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 1/2 -9/10 2/3 -8/9 3/5 1/1 -7/8 1/1 -13/15 0/1 -6/7 0/1 1/1 -17/20 0/1 -11/13 3/8 -16/19 2/5 3/7 -5/6 1/2 -19/23 1/2 -33/40 5/9 -14/17 1/2 3/5 -9/11 5/8 -22/27 3/5 7/11 -13/16 2/3 -17/21 2/3 -4/5 3/4 1/1 -19/24 1/1 -15/19 7/6 -11/14 2/1 -18/23 1/1 1/0 -7/9 0/1 -17/22 0/1 -10/13 0/1 1/5 -13/17 1/4 -3/4 1/2 -17/23 1/2 -31/42 1/2 -14/19 4/7 3/5 -11/15 2/3 -19/26 2/3 -8/11 2/3 5/7 -13/18 2/3 -18/25 5/7 3/4 -5/7 5/6 -17/24 1/1 -12/17 1/1 9/8 -19/27 4/3 -26/37 7/5 10/7 -33/47 3/2 -7/10 2/1 -30/43 -3/1 1/0 -23/33 0/1 -39/56 1/1 -16/23 -1/1 1/0 -25/36 0/1 -9/13 1/2 -20/29 -1/1 0/1 -11/16 0/1 -13/19 1/0 -2/3 1/3 1/1 -13/20 1/2 -11/17 1/2 -9/14 2/3 -16/25 1/2 1/1 -23/36 2/3 -30/47 2/3 1/1 -7/11 1/2 -12/19 4/5 1/1 -5/8 1/1 -18/29 1/1 6/5 -31/50 16/13 -44/71 5/4 39/31 -13/21 4/3 -47/76 4/3 -34/55 9/7 4/3 -21/34 4/3 -29/47 3/2 -8/13 5/3 2/1 -19/31 3/2 -49/80 2/1 -30/49 1/1 2/1 -11/18 2/1 -14/23 1/1 1/0 -17/28 2/1 -20/33 3/1 5/1 -3/5 1/0 -16/27 -1/1 1/1 -29/49 1/0 -13/22 0/1 -23/39 0/1 -10/17 -1/1 1/0 -7/12 0/1 -18/31 1/6 1/5 -29/50 2/9 -11/19 1/4 -26/45 1/3 1/1 -41/71 1/2 -15/26 0/1 -19/33 0/1 -4/7 0/1 1/3 -13/23 1/2 -9/16 1/2 -14/25 1/2 3/5 -5/9 2/3 -21/38 2/3 -16/29 2/3 5/7 -11/20 3/4 -6/11 6/7 1/1 -13/24 1/1 -7/13 7/6 -15/28 4/3 -8/15 1/1 5/3 -1/2 0/1 -8/17 3/4 1/1 -7/15 2/3 -6/13 6/7 1/1 -11/24 1/1 -5/11 5/4 -14/31 1/1 3/2 -9/20 2/1 -13/29 3/2 -43/96 2/1 -30/67 2/1 7/3 -17/38 2/1 -4/9 1/1 3/1 -11/25 1/0 -7/16 1/0 -10/23 -3/1 1/0 -3/7 -1/2 -11/26 0/1 -41/97 1/0 -71/168 -1/1 -30/71 -1/1 -1/2 -19/45 0/1 -8/19 -1/3 0/1 -5/12 0/1 -12/29 0/1 1/7 -19/46 2/11 -26/63 1/5 1/3 -33/80 0/1 -7/17 1/4 -9/22 0/1 -29/71 1/4 -49/120 1/3 -20/49 0/1 1/3 -11/27 0/1 -2/5 1/3 1/2 -13/33 2/3 -11/28 1/2 -20/51 1/3 1/1 -9/23 1/2 -7/18 1/2 -19/49 1/2 -31/80 4/7 -43/111 4/7 -12/31 7/12 3/5 -5/13 3/4 -23/60 2/3 -18/47 2/3 1/1 -13/34 2/3 -34/89 7/11 2/3 -55/144 2/3 -21/55 7/10 -8/21 5/7 1/1 -3/8 1/1 -10/27 1/1 7/5 -27/73 3/2 -71/192 3/2 -44/119 3/2 41/27 -17/46 8/5 -7/19 3/2 -25/68 2/1 -43/117 2/1 -18/49 1/1 2/1 -11/30 2/1 -4/11 2/1 3/1 -17/47 1/0 -13/36 1/0 -9/25 1/0 -5/14 0/1 -11/31 1/0 -17/48 1/0 -6/17 -1/1 1/0 -7/20 0/1 -8/23 -1/1 1/0 -1/3 0/1 -6/19 0/1 1/3 -5/16 0/1 -9/29 1/4 -4/13 1/3 2/5 -15/49 1/2 -11/36 1/2 -7/23 1/2 -10/33 3/5 1/1 -13/43 1/2 -29/96 1/2 -16/53 1/2 7/13 -3/10 2/3 -14/47 2/3 1/1 -11/37 3/4 -8/27 5/7 1/1 -21/71 3/4 -13/44 3/4 -5/17 5/6 -7/24 1/1 -2/7 1/1 2/1 -7/25 1/0 -5/18 1/0 -13/47 1/0 -21/76 1/0 -8/29 -2/1 -1/1 -3/11 -1/2 -13/48 0/1 -10/37 0/1 1/7 -7/26 0/1 -11/41 1/2 -4/15 1/3 1/1 -17/64 0/1 -13/49 1/2 -9/34 2/3 -5/19 3/2 -6/23 5/1 1/0 -1/4 0/1 -6/25 5/11 1/2 -5/21 2/3 -4/17 1/1 3/2 -3/13 -1/2 -11/48 0/1 -8/35 0/1 1/9 -5/22 0/1 -7/31 1/4 -9/40 1/3 -2/9 1/3 1/1 -5/23 1/2 -3/14 2/3 -10/47 2/3 1/1 -17/80 2/3 -7/33 2/3 -4/19 4/5 1/1 -5/24 1/1 -1/5 1/0 -4/21 -1/1 1/1 -3/16 0/1 -5/27 0/1 -2/11 2/3 1/1 -5/28 1/0 -3/17 1/0 -7/40 1/1 -4/23 3/1 1/0 -1/6 0/1 -4/25 3/7 1/2 -3/19 1/0 -2/13 2/3 1/1 -5/33 2/1 -3/20 1/0 -7/47 1/0 -4/27 -1/1 1/1 -1/7 1/2 -2/15 1/3 1/1 -3/23 1/2 -1/8 1/1 -2/17 -1/1 1/0 -1/9 0/1 -1/10 0/1 0/1 0/1 1/1 1/10 0/1 1/9 0/1 1/8 1/1 2/15 -1/1 1/1 1/7 1/0 3/20 1/2 2/13 1/1 2/1 3/19 1/2 1/6 0/1 4/23 1/2 3/5 7/40 1/1 3/17 1/2 2/11 1/1 2/1 5/27 0/1 3/16 0/1 4/21 1/3 1/1 1/5 1/2 5/24 1/1 4/19 1/1 4/3 3/14 2/1 5/23 1/0 2/9 -1/1 1/1 5/22 0/1 3/13 1/4 4/17 3/4 1/1 1/4 0/1 6/23 1/2 5/9 11/42 2/3 5/19 3/4 4/15 -1/1 1/1 7/26 0/1 3/11 1/4 5/18 1/2 7/25 1/2 2/7 2/3 1/1 7/24 1/1 5/17 5/4 8/27 1/1 5/3 11/37 3/2 14/47 1/1 2/1 3/10 2/1 13/43 1/0 10/33 1/1 3/1 17/56 3/1 7/23 1/0 11/36 1/0 4/13 -2/1 -1/1 9/29 -1/2 5/16 0/1 6/19 -1/1 0/1 1/3 0/1 7/20 0/1 6/17 1/3 1/2 5/14 0/1 9/25 1/2 13/36 1/2 17/47 1/2 4/11 3/5 2/3 7/19 3/4 3/8 1/1 11/29 3/2 19/50 10/7 27/71 3/2 8/21 1/1 5/3 29/76 3/2 21/55 7/4 13/34 2/1 18/47 1/1 2/1 5/13 3/2 12/31 3/1 7/2 31/80 4/1 19/49 1/0 7/18 1/0 9/23 1/0 11/28 1/0 13/33 2/1 2/5 -1/1 1/0 11/27 0/1 20/49 -1/1 0/1 9/22 0/1 16/39 -1/1 1/1 7/17 -1/2 5/12 0/1 13/31 1/8 21/50 2/13 8/19 0/1 1/5 19/45 0/1 30/71 1/4 1/3 11/26 0/1 14/33 1/5 1/3 3/7 1/4 10/23 3/7 1/2 7/16 1/2 11/25 1/2 4/9 3/5 1/1 17/38 2/3 13/29 3/4 9/20 2/3 5/11 5/6 11/24 1/1 6/13 1/1 6/5 13/28 3/2 7/15 2/1 1/2 0/1 9/17 3/4 8/15 5/7 1/1 7/13 7/8 13/24 1/1 6/11 1/1 6/5 17/31 3/2 11/20 3/2 16/29 5/3 2/1 53/96 2/1 37/67 5/2 21/38 2/1 5/9 2/1 14/25 3/1 1/0 9/16 1/0 13/23 1/0 4/7 -1/1 0/1 15/26 0/1 56/97 0/1 1/1 97/168 1/1 41/71 1/0 26/45 -1/1 1/1 11/19 -1/2 7/12 0/1 17/29 1/4 27/46 2/7 37/63 0/1 47/80 0/1 10/17 1/3 1/2 13/22 0/1 42/71 1/4 1/3 71/120 1/3 29/49 1/2 16/27 1/3 1/1 3/5 1/2 20/33 5/9 3/5 17/28 2/3 31/51 2/3 14/23 1/2 1/1 11/18 2/3 30/49 2/3 1/1 49/80 