239,212,540,479) (-8/9,-15/17) -> (19/43,4/9) Hyperbolic Matrix(1081,952,1500,1321) (-15/17,-7/8) -> (49/68,31/43) Hyperbolic Matrix(181,158,-480,-419) (-7/8,-13/15) -> (-17/45,-3/8) Hyperbolic Matrix(839,726,-2220,-1921) (-13/15,-19/22) -> (-31/82,-17/45) Hyperbolic Matrix(121,104,420,361) (-19/22,-6/7) -> (2/7,11/38) Hyperbolic Matrix(241,206,-420,-359) (-6/7,-17/20) -> (-23/40,-4/7) Hyperbolic Matrix(841,714,1980,1681) (-17/20,-28/33) -> (14/33,17/40) Hyperbolic Matrix(1559,1322,1980,1679) (-28/33,-11/13) -> (37/47,26/33) Hyperbolic Matrix(419,354,780,659) (-11/13,-27/32) -> (15/28,7/13) Hyperbolic Matrix(1499,1264,1920,1619) (-27/32,-16/19) -> (32/41,25/32) Hyperbolic Matrix(659,554,-1500,-1261) (-16/19,-5/6) -> (-29/66,-18/41) Hyperbolic Matrix(1081,894,-1740,-1439) (-5/6,-19/23) -> (-23/37,-41/66) Hyperbolic Matrix(359,296,-1020,-841) (-19/23,-14/17) -> (-6/17,-13/37) Hyperbolic Matrix(479,394,1020,839) (-14/17,-37/45) -> (7/15,8/17) Hyperbolic Matrix(781,642,1680,1381) (-37/45,-23/28) -> (13/28,7/15) Hyperbolic Matrix(1681,1380,2340,1921) (-23/28,-32/39) -> (28/39,23/32) Hyperbolic Matrix(1141,936,3000,2461) (-32/39,-9/11) -> (27/71,8/21) Hyperbolic Matrix(959,782,-1620,-1321) (-9/11,-22/27) -> (-16/27,-29/49) Hyperbolic Matrix(479,390,1620,1319) (-22/27,-13/16) -> (13/44,8/27) Hyperbolic Matrix(419,340,960,779) (-13/16,-17/21) -> (17/39,7/16) Hyperbolic Matrix(779,630,1260,1019) (-17/21,-4/5) -> (34/55,13/21) Hyperbolic Matrix(419,332,-1440,-1141) (-4/5,-19/24) -> (-7/24,-16/55) Hyperbolic Matrix(1019,806,1440,1139) (-19/24,-15/19) -> (29/41,17/24) Hyperbolic Matrix(421,332,-1140,-899) (-15/19,-11/14) -> (-17/46,-7/19) Hyperbolic Matrix(181,142,-840,-659) (-11/14,-18/23) -> (-8/37,-3/14) Hyperbolic Matrix(839,656,1380,1079) (-18/23,-25/32) -> (17/28,14/23) Hyperbolic Matrix(1619,1264,1920,1499) (-25/32,-32/41) -> (16/19,27/32) Hyperbolic Matrix(1261,984,3000,2341) (-32/41,-7/9) -> (29/69,8/19) Hyperbolic Matrix(299,232,540,419) (-7/9,-24/31) -> (16/29,5/9) Hyperbolic Matrix(1321,1022,-1860,-1439) (-24/31,-17/22) -> (-27/38,-22/31) Hyperbolic Matrix(899,694,1320,1019) (-17/22,-44/57) -> (2/3,15/22) Hyperbolic Matrix(959,740,3420,2639) (-44/57,-27/35) -> (7/25,16/57) Hyperbolic Matrix(1559,1202,-5760,-4441) (-27/35,-37/48) -> (-13/48,-23/85) Hyperbolic Matrix(4199,3236,5760,4439) (-37/48,-47/61) -> (43/59,35/48) Hyperbolic Matrix(3781,2912,6000,4621) (-47/61,-10/13) -> (46/73,75/119) Hyperbolic Matrix(599,460,780,599) (-10/13,-23/30) -> (23/30,10/13) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(419,320,1020,779) (-13/17,-16/21) -> (16/39,7/17) Hyperbolic Matrix(539,410,-1500,-1141) (-16/21,-3/4) -> (-23/64,-14/39) Hyperbolic Matrix(481,356,-1620,-1199) (-3/4,-17/23) -> (-11/37,-19/64) Hyperbolic Matrix(539,398,1380,1019) (-17/23,-14/19) -> (16/41,9/23) Hyperbolic Matrix(481,354,-1140,-839) (-14/19,-11/15) -> (-19/45,-8/19) Hyperbolic Matrix(659,482,-1560,-1141) (-11/15,-19/26) -> (-11/26,-19/45) Hyperbolic Matrix(3299,2410,-5340,-3901) (-19/26,-46/63) -> (-76/123,-21/34) Hyperbolic Matrix(1019,744,1560,1139) (-46/63,-27/37) -> (15/23,2/3) Hyperbolic Matrix(1319,962,-5760,-4201) (-27/37,-35/48) -> (-11/48,-19/83) Hyperbolic Matrix(4439,3236,5760,4199) (-35/48,-43/59) -> (47/61,37/48) Hyperbolic Matrix(601,438,660,481) (-43/59,-8/11) -> (10/11,1/1) Hyperbolic Matrix(361,262,-660,-479) (-8/11,-21/29) -> (-17/31,-6/11) Hyperbolic Matrix(661,478,1080,781) (-21/29,-13/18) -> (11/18,19/31) Hyperbolic Matrix(1319,952,2160,1559) (-13/18,-44/61) -> (36/59,11/18) Hyperbolic Matrix(1079,778,3660,2639) (-44/61,-31/43) -> (5/17,18/61) Hyperbolic Matrix(1621,1168,-2580,-1859) (-31/43,-18/25) -> (-22/35,-27/43) Hyperbolic Matrix(781,562,3420,2461) (-18/25,-41/57) -> (13/57,8/35) Hyperbolic Matrix(6121,4402,16020,11521) (-41/57,-64/89) -> (34/89,47/123) Hyperbolic Matrix(5519,3968,-13020,-9361) (-64/89,-23/32) -> (-39/92,-64/151) Hyperbolic Matrix(1921,1380,2340,1681) (-23/32,-28/39) -> (32/39,23/28) Hyperbolic Matrix(839,602,2340,1679) (-28/39,-5/7) -> (19/53,14/39) Hyperbolic Matrix(59,42,420,299) (-5/7,-27/38) -> (3/22,1/7) Hyperbolic Matrix(299,212,-1440,-1021) (-22/31,-17/24) -> (-5/24,-6/29) Hyperbolic Matrix(1139,806,1440,1019) (-17/24,-29/41) -> (15/19,19/24) Hyperbolic Matrix(4741,3352,-8400,-5939) (-29/41,-41/58) -> (-35/62,-57/101) Hyperbolic Matrix(481,340,1020,721) (-41/58,-12/17) -> (8/17,1/2) Hyperbolic Matrix(1021,720,3660,2581) (-12/17,-43/61) -> (17/61,12/43) Hyperbolic Matrix(1141,804,-3660,-2579) (-43/61,-31/44) -> (-5/16,-19/61) Hyperbolic Matrix(301,212,1620,1141) (-31/44,-19/27) -> (5/27,3/16) Hyperbolic Matrix(419,294,-600,-421) (-19/27,-7/10) -> (-7/10,-23/33) Parabolic Matrix(359,250,-1380,-961) (-23/33,-16/23) -> (-6/23,-7/27) Hyperbolic Matrix(2581,1794,-6300,-4379) (-16/23,-41/59) -> (-25/61,-34/83) Hyperbolic Matrix(2761,1918,4320,3001) (-41/59,-25/36) -> (23/36,39/61) Hyperbolic Matrix(421,292,780,541) (-25/36,-9/13) -> (7/13,13/24) Hyperbolic Matrix(301,208,-780,-539) (-9/13,-11/16) -> (-17/44,-5/13) Hyperbolic Matrix(539,370,960,659) (-11/16,-13/19) -> (23/41,9/16) Hyperbolic Matrix(419,286,-1320,-901) (-13/19,-15/22) -> (-7/22,-13/41) Hyperbolic Matrix(1019,694,1320,899) (-15/22,-2/3) -> (44/57,17/22) Hyperbolic Matrix(1139,744,1560,1019) (-2/3,-15/23) -> (27/37,46/63) Hyperbolic Matrix(1139,742,1380,899) (-15/23,-13/20) -> (33/40,19/23) Hyperbolic Matrix(179,116,-1020,-661) (-13/20,-11/17) -> (-3/17,-7/40) Hyperbolic Matrix(421,272,-1020,-659) (-11/17,-9/14) -> (-19/46,-7/17) Hyperbolic Matrix(601,386,-1680,-1079) (-9/14,-34/53) -> (-24/67,-5/14) Hyperbolic Matrix(661,424,2340,1501) (-34/53,-25/39) -> (11/39,2/7) Hyperbolic Matrix(359,230,-1500,-961) (-25/39,-16/25) -> (-6/25,-5/21) Hyperbolic Matrix(1679,1074,3000,1919) (-16/25,-39/61) -> (33/59,14/25) Hyperbolic Matrix(3001,1918,4320,2761) (-39/61,-23/36) -> (25/36,41/59) Hyperbolic Matrix(301,192,660,421) (-23/36,-7/11) -> (5/11,11/24) Hyperbolic Matrix(419,266,660,419) (-7/11,-19/30) -> (19/30,7/11) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(241,152,-1140,-719) (-12/19,-17/27) -> (-7/33,-4/19) Hyperbolic Matrix(3419,2152,4860,3059) (-17/27,-56/89) -> (64/91,19/27) Hyperbolic Matrix(5519,3472,-14880,-9361) (-56/89,-39/62) -> (-23/62,-56/151) Hyperbolic Matrix(4201,2642,-7440,-4679) (-39/62,-22/35) -> (-48/85,-35/62) Hyperbolic Matrix(421,264,480,301) (-27/43,-5/8) -> (7/8,15/17) Hyperbolic Matrix(61,38,-480,-299) (-5/8,-23/37) -> (-3/23,-1/8) Hyperbolic Matrix(3481,2162,-7920,-4919) (-41/66,-18/29) -> (-40/91,-29/66) Hyperbolic Matrix(1741,1080,3000,1861) (-18/29,-31/50) -> (29/50,18/31) Hyperbolic Matrix(4021,2492,5520,3421) (-75/121,-44/71) -> (8/11,43/59) Hyperbolic Matrix(539,334,3000,1859) (-44/71,-13/21) -> (7/39,2/11) Hyperbolic Matrix(1019,630,1260,779) (-13/21,-34/55) -> (4/5,17/21) Hyperbolic Matrix(1621,1002,2040,1261) (-34/55,-55/89) -> (23/29,4/5) Hyperbolic Matrix(4499,2780,16020,9899) (-55/89,-76/123) -> (16/57,25/89) Hyperbolic Matrix(781,482,-2040,-1259) (-21/34,-8/13) -> (-18/47,-13/34) Hyperbolic Matrix(241,148,-780,-479) (-8/13,-19/31) -> (-9/29,-4/13) Hyperbolic Matrix(781,478,1080,661) (-19/31,-11/18) -> (13/18,21/29) Hyperbolic Matrix(1559,952,2160,1319) (-11/18,-36/59) -> (44/61,13/18) Hyperbolic Matrix(7081,4320,12000,7321) (-36/59,-61/100) -> (59/100,36/61) Hyperbolic Matrix(7381,4502,-18000,-10979) (-61/100,-25/41) -> (-57/139,-41/100) Hyperbolic Matrix(361,220,1380,841) (-25/41,-14/23) -> (6/23,5/19) Hyperbolic Matrix(1079,656,1380,839) (-14/23,-17/28) -> (25/32,18/23) Hyperbolic Matrix(179,108,-300,-181) (-17/28,-3/5) -> (-3/5,-19/32) Parabolic Matrix(1501,890,-3540,-2099) (-19/32,-16/27) -> (-14/33,-39/92) Hyperbolic Matrix(541,320,-2940,-1739) (-29/49,-13/22) -> (-7/38,-9/49) Hyperbolic Matrix(1921,1134,-6300,-3719) (-13/22,-36/61) -> (-18/59,-25/82) Hyperbolic Matrix(7321,4320,12000,7081) (-36/61,-59/100) -> (61/100,36/59) Hyperbolic Matrix(4499,2654,-15360,-9061) (-59/100,-23/39) -> (-29/99,-41/140) Hyperbolic Matrix(241,142,1020,601) (-23/39,-10/17) -> (4/17,5/21) Hyperbolic Matrix(361,212,-1020,-599) (-10/17,-17/29) -> (-11/31,-6/17) Hyperbolic Matrix(301,176,720,421) (-17/29,-7/12) -> (5/12,13/31) Hyperbolic Matrix(299,174,720,419) (-7/12,-18/31) -> (12/29,5/12) Hyperbolic Matrix(1861,1080,3000,1741) (-18/31,-29/50) -> (31/50,18/29) Hyperbolic Matrix(1021,592,1140,661) (-29/50,-40/69) -> (8/9,9/10) Hyperbolic Matrix(659,382,3000,1739) (-40/69,-11/19) -> (9/41,2/9) Hyperbolic Matrix(301,174,-1140,-659) (-11/19,-15/26) -> (-9/34,-5/19) Hyperbolic Matrix(1561,900,3540,2041) (-15/26,-34/59) -> (26/59,15/34) Hyperbolic Matrix(1559,898,-3960,-2281) (-34/59,-19/33) -> (-13/33,-24/61) Hyperbolic Matrix(299,172,1980,1139) (-19/33,-23/40) -> (3/20,5/33) Hyperbolic Matrix(239,136,420,239) (-4/7,-17/30) -> (17/30,4/7) Hyperbolic Matrix(781,442,1380,781) (-17/30,-13/23) -> (13/23,17/30) Hyperbolic Matrix(3721,2102,5100,2881) (-13/23,-48/85) -> (62/85,27/37) Hyperbolic Matrix(3839,2166,-9360,-5281) (-57/101,-22/39) -> (-16/39,-57/139) Hyperbolic Matrix(181,102,960,541) (-22/39,-9/16) -> (3/16,4/21) Hyperbolic Matrix(659,370,960,539) (-9/16,-23/41) -> (13/19,11/16) Hyperbolic Matrix(239,134,-1500,-841) (-23/41,-14/25) -> (-4/25,-3/19) Hyperbolic Matrix(1919,1074,3000,1679) (-14/25,-33/59) -> (39/61,16/25) Hyperbolic Matrix(1499,838,3540,1979) (-33/59,-19/34) -> (11/26,25/59) Hyperbolic Matrix(1801,1006,-4080,-2279) (-19/34,-24/43) -> (-34/77,-15/34) Hyperbolic Matrix(61,34,540,301) (-24/43,-5/9) -> (1/9,2/17) Hyperbolic Matrix(419,232,540,299) (-5/9,-16/29) -> (24/31,7/9) Hyperbolic Matrix(541,298,1200,661) (-16/29,-11/20) -> (9/20,14/31) Hyperbolic Matrix(539,296,1200,659) (-11/20,-17/31) -> (13/29,9/20) Hyperbolic Matrix(239,130,660,359) (-6/11,-13/24) -> (13/36,4/11) Hyperbolic Matrix(541,292,780,421) (-13/24,-7/13) -> (9/13,25/36) Hyperbolic Matrix(659,354,780,419) (-7/13,-15/28) -> (27/32,11/13) Hyperbolic Matrix(299,160,1680,899) (-15/28,-8/15) -> (8/45,5/28) Hyperbolic Matrix(181,96,1020,541) (-8/15,-9/17) -> (3/17,8/45) Hyperbolic Matrix(299,158,1020,539) (-9/17,-1/2) -> (17/58,5/17) Hyperbolic Matrix(721,340,1020,481) (-1/2,-8/17) -> (12/17,41/58) Hyperbolic Matrix(839,394,1020,479) (-8/17,-7/15) -> (37/45,14/17) Hyperbolic Matrix(1381,642,1680,781) (-7/15,-13/28) -> (23/28,37/45) Hyperbolic Matrix(121,56,780,361) (-13/28,-6/13) -> (2/13,5/32) Hyperbolic Matrix(239,110,780,359) (-6/13,-11/24) -> (11/36,4/13) Hyperbolic Matrix(421,192,660,301) (-11/24,-5/11) -> (7/11,23/36) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(1261,566,1740,781) (-9/20,-13/29) -> (21/29,29/40) Hyperbolic Matrix(121,54,540,241) (-13/29,-4/9) -> (2/9,7/31) Hyperbolic Matrix(479,212,540,239) (-4/9,-19/43) -> (15/17,8/9) Hyperbolic Matrix(8041,3552,14400,6361) (-19/43,-53/120) -> (67/120,43/77) Hyperbolic Matrix(8039,3550,14400,6359) (-53/120,-34/77) -> (24/43,67/120) Hyperbolic Matrix(2041,900,3540,1561) (-15/34,-26/59) -> (34/59,15/26) Hyperbolic Matrix(1081,476,3000,1321) (-26/59,-11/25) -> (9/25,22/61) Hyperbolic Matrix(2279,1002,3000,1319) (-11/25,-40/91) -> (22/29,19/25) Hyperbolic