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 1/0 -9/1 -1/1 -8/1 1/0 -15/2 -2/1 -7/1 -3/2 -1/1 -20/3 1/0 -13/2 -2/1 -5/3 -19/3 -7/5 -4/3 -6/1 -1/1 -23/4 -2/3 -1/2 -40/7 -1/2 -17/3 -1/3 0/1 -11/2 -1/1 0/1 -27/5 -1/1 -16/3 1/0 -21/4 -2/1 -5/1 -3/2 -1/1 -24/5 -1/1 -19/4 -1/1 -8/9 -14/3 -3/4 -23/5 -1/1 0/1 -9/2 0/1 -22/5 1/0 -13/3 -1/1 -1/2 -17/4 0/1 1/0 -4/1 1/0 -23/6 -2/1 1/0 -42/11 -3/1 -19/5 -7/3 -2/1 -15/4 -2/1 -26/7 -5/2 -11/3 -2/1 -5/3 -18/5 -2/1 -25/7 -5/3 -8/5 -7/2 -2/1 -1/1 -24/7 -2/1 -17/5 -2/1 -5/3 -27/8 -2/1 -37/11 -2/1 -5/3 -47/14 -2/1 -5/3 -10/3 -3/2 -43/13 -3/2 -1/1 -33/10 -2/1 -56/17 -3/2 -23/7 -2/1 -5/3 -36/11 -3/2 -13/4 -2/1 -1/1 -29/9 -8/5 -11/7 -16/5 -3/2 -19/6 -7/5 -4/3 -3/1 -1/1 -20/7 1/0 -17/6 -5/2 -2/1 -14/5 -7/4 -25/9 -5/3 -8/5 -36/13 -3/2 -47/17 -4/3 -1/1 -11/4 -2/1 -1/1 -19/7 -5/3 -8/5 -8/3 -3/2 -29/11 -13/9 -10/7 -50/19 -3/2 -71/27 -10/7 -7/5 -21/8 -10/7 -76/29 -17/12 -55/21 -31/22 -7/5 -34/13 -3/2 -47/18 -7/5 -4/3 -13/5 -3/2 -7/5 -31/12 -11/8 -4/3 -80/31 -11/8 -49/19 -15/11 -4/3 -18/7 -4/3 -23/9 -6/5 -1/1 -28/11 -3/2 -33/13 -1/1 -5/2 -3/2 -4/3 -27/11 -1/1 -49/20 -8/7 -1/1 -22/9 -3/2 -39/16 -2/1 -17/7 -4/3 -1/1 -12/5 -3/2 -5/4 -31/13 -4/3 -1/1 -50/21 -3/2 -19/8 -4/3 -1/1 -45/19 -7/5 -71/30 -11/8 -4/3 -26/11 -3/2 -33/14 -4/3 -7/3 -3/2 -1/1 -23/10 -2/1 -3/2 -16/7 -3/2 -25/11 -7/5 -4/3 -9/4 -4/3 -38/17 -3/2 -29/13 -7/5 -4/3 -20/9 -11/8 -11/5 -15/11 -4/3 -24/11 -4/3 -13/6 -4/3 -25/19 -28/13 -13/10 -15/7 -9/7 -2/1 -5/4 -17/9 -6/5 -1/1 -15/8 -6/5 -13/7 -7/6 -1/1 -24/13 -1/1 -11/6 -4/3 -1/1 -31/17 -7/5 -4/3 -20/11 -5/4 -29/16 -6/5 -1/1 -96/53 -1/1 -67/37 -4/3 -1/1 -38/21 -5/4 -9/5 -1/1 -25/14 -4/3 -5/4 -16/9 -5/4 -23/13 -16/13 -11/9 -7/4 -6/5 -1/1 -26/15 -7/6 -97/56 -12/11 -1/1 -168/97 -1/1 -71/41 -1/1 0/1 -45/26 -4/3 -19/11 -6/5 -1/1 -12/7 -5/4 -7/6 -29/17 -6/5 -1/1 -46/27 -5/4 -63/37 -1/1 -80/47 -5/4 -17/10 -5/4 -6/5 -22/13 -5/4 -71/42 -17/14 -6/5 -120/71 -6/5 -49/29 -6/5 -13/11 -27/16 -6/5 -5/3 -5/4 -1/1 -33/20 -6/5 -28/17 -5/4 -51/31 -1/1 -23/14 -6/5 -7/6 -18/11 -1/1 -49/30 -2/1 -1/1 -80/49 -3/2 -111/68 -4/3 -31/19 -4/3 -1/1 -13/8 -4/3 -1/1 -60/37 -5/4 -47/29 -11/9 -6/5 -34/21 -7/6 -89/55 -11/10 -1/1 -144/89 -1/1 -55/34 -2/1 -1/1 -21/13 -1/1 -8/5 -5/4 -27/17 -11/9 -73/46 -17/14 -6/5 -192/121 -6/5 -119/75 -6/5 -1/1 -46/29 -5/4 -19/12 -11/9 -6/5 -68/43 -17/14 -117/74 -6/5 -49/31 -11/9 -6/5 -30/19 -6/5 -11/7 -6/5 -1/1 -47/30 -6/5 -1/1 -36/23 -5/4 -7/6 -25/16 -5/4 -6/5 -14/9 -5/4 -31/20 -41/34 -6/5 -48/31 -6/5 -17/11 -6/5 -25/21 -20/13 -7/6 -23/15 -10/9 -1/1 -3/2 -6/5 -19/13 -13/11 -20/17 -16/11 -7/6 -29/20 -22/19 -15/13 -13/9 -7/6 -1/1 -49/34 -6/5 -1/1 -36/25 -5/4 -7/6 -23/16 -6/5 -7/6 -33/23 -1/1 -43/30 -6/5 -7/6 -96/67 -7/6 -53/37 -7/6 -1/1 -10/7 -7/6 -47/33 -6/5 -1/1 -37/26 -8/7 -1/1 -27/19 -1/1 -71/50 -6/5 -7/6 -44/31 -7/6 -17/12 -6/5 -7/6 -24/17 -7/6 -7/5 -7/6 -1/1 -25/18 -7/6 -8/7 -18/13 -1/1 -47/34 -6/5 -1/1 -76/55 -3/2 -29/21 -4/3 -1/1 -11/8 -11/9 -6/5 -48/35 -6/5 -37/27 -6/5 -61/51 -26/19 -31/26 -41/30 -6/5 -25/21 -15/11 -13/11 -64/47 -19/16 -49/36 -6/5 -13/11 -34/25 -19/16 -19/14 -13/11 -46/39 -23/17 -13/11 -20/17 -4/3 -7/6 -25/19 -29/25 -22/19 -21/16 -22/19 -17/13 -22/19 -15/13 -13/10 -22/19 -15/13 -48/37 -15/13 -35/27 -15/13 -53/46 -22/17 -23/20 -31/24 -23/20 -8/7 -40/31 -7/6 -9/7 -15/13 -23/18 -23/20 -8/7 -14/11 -23/20 -47/37 -47/41 -8/7 -80/63 -39/34 -33/26 -8/7 -19/15 -63/55 -8/7 -24/19 -8/7 -5/4 -8/7 -9/8 -21/17 -1/1 -16/13 -7/6 -27/22 -8/7 -11/9 -15/13 -8/7 -28/23 -7/6 -17/14 -8/7 -9/8 -40/33 -7/6 -23/19 -15/13 -8/7 -6/5 -8/7 -25/21 -8/7 -33/29 -19/16 -33/29 -58/51 -13/11 -25/22 -17/15 -33/28 -8/7 -20/17 -25/22 -47/40 -76/67 -17/15 -27/23 -17/15 -7/6 -17/15 -26/23 -15/13 -35/31 -23/20 -44/39 -9/8 -8/7 -9/8 -17/15 -28/25 -19/17 -9/8 -10/9 -10/9 -9/8 -1/1 -10/9 -1/1 0/1 -1/1 1/1 -1/1 -10/11 10/9 -9/10 9/8 -10/11 8/7 -9/10 15/13 -35/39 7/6 -26/29 -17/19 20/17 -25/28 13/11 -17/19 -25/28 19/16 -58/65 -33/37 6/5 -8/9 23/19 -8/9 -15/17 40/33 -7/8 17/14 -9/10 -8/9 11/9 -8/9 -15/17 27/22 -8/9 16/13 -7/8 21/17 -1/1 5/4 -9/10 -8/9 24/19 -8/9 19/15 -8/9 -63/71 14/11 -23/26 23/18 -8/9 -23/26 9/7 -15/17 22/17 -23/26 13/10 -15/17 -22/25 17/13 -15/17 -22/25 4/3 -7/8 23/17 -20/23 -13/15 42/31 -20/23 19/14 -46/53 -13/15 15/11 -13/15 26/19 -31/36 11/8 -6/7 -11/13 18/13 -1/1 25/18 -8/9 -7/8 7/5 -1/1 -7/8 24/17 -7/8 17/12 -7/8 -6/7 27/19 -1/1 37/26 -1/1 -8/9 47/33 -1/1 -6/7 10/7 -7/8 43/30 -7/8 -6/7 33/23 -1/1 56/39 -7/8 23/16 -7/8 -6/7 36/25 -7/8 -5/6 13/9 -1/1 -7/8 29/20 -15/17 -22/25 16/11 -7/8 19/13 -20/23 -13/15 3/2 -6/7 20/13 -7/8 17/11 -25/29 -6/7 14/9 -5/6 25/16 -6/7 -5/6 36/23 -7/8 -5/6 47/30 -1/1 -6/7 11/7 -1/1 -6/7 19/12 -6/7 -11/13 8/5 -5/6 29/18 -1/1 -4/5 50/31 -5/6 71/44 -4/5 -3/4 21/13 -1/1 76/47 -5/6 55/34 -1/1 -2/3 34/21 -7/8 47/29 -6/7 -11/13 13/8 -1/1 -4/5 31/19 -1/1 -4/5 80/49 -3/4 49/30 -1/1 -2/3 18/11 -1/1 23/14 -7/8 -6/7 28/17 -5/6 33/20 -6/7 5/3 -1/1 -5/6 27/16 -6/7 49/29 -13/15 -6/7 22/13 -5/6 39/23 -1/1 17/10 -6/7 -5/6 12/7 -7/8 -5/6 31/18 -6/7 -5/6 50/29 -5/6 19/11 -1/1 -6/7 45/26 -4/5 71/41 -1/1 0/1 26/15 -7/8 33/19 -11/13 7/4 -1/1 -6/7 23/13 -11/13 -16/19 16/9 -5/6 25/14 -5/6 -4/5 9/5 -1/1 38/21 -5/6 29/16 -1/1 -6/7 20/11 -5/6 11/6 -1/1 -4/5 24/13 -1/1 13/7 -1/1 -7/8 28/15 -7/8 15/8 -6/7 2/1 -5/6 17/8 -5/6 -4/5 15/7 -9/11 13/6 -25/31 -4/5 24/11 -4/5 11/5 -4/5 -15/19 31/14 -4/5 -3/4 20/9 -11/14 29/13 -4/5 -7/9 96/43 -7/9 67/30 -7/9 -10/13 38/17 -3/4 9/4 -4/5 25/11 -4/5 -7/9 16/7 -3/4 23/10 -3/4 -2/3 7/3 -1/1 -3/4 26/11 -3/4 97/41 -9/11 -4/5 168/71 -4/5 71/30 -4/5 -11/14 45/19 -7/9 19/8 -1/1 -4/5 12/5 -5/6 -3/4 29/12 -1/1 -4/5 46/19 -3/4 63/26 -4/5 80/33 -3/4 17/7 -1/1 -4/5 22/9 -3/4 71/29 -4/3 -1/1 120/49 -1/1 49/20 -1/1 -8/9 27/11 -1/1 5/2 -4/5 -3/4 33/13 -1/1 28/11 -3/4 51/20 -2/3 23/9 -1/1 -6/7 18/7 -4/5 49/19 -4/5 -15/19 80/31 -11/14 111/43 -7/9 31/12 -4/5 -11/14 13/5 -7/9 -3/4 60/23 -11/14 -3/4 47/18 -4/5 -7/9 34/13 -3/4 89/34 -32/41 -7/9 144/55 -7/9 55/21 -7/9 -31/40 21/8 -10/13 8/3 -3/4 27/10 -8/11 73/27 -11/15 -8/11 192/71 -8/11 119/44 -8/11 -13/18 46/17 -3/4 19/7 -8/11 -5/7 68/25 -13/18 117/43 -5/7 49/18 -5/7 -2/3 30/11 -5/7 11/4 -1/1 -2/3 47/17 -1/1 -4/5 36/13 -3/4 25/9 -8/11 -5/7 14/5 -7/10 31/11 -17/25 -2/3 48/17 -2/3 17/6 -2/3 -5/8 20/7 -1/2 23/8 -3/4 -2/3 3/1 -1/1 19/6 -4/5 -7/9 16/5 -3/4 29/9 -11/15 -8/11 13/4 -1/1 -2/3 49/15 -4/5 -7/9 36/11 -3/4 23/7 -5/7 -2/3 33/10 -2/3 43/13 -1/1 -3/4 96/29 -3/4 53/16 -3/4 -2/3 10/3 -3/4 47/14 -5/7 -2/3 37/11 -5/7 -2/3 27/8 -2/3 71/21 -1/1 -2/3 44/13 -3/4 17/5 -5/7 -2/3 24/7 -2/3 7/2 -1/1 -2/3 25/7 -8/11 -5/7 18/5 -2/3 47/13 -1/1 -2/3 76/21 -1/2 29/8 -1/1 -2/3 11/3 -5/7 -2/3 48/13 -2/3 37/10 -2/3 -19/29 26/7 -5/8 41/11 -5/8 -3/5 15/4 -2/3 64/17 -1/2 49/13 -2/3 -3/5 34/9 -3/4 19/5 -2/3 -7/11 23/6 -2/3 -1/2 4/1 -1/2 25/6 -1/2 0/1 21/5 -1/1 17/4 -1/2 0/1 13/3 -1/1 1/0 48/11 -1/1 35/8 -1/1 -4/5 22/5 -1/2 31/7 -1/1 -2/3 40/9 -1/2 9/2 0/1 23/5 -1/1 0/1 14/3 -3/2 47/10 -4/3 -1/1 80/17 -3/2 33/7 -1/1 19/4 -8/7 -1/1 24/5 -1/1 5/1 -1/1 -3/4 21/4 -2/3 16/3 -1/2 27/5 -1/1 11/2 -1/1 0/1 28/5 -1/2 17/3 0/1 1/1 40/7 1/0 23/4 -2/1 1/0 6/1 -1/1 25/4 -5/6 -4/5 19/3 -4/5 -7/9 13/2 -5/7 -2/3 33/5 -3/5 20/3 -1/2 47/7 -1/3 0/1 27/4 0/1 7/1 -1/1 -3/4 15/2 -2/3 23/3 -1/1 -2/3 8/1 -1/2 17/2 0/1 1/0 9/1 -1/1 10/1 -1/2 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(3,-2,-4,3) Matrix(47,432,26,239) -> Matrix(5,6,-6,-7) Matrix(49,432,-38,-335) -> Matrix(7,-8,-6,7) Matrix(145,1104,-44,-335) -> Matrix(3,8,-2,-5) Matrix(97,720,26,193) -> Matrix(1,4,-2,-7) Matrix(241,1632,-92,-623) -> Matrix(17,10,-12,-7) Matrix(95,624,-44,-289) -> Matrix(13,30,-10,-23) Matrix(97,624,30,193) -> Matrix(7,12,-10,-17) Matrix(145,912,-38,-239) -> Matrix(11,14,-4,-5) Matrix(191,1104,-50,-289) -> Matrix(7,4,-2,-1) Matrix(385,2208,268,1537) -> Matrix(33,20,-38,-23) Matrix(337,1920,76,433) -> Matrix(5,2,-8,-3) Matrix(95,528,-52,-289) -> Matrix(5,4,-4,-3) Matrix(239,1296,168,911) -> Matrix(7,8,-8,-9) Matrix(143,768,116,623) -> Matrix(7,8,-8,-9) Matrix(145,768,118,625) -> Matrix(7,22,-8,-25) Matrix(47,240,28,143) -> Matrix(7,8,-8,-9) Matrix(49,240,10,49) -> Matrix(5,6,-6,-7) Matrix(191,912,40,191) -> Matrix(17,16,-16,-15) Matrix(193,912,-142,-671) -> Matrix(71,58,-60,-49) Matrix(145,672,52,241) -> Matrix(13,8,-18,-11) Matrix(95,432,42,191) -> Matrix(11,4,-14,-5) Matrix(239,1056,-98,-433) -> Matrix(3,2,-2,-1) Matrix(241,1056,-186,-815) -> Matrix(23,38,-20,-33) Matrix(145,624,56,241) -> Matrix(11,4,-14,-5) Matrix(193,816,-136,-575) -> Matrix(7,6,-6,-5) Matrix(335,1296,-236,-913) -> Matrix(7,20,-6,-17) Matrix(241,912,-190,-719) -> Matrix(39,70,-34,-61) Matrix(335,1248,-142,-529) -> Matrix(5,14,-4,-11) Matrix(337,1248,-246,-911) -> Matrix(43,92,-36,-77) Matrix(145,528,-92,-335) -> Matrix(17,28,-14,-23) Matrix(241,864,94,337) -> Matrix(13,22,-16,-27) Matrix(95,336,54,191) -> Matrix(7,8,-8,-9) Matrix(97,336,28,97) -> Matrix(3,4,-4,-5) Matrix(239,816,70,239) -> Matrix(11,20,-16,-29) Matrix(241,816,-184,-623) -> Matrix(51,80,-44,-69) Matrix(385,1296,314,1057) -> Matrix(9,10,-10,-11) Matrix(671,2256,428,1439) -> Matrix(19,32,-22,-37) Matrix(143,480,14,47) -> Matrix(1,2,-4,-7) Matrix(289,960,-202,-671) -> Matrix(5,4,-4,-3) Matrix(479,1584,290,959) -> Matrix(7,8,-8,-9) Matrix(671,2208,554,1823) -> Matrix(9,10,-10,-11) Matrix(527,1728,190,623) -> Matrix(19,30,-26,-41) Matrix(383,1248,-236,-769) -> Matrix(3,2,-2,-1) Matrix(193,624,30,97) -> Matrix(7,12,-10,-17) Matrix(239,768,164,527) -> Matrix(75,116,-86,-133) Matrix(241,768,166,529) -> Matrix(65,94,-74,-107) Matrix(289,912,122,385) -> Matrix(17,24,-22,-31) Matrix(385,1104,-234,-671) -> Matrix(5,4,-4,-3) Matrix(337,960,152,433) -> Matrix(11,26,-14,-33) Matrix(239,672,-154,-433) -> Matrix(29,52,-24,-43) Matrix(241,672,52,145) -> Matrix(5,8,-2,-3) Matrix(623,1728,190,527) -> Matrix(19,30,-26,-41) Matrix(1249,3456,382,1057) -> Matrix(17,24,-22,-31) Matrix(817,2256,574,1585) -> Matrix(9,10,-10,-11) Matrix(193,528,-140,-383) -> Matrix(17,28,-14,-23) Matrix(143,384,-54,-145) -> Matrix(35,54,-24,-37) Matrix(911,2400,528,1391) -> Matrix(47,68,-56,-81) Matrix(3503,9216,-2208,-5809) -> Matrix(23,32,-18,-25) Matrix(1297,3408,384,1009) -> Matrix(17,24,-22,-31) Matrix(3937,10320,-2490,-6527) -> Matrix(191,272,-158,-225) Matrix(1871,4896,-1156,-3025) -> Matrix(33,46,-28,-39) Matrix(1249,3264,-918,-2399) -> Matrix(69,94,-58,-79) Matrix(479,1248,-332,-865) -> Matrix(33,46,-28,-39) Matrix(241,624,56,145) -> Matrix(3,4,2,3) Matrix(1487,3840,-874,-2257) -> Matrix(33,46,-28,-39) Matrix(2977,7680,-2344,-6047) -> Matrix(53,68,-46,-59) Matrix(671,1728,186,479) -> Matrix(19,26,-30,-41) Matrix(337,864,94,241) -> Matrix(17,22,-24,-31) Matrix(433,1104,-282,-719) -> Matrix(5,4,-4,-3) Matrix(623,1584,94,239) -> Matrix(7,10,-12,-17) Matrix(625,1584,436,1105) -> Matrix(9,10,-10,-11) Matrix(97,240,78,193) -> Matrix(11,12,-12,-13) Matrix(1057,2592,-900,-2207) -> Matrix(43,60,-38,-53) Matrix(1393,3408,-804,-1967) -> Matrix(5,4,-4,-3) Matrix(335,816,-296,-721) -> Matrix(29,48,-26,-43) Matrix(239,576,-100,-241) -> Matrix(1,0,0,1) Matrix(383,912,-202,-481) -> Matrix(3,2,-2,-1) Matrix(1009,2400,626,1489) -> Matrix(7,8,-8,-9) Matrix(385,912,122,289) -> Matrix(17,24,-22,-31) Matrix(527,1248,182,431) -> Matrix(7,10,-12,-17) Matrix(1441,3408,-852,-2015) -> Matrix(3,2,-2,-1) Matrix(143,336,20,47) -> Matrix(5,6,-6,-7) Matrix(145,336,104,241) -> Matrix(9,10,-10,-11) Matrix(335,768,188,431) -> Matrix(13,22,-16,-27) Matrix(337,768,190,433) -> Matrix(47,68,-56,-81) Matrix(191,432,42,95) -> Matrix(3,4,2,3) Matrix(193,432,172,385) -> Matrix(47,66,-52,-73) Matrix(1633,3648,-902,-2015) -> Matrix(23,32,-18,-25) Matrix(1249,2784,-904,-2015) -> Matrix(23,32,-18,-25) Matrix(239,528,-196,-433) -> Matrix(43,60,-38,-53) Matrix(241,528,110,241) -> Matrix(89,120,-112,-151) Matrix(287,624,132,287) -> Matrix(151,200,-188,-249) Matrix(625,1344,246,529) -> Matrix(31,40,-38,-49) Matrix(385,816,-226,-479) -> Matrix(39,50,-32,-41) Matrix(1247,2352,-764,-1441) -> Matrix(1,2,-2,-3) Matrix(335,624,-284,-529) -> Matrix(77,94,-68,-83) Matrix(337,624,182,337) -> Matrix(13,14,-14