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 1/2 -8/9 3/8 -15/17 1/2 -7/8 3/5 -6/7 3/4 -17/20 1/1 -11/13 1/2 -16/19 1/0 -21/25 -1/2 -5/6 0/1 -14/17 1/2 -23/28 5/9 -9/11 1/2 -13/16 5/7 -4/5 3/4 -19/24 1/1 -34/43 7/4 -15/19 3/2 -26/33 1/0 -37/47 -1/2 -48/61 -1/4 -11/14 0/1 -7/9 3/2 -31/40 1/1 -24/31 1/0 -17/22 0/1 -44/57 1/4 -27/35 1/2 -10/13 1/0 -33/43 -1/2 -23/30 0/1 -13/17 1/2 -3/4 1/1 -11/15 7/6 -19/26 2/1 -46/63 5/4 -27/37 3/2 -8/11 1/0 -13/18 2/3 -18/25 9/8 -23/32 1/1 -5/7 3/2 -22/31 1/0 -17/24 3/1 -12/17 1/0 -7/10 0/1 -37/53 1/2 -30/43 3/8 -23/33 1/2 -39/56 1/1 -16/23 1/0 -25/36 1/1 -34/49 1/0 -9/13 1/2 -29/42 4/3 -20/29 1/0 -11/16 3/1 -35/51 1/0 -24/35 1/0 -13/19 -1/2 -2/3 1/0 -13/20 3/1 -11/17 1/0 -9/14 -2/1 -7/11 -1/2 -19/30 0/1 -12/19 1/4 -29/46 0/1 -17/27 1/2 -5/8 -1/1 -8/13 1/4 -27/44 1/3 -19/31 1/2 -11/18 2/3 -14/23 1/0 -17/28 -1/1 -20/33 1/0 -3/5 1/2 -16/27 1/0 -13/22 2/1 -10/17 1/0 -7/12 -1/1 -32/55 1/0 -25/43 1/2 -43/74 0/1 -18/31 1/0 -11/19 -3/2 -15/26 -2/3 -49/85 -1/2 -34/59 -5/12 -19/33 -1/2 -23/40 -1/3 -4/7 1/0 -17/30 0/1 -13/23 -1/2 -9/16 -1/5 -5/9 1/6 -21/38 0/1 -16/29 1/0 -43/78 0/1 -27/49 1/6 -11/20 1/3 -17/31 1/2 -6/11 1/0 -19/35 1/2 -32/59 5/8 -13/24 1/1 -7/13 1/2 -22/41 1/4 -15/28 1/1 -23/43 3/2 -8/15 1/0 -17/32 1/1 -9/17 1/0 -1/2 0/1 -8/17 1/2 -7/15 1/2 -13/28 1/1 -6/13 1/0 -11/24 1/1 -16/35 1/0 -5/11 1/2 -14/31 1/0 -9/20 -1/1 -22/49 -1/4 -35/78 0/1 -48/107 -1/12 -61/136 0/1 -13/29 1/2 -30/67 1/0 -17/38 0/1 -4/9 -1/4 -15/34 0/1 -11/25 1/18 -7/16 1/7 -10/23 1/4 -3/7 1/2 -20/47 1/4 -17/40 1/5 -14/33 1/4 -25/59 5/22 -11/26 2/7 -8/19 3/8 -29/69 1/2 -50/119 1/2 -21/50 2/3 -13/31 1/2 -57/136 0/1 -44/105 1/4 -31/74 0/1 -18/43 1/0 -23/55 1/2 -5/12 1/3 -7/17 1/2 -9/22 2/3 -11/27 1/2 -13/32 1/1 -15/37 1/2 -2/5 1/0 -7/18 2/1 -33/85 1/0 -26/67 1/0 -19/49 -3/2 -12/31 1/0 -17/44 -1/1 -5/13 -1/2 -13/34 0/1 -8/21 1/8 -3/8 1/3 -10/27 1/0 -17/46 0/1 -24/65 1/0 -7/19 -1/2 -25/68 0/1 -18/49 1/12 -11/30 0/1 -37/101 1/6 -26/71 1/4 -15/41 1/2 -4/11 1/4 -13/36 1/3 -9/25 5/14 -5/14 2/5 -6/17 1/2 -7/20 3/5 -1/3 1/2 -6/19 1/4 -5/16 3/5 -4/13 1/0 -11/36 1/1 -7/23 1/2 -31/102 1/1 -24/79 5/4 -17/56 1/1 -27/89 3/2 -10/33 1/0 -3/10 0/1 -5/17 1/2 -7/24 3/5 -9/31 1/2 -29/100 3/5 -20/69 5/8 -11/38 2/3 -2/7 3/4 -11/39 5/6 -9/32 1/1 -7/25 9/10 -19/68 1/1 -12/43 13/12 -5/18 2/1 -8/29 1/0 -27/98 0/1 -19/69 1/2 -11/40 1/3 -3/11 1/2 -10/37 3/4 -37/137 5/6 -101/374 1/1 -64/237 3/4 -27/100 1/1 -17/63 5/6 -7/26 2/3 -4/15 7/8 -9/34 1/1 -5/19 7/6 -1/4 1/1 -4/17 1/0 -7/30 0/1 -10/43 1/4 -3/13 1/2 -11/48 1/1 -19/83 5/2 -8/35 1/0 -13/57 -1/2 -31/136 0/1 -18/79 1/4 -5/22 0/1 -12/53 1/4 -7/31 1/2 -23/102 1/1 -16/71 1/0 -9/40 1/1 -11/49 1/2 -2/9 3/4 -7/32 1/1 -5/23 3/2 -3/14 0/1 -16/75 -1/4 -29/136 0/1 -13/61 1/6 -10/47 1/4 -17/80 1/3 -7/33 1/2 -18/85 1/2 -11/52 5/9 -4/19 3/4 -9/43 7/10 -14/67 3/4 -5/24 1/1 -6/29 11/12 -7/34 1/1 -1/5 3/2 -5/26 0/1 -9/47 5/6 -13/68 1/1 -4/21 5/4 -3/16 5/3 -2/11 1/0 -5/28 5/1 -3/17 1/0 -1/6 0/1 -4/25 1/4 -3/19 1/2 -8/51 1/2 -5/32 1/1 -2/13 1/0 -5/33 1/2 -8/53 5/8 -3/20 1/1 -4/27 7/8 -5/34 1/1 -1/7 3/2 -1/8 3/1 -2/17 1/0 -3/26 -6/1 -1/9 -3/2 -2/19 1/0 -1/10 0/1 0/1 1/0 1/9 3/2 2/17 1/0 1/8 -3/1 1/7 -3/2 3/20 -1/1 2/13 1/0 3/19 -1/2 4/25 -1/4 1/6 0/1 3/17 1/0 5/28 -5/1 2/11 1/0 3/16 -5/3 1/5 -3/2 5/24 -1/1 9/43 -7/10 4/19 -3/4 7/33 -1/2 10/47 -1/4 13/61 -1/6 3/14 0/1 2/9 -3/4 9/40 -1/1 7/31 -1/2 5/22 0/1 13/57 1/2 8/35 1/0 3/13 -1/2 10/43 -1/4 7/30 0/1 4/17 1/0 1/4 -1/1 4/15 -7/8 7/26 -2/3 17/63 -5/6 10/37 -3/4 3/11 -1/2 5/18 -2/1 7/25 -9/10 9/32 -1/1 2/7 -3/4 9/31 -1/2 7/24 -3/5 5/17 -1/2 3/10 0/1 16/53 1/0 13/43 3/2 10/33 1/0 17/56 -1/1 7/23 -1/2 11/36 -1/1 15/49 -1/2 4/13 