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): 768 Minimal number of generators: 129 Number of equivalence classes of cusps: 64 Genus: 33 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/1 -8/1 -6/1 -16/3 -14/3 -9/2 -4/1 -26/7 -18/5 -10/3 -36/11 -3/1 -20/7 -8/3 -12/5 -16/7 -2/1 -20/11 -12/7 -18/11 -36/23 -3/2 -4/3 -6/5 0/1 1/1 6/5 4/3 3/2 36/23 18/11 12/7 2/1 24/11 16/7 12/5 120/49 5/2 8/3 48/17 20/7 3/1 36/11 96/29 10/3 24/7 7/2 18/5 11/3 4/1 48/11 22/5 9/2 14/3 24/5 5/1 16/3 11/2 6/1 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -1/3 -8/1 -1/3 -15/2 -1/3 -7/1 -3/10 -6/1 -1/4 -17/3 -1/6 -11/2 -1/4 -16/3 -2/9 -5/1 -1/4 -14/3 -1/5 -23/5 -3/20 -9/2 -1/5 -4/1 -2/11 0/1 -15/4 -1/5 -26/7 -1/5 -11/3 -1/6 -18/5 -1/6 -25/7 -3/22 -7/2 -1/6 -10/3 -1/7 -33/10 -1/5 -23/7 -5/28 -36/11 -1/6 -13/4 -1/6 -16/5 -2/13 -3/1 -1/7 -20/7 -4/29 -2/15 -17/6 -7/52 -14/5 -3/23 -25/9 -11/86 -36/13 -1/8 -11/4 -1/8 -8/3 -1/8 -13/5 -1/8 -18/7 -1/8 -23/9 -13/108 -28/11 -8/67 -2/17 -5/2 -3/26 -12/5 -1/9 -19/8 -5/46 -45/19 -1/9 -71/30 -5/44 -26/11 -1/9 -33/14 -1/9 -7/3 -3/28 -23/10 -17/160 -16/7 -2/19 -25/11 -19/182 -9/4 -3/29 -38/17 -11/107 -29/13 -17/166 -20/9 -4/39 -6/59 -11/5 -1/10 -2/1 -1/11 -13/7 -1/12 -24/13 -1/12 -11/6 -1/12 -31/17 -13/158 -20/11 -6/73 -4/49 -29/16 -17/208 -9/5 -3/37 -25/14 -19/236 -16/9 -2/25 -23/13 -17/214 -7/4 -3/38 -12/7 -1/13 -17/10 -5/66 -22/13 -1/13 -71/42 -7/90 -120/71 -1/13 -49/29 -13/170 -27/16 -1/13 -5/3 -3/40 -28/17 -2/27 -8/109 -51/31 -3/41 -23/14 -13/178 -18/11 -1/14 -13/8 -1/14 -8/5 -1/14 -11/7 -1/14 -36/23 -1/14 -25/16 -11/156 -14/9 -3/43 -31/20 -13/188 -48/31 -2/29 -17/11 -7/102 -20/13 -2/29 -4/59 -23/15 -9/134 -3/2 -1/15 -19/13 -3/46 -16/11 -2/31 -13/9 -1/16 -36/25 -1/16 -23/16 -5/82 -33/23 -1/17 -43/30 -1/22 -96/67 0/1 -53/37 -1/8 -10/7 -1/15 -17/12 -1/16 -24/17 -1/16 -7/5 -1/16 -25/18 -3/44 -18/13 -1/16 -11/8 -1/16 -4/3 -2/33 0/1 -13/10 -1/16 -48/37 -2/33 -35/27 -3/50 -22/17 -1/17 -31/24 -1/18 -9/7 -1/17 -23/18 -3/46 -14/11 -1/17 -19/15 -3/50 -24/19 -1/17 -5/4 -1/18 -21/17 -1/17 -16/13 -2/35 -11/9 -1/18 -6/5 -1/18 -13/11 -1/18 -20/17 -4/73 -2/37 -7/6 -3/56 -15/13 -1/19 -8/7 -1/19 -9/8 -1/19 -1/1 -1/22 0/1 0/1 1/1 1/22 9/8 1/19 8/7 1/19 15/13 1/19 7/6 3/56 6/5 1/18 17/14 1/16 11/9 1/18 16/13 2/35 5/4 1/18 14/11 1/17 23/18 3/46 9/7 1/17 4/3 0/1 2/33 15/11 1/17 26/19 1/17 11/8 1/16 18/13 1/16 25/18 3/44 7/5 1/16 10/7 1/15 33/23 1/17 23/16 5/82 36/25 1/16 13/9 1/16 16/11 2/31 3/2 1/15 20/13 4/59 2/29 17/11 7/102 14/9 3/43 25/16 11/156 36/23 1/14 11/7 1/14 8/5 1/14 13/8 1/14 18/11 1/14 23/14 13/178 28/17 8/109 2/27 5/3 3/40 12/7 1/13 19/11 5/64 45/26 1/13 71/41 5/66 26/15 1/13 33/19 1/13 7/4 3/38 23/13 17/214 16/9 2/25 25/14 19/236 9/5 3/37 38/21 11/135 29/16 17/208 20/11 4/49 6/73 11/6 1/12 2/1 1/11 13/6 1/10 24/11 1/10 11/5 1/10 31/14 13/128 20/9 6/59 4/39 29/13 17/166 9/4 3/29 25/11 19/182 16/7 2/19 23/10 17/160 7/3 3/28 12/5 1/9 17/7 5/44 22/9 1/9 71/29 7/64 120/49 1/9 49/20 13/116 27/11 1/9 5/2 3/26 28/11 2/17 8/67 51/20 3/25 23/9 13/108 18/7 1/8 13/5 1/8 8/3 1/8 11/4 1/8 36/13 1/8 25/9 11/86 14/5 3/23 31/11 13/98 48/17 2/15 17/6 7/52 20/7 2/15 4/29 23/8 9/64 3/1 1/7 19/6 3/20 16/5 2/13 13/4 1/6 36/11 1/6 23/7 5/28 33/10 1/5 43/13 1/0 96/29 0/1 53/16 1/14 10/3 1/7 17/5 1/6 24/7 1/6 7/2 1/6 25/7 3/22 18/5 1/6 11/3 1/6 4/1 0/1 2/11 13/3 1/6 48/11 2/11 35/8 3/16 22/5 1/5 31/7 1/4 9/2 1/5 23/5 3/20 14/3 1/5 19/4 3/16 24/5 1/5 5/1 1/4 21/4 1/5 16/3 2/9 11/2 1/4 6/1 1/4 13/2 1/4 20/3 4/15 2/7 7/1 3/10 15/2 1/3 8/1 1/3 9/1 1/3 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(23,240,16,167) (-9/1,1/0) -> (33/23,23/16) Hyperbolic Matrix(23,192,20,167) (-9/1,-8/1) -> (8/7,15/13) Hyperbolic Matrix(25,192,22,169) (-8/1,-15/2) -> (9/8,8/7) Hyperbolic Matrix(71,528,16,119) (-15/2,-7/1) -> (31/7,9/2) Hyperbolic Matrix(23,144,-4,-25) (-7/1,-6/1) -> (-6/1,-17/3) Parabolic Matrix(95,528,-52,-289) (-17/3,-11/2) -> (-11/6,-31/17) Hyperbolic Matrix(71,384,22,119) (-11/2,-16/3) -> (16/5,13/4) Hyperbolic Matrix(73,384,-50,-263) (-16/3,-5/1) -> (-19/13,-16/11) Hyperbolic Matrix(71,336,-56,-265) (-5/1,-14/3) -> (-14/11,-19/15) Hyperbolic