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): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -9/1 -8/1 -15/2 -20/3 -6/1 -16/3 -21/4 -14/3 -9/2 -22/5 -4/1 -18/5 -36/11 -16/5 -3/1 -20/7 -8/3 -12/5 -16/7 -15/7 -2/1 -12/7 -120/71 -18/11 -8/5 -36/23 -3/2 -4/3 -6/5 -8/7 0/1 1/1 8/7 6/5 24/19 4/3 24/17 3/2 36/23 8/5 18/11 12/7 24/13 2/1 24/11 96/43 16/7 12/5 120/49 5/2 144/55 8/3 192/71 48/17 20/7 3/1 16/5 36/11 96/29 24/7 7/2 18/5 11/3 48/13 64/17 4/1 21/5 13/3 48/11 22/5 9/2 14/3 80/17 19/4 24/5 5/1 21/4 16/3 27/5 11/2 17/3 23/4 6/1 19/3 13/2 33/5 20/3 7/1 15/2 23/3 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/1 -1/3 -9/1 0/1 -8/1 0/1 -15/2 1/0 -7/1 -1/1 1/0 -20/3 0/1 -13/2 -4/1 1/0 -19/3 -2/1 1/0 -6/1 -1/1 -23/4 -1/1 -2/3 -40/7 -1/2 -17/3 -1/2 0/1 -11/2 0/1 1/2 -27/5 0/1 -16/3 -1/1 1/1 -21/4 1/0 -5/1 1/1 1/0 -24/5 1/0 -19/4 -6/1 1/0 -14/3 -3/1 -1/1 -23/5 -1/1 1/0 -9/2 1/0 -22/5 -3/1 -1/1 -13/3 -2/1 1/0 -17/4 0/1 1/0 -4/1 1/0 -23/6 -3/1 -8/3 -42/11 -3/1 -19/5 -5/2 -2/1 -15/4 1/0 -26/7 -3/1 -1/1 -11/3 -2/1 1/0 -18/5 -3/1 -25/7 -3/1 -5/2 -7/2 -3/1 -2/1 -24/7 -2/1 -17/5 -2/1 -7/4 -27/8 -3/2 -37/11 -3/2 -4/3 -47/14 -2/1 -1/1 -10/3 -5/3 -1/1 -43/13 -1/1 -3/4 -33/10 1/0 -56/17 -2/1 -23/7 -1/1 1/0 -36/11 -1/1 -13/4 0/1 1/0 -29/9 -2/1 1/0 -16/5 -3/1 -1/1 -19/6 -2/1 1/0 -3/1 -2/1 -20/7 -3/2 -17/6 -2/1 -3/2 -14/5 -5/3 -1/1 -25/9 -3/2 -1/1 -36/13 -1/1 -47/17 -1/1 1/0 -11/4 -2/1 -3/2 -19/7 -2/1 1/0 -8/3 -2/1 -29/11 -2/1 -7/4 -50/19 -31/17 -9/5 -71/27 -9/5 -43/24 -21/8 -7/4 -76/29 -2/1 -55/21 -7/4 -5/3 -34/13 -9/5 -5/3 -47/18 -2/1 -5/3 -13/5 -2/1 -7/4 -31/12 -7/4 -12/7 -80/31 -5/3 -49/19 -7/4 -5/3 -18/7 -5/3 -23/9 -7/4 -5/3 -28/11 -2/1 -33/13 -12/7 -5/2 -5/3 -8/5 -27/11 -8/5 -49/20 -30/19 -11/7 -22/9 -11/7 -17/11 -39/16 -3/2 -17/7 -14/9 -3/2 -12/5 -3/2 -31/13 -3/2 -22/15 -50/21 -45/31 -13/9 -19/8 -3/2 -10/7 -45/19 -10/7 -71/30 -24/17 -7/5 -26/11 -7/5 -1/1 -33/14 -3/2 -7/3 -3/2 -1/1 -23/10 -2/1 -1/1 -16/7 -5/3 -1/1 -25/11 -5/3 -3/2 -9/4 -3/2 -38/17 -5/3 -1/1 -29/13 -2/1 -3/2 -20/9 -3/2 -11/5 -20/13 -3/2 -24/11 -3/2 -13/6 -3/2 -34/23 -28/13 -22/15 -15/7 -16/11 -2/1 -7/5 -1/1 -17/9 -11/8 -26/19 -15/8 -19/14 -13/7 -43/32 -4/3 -24/13 -4/3 -11/6 -4/3 -29/22 -31/17 -4/3 -13/10 -20/11 -4/3 -29/16 -4/3 -5/4 -96/53 -9/7 -1/1 -67/37 -4/3 -5/4 -38/21 -9/7 -1/1 -9/5 -4/3 -25/14 -4/3 -9/7 -16/9 -9/7 -1/1 -23/13 -5/4 -1/1 -7/4 -4/3 -1/1 -26/15 -7/5 -1/1 -97/56 -24/17 -7/5 -168/97 -7/5 -71/41 -7/5 -25/18 -45/26 -11/8 -19/11 -11/8 -4/3 -12/7 -4/3 -29/17 -4/3 -37/28 -46/27 -33/25 -91/69 -63/37 -54/41 -80/47 -25/19 -17/10 -4/3 -21/16 -22/13 -25/19 -17/13 -71/42 -72/55 -17/13 -120/71 -17/13 -49/29 -17/13 -47/36 -27/16 -13/10 -5/3 -13/10 -9/7 -33/20 -23/18 -28/17 -5/4 -51/31 -4/3 -23/14 -9/7 -14/11 -18/11 -9/7 -49/30 -9/7 -14/11 -80/49 -9/7 -111/68 -41/32 -31/19 -23/18 -14/11 -13/8 -14/11 -5/4 -60/37 -9/7 -47/29 -9/7 -5/4 -34/21 -9/7 -19/15 -89/55 -9/7 -5/4 -144/89 -9/7 -55/34 -9/7 -14/11 -21/13 -14/11 -8/5 -5/4 -27/17 -6/5 -73/46 -10/9 -1/1 -192/121 -1/1 -119/75 -1/1 -3/4 -46/29 -7/5 -1/1 -19/12 -5/4 -6/5 -68/43 -6/5 -117/74 -7/6 -49/31 -5/4 -1/1 -30/19 -1/1 -11/7 -4/3 -5/4 -47/30 -6/5 -1/1 -36/23 -1/1 -25/16 -4/3 -1/1 -14/9 -9/7 -1/1 -31/20 -4/3 -5/4 -48/31 -9/7 -1/1 -17/11 -4/3 -5/4 -20/13 -4/3 -23/15 -13/10 -9/7 -3/2 -5/4 -19/13 -5/4 -6/5 -16/11 -11/9 -1/1 -29/20 -5/4 -6/5 -13/9 -6/5 -7/6 -49/34 -6/5 -1/1 -36/25 -1/1 -23/16 -6/5 -1/1 -33/23 -6/5 -43/30 -10/9 -1/1 -96/67 -1/1 -53/37 -1/1 -1/2 -10/7 -9/7 -1/1 -47/33 -5/4 -1/1 -37/26 -3/2 -4/3 -27/19 -4/3 -71/50 -9/7 -32/25 -44/31 -5/4 -17/12 -14/11 -5/4 -24/17 -5/4 -7/5 -5/4 -11/9 -25/18 -16/13 -11/9 -18/13 -11/9 -47/34 -11/9 -6/5 -76/55 -17/14 -29/21 -17/14 -6/5 -11/8 -5/4 -6/5 -48/35 -11/9 -1/1 -37/27 -5/4 -6/5 -26/19 -11/9 -1/1 -41/30 -6/5 -1/1 -15/11 -6/5 -64/47 -1/1 -49/36 -4/3 -1/1 -34/25 -9/7 -1/1 -19/14 -5/4 -16/13 -23/17 -27/22 -11/9 -4/3 -6/5 -25/19 -9/8 -1/1 -21/16 -5/4 -17/13 -6/5 -7/6 -13/10 -5/4 -6/5 -48/37 -11/9 -1/1 -35/27 -5/4 -6/5 -22/17 -11/9 -1/1 -31/24 -5/4 -6/5 -40/31 -6/5 -9/7 -6/5 -23/18 -6/5 -1/1 -14/11 -11/9 -1/1 -47/37 -5/4 -11/9 -80/63 -11/9 -33/26 -17/14 -19/15 -29/24 -6/5 -24/19 -6/5 -5/4 -6/5 -13/11 -21/17 -6/5 -16/13 -13/11 -1/1 -27/22 -7/6 -11/9 -20/17 -7/6 -28/23 -7/6 -17/14 -7/6 -8/7 -40/33 -8/7 -23/19 -9/8 -1/1 -6/5 -1/1 -25/21 -7/6 -1/1 -19/16 -5/4 -6/5 -13/11 -17/14 -6/5 -33/28 -19/16 -20/17 -7/6 -47/40 -8/7 -1/1 -27/23 -6/5 -7/6 -6/5 -1/1 -15/13 -6/5 -23/20 -6/5 -13/11 -8/7 -7/6 -17/15 -6/5 -7/6 -9/8 -7/6 -10/9 -15/13 -1/1 -1/1 -7/6 -1/1 0/1 -1/1 1/1 -1/1 -7/8 10/9 -1/1 -15/17 9/8 -7/8 8/7 -7/8 15/13 -6/7 7/6 -1/1 -6/7 20/17 -7/8 13/11 -6/7 -17/20 19/16 -6/7 -5/6 6/5 -1/1 23/19 -1/1 -9/10 40/33 -8/9 17/14 -8/9 -7/8 11/9 -7/8 -20/23 27/22 -7/8 16/13 -1/1 -13/15 21/17 -6/7 5/4 -13/15 -6/7 24/19 -6/7 19/15 -6/7 -29/34 14/11 -1/1 -11/13 23/18 -1/1 -6/7 9/7 -6/7 22/17 -1/1 -11/13 13/10 -6/7 -5/6 17/13 -7/8 -6/7 4/3 -6/7 23/17 -11/13 -27/32 42/31 -11/13 19/14 -16/19 -5/6 15/11 -6/7 26/19 -1/1 -11/13 11/8 -6/7 -5/6 18/13 -11/13 25/18 -11/13 -16/19 7/5 -11/13 -5/6 24/17 -5/6 17/12 -5/6 -14/17 27/19 -4/5 37/26 -4/5 -3/4 47/33 -1/1 -5/6 10/7 -1/1 -9/11 43/30 -1/1 -10/11 33/23 -6/7 56/39 -5/6 23/16 -1/1 -6/7 36/25 -1/1 13/9 -7/8 -6/7 29/20 -6/7 -5/6 16/11 -1/1 -11/13 19/13 -6/7 -5/6 3/2 -5/6 20/13 -4/5 17/11 -5/6 -4/5 14/9 -1/1 -9/11 25/16 -1/1 -4/5 36/23 -1/1 47/30 -1/1 -6/7 11/7 -5/6 -4/5 19/12 -6/7 -5/6 8/5 -5/6 29/18 -5/6 -14/17 50/31 -67/81 -19/23 71/44 -19/23 -90/109 21/13 -14/17 76/47 -5/6 55/34 -14/17 -9/11 34/21 -19/23 -9/11 47/29 -5/6 -9/11 13/8 -5/6 -14/17 31/19 -14/17 -23/28 80/49 -9/11 49/30 -14/17 -9/11 18/11 -9/11 23/14 -14/17 -9/11 28/17 -5/6 33/20 -23/28 5/3 -9/11 -13/16 27/16 -13/16 49/29 -47/58 -17/21 22/13 -17/21 -25/31 39/23 -4/5 17/10 -21/26 -4/5 12/7 -4/5 31/18 -4/5 -27/34 50/29 -53/67 -15/19 19/11 -4/5 -11/14 45/26 -11/14 71/41 -25/32 -7/9 26/15 -1/1 -7/9 33/19 -4/5 7/4 -1/1 -4/5 23/13 -1/1 -5/6 16/9 -1/1 -9/11 25/14 -9/11 -4/5 9/5 -4/5 38/21 -1/1 -9/11 29/16 -5/6 -4/5 20/11 -4/5 11/6 -29/36 -4/5 24/13 -4/5 13/7 -4/5 -43/54 28/15 -27/34 15/8 -19/24 2/1 -1/1 -7/9 17/8 -10/13 -23/30 15/7 -16/21 13/6 -34/45 -3/4 24/11 -3/4 11/5 -3/4 -20/27 31/14 -3/4 -8/11 20/9 -3/4 29/13 -3/4 -2/3 96/43 -1/1 -5/7 67/30 -3/4 -2/3 38/17 -1/1 -5/7 9/4 -3/4 25/11 -3/4 -5/7 16/7 -1/1 -5/7 23/10 -1/1 -2/3 7/3 -1/1 -3/4 26/11 -1/1 -7/9 97/41 -25/32 -7/9 168/71 -7/9 71/30 -7/9 -24/31 45/19 -10/13 19/8 -10/13 -3/4 12/5 -3/4 29/12 -3/4 -26/35 46/19 -23/31 -63/85 63/26 -37/50 80/33 -17/23 17/7 -3/4 -14/19 22/9 -17/23 -11/15 71/29 -47/64 -11/15 120/49 -11/15 49/20 -11/15 -30/41 27/11 -8/11 5/2 -8/11 -5/7 33/13 -12/17 28/11 -2/3 51/20 -3/4 23/9 -5/7 -7/10 18/7 -5/7 49/19 -5/7 -7/10 80/31 -5/7 111/43 -22/31 31/12 -12/17 -7/10 13/5 -7/10 -2/3 60/23 -5/7 47/18 -5/7 -2/3 34/13 -5/7 -9/13 89/34 -5/7 -2/3 144/55 -5/7 55/21 -5/7 -7/10 21/8 -7/10 8/3 -2/3 27/10 -1/2 73/27 -3/2 -1/1 192/71 -1/1 119/44 -1/1 -10/11 46/17 -1/1 -7/9 19/7 -2/3 -1/2 68/25 -1/2 117/43 0/1 49/18 -1/1 -2/3 30/11 -1/1 11/4 -3/4 -2/3 47/17 -1/1 -1/2 36/13 -1/1 25/9 -1/1 -3/4 14/5 -1/1 -5/7 31/11 -3/4 -2/3 48/17 -1/1 -5/7 17/6 -3/4 -2/3 20/7 -3/4 23/8 -8/11 -5/7 3/1 -2/3 19/6 -2/3 -1/2 16/5 -1/1 -3/5 29/9 -2/3 -1/2 13/4 -1/2 0/1 49/15 -1/1 -1/2 36/11 -1/1 23/7 -1/1 -1/2 33/10 -1/2 43/13 -3/2 -1/1 96/29 -1/1 53/16 -1/1 -8/9 10/3 -1/1 -5/7 47/14 -1/1 -2/3 37/11 -4/5 -3/4 27/8 -3/4 71/21 -5/7 -17/24 44/13 -2/3 17/5 -7/10 -2/3 24/7 -2/3 7/2 -2/3 -3/5 25/7 -5/8 -3/5 18/5 -3/5 47/13 -3/5 -1/2 76/21 -4/7 29/8 -4/7 -1/2 11/3 -2/3 -1/2 48/13 -1/1 -3/5 37/10 -2/3 -1/2 26/7 -1/1 -3/5 41/11 -1/1 -1/2 15/4 -1/2 64/17 -1/1 49/13 -1/1 -3/4 34/9 -1/1 -5/7 19/5 -2/3 -5/8 23/6 -8/13 -3/5 4/1 -1/2 25/6 -2/1 -1/1 21/5 -2/3 17/4 -1/2 0/1 13/3 -2/3 -1/2 48/11 -1/1 -3/5 35/8 -2/3 -1/2 22/5 -1/1 -3/5 31/7 -2/3 -1/2 40/9 -1/2 9/2 -1/2 23/5 -1/1 -1/2 14/3 -1/1 -3/5 47/10 -2/3 -3/5 80/17 -3/5 33/7 -4/7 19/4 -6/11 -1/2 24/5 -1/2 5/1 -1/2 -1/3 21/4 -1/2 16/3 -1/1 -1/3 27/5 0/1 11/2 -1/4 0/1 28/5 0/1 17/3 0/1 1/0 40/7 1/0 23/4 -2/1 -1/1 6/1 -1/1 25/4 -1/1 0/1 19/3 -2/3 -1/2 13/2 -4/7 -1/2 33/5 -2/5 20/3 0/1 47/7 -1/1 1/0 27/4 -1/2 7/1 -1/1 -1/2 15/2 -1/2 23/3 -1/2 -1/3 8/1 0/1 17/2 -1/2 0/1 9/1 0/1 10/1 -1/1 1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(47,480,14,143) (-10/1,1/0) -> (10/3,47/14) Hyperbolic Matrix(47,432,26,239) (-10/1,-9/1) -> (9/5,38/21) Hyperbolic Matrix(49,432,-38,-335) (-9/1,-8/1) -> (-40/31,-9/7) Hyperbolic Matrix(145,1104,-44,-335) (-8/1,-15/2) -> (-33/10,-56/17) Hyperbolic Matrix(97,720,26,193) (-15/2,-7/1) -> (41/11,15/4) Hyperbolic Matrix(241,1632,-92,-623) (-7/1,-20/3) -> (-76/29,-55/21) Hyperbolic Matrix(95,624,-44,-289) (-20/3,-13/2) -> (-13/6,-28/13) Hyperbolic Matrix(97,624,30,193) (-13/2,-19/3) -> (29/9,13/4) Hyperbolic Matrix(145,912,-38,-239) (-19/3,-6/1) -> (-42/11,-19/5) Hyperbolic