Matrix(301,132,960,421) (-18/41,-7/16) -> (5/16,6/19) Hyperbolic Matrix(779,340,960,419) (-7/16,-17/39) -> (17/21,13/16) Hyperbolic Matrix(2461,1072,-8400,-3659) (-17/39,-27/62) -> (-17/58,-29/99) Hyperbolic Matrix(2761,1202,-7440,-3239) (-27/62,-10/23) -> (-36/97,-23/62) Hyperbolic Matrix(599,260,1380,599) (-10/23,-13/30) -> (13/30,10/23) Hyperbolic Matrix(181,78,420,181) (-13/30,-3/7) -> (3/7,13/30) Hyperbolic Matrix(61,26,-420,-179) (-3/7,-14/33) -> (-4/27,-1/7) Hyperbolic Matrix(36241,15360,50400,21361) (-64/151,-89/210) -> (151/210,64/89) Hyperbolic Matrix(27179,11518,37800,16019) (-89/210,-25/59) -> (87/121,151/210) Hyperbolic Matrix(1979,838,3540,1499) (-25/59,-11/26) -> (19/34,33/59) Hyperbolic Matrix(2341,984,3000,1261) (-8/19,-29/69) -> (7/9,32/41) Hyperbolic Matrix(119,50,1140,479) (-29/69,-21/50) -> (1/10,1/9) Hyperbolic Matrix(1139,478,3000,1259) (-21/50,-13/31) -> (11/29,19/50) Hyperbolic Matrix(421,176,720,301) (-13/31,-5/12) -> (7/12,17/29) Hyperbolic Matrix(419,174,720,299) (-5/12,-12/29) -> (18/31,7/12) Hyperbolic Matrix(2399,992,3480,1439) (-12/29,-31/75) -> (31/45,20/29) Hyperbolic Matrix(6901,2852,10020,4141) (-31/75,-50/121) -> (42/61,31/45) Hyperbolic Matrix(3539,1462,4500,1859) (-50/121,-19/46) -> (11/14,48/61) Hyperbolic Matrix(779,320,1020,419) (-7/17,-16/39) -> (16/21,13/17) Hyperbolic Matrix(4679,1918,12000,4919) (-41/100,-25/61) -> (23/59,39/100) Hyperbolic Matrix(3179,1302,3660,1499) (-34/83,-9/22) -> (33/38,20/23) Hyperbolic Matrix(299,122,-1620,-661) (-9/22,-11/27) -> (-5/27,-7/38) Hyperbolic Matrix(119,48,-300,-121) (-11/27,-2/5) -> (-2/5,-13/33) Parabolic Matrix(1501,590,-5340,-2099) (-24/61,-11/28) -> (-9/32,-34/121) Hyperbolic Matrix(301,118,1380,541) (-11/28,-9/23) -> (5/23,7/32) Hyperbolic Matrix(1019,398,1380,539) (-9/23,-16/41) -> (14/19,17/23) Hyperbolic Matrix(2881,1124,-9840,-3839) (-16/41,-39/100) -> (-41/140,-12/41) Hyperbolic Matrix(4919,1918,12000,4679) (-39/100,-23/59) -> (25/61,41/100) Hyperbolic Matrix(601,234,2160,841) (-23/59,-7/18) -> (5/18,17/61) Hyperbolic Matrix(299,116,1080,419) (-7/18,-12/31) -> (8/29,5/18) Hyperbolic Matrix(2399,928,3720,1439) (-12/31,-29/75) -> (29/45,20/31) Hyperbolic Matrix(2339,904,-7920,-3061) (-29/75,-17/44) -> (-13/44,-31/105) Hyperbolic Matrix(2221,852,3600,1381) (-5/13,-23/60) -> (37/60,29/47) Hyperbolic Matrix(2219,850,3600,1379) (-23/60,-18/47) -> (8/13,37/60) Hyperbolic Matrix(1439,550,-5340,-2041) (-13/34,-34/89) -> (-24/89,-7/26) Hyperbolic Matrix(4681,1788,6600,2521) (-34/89,-21/55) -> (39/55,22/31) Hyperbolic Matrix(241,92,1260,481) (-21/55,-8/21) -> (4/21,1/5) Hyperbolic Matrix(2461,936,3000,1141) (-8/21,-27/71) -> (9/11,32/39) Hyperbolic Matrix(121,46,-1260,-479) (-27/71,-19/50) -> (-1/10,-1/11) Hyperbolic Matrix(1259,478,3000,1139) (-19/50,-11/29) -> (13/31,21/50) Hyperbolic Matrix(301,114,-1740,-659) (-11/29,-14/37) -> (-4/23,-5/29) Hyperbolic Matrix(3421,1294,4920,1861) (-14/37,-31/82) -> (57/82,16/23) Hyperbolic Matrix(721,268,-2580,-959) (-3/8,-13/35) -> (-7/25,-19/68) Hyperbolic Matrix(4859,1804,6300,2339) (-13/35,-36/97) -> (64/83,27/35) Hyperbolic Matrix(36241,13440,57600,21361) (-56/151,-89/240) -> (151/240,56/89) Hyperbolic Matrix(36239,13438,57600,21359) (-89/240,-33/89) -> (95/151,151/240) Hyperbolic Matrix(2401,890,3240,1201) (-33/89,-10/27) -> (20/27,23/31) Hyperbolic Matrix(2341,866,2760,1021) (-10/27,-27/73) -> (11/13,28/33) Hyperbolic Matrix(1379,510,6000,2219) (-27/73,-44/119) -> (14/61,3/13) Hyperbolic Matrix(2819,1042,4380,1619) (-44/119,-17/46) -> (9/14,38/59) Hyperbolic Matrix(419,154,1140,419) (-7/19,-11/30) -> (11/30,7/19) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(359,130,660,239) (-4/11,-13/36) -> (13/24,6/11) Hyperbolic Matrix(1319,476,4320,1559) (-13/36,-22/61) -> (18/59,11/36) Hyperbolic Matrix(1321,476,3000,1081) (-22/61,-9/25) -> (11/25,26/59) Hyperbolic Matrix(2519,906,3000,1079) (-9/25,-32/89) -> (26/31,21/25) Hyperbolic Matrix(8101,2912,11520,4141) (-32/89,-23/64) -> (45/64,64/91) Hyperbolic Matrix(1679,602,2340,839) (-14/39,-19/53) -> (5/7,28/39) Hyperbolic Matrix(9241,3312,14400,5161) (-19/53,-43/120) -> (77/120,43/67) Hyperbolic Matrix(9239,3310,14400,5159) (-43/120,-24/67) -> (34/53,77/120) Hyperbolic Matrix(2761,984,4380,1561) (-5/14,-21/59) -> (75/119,29/46) Hyperbolic Matrix(6301,2242,8940,3181) (-21/59,-16/45) -> (74/105,43/61) Hyperbolic Matrix(2281,810,3720,1321) (-16/45,-11/31) -> (19/31,46/75) Hyperbolic Matrix(781,274,1200,421) (-13/37,-7/20) -> (13/20,15/23) Hyperbolic Matrix(779,272,1200,419) (-7/20,-8/23) -> (24/37,13/20) Hyperbolic Matrix(421,146,1560,541) (-8/23,-1/3) -> (17/63,10/37) Hyperbolic Matrix(301,96,1320,421) (-1/3,-7/22) -> (5/22,13/57) Hyperbolic Matrix(2461,780,3600,1141) (-13/41,-19/60) -> (41/60,13/19) Hyperbolic Matrix(2459,778,3600,1139) (-19/60,-6/19) -> (28/41,41/60) Hyperbolic Matrix(421,132,960,301) (-6/19,-5/16) -> (7/16,18/41) Hyperbolic Matrix(5879,1830,10020,3119) (-19/61,-14/45) -> (44/75,71/121) Hyperbolic Matrix(2041,634,3480,1081) (-14/45,-9/29) -> (17/29,44/75) Hyperbolic Matrix(359,110,780,239) (-4/13,-11/36) -> (11/24,6/13) Hyperbolic Matrix(1559,476,4320,1319) (-11/36,-18/59) -> (22/61,13/36) Hyperbolic Matrix(3059,932,4920,1499) (-25/82,-7/23) -> (23/37,51/82) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(7379,2190,11520,3419) (-19/64,-27/91) -> (57/89,41/64) Hyperbolic Matrix(1801,534,4860,1441) (-27/91,-8/27) -> (10/27,33/89) Hyperbolic Matrix(1319,390,1620,479) (-8/27,-13/44) -> (13/16,22/27) Hyperbolic Matrix(5759,1700,8940,2639) (-31/105,-18/61) -> (38/59,29/45) Hyperbolic Matrix(2639,778,3660,1079) (-18/61,-5/17) -> (31/43,44/61) Hyperbolic Matrix(539,158,1020,299) (-5/17,-17/58) -> (1/2,9/17) Hyperbolic Matrix(301,88,1440,421) (-12/41,-7/24) -> (5/24,4/19) Hyperbolic Matrix(4079,1186,6600,1919) (-16/55,-9/31) -> (55/89,34/55) Hyperbolic Matrix(421,122,-1860,-539) (-9/31,-2/7) -> (-12/53,-7/31) Hyperbolic Matrix(1501,424,2340,661) (-2/7,-11/39) -> (25/39,34/53) Hyperbolic Matrix(419,118,2340,659) (-11/39,-9/32) -> (5/28,7/39) Hyperbolic Matrix(21781,6120,37800,10621) (-34/121,-59/210) -> (121/210,34/59) Hyperbolic Matrix(29039,8158,50400,14159) (-59/210,-25/89) -> (87/151,121/210) Hyperbolic Matrix(7799,2190,10680,2999) (-25/89,-16/57) -> (46/63,65/89) Hyperbolic Matrix(2639,740,3420,959) (-16/57,-7/25) -> (27/35,44/57) Hyperbolic Matrix(179,50,1500,419) (-19/68,-12/43) -> (2/17,1/8) Hyperbolic Matrix(2581,720,3660,1021) (-12/43,-17/61) -> (43/61,12/17) Hyperbolic Matrix(841,234,2160,601) (-17/61,-5/18) -> (7/18,23/59) Hyperbolic Matrix(419,116,1080,299) (-5/18,-8/29) -> (12/31,7/18) Hyperbolic Matrix(959,264,1740,479) (-8/29,-11/40) -> (11/20,16/29) Hyperbolic Matrix(2099,570,5520,1499) (-3/11,-16/59) -> (46/121,27/71) Hyperbolic Matrix(1321,358,5760,1561) (-16/59,-13/48) -> (11/48,14/61) Hyperbolic Matrix(2219,600,5100,1379) (-23/85,-10/37) -> (10/23,37/85) Hyperbolic Matrix(541,146,1560,421) (-10/37,-17/63) -> (1/3,8/23) Hyperbolic Matrix(7681,2072,10680,2881) (-17/63,-24/89) -> (64/89,41/57) Hyperbolic Matrix(239,64,-900,-241) (-7/26,-4/15) -> (-4/15,-9/34) Parabolic Matrix(841,220,1380,361) (-5/19,-6/23) -> (14/23,25/41) Hyperbolic Matrix(2039,528,3240,839) (-7/27,-8/31) -> (56/89,17/27) Hyperbolic Matrix(181,46,240,61) (-8/31,-1/4) -> (3/4,22/29) Hyperbolic Matrix(179,44,240,59) (-1/4,-7/29) -> (23/31,3/4) Hyperbolic Matrix(1681,404,3000,721) (-7/29,-6/25) -> (14/25,51/91) Hyperbolic Matrix(601,142,1020,241) (-5/21,-4/17) -> (10/17,23/39) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(181,42,780,181) (-7/30,-3/13) -> (3/13,7/30) Hyperbolic Matrix(2881,662,3660,841) (-3/13,-14/61) -> (48/61,37/47) Hyperbolic Matrix(1561,358,5760,1321) (-14/61,-11/48) -> (13/48,16/59) Hyperbolic Matrix(3961,906,6300,1441) (-19/83,-8/35) -> (22/35,61/97) Hyperbolic Matrix(2461,562,3420,781) (-8/35,-13/57) -> (41/57,18/25) Hyperbolic Matrix(421,96,1320,301) (-13/57,-5/22) -> (7/22,1/3) Hyperbolic Matrix(1139,258,1320,299) (-5/22,-12/53) -> (6/7,19/22) Hyperbolic Matrix(241,54,540,121) (-7/31,-2/9) -> (4/9,13/29) Hyperbolic Matrix(1739,382,3000,659) (-2/9,-9/41) -> (11/19,40/69) Hyperbolic Matrix(301,66,1920,421) (-9/41,-7/32) -> (5/32,3/19) Hyperbolic Matrix(541,118,1380,301) (-7/32,-5/23) -> (9/23,11/28) Hyperbolic Matrix(2821,612,3600,781) (-5/23,-13/60) -> (47/60,29/37) Hyperbolic Matrix(2819,610,3600,779) (-13/60,-8/37) -> (18/23,47/60) Hyperbolic Matrix(2641,564,4500,961) (-3/14,-13/61) -> (71/121,27/46) Hyperbolic Matrix(2819,600,3660,779) (-13/61,-10/47) -> (10/13,47/61) Hyperbolic Matrix(301,64,1980,421) (-10/47,-7/33) -> (5/33,2/13) Hyperbolic Matrix(421,88,1440,301) (-4/19,-5/24) -> (7/24,12/41) Hyperbolic Matrix(779,160,2040,419) (-6/29,-1/5) -> (21/55,34/89) Hyperbolic Matrix(481,92,1260,241) (-1/5,-4/21) -> (8/21,21/55) Hyperbolic Matrix(541,102,960,181) (-4/21,-3/16) -> (9/16,22/39) Hyperbolic Matrix(1141,212,1620,301) (-3/16,-5/27) -> (19/27,31/44) Hyperbolic Matrix(2941,540,3600,661) (-9/49,-11/60) -> (49/60,9/11) Hyperbolic Matrix(2939,538,3600,659) (-11/60,-2/11) -> (40/49,49/60) Hyperbolic Matrix(1859,334,3000,539) (-2/11,-7/39) -> (13/21,44/71) Hyperbolic Matrix(659,118,2340,419) (-7/39,-5/28) -> (9/32,11/39) Hyperbolic Matrix(899,160,1680,299) (-5/28,-8/45) -> (8/15,15/28) Hyperbolic Matrix(541,96,1020,181) (-8/45,-3/17) -> (9/17,8/15) Hyperbolic Matrix(481,84,1380,241) (-7/40,-4/23) -> (8/23,7/20) Hyperbolic Matrix(59,10,-360,-61) (-5/29,-1/6) -> (-1/6,-5/31) Parabolic Matrix(1921,308,3000,481) (-5/31,-4/25) -> (16/25,57/89) Hyperbolic Matrix(421,66,1920,301) (-3/19,-5/32) -> (7/32,9/41) Hyperbolic Matrix(361,56,780,121) (-5/32,-2/13) -> (6/13,13/28) Hyperbolic Matrix(1739,264,2760,419) (-2/13,-5/33) -> (17/27,46/73) Hyperbolic Matrix(1021,154,1200,181) (-5/33,-3/20) -> (17/20,23/27) Hyperbolic Matrix(1019,152,1200,179) (-3/20,-4/27) -> (28/33,17/20) Hyperbolic Matrix(1021,140,1320,181) (-1/7,-3/22) -> (17/22,41/53) Hyperbolic Matrix(119,16,-900,-121) (-3/22,-2/15) -> (-2/15,-5/38) Parabolic Matrix(2161,284,3660,481) (-5/38,-3/23) -> (49/83,13/22) Hyperbolic Matrix(179,22,480,59) (-1/8,-2/17) -> (16/43,3/8) Hyperbolic Matrix(301,34,540,61) (-2/17,-1/9) -> (5/9,24/43) Hyperbolic Matrix(479,50,1140,119) (-1/9,-1/10) -> (21/50,29/69) Hyperbolic Matrix(179,16,660,59) (-1/11,0/1) -> (16/59,3/11) Hyperbolic Matrix(479,-46,1260,-121) (0/1,1/10) -> (19/50,46/121) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(1381,-186,2220,-299) (2/15,3/22) -> (51/82,28/45) Hyperbolic Matrix(179,-26,420,-61) (1/7,3/20) -> (17/40,3/7) Hyperbolic Matrix(841,-134,1500,-239) (3/19,1/6) -> (37/66,23/41) Hyperbolic Matrix(659,-114,1740,-301) (1/6,4/23) -> (14/37,25/66) Hyperbolic Matrix(661,-116,1020,-179) (4/23,3/17) -> (11/17,24/37) Hyperbolic Matrix(661,-122,1620,-299) (2/11,5/27) -> (11/27,20/49) Hyperbolic Matrix(1021,-212,1440,-299) (1/5,5/24) -> (17/24,39/55) Hyperbolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(659,-142,840,-181) (3/14,5/23) -> (29/37,11/14) Hyperbolic Matrix(539,-122,1860,-421) (7/31,5/22) -> (11/38,9/31) Hyperbolic Matrix(4201,-962,5760,-1319) (8/35,11/48) -> (35/48,62/85) Hyperbolic