2/3 68/111 5/7 1/1 19/31 3/4 8/13 2/3 5/7 37/60 3/4 29/47 3/4 21/34 4/5 55/89 19/24 89/144 4/5 34/55 4/5 9/11 13/21 4/5 5/8 1/1 17/27 6/5 46/73 41/33 5/4 121/192 5/4 75/119 5/4 29/46 14/11 12/19 1/1 4/3 43/68 3/2 74/117 1/1 7/5 31/49 3/2 19/30 3/2 7/11 1/0 30/47 1/1 2/1 23/36 2/1 16/25 1/1 1/0 9/14 2/1 20/31 3/1 1/0 31/48 1/0 11/17 1/0 13/20 1/0 15/23 1/0 2/3 -1/1 1/1 13/19 1/2 11/16 0/1 20/29 0/1 1/3 9/13 1/0 34/49 0/1 1/1 25/36 0/1 16/23 1/3 1/2 23/33 0/1 30/43 3/7 1/2 67/96 1/2 37/53 1/2 7/10 2/3 33/47 3/4 26/37 10/13 7/9 19/27 4/5 50/71 5/6 31/37 31/44 6/7 12/17 9/10 1/1 17/24 1/1 5/7 5/4 18/25 3/2 5/3 13/18 2/1 34/47 1/1 2/1 55/76 2/1 21/29 1/0 8/11 5/3 2/1 35/48 2/1 27/37 13/6 19/26 2/1 30/41 2/1 3/1 11/15 2/1 47/64 2/1 36/49 2/1 3/1 25/34 2/1 14/19 3/1 4/1 17/23 1/0 3/4 1/0 19/25 1/0 16/21 -3/1 -1/1 13/17 -1/2 10/13 -1/3 0/1 37/48 0/1 27/35 1/8 17/22 0/1 24/31 1/3 1/2 31/40 1/1 7/9 0/1 18/23 1/2 1/1 11/14 2/3 37/47 3/4 63/80 4/5 26/33 7/9 1/1 15/19 7/8 19/24 1/1 4/5 1/1 3/2 17/21 2/1 13/16 2/1 22/27 7/3 3/1 9/11 5/2 23/28 4/1 14/17 3/1 1/0 33/40 5/1 19/23 1/0 5/6 1/0 21/25 1/0 16/19 -3/1 -2/1 11/13 -3/2 28/33 -1/1 -3/5 17/20 0/1 40/47 -1/1 0/1 23/27 0/1 6/7 0/1 1/1 13/15 0/1 20/23 1/3 1/2 7/8 1/1 15/17 3/2 8/9 1/1 3/1 9/10 2/1 1/1 1/0 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(13,-8,18,-11) Matrix(193,172,432,385) -> Matrix(1,0,0,1) Matrix(97,86,-432,-383) -> Matrix(3,-2,8,-5) Matrix(769,668,-1104,-959) -> Matrix(1,0,0,1) Matrix(527,456,720,623) -> Matrix(1,2,0,1) Matrix(1009,860,-1632,-1391) -> Matrix(13,-4,10,-3) Matrix(335,284,-624,-529) -> Matrix(13,-4,10,-3) Matrix(431,364,624,527) -> Matrix(5,-2,8,-3) Matrix(673,566,-912,-767) -> Matrix(13,-6,24,-11) Matrix(815,674,-1104,-913) -> Matrix(1,0,0,1) Matrix(671,554,2208,1823) -> Matrix(15,-8,2,-1) Matrix(1487,1226,1920,1583) -> Matrix(7,-4,16,-9) Matrix(239,196,-528,-433) -> Matrix(17,-10,12,-7) Matrix(385,314,1296,1057) -> Matrix(7,-4,2,-1) Matrix(145,118,768,625) -> Matrix(3,-2,14,-9) Matrix(143,116,768,623) -> Matrix(3,-2,-4,3) Matrix(97,78,240,193) -> Matrix(3,-2,-4,3) Matrix(191,152,240,191) -> Matrix(7,-6,6,-5) Matrix(721,570,912,721) -> Matrix(13,-14,14,-15) Matrix(241,190,-912,-719) -> Matrix(3,-4,4,-5) Matrix(431,338,672,527) -> Matrix(1,0,0,1) Matrix(241,188,432,337) -> Matrix(1,2,0,1) Matrix(623,482,-1056,-817) -> Matrix(1,0,0,1) Matrix(241,186,-1056,-815) -> Matrix(1,0,4,1) Matrix(383,294,624,479) -> Matrix(5,-2,8,-3) Matrix(241,184,-816,-623) -> Matrix(11,-4,14,-5) Matrix(383,284,-1296,-961) -> Matrix(1,-2,2,-3) Matrix(193,142,-912,-671) -> Matrix(13,-8,18,-11) Matrix(719,526,-1248,-913) -> Matrix(3,-2,14,-9) Matrix(337,246,-1248,-911) -> Matrix(3,-2,14,-9) Matrix(193,140,-528,-383) -> Matrix(5,-4,4,-3) Matrix(527,380,864,623) -> Matrix(11,-8,18,-13) Matrix(145,104,336,241) -> Matrix(5,-4,14,-11) Matrix(239,170,336,239) -> Matrix(11,-10,10,-9) Matrix(577,408,816,577) -> Matrix(17,-18,18,-19) Matrix(193,136,-816,-575) -> Matrix(5,-6,6,-7) Matrix(239,168,1296,911) -> Matrix(3,-4,-2,3) Matrix(817,574,2256,1585) -> Matrix(11,-16,20,-29) Matrix(433,304,480,337) -> Matrix(5,-8,2,-3) Matrix(289,202,-960,-671) -> Matrix(1,-4,2,-7) Matrix(625,436,1584,1105) -> Matrix(1,2,0,1) Matrix(385,268,2208,1537) -> Matrix(1,-2,2,-3) Matrix(1105,768,1728,1201) -> Matrix(1,2,0,1) Matrix(479,332,-1248,-865) -> Matrix(1,-2,2,-3) Matrix(527,364,624,431) -> Matrix(1,-2,0,1) Matrix(241,166,768,529) -> Matrix(1,0,0,1) Matrix(239,164,768,527) -> Matrix(1,0,-2,1) Matrix(527,360,912,623) -> Matrix(1,0,-2,1) Matrix(433,282,-1104,-719) -> Matrix(1,0,0,1) Matrix(527,342,960,623) -> Matrix(5,-4,4,-3) Matrix(239,154,-672,-433) -> Matrix(3,-2,2,-1) Matrix(527,338,672,431) -> Matrix(1,0,0,1) Matrix(1201,768,1728,1105) -> Matrix(3,-2,8,-5) Matrix(2399,1532,3456,2207) -> Matrix(3,-2,2,-1) Matrix(671,428,2256,1439) -> Matrix(5,-4,4,-3) Matrix(145,92,-528,-335) -> Matrix(3,-2,-4,3) Matrix(239,150,-384,-241) -> Matrix(11,-10,10,-9) Matrix(1009,626,2400,1489) -> Matrix(5,-6,26,-31) Matrix(3407,2112,-9216,-5713) -> Matrix(71,-88,46,-57) Matrix(2399,1486,3408,2111) -> Matrix(31,-40,38,-49) Matrix(3793,2346,-10320,-6383) -> Matrix(1,-2,2,-3) Matrix(1871,1156,-4896,-3025) -> Matrix(7,-10,12,-17) Matrix(865,534,-3264,-2015) -> Matrix(7,-10,12,-17) Matrix(383,236,-1248,-769) -> Matrix(5,-8,12,-19) Matrix(479,294,624,383) -> Matrix(1,-2,0,1) Matrix(1583,970,-3840,-2353) -> Matrix(1,-2,6,-11) Matrix(1633,1000,-7680,-4703) -> Matrix(3,-4,4,-5) Matrix(1249,764,1728,1057) -> Matrix(1,0,0,1) Matrix(623,380,864,527) -> Matrix(3,-8,2,-5) Matrix(385,234,-1104,-671) -> Matrix(1,-2,0,1) Matrix(1345,816,1584,961) -> Matrix(1,-2,-2,5) Matrix(479,290