Matrix(191,1104,-50,-289) (-6/1,-23/4) -> (-23/6,-42/11) Hyperbolic Matrix(385,2208,268,1537) (-23/4,-40/7) -> (56/39,23/16) Hyperbolic Matrix(337,1920,76,433) (-40/7,-17/3) -> (31/7,40/9) Hyperbolic Matrix(95,528,-52,-289) (-17/3,-11/2) -> (-11/6,-31/17) Hyperbolic Matrix(239,1296,168,911) (-11/2,-27/5) -> (27/19,37/26) Hyperbolic Matrix(143,768,116,623) (-27/5,-16/3) -> (16/13,21/17) Hyperbolic Matrix(145,768,118,625) (-16/3,-21/4) -> (27/22,16/13) Hyperbolic Matrix(47,240,28,143) (-21/4,-5/1) -> (5/3,27/16) Hyperbolic Matrix(49,240,10,49) (-5/1,-24/5) -> (24/5,5/1) Hyperbolic Matrix(191,912,40,191) (-24/5,-19/4) -> (19/4,24/5) Hyperbolic Matrix(193,912,-142,-671) (-19/4,-14/3) -> (-34/25,-19/14) Hyperbolic Matrix(145,672,52,241) (-14/3,-23/5) -> (25/9,14/5) Hyperbolic Matrix(95,432,42,191) (-23/5,-9/2) -> (9/4,25/11) Hyperbolic Matrix(239,1056,-98,-433) (-9/2,-22/5) -> (-22/9,-39/16) Hyperbolic Matrix(241,1056,-186,-815) (-22/5,-13/3) -> (-35/27,-22/17) Hyperbolic Matrix(145,624,56,241) (-13/3,-17/4) -> (31/12,13/5) Hyperbolic Matrix(193,816,-136,-575) (-17/4,-4/1) -> (-44/31,-17/12) Hyperbolic Matrix(335,1296,-236,-913) (-4/1,-23/6) -> (-71/50,-44/31) Hyperbolic Matrix(241,912,-190,-719) (-19/5,-15/4) -> (-33/26,-19/15) Hyperbolic Matrix(335,1248,-142,-529) (-15/4,-26/7) -> (-26/11,-33/14) Hyperbolic Matrix(337,1248,-246,-911) (-26/7,-11/3) -> (-37/27,-26/19) Hyperbolic Matrix(145,528,-92,-335) (-11/3,-18/5) -> (-30/19,-11/7) Hyperbolic Matrix(241,864,94,337) (-18/5,-25/7) -> (23/9,18/7) Hyperbolic Matrix(95,336,54,191) (-25/7,-7/2) -> (7/4,23/13) Hyperbolic Matrix(97,336,28,97) (-7/2,-24/7) -> (24/7,7/2) Hyperbolic Matrix(239,816,70,239) (-24/7,-17/5) -> (17/5,24/7) Hyperbolic Matrix(241,816,-184,-623) (-17/5,-27/8) -> (-21/16,-17/13) Hyperbolic Matrix(385,1296,314,1057) (-27/8,-37/11) -> (11/9,27/22) Hyperbolic Matrix(671,2256,428,1439) (-37/11,-47/14) -> (47/30,11/7) Hyperbolic Matrix(143,480,14,47) (-47/14,-10/3) -> (10/1,1/0) Hyperbolic Matrix(289,960,-202,-671) (-10/3,-43/13) -> (-53/37,-10/7) Hyperbolic Matrix(479,1584,290,959) (-43/13,-33/10) -> (33/20,5/3) Hyperbolic Matrix(671,2208,554,1823) (-56/17,-23/7) -> (23/19,40/33) Hyperbolic Matrix(527,1728,190,623) (-23/7,-36/11) -> (36/13,25/9) Hyperbolic Matrix(383,1248,-236,-769) (-36/11,-13/4) -> (-13/8,-60/37) Hyperbolic Matrix(193,624,30,97) (-13/4,-29/9) -> (19/3,13/2) Hyperbolic Matrix(239,768,164,527) (-29/9,-16/5) -> (16/11,19/13) Hyperbolic Matrix(241,768,166,529) (-16/5,-19/6) -> (29/20,16/11) Hyperbolic Matrix(289,912,122,385) (-19/6,-3/1) -> (45/19,19/8) Hyperbolic Matrix(385,1104,-234,-671) (-3/1,-20/7) -> (-28/17,-51/31) Hyperbolic Matrix(337,960,152,433) (-20/7,-17/6) -> (31/14,20/9) Hyperbolic Matrix(239,672,-154,-433) (-17/6,-14/5) -> (-14/9,-31/20) Hyperbolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,190,527) (-25/9,-36/13) -> (36/11,23/7) Hyperbolic Matrix(1249,3456,382,1057) (-36/13,-47/17) -> (49/15,36/11) Hyperbolic Matrix(817,2256,574,1585) (-47/17,-11/4) -> (37/26,47/33) Hyperbolic Matrix(193,528,-140,-383) (-11/4,-19/7) -> (-29/21,-11/8) Hyperbolic Matrix(143,384,-54,-145) (-19/7,-8/3) -> (-8/3,-29/11) Parabolic Matrix(911,2400,528,1391) (-29/11,-50/19) -> (50/29,19/11) Hyperbolic Matrix(3503,9216,-2208,-5809) (-50/19,-71/27) -> (-119/75,-46/29) Hyperbolic Matrix(1297,3408,384,1009) (-71/27,-21/8) -> (27/8,71/21) Hyperbolic Matrix(3937,10320,-2490,-6527) (-21/8,-76/29) -> (-68/43,-117/74) Hyperbolic Matrix(1871,4896,-1156,-3025) (-55/21,-34/13) -> (-34/21,-89/55) Hyperbolic Matrix(1249,3264,-918,-2399) (-34/13,-47/18) -> (-49/36,-34/25) Hyperbolic Matrix(479,1248,-332,-865) (-47/18,-13/5) -> (-13/9,-49/34) Hyperbolic Matrix(241,624,56,145) (-13/5,-31/12) -> (17/4,13/3) Hyperbolic Matrix(1487,3840,-874,-2257) (-31/12,-80/31) -> (-80/47,-17/10) Hyperbolic Matrix(2977,7680,-2344,-6047) (-80/31,-49/19) -> (-47/37,-80/63) Hyperbolic Matrix(671,1728,186,479) (-49/19,-18/7) -> (18/5,47/13) Hyperbolic Matrix(337,864,94,241) (-18/7,-23/9) -> (25/7,18/5) Hyperbolic Matrix(433,1104,-282,-719) (-23/9,-28/11) -> (-20/13,-23/15) Hyperbolic Matrix(623,1584,94,239) (-28/11,-33/13) -> (33/5,20/3) Hyperbolic Matrix(625,1584,436,1105) (-33/13,-5/2) -> (43/30,33/23) Hyperbolic Matrix(97,240,78,193) (-5/2,-27/11) -> (21/17,5/4) Hyperbolic Matrix(1057,2592,-900,-2207) (-27/11,-49/20) -> (-47/40,-27/23) Hyperbolic Matrix(1393,3408,-804,-1967) (-49/20,-22/9) -> (-26/15,-97/56) Hyperbolic Matrix(335,816,-296,-721) (-39/16,-17/7) -> (-17/15,-9/8) Hyperbolic Matrix(239,576,-100,-241) (-17/7,-12/5) -> (-12/5,-31/13) Parabolic Matrix(383,912,-202,-481) (-31/13,-50/21) -> (-2/1,-17/9) Hyperbolic Matrix(1009,2400,626,1489) (-50/21,-19/8) -> (29/18,50/31) Hyperbolic Matrix(385,912,122,289) (-19/8,-45/19) -> (3/1,19/6) Hyperbolic Matrix(527,1248,182,431) (-45/19,-71/30) -> (23/8,3/1) Hyperbolic Matrix(1441,3408,-852,-2015) (-71/30,-26/11) -> (-22/13,-71/42) Hyperbolic Matrix(143,336,20,47) (-33/14,-7/3) -> (7/1,15/2) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(337,768,190,433) (-16/7,-25/11) -> (23/13,16/9) Hyperbolic Matrix(191,432,42,95) (-25/11,-9/4) -> (9/2,23/5) Hyperbolic Matrix(193,432,172,385) (-9/4,-38/17) -> (10/9,9/8) Hyperbolic Matrix(1633,3648,-902,-2015) (-38/17,-29/13) -> (-67/37,-38/21) Hyperbolic Matrix(1249,2784,-904,-2015) (-29/13,-20/9) -> (-76/55,-29/21) Hyperbolic Matrix(239,528,-196,-433) (-20/9,-11/5) -> (-11/9,-28/23) Hyperbolic Matrix(241,528,110,241) (-11/5,-24/11) -> (24/11,11/5) Hyperbolic Matrix(287,624,132,287) (-24/11,-13/6) -> (13/6,24/11) Hyperbolic Matrix(625,1344,246,529) (-28/13,-15/7) -> (33/13,28/11) Hyperbolic Matrix(385,816,-226,-479) (-15/7,-2/1) -> (-46/27,-63/37) Hyperbolic Matrix(1247,2352,-764,-1441) (-17/9,-15/8) -> (-111/68,-31/19) Hyperbolic Matrix(335,624,-284,-529) (-15/8,-13/7) -> (-13/11,-33/28) Hyperbolic Matrix(337,624,182,337) (-13/7,-24/13) -> (24/13,13/7) Hyperbolic Matrix(287,528,156,287) (-24/13,-11/6) -> (11/6,24/13) Hyperbolic Matrix(527,960,342,623) (-31/17,-20/11) -> (20/13,17/11) Hyperbolic Matrix(1297,2352,-820,-1487) (-20/11,-29/16) -> (-19/12,-68/43) Hyperbolic Matrix(5087,9216,2278,4127) (-29/16,-96/53) -> (96/43,67/30) Hyperbolic Matrix(5089,9216,2280,4129) (-96/53,-67/37) -> (29/13,96/43) Hyperbolic Matrix(239,432,26,47) (-38/21,-9/5) -> (9/1,10/1) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(431,768,188,335) (-25/14,-16/9) -> (16/7,23/10) Hyperbolic Matrix(433,768,190,337) (-16/9,-23/13) -> (25/11,16/7) Hyperbolic Matrix(191,336,54,95) (-23/13,-7/4) -> (7/2,25/7) Hyperbolic Matrix(719,1248,-526,-913) (-7/4,-26/15) -> (-26/19,-41/30) Hyperbolic Matrix(11473,19872,4684,8113) (-97/56,-168/97) -> (120/49,49/20) Hyperbolic Matrix(11807,20448,4822,8351) (-168/97,-71/41) -> (71/29,120/49) Hyperbolic Matrix(2689,4656,1054,1825) (-71/41,-45/26) -> (51/20,23/9) Hyperbolic Matrix(527,912,360,623) (-45/26,-19/11) -> (19/13,3/2) Hyperbolic Matrix(335,576,-196,-337) (-19/11,-12/7) -> (-12/7,-29/17) Parabolic Matrix(1295,2208,478,815) (-29/17,-46/27) -> (46/17,19/7) Hyperbolic Matrix(4511,7680,958,1631) (-63/37,-80/47) -> (80/17,33/7) Hyperbolic Matrix(623,1056,-482,-817) (-17/10,-22/13) -> (-22/17,-31/24) Hyperbolic Matrix(12097,20448,5112,8641) (-71/42,-120/71) -> (168/71,71/30) Hyperbolic Matrix(11759,19872,4970,8399) (-120/71,-49/29) -> (97/41,168/71) Hyperbolic Matrix(4177,7056,-2642,-4463) (-49/29,-27/16) -> (-117/74,-49/31) Hyperbolic Matrix(143,240,28,47) (-27/16,-5/3) -> (5/1,21/4) Hyperbolic Matrix(959,1584,290,479) (-5/3,-33/20) -> (33/10,43/13) Hyperbolic Matrix(815,1344,436,719) (-33/20,-28/17) -> (28/15,15/8) Hyperbolic Matrix(2831,4656,1196,1967) (-51/31,-23/14) -> (71/30,45/19) Hyperbolic Matrix(527,864,380,623) (-23/14,-18/11) -> (18/13,25/18) Hyperbolic Matrix(1439,2352,528,863) (-18/11,-49/30) -> (49/18,30/11) Hyperbolic Matrix(4321,7056,-3174,-5183) (-49/30,-80/49) -> (-64/47,-49/36) Hyperbolic Matrix(5087,8304,1352,2207) (-80/49,-111/68) -> (15/4,64/17) Hyperbolic Matrix(383,624,294,479) (-31/19,-13/8) -> (13/10,17/13) Hyperbolic Matrix(2783,4512,1006,1631) (-60/37,-47/29) -> (47/17,36/13) Hyperbolic Matrix(1393,2256,-1096,-1775) (-47/29,-34/21) -> (-14/11,-47/37) Hyperbolic Matrix(12815,20736,4894,7919) (-89/55,-144/89) -> (144/55,55/21) Hyperbolic Matrix(12817,20736,4896,7921) (-144/89,-55/34) -> (89/34,144/55) Hyperbolic Matrix(1009,1632,-860,-1391) (-55/34,-21/13) -> (-27/23,-7/6) Hyperbolic Matrix(239,384,-150,-241) (-21/13,-8/5) -> (-8/5,-27/17) Parabolic Matrix(1391,2208,332,527) (-27/17,-73/46) -> (25/6,21/5) Hyperbolic Matrix(23231,36864,8590,13631) (-73/46,-192/121) -> (192/71,119/44) Hyperbolic Matrix(23233,36864,8592,13633) (-192/121,-119/75) -> (73/27,192/71) Hyperbolic Matrix(1393,2208,576,913) (-46/29,-19/12) -> (29/12,46/19) Hyperbolic