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 -7/8 -5/6 -3/4 -2/3 -23/36 -5/8 -13/21 -11/18 -7/12 -1/2 -7/15 -43/96 -7/16 -5/12 -49/120 -55/144 -3/8 -71/192 -17/48 -7/20 -1/3 -5/16 -11/36 -29/96 -5/18 -13/48 -17/64 -1/4 -5/21 -11/48 -5/22 -2/9 -3/14 -17/80 -4/21 -3/16 -1/6 -3/20 -2/15 -3/23 -1/8 -2/17 -1/9 -1/10 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 3/19 1/6 4/23 3/17 2/11 3/16 4/21 1/5 5/24 4/19 3/14 2/9 5/22 3/13 1/4 3/11 5/18 2/7 7/24 11/36 5/16 1/3 7/20 3/8 2/5 5/12 7/16 11/24 7/15 1/2 13/24 7/12 71/120 11/18 5/8 23/36 2/3 17/24 3/4 19/24 5/6 7/8 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 0/1 -9/10 -1/2 1/0 -8/9 -1/1 -7/8 -1/1 -13/15 0/1 -6/7 -1/1 0/1 -17/20 0/1 -11/13 -1/1 0/1 -16/19 -1/1 0/1 -5/6 -1/1 -19/23 -1/2 -2/5 -33/40 0/1 -14/17 -1/1 -1/2 -9/11 -1/1 0/1 -22/27 -1/1 -13/16 -1/2 1/0 -17/21 0/1 -4/5 -1/1 1/0 -19/24 -1/1 -15/19 -1/1 -4/5 -11/14 -3/4 -1/2 -18/23 -1/1 -1/2 -7/9 0/1 -17/22 -1/2 1/0 -10/13 -1/1 0/1 -13/17 -1/2 0/1 -3/4 -1/1 -17/23 -1/2 -4/9 -31/42 -1/3 -14/19 -1/3 0/1 -11/15 0/1 -19/26 -1/2 1/0 -8/11 -1/1 0/1 -13/18 0/1 -18/25 1/1 1/0 -5/7 -2/1 -1/1 -17/24 -1/1 -12/17 -1/1 -5/6 -19/27 -2/3 -26/37 -1/1 -2/3 -33/47 -1/1 -2/3 -7/10 -3/4 -1/2 -30/43 -1/2 -3/7 -23/33 0/1 -39/56 -1/1 -16/23 -1/2 -1/3 -25/36 0/1 -9/13 -1/1 0/1 -20/29 -1/1 0/1 -11/16 -1/2 1/0 -13/19 -1/1 0/1 -2/3 -1/1 -13/20 -1/1 -11/17 -2/3 -1/2 -9/14 -1/2 1/0 -16/25 -1/1 -1/2 -23/36 0/1 -30/47 -1/1 0/1 -7/11 -1/1 0/1 -12/19 -1/1 0/1 -5/8 -1/1 -18/29 -1/1 -4/5 -31/50 -17/22 -3/4 -44/71 -3/4 -23/31 -13/21 -2/3 -47/76 -2/3 -34/55 -1/1 -2/3 -21/34 -3/4 -1/2 -29/47 -1/1 -2/3 -8/13 -1/1 -2/3 -19/31 -2/3 -1/2 -49/80 -3/4 -1/2 -30/49 -1/1 -2/3 -11/18 -2/3 -14/23 -1/1 -1/2 -17/28 -2/3 -20/33 -3/5 -3/5 -1/2 0/1 -16/27 -1/1 -29/49 -1/1 0/1 -13/22 -1/2 1/0 -23/39 0/1 -10/17 -1/1 1/0 -7/12 -1/1 -18/31 -1/1 -3/4 -29/50 -11/14 -3/4 -11/19 -1/1 -2/3 -26/45 -1/1 -41/71 -3/4 -2/3 -15/26 -3/4 -1/2 -19/33 -2/3 -4/7 -1/1 -2/3 -13/23 -4/7 -1/2 -9/16 -1/2 -14/25 -1/2 -1/3 -5/9 0/1 -21/38 -1/2 1/0 -16/29 -1/1 0/1 -11/20 -1/1 -6/11 -1/1 0/1 -13/24 -1/1 -7/13 -1/1 -2/3 -15/28 -2/3 -8/15 -1/1 -1/2 -1/2 1/0 -8/17 -1/2 -1/3 -7/15 0/1 -6/13 -1/3 0/1 -11/24 0/1 -5/11 -1/1 0/1 -14/31 -1/1 -1/2 -9/20 0/1 -13/29 -1/1 0/1 -43/96 -1/2 1/0 -30/67 -1/1 0/1 -17/38 -1/2 1/0 -4/9 -1/1 -11/25 -2/3 -1/2 -7/16 -1/2 -10/23 -1/2 -3/7 -3/7 -1/3 0/1 -11/26 -1/2 -1/4 -41/97 -1/3 0/1 -71/168 -1/3 -30/71 -1/3 -1/4 -19/45 0/1 -8/19 -1/3 0/1 -5/12 0/1 -12/29 0/1 1/1 -19/46 -3/2 1/0 -26/63 -1/1 -33/80 -1/2 1/0 -7/17 0/1 1/0 -9/22 -1/2 1/0 -29/71 -1/2 0/1 -49/120 0/1 -20/49 -1/1 0/1 -11/27 0/1 -2/5 -1/1 -1/2 -13/33 -2/5 -11/28 -1/3 -20/51 -1/3 -9/23 -1/2 0/1 -7/18 -1/3 -19/49 -1/3 0/1 -31/80 -1/2 -1/4 -43/111 0/1 -12/31 -1/2 -1/3 -5/13 -1/3 0/1 -23/60 0/1 -18/47 -1/3 0/1 -13/34 -1/2 -1/4 -34/89 -1/3 0/1 -55/144 -1/2 -1/4 -21/55 -1/3 0/1 -8/21 -1/3 -3/8 0/1 -10/27 1/1 -27/73 8/1 1/0 -71/192 1/0 -44/119 -13/1 1/0 -17/46 -5/2 1/0 -7/19 -1/1 0/1 -25/68 0/1 -43/117 0/1 -18/49 -1/1 0/1 -11/30 0/1 -4/11 -1/1 0/1 -17/47 -1/1 0/1 -13/36 -1/1 -9/25 -1/2 0/1 -5/14 -1/2 1/0 -11/31 -2/3 -1/2 -17/48 -1/2 -6/17 -1/2 -1/3 -7/20 0/1 -8/23 -1/2 -1/3 -1/3 0/1 -6/19 -1/1 0/1 -5/16 -1/2 1/0 -9/29 -1/1 0/1 -4/13 -1/1 0/1 -15/49 -1/1 0/1 -11/36 -1/1 -7/23 -2/3 -1/2 -10/33 -1/1 -13/43 -4/7 -1/2 -29/96 -1/2 -16/53 -1/2 -5/11 -3/10 -1/2 -1/4 -14/47 -1/3 0/1 -11/37 -1/3 0/1 -8/27 -1/3 -21/71 -1/4 -6/25 -13/44 -1/5 -5/17 -1/6 0/1 -7/24 0/1 -2/7 0/1 1/1 -7/25 -2/1 1/0 -5/18 -1/1 -13/47 -1/1 0/1 -21/76 -1/1 -8/29 -1/1 0/1 -3/11 -1/1 0/1 -13/48 -1/2 1/0 -10/37 -1/1 0/1 -7/26 -1/2 1/0 -11/41 -1/1 0/1 -4/15 -1/1 -17/64 -1/2 1/0 -13/49 -1/1 0/1 -9/34 -1/2 1/0 -5/19 -1/1 -2/3 -6/23 -5/9 -1/2 -1/4 0/1 -6/25 5/1 1/0 -5/21 -2/1 -4/17 -1/1 -1/2 -3/13 -1/1 0/1 -11/48 -1/2 1/0 -8/35 -1/1 0/1 -5/22 -1/2 1/0 -7/31 0/1 1/0 -9/40 -1/1 -2/9 -1/1 -5/23 -1/2 0/1 -3/14 -1/2 -1/4 -10/47 -1/3 0/1 -17/80 -1/2 -1/4 -7/33 0/1 -4/19 -1/5 0/1 -5/24 0/1 -1/5 0/1 1/0 -4/21 -1/1 -3/16 -1/2 1/0 -5/27 0/1 -2/11 -1/1 0/1 -5/28 -1/1 -3/17 -1/2 0/1 -7/40 -1/1 -4/23 -3/5 -1/2 -1/6 0/1 -4/25 3/1 1/0 -3/19 -1/1 0/1 -2/13 -1/1 0/1 -5/33 0/1 -3/20 -1/1 -7/47 -1/1 0/1 -4/27 -1/1 -1/7 -1/1 0/1 -2/15 -1/1 -3/23 -2/3 -1/2 -1/8 0/1 -2/17 -1/1 1/0 -1/9 0/1 -1/10 -1/2 1/0 0/1 -1/1 0/1 1/10 -1/2 1/0 1/9 0/1 1/8 0/1 2/15 -1/1 1/7 -1/1 0/1 3/20 -1/1 2/13 -1/1 0/1 3/19 -1/1 0/1 1/6 0/1 4/23 -3/1 1/0 7/40 -1/1 3/17 0/1 1/0 2/11 -1/1 0/1 5/27 0/1 3/16 -1/2 1/0 4/21 -1/1 1/5 -1/2 0/1 5/24 0/1 4/19 0/1 1/3 3/14 1/2 1/0 5/23 0/1 1/0 2/9 -1/1 5/22 -1/2 1/0 3/13 -1/1 0/1 4/17 -1/1 1/0 1/4 0/1 6/23 -5/1 1/0 11/42 -2/1 5/19 -2/1 -1/1 4/15 -1/1 7/26 -1/2 1/0 3/11 -1/1 0/1 5/18 -1/1 7/25 -2/3 -1/2 2/7 -1/3 0/1 7/24 0/1 5/17 0/1 1/4 8/27 1/1 11/37 0/1 1/1 14/47 0/1 1/1 3/10 1/2 1/0 13/43 -4/1 1/0 10/33 -1/1 17/56 0/1 7/23 -2/1 1/0 11/36 -1/1 4/13 -1/1 0/1 9/29 -1/1 0/1 5/16 -1/2 1/0 6/19 -1/1 0/1 1/3 0/1 7/20 0/1 6/17 1/1 1/0 5/14 -1/2 1/0 9/25 0/1 1/0 13/36 -1/1 17/47 -1/1 0/1 4/11 -1/1 0/1 7/19 -1/1 0/1 3/8 0/1 11/29 0/1 1/3 19/50 5/12 1/2 27/71 1/2 8/15 8/21 1/1 29/76 1/1 21/55 0/1 1/1 13/34 1/2 1/0 18/47 0/1 1/1 5/13 0/1 1/1 12/31 1/1 1/0 31/80 1/2 1/0 19/49 0/1 1/1 7/18 1/1 9/23 0/1 1/0 11/28 1/1 13/33 2/1 2/5 -1/1 1/0 11/27 0/1 20/49 -1/1 0/1 9/22 -1/2 1/0 16/39 -1/1 7/17 -1/2 0/1 5/12 0/1 13/31 0/1 1/2 21/50 3/8 1/2 8/19 0/1 1/1 19/45 0/1 30/71 1/2 1/1 11/26 1/2 1/0 14/33 1/1 3/7 0/1 1/1 10/23 3/1 1/0 7/16 1/0 11/25 -2/1 1/0 4/9 -1/1 17/38 -1/2 1/0 13/29 -1/1 0/1 9/20 0/1 5/11 -1/1 0/1 11/24 0/1 6/13 0/1 1/1 13/28 1/1 7/15 0/1 1/2 -1/2 1/0 9/17 -2/1 1/0 8/15 -1/1 7/13 -2/1 -1/1 13/24 -1/1 6/11 -1/1 0/1 17/31 0/1 1/0 11/20 -1/1 16/29 -1/1 0/1 53/96 -1/2 1/0 37/67 -1/1 0/1 21/38 -1/2 1/0 5/9 0/1 14/25 1/1 1/0 9/16 1/0 13/23 -4/1 1/0 4/7 -2/1 -1/1 15/26 -3/2 1/0 56/97 -2/1 -1/1 97/168 -2/1 41/71 -2/1 -3/2 26/45 -1/1 11/19 -2/1 -1/1 7/12 -1/1 17/29 -1/1 -2/3 27/46 -1/2 -1/4 37/63 0/1 47/80 -1/2 1/0 10/17 -1/1 -1/2 13/22 -1/2 1/0 42/71 -1/1 1/0 71/120 -1/1 29/49 -1/1 0/1 16/27 -1/1 3/5 0/1 1/0 20/33 -3/1 17/28 -2/1 31/51 -2/1 14/23 -1/1 1/0 11/18 -2/1 30/49 -2/1 -1/1 49/80 -3/2 1/0 68/111 -1/1 19/31 -2/1 1/0 8/13 -2/1 -1/1 37/60 -1/1 29/47 -2/1 -1/1 21/34 -3/2 1/0 55/89 -2/1 -1/1 89/144 -3/2 1/0 34/55 -2/1 -1/1 13/21 -2/1 5/8 -1/1 17/27 -2/3 46/73 -9/17 -1/2 121/192 -1/2 75/119 -1/2 -12/25 29/46 -1/2 -3/8 12/19 -1/1 0/1 43/68 -1/1 74/117 -1/1 31/49 -1/1 0/1 19/30 -1/1 7/11 -1/1 0/1 30/47 -1/1 0/1 23/36 0/1 16/25 -1/1 1/0 9/14 -1/2 1/0 20/31 1/1 1/0 31/48 1/0 11/17 -2/1 1/0 13/20 -1/1 15/23 -2/1 1/0 2/3 -1/1 13/19 -1/1 0/1 11/16 -1/2 1/0 20/29 -1/1 0/1 9/13 -1/1 0/1 34/49 -1/1 0/1 25/36 0/1 16/23 1/1 1/0 23/33 0/1 30/43 3/1 1/0 67/96 1/0 37/53 -6/1 1/0 7/10 -3/2 1/0 33/47 -2/1 -1/1 26/37 -2/1 -1/1 19/27 -2/1 50/71 -3/2 -19/13 31/44 -4/3 12/17 -5/4 -1/1 17/24 -1/1 5/7 -1/1 -2/3 18/25 -1/2 -1/3 13/18 0/1 34/47 -1/1 0/1 55/76 0/1 21/29 -1/1 0/1 8/11 -1/1 0/1 35/48 -1/2 1/0 27/37 -1/1 0/1 19/26 -1/2 1/0 30/41 -1/1 0/1 11/15 0/1 47/64 -1/2 1/0 36/49 -1/1 0/1 25/34 -1/2 1/0 14/19 0/1 1/1 17/23 4/1 1/0 3/4 -1/1 19/25 -6/11 -1/2 16/21 -1/3 13/17 0/1 1/0 10/13 -1/1 0/1 37/48 -1/2 1/0 27/35 -1/1 0/1 17/22 -1/2 1/0 24/31 -1/1 -1/2 31/40 0/1 7/9 0/1 18/23 -1/1 1/0 11/14 -3/2 1/0 37/47 -2/1 -1/1 63/80 -3/2 1/0 26/33 -1/1 15/19 -4/3 -1/1 19/24 -1/1 4/5 -1/1 -1/2 17/21 0/1 13/16 -1/2 1/0 22/27 -1/1 9/11 -1/1 0/1 23/28 0/1 14/17 -1/1 1/0 33/40 0/1 19/23 2/1 1/0 5/6 -1/1 21/25 -4/7 -1/2 16/19 -1/1 0/1 11/13 -1/1 0/1 28/33 -1/1 17/20 0/1 40/47 -1/1 0/1 23/27 0/1 6/7 -1/1 0/1 13/15 0/1 20/23 1/1 1/0 7/8 -1/1 15/17 -1/2 0/1 8/9 -1/1 9/10 -1/2 1/0 1/1 -1/1 0/1 1/0 -1/2 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(337,304,480,433) (-1/1,-9/10) -> (7/10,33/47) Hyperbolic Matrix(193,172,432,385) (-9/10,-8/9) -> (4/9,17/38) Hyperbolic Matrix(97,86,-432,-383) (-8/9,-7/8) -> (-9/40,-2/9) Hyperbolic Matrix(769,668,-1104,-959) (-7/8,-13/15) -> (-23/33,-39/56) Hyperbolic Matrix(527,456,720,623) (-13/15,-6/7) -> (30/41,11/15) Hyperbolic Matrix(1009,860,-1632,-1391) (-6/7,-17/20) -> (-47/76,-34/55) Hyperbolic Matrix(335,284,-624,-529) (-17/20,-11/13) -> (-7/13,-15/28) Hyperbolic Matrix(431,364,624,527) (-11/13,-16/19) -> (20/29,9/13) Hyperbolic Matrix(673,566,-912,-767) (-16/19,-5/6) -> (-31/42,-14/19) Hyperbolic Matrix(815,674,-1104,-913) (-5/6,-19/23) -> (-17/23,-31/42) Hyperbolic Matrix(671,554,2208,1823) (-19/23,-33/40) -> (17/56,7/23) Hyperbolic Matrix(1487,1226,1920,1583) (-33/40,-14/17) -> (24/31,31/40) Hyperbolic Matrix(239,196,-528,-433) (-14/17,-9/11) -> (-5/11,-14/31) Hyperbolic