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 -8/1 -6/1 -11/2 -4/1 -10/3 -11/4 -2/1 -11/6 -55/34 -22/15 -11/8 -22/19 0/1 1/1 11/9 22/17 11/8 3/2 11/7 22/13 11/6 2/1 11/5 22/9 5/2 55/21 11/4 3/1 22/7 33/10 10/3 7/2 11/3 4/1 17/4 22/5 9/2 19/4 110/23 5/1 11/2 23/4 6/1 13/2 7/1 22/3 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/1 -8/1 -1/1 -1/3 -7/1 1/3 -13/2 0/1 1/1 -6/1 -1/1 1/1 -11/2 -1/1 1/1 -16/3 -1/1 1/1 -5/1 1/1 -14/3 -1/1 1/1 -23/5 -1/1 -32/7 -1/1 1/1 -9/2 -1/1 1/0 -22/5 -1/1 -13/3 -1/1 -17/4 0/1 1/0 -21/5 1/1 -4/1 -1/1 1/1 -19/5 -1/1 -15/4 -2/1 -1/1 -11/3 -1/1 -7/2 -1/1 -1/2 -10/3 -1/1 1/1 -13/4 -1/1 0/1 -16/5 -1/1 1/1 -3/1 -1/1 -11/4 -1/1 -19/7 -1/1 -27/10 -2/3 -1/2 -35/13 -1/1 -8/3 -1/1 -3/5 -29/11 -3/7 -21/8 -1/2 0/1 -13/5 -1/1 -5/2 -2/3 -1/2 -22/9 -1/2 -17/7 -7/15 -46/19 -7/15 -5/11 -29/12 -4/9 -3/7 -41/17 -3/7 -12/5 -3/7 -1/3 -43/18 -1/2 -2/5 -31/13 -1/3 -19/8 -1/2 -1/3 -7/3 -1/1 -23/10 -1/2 -2/5 -16/7 -3/7 -1/3 -25/11 -1/3 -34/15 -3/7 -1/3 -9/4 -1/2 -1/3 -11/5 -1/3 -13/6 -1/3 0/1 -2/1 -1/1 -1/3 -11/6 -1/3 -20/11 -1/3 -7/23 -29/16 -5/17 -2/7 -9/5 -1/3 -25/14 -1/3 -1/4 -66/37 -1/3 -41/23 -1/3 -16/9 -1/3 -3/11 -7/4 -1/4 -1/5 -12/7 -1/5 -1/7 -17/10 -1/10 0/1 -22/13 0/1 -5/3 -1/1 -28/17 -1/1 -1/3 -23/14 -1/2 0/1 -41/25 -1/3 -18/11 -1/1 -1/3 -13/8 -1/3 0/1 -34/21 -1/1 -1/3 -55/34 -1/3 -76/47 -1/3 -3/11 -21/13 -1/3 -50/31 -1/3 -1/5 -29/18 -1/7 0/1 -66/41 0/1 -37/23 1/3 -8/5 -1/1 -1/3 -27/17 -1/1 -46/29 -1/1 -1/3 -19/12 -1/2 -1/3 -11/7 -1/3 -3/2 -1/3 0/1 -22/15 -1/3 -19/13 -1/3 -16/11 -1/3 -1/5 -29/20 -1/1 0/1 -13/9 -1/3 -23/16 -1/4 0/1 -33/23 -1/3 -1/5 -43/30 -1/4 0/1 -10/7 -1/3 -1/5 -17/12 0/1 1/0 -41/29 -1/1 -65/46 -2/3 -1/2 -24/17 -1/1 -1/3 -31/22 -1/3 0/1 -7/5 -1/1 -11/8 -1/3 -15/11 -3/11 -19/14 -1/3 -1/4 -42/31 -1/3 -3/11 -65/48 -4/15 -1/4 -88/65 -1/4 -23/17 -1/5 -4/3 -1/3 -1/5 -13/10 -1/3 0/1 -22/17 -1/3 -9/7 -1/3 -5/4 -1/4 0/1 -11/9 -1/3 -1/5 -17/14 -1/4 0/1 -23/19 -1/5 -6/5 -1/3 -1/5 -7/6 -3/11 -1/4 -22/19 -1/4 -15/13 -7/29 -8/7 -3/13 -1/5 -1/1 -1/5 0/1 0/1 1/1 1/5 8/7 1/5 3/13 7/6 1/4 3/11 6/5 1/5 1/3 23/19 1/5 17/14 0/1 1/4 11/9 1/5 1/3 5/4 0/1 1/4 9/7 1/3 22/17 1/3 13/10 0/1 1/3 4/3 1/5 1/3 11/8 1/3 18/13 1/3 3/7 7/5 1/1 24/17 1/3 1/1 17/12 0/1 1/0 10/7 1/5 1/3 13/9 1/3 29/20 0/1 1/1 16/11 1/5 1/3 3/2 0/1 1/3 11/7 1/3 19/12 1/3 1/2 8/5 1/3 1/1 29/18 0/1 1/7 50/31 1/5 1/3 21/13 1/3 13/8 0/1 1/3 18/11 1/3 1/1 23/14 0/1 1/2 5/3 1/1 22/13 0/1 17/10 0/1 1/10 12/7 1/7 1/5 7/4 1/5 1/4 16/9 3/11 1/3 25/14 1/4 1/3 9/5 1/3 11/6 1/3 13/7 1/3 15/8 2/5 3/7 2/1 1/3 1/1 13/6 0/1 1/3 11/5 1/3 9/4 1/3 1/2 34/15 1/3 3/7 25/11 1/3 66/29 1/3 41/18 1/3 2/5 16/7 1/3 3/7 23/10 2/5 1/2 7/3 1/1 26/11 1/3 3/7 45/19 3/7 19/8 1/3 1/2 31/13 1/3 43/18 2/5 1/2 12/5 1/3 3/7 29/12 3/7 4/9 46/19 5/11 7/15 17/7 7/15 22/9 1/2 5/2 1/2 2/3 13/5 1/1 34/13 1/3 1/1 89/34 0/1 1/2 55/21 1/3 1/1 21/8 0/1 1/2 29/11 3/7 66/25 1/2 37/14 1/2 7/13 8/3 3/5 1/1 11/4 1/1 14/5 -1/1 1/1 17/6 0/1 1/0 20/7 1/3 1/1 3/1 1/1 22/7 1/1 19/6 1/1 1/0 16/5 -1/1 1/1 13/4 0/1 1/1 23/7 1/1 33/10 1/1 10/3 -1/1 1/1 7/2 1/2 1/1 11/3 1/1 15/4 1/1 2/1 34/9 -1/1 1/1 19/5 1/1 42/11 1/1 3/1 23/6 0/1 1/0 4/1 -1/1 1/1 21/5 -1/1 17/4 0/1 1/0 30/7 -1/1 1/1 13/3 1/1 22/5 1/1 9/2 1/1 1/0 32/7 -1/1 1/1 55/12 1/1 23/5 1/1 14/3 -1/1 1/1 19/4 1/1 1/0 43/9 3/1 110/23 1/0 67/14 -2/1 1/0 24/5 -1/1 1/1 5/1 -1/1 11/2 -1/1 1/1 17/3 -1/1 23/4 0/1 1/0 6/1 -1/1 1/1 13/2 -1/1 0/1 20/3 -1/1 -1/3 7/1 -1/3 22/3 0/1 15/2 0/1 1/7 8/1 1/3 1/1 9/1 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(43,418,18,175) (-9/1,1/0) -> (31/13,43/18) Hyperbolic Matrix(43,374,10,87) (-9/1,-8/1) -> (30/7,13/3) Hyperbolic Matrix(45,352,-28,-219) (-8/1,-7/1) -> (-37/23,-8/5) Hyperbolic Matrix(45,308,-32,-219) (-7/1,-13/2) -> (-31/22,-7/5) Hyperbolic Matrix(45,286,14,89) (-13/2,-6/1) -> (16/5,13/4) Hyperbolic Matrix(43,242,-8,-45) (-6/1,-11/2) -> (-11/2,-16/3) Parabolic