Matrix(145,672,52,241) (-14/3,-23/5) -> (25/9,14/5) Hyperbolic Matrix(95,432,42,191) (-23/5,-9/2) -> (9/4,25/11) Hyperbolic Matrix(23,96,-6,-25) (-9/2,-4/1) -> (-4/1,-15/4) Parabolic Matrix(335,1248,-142,-529) (-15/4,-26/7) -> (-26/11,-33/14) Hyperbolic Matrix(311,1152,-240,-889) (-26/7,-11/3) -> (-35/27,-22/17) Hyperbolic Matrix(119,432,46,167) (-11/3,-18/5) -> (18/7,13/5) Hyperbolic Matrix(241,864,94,337) (-18/5,-25/7) -> (23/9,18/7) Hyperbolic Matrix(95,336,54,191) (-25/7,-7/2) -> (7/4,23/13) Hyperbolic Matrix(71,240,-50,-169) (-7/2,-10/3) -> (-10/7,-17/12) Hyperbolic Matrix(407,1344,-182,-601) (-10/3,-33/10) -> (-9/4,-38/17) Hyperbolic Matrix(73,240,66,217) (-33/10,-23/7) -> (1/1,9/8) Hyperbolic Matrix(527,1728,190,623) (-23/7,-36/11) -> (36/13,25/9) Hyperbolic Matrix(265,864,96,313) (-36/11,-13/4) -> (11/4,36/13) Hyperbolic Matrix(119,384,22,71) (-13/4,-16/5) -> (16/3,11/2) Hyperbolic Matrix(121,384,-98,-311) (-16/5,-3/1) -> (-21/17,-16/13) Hyperbolic Matrix(385,1104,-234,-671) (-3/1,-20/7) -> (-28/17,-51/31) Hyperbolic Matrix(337,960,152,433) (-20/7,-17/6) -> (31/14,20/9) Hyperbolic Matrix(239,672,-154,-433) (-17/6,-14/5) -> (-14/9,-31/20) Hyperbolic Matrix(241,672,52,145) (-14/5,-25/9) -> (23/5,14/3) Hyperbolic Matrix(623,1728,190,527) (-25/9,-36/13) -> (36/11,23/7) Hyperbolic Matrix(313,864,96,265) (-36/13,-11/4) -> (13/4,36/11) Hyperbolic Matrix(71,192,44,119) (-11/4,-8/3) -> (8/5,13/8) Hyperbolic Matrix(73,192,46,121) (-8/3,-13/5) -> (11/7,8/5) Hyperbolic Matrix(167,432,46,119) (-13/5,-18/7) -> (18/5,11/3) Hyperbolic Matrix(337,864,94,241) (-18/7,-23/9) -> (25/7,18/5) Hyperbolic Matrix(433,1104,-282,-719) (-23/9,-28/11) -> (-20/13,-23/15) Hyperbolic Matrix(359,912,198,503) (-28/11,-5/2) -> (29/16,20/11) Hyperbolic Matrix(119,288,-50,-121) (-5/2,-12/5) -> (-12/5,-19/8) Parabolic Matrix(385,912,122,289) (-19/8,-45/19) -> (3/1,19/6) Hyperbolic Matrix(527,1248,182,431) (-45/19,-71/30) -> (23/8,3/1) Hyperbolic Matrix(1441,3408,-852,-2015) (-71/30,-26/11) -> (-22/13,-71/42) Hyperbolic Matrix(143,336,20,47) (-33/14,-7/3) -> (7/1,15/2) Hyperbolic Matrix(145,336,104,241) (-7/3,-23/10) -> (25/18,7/5) Hyperbolic Matrix(335,768,188,431) (-23/10,-16/7) -> (16/9,25/14) Hyperbolic Matrix(337,768,190,433) (-16/7,-25/11) -> (23/13,16/9) Hyperbolic Matrix(191,432,42,95) (-25/11,-9/4) -> (9/2,23/5) Hyperbolic Matrix(1031,2304,-720,-1609) (-38/17,-29/13) -> (-53/37,-10/7) Hyperbolic Matrix(409,912,248,553) (-29/13,-20/9) -> (28/17,5/3) Hyperbolic Matrix(217,480,-184,-407) (-20/9,-11/5) -> (-13/11,-20/17) Hyperbolic Matrix(23,48,-12,-25) (-11/5,-2/1) -> (-2/1,-13/7) Parabolic Matrix(311,576,142,263) (-13/7,-24/13) -> (24/11,11/5) Hyperbolic Matrix(313,576,144,265) (-24/13,-11/6) -> (13/6,24/11) Hyperbolic Matrix(527,960,342,623) (-31/17,-20/11) -> (20/13,17/11) Hyperbolic Matrix(503,912,198,359) (-20/11,-29/16) -> (5/2,28/11) Hyperbolic Matrix(743,1344,-518,-937) (-29/16,-9/5) -> (-33/23,-43/30) Hyperbolic Matrix(241,432,188,337) (-9/5,-25/14) -> (23/18,9/7) Hyperbolic Matrix(431,768,188,335) (-25/14,-16/9) -> (16/7,23/10) Hyperbolic Matrix(433,768,190,337) (-16/9,-23/13) -> (25/11,16/7) Hyperbolic Matrix(191,336,54,95) (-23/13,-7/4) -> (7/2,25/7) Hyperbolic Matrix(167,288,-98,-169) (-7/4,-12/7) -> (-12/7,-17/10) Parabolic Matrix(623,1056,-482,-817) (-17/10,-22/13) -> (-22/17,-31/24) Hyperbolic Matrix(8519,14400,3478,5879) (-71/42,-120/71) -> (120/49,49/20) Hyperbolic Matrix(8521,14400,3480,5881) (-120/71,-49/29) -> (71/29,120/49) Hyperbolic Matrix(1847,3120,724,1223) (-49/29,-27/16) -> (51/20,23/9) Hyperbolic Matrix(143,240,28,47) (-27/16,-5/3) -> (5/1,21/4) Hyperbolic Matrix(553,912,248,409) (-5/3,-28/17) -> (20/9,29/13) Hyperbolic Matrix(1897,3120,774,1273) (-51/31,-23/14) -> (49/20,27/11) Hyperbolic Matrix(527,864,380,623) (-23/14,-18/11) -> (18/13,25/18) Hyperbolic Matrix(265,432,192,313) (-18/11,-13/8) -> (11/8,18/13) Hyperbolic Matrix(119,192,44,71) (-13/8,-8/5) -> (8/3,11/4) Hyperbolic Matrix(121,192,46,73) (-8/5,-11/7) -> (13/5,8/3) Hyperbolic Matrix(551,864,382,599) (-11/7,-36/23) -> (36/25,13/9) Hyperbolic Matrix(1105,1728,768,1201) (-36/23,-25/16) -> (23/16,36/25) Hyperbolic