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 1/0 -9/10 1/0 -8/9 1/0 -7/8 -1/1 -13/15 1/0 -6/7 -1/1 0/1 -17/20 1/0 -11/13 3/2 -16/19 8/3 3/1 -5/6 1/0 -19/23 -23/4 -33/40 -5/1 -14/17 -13/3 -4/1 -9/11 -5/2 -22/27 -5/2 -13/16 -2/1 -17/21 -3/2 -4/5 -2/1 -1/1 -19/24 -1/1 -15/19 -3/4 -11/14 -1/2 -18/23 -1/1 0/1 -7/9 1/0 -17/22 -1/2 -10/13 0/1 1/3 -13/17 3/4 -3/4 1/0 -17/23 -23/6 -31/42 -7/2 -14/19 -16/5 -3/1 -11/15 -5/2 -19/26 -9/4 -8/11 -2/1 -5/3 -13/18 1/0 -18/25 -3/1 -2/1 -5/7 -3/2 -17/24 -1/1 -12/17 -1/1 -4/5 -19/27 -1/2 -26/37 -3/5 -4/7 -33/47 -1/2 -7/10 -1/2 -30/43 0/1 1/7 -23/33 1/0 -39/56 -1/1 -16/23 0/1 1/1 -25/36 1/0 -9/13 1/0 -20/29 -1/3 -2/7 -11/16 0/1 -13/19 1/2 -2/3 1/0 -13/20 -5/2 -11/17 -13/6 -9/14 -3/2 -16/25 -2/1 -1/1 -23/36 -3/2 -30/47 -2/1 -1/1 -7/11 1/0 -12/19 -4/3 -1/1 -5/8 -1/1 -18/29 -1/1 -2/3 -31/50 -7/10 -44/71 -2/3 -15/23 -13/21 -1/2 -47/76 -3/4 -34/55 -5/7 -2/3 -21/34 -1/2 -29/47 -1/2 -8/13 -1/3 0/1 -19/31 -3/4 -49/80 0/1 -30/49 -2/1 -1/1 -11/18 -1/2 -14/23 -1/1 0/1 -17/28 -1/2 -20/33 -1/4 -3/5 1/2 -16/27 1/0 -29/49 1/0 -13/22 1/0 -23/39 5/2 -10/17 4/1 5/1 -7/12 1/0 -18/31 -10/1 -9/1 -29/50 -17/2 -11/19 1/0 -26/45 -11/2 -41/71 -51/10 -15/26 -9/2 -19/33 1/0 -4/7 -4/1 -3/1 -13/23 -23/10 -9/16 -2/1 -14/25 -2/1 -5/3 -5/9 -3/2 -21/38 1/0 -16/29 -2/1 -5/3 -11/20 -3/2 -6/11 -6/5 -1/1 -13/24 -1/1 -7/13 -5/6 -15/28 -3/4 -8/15 -1/2 -1/2 1/0 -8/17 -4/3 -1/1 -7/15 -3/2 -6/13 -8/7 -1/1 -11/24 -1/1 -5/11 -5/6 -14/31 -9/13 -2/3 -9/20 -1/2 -13/29 -3/4 -43/96 -2/3 -30/67 -2/3 -7/11 -17/38 -1/2 -4/9 -1/2 -11/25 -3/14 -7/16 0/1 -10/23 0/1 1/3 -3/7 1/0 -11/26 1/0 -41/97 1/0 -71/168 1/1 -30/71 1/1 2/1 -19/45 1/0 -8/19 3/1 4/1 -5/12 1/0 -12/29 -7/1 -6/1 -19/46 -11/2 -26/63 1/0 -33/80 -6/1 -7/17 -9/2 -9/22 -7/2 -29/71 -43/14 -49/120 -3/1 -20/49 -3/1 -26/9 -11/27 -5/2 -2/5 -3/1 -2/1 -13/33 -11/6 -11/28 -7/4 -20/51 -17/10 -9/23 -23/14 -7/18 -3/2 -19/49 -3/2 -31/80 -10/7 -43/111 -3/2 -12/31 -10/7 -7/5 -5/13 -5/4 -23/60 -5/4 -18/47 -6/5 -1/1 -13/34 -3/2 -34/89 -15/11 -4/3 -55/144 -4/3 -21/55 -13/10 -8/21 -5/4 -3/8 -1/1 -10/27 -5/6 -27/73 -37/46 -71/192 -4/5 -44/119 -4/5 -55/69 -17/46 -11/14 -7/19 -3/4 -25/68 -1/2 -43/117 1/0 -18/49 -1/1 -6/7 -11/30 -3/4 -4/11 -2/3 -3/5 -17/47 -1/2 -13/36 -1/2 -9/25 -7/16 -5/14 -1/4 -11/31 -1/12 -17/48 0/1 -6/17 0/1 1/5 -7/20 1/0 -8/23 0/1 1/1 -1/3 1/0 -6/19 -4/1 -3/1 -5/16 -2/1 -9/29 -7/4 -4/13 -5/3 -8/5 -15/49 -3/2 -11/36 -3/2 -7/23 -23/16 -10/33 -11/8 -13/43 -35/26 -29/96 -4/3 -16/53 -4/3 -41/31 -3/10 -5/4 -14/47 -6/5 -1/1 -11/37 -7/6 -8/27 -7/6 -21/71 -57/50 -13/44 -9/8 -5/17 -13/12 -7/24 -1/1 -2/7 -1/1 -4/5 -7/25 -11/18 -5/18 -1/2 -13/47 -1/2 -21/76 -1/2 -8/29 -2/5 -1/3 -3/11 -1/4 -13/48 0/1 -10/37 0/1 1/9 -7/26 1/2 -11/41 1/2 -4/15 1/0 -17/64 0/1 -13/49 1/0 -9/34 1/0 -5/19 -1/2 -6/23 -1/5 0/1 -1/4 1/0 -6/25 -11/5 -2/1 -5/21 -3/2 -4/17 -1/1 0/1 -3/13 -5/2 -11/48 -2/1 -8/35 -2/1 -17/9 -5/22 -7/4 -7/31 1/0 -9/40 -5/3 -2/9 -3/2 -5/23 -23/18 -3/14 -7/6 -10/47 -10/9 -1/1 -17/80 -8/7 -7/33 -9/8 -4/19 -16/15 -1/1 -5/24 -1/1 -1/5 -3/4 -4/21 -1/2 -3/16 0/1 -5/27 1/0 -2/11 -2/1 -1/1 -5/28 -1/2 -3/17 1/2 -7/40 -1/1 -4/23 -1/3 0/1 -1/6 1/0 -4/25 -7/3 -2/1 -3/19 1/0 -2/13 -4/3 -1/1 -5/33 -1/2 -3/20 1/0 -7/47 1/0 -4/27 1/0 -1/7 -3/2 -2/15 -5/4 -3/23 -23/20 -1/8 -1/1 -2/17 -4/5 -7/9 -1/9 -1/2 -1/10 1/0 0/1 -1/1 0/1 1/10 -1/2 1/9 1/0 1/8 -1/1 2/15 -5/6 1/7 -3/4 3/20 -1/2 2/13 -1/1 -4/5 3/19 -1/2 1/6 -1/2 4/23 0/1 1/1 7/40 -1/1 3/17 -1/4 2/11 -1/1 -2/3 5/27 -1/2 3/16 0/1 4/21 1/0 1/5 -3/2 5/24 -1/1 4/19 -1/1 -16/17 3/14 -7/8 5/23 -23/28 2/9 -3/4 5/22 -7/10 3/13 -5/8 4/17 -1/1 0/1 1/4 -1/2 6/23 0/1 1/3 11/42 1/0 5/19 1/0 4/15 -1/2 7/26 -1/4 3/11 1/2 5/18 1/0 7/25 -11/4 2/7 -4/3 -1/1 7/24 -1/1 5/17 -13/14 8/27 -7/8 11/37 -7/8 14/47 -1/1 -6/7 3/10 -5/6 13/43 -35/44 10/33 -11/14 17/56 -7/9 7/23 -23/30 11/36 -3/4 4/13 -8/11 -5/7 9/29 -7/10 5/16 -2/3 6/19 -3/5 -4/7 1/3 -1/2 7/20 -1/2 6/17 -1/7 0/1 5/14 1/2 9/25 7/2 13/36 1/0 17/47 1/0 4/11 -3/1 -2/1 7/19 -3/2 3/8 -1/1 11/29 -7/8 19/50 -19/22 27/71 -53/62 8/21 -5/6 29/76 -5/6 21/55 -13/16 13/34 -3/4 18/47 -1/1 -6/7 5/13 -5/6 12/31 -7/9 -10/13 31/80 -10/13 19/49 -3/4 7/18 -3/4 9/23 -23/32 11/28 -7/10 13/33 -11/16 2/5 -2/3 -3/5 11/27 -5/8 20/49 -26/43 -3/5 9/22 -7/12 16/39 -1/2 7/17 -9/16 5/12 -1/2 13/31 -11/24 21/50 -9/20 8/19 -4/9 -3/7 19/45 -1/2 30/71 -2/5 -1/3 11/26 -1/2 14/33 -3/8 3/7 -1/2 10/23 -1/5 0/1 7/16 0/1 11/25 3/8 4/9 1/0 17/38 1/0 13/29 -3/2 9/20 1/0 5/11 -5/4 11/24 -1/1 6/13 -1/1 -8/9 13/28 -5/6 7/15 -3/4 1/2 -1/2 9/17 -3/2 8/15 1/0 7/13 -5/4 13/24 -1/1 6/11 -1/1 -6/7 17/31 -13/16 11/20 -3/4 16/29 -5/7 -2/3 53/96 -2/3 37/67 -5/8 21/38 -1/2 5/9 -3/4 14/25 -5/7 -2/3 9/16 -2/3 13/23 -23/36 4/7 -3/5 -4/7 15/26 -9/16 56/97 -64/115 -5/9 97/168 -5/9 41/71 -51/92 26/45 -11/20 11/19 -1/2 7/12 -1/2 17/29 -1/2 27/46 -11/24 37/63 -1/2 47/80 -4/9 10/17 -5/11 -4/9 13/22 -1/2 42/71 -2/5 -1/3 71/120 -1/3 29/49 -1/2 16/27 -1/2 3/5 -1/4 20/33 1/2 17/28 1/0 31/51 1/0 14/23 -1/1 0/1 11/18 1/0 30/49 -1/1 -2/3 49/80 0/1 68/111 1/0 19/31 -3/2 8/13 0/1 1/1 37/60 1/0 29/47 1/0 21/34 1/0 55/89 -9/4 89/144 -2/1 34/55 -2/1 -5/3 13/21 1/0 5/8 -1/1 17/27 -5/6 46/73 -33/41 -4/5 121/192 -4/5 75/119 -59/74 29/46 -11/14 12/19 -1/1 -4/5 43/68 -3/4 74/117 -3/4 31/49 -3/4 19/30 -3/4 7/11 -1/2 30/47 -1/1 -2/3 23/36 -3/4 16/25 -1/1 -2/3 9/14 -3/4 20/31 -21/31 -2/3 31/48 -2/3 11/17 -13/20 13/20 -5/8 15/23 -23/38 2/3 -1/2 13/19 -1/4 11/16 0/1 20/29 2/3 1/1 9/13 -1/2 34/49 -1/1 -2/3 25/36 -1/2 16/23 -1/3 0/1 23/33 -1/2 30/43 -1/9 0/1 67/96 0/1 37/53 1/10 7/10 1/0 33/47 1/0 26/37 -4/1 -3/1 19/27 1/0 50/71 -2/1 -13/7 31/44 -3/2 12/17 -4/3 -1/1 17/24 -1/1 5/7 -3/4 18/25 -2/3 -3/5 13/18 -1/2 34/47 -2/1 -1/1 55/76 -3/4 