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): 1440 Minimal number of generators: 241 Number of equivalence classes of cusps: 80 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/11 -8/11 -7/11 -32/55 -6/11 -1/2 -5/11 -9/20 -5/12 -17/44 -21/55 -49/132 -4/11 -7/22 -10/33 -3/10 -13/44 -5/18 -3/11 -35/132 -23/88 -1/4 -41/176 -29/132 -19/88 -3/14 -23/110 -4/21 -3/16 -2/11 -1/6 -7/44 -3/19 -3/20 -3/22 -2/15 -1/8 -1/10 0/1 1/9 1/8 1/7 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 2/9 5/22 3/13 4/17 5/21 1/4 3/11 5/18 2/7 1/3 4/11 2/5 9/22 5/12 5/11 7/15 1/2 6/11 13/22 7/11 2/3 15/22 23/33 8/11 17/22 87/110 9/11 19/22 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -8/9 -3/1 -2/1 -7/8 -2/1 -6/7 -1/1 0/1 -11/13 -3/2 -5/6 1/1 -19/23 15/4 -14/17 6/1 7/1 -9/11 1/0 -22/27 -12/1 -11/1 -35/43 1/0 -13/16 -8/1 -4/5 -3/1 -2/1 -19/24 -4/3 -15/19 1/0 -11/14 -3/1 -18/23 -2/1 -1/1 -25/32 -2/1 -7/9 -3/2 -17/22 -1/1 -10/13 -1/1 -2/3 -13/17 1/0 -16/21 -1/5 0/1 -3/4 0/1 -17/23 11/6 -14/19 8/3 3/1 -25/34 3/1 -36/49 4/1 13/3 -11/15 1/0 -8/11 1/0 -21/29 1/0 -34/47 -10/1 -29/3 -13/18 -7/1 -5/7 -7/2 -17/24 -2/1 -12/17 -11/5 -2/1 -7/10 -1/1 -9/13 -7/4 -20/29 -2/1 -1/1 -31/45 -3/2 -11/16 -4/3 -2/3 -1/1 0/1 -11/17 5/2 -20/31 3/1 4/1 -9/14 3/1 -7/11 1/0 -19/30 -11/1 -12/19 -8/1 -7/1 -41/65 -49/8 -29/46 -17/3 -17/27 -9/2 -39/62 -5/1 -22/35 -4/1 -3/1 -5/8 -4/1 -18/29 -3/1 -26/9 -31/50 -25/9 -13/21 -21/8 -8/13 -11/5 -2/1 -11/18 -5/3 -25/41 -7/4 -14/23 -2/1 -1/1 -3/5 -3/2 -13/22 -1/1 -10/17 -1/1 -6/7 -27/46 -7/9 -17/29 -3/4 -24/41 -9/13 -2/3 -31/53 -1/2 -7/12 -2/3 -32/55 -1/2 -25/43 -1/2 -68/117 -3/7 -2/5 -43/74 -1/3 -18/31 -1/3 0/1 -11/19 1/0 -4/7 -1/3 0/1 -13/23 3/10 -9/16 2/3 -14/25 1/1 6/5 -19/34 1/1 -5/9 1/0 -26/47 9/5 2/1 -21/38 7/3 -16/29 3/1 10/3 -11/20 4/1 -6/11 1/0 -13/24 -8/1 -7/13 -9/2 -8/15 -4/1 -3/1 -1/2 -1/1 -7/15 1/0 -6/13 2/1 3/1 -5/11 1/0 -14/31 -8/1 -7/1 -9/20 -6/1 -22/49 -13/3 -4/1 -13/29 1/0 -4/9 -3/1 -2/1 -19/43 1/0 -15/34 -5/1 -11/25 -7/2 -29/66 -3/1 -18/41 -3/1 -14/5 -7/16 -2/1 -10/23 -7/3 -2/1 -13/30 -11/5 -3/7 -7/4 -11/26 -7/5 -30/71 -2/1 -1/1 -19/45 -3/2 -8/19 -7/5 -4/3 -21/50 -9/7 -13/31 -7/6 -18/43 -2/1 -1/1 -23/55 -3/2 -5/12 -4/3 -17/41 -19/16 -12/29 -6/5 -1/1 -19/46 -15/13 -7/17 -11/10 -9/22 -1/1 -2/5 -1/1 -2/3 -11/28 -4/9 -9/23 -5/14 -16/41 -5/17 -2/7 -7/18 -1/5 -12/31 -1/13 0/1 -17/44 0/1 -5/13 1/4 -13/34 1/1 -34/89 0/1 1/1 -21/55 1/0 -29/76 0/1 -8/21 -1/1 0/1 -19/50 1/1 -30/79 1/3 2/5 -11/29 1/2 -25/66 1/1 -14/37 1/1 2/1 -3/8 0/1 -13/35 3/2 -49/132 2/1 -36/97 2/1 7/3 -23/62 3/1 -10/27 0/1 1/1 -17/46 5/3 -7/19 1/0 -4/11 1/0 -9/25 1/0 -5/14 -3/1 -6/17 -7/3 -2/1 -7/20 -2/1 -8/23 -3/1 -2/1 -1/3 -3/2 -7/22 -1/1 -6/19 -1/1 -12/13 -5/16 -4/5 -14/45 -1/1 -6/7 -9/29 -3/4 -4/13 -5/7 -2/3 -7/23 -9/16 -10/33 -1/2 -13/43 -1/2 -3/10 -1/3 -8/27 -1/9 0/1 -13/44 0/1 -5/17 1/4 -12/41 3/5 2/3 -19/65 9/10 -7/24 2/1 -9/31 -3/2 -2/7 -1/1 0/1 -7/25 1/2 -19/68 4/5 -31/111 15/16 -43/154 1/1 -12/43 1/1 6/5 -17/61 1/0 -5/18 1/1 -3/11 1/0 -7/26 -5/1 -11/41 -9/2 -4/15 -4/1 -3/1 -13/49 -9/4 -35/132 -2/1 -22/83 -2/1 -9/5 -9/34 -1/1 -5/19 -5/2 -11/42 -11/5 -17/65 -33/16 -23/88 -2/1 -6/23 -2/1 -9/5 -1/4 -2/1 -5/21 -21/16 -4/17 -11/9 -6/5 -7/30 -1/1 -24/103 -15/13 -8/7 -41/176 -8/7 -17/73 -9/8 -10/43 -6/5 -1/1 -3/13 -11/10 -5/22 -1/1 -2/9 -1/1 -6/7 -11/50 -9/11 -20/91 -41/51 -4/5 -29/132 -4/5 -9/41 -19/24 -7/32 -10/13 -12/55 -3/4 -5/23 -13/18 -8/37 -17/25 -2/3 -19/88 -2/3 -11/51 -21/32 -3/14 -3/5 -4/19 -1/3 0/1 -9/43 -1/2 -23/110 -1/3 -14/67 -1/3 0/1 -5/24 0/1 -6/29 -1/3 -2/7 -1/5 1/0 -4/21 -1/1 0/1 -3/16 0/1 -2/11 1/0 -5/28 -4/1 -8/45 -10/3 -3/1 -3/17 -5/2 -4/23 -2/1 -5/3 -1/6 -1/1 -4/25 -7/3 -2/1 -7/44 -2/1 -3/19 -7/4 -2/13 -2/1 -1/1 -3/20 -4/3 -1/7 -7/6 -3/22 -1/1 -2/15 -1/1 -12/13 -1/8 -2/3 -1/9 1/0 -1/10 -1/1 0/1 -1/1 0/1 1/9 -1/2 1/8 -2/1 1/7 -7/8 2/13 -1/1 -2/3 1/6 -1/1 4/23 -5/7 -2/3 3/17 -5/8 2/11 -1/2 5/27 -3/8 8/43 -1/3 -2/7 3/16 0/1 1/5 -1/2 5/24 0/1 4/19 0/1 1/1 3/14 -3/1 5/23 -13/8 7/32 -10/7 2/9 -6/5 -1/1 5/22 -1/1 3/13 -11/12 4/17 -6/7 -11/13 5/21 -21/26 1/4 -2/3 6/23 -9/13 -2/3 5/19 -5/8 9/34 -1/1 13/49 -9/14 4/15 -3/5 -4/7 3/11 -1/2 8/29 -3/7 -2/5 13/47 -3/8 5/18 -1/3 2/7 -1/1 0/1 7/24 -2/5 5/17 -1/6 3/10 1/1 4/13 -2/1 -5/3 9/29 -3/2 14/45 -6/5 -1/1 5/16 -4/3 1/3 -3/4 6/17 -2/3 -7/11 11/31 -13/22 5/14 -3/5 4/11 -1/2 11/30 -5/11 7/19 -1/2 24/65 -15/37 -2/5 17/46 -5/13 10/27 -1/3 0/1 23/62 -3/7 13/35 -3/8 3/8 0/1 11/29 -1/4 19/50 -1/3 8/21 -1/1 0/1 5/13 -1/6 7/18 1/3 16/41 2/3 5/7 9/23 5/4 2/5 -2/1 -1/1 9/22 -1/1 7/17 -11/12 19/46 -15/17 12/29 -1/1 -6/7 17/41 -19/22 22/53 -28/33 -11/13 5/12 -4/5 23/55 -3/4 18/43 -1/1 -2/3 49/117 -5/6 31/74 -1/1 13/31 -7/8 8/19 -4/5 -7/9 3/7 -7/10 10/23 -2/3 -7/11 7/16 -2/3 11/25 -7/12 15/34 -5/9 4/9 -2/3 -3/5 21/47 -23/40 17/38 -5/9 13/29 -1/2 9/20 -6/11 5/11 -1/2 11/24 -4/9 6/13 -3/7 -2/5 7/15 -1/2 1/2 -1/1 8/15 -3/5 -4/7 7/13 -9/16 6/11 -1/2 17/31 -15/32 11/20 -4/9 27/49 -9/20 16/29 -10/23 -3/7 5/9 -1/2 24/43 -2/5 -1/3 19/34 -1/3 14/25 -6/17 -1/3 37/66 -1/3 23/41 -9/28 9/16 -2/7 13/23 -3/16 17/30 -1/9 4/7 0/1 1/1 15/26 -1/1 41/71 1/0 26/45 -6/5 -1/1 11/19 -1/2 29/50 1/1 18/31 0/1 1/1 25/43 1/0 32/55 1/0 7/12 -2/1 24/41 -2/1 -9/5 17/29 -3/2 27/46 -7/5 10/17 -6/5 -1/1 13/22 -1/1 3/5 -3/4 17/28 -2/3 14/23 -1/1 -2/3 25/41 -7/10 11/18 -5/7 19/31 -23/34 27/44 -2/3 8/13 -2/3 -11/17 21/34 -17/27 55/89 -5/8 34/55 -5/8 47/76 -38/61 13/21 -21/34 31/50 -25/41 49/79 -17/28 18/29 -26/43 -3/5 41/66 -3/5 23/37 -31/52 5/8 -4/7 22/35 -3/5 -4/7 83/132 -4/7 61/97 -17/30 39/62 -5/9 17/27 -9/16 29/46 -17/31 12/19 -7/13 -8/15 7/11 -1/2 16/25 -7/15 -6/13 9/14 -3/7 11/17 -5/12 13/20 -4/11 15/23 -7/22 2/3 -1/1 0/1 15/22 -1/1 13/19 -7/8 11/16 -4/5 31/45 -3/4 20/29 -1/1 -2/3 9/13 -7/10 16/23 -2/3 -3/5 23/33 -1/2 30/43 -1/1 -2/3 7/10 -1/1 19/27 -15/22 31/44 -2/3 12/17 -2/3 -11/17 29/41 -1/2 46/65 -2/3 -7/11 17/24 -2/3 22/31 -8/13 -3/5 5/7 -7/12 18/25 -6/11 -7/13 49/68 -6/11 80/111 -6/11 -7/13 111/154 -7/13 31/43 -1/2 44/61 -4/7 -5/9 13/18 -7/13 8/11 -1/2 19/26 -9/19 30/41 -19/41 -6/13 11/15 -1/2 36/49 -13/29 -4/9 97/132 -4/9 61/83 -23/52 25/34 -3/7 14/19 -3/7 -8/19 31/42 -11/27 48/65 -31/77 -2/5 65/88 -2/5 17/23 -11/28 3/4 0/1 16/21 0/1 1/3 13/17 -1/2 23/30 -1/1 79/103 -1/2 135/176 0/1 56/73 0/1 1/1 33/43 1/0 10/13 -2/1 -1/1 17/22 -1/1 7/9 -3/4 39/50 -9/13 71/91 -23/34 103/132 -2/3 32/41 -2/3 -7/11 25/32 -2/3 43/55 -3/4 18/23 -1/1 -2/3 29/37 -15/22 69/88 -2/3 40/51 -2/3 -23/35 11/14 -3/5 15/19 -1/2 34/43 -6/5 -1/1 87/110 -1/1 53/67 -15/16 19/24 -4/5 23/29 -3/4 4/5 -2/3 -3/5 17/21 -21/38 13/16 -8/15 9/11 -1/2 23/28 -10/21 37/45 -1/2 14/17 -7/15 -6/13 19/23 -15/34 5/6 -1/3 21/25 -1/6 37/44 0/1 16/19 0/1 1/1 11/13 -3/4 17/20 -2/5 6/7 -1/1 0/1 19/22 -1/1 13/15 -3/4 7/8 -2/3 8/9 -2/3 -3/5 9/10 -5/9 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(175,156,-396,-353) (-1/1,-8/9) -> (-4/9,-19/43) Hyperbolic Matrix(221,194,352,309) (-8/9,-7/8) -> (5/8,22/35) Hyperbolic Matrix(133,116,-352,-307) (-7/8,-6/7) -> (-14/37,-3/8) Hyperbolic Matrix(89,76,-308,-263) (-6/7,-11/13) -> (-9/31,-2/7) Hyperbolic Matrix(351,296,-836,-705) (-11/13,-5/6) -> (-21/50,-13/31) Hyperbolic Matrix(791,654,1276,1055) (-5/6,-19/23) -> (13/21,31/50) Hyperbolic Matrix(177,146,748,617) (-19/23,-14/17) -> (4/17,5/21) Hyperbolic Matrix(395,324,-484,-397) (-14/17,-9/11) -> (-9/11,-22/27) Parabolic Matrix(2729,2222,3784,3081) (-22/27,-35/43) -> (31/43,44/61) Hyperbolic Matrix(969,788,1408,1145) (-35/43,-13/16) -> (11/16,31/45) Hyperbolic Matrix(87,70,-220,-177) (-13/16,-4/5) -> (-2/5,-11/28) Hyperbolic Matrix(573,454,-1276,-1011) (-4/5,-19/24) -> (-9/20,-22/49) Hyperbolic Matrix(529,418,-1892,-1495) (-19/24,-15/19) -> (-7/25,-19/68) Hyperbolic Matrix(307,242,836,659) (-15/19,-11/14) -> (11/30,7/19) Hyperbolic Matrix(439,344,-1012,-793) (-11/14,-18/23) -> (-10/23,-13/30) Hyperbolic Matrix(923,722,-2420,-1893) (-18/23,-25/32) -> (-29/76,-8/21) Hyperbolic