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 0/1 1/20 -8/9 0/1 1/17 -7/8 2/37 -6/7 1/18 2/35 -11/13 2/35 1/17 -5/6 0/1 2/35 -19/23 2/35 1/17 -14/17 2/35 3/52 -9/11 1/17 -22/27 6/101 5/84 -35/43 5/84 4/67 -13/16 2/33 -4/5 1/17 2/33 -19/24 2/33 -15/19 4/65 1/16 -11/14 0/1 2/33 -18/23 2/33 1/16 -25/32 2/33 -7/9 4/65 1/16 -17/22 1/16 -10/13 1/16 6/95 -13/17 2/31 1/15 -16/21 1/16 2/31 -3/4 2/31 -17/23 2/31 1/15 -14/19 4/61 1/15 -25/34 0/1 2/31 -36/49 2/31 5/77 -11/15 3/46 4/61 -8/11 1/15 -21/29 9/134 8/119 -34/47 6/89 5/74 -13/18 6/89 4/59 -5/7 1/15 2/29 -17/24 2/29 -12/17 7/102 2/29 -7/10 2/29 4/57 -9/13 2/29 3/43 -20/29 11/157 4/57 -31/45 4/57 9/128 -11/16 6/85 -2/3 1/14 2/27 -11/17 2/27 5/67 -20/31 3/40 10/133 -9/14 4/53 6/79 -7/11 1/13 -19/30 8/103 6/77 -12/19 1/13 4/51 -41/65 1/13 6/77 -29/46 6/77 4/51 -17/27 1/13 6/77 -39/62 14/179 4/51 -22/35 4/51 7/89 -5/8 2/25 -18/29 1/13 4/51 -31/50 0/1 2/25 -13/21 1/13 2/25 -8/13 3/38 2/25 -11/18 2/25 4/49 -25/41 2/25 3/37 -14/23 2/25 1/12 -3/5 2/25 1/12 -13/22 1/12 -10/17 1/12 6/71 -27/46 6/71 4/47 -17/29 4/47 7/82 -24/41 5/58 2/23 -31/53 0/1 1/12 -7/12 2/23 -32/55 1/11 -25/43 0/1 1/12 -68/117 0/1 1/7 -43/74 0/1 2/27 -18/31 1/12 2/23 -11/19 0/1 1/12 -4/7 1/12 2/23 -13/23 2/23 1/11 -9/16 2/23 -14/25 1/11 4/43 -19/34 0/1 2/21 -5/9 0/1 1/12 -26/47 5/58 2/23 -21/38 2/23 4/45 -16/29 0/1 1/11 -11/20 2/23 -6/11 1/11 -13/24 2/21 -7/13 1/11 2/21 -8/15 0/1 1/13 -1/2 0/1 2/21 -7/15 0/1 1/8 -6/13 2/21 1/10 -5/11 1/10 -14/31 1/10 2/19 -9/20 2/19 -22/49 3/29 2/19 -13/29 0/1 1/10 -4/9 0/1 1/9 -19/43 0/1 1/12 -15/34 0/1 2/21 -11/25 4/41 1/10 -29/66 1/10 -18/41 1/10 10/99 -7/16 2/19 -10/23 1/10 2/19 -13/30 4/39 2/19 -3/7 2/19 1/9 -11/26 0/1 2/17 -30/71 1/10 2/19 -19/45 0/1 1/10 -8/19 0/1 1/9 -21/50 0/1 2/19 -13/31 2/19 1/9 -18/43 0/1 1/9 -23/55 1/10 -5/12 2/19 -17/41 2/19 5/47 -12/29 7/65 4/37 -19/46 4/37 6/55 -7/17 6/55 1/9 -9/22 1/9 -2/5 1/9 2/17 -11/28 2/17 -9/23 1/9 2/17 -16/41 3/26 2/17 -7/18 4/35 2/17 -12/31 7/60 2/17 -17/44 2/17 -5/13 2/17 3/25 -13/34 2/17 4/33 -34/89 4/33 5/41 -21/55 1/8 -29/76 2/17 -8/21 2/17 1/8 -19/50 0/1 2/17 -30/79 3/25 4/33 -11/29 4/33 1/8 -25/66 1/8 -14/37 1/8 2/15 -3/8 2/17 -13/35 7/58 4/33 -49/132 4/33 -36/97 4/33 21/173 -23/62 4/33 14/115 -10/27 6/49 1/8 -17/46 4/33 6/49 -7/19 4/33 1/8 -4/11 1/8 -9/25 1/8 8/63 -5/14 6/47 4/31 -6/17 5/38 2/15 -7/20 2/15 -8/23 1/8 2/15 -1/3 2/15 1/7 -7/22 1/7 -6/19 1/7 12/83 -5/16 6/41 -14/45 9/61 4/27 -9/29 4/27 11/74 -4/13 3/20 2/13 -7/23 1/7 2/13 -10/33 1/7 -13/43 5/34 4/27 -3/10 4/27 2/13 -8/27 11/72 2/13 -13/44 2/13 -5/17 2/13 7/45 -12/41 2/13 1/6 -19/65 2/13 3/19 -7/24 2/13 -9/31 2/13 3/19 -2/7 2/13 1/6 -7/25 4/25 1/6 -19/68 2/13 -31/111 2/13 3/19 -43/154 3/19 -12/43 3/19 4/25 -17/61 2/13 3/19 -5/18 4/25 6/37 -3/11 1/6 -7/26 8/47 6/35 -11/41 7/41 6/35 -4/15 4/23 3/17 -13/49 5/28 2/11 -35/132 2/11 -22/83 2/11 5/27 -9/34 0/1 2/11 -5/19 1/6 4/23 -11/42 4/23 2/11 -17/65 3/17 2/11 -23/88 2/11 -6/23 1/6 2/11 -1/4 2/11 -5/21 2/11 1/5 -4/17 1/6 2/11 -7/30 10/53 4/21 -24/103 31/163 4/21 -41/176 4/21 -17/73 4/21 21/110 -10/43 4/21 1/5 -3/13 6/31 1/5 -5/22 1/5 -2/9 1/5 4/19 -11/50 8/37 2/9 -20/91 11/50 2/9 -29/132 2/9 -9/41 2/9 3/13 -7/32 2/9 -12/55 1/5 -5/23 1/5 2/9 -8/37 3/14 2/9 -19/88 2/9 -11/51 2/9 3/13 -3/14 0/1 2/9 -4/19 1/5 4/19 -9/43 4/19 3/14 -23/110 3/14 -14/67 3/14 2/9 -5/24 2/9 -6/29 1/5 4/19 -1/5 2/9 1/4 -4/21 2/9 1/4 -3/16 2/9 -2/11 1/4 -5/28 6/23 -8/45 4/15 3/11 -3/17 3/11 2/7 -4/23 1/4 2/7 -1/6 0/1 2/7 -4/25 0/1 1/3 -7/44 0/1 -3/19 0/1 1/4 -2/13 1/4 2/7 -3/20 2/7 -1/7 2/7 1/3 -3/22 1/3 -2/15 1/3 4/11 -1/8 2/5 -1/9 0/1 1/4 -1/10 0/1 2/5 0/1 0/1 1/1 1/9 -1/2 0/1 1/8 -2/1 1/7 -1/1 -2/3 2/13 -2/3 -1/2 1/6 -2/3 0/1 4/23 -2/3 -1/2 3/17 -2/3 -3/5 2/11 -1/2 5/27 -6/13 -5/11 8/43 -5/11 -4/9 3/16 -2/5 1/5 -1/2 -2/5 5/24 -2/5 4/19 -4/11 -1/3 3/14 -2/5 0/1 5/23 -2/5 -1/3 7/32 -2/5 2/9 -4/11 -1/3 5/22 -1/3 3/13 -1/3 -6/19 4/17 -2/7 -1/4 5/21 -1/3 -2/7 1/4 -2/7 6/23 -2/7 -1/4 5/19 -4/15 -1/4 9/34 -2/7 0/1 13/49 -2/7 -5/18 4/15 -3/11 -4/15 3/11 -1/4 8/29 -9/37 -8/33 13/47 -6/25 -5/21 5/18 -6/25 -4/17 2/7 -1/4 -2/9 7/24 -2/9 5/17 -7/31 -2/9 3/10 -2/9 -4/19 4/13 -2/9 -3/14 9/29 -11/52 -4/19 14/45 -4/19 -9/43 5/16 -6/29 1/3 -1/5 -2/11 6/17 -2/11 -5/28 11/31 -3/17 -10/57 5/14 -4/23 -6/35 4/11 -1/6 11/30 -8/49 -6/37 7/19 -1/6 -4/25 24/65 -1/6 -6/37 17/46 -6/37 -4/25 10/27 -1/6 -6/37 23/62 -14/87 -4/25 13/35 -4/25 -7/44 3/8 -2/13 11/29 -1/6 -4/25 19/50 -2/13 0/1 8/21 -1/6 -2/13 5/13 -3/19 -2/13 7/18 -2/13 -4/27 16/41 -2/13 -3/20 9/23 -2/13 -1/7 2/5 -2/13 -1/7 9/22 -1/7 7/17 -1/7 -6/43 19/46 -6/43 -4/29 12/29 -4/29 -7/51 17/41 -5/37 -2/15 22/53 -1/7 0/1 5/12 -2/15 23/55 -1/8 18/43 -1/7 0/1 49/117 -1/12 0/1 31/74 -2/11 0/1 13/31 -1/7 -2/15 8/19 -1/7 0/1 3/7 -1/7 -2/15 10/23 -2/15 -1/8 7/16 -2/15 11/25 -1/8 -4/33 15/34 -2/17 0/1 4/9 -1/7 0/1 21/47 -5/37 -2/15 17/38 -2/15 -4/31 13/29 -1/8 0/1 9/20 -2/15 5/11 -1/8 11/24 -2/17 6/13 -1/8 -2/17 7/15 -1/6 0/1 1/2 -2/17 0/1 8/15 -1/11 0/1 7/13 -2/17 -1/9 6/11 -1/9 17/31 -1/9 -2/19 11/20 -2/19 27/49 -3/28 -2/19 16/29 -1/9 0/1 5/9 -1/10 0/1 24/43 -1/7 0/1 19/34 -2/17 0/1 14/25 -4/35 -1/9 37/66 -1/9 23/41 -1/9 -10/91 9/16 -2/19 13/23 -1/9 -2/19 17/30 -4/37 -2/19 4/7 -2/19 -1/10 15/26 -2/21 0/1 41/71 -1/9 -2/19 26/45 -1/9 0/1 11/19 -1/10 0/1 29/50 -2/19 0/1 18/31 -2/19 -1/10 25/43 -1/10 0/1 32/55 -1/9 7/12 -2/19 24/41 -2/19 -5/48 17/29 -7/68 -4/39 27/46 -4/39 -6/59 10/17 -6/59 -1/10 13/22 -1/10 3/5 -1/10 -2/21 17/28 -2/21 14/23 -1/10 -2/21 25/41 -3/31 -2/21 11/18 -4/41 -2/21 19/31 -7/73 -2/21 27/44 -2/21 8/13 -2/21 -3/32 21/34 -2/21 -4/43 55/89 -4/43 -5/54 34/55 -1/11 47/76 -2/21 13/21 -2/21 -1/11 31/50 -2/21 0/1 49/79 -3/32 -4/43 18/29 -4/43 -1/11 41/66 -1/11 23/37 -1/11 -2/23 5/8 -2/21 22/35 -7/75 -4/43 83/132 -4/43 61/97 -4/43 -21/226 39/62 -4/43 -14/151 17/27 -6/65 -1/11 29/46 -4/43 -6/65 12/19 -4/43 -1/11 7/11 -1/11 16/25 -1/11 -8/89 9/14 -6/67 -4/45 11/17 -5/57 -2/23 13/20 -2/23 15/23 -1/11 -2/23 2/3 -2/23 -1/12 15/22 -1/12 13/19 -1/12 -12/145 11/16 -6/73 31/45 -9/110 -4/49 20/29 -4/49 -11/135 9/13 -3/37 -2/25 16/23 -1/12 -2/25 23/33 -1/12 30/43 -5/61 -4/49 7/10 -4/49 -2/25 19/27 -11/137 -2/25 31/44 -2/25 12/17 -2/25 -7/88 29/41 -2/25 -1/13 46/65 -2/25 -3/38 17/24 -2/25 22/31 -2/25 -3/38 5/7 -2/25 -1/13 18/25 -4/51 -1/13 49/68 -2/25 80/111 -2/25 -3/38 111/154 -3/38 31/43 -3/38 -4/51 44/61 -2/25 -3/38 13/18 -4/51 -6/77 8/11 -1/13 19/26 -8/105 -6/79 30/41 -7/92 -6/79 11/15 -4/53 -3/40 36/49 -5/67 -2/27 97/132 -2/27 61/83 -2/27 -5/68 25/34 -2/27 0/1 14/19 -1/13 -4/53 31/42 -4/53 -2/27 48/65 -3/40 -2/27 65/88 -2/27 17/23 -1/13 -2/27 3/4 -2/27 16/21 -2/27 -1/14 13/17 -1/13 -2/27 23/30 -10/137 -4/55 79/103 -31/426 -4/55 135/176 -4/55 56/73 -4/55 -21/289 33/43 -4/55 -1/14 10/13 -6/83 -1/14 17/22 -1/14 7/9 -1/14 -4/57 39/50 -8/115 -2/29 71/91 -11/159 -2/29 103/132 -2/29 32/41 -2/29 -3/44 25/32 -2/29 43/55 -1/14 18/23 -1/14 -2/29 29/37 -3/43 -2/29 69/88 -2/29 40/51 -2/29 -3/44 11/14 -2/29 0/1 15/19 -1/14 -4/57 34/43 -4/57 -3/43 87/110 -3/43 53/67 -3/43 -2/29 19/24 -2/29 23/29 -1/14 -4/57 4/5 -2/29 -1/15 17/21 -2/29 -1/15 13/16 -2/29 9/11 -1/15 23/28 -6/91 37/45 -4/61 -3/46 14/17 -3/46 -2/31 19/23 -1/15 -2/31 5/6 -2/31 0/1 21/25 -1/16 0/1 37/44 0/1 16/19 -1/15 0/1 11/13 -1/15 -2/31 17/20 -2/31 6/7 -2/31 -1/16 19/22 -1/16 13/15 -1/16 -4/65 7/8 -2/33 8/9 -1/15 0/1 9/10 -2/33 0/1 1/1 -1/18 0/1 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,-38,1) Matrix(175,156,-396,-353) -> Matrix(1,0,-8,1) Matrix(221,194,352,309) -> Matrix(75,-4,-806,43) Matrix(133,116,-352,-307) -> Matrix(1,0,-10,1) Matrix(89,76,-308,-263) -> Matrix(71,-4,444,-25) Matrix(351,296,-836,-705) -> Matrix(1,0,-8,1) Matrix(791,654,1276,1055) -> Matrix(1,0,-28,1) Matrix(177,146,748,617) -> Matrix(69,-4,-224,13) Matrix(395,324,-484,-397) -> Matrix(137,-8,2312,-135) Matrix(2729,2222,3784,3081) -> Matrix(135,-8,-1738,103) Matrix(969,788,1408,1145) -> Matrix(267,-16,-3254,195) Matrix(87,70,-220,-177) -> Matrix(1,0,-8,1) Matrix(573,454,-1276,-1011) -> Matrix(65,-4,634,-39) Matrix(529,418,-1892,-1495) -> Matrix(1,0,-10,1) Matrix(307,242,836,659) -> Matrix(129,-8,-790,49) Matrix(439,344,-1012,-793) -> Matrix(65,-4,634,-39) Matrix(923,722,-2420,-1893) -> Matrix(1,0,-8,1) Matrix(1055,824,-1804,-1409) -> Matrix(65,-4,764,-47) Matrix(307,238,396,307) -> Matrix(129,-8,-1822,113) Matrix(441,340,572,441) -> Matrix(191,-12,-2658,167) Matrix(483,370,-748,-573) -> Matrix(125,-8,1672,-107) Matrix(131,100,748,571) -> Matrix(63,-4,-110,7) Matrix(45,34,176,133) -> Matrix(63,-4,-236,15) Matrix(43,32,176,131) -> Matrix(61,-4,-198,13) Matrix(1055,778,-1672,-1233) -> Matrix(121,-8,1558,-103) Matrix(837,616,1496,1101) -> Matrix(1,0,-24,1) Matrix(1189,874,-4488,-3299) -> Matrix(1,0,-10,1) Matrix(1187,872,1496,1099) -> Matrix(123,-8,-1768,115) Matrix(351,256,-484,-353) -> Matrix(181,-12,2700,-179) Matrix(1495,1082,2552,1847) -> Matrix(297,-20,-2866,193) Matrix(617,446,1584,1145) -> Matrix(119,-8,-818,55) Matrix(131,94,-308,-221) -> Matrix(59,-4,546,-37) Matrix(45,32,-308,-219) -> Matrix(59,-4,192,-13) Matrix(263,186,-748,-529) -> Matrix(59,-4,428,-29) Matrix(131,92,-440,-309) -> Matrix(115,-8,762,-53) Matrix(219,152,-572,-397) -> Matrix(1,0,-6,1) Matrix(307,212,572,395) -> Matrix(57,-4,-470,33) Matrix(3785,2608,-6512,-4487) -> Matrix(57,-4,556,-39) Matrix(1627,1120,1980,1363) -> Matrix(341,-24,-5186,365) Matrix(309,212,-704,-483) -> Matrix(113,-8,1116,-79) Matrix(219,142,-748,-485) -> Matrix(55,-4,344,-25) Matrix(1585,1022,-2728,-1759) -> Matrix(53,-4,676,-51) Matrix(307,196,-484,-309) -> Matrix(157,-12,2028,-155) Matrix(177,112,836,529) -> Matrix(103,-8,-296,23) Matrix(1497,944,-5720,-3607) -> Matrix(205,-16,1166,-91) Matrix(835,526,2024,1275) -> Matrix(1,0,-20,1) Matrix(2947,1854,5104,3211) -> Matrix(51,-4,-446,35) Matrix(3037,1910,-8184,-5147) -> Matrix(715,-56,5886,-461) Matrix(309,194,352,221) -> Matrix(51,-4,-854,67) Matrix(45,28,-352,-219) -> Matrix(1,0,-10,1) Matrix(1409,874,-2552,-1583) -> Matrix(51,-4,574,-45) Matrix(1055,654,1276,791) -> Matrix(1,0,-28,1) Matrix(175,108,-572,-353) -> Matrix(1,0,-6,1) Matrix(307,188,-792,-485) -> Matrix(99,-8,854,-69) Matrix(439,268,1584,967) -> Matrix(97,-8,-400,33) Matrix(351,214,-1012,-617) -> Matrix(49,-4,380,-31) Matrix(43,26,-220,-133) -> Matrix(1,0,-8,1) Matrix(131,78,220,131) -> Matrix(49,-4,-502,41) Matrix(441,260,748,441) -> Matrix(143,-12,-1418,119) Matrix(749,440,2024,1189) -> Matrix(1,0,-18,1) Matrix(351,206,748,439) -> Matrix(47,-4,-364,31) Matrix(1321,774,1804,1057) -> Matrix(187,-16,-2466,211) Matrix(1583,926,-2860,-1673) -> Matrix(1,0,0,1) Matrix(2993,1742,4840,2817) -> Matrix(1,0,-22,1) Matrix(4487,2610,7260,4223) -> Matrix(43,-4,-462,43) Matrix(2595,1508,-11132,-6469) -> Matrix(59,-4,310,-21) Matrix(131,76,-836,-485) -> Matrix(1,0,-8,1) Matrix(87,50,-308,-177) -> Matrix(47,-4,294,-25) Matrix(219,124,-1012,-573) -> Matrix(45,-4,214,-19) Matrix(397,224,-1012,-571) -> Matrix(45,-4,394,-35) Matrix(221,124,-704,-395) -> Matrix(89,-8,612,-55) Matrix(1101,616,1496,837) -> Matrix(1,0,-24,1) Matrix(43,24,-396,-221) -> Matrix(1,0,-8,1) Matrix(1277,706,-5808,-3211) -> Matrix(137,-12,628,-55) Matrix(265,146,-1276,-703) -> Matrix(45,-4,214,-19) Matrix(263,144,-484,-265) -> Matrix(45,-4,484,-43) Matrix(485,262,572,309) -> Matrix(1,0,-26,1) Matrix(395,212,572,307) -> Matrix(41,-4,-502,49) Matrix(309,164,748,397) -> Matrix(45,-4,-326,29) Matrix(439,206,748,351) -> Matrix(39,-4,-380,39) Matrix(177,82,572,265) -> Matrix(43,-4,-204,19) Matrix(219,100,-484,-221) -> Matrix(41,-4,400,-39) Matrix(967,436,1364,615) -> Matrix(77,-8,-972,101) Matrix(1583,710,2156,967) -> Matrix(37,-4,-490,53) Matrix(969,434,-2552,-1143) -> Matrix(39,-4,322,-33) Matrix(2773,1224,4488,1981) -> Matrix(43,-4,-462,43) Matrix(395,174,1496,659) -> Matrix(1,0,-14,1) Matrix(1233,542,1804,793) -> Matrix(161,-16,-1942,193) Matrix(747,328,1100,483) -> Matrix(119,-12,-1418,143) Matrix(133,58,-704,-307) -> Matrix(39,-4,166,-17) Matrix(351,152,-1628,-705) -> Matrix(39,-4,166,-17) Matrix(1893,800,5104,2157) -> Matrix(41,-4,-256,25) Matrix(3257,1376,3960,1673) -> Matrix(37,-4,-564,61) Matrix(351,148,-1672