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: 40 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 11/9 11/8 3/2 11/7 11/6 2/1 11/5 12/5 22/9 5/2 44/17 55/21 11/4 3/1 22/7 33/10 10/3 44/13 7/2 18/5 11/3 4/1 13/3 22/5 9/2 88/19 14/3 110/23 5/1 16/3 11/2 6/1 44/7 20/3 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 -1/1 -4/5 -13/2 -2/3 -3/5 -6/1 0/1 -11/2 -1/1 -16/3 -1/1 -3/4 -5/1 -2/3 -1/2 -14/3 0/1 -23/5 -1/1 0/1 -9/2 -1/1 0/1 -4/1 -1/1 -1/2 -11/3 -1/2 -18/5 0/1 -7/2 -1/1 0/1 -24/7 -2/3 -3/5 -17/5 -4/7 -1/2 -10/3 0/1 -13/4 -1/1 -2/3 -3/1 -1/2 0/1 -14/5 0/1 -11/4 -1/2 -8/3 -1/2 -1/3 -29/11 -1/3 -4/13 -21/8 -1/3 0/1 -13/5 -1/3 0/1 -18/7 0/1 -23/9 -1/3 0/1 -5/2 -1/4 0/1 -12/5 -1/1 0/1 -31/13 -1/1 -2/3 -19/8 -1/2 -2/5 -7/3 -1/3 0/1 -23/10 -1/3 0/1 -16/7 -1/3 -1/4 -25/11 -1/4 -2/9 -9/4 -1/5 0/1 -20/9 -1/9 0/1 -11/5 0/1 -2/1 0/1 -11/6 0/1 -20/11 0/1 1/7 -9/5 0/1 1/3 -16/9 1/2 1/1 -23/13 0/1 1/1 -30/17 0/1 -7/4 0/1 1/1 -26/15 0/1 -19/11 2/1 1/0 -50/29 -4/1 -31/18 -2/1 -1/1 -43/25 -2/1 -1/1 -12/7 -1/1 0/1 -17/10 -1/4 0/1 -22/13 0/1 -5/3 0/1 1/2 -28/17 1/1 1/0 -23/14 0/1 1/1 -41/25 2/1 1/0 -18/11 0/1 -31/19 0/1 1/1 -44/27 1/2 1/0 -13/8 0/1 1/1 -34/21 2/3 -55/34 1/1 -76/47 1/1 2/1 -21/13 0/1 1/1 -8/5 1/1 1/0 -11/7 1/0 -14/9 0/1 -17/11 2/1 1/0 -20/13 0/1 1/1 -3/2 0/1 1/0 -22/15 1/0 -19/13 -6/1 1/0 -16/11 -3/1 1/0 -13/9 -2/1 -1/1 -23/16 -2/1 -1/1 -33/23 -1/1 -10/7 0/1 -27/19 4/1 1/0 -44/31 1/0 -17/12 -4/1 1/0 -24/17 -3/1 -2/1 -31/22 -2/1 -5/3 -7/5 -1/1 0/1 -25/18 -2/1 1/0 -68/49 -2/1 -1/1 -43/31 -1/1 0/1 -18/13 0/1 -11/8 1/0 -4/3 -1/1 1/0 -13/10 -2/1 -1/1 -22/17 -1/1 -9/7 -1/1 0/1 -32/25 -2/1 -1/1 -55/43 -1/1 -23/18 -1/1 0/1 -37/29 -1/1 0/1 -88/69 -1/2 1/0 -51/40 -1/1 0/1 -14/11 0/1 -19/15 0/1 1/0 -43/34 -2/1 -1/1 -110/87 -1/1 -67/53 -1/1 -2/3 -24/19 -1/1 0/1 -5/4 -2/1 1/0 -21/17 -2/1 -1/1 -16/13 -3/2 -1/1 -11/9 -1/1 -6/5 0/1 -25/21 6/1 1/0 -44/37 1/0 -19/16 -6/1 1/0 -13/11 -3/1 -2/1 -20/17 -2/1 -5/3 -7/6 -4/3 -1/1 -22/19 -1/1 -15/13 -1/1 -6/7 -8/7 -1/1 -1/2 -1/1 -1/1 0/1 0/1 -1/2 1/0 1/1 -1/1 0/1 7/6 -1/1 -4/5 13/11 -2/3 -3/5 6/5 0/1 11/9 -1/1 16/13 -1/1 -3/4 5/4 -2/3 -1/2 14/11 0/1 23/18 -1/1 0/1 9/7 -1/1 0/1 4/3 -1/1 -1/2 11/8 -1/2 18/13 0/1 7/5 -1/1 0/1 24/17 -2/3 -3/5 17/12 -4/7 -1/2 10/7 0/1 13/9 -1/1 -2/3 3/2 -1/2 0/1 14/9 0/1 11/7 -1/2 8/5 -1/2 -1/3 29/18 -1/3 -4/13 21/13 -1/3 0/1 13/8 -1/3 0/1 18/11 0/1 23/14 -1/3 0/1 5/3 -1/4 0/1 12/7 -1/1 0/1 31/18 -1/1 -2/3 19/11 -1/2 -2/5 7/4 -1/3 0/1 23/13 -1/3 0/1 16/9 -1/3 -1/4 25/14 -1/4 -2/9 9/5 -1/5 0/1 20/11 -1/9 0/1 11/6 0/1 2/1 0/1 11/5 0/1 20/9 0/1 1/7 9/4 0/1 1/3 16/7 1/2 1/1 23/10 0/1 1/1 30/13 0/1 7/3 0/1 1/1 26/11 0/1 19/8 2/1 1/0 50/21 -4/1 31/13 -2/1 -1/1 43/18 -2/1 -1/1 12/5 -1/1 0/1 17/7 -1/4 0/1 22/9 0/1 5/2 0/1 1/2 28/11 1/1 1/0 23/9 0/1 1/1 41/16 2/1 1/0 18/7 0/1 31/12 0/1 1/1 44/17 1/2 1/0 13/5 0/1 1/1 34/13 2/3 55/21 1/1 76/29 1/1 2/1 21/8 0/1 1/1 8/3 1/1 1/0 11/4 1/0 14/5 0/1 17/6 2/1 1/0 20/7 0/1 1/1 3/1 0/1 1/0 22/7 1/0 19/6 -6/1 1/0 16/5 -3/1 1/0 13/4 -2/1 -1/1 23/7 -2/1 -1/1 33/10 -1/1 10/3 0/1 27/8 4/1 1/0 44/13 1/0 17/5 -4/1 1/0 24/7 -3/1 -2/1 31/9 -2/1 -5/3 7/2 -1/1 0/1 25/7 -2/1 1/0 68/19 -2/1 -1/1 43/12 -1/1 0/1 18/5 0/1 11/3 1/0 4/1 -1/1 1/0 13/3 -2/1 -1/1 22/5 -1/1 9/2 -1/1 0/1 32/7 -2/1 -1/1 55/12 -1/1 23/5 -1/1 0/1 37/8 -1/1 0/1 88/19 -1/2 1/0 51/11 -1/1 0/1 14/3 0/1 19/4 0/1 1/0 43/9 -2/1 -1/1 110/23 -1/1 67/14 -1/1 -2/3 24/5 -1/1 0/1 5/1 -2/1 1/0 21/4 -2/1 -1/1 16/3 -3/2 -1/1 11/2 -1/1 6/1 0/1 25/4 6/1 1/0 44/7 1/0 19/3 -6/1 1/0 13/2 -3/1 -2/1 20/3 -2/1 -5/3 7/1 -4/3 -1/1 22/3 -1/1 15/2 -1/1 -6/7 8/1 -1/1 -1/2 1/0 -1/1 0/1 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(45,308,-32,-219) (-7/1,-13/2) -> (-31/22,-7/5) Hyperbolic Matrix(131,836,-76,-485) (-13/2,-6/1) -> (-50/29,-31/18) Hyperbolic Matrix(23,132,4,23) (-6/1,-11/2) -> (11/2,6/1) Hyperbolic