Matrix(1055,824,-1804,-1409) (-25/32,-7/9) -> (-31/53,-7/12) Hyperbolic Matrix(307,238,396,307) (-7/9,-17/22) -> (17/22,7/9) Hyperbolic Matrix(441,340,572,441) (-17/22,-10/13) -> (10/13,17/22) Hyperbolic Matrix(483,370,-748,-573) (-10/13,-13/17) -> (-11/17,-20/31) Hyperbolic Matrix(131,100,748,571) (-13/17,-16/21) -> (4/23,3/17) Hyperbolic Matrix(45,34,176,133) (-16/21,-3/4) -> (1/4,6/23) Hyperbolic Matrix(43,32,176,131) (-3/4,-17/23) -> (5/21,1/4) Hyperbolic Matrix(1055,778,-1672,-1233) (-17/23,-14/19) -> (-12/19,-41/65) Hyperbolic Matrix(837,616,1496,1101) (-14/19,-25/34) -> (19/34,14/25) Hyperbolic Matrix(1189,874,-4488,-3299) (-25/34,-36/49) -> (-22/83,-9/34) Hyperbolic Matrix(1187,872,1496,1099) (-36/49,-11/15) -> (23/29,4/5) Hyperbolic Matrix(351,256,-484,-353) (-11/15,-8/11) -> (-8/11,-21/29) Parabolic Matrix(1495,1082,2552,1847) (-21/29,-34/47) -> (24/41,17/29) Hyperbolic Matrix(617,446,1584,1145) (-34/47,-13/18) -> (7/18,16/41) Hyperbolic Matrix(131,94,-308,-221) (-13/18,-5/7) -> (-3/7,-11/26) Hyperbolic Matrix(45,32,-308,-219) (-5/7,-17/24) -> (-3/20,-1/7) Hyperbolic Matrix(263,186,-748,-529) (-17/24,-12/17) -> (-6/17,-7/20) Hyperbolic Matrix(131,92,-440,-309) (-12/17,-7/10) -> (-3/10,-8/27) Hyperbolic Matrix(219,152,-572,-397) (-7/10,-9/13) -> (-5/13,-13/34) Hyperbolic Matrix(307,212,572,395) (-9/13,-20/29) -> (8/15,7/13) Hyperbolic Matrix(3785,2608,-6512,-4487) (-20/29,-31/45) -> (-25/43,-68/117) Hyperbolic Matrix(1627,1120,1980,1363) (-31/45,-11/16) -> (23/28,37/45) Hyperbolic Matrix(309,212,-704,-483) (-11/16,-2/3) -> (-18/41,-7/16) Hyperbolic Matrix(219,142,-748,-485) (-2/3,-11/17) -> (-5/17,-12/41) Hyperbolic Matrix(1585,1022,-2728,-1759) (-20/31,-9/14) -> (-43/74,-18/31) Hyperbolic Matrix(307,196,-484,-309) (-9/14,-7/11) -> (-7/11,-19/30) Parabolic Matrix(177,112,836,529) (-19/30,-12/19) -> (4/19,3/14) Hyperbolic Matrix(1497,944,-5720,-3607) (-41/65,-29/46) -> (-11/42,-17/65) Hyperbolic Matrix(835,526,2024,1275) (-29/46,-17/27) -> (7/17,19/46) Hyperbolic Matrix(2947,1854,5104,3211) (-17/27,-39/62) -> (15/26,41/71) Hyperbolic Matrix(3037,1910,-8184,-5147) (-39/62,-22/35) -> (-36/97,-23/62) Hyperbolic Matrix(309,194,352,221) (-22/35,-5/8) -> (7/8,8/9) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) Hyperbolic Matrix(1409,874,-2552,-1583) (-18/29,-31/50) -> (-21/38,-16/29) Hyperbolic Matrix(1055,654,1276,791) (-31/50,-13/21) -> (19/23,5/6) Hyperbolic Matrix(175,108,-572,-353) (-13/21,-8/13) -> (-4/13,-7/23) Hyperbolic Matrix(307,188,-792,-485) (-8/13,-11/18) -> (-7/18,-12/31) Hyperbolic Matrix(439,268,1584,967) (-11/18,-25/41) -> (13/47,5/18) Hyperbolic Matrix(351,214,-1012,-617) (-25/41,-14/23) -> (-8/23,-1/3) Hyperbolic Matrix(43,26,-220,-133) (-14/23,-3/5) -> (-1/5,-4/21) Hyperbolic Matrix(131,78,220,131) (-3/5,-13/22) -> (13/22,3/5) Hyperbolic Matrix(441,260,748,441) (-13/22,-10/17) -> (10/17,13/22) Hyperbolic Matrix(749,440,2024,1189) (-10/17,-27/46) -> (17/46,10/27) Hyperbolic Matrix(351,206,748,439) (-27/46,-17/29) -> (7/15,1/2) Hyperbolic Matrix(1321,774,1804,1057) (-17/29,-24/41) -> (30/41,11/15) Hyperbolic Matrix(1583,926,-2860,-1673) (-24/41,-31/53) -> (-5/9,-26/47) Hyperbolic Matrix(2993,1742,4840,2817) (-7/12,-32/55) -> (34/55,47/76) Hyperbolic Matrix(4487,2610,7260,4223) (-32/55,-25/43) -> (55/89,34/55) Hyperbolic Matrix(2595,1508,-11132,-6469) (-68/117,-43/74) -> (-7/30,-24/103) Hyperbolic Matrix(131,76,-836,-485) (-18/31,-11/19) -> (-3/19,-2/13) Hyperbolic Matrix(87,50,-308,-177) (-11/19,-4/7) -> (-2/7,-7/25) Hyperbolic Matrix(219,124,-1012,-573) (-4/7,-13/23) -> (-5/23,-8/37) Hyperbolic Matrix(397,224,-1012,-571) (-13/23,-9/16) -> (-11/28,-9/23) Hyperbolic Matrix(221,124,-704,-395) (-9/16,-14/25) -> (-6/19,-5/16) Hyperbolic Matrix(1101,616,1496,837) (-14/25,-19/34) -> (25/34,14/19) Hyperbolic Matrix(43,24,-396,-221) (-19/34,-5/9) -> (-1/9,-1/10) Hyperbolic Matrix(1277,706,-5808,-3211) (-26/47,-21/38) -> (-11/50,-20/91) Hyperbolic Matrix(265,146,-1276,-703) (-16/29,-11/20) -> (-5/24,-6/29) Hyperbolic Matrix(263,144,-484,-265) (-11/20,-6/11) -> (-6/11,-13/24) Parabolic Matrix(485,262,572,309) (-13/24,-7/13) -> (11/13,17/20) Hyperbolic Matrix(395,212,572,307) (-7/13,-8/15) -> (20/29,9/13) Hyperbolic Matrix(309,164,748,397) (-8/15,-1/2) -> (19/46,12/29) Hyperbolic Matrix(439,206,748,351) (-1/2,-7/15) -> (17/29,27/46) Hyperbolic Matrix(177,82,572,265) (-7/15,-6/13) -> (4/13,9/29) Hyperbolic Matrix(219,100,-484,-221) (-6/13,-5/11) -> (-5/11,-14/31) Parabolic Matrix(967,436,1364,615) (-14/31,-9/20) -> (17/24,22/31) Hyperbolic Matrix(1583,710,2156,967) (-22/49,-13/29) -> (11/15,36/49) Hyperbolic Matrix(969,434,-2552,-1143) (-13/29,-4/9) -> (-30/79,-11/29) Hyperbolic Matrix(2773,1224,4488,1981) (-19/43,-15/34) -> (21/34,55/89) Hyperbolic Matrix(395,174,1496,659) (-15/34,-11/25) -> (5/19,9/34) Hyperbolic Matrix(1233,542,1804,793) (-11/25,-29/66) -> (15/22,13/19) Hyperbolic Matrix(747,328,1100,483) (-29/66,-18/41) -> (2/3,15/22) Hyperbolic Matrix(133,58,-704,-307) (-7/16,-10/23) -> (-4/21,-3/16) Hyperbolic Matrix(351,152,-1628,-705) (-13/30,-3/7) -> (-11/51,-3/14) Hyperbolic Matrix(1893,800,5104,2157) (-11/26,-30/71) -> (10/27,23/62) Hyperbolic Matrix(3257,1376,3960,1673) (-30/71,-19/45) -> (37/45,14/17) Hyperbolic Matrix(351,148,-1672,-705) (-19/45,-8/19) -> (-4/19,-9/43) Hyperbolic Matrix(219,92,-1364,-573) (-8/19,-21/50) -> (-1/6,-4/25) Hyperbolic Matrix(439,184,-1892,-793) (-13/31,-18/43) -> (-10/43,-3/13) Hyperbolic Matrix(2639,1104,3784,1583) (-18/43,-23/55) -> (23/33,30/43) Hyperbolic Matrix(1891,790,2420,1011) (-23/55,-5/12) -> (25/32,43/55) Hyperbolic Matrix(395,164,-1804,-749) (-5/12,-17/41) -> (-9/41,-7/32) Hyperbolic Matrix(705,292,2552,1057) (-17/41,-12/29) -> (8/29,13/47) Hyperbolic Matrix(397,164,748,309) (-12/29,-19/46) -> (1/2,8/15) Hyperbolic Matrix(1275,526,2024,835) (-19/46,-7/17) -> (17/27,29/46) Hyperbolic Matrix(307,126,748,307) (-7/17,-9/22) -> (9/22,7/17) Hyperbolic Matrix(89,36,220,89) (-9/22,-2/5) -> (2/5,9/22) Hyperbolic Matrix(1055,412,-3608,-1409) (-9/23,-16/41) -> (-12/41,-19/65) Hyperbolic Matrix(1319,514,1804,703) (-16/41,-7/18) -> (19/26,30/41) Hyperbolic Matrix(1189,460,1936,749) (-12/31,-17/44) -> (27/44,8/13) Hyperbolic Matrix(1187,458,1936,747) (-17/44,-5/13) -> (19/31,27/44) Hyperbolic Matrix(2507,958,4488,1715) (-13/34,-34/89) -> (24/43,19/34) Hyperbolic Matrix(3037,1160,7260,2773) (-34/89,-21/55) -> (23/55,18/43) Hyperbolic Matrix(2023,772,4840,1847) (-21/55,-29/76) -> (5/12,23/55) Hyperbolic Matrix(221,84,1276,485) (-8/21,-19/50) -> (1/6,4/23) Hyperbolic Matrix(969,368,-4400,-1671) (-19/50,-30/79) -> (-2/9,-11/50) Hyperbolic Matrix(1409,534,1628,617) (-11/29,-25/66) -> (19/22,13/15) Hyperbolic Matrix(1099,416,1276,483) (-25/66,-14/37) -> (6/7,19/22) Hyperbolic Matrix(43,16,352,131) (-3/8,-13/35) -> (1/9,1/8) Hyperbolic Matrix(10957,4068,17424,6469) (-13/35,-49/132) -> (83/132,61/97) Hyperbolic Matrix(10955,4066,17424,6467) (-49/132,-36/97) -> (22/35,83/132) Hyperbolic Matrix(3079,1142,4268,1583) (-23/62,-10/27) -> (44/61,13/18) Hyperbolic Matrix(1189,440,2024,749) (-10/27,-17/46) -> (27/46,10/17) Hyperbolic Matrix(439,162,-1672,-617) (-17/46,-7/19) -> (-5/19,-11/42) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(485,174,616,221) (-9/25,-5/14) -> (11/14,15/19) Hyperbolic Matrix(175,62,-748,-265) (-5/14,-6/17) -> (-4/17,-7/30) Hyperbolic Matrix(395,138,-1892,-661) (-7/20,-8/23) -> (-14/67,-5/24) Hyperbolic Matrix(617,198,1100,353) (-1/3,-7/22) -> (37/66,23/41) Hyperbolic Matrix(1011,320,1804,571) (-7/22,-6/19) -> (14/25,37/66) Hyperbolic Matrix(263,82,1408,439) (-5/16,-14/45) -> (8/43,3/16) Hyperbolic Matrix(1055,328,-4532,-1409) (-14/45,-9/29) -> (-17/73,-10/43) Hyperbolic Matrix(265,82,572,177) (-9/29,-4/13) -> (6/13,7/15) Hyperbolic Matrix(441,134,-2024,-615) (-7/23,-10/33) -> (-12/55,-5/23) Hyperbolic Matrix(2201,666,3784,1145) (-10/33,-13/43) -> (25/43,32/55) Hyperbolic