,1584,959) -> Matrix(1,-2,0,1) Matrix(47,28,240,143) -> Matrix(1,0,2,1) Matrix(385,228,-2592,-1535) -> Matrix(1,0,0,1) Matrix(1441,852,-3408,-2015) -> Matrix(1,0,0,1) Matrix(95,56,-816,-481) -> Matrix(1,0,0,1) Matrix(335,196,-576,-337) -> Matrix(1,0,6,1) Matrix(431,250,-912,-529) -> Matrix(9,-2,14,-3) Matrix(911,528,2400,1391) -> Matrix(13,-4,10,-3) Matrix(623,360,912,527) -> Matrix(1,0,-2,1) Matrix(817,472,1248,721) -> Matrix(1,0,-2,1) Matrix(1393,804,-3408,-1967) -> Matrix(1,0,2,1) Matrix(289,166,336,193) -> Matrix(1,0,-2,1) Matrix(95,54,336,191) -> Matrix(5,-2,8,-3) Matrix(337,190,768,433) -> Matrix(9,-4,16,-7) Matrix(335,188,768,431) -> Matrix(11,-6,24,-13) Matrix(337,188,432,241) -> Matrix(3,-2,8,-5) Matrix(47,26,432,239) -> Matrix(3,-2,2,-1) Matrix(1633,902,-3648,-2015) -> Matrix(7,-4,2,-1) Matrix(769,424,-2784,-1535) -> Matrix(11,-8,-4,3) Matrix(95,52,-528,-289) -> Matrix(5,-4,4,-3) Matrix(287,156,528,287) -> Matrix(13,-12,12,-11) Matrix(337,182,624,337) -> Matrix(13,-14,14,-15) Matrix(815,436,1344,719) -> Matrix(7,-10,12,-17) Matrix(337,178,-816,-431) -> Matrix(1,-2,6,-11) Matrix(911,428,-2352,-1105) -> Matrix(5,-2,8,-3) Matrix(95,44,-624,-289) -> Matrix(5,-4,4,-3) Matrix(287,132,624,287) -> Matrix(13,-12,12,-11) Matrix(241,110,528,241) -> Matrix(9,-10,10,-11) Matrix(337,152,960,433) -> Matrix(1,-2,4,-7) Matrix(865,388,-2352,-1055) -> Matrix(1,0,0,1) Matrix(5089,2280,9216,4129) -> Matrix(9,-16,4,-7) Matrix(5087,2278,9216,4127) -> Matrix(11,-24,6,-13) Matrix(385,172,432,193) -> Matrix(1,0,0,1) Matrix(95,42,432,191) -> Matrix(1,-2,0,1) Matrix(433,190,768,337) -> Matrix(1,-4,0,1) Matrix(431,188,768,335) -> Matrix(1,6,0,1) Matrix(241,104,336,145) -> Matrix(3,4,2,3) Matrix(335,142,-1248,-529) -> Matrix(1,0,4,1) Matrix(11759,4970,19872,8399) -> Matrix(1,2,2,5) Matrix(12097,5112,20448,8641) -> Matrix(3,2,10,7) Matrix(2831,1196,4656,1967) -> Matrix(3,2,4,3) Matrix(289,122,912,385) -> Matrix(1,0,2,1) Matrix(239,100,-576,-241) -> Matrix(1,0,10,1) Matrix(1393,576,2208,913) -> Matrix(29,-4,22,-3) Matrix(6049,2496,7680,3169) -> Matrix(19,-4,24,-5) 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(1,0,-2,1) Matrix(2593,1058,-7056,-2879) -> Matrix(7,-2,4,-1) Matrix(193,78,240,97) -> Matrix(7,-2,4,-1) Matrix(1105,436,1584,625) -> Matrix(3,-2,8,-5) Matrix(625,246,1344,529) -> Matrix(5,-4,4,-3) Matrix(2689,1054,4656,1825) -> Matrix(1,0,-2,1) Matrix(241,94,864,337) -> Matrix(1,0,0,1) Matrix(1489,578,2352,913) -> Matrix(29,-16,20,-11) Matrix(1873,726,-7056,-2735) -> Matrix(7,-4,16,-9) Matrix(6097,2362,8304,3217) -> Matrix(11,-6,2,-1) Matrix(145,56,624,241) -> Matrix(3,-2,8,-5) Matrix(2881,1104,4512,1729) -> Matrix(5,-4,4,-3) Matrix(481,184,-2256,-863) -> Matrix(1,0,0,1) Matrix(12817,4896,20736,7921) -> Matrix(71,-46,88,-57) Matrix(12815,4894,20736,7919) -> Matrix(97,-66,122,-83) Matrix(241,92,-1632,-623) -> Matrix(3,-2,-4,3) Matrix(143,54,-384,-145) -> Matrix(7,-6,6,-5) Matrix(1681,622,2208,817) -> Matrix(7,-10,-2,3) Matrix(23233,8592,36864,13633) -> Matrix(203,-302,162,-241) Matrix(23231,8590,36864,13631) -> Matrix(217,-328,174,-263) Matrix(1295,478,2208,815) -> Matrix(1,-2,6,-11) Matrix(1439,528,2352,863) -> Matrix(3,-4,4,-5) Matrix(1585,574,2256,817) -> Matrix(3,-16,4,-21) Matrix(2783,1006,4512,1631) -> Matrix(3,-34,4,-45) Matrix(527,190,1728,623) -> Matrix(1,4,0,1) Matrix(145,52,672,241) -> Matrix(1,2,0,1) Matrix(1489,528,2304,817) -> Matrix(1,-2,0,1) Matrix(1487,526,2304,815) -> Matrix(1,4,0,1) Matrix(671,236,816,287) -> Matrix(1,4,0,1) 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,-2,1) Matrix(97,30,624,193) -> Matrix(1,0,-2,1) Matrix(1249,382,3456,1057) -> Matrix(29,-14,56,-27) Matrix(623,190,1728,527) -> Matrix(7,-4,16,-9) Matrix(145,44,-1104,-335) -> Matrix(3,-2,8,-5) Matrix(959,290,1584,479) -> Matrix(5,-2,8,-3) Matrix(6433,1944,9216,2785) -> Matrix(17,-8,32,-15) Matrix(6431,1942,9216,2783) -> Matrix(19,-10,40,-21) Matrix(47,14,480,143) -> Matrix(3,-2,2,-1) Matrix(1439,428,2256,671) -> Matrix(5,-4,4,-3) Matrix(1057,314,1296,385) -> Matrix(7,-4,2,-1) Matrix(1297,384,3408,1009) -> Matrix(17,-12,10,-7) Matrix(239,70,816,239) -> Matrix(11,-10,10,-9) Matrix(97,28,336,97) -> Matrix(3,-4,4,-5) Matrix(191,54,336,95) -> Matrix(1,-2,0,1) Matrix(337,94,864,241) -> Matrix(1,0,0,1) Matrix(671,186,1728,479) -> Matrix(1,6,0,1) Matrix(673,186,-4512,-1247) -> Matrix(1,2,0,1) Matrix(1681,456,2304,625) -> Matrix(17,2,8,1) Matrix(1679,454,2304,623) -> Matrix(19,-2,10,-1) Matrix(97,26,720,193) -> Matrix(1,0,-2,1) Matrix(5087,1352,8304,2207) -> Matrix(1,-2,2,-3) Matrix(145,38,-912,-239) -> Matrix(1,-2,2,-3) Matrix(47,12,-192,-49) -> Matrix(1,0,2,1) Matrix(1391,332,2208,527) -> Matrix(27,-16,22,-13) Matrix(241,56,624,145) -> Matrix(1,2,0,1) Matrix(1777,408,2304,529) -> Matrix(1,0,10,1) Matrix(1775,406,2304,527) -> Matrix(1,0,-12,1) Matrix(337,76,1920,433) -> Matrix(1,0,-2,1) Matrix(191,42,432,95) -> Matrix(5,-2,8,-3) Matrix(241,52,672,145) -> Matrix(3,-2,8,-5) Matrix(4511,958,7680,1631) -> Matrix(3,-2,8,-5) Matrix(191,40,912,191) -> Matrix(9,-8,8,-7) Matrix(49,10,240,49) -> Matrix(1,-2,2,-3) Matrix(143,28,240,47) -> Matrix(1,0,2,1) Matrix(625,118,768,145) -> Matrix(5,2,2,1) Matrix(623,116,768,143) -> Matrix(7,-2,4,-1) Matrix(911,168,1296,239) -> Matrix(11,-4,14,-5) Matrix(529,94,816,145) -> Matrix(1,0,0,1) Matrix(719,126,816,143) -> Matrix(3,-2,2,-1) Matrix(961,168,1104,193) -> Matrix(1,-2,2,-3) Matrix(47,8,-288,-49) -> Matrix(1,0,2,1) Matrix(193,30,624,97) -> Matrix(1,0,-2,1) Matrix(623,94,1584,239) -> Matrix(1,0,0,1) Matrix(143,20,336,47) -> Matrix(1,0,2,1) Matrix(911,118,1104,143) -> Matrix(11,-6,2,-1) Matrix(673,80,816,97) -> Matrix(1,4,0,1) Matrix(239,26,432,47) -> Matrix(3,-2,2,-1) Matrix(143,14,480,47) -> Matrix(3,-2,2,-1) Matrix(335,-38,432,-49) -> Matrix(1,0,0,1) Matrix(335,-44,1104,-145) -> Matrix(1,2,0,1) Matrix(623,-92,1632,-241) -> Matrix(7,-2,4,-1) Matrix(289,-44,624,-95) -> Matrix(5,-4,4,-3) Matrix(239,-38,912,-145) -> Matrix(1,-2,2,-3) Matrix(289,-50,1104,-191) -> Matrix(5,-2,8,-3) Matrix(289,-52,528,-95) -> Matrix(5,-4,4,-3) Matrix(671,-142,912,-193) -> Matrix(5,-8,2,-3) Matrix(433,-98,1056,-239) -> Matrix(1,0,0,1) Matrix(815,-186,1056,-241) -> Matrix(1,0,4,1) Matrix(575,-136,816,-193) -> Matrix(5,-6,6,-7) Matrix(913,-236,1296,-335) -> Matrix(17,-6,20,-7) Matrix(719,-190,912,-241) -> Matrix(3,-4,4,-5) Matrix(529,-142,1248,-335) -> Matrix(1,0,4,1) Matrix(911,-246,1248,-337) -> Matrix(5,2,2,1) Matrix(335,-92,528,-145) -> Matrix(7,-2,4,-1) Matrix(623,-184,816,-241) -> Matrix(3,-4,-2,3) Matrix(671,-202,960,-289) -> Matrix(1,-4,2,-7) Matrix(769,-236,1248,-383) -> Matrix(3,8,4,11) Matrix(671,-234,1104,-385) -> Matrix(5,-2,8,-3) Matrix(433,-154,672,-239) -> Matrix(3,-2,2,-1) Matrix(383,-140,528,-193) -> Matrix(5,-4,4,-3) Matrix(145,-54,384,-143) -> Matrix(7,-6,6,-5) Matrix(5809,-2208,9216,-3503) -> Matrix(63,-92,50,-73) Matrix(6527,-2490,10320,-3937) -> Matrix(11,-18,8,-13) Matrix(3025,-1156,4896,-1871) -> Matrix(3,-10,4,-13) Matrix(2399,-918,3264,-1249) -> Matrix(5,-8,2,-3) Matrix(865,-332,1248,-479) -> Matrix(1,-2,2,-3) Matrix(2257,-874,3840,-1487) -> Matrix(1,-4,4,-15) Matrix(6047,-2344,7680,-2977) -> Matrix(3,-16,4,-21) Matrix(719,-282,1104,-433) -> Matrix(1,0,0,1) Matrix(2207,-900,2592,-1057) -> Matrix(1,0,0,1) Matrix(1967,-804,3408,-1393) -> Matrix(1,0,2,1) Matrix(721,-296,816,-335) -> Matrix(1,2,0,1) Matrix(241,-100,576,-239) -> Matrix(1,0,10,1) Matrix(481,-202,912,-383) -> Matrix(13,-2,20,-3) Matrix(2015,-852,3408,-1441) -> Matrix(1,0,0,1) Matrix(2015,-902,3648,-1633) -> Matrix(7,-4,2,-1) Matrix(2015,-904,2784,-1249) -> Matrix(5,-4,4,-3) Matrix(433,-196,528,-239) -> Matrix(13,-10,4,-3) Matrix(479,-226,816,-385) -> Matrix(1,-2,4,-7) Matrix(1441,-764,2352,-1247) -> Matrix(1,0,0,1) Matrix(529,-284,624,-335) -> Matrix(5,-4,-6,5) Matrix(1487,-820,2352,-1297) -> Matrix(11,-18,8,-13) Matrix(913,-526,1248,-719) -> Matrix(5,2,2,1) Matrix(337,-196,576,-335) -> Matrix(1,0,6,1) Matrix(817,-482,1056,-623) -> Matrix(1,0,0,1) Matrix(4463,-2642,7056,-4177) -> Matrix(5,-4,4,-3) Matrix(5183,-3174,7056,-4321) -> Matrix(7,-4,2,-1) Matrix(1775,-1096,2256,-1393) -> Matrix(23,-18,32,-25) Matrix(1391,-860,1632,-1009) -> Matrix(5,-4,-6,5) Matrix(241,-150,384,-239) -> Matrix(11,-10,10,-9) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(3839,-2778,4512,-3265) -> Matrix(1,-2,0,1) Matrix(767,-566,912,-673) -> Matrix(1,-6,0,1) Matrix(145,-108,192,-143) -> Matrix(1,-2,0,1) Matrix(241,-200,288,-239) -> Matrix(1,-6,0,1) 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): 85 Degree of the the map X: 85 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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 (0/1,1/1) 0 24 1/10 0/1 1 12 1/9 0/1 1 8 1/8 1/1 1 3 2/15 0 8 1/7 1/0 1 24 3/20 1/2 1 6 2/13 (1/1,2/1) 0 24 3/19 1/2 1 24 1/6 0/1 1 4 4/23 (1/2,3/5) 0 24 7/40 1/1 2 3 3/17 1/2 1 24 2/11 (1/1,2/1) 0 24 5/27 0/1 1 8 3/16 0/1 3 3 4/21 0 8 1/5 1/2 1 24 5/24 1/1 5 1 4/19 (1/1,4/3) 0 24 3/14 2/1 1 12 5/23 1/0 1 24 2/9 0 8 5/22 0/1 1 12 3/13 1/4 1 24 4/17 (3/4,1/1) 0 24 1/4 0/1 1 6 6/23 (1/2,5/9) 0 24 11/42 2/3 1 4 5/19 3/4 1 24 4/15 0 8 7/26 0/1 1 12 3/11 1/4 1 24 5/18 1/2 3 4 7/25 1/2 1 24 2/7 (2/3,1/1) 0 24 7/24 1/1 7 1 5/17 5/4 1 24 8/27 0 8 11/37 3/2 1 24 14/47 (1/1,2/1) 0 24 3/10 2/1 1 12 13/43 1/0 1 24 10/33 0 8 17/56 3/1 1 3 7/23 1/0 1 24 11/36 1/0 