,-15) Matrix(287,528,156,287) -> Matrix(7,8,-8,-9) Matrix(527,960,342,623) -> Matrix(45,58,-52,-67) Matrix(1297,2352,-820,-1487) -> Matrix(61,72,-50,-59) Matrix(5087,9216,2278,4127) -> Matrix(45,52,-58,-67) Matrix(5089,9216,2280,4129) -> Matrix(17,24,-22,-31) Matrix(239,432,26,47) -> Matrix(5,6,-6,-7) Matrix(241,432,188,337) -> Matrix(37,52,-42,-59) Matrix(431,768,188,335) -> Matrix(17,22,-24,-31) Matrix(433,768,190,337) -> Matrix(55,68,-72,-89) Matrix(191,336,54,95) -> Matrix(7,8,-8,-9) Matrix(719,1248,-526,-913) -> Matrix(119,144,-100,-121) Matrix(11473,19872,4684,8113) -> Matrix(19,20,-20,-21) Matrix(11807,20448,4822,8351) -> Matrix(5,4,-4,-3) Matrix(2689,4656,1054,1825) -> Matrix(5,6,-6,-7) Matrix(527,912,360,623) -> Matrix(45,58,-52,-67) Matrix(335,576,-196,-337) -> Matrix(1,0,0,1) Matrix(1295,2208,478,815) -> Matrix(17,22,-24,-31) Matrix(4511,7680,958,1631) -> Matrix(1,2,-2,-3) Matrix(623,1056,-482,-817) -> Matrix(83,98,-72,-85) Matrix(12097,20448,5112,8641) -> Matrix(111,134,-140,-169) Matrix(11759,19872,4970,8399) -> Matrix(89,106,-110,-131) Matrix(4177,7056,-2642,-4463) -> Matrix(121,144,-100,-119) Matrix(143,240,28,47) -> Matrix(7,8,-8,-9) Matrix(959,1584,290,479) -> Matrix(7,8,-8,-9) Matrix(815,1344,436,719) -> Matrix(11,12,-12,-13) Matrix(2831,4656,1196,1967) -> Matrix(31,38,-40,-49) Matrix(527,864,380,623) -> Matrix(13,14,-14,-15) Matrix(1439,2352,528,863) -> Matrix(7,12,-10,-17) Matrix(4321,7056,-3174,-5183) -> Matrix(7,20,-6,-17) Matrix(5087,8304,1352,2207) -> Matrix(7,10,-12,-17) Matrix(383,624,294,479) -> Matrix(67,82,-76,-93) Matrix(2783,4512,1006,1631) -> Matrix(31,38,-40,-49) Matrix(1393,2256,-1096,-1775) -> Matrix(163,194,-142,-169) Matrix(12815,20736,4894,7919) -> Matrix(101,108,-130,-139) Matrix(12817,20736,4896,7921) -> Matrix(25,18,-32,-23) Matrix(1009,1632,-860,-1391) -> Matrix(43,60,-38,-53) Matrix(239,384,-150,-241) -> Matrix(39,50,-32,-41) Matrix(1391,2208,332,527) -> Matrix(5,6,4,5) Matrix(23231,36864,8590,13631) -> Matrix(177,214,-244,-295) Matrix(23233,36864,8592,13633) -> Matrix(63,74,-86,-101) Matrix(1393,2208,576,913) -> Matrix(31,38,-40,-49) Matrix(1489,2352,578,913) -> Matrix(111,134,-140,-169) Matrix(1439,2256,428,671) -> Matrix(27,32,-38,-45) Matrix(2881,4512,1104,1729) -> Matrix(31,38,-40,-49) Matrix(1105,1728,768,1201) -> Matrix(11,12,-12,-13) Matrix(431,672,338,527) -> Matrix(147,178,-166,-201) Matrix(1487,2304,526,815) -> Matrix(93,112,-142,-171) Matrix(1489,2304,528,817) -> Matrix(127,152,-188,-225) Matrix(529,816,94,145) -> Matrix(5,6,-16,-19) Matrix(817,1248,472,721) -> Matrix(9,10,-10,-11) Matrix(623,912,360,527) -> Matrix(49,58,-60,-71) Matrix(527,768,164,239) -> Matrix(99,116,-134,-157) Matrix(529,768,166,241) -> Matrix(81,94,-106,-123) Matrix(431,624,364,527) -> Matrix(127,144,-142,-161) Matrix(2399,3456,1532,2207) -> Matrix(11,12,-12,-13) Matrix(1201,1728,768,1105) -> Matrix(11,12,-12,-13) Matrix(769,1104,-668,-959) -> Matrix(219,254,-194,-225) Matrix(1105,1584,436,625) -> Matrix(9,10,-10,-11) Matrix(6431,9216,1942,2783) -> Matrix(27,32,-38,-45) Matrix(6433,9216,1944,2785) -> Matrix(9,10,-10,-11) Matrix(337,480,304,433) -> Matrix(15,16,-16,-17) Matrix(1585,2256,574,817) -> Matrix(9,10,-10,-11) Matrix(911,1296,168,239) -> Matrix(7,8,-8,-9) Matrix(2399,3408,1486,2111) -> Matrix(9,10,-10,-11) Matrix(577,816,408,577) -> Matrix(71,84,-82,-97) Matrix(239,336,170,239) -> Matrix(13,14,-14,-15) Matrix(241,336,104,145) -> Matrix(9,10,-10,-11) Matrix(623,864,380,527) -> Matrix(13,14,-14,-15) Matrix(1249,1728,764,1057) -> Matrix(7,8,-8,-9) Matrix(3265,4512,-2778,-3839) -> Matrix(9,26,-8,-23) Matrix(1679,2304,454,623) -> Matrix(113,136,-172,-207) Matrix(1681,2304,456,625) -> Matrix(127,152,-188,-225) Matrix(527,720,456,623) -> Matrix(461,548,-514,-611) Matrix(6097,8304,2362,3217) -> Matrix(9,10,-10,-11) Matrix(673,912,-566,-767) -> Matrix(649,764,-570,-671) Matrix(143,192,-108,-145) -> Matrix(251,294,-216,-253) Matrix(1681,2208,622,817) -> Matrix(9,10,-10,-11) Matrix(479,624,294,383) -> Matrix(71,82,-84,-97) Matrix(1775,2304,406,527) -> Matrix(71,82,-84,-97) Matrix(1777,2304,408,529) -> Matrix(59,68,-46,-53) Matrix(1487,1920,1226,1583) -> Matrix(97,112,-110,-127) Matrix(337,432,188,241) -> Matrix(45,52,-58,-67) Matrix(527,672,338,431) -> Matrix(155,178,-182,-209) Matrix(6049,7680,2496,3169) -> Matrix(157,180,-198,-227) Matrix(721,912,570,721) -> Matrix(881,1008,-992,-1135) Matrix(191,240,152,191) -> Matrix(127,144,-142,-161) Matrix(193,240,78,97) -> Matrix(11,12,-12,-13) Matrix(623,768,116,143) -> Matrix(7,8,-8,-9) Matrix(625,768,118,145) -> Matrix(19,22,-32,-37) Matrix(1057,1296,314,385) -> Matrix(9,10,-10,-11) Matrix(671,816,236,287) -> Matrix(19,22,-32,-37) Matrix(673,816,80,97) -> Matrix(7,8,-8,-9) Matrix(911,1104,118,143) -> Matrix(19,22,-32,-37) Matrix(239,288,-200,-241) -> Matrix(335,384,-294,-337) Matrix(527,624,364,431) -> Matrix(127,144,-142,-161) Matrix(1345,1584,816,961) -> Matrix(97,110,-112,-127) Matrix(289,336,166,193) -> Matrix(67,76,-82,-93) Matrix(961,1104,168,193) -> Matrix(55,62,-8,-9) Matrix(719,816,126,143) -> Matrix(25,28,8,9) Matrix(385,432,172,193) -> Matrix(59,66,-76,-85) Matrix(433,480,304,337) -> Matrix(15,16,-16,-17) Matrix(1,0,2,1) -> Matrix(19,20,-20,-21) Matrix(383,-432,86,-97) -> Matrix(11,10,-32,-29) Matrix(959,-1104,668,-769) -> Matrix(283,254,-322,-289) Matrix(1391,-1632,860,-1009) -> Matrix(67,60,-86,-77) Matrix(529,-624,284,-335) -> Matrix(105,94,-124,-111) Matrix(767,-912,566,-673) -> Matrix(857,764,-986,-879) Matrix(913,-1104,674,-815) -> Matrix(223,196,-256,-225) Matrix(433,-528,196,-239) -> Matrix(67,60,-86,-77) Matrix(719,-912,190,-241) -> Matrix(79,70,-114,-101) Matrix(817,-1056,482,-623) -> Matrix(111,98,-128,-113) Matrix(815,-1056,186,-241) -> Matrix(43,38,-60,-53) Matrix(623,-816,184,-241) -> Matrix(91,80,-124,-109) Matrix(961,-1296,284,-383) -> Matrix(53,46,-68,-59) Matrix(671,-912,142,-193) -> Matrix(67,58,-52,-45) Matrix(913,-1248,526,-719) -> Matrix(167,144,-196,-169) Matrix(911,-1248,246,-337) -> Matrix(107,92