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): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 64 Genus: 113 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -35/51 -61/136 -15/34 -57/136 -13/34 -25/68 -31/102 -19/68 -101/374 -9/34 -31/136 -23/102 -29/136 -7/34 -13/68 -5/32 -5/34 -3/26 -1/10 0/1 1/9 2/17 1/8 1/7 3/20 2/13 1/6 3/17 5/28 2/11 3/16 1/5 5/24 3/14 2/9 5/22 3/13 7/30 4/17 1/4 4/15 3/11 5/18 2/7 5/17 16/51 1/3 6/17 2/5 7/17 5/12 7/15 8/17 1/2 9/17 10/17 11/17 2/3 12/17 13/17 14/17 15/17 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/32 -8/9 1/28 -15/17 1/28 -7/8 1/28 3/83 -6/7 5/136 -17/20 1/27 7/188 -11/13 3/80 -16/19 3/80 -21/25 3/80 -5/6 2/53 1/26 -14/17 1/26 -23/28 1/26 9/233 -9/11 7/180 -13/16 1/26 1/25 -4/5 3/76 -19/24 1/25 7/174 -34/43 5/124 -15/19 5/124 -26/33 19/468 -37/47 7/172 -48/61 23/564 -11/14 2/49 1/24 -7/9 1/24 -31/40 1/26 1/25 -24/31 5/124 -17/22 3/74 2/49 -44/57 25/612 -27/35 19/464 -10/13 1/24 -33/43 1/24 -23/30 8/193 1/24 -13/17 1/24 -3/4 1/24 1/23 -11/15 7/160 -19/26 3/68 2/45 -46/63 3/68 -27/37 3/68 -8/11 5/112 -13/18 0/1 1/22 -18/25 1/24 -23/32 1/24 1/23 -5/7 3/68 -22/31 7/156 -17/24 5/111 1/22 -12/17 1/22 -7/10 1/22 2/43 -37/53 3/64 -30/43 3/64 -23/33 13/276 -39/56 9/190 1/21 -16/23 5/104 -25/36 1/21 1/20 -34/49 1/20 -9/13 1/20 -29/42 0/1 1/24 -20/29 1/24 -11/16 1/23 1/22 -35/51 1/22 -24/35 13/284 -13/19 5/108 -2/3 1/20 -13/20 3/61 1/20 -11/17 1/20 -9/14 1/20 2/39 -7/11 3/56 -19/30 0/1 1/16 -12/19 1/24 -29/46 0/1 1/22 -17/27 3/64 -5/8 1/20 1/19 -8/13 3/56 -27/44 3/55 1/18 -19/31 3/56 -11/18 0/1 1/18 -14/23 5/92 -17/28 1/18 3/53 -20/33 7/120 -3/5 1/20 -16/27 1/20 -13/22 2/37 1/18 -10/17 1/18 -7/12 1/18 1/17 -32/55 1/16 -25/43 1/16 -43/74 0/1 1/14 -18/31 1/20 -11/19 3/52 -15/26 2/33 1/16 -49/85 1/16 -34/59 1/16 -19/33 5/76 -23/40 1/14 1/13 -4/7 1/20 -17/30 0/1 1/16 -13/23 3/56 -9/16 1/18 1/17 -5/9 1/16 -21/38 1/16 2/31 -16/29 1/12 -43/78 0/1 1/22 -27/49 1/20 -11/20 1/17 1/16 -17/31 1/16 -6/11 1/12 -19/35 3/64 -32/59 1/20 -13/24 1/19 1/18 -7/13 1/16 -22/41 1/24 -15/28 1/18 1/17 -23/43 1/16 -8/15 1/16 -17/32 1/17 1/16 -9/17 1/16 -1/2 0/1 1/16 -8/17 1/16 -7/15 1/16 -13/28 1/15 1/14 -6/13 1/16 -11/24 1/14 1/13 -16/35 3/32 -5/11 1/20 -14/31 1/16 -9/20 1/16 1/15 -22/49 1/12 -35/78 0/1 1/10 -48/107 1/0 -61/136 0/1 -13/29 1/20 -30/67 7/120 -17/38 2/33 1/16 -4/9 1/16 -15/34 1/15 -11/25 3/44 -7/16 1/15 1/14 -10/23 3/40 -3/7 1/12 -20/47 1/20 -17/40 1/19 1/18 -14/33 5/84 -25/59 1/16 -11/26 1/16 2/31 -8/19 3/44 -29/69 11/156 -50/119 1/14 -21/50 1/14 2/27 -13/31 1/12 -57/136 0/1 -44/105 1/24 -31/74 0/1 1/18 -18/43 1/16 -23/55 1/16 -5/12 1/15 1/14 -7/17 1/14 -9/22 1/14 2/27 -11/27 1/12 -13/32 3/40 1/13 -15/37 1/12 -2/5 1/12 -7/18 0/1 1/14 -33/85 1/14 -26/67 15/208 -19/49 7/96 -12/31 3/40 -17/44 1/14 3/41 -5/13 3/40 -13/34 1/13 -8/21 5/64 -3/8 1/13 1/12 -10/27 3/32 -17/46 0/1 1/10 -24/65 3/32 -7/19 1/8 -25/68 0/1 -18/49 1/24 -11/30 0/1 1/16 -37/101 9/136 -26/71 3/44 -15/41 1/12 -4/11 3/40 -13/36 1/13 1/12 -9/25 1/12 -5/14 2/25 1/12 -6/17 1/12 -7/20 1/12 3/35 -1/3 1/12 -6/19 5/52 -5/16 1/10 1/9 -4/13 1/12 -11/36 1/12 1/11 -7/23 5/56 -31/102 1/11 -24/79 23/252 -17/56 1/11 9/98 -27/89 7/76 -10/33 13/140 -3/10 2/21 1/10 -5/17 1/10 -7/24 1/10 5/49 -9/31 7/68 -29/100 19/184 3/29 -20/69 29/280 -11/38 5/48 2/19 -2/7 3/28 -11/39 3/28 -9/32 1/9 1/8 -7/25 1/8 -19/68 0/1 -12/43 1/12 -5/18 0/1 1/10 -8/29 1/8 -27/98 1/12 2/23 -19/69 7/76 -11/40 3/31 1/10 -3/11 5/48 -10/37 3/28 -37/137 15/136 -101/374 1/9 -64/237 17/152 -27/100 1/9 1/8 -17/63 3/28 -7/26 2/19 3/28 -4/15 7/64 -9/34 1/9 -5/19 9/80 -1/4 1/9 1/8 -4/17 1/8 -7/30 1/8 8/63 -10/43 1/8 -3/13 1/8 -11/48 3/23 11/84 -19/83 21/160 -8/35 19/144 -13/57 25/188 -31/136 2/15 -18/79 31/232 -5/22 2/15 3/22 -12/53 7/52 -7/31 5/36 -23/102 1/7 -16/71 7/48 -9/40 1/7 1/6 -11/49 1/8 -2/9 1/8 -7/32 1/8 1/7 -5/23 3/20 -3/14 1/8 2/15 -16/75 25/188 -29/136 2/15 -13/61 23/172 -10/47 7/52 -17/80 17/126 5/37 -7/33 19/140 -18/85 3/22 -11/52 3/22 13/95 -4/19 5/36 -9/43 5/36 -14/67 39/280 -5/24 7/50 1/7 -6/29 17/120 -7/34 1/7 -1/5 3/20 -5/26 3/20 2/13 -9/47 11/72 -13/68 2/13 -4/21 5/32 -3/16 1/7 1/6 -2/11 7/44 -5/28 9/55 1/6 -3/17 1/6 -1/6 1/6 2/11 -4/25 3/16 -3/19 3/16 -8/51 3/16 -5/32 3/16 1/5 -2/13 3/16 -5/33 23/120 -8/53 17/88 -3/20 7/36 1/5 -4/27 19/96 -5/34 1/5 -1/7 5/24 -1/8 3/13 1/4 -2/17 1/4 -3/26 1/4 10/39 -1/9 1/4 -2/19 1/4 -1/10 2/7 3/10 0/1 1/0 1/9 -1/4 2/17 -1/4 1/8 -1/4 -3/13 1/7 -5/24 3/20 -1/5 -7/36 2/13 -3/16 3/19 -3/16 4/25 -3/16 1/6 -2/11 -1/6 3/17 -1/6 5/28 -1/6 -9/55 2/11 -7/44 3/16 -1/6 -1/7 1/5 -3/20 5/24 -1/7 -7/50 9/43 -5/36 4/19 -5/36 7/33 -19/140 10/47 -7/52 13/61 -23/172 3/14 -2/15 -1/8 2/9 -1/8 9/40 -1/6 -1/7 7/31 -5/36 5/22 -3/22 -2/15 13/57 -25/188 8/35 -19/144 3/13 -1/8 10/43 -1/8 7/30 -8/63 -1/8 4/17 -1/8 1/4 -1/8 -1/9 4/15 -7/64 7/26 -3/28 -2/19 17/63 -3/28 10/37 -3/28 3/11 -5/48 5/18 -1/10 0/1 7/25 -1/8 9/32 -1/8 -1/9 2/7 -3/28 9/31 -7/68 7/24 -5/49 -1/10 5/17 -1/10 3/10 -1/10 -2/21 16/53 -3/32 13/43 -3/32 10/33 -13/140 17/56 -9/98 -1/11 7/23 -5/56 11/36 -1/11 -1/12 15/49 -1/12 4/13 -1/12 13/42 -1/8 0/1 9/29 -1/8 5/16 -1/9 -1/10 16/51 -1/10 11/35 -13/132 6/19 -5/52 1/3 -1/12 7/20 -3/35 -1/12 6/17 -1/12 5/14 -1/12 -2/25 4/11 -3/40 11/30 -1/16 0/1 7/19 -1/8 17/46 -1/10 0/1 10/27 -3/32 3/8 -1/12 -1/13 5/13 -3/40 17/44 -3/41 -1/14 12/31 -3/40 7/18 -1/14 0/1 9/23 -5/68 11/28 -1/14 -3/43 13/33 -7/104 2/5 -1/12 11/27 -1/12 9/22 -2/27 -1/14 7/17 -1/14 5/12 -1/14 -1/15 23/55 -1/16 18/43 -1/16 31/74 -1/18 0/1 13/31 -1/12 8/19 -3/44 11/26 -2/31 -1/16 36/85 -1/16 25/59 -1/16 14/33 -5/84 17/40 -1/18 -1/19 3/7 -1/12 13/30 -1/16 0/1 10/23 -3/40 7/16 -1/14 -1/15 4/9 -1/16 17/38 -1/16 -2/33 13/29 -1/20 35/78 -1/10 0/1 22/49 -1/12 9/20 -1/15 -1/16 14/31 -1/16 5/11 -1/20 16/35 -3/32 27/59 -1/12 11/24 -1/13 -1/14 6/13 -1/16 19/41 -1/8 13/28 -1/14 -1/15 20/43 -1/16 7/15 -1/16 15/32 -1/15 -1/16 8/17 -1/16 1/2 -1/16 0/1 9/17 -1/16 8/15 -1/16 15/28 -1/17 -1/18 7/13 -1/16 13/24 -1/18 -1/19 19/35 -3/64 6/11 -1/12 17/31 -1/16 11/20 -1/16 -1/17 27/49 -1/20 43/78 -1/22 0/1 59/107 -1/32 75/136 0/1 16/29 -1/12 37/67 -7/104 21/38 -2/31 -1/16 5/9 -1/16 19/34 -1/17 14/25 -3/52 9/16 -1/17 -1/18 13/23 -3/56 4/7 -1/20 27/47 -1/12 23/40 -1/13 -1/14 19/33 -5/76 34/59 -1/16 15/26 -1/16 -2/33 11/19 -3/52 40/69 -11/196 69/119 -1/18 29/50 -1/18 -2/37 18/31 -1/20 79/136 0/1 61/105 -1/8 43/74 -1/14 0/1 25/43 -1/16 32/55 -1/16 7/12 -1/17 -1/18 10/17 -1/18 13/22 -1/18 -2/37 16/27 -1/20 19/32 -3/56 -1/19 22/37 -1/20 3/5 -1/20 11/18 -1/18 0/1 52/85 -1/18 41/67 -15/272 30/49 -7/128 19/31 -3/56 27/44 -1/18 -3/55 8/13 -3/56 21/34 -1/19 13/21 -5/96 5/8 -1/19 -1/20 17/27 -3/64 29/46 -1/22 0/1 41/65 -3/64 12/19 -1/24 43/68 0/1 31/49 -1/8 19/30 -1/16 0/1 64/101 -9/152 45/71 -3/52 26/41 -1/20 7/11 -3/56 23/36 -1/19 -1/20 16/25 -1/20 9/14 -2/39 -1/20 11/17 -1/20 13/20 -1/20 -3/61 2/3 -1/20 13/19 -5/108 11/16 -1/22 -1/23 9/13 -1/20 25/36 -1/20 -1/21 16/23 -5/104 71/102 -1/21 55/79 -23/484 39/56 -1/21 -9/190 62/89 -7/148 23/33 -13/276 7/10 -2/43 -1/22 12/17 -1/22 17/24 -1/22 -5/111 22/31 -7/156 71/100 -19/424 -3/67 49/69 -29/648 27/38 -5/112 -2/45 5/7 -3/68 28/39 -3/68 23/32 -1/23 -1/24 18/25 -1/24 49/68 0/1 31/43 -1/20 13/18 -1/22 0/1 21/29 -1/24 71/98 -1/20 -2/41 50/69 -7/148 29/40 -3/65 -1/22 8/11 -5/112 27/37 -3/68 100/137 -15/344 273/374 -1/23 173/237 -17/392 73/100 -1/23 -1/24 46/63 -3/68 19/26 -2/45 -3/68 11/15 -7/160 25/34 -1/23 14/19 -9/208 3/4 -1/23 -1/24 13/17 -1/24 23/30 -1/24 -8/193 33/43 -1/24 10/13 -1/24 37/48 -3/73 -11/268 64/83 -21/512 27/35 -19/464 44/57 -25/612 105/136 -2/49 61/79 -31/760 17/22 -2/49 -3/74 41/53 -7/172 24/31 -5/124 79/102 -1/25 55/71 -7/176 31/40 -1/25 -1/26 38/49 -1/24 7/9 -1/24 25/32 -1/24 -1/25 18/23 -3/76 11/14 -1/24 -2/49 59/75 -25/612 107/136 -2/49 48/61 -23/564 37/47 -7/172 63/80 -17/418 -5/123 26/33 -19/468 67/85 -3/74 41/52 -3/74 -13/321 15/19 -5/124 34/43 -5/124 53/67 -39/968 19/24 -7/174 -1/25 23/29 -17/424 27/34 -1/25 4/5 -3/76 21/26 -3/76 -2/51 38/47 -11/280 55/68 -2/51 17/21 -5/128 13/16 -1/25 -1/26 9/11 -7/180 23/28 -9/233 -1/26 14/17 -1/26 5/6 -1/26 -2/53 21/25 -3/80 16/19 -3/80 43/51 -3/80 27/32 -3/80 -1/27 11/13 -3/80 28/33 -23/616 45/53 -17/456 17/20 -7/188 -1/27 23/27 -19/512 29/34 -1/27 6/7 -5/136 7/8 -3/83 -1/28 15/17 -1/28 23/26 -1/28 -10/281 8/9 -1/28 17/19 -1/28 9/10 -2/57 -3/86 1/1 -1/32 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(237,214,-340,-307) (-1/1,-8/9) -> (-30/43,-23/33) Hyperbolic Matrix(1019,902,-1768,-1565) (-8/9,-15/17) -> (-49/85,-34/59) Hyperbolic Matrix(239,210,272,239) (-15/17,-7/8) -> (7/8,15/17) Hyperbolic Matrix(101,88,272,237) (-7/8,-6/7) -> (10/27,3/8) Hyperbolic Matrix(101,86,-680,-579) (-6/7,-17/20) -> (-3/20,-4/27) Hyperbolic Matrix(203,172,-884,-749) (-17/20,-11/13) -> (-3/13,-11/48) Hyperbolic Matrix(613,518,-884,-747) (-11/13,-16/19) -> (-34/49,-9/13) Hyperbolic Matrix(271,228,1292,1087) (-16/19,-21/25) -> (9/43,4/19) Hyperbolic Matrix(1225,1028,2108,1769) (-21/25,-5/6) -> (43/74,25/43) Hyperbolic Matrix(169,140,204,169) (-5/6,-14/17) -> (14/17,5/6) Hyperbolic Matrix(783,644,952,783) (-14/17,-23/28) -> (23/28,14/17) Hyperbolic Matrix(373,306,952,781) (-23/28,-9/11) -> (9/23,11/28) Hyperbolic Matrix(307,250,544,443) (-9/11,-13/16) -> (9/16,13/23) Hyperbolic Matrix(375,304,-544,-441) (-13/16,-4/5) -> (-20/29,-11/16) Hyperbolic Matrix(169,134,-816,-647) (-4/5,-19/24) -> (-5/24,-6/29) Hyperbolic Matrix(1327,1050,-2448,-1937) (-19/24,-34/43) -> (-32/59,-13/24) Hyperbolic Matrix(205,162,1292,1021) (-34/43,-15/19) -> (3/19,4/25) Hyperbolic Matrix(885,698,-1292,-1019) (-15/19,-26/33) -> (-24/35,-13/19) Hyperbolic Matrix(1361,1072,-4488,-3535) (-26/33,-37/47) -> (-27/89,-10/33) Hyperbolic Matrix(1835,1444,3196,2515) (-37/47,-48/61) -> (4/7,27/47) Hyperbolic Matrix(407,320,-1904,-1497) (-48/61,-11/14) -> (-3/14,-16/75) Hyperbolic Matrix(171,134,-476,-373) (-11/14,-7/9) -> (-9/25,-5/14) Hyperbolic Matrix(1055,818,-1972,-1529) (-7/9,-31/40) -> (-15/28,-23/43) Hyperbolic Matrix(919,712,-4080,-3161) (-31/40,-24/31) -> (-16/71,-9/40) Hyperbolic Matrix(1055,816,-2856,-2209) (-24/31,-17/22) -> (-17/46,-24/65) Hyperbolic Matrix(681,526,-2992,-2311) (-17/22,-44/57) -> (-18/79,-5/22) Hyperbolic Matrix(1293,998,2380,1837) (-44/57,-27/35) -> (19/35,6/11) Hyperbolic Matrix(135,104,-884,-681) (-27/35,-10/13) -> (-2/13,-5/33) Hyperbolic Matrix(1701,1306,2924,2245) (-10/13,-33/43) -> (25/43,32/55) Hyperbolic Matrix(1053,808,1904,1461) (-33/43,-23/30) -> (21/38,5/9) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(103,78,136,103) (-13/17,-3/4) -> (3/4,13/17) Hyperbolic Matrix(35,26,-136,-101) (-3/4,-11/15) -> (-5/19,-1/4) Hyperbolic Matrix(511,374,884,647) (-11/15,-19/26) -> (15/26,11/19) Hyperbolic Matrix(1427,1042,1768,1291) (-19/26,-46/63) -> (4/5,21/26) Hyperbolic Matrix(1019,744,-2516,-1837) (-46/63,-27/37) -> (-15/37,-2/5) Hyperbolic Matrix(409,298,748,545) (-27/37,-8/11) -> (6/11,17/31) Hyperbolic Matrix(373,270,-612,-443) (-8/11,-13/18) -> (-11/18,-14/23) Hyperbolic Matrix(341,246,-1224,-883) (-13/18,-18/25) -> (-12/43,-5/18) Hyperbolic Matrix(1087,782,1700,1223) (-18/25,-23/32) -> (23/36,16/25) Hyperbolic Matrix(443,318,-1088,-781) (-23/32,-5/7) -> (-11/27,-13/32) Hyperbolic Matrix(647,460,-1768,-1257) (-5/7,-22/31) -> (-26/71,-15/41) Hyperbolic Matrix(815,578,2108,1495) (-22/31,-17/24) -> (17/44,12/31) Hyperbolic Matrix(577,408,816,577) (-17/24,-12/17) -> (12/17,17/24) Hyperbolic Matrix(239,168,340,239) (-12/17,-7/10) -> (7/10,12/17) Hyperbolic Matrix(2549,1780,4624,3229) (-7/10,-37/53) -> (27/49,43/78) Hyperbolic Matrix(1361,950,2924,2041) (-37/53,-30/43) -> (20/43,7/15) Hyperbolic Matrix(953,664,-4488,-3127) (-23/33,-39/56) -> (-17/80,-7/33) Hyperbolic Matrix(1735,1208,-5712,-3977) (-39/56,-16/23) -> (-24/79,-17/56) Hyperbolic Matrix(1223,850,1564,1087) (-16/23,-25/36) -> (25/32,18/23) Hyperbolic Matrix(1121,778,-2108,-1463) (-25/36,-34/49) -> (-8/15,-17/32) Hyperbolic Matrix(443,306,-2312,-1597) (-9/13,-29/42) -> (-5/26,-9/47) Hyperbolic Matrix(2483,1714,3400,2347) (-29/42,-20/29) -> (46/63,19/26) Hyperbolic Matrix(3163,2172,4012,2755) (-11/16,-35/51) -> (67/85,41/52) Hyperbolic Matrix(4455,3056,7684,5271) (-35/51,-24/35) -> (40/69,69/119) Hyperbolic Matrix(477,326,-1292,-883) (-13/19,-2/3) -> (-24/65,-7/19) Hyperbolic Matrix(307,200,680,443) (-2/3,-13/20) -> (9/20,14/31) Hyperbolic Matrix(441,286,680,441) (-13/20,-11/17) -> (11/17,13/20) Hyperbolic Matrix(307,198,476,307) (-11/17,-9/14) -> (9/14,11/17) Hyperbolic Matrix(103,66,-476,-305) (-9/14,-7/11) -> (-5/23,-3/14) Hyperbolic Matrix(577,366,-1020,-647) (-7/11,-19/30) -> (-17/30,-13/23) Hyperbolic Matrix(749,474,-2040,-1291) (-19/30,-12/19) -> (-18/49,-11/30) Hyperbolic Matrix(647,408,-2856,-1801) (-12/19,-29/46) -> (-5/22,-12/53) Hyperbolic Matrix(749,472,1836,1157) (-29/46,-17/27) -> (11/27,9/22) Hyperbolic Matrix(35,22,272,171) (-17/27,-5/8) -> (1/8,1/7) Hyperbolic Matrix(103,64,-272,-169) (-5/8,-8/13) -> (-8/21,-3/8) Hyperbolic Matrix(407,250,884,543) (-8/13,-27/44) -> (11/24,6/13) Hyperbolic Matrix(613,376,2108,1293) (-27/44,-19/31) -> (9/31,7/24) Hyperbolic Matrix(885,542,-2108,-1291) (-19/31,-11/18) -> (-21/50,-13/31) Hyperbolic Matrix(171,104,952,579) (-14/23,-17/28) -> (5/28,2/11) Hyperbolic Matrix(953,578,2244,1361) (-17/28,-20/33) -> (14/33,17/40) Hyperbolic Matrix(579,350,-1292,-781) (-20/33,-3/5) -> (-13/29,-30/67) Hyperbolic Matrix(307,182,-1088,-645) (-3/5,-16/27) -> (-2/7,-11/39) Hyperbolic Matrix(679,402,1836,1087) (-16/27,-13/22) -> (17/46,10/27) Hyperbolic Matrix(441,260,748,441) (-13/22,-10/17) -> (10/17,13/22) Hyperbolic Matrix(239,140,408,239) (-10/17,-7/12) -> (7/12,10/17) Hyperbolic Matrix(1055,614,-4964,-2889) (-7/12,-32/55) -> (-10/47,-17/80) Hyperbolic Matrix(2245,1306,2924,1701) (-32/55,-25/43) -> (33/43,10/13) Hyperbolic Matrix(1769,1028,2108,1225) (-25/43,-43/74) -> (5/6,21/25) Hyperbolic Matrix(4217,2450,-10064,-5847) (-43/74,-18/31) -> (-44/105,-31/74) Hyperbolic Matrix(817,474,-2108,-1223) (-18/31,-11/19) -> (-19/49,-12/31) Hyperbolic Matrix(647,374,884,511) (-11/19,-15/26) -> (19/26,11/15) Hyperbolic Matrix(2345,1352,2652,1529) (-15/26,-49/85) -> (15/17,23/26) Hyperbolic Matrix(2177,1254,-4012,-2311) (-34/59,-19/33) -> (-19/35,-32/59) Hyperbolic Matrix(883,508,2244,1291) (-19/33,-23/40) -> (11/28,13/33) Hyperbolic Matrix(985,566,-1836,-1055) (-23/40,-4/7) -> (-22/41,-15/28) Hyperbolic Matrix(137,78,-476,-271) (-4/7,-17/30) -> (-11/38,-2/7) Hyperbolic Matrix(443,250,544,307) (-13/23,-9/16) -> (13/16,9/11) Hyperbolic Matrix(239,134,-544,-305) (-9/16,-5/9) -> (-11/25,-7/16) Hyperbolic Matrix(1461,808,1904,1053) (-5/9,-21/38) -> (23/30,33/43) Hyperbolic Matrix(1087,600,-3944,-2177) (-21/38,-16/29) -> (-8/29,-27/98) Hyperbolic Matrix(4759,2624,-10608,-5849) (-16/29,-43/78) -> (-35/78,-48/107) Hyperbolic Matrix(1767,974,1972,1087) (-43/78,-27/49) -> (17/19,9/10) Hyperbolic Matrix(919,506,-4012,-2209) (-27/49,-11/20) -> (-11/48,-19/83) Hyperbolic Matrix(237,130,680,373) (-11/20,-17/31) -> (1/3,7/20) Hyperbolic Matrix(545,298,748,409) (-17/31,-6/11) -> (8/11,27/37) Hyperbolic Matrix(1837,998,2380,1293) (-6/11,-19/35) -> (27/35,44/57) Hyperbolic Matrix(341,184,884,477) (-13/24,-7/13) -> (5/13,17/44) Hyperbolic Matrix(2141,1150,2720,1461) (-7/13,-22/41) -> (48/61,37/47) Hyperbolic Matrix(883,472,2924,1563) (-23/43,-8/15) -> (16/53,13/43) Hyperbolic Matrix(1835,974,2176,1155) (-17/32,-9/17) -> (43/51,27/32) Hyperbolic Matrix(35,18,68,35) (-9/17,-1/2) -> (1/2,9/17) Hyperbolic Matrix(33,16,68,33) (-1/2,-8/17) -> (8/17,1/2) Hyperbolic Matrix(171,80,-1088,-509) (-8/17,-7/15) -> (-3/19,-8/51) Hyperbolic Matrix(443,206,-1972,-917) (-7/15,-13/28) -> (-9/40,-11/49) Hyperbolic