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 -1/2 0/1 -9/1 0/1 -8/1 -1/1 0/1 1/0 -15/2 -2/1 0/1 -7/1 -2/1 -20/3 0/1 -13/2 -2/1 1/0 -19/3 -2/1 -6/1 -1/1 -23/4 -1/2 0/1 -40/7 -1/1 -1/2 0/1 -17/3 -2/3 -11/2 0/1 1/1 -27/5 -2/1 -16/3 -2/1 0/1 -21/4 -2/1 0/1 -5/1 -2/1 -24/5 -1/1 -19/4 -1/1 -4/5 -14/3 -1/1 -2/3 -1/2 -23/5 -2/5 -9/2 -2/1 0/1 -22/5 -1/1 -1/2 0/1 -13/3 0/1 -17/4 2/1 1/0 -4/1 -2/1 0/1 -23/6 -4/1 1/0 -42/11 -3/1 -19/5 -2/1 -15/4 -2/1 -4/3 -26/7 -3/2 -4/3 -1/1 -11/3 0/1 -18/5 1/0 -25/7 -8/3 -7/2 -2/1 -1/1 -24/7 -1/1 -17/5 0/1 -27/8 -2/1 0/1 -37/11 -2/1 -47/14 -1/1 0/1 -10/3 -1/1 0/1 1/0 -43/13 -4/1 -33/10 -2/1 0/1 -56/17 -1/1 0/1 1/0 -23/7 -2/1 -36/11 1/0 -13/4 -2/1 1/0 -29/9 -2/1 -16/5 -2/1 -19/6 -2/1 -1/1 -3/1 -2/1 -20/7 -2/1 -8/5 -17/6 -8/5 -3/2 -14/5 -3/2 -4/3 -1/1 -25/9 -8/5 -36/13 -3/2 -47/17 -10/7 -11/4 -4/3 -1/1 -19/7 -2/1 -8/3 -2/1 -3/2 -1/1 -29/11 -2/1 -50/19 -2/1 -3/2 -1/1 -71/27 -10/7 -21/8 -2/1 -4/3 -76/29 -4/3 -55/21 -6/5 -34/13 -2/1 -3/2 -1/1 -47/18 -2/1 -1/1 -13/5 -2/1 -31/12 -3/2 -4/3 -80/31 -2/1 -4/3 -49/19 -2/1 -18/7 -3/2 -23/9 -6/5 -28/11 -2/1 -33/13 -2/1 -5/2 -3/2 -4/3 -27/11 -6/5 -49/20 -10/9 -1/1 -22/9 -3/2 -4/3 -1/1 -39/16 -4/3 -6/5 -17/7 -6/5 -12/5 -1/1 -31/13 -2/3 -50/21 -2/3 -3/5 -1/2 -19/8 -1/1 0/1 -45/19 0/1 -71/30 0/1 1/0 -26/11 -2/1 -1/1 1/0 -33/14 -2/1 0/1 -7/3 0/1 -23/10 -5/2 -2/1 -16/7 -2/1 -25/11 -16/9 -9/4 -2/1 -8/5 -38/17 -2/1 -3/2 -1/1 -29/13 -2/1 -20/9 -2/1 -8/5 -11/5 -8/5 -24/11 -3/2 -13/6 -3/2 -10/7 -28/13 -4/3 -15/7 -4/3 -2/1 -3/2 -4/3 -1/1 -17/9 -4/3 -15/8 -18/13 -4/3 -13/7 -4/3 -24/13 -4/3 -11/6 -4/3 -17/13 -31/17 -14/11 -20/11 -4/3 -29/16 -4/3 -1/1 -96/53 -4/3 -67/37 -4/3 -38/21 -4/3 -5/4 -1/1 -9/5 -4/3 -25/14 -3/2 -4/3 -16/9 -4/3 -23/13 -38/29 -7/4 -4/3 -9/7 -26/15 -4/3 -9/7 -5/4 -97/56 -58/45 -9/7 -168/97 -9/7 -71/41 -68/53 -45/26 -32/25 -14/11 -19/11 -14/11 -12/7 -5/4 -29/17 -6/5 -46/27 -5/4 -6/5 -1/1 -63/37 -6/5 -80/47 -4/3 -6/5 -17/10 -5/4 -6/5 -22/13 -5/4 -6/5 -1/1 -71/42 -4/3 -5/4 -120/71 -5/4 -49/29 -6/5 -27/16 -4/3 -6/5 -5/3 -4/3 -33/20 -16/13 -6/5 -28/17 -4/3 -6/5 -51/31 -6/5 -23/14 -5/4 -6/5 -18/11 -1/1 -49/30 -2/1 -1/1 -80/49 -2/1 -4/3 -111/68 -2/1 -4/3 -31/19 -4/3 -13/8 -4/3 -5/4 -60/37 -5/4 -47/29 -6/5 -34/21 -6/5 -7/6 -1/1 -89/55 -10/9 -144/89 -1/1 -55/34 -2/1 -1/1 -21/13 -4/3 -8/5 -4/3 -5/4 -1/1 -27/17 -4/3 -73/46 -14/11 -5/4 -192/121 -5/4 -119/75 -26/21 -46/29 -5/4 -11/9 -6/5 -19/12 -4/3 -1/1 -68/43 -4/3 -117/74 -4/3 -14/11 -49/31 -4/3 -30/19 -5/4 -11/7 -4/3 -47/30 -6/5 -1/1 -36/23 -1/1 -25/16 -3/2 -4/3 -14/9 -4/3 -9/7 -5/4 -31/20 -24/19 -5/4 -48/31 -5/4 -17/11 -16/13 -20/13 -6/5 -23/15 -10/9 -3/2 -4/3 -6/5 -19/13 -4/3 -16/11 -4/3 -29/20 -4/3 -9/7 -13/9 -4/3 -49/34 -4/3 -9/7 -36/25 -9/7 -23/16 -14/11 -5/4 -33/23 -14/11 -43/30 -24/19 -5/4 -96/67 -5/4 -53/37 -6/5 -10/7 -9/7 -14/11 -5/4 -47/33 -24/19 -37/26 -9/7 -14/11 -27/19 -24/19 -71/50 -14/11 -5/4 -44/31 -24/19 -34/27 -17/12 -44/35 -5/4 -24/17 -5/4 -7/5 -26/21 -25/18 -16/13 -27/22 -18/13 -11/9 -47/34 -16/13 -11/9 -76/55 -28/23 -6/5 -29/21 -6/5 -11/8 -16/13 -11/9 -48/35 -11/9 -37/27 -50/41 -26/19 -11/9 -17/14 -6/5 -41/30 -11/9 -6/5 -15/11 -6/5 -64/47 -16/13 -6/5 -49/36 -11/9 -6/5 -34/25 -5/4 -11/9 -6/5 -19/14 -11/9 -28/23 -23/17 -28/23 -4/3 -6/5 -25/19 -20/17 -21/16 -6/5 -8/7 -17/13 -6/5 -13/10 -5/4 -6/5 -48/37 -6/5 -35/27 -6/5 -22/17 -5/4 -6/5 -1/1 -31/24 -5/4 -6/5 -40/31 -5/4 -11/9 -6/5 -9/7 -6/5 -23/18 -6/5 -7/6 -14/11 -5/4 -11/9 -6/5 -47/37 -6/5 -80/63 -40/33 -6/5 -33/26 -40/33 -6/5 -19/15 -6/5 -24/19 -6/5 -5/4 -6/5 -19/16 -21/17 -20/17 -16/13 -6/5 -20/17 -27/22 -6/5 -20/17 -11/9 -20/17 -28/23 -6/5 -20/17 -17/14 -6/5 -7/6 -40/33 -6/5 -13/11 -7/6 -23/19 -20/17 -6/5 -7/6 -25/21 -8/7 -19/16 -15/13 -8/7 -13/11 -8/7 -33/28 -8/7 -26/23 -20/17 -8/7 -10/9 -47/40 -12/11 -1/1 -27/23 -8/7 -7/6 -6/5 -1/1 -15/13 -6/5 -23/20 -6/5 -7/6 -8/7 -6/5 -7/6 -1/1 -17/15 -8/7 -9/8 -6/5 -8/7 -10/9 -6/5 -13/11 -7/6 -1/1 -8/7 0/1 -1/1 1/1 -8/9 10/9 -7/8 -13/15 -6/7 9/8 -8/9 -6/7 8/7 -1/1 -7/8 -6/7 15/13 -6/7 7/6 -1/1 -6/7 20/17 -10/11 -8/9 13/11 -8/9 19/16 -8/9 -15/17 6/5 -7/8 23/19 -20/23 40/33 -7/8 -13/15 -6/7 17/14 -7/8 -6/7 11/9 -20/23 27/22 -20/23 -6/7 16/13 -20/23 -6/7 21/17 -20/23 5/4 -19/22 -6/7 24/19 -6/7 19/15 -6/7 14/11 -6/7 -11/13 -5/6 23/18 -7/8 -6/7 9/7 -6/7 22/17 -1/1 -6/7 -5/6 13/10 -6/7 -5/6 17/13 -6/7 4/3 -6/7 23/17 -28/33 42/31 -17/20 19/14 -28/33 -11/13 15/11 -6/7 26/19 -6/7 -17/20 -11/13 11/8 -11/13 -16/19 18/13 -11/13 25/18 -27/32 -16/19 7/5 -26/31 24/17 -5/6 17/12 -5/6 -44/53 27/19 -24/29 37/26 -14/17 -9/11 47/33 -24/29 10/7 -5/6 -14/17 -9/11 43/30 -5/6 -24/29 33/23 -14/17 56/39 -5/6 -14/17 -9/11 23/16 -5/6 -14/17 36/25 -9/11 13/9 -4/5 29/20 -9/11 -4/5 16/11 -4/5 19/13 -4/5 3/2 -6/7 -4/5 20/13 -6/7 17/11 -16/19 14/9 -5/6 -9/11 -4/5 25/16 -4/5 -3/4 36/23 -1/1 47/30 -1/1 -6/7 11/7 -4/5 19/12 -1/1 -4/5 8/5 -1/1 -5/6 -4/5 29/18 -1/1 -4/5 50/31 -6/7 -11/13 -5/6 71/44 -5/6 -14/17 21/13 -4/5 76/47 -6/7 -4/5 55/34 -1/1 -2/3 34/21 -1/1 -7/8 -6/7 47/29 -6/7 13/8 -5/6 -4/5 31/19 -4/5 80/49 -4/5 -2/3 49/30 -1/1 -2/3 18/11 -1/1 23/14 -6/7 -5/6 28/17 -6/7 -4/5 33/20 -6/7 -16/19 5/3 -4/5 27/16 -6/7 -4/5 49/29 -6/7 22/13 -1/1 -6/7 -5/6 39/23 -6/7 17/10 -6/7 -5/6 12/7 -5/6 31/18 -5/6 -14/17 50/29 -5/6 -19/23 -14/17 19/11 -14/17 45/26 -14/17 -32/39 71/41 -68/83 26/15 -5/6 -9/11 -4/5 33/19 -4/5 7/4 -9/11 -4/5 23/13 -38/47 16/9 -4/5 25/14 -4/5 -3/4 9/5 -4/5 38/21 -1/1 -5/6 -4/5 29/16 -1/1 -4/5 20/11 -4/5 11/6 -17/21 -4/5 24/13 -4/5 13/7 -4/5 28/15 -4/5 -26/33 15/8 -4/5 -18/23 2/1 -1/1 -4/5 -3/4 17/8 -4/5 -3/4 15/7 -4/5 13/6 -10/13 -3/4 24/11 -3/4 11/5 -8/11 31/14 -3/4 -2/3 20/9 -8/11 -2/3 29/13 -2/3 96/43 -2/3 67/30 -1/1 -2/3 38/17 -1/1 -3/4 -2/3 9/4 -8/11 -2/3 25/11 -16/23 16/7 -2/3 23/10 -2/3 -5/8 7/3 0/1 26/11 -1/1 -2/3 -1/2 97/41 -2/3 168/71 -1/2 71/30 -1/2 0/1 45/19 0/1 19/8 -1/1 0/1 12/5 -1/1 29/12 -1/1 -8/9 46/19 -7/8 -13/15 -6/7 63/26 -6/7 -4/5 80/33 -6/7 -4/5 17/7 -6/7 22/9 -1/1 -4/5 -3/4 71/29 -4/3 120/49 -1/1 49/20 -1/1 -10/11 27/11 -6/7 5/2 -4/5 -3/4 33/13 -2/3 28/11 -2/3 51/20 -2/3 0/1 23/9 -6/7 