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): 720 Minimal number of generators: 121 Number of equivalence classes of cusps: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/11 -6/11 -1/2 -4/11 -7/22 -10/33 -3/10 -1/4 -4/19 -2/11 -1/6 -3/22 -2/15 -1/8 0/1 1/9 1/8 1/7 2/13 1/6 2/11 1/5 2/9 5/22 4/17 1/4 3/11 2/7 3/10 1/3 4/11 8/21 2/5 9/22 5/11 1/2 6/11 13/22 34/55 7/11 2/3 15/22 23/33 8/11 65/88 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 -7/8 -3/2 1/0 -6/7 -1/1 -1/2 -5/6 1/2 1/0 -19/23 1/0 -14/17 3/1 1/0 -9/11 1/0 -4/5 -2/1 1/0 -7/9 -5/4 -17/22 -1/1 -10/13 -1/1 -5/6 -3/4 -1/2 1/0 -8/11 1/0 -13/18 -5/2 1/0 -5/7 1/0 -17/24 -3/2 -5/4 -12/17 -5/4 -1/1 -7/10 -3/2 1/0 -9/13 1/0 -20/29 -3/2 -4/3 -11/16 -5/4 -7/6 -2/3 -1/1 -1/2 -7/11 -1/2 -12/19 -1/2 0/1 -5/8 -1/2 1/0 -18/29 0/1 1/2 -31/50 3/2 1/0 -13/21 1/0 -8/13 -3/2 -1/1 -11/18 -3/4 -1/2 -14/23 -1/1 -1/2 -3/5 1/0 -13/22 -1/1 -10/17 -1/1 -7/8 -7/12 -5/6 -3/4 -4/7 -1/1 -1/2 -9/16 -3/4 -7/10 -14/25 -2/3 -9/14 -5/9 -5/8 -6/11 -1/2 -7/13 -3/8 -8/15 -1/2 0/1 -1/2 -1/2 1/0 -6/13 -3/5 -1/2 -5/11 -1/2 -4/9 -1/2 -2/5 -15/34 -3/8 -11/30 -11/25 -7/20 -29/66 -1/3 -18/41 -1/3 -7/22 -7/16 -1/2 -1/4 -10/23 -1/2 -1/3 -3/7 -1/4 -11/26 -1/4 -1/6 -19/45 -1/4 -8/19 -1/6 0/1 -13/31 -1/4 -18/43 -1/2 0/1 -5/12 -1/2 -1/4 -12/29 -1/6 0/1 -19/46 -1/6 -1/8 -7/17 -1/8 -9/22 0/1 -2/5 0/1 1/0 -5/13 -3/4 -13/34 -3/4 -1/2 -34/89 -2/3 -1/2 -21/55 -1/2 -8/21 -1/1 -1/2 -11/29 1/0 -25/66 -1/1 -14/37 -1/1 -5/6 -3/8 -3/4 -1/2 -4/11 -1/2 -5/14 -1/2 -5/12 -6/17 -3/8 -1/3 -7/20 -1/2 -3/8 -1/3 -1/4 -7/22 0/1 -6/19 0/1 1/10 -5/16 1/4 1/2 -4/13 1/2 1/1 -7/23 1/0 -10/33 1/0 -3/10 -3/2 1/0 -2/7 -1/1 -1/2 -3/11 -1/2 -4/15 -1/2 -2/5 -9/34 -7/18 -3/8 -5/19 -1/4 -11/42 -1/2 -3/8 -6/23 -1/2 -1/3 -1/4 -1/2 -1/4 -5/21 -1/4 -4/17 -1/4 -1/5 -7/30 -1/6 -1/8 -3/13 -1/8 -5/22 0/1 -2/9 0/1 1/2 -7/32 5/2 1/0 -12/55 1/0 -5/23 1/0 -3/14 -1/2 1/0 -4/19 -1/2 0/1 -9/43 1/0 -23/110 -1/1 -14/67 -1/1 -1/2 -5/24 -1/2 1/0 -1/5 1/0 -2/11 -1/2 -3/17 -3/8 -4/23 -1/2 -1/3 -1/6 -1/2 -1/4 -2/13 -1/1 -1/2 -3/20 -1/2 -3/8 -1/7 -1/4 -3/22 0/1 -2/15 0/1 1/2 -1/8 -1/2 1/0 -1/9 1/0 0/1 -1/2 0/1 1/9 -1/4 1/8 -1/2 -1/4 1/7 1/0 2/13 -1/2 -1/3 1/6 -1/2 1/0 2/11 -1/2 3/16 -1/2 -3/8 1/5 -1/4 3/14 -1/2 -1/4 5/23 -1/4 7/32 -1/4 -5/22 2/9 -1/6 0/1 5/22 0/1 3/13 1/4 4/17 1/1 1/0 5/21 1/0 1/4 -1/2 1/0 5/19 1/0 4/15 -2/3 -1/2 3/11 -1/2 2/7 -1/2 -1/3 3/10 -3/10 -1/4 4/13 -1/5 -1/6 5/16 -1/6 -1/8 1/3 1/0 4/11 -1/2 7/19 -7/16 10/27 -3/7 -5/12 13/35 -3/8 3/8 -1/2 -3/8 11/29 -1/4 8/21 -1/2 -1/3 5/13 -3/8 2/5 -1/4 0/1 9/22 0/1 7/17 1/4 19/46 1/4 1/2 12/29 0/1 1/2 17/41 3/4 5/12 -1/2 1/0 18/43 -1/2 0/1 13/31 1/0 8/19 0/1 1/2 3/7 1/0 10/23 -1/1 -1/2 7/16 -1/2 1/0 11/25 -7/8 15/34 -11/14 -3/4 4/9 -2/3 -1/2 5/11 -1/2 6/13 -1/2 -3/7 1/2 -1/2 -1/4 6/11 -1/2 11/20 -1/2 -9/20 16/29 -1/2 -4/9 5/9 -5/12 14/25 -9/22 -2/5 37/66 -2/5 23/41 -19/48 9/16 -7/18 -3/8 4/7 -1/2 -1/3 7/12 -3/8 -5/14 10/17 -7/20 -1/3 13/22 -1/3 3/5 -1/4 17/28 -1/2 -3/8 14/23 -1/2 -1/3 25/41 -3/8 11/18 -1/2 -3/8 8/13 -1/3 -3/10 21/34 -7/26 -1/4 34/55 -1/4 47/76 -1/4 -9/38 13/21 -1/4 31/50 -1/4 -3/14 18/29 -1/6 0/1 41/66 0/1 23/37 1/0 5/8 -1/2 -1/4 17/27 -1/4 29/46 -1/2 -1/4 12/19 -1/2 0/1 7/11 -1/2 2/3 -1/2 -1/3 15/22 -1/3 13/19 -13/40 11/16 -7/22 -5/16 20/29 -4/13 -3/10 9/13 -1/4 16/23 -1/3 -3/10 23/33 -3/10 30/43 -3/10 -2/7 7/10 -3/10 -1/4 12/17 -1/3 -5/16 29/41 -1/4 46/65 -1/3 -3/10 17/24 -5/16 -3/10 22/31 -3/10 -5/17 5/7 -1/4 8/11 -1/4 11/15 -1/4 14/19 -1/2 0/1 31/42 -1/2 -1/4 48/65 -1/2 -1/3 65/88 -1/3 17/23 -1/4 3/4 -1/2 -1/4 10/13 -5/14 -1/3 17/22 -1/3 7/9 -5/16 4/5 -2/7 -1/4 9/11 -1/4 14/17 -1/4 -3/13 19/23 -1/4 5/6 -1/4 -1/6 6/7 -1/2 -1/3 19/22 -1/3 13/15 -5/16 7/8 -3/10 -1/4 1/1 -1/4 