9 2 4/13 (-2/1,-1/1) 0 24 9/29 -1/2 1 24 5/16 0/1 1 3 6/19 (-1/1,0/1) 0 24 1/3 0/1 1 8 7/20 0/1 1 6 6/17 (1/3,1/2) 0 24 5/14 0/1 1 12 9/25 1/2 1 24 13/36 1/2 9 2 17/47 1/2 1 24 4/11 (3/5,2/3) 0 24 7/19 3/4 1 24 3/8 1/1 3 3 11/29 3/2 1 24 19/50 10/7 1 12 27/71 3/2 1 24 8/21 0 8 29/76 3/2 1 6 21/55 7/4 1 24 13/34 2/1 1 12 18/47 (1/1,2/1) 0 24 5/13 3/2 1 24 12/31 (3/1,7/2) 0 24 31/80 4/1 1 3 19/49 1/0 1 24 7/18 1/0 3 4 9/23 1/0 1 24 11/28 1/0 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 0/1 1 12 16/39 0 8 7/17 -1/2 1 24 5/12 0/1 5 2 13/31 1/8 1 24 21/50 2/13 1 12 8/19 (0/1,1/5) 0 24 19/45 0/1 1 8 30/71 (1/4,1/3) 0 24 11/26 0/1 1 12 14/33 0 8 3/7 1/4 1 24 10/23 (3/7,1/2) 0 24 7/16 1/2 5 3 11/25 1/2 1 24 4/9 0 8 17/38 2/3 1 12 13/29 3/4 1 24 9/20 2/3 1 6 5/11 5/6 1 24 11/24 1/1 11 1 6/13 (1/1,6/5) 0 24 13/28 3/2 1 6 7/15 2/1 1 8 1/2 0/1 1 12 9/17 3/4 1 24 8/15 0 8 7/13 7/8 1 24 13/24 1/1 13 1 6/11 (1/1,6/5) 0 24 17/31 3/2 1 24 11/20 3/2 1 6 16/29 (5/3,2/1) 0 24 53/96 2/1 5 1 37/67 5/2 1 24 21/38 2/1 1 12 5/9 2/1 1 8 14/25 (3/1,1/0) 0 24 9/16 1/0 5 3 13/23 1/0 1 24 4/7 (-1/1,0/1) 0 24 15/26 0/1 1 12 56/97 (0/1,1/1) 0 24 97/168 1/1 1 1 41/71 1/0 1 24 26/45 0 8 11/19 -1/2 1 24 7/12 0/1 3 2 17/29 1/4 1 24 27/46 2/7 1 12 37/63 0/1 1 8 47/80 0/1 1 3 10/17 (1/3,1/2) 0 24 13/22 0/1 1 12 42/71 (1/4,1/3) 0 24 71/120 1/3 2 1 29/49 1/2 1 24 16/27 0 8 3/5 1/2 1 24 20/33 0 8 17/28 2/3 1 6 31/51 2/3 1 8 14/23 (1/2,1/1) 0 24 11/18 2/3 1 4 30/49 (2/3,1/1) 0 24 49/80 2/3 1 3 68/111 0 8 19/31 3/4 1 24 8/13 (2/3,5/7) 0 24 37/60 3/4 9 2 29/47 3/4 1 24 21/34 4/5 1 12 55/89 19/24 1 24 89/144 4/5 7 1 34/55 (4/5,9/11) 0 24 13/21 4/5 1 8 5/8 1/1 5 3 17/27 6/5 1 8 46/73 (41/33,5/4) 0 24 121/192 5/4 21 1 75/119 5/4 1 24 29/46 14/11 1 12 12/19 (1/1,4/3) 0 24 43/68 3/2 1 6 74/117 0 8 31/49 3/2 1 24 19/30 3/2 3 4 7/11 1/0 1 24 30/47 (1/1,2/1) 0 24 23/36 2/1 1 2 16/25 (1/1,1/0) 0 24 9/14 2/1 1 12 20/31 (3/1,1/0) 0 24 31/48 1/0 3 1 11/17 1/0 1 24 13/20 1/0 1 6 15/23 1/0 1 24 2/3 0 8 13/19 1/2 1 24 11/16 0/1 1 3 20/29 (0/1,1/3) 0 24 9/13 1/0 1 24 34/49 (0/1,1/1) 0 24 25/36 0/1 1 2 16/23 (1/3,1/2) 0 24 23/33 0/1 1 8 30/43 (3/7,1/2) 0 24 67/96 1/2 9 1 37/53 1/2 1 24 7/10 2/3 1 12 33/47 3/4 1 24 26/37 (10/13,7/9) 0 24 19/27 4/5 1 8 50/71 (5/6,31/37) 0 24 31/44 6/7 1 6 12/17 (9/10,1/1) 0 24 17/24 1/1 14 1 5/7 5/4 1 24 18/25 (3/2,5/3) 0 24 13/18 2/1 1 4 34/47 (1/1,2/1) 0 24 55/76 2/1 1 6 21/29 1/0 1 24 8/11 (5/3,2/1) 0 24 35/48 2/1 9 1 27/37 13/6 1 24 19/26 2/1 1 12 30/41 (2/1,3/1) 0 24 11/15 2/1 1 8 47/64 2/1 1 3 36/49 (2/1,3/1) 0 24 25/34 2/1 1 12 14/19 (3/1,4/1) 0 24 17/23 1/0 1 24 3/4 1/0 1 6 19/25 1/0 1 24 16/21 0 8 13/17 -1/2 1 24 10/13 (-1/3,0/1) 0 24 37/48 0/1 11 1 27/35 1/8 1 24 17/22 0/1 1 12 24/31 (1/3,1/2) 0 24 31/40 1/1 1 3 7/9 0/1 1 8 18/23 (1/2,1/1) 0 24 11/14 2/3 1 12 37/47 3/4 1 24 63/80 4/5 1 3 26/33 0 8 15/19 7/8 1 24 19/24 1/1 10 1 4/5 (1/1,3/2) 0 24 17/21 2/1 1 8 13/16 2/1 3 3 22/27 0 8 9/11 5/2 1 24 23/28 4/1 1 6 14/17 (3/1,1/0) 0 24 33/40 5/1 1 3 19/23 1/0 1 24 5/6 1/0 3 4 21/25 1/0 1 24 16/19 (-3/1,-2/1) 0 24 11/13 -3/2 1 24 28/33 0 8 17/20 0/1 1 6 40/47 (-1/1,0/1) 0 24 23/27 0/1 1 8 6/7 (0/1,1/1) 0 24 13/15 0/1 1 8 20/23 (1/3,1/2) 0 24 7/8 1/1 2 3 15/17 3/2 1 24 8/9 0 8 9/10 2/1 1 12 1/1 1/0 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(143,-14,480,-47) (0/1,1/10) -> (14/47,3/10) Glide Reflection Matrix(239,-26,432,-47) (1/10,1/9) -> (21/38,5/9) Glide Reflection 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(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(961,-168,1104,-193) (4/23,7/40) -> (20/23,7/8) Glide Reflection Matrix(719,-126,816,-143) (7/40,3/17) -> (7/8,15/17) Glide Reflection Matrix(289,-52,528,-95) (3/17,2/11) -> (6/11,17/31) Hyperbolic Matrix(911,-168,1296,-239) (2/11,5/27) -> (26/37,19/27) Glide Reflection Matrix(623,-116,768,-143) (5/27,3/16) -> (17/21,13/16) Glide Reflection Matrix(625,-118,768,-145) (3/16,4/21) -> (13/16,22/27) Glide Reflection Matrix(143,-28,240,-47) (4/21,1/5) -> (16/27,3/5) Glide Reflection 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(815,-186,1056,-241) (5/22,3/13) -> (27/35,17/22) Hyperbolic Matrix(241,-56,624,-145) (3/13,4/17) -> (5/13,12/31) 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(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(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(623,-184,816,-241) (5/17,8/27) -> (16/21,13/17) Hyperbolic Matrix(1057,-314,1296,-385) (8/27,11/37) -> (22/27,9/11) Glide Reflection Matrix(1439,-428,2256,-671) (11/37,14/47) -> (7/11,30/47) Glide Reflection Matrix(671,-202,960,-289) (3/10,13/43) -> (37/53,7/10) Hyperbolic Matrix(959,-290,1584,-479) (13/43,10/33) -> (3/5,20/33) Glide