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): 2160 Minimal number of generators: 361 Number of equivalence classes of cusps: 72 Genus: 145 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -57/37 -19/17 0/1 1/1 19/16 19/15 19/14 19/13 3/2 19/12 19/11 19/10 2/1 19/9 38/17 76/33 19/8 12/5 152/63 76/31 5/2 38/15 76/29 19/7 418/153 114/41 76/27 3/1 19/6 76/23 38/11 7/2 18/5 76/21 11/3 152/41 34/9 19/5 4/1 38/9 17/4 30/7 13/3 9/2 114/25 14/3 19/4 24/5 5/1 26/5 95/18 16/3 38/7 11/2 17/3 40/7 6/1 19/3 32/5 13/2 20/3 7/1 22/3 15/2 38/5 23/3 8/1 9/1 28/3 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 -2/1 -1/1 -15/2 -3/4 -7/1 1/0 -20/3 1/1 1/0 -33/5 1/0 -13/2 1/0 -19/3 1/0 -6/1 -2/1 1/0 -29/5 1/0 -23/4 -5/2 -17/3 -7/4 -28/5 -5/3 -3/2 -11/2 -5/4 -16/3 -1/1 -2/3 -21/4 -1/2 -5/1 1/0 -29/6 1/0 -24/5 1/1 1/0 -19/4 1/0 -14/3 -2/1 1/0 -37/8 1/0 -23/5 1/0 -32/7 -3/2 -1/1 -41/9 -3/4 -9/2 1/0 -31/7 -3/2 -53/12 -1/2 -22/5 -2/1 1/0 -35/8 -3/2 -48/11 -3/2 -1/1 -13/3 -3/2 -43/10 -3/2 -30/7 -4/3 -5/4 -17/4 -9/8 -4/1 -1/1 0/1 -19/5 0/1 -34/9 0/1 1/0 -49/13 1/0 -15/4 1/0 -41/11 -3/2 -26/7 0/1 1/0 -63/17 1/0 -37/10 1/0 -11/3 -1/2 -40/11 0/1 1/1 -69/19 1/2 -29/8 1/0 -18/5 0/1 1/0 -7/2 -3/2 -24/7 -1/1 -5/6 -41/12 -3/4 -17/5 -3/4 -44/13 -3/5 -1/2 -27/8 -1/2 -64/19 -2/3 -3/5 -37/11 -1/2 -10/3 -1/2 0/1 -33/10 -1/2 -56/17 -1/1 -1/2 -23/7 -1/2 -36/11 0/1 1/1 -13/4 -1/2 -16/5 -1/3 0/1 -19/6 0/1 -3/1 1/0 -23/8 -1/2 -20/7 -3/5 -1/2 -17/6 -1/4 -31/11 -1/2 -14/5 -1/2 0/1 -39/14 -1/2 -64/23 -2/5 -1/3 -25/9 -1/4 -36/13 -1/1 0/1 -11/4 -1/4 -41/15 -1/6 -71/26 -1/6 -30/11 -1/8 0/1 -19/7 0/1 -8/3 0/1 1/1 -37/14 1/0 -29/11 1/0 -50/19 -1/2 0/1 -21/8 1/0 -34/13 0/1 1/0 -13/5 1/0 -44/17 -3/1 1/0 -75/29 1/0 -31/12 -3/2 -18/7 0/1 1/0 -59/23 1/0 -41/16 1/0 -23/9 1/0 -28/11 -3/2 -1/1 -5/2 -1/2 -27/11 -1/2 -22/9 -1/2 0/1 -61/25 -3/4 -39/16 -1/2 -17/7 -3/8 -46/19 -2/7 -1/4 -75/31 -1/4 -29/12 -1/4 -70/29 -1/4 0/1 -41/17 -1/4 -12/5 -1/5 0/1 -19/8 0/1 -26/11 0/1 1/8 -33/14 1/4 -73/31 1/4 -113/48 1/4 -40/17 0/1 1/3 -7/3 1/2 -37/16 1/0 -30/13 0/1 1/0 -23/10 1/0 -39/17 1/0 -55/24 1/0 -16/7 -1/1 0/1 -25/11 1/0 -34/15 0/1 1/0 -77/34 1/0 -43/19 1/0 -9/4 1/0 -20/9 -1/1 -1/2 -31/14 -1/2 -73/33 -1/2 -115/52 -1/2 -42/19 -1/2 0/1 -11/5 -1/2 -24/11 -1/1 -1/2 -37/17 -1/2 -13/6 -1/2 -28/13 -1/2 -1/3 -15/7 -1/4 -17/8 -1/8 -19/9 0/1 -2/1 0/1 1/0 -19/10 0/1 -17/9 1/8 -15/8 1/4 -13/7 1/2 -37/20 1/2 -61/33 1/0 -24/13 1/2 1/1 -11/6 1/2 -42/23 0/1 1/2 -73/40 1/2 -31/17 1/2 -20/11 1/2 1/1 -29/16 3/4 -38/21 1/1 -9/5 1/0 -25/14 1/0 -16/9 0/1 1/1 -39/22 1/0 -23/13 1/0 -76/43 -1/1 1/1 -53/30 1/0 -30/17 0/1 1/0 -37/21 1/0 -7/4 -1/2 -40/23 -1/3 0/1 -33/19 -1/4 -59/34 -1/6 -26/15 -1/8 0/1 -19/11 0/1 -12/7 0/1 1/5 -53/31 1/4 -41/24 1/4 -152/89 1/5 1/3 -111/65 1/4 -70/41 0/1 1/4 -29/17 1/4 -75/44 1/4 -46/27 1/4 2/7 -17/10 3/8 -56/33 5/11 1/2 -95/56 1/2 -39/23 1/2 -100/59 1/2 1/1 -61/36 3/4 -22/13 0/1 1/2 -49/29 1/2 -76/45 1/3 1/1 -27/16 1/2 -32/19 1/3 1/2 -5/3 1/2 -38/23 1/1 -33/20 7/6 -28/17 1/1 3/2 -51/31 3/2 -23/14 1/0 -64/39 1/1 2/1 -41/25 1/0 -18/11 0/1 1/0 -13/8 1/0 -47/29 1/0 -81/50 1/0 -115/71 1/0 -149/92 1/0 -34/21 0/1 1/0 -55/34 1/0 -76/47 -1/1 1/1 -21/13 1/0 -50/31 0/1 1/2 -79/49 3/4 -29/18 1/0 -8/5 -1/1 0/1 -19/12 0/1 -30/19 0/1 1/8 -71/45 1/6 -112/71 0/1 1/7 -265/168 1/8 -418/265 1/7 -153/97 1/6 -41/26 1/6 -52/33 1/5 1/4 -11/7 1/4 -36/23 0/1 1/1 -25/16 1/4 -114/73 1/3 -89/57 5/14 -64/41 1/3 2/5 -39/25 1/2 -14/9 0/1 1/2 -45/29 1/2 -76/49 1/3 1/1 -31/20 1/2 -48/31 1/3 1/2 -17/11 1/4 -37/24 1/2 -57/37 1/2 -20/13 1/2 3/5 -3/2 1/0 -22/15 -1/2 0/1 -19/13 0/1 -16/11 0/1 1/3 -13/9 1/2 -36/25 -1/1 0/1 -95/66 0/1 -59/41 1/8 -23/16 1/2 -56/39 1/2 1/1 -33/23 1/2 -76/53 1/3 1/1 -43/30 1/2 -10/7 0/1 1/2 -57/40 1/2 -47/33 1/2 -37/26 1/2 -64/45 3/5 2/3 -91/64 1/2 -27/19 1/2 -71/50 1/2 -115/81 1/2 -44/31 1/2 3/5 -61/43 5/8 -17/12 3/4 -75/53 3/4 -133/94 3/4 -58/41 3/4 10/13 -41/29 3/4 -65/46 5/6 -24/17 5/6 1/1 -31/22 13/14 -38/27 1/1 -7/5 3/2 -39/28 1/0 -71/51 1/0 -32/23 3/1 1/0 -57/41 1/0 -25/18 1/0 -18/13 0/1 1/0 -47/34 1/0 -76/55 -1/1 1/1 -29/21 1/0 -40/29 -1/1 0/1 -11/8 1/2 -48/35 3/1 1/0 -85/62 1/0 -37/27 1/0 -63/46 1/0 -152/111 -1/1 1/1 -89/65 1/0 -26/19 0/1 1/0 -67/49 1/2 -41/30 3/2 -56/41 -1/1 1/0 -15/11 1/0 -64/47 0/1 1/1 -49/36 1/0 -34/25 0/1 1/0 -19/14 0/1 -4/3 0/1 1/1 -21/16 9/10 -38/29 1/1 -17/13 9/8 -30/23 5/4 4/3 -43/33 3/2 -13/10 3/2 -48/37 1/1 3/2 -83/64 3/2 -35/27 3/2 -57/44 2/1 -22/17 2/1 1/0 -31/24 3/2 -40/31 1/1 2/1 -9/7 1/0 -41/32 3/4 -114/89 1/1 -73/57 9/8 -32/25 1/1 3/2 -55/43 7/4 -23/18 1/0 -37/29 1/0 -14/11 2/1 1/0 -19/15 1/0 -24/19 -1/1 1/0 -53/42 -1/2 -29/23 1/0 -5/4 1/0 -26/21 0/1 1/4 -21/17 1/2 -58/47 4/9 1/2 -95/77 1/2 -37/30 1/2 -16/13 2/3 1/1 -27/22 9/10 -38/31 1/1 -11/9 5/4 -39/32 3/2 -67/55 3/2 -95/78 3/2 -28/23 3/2 5/3 -73/60 3/2 -45/37 3/2 -17/14 7/4 -57/47 2/1 -40/33 2/1 11/5 -23/19 5/2 -52/43 3/1 1/0 -29/24 1/0 -6/5 2/1 1/0 -19/16 1/0 -32/27 -5/1 1/0 -13/11 1/0 -33/28 1/0 -20/17 -1/1 1/0 -7/6 1/0 -22/19 0/1 1/2 -15/13 3/4 -38/33 1/1 -23/20 7/6 -8/7 1/1 2/1 -9/8 1/0 -28/25 9/1 1/0 -19/17 1/0 -10/9 -2/1 1/0 -1/1 1/0 0/1 -1/1 1/1 1/1 1/0 8/7 -2/1 -1/1 15/13 -3/4 7/6 1/0 20/17 1/1 1/0 33/28 1/0 13/11 1/0 19/16 1/0 6/5 -2/1 1/0 29/24 1/0 23/19 -5/2 17/14 -7/4 28/23 -5/3 -3/2 11/9 -5/4 16/13 -1/1 -2/3 21/17 -1/2 5/4 1/0 29/23 1/0 24/19 1/1 1/0 19/15 1/0 14/11 -2/1 1/0 37/29 1/0 23/18 1/0 32/25 -3/2 -1/1 41/32 -3/4 9/7 1/0 31/24 -3/2 53/41 -1/2 22/17 -2/1 1/0 35/27 -3/2 48/37 -3/2 -1/1 13/10 -3/2 43/33 -3/2 30/23 -4/3 -5/4 17/13 -9/8 4/3 -1/1 0/1 19/14 0/1 34/25 0/1 1/0 49/36 1/0 15/11 1/0 41/30 -3/2 26/19 0/1 1/0 63/46 1/0 37/27 1/0 11/8 -1/2 40/29 0/1 1/1 69/50 1/2 29/21 1/0 18/13 0/1 1/0 7/5 -3/2 24/17 -1/1 -5/6 41/29 -3/4 17/12 -3/4 44/31 -3/5 -1/2 27/19 -1/2 64/45 -2/3 -3/5 37/26 -1/2 10/7 -1/2 0/1 33/23 -1/2 56/39 -1/1 -1/2 23/16 -1/2 36/25 0/1 1/1 13/9 -1/2 16/11 -1/3 0/1 19/13 0/1 3/2 1/0 23/15 -1/2 20/13 -3/5 -1/2 17/11 -1/4 31/20 -1/2 14/9 -1/2 0/1 39/25 -1/2 64/41 -2/5 -1/3 25/16 -1/4 36/23 -1/1 0/1 11/7 -1/4 41/26 -1/6 71/45 -1/6 30/19 -1/8 0/1 19/12 0/1 8/5 0/1 1/1 37/23 1/0 29/18 1/0 50/31 -1/2 0/1 21/13 1/0 34/21 0/1 1/0 13/8 1/0 44/27 -3/1 1/0 75/46 1/0 31/19 -3/2 18/11 0/1 1/0 59/36 1/0 41/25 1/0 23/14 1/0 28/17 -3/2 -1/1 5/3 -1/2 27/16 -1/2 22/13 -1/2 0/1 61/36 -3/4 39/23 -1/2 17/10 -3/8 46/27 -2/7 -1/4 75/44 -1/4 29/17 -1/4 70/41 -1/4 0/1 41/24 -1/4 12/7 -1/5 0/1 19/11 0/1 26/15 0/1 1/8 33/19 1/4 73/42 1/4 113/65 1/4 40/23 0/1 1/3 7/4 1/2 37/21 1/0 30/17 0/1 1/0 23/13 1/0 39/22 1/0 55/31 1/0 16/9 -1/1 0/1 25/14 1/0 34/19 0/1 1/0 77/43 1/0 43/24 1/0 9/5 1/0 20/11 -1/1 -1/2 31/17 -1/2 73/40 -1/2 115/63 -1/2 42/23 -1/2 0/1 11/6 -1/2 24/13 -1/1 -1/2 37/20 -1/2 13/7 -1/2 28/15 -1/2 -1/3 15/8 -1/4 17/9 -1/8 19/10 0/1 2/1 0/1 1/0 19/9 0/1 17/8 1/8 15/7 1/4 13/6 1/2 37/17 1/2 61/28 1/0 24/11 1/2 1/1 11/5 1/2 42/19 0/1 1/2 73/33 1/2 31/14 1/2 20/9 1/2 1/1 29/13 3/4 38/17 1/1 9/4 1/0 25/11 1/0 16/7 0/1 1/1 39/17 1/0 23/10 1/0 76/33 -1/1 1/1 53/23 1/0 30/13 0/1 1/0 37/16 1/0 7/3 -1/2 40/17 -1/3 0/1 33/14 -1/4 59/25 -1/6 26/11 -1/8 0/1 19/8 0/1 12/5 0/1 1/5 53/22 1/4 41/17 1/4 152/63 1/5 1/3 111/46 1/4 70/29 0/1 1/4 29/12 1/4 75/31 1/4 46/19 1/4 2/7 17/7 3/8 56/23 5/11 1/2 95/39 1/2 39/16 1/2 100/41 1/2 1/1 61/25 3/4 22/9 0/1 1/2 49/20 1/2 76/31 1/3 1/1 27/11 1/2 32/13 1/3 1/2 5/2 1/2 38/15 1/1 33/13 7/6 28/11 1/1 3/2 51/20 3/2 23/9 1/0 64/25 1/1 2/1 41/16 1/0 18/7 0/1 1/0 13/5 1/0 47/18 1/0 81/31 1/0 115/44 1/0 149/57 1/0 34/13 0/1 1/0 55/21 1/0 76/29 -1/1 1/1 21/8 1/0 50/19 0/1 1/2 79/30 3/4 29/11 1/0 8/3 -1/1 0/1 19/7 0/1 30/11 0/1 1/8 71/26 1/6 112/41 0/1 1/7 265/97 1/8 418/153 1/7 153/56 1/6 41/15 1/6 52/19 1/5 1/4 11/4 1/4 36/13 0/1 1/1 25/9 1/4 114/41 1/3 89/32 5/14 64/23 1/3 2/5 39/14 1/2 14/5 0/1 1/2 45/16 1/2 76/27 1/3 1/1 31/11 1/2 48/17 1/3 1/2 17/6 1/4 37/13 1/2 57/20 1/2 20/7 1/2 3/5 3/1 1/0 22/7 -1/2 0/1 19/6 0/1 16/5 0/1 1/3 13/4 1/2 36/11 -1/1 0/1 95/29 0/1 59/18 1/8 23/7 1/2 56/17 1/2 1/1 33/10 1/2 76/23 1/3 1/1 43/13 1/2 10/3 0/1 1/2 57/17 1/2 47/14 1/2 37/11 1/2 64/19 3/5 2/3 91/27 1/2 27/8 1/2 71/21 1/2 115/34 1/2 44/13 1/2 3/5 61/18 5/8 17/5 3/4 75/22 3/4 133/39 3/4 58/17 3/4 10/13 41/12 3/4 65/19 5/6 24/7 5/6 1/1 31/9 13/14 38/11 1/1 7/2 3/2 39/11 1/0 71/20 1/0 32/9 3/1 1/0 57/16 1/0 25/7 1/0 18/5 0/1 1/0 47/13 1/0 76/21 -1/1 1/1 29/8 1/0 40/11 -1/1 0/1 11/3 1/2 48/13 3/1 1/0 85/23 1/0 37/10 1/0 63/17 1/0 152/41 -1/1 1/1 89/24 1/0 26/7 0/1 1/0 67/18 1/2 41/11 3/2 56/15 -1/1 1/0 15/4 1/0 64/17 0/1 1/1 49/13 1/0 34/9 0/1 1/0 19/5 0/1 4/1 0/1 1/1 21/5 9/10 38/9 1/1 17/4 9/8 30/7 5/4 4/3 43/10 3/2 13/3 3/2 48/11 1/1 3/2 83/19 3/2 35/8 3/2 57/13 2/1 22/5 2/1 1/0 31/7 3/2 40/9 1/1 2/1 9/2 1/0 41/9 3/4 114/25 1/1 73/16 9/8 32/7 1/1 3/2 55/12 7/4 23/5 1/0 37/8 1/0 14/3 2/1 1/0 19/4 1/0 24/5 -1/1 1/0 53/11 -1/2 29/6 1/0 5/1 1/0 26/5 0/1 1/4 21/4 1/2 58/11 4/9 1/2 95/18 1/2 37/7 1/2 16/3 2/3 1/1 27/5 9/10 38/7 1/1 11/2 5/4 39/7 3/2 67/12 3/2 95/17 3/2 28/5 3/2 5/3 73/13 3/2 45/8 3/2 17/3 7/4 57/10 2/1 40/7 2/1 11/5 23/4 5/2 52/9 3/1 1/0 29/5 1/0 6/1 2/1 1/0 19/3 1/0 32/5 -5/1 1/0 13/2 1/0 33/5 1/0 20/3 -1/1 1/0 7/1 1/0 22/3 0/1 1/2 15/2 3/4 38/5 1/1 23/3 7/6 8/1 1/1 2/1 9/1 1/0 28/3 9/1 1/0 19/2 1/0 10/1 -2/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(37,304,-14,-115) (-8/1,1/0) -> (-8/3,-37/14) Hyperbolic Matrix(39,304,-34,-265) (-8/1,-15/2) -> (-23/20,-8/7) Hyperbolic Matrix(115,836,-26,-189) (-15/2,-7/1) -> (-31/7,-53/12) Hyperbolic Matrix(113,760,62,417) (-7/1,-20/3) -> (20/11,31/17) Hyperbolic Matrix(379,2508,264,1747) (-20/3,-33/5) -> (33/23,56/39) Hyperbolic Matrix(151,988,116,759) (-33/5,-13/2) -> (13/10,43/33) Hyperbolic Matrix(189,1216,-136,-875) (-13/2,-19/3) -> (-57/41,-25/18) Hyperbolic Matrix(37,228,6,37) (-19/3,-6/1) -> (6/1,19/3) Hyperbolic Matrix(379,2204,222,1291) (-6/1,-29/5) -> (29/17,70/41) Hyperbolic Matrix(381,2204,-302,-1747) (-29/5,-23/4) -> (-53/42,-29/23) Hyperbolic Matrix(305,1748,-212,-1215) (-23/4,-17/3) -> (-59/41,-23/16) Hyperbolic Matrix(229,1292,-148,-835) (-17/3,-28/5) -> (-48/31,-17/11) Hyperbolic Matrix(151,836,-110,-609) (-28/5,-11/2) -> (-11/8,-48/35) Hyperbolic Matrix(113,608,-92,-495) (-11/2,-16/3) -> (-16/13,-27/22) Hyperbolic Matrix(229,1216,-100,-531) (-16/3,-21/4) -> (-55/24,-16/7) Hyperbolic Matrix(191,988,-110,-569) (-21/4,-5/1) -> (-33/19,-59/34) Hyperbolic Matrix(533,2584,204,989) (-5/1,-29/6) -> (47/18,81/31) Hyperbolic Matrix(457,2204,-378,-1823) (-29/6,-24/5) -> (-52/43,-29/24) Hyperbolic Matrix(191,912,40,191) (-24/5,-19/4) -> (19/4,24/5) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(229,1064,82,381) (-14/3,-37/8) -> (39/14,14/5) Hyperbolic Matrix(379,1748,214,987) (-37/8,-23/5) -> (23/13,39/22) Hyperbolic Matrix(647,2964,-456,-2089) (-23/5,-32/7) -> (-44/31,-61/43) Hyperbolic Matrix(799,3648,-624,-2849) (-32/7,-41/9) -> (-73/57,-32/25) Hyperbolic Matrix(685,3116,184,837) (-41/9,-9/2) -> (67/18,41/11) Hyperbolic Matrix(341,1520,-94,-419) (-9/2,-31/7) -> (-69/19,-29/8) Hyperbolic Matrix(569,2508,336,1481) (-53/12,-22/5) -> (22/13,61/36) Hyperbolic Matrix(191,836,-130,-569) (-22/5,-35/8) -> (-3/2,-22/15) Hyperbolic Matrix(1027,4484,-844,-3685) (-35/8,-48/11) -> (-28/23,-73/60) Hyperbolic Matrix(227,988,122,531) (-48/11,-13/3) -> (13/7,28/15) Hyperbolic Matrix(229,988,194,837) (-13/3,-43/10) -> (33/28,13/11) Hyperbolic Matrix(797,3420,292,1253) (-43/10,-30/7) -> (30/11,71/26) Hyperbolic Matrix(303,1292,178,759) (-30/7,-17/4) -> (17/10,46/27) Hyperbolic Matrix(37,152,-28,-115) (-17/4,-4/1) -> (-4/3,-21/16) Hyperbolic Matrix(39,152,10,39) (-4/1,-19/5) -> (19/5,4/1) Hyperbolic Matrix(341,1292,90,341) (-19/5,-34/9) -> (34/9,19/5) Hyperbolic Matrix(645,2432,292,1101) (-34/9,-49/13) -> (11/5,42/19) Hyperbolic Matrix(1291,4864,-908,-3421) (-49/13,-15/4) -> (-91/64,-27/19) Hyperbolic Matrix(265,988,-92,-343) (-15/4,-41/11) -> (-3/1,-23/8) Hyperbolic Matrix(1103,4104,-684,-2545) (-41/11,-26/7) -> (-50/31,-79/49) Hyperbolic Matrix(1065,3952,-778,-2887) (-26/7,-63/17) -> (-89/65,-26/19) Hyperbolic