,-164,-141) Matrix(383,-528,140,-193) -> Matrix(33,28,-46,-39) Matrix(575,-816,136,-193) -> Matrix(7,6,-6,-5) Matrix(671,-960,202,-289) -> Matrix(5,4,-4,-3) Matrix(865,-1248,332,-479) -> Matrix(53,46,-68,-59) Matrix(719,-1104,282,-433) -> Matrix(5,4,-4,-3) Matrix(433,-672,154,-239) -> Matrix(61,52,-88,-75) Matrix(335,-528,92,-145) -> Matrix(33,28,-46,-39) Matrix(241,-384,150,-239) -> Matrix(59,50,-72,-61) Matrix(5713,-9216,2112,-3407) -> Matrix(33,28,-46,-39) Matrix(6383,-10320,2346,-3793) -> Matrix(43,38,-60,-53) Matrix(3025,-4896,1156,-1871) -> Matrix(53,46,-68,-59) Matrix(2015,-3264,534,-865) -> Matrix(5,4,-4,-3) Matrix(769,-1248,236,-383) -> Matrix(3,2,-2,-1) Matrix(2353,-3840,970,-1583) -> Matrix(1,0,0,1) Matrix(4703,-7680,1000,-1633) -> Matrix(7,6,-6,-5) Matrix(671,-1104,234,-385) -> Matrix(5,4,-4,-3) Matrix(1535,-2592,228,-385) -> Matrix(7,6,-6,-5) Matrix(2015,-3408,852,-1441) -> Matrix(3,2,-2,-1) Matrix(481,-816,56,-95) -> Matrix(7,6,-6,-5) Matrix(337,-576,196,-335) -> Matrix(1,0,0,1) Matrix(529,-912,250,-431) -> Matrix(59,50,-72,-61) Matrix(1967,-3408,804,-1393) -> Matrix(5,4,-4,-3) Matrix(2015,-3648,902,-1633) -> Matrix(39,32,-50,-41) Matrix(1535,-2784,424,-769) -> Matrix(5,4,-4,-3) Matrix(289,-528,52,-95) -> Matrix(5,4,-4,-3) Matrix(431,-816,178,-337) -> Matrix(3,2,-2,-1) Matrix(1105,-2352,428,-911) -> Matrix(79,64,-100,-81) Matrix(289,-624,44,-95) -> Matrix(37,30,-58,-47) Matrix(1055,-2352,388,-865) -> Matrix(47,36,-64,-49) Matrix(529,-1248,142,-335) -> Matrix(17,14,-28,-23) Matrix(241,-576,100,-239) -> Matrix(1,0,0,1) Matrix(433,-1056,98,-239) -> Matrix(3,2,-2,-1) Matrix(2879,-7056,1058,-2593) -> Matrix(43,38,-60,-53) Matrix(2735,-7056,726,-1873) -> Matrix(23,18,-32,-25) Matrix(863,-2256,184,-481) -> Matrix(31,24,-22,-17) Matrix(623,-1632,92,-241) -> Matrix(13,10,-4,-3) Matrix(145,-384,54,-143) -> Matrix(71,54,-96,-73) Matrix(335,-1104,44,-145) -> Matrix(11,8,-18,-13) Matrix(1247,-4512,186,-673) -> Matrix(3,2,-8,-5) Matrix(239,-912,38,-145) -> Matrix(23,14,-28,-17) Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) Matrix(49,-288,8,-47) -> Matrix(5,6,-6,-7) 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): 72 Degree of the the map X: 72 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 -16/3 -21/4 -4/1 -18/5 -16/5 -3/1 -8/3 -8/5 -3/2 -4/3 0/1 1/1 24/19 4/3 24/17 3/2 36/23 8/5 12/7 24/13 2/1 12/5 8/3 3/1 16/5 36/11 10/3 24/7 7/2 18/5 48/13 15/4 4/1 13/3 48/11 22/5 14/3 24/5 5/1 11/2 17/3 6/1 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 -6/1 -1/1 -17/3 -1/3 0/1 -11/2 -1/1 0/1 -27/5 -1/1 -16/3 1/0 -21/4 -2/1 -5/1 -3/2 -1/1 -24/5 -1/1 -19/4 -1/1 -8/9 -14/3 -3/4 -9/2 0/1 -22/5 1/0 -13/3 -1/1 -1/2 -17/4 0/1 1/0 -4/1 1/0 -19/5 -7/3 -2/1 -15/4 -2/1 -26/7 -5/2 -11/3 -2/1 -5/3 -18/5 -2/1 -7/2 -2/1 -1/1 -24/7 -2/1 -17/5 -2/1 -5/3 -27/8 -2/1 -37/11 -2/1 -5/3 -10/3 -3/2 -23/7 -2/1 -5/3 -36/11 -3/2 -13/4 -2/1 -1/1 -16/5 -3/2 -19/6 -7/5 -4/3 -3/1 -1/1 -14/5 -7/4 -11/4 -2/1 -1/1 -19/7 -5/3 -8/5 -8/3 -3/2 -21/8 -10/7 -13/5 -3/2 -7/5 -18/7 -4/3 -5/2 -3/2 -4/3 -2/1 -5/4 -15/8 -6/5 -13/7 -7/6 -1/1 -24/13 -1/1 -11/6 -4/3 -1/1 -20/11 -5/4 -9/5 -1/1 -16/9 -5/4 -7/4 -6/5 -1/1 -12/7 -5/4 -7/6 -5/3 -5/4 -1/1 -18/11 -1/1 -31/19 -4/3 -1/1 -13/8 -4/3 -1/1 -34/21 -7/6 -21/13 -1/1 -8/5 -5/4 -27/17 -11/9 -46/29 -5/4 -19/12 -11/9 -6/5 -30/19 -6/5 -11/7 -6/5 -1/1 -36/23 -5/4 -7/6 -25/16 -5/4 -6/5 -14/9 -5/4 -17/11 -6/5 -25/21 -3/2 -6/5 -16/11 -7/6 -29/20 -22/19 -15/13 -13/9 -7/6 -1/1 -10/7 -7/6 -27/19 -1/1 -44/31 -7/6 -17/12 -6/5 -7/6 -24/17 -7/6 -7/5 -7/6 -1/1 -18/13 -1/1 -11/8 -11/9 -6/5 -48/35 -6/5 -37/27 -6/5 -61/51 -26/19 -31/26 -15/11 -13/11 -19/14 -13/11 -46/39 -4/3 -7/6 -17/13 -22/19 -15/13 -13/10 -22/19 -15/13 -48/37 -15/13 -35/27 -15/13 -53/46 -22/17 -23/20 -9/7 -15/13 -14/11 -23/20 -19/15 -63/55 -8/7 -24/19 -8/7 -5/4 -8/7 -9/8 -6/5 -8/7 -13/11 -25/22 -17/15 -7/6 -17/15 -26/23 -8/7 -9/8 -1/1 -10/9 -1/1 0/1 -1/1 1/1 -1/1 -10/11 8/7 -9/10 15/13 -35/39 7/6 -26/29 -17/19 20/17 -25/28 13/11 -17/19 -25/28 19/16 -58/65 -33/37 6/5 -8/9 11/9 -8/9 -15/17 27/22 -8/9 16/13 -7/8 21/17 -1/1 5/4 -9/10 -8/9 24/19 -8/9 19/15 -8/9 -63/71 14/11 -23/26 23/18 -8/9 -23/26 9/7 -15/17 22/17 -23/26 13/10 -15/17 -22/25 17/13 -15/17 -22/25 4/3 -7/8 23/17 -20/23 -13/15 19/14 -46/53 -13/15 15/11 -13/15 26/19 -31/36 11/8 -6/7 -11/13 18/13 -1/1 7/5 -1/1 -7/8 24/17 -7/8 17/12 -7/8 -6/7 27/19 -1/1 37/26 -1/1 -8/9 10/7 -7/8 23/16 -7/8 -6/7 36/25 -7/8 -5/6 13/9 -1/1 -7/8 29/20 -15/17 -22/25 16/11 -7/8 19/13 -20/23 -13/15 3/2 -6/7 17/11 -25/29 -6/7 14/9 -5/6 25/16 -6/7 -5/6 36/23 -7/8 -5/6 47/30 -1/1 -6/7 11/7 -1/1 -6/7 19/12 -6/7 -11/13 8/5 -5/6 29/18 -1/1 -4/5 50/31 -5/6 21/13 -1/1 55/34 -1/1 -2/3 34/21 -7/8 47/29 -6/7 -11/13 13/8 -1/1 -4/5 31/19 -1/1 -4/5 18/11 -1/1 23/14 -7/8 -6/7 5/3 -1/1 -5/6 27/16 -6/7 22/13 -5/6 39/23 -1/1 17/10 -6/7 -5/6 12/7 -7/8 -5/6 19/11 -1/1 -6/7 45/26 -4/5 26/15 -7/8 33/19 -11/13 7/4 -1/1 -6/7 16/9 -5/6 9/5 -1/1 29/16 -1/1 -6/7 20/11 -5/6 11/6 -1/1 -4/5 24/13 -1/1 13/7 -1/1 -7/8 28/15 -7/8 15/8 -6/7 2/1 -5/6 7/3 -1/1 -3/4 26/11 -3/4 45/19 -7/9 19/8 -1/1 -4/5 12/5 -5/6 -3/4 29/12 -1/1 -4/5 46/19 -3/4 17/7 -1/1 -4/5 22/9 -3/4 27/11 -1/1 5/2 -4/5 -3/4 18/7 -4/5 31/12 -4/5 -11/14 13/5 -7/9 -3/4 34/13 -3/4 21/8 -10/13 8/3 -3/4 19/7 -8/11 -5/7 30/11 -5/7 11/4 -1/1 -2/3 36/13 -3/4 25/9 -8/11 -5/7 14/5 -7/10 3/1 -1/1 19/6 -4/5 -7/9 16/5 -3/4 13/4 -1/1 -2/3 49/15 -4/5 -7/9 36/11 -3/4 23/7 -5/7 -2/3 33/10 -2/3 10/3 -3/4 47/14 -5/7 -2/3 37/11 -5/7 -2/3 27/8 -2/3 44/13 -3/4 17/5 -5/7 -2/3 24/7 -2/3 7/2 -1/1 -2/3 25/7 -8/11 -5/7 18/5 -2/3 29/8 -1/1 -2/3 11/3 -5/7 -2/3 48/13 -2/3 37/10 -2/3 -19/29 26/7 -5/8 41/11 -5/8 -3/5 15/4 -2/3 34/9 -3/4 19/5 -2/3 -7/11 23/6 -2/3 -1/2 4/1 -1/2 25/6 -1/2 0/1 21/5 -1/1 17/4 -1/2 0/1 13/3 -1/1 1/0 48/11 -1/1 35/8 -1/1 -4/5 22/5 -1/2 31/7 -1/1 -2/3 9/2 0/1 14/3 -3/2 19/4 -8/7 -1/1 24/5 -1/1 5/1 -1/1 -3/4 21/4 -2/3 16/3 -1/2 27/5 -1/1 11/2 -1/1 0/1 28/5 -1/2 17/3 0/1 1/1 23/4 -2/1 1/0 6/1 -1/1 7/1 -1/1 -3/4 15/2 -2/3 8/1 -1/2 