21/29 -1/2 8/11 -5/7 -2/3 35/48 -2/3 27/37 -21/32 19/26 -9/14 30/41 -2/3 -3/5 11/15 -5/8 47/64 -8/13 36/49 -2/3 -3/5 25/34 -11/18 14/19 -3/5 -16/27 17/23 -23/40 3/4 -1/2 19/25 -13/32 16/21 -3/8 13/17 -3/10 10/13 -1/5 0/1 37/48 0/1 27/35 1/6 17/22 1/0 24/31 -3/1 -2/1 31/40 -1/1 7/9 -1/2 18/23 -1/1 0/1 11/14 1/0 37/47 1/0 63/80 -2/1 26/33 1/0 15/19 -3/2 19/24 -1/1 4/5 -1/1 -2/3 17/21 -3/4 13/16 -2/3 22/27 -5/8 9/11 -5/8 23/28 -7/12 14/17 -4/7 -13/23 33/40 -5/9 19/23 -23/42 5/6 -1/2 21/25 -17/38 16/19 -3/7 -8/19 11/13 -3/8 28/33 -1/4 17/20 -1/2 40/47 -6/17 -1/3 23/27 -1/4 6/7 -1/1 0/1 13/15 -1/2 20/23 -1/3 0/1 7/8 -1/1 15/17 -5/8 8/9 -1/2 9/10 -1/2 1/1 -1/2 1/0 0/1 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,-2,1) Matrix(337,304,480,433) -> Matrix(1,2,0,1) Matrix(193,172,432,385) -> Matrix(1,0,0,1) Matrix(97,86,-432,-383) -> Matrix(3,8,-2,-5) Matrix(769,668,-1104,-959) -> Matrix(1,0,0,1) Matrix(527,456,720,623) -> Matrix(5,2,-8,-3) Matrix(1009,860,-1632,-1391) -> Matrix(3,-2,-4,3) Matrix(335,284,-624,-529) -> Matrix(3,-2,-4,3) Matrix(431,364,624,527) -> Matrix(1,-2,0,1) Matrix(673,566,-912,-767) -> Matrix(7,-24,-2,7) Matrix(815,674,-1104,-913) -> Matrix(7,46,-2,-13) Matrix(671,554,2208,1823) -> Matrix(17,92,-22,-119) Matrix(1487,1226,1920,1583) -> Matrix(3,14,-2,-9) Matrix(239,196,-528,-433) -> Matrix(3,10,-4,-13) Matrix(385,314,1296,1057) -> Matrix(5,16,-6,-19) Matrix(145,118,768,625) -> Matrix(1,2,2,5) Matrix(143,116,768,623) -> Matrix(1,2,-4,-7) Matrix(97,78,240,193) -> Matrix(1,4,-2,-7) Matrix(191,152,240,191) -> Matrix(3,4,-4,-5) Matrix(721,570,912,721) -> Matrix(7,6,-6,-5) Matrix(241,190,-912,-719) -> Matrix(3,2,-2,-1) Matrix(431,338,672,527) -> Matrix(1,2,-2,-3) Matrix(241,188,432,337) -> Matrix(3,-2,-4,3) Matrix(623,482,-1056,-817) -> Matrix(5,2,2,1) Matrix(241,186,-1056,-815) -> Matrix(11,2,-6,-1) Matrix(383,294,624,479) -> Matrix(1,0,-2,1) Matrix(241,184,-816,-623) -> Matrix(9,-10,-8,9) Matrix(383,284,-1296,-961) -> Matrix(9,44,-8,-39) Matrix(193,142,-912,-671) -> Matrix(11,32,-10,-29) Matrix(719,526,-1248,-913) -> Matrix(7,18,-2,-5) Matrix(337,246,-1248,-911) -> Matrix(1,2,6,13) Matrix(193,140,-528,-383) -> Matrix(3,4,-4,-5) Matrix(527,380,864,623) -> Matrix(1,2,0,1) Matrix(145,104,336,241) -> Matrix(1,2,-4,-7) Matrix(239,170,336,239) -> Matrix(5,6,-6,-7) Matrix(577,408,816,577) -> Matrix(9,8,-8,-7) Matrix(193,136,-816,-575) -> Matrix(5,4,-4,-3) Matrix(239,168,1296,911) -> Matrix(3,2,-8,-5) Matrix(817,574,2256,1585) -> Matrix(11,6,-2,-1) Matrix(433,304,480,337) -> Matrix(5,2,-8,-3) Matrix(289,202,-960,-671) -> Matrix(13,4,-10,-3) Matrix(625,436,1584,1105) -> Matrix(11,-2,-16,3) Matrix(385,268,2208,1537) -> Matrix(1,0,0,1) Matrix(1105,768,1728,1201) -> Matrix(3,-2,-4,3) Matrix(479,332,-1248,-865) -> Matrix(5,4,-4,-3) Matrix(527,364,624,431) -> Matrix(3,2,-8,-5) Matrix(241,166,768,529) -> Matrix(9,2,-14,-3) Matrix(239,164,768,527) -> Matrix(11,-2,-16,3) Matrix(527,360,912,623) -> Matrix(11,-6,-20,11) Matrix(433,282,-1104,-719) -> Matrix(17,46,-10,-27) Matrix(527,342,960,623) -> Matrix(11,26,-14,-33) Matrix(239,154,-672,-433) -> Matrix(1,2,-6,-11) Matrix(527,338,672,431) -> Matrix(1,2,-2,-3) Matrix(1201,768,1728,1105) -> Matrix(1,2,-4,-7) Matrix(2399,1532,3456,2207) -> Matrix(3,4,-4,-5) Matrix(671,428,2256,1439) -> Matrix(7,8,-8,-9) Matrix(145,92,-528,-335) -> Matrix(1,2,-4,-7) Matrix(239,150,-384,-241) -> Matrix(5,6,-6,-7) Matrix(1009,626,2400,1489) -> Matrix(13,10,-30,-23) Matrix(3407,2112,-9216,-5713) -> Matrix(73,50,-92,-63) Matrix(2399,1486,3408,2111) -> Matrix(7,4,-2,-1) Matrix(3793,2346,-10320,-6383) -> Matrix(3,2,-2,-1) Matrix(1871,1156,-4896,-3025) -> Matrix(17,10,-12,-7) Matrix(865,534,-3264,-2015) -> Matrix(7,4,-2,-1) Matrix(383,236,-1248,-769) -> Matrix(19,8,-12,-5) Matrix(479,294,624,383) -> Matrix(1,0,-2,1) Matrix(1583,970,-3840,-2353) -> Matrix(11,6,-2,-1) Matrix(1633,1000,-7680,-4703) -> Matrix(9,8,-8,-7) Matrix(1249,764,1728,1057) -> Matrix(1,0,0,1) Matrix(623,380,864,527) -> Matrix(5,2,-8,-3) Matrix(385,234,-1104,-671) -> Matrix(1,0,2,1) Matrix(1345,816,1584,961) -> Matrix(1,0,0,1) Matrix(479,290,1584,959) -> Matrix(27,4,-34,-5) Matrix(47,28,240,143) -> Matrix(1,-2,0,1) Matrix(385,228,-2592,-1535) -> Matrix(1,-4,0,1) Matrix(1441,852,-3408,-2015) -> Matrix(1,0,0,1) Matrix(95,56,-816,-481) -> Matrix(3,-8,-4,11) Matrix(335,196,-576,-337) -> Matrix(1,-14,0,1) Matrix(431,250,-912,-529) -> Matrix(3,26,-2,-17) Matrix(911,528,2400,1391) -> Matrix(7,50,-8,-57) Matrix(623,360,912,527) -> Matrix(1,6,-4,-23) Matrix(817,472,1248,721) -> Matrix(7,38,-12,-65) Matrix(1393,804,-3408,-1967) -> Matrix(13,62,-4,-19) Matrix(289,166,336,193) -> Matrix(1,4,-2,-7) Matrix(95,54,336,191) -> Matrix(3,8,-2,-5) Matrix(337,190,768,433) -> Matrix(1,2,6,13) Matrix(335,188,768,431) -> Matrix(1,2,-8,-15) Matrix(337,188,432,241) -> Matrix(1,2,-4,-7) Matrix(47,26,432,239) -> Matrix(1,2,-2,-3) Matrix(1633,902,-3648,-2015) -> Matrix(1,4,-2,-7) Matrix(769,424,-2784,-1535) -> Matrix(5,8,-12,-19) Matrix(95,52,-528,-289) -> Matrix(3,4,-4,-5) Matrix(287,156,528,287) -> Matrix(11,12,-12,-13) Matrix(337,182,624,337) -> Matrix(11,10,-10,-9) Matrix(815,436,1344,719) -> Matrix(3,2,4,3) Matrix(337,178,-816,-431) -> Matrix(11,6,-2,-1) Matrix(911,428,-2352,-1105) -> Matrix(11,18,-8,-13) Matrix(95,44,-624,-289) -> Matrix(3,4,-4,-5) Matrix(287,132,624,287) -> Matrix(15,16,-16,-17) Matrix(241,110,528,241) -> Matrix(11,10,-10,-9) Matrix(337,152,960,433) -> Matrix(3,2,-8,-5) Matrix(865,388,-2352,-1055) -> Matrix(1,0,0,1) Matrix(5089,2280,9216,4129) -> Matrix(23,16,-36,-25) Matrix(5087,2278,9216,4127) -> Matrix(37,24,-54,-35) Matrix(385,172,432,193) -> Matrix(1,0,0,1) Matrix(95,42,432