Matrix(43,220,-26,-133) (-16/3,-5/1) -> (-5/3,-28/17) Hyperbolic Matrix(89,418,-56,-263) (-5/1,-14/3) -> (-8/5,-27/17) Hyperbolic Matrix(43,198,38,175) (-14/3,-23/5) -> (1/1,8/7) Hyperbolic Matrix(527,2420,-326,-1497) (-23/5,-32/7) -> (-76/47,-21/13) Hyperbolic Matrix(131,594,58,263) (-32/7,-9/2) -> (9/4,34/15) Hyperbolic Matrix(89,396,20,89) (-9/2,-22/5) -> (22/5,9/2) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(221,946,-82,-351) (-13/3,-17/4) -> (-27/10,-35/13) Hyperbolic Matrix(177,748,146,617) (-17/4,-21/5) -> (23/19,17/14) Hyperbolic Matrix(175,726,74,307) (-21/5,-4/1) -> (26/11,45/19) Hyperbolic Matrix(131,506,-80,-309) (-4/1,-19/5) -> (-41/25,-18/11) Hyperbolic Matrix(309,1166,-128,-483) (-19/5,-15/4) -> (-29/12,-41/17) Hyperbolic Matrix(89,330,24,89) (-15/4,-11/3) -> (11/3,15/4) Hyperbolic Matrix(43,154,12,43) (-11/3,-7/2) -> (7/2,11/3) Hyperbolic Matrix(45,154,26,89) (-7/2,-10/3) -> (12/7,7/4) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(89,286,14,45) (-13/4,-16/5) -> (6/1,13/2) Hyperbolic Matrix(221,704,-124,-395) (-16/5,-3/1) -> (-41/23,-16/9) Hyperbolic Matrix(87,242,-32,-89) (-3/1,-11/4) -> (-11/4,-19/7) Parabolic Matrix(529,1430,-374,-1011) (-19/7,-27/10) -> (-17/12,-41/29) Hyperbolic Matrix(131,352,16,43) (-35/13,-8/3) -> (8/1,9/1) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(309,814,134,353) (-29/11,-21/8) -> (23/10,7/3) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(43,110,34,87) (-13/5,-5/2) -> (5/4,9/7) Hyperbolic Matrix(89,220,36,89) (-5/2,-22/9) -> (22/9,5/2) Hyperbolic Matrix(307,748,126,307) (-22/9,-17/7) -> (17/7,22/9) Hyperbolic Matrix(263,638,54,131) (-17/7,-46/19) -> (24/5,5/1) Hyperbolic Matrix(309,748,164,397) (-46/19,-29/12) -> (15/8,2/1) Hyperbolic Matrix(703,1694,310,747) (-41/17,-12/5) -> (34/15,25/11) Hyperbolic Matrix(395,946,-276,-661) (-12/5,-43/18) -> (-43/30,-10/7) Hyperbolic Matrix(175,418,18,43) (-43/18,-31/13) -> (9/1,1/0) Hyperbolic Matrix(397,946,222,529) (-31/13,-19/8) -> (25/14,9/5) Hyperbolic Matrix(177,418,-130,-307) (-19/8,-7/3) -> (-15/11,-19/14) Hyperbolic Matrix(353,814,134,309) (-7/3,-23/10) -> (21/8,29/11) Hyperbolic Matrix(441,1012,-268,-615) (-23/10,-16/7) -> (-28/17,-23/14) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(659,1496,174,395) (-25/11,-34/15) -> (34/9,19/5) Hyperbolic Matrix(263,594,58,131) (-34/15,-9/4) -> (9/2,32/7) Hyperbolic Matrix(89,198,40,89) (-9/4,-11/5) -> (11/5,9/4) Hyperbolic Matrix(131,286,60,131) (-11/5,-13/6) -> (13/6,11/5) Hyperbolic Matrix(175,374,-124,-265) (-13/6,-2/1) -> (-24/17,-31/22) Hyperbolic Matrix(131,242,-72,-133) (-2/1,-11/6) -> (-11/6,-20/11) Parabolic Matrix(1055,1914,436,791) (-20/11,-29/16) -> (29/12,46/19) Hyperbolic Matrix(353,638,244,441) (-29/16,-9/5) -> (13/9,29/20) Hyperbolic Matrix(529,946,222,397) (-9/5,-25/14) -> (19/8,31/13) Hyperbolic Matrix(1011,1804,320,571) (-25/14,-66/37) -> (22/7,19/6) Hyperbolic Matrix(617,1100,198,353) (-66/37,-41/23) -> (3/1,22/7) Hyperbolic Matrix(87,154,74,131) (-16/9,-7/4) -> (7/6,6/5) Hyperbolic Matrix(89,154,26,45) (-7/4,-12/7) -> (10/3,7/2) Hyperbolic Matrix(219,374,154,263) (-12/7,-17/10) -> (17/12,10/7) Hyperbolic Matrix(441,748,260,441) (-17/10,-22/13) -> (22/13,17/10) Hyperbolic Matrix(131,220,78,131) (-22/13,-5/3) -> (5/3,22/13) Hyperbolic Matrix(2199,3608,-1556,-2553) (-23/14,-41/25) -> (-41/29,-65/46) Hyperbolic Matrix(175,286,134,219) (-18/11,-13/8) -> (13/10,4/3) Hyperbolic Matrix(3739,6050,-2312,-3741) (-34/21,-55/34) -> (-55/34,-76/47) Parabolic Matrix(791,1276,654,1055) (-21/13,-50/31) -> (6/5,23/19) Hyperbolic Matrix(1187,1914,818,1319) (-50/31,-29/18) -> (29/20,16/11) Hyperbolic Matrix(1011,1628,136,219) (-29/18,-66/41) -> (22/3,15/2) Hyperbolic Matrix(793,1276,110,177) (-66/41,-37/23) -> (7/1,22/3) Hyperbolic Matrix(1275,2024,526,835) (-27/17,-46/29) -> (46/19,17/7) Hyperbolic Matrix(1055,1672,-778,-1233) (-46/29,-19/12) -> (-19/14,-42/31) Hyperbolic