9/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,72,9,59) (-6/1,1/0) -> (6/5,11/9) Hyperbolic Matrix(37,216,31,181) (-6/1,-17/3) -> (19/16,6/5) Hyperbolic Matrix(107,600,79,443) (-17/3,-11/2) -> (23/17,19/14) 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(107,504,-69,-325) (-19/4,-14/3) -> (-14/9,-17/11) Hyperbolic Matrix(37,168,-13,-59) (-14/3,-9/2) -> (-3/1,-14/5) Hyperbolic Matrix(277,1224,117,517) (-9/2,-22/5) -> (26/11,45/19) 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(107,408,91,347) (-4/1,-19/5) -> (7/6,20/17) Hyperbolic Matrix(325,1224,201,757) (-19/5,-15/4) -> (21/13,55/34) Hyperbolic Matrix(277,1032,113,421) (-15/4,-26/7) -> (22/9,27/11) 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(155,552,57,203) (-18/5,-7/2) -> (19/7,30/11) 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(277,936,153,517) (-17/5,-27/8) -> (9/5,29/16) Hyperbolic Matrix(385,1296,314,1057) (-27/8,-37/11) -> (11/9,27/22) Hyperbolic Matrix(251,840,75,251) (-37/11,-10/3) -> (10/3,47/14) Hyperbolic Matrix(181,600,127,421) (-10/3,-23/7) -> (37/26,10/7) Hyperbolic Matrix(527,1728,190,623) (-23/7,-36/11) -> (36/13,25/9) Hyperbolic Matrix(683,2232,209,683) (-36/11,-13/4) -> (49/15,36/11) Hyperbolic Matrix(37,120,-33,-107) (-13/4,-16/5) -> (-8/7,-1/1) 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(181,504,65,181) (-14/5,-11/4) -> (25/9,14/5) Hyperbolic Matrix(203,552,57,155) (-11/4,-19/7) -> (7/2,25/7) Hyperbolic Matrix(133,360,-75,-203) (-19/7,-8/3) -> (-16/9,-7/4) Hyperbolic Matrix(155,408,-87,-229) (-8/3,-21/8) -> (-9/5,-16/9) Hyperbolic Matrix(229,600,179,469) (-21/8,-13/5) -> (23/18,9/7) Hyperbolic Matrix(251,648,153,395) (-13/5,-18/7) -> (18/11,23/14) Hyperbolic Matrix(85,216,-61,-155) (-18/7,-5/2) -> (-7/5,-18/13) Hyperbolic Matrix(11,24,5,11) (-5/2,-2/1) -> (2/1,7/3) Hyperbolic Matrix(395,744,-249,-469) (-2/1,-15/8) -> (-27/17,-46/29) Hyperbolic Matrix(347,648,83,155) (-15/8,-13/7) -> (25/6,21/5) 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(277,504,205,373) (-11/6,-20/11) -> (4/3,23/17) Hyperbolic Matrix(517,936,153,277) (-20/11,-9/5) -> (27/8,44/13) Hyperbolic Matrix(181,312,105,181) (-7/4,-12/7) -> (12/7,19/11) Hyperbolic Matrix(155,264,91,155) (-12/7,-5/3) -> (17/10,12/7) Hyperbolic Matrix(395,648,153,251) (-5/3,-18/11) -> (18/7,31/12) Hyperbolic Matrix(779,1272,-493,-805) (-18/11,-31/19) -> (-19/12,-30/19) Hyperbolic Matrix(383,624,294,479) (-31/19,-13/8) -> (13/10,17/13) Hyperbolic Matrix(1259,2040,777,1259) (-13/8,-34/21) -> (34/21,47/29) Hyperbolic Matrix(757,1224,201,325) (-34/21,-21/13) -> (15/4,34/9) Hyperbolic Matrix(239,384,-150,-241) (-21/13,-8/5) -> (-8/5,-27/17) Parabolic Matrix(1393,2208,576,913) (-46/29,-19/12) -> (29/12,46/19) Hyperbolic Matrix(1333,2088,851,1333) (-11/7,-36/23) -> (36/23,47/30) 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(203,312,-149,-229) (-17/11,-3/2) -> (-15/11,-19/14) Hyperbolic Matrix(181,264,157,229) (-3/2,-16/11) -> (8/7,15/13) 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(251,360,175,251) (-13/9,-10/7) -> (10/7,23/16) Hyperbolic Matrix(421,600,127,181) (-10/7,-27/19) -> (33/10,10/3) Hyperbolic Matrix(997,1416,533,757) (-27/19,-44/31) -> (28/15,15/8) 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(469,648,131,181) (-18/13,-11/8) -> (25/7,18/5) 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(1141,1560,659,901) (-26/19,-15/11) -> (45/26,26/15) Hyperbolic Matrix(443,600,79,107) (-19/14,-4/3) -> (28/5,17/3) Hyperbolic Matrix(347,456,191,251) (-4/3,-17/13) -> (29/16,20/11) 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(613,792,363,469) (-22/17,-9/7) -> (27/16,22/13) Hyperbolic Matrix(469,600,179,229) (-9/7,-14/11) -> (34/13,21/8) Hyperbolic Matrix(1115,1416,689,875) (-14/11,-19/15) -> (55/34,34/21) 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(59,72,9,11) (-5/4,-6/5) -> (6/1,7/1) Hyperbolic Matrix(181,216,31,37) (-6/5,-13/11) -> (23/4,6/1) Hyperbolic Matrix(347,408,91,107) (-13/11,-7/6) -> (19/5,23/6) Hyperbolic Matrix(229,264,157,181) (-7/6,-8/7) -> (16/11,19/13) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(107,-120,33,-37) (1/1,8/7) -> (16/5,13/4) Hyperbolic Matrix(517,-600,299,-347) (15/13,7/6) -> (19/11,45/26) Hyperbolic Matrix(529,-624,284,-335) (20/17,13/11) -> (13/7,28/15) Hyperbolic Matrix(757,-936,203,-251) (21/17,5/4) -> (41/11,15/4) 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(229,-312,149,-203) (19/14,15/11) -> (3/2,17/11) 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(155,-216,61,-85) (18/13,7/5) -> (5/2,18/7) Hyperbolic Matrix(575,-816,136,-193) (17/12,27/19) -> (21/5,17/4) Hyperbolic Matrix(949,-1368,607,-875) (36/25,13/9) -> (25/16,36/23) Hyperbolic Matrix(613,-888,107,-155) (13/9,29/20) -> (17/3,23/4) Hyperbolic Matrix(443,-648,255,-373) (19/13,3/2) -> (33/19,7/4) Hyperbolic Matrix(325,-504,69,-107) (17/11,14/9) -> (14/3,19/4) Hyperbolic Matrix(661,-1032,253,-395) (14/9,25/16) -> (13/5,34/13) Hyperbolic Matrix(1669,-2616,497,-779) (47/30,11/7) -> (47/14,37/11) 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(1355,-2184,559,-901) (29/18,50/31) -> (46/19,17/7) Hyperbolic Matrix(491,-792,261,-421) (50/31,21/13) -> (15/8,2/1) Hyperbolic Matrix(769,-1248,236,-383) (47/29,13/8) -> (13/4,49/15) Hyperbolic Matrix(661,-1080,183,-299) (31/19,18/11) -> (18/5,29/8) Hyperbolic Matrix(277,-456,65,-107) (23/14,5/3) -> (17/4,13/3) Hyperbolic Matrix(325,-552,63,-107) (39/23,17/10) -> (5/1,21/4) Hyperbolic Matrix(203,-360,75,-133) (7/4,16/9) -> (8/3,19/7) Hyperbolic Matrix(229,-408,87,-155) (16/9,9/5) -> (21/8,8/3) Hyperbolic Matrix(289,-528,52,-95) (20/11,11/6) -> (11/2,28/5) 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(107,-264,15,-37) (27/11,5/2) -> (7/1,15/2) Hyperbolic Matrix(443,-1224,135,-373) (11/4,36/13) -> (36/11,23/7) Hyperbolic Matrix(59,-168,13,-37) (14/5,3/1) -> (9/2,14/3) Hyperbolic Matrix(85,-264,19,-59) (3/1,19/6) -> (31/7,9/2) Hyperbolic Matrix(299,-984,55,-181) (23/7,33/10) -> (27/5,11/2) Hyperbolic Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) Hyperbolic