Matrix(397,120,440,133) (-13/43,-3/10) -> (9/10,1/1) Hyperbolic Matrix(1365,404,1936,573) (-8/27,-13/44) -> (31/44,12/17) Hyperbolic Matrix(1363,402,1936,571) (-13/44,-5/17) -> (19/27,31/44) Hyperbolic Matrix(1979,578,-7084,-2069) (-19/65,-7/24) -> (-19/68,-31/111) Hyperbolic Matrix(749,218,1364,397) (-7/24,-9/31) -> (17/31,11/20) Hyperbolic Matrix(17819,4976,22528,6291) (-31/111,-43/154) -> (87/110,53/67) Hyperbolic Matrix(8977,2506,11352,3169) (-43/154,-12/43) -> (34/43,87/110) Hyperbolic Matrix(703,196,3784,1055) (-12/43,-17/61) -> (5/27,8/43) Hyperbolic Matrix(2685,748,4268,1189) (-17/61,-5/18) -> (39/62,17/27) Hyperbolic Matrix(131,36,-484,-133) (-5/18,-3/11) -> (-3/11,-7/26) Parabolic Matrix(1101,296,1804,485) (-7/26,-11/41) -> (25/41,11/18) Hyperbolic Matrix(747,200,1804,483) (-11/41,-4/15) -> (12/29,17/41) Hyperbolic Matrix(1189,316,2156,573) (-4/15,-13/49) -> (27/49,16/29) Hyperbolic Matrix(12805,3396,17424,4621) (-13/49,-35/132) -> (97/132,61/83) Hyperbolic Matrix(12803,3394,17424,4619) (-35/132,-22/83) -> (36/49,97/132) Hyperbolic Matrix(659,174,1496,395) (-9/34,-5/19) -> (11/25,15/34) Hyperbolic Matrix(5721,1496,7744,2025) (-17/65,-23/88) -> (65/88,17/23) Hyperbolic Matrix(5719,1494,7744,2023) (-23/88,-6/23) -> (48/65,65/88) Hyperbolic Matrix(133,34,176,45) (-6/23,-1/4) -> (3/4,16/21) Hyperbolic Matrix(131,32,176,43) (-1/4,-5/21) -> (17/23,3/4) Hyperbolic Matrix(617,146,748,177) (-5/21,-4/17) -> (14/17,19/23) Hyperbolic Matrix(23761,5536,30976,7217) (-24/103,-41/176) -> (135/176,56/73) Hyperbolic Matrix(23759,5534,30976,7215) (-41/176,-17/73) -> (79/103,135/176) Hyperbolic Matrix(131,30,572,131) (-3/13,-5/22) -> (5/22,3/13) Hyperbolic Matrix(89,20,396,89) (-5/22,-2/9) -> (2/9,5/22) Hyperbolic Matrix(13597,2988,17424,3829) (-20/91,-29/132) -> (103/132,32/41) Hyperbolic Matrix(13595,2986,17424,3827) (-29/132,-9/41) -> (71/91,103/132) Hyperbolic Matrix(1409,308,2420,529) (-7/32,-12/55) -> (32/55,7/12) Hyperbolic Matrix(6073,1312,7744,1673) (-8/37,-19/88) -> (69/88,40/51) Hyperbolic Matrix(6071,1310,7744,1671) (-19/88,-11/51) -> (29/37,69/88) Hyperbolic Matrix(395,84,616,131) (-3/14,-4/19) -> (16/25,9/14) Hyperbolic Matrix(8183,1712,11352,2375) (-9/43,-23/110) -> (111/154,31/43) Hyperbolic Matrix(16237,3394,22528,4709) (-23/110,-14/67) -> (80/111,111/154) Hyperbolic Matrix(397,82,1496,309) (-6/29,-1/5) -> (13/49,4/15) Hyperbolic Matrix(87,16,-484,-89) (-3/16,-2/11) -> (-2/11,-5/28) Parabolic Matrix(617,110,1980,353) (-5/28,-8/45) -> (14/45,5/16) Hyperbolic Matrix(2287,406,3960,703) (-8/45,-3/17) -> (41/71,26/45) Hyperbolic Matrix(571,100,748,131) (-3/17,-4/23) -> (16/21,13/17) Hyperbolic Matrix(485,84,1276,221) (-4/23,-1/6) -> (19/50,8/21) Hyperbolic Matrix(1629,260,1936,309) (-4/25,-7/44) -> (37/44,16/19) Hyperbolic Matrix(1627,258,1936,307) (-7/44,-3/19) -> (21/25,37/44) Hyperbolic Matrix(263,40,572,87) (-2/13,-3/20) -> (11/24,6/13) Hyperbolic Matrix(793,110,1276,177) (-1/7,-3/22) -> (41/66,23/37) Hyperbolic Matrix(1011,136,1628,219) (-3/22,-2/15) -> (18/29,41/66) Hyperbolic Matrix(131,16,352,43) (-1/8,-1/9) -> (13/35,3/8) Hyperbolic Matrix(307,30,440,43) (-1/10,0/1) -> (30/43,7/10) Hyperbolic Matrix(221,-24,396,-43) (0/1,1/9) -> (5/9,24/43) Hyperbolic Matrix(219,-28,352,-45) (1/8,1/7) -> (23/37,5/8) Hyperbolic Matrix(219,-32,308,-45) (1/7,2/13) -> (22/31,5/7) Hyperbolic Matrix(485,-76,836,-131) (2/13,1/6) -> (29/50,18/31) Hyperbolic Matrix(89,-16,484,-87) (3/17,2/11) -> (2/11,5/27) Parabolic Matrix(133,-26,220,-43) (3/16,1/5) -> (3/5,17/28) Hyperbolic Matrix(703,-146,1276,-265) (1/5,5/24) -> (11/20,27/49) Hyperbolic Matrix(1363,-286,1892,-397) (5/24,4/19) -> (18/25,49/68) Hyperbolic Matrix(573,-124,1012,-219) (3/14,5/23) -> (13/23,17/30) Hyperbolic Matrix(1497,-326,2420,-527) (5/23,7/32) -> (47/76,13/21) Hyperbolic Matrix(749,-164,1804,-395) (7/32,2/9) -> (22/53,5/12) Hyperbolic Matrix(265,-62,748,-175) (3/13,4/17) -> (6/17,11/31) Hyperbolic Matrix(617,-162,1672,-439) (6/23,5/19) -> (7/19,24/65) Hyperbolic Matrix(3299,-874,4488,-1189) (9/34,13/49) -> (61/83,25/34) Hyperbolic Matrix(133,-36,484,-131) (4/15,3/11) -> (3/11,8/29) Parabolic Matrix(177,-50,308,-87) (5/18,2/7) -> (4/7,15/26) Hyperbolic Matrix(263,-76,308,-89) (2/7,7/24) -> (17/20,6/7) Hyperbolic Matrix(485,-142,748,-219) (7/24,5/17) -> (11/17,13/20) Hyperbolic Matrix(309,-92,440,-131) (5/17,3/10) -> (7/10,19/27) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(2727,-848,6512,-2025) (9/29,14/45) -> (18/43,49/117) Hyperbolic Matrix(395,-124,704,-221) (5/16,1/3) -> (23/41,9/16) Hyperbolic Matrix(529,-186,748,-263) (1/3,6/17) -> (12/17,29/41) Hyperbolic Matrix(1143,-406,2728,-969) (11/31,5/14) -> (31/74,13/31) Hyperbolic Matrix(177,-64,484,-175) (5/14,4/11) -> (4/11,11/30) Parabolic Matrix(4223,-1560,5720,-2113) (24/65,17/46) -> (31/42,48/65) Hyperbolic Matrix(5147,-1910,8184,-3037) (23/62,13/35) -> (61/97,39/62) Hyperbolic Matrix(307,-116,352,-133) (3/8,11/29) -> (13/15,7/8) Hyperbolic Matrix(1143,-434,2552,-969) (11/29,19/50) -> (17/38,13/29) Hyperbolic Matrix(397,-152,572,-219) (8/21,5/13) -> (9/13,16/23) Hyperbolic Matrix(485,-188,792,-307) (5/13,7/18) -> (11/18,19/31) Hyperbolic Matrix(661,-258,1012,-395) (16/41,9/23) -> (15/23,2/3) Hyperbolic Matrix(177,-70,220,-87) (9/23,2/5) -> (4/5,17/21) Hyperbolic Matrix(1277,-530,2860,-1187) (17/41,22/53) -> (4/9,21/47) Hyperbolic Matrix(8537,-3576,11132,-4663) (49/117,31/74) -> (23/30,79/103) Hyperbolic Matrix(705,-296,836,-351) (13/31,8/19) -> (16/19,11/13) Hyperbolic Matrix(221,-94,308,-131) (8/19,3/7) -> (5/7,18/25) Hyperbolic Matrix(793,-344,1012,-439) (3/7,10/23) -> (18/23,29/37) Hyperbolic Matrix(615,-268,1012,-441) (10/23,7/16) -> (17/28,14/23) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(353,-156,396,-175) (15/34,4/9) -> (8/9,9/10) Hyperbolic Matrix(4531,-2026,5808,-2597) (21/47,17/38) -> (39/50,71/91) Hyperbolic Matrix(1011,-454,1276,-573) (13/29,9/20) -> (19/24,23/29) Hyperbolic Matrix(221,-100,484,-219) (9/20,5/11) -> (5/11,11/24) Parabolic Matrix(265,-144,484,-263) (7/13,6/11) -> (6/11,17/31) Parabolic Matrix(1583,-874,2552,-1409) (16/29,5/9) -> (49/79,18/29) Hyperbolic Matrix(571,-322,704,-397) (9/16,13/23) -> (17/21,13/16) Hyperbolic Matrix(1277,-724,1628,-923) (17/30,4/7) -> (40/51,11/14) Hyperbolic Matrix(1321,-764,1672,-967) (26/45,11/19) -> (15/19,34/43) Hyperbolic Matrix(1145,-664,1364,-791) (11/19,29/50) -> (5/6,21/25) Hyperbolic Matrix(1453,-844,1892,-1099) (18/31,25/43) -> (33/43,10/13) Hyperbolic Matrix(1409,-824,1804,-1055) (7/12,24/41) -> (32/41,25/32) Hyperbolic Matrix(2553,-1556,3608,-2199) (14/23,25/41) -> (29/41,46/65) Hyperbolic Matrix(3431,-2128,4400,-2729) (31/50,49/79) -> (7/9,39/50) Hyperbolic Matrix(1233,-778,1672,-1055) (29/46,12/19) -> (14/19,31/42) Hyperbolic Matrix(309,-196,484,-307) (12/19,7/11) -> (7/11,16/25) Parabolic Matrix(573,-370,748,-483) (9/14,11/17) -> (13/17,23/30) Hyperbolic Matrix(1497,-974,1892,-1231) (13/20,15/23) -> (53/67,19/24) Hyperbolic Matrix(3477,-2396,4532,-3123) (31/45,20/29) -> (56/73,33/43) Hyperbolic Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(5105,-3614,7084,-5015) (46/65,17/24) -> (49/68,80/111) Hyperbolic Matrix(353,-256,484,-351) (13/18,8/11) -> (8/11,19/26) Parabolic