Matrix(65,352,12,65) (-11/2,-16/3) -> (16/3,11/2) Hyperbolic Matrix(43,220,-26,-133) (-16/3,-5/1) -> (-5/3,-28/17) Hyperbolic Matrix(65,308,-42,-199) (-5/1,-14/3) -> (-14/9,-17/11) Hyperbolic Matrix(219,1012,-124,-573) (-14/3,-23/5) -> (-23/13,-30/17) Hyperbolic Matrix(241,1100,-140,-639) (-23/5,-9/2) -> (-31/18,-43/25) 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(109,396,30,109) (-11/3,-18/5) -> (18/5,11/3) Hyperbolic Matrix(87,308,-50,-177) (-18/5,-7/2) -> (-7/4,-26/15) Hyperbolic Matrix(89,308,-76,-263) (-7/2,-24/7) -> (-20/17,-7/6) Hyperbolic Matrix(219,748,-142,-485) (-24/7,-17/5) -> (-17/11,-20/13) Hyperbolic Matrix(131,440,-92,-309) (-17/5,-10/3) -> (-10/7,-27/19) 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(109,308,-86,-243) (-3/1,-14/5) -> (-14/11,-19/15) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) 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(307,792,-188,-485) (-13/5,-18/7) -> (-18/11,-31/19) Hyperbolic Matrix(463,1188,-334,-857) (-18/7,-23/9) -> (-43/31,-18/13) Hyperbolic Matrix(87,220,-70,-177) (-23/9,-5/2) -> (-5/4,-21/17) Hyperbolic Matrix(109,264,-64,-155) (-5/2,-12/5) -> (-12/7,-17/10) Hyperbolic Matrix(461,1100,-360,-859) (-12/5,-31/13) -> (-9/7,-32/25) Hyperbolic Matrix(351,836,-296,-705) (-31/13,-19/8) -> (-19/16,-13/11) Hyperbolic Matrix(131,308,-94,-221) (-19/8,-7/3) -> (-7/5,-25/18) Hyperbolic Matrix(439,1012,-344,-793) (-7/3,-23/10) -> (-23/18,-37/29) 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(375,836,-266,-593) (-9/4,-20/9) -> (-24/17,-31/22) Hyperbolic Matrix(199,440,90,199) (-20/9,-11/5) -> (11/5,20/9) 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(241,440,132,241) (-11/6,-20/11) -> (20/11,11/6) Hyperbolic Matrix(243,440,-206,-373) (-20/11,-9/5) -> (-13/11,-20/17) Hyperbolic Matrix(197,352,-136,-243) (-9/5,-16/9) -> (-16/11,-13/9) Hyperbolic Matrix(397,704,-322,-571) (-16/9,-23/13) -> (-21/17,-16/13) Hyperbolic Matrix(923,1628,-724,-1277) (-30/17,-7/4) -> (-51/40,-14/11) Hyperbolic Matrix(813,1408,-496,-859) (-26/15,-19/11) -> (-41/25,-18/11) Hyperbolic Matrix(791,1364,-664,-1145) (-19/11,-50/29) -> (-6/5,-25/21) Hyperbolic Matrix(2047,3520,-1266,-2177) (-43/25,-12/7) -> (-76/47,-21/13) 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(1341,2200,-1060,-1739) (-23/14,-41/25) -> (-19/15,-43/34) Hyperbolic Matrix(1187,1936,458,747) (-31/19,-44/27) -> (44/17,13/5) Hyperbolic Matrix(1189,1936,460,749) (-44/27,-13/8) -> (31/12,44/17) Hyperbolic Matrix(1033,1672,312,505) (-34/21,-55/34) -> (33/10,10/3) Hyperbolic Matrix(3673,5940,802,1297) (-55/34,-76/47) -> (32/7,55/12) 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(197,308,126,197) (-11/7,-14/9) -> (14/9,11/7) Hyperbolic Matrix(461,704,-332,-507) (-20/13,-3/2) -> (-25/18,-68/49) 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(1409,2024,-1102,-1583) (-23/16,-33/23) -> (-55/43,-23/18) Hyperbolic Matrix(1167,1672,446,639) (-33/23,-10/7) -> (34/13,55/21) Hyperbolic Matrix(1363,1936,402,571) (-27/19,-44/31) -> (44/13,17/5) Hyperbolic Matrix(1365,1936,404,573) (-44/31,-17/12) -> (27/8,44/13) Hyperbolic Matrix(373,528,-296,-419) (-17/12,-24/17) -> (-24/19,-5/4) Hyperbolic Matrix(4027,5588,-3186,-4421) (-68/49,-43/31) -> (-67/53,-24/19) Hyperbolic Matrix(287,396,208,287) (-18/13,-11/8) -> (11/8,18/13) 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(4643,5940,1772,2267) (-32/25,-55/43) -> (55/21,76/29) Hyperbolic Matrix(6071,7744,1310,1671) (-37/29,-88/69) -> (88/19,51/11) Hyperbolic Matrix(6073,7744,1312,1673) (-88/69,-51/40) -> (37/8,88/19) Hyperbolic Matrix(9569,12100,2000,2529) (-43/34,-110/87) -> (110/23,67/14) Hyperbolic Matrix(9571,12100,2002,2531) (-110/87,-67/53) -> (43/9,110/23) Hyperbolic Matrix(287,352,234,287) (-16/13,-11/9) -> (11/9,16/13) Hyperbolic