Matrix(49,-192,12,-47) (23/6,4/1) -> (4/1,25/6) Parabolic Matrix(59,-312,7,-37) (21/4,16/3) -> (8/1,9/1) Hyperbolic Matrix(85,-456,11,-59) (16/3,27/5) -> (15/2,8/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(11,72,9,59) -> Matrix(7,15,-8,-17) Matrix(37,216,31,181) -> Matrix(41,33,-46,-37) Matrix(107,600,79,443) -> Matrix(7,-13,-8,15) Matrix(239,1296,168,911) -> Matrix(7,8,-8,-9) Matrix(143,768,116,623) -> Matrix(7,8,-8,-9) Matrix(145,768,118,625) -> Matrix(7,22,-8,-25) Matrix(47,240,28,143) -> Matrix(7,8,-8,-9) Matrix(49,240,10,49) -> Matrix(5,6,-6,-7) Matrix(191,912,40,191) -> Matrix(17,16,-16,-15) Matrix(107,504,-69,-325) -> Matrix(29,23,-24,-19) Matrix(37,168,-13,-59) -> Matrix(1,-1,0,1) Matrix(277,1224,117,517) -> Matrix(3,7,-4,-9) Matrix(241,1056,-186,-815) -> Matrix(23,38,-20,-33) Matrix(145,624,56,241) -> Matrix(11,4,-14,-5) Matrix(193,816,-136,-575) -> Matrix(7,6,-6,-5) Matrix(107,408,91,347) -> Matrix(25,67,-28,-75) Matrix(325,1224,201,757) -> Matrix(5,11,-6,-13) Matrix(277,1032,113,421) -> Matrix(5,11,-6,-13) Matrix(337,1248,-246,-911) -> Matrix(43,92,-36,-77) Matrix(145,528,-92,-335) -> Matrix(17,28,-14,-23) Matrix(155,552,57,203) -> Matrix(13,21,-18,-29) Matrix(97,336,28,97) -> Matrix(3,4,-4,-5) Matrix(239,816,70,239) -> Matrix(11,20,-16,-29) Matrix(277,936,153,517) -> Matrix(3,7,-4,-9) Matrix(385,1296,314,1057) -> Matrix(9,10,-10,-11) Matrix(251,840,75,251) -> Matrix(13,21,-18,-29) Matrix(181,600,127,421) -> Matrix(5,11,-6,-13) Matrix(527,1728,190,623) -> Matrix(19,30,-26,-41) Matrix(683,2232,209,683) -> Matrix(11,15,-14,-19) Matrix(37,120,-33,-107) -> Matrix(11,21,-10,-19) Matrix(241,768,166,529) -> Matrix(65,94,-74,-107) Matrix(289,912,122,385) -> Matrix(17,24,-22,-31) Matrix(181,504,65,181) -> Matrix(13,21,-18,-29) Matrix(203,552,57,155) -> Matrix(13,21,-18,-29) Matrix(133,360,-75,-203) -> Matrix(27,43,-22,-35) Matrix(155,408,-87,-229) -> Matrix(33,47,-26,-37) Matrix(229,600,179,469) -> Matrix(131,185,-148,-209) Matrix(251,648,153,395) -> Matrix(23,31,-26,-35) Matrix(85,216,-61,-155) -> Matrix(19,25,-16,-21) Matrix(11,24,5,11) -> Matrix(11,15,-14,-19) Matrix(395,744,-249,-469) -> Matrix(19,25,-16,-21) Matrix(347,648,83,155) -> Matrix(1,1,4,5) Matrix(337,624,182,337) -> Matrix(13,14,-14,-15) Matrix(287,528,156,287) -> Matrix(7,8,-8,-9) Matrix(277,504,205,373) -> Matrix(73,93,-84,-107) Matrix(517,936,153,277) -> Matrix(5,7,-8,-11) Matrix(181,312,105,181) -> Matrix(29,35,-34,-41) Matrix(155,264,91,155) -> Matrix(29,35,-34,-41) Matrix(395,648,153,251) -> Matrix(27,31,-34,-39) Matrix(779,1272,-493,-805) -> Matrix(7,13,-6,-11) Matrix(383,624,294,479) -> Matrix(67,82,-76,-93) Matrix(1259,2040,777,1259) -> Matrix(29,35,-34,-41) Matrix(757,1224,201,325) -> Matrix(9,11,-14,-17) Matrix(239,384,-150,-241) -> Matrix(39,50,-32,-41) Matrix(1393,2208,576,913) -> Matrix(31,38,-40,-49) Matrix(1333,2088,851,1333) -> Matrix(29,35,-34,-41) Matrix(1105,1728,768,1201) -> Matrix(11,12,-12,-13) Matrix(431,672,338,527) -> Matrix(147,178,-166,-201) Matrix(203,312,-149,-229) -> Matrix(43,49,-36,-41) Matrix(181,264,157,229) -> Matrix(255,299,-284,-333) Matrix(529,768,166,241) -> Matrix(81,94,-106,-123) Matrix(431,624,364,527) -> Matrix(127,144,-142,-161) Matrix(251,360,175,251) -> Matrix(29,35,-34,-41) Matrix(421,600,127,181) -> Matrix(9,11,-14,-17) Matrix(997,1416,533,757) -> Matrix(29,35,-34,-41) Matrix(577,816,408,577) -> Matrix(71,84,-82,-97) Matrix(239,336,170,239) -> Matrix(13,14,-14,-15) Matrix(469,648,131,181) -> Matrix(5,7,-8,-11) Matrix(1679,2304,454,623) -> Matrix(113,136,-172,-207) Matrix(1681,2304,456,625) -> Matrix(127,152,-188,-225) Matrix(1141,1560,659,901) -> Matrix(9,11,-14,-17) Matrix(443,600,79,107) -> Matrix(11,13,-28,-33) Matrix(347,456,191,251) -> Matrix(101,117,-120,-139) Matrix(479,624,294,383) -> Matrix(71,82,-84,-97) Matrix(1775,2304,406,527) -> Matrix(71,82,-84,-97) Matrix(1777,2304,408,529) -> Matrix(59,68,-46,-53) Matrix(613,792,363,469) -> Matrix(55,63,-62,-71) Matrix(469,600,179,229) -> Matrix(161,185,-208,-239) Matrix(1115,1416,689,875) -> Matrix(69,79,-76,-87) Matrix(721,912,570,721) -> Matrix(881,1008,-992,-1135) Matrix(191,240,152,191) -> Matrix(127,144,-142,-161) Matrix(59,72,9,11) -> Matrix(13,15,-20,-23) Matrix(181,216,31,37) -> Matrix(29,33,-22,-25) Matrix(347,408,91,107) -> Matrix(59,67,-96,-109) Matrix(229,264,157,181) -> Matrix(265,299,-304,-343) Matrix(1,0,2,1) -> Matrix(19,20,-20,-21) Matrix(107,-120,33,-37) -> Matrix(23,21,-34,-31) Matrix(517,-600,299,-347) -> Matrix(155,139,-184,-165) Matrix(529,-624,284,-335) -> Matrix(105,94,-124,-111) Matrix(757,-936,203,-251) -> Matrix(15,13,-22,-19) Matrix(719,-912,190,-241) -> Matrix(79,70,-114,-101) Matrix(817,-1056,482,-623) -> Matrix(111,98,-128,-113) Matrix(815,-1056,186,-241) -> Matrix(43,38,-60,-53) Matrix(623,-816,184,-241) -> Matrix(91,80,-124,-109) Matrix(229,-312,149,-203) -> Matrix(57,49,-64,-55) Matrix(913,-1248,526,-719) -> Matrix(167,144,-196,-169) Matrix(911,-1248,246,-337) -> Matrix(107,92,-164,-141) Matrix(383,-528,140,-193) -> Matrix(33,28,-46,-39) Matrix(155,-216,61,-85) -> Matrix(29,25,-36,-31) Matrix(575,-816,136,-193) -> Matrix(7,6,-6,-5) Matrix(949,-1368,607,-875) -> Matrix(43,37,-50,-43) Matrix(613,-888,107,-155) -> Matrix(17,15,-8,-7) Matrix(443,-648,255,-373) -> Matrix(123,107,-146,-127) Matrix(325,-504,69,-107) -> Matrix(27,23,-20,-17) Matrix(661,-1032,253,-395) -> Matrix(21,17,-26,-21) Matrix(1669,-2616,497,-779) -> Matrix(19,17,-28,-25) Matrix(335,-528,92,-145) -> Matrix(33,28,-46,-39) Matrix(241,-384,150,-239) -> Matrix(59,50,-72,-61) Matrix(1355,-2184,559,-901) -> Matrix(21,17,-26,-21) Matrix(491,-792,261,-421) -> Matrix(31,25,-36,-29) Matrix(769,-1248,236,-383) -> Matrix(3,2,-2,-1) Matrix(661,-1080,183,-299) -> Matrix(11,9,-16,-13) Matrix(277,-456,65,-107) -> Matrix(1,1,-8,-7) Matrix(325,-552,63,-107) -> Matrix(15,13,-22,-19) Matrix(203,-360,75,-133) -> Matrix(51,43,-70,-59) Matrix(229,-408,87,-155) -> Matrix(57,47,-74,-61) Matrix(289,-528,52,-95) -> Matrix(5,4,-4,-3) Matrix(529,-1248,142,-335) -> Matrix(17,14,-28,-23) Matrix(241,-576,100,-239) -> Matrix(1,0,0,1) Matrix(433,-1056,98,-239) -> Matrix(3,2,-2,-1) Matrix(107,-264,15,-37) -> Matrix(11,9,-16,-13) Matrix(443,-1224,135,-373) -> Matrix(11,9,-16,-13) Matrix(59,-168,13,-37) -> Matrix(1,1,-4,-3) Matrix(85,-264,19,-59) -> Matrix(1,1,-6,-5) Matrix(299,-984,55,-181) -> Matrix(7,5,-10,-7) Matrix(107,-360,11,-37) -> Matrix(7,5,-10,-7) Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) Matrix(59,-312,7,-37) -> Matrix(1,1,-4,-3) Matrix(85,-456,11,-59) -> Matrix(3,1,-4,-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): 