Matrix(397,-324,484,-395) (13/16,9/11) -> (9/11,23/28) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(175,156,-396,-353) -> Matrix(1,0,0,1) Matrix(221,194,352,309) -> Matrix(1,6,-2,-11) Matrix(133,116,-352,-307) -> Matrix(1,2,0,1) Matrix(89,76,-308,-263) -> Matrix(1,0,0,1) Matrix(351,296,-836,-705) -> Matrix(5,4,-4,-3) Matrix(791,654,1276,1055) -> Matrix(11,-36,-18,59) Matrix(177,146,748,617) -> Matrix(5,-24,-6,29) Matrix(395,324,-484,-397) -> Matrix(1,-18,0,1) Matrix(2729,2222,3784,3081) -> Matrix(1,16,-2,-31) Matrix(969,788,1408,1145) -> Matrix(3,28,-4,-37) Matrix(87,70,-220,-177) -> Matrix(1,4,-2,-7) Matrix(573,454,-1276,-1011) -> Matrix(9,14,-2,-3) Matrix(529,418,-1892,-1495) -> Matrix(1,0,2,1) Matrix(307,242,836,659) -> Matrix(1,-2,-2,5) Matrix(439,344,-1012,-793) -> Matrix(9,16,-4,-7) Matrix(923,722,-2420,-1893) -> Matrix(1,2,-2,-3) Matrix(1055,824,-1804,-1409) -> Matrix(3,4,-4,-5) Matrix(307,238,396,307) -> Matrix(5,6,-6,-7) Matrix(441,340,572,441) -> Matrix(5,4,-4,-3) Matrix(483,370,-748,-573) -> Matrix(5,2,2,1) Matrix(131,100,748,571) -> Matrix(5,2,-8,-3) Matrix(45,34,176,133) -> Matrix(1,2,-2,-3) Matrix(43,32,176,131) -> Matrix(3,-2,-4,3) Matrix(1055,778,-1672,-1233) -> Matrix(13,-32,-2,5) Matrix(837,616,1496,1101) -> Matrix(3,-10,-8,27) Matrix(1189,874,-4488,-3299) -> Matrix(3,-10,-2,7) Matrix(1187,872,1496,1099) -> Matrix(3,-14,-4,19) Matrix(351,256,-484,-353) -> Matrix(1,-16,0,1) Matrix(1495,1082,2552,1847) -> Matrix(3,32,-2,-21) Matrix(617,446,1584,1145) -> Matrix(1,8,2,17) Matrix(131,94,-308,-221) -> Matrix(3,14,-2,-9) Matrix(45,32,-308,-219) -> Matrix(5,14,-4,-11) Matrix(263,186,-748,-529) -> Matrix(3,8,-2,-5) Matrix(131,92,-440,-309) -> Matrix(1,2,-4,-7) Matrix(219,152,-572,-397) -> Matrix(1,2,0,1) Matrix(307,212,572,395) -> Matrix(7,10,-12,-17) Matrix(3785,2608,-6512,-4487) -> Matrix(5,8,-12,-19) Matrix(1627,1120,1980,1363) -> Matrix(17,26,-36,-55) Matrix(309,212,-704,-483) -> Matrix(11,14,-4,-5) Matrix(219,142,-748,-485) -> Matrix(1,-2,2,-3) Matrix(1585,1022,-2728,-1759) -> Matrix(1,-4,-2,9) Matrix(307,196,-484,-309) -> Matrix(1,-14,0,1) Matrix(177,112,836,529) -> Matrix(1,8,0,1) Matrix(1497,944,-5720,-3607) -> Matrix(17,100,-8,-47) Matrix(835,526,2024,1275) -> Matrix(9,46,-10,-51) Matrix(2947,1854,5104,3211) -> Matrix(3,14,-2,-9) Matrix(3037,1910,-8184,-5147) -> Matrix(5,22,2,9) Matrix(309,194,352,221) -> Matrix(1,6,-2,-11) Matrix(45,28,-352,-219) -> Matrix(3,10,-4,-13) Matrix(1409,874,-2552,-1583) -> Matrix(17,48,6,17) Matrix(1055,654,1276,791) -> Matrix(13,36,-30,-83) Matrix(175,108,-572,-353) -> Matrix(5,12,-8,-19) Matrix(307,188,-792,-485) -> Matrix(1,2,-8,-15) Matrix(439,268,1584,967) -> Matrix(5,8,-12,-19) Matrix(351,214,-1012,-617) -> Matrix(5,8,-2,-3) Matrix(43,26,-220,-133) -> Matrix(1,2,-2,-3) Matrix(131,78,220,131) -> Matrix(5,6,-6,-7) Matrix(441,260,748,441) -> Matrix(13,12,-12,-11) Matrix(749,440,2024,1189) -> Matrix(7,6,-20,-17) Matrix(351,206,748,439) -> Matrix(5,4,-14,-11) Matrix(1321,774,1804,1057) -> Matrix(21,16,-46,-35) Matrix(1583,926,-2860,-1673) -> Matrix(1,0,2,1) Matrix(2993,1742,4840,2817) -> Matrix(91,48,-146,-77) Matrix(4487,2610,7260,4223) -> Matrix(109,52,-174,-83) Matrix(2595,1508,-11132,-6469) -> Matrix(19,6,-16,-5) Matrix(131,76,-836,-485) -> Matrix(7,2,-4,-1) Matrix(87,50,-308,-177) -> Matrix(1,0,2,1) Matrix(219,124,-1012,-573) -> Matrix(11,-2,-16,3) Matrix(397,224,-1012,-571) -> Matrix(5,-2,-12,5) Matrix(221,124,-704,-395) -> Matrix(7,-6,-8,7) Matrix(1101,616,1496,837) -> Matrix(7,-10,-16,23) Matrix(43,24,-396,-221) -> Matrix(1,-2,0,1) Matrix(1277,706,-5808,-3211) -> Matrix(21,-46,-26,57) Matrix(265,146,-1276,-703) -> Matrix(1,-4,-2,9) Matrix(263,144,-484,-265) -> Matrix(1,-12,0,1) Matrix(485,262,572,309) -> Matrix(1,6,-2,-11) Matrix(395,212,572,307) -> Matrix(3,10,-4,-13) Matrix(309,164,748,397) -> Matrix(7,22,-8,-25) Matrix(439,206,748,351) -> Matrix(3,-4,-2,3) Matrix(177,82,572,265) -> Matrix(3,-4,-2,3) Matrix(219,100,-484,-221) -> Matrix(1,-10,0,1) Matrix(967,436,1364,615) -> Matrix(5,32,-8,-51) Matrix(1583,710,2156,967) -> Matrix(1,0,-2,1) Matrix(969,434,-2552,-1143) -> Matrix(1,4,2,9) Matrix(2773,1224,4488,1981) -> Matrix(5,42,-8,-67) Matrix(395,174,1496,659) -> Matrix(1,6,-2,-11) Matrix(1233,542,1804,793) -> Matrix(9,28,-10,-31) Matrix(747,328,1100,483) -> Matrix(5,14,-4,-11) Matrix(133,58,-704,-307) -> Matrix(1,2,2,5) Matrix(351,152,-1628,-705) -> Matrix(13,28,-20,-43) Matrix(1893,800,5104,2157) -> Matrix(1,2,-4,-7) Matrix(3257,1376,3960,1673) -> Matrix(13,20,-28,-43) Matrix(351,148,-1672,-705) -> Matrix(3,4,-4,-5) Matrix(219,92,-1364,-573) -> Matrix(11,14,-4,-5) Matrix(439,184,-1892,-793) -> Matrix(5,4,-4,-3) Matrix(2639,1104,3784,1583) -> Matrix(3,4,-4,-5) Matrix(1891,790,2420,1011) -> Matrix(5,6,-6,-7) Matrix(395,164,-1804,-749) -> Matrix(31,38,-40,-49) Matrix(705,292,2552,1057) -> Matrix(17,20,-40,-47) Matrix(397,164,748,309) -> Matrix(19,22,-32,-37) Matrix(1275,526,2024,835) -> Matrix(41,46,-74,-83) Matrix(307,126,748,307) -> Matrix(21,22,-22,-23) Matrix(89,36,220,89) -> Matrix(5,4,-4,-3) Matrix(1055,412,-3608,-1409) -> Matrix(13,4,16,5) Matrix(1319,514,1804,703) -> Matrix(31,8,-66,-17) Matrix(1189,460,1936,749) -> Matrix(37,2,-56,-3) Matrix(1187,458,1936,747) -> Matrix(31,-2,-46,3) Matrix(2507,958,4488,1715) -> Matrix(1,-2,-2,5) Matrix(3037,1160,7260,2773) -> Matrix(3,-2,-4,3) Matrix(2023,772,4840,1847) -> Matrix(3,4,-4,-5) Matrix(221,84,1276,485) -> Matrix(3,-2,-4,3) Matrix(969,368,-4400,-1671) -> Matrix(13,-4,-16,5) Matrix(1409,534,1628,617) -> Matrix(5,-4,-6,5) Matrix(1099,416,1276,483) -> Matrix(1,-2,0,1) Matrix(43,16,352,131) -> Matrix(1,-2,0,1) Matrix(10957,4068,17424,6469) -> Matrix(25,-46,-44,81) Matrix(10955,4066,17424,6467) -> Matrix(15,-34,-26,59) Matrix(3079,1142,4268,1583) -> Matrix(1,4,-2,-7) Matrix(1189,440,2024,749) -> Matrix(5,-6,-4,5) Matrix(439,162,-1672,-617) -> Matrix(5,-12,-2,5) Matrix(175,64,-484,-177) -> Matrix(1,-8,0,1) Matrix(485,174,616,221) -> Matrix(1,6,-2,-11) Matrix(175,62,-748,-265) -> Matrix(7,20,-6,-17) Matrix(395,138,-1892,-661) -> Matrix(1,2,-2,-3) Matrix(617,198,1100,353) -> Matrix(11,12,-34,-37) Matrix(1011,320,1804,571) -> Matrix(19,18,-56,-53) Matrix(263,82,1408,439) -> Matrix(5,4,-14,-11) Matrix(1055,328,-4532,-1409) -> Matrix(13,12,-12,-11) Matrix(265,82,572,177) -> Matrix(5,4,-14,-11) Matrix(441,134,-2024,-615) -> Matrix(37,20,-50,-27) Matrix(2201,666,3784,1145) -> Matrix(17,8,2,1) Matrix(397,120,440,133) -> Matrix(13,6,-24,-11) Matrix(1365,404,1936,573) -> Matrix(29,2,-44,-3) Matrix(1363,402,1936,571) -> Matrix(23,-2,-34,3) Matrix(1979,578,-7084,-2069) -> Matrix(5,-6,6,-7) Matrix(749,218,1364,397) -> Matrix(1,-6,-2,13) Matrix(17819,4976,22528,6291) -> Matrix(31,-30,-32,31) Matrix(8977,2506,11352,3169) -> Matrix(11,-12,-10,11) Matrix(703,196,3784,1055) -> Matrix(3,-4,-8,11) Matrix(2685,748,4268,1189) -> Matrix(9,-14,-16,25) Matrix(131,36,-484,-133) -> Matrix(1,-6,0,1) Matrix(1101,296,1804,485) -> Matrix(3,10,-4,-13) Matrix(747,200,1804,483) -> Matrix(7,22,-8,-25) Matrix(1189,316,2156,573) -> Matrix(7,18,-16,-41) Matrix(12805,3396,17424,4621) -> Matrix(39,82,-88,-185) Matrix(12803,3394,17424,4619) -> Matrix(33,62,-74,-139) Matrix(659,174,1496,395) -> Matrix(1,6,-2,-11) Matrix(5721,1496,7744,2025) -> Matrix(43,88,-108,-221) Matrix(5719,1494,7744,2023) -> Matrix(41,80,-102,-199) Matrix(133,34,176,45) -> Matrix(1,2,-2,-3) Matrix(131,32,176,43) -> Matrix(1,2,-4,-7) Matrix(617,146,748,177) -> Matrix(19,24,-42,-53) Matrix(23761,5536,30976,7217) -> Matrix(7,8,20,23) Matrix(23759,5534,30976,7215) -> Matrix(7,8,-22,-25) Matrix(131,30,572,131) -> Matrix(21,22,-22,-23) Matrix(89,20,396,89) -> Matrix(13,12,-12,-11) Matrix(13597,2988,17424,3829) -> Matrix(137,110,-208,-167) Matrix(13595,2986,17424,3827) -> Matrix(163,130,-242,-193) Matrix(1409,308,2420,529) -> Matrix(21,16,-4,-3) Matrix(6073,1312,7744,1673) -> Matrix(119,80,-180,-121) Matrix(6071,1310,7744,1671) -> Matrix(109,72,-162,-107) Matrix(395,84,616,131) -> Matrix(11,6,-24,-13) Matrix(8183,1712,11352,2375) -> Matrix(17,8,-32,-15) Matrix(16237,3394,22528,4709) -> Matrix(25,6,-46,-11) Matrix(397,82,1496,309) -> Matrix(9,2,-14,-3) Matrix(87,16,-484,-89) -> Matrix(1,-4,0,1) Matrix(617,110,1980,353) -> Matrix(3,8,-2,-5) Matrix(2287,406,3960,703) -> Matrix(3,8,-2,-5) Matrix(571,100,748,131) -> Matrix(1,2,0,1) Matrix(485,84,1276,221) -> Matrix(1,2,-4,-7) Matrix(1629,260,1936,309) -> Matrix(1,2,4,9) Matrix(1627,258,1936,307) -> Matrix(1,2,-10,-19) Matrix(263,40,572,87) -> Matrix(5,8,-12,-19) Matrix(793,110,1276,177) -> Matrix(49,52,-82,-87) Matrix(1011,136,1