Matrix(759,2812,410,1519) (-63/17,-37/10) -> (37/20,13/7) Hyperbolic Matrix(227,836,-186,-685) (-37/10,-11/3) -> (-11/9,-39/32) Hyperbolic Matrix(229,836,146,533) (-11/3,-40/11) -> (36/23,11/7) Hyperbolic Matrix(837,3040,356,1293) (-40/11,-69/19) -> (7/3,40/17) Hyperbolic Matrix(379,1368,-274,-989) (-29/8,-18/5) -> (-18/13,-47/34) Hyperbolic Matrix(191,684,-74,-265) (-18/5,-7/2) -> (-31/12,-18/7) Hyperbolic Matrix(265,912,-188,-647) (-7/2,-24/7) -> (-24/17,-31/22) Hyperbolic Matrix(911,3116,-578,-1977) (-24/7,-41/12) -> (-41/26,-52/33) Hyperbolic Matrix(913,3116,-356,-1215) (-41/12,-17/5) -> (-59/23,-41/16) Hyperbolic Matrix(875,2964,-684,-2317) (-17/5,-44/13) -> (-32/25,-55/43) Hyperbolic Matrix(607,2052,-360,-1217) (-44/13,-27/8) -> (-27/16,-32/19) Hyperbolic Matrix(1443,4864,-1060,-3573) (-27/8,-64/19) -> (-64/47,-49/36) Hyperbolic Matrix(1445,4864,926,3117) (-64/19,-37/11) -> (39/25,64/41) Hyperbolic Matrix(113,380,-102,-343) (-37/11,-10/3) -> (-10/9,-1/1) Hyperbolic Matrix(229,760,-160,-531) (-10/3,-33/10) -> (-43/30,-10/7) Hyperbolic Matrix(761,2508,646,2129) (-33/10,-56/17) -> (20/17,33/28) Hyperbolic Matrix(531,1748,346,1139) (-56/17,-23/7) -> (23/15,20/13) Hyperbolic Matrix(533,1748,-440,-1443) (-23/7,-36/11) -> (-40/33,-23/19) Hyperbolic Matrix(419,1368,268,875) (-36/11,-13/4) -> (25/16,36/23) Hyperbolic Matrix(189,608,106,341) (-13/4,-16/5) -> (16/9,25/14) Hyperbolic Matrix(191,608,60,191) (-16/5,-19/6) -> (19/6,16/5) Hyperbolic Matrix(267,836,-206,-645) (-19/6,-3/1) -> (-35/27,-57/44) Hyperbolic Matrix(609,1748,424,1217) (-23/8,-20/7) -> (56/39,23/16) Hyperbolic Matrix(455,1292,-268,-761) (-20/7,-17/6) -> (-17/10,-56/33) Hyperbolic Matrix(457,1292,-376,-1063) (-17/6,-31/11) -> (-45/37,-17/14) Hyperbolic Matrix(379,1064,-244,-685) (-31/11,-14/5) -> (-14/9,-45/29) Hyperbolic Matrix(381,1064,82,229) (-14/5,-39/14) -> (37/8,14/3) Hyperbolic Matrix(1747,4864,1228,3419) (-39/14,-64/23) -> (64/45,37/26) Hyperbolic Matrix(2623,7296,-1680,-4673) (-64/23,-25/9) -> (-89/57,-64/41) Hyperbolic Matrix(493,1368,342,949) (-25/9,-36/13) -> (36/25,13/9) Hyperbolic Matrix(303,836,220,607) (-36/13,-11/4) -> (11/8,40/29) Hyperbolic Matrix(1139,3116,-806,-2205) (-11/4,-41/15) -> (-41/29,-65/46) Hyperbolic Matrix(2393,6536,-1016,-2775) (-41/15,-71/26) -> (-33/14,-73/31) Hyperbolic Matrix(1253,3420,292,797) (-71/26,-30/11) -> (30/7,43/10) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(113,304,42,113) (-19/7,-8/3) -> (8/3,19/7) Hyperbolic Matrix(1065,2812,-748,-1975) (-37/14,-29/11) -> (-47/33,-37/26) Hyperbolic Matrix(1559,4104,-1140,-3001) (-29/11,-50/19) -> (-26/19,-67/49) Hyperbolic Matrix(1329,3496,-766,-2015) (-50/19,-21/8) -> (-59/34,-26/15) Hyperbolic Matrix(987,2584,-610,-1597) (-21/8,-34/13) -> (-34/21,-55/34) Hyperbolic Matrix(495,1292,-218,-569) (-34/13,-13/5) -> (-25/11,-34/15) Hyperbolic Matrix(381,988,-322,-835) (-13/5,-44/17) -> (-32/27,-13/11) Hyperbolic Matrix(3231,8360,-2276,-5889) (-44/17,-75/29) -> (-115/81,-44/31) Hyperbolic Matrix(647,1672,368,951) (-75/29,-31/12) -> (7/4,37/21) Hyperbolic Matrix(1481,3800,-1200,-3079) (-18/7,-59/23) -> (-21/17,-58/47) Hyperbolic Matrix(1217,3116,-712,-1823) (-41/16,-23/9) -> (-53/31,-41/24) Hyperbolic Matrix(417,1064,-194,-495) (-23/9,-28/11) -> (-28/13,-15/7) Hyperbolic Matrix(419,1064,-254,-645) (-28/11,-5/2) -> (-33/20,-28/17) Hyperbolic Matrix(835,2052,-588,-1445) (-5/2,-27/11) -> (-27/19,-71/50) Hyperbolic Matrix(683,1672,-404,-989) (-27/11,-22/9) -> (-22/13,-49/29) Hyperbolic Matrix(1027,2508,794,1939) (-22/9,-61/25) -> (53/41,22/17) Hyperbolic Matrix(1901,4636,-1028,-2507) (-61/25,-39/16) -> (-37/20,-61/33) Hyperbolic Matrix(531,1292,-344,-837) (-39/16,-17/7) -> (-17/11,-37/24) Hyperbolic Matrix(533,1292,408,989) (-17/7,-46/19) -> (30/23,17/13) Hyperbolic Matrix(1633,3952,926,2241) (-46/19,-75/31) -> (37/21,30/17) Hyperbolic Matrix(3079,7448,-2246,-5433) (-75/31,-29/12) -> (-85/62,-37/27) Hyperbolic Matrix(913,2204,756,1825) (-29/12,-70/29) -> (6/5,29/24) Hyperbolic Matrix(4409,10640,-2582,-6231) (-70/29,-41/17) -> (-111/65,-70/41) Hyperbolic Matrix(1293,3116,-788,-1899) (-41/17,-12/5) -> (-64/39,-41/25) Hyperbolic Matrix(191,456,80,191) (-12/5,-19/8) -> (19/8,12/5) Hyperbolic Matrix(417,988,176,417) (-19/8,-26/11) -> (26/11,19/8) Hyperbolic Matrix(419,988,-338,-797) (-26/11,-33/14) -> (-5/4,-26/21) Hyperbolic Matrix(10717,25232,4100,9653) (-73/31,-113/48) -> (115/44,149/57) Hyperbolic Matrix(9881,23256,-6264,-14743) (-113/48,-40/17) -> (-112/71,-265/168) Hyperbolic Matrix(647,1520,146,343) (-40/17,-7/3) -> (31/7,40/9) Hyperbolic Matrix(721,1672,442,1025) (-7/3,-37/16) -> (75/46,31/19) Hyperbolic Matrix(1711,3952,1004,2319) (-37/16,-30/13) -> (46/27,75/44) Hyperbolic Matrix(989,2280,-560,-1291) (-30/13,-23/10) -> (-53/30,-30/17) Hyperbolic Matrix(761,1748,596,1369) (-23/10,-39/17) -> (37/29,23/18) Hyperbolic Matrix(2089,4788,-1476,-3383) (-39/17,-55/24) -> (-17/12,-75/53) Hyperbolic Matrix(267,608,184,419) (-16/7,-25/11) -> (13/9,16/11) Hyperbolic Matrix(3153,7144,-1426,-3231) (-34/15,-77/34) -> (-115/52,-42/19) Hyperbolic Matrix(4599,10412,1360,3079) (-77/34,-43/19) -> (71/21,115/34) Hyperbolic Matrix(571,1292,118,267) (-43/19,-9/4) -> (29/6,5/1) Hyperbolic Matrix(341,760,-188,-419) (-9/4,-20/9) -> (-20/11,-29/16) Hyperbolic Matrix(343,760,292,647) (-20/9,-31/14) -> (7/6,20/17) Hyperbolic Matrix(2507,5548,446,987) (-31/14,-73/33) -> (73/13,45/8) Hyperbolic Matrix(7181,15884,2628,5813) (-73/33,-115/52) -> (153/56,41/15) Hyperbolic Matrix(1101,2432,292,645) (-42/19,-11/5) -> (49/13,34/9) Hyperbolic Matrix(381,836,-242,-531) (-11/5,-24/11) -> (-52/33,-11/7) Hyperbolic Matrix(2129,4636,-1256,-2735) (-24/11,-37/17) -> (-39/23,-100/59) Hyperbolic Matrix(1293,2812,944,2053) (-37/17,-13/6) -> (63/46,37/27) Hyperbolic Matrix(457,988,352,761) (-13/6,-28/13) -> (48/37,13/10) Hyperbolic Matrix(569,1216,124,265) (-15/7,-17/8) -> (55/12,23/5) Hyperbolic Matrix(1291,2736,394,835) (-17/8,-19/9) -> (95/29,59/18) Hyperbolic Matrix(37,76,18,37) (-19/9,-2/1) -> (2/1,19/9) Hyperbolic Matrix(39,76,20,39) (-2/1,-19/10) -> (19/10,2/1) Hyperbolic Matrix(683,1292,120,227) (-19/10,-17/9) -> (17/3,57/10) Hyperbolic Matrix(685,1292,202,381) (-17/9,-15/8) -> (61/18,17/5) Hyperbolic Matrix(569,1064,-346,-647) (-15/8,-13/7) -> (-51/31,-23/14) Hyperbolic Matrix(1519,2812,410,759) (-13/7,-37/20) -> (37/10,63/17) Hyperbolic Matrix(1481,2736,308,569) (-61/33,-24/13) -> (24/5,53/11) Hyperbolic Matrix(989,1824,-700,-1291) (-24/13,-11/6) -> (-65/46,-24/17) Hyperbolic Matrix(1331,2432,978,1787) (-11/6,-42/23) -> (34/25,49/36) Hyperbolic Matrix(4787,8740,-2956,-5397) (-42/23,-73/40) -> (-149/92,-34/21) Hyperbolic Matrix(3915,7144,896,1635) (-73/40,-31/17) -> (83/19,35/8) Hyperbolic Matrix(417,760,62,113) (-31/17,-20/11) -> (20/3,7/1) Hyperbolic Matrix(797,1444,356,645) (-29/16,-38/21) -> (38/17,9/4) Hyperbolic Matrix(799,1444,358,647) (-38/21,-9/5) -> (29/13,38/17) Hyperbolic Matrix(723,1292,-446,-797) (-9/5,-25/14) -> (-13/8,-47/29) Hyperbolic Matrix(341,608,106,189) (-25/14,-16/9) -> (16/5,13/4) Hyperbolic Matrix(685,1216,-556,-987) (-16/9,-39/22) -> (-37/30,-16/13) Hyperbolic Matrix(987,1748,214,379) (-39/22,-23/13) -> (23/5,37/8) Hyperbolic Matrix(3267,5776,1418,2507) (-23/13,-76/43) -> (76/33,53/23) Hyperbolic Matrix(3269,5776,1420,2509) (-76/43,-53/30) -> (23/10,76/33) Hyperbolic Matrix(2241,3952,926,1633) (-30/17,-37/21) -> (75/31,46/19) Hyperbolic Matrix(303,532,86,151) (-37/21,-7/4) -> (7/2,39/11) Hyperbolic Matrix(1747,3040,1266,2203) (-7/4,-40/23) -> (40/29,69/50) Hyperbolic Matrix(3761,6536,-2384,-4143) (-40/23,-33/19) -> (-71/45,-112/71) Hyperbolic Matrix(571,988,330,571) (-26/15,-19/11) -> (19/11,26/15) Hyperbolic Matrix(265,456,154,265) (-19/11,-12/7) -> (12/7,19/11) Hyperbolic Matrix(2089,3572,-1534,-2623) (-12/7,-53/31) -> (-15/11,-64/47) Hyperbolic Matrix(13527,23104,5606,9575) (-41/24,-152/89) -> (152/63,111/46) Hyperbolic Matrix(13529,23104,5608,9577) (-152/89,-111/65) -> (41/17,152/63) Hyperbolic Matrix(1291,2204,222,379) (-70/41,-29/17) -> (29/5,6/1) Hyperbolic Matrix(3611,6156,-2964,-5053) (-29/17,-75/44) -> (-39/32,-67/55) Hyperbolic Matrix(2319,3952,1004,1711) (-75/44,-46/27) -> (30/13,37/16) Hyperbolic Matrix(759,1292,178,303) (-46/27,-17/10) -> (17/4,30/7) Hyperbolic Matrix(3001,5092,1052,1785) (-56/33,-95/56) -> (57/20,20/7) Hyperbolic Matrix(7259,12312,-5130,-8701) (-95/56,-39/23) -> (-75/53,-133/94) Hyperbolic Matrix(3229,5472,560,949) (-100/59,-61/36) -> (23/4,52/9) Hyperbolic Matrix(987,1672,134,227) (-61/36,-22/13) -> (22/3,15/2) Hyperbolic Matrix(3419,5776,1394,2355) (-49/29,-76/45) -> (76/31,27/11) Hyperbolic Matrix(3421,5776,1396,2357) (-76/45,-27/16) -> (49/20,76/31) Hyperbolic Matrix(1445,2432,-1038,-1747) (-32/19,-5/3) -> (-71/51,-32/23) Hyperbolic Matrix(873,1444,344,569) (-5/3,-38/23) -> (38/15,33/13) Hyperbolic Matrix(875,1444,346,571) (-38/23,-33/20) -> (5/2,38/15) Hyperbolic Matrix(1709,2812,392,645) (-28/17,-51/31) -> (13/3,48/11) Hyperbolic Matrix(4445,7296,-3126,-5131) (-23/14,-64/39) -> (-64/45,-91/64) Hyperbolic Matrix(1901,3116,-1344,-2203) (-41/25,-18/11) -> (-58/41,-41/29) Hyperbolic Matrix(419,684,-302,-493) (-18/11,-13/8) -> (-25/18,-18/13) Hyperbolic Matrix(1595,2584,1266,2051) (-47/29,-81/50) -> (5/4,29/23) Hyperbolic Matrix(6991,11324,1970,3191) (-81/50,-115/71) -> (39/11,71/20) Hyperbolic Matrix(15579,25232,8962,14515) (-115/71,-149/92) -> (73/42,113/65) Hyperbolic Matrix(3571,5776,1362,2203) (-55/34,-76/47) -> (76/29,21/8) Hyperbolic Matrix(3573,5776,1364,2205) (-76/47,-21/13) -> (55/21,76/29) Hyperbolic Matrix(989,1596,-800,-1291) (-21/13,-50/31) -> (-26/21,-21/17) Hyperbolic Matrix(1179,1900,260,419) (-79/49,-29/18) -> (9/2,41/9) Hyperbolic Matrix(189,304,-166,-267) (-29/18,-8/5) -> (-8/7,-9/8) Hyperbolic Matrix(191,304,120,191) (-8/5,-19/12) -> (19/12,8/5) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(2167,3420,1662,2623) (-30/19,-71/45) -> (43/33,30/23) Hyperbolic Matrix(110769,174724,40544,63953) (-265/168,-418/265) -> (418/153,153/56) Hyperbolic Matrix(110771,174724,40546,63955) (-418/265,-153/97) -> (265/97,418/153) Hyperbolic Matrix(10071,15884,5518,8703) (-153/97,-41/26) -> (73/40,115/63) Hyperbolic Matrix(533,836,146,229) (-11/7,-36/23) -> (40/11,11/3) Hyperbolic Matrix(875,1368,268,419) (-36/23,-25/16) -> (13/4,36/11) Hyperbolic Matrix(8321,12996,2992,4673) (-25/16,-114/73) -> (114/41,89/32) Hyperbolic Matrix(8323,12996,2994,4675) (-114/73,-89/57) -> (25/9,114/41) Hyperbolic Matrix(3117,4864,926,1445) (-64/41,-39/25) -> (37/11,64/19) Hyperbolic Matrix(683,1064,536,835) (-39/25,-14/9) -> (14/11,37/29) Hyperbolic Matrix(3723,5776,1322,2051) (-45/29,-76/49) -> (76/27,31/11) Hyperbolic Matrix(3725,5776,1324,2053) (-76/49,-31/20) -> (45/16,76/27) Hyperbolic Matrix(3533,5472,-2724,-4219) (-31/20,-48/31) -> (-48/37,-83/64) Hyperbolic Matrix(3649,5624,-2958,-4559) (-37/24,-57/37) -> (-95/77,-37/30) Hyperbolic Matrix(3307,5092,1358,2091) (-57/37,-20/13) -> (56/23,95/39) Hyperbolic Matrix(645,988,-472,-723) (-20/13,-3/2) -> (-41/30,-56/41) Hyperbolic Matrix(1141,1672,260,381) (-22/15,-19/13) -> (57/13,22/5) Hyperbolic Matrix(417,608,286,417) (-19/13,-16/11) -> (16/11,19/13) Hyperbolic Matrix(419,608,184,267) (-16/11,-13/9) -> (25/11,16/7) Hyperbolic Matrix(949,1368,342,493) (-13/9,-36/25) -> (36/13,25/9) Hyperbolic Matrix(4065,5852,712,1025) (-36/25,-95/66) -> (57/10,40/7) Hyperbolic Matrix(1901,2736,1004,1445) (-95/66,-59/41) -> (17/9,19/10) Hyperbolic Matrix(1481,2128,396,569) (-23/16,-56/39) -> (56/15,15/4) Hyperbolic Matrix(1747,2508,264,379) (-56/39,-33/23) -> (33/5,20/3) Hyperbolic Matrix(4027,5776,1218,1747) (-33/23,-76/53) -> (76/23,43/13) Hyperbolic Matrix(4029,5776,1220,1749) (-76/53,-43/30) -> (33/10,76/23) Hyperbolic Matrix(533,760,54,77) (-10/7,-57/40) -> (19/2,10/1) Hyperbolic Matrix(5815,8284,-4774,-6801) (-57/40,-47/33) -> (-67/55,-95/78) Hyperbolic Matrix(3419,4864,1228,1747) (-37/26,-64/45) -> (64/23,39/14) Hyperbolic