1/0 13/42 -4/5 9/29 -1/2 5/16 -3/5 16/51 -1/2 11/35 -1/2 6/19 -1/4 1/3 -1/2 7/20 -3/5 6/17 -1/2 5/14 -2/5 4/11 -1/4 11/30 0/1 7/19 1/2 17/46 0/1 10/27 1/0 3/8 -1/3 5/13 1/2 17/44 1/1 12/31 1/0 7/18 -2/1 9/23 -1/2 11/28 -1/3 13/33 -1/2 2/5 1/0 11/27 -1/2 9/22 -2/3 7/17 -1/2 5/12 -1/3 23/55 -1/2 18/43 1/0 31/74 0/1 13/31 -1/2 8/19 -3/8 11/26 -2/7 36/85 -1/4 25/59 -5/22 14/33 -1/4 17/40 -1/5 3/7 -1/2 13/30 0/1 10/23 -1/4 7/16 -1/7 4/9 1/4 17/38 0/1 13/29 -1/2 35/78 0/1 22/49 1/4 9/20 1/1 14/31 1/0 5/11 -1/2 16/35 1/0 27/59 -5/2 11/24 -1/1 6/13 1/0 19/41 1/2 13/28 -1/1 20/43 -3/4 7/15 -1/2 15/32 -1/1 8/17 -1/2 1/2 0/1 9/17 1/0 8/15 1/0 15/28 -1/1 7/13 -1/2 13/24 -1/1 19/35 -1/2 6/11 1/0 17/31 -1/2 11/20 -1/3 27/49 -1/6 43/78 0/1 59/107 -1/14 75/136 0/1 16/29 1/0 37/67 -1/2 21/38 0/1 5/9 -1/6 19/34 0/1 14/25 1/16 9/16 1/5 13/23 1/2 4/7 1/0 27/47 1/2 23/40 1/3 19/33 1/2 34/59 5/12 15/26 2/3 11/19 3/2 40/69 1/0 69/119 1/0 29/50 -2/1 18/31 1/0 79/136 0/1 61/105 1/2 43/74 0/1 25/43 -1/2 32/55 1/0 7/12 1/1 10/17 1/0 13/22 -2/1 16/27 1/0 19/32 -1/1 22/37 1/0 3/5 -1/2 11/18 -2/3 52/85 -1/2 41/67 -1/2 30/49 -3/8 19/31 -1/2 27/44 -1/3 8/13 -1/4 21/34 0/1 13/21 1/6 5/8 1/1 17/27 -1/2 29/46 0/1 41/65 -1/2 12/19 -1/4 43/68 0/1 31/49 1/10 19/30 0/1 64/101 1/4 45/71 1/2 26/41 1/0 7/11 1/2 23/36 1/1 16/25 5/4 9/14 2/1 11/17 1/0 13/20 -3/1 2/3 1/0 13/19 1/2 11/16 -3/1 9/13 -1/2 25/36 -1/1 16/23 1/0 71/102 -1/1 55/79 -5/6 39/56 -1/1 62/89 -3/4 23/33 -1/2 7/10 0/1 12/17 1/0 17/24 -3/1 22/31 1/0 71/100 -3/1 49/69 -5/2 27/38 -2/1 5/7 -3/2 28/39 -5/4 23/32 -1/1 18/25 -9/8 49/68 -1/1 31/43 -13/14 13/18 -2/3 21/29 -1/2 71/98 0/1 50/69 1/0 29/40 1/1 8/11 1/0 27/37 -3/2 100/137 -5/4 273/374 -1/1 173/237 -3/2 73/100 -1/1 46/63 -5/4 19/26 -2/1 11/15 -7/6 25/34 -1/1 14/19 -7/8 3/4 -1/1 13/17 -1/2 23/30 0/1 33/43 1/2 10/13 1/0 37/48 -1/1 64/83 -5/8 27/35 -1/2 44/57 -1/4 105/136 0/1 61/79 1/2 17/22 0/1 41/53 1/2 24/31 1/0 79/102 -1/1 55/71 -1/2 31/40 -1/1 38/49 1/0 7/9 -3/2 25/32 -1/1 18/23 -3/4 11/14 0/1 59/75 -1/6 107/136 0/1 48/61 1/4 37/47 1/2 63/80 1/1 26/33 1/0 67/85 1/0 41/52 -5/1 15/19 -3/2 34/43 -7/4 53/67 -3/2 19/24 -1/1 23/29 -11/10 27/34 -1/1 4/5 -3/4 21/26 0/1 38/47 -5/4 55/68 -1/1 17/21 -5/6 13/16 -5/7 9/11 -1/2 23/28 -5/9 14/17 -1/2 5/6 0/1 21/25 1/2 16/19 1/0 43/51 1/0 27/32 -1/1 11/13 -1/2 28/33 1/0 45/53 -5/2 17/20 -1/1 23/27 -7/6 29/34 -1/1 6/7 -3/4 7/8 -3/5 15/17 -1/2 23/26 -6/13 8/9 -3/8 17/19 -1/2 9/10 0/1 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(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,-4,1) Matrix(237,214,-340,-307) -> Matrix(1,0,0,1) Matrix(1019,902,-1768,-1565) -> Matrix(9,-4,-20,9) Matrix(239,210,272,239) -> Matrix(11,-6,-20,11) Matrix(101,88,272,237) -> Matrix(3,-2,-4,3) Matrix(101,86,-680,-579) -> Matrix(3,-4,4,-5) Matrix(203,172,-884,-749) -> Matrix(1,0,0,1) Matrix(613,518,-884,-747) -> Matrix(1,0,0,1) Matrix(271,228,1292,1087) -> Matrix(3,-2,-4,3) Matrix(1225,1028,2108,1769) -> Matrix(1,0,0,1) Matrix(169,140,204,169) -> Matrix(1,0,-4,1) Matrix(783,644,952,783) -> Matrix(19,-10,-36,19) Matrix(373,306,952,781) -> Matrix(7,-4,-12,7) Matrix(307,250,544,443) -> Matrix(3,-2,8,-5) Matrix(375,304,-544,-441) -> Matrix(5,-4,4,-3) Matrix(169,134,-816,-647) -> Matrix(7,-8,8,-9) Matrix(1327,1050,-2448,-1937) -> Matrix(3,-4,4,-5) Matrix(205,162,1292,1021) -> Matrix(1,-2,0,1) Matrix(885,698,-1292,-1019) -> Matrix(1,-2,0,1) Matrix(1361,1072,-4488,-3535) -> Matrix(1,2,0,1) Matrix(1835,1444,3196,2515) -> Matrix(1,0,4,1) Matrix(407,320,-1904,-1497) -> Matrix(1,0,0,1) Matrix(171,134,-476,-373) -> Matrix(3,-2,8,-5) Matrix(1055,818,-1972,-1529) -> Matrix(1,0,0,1) Matrix(919,712,-4080,-3161