,-705) -> Matrix(37,-4,176,-19) Matrix(219,92,-1364,-573) -> Matrix(1,0,-6,1) Matrix(439,184,-1892,-793) -> Matrix(35,-4,184,-21) Matrix(2639,1104,3784,1583) -> Matrix(41,-4,-502,49) Matrix(1891,790,2420,1011) -> Matrix(1,0,-24,1) Matrix(395,164,-1804,-749) -> Matrix(37,-4,176,-19) Matrix(705,292,2552,1057) -> Matrix(187,-20,-776,83) Matrix(397,164,748,309) -> Matrix(37,-4,-342,37) Matrix(1275,526,2024,835) -> Matrix(1,0,-20,1) Matrix(307,126,748,307) -> Matrix(109,-12,-772,85) Matrix(89,36,220,89) -> Matrix(35,-4,-236,27) Matrix(1055,412,-3608,-1409) -> Matrix(69,-8,440,-51) Matrix(1319,514,1804,703) -> Matrix(37,-4,-490,53) Matrix(1189,460,1936,749) -> Matrix(171,-20,-1804,211) Matrix(1187,458,1936,747) -> Matrix(169,-20,-1766,209) Matrix(2507,958,4488,1715) -> Matrix(33,-4,-272,33) Matrix(3037,1160,7260,2773) -> Matrix(33,-4,-272,33) Matrix(2023,772,4840,1847) -> Matrix(1,0,-16,1) Matrix(221,84,1276,485) -> Matrix(1,0,-10,1) Matrix(969,368,-4400,-1671) -> Matrix(67,-8,310,-37) Matrix(1409,534,1628,617) -> Matrix(65,-8,-1048,129) Matrix(1099,416,1276,483) -> Matrix(31,-4,-488,63) Matrix(43,16,352,131) -> Matrix(33,-4,-8,1) Matrix(10957,4068,17424,6469) -> Matrix(925,-112,-9952,1205) Matrix(10955,4066,17424,6467) -> Matrix(923,-112,-9914,1203) Matrix(3079,1142,4268,1583) -> Matrix(131,-16,-1662,203) Matrix(1189,440,2024,749) -> Matrix(1,0,-18,1) Matrix(439,162,-1672,-617) -> Matrix(65,-8,382,-47) Matrix(175,64,-484,-177) -> Matrix(97,-12,768,-95) Matrix(485,174,616,221) -> Matrix(31,-4,-426,55) Matrix(175,62,-748,-265) -> Matrix(61,-8,328,-43) Matrix(395,138,-1892,-661) -> Matrix(29,-4,138,-19) Matrix(617,198,1100,353) -> Matrix(85,-12,-772,109) Matrix(1011,320,1804,571) -> Matrix(111,-16,-992,143) Matrix(263,82,1408,439) -> Matrix(109,-16,-252,37) Matrix(1055,328,-4532,-1409) -> Matrix(271,-40,1416,-209) Matrix(265,82,572,177) -> Matrix(27,-4,-236,35) Matrix(441,134,-2024,-615) -> Matrix(1,0,-2,1) Matrix(2201,666,3784,1145) -> Matrix(27,-4,-236,35) Matrix(397,120,440,133) -> Matrix(27,-4,-452,67) Matrix(1365,404,1936,573) -> Matrix(235,-36,-2944,451) Matrix(1363,402,1936,571) -> Matrix(233,-36,-2906,449) Matrix(1979,578,-7084,-2069) -> Matrix(1,0,0,1) Matrix(749,218,1364,397) -> Matrix(51,-8,-478,75) Matrix(17819,4976,22528,6291) -> Matrix(77,-12,-1110,173) Matrix(8977,2506,11352,3169) -> Matrix(151,-24,-2158,343) Matrix(703,196,3784,1055) -> Matrix(49,-8,-104,17) Matrix(2685,748,4268,1189) -> Matrix(101,-16,-1092,173) Matrix(131,36,-484,-133) -> Matrix(73,-12,432,-71) Matrix(1101,296,1804,485) -> Matrix(23,-4,-224,39) Matrix(747,200,1804,483) -> Matrix(93,-16,-680,117) Matrix(1189,316,2156,573) -> Matrix(23,-4,-224,39) Matrix(12805,3396,17424,4621) -> Matrix(111,-20,-1504,271) Matrix(12803,3394,17424,4619) -> Matrix(109,-20,-1466,269) Matrix(659,174,1496,395) -> Matrix(1,0,-14,1) Matrix(5721,1496,7744,2025) -> Matrix(23,-4,-316,55) Matrix(5719,1494,7744,2023) -> Matrix(21,-4,-278,53) Matrix(133,34,176,45) -> Matrix(23,-4,-316,55) Matrix(131,32,176,43) -> Matrix(21,-4,-278,53) Matrix(617,146,748,177) -> Matrix(21,-4,-320,61) Matrix(23761,5536,30976,7217) -> Matrix(1093,-208,-15034,2861) Matrix(23759,5534,30976,7215) -> Matrix(1091,-208,-14996,2859) Matrix(131,30,572,131) -> Matrix(61,-12,-188,37) Matrix(89,20,396,89) -> Matrix(39,-8,-112,23) Matrix(13597,2988,17424,3829) -> Matrix(127,-28,-1846,407) Matrix(13595,2986,17424,3827) -> Matrix(125,-28,-1808,405) Matrix(1409,308,2420,529) -> Matrix(1,0,-14,1) Matrix(6073,1312,7744,1673) -> Matrix(55,-12,-802,175) Matrix(6071,1310,7744,1671) -> Matrix(53,-12,-764,173) Matrix(395,84,616,131) -> Matrix(21,-4,-236,45) Matrix(8183,1712,11352,2375) -> Matrix(113,-24,-1436,305) Matrix(16237,3394,22528,4709) -> Matrix(55,-12,-692,151) Matrix(397,82,1496,309) -> Matrix(37,-8,-134,29) Matrix(87,16,-484,-89) -> Matrix(33,-8,128,-31) Matrix(617,110,1980,353) -> Matrix(91,-24,-436,115) Matrix(2287,406,3960,703) -> Matrix(15,-4,-146,39) Matrix(571,100,748,131) -> Matrix(15,-4,-206,55) Matrix(485,84,1276,221) -> Matrix(1,0,-10,1) Matrix(1629,260,1936,309) -> Matrix(1,0,-18,1) Matrix(1627,258,1936,307) -> Matrix(1,0,-20,1) Matrix(263,40,572,87) -> Matrix(1,0,-12,1) Matrix(793,110,1276,177) -> Matrix(13,-4,-146,45) Matrix(1011,136,1628,219) -> Matrix(23,-8,-250,87) Matrix(131,16,352,43) -> Matrix(9,-4,-56,25) Matrix(307,30,440,43) -> Matrix(9,-4,-110,49) Matrix(221,-24,396,-43) -> Matrix(1,0,-8,1) Matrix(219,-28,352,-45) -> Matrix(1,0,-10,1) Matrix(219,-32,308,-45) -> Matrix(5,4,-64,-51) Matrix(485,-76,836,-131) -> Matrix(1,0,-8,1) Matrix(89,-16,484,-87) -> Matrix(15,8,-32,-17) Matrix(133,-26,220,-43) -> Matrix(1,0,-8,1) Matrix(703,-146,1276,-265) -> Matrix(11,4,-102,-37) Matrix(1363,-286,1892,-397) -> Matrix(1,0,-10,1) Matrix(573,-124,1012,-219) -> Matrix(11,4,-102,-37) Matrix(1497,-326,2420,-527) -> Matrix(1,0,-8,1) Matrix(749,-164,1804,-395) -> Matrix(11,4,-80,-29) Matrix(265,-62,748,-175) -> Matrix(27,8,-152,-45) Matrix(617,-162,1672,-439) -> Matrix(31,8,-190,-49) Matrix(3299,-874,4488,-1189) -> Matrix(1,0,-10,1) Matrix(133,-36,484,-131) -> Matrix(47,12,-192,-49) Matrix(177,-50,308,-87) -> Matrix(17,4,-166,-39) Matrix(263,-76,308,-89) -> Matrix(17,4,-268,-63) Matrix(485,-142,748,-219) -> Matrix(17,4,-200,-47) Matrix(309,-92,440,-131) -> Matrix(37,8,-458,-99) Matrix(353,-108,572,-175) -> Matrix(1,0,-6,1) Matrix(2727,-848,6512,-2025) -> Matrix(19,4,-176,-37) Matrix(395,-124,704,-221) -> Matrix(39,8,-356,-73) Matrix(529,-186,748,-263) -> Matrix(21,4,-268,-51) Matrix(1143,-406,2728,-969) -> Matrix(23,4,-144,-25) Matrix(177,-64,484,-175) -> Matrix(71,12,-432,-73) Matrix(4223,-1560,5720,-2113) -> Matrix(99,16,-1318,-213) Matrix(5147,-1910,8184,-3037) -> Matrix(349,56,-3758,-603) Matrix(307,-116,352,-133) -> Matrix(1,0,-10,1) Matrix(1143,-434,2552,-969) -> Matrix(25,4,-194,-31) Matrix(397,-152,572,-219) -> Matrix(1,0,-6,1) Matrix(485,-188,792,-307) -> Matrix(53,8,-550,-83) Matrix(661,-258,1012,-395) -> Matrix(27,4,-304,-45) Matrix(177,-70,220,-87) -> Matrix(1,0,-8,1) Matrix(1277,-530,2860,-1187) -> Matrix(1,