Reflection Matrix(1823,-554,2208,-671) (17/56,7/23) -> (33/40,19/23) Glide Reflection Matrix(623,-190,1728,-527) (7/23,11/36) -> (9/25,13/36) Glide Reflection Matrix(769,-236,1248,-383) (11/36,4/13) -> (8/13,37/60) Hyperbolic Matrix(527,-164,768,-239) (9/29,5/16) -> (13/19,11/16) Glide Reflection Matrix(529,-166,768,-241) (5/16,6/19) -> (11/16,20/29) Glide Reflection Matrix(385,-122,912,-289) (6/19,1/3) -> (8/19,19/45) Glide Reflection Matrix(671,-234,1104,-385) (1/3,7/20) -> (17/28,31/51) Hyperbolic Matrix(671,-236,816,-287) (7/20,6/17) -> (23/28,14/17) Glide Reflection Matrix(433,-154,672,-239) (6/17,5/14) -> (9/14,20/31) Hyperbolic Matrix(2783,-1006,4512,-1631) (13/36,17/47) -> (37/60,29/47) Glide Reflection Matrix(1585,-574,2256,-817) (17/47,4/11) -> (33/47,26/37) Glide Reflection 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(1633,-620,2784,-1057) (11/29,19/50) -> (17/29,27/46) Glide Reflection Matrix(5809,-2208,9216,-3503) (19/50,27/71) -> (75/119,29/46) Hyperbolic Matrix(1535,-584,2016,-767) (27/71,8/21) -> (19/25,16/21) Glide Reflection 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(1489,-578,2352,-913) (19/49,7/18) -> (31/49,19/30) Glide Reflection Matrix(719,-282,1104,-433) (9/23,11/28) -> (13/20,15/23) Hyperbolic Matrix(625,-246,1344,-529) (11/28,13/33) -> (13/28,7/15) Glide Reflection Matrix(1105,-436,1584,-625) (13/33,2/5) -> (23/33,30/43) Glide Reflection Matrix(193,-78,240,-97) (2/5,11/27) -> (4/5,17/21) Glide Reflection 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(1151,-484,1824,-767) (21/50,8/19) -> (29/46,12/19) Glide Reflection Matrix(2831,-1196,4656,-1967) (19/45,30/71) -> (31/51,14/23) Glide Reflection Matrix(2015,-852,3408,-1441) (30/71,11/26) -> (13/22,42/71) Hyperbolic Matrix(241,-104,336,-145) (3/7,10/23) -> (5/7,18/25) Glide 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(385,-172,432,-193) (4/9,17/38) -> (8/9,9/10) Glide Reflection 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(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(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(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(623,-342,960,-527) (17/31,11/20) -> (11/17,13/20) Glide Reflection Matrix(1487,-820,2352,-1297) (11/20,16/29) -> (12/19,43/68) Hyperbolic Matrix(3073,-1696,5568,-3073) (16/29,53/96) -> (16/29,53/96) Reflection Matrix(7103,-3922,12864,-7103) (53/96,37/67) -> (53/96,37/67) 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(18817,-10864,32592,-18817) (56/97,97/168) -> (56/97,97/168) Reflection Matrix(13775,-7954,23856,-13775) (97/168,41/71) -> (97/168,41/71) Reflection Matrix(817,-472,1248,-721) (41/71,26/45) -> (15/23,2/3) Glide Reflection Matrix(623,-360,912,-527) (26/45,11/19) -> (2/3,13/19) Glide Reflection Matrix(337,-196,576,-335) (11/19,7/12) -> (7/12,17/29) Parabolic Matrix(3841,-2256,5232,-3073) (37/63,47/80) -> (11/15,47/64) Glide Reflection Matrix(817,-482,1056,-623) (10/17,13/22) -> (17/22,24/31) Hyperbolic Matrix(10081,-5964,17040,-10081) (42/71,71/120) -> (42/71,71/120) Reflection Matrix(6959,-4118,11760,-6959) (71/120,29/49) -> (71/120,29/49) Reflection Matrix(4463,-2642,7056,-4177) (29/49,16/27) -> (74/117,31/49) Hyperbolic Matrix(1345,-816,1584,-961) (20/33,17/28) -> (28/33,17/20) Glide Reflection Matrix(623,-380,864,-527) (14/23,11/18) -> (18/25,13/18) Glide Reflection Matrix(1249,-764,1728,-1057) (11/18,30/49) -> (13/18,34/47) Glide Reflection Matrix(5183,-3174,7056,-4321) (30/49,49/80) -> (47/64,36/49) Hyperbolic Matrix(9073,-5558,11520,-7057) (49/80,68/111) -> (63/80,26/33) Glide Reflection Matrix(479,-294,624,-383) (19/31,8/13) -> (13/17,10/13) Glide Reflection Matrix(1775,-1096,2256,-1393) (29/47,21/34) -> (11/14,37/47) Hyperbolic Matrix(15841,-9790,25632,-15841) (55/89,89/144) -> (55/89,89/144) Reflection Matrix(9791,-6052,15840,-9791) (89/144,34/55) -> (89/144,34/55) Reflection 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(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(2399,-1532,3456,-2207) (30/47,23/36) -> (34/49,25/36) Glide 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(1921,-1240,2976,-1921) (20/31,31/48) -> (20/31,31/48) Reflection Matrix(1055,-682,1632,-1055) (31/48,11/17) -> (31/48,11/17) Reflection Matrix(527,-364,624,-431) (20/29,9/13) -> (16/19,11/13) Glide Reflection Matrix(959,-668,1104,-769) (16/23,23/33) -> (13/15,20/23) Hyperbolic Matrix(5761,-4020,8256,-5761) (30/43,67/96) -> (30/43,67/96) Reflection Matrix(7103,-4958,10176,-7103) (67/96,37/53) -> (67/96,37/53) Reflection Matrix(433,-304,480,-337) (7/10,33/47) -> (9/10,1/1) 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(3839,-2778,4512,-3265) (34/47,55/76) -> (17/20,40/47) Hyperbolic