Matrix(781,362,-1836,-851) (-13/28,-6/13) -> (-20/47,-17/40) Hyperbolic Matrix(543,250,884,407) (-6/13,-11/24) -> (27/44,8/13) Hyperbolic Matrix(511,234,-2448,-1121) (-11/24,-16/35) -> (-14/67,-5/24) Hyperbolic Matrix(543,248,2380,1087) (-16/35,-5/11) -> (13/57,8/35) Hyperbolic Matrix(203,92,748,339) (-5/11,-14/31) -> (10/37,3/11) Hyperbolic Matrix(443,200,680,307) (-14/31,-9/20) -> (13/20,2/3) Hyperbolic Matrix(307,138,-2040,-917) (-9/20,-22/49) -> (-8/53,-3/20) Hyperbolic Matrix(1395,626,4624,2075) (-22/49,-35/78) -> (3/10,16/53) Hyperbolic Matrix(10201,4576,18496,8297) (-48/107,-61/136) -> (75/136,16/29) Hyperbolic Matrix(10199,4574,18496,8295) (-61/136,-13/29) -> (59/107,75/136) Hyperbolic Matrix(3705,1658,5848,2617) (-30/67,-17/38) -> (19/30,64/101) Hyperbolic Matrix(443,198,1904,851) (-17/38,-4/9) -> (10/43,7/30) Hyperbolic Matrix(647,286,1156,511) (-4/9,-15/34) -> (19/34,14/25) Hyperbolic Matrix(645,284,1156,509) (-15/34,-11/25) -> (5/9,19/34) Hyperbolic Matrix(101,44,544,237) (-7/16,-10/23) -> (2/11,3/16) Hyperbolic Matrix(373,162,-1020,-443) (-10/23,-3/7) -> (-15/41,-4/11) Hyperbolic Matrix(681,290,3196,1361) (-3/7,-20/47) -> (10/47,13/61) Hyperbolic Matrix(2957,1256,4080,1733) (-17/40,-14/33) -> (50/69,29/40) Hyperbolic Matrix(1123,476,-5372,-2277) (-14/33,-25/59) -> (-9/43,-14/67) Hyperbolic Matrix(203,86,-1768,-749) (-25/59,-11/26) -> (-3/26,-1/9) Hyperbolic Matrix(237,100,884,373) (-11/26,-8/19) -> (4/15,7/26) Hyperbolic Matrix(647,272,-4284,-1801) (-8/19,-29/69) -> (-5/33,-8/53) Hyperbolic Matrix(2413,1014,7684,3229) (-29/69,-50/119) -> (16/51,11/35) Hyperbolic Matrix(3909,1642,6392,2685) (-50/119,-21/50) -> (11/18,52/85) Hyperbolic Matrix(10745,4504,18496,7753) (-13/31,-57/136) -> (79/136,61/105) Hyperbolic Matrix(10743,4502,18496,7751) (-57/136,-44/105) -> (18/31,79/136) Hyperbolic Matrix(339,142,2108,883) (-31/74,-18/43) -> (4/25,1/6) Hyperbolic Matrix(679,284,2924,1223) (-18/43,-23/55) -> (3/13,10/43) Hyperbolic Matrix(1259,526,-4148,-1733) (-23/55,-5/12) -> (-17/56,-27/89) Hyperbolic Matrix(169,70,408,169) (-5/12,-7/17) -> (7/17,5/12) Hyperbolic Matrix(307,126,748,307) (-7/17,-9/22) -> (9/22,7/17) Hyperbolic Matrix(1157,472,1836,749) (-9/22,-11/27) -> (17/27,29/46) Hyperbolic Matrix(1361,552,-4692,-1903) (-13/32,-15/37) -> (-9/31,-29/100) Hyperbolic Matrix(169,66,-612,-239) (-2/5,-7/18) -> (-5/18,-8/29) Hyperbolic Matrix(3707,1440,6392,2483) (-7/18,-33/85) -> (69/119,29/50) Hyperbolic Matrix(6699,2600,8500,3299) (-33/85,-26/67) -> (26/33,67/85) Hyperbolic Matrix(1665,646,-7276,-2823) (-26/67,-19/49) -> (-19/83,-8/35) Hyperbolic Matrix(1495,578,2108,815) (-12/31,-17/44) -> (17/24,22/31) Hyperbolic Matrix(477,184,884,341) (-17/44,-5/13) -> (7/13,13/24) Hyperbolic Matrix(715,274,1156,443) (-5/13,-13/34) -> (21/34,13/21) Hyperbolic Matrix(713,272,1156,441) (-13/34,-8/21) -> (8/13,21/34) Hyperbolic Matrix(237,88,272,101) (-3/8,-10/27) -> (6/7,7/8) Hyperbolic Matrix(1087,402,1836,679) (-10/27,-17/46) -> (13/22,16/27) Hyperbolic Matrix(2925,1076,4624,1701) (-7/19,-25/68) -> (43/68,31/49) Hyperbolic Matrix(2923,1074,4624,1699) (-25/68,-18/49) -> (12/19,43/68) Hyperbolic Matrix(3231,1184,5848,2143) (-11/30,-37/101) -> (37/67,21/38) Hyperbolic Matrix(3637,1332,-13464,-4931) (-37/101,-26/71) -> (-10/37,-37/137) Hyperbolic Matrix(851,308,1224,443) (-4/11,-13/36) -> (25/36,16/23) Hyperbolic Matrix(477,172,1700,613) (-13/36,-9/25) -> (7/25,9/32) Hyperbolic Matrix(169,60,476,169) (-5/14,-6/17) -> (6/17,5/14) Hyperbolic Matrix(239,84,680,239) (-6/17,-7/20) -> (7/20,6/17) Hyperbolic Matrix(373,130,680,237) (-7/20,-1/3) -> (17/31,11/20) Hyperbolic Matrix(169,54,-748,-239) (-1/3,-6/19) -> (-12/53,-7/31) Hyperbolic Matrix(273,86,-1292,-407) (-6/19,-5/16) -> (-11/52,-4/19) Hyperbolic Matrix(103,32,-544,-169) (-5/16,-4/13) -> (-4/21,-3/16) Hyperbolic Matrix(137,42,-884,-271) (-4/13,-11/36) -> (-5/32,-2/13) Hyperbolic Matrix(781,238,1224,373) (-11/36,-7/23) -> (7/11,23/36) Hyperbolic Matrix(7243,2202,10404,3163) (-7/23,-31/102) -> (71/102,55/79) Hyperbolic Matrix(7241,2200,10404,3161) (-31/102,-24/79) -> (16/23,71/102) Hyperbolic Matrix(33,10,-340,-103) (-10/33,-3/10) -> (-1/10,0/1) Hyperbolic Matrix(101,30,340,101) (-3/10,-5/17) -> (5/17,3/10) Hyperbolic Matrix(239,70,816,239) (-5/17,-7/24) -> (7/24,5/17) Hyperbolic Matrix(1293,376,2108,613) (-7/24,-9/31) -> (19/31,27/44) Hyperbolic Matrix(8263,2396,-30600,-8873) (-29/100,-20/69) -> (-64/237,-27/100) Hyperbolic Matrix(6799,1970,9384,2719) (-20/69,-11/38) -> (71/98,50/69) Hyperbolic Matrix(1597,450,-5916,-1667) (-11/39,-9/32) -> (-27/100,-17/63) Hyperbolic Matrix(849,238,1088,305) (-9/32,-7/25) -> (7/9,25/32) Hyperbolic Matrix(3333,932,4624,1293) (-7/25,-19/68) -> (49/68,31/43) Hyperbolic Matrix(3331,930,4624,1291) (-19/68,-12/43) -> (18/25,49/68) Hyperbolic Matrix(6665,1836,9384,2585) (-27/98,-19/69) -> (49/69,27/38) Hyperbolic Matrix(2347,646,4080,1123) (-19/69,-11/40) -> (23/40,19/33) Hyperbolic Matrix(613,168,748,205) (-11/40,-3/11) -> (9/11,23/28) Hyperbolic Matrix(339,92,748,203) (-3/11,-10/37) -> (14/31,5/11) Hyperbolic Matrix(102103,27574,139876,37775) (-37/137,-101/374) -> (273/374,173/237) Hyperbolic Matrix(102101,27572,139876,37773) (-101/374,-64/237) -> (100/137,273/374) Hyperbolic Matrix(1053,284,3400,917) (-17/63,-7/26) -> (13/42,9/29) Hyperbolic Matrix(373,100,884,237) (-7/26,-4/15) -> (8/19,11/26) Hyperbolic Matrix(851,226,1156,307) (-4/15,-9/34) -> (25/34,14/19) Hyperbolic Matrix(849,224,1156,305) (-9/34,-5/19) -> (11/15,25/34) Hyperbolic Matrix(33,8,136,33) (-1/4,-4/17) -> (4/17,1/4) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(851,198,1904,443) (-7/30,-10/43) -> (4/9,17/38) Hyperbolic Matrix(1223,284,2924,679) (-10/43,-3/13) -> (23/55,18/43) Hyperbolic Matrix(1087,248,2380,543) (-8/35,-13/57) -> (5/11,16/35) Hyperbolic Matrix(14281,3256,18496,4217) (-13/57,-31/136) -> (105/136,61/79) Hyperbolic Matrix(14279,3254,18496,4215) (-31/136,-18/79) -> (44/57,105/136) Hyperbolic Matrix(8059,1818,10404,2347) (-7/31,-23/102) -> (79/102,55/71) Hyperbolic Matrix(8057,1816,10404,2345) (-23/102,-16/71) -> (24/31,79/102) Hyperbolic Matrix(545,122,612,137) (-11/49,-2/9) -> (8/9,17/19) Hyperbolic Matrix(783,172,1088,239) (-2/9,-7/32) -> (23/32,18/25) Hyperbolic Matrix(477,104,1564,341) (-7/32,-5/23) -> (7/23,11/36) Hyperbolic Matrix(14553,3104,18496,3945) (-16/75,-29/136) -> (107/136,48/61) Hyperbolic Matrix(14551,3102,18496,3943) (-29/136,-13/61) -> (59/75,107/136) Hyperbolic Matrix(1259,268,2720,579) (-13/61,-10/47) -> (6/13,19/41) Hyperbolic Matrix(5201,1102,8500,1801) (-7/33,-18/85) -> (52/85,41/67) Hyperbolic Matrix(1257,266,4012,849) (-18/85,-11/52) -> (5/16,16/51) Hyperbolic Matrix(1087,228,1292,271) (-4/19,-9/43) -> (21/25,16/19) Hyperbolic Matrix(919,190,1156,239) (-6/29,-7/34) -> (27/34,4/5) Hyperbolic Matrix(917,188,1156,237) (-7/34,-1/5) -> (23/29,27/34) Hyperbolic Matrix(477,92,1768,341) (-1/5,-5/26) -> (7/26,17/63) Hyperbolic Matrix(3741,716,4624,885) (-9/47,-13/68) -> (55/68,17/21) Hyperbolic Matrix(3739,714,4624,883) (-13/68,-4/21) -> (38/47,55/68) Hyperbolic Matrix(237,44,544,101) (-3/16,-2/11) -> (10/23,7/16) Hyperbolic Matrix(543,98,748,135) (-2/11,-5/28) -> (29/40,8/11) Hyperbolic Matrix(169,30,952,169) (-5/28,-3/17) -> (3/17,5/28) Hyperbolic Matrix(35,6,204,35) (-3/17,-1/6) -> (1/6,3/17) Hyperbolic Matrix(883,142,2108,339) (-1/6,-4/25) -> (18/43,31/74) Hyperbolic Matrix(1021,162,1292,205) (-4/25,-3/19) -> (15/19,34/43) Hyperbolic Matrix(1021,160,2176,341) (-8/51,-5/32) -> (15/32,8/17) Hyperbolic Matrix(987,146,1156,171) (-4/27,-5/34) -> (29/34,6/7) Hyperbolic Matrix(985,144,1156,169) (-5/34,-1/7) -> (23/27,29/34) Hyperbolic Matrix(171,22,272,35) (-1/7,-1/8) -> (5/8,17/27) Hyperbolic Matrix(33,4,272,33) (-1/8,-2/17) -> (2/17,1/8) Hyperbolic Matrix(1123,130,2652,307) (-2/17,-3/26) -> (11/26,36/85) Hyperbolic