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(43,38,198,175) (-1/1,-7/8) -> (3/14,5/23) Hyperbolic Matrix(133,116,-352,-307) (-7/8,-6/7) -> (-14/37,-3/8) Hyperbolic Matrix(87,74,154,131) (-6/7,-5/6) -> (9/16,4/7) 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(307,252,374,307) (-14/17,-9/11) -> (9/11,14/17) Hyperbolic Matrix(89,72,110,89) (-9/11,-4/5) -> (4/5,9/11) Hyperbolic Matrix(43,34,110,87) (-4/5,-7/9) -> (5/13,2/5) 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(175,134,286,219) (-10/13,-3/4) -> (11/18,8/13) Hyperbolic Matrix(175,128,-242,-177) (-3/4,-8/11) -> (-8/11,-13/18) Parabolic 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(219,154,374,263) (-12/17,-7/10) -> (7/12,10/17) Hyperbolic Matrix(219,152,-572,-397) (-7/10,-9/13) -> (-5/13,-13/34) Hyperbolic Matrix(353,244,638,441) (-9/13,-20/29) -> (16/29,5/9) Hyperbolic Matrix(1187,818,1914,1319) (-20/29,-11/16) -> (31/50,18/29) Hyperbolic Matrix(309,212,-704,-483) (-11/16,-2/3) -> (-18/41,-7/16) Hyperbolic Matrix(43,28,66,43) (-2/3,-7/11) -> (7/11,2/3) Hyperbolic Matrix(265,168,418,265) (-7/11,-12/19) -> (12/19,7/11) Hyperbolic Matrix(89,56,-418,-263) (-12/19,-5/8) -> (-3/14,-4/19) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) Hyperbolic Matrix(1319,818,1914,1187) (-18/29,-31/50) -> (11/16,20/29) 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(219,134,286,175) (-8/13,-11/18) -> (3/4,10/13) Hyperbolic Matrix(131,80,-506,-309) (-11/18,-14/23) -> (-6/23,-1/4) Hyperbolic Matrix(89,54,-506,-307) (-14/23,-3/5) -> (-3/17,-4/23) 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(263,154,374,219) (-10/17,-7/12) -> (7/10,12/17) Hyperbolic Matrix(45,26,154,89) (-7/12,-4/7) -> (2/7,3/10) Hyperbolic Matrix(131,74,154,87) (-4/7,-9/16) -> (5/6,6/7) Hyperbolic Matrix(221,124,-704,-395) (-9/16,-14/25) -> (-6/19,-5/16) Hyperbolic Matrix(397,222,946,529) (-14/25,-5/9) -> (13/31,8/19) Hyperbolic Matrix(131,72,-242,-133) (-5/9,-6/11) -> (-6/11,-7/13) Parabolic 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(43,20,-286,-133) (-1/2,-6/13) -> (-2/13,-3/20) Hyperbolic Matrix(131,60,286,131) (-6/13,-5/11) -> (5/11,6/13) Hyperbolic Matrix(89,40,198,89) (-5/11,-4/9) -> (4/9,5/11) Hyperbolic Matrix(131,58,594,263) (-4/9,-15/34) -> (7/32,2/9) Hyperbolic Matrix(703,310,1694,747) (-15/34,-11/25) -> (17/41,5/12) 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(87,38,-506,-221) (-7/16,-10/23) -> (-4/23,-1/6) Hyperbolic Matrix(309,134,814,353) (-10/23,-3/7) -> (11/29,8/21) Hyperbolic Matrix(175,74,726,307) (-11/26,-19/45) -> (5/21,1/4) Hyperbolic Matrix(351,148,-1672,-705) (-19/45,-8/19) -> (-4/19,-9/43) Hyperbolic Matrix(529,222,946,397) (-8/19,-13/31) -> (5/9,14/25) Hyperbolic Matrix(43,18,418,175) (-13/31,-18/43) -> (0/1,1/9) Hyperbolic Matrix(967,404,-2530,-1057) (-18/43,-5/12) -> (-13/34,-34/89) Hyperbolic Matrix(309,128,-1166,-483) (-5/12,-12/29) -> (-4/15,-9/34) Hyperbolic Matrix(1055,436,1914,791) (-12/29,-19/46) -> (11/20,16/29) 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(87,34,110,43) (-2/5,-5/13) -> (7/9,4/5) Hyperbolic Matrix(3697,1412,5302,2025) (-34/89,-21/55) -> (23/33,30/43) Hyperbolic Matrix(1363,520,1958,747) (-21/55,-8/21) -> (16/23,23/33) Hyperbolic Matrix(353,134,814,309) (-8/21,-11/29) -> (3/7,10/23) 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(87,32,-242,-89) (-3/8,-4/11) -> (-4/11,-5/14) Parabolic Matrix(175,62,-748,-265) (-5/14,-6/17) -> (-4/17,-7/30) Hyperbolic Matrix(133,46,-506,-175) (-7/20,-1/3) -> (-5/19,-11/42) 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(45,14,286,89) (-5/16,-4/13) -> (2/13,1/6) Hyperbolic Matrix(441,134,-2024,-615) (-7/23,-10/33) -> (-12/55,-5/23) Hyperbolic Matrix(351,106,-1606,-485) (-10/33,-3/10) -> (-7/32,-12/55) Hyperbolic Matrix(89,26,154,45) (-3/10,-2/7) -> (4/7,7/12) Hyperbolic