72 ----------------------------------------------------------------------- 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 10 1 1/1 (-1/1,-10/11) 0 24 8/7 -9/10 5 3 7/6 (-26/29,-17/19) 0 24 13/11 (-17/19,-25/28) 0 24 6/5 -8/9 3 4 5/4 (-9/10,-8/9) 0 24 24/19 -8/9 9 1 19/15 (-8/9,-63/71) 0 24 14/11 -23/26 1 12 9/7 -15/17 1 8 22/17 -23/26 1 12 13/10 (-15/17,-22/25) 0 24 17/13 (-15/17,-22/25) 0 24 4/3 -7/8 3 6 19/14 (-46/53,-13/15) 0 24 15/11 -13/15 1 8 26/19 -31/36 1 12 11/8 (-6/7,-11/13) 0 24 18/13 -1/1 3 4 7/5 (-1/1,-7/8) 0 24 24/17 -7/8 1 1 17/12 (-7/8,-6/7) 0 24 27/19 -1/1 1 8 10/7 -7/8 1 12 36/25 (-7/8,-5/6) 0 2 13/9 (-1/1,-7/8) 0 24 29/20 (-15/17,-22/25) 0 24 16/11 -7/8 5 3 19/13 (-20/23,-13/15) 0 24 3/2 -6/7 1 8 17/11 (-25/29,-6/7) 0 24 14/9 -5/6 1 12 25/16 (-6/7,-5/6) 0 24 36/23 (-7/8,-5/6) 0 2 11/7 (-1/1,-6/7) 0 24 19/12 (-6/7,-11/13) 0 24 8/5 -5/6 1 3 29/18 (-1/1,-4/5) 0 24 50/31 -5/6 1 12 21/13 -1/1 1 8 34/21 -7/8 1 12 13/8 (-1/1,-4/5) 0 24 31/19 (-1/1,-4/5) 0 24 18/11 -1/1 3 4 5/3 (-1/1,-5/6) 0 24 27/16 -6/7 1 8 22/13 -5/6 1 12 12/7 (-7/8,-5/6) 0 2 26/15 -7/8 1 12 33/19 -11/13 1 8 7/4 (-1/1,-6/7) 0 24 16/9 -5/6 3 3 9/5 -1/1 1 8 20/11 -5/6 3 6 11/6 (-1/1,-4/5) 0 24 24/13 -1/1 3 1 13/7 (-1/1,-7/8) 0 24 15/8 -6/7 1 8 2/1 -5/6 1 12 12/5 (-5/6,-3/4) 0 2 46/19 -3/4 1 12 17/7 (-1/1,-4/5) 0 24 22/9 -3/4 1 12 5/2 (-4/5,-3/4) 0 24 18/7 -4/5 3 4 31/12 (-4/5,-11/14) 0 24 13/5 (-7/9,-3/4) 0 24 34/13 -3/4 1 12 21/8 -10/13 1 8 8/3 -3/4 3 3 19/7 (-8/11,-5/7) 0 24 11/4 (-1/1,-2/3) 0 24 36/13 -3/4 3 2 14/5 -7/10 1 12 3/1 -1/1 1 8 19/6 (-4/5,-7/9) 0 24 16/5 -3/4 5 3 13/4 (-1/1,-2/3) 0 24 36/11 -3/4 3 2 23/7 (-5/7,-2/3) 0 24 33/10 -2/3 1 8 10/3 -3/4 1 12 37/11 (-5/7,-2/3) 0 24 27/8 -2/3 1 8 44/13 -3/4 3 6 17/5 (-5/7,-2/3) 0 24 24/7 -2/3 2 1 7/2 (-1/1,-2/3) 0 24 25/7 (-8/11,-5/7) 0 24 18/5 -2/3 3 4 29/8 (-1/1,-2/3) 0 24 11/3 (-5/7,-2/3) 0 24 48/13 -2/3 12 1 37/10 (-2/3,-19/29) 0 24 26/7 -5/8 1 12 41/11 (-5/8,-3/5) 0 24 15/4 -2/3 1 8 34/9 -3/4 1 12 19/5 (-2/3,-7/11) 0 24 23/6 (-2/3,-1/2) 0 24 4/1 -1/2 1 6 25/6 (-1/2,0/1) 0 24 21/5 -1/1 1 8 17/4 (-1/2,0/1) 0 24 13/3 (-1/1,1/0) 0 24 48/11 -1/1 5 1 35/8 (-1/1,-4/5) 0 24 22/5 -1/2 1 12 31/7 (-1/1,-2/3) 0 24 9/2 0/1 1 8 14/3 -3/2 1 12 19/4 (-8/7,-1/1) 0 24 24/5 -1/1 11 1 5/1 (-1/1,-3/4) 0 24 21/4 -2/3 1 8 16/3 -1/2 1 3 27/5 -1/1 1 8 11/2 (-1/1,0/1) 0 24 28/5 -1/2 3 6 17/3 (0/1,1/1) 0 24 23/4 (-2/1,1/0) 0 24 6/1 -1/1 3 4 7/1 (-1/1,-3/4) 0 24 15/2 -2/3 1 8 8/1 -1/2 1 3 9/1 -1/1 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(107,-120,33,-37) (1/1,8/7) -> (16/5,13/4) Hyperbolic Matrix(229,-264,157,-181) (8/7,7/6) -> (16/11,19/13) Glide Reflection Matrix(347,-408,91,-107) (7/6,13/11) -> (19/5,23/6) Glide Reflection Matrix(181,-216,31,-37) (13/11,6/5) -> (23/4,6/1) Glide Reflection Matrix(59,-72,9,-11) (6/5,5/4) -> (6/1,7/1) Glide Reflection Matrix(191,-240,152,-191) (5/4,24/19) -> (5/4,24/19) Reflection Matrix(721,-912,570,-721) (24/19,19/15) -> (24/19,19/15) Reflection Matrix(719,-912,190,-241) (19/15,14/11) -> (34/9,19/5) Hyperbolic Matrix(469,-600,179,-229) (14/11,9/7) -> (34/13,21/8) Glide Reflection Matrix(613,-792,363,-469) (9/7,22/17) -> (27/16,22/13) Glide Reflection 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(443,-600,79,-107) (4/3,19/14) -> (28/5,17/3) Glide Reflection Matrix(229,-312,149,-203) (19/14,15/11) -> (3/2,17/11) 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(469,-648,131,-181) (11/8,18/13) -> (25/7,18/5) Glide Reflection Matrix(155,-216,61,-85) (18/13,7/5) -> (5/2,18/7) 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(421,-600,127,-181) (27/19,10/7) -> (33/10,10/3) Glide Reflection Matrix(251,-360,175,-251) (10/7,36/25) -> (10/7,36/25) Reflection Matrix(949,-1368,607,-875) (36/25,13/9) -> (25/16,36/23) Hyperbolic Matrix(613,-888,107,-155) (13/9,29/20) -> (17/3,23/4) Hyperbolic Matrix(529,-768,166,-241) (29/20,16/11) -> (19/6,16/5) Glide Reflection Matrix(443,-648,255,-373) (19/13,3/2) -> (33/19,7/4) Hyperbolic Matrix(325,-504,69,-107) (17/11,14/9) -> (14/3,19/4) Hyperbolic Matrix(661,-1032,253,-395) (14/9,25/16) -> (13/5,34/13) Hyperbolic Matrix(1333,-2088,851,-1333) (36/23,58/37) -> (36/23,58/37) Reflection Matrix(1439,-2256,428,-671) (47/30,11/7) -> (47/14,37/11) Glide Reflection 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(1355,-2184,559,-901) (29/18,50/31) -> (46/19,17/7) Hyperbolic Matrix(491,-792,261,-421) (50/31,21/13) -> (15/8,2/1) Hyperbolic Matrix(757,-1224,201,-325) (21/13,34/21) -> (15/4,34/9) Glide Reflection Matrix(1259,-2040,777,-1259) (34/21,60/37) -> (34/21,60/37) Reflection Matrix(769,-1248,236,-383) (47/29,13/8) -> (13/4,49/15) Hyperbolic Matrix(661,-1080,183,-299) (31/19,18/11) -> (18/5,29/8) Hyperbolic Matrix(395,-648,153,-251) (18/11,5/3) -> (18/7,31/12) Glide Reflection Matrix(143,-240,28,-47) (5/3,27/16) -> (5/1,21/4) Glide Reflection Matrix(155,-264,91,-155) (22/13,12/7) -> (22/13,12/7) Reflection Matrix(181,-312,105,-181) (12/7,26/15) -> (12/7,26/15) Reflection Matrix(203,-360,75,-133) (7/4,16/9) -> (8/3,19/7) Hyperbolic Matrix(229,-408,87,-155) (16/9,9/5) -> (21/8,8/3) Hyperbolic Matrix(517,-936,153,-277) (9/5,20/11) -> (27/8,44/13) Glide Reflection Matrix(289,-528,52,-95) (20/11,11/6) -> (11/2,28/5) Hyperbolic 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(347,-648,83,-155) (13/7,15/8) -> (25/6,21/5) Glide Reflection Matrix(11,-24,5,-11) (2/1,12/5) -> (2/1,12/5) Reflection