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): 864 Minimal number of generators: 145 Number of equivalence classes of cusps: 64 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -7/1 -6/1 -11/2 -5/1 -4/1 -37/10 -13/4 -3/1 -5/2 -2/1 -1/1 -5/8 -13/22 -1/2 -7/16 -2/5 -5/14 -7/22 -4/13 -1/4 -2/11 0/1 1/8 1/5 1/4 2/7 5/13 1/2 10/17 7/11 11/16 3/4 4/5 1/1 5/4 7/5 3/2 11/7 17/10 7/4 2/1 9/4 19/8 5/2 13/5 11/4 3/1 7/2 15/4 4/1 17/4 73/17 9/2 5/1 11/2 28/5 6/1 13/2 7/1 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 -1/2 -8/1 -1/2 1/0 -7/1 -1/2 1/0 -13/2 -1/1 0/1 -6/1 -1/2 1/0 -11/2 -1/1 -16/3 -3/4 -1/2 -5/1 -1/2 -19/4 -1/1 -14/3 -1/2 1/0 -9/2 -1/1 0/1 -13/3 1/0 -4/1 -1/1 -15/4 -1/1 0/1 -26/7 -3/2 1/0 -37/10 -1/1 -11/3 -1/2 -40/11 -1/2 1/0 -29/8 -1/1 -18/5 -1/2 1/0 -7/2 -1/1 0/1 -17/5 -1/2 -10/3 -1/2 1/0 -13/4 -1/1 -16/5 -3/4 -1/2 -3/1 -1/2 -11/4 -1/1 0/1 -19/7 -1/2 -27/10 -1/1 -1/2 -8/3 -1/2 1/0 -21/8 -1/2 -1/3 -55/21 -1/2 -34/13 -1/3 -13/5 -1/2 -5/2 0/1 -17/7 1/0 -12/5 -1/2 1/0 -19/8 -1/1 0/1 -26/11 -1/1 -7/3 -1/2 -9/4 0/1 1/1 -11/5 1/0 -2/1 -1/2 1/0 -1/1 -1/2 1/0 -2/3 -1/2 1/0 -9/14 -2/1 -1/1 -7/11 -1/2 -19/30 -1/1 0/1 -12/19 -1/2 1/0 -5/8 -1/1 -18/29 -3/4 -1/2 -13/21 -1/2 -21/34 -2/3 -1/2 -8/13 -1/2 1/0 -11/18 -1/1 0/1 -3/5 -1/2 -13/22 0/1 -23/39 1/0 -10/17 -1/2 1/0 -17/29 -1/2 -7/12 -1/1 0/1 -18/31 -1/2 1/0 -29/50 0/1 -11/19 -1/2 -15/26 -1/1 0/1 -19/33 -1/2 -4/7 0/1 -17/30 0/1 1/0 -13/23 1/0 -9/16 -1/1 0/1 -14/25 -1/2 1/0 -33/59 -1/2 -19/34 0/1 -5/9 -1/2 -11/20 0/1 -6/11 -1/2 1/0 -7/13 -1/2 1/0 -8/15 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -1/2 1/0 -17/37 1/0 -11/24 -1/1 1/0 -5/11 -1/2 1/0 -14/31 -3/2 1/0 -9/20 -1/1 0/1 -4/9 -1/2 1/0 -7/16 0/1 -10/23 1/2 1/0 -3/7 1/0 -14/33 -5/8 -1/2 -11/26 0/1 -8/19 -1/2 1/0 -5/12 -1/1 0/1 -7/17 -1/2 -2/5 0/1 -7/18 -1/1 0/1 -19/49 -1/2 1/0 -12/31 -1/2 -1/4 -5/13 1/0 -13/34 0/1 -34/89 5/2 1/0 -21/55 1/0 -8/21 -1/2 1/0 -3/8 -1/1 0/1 -4/11 -1/2 1/0 -5/14 0/1 -6/17 1/2 1/0 -1/3 1/0 -7/22 -2/1 -6/19 -3/2 1/0 -5/16 -2/1 -1/1 -4/13 -1/1 -11/36 -1/1 -2/3 -7/23 -1/2 -3/10 -1/1 0/1 -5/17 1/0 -2/7 -1/2 1/0 -5/18 -2/1 1/0 -8/29 -2/1 -3/11 1/0 -1/4 -1/1 -3/13 -1/2 -8/35 -1/1 -5/22 -1/1 -1/2 -7/31 -1/2 -2/9 -1/2 1/0 -3/14 -1/1 0/1 -4/19 0/1 -1/5 1/0 -5/26 -2/1 -9/47 -3/2 -4/21 -3/2 -11/8 -7/37 -3/2 -5/4 -3/16 -5/4 -1/1 -2/11 -1/1 -5/28 -1/1 -9/10 -3/17 -5/6 -1/6 -1/1 -2/3 0/1 -1/2 1/0 1/8 0/1 1/7 1/0 1/6 -1/1 0/1 2/11 -1/2 1/0 1/5 -1/2 2/9 -1/2 -1/4 1/4 -1/3 0/1 3/11 -1/6 2/7 0/1 5/17 1/8 3/10 0/1 1/4 4/13 3/8 1/2 5/16 1/1 1/3 1/0 3/8 -1/1 0/1 8/21 -1/2 1/0 5/13 -1/2 1/0 12/31 -1/2 1/0 7/18 -1/1 0/1 2/5 -1/2 1/0 1/2 0/1 4/7 1/2 1/0 11/19 1/0 7/12 0/1 1/0 10/17 0/1 13/22 0/1 1/1 16/27 1/2 1/0 3/5 1/0 5/8 1/1 1/0 12/19 5/2 1/0 7/11 1/0 16/25 -7/2 1/0 9/14 -2/1 1/0 2/3 -1/2 1/0 11/16 0/1 9/13 1/0 16/23 1/1 23/33 1/0 7/10 -1/1 1/0 19/27 1/0 12/17 -1/2 1/0 5/7 1/0 13/18 -2/1 -1/1 8/11 -1/2 1/0 11/15 -1/2 3/4 -1/1 0/1 7/9 -1/2 4/5 0/1 9/11 1/2 5/6 0/1 1/1 1/1 1/0 5/4 -1/1 9/7 -1/2 22/17 0/1 13/10 -1/2 0/1 17/13 -1/2 1/0 4/3 -1/2 1/0 15/11 1/0 26/19 0/1 11/8 0/1 1/0 40/29 -2/1 29/21 1/0 18/13 -1/2 1/0 7/5 1/0 17/12 -2/1 -1/1 27/19 -3/2 37/26 -1/1 10/7 -3/2 1/0 3/2 -1/1 0/1 14/9 -1/2 1/0 11/7 -1/2 1/0 30/19 -1/2 1/0 19/12 -1/1 0/1 8/5 -1/2 1/0 29/18 -1/1 0/1 21/13 1/0 13/8 -1/1 5/3 1/0 17/10 -1/1 29/17 -3/4 12/7 -3/4 -1/2 19/11 -1/2 