18/7 -3/4 49/19 -2/3 80/31 -4/5 -2/3 111/43 -4/5 31/12 -4/5 -3/4 13/5 -2/3 60/23 -1/1 47/18 -1/1 -2/3 34/13 -1/1 -3/4 -2/3 89/34 -2/1 -1/1 144/55 -1/1 55/21 -6/7 21/8 -4/5 -2/3 8/3 -1/1 -3/4 -2/3 27/10 -4/5 -2/3 73/27 -10/13 192/71 -3/4 119/44 -3/4 -14/19 46/17 -1/1 -3/4 -2/3 19/7 -2/3 68/25 -2/3 0/1 117/43 0/1 49/18 -1/1 -4/5 30/11 -1/1 11/4 -1/1 -4/5 47/17 -10/13 36/13 -3/4 25/9 -8/11 14/5 -1/1 -4/5 -3/4 31/11 -16/21 48/17 -3/4 17/6 -3/4 -8/11 20/7 -8/11 -2/3 23/8 -3/4 -2/3 3/1 -2/3 19/6 -1/1 -2/3 16/5 -2/3 29/9 -2/3 13/4 -2/3 -1/2 49/15 -4/7 36/11 -1/2 23/7 -2/3 33/10 -2/3 0/1 43/13 -4/7 96/29 -1/2 53/16 -1/2 -2/5 10/3 -1/1 -1/2 0/1 47/14 -1/1 0/1 37/11 -2/3 27/8 -2/3 0/1 71/21 -2/5 44/13 0/1 17/5 0/1 24/7 -1/1 7/2 -1/1 -2/3 25/7 -8/13 18/5 -1/2 47/13 0/1 76/21 0/1 29/8 -1/1 0/1 11/3 0/1 48/13 -1/1 37/10 -1/1 -6/7 26/7 -1/1 -4/5 -3/4 41/11 -2/3 15/4 -4/5 -2/3 64/17 -4/5 -2/3 49/13 -2/3 34/9 -5/7 -7/10 -2/3 19/5 -2/3 23/6 -4/7 -1/2 4/1 -2/3 0/1 25/6 -4/7 -1/2 21/5 -2/3 17/4 -1/2 -2/5 13/3 0/1 48/11 0/1 35/8 0/1 1/0 22/5 -1/1 0/1 1/0 31/7 -2/3 40/9 -1/1 -1/2 0/1 9/2 -2/3 0/1 23/5 2/1 14/3 -2/1 -1/1 1/0 47/10 -2/1 -1/1 80/17 -2/1 0/1 33/7 -2/1 19/4 -4/3 -1/1 24/5 -1/1 5/1 -2/3 21/4 -2/3 0/1 16/3 -2/3 0/1 27/5 -2/3 11/2 -1/3 0/1 28/5 0/1 17/3 -2/1 40/7 -1/1 0/1 1/0 23/4 0/1 1/0 6/1 -1/1 25/4 -4/5 -3/4 19/3 -2/3 13/2 -2/3 -1/2 33/5 0/1 20/3 0/1 47/7 0/1 27/4 -2/1 0/1 7/1 -2/3 15/2 -2/3 0/1 23/3 -2/3 8/1 -1/1 -1/2 0/1 17/2 -1/2 0/1 9/1 0/1 10/1 -1/1 0/1 1/0 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(1,0,0,1) 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(1,0,0,1) Matrix(97,720,26,193) -> Matrix(3,4,-4,-5) Matrix(241,1632,-92,-623) -> Matrix(5,4,-4,-3) Matrix(95,624,-44,-289) -> Matrix(3,-4,-2,3) 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(7,4,-2,-1) Matrix(385,2208,268,1537) -> Matrix(23,14,-28,-17) Matrix(337,1920,76,433) -> Matrix(1,0,0,1) Matrix(95,528,-52,-289) -> Matrix(13,4,-10,-3) Matrix(239,1296,168,911) -> Matrix(5,-14,-6,17) 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(5,6,-6,-7) Matrix(49,240,10,49) -> Matrix(3,4,-4,-5) Matrix(191,912,40,191) -> Matrix(9,8,-8,-7) Matrix(193,912,-142,-671) -> Matrix(27,16,-22,-13) Matrix(145,672,52,241) -> Matrix(1,2,-2,-3) Matrix(95,432,42,191) -> Matrix(3,-2,-4,3) Matrix(239,1056,-98,-433) -> Matrix(5,4,-4,-3) Matrix(241,1056,-186,-815) -> Matrix(7,6,-6,-5) Matrix(145,624,56,241) -> Matrix(3,-2,-4,3) Matrix(193,816,-136,-575) -> Matrix(5,34,-4,-27) Matrix(335,1296,-236,-913) -> Matrix(5,34,-4,-27) Matrix(241,912,-190,-719) -> Matrix(29,52,-24,-43) Matrix(335,1248,-142,-529) -> Matrix(1,2,-2,-3) Matrix(337,1248,-246,-911) -> Matrix(39,50,-32,-41) Matrix(145,528,-92,-335) -> Matrix(5,4,-4,-3) Matrix(241,864,94,337) -> Matrix(3,10,-4,-13) Matrix(95,336,54,191) -> Matrix(13,22,-16,-27) Matrix(97,336,28,97) -> Matrix(3,4,-4,-5) Matrix(239,816,70,239) -> Matrix(1,0,0,1) Matrix(241,816,-184,-623) -> Matrix(7,6,-6,-5) Matrix(385,1296,314,1057) -> Matrix(7,-6,-8,7) Matrix(671,2256,428,1439) -> Matrix(5,6,-6,-7) Matrix(143,480,14,47) -> Matrix(1,0,0,1) Matrix(289,960,-202,-671) -> Matrix(5,14,-4,-11) Matrix(479,1584,290,959) -> Matrix(5,16,-6,-19) Matrix(671,2208,554,1823) -> Matrix(7,-6,-8,7) Matrix(527,1728,190,623) -> Matrix(3,-2,-4,3) 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(3,10,-4,-13) Matrix(241,768,166,529) -> Matrix(13,22,-16,-27) Matrix(289,912,122,385) -> Matrix(1,2,-2,-3) Matrix(385,1104,-234,-671) -> Matrix(17,28,-14,-23) Matrix(337,960,152,433) -> Matrix(19,30,-26,-41) Matrix(239,672,-154,-433) -> Matrix(23,32,-18,-25) Matrix(241,672,52,145) -> Matrix(1,2,-2,-3) Matrix(623,1728,190,527) -> Matrix(1,2,-4,-7) Matrix(1249,3456,382,1057) -> Matrix(15,22,-28,-41) Matrix(817,2256,574,1585) -> Matrix(13,22,-16,-27) Matrix(193,528,-140,-383) -> Matrix(17,28,-14,-23) Matrix(143,384,-54,-145) -> Matrix(1,0,0,1) Matrix(911,2400,528,1391) -> Matrix(33,52,-40,-63) Matrix(3503,9216,-2208,-5809) -> Matrix(17,28,-14,-23) Matrix(1297,3408,384,1009) -> Matrix(3,4,-4,-5) Matrix(3937,10320,-2490,-6527) -> Matrix(23,32,-18,-25) Matrix(1871,4896,-1156,-3025) -> Matrix(5,4,-4,-3) Matrix(1249,3264,-918,-2399) -> Matrix(17,28,-14,-23) Matrix(479,1248,-332,-865) -> Matrix(5,14,-4,-11) Matrix(241,624,56,145) -> Matrix(1,2,-4,-7) Matrix(1487,3840,-874,-2257) -> Matrix(3,2,-2,-1) Matrix(2977,7680,-2344,-6047) -> Matrix(29,52,-24,-43) Matrix(671,1728,186,479) -> Matrix(1,2,-4,-7) Matrix(337,864,94,241) -> Matrix(7,10,-12,-17) Matrix(433,1104,-282,-719) -> Matrix(5,4,-4,-3) Matrix(623,1584,94,239) -> Matrix(1,2,-4,-7) Matrix(625,1584,436,1105) -> Matrix(33,52,-40,-63) Matrix(97,240,78,193) -> Matrix(45,58,-52,-67) Matrix(1057,2592,-900,-2207) -> Matrix(3,2,-2,-1) Matrix(1393,3408,-804,-1967) -> Matrix(23,32,-18,-25) Matrix(335,816,-296,-721) -> Matrix(3,2,-2,-1) Matrix(239,576,-100,-241) -> Matrix(7,8,-8,-9) Matrix(383,912,-202,-481) -> Matrix(17,10,-12,-7) Matrix(1009,2400,626,1489) -> Matrix(3,4,-4,-5) Matrix(385,912,122,289) -> Matrix(1,2,-2,-3) Matrix(527,1248,182,431) -> Matrix(3,-2,-4,3) Matrix(1441,3408,-852,-2015) -> Matrix(5,4,-4,-3) Matrix(143,336,20,47) -> Matrix(1,2,-2,-3) Matrix(145,336,104,241) -> Matrix(5,26,-6,-31) Matrix(335,768,188,431) -> Matrix(11,26,-14,-33) Matrix(337,768,190,433) -> Matrix(37,70,-46,-87) Matrix(191,432,42,95) -> Matrix(1,2,-4,-7) Matrix(193,432,172,385) -> Matrix(19,32,-22,-37) 