Matrix(109,132,90,109) (-11/9,-6/5) -> (6/5,11/9) Hyperbolic Matrix(1627,1936,258,307) (-25/21,-44/37) -> (44/7,19/3) Hyperbolic Matrix(1629,1936,260,309) (-44/37,-19/16) -> (25/4,44/7) 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(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(705,-836,296,-351) (13/11,6/5) -> (50/21,31/13) Hyperbolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(243,-308,86,-109) (5/4,14/11) -> (14/5,17/6) Hyperbolic Matrix(793,-1012,344,-439) (14/11,23/18) -> (23/10,30/13) Hyperbolic Matrix(859,-1100,360,-461) (23/18,9/7) -> (31/13,43/18) Hyperbolic Matrix(67,-88,16,-21) (9/7,4/3) -> (4/1,13/3) Hyperbolic 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(309,-440,92,-131) (17/12,10/7) -> (10/3,27/8) 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(199,-308,42,-65) (3/2,14/9) -> (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(485,-792,188,-307) (13/8,18/11) -> (18/7,31/12) Hyperbolic Matrix(725,-1188,202,-331) (18/11,23/14) -> (43/12,18/5) Hyperbolic Matrix(133,-220,26,-43) (23/14,5/3) -> (5/1,21/4) Hyperbolic Matrix(155,-264,64,-109) (5/3,12/7) -> (12/5,17/7) Hyperbolic Matrix(639,-1100,140,-241) (12/7,31/18) -> (9/2,32/7) Hyperbolic Matrix(485,-836,76,-131) (31/18,19/11) -> (19/3,13/2) Hyperbolic Matrix(177,-308,50,-87) (19/11,7/4) -> (7/2,25/7) Hyperbolic Matrix(573,-1012,124,-219) (7/4,23/13) -> (23/5,37/8) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(461,-836,134,-243) (9/5,20/11) -> (24/7,31/9) Hyperbolic Matrix(197,-440,30,-67) (20/9,9/4) -> (13/2,20/3) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(705,-1628,152,-351) (30/13,7/3) -> (51/11,14/3) Hyperbolic Matrix(595,-1408,232,-549) (26/11,19/8) -> (41/16,18/7) Hyperbolic Matrix(573,-1364,92,-219) (19/8,50/21) -> (6/1,25/4) Hyperbolic Matrix(1473,-3520,562,-1343) (43/18,12/5) -> (76/29,21/8) Hyperbolic Matrix(859,-2200,180,-461) (23/9,41/16) -> (19/4,43/9) Hyperbolic Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic Matrix(243,-704,68,-197) (20/7,3/1) -> (25/7,68/19) Hyperbolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(155,-528,32,-109) (17/5,24/7) -> (24/5,5/1) Hyperbolic Matrix(1561,-5588,326,-1167) (68/19,43/12) -> (67/14,24/5) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(21,176,-8,-67) -> Matrix(1,0,-2,1) Matrix(45,308,-32,-219) -> Matrix(5,4,-4,-3) Matrix(131,836,-76,-485) -> Matrix(7,4,-2,-1) Matrix(23,132,4,23) -> Matrix(1,0,0,1) Matrix(65,352,12,65) -> Matrix(7,6,-6,-5) Matrix(43,220,-26,-133) -> Matrix(3,2,4,3) Matrix(65,308,-42,-199) -> Matrix(1,0,2,1) Matrix(219,1012,-124,-573) -> Matrix(1,0,2,1) Matrix(241,1100,-140,-639) -> Matrix(3,2,-2,-1) Matrix(21,88,-16,-67) -> Matrix(3,2,-2,-1) Matrix(23,88,6,23) -> Matrix(3,2,-2,-1) Matrix(109,396,30,109) -> Matrix(1,0,2,1) Matrix(87,308,-50,-177) -> Matrix(1,0,2,1) Matrix(89,308,-76,-263) -> Matrix(5,4,-4,-3) Matrix(219,748,-142,-485) -> Matrix(3,2,-2,-1) Matrix(131,440,-92,-309) -> Matrix(1,0,2,1) Matrix(175,572,-108,-353) -> Matrix(3,2,4,3) Matrix(109,352,-48,-155) -> Matrix(3,2,-14,-9) Matrix(109,308,-86,-243) -> Matrix(1,0,2,1) Matrix(111,308,40,111) -> Matrix(1,0,2,1) Matrix(65,176,24,65) -> Matrix(5,2,2,1) Matrix(133,352,-116,-307) -> Matrix(5,2,-8,-3) Matrix(219,572,-152,-397) -> Matrix(7,2,-4,-1) Matrix(307,792,-188,-485) -> Matrix(1,0,4,1) Matrix(463,1188,-334,-857) -> Matrix(1,0,2,1) Matrix(87,220,-70,-177) -> Matrix(7,2,-4,-1) Matrix(109,264,-64,-155) -> Matrix(1,0,0,1) Matrix(461,1100,-360,-859) -> Matrix(3,2,-2,-1) Matrix(351,836,-296,-705) -> Matrix(7,4,-2,-1) Matrix(131,308,-94,-221) -> Matrix(1,0,2,1) Matrix(439,1012,-344,-793) -> Matrix(1,0,2,1) Matrix(441,1012,-268,-615) -> Matrix(1,0,4,1) Matrix(309,704,-212,-483) -> Matrix(15,4,-4,-1) Matrix(375,836,-266,-593) -> Matrix(15,2,-8,-1) Matrix(199,440,90,199) -> Matrix(1,0,16