Matrix(229,-552,95,-229) (12/5,46/19) -> (12/5,46/19) Reflection Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(421,-1032,113,-277) (22/9,5/2) -> (26/7,41/11) Glide Reflection Matrix(241,-624,56,-145) (31/12,13/5) -> (17/4,13/3) Glide Reflection Matrix(203,-552,57,-155) (19/7,11/4) -> (7/2,25/7) Glide Reflection Matrix(443,-1224,135,-373) (11/4,36/13) -> (36/11,23/7) Hyperbolic Matrix(181,-504,65,-181) (36/13,14/5) -> (36/13,14/5) Reflection Matrix(59,-168,13,-37) (14/5,3/1) -> (9/2,14/3) Hyperbolic Matrix(85,-264,19,-59) (3/1,19/6) -> (31/7,9/2) Hyperbolic Matrix(683,-2232,209,-683) (62/19,36/11) -> (62/19,36/11) Reflection Matrix(299,-984,55,-181) (23/7,33/10) -> (27/5,11/2) Hyperbolic Matrix(251,-840,75,-251) (10/3,84/25) -> (10/3,84/25) Reflection Matrix(107,-360,11,-37) (37/11,27/8) -> (9/1,1/0) 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(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(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(59,-312,7,-37) (21/4,16/3) -> (8/1,9/1) Hyperbolic Matrix(85,-456,11,-59) (16/3,27/5) -> (15/2,8/1) Hyperbolic 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(21,20,-22,-21) (0/1,1/1) -> (-1/1,-10/11) Matrix(107,-120,33,-37) -> Matrix(23,21,-34,-31) Matrix(229,-264,157,-181) -> Matrix(333,299,-382,-343) Matrix(347,-408,91,-107) -> Matrix(75,67,-122,-109) Matrix(181,-216,31,-37) -> Matrix(37,33,-28,-25) Matrix(59,-72,9,-11) -> Matrix(17,15,-26,-23) Matrix(191,-240,152,-191) -> Matrix(161,144,-180,-161) (5/4,24/19) -> (-9/10,-8/9) Matrix(721,-912,570,-721) -> Matrix(1135,1008,-1278,-1135) (24/19,19/15) -> (-8/9,-63/71) Matrix(719,-912,190,-241) -> Matrix(79,70,-114,-101) Matrix(469,-600,179,-229) -> Matrix(209,185,-270,-239) Matrix(613,-792,363,-469) -> Matrix(71,63,-80,-71) *** -> (-9/10,-7/8) Matrix(815,-1056,186,-241) -> Matrix(43,38,-60,-53) Matrix(479,-624,294,-383) -> Matrix(93,82,-110,-97) Matrix(623,-816,184,-241) -> Matrix(91,80,-124,-109) Matrix(443,-600,79,-107) -> Matrix(15,13,-38,-33) Matrix(229,-312,149,-203) -> Matrix(57,49,-64,-55) -7/8 Matrix(913,-1248,526,-719) -> Matrix(167,144,-196,-169) -6/7 Matrix(911,-1248,246,-337) -> Matrix(107,92,-164,-141) Matrix(469,-648,131,-181) -> Matrix(9,7,-14,-11) Matrix(155,-216,61,-85) -> Matrix(29,25,-36,-31) -5/6 Matrix(239,-336,170,-239) -> Matrix(15,14,-16,-15) (7/5,24/17) -> (-1/1,-7/8) Matrix(577,-816,408,-577) -> Matrix(97,84,-112,-97) (24/17,17/12) -> (-7/8,-6/7) Matrix(575,-816,136,-193) -> Matrix(7,6,-6,-5) -1/1 Matrix(421,-600,127,-181) -> Matrix(13,11,-20,-17) Matrix(251,-360,175,-251) -> Matrix(41,35,-48,-41) (10/7,36/25) -> (-7/8,-5/6) Matrix(949,-1368,607,-875) -> Matrix(43,37,-50,-43) (-1/1,-6/7).(-7/8,-5/6) Matrix(613,-888,107,-155) -> Matrix(17,15,-8,-7) Matrix(529,-768,166,-241) -> Matrix(107,94,-140,-123) Matrix(443,-648,255,-373) -> Matrix(123,107,-146,-127) Matrix(325,-504,69,-107) -> Matrix(27,23,-20,-17) Matrix(661,-1032,253,-395) -> Matrix(21,17,-26,-21) (-1/1,-4/5).(-5/6,-3/4) Matrix(1333,-2088,851,-1333) -> Matrix(41,35,-48,-41) (36/23,58/37) -> (-7/8,-5/6) Matrix(1439,-2256,428,-671) -> Matrix(37,32,-52,-45) Matrix(335,-528,92,-145) -> Matrix(33,28,-46,-39) Matrix(241,-384,150,-239) -> Matrix(59,50,-72,-61) -5/6 Matrix(1355,-2184,559,-901) -> Matrix(21,17,-26,-21) (-1/1,-4/5).(-5/6,-3/4) Matrix(491,-792,261,-421) -> Matrix(31,25,-36,-29) -5/6 Matrix(757,-1224,201,-325) -> Matrix(13,11,-20,-17) Matrix(1259,-2040,777,-1259) -> Matrix(41,35,-48,-41) (34/21,60/37) -> (-7/8,-5/6) Matrix(769,-1248,236,-383) -> Matrix(3,2,-2,-1) -1/1 Matrix(661,-1080,183,-299) -> Matrix(11,9,-16,-13) -3/4 Matrix(395,-648,153,-251) -> Matrix(35,31,-44,-39) Matrix(143,-240,28,-47) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(155,-264,91,-155) -> Matrix(41,35,-48,-41) (22/13,12/7) -> (-7/8,-5/6) Matrix(181,-312,105,-181) -> Matrix(41,35,-48,-41) (12/7,26/15) -> (-7/8,-5/6) Matrix(203,-360,75,-133) -> Matrix(51,43,-70,-59) Matrix(229,-408,87,-155) -> Matrix(57,47,-74,-61) Matrix(517,-936,153,-277) -> Matrix(9,7,-14,-11) Matrix(289,-528,52,-95) -> Matrix(5,4,-4,-3) -1/1 Matrix(287,-528,156,-287) -> Matrix(9,8,-10,-9) (11/6,24/13) -> (-1/1,-4/5) Matrix(337,-624,182,-337) -> Matrix(15,14,-16,-15) (24/13,13/7) -> (-1/1,-7/8) Matrix(347,-648,83,-155) -> Matrix(1,1,6,5) Matrix(11,-24,5,-11) -> Matrix(19,15,-24,-19) (2/1,12/5) -> (-5/6,-3/4) Matrix(229,-552,95,-229) -> Matrix(19,15,-24,-19) (12/5,46/19) -> (-5/6,-3/4) Matrix(433,-1056,98,-239) -> Matrix(3,2,-2,-1) -1/1 Matrix(421,-1032,113,-277) -> Matrix(13,11,-20,-17) Matrix(241,-624,56,-145) -> Matrix(5,4,4,3) Matrix(203,-552,57,-155) -> Matrix(29,21,-40,-29) *** -> (-3/4,-7/10) Matrix(443,-1224,135,-373) -> Matrix(11,9,-16,-13) -3/4 Matrix(181,-504,65,-181) -> Matrix(29,21,-40,-29) (36/13,14/5) -> (-3/4,-7/10) Matrix(59,-168,13,-37) -> Matrix(1,1,-4,-3) -1/2 Matrix(85,-264,19,-59) -> Matrix(1,1,-6,-5) Matrix(683,-2232,209,-683) -> Matrix(19,15,-24,-19) (62/19,36/11) -> (-5/6,-3/4) Matrix(299,-984,55,-181) -> Matrix(7,5,-10,-7) (-1/1,-2/3).(-3/4,-1/2) Matrix(251,-840,75,-251) -> Matrix(29,21,-40,-29) (10/3,84/25) -> (-3/4,-7/10) Matrix(107,-360,11,-37) -> Matrix(7,5,-10,-7) (-1/1,-2/3).(-3/4,-1/2) Matrix(239,-816,70,-239) -> Matrix(29,20,-42,-29) (17/5,24/7) -> (-5/7,-2/3) Matrix(97,-336,28,-97) -> Matrix(5,4,-6,-5) (24/7,7/2) -> (-1/1,-2/3) Matrix(287,-1056,78,-287) -> Matrix(29,20,-42,-29) (11/3,48/13) -> (-5/7,-2/3) Matrix(961,-3552,260,-961) -> Matrix(115,76,-174,-115) (48/13,37/10) -> (-2/3,-19/29) Matrix(193,-720,26,-97) -> Matrix(7,4,-12,-7) *** -> (-2/3,-1/2) Matrix(49,-192,12,-47) -> Matrix(3,2,-8,-5) -1/2 Matrix(287,-1248,66,-287) -> Matrix(1,2,0,-1) (13/3,48/11) -> (-1/1,1/0) Matrix(769,-3360,176,-769) -> Matrix(9,8,-10,-9) (48/11,35/8) -> (-1/1,-4/5) Matrix(191,-912,40,-191) -> Matrix(15,16,-14,-15) (19/4,24/5) -> (-8/7,-1/1) Matrix(49,-240,10,-49) -> Matrix(7,6,-8,-7) (24/5,5/1) -> (-1/1,-3/4) Matrix(59,-312,7,-37) -> Matrix(1,1,-4,-3) -1/2 Matrix(85,-456,11,-59) -> Matrix(3,1,-4,-1) -1/2 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.