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(5,4,-4,-3) Matrix(241,528,110,241) -> Matrix(31,48,-42,-65) Matrix(287,624,132,287) -> Matrix(41,60,-54,-79) Matrix(625,1344,246,529) -> Matrix(5,6,-6,-7) Matrix(385,816,-226,-479) -> Matrix(3,2,-2,-1) Matrix(1247,2352,-764,-1441) -> Matrix(23,32,-18,-25) Matrix(335,624,-284,-529) -> Matrix(91,124,-80,-109) Matrix(337,624,182,337) -> Matrix(137,184,-172,-231) Matrix(287,528,156,287) -> Matrix(103,136,-128,-169) Matrix(527,960,342,623) -> Matrix(9,10,-10,-11) Matrix(1297,2352,-820,-1487) -> Matrix(1,0,0,1) Matrix(5087,9216,2278,4127) -> Matrix(5,6,-6,-7) Matrix(5089,9216,2280,4129) -> Matrix(29,38,-42,-55) Matrix(239,432,26,47) -> Matrix(3,4,-4,-5) Matrix(241,432,188,337) -> Matrix(9,10,-10,-11) Matrix(431,768,188,335) -> Matrix(19,26,-30,-41) Matrix(433,768,190,337) -> Matrix(53,70,-78,-103) Matrix(191,336,54,95) -> Matrix(17,22,-24,-31) Matrix(719,1248,-526,-913) -> Matrix(75,98,-62,-81) Matrix(11473,19872,4684,8113) -> Matrix(115,148,-122,-157) Matrix(11807,20448,4822,8351) -> Matrix(81,104,-74,-95) Matrix(2689,4656,1054,1825) -> Matrix(11,14,-4,-5) Matrix(527,912,360,623) -> Matrix(17,22,-24,-31) Matrix(335,576,-196,-337) -> Matrix(79,100,-64,-81) Matrix(1295,2208,478,815) -> Matrix(7,8,-8,-9) Matrix(4511,7680,958,1631) -> Matrix(3,4,-4,-5) Matrix(623,1056,-482,-817) -> Matrix(1,0,0,1) Matrix(12097,20448,5112,8641) -> Matrix(3,4,-10,-13) Matrix(11759,19872,4970,8399) -> Matrix(13,16,-22,-27) Matrix(4177,7056,-2642,-4463) -> Matrix(41,50,-32,-39) Matrix(143,240,28,47) -> Matrix(5,6,-6,-7) Matrix(959,1584,290,479) -> Matrix(13,16,-22,-27) Matrix(815,1344,436,719) -> Matrix(71,86,-90,-109) Matrix(2831,4656,1196,1967) -> Matrix(5,6,-6,-7) Matrix(527,864,380,623) -> Matrix(71,82,-84,-97) Matrix(1439,2352,528,863) -> Matrix(5,6,-6,-7) Matrix(4321,7056,-3174,-5183) -> Matrix(17,28,-14,-23) Matrix(5087,8304,1352,2207) -> Matrix(5,6,-6,-7) Matrix(383,624,294,479) -> Matrix(9,10,-10,-11) Matrix(2783,4512,1006,1631) -> Matrix(55,68,-72,-89) Matrix(1393,2256,-1096,-1775) -> Matrix(61,72,-50,-59) Matrix(12815,20736,4894,7919) -> Matrix(15,16,-16,-17) Matrix(12817,20736,4896,7921) -> Matrix(1,0,0,1) Matrix(1009,1632,-860,-1391) -> Matrix(5,4,-4,-3) Matrix(239,384,-150,-241) -> Matrix(1,0,0,1) Matrix(1391,2208,332,527) -> Matrix(5,6,-6,-7) Matrix(23231,36864,8590,13631) -> Matrix(89,112,-120,-151) Matrix(23233,36864,8592,13633) -> Matrix(103,128,-136,-169) Matrix(1393,2208,576,913) -> Matrix(11,12,-12,-13) Matrix(1489,2352,578,913) -> Matrix(17,22,-24,-31) Matrix(1439,2256,428,671) -> Matrix(5,6,-6,-7) Matrix(2881,4512,1104,1729) -> Matrix(7,8,-8,-9) Matrix(1105,1728,768,1201) -> Matrix(13,22,-16,-27) Matrix(431,672,338,527) -> Matrix(9,10,-10,-11) Matrix(1487,2304,526,815) -> Matrix(89,112,-120,-151) Matrix(1489,2304,528,817) -> Matrix(103,128,-136,-169) Matrix(529,816,94,145) -> Matrix(5,6,4,5) Matrix(817,1248,472,721) -> Matrix(13,22,-16,-27) Matrix(623,912,360,527) -> Matrix(13,22,-16,-27) Matrix(527,768,164,239) -> Matrix(7,10,-12,-17) Matrix(529,768,166,241) -> Matrix(17,22,-24,-31) Matrix(431,624,364,527) -> Matrix(11,12,-12,-13) Matrix(2399,3456,1532,2207) -> Matrix(45,58,-52,-67) Matrix(1201,1728,768,1105) -> Matrix(17,22,-24,-31) Matrix(769,1104,-668,-959) -> Matrix(53,68,-46,-59) Matrix(1105,1584,436,625) -> Matrix(41,52,-56,-71) Matrix(6431,9216,1942,2783) -> Matrix(27,34,-58,-73) Matrix(6433,9216,1944,2785) -> Matrix(21,26,-38,-47) Matrix(337,480,304,433) -> Matrix(101,128,-116,-147) Matrix(1585,2256,574,817) -> Matrix(17,22,-24,-31) Matrix(911,1296,168,239) -> Matrix(11,14,-26,-33) Matrix(2399,3408,1486,2111) -> Matrix(111,140,-134,-169) Matrix(577,816,408,577) -> Matrix(351,440,-422,-529) Matrix(239,336,170,239) -> Matrix(209,260,-250,-311) Matrix(241,336,104,145) -> Matrix(21,26,-38,-47) Matrix(623,864,380,527) -> Matrix(67,82,-76,-93) Matrix(1249,1728,764,1057) -> Matrix(31,38,-40,-49) Matrix(3265,4512,-2778,-3839) -> Matrix(95,116,-86,-105) Matrix(1679,2304,454,623) -> Matrix(67,82,-76,-93) Matrix(1681,2304,456,625) -> Matrix(41,50,-32,-39) Matrix(527,720,456,623) -> Matrix(49,60,-58,-71) Matrix(6097,8304,2362,3217) -> Matrix(31,38,-40,-49) Matrix(673,912,-566,-767) -> Matrix(273,332,-236,-287) Matrix(143,192,-108,-145) -> Matrix(119,144,-100,-121) Matrix(1681,2208,622,817) -> Matrix(9,10,-10,-11) Matrix(479,624,294,383) -> Matrix(9,10,-10,-11) Matrix(1775,2304,406,527) -> Matrix(5,6,4,5) Matrix(1777,2304,408,529) -> Matrix(5,6,-16,-19) Matrix(1487,1920,1226,1583) -> Matrix(11,12,-12,-13) Matrix(337,432,188,241) -> Matrix(9,10,-10,-11) Matrix(527,672,338,431) -> Matrix(9,10,-10,-11) Matrix(6049,7680,2496,3169) -> Matrix(109,132,-128,-155) Matrix(721,912,570,721) -> Matrix(409,492,-478,-575) Matrix(191,240,152,191) -> Matrix(191,228,-222,-265) Matrix(193,240,78,97) -> Matrix(49,58,-60,-71) 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(5,6,-16,-19) Matrix(671,816,236,287) -> Matrix(63,74,-86,-101) Matrix(673,816,80,97) -> Matrix(5,6,-16,-19) Matrix(911,1104,118,143) -> Matrix(5,6,-16,-19) Matrix(239,288,-200,-241) -> Matrix(167,196,-144,-169) Matrix(527,624,364,431) -> Matrix(11,12,-12,-13) Matrix(1345,1584,816,961) -> Matrix(13,14,-14,-15) Matrix(289,336,166,193) -> Matrix(49,58,-60,-71) Matrix(961,1104,168,193) -> Matrix(5,6,-6,-7) Matrix(719,816,126,143) -> Matrix(5,6,-6,-7) Matrix(385,432,172,193) -> Matrix(27,32,-38,-45) Matrix(433,480,304,337) -> Matrix(109,128,-132,-155) Matrix(1,0,2,1) -> Matrix(15,16,-16,-17) Matrix(383,-432,86,-97) -> Matrix(7,6,-6,-5) Matrix(959,-1104,668,-769) -> Matrix(77,68,-94,-83) Matrix(1391,-1632,860,-1009) -> Matrix(5,4,-4,-3) Matrix(529,-624,284,-335) -> Matrix(139,124,-176,-157) Matrix(767,-912,566,-673) -> Matrix(377,332,-444,-391) Matrix(913,-1104,674,-815) -> Matrix(167,144,-196,-169) Matrix(433,-528,196,-239) -> Matrix(5,4,-4,-3) Matrix(719,-912,190,-241) -> Matrix(61,52,-88,-75) Matrix(817,-1056,482,-623) -> Matrix(1,0,0,1) Matrix(815,-1056,186,-241) -> Matrix(7,6,-6,-5) Matrix(623,-816,184,-241) -> Matrix(7,6,-6,-5) Matrix(961,-1296,284,-383) -> Matrix(7,6,-34,-29) Matrix(671,-912,142,-193) -> Matrix(19,16,-6,-5) Matrix(913,-1248,526,-719) -> Matrix(115,98,-142,-121) Matrix(911,-1248,246,-337) -> Matrix(59,50,-72,-61) Matrix(383,-528,140,-193) -> Matrix(33,28,-46,-39) Matrix(575,-816,136,-193) -> Matrix(41,34,-76,-63) Matrix(671,-960,202,-289) -> Matrix(17,14,-28,-23) Matrix(865,-1248,332,-479) -> Matrix(17,14,-28,-23) Matrix(719,-1104,282,-433) -> Matrix(5,4,-4,-3) Matrix(433,-672,154,-239) -> Matrix(39,32,-50,-41) Matrix(335,-528,92,-145) -> Matrix(5,4,-4,-3) Matrix(241,-384,150,-239) -> Matrix(1,0,0,1) Matrix(5713,-9216,2112,-3407) -> Matrix(33,28,-46,-39) Matrix(6383,-10320,2346,-3793) -> Matrix(5,4,-4,-3) Matrix(3025,-4896,1156,-1871) -> Matrix(5,4,-4,-3) Matrix(2015,-3264,534,-865) -> Matrix(33,28,-46,-39) Matrix(769,-1248,236,-383) -> Matrix(17,14,-28,-23) Matrix(2353,-3840,970,-1583) -> Matrix(1,2,-2,-3) Matrix(4703,-7680,1000,-1633) -> Matrix(5,4,-4,-3) Matrix(671,-1104,234,-385) -> Matrix(33,28,-46,-39) Matrix(1535,-2592,228,-385) -> Matrix(7,6,-6,-5) Matrix(2015,-3408,852,-1441) -> Matrix(5,4,-4,-3) Matrix(481,-816,56,-95) -> Matrix(7,6,-20,-17) Matrix(337,-576,196,-335) -> Matrix(119,100,-144,-121) Matrix(529,-912,250,-431) -> Matrix(75,62,-98,-81) Matrix(1967,-3408,804,-1393) -> Matrix(39,32,-50,-41) Matrix(2015,-3648,902,-1633) -> Matrix(3,2,-2,-1) Matrix(1535,-2784,424,-769) -> Matrix(5,4,-4,-3) Matrix(289,-528,52,-95) -> Matrix(5,4,6,5) Matrix(431,-816,178,-337) -> Matrix(59,46,-68,-53) Matrix(1105,-2352,428,-911) -> Matrix(1,0,0,1) Matrix(289,-624,44,-95) -> Matrix(5,4,-14,-11) Matrix(1055,-2352,388,-865) -> Matrix(11,8,-18,-13) Matrix(529,-1248,142,-335) -> Matrix(1,2,-2,-3) Matrix(241,-576,100,-239) -> Matrix(7,8,-8,-9) Matrix(433,-1056,98,-239) -> Matrix(5,4,-4,-3) Matrix(2879,-7056,1058,-2593) -> Matrix(7,6,-6,-5) Matrix(2735,-7056,726,-1873) -> Matrix(1,0,0,1) Matrix(863,-2256,184,-481) -> Matrix(5,4,-4,-3) Matrix(623,-1632,92,-241) -> Matrix(5,4,-4,-3) Matrix(145,-384,54,-143) -> Matrix(1,0,0,1) Matrix(335,-1104,44,-145) -> Matrix(1,0,0,1) Matrix(1247,-4512,186,-673) -> Matrix(1,0,2,1) Matrix(239,-912,38,-145) -> Matrix(13,8,-18,-11) Matrix(49,-192,12,-47) -> Matrix(1,0,0,1) Matrix(49,-288,8,-47) -> Matrix(3,4,-4,-5) 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): 64 Degree of the the map X: 64 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: 48 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -4/1 -18/5 -10/3 -12/5 -2/1 -12/7 -4/3 0/1 1/1 8/7 4/3 24/17 3/2 8/5 12/7 24/13 2/1 16/7 12/5 5/2 144/55 8/3 3/1 16/5 10/3 24/7 7/2 18/5 48/13 64/17 4/1 21/5 13/3 48/11 9/2 33/7 24/5 5/1 21/4 16/3 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 -9/1 0/1 -8/1 -1/1 0/1 1/0 -15/2 -2/1 0/1 -7/1 -2/1 -13/2 -2/1 1/0 -6/1 -1/1 -5/1 -2/1 -9/2 -2/1 0/1 -22/5 -1/1 -1/2 0/1 -13/3 0/1 -17/4 2/1 1/0 -4/1 -2/1 0/1 -19/5 -2/1 -15/4 -2/1 -4/3 -26/7 -3/2 -4/3 -1/1 -11/3 0/1 -18/5 1/0 -7/2 -2/1 -1/1 -24/7 -1/1 -17/5 0/1 -27/8 -2/1 0/1 -10/3 -1/1 0/1 1/0 -13/4 -2/1 1/0 -16/5 -2/1 -3/1 -2/1 -8/3 -2/1 -3/2 -1/1 -21/8 -2/1 -4/3 -55/21 -6/5 -34/13 -2/1 -3/2 -1/1 -13/5 -2/1 -31/12 -3/2 -4/3 -18/7 -3/2 -5/2 -3/2 -4/3 -22/9 -3/2 -4/3 -1/1 -39/16 -4/3 -6/5 -17/7 -6/5 -12/5 -1/1 -31/13 -2/3 -19/8 -1/1 0/1 -26/11 -2/1 -1/1 1/0 -33/14 -2/1 0/1 -7/3 0/1 -16/7 -2/1 -9/4 -2/1 -8/5 -11/5 -8/5 -24/11 -3/2 -13/6 -3/2 -10/7 -2/1 -3/2 -4/3 -1/1 -9/5 -4/3 -16/9 -4/3 -23/13 -38/29 -7/4 -4/3 -9/7 -19/11 -14/11 -12/7 -5/4 -29/17 -6/5 -46/27 -5/4 -6/5 -1/1 -17/10 -5/4 -6/5 -22/13 -5/4 -6/5 -1/1 -27/16 -4/3 -6/5 -5/3 -4/3 -18/11 -1/1 -49/30 -2/1 -1/1 -80/49 -2/1 -4/3 -31/19 -4/3 -13/8 -4/3 -5/4 -47/29 -6/5 -34/21 -6/5 -7/6 -1/1 -89/55 -10/9 -144/89 -1/1 -55/34 -2/1 -1/1 -21/13 -4/3 -8/5 -4/3 -5/4 -1/1 -3/2 -4/3 -6/5 -16/11 -4/3 -29/20 -4/3 -9/7 -13/9 -4/3 -23/16 -14/11 -5/4 -10/7 -9/7 -14/11 -5/4 -37/26 -9/7 -14/11 -27/19 -24/19 -44/31 -24/19 -34/27 -17/12 -44/35 -5/4 -24/17 -5/4 -7/5 -26/21 -25/18 -16/13 -27/22 -18/13 -11/9 -11/8 -16/13 -11/9 -48/35 -11/9 -37/27 -50/41 -26/19 -11/9 -17/14 -6/5 -41/30 -11/9 -6/5 -15/11 -6/5 -64/47 -16/13 -6/5 -49/36 -11/9 -6/5 -34/25 -5/4 -11/9 -6/5 -19/14 -11/9 -28/23 -23/17 -28/23 -4/3 -6/5 -25/19 -20/17 -21/16 -6/5 -8/7 -17/13 -6/5 -13/10 -5/4 -6/5 -48/37 -6/5 -35/27 -6/5 -22/17 -5/4 -6/5 -1/1 -31/24 -5/4 -6/5 -9/7 -6/5 -14/11 -5/4 -11/9 -6/5 -47/37 -6/5 -80/63 -40/33 -6/5 -33/26 -40/33 -6/5 -19/15 -6/5 -24/19 -6/5 -5/4 -6/5 -19/16 -21/17 -20/17 -16/13 -6/5 -20/17 -27/22 -6/5 -20/17 -11/9 -20/17 -6/5 -7/6 -19/16 -15/13 -8/7 -13/11 -8/7 -20/17 -8/7 -10/9 -27/23 -8/7 -7/6 -6/5 -1/1 -15/13 -6/5 -8/7 -6/5 -7/6 -1/1 -9/8 -6/5 -8/7 -1/1 -8/7 0/1 -1/1 1/1 -8/9 9/8 -8/9 -6/7 8/7 -1/1 -7/8 -6/7 15/13 -6/7 7/6 -1/1 -6/7 13/11 -8/9 6/5 -7/8 5/4 -19/22 -6/7 9/7 -6/7 22/17 -1/1 -6/7 -5/6 13/10 -6/7 -5/6 17/13 -6/7 4/3 -6/7 19/14 -28/33 -11/13 15/11 -6/7 26/19 -6/7 -17/20 -11/13 11/8 -11/13 -16/19 18/13 -11/13 7/5 -26/31 24/17 -5/6 17/12 -5/6 -44/53 27/19 -24/29 10/7 -5/6 -14/17 -9/11 13/9 -4/5 16/11 -4/5 3/2 -6/7 -4/5 8/5 -1/1 -5/6 -4/5 21/13 -4/5 55/34 -1/1 -2/3 34/21 -1/1 -7/8 -6/7 13/8 -5/6 -4/5 31/19 -4/5 18/11 -1/1 5/3 -4/5 22/13 -1/1 -6/7 -5/6 39/23 -6/7 17/10 -6/7 -5/6 12/7 -5/6 31/18 -5/6 -14/17 19/11 -14/17 26/15 -5/6 -9/11 -4/5 33/19 -4/5 7/4 -9/11 -4/5 16/9 -4/5 9/5 -4/5 11/6 -17/21 -4/5 24/13 -4/5 13/7 -4/5 2/1 -1/1 -4/5 -3/4 9/4 -8/11 -2/3 16/7 -2/3 23/10 -2/3 -5/8 7/3 0/1 19/8 -1/1 0/1 12/5 -1/1 29/12 -1/1 -8/9 46/19 -7/8 -13/15 -6/7 17/7 -6/7 22/9 -1/1 -4/5 -3/4 27/11 -6/7 5/2 -4/5 -3/4 18/7 -3/4 49/19 -2/3 80/31 -4/5 -2/3 31/12 -4/5 -3/4 13/5 -2/3 47/18 -1/1 -2/3 34/13 -1/1 -3/4 -2/3 89/34 -2/1 -1/1 144/55 -1/1 55/21 -6/7 21/8 -4/5 -2/3 8/3 -1/1 -3/4 -2/3 3/1 -2/3 16/5 -2/3 29/9 -2/3 13/4 -2/3 -1/2 23/7 -2/3 10/3 -1/1 -1/2 0/1 37/11 -2/3 27/8 -2/3 0/1 44/13 0/1 17/5 0/1 24/7 -1/1 7/2 -1/1 -2/3 25/7 -8/13 18/5 -1/2 11/3 0/1 48/13 -1/1 37/10 -1/1 -6/7 26/7 -1/1 -4/5 -3/4 41/11 -2/3 15/4 -4/5 -2/3 64/17 -4/5 -2/3 49/13 -2/3 34/9 -5/7 -7/10 -2/3 19/5 -2/3 23/6 -4/7 -1/2 4/1 -2/3 0/1 25/6 -4/7 -1/2 21/5 -2/3 17/4 -1/2 -2/5 13/3 0/1 48/11 0/1 35/8 0/1 1/0 22/5 -1/1 0/1 1/0 31/7 -2/3 9/2 -2/3 0/1 14/3 -2/1 -1/1 1/0 47/10 -2/1 -1/1 80/17 -2/1 0/1 33/7 -2/1 19/4 -4/3 -1/1 24/5 -1/1 5/1 -2/3 21/4 -2/3 0/1 16/3 -2/3 0/1 27/5 -2/3 11/2 -1/3 0/1 6/1 -1/1 19/3 -2/3 13/2 -2/3 -1/2 20/3 0/1 27/4 -2/1 0/1 7/1 -2/3 15/2 -2/3 0/1 8/1 -1/1 -1/2 0/1 9/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(17,192,10,113) (-9/1,1/0) -> (39/23,17/10) Hyperbolic Matrix(17,144,2,17) (-9/1,-8/1) -> (8/1,9/1) Hyperbolic Matrix(31,240,4,31) (-8/1,-15/2) -> (15/2,8/1) Hyperbolic Matrix(97,720,26,193) (-15/2,-7/1) -> (41/11,15/4) Hyperbolic