1/0 26/15 -1/2 1/0 33/19 1/0 7/4 -1/1 0/1 9/5 1/0 20/11 1/2 1/0 11/6 1/1 1/0 2/1 -1/1 13/6 -3/5 -1/2 11/5 -1/2 20/9 -1/2 1/0 9/4 -1/1 -1/2 7/3 -1/2 19/8 0/1 31/13 1/2 12/5 -1/2 1/0 17/7 1/0 5/2 -1/1 0/1 18/7 -1/2 1/0 13/5 -1/2 1/0 34/13 -1/2 1/0 21/8 -1/1 0/1 8/3 -1/2 1/0 27/10 -1/1 0/1 46/17 0/1 19/7 1/0 11/4 -1/1 25/9 -1/2 39/14 -5/9 -1/2 53/19 -1/2 14/5 -1/2 -3/8 31/11 -1/2 -1/4 17/6 -1/4 0/1 3/1 1/0 7/2 -1/1 11/3 -1/2 26/7 -2/3 41/11 -1/2 56/15 -13/24 -1/2 71/19 -1/2 15/4 -1/2 0/1 19/5 -1/2 4/1 -1/2 1/0 17/4 -1/1 30/7 -7/12 -1/2 73/17 -1/2 43/10 -1/2 -3/7 13/3 -1/2 9/2 -1/1 0/1 23/5 -1/2 37/8 0/1 14/3 1/2 1/0 33/7 -3/2 19/4 -1/1 -1/2 24/5 -1/2 1/0 5/1 -1/2 1/0 16/3 -3/4 -1/2 11/2 0/1 1/0 28/5 0/1 45/8 2/1 1/0 107/19 1/0 62/11 -9/2 1/0 17/3 1/0 6/1 -1/2 1/0 13/2 0/1 7/1 1/0 15/2 -1/1 1/0 8/1 -1/1 9/1 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,18,0,1) (-9/1,1/0) -> (9/1,1/0) Parabolic Matrix(47,390,-84,-697) (-9/1,-8/1) -> (-14/25,-33/59) Hyperbolic Matrix(21,164,16,125) (-8/1,-7/1) -> (17/13,4/3) Hyperbolic Matrix(45,296,-116,-763) (-7/1,-13/2) -> (-7/18,-19/49) Hyperbolic Matrix(45,278,28,173) (-13/2,-6/1) -> (8/5,29/18) Hyperbolic Matrix(43,242,-8,-45) (-6/1,-11/2) -> (-11/2,-16/3) Parabolic Matrix(105,554,76,401) (-16/3,-5/1) -> (29/21,18/13) Hyperbolic Matrix(9,44,28,137) (-5/1,-19/4) -> (5/16,1/3) Hyperbolic Matrix(247,1166,-68,-321) (-19/4,-14/3) -> (-40/11,-29/8) Hyperbolic Matrix(51,232,20,91) (-14/3,-9/2) -> (5/2,18/7) Hyperbolic Matrix(5,22,32,141) (-9/2,-13/3) -> (1/7,1/6) Hyperbolic Matrix(115,494,-44,-189) (-13/3,-4/1) -> (-34/13,-13/5) Hyperbolic Matrix(123,466,-52,-197) (-4/1,-15/4) -> (-19/8,-26/11) Hyperbolic Matrix(119,444,-264,-985) (-15/4,-26/7) -> (-14/31,-9/20) Hyperbolic Matrix(359,1332,252,935) (-26/7,-37/10) -> (37/26,10/7) Hyperbolic Matrix(381,1406,268,989) (-37/10,-11/3) -> (27/19,37/26) Hyperbolic Matrix(81,296,136,497) (-11/3,-40/11) -> (16/27,3/5) Hyperbolic Matrix(117,422,28,101) (-29/8,-18/5) -> (4/1,17/4) Hyperbolic Matrix(43,152,28,99) (-18/5,-7/2) -> (3/2,14/9) Hyperbolic Matrix(75,256,104,355) (-7/2,-17/5) -> (5/7,13/18) Hyperbolic Matrix(53,178,92,309) (-17/5,-10/3) -> (4/7,11/19) Hyperbolic Matrix(103,338,-32,-105) (-10/3,-13/4) -> (-13/4,-16/5) Parabolic Matrix(91,290,16,51) (-16/5,-3/1) -> (17/3,6/1) Hyperbolic Matrix(31,86,40,111) (-3/1,-11/4) -> (3/4,7/9) Hyperbolic Matrix(147,400,104,283) (-11/4,-19/7) -> (7/5,17/12) Hyperbolic Matrix(105,284,-464,-1255) (-19/7,-27/10) -> (-5/22,-7/31) Hyperbolic Matrix(233,628,128,345) (-27/10,-8/3) -> (20/11,11/6) Hyperbolic Matrix(111,292,176,463) (-8/3,-21/8) -> (5/8,12/19) Hyperbolic Matrix(367,962,-800,-2097) (-21/8,-55/21) -> (-17/37,-11/24) Hyperbolic Matrix(635,1662,912,2387) (-55/21,-34/13) -> (16/23,23/33) Hyperbolic Matrix(59,150,-24,-61) (-13/5,-5/2) -> (-5/2,-17/7) Parabolic Matrix(103,248,76,183) (-17/7,-12/5) -> (4/3,15/11) Hyperbolic Matrix(79,188,208,495) (-12/5,-19/8) -> (3/8,8/21) Hyperbolic Matrix(147,346,212,499) (-26/11,-7/3) -> (9/13,16/23) Hyperbolic Matrix(15,34,56,127) (-7/3,-9/4) -> (1/4,3/11) Hyperbolic Matrix(103,230,-176,-393) (-9/4,-11/5) -> (-17/29,-7/12) Hyperbolic Matrix(77,166,32,69) (-11/5,-2/1) -> (12/5,17/7) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(151,98,208,135) (-2/3,-9/14) -> (13/18,8/11) Hyperbolic