Matrix(769,-560,1056,-769) (8/11,35/48) -> (8/11,35/48) Reflection Matrix(2591,-1890,3552,-2591) (35/48,27/37) -> (35/48,27/37) Reflection Matrix(623,-456,720,-527) (30/41,11/15) -> (6/7,13/15) Glide Reflection 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(961,-740,1248,-961) (10/13,37/48) -> (10/13,37/48) Reflection Matrix(2591,-1998,3360,-2591) (37/48,27/35) -> (37/48,27/35) Reflection Matrix(1583,-1226,1920,-1487) (24/31,31/40) -> (14/17,33/40) Glide Reflection 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(241,-200,288,-239) (19/23,5/6) -> (5/6,21/25) Parabolic 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) -> (0/1,1/1) Matrix(143,-14,480,-47) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(239,-26,432,-47) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(335,-38,432,-49) -> Matrix(1,0,0,1) Matrix(335,-44,1104,-145) -> Matrix(1,2,0,1) 1/0 Matrix(143,-20,336,-47) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(623,-92,1632,-241) -> Matrix(7,-2,4,-1) Matrix(289,-44,624,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(193,-30,624,-97) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(239,-38,912,-145) -> Matrix(1,-2,2,-3) 1/1 Matrix(289,-50,1104,-191) -> Matrix(5,-2,8,-3) 1/2 Matrix(961,-168,1104,-193) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(719,-126,816,-143) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(289,-52,528,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(911,-168,1296,-239) -> Matrix(3,4,4,5) Matrix(623,-116,768,-143) -> Matrix(3,2,2,1) Matrix(625,-118,768,-145) -> Matrix(9,-2,4,-1) Matrix(143,-28,240,-47) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(49,-10,240,-49) -> Matrix(3,-2,4,-3) (1/5,5/24) -> (1/2,1/1) Matrix(191,-40,912,-191) -> Matrix(7,-8,6,-7) (5/24,4/19) -> (1/1,4/3) Matrix(671,-142,912,-193) -> Matrix(5,-8,2,-3) 2/1 Matrix(241,-52,672,-145) -> Matrix(1,-2,2,-5) Matrix(191,-42,432,-95) -> Matrix(1,2,2,3) Matrix(433,-98,1056,-239) -> Matrix(1,0,0,1) Matrix(815,-186,1056,-241) -> Matrix(1,0,4,1) 0/1 Matrix(241,-56,624,-145) -> Matrix(5,-2,2,-1) Matrix(575,-136,816,-193) -> Matrix(5,-6,6,-7) 1/1 Matrix(913,-236,1296,-335) -> Matrix(17,-6,20,-7) Matrix(719,-190,912,-241) -> Matrix(3,-4,4,-5) 1/1 Matrix(529,-142,1248,-335) -> Matrix(1,0,4,1) 0/1 Matrix(911,-246,1248,-337) -> Matrix(5,2,2,1) Matrix(335,-92,528,-145) -> Matrix(7,-2,4,-1) Matrix(337,-94,864,-241) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(191,-54,336,-95) -> Matrix(3,-2,-2,1) Matrix(97,-28,336,-97) -> Matrix(5,-4,6,-5) (2/7,7/24) -> (2/3,1/1) Matrix(239,-70,816,-239) -> Matrix(9,-10,8,-9) (7/24,5/17) -> (1/1,5/4) Matrix(623,-184,816,-241) -> Matrix(3,-4,-2,3) Matrix(1057,-314,1296,-385) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1439,-428,2256,-671) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(671,-202,960,-289) -> Matrix(1,-4,2,-7) Matrix(959,-290,1584,-479) -> Matrix(1,2,2,3) Matrix(1823,-554,2208,-671) -> Matrix(-1,8,0,1) *** -> (4/1,1/0) Matrix(623,-190,1728,-527) -> Matrix(1,-4,2,-9) Matrix(769,-236,1248,-383) -> Matrix(3,8,4,11) Matrix(527,-164,768,-239) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(529,-166,768,-241) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(385,-122,912,-289) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(671,-234,1104,-385) -> Matrix(5,-2,8,-3) 1/2 Matrix(671,-236,816,-287) -> Matrix(9,-4,2,-1) Matrix(433,-154,672,-239) -> Matrix(3,-2,2,-1) 1/1 Matrix(2783,-1006,4512,-1631) -> Matrix(65,-34,86,-45) Matrix(1585,-574,2256,-817) -> Matrix(29,-16,38,-21) Matrix(383,-140,528,-193) -> Matrix(5,-4,4,-3) 1/1 Matrix(145,-54,384,-143) -> Matrix(7,-6,6,-5) 1/1 Matrix(1633,-620,2784,-1057) -> Matrix(3,-4,14,-19) Matrix(5809,-2208,9216,-3503) -> Matrix(63,-92,50,-73) Matrix(1535,-584,2016,-767) -> Matrix(5,-8,-2,3) Matrix(6527,-2490,10320,-3937) -> Matrix(11,-18,8,-13) 3/2 Matrix(3025,-1156,4896,-1871) -> Matrix(3,-10,4,-13) Matrix(2399,-918,3264,-1249) -> Matrix(5,-8,2,-3) 2/1 Matrix(865,-332,1248,-479) -> Matrix(1,-2,2,-3) 1/1 Matrix(2257,-874,3840,-1487) -> Matrix(1,-4,4,-15) Matrix(6047,-2344,7680,-2977) -> Matrix(3,-16,4,-21) Matrix(1489,-578,2352,-913) -> Matrix(3,-16,2,-11) Matrix(719,-282,1104,-433) -> Matrix(1,0,0,1) Matrix(625,-246,1344,-529) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1105,-436,1584,-625) -> Matrix(1,-2,2,-5) Matrix(193,-78,240,-97) -> Matrix(3,2,2,1) Matrix(2207,-900,2592,-1057) -> Matrix(1,0,0,1) Matrix(1967,-804,3408,-1393) -> Matrix(1,0,2,1) 0/1 Matrix(721,-296,816,-335) -> Matrix(1,2,0,1) 1/0 Matrix(241,-100,576,-239) -> Matrix(1,0,10,1) 0/1 