Matrix(475,52,612,67) (-1/9,-2/19) -> (38/49,7/9) Hyperbolic Matrix(885,92,1972,205) (-2/19,-1/10) -> (35/78,22/49) Hyperbolic Matrix(103,-10,340,-33) (0/1,1/9) -> (13/43,10/33) Hyperbolic Matrix(749,-86,1768,-203) (1/9,2/17) -> (36/85,25/59) Hyperbolic Matrix(579,-86,680,-101) (1/7,3/20) -> (17/20,23/27) Hyperbolic Matrix(681,-104,884,-135) (3/20,2/13) -> (10/13,37/48) Hyperbolic Matrix(271,-42,884,-137) (2/13,3/19) -> (15/49,4/13) Hyperbolic Matrix(169,-32,544,-103) (3/16,1/5) -> (9/29,5/16) Hyperbolic Matrix(647,-134,816,-169) (1/5,5/24) -> (19/24,23/29) Hyperbolic Matrix(1121,-234,2448,-511) (5/24,9/43) -> (27/59,11/24) Hyperbolic Matrix(407,-86,1292,-273) (4/19,7/33) -> (11/35,6/19) Hyperbolic Matrix(3127,-664,4488,-953) (7/33,10/47) -> (62/89,23/33) Hyperbolic Matrix(1497,-320,1904,-407) (13/61,3/14) -> (11/14,59/75) Hyperbolic Matrix(305,-66,476,-103) (3/14,2/9) -> (16/25,9/14) Hyperbolic Matrix(917,-206,1972,-443) (2/9,9/40) -> (13/28,20/43) Hyperbolic Matrix(3161,-712,4080,-919) (9/40,7/31) -> (55/71,31/40) Hyperbolic Matrix(1801,-408,2856,-647) (7/31,5/22) -> (29/46,41/65) Hyperbolic Matrix(2311,-526,2992,-681) (5/22,13/57) -> (61/79,17/22) Hyperbolic Matrix(749,-172,884,-203) (8/35,3/13) -> (11/13,28/33) Hyperbolic Matrix(101,-26,136,-35) (1/4,4/15) -> (14/19,3/4) Hyperbolic Matrix(1497,-404,2516,-679) (17/63,10/37) -> (22/37,3/5) Hyperbolic Matrix(239,-66,612,-169) (3/11,5/18) -> (7/18,9/23) Hyperbolic Matrix(883,-246,1224,-341) (5/18,7/25) -> (31/43,13/18) Hyperbolic Matrix(645,-182,1088,-307) (9/32,2/7) -> (16/27,19/32) Hyperbolic Matrix(1121,-324,1768,-511) (2/7,9/31) -> (45/71,26/41) Hyperbolic Matrix(3535,-1072,4488,-1361) (10/33,17/56) -> (63/80,26/33) Hyperbolic Matrix(3977,-1208,5712,-1735) (17/56,7/23) -> (55/79,39/56) Hyperbolic Matrix(987,-302,2108,-645) (11/36,15/49) -> (7/15,15/32) Hyperbolic Matrix(1869,-578,2312,-715) (4/13,13/42) -> (21/26,38/47) Hyperbolic Matrix(815,-258,1292,-409) (6/19,1/3) -> (41/65,12/19) Hyperbolic Matrix(373,-134,476,-171) (5/14,4/11) -> (18/23,11/14) Hyperbolic Matrix(443,-162,1020,-373) (4/11,11/30) -> (13/30,10/23) Hyperbolic Matrix(1291,-474,2040,-749) (11/30,7/19) -> (31/49,19/30) Hyperbolic Matrix(2209,-816,2856,-1055) (7/19,17/46) -> (17/22,41/53) Hyperbolic Matrix(169,-64,272,-103) (3/8,5/13) -> (13/21,5/8) Hyperbolic Matrix(1223,-474,2108,-817) (12/31,7/18) -> (29/50,18/31) Hyperbolic Matrix(713,-282,1292,-511) (13/33,2/5) -> (16/29,37/67) Hyperbolic Matrix(781,-318,1088,-443) (2/5,11/27) -> (5/7,28/39) Hyperbolic Matrix(3909,-1634,4964,-2075) (5/12,23/55) -> (37/47,63/80) Hyperbolic Matrix(5847,-2450,10064,-4217) (31/74,13/31) -> (61/105,43/74) Hyperbolic Matrix(1291,-542,2108,-885) (13/31,8/19) -> (30/49,19/31) Hyperbolic Matrix(1835,-778,4012,-1701) (25/59,14/33) -> (16/35,27/59) Hyperbolic Matrix(851,-362,1836,-781) (17/40,3/7) -> (19/41,13/28) Hyperbolic Matrix(339,-146,476,-205) (3/7,13/30) -> (27/38,5/7) Hyperbolic Matrix(305,-134,544,-239) (7/16,4/9) -> (14/25,9/16) Hyperbolic Matrix(2857,-1280,3944,-1767) (17/38,13/29) -> (21/29,71/98) Hyperbolic Matrix(5849,-2624,10608,-4759) (13/29,35/78) -> (43/78,59/107) Hyperbolic Matrix(3093,-1390,4012,-1803) (22/49,9/20) -> (37/48,64/83) Hyperbolic Matrix(917,-488,1088,-579) (9/17,8/15) -> (16/19,43/51) Hyperbolic Matrix(1529,-818,1972,-1055) (8/15,15/28) -> (31/40,38/49) Hyperbolic Matrix(1055,-566,1836,-985) (15/28,7/13) -> (27/47,23/40) Hyperbolic Matrix(1937,-1050,2448,-1327) (13/24,19/35) -> (53/67,19/24) Hyperbolic Matrix(1733,-954,2040,-1123) (11/20,27/49) -> (45/53,17/20) Hyperbolic Matrix(647,-366,1020,-577) (13/23,4/7) -> (26/41,7/11) Hyperbolic Matrix(4249,-2448,5372,-3095) (19/33,34/59) -> (34/43,53/67) Hyperbolic Matrix(1565,-902,1768,-1019) (34/59,15/26) -> (23/26,8/9) Hyperbolic Matrix(3637,-2108,4284,-2483) (11/19,40/69) -> (28/33,45/53) Hyperbolic Matrix(2889,-1682,4148,-2415) (32/55,7/12) -> (39/56,62/89) Hyperbolic Matrix(3331,-1980,4692,-2789) (19/32,22/37) -> (22/31,71/100) Hyperbolic Matrix(443,-270,612,-373) (3/5,11/18) -> (13/18,21/29) Hyperbolic Matrix(5611,-3434,7276,-4453) (41/67,30/49) -> (64/83,27/35) Hyperbolic Matrix(9827,-6228,13464,-8533) (64/101,45/71) -> (27/37,100/137) Hyperbolic Matrix(579,-394,748,-509) (2/3,13/19) -> (41/53,24/31) Hyperbolic Matrix(1019,-698,1292,-885) (13/19,11/16) -> (41/52,15/19) Hyperbolic Matrix(441,-304,544,-375) (11/16,9/13) -> (17/21,13/16) Hyperbolic Matrix(747,-518,884,-613) (9/13,25/36) -> (27/32,11/13) Hyperbolic Matrix(307,-214,340,-237) (23/33,7/10) -> (9/10,1/1) Hyperbolic Matrix(22337,-15860,30600,-21727) (71/100,49/69) -> (173/237,73/100) Hyperbolic Matrix(4319,-3102,5916,-4249) (28/39,23/32) -> (73/100,46/63) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-64,1) Matrix(237,214,-340,-307) -> Matrix(115,-4,2444,-85) Matrix(1019,902,-1768,-1565) -> Matrix(225,-8,3572,-127) Matrix(239,210,272,239) -> Matrix(167,-6,-4648,167) Matrix(101,88,272,237) -> Matrix(55,-2,-632,23) Matrix(101,86,-680,-579) -> Matrix(377,-14,1912,-71) Matrix(203,172,-884,-749) -> Matrix(267,-10,2056,-77) Matrix(613,518,-884,-747) -> Matrix(53,-2,1140,-43) Matrix(271,228,1292,1087) -> Matrix(55,-2,-412,15) Matrix(1225,1028,2108,1769) -> Matrix(53,-2,-768,29) Matrix(169,140,204,169) -> Matrix(105,-4,-2756,105) Matrix(783,644,952,783) -> Matrix(467,-18,-12116,467) Matrix(373,306,952,781) -> Matrix(155,-6,-2144,83) Matrix(307,250,544,443) -> Matrix(51,-2,-892,35) Matrix(375,304,-544,-441) -> Matrix(51,-2,1148,-45) Matrix(169,134,-816,-647) -> Matrix(349,-14,2468,-99) Matrix(1327,1050,-2448,-1937) -> Matrix(149,-6,2856,-115) Matrix(205,162,1292,1021) -> Matrix(49,-2,-220,9) Matrix(885,698,-1292,-1019) -> Matrix(247,-10,5360,-217) Matrix(1361,1072,-4488,-3535) -> Matrix(689,-28,7456,-303) Matrix(1835,1444,3196,2515) -> Matrix(49,-2,-416,17) Matrix(407,320,-1904,-1497) -> Matrix(97,-4,752,-31) Matrix(171,134,-476,-373) -> Matrix(1,0,-12,1) Matrix(1055,818,-1972,-1529) -> Matrix(1,0,-8,1) Matrix(919,712,-4080,-3161) -> Matrix(51,-2,332,-13) Matrix(1055,816,-2856,-2209) -> Matrix(49,-2,564,-23) Matrix(681,526,-2992,-2311) -> Matrix(295,-12,2188,-89) Matrix(1293,998,2380,1837) -> Matrix(49,-2,-1200,49) Matrix(135,104,-884,-681) -> Matrix(243,-10,1288,-53) Matrix(1701,1306,2924,2245) -> Matrix(145,-6,-2344,97) Matrix(1053,808,1904,1461) -> Matrix(145,-6,-2344,97) Matrix(781,598,1020,781) -> Matrix(385,-16,-9264,385) Matrix(103,78,136,103) -> Matrix(47,-2,-1104,47) Matrix(35,26,-136,-101) -> Matrix(47,-2,400,-17) Matrix(511,374,884,647) -> Matrix(91,-4,-1524,67) Matrix(1427,1042,1768,1291) -> Matrix(1,0,-48,1) Matrix(1019,744,-2516,-1837) -> Matrix(45,-2,608,-27) Matrix(409,298,748,545) -> Matrix(45,-2,-652,29) Matrix(373,270,-612,-443) -> Matrix(1,0,-4,1) Matrix(341,246,-1224,-883) -> Matrix(1,0,-12,1) Matrix(1087,782,1700,1223) -> Matrix(47,-2,-916,39) Matrix(443,318,-1088,-781) -> Matrix(45,-2,608,-27) Matrix(647,460,-1768,-1257) -> Matrix(45,-2,608,-27) Matrix(815,578,2108,1495) -> Matrix(45,-2,-652,29) Matrix(577,408,816,577) -> Matrix(221,-10,-4884,221) Matrix(239,168,340,239) -> Matrix(87,-4,-1892,87) Matrix(2549,1780,4624,3229) -> Matrix(43,-2,-924,43) Matrix(1361,950,2924,2041) -> Matrix(43,-2,-752,35) Matrix(953,664,-4488,-3127) -> Matrix(593,-28,4384,-207) Matrix(1735,1208,-5712,-3977) -> Matrix(379,-18,4148,-197) Matrix(1223,850,1564,1087) -> Matrix(41,-2,-1004,49) Matrix(1121,778,-2108,-1463) -> Matrix(1,0,-4,1) Matrix(443,306,-2312,-1597) -> Matrix(51,-2,332,-13) Matrix(2483,1714,3400,2347) -> Matrix(45,-2,-1012,45) Matrix(3163,2172,4012,2755) -> Matrix(355,-16,-8764,395) Matrix(4455,3056,7684,5271) -> Matrix(263,-12,-4712,215) Matrix(477,326,-1292,-883) -> Matrix(43,-2,452,-21) Matrix(307,200,680,443) -> Matrix(41,-2,-676,33) Matrix(441,286,680,441) -> Matrix(121,-6,-2440,121) Matrix(307,198,476,307) -> Matrix(79,-4,-1560,79) Matrix(103,66,-476,-305) -> Matrix(1,0,-12,1) Matrix(577,366,-1020,-647) -> Matrix(1,0,0,1) Matrix(749,474,-2040,-1291) -> Matrix(1,0,0,1) Matrix(647,408,-2856,-1801) -> Matrix(41,-2,308,-15) Matrix(749,472,1836,1157) -> Matrix(43,-2,-580,27) Matrix(35,22,272,171) -> Matrix(41,-2,-184,9) Matrix(103,64,-272,-169) -> Matrix(39,-2,488,-25) Matrix(407,250,884,543) -> Matrix(37,-2,-536,29) Matrix(613,376,2108,1293) -> Matrix(35,-2,-332,19) Matrix(885,542,-2108,-1291) -> Matrix(37,-2,500,-27) Matrix(171,104,952,579) -> Matrix(109,-6,-672,37) Matrix(953,578,2244,1361) -> Matrix(35,-2,-612,35) Matrix(579,350,-1292,-781) -> Matrix(1,0,0,1) Matrix(307,182,-1088,-645) -> Matrix(37,-2,352,-19) Matrix(679,402,1836,1087) -> Matrix(37,-2,-388,21) Matrix(441,260,748,441) -> Matrix(73,-4,-1332,73) Matrix(239,140,408,239) -> Matrix(35,-2,-612,35) Matrix(1055,614,-4964,-2889) -> Matrix(199,-12,1476,-89) Matrix(2245,1306,2924,1701) -> Matrix(97,-6,-2344,145) Matrix(1769,1028,2108,1225) -> Matrix(29,-2,-768,53) Matrix(4217,2450,-10064,-5847) -> Matrix(1,0,4,1) Matrix(817,474,-2108,-1223) -> Matrix(37,-2,500,-27) Matrix(647,374,884,511) -> Matrix(67,-4,-1524,91) Matrix(2345,1352,2652,1529) -> Matrix(193,-12,-5420,337) Matrix(2177,1254,-4012,-2311) -> Matrix(31,-2,636,-41) Matrix(883,508,2244,1291) -> Matrix(29,-2,-420,29) Matrix(985,566,-1836,-1055) -> Matrix(1,0,4,1) Matrix(137,78,-476,-271) -> Matrix(37,-2,352,-19) Matrix(443,250,544,307) -> Matrix(35,-2,-892,51) Matrix(239,134,-544,-305) -> Matrix(35,-2,508,-29) Matrix(1461,808,1904,1053) -> Matrix(97,-6,-2344,145) Matrix(1087,600,-3944,-2177) -> Matrix(1,0,-4,1) Matrix(4759,2624,-10608,-5849) -> Matrix(1,0,-12,1) Matrix(1767,974,1972,1087) -> Matrix(41,-2,-1168,57) Matrix(919,506,-4012,-2209) -> Matrix(139,-8,1060,-61) Matrix(237,130,680,373) -> Matrix(31,-2,-356,23) Matrix(545,298,748,409) -> Matrix(29,-2,-652,45) Matrix(1837,998,2380,1293) -> Matrix(49,-2,-1200,49) Matrix(341,184,884,477) -> Matrix(35,-2,-472,27) Matrix(2141,1150,2720,1461) -> Matrix(25,-2,-612,49) Matrix(883,472,2924,1563) -> Matrix(29,-2,-304,21) Matrix(1835,974,2176,1155) -> Matrix(67,-4,-1792,107) Matrix(35,18,68,35) -> Matrix(1,0,-32,1) Matrix(33,16,68,33) -> Matrix(1,0,-32,1) Matrix(171,80,-1088,-509) -> Matrix(29,-2,160,-11) Matrix(443,206,-1972,-917) -> Matrix(1,0,-8,1) Matrix(781,362,-1836,-851) -> Matrix(1,0,4,1) Matrix(543,250,884,407) -> Matrix(29,-2,-536,37) Matrix(511,234,-2448,-1121) -> Matrix(77,-6,552,-43) Matrix(543,248,2380,1087) -> Matrix(15,-2,-112,15) Matrix(203,92,748,339) -> Matrix(35,-2,-332,19) Matrix(443,200,680,307) -> Matrix(33,-2,-676,41) Matrix(307,138,-2040,-917) -> Matrix(89,-6,460,-31) Matrix(1395,626,4624,2075) -> Matrix(21,-2,-220,21) Matrix(10201,4576,18496,8297) -> Matrix(1,0,-12,1) Matrix(10199,4574,18496,8295) -> Matrix(1,0,-52,1) Matrix(3705,1658,5848,2617) -> Matrix(33,-2,-544,33) Matrix(443,198,1904,851) -> Matrix(95,-6,-744,47) Matrix(647,286,1156,511) -> Matrix(61,-4,-1052,69) Matrix(645,284,1156,509) -> Matrix(59,-4,-988,67) Matrix(101,44,544,237) -> Matrix(29,-2,-188,13) Matrix(373,162,-1020,-443) -> Matrix(1,0,0,1) Matrix(681,290,3196,1361) -> Matrix(47,-2,-352,15) Matrix(2957,1256,4080,1733) -> Matrix(35,-2,-752,43) Matrix(1123,476,-5372,-2277) -> Matrix(261,-16,1876,-115) Matrix(203,86,-1768,-749) -> Matrix(129,-8,500,-31) Matrix(237,100,884,373) -> Matrix(61,-4,-564,37) Matrix(647,272,-4284,-1801) -> Matrix(229,-16,1188,-83) Matrix(2413,1014,7684,3229) -> Matrix(169,-12,-1704,121) Matrix(3909,1642,6392,2685) -> Matrix(27,-2,-472,35) Matrix(10745,4504,18496,7753) -> Matrix(1,0,-20,1) Matrix(10743,4502,18496,7751) -> Matrix(1,0,-44,1) Matrix(339,142,2108,883) -> Matrix(35,-2,-192,11) Matrix(679,284,2924,1223) -> Matrix(95,-6,-744,47) Matrix(1259,526,-4148,-1733) -> Matrix(121,-8,1316,-87) Matrix(169,70,408,169) -> Matrix(29,-2,-420,29) Matrix(307,126,748,307) -> Matrix(55,-4,-756,55) Matrix(1157,472,1836,749) -> Matrix(27,-2,-580,43) Matrix(1361,552,-4692,-1903) -> Matrix(127,-10,1232,-97) Matrix(169,66,-612,-239) -> Matrix(1,0,-4,1) Matrix(3707,1440,6392,2483) -> Matrix(29,-2,-536,37) Matrix(6699,2600,8500,3299) -> Matrix(445,-32,-10972,789) Matrix(1665,646,-7276,-2823) -> Matrix(387,-28,2944,-213) Matrix(1495,578,2108,815) -> Matrix(29,-2,-652,45) Matrix(477,184,884,341) -> Matrix(27,-2,-472,35) Matrix(715,274,1156,443) -> Matrix(105,-8,-2008,153) Matrix(713,272,1156,441) -> Matrix(103,-8,-1944,151) Matrix(237,88,272,101) -> Matrix(23,-2,-632,55) Matrix(1087,402,1836,679) -> Matrix(21,-2,-388,37) Matrix(2925,1076,4624,1701) -> Matrix(1,0,-16,1) Matrix(2923,1074,4624,1699) -> Matrix(1,0,-48,1) Matrix(3231,1184,5848,2143) -> Matrix(31,-2,-480,31) Matrix(3637,1332,-13464,-4931) -> Matrix(89,-6,816,-55) Matrix(851,308,1224,443) -> Matrix(25,-2,-512,41) Matrix(477,172,1700,613) -> Matrix(25,-2,-212,17) Matrix(169,60,476,169) -> Matrix(49,-4,-600,49) Matrix(239,84,680,239) -> Matrix(71,-6,-840,71) Matrix(373,130,680,237) -> Matrix(23,-2,-356,31) Matrix(169,54,-748,-239) -> Matrix(43,-4,312,-29) Matrix(273,86,-1292,-407) -> Matrix(103,-10,752,-73) Matrix(103,32,-544,-169) -> Matrix(19,-2,124,-13) Matrix(137,42,-884,-271) -> Matrix(21,-2,116,-11) Matrix(781,238,1224,373) -> Matrix(23,-2,-448,39) Matrix(7243,2202,10404,3163) -> Matrix(309,-28,-6500,589) Matrix(7241,2200,10404,3161) -> Matrix(307,-28,-6436,587) Matrix(33,10,-340,-103) -> Matrix(43,-4,140,-13) Matrix(101,30,340,101) -> Matrix(41,-4,-420,41) Matrix(239,70,816,239) -> Matrix(99,-10,-980,99) Matrix(1293,376,2108,613) -> Matrix(19,-2,-332,35) Matrix(8263,2396,-30600,-8873) -> Matrix(213,-22,1888,-195) Matrix(6799,1970,9384,2719) -> Matrix(77,-8,-1588,165) Matrix(1597,450,-5916,-1667) -> Matrix(1,0,0,1) Matrix(849,238,1088,305) -> Matrix(17,-2,-416,49) Matrix(3333,932,4624,1293) -> Matrix(1,0,-28,1) Matrix(3331,930,4624,1291) -> Matrix(1,0,-36,1) Matrix(6665,1836,9384,2585) -> Matrix(91,-8,-2036,179) Matrix(2347,646,4080,1123) -> Matrix(21,-2,-304,29) Matrix(613,168,748,205) -> Matrix(59,-6,-1524,155) Matrix(339,92,748,203) -> Matrix(19,-2,-332,35) Matrix(102103,27574,139876,37775) -> Matrix(289,-32,-6656,737) Matrix(102101,27572,139876,37773) -> Matrix(287,-32,-6592,735) Matrix(1053,284,3400,917) -> Matrix(19,-2,-180,19) Matrix(373,100,884,237) -> Matrix(37,-4,-564,61) Matrix(851,226,1156,307) -> Matrix(145,-16,-3344,369) Matrix(849,224,1156,305) -> Matrix(143,-16,-3280,367) Matrix(33,8,136,33) -> Matrix(17,-2,-144,17) Matrix(239,56,1020,239) -> Matrix(127,-16,-1008,127) Matrix(851,198,1904,443) -> Matrix(47,-6,-744,95) Matrix(1223,284,2924,679) -> Matrix(47,-6,-744,95) Matrix(1087,248,2380,543) -> Matrix(15,-2,-112,15) Matrix(14281,3256,18496,4217) -> Matrix(841,-112,-20612,2745) Matrix(14279,3254,18496,4215) -> Matrix(839,-112,-20548,2743) Matrix(8059,1818,10404,2347) -> Matrix(85,-12,-2132,301) Matrix(8057,1816,10404,2345) -> Matrix(83,-12,-2068,299) Matrix(545,122,612,137) -> Matrix(17,-2,-484,57) Matrix(783,172,1088,239) -> Matrix(15,-2,-352,47) Matrix(477,104,1564,341) -> Matrix(15,-2,-172,23) Matrix(14553,3104,18496,3945) -> Matrix(721,-96,-17672,2353) Matrix(14551,3102,18496,3943) -> Matrix(719,-96,-17608,2351) Matrix(1259,268,2720,579) -> Matrix(15,-2,-292,39) Matrix(5201,1102,8500,1801) -> Matrix(235,-32,-4252,579) Matrix(1257,266,4012,849) -> Matrix(117,-16,-1148,157) Matrix(1087,228,1292,271) -> Matrix(15,-2,-412,55) Matrix(919,190,1156,239) -> Matrix(141,-20,-3532,501) Matrix(917,188,1156,237) -> Matrix(139,-20,-3468,499) Matrix(477,92,1768,341) -> Matrix(1,0,-16,1) Matrix(3741,716,4624,885) -> Matrix(209,-32,-5336,817) Matrix(3739,714,4624,883) -> Matrix(207,-32,-5272,815) Matrix(237,44,544,101) -> Matrix(13,-2,-188,29) Matrix(543,98,748,135) -> Matrix(37,-6,-820,133) Matrix(169,30,952,169) -> Matrix(109,-18,-660,109) Matrix(35,6,204,35