Matrix(7333,10412,4094,5813) (-71/50,-115/81) -> (77/43,43/24) Hyperbolic Matrix(911,1292,428,607) (-61/43,-17/12) -> (17/8,15/7) Hyperbolic Matrix(9347,13224,1772,2507) (-133/94,-58/41) -> (58/11,95/18) Hyperbolic Matrix(1025,1444,296,417) (-31/22,-38/27) -> (38/11,7/2) Hyperbolic Matrix(1027,1444,298,419) (-38/27,-7/5) -> (31/9,38/11) Hyperbolic Matrix(381,532,164,229) (-7/5,-39/28) -> (37/16,7/3) Hyperbolic Matrix(8133,11324,3112,4333) (-39/28,-71/51) -> (81/31,115/44) Hyperbolic Matrix(1749,2432,274,381) (-32/23,-57/41) -> (19/3,32/5) Hyperbolic Matrix(4179,5776,1154,1595) (-47/34,-76/55) -> (76/21,29/8) Hyperbolic Matrix(4181,5776,1156,1597) (-76/55,-29/21) -> (47/13,76/21) Hyperbolic Matrix(1101,1520,-854,-1179) (-29/21,-40/29) -> (-40/31,-9/7) Hyperbolic Matrix(607,836,220,303) (-40/29,-11/8) -> (11/4,36/13) Hyperbolic Matrix(2051,2812,-1830,-2509) (-48/35,-85/62) -> (-9/8,-28/25) Hyperbolic Matrix(2053,2812,944,1293) (-37/27,-63/46) -> (13/6,37/17) Hyperbolic Matrix(16871,23104,4550,6231) (-63/46,-152/111) -> (152/41,89/24) Hyperbolic Matrix(16873,23104,4552,6233) (-152/111,-89/65) -> (63/17,152/41) Hyperbolic Matrix(2279,3116,1778,2431) (-67/49,-41/30) -> (41/32,9/7) Hyperbolic Matrix(1559,2128,474,647) (-56/41,-15/11) -> (23/7,56/17) Hyperbolic Matrix(1787,2432,978,1331) (-49/36,-34/25) -> (42/23,11/6) Hyperbolic Matrix(951,1292,700,951) (-34/25,-19/14) -> (19/14,34/25) Hyperbolic Matrix(113,152,84,113) (-19/14,-4/3) -> (4/3,19/14) Hyperbolic Matrix(1101,1444,260,341) (-21/16,-38/29) -> (38/9,17/4) Hyperbolic Matrix(1103,1444,262,343) (-38/29,-17/13) -> (21/5,38/9) Hyperbolic Matrix(989,1292,408,533) (-17/13,-30/23) -> (46/19,17/7) Hyperbolic Matrix(2623,3420,1662,2167) (-30/23,-43/33) -> (71/45,30/19) Hyperbolic Matrix(759,988,116,151) (-43/33,-13/10) -> (13/2,33/5) Hyperbolic Matrix(2167,2812,850,1103) (-13/10,-48/37) -> (28/11,51/20) Hyperbolic Matrix(5509,7144,2490,3229) (-83/64,-35/27) -> (73/33,31/14) Hyperbolic Matrix(1291,1672,410,531) (-57/44,-22/17) -> (22/7,19/6) Hyperbolic Matrix(647,836,-558,-721) (-22/17,-31/24) -> (-7/6,-22/19) Hyperbolic Matrix(1177,1520,676,873) (-31/24,-40/31) -> (40/23,7/4) Hyperbolic Matrix(1481,1900,562,721) (-9/7,-41/32) -> (79/30,29/11) Hyperbolic Matrix(10145,12996,2224,2849) (-41/32,-114/89) -> (114/25,73/16) Hyperbolic Matrix(10147,12996,2226,2851) (-114/89,-73/57) -> (41/9,114/25) Hyperbolic Matrix(951,1216,506,647) (-55/43,-23/18) -> (15/8,17/9) Hyperbolic Matrix(1369,1748,596,761) (-23/18,-37/29) -> (39/17,23/10) Hyperbolic Matrix(835,1064,536,683) (-37/29,-14/11) -> (14/9,39/25) Hyperbolic Matrix(419,532,330,419) (-14/11,-19/15) -> (19/15,14/11) Hyperbolic Matrix(721,912,570,721) (-19/15,-24/19) -> (24/19,19/15) Hyperbolic Matrix(2167,2736,994,1255) (-24/19,-53/42) -> (61/28,24/11) Hyperbolic Matrix(1025,1292,572,721) (-29/23,-5/4) -> (43/24,9/5) Hyperbolic Matrix(10717,13224,3142,3877) (-58/47,-95/77) -> (133/39,58/17) Hyperbolic Matrix(1177,1444,216,265) (-27/22,-38/31) -> (38/7,11/2) Hyperbolic Matrix(1179,1444,218,267) (-38/31,-11/9) -> (27/5,38/7) Hyperbolic Matrix(2621,3192,280,341) (-95/78,-28/23) -> (28/3,19/2) Hyperbolic Matrix(4561,5548,2500,3041) (-73/60,-45/37) -> (31/17,73/40) Hyperbolic Matrix(1065,1292,502,609) (-17/14,-57/47) -> (19/9,17/8) Hyperbolic Matrix(4827,5852,1474,1787) (-57/47,-40/33) -> (36/11,95/29) Hyperbolic Matrix(4523,5472,1854,2243) (-23/19,-52/43) -> (100/41,61/25) Hyperbolic Matrix(1825,2204,756,913) (-29/24,-6/5) -> (70/29,29/12) Hyperbolic Matrix(191,228,160,191) (-6/5,-19/16) -> (19/16,6/5) Hyperbolic Matrix(2051,2432,576,683) (-19/16,-32/27) -> (32/9,57/16) Hyperbolic Matrix(837,988,194,229) (-13/11,-33/28) -> (43/10,13/3) Hyperbolic Matrix(2129,2508,646,761) (-33/28,-20/17) -> (56/17,33/10) Hyperbolic Matrix(647,760,292,343) (-20/17,-7/6) -> (31/14,20/9) Hyperbolic Matrix(1445,1672,592,685) (-22/19,-15/13) -> (61/25,22/9) Hyperbolic Matrix(1253,1444,164,189) (-15/13,-38/33) -> (38/5,23/3) Hyperbolic Matrix(1255,1444,166,191) (-38/33,-23/20) -> (15/2,38/5) Hyperbolic Matrix(2851,3192,510,571) (-28/25,-19/17) -> (95/17,28/5) Hyperbolic Matrix(683,760,204,227) (-19/17,-10/9) -> (10/3,57/17) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(267,-304,166,-189) (1/1,8/7) -> (8/5,37/23) Hyperbolic Matrix(265,-304,34,-39) (8/7,15/13) -> (23/3,8/1) Hyperbolic Matrix(721,-836,558,-647) (15/13,7/6) -> (31/24,53/41) Hyperbolic Matrix(1027,-1216,288,-341) (13/11,19/16) -> (57/16,25/7) Hyperbolic Matrix(1823,-2204,378,-457) (29/24,23/19) -> (53/11,29/6) Hyperbolic Matrix(1443,-1748,440,-533) (23/19,17/14) -> (59/18,23/7) Hyperbolic Matrix(1063,-1292,376,-457) (17/14,28/23) -> (48/17,17/6) Hyperbolic Matrix(685,-836,186,-227) (28/23,11/9) -> (11/3,48/13) Hyperbolic Matrix(495,-608,92,-113) (11/9,16/13) -> (16/3,27/5) Hyperbolic Matrix(987,-1216,556,-685) (16/13,21/17) -> (55/31,16/9) Hyperbolic Matrix(797,-988,338,-419) (21/17,5/4) -> (33/14,59/25) Hyperbolic Matrix(1747,-2204,302,-381) (29/23,24/19) -> (52/9,29/5) Hyperbolic Matrix(2317,-2964,684,-875) (23/18,32/25) -> (44/13,61/18) Hyperbolic Matrix(2849,-3648,624,-799) (32/25,41/32) -> (73/16,32/7) Hyperbolic Matrix(1179,-1520,854,-1101) (9/7,31/24) -> (69/50,29/21) Hyperbolic Matrix(645,-836,206,-267) (22/17,35/27) -> (3/1,22/7) Hyperbolic Matrix(3457,-4484,616,-799) (35/27,48/37) -> (28/5,73/13) Hyperbolic Matrix(115,-152,28,-37) (17/13,4/3) -> (4/1,21/5) Hyperbolic Matrix(3573,-4864,1060,-1443) (49/36,15/11) -> (91/27,27/8) Hyperbolic Matrix(723,-988,472,-645) (15/11,41/30) -> (3/2,23/15) Hyperbolic Matrix(3001,-4104,1140,-1559) (41/30,26/19) -> (50/19,79/30) Hyperbolic Matrix(2887,-3952,778,-1065) (26/19,63/46) -> (89/24,26/7) Hyperbolic Matrix(609,-836,110,-151) (37/27,11/8) -> (11/2,39/7) Hyperbolic Matrix(989,-1368,274,-379) (29/21,18/13) -> (18/5,47/13) Hyperbolic Matrix(493,-684,302,-419) (18/13,7/5) -> (31/19,18/11) Hyperbolic Matrix(647,-912,188,-265) (7/5,24/17) -> (24/7,31/9) Hyperbolic Matrix(2205,-3116,806,-1139) (24/17,41/29) -> (41/15,52/19) Hyperbolic Matrix(2203,-3116,1344,-1901) (41/29,17/12) -> (59/36,41/25) Hyperbolic Matrix(2089,-2964,456,-647) (17/12,44/31) -> (32/7,55/12) Hyperbolic Matrix(1445,-2052,588,-835) (44/31,27/19) -> (27/11,32/13) Hyperbolic Matrix(3421,-4864,908,-1291) (27/19,64/45) -> (64/17,49/13) Hyperbolic Matrix(267,-380,26,-37) (37/26,10/7) -> (10/1,1/0) Hyperbolic Matrix(531,-760,160,-229) (10/7,33/23) -> (43/13,10/3) Hyperbolic Matrix(1215,-1748,212,-305) (23/16,36/25) -> (40/7,23/4) Hyperbolic Matrix(569,-836,130,-191) (19/13,3/2) -> (35/8,57/13) Hyperbolic Matrix(837,-1292,344,-531) (20/13,17/11) -> (17/7,56/23) Hyperbolic Matrix(835,-1292,148,-229) (17/11,31/20) -> (45/8,17/3) Hyperbolic Matrix(685,-1064,244,-379) (31/20,14/9) -> (14/5,45/16) Hyperbolic Matrix(4673,-7296,1680,-2623) (64/41,25/16) -> (89/32,64/23) Hyperbolic Matrix(1977,-3116,578,-911) (11/7,41/26) -> (41/12,65/19) Hyperbolic Matrix(4143,-6536,2384,-3761) (41/26,71/45) -> (33/19,73/42) Hyperbolic Matrix(1747,-2812,520,-837) (37/23,29/18) -> (47/14,37/11) Hyperbolic Matrix(2545,-4104,684,-1103) (29/18,50/31) -> (26/7,67/18) Hyperbolic Matrix(2167,-3496,918,-1481) (50/31,21/13) -> (59/25,26/11) Hyperbolic Matrix(1597,-2584,610,-987) (21/13,34/21) -> (34/13,55/21) Hyperbolic Matrix(797,-1292,446,-723) (34/21,13/8) -> (25/14,34/19) Hyperbolic Matrix(607,-988,94,-153) (13/8,44/27) -> (32/5,13/2) Hyperbolic Matrix(5129,-8360,1516,-2471) (44/27,75/46) -> (115/34,44/13) Hyperbolic Matrix(2319,-3800,440,-721) (18/11,59/36) -> (21/4,58/11) Hyperbolic Matrix(1899,-3116,788,-1293) (41/25,23/14) -> (53/22,41/17) Hyperbolic Matrix(647,-1064,346,-569) (23/14,28/17) -> (28/15,15/8) Hyperbolic Matrix(645,-1064,254,-419) (28/17,5/3) -> (33/13,28/11) Hyperbolic Matrix(1217,-2052,360,-607) (5/3,27/16) -> (27/8,71/21) Hyperbolic Matrix(989,-1672,404,-683) (27/16,22/13) -> (22/9,49/20) Hyperbolic Matrix(2735,-4636,1256,-2129) (61/36,39/23) -> (37/17,61/28) Hyperbolic Matrix(761,-1292,268,-455) (39/23,17/10) -> (17/6,37/13) Hyperbolic Matrix(4369,-7448,1182,-2015) (75/44,29/17) -> (85/23,37/10) Hyperbolic Matrix(6231,-10640,2582,-4409) (70/41,41/24) -> (111/46,70/29) Hyperbolic Matrix(1823,-3116,712,-1217) (41/24,12/7) -> (64/25,41/16) Hyperbolic Matrix(569,-988,110,-191) (26/15,33/19) -> (5/1,26/5) Hyperbolic Matrix(13375,-23256,4896,-8513) (113/65,40/23) -> (112/41,265/97) Hyperbolic Matrix(1291,-2280,560,-989) (30/17,23/13) -> (53/23,30/13) Hyperbolic Matrix(2699,-4788,792,-1405) (39/22,55/31) -> (17/5,75/22) Hyperbolic Matrix(3991,-7144,2186,-3913) (34/19,77/43) -> (115/63,42/23) Hyperbolic Matrix(419,-760,188,-341) (9/5,20/11) -> (20/9,29/13) Hyperbolic Matrix(455,-836,166,-305) (11/6,24/13) -> (52/19,11/4) Hyperbolic Matrix(2507,-4636,1028,-1901) (24/13,37/20) -> (39/16,100/41) Hyperbolic Matrix(495,-1064,194,-417) (15/7,13/6) -> (51/20,23/9) Hyperbolic Matrix(835,-1824,244,-533) (24/11,11/5) -> (65/19,24/7) Hyperbolic Matrix(3953,-8740,1512,-3343) (42/19,73/33) -> (149/57,34/13) Hyperbolic Matrix(569,-1292,218,-495) (9/4,25/11) -> (13/5,47/18) Hyperbolic Matrix(531,-1216,100,-229) (16/7,39/17) -> (37/7,16/3) Hyperbolic Matrix(2775,-6536,1016,-2393) (40/17,33/14) -> (71/26,112/41) Hyperbolic Matrix(1483,-3572,394,-949) (12/5,53/22) -> (15/4,64/17) Hyperbolic Matrix(2545,-6156,456,-1103) (29/12,75/31) -> (39/7,67/12) Hyperbolic Matrix(5053,-12312,1482,-3611) (95/39,39/16) -> (75/22,133/39) Hyperbolic Matrix(987,-2432,278,-685) (32/13,5/2) -> (71/20,32/9) Hyperbolic Matrix(2851,-7296,846,-2165) (23/9,64/25) -> (64/19,91/27) Hyperbolic Matrix(1215,-3116,356,-913) (41/16,18/7) -> (58/17,41/12) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(607,-1596,116,-305) (21/8,50/19) -> (26/5,21/4) Hyperbolic Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(1939,-5472,444,-1253) (31/11,48/17) -> (48/11,83/19) Hyperbolic Matrix(1975,-5624,374,-1065) (37/13,57/20) -> (95/18,37/7) Hyperbolic Matrix(343,-988,92,-265) (20/7,3/1) -> (41/11,56/15) Hyperbolic Matrix(2469,-8284,442,-1483) (57/17,47/14) -> (67/12,95/17) Hyperbolic Matrix(419,-1520,94,-341) (29/8,40/11) -> (40/9,9/2) Hyperbolic Matrix(761,-2812,82,-303) (48/13,85/23) -> (9/1,28/3) Hyperbolic