Matrix(65,432,-48,-319) (-7/1,-13/2) -> (-19/14,-23/17) Hyperbolic Matrix(31,192,-26,-161) (-13/2,-6/1) -> (-6/5,-19/16) Hyperbolic Matrix(17,96,-14,-79) (-6/1,-5/1) -> (-11/9,-6/5) Hyperbolic Matrix(31,144,-14,-65) (-5/1,-9/2) -> (-9/4,-11/5) 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(113,432,-96,-367) (-4/1,-19/5) -> (-13/11,-20/17) 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(79,288,48,175) (-11/3,-18/5) -> (18/11,5/3) Hyperbolic Matrix(161,576,-116,-415) (-18/5,-7/2) -> (-25/18,-18/13) 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(257,864,-152,-511) (-27/8,-10/3) -> (-22/13,-27/16) Hyperbolic Matrix(161,528,-68,-223) (-10/3,-13/4) -> (-19/8,-26/11) Hyperbolic Matrix(209,672,-144,-463) (-13/4,-16/5) -> (-16/11,-29/20) Hyperbolic Matrix(31,96,10,31) (-16/5,-3/1) -> (3/1,16/5) Hyperbolic Matrix(17,48,6,17) (-3/1,-8/3) -> (8/3,3/1) Hyperbolic Matrix(127,336,48,127) (-8/3,-21/8) -> (21/8,8/3) Hyperbolic Matrix(641,1680,-488,-1279) (-21/8,-55/21) -> (-25/19,-21/16) Hyperbolic Matrix(1871,4896,-1156,-3025) (-55/21,-34/13) -> (-34/21,-89/55) Hyperbolic Matrix(607,1584,-356,-929) (-34/13,-13/5) -> (-29/17,-46/27) Hyperbolic Matrix(241,624,56,145) (-13/5,-31/12) -> (17/4,13/3) Hyperbolic Matrix(559,1440,-342,-881) (-31/12,-18/7) -> (-18/11,-49/30) Hyperbolic Matrix(113,288,82,209) (-18/7,-5/2) -> (11/8,18/13) Hyperbolic Matrix(353,864,-248,-607) (-5/2,-22/9) -> (-10/7,-37/26) Hyperbolic Matrix(79,192,72,175) (-39/16,-17/7) -> (1/1,9/8) Hyperbolic Matrix(239,576,-100,-241) (-17/7,-12/5) -> (-12/5,-31/13) Parabolic Matrix(545,1296,-336,-799) (-31/13,-19/8) -> (-13/8,-47/29) Hyperbolic Matrix(143,336,20,47) (-33/14,-7/3) -> (7/1,15/2) Hyperbolic Matrix(209,480,-118,-271) (-7/3,-16/7) -> (-16/9,-23/13) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(175,384,36,79) (-11/5,-24/11) -> (24/5,5/1) Hyperbolic Matrix(353,768,74,161) (-24/11,-13/6) -> (19/4,24/5) Hyperbolic Matrix(223,480,-164,-353) (-13/6,-2/1) -> (-34/25,-19/14) Hyperbolic Matrix(79,144,-62,-113) (-2/1,-9/5) -> (-9/7,-14/11) Hyperbolic Matrix(161,288,90,161) (-9/5,-16/9) -> (16/9,9/5) Hyperbolic Matrix(191,336,54,95) (-23/13,-7/4) -> (7/2,25/7) Hyperbolic Matrix(305,528,-212,-367) (-7/4,-19/11) -> (-13/9,-23/16) Hyperbolic Matrix(335,576,-196,-337) (-19/11,-12/7) -> (-12/7,-29/17) Parabolic Matrix(1663,2832,-1222,-2081) (-46/27,-17/10) -> (-49/36,-34/25) Hyperbolic Matrix(623,1056,-482,-817) (-17/10,-22/13) -> (-22/17,-31/24) Hyperbolic Matrix(143,240,28,47) (-27/16,-5/3) -> (5/1,21/4) Hyperbolic Matrix(175,288,48,79) (-5/3,-18/11) -> (18/5,11/3) Hyperbolic Matrix(4321,7056,-3174,-5183) (-49/30,-80/49) -> (-64/47,-49/36) Hyperbolic Matrix(3823,6240,-3010,-4913) (-80/49,-31/19) -> (-47/37,-80/63) Hyperbolic Matrix(383,624,294,479) (-31/19,-13/8) -> (13/10,17/13) 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(209,336,130,209) (-21/13,-8/5) -> (8/5,21/13) Hyperbolic Matrix(31,48,20,31) (-8/5,-3/2) -> (3/2,8/5) Hyperbolic Matrix(65,96,44,65) (-3/2,-16/11) -> (16/11,3/2) Hyperbolic Matrix(497,720,78,113) (-29/20,-13/9) -> (19/3,13/2) Hyperbolic Matrix(703,1008,-514,-737) (-23/16,-10/7) -> (-26/19,-41/30) Hyperbolic Matrix(911,1296,168,239) (-37/26,-27/19) -> (27/5,11/2) Hyperbolic Matrix(1217,1728,-1036,-1471) (-27/19,-44/31) -> (-20/17,-27/23) 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(209,288,82,113) (-18/13,-11/8) -> (5/2,18/7) 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(2431,3312,516,703) (-15/11,-64/47) -> (80/17,33/7) Hyperbolic Matrix(143,192,-108,-145) (-23/17,-4/3) -> (-4/3,-25/19) Parabolic 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(223,288,24,31) (-31/24,-9/7) -> (9/1,1/0) Hyperbolic Matrix(2609,3312,694,881) (-80/63,-33/26) -> (15/4,64/17) Hyperbolic Matrix(607,768,328,415) (-19/15,-24/19) -> (24/13,13/7) Hyperbolic Matrix(305,384,166,209) (-24/19,-5/4) -> (11/6,24/13) 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(607,720,188,223) (-19/16,-13/11) -> (29/9,13/4) Hyperbolic Matrix(289,336,166,193) (-7/6,-15/13) -> (33/19,7/4) Hyperbolic Matrix(209,240,182,209) (-15/13,-8/7) -> (8/7,15/13) Hyperbolic Matrix(127,144,112,127) (-8/7,-9/8) -> (9/8,8/7) Hyperbolic Matrix(257,288,58,65) (-9/8,-1/1) -> (31/7,9/2) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(367,-432,96,-113) (7/6,13/11) -> (19/5,23/6) Hyperbolic Matrix(161,-192,26,-31) (13/11,6/5) -> (6/1,19/3) Hyperbolic Matrix(79,-96,14,-17) (6/5,5/4) -> (11/2,6/1) Hyperbolic Matrix(113,-144,62,-79) (5/4,9/7) -> (9/5,11/6) 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(319,-432,48,-65) (4/3,19/14) -> (13/2,20/3) 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(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(607,-864,248,-353) (27/19,10/7) -> (22/9,27/11) Hyperbolic Matrix(367,-528,212,-305) (10/7,13/9) -> (19/11,26/15) Hyperbolic Matrix(463,-672,144,-209) (13/9,16/11) -> (16/5,29/9) Hyperbolic Matrix(1039,-1680,248,-401) (21/13,55/34) -> (25/6,21/5) Hyperbolic Matrix(3025,-4896,1156,-1871) (55/34,34/21) -> (34/13,89/34) Hyperbolic Matrix(977,-1584,404,-655) (34/21,13/8) -> (29/12,46/19) Hyperbolic Matrix(881,-1440,342,-559) (31/19,18/11) -> (18/7,49/19) Hyperbolic Matrix(511,-864,152,-257) (5/3,22/13) -> (10/3,37/11) Hyperbolic Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(751,-1296,288,-497) (31/18,19/11) -> (13/5,47/18) Hyperbolic Matrix(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(257,-480,68,-127) (13/7,2/1) -> (34/9,19/5) Hyperbolic Matrix(65,-144,14,-31) (2/1,9/4) -> (9/2,14/3) Hyperbolic Matrix(223,-528,68,-161) (7/3,19/8) -> (13/4,23/7) Hyperbolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(1169,-2832,310,-751) (46/19,17/7) -> (49/13,34/9) Hyperbolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(2735,-7056,726,-1873) (49/19,80/31) -> (64/17,49/13) Hyperbolic Matrix(2417,-6240,514,-1327) (80/31,31/12) -> (47/10,80/17) 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(305,-1008,82,-271) (23/7,10/3) -> (26/7,41/11) Hyperbolic