,191) -> Matrix(11,4,-14,-5) Matrix(433,190,768,337) -> Matrix(17,2,-26,-3) Matrix(431,188,768,335) -> Matrix(11,-2,-16,3) Matrix(241,104,336,145) -> Matrix(3,-2,-4,3) Matrix(335,142,-1248,-529) -> Matrix(1,-2,2,-3) Matrix(11759,4970,19872,8399) -> Matrix(1,-2,-2,5) Matrix(12097,5112,20448,8641) -> Matrix(3,-4,-8,11) Matrix(2831,1196,4656,1967) -> Matrix(1,-2,0,1) Matrix(289,122,912,385) -> Matrix(1,0,-2,1) Matrix(239,100,-576,-241) -> Matrix(1,-10,0,1) Matrix(1393,576,2208,913) -> Matrix(3,22,-4,-29) Matrix(6049,2496,7680,3169) -> Matrix(1,4,0,1) Matrix(239,98,-1056,-433) -> Matrix(3,14,-2,-9) Matrix(11807,4822,20448,8351) -> Matrix(121,368,-218,-663) Matrix(11473,4684,19872,8113) -> Matrix(109,322,-196,-579) Matrix(2593,1058,-7056,-2879) -> Matrix(3,8,-2,-5) Matrix(193,78,240,97) -> Matrix(1,4,-2,-7) Matrix(1105,436,1584,625) -> Matrix(1,2,-8,-15) Matrix(625,246,1344,529) -> Matrix(21,38,-26,-47) Matrix(2689,1054,4656,1825) -> Matrix(83,140,-150,-253) Matrix(241,94,864,337) -> Matrix(9,14,-2,-3) Matrix(1489,578,2352,913) -> Matrix(29,42,-38,-55) Matrix(1873,726,-7056,-2735) -> Matrix(7,10,2,3) Matrix(6097,2362,8304,3217) -> Matrix(19,26,-30,-41) Matrix(145,56,624,241) -> Matrix(7,10,-12,-17) Matrix(2881,1104,4512,1729) -> Matrix(7,8,-8,-9) Matrix(481,184,-2256,-863) -> Matrix(5,4,-4,-3) Matrix(12817,4896,20736,7921) -> Matrix(37,50,-20,-27) Matrix(12815,4894,20736,7919) -> Matrix(47,62,-22,-29) Matrix(241,92,-1632,-623) -> Matrix(11,14,-4,-5) Matrix(143,54,-384,-145) -> Matrix(9,10,-10,-11) Matrix(1681,622,2208,817) -> Matrix(27,22,-70,-57) Matrix(23233,8592,36864,13633) -> Matrix(479,384,-600,-481) Matrix(23231,8590,36864,13631) -> Matrix(441,352,-550,-439) Matrix(1295,478,2208,815) -> Matrix(29,22,-62,-47) Matrix(1439,528,2352,863) -> Matrix(5,4,-4,-3) Matrix(1585,574,2256,817) -> Matrix(11,6,-2,-1) Matrix(2783,1006,4512,1631) -> Matrix(23,12,-2,-1) Matrix(527,190,1728,623) -> Matrix(47,22,-62,-29) Matrix(145,52,672,241) -> Matrix(17,6,-20,-7) Matrix(1489,528,2304,817) -> Matrix(37,2,-56,-3) Matrix(1487,526,2304,815) -> Matrix(31,-2,-46,3) Matrix(671,236,816,287) -> Matrix(7,-4,-12,7) Matrix(527,182,1248,431) -> Matrix(1,-2,-2,5) Matrix(385,122,912,289) -> Matrix(1,0,-2,1) Matrix(529,166,768,241) -> Matrix(1,2,2,5) Matrix(527,164,768,239) -> Matrix(1,2,-8,-15) Matrix(97,30,624,193) -> Matrix(7,12,-10,-17) Matrix(1249,382,3456,1057) -> Matrix(29,44,-2,-3) Matrix(623,190,1728,527) -> Matrix(15,22,2,3) Matrix(145,44,-1104,-335) -> Matrix(33,46,-28,-39) Matrix(959,290,1584,479) -> Matrix(3,4,14,19) Matrix(6433,1944,9216,2785) -> Matrix(3,4,56,75) Matrix(6431,1942,9216,2783) -> Matrix(3,4,-58,-77) Matrix(47,14,480,143) -> Matrix(5,6,-6,-7) Matrix(1439,428,2256,671) -> Matrix(7,8,-8,-9) Matrix(1057,314,1296,385) -> Matrix(13,16,-22,-27) Matrix(1297,384,3408,1009) -> Matrix(71,82,-84,-97) Matrix(239,70,816,239) -> Matrix(25,26,-26,-27) Matrix(97,28,336,97) -> Matrix(9,8,-8,-7) Matrix(191,54,336,95) -> Matrix(11,8,-18,-13) Matrix(337,94,864,241) -> Matrix(25,14,-34,-19) Matrix(671,186,1728,479) -> Matrix(35,16,-46,-21) Matrix(673,186,-4512,-1247) -> Matrix(1,0,2,1) Matrix(1681,456,2304,625) -> Matrix(29,2,-44,-3) Matrix(1679,454,2304,623) -> Matrix(23,-2,-34,3) Matrix(97,26,720,193) -> Matrix(5,-4,-6,5) Matrix(5087,1352,8304,2207) -> Matrix(1,0,0,1) Matrix(145,38,-912,-239) -> Matrix(3,2,-2,-1) Matrix(47,12,-192,-49) -> Matrix(1,-2,0,1) Matrix(1391,332,2208,527) -> Matrix(13,22,-16,-27) Matrix(241,56,624,145) -> Matrix(3,10,-4,-13) Matrix(1777,408,2304,529) -> Matrix(1,2,8,17) Matrix(1775,406,2304,527) -> Matrix(1,2,-14,-27) Matrix(337,76,1920,433) -> Matrix(1,2,-4,-7) Matrix(191,42,432,95) -> Matrix(3,4,2,3) Matrix(241,52,672,145) -> Matrix(5,6,4,5) Matrix(4511,958,7680,1631) -> Matrix(39,44,-86,-97) Matrix(191,40,912,191) -> Matrix(31,32,-32,-33) Matrix(49,10,240,49) -> Matrix(7,6,-6,-5) Matrix(143,28,240,47) -> Matrix(3,2,-8,-5) Matrix(625,118,768,145) -> Matrix(9,2,-14,-3) Matrix(623,116,768,143) -> Matrix(3,-2,-4,3) Matrix(911,168,1296,239) -> Matrix(1,-2,0,1) Matrix(529,94,816,145) -> Matrix(9,2,-14,-3) Matrix(719,126,816,143) -> Matrix(1,2,-2,-3) Matrix(961,168,1104,193) -> Matrix(1,0,0,1) Matrix(47,8,-288,-49) -> Matrix(1,-2,0,1) Matrix(193,30,624,97) -> Matrix(7,12,-10,-17) Matrix(623,94,1584,239) -> Matrix(7,-2,-10,3) Matrix(143,20,336,47) -> Matrix(1,2,-4,-7) Matrix(911,118,1104,143) -> Matrix(41,46,-74,-83) Matrix(673,80,816,97) -> Matrix(29,24,-52,-43) Matrix(239,26,432,47) -> Matrix(1,2,-2,-3) Matrix(143,14,480,47) -> Matrix(5,6,-6,-7) Matrix(335,-38,432,-49) -> Matrix(1,2,-2,-3) Matrix(335,-44,1104,-145) -> Matrix(53,46,-68,-59) Matrix(623,-92,1632,-241) -> Matrix(23,14,-28,-17) Matrix(289,-44,624,-95) -> Matrix(3,4,-4,-5) Matrix(239,-38,912,-145) -> Matrix(3,2,-2,-1) Matrix(289,-50,1104,-191) -> Matrix(1,0,2,1) Matrix(289,-52,528,-95) -> Matrix(3,4,-4,-5) Matrix(671,-142,912,-193) -> Matrix(35,32,-58,-53) Matrix(433,-98,1056,-239) -> Matrix(19,14,-34,-25) Matrix(815,-186,1056,-241) -> Matrix(3,2,10,7) Matrix(575,-136,816,-193) -> Matrix(5,4,-4,-3) Matrix(913,-236,1296,-335) -> Matrix(7,2,-4,-1) Matrix(719,-190,912,-241) -> Matrix(3,2,-2,-1) Matrix(529,-142,1248,-335) -> Matrix(7,2,-18,-5) Matrix(911,-246,1248,-337) -> Matrix(17,2,-26,-3) Matrix(335,-92,528,-145) -> Matrix(3,-2,-4,3) Matrix(623,-184,816,-241) -> Matrix(11,10,-32,-29) Matrix(671,-202,960,-289) -> Matrix(5,4,6,5) Matrix(769,-236,1248,-383) -> Matrix(11,8,4,3) Matrix(671,-234,1104,-385) -> Matrix(1,0,2,1) Matrix(433,-154,672,-239) -> Matrix(7,-2,-10,3) Matrix(383,-140,528,-193) -> Matrix(3,4,-4,-5) Matrix(145,-54,384,-143) -> Matrix(9,10,-10,-11) Matrix(5809,-2208,9216,-3503) -> Matrix(165,142,-208,-179) Matrix(6527,-2490,10320,-3937) -> Matrix(39,32,-50,-41) Matrix(3025,-1156,4896,-1871) -> Matrix(13,10,-4,-3) Matrix(2399,-918,3264,-1249) -> Matrix(23,20,-38,-33) Matrix(865,-332,1248,-479) -> Matrix(5,4,-4,-3) Matrix(2257,-874,3840,-1487) -> Matrix(29,22,-62,-47) Matrix(6047,-2344,7680,-2977) -> Matrix(21,16,-4,-3) Matrix(719,-282,1104,-433) -> Matrix(65,46,-106,-75) Matrix(2207,-900,2592,-1057) -> Matrix(13,8,-44,-27) Matrix(1967,-804,3408,-1393) -> Matrix(105,62,-188,-111) Matrix(721,-296,816,-335) -> Matrix(3,2,-8,-5) Matrix(241,-100,576,-239) -> Matrix(19,10,-40,-21) Matrix(481,-202,912,-383) -> Matrix(9,4,2,1) Matrix(2015,-852,3408,-1441) -> Matrix(1,0,0,1) Matrix(2015,-902,3648,-1633) -> Matrix(1,4,-2,-7) Matrix(2015,-904,2784,-1249) -> Matrix(3,4,-4,-5) Matrix(433,-196,528,-239) -> Matrix(7,10,-12,-17) Matrix(479,-226,816,-385) -> Matrix(21,16,-46,-35) Matrix(1441,-764,2352,-1247) -> Matrix(1,0,0,1) Matrix(529,-284,624,-335) -> Matrix(1,2,-4,-7) Matrix(1487,-820,2352,-1297) -> Matrix(25,18,-32,-23) Matrix(913,-526,1248,-719) -> Matrix(31,18,-50,-29) Matrix(337,-196,576,-335) -> Matrix(27,14,-56,-29) Matrix(817,-482,1056,-623) -> Matrix(5,2,2,1) Matrix(4463,-2642,7056,-4177) -> Matrix(23,10,-30,-13) Matrix(5183,-3174,7056,-4321) -> Matrix(11,8,-18,-13) Matrix(1775,-1096,2256,-1393) -> Matrix(1,2,0,1) Matrix(1391,-860,1632,-1009) -> Matrix(1,2,-4,-7) Matrix(241,-150,384,-239) -> Matrix(5,6,-6,-7) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(3839,-2778,4512,-3265) -> Matrix(5,4,-14,-11) Matrix(767,-566,912,-673) -> Matrix(41,24,-94,-55) Matrix(145,-108,192,-143) -> Matrix(11,6,-24,-13) Matrix(241,-200,288,-239) -> Matrix(19,10,-40,-21) 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): 128 Degree of the the map X: 128 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 -7/8 -5/6 -3/4 -11/15 -2/3 -5/8 -13/21 -5/9 -1/2 -3/8 -71/192 -1/3 -11/36 -3/10 -1/4 -5/21 -2/9 -2/11 -3/17 -1/6 -1/8 0/1 1/7 1/6 1/5 5/24 5/23 2/9 3/13 1/4 5/19 3/11 2/7 7/24 3/10 1/3 3/8 2/5 5/12 7/16 11/24 1/2 13/24 5/9 7/12 5/8 23/36 2/3 17/24 11/15 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 1/0 -8/9 1/0 -7/8 -1/1 -13/15 1/0 -6/7 -1/1 0/1 -5/6 1/0 -9/11 -5/2 -4/5 -2/1 -1/1 -19/24 -1/1 -15/19 -3/4 -11/14 -1/2 -18/23 -1/1 0/1 -7/9 1/0 -10/13 0/1 1/3 -13/17 3/4 -3/4 1/0 -14/19 -16/5 -3/1 -11/15 -5/2 -19/26 -9/4 -8/11 -2/1 -5/3 -13/18 1/0 -5/7 -3/2 -17/24 -1/1 -12/17 -1/1 -4/5 -19/27 -1/2 -7/10 -1/2 -23/33 1/0 -39/56 -1/1 -16/23 0/1 1/1 -25/36 1/0 -9/13 1/0 -2/3 1/0 -9/14 -3/2 -16/25 -2/1 -1/1 -23/36 -3/2 -7/11 1/0 -12/19 -4/3 -1/1 -5/8 -1/1 -18/29 -1/1 -2/3 -13/21 -1/2 -21/34 -1/2 -29/47 -1/2 -8/13 -1/3 0/1 -3/5 1/2 -7/12 1/0 -11/19 1/0 -15/26 -9/2 -19/33 1/0 -4/7 -4/1 -3/1 -13/23 -23/10 -9/16 -2/1 -14/25 -2/1 -5/3 -5/9 -3/2 -6/11 -6/5 -1/1 -13/24 -1/1 -7/13 -5/6 -1/2 1/0 -6/13 -8/7 -1/1 -11/24 -1/1 -5/11 -5/6 -4/9 -1/2 -11/25 -3/14 -7/16 0/1 -3/7 1/0 -5/12 1/0 -7/17 -9/2 -9/22 -7/2 -20/49 -3/1 -26/9 -11/27 -5/2 -2/5 -3/1 -2/1 -11/28 -7/4 -9/23 -23/14 -7/18 -3/2 -12/31 -10/7 -7/5 -5/13 -5/4 -8/21 -5/4 -3/8 -1/1 -10/27 -5/6 -27/73 -37/46 -71/192 -4/5 -44/119 -4/5 -55/69 -17/46 -11/14 -7/19 -3/4 -18/49 -1/1 -6/7 -11/30 -3/4 -4/11 -2/3 -3/5 -1/3 1/0 -4/13 -5/3 -8/5 -15/49 -3/2 -11/36 -3/2 -7/23 -23/16 -3/10 -5/4 -8/27 -7/6 -21/71 -57/50 -13/44 -9/8 -5/17 -13/12 -7/24 -1/1 -2/7 -1/1 -4/5 -7/25 -11/18 -5/18 -1/2 -3/11 -1/4 -4/15 1/0 -13/49 1/0 -9/34 1/0 -5/19 -1/2 -6/23 -1/5 0/1 -1/4 1/0 -6/25 -11/5 -2/1 -5/21 -3/2 -4/17 -1/1 0/1 -3/13 -5/2 -5/22 -7/4 -7/31 1/0 -9/40 -5/3 -2/9 -3/2 -5/23 -23/18 -3/14 -7/6 -7/33 -9/8 -4/19 -16/15 -1/1 -5/24 -1/1 -1/5 -3/4 -2/11 -2/1 -1/1 -3/17 1/2 -7/40 -1/1 -4/23 -1/3 0/1 -1/6 1/0 -1/7 -3/2 -1/8 -1/1 0/1 -1/1 0/1 1/7 -3/4 1/6 -1/2 1/5 -3/2 5/24 -1/1 4/19 -1/1 -16/17 3/14 -7/8 5/23 -23/28 2/9 -3/4 5/22 -7/10 3/13 -5/8 4/17 -1/1 0/1 1/4 -1/2 6/23 0/1 1/3 5/19 1/0 4/15 -1/2 3/11 1/2 5/18 1/0 7/25 -11/4 2/7 -4/3 -1/1 7/24 -1/1 5/17 -13/14 3/10 -5/6 1/3 -1/2 5/14 1/2 9/25 7/2 13/36 1/0 4/11 -3/1 -2/1 7/19 -3/2 3/8 -1/1 11/29 -7/8 8/21 -5/6 5/13 -5/6 7/18 -3/4 9/23 -23/32 2/5 -2/3 -3/5 9/22 -7/12 16/39 -1/2 7/17 -9/16 5/12 -1/2 3/7 -1/2 10/23 -1/5 0/1 7/16 0/1 11/25 3/8 4/9 1/0 5/11 -5/4 11/24 -1/1 6/13 -1/1 -8/9 1/2 -1/2 7/13 -5/4 13/24 -1/1 6/11 -1/1 -6/7 5/9 -3/4 14/25 -5/7 -2/3 9/16 -2/3 13/23 -23/36 4/7 -3/5 -4/7 15/26 -9/16 41/71 -51/92 26/45 -11/20 11/19 -1/2 7/12 -1/2 3/5 -1/4 11/18 1/0 30/49 -1/1 -2/3 49/80 0/1 19/31 -3/2 8/13 0/1 1/1 37/60 1/0 29/47 1/0 21/34 1/0 13/21 1/0 5/8 -1/1 17/27 -5/6 46/73 -33/41 -4/5 121/192 -4/5 75/119 -59/74 29/46 -11/14 12/19 -1/1 -4/5 7/11 -1/2 23/36 -3/4 16/25 -1/1 -2/3 9/14 -3/4 11/17 -13/20 2/3 -1/2 9/13 -1/2 25/36 -1/2 16/23 -1/3 0/1 23/33 -1/2 7/10 1/0 19/27 1/0 50/71 -2/1 -13/7 31/44 -3/2 12/17 -4/3 -1/1 17/24 -1/1 5/7 -3/4 13/18 -1/2 34/47 -2/1 -1/1 21/29 -1/2 8/11 -5/7 -2/3 19/26 -9/14 30/41 -2/3 -3/5 11/15 -5/8 25/34 -11/18 14/19 -3/5 -16/27 17/23 -23/40 3/4 -1/2 19/25 -13/32 16/21 -3/8 13/17 -3/10 10/13 -1/5 0/1 7/9 -1/2 18/23 -1/1 0/1 11/14 1/0 26/33 1/0 15/19 -3/2 19/24 -1/1 4/5 -1/1 -2/3 9/11 -5/8 5/6 -1/2 11/13 -3/8 6/7 -1/1 0/1 13/15 -1/2 20/23 -1/3 0/1 7/8 -1/1 15/17 -5/8 8/9 -1/2 9/10 -1/2 1/1 -1/2 1/0 0/1 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(121,108,-456,-407) (-1/1,-8/9) -> (-4/15,-13/49) 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(121,102,-312,-263) (-6/7,-5/6) -> (-7/18,-12/31) Hyperbolic Matrix(73,60,264,217) (-5/6,-9/11) -> (3/11,5/18) Hyperbolic Matrix(167,136,264,215) (-9/11,-4/5) -> (12/19,7/11) 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(119,92,216,167) (-7/9,-10/13) -> (6/11,5/9) 