,1) Matrix(21,44,10,21) -> Matrix(1,0,2,1) Matrix(23,44,12,23) -> Matrix(1,0,-2,1) Matrix(241,440,132,241) -> Matrix(1,0,-16,1) Matrix(243,440,-206,-373) -> Matrix(9,-2,-4,1) Matrix(197,352,-136,-243) -> Matrix(5,-2,-2,1) Matrix(397,704,-322,-571) -> Matrix(1,-2,0,1) Matrix(923,1628,-724,-1277) -> Matrix(1,0,-2,1) Matrix(813,1408,-496,-859) -> Matrix(1,0,0,1) Matrix(791,1364,-664,-1145) -> Matrix(1,4,0,1) Matrix(2047,3520,-1266,-2177) -> Matrix(1,2,0,1) Matrix(285,484,116,197) -> Matrix(1,0,6,1) Matrix(287,484,118,199) -> Matrix(1,0,-6,1) Matrix(1341,2200,-1060,-1739) -> Matrix(1,-2,0,1) Matrix(1187,1936,458,747) -> Matrix(1,0,0,1) Matrix(1189,1936,460,749) -> Matrix(1,0,0,1) Matrix(1033,1672,312,505) -> Matrix(3,-2,-4,3) Matrix(3673,5940,802,1297) -> Matrix(3,-4,-2,3) Matrix(109,176,-96,-155) -> Matrix(1,0,-2,1) Matrix(111,176,70,111) -> Matrix(1,-2,-2,5) Matrix(197,308,126,197) -> Matrix(1,0,-2,1) Matrix(461,704,-332,-507) -> Matrix(1,-2,0,1) Matrix(329,484,104,153) -> Matrix(1,-6,0,1) Matrix(331,484,106,155) -> Matrix(1,6,0,1) Matrix(1409,2024,-1102,-1583) -> Matrix(1,2,-2,-3) Matrix(1167,1672,446,639) -> Matrix(3,2,4,3) Matrix(1363,1936,402,571) -> Matrix(1,-8,0,1) Matrix(1365,1936,404,573) -> Matrix(1,8,0,1) Matrix(373,528,-296,-419) -> Matrix(1,2,0,1) Matrix(4027,5588,-3186,-4421) -> Matrix(1,2,-2,-3) Matrix(287,396,208,287) -> Matrix(1,0,-2,1) Matrix(65,88,48,65) -> Matrix(1,2,-2,-3) Matrix(373,484,84,109) -> Matrix(1,2,-2,-3) Matrix(375,484,86,111) -> Matrix(3,2,-2,-1) Matrix(4643,5940,1772,2267) -> Matrix(3,4,2,3) Matrix(6071,7744,1310,1671) -> Matrix(1,0,0,1) Matrix(6073,7744,1312,1673) -> Matrix(1,0,0,1) Matrix(9569,12100,2000,2529) -> Matrix(3,4,-4,-5) Matrix(9571,12100,2002,2531) -> Matrix(5,4,-4,-3) Matrix(287,352,234,287) -> Matrix(5,6,-6,-7) Matrix(109,132,90,109) -> Matrix(1,0,0,1) Matrix(1627,1936,258,307) -> Matrix(1,-12,0,1) Matrix(1629,1936,260,309) -> Matrix(1,12,0,1) Matrix(417,484,56,65) -> Matrix(9,10,-10,-11) Matrix(419,484,58,67) -> Matrix(11,10,-10,-9) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(155,-176,96,-109) -> Matrix(1,0,-2,1) Matrix(263,-308,76,-89) -> Matrix(5,4,-4,-3) Matrix(705,-836,296,-351) -> Matrix(7,4,-2,-1) Matrix(177,-220,70,-87) -> Matrix(3,2,4,3) Matrix(243,-308,86,-109) -> Matrix(1,0,2,1) Matrix(793,-1012,344,-439) -> Matrix(1,0,2,1) Matrix(859,-1100,360,-461) -> Matrix(3,2,-2,-1) Matrix(67,-88,16,-21) -> Matrix(3,2,-2,-1) Matrix(221,-308,94,-131) -> Matrix(1,0,2,1) Matrix(219,-308,32,-45) -> Matrix(5,4,-4,-3) Matrix(529,-748,186,-263) -> Matrix(3,2,-2,-1) Matrix(309,-440,92,-131) -> Matrix(1,0,2,1) Matrix(397,-572,152,-219) -> Matrix(3,2,4,3) Matrix(243,-352,136,-197) -> Matrix(3,2,-14,-9) Matrix(199,-308,42,-65) -> Matrix(1,0,2,1) Matrix(219,-352,28,-45) -> Matrix(5,2,-8,-3) Matrix(353,-572,108,-175) -> Matrix(7,2,-4,-1) Matrix(485,-792,188,-307) -> Matrix(1,0,4,1) Matrix(725,-1188,202,-331) -> Matrix(1,0,2,1) Matrix(133,-220,26,-43) -> Matrix(7,2,-4,-1) Matrix(155,-264,64,-109) -> Matrix(1,0,0,1) Matrix(639,-1100,140,-241) -> Matrix(3,2,-2,-1) Matrix(485,-836,76,-131) -> Matrix(7,4,-2,-1) Matrix(177,-308,50,-87) -> Matrix(1,0,2,1) Matrix(573,-1012,124,-219) -> Matrix(1,0,2,1) Matrix(571,-1012,224,-397) -> Matrix(1,0,4,1) Matrix(395,-704,124,-221) -> Matrix(15,4,-4,-1) Matrix(461,-836,134,-243) -> Matrix(15,2,-8,-1) Matrix(197,-440,30,-67) -> Matrix(9,-2,-4,1) Matrix(155,-352,48,-109) -> Matrix(5,-2,-2,1) Matrix(307,-704,58,-133) -> Matrix(1,-2,0,1) Matrix(705,-1628,152,-351) -> Matrix(1,0,-2,1) Matrix(595,-1408,232,-549) -> Matrix(1,0,0,1) Matrix(573,-1364,92,-219) -> Matrix(1,4,0,1) Matrix(1473,-3520,562,-1343) -> Matrix(1,2,0,1) Matrix(859,-2200,180,-461) -> Matrix(1,-2,0,1) Matrix(67,-176,8,-21) -> Matrix(1,0,-2,1) Matrix(243,-704,68,-197) -> Matrix(1,-2,0,1) Matrix(615,-2024,134,-441) -> Matrix(1,2,-2,-3) Matrix(155,-528,32,-109) -> Matrix(1,2,0,1) Matrix(1561,-5588,326,-1167) -> Matrix(1,2,-2,-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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 