Matrix(53,34,-304,-195) (-9/14,-7/11) -> (-3/17,-1/6) Hyperbolic Matrix(735,466,-1276,-809) (-7/11,-19/30) -> (-15/26,-19/33) Hyperbolic Matrix(493,312,1272,805) (-19/30,-12/19) -> (12/31,7/18) Hyperbolic Matrix(239,150,-384,-241) (-12/19,-5/8) -> (-5/8,-18/29) Parabolic Matrix(803,498,1140,707) (-18/29,-13/21) -> (19/27,12/17) Hyperbolic Matrix(799,494,-1412,-873) (-13/21,-21/34) -> (-17/30,-13/23) Hyperbolic Matrix(661,408,1032,637) (-21/34,-8/13) -> (16/25,9/14) Hyperbolic Matrix(49,30,276,169) (-8/13,-11/18) -> (1/6,2/11) Hyperbolic Matrix(141,86,-464,-283) (-11/18,-3/5) -> (-7/23,-3/10) Hyperbolic Matrix(571,338,-968,-573) (-3/5,-13/22) -> (-13/22,-23/39) Parabolic Matrix(523,308,-1136,-669) (-23/39,-10/17) -> (-6/13,-17/37) Hyperbolic Matrix(177,104,-788,-463) (-10/17,-17/29) -> (-7/31,-2/9) Hyperbolic Matrix(949,552,600,349) (-7/12,-18/31) -> (30/19,19/12) Hyperbolic Matrix(517,300,-1632,-947) (-18/31,-29/50) -> (-7/22,-6/19) Hyperbolic Matrix(2011,1166,-3596,-2085) (-29/50,-11/19) -> (-33/59,-19/34) Hyperbolic Matrix(769,444,168,97) (-11/19,-15/26) -> (9/2,23/5) Hyperbolic Matrix(1523,876,1104,635) (-19/33,-4/7) -> (40/29,29/21) Hyperbolic Matrix(917,520,164,93) (-4/7,-17/30) -> (11/2,28/5) Hyperbolic Matrix(823,464,580,327) (-13/23,-9/16) -> (17/12,27/19) Hyperbolic Matrix(1069,600,408,229) (-9/16,-14/25) -> (34/13,21/8) Hyperbolic Matrix(79,44,-404,-225) (-19/34,-5/9) -> (-1/5,-5/26) Hyperbolic Matrix(279,154,404,223) (-5/9,-11/20) -> (11/16,9/13) Hyperbolic Matrix(161,88,236,129) (-11/20,-6/11) -> (2/3,11/16) Hyperbolic Matrix(547,296,316,171) (-6/11,-7/13) -> (19/11,26/15) Hyperbolic Matrix(387,208,80,43) (-7/13,-8/15) -> (24/5,5/1) Hyperbolic Matrix(227,120,384,203) (-8/15,-1/2) -> (13/22,16/27) Hyperbolic Matrix(367,170,136,63) (-1/2,-6/13) -> (8/3,27/10) Hyperbolic Matrix(201,92,-1064,-487) (-11/24,-5/11) -> (-7/37,-3/16) Hyperbolic Matrix(1115,504,396,179) (-5/11,-14/31) -> (14/5,31/11) Hyperbolic Matrix(165,74,-524,-235) (-9/20,-4/9) -> (-6/19,-5/16) Hyperbolic Matrix(223,98,-512,-225) (-4/9,-7/16) -> (-7/16,-10/23) Parabolic Matrix(347,150,192,83) (-10/23,-3/7) -> (9/5,20/11) Hyperbolic Matrix(1187,504,252,107) (-3/7,-14/33) -> (14/3,33/7) Hyperbolic Matrix(1313,556,-3436,-1455) (-14/33,-11/26) -> (-13/34,-34/89) Hyperbolic Matrix(403,170,64,27) (-11/26,-8/19) -> (6/1,13/2) Hyperbolic Matrix(495,208,188,79) (-8/19,-5/12) -> (21/8,8/3) Hyperbolic Matrix(183,76,248,103) (-5/12,-7/17) -> (11/15,3/4) Hyperbolic Matrix(151,62,-548,-225) (-7/17,-2/5) -> (-8/29,-3/11) Hyperbolic Matrix(87,34,-412,-161) (-2/5,-7/18) -> (-3/14,-4/19) Hyperbolic Matrix(413,160,-2176,-843) (-19/49,-12/31) -> (-4/21,-7/37) Hyperbolic Matrix(1117,432,468,181) (-12/31,-5/13) -> (31/13,12/5) Hyperbolic Matrix(407,156,60,23) (-5/13,-13/34) -> (13/2,7/1) Hyperbolic Matrix(6729,2570,1804,689) (-34/89,-21/55) -> (41/11,56/15) Hyperbolic Matrix(2123,810,1224,467) (-21/55,-8/21) -> (26/15,33/19) Hyperbolic Matrix(463,176,292,111) (-8/21,-3/8) -> (19/12,8/5) Hyperbolic Matrix(27,10,116,43) (-3/8,-4/11) -> (2/9,1/4) Hyperbolic Matrix(139,50,-392,-141) (-4/11,-5/14) -> (-5/14,-6/17) Parabolic Matrix(247,86,112,39) (-6/17,-1/3) -> (11/5,20/9) Hyperbolic Matrix(213,68,-1112,-355) (-1/3,-7/22) -> (-5/26,-9/47) Hyperbolic Matrix(207,64,-676,-209) (-5/16,-4/13) -> (-4/13,-11/36) Parabolic Matrix(1349,412,776,237) (-11/36,-7/23) -> (33/19,7/4) Hyperbolic