Matrix(43,12,154,43) (-2/7,-3/11) -> (3/11,2/7) Hyperbolic Matrix(89,24,330,89) (-3/11,-4/15) -> (4/15,3/11) Hyperbolic Matrix(659,174,1496,395) (-9/34,-5/19) -> (11/25,15/34) Hyperbolic Matrix(703,184,-3366,-881) (-11/42,-6/23) -> (-14/67,-5/24) 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(43,10,374,87) (-7/30,-3/13) -> (1/9,1/8) 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(263,58,594,131) (-2/9,-7/32) -> (15/34,4/9) Hyperbolic Matrix(175,38,198,43) (-5/23,-3/14) -> (7/8,1/1) Hyperbolic Matrix(4665,976,6314,1321) (-9/43,-23/110) -> (65/88,17/23) Hyperbolic Matrix(9635,2014,13046,2727) (-23/110,-14/67) -> (48/65,65/88) Hyperbolic Matrix(263,54,638,131) (-5/24,-1/5) -> (7/17,19/46) Hyperbolic Matrix(43,8,-242,-45) (-1/5,-2/11) -> (-2/11,-3/17) Parabolic Matrix(89,14,286,45) (-1/6,-2/13) -> (4/13,5/16) 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(131,16,352,43) (-1/8,-1/9) -> (13/35,3/8) Hyperbolic Matrix(175,18,418,43) (-1/9,0/1) -> (18/43,13/31) 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(45,-8,242,-43) (1/6,2/11) -> (2/11,3/16) Parabolic Matrix(133,-26,220,-43) (3/16,1/5) -> (3/5,17/28) Hyperbolic Matrix(263,-56,418,-89) (1/5,3/14) -> (5/8,17/27) Hyperbolic Matrix(1497,-326,2420,-527) (5/23,7/32) -> (47/76,13/21) Hyperbolic Matrix(351,-82,946,-221) (3/13,4/17) -> (10/27,13/35) Hyperbolic Matrix(309,-80,506,-131) (1/4,5/19) -> (25/41,11/18) Hyperbolic Matrix(483,-128,1166,-309) (5/19,4/15) -> (12/29,17/41) 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(89,-32,242,-87) (1/3,4/11) -> (4/11,7/19) Parabolic Matrix(1011,-374,1430,-529) (7/19,10/27) -> (12/17,29/41) 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(661,-276,946,-395) (5/12,18/43) -> (30/43,7/10) Hyperbolic Matrix(307,-130,418,-177) (8/19,3/7) -> (11/15,14/19) 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(265,-124,374,-175) (6/13,1/2) -> (17/24,22/31) Hyperbolic Matrix(133,-72,242,-131) (1/2,6/11) -> (6/11,11/20) Parabolic Matrix(2553,-1556,3608,-2199) (14/23,25/41) -> (29/41,46/65) Hyperbolic Matrix(3741,-2312,6050,-3739) (21/34,34/55) -> (34/55,47/76) Parabolic Matrix(1233,-778,1672,-1055) (29/46,12/19) -> (14/19,31/42) Hyperbolic Matrix(3167,-2242,4290,-3037) (46/65,17/24) -> (31/42,48/65) Hyperbolic Matrix(177,-128,242,-175) (5/7,8/11) -> (8/11,11/15) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(43,38,198,175) -> Matrix(1,2,-4,-7) Matrix(133,116,-352,-307) -> Matrix(3,4,-4,-5) Matrix(87,74,154,131) -> Matrix(3,2,-8,-5) Matrix(791,654,1276,1055) -> Matrix(1,-2,-4,9) Matrix(177,146,748,617) -> Matrix(1,-2,0,1) Matrix(307,252,374,307) -> Matrix(1,-6,-4,25) Matrix(89,72,110,89) -> Matrix(1,4,-4,-15) Matrix(43,34,110,87) -> Matrix(1,2,-4,-7) Matrix(307,238,396,307) -> Matrix(9,10,-28,-31) Matrix(441,340,572,441) -> Matrix(11,10,-32,-29) Matrix(175,134,286,219) -> Matrix(3,2,-8,-5) Matrix(175,128,-242,-177) -> Matrix(1,-2,0,1) Matrix(131,94,-308,-221) -> Matrix(1,2,-4,-7) Matrix(45,32,-308,-219) -> Matrix(1,2,-4,-7) Matrix(263,186,-748,-529) -> Matrix(1,2,-4,-7) Matrix(219,154,374,263) -> Matrix(3,2,-8,-5) Matrix(219,152,-572,-397) -> Matrix(3,4,-4,-5) Matrix(353,244,638,441) -> Matrix(5,8,-12,-19) Matrix(1187,818,1914,1319) -> Matrix(3,4,-16,-21) Matrix(309,212,-704,-483) -> Matrix(5,6,-16,-19) Matrix(43,28,66,43) -> Matrix(3,2,-8,-5) Matrix(265,168,418,265) -> Matrix(1,0,0,1) Matrix(89,56,-418,-263) -> Matrix(1,0,0,1) Matrix(45,28,-352,-219) -> Matrix(1,0,0,1) Matrix(1319,818,1914,1187) -> Matrix(5,-4,-16,13) Matrix(1055,654,1276,791) -> Matrix(1,-2,-4,9) Matrix(175,108,-572,-353) -> Matrix(1,2,0,1) Matrix(219,134,286,175) -> Matrix(3,2,-8,-5) Matrix(131,80,-506,-309) -> Matrix(3,2,-8,-5) Matrix(89,54,-506,-307) -> Matrix(3,2,-8,-5) Matrix(131,78,220,131) -> Matrix(1,2,-4,-7) Matrix(441,260,748,441) -> Matrix(15,14,-44,-41) Matrix(263,154,374,219) -> Matrix(3,2,-8,-5) Matrix(45,26,154,89) -> Matrix(3,2,-8,-5) Matrix(131,74,154,87) -> Matrix(3,2,-8,-5) Matrix(221,124,-704,-395) -> Matrix(3,2,16,11) Matrix(397,222,946,529) -> Matrix(3,2,-8,-5) Matrix(131,72,-242,-133) -> Matrix(7,4,-16,-9) Matrix(395,212,572,307) -> Matrix(11,4,-36,-13) Matrix(309,164,748,397) -> Matrix(1,0,4,1) Matrix(43,20,-286,-133) -> Matrix(3,2,-8,-5) Matrix(131,60,286,131) -> Matrix(11,6,-24,-13) Matrix(89,40,198,89) -> Matrix(9,4,-16,-7) Matrix(131,58,594,263) -> Matrix(5,2,-28,-11) Matrix(703,310,1694,747) -> Matrix(11,4,8,3) Matrix(1233,542,1804,793) -> Matrix(59,20,-180,-61) Matrix(747,328,1100,483) -> Matrix(25,8,-72,-23) Matrix(87,38,-506,-221) -> Matrix(1,0,0,1) Matrix(309,134,814,353) -> Matrix(1,0,0,1) Matrix(175,74,726,307) -> Matrix(1,0,4,1) Matrix(351,148,-1672,-705) -> Matrix(1,0,4,1) Matrix(529,222,946,397) -> Matrix(3,2,-8,-5) Matrix(43,18,418,175) -> Matrix(1,0,0,1) Matrix(967,404,-2530,-1057) -> Matrix(5,2,-8,-3) Matrix(309,128,-1166,-483) -> Matrix(11,2,-28,-5) Matrix(1055,436,1914,791) -> Matrix(23,4,-52,-9) Matrix(1275,526,2024,835) -> Matrix(1,0,4,1) Matrix(307,126,748,307) -> Matrix(1,0,12,1) Matrix(89,36,220,89) -> Matrix(1,0,-4,1) Matrix(87,34,110,43) -> Matrix(1,2,-4,-7) Matrix(3697,1412,5302,2025) -> Matrix(13,8,-44,-27) Matrix(1363,520,1958,747) -> Matrix(1,2,-4,-7) Matrix(353,134,814,309) -> Matrix(1,0,0,1) Matrix(1409,534,1628,617) -> Matrix(5,6,-16,-19) Matrix(1099,416,1276,483) -> Matrix(7,6,-20,-17) Matrix(87,32,-242,-89) -> Matrix(7,4,-16,-9) Matrix(175,62,-748,-265) -> Matrix(5,2,-28,-11) Matrix(133,46,-506,-175) -> Matrix(1,0,0,1) Matrix(617,198,1100,353) -> Matrix(27,2,-68,-5) Matrix(1011,320,1804,571) -> Matrix(29,-2,-72,5) Matrix(45,14,286,89) -> Matrix(1,0,-4,1) Matrix(441,134,-2024,-615) -> Matrix(1,-4,0,1) Matrix(351,106,-1606,-485) -> Matrix(1,4,0,1) Matrix(89,26,154,45) -> Matrix(3,2,-8,-5) Matrix(43,12,154,43) -> Matrix(3,2,-8,-5) Matrix(89,24,330,89) -> Matrix(9,4,-16,-7) Matrix(659,174,1496,395) -> Matrix(17,6,-20,-7) Matrix(703,184,-3366,-881) -> Matrix(5,2,-8,-3) Matrix(131,32,176,43) -> Matrix(1,0,0,1) Matrix(617,146,748,177) -> Matrix(7,2,-32,-9) Matrix(43,10,374,87) -> Matrix(1,0,4,1) Matrix(131,30,572,131) -> Matrix(1,0,12,1) Matrix(89,20,396,89) -> Matrix(1,0,-8,1) Matrix(263,58,594,131) -> Matrix(3,-2,-4,3) Matrix(175,38,198,43) -> Matrix(1,2,-4,-7) Matrix(4665,976,6314,1321) -> Matrix(1,2,-4,-7) Matrix(9635,2014,13046,2727) -> Matrix(3,2,-8,-5) Matrix(263,54,638,131) -> Matrix(1,0,4,1) Matrix(43,8,-242,-45) -> Matrix(3,2,-8,-5) Matrix(89,14,286,45) -> Matrix(1,0,-4,1) Matrix(793,110,1276,177) -> Matrix(1,0,4,1) Matrix(1011,136,1628,219) -> Matrix(1,0,-8,1) Matrix(131,16,352,43) -> Matrix(3,2,-8,-5) Matrix(175,18,418,43) -> Matrix(1,0,0,1) Matrix(219,-28,352,-45) -> Matrix(1,0,0,1) Matrix(219,-32,308,-45) -> Matrix(1,2,-4,-7) Matrix(45,-8,242,-43) -> Matrix(3,2,-8,-5) Matrix(133,-26,220,-43) -> Matrix(1,0,0,1) Matrix(263,-56,418,-89) -> Matrix(1,0,0,1) Matrix(1497,-326,2420,-527) -> Matrix(7,2,-32,-9) Matrix(351,-82,946,-221) -> Matrix(5,-2,-12,5) Matrix(309,-80,506,-131) -> Matrix(3,2,-8,-5) Matrix(483,-128,1166,-309) -> Matrix(3,2,4,3) Matrix(353,-108,572,-175) -> Matrix(9,2,-32,-7) Matrix(395,-124,704,-221) -> Matrix(19,2,-48,-5) Matrix(89,-32,242,-87) -> Matrix(7,4,-16,-9) Matrix(1011,-374,1430,-529) -> Matrix(23,10,-76,-33) Matrix(307,-116,352,-133) -> Matrix(11,4,-36,-13) Matrix(397,-152,572,-219) -> Matrix(11,4,-36,-13) Matrix(661,-276,946,-395) -> Matrix(1,2,-4,-7) Matrix(307,-130,418,-177) -> Matrix(1,0,-4,1) Matrix(615,-268,1012,-441) -> Matrix(3,2,-8,-5) Matrix(483,-212,704,-309) -> Matrix(5,6,-16,-19) Matrix(265,-124,374,-175) -> Matrix(11,4,-36,-13) Matrix(133,-72,242,-131) -> Matrix(7,4,-16,-9) Matrix(2553,-1556,3608,-2199) -> Matrix(11,4,-36,-13) Matrix(3741,-2312,6050,-3739) -> Matrix(31,8,-128,-33) Matrix(1233,-778,1672,-1055) -> Matrix(1,0,0,1) Matrix(3167,-2242,4290,-3037) -> Matrix(13,4,-36,-11) Matrix(177,-128,242,-175) -> Matrix(7,2,-32,-9) 