Matrix(511,-1728,76,-257) (27/8,44/13) -> (20/3,27/4) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(17,192,10,113) -> Matrix(11,6,-13,-7) Matrix(17,144,2,17) -> Matrix(1,0,-1,1) Matrix(31,240,4,31) -> Matrix(1,0,-1,1) Matrix(97,720,26,193) -> Matrix(3,4,-4,-5) Matrix(65,432,-48,-319) -> Matrix(11,-6,-9,5) Matrix(31,192,-26,-161) -> Matrix(15,22,-13,-19) Matrix(17,96,-14,-79) -> Matrix(13,6,-11,-5) Matrix(31,144,-14,-65) -> Matrix(5,2,-3,-1) Matrix(239,1056,-98,-433) -> Matrix(5,4,-4,-3) Matrix(241,1056,-186,-815) -> Matrix(7,6,-6,-5) Matrix(145,624,56,241) -> Matrix(3,-2,-4,3) Matrix(193,816,-136,-575) -> Matrix(5,34,-4,-27) Matrix(113,432,-96,-367) -> Matrix(1,10,-1,-9) Matrix(241,912,-190,-719) -> Matrix(29,52,-24,-43) Matrix(335,1248,-142,-529) -> Matrix(1,2,-2,-3) Matrix(337,1248,-246,-911) -> Matrix(39,50,-32,-41) Matrix(79,288,48,175) -> Matrix(1,-4,-1,5) Matrix(161,576,-116,-415) -> Matrix(11,38,-9,-31) Matrix(97,336,28,97) -> Matrix(3,4,-4,-5) Matrix(239,816,70,239) -> Matrix(1,0,0,1) Matrix(241,816,-184,-623) -> Matrix(7,6,-6,-5) Matrix(257,864,-152,-511) -> Matrix(1,6,-1,-5) Matrix(161,528,-68,-223) -> Matrix(1,2,-1,-1) Matrix(209,672,-144,-463) -> Matrix(9,22,-7,-17) Matrix(31,96,10,31) -> Matrix(1,0,-1,1) Matrix(17,48,6,17) -> Matrix(5,8,-7,-11) Matrix(127,336,48,127) -> Matrix(5,8,-7,-11) Matrix(641,1680,-488,-1279) -> Matrix(15,22,-13,-19) Matrix(1871,4896,-1156,-3025) -> Matrix(5,4,-4,-3) Matrix(607,1584,-356,-929) -> Matrix(11,16,-9,-13) Matrix(241,624,56,145) -> Matrix(1,2,-4,-7) Matrix(559,1440,-342,-881) -> Matrix(7,10,-5,-7) Matrix(113,288,82,209) -> Matrix(1,-4,-1,5) Matrix(353,864,-248,-607) -> Matrix(1,6,-1,-5) Matrix(79,192,72,175) -> Matrix(27,34,-31,-39) Matrix(239,576,-100,-241) -> Matrix(7,8,-8,-9) Matrix(545,1296,-336,-799) -> Matrix(9,4,-7,-3) Matrix(143,336,20,47) -> Matrix(1,2,-2,-3) Matrix(209,480,-118,-271) -> Matrix(17,38,-13,-29) Matrix(127,288,56,127) -> Matrix(9,16,-13,-23) Matrix(175,384,36,79) -> Matrix(9,14,-11,-17) Matrix(353,768,74,161) -> Matrix(15,22,-13,-19) Matrix(223,480,-164,-353) -> Matrix(21,26,-17,-21) Matrix(79,144,-62,-113) -> Matrix(21,26,-17,-21) Matrix(161,288,90,161) -> Matrix(19,24,-23,-29) Matrix(191,336,54,95) -> Matrix(17,22,-24,-31) Matrix(305,528,-212,-367) -> Matrix(83,106,-65,-83) Matrix(335,576,-196,-337) -> Matrix(79,100,-64,-81) Matrix(1663,2832,-1222,-2081) -> Matrix(31,36,-25,-29) Matrix(623,1056,-482,-817) -> Matrix(1,0,0,1) Matrix(143,240,28,47) -> Matrix(5,6,-6,-7) Matrix(175,288,48,79) -> Matrix(3,4,-7,-9) Matrix(4321,7056,-3174,-5183) -> Matrix(17,28,-14,-23) Matrix(3823,6240,-3010,-4913) -> Matrix(57,74,-47,-61) Matrix(383,624,294,479) -> Matrix(9,10,-10,-11) Matrix(1393,2256,-1096,-1775) -> Matrix(61,72,-50,-59) Matrix(12815,20736,4894,7919) -> Matrix(15,16,-16,-17) Matrix(12817,20736,4896,7921) -> Matrix(1,0,0,1) Matrix(1009,1632,-860,-1391) -> Matrix(5,4,-4,-3) Matrix(209,336,130,209) -> Matrix(19,24,-23,-29) Matrix(31,48,20,31) -> Matrix(19,24,-23,-29) Matrix(65,96,44,65) -> Matrix(19,24,-23,-29) Matrix(497,720,78,113) -> Matrix(11,14,-15,-19) Matrix(703,1008,-514,-737) -> Matrix(145,184,-119,-151) Matrix(911,1296,168,239) -> Matrix(11,14,-26,-33) Matrix(1217,1728,-1036,-1471) -> Matrix(13,16,-9,-11) Matrix(577,816,408,577) -> Matrix(351,440,-422,-529) Matrix(239,336,170,239) -> Matrix(209,260,-250,-311) Matrix(241,336,104,145) -> Matrix(21,26,-38,-47) Matrix(209,288,82,113) -> Matrix(3,4,-7,-9) Matrix(1679,2304,454,623) -> Matrix(67,82,-76,-93) Matrix(1681,2304,456,625) -> Matrix(41,50,-32,-39) Matrix(527,720,456,623) -> Matrix(49,60,-58,-71) Matrix(2431,3312,516,703) -> Matrix(13,16,-9,-11) Matrix(143,192,-108,-145) -> Matrix(119,144,-100,-121) Matrix(479,624,294,383) -> Matrix(9,10,-10,-11) Matrix(1775,2304,406,527) -> Matrix(5,6,4,5) Matrix(1777,2304,408,529) -> Matrix(5,6,-16,-19) Matrix(223,288,24,31) -> Matrix(5,6,-1,-1) Matrix(2609,3312,694,881) -> Matrix(23,28,-37,-45) Matrix(607,768,328,415) -> Matrix(251,302,-315,-379) Matrix(305,384,166,209) -> Matrix(149,178,-185,-221) Matrix(193,240,78,97) -> Matrix(49,58,-60,-71) 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(5,6,-16,-19) Matrix(607,720,188,223) -> Matrix(33,38,-53,-61) Matrix(289,336,166,193) -> Matrix(49,58,-60,-71) Matrix(209,240,182,209) -> Matrix(41,48,-47,-55) Matrix(127,144,112,127) -> Matrix(41,48,-47,-55) Matrix(257,288,58,65) -> Matrix(5,6,-11,-13) Matrix(1,0,2,1) -> Matrix(15,16,-16,-17) Matrix(367,-432,96,-113) -> Matrix(11,10,-21,-19) Matrix(161,-192,26,-31) -> Matrix(25,22,-33,-29) Matrix(79,-96,14,-17) -> Matrix(7,6,1,1) Matrix(113,-144,62,-79) -> Matrix(31,26,-37,-31) Matrix(817,-1056,482,-623) -> Matrix(1,0,0,1) Matrix(815,-1056,186,-241) -> Matrix(7,6,-6,-5) Matrix(623,-816,184,-241) -> Matrix(7,6,-6,-5) Matrix(319,-432,48,-65) -> Matrix(7,6,-27,-23) Matrix(671,-912,142,-193) -> Matrix(19,16,-6,-5) Matrix(913,-1248,526,-719) -> Matrix(115,98,-142,-121) Matrix(911,-1248,246,-337) -> Matrix(59,50,-72,-61) Matrix(415,-576,116,-161) -> Matrix(45,38,-77,-65) Matrix(575,-816,136,-193) -> Matrix(41,34,-76,-63) Matrix(607,-864,248,-353) -> Matrix(7,6,-13,-11) Matrix(367,-528,212,-305) -> Matrix(129,106,-157,-129) Matrix(463,-672,144,-209) -> Matrix(27,22,-43,-35) Matrix(1039,-1680,248,-401) -> Matrix(7,6,-13,-11) Matrix(3025,-4896,1156,-1871) -> Matrix(5,4,-4,-3) Matrix(977,-1584,404,-655) -> Matrix(43,36,-49,-41) Matrix(881,-1440,342,-559) -> Matrix(13,10,-17,-13) Matrix(511,-864,152,-257) -> Matrix(7,6,-13,-11) Matrix(337,-576,196,-335) -> Matrix(119,100,-144,-121) Matrix(751,-1296,288,-497) -> Matrix(5,4,1,1) Matrix(271,-480,118,-209) -> Matrix(47,38,-73,-59) Matrix(257,-480,68,-127) -> Matrix(33,26,-47,-37) Matrix(65,-144,14,-31) -> Matrix(3,2,1,1) Matrix(223,-528,68,-161) -> Matrix(3,2,-5,-3) Matrix(241,-576,100,-239) -> Matrix(7,8,-8,-9) Matrix(1169,-2832,310,-751) -> Matrix(19,16,-25,-21) Matrix(433,-1056,98,-239) -> Matrix(5,4,-4,-3) Matrix(2735,-7056,726,-1873) -> Matrix(1,0,0,1) Matrix(2417,-6240,514,-1327) -> Matrix(3,2,1,1) Matrix(863,-2256,184,-481) -> Matrix(5,4,-4,-3) Matrix(623,-1632,92,-241) -> Matrix(5,4,-4,-3) Matrix(305,-1008,82,-271) -> Matrix(7,4,-9,-5) Matrix(511,-1728,76,-257) -> Matrix(1,0,1,1) Matrix(49,-192,12,-47) -> Matrix(1,0,0,1) 