Matrix(265,418,168,265) (-19/12,-11/7) -> (11/7,19/12) Hyperbolic Matrix(43,66,28,43) (-11/7,-3/2) -> (3/2,11/7) Hyperbolic Matrix(747,1100,328,483) (-3/2,-22/15) -> (66/29,41/18) Hyperbolic Matrix(1233,1804,542,793) (-22/15,-19/13) -> (25/11,66/29) Hyperbolic Matrix(1319,1914,818,1187) (-16/11,-29/20) -> (29/18,50/31) Hyperbolic Matrix(395,572,212,307) (-29/20,-13/9) -> (13/7,15/8) Hyperbolic Matrix(1363,1958,520,747) (-23/16,-33/23) -> (55/21,21/8) Hyperbolic Matrix(3697,5302,1412,2025) (-33/23,-43/30) -> (89/34,55/21) Hyperbolic Matrix(263,374,154,219) (-10/7,-17/12) -> (17/10,12/7) Hyperbolic Matrix(3037,4290,-2242,-3167) (-65/46,-24/17) -> (-42/31,-65/48) Hyperbolic Matrix(175,242,-128,-177) (-7/5,-11/8) -> (-11/8,-15/11) Parabolic Matrix(9635,13046,2014,2727) (-65/48,-88/65) -> (110/23,67/14) Hyperbolic Matrix(4665,6314,976,1321) (-88/65,-23/17) -> (43/9,110/23) Hyperbolic Matrix(131,176,32,43) (-23/17,-4/3) -> (4/1,21/5) Hyperbolic Matrix(219,286,134,175) (-4/3,-13/10) -> (13/8,18/11) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(307,396,238,307) (-22/17,-9/7) -> (9/7,22/17) Hyperbolic Matrix(87,110,34,43) (-9/7,-5/4) -> (5/2,13/5) Hyperbolic Matrix(89,110,72,89) (-5/4,-11/9) -> (11/9,5/4) Hyperbolic Matrix(307,374,252,307) (-11/9,-17/14) -> (17/14,11/9) Hyperbolic Matrix(617,748,146,177) (-17/14,-23/19) -> (21/5,17/4) Hyperbolic Matrix(1055,1276,654,791) (-23/19,-6/5) -> (50/31,21/13) Hyperbolic Matrix(131,154,74,87) (-6/5,-7/6) -> (7/4,16/9) Hyperbolic Matrix(1099,1276,416,483) (-7/6,-22/19) -> (66/25,37/14) Hyperbolic Matrix(1409,1628,534,617) (-22/19,-15/13) -> (29/11,66/25) Hyperbolic Matrix(175,198,38,43) (-8/7,-1/1) -> (23/5,14/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(307,-352,116,-133) (8/7,7/6) -> (37/14,8/3) Hyperbolic Matrix(177,-242,128,-175) (4/3,11/8) -> (11/8,18/13) Parabolic Matrix(221,-308,94,-131) (18/13,7/5) -> (7/3,26/11) Hyperbolic Matrix(219,-308,32,-45) (7/5,24/17) -> (20/3,7/1) Hyperbolic Matrix(529,-748,186,-263) (24/17,17/12) -> (17/6,20/7) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(483,-704,212,-309) (16/11,3/2) -> (41/18,16/7) Hyperbolic Matrix(263,-418,56,-89) (19/12,8/5) -> (14/3,19/4) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(309,-506,80,-131) (18/11,23/14) -> (23/6,4/1) Hyperbolic Matrix(307,-506,54,-89) (23/14,5/3) -> (17/3,23/4) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(133,-242,72,-131) (9/5,11/6) -> (11/6,13/7) Parabolic Matrix(133,-286,20,-43) (2/1,13/6) -> (13/2,20/3) Hyperbolic Matrix(221,-506,38,-87) (16/7,23/10) -> (23/4,6/1) Hyperbolic Matrix(705,-1672,148,-351) (45/19,19/8) -> (19/4,43/9) Hyperbolic Matrix(1057,-2530,404,-967) (43/18,12/5) -> (34/13,89/34) Hyperbolic Matrix(483,-1166,128,-309) (12/5,29/12) -> (15/4,34/9) Hyperbolic Matrix(89,-242,32,-87) (8/3,11/4) -> (11/4,14/5) Parabolic Matrix(265,-748,62,-175) (14/5,17/6) -> (17/4,30/7) Hyperbolic Matrix(175,-506,46,-133) (20/7,3/1) -> (19/5,42/11) Hyperbolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(485,-1606,106,-351) (33/10,10/3) -> (32/7,55/12) Hyperbolic Matrix(881,-3366,184,-703) (42/11,23/6) -> (67/14,24/5) Hyperbolic Matrix(45,-242,8,-43) (5/1,11/2) -> (11/2,17/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(43,418,18,175) -> Matrix(1,2,2,5) Matrix(43,374,10,87) -> Matrix(1,0,2,1) Matrix(45,352,-28,-219) -> Matrix(1,0,0,1) Matrix(45,308,-32,-219) -> Matrix(1,0,-4,1) Matrix(45,286,14,89) -> Matrix(1,0,0,1) Matrix(43,242,-8,-45) -> Matrix(1,0,0,1) Matrix(43,220,-26,-133) -> Matrix(1,0,-2,1) Matrix(89,418,-56,-263) -> Matrix(1,0,-2,1) Matrix(43,198,38,175) -> Matrix(1,2,4,9) Matrix(527,2420,-326,-1497) -> Matrix(1,2,-4,-7) Matrix(131,594,58,263) -> Matrix(1,2,2,5) Matrix(89,396,20,89) -> Matrix(1,2,0,1) Matrix(131,572,30,131) -> Matrix(1,0,2,1) Matrix(221,946,-82,-351) -> Matrix(1,2,-2,-3) Matrix(177,748,146,617) -> Matrix(1,0,4,1) Matrix(175,726,74,307) -> Matrix(1,2,2,5) Matrix(131,506,-80,-309) -> Matrix(1,0,-2,1) Matrix(309,1166,-128,-483) -> Matrix(1,-2,-2,5) Matrix(89,330,24,89) -> Matrix(3,4,2,3) Matrix(43,154,12,43) -> Matrix(3,2,4,3) Matrix(45,154,26,89) -> Matrix(1,0,6,1) Matrix(175,572,-108,-353) -> Matrix(1,0,-2,1) Matrix(89,286,14,45) -> Matrix(1,0,0,1) Matrix(221,704,-124,-395) -> Matrix(1,2,-4,-7) Matrix(87,242,-32,-89) -> Matrix(1,2,-2,-3) Matrix(529,1430,-374,-1011) -> Matrix(3,2,-2,-1) Matrix(131,352,16,43) -> Matrix(3,2,4,3) Matrix(133,352,-116,-307) -> Matrix(7,4,-30,-17) Matrix(309,814,134,353) -> Matrix(5,2,12,5) Matrix(219,572,-152,-397) -> Matrix(1,0,-2,1) Matrix(43,110,34,87) -> Matrix(3,2,10,7) Matrix(89,220,36,89) -> Matrix(7,4,12,7) Matrix(307,748,126,307) -> Matrix(29,14,60,29) Matrix(263,638,54,131) -> Matrix(13,6,2,1) Matrix(309,748,164,397) -> Matrix(13,6,28,13) Matrix(703,1694,310,747) -> Matrix(9,4,20,9) Matrix(395,946,-276,-661) -> Matrix(5,2,-18,-7) Matrix(175,418,18,43) -> Matrix(5,2,2,1) Matrix(397,946,222,529) -> Matrix(1,0,6,1) Matrix(177,418,-130,-307) -> Matrix(5,2,-18,-7) Matrix(353,814,134,309) -> Matrix(5,2,12,5) Matrix(441,1012,-268,-615) -> Matrix(5,2,-8,-3) Matrix(309,704,-212,-483) -> Matrix(5,2,-18,-7) Matrix(659,1496,174,395) -> Matrix(5,2,2,1) Matrix(263,594,58,131) -> Matrix(5,2,2,1) Matrix(89,198,40,89) -> Matrix(5,2,12,5) Matrix(131,286,60,131) -> Matrix(1,0,6,1) Matrix(175,374,-124,-265) -> Matrix(1,0,0,1) Matrix(131,242,-72,-133) -> Matrix(11,4,-36,-13) Matrix(1055,1914,436,791) -> Matrix(47,14,104,31) Matrix(353,638,244,441) -> Matrix(7,2,24,7) Matrix(529,946,222,397) -> Matrix(1,0,6,1) Matrix(1011,1804,320,571) -> Matrix(1,0,4,1) Matrix(617,1100,198,353) -> Matrix(7,2,10,3) Matrix(87,154,74,131) -> Matrix(7,2,24,7) Matrix(89,154,26,45) -> Matrix(1,0,6,1) Matrix(219,374,154,263) -> Matrix(1,0,10,1) Matrix(441,748,260,441) -> Matrix(1,0,20,1) Matrix(131,220,78,131) -> Matrix(1,0,2,1) Matrix(2199,3608,-1556,-2553) -> Matrix(5,2,-8,-3) Matrix(175,286,134,219) -> Matrix(1,0,6,1) Matrix(3739,6050,-2312,-3741) -> Matrix(5,2,-18,-7) Matrix(791,1276,654,1055) -> Matrix(1,0,8,1) Matrix(1187,1914,818,1319) -> Matrix(1,0,8,1) Matrix(1011,1628,136,219) -> Matrix(1,0,14,1) Matrix(793,1276,110,177) -> Matrix(1,0,-6,1) Matrix(1275,2024,526,835) -> Matrix(13,6,28,13) Matrix(1055,1672,-778,-1233) -> Matrix(5,2,-18,-7) Matrix(265,418,168,265) -> Matrix(5,2,12,5) Matrix(43,66,28,43) -> Matrix(1,0,6,1) Matrix(747,1100,328,483) -> Matrix(5,2,12,5) Matrix(1233,1804,542,793) -> Matrix(1,0,6,1) Matrix(1319,1914,818,1187) -> Matrix(1,0,8,1) Matrix(395,572,212,307) -> Matrix(5,2,12,5) Matrix(1363,1958,520,747) -> Matrix(1,0,6,1) Matrix(3697,5302,1412,2025) -> Matrix(1,0,6,1) Matrix(263,374,154,219) -> Matrix(1,0,10,1) Matrix(3037,4290,-2242,-3167) -> Matrix(5,2,-18,-7) Matrix(175,242,-128,-177) -> Matrix(5,2,-18,-7) Matrix(9635,13046,2014,2727) -> Matrix(23,6,-4,-1) Matrix(4665,6314,976,1321) -> Matrix(17,4,4,1) Matrix(131,176,32,43) -> Matrix(1,0,4,1) Matrix(219,286,134,175) -> Matrix(1,0,6,1) Matrix(441,572,340,441) -> Matrix(1,0,6,1) Matrix(307,396,238,307) -> Matrix(7,2,24,7) Matrix(87,110,34,43) -> Matrix(7,2,10,3) Matrix(89,110,72,89) -> Matrix(1,0,8,1) Matrix(307,374,252,307) -> Matrix(1,0,8,1) Matrix(617,748,146,177) -> Matrix(1,0,4,1) Matrix(1055,1276,654,791) -> Matrix(1,0,8,1) Matrix(131,154,74,87) -> Matrix(7,2,24,7) Matrix(1099,1276,416,483) -> Matrix(39,10,74,19) Matrix(1409,1628,534,617) -> Matrix(41,10,86,21) Matrix(175,198,38,43) -> Matrix(9,2,4,1) Matrix(1,0,2,1) -> Matrix(1,0,10,1) Matrix(307,-352,116,-133) -> Matrix(17,-4,30,-7) Matrix(177,-242,128,-175) -> Matrix(7,-2,18,-5) Matrix(221,-308,94,-131) -> Matrix(1,0,0,1) Matrix(219,-308,32,-45) -> Matrix(1,0,-4,1) Matrix(529,-748,186,-263) -> Matrix(1,0,0,1) Matrix(397,-572,152,-219) -> Matrix(1,0,-2,1) Matrix(483,-704,212