Matrix(189,-836,26,-115) (22/5,31/7) -> (7/1,22/3) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(37,304,-14,-115) -> Matrix(1,2,0,1) Matrix(39,304,-34,-265) -> Matrix(3,4,2,3) Matrix(115,836,-26,-189) -> Matrix(3,2,-2,-1) Matrix(113,760,62,417) -> Matrix(1,0,-2,1) Matrix(379,2508,264,1747) -> Matrix(1,0,-2,1) Matrix(151,988,116,759) -> Matrix(3,-4,-2,3) Matrix(189,1216,-136,-875) -> Matrix(1,-2,0,1) Matrix(37,228,6,37) -> Matrix(1,4,0,1) Matrix(379,2204,222,1291) -> Matrix(1,2,-4,-7) Matrix(381,2204,-302,-1747) -> Matrix(1,2,0,1) Matrix(305,1748,-212,-1215) -> Matrix(1,2,4,9) Matrix(229,1292,-148,-835) -> Matrix(1,2,0,1) Matrix(151,836,-110,-609) -> Matrix(3,4,2,3) Matrix(113,608,-92,-495) -> Matrix(5,4,6,5) Matrix(229,1216,-100,-531) -> Matrix(3,2,-2,-1) Matrix(191,988,-110,-569) -> Matrix(1,0,-4,1) Matrix(533,2584,204,989) -> Matrix(1,0,0,1) Matrix(457,2204,-378,-1823) -> Matrix(1,2,0,1) Matrix(191,912,40,191) -> Matrix(1,-2,0,1) Matrix(113,532,24,113) -> Matrix(1,4,0,1) Matrix(229,1064,82,381) -> Matrix(1,2,2,5) Matrix(379,1748,214,987) -> Matrix(1,2,0,1) Matrix(647,2964,-456,-2089) -> Matrix(5,8,8,13) Matrix(799,3648,-624,-2849) -> Matrix(5,6,4,5) Matrix(685,3116,184,837) -> Matrix(1,0,2,1) Matrix(341,1520,-94,-419) -> Matrix(1,2,0,1) Matrix(569,2508,336,1481) -> Matrix(1,2,-2,-3) Matrix(191,836,-130,-569) -> Matrix(1,2,-2,-3) Matrix(1027,4484,-844,-3685) -> Matrix(7,12,4,7) Matrix(227,988,122,531) -> Matrix(1,2,-4,-7) Matrix(229,988,194,837) -> Matrix(3,4,2,3) Matrix(797,3420,292,1253) -> Matrix(3,4,20,27) Matrix(303,1292,178,759) -> Matrix(5,6,-16,-19) Matrix(37,152,-28,-115) -> Matrix(1,0,2,1) Matrix(39,152,10,39) -> Matrix(1,0,2,1) Matrix(341,1292,90,341) -> Matrix(1,0,0,1) Matrix(645,2432,292,1101) -> Matrix(1,0,2,1) Matrix(1291,4864,-908,-3421) -> Matrix(1,-2,2,-3) Matrix(265,988,-92,-343) -> Matrix(1,2,-2,-3) Matrix(1103,4104,-684,-2545) -> Matrix(1,0,2,1) Matrix(1065,3952,-778,-2887) -> Matrix(1,0,0,1) Matrix(759,2812,410,1519) -> Matrix(1,0,-2,1) Matrix(227,836,-186,-685) -> Matrix(3,4,2,3) Matrix(229,836,146,533) -> Matrix(1,0,-2,1) Matrix(837,3040,356,1293) -> Matrix(1,0,-4,1) Matrix(379,1368,-274,-989) -> Matrix(1,0,0,1) Matrix(191,684,-74,-265) -> Matrix(1,0,0,1) Matrix(265,912,-188,-647) -> Matrix(11,10,12,11) Matrix(911,3116,-578,-1977) -> Matrix(5,4,26,21) Matrix(913,3116,-356,-1215) -> Matrix(13,10,-4,-3) Matrix(875,2964,-684,-2317) -> Matrix(13,8,8,5) Matrix(607,2052,-360,-1217) -> Matrix(3,2,4,3) Matrix(1443,4864,-1060,-3573) -> Matrix(3,2,-2,-1) Matrix(1445,4864,926,3117) -> Matrix(7,4,-16,-9) Matrix(113,380,-102,-343) -> Matrix(3,2,-2,-1) Matrix(229,760,-160,-531) -> Matrix(1,0,4,1) Matrix(761,2508,646,2129) -> Matrix(1,0,2,1) Matrix(531,1748,346,1139) -> Matrix(5,2,-8,-3) Matrix(533,1748,-440,-1443) -> Matrix(9,2,4,1) Matrix(419,1368,268,875) -> Matrix(1,0,-2,1) Matrix(189,608,106,341) -> Matrix(1,0,2,1) Matrix(191,608,60,191) -> Matrix(1,0,6,1) Matrix(267,836,-206,-645) -> Matrix(3,-2,2,-1) Matrix(609,1748,424,1217) -> Matrix(3,2,-8,-5) Matrix(455,1292,-268,-761) -> Matrix(5,2,12,5) Matrix(457,1292,-376,-1063) -> Matrix(1,2,0,1) Matrix(379,1064,-244,-685) -> Matrix(1,0,4,1) Matrix(381,1064,82,229) -> Matrix(5,2,2,1) Matrix(1747,4864,1228,3419) -> Matrix(9,4,-16,-7) Matrix(2623,7296,-1680,-4673) -> Matrix(11,4,30,11) Matrix(493,1368,342,949) -> Matrix(1,0,2,1) Matrix(303,836,220,607) -> Matrix(1,0,2,1) Matrix(1139,3116,-806,-2205) -> Matrix(21,4,26,5) Matrix(2393,6536,-1016,-2775) -> Matrix(1,0,10,1) Matrix(1253,3420,292,797) -> Matrix(27,4,20,3) Matrix(419,1140,154,419) -> Matrix(1,0,16,1) Matrix(113,304,42,113) -> Matrix(1,0,-2,1) Matrix(1065,2812,-748,-1975) -> Matrix(1,-4,2,-7) Matrix(1559,4104,-1140,-3001) -> Matrix(1,0,2,1) Matrix(1329,3496,-766,-2015) -> Matrix(1,0,-6,1) Matrix(987,2584,-610,-1597) -> Matrix(1,0,0,1) Matrix(495,1292,-218,-569) -> Matrix(1,0,0,1) Matrix(381,988,-322,-835) -> Matrix(1,-2,0,1) Matrix(3231,8360,-2276,-5889) -> Matrix(1,0,2,1) Matrix(647,1672,368,951) -> Matrix(1,2,0,1) Matrix(1481,3800,-1200,-3079) -> Matrix(1,4,2,9) Matrix(1217,3116,-712,-1823) -> Matrix(1,2,4,9) Matrix(417,1064,-194,-495) -> Matrix(1,2,-4,-7) Matrix(419,1064,-254,-645) -> Matrix(5,6,4,5) Matrix(835,2052,-588,-1445) -> Matrix(3,2,4,3) Matrix(683,1672,-404,-989) -> Matrix(1,0,4,1) Matrix(1027,2508,794,1939) -> Matrix(3,2,-2,-1) Matrix(1901,4636,-1028,-2507) -> Matrix(3,2,4,3) Matrix(531,1292,-344,-837) -> Matrix(5,2,12,5) Matrix(533,1292,408,989) -> Matrix(19,6,-16,-5) Matrix(1633,3952,926,2241) -> Matrix(7,2,-4,-1) Matrix(3079,7448,-2246,-5433) -> Matrix(7,2,-4,-1) Matrix(913,2204,756,1825) -> Matrix(7,2,-4,-1) Matrix(4409,10640,-2582,-6231) -> Matrix(1,0,8,1) Matrix(1293,3116,-788,-1899) -> Matrix(9,2,4,1) Matrix(191,456,80,191) -> Matrix(1,0,10,1) Matrix(417,988,176,417) -> Matrix(1,0,-16,1) Matrix(419,988,-338,-797) -> Matrix(1,0,-4,1) Matrix(10717,25232,4100,9653) -> Matrix(1,0,-4,1) Matrix(9881,23256,-6264,-14743) -> Matrix(1,0,4,1) Matrix(647,1520,146,343) -> Matrix(7,-2,4,-1) Matrix(721,1672,442,1025) -> Matrix(1,-2,0,1) Matrix(1711,3952,1004,2319) -> Matrix(1,2,-4,-7) Matrix(989,2280,-560,-1291) -> Matrix(1,0,0,1) Matrix(761,1748,596,1369) -> Matrix(1,-2,0,1) Matrix(2089,4788,-1476,-3383) -> Matrix(3,8,4,11) Matrix(267,608,184,419) -> Matrix(1,0,-2,1) Matrix(3153,7144,-1426,-3231) -> Matrix(1,0,-2,1) Matrix(4599,10412,1360,3079) -> Matrix(1,-2,2,-3) Matrix(571,1292,118,267) -> Matrix(1,0,0,1) Matrix(341,760,-188,-419) -> Matrix(3,2,4,3) Matrix(343,760,292,647) -> Matrix(1,0,2,1) Matrix(2507,5548,446,987) -> Matrix(1,2,0,1) Matrix(7181,15884,2628,5813) -> Matrix(1,0,8,1) Matrix(1101,2432,292,645) -> Matrix(1,0,2,1) Matrix(381,836,-242,-531) -> Matrix(1,0,6,1) Matrix(2129,4636,-1256,-2735) -> Matrix(3,2,4,3) Matrix(1293,2812,944,2053) -> Matrix(1,0,2,1) Matrix(457,988,352,761) -> Matrix(7,2,-4,-1) Matrix(569,1216,124,265) -> Matrix(9,2,4,1) Matrix(1291,2736,394,835) -> Matrix(1,0,16,1) Matrix(37,76,18,37) -> Matrix(1,0,0,1) Matrix(39,76,20,39) -> Matrix(1,0,0,1) Matrix(683,1292,120,227) -> Matrix(23,-2,12,-1) Matrix(685,1292,202,381) -> Matrix(13,-2,20,-3) Matrix(569,1064,-346,-647) -> Matrix(7,-2,4,-1) Matrix(1519,2812,410,759) -> Matrix(1,0,-2,1) Matrix(1481,2736,308,569) -> Matrix(1,0,-2,1) Matrix(989,1824,-700,-1291) -> Matrix(3,-4,4,-5) Matrix(1331,2432,978,1787) -> Matrix(1,0,-2,1) Matrix(4787,8740,-2956,-5397) -> Matrix(1,0,-2,1) Matrix(3915,7144,896,1635) -> Matrix(7,-2,4,-1) Matrix(417,760,62,113) -> Matrix(1,0,-2,1) Matrix(797,1444,356,645) -> Matrix(5,-4,4,-3) Matrix(799,1444,358,647) -> Matrix(3,-4,4,-5) Matrix(723,1292,-446,-797) -> Matrix(1,0,0,1) Matrix(341,608,106,189) -> Matrix(1,0,2,1) Matrix(685,1216,-556,-987) -> Matrix(1,-2,2,-3) Matrix(987,1748,214,379) -> Matrix(1,2,0,1) Matrix(3267,5776,1418,2507) -> Matrix(1,0,0,1) Matrix(3269,5776,1420,2509) -> Matrix(1,0,0,1) Matrix(2241,3952,926,1633) -> Matrix(1,-2,4,-7) Matrix(303,532,86,151) -> Matrix(1,2,0,1) Matrix(1747,3040,1266,2203) -> Matrix(1,0,4,1) Matrix(3761,6536,-2384,-4143) -> Matrix(1,0,10,1) Matrix(571,988,330,571) -> Matrix(1,0,16,1) Matrix(265,456,154,265) -> Matrix(1,0,-10,1) Matrix(2089,3572,-1534,-2623) -> Matrix(1,0,-4,1) Matrix(13527,23104,5606,9575) -> Matrix(1,0,0,1) Matrix(13529,23104,5608,9577) -> Matrix(1,0,0,1) Matrix(1291,2204,222,379) -> Matrix(7,-2,4,-1) Matrix(3611,6156,-2964,-5053) -> Matrix(37,-10,26,-7) Matrix(2319,3952,1004,1711) -> Matrix(7,-2,4,-1) Matrix(759,1292,178,303) -> Matrix(19,-6,16,-5) Matrix(3001,5092,1052,1785) -> Matrix(17,-8,32,-15) Matrix(7259,12312,-5130,-8701) -> Matrix(37,-20,50,-27) Matrix(3229,5472,560,949) -> Matrix(7,-4,2,-1) Matrix(987,1672,134,227) -> Matrix(1,0,0,1) Matrix(3419,5776,1394,2355) -> Matrix(1,0,0,1) Matrix(3421,5776,1396,2357) -> Matrix(1,0,0,1) Matrix(1445,2432,-1038,-1747) -> Matrix(3,-2,2,-1) Matrix(873,1444,344,569) -> Matrix(9,-8,8,-7) Matrix(875,1444,346,571) -> Matrix(7,-8,8,-9) Matrix(1709,2812,392,645) -> Matrix(1,0,0,1) Matrix(4445,7296,-3126,-5131) -> Matrix(1,-4,2,-7) Matrix(1901,3116,-1344,-2203) -> Matrix(3,-10,4,-13) Matrix(419,684,-302,-493) -> Matrix(1,0,0,1) Matrix(1595,2584,1266,2051) -> Matrix(1,0,0,1) Matrix(6991,11324,1970,3191) -> Matrix(1,2,0,1) Matrix(15579,25232,8962,14515) -> Matrix(1,0,4,1) Matrix(3571,5776,1362,2203) -> Matrix(1,0,0,1) Matrix(3573,5776,1364,2205) -> Matrix(1,0,0,1) Matrix(989,1596,-800,-1291) -> Matrix(1,0,2,1) Matrix(1179,1900,260,419) -> Matrix(1,0,0,1) Matrix(189,304,-166,-267) -> Matrix(1,2,0,1) Matrix(191,304,120,191) -> Matrix(1,0,2,1) Matrix(721,1140,456,721) -> Matrix(1,0,-16,1) Matrix(2167,3420,1662,2623) -> Matrix(27,-4,-20,3) Matrix(110769,174724,40544,63953) -> Matrix(15,-2,98,-13) Matrix(110771,174724,40546,63955) -> Matrix(13,-2,98,-15) Matrix(10071,15884,5518,8703) -> Matrix(1,0,-8,1) Matrix(533,836,146,229) -> Matrix(1,0,-2,1) Matrix(875,1368,268,419) -> Matrix(1,0,-2,1) Matrix(8321,12996,2992,4673) -> Matrix(19,-6,54,-17) Matrix(8323,12996,2994,4675) -> Matrix(17,-6,54,-19) Matrix(3117,4864,926,1445) -> Matrix(9,-4,16,-7) Matrix(683,1064,536,835) -> Matrix(5,-2,-2,1) Matrix(3723,5776,1322,2051) -> Matrix(1,0,0,1) Matrix(3725,5776,1324,2053) -> Matrix(1,0,0,1) Matrix(3533,5472,-2724,-4219) -> Matrix(7,-2,4,-1) Matrix(3649,5624,-2958,-4559) -> Matrix(17,-8,32,-15) Matrix(3307,5092,1358,2091) -> Matrix(15,-8,32,-17) Matrix(645,988,-472,-723) -> Matrix(3,-2,2,-1) Matrix(1141,1672,260,381) -> Matrix(5,2,2,1) Matrix(417,608,286,417) -> Matrix(1,0,-6,1) Matrix(419,608,184,267) -> Matrix(1,0,-2,1) Matrix(949,1368,342,493) -> Matrix(1,0,2,1) Matrix(4065,5852,712,1025) -> Matrix(13,2,6,1) Matrix(1901,2736,1004,1445) -> Matrix(1,0,-16,1) Matrix(1481,2128,396,569) -> Matrix(1,0,-2,1) Matrix(1747,2508,264,379) -> Matrix(1,0,-2,1) Matrix(4027,5776,1218,1747) -> Matrix(1,0,0,1) Matrix(4029,5776,1220,1749) -> Matrix(1,0,0,1) Matrix(533,760,54,77) -> Matrix(5,-2,-2,1) Matrix(5815,8284,-4774,-6801) -> Matrix(53,-28,36,-19) Matrix(3419,4864,1228,1747) -> Matrix(7,-4,16,-9) Matrix(7333,10412,4094,5813) -> Matrix(3,-2,2,-1) Matrix(911,1292,428,607) -> Matrix(3,-2,20,-13) Matrix(9347,13224,1772,2507) -> Matrix(29,-22,62,-47) Matrix(1025,1444,296,417) -> Matrix(17,-16,16,-15) Matrix(1027,1444,298,419) -> Matrix(15,-16,16,-17) Matrix(381,532,164,229) -> Matrix(1,-2,0,1) Matrix(8133,11324,3112,4333) -> Matrix(1,-2,0,1) Matrix(1749,2432,274,381) -> Matrix(1,-8,0,1) Matrix(4179,5776,1154,1595) -> Matrix(1,0,0,1) Matrix(4181,5776,1156,1597) -> Matrix(1,0,0,1) Matrix(1101,1520,-854,-1179) -> Matrix(1,2,0,1) Matrix(607,836,220,303) -> Matrix(1,0,2,1) Matrix(2051,2812,-1830,-2509) -> Matrix(1,6,0,1) Matrix(2053,2812,944,1293) -> Matrix(1,0,2,1) Matrix(16871,23104,4550,6231) -> Matrix(1,0,0,1) Matrix(16873,23104,4552,6233) -> Matrix(1,0,0,1) Matrix(2279,3116,1778,2431) -> Matrix(1,0,-2,1) Matrix(1559,2128,474,647) -> Matrix(1,0,2,1) Matrix(1787,2432,978,1331) -> Matrix(1,0,-2,1) Matrix(951,1292,700,951) -> Matrix(1,0,0,1) Matrix(113,152,84,113) -> Matrix(1,0,-2,1) Matrix(1101,1444,260,341) -> Matrix(19,-18,18,-17) Matrix(1103,1444,262,343) -> Matrix(17,-18,18,-19) Matrix(989,1292,408,533) -> Matrix(5,-6,16,-19) Matrix(2623,3420,1662,2167) -> Matrix(3,-4,-20,27) Matrix(759,988,116,151) -> Matrix(3,-4,-2,3) Matrix(2167,2812,850,1103) -> Matrix(1,0,0,1) Matrix(5509,7144,2490,3229) -> Matrix(1,-2,4,-7) Matrix(1291,1672,410,531) -> Matrix(1,-2,-2,5) Matrix(647,836,-558,-721) -> Matrix(1,-2,2,-3) Matrix(1177,1520,676,873) -> Matrix(1,-2,4,-7) Matrix(1481,1900,562,721) -> Matrix(1,0,0,1) Matrix(10145,12996,2224,2849) -> Matrix(13,-12,12,-11) Matrix(10147,12996,2226,2851) -> Matrix(11,-12,12,-13) Matrix(951,1216,506,647) -> Matrix(1,-2,-4,9) Matrix(1369,1748,596,761) -> Matrix(1,-2,0,1) Matrix(835,1064,536,683) -> Matrix(1,-2,-2,5) Matrix(419,532,330,419) -> Matrix(1,-4,0,1) Matrix(721,912,570,721) -> Matrix(1,2,0,1) Matrix(2167,2736,994,1255) -> Matrix(1,0,2,1) Matrix(1025,1292,572,721) -> Matrix(1,0,0,1) Matrix(10717,13224,3142,3877) -> Matrix(47,-22,62,-29) Matrix(1177,1444,216,265) -> Matrix(15,-14,14,-13) Matrix(1179,1444,218,267) -> Matrix(13,-14,14,-15) Matrix(2621,3192,280,341) -> Matrix(21,-32,2,-3) Matrix(4561,5548,2500,3041) -> Matrix(1,-2,0,1) Matrix(1065,1292,502,609) -> Matrix(1,-2,12,-23) Matrix(4827,5852,1474,1787) -> Matrix(1,-2,-6,13) Matrix(4523,5472,1854,2243) -> Matrix(1,-4,2,-7) Matrix(1825,2204,756,913) -> Matrix(1,-2,4,-7) Matrix(191,228,160,191) -> Matrix(1,-4,0,1) Matrix(2051,2432,576,683) -> Matrix(1,8,0,1) Matrix(837,988,194,229) -> Matrix(3,4,2,3) Matrix(2129,2508,646,761) -> Matrix(1,0,2,1) Matrix(647,760,292,343) -> Matrix(1,0,2,1) Matrix(1445,1672,592,685) -> Matrix(1,0,0,1) Matrix(1253,1444,164,189) -> Matrix(11,-10,10,-9) Matrix(1255,1444,166,191) -> Matrix(9,-10,10,-11) Matrix(2851,3192,510,571) -> Matrix(3,-32,2,-21) Matrix(683,760,204,227) -> Matrix(1,2,2,5) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(267,-304,166,-189) -> Matrix(1,2,0,1) Matrix(265,-304,34,-39) -> Matrix(3,4,2,3) Matrix(721,-836,558,-647) -> Matrix(3,2,-2,-1) Matrix(1027,-1216,288,-341) -> Matrix(1,-2,0,1) Matrix(1823,-2204,378,-457) -> Matrix(1,2,0,1) Matrix(1443,-1748,440,-533) -> Matrix(1,2,4,9) Matrix(1063,-1292,376,-457) -> Matrix(1,2,0,1) Matrix(685,-836,186,-227) -> Matrix(3,4,2,3) Matrix(495,-608,92,-113) -> Matrix(5,4,6,5) Matrix(987,-1216,556,-685) -> Matrix(3,2,-2,-1) Matrix(797,-988,338,-419) -> Matrix(1,0,-4,1) Matrix(1747,-2204,302,-381) -> Matrix(1,2,0,1) Matrix(2317,-2964,684,-875) -> Matrix(5,8,8,13) Matrix(2849,-3648,624,-799) -> Matrix(5,6,4,5) Matrix(1179,-1520,854,-1101) -> Matrix(1,2,0,1) Matrix(645,-836,206,-267) -> Matrix(1,2,-2,-3) Matrix(3457,-4484,616,-799) -> Matrix(7,12,4,7) Matrix(