) -> Matrix(23,-4,-132,23) Matrix(883,142,2108,339) -> Matrix(11,-2,-192,35) Matrix(1021,162,1292,205) -> Matrix(9,-2,-220,49) Matrix(1021,160,2176,341) -> Matrix(21,-4,-320,61) Matrix(987,146,1156,171) -> Matrix(121,-24,-3272,649) Matrix(985,144,1156,169) -> Matrix(119,-24,-3208,647) Matrix(171,22,272,35) -> Matrix(9,-2,-184,41) Matrix(33,4,272,33) -> Matrix(25,-6,-104,25) Matrix(1123,130,2652,307) -> Matrix(47,-12,-748,191) Matrix(475,52,612,67) -> Matrix(7,-2,-164,47) Matrix(885,92,1972,205) -> Matrix(7,-2,-80,23) Matrix(103,-10,340,-33) -> Matrix(13,4,-140,-43) Matrix(749,-86,1768,-203) -> Matrix(31,8,-500,-129) Matrix(579,-86,680,-101) -> Matrix(71,14,-1912,-377) Matrix(681,-104,884,-135) -> Matrix(53,10,-1288,-243) Matrix(271,-42,884,-137) -> Matrix(11,2,-116,-21) Matrix(169,-32,544,-103) -> Matrix(13,2,-124,-19) Matrix(647,-134,816,-169) -> Matrix(99,14,-2468,-349) Matrix(1121,-234,2448,-511) -> Matrix(43,6,-552,-77) Matrix(407,-86,1292,-273) -> Matrix(73,10,-752,-103) Matrix(3127,-664,4488,-953) -> Matrix(207,28,-4384,-593) Matrix(1497,-320,1904,-407) -> Matrix(31,4,-752,-97) Matrix(305,-66,476,-103) -> Matrix(1,0,-12,1) Matrix(917,-206,1972,-443) -> Matrix(1,0,-8,1) Matrix(3161,-712,4080,-919) -> Matrix(13,2,-332,-51) Matrix(1801,-408,2856,-647) -> Matrix(15,2,-308,-41) Matrix(2311,-526,2992,-681) -> Matrix(89,12,-2188,-295) Matrix(749,-172,884,-203) -> Matrix(77,10,-2056,-267) Matrix(101,-26,136,-35) -> Matrix(17,2,-400,-47) Matrix(1497,-404,2516,-679) -> Matrix(19,2,-352,-37) Matrix(239,-66,612,-169) -> Matrix(1,0,-4,1) Matrix(883,-246,1224,-341) -> Matrix(1,0,-12,1) Matrix(645,-182,1088,-307) -> Matrix(19,2,-352,-37) Matrix(1121,-324,1768,-511) -> Matrix(19,2,-352,-37) Matrix(3535,-1072,4488,-1361) -> Matrix(303,28,-7456,-689) Matrix(3977,-1208,5712,-1735) -> Matrix(197,18,-4148,-379) Matrix(987,-302,2108,-645) -> Matrix(1,0,-4,1) Matrix(1869,-578,2312,-715) -> Matrix(13,2,-332,-51) Matrix(815,-258,1292,-409) -> Matrix(21,2,-452,-43) Matrix(373,-134,476,-171) -> Matrix(1,0,-12,1) Matrix(443,-162,1020,-373) -> Matrix(1,0,0,1) Matrix(1291,-474,2040,-749) -> Matrix(1,0,0,1) Matrix(2209,-816,2856,-1055) -> Matrix(23,2,-564,-49) Matrix(169,-64,272,-103) -> Matrix(25,2,-488,-39) Matrix(1223,-474,2108,-817) -> Matrix(27,2,-500,-37) Matrix(713,-282,1292,-511) -> Matrix(1,0,0,1) Matrix(781,-318,1088,-443) -> Matrix(27,2,-608,-45) Matrix(3909,-1634,4964,-2075) -> Matrix(185,12,-4548,-295) Matrix(5847,-2450,10064,-4217) -> Matrix(1,0,4,1) Matrix(1291,-542,2108,-885) -> Matrix(27,2,-500,-37) Matrix(1835,-778,4012,-1701) -> Matrix(33,2,-380,-23) Matrix(851,-362,1836,-781) -> Matrix(1,0,4,1) Matrix(339,-146,476,-205) -> Matrix(27,2,-608,-45) Matrix(305,-134,544,-239) -> Matrix(29,2,-508,-35) Matrix(2857,-1280,3944,-1767) -> Matrix(1,0,-4,1) Matrix(5849,-2624,10608,-4759) -> Matrix(1,0,-12,1) Matrix(3093,-1390,4012,-1803) -> Matrix(117,8,-2852,-195) Matrix(917,-488,1088,-579) -> Matrix(35,2,-928,-53) Matrix(1529,-818,1972,-1055) -> Matrix(1,0,-8,1) Matrix(1055,-566,1836,-985) -> Matrix(1,0,4,1) Matrix(1937,-1050,2448,-1327) -> Matrix(115,6,-2856,-149) Matrix(1733,-954,2040,-1123) -> Matrix(103,6,-2764,-161) Matrix(647,-366,1020,-577) -> Matrix(1,0,0,1) Matrix(4249,-2448,5372,-3095) -> Matrix(251,16,-6228,-397) Matrix(1565,-902,1768,-1019) -> Matrix(127,8,-3572,-225) Matrix(3637,-2108,4284,-2483) -> Matrix(283,16,-7588,-429) Matrix(2889,-1682,4148,-2415) -> Matrix(135,8,-2852,-169) Matrix(3331,-1980,4692,-2789) -> Matrix(193,10,-4304,-223) Matrix(443,-270,612,-373) -> Matrix(1,0,-4,1) Matrix(5611,-3434,7276,-4453) -> Matrix(509,28,-12416,-683) Matrix(9827,-6228,13464,-8533) -> Matrix(103,6,-2352,-137) Matrix(579,-394,748,-509) -> Matrix(85,4,-2104,-99) Matrix(1019,-698,1292,-885) -> Matrix(217,10,-5360,-247) Matrix(441,-304,544,-375) -> Matrix(45,2,-1148,-51) Matrix(747,-518,884,-613) -> Matrix(43,2,-1140,-53) Matrix(307,-214,340,-237) -> Matrix(85,4,-2444,-115) Matrix(22337,-15860,30600,-21727) -> Matrix(491,22,-11360,-509) Matrix(4319,-3102,5916,-4249) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 72 Degree of the the map X: 144 Degree of the the map Y: 288 ----------------------------------------------------------------------- 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): 432 Minimal number of generators: 73 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: 32 Genus: 21 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/9 2/17 1/8 1/7 2/13 1/6 3/17 2/11 1/5 3/14 4/17 1/4 4/15 5/17 3/10 1/3 6/17 7/17 5/12 7/16 8/17 1/2 19/34 52/85 21/34 25/34 105/136 79/102 27/34 29/34 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/9 -1/4 2/17 -1/4 1/8 -1/4 -3/13 1/7 -5/24 3/20 -1/5 -7/36 2/13 -3/16 3/19 -3/16 4/25 -3/16 1/6 -2/11 -1/6 3/17 -1/6 2/11 -7/44 1/5 -3/20 5/24 -1/7 -7/50 9/43 -5/36 4/19 -5/36 7/33 -19/140 3/14 -2/15 -1/8 2/9 -1/8 5/22 -3/22 -2/15 8/35 -19/144 3/13 -1/8 4/17 -1/8 1/4 -1/8 -1/9 4/15 -7/64 3/11 -5/48 5/18 -1/10 0/1 2/7 -3/28 5/17 -1/10 3/10 -1/10 -2/21 13/43 -3/32 10/33 -13/140 17/56 -9/98 -1/11 7/23 -5/56 4/13 -1/12 1/3 -1/12 6/17 -1/12 5/14 -1/12 -2/25 4/11 -3/40 7/19 -1/8 3/8 -1/12 -1/13 5/13 -3/40 7/18 -1/14 0/1 2/5 -1/12 7/17 -1/14 5/12 -1/14 -1/15 18/43 -1/16 31/74 -1/18 0/1 13/31 -1/12 8/19 -3/44 3/7 -1/12 7/16 -1/14 -1/15 4/9 -1/16 5/11 -1/20 6/13 -1/16 7/15 -1/16 8/17 -1/16 1/2 -1/16 0/1 9/17 -1/16 8/15 -1/16 7/13 -1/16 6/11 -1/12 5/9 -1/16 19/34 -1/17 14/25 -3/52 9/16 -1/17 -1/18 4/7 -1/20 15/26 -1/16 -2/33 11/19 -3/52 18/31 -1/20 7/12 -1/17 -1/18 10/17 -1/18 3/5 -1/20 11/18 -1/18 0/1 52/85 -1/18 41/67 -15/272 30/49 -7/128 19/31 -3/56 8/13 -3/56 21/34 -1/19 13/21 -5/96 5/8 -1/19 -1/20 17/27 -3/64 12/19 -1/24 7/11 -3/56 16/25 -1/20 9/14 -2/39 -1/20 11/17 -1/20 2/3 -1/20 13/19 -5/108 11/16 -1/22 -1/23 9/13 -1/20 16/23 -5/104 23/33 -13/276 7/10 -2/43 -1/22 12/17 -1/22 5/7 -3/68 13/18 -1/22 0/1 21/29 -1/24 8/11 -5/112 11/15 -7/160 25/34 -1/23 14/19 -9/208 3/4 -1/23 -1/24 13/17 -1/24 10/13 -1/24 37/48 -3/73 -11/268 27/35 -19/464 44/57 -25/612 105/136 -2/49 61/79 -31/760 17/22 -2/49 -3/74 24/31 -5/124 79/102 -1/25 55/71 -7/176 31/40 -1/25 -1/26 7/9 -1/24 18/23 -3/76 11/14 -1/24 -2/49 26/33 -19/468 67/85 -3/74 41/52 -3/74 -13/321 15/19 -5/124 34/43 -5/124 19/24 -7/174 -1/25 23/29 -17/424 27/34 -1/25 4/5 -3/76 13/16 -1/25 -1/26 9/11 -7/180 14/17 -1/26 5/6 -1/26 -2/53 21/25 -3/80 16/19 -3/80 11/13 -3/80 28/33 -23/616 17/20 -7/188 -1/27 23/27 -19/512 29/34 -1/27 6/7 -5/136 7/8 -3/83 -1/28 15/17 -1/28 8/9 -1/28 9/10 -2/57 -3/86 1/1 -1/32 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(103,-10,340,-33) (0/1,1/9) -> (13/43,10/33) Hyperbolic Matrix(271,-31,306,-35) (1/9,2/17) -> (15/17,8/9) Hyperbolic Matrix(239,-29,272,-33) (2/17,1/8) -> (7/8,15/17) Hyperbolic Matrix(137,-19,238,-33) (1/8,1/7) -> (4/7,15/26) Hyperbolic Matrix(579,-86,680,-101) (1/7,3/20) -> (17/20,23/27) Hyperbolic Matrix(681,-104,884,-135) (3/20,2/13) -> (10/13,37/48) Hyperbolic Matrix(237,-37,442,-69) (2/13,3/19) -> (8/15,7/13) Hyperbolic Matrix(271,-43,1292,-205) (3/19,4/25) -> (9/43,4/19) Hyperbolic Matrix(817,-131,1054,-169) (4/25,1/6) -> (31/40,7/9) Hyperbolic Matrix(169,-29,204,-35) (1/6,3/17) -> (14/17,5/6) Hyperbolic Matrix(307,-55,374,-67) (3/17,2/11) -> (9/11,14/17) Hyperbolic Matrix(271,-50,374,-69) (2/11,1/5) -> (21/29,8/11) Hyperbolic Matrix(647,-134,816,-169) (1/5,5/24) -> (19/24,23/29) Hyperbolic Matrix(579,-121,646,-135) (5/24,9/43) -> (8/9,9/10) Hyperbolic Matrix(1769,-374,2890,-611) (4/19,7/33) -> (41/67,30/49) Hyperbolic Matrix(1599,-340,2074,-441) (7/33,3/14) -> (37/48,27/35) Hyperbolic Matrix(305,-66,476,-103) (3/14,2/9) -> (16/25,9/14) Hyperbolic Matrix(441,-100,1054,-239) (2/9,5/22) -> (5/12,18/43) Hyperbolic Matrix(815,-186,2686,-613) (5/22,8/35) -> (10/33,17/56) Hyperbolic Matrix(749,-172,884,-203) (8/35,3/13) -> (11/13,28/33) Hyperbolic