) -> Matrix(1,0,0,1) Matrix(1055,816,-2856,-2209) -> Matrix(1,0,0,1) Matrix(681,526,-2992,-2311) -> Matrix(1,0,0,1) Matrix(1293,998,2380,1837) -> Matrix(1,0,-4,1) Matrix(135,104,-884,-681) -> Matrix(1,0,0,1) Matrix(1701,1306,2924,2245) -> Matrix(1,0,0,1) Matrix(1053,808,1904,1461) -> Matrix(1,0,-4,1) Matrix(781,598,1020,781) -> Matrix(1,0,-4,1) Matrix(103,78,136,103) -> Matrix(3,-2,-4,3) Matrix(35,26,-136,-101) -> Matrix(1,0,0,1) Matrix(511,374,884,647) -> Matrix(3,-4,4,-5) Matrix(1427,1042,1768,1291) -> Matrix(1,-2,0,1) Matrix(1019,744,-2516,-1837) -> Matrix(3,-4,4,-5) Matrix(409,298,748,545) -> Matrix(1,-2,0,1) Matrix(373,270,-612,-443) -> Matrix(1,0,0,1) Matrix(341,246,-1224,-883) -> Matrix(5,-4,4,-3) Matrix(1087,782,1700,1223) -> Matrix(3,-4,4,-5) Matrix(443,318,-1088,-781) -> Matrix(3,-4,4,-5) Matrix(647,460,-1768,-1257) -> Matrix(1,-2,4,-7) Matrix(815,578,2108,1495) -> Matrix(1,-2,0,1) Matrix(577,408,816,577) -> Matrix(1,-6,0,1) Matrix(239,168,340,239) -> Matrix(1,0,0,1) Matrix(2549,1780,4624,3229) -> Matrix(1,0,-8,1) Matrix(1361,950,2924,2041) -> Matrix(1,0,-4,1) Matrix(953,664,-4488,-3127) -> Matrix(3,-2,8,-5) Matrix(1735,1208,-5712,-3977) -> Matrix(5,-4,4,-3) Matrix(1223,850,1564,1087) -> Matrix(3,-2,-4,3) Matrix(1121,778,-2108,-1463) -> Matrix(1,0,0,1) Matrix(443,306,-2312,-1597) -> Matrix(3,-4,4,-5) Matrix(2483,1714,3400,2347) -> Matrix(5,-6,-4,5) Matrix(3163,2172,4012,2755) -> Matrix(1,-8,0,1) Matrix(4455,3056,7684,5271) -> Matrix(1,8,0,1) Matrix(477,326,-1292,-883) -> Matrix(1,0,0,1) Matrix(307,200,680,443) -> Matrix(1,-2,0,1) Matrix(441,286,680,441) -> Matrix(1,-6,0,1) Matrix(307,198,476,307) -> Matrix(1,4,0,1) Matrix(103,66,-476,-305) -> Matrix(1,2,0,1) Matrix(577,366,-1020,-647) -> Matrix(1,0,0,1) Matrix(749,474,-2040,-1291) -> Matrix(1,0,8,1) Matrix(647,408,-2856,-1801) -> Matrix(1,0,0,1) Matrix(749,472,1836,1157) -> Matrix(3,-2,-4,3) Matrix(35,22,272,171) -> Matrix(1,-2,0,1) Matrix(103,64,-272,-169) -> Matrix(1,0,4,1) Matrix(407,250,884,543) -> Matrix(1,0,-4,1) Matrix(613,376,2108,1293) -> Matrix(3,-2,-4,3) Matrix(885,542,-2108,-1291) -> Matrix(1,0,0,1) Matrix(171,104,952,579) -> Matrix(1,-4,0,1) Matrix(953,578,2244,1361) -> Matrix(1,0,-4,1) Matrix(579,350,-1292,-781) -> Matrix(1,0,0,1) Matrix(307,182,-1088,-645) -> Matrix(3,-4,4,-5) Matrix(679,402,1836,1087) -> Matrix(1,-2,0,1) Matrix(441,260,748,441) -> Matrix(1,-4,0,1) Matrix(239,140,408,239) -> Matrix(1,2,0,1) Matrix(1055,614,-4964,-2889) -> Matrix(1,0,4,1) Matrix(2245,1306,2924,1701) -> Matrix(1,0,0,1) Matrix(1769,1028,2108,1225) -> Matrix(1,0,0,1) Matrix(4217,2450,-10064,-5847) -> Matrix(1,0,4,1) Matrix(817,474,-2108,-1223) -> Matrix(1,0,0,1) Matrix(647,374,884,511) -> Matrix(5,4,-4,-3) Matrix(2345,1352,2652,1529) -> Matrix(15,8,-32,-17) Matrix(2177,1254,-4012,-2311) -> Matrix(1,0,4,1) Matrix(883,508,2244,1291) -> Matrix(1,0,0,1) Matrix(985,566,-1836,-1055) -> Matrix(1,0,4,1) Matrix(137,78,-476,-271) -> Matrix(3,2,4,3) Matrix(443,250,544,307) -> Matrix(5,2,-8,-3) Matrix(239,134,-544,-305) -> Matrix(1,0,12,1) Matrix(1461,808,1904,1053) -> Matrix(1,0,-4,1) Matrix(1087,600,-3944,-2177) -> Matrix(1,0,0,1) Matrix(4759,2624,-10608,-5849) -> Matrix(1,0,-12,1) Matrix(1767,974,1972,1087) -> Matrix(1,0,-8,1) Matrix(919,506,-4012,-2209) -> Matrix(7,-2,4,-1) Matrix(237,130,680,373) -> Matrix(3,-2,-4,3) Matrix(545,298,748,409) -> Matrix(1,-2,0,1) Matrix(1837,998,2380,1293) -> Matrix(1,0,-4,1) Matrix(341,184,884,477) -> Matrix(1,0,0,1) Matrix(2141,1150,2720,1461) -> Matrix(1,0,0,1) Matrix(883,472,2924,1563) -> Matrix(1,0,0,1) Matrix(1835,974,2176,1155) -> Matrix(1,-2,0,1) Matrix(35,18,68,35) -> Matrix(1,0,0,1) Matrix(33,16,68,33) -> Matrix(1,0,-4,1) Matrix(171,80,-1088,-509) -> Matrix(1,0,0,1) Matrix(443,206,-1972,-917) -> Matrix(1,0,0,1) Matrix(781,362,-1836,-851) -> Matrix(1,0,4,1) Matrix(543,250,884,407) -> Matrix(1,0,-4,1) Matrix(511,234,-2448,-1121) -> Matrix(3,-4,4,-5) Matrix(543,248,2380,1087) -> Matrix(1,0,0,1) Matrix(203,92,748,339) -> Matrix(3,-2,-4,3) Matrix(443,200,680,307) -> Matrix(1,-2,0,1) Matrix(307,138,-2040,-917) -> Matrix(3,2,4,3) Matrix(1395,626,4624,2075) -> Matrix(1,0,4,1) Matrix(10201,4576,18496,8297) -> Matrix(1,0,12,1) Matrix(10199,4574,18496,8295) -> Matrix(1,0,-16,1) Matrix(3705,1658,5848,2617) -> Matrix(1,0,4,1) Matrix(443,198,1904,851) -> Matrix(1,0,0,1) Matrix(647,286,1156,511) -> Matrix(1,0,20,1) Matrix(645,284,1156,509) -> Matrix(1,0,-24,1) Matrix(101,44,544,237) -> Matrix(9,-2,-4,1) Matrix(373,162,-1020,-443) -> Matrix(1,0,0,1) Matrix(681,290,3196,1361) -> Matrix(1,0,-8,1) Matrix(2957,1256,4080,1733) -> Matrix(1,0,-4,1) Matrix(1123,476,-5372,-2277) -> Matrix(19,-4,24,-5) Matrix(203,86,-1768,-749) -> Matrix(17,-4,-4,1) Matrix(237,100,884,373) -> Matrix(13,-4,-16,5) Matrix(647,272,-4284,-1801) -> Matrix(9,-4,16,-7) Matrix(2413,1014,7684,3229) -> Matrix(17,-8,-36,17) Matrix(3909,1642,6392,2685) -> Matrix(7,-4,-12,7) Matrix(10745,4504,18496,7753) -> Matrix(1,0,0,1) Matrix(10743,4502,18496,7751) -> Matrix(1,0,-4,1) Matrix(339,142,2108,883) -> Matrix(1,0,-4,1) Matrix(679,284,2924,1223) -> Matrix(1,0,-4,1) Matrix(1259,526,-4148,-1733) -> Matrix(7,-2,4,-1) Matrix(169,70,408,169) -> Matrix(5,-2,-12,5) Matrix(307,126,748,307) -> Matrix(7,-4,-12,7) Matrix(1157,472,1836,749) -> Matrix(3,-2,-4,3) Matrix(1361,552,-4692,-1903) -> Matrix(5,-2,8,-3) Matrix(169,66,-612,-239) -> Matrix(1,0,0,1) Matrix(3707,1440,6392,2483) -> Matrix(1,-4,0,1) Matrix(6699,2600,8500,3299) -> Matrix(1,6,0,1) Matrix(1665,646,-7276,-2823) -> Matrix(1,4,0,1) Matrix(1495,578,2108,815) -> Matrix(1,-2,0,1) Matrix(477,184,884,341) -> Matrix(1,0,0,1) Matrix(715,274,1156,443) -> Matrix(1,0,8,1) Matrix(713,272,1156,441) -> Matrix(1,0,-12,1) Matrix(237,88,272,101) -> Matrix(3,-2,-4,3) Matrix(1087,402,1836,679) -> Matrix(1,-2,0,1) Matrix(2925,1076,4624,1701) -> Matrix(1,0,12,1) Matrix(2923,1074,4624,1699) -> Matrix(1,0,-16,1) Matrix(3231,1184,5848,2143) -> Matrix(1,0,-8,1) Matrix(3637,1332,-13464,-4931) -> Matrix(19,-4,24,-5) Matrix(851,308,1224,443) -> Matrix(1,0,-4,1) Matrix(477,172,1700,613) -> Matrix(13,-4,-16,5) Matrix(169,60,476,169) -> Matrix(9,-4,-20,9) Matrix(239,84,680,239) -> Matrix(11,-6,-20,11) Matrix(373,130,680,237) -> Matrix(3,-2,-4,3) Matrix(169,54,-748,-239) -> Matrix(1,0,0,1) Matrix(273,86,-1292,-407) -> Matrix(5,-2,8,-3) Matrix(103,32,-544,-169) -> Matrix(5,-4,4,-3) Matrix(137,42,-884,-271) -> Matrix(1,0,0,1) Matrix(781,238,1224,373) -> Matrix(1,0,0,1) Matrix(7243,2202,10404,3163) -> Matrix(7,-6,-8,7) Matrix(7241,2200,10404,3161) -> Matrix(5,-6,-4,5) Matrix(33,10,-340,-103) -> Matrix(1,0,0,1) Matrix(101,30,340,101) -> Matrix(1,0,-4,1) Matrix(239,70,816,239) -> Matrix(11,-6,-20,11) Matrix(1293,376,2108,613) -> Matrix(3,-2,-4,3) Matrix(8263,2396,-30600,-8873) -> Matrix(23,-14,28,-17) Matrix(6799,1970,9384,2719) -> Matrix(3,-2,8,-5) Matrix(1597,450,-5916,-1667) -> Matrix(1,0,0,1) Matrix(849,238,1088,305) -> Matrix(7,-6,-8,7) Matrix(3333,932,4624,1293) -> Matrix(23,-22,-24,23) Matrix(3331,930,4624,1291) -> Matrix(21,-22,-20,21) Matrix(6665,1836,9384,2585) -> Matrix(9,-2,-4,1) Matrix(2347,646,4080,1123) -> Matrix(1,0,0,1) Matrix(613,168,748,205) -> Matrix(7,-4,-12,7) Matrix(339,92,748,203) -> Matrix(3,-2,-4,3) Matrix(102103,27574,139876,37775) -> Matrix(3,-2,-4,3) Matrix(102101,27572,139876,37773) -> Matrix(1,-2,0,1) Matrix(1053,284,3400,917) -> Matrix(7,-6,-8,7) Matrix(373,100,884,237) -> Matrix(5,-4,-16,13) Matrix(851,226,1156,307) -> Matrix(15,-14,-16,15) Matrix(849,224,1156,305) -> Matrix(13,-14,-12,13) Matrix(33,8,136,33) -> Matrix(1,-2,0,1) Matrix(239,56,1020,239) -> Matrix(1,0,0,1) Matrix(851,198,1904,443) -> Matrix(1,0,0,1) Matrix(1223,284,2924,679) -> Matrix(1,0,-4,1) Matrix(1087,248,2380,543) -> Matrix(1,0,0,1) Matrix(14281,3256,18496,4217) -> Matrix(1,0,4,1) Matrix(14279,3254,18496,4215) -> Matrix(1,0,-8,1) Matrix(8059,1818,10404,2347) -> Matrix(3,-2,-4,3) Matrix(8057,1816,10404,2345) -> Matrix(1,-2,0,1) Matrix(545,122,612,137) -> Matrix(1,0,-4,1) Matrix(783,172,1088,239) -> Matrix(5,-6,-4,5) Matrix(477,104,1564,341) -> Matrix(1,-2,0,1) Matrix(14553,3104,18496,3945) -> Matrix(1,0,8,1) Matrix(14551,3102,18496,3943) -> Matrix(1,0,-12,1) Matrix(1259,268,2720,579) -> Matrix(1,0,-4,1) Matrix(5201,1102,8500,1801) -> Matrix(13,-6,-28,13) Matrix(1257,266,4012,849) -> Matrix(15,-8,-28,15) Matrix(1087,228,1292,271) -> Matrix(3,-2,-4,3) Matrix(919,190,1156,239) -> Matrix(15,-14,-16,15) Matrix(917,188,1156,237) -> Matrix(13,-14,-12,13) Matrix(477,92,1768,341) -> Matrix(3,-2,-4,3) Matrix(3741,716,4624,885) -> Matrix(11,-10,-12,11) Matrix(3739,714,4624,883) -> Matrix(9,-10,-8,9) Matrix(237,44,544,101) -> Matrix(1,-2,-4,9) Matrix(543,98,748,135) -> Matrix(1,-4,0,1) Matrix(169,30,952,169) -> Matrix(1,-10,0,1) Matrix(35,6,204,35) -> Matrix(1,0,0,1) Matrix(883,142,2108,339) -> Matrix(1,0,-4,1) Matrix(1021,162,1292,205) -> Matrix(1,-2,0,1) Matrix(1021,160,2176,341) -> Matrix(3,-2,-4,3) Matrix(987,146,1156,171) -> Matrix(11,-10,-12,11) Matrix(985,144,1156,169) -> Matrix(9,-10,-8,9) Matrix(171,22,272,35) -> Matrix(1,-2,0,1) Matrix(33,4,272,33) -> Matrix(1,-6,0,1) Matrix(1123,130,2652,307) -> Matrix(1,8,-4,-31) Matrix(475,52,612,67) -> Matrix(1,0,0,1) Matrix(885,92,1972,205) -> Matrix(1,0,4,1) Matrix(103,-10,340,-33) -> Matrix(1,0,0,1) Matrix(749,-86,1768,-203) -> Matrix(1,-4,-4,17) Matrix(579,-86,680,-101) -> Matrix(5,4,-4,-3) Matrix(681,-104,884,-135) -> Matrix(1,0,0,1) Matrix(271,-42,884,-137) -> Matrix(1,0,0,1) Matrix(169,-32,544,-103) -> Matrix(3,4,-4,-5) Matrix(647,-134,816,-169) -> Matrix(9,8,-8,-7) Matrix(1121,-234,2448,-511) -> Matrix(5,4,-4,-3) Matrix(407,-86,1292,-273) -> Matrix(3,2,-8,-5) Matrix(3127,-664,4488,-953) -> Matrix(5,2,-8,-3) Matrix(1497,-320,1904,-407) -> Matrix(1,0,0,1) Matrix(305,-66,476,-103) -> Matrix(1,2,0,1) Matrix(917,-206,1972,-443) -> Matrix(1,0,0,1) Matrix(3161,-712,4080,-919) -> Matrix(1,0,0,1) Matrix(1801,-408,2856,-647) -> Matrix(1,0,0,1) Matrix(2311,-526,2992,-681) -> Matrix(1,0,0,1) Matrix(749,-172,884,-203) -> Matrix(1,0,0,1) Matrix(101,-26,136,-35) -> Matrix(1,0,0,1) Matrix(1497,-404,2516,-679) -> Matrix(5,4,-4,-3) Matrix(239,-66,612,-169) -> Matrix(1,0,0,1) Matrix(883,-246,1224,-341) -> Matrix(3,4,-4,-5) Matrix(645,-182,1088,-307) -> Matrix(5,4,-4,-3) Matrix(1121,-324,1768,-511) -> Matrix(3,2,4,3) Matrix(3535,-1072,4488,-1361) -> Matrix(1,2,0,1) Matrix(3977,-1208,5712,-1735) -> Matrix(3,4,-4,-5) Matrix(987,-302,2108,-645) -> Matrix(1,0,0,1) Matrix(1869,-578,2312,-715) -> Matrix(5,4,-4,-3) Matrix(815,-258,1292,-409) -> Matrix(1,0,0,1) Matrix(373,-134,476,-171) -> Matrix(5,2,-8,-3) Matrix(443,-162,1020,-373) -> Matrix(1,0,0,1) Matrix(1291,-474,2040,-749) -> Matrix(1,0,8,1) Matrix(2209,-816,2856,-1055) -> Matrix(1,0,0,1) Matrix(169,-64,272,-103) -> Matrix(1,0,4,1) Matrix(1223,-474,2108,-817) -> Matrix(1,0,0,1) Matrix(713,-282,1292,-511) -> Matrix(1,0,0,1) Matrix(781,-318,1088,-443) -> Matrix(5,4,-4,-3) Matrix(3909,-1634,4964,-2075) -> Matrix(1,0,4,1) Matrix(5847,-2450,10064,