Matrix(255,76,104,31) (-3/10,-5/17) -> (17/7,5/2) Hyperbolic Matrix(355,104,256,75) (-5/17,-2/7) -> (18/13,7/5) Hyperbolic Matrix(99,28,152,43) (-2/7,-5/18) -> (9/14,2/3) Hyperbolic Matrix(773,214,596,165) (-5/18,-8/29) -> (22/17,13/10) Hyperbolic Matrix(23,6,-96,-25) (-3/11,-1/4) -> (-1/4,-3/13) Parabolic Matrix(419,96,48,11) (-3/13,-8/35) -> (8/1,9/1) Hyperbolic Matrix(701,160,92,21) (-8/35,-5/22) -> (15/2,8/1) Hyperbolic Matrix(91,20,232,51) (-2/9,-3/14) -> (7/18,2/5) Hyperbolic Matrix(339,70,92,19) (-4/19,-1/5) -> (11/3,26/7) Hyperbolic Matrix(3271,626,580,111) (-9/47,-4/21) -> (62/11,17/3) Hyperbolic Matrix(87,16,-484,-89) (-3/16,-2/11) -> (-2/11,-5/28) Parabolic Matrix(1247,222,264,47) (-5/28,-3/17) -> (33/7,19/4) Hyperbolic Matrix(63,10,44,7) (-1/6,0/1) -> (10/7,3/2) Hyperbolic Matrix(149,-14,32,-3) (0/1,1/8) -> (37/8,14/3) Hyperbolic Matrix(443,-60,96,-13) (1/8,1/7) -> (23/5,37/8) Hyperbolic Matrix(229,-42,60,-11) (2/11,1/5) -> (19/5,4/1) Hyperbolic Matrix(105,-22,148,-31) (1/5,2/9) -> (12/17,5/7) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(319,-94,112,-33) (5/17,3/10) -> (17/6,3/1) Hyperbolic Matrix(303,-92,56,-17) (3/10,4/13) -> (16/3,11/2) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(93,-34,52,-19) (1/3,3/8) -> (7/4,9/5) Hyperbolic Matrix(261,-100,676,-259) (8/21,5/13) -> (5/13,12/31) Parabolic Matrix(13,-6,24,-11) (2/5,1/2) -> (1/2,4/7) Parabolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(499,-292,364,-213) (7/12,10/17) -> (26/19,11/8) Hyperbolic Matrix(1471,-868,544,-321) (10/17,13/22) -> (27/10,46/17) Hyperbolic Matrix(101,-62,44,-27) (3/5,5/8) -> (9/4,7/3) Hyperbolic Matrix(309,-196,484,-307) (12/19,7/11) -> (7/11,16/25) Parabolic Matrix(1549,-1080,360,-251) (23/33,7/10) -> (43/10,13/3) Hyperbolic Matrix(475,-334,64,-45) (7/10,19/27) -> (7/1,15/2) Hyperbolic Matrix(499,-364,292,-213) (8/11,11/15) -> (29/17,12/7) Hyperbolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(445,-366,276,-227) (9/11,5/6) -> (29/18,21/13) Hyperbolic Matrix(87,-74,20,-17) (5/6,1/1) -> (13/3,9/2) Hyperbolic Matrix(41,-50,32,-39) (1/1,5/4) -> (5/4,9/7) Parabolic Matrix(879,-1136,236,-305) (9/7,22/17) -> (26/7,41/11) Hyperbolic Matrix(531,-692,188,-245) (13/10,17/13) -> (31/11,17/6) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(1529,-2108,272,-375) (11/8,40/29) -> (28/5,45/8) Hyperbolic Matrix(309,-484,196,-307) (14/9,11/7) -> (11/7,30/19) Parabolic Matrix(343,-556,124,-201) (21/13,13/8) -> (11/4,25/9) Hyperbolic Matrix(185,-302,68,-111) (13/8,5/3) -> (19/7,11/4) Hyperbolic Matrix(341,-578,200,-339) (5/3,17/10) -> (17/10,29/17) Parabolic Matrix(211,-364,40,-69) (12/7,19/11) -> (5/1,16/3) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(345,-754,124,-271) (13/6,11/5) -> (25/9,39/14) Hyperbolic Matrix(267,-596,56,-125) (20/9,9/4) -> (19/4,24/5) Hyperbolic Matrix(305,-722,128,-303) (7/3,19/8) -> (19/8,31/13) Parabolic Matrix(261,-676,100,-259) (18/7,13/5) -> (13/5,34/13) Parabolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(1419,-3962,380,-1061) (53/19,14/5) -> (56/15,71/19) Hyperbolic Matrix(29,-98,8,-27) (3/1,7/2) -> (7/2,11/3) Parabolic Matrix(1283,-4800,228,-853) (71/19,15/4) -> (45/8,107/19) Hyperbolic