628,219) -> Matrix(65,62,-108,-103) Matrix(131,16,352,43) -> Matrix(3,2,-8,-5) Matrix(307,30,440,43) -> Matrix(1,2,-2,-3) Matrix(221,-24,396,-43) -> Matrix(3,2,-8,-5) Matrix(219,-28,352,-45) -> Matrix(7,10,-12,-17) Matrix(219,-32,308,-45) -> Matrix(17,14,-28,-23) Matrix(485,-76,836,-131) -> Matrix(3,2,4,3) Matrix(89,-16,484,-87) -> Matrix(7,4,-16,-9) Matrix(133,-26,220,-43) -> Matrix(1,2,-2,-3) Matrix(703,-146,1276,-265) -> Matrix(1,-4,-2,9) Matrix(1363,-286,1892,-397) -> Matrix(1,6,-2,-11) Matrix(573,-124,1012,-219) -> Matrix(1,2,-8,-15) Matrix(1497,-326,2420,-527) -> Matrix(41,64,-66,-103) Matrix(749,-164,1804,-395) -> Matrix(27,38,-32,-45) Matrix(265,-62,748,-175) -> Matrix(23,20,-38,-33) Matrix(617,-162,1672,-439) -> Matrix(19,12,-46,-29) Matrix(3299,-874,4488,-1189) -> Matrix(13,10,-30,-23) Matrix(133,-36,484,-131) -> Matrix(11,6,-24,-13) Matrix(177,-50,308,-87) -> Matrix(1,0,2,1) Matrix(263,-76,308,-89) -> Matrix(1,0,0,1) Matrix(485,-142,748,-219) -> Matrix(7,2,-18,-5) Matrix(309,-92,440,-131) -> Matrix(3,-2,-4,3) Matrix(353,-108,572,-175) -> Matrix(5,12,-8,-19) Matrix(2727,-848,6512,-2025) -> Matrix(7,8,-8,-9) Matrix(395,-124,704,-221) -> Matrix(5,6,-16,-19) Matrix(529,-186,748,-263) -> Matrix(11,8,-18,-13) Matrix(1143,-406,2728,-969) -> Matrix(13,8,-18,-11) Matrix(177,-64,484,-175) -> Matrix(15,8,-32,-17) Matrix(4223,-1560,5720,-2113) -> Matrix(81,32,-200,-79) Matrix(5147,-1910,8184,-3037) -> Matrix(53,22,-94,-39) Matrix(307,-116,352,-133) -> Matrix(5,2,-8,-3) Matrix(1143,-434,2552,-969) -> Matrix(17,4,-30,-7) Matrix(397,-152,572,-219) -> Matrix(5,2,-8,-3) Matrix(485,-188,792,-307) -> Matrix(11,-2,-16,3) Matrix(661,-258,1012,-395) -> Matrix(3,-2,-10,7) Matrix(177,-70,220,-87) -> Matrix(1,4,-2,-7) Matrix(1277,-530,2860,-1187) -> Matrix(73,62,-126,-107) Matrix(8537,-3576,11132,-4663) -> Matrix(5,4,-4,-3) Matrix(705,-296,836,-351) -> Matrix(5,4,-4,-3) Matrix(221,-94,308,-131) -> Matrix(19,14,-34,-25) Matrix(793,-344,1012,-439) -> Matrix(25,16,-36,-23) Matrix(615,-268,1012,-441) -> Matrix(25,16,-36,-23) Matrix(483,-212,704,-309) -> Matrix(23,14,-28,-17) Matrix(353,-156,396,-175) -> Matrix(1,0,0,1) Matrix(4531,-2026,5808,-2597) -> Matrix(81,46,-118,-67) Matrix(1011,-454,1276,-573) -> Matrix(25,14,-34,-19) Matrix(221,-100,484,-219) -> Matrix(19,10,-40,-21) Matrix(265,-144,484,-263) -> Matrix(23,12,-48,-25) Matrix(1583,-874,2552,-1409) -> Matrix(113,48,-186,-79) Matrix(571,-322,704,-397) -> Matrix(25,6,-46,-11) Matrix(1277,-724,1628,-923) -> Matrix(21,2,-32,-3) Matrix(1321,-764,1672,-967) -> Matrix(1,0,0,1) Matrix(1145,-664,1364,-791) -> Matrix(1,0,-4,1) Matrix(1453,-844,1892,-1099) -> Matrix(1,-2,0,1) Matrix(1409,-824,1804,-1055) -> Matrix(3,4,-4,-5) Matrix(2553,-1556,3608,-2199) -> Matrix(23,16,-36,-25) Matrix(3431,-2128,4400,-2729) -> Matrix(125,76,-176,-107) Matrix(1233,-778,1672,-1055) -> Matrix(59,32,-142,-77) Matrix(309,-196,484,-307) -> Matrix(27,14,-56,-29) Matrix(573,-370,748,-483) -> Matrix(5,2,2,1) Matrix(1497,-974,1892,-1231) -> Matrix(23,8,-26,-9) Matrix(3477,-2396,4532,-3123) -> Matrix(3,2,4,3) Matrix(1583,-1102,2024,-1409) -> Matrix(13,8,-18,-11) Matrix(5105,-3614,7084,-5015) -> Matrix(45,28,-82,-51) Matrix(353,-256,484,-351) -> Matrix(31,16,-64,-33) Matrix(397,-324,484,-395) -> Matrix(35,18,-72,-37) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 120 Degree of the the map X: 120 Degree of the the map Y: 240 ----------------------------------------------------------------------- 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): 720 Minimal number of generators: 121 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: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/11 -7/11 -1/2 -5/11 -21/55 -7/22 -10/33 -3/10 -3/11 -5/19 -23/88 -1/4 -1/6 -3/22 -1/8 0/1 1/8 1/7 1/6 3/17 2/11 1/5 2/9 5/22 3/13 1/4 3/11 2/7 3/10 1/3 4/11 2/5 9/22 5/11 7/15 1/2 6/11 5/9 13/22 13/21 7/11 2/3 15/22 23/33 8/11 17/22 9/11 19/22 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -8/9 -3/1 -2/1 -7/8 -2/1 -6/7 -1/1 0/1 -11/13 -3/2 -5/6 1/1 -9/11 1/0 -13/16 -8/1 -4/5 -3/1 -2/1 -11/14 -3/1 -18/23 -2/1 -1/1 -25/32 -2/1 -7/9 -3/2 -17/22 -1/1 -10/13 -1/1 -2/3 -13/17 1/0 -16/21 -1/5 0/1 -3/4 0/1 -14/19 8/3 3/1 -11/15 1/0 -8/11 1/0 -5/7 -7/2 -7/10 -1/1 -9/13 -7/4 -11/16 -4/3 -2/3 -1/1 0/1 -7/11 1/0 -12/19 -8/1 -7/1 -17/27 -9/2 -22/35 -4/1 -3/1 -5/8 -4/1 -18/29 -3/1 -26/9 -13/21 -21/8 -8/13 -11/5 -2/1 -3/5 -3/2 -13/22 -1/1 -10/17 -1/1 -6/7 -27/46 -7/9 -17/29 -3/4 -24/41 -9/13 -2/3 -7/12 -2/3 -25/43 -1/2 -18/31 -1/3 0/1 -11/19 1/0 -4/7 -1/3 0/1 -13/23 3/10 -9/16 2/3 -14/25 1/1 6/5 -19/34 1/1 -5/9 1/0 -6/11 1/0 -7/13 -9/2 -1/2 -1/1 -5/11 1/0 -9/20 -6/1 -13/29 1/0 -4/9 -3/1 -2/1 -11/25 -7/2 -29/66 -3/1 -18/41 -3/1 -14/5 -7/16 -2/1 -3/7 -7/4 -5/12 -4/3 -7/17 -11/10 -9/22 -1/1 -2/5 -1/1 -2/3 -11/28 -4/9 -9/23 -5/14 -16/41 -5/17 -2/7 -7/18 -1/5 -5/13 1/4 -13/34 1/1 -21/55 1/0 -29/76 0/1 -8/21 -1/1 0/1 -19/50 1/1 -11/29 1/2 -25/66 1/1 -14/37 1/1 2/1 -3/8 0/1 -10/27 0/1 1/1 -17/46 5/3 -7/19 1/0 -4/11 1/0 -1/3 -3/2 -7/22 -1/1 -6/19 -1/1 -12/13 -5/16 -4/5 -9/29 -3/4 -4/13 -5/7 -2/3 -7/23 -9/16 -10/33 -1/2 -13/43 -1/2 -3/10 -1/3 -5/17 1/4 -12/41 3/5 2/3 -19/65 9/10 -7/24 2/1 -9/31 -3/2 -2/7 -1/1 0/1 -3/11 1/0 -4/15 -4/1 -3/1 -5/19 -5/2 -11/42 -11/5 -17/65 -33/16 -23/88 -2/1 -6/23 -2/1 -9/5 -1/4 -2/1 -3/13 -11/10 -5/22 -1/1 -2/9 -1/1 -6/7 -1/5 1/0 -2/11 1/0 -3/17 -5/2 -4/23 -2/1 -5/3 -1/6 -1/1 -1/7 -7/6 -3/22 -1/1 -2/15 -1/1 -12/13 -1/8 -2/3 0/1 -1/1 0/1 1/8 -2/1 1/7 -7/8 1/6 -1/1 4/23 -5/7 -2/3 3/17 -5/8 2/11 -1/2 1/5 -1/2 2/9 -6/5 -1/1 5/22 -1/1 3/13 -11/12 1/4 -2/3 3/11 -1/2 5/18 -1/3 2/7 -1/1 0/1 7/24 -2/5 5/17 -1/6 3/10 1/1 4/13 -2/1 -5/3 9/29 -3/2 5/16 -4/3 1/3 -3/4 4/11 -1/2 7/19 -1/2 3/8 0/1 11/29 -1/4 19/50 -1/3 8/21 -1/1 0/1 5/13 -1/6 7/18 1/3 9/23 5/4 2/5 -2/1 -1/1 9/22 -1/1 7/17 -11/12 5/12 -4/5 3/7 -7/10 7/16 -2/3 11/25 -7/12 4/9 -2/3 -3/5 5/11 -1/2 6/13 -3/7 -2/5 7/15 -1/2 1/2 -1/1 7/13 -9/16 6/11 -1/2 5/9 -1/2 19/34 -1/3 14/25 -6/17 -1/3 37/66 -1/3 23/41 -9/28 9/16 -2/7 13/23 -3/16 4/7 0/1 1/1 15/26 -1/1 26/45 -6/5 -1/1 11/19 -1/2 18/31 0/1 1/1 25/43 1/0 7/12 -2/1 17/29 -3/2 27/46 -7/5 10/17 -6/5 -1/1 13/22 -1/1 3/5 -3/4 8/13 -2/3 -11/17 21/34 -17/27 55/89 -5/8 34/55 -5/8 13/21 -21/34 18/29 -26/43 -3/5 41/66 -3/5 23/37 -31/52 5/8 -4/7 7/11 -1/2 9/14 -3/7 11/17 -5/12 13/20 -4/11 2/3 -1/1 0/1 15/22 -1/1 13/19 -7/8 11/16 -4/5 9/13 -7/10 16/23 -2/3 -3/5 23/33 -1/2 7/10 -1/1 5/7 -7/12 8/11 -1/2 11/15 -1/2 25/34 -3/7 14/19 -3/7 -8/19 31/42 -11/27 17/23 -11/28 3/4 0/1 16/21 0/1 1/3 13/17 -1/2 23/30 -1/1 10/13 -2/1 -1/1 17/22 -1/1 7/9 -3/4 25/32 -2/3 43/55 -3/4 18/23 -1/1 -2/3 11/14 -3/5 15/19 -1/2 34/43 -6/5 -1/1 87/110 -1/1 53/67 -15/16 19/24 -4/5 4/5 -2/3 -3/5 9/11 -1/2 14/17 -7/15 -6/13 19/23 -15/34 5/6 -1/3 11/13 -3/4 17/20 -2/5 6/7 -1/1 0/1 19/22 -1/1 13/15 -3/4 7/8 -2/3 8/9 -2/3 -3/5 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(243,218,418,375) (-1/1,-8/9) -> (18/31,25/43) Hyperbolic Matrix(287,254,374,331) (-8/9,-7/8) -> (23/30,10/13) Hyperbolic Matrix(133,116,-352,-307) (-7/8,-6/7) -> (-14/37,-3/8) Hyperbolic Matrix(89,76,-308,-263) (-6/7,-11/13) -> (-9/31,-2/7) Hyperbolic Matrix(197,166,286,241) (-11/13,-5/6) -> (11/16,9/13) Hyperbolic Matrix(197,162,-242,-199) (-5/6,-9/11) -> (-9/11,-13/16) Parabolic Matrix(87,70,-220,-177) (-13/16,-4/5) -> (-2/5,-11/28) Hyperbolic Matrix(155,122,-418,-329) (-4/5,-11/14) -> (-3/8,-10/27) Hyperbolic Matrix(23,18,198,155) (-11/14,-18/23) -> (0/1,1/8) Hyperbolic Matrix(923,722,-2420,-1893) (-18/23,-25/32) -> (-29/76,-8/21) Hyperbolic Matrix(331,258,594,463) (-25/32,-7/9) -> (5/9,19/34) Hyperbolic Matrix(307,238,396,307) (-7/9,-17/22) -> (17/22,7/9) Hyperbolic Matrix(441,340,572,441) (-17/22,-10/13) -> (10/13,17/22) Hyperbolic Matrix(595,456,-946,-725) (-10/13,-13/17) -> (-17/27,-22/35) Hyperbolic Matrix(131,100,748,571) (-13/17,-16/21) -> (4/23,3/17) Hyperbolic