-4217) -> Matrix(1,0,4,1) Matrix(1291,-542,2108,-885) -> Matrix(1,0,0,1) Matrix(1835,-778,4012,-1701) -> Matrix(1,0,4,1) Matrix(851,-362,1836,-781) -> Matrix(1,0,4,1) Matrix(339,-146,476,-205) -> Matrix(7,2,-4,-1) Matrix(305,-134,544,-239) -> Matrix(1,0,12,1) Matrix(2857,-1280,3944,-1767) -> Matrix(1,0,0,1) Matrix(5849,-2624,10608,-4759) -> Matrix(1,0,-12,1) Matrix(3093,-1390,4012,-1803) -> Matrix(3,-2,-4,3) Matrix(917,-488,1088,-579) -> Matrix(1,0,0,1) Matrix(1529,-818,1972,-1055) -> Matrix(1,0,0,1) Matrix(1055,-566,1836,-985) -> Matrix(1,0,4,1) Matrix(1937,-1050,2448,-1327) -> Matrix(5,4,-4,-3) Matrix(1733,-954,2040,-1123) -> Matrix(7,2,-4,-1) Matrix(647,-366,1020,-577) -> Matrix(1,0,0,1) Matrix(4249,-2448,5372,-3095) -> Matrix(11,-4,-8,3) Matrix(1565,-902,1768,-1019) -> Matrix(9,-4,-20,9) Matrix(3637,-2108,4284,-2483) -> Matrix(1,-4,0,1) Matrix(2889,-1682,4148,-2415) -> Matrix(3,-2,-4,3) Matrix(3331,-1980,4692,-2789) -> Matrix(1,-2,0,1) Matrix(443,-270,612,-373) -> Matrix(1,0,0,1) Matrix(5611,-3434,7276,-4453) -> Matrix(9,4,-16,-7) Matrix(9827,-6228,13464,-8533) -> Matrix(11,-4,-8,3) Matrix(579,-394,748,-509) -> Matrix(1,0,0,1) Matrix(1019,-698,1292,-885) -> Matrix(1,-2,0,1) Matrix(441,-304,544,-375) -> Matrix(3,4,-4,-5) Matrix(747,-518,884,-613) -> Matrix(1,0,0,1) Matrix(307,-214,340,-237) -> Matrix(1,0,0,1) Matrix(22337,-15860,30600,-21727) -> Matrix(5,14,-4,-11) 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): 48 Degree of the the map X: 96 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 3/2 2/17 1/0 1/8 -3/1 1/7 -3/2 3/20 -1/1 2/13 1/0 3/19 -1/2 4/25 -1/4 1/6 0/1 3/17 1/0 2/11 1/0 1/5 -3/2 5/24 -1/1 9/43 -7/10 4/19 -3/4 7/33 -1/2 3/14 0/1 2/9 -3/4 5/22 0/1 8/35 1/0 3/13 -1/2 4/17 1/0 1/4 -1/1 4/15 -7/8 3/11 -1/2 5/18 -2/1 2/7 -3/4 5/17 -1/2 3/10 0/1 13/43 3/2 10/33 1/0 17/56 -1/1 7/23 -1/2 4/13 1/0 1/3 -1/2 6/17 -1/2 5/14 -2/5 4/11 -1/4 7/19 1/2 3/8 -1/3 5/13 1/2 7/18 -2/1 2/5 1/0 7/17 -1/2 5/12 -1/3 18/43 1/0 31/74 0/1 13/31 -1/2 8/19 -3/8 3/7 -1/2 7/16 -1/7 4/9 1/4 5/11 -1/2 6/13 1/0 7/15 -1/2 8/17 -1/2 1/2 0/1 9/17 1/0 8/15 1/0 7/13 -1/2 6/11 1/0 5/9 -1/6 19/34 0/1 14/25 1/16 9/16 1/5 4/7 1/0 15/26 2/3 11/19 3/2 18/31 1/0 7/12 1/1 10/17 1/0 3/5 -1/2 11/18 -2/3 52/85 -1/2 41/67 -1/2 30/49 -3/8 19/31 -1/2 8/13 -1/4 21/34 0/1 13/21 1/6 5/8 1/1 17/27 -1/2 12/19 -1/4 7/11 1/2 16/25 5/4 9/14 2/1 11/17 1/0 2/3 1/0 13/19 1/2 11/16 -3/1 9/13 -1/2 16/23 1/0 23/33 -1/2 7/10 0/1 12/17 1/0 5/7 -3/2 13/18 -2/3 21/29 -1/2 8/11 1/0 11/15 -7/6 25/34 -1/1 14/19 -7/8 3/4 -1/1 13/17 -1/2 10/13 1/0 37/48 -1/1 27/35 -1/2 44/57 -1/4 105/136 0/1 61/79 1/2 17/22 0/1 24/31 1/0 79/102 -1/1 55/71 -1/2 31/40 -1/1 7/9 -3/2 18/23 -3/4 11/14 0/1 26/33 1/0 67/85 1/0 41/52 -5/1 15/19 -3/2 34/43 -7/4 19/24 -1/1 23/29 -11/10 27/34 -1/1 4/5 -3/4 13/16 -5/7 9/11 -1/2 14/17 -1/2 5/6 0/1 21/25 1/2 16/19 1/0 11/13 -1/2 28/33 1/0 17/20 -1/1 23/27 -7/6 29/34 -1/1 6/7 -3/4 7/8 -3/5 15/17 -1/2 8/9 -3/8 9/10 0/1 1/1 -1/2 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,-2,1) Matrix(103,-10,340,-33) -> Matrix(1,0,0,1) Matrix(271,-31,306,-35) -> Matrix(1,-3,-2,7) Matrix(239,-29,272,-33) -> Matrix(1,6,-2,-11) Matrix(137,-19,238,-33) -> Matrix(1,1,2,3) Matrix(579,-86,680,-101) -> Matrix(5,4,-4,-3) Matrix(681,-104,884,-135) -> Matrix(1,0,0,1) Matrix(237,-37,442,-69) -> Matrix(1,1,-2,-1) Matrix(271,-43,1292,-205) -> Matrix(1,2,-2,-3) Matrix(817,-131,1054,-169) -> Matrix(1,1,-2,-1) Matrix(169,-29,204,-35) -> Matrix(1,0,-2,1) Matrix(307,-55,374,-67) -> Matrix(1,5,-2,-9) Matrix(271,-50,374,-69) -> Matrix(1,1,0,1) Matrix(647,-134,816,-169) -> Matrix(9,8,-8,-7) Matrix(579,-121,646,-135) -> Matrix(1,1,-6,-5) Matrix(1769