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): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 80 Genus: 105 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -14/31 -12/29 -10/27 -1/3 -4/21 -2/19 0/1 2/15 5/29 3/14 7/27 23/79 4/13 1/3 9/25 5/12 1/2 6/11 13/21 7/10 5/7 15/19 8/9 1/1 9/8 8/7 19/15 7/5 10/7 3/2 52/33 21/13 5/3 76/43 9/5 11/6 2/1 11/5 71/31 7/3 12/5 5/2 171/67 25/9 3/1 16/5 13/4 10/3 118/35 105/31 7/2 40/11 11/3 67/18 27/7 4/1 13/3 22/5 9/2 14/3 5/1 57/11 26/5 16/3 11/2 28/5 29/5 6/1 13/2 20/3 7/1 22/3 15/2 8/1 25/3 26/3 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/4 -6/13 3/10 1/3 -23/50 7/20 -17/37 3/8 1/2 -11/24 1/4 -16/35 1/2 1/1 -5/11 1/6 1/4 -14/31 1/4 -9/20 1/4 -4/9 3/10 1/3 -23/52 11/32 -19/43 5/14 3/8 -15/34 1/4 -26/59 1/3 1/2 -11/25 3/8 1/2 -18/41 0/1 1/2 -7/16 1/4 -17/39 1/6 1/4 -27/62 1/4 -10/23 1/5 1/4 -3/7 1/4 3/10 -8/19 1/3 1/2 -13/31 1/4 3/10 -5/12 1/4 -12/29 1/4 -19/46 1/4 -7/17 1/4 3/10 -23/56 1/4 -39/95 1/4 5/18 -55/134 9/32 -16/39 2/7 3/10 -9/22 5/16 -11/27 1/4 3/10 -24/59 3/10 1/3 -13/32 5/16 -2/5 1/3 1/2 -9/23 1/4 1/2 -34/87 2/7 3/10 -25/64 3/8 -16/41 1/4 1/3 -7/18 1/4 -12/31 1/3 5/14 -5/13 1/4 1/2 -23/60 5/16 -18/47 3/10 4/13 -13/34 9/28 -8/21 1/3 7/20 -11/29 3/8 7/18 -3/8 3/8 -10/27 1/2 -17/46 5/8 -7/19 1/2 1/0 -25/68 1/0 -18/49 0/1 1/6 -11/30 1/0 -4/11 1/3 1/2 -5/14 3/8 -6/17 1/3 1/2 -7/20 5/12 -15/43 5/12 11/26 -8/23 4/9 1/2 -1/3 1/4 1/2 -5/16 1/0 -4/13 0/1 1/0 -11/36 1/8 -7/23 1/6 1/4 -3/10 1/4 -14/47 1/3 1/2 -11/37 1/4 1/2 -8/27 1/3 5/14 -13/44 11/28 -18/61 5/12 3/7 -5/17 5/12 1/2 -2/7 1/2 1/1 -9/32 1/0 -7/25 -1/2 1/0 -26/93 -1/2 0/1 -19/68 -1/4 -12/43 0/1 1/2 -5/18 -1/4 -8/29 0/1 1/12 -11/40 1/8 -3/11 1/6 1/4 -4/15 1/3 1/2 -9/34 3/8 -14/53 7/18 2/5 -19/72 3/8 -24/91 2/5 1/2 -5/19 5/12 1/2 -6/23 1/2 -1/4 1/0 -6/25 1/5 3/14 -5/21 1/4 5/18 -4/17 1/3 3/8 -3/13 3/8 1/2 -2/9 1/2 1/1 -3/14 1/0 -7/33 -1/2 1/0 -4/19 -1/6 0/1 -5/24 1/12 -1/5 1/4 1/2 -4/21 1/2 -7/37 1/2 7/12 -3/16 3/4 -11/59 1/2 1/0 -8/43 1/2 1/1 -5/27 1/2 1/0 -7/38 7/8 -16/87 1/1 15/14 -9/49 5/4 3/2 -2/11 0/1 1/0 -5/28 1/0 -3/17 1/2 1/0 -10/57 2/1 1/0 -7/40 1/0 -18/103 1/0 -11/63 -9/2 1/0 -4/23 -1/1 -1/2 -5/29 -1/2 -1/4 -6/35 -1/10 0/1 -1/6 1/4 -4/25 0/1 1/8 -3/19 1/4 3/10 -2/13 1/3 1/2 -1/7 1/2 1/0 -2/15 1/1 1/0 -5/38 1/0 -8/61 -2/1 -3/2 -3/23 -1/2 1/0 -4/31 -1/6 0/1 -1/8 1/4 -2/17 -1/2 0/1 -1/9 1/4 1/2 -2/19 1/2 -1/10 1/0 0/1 0/1 1/2 1/10 1/4 1/9 1/2 1/0 1/8 1/4 2/15 1/2 1/7 1/2 1/0 1/6 1/0 5/29 0/1 9/52 1/20 4/23 0/1 1/10 7/40 1/8 3/17 1/6 1/4 2/11 1/4 1/3 3/16 3/4 4/21 -1/1 1/0 5/26 -1/8 1/5 1/4 1/2 4/19 2/5 1/2 3/14 1/2 5/23 1/2 5/8 2/9 1/2 1/1 1/4 1/0 7/27 0/1 13/50 1/28 6/23 0/1 1/14 5/19 1/8 1/6 14/53 0/1 1/6 9/34 1/4 4/15 1/6 1/5 7/26 1/4 10/37 1/4 2/7 3/11 1/4 1/2 2/7 0/1 1/4 11/38 7/24 9/31 3/10 5/16 16/55 15/46 1/3 23/79 1/3 30/103 1/3 29/86 7/24 7/20 12/41 7/18 2/5 5/17 1/4 1/2 8/27 1/3 1/2 3/10 3/8 4/13 1/2 5/16 5/8 16/51 1/2 2/3 11/35 1/2 3/4 6/19 3/4 1/1 7/22 1/0 1/3 1/2 1/0 6/17 -1/2 0/1 5/14 -1/8 9/25 0/1 13/36 1/28 4/11 0/1 1/10 11/30 1/4 7/19 1/6 1/4 17/46 1/8 10/27 0/1 1/6 3/8 1/4 14/37 1/4 11/29 1/4 7/26 19/50 1/4 8/21 2/7 3/10 5/13 1/4 1/2 7/18 3/8 2/5 1/3 1/2 7/17 7/16 1/2 5/12 1/2 13/31 1/2 13/24 21/50 9/16 8/19 1/2 4/7 11/26 7/12 25/59 5/8 19/30 14/33 2/3 3/4 3/7 1/2 3/4 19/44 5/4 16/37 0/1 1/2 29/67 3/4 5/6 13/30 1/0 36/83 1/2 23/53 1/2 3/4 10/23 1/2 1/1 17/39 1/2 3/4 7/16 1/0 11/25 1/4 1/2 26/59 1/2 15/34 7/12 4/9 3/4 1/1 1/2 1/4 6/11 1/2 11/20 11/20 16/29 1/2 4/7 5/9 1/2 5/8 4/7 1/2 1/1 11/19 3/4 5/6 7/12 5/4 17/29 5/4 3/2 27/46 7/4 10/17 3/2 2/1 23/39 7/2 1/0 13/22 1/0 16/27 5/1 1/0 3/5 -1/2 1/0 14/23 -1/2 0/1 39/64 1/0 25/41 -1/2 1/0 11/18 -1/4 8/13 -1/8 0/1 13/21 0/1 18/29 0/1 1/24 5/8 1/8 22/35 1/6 1/5 17/27 1/6 1/4 29/46 1/4 12/19 0/1 1/2 7/11 1/6 1/4 2/3 1/3 1/2 9/13 9/20 1/2 7/10 1/2 19/27 1/2 19/36 50/71 33/62 8/15 31/44 15/28 12/17 1/2 6/11 17/24 9/16 22/31 4/7 15/26 49/69 7/12 41/70 27/38 19/32 5/7 1/2 5/8 28/39 1/2 2/3 23/32 3/4 18/25 3/5 5/8 31/43 9/14 13/20 13/18 11/16 8/11 5/6 1/1 3/4 1/0 13/17 -1/2 1/0 10/13 0/1 1/2 27/35 1/2 3/4 17/22 1/0 7/9 -1/2 1/0 18/23 -1/2 0/1 11/14 -1/4 15/19 0/1 19/24 1/12 4/5 0/1 1/4 9/11 1/4 1/2 14/17 0/1 1/2 19/23 1/4 1/2 5/6 1/4 21/25 3/8 1/2 16/19 1/3 1/2 11/13 3/8 1/2 6/7 1/3 3/8 13/15 3/8 1/2 7/8 7/16 8/9 1/2 9/10 9/16 1/1 1/2 1/0 9/8 1/2 17/15 1/2 15/28 8/7 1/2 4/7 23/20 7/12 15/13 11/18 5/8 22/19 9/14 2/3 29/25 1/2 3/4 36/31 1/2 2/3 7/6 5/8 13/11 1/2 3/4 19/16 3/4 25/21 3/4 5/6 31/26 7/8 6/5 1/2 1/1 11/9 1/2 5/8 27/22 3/4 43/35 5/8 9/14 16/13 2/3 7/10 37/30 3/4 21/17 7/10 3/4 5/4 3/4 19/15 1/1 14/11 1/1 5/4 23/18 1/0 9/7 1/2 1/0 31/24 3/4 22/17 3/2 2/1 13/10 1/0 4/3 1/2 1/1 19/14 1/0 53/39 3/2 1/0 87/64 9/4 34/25 4/1 1/0 15/11 -3/2 1/0 26/19 -1/2 0/1 37/27 -1/4 -1/6 11/8 1/4 51/37 1/2 1/0 91/66 1/4 40/29 0/1 1/2 69/50 1/2 29/21 1/2 1/0 18/13 -1/2 0/1 7/5 1/4 1/2 10/7 1/2 13/9 1/2 7/12 16/11 1/2 2/3 19/13 1/2 5/8 22/15 1/2 2/3 3/2 3/4 20/13 1/2 1/1 37/24 3/4 17/11 1/2 1/0 31/20 1/2 14/9 1/2 2/3 39/25 7/10 3/4 103/66 3/4 64/41 1/2 2/3 25/16 3/4 11/7 7/10 3/4 52/33 3/4 93/59 3/4 77/102 134/85 28/37 53/70 41/26 3/4 30/19 17/22 7/9 19/12 13/16 8/5 7/8 1/1 21/13 1/1 34/21 1/1 25/24 13/8 9/8 18/11 4/3 3/2 41/25 3/2 1/0 105/64 1/0 169/103 1/1 64/39 1/1 3/2 23/14 5/4 5/3 1/2 1/0 32/19 1/2 27/16 3/4 49/29 1/2 1/0 22/13 1/2 1/1 61/36 1/0 39/23 1/2 3/4 56/33 2/3 3/4 73/43 3/4 5/6 17/10 1/0 12/7 5/6 1/1 31/18 13/12 19/11 5/4 3/2 83/48 5/4 64/37 1/1 3/2 45/26 1/0 26/15 3/2 2/1 33/19 3/2 1/0 7/4 1/0 51/29 1/4 1/2 44/25 0/1 1/2 37/21 1/4 1/2 30/17 0/1 1/4 83/47 1/4 1/2 53/30 5/12 76/43 1/2 23/13 1/2 3/4 62/35 0/1 1/2 39/22 3/4 16/9 1/1 1/0 57/32 1/4 41/23 1/2 3/4 66/37 1/2 1/1 25/14 3/4 34/19 3/2 2/1 9/5 1/2 1/0 29/16 1/0 20/11 0/1 1/2 11/6 1/2 24/13 1/2 2/3 13/7 1/2 3/4 2/1 1/2 1/1 19/9 11/10 9/8 17/8 5/4 15/7 5/4 3/2 13/6 5/4 11/5 3/2 1/0 20/9 0/1 1/2 9/4 5/4 25/11 3/2 7/4 41/18 1/0 16/7 3/2 2/1 71/31 2/1 126/55 2/1 21/10 55/24 9/4 94/41 2/1 5/2 39/17 5/2 1/0 62/27 2/1 1/0 23/10 1/0 30/13 -1/1 1/0 37/16 3/4 7/3 3/2 1/0 12/5 1/0 17/7 -1/2 1/0 39/16 -1/4 22/9 0/1 1/2 71/29 1/2 1/0 49/20 1/0 27/11 -1/2 1/0 5/2 1/0 28/11 1/2 2/3 51/20 3/4 74/29 1/2 1/1 171/67 1/1 97/38 1/0 23/9 1/2 1/0 87/34 9/16 64/25 5/8 2/3 41/16 3/4 18/7 3/4 1/1 49/19 1/1 31/12 5/4 13/5 3/2 1/0 60/23 -5/2 -2/1 47/18 -3/4 81/31 -1/2 -1/4 115/44 1/0 34/13 -1/4 0/1 21/8 1/0 8/3 1/2 1/1 19/7 7/10 3/4 68/25 3/4 13/17 49/18 3/4 79/29 3/4 17/22 109/40 3/4 30/11 4/5 5/6 41/15 5/6 7/8 52/19 1/2 1/1 11/4 7/8 25/9 1/1 39/14 29/28 14/5 1/1 11/10 17/6 5/4 3/1 3/2 1/0 22/7 3/2 2/1 19/6 1/0 73/23 11/4 17/6 54/17 3/1 19/6 35/11 7/2 1/0 51/16 1/0 16/5 4/1 1/0 13/4 1/0 36/11 -6/1 1/0 95/29 -11/2 1/0 59/18 1/0 23/7 -7/2 1/0 10/3 -1/1 1/0 37/11 1/2 1/0 64/19 3/2 2/1 91/27 11/2 1/0 118/35 1/0 27/8 1/0 44/13 -3/2 -1/1 105/31 -1/1 166/49 -1/1 -9/10 61/18 -3/4 17/5 -1/2 1/0 24/7 -1/6 0/1 79/23 0/1 55/16 1/16 31/9 1/6 1/4 38/11 1/2 1/1 7/2 1/0 32/9 0/1 1/2 57/16 1/0 25/7 1/4 1/2 68/19 1/2 3/5 43/12 3/4 18/5 0/1 1/2 47/13 1/4 3/10 29/8 3/8 40/11 1/2 11/3 1/2 3/4 26/7 1/2 1/1 93/25 1/2 1/0 67/18 1/2 108/29 1/2 2/3 41/11 1/2 3/4 15/4 1/0 49/13 1/2 5/8 34/9 5/7 3/4 53/14 3/4 19/5 3/4 5/6 61/16 7/8 42/11 5/6 6/7 23/6 11/12 27/7 1/1 31/8 17/16 4/1 1/1 3/2 13/3 5/2 1/0 35/8 9/4 57/13 5/2 1/0 22/5 2/1 5/2 53/12 1/0 84/19 5/2 3/1 31/7 5/2 11/4 9/2 1/0 14/3 1/0 19/4 1/0 24/5 -5/2 -2/1 53/11 -5/2 1/0 29/6 1/0 5/1 -1/2 1/0 31/6 -1/12 57/11 0/1 26/5 0/1 1/10 21/4 1/4 37/7 1/2 1/0 16/3 1/3 1/2 59/11 9/20 1/2 43/8 1/2 27/5 1/2 5/8 11/2 1/0 28/5 1/2 1/1 17/3 1/2 3/4 40/7 3/4 4/5 63/11 3/4 5/6 23/4 7/8 29/5 1/1 35/6 13/12 6/1 1/1 3/2 13/2 7/4 20/3 2/1 5/2 27/4 11/4 7/1 7/2 1/0 22/3 9/1 1/0 15/2 1/0 38/5 -13/1 1/0 23/3 -15/2 1/0 8/1 -2/1 1/0 25/3 -3/4 -1/2 42/5 -3/4 -2/3 17/2 -1/4 26/3 -1/6 0/1 9/1 1/2 1/0 10/1 1/2 1/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(255,118,188,87) (-1/2,-6/13) -> (4/3,19/14) Hyperbolic Matrix(755,348,128,59) (-6/13,-23/50) -> (35/6,6/1) Hyperbolic Matrix(4279,1968,2520,1159) (-23/50,-17/37) -> (73/43,17/10) Hyperbolic Matrix(375,172,-2008,-921) (-17/37,-11/24) -> (-3/16,-11/59) Hyperbolic Matrix(3137,1436,876,401) (-11/24,-16/35) -> (68/19,43/12) Hyperbolic Matrix(1503,686,436,199) (-16/35,-5/11) -> (31/9,38/11) Hyperbolic Matrix(495,224,1306,591) (-5/11,-14/31) -> (14/37,11/29) Hyperbolic Matrix(373,168,988,445) (-14/31,-9/20) -> (3/8,14/37) Hyperbolic Matrix(121,54,-428,-191) (-9/20,-4/9) -> (-2/7,-9/32) Hyperbolic Matrix(487,216,124,55) (-4/9,-23/52) -> (31/8,4/1) Hyperbolic Matrix(973,430,2256,997) (-23/52,-19/43) -> (3/7,19/44) Hyperbolic Matrix(1829,808,790,349) (-19/43,-15/34) -> (37/16,7/3) Hyperbolic Matrix(1583,698,-3894,-1717) (-15/34,-26/59) -> (-24/59,-13/32) Hyperbolic Matrix(849,374,-4556,-2007) (-26/59,-11/25) -> (-11/59,-8/43) Hyperbolic Matrix(605,266,1094,481) (-11/25,-18/41) -> (16/29,5/9) Hyperbolic Matrix(1937,850,850,373) (-18/41,-7/16) -> (41/18,16/7) Hyperbolic Matrix(1087,474,-2956,-1289) (-7/16,-17/39) -> (-7/19,-25/68) Hyperbolic Matrix(2291,998,1926,839) (-17/39,-27/62) -> (19/16,25/21) Hyperbolic Matrix(239,104,-1804,-785) (-27/62,-10/23) -> (-2/15,-5/38) Hyperbolic Matrix(599,260,182,79) (-10/23,-3/7) -> (23/7,10/3) Hyperbolic Matrix(237,100,410,173) (-3/7,-8/19) -> (4/7,11/19) Hyperbolic Matrix(119,50,-764,-321) (-8/19,-13/31) -> (-3/19,-2/13) Hyperbolic Matrix(821,344,642,269) (-13/31,-5/12) -> (23/18,9/7) Hyperbolic