Matrix(385,314,1296,1057) (-9/11,-22/27) -> (8/27,11/37) Hyperbolic Matrix(145,118,768,625) (-22/27,-13/16) -> (3/16,4/21) Hyperbolic Matrix(143,116,768,623) (-13/16,-17/21) -> (5/27,3/16) Hyperbolic Matrix(97,78,240,193) (-17/21,-4/5) -> (2/5,11/27) Hyperbolic Matrix(191,152,240,191) (-4/5,-19/24) -> (19/24,4/5) Hyperbolic Matrix(721,570,912,721) (-19/24,-15/19) -> (15/19,19/24) Hyperbolic Matrix(241,190,-912,-719) (-15/19,-11/14) -> (-9/34,-5/19) Hyperbolic Matrix(431,338,672,527) (-11/14,-18/23) -> (16/25,9/14) Hyperbolic Matrix(241,188,432,337) (-18/23,-7/9) -> (5/9,14/25) Hyperbolic Matrix(623,482,-1056,-817) (-7/9,-17/22) -> (-13/22,-23/39) Hyperbolic Matrix(241,186,-1056,-815) (-17/22,-10/13) -> (-8/35,-5/22) Hyperbolic Matrix(383,294,624,479) (-10/13,-13/17) -> (19/31,8/13) Hyperbolic Matrix(241,184,-816,-623) (-13/17,-3/4) -> (-13/44,-5/17) Hyperbolic Matrix(383,284,-1296,-961) (-3/4,-17/23) -> (-21/71,-13/44) Hyperbolic Matrix(193,142,-912,-671) (-14/19,-11/15) -> (-7/33,-4/19) Hyperbolic Matrix(719,526,-1248,-913) (-11/15,-19/26) -> (-15/26,-19/33) Hyperbolic Matrix(337,246,-1248,-911) (-19/26,-8/11) -> (-10/37,-7/26) Hyperbolic Matrix(193,140,-528,-383) (-8/11,-13/18) -> (-11/30,-4/11) Hyperbolic Matrix(527,380,864,623) (-13/18,-18/25) -> (14/23,11/18) Hyperbolic Matrix(145,104,336,241) (-18/25,-5/7) -> (3/7,10/23) Hyperbolic Matrix(239,170,336,239) (-5/7,-17/24) -> (17/24,5/7) Hyperbolic Matrix(577,408,816,577) (-17/24,-12/17) -> (12/17,17/24) Hyperbolic Matrix(193,136,-816,-575) (-12/17,-19/27) -> (-5/21,-4/17) Hyperbolic Matrix(239,168,1296,911) (-19/27,-26/37) -> (2/11,5/27) Hyperbolic Matrix(817,574,2256,1585) (-26/37,-33/47) -> (17/47,4/11) Hyperbolic Matrix(433,304,480,337) (-33/47,-7/10) -> (9/10,1/1) Hyperbolic Matrix(289,202,-960,-671) (-7/10,-30/43) -> (-16/53,-3/10) Hyperbolic Matrix(625,436,1584,1105) (-30/43,-23/33) -> (13/33,2/5) Hyperbolic Matrix(385,268,2208,1537) (-39/56,-16/23) -> (4/23,7/40) Hyperbolic Matrix(1105,768,1728,1201) (-16/23,-25/36) -> (23/36,16/25) Hyperbolic Matrix(479,332,-1248,-865) (-25/36,-9/13) -> (-5/13,-23/60) Hyperbolic Matrix(527,364,624,431) (-9/13,-20/29) -> (16/19,11/13) Hyperbolic Matrix(241,166,768,529) (-20/29,-11/16) -> (5/16,6/19) Hyperbolic Matrix(239,164,768,527) (-11/16,-13/19) -> (9/29,5/16) Hyperbolic Matrix(527,360,912,623) (-13/19,-2/3) -> (26/45,11/19) Hyperbolic Matrix(433,282,-1104,-719) (-2/3,-13/20) -> (-11/28,-20/51) Hyperbolic Matrix(527,342,960,623) (-13/20,-11/17) -> (17/31,11/20) Hyperbolic Matrix(239,154,-672,-433) (-11/17,-9/14) -> (-5/14,-11/31) Hyperbolic Matrix(527,338,672,431) (-9/14,-16/25) -> (18/23,11/14) Hyperbolic Matrix(1201,768,1728,1105) (-16/25,-23/36) -> (25/36,16/23) Hyperbolic Matrix(2399,1532,3456,2207) (-23/36,-30/47) -> (34/49,25/36) Hyperbolic Matrix(671,428,2256,1439) (-30/47,-7/11) -> (11/37,14/47) Hyperbolic Matrix(145,92,-528,-335) (-7/11,-12/19) -> (-8/29,-3/11) Hyperbolic Matrix(239,150,-384,-241) (-12/19,-5/8) -> (-5/8,-18/29) Parabolic Matrix(1009,626,2400,1489) (-18/29,-31/50) -> (21/50,8/19) Hyperbolic Matrix(3407,2112,-9216,-5713) (-31/50,-44/71) -> (-44/119,-17/46) Hyperbolic Matrix(2399,1486,3408,2111) (-44/71,-13/21) -> (19/27,50/71) Hyperbolic Matrix(3793,2346,-10320,-6383) (-13/21,-47/76) -> (-25/68,-43/117) Hyperbolic Matrix(1871,1156,-4896,-3025) (-34/55,-21/34) -> (-13/34,-34/89) Hyperbolic Matrix(865,534,-3264,-2015) (-21/34,-29/47) -> (-13/49,-9/34) Hyperbolic Matrix(383,236,-1248,-769) (-29/47,-8/13) -> (-4/13,-15/49) Hyperbolic Matrix(479,294,624,383) (-8/13,-19/31) -> (13/17,10/13) Hyperbolic Matrix(1583,970,-3840,-2353) (-19/31,-49/80) -> (-33/80,-7/17) Hyperbolic Matrix(1633,1000,-7680,-4703) (-49/80,-30/49) -> (-10/47,-17/80) Hyperbolic Matrix(1249,764,1728,1057) (-30/49,-11/18) -> (13/18,34/47) Hyperbolic Matrix(623,380,864,527) (-11/18,-14/23) -> (18/25,13/18) Hyperbolic Matrix(385,234,-1104,-671) (-14/23,-17/28) -> (-7/20,-8/23) Hyperbolic Matrix(1345,816,1584,961) (-17/28,-20/33) -> (28/33,17/20) Hyperbolic Matrix(479,290,1584,959) (-20/33,-3/5) -> (13/43,10/33) Hyperbolic Matrix(47,28,240,143) (-3/5,-16/27) -> (4/21,1/5) Hyperbolic Matrix(385,228,-2592,-1535) (-16/27,-29/49) -> (-7/47,-4/27) Hyperbolic Matrix(1441,852,-3408,-2015) (-29/49,-13/22) -> (-11/26,-41/97) Hyperbolic Matrix(95,56,-816,-481) (-23/39,-10/17) -> (-2/17,-1/9) Hyperbolic Matrix(335,196,-576,-337) (-10/17,-7/12) -> (-7/12,-18/31) Parabolic Matrix(431,250,-912,-529) (-18/31,-29/50) -> (-1/2,-8/17) Hyperbolic Matrix(911,528,2400,1391) (-29/50,-11/19) -> (11/29,19/50) Hyperbolic Matrix(623,360,912,527) (-11/19,-26/45) -> (2/3,13/19) Hyperbolic Matrix(817,472,1248,721) (-26/45,-41/71) -> (15/23,2/3) Hyperbolic Matrix(1393,804,-3408,-1967) (-41/71,-15/26) -> (-9/22,-29/71) Hyperbolic Matrix(289,166,336,193) (-19/33,-4/7) -> (6/7,13/15) Hyperbolic Matrix(95,54,336,191) (-4/7,-13/23) -> (7/25,2/7) Hyperbolic Matrix(337,190,768,433) (-13/23,-9/16) -> (7/16,11/25) Hyperbolic Matrix(335,188,768,431) (-9/16,-14/25) -> (10/23,7/16) Hyperbolic Matrix(337,188,432,241) (-14/25,-5/9) -> (7/9,18/23) Hyperbolic Matrix(47,26,432,239) (-5/9,-21/38) -> (1/10,1/9) Hyperbolic Matrix(1633,902,-3648,-2015) (-21/38,-16/29) -> (-30/67,-17/38) Hyperbolic Matrix(769,424,-2784,-1535) (-16/29,-11/20) -> (-21/76,-8/29) Hyperbolic Matrix(95,52,-528,-289) (-11/20,-6/11) -> (-2/11,-5/28) Hyperbolic Matrix(287,156,528,287) (-6/11,-13/24) -> (13/24,6/11) Hyperbolic Matrix(337,182,624,337) (-13/24,-7/13) -> (7/13,13/24) Hyperbolic Matrix(815,436,1344,719) (-15/28,-8/15) -> (20/33,17/28) Hyperbolic Matrix(337,178,-816,-431) (-8/15,-1/2) -> (-19/46,-26/63) Hyperbolic Matrix(911,428,-2352,-1105) (-8/17,-7/15) -> (-43/111,-12/31) Hyperbolic Matrix(95,44,-624,-289) (-7/15,-6/13) -> (-2/13,-5/33) Hyperbolic Matrix(287,132,624,287) (-6/13,-11/24) -> (11/24,6/13) Hyperbolic Matrix(241,110,528,241) (-11/24,-5/11) -> (5/11,11/24) Hyperbolic Matrix(337,152,960,433) (-14/31,-9/20) -> (7/20,6/17) Hyperbolic Matrix(865,388,-2352,-1055) (-9/20,-13/29) -> (-7/19,-25/68) Hyperbolic Matrix(5089,2280,9216,4129) (-13/29,-43/96) -> (53/96,37/67) Hyperbolic Matrix(5087,2278,9216,4127) (-43/96,-30/67) -> (16/29,53/96) Hyperbolic Matrix(385,172,432,193) (-17/38,-4/9) -> (8/9,9/10) Hyperbolic Matrix(95,42,432,191) (-4/9,-11/25) -> (5/23,2/9) Hyperbolic Matrix(433,190,768,337) (-11/25,-7/16) -> (9/16,13/23) Hyperbolic Matrix(431,188,768,335) (-7/16,-10/23) -> (14/25,9/16) Hyperbolic Matrix(241,104,336,145) (-10/23,-3/7) -> (5/7,18/25) Hyperbolic Matrix(335,142,-1248,-529) (-3/7,-11/26) -> (-7/26,-11/41) Hyperbolic Matrix(11759,4970,19872,8399) (-41/97,-71/168) -> (71/120,29/49) Hyperbolic Matrix(12097,5112,20448,8641) (-71/168,-30/71) -> (42/71,71/120) Hyperbolic Matrix(2831,1196,4656,1967) (-30/71,-19/45) -> (31/51,14/23) Hyperbolic Matrix(289,122,912,385) (-19/45,-8/19) -> (6/19,1/3) Hyperbolic Matrix(239,100,-576,-241) (-8/19,-5/12) -> (-5/12,-12/29) Parabolic Matrix(1393,576,2208,913) (-12/29,-19/46) -> (29/46,12/19) Hyperbolic Matrix(6049,2496,7680,3169) (-26/63,-33/80) -> (63/80,26/33) Hyperbolic Matrix(239,98,-1056,-433) (-7/17,-9/22) -> (-5/22,-7/31) Hyperbolic Matrix(11807,4822,20448,8351) (-29/71,-49/120) -> (97/168,41/71) Hyperbolic Matrix(11473,4684,19872,8113) (-49/120,-20/49) -> (56/97,97/168) Hyperbolic Matrix(2593,1058,-7056,-2879) (-20/49,-11/27) -> (-43/117,-18/49) Hyperbolic Matrix(193,78,240,97) (-11/27,-2/5) -> (4/5,17/21) Hyperbolic Matrix(1105,436,1584,625) (-2/5,-13/33) -> (23/33,30/43) Hyperbolic Matrix(625,246,1344,529) (-13/33,-11/28) -> (13/28,7/15) Hyperbolic Matrix(2689,1054,4656,1825) (-20/51,-9/23) -> (41/71,26/45) Hyperbolic Matrix(241,94,864,337) (-9/23,-7/18) -> (5/18,7/25) Hyperbolic Matrix(1489,578,2352,913) (-7/18,-19/49) -> (31/49,19/30) Hyperbolic Matrix(1873,726,-7056,-2735) (-19/49,-31/80) -> (-17/64,-13/49) Hyperbolic Matrix(6097,2362,8304,3217) (-31/80,-43/111) -> (11/15,47/64) Hyperbolic Matrix(145,56,624,241) (-12/31,-5/13) -> (3/13,4/17) Hyperbolic Matrix(2881,1104,4512,1729) (-23/60,-18/47) -> (30/47,23/36) Hyperbolic Matrix(481,184,-2256,-863) (-18/47,-13/34) -> (-3/14,-10/47) Hyperbolic Matrix(12817,4896,20736,7921) (-34/89,-55/144) -> (89/144,34/55) Hyperbolic Matrix(12815,4894,20736,7919) (-55/144,-21/55) -> (55/89,89/144) Hyperbolic Matrix(241,92,-1632,-623) (-21/55,-8/21) -> (-4/27,-1/7) Hyperbolic Matrix(143,54,-384,-145) (-8/21,-3/8) -> (-3/8,-10/27) Parabolic Matrix(1681,622,2208,817) (-10/27,-27/73) -> (19/25,16/21) Hyperbolic