,-374,2890,-611) -> Matrix(5,3,-12,-7) Matrix(1599,-340,2074,-441) -> Matrix(3,1,-4,-1) Matrix(305,-66,476,-103) -> Matrix(1,2,0,1) Matrix(441,-100,1054,-239) -> Matrix(1,1,-4,-3) Matrix(815,-186,2686,-613) -> Matrix(1,-1,0,1) Matrix(749,-172,884,-203) -> Matrix(1,0,0,1) Matrix(339,-79,442,-103) -> Matrix(1,1,-2,-1) Matrix(103,-25,136,-33) -> Matrix(1,2,-2,-3) Matrix(101,-26,136,-35) -> Matrix(1,0,0,1) Matrix(137,-37,374,-101) -> Matrix(1,1,-6,-5) Matrix(305,-84,374,-103) -> Matrix(3,1,-4,-1) Matrix(103,-29,238,-67) -> Matrix(1,1,-6,-5) Matrix(169,-49,238,-69) -> Matrix(5,3,-2,-1) Matrix(239,-71,340,-101) -> Matrix(1,0,2,1) Matrix(1157,-349,1462,-441) -> Matrix(3,-1,-2,1) Matrix(3807,-1156,4930,-1497) -> Matrix(1,1,0,1) Matrix(239,-73,442,-135) -> Matrix(1,1,-2,-1) Matrix(271,-84,442,-137) -> Matrix(1,1,-4,-3) Matrix(67,-23,102,-35) -> Matrix(1,1,-2,-1) Matrix(307,-109,476,-169) -> Matrix(9,4,2,1) Matrix(373,-134,476,-171) -> Matrix(5,2,-8,-3) Matrix(373,-138,646,-239) -> Matrix(1,1,0,1) Matrix(169,-64,272,-103) -> Matrix(1,0,4,1) Matrix(305,-118,442,-171) -> Matrix(1,-1,0,1) Matrix(137,-54,170,-67) -> Matrix(3,1,-4,-1) Matrix(101,-41,170,-69) -> Matrix(1,1,-2,-1) Matrix(239,-99,408,-169) -> Matrix(5,2,2,1) Matrix(1769,-741,2108,-883) -> Matrix(1,0,2,1) Matrix(5031,-2108,6494,-2721) -> Matrix(3,1,-4,-1) Matrix(1291,-542,2108,-885) -> Matrix(1,0,0,1) Matrix(407,-172,646,-273) -> Matrix(3,1,-4,-1) Matrix(305,-134,544,-239) -> Matrix(1,0,12,1) Matrix(239,-108,374,-169) -> Matrix(1,1,0,1) Matrix(307,-141,442,-203) -> Matrix(1,1,-2,-1) Matrix(373,-173,442,-205) -> Matrix(1,1,-2,-1) Matrix(271,-127,510,-239) -> Matrix(1,1,-2,-1) Matrix(35,-17,68,-33) -> Matrix(1,0,2,1) Matrix(239,-132,306,-169) -> Matrix(3,1,-4,-1) Matrix(647,-361,1156,-645) -> Matrix(1,0,22,1) Matrix(171,-97,238,-135) -> Matrix(3,-1,-2,1) Matrix(441,-256,646,-375) -> Matrix(1,-1,0,1) Matrix(815,-474,1054,-613) -> Matrix(1,-1,0,1) Matrix(443,-270,612,-373) -> Matrix(1,0,0,1) Matrix(4691,-2869,5950,-3639) -> Matrix(13,7,-2,-1) Matrix(6699,-4099,8500,-5201) -> Matrix(13,6,2,1) Matrix(715,-441,1156,-713) -> Matrix(1,0,10,1) Matrix(237,-149,272,-171) -> Matrix(1,2,-2,-3) Matrix(273,-173,374,-237) -> Matrix(3,-1,-2,1) Matrix(1019,-698,1292,-885) -> Matrix(1,-2,0,1) Matrix(2073,-1444,2686,-1871) -> Matrix(1,1,-4,-3) Matrix(307,-214,340,-237) -> Matrix(1,0,0,1) Matrix(851,-625,1156,-849) -> Matrix(13,14,-14,-15) Matrix(14281,-11025,18496,-14279) -> Matrix(1,0,6,1) Matrix(8059,-6241,10404,-8057) -> Matrix(1,2,-2,-3) Matrix(953,-750,1122,-883) -> Matrix(1,-1,0,1) Matrix(1087,-859,1292,-1021) -> Matrix(1,2,-2,-3) Matrix(919,-729,1156,-917) -> Matrix(13,14,-14,-15) Matrix(987,-841,1156,-985) -> Matrix(9,10,-10,-11) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 ----------------------------------------------------------------------- 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 3/2 1 34 2/17 1/0 9 2 1/8 -3/1 2 17 1/7 -3/2 1 34 5/34 -1/1 10 1 3/20 -1/1 2 17 2/13 1/0 1 34 3/19 -1/2 1 34 4/25 -1/4 1 34 1/6 0/1 2 17 3/17 1/0 5 2 2/11 1/0 1 34 1/5 -3/2 1 34 7/34 -1/1 14 1 5/24 -1/1 2 17 9/43 -7/10 1 34 4/19 -3/4 1 34 7/33 -1/2 1 34 3/14 0/1 2 17 2/9 -3/4 1 34 5/22 0/1 2 17 8/35 1/0 1 34 11/48 -1/1 2 17 3/13 -1/2 1 34 4/17 1/0 1 2 1/4 -1/1 2 17 9/34 -1/1 14 1 4/15 -7/8 1 34 3/11 -1/2 1 34 5/18 -2/1 2 17 2/7 -3/4 1 34 5/17 -1/2 3 2 3/10 0/1 2 17 13/43 3/2 1 34 10/33 1/0 1 34 17/56 -1/1 2 17 31/102 -1/1 6 1 7/23 -1/2 1 34 4/13 1/0 1 34 1/3 -1/2 1 34 6/17 -1/2 5 2 5/14 -2/5 2 17 4/11 -1/4 1 34 7/19 1/2 1 34 3/8 -1/3 2 17 13/34 0/1 10 1 5/13 1/2 1 34 12/31 1/0 1 34 7/18 -2/1 2 17 9/23 -1/2 1 34 2/5 1/0 1 34 7/17 -1/2 3 2 5/12 -1/3 2 17 