Matrix(431,672,338,527) (-25/16,-14/9) -> (14/11,23/18) Hyperbolic Matrix(1487,2304,526,815) (-31/20,-48/31) -> (48/17,17/6) Hyperbolic Matrix(1489,2304,528,817) (-48/31,-17/11) -> (31/11,48/17) Hyperbolic Matrix(311,480,46,71) (-17/11,-20/13) -> (20/3,7/1) Hyperbolic Matrix(817,1248,472,721) (-23/15,-3/2) -> (45/26,71/41) Hyperbolic Matrix(623,912,360,527) (-3/2,-19/13) -> (19/11,45/26) Hyperbolic Matrix(265,384,216,313) (-16/11,-13/9) -> (11/9,16/13) Hyperbolic Matrix(599,864,382,551) (-13/9,-36/25) -> (36/23,11/7) Hyperbolic Matrix(1201,1728,768,1105) (-36/25,-23/16) -> (25/16,36/23) Hyperbolic Matrix(167,240,16,23) (-23/16,-33/23) -> (9/1,1/0) Hyperbolic Matrix(6431,9216,1942,2783) (-43/30,-96/67) -> (96/29,53/16) Hyperbolic Matrix(6433,9216,1944,2785) (-96/67,-53/37) -> (43/13,96/29) Hyperbolic Matrix(407,576,118,167) (-17/12,-24/17) -> (24/7,7/2) Hyperbolic Matrix(409,576,120,169) (-24/17,-7/5) -> (17/5,24/7) Hyperbolic Matrix(241,336,104,145) (-7/5,-25/18) -> (23/10,7/3) Hyperbolic Matrix(623,864,380,527) (-25/18,-18/13) -> (18/11,23/14) Hyperbolic Matrix(313,432,192,265) (-18/13,-11/8) -> (13/8,18/11) Hyperbolic Matrix(71,96,-54,-73) (-11/8,-4/3) -> (-4/3,-13/10) Parabolic Matrix(1775,2304,406,527) (-13/10,-48/37) -> (48/11,35/8) Hyperbolic Matrix(1777,2304,408,529) (-48/37,-35/27) -> (13/3,48/11) Hyperbolic Matrix(409,528,354,457) (-31/24,-9/7) -> (15/13,7/6) Hyperbolic Matrix(337,432,188,241) (-9/7,-23/18) -> (25/14,9/5) Hyperbolic Matrix(527,672,338,431) (-23/18,-14/11) -> (14/9,25/16) Hyperbolic Matrix(455,576,94,119) (-19/15,-24/19) -> (24/5,5/1) Hyperbolic Matrix(457,576,96,121) (-24/19,-5/4) -> (19/4,24/5) Hyperbolic Matrix(193,240,78,97) (-5/4,-21/17) -> (27/11,5/2) Hyperbolic Matrix(313,384,216,265) (-16/13,-11/9) -> (13/9,16/11) Hyperbolic Matrix(119,144,-100,-121) (-11/9,-6/5) -> (-6/5,-13/11) Parabolic Matrix(409,480,144,169) (-20/17,-7/6) -> (17/6,20/7) Hyperbolic Matrix(289,336,166,193) (-7/6,-15/13) -> (33/19,7/4) Hyperbolic Matrix(167,192,20,23) (-15/13,-8/7) -> (8/1,9/1) Hyperbolic Matrix(169,192,22,25) (-8/7,-9/8) -> (15/2,8/1) Hyperbolic Matrix(217,240,66,73) (-9/8,-1/1) -> (23/7,33/10) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(433,-528,196,-239) (17/14,11/9) -> (11/5,31/14) Hyperbolic Matrix(311,-384,98,-121) (16/13,5/4) -> (19/6,16/5) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(913,-1248,526,-719) (15/11,26/19) -> (26/15,33/19) Hyperbolic Matrix(841,-1152,192,-263) (26/19,11/8) -> (35/8,22/5) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(937,-1344,518,-743) (10/7,33/23) -> (9/5,38/21) Hyperbolic Matrix(263,-384,50,-73) (16/11,3/2) -> (21/4,16/3) Hyperbolic Matrix(719,-1104,282,-433) (3/2,20/13) -> (28/11,51/20) Hyperbolic Matrix(433,-672,154,-239) (17/11,14/9) -> (14/5,31/11) Hyperbolic Matrix(671,-1104,234,-385) (23/14,28/17) -> (20/7,23/8) Hyperbolic Matrix(169,-288,98,-167) (5/3,12/7) -> (12/7,19/11) Parabolic Matrix(1967,-3408,804,-1393) (71/41,26/15) -> (22/9,71/29) Hyperbolic Matrix(1273,-2304,384,-695) (38/21,29/16) -> (53/16,10/3) Hyperbolic Matrix(263,-480,40,-73) (20/11,11/6) -> (13/2,20/3) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(601,-1344,182,-407) (29/13,9/4) -> (33/10,43/13) Hyperbolic Matrix(121,-288,50,-119) (7/3,12/5) -> (12/5,17/7) Parabolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(23,240,16,167) -> Matrix(5,2,82,33) Matrix(23,192,20,167) -> Matrix(11,4,206,75) Matrix(25,192,22,169) -> Matrix(13,4,250,77) Matrix(71,528,16,119) -> Matrix(7,2,38,11) Matrix(23,144,-4,-25) -> Matrix(7,2,-32,-9) Matrix(95,528,-52,-289) -> Matrix(23,6,-280,-73) Matrix(71,384,22,119) -> Matrix(17,4,106,25) Matrix(73,384,-50,-263) -> Matrix(19,4,-290,-61) Matrix(71,336,-56,-265) -> Matrix(11,2,-182,-33) Matrix(145,672,52,241) -> Matrix(23,4,178,31) Matrix(95,432,42,191) -> Matrix(7,2,66,19) Matrix(23,96,-6,-25) -> Matrix(1,0,0,1) Matrix(335,1248,-142,-529) -> Matrix(19,4,-176,-37) Matrix(311,1152,-240,-889) -> Matrix(21,4,-352,-67) Matrix(119,432,46,167) -> Matrix(13,2,110,17) Matrix(241,864,94,337) -> Matrix(25,4,206,33) Matrix(95,336,54,191) -> Matrix(9,2,112,25) Matrix(71,240,-50,-169) -> Matrix(13,2,-202,-31) Matrix(407,