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): 20 Degree of the the map X: 40 Degree of the the map Y: 120 ----------------------------------------------------------------------- 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): 360 Minimal number of generators: 61 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: 30 Genus: 16 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/22 -7/22 -10/33 -5/22 -3/22 -1/8 0/1 1/7 1/6 2/11 1/5 2/9 1/4 3/11 2/7 3/10 1/3 4/11 2/5 5/11 1/2 6/11 5/9 7/11 2/3 23/33 8/11 9/11 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -6/7 -1/1 -1/2 -5/6 1/2 1/0 -9/11 1/0 -4/5 -2/1 1/0 -7/9 -5/4 -3/4 -1/2 1/0 -8/11 1/0 -5/7 1/0 -7/10 -3/2 1/0 -9/13 1/0 -2/3 -1/1 -1/2 -7/11 -1/2 -5/8 -1/2 1/0 -18/29 0/1 1/2 -13/21 1/0 -8/13 -3/2 -1/1 -3/5 1/0 -7/12 -5/6 -3/4 -4/7 -1/1 -1/2 -9/16 -3/4 -7/10 -14/25 -2/3 -9/14 -5/9 -5/8 -6/11 -1/2 -1/2 -1/2 1/0 -5/11 -1/2 -4/9 -1/2 -2/5 -7/16 -1/2 -1/4 -3/7 -1/4 -5/12 -1/2 -1/4 -7/17 -1/8 -9/22 0/1 -2/5 0/1 1/0 -5/13 -3/4 -13/34 -3/4 -1/2 -21/55 -1/2 -8/21 -1/1 -1/2 -3/8 -3/4 -1/2 -4/11 -1/2 -1/3 -1/4 -7/22 0/1 -6/19 0/1 1/10 -5/16 1/4 1/2 -4/13 1/2 1/1 -7/23 1/0 -10/33 1/0 -3/10 -3/2 1/0 -2/7 -1/1 -1/2 -3/11 -1/2 -1/4 -1/2 -1/4 -3/13 -1/8 -5/22 0/1 -2/9 0/1 1/2 -1/5 1/0 -2/11 -1/2 -1/6 -1/2 -1/4 -1/7 -1/4 -3/22 0/1 -2/15 0/1 1/2 -1/8 -1/2 1/0 0/1 -1/2 0/1 1/7 1/0 1/6 -1/2 1/0 2/11 -1/2 1/5 -1/4 2/9 -1/6 0/1 1/4 -1/2 1/0 3/11 -1/2 2/7 -1/2 -1/3 3/10 -3/10 -1/4 4/13 -1/5 -1/6 1/3 1/0 4/11 -1/2 3/8 -1/2 -3/8 11/29 -1/4 8/21 -1/2 -1/3 5/13 -3/8 2/5 -1/4 0/1 5/12 -1/2 1/0 3/7 1/0 7/16 -1/2 1/0 11/25 -7/8 4/9 -2/3 -1/2 5/11 -1/2 1/2 -1/2 -1/4 6/11 -1/2 5/9 -5/12 9/16 -7/18 -3/8 4/7 -1/2 -1/3 7/12 -3/8 -5/14 10/17 -7/20 -1/3 13/22 -1/3 3/5 -1/4 8/13 -1/3 -3/10 21/34 -7/26 -1/4 34/55 -1/4 13/21 -1/4 5/8 -1/2 -1/4 7/11 -1/2 2/3 -1/2 -1/3 15/22 -1/3 13/19 -13/40 11/16 -7/22 -5/16 9/13 -1/4 16/23 -1/3 -3/10 23/33 -3/10 7/10 -3/10 -1/4 5/7 -1/4 8/11 -1/4 3/4 -1/2 -1/4 10/13 -5/14 -1/3 17/22 -1/3 7/9 -5/16 4/5 -2/7 -1/4 9/11 -1/4 5/6 -1/4 -1/6 6/7 -1/2 -1/3 19/22 -1/3 13/15 -5/16 7/8 -3/10 -1/4 1/1 -1/4 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(109,96,-176,-155) (-1/1,-6/7) -> (-18/29,-13/21) Hyperbolic Matrix(87,74,154,131) (-6/7,-5/6) -> (9/16,4/7) Hyperbolic Matrix(109,90,132,109) (-5/6,-9/11) -> (9/11,5/6) Hyperbolic Matrix(89,72,110,89) (-9/11,-4/5) -> (4/5,9/11) Hyperbolic Matrix(43,34,110,87) (-4/5,-7/9) -> (5/13,2/5) Hyperbolic Matrix(21,16,-88,-67) (-7/9,-3/4) -> (-1/4,-3/13) Hyperbolic Matrix(65,48,88,65) (-3/4,-8/11) -> (8/11,3/4) 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(197,136,-352,-243) (-9/13,-2/3) -> (-14/25,-5/9) Hyperbolic Matrix(43,28,66,43) (-2/3,-7/11) -> (7/11,2/3) Hyperbolic Matrix(111,70,176,111) (-7/11,-5/8) -> (5/8,7/11) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) 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(109,64,-264,-155) (-3/5,-7/12) -> (-5/12,-7/17) Hyperbolic Matrix(45,26,154,89) (-7/12,-4/7) -> (2/7,3/10) Hyperbolic Matrix(131,74,154,87) (-4/7,-9/16) -> (5/6,6/7) Hyperbolic Matrix(221,124,-704,-395) (-9/16,-14/25) -> (-6/19,-5/16) Hyperbolic Matrix(109,60,198,109) (-5/9,-6/11) -> (6/11,5/9) Hyperbolic Matrix(23,12,44,23) (-6/11,-1/2) -> (1/2,6/11) Hyperbolic Matrix(21,10,44,21) (-1/2,-5/11) -> (5/11,1/2) Hyperbolic Matrix(89,40,198,89) (-5/11,-4/9) -> (4/9,5/11) Hyperbolic