,-309) -> Matrix(7,-2,18,-5) Matrix(263,-418,56,-89) -> Matrix(1,0,-2,1) Matrix(219,-352,28,-45) -> Matrix(1,0,0,1) Matrix(353,-572,108,-175) -> Matrix(1,0,-2,1) Matrix(309,-506,80,-131) -> Matrix(1,0,-2,1) Matrix(307,-506,54,-89) -> Matrix(1,0,-2,1) Matrix(395,-704,124,-221) -> Matrix(7,-2,4,-1) Matrix(133,-242,72,-131) -> Matrix(13,-4,36,-11) Matrix(133,-286,20,-43) -> Matrix(1,0,-4,1) Matrix(221,-506,38,-87) -> Matrix(5,-2,-2,1) Matrix(705,-1672,148,-351) -> Matrix(1,0,-2,1) Matrix(1057,-2530,404,-967) -> Matrix(5,-2,8,-3) Matrix(483,-1166,128,-309) -> Matrix(5,-2,-2,1) Matrix(89,-242,32,-87) -> Matrix(3,-2,2,-1) Matrix(265,-748,62,-175) -> Matrix(1,0,0,1) Matrix(175,-506,46,-133) -> Matrix(3,-2,2,-1) Matrix(615,-2024,134,-441) -> Matrix(3,-2,2,-1) Matrix(485,-1606,106,-351) -> Matrix(1,0,0,1) Matrix(881,-3366,184,-703) -> Matrix(1,-2,0,1) Matrix(45,-242,8,-43) -> Matrix(1,0,0,1) 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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 Degree of the the map X: 24 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 0/1 1/1 11/9 11/8 3/2 11/7 11/6 2/1 11/5 22/9 5/2 55/21 11/4 3/1 22/7 33/10 10/3 7/2 11/3 4/1 13/3 22/5 9/2 5/1 11/2 6/1 7/1 22/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 1/3 -6/1 -1/1 1/1 -11/2 -1/1 1/1 -5/1 1/1 -9/2 -1/1 1/0 -4/1 -1/1 1/1 -11/3 -1/1 -7/2 -1/1 -1/2 -10/3 -1/1 1/1 -13/4 -1/1 0/1 -3/1 -1/1 -11/4 -1/1 -8/3 -1/1 -3/5 -29/11 -3/7 -21/8 -1/2 0/1 -13/5 -1/1 -5/2 -2/3 -1/2 -12/5 -3/7 -1/3 -7/3 -1/1 -16/7 -3/7 -1/3 -25/11 -1/3 -9/4 -1/2 -1/3 -11/5 -1/3 -2/1 -1/1 -1/3 -11/6 -1/3 -9/5 -1/3 -16/9 -1/3 -3/11 -7/4 -1/4 -1/5 -12/7 -1/5 -1/7 -17/10 -1/10 0/1 -22/13 0/1 -5/3 -1/1 -13/8 -1/3 0/1 -34/21 -1/1 -1/3 -55/34 -1/3 -21/13 -1/3 -8/5 -1/1 -1/3 -11/7 -1/3 -3/2 -1/3 0/1 -22/15 -1/3 -19/13 -1/3 -16/11 -1/3 -1/5 -13/9 -1/3 -23/16 -1/4 0/1 -33/23 -1/3 -1/5 -10/7 -1/3 -1/5 -7/5 -1/1 -11/8 -1/3 -4/3 -1/3 -1/5 -13/10 -1/3 0/1 -22/17 -1/3 -9/7 -1/3 -5/4 -1/4 0/1 -11/9 -1/3 -1/5 -6/5 -1/3 -1/5 -7/6 -3/11 -1/4 -22/19 -1/4 -15/13 -7/29 -8/7 -3/13 -1/5 -1/1 -1/5 0/1 0/1 1/1 1/5 7/6 1/4 3/11 6/5 1/5 1/3 11/9 1/5 1/3 5/4 0/1 1/4 9/7 1/3 4/3 1/5 1/3 11/8 1/3 7/5 1/1 10/7 1/5 1/3 13/9 1/3 3/2 0/1 1/3 11/7 1/3 8/5 1/3 1/1 29/18 0/1 1/7 21/13 1/3 13/8 0/1 1/3 5/3 1/1 12/7 1/7 1/5 7/4 1/5 1/4 16/9 3/11 1/3 25/14 1/4 1/3 9/5 1/3 11/6 1/3 2/1 1/3 1/1 11/5 1/3 9/4 1/3 1/2 16/7 1/3 3/7 7/3 1/1 12/5 1/3 3/7 17/7 7/15 22/9 1/2 5/2 1/2 2/3 13/5 1/1 34/13 1/3 1/1 55/21 1/3 1/1 21/8 0/1 1/2 8/3 3/5 1/1 11/4 1/1 3/1 1/1 22/7 1/1 19/6 1/1 1/0 16/5 -1/1 1/1 13/4 0/1 1/1 23/7 1/1 33/10 1/1 10/3 -1/1 1/1 7/2 1/2 1/1 11/3 1/1 4/1 -1/1 1/1 13/3 1/1 22/5 1/1 9/2 1/1 1/0 5/1 -1/1 11/2 -1/1 1/1 6/1 -1/1 1/1 7/1 -1/3 22/3 0/1 15/2 0/1 1/7 8/1 1/3 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(21,176,-8,-67) (-7/1,1/0) -> (-29/11,-21/8) Hyperbolic Matrix(23,154,10,67) (-7/1,-6/1) -> (16/7,7/3) Hyperbolic Matrix(23,132,4,23) (-6/1,-11/2) -> (11/2,6/1) Hyperbolic Matrix(21,110,4,21) (-11/2,-5/1) -> (5/1,11/2) Hyperbolic Matrix(23,110,14,67) (-5/1,-9/2) -> (13/8,5/3) Hyperbolic Matrix(21,88,-16,-67) (-9/2,-4/1) -> (-4/3,-13/10) Hyperbolic Matrix(23,88,6,23) (-4/1,-11/3) -> (11/3,4/1) Hyperbolic Matrix(43,154,12,43) (-11/3,-7/2) -> (7/2,11/3) Hyperbolic Matrix(45,154,26,89) (-7/2,-10/3) -> (12/7,7/4) Hyperbolic Matrix(175,572,-108,-353) (-10/3,-13/4) -> (-13/8,-34/21) Hyperbolic Matrix(109,352,-48,-155) (-13/4,-3/1) -> (-25/11,-9/4) Hyperbolic Matrix(23,66,8,23) (-3/1,-11/4) -> (11/4,3/1) Hyperbolic Matrix(65,176,24,65) (-11/4,-8/3) -> (8/3,11/4) Hyperbolic Matrix(133,352,-116,-307) (-8/3,-29/11) -> (-15/13,-8/7) Hyperbolic Matrix(219,572,-152,-397) (-21/8,-13/5) -> (-13/9,-23/16) Hyperbolic Matrix(43,110,34,87) (-13/5,-5/2) -> (5/4,9/7) Hyperbolic Matrix(109,264,-64,-155) (-5/2,-12/5) -> (-12/7,-17/10) Hyperbolic Matrix(65,154,46,109) (-12/5,-7/3) -> (7/5,10/7) Hyperbolic