Matrix(1489,2352,578,913) (-49/31,-30/19) -> (18/7,49/19) Hyperbolic Matrix(1439,2256,428,671) (-11/7,-47/30) -> (47/14,37/11) Hyperbolic Matrix(2881,4512,1104,1729) (-47/30,-36/23) -> (60/23,47/18) Hyperbolic Matrix(1105,1728,768,1201) (-36/23,-25/16) -> (23/16,36/25) Hyperbolic Matrix(431,672,338,527) (-25/16,-14/9) -> (14/11,23/18) Hyperbolic Matrix(1487,2304,526,815) (-31/20,-48/31) -> (48/17,17/6) Hyperbolic Matrix(1489,2304,528,817) (-48/31,-17/11) -> (31/11,48/17) Hyperbolic Matrix(529,816,94,145) (-17/11,-20/13) -> (28/5,17/3) Hyperbolic Matrix(817,1248,472,721) (-23/15,-3/2) -> (45/26,71/41) Hyperbolic Matrix(623,912,360,527) (-3/2,-19/13) -> (19/11,45/26) Hyperbolic Matrix(527,768,164,239) (-19/13,-16/11) -> (16/5,29/9) Hyperbolic Matrix(529,768,166,241) (-16/11,-29/20) -> (19/6,16/5) Hyperbolic Matrix(431,624,364,527) (-29/20,-13/9) -> (13/11,19/16) Hyperbolic Matrix(2399,3456,1532,2207) (-49/34,-36/25) -> (36/23,47/30) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(769,1104,-668,-959) (-23/16,-33/23) -> (-15/13,-23/20) Hyperbolic Matrix(1105,1584,436,625) (-33/23,-43/30) -> (5/2,33/13) Hyperbolic Matrix(6431,9216,1942,2783) (-43/30,-96/67) -> (96/29,53/16) Hyperbolic Matrix(6433,9216,1944,2785) (-96/67,-53/37) -> (43/13,96/29) Hyperbolic Matrix(337,480,304,433) (-10/7,-47/33) -> (1/1,10/9) Hyperbolic Matrix(1585,2256,574,817) (-47/33,-37/26) -> (11/4,47/17) Hyperbolic Matrix(911,1296,168,239) (-37/26,-27/19) -> (27/5,11/2) Hyperbolic Matrix(2399,3408,1486,2111) (-27/19,-71/50) -> (71/44,21/13) Hyperbolic Matrix(577,816,408,577) (-17/12,-24/17) -> (24/17,17/12) Hyperbolic Matrix(239,336,170,239) (-24/17,-7/5) -> (7/5,24/17) Hyperbolic Matrix(241,336,104,145) (-7/5,-25/18) -> (23/10,7/3) Hyperbolic Matrix(623,864,380,527) (-25/18,-18/13) -> (18/11,23/14) Hyperbolic Matrix(1249,1728,764,1057) (-18/13,-47/34) -> (49/30,18/11) Hyperbolic Matrix(3265,4512,-2778,-3839) (-47/34,-76/55) -> (-20/17,-47/40) Hyperbolic Matrix(1679,2304,454,623) (-11/8,-48/35) -> (48/13,37/10) Hyperbolic Matrix(1681,2304,456,625) (-48/35,-37/27) -> (11/3,48/13) Hyperbolic Matrix(527,720,456,623) (-41/30,-15/11) -> (15/13,7/6) Hyperbolic Matrix(6097,8304,2362,3217) (-15/11,-64/47) -> (80/31,111/43) Hyperbolic Matrix(673,912,-566,-767) (-19/14,-23/17) -> (-25/21,-19/16) Hyperbolic Matrix(143,192,-108,-145) (-23/17,-4/3) -> (-4/3,-25/19) Parabolic Matrix(1681,2208,622,817) (-25/19,-21/16) -> (27/10,73/27) Hyperbolic Matrix(479,624,294,383) (-17/13,-13/10) -> (13/8,31/19) Hyperbolic Matrix(1775,2304,406,527) (-13/10,-48/37) -> (48/11,35/8) Hyperbolic Matrix(1777,2304,408,529) (-48/37,-35/27) -> (13/3,48/11) Hyperbolic Matrix(1487,1920,1226,1583) (-31/24,-40/31) -> (40/33,17/14) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,338,431) (-23/18,-14/11) -> (14/9,25/16) Hyperbolic Matrix(6049,7680,2496,3169) (-80/63,-33/26) -> (63/26,80/33) Hyperbolic Matrix(721,912,570,721) (-19/15,-24/19) -> (24/19,19/15) Hyperbolic Matrix(191,240,152,191) (-24/19,-5/4) -> (5/4,24/19) Hyperbolic Matrix(193,240,78,97) (-5/4,-21/17) -> (27/11,5/2) Hyperbolic Matrix(623,768,116,143) (-21/17,-16/13) -> (16/3,27/5) Hyperbolic Matrix(625,768,118,145) (-16/13,-27/22) -> (21/4,16/3) Hyperbolic Matrix(1057,1296,314,385) (-27/22,-11/9) -> (37/11,27/8) Hyperbolic Matrix(671,816,236,287) (-28/23,-17/14) -> (17/6,20/7) Hyperbolic Matrix(673,816,80,97) (-17/14,-40/33) -> (8/1,17/2) Hyperbolic Matrix(911,1104,118,143) (-40/33,-23/19) -> (23/3,8/1) Hyperbolic Matrix(239,288,-200,-241) (-23/19,-6/5) -> (-6/5,-25/21) Parabolic Matrix(527,624,364,431) (-19/16,-13/11) -> (13/9,29/20) Hyperbolic Matrix(1345,1584,816,961) (-33/28,-20/17) -> (28/17,33/20) Hyperbolic Matrix(289,336,166,193) (-7/6,-15/13) -> (33/19,7/4) Hyperbolic Matrix(961,1104,168,193) (-23/20,-8/7) -> (40/7,23/4) Hyperbolic Matrix(719,816,126,143) (-8/7,-17/15) -> (17/3,40/7) Hyperbolic Matrix(385,432,172,193) (-9/8,-10/9) -> (38/17,9/4) Hyperbolic Matrix(433,480,304,337) (-10/9,-1/1) -> (47/33,10/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(383,-432,86,-97) (9/8,8/7) -> (40/9,9/2) Hyperbolic Matrix(959,-1104,668,-769) (8/7,15/13) -> (33/23,56/39) Hyperbolic Matrix(1391,-1632,860,-1009) (7/6,20/17) -> (76/47,55/34) Hyperbolic Matrix(529,-624,284,-335) (20/17,13/11) -> (13/7,28/15) Hyperbolic Matrix(767,-912,566,-673) (19/16,6/5) -> (42/31,19/14) Hyperbolic Matrix(913,-1104,674,-815) (6/5,23/19) -> (23/17,42/31) Hyperbolic Matrix(433,-528,196,-239) (17/14,11/9) -> (11/5,31/14) Hyperbolic Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(817,-1056,482,-623) (9/7,22/17) -> (22/13,39/23) Hyperbolic Matrix(815,-1056,186,-241) (22/17,13/10) -> (35/8,22/5) Hyperbolic Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(961,-1296,284,-383) (4/3,23/17) -> (71/21,44/13) Hyperbolic Matrix(671,-912,142,-193) (19/14,15/11) -> (33/7,19/4) Hyperbolic Matrix(913,-1248,526,-719) (15/11,26/19) -> (26/15,33/19) Hyperbolic Matrix(911,-1248,246,-337) (26/19,11/8) -> (37/10,26/7) Hyperbolic Matrix(383,-528,140,-193) (11/8,18/13) -> (30/11,11/4) Hyperbolic Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(671,-960,202,-289) (10/7,43/30) -> (53/16,10/3) Hyperbolic Matrix(865,-1248,332,-479) (36/25,13/9) -> (13/5,60/23) Hyperbolic Matrix(719,-1104,282,-433) (3/2,20/13) -> (28/11,51/20) Hyperbolic Matrix(433,-672,154,-239) (17/11,14/9) -> (14/5,31/11) Hyperbolic Matrix(335,-528,92,-145) (11/7,19/12) -> (29/8,11/3) Hyperbolic Matrix(241,-384,150,-239) (19/12,8/5) -> (8/5,29/18) Parabolic Matrix(5713,-9216,2112,-3407) (50/31,71/44) -> (119/44,46/17) Hyperbolic Matrix(6383,-10320,2346,-3793) (21/13,76/47) -> (68/25,117/43) Hyperbolic Matrix(3025,-4896,1156,-1871) (55/34,34/21) -> (34/13,89/34) Hyperbolic Matrix(2015,-3264,534,-865) (34/21,47/29) -> (49/13,34/9) Hyperbolic Matrix(769,-1248,236,-383) (47/29,13/8) -> (13/4,49/15) Hyperbolic Matrix(2353,-3840,970,-1583) (31/19,80/49) -> (80/33,17/7) Hyperbolic Matrix(4703,-7680,1000,-1633) (80/49,49/30) -> (47/10,80/17) Hyperbolic Matrix(671,-1104,234,-385) (23/14,28/17) -> (20/7,23/8) Hyperbolic Matrix(1535,-2592,228,-385) (27/16,49/29) -> (47/7,27/4) Hyperbolic Matrix(2015,-3408,852,-1441) (49/29,22/13) -> (26/11,97/41) Hyperbolic Matrix(481,-816,56,-95) (39/23,17/10) -> (17/2,9/1) Hyperbolic Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(529,-912,250,-431) (31/18,50/29) -> (2/1,17/8) Hyperbolic Matrix(1967,-3408,804,-1393) (71/41,26/15) -> (22/9,71/29) Hyperbolic Matrix(2015,-3648,902,-1633) (38/21,29/16) -> (67/30,38/17) Hyperbolic Matrix(1535,-2784,424,-769) (29/16,20/11) -> (76/21,29/8) Hyperbolic Matrix(289,-528,52,-95) (20/11,11/6) -> (11/2,28/5) Hyperbolic Matrix(431,-816,178,-337) (15/8,2/1) -> (46/19,63/26) Hyperbolic Matrix(1105,-2352,428,-911) (17/8,15/7) -> (111/43,31/12) Hyperbolic Matrix(289,-624,44,-95) (15/7,13/6) -> (13/2,33/5) Hyperbolic Matrix(1055,-2352,388,-865) (20/9,29/13) -> (19/7,68/25) Hyperbolic Matrix(529,-1248,142,-335) (7/3,26/11) -> (26/7,41/11) Hyperbolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(2879,-7056,1058,-2593) (49/20,27/11) -> (117/43,49/18) Hyperbolic Matrix(2735,-7056,726,-1873) (49/19,80/31) -> (64/17,49/13) Hyperbolic Matrix(863,-2256,184,-481) (47/18,34/13) -> (14/3,47/10) Hyperbolic Matrix(623,-1632,92,-241) (55/21,21/8) -> (27/4,7/1) Hyperbolic Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(335,-1104,44,-145) (23/7,33/10) -> (15/2,23/3) Hyperbolic Matrix(1247,-4512,186,-673) (47/13,76/21) -> (20/3,47/7) Hyperbolic