0,0,1) Matrix(8537,-3576,11132,-4663) -> Matrix(17,4,-234,-55) Matrix(705,-296,836,-351) -> Matrix(1,0,-8,1) Matrix(221,-94,308,-131) -> Matrix(29,4,-370,-51) Matrix(793,-344,1012,-439) -> Matrix(31,4,-442,-57) Matrix(615,-268,1012,-441) -> Matrix(31,4,-318,-41) Matrix(483,-212,704,-309) -> Matrix(63,8,-764,-97) Matrix(353,-156,396,-175) -> Matrix(1,0,-8,1) Matrix(4531,-2026,5808,-2597) -> Matrix(91,12,-1312,-173) Matrix(1011,-454,1276,-573) -> Matrix(31,4,-442,-57) Matrix(221,-100,484,-219) -> Matrix(31,4,-256,-33) Matrix(265,-144,484,-263) -> Matrix(35,4,-324,-37) Matrix(1583,-874,2552,-1409) -> Matrix(37,4,-398,-43) Matrix(571,-322,704,-397) -> Matrix(37,4,-546,-59) Matrix(1277,-724,1628,-923) -> Matrix(37,4,-546,-59) Matrix(1321,-764,1672,-967) -> Matrix(39,4,-556,-57) Matrix(1145,-664,1364,-791) -> Matrix(1,0,-6,1) Matrix(1453,-844,1892,-1099) -> Matrix(41,4,-564,-55) Matrix(1409,-824,1804,-1055) -> Matrix(39,4,-556,-57) Matrix(2553,-1556,3608,-2199) -> Matrix(83,8,-1048,-101) Matrix(3431,-2128,4400,-2729) -> Matrix(85,8,-1222,-115) Matrix(1233,-778,1672,-1055) -> Matrix(87,8,-1142,-105) Matrix(309,-196,484,-307) -> Matrix(131,12,-1452,-133) Matrix(573,-370,748,-483) -> Matrix(91,8,-1240,-109) Matrix(1497,-974,1892,-1231) -> Matrix(47,4,-670,-57) Matrix(3477,-2396,4532,-3123) -> Matrix(489,40,-6736,-551) Matrix(1583,-1102,2024,-1409) -> Matrix(1,0,-2,1) Matrix(5105,-3614,7084,-5015) -> Matrix(1,0,0,1) Matrix(353,-256,484,-351) -> Matrix(155,12,-2028,-157) Matrix(397,-324,484,-395) -> Matrix(119,8,-1800,-121) 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): 40 Degree of the the map X: 80 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 0/1 1/9 1/8 1/7 2/13 1/6 3/17 2/11 3/16 1/5 4/19 3/14 5/22 5/21 1/4 4/15 3/11 5/18 3/10 5/16 1/3 4/11 3/8 9/22 5/12 23/55 9/20 5/11 1/2 6/11 11/20 7/12 27/44 83/132 7/11 15/22 23/33 31/44 8/11 97/132 65/88 3/4 135/176 103/132 69/88 87/110 9/11 37/44 19/22 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/9 -1/2 0/1 1/8 -2/1 1/7 -1/1 -2/3 2/13 -2/3 -1/2 1/6 -2/3 0/1 4/23 -2/3 -1/2 3/17 -2/3 -3/5 2/11 -1/2 5/27 -6/13 -5/11 8/43 -5/11 -4/9 3/16 -2/5 1/5 -1/2 -2/5 5/24 -2/5 4/19 -4/11 -1/3 3/14 -2/5 0/1 5/23 -2/5 -1/3 7/32 -2/5 2/9 -4/11 -1/3 5/22 -1/3 3/13 -1/3 -6/19 4/17 -2/7 -1/4 5/21 -1/3 -2/7 1/4 -2/7 6/23 -2/7 -1/4 5/19 -4/15 -1/4 9/34 -2/7 0/1 13/49 -2/7 -5/18 4/15 -3/11 -4/15 3/11 -1/4 8/29 -9/37 -8/33 13/47 -6/25 -5/21 5/18 -6/25 -4/17 2/7 -1/4 -2/9 7/24 -2/9 5/17 -7/31 -2/9 3/10 -2/9 -4/19 4/13 -2/9 -3/14 9/29 -11/52 -4/19 14/45 -4/19 -9/43 5/16 -6/29 1/3 -1/5 -2/11 6/17 -2/11 -5/28 11/31 -3/17 -10/57 5/14 -4/23 -6/35 4/11 -1/6 11/30 -8/49 -6/37 7/19 -1/6 -4/25 24/65 -1/6 -6/37 17/46 -6/37 -4/25 10/27 -1/6 -6/37 23/62 -14/87 -4/25 13/35 -4/25 -7/44 3/8 -2/13 11/29 -1/6 -4/25 19/50 -2/13 0/1 8/21 -1/6 -2/13 5/13 -3/19 -2/13 7/18 -2/13 -4/27 16/41 -2/13 -3/20 9/23 -2/13 -1/7 2/5 -2/13 -1/7 9/22 -1/7 7/17 -1/7 -6/43 19/46 -6/43 -4/29 12/29 -4/29 -7/51 17/41 -5/37 -2/15 22/53 -1/7 0/1 5/12 -2/15 23/55 -1/8 18/43 -1/7 0/1 49/117 -1/12 0/1 31/74 -2/11 0/1 13/31 -1/7 -2/15 8/19 -1/7 0/1 3/7 -1/7 -2/15 10/23 -2/15 -1/8 7/16 -2/15 11/25 -1/8 -4/33 15/34 -2/17 0/1 4/9 -1/7 0/1 21/47 -5/37 -2/15 17/38 -2/15 -4/31 13/29 -1/8 0/1 9/20 -2/15 5/11 -1/8 11/24 -2/17 6/13 -1/8 -2/17 7/15 -1/6 0/1 1/2 -2/17 0/1 8/15 -1/11 0/1 7/13 -2/17 -1/9 6/11 -1/9 17/31 -1/9 -2/19 11/20 -2/19 27/49 -3/28 -2/19 16/29 -1/9 0/1 5/9 -1/10 0/1 24/43 -1/7 0/1 19/34 -2/17 0/1 14/25 -4/35 -1/9 37/66 -1/9 23/41 -1/9 -10/91 9/16 -2/19 13/23 -1/9 -2/19 17/30 -4/37 -2/19 4/7 -2/19 -1/10 15/26 -2/21 0/1 41/71 -1/9 -2/19 26/45 -1/9 0/1 11/19 -1/10 0/1 29/50 -2/19 0/1 18/31 -2/19 -1/10 25/43 -1/10 0/1 32/55 -1/9 7/12 -2/19 24/41 -2/19 -5/48 17/29 -7/68 -4/39 27/46 -4/39 -6/59 10/17 -6/59 -1/10 13/22 -1/10 3/5 -1/10 -2/21 17/28 -2/21 14/23 -1/10 -2/21 25/41 -3/31 -2/21 11/18 -4/41 -2/21 19/31 -7/73 -2/21 27/44 -2/21 8/13 -2/21 -3/32 21/34 -2/21 -4/43 55/89 -4/43 -5/54 34/55 -1/11 47/76 -2/21 13/21 -2/21 -1/11 31/50 -2/21 0/1 49/79 -3/32 -4/43 18/29 -4/43 -1/11 41/66 -1/11 23/37 -1/11 -2/23 5/8 -2/21 22/35 -7/75 -4/43 83/132 -4/43 61/97 -4/43 -21/226 39/62 -4/43 -14/151 17/27 -6/65 -1/11 29/46 -4/43 -6/65 12/19 -4/43 -1/11 7/11 -1/11 16/25 -1/11 -8/89 9/14 -6/67 -4/45 11/17 -5/57 -2/23 13/20 -2/23 15/23 -1/11 -2/23 2/3 -2/23 -1/12 15/22 -1/12 13/19 -1/12 -12/145 11/16 -6/73 31/45 -9/110 -4/49 20/29 -4/49 -11/135 9/13 -3/37 -2/25 16/23 -1/12 -2/25 23/33 -1/12 30/43 -5/61 -4/49 7/10 -4/49 -2/25 19/27 -11/137 -2/25 31/44 -2/25 12/17 -2/25 -7/88 29/41 -2/25 -1/13 46/65 -2/25 -3/38 17/24 -2/25 22/31 -2/25 -3/38 5/7 -2/25 -1/13 18/25 -4/51 -1/13 49/68 -2/25 80/111 -2/25 -3/38 111/154 -3/38 31/43 -3/38 -4/51 44/61 -2/25 -3/38 13/18 -4/51 -6/77 8/11 -1/13 19/26 -8/105 -6/79 30/41 -7/92 -6/79 11/15 -4/53 -3/40 36/49 -5/67 -2/27 97/132 -2/27 61/83 -2/27 -5/68 25/34 -2/27 0/1 14/19 -1/13 -4/53 31/42 -4/53 -2/27 48/65 -3/40 -2/27 65/88 -2/27 17/23 -1/13 -2/27 3/4 -2/27 16/21 -2/27 -1/14 13/17 -1/13 -2/27 23/30 -10/137 -4/55 79/103 -31/426 -4/55 135/176 -4/55 56/73 -4/55 -21/289 33/43 -4/55 -1/14 10/13 -6/83 -1/14 17/22 -1/14 7/9 -1/14 -4/57 39/50 -8/115 -2/29 71/91 -11/159 -2/29 103/132 -2/29 32/41 -2/29 -3/44 25/32 -2/29 43/55 -1/14 18/23 -1/14 -2/29 29/37 -3/43 -2/29 69/88 -2/29 40/51 -2/29 -3/44 11/14 -2/29 0/1 15/19 -1/14 -4/57 34/43 -4/57 -3/43 87/110 -3/43 53/67 -3/43 -2/29 19/24 -2/29 23/29 -1/14 -4/57 4/5 -2/29 -1/15 17/21 -2/29 -1/15 13/16 -2/29 9/11 -1/15 23/28 -6/91 37/45 -4/61 -3/46 14/17 -3/46 -2/31 19/23 -1/15 -2/31 5/6 -2/31 0/1 21/25 -1/16 0/1 37/44 0/1 16/19 -1/15 0/1 11/13 -1/15 -2/31 17/20 -2/31 6/7 -2/31 -1/16 19/22 -1/16 13/15 -1/16 -4/65 7/8 -2/33 8/9 -1/15 0/1 9/10 -2/33 0/1 1/1 -1/18 0/1 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(221,-24,396,-43) (0/1,1/9) -> (5/9,24/43) Hyperbolic Matrix(221,-27,352,-43) (1/9,1/8) -> (5/8,22/35) 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(791,-137,1276,-221) (1/6,4/23) -> (13/21,31/50) Hyperbolic Matrix(177,-31,748,-131) (4/23,3/17) -> (4/17,5/21) Hyperbolic