Matrix(23233,8592,36864,13633) (-27/73,-71/192) -> (121/192,75/119) Hyperbolic Matrix(23231,8590,36864,13631) (-71/192,-44/119) -> (46/73,121/192) Hyperbolic Matrix(1295,478,2208,815) (-17/46,-7/19) -> (17/29,27/46) Hyperbolic Matrix(1439,528,2352,863) (-18/49,-11/30) -> (11/18,30/49) Hyperbolic Matrix(1585,574,2256,817) (-4/11,-17/47) -> (33/47,26/37) Hyperbolic Matrix(2783,1006,4512,1631) (-17/47,-13/36) -> (37/60,29/47) Hyperbolic Matrix(527,190,1728,623) (-13/36,-9/25) -> (7/23,11/36) Hyperbolic Matrix(145,52,672,241) (-9/25,-5/14) -> (3/14,5/23) Hyperbolic Matrix(1489,528,2304,817) (-11/31,-17/48) -> (31/48,11/17) Hyperbolic Matrix(1487,526,2304,815) (-17/48,-6/17) -> (20/31,31/48) Hyperbolic Matrix(671,236,816,287) (-6/17,-7/20) -> (23/28,14/17) Hyperbolic Matrix(527,182,1248,431) (-8/23,-1/3) -> (19/45,30/71) Hyperbolic Matrix(385,122,912,289) (-1/3,-6/19) -> (8/19,19/45) Hyperbolic Matrix(529,166,768,241) (-6/19,-5/16) -> (11/16,20/29) Hyperbolic Matrix(527,164,768,239) (-5/16,-9/29) -> (13/19,11/16) Hyperbolic Matrix(97,30,624,193) (-9/29,-4/13) -> (2/13,3/19) Hyperbolic Matrix(1249,382,3456,1057) (-15/49,-11/36) -> (13/36,17/47) Hyperbolic Matrix(623,190,1728,527) (-11/36,-7/23) -> (9/25,13/36) Hyperbolic Matrix(145,44,-1104,-335) (-7/23,-10/33) -> (-2/15,-3/23) Hyperbolic Matrix(959,290,1584,479) (-10/33,-13/43) -> (3/5,20/33) Hyperbolic Matrix(6433,1944,9216,2785) (-13/43,-29/96) -> (67/96,37/53) Hyperbolic Matrix(6431,1942,9216,2783) (-29/96,-16/53) -> (30/43,67/96) Hyperbolic Matrix(47,14,480,143) (-3/10,-14/47) -> (0/1,1/10) Hyperbolic Matrix(1439,428,2256,671) (-14/47,-11/37) -> (7/11,30/47) Hyperbolic Matrix(1057,314,1296,385) (-11/37,-8/27) -> (22/27,9/11) Hyperbolic Matrix(1297,384,3408,1009) (-8/27,-21/71) -> (27/71,8/21) Hyperbolic Matrix(239,70,816,239) (-5/17,-7/24) -> (7/24,5/17) Hyperbolic Matrix(97,28,336,97) (-7/24,-2/7) -> (2/7,7/24) Hyperbolic Matrix(191,54,336,95) (-2/7,-7/25) -> (13/23,4/7) Hyperbolic Matrix(337,94,864,241) (-7/25,-5/18) -> (7/18,9/23) Hyperbolic Matrix(671,186,1728,479) (-5/18,-13/47) -> (19/49,7/18) Hyperbolic Matrix(673,186,-4512,-1247) (-13/47,-21/76) -> (-3/20,-7/47) Hyperbolic Matrix(1681,456,2304,625) (-3/11,-13/48) -> (35/48,27/37) Hyperbolic Matrix(1679,454,2304,623) (-13/48,-10/37) -> (8/11,35/48) Hyperbolic Matrix(97,26,720,193) (-11/41,-4/15) -> (2/15,1/7) Hyperbolic Matrix(5087,1352,8304,2207) (-4/15,-17/64) -> (49/80,68/111) Hyperbolic Matrix(145,38,-912,-239) (-5/19,-6/23) -> (-4/25,-3/19) Hyperbolic Matrix(47,12,-192,-49) (-6/23,-1/4) -> (-1/4,-6/25) Parabolic Matrix(1391,332,2208,527) (-6/25,-5/21) -> (17/27,46/73) Hyperbolic Matrix(241,56,624,145) (-4/17,-3/13) -> (5/13,12/31) Hyperbolic Matrix(1777,408,2304,529) (-3/13,-11/48) -> (37/48,27/35) Hyperbolic Matrix(1775,406,2304,527) (-11/48,-8/35) -> (10/13,37/48) Hyperbolic Matrix(337,76,1920,433) (-7/31,-9/40) -> (7/40,3/17) Hyperbolic Matrix(191,42,432,95) (-2/9,-5/23) -> (11/25,4/9) Hyperbolic Matrix(241,52,672,145) (-5/23,-3/14) -> (5/14,9/25) Hyperbolic Matrix(4511,958,7680,1631) (-17/80,-7/33) -> (37/63,47/80) Hyperbolic Matrix(191,40,912,191) (-4/19,-5/24) -> (5/24,4/19) Hyperbolic Matrix(49,10,240,49) (-5/24,-1/5) -> (1/5,5/24) Hyperbolic Matrix(143,28,240,47) (-1/5,-4/21) -> (16/27,3/5) Hyperbolic Matrix(625,118,768,145) (-4/21,-3/16) -> (13/16,22/27) Hyperbolic Matrix(623,116,768,143) (-3/16,-5/27) -> (17/21,13/16) Hyperbolic Matrix(911,168,1296,239) (-5/27,-2/11) -> (26/37,19/27) Hyperbolic Matrix(529,94,816,145) (-5/28,-3/17) -> (11/17,13/20) Hyperbolic Matrix(719,126,816,143) (-3/17,-7/40) -> (7/8,15/17) Hyperbolic Matrix(961,168,1104,193) (-7/40,-4/23) -> (20/23,7/8) Hyperbolic Matrix(47,8,-288,-49) (-4/23,-1/6) -> (-1/6,-4/25) Parabolic Matrix(193,30,624,97) (-3/19,-2/13) -> (4/13,9/29) Hyperbolic Matrix(623,94,1584,239) (-5/33,-3/20) -> (11/28,13/33) Hyperbolic Matrix(143,20,336,47) (-1/7,-2/15) -> (14/33,3/7) Hyperbolic Matrix(911,118,1104,143) (-3/23,-1/8) -> (33/40,19/23) Hyperbolic Matrix(673,80,816,97) (-1/8,-2/17) -> (14/17,33/40) Hyperbolic Matrix(239,26,432,47) (-1/9,-1/10) -> (21/38,5/9) Hyperbolic Matrix(143,14,480,47) (-1/10,0/1) -> (14/47,3/10) Hyperbolic Matrix(335,-38,432,-49) (1/9,1/8) -> (31/40,7/9) Hyperbolic Matrix(335,-44,1104,-145) (1/8,2/15) -> (10/33,17/56) Hyperbolic Matrix(623,-92,1632,-241) (1/7,3/20) -> (29/76,21/55) Hyperbolic Matrix(289,-44,624,-95) (3/20,2/13) -> (6/13,13/28) Hyperbolic Matrix(239,-38,912,-145) (3/19,1/6) -> (11/42,5/19) Hyperbolic Matrix(289,-50,1104,-191) (1/6,4/23) -> (6/23,11/42) Hyperbolic Matrix(289,-52,528,-95) (3/17,2/11) -> (6/11,17/31) Hyperbolic Matrix(671,-142,912,-193) (4/19,3/14) -> (25/34,14/19) Hyperbolic Matrix(433,-98,1056,-239) (2/9,5/22) -> (9/22,16/39) Hyperbolic Matrix(815,-186,1056,-241) (5/22,3/13) -> (27/35,17/22) Hyperbolic Matrix(575,-136,816,-193) (4/17,1/4) -> (31/44,12/17) Hyperbolic Matrix(913,-236,1296,-335) (1/4,6/23) -> (50/71,31/44) Hyperbolic Matrix(719,-190,912,-241) (5/19,4/15) -> (26/33,15/19) Hyperbolic Matrix(529,-142,1248,-335) (4/15,7/26) -> (11/26,14/33) Hyperbolic Matrix(911,-246,1248,-337) (7/26,3/11) -> (27/37,19/26) Hyperbolic Matrix(335,-92,528,-145) (3/11,5/18) -> (19/30,7/11) Hyperbolic Matrix(623,-184,816,-241) (5/17,8/27) -> (16/21,13/17) Hyperbolic Matrix(671,-202,960,-289) (3/10,13/43) -> (37/53,7/10) Hyperbolic Matrix(769,-236,1248,-383) (11/36,4/13) -> (8/13,37/60) Hyperbolic Matrix(671,-234,1104,-385) (1/3,7/20) -> (17/28,31/51) Hyperbolic Matrix(433,-154,672,-239) (6/17,5/14) -> (9/14,20/31) Hyperbolic Matrix(383,-140,528,-193) (4/11,7/19) -> (21/29,8/11) Hyperbolic Matrix(145,-54,384,-143) (7/19,3/8) -> (3/8,11/29) Parabolic Matrix(5809,-2208,9216,-3503) (19/50,27/71) -> (75/119,29/46) Hyperbolic Matrix(6527,-2490,10320,-3937) (8/21,29/76) -> (43/68,74/117) Hyperbolic Matrix(3025,-1156,4896,-1871) (21/55,13/34) -> (21/34,55/89) Hyperbolic Matrix(2399,-918,3264,-1249) (13/34,18/47) -> (36/49,25/34) Hyperbolic Matrix(865,-332,1248,-479) (18/47,5/13) -> (9/13,34/49) Hyperbolic Matrix(2257,-874,3840,-1487) (12/31,31/80) -> (47/80,10/17) Hyperbolic Matrix(6047,-2344,7680,-2977) (31/80,19/49) -> (37/47,63/80) Hyperbolic Matrix(719,-282,1104,-433) (9/23,11/28) -> (13/20,15/23) Hyperbolic Matrix(2207,-900,2592,-1057) (11/27,20/49) -> (40/47,23/27) Hyperbolic Matrix(1967,-804,3408,-1393) (20/49,9/22) -> (15/26,56/97) Hyperbolic Matrix(721,-296,816,-335) (16/39,7/17) -> (15/17,8/9) Hyperbolic Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic Matrix(481,-202,912,-383) (13/31,21/50) -> (1/2,9/17) Hyperbolic Matrix(2015,-852,3408,-1441) (30/71,11/26) -> (13/22,42/71) Hyperbolic Matrix(2015,-902,3648,-1633) (17/38,13/29) -> (37/67,21/38) Hyperbolic Matrix(2015,-904,2784,-1249) (13/29,9/20) -> (55/76,21/29) Hyperbolic Matrix(433,-196,528,-239) (9/20,5/11) -> (9/11,23/28) Hyperbolic Matrix(479,-226,816,-385) (7/15,1/2) -> (27/46,37/63) Hyperbolic Matrix(1441,-764,2352,-1247) (9/17,8/15) -> (68/111,19/31) Hyperbolic Matrix(529,-284,624,-335) (8/15,7/13) -> (11/13,28/33) Hyperbolic Matrix(1487,-820,2352,-1297) (11/20,16/29) -> (12/19,43/68) Hyperbolic Matrix(913,-526,1248,-719) (4/7,15/26) -> (19/26,30/41) Hyperbolic Matrix(337,-196,576,-335) (11/19,7/12) -> (7/12,17/29) Parabolic Matrix(817,-482,1056,-623) (10/17,13/22) -> (17/22,24/31) Hyperbolic Matrix(4463,-2642,7056,-4177) (29/49,16/27) -> (74/117,31/49) Hyperbolic Matrix(5183,-3174,7056,-4321) (30/49,49/80) -> (47/64,36/49) Hyperbolic Matrix(1775,-1096,2256,-1393) (29/47,21/34) -> (11/14,37/47) Hyperbolic Matrix(1391,-860,1632,-1009) (34/55,13/21) -> (23/27,6/7) Hyperbolic Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(959,-668,1104,-769) (16/23,23/33) -> (13/15,20/23) Hyperbolic Matrix(3839,-2778,4512,-3265) (34/47,55/76) -> (17/20,40/47) Hyperbolic Matrix(767,-566,912,-673) (14/19,17/23) -> (21/25,16/19) Hyperbolic Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic Matrix(241,-200,288,-239) (19/23,5/6) -> (5/6,21/25) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,0,1) Matrix(337,304,480,433) -> Matrix(3,2,-2,-1) Matrix(193,172,432,385) -> Matrix(1,0,0,1) Matrix(97,86,-432,-383) -> Matrix(1,0,0,1) Matrix(769,668,-1104,-959) -> Matrix(1,0,0,1) Matrix(527,456,720,623) -> Matrix(1,0,0,1) Matrix(1009,860,-1632,-1391) -> Matrix(1,2,-2,-3) Matrix(335,284,-624,-529) -> Matrix(1,2,-2,-3) Matrix(431,364,624,527) -> Matrix(1,0,0,1) Matrix(673,566,-912,-767) -> Matrix(1,0,-2,1) Matrix(815,674,-1104,-913) -> Matrix(3,2,-8,-5) Matrix(671,554,2208,1823) -> Matrix(1,0,2,1) Matrix(1487,1226,1920,1583) -> Matrix(1,0,0,1) Matrix(239,196,-528,-433) -> Matrix(1,0,0,1) Matrix(385,314,1296,1057) -> Matrix(1,0,2,1) Matrix(145,118,768,625) -> Matrix(1,0,0,1) Matrix(143,116,768,623) -> Matrix(1,0,0,1) Matrix(97,78,240,193) -> Matrix(1,0,0,1) Matrix(191,152,240,191) -> Matrix(1,2,-2,-3) Matrix(721,570,912,721) -> Matrix(9,8,-8,-7) Matrix(241,190,-912,-719) -> Matrix(3,2,-2,-1) Matrix(431,338,672,527) -> Matrix(3,2,-2,-1) Matrix(241,188,432,337) -> Matrix(1,0,2,1) Matrix(623,482,-1056,-817) -> Matrix(1,0,0,1) Matrix(241,186,-1056,-815) -> Matrix(1,0,0,1) Matrix(383,294,624,479) -> Matrix(3,2,-2,-1) Matrix(241,184,-816,-623) -> Matrix(1,0,-4,1) Matrix(383,284,-1296,-961) -> Matrix(3,2,-14,-9) Matrix(193,142,-912,-671) -> Matrix(1,0,-2,1) Matrix(719,526,-1248,-913) -> Matrix(1,2,-2,-3) Matrix(337,246,-1248,-911) -> Matrix(1,0,0,1) Matrix(193,140,-528,-383) -> Matrix(1,0,0,1) Matrix(527,380,864,623) -> Matrix(1,-2,0,1) Matrix(145,104,336,241) -> Matrix(1,2,0,1) Matrix(239,170,336,239) -> Matrix(3,4,-4,-5) Matrix(577,408,816,577) -> Matrix(11,10,-10,-9) Matrix(193,136,-816,-575) -> Matrix(5,4,-4,-3) Matrix(239,168,1296,911) -> Matrix(3,2,-2,-1) Matrix(817,574,2256,1585) -> Matrix(3,2,-2,-1) Matrix(433,304,480,337) -> Matrix(3,2,-2,-1) Matrix(289,202,-960,-671) -> Matrix(3,2,-8,-5) Matrix(625,436,1584,1105) -> Matrix(5,2,2,1) Matrix(385,268,2208,1537) -> Matrix(3,2,-2,-1) Matrix(1105,768,1728,1201) -> Matrix(1,0,2,1) Matrix(479,332,-1248,-865) -> Matrix(1,0,-2,1) Matrix(527,364,624,431) -> Matrix(1,0,0,1) Matrix(241,166,768,529) -> Matrix(1,0,0,1) Matrix(239,164,768,527) -> Matrix(1,0,0,1) Matrix(527,360,912,623) -> Matrix(3,2,-2,-1) Matrix(433,282,-1104,-719) -> Matrix(3,2,-8,-5) Matrix(527,342,960,623) -> Matrix(3,2,-2,-1) Matrix(239,154,-672,-433) -> Matrix(1,0,0,1) Matrix(527,338,672,431) -> Matrix(3,2,-2,-1) Matrix(1201,768,1728,1105) -> Matrix(1,0,2,1) Matrix(2399,1532,3456,2207) -> Matrix(1,0,0,1) Matrix(671,428,2256,1439) -> Matrix(1,0,2,1) Matrix(145,92,-528,-335) -> Matrix(1,0,0,1) Matrix(239,150,-384,-241) -> Matrix(3,4,-4,-5) Matrix(1009,626,2400,1489) -> Matrix(5,4,6,5) Matrix(3407,2112,-9216,-5713) -> Matrix(21,16,-4,-3) Matrix(2399,1486,3408,2111) -> Matrix(17,12,-10,-7) Matrix(3793,2346,-10320,-6383) -> Matrix(3,2,-2,-1) Matrix(1871,1156,-4896,-3025) -> Matrix(3,2,-8,-5) Matrix(865,534,-3264,-2015) -> Matrix(3,2,-2,-1) Matrix(383,236,-1248,-769) -> Matrix(3,2,-2,-1) Matrix(479,294,624,383) -> Matrix(3,2,-2,-1) Matrix(1583,970,-3840,-2353) -> Matrix(3,2,-2,-1) Matrix(1633,1000,-7680,-4703) -> Matrix(3,2,-8,-5) Matrix(1249,764,1728,1057) -> Matrix(3,2,-2,-1) Matrix(623,380,864,527) -> Matrix(3,2,-8,-5) Matrix(385,234,-1104,-671) -> Matrix(3,2,-8,-5) Matrix(1345,816,1584,961) -> Matrix(3,2,-8,-5) Matrix(479,290,1584,959) -> Matrix(7,4,-2,-1) Matrix(47,28,240,143) -> Matrix(1,0,0,1) Matrix(385,228,-2592,-1535) -> Matrix(1,0,0,1) Matrix(1441,852,-3408,-2015) -> Matrix(1,0,-2,1) Matrix(95,56,-816,-481) -> Matrix(1,0,0,1) Matrix(335,196,-576,-337) -> Matrix(3,4,-4,-5) Matrix(431,250,-912,-529) -> Matrix(5,4,-14,-11) Matrix(911,528,2400,1391) -> Matrix(3,2,10,7) Matrix(623,360,912,527) -> Matrix(3,2,-2,-1) Matrix(817,472,1248,721) -> Matrix(5,4,-4,-3) Matrix(1393,804,-3408,-1967) -> Matrix(3,2,-2,-1) Matrix(289,166,336,193) -> Matrix(3,2,-2,-1) Matrix(95,54,336,191) -> Matrix(3,2,-8,-5) Matrix(337,190,768,433) -> Matrix(11,6,-2,-1) Matrix(335,188,768,431) -> Matrix(9,4,2,1) Matrix(337,188,432,241) -> Matrix(1,0,2,1) Matrix(47,26,432,239) -> Matrix(1,0,0,1) Matrix(1633,902,-3648,-2015) -> Matrix(1,0,0,1) Matrix(769,424,-2784,-1535) -> Matrix(1,0,0,1) Matrix(95,52,-528,-289) -> Matrix(1,0,0,1) Matrix(287,156,528,287) -> Matrix(1,0,0,1) Matrix(337,182,624,337) -> Matrix(5,4,-4,-3) Matrix(815,436,1344,719) -> Matrix(7,4,-2,-1) Matrix(337,178,-816,-431) -> Matrix(3,2,-2,-1) Matrix(911,428,-2352,-1105) -> Matrix(1,0,0,1) Matrix(95,44,-624,-289) -> Matrix(1,0,2,1) Matrix(287,132,624,287) -> Matrix(1,0,4,1) Matrix(241,110,528,241) -> Matrix(1,0,0,1) Matrix(337,152,960,433) -> Matrix(1,0,2,1) Matrix(865,388,-2352,-1055) -> Matrix(1,0,0,1) Matrix(5089,2280,9216,4129) -> Matrix(1,0,0,1) Matrix(5087,2278,9216,4127) -> Matrix(1,0,0,1) Matrix(385,172,432,193) -> Matrix(1,0,0,1) Matrix(95,42,432,191) -> Matrix(3,2,-2,-1) Matrix(433,190,768,337) -> Matrix(11,6,-2,-1) Matrix(431,188,768,335) -> Matrix(9,4,2,1) Matrix(241,104,336,145) -> Matrix(5,2,-8,-3) Matrix(335,142,-1248,-529) -> Matrix(1,0,2,1) Matrix(11759,4970,19872,8399) -> Matrix(1,0,2,1) Matrix(12097,5112,20448,8641) -> Matrix(7,2,-4,-1) Matrix(2831,1196,4656,1967) -> Matrix(7,2,-4,-1) Matrix(289,122,912,385) -> Matrix(1,0,2,1) Matrix(239,100,-576,-241) -> Matrix(1,0,4,1) Matrix(1393,576,2208,913) -> Matrix(1,0,-2,1) Matrix(6049,2496,7680,3169) -> Matrix(3,2,-2,-1) Matrix(239,98,-1056,-433) -> Matrix(1,0,0,1) Matrix(11807,4822,20448,8351) -> Matrix(7,2,-4,-1) Matrix(11473,4684,19872,8113) -> Matrix(3,2,-2,-1) Matrix(2593,1058,-7056,-2879) -> Matrix(1,0,0,1) Matrix(193,78,240,97) -> Matrix(1,0,0,1) Matrix(1105,436,1584,625) -> Matrix(5,2,2,1) Matrix(625,246,1344,529) -> Matrix(5,2,2,1) Matrix(2689,1054,4656,1825) -> Matrix(7,2,-4,-1) Matrix(241,94,864,337) -> Matrix(5,2,-8,-3) Matrix(1489,578,2352,913) -> Matrix(1,0,2,1) Matrix(1873,726,-7056,-2735) -> Matrix(1,0,2,1) Matrix(6097,2362,8304,3217) -> Matrix(1,0,2,1) Matrix(145,56,624,241) -> Matrix(1,0,2,1) Matrix(2881,1104,4512,1729) -> Matrix(1,0,2,1) Matrix(481,184,-2256,-863) -> Matrix(1,0,0,1) Matrix(12817,4896,20736,7921) -> Matrix(7,2,-4,-1) Matrix(12815,4894,20736,7919) -> Matrix(7,2,-4,-1) Matrix(241,92,-1632,-623) -> Matrix(1,0,2,1) Matrix(143,54,-384,-145) -> Matrix(1,0,4,1) Matrix(1681,622,2208,817) -> Matrix(1,-2,-2,5) Matrix(23233,8592,36864,13633) -> Matrix(1,-20,-2,41) Matrix(23231,8590,36864,13631) -> Matrix(1,22,-2,-43) Matrix(1295,478,2208,815) -> Matrix(1,2,-2,-3) Matrix(1439,528,2352,863) -> Matrix(3,2,-2,-1) Matrix(1585,574,2256,817) -> Matrix(3,2,-2,-1) Matrix(2783,1006,4512,1631) -> Matrix(3,2,-2,-1) Matrix(527,190,1728,623) -> Matrix(3,2,-2,-1) Matrix(145,52,672,241) -> Matrix(1,0,2,1) Matrix(1489,528,2304,817) -> Matrix(7,4,-2,-1) Matrix(1487,526,2304,815) -> Matrix(5,2,2,1) Matrix(671,236,816,287) -> Matrix(1,0,2,1) Matrix(527,182,1248,431) -> Matrix(1,0,4,1) Matrix(385,122,912,289) -> Matrix(1,0,2,1) Matrix(529,166,768,241) -> Matrix(1,0,0,1) Matrix(527,164,768,239) -> Matrix(1,0,0,1) Matrix(97,30,624,193) -> Matrix(1,0,0,1) Matrix(1249,382,3456,1057) -> Matrix(1,0,0,1) Matrix(623,190,1728,527) -> Matrix(3,2,-2,-1) Matrix(145,44,-1104,-335) -> Matrix(1,0,0,1) Matrix(959,290,1584,479) -> Matrix(7,4,-2,-1) Matrix(6433,1944,9216,2785) -> Matrix(19,10,-2,-1) Matrix(6431,1942,9216,2783) -> Matrix(17,8,2,1) Matrix(47,14,480,143) -> Matrix(1,0,2,1) Matrix(1439,428,2256,671) -> Matrix(1,0,2,1) Matrix(1057,314,1296,385) -> Matrix(1,0,2,1) Matrix(1297,384,3408,1009) -> Matrix(7,2,10,3) Matrix(239,70,816,239) -> Matrix(1,0,10,1) Matrix(97,28,336,97) -> Matrix(1,0,-4,1) Matrix(191,54,336,95) -> Matrix(1,-2,0,1) Matrix(337,94,864,241) -> Matrix(1,2,0,1) Matrix(671,186,1728,479) -> Matrix(1,0,2,1) Matrix(673,186,-4512,-1247) -> Matrix(1,0,0,1) Matrix(1681,456,2304,625) -> Matrix(1,0,0,1) Matrix(1679,454,2304,623) -> Matrix(1,0,0,1) Matrix(97,26,720,193) -> Matrix(1,0,0,1) Matrix(5087,1352,8304,2207) -> Matrix(3,2,-2,-1) Matrix(145,38,-912,-239) -> Matrix(3,2,-2,-1) Matrix(47,12,-192,-49) -> Matrix(1,0,2,1) Matrix(1391,332,2208,527) -> Matrix(1,4,-2,-7) Matrix(241,56,624,145) -> Matrix(1,0,2,1) Matrix(1777,408,2304,529) -> Matrix(1,0,0,1) Matrix(1775,406,2304,527) -> Matrix(1,0,0,1) Matrix(337,76,1920,433) -> Matrix(1,0,0,1) Matrix(191,42,432,95) -> Matrix(3,2,-2,-1) Matrix(241,52,672,145) -> Matrix(1,0,2,1) Matrix(4511,958,7680,1631) -> Matrix(1,0,2,1) Matrix(191,40,912,191) -> Matrix(1,0,8,1) Matrix(49,10,240,49) -> Matrix(1,0,-2,1) Matrix(143,28,240,47) -> Matrix(1,0,0,1) Matrix(625,118,768,145) -> Matrix(1,0,0,1) Matrix(623,116,768,143) -> Matrix(1,0,0,1) Matrix(911,168,1296,239) -> Matrix(3,2,-2,-1) Matrix(529,94,816,145) -> Matrix(3,2,-2,-1) Matrix(719,126,816,143) -> Matrix(1,0,0,1) Matrix(961,168,1104,193) -> Matrix(3,2,-2,-1) Matrix(47,8,-288,-49) -> Matrix(1,0,2,1) Matrix(193,30,624,97) -> Matrix(1,0,0,1) Matrix(623,94,1584,239) -> Matrix(1,2,0,1) Matrix(143,20,336,47) -> Matrix(1,0,2,1) Matrix(911,118,1104,143) -> Matrix(1,0,2,1) Matrix(673,80,816,97) -> Matrix(1,0,