Matrix(239,-912,38,-145) (19/5,23/6) -> (25/4,19/3) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(49,-288,8,-47) (23/4,6/1) -> (6/1,25/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(47,480,14,143) -> Matrix(1,2,-2,-3) Matrix(47,432,26,239) -> Matrix(3,4,-4,-5) Matrix(49,432,-38,-335) -> Matrix(5,-6,-4,5) Matrix(145,1104,-44,-335) -> Matrix(1,-2,0,1) Matrix(97,720,26,193) -> Matrix(1,2,-2,-3) Matrix(241,1632,-92,-623) -> Matrix(7,2,-4,-1) Matrix(95,624,-44,-289) -> Matrix(3,-22,-2,15) Matrix(97,624,30,193) -> Matrix(1,4,-2,-7) Matrix(145,912,-38,-239) -> Matrix(5,8,-2,-3) Matrix(191,1104,-50,-289) -> Matrix(1,-2,0,1) Matrix(385,2208,268,1537) -> Matrix(3,4,-4,-5) Matrix(337,1920,76,433) -> Matrix(5,2,-8,-3) Matrix(95,528,-52,-289) -> Matrix(21,4,-16,-3) Matrix(239,1296,168,911) -> Matrix(5,-4,-6,5) Matrix(143,768,116,623) -> Matrix(7,-6,-8,7) Matrix(145,768,118,625) -> Matrix(7,-6,-8,7) Matrix(47,240,28,143) -> Matrix(13,-4,-16,5) Matrix(49,240,10,49) -> Matrix(1,-2,-2,5) Matrix(191,912,40,191) -> Matrix(1,12,-2,-23) Matrix(193,912,-142,-671) -> Matrix(5,14,-4,-11) Matrix(145,672,52,241) -> Matrix(3,4,-4,-5) Matrix(95,432,42,191) -> Matrix(3,-2,-4,3) Matrix(239,1056,-98,-433) -> Matrix(3,20,-2,-13) Matrix(241,1056,-186,-815) -> Matrix(5,4,-4,-3) Matrix(145,624,56,241) -> Matrix(7,12,-10,-17) Matrix(193,816,-136,-575) -> Matrix(5,14,-4,-11) Matrix(335,1296,-236,-913) -> Matrix(5,24,-4,-19) Matrix(241,912,-190,-719) -> Matrix(17,28,-14,-23) Matrix(335,1248,-142,-529) -> Matrix(3,2,-2,-1) Matrix(337,1248,-246,-911) -> Matrix(5,4,-4,-3) Matrix(145,528,-92,-335) -> Matrix(5,14,-4,-11) Matrix(241,864,94,337) -> Matrix(3,4,-4,-5) Matrix(95,336,54,191) -> Matrix(3,10,-4,-13) Matrix(97,336,28,97) -> Matrix(5,12,-8,-19) Matrix(239,816,70,239) -> Matrix(15,28,-22,-41) Matrix(241,816,-184,-623) -> Matrix(17,28,-14,-23) Matrix(385,1296,314,1057) -> Matrix(19,32,-22,-37) Matrix(671,2256,428,1439) -> Matrix(7,8,-8,-9) Matrix(143,480,14,47) -> Matrix(1,2,-2,-3) Matrix(289,960,-202,-671) -> Matrix(3,2,-2,-1) Matrix(479,1584,290,959) -> Matrix(23,14,-28,-17) Matrix(671,2208,554,1823) -> Matrix(9,10,-10,-11) Matrix(527,1728,190,623) -> Matrix(3,4,-4,-5) Matrix(383,1248,-236,-769) -> Matrix(5,14,-4,-11) Matrix(193,624,30,97) -> Matrix(1,4,-2,-7) Matrix(239,768,164,527) -> Matrix(5,16,-6,-19) Matrix(241,768,166,529) -> Matrix(5,16,-6,-19) Matrix(289,912,122,385) -> Matrix(3,16,-4,-21) Matrix(385,1104,-234,-671) -> Matrix(3,2,-2,-1) Matrix(337,960,152,433) -> Matrix(19,30,-26,-41) Matrix(239,672,-154,-433) -> Matrix(3,2,-2,-1) Matrix(241,672,52,145) -> Matrix(3,4,-4,-5) Matrix(623,1728,190,527) -> Matrix(3,4,-4,-5) Matrix(1249,3456,382,1057) -> Matrix(1,2,-2,-3) Matrix(817,2256,574,1585) -> Matrix(5,6,-6,-7) Matrix(193,528,-140,-383) -> Matrix(17,28,-14,-23) Matrix(143,384,-54,-145) -> Matrix(7,16,-4,-9) Matrix(911,2400,528,1391) -> Matrix(5,6,-6,-7) Matrix(3503,9216,-2208,-5809) -> Matrix(9,16,-4,-7) Matrix(1297,3408,384,1009) -> Matrix(35,62,-48,-85) Matrix(3937,10320,-2490,-6527) -> Matrix(17,28,-14,-23) Matrix(1871,4896,-1156,-3025) -> Matrix(51,88,-40,-69) Matrix(1249,3264,-918,-2399) -> Matrix(11,18,-8,-13) Matrix(479,1248,-332,-865) -> Matrix(17,28,-14,-23) Matrix(241,624,56,145) -> Matrix(7,12,-10,-17) Matrix(1487,3840,-874,-2257) -> Matrix(163,280,-124,-213) Matrix(2977,7680,-2344,-6047) -> Matrix(29,52,-24,-43) Matrix(671,1728,186,479) -> Matrix(15,26,-26,-45) Matrix(337,864,94,241) -> Matrix(3,4,-4,-5) Matrix(433,1104,-282,-719) -> Matrix(3,2,-2,-1) Matrix(623,1584,94,239) -> Matrix(1,2,-6,-11) Matrix(625,1584,436,1105) -> Matrix(25,42,-28,-47) Matrix(97,240,78,193) -> Matrix(47,74,-54,-85) Matrix(1057,2592,-900,-2207) -> Matrix(37,58,-30,-47) Matrix(1393,3408,-804,-1967) -> Matrix(35,54,-24,-37) Matrix(335,816,-296,-721) -> Matrix(51,80,-44,-69) Matrix(239,576,-100,-241) -> Matrix(71,108,-48,-73) Matrix(383,912,-202,-481) -> Matrix(113,164,-82,-119) Matrix(1009,2400,626,1489) -> Matrix(7,8,-8,-9) Matrix(385,912,122,289) -> Matrix(11,16,-20,-29) Matrix(527,1248,182,431) -> Matrix(45,64,-64,-91) Matrix(1441,3408,-852,-2015) -> Matrix(71,96,-54,-73) Matrix(143,336,20,47) -> Matrix(3,4,-4,-5) Matrix(145,336,104,241) -> Matrix(27,38,-32,-45) Matrix(335,768,188,431) -> Matrix(13,22,-16,-27) Matrix(337,768,190,433) -> Matrix(13,22,-16,-27) Matrix(191,432,42,95) -> Matrix(1,2,-4,-7) Matrix(193,432,172,385) -> Matrix(9,10,-10,-11) Matrix(1633,3648,-902,-2015) -> Matrix(3,2,-2,-1) Matrix(1249,2784,-904,-2015) -> Matrix(29,52,-24,-43) Matrix(239,528,-196,-433) -> Matrix(51,80,-44,-69) Matrix(241,528,110,241) -> Matrix(79,120,-106,-161) Matrix(287,624,132,287) -> Matrix(137,204,-182,-271) Matrix(625,1344,246,529) -> Matrix(101,148,-144,-211) Matrix(385,816,-226,-479) -> Matrix(211,302,-160,-229) Matrix(1247,2352,-764,-1441) -> Matrix(325,444,-254,-347) Matrix(335,624,-284,-529) -> Matrix(141,190,-118,-159) Matrix(337,624,182,337) -> Matrix(257,344,-322,-431) Matrix(287,528,156,287) -> Matrix(175,232,-218,-289) Matrix(527,960,342,623) -> Matrix(55,72,-68,-89) Matrix(1297,2352,-820,-1487) -> Matrix(39,50,-32,-41) Matrix(5087,9216,2278,4127) -> Matrix(17,22,-24,-31) Matrix(5089,9216,2280,4129) -> Matrix(17,22,-24,-31) Matrix(239,432,26,47) -> Matrix(3,4,-4,-5) Matrix(241,432,188,337) -> Matrix(45,58,-52,-67) Matrix(431,768,188,335) -> Matrix(17,22,-24,-31) Matrix(433,768,190,337) -> Matrix(17,22,-24,-31) Matrix(191,336,54,95) -> Matrix(7,10,-12,-17) Matrix(719,1248,-526,-913) -> Matrix(3,2,-2,-1) Matrix(11473,19872,4684,8113) -> Matrix(337,474,-460,-647) Matrix(11807,20448,4822,8351) -> Matrix(433,604,-590,-823) Matrix(2689,4656,1054,1825) -> Matrix(55,76,-76,-105) Matrix(527,912,360,623) -> Matrix(63,86,-74,-101) Matrix(335,576,-196,-337) -> Matrix(143,192,-108,-145) Matrix(1295,2208,478,815) -> Matrix(53,70,-78,-103) Matrix(4511,7680,958,1631) -> Matrix(199,262,-338,-445) Matrix(623,1056,-482,-817) -> Matrix(111,146,-92,-121) Matrix(12097,20448,5112,8641) -> Matrix(697,912,-898,-1175) Matrix(11759,19872,4970,8399) -> Matrix(577,754,-740,-967) Matrix(4177,7056,-2642,-4463) -> Matrix(101,132,-88,-115) Matrix(143,240,28,47) -> Matrix(3,4,-16,-21) Matrix(959,1584,290,479) -> Matrix(11,14,-4,-5) Matrix(815,1344,436,719) -> Matrix(281,358,-354,-451) Matrix(2831,4656,1196,1967) -> Matrix(91,118,-118,-153) Matrix(527,864,380,623) -> Matrix(9,10,-10,-11) Matrix(1439,2352,528,863) -> Matrix(3,4,-10,-13) Matrix(4321,7056,-3174,-5183) -> Matrix(39,50,-32,-41) Matrix(5087,8304,1352,2207) -> Matrix(25,32,-18,-23) Matrix(383,624,294,479) -> Matrix(31,40,-38,-49) Matrix(2783,4512,1006,1631) -> Matrix(3,4,-10,-13) Matrix(1393,2256,-1096,-1775) -> Matrix(79,100,-64,-81) Matrix(12815,20736,4894,7919) -> Matrix(29,38,-42,-55) Matrix(12817,20736,4896,7921) -> Matrix(41,52,-56,-71) Matrix(1009,1632,-860,-1391) -> Matrix(53,68,-46,-59) Matrix(239,384,-150,-241) -> Matrix(79,100,-64,-81) Matrix(1391,2208,332,527) -> Matrix(7,8,-8,-9) Matrix(23231,36864,8590,13631) -> Matrix(19,20,-20,-21) Matrix(23233,36864,8592,13633) -> Matrix(7,6,-6,-5) Matrix(1393,2208,576,913) -> Matrix(89,112,-120,-151) Matrix(1489,2352,578,913) -> Matrix(27,32,-38,-45) Matrix(1439,2256,428,671) -> Matrix(7,8,-8,-9) Matrix(2881,4512,1104,1729) -> Matrix(27,32,-38,-45) Matrix(1105,1728,768,1201) -> Matrix(9,10,-10,-11) Matrix(431,672,338,527) -> Matrix(9,10,-10,-11) Matrix(1487,2304,526,815) -> Matrix(17,22,-24,-31) Matrix(1489,2304,528,817) -> Matrix(17,22,-24,-31) Matrix(529,816,94,145) -> Matrix(3,4,-4,-5) Matrix(817,1248,472,721) -> Matrix(105,134,-134,-171) Matrix(623,912,360,527) -> Matrix(71,86,-90,-109) Matrix(527,768,164,239) -> Matrix(13,16,-22,-27) Matrix(529,768,166,241) -> Matrix(13,16,-22,-27) Matrix(431,624,364,527) -> Matrix(49,60,-58,-71) Matrix(2399,3456,1532,2207) -> Matrix(11,12,-12,-13) Matrix(1201,1728,768,1105) -> Matrix(9,10,-10,-11) Matrix(769,1104,-668,-959) -> Matrix(59,72,-50,-61) Matrix(1105,1584,436,625) -> Matrix(37,42,-52,-59) Matrix(6431,9216,1942,2783) -> Matrix(17,18,-18,-19) Matrix(6433,9216,1944,2785) -> Matrix(5,4,-4,-3) Matrix(337,480,304,433) -> Matrix(11,12,-12,-13) Matrix(1585,2256,574,817) -> Matrix(5,6,-6,-7) Matrix(911,1296,168,239) -> Matrix(3,4,-10,-13) Matrix(2399,3408,1486,2111) -> Matrix(155,202,-188,-245) Matrix(577,816,408,577) -> Matrix(111,140,-134,-169) Matrix(239,336,170,239) -> Matrix(89,110,-106,-131) Matrix(241,336,104,145) -> Matrix(31,38,-40,-49) Matrix(623,864,380,527) -> Matrix(9,10,-10,-11) Matrix(1249,1728,764,1057) -> Matrix(171,208,-208,-253) Matrix(3265,4512,-2778,-3839) -> Matrix(77,94,-68,-83) Matrix(1679,2304,454,623) -> Matrix(13,16,-22,-27) Matrix(1681,2304,456,625) -> Matrix(13,16,-22,-27) Matrix(527,720,456,623) -> Matrix(11,12,-12,-13) Matrix(6097,8304,2362,3217) -> Matrix(47,52,-66,-73) Matrix(673,912,-566,-767) -> Matrix(41,50,-32,-39) Matrix(143,192,-108,-145) -> Matrix(59,72,-50,-61) Matrix(1681,2208,622,817) -> Matrix(5,6,-6,-7) Matrix(479,624,294,383) -> Matrix(31,40,-38,-49) Matrix(1775,2304,406,527) -> Matrix(13,16,-22,-27) Matrix(1777,2304,408,529) -> Matrix(13,16,-22,-27) Matrix(1487,1920,1226,1583) -> Matrix(67,82,-76,-93) Matrix(337,432,188,241) -> Matrix(49,58,-60,-71) Matrix(527,672,338,431) -> Matrix(9,10,-10,-11) Matrix(6049,7680,2496,3169) -> Matrix(571,696,-772,-941) Matrix(721,912,570,721) -> Matrix(289,348,-338,-407) Matrix(191,240,152,191) -> Matrix(131,156,-152,-181) Matrix(193,240,78,97) -> Matrix(63,74,-86,-101) Matrix(623,768,116,143) -> Matrix(5,6,-16,-19) Matrix(625,768,118,145) -> Matrix(5,6,-16,-19) Matrix(1057,1296,314,385) -> Matrix(27,32,-38,-45) Matrix(671,816,236,287) -> Matrix(9,10,-10,-11) Matrix(673,816,80,97) -> Matrix(7,8,-8,-9) Matrix(911,1104,118,143) -> Matrix(7,8,-22,-25) Matrix(239,288,-200,-241) -> Matrix(1,2,-2,-3) Matrix(527,624,364,431) -> Matrix(49,60,-58,-71) Matrix(1345,1584,816,961) -> Matrix(109,128,-132,-155) Matrix(289,336,166,193) -> Matrix(9,10,-10,-11) Matrix(961,1104,168,193) -> Matrix(17,20,-6,-7) Matrix(719,816,126,143) -> Matrix(5,6,-6,-7) Matrix(385,