Matrix(695,288,-1682,-697) (-5/12,-12/29) -> (-12/29,-19/46) Parabolic Matrix(1275,526,2024,835) (-19/46,-7/17) -> (17/27,29/46) Hyperbolic Matrix(1965,808,518,213) (-7/17,-23/56) -> (53/14,19/5) Hyperbolic Matrix(6805,2794,2136,877) (-23/56,-39/95) -> (35/11,51/16) Hyperbolic Matrix(7499,3078,4266,1751) (-39/95,-55/134) -> (7/4,51/29) Hyperbolic Matrix(19029,7810,8306,3409) (-55/134,-16/39) -> (126/55,55/24) Hyperbolic Matrix(2073,850,578,237) (-16/39,-9/22) -> (43/12,18/5) Hyperbolic Matrix(1035,422,802,327) (-9/22,-11/27) -> (9/7,31/24) Hyperbolic Matrix(6189,2518,1664,677) (-11/27,-24/59) -> (26/7,93/25) Hyperbolic Matrix(1719,698,628,255) (-13/32,-2/5) -> (52/19,11/4) Hyperbolic Matrix(111,44,58,23) (-2/5,-9/23) -> (13/7,2/1) Hyperbolic Matrix(445,174,-3404,-1331) (-9/23,-34/87) -> (-8/61,-3/23) Hyperbolic Matrix(2677,1046,6196,2421) (-34/87,-25/64) -> (19/44,16/37) Hyperbolic Matrix(671,262,2118,827) (-25/64,-16/41) -> (6/19,7/22) Hyperbolic Matrix(2005,782,782,305) (-16/41,-7/18) -> (41/16,18/7) Hyperbolic Matrix(779,302,276,107) (-7/18,-12/31) -> (14/5,17/6) Hyperbolic Matrix(445,172,-1498,-579) (-12/31,-5/13) -> (-11/37,-8/27) Hyperbolic Matrix(771,296,112,43) (-5/13,-23/60) -> (27/4,7/1) Hyperbolic Matrix(4077,1562,1600,613) (-23/60,-18/47) -> (28/11,51/20) Hyperbolic Matrix(2205,844,1706,653) (-18/47,-13/34) -> (31/24,22/17) Hyperbolic Matrix(1429,546,882,337) (-13/34,-8/21) -> (34/21,13/8) Hyperbolic Matrix(221,84,-934,-355) (-8/21,-11/29) -> (-5/21,-4/17) Hyperbolic Matrix(549,208,710,269) (-11/29,-3/8) -> (17/22,7/9) Hyperbolic Matrix(539,200,-1458,-541) (-3/8,-10/27) -> (-10/27,-17/46) Parabolic Matrix(1295,478,2208,815) (-17/46,-7/19) -> (17/29,27/46) Hyperbolic Matrix(2797,1028,536,197) (-25/68,-18/49) -> (26/5,21/4) Hyperbolic Matrix(1291,474,-4622,-1697) (-18/49,-11/30) -> (-19/68,-12/43) Hyperbolic Matrix(323,118,52,19) (-11/30,-4/11) -> (6/1,13/2) Hyperbolic Matrix(105,38,268,97) (-4/11,-5/14) -> (7/18,2/5) Hyperbolic Matrix(209,74,-788,-279) (-5/14,-6/17) -> (-4/15,-9/34) Hyperbolic Matrix(525,184,836,293) (-6/17,-7/20) -> (5/8,22/35) Hyperbolic Matrix(6267,2188,2300,803) (-7/20,-15/43) -> (79/29,109/40) Hyperbolic Matrix(1355,472,3132,1091) (-15/43,-8/23) -> (16/37,29/67) Hyperbolic Matrix(415,144,366,127) (-8/23,-1/3) -> (17/15,8/7) Hyperbolic Matrix(197,62,448,141) (-1/3,-5/16) -> (7/16,11/25) Hyperbolic Matrix(97,30,-540,-167) (-5/16,-4/13) -> (-2/11,-5/28) Hyperbolic Matrix(391,120,492,151) (-4/13,-11/36) -> (19/24,4/5) Hyperbolic Matrix(1273,388,292,89) (-11/36,-7/23) -> (13/3,35/8) Hyperbolic Matrix(685,208,438,133) (-7/23,-3/10) -> (25/16,11/7) Hyperbolic Matrix(1939,578,1258,375) (-3/10,-14/47) -> (20/13,37/24) Hyperbolic Matrix(1451,432,3342,995) (-14/47,-11/37) -> (23/53,10/23) Hyperbolic Matrix(291,86,-1208,-357) (-8/27,-13/44) -> (-1/4,-6/25) Hyperbolic Matrix(481,142,2510,741) (-13/44,-18/61) -> (4/21,5/26) Hyperbolic Matrix(773,228,2458,725) (-18/61,-5/17) -> (11/35,6/19) Hyperbolic Matrix(97,28,142,41) (-5/17,-2/7) -> (2/3,9/13) Hyperbolic Matrix(1231,346,708,199) (-9/32,-7/25) -> (33/19,7/4) Hyperbolic Matrix(6513,1822,1748,489) (-7/25,-26/93) -> (108/29,41/11) Hyperbolic Matrix(3399,950,-12884,-3601) (-26/93,-19/68) -> (-19/72,-24/91) Hyperbolic Matrix(2073,578,850,237) (-12/43,-5/18) -> (39/16,22/9) Hyperbolic Matrix(469,130,754,209) (-5/18,-8/29) -> (18/29,5/8) Hyperbolic Matrix(189,52,-1174,-323) (-8/29,-11/40) -> (-1/6,-4/25) Hyperbolic Matrix(467,128,1266,347) (-11/40,-3/11) -> (7/19,17/46) Hyperbolic Matrix(373,100,138,37) (-3/11,-4/15) -> (8/3,19/7) Hyperbolic Matrix(1755,464,556,147) (-9/34,-14/53) -> (22/7,19/6) Hyperbolic Matrix(2773,732,322,85) (-14/53,-19/72) -> (17/2,26/3) Hyperbolic Matrix(3323,876,2864,755) (-24/91,-5/19) -> (29/25,36/31) Hyperbolic Matrix(1013,266,278,73) (-5/19,-6/23) -> (40/11,11/3) Hyperbolic Matrix(827,214,228,59) (-6/23,-1/4) -> (29/8,40/11) Hyperbolic Matrix(359,86,-2058,-493) (-6/25,-5/21) -> (-11/63,-4/23) Hyperbolic Matrix(265,62,312,73) (-4/17,-3/13) -> (11/13,6/7) Hyperbolic Matrix(89,20,218,49) (-3/13,-2/9) -> (2/5,7/17) Hyperbolic Matrix(173,38,132,29) (-2/9,-3/14) -> (13/10,4/3) Hyperbolic Matrix(431,92,520,111) (-3/14,-7/33) -> (19/23,5/6) Hyperbolic Matrix(85,18,-732,-155) (-7/33,-4/19) -> (-2/17,-1/9) Hyperbolic Matrix(343,72,948,199) (-4/19,-5/24) -> (13/36,4/11) Hyperbolic Matrix(943,196,688,143) (-5/24,-1/5) -> (37/27,11/8) Hyperbolic Matrix(167,32,-882,-169) (-1/5,-4/21) -> (-4/21,-7/37) Parabolic Matrix(2765,522,1552,293) (-7/37,-3/16) -> (57/32,41/23) Hyperbolic Matrix(1335,248,1588,295) (-8/43,-5/27) -> (21/25,16/19) Hyperbolic Matrix(919,170,1292,239) (-5/27,-7/38) -> (27/38,5/7) Hyperbolic Matrix(1749,322,6002,1105) (-7/38,-16/87) -> (30/103,7/24) Hyperbolic Matrix(8997,1654,2834,521) (-16/87,-9/49) -> (73/23,54/17) Hyperbolic Matrix(667,122,82,15) (-9/49,-2/11) -> (8/1,25/3) Hyperbolic Matrix(745,132,412,73) (-5/28,-3/17) -> (9/5,29/16) Hyperbolic Matrix(5113,898,3012,529) (-3/17,-10/57) -> (56/33,73/43) Hyperbolic Matrix(3547,622,1112,195) (-10/57,-7/40) -> (51/16,16/5) Hyperbolic Matrix(7501,1312,2224,389) (-7/40,-18/103) -> (118/35,27/8) Hyperbolic Matrix(16807,2936,4986,871) (-18/103,-11/63) -> (91/27,118/35) Hyperbolic Matrix(1315,228,248,43) (-4/23,-5/29) -> (37/7,16/3) Hyperbolic Matrix(1069,184,122,21) (-5/29,-6/35) -> (26/3,9/1) Hyperbolic Matrix(491,84,1888,323) (-6/35,-1/6) -> (13/50,6/23) Hyperbolic Matrix(891,142,2102,335) (-4/25,-3/19) -> (25/59,14/33) Hyperbolic Matrix(79,12,362,55) (-2/13,-1/7) -> (5/23,2/9) Hyperbolic Matrix(237,32,274,37) (-1/7,-2/15) -> (6/7,13/15) Hyperbolic Matrix(7593,998,4816,633) (-5/38,-8/61) -> (134/85,41/26) Hyperbolic Matrix(1405,182,1212,157) (-3/23,-4/31) -> (22/19,29/25) Hyperbolic Matrix(311,40,1796,231) (-4/31,-1/8) -> (9/52,4/23) Hyperbolic Matrix(927,112,1316,159) (-1/8,-2/17) -> (50/71,31/44) Hyperbolic Matrix(761,82,1754,189) (-1/9,-2/19) -> (36/83,23/53) Hyperbolic Matrix(607,62,1400,143) (-2/19,-1/10) -> (13/30,36/83) Hyperbolic Matrix(149,14,564,53) (-1/10,0/1) -> (14/53,9/34) Hyperbolic Matrix(995,-94,434,-41) (0/1,1/10) -> (55/24,94/41) Hyperbolic Matrix(1845,-196,706,-75) (1/10,1/9) -> (81/31,115/44) Hyperbolic Matrix(485,-58,92,-11) (1/9,1/8) -> (21/4,37/7) Hyperbolic Matrix(661,-86,392,-51) (1/8,2/15) -> (32/19,27/16) Hyperbolic Matrix(299,-42,178,-25) (2/15,1/7) -> (5/3,32/19) Hyperbolic Matrix(119,-18,324,-49) (1/7,1/6) -> (11/30,7/19) Hyperbolic Matrix(291,-50,1682,-289) (1/6,5/29) -> (5/29,9/52) Parabolic Matrix(3707,-646,1360,-237) (4/23,7/40) -> (109/40,30/11) Hyperbolic Matrix(3587,-630,2602,-457) (7/40,3/17) -> (51/37,91/66) Hyperbolic Matrix(577,-104,172,-31) (3/17,2/11) -> (10/3,37/11) Hyperbolic Matrix(229,-42,518,-95) (2/11,3/16) -> (15/34,4/9) Hyperbolic Matrix(1257,-238,544,-103) (3/16,4/21) -> (30/13,37/16) Hyperbolic Matrix(285,-56,56,-11) (5/26,1/5) -> (5/1,31/6) Hyperbolic Matrix(563,-118,730,-153) (1/5,4/19) -> (10/13,27/35) Hyperbolic Matrix(785,-166,506,-107) (4/19,3/14) -> (31/20,14/9) Hyperbolic Matrix(951,-206,614,-133) (3/14,5/23) -> (17/11,31/20) Hyperbolic Matrix(221,-50,84,-19) (2/9,1/4) -> (21/8,8/3) Hyperbolic Matrix(379,-98,1458,-377) (1/4,7/27) -> (7/27,13/50) Parabolic Matrix(1293,-338,1052,-275) (6/23,5/19) -> (43/35,16/13) Hyperbolic Matrix(2797,-738,1588,-419) (5/19,14/53) -> (44/25,37/21) Hyperbolic Matrix(1397,-370,404,-107) (9/34,4/15) -> (38/11,7/2) Hyperbolic Matrix(1395,-374,884,-237) (4/15,7/26) -> (41/26,30/19) Hyperbolic Matrix(2463,-664,1072,-289) (7/26,10/37) -> (62/27,23/10) Hyperbolic Matrix(1069,-290,188,-51) (10/37,3/11) -> (17/3,40/7) Hyperbolic Matrix(107,-30,132,-37) (3/11,2/7) -> (4/5,9/11) Hyperbolic Matrix(1901,-548,1398,-403) (2/7,11/38) -> (87/64,34/25) Hyperbolic Matrix(4797,-1390,2716,-787) (11/38,9/31) -> (83/47,53/30) Hyperbolic Matrix(1107,-322,526,-153) (9/31,16/55) -> (2/1,19/9) Hyperbolic Matrix(3635,-1058,12482,-3633) (16/55,23/79) -> (23/79,30/103) Parabolic Matrix(3367,-984,1290,-377) (7/24,12/41) -> (60/23,47/18) Hyperbolic Matrix(1629,-478,2314,-679) (12/41,5/17) -> (19/27,50/71) Hyperbolic Matrix(629,-186,1444,-427) (5/17,8/27) -> (10/23,17/39) Hyperbolic Matrix(577,-172,104,-31) (8/27,3/10) -> (11/2,28/5) Hyperbolic Matrix(105,-32,338,-103) (3/10,4/13) -> (4/13,5/16) Parabolic Matrix(933,-292,802,-251) (5/16,16/51) -> (36/31,7/6) Hyperbolic Matrix(4141,-1300,2354,-739) (16/51,11/35) -> (51/29,44/25) Hyperbolic Matrix(667,-216,386,-125) (7/22,1/3) -> (19/11,83/48) Hyperbolic Matrix(705,-248,452,-159) (1/3,6/17) -> (14/9,39/25) Hyperbolic Matrix(501,-178,76,-27) (6/17,5/14) -> (13/2,20/3) Hyperbolic Matrix(451,-162,1250,-449) (5/14,9/25) -> (9/25,13/36) Parabolic Matrix(847,-310,1194,-437) (4/11,11/30) -> (17/24,22/31) Hyperbolic Matrix(1093,-404,744,-275) (17/46,10/27) -> (22/15,3/2) Hyperbolic Matrix(943,-350,520,-193) (10/27,3/8) -> (29/16,20/11) Hyperbolic Matrix(5371,-2040,1972,-749) (11/29,19/50) -> (49/18,79/29) Hyperbolic Matrix(1577,-600,1280,-487) (19/50,8/21) -> (16/13,37/30) Hyperbolic Matrix(491,-188,222,-85) (8/21,5/13) -> (11/5,20/9) Hyperbolic Matrix(637,-246,246,-95) (5/13,7/18) -> (31/12,13/5) Hyperbolic Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic Matrix(5507,-2312,2108,-885) (13/31,21/50) -> (47/18,81/31) Hyperbolic Matrix(2107,-886,478,-201) (21/50,8/19) -> (22/5,53/12) Hyperbolic Matrix(1531,-646,884,-373) (8/19,11/26) -> (45/26,26/15) Hyperbolic Matrix(2867,-1214,4036,-1709) (11/26,25/59) -> (49/69,27/38) Hyperbolic