0,1) Matrix(239,26,432,47) -> Matrix(1,0,0,1) Matrix(143,14,480,47) -> Matrix(1,0,2,1) Matrix(335,-38,432,-49) -> Matrix(1,0,0,1) Matrix(335,-44,1104,-145) -> Matrix(1,0,0,1) Matrix(623,-92,1632,-241) -> Matrix(1,0,2,1) Matrix(289,-44,624,-95) -> Matrix(1,0,2,1) Matrix(239,-38,912,-145) -> Matrix(3,2,-2,-1) Matrix(289,-50,1104,-191) -> Matrix(1,-2,0,1) Matrix(289,-52,528,-95) -> Matrix(1,0,0,1) Matrix(671,-142,912,-193) -> Matrix(1,0,-2,1) Matrix(433,-98,1056,-239) -> Matrix(1,0,0,1) Matrix(815,-186,1056,-241) -> Matrix(1,0,0,1) Matrix(575,-136,816,-193) -> Matrix(5,4,-4,-3) Matrix(913,-236,1296,-335) -> Matrix(3,-4,-2,3) Matrix(719,-190,912,-241) -> Matrix(3,2,-2,-1) Matrix(529,-142,1248,-335) -> Matrix(1,0,2,1) Matrix(911,-246,1248,-337) -> Matrix(1,0,0,1) Matrix(335,-92,528,-145) -> Matrix(1,0,0,1) Matrix(623,-184,816,-241) -> Matrix(1,0,-4,1) Matrix(671,-202,960,-289) -> Matrix(1,-2,0,1) Matrix(769,-236,1248,-383) -> Matrix(3,2,-2,-1) Matrix(671,-234,1104,-385) -> Matrix(1,-2,0,1) Matrix(433,-154,672,-239) -> Matrix(1,0,0,1) Matrix(383,-140,528,-193) -> Matrix(1,0,0,1) Matrix(145,-54,384,-143) -> Matrix(1,0,4,1) Matrix(5809,-2208,9216,-3503) -> Matrix(9,-4,-20,9) Matrix(6527,-2490,10320,-3937) -> Matrix(1,0,-2,1) Matrix(3025,-1156,4896,-1871) -> Matrix(1,-2,0,1) Matrix(2399,-918,3264,-1249) -> Matrix(1,0,-2,1) Matrix(865,-332,1248,-479) -> Matrix(1,0,-2,1) Matrix(2257,-874,3840,-1487) -> Matrix(1,0,-2,1) Matrix(6047,-2344,7680,-2977) -> Matrix(1,-2,0,1) Matrix(719,-282,1104,-433) -> Matrix(1,-2,0,1) Matrix(2207,-900,2592,-1057) -> Matrix(1,0,0,1) Matrix(1967,-804,3408,-1393) -> Matrix(3,2,-2,-1) Matrix(721,-296,816,-335) -> Matrix(1,0,0,1) Matrix(241,-100,576,-239) -> Matrix(1,0,4,1) Matrix(481,-202,912,-383) -> Matrix(5,-2,-2,1) Matrix(2015,-852,3408,-1441) -> Matrix(1,0,-2,1) Matrix(2015,-902,3648,-1633) -> Matrix(1,0,0,1) Matrix(2015,-904,2784,-1249) -> Matrix(1,0,0,1) Matrix(433,-196,528,-239) -> Matrix(1,0,0,1) Matrix(479,-226,816,-385) -> Matrix(1,0,-2,1) Matrix(1441,-764,2352,-1247) -> Matrix(1,0,0,1) Matrix(529,-284,624,-335) -> Matrix(1,2,-2,-3) Matrix(1487,-820,2352,-1297) -> Matrix(1,0,0,1) Matrix(913,-526,1248,-719) -> Matrix(1,2,-2,-3) Matrix(337,-196,576,-335) -> Matrix(3,4,-4,-5) Matrix(817,-482,1056,-623) -> Matrix(1,0,0,1) Matrix(4463,-2642,7056,-4177) -> Matrix(1,0,0,1) Matrix(5183,-3174,7056,-4321) -> Matrix(1,2,-2,-3) Matrix(1775,-1096,2256,-1393) -> Matrix(1,0,0,1) Matrix(1391,-860,1632,-1009) -> Matrix(1,2,-2,-3) Matrix(241,-150,384,-239) -> Matrix(3,4,-4,-5) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(3839,-2778,4512,-3265) -> Matrix(1,0,0,1) Matrix(767,-566,912,-673) -> Matrix(1,0,-2,1) Matrix(145,-108,192,-143) -> Matrix(1,2,-2,-3) Matrix(241,-200,288,-239) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 43 Degree of the the map X: 43 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 768 Minimal number of generators: 129 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/10 1/9 1/8 2/15 1/7 3/20 2/13 3/19 1/6 4/23 3/17 2/11 3/16 4/21 1/5 5/24 3/14 2/9 5/22 1/4 4/15 5/18 7/24 11/36 5/16 1/3 13/36 3/8 8/21 31/80 7/18 5/12 7/16 9/20 11/24 1/2 53/96 9/16 7/12 71/120 89/144 5/8 121/192 31/48 2/3 11/16 67/96 35/48 47/64 3/4 37/48 13/16 5/6 7/8 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/1 0/1 1/10 -1/2 1/0 1/9 0/1 1/8 0/1 2/15 -1/1 1/7 -1/1 0/1 3/20 -1/1 2/13 -1/1 0/1 3/19 -1/1 0/1 1/6 0/1 4/23 -3/1 1/0 7/40 -1/1 3/17 0/1 1/0 2/11 -1/1 0/1 5/27 0/1 3/16 -1/2 1/0 4/21 -1/1 1/5 -1/2 0/1 5/24 0/1 4/19 0/1 1/3 3/14 1/2 1/0 5/23 0/1 1/0 2/9 -1/1 5/22 -1/2 1/0 3/13 -1/1 0/1 4/17 -1/1 1/0 1/4 0/1 6/23 -5/1 1/0 11/42 -2/1 5/19 -2/1 -1/1 4/15 -1/1 7/26 -1/2 1/0 3/11 -1/1 0/1 5/18 -1/1 7/25 -2/3 -1/2 2/7 -1/3 0/1 7/24 0/1 5/17 0/1 1/4 8/27 1/1 11/37 0/1 1/1 14/47 0/1 1/1 3/10 1/2 1/0 13/43 -4/1 1/0 10/33 -1/1 17/56 0/1 7/23 -2/1 1/0 11/36 -1/1 4/13 -1/1 0/1 9/29 -1/1 0/1 5/16 -1/2 1/0 6/19 -1/1 0/1 1/3 0/1 7/20 0/1 6/17 1/1 1/0 5/14 -1/2 1/0 9/25 0/1 1/0 13/36 -1/1 17/47 -1/1 0/1 4/11 -1/1 0/1 7/19 -1/1 0/1 3/8 0/1 11/29 0/1 1/3 19/50 5/12 1/2 27/71 1/2 8/15 8/21 1/1 29/76 1/1 21/55 0/1 1/1 13/34 1/2 1/0 18/47 0/1 1/1 5/13 0/1 1/1 12/31 1/1 1/0 31/80 1/2 1/0 19/49 0/1 1/1 7/18 1/1 9/23 0/1 1/0 11/28 1/1 13/33 2/1 2/5 -1/1 1/0 11/27 0/1 20/49 -1/1 0/1 9/22 -1/2 1/0 16/39 -1/1 7/17 -1/2 0/1 5/12 0/1 13/31 0/1 1/2 21/50 3/8 1/2 8/19 0/1 1/1 19/45 0/1 30/71 1/2 1/1 11/26 1/2 1/0 14/33 1/1 3/7 0/1 1/1 10/23 3/1 1/0 7/16 1/0 11/25 -2/1 1/0 4/9 -1/1 17/38 -1/2 1/0 13/29 -1/1 0/1 9/20 0/1 5/11 -1/1 0/1 11/24 0/1 6/13 0/1 1/1 13/28 1/1 7/15 0/1 1/2 -1/2 1/0 9/17 -2/1 1/0 8/15 -1/1 7/13 -2/1 -1/1 13/24 -1/1 6/11 -1/1 0/1 17/31 0/1 1/0 11/20 -1/1 16/29 -1/1 0/1 53/96 -1/2 1/0 37/67 -1/1 0/1 21/38 -1/2 1/0 5/9 0/1 14/25 1/1 1/0 9/16 1/0 13/23 -4/1 1/0 4/7 -2/1 -1/1 15/26 -3/2 1/0 56/97 -2/1 -1/1 97/168 -2/1 41/71 -2/1 -3/2 26/45 -1/1 11/19 -2/1 -1/1 7/12 -1/1 17/29 -1/1 -2/3 27/46 -1/2 -1/4 37/63 0/1 47/80 -1/2 1/0 10/17 -1/1 -1/2 13/22 -1/2 1/0 42/71 -1/1 1/0 71/120 -1/1 29/49 -1/1 0/1 16/27 -1/1 3/5 0/1 1/0 20/33 -3/1 17/28 -2/1 31/51 -2/1 14/23 -1/1 1/0 11/18 -2/1 30/49 -2/1 -1/1 49/80 -3/2 1/0 68/111 -1/1 19/31 -2/1 1/0 8/13 -2/1 -1/1 37/60 -1/1 29/47 -2/1 -1/1 21/34 -3/2 1/0 55/89 -2/1 -1/1 89/144 -3/2 1/0 34/55 -2/1 -1/1 13/21 -2/1 5/8 -1/1 17/27 -2/3 46/73 -9/17 -1/2 121/192 -1/2 75/119 -1/2 -12/25 29/46 -1/2 -3/8 12/19 -1/1 0/1 43/68 -1/1 74/117 -1/1 31/49 -1/1 0/1 19/30 -1/1 7/11 -1/1 0/1 30/47 -1/1 0/1 23/36 0/1 16/25 -1/1 1/0 9/14 -1/2 1/0 20/31 1/1 1/0 31/48 1/0 11/17 -2/1 1/0 13/20 -1/1 15/23 -2/1 1/0 2/3 -1/1 13/19 -1/1 0/1 11/16 -1/2 1/0 20/29 -1/1 0/1 9/13 -1/1 0/1 34/49 -1/1 0/1 25/36 0/1 16/23 1/1 1/0 23/33 0/1 30/43 3/1 1/0 67/96 1/0 37/53 -6/1 1/0 7/10 -3/2 1/0 33/47 -2/1 -1/1 26/37 -2/1 -1/1 19/27 -2/1 50/71 -3/2 -19/13 31/44 -4/3 12/17 -5/4 -1/1 17/24 -1/1 5/7 -1/1 -2/3 18/25 -1/2 -1/3 13/18 0/1 34/47 -1/1 0/1 55/76 0/1 21/29 -1/1 0/1 8/11 -1/1 0/1 35/48 -1/2 1/0 27/37 -1/1 0/1 19/26 -1/2 1/0 30/41 -1/1 0/1 11/15 0/1 47/64 -1/2 1/0 36/49 -1/1 0/1 25/34 -1/2 1/0 14/19 0/1 1/1 17/23 4/1 1/0 3/4 -1/1 19/25 -6/11 -1/2 16/21 -1/3 13/17 0/1 1/0 10/13 -1/1 0/1 37/48 -1/2 1/0 27/35 -1/1 0/1 17/22 -1/2 1/0 24/31 -1/1 -1/2 31/40 0/1 7/9 0/1 18/23 -1/1 1/0 11/14 -3/2 1/0 37/47 -2/1 -1/1 63/80 -3/2 1/0 26/33 -1/1 15/19 -4/3 -1/1 19/24 -1/1 4/5 -1/1 -1/2 17/21 0/1 13/16 -1/2 1/0 22/27 -1/1 9/11 -1/1 0/1 23/28 0/1 14/17 -1/1 1/0 33/40 0/1 19/23 2/1 1/0 5/6 -1/1 21/25 -4/7 -1/2 16/19 -1/1 0/1 11/13 -1/1 0/1 28/33 -1/1 17/20 0/1 40/47 -1/1 0/1 23/27 0/1 6/7 -1/1 0/1 13/15 0/1 20/23 1/1 1/0 7/8 -1/1 15/17 -1/2 0/1 8/9 -1/1 9/10 -1/2 1/0 1/1 -1/1 0/1 1/0 -1/2 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(337,-33,480,-47) (0/1,1/10) -> (7/10,33/47) Hyperbolic Matrix(193,-21,432,-47) (1/10,1/9) -> (4/9,17/38) Hyperbolic Matrix(335,-38,432,-49) (1/9,1/8) -> (31/40,7/9) Hyperbolic Matrix(335,-44,1104,-145) (1/8,2/15) -> (10/33,17/56) Hyperbolic Matrix(527,-71,720,-97) (2/15,1/7) -> (30/41,11/15) Hyperbolic Matrix(623,-92,1632,-241) (1/7,3/20) -> (29/76,21/55) Hyperbolic Matrix(289,-44,624,-95) (3/20,2/13) -> (6/13,13/28) Hyperbolic Matrix(431,-67,624,-97) (2/13,3/19) -> (20/29,9/13) Hyperbolic Matrix(239,-38,912,-145) (3/19,1/6) -> (11/42,5/19) Hyperbolic Matrix(289,-50,1104,-191) (1/6,4/23) -> (6/23,11/42) Hyperbolic Matrix(671,-117,2208,-385) (4/23,7/40) -> (17/56,7/23) Hyperbolic Matrix(1487,-261,1920,-337) (7/40,3/17) -> (24/31,31/40) Hyperbolic Matrix(289,-52,528,-95) (3/17,2/11) -> (6/11,17/31) Hyperbolic Matrix(385,-71,1296,-239) (2/11,5/27) -> (8/27,11/37) Hyperbolic Matrix(145,-27,768,-143) (5/27,3/16) -> (3/16,4/21) Parabolic Matrix(97,-19,240,-47) (4/21,1/5) -> (2/5,11/27) Hyperbolic Matrix(191,-39,240,-49) (1/5,5/24) -> (19/24,4/5) Hyperbolic Matrix(721,-151,912,-191) (5/24,4/19) -> (15/19,19/24) Hyperbolic Matrix(671,-142,912,-193) (4/19,3/14) -> (25/34,14/19) Hyperbolic Matrix(431,-93,672,-145) (3/14,5/23) -> (16/25,9/14) Hyperbolic Matrix(241,-53,432,-95) (5/23,2/9) -> (5/9,14/25) Hyperbolic Matrix(433,-98,1056,-239) (2/9,5/22) -> (9/22,16/39) Hyperbolic Matrix(815,-186,1056,-241) (5/22,3/13) -> (27/35,17/22) Hyperbolic Matrix(383,-89,624,-145) (3/13,4/17) -> (19/31,8/13) Hyperbolic Matrix(575,-136,816,-193) (4/17,1/4) -> (31/44,12/17) Hyperbolic Matrix(913,-236,1296,-335) (1/4,6/23) -> (50/71,31/44) Hyperbolic Matrix(719,-190,912,-241) (5/19,4/15) -> (26/33,15/19) Hyperbolic Matrix(529,-142,1248,-335) (4/15,7/26) -> (11/26,14/33) Hyperbolic Matrix(911,-246,1248,-337) (7/26,3/11) -> (27/37,19/26) Hyperbolic