432,172,193) -> Matrix(9,10,-10,-11) Matrix(433,480,304,337) -> Matrix(11,12,-12,-13) Matrix(1,0,2,1) -> Matrix(13,14,-14,-15) Matrix(383,-432,86,-97) -> Matrix(23,20,-38,-33) Matrix(959,-1104,668,-769) -> Matrix(83,72,-98,-85) Matrix(1391,-1632,860,-1009) -> Matrix(77,68,-94,-83) Matrix(529,-624,284,-335) -> Matrix(221,190,-278,-239) Matrix(767,-912,566,-673) -> Matrix(61,50,-72,-59) Matrix(913,-1104,674,-815) -> Matrix(83,72,-98,-85) Matrix(433,-528,196,-239) -> Matrix(91,80,-124,-109) Matrix(719,-912,190,-241) -> Matrix(33,28,-46,-39) Matrix(817,-1056,482,-623) -> Matrix(171,146,-212,-181) Matrix(815,-1056,186,-241) -> Matrix(5,4,-4,-3) Matrix(623,-816,184,-241) -> Matrix(33,28,-46,-39) Matrix(961,-1296,284,-383) -> Matrix(61,52,-88,-75) Matrix(671,-912,142,-193) -> Matrix(17,14,-28,-23) Matrix(913,-1248,526,-719) -> Matrix(3,2,-2,-1) Matrix(911,-1248,246,-337) -> Matrix(5,4,-4,-3) Matrix(383,-528,140,-193) -> Matrix(33,28,-46,-39) Matrix(575,-816,136,-193) -> Matrix(17,14,-28,-23) Matrix(671,-960,202,-289) -> Matrix(3,2,-2,-1) Matrix(865,-1248,332,-479) -> Matrix(33,28,-46,-39) Matrix(719,-1104,282,-433) -> Matrix(3,2,-2,-1) Matrix(433,-672,154,-239) -> Matrix(3,2,-2,-1) Matrix(335,-528,92,-145) -> Matrix(17,14,-28,-23) Matrix(241,-384,150,-239) -> Matrix(119,100,-144,-121) Matrix(5713,-9216,2112,-3407) -> Matrix(121,100,-144,-119) Matrix(6383,-10320,2346,-3793) -> Matrix(17,14,-28,-23) Matrix(3025,-4896,1156,-1871) -> Matrix(107,88,-152,-125) Matrix(2015,-3264,534,-865) -> Matrix(39,32,-50,-41) Matrix(769,-1248,236,-383) -> Matrix(17,14,-28,-23) Matrix(2353,-3840,970,-1583) -> Matrix(443,364,-600,-493) Matrix(4703,-7680,1000,-1633) -> Matrix(29,24,-52,-43) Matrix(671,-1104,234,-385) -> Matrix(3,2,-2,-1) Matrix(1535,-2592,228,-385) -> Matrix(37,30,-58,-47) Matrix(2015,-3408,852,-1441) -> Matrix(119,96,-150,-121) Matrix(481,-816,56,-95) -> Matrix(5,4,16,13) Matrix(337,-576,196,-335) -> Matrix(239,192,-300,-241) Matrix(529,-912,250,-431) -> Matrix(225,178,-292,-231) Matrix(1967,-3408,804,-1393) -> Matrix(71,54,-96,-73) Matrix(2015,-3648,902,-1633) -> Matrix(3,2,-2,-1) Matrix(1535,-2784,424,-769) -> Matrix(29,24,-52,-43) Matrix(289,-528,52,-95) -> Matrix(5,4,16,13) Matrix(431,-816,178,-337) -> Matrix(295,232,-398,-313) Matrix(1105,-2352,428,-911) -> Matrix(269,206,-380,-291) Matrix(289,-624,44,-95) -> Matrix(29,22,-62,-47) Matrix(1055,-2352,388,-865) -> Matrix(11,8,-18,-13) Matrix(529,-1248,142,-335) -> Matrix(3,2,-2,-1) Matrix(241,-576,100,-239) -> Matrix(143,108,-192,-145) Matrix(433,-1056,98,-239) -> Matrix(27,20,-50,-37) Matrix(2879,-7056,1058,-2593) -> Matrix(11,8,4,3) Matrix(2735,-7056,726,-1873) -> Matrix(11,8,-18,-13) Matrix(863,-2256,184,-481) -> Matrix(23,16,-36,-25) Matrix(623,-1632,92,-241) -> Matrix(3,2,4,3) Matrix(145,-384,54,-143) -> Matrix(23,16,-36,-25) Matrix(335,-1104,44,-145) -> Matrix(3,2,-8,-5) Matrix(1247,-4512,186,-673) -> Matrix(7,4,-2,-1) Matrix(239,-912,38,-145) -> Matrix(13,8,-18,-11) Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) Matrix(49,-288,8,-47) -> 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): 68 Degree of the the map X: 68 Degree of the the map Y: 256 ----------------------------------------------------------------------- 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): 768 Minimal number of generators: 129 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: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 8/7 6/5 16/13 4/3 16/11 3/2 8/5 12/7 16/9 2/1 24/11 20/9 96/43 16/7 12/5 120/49 18/7 144/55 8/3 192/71 36/13 48/17 3/1 16/5 36/11 96/29 24/7 18/5 48/13 15/4 64/17 4/1 48/11 22/5 9/2 14/3 80/17 24/5 5/1 21/4 16/3 11/2 6/1 19/3 13/2 20/3 27/4 7/1 15/2 23/3 8/1 17/2 9/1 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 -7/8 10/9 -1/1 -15/17 9/8 -7/8 8/7 -7/8 15/13 -6/7 7/6 -1/1 -6/7 20/17 -7/8 13/11 -6/7 -17/20 19/16 -6/7 -5/6 6/5 -1/1 23/19 -1/1 -9/10 40/33 -8/9 17/14 -8/9 -7/8 11/9 -7/8 -20/23 27/22 -7/8 16/13 -1/1 -13/15 21/17 -6/7 5/4 -13/15 -6/7 24/19 -6/7 19/15 -6/7 -29/34 14/11 -1/1 -11/13 23/18 -1/1 -6/7 9/7 -6/7 22/17 -1/1 -11/13 13/10 -6/7 -5/6 17/13 -7/8 -6/7 4/3 -6/7 23/17 -11/13 -27/32 42/31 -11/13 19/14 -16/19 -5/6 15/11 -6/7 26/19 -1/1 -11/13 11/8 -6/7 -5/6 18/13 -11/13 25/18 -11/13 -16/19 7/5 -11/13 -5/6 24/17 -5/6 17/12 -5/6 -14/17 27/19 -4/5 37/26 -4/5 -3/4 47/33 -1/1 -5/6 10/7 -1/1 -9/11 43/30 -1/1 -10/11 33/23 -6/7 56/39 -5/6 23/16 -1/1 -6/7 36/25 -1/1 13/9 -7/8 -6/7 29/20 -6/7 -5/6 16/11 -1/1 -11/13 19/13 -6/7 -5/6 3/2 -5/6 20/13 -4/5 17/11 -5/6 -4/5 14/9 -1/1 -9/11 25/16 -1/1 -4/5 36/23 -1/1 47/30 -1/1 -6/7 11/7 -5/6 -4/5 19/12 -6/7 -5/6 8/5 -5/6 29/18 -5/6 -14/17 50/31 -67/81 -19/23 71/44 -19/23 -90/109 21/13 -14/17 76/47 -5/6 55/34 -14/17 -9/11 34/21 -19/23 -9/11 47/29 -5/6 -9/11 13/8 -5/6 -14/17 31/19 -14/17 -23/28 80/49 -9/11 49/30 -14/17 -9/11 18/11 -9/11 23/14 -14/17 -9/11 28/17 -5/6 33/20 -23/28 5/3 -9/11 -13/16 27/16 -13/16 49/29 -47/58 -17/21 22/13 -17/21 -25/31 39/23 -4/5 17/10 -21/26 -4/5 12/7 -4/5 31/18 -4/5 -27/34 50/29 -53/67 -15/19 19/11 -4/5 -11/14 45/26 -11/14 71/41 -25/32 -7/9 26/15 -1/1 -7/9 33/19 -4/5 7/4 -1/1 -4/5 23/13 -1/1 -5/6 16/9 -1/1 -9/11 25/14 -9/11 -4/5 9/5 -4/5 38/21 -1/1 -9/11 29/16 -5/6 -4/5 20/11 -4/5 11/6 -29/36 -4/5 24/13 -4/5 13/7 -4/5 -43/54 28/15 -27/34 15/8 -19/24 2/1 -1/1 -7/9 17/8 -10/13 -23/30 15/7 -16/21 13/6 -34/45 -3/4 24/11 -3/4 11/5 -3/4 -20/27 31/14 -3/4 -8/11 20/9 -3/4 29/13 -3/4 -2/3 96/43 -1/1 -5/7 67/30 -3/4 -2/3 38/17 -1/1 -5/7 9/4 -3/4 25/11 -3/4 -5/7 16/7 -1/1 -5/7 23/10 -1/1 -2/3 7/3 -1/1 -3/4 26/11 -1/1 -7/9 97/41 -25/32 -7/9 168/71 -7/9 71/30 -7/9 -24/31 45/19 -10/13 19/8 -10/13 -3/4 12/5 -3/4 29/12 -3/4 -26/35 46/19 -23/31 -63/85 63/26 -37/50 80/33 -17/23 17/7 -3/4 -14/19 22/9 -17/23 -11/15 71/29 -47/64 -11/15 120/49 -11/15 49/20 -11/15 -30/41 27/11 -8/11 5/2 -8/11 -5/7 33/13 -12/17 28/11 -2/3 51/20 -3/4 23/9 -5/7 -7/10 18/7 -5/7 49/19 -5/7 -7/10 80/31 -5/7 111/43 -22/31 31/12 -12/17 -7/10 13/5 -7/10 -2/3 60/23 -5/7 47/18 -5/7 -2/3 34/13 -5/7 -9/13 89/34 -5/7 -2/3 144/55 -5/7 55/21 -5/7 -7/10 21/8 -7/10 8/3 -2/3 27/10 -1/2 73/27 -3/2 -1/1 192/71 -1/1 119/44 -1/1 -10/11 46/17 -1/1 -7/9 19/7 -2/3 -1/2 68/25 -1/2 117/43 0/1 49/18 -1/1 -2/3 30/11 -1/1 11/4 -3/4 -2/3 47/17 -1/1 -1/2 36/13 -1/1 25/9 -1/1 -3/4 14/5 -1/1 -5/7 31/11 -3/4 -2/3 48/17 -1/1 -5/7 17/6 -3/4 -2/3 20/7 -3/4 23/8 -8/11 -5/7 3/1 -2/3 19/6 -2/3 -1/2 16/5 -1/1 -3/5 29/9 -2/3 -1/2 13/4 -1/2 0/1 49/15 -1/1 -1/2 36/11 -1/1 23/7 -1/1 -1/2 33/10 -1/2 43/13 -3/2 -1/1 96/29 -1/1 53/16 -1/1 -8/9 10/3 -1/1 -5/7 47/14 -1/1 -2/3 37/11 -4/5 -3/4 27/8 -3/4 71/21 -5/7 -17/24 44/13 -2/3 17/5 -7/10 -2/3 24/7 -2/3 7/2 -2/3 -3/5 25/7 -5/8 -3/5 18/5 -3/5 47/13 -3/5 -1/2 76/21 -4/7 29/8 -4/7 -1/2 11/3 -2/3 -1/2 48/13 -1/1 -3/5 37/10 -2/3 -1/2 26/7 -1/1 -3/5 41/11 -1/1 -1/2 15/4 -1/2 64/17 -1/1 49/13 -1/1 -3/4 34/9 -1/1 -5/7 19/5 -2/3 -5/8 23/6 -8/13 -3/5 4/1 -1/2 25/6 -2/1 -1/1 21/5 -2/3 17/4 -1/2 0/1 13/3 -2/3 -1/2 48/11 -1/1 -3/5 35/8 -2/3 -1/2 22/5 -1/1 -3/5 31/7 -2/3 -1/2 40/9 -1/2 9/2 -1/2 23/5 -1/1 -1/2 14/3 -1/1 -3/5 47/10 -2/3 -3/5 80/17 -3/5 33/7 -4/7 19/4 -6/11 -1/2 24/5 -1/2 5/1 -1/2 -1/3 21/4 -1/2 16/3 -1/1 -1/3 27/5 0/1 11/2 -1/4 0/1 28/5 0/1 17/3 0/1 1/0 40/7 1/0 23/4 -2/1 -1/1 6/1 -1/1 25/4 -1/1 0/1 19/3 -2/3 -1/2 13/2 -4/7 -1/2 33/5 -2/5 20/3 0/1 47/7 -1/1 1/0 27/4 -1/2 7/1 -1/1 -1/2 15/2 -1/2 23/3 -1/2 -1/3 8/1 0/1 17/2 -1/2 0/1 9/1 0/1 10/1 -1/1 1/1 1/0 -1/1 0/1 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(433,-480,129,-143) (1/1,10/9) -> (10/3,47/14) Hyperbolic Matrix(385,-432,213,-239) (10/9,9/8) -> (9/5,38/21) Hyperbolic Matrix(383,-432,86,-97) (9/8,8/7) -> (40/9,9/2) Hyperbolic Matrix(959,-1104,668,-769) (8/7,15/13) -> (33/23,56/39) Hyperbolic Matrix(623,-720,167,-193) (15/13,7/6) -> (41/11,15/4) Hyperbolic Matrix(1391,-1632,860,-1009) (7/6,20/17) -> (76/47,55/34) Hyperbolic Matrix(529,-624,284,-335) (20/17,13/11) -> (13/7,28/15) Hyperbolic Matrix(527,-624,163,-193) (13/11,19/16) -> (29/9,13/4) Hyperbolic Matrix(767,-912,566,-673) (19/16,6/5) -> (42/31,19/14) Hyperbolic Matrix(913,-1104,674,-815) (6/5,23/19) -> (23/17,42/31) Hyperbolic Matrix(1823,-2208,1269,-1537) (23/19,40/33) -> (56/39,23/16) Hyperbolic Matrix(1583,-1920,357,-433) (40/33,17/14) -> (31/7,40/9) Hyperbolic Matrix(433,-528,196,-239) (17/14,11/9) -> (11/5,31/14) Hyperbolic Matrix(1057,-1296,743,-911) (11/9,27/22) -> (27/19,37/26) Hyperbolic Matrix(625,-768,507,-623) (27/22,16/13) -> (16/13,21/17) Parabolic Matrix(193,-240,115,-143) (21/17,5/4) -> (5/3,27/16) Hyperbolic Matrix(191,-240,39,-49) (5/4,24/19) -> (24/5,5/1) Hyperbolic Matrix(721,-912,151,-191) (24/19,19/15) -> (19/4,24/5) Hyperbolic Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(527,-672,189,-241) (14/11,23/18) -> (25/9,14/5) Hyperbolic