Matrix(1431,-608,812,-345) (14/33,3/7) -> (37/21,30/17) Hyperbolic Matrix(3463,-1500,1092,-473) (29/67,13/30) -> (19/6,73/23) Hyperbolic Matrix(2651,-1156,782,-341) (17/39,7/16) -> (61/18,17/5) Hyperbolic Matrix(3257,-1434,1842,-811) (11/25,26/59) -> (76/43,23/13) Hyperbolic Matrix(5711,-2518,3232,-1425) (26/59,15/34) -> (53/30,76/43) Hyperbolic Matrix(187,-84,118,-53) (4/9,1/2) -> (19/12,8/5) Hyperbolic Matrix(133,-72,242,-131) (1/2,6/11) -> (6/11,11/20) Parabolic Matrix(1183,-652,176,-97) (11/20,16/29) -> (20/3,27/4) Hyperbolic Matrix(131,-74,108,-61) (5/9,4/7) -> (6/5,11/9) Hyperbolic Matrix(817,-474,474,-275) (11/19,7/12) -> (31/18,19/11) Hyperbolic Matrix(557,-326,258,-151) (7/12,17/29) -> (15/7,13/6) Hyperbolic Matrix(2441,-1434,686,-403) (27/46,10/17) -> (32/9,57/16) Hyperbolic Matrix(1113,-656,962,-567) (10/17,23/39) -> (15/13,22/19) Hyperbolic Matrix(1241,-732,256,-151) (23/39,13/22) -> (29/6,5/1) Hyperbolic Matrix(2179,-1290,576,-341) (13/22,16/27) -> (34/9,53/14) Hyperbolic Matrix(299,-178,42,-25) (16/27,3/5) -> (7/1,22/3) Hyperbolic Matrix(507,-308,614,-373) (3/5,14/23) -> (14/17,19/23) Hyperbolic Matrix(6465,-3938,4142,-2523) (14/23,39/64) -> (103/66,64/41) Hyperbolic Matrix(6929,-4224,4224,-2575) (39/64,25/41) -> (41/25,105/64) Hyperbolic Matrix(2787,-1700,782,-477) (25/41,11/18) -> (57/16,25/7) Hyperbolic Matrix(885,-542,338,-207) (11/18,8/13) -> (34/13,21/8) Hyperbolic Matrix(547,-338,882,-545) (8/13,13/21) -> (13/21,18/29) Parabolic Matrix(585,-368,62,-39) (22/35,17/27) -> (9/1,10/1) Hyperbolic Matrix(3419,-2156,2190,-1381) (29/46,12/19) -> (64/41,25/16) Hyperbolic Matrix(749,-474,542,-343) (12/19,7/11) -> (29/21,18/13) Hyperbolic Matrix(83,-54,20,-13) (7/11,2/3) -> (4/1,13/3) Hyperbolic Matrix(281,-196,400,-279) (9/13,7/10) -> (7/10,19/27) Parabolic Matrix(3391,-2390,1914,-1349) (31/44,12/17) -> (62/35,39/22) Hyperbolic Matrix(757,-536,298,-211) (12/17,17/24) -> (5/2,28/11) Hyperbolic Matrix(12129,-8612,7694,-5463) (22/31,49/69) -> (93/59,134/85) Hyperbolic Matrix(2179,-1562,950,-681) (5/7,28/39) -> (94/41,39/17) Hyperbolic Matrix(4829,-3468,3502,-2515) (28/39,23/32) -> (91/66,40/29) Hyperbolic Matrix(1937,-1394,1088,-783) (23/32,18/25) -> (16/9,57/32) Hyperbolic Matrix(2687,-1936,712,-513) (18/25,31/43) -> (49/13,34/9) Hyperbolic Matrix(2923,-2108,850,-613) (31/43,13/18) -> (55/16,31/9) Hyperbolic Matrix(749,-542,474,-343) (13/18,8/11) -> (30/19,19/12) Hyperbolic Matrix(235,-172,138,-101) (8/11,3/4) -> (17/10,12/7) Hyperbolic Matrix(193,-146,78,-59) (3/4,13/17) -> (27/11,5/2) Hyperbolic Matrix(923,-708,674,-517) (13/17,10/13) -> (26/19,37/27) Hyperbolic Matrix(2993,-2310,1766,-1363) (27/35,17/22) -> (61/36,39/23) Hyperbolic Matrix(993,-776,572,-447) (7/9,18/23) -> (26/15,33/19) Hyperbolic Matrix(609,-478,172,-135) (18/23,11/14) -> (7/2,32/9) Hyperbolic Matrix(571,-450,722,-569) (11/14,15/19) -> (15/19,19/24) Parabolic Matrix(485,-398,262,-215) (9/11,14/17) -> (24/13,13/7) Hyperbolic Matrix(925,-776,776,-651) (5/6,21/25) -> (25/21,31/26) Hyperbolic Matrix(1217,-1026,720,-607) (16/19,11/13) -> (49/29,22/13) Hyperbolic Matrix(617,-538,164,-143) (13/15,7/8) -> (15/4,49/13) Hyperbolic Matrix(145,-128,162,-143) (7/8,8/9) -> (8/9,9/10) Parabolic Matrix(317,-294,124,-115) (9/10,1/1) -> (23/9,87/34) Hyperbolic Matrix(259,-286,48,-53) (1/1,9/8) -> (43/8,27/5) Hyperbolic Matrix(1117,-1262,208,-235) (9/8,17/15) -> (59/11,43/8) Hyperbolic Matrix(1267,-1454,332,-381) (8/7,23/20) -> (61/16,42/11) Hyperbolic Matrix(601,-692,284,-327) (23/20,15/13) -> (19/9,17/8) Hyperbolic Matrix(531,-626,218,-257) (7/6,13/11) -> (17/7,39/16) Hyperbolic Matrix(1057,-1254,778,-923) (13/11,19/16) -> (19/14,53/39) Hyperbolic Matrix(4621,-5512,1364,-1627) (31/26,6/5) -> (166/49,61/18) Hyperbolic Matrix(1221,-1498,886,-1087) (11/9,27/22) -> (11/8,51/37) Hyperbolic Matrix(4211,-5172,3098,-3805) (27/22,43/35) -> (53/39,87/64) Hyperbolic Matrix(2921,-3606,1872,-2311) (37/30,21/17) -> (39/25,103/66) Hyperbolic Matrix(1095,-1354,334,-413) (21/17,5/4) -> (59/18,23/7) Hyperbolic Matrix(661,-834,256,-323) (5/4,19/15) -> (49/19,31/12) Hyperbolic Matrix(809,-1028,314,-399) (19/15,14/11) -> (18/7,49/19) Hyperbolic Matrix(717,-914,404,-515) (14/11,23/18) -> (39/22,16/9) Hyperbolic Matrix(563,-730,118,-153) (22/17,13/10) -> (19/4,24/5) Hyperbolic Matrix(663,-902,86,-117) (34/25,15/11) -> (23/3,8/1) Hyperbolic Matrix(1091,-1492,302,-413) (15/11,26/19) -> (18/5,47/13) Hyperbolic Matrix(7343,-10132,1972,-2721) (40/29,69/50) -> (67/18,108/29) Hyperbolic Matrix(6057,-8360,1628,-2247) (69/50,29/21) -> (93/25,67/18) Hyperbolic Matrix(341,-474,100,-139) (18/13,7/5) -> (17/5,24/7) Hyperbolic Matrix(141,-200,98,-139) (7/5,10/7) -> (10/7,13/9) Parabolic Matrix(721,-1046,264,-383) (13/9,16/11) -> (30/11,41/15) Hyperbolic Matrix(913,-1330,208,-303) (16/11,19/13) -> (57/13,22/5) Hyperbolic Matrix(1351,-1980,552,-809) (19/13,22/15) -> (22/9,71/29) Hyperbolic Matrix(457,-698,256,-391) (3/2,20/13) -> (66/37,25/14) Hyperbolic Matrix(1765,-2722,308,-475) (37/24,17/11) -> (63/11,23/4) Hyperbolic Matrix(3433,-5408,2178,-3431) (11/7,52/33) -> (52/33,93/59) Parabolic Matrix(547,-882,338,-545) (8/5,21/13) -> (21/13,34/21) Parabolic Matrix(259,-422,116,-189) (13/8,18/11) -> (20/9,9/4) Hyperbolic Matrix(1803,-2956,1018,-1669) (18/11,41/25) -> (23/13,62/35) Hyperbolic Matrix(20935,-34348,8202,-13457) (105/64,169/103) -> (171/67,97/38) Hyperbolic Matrix(14291,-23450,5600,-9189) (169/103,64/39) -> (74/29,171/67) Hyperbolic Matrix(3243,-5324,734,-1205) (64/39,23/14) -> (53/12,84/19) Hyperbolic Matrix(745,-1226,206,-339) (23/14,5/3) -> (47/13,29/8) Hyperbolic Matrix(2073,-3502,544,-919) (27/16,49/29) -> (19/5,61/16) Hyperbolic Matrix(3383,-5730,1956,-3313) (22/13,61/36) -> (83/48,64/37) Hyperbolic Matrix(3429,-5818,1942,-3295) (39/23,56/33) -> (30/17,83/47) Hyperbolic Matrix(525,-902,188,-323) (12/7,31/18) -> (39/14,14/5) Hyperbolic Matrix(3811,-6594,1494,-2585) (64/37,45/26) -> (51/20,74/29) Hyperbolic Matrix(3079,-5490,696,-1241) (41/23,66/37) -> (84/19,31/7) Hyperbolic Matrix(1025,-1832,268,-479) (25/14,34/19) -> (42/11,23/6) Hyperbolic Matrix(1023,-1834,304,-545) (34/19,9/5) -> (37/11,64/19) Hyperbolic Matrix(265,-484,144,-263) (20/11,11/6) -> (11/6,24/13) Parabolic Matrix(1173,-2500,358,-763) (17/8,15/7) -> (95/29,59/18) Hyperbolic Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(229,-518,42,-95) (9/4,25/11) -> (27/5,11/2) Hyperbolic Matrix(1411,-3212,322,-733) (25/11,41/18) -> (35/8,57/13) Hyperbolic Matrix(4403,-10082,1922,-4401) (16/7,71/31) -> (71/31,126/55) Parabolic Matrix(3177,-7294,970,-2227) (39/17,62/27) -> (36/11,95/29) Hyperbolic Matrix(1317,-3034,484,-1115) (23/10,30/13) -> (68/25,49/18) Hyperbolic Matrix(121,-288,50,-119) (7/3,12/5) -> (12/5,17/7) Parabolic Matrix(3273,-8014,1282,-3139) (71/29,49/20) -> (97/38,23/9) Hyperbolic Matrix(1379,-3380,286,-701) (49/20,27/11) -> (53/11,29/6) Hyperbolic Matrix(1853,-4742,220,-563) (87/34,64/25) -> (42/5,17/2) Hyperbolic Matrix(3419,-8754,1308,-3349) (64/25,41/16) -> (115/44,34/13) Hyperbolic Matrix(2413,-6292,716,-1867) (13/5,60/23) -> (64/19,91/27) Hyperbolic Matrix(841,-2286,110,-299) (19/7,68/25) -> (38/5,23/3) Hyperbolic Matrix(1475,-4034,464,-1269) (41/15,52/19) -> (54/17,35/11) Hyperbolic Matrix(451,-1250,162,-449) (11/4,25/9) -> (25/9,39/14) Parabolic Matrix(195,-554,44,-125) (17/6,3/1) -> (31/7,9/2) Hyperbolic Matrix(395,-1238,82,-257) (3/1,22/7) -> (24/5,53/11) Hyperbolic Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(93,-314,8,-27) (27/8,44/13) -> (10/1,1/0) Hyperbolic Matrix(6511,-22050,1922,-6509) (44/13,105/31) -> (105/31,166/49) Parabolic Matrix(997,-3422,192,-659) (24/7,79/23) -> (57/11,26/5) Hyperbolic Matrix(1625,-5584,314,-1079) (79/23,55/16) -> (31/6,57/11) Hyperbolic Matrix(1233,-4412,230,-823) (25/7,68/19) -> (16/3,59/11) Hyperbolic Matrix(203,-750,36,-133) (11/3,26/7) -> (28/5,17/3) Hyperbolic Matrix(379,-1458,98,-377) (23/6,27/7) -> (27/7,31/8) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(637,-3646,76,-435) (40/7,63/11) -> (25/3,42/5) Hyperbolic Matrix(291,-1682,50,-289) (23/4,29/5) -> (29/5,35/6) Parabolic