Degree of the the map X: 30 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 2/1 11/5 12/5 22/9 44/17 11/4 3/1 22/7 33/10 10/3 44/13 18/5 11/3 4/1 22/5 9/2 88/19 14/3 110/23 5/1 16/3 11/2 6/1 44/7 20/3 7/1 22/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 -1/2 1/0 1/1 -1/1 0/1 7/6 -1/1 -4/5 13/11 -2/3 -3/5 6/5 0/1 11/9 -1/1 16/13 -1/1 -3/4 5/4 -2/3 -1/2 14/11 0/1 23/18 -1/1 0/1 9/7 -1/1 0/1 4/3 -1/1 -1/2 11/8 -1/2 18/13 0/1 7/5 -1/1 0/1 24/17 -2/3 -3/5 17/12 -4/7 -1/2 10/7 0/1 13/9 -1/1 -2/3 3/2 -1/2 0/1 14/9 0/1 11/7 -1/2 8/5 -1/2 -1/3 29/18 -1/3 -4/13 21/13 -1/3 0/1 13/8 -1/3 0/1 18/11 0/1 23/14 -1/3 0/1 5/3 -1/4 0/1 12/7 -1/1 0/1 31/18 -1/1 -2/3 19/11 -1/2 -2/5 7/4 -1/3 0/1 23/13 -1/3 0/1 16/9 -1/3 -1/4 25/14 -1/4 -2/9 9/5 -1/5 0/1 20/11 -1/9 0/1 11/6 0/1 2/1 0/1 11/5 0/1 20/9 0/1 1/7 9/4 0/1 1/3 16/7 1/2 1/1 23/10 0/1 1/1 30/13 0/1 7/3 0/1 1/1 26/11 0/1 19/8 2/1 1/0 50/21 -4/1 31/13 -2/1 -1/1 43/18 -2/1 -1/1 12/5 -1/1 0/1 17/7 -1/4 0/1 22/9 0/1 5/2 0/1 1/2 28/11 1/1 1/0 23/9 0/1 1/1 41/16 2/1 1/0 18/7 0/1 31/12 0/1 1/1 44/17 1/2 1/0 13/5 0/1 1/1 34/13 2/3 55/21 1/1 76/29 1/1 2/1 21/8 0/1 1/1 8/3 1/1 1/0 11/4 1/0 14/5 0/1 17/6 2/1 1/0 20/7 0/1 1/1 3/1 0/1 1/0 22/7 1/0 19/6 -6/1 1/0 16/5 -3/1 1/0 13/4 -2/1 -1/1 23/7 -2/1 -1/1 33/10 -1/1 10/3 0/1 27/8 4/1 1/0 44/13 1/0 17/5 -4/1 1/0 24/7 -3/1 -2/1 31/9 -2/1 -5/3 7/2 -1/1 0/1 25/7 -2/1 1/0 68/19 -2/1 -1/1 43/12 -1/1 0/1 18/5 0/1 11/3 1/0 4/1 -1/1 1/0 13/3 -2/1 -1/1 22/5 -1/1 9/2 -1/1 0/1 32/7 -2/1 -1/1 55/12 -1/1 23/5 -1/1 0/1 37/8 -1/1 0/1 88/19 -1/2 1/0 51/11 -1/1 0/1 14/3 0/1 19/4 0/1 1/0 43/9 -2/1 -1/1 110/23 -1/1 67/14 -1/1 -2/3 24/5 -1/1 0/1 5/1 -2/1 1/0 21/4 -2/1 -1/1 16/3 -3/2 -1/1 11/2 -1/1 6/1 0/1 25/4 6/1 1/0 44/7 1/0 19/3 -6/1 1/0 13/2 -3/1 -2/1 20/3 -2/1 -5/3 7/1 -4/3 -1/1 22/3 -1/1 15/2 -1/1 -6/7 8/1 -1/1 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(155,-176,96,-109) (1/1,7/6) -> (29/18,21/13) Hyperbolic Matrix(263,-308,76,-89) (7/6,13/11) -> (31/9,7/2) Hyperbolic Matrix(705,-836,296,-351) (13/11,6/5) -> (50/21,31/13) Hyperbolic Matrix(109,-132,19,-23) (6/5,11/9) -> (11/2,6/1) Hyperbolic Matrix(287,-352,53,-65) (11/9,16/13) -> (16/3,11/2) Hyperbolic Matrix(177,-220,70,-87) (16/13,5/4) -> (5/2,28/11) Hyperbolic Matrix(243,-308,86,-109) (5/4,14/11) -> (14/5,17/6) Hyperbolic Matrix(793,-1012,344,-439) (14/11,23/18) -> (23/10,30/13) Hyperbolic Matrix(859,-1100,360,-461) (23/18,9/7) -> (31/13,43/18) Hyperbolic Matrix(67,-88,16,-21) (9/7,4/3) -> (4/1,13/3) Hyperbolic Matrix(65,-88,17,-23) (4/3,11/8) -> (11/3,4/1) Hyperbolic Matrix(287,-396,79,-109) (11/8,18/13) -> (18/5,11/3) Hyperbolic 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(309,-440,92,-131) (17/12,10/7) -> (10/3,27/8) 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(199,-308,42,-65) (3/2,14/9) -> (14/3,19/4) Hyperbolic Matrix(197,-308,71,-111) (14/9,11/7) -> (11/4,14/5) Hyperbolic Matrix(111,-176,41,-65) (11/7,8/5) -> (8/3,11/4) 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(485,-792,188,-307) (13/8,18/11) -> (18/7,31/12) Hyperbolic Matrix(725,-1188,202,-331) (18/11,23/14) -> (43/12,18/5) Hyperbolic Matrix(133,-220,26,-43) (23/14,5/3) -> (5/1,21/4) Hyperbolic Matrix(155,-264,64,-109) (5/3,12/7) -> (12/5,17/7) Hyperbolic Matrix(639,-1100,140,-241) (12/7,31/18) -> (9/2,32/7) Hyperbolic Matrix(485,-836,76,-131) (31/18,19/11) -> (19/3,13/2) Hyperbolic Matrix(177,-308,50,-87) (19/11,7/4) -> (7/2,25/7) Hyperbolic Matrix(573,-1012,124,-219) (7/4,23/13) -> (23/5,37/8) Hyperbolic Matrix(571,-1012,224,-397) (23/13,16/9) -> (28/11,23/9) Hyperbolic