Matrix(339,-79,442,-103) (3/13,4/17) -> (13/17,10/13) Hyperbolic Matrix(103,-25,136,-33) (4/17,1/4) -> (3/4,13/17) Hyperbolic Matrix(101,-26,136,-35) (1/4,4/15) -> (14/19,3/4) Hyperbolic Matrix(137,-37,374,-101) (4/15,3/11) -> (4/11,7/19) Hyperbolic Matrix(305,-84,374,-103) (3/11,5/18) -> (13/16,9/11) Hyperbolic Matrix(103,-29,238,-67) (5/18,2/7) -> (3/7,7/16) Hyperbolic Matrix(169,-49,238,-69) (2/7,5/17) -> (12/17,5/7) Hyperbolic Matrix(239,-71,340,-101) (5/17,3/10) -> (7/10,12/17) Hyperbolic Matrix(1157,-349,1462,-441) (3/10,13/43) -> (34/43,19/24) Hyperbolic Matrix(3807,-1156,4930,-1497) (17/56,7/23) -> (61/79,17/22) Hyperbolic Matrix(239,-73,442,-135) (7/23,4/13) -> (7/13,6/11) Hyperbolic Matrix(271,-84,442,-137) (4/13,1/3) -> (19/31,8/13) Hyperbolic Matrix(67,-23,102,-35) (1/3,6/17) -> (11/17,2/3) Hyperbolic Matrix(307,-109,476,-169) (6/17,5/14) -> (9/14,11/17) Hyperbolic Matrix(373,-134,476,-171) (5/14,4/11) -> (18/23,11/14) Hyperbolic Matrix(373,-138,646,-239) (7/19,3/8) -> (15/26,11/19) Hyperbolic Matrix(169,-64,272,-103) (3/8,5/13) -> (13/21,5/8) Hyperbolic Matrix(305,-118,442,-171) (5/13,7/18) -> (11/16,9/13) Hyperbolic Matrix(137,-54,170,-67) (7/18,2/5) -> (4/5,13/16) Hyperbolic Matrix(101,-41,170,-69) (2/5,7/17) -> (10/17,3/5) Hyperbolic Matrix(239,-99,408,-169) (7/17,5/12) -> (7/12,10/17) Hyperbolic Matrix(1769,-741,2108,-883) (18/43,31/74) -> (5/6,21/25) Hyperbolic Matrix(5031,-2108,6494,-2721) (31/74,13/31) -> (55/71,31/40) Hyperbolic Matrix(1291,-542,2108,-885) (13/31,8/19) -> (30/49,19/31) Hyperbolic Matrix(407,-172,646,-273) (8/19,3/7) -> (17/27,12/19) Hyperbolic Matrix(305,-134,544,-239) (7/16,4/9) -> (14/25,9/16) Hyperbolic Matrix(239,-108,374,-169) (4/9,5/11) -> (7/11,16/25) Hyperbolic Matrix(307,-141,442,-203) (5/11,6/13) -> (9/13,16/23) Hyperbolic Matrix(373,-173,442,-205) (6/13,7/15) -> (16/19,11/13) Hyperbolic Matrix(271,-127,510,-239) (7/15,8/17) -> (9/17,8/15) Hyperbolic Matrix(35,-17,68,-33) (8/17,1/2) -> (1/2,9/17) Parabolic Matrix(239,-132,306,-169) (6/11,5/9) -> (7/9,18/23) Hyperbolic Matrix(647,-361,1156,-645) (5/9,19/34) -> (19/34,14/25) Parabolic Matrix(171,-97,238,-135) (9/16,4/7) -> (5/7,13/18) Hyperbolic Matrix(441,-256,646,-375) (11/19,18/31) -> (2/3,13/19) Hyperbolic Matrix(815,-474,1054,-613) (18/31,7/12) -> (17/22,24/31) Hyperbolic Matrix(443,-270,612,-373) (3/5,11/18) -> (13/18,21/29) Hyperbolic Matrix(4691,-2869,5950,-3639) (11/18,52/85) -> (67/85,41/52) Hyperbolic Matrix(6699,-4099,8500,-5201) (52/85,41/67) -> (26/33,67/85) Hyperbolic Matrix(715,-441,1156,-713) (8/13,21/34) -> (21/34,13/21) Parabolic Matrix(237,-149,272,-171) (5/8,17/27) -> (6/7,7/8) Hyperbolic Matrix(273,-173,374,-237) (12/19,7/11) -> (8/11,11/15) Hyperbolic Matrix(1019,-698,1292,-885) (13/19,11/16) -> (41/52,15/19) Hyperbolic Matrix(2073,-1444,2686,-1871) (16/23,23/33) -> (27/35,44/57) Hyperbolic Matrix(307,-214,340,-237) (23/33,7/10) -> (9/10,1/1) Hyperbolic Matrix(851,-625,1156,-849) (11/15,25/34) -> (25/34,14/19) Parabolic Matrix(14281,-11025,18496,-14279) (44/57,105/136) -> (105/136,61/79) Parabolic Matrix(8059,-6241,10404,-8057) (24/31,79/102) -> (79/102,55/71) Parabolic Matrix(953,-750,1122,-883) (11/14,26/33) -> (28/33,17/20) Hyperbolic Matrix(1087,-859,1292,-1021) (15/19,34/43) -> (21/25,16/19) Hyperbolic Matrix(919,-729,1156,-917) (23/29,27/34) -> (27/34,4/5) Parabolic Matrix(987,-841,1156,-985) (23/27,29/34) -> (29/34,6/7) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-32,1) Matrix(103,-10,340,-33) -> Matrix(13,4,-140,-43) Matrix(271,-31,306,-35) -> Matrix(27,7,-760,-197) Matrix(239,-29,272,-33) -> Matrix(25,6,-696,-167) Matrix(137,-19,238,-33) -> Matrix(5,1,-76,-15) Matrix(579,-86,680,-101) -> Matrix(71,14,-1912,-377) Matrix(681,-104,884,-135) -> Matrix(53,10,-1288,-243) Matrix(237,-37,442,-69) -> Matrix(5,1,-96,-19) Matrix(271,-43,1292,-205) -> Matrix(9,2,-68,-15) Matrix(817,-131,1054,-169) -> Matrix(5,1,-136,-27) Matrix(169,-29,204,-35) -> Matrix(23,4,-604,-105) Matrix(307,-55,374,-67) -> Matrix(43,7,-1112,-181) Matrix(271,-50,374,-69) -> Matrix(7,1,-148,-21) Matrix(647,-134,816,-169) -> Matrix(99,14,-2468,-349) Matrix(579,-121,646,-135) -> Matrix(79,11,-2248,-313) Matrix(1769,-374,2890,-611) -> Matrix(95,13,-1732,-237) Matrix(1599,-340,2074,-441) -> Matrix(141,19,-3436,-463) Matrix(305,-66,476,-103) -> Matrix(1,0,-12,1) Matrix(441,-100,1054,-239) -> Matrix(7,1,-120,-17) Matrix(815,-186,2686,-613) -> Matrix(113,15,-1228,-163) Matrix(749,-172,884,-203) -> Matrix(77,10,-2056,-267) Matrix(339,-79,442,-103) -> Matrix(55,7,-1328,-169) Matrix(103,-25,136,-33) -> Matrix(17,2,-400,-47) Matrix(101,-26,136,-35) -> Matrix(17,2,-400,-47) Matrix(137,-37,374,-101) -> Matrix(9,1,-136,-15) Matrix(305,-84,374,-103) -> Matrix(11,1,-276,-25) Matrix(103,-29,238,-67) -> Matrix(9,1,-136,-15) Matrix(169,-49,238,-69) -> Matrix(29,3,-648,-67) Matrix(239,-71,340,-101) -> Matrix(41,4,-892,-87) Matrix(1157,-349,1462,-441) -> Matrix(137,13,-3404,-323) Matrix(3807,-1156,4930,-1497) -> Matrix(229,21,-5616,-515) Matrix(239,-73,442,-135) -> Matrix(11,1,-188,-17) Matrix(271,-84,442,-137) -> Matrix(9,1,-172,-19) Matrix(67,-23,102,-35) -> Matrix(11,1,-232,-21) Matrix(307,-109,476,-169) -> Matrix(49,4,-968,-79) Matrix(373,-134,476,-171) -> Matrix(1,0,-12,1) Matrix(373,-138,646,-239) -> Matrix(11,1,-188,-17) Matrix(169,-64,272,-103) -> Matrix(25,2,-488,-39) Matrix(305,-118,442,-171) -> Matrix(13,1,-300,-23) Matrix(137,-54,170,-67) -> Matrix(15,1,-376,-25) Matrix(101,-41,170,-69) -> Matrix(13,1,-248,-19) Matrix(239,-99,408,-169) -> Matrix(29,2,-508,-35) Matrix(1769,-741,2108,-883) -> Matrix(35,2,-928,-53) Matrix(5031,-2108,6494,-2721) -> Matrix(19,1,-476,-25) Matrix(1291,-542,2108,-885) -> Matrix(27,2,-500,-37) Matrix(407,-172,646,-273) -> Matrix(15,1,-316,-21) Matrix(305,-134,544,-239) -> Matrix(29,2,-508,-35) Matrix(239,-108,374,-169) -> Matrix(17,1,-324,-19) Matrix(307,-141,442,-203) -> Matrix(15,1,-316,-21) Matrix(373,-173,442,-205) -> Matrix(13,1,-352,-27) Matrix(271,-127,510,-239) -> Matrix(15,1,-256,-17) Matrix(35,-17,68,-33) -> Matrix(1,0,0,1) Matrix(239,-132,306,-169) -> Matrix(15,1,-376,-25) Matrix(647,-361,1156,-645) -> Matrix(67,4,-1156,-69) Matrix(171,-97,238,-135) -> Matrix(17,1,-392,-23) Matrix(441,-256,646,-375) -> Matrix(19,1,-400,-21) Matrix(815,-474,1054,-613) -> Matrix(15,1,-376,-25) Matrix(443,-270,612,-373) -> Matrix(1,0,-4,1) Matrix(4691,-2869,5950,-3639) -> Matrix(231,13,-5704,-321) Matrix(6699,-4099,8500,-5201) -> Matrix(579,32,-14276,-789) Matrix(715,-441,1156,-713) -> Matrix(151,8,-2888,-153) Matrix(237,-149,272,-171) -> Matrix(41,2,-1128,-55) Matrix(273,-173,374,-237) -> Matrix(17,1,-392,-23) Matrix(1019,-698,1292,-885) -> Matrix(217,10,-5360,-247) Matrix(2073,-1444,2686,-1871) -> Matrix(317,15,-7756,-367) Matrix(307,-214,340,-237) -> Matrix(85,4,-2444,-115) Matrix(851,-625,1156,-849) -> Matrix(367,16,-8464,-369) Matrix(14281,-11025,18496,-14279) -> Matrix(2743,112,-67228,-2745) Matrix(8059,-6241,10404,-8057) -> Matrix(299,12,-7500,-301) Matrix(953,-750,1122,-883) -> Matrix(319,13,-8564,-349) Matrix(1087,-859,1292,-1021) -> Matrix(49,2,-1348,-55) Matrix(919,-729,1156,-917) -> Matrix(499,20,-12500,-501) Matrix(987,-841,1156,-985) -> Matrix(647,24,-17496,-649) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 36 ----------------------------------------------------------------------- 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 1/0 1 34 1/9 -1/4 1 34 2/17 -1/4 13 2 1/8 (-1/4,-3/13) 0 17 1/7 -5/24 1 34 5/34 -1/5 24 1 3/20 (-1/5,-7/36) 0 17 2/13 -3/16 1 34 3/19 -3/16 1 34 4/25 -3/16 1 34 1/6 (-2/11,-1/6) 0 17 3/17 -1/6 11 2 2/11 -7/44 1 34 1/5 -3/20 1 34 7/34 -1/7 20 1 5/24 (-1/7,-7/50) 0 17 9/43 -5/36 1 34 4/19 -5/36 1 34 7/33 -19/140 1 34 3/14 (-2/15,-1/8) 0 17 2/9 -1/8 1 34 5/22 (-3/22,-2/15) 0 17 8/35 -19/144 1 34 11/48 (-11/84,-3/23) 0 17 3/13 -1/8 1 34 