Matrix(109,48,-352,-155) (-4/9,-7/16) -> (-5/16,-4/13) 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(287,118,484,199) (-7/17,-9/22) -> (13/22,3/5) Hyperbolic Matrix(285,116,484,197) (-9/22,-2/5) -> (10/17,13/22) Hyperbolic Matrix(87,34,110,43) (-2/5,-5/13) -> (7/9,4/5) Hyperbolic Matrix(1167,446,1672,639) (-13/34,-21/55) -> (23/33,7/10) Hyperbolic Matrix(1363,520,1958,747) (-21/55,-8/21) -> (16/23,23/33) Hyperbolic Matrix(21,8,-176,-67) (-8/21,-3/8) -> (-1/8,0/1) Hyperbolic Matrix(65,24,176,65) (-3/8,-4/11) -> (4/11,3/8) Hyperbolic Matrix(23,8,66,23) (-4/11,-1/3) -> (1/3,4/11) Hyperbolic Matrix(331,106,484,155) (-1/3,-7/22) -> (15/22,13/19) Hyperbolic Matrix(329,104,484,153) (-7/22,-6/19) -> (2/3,15/22) Hyperbolic Matrix(1211,368,1958,595) (-7/23,-10/33) -> (34/55,13/21) Hyperbolic Matrix(1033,312,1672,505) (-10/33,-3/10) -> (21/34,34/55) Hyperbolic Matrix(89,26,154,45) (-3/10,-2/7) -> (4/7,7/12) Hyperbolic Matrix(43,12,154,43) (-2/7,-3/11) -> (3/11,2/7) Hyperbolic Matrix(23,6,88,23) (-3/11,-1/4) -> (1/4,3/11) Hyperbolic Matrix(375,86,484,111) (-3/13,-5/22) -> (17/22,7/9) Hyperbolic Matrix(373,84,484,109) (-5/22,-2/9) -> (10/13,17/22) 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(23,4,132,23) (-2/11,-1/6) -> (1/6,2/11) Hyperbolic Matrix(67,10,154,23) (-1/6,-1/7) -> (3/7,7/16) Hyperbolic Matrix(419,58,484,67) (-1/7,-3/22) -> (19/22,13/15) Hyperbolic Matrix(417,56,484,65) (-3/22,-2/15) -> (6/7,19/22) Hyperbolic Matrix(67,-8,176,-21) (0/1,1/7) -> (11/29,8/21) Hyperbolic Matrix(67,-16,88,-21) (2/9,1/4) -> (3/4,10/13) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(155,-48,352,-109) (4/13,1/3) -> (11/25,4/9) 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(155,-64,264,-109) (2/5,5/12) -> (7/12,10/17) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(243,-136,352,-197) (5/9,9/16) -> (11/16,9/13) Hyperbolic Matrix(155,-96,176,-109) (13/21,5/8) -> (7/8,1/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(109,96,-176,-155) -> Matrix(1,1,0,1) Matrix(87,74,154,131) -> Matrix(3,2,-8,-5) Matrix(109,90,132,109) -> Matrix(1,-1,-4,5) Matrix(89,72,110,89) -> Matrix(1,4,-4,-15) Matrix(43,34,110,87) -> Matrix(1,2,-4,-7) Matrix(21,16,-88,-67) -> Matrix(1,1,-4,-3) Matrix(65,48,88,65) -> Matrix(1,1,-4,-3) Matrix(111,80,154,111) -> Matrix(1,3,-4,-11) Matrix(65,46,154,109) -> Matrix(1,1,0,1) Matrix(219,152,-572,-397) -> Matrix(3,4,-4,-5) Matrix(197,136,-352,-243) -> Matrix(5,7,-8,-11) Matrix(43,28,66,43) -> Matrix(3,2,-8,-5) Matrix(111,70,176,111) -> Matrix(1,1,-4,-3) Matrix(45,28,-352,-219) -> Matrix(1,0,0,1) Matrix(175,108,-572,-353) -> Matrix(1,2,0,1) Matrix(23,14,110,67) -> Matrix(1,1,-4,-3) Matrix(109,64,-264,-155) -> Matrix(1,1,-8,-7) Matrix(45,26,154,89) -> Matrix(3,2,-8,-5) Matrix(131,74,154,87) -> Matrix(3,2,-8,-5) Matrix(221,124,-704,-395) -> Matrix(3,2,16,11) Matrix(109,60,198,109) -> Matrix(9,5,-20,-11) Matrix(23,12,44,23) -> Matrix(1,1,-4,-3) Matrix(21,10,44,21) -> Matrix(1,1,-4,-3) Matrix(89,40,198,89) -> Matrix(9,4,-16,-7) Matrix(109,48,-352,-155) -> Matrix(3,1,8,3) Matrix(23,10,154,67) -> Matrix(3,1,-4,-1) Matrix(109,46,154,65) -> Matrix(5,1,-16,-3) Matrix(287,118,484,199) -> Matrix(9,1,-28,-3) Matrix(285,116,484,197) -> Matrix(7,-1,-20,3) Matrix(87,34,110,43) -> Matrix(1,2,-4,-7) Matrix(1167,446,1672,639) -> Matrix(7,5,-24,-17) Matrix(1363,520,1958,747) -> Matrix(1,2,-4,-7) Matrix(21,8,-176,-67) -> Matrix(1,1,-4,-3) Matrix(65,24,176,65) -> Matrix(5,3,-12,-7) Matrix(23,8,66,23) -> Matrix(3,1,-4,-1) Matrix(331,106,484,155) -> Matrix(17,1,-52,-3) Matrix(329,104,484,153) -> Matrix(11,-1,-32,3) Matrix(1211,368,1958,595) -> Matrix(1,-3,-4,13) Matrix(1033,312,1672,505) -> Matrix(1,5,-4,-19) Matrix(89,26,154,45) -> Matrix(3,2,-8,-5) Matrix(43,12,154,43) -> Matrix(3,2,-8,-5) Matrix(23,6,88,23) -> Matrix(3,1,-4,-1) Matrix(375,86,484,111) -> Matrix(13,1,-40,-3) Matrix(373,84,484,109) -> Matrix(7,-1,-20,3) Matrix(67,14,110,23) -> Matrix(1,1,-4,-3) Matrix(21,4,110,21) -> Matrix(1,1,-4,-3) Matrix(23,4,132,23) -> Matrix(3,1,-4,-1) Matrix(67,10,154,23) -> Matrix(3,1,-4,-1) Matrix(419,58,484,67) -> Matrix(9,1,-28,-3) Matrix(417,56,484,65) -> Matrix(3,-1,-8,3) Matrix(67,-8,176,-21) -> Matrix(1,1,-4,-3) Matrix(67,-16,88,-21) -> Matrix(1,1,-4,-3) Matrix(353,-108,572,-175) -> Matrix(9,2,-32,-7) Matrix(155,-48,352,-109) -> Matrix(7,1,-8,-1) Matrix(307,-116,352,-133) -> Matrix(11,4,-36,-13) Matrix(397,-152,572,-219) -> Matrix(11,4,-36,-13) Matrix(155,-64,264,-109) -> Matrix(3,-1,-8,3) Matrix(483,-212,704,-309) -> Matrix(5,6,-16,-19) Matrix(243,-136,352,-197) -> Matrix(17,7,-56,-23) Matrix(155,-96,176,-109) -> Matrix(5,1,-16,-3) 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): 20 ----------------------------------------------------------------------- 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 (-1/2,0/1) 0 22 1/7 1/0 1 22 1/6 (-1/2,1/0) 0 11 2/11 -1/2 2 2 1/5 -1/4 1 22 2/9 (-1/6,0/1) 0 22 1/4 (-1/2,1/0) 0 11 3/11 -1/2 3 2 2/7 (-1/2,-1/3) 0 22 3/10 (-3/10,-1/4) 0 11 4/13 (-1/5,-1/6) 0 22 1/3 1/0 1 22 4/11 -1/2 4 2 3/8 (-1/2,-3/8) 0 11 11/29 -1/4 1 22 8/21 (-1/2,-1/3) 0 22 5/13 -3/8 1 22 2/5 (-1/4,0/1) 0 22 5/12 (-1/2,1/0) 0 11 3/7 1/0 1 22 7/16 (-1/2,1/0) 0 11 11/25 -7/8 1 22 4/9 (-2/3,-1/2) 0 22 5/11 -1/2 5 2 1/2 (-1/2,-1/4) 0 11 6/11 -1/2 4 2 5/9 -5/12 1 22 9/16 (-7/18,-3/8) 0 11 4/7 (-1/2,-1/3) 0 22 7/12 (-3/8,-5/14) 0 11 10/17 (-7/20,-1/3) 0 22 13/22 -1/3 8 1 3/5 -1/4 1 22 8/13 (-1/3,-3/10) 0 22 21/34 (-7/26,-1/4) 0 11 34/55 -1/4 8 2 13/21 -1/4 1 22 5/8 (-1/2,-1/4) 0 11 7/11 -1/2 1 2 2/3 (-1/2,-1/3) 0 22 15/22 -1/3 14 1 13/19 -13/40 1 22 11/16 (-7/22,-5/16) 0 11 9/13 -1/4 1 22 16/23 (-1/3,-3/10) 0 22 23/33 -3/10 1 2 7/10 (-3/10,-1/4) 0 11 5/7 -1/4 1 22 8/11 -1/4 2 2 3/4 (-1/2,-1/4) 0 11 10/13 (-5/14,-1/3) 0 22 17/22 -1/3 10 1 7/9 -5/16 1 22 4/5 (-2/7,-1/4) 0 22 9/11 -1/4 5 2 5/6 (-1/4,-1/6) 0 11 6/7 (-1/2,-1/3) 0 22 19/22 -1/3 6 1 13/15 -5/16 1 22 7/8 (-3/10,-1/4) 0 11 1/1 -1/4 1 22 1/0 0/1 2 1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(67,-8,176,-21) (0/1,1/7) -> (11/29,8/21) Hyperbolic Matrix(67,-10,154,-23) (1/7,1/6) -> (3/7,7/16) Glide Reflection Matrix(23,-4,132,-23) (1/6,2/11) -> (1/6,2/11) 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(67,-16,88,-21) (2/9,1/4) -> (3/4,10/13) Hyperbolic Matrix(23,-6,88,-23) (1/4,3/11) -> (1/4,3/11) Reflection Matrix(43,-12,154,-43) (3/11,2/7) -> (3/11,2/7) Reflection Matrix(89,-26,154,-45) (2/7,3/10) -> (4/7,7/12) Glide Reflection Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(155,-48,352,-109) (4/13,1/3) -> (11/25,4/9) Hyperbolic Matrix(23,-8,66,-23) (1/3,4/11) -> (1/3,4/11) Reflection Matrix(65,-24,176,-65) (4/11,3/8) -> (4/11,3/8) Reflection 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(87,-34,110,-43) (5/13,2/5) -> (7/9,4/5) Glide Reflection Matrix(155,-64,264,-109) (2/5,5/12) -> (7/12,10/17) Hyperbolic 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(89,-40,198,-89) (4/9,5/11) -> (4/9,5/11) Reflection Matrix(21,-10,44,-21) (5/11,1/2) -> (5/11,1/2) Reflection Matrix(23,-12,44,-23) (1/2,6/11) -> (1/2,6/11) Reflection Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(243,-136,352,-197) (5/9,9/16) -> (11/16,9/13) Hyperbolic Matrix(131,-74,154,-87) (9/16,4/7) -> (5/6,6/7) 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(2311,-1428,3740,-2311) (21/34,34/55) -> (21/34,34/55) Reflection Matrix(1429,-884,2310,-1429) (34/55,13/21) -> (34/55,13/21) Reflection Matrix(155,-96,176,-109) (13/21,5/8) -> (7/8,1/1) Hyperbolic