Matrix(961,-230,1500,-359) (5/21,1/4) -> (41/64,25/39) Hyperbolic Matrix(1139,-296,1620,-421) (1/4,6/23) -> (26/37,45/64) Hyperbolic Matrix(659,-174,1140,-301) (5/19,4/15) -> (26/45,11/19) Hyperbolic Matrix(901,-242,1560,-419) (4/15,7/26) -> (15/26,26/45) Hyperbolic Matrix(2041,-550,5340,-1439) (7/26,17/63) -> (47/123,13/34) Hyperbolic Matrix(4441,-1202,5760,-1559) (10/37,13/48) -> (37/48,64/83) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(959,-268,2580,-721) (12/43,7/25) -> (13/35,16/43) Hyperbolic Matrix(7501,-2108,13020,-3659) (25/89,9/32) -> (53/92,87/151) Hyperbolic Matrix(1141,-332,1440,-419) (9/31,7/24) -> (19/24,23/29) Hyperbolic Matrix(3659,-1072,8400,-2461) (12/41,17/58) -> (27/62,44/101) Hyperbolic Matrix(2519,-744,3660,-1081) (18/61,13/44) -> (11/16,42/61) Hyperbolic Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(1021,-310,1380,-419) (10/33,7/23) -> (17/23,20/27) Hyperbolic Matrix(3719,-1134,6300,-1921) (7/23,18/59) -> (36/61,49/83) Hyperbolic Matrix(479,-148,780,-241) (4/13,5/16) -> (27/44,8/13) Hyperbolic Matrix(901,-286,1320,-419) (6/19,7/22) -> (15/22,28/41) Hyperbolic Matrix(841,-296,1020,-359) (7/20,6/17) -> (14/17,33/40) Hyperbolic Matrix(599,-212,1020,-361) (6/17,5/14) -> (27/46,10/17) Hyperbolic Matrix(1079,-386,1680,-601) (5/14,19/53) -> (43/67,9/14) Hyperbolic Matrix(1141,-410,1500,-539) (14/39,9/25) -> (19/25,16/21) Hyperbolic Matrix(899,-332,1140,-421) (7/19,10/27) -> (26/33,15/19) Hyperbolic Matrix(9361,-3472,14880,-5519) (33/89,23/62) -> (39/62,95/151) Hyperbolic Matrix(3239,-1202,7440,-2761) (23/62,13/35) -> (37/85,27/62) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(4439,-1682,7920,-3001) (25/66,11/29) -> (51/91,37/66) Hyperbolic Matrix(1259,-482,2040,-781) (13/34,5/13) -> (29/47,21/34) Hyperbolic Matrix(539,-208,780,-301) (5/13,12/31) -> (20/29,9/13) Hyperbolic Matrix(10619,-4142,18000,-7021) (39/100,16/41) -> (82/139,59/100) Hyperbolic Matrix(121,-48,300,-119) (11/28,2/5) -> (2/5,13/32) Parabolic Matrix(2039,-830,3540,-1441) (13/32,11/27) -> (19/33,53/92) Hyperbolic Matrix(2399,-980,2940,-1201) (20/49,9/22) -> (31/38,40/49) Hyperbolic Matrix(4379,-1794,6300,-2581) (9/22,25/61) -> (41/59,57/82) Hyperbolic Matrix(10861,-4454,15360,-6299) (41/100,16/39) -> (70/99,99/140) Hyperbolic Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(839,-354,1140,-481) (8/19,11/26) -> (25/34,14/19) Hyperbolic Matrix(2401,-1018,3960,-1679) (25/59,14/33) -> (20/33,37/61) Hyperbolic Matrix(5521,-2406,9360,-4079) (44/101,17/39) -> (23/39,82/139) Hyperbolic Matrix(1261,-554,1500,-659) (18/41,11/25) -> (21/25,16/19) Hyperbolic Matrix(2279,-1006,4080,-1801) (15/34,19/43) -> (43/77,19/34) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(5939,-3352,8400,-4741) (22/39,35/62) -> (41/58,70/99) Hyperbolic Matrix(4679,-2642,7440,-4201) (35/62,13/23) -> (61/97,39/62) Hyperbolic Matrix(359,-206,420,-241) (4/7,19/33) -> (23/27,6/7) Hyperbolic Matrix(1321,-782,1620,-959) (13/22,16/27) -> (22/27,31/38) Hyperbolic Matrix(181,-108,300,-179) (16/27,3/5) -> (3/5,20/33) Parabolic Matrix(3839,-2330,5340,-3241) (37/61,17/28) -> (23/32,87/121) Hyperbolic Matrix(6959,-4244,9840,-6001) (25/41,61/100) -> (99/140,29/41) Hyperbolic Matrix(5581,-3424,7920,-4859) (46/75,27/44) -> (31/44,74/105) Hyperbolic Matrix(3901,-2410,5340,-3299) (21/34,55/89) -> (65/89,19/26) Hyperbolic Matrix(1139,-706,1260,-781) (44/71,31/50) -> (9/10,10/11) Hyperbolic Matrix(1439,-894,1740,-1081) (18/29,23/37) -> (19/23,24/29) Hyperbolic Matrix(1859,-1168,2580,-1621) (5/8,22/35) -> (18/25,49/68) Hyperbolic Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(1439,-1022,1860,-1321) (22/31,5/7) -> (41/53,24/31) Hyperbolic Matrix(661,-484,900,-659) (19/26,11/15) -> (11/15,25/34) Parabolic Matrix(301,-250,360,-299) (24/29,5/6) -> (5/6,26/31) Parabolic Matrix(781,-676,900,-779) (19/22,13/15) -> (13/15,33/38) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(781,706,-1260,-1139) -> Matrix(1,2,-2,-3) Matrix(661,592,1140,1021) -> Matrix(3,-2,-4,3) Matrix(239,212,540,479) -> Matrix(3,4,-4,-5) Matrix(1081,952,1500,1321) -> Matrix(5,-8,-8,13) Matrix(181,158,-480,-419) -> Matrix(3,-10,-2,7) Matrix(839,726,-2220,-1921) -> Matrix(3,68,-2,-45) Matrix(121,104,420,361) -> Matrix(1,4,0,1) Matrix(241,206,-420,-359) -> Matrix(3,8,-2,-5) Matrix(841,714,1980,1681) -> Matrix(5,8,-2,-3) Matrix(1559,1322,1980,1679) -> Matrix(1,4,-2,-7) Matrix(419,354,780,659) -> Matrix(1,-2,-2,5) Matrix(1499,1264,1920,1619) -> Matrix(3,10,-4,-13) Matrix(659,554,-1500,-1261) -> Matrix(3,2,-2,-1) Matrix(1081,894,-1740,-1439) -> Matrix(1,0,-2,1) Matrix(359,296,-1020,-841) -> Matrix(1,0,-4,1) Matrix(479,394,1020,839) -> Matrix(1,-4,-2,9) Matrix(781,642,1680,1381) -> Matrix(1,10,-2,-19) Matrix(1681,1380,2340,1921) -> Matrix(5,12,-8,-19) Matrix(1141,936,3000,2461) -> Matrix(17,22,-24,-31) Matrix(959,782,-1620,-1321) -> Matrix(9,-4,-2,1) Matrix(479,390,1620,1319) -> Matrix(3,-4,-2,3) Matrix(419,340,960,779) -> Matrix(7,-6,-8,7) Matrix(779,630,1260,1019) -> Matrix(1,-2,2,-3) Matrix(419,332,-1440,-1141) -> Matrix(5,22,-8,-35) Matrix(1019,806,1440,1139) -> Matrix(7,26,-10,-37) Matrix(421,332,-1140,-899) -> Matrix(9,26,-8,-23) Matrix(181,142,-840,-659) -> Matrix(1,2,2,5) Matrix(839,656,1380,1079) -> Matrix(5,8,-12,-19) Matrix(1619,1264,1920,1499) -> Matrix(7,10,-12,-17) Matrix(1261,984,3000,2341) -> Matrix(5,6,4,5) Matrix(299,232,540,419) -> Matrix(1,2,0,1) Matrix(1321,1022,-1860,-1439) -> Matrix(5,8,-2,-3) Matrix(899,694,1320,1019) -> Matrix(1,2,-6,-11) Matrix(959,740,3420,2639) -> Matrix(5,8,-12,-19) Matrix(1559,1202,-5760,-4441) -> Matrix(3,4,2,3) Matrix(4199,3236,5760,4439) -> Matrix(11,16,-20,-29) Matrix(3781,2912,6000,4621) -> Matrix(13,18,-8,-11) Matrix(599,460,780,599) -> Matrix(7,8,-8,-9) Matrix(781,598,1020,781) -> Matrix(7,6,-6,-5) Matrix(419,320,1020,779) -> Matrix(3,2,-8,-5) Matrix(539,410,-1500,-1141) -> Matrix(1,2,-2,-3) Matrix(481,356,-1620,-1199) -> Matrix(7,-20,-8,23) Matrix(539,398,1380,1019) -> Matrix(1,-2,-2,5) Matrix(481,354,-1140,-839) -> Matrix(1,-8,-2,17) Matrix(659,482,-1560,-1141) -> Matrix(1,14,-2,-27) Matrix(3299,2410,-5340,-3901) -> Matrix(1,10,-6,-59) Matrix(1019,744,1560,1139) -> Matrix(5,42,-8,-67) Matrix(1319,962,-5760,-4201) -> Matrix(5,36,-6,-43) Matrix(4439,3236,5760,4199) -> Matrix(3,16,-4,-21) Matrix(601,438,660,481) -> Matrix(1,8,-2,-15) Matrix(361,262,-660,-479) -> Matrix(1,4,2,9) Matrix(661,478,1080,781) -> Matrix(3,10,-10,-33) Matrix(1319,952,2160,1559) -> Matrix(7,20,-20,-57) Matrix(1079,778,3660,2639) -> Matrix(7,20,-6,-17) Matrix(1621,1168,-2580,-1859) -> Matrix(1,2,0,1) Matrix(781,562,3420,2461) -> Matrix(13,30,-10,-23) Matrix(6121,4402,16020,11521) -> Matrix(7,12,-10,-17) Matrix(5519,3968,-13020,-9361) -> Matrix(5,12,-8,-19) Matrix(1921,1380,2340,1681) -> Matrix(5,12,-8,-19) Matrix(839,602,2340,1679) -> Matrix(11,24,-6,-13) Matrix(59,42,420,299) -> Matrix(1,2,-2,-3) Matrix(299,212,-1440,-1021) -> Matrix(1,2,0,1) Matrix(1139,806,1440,1019) -> Matrix(15,26,-26,-45) Matrix(4741,3352,-8400,-5939) -> Matrix(13,22,-16,-27) Matrix(481,340,1020,721) -> Matrix(5,8,-12,-19) Matrix(1021,720,3660,2581) -> Matrix(1,2,-4,-7) Matrix(1141,804,-3660,-2579) -> Matrix(37,54,-24,-35) Matrix(301,212,1620,1141) -> Matrix(7,10,-12,-17) Matrix(419,294,-600,-421) -> Matrix(5,6,-6,-7) Matrix(359,250,-1380,-961) -> Matrix(7,4,-2,-1) Matrix(2581,1794,-6300,-4379) -> Matrix(5,2,2,1) Matrix(2761,1918,4320,3001) -> Matrix(11,4,-14,-5) Matrix(421,292,780,541) -> Matrix(3,2,-8,-5) Matrix(301,208,-780,-539) -> Matrix(1,-2,0,1) Matrix(539,370,960,659) -> Matrix(3,2,-2,-1) Matrix(419,286,-1320,-901) -> Matrix(13,-2,-6,1) Matrix(1019,694,1320,899) -> Matrix(7,-2,-10,3) Matrix(1139,744,1560,1019) -> Matrix(17,42,-32,-79) Matrix(1139,742,1380,899) -> Matrix(1,2,2,5) Matrix(179,116,-1020,-661) -> Matrix(11,18,-8,-13) Matrix(421,272,-1020,-659) -> Matrix(1,2,0,1) Matrix(601,386,-1680,-1079) -> Matrix(1,4,-2,-7) Matrix(661,424,2340,1501) -> Matrix(1,2,-8,-15) Matrix(359,230,-1500,-961) -> Matrix(17,28,-14,-23) Matrix(1679,1074,3000,1919) -> Matrix(3,4,2,3) Matrix(3001,1918,4320,2761) -> Matrix(3,4,2,3) Matrix(301,192,660,421) -> Matrix(7,10,-12,-17) Matrix(419,266,660,419) -> Matrix(9,10,-10,-11) Matrix(721,456,1140,721) -> Matrix(13,12,-12,-11) Matrix(241,152,-1140,-719) -> Matrix(5,4,-4,-3) Matrix(3419,2152,4860,3059) -> Matrix(25,18,-32,-23) Matrix(5519,3472,-14880,-9361) -> Matrix(135,88,-112,-73) Matrix(4201,2642,-7440,-4679) -> Matrix(33,20,-38,-23) Matrix(421,264,480,301) -> Matrix(3,2,-8,-5) Matrix(61,38,-480,-299) -> Matrix(3,2,-2,-1) Matrix(3481,2162,-7920,-4919) -> Matrix(13,4,-10,-3) Matrix(1741,1080,3000,1861) -> Matrix(3,-2,-4,3) Matrix(4021,2492,5520,3421) -> Matrix(13,6,-24,-11) Matrix(539,334,3000,1859) -> Matrix(1,2,-2,-3) Matrix(1019,630,1260,779) -> Matrix(7,2,-18,-5) Matrix(1621,1002,2040,1261) -> Matrix(25,6,-46,-11) Matrix(4499,2780,16020,9899) -> Matrix(31,6,-88,-17) Matrix(781,482,-2040,-1259) -> Matrix(27,2,-14,-1) Matrix(241,148,-780,-479) -> Matrix(11,-4,-8,3) Matrix(781,478,1080,661) -> Matrix(13,-10,-22,17) Matrix(1559,952,2160,1319) -> Matrix(17,-20,-28,33) Matrix(7081,4320,12000,7321) -> Matrix(5,-8,-8,13) Matrix(7381,4502,-18000,-10979) -> Matrix(1,-2,2,-3) Matrix(361,220,1380,841) -> Matrix(5,-8,-8,13) Matrix(1079,656,1380,839) -> Matrix(3,-8,-4,11) Matrix(179,108,-300,-181) -> Matrix(1,-6,0,1) Matrix(1501,890,-3540,-2099) -> Matrix(1,6,-2,-11) Matrix(541,320,-2940,-1739) -> Matrix(9,34,-4,-15) Matrix(1921,1134,-6300,-3719) -> Matrix(3,8,-2,-5) Matrix(7321,4320,12000,7081) -> Matrix(3,8,-8,-21) Matrix(4499,2654,-15360,-9061) -> Matrix(7,26,-10,-37) Matrix(241,142,1020,601) -> Matrix(9,28,-10,-31) Matrix(361,212,-1020,-599) -> Matrix(3,8,-8,-21) Matrix(301,176,720,421) -> Matrix(1,2,4,9) Matrix(299,174,720,419) -> Matrix(1,2,-6,-11) Matrix(1861,1080,3000,1741) -> Matrix(1,2,-4,-7) Matrix(1021,592,1140,661) -> Matrix(1,2,-4,-7) Matrix(659,382,3000,1739) -> Matrix(1,2,-2,-3) Matrix(301,174,-1140,-659) -> Matrix(9,14,-2,-3) Matrix(1561,900,3540,2041) -> Matrix(7,8,-8,-9) Matrix(1559,898,-3960,-2281) -> Matrix(7,4,-2,-1) Matrix(299,172,1980,1139) -> Matrix(1,2,0,1) Matrix(239,136,420,239) -> Matrix(7,8,-8,-9) Matrix(781,442,1380,781) -> Matrix(19,18,-18,-17) Matrix(3721,2102,5100,2881) -> Matrix(55,48,-102,-89) Matrix(3839,2166,-9360,-5281) -> Matrix(5,4,6,5) Matrix(181,102,960,541) -> Matrix(3,2,-2,-1) Matrix(659,370,960,539) -> Matrix(3,2,-2,-1) Matrix(239,134,-1500,-841) -> Matrix(13,8,-18,-11) Matrix(1919,1074,3000,1679) -> Matrix(11,4,-14,-5) Matrix(1499,838,3540,1979) -> Matrix(3,2,-2,-1) Matrix(1801,1006,-4080,-2279) -> Matrix(13,4,-10,-3) Matrix(61,34,540,301) -> Matrix(1,2,-2,-3) Matrix(419,232,540,299) -> Matrix(5,2,-8,-3) Matrix(541,298,1200,661) -> Matrix(17,2,-26,-3) Matrix(539,296,1200,659) -> Matrix(19,-2,-28,3) Matrix(239,130,660,359) -> Matrix(3,-4,-2,3) Matrix(541,292,780,421) -> Matrix(1,-2,0,1) Matrix(659,354,780,419) -> Matrix(1,-2,-2,5) Matrix(299,160,1680,899) -> Matrix(3,-26,-4,35) Matrix(181,96,1020,541) -> Matrix(3,22,-4,-29) Matrix(299,158,1020,539) -> Matrix(3,14,-2,-9) Matrix(721,340,1020,481