Matrix(337,-432,149,-191) (23/18,9/7) -> (9/4,25/11) Hyperbolic Matrix(817,-1056,482,-623) (9/7,22/17) -> (22/13,39/23) Hyperbolic Matrix(815,-1056,186,-241) (22/17,13/10) -> (35/8,22/5) Hyperbolic Matrix(479,-624,185,-241) (13/10,17/13) -> (31/12,13/5) Hyperbolic Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(961,-1296,284,-383) (4/3,23/17) -> (71/21,44/13) Hyperbolic Matrix(671,-912,142,-193) (19/14,15/11) -> (33/7,19/4) Hyperbolic Matrix(913,-1248,526,-719) (15/11,26/19) -> (26/15,33/19) Hyperbolic Matrix(911,-1248,246,-337) (26/19,11/8) -> (37/10,26/7) Hyperbolic Matrix(383,-528,140,-193) (11/8,18/13) -> (30/11,11/4) Hyperbolic Matrix(623,-864,243,-337) (18/13,25/18) -> (23/9,18/7) Hyperbolic Matrix(241,-336,137,-191) (25/18,7/5) -> (7/4,23/13) Hyperbolic Matrix(239,-336,69,-97) (7/5,24/17) -> (24/7,7/2) Hyperbolic Matrix(577,-816,169,-239) (24/17,17/12) -> (17/5,24/7) Hyperbolic Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(1585,-2256,1011,-1439) (37/26,47/33) -> (47/30,11/7) Hyperbolic Matrix(337,-480,33,-47) (47/33,10/7) -> (10/1,1/0) Hyperbolic Matrix(671,-960,202,-289) (10/7,43/30) -> (53/16,10/3) Hyperbolic Matrix(1105,-1584,669,-959) (43/30,33/23) -> (33/20,5/3) Hyperbolic Matrix(1201,-1728,433,-623) (23/16,36/25) -> (36/13,25/9) Hyperbolic Matrix(865,-1248,332,-479) (36/25,13/9) -> (13/5,60/23) Hyperbolic Matrix(431,-624,67,-97) (13/9,29/20) -> (19/3,13/2) Hyperbolic Matrix(529,-768,363,-527) (29/20,16/11) -> (16/11,19/13) Parabolic Matrix(623,-912,263,-385) (19/13,3/2) -> (45/19,19/8) Hyperbolic Matrix(719,-1104,282,-433) (3/2,20/13) -> (28/11,51/20) Hyperbolic Matrix(623,-960,281,-433) (20/13,17/11) -> (31/14,20/9) Hyperbolic Matrix(433,-672,154,-239) (17/11,14/9) -> (14/5,31/11) Hyperbolic Matrix(431,-672,93,-145) (14/9,25/16) -> (23/5,14/3) Hyperbolic Matrix(1105,-1728,337,-527) (25/16,36/23) -> (36/11,23/7) Hyperbolic Matrix(2207,-3456,675,-1057) (36/23,47/30) -> (49/15,36/11) Hyperbolic Matrix(335,-528,92,-145) (11/7,19/12) -> (29/8,11/3) Hyperbolic Matrix(241,-384,150,-239) (19/12,8/5) -> (8/5,29/18) Parabolic Matrix(1489,-2400,863,-1391) (29/18,50/31) -> (50/29,19/11) Hyperbolic Matrix(5713,-9216,2112,-3407) (50/31,71/44) -> (119/44,46/17) Hyperbolic Matrix(2111,-3408,625,-1009) (71/44,21/13) -> (27/8,71/21) Hyperbolic Matrix(6383,-10320,2346,-3793) (21/13,76/47) -> (68/25,117/43) Hyperbolic Matrix(3025,-4896,1156,-1871) (55/34,34/21) -> (34/13,89/34) Hyperbolic Matrix(2015,-3264,534,-865) (34/21,47/29) -> (49/13,34/9) Hyperbolic Matrix(769,-1248,236,-383) (47/29,13/8) -> (13/4,49/15) Hyperbolic Matrix(383,-624,89,-145) (13/8,31/19) -> (17/4,13/3) Hyperbolic Matrix(2353,-3840,970,-1583) (31/19,80/49) -> (80/33,17/7) Hyperbolic Matrix(4703,-7680,1000,-1633) (80/49,49/30) -> (47/10,80/17) Hyperbolic Matrix(1057,-1728,293,-479) (49/30,18/11) -> (18/5,47/13) Hyperbolic Matrix(527,-864,147,-241) (18/11,23/14) -> (25/7,18/5) Hyperbolic Matrix(671,-1104,234,-385) (23/14,28/17) -> (20/7,23/8) Hyperbolic Matrix(961,-1584,145,-239) (28/17,33/20) -> (33/5,20/3) Hyperbolic Matrix(1535,-2592,228,-385) (27/16,49/29) -> (47/7,27/4) Hyperbolic Matrix(2015,-3408,852,-1441) (49/29,22/13) -> (26/11,97/41) Hyperbolic Matrix(481,-816,56,-95) (39/23,17/10) -> (17/2,9/1) Hyperbolic Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(529,-912,250,-431) (31/18,50/29) -> (2/1,17/8) Hyperbolic Matrix(527,-912,167,-289) (19/11,45/26) -> (3/1,19/6) Hyperbolic Matrix(721,-1248,249,-431) (45/26,71/41) -> (23/8,3/1) Hyperbolic Matrix(1967,-3408,804,-1393) (71/41,26/15) -> (22/9,71/29) Hyperbolic Matrix(193,-336,27,-47) (33/19,7/4) -> (7/1,15/2) Hyperbolic Matrix(433,-768,243,-431) (23/13,16/9) -> (16/9,25/14) Parabolic Matrix(241,-432,53,-95) (25/14,9/5) -> (9/2,23/5) Hyperbolic Matrix(2015,-3648,902,-1633) (38/21,29/16) -> (67/30,38/17) Hyperbolic Matrix(1535,-2784,424,-769) (29/16,20/11) -> (76/21,29/8) Hyperbolic Matrix(289,-528,52,-95) (20/11,11/6) -> (11/2,28/5) Hyperbolic Matrix(287,-528,131,-241) (11/6,24/13) -> (24/11,11/5) Hyperbolic Matrix(337,-624,155,-287) (24/13,13/7) -> (13/6,24/11) Hyperbolic Matrix(719,-1344,283,-529) (28/15,15/8) -> (33/13,28/11) Hyperbolic Matrix(431,-816,178,-337) (15/8,2/1) -> (46/19,63/26) Hyperbolic Matrix(1105,-2352,428,-911) (17/8,15/7) -> (111/43,31/12) Hyperbolic Matrix(289,-624,44,-95) (15/7,13/6) -> (13/2,33/5) Hyperbolic Matrix(1055,-2352,388,-865) (20/9,29/13) -> (19/7,68/25) Hyperbolic Matrix(4129,-9216,1849,-4127) (29/13,96/43) -> (96/43,67/30) Parabolic Matrix(193,-432,21,-47) (38/17,9/4) -> (9/1,10/1) Hyperbolic Matrix(337,-768,147,-335) (25/11,16/7) -> (16/7,23/10) Parabolic Matrix(145,-336,41,-95) (23/10,7/3) -> (7/2,25/7) Hyperbolic Matrix(529,-1248,142,-335) (7/3,26/11) -> (26/7,41/11) Hyperbolic Matrix(8399,-19872,3429,-8113) (97/41,168/71) -> (120/49,49/20) Hyperbolic Matrix(8641,-20448,3529,-8351) (168/71,71/30) -> (71/29,120/49) Hyperbolic Matrix(1967,-4656,771,-1825) (71/30,45/19) -> (51/20,23/9) Hyperbolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(913,-2208,337,-815) (29/12,46/19) -> (46/17,19/7) Hyperbolic Matrix(3169,-7680,673,-1631) (63/26,80/33) -> (80/17,33/7) Hyperbolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(2879,-7056,1058,-2593) (49/20,27/11) -> (117/43,49/18) Hyperbolic Matrix(97,-240,19,-47) (27/11,5/2) -> (5/1,21/4) Hyperbolic Matrix(625,-1584,189,-479) (5/2,33/13) -> (33/10,43/13) Hyperbolic Matrix(913,-2352,335,-863) (18/7,49/19) -> (49/18,30/11) Hyperbolic Matrix(2735,-7056,726,-1873) (49/19,80/31) -> (64/17,49/13) Hyperbolic Matrix(3217,-8304,855,-2207) (80/31,111/43) -> (15/4,64/17) Hyperbolic Matrix(1729,-4512,625,-1631) (60/23,47/18) -> (47/17,36/13) Hyperbolic Matrix(863,-2256,184,-481) (47/18,34/13) -> (14/3,47/10) Hyperbolic Matrix(7921,-20736,3025,-7919) (89/34,144/55) -> (144/55,55/21) Parabolic Matrix(623,-1632,92,-241) (55/21,21/8) -> (27/4,7/1) Hyperbolic Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(817,-2208,195,-527) (27/10,73/27) -> (25/6,21/5) Hyperbolic Matrix(13633,-36864,5041,-13631) (73/27,192/71) -> (192/71,119/44) Parabolic Matrix(817,-2256,243,-671) (11/4,47/17) -> (47/14,37/11) Hyperbolic Matrix(817,-2304,289,-815) (31/11,48/17) -> (48/17,17/6) Parabolic Matrix(287,-816,51,-145) (17/6,20/7) -> (28/5,17/3) Hyperbolic Matrix(241,-768,75,-239) (19/6,16/5) -> (16/5,29/9) Parabolic Matrix(335,-1104,44,-145) (23/7,33/10) -> (15/2,23/3) Hyperbolic Matrix(2785,-9216,841,-2783) (43/13,96/29) -> (96/29,53/16) Parabolic Matrix(385,-1296,71,-239) (37/11,27/8) -> (27/5,11/2) Hyperbolic Matrix(1247,-4512,186,-673) (47/13,76/21) -> (20/3,47/7) Hyperbolic Matrix(625,-2304,169,-623) (11/3,48/13) -> (48/13,37/10) Parabolic Matrix(239,-912,38,-145) (19/5,23/6) -> (25/4,19/3) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(529,-2304,121,-527) (13/3,48/11) -> (48/11,35/8) Parabolic Matrix(145,-768,27,-143) (21/4,16/3) -> (16/3,27/5) Parabolic Matrix(143,-816,17,-97) (17/3,40/7) -> (8/1,17/2) Hyperbolic Matrix(193,-1104,25,-143) (40/7,23/4) -> (23/3,8/1) Hyperbolic Matrix(49,-288,8,-47) (23/4,6/1) -> (6/1,25/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(6,7,-7,-8) Matrix(433,-480,129,-143) -> Matrix(6,5,-5,-4) Matrix(385,-432,213,-239) -> Matrix(4,3,-3,-2) Matrix(383,-432,86,-97) -> Matrix(23,20,-38,-33) Matrix(959,-1104,668,-769) -> Matrix(83,72,-98,-85) Matrix(623,-720,167,-193) -> Matrix(6,5,-5,-4) Matrix(1391,-1632,860,-1009) -> Matrix(77,68,-94,-83) Matrix(529,-624,284,-335) -> Matrix(221,190,-278,-239) Matrix(527,-624,163,-193) -> Matrix(20,17,-33,-28) Matrix(767,-912,566,-673) -> Matrix(61,50,-72,-59) Matrix(913,-1104,674,-815) -> Matrix(83,72,-98,-85) Matrix(1823,-2208,1269,-1537) -> Matrix(4,3,-3,-2) Matrix(1583,-1920,357,-433) -> Matrix(26,23,-43,-38) Matrix(433,-528,196,-239) -> Matrix(91,80,-124,-109) Matrix(1057,-1296,743,-911) -> Matrix(68,59,-83,-72) Matrix(625,-768,507,-623) -> Matrix(98,85,-113,-98) Matrix(193,-240,115,-143) -> Matrix(132,115,-163,-142) Matrix(191,-240,39,-49) -> Matrix(22,19,-51,-44) Matrix(721,-912,151,-191) -> Matrix(76,65,-145,-124) Matrix(719,-912,190,-241) -> Matrix(33,28,-46,-39) Matrix(527,-672,189,-241) -> Matrix(4,3,-3,-2) Matrix(337,-432,149,-191) -> Matrix(38,33,-53,-46) Matrix(817,-1056,482,-623) -> Matrix(171,146,-212,-181) Matrix(815,-1056,186,-241) -> Matrix(5,4,-4,-3) Matrix(479,-624,185,-241) -> Matrix(28,23,-39,-32) Matrix(623,-816,184,-241) -> Matrix(33,28,-46,-39) Matrix(961,-1296,284,-383) -> Matrix(61,52,-88,-75) Matrix(671,-912,142,-193) -> Matrix(17,14,-28,-23) Matrix(913,-1248,526,-719) -> Matrix(3,2,-2,-1) Matrix(911,-1248,246,-337) -> Matrix(5,4,-4,-3) Matrix(383,-528,140,-193) -> Matrix(33,28,-46,-39) Matrix(623,-864,243,-337) -> Matrix(4,3,-3,-2) Matrix(241,-336,137,-191) -> Matrix(46,39,-59,-50) Matrix(239,-336,69