1344,-182,-601) -> Matrix(17,4,-166,-39) Matrix(73,240,66,217) -> Matrix(11,2,214,39) Matrix(527,1728,190,623) -> Matrix(47,8,370,63) Matrix(265,864,96,313) -> Matrix(1,0,14,1) Matrix(119,384,22,71) -> Matrix(25,4,106,17) Matrix(121,384,-98,-311) -> Matrix(27,4,-466,-69) Matrix(385,1104,-234,-671) -> Matrix(101,14,-1378,-191) Matrix(337,960,152,433) -> Matrix(117,16,1148,157) Matrix(239,672,-154,-433) -> Matrix(91,12,-1312,-173) Matrix(241,672,52,145) -> Matrix(31,4,178,23) Matrix(623,1728,190,527) -> Matrix(63,8,370,47) Matrix(313,864,96,265) -> Matrix(1,0,14,1) Matrix(71,192,44,119) -> Matrix(31,4,426,55) Matrix(73,192,46,121) -> Matrix(33,4,470,57) Matrix(167,432,46,119) -> Matrix(17,2,110,13) Matrix(337,864,94,241) -> Matrix(33,4,206,25) Matrix(433,1104,-282,-719) -> Matrix(117,14,-1730,-207) Matrix(359,912,198,503) -> Matrix(185,22,2262,269) Matrix(119,288,-50,-121) -> Matrix(71,8,-648,-73) Matrix(385,912,122,289) -> Matrix(19,2,142,15) Matrix(527,1248,182,431) -> Matrix(37,4,268,29) Matrix(1441,3408,-852,-2015) -> Matrix(19,2,-238,-25) Matrix(143,336,20,47) -> Matrix(55,6,174,19) Matrix(145,336,104,241) -> Matrix(19,2,332,35) Matrix(335,768,188,431) -> Matrix(227,24,2828,299) Matrix(337,768,190,433) -> Matrix(229,24,2872,301) Matrix(191,432,42,95) -> Matrix(19,2,66,7) Matrix(1031,2304,-720,-1609) -> Matrix(39,4,-478,-49) Matrix(409,912,248,553) -> Matrix(215,22,2922,299) Matrix(217,480,-184,-407) -> Matrix(79,8,-1432,-145) Matrix(23,48,-12,-25) -> Matrix(21,2,-242,-23) Matrix(311,576,142,263) -> Matrix(239,20,2378,199) Matrix(313,576,144,265) -> Matrix(241,20,2422,201) Matrix(527,960,342,623) -> Matrix(195,16,2864,235) Matrix(503,912,198,359) -> Matrix(269,22,2262,185) Matrix(743,1344,-518,-937) -> Matrix(49,4,-870,-71) Matrix(241,432,188,337) -> Matrix(25,2,462,37) Matrix(431,768,188,335) -> Matrix(299,24,2828,227) Matrix(433,768,190,337) -> Matrix(301,24,2872,229) Matrix(191,336,54,95) -> Matrix(25,2,112,9) Matrix(167,288,-98,-169) -> Matrix(103,8,-1352,-105) Matrix(623,1056,-482,-817) -> Matrix(53,4,-888,-67) Matrix(8519,14400,3478,5879) -> Matrix(259,20,2318,179) Matrix(8521,14400,3480,5881) -> Matrix(261,20,2362,181) Matrix(1847,3120,724,1223) -> Matrix(341,26,2846,217) Matrix(143,240,28,47) -> Matrix(27,2,148,11) Matrix(553,912,248,409) -> Matrix(299,22,2922,215) Matrix(1897,3120,774,1273) -> Matrix(355,26,3154,231) Matrix(527,864,380,623) -> Matrix(55,4,866,63) Matrix(265,432,192,313) -> Matrix(27,2,418,31) Matrix(119,192,44,71) -> Matrix(55,4,426,31) Matrix(121,192,46,73) -> Matrix(57,4,470,33) Matrix(551,864,382,599) -> Matrix(1,0,30,1) Matrix(1105,1728,768,1201) -> Matrix(113,8,1822,129) Matrix(431,672,338,527) -> Matrix(57,4,926,65) Matrix(1487,2304,526,815) -> Matrix(579,40,4328,299) Matrix(1489,2304,528,817) -> Matrix(581,40,4372,301) Matrix(311,480,46,71) -> Matrix(117,8,424,29) Matrix(817,1248,472,721) -> Matrix(59,4,752,51) Matrix(623,912,360,527) -> Matrix(29,2,362,25) Matrix(265,384,216,313) -> Matrix(63,4,1118,71) Matrix(599,864,382,551) -> Matrix(1,0,30,1) Matrix(1201,1728,768,1105) -> Matrix(129,8,1822,113) Matrix(167,240,16,23) -> Matrix(33,2,82,5) Matrix(6431,9216,1942,2783) -> Matrix(1,0,36,1) Matrix(6433,9216,1944,2785) -> Matrix(1,0,8,1) Matrix(407,576,118,167) -> Matrix(63,4,362,23) Matrix(409,576,120,169) -> Matrix(65,4,406,25) Matrix(241,336,104,145) -> Matrix(35,2,332,19) Matrix(623,864,380,527) -> Matrix(63,4,866,55) Matrix(313,432,192,265) -> Matrix(31,2,418,27) Matrix(71,96,-54,-73) -> Matrix(1,0,0,1) Matrix(1775,2304,406,527) -> Matrix(131,8,704,43) Matrix(1777,2304,408,529) -> Matrix(133,8,748,45) Matrix(409,528,354,457) -> Matrix(33,2,610,37) Matrix(337,432,188,241) -> Matrix(37,2,462,25) Matrix(527,672,338,431) -> Matrix(65,4,926,57) Matrix(455,576,94,119) -> Matrix(67,4,318,19) Matrix(457,576,96,121) -> Matrix(69,4,362,21) Matrix(193,240,78,97) -> Matrix(33,2,280,17) Matrix(313,384,216,265) -> Matrix(71,4,1118,63) Matrix(119,144,-100,-121) -> Matrix(35,2,-648,-37) Matrix(409,480,144,169) -> Matrix(147,8,1084,59) Matrix(289,336,166,193) -> Matrix(113,6,1450,77) Matrix(167,192,20,23) -> Matrix(75,4,206,11) Matrix(169,192,22,25) -> Matrix(77,4,250,13) Matrix(217,240,66,73) -> Matrix(39,2,214,11) Matrix(1,0,2,1) -> Matrix(1,0,44,1) Matrix(121,-144,100,-119) -> Matrix(37,-2,648,-35) Matrix(433,-528,196,-239) -> Matrix(109,-6,1072,-59) Matrix(311,-384,98,-121) -> Matrix(69,-4,466,-27) Matrix(265,-336,56,-71) -> Matrix(33,-2,182,-11) Matrix(73,-96,54,-71) -> Matrix(1,0,0,1) Matrix(913,-1248,526,-719) -> Matrix(69,-4,880,-51) Matrix(841,-1152,192,-263) -> Matrix(67,-4,352,-21) Matrix(169,-240,50,-71) -> Matrix(31,-2,202,-13) Matrix(937,-1344,518,-743) -> Matrix(71,-4,870,-49) Matrix(263,-384,50,-73) -> Matrix(61,-4,290,-19) Matrix(719,-1104,282,-433) -> Matrix(207,-14,1730,-117) Matrix(433,-672,154,-239) -> Matrix(173,-12,1312,-91) Matrix(671,-1104,234,-385) -> Matrix(191,-14,1378,-101) Matrix(169,-288,98,-167) -> Matrix(105,-8,1352,-103) Matrix(1967,-3408,804,-1393) -> Matrix(25,-2,238,-19) Matrix(1273,-2304,384,-695) -> Matrix(49,-4,478,-39) Matrix(263,-480,40,-73) -> Matrix(97,-8,376,-31) Matrix(25,-48,12,-23) -> Matrix(23,-2,242,-21) Matrix(601,-1344,182,-407) -> Matrix(39,-4,166,-17) Matrix(121,-288,50,-119) -> Matrix(73,-8,648,-71) Matrix(433,-1056,98,-239) -> Matrix(35,-4,184,-21) Matrix(25,-96,6,-23) -> Matrix(1,0,0,1) Matrix(25,-144,4,-23) -> Matrix(9,-2,32,-7) 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): 64 Degree of the the map X: 64 Degree of the the map Y: 128 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 384 Minimal number of generators: 65 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 8/7 6/5 4/3 3/2 8/5 12/7 16/9 2/1 24/11 20/9 16/7 12/5 120/49 18/7 8/3 36/13 48/17 3/1 16/5 36/11 96/29 10/3 24/7 18/5 4/1 48/11 22/5 9/2 14/3 24/5 5/1 16/3 11/2 6/1 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/22 9/8 1/19 8/7 1/19 15/13 1/19 7/6 3/56 6/5 1/18 17/14 1/16 11/9 1/18 16/13 2/35 5/4 1/18 14/11 1/17 23/18 3/46 9/7 1/17 4/3 0/1 2/33 15/11 1/17 26/19 1/17 11/8 1/16 18/13 1/16 25/18 3/44 7/5 1/16 10/7 1/15 33/23 1/17 23/16 5/82 36/25 1/16 13/9 1/16 16/11 2/31 3/2 1/15 20/13 4/59 2/29 17/11 7/102 14/9 3/43 25/16 11/156 36/23 1/14 11/7 1/14 8/5 1/14 13/8 1/14 18/11 1/14 23/14 13/178 28/17 8/109 2/27 5/3 3/40 12/7 1/13 19/11 5/64 45/26 1/13 71/41 5/66 26/15 1/13 33/19 1/13 7/4 3/38 23/13 17/214 16/9 2/25 25/14 19/236 9/5 3/37 38/21 11/135 29/16 17/208 20/11 4/49 6/73 11/6 1/12 2/1 1/11 13/6 1/10 24/11 1/10 11/5 1/10 31/14 13/128 20/9 6/59 4/39 29/13 17/166 9/4 3/29 25/11 19/182 16/7 2/19 23/10 17/160 7/3 3/28 12/5 1/9 17/7 5/44 22/9 1/9 71/29 7/64 120/49 1/9 49/20 13/116 27/11 1/9 5/2 3/26 28/11 2/17 8/67 51/20 3/25 23/9 13/108 18/7 1/8 13/5 1/8 8/3 1/8 11/4 1/8 36/13 1/8 25/9 11/86 14/5 3/23 31/11 13/98 48/17 2/15 17/6 7/52 20/7 2/15 4/29 23/8 9/64 3/1 1/7 19/6 3/20 16/5 2/13 13/4 1/6 36/11 1/6 23/7 5/28 33/10 1/5 43/13 1/0 96/29 0/1 53/16 1/14 10/3 1/7 17/5 1/6 24/7 1/6 7/2 1/6 25/7 3/22 18/5 1/6 11/3 1/6 4/1 0/1 2/11 13/3 1/6 48/11 2/11 35/8 3/16 22/5 1/5 31/7 1/4 9/2 1/5 23/5 3/20 14/3 1/5 19/4 3/16 24/5 1/5 5/1 1/4 21/4 1/5 16/3 2/9 11/2 1/4 6/1 1/4 13/2 1/4 20/3 4/15 2/7 7/1 3/10 15/2 1/3 8/1 1/3 9/1 1/3 1/0 1/0 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(217,-240,151,-167) (1/1,9/8) -> (33/23,23/16) Hyperbolic Matrix(169,-192,147,-167) (9/8,8/7) -> (8/7,15/13) Parabolic Matrix(457,-528,103,-119) (15/13,7/6) -> (31/7,9/2) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(433,-528,196,-239) (17/14,11/9) -> (11/5,31/14) Hyperbolic Matrix(313,-384,97,-119) (11/9,16/13) -> (16/5,13/4) Hyperbolic Matrix(311,-384,98,-121) (16/13,5/4) -> (19/6,16/5) Hyperbolic Matrix(265,-336,56,-71) (5/4,14/11) -> (14/3,19/4) Hyperbolic Matrix(527,-672,189,-241) (14/11,23/18) -> (25/9,14/5) Hyperbolic Matrix(337,-432,149,-191) (23/18,9/7) -> (9/4,25/11) Hyperbolic Matrix(73,-96,54,-71) (9/7,4/3) -> (4/3,15/11) Parabolic Matrix(913,-1248,526,-719) (15/11,26/19) -> (26/15,33/19) Hyperbolic Matrix(841,-1152,192,-263) (26/19,11/8) -> (35/8,22/5) Hyperbolic Matrix(313,-432,121,-167) (11/8,18/13) -> (18/7,13/5) Hyperbolic Matrix(623,-864,243,-337) (18/13,25/18) -> (23/9,18/7) Hyperbolic Matrix(241,-336,137,-191) (25/18,7/5) -> (7/4,23/13) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(937,-1344,518,-743) (10/7,33/23) -> (9/5,38/21) Hyperbolic