Matrix(335,-92,528,-145) (3/11,5/18) -> (19/30,7/11) Hyperbolic Matrix(527,-147,864,-241) (5/18,7/25) -> (14/23,11/18) Hyperbolic Matrix(145,-41,336,-95) (7/25,2/7) -> (3/7,10/23) Hyperbolic Matrix(239,-69,336,-97) (2/7,7/24) -> (17/24,5/7) Hyperbolic Matrix(577,-169,816,-239) (7/24,5/17) -> (12/17,17/24) Hyperbolic Matrix(623,-184,816,-241) (5/17,8/27) -> (16/21,13/17) Hyperbolic Matrix(817,-243,2256,-671) (11/37,14/47) -> (17/47,4/11) Hyperbolic Matrix(433,-129,480,-143) (14/47,3/10) -> (9/10,1/1) Hyperbolic Matrix(671,-202,960,-289) (3/10,13/43) -> (37/53,7/10) Hyperbolic Matrix(625,-189,1584,-479) (13/43,10/33) -> (13/33,2/5) Hyperbolic Matrix(1105,-337,1728,-527) (7/23,11/36) -> (23/36,16/25) Hyperbolic Matrix(769,-236,1248,-383) (11/36,4/13) -> (8/13,37/60) Hyperbolic Matrix(527,-163,624,-193) (4/13,9/29) -> (16/19,11/13) Hyperbolic Matrix(241,-75,768,-239) (9/29,5/16) -> (5/16,6/19) Parabolic Matrix(527,-167,912,-289) (6/19,1/3) -> (26/45,11/19) Hyperbolic Matrix(671,-234,1104,-385) (1/3,7/20) -> (17/28,31/51) Hyperbolic Matrix(527,-185,960,-337) (7/20,6/17) -> (17/31,11/20) Hyperbolic Matrix(433,-154,672,-239) (6/17,5/14) -> (9/14,20/31) Hyperbolic Matrix(527,-189,672,-241) (5/14,9/25) -> (18/23,11/14) Hyperbolic Matrix(1201,-433,1728,-623) (9/25,13/36) -> (25/36,16/23) Hyperbolic Matrix(2399,-867,3456,-1249) (13/36,17/47) -> (34/49,25/36) Hyperbolic Matrix(383,-140,528,-193) (4/11,7/19) -> (21/29,8/11) Hyperbolic Matrix(145,-54,384,-143) (7/19,3/8) -> (3/8,11/29) Parabolic Matrix(1009,-383,2400,-911) (11/29,19/50) -> (21/50,8/19) Hyperbolic Matrix(5809,-2208,9216,-3503) (19/50,27/71) -> (75/119,29/46) Hyperbolic Matrix(2399,-913,3408,-1297) (27/71,8/21) -> (19/27,50/71) Hyperbolic Matrix(6527,-2490,10320,-3937) (8/21,29/76) -> (43/68,74/117) Hyperbolic Matrix(3025,-1156,4896,-1871) (21/55,13/34) -> (21/34,55/89) Hyperbolic Matrix(2399,-918,3264,-1249) (13/34,18/47) -> (36/49,25/34) Hyperbolic Matrix(865,-332,1248,-479) (18/47,5/13) -> (9/13,34/49) Hyperbolic Matrix(479,-185,624,-241) (5/13,12/31) -> (13/17,10/13) Hyperbolic Matrix(2257,-874,3840,-1487) (12/31,31/80) -> (47/80,10/17) Hyperbolic Matrix(6047,-2344,7680,-2977) (31/80,19/49) -> (37/47,63/80) Hyperbolic Matrix(1249,-485,1728,-671) (19/49,7/18) -> (13/18,34/47) Hyperbolic Matrix(623,-243,864,-337) (7/18,9/23) -> (18/25,13/18) Hyperbolic Matrix(719,-282,1104,-433) (9/23,11/28) -> (13/20,15/23) Hyperbolic Matrix(1345,-529,1584,-623) (11/28,13/33) -> (28/33,17/20) Hyperbolic Matrix(2207,-900,2592,-1057) (11/27,20/49) -> (40/47,23/27) Hyperbolic Matrix(1967,-804,3408,-1393) (20/49,9/22) -> (15/26,56/97) Hyperbolic Matrix(721,-296,816,-335) (16/39,7/17) -> (15/17,8/9) Hyperbolic Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic Matrix(481,-202,912,-383) (13/31,21/50) -> (1/2,9/17) Hyperbolic Matrix(623,-263,912,-385) (8/19,19/45) -> (2/3,13/19) Hyperbolic Matrix(817,-345,1248,-527) (19/45,30/71) -> (15/23,2/3) Hyperbolic Matrix(2015,-852,3408,-1441) (30/71,11/26) -> (13/22,42/71) Hyperbolic Matrix(289,-123,336,-143) (14/33,3/7) -> (6/7,13/15) Hyperbolic Matrix(337,-147,768,-335) (10/23,7/16) -> (7/16,11/25) Parabolic Matrix(337,-149,432,-191) (11/25,4/9) -> (7/9,18/23) Hyperbolic Matrix(2015,-902,3648,-1633) (17/38,13/29) -> (37/67,21/38) Hyperbolic Matrix(2015,-904,2784,-1249) (13/29,9/20) -> (55/76,21/29) Hyperbolic Matrix(433,-196,528,-239) (9/20,5/11) -> (9/11,23/28) Hyperbolic Matrix(287,-131,528,-241) (5/11,11/24) -> (13/24,6/11) Hyperbolic Matrix(337,-155,624,-287) (11/24,6/13) -> (7/13,13/24) Hyperbolic Matrix(815,-379,1344,-625) (13/28,7/15) -> (20/33,17/28) Hyperbolic Matrix(479,-226,816,-385) (7/15,1/2) -> (27/46,37/63) Hyperbolic Matrix(1441,-764,2352,-1247) (9/17,8/15) -> (68/111,19/31) Hyperbolic Matrix(529,-284,624,-335) (8/15,7/13) -> (11/13,28/33) Hyperbolic Matrix(1487,-820,2352,-1297) (11/20,16/29) -> (12/19,43/68) Hyperbolic Matrix(5089,-2809,9216,-5087) (16/29,53/96) -> (53/96,37/67) Parabolic Matrix(385,-213,432,-239) (21/38,5/9) -> (8/9,9/10) Hyperbolic Matrix(433,-243,768,-431) (14/25,9/16) -> (9/16,13/23) Parabolic Matrix(241,-137,336,-191) (13/23,4/7) -> (5/7,18/25) Hyperbolic Matrix(913,-526,1248,-719) (4/7,15/26) -> (19/26,30/41) Hyperbolic Matrix(11759,-6789,19872,-11473) (56/97,97/168) -> (71/120,29/49) Hyperbolic Matrix(12097,-6985,20448,-11807) (97/168,41/71) -> (42/71,71/120) Hyperbolic Matrix(2831,-1635,4656,-2689) (41/71,26/45) -> (31/51,14/23) Hyperbolic Matrix(337,-196,576,-335) (11/19,7/12) -> (7/12,17/29) Parabolic Matrix(1393,-817,2208,-1295) (17/29,27/46) -> (29/46,12/19) Hyperbolic Matrix(6049,-3553,7680,-4511) (37/63,47/80) -> (63/80,26/33) Hyperbolic Matrix(817,-482,1056,-623) (10/17,13/22) -> (17/22,24/31) Hyperbolic Matrix(4463,-2642,7056,-4177) (29/49,16/27) -> (74/117,31/49) Hyperbolic Matrix(193,-115,240,-143) (16/27,3/5) -> (4/5,17/21) Hyperbolic Matrix(1105,-669,1584,-959) (3/5,20/33) -> (23/33,30/43) Hyperbolic Matrix(1489,-911,2352,-1439) (11/18,30/49) -> (31/49,19/30) Hyperbolic Matrix(5183,-3174,7056,-4321) (30/49,49/80) -> (47/64,36/49) Hyperbolic Matrix(6097,-3735,8304,-5087) (49/80,68/111) -> (11/15,47/64) Hyperbolic Matrix(2881,-1777,4512,-2783) (37/60,29/47) -> (30/47,23/36) Hyperbolic Matrix(1775,-1096,2256,-1393) (29/47,21/34) -> (11/14,37/47) Hyperbolic Matrix(12817,-7921,20736,-12815) (55/89,89/144) -> (89/144,34/55) Parabolic Matrix(1391,-860,1632,-1009) (34/55,13/21) -> (23/27,6/7) Hyperbolic Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(1681,-1059,2208,-1391) (17/27,46/73) -> (19/25,16/21) Hyperbolic Matrix(23233,-14641,36864,-23231) (46/73,121/192) -> (121/192,75/119) Parabolic Matrix(1585,-1011,2256,-1439) (7/11,30/47) -> (33/47,26/37) Hyperbolic Matrix(1489,-961,2304,-1487) (20/31,31/48) -> (31/48,11/17) Parabolic Matrix(671,-435,816,-529) (11/17,13/20) -> (23/28,14/17) Hyperbolic Matrix(529,-363,768,-527) (13/19,11/16) -> (11/16,20/29) Parabolic Matrix(959,-668,1104,-769) (16/23,23/33) -> (13/15,20/23) Hyperbolic Matrix(6433,-4489,9216,-6431) (30/43,67/96) -> (67/96,37/53) Parabolic Matrix(1057,-743,1296,-911) (26/37,19/27) -> (22/27,9/11) Hyperbolic Matrix(3839,-2778,4512,-3265) (34/47,55/76) -> (17/20,40/47) Hyperbolic Matrix(1681,-1225,2304,-1679) (8/11,35/48) -> (35/48,27/37) Parabolic Matrix(767,-566,912,-673) (14/19,17/23) -> (21/25,16/19) Hyperbolic Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic Matrix(1777,-1369,2304,-1775) (10/13,37/48) -> (37/48,27/35) Parabolic Matrix(625,-507,768,-623) (17/21,13/16) -> (13/16,22/27) Parabolic Matrix(719,-593,816,-673) (14/17,33/40) -> (7/8,15/17) Hyperbolic Matrix(961,-793,1104,-911) (33/40,19/23) -> (20/23,7/8) Hyperbolic Matrix(241,-200,288,-239) (19/23,5/6) -> (5/6,21/25) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,1,-2,-1) Matrix(337,-33,480,-47) -> Matrix(1,-1,0,1) Matrix(193,-21,432,-47) -> Matrix(1,1,-2,-1) Matrix(335,-38,432,-49) -> Matrix(1,0,0,1) Matrix(335,-44,1104,-145) -> Matrix(1,0,0,1) Matrix(527,-71,720,-97) -> Matrix(1,1,-2,-1) Matrix(623,-92,1632,-241) -> Matrix(1,0,2,1) Matrix(289,-44,624,-95) -> Matrix(1,0,2,1) Matrix(431,-67,624,-97) -> Matrix(1,1,-2,-1) Matrix(239,-38,912,-145) -> Matrix(3,2,-2,-1) Matrix(289,-50,1104,-191) -> Matrix(1,-2,0,1) Matrix(671,-117,2208,-385) -> Matrix(1,1,0,1) Matrix(1487,-261,1920,-337) -> Matrix(1,1,-2,-1) Matrix(289,-52,528,-95) -> Matrix(1,0,0,1) Matrix(385,-71,1296,-239) -> Matrix(1,1,0,1) Matrix(145,-27,768,-143) -> Matrix(1,1,-2,-1) Matrix(97,-19,240,-47) -> Matrix(1,1,-2,-1) Matrix(191,-39,240,-49) -> Matrix(3,1,-4,-1) Matrix(721,-151,912,-191) -> Matrix(7,-1,-6,1) Matrix(671,-142,912,-193) -> Matrix(1,0,-2,1) Matrix(431,-93,672,-145) -> Matrix(1,-1,0,1) Matrix(241,-53,432,-95) -> Matrix(1,1,0,1) Matrix(433,-98,1056,-239) -> Matrix(1,0,0,1) Matrix(815,-186,1056,-241) -> Matrix(1,0,0,1) Matrix(383,-89,624,-145) -> Matrix(1,-1,0,1) Matrix(575,-136,816,-193) -> Matrix(5,4,-4,-3) Matrix(913,-236,1296,-335) -> Matrix(3,-4,-2,3) Matrix(719,-190,912,-241) -> Matrix(3,2,-2,-1) Matrix(529,-142,1248,-335) -> Matrix(1,0,2,1) Matrix(911,-246,1248,-337) -> Matrix(1,0,0,1) Matrix(335,-92,528,-145) -> Matrix(1,0,0,1) Matrix(527,-147,864,-241) -> Matrix(5,3,-2,-1) Matrix(145,-41,336,-95) -> Matrix(3,1,2,1) Matrix(239,-69,336,-97) -> Matrix(5,1,-6,-1) Matrix(577,-169,816,-239) -> Matrix(9,-1,-8,1) Matrix(623,-184,816,-241) -> Matrix(1,0,-4,1) Matrix(817,-243,2256,-671) -> Matrix(1,-1,0,1) Matrix(433,-129,480,-143) -> Matrix(1,-1,0,1) Matrix(671,-202