115,-152,28,-37) -> Matrix(1,0,2,1) Matrix(3573,-4864,1060,-1443) -> Matrix(1,-2,2,-3) Matrix(723,-988,472,-645) -> Matrix(1,2,-2,-3) Matrix(3001,-4104,1140,-1559) -> Matrix(1,0,2,1) Matrix(2887,-3952,778,-1065) -> Matrix(1,0,0,1) Matrix(609,-836,110,-151) -> Matrix(3,4,2,3) Matrix(989,-1368,274,-379) -> Matrix(1,0,0,1) Matrix(493,-684,302,-419) -> Matrix(1,0,0,1) Matrix(647,-912,188,-265) -> Matrix(11,10,12,11) Matrix(2205,-3116,806,-1139) -> Matrix(5,4,26,21) Matrix(2203,-3116,1344,-1901) -> Matrix(13,10,-4,-3) Matrix(2089,-2964,456,-647) -> Matrix(13,8,8,5) Matrix(1445,-2052,588,-835) -> Matrix(3,2,4,3) Matrix(3421,-4864,908,-1291) -> Matrix(3,2,-2,-1) Matrix(267,-380,26,-37) -> Matrix(3,2,-2,-1) Matrix(531,-760,160,-229) -> Matrix(1,0,4,1) Matrix(1215,-1748,212,-305) -> Matrix(9,2,4,1) Matrix(569,-836,130,-191) -> Matrix(3,-2,2,-1) Matrix(837,-1292,344,-531) -> Matrix(5,2,12,5) Matrix(835,-1292,148,-229) -> Matrix(1,2,0,1) Matrix(685,-1064,244,-379) -> Matrix(1,0,4,1) Matrix(4673,-7296,1680,-2623) -> Matrix(11,4,30,11) Matrix(1977,-3116,578,-911) -> Matrix(21,4,26,5) Matrix(4143,-6536,2384,-3761) -> Matrix(1,0,10,1) Matrix(1747,-2812,520,-837) -> Matrix(1,-4,2,-7) Matrix(2545,-4104,684,-1103) -> Matrix(1,0,2,1) Matrix(2167,-3496,918,-1481) -> Matrix(1,0,-6,1) Matrix(1597,-2584,610,-987) -> Matrix(1,0,0,1) Matrix(797,-1292,446,-723) -> Matrix(1,0,0,1) Matrix(607,-988,94,-153) -> Matrix(1,-2,0,1) Matrix(5129,-8360,1516,-2471) -> Matrix(1,0,2,1) Matrix(2319,-3800,440,-721) -> Matrix(1,4,2,9) Matrix(1899,-3116,788,-1293) -> Matrix(1,2,4,9) Matrix(647,-1064,346,-569) -> Matrix(1,2,-4,-7) Matrix(645,-1064,254,-419) -> Matrix(5,6,4,5) Matrix(1217,-2052,360,-607) -> Matrix(3,2,4,3) Matrix(989,-1672,404,-683) -> Matrix(1,0,4,1) Matrix(2735,-4636,1256,-2129) -> Matrix(3,2,4,3) Matrix(761,-1292,268,-455) -> Matrix(5,2,12,5) Matrix(4369,-7448,1182,-2015) -> Matrix(7,2,-4,-1) Matrix(6231,-10640,2582,-4409) -> Matrix(1,0,8,1) Matrix(1823,-3116,712,-1217) -> Matrix(9,2,4,1) Matrix(569,-988,110,-191) -> Matrix(1,0,-4,1) Matrix(13375,-23256,4896,-8513) -> Matrix(1,0,4,1) Matrix(1291,-2280,560,-989) -> Matrix(1,0,0,1) Matrix(2699,-4788,792,-1405) -> Matrix(3,8,4,11) Matrix(3991,-7144,2186,-3913) -> Matrix(1,0,-2,1) Matrix(419,-760,188,-341) -> Matrix(3,2,4,3) Matrix(455,-836,166,-305) -> Matrix(1,0,6,1) Matrix(2507,-4636,1028,-1901) -> Matrix(3,2,4,3) Matrix(495,-1064,194,-417) -> Matrix(7,-2,4,-1) Matrix(835,-1824,244,-533) -> Matrix(3,-4,4,-5) Matrix(3953,-8740,1512,-3343) -> Matrix(1,0,-2,1) Matrix(569,-1292,218,-495) -> Matrix(1,0,0,1) Matrix(531,-1216,100,-229) -> Matrix(1,-2,2,-3) Matrix(2775,-6536,1016,-2393) -> Matrix(1,0,10,1) Matrix(1483,-3572,394,-949) -> Matrix(1,0,-4,1) Matrix(2545,-6156,456,-1103) -> Matrix(37,-10,26,-7) Matrix(5053,-12312,1482,-3611) -> Matrix(37,-20,50,-27) Matrix(987,-2432,278,-685) -> Matrix(3,-2,2,-1) Matrix(2851,-7296,846,-2165) -> Matrix(1,-4,2,-7) Matrix(1215,-3116,356,-913) -> Matrix(3,-10,4,-13) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(607,-1596,116,-305) -> Matrix(1,0,2,1) Matrix(115,-304,14,-37) -> Matrix(1,2,0,1) Matrix(1939,-5472,444,-1253) -> Matrix(7,-2,4,-1) Matrix(1975,-5624,374,-1065) -> Matrix(17,-8,32,-15) Matrix(343,-988,92,-265) -> Matrix(3,-2,2,-1) Matrix(2469,-8284,442,-1483) -> Matrix(53,-28,36,-19) Matrix(419,-1520,94,-341) -> Matrix(1,2,0,1) Matrix(761,-2812,82,-303) -> Matrix(1,6,0,1) Matrix(189,-836,26,-115) -> Matrix(1,-2,2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 90 Degree of the the map X: 90 Degree of the the map Y: 360 ----------------------------------------------------------------------- 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): 1080 Minimal number of generators: 181 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: 54 Genus: 64 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 19/9 38/17 76/33 19/8 12/5 152/63 76/31 38/15 76/29 19/7 418/153 114/41 76/27 3/1 19/6 76/23 38/11 18/5 76/21 152/41 34/9 19/5 4/1 38/9 30/7 114/25 14/3 19/4 24/5 5/1 26/5 95/18 16/3 38/7 11/2 17/3 40/7 6/1 19/3 32/5 13/2 20/3 7/1 22/3 15/2 38/5 8/1 9/1 28/3 19/2 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 1/1 1/1 1/0 8/7 -2/1 -1/1 15/13 -3/4 7/6 1/0 20/17 1/1 1/0 33/28 1/0 13/11 1/0 19/16 1/0 6/5 -2/1 1/0 29/24 1/0 23/19 -5/2 17/14 -7/4 28/23 -5/3 -3/2 11/9 -5/4 16/13 -1/1 -2/3 21/17 -1/2 5/4 1/0 29/23 1/0 24/19 1/1 1/0 19/15 1/0 14/11 -2/1 1/0 37/29 1/0 23/18 1/0 32/25 -3/2 -1/1 41/32 -3/4 9/7 1/0 31/24 -3/2 53/41 -1/2 22/17 -2/1 1/0 35/27 -3/2 48/37 -3/2 -1/1 13/10 -3/2 43/33 -3/2 30/23 -4/3 -5/4 17/13 -9/8 4/3 -1/1 0/1 19/14 0/1 34/25 0/1 1/0 49/36 1/0 15/11 1/0 41/30 -3/2 26/19 0/1 1/0 63/46 1/0 37/27 1/0 11/8 -1/2 40/29 0/1 1/1 69/50 1/2 29/21 1/0 18/13 0/1 1/0 7/5 -3/2 24/17 -1/1 -5/6 41/29 -3/4 17/12 -3/4 44/31 -3/5 -1/2 27/19 -1/2 64/45 -2/3 -3/5 37/26 -1/2 10/7 -1/2 0/1 33/23 -1/2 56/39 -1/1 -1/2 23/16 -1/2 36/25 0/1 1/1 13/9 -1/2 16/11 -1/3 0/1 19/13 0/1 3/2 1/0 23/15 -1/2 20/13 -3/5 -1/2 17/11 -1/4 31/20 -1/2 14/9 -1/2 0/1 39/25 -1/2 64/41 -2/5 -1/3 25/16 -1/4 36/23 -1/1 0/1 11/7 -1/4 41/26 -1/6 71/45 -1/6 30/19 -1/8 0/1 19/12 0/1 8/5 0/1 1/1 37/23 1/0 29/18 1/0 50/31 -1/2 0/1 21/13 1/0 34/21 0/1 1/0 13/8 1/0 44/27 -3/1 1/0 75/46 1/0 31/19 -3/2 18/11 0/1 1/0 59/36 1/0 41/25 1/0 23/14 1/0 28/17 -3/2 -1/1 5/3 -1/2 27/16 -1/2 22/13 -1/2 0/1 61/36 -3/4 39/23 -1/2 17/10 -3/8 46/27 -2/7 -1/4 75/44 -1/4 29/17 -1/4 70/41 -1/4 0/1 41/24 -1/4 12/7 -1/5 0/1 19/11 0/1 26/15 0/1 1/8 33/19 1/4 73/42 1/4 113/65 1/4 40/23 0/1 1/3 7/4 1/2 37/21 1/0 30/17 0/1 1/0 23/13 1/0 39/22 1/0 55/31 1/0 16/9 -1/1 0/1 25/14 1/0 34/19 0/1 1/0 77/43 1/0 43/24 1/0 9/5 1/0 20/11 -1/1 -1/2 31/17 -1/2 73/40 -1/2 115/63 -1/2 42/23 -1/2 0/1 11/6 -1/2 24/13 -1/1 -1/2 37/20 -1/2 13/7 -1/2 28/15 -1/2 -1/3 15/8 -1/4 17/9 -1/8 19/10 0/1 2/1 0/1 1/0 19/9 0/1 17/8 1/8 15/7 1/4 13/6 1/2 37/17 1/2 61/28 1/0 24/11 1/2 1/1 11/5 1/2 42/19 0/1 1/2 73/33 1/2 31/14 1/2 20/9 1/2 1/1 29/13 3/4 38/17 1/1 9/4 1/0 25/11 1/0 16/7 0/1 1/1 39/17 1/0 23/10 1/0 76/33 -1/1 1/1 53/23 1/0 30/13 0/1 1/0 37/16 1/0 7/3 -1/2 40/17 -1/3 0/1 33/14 -1/4 59/25 -1/6 26/11 -1/8 0/1 19/8 0/1 12/5 0/1 1/5 53/22 1/4 41/17 1/4 152/63 1/5 1/3 111/46 1/4 70/29 0/1 1/4 29/12 1/4 75/31 1/4 46/19 1/4 2/7 17/7 3/8 56/23 5/11 1/2 95/39 1/2 39/16 1/2 100/41 1/2 1/1 61/25 3/4 22/9 0/1 1/2 49/20 1/2 76/31 1/3 1/1 27/11 1/2 32/13 1/3 1/2 5/2 1/2 38/15 1/1 33/13 7/6 28/11 1/1 3/2 51/20 3/2 23/9 1/0 64/25 1/1 2/1 41/16 1/0 18/7 0/1 1/0 13/5 1/0 47/18 1/0 81/31 1/0 115/44 1/0 149/57 1/0 34/13 0/1 1/0 55/21 1/0 76/29 -1/1 1/1 21/8 1/0 50/19 0/1 1/2 79/30 3/4 29/11 1/0 8/3 -1/1 0/1 19/7 0/1 30/11 0/1 1/8 71/26 1/6 112/41 0/1 1/7 265/97 1/8 418/153 1/7 153/56 1/6 41/15 1/6 52/19 1/5 1/4 11/4 1/4 36/13 0/1 1/1 25/9 1/4 114/41 1/3 89/32 5/14 64/23 1/3 2/5 39/14 1/2 14/5 0/1 1/2 45/16 1/2 76/27 1/3 1/1 31/11 1/2 48/17 1/3 1/2 17/6 1/4 37/13 1/2 57/20 1/2 20/7 1/2 3/5 3/1 1/0 22/7 -1/2 0/1 19/6 0/1 16/5 0/1 1/3 13/4 1/2 36/11 -1/1 0/1 95/29 0/1 59/18 1/8 23/7 1/2 56/17 1/2 1/1 33/10 1/2 76/23 1/3 1/1 43/13 1/2 10/3 0/1 1/2 57/17 1/2 47/14 1/2 37/11 1/2 64/19 3/5 2/3 91/27 1/2 27/8 1/2 71/21 1/2 115/34 1/2 44/13 1/2 3/5 61/18 5/8 17/5 3/4 75/22 3/4 133/39 3/4 58/17 3/4 10/13 41/12 3/4 65/19 5/6 24/7 5/6 1/1 31/9 13/14 38/11 1/1 7/2 3/2 39/11 1/0 71/20 1/0 32/9 3/1 1/0 57/16 1/0 25/7 1/0 18/5 0/1 1/0 47/13 1/0 76/21 -1/1 1/1 29/8 1/0 40/11 -1/1 0/1 11/3 1/2 48/13 3/1 1/0 85/23 1/0 37/10 1/0 63/17 1/0 152/41 -1/1 1/1 89/24 1/0 26/7 0/1 1/0 67/18 1/2 41/11 3/2 56/15 -1/1 1/0 15/4 1/0 64/17 0/1 1/1 49/13 1/0 34/9 0/1 1/0 19/5 0/1 4/1 0/1 1/1 21/5 9/10 38/9 1/1 17/4 9/8 30/7 5/4 4/3 43/10 3/2 13/3 3/2 48/11 1/1 3/2 83/19 3/2 35/8 3/2 57/13 2/1 22/5 2/1 1/0 31/7 3/2 40/9 1/1 2/1 9/2 1/0 41/9 3/4 114/25 1/1 73/16 9/8 32/7 1/1 3/2 55/12 7/4 23/5 1/0 37/8 1/0 14/3 2/1 1/0 19/4 1/0 24/5 -1/1 1/0 53/11 -1/2 29/6 1/0 5/1 1/0 26/5 0/1 1/4 21/4 1/2 58/11 4/9 1/2 95/18 1/2 37/7 1/2 16/3 2/3 1/1 27/5 9/10 38/7 1/1 11/2 5/4 39/7 3/2 67/12 3/2 95/17 3/2 28/5 3/2 5/3 73/13 3/2 45/8 3/2 17/3 7/4 57/10 2/1 40/7 2/1 11/5 23/4 5/2 52/9 3/1 1/0 29/5 1/0 6/1 2/1 1/0 19/3 1/0 32/5 -5/1 1/0 13/2 1/0 33/5 1/0 20/3 -1/1 1/0 7/1 1/0 22/3 0/1 1/2 15/2 3/4 38/5 1/1 23/3 7/6 8/1 1/1 2/1 9/1 1/0 28/3 9/1 1/0 19/2 1/0 10/1 -2/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(267,-304,166,-189) (1/1,8/7) -> (8/5,37/23) Hyperbolic Matrix(265,-304,34,-39) (8/7,15/13) -> (23/3,8/1) Hyperbolic Matrix(721,-836,558,-647) (15/13,7/6) -> (31/24,53/41) Hyperbolic Matrix(647,-760,355,-417) (7/6,20/17) -> (20/11,31/17) Hyperbolic Matrix(2129,-2508,1483,-1747) (20/17,33/28) -> (33/23,56/39) Hyperbolic Matrix(837,-988,643,-759) (33/28,13/11) -> (13/10,43/33) Hyperbolic Matrix(1027,-1216,288,-341) (13/11,19/16) -> (57/16,25/7) Hyperbolic Matrix(191,-228,31,-37) (19/16,6/5) -> (6/1,19/3) Hyperbolic Matrix(1825,-2204,1069,-1291) (6/5,29/24) -> (29/17,70/41) Hyperbolic Matrix(1823,-2204,378,-457) (29/24,23/19) -> (53/11,29/6) Hyperbolic Matrix(1443,-1748,440,-533) (23/19,17/14) -> (59/18,23/7) Hyperbolic Matrix(1063,-1292,376,-457) (17/14,28/23) -> (48/17,17/6) Hyperbolic Matrix(685,-836,186,-227) (28/23,11/9) -> (11/3,48/13) Hyperbolic Matrix(495,-608,92,-113) (11/9,16/13) -> (16/3,27/5) Hyperbolic Matrix(987,-1216,556,-685) (16/13,21/17) -> (55/31,16/9) Hyperbolic Matrix(797,-988,338,-419) (21/17,5/4) -> (33/14,59/25) Hyperbolic Matrix(2051,-2584,785,-989) (5/4,29/23) -> (47/18,81/31) Hyperbolic Matrix(1747,-2204,302,-381) (29/23,24/19) -> (52/9,29/5) Hyperbolic Matrix(721,-912,151,-191) (24/19,19/15) -> (19/4,24/5) Hyperbolic Matrix(419,-532,89,-113) (19/15,14/11) -> (14/3,19/4) Hyperbolic Matrix(835,-1064,299,-381) (14/11,37/29) -> (39/14,14/5) Hyperbolic Matrix(1369,-1748,773,-987) (37/29,23/18) -> (23/13,39/22) Hyperbolic Matrix(2317,-2964,684,-875) (23/18,32/25) -> (44/13,61/18) Hyperbolic Matrix(2849,-3648,624,-799) (32/25,41/32) -> (73/16,32/7) Hyperbolic Matrix(2431,-3116,653,-837) (41/32,9/7) -> (67/18,41/11) Hyperbolic Matrix(1179,-1520,854,-1101) (9/7,31/24) -> (69/50,29/21) Hyperbolic Matrix(1939,-2508,1145,-1481) (53/41,22/17) -> (22/13,61/36) Hyperbolic Matrix(645,-836,206,-267) (22/17,35/27) -> (3/1,22/7) Hyperbolic Matrix(3457,-4484,616,-799) (35/27,48/37) -> (28/5,73/13) Hyperbolic Matrix(761,-988,409,-531) (48/37,13/10) -> (13/7,28/15) Hyperbolic Matrix(2623,-3420,961,-1253) (43/33,30/23) -> (30/11,71/26) Hyperbolic Matrix(989,-1292,581,-759) (30/23,17/13) -> (17/10,46/27) Hyperbolic Matrix(115,-152,28,-37) (17/13,4/3) -> (4/1,21/5) Hyperbolic Matrix(113,-152,29,-39) (4/3,19/14) -> (19/5,4/1) Hyperbolic Matrix(951,-1292,251,-341) (19/14,34/25) -> (34/9,19/5) Hyperbolic Matrix(1787,-2432,809,-1101) (34/25,49/36) -> (11/5,42/19) Hyperbolic Matrix(3573,-4864,1060,-1443) (49/36,15/11) -> (91/27,27/8) Hyperbolic Matrix(723,-988,472,-645) (15/11,41/30) -> (3/2,23/15) Hyperbolic Matrix(3001,-4104,1140,-1559) (41/30,26/19) -> (50/19,79/30) Hyperbolic Matrix(2887,-3952,778,-1065) (26/19,63/46) -> (89/24,26/7) Hyperbolic Matrix(2053,-2812,1109,-1519) (63/46,37/27) -> (37/20,13/7) Hyperbolic Matrix(609,-836,110,-151) (37/27,11/8) -> (11/2,39/7) Hyperbolic Matrix(607,-836,387,-533) (11/8,40/29) -> (36/23,11/7) Hyperbolic Matrix(2203,-3040,937,-1293) (40/29,69/50) -> (7/3,40/17) Hyperbolic Matrix(989,-1368,274,-379) (29/21,18/13) -> (18/5,47/13) Hyperbolic Matrix(493,-684,302,-419) (18/13,7/5) -> (31/19,18/11) Hyperbolic Matrix(647,-912,188,-265) (7/5,24/17) -> (24/7,31/9) Hyperbolic Matrix(2205,-3116,806,-1139) (24/17,41/29) -> (41/15,52/19) Hyperbolic Matrix(2203,-3116,1344,-1901) (41/29,17/12) -> (59/36,41/25) Hyperbolic Matrix(2089,-2964,456,-647) (17/12,44/31) -> (32/7,55/12) Hyperbolic Matrix(1445,-2052,588,-835) (44/31,27/19) -> (27/11,32/13) Hyperbolic Matrix(3421,-4864,908,-1291) (27/19,64/45) -> (64/17,49/13) Hyperbolic Matrix(3419,-4864,2191,-3117) (64/45,37/26) -> (39/25,64/41) Hyperbolic Matrix(267,-380,26,-37) (37/26,10/7) -> (10/1,1/0) Hyperbolic