Matrix(121,-900,16,-119) (22/3,15/2) -> (15/2,38/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(255,118,188,87) -> Matrix(7,-2,4,-1) Matrix(755,348,128,59) -> Matrix(19,-6,16,-5) Matrix(4279,1968,2520,1159) -> Matrix(17,-6,20,-7) Matrix(375,172,-2008,-921) -> Matrix(5,-2,8,-3) Matrix(3137,1436,876,401) -> Matrix(5,-2,8,-3) Matrix(1503,686,436,199) -> Matrix(1,0,0,1) Matrix(495,224,1306,591) -> Matrix(17,-4,64,-15) Matrix(373,168,988,445) -> Matrix(15,-4,64,-17) Matrix(121,54,-428,-191) -> Matrix(7,-2,4,-1) Matrix(487,216,124,55) -> Matrix(19,-6,16,-5) Matrix(973,430,2256,997) -> Matrix(17,-6,20,-7) Matrix(1829,808,790,349) -> Matrix(5,-2,8,-3) Matrix(1583,698,-3894,-1717) -> Matrix(11,-4,36,-13) Matrix(849,374,-4556,-2007) -> Matrix(5,-2,8,-3) Matrix(605,266,1094,481) -> Matrix(9,-4,16,-7) Matrix(1937,850,850,373) -> Matrix(7,-2,4,-1) Matrix(1087,474,-2956,-1289) -> Matrix(1,0,-4,1) Matrix(2291,998,1926,839) -> Matrix(19,-4,24,-5) Matrix(239,104,-1804,-785) -> Matrix(1,0,-4,1) Matrix(599,260,182,79) -> Matrix(9,-2,-4,1) Matrix(237,100,410,173) -> Matrix(5,-2,8,-3) Matrix(119,50,-764,-321) -> Matrix(1,0,0,1) Matrix(821,344,642,269) -> Matrix(7,-2,4,-1) Matrix(695,288,-1682,-697) -> Matrix(9,-2,32,-7) Matrix(1275,526,2024,835) -> Matrix(7,-2,32,-9) Matrix(1965,808,518,213) -> Matrix(5,-2,8,-3) Matrix(6805,2794,2136,877) -> Matrix(23,-6,4,-1) Matrix(7499,3078,4266,1751) -> Matrix(7,-2,32,-9) Matrix(19029,7810,8306,3409) -> Matrix(127,-36,60,-17) Matrix(2073,850,578,237) -> Matrix(7,-2,4,-1) Matrix(1035,422,802,327) -> Matrix(7,-2,4,-1) Matrix(6189,2518,1664,677) -> Matrix(7,-2,4,-1) Matrix(1719,698,628,255) -> Matrix(5,-2,8,-3) Matrix(111,44,58,23) -> Matrix(5,-2,8,-3) Matrix(445,174,-3404,-1331) -> Matrix(1,0,-4,1) Matrix(2677,1046,6196,2421) -> Matrix(7,-2,4,-1) Matrix(671,262,2118,827) -> Matrix(5,-2,8,-3) Matrix(2005,782,782,305) -> Matrix(5,-2,8,-3) Matrix(779,302,276,107) -> Matrix(19,-6,16,-5) Matrix(445,172,-1498,-579) -> Matrix(1,0,0,1) Matrix(771,296,112,43) -> Matrix(15,-4,4,-1) Matrix(4077,1562,1600,613) -> Matrix(7,-2,4,-1) Matrix(2205,844,1706,653) -> Matrix(19,-6,16,-5) Matrix(1429,546,882,337) -> Matrix(55,-18,52,-17) Matrix(221,84,-934,-355) -> Matrix(11,-4,36,-13) Matrix(549,208,710,269) -> Matrix(5,-2,8,-3) Matrix(539,200,-1458,-541) -> Matrix(9,-4,16,-7) Matrix(1295,478,2208,815) -> Matrix(5,-4,4,-3) Matrix(2797,1028,536,197) -> Matrix(1,0,4,1) Matrix(1291,474,-4622,-1697) -> Matrix(1,0,-4,1) Matrix(323,118,52,19) -> Matrix(7,-2,4,-1) Matrix(105,38,268,97) -> Matrix(1,0,0,1) Matrix(209,74,-788,-279) -> Matrix(1,0,0,1) Matrix(525,184,836,293) -> Matrix(5,-2,28,-11) Matrix(6267,2188,2300,803) -> Matrix(63,-26,80,-33) Matrix(1355,472,3132,1091) -> Matrix(9,-4,16,-7) Matrix(415,144,366,127) -> Matrix(17,-8,32,-15) Matrix(197,62,448,141) -> Matrix(1,0,0,1) Matrix(97,30,-540,-167) -> Matrix(1,0,0,1) Matrix(391,120,492,151) -> Matrix(1,0,4,1) Matrix(1273,388,292,89) -> Matrix(7,-2,4,-1) Matrix(685,208,438,133) -> Matrix(5,-2,8,-3) Matrix(1939,578,1258,375) -> Matrix(5,-2,8,-3) Matrix(1451,432,3342,995) -> Matrix(5,-2,8,-3) Matrix(291,86,-1208,-357) -> Matrix(5,-2,28,-11) Matrix(481,142,2510,741) -> Matrix(5,-2,-12,5) Matrix(773,228,2458,725) -> Matrix(9,-4,16,-7) Matrix(97,28,142,41) -> Matrix(3,-2,8,-5) Matrix(1231,346,708,199) -> Matrix(1,2,0,1) Matrix(6513,1822,1748,489) -> Matrix(3,2,4,3) Matrix(3399,950,-12884,-3601) -> Matrix(5,2,12,5) Matrix(2073,578,850,237) -> Matrix(1,0,0,1) Matrix(469,130,754,209) -> Matrix(1,0,12,1) Matrix(189,52,-1174,-323) -> Matrix(1,0,-4,1) Matrix(467,128,1266,347) -> Matrix(1,0,0,1) Matrix(373,100,138,37) -> Matrix(5,-2,8,-3) Matrix(1755,464,556,147) -> Matrix(21,-8,8,-3) Matrix(2773,732,322,85) -> Matrix(5,-2,-12,5) Matrix(3323,876,2864,755) -> Matrix(9,-4,16,-7) Matrix(1013,266,278,73) -> Matrix(9,-4,16,-7) Matrix(827,214,228,59) -> Matrix(3,-2,8,-5) Matrix(359,86,-2058,-493) -> Matrix(9,-2,-4,1) Matrix(265,62,312,73) -> Matrix(1,0,0,1) Matrix(89,20,218,49) -> Matrix(3,-2,8,-5) Matrix(173,38,132,29) -> Matrix(1,0,0,1) Matrix(431,92,520,111) -> Matrix(1,0,4,1) Matrix(85,18,-732,-155) -> Matrix(1,0,4,1) Matrix(343,72,948,199) -> Matrix(1,0,16,1) Matrix(943,196,688,143) -> Matrix(1,0,-8,1) Matrix(167,32,-882,-169) -> Matrix(9,-4,16,-7) Matrix(2765,522,1552,293) -> Matrix(3,-2,8,-5) Matrix(1335,248,1588,295) -> Matrix(3,-2,8,-5) Matrix(919,170,1292,239) -> Matrix(5,-2,8,-3) Matrix(1749,322,6002,1105) -> Matrix(15,-14,44,-41) Matrix(8997,1654,2834,521) -> Matrix(23,-26,8,-9) Matrix(667,122,82,15) -> Matrix(1,-2,0,1) Matrix(745,132,412,73) -> Matrix(1,0,0,1) Matrix(5113,898,3012,529) -> Matrix(3,-4,4,-5) Matrix(3547,622,1112,195) -> Matrix(1,2,0,1) Matrix(7501,1312,2224,389) -> Matrix(1,-4,0,1) Matrix(16807,2936,4986,871) -> Matrix(1,10,0,1) Matrix(1315,228,248,43) -> Matrix(1,0,4,1) Matrix(1069,184,122,21) -> Matrix(1,0,4,1) Matrix(491,84,1888,323) -> Matrix(1,0,24,1) Matrix(891,142,2102,335) -> Matrix(13,-2,20,-3) Matrix(79,12,362,55) -> Matrix(5,-2,8,-3) Matrix(237,32,274,37) -> Matrix(3,-2,8,-5) Matrix(7593,998,4816,633) -> Matrix(3,-22,4,-29) Matrix(1405,182,1212,157) -> Matrix(3,2,4,3) Matrix(311,40,1796,231) -> Matrix(1,0,16,1) Matrix(927,112,1316,159) -> Matrix(17,-8,32,-15) Matrix(761,82,1754,189) -> Matrix(5,-2,8,-3) Matrix(607,62,1400,143) -> Matrix(1,0,0,1) Matrix(149,14,564,53) -> Matrix(1,0,4,1) Matrix(995,-94,434,-41) -> Matrix(1,2,0,1) Matrix(1845,-196,706,-75) -> Matrix(1,0,-4,1) Matrix(485,-58,92,-11) -> Matrix(1,0,0,1) Matrix(661,-86,392,-51) -> Matrix(5,-2,8,-3) Matrix(299,-42,178,-25) -> Matrix(1,0,0,1) Matrix(119,-18,324,-49) -> Matrix(1,0,4,1) Matrix(291,-50,1682,-289) -> Matrix(1,0,20,1) Matrix(3707,-646,1360,-237) -> Matrix(35,-4,44,-5) Matrix(3587,-630,2602,-457) -> Matrix(1,0,-4,1) Matrix(577,-104,172,-31) -> Matrix(1,0,-4,1) Matrix(229,-42,518,-95) -> Matrix(5,-2,8,-3) Matrix(1257,-238,544,-103) -> Matrix(1,0,0,1) Matrix(285,-56,56,-11) -> Matrix(1,0,-4,1) Matrix(563,-118,730,-153) -> Matrix(5,-2,8,-3) Matrix(785,-166,506,-107) -> Matrix(9,-4,16,-7) Matrix(951,-206,614,-133) -> Matrix(3,-2,8,-5) Matrix(221,-50,84,-19) -> Matrix(1,0,0,1) Matrix(379,-98,1458,-377) -> Matrix(1,0,28,1) Matrix(1293,-338,1052,-275) -> Matrix(21,-2,32,-3) Matrix(2797,-738,1588,-419) -> Matrix(1,0,-4,1) Matrix(1397,-370,404,-107) -> Matrix(1,0,-4,1) Matrix(1395,-374,884,-237) -> Matrix(43,-10,56,-13) Matrix(2463,-664,1072,-289) -> Matrix(15,-4,4,-1) Matrix(1069,-290,188,-51) -> Matrix(5,-2,8,-3) Matrix(107,-30,132,-37) -> Matrix(1,0,0,1) Matrix(1901,-548,1398,-403) -> Matrix(15,-4,4,-1) Matrix(4797,-1390,2716,-787) -> Matrix(13,-4,36,-11) Matrix(1107,-322,526,-153) -> Matrix(43,-14,40,-13) Matrix(3635,-1058,12482,-3633) -> Matrix(133,-44,396,-131) Matrix(3367,-984,1290,-377) -> Matrix(11,-4,-8,3) Matrix(1629,-478,2314,-679) -> Matrix(21,-10,40,-19) Matrix(629,-186,1444,-427) -> Matrix(5,-2,8,-3) Matrix(577,-172,104,-31) -> Matrix(5,-2,8,-3) Matrix(105,-32,338,-103) -> Matrix(9,-4,16,-7) Matrix(933,-292,802,-251) -> Matrix(1,0,0,1) Matrix(4141,-1300,2354,-739) -> Matrix(3,-2,8,-5) Matrix(667,-216,386,-125) -> Matrix(5,-4,4,-3) Matrix(705,-248,452,-159) -> Matrix(3,2,4,3) Matrix(501,-178,76,-27) -> Matrix(9,2,4,1) Matrix(451,-162,1250,-449) -> Matrix(1,0,36,1) Matrix(847,-310,1194,-437) -> Matrix(25,-4,44,-7) Matrix(1093,-404,744,-275) -> Matrix(13,-2,20,-3) Matrix(943,-350,520,-193) -> Matrix(1,0,-4,1) Matrix(5371,-2040,1972,-749) -> Matrix(5,-2,8,-3) Matrix(1577,-600,1280,-487) -> Matrix(29,-8,40,-11) Matrix(491,-188,222,-85) -> Matrix(7,-2,4,-1) Matrix(637,-246,246,-95) -> Matrix(7,-2,4,-1) Matrix(241,-100,576,-239) -> Matrix(21,-10,40,-19) Matrix(5507,-2312,2108,-885) -> Matrix(11,-6,-20,11) Matrix(2107,-886,478,-201) -> Matrix(39,-22,16,-9) Matrix(1531,-646,884,-373) -> Matrix(17,-10,12,-7) Matrix(2867,-1214,4036,-1709) -> Matrix(59,-36,100,-61) Matrix(1431,-608,812,-345) -> Matrix(3,-2,8,-5) Matrix(3463,-1500,1092,-473) -> Matrix(1,2,0,1) Matrix(2651,-1156,782,-341) -> Matrix(3,-2,-4,3) Matrix(3257,-1434,1842,-811) -> Matrix(5,-2,8,-3) Matrix(5711,-2518,3232,-1425) -> Matrix(11,-6,24,-13) Matrix(187,-84,118,-53) -> Matrix(3,-4,4,-5) Matrix(133,-72,242,-131) -> Matrix(13,-6,24,-11) Matrix(1183,-652,176,-97) -> Matrix(39,-22,16,-9) Matrix(131,-74,108,-61) -> Matrix(1,0,0,1) Matrix(817,-474,474,-275) -> Matrix(9,-8,8,-7) Matrix(557,-326,258,-151) -> Matrix(1,0,0,1) Matrix(2441,-1434,686,-403) -> Matrix(1,-2,4,-7) Matrix(1113,-656,962,-567) -> Matrix(5,-12,8,-19) Matrix(1241,-732,256,-151) -> Matrix(1,-4,0,1) Matrix(2179,-1290,576,-341) -> Matrix(3,-10,4,-13) Matrix(299,-178,42,-25) -> Matrix(1,4,0,1) Matrix(507,-308,614,-373) -> Matrix(1,0,4,1) Matrix(6465,-3938,4142,-2523) -> Matrix(3,2,4,3) Matrix(6929,-4224,4224,-2575) -> Matrix(1,2,0,1) Matrix(2787,-1700,782,-477) -> Matrix(1,0,4,1) Matrix(885,-542,338,-207) -> Matrix(1,0,4,1) Matrix(547,-338,882,-545) -> Matrix(1,0,32,1) Matrix(585,-368,62,-39) -> Matrix(1,0,-4,1) Matrix(3419,-2156,2190,-1381) -> Matrix(5,-2,8,-3) Matrix(749,-474,542,-343) -> Matrix(1,0,-4,1) Matrix(83,-54,20,-13) -> Matrix(7,-2,4,-1) Matrix(281,-196,400,-279) -> Matrix(29,-14,56,-27) Matrix(3391,-2390,1914,-1349) -> Matrix(11,-6,24,-13) Matrix(757,-536,298,-211) -> Matrix(7,-4,16,-9) Matrix(12129,-8612,7694,-5463) -> Matrix(357,-208,472,-275) Matrix(2179,-1562,950,-681) -> Matrix(19,-12,8,-5) Matrix(4829,-3468,3502,-2515) -> Matrix(3,-2,8,-5) Matrix(1937,-1394,1088,-783) -> Matrix(3,-2,8,-5) Matrix(2687,-1936,712,-513) -> Matrix(25,-16,36,-23) Matrix(2923,-2108,850,-613) -> Matrix(3,-2,32,-21) Matrix(749,-542,474,-343) -> Matrix(25,-18,32,-23) Matrix(235,-172,138,-101) -> Matrix(1,0,0,1) Matrix(193,-146,78,-59) -> Matrix(1,0,0,1) Matrix(923,-708,674,-517) -> Matrix(1,0,-4,1) Matrix(2993,-2310,1766,-1363) -> Matrix(1,0,0,1) Matrix(993,-776,572,-447) -> Matrix(1,2,0,1) Matrix(609,-478,172,-135) -> Matrix(1,0,4,1) Matrix(571,-450,722,-569) -> Matrix(1,0,16,1) Matrix(485,-398,262,-215) -> Matrix(5,-2,8,-3) Matrix(925,-776,776,-651) -> Matrix(17,-6,20,-7) Matrix(1217,-1026,720,-607) -> Matrix(5,-2,8,-3) Matrix(617,-538,164,-143) -> Matrix(9,-4,16,-7) Matrix(145,-128,162,-143) -> Matrix(17,-8,32,-15) Matrix(317,-294,124,-115) -> Matrix(1,0,0,1) Matrix(259,-286,48,-53) -> Matrix(5,-2,8,-3) Matrix(1117,-1262,208,-235) -> Matrix(23,-12,48,-25) Matrix(1267,-1454,332,-381) -> Matrix(23,-14,28,-17) Matrix(601,-692,284,-327) -> Matrix(37,-22,32,-19) Matrix(531,-626,218,-257) -> Matrix(3,-2,-4,3) Matrix(1057,-1254,778,-923) -> Matrix(5,-4,4,-3) Matrix(4621,-5512,1364,-1627) -> Matrix(11,-10,-12,11) Matrix(1221,-1498,886,-1087) -> Matrix(3,-2,8,-5) Matrix(4211,-5172,3098,-3805) -> Matrix(19,-12,8,-5) Matrix(2921,-3606,1872,-2311) -> Matrix(1,0,0,1) Matrix(1095