,960,-289) -> Matrix(1,-2,0,1) Matrix(625,-189,1584,-479) -> Matrix(1,3,0,1) Matrix(1105,-337,1728,-527) -> Matrix(1,1,0,1) Matrix(769,-236,1248,-383) -> Matrix(3,2,-2,-1) Matrix(527,-163,624,-193) -> Matrix(1,1,-2,-1) Matrix(241,-75,768,-239) -> Matrix(1,1,-2,-1) Matrix(527,-167,912,-289) -> Matrix(1,-1,0,1) Matrix(671,-234,1104,-385) -> Matrix(1,-2,0,1) Matrix(527,-185,960,-337) -> Matrix(1,-1,0,1) Matrix(433,-154,672,-239) -> Matrix(1,0,0,1) Matrix(527,-189,672,-241) -> Matrix(1,-1,0,1) Matrix(1201,-433,1728,-623) -> Matrix(1,1,0,1) Matrix(2399,-867,3456,-1249) -> Matrix(1,1,-2,-1) Matrix(383,-140,528,-193) -> Matrix(1,0,0,1) Matrix(145,-54,384,-143) -> Matrix(1,0,4,1) Matrix(1009,-383,2400,-911) -> Matrix(3,-1,4,-1) Matrix(5809,-2208,9216,-3503) -> Matrix(9,-4,-20,9) Matrix(2399,-913,3408,-1297) -> Matrix(7,-5,-4,3) Matrix(6527,-2490,10320,-3937) -> Matrix(1,0,-2,1) Matrix(3025,-1156,4896,-1871) -> Matrix(1,-2,0,1) Matrix(2399,-918,3264,-1249) -> Matrix(1,0,-2,1) Matrix(865,-332,1248,-479) -> Matrix(1,0,-2,1) Matrix(479,-185,624,-241) -> Matrix(1,-1,0,1) Matrix(2257,-874,3840,-1487) -> Matrix(1,0,-2,1) Matrix(6047,-2344,7680,-2977) -> Matrix(1,-2,0,1) Matrix(1249,-485,1728,-671) -> Matrix(1,-1,0,1) Matrix(623,-243,864,-337) -> Matrix(1,-1,-2,3) Matrix(719,-282,1104,-433) -> Matrix(1,-2,0,1) Matrix(1345,-529,1584,-623) -> Matrix(1,-1,-2,3) Matrix(2207,-900,2592,-1057) -> Matrix(1,0,0,1) Matrix(1967,-804,3408,-1393) -> Matrix(3,2,-2,-1) Matrix(721,-296,816,-335) -> Matrix(1,0,0,1) Matrix(241,-100,576,-239) -> Matrix(1,0,4,1) Matrix(481,-202,912,-383) -> Matrix(5,-2,-2,1) Matrix(623,-263,912,-385) -> Matrix(1,-1,0,1) Matrix(817,-345,1248,-527) -> Matrix(3,-1,-2,1) Matrix(2015,-852,3408,-1441) -> Matrix(1,0,-2,1) Matrix(289,-123,336,-143) -> Matrix(1,-1,0,1) Matrix(337,-147,768,-335) -> Matrix(1,-5,0,1) Matrix(337,-149,432,-191) -> Matrix(1,1,0,1) Matrix(2015,-902,3648,-1633) -> Matrix(1,0,0,1) Matrix(2015,-904,2784,-1249) -> Matrix(1,0,0,1) Matrix(433,-196,528,-239) -> Matrix(1,0,0,1) Matrix(287,-131,528,-241) -> Matrix(1,1,-2,-1) Matrix(337,-155,624,-287) -> Matrix(3,-1,-2,1) Matrix(815,-379,1344,-625) -> Matrix(1,-3,0,1) Matrix(479,-226,816,-385) -> Matrix(1,0,-2,1) Matrix(1441,-764,2352,-1247) -> Matrix(1,0,0,1) Matrix(529,-284,624,-335) -> Matrix(1,2,-2,-3) Matrix(1487,-820,2352,-1297) -> Matrix(1,0,0,1) Matrix(5089,-2809,9216,-5087) -> Matrix(1,1,-2,-1) Matrix(385,-213,432,-239) -> Matrix(1,1,-2,-1) Matrix(433,-243,768,-431) -> Matrix(1,-5,0,1) Matrix(241,-137,336,-191) -> Matrix(1,3,-2,-5) Matrix(913,-526,1248,-719) -> Matrix(1,2,-2,-3) Matrix(11759,-6789,19872,-11473) -> Matrix(1,1,0,1) Matrix(12097,-6985,20448,-11807) -> Matrix(3,5,-2,-3) Matrix(2831,-1635,4656,-2689) -> Matrix(3,5,-2,-3) Matrix(337,-196,576,-335) -> Matrix(3,4,-4,-5) Matrix(1393,-817,2208,-1295) -> Matrix(1,1,-4,-3) Matrix(6049,-3553,7680,-4511) -> Matrix(1,-1,0,1) Matrix(817,-482,1056,-623) -> Matrix(1,0,0,1) Matrix(4463,-2642,7056,-4177) -> Matrix(1,0,0,1) Matrix(193,-115,240,-143) -> Matrix(1,1,-2,-1) Matrix(1105,-669,1584,-959) -> Matrix(1,3,0,1) Matrix(1489,-911,2352,-1439) -> Matrix(1,1,0,1) Matrix(5183,-3174,7056,-4321) -> Matrix(1,2,-2,-3) Matrix(6097,-3735,8304,-5087) -> Matrix(1,1,0,1) Matrix(2881,-1777,4512,-2783) -> Matrix(1,1,0,1) Matrix(1775,-1096,2256,-1393) -> Matrix(1,0,0,1) Matrix(12817,-7921,20736,-12815) -> Matrix(3,5,-2,-3) Matrix(1391,-860,1632,-1009) -> Matrix(1,2,-2,-3) Matrix(241,-150,384,-239) -> Matrix(3,4,-4,-5) Matrix(1681,-1059,2208,-1391) -> Matrix(5,3,-12,-7) Matrix(23233,-14641,36864,-23231) -> Matrix(41,21,-84,-43) Matrix(1585,-1011,2256,-1439) -> Matrix(1,-1,0,1) Matrix(1489,-961,2304,-1487) -> Matrix(1,-3,0,1) Matrix(671,-435,816,-529) -> Matrix(1,1,0,1) Matrix(529,-363,768,-527) -> Matrix(1,1,-2,-1) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(6433,-4489,9216,-6431) -> Matrix(1,-9,0,1) Matrix(1057,-743,1296,-911) -> Matrix(1,1,0,1) Matrix(3839,-2778,4512,-3265) -> Matrix(1,0,0,1) Matrix(1681,-1225,2304,-1679) -> Matrix(1,1,-2,-1) Matrix(767,-566,912,-673) -> Matrix(1,0,-2,1) Matrix(145,-108,192,-143) -> Matrix(1,2,-2,-3) Matrix(1777,-1369,2304,-1775) -> Matrix(1,1,-2,-1) Matrix(625,-507,768,-623) -> Matrix(1,1,-2,-1) Matrix(719,-593,816,-673) -> Matrix(1,1,-2,-1) Matrix(961,-793,1104,-911) -> Matrix(1,-1,0,1) Matrix(241,-200,288,-239) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 43 ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 24 1/10 (-1/2,1/0) 0 12 1/9 0/1 1 8 1/8 0/1 1 3 2/15 -1/1 1 8 1/7 (-1/1,0/1) 0 24 3/20 -1/1 1 6 2/13 (-1/1,0/1) 0 24 3/19 (-1/1,0/1) 0 24 1/6 0/1 1 4 4/23 (-3/1,1/0) 0 24 7/40 -1/1 1 3 3/17 (0/1,1/0) 0 24 2/11 (-1/1,0/1) 0 24 5/27 0/1 1 8 3/16 (-1/1,0/1).(-1/2,1/0) 0 3 4/21 -1/1 1 8 1/5 (-1/2,0/1) 0 24 5/24 0/1 5 1 4/19 (0/1,1/3) 0 24 3/14 (1/2,1/0) 0 12 5/23 (0/1,1/0) 0 24 2/9 -1/1 1 8 5/22 (-1/2,1/0) 0 12 11/48 (-1/1,0/1).(-1/2,1/0) 0 1 3/13 (-1/1,0/1) 0 24 4/17 (-1/1,1/0) 0 24 1/4 0/1 1 6 6/23 (-5/1,1/0) 0 24 11/42 -2/1 1 4 5/19 (-2/1,-1/1) 0 24 9/34 (-1/2,1/0) 0 12 4/15 -1/1 1 8 7/26 (-1/2,1/0) 0 12 13/48 (-1/1,0/1).(-1/2,1/0) 0 1 3/11 (-1/1,0/1) 0 24 5/18 -1/1 1 4 7/25 (-2/3,-1/2) 0 24 2/7 (-1/3,0/1) 0 24 7/24 0/1 7 1 5/17 (0/1,1/4) 0 24 13/44 1/3 1 6 21/71 (6/13,1/2) 0 24 8/27 1/1 1 8 11/37 (0/1,1/1) 0 24 14/47 (0/1,1/1) 0 24 3/10 (1/2,1/0) 0 12 29/96 1/0 9 1 13/43 (-4/1,1/0) 0 24 10/33 -1/1 1 8 17/56 0/1 1 3 7/23 (-2/1,1/0) 0 24 11/36 -1/1 1 2 4/13 (-1/1,0/1) 0 24 9/29 (-1/1,0/1) 0 24 5/16 (-1/1,0/1).(-1/2,1/0) 0 3 6/19 (-1/1,0/1) 0 24 1/3 0/1 1 8 7/20 0/1 1 6 6/17 (1/1,1/0) 0 24 17/48 1/0 3 1 5/14 (-1/2,1/0) 0 12 9/25 (0/1,1/0) 0 24 13/36 -1/1 1 2 17/47 (-1/1,0/1) 0 24 4/11 (-1/1,0/1) 0 24 11/30 0/1 1 4 18/49 (-1/1,0/1) 0 24 7/19 (-1/1,0/1) 0 24 3/8 0/1 2 3 11/29 (0/1,1/3) 0 24 19/50 (5/12,1/2) 0 12 73/192 1/2 21 1 27/71 (1/2,8/15) 0 24 8/21 1/1 1 8 29/76 1/1 1 6 21/55 (0/1,1/1) 0 24 55/144 (0/1,1/1).(1/2,1/0) 0 1 13/34 (1/2,1/0) 0 12 31/81 0/1 1 8 18/47 (0/1,1/1) 0 24 23/60 0/1 1 2 5/13 (0/1,1/1) 0 24 12/31 (1/1,1/0) 0 24 31/80 (0/1,1/1).(1/2,1/0) 0 3 50/129 1/1 1 8 19/49 (0/1,1/1) 0 24 7/18 1/1 1 4 9/23 (0/1,1/0) 0 24 20/51 1/1 1 8 11/28 1/1 1 6 13/33 2/1 1 8 2/5 (-1/1,1/0) 0 24 11/27 0/1 1 8 20/49 (-1/1,0/1) 0 24 9/22 (-1/2,1/0) 0 12 16/39 -1/1 1 8 23/56 -1/1 1 3 7/17 (-1/2,0/1) 0 24 5/12 0/1 2 2 13/31 (0/1,1/2) 0 24 21/50 (3/8,1/2) 0 12 8/19 (0/1,1/1) 0 24 19/45 0/1 1 8 30/71 (1/2,1/1) 0 24 71/168 1/1 1 1 41/97 (0/1,1/1) 0 24 11/26 (1/2,1/0) 0 12 14/33 1/1 1 8 3/7 (0/1,1/1) 0 24 10/23 (3/1,1/0) 0 24 7/16 1/0 5 3 11/25 (-2/1,1/0) 0 24 4/9 -1/1 1 8 17/38 (-1/2,1/0) 0 12 43/96 (-1/1,0/1).(-1/2,1/0) 0 1 13/29 (-1/1,0/1) 0 24 22/49 (-1/1,0/1) 0 24 31/69 0/1 1 8 9/20 0/1 1 6 14/31 (-1/1,1/0) 0 24 5/11 (-1/1,0/1) 0 24 11/24 0/1 2 1 6/13 (0/1,1/1) 0 24 13/28 1/1 1 6 7/15 0/1 1 8 15/32 (0/1,1/1).(1/2,1/0) 0 3 8/17 (1/1,1/0) 0 24 1/2 (-1/2,1/0) 0 12 1/0 (-1/1,0/1).(-1/2,1/0) 0 1 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(143,-14,480,-47) (0/1,1/10) -> (14/47,3/10) Glide Reflection Matrix(193,-21,432,-47) (1/10,1/9) -> (4/9,17/38) Hyperbolic Matrix(335,-39,816,-95) (1/9,1/8) -> (16/39,23/56) Glide Reflection Matrix(335,-44,1104,-145) (1/8,2/15) -> (10/33,17/56) Hyperbolic Matrix(143,-20,336,-47) (2/15,1/7) -> (14/33,3/7) Glide Reflection Matrix(623,-92,1632,-241) (1/7,3/20) -> (29/76,21/55) Hyperbolic Matrix(289,-44,624,-95) (3/20,2/13) -> (6/13,13/28) Hyperbolic Matrix(193,-30,624,-97) (2/13,3/19) -> (4/13,9/29) Glide Reflection Matrix(239,-38,912,-145) (3/19,1/6) -> (11/42,5/19) Hyperbolic Matrix(289,-50,1104,-191) (1/6,4/23) -> (6/23,11/42) Hyperbolic Matrix(671,-117,2208,-385) (4/23,7/40) -> (17/56,7/23) Hyperbolic Matrix(671,-118,1632,-287) (7/40,3/17) -> (23/56,7/17) Glide Reflection Matrix(239,-43,528,-95) (3/17,2/11) -> (14/31,5/11) Glide Reflection Matrix(385,-71,1296,-239) (2/11,5/27) -> (8/27,11/37) Hyperbolic Matrix(145,-27,768,-143) (5/27,3/16) -> (3/16,4/21) Parabolic Matrix(97,-19,240,-47) (4/21,1/5) -> (2/5,11/27) Hyperbolic Matrix(49,-10,240,-49) (1/5,5/24) -> (1/5,5/24) Reflection Matrix(191,-40,912,-191) (5/24,4/19) -> (5/24,4/19) Reflection Matrix(241,-51,912,-193) (4/19,3/14) -> (5/19,9/34) Glide Reflection Matrix(241,-52,672,-145) (3/14,5/23) -> (5/14,9/25) Glide Reflection Matrix(191,-42,432,-95) (5/23,2/9) -> (11/25,4/9) Glide Reflection Matrix(433,-98,1056,-239) (2/9,5/22) -> (9/22,16/39) Hyperbolic Matrix(241,-55,1056,-241) (5/22,11/48) -> (5/22,11/48) Reflection Matrix(287,-66,1248,-287) (11/48,3/13) -> (11/48,3/13) Reflection