Matrix(1201,-1728,433,-623) (23/16,36/25) -> (36/13,25/9) Hyperbolic Matrix(599,-864,217,-313) (36/25,13/9) -> (11/4,36/13) Hyperbolic Matrix(265,-384,49,-71) (13/9,16/11) -> (16/3,11/2) Hyperbolic Matrix(263,-384,50,-73) (16/11,3/2) -> (21/4,16/3) Hyperbolic Matrix(719,-1104,282,-433) (3/2,20/13) -> (28/11,51/20) Hyperbolic Matrix(623,-960,281,-433) (20/13,17/11) -> (31/14,20/9) Hyperbolic Matrix(433,-672,154,-239) (17/11,14/9) -> (14/5,31/11) Hyperbolic Matrix(431,-672,93,-145) (14/9,25/16) -> (23/5,14/3) Hyperbolic Matrix(1105,-1728,337,-527) (25/16,36/23) -> (36/11,23/7) Hyperbolic Matrix(551,-864,169,-265) (36/23,11/7) -> (13/4,36/11) Hyperbolic Matrix(121,-192,75,-119) (11/7,8/5) -> (8/5,13/8) Parabolic Matrix(265,-432,73,-119) (13/8,18/11) -> (18/5,11/3) Hyperbolic Matrix(527,-864,147,-241) (18/11,23/14) -> (25/7,18/5) Hyperbolic Matrix(671,-1104,234,-385) (23/14,28/17) -> (20/7,23/8) Hyperbolic Matrix(553,-912,305,-503) (28/17,5/3) -> (29/16,20/11) Hyperbolic Matrix(169,-288,98,-167) (5/3,12/7) -> (12/7,19/11) Parabolic Matrix(527,-912,167,-289) (19/11,45/26) -> (3/1,19/6) Hyperbolic Matrix(721,-1248,249,-431) (45/26,71/41) -> (23/8,3/1) Hyperbolic Matrix(1967,-3408,804,-1393) (71/41,26/15) -> (22/9,71/29) Hyperbolic Matrix(193,-336,27,-47) (33/19,7/4) -> (7/1,15/2) Hyperbolic Matrix(433,-768,243,-431) (23/13,16/9) -> (16/9,25/14) Parabolic Matrix(241,-432,53,-95) (25/14,9/5) -> (9/2,23/5) Hyperbolic Matrix(1273,-2304,384,-695) (38/21,29/16) -> (53/16,10/3) Hyperbolic Matrix(263,-480,40,-73) (20/11,11/6) -> (13/2,20/3) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(265,-576,121,-263) (13/6,24/11) -> (24/11,11/5) Parabolic Matrix(409,-912,161,-359) (20/9,29/13) -> (5/2,28/11) Hyperbolic Matrix(601,-1344,182,-407) (29/13,9/4) -> (33/10,43/13) Hyperbolic Matrix(337,-768,147,-335) (25/11,16/7) -> (16/7,23/10) Parabolic Matrix(145,-336,41,-95) (23/10,7/3) -> (7/2,25/7) Hyperbolic Matrix(121,-288,50,-119) (7/3,12/5) -> (12/5,17/7) Parabolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(5881,-14400,2401,-5879) (71/29,120/49) -> (120/49,49/20) Parabolic Matrix(1273,-3120,499,-1223) (49/20,27/11) -> (51/20,23/9) Hyperbolic Matrix(97,-240,19,-47) (27/11,5/2) -> (5/1,21/4) Hyperbolic Matrix(73,-192,27,-71) (13/5,8/3) -> (8/3,11/4) Parabolic Matrix(817,-2304,289,-815) (31/11,48/17) -> (48/17,17/6) Parabolic Matrix(169,-480,25,-71) (17/6,20/7) -> (20/3,7/1) Hyperbolic Matrix(73,-240,7,-23) (23/7,33/10) -> (9/1,1/0) Hyperbolic Matrix(2785,-9216,841,-2783) (43/13,96/29) -> (96/29,53/16) Parabolic Matrix(169,-576,49,-167) (17/5,24/7) -> (24/7,7/2) Parabolic Matrix(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic Matrix(529,-2304,121,-527) (13/3,48/11) -> (48/11,35/8) Parabolic Matrix(121,-576,25,-119) (19/4,24/5) -> (24/5,5/1) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic Matrix(25,-192,3,-23) (15/2,8/1) -> (8/1,9/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,22,1) Matrix(217,-240,151,-167) -> Matrix(39,-2,644,-33) Matrix(169,-192,147,-167) -> Matrix(77,-4,1444,-75) Matrix(457,-528,103,-119) -> Matrix(37,-2,204,-11) Matrix(121,-144,100,-119) -> Matrix(37,-2,648,-35) Matrix(433,-528,196,-239) -> Matrix(109,-6,1072,-59) Matrix(313,-384,97,-119) -> Matrix(71,-4,444,-25) Matrix(311,-384,98,-121) -> Matrix(69,-4,466,-27) Matrix(265,-336,56,-71) -> Matrix(33,-2,182,-11) Matrix(527,-672,189,-241) -> Matrix(65,-4,504,-31) Matrix(337,-432,149,-191) -> Matrix(37,-2,352,-19) Matrix(73,-96,54,-71) -> Matrix(1,0,0,1) Matrix(913,-1248,526,-719) -> Matrix(69,-4,880,-51) Matrix(841,-1152,192,-263) -> Matrix(67,-4,352,-21) Matrix(313,-432,121,-167) -> Matrix(31,-2,264,-17) Matrix(623,-864,243,-337) -> Matrix(63,-4,520,-33) Matrix(241,-336,137,-191) -> Matrix(35,-2,438,-25) Matrix(169,-240,50,-71) -> Matrix(31,-2,202,-13) Matrix(937,-1344,518,-743) -> Matrix(71,-4,870,-49) Matrix(1201,-1728,433,-623) -> Matrix(129,-8,1016,-63) Matrix(599,-864,217,-313) -> Matrix(1,0,-8,1) Matrix(265,-384,49,-71) -> Matrix(63,-4,268,-17) Matrix(263,-384,50,-73) -> Matrix(61,-4,290,-19) Matrix(719,-1104,282,-433) -> Matrix(207,-14,1730,-117) Matrix(623,-960,281,-433) -> Matrix(235,-16,2306,-157) Matrix(433,-672,154,-239) -> Matrix(173,-12,1312,-91) Matrix(431,-672,93,-145) -> Matrix(57,-4,328,-23) Matrix(1105,-1728,337,-527) -> Matrix(113,-8,664,-47) Matrix(551,-864,169,-265) -> Matrix(1,0,-8,1) Matrix(121,-192,75,-119) -> Matrix(57,-4,784,-55) Matrix(265,-432,73,-119) -> Matrix(27,-2,176,-13) Matrix(527,-864,147,-241) -> Matrix(55,-4,344,-25) Matrix(671,-1104,234,-385) -> Matrix(191,-14,1378,-101) Matrix(553,-912,305,-503) -> Matrix(299,-22,3656,-269) Matrix(169,-288,98,-167) -> Matrix(105,-8,1352,-103) Matrix(527,-912,167,-289) -> Matrix(25,-2,188,-15) Matrix(721,-1248,249,-431) -> Matrix(51,-4,370,-29) Matrix(1967,-3408,804,-1393) -> Matrix(25,-2,238,-19) Matrix(193,-336,27,-47) -> Matrix(77,-6,244,-19) Matrix(433,-768,243,-431) -> Matrix(301,-24,3750,-299) Matrix(241,-432,53,-95) -> Matrix(25,-2,88,-7) Matrix(1273,-2304,384,-695) -> Matrix(49,-4,478,-39) Matrix(263,-480,40,-73) -> Matrix(97,-8,376,-31) Matrix(25,-48,12,-23) -> Matrix(23,-2,242,-21) Matrix(265,-576,121,-263) -> Matrix(201,-20,2000,-199) Matrix(409,-912,161,-359) -> Matrix(215,-22,1808,-185) Matrix(601,-1344,182,-407) -> Matrix(39,-4,166,-17) Matrix(337,-768,147,-335) -> Matrix(229,-24,2166,-227) Matrix(145,-336,41,-95) -> Matrix(19,-2,86,-9) Matrix(121,-288,50,-119) -> Matrix(73,-8,648,-71) Matrix(433,-1056,98,-239) -> Matrix(35,-4,184,-21) Matrix(5881,-14400,2401,-5879) -> Matrix(181,-20,1620,-179) Matrix(1273,-3120,499,-1223) -> Matrix(231,-26,1928,-217) Matrix(97,-240,19,-47) -> Matrix(17,-2,94,-11) Matrix(73,-192,27,-71) -> Matrix(33,-4,256,-31) Matrix(817,-2304,289,-815) -> Matrix(301,-40,2250,-299) Matrix(169,-480,25,-71) -> Matrix(59,-8,214,-29) Matrix(73,-240,7,-23) -> Matrix(11,-2,28,-5) Matrix(2785,-9216,841,-2783) -> Matrix(1,0,14,1) Matrix(169,-576,49,-167) -> Matrix(25,-4,144,-23) Matrix(25,-96,6,-23) -> Matrix(1,0,0,1) Matrix(529,-2304,121,-527) -> Matrix(45,-8,242,-43) Matrix(121,-576,25,-119) -> Matrix(21,-4,100,-19) Matrix(25,-144,4,-23) -> Matrix(9,-2,32,-7) Matrix(25,-192,3,-23) -> Matrix(13,-4,36,-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): 32 ----------------------------------------------------------------------- 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 22 1 2/1 1/11 2 12 24/11 1/10 20 1 11/5 1/10 1 24 20/9 0 6 29/13 17/166 1 24 9/4 3/29 1 8 25/11 19/182 1 24 16/7 2/19 6 3 23/10 17/160 1 24 7/3 3/28 1 24 12/5 1/9 8 2 17/7 5/44 1 24 22/9 1/9 2 12 120/49 1/9 20 1 49/20 13/116 1 24 27/11 1/9 1 8 5/2 3/26 1 24 28/11 0 6 23/9 13/108 1 24 18/7 1/8 2 4 13/5 1/8 1 24 8/3 1/8 4 3 11/4 1/8 1 24 36/13 1/8 8 2 25/9 11/86 1 24 14/5 3/23 2 12 48/17 2/15 10 1 17/6 7/52 1 24 20/7 0 6 23/8 9/64 1 24 3/1 1/7 1 8 16/5 2/13 2 3 13/4 1/6 1 24 36/11 1/6 8 2 23/7 5/28 1 24 33/10 1/5 1 8 43/13 1/0 1 24 96/29 0/1 14 1 10/3 1/7 2 12 24/7 1/6 4 1 7/2 1/6 1 24 25/7 3/22 1 24 18/5 1/6 2 4 11/3 1/6 1 24 4/1 0 6 13/3 1/6 1 24 48/11 2/11 2 1 22/5 1/5 2 12 31/7 1/4 1 24 9/2 1/5 1 8 23/5 3/20 1 24 14/3 1/5 2 12 24/5 1/5 4 1 5/1 1/4 1 24 21/4 1/5 1 8 16/3 2/9 2 3 11/2 1/4 1 24 6/1 1/4 2 4 13/2 1/4 1 24 20/3 0 6 7/1 3/10 1 24 15/2 1/3 1 8 8/1 1/3 4 3 9/1 1/3 1 8 1/0 1/0 1 24 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(23,-48,11,-23) (2/1,24/11) -> (2/1,24/11) Reflection Matrix(241,-528,110,-241) (24/11,11/5) -> (24/11,11/5) Reflection Matrix(217,-480,33,-73) (11/5,20/9) -> (13/2,20/3) Glide Reflection Matrix(409,-912,161,-359) (20/9,29/13) -> (5/2,28/11) Hyperbolic Matrix(601,-1344,182,-407) (29/13,9/4) -> (33/10,43/13) Hyperbolic Matrix(191,-432,42,-95) (9/4,25/11) -> (9/2,23/5) Glide Reflection Matrix(337,-768,147,-335) (25/11,16/7) -> (16/7,23/10) Parabolic Matrix(145,-336,41,-95) (23/10,7/3) -> (7/2,25/7) Hyperbolic Matrix(121,-288,50,-119) (7/3,12/5) -> (12/5,17/7) Parabolic Matrix(433,-1056,98,-239) (17/7,22/9) -> (22/5,31/7) Hyperbolic Matrix(1079,-2640,441,-1079) (22/9,120/49) -> (22/9,120/49) Reflection Matrix(4801,-11760,1960,-4801) (120/49,49/20) -> (120/49,49/20) Reflection Matrix(313,-768,108,-265) (49/20,27/11) -> (23/8,3/1) Glide Reflection Matrix(97,-240,19,-47) (27/11,5/2) -> (5/1,21/4) Hyperbolic