) -> Matrix(3,-8,-4,11) Matrix(839,394,1020,479) -> Matrix(1,-4,-2,9) Matrix(1381,642,1680,781) -> Matrix(1,10,-2,-19) Matrix(121,56,780,361) -> Matrix(1,4,0,1) Matrix(239,110,780,359) -> Matrix(5,16,-6,-19) Matrix(421,192,660,301) -> Matrix(3,10,-4,-13) Matrix(181,82,-660,-299) -> Matrix(1,2,2,5) Matrix(1261,566,1740,781) -> Matrix(31,58,-54,-101) Matrix(121,54,540,241) -> Matrix(5,8,-2,-3) Matrix(479,212,540,239) -> Matrix(3,4,-4,-5) Matrix(8041,3552,14400,6361) -> Matrix(3,4,20,27) Matrix(8039,3550,14400,6359) -> Matrix(3,4,-22,-29) Matrix(2041,900,3540,1561) -> Matrix(7,8,-8,-9) Matrix(1081,476,3000,1321) -> Matrix(1,0,0,1) Matrix(2279,1002,3000,1319) -> Matrix(3,4,2,3) Matrix(301,132,960,421) -> Matrix(17,22,-24,-31) Matrix(779,340,960,419) -> Matrix(5,6,-16,-19) Matrix(2461,1072,-8400,-3659) -> Matrix(37,42,-52,-59) Matrix(2761,1202,-7440,-3239) -> Matrix(105,116,-86,-95) Matrix(599,260,1380,599) -> Matrix(27,28,-28,-29) Matrix(181,78,420,181) -> Matrix(7,6,-6,-5) Matrix(61,26,-420,-179) -> Matrix(3,2,-2,-1) Matrix(36241,15360,50400,21361) -> Matrix(1,0,0,1) Matrix(27179,11518,37800,16019) -> Matrix(31,18,-50,-29) Matrix(1979,838,3540,1499) -> Matrix(3,2,-2,-1) Matrix(2341,984,3000,1261) -> Matrix(17,6,-20,-7) Matrix(119,50,1140,479) -> Matrix(23,8,-26,-9) Matrix(1139,478,3000,1259) -> Matrix(59,18,-82,-25) Matrix(421,176,720,301) -> Matrix(13,2,-20,-3) Matrix(419,174,720,299) -> Matrix(7,-2,-10,3) Matrix(2399,992,3480,1439) -> Matrix(1,0,-4,1) Matrix(6901,2852,10020,4141) -> Matrix(3,-2,-4,3) Matrix(3539,1462,4500,1859) -> Matrix(1,2,-2,-3) Matrix(779,320,1020,419) -> Matrix(1,-2,0,1) Matrix(4679,1918,12000,4919) -> Matrix(1,0,-2,1) Matrix(3179,1302,3660,1499) -> Matrix(1,-14,-2,29) Matrix(299,122,-1620,-661) -> Matrix(5,-2,-2,1) Matrix(119,48,-300,-121) -> Matrix(1,-4,0,1) Matrix(1501,590,-5340,-2099) -> Matrix(5,14,6,17) Matrix(301,118,1380,541) -> Matrix(1,2,2,5) Matrix(1019,398,1380,539) -> Matrix(1,-2,-2,5) Matrix(2881,1124,-9840,-3839) -> Matrix(3,4,-4,-5) Matrix(4919,1918,12000,4679) -> Matrix(1,0,-2,1) Matrix(601,234,2160,841) -> Matrix(1,4,-2,-7) Matrix(299,116,1080,419) -> Matrix(1,2,0,1) Matrix(2399,928,3720,1439) -> Matrix(3,4,-4,-5) Matrix(2339,904,-7920,-3061) -> Matrix(3,10,-4,-13) Matrix(2221,852,3600,1381) -> Matrix(1,2,20,41) Matrix(2219,850,3600,1379) -> Matrix(1,2,-26,-51) Matrix(1439,550,-5340,-2041) -> Matrix(11,20,6,11) Matrix(4681,1788,6600,2521) -> Matrix(11,20,-16,-29) Matrix(241,92,1260,481) -> Matrix(11,20,-16,-29) Matrix(2461,936,3000,1141) -> Matrix(13,22,-16,-27) Matrix(121,46,-1260,-479) -> Matrix(19,32,-22,-37) Matrix(1259,478,3000,1139) -> Matrix(11,18,14,23) Matrix(301,114,-1740,-659) -> Matrix(37,58,-30,-47) Matrix(3421,1294,4920,1861) -> Matrix(17,26,-2,-3) Matrix(721,268,-2580,-959) -> Matrix(3,4,-4,-5) Matrix(4859,1804,6300,2339) -> Matrix(31,38,-40,-49) Matrix(36241,13440,57600,21361) -> Matrix(283,340,-144,-173) Matrix(36239,13438,57600,21359) -> Matrix(297,356,-146,-175) Matrix(2401,890,3240,1201) -> Matrix(37,44,-90,-107) Matrix(2341,866,2760,1021) -> Matrix(9,10,-10,-11) Matrix(1379,510,6000,2219) -> Matrix(1,2,-2,-3) Matrix(2819,1042,4380,1619) -> Matrix(9,10,-10,-11) Matrix(419,154,1140,419) -> Matrix(25,26,-26,-27) Matrix(241,88,660,241) -> Matrix(13,12,-12,-11) Matrix(359,130,660,239) -> Matrix(5,4,-14,-11) Matrix(1319,476,4320,1559) -> Matrix(3,4,-4,-5) Matrix(1321,476,3000,1081) -> Matrix(1,0,0,1) Matrix(2519,906,3000,1079) -> Matrix(11,8,-18,-13) Matrix(8101,2912,11520,4141) -> Matrix(23,14,-28,-17) Matrix(1679,602,2340,839) -> Matrix(35,24,-54,-37) Matrix(9241,3312,14400,5161) -> Matrix(95,64,-144,-97) Matrix(9239,3310,14400,5159) -> Matrix(109,72,-162,-107) Matrix(2761,984,4380,1561) -> Matrix(29,16,-20,-11) Matrix(6301,2242,8940,3181) -> Matrix(73,38,-98,-51) Matrix(2281,810,3720,1321) -> Matrix(17,8,-66,-31) Matrix(781,274,1200,421) -> Matrix(17,2,-26,-3) Matrix(779,272,1200,419) -> Matrix(11,-2,-16,3) Matrix(421,146,1560,541) -> Matrix(1,-2,-2,5) Matrix(301,96,1320,421) -> Matrix(5,14,-4,-11) Matrix(2461,780,3600,1141) -> Matrix(1,2,16,33) Matrix(2459,778,3600,1139) -> Matrix(1,2,-22,-43) Matrix(421,132,960,301) -> Matrix(13,22,-16,-27) Matrix(5879,1830,10020,3119) -> Matrix(201,304,-322,-487) Matrix(2041,634,3480,1081) -> Matrix(79,116,-126,-185) Matrix(359,110,780,239) -> Matrix(13,16,-22,-27) Matrix(1559,476,4320,1319) -> Matrix(3,4,-4,-5) Matrix(3059,932,4920,1499) -> Matrix(5,6,4,5) Matrix(179,54,-600,-181) -> Matrix(13,14,-14,-15) Matrix(7379,2190,11520,3419) -> Matrix(155,134,-214,-185) Matrix(1801,534,4860,1441) -> Matrix(85,72,-98,-83) Matrix(1319,390,1620,479) -> Matrix(5,4,-14,-11) Matrix(5759,1700,8940,2639) -> Matrix(1,0,0,1) Matrix(2639,778,3660,1079) -> Matrix(23,20,-38,-33) Matrix(539,158,1020,299) -> Matrix(19,14,-34,-25) Matrix(301,88,1440,421) -> Matrix(3,2,4,3) Matrix(4079,1186,6600,1919) -> Matrix(13,8,34,21) Matrix(421,122,-1860,-539) -> Matrix(25,14,-34,-19) Matrix(1501,424,2340,661) -> Matrix(11,-2,-16,3) Matrix(419,118,2340,659) -> Matrix(7,-2,-10,3) Matrix(21781,6120,37800,10621) -> Matrix(27,-26,-28,27) Matrix(29039,8158,50400,14159) -> Matrix(31,-32,-30,31) Matrix(7799,2190,10680,2999) -> Matrix(35,-44,-66,83) Matrix(2639,740,3420,959) -> Matrix(3,-8,-4,11) Matrix(179,50,1500,419) -> Matrix(1,2,-2,-3) Matrix(2581,720,3660,1021) -> Matrix(3,-2,-4,3) Matrix(841,234,2160,601) -> Matrix(1,4,-2,-7) Matrix(419,116,1080,299) -> Matrix(5,2,-8,-3) Matrix(959,264,1740,479) -> Matrix(1,0,4,1) Matrix(2099,570,5520,1499) -> Matrix(27,-22,-38,31) Matrix(1321,358,5760,1561) -> Matrix(7,-8,-6,7) Matrix(2219,600,5100,1379) -> Matrix(11,-10,-12,11) Matrix(541,146,1560,421) -> Matrix(1,-2,-2,5) Matrix(7681,2072,10680,2881) -> Matrix(5,-8,-8,13) Matrix(239,64,-900,-241) -> Matrix(1,-8,0,1) Matrix(841,220,1380,361) -> Matrix(3,8,-8,-21) Matrix(2039,528,3240,839) -> Matrix(7,16,-4,-9) Matrix(181,46,240,61) -> Matrix(1,2,-2,-3) Matrix(179,44,240,59) -> Matrix(1,2,-4,-7) Matrix(1681,404,3000,721) -> Matrix(19,24,-4,-5) Matrix(601,142,1020,241) -> Matrix(25,28,-42,-47) Matrix(239,56,1020,239) -> Matrix(27,28,-28,-29) Matrix(181,42,780,181) -> Matrix(19,18,-18,-17) Matrix(2881,662,3660,841) -> Matrix(23,20,-38,-33) Matrix(1561,358,5760,1321) -> Matrix(9,8,-26,-23) Matrix(3961,906,6300,1441) -> Matrix(19,16,-6,-5) Matrix(2461,562,3420,781) -> Matrix(37,30,-58,-47) Matrix(421,96,1320,301) -> Matrix(17,14,-28,-23) Matrix(1139,258,1320,299) -> Matrix(35,26,-66,-49) Matrix(241,54,540,121) -> Matrix(13,8,-18,-11) Matrix(1739,382,3000,659) -> Matrix(1,2,-2,-3) Matrix(301,66,1920,421) -> Matrix(3,2,-2,-1) Matrix(541,118,1380,301) -> Matrix(9,2,-14,-3) Matrix(2821,612,3600,781) -> Matrix(29,2,-44,-3) Matrix(2819,610,3600,779) -> Matrix(23,-2,-34,3) Matrix(2641,564,4500,961) -> Matrix(5,-28,-8,45) Matrix(2819,600,3660,779) -> Matrix(3,10,-4,-13) Matrix(301,64,1980,421) -> Matrix(1,2,0,1) Matrix(421,88,1440,301) -> Matrix(7,2,-4,-1) Matrix(779,160,2040,419) -> Matrix(11,-2,-16,3) Matrix(481,92,1260,241) -> Matrix(11,20,-16,-29) Matrix(541,102,960,181) -> Matrix(3,2,-2,-1) Matrix(1141,212,1620,301) -> Matrix(3,10,-4,-13) Matrix(2941,540,3600,661) -> Matrix(1,2,8,17) Matrix(2939,538,3600,659) -> Matrix(1,2,-14,-27) Matrix(1859,334,3000,539) -> Matrix(1,2,-2,-3) Matrix(659,118,2340,419) -> Matrix(1,2,-6,-11) Matrix(899,160,1680,299) -> Matrix(17,26,-36,-55) Matrix(541,96,1020,181) -> Matrix(15,22,-28,-41) Matrix(481,84,1380,241) -> Matrix(3,4,-16,-21) Matrix(59,10,-360,-61) -> Matrix(9,10,-10,-11) Matrix(1921,308,3000,481) -> Matrix(47,36,-64,-49) Matrix(421,66,1920,301) -> Matrix(3,2,-2,-1) Matrix(361,56,780,121) -> Matrix(9,4,-16,-7) Matrix(1739,264,2760,419) -> Matrix(7,2,-4,-1) Matrix(1021,154,1200,181) -> Matrix(9,2,-14,-3) Matrix(1019,152,1200,179) -> Matrix(3,-2,-4,3) Matrix(1021,140,1320,181) -> Matrix(3,-2,-4,3) Matrix(119,16,-900,-121) -> Matrix(1,-4,0,1) Matrix(2161,284,3660,481) -> Matrix(7,24,-12,-41) Matrix(179,22,480,59) -> Matrix(5,6,-6,-7) Matrix(301,34,540,61) -> Matrix(1,2,-2,-3) Matrix(479,50,1140,119) -> Matrix(7,8,6,7) Matrix(179,16,660,59) -> Matrix(3,2,-8,-5) Matrix(479,-46,1260,-121) -> Matrix(27,32,-38,-45) Matrix(299,-38,480,-61) -> Matrix(3,2,-2,-1) Matrix(1381,-186,2220,-299) -> Matrix(5,2,2,1) Matrix(179,-26,420,-61) -> Matrix(3,2,-2,-1) Matrix(841,-134,1500,-239) -> Matrix(5,8,-2,-3) Matrix(659,-114,1740,-301) -> Matrix(69,58,-94,-79) Matrix(661,-116,1020,-179) -> Matrix(23,18,-32,-25) Matrix(661,-122,1620,-299) -> Matrix(3,2,-14,-9) Matrix(1021,-212,1440,-299) -> Matrix(5,2,-8,-3) Matrix(719,-152,1140,-241) -> Matrix(5,4,-4,-3) Matrix(659,-142,840,-181) -> Matrix(9,2,-14,-3) Matrix(539,-122,1860,-421) -> Matrix(9,14,-2,-3) Matrix(4201,-962,5760,-1319) -> Matrix(29,36,-54,-67) Matrix(961,-230,1500,-359) -> Matrix(33,28,-46,-39) Matrix(1139,-296,1620,-421) -> Matrix(23,14,-28,-17) Matrix(659,-174,1140,-301) -> Matrix(25,14,-34,-19) Matrix(901,-242,1560,-419) -> Matrix(23,10,-30,-13) Matrix(2041,-550,5340,-1439) -> Matrix(51,20,-74,-29) Matrix(4441,-1202,5760,-1559) -> Matrix(11,4,-14,-5) Matrix(299,-82,660,-181) -> Matrix(9,2,-14,-3) Matrix(959,-268,2580,-721) -> Matrix(3,4,-4,-5) Matrix(7501,-2108,13020,-3659) -> Matrix(19,6,-16,-5) Matrix(1141,-332,1440,-419) -> Matrix(9,22,-16,-39) Matrix(3659,-1072,8400,-2461) -> Matrix(25,42,-28,-47) Matrix(2519,-744,3660,-1081) -> Matrix(3,4,-4,-5) Matrix(181,-54,600,-179) -> Matrix(13,14,-14,-15) Matrix(1021,-310,1380,-419) -> Matrix(25,22,-58,-51) Matrix(3719,-1134,6300,-1921) -> Matrix(11,8,-18,-13) Matrix(479,-148,780,-241) -> Matrix(5,4,-24,-19) Matrix(901,-286,1320,-419) -> Matrix(3,2,-26,-17) Matrix(841,-296,1020,-359) -> Matrix(1,0,-4,1) Matrix(599,-212,1020,-361) -> Matrix(5,-8,-8,13) Matrix(1079,-386,1680,-601) -> Matrix(1,4,-2,-7) Matrix(1141,-410,1500,-539) -> Matrix(1,2,-2,-3) Matrix(899,-332,1140,-421) -> Matrix(29,26,-48,-43) Matrix(9361,-3472,14880,-5519) -> Matrix(103,88,-48,-41) Matrix(3239,-1202,7440,-2761) -> Matrix(137,116,-150,-127) Matrix(419,-158,480,-181) -> Matrix(13,10,-30,-23) Matrix(4439,-1682,7920,-3001) -> Matrix(93,68,-26,-19) Matrix(1259,-482,2040,-781) -> Matrix(3,2,34,23) Matrix(539,-208,780,-301) -> Matrix(3,2,-8,-5) Matrix(10619,-4142,18000,-7021) -> Matrix(29,18,-50,-31) Matrix(121,-48,300,-119) -> Matrix(7,4,-16,-9) Matrix(2039,-830,3540,-1441) -> Matrix(1,0,2,1) Matrix(2399,-980,2940,-1201) -> Matrix(1,0,-4,1) Matrix(4379,-1794,6300,-2581) -> Matrix(5,2,2,1) Matrix(10861,-4454,15360,-6299) -> Matrix(1,2,-2,-3) Matrix(659,-272,1020,-421) -> Matrix(5,2,-8,-3) Matrix(839,-354,1140,-481) -> Matrix(1,-8,-2,17) Matrix(2401,-1018,3960,-1679) -> Matrix(1,0,-2,1) Matrix(5521,-2406,9360,-4079) -> Matrix(23,20,-38,-33) Matrix(1261,-554,1500,-659) -> Matrix(3,2,-2,-1) Matrix(2279,-1006,4080,-1801) -> Matrix(5,4,6,5) Matrix(479,-262,660,-361) -> Matrix(17,4,-30,-7) Matrix(5939,-3352,8400,-4741) -> Matrix(17,22,-24,-31) Matrix(4679,-2642,7440,-4201) -> Matrix(17,20,-6,-7) Matrix(359,-206,420,-241) -> Matrix(11,8,-18,-13) Matrix(1321,-782,1620,-959) -> Matrix(7,4,-30,-17) Matrix(181,-108,300,-179) -> Matrix(11,6,-24,-13) Matrix(3839,-2330,5340,-3241) -> Matrix(29,12,-46,-19) Matrix(6959,-4244,9840,-6001) -> Matrix(31,12,-44,-17) Matrix(5581,-3424,7920,-4859) -> Matrix(91,22,-120,-29) Matrix(3901,-2410,5340,-3299) -> Matrix(39,-10,-74,19) Matrix(1139,-706,1260,-781) -> Matrix(1,2,-2,-3) Matrix(1439,-894,1740,-1081) -> Matrix(1,0,-2,1) Matrix(1859,-1168,2580,-1621) -> Matrix(5,2,-8,-3) Matrix(421,-294,600,-419) -> Matrix(5,6,-6,-7) Matrix(1439,-1022,1860,-1321) -> Matrix(13,8,-18,-11) Matrix(661,-484,900,-659) -> Matrix(43,22,-88,-45) Matrix(301,-250,360,-299) -> Matrix(1,2,-2,-3) Matrix(781,-676,900,-779) -> Matrix(51,26,-104,-53) 