Matrix(241,-56,624,-145) (3/13,4/17) -> (5/13,12/31) Glide Reflection Matrix(241,-57,816,-193) (4/17,1/4) -> (5/17,13/44) Glide Reflection Matrix(383,-99,1296,-335) (1/4,6/23) -> (13/44,21/71) Glide Reflection Matrix(1249,-331,3264,-865) (9/34,4/15) -> (13/34,31/81) Glide Reflection Matrix(529,-142,1248,-335) (4/15,7/26) -> (11/26,14/33) Hyperbolic Matrix(337,-91,1248,-337) (7/26,13/48) -> (7/26,13/48) Reflection Matrix(287,-78,1056,-287) (13/48,3/11) -> (13/48,3/11) Reflection Matrix(193,-53,528,-145) (3/11,5/18) -> (4/11,11/30) Glide Reflection Matrix(337,-94,864,-241) (5/18,7/25) -> (7/18,9/23) Glide Reflection Matrix(145,-41,336,-95) (7/25,2/7) -> (3/7,10/23) Hyperbolic Matrix(97,-28,336,-97) (2/7,7/24) -> (2/7,7/24) Reflection Matrix(239,-70,816,-239) (7/24,5/17) -> (7/24,5/17) Reflection Matrix(1297,-384,3408,-1009) (21/71,8/27) -> (27/71,8/21) Glide Reflection Matrix(817,-243,2256,-671) (11/37,14/47) -> (17/47,4/11) Hyperbolic Matrix(289,-87,960,-289) (3/10,29/96) -> (3/10,29/96) Reflection Matrix(2495,-754,8256,-2495) (29/96,13/43) -> (29/96,13/43) Reflection Matrix(625,-189,1584,-479) (13/43,10/33) -> (13/33,2/5) Hyperbolic Matrix(623,-190,1728,-527) (7/23,11/36) -> (9/25,13/36) Glide Reflection Matrix(479,-147,1248,-383) (11/36,4/13) -> (23/60,5/13) Glide Reflection Matrix(241,-75,768,-239) (9/29,5/16) -> (5/16,6/19) Parabolic Matrix(385,-122,912,-289) (6/19,1/3) -> (8/19,19/45) Glide Reflection Matrix(433,-151,1104,-385) (1/3,7/20) -> (20/51,11/28) Glide Reflection Matrix(433,-152,960,-337) (7/20,6/17) -> (9/20,14/31) Glide Reflection Matrix(577,-204,1632,-577) (6/17,17/48) -> (6/17,17/48) Reflection Matrix(239,-85,672,-239) (17/48,5/14) -> (17/48,5/14) Reflection Matrix(1729,-625,4512,-1631) (13/36,17/47) -> (18/47,23/60) Hyperbolic Matrix(913,-335,2352,-863) (11/30,18/49) -> (19/49,7/18) Hyperbolic Matrix(1055,-388,2352,-865) (18/49,7/19) -> (13/29,22/49) Hyperbolic Matrix(145,-54,384,-143) (7/19,3/8) -> (3/8,11/29) Parabolic Matrix(1009,-383,2400,-911) (11/29,19/50) -> (21/50,8/19) Hyperbolic Matrix(3649,-1387,9600,-3649) (19/50,73/192) -> (19/50,73/192) Reflection Matrix(10367,-3942,27264,-10367) (73/192,27/71) -> (73/192,27/71) Reflection Matrix(2545,-971,5664,-2161) (8/21,29/76) -> (31/69,9/20) Glide Reflection Matrix(6049,-2310,15840,-6049) (21/55,55/144) -> (21/55,55/144) Reflection Matrix(1871,-715,4896,-1871) (55/144,13/34) -> (55/144,13/34) Reflection Matrix(3889,-1489,10032,-3841) (31/81,18/47) -> (50/129,19/49) Glide Reflection Matrix(1105,-428,2352,-911) (12/31,31/80) -> (15/32,8/17) Hyperbolic Matrix(2495,-967,5328,-2065) (31/80,50/129) -> (7/15,15/32) Hyperbolic Matrix(1967,-771,4656,-1825) (9/23,20/51) -> (19/45,30/71) Hyperbolic Matrix(625,-246,1344,-529) (11/28,13/33) -> (13/28,7/15) Glide Reflection Matrix(2113,-862,4704,-1919) (11/27,20/49) -> (22/49,31/69) Hyperbolic Matrix(1441,-589,3408,-1393) (20/49,9/22) -> (41/97,11/26) Glide Reflection Matrix(241,-100,576,-239) (7/17,5/12) -> (5/12,13/31) Parabolic Matrix(431,-181,912,-383) (13/31,21/50) -> (8/17,1/2) Glide Reflection Matrix(10081,-4260,23856,-10081) (30/71,71/168) -> (30/71,71/168) Reflection Matrix(13775,-5822,32592,-13775) (71/168,41/97) -> (71/168,41/97) Reflection Matrix(337,-147,768,-335) (10/23,7/16) -> (7/16,11/25) Parabolic Matrix(1633,-731,3648,-1633) (17/38,43/96) -> (17/38,43/96) Reflection Matrix(2495,-1118,5568,-2495) (43/96,13/29) -> (43/96,13/29) Reflection Matrix(241,-110,528,-241) (5/11,11/24) -> (5/11,11/24) Reflection Matrix(287,-132,624,-287) (11/24,6/13) -> (11/24,6/13) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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(143,-14,480,-47) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(193,-21,432,-47) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(335,-39,816,-95) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(335,-44,1104,-145) -> Matrix(1,0,0,1) Matrix(143,-20,336,-47) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(623,-92,1632,-241) -> Matrix(1,0,2,1) 0/1 Matrix(289,-44,624,-95) -> Matrix(1,0,2,1) 0/1 Matrix(193,-30,624,-97) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(239,-38,912,-145) -> Matrix(3,2,-2,-1) -1/1 Matrix(289,-50,1104,-191) -> Matrix(1,-2,0,1) 1/0 Matrix(671,-117,2208,-385) -> Matrix(1,1,0,1) 1/0 Matrix(671,-118,1632,-287) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(239,-43,528,-95) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(385,-71,1296,-239) -> Matrix(1,1,0,1) 1/0 Matrix(145,-27,768,-143) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(97,-19,240,-47) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(49,-10,240,-49) -> Matrix(-1,0,4,1) (1/5,5/24) -> (-1/2,0/1) Matrix(191,-40,912,-191) -> Matrix(1,0,6,-1) (5/24,4/19) -> (0/1,1/3) Matrix(241,-51,912,-193) -> Matrix(1,-1,-2,1) Matrix(241,-52,672,-145) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(191,-42,432,-95) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(433,-98,1056,-239) -> Matrix(1,0,0,1) Matrix(241,-55,1056,-241) -> Matrix(1,1,0,-1) (5/22,11/48) -> (-1/2,1/0) Matrix(287,-66,1248,-287) -> Matrix(-1,0,2,1) (11/48,3/13) -> (-1/1,0/1) Matrix(241,-56,624,-145) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(241,-57,816,-193) -> Matrix(1,1,4,3) Matrix(383,-99,1296,-335) -> Matrix(1,-1,2,-3) Matrix(1249,-331,3264,-865) -> Matrix(1,1,2,1) Matrix(529,-142,1248,-335) -> Matrix(1,0,2,1) 0/1 Matrix(337,-91,1248,-337) -> Matrix(1,1,0,-1) (7/26,13/48) -> (-1/2,1/0) Matrix(287,-78,1056,-287) -> Matrix(-1,0,2,1) (13/48,3/11) -> (-1/1,0/1) Matrix(193,-53,528,-145) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(337,-94,864,-241) -> Matrix(3,2,2,1) Matrix(145,-41,336,-95) -> Matrix(3,1,2,1) Matrix(97,-28,336,-97) -> Matrix(-1,0,6,1) (2/7,7/24) -> (-1/3,0/1) Matrix(239,-70,816,-239) -> Matrix(1,0,8,-1) (7/24,5/17) -> (0/1,1/4) Matrix(1297,-384,3408,-1009) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(817,-243,2256,-671) -> Matrix(1,-1,0,1) 1/0 Matrix(289,-87,960,-289) -> Matrix(-1,1,0,1) (3/10,29/96) -> (1/2,1/0) Matrix(2495,-754,8256,-2495) -> Matrix(1,8,0,-1) (29/96,13/43) -> (-4/1,1/0) Matrix(625,-189,1584,-479) -> Matrix(1,3,0,1) 1/0 Matrix(623,-190,1728,-527) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(479,-147,1248,-383) -> Matrix(1,1,2,1) Matrix(241,-75,768,-239) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(385,-122,912,-289) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(433,-151,1104,-385) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(433,-152,960,-337) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(577,-204,1632,-577) -> Matrix(-1,2,0,1) (6/17,17/48) -> (1/1,1/0) Matrix(239,-85,672,-239) -> Matrix(1,1,0,-1) (17/48,5/14) -> (-1/2,1/0) Matrix(1729,-625,4512,-1631) -> Matrix(1,1,0,1) 1/0 Matrix(913,-335,2352,-863) -> Matrix(1,1,0,1) 1/0 Matrix(1055,-388,2352,-865) -> Matrix(1,0,0,1) Matrix(145,-54,384,-143) -> Matrix(1,0,4,1) 0/1 Matrix(1009,-383,2400,-911) -> Matrix(3,-1,4,-1) 1/2 Matrix(3649,-1387,9600,-3649) -> Matrix(11,-5,24,-11) (19/50,73/192) -> (5/12,1/2) Matrix(10367,-3942,27264,-10367) -> Matrix(31,-16,60,-31) (73/192,27/71) -> (1/2,8/15) Matrix(2545,-971,5664,-2161) -> Matrix(1,-1,-2,1) Matrix(6049,-2310,15840,-6049) -> Matrix(1,0,2,-1) (21/55,55/144) -> (0/1,1/1) Matrix(1871,-715,4896,-1871) -> Matrix(-1,1,0,1) (55/144,13/34) -> (1/2,1/0) Matrix(3889,-1489,10032,-3841) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(1105,-428,2352,-911) -> Matrix(1,0,0,1) Matrix(2495,-967,5328,-2065) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(1967,-771,4656,-1825) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(625,-246,1344,-529) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(2113,-862,4704,-1919) -> Matrix(1,0,0,1) Matrix(1441,-589,3408,-1393) -> Matrix(1,1,2,1) Matrix(241,-100,576,-239) -> Matrix(1,0,4,1) 0/1 Matrix(431,-181,912,-383) -> Matrix(3,-1,2,-1) Matrix(10081,-4260,23856,-10081) -> Matrix(3,-2,4,-3) (30/71,71/168) -> (1/2,1/1) Matrix(13775,-5822,32592,-13775) -> Matrix(1,0,2,-1) (71/168,41/97) -> (0/1,1/1) Matrix(337,-147,768,-335) -> Matrix(1,-5,0,1) 1/0 Matrix(1633,-731,3648,-1633) -> Matrix(1,1,0,-1) (17/38,43/96) -> (-1/2,1/0) Matrix(2495,-1118,5568,-2495) -> Matrix(-1,0,2,1) (43/96,13/29) -> (-1/1,0/1) Matrix(241,-110,528,-241) -> Matrix(-1,0,2,1) (5/11,11/24) -> (-1/1,0/1) Matrix(287,-132,624,-287) -> Matrix(1,0,2,-1) (11/24,6/13) -> (0/1,1/1) Matrix(-1,1,0,1) -> Matrix(1,1,0,-1) (1/2,1/0) -> (-1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.