,-97) -> Matrix(44,37,-69,-58) Matrix(577,-816,169,-239) -> Matrix(76,63,-111,-92) Matrix(575,-816,136,-193) -> Matrix(17,14,-28,-23) Matrix(1585,-2256,1011,-1439) -> Matrix(0,-1,1,2) Matrix(337,-480,33,-47) -> Matrix(6,5,-5,-4) Matrix(671,-960,202,-289) -> Matrix(3,2,-2,-1) Matrix(1105,-1584,669,-959) -> Matrix(86,77,-105,-94) Matrix(1201,-1728,433,-623) -> Matrix(4,3,-3,-2) Matrix(865,-1248,332,-479) -> Matrix(33,28,-46,-39) Matrix(431,-624,67,-97) -> Matrix(20,17,-33,-28) Matrix(529,-768,363,-527) -> Matrix(72,61,-85,-72) Matrix(623,-912,263,-385) -> Matrix(88,75,-115,-98) Matrix(719,-1104,282,-433) -> Matrix(3,2,-2,-1) Matrix(623,-960,281,-433) -> Matrix(58,47,-79,-64) Matrix(433,-672,154,-239) -> Matrix(3,2,-2,-1) Matrix(431,-672,93,-145) -> Matrix(4,3,-3,-2) Matrix(1105,-1728,337,-527) -> Matrix(4,3,-3,-2) Matrix(2207,-3456,675,-1057) -> Matrix(6,5,-5,-4) Matrix(335,-528,92,-145) -> Matrix(17,14,-28,-23) Matrix(241,-384,150,-239) -> Matrix(119,100,-144,-121) Matrix(1489,-2400,863,-1391) -> Matrix(2,1,-1,0) Matrix(5713,-9216,2112,-3407) -> Matrix(121,100,-144,-119) Matrix(2111,-3408,625,-1009) -> Matrix(154,127,-211,-174) Matrix(6383,-10320,2346,-3793) -> Matrix(17,14,-28,-23) Matrix(3025,-4896,1156,-1871) -> Matrix(107,88,-152,-125) Matrix(2015,-3264,534,-865) -> Matrix(39,32,-50,-41) Matrix(769,-1248,236,-383) -> Matrix(17,14,-28,-23) Matrix(383,-624,89,-145) -> Matrix(28,23,-39,-32) Matrix(2353,-3840,970,-1583) -> Matrix(443,364,-600,-493) Matrix(4703,-7680,1000,-1633) -> Matrix(29,24,-52,-43) Matrix(1057,-1728,293,-479) -> Matrix(62,51,-107,-88) Matrix(527,-864,147,-241) -> Matrix(4,3,-3,-2) Matrix(671,-1104,234,-385) -> Matrix(3,2,-2,-1) Matrix(961,-1584,145,-239) -> Matrix(6,5,-29,-24) Matrix(1535,-2592,228,-385) -> Matrix(37,30,-58,-47) Matrix(2015,-3408,852,-1441) -> Matrix(119,96,-150,-121) Matrix(481,-816,56,-95) -> Matrix(5,4,16,13) Matrix(337,-576,196,-335) -> Matrix(239,192,-300,-241) Matrix(529,-912,250,-431) -> Matrix(225,178,-292,-231) Matrix(527,-912,167,-289) -> Matrix(24,19,-43,-34) Matrix(721,-1248,249,-431) -> Matrix(88,69,-125,-98) Matrix(1967,-3408,804,-1393) -> Matrix(71,54,-96,-73) Matrix(193,-336,27,-47) -> Matrix(4,3,-3,-2) Matrix(433,-768,243,-431) -> Matrix(50,41,-61,-50) Matrix(241,-432,53,-95) -> Matrix(6,5,-17,-14) Matrix(2015,-3648,902,-1633) -> Matrix(3,2,-2,-1) Matrix(1535,-2784,424,-769) -> Matrix(29,24,-52,-43) Matrix(289,-528,52,-95) -> Matrix(5,4,16,13) Matrix(287,-528,131,-241) -> Matrix(208,167,-279,-224) Matrix(337,-624,155,-287) -> Matrix(332,265,-441,-352) Matrix(719,-1344,283,-529) -> Matrix(228,181,-325,-258) Matrix(431,-816,178,-337) -> Matrix(295,232,-398,-313) Matrix(1105,-2352,428,-911) -> Matrix(269,206,-380,-291) Matrix(289,-624,44,-95) -> Matrix(29,22,-62,-47) Matrix(1055,-2352,388,-865) -> Matrix(11,8,-18,-13) Matrix(4129,-9216,1849,-4127) -> Matrix(18,13,-25,-18) Matrix(193,-432,21,-47) -> Matrix(4,3,-3,-2) Matrix(337,-768,147,-335) -> Matrix(18,13,-25,-18) Matrix(145,-336,41,-95) -> Matrix(14,11,-23,-18) Matrix(529,-1248,142,-335) -> Matrix(3,2,-2,-1) Matrix(8399,-19872,3429,-8113) -> Matrix(622,485,-849,-662) Matrix(8641,-20448,3529,-8351) -> Matrix(764,593,-1041,-808) Matrix(1967,-4656,771,-1825) -> Matrix(92,71,-127,-98) Matrix(241,-576,100,-239) -> Matrix(143,108,-192,-145) Matrix(913,-2208,337,-815) -> Matrix(66,49,-97,-72) Matrix(3169,-7680,673,-1631) -> Matrix(242,179,-411,-304) Matrix(433,-1056,98,-239) -> Matrix(27,20,-50,-37) Matrix(2879,-7056,1058,-2593) -> Matrix(11,8,4,3) Matrix(97,-240,19,-47) -> Matrix(4,3,-19,-14) Matrix(625,-1584,189,-479) -> Matrix(10,7,-3,-2) Matrix(913,-2352,335,-863) -> Matrix(4,3,-11,-8) Matrix(2735,-7056,726,-1873) -> Matrix(11,8,-18,-13) Matrix(3217,-8304,855,-2207) -> Matrix(24,17,-17,-12) Matrix(1729,-4512,625,-1631) -> Matrix(4,3,-11,-8) Matrix(863,-2256,184,-481) -> Matrix(23,16,-36,-25) Matrix(7921,-20736,3025,-7919) -> Matrix(34,25,-49,-36) Matrix(623,-1632,92,-241) -> Matrix(3,2,4,3) Matrix(145,-384,54,-143) -> Matrix(23,16,-36,-25) Matrix(817,-2208,195,-527) -> Matrix(0,-1,1,2) Matrix(13633,-36864,5041,-13631) -> Matrix(12,13,-13,-14) Matrix(817,-2256,243,-671) -> Matrix(0,-1,1,2) Matrix(817,-2304,289,-815) -> Matrix(18,13,-25,-18) Matrix(287,-816,51,-145) -> Matrix(4,3,-3,-2) Matrix(241,-768,75,-239) -> Matrix(8,5,-13,-8) Matrix(335,-1104,44,-145) -> Matrix(3,2,-8,-5) Matrix(2785,-9216,841,-2783) -> Matrix(10,11,-11,-12) Matrix(385,-1296,71,-239) -> Matrix(4,3,-11,-8) Matrix(1247,-4512,186,-673) -> Matrix(7,4,-2,-1) Matrix(625,-2304,169,-623) -> Matrix(8,5,-13,-8) Matrix(239,-912,38,-145) -> Matrix(13,8,-18,-11) Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) Matrix(529,-2304,121,-527) -> Matrix(8,5,-13,-8) Matrix(145,-768,27,-143) -> Matrix(2,1,-5,-2) Matrix(143,-816,17,-97) -> Matrix(0,-1,1,2) Matrix(193,-1104,25,-143) -> Matrix(0,-1,1,4) Matrix(49,-288,8,-47) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 68 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 7 1 2/1 (-1/1,-7/9) 0 12 15/7 -16/21 2 8 13/6 (-34/45,-3/4) 0 24 24/11 -3/4 18 1 11/5 (-3/4,-20/27) 0 24 20/9 -3/4 1 6 29/13 (-3/4,-2/3) 0 24 96/43 (-1/1,-5/7).(-3/4,-2/3) 0 1 38/17 (-1/1,-5/7) 0 12 9/4 -3/4 2 8 25/11 (-3/4,-5/7) 0 24 16/7 (-1/1,-5/7).(-3/4,-2/3) 0 3 23/10 (-1/1,-2/3) 0 24 7/3 (-1/1,-3/4) 0 24 26/11 (-1/1,-7/9) 0 12 71/30 (-7/9,-24/31) 0 24 45/19 -10/13 2 8 19/8 (-10/13,-3/4) 0 24 12/5 -3/4 6 2 29/12 (-3/4,-26/35) 0 24 46/19 (-23/31,-63/85) 0 12 63/26 -37/50 2 8 17/7 (-3/4,-14/19) 0 24 22/9 (-17/23,-11/15) 0 12 71/29 (-47/64,-11/15) 0 24 120/49 -11/15 7 1 49/20 (-11/15,-30/41) 0 24 27/11 -8/11 2 8 5/2 (-8/11,-5/7) 0 24 33/13 -12/17 2 8 28/11 -2/3 1 6 23/9 (-5/7,-7/10) 0 24 18/7 -5/7 1 4 49/19 (-5/7,-7/10) 0 24 80/31 -5/7 5 3 111/43 -22/31 2 8 31/12 (-12/17,-7/10) 0 24 13/5 (-7/10,-2/3) 0 24 47/18 (-5/7,-2/3) 0 24 34/13 (-5/7,-9/13) 0 12 144/55 -5/7 1 1 55/21 (-5/7,-7/10) 0 24 21/8 -7/10 2 8 8/3 -2/3 2 3 27/10 -1/2 2 8 73/27 (-3/2,-1/1) 0 24 192/71 -1/1 13 1 46/17 (-1/1,-7/9) 0 12 19/7 (-2/3,-1/2) 0 24 11/4 (-3/4,-2/3) 0 24 47/17 (-1/1,-1/2) 0 24 36/13 -1/1 1 2 25/9 (-1/1,-3/4) 0 24 14/5 (-1/1,-5/7) 0 12 48/17 (-1/1,-5/7).(-3/4,-2/3) 0 1 17/6 (-3/4,-2/3) 0 24 20/7 -3/4 1 6 23/8 (-8/11,-5/7) 0 24 3/1 -2/3 2 8 19/6 (-2/3,-1/2) 0 24 16/5 (-1/1,-3/5).(-2/3,-1/2) 0 3 29/9 (-2/3,-1/2) 0 24 13/4 (-1/2,0/1) 0 24 49/15 (-1/1,-1/2) 0 24 36/11 -1/1 1 2 23/7 (-1/1,-1/2) 0 24 33/10 -1/2 2 8 43/13 (-3/2,-1/1) 0 24 96/29 -1/1 11 1 10/3 (-1/1,-5/7) 0 12 47/14 (-1/1,-2/3) 0 24 37/11 (-4/5,-3/4) 0 24 27/8 -3/4 2 8 17/5 (-7/10,-2/3) 0 24 24/7 -2/3 5 1 7/2 (-2/3,-3/5) 0 24 25/7 (-5/8,-3/5) 0 24 18/5 -3/5 1 4 47/13 (-3/5,-1/2) 0 24 76/21 -4/7 1 6 29/8 (-4/7,-1/2) 0 24 11/3 (-2/3,-1/2) 0 24 48/13 (-1/1,-3/5).(-2/3,-1/2) 0 1 26/7 (-1/1,-3/5) 0 12 41/11 (-1/1,-1/2) 0 24 15/4 -1/2 2 8 19/5 (-2/3,-5/8) 0 24 23/6 (-8/13,-3/5) 0 24 4/1 -1/2 1 6 25/6 (-2/1,-1/1) 0 24 21/5 -2/3 2 8 17/4 (-1/2,0/1) 0 24 13/3 (-2/3,-1/2) 0 24 48/11 (-1/1,-3/5).(-2/3,-1/2) 0 1 22/5 (-1/1,-3/5) 0 12 31/7 (-2/3,-1/2) 0 24 9/2 -1/2 2 8 23/5 (-1/1,-1/2) 0 24 14/3 (-1/1,-3/5) 0 12 47/10 (-2/3,-3/5) 0 24 80/17 -3/5 5 3 33/7 -4/7 2 8 19/4 (-6/11,-1/2) 0 24 24/5 -1/2 7 1 5/1 (-1/2,-1/3) 0 24 21/4 -1/2 2 8 16/3 (-1/1,-1/3).(-1/2,0/1) 0 3 27/5 0/1 2 8 11/2 (-1/4,0/1) 0 24 28/5 0/1 1 6 17/3 (0/1,1/0) 0 24 40/7 1/0 1 3 23/4 (-2/1,-1/1) 0 24 6/1 -1/1 1 4 25/4 (-1/1,0/1) 0 24 19/3 (-2/3,-1/2) 0 24 13/2 (-4/7,-1/2) 0 24 33/5 -2/5 2 8 20/3 0/1 1 6 47/7 (-1/1,1/0) 0 24 27/4 -1/2 2 8 7/1 (-1/1,-1/2) 0 24 15/2 -1/2 2 8 23/3 (-1/2,-1/3) 0 24 8/1 0/1 1 3 17/2 (-1/2,0/1) 0 24 9/1 0/1 2 8 10/1 (-1/1,1/1) 0 12 1/0 (-1/1,0/1) 0 24 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(385,-816,159,-337) (2/1,15/7) -> (46/19,63/26) Glide Reflection Matrix(289,-624,44,-95) (15/7,13/6) -> (13/2,33/5) Hyperbolic Matrix(287,-624,132,-287) (13/6,24/11) -> (13/6,24/11) Reflection Matrix(241,-528,110,-241) (24/11,11/5) -> (24/11,11/5) Reflection Matrix(239,-528,43,-95) (11/5,20/9) -> (11/2,28/5) Glide Reflection Matrix(1249,-2784,345,-769) (20/9,29/13) -> (76/21,29/8) Glide Reflection Matrix(2495,-5568,1118,-2495) (29/13,96/43) -> (29/13,96/43) Reflection Matrix(1633,-3648,731,-1633) (96/43,38/17) -> (96/43,38/17) Reflection Matrix(193,-432,21,-47) (38/17,9/4) -> (9/1,10/1) Hyperbolic Matrix(191,-432,42,-95) (9/4,25/11) -> (9/2,23/5) Glide Reflection Matrix(337,-768,147,-335) (25/11,16/7) -> (16/7,23/10) Parabolic Matrix(145,-336,41,-95) (23/10,7/3) -> (7/2,25/7) Hyperbolic Matrix(529,-1248,142,-335) (7/3,26/11) -> (26/7,41/11) Hyperbolic Matrix(1441,-3408,589,-1393) (26/11,71/30) -> (22/9,71/29) Glide Reflection Matrix(527,-1248,182,-431) (71/30,45/19) -> (23/8,3/1) Glide Reflection Matrix(385,-912,122,-289) (45/19,19/8) -> (3/1,19/6) Glide