Matrix(111,-70,176,-111) (5/8,7/11) -> (5/8,7/11) Reflection Matrix(43,-28,66,-43) (7/11,2/3) -> (7/11,2/3) Reflection 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(1057,-736,1518,-1057) (16/23,23/33) -> (16/23,23/33) Reflection Matrix(461,-322,660,-461) (23/33,7/10) -> (23/33,7/10) Reflection Matrix(111,-80,154,-111) (5/7,8/11) -> (5/7,8/11) Reflection Matrix(65,-48,88,-65) (8/11,3/4) -> (8/11,3/4) 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(89,-72,110,-89) (4/5,9/11) -> (4/5,9/11) Reflection Matrix(109,-90,132,-109) (9/11,5/6) -> (9/11,5/6) Reflection 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(-1,0,4,1) (0/1,1/0) -> (-1/2,0/1) Matrix(67,-8,176,-21) -> Matrix(1,1,-4,-3) -1/2 Matrix(67,-10,154,-23) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(23,-4,132,-23) -> Matrix(1,1,0,-1) (1/6,2/11) -> (-1/2,1/0) Matrix(21,-4,110,-21) -> Matrix(3,1,-8,-3) (2/11,1/5) -> (-1/2,-1/4) Matrix(67,-14,110,-23) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(67,-16,88,-21) -> Matrix(1,1,-4,-3) -1/2 Matrix(23,-6,88,-23) -> Matrix(1,1,0,-1) (1/4,3/11) -> (-1/2,1/0) Matrix(43,-12,154,-43) -> Matrix(5,2,-12,-5) (3/11,2/7) -> (-1/2,-1/3) Matrix(89,-26,154,-45) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(353,-108,572,-175) -> Matrix(9,2,-32,-7) -1/4 Matrix(155,-48,352,-109) -> Matrix(7,1,-8,-1) Matrix(23,-8,66,-23) -> Matrix(1,1,0,-1) (1/3,4/11) -> (-1/2,1/0) Matrix(65,-24,176,-65) -> Matrix(7,3,-16,-7) (4/11,3/8) -> (-1/2,-3/8) Matrix(307,-116,352,-133) -> Matrix(11,4,-36,-13) -1/3 Matrix(397,-152,572,-219) -> Matrix(11,4,-36,-13) -1/3 Matrix(87,-34,110,-43) -> Matrix(7,2,-24,-7) *** -> (-1/3,-1/4) Matrix(155,-64,264,-109) -> Matrix(3,-1,-8,3) Matrix(109,-46,154,-65) -> Matrix(1,-1,-4,3) Matrix(483,-212,704,-309) -> Matrix(5,6,-16,-19) Matrix(89,-40,198,-89) -> Matrix(7,4,-12,-7) (4/9,5/11) -> (-2/3,-1/2) Matrix(21,-10,44,-21) -> Matrix(3,1,-8,-3) (5/11,1/2) -> (-1/2,-1/4) Matrix(23,-12,44,-23) -> Matrix(3,1,-8,-3) (1/2,6/11) -> (-1/2,-1/4) Matrix(109,-60,198,-109) -> Matrix(11,5,-24,-11) (6/11,5/9) -> (-1/2,-5/12) Matrix(243,-136,352,-197) -> Matrix(17,7,-56,-23) Matrix(131,-74,154,-87) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(441,-260,748,-441) -> Matrix(41,14,-120,-41) (10/17,13/22) -> (-7/20,-1/3) Matrix(131,-78,220,-131) -> Matrix(7,2,-24,-7) (13/22,3/5) -> (-1/3,-1/4) Matrix(2311,-1428,3740,-2311) -> Matrix(27,7,-104,-27) (21/34,34/55) -> (-7/26,-1/4) Matrix(1429,-884,2310,-1429) -> Matrix(5,1,-24,-5) (34/55,13/21) -> (-1/4,-1/6) Matrix(155,-96,176,-109) -> Matrix(5,1,-16,-3) -1/4 Matrix(111,-70,176,-111) -> Matrix(3,1,-8,-3) (5/8,7/11) -> (-1/2,-1/4) Matrix(43,-28,66,-43) -> Matrix(5,2,-12,-5) (7/11,2/3) -> (-1/2,-1/3) Matrix(89,-60,132,-89) -> Matrix(5,2,-12,-5) (2/3,15/22) -> (-1/2,-1/3) Matrix(571,-390,836,-571) -> Matrix(79,26,-240,-79) (15/22,13/19) -> (-1/3,-13/40) Matrix(1057,-736,1518,-1057) -> Matrix(19,6,-60,-19) (16/23,23/33) -> (-1/3,-3/10) Matrix(461,-322,660,-461) -> Matrix(11,3,-40,-11) (23/33,7/10) -> (-3/10,-1/4) Matrix(111,-80,154,-111) -> Matrix(11,3,-40,-11) (5/7,8/11) -> (-3/10,-1/4) Matrix(65,-48,88,-65) -> Matrix(3,1,-8,-3) (8/11,3/4) -> (-1/2,-1/4) Matrix(441,-340,572,-441) -> Matrix(29,10,-84,-29) (10/13,17/22) -> (-5/14,-1/3) Matrix(307,-238,396,-307) -> Matrix(31,10,-96,-31) (17/22,7/9) -> (-1/3,-5/16) Matrix(89,-72,110,-89) -> Matrix(15,4,-56,-15) (4/5,9/11) -> (-2/7,-1/4) Matrix(109,-90,132,-109) -> Matrix(5,1,-24,-5) (9/11,5/6) -> (-1/4,-1/6) Matrix(265,-228,308,-265) -> Matrix(5,2,-12,-5) (6/7,19/22) -> (-1/2,-1/3) Matrix(571,-494,660,-571) -> Matrix(31,10,-96,-31) (19/22,13/15) -> (-1/3,-5/16) Matrix(-1,2,0,1) -> Matrix(-1,0,8,1) (1/1,1/0) -> (-1/4,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.