Matrix(1803,-7736,320,-1373) (30/7,73/17) -> (107/19,62/11) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,18,0,1) -> Matrix(1,0,0,1) Matrix(47,390,-84,-697) -> Matrix(1,0,0,1) Matrix(21,164,16,125) -> Matrix(1,0,0,1) Matrix(45,296,-116,-763) -> Matrix(1,0,0,1) Matrix(45,278,28,173) -> Matrix(1,0,0,1) Matrix(43,242,-8,-45) -> Matrix(1,2,-2,-3) Matrix(105,554,76,401) -> Matrix(3,2,-2,-1) Matrix(9,44,28,137) -> Matrix(1,0,2,1) Matrix(247,1166,-68,-321) -> Matrix(1,0,0,1) Matrix(51,232,20,91) -> Matrix(1,0,0,1) Matrix(5,22,32,141) -> Matrix(1,0,0,1) Matrix(115,494,-44,-189) -> Matrix(1,0,-2,1) Matrix(123,466,-52,-197) -> Matrix(1,0,0,1) Matrix(119,444,-264,-985) -> Matrix(1,0,0,1) Matrix(359,1332,252,935) -> Matrix(1,0,0,1) Matrix(381,1406,268,989) -> Matrix(5,4,-4,-3) Matrix(81,296,136,497) -> Matrix(1,0,2,1) Matrix(117,422,28,101) -> Matrix(1,0,0,1) Matrix(43,152,28,99) -> Matrix(1,0,0,1) Matrix(75,256,104,355) -> Matrix(3,2,-2,-1) Matrix(53,178,92,309) -> Matrix(1,0,2,1) Matrix(103,338,-32,-105) -> Matrix(1,2,-2,-3) Matrix(91,290,16,51) -> Matrix(3,2,-2,-1) Matrix(31,86,40,111) -> Matrix(1,0,0,1) Matrix(147,400,104,283) -> Matrix(3,2,-2,-1) Matrix(105,284,-464,-1255) -> Matrix(1,0,0,1) Matrix(233,628,128,345) -> Matrix(1,0,2,1) Matrix(111,292,176,463) -> Matrix(5,2,2,1) Matrix(367,962,-800,-2097) -> Matrix(1,0,2,1) Matrix(635,1662,912,2387) -> Matrix(5,2,2,1) Matrix(59,150,-24,-61) -> Matrix(1,0,2,1) Matrix(103,248,76,183) -> Matrix(1,0,0,1) Matrix(79,188,208,495) -> Matrix(1,0,0,1) Matrix(147,346,212,499) -> Matrix(1,0,2,1) Matrix(15,34,56,127) -> Matrix(1,0,-4,1) Matrix(103,230,-176,-393) -> Matrix(1,0,-2,1) Matrix(77,166,32,69) -> Matrix(1,0,0,1) Matrix(3,4,-4,-5) -> Matrix(1,0,0,1) Matrix(151,98,208,135) -> Matrix(1,0,0,1) Matrix(53,34,-304,-195) -> Matrix(3,4,-4,-5) Matrix(735,466,-1276,-809) -> Matrix(1,0,0,1) Matrix(493,312,1272,805) -> Matrix(1,0,0,1) Matrix(239,150,-384,-241) -> Matrix(1,2,-2,-3) Matrix(803,498,1140,707) -> Matrix(3,2,-2,-1) Matrix(799,494,-1412,-873) -> Matrix(3,2,-2,-1) Matrix(661,408,1032,637) -> Matrix(7,4,-2,-1) Matrix(49,30,276,169) -> Matrix(1,0,0,1) Matrix(141,86,-464,-283) -> Matrix(1,0,0,1) Matrix(571,338,-968,-573) -> Matrix(1,0,2,1) Matrix(523,308,-1136,-669) -> Matrix(1,0,0,1) Matrix(177,104,-788,-463) -> Matrix(1,0,0,1) Matrix(949,552,600,349) -> Matrix(1,0,0,1) Matrix(517,300,-1632,-947) -> Matrix(3,2,-2,-1) Matrix(2011,1166,-3596,-2085) -> Matrix(1,0,0,1) Matrix(769,444,168,97) -> Matrix(1,0,0,1) Matrix(1523,876,1104,635) -> Matrix(3,2,-2,-1) Matrix(917,520,164,93) -> Matrix(1,0,0,1) Matrix(823,464,580,327) -> Matrix(3,2,-2,-1) Matrix(1069,600,408,229) -> Matrix(1,0,0,1) Matrix(79,44,-404,-225) -> Matrix(3,2,-2,-1) Matrix(279,154,404,223) -> Matrix(1,0,2,1) Matrix(161,88,236,129) -> Matrix(1,0,0,1) Matrix(547,296,316,171) -> Matrix(1,0,0,1) Matrix(387,208,80,43) -> Matrix(1,0,0,1) Matrix(227,120,384,203) -> Matrix(1,0,2,1) Matrix(367,170,136,63) -> Matrix(1,0,0,1) Matrix(201,92,-1064,-487) -> Matrix(5,4,-4,-3) Matrix(1115,504,396,179) -> Matrix(1,0,-2,1) Matrix(165,74,-524,-235) -> Matrix(3,2,-2,-1) Matrix(223,98,-512,-225) -> Matrix(1,0,2,1) Matrix(347,150,192,83) -> Matrix(1,0,0,1) Matrix(1187,504,252,107) -> Matrix(3,2,-2,-1) Matrix(1313,556,-3436,-1455) -> Matrix(1,0,2,1) Matrix(403,170,64,27) -> Matrix(1,0,0,1) Matrix(495,208,188,79) -> Matrix(1,0,0,1) Matrix(183,76,248,103) -> Matrix(1,0,0,1) Matrix(151,62,-548,-225) -> Matrix(3,2,-2,-1) Matrix(87,34,-412,-161) -> Matrix(1,0,0,1) Matrix(413,160,-2176,-843) -> Matrix(5,4,-4,-3) Matrix(1117,432,468,181) -> Matrix(1,0,2,1) Matrix(407,156,60,23) -> Matrix(1,0,0,1) Matrix(6729,2570,1804,689) -> Matrix(1,4,-2,-7) Matrix(2123,810,1224,467) -> Matrix(1,0,0,1) Matrix(463,176,292,111) -> Matrix(1,0,0,1) Matrix(27,10,116,43) -> Matrix(1,0,-2,1) Matrix(139,50,-392,-141) -> Matrix(1,0,2,1) Matrix(247,86,112,39) -> Matrix(1,0,-2,1) Matrix(213,68,-1112,-355) -> Matrix(3,8,-2,-5) Matrix(207,64,-676,-209) -> Matrix(3,4,-4,-5) Matrix(1349,412,776,237) -> Matrix(3,2,-2,-1) Matrix(255,76,104,31) -> Matrix(1,0,0,1) Matrix(355,104,256,75) -> Matrix(1,0,0,1) Matrix(99,28,152,43) -> Matrix(1,0,0,1) Matrix(773,214,596,165) -> Matrix(1,2,-2,-3) Matrix(23,6,-96,-25) -> Matrix(1,2,-2,-3) Matrix(419,96,48,11) -> Matrix(1,0,0,1) Matrix(701,160,92,21) -> Matrix(3,2,-2,-1) Matrix(91,20,232,51) -> Matrix(1,0,0,1) Matrix(339,70,92,19) -> Matrix(1,2,-2,-3) Matrix(3271,626,580,111) -> Matrix(5,8,-2,-3) Matrix(87,16,-484,-89) -> Matrix(13,14,-14,-15) Matrix(1247,222,264,47) -> Matrix(9,8,-8,-7) Matrix(63,10,44,7) -> Matrix(3,2,-2,-1) Matrix(149,-14,32,-3) -> Matrix(1,0,2,1) Matrix(443,-60,96,-13) -> Matrix(1,0,-2,1) Matrix(229,-42,60,-11) -> Matrix(1,0,0,1) Matrix(105,-22,148,-31) -> Matrix(1,0,2,1) Matrix(57,-16,196,-55) -> Matrix(1,0,14,1) Matrix(319,-94,112,-33) -> Matrix(1,0,-8,1) Matrix(303,-92,56,-17) -> Matrix(1,0,-4,1) Matrix(701,-218,164,-51) -> Matrix(3,-2,-4,3) Matrix(93,-34,52,-19) -> Matrix(1,0,0,1) Matrix(261,-100,676,-259) -> Matrix(1,0,0,1) Matrix(13,-6,24,-11) -> Matrix(1,0,2,1) Matrix(513,-298,136,-79) -> Matrix(1,0,-2,1) Matrix(499,-292,364,-213) -> Matrix(1,0,0,1) Matrix(1471,-868,544,-321) -> Matrix(1,0,-2,1) Matrix(101,-62,44,-27) -> Matrix(1,0,-2,1) Matrix(309,-196,484,-307) -> Matrix(1,-6,0,1) Matrix(1549,-1080,360,-251) -> Matrix(1,-2,-2,5) Matrix(475,-334,64,-45) -> Matrix(1,0,0,1) Matrix(499,-364,292,-213) -> Matrix(1,2,-2,-3) Matrix(81,-64,100,-79) -> Matrix(1,0,4,1) Matrix(445,-366,276,-227) -> Matrix(1,0,-2,1) Matrix(87,-74,20,-17) -> Matrix(1,0,-2,1) Matrix(41,-50,32,-39) -> Matrix(1,2,-2,-3) Matrix(879,-1136,236,-305) -> Matrix(5,2,-8,-3) Matrix(531,-692,188,-245) -> Matrix(1,0,-2,1) Matrix(867,-1184,320,-437) -> Matrix(1,0,0,1) Matrix(1529,-2108,272,-375) -> Matrix(1,2,0,1) Matrix(309,-484,196,-307) -> Matrix(1,0,0,1) Matrix(343,-556,124,-201) -> Matrix(1,2,-2,-3) Matrix(185,-302,68,-111) -> Matrix(1,0,0,1) Matrix(341,-578,200,-339) -> Matrix(3,4,-4,-5) Matrix(211,-364,40,-69) -> Matrix(1,0,0,1) Matrix(25,-48,12,-23) -> Matrix(1,2,-2,-3) Matrix(345,-754,124,-271) -> Matrix(5,2,-8,-3) Matrix(267,-596,56,-125) -> Matrix(1,0,0,1) Matrix(305,-722,128,-303) -> Matrix(1,0,4,1) Matrix(261,-676,100,-259) -> Matrix(1,0,0,1) Matrix(1839,-5126,428,-1193) -> Matrix(15,8,-32,-17) Matrix(1419,-3962,380,-1061) -> Matrix(17,8,-32,-15) Matrix(29,-98,8,-27) -> Matrix(1,2,-2,-3) Matrix(1283,-4800,228,-853) -> Matrix(5,2,2,1) Matrix(1803,-7736,320,-1373) -> Matrix(15,8,-2,-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: 144 ----------------------------------------------------------------------- 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): 432 Minimal number of generators: 73 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: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -5/11 -7/16 -2/5 -5/14 -1/3 -1/4 0/1 1/5 2/7 1/3 5/13 1/2 7/11 4/5 1/1 5/4 7/5 3/2 11/7 17/10 2/1 19/8 5/2 13/5 11/4 3/1 7/2 15/4 4/1 73/17 9/2 5/1 11/2 6/1 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 -1/2 -1/1 0/1 -6/13 -1/2 1/0 -5/11 -1/2 1/0 -9/20 -1/1 0/1 -4/9 -1/2 1/0 -7/16 0/1 -10/23 1/2 1/0 -3/7 1/0 -11/26 0/1 -8/19 -1/2 1/0 -5/12 -1/1 0/1 -7/17 -1/2 -2/5 0/1 -7/18 -1/1 0/1 -19/49 -1/2 1/0 -12/31 -1/2 -1/4 -5/13 1/0 -13/34 0/1 -8/21 -1/2 1/0 -3/8 -1/1 0/1 -4/11 -1/2 1/0 -5/14 0/1 -6/17 1/2 1/0 -1/3 1/0 -3/10 -1/1 0/1 -5/17 1/0 -2/7 -1/2 1/0 -5/18 -2/1 1/0 -8/29 -2/1 -3/11 1/0 -1/4 -1/1 -3/13 -1/2 -2/9 -1/2 1/0 -3/14 -1/1 0/1 -4/19 0/1 -1/5 1/0 -1/6 -1/1 -2/3 0/1 -1/2 1/0 1/5 -1/2 2/9 -1/2 -1/4 1/4 -1/3 0/1 3/11 -1/6 2/7 0/1 5/17 1/8 3/10 0/1 1/4 4/13 3/8 1/2 5/16 1/1 1/3 1/0 3/8 -1/1 0/1 5/13 -1/2 1/0 7/18 -1/1 0/1 2/5 -1/2 1/0 1/2 0/1 4/7 1/2 1/0 7/12 0/1 1/0 10/17 0/1 3/5 1/0 5/8 1/1 1/0 7/11 1/0 9/14 -2/1 1/0 2/3 -1/2 1/0 7/10 -1/1 1/0 12/17 -1/2 1/0 5/7 1/0 8/11 -1/2 1/0 11/15 -1/2 3/4 -1/1 0/1 7/9 -1/2 4/5 0/1 9/11 1/2 5/6 0/1 1/1 1/1 1/0 5/4 -1/1 9/7 -1/2 22/17 0/1 13/10 -1/2 0/1 17/13 -1/2 1/0 4/3 -1/2 1/0 15/11 1/0 26/19 0/1 11/8 0/1 1/0 18/13 -1/2 1/0 7/5 1/0 10/7 -3/2 1/0 3/2 -1/1 0/1 11/7 -1/2 1/0 19/12 -1/1 0/1 8/5 -1/2 1/0 29/18 -1/1 0/1 21/13 1/0 13/8 -1/1 5/3 1/0 17/10 -1/1 29/17 -3/4 12/7 -3/4 -1/2 7/4 -1/1 0/1 9/5 1/0 20/11 1/2 1/0 11/6 1/1 1/0 2/1 -1/1 13/6 -3/5 -1/2 11/5 -1/2 9/4 -1/1 -1/2 7/3 -1/2 19/8 0/1 31/13 1/2 12/5 -1/2 1/0 17/7 1/0 5/2 -1/1 0/1 13/5 -1/2 1/0 21/8 -1/1 0/1 8/3 -1/2 1/0 27/10 -1/1 0/1 19/7 1/0 11/4 -1/1 25/9 -1/2 39/14 -5/9 -1/2 53/19 -1/2 14/5 -1/2 -3/8 31/11 -1/2 -1/4 17/6 -1/4 0/1 3/1 1/0 7/2 -1/1 11/3 -1/2 26/7 -2/3 41/11 -1/2 15/4 -1/2 0/1 4/1 -1/2 1/0 17/4 -1/1 30/7 -7/12 -1/2 73/17 -1/2 43/10 -1/2 -3/7 13/3 -1/2 9/2 -1/1 0/1 14/3 1/2 1/0 5/1 -1/2 1/0 16/3 -3/4 -1/2 11/2 0/1 1/0 17/3 1/0 6/1 -1/2 1/0 13/2 0/1 7/1 1/0 8/1 -1/1 9/1 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(367,170,136,63) (-1/2,-6/13) -> (8/3,27/10) Hyperbolic Matrix(265,122,202,93) (-6/13,-5/11) -> (17/13,4/3) Hyperbolic Matrix(457,206,-1178,-531) (-5/11,-9/20) -> (-7/18,-19/49) Hyperbolic Matrix(421,188,262,117) (-9/20,-4/9) -> (8/5,29/18) Hyperbolic Matrix(223,98,-512,-225) (-4/9,-7/16) -> (-7/16,-10/23) Parabolic Matrix(347,150,192,83) (-10/23,-3/7) -> (9/5,20/11) Hyperbolic Matrix(61,26,190,81) (-3/7,-11/26) -> (5/16,1/3) Hyperbolic Matrix(403,170,64,27) (-11/26,-8/19) -> (6/1,13/2) Hyperbolic Matrix(495,208,188,79) (-8/19,-5/12) -> (21/8,8/3) Hyperbolic Matrix(183,76,248,103) (-5/12,-7/17) -> (11/15,3/4) Hyperbolic Matrix(151,62,-548,-225) (-7/17,-2/5) -> (-8/29,-3/11) Hyperbolic Matrix(87,34,-412,-161) (-2/5,-7/18) -> (-3/14,-4/19) Hyperbolic Matrix(1647,638,586,227) (-19/49,-12/31) -> (14/5,31/11) Hyperbolic Matrix(1117,432,468,181) (-12/31,-5/13) -> (31/13,12/5) Hyperbolic Matrix(407,156,60,23) (-5/13,-13/34) -> (13/2,7/1) Hyperbolic Matrix(493,188,118,45) (-13/34,-8/21) -> (4/1,17/4) Hyperbolic Matrix(463,176,292,111) (-8/21,-3/8) -> (19/12,8/5) Hyperbolic Matrix(27,10,116,43) (-3/8,-4/11) -> (2/9,1/4) Hyperbolic Matrix(139,50,-392,-141) (-4/11,-5/14) -> (-5/14,-6/17) Parabolic Matrix(307,108,54,19) (-6/17,-1/3) -> (17/3,6/1) Hyperbolic Matrix(79,24,102,31) (-1/3,-3/10) -> (3/4,7/9) Hyperbolic