,-1354,334,-413) -> Matrix(19,-14,-4,3) Matrix(661,-834,256,-323) -> Matrix(9,-8,8,-7) Matrix(809,-1028,314,-399) -> Matrix(7,-8,8,-9) Matrix(717,-914,404,-515) -> Matrix(3,-4,4,-5) Matrix(563,-730,118,-153) -> Matrix(1,-4,0,1) Matrix(663,-902,86,-117) -> Matrix(1,-6,0,1) Matrix(1091,-1492,302,-413) -> Matrix(1,0,4,1) Matrix(7343,-10132,1972,-2721) -> Matrix(5,-2,8,-3) Matrix(6057,-8360,1628,-2247) -> Matrix(1,0,0,1) Matrix(341,-474,100,-139) -> Matrix(1,0,-4,1) Matrix(141,-200,98,-139) -> Matrix(9,-4,16,-7) Matrix(721,-1046,264,-383) -> Matrix(23,-14,28,-17) Matrix(913,-1330,208,-303) -> Matrix(19,-12,8,-5) Matrix(1351,-1980,552,-809) -> Matrix(3,-2,8,-5) Matrix(457,-698,256,-391) -> Matrix(1,0,0,1) Matrix(1765,-2722,308,-475) -> Matrix(3,-4,4,-5) Matrix(3433,-5408,2178,-3431) -> Matrix(169,-126,224,-167) Matrix(547,-882,338,-545) -> Matrix(33,-32,32,-31) Matrix(259,-422,116,-189) -> Matrix(3,-4,4,-5) Matrix(1803,-2956,1018,-1669) -> Matrix(3,-4,4,-5) Matrix(20935,-34348,8202,-13457) -> Matrix(1,0,0,1) Matrix(14291,-23450,5600,-9189) -> Matrix(3,-4,4,-5) Matrix(3243,-5324,734,-1205) -> Matrix(11,-14,4,-5) Matrix(745,-1226,206,-339) -> Matrix(1,-2,4,-7) Matrix(2073,-3502,544,-919) -> Matrix(3,-4,4,-5) Matrix(3383,-5730,1956,-3313) -> Matrix(5,-4,4,-3) Matrix(3429,-5818,1942,-3295) -> Matrix(3,-2,8,-5) Matrix(525,-902,188,-323) -> Matrix(17,-16,16,-15) Matrix(3811,-6594,1494,-2585) -> Matrix(3,-4,4,-5) Matrix(3079,-5490,696,-1241) -> Matrix(1,2,0,1) Matrix(1025,-1832,268,-479) -> Matrix(7,-8,8,-9) Matrix(1023,-1834,304,-545) -> Matrix(1,0,0,1) Matrix(265,-484,144,-263) -> Matrix(5,-2,8,-3) Matrix(1173,-2500,358,-763) -> Matrix(21,-26,-4,5) Matrix(321,-698,86,-187) -> Matrix(3,-4,4,-5) Matrix(229,-518,42,-95) -> Matrix(3,-4,4,-5) Matrix(1411,-3212,322,-733) -> Matrix(9,-16,4,-7) Matrix(4403,-10082,1922,-4401) -> Matrix(25,-48,12,-23) Matrix(3177,-7294,970,-2227) -> Matrix(1,-8,0,1) Matrix(1317,-3034,484,-1115) -> Matrix(3,-10,4,-13) Matrix(121,-288,50,-119) -> Matrix(1,-2,0,1) Matrix(3273,-8014,1282,-3139) -> Matrix(1,0,0,1) Matrix(1379,-3380,286,-701) -> Matrix(1,-2,0,1) Matrix(1853,-4742,220,-563) -> Matrix(7,-4,-12,7) Matrix(3419,-8754,1308,-3349) -> Matrix(3,-2,-4,3) Matrix(2413,-6292,716,-1867) -> Matrix(1,4,0,1) Matrix(841,-2286,110,-299) -> Matrix(35,-26,-4,3) Matrix(1475,-4034,464,-1269) -> Matrix(25,-22,8,-7) Matrix(451,-1250,162,-449) -> Matrix(37,-36,36,-35) Matrix(195,-554,44,-125) -> Matrix(11,-14,4,-5) Matrix(395,-1238,82,-257) -> Matrix(1,-4,0,1) Matrix(209,-676,64,-207) -> Matrix(1,-10,0,1) Matrix(93,-314,8,-27) -> Matrix(1,2,0,1) Matrix(6511,-22050,1922,-6509) -> Matrix(11,12,-12,-13) Matrix(997,-3422,192,-659) -> Matrix(1,0,16,1) Matrix(1625,-5584,314,-1079) -> Matrix(1,0,-28,1) Matrix(1233,-4412,230,-823) -> Matrix(7,-4,16,-9) Matrix(203,-750,36,-133) -> Matrix(1,0,0,1) Matrix(379,-1458,98,-377) -> Matrix(29,-28,28,-27) Matrix(85,-392,18,-83) -> Matrix(1,-8,0,1) Matrix(637,-3646,76,-435) -> Matrix(7,-6,-8,7) Matrix(291,-1682,50,-289) -> Matrix(21,-20,20,-19) Matrix(121,-900,16,-119) -> Matrix(1,-22,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 Degree of the the map X: 96 Degree of the the map Y: 288 ----------------------------------------------------------------------- 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): 864 Minimal number of generators: 145 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: 48 Genus: 49 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 0/1 2/15 3/14 4/13 5/12 1/2 6/11 7/10 8/9 1/1 9/8 19/15 7/5 10/7 3/2 52/33 21/13 11/6 2/1 12/5 5/2 8/3 25/9 3/1 13/4 10/3 105/31 7/2 11/3 67/18 27/7 4/1 13/3 9/2 14/3 5/1 57/11 16/3 11/2 29/5 6/1 13/2 7/1 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/4 -6/13 3/10 1/3 -17/37 3/8 1/2 -11/24 1/4 -5/11 1/6 1/4 -9/20 1/4 -4/9 3/10 1/3 -19/43 5/14 3/8 -15/34 1/4 -26/59 1/3 1/2 -11/25 3/8 1/2 -7/16 1/4 -17/39 1/6 1/4 -27/62 1/4 -10/23 1/5 1/4 -3/7 1/4 3/10 -8/19 1/3 1/2 -5/12 1/4 -7/17 1/4 3/10 -9/22 5/16 -2/5 1/3 1/2 -9/23 1/4 1/2 -7/18 1/4 -5/13 1/4 1/2 -8/21 1/3 7/20 -11/29 3/8 7/18 -3/8 3/8 -7/19 1/2 1/0 -25/68 1/0 -18/49 0/1 1/6 -11/30 1/0 -4/11 1/3 1/2 -5/14 3/8 -6/17 1/3 1/2 -1/3 1/4 1/2 -5/16 1/0 -4/13 0/1 1/0 -3/10 1/4 -8/27 1/3 5/14 -13/44 11/28 -5/17 5/12 1/2 -2/7 1/2 1/1 -7/25 -1/2 1/0 -26/93 -1/2 0/1 -19/68 -1/4 -12/43 0/1 1/2 -5/18 -1/4 -8/29 0/1 1/12 -3/11 1/6 1/4 -4/15 1/3 1/2 -9/34 3/8 -5/19 5/12 1/2 -1/4 1/0 -6/25 1/5 3/14 -5/21 1/4 5/18 -4/17 1/3 3/8 -3/13 3/8 1/2 -2/9 1/2 1/1 -3/14 1/0 -1/5 1/4 1/2 -3/16 3/4 -11/59 1/2 1/0 -8/43 1/2 1/1 -5/27 1/2 1/0 -7/38 7/8 -2/11 0/1 1/0 -5/28 1/0 -3/17 1/2 1/0 -7/40 1/0 -11/63 -9/2 1/0 -4/23 -1/1 -1/2 -5/29 -1/2 -1/4 -6/35 -1/10 0/1 -1/6 1/4 -2/13 1/3 1/2 -1/7 1/2 1/0 -2/15 1/1 1/0 -5/38 1/0 -3/23 -1/2 1/0 -4/31 -1/6 0/1 -1/8 1/4 0/1 0/1 1/2 1/8 1/4 2/15 1/2 1/7 1/2 1/0 1/6 1/0 3/17 1/6 1/4 2/11 1/4 1/3 3/16 3/4 4/21 -1/1 1/0 5/26 -1/8 1/5 1/4 1/2 3/14 1/2 5/23 1/2 5/8 2/9 1/2 1/1 1/4 1/0 5/19 1/8 1/6 9/34 1/4 4/15 1/6 1/5 7/26 1/4 3/11 1/4 1/2 2/7 0/1 1/4 5/17 1/4 1/2 8/27 1/3 1/2 3/10 3/8 4/13 1/2 5/16 5/8 1/3 1/2 1/0 4/11 0/1 1/10 11/30 1/4 7/19 1/6 1/4 3/8 1/4 5/13 1/4 1/2 7/18 3/8 2/5 1/3 1/2 5/12 1/2 8/19 1/2 4/7 3/7 1/2 3/4 13/30 1/0 10/23 1/2 1/1 17/39 1/2 3/4 7/16 1/0 11/25 1/4 1/2 15/34 7/12 4/9 3/4 1/1 1/2 1/4 6/11 1/2 11/20 11/20 5/9 1/2 5/8 4/7 1/2 1/1 11/19 3/4 5/6 7/12 5/4 3/5 -1/2 1/0 5/8 1/8 7/11 1/6 1/4 2/3 1/3 1/2 7/10 1/2 12/17 1/2 6/11 5/7 1/2 5/8 18/25 3/5 5/8 31/43 9/14 13/20 13/18 11/16 8/11 5/6 1/1 3/4 1/0 10/13 0/1 1/2 17/22 1/0 7/9 -1/2 1/0 4/5 0/1 1/4 5/6 1/4 21/25 3/8 1/2 16/19 1/3 1/2 11/13 3/8 1/2 6/7 1/3 3/8 13/15 3/8 1/2 7/8 7/16 8/9 1/2 9/10 9/16 1/1 1/2 1/0 9/8 1/2 8/7 1/2 4/7 15/13 11/18 5/8 7/6 5/8 13/11 1/2 3/4 19/16 3/4 25/21 3/4 5/6 31/26 7/8 6/5 1/2 1/1 5/4 3/4 19/15 1/1 14/11 1/1 5/4 9/7 1/2 1/0 22/17 3/2 2/1 13/10 1/0 4/3 1/2 1/1 19/14 1/0 34/25 4/1 1/0 15/11 -3/2 1/0 11/8 1/4 18/13 -1/2 0/1 7/5 1/4 1/2 10/7 1/2 13/9 1/2 7/12 3/2 3/4 11/7 7/10 3/4 52/33 3/4 93/59 3/4 77/102 41/26 3/4 30/19 17/22 7/9 19/12 13/16 8/5 7/8 1/1 21/13 1/1 34/21 1/1 25/24 13/8 9/8 5/3 1/2 1/0 32/19 1/2 27/16 3/4 49/29 1/2 1/0 22/13 1/2 1/1 17/10 1/0 12/7 5/6 1/1 31/18 13/12 19/11 5/4 3/2 7/4 1/0 16/9 1/1 1/0 9/5 1/2 1/0 11/6 1/2 13/7 1/2 3/4 2/1 1/2 1/1 13/6 5/4 11/5 3/2 1/0 9/4 5/4 25/11 3/2 7/4 16/7 3/2 2/1 23/10 1/0 7/3 3/2 1/0 12/5 1/0 17/7 -1/2 1/0 5/2 1/0 18/7 3/4 1/1 49/19 1/1 31/12 5/4 13/5 3/2 1/0 21/8 1/0 8/3 1/2 1/1 19/7 7/10 3/4 11/4 7/8 25/9 1/1 39/14 29/28 14/5 1/1 11/10 3/1 3/2 1/0 13/4 1/0 23/7 -7/2 1/0 10/3 -1/1 1/0 37/11 1/2 1/0 27/8 1/0 44/13 -3/2 -1/1 105/31 -1/1 166/49 -1/1 -9/10 61/18 -3/4 17/5 -1/2 1/0 24/7 -1/6 0/1 79/23 0/1 55/16 1/16 31/9 1/6 1/4 38/11 1/2 1/1 7/2 1/0 18/5 0/1 1/2 11/3 1/2 3/4 26/7 1/2 1/1 67/18 1/2 108/29 1/2 2/3 41/11 1/2 3/4 15/4 1/0 49/13 1/2 5/8 34/9 5/7 3/4 53/14 3/4 19/5 3/4 5/6 23/6 11/12 27/7 1/1 31/8 17/16 4/1 1/1 3/2 13/3 5/2 1/0 9/2 1/0 14/3 1/0 19/4 1/0 5/1 -1/2 1/0 31/6 -1/12 57/11 0/1 26/5 0/1 1/10 21/4 1/4 37/7 1/2 1/0 16/3 1/3 1/2 43/8 1/2 27/5 1/2 5/8 11/2 1/0 28/5 1/2 1/1 17/3 1/2 3/4 23/4 7/8 29/5 1/1 35/6 13/12 6/1 1/1 3/2 13/2 7/4 7/1 7/2 1/0 15/2 1/0 23/3 -15/2 1/0 8/1 -2/1 1/0 17/2 -1/4 9/1 1/2 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(255,118,188,87) (-1/2,-6/13) -> (4/3,19/14) Hyperbolic Matrix(187,86,-1446,-665) (-6/13,-17/37) -> (-3/23,-4/31) Hyperbolic Matrix(375,172,-2008,-921) (-17/37,-11/24) -> (-3/16,-11/59) Hyperbolic Matrix(437,200,378,173) (-11/24,-5/11) -> (15/13,7/6) Hyperbolic Matrix(309,140,64,29) (-5/11,-9/20) -> (19/4,5/1) Hyperbolic Matrix(557,250,430,193) (-9/20,-4/9) -> (22/17,13/10) Hyperbolic Matrix(303,134,-1766,-781) (-4/9,-19/43) -> (-5/29,-6/35) Hyperbolic Matrix(1037,458,120,53) (-19/43,-15/34) -> (17/2,9/1) Hyperbolic Matrix(2005,884,-7174,-3163) (-15/34,-26/59) -> (-26/93,-19/68) Hyperbolic Matrix(849,374,-4556,-2007) (-26/59,-11/25) -> (-11/59,-8/43) Hyperbolic Matrix(305,134,-1154,-507) (-11/25,-7/16) -> (-9/34,-5/19) Hyperbolic Matrix(1087,474,-2956,-1289) (-7/16,-17/39) -> (-7/19,-25/68) Hyperbolic Matrix(2291,998,1926,839) (-17/39,-27/62) -> (19/16,25/21) Hyperbolic Matrix(239,104,-1804,-785) (-27/62,-10/23) -> (-2/15,-5/38) Hyperbolic Matrix(599,260,182,79) (-10/23,-3/7) -> (23/7,10/3) Hyperbolic Matrix(237,100,410,173) (-3/7,-8/19) -> (4/7,11/19) Hyperbolic Matrix(177,74,232,97) (-8/19,-5/12) -> (3/4,10/13) Hyperbolic Matrix(289,120,118,49) (-5/12,-7/17) -> (17/7,5/2) Hyperbolic Matrix(405,166,344,141) (-7/17,-9/22) -> (7/6,13/11) Hyperbolic Matrix(289,118,-1036,-423) (-9/22,-2/5) -> (-12/43,-5/18) Hyperbolic Matrix(111,44,58,23) (-2/5,-9/23) -> (13/7,2/1) Hyperbolic Matrix(169,66,-950,-371) (-9/23,-7/18) -> (-5/28,-3/17) Hyperbolic Matrix(165,64,446,173) (-7/18,-5/13) -> (7/19,3/8) Hyperbolic Matrix(167,64,-608,-233) (-5/13,-8/21) -> (-8/29,-3/11) Hyperbolic Matrix(221,84,-934,-355) (-8/21,-11/29) -> (-5/21,-4/17) Hyperbolic Matrix(549,208,710,269) (-11/29,-3/8) -> (17/22,7/9) Hyperbolic Matrix(161,60,110,41) (-3/8,-7/19) -> (13/9,3/2) Hyperbolic Matrix(2797,1028,536,197) (-25/68,-18/49) -> (26/5,21/4) Hyperbolic Matrix(1291,474,-4622,-1697) (-18/49,-11/30) -> (-19/68,-12/43) Hyperbolic Matrix(323,118,52,19) (-11/30,-4/11) -> (6/1,13/2) Hyperbolic Matrix(105,38,268,97) (-4/11,-5/14) -> (7/18,2/5) Hyperbolic Matrix(209,74,-788,-279) (-5/14,-6/17) -> (-4/15,-9/34) Hyperbolic Matrix(473,166,208,73) (-6/17,-1/3) -> (25/11,16/7) Hyperbolic