Matrix(89,-16,484,-87) (3/17,2/11) -> (2/11,5/27) Parabolic Matrix(2729,-507,3784,-703) (5/27,8/43) -> (31/43,44/61) Hyperbolic Matrix(969,-181,1408,-263) (8/43,3/16) -> (11/16,31/45) Hyperbolic 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(307,-65,836,-177) (4/19,3/14) -> (11/30,7/19) 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(307,-69,396,-89) (2/9,5/22) -> (17/22,7/9) Hyperbolic Matrix(441,-101,572,-131) (5/22,3/13) -> (10/13,17/22) Hyperbolic Matrix(265,-62,748,-175) (3/13,4/17) -> (6/17,11/31) Hyperbolic Matrix(45,-11,176,-43) (5/21,1/4) -> (1/4,6/23) Parabolic Matrix(617,-162,1672,-439) (6/23,5/19) -> (7/19,24/65) Hyperbolic Matrix(837,-221,1496,-395) (5/19,9/34) -> (19/34,14/25) Hyperbolic Matrix(3299,-874,4488,-1189) (9/34,13/49) -> (61/83,25/34) Hyperbolic Matrix(1187,-315,1496,-397) (13/49,4/15) -> (23/29,4/5) Hyperbolic Matrix(133,-36,484,-131) (4/15,3/11) -> (3/11,8/29) Parabolic Matrix(1495,-413,2552,-705) (8/29,13/47) -> (24/41,17/29) Hyperbolic Matrix(617,-171,1584,-439) (13/47,5/18) -> (7/18,16/41) Hyperbolic 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(307,-95,572,-177) (4/13,9/29) -> (8/15,7/13) Hyperbolic Matrix(2727,-848,6512,-2025) (9/29,14/45) -> (18/43,49/117) Hyperbolic Matrix(1627,-507,1980,-617) (14/45,5/16) -> (23/28,37/45) 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(835,-309,2024,-749) (17/46,10/27) -> (7/17,19/46) Hyperbolic Matrix(2947,-1093,5104,-1893) (10/27,23/62) -> (15/26,41/71) Hyperbolic Matrix(5147,-1910,8184,-3037) (23/62,13/35) -> (61/97,39/62) Hyperbolic Matrix(309,-115,352,-131) (13/35,3/8) -> (7/8,8/9) 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(1055,-401,1276,-485) (19/50,8/21) -> (19/23,5/6) 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(131,-53,220,-89) (2/5,9/22) -> (13/22,3/5) Hyperbolic Matrix(441,-181,748,-307) (9/22,7/17) -> (10/17,13/22) Hyperbolic Matrix(351,-145,748,-309) (19/46,12/29) -> (7/15,1/2) Hyperbolic Matrix(1321,-547,1804,-747) (12/29,17/41) -> (30/41,11/15) Hyperbolic Matrix(1277,-530,2860,-1187) (17/41,22/53) -> (4/9,21/47) Hyperbolic Matrix(2993,-1251,4840,-2023) (5/12,23/55) -> (34/55,47/76) Hyperbolic Matrix(4487,-1877,7260,-3037) (23/55,18/43) -> (55/89,34/55) 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(1101,-485,1496,-659) (11/25,15/34) -> (25/34,14/19) 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(485,-223,572,-263) (11/24,6/13) -> (11/13,17/20) Hyperbolic Matrix(395,-183,572,-265) (6/13,7/15) -> (20/29,9/13) Hyperbolic Matrix(439,-233,748,-397) (1/2,8/15) -> (17/29,27/46) Hyperbolic Matrix(265,-144,484,-263) (7/13,6/11) -> (6/11,17/31) Parabolic Matrix(967,-531,1364,-749) (17/31,11/20) -> (17/24,22/31) Hyperbolic Matrix(1583,-873,2156,-1189) (27/49,16/29) -> (11/15,36/49) Hyperbolic Matrix(1583,-874,2552,-1409) (16/29,5/9) -> (49/79,18/29) Hyperbolic Matrix(2773,-1549,4488,-2507) (24/43,19/34) -> (21/34,55/89) Hyperbolic Matrix(1233,-691,1804,-1011) (14/25,37/66) -> (15/22,13/19) Hyperbolic Matrix(747,-419,1100,-617) (37/66,23/41) -> (2/3,15/22) 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(3257,-1881,3960,-2287) (41/71,26/45) -> (37/45,14/17) 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(2639,-1535,3784,-2201) (25/43,32/55) -> (23/33,30/43) Hyperbolic Matrix(1891,-1101,2420,-1409) (32/55,7/12) -> (25/32,43/55) Hyperbolic Matrix(1409,-824,1804,-1055) (7/12,24/41) -> (32/41,25/32) Hyperbolic Matrix(1275,-749,2024,-1189) (27/46,10/17) -> (17/27,29/46) Hyperbolic Matrix(2553,-1556,3608,-2199) (14/23,25/41) -> (29/41,46/65) Hyperbolic Matrix(1319,-805,1804,-1101) (25/41,11/18) -> (19/26,30/41) Hyperbolic Matrix(1189,-729,1936,-1187) (19/31,27/44) -> (27/44,8/13) Parabolic Matrix(3431,-2128,4400,-2729) (31/50,49/79) -> (7/9,39/50) Hyperbolic Matrix(1409,-875,1628,-1011) (18/29,41/66) -> (19/22,13/15) Hyperbolic Matrix(1099,-683,1276,-793) (41/66,23/37) -> (6/7,19/22) Hyperbolic Matrix(10957,-6889,17424,-10955) (22/35,83/132) -> (83/132,61/97) Parabolic Matrix(3079,-1937,4268,-2685) (39/62,17/27) -> (44/61,13/18) 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(485,-311,616,-395) (16/25,9/14) -> (11/14,15/19) Hyperbolic 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(397,-277,440,-307) (30/43,7/10) -> (9/10,1/1) Hyperbolic Matrix(1365,-961,1936,-1363) (19/27,31/44) -> (31/44,12/17) Parabolic Matrix(5105,-3614,7084,-5015) (46/65,17/24) -> (49/68,80/111) Hyperbolic Matrix(17819,-12843,22528,-16237) (80/111,111/154) -> (87/110,53/67) Hyperbolic Matrix(8977,-6471,11352,-8183) (111/154,31/43) -> (34/43,87/110) Hyperbolic Matrix(353,-256,484,-351) (13/18,8/11) -> (8/11,19/26) Parabolic Matrix(12805,-9409,17424,-12803) (36/49,97/132) -> (97/132,61/83) Parabolic Matrix(5721,-4225,7744,-5719) (48/65,65/88) -> (65/88,17/23) Parabolic Matrix(133,-99,176,-131) (17/23,3/4) -> (3/4,16/21) Parabolic Matrix(617,-471,748,-571) (16/21,13/17) -> (14/17,19/23) Hyperbolic Matrix(23761,-18225,30976,-23759) (79/103,135/176) -> (135/176,56/73) Parabolic Matrix(13597,-10609,17424,-13595) (71/91,103/132) -> (103/132,32/41) Parabolic Matrix(6073,-4761,7744,-6071) (29/37,69/88) -> (69/88,40/51) Parabolic Matrix(397,-324,484,-395) (13/16,9/11) -> (9/11,23/28) Parabolic