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(217,160,-552,-407) (-3/4,-14/19) -> (-2/5,-11/28) 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(167,122,360,263) (-19/26,-8/11) -> (6/13,1/2) Hyperbolic Matrix(193,140,-528,-383) (-8/11,-13/18) -> (-11/30,-4/11) Hyperbolic Matrix(25,18,168,121) (-13/18,-5/7) -> (1/7,1/6) 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(697,490,1128,793) (-19/27,-7/10) -> (21/34,13/21) Hyperbolic Matrix(935,652,1272,887) (-7/10,-23/33) -> (11/15,25/34) Hyperbolic Matrix(2807,1954,4584,3191) (-39/56,-16/23) -> (30/49,49/80) Hyperbolic Matrix(1105,768,1728,1201) (-16/23,-25/36) -> (23/36,16/25) Hyperbolic Matrix(649,450,936,649) (-25/36,-9/13) -> (9/13,25/36) Hyperbolic Matrix(119,82,312,215) (-9/13,-2/3) -> (8/21,5/13) Hyperbolic Matrix(121,78,-408,-263) (-2/3,-9/14) -> (-3/10,-8/27) 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(505,322,792,505) (-23/36,-7/11) -> (7/11,23/36) Hyperbolic Matrix(215,136,264,167) (-7/11,-12/19) -> (4/5,9/11) Hyperbolic Matrix(239,150,-384,-241) (-12/19,-5/8) -> (-5/8,-18/29) Parabolic Matrix(361,224,-888,-551) (-18/29,-13/21) -> (-11/27,-2/5) Hyperbolic Matrix(793,490,1128,697) (-13/21,-21/34) -> (7/10,19/27) 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(23,14,-120,-73) (-8/13,-3/5) -> (-1/5,-2/11) Hyperbolic Matrix(71,42,120,71) (-3/5,-7/12) -> (7/12,3/5) Hyperbolic Matrix(265,154,456,265) (-7/12,-11/19) -> (11/19,7/12) Hyperbolic Matrix(505,292,-1368,-791) (-11/19,-15/26) -> (-17/46,-7/19) 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(167,92,216,119) (-5/9,-6/11) -> (10/13,7/9) 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(71,38,312,167) (-7/13,-1/2) -> (5/22,3/13) Hyperbolic Matrix(263,122,360,167) (-1/2,-6/13) -> (8/11,19/26) 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(71,32,264,119) (-5/11,-4/9) -> (4/15,3/11) 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(23,10,-168,-73) (-7/16,-3/7) -> (-1/7,-1/8) Hyperbolic Matrix(71,30,168,71) (-3/7,-5/12) -> (5/12,3/7) Hyperbolic Matrix(169,70,408,169) (-5/12,-7/17) -> (7/17,5/12) Hyperbolic Matrix(239,98,-1056,-433) (-7/17,-9/22) -> (-5/22,-7/31) Hyperbolic Matrix(1801,736,-4872,-1991) (-9/22,-20/49) -> (-44/119,-17/46) Hyperbolic Matrix(2281,930,3240,1321) (-20/49,-11/27) -> (19/27,50/71) Hyperbolic Matrix(887,348,-3000,-1177) (-11/28,-9/23) -> (-21/71,-13/44) Hyperbolic Matrix(241,94,864,337) (-9/23,-7/18) -> (5/18,7/25) Hyperbolic Matrix(145,56,624,241) (-12/31,-5/13) -> (3/13,4/17) Hyperbolic Matrix(215,82,312,119) (-5/13,-8/21) -> (2/3,9/13) 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(359,132,1368,503) (-7/19,-18/49) -> (6/23,5/19) Hyperbolic Matrix(1439,528,2352,863) (-18/49,-11/30) -> (11/18,30/49) Hyperbolic Matrix(23,8,-72,-25) (-4/11,-1/3) -> (-1/3,-4/13) Parabolic Matrix(2857,874,4632,1417) (-15/49,-11/36) -> (37/60,29/47) Hyperbolic Matrix(623,190,1728,527) (-11/36,-7/23) -> (9/25,13/36) Hyperbolic Matrix(119,36,552,167) (-7/23,-3/10) -> (3/14,5/23) Hyperbolic Matrix(2953,874,5112,1513) (-8/27,-21/71) -> (41/71,26/45) 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(217,60,264,73) (-5/18,-3/11) -> (9/11,5/6) Hyperbolic Matrix(119,32,264,71) (-3/11,-4/15) -> (4/9,5/11) Hyperbolic Matrix(1129,296,1560,409) (-5/19,-6/23) -> (34/47,21/29) 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(265,62,312,73) (-4/17,-3/13) -> (11/13,6/7) Hyperbolic Matrix(167,38,312,71) (-3/13,-5/22) -> (1/2,7/13) Hyperbolic Matrix(2279,514,3720,839) (-7/31,-9/40) -> (49/80,19/31) 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(553,118,792,169) (-3/14,-7/33) -> (23/33,7/10) 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(313,56,408,73) (-2/11,-3/17) -> (13/17,10/13) 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(503,86,696,119) (-4/23,-1/6) -> (13/18,34/47) Hyperbolic Matrix(121,18,168,25) (-1/6,-1/7) -> (5/7,13/18) Hyperbolic Matrix(121,14,216,25) (-1/8,0/1) -> (14/25,9/16) Hyperbolic Matrix(73,-10,168,-23) (0/1,1/7) -> (3/7,10/23) Hyperbolic Matrix(73,-14,120,-23) (1/6,1/5) -> (3/5,11/18) 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(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(263,-78,408,-121) (5/17,3/10) -> (9/14,11/17) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(695,-252,1128,-409) (13/36,4/11) -> (8/13,37/60) 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(985,-374,1704,-647) (11/29,8/21) -> (26/45,11/19) Hyperbolic Matrix(263,-102,312,-121) (5/13,7/18) -> (5/6,11/13) Hyperbolic Matrix(407,-160,552,-217) (9/23,2/5) -> (14/19,17/23) Hyperbolic Matrix(409,-166,648,-263) (2/5,9/22) -> (29/46,12/19) Hyperbolic Matrix(721,-296,816,-335) (16/39,7/17) -> (15/17,8/9) Hyperbolic Matrix(913,-526,1248,-719) (4/7,15/26) -> (19/26,30/41) Hyperbolic Matrix(4009,-2314,6360,-3671) (15/26,41/71) -> (75/119,29/46) Hyperbolic Matrix(457,-282,504,-311) (29/47,21/34) -> (9/10,1/1) Hyperbolic Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(311,-202,408,-265) (11/17,2/3) -> (16/21,13/17) Hyperbolic Matrix(959,-668,1104,-769) (16/23,23/33) -> (13/15,20/23) Hyperbolic Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic Matrix(409,-322,456,-359) (11/14,26/33) -> (8/9,9/10) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(121,108,-456,-407) -> Matrix(1,1,0,1) Matrix(97,86,-432,-383) -> Matrix(3,8,-2,-5) Matrix(769,668,-1104,-959) -> Matrix(1,0,0,1) Matrix(527,456,720,623) -> Matrix(5,2,-8,-3) Matrix(121,102,-312,-263) -> Matrix(3,-7,-2,5) Matrix(73,60,264,217) -> Matrix(1,3,0,1) Matrix(167,136,264,215) -> Matrix(3,7,-4,-9) Matrix(191,152,240,191) -> Matrix(3,4,-4,-5) Matrix(721,570,912,721) -> Matrix(7,6,-6,-5) Matrix(241,190,-912,-719) -> Matrix(3,2,-2,-1) Matrix(431,338,672,527) -> Matrix(1,2,-2,-3) Matrix(241,188,432,337) -> Matrix(3,-2,-4,3) Matrix(119,92,216,167) -> Matrix(3,1,-4,-1) Matrix(383,294,624,479) -> Matrix(1,0,-2,1) Matrix(241,184,-816,-623) -> Matrix(9,-10,-8,9) Matrix(217,160,-552,-407) -> Matrix(7,23,-4,-13) Matrix(193,142,-912,-671) -> Matrix(11,32,-10,-29) Matrix(719,526,-1248,-913) -> Matrix(7,18,-2,-5) Matrix(167,122,360,263) -> Matrix(5,11,-6,-13) Matrix(193,140,-528,-383) -> Matrix(3,4,-4,-5) Matrix(25,18,168,121) -> Matrix(1,3,-2,-5) Matrix(239,170,336,239) -> Matrix(5,6,-6,-7) Matrix(577,408,816,577) -> Matrix(9,8,-8,-7) Matrix(193,136,-816,-575) -> Matrix(5,4,-4,-3) Matrix(697,490,1128,793) -> Matrix(5,3,-2,-1) Matrix(935,652,1272,887) -> Matrix(5,-3,-8,5) Matrix(2807,1954,4584,3191) -> Matrix(1,1,-2,-1) Matrix(1105,768,1728,1201) -> Matrix(3,-2,-4,3) Matrix(649,450,936,649) -> Matrix(1,1,-2,-1) Matrix(119,82,312,215) -> Matrix(5,1,-6,-1) Matrix(121,78,-408,-263) -> Matrix(7,13,-6,-11) Matrix(527,338,672,431) -> Matrix(1,2,-2,-3) Matrix(1201,768,1728,1105) -> Matrix(1,2,-4,-7) Matrix(505,322,792,505) -> Matrix(1,3,-2,-5) Matrix(215,136,264,167) -> Matrix(5,7,-8,-11) Matrix(239,150,-384,-241) -> Matrix(5,6,-6,-7) Matrix(361,224,-888,-551) -> Matrix(9,7,-4,-3) Matrix(793,490,1128,697) -> Matrix(5,3,-2,-1) Matrix(865,534,-3264,-2015) -> Matrix(7,4,-2,-1) Matrix(383,236,-1248,-769) -> Matrix(19,8,-12,-5) Matrix(23,14,-120,-73) -> Matrix(1,1,-2,-1) Matrix(71,42,120,71) -> Matrix(1,-1,-2,3) Matrix(265,154,456,265) -> Matrix(1,13,-2,-25) Matrix(505,292,-1368,-791) -> Matrix(3,19,-4,-25) Matrix(289,166,336,193) -> Matrix(1,4,-2,-7) Matrix(95,54,336,191) -> Matrix(3,8,-2,-5) Matrix(337,190,768,433) -> Matrix(1,2,6,13) Matrix(335,188,768,431) -> Matrix(1,2,-8,-15) Matrix(337,188,432,241) -> Matrix(1,2,-4,-7) Matrix(167,92,216,119) -> Matrix(1,1,0,1) Matrix(287,156,528,287) -> Matrix(11,12,-12,-13) Matrix(337,182,624,337) -> Matrix(11,10,-10,-9) Matrix(71,38,312,167) -> Matrix(7,5,-10,-7) Matrix(263,122,360,167) -> Matrix(9,11,-14,-17) Matrix(287,132,624,287) -> Matrix(15,16,-16,-17) Matrix(241,110,528,241) -> Matrix(11,10,-10,-9) Matrix(71,32,264,119) -> Matrix(1,1,-4,-3) Matrix(95,42,432,191) -> Matrix(11,4,-14,-5) Matrix(433,190,768,337) -> Matrix(17,2,-26,-3) Matrix(23,10,-168,-73) -> Matrix(3,-1,-2,1) Matrix(71,30,168,71) -> Matrix(1,-1,-2,3) Matrix(169,70,408,169) -> Matrix(1,9,-2,-17) Matrix(239,98,-1056,-433) -> Matrix(3,14,-2,-9) Matrix(1801,736,-4872,-1991) -> Matrix(19,61,-24,-77) Matrix(2281,930,3240,1321) -> Matrix(5,13,-2,-5) Matrix(887,348,-3000,-1177) -> Matrix(59,101,-52,-89) Matrix(241,94,864,337) -> Matrix(9,14,-2,-3) Matrix(145,56,624,241) -> Matrix(7,10,-12,-17) Matrix(215,82,312,119) -> Matrix(1,1,2,3) Matrix(143,54,-384,-145) -> Matrix(9,10,-10,-11) Matrix(1681,622,2208,817) -> Matrix(27,22,-70,-57) Matrix(23233,8592,36864,13633) -> Matrix(479,384,-600,-481) Matrix(23231,8590,36864,13631) -> Matrix(441,352,-550,-439) Matrix(359,132,1368,503) -> Matrix(1,1,-4,-3) Matrix(1439,528,2352,863) -> Matrix(5,4,-4,-3) Matrix(23,8,-72,-25) -> Matrix(1,-1,0,1) Matrix(2857,874,4632,1417) -> Matrix(23,35,-2,-3) Matrix(623,190,1728,527) -> Matrix(15,22,2,3) Matrix(119,36,552,167) -> Matrix(17,23,-20,-27) Matrix(2953,874,5112,1513) -> Matrix(107,123,-194,-223) Matrix(239,70,816,239) -> Matrix(25,26,-26,-27) Matrix(97,28,336,97) -> Matrix(9,8,-8,-7) Matrix(191,54,336,95) -> Matrix(11,8,-18,-13) Matrix(337,94,864,241) -> Matrix(25,14,-34,-19) Matrix(217,60,264,73) -> Matrix(7,3,-12,-5) Matrix(119,32,264,71) -> Matrix(1,-1,0,1) Matrix(1129,296,1560,409) -> Matrix(3,1,-4,-1) Matrix(47,12,-192,-49) -> Matrix(1,-2,0,1) Matrix(1391,332,2208,527) -> Matrix(13,22,-16,-27) Matrix(265,62,312,73) -> Matrix(1,1,-2,-1) Matrix(167,38,312,71) -> Matrix(3,5,-2,-3) Matrix(2279,514,3720,839) -> Matrix(3,5,-2,-3) Matrix(191,42,432,95) -> Matrix(3,4,2,3) Matrix(241,52,672,145) -> Matrix(5,6,4,5) Matrix(553,118,792,169) -> Matrix(1,1,6,7) Matrix(191,40,912,191) -> Matrix(31,32,-32,-33) Matrix(49,10,240,49) -> Matrix(7,6,-6,-5) Matrix(313,56,408,73) -> Matrix(1,1,-4,-3) Matrix(719,126,816,143) -> Matrix(1,2,-2,-3) Matrix(961,168,1104,193) -> Matrix(1,0,0,1) Matrix(503,86,696,119) -> Matrix(1,1,-2,-1) Matrix(121,18,168,25) -> Matrix(1,3,-2,-5) Matrix(121,14,216,25) -> Matrix(7,5,-10,-7) Matrix(73,-10,168,-23) -> Matrix(1,1,-6,-5) Matrix(73,-14,120,-23) -> Matrix(1,1,-2,-1) Matrix(671,-142,912,-193) -> Matrix(35,32,-58,-53) Matrix(433,-98,1056,-239) -> Matrix(19,14,-34,-25) Matrix(575,-136,816,-193) -> Matrix(5,4,-4,-3) Matrix(913,-236,1296,-335) -> Matrix(7,2,-4,-1) Matrix(719,-190,912,-241) -> Matrix(3,2,-2,-1) Matrix(263,-78,408,-121) -> Matrix(15,13,-22,-19) Matrix(25,-8,72,-23) -> Matrix(1,1,-4,-3) Matrix(695,-252,1128,-409) -> Matrix(1,3,0,1) Matrix(383,-140,528,-193) -> Matrix(3,4,-4,-5) Matrix(145,-54,384,-143) -> Matrix(9,10,-10,-11) Matrix(985,-374,1704,-647) -> Matrix(47,41,-86,-75) Matrix(263,-102,312,-121) -> Matrix(9,7,-22,-17) Matrix(407,-160,552,-217) -> Matrix(33,23,-56,-39) Matrix(409,-166,648,-263) -> Matrix(7,5,-10,-7) Matrix(721,-296,816,-335) -> Matrix(3,2,-8,-5) Matrix(913,-526,1248,-719) -> Matrix(31,18,-50,-29) Matrix(4009,-2314,6360,-3671) -> Matrix(163,91,-206,-115) Matrix(457,-282,504,-311) -> Matrix(1,5,-2,-9) Matrix(241,-150,384,-239) -> Matrix(5,6,-6,-7) Matrix(311,-202,408,-265) -> Matrix(11,7,-30,-19) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(145,-108,192,-143) -> Matrix(11,6,-24,-13) Matrix(409,-322,456,-359) -> Matrix(1,3,-2,-5) 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): 128 ----------------------------------------------------------------------- 