Matrix(481,-202,912,-383) -> Matrix(13,-2,20,-3) Matrix(1151,-484,1824,-767) -> Matrix(19,-4,14,-3) Matrix(2831,-1196,4656,-1967) -> Matrix(7,-2,10,-3) Matrix(2015,-852,3408,-1441) -> Matrix(1,0,0,1) Matrix(241,-104,336,-145) -> Matrix(11,-4,8,-3) Matrix(431,-188,768,-335) -> Matrix(13,-6,2,-1) Matrix(433,-190,768,-337) -> Matrix(7,-4,-2,1) Matrix(385,-172,432,-193) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(2015,-902,3648,-1633) -> Matrix(7,-4,2,-1) Matrix(2015,-904,2784,-1249) -> Matrix(5,-4,4,-3) 1/1 Matrix(433,-196,528,-239) -> Matrix(13,-10,4,-3) Matrix(241,-110,528,-241) -> Matrix(11,-10,12,-11) (5/11,11/24) -> (5/6,1/1) Matrix(287,-132,624,-287) -> Matrix(11,-12,10,-11) (11/24,6/13) -> (1/1,6/5) Matrix(479,-226,816,-385) -> Matrix(1,-2,4,-7) Matrix(1441,-764,2352,-1247) -> Matrix(1,0,0,1) Matrix(529,-284,624,-335) -> Matrix(5,-4,-6,5) Matrix(337,-182,624,-337) -> Matrix(15,-14,16,-15) (7/13,13/24) -> (7/8,1/1) Matrix(287,-156,528,-287) -> Matrix(11,-12,10,-11) (13/24,6/11) -> (1/1,6/5) Matrix(623,-342,960,-527) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1487,-820,2352,-1297) -> Matrix(11,-18,8,-13) 3/2 Matrix(3073,-1696,5568,-3073) -> Matrix(11,-20,6,-11) (16/29,53/96) -> (5/3,2/1) Matrix(7103,-3922,12864,-7103) -> Matrix(9,-20,4,-9) (53/96,37/67) -> (2/1,5/2) Matrix(337,-188,432,-241) -> Matrix(1,-2,2,-5) Matrix(913,-526,1248,-719) -> Matrix(5,2,2,1) Matrix(18817,-10864,32592,-18817) -> Matrix(1,0,2,-1) (56/97,97/168) -> (0/1,1/1) Matrix(13775,-7954,23856,-13775) -> Matrix(-1,2,0,1) (97/168,41/71) -> (1/1,1/0) Matrix(817,-472,1248,-721) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(623,-360,912,-527) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(337,-196,576,-335) -> Matrix(1,0,6,1) 0/1 Matrix(3841,-2256,5232,-3073) -> Matrix(9,-2,4,-1) Matrix(817,-482,1056,-623) -> Matrix(1,0,0,1) Matrix(10081,-5964,17040,-10081) -> Matrix(7,-2,24,-7) (42/71,71/120) -> (1/4,1/3) Matrix(6959,-4118,11760,-6959) -> Matrix(5,-2,12,-5) (71/120,29/49) -> (1/3,1/2) Matrix(4463,-2642,7056,-4177) -> Matrix(5,-4,4,-3) 1/1 Matrix(1345,-816,1584,-961) -> Matrix(3,-2,-8,5) Matrix(623,-380,864,-527) -> Matrix(13,-8,8,-5) Matrix(1249,-764,1728,-1057) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(5183,-3174,7056,-4321) -> Matrix(7,-4,2,-1) Matrix(9073,-5558,11520,-7057) -> Matrix(7,-6,8,-7) *** -> (3/4,1/1) Matrix(479,-294,624,-383) -> Matrix(3,-2,-2,1) Matrix(1775,-1096,2256,-1393) -> Matrix(23,-18,32,-25) 3/4 Matrix(15841,-9790,25632,-15841) -> Matrix(191,-152,240,-191) (55/89,89/144) -> (19/24,4/5) Matrix(9791,-6052,15840,-9791) -> Matrix(89,-72,110,-89) (89/144,34/55) -> (4/5,9/11) Matrix(1391,-860,1632,-1009) -> Matrix(5,-4,-6,5) Matrix(241,-150,384,-239) -> Matrix(11,-10,10,-9) 1/1 Matrix(2737,-1724,3888,-2449) -> Matrix(41,-50,50,-61) Matrix(17665,-11132,28032,-17665) -> Matrix(329,-410,264,-329) (46/73,121/192) -> (41/33,5/4) Matrix(28799,-18150,45696,-28799) -> Matrix(511,-640,408,-511) (121/192,75/119) -> (5/4,64/51) Matrix(2399,-1532,3456,-2207) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(1201,-768,1728,-1105) -> Matrix(1,-2,2,-5) Matrix(527,-338,672,-431) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1921,-1240,2976,-1921) -> Matrix(-1,6,0,1) (20/31,31/48) -> (3/1,1/0) Matrix(1055,-682,1632,-1055) -> Matrix(1,0,0,-1) (31/48,11/17) -> (0/1,1/0) Matrix(527,-364,624,-431) -> Matrix(3,-2,-2,1) Matrix(959,-668,1104,-769) -> Matrix(1,0,0,1) Matrix(5761,-4020,8256,-5761) -> Matrix(13,-6,28,-13) (30/43,67/96) -> (3/7,1/2) Matrix(7103,-4958,10176,-7103) -> Matrix(23,-12,44,-23) (67/96,37/53) -> (1/2,6/11) Matrix(433,-304,480,-337) -> Matrix(11,-8,4,-3) Matrix(577,-408,816,-577) -> Matrix(19,-18,20,-19) (12/17,17/24) -> (9/10,1/1) Matrix(239,-170,336,-239) -> Matrix(9,-10,8,-9) (17/24,5/7) -> (1/1,5/4) Matrix(3839,-2778,4512,-3265) -> Matrix(1,-2,0,1) 1/0 Matrix(769,-560,1056,-769) -> Matrix(11,-20,6,-11) (8/11,35/48) -> (5/3,2/1) Matrix(2591,-1890,3552,-2591) -> Matrix(25,-52,12,-25) (35/48,27/37) -> (2/1,13/6) Matrix(623,-456,720,-527) -> Matrix(1,-2,2,-5) Matrix(767,-566,912,-673) -> Matrix(1,-6,0,1) 1/0 Matrix(145,-108,192,-143) -> Matrix(1,-2,0,1) 1/0 Matrix(961,-740,1248,-961) -> Matrix(-1,0,6,1) (10/13,37/48) -> (-1/3,0/1) Matrix(2591,-1998,3360,-2591) -> Matrix(1,0,16,-1) (37/48,27/35) -> (0/1,1/8) Matrix(1583,-1226,1920,-1487) -> Matrix(9,-4,2,-1) Matrix(721,-570,912,-721) -> Matrix(15,-14,16,-15) (15/19,19/24) -> (7/8,1/1) Matrix(191,-152,240,-191) -> Matrix(5,-6,4,-5) (19/24,4/5) -> (1/1,3/2) Matrix(241,-200,288,-239) -> Matrix(1,-6,0,1) 1/0 Matrix(-1,2,0,1) -> Matrix(1,0,0,-1) (1/1,1/0) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.