Matrix(1629,-1369,1936,-1627) (21/25,37/44) -> (37/44,16/19) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-19,1) Matrix(221,-24,396,-43) -> Matrix(1,0,-8,1) Matrix(221,-27,352,-43) -> Matrix(1,4,-11,-43) Matrix(219,-28,352,-45) -> Matrix(1,0,-10,1) Matrix(219,-32,308,-45) -> Matrix(5,4,-64,-51) Matrix(485,-76,836,-131) -> Matrix(1,0,-8,1) Matrix(791,-137,1276,-221) -> Matrix(1,0,-9,1) Matrix(177,-31,748,-131) -> Matrix(7,4,-23,-13) Matrix(89,-16,484,-87) -> Matrix(15,8,-32,-17) Matrix(2729,-507,3784,-703) -> Matrix(17,8,-219,-103) Matrix(969,-181,1408,-263) -> Matrix(37,16,-451,-195) Matrix(133,-26,220,-43) -> Matrix(1,0,-8,1) Matrix(703,-146,1276,-265) -> Matrix(11,4,-102,-37) Matrix(1363,-286,1892,-397) -> Matrix(1,0,-10,1) Matrix(307,-65,836,-177) -> Matrix(23,8,-141,-49) Matrix(573,-124,1012,-219) -> Matrix(11,4,-102,-37) Matrix(1497,-326,2420,-527) -> Matrix(1,0,-8,1) Matrix(749,-164,1804,-395) -> Matrix(11,4,-80,-29) Matrix(307,-69,396,-89) -> Matrix(23,8,-325,-113) Matrix(441,-101,572,-131) -> Matrix(37,12,-515,-167) Matrix(265,-62,748,-175) -> Matrix(27,8,-152,-45) Matrix(45,-11,176,-43) -> Matrix(13,4,-49,-15) Matrix(617,-162,1672,-439) -> Matrix(31,8,-190,-49) Matrix(837,-221,1496,-395) -> Matrix(1,0,-5,1) Matrix(3299,-874,4488,-1189) -> Matrix(1,0,-10,1) Matrix(1187,-315,1496,-397) -> Matrix(29,8,-417,-115) Matrix(133,-36,484,-131) -> Matrix(47,12,-192,-49) Matrix(1495,-413,2552,-705) -> Matrix(83,20,-801,-193) Matrix(617,-171,1584,-439) -> Matrix(33,8,-227,-55) Matrix(177,-50,308,-87) -> Matrix(17,4,-166,-39) Matrix(263,-76,308,-89) -> Matrix(17,4,-268,-63) Matrix(485,-142,748,-219) -> Matrix(17,4,-200,-47) Matrix(309,-92,440,-131) -> Matrix(37,8,-458,-99) Matrix(353,-108,572,-175) -> Matrix(1,0,-6,1) Matrix(307,-95,572,-177) -> Matrix(19,4,-157,-33) Matrix(2727,-848,6512,-2025) -> Matrix(19,4,-176,-37) Matrix(1627,-507,1980,-617) -> Matrix(115,24,-1749,-365) Matrix(395,-124,704,-221) -> Matrix(39,8,-356,-73) Matrix(529,-186,748,-263) -> Matrix(21,4,-268,-51) Matrix(1143,-406,2728,-969) -> Matrix(23,4,-144,-25) Matrix(177,-64,484,-175) -> Matrix(71,12,-432,-73) Matrix(4223,-1560,5720,-2113) -> Matrix(99,16,-1318,-213) Matrix(835,-309,2024,-749) -> Matrix(1,0,-1,1) Matrix(2947,-1093,5104,-1893) -> Matrix(25,4,-219,-35) Matrix(5147,-1910,8184,-3037) -> Matrix(349,56,-3758,-603) Matrix(309,-115,352,-131) -> Matrix(25,4,-419,-67) Matrix(307,-116,352,-133) -> Matrix(1,0,-10,1) Matrix(1143,-434,2552,-969) -> Matrix(25,4,-194,-31) Matrix(1055,-401,1276,-485) -> Matrix(1,0,-9,1) Matrix(397,-152,572,-219) -> Matrix(1,0,-6,1) Matrix(485,-188,792,-307) -> Matrix(53,8,-550,-83) Matrix(661,-258,1012,-395) -> Matrix(27,4,-304,-45) Matrix(177,-70,220,-87) -> Matrix(1,0,-8,1) Matrix(131,-53,220,-89) -> Matrix(27,4,-277,-41) Matrix(441,-181,748,-307) -> Matrix(85,12,-843,-119) Matrix(351,-145,748,-309) -> Matrix(29,4,-225,-31) Matrix(1321,-547,1804,-747) -> Matrix(117,16,-1543,-211) Matrix(1277,-530,2860,-1187) -> Matrix(1,0,0,1) Matrix(2993,-1251,4840,-2023) -> Matrix(1,0,-3,1) Matrix(4487,-1877,7260,-3037) -> Matrix(33,4,-355,-43) Matrix(8537,-3576,11132,-4663) -> Matrix(17,4,-234,-55) Matrix(705,-296,836,-351) -> Matrix(1,0,-8,1) Matrix(221,-94,308,-131) -> Matrix(29,4,-370,-51) Matrix(793,-344,1012,-439) -> Matrix(31,4,-442,-57) Matrix(615,-268,1012,-441) -> Matrix(31,4,-318,-41) Matrix(483,-212,704,-309) -> Matrix(63,8,-764,-97) Matrix(1101,-485,1496,-659) -> Matrix(1,0,-5,1) Matrix(353,-156,396,-175) -> Matrix(1,0,-8,1) Matrix(4531,-2026,5808,-2597) -> Matrix(91,12,-1312,-173) Matrix(1011,-454,1276,-573) -> Matrix(31,4,-442,-57) Matrix(221,-100,484,-219) -> Matrix(31,4,-256,-33) Matrix(485,-223,572,-263) -> Matrix(1,0,-7,1) Matrix(395,-183,572,-265) -> Matrix(35,4,-429,-49) Matrix(439,-233,748,-397) -> Matrix(37,4,-361,-39) Matrix(265,-144,484,-263) -> Matrix(35,4,-324,-37) Matrix(967,-531,1364,-749) -> Matrix(75,8,-947,-101) Matrix(1583,-873,2156,-1189) -> Matrix(39,4,-517,-53) Matrix(1583,-874,2552,-1409) -> Matrix(37,4,-398,-43) Matrix(2773,-1549,4488,-2507) -> Matrix(33,4,-355,-43) Matrix(1233,-691,1804,-1011) -> Matrix(143,16,-1725,-193) Matrix(747,-419,1100,-617) -> Matrix(109,12,-1299,-143) Matrix(571,-322,704,-397) -> Matrix(37,4,-546,-59) Matrix(1277,-724,1628,-923) -> Matrix(37,4,-546,-59) Matrix(3257,-1881,3960,-2287) -> Matrix(39,4,-595,-61) Matrix(1321,-764,1672,-967) -> Matrix(39,4,-556,-57) Matrix(1145,-664,1364,-791) -> Matrix(1,0,-6,1) Matrix(1453,-844,1892,-1099) -> Matrix(41,4,-564,-55) Matrix(2639,-1535,3784,-2201) -> Matrix(35,4,-429,-49) Matrix(1891,-1101,2420,-1409) -> Matrix(1,0,-5,1) Matrix(1409,-824,1804,-1055) -> Matrix(39,4,-556,-57) Matrix(1275,-749,2024,-1189) -> Matrix(1,0,-1,1) Matrix(2553,-1556,3608,-2199) -> Matrix(83,8,-1048,-101) Matrix(1319,-805,1804,-1101) -> Matrix(39,4,-517,-53) Matrix(1189,-729,1936,-1187) -> Matrix(209,20,-2205,-211) Matrix(3431,-2128,4400,-2729) -> Matrix(85,8,-1222,-115) Matrix(1409,-875,1628,-1011) -> Matrix(87,8,-1403,-129) Matrix(1099,-683,1276,-793) -> Matrix(45,4,-709,-63) Matrix(10957,-6889,17424,-10955) -> Matrix(1203,112,-12943,-1205) Matrix(3079,-1937,4268,-2685) -> Matrix(173,16,-2195,-203) Matrix(1233,-778,1672,-1055) -> Matrix(87,8,-1142,-105) Matrix(309,-196,484,-307) -> Matrix(131,12,-1452,-133) Matrix(485,-311,616,-395) -> Matrix(45,4,-619,-55) Matrix(573,-370,748,-483) -> Matrix(91,8,-1240,-109) Matrix(1497,-974,1892,-1231) -> Matrix(47,4,-670,-57) Matrix(3477,-2396,4532,-3123) -> Matrix(489,40,-6736,-551) Matrix(1583,-1102,2024,-1409) -> Matrix(1,0,-2,1) Matrix(397,-277,440,-307) -> Matrix(49,4,-821,-67) Matrix(1365,-961,1936,-1363) -> Matrix(449,36,-5625,-451) Matrix(5105,-3614,7084,-5015) -> Matrix(1,0,0,1) Matrix(17819,-12843,22528,-16237) -> Matrix(151,12,-2177,-173) Matrix(8977,-6471,11352,-8183) -> Matrix(305,24,-4359,-343) Matrix(353,-256,484,-351) -> Matrix(155,12,-2028,-157) Matrix(12805,-9409,17424,-12803) -> Matrix(269,20,-3645,-271) Matrix(5721,-4225,7744,-5719) -> Matrix(53,4,-729,-55) Matrix(133,-99,176,-131) -> Matrix(53,4,-729,-55) Matrix(617,-471,748,-571) -> Matrix(55,4,-839,-61) Matrix(23761,-18225,30976,-23759) -> Matrix(2859,208,-39325,-2861) Matrix(13597,-10609,17424,-13595) -> Matrix(405,28,-5887,-407) Matrix(6073,-4761,7744,-6071) -> Matrix(173,12,-2523,-175) Matrix(397,-324,484,-395) -> Matrix(119,8,-1800,-121) Matrix(1629,-1369,1936,-1627) -> Matrix(1,0,1,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 40 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (0/1,1/1) 0 22 1/9 (-1/2,0/1) 0 22 1/8 -2/1 1 11 1/7 (-1/1,-2/3) 0 22 2/13 (-2/3,-1/2) 0 22 1/6 (-2/3,0/1) 0 11 4/23 (-2/3,-1/2) 0 22 3/17 (-2/3,-3/5) 0 22 2/11 -1/2 4 2 5/27 (-6/13,-5/11) 0 22 8/43 (-5/11,-4/9) 0 22 3/16 -2/5 1 11 1/5 (-1/2,-2/5) 0 22 5/24 -2/5 1 11 4/19 (-4/11,-1/3) 0 22 3/14 (-2/5,0/1) 0 11 5/23 (-2/5,-1/3) 0 22 7/32 -2/5 1 11 2/9 (-4/11,-1/3) 0 22 5/22 -1/3 10 1 3/13 (-1/3,-6/19) 