4/17 -1/8 9 2 1/4 (-1/8,-1/9) 0 17 9/34 -1/9 16 1 4/15 -7/64 1 34 3/11 -5/48 1 34 5/18 (-1/10,0/1) 0 17 2/7 -3/28 1 34 5/17 -1/10 7 2 3/10 (-1/10,-2/21) 0 17 13/43 -3/32 1 34 10/33 -13/140 1 34 17/56 (-9/98,-1/11) 0 17 31/102 -1/11 28 1 7/23 -5/56 1 34 4/13 -1/12 1 34 1/3 -1/12 1 34 6/17 -1/12 5 2 5/14 (-1/12,-2/25) 0 17 4/11 -3/40 1 34 7/19 -1/8 1 34 3/8 (-1/12,-1/13) 0 17 13/34 -1/13 8 1 5/13 -3/40 1 34 12/31 -3/40 1 34 7/18 (-1/14,0/1) 0 17 9/23 -5/68 1 34 2/5 -1/12 1 34 7/17 -1/14 3 2 5/12 (-1/14,-1/15) 0 17 18/43 -1/16 1 34 31/74 (-1/18,0/1) 0 17 57/136 0/1 12 1 13/31 -1/12 1 34 21/50 (-2/27,-1/14) 0 17 50/119 -1/14 15 2 29/69 -11/156 1 34 8/19 -3/44 1 34 11/26 (-2/31,-1/16) 0 17 3/7 -1/12 1 34 7/16 (-1/14,-1/15) 0 17 15/34 -1/15 4 1 4/9 -1/16 1 34 9/20 (-1/15,-1/16) 0 17 5/11 -1/20 1 34 6/13 -1/16 1 34 7/15 -1/16 1 34 8/17 -1/16 1 2 1/2 (-1/16,0/1) 0 17 1/0 0/1 32 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(103,-10,340,-33) (0/1,1/9) -> (13/43,10/33) Hyperbolic Matrix(35,-4,306,-35) (1/9,2/17) -> (1/9,2/17) Reflection Matrix(33,-4,272,-33) (2/17,1/8) -> (2/17,1/8) Reflection Matrix(101,-14,238,-33) (1/8,1/7) -> (11/26,3/7) Glide Reflection Matrix(69,-10,476,-69) (1/7,5/34) -> (1/7,5/34) Reflection Matrix(101,-15,680,-101) (5/34,3/20) -> (5/34,3/20) Reflection Matrix(203,-31,884,-135) (3/20,2/13) -> (11/48,3/13) Glide Reflection Matrix(205,-32,442,-69) (2/13,3/19) -> (6/13,7/15) Glide Reflection Matrix(271,-43,1292,-205) (3/19,4/25) -> (9/43,4/19) Hyperbolic Matrix(883,-142,2108,-339) (4/25,1/6) -> (18/43,31/74) Glide Reflection Matrix(35,-6,204,-35) (1/6,3/17) -> (1/6,3/17) Reflection Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(67,-13,170,-33) (2/11,1/5) -> (9/23,2/5) Glide Reflection Matrix(69,-14,340,-69) (1/5,7/34) -> (1/5,7/34) Reflection Matrix(169,-35,816,-169) (7/34,5/24) -> (7/34,5/24) Reflection Matrix(441,-92,1462,-305) (5/24,9/43) -> (3/10,13/43) Glide Reflection Matrix(815,-172,1938,-409) (4/19,7/33) -> (29/69,8/19) Hyperbolic Matrix(475,-101,2074,-441) (7/33,3/14) -> (8/35,11/48) Glide Reflection Matrix(137,-30,306,-67) (3/14,2/9) -> (4/9,9/20) Hyperbolic Matrix(441,-100,1054,-239) (2/9,5/22) -> (5/12,18/43) Hyperbolic Matrix(815,-186,2686,-613) (5/22,8/35) -> (10/33,17/56) Hyperbolic Matrix(103,-24,442,-103) (3/13,4/17) -> (3/13,4/17) Reflection Matrix(33,-8,136,-33) (4/17,1/4) -> (4/17,1/4) Reflection Matrix(35,-9,136,-35) (1/4,9/34) -> (1/4,9/34) Reflection Matrix(271,-72,1020,-271) (9/34,4/15) -> (9/34,4/15) Reflection Matrix(137,-37,374,-101) (4/15,3/11) -> (4/11,7/19) Hyperbolic Matrix(239,-66,612,-169) (3/11,5/18) -> (7/18,9/23) Hyperbolic Matrix(103,-29,238,-67) (5/18,2/7) -> (3/7,7/16) Hyperbolic Matrix(69,-20,238,-69) (2/7,5/17) -> (2/7,5/17) Reflection Matrix(101,-30,340,-101) (5/17,3/10) -> (5/17,3/10) Reflection Matrix(1735,-527,5712,-1735) (17/56,31/102) -> (17/56,31/102) Reflection Matrix(1427,-434,4692,-1427) (31/102,7/23) -> (31/102,7/23) Reflection Matrix(203,-62,442,-135) (7/23,4/13) -> (5/11,6/13) Glide Reflection Matrix(171,-53,442,-137) (4/13,1/3) -> (5/13,12/31) Glide Reflection Matrix(35,-12,102,-35) (1/3,6/17) -> (1/3,6/17) Reflection Matrix(169,-60,476,-169) (6/17,5/14) -> (6/17,5/14) Reflection Matrix(169,-61,374,-135) (5/14,4/11) -> (9/20,5/11) Glide Reflection Matrix(273,-101,646,-239) (7/19,3/8) -> (8/19,11/26) Glide Reflection Matrix(103,-39,272,-103) (3/8,13/34) -> (3/8,13/34) Reflection Matrix(339,-130,884,-339) (13/34,5/13) -> (13/34,5/13) Reflection Matrix(885,-343,2108,-817) (12/31,7/18) -> (13/31,21/50) Glide Reflection Matrix(69,-28,170,-69) (2/5,7/17) -> (2/5,7/17) Reflection Matrix(169,-70,408,-169) (7/17,5/12) -> (7/17,5/12) Reflection Matrix(4217,-1767,10064,-4217) (31/74,57/136) -> (31/74,57/136) Reflection Matrix(3535,-1482,8432,-3535) (57/136,13/31) -> (57/136,13/31) Reflection Matrix(4999,-2100,11900,-4999) (21/50,50/119) -> (21/50,50/119) Reflection Matrix(6901,-2900,16422,-6901) (50/119,29/69) -> (50/119,29/69) Reflection Matrix(239,-105,544,-239) (7/16,15/34) -> (7/16,15/34) Reflection Matrix(271,-120,612,-271) (15/34,4/9) -> (15/34,4/9) Reflection Matrix(239,-112,510,-239) (7/15,8/17) -> (7/15,8/17) Reflection Matrix(33,-16,68,-33) (8/17,1/2) -> (8/17,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(103,-10,340,-33) -> Matrix(13,4,-140,-43) Matrix(35,-4,306,-35) -> Matrix(27,7,-104,-27) (1/9,2/17) -> (-7/26,-1/4) Matrix(33,-4,272,-33) -> Matrix(25,6,-104,-25) (2/17,1/8) -> (-1/4,-3/13) Matrix(101,-14,238,-33) -> Matrix(5,1,-84,-17) Matrix(69,-10,476,-69) -> Matrix(49,10,-240,-49) (1/7,5/34) -> (-5/24,-1/5) Matrix(101,-15,680,-101) -> Matrix(71,14,-360,-71) (5/34,3/20) -> (-1/5,-7/36) Matrix(203,-31,884,-135) -> Matrix(53,10,-408,-77) Matrix(205,-32,442,-69) -> Matrix(5,1,-64,-13) Matrix(271,-43,1292,-205) -> Matrix(9,2,-68,-15) Matrix(883,-142,2108,-339) -> Matrix(11,2,-192,-35) Matrix(35,-6,204,-35) -> Matrix(23,4,-132,-23) (1/6,3/17) -> (-2/11,-1/6) Matrix(67,-12,374,-67) -> Matrix(43,7,-264,-43) (3/17,2/11) -> (-1/6,-7/44) Matrix(67,-13,170,-33) -> Matrix(7,1,-104,-15) Matrix(69,-14,340,-69) -> Matrix(41,6,-280,-41) (1/5,7/34) -> (-3/20,-1/7) Matrix(169,-35,816,-169) -> Matrix(99,14,-700,-99) (7/34,5/24) -> (-1/7,-7/50) Matrix(441,-92,1462,-305) -> Matrix(93,13,-980,-137) Matrix(815,-172,1938,-409) -> Matrix(51,7,-736,-101) Matrix(475,-101,2074,-441) -> Matrix(141,19,-1076,-145) Matrix(137,-30,306,-67) -> Matrix(7,1,-120,-17) Matrix(441,-100,1054,-239) -> Matrix(7,1,-120,-17) Matrix(815,-186,2686,-613) -> Matrix(113,15,-1228,-163) Matrix(103,-24,442,-103) -> Matrix(55,7,-432,-55) (3/13,4/17) -> (-7/54,-1/8) Matrix(33,-8,136,-33) -> Matrix(17,2,-144,-17) (4/17,1/4) -> (-1/8,-1/9) Matrix(35,-9,136,-35) -> Matrix(17,2,-144,-17) (1/4,9/34) -> (-1/8,-1/9) Matrix(271,-72,1020,-271) -> Matrix(127,14,-1152,-127) (9/34,4/15) -> (-1/9,-7/64) Matrix(137,-37,374,-101) -> Matrix(9,1,-136,-15) Matrix(239,-66,612,-169) -> Matrix(1,0,-4,1) 0/1 Matrix(103,-29,238,-67) -> Matrix(9,1,-136,-15) Matrix(69,-20,238,-69) -> Matrix(29,3,-280,-29) (2/7,5/17) -> (-3/28,-1/10) Matrix(101,-30,340,-101) -> Matrix(41,4,-420,-41) (5/17,3/10) -> (-1/10,-2/21) Matrix(1735,-527,5712,-1735) -> Matrix(197,18,-2156,-197) (17/56,31/102) -> (-9/98,-1/11) Matrix(1427,-434,4692,-1427) -> Matrix(111,10,-1232,-111) (31/102,7/23) -> (-1/11,-5/56) Matrix(203,-62,442,-135) -> Matrix(11,1,-164,-15) Matrix(171,-53,442,-137) -> Matrix(9,1,-116,-13) Matrix(35,-12,102,-35) -> Matrix(11,1,-120,-11) (1/3,6/17) -> (-1/10,-1/12) Matrix(169,-60,476,-169) -> Matrix(49,4,-600,-49) (6/17,5/14) -> (-1/12,-2/25) Matrix(169,-61,374,-135) -> Matrix(13,1,-220,-17) Matrix(273,-101,646,-239) -> Matrix(11,1,-164,-15) Matrix(103,-39,272,-103) -> Matrix(25,2,-312,-25) (3/8,13/34) -> (-1/12,-1/13) Matrix(339,-130,884,-339) -> Matrix(79,6,-1040,-79) (13/34,5/13) -> (-1/13,-3/40) Matrix(885,-343,2108,-817) -> Matrix(27,2,-364,-27) *** -> (-1/13,-1/14) Matrix(69,-28,170,-69) -> Matrix(13,1,-168,-13) (2/5,7/17) -> (-1/12,-1/14) Matrix(169,-70,408,-169) -> Matrix(29,2,-420,-29) (7/17,5/12) -> (-1/14,-1/15) Matrix(4217,-1767,10064,-4217) -> Matrix(-1,0,36,1) (31/74,57/136) -> (-1/18,0/1) Matrix(3535,-1482,8432,-3535) -> Matrix(-1,0,24,1) (57/136,13/31) -> (-1/12,0/1) Matrix(4999,-2100,11900,-4999) -> Matrix(55,4,-756,-55) (21/50,50/119) -> (-2/27,-1/14) Matrix(6901,-2900,16422,-6901) -> Matrix(155,11,-2184,-155) (50/119,29/69) -> (-1/14,-11/156) Matrix(239,-105,544,-239) -> Matrix(29,2,-420,-29) (7/16,15/34) -> (-1/14,-1/15) Matrix(271,-120,612,-271) -> Matrix(31,2,-480,-31) (15/34,4/9) -> (-1/15,-1/16) Matrix(239,-112,510,-239) -> Matrix(15,1,-224,-15) (7/15,8/17) -> (-1/14,-1/16) Matrix(33,-16,68,-33) -> Matrix(-1,0,32,1) (8/17,1/2) -> (-1/16,0/1) Matrix(-1,1,0,1) -> Matrix(-1,0,32,1) (1/2,1/0) -> (-1/16,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.