Matrix(433,-1104,151,-385) (28/11,23/9) -> (20/7,23/8) Glide Reflection Matrix(337,-864,94,-241) (23/9,18/7) -> (25/7,18/5) Glide Reflection Matrix(167,-432,46,-119) (18/7,13/5) -> (18/5,11/3) Glide Reflection Matrix(73,-192,27,-71) (13/5,8/3) -> (8/3,11/4) Parabolic Matrix(313,-864,96,-265) (11/4,36/13) -> (13/4,36/11) Glide Reflection Matrix(623,-1728,190,-527) (36/13,25/9) -> (36/11,23/7) Glide Reflection Matrix(241,-672,52,-145) (25/9,14/5) -> (23/5,14/3) Glide Reflection Matrix(239,-672,85,-239) (14/5,48/17) -> (14/5,48/17) Reflection Matrix(577,-1632,204,-577) (48/17,17/6) -> (48/17,17/6) Reflection Matrix(169,-480,25,-71) (17/6,20/7) -> (20/3,7/1) Hyperbolic Matrix(121,-384,23,-73) (3/1,16/5) -> (21/4,16/3) Glide Reflection Matrix(119,-384,22,-71) (16/5,13/4) -> (16/3,11/2) Glide Reflection Matrix(73,-240,7,-23) (23/7,33/10) -> (9/1,1/0) Hyperbolic Matrix(2495,-8256,754,-2495) (43/13,96/29) -> (43/13,96/29) Reflection Matrix(289,-960,87,-289) (96/29,10/3) -> (96/29,10/3) Reflection Matrix(71,-240,21,-71) (10/3,24/7) -> (10/3,24/7) Reflection Matrix(97,-336,28,-97) (24/7,7/2) -> (24/7,7/2) Reflection Matrix(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic Matrix(287,-1248,66,-287) (13/3,48/11) -> (13/3,48/11) Reflection Matrix(241,-1056,55,-241) (48/11,22/5) -> (48/11,22/5) Reflection Matrix(119,-528,16,-71) (31/7,9/2) -> (7/1,15/2) Glide Reflection Matrix(71,-336,15,-71) (14/3,24/5) -> (14/3,24/5) Reflection Matrix(49,-240,10,-49) (24/5,5/1) -> (24/5,5/1) Reflection Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic Matrix(25,-192,3,-23) (15/2,8/1) -> (8/1,9/1) Parabolic 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(1,0,1,-1) -> Matrix(1,0,22,-1) (0/1,2/1) -> (0/1,1/11) Matrix(23,-48,11,-23) -> Matrix(21,-2,220,-21) (2/1,24/11) -> (1/11,1/10) Matrix(241,-528,110,-241) -> Matrix(179,-18,1780,-179) (24/11,11/5) -> (1/10,9/89) Matrix(217,-480,33,-73) -> Matrix(79,-8,306,-31) Matrix(409,-912,161,-359) -> Matrix(215,-22,1808,-185) Matrix(601,-1344,182,-407) -> Matrix(39,-4,166,-17) Matrix(191,-432,42,-95) -> Matrix(19,-2,66,-7) Matrix(337,-768,147,-335) -> Matrix(229,-24,2166,-227) 2/19 Matrix(145,-336,41,-95) -> Matrix(19,-2,86,-9) Matrix(121,-288,50,-119) -> Matrix(73,-8,648,-71) 1/9 Matrix(433,-1056,98,-239) -> Matrix(35,-4,184,-21) Matrix(1079,-2640,441,-1079) -> Matrix(53,-6,468,-53) (22/9,120/49) -> (1/9,3/26) Matrix(4801,-11760,1960,-4801) -> Matrix(233,-26,2088,-233) (120/49,49/20) -> (1/9,13/116) Matrix(313,-768,108,-265) -> Matrix(35,-4,236,-27) Matrix(97,-240,19,-47) -> Matrix(17,-2,94,-11) Matrix(433,-1104,151,-385) -> Matrix(117,-14,844,-101) Matrix(337,-864,94,-241) -> Matrix(33,-4,206,-25) Matrix(167,-432,46,-119) -> Matrix(17,-2,110,-13) Matrix(73,-192,27,-71) -> Matrix(33,-4,256,-31) 1/8 Matrix(313,-864,96,-265) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(623,-1728,190,-527) -> Matrix(63,-8,370,-47) Matrix(241,-672,52,-145) -> Matrix(31,-4,178,-23) Matrix(239,-672,85,-239) -> Matrix(91,-12,690,-91) (14/5,48/17) -> (3/23,2/15) Matrix(577,-1632,204,-577) -> Matrix(209,-28,1560,-209) (48/17,17/6) -> (2/15,7/52) Matrix(169,-480,25,-71) -> Matrix(59,-8,214,-29) Matrix(121,-384,23,-73) -> Matrix(27,-4,128,-19) Matrix(119,-384,22,-71) -> Matrix(25,-4,106,-17) Matrix(73,-240,7,-23) -> Matrix(11,-2,28,-5) Matrix(2495,-8256,754,-2495) -> Matrix(1,0,0,-1) (43/13,96/29) -> (0/1,1/0) Matrix(289,-960,87,-289) -> Matrix(1,0,14,-1) (96/29,10/3) -> (0/1,1/7) Matrix(71,-240,21,-71) -> Matrix(13,-2,84,-13) (10/3,24/7) -> (1/7,1/6) Matrix(97,-336,28,-97) -> Matrix(11,-2,60,-11) (24/7,7/2) -> (1/6,1/5) Matrix(25,-96,6,-23) -> Matrix(1,0,0,1) Matrix(287,-1248,66,-287) -> Matrix(23,-4,132,-23) (13/3,48/11) -> (1/6,2/11) Matrix(241,-1056,55,-241) -> Matrix(21,-4,110,-21) (48/11,22/5) -> (2/11,1/5) Matrix(119,-528,16,-71) -> Matrix(11,-2,38,-7) Matrix(71,-336,15,-71) -> Matrix(11,-2,60,-11) (14/3,24/5) -> (1/6,1/5) Matrix(49,-240,10,-49) -> Matrix(9,-2,40,-9) (24/5,5/1) -> (1/5,1/4) Matrix(25,-144,4,-23) -> Matrix(9,-2,32,-7) 1/4 Matrix(25,-192,3,-23) -> Matrix(13,-4,36,-11) 1/3 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.