0 22 4/17 (-2/7,-1/4) 0 22 5/21 (-1/3,-2/7) 0 22 1/4 -2/7 1 11 6/23 (-2/7,-1/4) 0 22 5/19 (-4/15,-1/4) 0 22 9/34 (-2/7,0/1) 0 11 35/132 -2/7 5 1 13/49 (-2/7,-5/18) 0 22 4/15 (-3/11,-4/15) 0 22 3/11 -1/4 6 2 8/29 (-9/37,-8/33) 0 22 13/47 (-6/25,-5/21) 0 22 5/18 (-6/25,-4/17) 0 11 2/7 (-1/4,-2/9) 0 22 9/31 (-3/13,-2/9) 0 22 7/24 -2/9 1 11 5/17 (-7/31,-2/9) 0 22 13/44 -2/9 9 1 3/10 (-2/9,-4/19) 0 11 4/13 (-2/9,-3/14) 0 22 9/29 (-11/52,-4/19) 0 22 14/45 (-4/19,-9/43) 0 22 5/16 -6/29 1 11 1/3 (-1/5,-2/11) 0 22 7/20 -2/11 1 11 6/17 (-2/11,-5/28) 0 22 11/31 (-3/17,-10/57) 0 22 5/14 (-4/23,-6/35) 0 11 4/11 -1/6 6 2 11/30 (-8/49,-6/37) 0 11 7/19 (-1/6,-4/25) 0 22 24/65 (-1/6,-6/37) 0 22 65/176 -6/37 1 1 17/46 (-6/37,-4/25) 0 11 10/27 (-1/6,-6/37) 0 22 23/62 (-14/87,-4/25) 0 11 49/132 -4/25 7 1 13/35 (-4/25,-7/44) 0 22 3/8 -2/13 1 11 14/37 (-2/11,-1/6) 0 22 25/66 -1/6 6 1 11/29 (-1/6,-4/25) 0 22 19/50 (-2/13,0/1) 0 11 8/21 (-1/6,-2/13) 0 22 29/76 -2/13 1 11 21/55 -1/6 2 2 34/89 (-5/31,-4/25) 0 22 13/34 (-4/25,-2/13) 0 11 5/13 (-3/19,-2/13) 0 22 17/44 -2/13 5 1 7/18 (-2/13,-4/27) 0 11 16/41 (-2/13,-3/20) 0 22 25/64 -2/13 1 11 9/23 (-2/13,-1/7) 0 22 2/5 (-2/13,-1/7) 0 22 9/22 -1/7 8 1 7/17 (-1/7,-6/43) 0 22 19/46 (-6/43,-4/29) 0 11 12/29 (-4/29,-7/51) 0 22 17/41 (-5/37,-2/15) 0 22 22/53 (-1/7,0/1) 0 22 5/12 -2/15 1 11 23/55 -1/8 2 2 18/43 (-1/7,0/1) 0 22 49/117 (-1/12,0/1) 0 22 129/308 0/1 13 1 31/74 (-2/11,0/1) 0 11 13/31 (-1/7,-2/15) 0 22 21/50 (-2/15,0/1) 0 11 37/88 0/1 1 1 8/19 (-1/7,0/1) 0 22 27/64 -2/15 1 11 46/109 (-2/15,-1/8) 0 22 65/154 -1/8 2 1 19/45 (-1/8,0/1) 0 22 30/71 (-2/15,-1/8) 0 22 11/26 (-2/13,0/1) 0 11 3/7 (-1/7,-2/15) 0 22 19/44 -2/15 3 1 13/30 (-2/15,-4/31) 0 11 10/23 (-2/15,-1/8) 0 22 17/39 (-2/15,-1/8) 0 22 7/16 -2/15 1 11 18/41 (-10/79,-1/8) 0 22 29/66 -1/8 14 1 11/25 (-1/8,-4/33) 0 22 15/34 (-2/17,0/1) 0 11 19/43 (-1/10,0/1) 0 22 4/9 (-1/7,0/1) 0 22 21/47 (-5/37,-2/15) 0 22 59/132 -2/15 7 1 17/38 (-2/15,-4/31) 0 11 13/29 (-1/8,0/1) 0 22 22/49 (-2/15,-3/23) 0 22 9/20 -2/15 1 11 5/11 -1/8 2 2 11/24 -2/17 1 11 6/13 (-1/8,-2/17) 0 22 7/15 (-1/6,0/1) 0 22 1/2 (-2/17,0/1) 0 11 1/0 0/1 19 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(175,-19,396,-43) (0/1,1/9) -> (19/43,4/9) Glide Reflection Matrix(131,-16,352,-43) (1/9,1/8) -> (13/35,3/8) Glide Reflection Matrix(133,-17,352,-45) (1/8,1/7) -> (3/8,14/37) Glide Reflection Matrix(89,-13,308,-45) (1/7,2/13) -> (2/7,9/31) Glide Reflection Matrix(351,-55,836,-131) (2/13,1/6) -> (13/31,21/50) Glide Reflection Matrix(485,-84,1276,-221) (1/6,4/23) -> (19/50,8/21) Glide Reflection Matrix(177,-31,748,-131) (4/23,3/17) -> (4/17,5/21) Hyperbolic Matrix(89,-16,484,-87) (3/17,2/11) -> (2/11,5/27) Parabolic Matrix(1803,-335,4268,-793) (5/27,8/43) -> (19/45,30/71) Hyperbolic Matrix(439,-82,1408,-263) (8/43,3/16) -> (14/45,5/16) Glide Reflection Matrix(307,-58,704,-133) (3/16,1/5) -> (17/39,7/16) Hyperbolic Matrix(573,-119,1276,-265) (1/5,5/24) -> (22/49,9/20) Glide Reflection Matrix(705,-148,1672,-351) (5/24,4/19) -> (8/19,27/64) Hyperbolic Matrix(307,-65,836,-177) (4/19,3/14) -> (11/30,7/19) Hyperbolic Matrix(439,-95,1012,-219) (3/14,5/23) -> (13/30,10/23) Glide Reflection Matrix(923,-201,2420,-527) (5/23,7/32) -> (8/21,29/76) Glide Reflection Matrix(749,-164,1804,-395) (7/32,2/9) -> (22/53,5/12) Hyperbolic 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(265,-62,748,-175) (3/13,4/17) -> (6/17,11/31) Hyperbolic Matrix(45,-11,176,-43) (5/21,1/4) -> (1/4,6/23) Parabolic Matrix(617,-162,1672,-439) (6/23,5/19) -> (7/19,24/65) Hyperbolic Matrix(659,-174,1496,-395) (5/19,9/34) -> (11/25,15/34) Glide Reflection Matrix(1189,-315,4488,-1189) (9/34,35/132) -> (9/34,35/132) Reflection Matrix(3431,-910,12936,-3431) (35/132,13/49) -> (35/132,13/49) Reflection Matrix(967,-257,2156,-573) (13/49,4/15) -> (13/29,22/49) Hyperbolic Matrix(133,-36,484,-131) (4/15,3/11) -> (3/11,8/29) Parabolic Matrix(1057,-292,2552,-705) (8/29,13/47) -> (12/29,17/41) Glide Reflection Matrix(617,-171,1584,-439) (13/47,5/18) -> (7/18,16/41) Hyperbolic Matrix(131,-37,308,-87) (5/18,2/7) -> (11/26,3/7) Glide Reflection Matrix(485,-141,1056,-307) (9/31,7/24) -> (11/24,6/13) Hyperbolic Matrix(263,-77,748,-219) (7/24,5/17) -> (7/20,6/17) Glide Reflection Matrix(441,-130,1496,-441) (5/17,13/44) -> (5/17,13/44) Reflection Matrix(131,-39,440,-131) (13/44,3/10) -> (13/44,3/10) Reflection Matrix(219,-67,572,-175) (3/10,4/13) -> (13/34,5/13) Glide Reflection Matrix(265,-82,572,-177) (4/13,9/29) -> (6/13,7/15) Glide Reflection Matrix(2727,-848,6512,-2025) (9/29,14/45) -> (18/43,49/117) Hyperbolic Matrix(309,-97,704,-221) (5/16,1/3) -> (7/16,18/41) Glide Reflection Matrix(395,-137,1012,-351) (1/3,7/20) -> (16/41,25/64) Glide Reflection 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(8449,-3120,22880,-8449) (24/65,65/176) -> (24/65,65/176) Reflection Matrix(2991,-1105,8096,-2991) (65/176,17/46) -> (65/176,17/46) Reflection Matrix(835,-309,2024,-749) (17/46,10/27) -> (7/17,19/46) Hyperbolic Matrix(2157,-800,5104,-1893) (10/27,23/62) -> (30/71,11/26) Glide Reflection Matrix(3037,-1127,8184,-3037) (23/62,49/132) -> (23/62,49/132) Reflection Matrix(3431,-1274,9240,-3431) (49/132,13/35) -> (49/132,13/35) Reflection Matrix(1849,-700,4884,-1849) (14/37,25/66) -> (14/37,25/66) Reflection Matrix(1451,-550,3828,-1451) (25/66,11/29) -> (25/66,11/29) Reflection Matrix(1143,-434,2552,-969) (11/29,19/50) -> (17/38,13/29) Hyperbolic Matrix(2023,-772,4840,-1847) (29/76,21/55) -> (5/12,23/55) Glide Reflection Matrix(3037,-1160,7260,-2773) (21/55,34/89) -> (23/55,18/43) Glide Reflection Matrix(1981,-757,4488,-1715) (34/89,13/34) -> (15/34,19/43) Hyperbolic Matrix(441,-170,1144,-441) (5/13,17/44) -> (5/13,17/44) Reflection Matrix(307,-119,792,-307) (17/44,7/18) -> (17/44,7/18) Reflection Matrix(3565,-1393,8448,-3301) (25/64,9/23) -> (27/64,46/109) Glide Reflection Matrix(441,-173,1012,-397) (9/23,2/5) -> (10/23,17/39) Glide Reflection 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(351,-145,748,-309) (19/46,12/29) -> (7/15,1/2) Hyperbolic