Matrix(395,-704,124,-221) (16/9,25/14) -> (19/6,16/5) Hyperbolic Matrix(461,-836,134,-243) (9/5,20/11) -> (24/7,31/9) Hyperbolic Matrix(241,-440,109,-199) (20/11,11/6) -> (11/5,20/9) Hyperbolic Matrix(23,-44,11,-21) (11/6,2/1) -> (2/1,11/5) Parabolic Matrix(197,-440,30,-67) (20/9,9/4) -> (13/2,20/3) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(705,-1628,152,-351) (30/13,7/3) -> (51/11,14/3) Hyperbolic Matrix(595,-1408,232,-549) (26/11,19/8) -> (41/16,18/7) Hyperbolic Matrix(573,-1364,92,-219) (19/8,50/21) -> (6/1,25/4) Hyperbolic Matrix(1473,-3520,562,-1343) (43/18,12/5) -> (76/29,21/8) Hyperbolic Matrix(199,-484,81,-197) (17/7,22/9) -> (22/9,5/2) Parabolic Matrix(859,-2200,180,-461) (23/9,41/16) -> (19/4,43/9) Hyperbolic Matrix(749,-1936,289,-747) (31/12,44/17) -> (44/17,13/5) Parabolic Matrix(639,-1672,193,-505) (34/13,55/21) -> (33/10,10/3) Hyperbolic Matrix(2267,-5940,495,-1297) (55/21,76/29) -> (32/7,55/12) Hyperbolic Matrix(67,-176,8,-21) (21/8,8/3) -> (8/1,1/0) Hyperbolic Matrix(243,-704,68,-197) (20/7,3/1) -> (25/7,68/19) Hyperbolic Matrix(155,-484,49,-153) (3/1,22/7) -> (22/7,19/6) Parabolic Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(573,-1936,169,-571) (27/8,44/13) -> (44/13,17/5) Parabolic Matrix(155,-528,32,-109) (17/5,24/7) -> (24/5,5/1) Hyperbolic Matrix(1561,-5588,326,-1167) (68/19,43/12) -> (67/14,24/5) Hyperbolic Matrix(111,-484,25,-109) (13/3,22/5) -> (22/5,9/2) Parabolic Matrix(1673,-7744,361,-1671) (37/8,88/19) -> (88/19,51/11) Parabolic Matrix(2531,-12100,529,-2529) (43/9,110/23) -> (110/23,67/14) Parabolic Matrix(309,-1936,49,-307) (25/4,44/7) -> (44/7,19/3) Parabolic Matrix(67,-484,9,-65) (7/1,22/3) -> (22/3,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,0,1) Matrix(155,-176,96,-109) -> Matrix(1,0,-2,1) Matrix(263,-308,76,-89) -> Matrix(5,4,-4,-3) Matrix(705,-836,296,-351) -> Matrix(7,4,-2,-1) Matrix(109,-132,19,-23) -> Matrix(1,0,0,1) Matrix(287,-352,53,-65) -> Matrix(7,6,-6,-5) Matrix(177,-220,70,-87) -> Matrix(3,2,4,3) Matrix(243,-308,86,-109) -> Matrix(1,0,2,1) Matrix(793,-1012,344,-439) -> Matrix(1,0,2,1) Matrix(859,-1100,360,-461) -> Matrix(3,2,-2,-1) Matrix(67,-88,16,-21) -> Matrix(3,2,-2,-1) Matrix(65,-88,17,-23) -> Matrix(3,2,-2,-1) Matrix(287,-396,79,-109) -> Matrix(1,0,2,1) Matrix(221,-308,94,-131) -> Matrix(1,0,2,1) Matrix(219,-308,32,-45) -> Matrix(5,4,-4,-3) Matrix(529,-748,186,-263) -> Matrix(3,2,-2,-1) Matrix(309,-440,92,-131) -> Matrix(1,0,2,1) Matrix(397,-572,152,-219) -> Matrix(3,2,4,3) Matrix(243,-352,136,-197) -> Matrix(3,2,-14,-9) Matrix(199,-308,42,-65) -> Matrix(1,0,2,1) Matrix(197,-308,71,-111) -> Matrix(1,0,2,1) Matrix(111,-176,41,-65) -> Matrix(5,2,2,1) Matrix(219,-352,28,-45) -> Matrix(5,2,-8,-3) Matrix(353,-572,108,-175) -> Matrix(7,2,-4,-1) Matrix(485,-792,188,-307) -> Matrix(1,0,4,1) Matrix(725,-1188,202,-331) -> Matrix(1,0,2,1) Matrix(133,-220,26,-43) -> Matrix(7,2,-4,-1) Matrix(155,-264,64,-109) -> Matrix(1,0,0,1) Matrix(639,-1100,140,-241) -> Matrix(3,2,-2,-1) Matrix(485,-836,76,-131) -> Matrix(7,4,-2,-1) Matrix(177,-308,50,-87) -> Matrix(1,0,2,1) Matrix(573,-1012,124,-219) -> Matrix(1,0,2,1) Matrix(571,-1012,224,-397) -> Matrix(1,0,4,1) Matrix(395,-704,124,-221) -> Matrix(15,4,-4,-1) Matrix(461,-836,134,-243) -> Matrix(15,2,-8,-1) Matrix(241,-440,109,-199) -> Matrix(1,0,16,1) Matrix(23,-44,11,-21) -> Matrix(1,0,2,1) Matrix(197,-440,30,-67) -> Matrix(9,-2,-4,1) Matrix(155,-352,48,-109) -> Matrix(5,-2,-2,1) Matrix(307,-704,58,-133) -> Matrix(1,-2,0,1) Matrix(705,-1628,152,-351) -> Matrix(1,0,-2,1) Matrix(595,-1408,232,-549) -> Matrix(1,0,0,1) Matrix(573,-1364,92,-219) -> Matrix(1,4,0,1) Matrix(1473,-3520,562,-1343) -> Matrix(1,2,0,1) Matrix(199,-484,81,-197) -> Matrix(1,0,6,1) Matrix(859,-2200,180,-461) -> Matrix(1,-2,0,1) Matrix(749,-1936,289,-747) -> Matrix(1,0,0,1) Matrix(639,-1672,193,-505) -> Matrix(3,-2,-4,3) Matrix(2267,-5940,495,-1297) -> Matrix(3,-4,-2,3) Matrix(67,-176,8,-21) -> Matrix(1,0,-2,1) Matrix(243,-704,68,-197) -> Matrix(1,-2,0,1) Matrix(155,-484,49,-153) -> Matrix(1,-6,0,1) Matrix(615,-2024,134,-441) -> Matrix(1,2,-2,-3) Matrix(573,-1936,169,-571) -> Matrix(1,-8,0,1) Matrix(155,-528,32,-109) -> Matrix(1,2,0,1) Matrix(1561,-5588,326,-1167) -> Matrix(1,2,-2,-3) Matrix(111,-484,25,-109) -> Matrix(1,2,-2,-3) Matrix(1673,-7744,361,-1671) -> Matrix(1,0,0,1) Matrix(2531,-12100,529,-2529) -> Matrix(3,4,-4,-5) Matrix(309,-1936,49,-307) -> Matrix(1,-12,0,1) Matrix(67,-484,9,-65) -> Matrix(9,10,-10,-11) 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): 15 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (-1/1,0/1) 0 1 2/1 0/1 2 11 11/5 0/1 7 2 20/9 (0/1,1/7) 0 11 9/4 (0/1,1/3) 0 22 16/7 (1/2,1/1) 0 11 23/10 (0/1,1/1) 0 22 7/3 (0/1,1/1) 0 22 19/8 (2/1,1/0) 0 22 31/13 (-2/1,-1/1) 0 22 12/5 (-1/1,0/1) 0 11 22/9 0/1 6 1 5/2 (0/1,1/2) 0 22 23/9 (0/1,1/1) 0 22 18/7 0/1 2 11 44/17 (0/1,1/1) 0 1 13/5 (0/1,1/1) 0 22 21/8 (0/1,1/1) 0 22 8/3 (1/1,1/0) 0 11 11/4 1/0 1 2 14/5 0/1 2 11 3/1 (0/1,1/0) 0 22 22/7 1/0 6 1 16/5 (-3/1,1/0) 0 11 13/4 (-2/1,-1/1) 0 22 23/7 (-2/1,-1/1) 0 22 33/10 -1/1 4 2 10/3 0/1 2 11 44/13 1/0 8 1 17/5 (-4/1,1/0) 0 22 24/7 (-3/1,-2/1) 0 11 7/2 (-1/1,0/1) 0 22 25/7 (-2/1,1/0) 0 22 43/12 (-1/1,0/1) 0 22 18/5 0/1 2 11 11/3 1/0 1 2 4/1 (-1/1,1/0) 0 11 22/5 -1/1 2 1 9/2 (-1/1,0/1) 0 22 32/7 (-2/1,-1/1) 0 11 55/12 -1/1 4 2 23/5 (-1/1,0/1) 0 22 37/8 (-1/1,0/1) 0 22 88/19 (-1/1,0/1) 0 1 14/3 0/1 2 11 19/4 (0/1,1/0) 0 22 43/9 (-2/1,-1/1) 0 22 110/23 -1/1 4 1 24/5 (-1/1,0/1) 0 11 5/1 (-2/1,1/0) 0 22 21/4 (-2/1,-1/1) 0 22 16/3 (-3/2,-1/1) 0 11 11/2 -1/1 3 2 6/1 0/1 2 11 44/7 1/0 12 1 19/3 (-6/1,1/0) 0 22 13/2 (-3/1,-2/1) 0 22 20/3 (-2/1,-5/3) 0 11 7/1 (-4/3,-1/1) 0 22 22/3 -1/1 10 1 8/1 (-1/1,-1/2) 0 11 1/0 (-1/1,0/1) 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(21,-44,10,-21) (2/1,11/5) -> (2/1,11/5) Reflection Matrix(199,-440,90,-199) (11/5,20/9) -> (11/5,20/9) Reflection Matrix(197,-440,30,-67) (20/9,9/4) -> (13/2,20/3) Hyperbolic Matrix(155,-352,48,-109) (9/4,16/7) -> (16/5,13/4) Hyperbolic Matrix(307,-704,58,-133) (16/7,23/10) -> (21/4,16/3) Hyperbolic Matrix(439,-1012,95,-219) (23/10,7/3) -> (23/5,37/8) Glide Reflection Matrix(131,-308,37,-87) (7/3,19/8) -> (7/2,25/7) Glide Reflection Matrix(351,-836,55,-131) (19/8,31/13) -> (19/3,13/2) Glide Reflection Matrix(461,-1100,101,-241) (31/13,12/5) -> (9/2,32/7) Glide Reflection Matrix(109,-264,45,-109) (12/5,22/9) -> (12/5,22/9) Reflection Matrix(89,-220,36,-89) (22/9,5/2) -> (22/9,5/2) Reflection Matrix(87,-220,17,-43) (5/2,23/9) -> (5/1,21/4) Glide Reflection Matrix(463,-1188,129,-331) (23/9,18/7) -> (43/12,18/5) Glide Reflection Matrix(307,-792,119,-307) (18/7,44/17) -> (18/7,44/17) Reflection Matrix(441,-1144,170,-441) (44/17,13/5) -> (44/17,13/5) Reflection Matrix(219,-572,67,-175) (13/5,21/8) -> (13/4,23/7) Glide 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(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(109,-308,23,-65) (14/5,3/1) -> (14/3,19/4) Glide Reflection Matrix(43,-132,14,-43) (3/1,22/7) -> (3/1,22/7) Reflection Matrix(111,-352,35,-111) (22/7,16/5) -> (22/7,16/5) Reflection Matrix(615,-2024,134,-441) (23/7,33/10) -> (55/12,23/5) Hyperbolic Matrix(199,-660,60,-199) (33/10,10/3) -> (33/10,10/3) Reflection Matrix(131,-440,39,-131) (10/3,44/13) -> (10/3,44/13) Reflection Matrix(441,-1496,130,-441) (44/13,17/5) -> (44/13,17/5) Reflection Matrix(155,-528,32,-109) (17/5,24/7) -> (24/5,5/1) Hyperbolic Matrix(89,-308,13,-45) (24/7,7/2) -> (20/3,7/1) Glide Reflection