Matrix(67,154,10,23) (-7/3,-16/7) -> (6/1,7/1) Hyperbolic Matrix(309,704,-212,-483) (-16/7,-25/11) -> (-19/13,-16/11) Hyperbolic Matrix(89,198,40,89) (-9/4,-11/5) -> (11/5,9/4) Hyperbolic Matrix(21,44,10,21) (-11/5,-2/1) -> (2/1,11/5) Hyperbolic Matrix(23,44,12,23) (-2/1,-11/6) -> (11/6,2/1) Hyperbolic Matrix(109,198,60,109) (-11/6,-9/5) -> (9/5,11/6) Hyperbolic Matrix(197,352,-136,-243) (-9/5,-16/9) -> (-16/11,-13/9) Hyperbolic Matrix(87,154,74,131) (-16/9,-7/4) -> (7/6,6/5) Hyperbolic Matrix(89,154,26,45) (-7/4,-12/7) -> (10/3,7/2) Hyperbolic Matrix(285,484,116,197) (-17/10,-22/13) -> (22/9,5/2) Hyperbolic Matrix(287,484,118,199) (-22/13,-5/3) -> (17/7,22/9) Hyperbolic Matrix(67,110,14,23) (-5/3,-13/8) -> (9/2,5/1) Hyperbolic Matrix(1033,1672,312,505) (-34/21,-55/34) -> (33/10,10/3) Hyperbolic Matrix(1211,1958,368,595) (-55/34,-21/13) -> (23/7,33/10) Hyperbolic Matrix(109,176,-96,-155) (-21/13,-8/5) -> (-8/7,-1/1) Hyperbolic Matrix(111,176,70,111) (-8/5,-11/7) -> (11/7,8/5) Hyperbolic Matrix(43,66,28,43) (-11/7,-3/2) -> (3/2,11/7) Hyperbolic Matrix(329,484,104,153) (-3/2,-22/15) -> (22/7,19/6) Hyperbolic Matrix(331,484,106,155) (-22/15,-19/13) -> (3/1,22/7) Hyperbolic Matrix(1363,1958,520,747) (-23/16,-33/23) -> (55/21,21/8) Hyperbolic Matrix(1167,1672,446,639) (-33/23,-10/7) -> (34/13,55/21) Hyperbolic Matrix(109,154,46,65) (-10/7,-7/5) -> (7/3,12/5) Hyperbolic Matrix(111,154,80,111) (-7/5,-11/8) -> (11/8,7/5) Hyperbolic Matrix(65,88,48,65) (-11/8,-4/3) -> (4/3,11/8) Hyperbolic Matrix(373,484,84,109) (-13/10,-22/17) -> (22/5,9/2) Hyperbolic Matrix(375,484,86,111) (-22/17,-9/7) -> (13/3,22/5) Hyperbolic Matrix(87,110,34,43) (-9/7,-5/4) -> (5/2,13/5) Hyperbolic Matrix(89,110,72,89) (-5/4,-11/9) -> (11/9,5/4) Hyperbolic Matrix(109,132,90,109) (-11/9,-6/5) -> (6/5,11/9) Hyperbolic Matrix(131,154,74,87) (-6/5,-7/6) -> (7/4,16/9) Hyperbolic Matrix(417,484,56,65) (-7/6,-22/19) -> (22/3,15/2) Hyperbolic Matrix(419,484,58,67) (-22/19,-15/13) -> (7/1,22/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(155,-176,96,-109) (1/1,7/6) -> (29/18,21/13) Hyperbolic Matrix(67,-88,16,-21) (9/7,4/3) -> (4/1,13/3) Hyperbolic Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(243,-352,136,-197) (13/9,3/2) -> (25/14,9/5) Hyperbolic Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(155,-264,64,-109) (5/3,12/7) -> (12/5,17/7) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(21,176,-8,-67) -> Matrix(0,-1,1,2) Matrix(23,154,10,67) -> Matrix(2,-1,5,-2) Matrix(23,132,4,23) -> Matrix(0,-1,1,0) Matrix(21,110,4,21) -> Matrix(0,-1,1,0) Matrix(23,110,14,67) -> Matrix(0,1,-1,2) Matrix(21,88,-16,-67) -> Matrix(0,-1,1,4) Matrix(23,88,6,23) -> Matrix(0,-1,1,0) Matrix(43,154,12,43) -> Matrix(3,2,4,3) Matrix(45,154,26,89) -> Matrix(1,0,6,1) Matrix(175,572,-108,-353) -> Matrix(1,0,-2,1) Matrix(109,352,-48,-155) -> Matrix(2,1,-5,-2) Matrix(23,66,8,23) -> Matrix(2,1,3,2) Matrix(65,176,24,65) -> Matrix(4,3,5,4) Matrix(133,352,-116,-307) -> Matrix(7,4,-30,-17) Matrix(219,572,-152,-397) -> Matrix(1,0,-2,1) Matrix(43,110,34,87) -> Matrix(3,2,10,7) Matrix(109,264,-64,-155) -> Matrix(2,1,-17,-8) Matrix(65,154,46,109) -> Matrix(2,1,3,2) Matrix(67,154,10,23) -> Matrix(2,1,-5,-2) Matrix(309,704,-212,-483) -> Matrix(5,2,-18,-7) Matrix(89,198,40,89) -> Matrix(5,2,12,5) Matrix(21,44,10,21) -> Matrix(2,1,3,2) Matrix(23,44,12,23) -> Matrix(2,1,3,2) Matrix(109,198,60,109) -> Matrix(10,3,33,10) Matrix(197,352,-136,-243) -> Matrix(4,1,-9,-2) Matrix(87,154,74,131) -> Matrix(7,2,24,7) Matrix(89,154,26,45) -> Matrix(1,0,6,1) Matrix(285,484,116,197) -> Matrix(12,1,23,2) Matrix(287,484,118,199) -> Matrix(6,-1,13,-2) Matrix(67,110,14,23) -> Matrix(2,1,-1,0) Matrix(1033,1672,312,505) -> Matrix(2,1,-1,0) Matrix(1211,1958,368,595) -> Matrix(4,1,7,2) Matrix(109,176,-96,-155) -> Matrix(4,1,-17,-4) Matrix(111,176,70,111) -> Matrix(2,1,3,2) Matrix(43,66