Matrix(531,-760,160,-229) (10/7,33/23) -> (43/13,10/3) Hyperbolic Matrix(1217,-1748,793,-1139) (56/39,23/16) -> (23/15,20/13) Hyperbolic Matrix(1215,-1748,212,-305) (23/16,36/25) -> (40/7,23/4) Hyperbolic Matrix(949,-1368,607,-875) (36/25,13/9) -> (25/16,36/23) Hyperbolic Matrix(419,-608,235,-341) (13/9,16/11) -> (16/9,25/14) Hyperbolic Matrix(417,-608,131,-191) (16/11,19/13) -> (19/6,16/5) Hyperbolic Matrix(569,-836,130,-191) (19/13,3/2) -> (35/8,57/13) Hyperbolic Matrix(837,-1292,344,-531) (20/13,17/11) -> (17/7,56/23) Hyperbolic Matrix(835,-1292,148,-229) (17/11,31/20) -> (45/8,17/3) Hyperbolic Matrix(685,-1064,244,-379) (31/20,14/9) -> (14/5,45/16) Hyperbolic Matrix(683,-1064,147,-229) (14/9,39/25) -> (37/8,14/3) Hyperbolic Matrix(4673,-7296,1680,-2623) (64/41,25/16) -> (89/32,64/23) Hyperbolic Matrix(1977,-3116,578,-911) (11/7,41/26) -> (41/12,65/19) Hyperbolic Matrix(4143,-6536,2384,-3761) (41/26,71/45) -> (33/19,73/42) Hyperbolic Matrix(2167,-3420,505,-797) (71/45,30/19) -> (30/7,43/10) Hyperbolic Matrix(721,-1140,265,-419) (30/19,19/12) -> (19/7,30/11) Hyperbolic Matrix(191,-304,71,-113) (19/12,8/5) -> (8/3,19/7) Hyperbolic Matrix(1747,-2812,520,-837) (37/23,29/18) -> (47/14,37/11) Hyperbolic Matrix(2545,-4104,684,-1103) (29/18,50/31) -> (26/7,67/18) Hyperbolic Matrix(2167,-3496,918,-1481) (50/31,21/13) -> (59/25,26/11) Hyperbolic Matrix(1597,-2584,610,-987) (21/13,34/21) -> (34/13,55/21) Hyperbolic Matrix(797,-1292,446,-723) (34/21,13/8) -> (25/14,34/19) Hyperbolic Matrix(607,-988,94,-153) (13/8,44/27) -> (32/5,13/2) Hyperbolic Matrix(5129,-8360,1516,-2471) (44/27,75/46) -> (115/34,44/13) Hyperbolic Matrix(1025,-1672,583,-951) (75/46,31/19) -> (7/4,37/21) Hyperbolic Matrix(2319,-3800,440,-721) (18/11,59/36) -> (21/4,58/11) Hyperbolic Matrix(1899,-3116,788,-1293) (41/25,23/14) -> (53/22,41/17) Hyperbolic Matrix(647,-1064,346,-569) (23/14,28/17) -> (28/15,15/8) Hyperbolic Matrix(645,-1064,254,-419) (28/17,5/3) -> (33/13,28/11) Hyperbolic Matrix(1217,-2052,360,-607) (5/3,27/16) -> (27/8,71/21) Hyperbolic Matrix(989,-1672,404,-683) (27/16,22/13) -> (22/9,49/20) Hyperbolic Matrix(2735,-4636,1256,-2129) (61/36,39/23) -> (37/17,61/28) Hyperbolic Matrix(761,-1292,268,-455) (39/23,17/10) -> (17/6,37/13) Hyperbolic Matrix(2319,-3952,1315,-2241) (46/27,75/44) -> (37/21,30/17) Hyperbolic Matrix(4369,-7448,1182,-2015) (75/44,29/17) -> (85/23,37/10) Hyperbolic Matrix(6231,-10640,2582,-4409) (70/41,41/24) -> (111/46,70/29) Hyperbolic Matrix(1823,-3116,712,-1217) (41/24,12/7) -> (64/25,41/16) Hyperbolic Matrix(265,-456,111,-191) (12/7,19/11) -> (19/8,12/5) Hyperbolic Matrix(571,-988,241,-417) (19/11,26/15) -> (26/11,19/8) Hyperbolic Matrix(569,-988,110,-191) (26/15,33/19) -> (5/1,26/5) Hyperbolic Matrix(14515,-25232,5553,-9653) (73/42,113/65) -> (115/44,149/57) Hyperbolic Matrix(13375,-23256,4896,-8513) (113/65,40/23) -> (112/41,265/97) Hyperbolic Matrix(873,-1520,197,-343) (40/23,7/4) -> (31/7,40/9) Hyperbolic Matrix(1291,-2280,560,-989) (30/17,23/13) -> (53/23,30/13) Hyperbolic Matrix(2699,-4788,792,-1405) (39/22,55/31) -> (17/5,75/22) Hyperbolic Matrix(3991,-7144,2186,-3913) (34/19,77/43) -> (115/63,42/23) Hyperbolic Matrix(5813,-10412,1719,-3079) (77/43,43/24) -> (71/21,115/34) Hyperbolic Matrix(721,-1292,149,-267) (43/24,9/5) -> (29/6,5/1) Hyperbolic Matrix(419,-760,188,-341) (9/5,20/11) -> (20/9,29/13) Hyperbolic Matrix(3041,-5548,541,-987) (31/17,73/40) -> (73/13,45/8) Hyperbolic Matrix(8703,-15884,3185,-5813) (73/40,115/63) -> (153/56,41/15) Hyperbolic Matrix(1331,-2432,353,-645) (42/23,11/6) -> (49/13,34/9) Hyperbolic Matrix(455,-836,166,-305) (11/6,24/13) -> (52/19,11/4) Hyperbolic Matrix(2507,-4636,1028,-1901) (24/13,37/20) -> (39/16,100/41) Hyperbolic Matrix(647,-1216,141,-265) (15/8,17/9) -> (55/12,23/5) Hyperbolic Matrix(1445,-2736,441,-835) (17/9,19/10) -> (95/29,59/18) Hyperbolic Matrix(39,-76,19,-37) (19/10,2/1) -> (2/1,19/9) Parabolic Matrix(609,-1292,107,-227) (19/9,17/8) -> (17/3,57/10) Hyperbolic Matrix(607,-1292,179,-381) (17/8,15/7) -> (61/18,17/5) Hyperbolic Matrix(495,-1064,194,-417) (15/7,13/6) -> (51/20,23/9) Hyperbolic Matrix(1293,-2812,349,-759) (13/6,37/17) -> (37/10,63/17) Hyperbolic Matrix(1255,-2736,261,-569) (61/28,24/11) -> (24/5,53/11) Hyperbolic Matrix(835,-1824,244,-533) (24/11,11/5) -> (65/19,24/7) Hyperbolic Matrix(3953,-8740,1512,-3343) (42/19,73/33) -> (149/57,34/13) Hyperbolic Matrix(3229,-7144,739,-1635) (73/33,31/14) -> (83/19,35/8) Hyperbolic Matrix(343,-760,51,-113) (31/14,20/9) -> (20/3,7/1) Hyperbolic Matrix(647,-1444,289,-645) (29/13,38/17) -> (38/17,9/4) Parabolic Matrix(569,-1292,218,-495) (9/4,25/11) -> (13/5,47/18) Hyperbolic Matrix(267,-608,83,-189) (25/11,16/7) -> (16/5,13/4) Hyperbolic Matrix(531,-1216,100,-229) (16/7,39/17) -> (37/7,16/3) Hyperbolic Matrix(761,-1748,165,-379) (39/17,23/10) -> (23/5,37/8) Hyperbolic Matrix(2509,-5776,1089,-2507) (23/10,76/33) -> (76/33,53/23) Parabolic Matrix(1711,-3952,707,-1633) (30/13,37/16) -> (75/31,46/19) Hyperbolic Matrix(229,-532,65,-151) (37/16,7/3) -> (7/2,39/11) Hyperbolic Matrix(2775,-6536,1016,-2393) (40/17,33/14) -> (71/26,112/41) Hyperbolic Matrix(1483,-3572,394,-949) (12/5,53/22) -> (15/4,64/17) Hyperbolic Matrix(9577,-23104,3969,-9575) (41/17,152/63) -> (152/63,111/46) Parabolic Matrix(913,-2204,157,-379) (70/29,29/12) -> (29/5,6/1) Hyperbolic Matrix(2545,-6156,456,-1103) (29/12,75/31) -> (39/7,67/12) Hyperbolic Matrix(533,-1292,125,-303) (46/19,17/7) -> (17/4,30/7) Hyperbolic Matrix(2091,-5092,733,-1785) (56/23,95/39) -> (57/20,20/7) Hyperbolic Matrix(5053,-12312,1482,-3611) (95/39,39/16) -> (75/22,133/39) Hyperbolic Matrix(2243,-5472,389,-949) (100/41,61/25) -> (23/4,52/9) Hyperbolic Matrix(685,-1672,93,-227) (61/25,22/9) -> (22/3,15/2) Hyperbolic Matrix(2357,-5776,961,-2355) (49/20,76/31) -> (76/31,27/11) Parabolic Matrix(987,-2432,278,-685) (32/13,5/2) -> (71/20,32/9) Hyperbolic Matrix(571,-1444,225,-569) (5/2,38/15) -> (38/15,33/13) Parabolic Matrix(1103,-2812,253,-645) (28/11,51/20) -> (13/3,48/11) Hyperbolic Matrix(2851,-7296,846,-2165) (23/9,64/25) -> (64/19,91/27) Hyperbolic Matrix(1215,-3116,356,-913) (41/16,18/7) -> (58/17,41/12) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(4333,-11324,1221,-3191) (81/31,115/44) -> (39/11,71/20) Hyperbolic Matrix(2205,-5776,841,-2203) (55/21,76/29) -> (76/29,21/8) Parabolic Matrix(607,-1596,116,-305) (21/8,50/19) -> (26/5,21/4) Hyperbolic Matrix(721,-1900,159,-419) (79/30,29/11) -> (9/2,41/9) Hyperbolic Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(63955,-174724,23409,-63953) (265/97,418/153) -> (418/153,153/56) Parabolic Matrix(303,-836,83,-229) (11/4,36/13) -> (40/11,11/3) Hyperbolic Matrix(493,-1368,151,-419) (36/13,25/9) -> (13/4,36/11) Hyperbolic Matrix(4675,-12996,1681,-4673) (25/9,114/41) -> (114/41,89/32) Parabolic Matrix(1747,-4864,519,-1445) (64/23,39/14) -> (37/11,64/19) Hyperbolic Matrix(2053,-5776,729,-2051) (45/16,76/27) -> (76/27,31/11) Parabolic Matrix(1939,-5472,444,-1253) (31/11,48/17) -> (48/11,83/19) Hyperbolic Matrix(1975,-5624,374,-1065) (37/13,57/20) -> (95/18,37/7) Hyperbolic Matrix(343,-988,92,-265) (20/7,3/1) -> (41/11,56/15) Hyperbolic Matrix(531,-1672,121,-381) (22/7,19/6) -> (57/13,22/5) Hyperbolic Matrix(1787,-5852,313,-1025) (36/11,95/29) -> (57/10,40/7) Hyperbolic Matrix(647,-2128,173,-569) (23/7,56/17) -> (56/15,15/4) Hyperbolic Matrix(761,-2508,115,-379) (56/17,33/10) -> (33/5,20/3) Hyperbolic Matrix(1749,-5776,529,-1747) (33/10,76/23) -> (76/23,43/13) Parabolic Matrix(227,-760,23,-77) (10/3,57/17) -> (19/2,10/1) Hyperbolic Matrix(2469,-8284,442,-1483) (57/17,47/14) -> (67/12,95/17) Hyperbolic Matrix(3877,-13224,735,-2507) (133/39,58/17) -> (58/11,95/18) Hyperbolic Matrix(419,-1444,121,-417) (31/9,38/11) -> (38/11,7/2) Parabolic Matrix(683,-2432,107,-381) (32/9,57/16) -> (19/3,32/5) Hyperbolic Matrix(1597,-5776,441,-1595) (47/13,76/21) -> (76/21,29/8) Parabolic Matrix(419,-1520,94,-341) (29/8,40/11) -> (40/9,9/2) Hyperbolic Matrix(761,-2812,82,-303) (48/13,85/23) -> (9/1,28/3) Hyperbolic Matrix(6233,-23104,1681,-6231) (63/17,152/41) -> (152/41,89/24) Parabolic Matrix(343,-1444,81,-341) (21/5,38/9) -> (38/9,17/4) Parabolic Matrix(229,-988,35,-151) (43/10,13/3) -> (13/2,33/5) Hyperbolic Matrix(189,-836,26,-115) (22/5,31/7) -> (7/1,22/3) Hyperbolic Matrix(2851,-12996,625,-2849) (41/9,114/25) -> (114/25,73/16) Parabolic Matrix(267,-1444,49,-265) (27/5,38/7) -> (38/7,11/2) Parabolic Matrix(571,-3192,61,-341) (95/17,28/5) -> (28/3,19/2) Hyperbolic Matrix(191,-1444,25,-189) (15/2,38/5) -> (38/5,23/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,0,1) Matrix(267,-304,166,-189) -> Matrix(1,2,0,1) Matrix(265,-304,34,-39) -> Matrix(3,4,2,3) Matrix(721,-836,558,-647) -> Matrix(3,2,-2,-1) Matrix(647,-760,355,-417) -> Matrix(1,0,-2,1) Matrix(2129,-2508,1483,-1747) -> Matrix(1,0,-2,1) Matrix(837,-988,643,-759) -> Matrix(3,-4,-2,3) Matrix(1027,-1216,288,-341) -> Matrix(1,-2,0,1) Matrix(191,-228,31,-37) -> Matrix(1,4,0,1) Matrix(1825,-2204,1069,-1291) -> Matrix(1,2,-4,-7) Matrix(1823,-2204,378,-457) -> Matrix(1,2,0,1) Matrix(1443,-1748,440,-533) -> Matrix(1,2,4,9) Matrix(1063,-1292,376,-457) -> Matrix(1,2,0,1) Matrix(685,-836,186,-227) -> Matrix(3,4,2,3) Matrix(495,-608,92,-113) -> Matrix(5,4,6,5) Matrix(987,-1216,556,-685) -> Matrix(3,2,-2,-1) Matrix(797,-988,338,-419) -> Matrix(1,0,-4,1) Matrix(2051,-2584,785,-989) -> Matrix(1,0,0,1) Matrix(1747,-2204,302,-381) -> Matrix(1,2,0,1) Matrix(721,-912,151,-191) -> Matrix(1,-2,0,1) Matrix(419,-532,89,-113) -> Matrix(1,4,0,1) Matrix(835,-1064,299,-381) -> Matrix(1,2,2,5) Matrix(1369,-1748,773,-987) -> Matrix(1,2,0,1) Matrix(2317,-2964,684,-875) -> Matrix(5,8,8,13) Matrix(2849,-3648,624,-799) -> Matrix(5,6,4,5) Matrix(2431,-3116,653,-837) -> Matrix(1,0,2,1) Matrix(1179,-1520,854,-1101) -> Matrix(1,2,0,1) Matrix(1939,-2508,1145,-1481) -> Matrix(1,2,-2,-3) Matrix(645,-836,206,-267) -> Matrix(1,2,-2,-3) Matrix(3457,-4484,616,-799) -> Matrix(7,12,4,7) Matrix(761,-988,409,-531) -> Matrix(1,2,-4,-7) Matrix(2623,-3420,961,-1253) -> Matrix(3,4,20,27) Matrix(989,-1292,581,-759) -> Matrix(5,6,-16,-19) Matrix(115,-152,28,-37) -> Matrix(1,0,2,1) Matrix(113,-152,29,-39) -> Matrix(1,0,2,1) Matrix(951,-1292,251,-341) -> Matrix(1,0,0,1) Matrix(1787,-2432,809,-1101) -> Matrix(1,0,2,1) Matrix(3573,-4864,1060,-1443) -> Matrix(1,-2,2,-3) Matrix(723,-988,472,-645) -> Matrix(1,2,-2,-3) Matrix(3001,-4104,1140,-1559) -> Matrix(1,0,2,1) Matrix(2887,-3952,778,-1065) -> Matrix(1,0,0,1) Matrix(2053,-2812,1109,-1519) -> Matrix(1,0,-2,1) Matrix(609,-836,110,-151) -> Matrix(3,4,2,3) Matrix(607,-836,387,-533) -> Matrix(1,0,-2,1) Matrix(2203,-3040,937,-1293) -> Matrix(1,0,-4,1) Matrix(989,-1368,274,-379) -> Matrix(1,0,0,1) Matrix(493,-684,302,-419) -> Matrix(1,0,0,1) Matrix(647,-912,188,-265) -> Matrix(11,10,12,11) Matrix(2205,-3116,806,-1139) -> Matrix(5,4,26,21) Matrix(2203,-3116,1344,-1901) -> Matrix(13,10,-4,-3) Matrix(2089,-2964,456,-647) -> Matrix(13,8,8,5) Matrix(1445,-2052,588,-835) -> Matrix(3,2,4,3) Matrix(3421,-4864,908,-1291) -> Matrix(3,2,-2,-1) Matrix(3419,-4864,2191,-3117) -> Matrix(7,4,-16,-9) Matrix(267,-380,26,-37) -> Matrix(3,2,-2,-1) Matrix(531,-760,160,-229) -> Matrix(1,0,4,1) Matrix(1217,-1748,793,-1139) -> Matrix(5,2,-8,-3) Matrix(1215,-1748,212,-305) -> Matrix(9,2,4,1) Matrix(949,-1368,607,-875) -> Matrix(1,0,-2,1) Matrix(419,-608,235,-341) -> Matrix(1,0,2,1) Matrix(417,-608,131,-191) -> Matrix(1,0,6,1) Matrix(569,-836,130,-191) -> Matrix(3,-2,2,-1) Matrix(837,-1292,344,-531) -> Matrix(5,2,12,5) Matrix(835,-1292,148,-229) -> Matrix(1,2,0,1) Matrix(685,-1064,244,-379) -> Matrix(1,0,4,1) Matrix(683,-1064,147,-229) -> Matrix(5,2,2,1) Matrix(4673,-7296,1680,-2623) -> Matrix(11,4,30,11) Matrix(1977,-3116,578,-911) -> Matrix(21,4,26,5) Matrix(4143,-6536,2384,-3761) -> Matrix(1,0,10,1) Matrix(2167,-3420,505,-797) -> Matrix(27,4,20,3) Matrix(721,-1140,265,-419) -> Matrix(1,0,16,1) Matrix(191,-304,71,-113) -> Matrix(1,0,-2,1) Matrix(1747,-2812,520,-837) -> Matrix(1,-4,2,-7) Matrix(2545,-4104,684,-1103) -> Matrix(1,0,2,1) Matrix(2167,-3496,918,-1481) -> Matrix(1,0,-6,1) Matrix(1597,-2584,610,-987) -> Matrix(1,0,0,1) Matrix(797,-1292,446,-723) -> Matrix(1,0,0,1) Matrix(607,-988,94,-153) -> Matrix(1,-2,0,1) Matrix(5129,-8360,1516,-2471) -> Matrix(1,0,2,1) Matrix(1025,-1672,583,-951) -> Matrix(1,2,0,1) Matrix(2319,-3800,440,-721) -> Matrix(1,4,2,9) Matrix(1899,-3116,788,-1293) -> Matrix(1,2,4,9) Matrix(647,-1064,346,-569) -> Matrix(1,2,-4,-7) Matrix(645,-1064,254,-419) -> Matrix(5,6,4,5) Matrix(1217,-2052,360,-607) -> Matrix(3,2,4,3) Matrix(989,-1672,404,-683) -> Matrix(1,0,4,1) Matrix(2735,-4636,1256,-2129) -> Matrix(3,2,4,3) Matrix(761,-1292,268,-455) -> Matrix(5,2,12,5) Matrix(2319,-3952,1315,-2241) -> Matrix(7,2,-4,-1) Matrix(4369,-7448,1182,-2015) -> Matrix(7,2,-4,-1) Matrix(6231,-10640,2582,-4409) -> Matrix(1,0,8,1) Matrix(1823,-3116,712,-1217) -> Matrix(9,2,4,1) Matrix(265,-456,111,-191) -> Matrix(1,0,10,1) Matrix(571,-988,241,-417) -> Matrix(1,0,-16,1) Matrix(569,-988,110,-191) -> Matrix(1,0,-4,1) Matrix(14515,-25232,5553,-9653) -> Matrix(1,0,-4,1) Matrix(13375,-23256,4896,-8513) -> Matrix(1,0,4,1) Matrix(873,-1520,197,-343) -> Matrix(7,-2,4,-1) Matrix(1291,-2280,560,-989) -> Matrix(1,0,0,1) Matrix(2699,-4788,792,-1405) -> Matrix(3,8,4,11) Matrix(3991,-7144,2186,-3913) -> Matrix(1,0,-2,1) Matrix(5813,-10412,1719,-3079) -> Matrix(1,-2,2,-3) Matrix(721,-1292,149,-267) -> Matrix(1,0,0,1) Matrix(419,-760,188,-341) -> Matrix(3,2,4,3) Matrix(3041,-5548,541,-987) -> Matrix(1,2,0,1) Matrix(8703,-15884,3185,-5813) -> Matrix(1,0,8,1) Matrix(1331,-2432,353,-645) -> Matrix(1,0,2,1) Matrix(455,-836,166,-305) -> Matrix(1,0,6,1) Matrix(2507,-4636,1028,-1901) -> Matrix(3,2,4,3) Matrix(647,-1216,141,-265) -> Matrix(9,2,4,1) Matrix(1445,-2736,441,-835) -> Matrix(1,0,16,1) Matrix(39,-76,19,-37) -> Matrix(1,0,0,1) Matrix(609,-1292,107,-227) -> Matrix(23,-2,12,-1) Matrix(607,-1292,179,-381) -> Matrix(13,-2,20,-3) Matrix(495,-1064,194,-417) -> Matrix(7,-2,4,-1) Matrix(1293,-2812,349,-759) -> Matrix(1,0,-2,1) Matrix(1255,-2736,261,-569) -> Matrix(1,0,-2,1) Matrix(835,-1824,244,-533) -> Matrix(3,-4,4,-5) Matrix(3953,-8740,1512,-3343) -> Matrix(1,0,-2,1) Matrix(3229,-7144,739,-1635) -> Matrix(7,-2,4,-1) Matrix(343,-760,51,-113) -> Matrix(1,0,-2,1) Matrix(647,-1444,289,-645) -> Matrix(5,-4,4,-3) Matrix(569,-1292,218,-495) -> Matrix(1,0,0,1) Matrix(267,-608,83,-189) -> Matrix(1,0,2,1) Matrix(531,-1216,100,-229) -> Matrix(1,-2,2,-3) Matrix(761,-1748,165,-379) -> Matrix(1,2,0,1) Matrix(2509,-5776,1089,-2507) -> Matrix(1,0,0,1) Matrix(1711,-3952,707,-1633) -> Matrix(1,-2,4,-7) Matrix(229,-532,65,-151) -> Matrix(1,2,0,1) Matrix(2775,-6536,1016,-2393) -> Matrix(1,0,10,1) Matrix(1483,-3572,394,-949) -> Matrix(1,0,-4,1) Matrix(9577,-23104,3969,-9575) -> Matrix(1,0,0,1) Matrix(913,-2204,157,-379) -> Matrix(7,-2,4,-1) Matrix(2545,-6156,456,-1103) -> Matrix(37,-10,26,-7) Matrix(533,-1292,125,-303) -> Matrix(19,-6,16,-5) Matrix(2091,-5092,733,-1785) -> Matrix(17,-8,32,-15) Matrix(5053,-12312,1482,-3611) -> Matrix(37,-20,50,-27) Matrix(2243,-5472,389,-949) -> Matrix(7,-4,2,-1) Matrix(685,-1672,93,-227) -> Matrix(1,0,0,1) Matrix(2357,-5776,961,-2355) -> Matrix(1,0,0,1) Matrix(987,-2432,278,-685) -> Matrix(3,-2,2,-1) Matrix(571,-1444,225,-569) -> Matrix(9,-8,8,-7) Matrix(1103,-2812,253,-645) -> Matrix(1,0,0,1) Matrix(2851,-7296,846,-2165) -> Matrix(1,-4,2,-7) Matrix(1215,-3116,356,-913) -> Matrix(3,-10,4,-13) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(4333,-11324,1221,-3191) -> Matrix(1,2,0,1) Matrix(2205,-5776,841,-2203) -> Matrix(1,0,0,1) Matrix(607,-1596,116,-305) -> Matrix(1,0,2,1) Matrix(721,-1900,159,-419) -> Matrix(1,0,0,1) Matrix(115,-304,14,-37) -> Matrix(1,2,0,1) Matrix(63955,-174724,23409,-63953) -> Matrix(15,-2,98,-13) Matrix(303,-836,83,-229) -> Matrix(1,0,-2,1) Matrix(493,-1368,151,-419) -> Matrix(1,0,-2,1) Matrix(4675,-12996,1681,-4673) -> Matrix(19,-6,54,-17) Matrix(1747,-4864,519,-1445) -> Matrix(9,-4,16,-7) Matrix(2053,-5776,729,-2051) -> Matrix(1,0,0,1) Matrix(1939,-5472,444,-1253) -> Matrix(7,-2,4,-1) Matrix(1975,-5624,374,-1065) -> Matrix(17,-8,32,-15) Matrix(343,-988,92,-265) -> Matrix(3,-2,2,-1) Matrix(531,-1672,121,-381) -> Matrix(5,2,2,1) Matrix(1787,-5852,313,-1025) -> Matrix(13,2,6,1) Matrix(647,-2128,173,-569) -> Matrix(1,0,-2,1) Matrix(761,-2508,115,-379) -> Matrix(1,0,-2,1) Matrix(1749,-5776,529,-1747) -> Matrix(1,0,0,1) Matrix(227,-760,23,-77) -> Matrix(5,-2,-2,1) Matrix(2469,-8284,442,-1483) -> Matrix(53,-28,36,-19) Matrix(3877,-13224,735,-2507) -> Matrix(29,-22,62,-47) Matrix(419,-1444,121,-417) -> Matrix(17,-16,16,-15) Matrix(683,-2432,107,-381) -> Matrix(1,-8,0,1) Matrix(1597,-5776,441,-1595) -> Matrix(1,0,0,1) Matrix(419,-1520,94,-341) -> Matrix(1,2,0,1) Matrix(761,-2812,82,-303) -> Matrix(1,6,0,1) Matrix(6233,-23104,1681,-6231) -> Matrix(1,0,0,1) Matrix(343,-1444,81,-341) -> Matrix(19,-18,18,-17) Matrix(229,-988,35,-151) -> Matrix(3,-4,-2,3) Matrix(189,-836,26,-115) -> Matrix(1,-2,2,-3) Matrix(2851,-12996,625,-2849) -> Matrix(13,-12,12,-11) Matrix(267,-1444,49,-265) -> Matrix(15,-14,14,-13) Matrix(571,-3192,61,-341) -> Matrix(21,-32,2,-3) Matrix(191,-1444,25,-189) -> Matrix(11,-10,10,-9) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 45 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (0/1,1/0) 0 1 2/1 (0/1,1/0) 0 19 19/9 0/1 17 2 17/8 1/8 1 38 15/7 1/4 1 38 13/6 1/2 1 38 37/17 1/2 1 38 24/11 (1/2,1/1) 0 19 11/5 1/2 1 38 42/19 (0/1,1/2) 0 19 73/33 1/2 1 38 31/14 1/2 1 38 20/9 (1/2,1/1) 0 19 38/17 1/1 4 1 9/4 1/0 1 38 25/11 1/0 1 38 16/7 (0/1,1/1) 0 19 39/17 1/0 1 38 23/10 1/0 1 38 76/33 (0/1,1/0) 0 1 30/13 (0/1,1/0) 0 19 37/16 1/0 1 38 7/3 -1/2 1 38 40/17 (-1/3,0/1) 0 19 33/14 -1/4 1 38 26/11 (-1/8,0/1) 0 19 19/8 0/1 13 2 12/5 (0/1,1/5) 0 19 41/17 1/4 1 38 152/63 (0/1,1/4) 0 1 70/29 (0/1,1/4) 0 19 29/12 1/4 1 38 75/31 1/4 1 38 46/19 (1/4,2/7) 0 19 17/7 3/8 1 38 39/16 1/2 1 38 100/41 (1/2,1/1) 0 19 61/25 3/4 1 38 22/9 (0/1,1/2) 0 19 76/31 (0/1,1/2) 0 1 27/11 1/2 1 38 5/2 1/2 1 38 38/15 1/1 8 1 28/11 (1/1,3/2) 0 19 51/20 3/2 1 38 23/9 1/0 1 38 64/25 (1/1,2/1) 0 19 41/16 1/0 1 38 18/7 (0/1,1/0) 0 19 13/5 1/0 1 38 47/18 1/0 1 38 81/31 1/0 1 38 115/44 1/0 1 38 149/57 1/0 1 38 34/13 (0/1,1/0) 0 19 76/29 (0/1,1/0) 0 1 21/8 1/0 1 38 50/19 (0/1,1/2) 0 19 29/11 1/0 1 38 8/3 (-1/1,0/1) 0 19 19/7 0/1 9 2 30/11 (0/1,1/8) 0 19 71/26 1/6 1 38 112/41 (0/1,1/7) 0 19 418/153 1/7 2 1 153/56 1/6 1 38 41/15 1/6 1 38 11/4 1/4 1 38 36/13 (0/1,1/1) 0 19 25/9 1/4 1 38 114/41 1/3 6 1 64/23 (1/3,2/5) 0 19 39/14 1/2 1 38 14/5 (0/1,1/2) 0 19 76/27 (0/1,1/2) 0 1 31/11 1/2 1 38 17/6 1/4 1 38 37/13 1/2 1 38 57/20 1/2 15 2 20/7 (1/2,3/5) 0 19 3/1 1/0 1 38 19/6 0/1 5 2 16/5 (0/1,1/3) 0 19 13/4 1/2 1 38 36/11 (-1/1,0/1) 0 19 23/7 1/2 1 38 56/17 (1/2,1/1) 0 19 33/10 1/2 1 38 76/23 (0/1,1/2) 0 1 10/3 (0/1,1/2) 0 19 37/11 1/2 1 38 64/19 (3/5,2/3) 0 19 27/8 1/2 1 38 71/21 1/2 1 38 44/13 (1/2,3/5) 0 19 17/5 3/4 1 38 58/17 (3/4,10/13) 0 19 41/12 3/4 1 38 65/19 5/6 1 38 24/7 (5/6,1/1) 0 19 38/11 1/1 16 1 7/2 3/2 1 38 39/11 1/0 1 38 71/20 1/0 1 38 32/9 (3/1,1/0) 0 19 25/7 1/0 1 38 18/5 (0/1,1/0) 0 19 76/21 (0/1,1/0) 0 1 29/8 1/0 1 38 40/11 (-1/1,0/1) 0 19 11/3 1/2 1 38 37/10 1/0 1 38 63/17 1/0 1 38 152/41 (0/1,1/0) 0 1 26/7 (0/1,1/0) 0 19 67/18 1/2 1 38 41/11 3/2 1 38 56/15 (-1/1,1/0) 0 19 15/4 1/0 1 38 64/17 (0/1,1/1) 0 19 49/13 1/0 1 38 34/9 (0/1,1/0) 0 19 19/5 0/1 1 2 4/1 (0/1,1/1) 0 19 38/9 1/1 18 1 17/4 9/8 1 38 30/7 (5/4,4/3) 0 19 43/10 3/2 1 38 13/3 3/2 1 38 48/11 (1/1,3/2) 0 19 35/8 3/2 1 38 57/13 2/1 5 2 22/5 (2/1,1/0) 0 19 31/7 3/2 1 38 40/9 (1/1,2/1) 0 19 9/2 1/0 1 38 41/9 3/4 1 38 114/25 1/1 12 1 32/7 (1/1,3/2) 0 19 55/12 7/4 1 38 23/5 1/0 1 38 37/8 1/0 1 38 14/3 (2/1,1/0) 0 19 19/4 1/0 3 2 24/5 (-1/1,1/0) 0 19 29/6 1/0 1 38 5/1 1/0 1 38 26/5 (0/1,1/4) 0 19 21/4 1/2 1 38 58/11 (4/9,1/2) 0 19 95/18 1/2 15 2 37/7 1/2 1 38 16/3 (2/3,1/1) 0 19 38/7 1/1 14 1 11/2 5/4 1 38 39/7 3/2 1 38 67/12 3/2 1 38 28/5 (3/2,5/3) 0 19 73/13 3/2 1 38 45/8 3/2 1 38 17/3 7/4 1 38 57/10 2/1 17 2 40/7 (2/1,11/5) 0 19 23/4 5/2 1 38 52/9 (3/1,1/0) 0 19 29/5 1/0 1 38 6/1 (2/1,1/0) 0 19 19/3 1/0 7 2 32/5 (-5/1,1/0) 0 19 13/2 1/0 1 38 33/5 1/0 1 38 20/3 (-1/1,1/0) 0 19 7/1 1/0 1 38 22/3 (0/1,1/2) 0 19 15/2 3/4 1 38 38/5 1/1 10 1 8/1 (1/1,2/1) 0 19 9/1 1/0 1 38 28/3 (9/1,1/0) 0 19 19/2 1/0 11 2 10/1 (-2/1,1/0) 0 19 1/0 1/0 1 38 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(37,-76,18,-37) (2/1,19/9) -> (2/1,19/9) Reflection Matrix(609,-1292,107,-227) (19/9,17/8) -> (17/3,57/10) Hyperbolic Matrix(569,-1216,124,-265) (17/8,15/7) -> (55/12,23/5) Glide Reflection Matrix(495,-1064,194,-417) (15/7,13/6) -> (51/20,23/9) Hyperbolic Matrix(1293,-2812,349,-759) (13/6,37/17) -> (37/10,63/17) Hyperbolic Matrix(2129,-4636,873,-1901) (37/17,24/11) -> (39/16,100/41) Glide Reflection Matrix(835,-1824,244,-533) (24/11,11/5) -> (65/19,24/7) Hyperbolic Matrix(1101,-2432,292,-645) (11/5,42/19) -> (49/13,34/9) Glide Reflection Matrix(3953,-8740,1512,-3343) (42/19,73/33) -> (149/57,34/13) Hyperbolic Matrix(2507,-5548,446,-987) (73/33,31/14) -> (73/13,45/8) Glide Reflection Matrix(343,-760,51,-113) (31/14,20/9) -> (20/3,7/1) Hyperbolic Matrix(341,-760,153,-341) (20/9,38/17) -> (20/9,38/17) Reflection Matrix(305,-684,136,-305) (38/17,9/4) -> (38/17,9/4) Reflection Matrix(569,-1292,218,-495) (9/4,25/11) -> (13/5,47/18) Hyperbolic Matrix(267,-608,83,-189) (25/11,16/7) -> (16/5,13/4) Hyperbolic Matrix(531,-1216,100,-229) (16/7,39/17) -> (37/7,16/3) Hyperbolic Matrix(761,-1748,165,-379) (39/17,23/10) -> (23/5,37/8) Hyperbolic Matrix(1519,-3496,660,-1519) (23/10,76/33) -> (23/10,76/33) Reflection Matrix(989,-2280,429,-989) (76/33,30/13) -> (76/33,30/13) Reflection Matrix(1711,-3952,707,-1633) (30/13,37/16) -> (75/31,46/19) Hyperbolic Matrix(229,-532,65,-151) (37/16,7/3) -> (7/2,39/11) Hyperbolic Matrix(647,-1520,146,-343) (7/3,40/17) -> (31/7,40/9) Glide Reflection Matrix(2775,-6536,1016,-2393) (40/17,33/14) -> (71/26,112/41) Hyperbolic Matrix(419,-988,81,-191) (33/14,26/11) -> (5/1,26/5) Glide Reflection Matrix(417,-988,176,-417) (26/11,19/8) -> (26/11,19/8) Reflection Matrix(191,-456,80,-191) (19/8,12/5) -> (19/8,12/5) Reflection Matrix(1293,-3116,505,-1217) (12/5,41/17) -> (64/25,41/16) Glide Reflection Matrix(5167,-12464,2142,-5167) (41/17,152/63) -> (41/17,152/63) Reflection Matrix(4409,-10640,1827,-4409) (152/63,70/29) -> (152/63,70/29) Reflection Matrix(913,-2204,157,-379) (70/29,29/12) -> (29/5,6/1) Hyperbolic Matrix(2545,-6156,456,-1103) (29/12,75/31) -> (39/7,67/12) Hyperbolic Matrix(533,-1292,125,-303) (46/19,17/7) -> (17/4,30/7) Hyperbolic Matrix(531,-1292,187,-455) (17/7,39/16) -> (17/6,37/13) Glide Reflection Matrix(2243,-5472,389,-949) (100/41,61/25) -> (23/4,52/9) Hyperbolic Matrix(685,-1672,93,-227) (61/25,22/9) -> (22/3,15/2) Hyperbolic Matrix(683,-1672,279,-683) (22/9,76/31) -> (22/9,76/31) Reflection Matrix(1673,-4104,682,-1673) (76/31,27/11) -> (76/31,27/11) Reflection Matrix(835,-2052,247,-607) (27/11,5/2) -> (27/8,71/21) Glide Reflection Matrix(151,-380,60,-151) (5/2,38/15) -> (5/2,38/15) Reflection Matrix(419,-1064,165,-419) (38/15,28/11) -> (38/15,28/11) Reflection Matrix(1103,-2812,253,-645) (28/11,51/20) -> (13/3,48/11) Hyperbolic Matrix(951,-2432,253,-647) (23/9,64/25) -> (15/4,64/17) Glide Reflection Matrix(1215,-3116,356,-913) (41/16,18/7) -> (58/17,41/12) Hyperbolic Matrix(265,-684,74,-191) (18/7,13/5) -> (25/7,18/5) Hyperbolic Matrix(989,-2584,204,-533) (47/18,81/31) -> (29/6,5/1) Glide Reflection Matrix(4333,-11324,1221,-3191) (81/31,115/44) -> (39/11,71/20) Hyperbolic Matrix(10525,-27512,3852,-10069) (115/44,149/57) -> (153/56,41/15) Glide Reflection Matrix(987,-2584,377,-987) (34/13,76/29) -> (34/13,76/29) Reflection Matrix(1217,-3192,464,-1217) (76/29,21/8) -> (76/29,21/8) Reflection Matrix(607,-1596,116,-305) (21/8,50/19) -> (26/5,21/4) Hyperbolic