Matrix(1277,-530,2860,-1187) (17/41,22/53) -> (4/9,21/47) Hyperbolic Matrix(30185,-12642,72072,-30185) (49/117,129/308) -> (49/117,129/308) Reflection Matrix(9547,-3999,22792,-9547) (129/308,31/74) -> (129/308,31/74) Reflection Matrix(1849,-777,4400,-1849) (21/50,37/88) -> (21/50,37/88) Reflection Matrix(1407,-592,3344,-1407) (37/88,8/19) -> (37/88,8/19) Reflection Matrix(14169,-5980,33572,-14169) (46/109,65/154) -> (46/109,65/154) Reflection Matrix(5851,-2470,13860,-5851) (65/154,19/45) -> (65/154,19/45) Reflection Matrix(265,-114,616,-265) (3/7,19/44) -> (3/7,19/44) Reflection Matrix(571,-247,1320,-571) (19/44,13/30) -> (19/44,13/30) Reflection Matrix(2377,-1044,5412,-2377) (18/41,29/66) -> (18/41,29/66) Reflection Matrix(1451,-638,3300,-1451) (29/66,11/25) -> (29/66,11/25) Reflection Matrix(5545,-2478,12408,-5545) (21/47,59/132) -> (21/47,59/132) Reflection Matrix(2243,-1003,5016,-2243) (59/132,17/38) -> (59/132,17/38) Reflection Matrix(221,-100,484,-219) (9/20,5/11) -> (5/11,11/24) Parabolic 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(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(175,-19,396,-43) -> Matrix(-1,0,9,1) *** -> (-2/9,0/1) Matrix(131,-16,352,-43) -> Matrix(1,4,-6,-25) Matrix(133,-17,352,-45) -> Matrix(-1,0,7,1) *** -> (-2/7,0/1) Matrix(89,-13,308,-45) -> Matrix(5,4,-21,-17) Matrix(351,-55,836,-131) -> Matrix(-1,0,9,1) *** -> (-2/9,0/1) Matrix(485,-84,1276,-221) -> Matrix(-1,0,8,1) *** -> (-1/4,0/1) Matrix(177,-31,748,-131) -> Matrix(7,4,-23,-13) Matrix(89,-16,484,-87) -> Matrix(15,8,-32,-17) -1/2 Matrix(1803,-335,4268,-793) -> Matrix(9,4,-61,-27) Matrix(439,-82,1408,-263) -> Matrix(37,16,-178,-77) Matrix(307,-58,704,-133) -> Matrix(9,4,-70,-31) Matrix(573,-119,1276,-265) -> Matrix(11,4,-85,-31) Matrix(705,-148,1672,-351) -> Matrix(11,4,-80,-29) Matrix(307,-65,836,-177) -> Matrix(23,8,-141,-49) Matrix(439,-95,1012,-219) -> Matrix(11,4,-85,-31) Matrix(923,-201,2420,-527) -> Matrix(-1,0,9,1) *** -> (-2/9,0/1) Matrix(749,-164,1804,-395) -> Matrix(11,4,-80,-29) Matrix(89,-20,396,-89) -> Matrix(23,8,-66,-23) (2/9,5/22) -> (-4/11,-1/3) Matrix(131,-30,572,-131) -> Matrix(37,12,-114,-37) (5/22,3/13) -> (-1/3,-6/19) Matrix(265,-62,748,-175) -> Matrix(27,8,-152,-45) Matrix(45,-11,176,-43) -> Matrix(13,4,-49,-15) -2/7 Matrix(617,-162,1672,-439) -> Matrix(31,8,-190,-49) Matrix(659,-174,1496,-395) -> Matrix(-1,0,12,1) *** -> (-1/6,0/1) Matrix(1189,-315,4488,-1189) -> Matrix(-1,0,7,1) (9/34,35/132) -> (-2/7,0/1) Matrix(3431,-910,12936,-3431) -> Matrix(71,20,-252,-71) (35/132,13/49) -> (-2/7,-5/18) Matrix(967,-257,2156,-573) -> Matrix(15,4,-109,-29) Matrix(133,-36,484,-131) -> Matrix(47,12,-192,-49) -1/4 Matrix(1057,-292,2552,-705) -> Matrix(83,20,-610,-147) Matrix(617,-171,1584,-439) -> Matrix(33,8,-227,-55) Matrix(131,-37,308,-87) -> Matrix(17,4,-123,-29) Matrix(485,-141,1056,-307) -> Matrix(17,4,-149,-35) Matrix(263,-77,748,-219) -> Matrix(17,4,-89,-21) Matrix(441,-130,1496,-441) -> Matrix(125,28,-558,-125) (5/17,13/44) -> (-7/31,-2/9) Matrix(131,-39,440,-131) -> Matrix(37,8,-171,-37) (13/44,3/10) -> (-2/9,-4/19) Matrix(219,-67,572,-175) -> Matrix(-1,0,11,1) *** -> (-2/11,0/1) Matrix(265,-82,572,-177) -> Matrix(19,4,-166,-35) Matrix(2727,-848,6512,-2025) -> Matrix(19,4,-176,-37) Matrix(309,-97,704,-221) -> Matrix(39,8,-307,-63) Matrix(395,-137,1012,-351) -> Matrix(23,4,-155,-27) Matrix(1143,-406,2728,-969) -> Matrix(23,4,-144,-25) -1/6 Matrix(177,-64,484,-175) -> Matrix(71,12,-432,-73) -1/6 Matrix(8449,-3120,22880,-8449) -> Matrix(73,12,-444,-73) (24/65,65/176) -> (-1/6,-6/37) Matrix(2991,-1105,8096,-2991) -> Matrix(149,24,-925,-149) (65/176,17/46) -> (-6/37,-4/25) Matrix(835,-309,2024,-749) -> Matrix(1,0,-1,1) 0/1 Matrix(2157,-800,5104,-1893) -> Matrix(25,4,-206,-33) Matrix(3037,-1127,8184,-3037) -> Matrix(349,56,-2175,-349) (23/62,49/132) -> (-14/87,-4/25) Matrix(3431,-1274,9240,-3431) -> Matrix(351,56,-2200,-351) (49/132,13/35) -> (-4/25,-7/44) Matrix(1849,-700,4884,-1849) -> Matrix(23,4,-132,-23) (14/37,25/66) -> (-2/11,-1/6) Matrix(1451,-550,3828,-1451) -> Matrix(49,8,-300,-49) (25/66,11/29) -> (-1/6,-4/25) Matrix(1143,-434,2552,-969) -> Matrix(25,4,-194,-31) Matrix(2023,-772,4840,-1847) -> Matrix(-1,0,14,1) *** -> (-1/7,0/1) Matrix(3037,-1160,7260,-2773) -> Matrix(25,4,-206,-33) Matrix(1981,-757,4488,-1715) -> Matrix(25,4,-219,-35) Matrix(441,-170,1144,-441) -> Matrix(77,12,-494,-77) (5/13,17/44) -> (-3/19,-2/13) Matrix(307,-119,792,-307) -> Matrix(53,8,-351,-53) (17/44,7/18) -> (-2/13,-4/27) Matrix(3565,-1393,8448,-3301) -> Matrix(27,4,-209,-31) Matrix(441,-173,1012,-397) -> Matrix(27,4,-209,-31) Matrix(89,-36,220,-89) -> Matrix(27,4,-182,-27) (2/5,9/22) -> (-2/13,-1/7) Matrix(307,-126,748,-307) -> Matrix(85,12,-602,-85) (9/22,7/17) -> (-1/7,-6/43) Matrix(351,-145,748,-309) -> Matrix(29,4,-225,-31) -2/15 Matrix(1277,-530,2860,-1187) -> Matrix(1,0,0,1) Matrix(30185,-12642,72072,-30185) -> Matrix(-1,0,24,1) (49/117,129/308) -> (-1/12,0/1) Matrix(9547,-3999,22792,-9547) -> Matrix(-1,0,11,1) (129/308,31/74) -> (-2/11,0/1) Matrix(1849,-777,4400,-1849) -> Matrix(-1,0,15,1) (21/50,37/88) -> (-2/15,0/1) Matrix(1407,-592,3344,-1407) -> Matrix(-1,0,14,1) (37/88,8/19) -> (-1/7,0/1) Matrix(14169,-5980,33572,-14169) -> Matrix(31,4,-240,-31) (46/109,65/154) -> (-2/15,-1/8) Matrix(5851,-2470,13860,-5851) -> Matrix(-1,0,16,1) (65/154,19/45) -> (-1/8,0/1) Matrix(265,-114,616,-265) -> Matrix(29,4,-210,-29) (3/7,19/44) -> (-1/7,-2/15) Matrix(571,-247,1320,-571) -> Matrix(61,8,-465,-61) (19/44,13/30) -> (-2/15,-4/31) Matrix(2377,-1044,5412,-2377) -> Matrix(159,20,-1264,-159) (18/41,29/66) -> (-10/79,-1/8) Matrix(1451,-638,3300,-1451) -> Matrix(65,8,-528,-65) (29/66,11/25) -> (-1/8,-4/33) Matrix(5545,-2478,12408,-5545) -> Matrix(149,20,-1110,-149) (21/47,59/132) -> (-5/37,-2/15) Matrix(2243,-1003,5016,-2243) -> Matrix(61,8,-465,-61) (59/132,17/38) -> (-2/15,-4/31) Matrix(221,-100,484,-219) -> Matrix(31,4,-256,-33) -1/8 Matrix(-1,1,0,1) -> Matrix(-1,0,17,1) (1/2,1/0) -> (-2/17,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.