Matrix(197,62,448,141) (-1/3,-5/16) -> (7/16,11/25) Hyperbolic Matrix(97,30,-540,-167) (-5/16,-4/13) -> (-2/11,-5/28) Hyperbolic Matrix(245,74,96,29) (-4/13,-3/10) -> (5/2,18/7) Hyperbolic Matrix(337,100,920,273) (-3/10,-8/27) -> (4/11,11/30) Hyperbolic Matrix(291,86,-1208,-357) (-8/27,-13/44) -> (-1/4,-6/25) Hyperbolic Matrix(339,100,-1834,-541) (-13/44,-5/17) -> (-5/27,-7/38) Hyperbolic Matrix(239,70,338,99) (-5/17,-2/7) -> (12/17,5/7) Hyperbolic Matrix(613,172,474,133) (-2/7,-7/25) -> (9/7,22/17) Hyperbolic Matrix(6513,1822,1748,489) (-7/25,-26/93) -> (108/29,41/11) Hyperbolic Matrix(989,274,610,169) (-5/18,-8/29) -> (34/21,13/8) Hyperbolic Matrix(373,100,138,37) (-3/11,-4/15) -> (8/3,19/7) Hyperbolic Matrix(229,60,416,109) (-5/19,-1/4) -> (11/20,5/9) Hyperbolic Matrix(359,86,-2058,-493) (-6/25,-5/21) -> (-11/63,-4/23) Hyperbolic Matrix(265,62,312,73) (-4/17,-3/13) -> (11/13,6/7) Hyperbolic Matrix(131,30,310,71) (-3/13,-2/9) -> (8/19,3/7) Hyperbolic Matrix(173,38,132,29) (-2/9,-3/14) -> (13/10,4/3) Hyperbolic Matrix(301,64,174,37) (-3/14,-1/5) -> (19/11,7/4) Hyperbolic Matrix(41,8,128,25) (-1/5,-3/16) -> (5/16,1/3) Hyperbolic Matrix(1335,248,1588,295) (-8/43,-5/27) -> (21/25,16/19) Hyperbolic Matrix(207,38,1084,199) (-7/38,-2/11) -> (4/21,5/26) Hyperbolic Matrix(205,36,-1566,-275) (-3/17,-7/40) -> (-5/38,-3/23) Hyperbolic Matrix(6303,1102,3998,699) (-7/40,-11/63) -> (93/59,41/26) Hyperbolic Matrix(1315,228,248,43) (-4/23,-5/29) -> (37/7,16/3) Hyperbolic Matrix(1109,190,286,49) (-6/35,-1/6) -> (31/8,4/1) Hyperbolic Matrix(281,44,364,57) (-1/6,-2/13) -> (10/13,17/22) Hyperbolic Matrix(79,12,362,55) (-2/13,-1/7) -> (5/23,2/9) Hyperbolic Matrix(237,32,274,37) (-1/7,-2/15) -> (6/7,13/15) Hyperbolic Matrix(1133,146,194,25) (-4/31,-1/8) -> (35/6,6/1) Hyperbolic Matrix(193,22,114,13) (-1/8,0/1) -> (22/13,17/10) Hyperbolic Matrix(93,-10,214,-23) (0/1,1/8) -> (13/30,10/23) Hyperbolic Matrix(661,-86,392,-51) (1/8,2/15) -> (32/19,27/16) Hyperbolic Matrix(299,-42,178,-25) (2/15,1/7) -> (5/3,32/19) Hyperbolic Matrix(119,-18,324,-49) (1/7,1/6) -> (11/30,7/19) Hyperbolic Matrix(493,-86,86,-15) (1/6,3/17) -> (17/3,23/4) Hyperbolic Matrix(577,-104,172,-31) (3/17,2/11) -> (10/3,37/11) Hyperbolic Matrix(229,-42,518,-95) (2/11,3/16) -> (15/34,4/9) Hyperbolic Matrix(485,-92,58,-11) (3/16,4/21) -> (8/1,17/2) Hyperbolic Matrix(285,-56,56,-11) (5/26,1/5) -> (5/1,31/6) Hyperbolic Matrix(85,-18,392,-83) (1/5,3/14) -> (3/14,5/23) Parabolic Matrix(221,-50,84,-19) (2/9,1/4) -> (21/8,8/3) Hyperbolic Matrix(513,-134,134,-35) (1/4,5/19) -> (19/5,23/6) Hyperbolic Matrix(2179,-576,1290,-341) (5/19,9/34) -> (27/16,49/29) Hyperbolic Matrix(1397,-370,404,-107) (9/34,4/15) -> (38/11,7/2) Hyperbolic Matrix(1395,-374,884,-237) (4/15,7/26) -> (41/26,30/19) Hyperbolic Matrix(1259,-340,374,-101) (7/26,3/11) -> (37/11,27/8) Hyperbolic Matrix(239,-66,134,-37) (3/11,2/7) -> (16/9,9/5) Hyperbolic Matrix(341,-100,474,-139) (2/7,5/17) -> (5/7,18/25) Hyperbolic Matrix(629,-186,1444,-427) (5/17,8/27) -> (10/23,17/39) Hyperbolic Matrix(577,-172,104,-31) (8/27,3/10) -> (11/2,28/5) Hyperbolic Matrix(105,-32,338,-103) (3/10,4/13) -> (4/13,5/16) Parabolic Matrix(75,-26,26,-9) (1/3,4/11) -> (14/5,3/1) Hyperbolic Matrix(221,-84,50,-19) (3/8,5/13) -> (13/3,9/2) Hyperbolic Matrix(637,-246,246,-95) (5/13,7/18) -> (31/12,13/5) Hyperbolic Matrix(121,-50,288,-119) (2/5,5/12) -> (5/12,8/19) Parabolic Matrix(1257,-544,238,-103) (3/7,13/30) -> (21/4,37/7) Hyperbolic Matrix(2651,-1156,782,-341) (17/39,7/16) -> (61/18,17/5) Hyperbolic Matrix(259,-114,284,-125) (11/25,15/34) -> (9/10,1/1) Hyperbolic Matrix(187,-84,118,-53) (4/9,1/2) -> (19/12,8/5) Hyperbolic Matrix(133,-72,242,-131) (1/2,6/11) -> (6/11,11/20) Parabolic Matrix(239,-134,66,-37) (5/9,4/7) -> (18/5,11/3) Hyperbolic Matrix(817,-474,474,-275) (11/19,7/12) -> (31/18,19/11) Hyperbolic Matrix(235,-138,172,-101) (7/12,3/5) -> (15/11,11/8) Hyperbolic Matrix(105,-64,64,-39) (3/5,5/8) -> (13/8,5/3) Hyperbolic Matrix(187,-118,84,-53) (5/8,7/11) -> (11/5,9/4) Hyperbolic Matrix(83,-54,20,-13) (7/11,2/3) -> (4/1,13/3) Hyperbolic Matrix(141,-98,200,-139) (2/3,7/10) -> (7/10,12/17) Parabolic Matrix(2687,-1936,712,-513) (18/25,31/43) -> (49/13,34/9) Hyperbolic Matrix(2923,-2108,850,-613) (31/43,13/18) -> (55/16,31/9) Hyperbolic Matrix(749,-542,474,-343) (13/18,8/11) -> (30/19,19/12) Hyperbolic Matrix(235,-172,138,-101) (8/11,3/4) -> (17/10,12/7) Hyperbolic Matrix(171,-134,134,-105) (7/9,4/5) -> (14/11,9/7) Hyperbolic Matrix(131,-108,74,-61) (4/5,5/6) -> (7/4,16/9) Hyperbolic Matrix(925,-776,776,-651) (5/6,21/25) -> (25/21,31/26) Hyperbolic Matrix(1217,-1026,720,-607) (16/19,11/13) -> (49/29,22/13) Hyperbolic Matrix(617,-538,164,-143) (13/15,7/8) -> (15/4,49/13) Hyperbolic Matrix(145,-128,162,-143) (7/8,8/9) -> (8/9,9/10) Parabolic Matrix(259,-286,48,-53) (1/1,9/8) -> (43/8,27/5) Hyperbolic Matrix(429,-488,80,-91) (9/8,8/7) -> (16/3,43/8) Hyperbolic Matrix(711,-818,206,-237) (8/7,15/13) -> (31/9,38/11) Hyperbolic Matrix(887,-1050,234,-277) (13/11,19/16) -> (53/14,19/5) Hyperbolic Matrix(4621,-5512,1364,-1627) (31/26,6/5) -> (166/49,61/18) Hyperbolic Matrix(107,-132,30,-37) (6/5,5/4) -> (7/2,18/5) Hyperbolic Matrix(661,-834,256,-323) (5/4,19/15) -> (49/19,31/12) Hyperbolic Matrix(809,-1028,314,-399) (19/15,14/11) -> (18/7,49/19) Hyperbolic Matrix(1801,-2448,476,-647) (19/14,34/25) -> (34/9,53/14) Hyperbolic Matrix(663,-902,86,-117) (34/25,15/11) -> (23/3,8/1) Hyperbolic Matrix(185,-256,86,-119) (11/8,18/13) -> (2/1,13/6) Hyperbolic Matrix(341,-474,100,-139) (18/13,7/5) -> (17/5,24/7) Hyperbolic Matrix(141,-200,98,-139) (7/5,10/7) -> (10/7,13/9) Parabolic Matrix(173,-270,66,-103) (3/2,11/7) -> (13/5,21/8) Hyperbolic Matrix(3433,-5408,2178,-3431) (11/7,52/33) -> (52/33,93/59) Parabolic Matrix(547,-882,338,-545) (8/5,21/13) -> (21/13,34/21) Parabolic Matrix(525,-902,188,-323) (12/7,31/18) -> (39/14,14/5) Hyperbolic Matrix(133,-242,72,-131) (9/5,11/6) -> (11/6,13/7) Parabolic Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(229,-518,42,-95) (9/4,25/11) -> (27/5,11/2) Hyperbolic Matrix(629,-1444,186,-427) (16/7,23/10) -> (27/8,44/13) Hyperbolic Matrix(93,-214,10,-23) (23/10,7/3) -> (9/1,1/0) Hyperbolic Matrix(121,-288,50,-119) (7/3,12/5) -> (12/5,17/7) Parabolic Matrix(119,-324,18,-49) (19/7,11/4) -> (13/2,7/1) Hyperbolic Matrix(451,-1250,162,-449) (11/4,25/9) -> (25/9,39/14) Parabolic Matrix(105,-338,32,-103) (3/1,13/4) -> (13/4,23/7) Parabolic Matrix(6511,-22050,1922,-6509) (44/13,105/31) -> (105/31,166/49) Parabolic Matrix(997,-3422,192,-659) (24/7,79/23) -> (57/11,26/5) Hyperbolic Matrix(1625,-5584,314,-1079) (79/23,55/16) -> (31/6,57/11) Hyperbolic Matrix(203,-750,36,-133) (11/3,26/7) -> (28/5,17/3) Hyperbolic Matrix(2413,-8978,648,-2411) (26/7,67/18) -> (67/18,108/29) Parabolic Matrix(379,-1458,98,-377) (23/6,27/7) -> (27/7,31/8) Parabolic Matrix(85,-392,18,-83) (9/2,14/3) -> (14/3,19/4) Parabolic Matrix(291,-1682,50,-289) (23/4,29/5) -> (29/5,35/6) Parabolic Matrix(61,-450,8,-59) (7/1,15/2) -> (15/2,23/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,4,1) Matrix(255,118,188,87) -> Matrix(7,-2,4,-1) Matrix(187,86,-1446,-665) -> Matrix(3,-1,-8,3) Matrix(375,172,-2008,-921) -> Matrix(5,-2,8,-3) Matrix(437,200,378,173) -> Matrix(7,-3,12,-5) Matrix(309,140,64,29) -> Matrix(5,-1,-4,1) Matrix(557,250,430,193) -> Matrix(11,-3,4,-1) Matrix(303,134,-1766,-781) -> Matrix(3,-1,-20,7) Matrix(1037,458,120,53) -> Matrix(3,-1,-8,3) Matrix(2005,884,-7174,-3163) -> Matrix(3,-1,-8,3) Matrix(849,374,-4556,-2007) -> Matrix(5,-2,8,-3) Matrix(305,134,-1154,-507) -> Matrix(1,-1,4,-3) Matrix(1087,474,-2956,-1289) -> Matrix(1,0,-4,1) Matrix(2291,998,1926,839) -> Matrix(19,-4,24,-5) Matrix(239,104,-1804,-785) -> Matrix(1,0,-4,1) Matrix(599,260,182,79) -> Matrix(9,-2,-4,1) Matrix(237,100,410,173) -> Matrix(5,-2,8,-3) Matrix(177,74,232,97) -> Matrix(3,-1,4,-1) Matrix(289,120,118,49) -> Matrix(3,-1,4,-1) Matrix(405,166,344,141) -> Matrix(17,-5,24,-7) Matrix(289,118,-1036,-423) -> Matrix(3,-1,4,-1) Matrix(111,44,58,23) -> Matrix(5,-2,8,-3) Matrix(169,66,-950,-371) -> Matrix(3,-1,4,-1) Matrix(165,64,446,173) -> Matrix(3,-1,16,-5) Matrix(167,64,-608,-233) -> Matrix(3,-1,16,-5) Matrix(221,84,-934,-355) -> Matrix(11,-4,36,-13) Matrix(549,208,710,269) -> Matrix(5,-2,8,-3) Matrix(161,60,110,41) -> Matrix(7,-3,12,-5) Matrix(2797,1028,536,197) -> Matrix(1,0,4,1) Matrix(1291,474,-4622,-1697) -> Matrix(1,0,-4,1) Matrix(323,118,52,19) -> Matrix(7,-2,4,-1) Matrix(105,38,268,97) -> Matrix(1,0,0,1) Matrix(209,74,-788,-279) -> Matrix(1,0,0,1) Matrix(473,166,208,73) -> Matrix(13,-5,8,-3) Matrix(197,62,448,141) -> Matrix(1,0,0,1) Matrix(97,30,-540,-167) -> Matrix(1,0,0,1) Matrix(245,74,96,29) -> Matrix(3,-1,4,-1) Matrix(337,100,920,273) -> Matrix(3,-1,16,-5) Matrix(291,86,-1208,-357) -> Matrix(5,-2,28,-11) Matrix(339,100,-1834,-541) -> Matrix(7,-3,12,-5) Matrix(239,70,338,99) -> Matrix(11,-5,20,-9) Matrix(613,172,474,133) -> Matrix(1,1,0,1) Matrix(6513,1822,1748,489) -> Matrix(3,2,4,3) Matrix(989,274,610,169) -> Matrix(13,1,12,1) Matrix(373,100,138,37) -> Matrix(5,-2,8,-3) Matrix(229,60,416,109) -> Matrix(11,-5,20,-9) Matrix(359,86,-2058,-493) -> Matrix(9,-2,-4,1) Matrix(265,62,312,73) -> Matrix(1,0,0,1) Matrix(131,30,310,71) -> Matrix(7,-3,12,-5) Matrix(173,38,132,29) -> Matrix(1,0,0,1) Matrix(301,64,174,37) -> Matrix(1,1,0,1) Matrix(41,8,128,25) -> Matrix(3,-1,4,-1) Matrix(1335,248,1588,295) -> Matrix(3,-2,8,-5) Matrix(207,38,1084,199) -> Matrix(1,-1,0,1) Matrix(205,36,-1566,-275) -> Matrix(1,-1,0,1) Matrix(6303,1102,3998,699) -> Matrix(3,-25,4,-33) Matrix(1315,228,248,43) -> Matrix(1,0,4,1) Matrix(1109,190,286,49) -> Matrix(13,1,12,1) Matrix(281,44,364,57) -> Matrix(3,-1,4,-1) Matrix(79,12,362,55) -> Matrix(5,-2,8,-3) Matrix(237,32,274,37) -> Matrix(3,-2,8,-5) Matrix(1133,146,194,25) -> Matrix(9,1,8,1) Matrix(193,22,114,13) -> Matrix(3,-1,4,-1) Matrix(93,-10,214,-23) -> Matrix(3,-1,4,-1) Matrix(661,-86,392,-51) -> Matrix(5,-2,8,-3) Matrix(299,-42,178,-25) -> Matrix(1,0,0,1) Matrix(119,-18,324,-49) -> Matrix(1,0,4,1) Matrix(493,-86,86,-15) -> Matrix(7,-1,8,-1) Matrix(577,-104,172,-31) -> Matrix(1,0,-4,1) Matrix(229,-42,518,-95) -> Matrix(5,-2,8,-3) Matrix(485,-92,58,-11) -> Matrix(1,-1,0,1) Matrix(285,-56,56,-11) -> Matrix(1,0,-4,1) Matrix(85,-18,392,-83) -> Matrix(7,-3,12,-5) Matrix(221,-50,84,-19) -> Matrix(1,0,0,1) Matrix(513,-134,134,-35) -> Matrix(11,-1,12,-1) Matrix(2179,-576,1290,-341) -> Matrix(7,-1,8,-1) Matrix(1397,-370,404,-107) -> Matrix(1,0,-4,1) Matrix(1395,-374,884,-237) -> Matrix(43,-10,56,-13) Matrix(1259,-340,374,-101) -> Matrix(3,-1,4,-1) Matrix(239,-66,134,-37) -> Matrix(3,-1,4,-1) Matrix(341,-100,474,-139) -> Matrix(7,-3,12,-5) Matrix(629,-186,1444,-427) -> Matrix(5,-2,8,-3) Matrix(577,-172,104,-31) -> Matrix(5,-2,8,-3) Matrix(105,-32,338,-103) -> Matrix(9,-4,16,-7) Matrix(75,-26,26,-9) -> Matrix(1,1,0,1) Matrix(221,-84,50,-19) -> Matrix(11,-3,4,-1) Matrix(637,-246,246,-95) -> Matrix(7,-2,4,-1) Matrix(121,-50,288,-119) -> Matrix(11,-5,20,-9) Matrix(1257,-544,238,-103) -> Matrix(1,-1,4,-3) Matrix(2651,-1156,782,-341) -> Matrix(3,-2,-4,3) Matrix(259,-114,284,-125) -> Matrix(3,-1,4,-1) Matrix(187,-84,118,-53) -> Matrix(3,-4,4,-5) Matrix(133,-72,242,-131) -> Matrix(13,-6,24,-11) Matrix(239,-134,66,-37) -> Matrix(1,-1,4,-3) Matrix(817,-474,474,-275) -> Matrix(9,-8,8,-7) Matrix(235,-138,172,-101) -> Matrix(1,-1,0,1) Matrix(105,-64,64,-39) -> Matrix(1,1,0,1) Matrix(187,-118,84,-53) -> Matrix(3,-1,4,-1) Matrix(83,-54,20,-13) -> Matrix(7,-2,4,-1) Matrix(141,-98,200,-139) -> Matrix(15,-7,28,-13) Matrix(2687,-1936,712,-513) -> Matrix(25,-16,36,-23) Matrix(2923,-2108,850,-613) -> Matrix(3,-2,32,-21) Matrix(749,-542,474,-343) -> Matrix(25,-18,32,-23) Matrix(235,-172,138,-101) -> Matrix(1,0,0,1) Matrix(171,-134,134,-105) -> Matrix(1,1,0,1) Matrix(131,-108,74,-61) -> Matrix(3,-1,4,-1) Matrix(925,-776,776,-651) -> Matrix(17,-6,20,-7) Matrix(1217,-1026,720,-607) -> Matrix(5,-2,8,-3) Matrix(617,-538,164,-143) -> Matrix(9,-4,16,-7) Matrix(145,-128,162,-143) -> Matrix(17,-8,32,-15) Matrix(259,-286,48,-53) -> Matrix(5,-2,8,-3) Matrix(429,-488,80,-91) -> Matrix(9,-5,20,-11) Matrix(711,-818,206,-237) -> Matrix(5,-3,12,-7) Matrix(887,-1050,234,-277) -> Matrix(13,-9,16,-11) Matrix(4621,-5512,1364,-1627) -> Matrix(11,-10,-12,11) Matrix(107,-132,30,-37) -> Matrix(1,-1,4,-3) Matrix(661,-834,256,-323) -> Matrix(9,-8,8,-7) Matrix(809,-1028,314,-399) -> Matrix(7,-8,8,-9) Matrix(1801,-2448,476,-647) -> Matrix(3,-7,4,-9) Matrix(663,-902,86,-117) -> Matrix(1,-6,0,1) Matrix(185,-256,86,-119) -> Matrix(1,1,0,1) Matrix(341,-474,100,-139) -> Matrix(1,0,-4,1) Matrix(141,-200,98,-139) -> Matrix(9,-4,16,-7) Matrix(173,-270,66,-103) -> Matrix(1,-1,4,-3) Matrix(3433,-5408,2178,-3431) -> Matrix(169,-126,224,-167) Matrix(547,-882,338,-545) -> Matrix(33,-32,32,-31) Matrix(525,-902,188,-323) -> Matrix(17,-16,16,-15) Matrix(133,-242,72,-131) -> Matrix(3,-1,4,-1) Matrix(321,-698,86,-187) -> Matrix(3,-4,4,-5) Matrix(229,-518,42,-95) -> Matrix(3,-4,4,-5) Matrix(629,-1444,186,-427) -> Matrix(1,-3,0,1) Matrix(93,-214,10,-23) -> Matrix(1,-1,0,1) Matrix(121,-288,50,-119) -> Matrix(1,-2,0,1) Matrix(119,-324,18,-49) -> Matrix(9,-7,4,-3) Matrix(451,-1250,162,-449) -> Matrix(37,-36,36,-35) Matrix(105,-338,32,-103) -> Matrix(1,-5,0,1) Matrix(6511,-22050,1922,-6509) -> Matrix(11,12,-12,-13) Matrix(997,-3422,192,-659) -> Matrix(1,0,16,1) Matrix(1625,-5584,314,-1079) -> Matrix(1,0,-28,1) Matrix(203,-750,36,-133) -> Matrix(1,0,0,1) Matrix(2413,-8978,648,-2411) -> Matrix(3,-1,4,-1) Matrix(379,-1458,98,-377) -> Matrix(29,-28,28,-27) Matrix(85,-392,18,-83) -> Matrix(1,-8,0,1) Matrix(291,-1682,50,-289) -> Matrix(21,-20,20,-19) Matrix(61,-450,8,-59) -> Matrix(1,-11,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of 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): 48 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 2 1 0/1 (0/1,1/2) 0 34 1/8 1/4 1 34 2/15 1/2 2 2 1/7 (1/2,1/0) 0 17 1/6 1/0 1 34 3/17 (1/6,1/4) 0 17 2/11 (1/4,1/3) 0 34 3/16 3/4 1 34 4/21 (-1/1,1/0) 0 34 1/5 (1/4,1/2) 0 17 3/14 1/2 3 2 2/9 (1/2,1/1) 0 34 1/4 1/0 1 34 5/19 (1/8,1/6) 0 17 9/34 1/4 1 34 4/15 (1/6,1/5) 0 34 7/26 1/4 1 34 3/11 (1/4,1/2) 0 17 2/7 (0/1,1/4) 0 34 5/17 (1/4,1/2) 0 17 8/27 (1/3,1/2) 0 34 3/10 3/8 1 34 4/13 1/2 4 2 1/3 (1/2,1/0) 0 17 4/11 (0/1,1/10) 0 34 3/8 1/4 1 34 5/13 (1/4,1/2) 0 17 2/5 (1/3,1/2) 0 34 5/12 1/2 5 2 3/7 (1/2,3/4) 0 17 13/30 1/0 1 34 10/23 (1/2,1/1) 0 34 17/39 (1/2,3/4) 0 17 7/16 1/0 1 34 4/9 (3/4,1/1) 0 34 1/2 1/4 1 34 6/11 1/2 6 2 5/9 (1/2,5/8) 0 17 4/7 (1/2,1/1) 0 34 7/12 5/4 1 34 3/5 (-1/2,1/0) 0 17 5/8 1/8 1 34 7/11 (1/6,1/4) 0 17 2/3 (1/3,1/2) 0 34 7/10 1/2 7 2 5/7 (1/2,5/8) 0 17 18/25 (3/5,5/8) 0 34 31/43 (9/14,13/20) 0 17 13/18 11/16 1 34 8/11 (5/6,1/1) 0 34 3/4 1/0 1 34 7/9 (-1/2,1/0) 0 17 4/5 (0/1,1/4) 0 34 5/6 1/4 1 34 6/7 (1/3,3/8) 0 34 7/8 7/16 1 34 8/9 1/2 8 2 1/1 (1/2,1/0) 0 17 9/8 1/2 7 2 8/7 (1/2,4/7) 0 34 7/6 5/8 1 34 6/5 (1/2,1/1) 0 34 5/4 3/4 1 34 19/15 1/1 8 1 14/11 (1/1,5/4) 0 34 9/7 (1/2,1/0) 0 17 4/3 (1/2,1/1) 0 34 15/11 (-3/2,1/0) 0 17 11/8 1/4 1 34 18/13 (-1/2,0/1) 0 34 7/5 (1/4,1/2) 0 17 10/7 1/2 4 2 3/2 3/4 1 34 11/7 (7/10,3/4) 0 17 52/33 3/4 14 2 41/26 3/4 1 34 30/19 (17/22,7/9) 0 34 19/12 13/16 1 34 8/5 (7/8,1/1) 0 34 21/13 1/1 16 1 13/8 9/8 1 34 5/3 (1/2,1/0) 0 17 17/10 1/0 1 34 12/7 (5/6,1/1) 0 34 7/4 1/0 1 34 16/9 (1/1,1/0) 0 34 9/5 (1/2,1/0) 0 17 11/6 1/2 1 2 2/1 (1/2,1/1) 0 34 13/6 5/4 1 34 11/5 (3/2,1/0) 0 17 9/4 5/4 1 34 16/7 (3/2,2/1) 0 34 23/10 1/0 1 34 7/3 (3/2,1/0) 0 17 12/5 1/0 2 2 5/2 1/0 1 34 13/5 (3/2,1/0) 0 17 21/8 1/0 1 34 8/3 (1/2,1/1) 0 34 11/4 7/8 1 34 25/9 1/1 18 1 14/5 (1/1,11/10) 0 34 3/1 (3/2,1/0) 0 17 13/4 1/0 5 2 10/3 (-1/1,1/0) 0 34 37/11 (1/2,1/0) 0 17 27/8 1/0 1 34 44/13 (-3/2,-1/1) 0 34 105/31 -1/1 6 1 61/18 -3/4 1 34 17/5 (-1/2,1/0) 0 17 24/7 (-1/6,0/1) 0 34 79/23 0/1 22 1 55/16 1/16 1 34 31/9 (1/6,1/4) 0 17 7/2 1/0 1 34 18/5 (0/1,1/2) 0 34 11/3 (1/2,3/4) 0 17 26/7 (1/2,1/1) 0 34 67/18 1/2 1 2 41/11 (1/2,3/4) 0 17 15/4 1/0 1 34 34/9 (5/7,3/4) 0 34 19/5 (3/4,5/6) 0 17 23/6 11/12 1 34 27/7 1/1 14 1 4/1 (1/1,3/2) 0 34 13/3 (5/2,1/0) 0 17 9/2 1/0 1 34 14/3 1/0 8 2 5/1 (-1/2,1/0) 0 17 21/4 1/4 1 34 16/3 (1/3,1/2) 0 34 11/2 1/0 1 34 28/5 (1/2,1/1) 0 34 17/3 (1/2,3/4) 0 17 23/4 7/8 1 34 29/5 1/1 10 1 6/1 (1/1,3/2) 0 34 7/1 (7/2,1/0) 0 17 15/2 1/0 11 2 8/1 (-2/1,1/0) 0 34 9/1 (1/2,1/0) 0 17 1/0 1/0 1 34 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(93,-10,214,-23) (0/1,1/8) -> (13/30,10/23) Hyperbolic Matrix(31,-4,240,-31) (1/8,2/15) -> (1/8,2/15) Reflection Matrix(29,-4,210,-29) (2/15,1/7) -> (2/15,1/7) Reflection Matrix(149,-22,88,-13) (1/7,1/6) -> (5/3,17/10) Glide Reflection Matrix(493,-86,86,-15) (1/6,3/17) -> (17/3,23/4) Hyperbolic Matrix(577,-104,172,-31) (3/17,2/11) -> (10/3,37/11) Hyperbolic Matrix(173,-32,200,-37) (2/11,3/16) -> (6/7,7/8) Glide Reflection Matrix(859,-162,228,-43) (3/16,4/21) -> (15/4,34/9) Glide Reflection Matrix(741,-142,1028,-197) (4/21,1/5) -> (18/25,31/43) Glide Reflection Matrix(29,-6,140,-29) (1/5,3/14) -> (1/5,3/14) Reflection Matrix(55,-12,252,-55) (3/14,2/9) -> (3/14,2/9) Reflection Matrix(221,-50,84,-19) (2/9,1/4) -> (21/8,8/3) Hyperbolic Matrix(513,-134,134,-35) (1/4,5/19) -> (19/5,23/6) Hyperbolic Matrix(349,-92,808,-213) (5/19,9/34) -> (3/7,13/30) Glide Reflection Matrix(859,-228,162,-43) (9/34,4/15) -> (21/4,16/3) Glide Reflection Matrix(1395,-374,884,-237) (4/15,7/26) -> (41/26,30/19) Hyperbolic Matrix(1259,-340,374,-101) (7/26,3/11) -> (37/11,27/8) Hyperbolic Matrix(239,-66,134,-37) (3/11,2/7) -> (16/9,9/5) Hyperbolic Matrix(341,-100,474,-139) (2/7,5/17) -> (5/7,18/25) Hyperbolic Matrix(629,-186,1444,-427) (5/17,8/27) -> (10/23,17/39) Hyperbolic Matrix(577,-172,104,-31) (8/27,3/10) -> (11/2,28/5) Hyperbolic Matrix(79,-24,260,-79) (3/10,4/13) -> (3/10,4/13) Reflection Matrix(25,-8,78,-25) (4/13,1/3) -> (4/13,1/3) Reflection Matrix(75,-26,26,-9) (1/3,4/11) -> (14/5,3/1) Hyperbolic Matrix(173,-64,100,-37) (4/11,3/8) -> (12/7,7/4) Glide Reflection Matrix(221,-84,50,-19) (3/8,5/13) -> (13/3,9/2) Hyperbolic Matrix(97,-38,74,-29) (5/13,2/5) -> (9/7,4/3) Glide Reflection Matrix(49,-20,120,-49) (2/5,5/12) -> (2/5,5/12) Reflection Matrix(71,-30,168,-71) (5/12,3/7) -> (5/12,3/7) Reflection Matrix(2651,-1156,782,-341) (17/39,7/16) -> (61/18,17/5) Hyperbolic Matrix(141,-62,166,-73) (7/16,4/9) -> (5/6,6/7) Glide Reflection Matrix(187,-84,118,-53) (4/9,1/2) -> (19/12,8/5) Hyperbolic Matrix(23,-12,44,-23) (1/2,6/11) -> (1/2,6/11) Reflection Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(239,-134,66,-37) (5/9,4/7) -> (18/5,11/3) Hyperbolic Matrix(173,-100,64,-37) (4/7,7/12) -> (8/3,11/4) Glide Reflection Matrix(235,-138,172,-101) (7/12,3/5) -> (15/11,11/8) Hyperbolic Matrix(105,-64,64,-39) (3/5,5/8) -> (13/8,5/3) Hyperbolic Matrix(187,-118,84,-53) (5/8,7/11) -> (11/5,9/4) Hyperbolic