,28,43) -> Matrix(1,0,6,1) Matrix(329,484,104,153) -> Matrix(2,1,-1,0) Matrix(331,484,106,155) -> Matrix(4,1,7,2) Matrix(1363,1958,520,747) -> Matrix(1,0,6,1) Matrix(1167,1672,446,639) -> Matrix(4,1,7,2) Matrix(109,154,46,65) -> Matrix(2,1,3,2) Matrix(111,154,80,111) -> Matrix(2,1,3,2) Matrix(65,88,48,65) -> Matrix(4,1,15,4) Matrix(373,484,84,109) -> Matrix(2,1,-1,0) Matrix(375,484,86,111) -> Matrix(4,1,7,2) Matrix(87,110,34,43) -> Matrix(7,2,10,3) Matrix(89,110,72,89) -> Matrix(1,0,8,1) Matrix(109,132,90,109) -> Matrix(4,1,15,4) Matrix(131,154,74,87) -> Matrix(7,2,24,7) Matrix(417,484,56,65) -> Matrix(4,1,39,10) Matrix(419,484,58,67) -> Matrix(4,1,-41,-10) Matrix(1,0,2,1) -> Matrix(1,0,10,1) Matrix(155,-176,96,-109) -> Matrix(4,-1,17,-4) Matrix(67,-88,16,-21) -> Matrix(4,-1,1,0) Matrix(397,-572,152,-219) -> Matrix(1,0,-2,1) Matrix(243,-352,136,-197) -> Matrix(2,-1,9,-4) Matrix(219,-352,28,-45) -> Matrix(1,0,0,1) Matrix(353,-572,108,-175) -> Matrix(1,0,-2,1) Matrix(155,-264,64,-109) -> Matrix(8,-1,17,-2) Matrix(395,-704,124,-221) -> Matrix(7,-2,4,-1) Matrix(155,-352,48,-109) -> Matrix(2,-1,5,-2) Matrix(67,-176,8,-21) -> Matrix(2,-1,1,0) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 24 ----------------------------------------------------------------------- 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 5 1 1/1 1/5 1 22 7/6 (1/4,3/11) 0 22 6/5 (1/5,1/3) 0 11 11/9 (0/1,1/4).(1/5,1/3) 0 2 5/4 (0/1,1/4) 0 22 9/7 1/3 1 22 4/3 (1/5,1/3) 0 11 11/8 1/3 2 2 7/5 1/1 1 22 10/7 (1/5,1/3) 0 11 13/9 1/3 1 22 3/2 (0/1,1/3) 0 22 11/7 1/3 1 2 8/5 (1/3,1/1) 0 11 29/18 (0/1,1/7) 0 22 21/13 1/3 1 22 13/8 (0/1,1/3) 0 22 5/3 1/1 1 22 12/7 (1/7,1/5) 0 11 7/4 (1/5,1/4) 0 22 16/9 (3/11,1/3) 0 11 25/14 (1/4,1/3) 0 22 9/5 1/3 1 22 11/6 1/3 4 2 2/1 (1/3,1/1) 0 11 11/5 1/3 1 2 9/4 (1/3,1/2) 0 22 16/7 (1/3,3/7) 0 11 7/3 1/1 1 22 12/5 (1/3,3/7) 0 11 17/7 7/15 1 22 22/9 1/2 9 1 5/2 (1/2,2/3) 0 22 13/5 1/1 1 22 34/13 (1/3,1/1) 0 11 55/21 (0/1,1/2).(1/3,1/1) 0 2 21/8 (0/1,1/2) 0 22 8/3 (3/5,1/1) 0 11 11/4 1/1 2 2 3/1 1/1 1 22 22/7 1/1 1 1 19/6 (1/1,1/0) 0 22 16/5 (-1/1,1/1) 0 11 13/4 (0/1,1/1) 0 22 23/7 1/1 1 22 33/10 1/1 2 2 10/3 (-1/1,1/1) 0 11 7/2 (1/2,1/1) 0 22 11/3 1/1 3 2 4/1 (-1/1,1/1) 0 11 13/3 1/1 1 22 22/5 1/1 1 1 9/2 (1/1,1/0) 0 22 5/1 -1/1 1 22 11/2 (-1/1,1/1) 0 2 6/1 (-1/1,1/1) 0 11 7/1 -1/3 1 22 22/3 0/1 10 1 15/2 (0/1,1/7) 0 22 8/1 (1/3,1/1) 0 11 1/0 (0/1,1/0) 0 22 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(155,-176,96,-109) (1/1,7/6) -> (29/18,21/13) Hyperbolic Matrix(131,-154,74,-87) (7/6,6/5) -> (7/4,16/9) Glide Reflection Matrix(109,-132,90,-109) (6/5,11/9) -> (6/5,11/9) Reflection Matrix(89,-110,72,-89) (11/9,5/4) -> (11/9,5/4) Reflection Matrix(87,-110,34,-43) (5/4,9/7) -> (5/2,13/5) Glide Reflection Matrix(67,-88,16,-21) (9/7,4/3) -> (4/1,13/3) Hyperbolic Matrix(65,-88,48,-65) (4/3,11/8) -> (4/3,11/8) Reflection Matrix(111,-154,80,-111) (11/8,7/5) -> (11/8,7/5) Reflection Matrix(109,-154,46,-65) (7/5,10/7) -> (7/3,12/5) Glide Reflection Matrix(397,-572,152,-219) (10/7,13/9) -> (13/5,34/13) Hyperbolic Matrix(243,-352,136,-197) (13/9,3/2) -> (25/14,9/5) Hyperbolic Matrix(43,-66,28,-43) (3/2,11/7) -> (3/2,11/7) Reflection Matrix(111,-176,70,-111) (11/7,8/5) -> (11/7,8/5) Reflection Matrix(219,-352,28,-45) (8/5,29/18) -> (15/2,8/1) Hyperbolic Matrix(353,-572,108,-175) (21/13,13/8) -> (13/4,23/7) Hyperbolic Matrix(67,-110,14,-23) (13/8,5/3) -> (9/2,5/1) Glide Reflection Matrix(155,-264,64,-109) (5/3,12/7) -> (12/5,17/7) Hyperbolic Matrix(89,-154,26,-45) (12/7,7/4) -> (10/3,7/2) Glide Reflection Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(23,-44,12,-23) (11/6,2/1) -> (11/6,2/1) Reflection Matrix(21,-44,10,-21) (2/1,11/5) -> (2/1,11/5) Reflection Matrix(89,-198,40,-89) (11/5,9/4) -> (11/5,9/4) Reflection Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(67,-154,10,-23) (16/7,7/3) -> (6/1,7/1) Glide