Reflection Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(913,-2208,337,-815) (29/12,46/19) -> (46/17,19/7) Hyperbolic Matrix(1583,-3840,613,-1487) (63/26,17/7) -> (111/43,31/12) Glide Reflection Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(6959,-17040,2842,-6959) (71/29,120/49) -> (71/29,120/49) Reflection Matrix(4801,-11760,1960,-4801) (120/49,49/20) -> (120/49,49/20) Reflection Matrix(1057,-2592,157,-385) (49/20,27/11) -> (47/7,27/4) Glide Reflection Matrix(97,-240,19,-47) (27/11,5/2) -> (5/1,21/4) Hyperbolic Matrix(625,-1584,189,-479) (5/2,33/13) -> (33/10,43/13) Hyperbolic Matrix(623,-1584,94,-239) (33/13,28/11) -> (33/5,20/3) Glide Reflection Matrix(433,-1104,151,-385) (28/11,23/9) -> (20/7,23/8) Glide Reflection Matrix(337,-864,94,-241) (23/9,18/7) -> (25/7,18/5) Glide Reflection Matrix(671,-1728,186,-479) (18/7,49/19) -> (18/5,47/13) Glide Reflection Matrix(2977,-7680,633,-1633) (49/19,80/31) -> (47/10,80/17) Glide Reflection Matrix(4463,-11520,948,-2447) (80/31,111/43) -> (80/17,33/7) Glide Reflection Matrix(241,-624,56,-145) (31/12,13/5) -> (17/4,13/3) Glide Reflection Matrix(479,-1248,147,-383) (13/5,47/18) -> (13/4,49/15) Glide Reflection Matrix(863,-2256,184,-481) (47/18,34/13) -> (14/3,47/10) Hyperbolic Matrix(1871,-4896,715,-1871) (34/13,144/55) -> (34/13,144/55) Reflection Matrix(6049,-15840,2310,-6049) (144/55,55/21) -> (144/55,55/21) Reflection Matrix(623,-1632,92,-241) (55/21,21/8) -> (27/4,7/1) Hyperbolic Matrix(145,-384,54,-143) (21/8,8/3) -> (8/3,27/10) Parabolic Matrix(817,-2208,195,-527) (27/10,73/27) -> (25/6,21/5) Hyperbolic Matrix(10367,-28032,3834,-10367) (73/27,192/71) -> (73/27,192/71) Reflection Matrix(3265,-8832,1207,-3265) (192/71,46/17) -> (192/71,46/17) Reflection Matrix(193,-528,53,-145) (19/7,11/4) -> (29/8,11/3) Glide Reflection Matrix(817,-2256,243,-671) (11/4,47/17) -> (47/14,37/11) Hyperbolic Matrix(1249,-3456,382,-1057) (47/17,36/13) -> (49/15,36/11) Glide Reflection Matrix(623,-1728,190,-527) (36/13,25/9) -> (36/11,23/7) Glide Reflection Matrix(241,-672,52,-145) (25/9,14/5) -> (23/5,14/3) Glide Reflection Matrix(239,-672,85,-239) (14/5,48/17) -> (14/5,48/17) Reflection Matrix(577,-1632,204,-577) (48/17,17/6) -> (48/17,17/6) Reflection Matrix(287,-816,51,-145) (17/6,20/7) -> (28/5,17/3) Hyperbolic Matrix(241,-768,75,-239) (19/6,16/5) -> (16/5,29/9) Parabolic Matrix(193,-624,30,-97) (29/9,13/4) -> (19/3,13/2) Glide Reflection Matrix(335,-1104,44,-145) (23/7,33/10) -> (15/2,23/3) Hyperbolic Matrix(2495,-8256,754,-2495) (43/13,96/29) -> (43/13,96/29) Reflection Matrix(289,-960,87,-289) (96/29,10/3) -> (96/29,10/3) Reflection Matrix(143,-480,14,-47) (10/3,47/14) -> (10/1,1/0) Glide Reflection Matrix(385,-1296,71,-239) (37/11,27/8) -> (27/5,11/2) Hyperbolic Matrix(241,-816,57,-193) (27/8,17/5) -> (21/5,17/4) Glide Reflection Matrix(239,-816,70,-239) (17/5,24/7) -> (17/5,24/7) Reflection Matrix(97,-336,28,-97) (24/7,7/2) -> (24/7,7/2) Reflection Matrix(1247,-4512,186,-673) (47/13,76/21) -> (20/3,47/7) Hyperbolic Matrix(287,-1056,78,-287) (11/3,48/13) -> (11/3,48/13) Reflection Matrix(337,-1248,91,-337) (48/13,26/7) -> (48/13,26/7) Reflection Matrix(193,-720,26,-97) (41/11,15/4) -> (7/1,15/2) Glide Reflection Matrix(241,-912,51,-193) (15/4,19/5) -> (33/7,19/4) Glide Reflection Matrix(239,-912,38,-145) (19/5,23/6) -> (25/4,19/3) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(287,-1248,66,-287) (13/3,48/11) -> (13/3,48/11) Reflection Matrix(241,-1056,55,-241) (48/11,22/5) -> (48/11,22/5) Reflection Matrix(97,-432,11,-49) (31/7,9/2) -> (17/2,9/1) Glide Reflection Matrix(191,-912,40,-191) (19/4,24/5) -> (19/4,24/5) Reflection Matrix(49,-240,10,-49) (24/5,5/1) -> (24/5,5/1) Reflection Matrix(145,-768,27,-143) (21/4,16/3) -> (16/3,27/5) Parabolic Matrix(143,-816,17,-97) (17/3,40/7) -> (8/1,17/2) Hyperbolic Matrix(193,-1104,25,-143) (40/7,23/4) -> (23/3,8/1) Hyperbolic Matrix(49,-288,8,-47) (23/4,6/1) -> (6/1,25/4) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(8,7,-9,-8) (0/1,2/1) -> (-1/1,-7/9) Matrix(385,-816,159,-337) -> Matrix(272,209,-367,-282) Matrix(289,-624,44,-95) -> Matrix(29,22,-62,-47) Matrix(287,-624,132,-287) -> Matrix(271,204,-360,-271) (13/6,24/11) -> (-34/45,-3/4) Matrix(241,-528,110,-241) -> Matrix(161,120,-216,-161) (24/11,11/5) -> (-3/4,-20/27) Matrix(239,-528,43,-95) -> Matrix(4,3,11,8) Matrix(1249,-2784,345,-769) -> Matrix(16,11,-29,-20) Matrix(2495,-5568,1118,-2495) -> Matrix(17,12,-24,-17) (29/13,96/43) -> (-3/4,-2/3) Matrix(1633,-3648,731,-1633) -> Matrix(6,5,-7,-6) (96/43,38/17) -> (-1/1,-5/7) Matrix(193,-432,21,-47) -> Matrix(4,3,-3,-2) -1/1 Matrix(191,-432,42,-95) -> Matrix(3,2,-10,-7) Matrix(337,-768,147,-335) -> Matrix(18,13,-25,-18) (-1/1,-5/7).(-3/4,-2/3) Matrix(145,-336,41,-95) -> Matrix(14,11,-23,-18) Matrix(529,-1248,142,-335) -> Matrix(3,2,-2,-1) -1/1 Matrix(1441,-3408,589,-1393) -> Matrix(82,65,-111,-88) Matrix(527,-1248,182,-431) -> Matrix(83,64,-118,-91) Matrix(385,-912,122,-289) -> Matrix(21,16,-38,-29) Matrix(241,-576,100,-239) -> Matrix(143,108,-192,-145) -3/4 Matrix(913,-2208,337,-815) -> Matrix(66,49,-97,-72) Matrix(1583,-3840,613,-1487) -> Matrix(256,189,-363,-268) Matrix(433,-1056,98,-239) -> Matrix(27,20,-50,-37) Matrix(6959,-17040,2842,-6959) -> Matrix(1409,1034,-1920,-1409) (71/29,120/49) -> (-47/64,-11/15) Matrix(4801,-11760,1960,-4801) -> Matrix(901,660,-1230,-901) (120/49,49/20) -> (-11/15,-30/41) Matrix(1057,-2592,157,-385) -> Matrix(26,19,-41,-30) Matrix(97,-240,19,-47) -> Matrix(4,3,-19,-14) Matrix(625,-1584,189,-479) -> Matrix(10,7,-3,-2) Matrix(623,-1584,94,-239) -> Matrix(3,2,-16,-11) Matrix(433,-1104,151,-385) -> Matrix(6,5,-7,-6) *** -> (-1/1,-5/7) Matrix(337,-864,94,-241) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(671,-1728,186,-479) -> Matrix(37,26,-64,-45) Matrix(2977,-7680,633,-1633) -> Matrix(16,11,-29,-20) Matrix(4463,-11520,948,-2447) -> Matrix(121,86,-204,-145) Matrix(241,-624,56,-145) -> Matrix(17,12,-24,-17) *** -> (-3/4,-2/3) Matrix(479,-1248,147,-383) -> Matrix(10,7,-17,-12) Matrix(863,-2256,184,-481) -> Matrix(23,16,-36,-25) -2/3 Matrix(1871,-4896,715,-1871) -> Matrix(64,45,-91,-64) (34/13,144/55) -> (-5/7,-9/13) Matrix(6049,-15840,2310,-6049) -> Matrix(99,70,-140,-99) (144/55,55/21) -> (-5/7,-7/10) Matrix(623,-1632,92,-241) -> Matrix(3,2,4,3) Matrix(145,-384,54,-143) -> Matrix(23,16,-36,-25) -2/3 Matrix(817,-2208,195,-527) -> Matrix(0,-1,1,2) -1/1 Matrix(10367,-28032,3834,-10367) -> Matrix(5,6,-4,-5) (73/27,192/71) -> (-3/2,-1/1) Matrix(3265,-8832,1207,-3265) -> Matrix(8,7,-9,-8) (192/71,46/17) -> (-1/1,-7/9) Matrix(193,-528,53,-145) -> Matrix(10,7,-17,-12) Matrix(817,-2256,243,-671) -> Matrix(0,-1,1,2) -1/1 Matrix(1249,-3456,382,-1057) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(623,-1728,190,-527) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(241,-672,52,-145) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(239,-672,85,-239) -> Matrix(6,5,-7,-6) (14/5,48/17) -> (-1/1,-5/7) Matrix(577,-1632,204,-577) -> Matrix(17,12,-24,-17) (48/17,17/6) -> (-3/4,-2/3) Matrix(287,-816,51,-145) -> Matrix(4,3,-3,-2) -1/1 Matrix(241,-768,75,-239) -> Matrix(8,5,-13,-8) (-1/1,-3/5).(-2/3,-1/2) Matrix(193,-624,30,-97) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(335,-1104,44,-145) -> Matrix(3,2,-8,-5) -1/2 Matrix(2495,-8256,754,-2495) -> Matrix(5,6,-4,-5) (43/13,96/29) -> (-3/2,-1/1) Matrix(289,-960,87,-289) -> Matrix(6,5,-7,-6) (96/29,10/3) -> (-1/1,-5/7) Matrix(143,-480,14,-47) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(385,-1296,71,-239) -> Matrix(4,3,-11,-8) Matrix(241,-816,57,-193) -> Matrix(10,7,-17,-12) Matrix(239,-816,70,-239) -> Matrix(41,28,-60,-41) (17/5,24/7) -> (-7/10,-2/3) Matrix(97,-336,28,-97) -> Matrix(19,12,-30,-19) (24/7,7/2) -> (-2/3,-3/5) Matrix(1247,-4512,186,-673) -> Matrix(7,4,-2,-1) Matrix(287,-1056,78,-287) -> Matrix(7,4,-12,-7) (11/3,48/13) -> (-2/3,-1/2) Matrix(337,-1248,91,-337) -> Matrix(4,3,-5,-4) (48/13,26/7) -> (-1/1,-3/5) Matrix(193,-720,26,-97) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(241,-912,51,-193) -> Matrix(10,7,-17,-12) Matrix(239,-912,38,-145) -> Matrix(13,8,-18,-11) -2/3 Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) -1/2 Matrix(287,-1248,66,-287) -> Matrix(7,4,-12,-7) (13/3,48/11) -> (-2/3,-1/2) Matrix(241,-1056,55,-241) -> Matrix(4,3,-5,-4) (48/11,22/5) -> (-1/1,-3/5) Matrix(97,-432,11,-49) -> Matrix(2,1,-7,-4) Matrix(191,-912,40,-191) -> Matrix(23,12,-44,-23) (19/4,24/5) -> (-6/11,-1/2) Matrix(49,-240,10,-49) -> Matrix(5,2,-12,-5) (24/5,5/1) -> (-1/2,-1/3) Matrix(145,-768,27,-143) -> Matrix(2,1,-5,-2) (-1/1,-1/3).(-1/2,0/1) Matrix(143,-816,17,-97) -> Matrix(0,-1,1,2) -1/1 Matrix(193,-1104,25,-143) -> Matrix(0,-1,1,4) Matrix(49,-288,8,-47) -> Matrix(1,2,-2,-3) -1/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.