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): 192 Degree of the the map X: 192 Degree of the the map Y: 384 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/10 -13/15 -5/6 -4/5 -11/15 -7/10 -2/3 -13/21 -3/5 -5/9 -1/2 -7/15 -9/20 -5/12 -2/5 -9/25 -1/3 -14/45 -9/29 -3/10 -59/210 -7/25 -5/18 -1/4 -2/9 -3/14 -1/5 -5/27 -1/6 -3/19 -2/13 -3/23 -1/8 -1/9 0/1 1/8 2/15 1/7 1/6 3/17 2/11 1/5 3/14 2/9 3/13 7/30 1/4 4/15 3/11 5/18 7/25 2/7 3/10 1/3 9/25 11/30 2/5 5/12 13/30 9/20 7/15 1/2 8/15 17/30 3/5 13/21 17/27 19/30 29/45 2/3 31/45 7/10 11/15 23/30 4/5 5/6 13/15 9/10 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 -1/1 -8/9 1/0 -7/8 2/1 -13/15 1/0 -6/7 -4/1 -3/1 -11/13 -1/2 -5/6 -1/1 -14/17 1/1 2/1 -9/11 -1/2 -4/5 1/0 -19/24 -4/1 -15/19 -13/4 -11/14 -3/1 -7/9 1/0 -17/22 -1/1 -27/35 -3/2 -10/13 -4/3 -1/1 -23/30 -1/1 -13/17 -3/4 -16/21 -1/2 -3/4 0/1 -11/15 1/0 -19/26 -11/1 -27/37 -15/2 -8/11 -6/1 -5/1 -5/7 -3/2 -12/17 -2/1 -1/1 -43/61 -3/2 -31/44 -10/7 -19/27 -3/2 -7/10 -1/1 -23/33 -3/4 -16/23 -2/3 -3/5 -9/13 -1/4 -11/16 0/1 -2/3 1/0 -11/17 -3/2 -9/14 -1/1 -25/39 -7/4 -16/25 -3/2 -7/11 -5/4 -19/30 -1/1 -12/19 -1/1 -6/7 -17/27 -3/4 -5/8 0/1 -23/37 -1/2 -18/29 0/1 1/1 -31/50 -1/1 -44/71 -1/3 0/1 -13/21 -1/2 -34/55 -1/4 -55/89 -7/34 -21/34 -1/7 -8/13 0/1 1/5 -3/5 1/0 -10/17 -3/1 -14/5 -17/29 -29/12 -7/12 -2/1 -18/31 -2/1 -1/1 -29/50 -5/3 -40/69 -3/2 -11/19 -7/4 -15/26 -1/1 -34/59 -10/9 -1/1 -19/33 1/0 -4/7 -4/3 -1/1 -17/30 -1/1 -13/23 -9/10 -9/16 -2/3 -5/9 -1/2 -16/29 -1/5 0/1 -11/20 0/1 -6/11 2/3 1/1 -13/24 2/1 -7/13 5/2 -8/15 1/0 -1/2 -1/1 -7/15 1/0 -13/28 -8/1 -6/13 -5/1 -4/1 -5/11 -5/2 -9/20 -2/1 -4/9 -3/2 -15/34 -1/1 -26/59 -1/1 -2/3 -11/25 -3/2 -7/16 -6/5 -17/39 -9/8 -10/23 -14/13 -1/1 -13/30 -1/1 -3/7 -3/4 -8/19 -3/7 -2/5 -21/50 -1/3 -13/31 -5/18 -5/12 0/1 -12/29 0/1 1/3 -31/75 1/2 -19/46 1/1 -7/17 1/2 -16/39 1/0 -9/22 -1/1 -11/27 1/2 -2/5 1/0 -13/33 -7/2 -24/61 -34/11 -3/1 -11/28 -8/3 -9/23 -3/2 -16/41 -4/1 -3/1 -39/100 -2/1 -23/59 1/0 -7/18 -3/1 -12/31 -3/1 -2/1 -29/75 1/0 -17/44 -2/1 -5/13 -9/4 -8/21 -7/4 -19/50 -5/3 -11/29 -29/18 -14/37 -17/11 -20/13 -17/45 -3/2 -3/8 -4/3 -13/35 -5/4 -10/27 -7/6 -17/46 -1/1 -7/19 -13/12 -11/30 -1/1 -4/11 -1/1 -6/7 -13/36 -2/3 -22/61 -2/1 -1/1 -9/25 -3/4 -5/14 -3/5 -1/3 1/0 -5/16 -8/5 -19/61 -3/2 -14/45 -3/2 -9/29 -29/20 -4/13 -4/3 -9/7 -11/36 -6/5 -18/59 -2/1 -1/1 -7/23 -5/4 -3/10 -1/1 -11/37 -9/10 -19/64 -20/23 -27/91 -55/64 -8/27 -5/6 -5/17 -3/4 -7/24 -2/3 -16/55 -5/8 -9/31 -13/22 -2/7 -1/3 0/1 -11/39 1/2 -9/32 2/3 -34/121 16/17 1/1 -59/210 1/1 -25/89 13/12 -16/57 3/2 -7/25 1/0 -12/43 0/1 1/1 -17/61 1/0 -5/18 -1/1 -8/29 -1/1 0/1 -11/40 0/1 -3/11 1/0 -4/15 1/0 -5/19 -7/2 -1/4 -2/1 -4/17 -14/13 -1/1 -7/30 -1/1 -3/13 -9/10 -2/9 -1/2 -9/41 -1/4 -7/32 -2/5 -5/23 -1/6 -3/14 1/1 -1/5 1/0 -3/16 0/1 -5/27 1/0 -2/11 -2/1 -5/3 -7/39 -3/2 -5/28 -8/5 -8/45 -3/2 -3/17 -3/2 -1/6 -1/1 -3/19 -5/8 -5/32 -4/7 -2/13 -1/1 0/1 -1/7 -1/2 -2/15 1/0 -3/23 1/0 -1/8 -2/1 -1/9 -3/2 0/1 -1/1 0/1 1/8 -2/3 2/15 -1/2 1/7 1/0 1/6 -1/1 3/17 -3/4 5/28 -8/11 7/39 -3/4 2/11 -5/7 -2/3 1/5 -1/2 4/19 -2/1 -1/1 3/14 -1/3 5/23 1/4 7/32 2/1 9/41 1/2 2/9 1/0 3/13 -9/8 7/30 -1/1 4/17 -1/1 -14/15 1/4 -2/3 5/19 -7/12 4/15 -1/2 3/11 -1/2 8/29 -1/1 0/1 5/18 -1/1 17/61 -1/2 12/43 -1/3 0/1 7/25 -1/2 9/32 -2/7 2/7 0/1 1/1 9/31 -13/4 7/24 -2/1 5/17 -3/2 8/27 -5/4 3/10 -1/1 10/33 -9/10 7/23 -5/6 4/13 -9/11 -4/5 1/3 -1/2 6/17 2/3 1/1 5/14 -3/1 9/25 -3/2 22/61 -1/1 -2/3 13/36 -2/1 4/11 -6/5 -1/1 11/30 -1/1 7/19 -13/14 10/27 -7/8 33/89 -67/78 23/62 -23/27 13/35 -5/6 3/8 -4/5 14/37 -20/27 -17/23 11/29 -29/40 8/21 -7/10 5/13 -9/14 12/31 -2/3 -3/5 7/18 -3/5 23/59 -1/2 16/41 -3/5 -4/7 9/23 -3/4 11/28 -8/13 2/5 -1/2 9/22 -1/1 16/39 -1/2 7/17 -1/4 12/29 -1/5 0/1 5/12 0/1 3/7 -3/2 13/30 -1/1 10/23 -1/1 -14/15 27/62 -19/21 17/39 -9/10 7/16 -6/7 11/25 -3/4 26/59 -2/1 -1/1 15/34 -1/1 4/9 -3/4 13/29 -29/42 9/20 -2/3 14/31 -2/3 -7/11 5/11 -5/8 6/13 -4/7 -5/9 7/15 -1/2 8/17 -3/7 -2/5 1/2 -1/1 9/17 -1/2 8/15 -1/2 7/13 -5/12 6/11 -1/3 -2/7 11/20 0/1 16/29 0/1 1/3 5/9 1/0 9/16 -2/1 13/23 -9/8 17/30 -1/1 4/7 -1/1 -4/5 19/33 -1/2 34/59 -1/1 -10/11 15/26 -1/1 11/19 -7/10 40/69 -3/4 29/50 -5/7 18/31 -1/1 -2/3 7/12 -2/3 3/5 -1/2 11/18 -1/3 19/31 -7/26 46/75 -1/4 27/44 -4/17 8/13 -1/7 0/1 21/34 1/5 55/89 7/20 34/55 1/2 13/21 1/0 44/71 0/1 1/1 31/50 -1/1 18/29 -1/3 0/1 23/37 1/0 28/45 1/0 5/8 0/1 22/35 1/0 39/62 -7/3 95/151 -37/18 151/240 -2/1 56/89 -2/1 -21/11 17/27 -3/2 29/46 -7/5 12/19 -6/5 -1/1 19/30 -1/1 7/11 -5/6 9/14 -1/1 29/45 -3/4 20/31 -5/7 -2/3 11/17 -3/4 2/3 -1/2 11/16 0/1 31/45 -1/2 20/29 -1/1 0/1 9/13 1/2 16/23 -3/1 -2/1 7/10 -1/1 26/37 -9/11 -4/5 19/27 -3/4 31/44 -10/13 74/105 -3/4 43/61 -3/4 12/17 -1/1 -2/3 41/58 -11/15 29/41 -13/18 17/24 -2/3 5/7 -3/4 13/18 -3/5 21/29 -29/50 29/40 -4/7 8/11 -5/9 -6/11 11/15 -1/2 14/19 -6/13 -5/11 17/23 -7/16 20/27 -5/12 23/31 -15/38 3/4 0/1 16/21 1/0 13/17 -3/2 23/30 -1/1 10/13 -1/1 -4/5 27/35 -3/4 17/22 -1/1 24/31 -5/7 -2/3 7/9 -1/2 11/14 -3/5 26/33 -5/8 15/19 -13/22 19/24 -4/7 23/29 -29/52 4/5 -1/2 17/21 -3/8 13/16 0/1 9/11 1/0 14/17 -2/5 -1/3 19/23 -1/2 24/29 -1/5 0/1 5/6 -1/1 16/19 -2/3 -7/11 11/13 1/0 6/7 -3/5 -4/7 13/15 -1/2 20/23 -10/21 -9/19 7/8 -2/5 8/9 -1/2 9/10 -1/1 10/11 -2/3 -3/5 1/1 -1/2 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(269,246,-690,-631) (-1/1,-9/10) -> (-39/100,-23/59) Hyperbolic Matrix(661,592,1140,1021) (-9/10,-8/9) -> (40/69,29/50) Hyperbolic Matrix(209,184,510,449) (-8/9,-7/8) -> (9/22,16/39) Hyperbolic Matrix(181,158,-480,-419) (-7/8,-13/15) -> (-17/45,-3/8) Hyperbolic Matrix(329,284,-870,-751) (-13/15,-6/7) -> (-14/37,-17/45) Hyperbolic Matrix(271,230,390,331) (-6/7,-11/13) -> (9/13,16/23) Hyperbolic Matrix(211,178,-390,-329) (-11/13,-5/6) -> (-13/24,-7/13) Hyperbolic Matrix(211,174,-690,-569) (-5/6,-14/17) -> (-4/13,-11/36) Hyperbolic Matrix(151,124,330,271) (-14/17,-9/11) -> (5/11,6/13) Hyperbolic Matrix(211,172,-330,-269) (-9/11,-4/5) -> (-16/25,-7/11) Hyperbolic Matrix(419,332,-1440,-1141) (-4/5,-19/24) -> (-7/24,-16/55) Hyperbolic Matrix(1019,806,1440,1139) (-19/24,-15/19) -> (29/41,17/24) Hyperbolic Matrix(421,332,-1140,-899) (-15/19,-11/14) -> (-17/46,-7/19) Hyperbolic Matrix(151,118,270,211) (-11/14,-7/9) -> (5/9,9/16) Hyperbolic Matrix(31,24,-270,-209) (-7/9,-17/22) -> (-1/8,-1/9) Hyperbolic Matrix(391,302,1050,811) (-17/22,-27/35) -> (13/35,3/8) Hyperbolic Matrix(511,394,1830,1411) (-27/35,-10/13) -> (12/43,7/25) Hyperbolic Matrix(599,460,780,599) (-10/13,-23/30) -> (23/30,10/13) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(419,320,1020,779) (-13/17,-16/21) -> (16/39,7/17) Hyperbolic Matrix(331,252,750,571) (-16/21,-3/4) -> (15/34,4/9) Hyperbolic Matrix(329,242,-450,-331) (-3/4,-11/15) -> (-11/15,-19/26) Parabolic Matrix(989,722,-3330,-2431) (-19/26,-27/37) -> (-11/37,-19/64) Hyperbolic Matrix(691,504,1770,1291) (-27/37,-8/11) -> (16/41,9/23) Hyperbolic Matrix(89,64,-210,-151) (-8/11,-5/7) -> (-3/7,-8/19) Hyperbolic Matrix(31,22,-210,-149) (-5/7,-12/17) -> (-2/13,-1/7) Hyperbolic Matrix(1021,720,3660,2581) (-12/17,-43/61) -> (17/61,12/43) Hyperbolic Matrix(1141,804,-3660,-2579) (-43/61,-31/44) -> (-5/16,-19/61) Hyperbolic Matrix(1531,1078,2430,1711) (-31/44,-19/27) -> (17/27,29/46) Hyperbolic Matrix(419,294,-600,-421) (-19/27,-7/10) -> (-7/10,-23/33) Parabolic Matrix(569,396,990,689) (-23/33,-16/23) -> (4/7,19/33) Hyperbolic Matrix(331,230,390,271) (-16/23,-9/13) -> (11/13,6/7) Hyperbolic Matrix(301,208,-780,-539) (-9/13,-11/16) -> (-17/44,-5/13) Hyperbolic Matrix(211,144,-570,-389) (-11/16,-2/3) -> (-10/27,-17/46) Hyperbolic Matrix(151,98,510,331) (-2/3,-11/17) -> (5/17,8/27) Hyperbolic Matrix(421,272,-1020,-659) (-11/17,-9/14) -> (-19/46,-7/17) Hyperbolic Matrix(511,328,1170,751) (-9/14,-25/39) -> (17/39,7/16) Hyperbolic Matrix(1651,1058,2670,1711) (-25/39,-16/25) -> (34/55,13/21) Hyperbolic Matrix(419,266,660,419) (-7/11,-19/30) -> (19/30,7/11) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(149,94,-810,-511) (-12/19,-17/27) -> (-5/27,-2/11) Hyperbolic Matrix(331,208,-810,-509) (-17/27,-5/8) -> (-9/22,-11/27) Hyperbolic Matrix(61,38,-480,-299) (-5/8,-23/37) -> (-3/23,-1/8) Hyperbolic Matrix(869,540,-2850,-1771) (-23/37,-18/29) -> (-18/59,-7/23) Hyperbolic Matrix(1741,1080,3000,1861) (-18/29,-31/50) -> (29/50,18/31) Hyperbolic Matrix(3569,2212,-9150,-5671) (-31/50,-44/71) -> (-16/41,-39/100) Hyperbolic Matrix(539,334,3000,1859) (-44/71,-13/21) -> (7/39,2/11) Hyperbolic Matrix(1019,630,1260,779) (-13/21,-34/55) -> (4/5,17/21) Hyperbolic Matrix(1621,1002,2040,1261) (-34/55,-55/89) -> (23/29,4/5) Hyperbolic Matrix(2609,1612,-8790,-5431) (-55/89,-21/34) -> (-19/64,-27/91) Hyperbolic Matrix(149,92,630,389) (-21/34,-8/13) -> (4/17,1/4) Hyperbolic Matrix(89,54,-150,-91) (-8/13,-3/5) -> (-3/5,-10/17) Parabolic Matrix(269,158,-870,-511) (-10/17,-17/29) -> (-9/29,-4/13) Hyperbolic Matrix(629,368,870,509) (-17/29,-7/12) -> (13/18,21/29) Hyperbolic Matrix(299,174,720,419) (-7/12,-18/31) -> (12/29,5/12) Hyperbolic Matrix(1861,1080,3000,1741) (-18/31,-29/50) -> (31/50,18/29) Hyperbolic Matrix(1021,592,1140,661) (-29/50,-40/69) -> (8/9,9/10) Hyperbolic Matrix(659,382,3000,1739) (-40/69,-11/19) -> (9/41,2/9) Hyperbolic Matrix(149,86,570,329) (-11/19,-15/26) -> (1/4,5/19) Hyperbolic Matrix(1561,900,3540,2041) (-15/26,-34/59) -> (26/59,15/34) Hyperbolic Matrix(1559,898,-3960,-2281) (-34/59,-19/33) -> (-13/33,-24/61) Hyperbolic Matrix(991,570,1410,811) (-19/33,-4/7) -> (26/37,19/27) Hyperbolic Matrix(239,136,420,239) (-4/7,-17/30) -> (17/30,4/7) Hyperbolic Matrix(781,442,1380,781) (-17/30,-13/23) -> (13/23,17/30) Hyperbolic Matrix(149,84,690,389) (-13/23,-9/16) -> (3/14,5/23) Hyperbolic Matrix(211,118,270,151) (-9/16,-5/9) -> (7/9,11/14) Hyperbolic Matrix(419,232,540,299) (-5/9,-16/29) -> (24/31,7/9) Hyperbolic Matrix(541,298,1200,661) (-16/29,-11/20) -> (9/20,14/31) Hyperbolic Matrix(391,214,-930,-509) (-11/20,-6/11) -> (-8/19,-21/50) Hyperbolic Matrix(239,130,660,359) (-6/11,-13/24) -> (13/36,4/11) Hyperbolic Matrix(209,112,390,209) (-7/13,-8/15) -> (8/15,7/13) Hyperbolic Matrix(91,48,-510,-269) (-8/15,-1/2) -> (-5/28,-8/45) Hyperbolic Matrix(209,98,-450,-211) (-1/2,-7/15) -> (-7/15,-13/28) Parabolic Matrix(869,402,1230,569) (-13/28,-6/13) -> (12/17,41/58) Hyperbolic Matrix(271,124,330,151) (-6/13,-5/11) -> (9/11,14/17) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(331,148,-870,-389) (-9/20,-4/9) -> (-8/21,-19/50) Hyperbolic Matrix(571,252,750,331) (-4/9,-15/34) -> (3/4,16/21) Hyperbolic Matrix(2041,900,3540,1561) (-15/34,-26/59) -> (34/59,15/26) Hyperbolic