18/43 1/0 1 34 31/74 0/1 2 17 57/136 0/1 2 1 13/31 -1/2 1 34 21/50 -2/3 2 17 50/119 -1/2 13 2 29/69 -1/2 1 34 8/19 -3/8 1 34 11/26 -2/7 2 17 3/7 -1/2 1 34 7/16 -1/7 2 17 15/34 0/1 22 1 4/9 1/4 1 34 9/20 1/1 2 17 5/11 -1/2 1 34 6/13 1/0 1 34 7/15 -1/2 1 34 8/17 -1/2 1 2 1/2 0/1 2 17 1/0 0/1 2 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(1,0,0,1) Matrix(35,-4,306,-35) -> Matrix(-1,3,0,1) (1/9,2/17) -> (3/2,1/0) Matrix(33,-4,272,-33) -> Matrix(1,6,0,-1) (2/17,1/8) -> (-3/1,1/0) Matrix(101,-14,238,-33) -> Matrix(1,1,-4,-5) Matrix(69,-10,476,-69) -> Matrix(5,6,-4,-5) (1/7,5/34) -> (-3/2,-1/1) Matrix(101,-15,680,-101) -> Matrix(5,4,-6,-5) (5/34,3/20) -> (-1/1,-2/3) Matrix(203,-31,884,-135) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(205,-32,442,-69) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(271,-43,1292,-205) -> Matrix(1,2,-2,-3) -1/1 Matrix(883,-142,2108,-339) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(35,-6,204,-35) -> Matrix(1,0,0,-1) (1/6,3/17) -> (0/1,1/0) Matrix(67,-12,374,-67) -> Matrix(1,5,0,-1) (3/17,2/11) -> (-5/2,1/0) Matrix(67,-13,170,-33) -> Matrix(1,1,-2,-3) Matrix(69,-14,340,-69) -> Matrix(5,6,-4,-5) (1/5,7/34) -> (-3/2,-1/1) Matrix(169,-35,816,-169) -> Matrix(9,8,-10,-9) (7/34,5/24) -> (-1/1,-4/5) Matrix(441,-92,1462,-305) -> Matrix(1,1,4,3) Matrix(815,-172,1938,-409) -> Matrix(5,3,-12,-7) -1/2 Matrix(475,-101,2074,-441) -> Matrix(3,1,-2,-1) Matrix(137,-30,306,-67) -> Matrix(1,1,0,1) 1/0 Matrix(441,-100,1054,-239) -> Matrix(1,1,-4,-3) -1/2 Matrix(815,-186,2686,-613) -> Matrix(1,-1,0,1) 1/0 Matrix(103,-24,442,-103) -> Matrix(1,1,0,-1) (3/13,4/17) -> (-1/2,1/0) Matrix(33,-8,136,-33) -> Matrix(1,2,0,-1) (4/17,1/4) -> (-1/1,1/0) Matrix(35,-9,136,-35) -> Matrix(-1,0,2,1) (1/4,9/34) -> (-1/1,0/1) Matrix(271,-72,1020,-271) -> Matrix(15,14,-16,-15) (9/34,4/15) -> (-1/1,-7/8) Matrix(137,-37,374,-101) -> Matrix(1,1,-6,-5) Matrix(239,-66,612,-169) -> Matrix(1,0,0,1) Matrix(103,-29,238,-67) -> Matrix(1,1,-6,-5) Matrix(69,-20,238,-69) -> Matrix(5,3,-8,-5) (2/7,5/17) -> (-3/4,-1/2) Matrix(101,-30,340,-101) -> Matrix(-1,0,4,1) (5/17,3/10) -> (-1/2,0/1) Matrix(1735,-527,5712,-1735) -> Matrix(3,4,-2,-3) (17/56,31/102) -> (-2/1,-1/1) Matrix(1427,-434,4692,-1427) -> Matrix(3,2,-4,-3) (31/102,7/23) -> (-1/1,-1/2) Matrix(203,-62,442,-135) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(171,-53,442,-137) -> Matrix(1,1,2,1) Matrix(35,-12,102,-35) -> Matrix(1,1,0,-1) (1/3,6/17) -> (-1/2,1/0) Matrix(169,-60,476,-169) -> Matrix(9,4,-20,-9) (6/17,5/14) -> (-1/2,-2/5) Matrix(169,-61,374,-135) -> Matrix(3,1,-2,-1) Matrix(273,-101,646,-239) -> Matrix(1,1,-2,-3) Matrix(103,-39,272,-103) -> Matrix(-1,0,6,1) (3/8,13/34) -> (-1/3,0/1) Matrix(339,-130,884,-339) -> Matrix(1,0,4,-1) (13/34,5/13) -> (0/1,1/2) Matrix(885,-343,2108,-817) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(69,-28,170,-69) -> Matrix(1,1,0,-1) (2/5,7/17) -> (-1/2,1/0) Matrix(169,-70,408,-169) -> Matrix(5,2,-12,-5) (7/17,5/12) -> (-1/2,-1/3) Matrix(4217,-1767,10064,-4217) -> Matrix(-1,0,6,1) (31/74,57/136) -> (-1/3,0/1) Matrix(3535,-1482,8432,-3535) -> Matrix(-1,0,4,1) (57/136,13/31) -> (-1/2,0/1) Matrix(4999,-2100,11900,-4999) -> Matrix(7,4,-12,-7) (21/50,50/119) -> (-2/3,-1/2) Matrix(6901,-2900,16422,-6901) -> Matrix(19,9,-40,-19) (50/119,29/69) -> (-1/2,-9/20) Matrix(239,-105,544,-239) -> Matrix(-1,0,14,1) (7/16,15/34) -> (-1/7,0/1) Matrix(271,-120,612,-271) -> Matrix(1,0,8,-1) (15/34,4/9) -> (0/1,1/4) Matrix(239,-112,510,-239) -> Matrix(1,1,0,-1) (7/15,8/17) -> (-1/2,1/0) Matrix(33,-16,68,-33) -> Matrix(-1,0,4,1) (8/17,1/2) -> (-1/2,0/1) Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.