Matrix(1559,-4104,419,-1103) (50/19,29/11) -> (26/7,67/18) Glide Reflection Matrix(115,-304,14,-37) (29/11,8/3) -> (8/1,9/1) Hyperbolic Matrix(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(1253,-3420,292,-797) (30/11,71/26) -> (30/7,43/10) Glide Reflection Matrix(17137,-46816,6273,-17137) (112/41,418/153) -> (112/41,418/153) Reflection Matrix(46817,-127908,17136,-46817) (418/153,153/56) -> (418/153,153/56) Reflection Matrix(1139,-3116,333,-911) (41/15,11/4) -> (41/12,65/19) Glide Reflection Matrix(303,-836,83,-229) (11/4,36/13) -> (40/11,11/3) Hyperbolic Matrix(493,-1368,151,-419) (36/13,25/9) -> (13/4,36/11) Hyperbolic Matrix(2051,-5700,738,-2051) (25/9,114/41) -> (25/9,114/41) Reflection Matrix(2623,-7296,943,-2623) (114/41,64/23) -> (114/41,64/23) Reflection Matrix(1747,-4864,519,-1445) (64/23,39/14) -> (37/11,64/19) Hyperbolic Matrix(381,-1064,82,-229) (39/14,14/5) -> (37/8,14/3) Glide Reflection Matrix(379,-1064,135,-379) (14/5,76/27) -> (14/5,76/27) Reflection Matrix(1673,-4712,594,-1673) (76/27,31/11) -> (76/27,31/11) Reflection Matrix(457,-1292,81,-229) (31/11,17/6) -> (45/8,17/3) Glide Reflection Matrix(1975,-5624,374,-1065) (37/13,57/20) -> (95/18,37/7) Hyperbolic Matrix(799,-2280,280,-799) (57/20,20/7) -> (57/20,20/7) Reflection Matrix(343,-988,92,-265) (20/7,3/1) -> (41/11,56/15) Hyperbolic Matrix(267,-836,61,-191) (3/1,19/6) -> (35/8,57/13) Glide Reflection Matrix(191,-608,60,-191) (19/6,16/5) -> (19/6,16/5) Reflection Matrix(533,-1748,93,-305) (36/11,23/7) -> (40/7,23/4) Glide Reflection Matrix(647,-2128,173,-569) (23/7,56/17) -> (56/15,15/4) Hyperbolic Matrix(761,-2508,115,-379) (56/17,33/10) -> (33/5,20/3) Hyperbolic Matrix(1519,-5016,460,-1519) (33/10,76/23) -> (33/10,76/23) Reflection Matrix(229,-760,69,-229) (76/23,10/3) -> (76/23,10/3) Reflection Matrix(113,-380,11,-37) (10/3,37/11) -> (10/1,1/0) Glide Reflection Matrix(1443,-4864,383,-1291) (64/19,27/8) -> (64/17,49/13) Glide Reflection Matrix(1595,-5396,449,-1519) (71/21,44/13) -> (71/20,32/9) Glide Reflection Matrix(875,-2964,191,-647) (44/13,17/5) -> (32/7,55/12) Glide Reflection Matrix(647,-2204,123,-419) (17/5,58/17) -> (21/4,58/11) Glide Reflection Matrix(265,-912,77,-265) (24/7,38/11) -> (24/7,38/11) Reflection Matrix(153,-532,44,-153) (38/11,7/2) -> (38/11,7/2) Reflection Matrix(341,-1216,53,-189) (32/9,25/7) -> (32/5,13/2) Glide Reflection Matrix(379,-1368,105,-379) (18/5,76/21) -> (18/5,76/21) Reflection Matrix(1217,-4408,336,-1217) (76/21,29/8) -> (76/21,29/8) Reflection Matrix(419,-1520,94,-341) (29/8,40/11) -> (40/9,9/2) Hyperbolic Matrix(227,-836,41,-151) (11/3,37/10) -> (11/2,39/7) Glide Reflection Matrix(5167,-19152,1394,-5167) (63/17,152/41) -> (63/17,152/41) Reflection Matrix(1065,-3952,287,-1065) (152/41,26/7) -> (152/41,26/7) Reflection Matrix(837,-3116,184,-685) (67/18,41/11) -> (9/2,41/9) Glide Reflection Matrix(341,-1292,90,-341) (34/9,19/5) -> (34/9,19/5) Reflection Matrix(39,-152,10,-39) (19/5,4/1) -> (19/5,4/1) Reflection Matrix(37,-152,9,-37) (4/1,38/9) -> (4/1,38/9) Reflection Matrix(305,-1292,72,-305) (38/9,17/4) -> (38/9,17/4) Reflection Matrix(229,-988,35,-151) (43/10,13/3) -> (13/2,33/5) Hyperbolic Matrix(1027,-4484,183,-799) (48/11,35/8) -> (28/5,73/13) Glide Reflection Matrix(571,-2508,130,-571) (57/13,22/5) -> (57/13,22/5) Reflection Matrix(189,-836,26,-115) (22/5,31/7) -> (7/1,22/3) Hyperbolic Matrix(2051,-9348,450,-2051) (41/9,114/25) -> (41/9,114/25) Reflection Matrix(799,-3648,175,-799) (114/25,32/7) -> (114/25,32/7) Reflection Matrix(113,-532,24,-113) (14/3,19/4) -> (14/3,19/4) Reflection Matrix(191,-912,40,-191) (19/4,24/5) -> (19/4,24/5) Reflection Matrix(457,-2204,79,-381) (24/5,29/6) -> (52/9,29/5) Glide Reflection Matrix(2089,-11020,396,-2089) (58/11,95/18) -> (58/11,95/18) Reflection Matrix(113,-608,21,-113) (16/3,38/7) -> (16/3,38/7) Reflection Matrix(153,-836,28,-153) (38/7,11/2) -> (38/7,11/2) Reflection Matrix(381,-2128,41,-229) (67/12,28/5) -> (9/1,28/3) Glide Reflection Matrix(799,-4560,140,-799) (57/10,40/7) -> (57/10,40/7) Reflection Matrix(37,-228,6,-37) (6/1,19/3) -> (6/1,19/3) Reflection Matrix(191,-1216,30,-191) (19/3,32/5) -> (19/3,32/5) Reflection Matrix(151,-1140,20,-151) (15/2,38/5) -> (15/2,38/5) Reflection Matrix(39,-304,5,-39) (38/5,8/1) -> (38/5,8/1) Reflection Matrix(113,-1064,12,-113) (28/3,19/2) -> (28/3,19/2) Reflection Matrix(39,-380,4,-39) (19/2,10/1) -> (19/2,10/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,0,-1) (0/1,2/1) -> (0/1,1/0) Matrix(37,-76,18,-37) -> Matrix(1,0,0,-1) (2/1,19/9) -> (0/1,1/0) Matrix(609,-1292,107,-227) -> Matrix(23,-2,12,-1) Matrix(569,-1216,124,-265) -> Matrix(9,-2,4,-1) Matrix(495,-1064,194,-417) -> Matrix(7,-2,4,-1) Matrix(1293,-2812,349,-759) -> Matrix(1,0,-2,1) 0/1 Matrix(2129,-4636,873,-1901) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(835,-1824,244,-533) -> Matrix(3,-4,4,-5) 1/1 Matrix(1101,-2432,292,-645) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(3953,-8740,1512,-3343) -> Matrix(1,0,-2,1) 0/1 Matrix(2507,-5548,446,-987) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(343,-760,51,-113) -> Matrix(1,0,-2,1) 0/1 Matrix(341,-760,153,-341) -> Matrix(3,-2,4,-3) (20/9,38/17) -> (1/2,1/1) Matrix(305,-684,136,-305) -> Matrix(-1,2,0,1) (38/17,9/4) -> (1/1,1/0) Matrix(569,-1292,218,-495) -> Matrix(1,0,0,1) Matrix(267,-608,83,-189) -> Matrix(1,0,2,1) 0/1 Matrix(531,-1216,100,-229) -> Matrix(1,-2,2,-3) 1/1 Matrix(761,-1748,165,-379) -> Matrix(1,2,0,1) 1/0 Matrix(1519,-3496,660,-1519) -> Matrix(1,0,0,-1) (23/10,76/33) -> (0/1,1/0) Matrix(989,-2280,429,-989) -> Matrix(1,0,0,-1) (76/33,30/13) -> (0/1,1/0) Matrix(1711,-3952,707,-1633) -> Matrix(1,-2,4,-7) Matrix(229,-532,65,-151) -> Matrix(1,2,0,1) 1/0 Matrix(647,-1520,146,-343) -> Matrix(7,2,4,1) Matrix(2775,-6536,1016,-2393) -> Matrix(1,0,10,1) 0/1 Matrix(419,-988,81,-191) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(417,-988,176,-417) -> Matrix(-1,0,16,1) (26/11,19/8) -> (-1/8,0/1) Matrix(191,-456,80,-191) -> Matrix(1,0,10,-1) (19/8,12/5) -> (0/1,1/5) Matrix(1293,-3116,505,-1217) -> Matrix(9,-2,4,-1) Matrix(5167,-12464,2142,-5167) -> Matrix(1,0,8,-1) (41/17,152/63) -> (0/1,1/4) Matrix(4409,-10640,1827,-4409) -> Matrix(1,0,8,-1) (152/63,70/29) -> (0/1,1/4) Matrix(913,-2204,157,-379) -> Matrix(7,-2,4,-1) Matrix(2545,-6156,456,-1103) -> Matrix(37,-10,26,-7) Matrix(533,-1292,125,-303) -> Matrix(19,-6,16,-5) Matrix(531,-1292,187,-455) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(2243,-5472,389,-949) -> Matrix(7,-4,2,-1) Matrix(685,-1672,93,-227) -> Matrix(1,0,0,1) Matrix(683,-1672,279,-683) -> Matrix(1,0,4,-1) (22/9,76/31) -> (0/1,1/2) Matrix(1673,-4104,682,-1673) -> Matrix(1,0,4,-1) (76/31,27/11) -> (0/1,1/2) Matrix(835,-2052,247,-607) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(151,-380,60,-151) -> Matrix(3,-2,4,-3) (5/2,38/15) -> (1/2,1/1) Matrix(419,-1064,165,-419) -> Matrix(5,-6,4,-5) (38/15,28/11) -> (1/1,3/2) Matrix(1103,-2812,253,-645) -> Matrix(1,0,0,1) Matrix(951,-2432,253,-647) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1215,-3116,356,-913) -> Matrix(3,-10,4,-13) Matrix(265,-684,74,-191) -> Matrix(1,0,0,1) Matrix(989,-2584,204,-533) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(4333,-11324,1221,-3191) -> Matrix(1,2,0,1) 1/0 Matrix(10525,-27512,3852,-10069) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(987,-2584,377,-987) -> Matrix(1,0,0,-1) (34/13,76/29) -> (0/1,1/0) Matrix(1217,-3192,464,-1217) -> Matrix(1,0,0,-1) (76/29,21/8) -> (0/1,1/0) Matrix(607,-1596,116,-305) -> Matrix(1,0,2,1) 0/1 Matrix(1559,-4104,419,-1103) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(115,-304,14,-37) -> Matrix(1,2,0,1) 1/0 Matrix(113,-304,42,-113) -> Matrix(-1,0,2,1) (8/3,19/7) -> (-1/1,0/1) Matrix(419,-1140,154,-419) -> Matrix(1,0,16,-1) (19/7,30/11) -> (0/1,1/8) Matrix(1253,-3420,292,-797) -> Matrix(27,-4,20,-3) Matrix(17137,-46816,6273,-17137) -> Matrix(1,0,14,-1) (112/41,418/153) -> (0/1,1/7) Matrix(46817,-127908,17136,-46817) -> Matrix(13,-2,84,-13) (418/153,153/56) -> (1/7,1/6) Matrix(1139,-3116,333,-911) -> Matrix(21,-4,26,-5) Matrix(303,-836,83,-229) -> Matrix(1,0,-2,1) 0/1 Matrix(493,-1368,151,-419) -> Matrix(1,0,-2,1) 0/1 Matrix(2051,-5700,738,-2051) -> Matrix(7,-2,24,-7) (25/9,114/41) -> (1/4,1/3) Matrix(2623,-7296,943,-2623) -> Matrix(11,-4,30,-11) (114/41,64/23) -> (1/3,2/5) Matrix(1747,-4864,519,-1445) -> Matrix(9,-4,16,-7) 1/2 Matrix(381,-1064,82,-229) -> Matrix(5,-2,2,-1) Matrix(379,-1064,135,-379) -> Matrix(1,0,4,-1) (14/5,76/27) -> (0/1,1/2) Matrix(1673,-4712,594,-1673) -> Matrix(1,0,4,-1) (76/27,31/11) -> (0/1,1/2) Matrix(457,-1292,81,-229) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1975,-5624,374,-1065) -> Matrix(17,-8,32,-15) 1/2 Matrix(799,-2280,280,-799) -> Matrix(11,-6,20,-11) (57/20,20/7) -> (1/2,3/5) Matrix(343,-988,92,-265) -> Matrix(3,-2,2,-1) 1/1 Matrix(267,-836,61,-191) -> Matrix(3,2,2,1) Matrix(191,-608,60,-191) -> Matrix(1,0,6,-1) (19/6,16/5) -> (0/1,1/3) Matrix(533,-1748,93,-305) -> Matrix(9,-2,4,-1) Matrix(647,-2128,173,-569) -> Matrix(1,0,-2,1) 0/1 Matrix(761,-2508,115,-379) -> Matrix(1,0,-2,1) 0/1 Matrix(1519,-5016,460,-1519) -> Matrix(1,0,4,-1) (33/10,76/23) -> (0/1,1/2) Matrix(229,-760,69,-229) -> Matrix(1,0,4,-1) (76/23,10/3) -> (0/1,1/2) Matrix(113,-380,11,-37) -> Matrix(3,-2,-2,1) Matrix(1443,-4864,383,-1291) -> Matrix(3,-2,-2,1) Matrix(1595,-5396,449,-1519) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(875,-2964,191,-647) -> Matrix(13,-8,8,-5) Matrix(647,-2204,123,-419) -> Matrix(3,-2,10,-7) Matrix(265,-912,77,-265) -> Matrix(11,-10,12,-11) (24/7,38/11) -> (5/6,1/1) Matrix(153,-532,44,-153) -> Matrix(5,-6,4,-5) (38/11,7/2) -> (1/1,3/2) Matrix(341,-1216,53,-189) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(379,-1368,105,-379) -> Matrix(1,0,0,-1) (18/5,76/21) -> (0/1,1/0) Matrix(1217,-4408,336,-1217) -> Matrix(1,0,0,-1) (76/21,29/8) -> (0/1,1/0) Matrix(419,-1520,94,-341) -> Matrix(1,2,0,1) 1/0 Matrix(227,-836,41,-151) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(5167,-19152,1394,-5167) -> Matrix(1,0,0,-1) (63/17,152/41) -> (0/1,1/0) Matrix(1065,-3952,287,-1065) -> Matrix(1,0,0,-1) (152/41,26/7) -> (0/1,1/0) Matrix(837,-3116,184,-685) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(341,-1292,90,-341) -> Matrix(1,0,0,-1) (34/9,19/5) -> (0/1,1/0) Matrix(39,-152,10,-39) -> Matrix(1,0,2,-1) (19/5,4/1) -> (0/1,1/1) Matrix(37,-152,9,-37) -> Matrix(1,0,2,-1) (4/1,38/9) -> (0/1,1/1) Matrix(305,-1292,72,-305) -> Matrix(17,-18,16,-17) (38/9,17/4) -> (1/1,9/8) Matrix(229,-988,35,-151) -> Matrix(3,-4,-2,3) Matrix(1027,-4484,183,-799) -> Matrix(7,-12,4,-7) *** -> (3/2,2/1) Matrix(571,-2508,130,-571) -> Matrix(-1,4,0,1) (57/13,22/5) -> (2/1,1/0) Matrix(189,-836,26,-115) -> Matrix(1,-2,2,-3) 1/1 Matrix(2051,-9348,450,-2051) -> Matrix(7,-6,8,-7) (41/9,114/25) -> (3/4,1/1) Matrix(799,-3648,175,-799) -> Matrix(5,-6,4,-5) (114/25,32/7) -> (1/1,3/2) Matrix(113,-532,24,-113) -> Matrix(-1,4,0,1) (14/3,19/4) -> (2/1,1/0) Matrix(191,-912,40,-191) -> Matrix(1,2,0,-1) (19/4,24/5) -> (-1/1,1/0) Matrix(457,-2204,79,-381) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(2089,-11020,396,-2089) -> Matrix(17,-8,36,-17) (58/11,95/18) -> (4/9,1/2) Matrix(113,-608,21,-113) -> Matrix(5,-4,6,-5) (16/3,38/7) -> (2/3,1/1) Matrix(153,-836,28,-153) -> Matrix(9,-10,8,-9) (38/7,11/2) -> (1/1,5/4) Matrix(381,-2128,41,-229) -> Matrix(15,-22,2,-3) Matrix(799,-4560,140,-799) -> Matrix(21,-44,10,-21) (57/10,40/7) -> (2/1,11/5) Matrix(37,-228,6,-37) -> Matrix(-1,4,0,1) (6/1,19/3) -> (2/1,1/0) Matrix(191,-1216,30,-191) -> Matrix(1,10,0,-1) (19/3,32/5) -> (-5/1,1/0) Matrix(151,-1140,20,-151) -> Matrix(7,-6,8,-7) (15/2,38/5) -> (3/4,1/1) Matrix(39,-304,5,-39) -> Matrix(3,-4,2,-3) (38/5,8/1) -> (1/1,2/1) Matrix(113,-1064,12,-113) -> Matrix(-1,18,0,1) (28/3,19/2) -> (9/1,1/0) Matrix(39,-380,4,-39) -> Matrix(1,4,0,-1) (19/2,10/1) -> (-2/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.