Reflection Matrix(307,-748,126,-307) (17/7,22/9) -> (17/7,22/9) Reflection Matrix(89,-220,36,-89) (22/9,5/2) -> (22/9,5/2) Reflection Matrix(1429,-3740,546,-1429) (34/13,55/21) -> (34/13,55/21) Reflection Matrix(881,-2310,336,-881) (55/21,21/8) -> (55/21,21/8) Reflection Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic Matrix(65,-176,24,-65) (8/3,11/4) -> (8/3,11/4) Reflection Matrix(23,-66,8,-23) (11/4,3/1) -> (11/4,3/1) Reflection Matrix(43,-132,14,-43) (3/1,22/7) -> (3/1,22/7) Reflection Matrix(265,-836,84,-265) (22/7,19/6) -> (22/7,19/6) Reflection Matrix(461,-1518,140,-461) (23/7,33/10) -> (23/7,33/10) Reflection Matrix(199,-660,60,-199) (33/10,10/3) -> (33/10,10/3) Reflection Matrix(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(21,-110,4,-21) (5/1,11/2) -> (5/1,11/2) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(43,-308,6,-43) (7/1,22/3) -> (7/1,22/3) Reflection Matrix(89,-660,12,-89) (22/3,15/2) -> (22/3,15/2) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,10,-1) (0/1,1/1) -> (0/1,1/5) Matrix(155,-176,96,-109) -> Matrix(4,-1,17,-4) (0/1,1/4).(1/5,1/3) Matrix(131,-154,74,-87) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(109,-132,90,-109) -> Matrix(4,-1,15,-4) (6/5,11/9) -> (1/5,1/3) Matrix(89,-110,72,-89) -> Matrix(1,0,8,-1) (11/9,5/4) -> (0/1,1/4) Matrix(87,-110,34,-43) -> Matrix(7,-2,10,-3) Matrix(67,-88,16,-21) -> Matrix(4,-1,1,0) Matrix(65,-88,48,-65) -> Matrix(4,-1,15,-4) (4/3,11/8) -> (1/5,1/3) Matrix(111,-154,80,-111) -> Matrix(2,-1,3,-2) (11/8,7/5) -> (1/3,1/1) Matrix(109,-154,46,-65) -> Matrix(2,-1,3,-2) *** -> (1/3,1/1) Matrix(397,-572,152,-219) -> Matrix(1,0,-2,1) 0/1 Matrix(243,-352,136,-197) -> Matrix(2,-1,9,-4) 1/3 Matrix(43,-66,28,-43) -> Matrix(1,0,6,-1) (3/2,11/7) -> (0/1,1/3) Matrix(111,-176,70,-111) -> Matrix(2,-1,3,-2) (11/7,8/5) -> (1/3,1/1) Matrix(219,-352,28,-45) -> Matrix(1,0,0,1) Matrix(353,-572,108,-175) -> Matrix(1,0,-2,1) 0/1 Matrix(67,-110,14,-23) -> Matrix(-2,1,1,0) Matrix(155,-264,64,-109) -> Matrix(8,-1,17,-2) Matrix(89,-154,26,-45) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(395,-704,124,-221) -> Matrix(7,-2,4,-1) Matrix(109,-198,60,-109) -> Matrix(10,-3,33,-10) (9/5,11/6) -> (3/11,1/3) Matrix(23,-44,12,-23) -> Matrix(2,-1,3,-2) (11/6,2/1) -> (1/3,1/1) Matrix(21,-44,10,-21) -> Matrix(2,-1,3,-2) (2/1,11/5) -> (1/3,1/1) Matrix(89,-198,40,-89) -> Matrix(5,-2,12,-5) (11/5,9/4) -> (1/3,1/2) Matrix(155,-352,48,-109) -> Matrix(2,-1,5,-2) (0/1,1/2).(1/3,1/1) Matrix(67,-154,10,-23) -> Matrix(2,-1,-5,2) Matrix(307,-748,126,-307) -> Matrix(29,-14,60,-29) (17/7,22/9) -> (7/15,1/2) Matrix(89,-220,36,-89) -> Matrix(7,-4,12,-7) (22/9,5/2) -> (1/2,2/3) Matrix(1429,-3740,546,-1429) -> Matrix(2,-1,3,-2) (34/13,55/21) -> (1/3,1/1) Matrix(881,-2310,336,-881) -> Matrix(1,0,4,-1) (55/21,21/8) -> (0/1,1/2) Matrix(67,-176,8,-21) -> Matrix(2,-1,1,0) 1/1 Matrix(65,-176,24,-65) -> Matrix(4,-3,5,-4) (8/3,11/4) -> (3/5,1/1) Matrix(23,-66,8,-23) -> Matrix(2,-1,3,-2) (11/4,3/1) -> (1/3,1/1) Matrix(43,-132,14,-43) -> Matrix(1,0,2,-1) (3/1,22/7) -> (0/1,1/1) Matrix(265,-836,84,-265) -> Matrix(-1,2,0,1) (22/7,19/6) -> (1/1,1/0) Matrix(461,-1518,140,-461) -> Matrix(2,-1,3,-2) (23/7,33/10) -> (1/3,1/1) Matrix(199,-660,60,-199) -> Matrix(0,1,1,0) (33/10,10/3) -> (-1/1,1/1) Matrix(43,-154,12,-43) -> Matrix(3,-2,4,-3) (7/2,11/3) -> (1/2,1/1) Matrix(23,-88,6,-23) -> Matrix(0,1,1,0) (11/3,4/1) -> (-1/1,1/1) Matrix(131,-572,30,-131) -> Matrix(1,0,2,-1) (13/3,22/5) -> (0/1,1/1) Matrix(89,-396,20,-89) -> Matrix(-1,2,0,1) (22/5,9/2) -> (1/1,1/0) Matrix(21,-110,4,-21) -> Matrix(0,1,1,0) (5/1,11/2) -> (-1/1,1/1) Matrix(23,-132,4,-23) -> Matrix(0,1,1,0) (11/2,6/1) -> (-1/1,1/1) Matrix(43,-308,6,-43) -> Matrix(-1,0,6,1) (7/1,22/3) -> (-1/3,0/1) Matrix(89,-660,12,-89) -> Matrix(1,0,14,-1) (22/3,15/2) -> (0/1,1/7) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.