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 1/7 -3/4 1 24 1/6 -1/2 1 4 1/5 -3/2 1 24 5/24 -1/1 19 1 4/19 (-1/1,-16/17) 0 24 3/14 -7/8 1 12 5/23 -23/28 1 24 2/9 -3/4 2 8 5/22 -7/10 1 12 3/13 -5/8 1 24 4/17 (-1/1,0/1) 0 24 1/4 -1/2 1 6 6/23 (0/1,1/3) 0 24 5/19 1/0 1 24 4/15 -1/2 2 8 3/11 1/2 1 24 5/18 1/0 5 4 7/25 -11/4 1 24 2/7 (-4/3,-1/1) 0 24 7/24 -1/1 17 1 5/17 -13/14 1 24 3/10 -5/6 1 12 1/3 -1/2 1 8 5/14 1/2 1 12 9/25 7/2 1 24 13/36 1/0 11 2 4/11 (-3/1,-2/1) 0 24 7/19 -3/2 1 24 3/8 -1/1 5 3 11/29 -7/8 1 24 8/21 -5/6 2 8 5/13 -5/6 1 24 7/18 -3/4 5 4 9/23 -23/32 1 24 2/5 (-2/3,-3/5) 0 24 9/22 -7/12 1 12 16/39 -1/2 2 8 7/17 -9/16 1 24 5/12 -1/2 5 2 3/7 -1/2 1 24 10/23 (-1/5,0/1) 0 24 7/16 0/1 7 3 11/25 3/8 1 24 4/9 1/0 2 8 5/11 -5/4 1 24 11/24 -1/1 13 1 6/13 (-1/1,-8/9) 0 24 1/2 -1/2 1 12 7/13 -5/4 1 24 13/24 -1/1 11 1 6/11 (-1/1,-6/7) 0 24 5/9 -3/4 1 8 14/25 (-5/7,-2/3) 0 24 9/16 -2/3 7 3 13/23 -23/36 1 24 4/7 (-3/5,-4/7) 0 24 15/26 -9/16 1 12 41/71 -51/92 1 24 26/45 -11/20 2 8 11/19 -1/2 1 24 7/12 -1/2 7 2 3/5 -1/4 1 24 11/18 1/0 1 4 30/49 (-1/1,-2/3) 0 24 49/80 0/1 1 3 19/31 -3/2 1 24 8/13 (0/1,1/1) 0 24 37/60 1/0 11 2 29/47 1/0 1 24 21/34 1/0 1 12 13/21 1/0 1 8 5/8 -1/1 3 3 17/27 -5/6 1 8 46/73 (-33/41,-4/5) 0 24 121/192 -4/5 23 1 75/119 -59/74 1 24 29/46 -11/14 1 12 12/19 (-1/1,-4/5) 0 24 7/11 -1/2 1 24 23/36 -3/4 1 2 16/25 (-1/1,-2/3) 0 24 9/14 -3/4 1 12 11/17 -13/20 1 24 2/3 -1/2 2 8 9/13 -1/2 1 24 25/36 -1/2 1 2 16/23 (-1/3,0/1) 0 24 23/33 -1/2 1 8 7/10 1/0 1 12 19/27 1/0 1 8 50/71 (-2/1,-13/7) 0 24 31/44 -3/2 1 6 12/17 (-4/3,-1/1) 0 24 17/24 -1/1 7 1 5/7 -3/4 1 24 13/18 -1/2 1 4 34/47 (-2/1,-1/1) 0 24 21/29 -1/2 1 24 8/11 (-5/7,-2/3) 0 24 19/26 -9/14 1 12 30/41 (-2/3,-3/5) 0 24 11/15 -5/8 1 8 25/34 -11/18 1 12 14/19 (-3/5,-16/27) 0 24 17/23 -23/40 1 24 3/4 -1/2 3 6 19/25 -13/32 1 24 16/21 -3/8 2 8 13/17 -3/10 1 24 10/13 (-1/5,0/1) 0 24 7/9 -1/2 1 8 18/23 (-1/1,0/1) 0 24 11/14 1/0 1 12 26/33 1/0 2 8 15/19 -3/2 1 24 19/24 -1/1 5 1 4/5 (-1/1,-2/3) 0 24 9/11 -5/8 1 24 5/6 -1/2 5 4 11/13 -3/8 1 24 6/7 (-1/1,0/1) 0 24 13/15 -1/2 1 8 20/23 (-1/3,0/1) 0 24 7/8 -1/1 1 3 15/17 -5/8 1 24 8/9 -1/2 2 8 9/10 -1/2 1 12 1/1 -1/2 1 24 1/0 0/1 1 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(73,-10,168,-23) (0/1,1/7) -> (3/7,10/23) Hyperbolic Matrix(121,-18,168,-25) (1/7,1/6) -> (5/7,13/18) Glide Reflection Matrix(73,-14,120,-23) (1/6,1/5) -> (3/5,11/18) 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(671,-142,912,-193) (4/19,3/14) -> (25/34,14/19) Hyperbolic 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(167,-38,312,-71) (5/22,3/13) -> (1/2,7/13) Glide Reflection Matrix(265,-62,312,-73) (3/13,4/17) -> (11/13,6/7) Glide Reflection 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(1129,-296,1560,-409) (6/23,5/19) -> (34/47,21/29) Glide Reflection Matrix(719,-190,912,-241) (5/19,4/15) -> (26/33,15/19) Hyperbolic Matrix(119,-32,264,-71) (4/15,3/11) -> (4/9,5/11) Glide Reflection Matrix(217,-60,264,-73) (3/11,5/18) -> (9/11,5/6) Glide Reflection Matrix(337,-94,864,-241) (5/18,7/25) -> (7/18,9/23) Glide Reflection Matrix(191,-54,336,-95) (7/25,2/7) -> (13/23,4/7) Glide Reflection 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(263,-78,408,-121) (5/17,3/10) -> (9/14,11/17) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(649,-234,1800,-649) (9/25,13/36) -> (9/25,13/36) Reflection Matrix(695,-252,1128,-409) (13/36,4/11) -> (8/13,37/60) 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(985,-374,1704,-647) (11/29,8/21) -> (26/45,11/19) Hyperbolic Matrix(215,-82,312,-119) (8/21,5/13) -> (2/3,9/13) Glide Reflection Matrix(263,-102,312,-121) (5/13,7/18) -> (5/6,11/13) Hyperbolic Matrix(407,-160,552,-217) (9/23,2/5) -> (14/19,17/23) Hyperbolic Matrix(409,-166,648,-263) (2/5,9/22) -> (29/46,12/19) Hyperbolic Matrix(721,-296,816,-335) (16/39,7/17) -> (15/17,8/9) Hyperbolic Matrix(169,-70,408,-169) (7/17,5/12) -> (7/17,5/12) Reflection Matrix(71,-30,168,-71) (5/12,3/7) -> (5/12,3/7) Reflection Matrix(431,-188,768,-335) (10/23,7/16) -> (14/25,9/16) Glide Reflection Matrix(433,-190,768,-337) (7/16,11/25) -> (9/16,13/23) Glide 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(263,-122,360,-167) (6/13,1/2) -> (8/11,19/26) Glide Reflection Matrix(337,-182,624,-337) (7/13,13/24) -> (7/13,13/24) Reflection Matrix(287,-156,528,-287) (13/24,6/11) -> (13/24,6/11) Reflection Matrix(167,-92,216,-119) (6/11,5/9) -> (10/13,7/9) Glide Reflection Matrix(337,-188,432,-241) (5/9,14/25) -> (7/9,18/23) Glide Reflection Matrix(913,-526,1248,-719) (4/7,15/26) -> (19/26,30/41) Hyperbolic Matrix(4009,-2314,6360,-3671) (15/26,41/71) -> (75/119,29/46) Hyperbolic Matrix(1991,-1150,2616,-1511) (41/71,26/45) -> (19/25,16/21) Glide Reflection Matrix(265,-154,456,-265) (11/19,7/12) -> (11/19,7/12) Reflection Matrix(71,-42,120,-71) (7/12,3/5) -> (7/12,3/5) Reflection Matrix(1249,-764,1728,-1057) (11/18,30/49) -> (13/18,34/47) Glide Reflection Matrix(1943,-1190,2232,-1367) (30/49,49/80) -> (20/23,7/8) Glide Reflection Matrix(1417,-868,1608,-985) (49/80,19/31) -> (7/8,15/17) Glide Reflection Matrix(479,-294,624,-383) (19/31,8/13) -> (13/17,10/13) Glide Reflection Matrix(3479,-2146,5640,-3479) (37/60,29/47) -> (37/60,29/47) Reflection Matrix(457,-282,504,-311) (29/47,21/34) -> (9/10,1/1) Hyperbolic Matrix(793,-490,1128,-697) (21/34,13/21) -> (7/10,19/27) Glide Reflection Matrix(241,-150,384,-239) (13/21,5/8) -> (5/8,17/27) Parabolic Matrix(2737,-1724,3888,-2449) (17/27,46/73) -> (19/27,50/71) Glide Reflection Matrix(17665,-11132,28032,-17665) (46/73,121/192) -> (46/73,121/192) Reflection Matrix(28799,-18150,45696,-28799) (121/192,75/119) -> (121/192,75/119) Reflection