Matrix(83,-54,20,-13) (7/11,2/3) -> (4/1,13/3) Hyperbolic Matrix(41,-28,60,-41) (2/3,7/10) -> (2/3,7/10) Reflection Matrix(99,-70,140,-99) (7/10,5/7) -> (7/10,5/7) Reflection Matrix(2923,-2108,850,-613) (31/43,13/18) -> (55/16,31/9) Hyperbolic Matrix(749,-542,474,-343) (13/18,8/11) -> (30/19,19/12) Hyperbolic Matrix(235,-172,138,-101) (8/11,3/4) -> (17/10,12/7) Hyperbolic Matrix(97,-74,38,-29) (3/4,7/9) -> (5/2,13/5) Glide Reflection Matrix(171,-134,134,-105) (7/9,4/5) -> (14/11,9/7) Hyperbolic Matrix(131,-108,74,-61) (4/5,5/6) -> (7/4,16/9) Hyperbolic Matrix(127,-112,144,-127) (7/8,8/9) -> (7/8,8/9) Reflection Matrix(17,-16,18,-17) (8/9,1/1) -> (8/9,1/1) Reflection Matrix(17,-18,16,-17) (1/1,9/8) -> (1/1,9/8) Reflection Matrix(127,-144,112,-127) (9/8,8/7) -> (9/8,8/7) Reflection Matrix(173,-200,32,-37) (8/7,7/6) -> (16/3,11/2) Glide Reflection Matrix(141,-166,62,-73) (7/6,6/5) -> (9/4,16/7) Glide Reflection Matrix(107,-132,30,-37) (6/5,5/4) -> (7/2,18/5) Hyperbolic Matrix(151,-190,120,-151) (5/4,19/15) -> (5/4,19/15) Reflection Matrix(419,-532,330,-419) (19/15,14/11) -> (19/15,14/11) Reflection Matrix(87,-118,14,-19) (4/3,15/11) -> (6/1,7/1) Glide Reflection Matrix(185,-256,86,-119) (11/8,18/13) -> (2/1,13/6) Hyperbolic Matrix(341,-474,100,-139) (18/13,7/5) -> (17/5,24/7) Hyperbolic Matrix(99,-140,70,-99) (7/5,10/7) -> (7/5,10/7) Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(173,-270,66,-103) (3/2,11/7) -> (13/5,21/8) Hyperbolic Matrix(727,-1144,462,-727) (11/7,52/33) -> (11/7,52/33) Reflection Matrix(2705,-4264,1716,-2705) (52/33,41/26) -> (52/33,41/26) Reflection Matrix(209,-336,130,-209) (8/5,21/13) -> (8/5,21/13) Reflection Matrix(337,-546,208,-337) (21/13,13/8) -> (21/13,13/8) Reflection Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(23,-44,12,-23) (11/6,2/1) -> (11/6,2/1) Reflection Matrix(321,-698,86,-187) (13/6,11/5) -> (41/11,15/4) Hyperbolic Matrix(629,-1444,186,-427) (16/7,23/10) -> (27/8,44/13) Hyperbolic Matrix(93,-214,10,-23) (23/10,7/3) -> (9/1,1/0) Hyperbolic Matrix(71,-168,30,-71) (7/3,12/5) -> (7/3,12/5) Reflection Matrix(49,-120,20,-49) (12/5,5/2) -> (12/5,5/2) Reflection Matrix(199,-550,72,-199) (11/4,25/9) -> (11/4,25/9) Reflection Matrix(251,-700,90,-251) (25/9,14/5) -> (25/9,14/5) Reflection Matrix(25,-78,8,-25) (3/1,13/4) -> (3/1,13/4) Reflection Matrix(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(2729,-9240,806,-2729) (44/13,105/31) -> (44/13,105/31) Reflection Matrix(3781,-12810,1116,-3781) (105/31,61/18) -> (105/31,61/18) Reflection Matrix(1105,-3792,322,-1105) (24/7,79/23) -> (24/7,79/23) Reflection Matrix(2529,-8690,736,-2529) (79/23,55/16) -> (79/23,55/16) Reflection Matrix(199,-686,38,-131) (31/9,7/2) -> (5/1,21/4) Glide Reflection Matrix(203,-750,36,-133) (11/3,26/7) -> (28/5,17/3) Hyperbolic Matrix(937,-3484,252,-937) (26/7,67/18) -> (26/7,67/18) Reflection Matrix(1475,-5494,396,-1475) (67/18,41/11) -> (67/18,41/11) Reflection Matrix(121,-458,14,-53) (34/9,19/5) -> (8/1,9/1) Glide Reflection Matrix(323,-1242,84,-323) (23/6,27/7) -> (23/6,27/7) Reflection Matrix(55,-216,14,-55) (27/7,4/1) -> (27/7,4/1) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(231,-1334,40,-231) (23/4,29/5) -> (23/4,29/5) Reflection Matrix(59,-348,10,-59) (29/5,6/1) -> (29/5,6/1) Reflection Matrix(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(31,-240,4,-31) (15/2,8/1) -> (15/2,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(-1,0,2,1) -> Matrix(1,0,4,-1) (-1/1,0/1) -> (0/1,1/2) Matrix(93,-10,214,-23) -> Matrix(3,-1,4,-1) 1/2 Matrix(31,-4,240,-31) -> Matrix(3,-1,8,-3) (1/8,2/15) -> (1/4,1/2) Matrix(29,-4,210,-29) -> Matrix(-1,1,0,1) (2/15,1/7) -> (1/2,1/0) Matrix(149,-22,88,-13) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(493,-86,86,-15) -> Matrix(7,-1,8,-1) Matrix(577,-104,172,-31) -> Matrix(1,0,-4,1) 0/1 Matrix(173,-32,200,-37) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(859,-162,228,-43) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(741,-142,1028,-197) -> Matrix(5,2,8,3) Matrix(29,-6,140,-29) -> Matrix(3,-1,8,-3) (1/5,3/14) -> (1/4,1/2) Matrix(55,-12,252,-55) -> Matrix(3,-2,4,-3) (3/14,2/9) -> (1/2,1/1) Matrix(221,-50,84,-19) -> Matrix(1,0,0,1) Matrix(513,-134,134,-35) -> Matrix(11,-1,12,-1) Matrix(349,-92,808,-213) -> Matrix(5,-1,4,-1) Matrix(859,-228,162,-43) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(1395,-374,884,-237) -> Matrix(43,-10,56,-13) Matrix(1259,-340,374,-101) -> Matrix(3,-1,4,-1) 1/2 Matrix(239,-66,134,-37) -> Matrix(3,-1,4,-1) 1/2 Matrix(341,-100,474,-139) -> Matrix(7,-3,12,-5) 1/2 Matrix(629,-186,1444,-427) -> Matrix(5,-2,8,-3) 1/2 Matrix(577,-172,104,-31) -> Matrix(5,-2,8,-3) 1/2 Matrix(79,-24,260,-79) -> Matrix(7,-3,16,-7) (3/10,4/13) -> (3/8,1/2) Matrix(25,-8,78,-25) -> Matrix(-1,1,0,1) (4/13,1/3) -> (1/2,1/0) Matrix(75,-26,26,-9) -> Matrix(1,1,0,1) 1/0 Matrix(173,-64,100,-37) -> Matrix(5,-1,4,-1) Matrix(221,-84,50,-19) -> Matrix(11,-3,4,-1) Matrix(97,-38,74,-29) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(49,-20,120,-49) -> Matrix(5,-2,12,-5) (2/5,5/12) -> (1/3,1/2) Matrix(71,-30,168,-71) -> Matrix(5,-3,8,-5) (5/12,3/7) -> (1/2,3/4) Matrix(2651,-1156,782,-341) -> Matrix(3,-2,-4,3) Matrix(141,-62,166,-73) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(187,-84,118,-53) -> Matrix(3,-4,4,-5) 1/1 Matrix(23,-12,44,-23) -> Matrix(3,-1,8,-3) (1/2,6/11) -> (1/4,1/2) Matrix(109,-60,198,-109) -> Matrix(9,-5,16,-9) (6/11,5/9) -> (1/2,5/8) Matrix(239,-134,66,-37) -> Matrix(1,-1,4,-3) 1/2 Matrix(173,-100,64,-37) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(235,-138,172,-101) -> Matrix(1,-1,0,1) 1/0 Matrix(105,-64,64,-39) -> Matrix(1,1,0,1) 1/0 Matrix(187,-118,84,-53) -> Matrix(3,-1,4,-1) 1/2 Matrix(83,-54,20,-13) -> Matrix(7,-2,4,-1) Matrix(41,-28,60,-41) -> Matrix(5,-2,12,-5) (2/3,7/10) -> (1/3,1/2) Matrix(99,-70,140,-99) -> Matrix(9,-5,16,-9) (7/10,5/7) -> (1/2,5/8) Matrix(2923,-2108,850,-613) -> Matrix(3,-2,32,-21) Matrix(749,-542,474,-343) -> Matrix(25,-18,32,-23) 3/4 Matrix(235,-172,138,-101) -> Matrix(1,0,0,1) Matrix(97,-74,38,-29) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(171,-134,134,-105) -> Matrix(1,1,0,1) 1/0 Matrix(131,-108,74,-61) -> Matrix(3,-1,4,-1) 1/2 Matrix(127,-112,144,-127) -> Matrix(15,-7,32,-15) (7/8,8/9) -> (7/16,1/2) Matrix(17,-16,18,-17) -> Matrix(-1,1,0,1) (8/9,1/1) -> (1/2,1/0) Matrix(17,-18,16,-17) -> Matrix(-1,1,0,1) (1/1,9/8) -> (1/2,1/0) Matrix(127,-144,112,-127) -> Matrix(15,-8,28,-15) (9/8,8/7) -> (1/2,4/7) Matrix(173,-200,32,-37) -> Matrix(5,-3,8,-5) *** -> (1/2,3/4) Matrix(141,-166,62,-73) -> Matrix(7,-5,4,-3) Matrix(107,-132,30,-37) -> Matrix(1,-1,4,-3) 1/2 Matrix(151,-190,120,-151) -> Matrix(7,-6,8,-7) (5/4,19/15) -> (3/4,1/1) Matrix(419,-532,330,-419) -> Matrix(9,-10,8,-9) (19/15,14/11) -> (1/1,5/4) Matrix(87,-118,14,-19) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(185,-256,86,-119) -> Matrix(1,1,0,1) 1/0 Matrix(341,-474,100,-139) -> Matrix(1,0,-4,1) 0/1 Matrix(99,-140,70,-99) -> Matrix(3,-1,8,-3) (7/5,10/7) -> (1/4,1/2) Matrix(41,-60,28,-41) -> Matrix(5,-3,8,-5) (10/7,3/2) -> (1/2,3/4) Matrix(173,-270,66,-103) -> Matrix(1,-1,4,-3) 1/2 Matrix(727,-1144,462,-727) -> Matrix(29,-21,40,-29) (11/7,52/33) -> (7/10,3/4) Matrix(2705,-4264,1716,-2705) -> Matrix(139,-105,184,-139) (52/33,41/26) -> (3/4,35/46) Matrix(209,-336,130,-209) -> Matrix(15,-14,16,-15) (8/5,21/13) -> (7/8,1/1) Matrix(337,-546,208,-337) -> Matrix(17,-18,16,-17) (21/13,13/8) -> (1/1,9/8) Matrix(109,-198,60,-109) -> Matrix(-1,1,0,1) (9/5,11/6) -> (1/2,1/0) Matrix(23,-44,12,-23) -> Matrix(3,-2,4,-3) (11/6,2/1) -> (1/2,1/1) Matrix(321,-698,86,-187) -> Matrix(3,-4,4,-5) 1/1 Matrix(629,-1444,186,-427) -> Matrix(1,-3,0,1) 1/0 Matrix(93,-214,10,-23) -> Matrix(1,-1,0,1) 1/0 Matrix(71,-168,30,-71) -> Matrix(-1,3,0,1) (7/3,12/5) -> (3/2,1/0) Matrix(49,-120,20,-49) -> Matrix(-1,1,0,1) (12/5,5/2) -> (1/2,1/0) Matrix(199,-550,72,-199) -> Matrix(15,-14,16,-15) (11/4,25/9) -> (7/8,1/1) Matrix(251,-700,90,-251) -> Matrix(21,-22,20,-21) (25/9,14/5) -> (1/1,11/10) Matrix(25,-78,8,-25) -> Matrix(-1,3,0,1) (3/1,13/4) -> (3/2,1/0) Matrix(79,-260,24,-79) -> Matrix(1,2,0,-1) (13/4,10/3) -> (-1/1,1/0) Matrix(2729,-9240,806,-2729) -> Matrix(5,6,-4,-5) (44/13,105/31) -> (-3/2,-1/1) Matrix(3781,-12810,1116,-3781) -> Matrix(7,6,-8,-7) (105/31,61/18) -> (-1/1,-3/4) Matrix(1105,-3792,322,-1105) -> Matrix(-1,0,12,1) (24/7,79/23) -> (-1/6,0/1) Matrix(2529,-8690,736,-2529) -> Matrix(1,0,32,-1) (79/23,55/16) -> (0/1,1/16) Matrix(199,-686,38,-131) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(203,-750,36,-133) -> Matrix(1,0,0,1) Matrix(937,-3484,252,-937) -> Matrix(3,-2,4,-3) (26/7,67/18) -> (1/2,1/1) Matrix(1475,-5494,396,-1475) -> Matrix(5,-3,8,-5) (67/18,41/11) -> (1/2,3/4) Matrix(121,-458,14,-53) -> Matrix(1,-1,-4,3) Matrix(323,-1242,84,-323) -> Matrix(23,-22,24,-23) (23/6,27/7) -> (11/12,1/1) Matrix(55,-216,14,-55) -> Matrix(5,-6,4,-5) (27/7,4/1) -> (1/1,3/2) Matrix(55,-252,12,-55) -> Matrix(-1,7,0,1) (9/2,14/3) -> (7/2,1/0) Matrix(29,-140,6,-29) -> Matrix(1,1,0,-1) (14/3,5/1) -> (-1/2,1/0) Matrix(231,-1334,40,-231) -> Matrix(15,-14,16,-15) (23/4,29/5) -> (7/8,1/1) Matrix(59,-348,10,-59) -> Matrix(5,-6,4,-5) (29/5,6/1) -> (1/1,3/2) Matrix(29,-210,4,-29) -> Matrix(-1,7,0,1) (7/1,15/2) -> (7/2,1/0) Matrix(31,-240,4,-31) -> Matrix(1,4,0,-1) (15/2,8/1) -> (-2/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.