Matrix(419,318,726,551) (-16/21,-3/4) -> (15/26,26/45) Hyperbolic Matrix(197,146,-506,-375) (-3/4,-14/19) -> (-16/41,-7/18) Hyperbolic Matrix(683,502,-1166,-857) (-14/19,-11/15) -> (-17/29,-24/41) Hyperbolic Matrix(241,176,330,241) (-11/15,-8/11) -> (8/11,11/15) Hyperbolic Matrix(111,80,154,111) (-8/11,-5/7) -> (5/7,8/11) Hyperbolic Matrix(65,46,154,109) (-5/7,-7/10) -> (5/12,3/7) Hyperbolic Matrix(219,152,-572,-397) (-7/10,-9/13) -> (-5/13,-13/34) Hyperbolic Matrix(241,166,286,197) (-9/13,-11/16) -> (5/6,11/13) Hyperbolic Matrix(309,212,-704,-483) (-11/16,-2/3) -> (-18/41,-7/16) Hyperbolic Matrix(153,98,-242,-155) (-2/3,-7/11) -> (-7/11,-12/19) Parabolic Matrix(419,264,-1430,-901) (-12/19,-17/27) -> (-5/17,-12/41) Hyperbolic Matrix(309,194,352,221) (-22/35,-5/8) -> (7/8,8/9) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) Hyperbolic Matrix(461,286,814,505) (-18/29,-13/21) -> (13/23,4/7) Hyperbolic Matrix(175,108,-572,-353) (-13/21,-8/13) -> (-4/13,-7/23) Hyperbolic Matrix(23,14,110,67) (-8/13,-3/5) -> (1/5,2/9) Hyperbolic Matrix(131,78,220,131) (-3/5,-13/22) -> (13/22,3/5) Hyperbolic Matrix(441,260,748,441) (-13/22,-10/17) -> (10/17,13/22) Hyperbolic Matrix(507,298,638,375) (-10/17,-27/46) -> (19/24,4/5) Hyperbolic Matrix(351,206,748,439) (-27/46,-17/29) -> (7/15,1/2) Hyperbolic Matrix(947,554,1694,991) (-24/41,-7/12) -> (19/34,14/25) Hyperbolic Matrix(285,166,-946,-551) (-7/12,-25/43) -> (-13/43,-3/10) Hyperbolic Matrix(375,218,418,243) (-25/43,-18/31) -> (8/9,1/1) Hyperbolic Matrix(417,242,946,549) (-18/31,-11/19) -> (11/25,4/9) Hyperbolic Matrix(111,64,-418,-241) (-11/19,-4/7) -> (-4/15,-5/19) Hyperbolic Matrix(505,286,814,461) (-4/7,-13/23) -> (13/21,18/29) Hyperbolic Matrix(397,224,-1012,-571) (-13/23,-9/16) -> (-11/28,-9/23) Hyperbolic Matrix(221,124,-704,-395) (-9/16,-14/25) -> (-6/19,-5/16) Hyperbolic Matrix(1101,616,1496,837) (-14/25,-19/34) -> (25/34,14/19) Hyperbolic Matrix(463,258,594,331) (-19/34,-5/9) -> (7/9,25/32) Hyperbolic Matrix(109,60,198,109) (-5/9,-6/11) -> (6/11,5/9) Hyperbolic Matrix(155,84,286,155) (-6/11,-7/13) -> (7/13,6/11) Hyperbolic Matrix(109,58,-374,-199) (-7/13,-1/2) -> (-7/24,-9/31) Hyperbolic Matrix(109,50,-242,-111) (-1/2,-5/11) -> (-5/11,-9/20) Parabolic Matrix(1123,504,1914,859) (-9/20,-13/29) -> (17/29,27/46) Hyperbolic Matrix(197,88,638,285) (-13/29,-4/9) -> (4/13,9/29) Hyperbolic Matrix(549,242,946,417) (-4/9,-11/25) -> (11/19,18/31) Hyperbolic Matrix(1233,542,1804,793) (-11/25,-29/66) -> (15/22,13/19) Hyperbolic Matrix(747,328,1100,483) (-29/66,-18/41) -> (2/3,15/22) Hyperbolic Matrix(23,10,154,67) (-7/16,-3/7) -> (1/7,1/6) Hyperbolic Matrix(109,46,154,65) (-3/7,-5/12) -> (7/10,5/7) Hyperbolic Matrix(111,46,374,155) (-5/12,-7/17) -> (5/17,3/10) Hyperbolic Matrix(307,126,748,307) (-7/17,-9/22) -> (9/22,7/17) Hyperbolic Matrix(89,36,220,89) (-9/22,-2/5) -> (2/5,9/22) Hyperbolic Matrix(1055,412,-3608,-1409) (-9/23,-16/41) -> (-12/41,-19/65) Hyperbolic Matrix(67,26,286,111) (-7/18,-5/13) -> (3/13,1/4) Hyperbolic Matrix(2309,882,-6050,-2311) (-13/34,-21/55) -> (-21/55,-29/76) Parabolic Matrix(221,84,1276,485) (-8/21,-19/50) -> (1/6,4/23) Hyperbolic Matrix(595,226,1914,727) (-19/50,-11/29) -> (9/29,5/16) Hyperbolic Matrix(1409,534,1628,617) (-11/29,-25/66) -> (19/22,13/15) Hyperbolic Matrix(1099,416,1276,483) (-25/66,-14/37) -> (6/7,19/22) Hyperbolic Matrix(1189,440,2024,749) (-10/27,-17/46) -> (27/46,10/17) Hyperbolic Matrix(439,162,-1672,-617) (-17/46,-7/19) -> (-5/19,-11/42) Hyperbolic Matrix(153,56,418,153) (-7/19,-4/11) -> (4/11,7/19) Hyperbolic Matrix(23,8,66,23) (-4/11,-1/3) -> (1/3,4/11) Hyperbolic Matrix(617,198,1100,353) (-1/3,-7/22) -> (37/66,23/41) Hyperbolic Matrix(1011,320,1804,571) (-7/22,-6/19) -> (14/25,37/66) Hyperbolic Matrix(727,226,1914,595) (-5/16,-9/29) -> (11/29,19/50) Hyperbolic Matrix(265,82,572,177) (-9/29,-4/13) -> (6/13,7/15) Hyperbolic Matrix(1211,368,1958,595) (-7/23,-10/33) -> (34/55,13/21) Hyperbolic Matrix(3277,992,5302,1605) (-10/33,-13/43) -> (55/89,34/55) Hyperbolic Matrix(155,46,374,111) (-3/10,-5/17) -> (7/17,5/12) Hyperbolic Matrix(1123,328,-4290,-1253) (-19/65,-7/24) -> (-11/42,-17/65) Hyperbolic Matrix(65,18,-242,-67) (-2/7,-3/11) -> (-3/11,-4/15) Parabolic Matrix(10319,2698,13046,3411) (-17/65,-23/88) -> (87/110,53/67) Hyperbolic Matrix(4993,1304,6314,1649) (-23/88,-6/23) -> (34/43,87/110) Hyperbolic Matrix(133,34,176,45) (-6/23,-1/4) -> (3/4,16/21) Hyperbolic Matrix(111,26,286,67) (-1/4,-3/13) -> (5/13,7/18) Hyperbolic Matrix(131,30,572,131) (-3/13,-5/22) -> (5/22,3/13) Hyperbolic Matrix(89,20,396,89) (-5/22,-2/9) -> (2/9,5/22) Hyperbolic Matrix(67,14,110,23) (-2/9,-1/5) -> (3/5,8/13) Hyperbolic Matrix(21,4,110,21) (-1/5,-2/11) -> (2/11,1/5) Hyperbolic Matrix(67,12,374,67) (-2/11,-3/17) -> (3/17,2/11) Hyperbolic Matrix(571,100,748,131) (-3/17,-4/23) -> (16/21,13/17) Hyperbolic Matrix(485,84,1276,221) (-4/23,-1/6) -> (19/50,8/21) Hyperbolic Matrix(67,10,154,23) (-1/6,-1/7) -> (3/7,7/16) Hyperbolic Matrix(793,110,1276,177) (-1/7,-3/22) -> (41/66,23/37) Hyperbolic Matrix(1011,136,1628,219) (-3/22,-2/15) -> (18/29,41/66) Hyperbolic Matrix(155,18,198,23) (-1/8,0/1) -> (18/23,11/14) Hyperbolic Matrix(219,-28,352,-45) (1/8,1/7) -> (23/37,5/8) Hyperbolic Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(177,-50,308,-87) (5/18,2/7) -> (4/7,15/26) Hyperbolic Matrix(263,-76,308,-89) (2/7,7/24) -> (17/20,6/7) Hyperbolic Matrix(485,-142,748,-219) (7/24,5/17) -> (11/17,13/20) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(395,-124,704,-221) (5/16,1/3) -> (23/41,9/16) Hyperbolic Matrix(329,-122,418,-155) (7/19,3/8) -> (11/14,15/19) Hyperbolic Matrix(307,-116,352,-133) (3/8,11/29) -> (13/15,7/8) Hyperbolic Matrix(397,-152,572,-219) (8/21,5/13) -> (9/13,16/23) Hyperbolic Matrix(375,-146,506,-197) (7/18,9/23) -> (17/23,3/4) Hyperbolic Matrix(417,-164,506,-199) (9/23,2/5) -> (14/17,19/23) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(243,-130,286,-153) (1/2,7/13) -> (11/13,17/20) Hyperbolic Matrix(419,-236,506,-285) (9/16,13/23) -> (19/23,5/6) Hyperbolic Matrix(1321,-764,1672,-967) (26/45,11/19) -> (15/19,34/43) Hyperbolic Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(857,-502,1166,-683) (7/12,17/29) -> (11/15,25/34) Hyperbolic Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(573,-370,748,-483) (9/14,11/17) -> (13/17,23/30) Hyperbolic Matrix(373,-244,506,-331) (13/20,2/3) -> (14/19,31/42) Hyperbolic Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(1255,-876,1606,-1121) (23/33,7/10) -> (25/32,43/55) Hyperbolic Matrix(2663,-1966,3366,-2485) (31/42,17/23) -> (53/67,19/24) Hyperbolic Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(243,218,418,375) -> Matrix(1,3,0,1) Matrix(287,254,374,331) -> Matrix(1,1,0,1) Matrix(133,116,-352,-307) -> Matrix(1,2,0,1) Matrix(89,76,-308,-263) -> Matrix(1,0,0,1) Matrix(197,166,286,241) -> Matrix(3,1,-4,-1) Matrix(197,162,-242,-199) -> Matrix(1,-9,0,1) Matrix(87,70,-220,-177) -> Matrix(1,4,-2,-7) Matrix(155,122,-418,-329) -> Matrix(1,3,0,1) Matrix(23,18,198,155) -> Matrix(1,1,0,1) Matrix(923,722,-2420,-1893) -> Matrix(1,2,-2,-3) Matrix(331,258,594,463) -> Matrix(3,5,-8,-13) Matrix(307,238,396,307) -> Matrix(5,6,-6,-7) Matrix(441,340,572,441) -> Matrix(5,4,-4,-3) Matrix(595,456,-946,-725) -> Matrix(9,5,-2,-1) Matrix(131,100,748,571) -> Matrix(5,2,-8,-3) Matrix(419,318,726,551) -> Matrix(1,-1,0,1) Matrix(197,146,-506,-375) -> Matrix(1,-1,-4,5) Matrix(683,502,-1166,-857) -> Matrix(3,-11,-4,15) Matrix(241,176,330,241) -> Matrix(1,-9,-2,19) Matrix(111,80,154,111) -> Matrix(1,7,-2,-13) Matrix(65,46,154,109) -> Matrix(3,7,-4,-9) Matrix(219,152,-572,-397) -> Matrix(1,2,0,1) Matrix(241,166,286,197) -> Matrix(1,1,0,1) Matrix(309,212,-704,-483) -> Matrix(11,14,-4,-5) Matrix(153,98,-242,-155) -> Matrix(1,-7,0,1) Matrix(419,264,-1430,-901) -> Matrix(1,5,2,11) Matrix(309,194,352,221) -> Matrix(1,6,-2,-11) Matrix(45,28,-352,-219) -> Matrix(3,10,-4,-13) Matrix(461,286,814,505) -> Matrix(1,3,-8,-23) Matrix(175,108,-572,-353) -> Matrix(5,12,-8,-19) Matrix(23,14,110,67) -> Matrix(1,1,0,1) Matrix(131,78,220,131) -> Matrix(5,6,-6,-7) Matrix(441,260,748,441) -> Matrix(13,12,-12,-11) Matrix(507,298,638,375) -> Matrix(11,9,-16,-13) Matrix(351,206,748,439) -> Matrix(5,4,-14,-11) Matrix(947,554,1694,991) -> Matrix(5,3,-12,-7) Matrix(285,166,-946,-551) -> Matrix(5,3,-12,-7) Matrix(375,218,418,243) -> Matrix(7,3,-12,-5) Matrix(417,242,946,549) -> Matrix(7,3,-12,-5) Matrix(111,64,-418,-241) -> Matrix(5,3,-2,-1) Matrix(505,286,814,461) -> Matrix(17,-3,-28,5) Matrix(397,224,-1012,-571) -> Matrix(5,-2,-12,5) Matrix(221,124,-704,-395) -> Matrix(7,-6,-8,7) Matrix(1101,616,1496,837) -> Matrix(7,-10,-16,23) Matrix(463,258,594,331) -> Matrix(3,-5,-4,7) Matrix(109,60,198,109) -> Matrix(1,-3,-2,7) Matrix(155,84,286,155) -> Matrix(1,9,-2,-17) Matrix(109,58,-374,-199) -> Matrix(1,3,0,1) Matrix(109,50,-242,-111) -> Matrix(1,-5,0,1) Matrix(1123,504,1914,859) -> Matrix(3,11,-2,-7) Matrix(197,88,638,285) -> Matrix(3,11,-2,-7) Matrix(549,242,946,417) -> Matrix(1,3,0,1) Matrix(1233,542,1804,793) -> Matrix(9,28,-10,-31) Matrix(747,328,1100,483) -> Matrix(5,14,-4,-11) Matrix(23,10,154,67) -> Matrix(3,7,-4,-9) Matrix(109,46,154,65) -> Matrix(5,7,-8,-11) Matrix(111,46,374,155) -> Matrix(1,1,4,5) Matrix(307,126,748,307) -> Matrix(21,22,-22,-23) Matrix(89,36,220,89) -> Matrix(5,4,-4,-3) Matrix(1055,412,-3608,-1409) -> Matrix(13,4,16,5) Matrix(67,26,286,111) -> Matrix(7,1,-8,-1) Matrix(2309,882,-6050,-2311) -> Matrix(1,-1,0,1) Matrix(221,84,1276,485) -> Matrix(3,-2,-4,3) Matrix(595,226,1914,727) -> Matrix(5,-1,-4,1) Matrix(1409,534,1628,617) -> Matrix(5,-4,-6,5) Matrix(1099,416,1276,483) -> Matrix(1,-2,0,1) Matrix(1189,440,2024,749) -> Matrix(5,-6,-4,5) Matrix(439,162,-1672,-617) -> Matrix(5,-12,-2,5) Matrix(153,56,418,153) -> Matrix(1,-5,-2,11) Matrix(23,8,66,23) -> Matrix(1,3,-2,-5) Matrix(617,198,1100,353) -> Matrix(11,12,-34,-37) Matrix(1011,320,1804,571) -> Matrix(19,18,-56,-53) Matrix(727,226,1914,595) -> Matrix(1,1,-8,-7) Matrix(265,82,572,177) -> Matrix(5,4,-14,-11) Matrix(1211,368,1958,595) -> Matrix(61,33,-98,-53) Matrix(3277,992,5302,1605) -> Matrix(139,67,-222,-107) Matrix(155,46,374,111) -> Matrix(7,1,-8,-1) Matrix(1123,328,-4290,-1253) -> Matrix(13,-15,-6,7) Matrix(65,18,-242,-67) -> Matrix(1,-3,0,1) Matrix(10319,2698,13046,3411) -> Matrix(31,63,-32,-65) Matrix(4993,1304,6314,1649) -> Matrix(11,21,-10,-19) Matrix(133,34,176,45) -> Matrix(1,2,-2,-3) Matrix(111,26,286,67) -> Matrix(1,1,4,5) Matrix(131,30,572,131) -> Matrix(21,22,-22,-23) Matrix(89,20,396,89) -> Matrix(13,12,-12,-11) Matrix(67,14,110,23) -> Matrix(3,1,-4,-1) Matrix(21,4,110,21) -> Matrix(1,1,-2,-1) Matrix(67,12,374,67) -> Matrix(1,5,-2,-9) Matrix(571,100,748,131) -> Matrix(1,2,0,1) Matrix(485,84,1276,221) -> Matrix(1,2,-4,-7) Matrix(67,10,154,23) -> Matrix(5,7,-8,-11) Matrix(793,110,1276,177) -> Matrix(49,52,-82,-87) Matrix(1011,136,1628,219) -> Matrix(65,62,-108,-103) Matrix(155,18,198,23) -> Matrix(3,1,-4,-1) Matrix(219,-28,352,-45) -> Matrix(7,10,-12,-17) Matrix(67,-18,242,-65) -> Matrix(5,3,-12,-7) Matrix(177,-50,308,-87) -> Matrix(1,0,2,1) Matrix(263,-76,308,-89) -> Matrix(1,0,0,1) Matrix(485,-142,748,-219) -> Matrix(7,2,-18,-5) Matrix(353,-108,572,-175) -> Matrix(5,12,-8,-19) Matrix(395,-124,704,-221) -> Matrix(5,6,-16,-19) Matrix(329,-122,418,-155) -> Matrix(7,3,-12,-5) Matrix(307,-116,352,-133) -> Matrix(5,2,-8,-3) Matrix(397,-152,572,-219) -> Matrix(5,2,-8,-3) Matrix(375,-146,506,-197) -> Matrix(3,-1,-8,3) Matrix(417,-164,506,-199) -> Matrix(1,-5,-2,11) Matrix(483,-212,704,-309) -> Matrix(23,14,-28,-17) Matrix(111,-50,242,-109) -> Matrix(9,5,-20,-11) Matrix(243,-130,286,-153) -> Matrix(5,3,-12,-7) Matrix(419,-236,506,-285) -> Matrix(11,3,-26,-7) Matrix(1321,-764,1672,-967) -> Matrix(1,0,0,1) Matrix(1563,-910,2530,-1473) -> Matrix(5,27,-8,-43) Matrix(857,-502,1166,-683) -> Matrix(7,11,-16,-25) Matrix(155,-98,242,-153) -> Matrix(13,7,-28,-15) Matrix(573,-370,748,-483) -> Matrix(5,2,2,1) Matrix(373,-244,506,-331) -> Matrix(11,3,-26,-7) Matrix(1583,-1102,2024,-1409) -> Matrix(13,8,-18,-11) Matrix(1255,-876,1606,-1121) -> Matrix(7,5,-10,-7) Matrix(2663,-1966,3366,-2485) -> Matrix(47,19,-52,-21) Matrix(199,-162,242,-197) -> Matrix(17,9,-36,-19) 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): 120 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 22 1/8 -2/1 1 11 1/7 -7/8 1 22 1/6 -1/1 1 11 4/23 (-5/7,-2/3) 0 22 3/17 -5/8 1 22 2/11 -1/2 2 2 1/5 -1/2 1 22 2/9 (-6/5,-1/1) 0 22 5/22 -1/1 17 1 3/13 -11/12 1 22 1/4 -2/3 1 11 3/11 -1/2 3 2 5/18 -1/3 1 11 2/7 (-1/1,0/1) 0 22 7/24 -2/5 1 11 5/17 -1/6 1 22 3/10 1/1 1 11 4/13 (-2/1,-5/3) 0 22 9/29 -3/2 1 22 5/16 -4/3 1 11 1/3 -3/4 1 22 4/11 -1/2 4 2 7/19 -1/2 1 22 3/8 0/1 1 11 11/29 -1/4 1 22 19/50 -1/3 1 11 8/21 (-1/1,0/1) 0 22 5/13 -1/6 1 22 7/18 1/3 1 11 9/23 5/4 1 22 2/5 (-2/1,-1/1) 0 22 9/22 -1/1 13 1 7/17 -11/12 1 22 5/12 -4/5 1 11 3/7 -7/10 1 22 7/16 -2/3 1 11 11/25 -7/12 1 22 4/9 (-2/3,-3/5) 0 22 5/11 -1/2 5 2 6/13 (-3/7,-2/5) 0 22 7/15 -1/2 1 22 1/2 -1/1 1 11 7/13 -9/16 1 22 6/11 -1/2 6 2 5/9 -1/2 1 22 19/34 -1/3 1 11 14/25 (-6/17,-1/3) 0 22 37/66 -1/3 15 1 23/41 -9/28 1 22 9/16 -2/7 1 11 13/23 -3/16 1 22 4/7 (0/1,1/1) 0 22 15/26 -1/1 1 11 26/45 (-6/5,-1/1) 0 22 11/19 -1/2 1 22 18/31 (0/1,1/1) 0 22 25/43 1/0 1 22 7/12 -2/1 1 11 17/29 -3/2 1 22 27/46 -7/5 1 11 10/17 (-6/5,-1/1) 0 22 13/22 -1/1 9 1 3/5 -3/4 1 22 8/13 (-2/3,-11/17) 0 22 21/34 -17/27 1 11 55/89 -5/8 1 22 34/55 -5/8 10 2 13/21 -21/34 1 22 18/29 (-26/43,-3/5) 0 22 41/66 -3/5 19 1 23/37 -31/52 1 22 5/8 -4/7 1 11 7/11 -1/2 7 2 9/14 -3/7 1 11 11/17 -5/12 1 22 13/20 -4/11 1 11 2/3 (-1/1,0/1) 0 22 15/22 -1/1 7 1 13/19 -7/8 1 22 11/16 -4/5 1 11 9/13 -7/10 1 22 16/23 (-2/3,-3/5) 0 22 23/33 -1/2 1 2 7/10 -1/1 1 11 5/7 -7/12 1 22 8/11 -1/2 8 2 11/15 -1/2 1 22 25/34 -3/7 1 11 14/19 (-3/7,-8/19) 0 22 31/42 -11/27 1 11 17/23 -11/28 1 22 3/4 0/1 1 11 16/21 (0/1,1/3) 0 22 13/17 -1/2 1 22 23/30 -1/1 1 11 10/13 (-2/1,-1/1) 0 22 17/22 -1/1 5 1 7/9 -3/4 1 22 25/32 -2/3 1 11 43/55 -3/4 1 2 18/23 (-1/1,-2/3) 0 22 11/14 -3/5 1 11 15/19 -1/2 1 22 34/43 (-6/5,-1/1) 0 22 87/110 -1/1 21 1 53/67 -15/16 1 22 19/24 -4/5 1 11 4/5 (-2/3,-3/5) 0 22 9/11 -1/2 9 2 14/17 (-7/15,-6/13) 0 22 19/23 -15/34 1 22 5/6 -1/3 1 11 11/13 -3/4 1 22 17/20 -2/5 1 11 6/7 (-1/1,0/1) 0 22 19/22 -1/1 3 1 13/15 -3/4 1 22 7/8 -2/3 1 11 8/9 (-2/3,-3/5) 0 22 1/1 -1/2 1 22 1/0 0/1 1 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(155,-18,198,-23) (0/1,1/8) -> (18/23,11/14) Glide Reflection Matrix(219,-28,352,-45) (1/8,1/7) -> (23/37,5/8) Hyperbolic Matrix(67,-10,154,-23) (1/7,1/6) -> (3/7,7/16) Glide Reflection Matrix(485,-84,1276,-221) (1/6,4/23) -> (19/50,8/21) Glide Reflection Matrix(571,-100,748,-131) (4/23,3/17) -> (16/21,13/17) Glide Reflection Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(21,-4,110,-21) (2/11,1/5) -> (2/11,1/5) Reflection Matrix(67,-14,110,-23) (1/5,2/9) -> (3/5,8/13) Glide Reflection Matrix(89,-20,396,-89) (2/9,5/22) -> (2/9,5/22) Reflection Matrix(131,-30,572,-131) (5/22,3/13) -> (5/22,3/13) Reflection Matrix(111,-26,286,-67) (3/13,1/4) -> (5/13,7/18) Glide Reflection Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(177,-50,308,-87) (5/18,2/7) -> (4/7,15/26) Hyperbolic Matrix(263,-76,308,-89) (2/7,7/24) -> (17/20,6/7) Hyperbolic Matrix(485,-142,748,-219) (7/24,5/17) -> (11/17,13/20) Hyperbolic Matrix(155,-46,374,-111) (5/17,3/10) -> (7/17,5/12) Glide Reflection Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(265,-82,572,-177) (4/13,9/29) -> (6/13,7/15) Glide Reflection Matrix(727,-226,1914,-595) (9/29,5/16) -> (11/29,19/50) Glide Reflection Matrix(395,-124,704,-221) (5/16,1/3) -> (23/41,9/16) Hyperbolic Matrix(23,-8,66,-23) (1/3,4/11) -> (1/3,4/11) Reflection Matrix(153,-56,418,-153) (4/11,7/19) -> (4/11,7/19) Reflection