Matrix(215,-136,264,-167) (12/19,7/11) -> (4/5,9/11) Glide Reflection Matrix(505,-322,792,-505) (7/11,23/36) -> (7/11,23/36) Reflection Matrix(1201,-768,1728,-1105) (23/36,16/25) -> (25/36,16/23) Glide Reflection Matrix(527,-338,672,-431) (16/25,9/14) -> (18/23,11/14) Glide Reflection Matrix(311,-202,408,-265) (11/17,2/3) -> (16/21,13/17) Hyperbolic Matrix(649,-450,936,-649) (9/13,25/36) -> (9/13,25/36) Reflection Matrix(959,-668,1104,-769) (16/23,23/33) -> (13/15,20/23) Hyperbolic Matrix(935,-652,1272,-887) (23/33,7/10) -> (11/15,25/34) Glide Reflection Matrix(577,-408,816,-577) (12/17,17/24) -> (12/17,17/24) Reflection Matrix(239,-170,336,-239) (17/24,5/7) -> (17/24,5/7) Reflection Matrix(623,-456,720,-527) (30/41,11/15) -> (6/7,13/15) Glide Reflection Matrix(145,-108,192,-143) (17/23,3/4) -> (3/4,19/25) Parabolic Matrix(409,-322,456,-359) (11/14,26/33) -> (8/9,9/10) Hyperbolic Matrix(721,-570,912,-721) (15/19,19/24) -> (15/19,19/24) Reflection Matrix(191,-152,240,-191) (19/24,4/5) -> (19/24,4/5) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) 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(73,-10,168,-23) -> Matrix(1,1,-6,-5) Matrix(121,-18,168,-25) -> Matrix(5,3,-8,-5) *** -> (-3/4,-1/2) Matrix(73,-14,120,-23) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(49,-10,240,-49) -> Matrix(5,6,-4,-5) (1/5,5/24) -> (-3/2,-1/1) Matrix(191,-40,912,-191) -> Matrix(33,32,-34,-33) (5/24,4/19) -> (-1/1,-16/17) Matrix(671,-142,912,-193) -> Matrix(35,32,-58,-53) Matrix(241,-52,672,-145) -> Matrix(7,6,6,5) Matrix(191,-42,432,-95) -> Matrix(5,4,4,3) Matrix(433,-98,1056,-239) -> Matrix(19,14,-34,-25) Matrix(167,-38,312,-71) -> Matrix(7,5,-4,-3) Matrix(265,-62,312,-73) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(575,-136,816,-193) -> Matrix(5,4,-4,-3) -1/1 Matrix(913,-236,1296,-335) -> Matrix(7,2,-4,-1) Matrix(1129,-296,1560,-409) -> Matrix(1,-1,-2,1) Matrix(719,-190,912,-241) -> Matrix(3,2,-2,-1) -1/1 Matrix(119,-32,264,-71) -> Matrix(3,1,-2,-1) Matrix(217,-60,264,-73) -> Matrix(1,-3,-2,5) Matrix(337,-94,864,-241) -> Matrix(3,14,-4,-19) Matrix(191,-54,336,-95) -> Matrix(5,8,-8,-13) Matrix(97,-28,336,-97) -> Matrix(7,8,-6,-7) (2/7,7/24) -> (-4/3,-1/1) Matrix(239,-70,816,-239) -> Matrix(27,26,-28,-27) (7/24,5/17) -> (-1/1,-13/14) Matrix(263,-78,408,-121) -> Matrix(15,13,-22,-19) Matrix(25,-8,72,-23) -> Matrix(1,1,-4,-3) -1/2 Matrix(649,-234,1800,-649) -> Matrix(-1,7,0,1) (9/25,13/36) -> (7/2,1/0) Matrix(695,-252,1128,-409) -> Matrix(1,3,0,1) 1/0 Matrix(383,-140,528,-193) -> Matrix(3,4,-4,-5) -1/1 Matrix(145,-54,384,-143) -> Matrix(9,10,-10,-11) -1/1 Matrix(985,-374,1704,-647) -> Matrix(47,41,-86,-75) Matrix(215,-82,312,-119) -> Matrix(1,1,4,3) Matrix(263,-102,312,-121) -> Matrix(9,7,-22,-17) Matrix(407,-160,552,-217) -> Matrix(33,23,-56,-39) Matrix(409,-166,648,-263) -> Matrix(7,5,-10,-7) (-1/1,-2/3).(-3/4,-1/2) Matrix(721,-296,816,-335) -> Matrix(3,2,-8,-5) -1/2 Matrix(169,-70,408,-169) -> Matrix(17,9,-32,-17) (7/17,5/12) -> (-9/16,-1/2) Matrix(71,-30,168,-71) -> Matrix(3,1,-8,-3) (5/12,3/7) -> (-1/2,-1/4) Matrix(431,-188,768,-335) -> Matrix(15,2,-22,-3) Matrix(433,-190,768,-337) -> Matrix(13,-2,-20,3) Matrix(241,-110,528,-241) -> Matrix(9,10,-8,-9) (5/11,11/24) -> (-5/4,-1/1) Matrix(287,-132,624,-287) -> Matrix(17,16,-18,-17) (11/24,6/13) -> (-1/1,-8/9) Matrix(263,-122,360,-167) -> Matrix(13,11,-20,-17) Matrix(337,-182,624,-337) -> Matrix(9,10,-8,-9) (7/13,13/24) -> (-5/4,-1/1) Matrix(287,-156,528,-287) -> Matrix(13,12,-14,-13) (13/24,6/11) -> (-1/1,-6/7) Matrix(167,-92,216,-119) -> Matrix(1,1,2,1) Matrix(337,-188,432,-241) -> Matrix(3,2,-10,-7) Matrix(913,-526,1248,-719) -> Matrix(31,18,-50,-29) -3/5 Matrix(4009,-2314,6360,-3671) -> Matrix(163,91,-206,-115) Matrix(1991,-1150,2616,-1511) -> Matrix(67,37,-172,-95) Matrix(265,-154,456,-265) -> Matrix(25,13,-48,-25) (11/19,7/12) -> (-13/24,-1/2) Matrix(71,-42,120,-71) -> Matrix(3,1,-8,-3) (7/12,3/5) -> (-1/2,-1/4) Matrix(1249,-764,1728,-1057) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1943,-1190,2232,-1367) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(1417,-868,1608,-985) -> Matrix(1,-1,-2,1) Matrix(479,-294,624,-383) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(3479,-2146,5640,-3479) -> Matrix(1,9,0,-1) (37/60,29/47) -> (-9/2,1/0) Matrix(457,-282,504,-311) -> Matrix(1,5,-2,-9) Matrix(793,-490,1128,-697) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(241,-150,384,-239) -> Matrix(5,6,-6,-7) -1/1 Matrix(2737,-1724,3888,-2449) -> Matrix(17,14,-6,-5) Matrix(17665,-11132,28032,-17665) -> Matrix(329,264,-410,-329) (46/73,121/192) -> (-33/41,-4/5) Matrix(28799,-18150,45696,-28799) -> Matrix(591,472,-740,-591) (121/192,75/119) -> (-4/5,-59/74) Matrix(215,-136,264,-167) -> Matrix(9,7,-14,-11) Matrix(505,-322,792,-505) -> Matrix(5,3,-8,-5) (7/11,23/36) -> (-3/4,-1/2) Matrix(1201,-768,1728,-1105) -> Matrix(3,2,-10,-7) Matrix(527,-338,672,-431) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(311,-202,408,-265) -> Matrix(11,7,-30,-19) Matrix(649,-450,936,-649) -> Matrix(1,1,0,-1) (9/13,25/36) -> (-1/2,1/0) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(935,-652,1272,-887) -> Matrix(11,3,-18,-5) Matrix(577,-408,816,-577) -> Matrix(7,8,-6,-7) (12/17,17/24) -> (-4/3,-1/1) Matrix(239,-170,336,-239) -> Matrix(7,6,-8,-7) (17/24,5/7) -> (-1/1,-3/4) Matrix(623,-456,720,-527) -> Matrix(3,2,2,1) Matrix(145,-108,192,-143) -> Matrix(11,6,-24,-13) -1/2 Matrix(409,-322,456,-359) -> Matrix(1,3,-2,-5) Matrix(721,-570,912,-721) -> Matrix(5,6,-4,-5) (15/19,19/24) -> (-3/2,-1/1) Matrix(191,-152,240,-191) -> Matrix(5,4,-6,-5) (19/24,4/5) -> (-1/1,-2/3) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.