Matrix(1081,476,3000,1321) (-26/59,-11/25) -> (9/25,22/61) Hyperbolic Matrix(269,118,750,329) (-11/25,-7/16) -> (5/14,9/25) Hyperbolic Matrix(779,340,960,419) (-7/16,-17/39) -> (17/21,13/16) Hyperbolic Matrix(331,144,-1170,-509) (-17/39,-10/23) -> (-2/7,-11/39) Hyperbolic Matrix(599,260,1380,599) (-10/23,-13/30) -> (13/30,10/23) Hyperbolic Matrix(181,78,420,181) (-13/30,-3/7) -> (3/7,13/30) Hyperbolic Matrix(929,390,2070,869) (-21/50,-13/31) -> (13/29,9/20) Hyperbolic Matrix(569,238,930,389) (-13/31,-5/12) -> (11/18,19/31) Hyperbolic Matrix(419,174,720,299) (-5/12,-12/29) -> (18/31,7/12) Hyperbolic Matrix(2399,992,3480,1439) (-12/29,-31/75) -> (31/45,20/29) Hyperbolic Matrix(2251,930,3270,1351) (-31/75,-19/46) -> (11/16,31/45) Hyperbolic Matrix(779,320,1020,419) (-7/17,-16/39) -> (16/21,13/17) Hyperbolic Matrix(449,184,510,209) (-16/39,-9/22) -> (7/8,8/9) Hyperbolic Matrix(119,48,-300,-121) (-11/27,-2/5) -> (-2/5,-13/33) Parabolic Matrix(1501,590,-5340,-2099) (-24/61,-11/28) -> (-9/32,-34/121) Hyperbolic Matrix(301,118,1380,541) (-11/28,-9/23) -> (5/23,7/32) Hyperbolic Matrix(1019,398,1380,539) (-9/23,-16/41) -> (14/19,17/23) Hyperbolic Matrix(601,234,2160,841) (-23/59,-7/18) -> (5/18,17/61) Hyperbolic Matrix(299,116,1080,419) (-7/18,-12/31) -> (8/29,5/18) Hyperbolic Matrix(2399,928,3720,1439) (-12/31,-29/75) -> (29/45,20/31) Hyperbolic Matrix(1951,754,3030,1171) (-29/75,-17/44) -> (9/14,29/45) Hyperbolic Matrix(89,34,390,149) (-5/13,-8/21) -> (2/9,3/13) Hyperbolic Matrix(1891,718,2610,991) (-19/50,-11/29) -> (21/29,29/40) Hyperbolic Matrix(391,148,1350,511) (-11/29,-14/37) -> (2/7,9/31) Hyperbolic Matrix(811,302,1050,391) (-3/8,-13/35) -> (27/35,17/22) Hyperbolic Matrix(749,278,-2670,-991) (-13/35,-10/27) -> (-16/57,-7/25) Hyperbolic Matrix(419,154,1140,419) (-7/19,-11/30) -> (11/30,7/19) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(631,228,750,271) (-4/11,-13/36) -> (5/6,16/19) Hyperbolic Matrix(1169,422,1410,509) (-13/36,-22/61) -> (24/29,5/6) Hyperbolic Matrix(1321,476,3000,1081) (-22/61,-9/25) -> (11/25,26/59) Hyperbolic Matrix(329,118,750,269) (-9/25,-5/14) -> (7/16,11/25) Hyperbolic Matrix(29,10,-90,-31) (-5/14,-1/3) -> (-1/3,-5/16) Parabolic Matrix(6449,2008,9150,2849) (-19/61,-14/45) -> (74/105,43/61) Hyperbolic Matrix(2189,680,3570,1109) (-14/45,-9/29) -> (19/31,46/75) Hyperbolic Matrix(1559,476,4320,1319) (-11/36,-18/59) -> (22/61,13/36) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(1801,534,4860,1441) (-27/91,-8/27) -> (10/27,33/89) Hyperbolic Matrix(331,98,510,151) (-8/27,-5/17) -> (11/17,2/3) Hyperbolic Matrix(89,26,510,149) (-5/17,-7/24) -> (1/6,3/17) Hyperbolic Matrix(4079,1186,6600,1919) (-16/55,-9/31) -> (55/89,34/55) Hyperbolic Matrix(511,148,1350,391) (-9/31,-2/7) -> (14/37,11/29) Hyperbolic Matrix(419,118,2340,659) (-11/39,-9/32) -> (5/28,7/39) Hyperbolic Matrix(30031,8438,47730,13411) (-34/121,-59/210) -> (151/240,56/89) Hyperbolic Matrix(33389,9380,53070,14909) (-59/210,-25/89) -> (95/151,151/240) Hyperbolic Matrix(3091,868,4170,1171) (-25/89,-16/57) -> (20/27,23/31) Hyperbolic Matrix(1411,394,1830,511) (-7/25,-12/43) -> (10/13,27/35) Hyperbolic Matrix(2581,720,3660,1021) (-12/43,-17/61) -> (43/61,12/17) Hyperbolic Matrix(841,234,2160,601) (-17/61,-5/18) -> (7/18,23/59) Hyperbolic Matrix(419,116,1080,299) (-5/18,-8/29) -> (12/31,7/18) Hyperbolic Matrix(959,264,1740,479) (-8/29,-11/40) -> (11/20,16/29) Hyperbolic Matrix(89,24,330,89) (-3/11,-4/15) -> (4/15,3/11) Hyperbolic Matrix(151,40,570,151) (-4/15,-5/19) -> (5/19,4/15) Hyperbolic Matrix(329,86,570,149) (-5/19,-1/4) -> (15/26,11/19) Hyperbolic Matrix(389,92,630,149) (-1/4,-4/17) -> (8/13,21/34) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(181,42,780,181) (-7/30,-3/13) -> (3/13,7/30) Hyperbolic Matrix(149,34,390,89) (-3/13,-2/9) -> (8/21,5/13) Hyperbolic Matrix(1739,382,3000,659) (-2/9,-9/41) -> (11/19,40/69) Hyperbolic Matrix(2609,572,3690,809) (-9/41,-7/32) -> (41/58,29/41) Hyperbolic Matrix(541,118,1380,301) (-7/32,-5/23) -> (9/23,11/28) Hyperbolic Matrix(389,84,690,149) (-5/23,-3/14) -> (9/16,13/23) Hyperbolic Matrix(29,6,-150,-31) (-3/14,-1/5) -> (-1/5,-3/16) Parabolic Matrix(1141,212,1620,301) (-3/16,-5/27) -> (19/27,31/44) Hyperbolic Matrix(1859,334,3000,539) (-2/11,-7/39) -> (13/21,44/71) Hyperbolic Matrix(1529,274,3510,629) (-7/39,-5/28) -> (27/62,17/39) Hyperbolic Matrix(541,96,1020,181) (-8/45,-3/17) -> (9/17,8/15) Hyperbolic Matrix(149,26,510,89) (-3/17,-1/6) -> (7/24,5/17) Hyperbolic Matrix(451,72,570,91) (-1/6,-3/19) -> (15/19,19/24) Hyperbolic Matrix(421,66,1920,301) (-3/19,-5/32) -> (7/32,9/41) Hyperbolic Matrix(269,42,570,89) (-5/32,-2/13) -> (8/17,1/2) Hyperbolic Matrix(29,4,210,29) (-1/7,-2/15) -> (2/15,1/7) Hyperbolic Matrix(989,130,1590,209) (-2/15,-3/23) -> (23/37,28/45) Hyperbolic Matrix(149,16,270,29) (-1/9,0/1) -> (16/29,5/9) Hyperbolic Matrix(209,-24,270,-31) (0/1,1/8) -> (17/22,24/31) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(149,-22,210,-31) (1/7,1/6) -> (17/24,5/7) Hyperbolic Matrix(269,-48,510,-91) (3/17,5/28) -> (1/2,9/17) Hyperbolic Matrix(31,-6,150,-29) (2/11,1/5) -> (1/5,4/19) Parabolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(991,-278,2670,-749) (7/25,9/32) -> (23/62,13/35) Hyperbolic Matrix(509,-144,1170,-331) (9/32,2/7) -> (10/23,27/62) Hyperbolic Matrix(1141,-332,1440,-419) (9/31,7/24) -> (19/24,23/29) Hyperbolic Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(1021,-310,1380,-419) (10/33,7/23) -> (17/23,20/27) Hyperbolic Matrix(569,-174,690,-211) (7/23,4/13) -> (14/17,19/23) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(571,-202,930,-329) (6/17,5/14) -> (27/44,8/13) Hyperbolic Matrix(899,-332,1140,-421) (7/19,10/27) -> (26/33,15/19) Hyperbolic Matrix(9361,-3472,14880,-5519) (33/89,23/62) -> (39/62,95/151) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(389,-148,870,-331) (11/29,8/21) -> (4/9,13/29) Hyperbolic Matrix(539,-208,780,-301) (5/13,12/31) -> (20/29,9/13) Hyperbolic Matrix(631,-246,690,-269) (23/59,16/41) -> (10/11,1/1) Hyperbolic Matrix(811,-320,1290,-509) (11/28,2/5) -> (22/35,39/62) Hyperbolic Matrix(509,-208,810,-331) (2/5,9/22) -> (5/8,22/35) Hyperbolic Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(151,-64,210,-89) (5/12,3/7) -> (5/7,13/18) Hyperbolic Matrix(211,-98,450,-209) (6/13,7/15) -> (7/15,8/17) Parabolic Matrix(329,-178,390,-211) (7/13,6/11) -> (16/19,11/13) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(2851,-1642,4530,-2609) (19/33,34/59) -> (56/89,17/27) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(5581,-3424,7920,-4859) (46/75,27/44) -> (31/44,74/105) Hyperbolic Matrix(1049,-648,1410,-871) (21/34,55/89) -> (23/31,3/4) Hyperbolic Matrix(1139,-706,1260,-781) (44/71,31/50) -> (9/10,10/11) Hyperbolic Matrix(1439,-894,1740,-1081) (18/29,23/37) -> (19/23,24/29) Hyperbolic Matrix(269,-172,330,-211) (7/11,9/14) -> (13/16,9/11) Hyperbolic Matrix(449,-308,570,-391) (2/3,11/16) -> (11/14,26/33) Hyperbolic Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(331,-242,450,-329) (8/11,11/15) -> (11/15,14/19) Parabolic Matrix(391,-338,450,-389) (6/7,13/15) -> (13/15,20/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(269,246,-690,-631) -> Matrix(1,-1,0,1) Matrix(661,592,1140,1021) -> Matrix(3,-2,-4,3) Matrix(209,184,510,449) -> Matrix(1,-1,-2,3) Matrix(181,158,-480,-419) -> Matrix(3,-10,-2,7) Matrix(329,284,-870,-751) -> Matrix(3,29,-2,-19) Matrix(271,230,390,331) -> Matrix(1,1,0,1) Matrix(211,178,-390,-329) -> Matrix(1,3,0,1) Matrix(211,174,-690,-569) -> Matrix(5,-1,-4,1) Matrix(151,124,330,271) -> Matrix(1,3,-2,-5) Matrix(211,172,-330,-269) -> Matrix(3,-1,-2,1) Matrix(419,332,-1440,-1141) -> Matrix(5,22,-8,-35) Matrix(1019,806,1440,1139) -> Matrix(7,26,-10,-37) Matrix(421,332,-1140,-899) -> Matrix(9,26,-8,-23) Matrix(151,118,270,211) -> Matrix(1,1,0,1) Matrix(31,24,-270,-209) -> Matrix(3,5,-2,-3) Matrix(391,302,1050,811) -> Matrix(3,7,-4,-9) Matrix(511,394,1830,1411) -> Matrix(1,1,0,1) Matrix(599,460,780,599) -> Matrix(7,8,-8,-9) Matrix(781,598,1020,781) -> Matrix(7,6,-6,-5) Matrix(419,320,1020,779) -> Matrix(3,2,-8,-5) Matrix(331,252,750,571) -> Matrix(5,1,-6,-1) Matrix(329,242,-450,-331) -> Matrix(1,-11,0,1) Matrix(989,722,-3330,-2431) -> Matrix(7,57,-8,-65) Matrix(691,504,1770,1291) -> Matrix(1,9,-2,-17) Matrix(89,64,-210,-151) -> Matrix(1,3,-2,-5) Matrix(31,22,-210,-149) -> Matrix(1,1,0,1) Matrix(1021,720,3660,2581) -> Matrix(1,2,-4,-7) Matrix(1141,804,-3660,-2579) -> Matrix(37,54,-24,-35) Matrix(1531,1078,2430,1711) -> Matrix(7,9,-4,-5) Matrix(419,294,-600,-421) -> Matrix(5,6,-6,-7) Matrix(569,396,990,689) -> Matrix(7,5,-10,-7) Matrix(331,230,390,271) -> Matrix(3,1,-4,-1) Matrix(301,208,-780,-539) -> Matrix(1,-2,0,1) Matrix(211,144,-570,-389) -> Matrix(7,-1,-6,1) Matrix(151,98,510,331) -> Matrix(5,9,-4,-7) Matrix(421,272,-1020,-659) -> Matrix(1,2,0,1) Matrix(511,328,1170,751) -> Matrix(5,11,-6,-13) Matrix(1651,1058,2670,1711) -> Matrix(3,5,4,7) Matrix(419,266,660,419) -> Matrix(9,10,-10,-11) Matrix(721,456,1140,721) -> Matrix(13,12,-12,-11) Matrix(149,94,-810,-511) -> Matrix(9,7,-4,-3) Matrix(331,208,-810,-509) -> Matrix(1,1,-2,-1) Matrix(61,38,-480,-299) -> Matrix(3,2,-2,-1) Matrix(869,540,-2850,-1771) -> Matrix(3,-1,-2,1) Matrix(1741,1080,3000,1861) -> Matrix(3,-2,-4,3) Matrix(3569,2212,-9150,-5671) -> Matrix(5,3,-2,-1) Matrix(539,334,3000,1859) -> Matrix(1,2,-2,-3) Matrix(1019,630,1260,779) -> Matrix(7,2,-18,-5) Matrix(1621,1002,2040,1261) -> Matrix(25,6,-46,-11) Matrix(2609,1612,-8790,-5431) -> Matrix(71,13,-82,-15) Matrix(149,92,630,389) -> Matrix(9,1,-10,-1) Matrix(89,54,-150,-91) -> Matrix(1,-3,0,1) Matrix(269,158,-870,-511) -> Matrix(11,29,-8,-21) Matrix(629,368,870,509) -> Matrix(13,29,-22,-49) Matrix(299,174,720,419) -> Matrix(1,2,-6,-11) Matrix(1861,1080,3000,1741) -> Matrix(1,2,-4,-7) Matrix(1021,592,1140,661) -> Matrix(1,2,-4,-7) Matrix(659,382,3000,1739) -> Matrix(1,2,-2,-3) Matrix(149,86,570,329) -> Matrix(5,7,-8,-11) Matrix(1561,900,3540,2041) -> Matrix(7,8,-8,-9) Matrix(1559,898,-3960,-2281) -> Matrix(7,4,-2,-1) Matrix(991,570,1410,811) -> Matrix(3,7,-4,-9) Matrix(239,136,420,239) -> Matrix(7,8,-8,-9) Matrix(781,442,1380,781) -> Matrix(19,18,-18,-17) Matrix(149,84,690,389) -> Matrix(1,1,-6,-5) Matrix(211,118,270,151) -> Matrix(3,1,-4,-1) Matrix(419,232,540,299) -> Matrix(5,2,-8,-3) Matrix(541,298,1200,661) -> Matrix(17,2,-26,-3) Matrix(391,214,-930,-509) -> Matrix(3,-1,-8,3) Matrix(239,130,660,359) -> Matrix(3,-4,-2,3) Matrix(209,112,390,209) -> Matrix(1,-5,-2,11) Matrix(91,48,-510,-269) -> Matrix(3,11,-2,-7) Matrix(209,98,-450,-211) -> Matrix(1,-7,0,1) Matrix(869,402,1230,569) -> Matrix(3,13,-4,-17) Matrix(271,124,330,151) -> Matrix(1,3,-2,-5) Matrix(181,82,-660,-299) -> Matrix(1,2,2,5) Matrix(331,148,-870,-389) -> Matrix(17,29,-10,-17) Matrix(571,252,750,331) -> Matrix(1,1,2,3) Matrix(2041,900,3540,1561) -> Matrix(7,8,-8,-9) Matrix(1081,476,3000,1321) -> Matrix(1,0,0,1) Matrix(269,118,750,329) -> Matrix(7,9,-4,-5) Matrix(779,340,960,419) -> Matrix(5,6,-16,-19) Matrix(331,144,-1170,-509) -> Matrix(1,1,10,11) Matrix(599,260,1380,599