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): 64 ----------------------------------------------------------------------- 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 8 1 1/1 -8/9 1 24 9/8 (-8/9,-6/7) 0 8 8/7 (-8/9,-6/7) 0 3 15/13 -6/7 1 8 7/6 (-1/1,-6/7) 0 24 13/11 -8/9 1 24 6/5 -7/8 2 4 5/4 (-19/22,-6/7) 0 24 9/7 -6/7 1 8 22/17 0 12 13/10 (-6/7,-5/6) 0 24 17/13 -6/7 1 24 4/3 -6/7 2 6 19/14 (-28/33,-11/13) 0 24 15/11 -6/7 1 8 26/19 0 12 11/8 (-11/13,-16/19) 0 24 18/13 -11/13 2 4 7/5 -26/31 1 24 24/17 -5/6 14 1 17/12 (-5/6,-44/53) 0 24 27/19 -24/29 1 8 10/7 0 12 13/9 -4/5 1 24 16/11 -4/5 2 3 3/2 (-6/7,-4/5) 0 8 8/5 (-6/7,-4/5) 0 3 21/13 -4/5 1 8 55/34 (-1/1,-2/3) 0 24 34/21 0 12 13/8 (-5/6,-4/5) 0 24 31/19 -4/5 1 24 18/11 -1/1 2 4 5/3 -4/5 1 24 22/13 0 12 39/23 -6/7 1 8 17/10 (-6/7,-5/6) 0 24 12/7 -5/6 2 2 31/18 (-5/6,-14/17) 0 24 19/11 -14/17 1 24 26/15 0 12 33/19 -4/5 1 8 7/4 (-9/11,-4/5) 0 24 16/9 -4/5 6 3 9/5 -4/5 1 8 11/6 (-17/21,-4/5) 0 24 24/13 -4/5 10 1 13/7 -4/5 1 24 2/1 0 12 9/4 (-8/11,-2/3) 0 8 16/7 -2/3 6 3 23/10 (-2/3,-5/8) 0 24 7/3 0/1 1 24 19/8 (-1/1,0/1) 0 24 12/5 -1/1 4 2 29/12 (-1/1,-8/9) 0 24 46/19 0 12 17/7 -6/7 1 24 22/9 0 12 27/11 -6/7 1 8 5/2 (-4/5,-3/4) 0 24 18/7 -3/4 2 4 49/19 -2/3 1 24 80/31 (-4/5,-2/3) 0 3 31/12 (-4/5,-3/4) 0 24 13/5 -2/3 1 24 47/18 (-1/1,-2/3) 0 24 34/13 0 12 89/34 (-2/1,-1/1) 0 24 144/55 -1/1 8 1 55/21 -6/7 1 24 21/8 (-4/5,-2/3) 0 8 8/3 (-4/5,-2/3) 0 3 3/1 -2/3 1 8 16/5 -2/3 2 3 29/9 -2/3 1 24 13/4 (-2/3,-1/2) 0 24 23/7 -2/3 1 24 10/3 0 12 37/11 -2/3 1 24 27/8 (-2/3,0/1) 0 8 44/13 0/1 2 6 17/5 0/1 1 24 24/7 -1/1 2 1 7/2 (-1/1,-2/3) 0 24 25/7 -8/13 1 24 18/5 -1/2 2 4 11/3 0/1 1 24 48/13 -1/1 6 1 37/10 (-1/1,-6/7) 0 24 26/7 0 12 41/11 -2/3 1 24 15/4 (-4/5,-2/3) 0 8 64/17 (-4/5,-2/3) 0 3 49/13 -2/3 1 24 34/9 0 12 19/5 -2/3 1 24 23/6 (-4/7,-1/2) 0 24 4/1 0 6 25/6 (-4/7,-1/2) 0 24 21/5 -2/3 1 8 17/4 (-1/2,-2/5) 0 24 13/3 0/1 1 24 48/11 0/1 2 1 35/8 (0/1,1/0) 0 24 22/5 0 12 31/7 -2/3 1 24 9/2 (-2/3,0/1) 0 8 14/3 0 12 47/10 (-2/1,-1/1) 0 24 80/17 (-2/1,0/1) 0 3 33/7 -2/1 1 8 19/4 (-4/3,-1/1) 0 24 24/5 -1/1 6 1 5/1 -2/3 1 24 21/4 (-2/3,0/1) 0 8 16/3 (-2/3,0/1) 0 3 27/5 -2/3 1 8 11/2 (-1/3,0/1) 0 24 6/1 -1/1 2 4 19/3 -2/3 1 24 13/2 (-2/3,-1/2) 0 24 20/3 0/1 2 6 27/4 (-2/1,0/1) 0 8 7/1 -2/3 1 24 15/2 (-2/3,0/1) 0 8 8/1 (-2/3,0/1) 0 3 9/1 0/1 1 8 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(257,-288,58,-65) (1/1,9/8) -> (31/7,9/2) Glide Reflection Matrix(127,-144,112,-127) (9/8,8/7) -> (9/8,8/7) Reflection Matrix(209,-240,182,-209) (8/7,15/13) -> (8/7,15/13) Reflection Matrix(289,-336,166,-193) (15/13,7/6) -> (33/19,7/4) Glide Reflection Matrix(367,-432,96,-113) (7/6,13/11) -> (19/5,23/6) Hyperbolic Matrix(161,-192,26,-31) (13/11,6/5) -> (6/1,19/3) Hyperbolic Matrix(79,-96,14,-17) (6/5,5/4) -> (11/2,6/1) Hyperbolic Matrix(113,-144,62,-79) (5/4,9/7) -> (9/5,11/6) 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,-624,294,-383) (13/10,17/13) -> (13/8,31/19) Glide Reflection Matrix(623,-816,184,-241) (17/13,4/3) -> (44/13,17/5) Hyperbolic Matrix(319,-432,48,-65) (4/3,19/14) -> (13/2,20/3) 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(209,-288,82,-113) (11/8,18/13) -> (5/2,18/7) Glide Reflection Matrix(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(239,-336,170,-239) (7/5,24/17) -> (7/5,24/17) Reflection Matrix(577,-816,408,-577) (24/17,17/12) -> (24/17,17/12) Reflection Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(607,-864,248,-353) (27/19,10/7) -> (22/9,27/11) Hyperbolic Matrix(367,-528,212,-305) (10/7,13/9) -> (19/11,26/15) Hyperbolic Matrix(463,-672,144,-209) (13/9,16/11) -> (16/5,29/9) Hyperbolic Matrix(65,-96,44,-65) (16/11,3/2) -> (16/11,3/2) Reflection Matrix(31,-48,20,-31) (3/2,8/5) -> (3/2,8/5) Reflection Matrix(209,-336,130,-209) (8/5,21/13) -> (8/5,21/13) Reflection Matrix(1039,-1680,248,-401) (21/13,55/34) -> (25/6,21/5) Hyperbolic Matrix(3025,-4896,1156,-1871) (55/34,34/21) -> (34/13,89/34) Hyperbolic Matrix(977,-1584,404,-655) (34/21,13/8) -> (29/12,46/19) Hyperbolic Matrix(881,-1440,342,-559) (31/19,18/11) -> (18/7,49/19) Hyperbolic Matrix(175,-288,48,-79) (18/11,5/3) -> (18/5,11/3) Glide Reflection Matrix(511,-864,152,-257) (5/3,22/13) -> (10/3,37/11) Hyperbolic Matrix(113,-192,10,-17) (39/23,17/10) -> (9/1,1/0) Glide Reflection Matrix(337,-576,196,-335) (17/10,12/7) -> (12/7,31/18) Parabolic Matrix(751,-1296,288,-497) (31/18,19/11) -> (13/5,47/18) Hyperbolic Matrix(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(161,-288,90,-161) (16/9,9/5) -> (16/9,9/5) Reflection Matrix(287,-528,156,-287) (11/6,24/13) -> (11/6,24/13) Reflection Matrix(337,-624,182,-337) (24/13,13/7) -> (24/13,13/7) Reflection Matrix(257,-480,68,-127) (13/7,2/1) -> (34/9,19/5) Hyperbolic Matrix(65,-144,14,-31) (2/1,9/4) -> (9/2,14/3) Hyperbolic Matrix(127,-288,56,-127) (9/4,16/7) -> (9/4,16/7) Reflection Matrix(271,-624,76,-175) (23/10,7/3) -> (7/2,25/7) Glide Reflection Matrix(223,-528,68,-161) (7/3,19/8) -> (13/4,23/7) Hyperbolic Matrix(241,-576,100,-239) (19/8,12/5) -> (12/5,29/12) Parabolic Matrix(1169,-2832,310,-751) (46/19,17/7) -> (49/13,34/9) Hyperbolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(175,-432,32,-79) (27/11,5/2) -> (27/5,11/2) Glide Reflection Matrix(2735,-7056,726,-1873) (49/19,80/31) -> (64/17,49/13) Hyperbolic Matrix(2417,-6240,514,-1327) (80/31,31/12) -> (47/10,80/17) Hyperbolic Matrix(241,-624,56,-145) (31/12,13/5) -> (17/4,13/3) Glide Reflection Matrix(863,-2256,184,-481) (47/18,34/13) -> (14/3,47/10) Hyperbolic Matrix(9791,-25632,3740,-9791) (89/34,144/55) -> (89/34,144/55) 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(127,-336,48,-127) (21/8,8/3) -> (21/8,8/3) Reflection Matrix(17,-48,6,-17) (8/3,3/1) -> (8/3,3/1) Reflection Matrix(31,-96,10,-31) (3/1,16/5) -> (3/1,16/5) Reflection Matrix(193,-624,30,-97) (29/9,13/4) -> (19/3,13/2) Glide