Matrix(529,-1892,111,-397) (25/7,43/12) -> (19/4,43/9) Glide Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(21,-88,5,-21) (4/1,22/5) -> (4/1,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(769,-3520,168,-769) (32/7,55/12) -> (32/7,55/12) Reflection Matrix(1407,-6512,304,-1407) (37/8,88/19) -> (37/8,88/19) Reflection Matrix(265,-1232,57,-265) (88/19,14/3) -> (88/19,14/3) Reflection Matrix(1979,-9460,414,-1979) (43/9,110/23) -> (43/9,110/23) Reflection Matrix(551,-2640,115,-551) (110/23,24/5) -> (110/23,24/5) Reflection Matrix(65,-352,12,-65) (16/3,11/2) -> (16/3,11/2) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(43,-264,7,-43) (6/1,44/7) -> (6/1,44/7) Reflection Matrix(265,-1672,42,-265) (44/7,19/3) -> (44/7,19/3) Reflection Matrix(43,-308,6,-43) (7/1,22/3) -> (7/1,22/3) Reflection Matrix(23,-176,3,-23) (22/3,8/1) -> (22/3,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(-1,0,2,1) (0/1,2/1) -> (-1/1,0/1) Matrix(21,-44,10,-21) -> Matrix(1,0,0,-1) (2/1,11/5) -> (0/1,1/0) Matrix(199,-440,90,-199) -> Matrix(1,0,14,-1) (11/5,20/9) -> (0/1,1/7) Matrix(197,-440,30,-67) -> Matrix(9,-2,-4,1) Matrix(155,-352,48,-109) -> Matrix(5,-2,-2,1) Matrix(307,-704,58,-133) -> Matrix(1,-2,0,1) 1/0 Matrix(439,-1012,95,-219) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(131,-308,37,-87) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(351,-836,55,-131) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(461,-1100,101,-241) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(109,-264,45,-109) -> Matrix(-1,0,2,1) (12/5,22/9) -> (-1/1,0/1) Matrix(89,-220,36,-89) -> Matrix(1,0,4,-1) (22/9,5/2) -> (0/1,1/2) Matrix(87,-220,17,-43) -> Matrix(3,-2,-2,1) Matrix(463,-1188,129,-331) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(307,-792,119,-307) -> Matrix(1,0,2,-1) (18/7,44/17) -> (0/1,1/1) Matrix(441,-1144,170,-441) -> Matrix(1,0,2,-1) (44/17,13/5) -> (0/1,1/1) Matrix(219,-572,67,-175) -> Matrix(3,-2,-2,1) Matrix(67,-176,8,-21) -> Matrix(1,0,-2,1) 0/1 Matrix(65,-176,24,-65) -> Matrix(-1,2,0,1) (8/3,11/4) -> (1/1,1/0) Matrix(111,-308,40,-111) -> Matrix(1,0,0,-1) (11/4,14/5) -> (0/1,1/0) Matrix(109,-308,23,-65) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(43,-132,14,-43) -> Matrix(1,0,0,-1) (3/1,22/7) -> (0/1,1/0) Matrix(111,-352,35,-111) -> Matrix(1,6,0,-1) (22/7,16/5) -> (-3/1,1/0) Matrix(615,-2024,134,-441) -> Matrix(1,2,-2,-3) -1/1 Matrix(199,-660,60,-199) -> Matrix(-1,0,2,1) (33/10,10/3) -> (-1/1,0/1) Matrix(131,-440,39,-131) -> Matrix(1,0,0,-1) (10/3,44/13) -> (0/1,1/0) Matrix(441,-1496,130,-441) -> Matrix(1,8,0,-1) (44/13,17/5) -> (-4/1,1/0) Matrix(155,-528,32,-109) -> Matrix(1,2,0,1) 1/0 Matrix(89,-308,13,-45) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(529,-1892,111,-397) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(109,-396,30,-109) -> Matrix(1,0,0,-1) (18/5,11/3) -> (0/1,1/0) Matrix(23,-88,6,-23) -> Matrix(1,2,0,-1) (11/3,4/1) -> (-1/1,1/0) Matrix(21,-88,5,-21) -> Matrix(1,2,0,-1) (4/1,22/5) -> (-1/1,1/0) Matrix(89,-396,20,-89) -> Matrix(-1,0,2,1) (22/5,9/2) -> (-1/1,0/1) Matrix(769,-3520,168,-769) -> Matrix(3,4,-2,-3) (32/7,55/12) -> (-2/1,-1/1) Matrix(1407,-6512,304,-1407) -> Matrix(-1,0,2,1) (37/8,88/19) -> (-1/1,0/1) Matrix(265,-1232,57,-265) -> Matrix(-1,0,2,1) (88/19,14/3) -> (-1/1,0/1) Matrix(1979,-9460,414,-1979) -> Matrix(3,4,-2,-3) (43/9,110/23) -> (-2/1,-1/1) Matrix(551,-2640,115,-551) -> Matrix(-1,0,2,1) (110/23,24/5) -> (-1/1,0/1) Matrix(65,-352,12,-65) -> Matrix(5,6,-4,-5) (16/3,11/2) -> (-3/2,-1/1) Matrix(23,-132,4,-23) -> Matrix(-1,0,2,1) (11/2,6/1) -> (-1/1,0/1) Matrix(43,-264,7,-43) -> Matrix(1,0,0,-1) (6/1,44/7) -> (0/1,1/0) Matrix(265,-1672,42,-265) -> Matrix(1,12,0,-1) (44/7,19/3) -> (-6/1,1/0) Matrix(43,-308,6,-43) -> Matrix(7,8,-6,-7) (7/1,22/3) -> (-4/3,-1/1) Matrix(23,-176,3,-23) -> Matrix(3,2,-4,-3) (22/3,8/1) -> (-1/1,-1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.