) -> Matrix(27,28,-28,-29) Matrix(181,78,420,181) -> Matrix(7,6,-6,-5) Matrix(929,390,2070,869) -> Matrix(41,13,-60,-19) Matrix(569,238,930,389) -> Matrix(5,1,-16,-3) Matrix(419,174,720,299) -> Matrix(7,-2,-10,3) Matrix(2399,992,3480,1439) -> Matrix(1,0,-4,1) Matrix(2251,930,3270,1351) -> Matrix(1,-1,0,1) Matrix(779,320,1020,419) -> Matrix(1,-2,0,1) Matrix(449,184,510,209) -> Matrix(1,-1,-2,3) Matrix(119,48,-300,-121) -> Matrix(1,-4,0,1) Matrix(1501,590,-5340,-2099) -> Matrix(5,14,6,17) Matrix(301,118,1380,541) -> Matrix(1,2,2,5) Matrix(1019,398,1380,539) -> Matrix(1,-2,-2,5) Matrix(601,234,2160,841) -> Matrix(1,4,-2,-7) Matrix(299,116,1080,419) -> Matrix(1,2,0,1) Matrix(2399,928,3720,1439) -> Matrix(3,4,-4,-5) Matrix(1951,754,3030,1171) -> Matrix(3,7,-4,-9) Matrix(89,34,390,149) -> Matrix(5,9,-4,-7) Matrix(1891,718,2610,991) -> Matrix(53,87,-92,-151) Matrix(391,148,1350,511) -> Matrix(11,17,-2,-3) Matrix(811,302,1050,391) -> Matrix(5,7,-8,-11) Matrix(749,278,-2670,-991) -> Matrix(9,11,4,5) Matrix(419,154,1140,419) -> Matrix(25,26,-26,-27) Matrix(241,88,660,241) -> Matrix(13,12,-12,-11) Matrix(631,228,750,271) -> Matrix(7,5,-10,-7) Matrix(1169,422,1410,509) -> Matrix(1,1,-4,-3) Matrix(1321,476,3000,1081) -> Matrix(1,0,0,1) Matrix(329,118,750,269) -> Matrix(13,9,-16,-11) Matrix(29,10,-90,-31) -> Matrix(1,-1,0,1) Matrix(6449,2008,9150,2849) -> Matrix(73,111,-98,-149) Matrix(2189,680,3570,1109) -> Matrix(17,25,-66,-97) Matrix(1559,476,4320,1319) -> Matrix(3,4,-4,-5) Matrix(179,54,-600,-181) -> Matrix(13,14,-14,-15) Matrix(1801,534,4860,1441) -> Matrix(85,72,-98,-83) Matrix(331,98,510,151) -> Matrix(11,9,-16,-13) Matrix(89,26,510,149) -> Matrix(13,9,-16,-11) Matrix(4079,1186,6600,1919) -> Matrix(13,8,34,21) Matrix(511,148,1350,391) -> Matrix(31,17,-42,-23) Matrix(419,118,2340,659) -> Matrix(7,-2,-10,3) Matrix(30031,8438,47730,13411) -> Matrix(55,-53,-28,27) Matrix(33389,9380,53070,14909) -> Matrix(61,-63,-30,31) Matrix(3091,868,4170,1171) -> Matrix(9,-11,-22,27) Matrix(1411,394,1830,511) -> Matrix(3,1,-4,-1) Matrix(2581,720,3660,1021) -> Matrix(3,-2,-4,3) Matrix(841,234,2160,601) -> Matrix(1,4,-2,-7) Matrix(419,116,1080,299) -> Matrix(5,2,-8,-3) Matrix(959,264,1740,479) -> Matrix(1,0,4,1) Matrix(89,24,330,89) -> Matrix(1,-1,-2,3) Matrix(151,40,570,151) -> Matrix(1,7,-2,-13) Matrix(329,86,570,149) -> Matrix(3,7,-4,-9) Matrix(389,92,630,149) -> Matrix(1,1,6,7) Matrix(239,56,1020,239) -> Matrix(27,28,-28,-29) Matrix(181,42,780,181) -> Matrix(19,18,-18,-17) Matrix(149,34,390,89) -> Matrix(11,9,-16,-13) Matrix(1739,382,3000,659) -> Matrix(1,2,-2,-3) Matrix(2609,572,3690,809) -> Matrix(7,5,-10,-7) Matrix(541,118,1380,301) -> Matrix(9,2,-14,-3) Matrix(389,84,690,149) -> Matrix(3,-1,-2,1) Matrix(29,6,-150,-31) -> Matrix(1,-1,0,1) Matrix(1141,212,1620,301) -> Matrix(3,10,-4,-13) Matrix(1859,334,3000,539) -> Matrix(1,2,-2,-3) Matrix(1529,274,3510,629) -> Matrix(7,15,-8,-17) Matrix(541,96,1020,181) -> Matrix(15,22,-28,-41) Matrix(149,26,510,89) -> Matrix(7,9,-4,-5) Matrix(451,72,570,91) -> Matrix(15,11,-26,-19) Matrix(421,66,1920,301) -> Matrix(3,2,-2,-1) Matrix(269,42,570,89) -> Matrix(5,3,-12,-7) Matrix(29,4,210,29) -> Matrix(1,1,-2,-1) Matrix(989,130,1590,209) -> Matrix(1,3,0,1) Matrix(149,16,270,29) -> Matrix(1,1,2,3) Matrix(209,-24,270,-31) -> Matrix(7,5,-10,-7) Matrix(299,-38,480,-61) -> Matrix(3,2,-2,-1) Matrix(149,-22,210,-31) -> Matrix(3,1,-4,-1) Matrix(269,-48,510,-91) -> Matrix(15,11,-26,-19) Matrix(31,-6,150,-29) -> Matrix(1,1,-4,-3) Matrix(719,-152,1140,-241) -> Matrix(5,4,-4,-3) Matrix(299,-82,660,-181) -> Matrix(9,2,-14,-3) Matrix(991,-278,2670,-749) -> Matrix(27,11,-32,-13) Matrix(509,-144,1170,-331) -> Matrix(13,1,-14,-1) Matrix(1141,-332,1440,-419) -> Matrix(9,22,-16,-39) Matrix(181,-54,600,-179) -> Matrix(13,14,-14,-15) Matrix(1021,-310,1380,-419) -> Matrix(25,22,-58,-51) Matrix(569,-174,690,-211) -> Matrix(1,1,-8,-7) Matrix(31,-10,90,-29) -> Matrix(1,1,-4,-3) Matrix(571,-202,930,-329) -> Matrix(1,-1,-4,5) Matrix(899,-332,1140,-421) -> Matrix(29,26,-48,-43) Matrix(9361,-3472,14880,-5519) -> Matrix(103,88,-48,-41) Matrix(419,-158,480,-181) -> Matrix(13,10,-30,-23) Matrix(389,-148,870,-331) -> Matrix(41,29,-58,-41) Matrix(539,-208,780,-301) -> Matrix(3,2,-8,-5) Matrix(631,-246,690,-269) -> Matrix(1,1,-4,-3) Matrix(811,-320,1290,-509) -> Matrix(9,5,-2,-1) Matrix(509,-208,810,-331) -> Matrix(1,1,-2,-1) Matrix(659,-272,1020,-421) -> Matrix(5,2,-8,-3) Matrix(151,-64,210,-89) -> Matrix(1,3,-2,-5) Matrix(211,-98,450,-209) -> Matrix(13,7,-28,-15) Matrix(329,-178,390,-211) -> Matrix(7,3,-12,-5) Matrix(479,-262,660,-361) -> Matrix(17,4,-30,-7) Matrix(2851,-1642,4530,-2609) -> Matrix(1,-1,0,1) Matrix(91,-54,150,-89) -> Matrix(5,3,-12,-7) Matrix(5581,-3424,7920,-4859) -> Matrix(91,22,-120,-29) Matrix(1049,-648,1410,-871) -> Matrix(5,-1,-14,3) Matrix(1139,-706,1260,-781) -> Matrix(1,2,-2,-3) Matrix(1439,-894,1740,-1081) -> Matrix(1,0,-2,1) Matrix(269,-172,330,-211) -> Matrix(1,1,-6,-5) Matrix(449,-308,570,-391) -> Matrix(1,3,-2,-5) Matrix(421,-294,600,-419) -> Matrix(5,6,-6,-7) Matrix(331,-242,450,-329) -> Matrix(21,11,-44,-23) Matrix(391,-338,450,-389) -> Matrix(25,13,-52,-27) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 192 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 30 1/8 -2/3 1 15 2/15 -1/2 2 2 1/7 1/0 1 30 1/6 -1/1 5 5 3/17 -3/4 1 30 5/28 -8/11 1 15 7/39 -3/4 1 10 2/11 (-5/7,-2/3) 0 30 1/5 -1/2 1 6 4/19 (-2/1,-1/1) 0 30 3/14 -1/3 1 15 5/23 1/4 1 30 7/32 2/1 1 15 9/41 1/2 1 30 2/9 1/0 2 10 3/13 -9/8 1 30 7/30 -1/1 23 1 4/17 (-1/1,-14/15) 0 30 1/4 -2/3 1 15 5/19 -7/12 1 30 4/15 -1/2 4 2 3/11 -1/2 1 30 8/29 (-1/1,0/1) 0 30 5/18 -1/1 1 5 17/61 -1/2 1 30 12/43 (-1/3,0/1) 0 30 7/25 -1/2 3 6 9/32 -2/7 1 15 2/7 (0/1,1/1) 0 30 9/31 -13/4 1 30 7/24 -2/1 5 5 5/17 -3/2 1 30 8/27 -5/4 2 10 3/10 -1/1 7 3 10/33 -9/10 2 10 7/23 -5/6 1 30 4/13 (-9/11,-4/5) 0 30 1/3 -1/2 1 10 6/17 (2/3,1/1) 0 30 5/14 -3/1 1 15 9/25 -3/2 1 6 22/61 (-1/1,-2/3) 0 30 13/36 -2/1 1 5 4/11 (-6/5,-1/1) 0 30 11/30 -1/1 19 1 7/19 -13/14 1 30 10/27 -7/8 2 10 33/89 -67/78 1 30 23/62 -23/27 1 15 13/35 -5/6 3 6 3/8 -4/5 1 15 14/37 (-20/27,-17/23) 0 30 11/29 -29/40 1 30 8/21 -7/10 2 10 5/13 -9/14 1 30 12/31 (-2/3,-3/5) 0 30 7/18 -3/5 1 5 23/59 -1/2 1 30 16/41 (-3/5,-4/7) 0 30 9/23 -3/4 1 30 11/28 -8/13 1 15 2/5 -1/2 2 6 9/22 -1/1 1 15 16/39 -1/2 2 10 7/17 -1/4 1 30 12/29 (-1/5,0/1) 0 30 5/12 0/1 5 5 3/7 -3/2 1 30 13/30 -1/1 17 1 10/23 (-1/1,-14/15) 0 30 27/62 -19/21 1 15 17/39 -9/10 1 10 7/16 -6/7 1 15 11/25 -3/4 1 6 26/59 (-2/1,-1/1) 0 30 15/34 -1/1 1 15 4/9 -3/4 2 10 13/29 -29/42 1 30 9/20 -2/3 9 3 14/31 (-2/3,-7/11) 0 30 5/11 -5/8 1 30 6/13 (-4/7,-5/9) 0 30 7/15 -1/2 7 2 8/17 (-3/7,-2/5) 0 30 1/2 -1/1 1 15 9/17 -1/2 1 30 8/15 -1/2 8 2 7/13 -5/12 1 30 6/11 (-1/3,-2/7) 0 30 11/20 0/1 9 3 16/29 (0/1,1/3) 0 30 5/9 1/0 1 10 9/16 -2/1 1 15 13/23 -9/8 1 30 17/30 -1/1 13 1 4/7 (-1/1,-4/5) 0 30 19/33 -1/2 1 10 34/59 (-1/1,-10/11) 0 30 15/26 -1/1 1 15 11/19 -7/10 1 30 40/69 -3/4 2 10 29/50 -5/7 1 3 18/31 (-1/1,-2/3) 0 30 7/12 -2/3 5 5 3/5 -1/2 3 6 11/18 -1/3 5 5 19/31 -7/26 1 30 46/75 -1/4 14 2 27/44 -4/17 1 15 8/13 (-1/7,0/1) 0 30 21/34 1/5 1 15 55/89 7/20 1 30 34/55 1/2 4 6 13/21 1/0 1 10 44/71 (0/1,1/1) 0 30 31/50 -1/1 1 3 18/29 (-1/3,0/1) 0 30 23/37 1/0 1 30 28/45 1/0 2 2 5/8 0/1 1 15 22/35 1/0 2 6 39/62 -7/3 1 15 95/151 -37/18 1 30 151/240 -2/1 29 1 56/89 (-2/1,-21/11) 0 30 17/27 -3/2 1 10 29/46 -7/5 1 15 12/19 (-6/5,-1/1) 0 30 19/30 -1/1 11 1 7/11 -5/6 1 30 9/14 -1/1 1 15 29/45 -3/4 1 2 20/31 (-5/7,-2/3) 0 30 11/17 -3/4 1 30 2/3 -1/2 2 10 11/16 0/1 1 15 31/45 -1/2 1 2 20/29 (-1/1,0/1) 0 30 9/13 1/2 1 30 16/23 (-3/1,-2/1) 0 30 7/10 -1/1 3 3 26/37 (-9/11,-4/5) 0 30 19/27 -3/4 1 10 31/44 -10/13 1 15 74/105 -3/4 14 2 43/61 -3/4 1 30 12/17 (-1/1,-2/3) 0 30 41/58 -11/15 1 15 29/41 -13/18 1 30 17/24 -2/3 5 5 5/7 -3/4 1 30 13/18 -3/5 5 5 21/29 -29/50 1 30 29/40 -4/7 9 3 8/11 (-5/9,-6/11) 0 30 11/15 -1/2 11 2 14/19 (-6/13,-5/11) 0 30 17/23 -7/16 1 30 20/27 -5/12 2 10 23/31 -15/38 1 30 3/4 0/1 1 15 16/21 1/0 2 10 13/17 -3/2 1 30 23/30 -1/1 7 1 10/13 (-1/1,-4/5) 0 30 27/35 -3/4 3 6 17/22 -1/1 1 15 24/31 (-5/7,-2/3) 0 30 7/9 -1/2 1 10 11/14 -3/5 1 15 26/33 -5/8 2 10 15/19 -13/22 1 30 19/24 -4/7 5 5 23/29 -29/52 1 30 4/5 -1/2 4 6 17/21 -3/8 1 10 13/16 0/1 1 15 9/11 1/0 1 30 14/17 (-2/5,-1/3) 0 30 19/23 -1/2 1 30 24/29 (-1/5,0/1) 0 30 5/6 -1/1 1 5 16/19 (-2/3,-7/11) 0 30 11/13 1/0 1 30 6/7 (-3/5,-4/7) 0 30 13/15 -1/2 13 2 20/23 (-10/21,-9/19) 0 30 7/8 -2/5 1 15 8/9 -1/2 2 10 9/10 -1/1 1 3 10/11 (-2/3,-3/5) 0 30 1/1 -1/2 1 30 1/0 0/1 1 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(209,-24,270,-31) (0/1,1/8) -> (17/22,24/31) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(29,-4,210,-29) (2/15,1/7) -> (2/15,1/7) Reflection Matrix(149,-22,210,-31) (1/7,1/6) -> (17/24,5/7) Hyperbolic Matrix(149,-26,510,-89) (1/6,3/17) -> (7/24,5/17) Glide Reflection Matrix(269,-48,510,-91) (3/17,5/28) -> (1/2,9/17) Hyperbolic Matrix(1529,-274,3510,-629) (5/28,7/39) -> (27/62,17/39) Glide Reflection Matrix(1859,-334,3000,-539) (7/39,2/11) -> (13/21,44/71) Glide Reflection Matrix(31,-6,150,-29) (2/11,1/5) -> (1/5,4/19) Parabolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(389,-84,690,-149) (3/14,5/23) -> (9/16,13/23) Glide Reflection Matrix(541,-118,1380,-301) (5/23,7/32) -> (9/23,11/28) Glide Reflection Matrix(2609,-572,3690,-809) (7/32,9/41) -> (41/58,29/41) Glide Reflection Matrix(1739,-382,3000,-659) (9/41,2/9) -> (11/19,40/69) Glide Reflection Matrix(149,-34,390,-89) (2/9,3/13) -> (8/21,5/13) Glide Reflection Matrix(181,-42,780,-181) (3/13,7/30) -> (3/13,7/30) Reflection Matrix(239,-56,1020,-239) (7/30,4/17) -> (7/30,4/17) Reflection Matrix(389,-92,630,-149) (4/17,1/4) -> (8/13,21/34) Glide Reflection Matrix(329,-86,570,-149) (1/4,5/19) -> (15/26,11/19) Glide Reflection Matrix(151,-40,570,-151) (5/19,4/15) -> (5/19,4/15) Reflection Matrix(89,-24,330,-89) (4/15,3/11) -> (4/15,3/11) Reflection Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(419,-116,1080,-299) (8/29,5/18) -> (12/31,7/18) Glide Reflection Matrix(841,-234,2160,-601) (5/18,17/61) -> (7/18,23/59) Glide Reflection Matrix(2581,-720,3660,-1021) (17/61,12/43) -> (43/61,12/17) Glide Reflection Matrix(1411,-394,1830,-511) (12/43,7/25) -> (10/13,27/35) Glide Reflection Matrix(991,-278,2670,-749) (7/25,9/32) -> (23/62,13/35) Hyperbolic Matrix(509,-144,1170,-331) (9/32,2/7) -> (10/23,27/62) Hyperbolic Matrix(511,-148,1350,-391) (2/7,9/31) -> (14/37,11/29) Glide Reflection Matrix(1141,-332,1440,-419) (9/31,7/24) -> (19/24,23/29) Hyperbolic Matrix(331,-98,510,-151) (5/17,8/27) -> (11/17,2/3) Glide Reflection Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(1021,-310,1380,-419) (10/33,7/23) -> (17/23,20/27) Hyperbolic Matrix(569,-174,690,-211) (7/23,4/13) -> (14/17,19/23) Hyperbolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(571,-202,930,-329) (6/17,5/14) -> (27/44,8/13) Hyperbolic Matrix(329,-118,750,-269) (5/14,9/25) -> (7/16,11/25) Glide Reflection Matrix(1321,-476,3000,-1081) (9/25,22/61) -> (11/25,26/59) Glide Reflection Matrix(1169,-422,1410,-509) (22/61,13/36) -> (24/29,5/6) Glide