Reflection Matrix(305,-1008,82,-271) (23/7,10/3) -> (26/7,41/11) Hyperbolic Matrix(271,-912,52,-175) (37/11,27/8) -> (5/1,21/4) Glide Reflection Matrix(511,-1728,76,-257) (27/8,44/13) -> (20/3,27/4) Hyperbolic 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(287,-1056,78,-287) (11/3,48/13) -> (11/3,48/13) Reflection Matrix(961,-3552,260,-961) (48/13,37/10) -> (48/13,37/10) Reflection Matrix(193,-720,26,-97) (41/11,15/4) -> (7/1,15/2) Glide Reflection Matrix(511,-1920,136,-511) (15/4,64/17) -> (15/4,64/17) Reflection 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(769,-3360,176,-769) (48/11,35/8) -> (48/11,35/8) Reflection Matrix(1121,-5280,238,-1121) (80/17,33/7) -> (80/17,33/7) 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(127,-672,24,-127) (21/4,16/3) -> (21/4,16/3) Reflection Matrix(161,-864,30,-161) (16/3,27/5) -> (16/3,27/5) Reflection Matrix(31,-240,4,-31) (15/2,8/1) -> (15/2,8/1) Reflection Matrix(17,-144,2,-17) (8/1,9/1) -> (8/1,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(17,16,-18,-17) (0/1,1/1) -> (-1/1,-8/9) Matrix(257,-288,58,-65) -> Matrix(7,6,-15,-13) Matrix(127,-144,112,-127) -> Matrix(55,48,-63,-55) (9/8,8/7) -> (-8/9,-6/7) Matrix(209,-240,182,-209) -> Matrix(55,48,-63,-55) (8/7,15/13) -> (-8/9,-6/7) Matrix(289,-336,166,-193) -> Matrix(67,58,-82,-71) Matrix(367,-432,96,-113) -> Matrix(11,10,-21,-19) Matrix(161,-192,26,-31) -> Matrix(25,22,-33,-29) Matrix(79,-96,14,-17) -> Matrix(7,6,1,1) Matrix(113,-144,62,-79) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(817,-1056,482,-623) -> Matrix(1,0,0,1) Matrix(815,-1056,186,-241) -> Matrix(7,6,-6,-5) -1/1 Matrix(479,-624,294,-383) -> Matrix(11,10,-12,-11) *** -> (-1/1,-5/6) Matrix(623,-816,184,-241) -> Matrix(7,6,-6,-5) -1/1 Matrix(319,-432,48,-65) -> Matrix(7,6,-27,-23) Matrix(671,-912,142,-193) -> Matrix(19,16,-6,-5) Matrix(913,-1248,526,-719) -> Matrix(115,98,-142,-121) Matrix(911,-1248,246,-337) -> Matrix(59,50,-72,-61) -5/6 Matrix(209,-288,82,-113) -> Matrix(5,4,-11,-9) Matrix(415,-576,116,-161) -> Matrix(45,38,-77,-65) Matrix(239,-336,170,-239) -> Matrix(311,260,-372,-311) (7/5,24/17) -> (-26/31,-5/6) Matrix(577,-816,408,-577) -> Matrix(529,440,-636,-529) (24/17,17/12) -> (-5/6,-44/53) Matrix(575,-816,136,-193) -> Matrix(41,34,-76,-63) Matrix(607,-864,248,-353) -> Matrix(7,6,-13,-11) Matrix(367,-528,212,-305) -> Matrix(129,106,-157,-129) (-5/6,-9/11).(-14/17,-4/5) Matrix(463,-672,144,-209) -> Matrix(27,22,-43,-35) Matrix(65,-96,44,-65) -> Matrix(29,24,-35,-29) (16/11,3/2) -> (-6/7,-4/5) Matrix(31,-48,20,-31) -> Matrix(29,24,-35,-29) (3/2,8/5) -> (-6/7,-4/5) Matrix(209,-336,130,-209) -> Matrix(29,24,-35,-29) (8/5,21/13) -> (-6/7,-4/5) Matrix(1039,-1680,248,-401) -> Matrix(7,6,-13,-11) Matrix(3025,-4896,1156,-1871) -> Matrix(5,4,-4,-3) -1/1 Matrix(977,-1584,404,-655) -> Matrix(43,36,-49,-41) -6/7 Matrix(881,-1440,342,-559) -> Matrix(13,10,-17,-13) (-1/1,-3/4).(-4/5,-2/3) Matrix(175,-288,48,-79) -> Matrix(5,4,-11,-9) Matrix(511,-864,152,-257) -> Matrix(7,6,-13,-11) Matrix(113,-192,10,-17) -> Matrix(7,6,-1,-1) Matrix(337,-576,196,-335) -> Matrix(119,100,-144,-121) -5/6 Matrix(751,-1296,288,-497) -> Matrix(5,4,1,1) Matrix(271,-480,118,-209) -> Matrix(47,38,-73,-59) Matrix(161,-288,90,-161) -> Matrix(29,24,-35,-29) (16/9,9/5) -> (-6/7,-4/5) Matrix(287,-528,156,-287) -> Matrix(169,136,-210,-169) (11/6,24/13) -> (-17/21,-4/5) Matrix(337,-624,182,-337) -> Matrix(231,184,-290,-231) (24/13,13/7) -> (-4/5,-23/29) Matrix(257,-480,68,-127) -> Matrix(33,26,-47,-37) Matrix(65,-144,14,-31) -> Matrix(3,2,1,1) Matrix(127,-288,56,-127) -> Matrix(23,16,-33,-23) (9/4,16/7) -> (-8/11,-2/3) Matrix(271,-624,76,-175) -> Matrix(13,8,-21,-13) *** -> (-2/3,-4/7) Matrix(223,-528,68,-161) -> Matrix(3,2,-5,-3) (-1/1,-1/2).(-2/3,0/1) Matrix(241,-576,100,-239) -> Matrix(7,8,-8,-9) -1/1 Matrix(1169,-2832,310,-751) -> Matrix(19,16,-25,-21) -4/5 Matrix(433,-1056,98,-239) -> Matrix(5,4,-4,-3) -1/1 Matrix(175,-432,32,-79) -> Matrix(5,4,-11,-9) Matrix(2735,-7056,726,-1873) -> Matrix(1,0,0,1) Matrix(2417,-6240,514,-1327) -> Matrix(3,2,1,1) Matrix(241,-624,56,-145) -> Matrix(3,2,-10,-7) Matrix(863,-2256,184,-481) -> Matrix(5,4,-4,-3) -1/1 Matrix(9791,-25632,3740,-9791) -> Matrix(3,4,-2,-3) (89/34,144/55) -> (-2/1,-1/1) Matrix(6049,-15840,2310,-6049) -> Matrix(13,12,-14,-13) (144/55,55/21) -> (-1/1,-6/7) Matrix(623,-1632,92,-241) -> Matrix(5,4,-4,-3) -1/1 Matrix(127,-336,48,-127) -> Matrix(11,8,-15,-11) (21/8,8/3) -> (-4/5,-2/3) Matrix(17,-48,6,-17) -> Matrix(11,8,-15,-11) (8/3,3/1) -> (-4/5,-2/3) Matrix(31,-96,10,-31) -> Matrix(-1,0,3,1) (3/1,16/5) -> (-2/3,0/1) Matrix(193,-624,30,-97) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(305,-1008,82,-271) -> Matrix(7,4,-9,-5) -2/3 Matrix(271,-912,52,-175) -> Matrix(-1,0,3,1) *** -> (-2/3,0/1) Matrix(511,-1728,76,-257) -> Matrix(1,0,1,1) 0/1 Matrix(239,-816,70,-239) -> Matrix(-1,0,2,1) (17/5,24/7) -> (-1/1,0/1) Matrix(97,-336,28,-97) -> Matrix(5,4,-6,-5) (24/7,7/2) -> (-1/1,-2/3) Matrix(287,-1056,78,-287) -> Matrix(-1,0,2,1) (11/3,48/13) -> (-1/1,0/1) Matrix(961,-3552,260,-961) -> Matrix(13,12,-14,-13) (48/13,37/10) -> (-1/1,-6/7) Matrix(193,-720,26,-97) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(511,-1920,136,-511) -> Matrix(11,8,-15,-11) (15/4,64/17) -> (-4/5,-2/3) Matrix(49,-192,12,-47) -> Matrix(1,0,0,1) Matrix(287,-1248,66,-287) -> Matrix(-1,0,4,1) (13/3,48/11) -> (-1/2,0/1) Matrix(769,-3360,176,-769) -> Matrix(1,0,0,-1) (48/11,35/8) -> (0/1,1/0) Matrix(1121,-5280,238,-1121) -> Matrix(-1,0,1,1) (80/17,33/7) -> (-2/1,0/1) Matrix(191,-912,40,-191) -> Matrix(7,8,-6,-7) (19/4,24/5) -> (-4/3,-1/1) Matrix(49,-240,10,-49) -> Matrix(5,4,-6,-5) (24/5,5/1) -> (-1/1,-2/3) Matrix(127,-672,24,-127) -> Matrix(-1,0,3,1) (21/4,16/3) -> (-2/3,0/1) Matrix(161,-864,30,-161) -> Matrix(-1,0,3,1) (16/3,27/5) -> (-2/3,0/1) Matrix(31,-240,4,-31) -> Matrix(-1,0,3,1) (15/2,8/1) -> (-2/3,0/1) Matrix(17,-144,2,-17) -> Matrix(-1,0,3,1) (8/1,9/1) -> (-2/3,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.