Matrix(329,-122,418,-155) (7/19,3/8) -> (11/14,15/19) Hyperbolic Matrix(307,-116,352,-133) (3/8,11/29) -> (13/15,7/8) Hyperbolic Matrix(397,-152,572,-219) (8/21,5/13) -> (9/13,16/23) Hyperbolic Matrix(375,-146,506,-197) (7/18,9/23) -> (17/23,3/4) Hyperbolic Matrix(417,-164,506,-199) (9/23,2/5) -> (14/17,19/23) Hyperbolic Matrix(89,-36,220,-89) (2/5,9/22) -> (2/5,9/22) Reflection Matrix(307,-126,748,-307) (9/22,7/17) -> (9/22,7/17) Reflection Matrix(109,-46,154,-65) (5/12,3/7) -> (7/10,5/7) Glide Reflection Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(549,-242,946,-417) (11/25,4/9) -> (11/19,18/31) Glide Reflection Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(439,-206,748,-351) (7/15,1/2) -> (17/29,27/46) Glide Reflection Matrix(243,-130,286,-153) (1/2,7/13) -> (11/13,17/20) Hyperbolic Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(463,-258,594,-331) (5/9,19/34) -> (7/9,25/32) Glide Reflection Matrix(1101,-616,1496,-837) (19/34,14/25) -> (25/34,14/19) Glide Reflection Matrix(1849,-1036,3300,-1849) (14/25,37/66) -> (14/25,37/66) Reflection Matrix(3035,-1702,5412,-3035) (37/66,23/41) -> (37/66,23/41) Reflection Matrix(419,-236,506,-285) (9/16,13/23) -> (19/23,5/6) Hyperbolic Matrix(505,-286,814,-461) (13/23,4/7) -> (13/21,18/29) Glide Reflection Matrix(551,-318,726,-419) (15/26,26/45) -> (3/4,16/21) Glide Reflection Matrix(1321,-764,1672,-967) (26/45,11/19) -> (15/19,34/43) Hyperbolic Matrix(375,-218,418,-243) (18/31,25/43) -> (8/9,1/1) Glide Reflection Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(857,-502,1166,-683) (7/12,17/29) -> (11/15,25/34) Hyperbolic Matrix(507,-298,638,-375) (27/46,10/17) -> (19/24,4/5) Glide Reflection Matrix(441,-260,748,-441) (10/17,13/22) -> (10/17,13/22) Reflection Matrix(131,-78,220,-131) (13/22,3/5) -> (13/22,3/5) Reflection Matrix(6051,-3740,9790,-6051) (55/89,34/55) -> (55/89,34/55) Reflection Matrix(1429,-884,2310,-1429) (34/55,13/21) -> (34/55,13/21) Reflection Matrix(2377,-1476,3828,-2377) (18/29,41/66) -> (18/29,41/66) Reflection Matrix(3035,-1886,4884,-3035) (41/66,23/37) -> (41/66,23/37) Reflection Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(573,-370,748,-483) (9/14,11/17) -> (13/17,23/30) Hyperbolic Matrix(373,-244,506,-331) (13/20,2/3) -> (14/19,31/42) Hyperbolic Matrix(89,-60,132,-89) (2/3,15/22) -> (2/3,15/22) Reflection Matrix(571,-390,836,-571) (15/22,13/19) -> (15/22,13/19) Reflection Matrix(241,-166,286,-197) (11/16,9/13) -> (5/6,11/13) Glide Reflection Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(1255,-876,1606,-1121) (23/33,7/10) -> (25/32,43/55) Hyperbolic Matrix(111,-80,154,-111) (5/7,8/11) -> (5/7,8/11) Reflection Matrix(241,-176,330,-241) (8/11,11/15) -> (8/11,11/15) Reflection Matrix(2663,-1966,3366,-2485) (31/42,17/23) -> (53/67,19/24) Hyperbolic Matrix(331,-254,374,-287) (23/30,10/13) -> (7/8,8/9) Glide Reflection Matrix(441,-340,572,-441) (10/13,17/22) -> (10/13,17/22) Reflection Matrix(307,-238,396,-307) (17/22,7/9) -> (17/22,7/9) Reflection Matrix(7481,-5916,9460,-7481) (34/43,87/110) -> (34/43,87/110) Reflection Matrix(11659,-9222,14740,-11659) (87/110,53/67) -> (87/110,53/67) Reflection Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic Matrix(265,-228,308,-265) (6/7,19/22) -> (6/7,19/22) Reflection Matrix(571,-494,660,-571) (19/22,13/15) -> (19/22,13/15) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(155,-18,198,-23) -> Matrix(1,-1,-2,1) Matrix(219,-28,352,-45) -> Matrix(7,10,-12,-17) Matrix(67,-10,154,-23) -> Matrix(9,7,-14,-11) Matrix(485,-84,1276,-221) -> Matrix(3,2,-10,-7) Matrix(571,-100,748,-131) -> Matrix(3,2,2,1) Matrix(67,-12,374,-67) -> Matrix(9,5,-16,-9) (3/17,2/11) -> (-5/8,-1/2) Matrix(21,-4,110,-21) -> Matrix(1,1,0,-1) (2/11,1/5) -> (-1/2,1/0) Matrix(67,-14,110,-23) -> Matrix(1,-1,-2,1) Matrix(89,-20,396,-89) -> Matrix(11,12,-10,-11) (2/9,5/22) -> (-6/5,-1/1) Matrix(131,-30,572,-131) -> Matrix(23,22,-24,-23) (5/22,3/13) -> (-1/1,-11/12) Matrix(111,-26,286,-67) -> Matrix(1,1,6,5) Matrix(67,-18,242,-65) -> Matrix(5,3,-12,-7) -1/2 Matrix(177,-50,308,-87) -> Matrix(1,0,2,1) 0/1 Matrix(263,-76,308,-89) -> Matrix(1,0,0,1) Matrix(485,-142,748,-219) -> Matrix(7,2,-18,-5) -1/3 Matrix(155,-46,374,-111) -> Matrix(5,-1,-6,1) Matrix(353,-108,572,-175) -> Matrix(5,12,-8,-19) Matrix(265,-82,572,-177) -> Matrix(3,4,-8,-11) Matrix(727,-226,1914,-595) -> Matrix(1,1,-6,-7) Matrix(395,-124,704,-221) -> Matrix(5,6,-16,-19) Matrix(23,-8,66,-23) -> Matrix(5,3,-8,-5) (1/3,4/11) -> (-3/4,-1/2) Matrix(153,-56,418,-153) -> Matrix(11,5,-24,-11) (4/11,7/19) -> (-1/2,-5/12) Matrix(329,-122,418,-155) -> Matrix(7,3,-12,-5) -1/2 Matrix(307,-116,352,-133) -> Matrix(5,2,-8,-3) -1/2 Matrix(397,-152,572,-219) -> Matrix(5,2,-8,-3) -1/2 Matrix(375,-146,506,-197) -> Matrix(3,-1,-8,3) Matrix(417,-164,506,-199) -> Matrix(1,-5,-2,11) Matrix(89,-36,220,-89) -> Matrix(3,4,-2,-3) (2/5,9/22) -> (-2/1,-1/1) Matrix(307,-126,748,-307) -> Matrix(23,22,-24,-23) (9/22,7/17) -> (-1/1,-11/12) Matrix(109,-46,154,-65) -> Matrix(9,7,-14,-11) Matrix(483,-212,704,-309) -> Matrix(23,14,-28,-17) Matrix(549,-242,946,-417) -> Matrix(5,3,2,1) Matrix(111,-50,242,-109) -> Matrix(9,5,-20,-11) -1/2 Matrix(439,-206,748,-351) -> Matrix(11,4,-8,-3) Matrix(243,-130,286,-153) -> Matrix(5,3,-12,-7) -1/2 Matrix(155,-84,286,-155) -> Matrix(17,9,-32,-17) (7/13,6/11) -> (-9/16,-1/2) Matrix(109,-60,198,-109) -> Matrix(7,3,-16,-7) (6/11,5/9) -> (-1/2,-3/8) Matrix(463,-258,594,-331) -> Matrix(13,5,-18,-7) Matrix(1101,-616,1496,-837) -> Matrix(27,10,-62,-23) Matrix(1849,-1036,3300,-1849) -> Matrix(35,12,-102,-35) (14/25,37/66) -> (-6/17,-1/3) Matrix(3035,-1702,5412,-3035) -> Matrix(55,18,-168,-55) (37/66,23/41) -> (-1/3,-9/28) Matrix(419,-236,506,-285) -> Matrix(11,3,-26,-7) Matrix(505,-286,814,-461) -> Matrix(23,3,-38,-5) Matrix(551,-318,726,-419) -> Matrix(1,1,-2,-3) Matrix(1321,-764,1672,-967) -> Matrix(1,0,0,1) Matrix(375,-218,418,-243) -> Matrix(1,-3,-2,5) Matrix(1563,-910,2530,-1473) -> Matrix(5,27,-8,-43) Matrix(857,-502,1166,-683) -> Matrix(7,11,-16,-25) Matrix(507,-298,638,-375) -> Matrix(7,9,-10,-13) Matrix(441,-260,748,-441) -> Matrix(11,12,-10,-11) (10/17,13/22) -> (-6/5,-1/1) Matrix(131,-78,220,-131) -> Matrix(7,6,-8,-7) (13/22,3/5) -> (-1/1,-3/4) Matrix(6051,-3740,9790,-6051) -> Matrix(631,395,-1008,-631) (55/89,34/55) -> (-79/126,-5/8) Matrix(1429,-884,2310,-1429) -> Matrix(169,105,-272,-169) (34/55,13/21) -> (-5/8,-21/34) Matrix(2377,-1476,3828,-2377) -> Matrix(259,156,-430,-259) (18/29,41/66) -> (-26/43,-3/5) Matrix(3035,-1886,4884,-3035) -> Matrix(311,186,-520,-311) (41/66,23/37) -> (-3/5,-31/52) Matrix(155,-98,242,-153) -> Matrix(13,7,-28,-15) -1/2 Matrix(573,-370,748,-483) -> Matrix(5,2,2,1) Matrix(373,-244,506,-331) -> Matrix(11,3,-26,-7) Matrix(89,-60,132,-89) -> Matrix(-1,0,2,1) (2/3,15/22) -> (-1/1,0/1) Matrix(571,-390,836,-571) -> Matrix(15,14,-16,-15) (15/22,13/19) -> (-1/1,-7/8) Matrix(241,-166,286,-197) -> Matrix(1,1,2,1) Matrix(1583,-1102,2024,-1409) -> Matrix(13,8,-18,-11) -2/3 Matrix(1255,-876,1606,-1121) -> Matrix(7,5,-10,-7) (-1/1,-2/3).(-3/4,-1/2) Matrix(111,-80,154,-111) -> Matrix(13,7,-24,-13) (5/7,8/11) -> (-7/12,-1/2) Matrix(241,-176,330,-241) -> Matrix(19,9,-40,-19) (8/11,11/15) -> (-1/2,-9/20) Matrix(2663,-1966,3366,-2485) -> Matrix(47,19,-52,-21) Matrix(331,-254,374,-287) -> Matrix(1,-1,-2,1) Matrix(441,-340,572,-441) -> Matrix(3,4,-2,-3) (10/13,17/22) -> (-2/1,-1/1) Matrix(307,-238,396,-307) -> Matrix(7,6,-8,-7) (17/22,7/9) -> (-1/1,-3/4) Matrix(7481,-5916,9460,-7481) -> Matrix(11,12,-10,-11) (34/43,87/110) -> (-6/5,-1/1) Matrix(11659,-9222,14740,-11659) -> Matrix(31,30,-32,-31) (87/110,53/67) -> (-1/1,-15/16) Matrix(199,-162,242,-197) -> Matrix(17,9,-36,-19) -1/2 Matrix(265,-228,308,-265) -> Matrix(-1,0,2,1) (6/7,19/22) -> (-1/1,0/1) Matrix(571,-494,660,-571) -> Matrix(7,6,-8,-7) (19/22,13/15) -> (-1/1,-3/4) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.