Reflection Matrix(631,-228,750,-271) (13/36,4/11) -> (5/6,16/19) Glide Reflection Matrix(241,-88,660,-241) (4/11,11/30) -> (4/11,11/30) Reflection Matrix(419,-154,1140,-419) (11/30,7/19) -> (11/30,7/19) Reflection Matrix(899,-332,1140,-421) (7/19,10/27) -> (26/33,15/19) Hyperbolic Matrix(2401,-890,3240,-1201) (10/27,33/89) -> (20/27,23/31) Glide Reflection Matrix(9361,-3472,14880,-5519) (33/89,23/62) -> (39/62,95/151) Hyperbolic Matrix(811,-302,1050,-391) (13/35,3/8) -> (27/35,17/22) Glide Reflection Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(389,-148,870,-331) (11/29,8/21) -> (4/9,13/29) Hyperbolic Matrix(539,-208,780,-301) (5/13,12/31) -> (20/29,9/13) Hyperbolic Matrix(631,-246,690,-269) (23/59,16/41) -> (10/11,1/1) Hyperbolic Matrix(1019,-398,1380,-539) (16/41,9/23) -> (14/19,17/23) Glide Reflection Matrix(811,-320,1290,-509) (11/28,2/5) -> (22/35,39/62) Hyperbolic Matrix(509,-208,810,-331) (2/5,9/22) -> (5/8,22/35) Hyperbolic Matrix(449,-184,510,-209) (9/22,16/39) -> (7/8,8/9) Glide Reflection Matrix(779,-320,1020,-419) (16/39,7/17) -> (16/21,13/17) Glide Reflection Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(419,-174,720,-299) (12/29,5/12) -> (18/31,7/12) Glide Reflection Matrix(151,-64,210,-89) (5/12,3/7) -> (5/7,13/18) Hyperbolic Matrix(181,-78,420,-181) (3/7,13/30) -> (3/7,13/30) Reflection Matrix(599,-260,1380,-599) (13/30,10/23) -> (13/30,10/23) Reflection Matrix(779,-340,960,-419) (17/39,7/16) -> (17/21,13/16) Glide Reflection Matrix(2041,-900,3540,-1561) (26/59,15/34) -> (34/59,15/26) Glide Reflection Matrix(571,-252,750,-331) (15/34,4/9) -> (3/4,16/21) Glide Reflection Matrix(1261,-566,1740,-781) (13/29,9/20) -> (21/29,29/40) Glide Reflection Matrix(661,-298,1200,-541) (9/20,14/31) -> (11/20,16/29) Glide Reflection Matrix(271,-124,330,-151) (5/11,6/13) -> (9/11,14/17) Glide Reflection Matrix(211,-98,450,-209) (6/13,7/15) -> (7/15,8/17) Parabolic Matrix(721,-340,1020,-481) (8/17,1/2) -> (12/17,41/58) Glide Reflection Matrix(271,-144,510,-271) (9/17,8/15) -> (9/17,8/15) Reflection Matrix(209,-112,390,-209) (8/15,7/13) -> (8/15,7/13) Reflection Matrix(329,-178,390,-211) (7/13,6/11) -> (16/19,11/13) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(419,-232,540,-299) (16/29,5/9) -> (24/31,7/9) Glide Reflection Matrix(211,-118,270,-151) (5/9,9/16) -> (7/9,11/14) Glide Reflection Matrix(781,-442,1380,-781) (13/23,17/30) -> (13/23,17/30) Reflection Matrix(239,-136,420,-239) (17/30,4/7) -> (17/30,4/7) Reflection Matrix(991,-570,1410,-811) (4/7,19/33) -> (26/37,19/27) Glide Reflection Matrix(2851,-1642,4530,-2609) (19/33,34/59) -> (56/89,17/27) Hyperbolic Matrix(1021,-592,1140,-661) (40/69,29/50) -> (8/9,9/10) Glide Reflection Matrix(1861,-1080,3000,-1741) (29/50,18/31) -> (31/50,18/29) Glide Reflection Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(781,-478,1080,-661) (11/18,19/31) -> (13/18,21/29) Glide Reflection Matrix(2851,-1748,4650,-2851) (19/31,46/75) -> (19/31,46/75) Reflection Matrix(5581,-3424,7920,-4859) (46/75,27/44) -> (31/44,74/105) Hyperbolic Matrix(1049,-648,1410,-871) (21/34,55/89) -> (23/31,3/4) Hyperbolic Matrix(1621,-1002,2040,-1261) (55/89,34/55) -> (23/29,4/5) Glide Reflection Matrix(1019,-630,1260,-779) (34/55,13/21) -> (4/5,17/21) Glide Reflection Matrix(1139,-706,1260,-781) (44/71,31/50) -> (9/10,10/11) Hyperbolic Matrix(1439,-894,1740,-1081) (18/29,23/37) -> (19/23,24/29) Hyperbolic Matrix(2071,-1288,3330,-2071) (23/37,28/45) -> (23/37,28/45) Reflection Matrix(45601,-28690,72480,-45601) (95/151,151/240) -> (95/151,151/240) Reflection Matrix(26879,-16912,42720,-26879) (151/240,56/89) -> (151/240,56/89) Reflection Matrix(1711,-1078,2430,-1531) (17/27,29/46) -> (19/27,31/44) Glide Reflection Matrix(721,-456,1140,-721) (12/19,19/30) -> (12/19,19/30) Reflection Matrix(419,-266,660,-419) (19/30,7/11) -> (19/30,7/11) Reflection Matrix(269,-172,330,-211) (7/11,9/14) -> (13/16,9/11) Hyperbolic Matrix(929,-598,1350,-869) (9/14,29/45) -> (11/16,31/45) Glide Reflection Matrix(1861,-1200,2700,-1741) (29/45,20/31) -> (31/45,20/29) Glide Reflection Matrix(449,-308,570,-391) (2/3,11/16) -> (11/14,26/33) Hyperbolic Matrix(331,-230,390,-271) (9/13,16/23) -> (11/13,6/7) Glide Reflection Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(9029,-6364,12810,-9029) (74/105,43/61) -> (74/105,43/61) Reflection Matrix(1139,-806,1440,-1019) (29/41,17/24) -> (15/19,19/24) Glide Reflection Matrix(331,-242,450,-329) (8/11,11/15) -> (11/15,14/19) Parabolic Matrix(781,-598,1020,-781) (13/17,23/30) -> (13/17,23/30) Reflection Matrix(599,-460,780,-599) (23/30,10/13) -> (23/30,10/13) Reflection Matrix(391,-338,450,-389) (6/7,13/15) -> (13/15,20/23) Parabolic 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(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(209,-24,270,-31) -> Matrix(7,5,-10,-7) (-1/1,-2/3).(-3/4,-1/2) Matrix(299,-38,480,-61) -> Matrix(3,2,-2,-1) -1/1 Matrix(29,-4,210,-29) -> Matrix(1,1,0,-1) (2/15,1/7) -> (-1/2,1/0) Matrix(149,-22,210,-31) -> Matrix(3,1,-4,-1) -1/2 Matrix(149,-26,510,-89) -> Matrix(11,9,-6,-5) Matrix(269,-48,510,-91) -> Matrix(15,11,-26,-19) Matrix(1529,-274,3510,-629) -> Matrix(23,15,-26,-17) Matrix(1859,-334,3000,-539) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(31,-6,150,-29) -> Matrix(1,1,-4,-3) -1/2 Matrix(719,-152,1140,-241) -> Matrix(5,4,-4,-3) -1/1 Matrix(389,-84,690,-149) -> Matrix(5,1,-4,-1) Matrix(541,-118,1380,-301) -> Matrix(5,-2,-8,3) Matrix(2609,-572,3690,-809) -> Matrix(3,5,-4,-7) Matrix(1739,-382,3000,-659) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(149,-34,390,-89) -> Matrix(7,9,-10,-13) Matrix(181,-42,780,-181) -> Matrix(17,18,-16,-17) (3/13,7/30) -> (-9/8,-1/1) Matrix(239,-56,1020,-239) -> Matrix(29,28,-30,-29) (7/30,4/17) -> (-1/1,-14/15) Matrix(389,-92,630,-149) -> Matrix(1,1,8,7) Matrix(329,-86,570,-149) -> Matrix(11,7,-14,-9) Matrix(151,-40,570,-151) -> Matrix(13,7,-24,-13) (5/19,4/15) -> (-7/12,-1/2) Matrix(89,-24,330,-89) -> Matrix(3,1,-8,-3) (4/15,3/11) -> (-1/2,-1/4) Matrix(299,-82,660,-181) -> Matrix(9,2,-14,-3) Matrix(419,-116,1080,-299) -> Matrix(1,-2,-2,3) Matrix(841,-234,2160,-601) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(2581,-720,3660,-1021) -> Matrix(7,2,-10,-3) Matrix(1411,-394,1830,-511) -> Matrix(1,-1,-2,1) Matrix(991,-278,2670,-749) -> Matrix(27,11,-32,-13) Matrix(509,-144,1170,-331) -> Matrix(13,1,-14,-1) Matrix(511,-148,1350,-391) -> Matrix(3,17,-4,-23) Matrix(1141,-332,1440,-419) -> Matrix(9,22,-16,-39) Matrix(331,-98,510,-151) -> Matrix(7,9,-10,-13) Matrix(181,-54,600,-179) -> Matrix(13,14,-14,-15) -1/1 Matrix(1021,-310,1380,-419) -> Matrix(25,22,-58,-51) Matrix(569,-174,690,-211) -> Matrix(1,1,-8,-7) Matrix(31,-10,90,-29) -> Matrix(1,1,-4,-3) -1/2 Matrix(571,-202,930,-329) -> Matrix(1,-1,-4,5) Matrix(329,-118,750,-269) -> Matrix(5,9,-6,-11) Matrix(1321,-476,3000,-1081) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1169,-422,1410,-509) -> Matrix(1,1,-2,-3) Matrix(631,-228,750,-271) -> Matrix(3,5,-4,-7) Matrix(241,-88,660,-241) -> Matrix(11,12,-10,-11) (4/11,11/30) -> (-6/5,-1/1) Matrix(419,-154,1140,-419) -> Matrix(27,26,-28,-27) (11/30,7/19) -> (-1/1,-13/14) Matrix(899,-332,1140,-421) -> Matrix(29,26,-48,-43) Matrix(2401,-890,3240,-1201) -> Matrix(51,44,-124,-107) Matrix(9361,-3472,14880,-5519) -> Matrix(103,88,-48,-41) Matrix(811,-302,1050,-391) -> Matrix(9,7,-14,-11) Matrix(419,-158,480,-181) -> Matrix(13,10,-30,-23) Matrix(389,-148,870,-331) -> Matrix(41,29,-58,-41) (-3/4,-7/10).(-5/7,-2/3) Matrix(539,-208,780,-301) -> Matrix(3,2,-8,-5) -1/2 Matrix(631,-246,690,-269) -> Matrix(1,1,-4,-3) -1/2 Matrix(1019,-398,1380,-539) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(811,-320,1290,-509) -> Matrix(9,5,-2,-1) Matrix(509,-208,810,-331) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(449,-184,510,-209) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(779,-320,1020,-419) -> Matrix(5,2,-2,-1) Matrix(659,-272,1020,-421) -> Matrix(5,2,-8,-3) -1/2 Matrix(419,-174,720,-299) -> Matrix(11,2,-16,-3) Matrix(151,-64,210,-89) -> Matrix(1,3,-2,-5) Matrix(181,-78,420,-181) -> Matrix(5,6,-4,-5) (3/7,13/30) -> (-3/2,-1/1) Matrix(599,-260,1380,-599) -> Matrix(29,28,-30,-29) (13/30,10/23) -> (-1/1,-14/15) Matrix(779,-340,960,-419) -> Matrix(7,6,-22,-19) Matrix(2041,-900,3540,-1561) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(571,-252,750,-331) -> Matrix(1,1,4,3) Matrix(1261,-566,1740,-781) -> Matrix(85,58,-148,-101) Matrix(661,-298,1200,-541) -> Matrix(3,2,20,13) Matrix(271,-124,330,-151) -> Matrix(5,3,-8,-5) *** -> (-3/4,-1/2) Matrix(211,-98,450,-209) -> Matrix(13,7,-28,-15) -1/2 Matrix(721,-340,1020,-481) -> Matrix(19,8,-26,-11) Matrix(271,-144,510,-271) -> Matrix(21,11,-40,-21) (9/17,8/15) -> (-11/20,-1/2) Matrix(209,-112,390,-209) -> Matrix(11,5,-24,-11) (8/15,7/13) -> (-1/2,-5/12) Matrix(329,-178,390,-211) -> Matrix(7,3,-12,-5) -1/2 Matrix(479,-262,660,-361) -> Matrix(17,4,-30,-7) Matrix(419,-232,540,-299) -> Matrix(1,-2,-2,3) Matrix(211,-118,270,-151) -> Matrix(1,-1,-2,1) Matrix(781,-442,1380,-781) -> Matrix(17,18,-16,-17) (13/23,17/30) -> (-9/8,-1/1) Matrix(239,-136,420,-239) -> Matrix(9,8,-10,-9) (17/30,4/7) -> (-1/1,-4/5) Matrix(991,-570,1410,-811) -> Matrix(11,7,-14,-9) Matrix(2851,-1642,4530,-2609) -> Matrix(1,-1,0,1) 1/0 Matrix(1021,-592,1140,-661) -> Matrix(3,2,-10,-7) Matrix(1861,-1080,3000,-1741) -> Matrix(3,2,-10,-7) Matrix(91,-54,150,-89) -> Matrix(5,3,-12,-7) -1/2 Matrix(781,-478,1080,-661) -> Matrix(33,10,-56,-17) Matrix(2851,-1748,4650,-2851) -> Matrix(27,7,-104,-27) (19/31,46/75) -> (-7/26,-1/4) Matrix(5581,-3424,7920,-4859) -> Matrix(91,22,-120,-29) Matrix(1049,-648,1410,-871) -> Matrix(5,-1,-14,3) Matrix(1621,-1002,2040,-1261) -> Matrix(13,-6,-24,11) Matrix(1019,-630,1260,-779) -> Matrix(3,-2,-8,5) Matrix(1139,-706,1260,-781) -> Matrix(1,2,-2,-3) -1/1 Matrix(1439,-894,1740,-1081) -> Matrix(1,0,-2,1) 0/1 Matrix(2071,-1288,3330,-2071) -> Matrix(-1,1,0,1) (23/37,28/45) -> (1/2,1/0) Matrix(45601,-28690,72480,-45601) -> Matrix(73,148,-36,-73) (95/151,151/240) -> (-37/18,-2/1) Matrix(26879,-16912,42720,-26879) -> Matrix(43,84,-22,-43) (151/240,56/89) -> (-2/1,-21/11) Matrix(1711,-1078,2430,-1531) -> Matrix(5,9,-6,-11) Matrix(721,-456,1140,-721) -> Matrix(11,12,-10,-11) (12/19,19/30) -> (-6/5,-1/1) Matrix(419,-266,660,-419) -> Matrix(11,10,-12,-11) (19/30,7/11) -> (-1/1,-5/6) Matrix(269,-172,330,-211) -> Matrix(1,1,-6,-5) Matrix(929,-598,1350,-869) -> Matrix(1,1,2,1) Matrix(1861,-1200,2700,-1741) -> Matrix(3,2,-10,-7) Matrix(449,-308,570,-391) -> Matrix(1,3,-2,-5) Matrix(331,-230,390,-271) -> Matrix(1,-1,-2,1) Matrix(421,-294,600,-419) -> Matrix(5,6,-6,-7) -1/1 Matrix(9029,-6364,12810,-9029) -> Matrix(77,57,-104,-77) (74/105,43/61) -> (-3/4,-19/26) Matrix(1139,-806,1440,-1019) -> Matrix(37,26,-64,-45) Matrix(331,-242,450,-329) -> Matrix(21,11,-44,-23) -1/2 Matrix(781,-598,1020,-781) -> Matrix(5,6,-4,-5) (13/17,23/30) -> (-3/2,-1/1) Matrix(599,-460,780,-599) -> Matrix(9,8,-10,-9) (23/30,10/13) -> (-1/1,-4/5) Matrix(391,-338,450,-389) -> Matrix(25,13,-52,-27) -1/2 Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.