Matrix(255,76,104,31) (-3/10,-5/17) -> (17/7,5/2) Hyperbolic Matrix(355,104,256,75) (-5/17,-2/7) -> (18/13,7/5) Hyperbolic Matrix(99,28,152,43) (-2/7,-5/18) -> (9/14,2/3) Hyperbolic Matrix(773,214,596,165) (-5/18,-8/29) -> (22/17,13/10) Hyperbolic Matrix(23,6,-96,-25) (-3/11,-1/4) -> (-1/4,-3/13) Parabolic Matrix(187,42,138,31) (-3/13,-2/9) -> (4/3,15/11) Hyperbolic Matrix(91,20,232,51) (-2/9,-3/14) -> (7/18,2/5) Hyperbolic Matrix(339,70,92,19) (-4/19,-1/5) -> (11/3,26/7) Hyperbolic Matrix(23,4,86,15) (-1/5,-1/6) -> (1/4,3/11) Hyperbolic Matrix(63,10,44,7) (-1/6,0/1) -> (10/7,3/2) Hyperbolic Matrix(45,-8,62,-11) (0/1,1/5) -> (5/7,8/11) Hyperbolic Matrix(105,-22,148,-31) (1/5,2/9) -> (12/17,5/7) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(319,-94,112,-33) (5/17,3/10) -> (17/6,3/1) Hyperbolic Matrix(303,-92,56,-17) (3/10,4/13) -> (16/3,11/2) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(93,-34,52,-19) (1/3,3/8) -> (7/4,9/5) Hyperbolic Matrix(131,-50,338,-129) (3/8,5/13) -> (5/13,7/18) Parabolic Matrix(13,-6,24,-11) (2/5,1/2) -> (1/2,4/7) Parabolic Matrix(193,-112,274,-159) (4/7,7/12) -> (7/10,12/17) Hyperbolic Matrix(499,-292,364,-213) (7/12,10/17) -> (26/19,11/8) Hyperbolic Matrix(159,-94,22,-13) (10/17,3/5) -> (7/1,8/1) Hyperbolic Matrix(101,-62,44,-27) (3/5,5/8) -> (9/4,7/3) Hyperbolic Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(85,-58,22,-15) (2/3,7/10) -> (15/4,4/1) Hyperbolic Matrix(499,-364,292,-213) (8/11,11/15) -> (29/17,12/7) Hyperbolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(445,-366,276,-227) (9/11,5/6) -> (29/18,21/13) Hyperbolic Matrix(87,-74,20,-17) (5/6,1/1) -> (13/3,9/2) Hyperbolic Matrix(41,-50,32,-39) (1/1,5/4) -> (5/4,9/7) Parabolic Matrix(879,-1136,236,-305) (9/7,22/17) -> (26/7,41/11) Hyperbolic Matrix(531,-692,188,-245) (13/10,17/13) -> (31/11,17/6) Hyperbolic Matrix(259,-354,30,-41) (15/11,26/19) -> (8/1,9/1) Hyperbolic Matrix(303,-418,166,-229) (11/8,18/13) -> (20/11,11/6) Hyperbolic Matrix(179,-254,74,-105) (7/5,10/7) -> (12/5,17/7) Hyperbolic Matrix(155,-242,98,-153) (3/2,11/7) -> (11/7,19/12) Parabolic Matrix(343,-556,124,-201) (21/13,13/8) -> (11/4,25/9) Hyperbolic Matrix(185,-302,68,-111) (13/8,5/3) -> (19/7,11/4) Hyperbolic Matrix(341,-578,200,-339) (5/3,17/10) -> (17/10,29/17) Parabolic Matrix(119,-206,26,-45) (12/7,7/4) -> (9/2,14/3) Hyperbolic Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(345,-754,124,-271) (13/6,11/5) -> (25/9,39/14) Hyperbolic Matrix(123,-274,22,-49) (11/5,9/4) -> (11/2,17/3) Hyperbolic Matrix(305,-722,128,-303) (7/3,19/8) -> (19/8,31/13) Parabolic Matrix(131,-338,50,-129) (5/2,13/5) -> (13/5,21/8) Parabolic Matrix(97,-262,10,-27) (27/10,19/7) -> (9/1,1/0) Hyperbolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(935,-2612,218,-609) (53/19,14/5) -> (30/7,73/17) Hyperbolic Matrix(29,-98,8,-27) (3/1,7/2) -> (7/2,11/3) Parabolic Matrix(525,-1958,122,-455) (41/11,15/4) -> (43/10,13/3) Hyperbolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,1,-2,-1) Matrix(367,170,136,63) -> Matrix(1,0,0,1) Matrix(265,122,202,93) -> Matrix(1,1,-2,-1) Matrix(457,206,-1178,-531) -> Matrix(1,1,-2,-1) Matrix(421,188,262,117) -> Matrix(1,1,-2,-1) Matrix(223,98,-512,-225) -> Matrix(1,0,2,1) Matrix(347,150,192,83) -> Matrix(1,0,0,1) Matrix(61,26,190,81) -> Matrix(1,1,0,1) Matrix(403,170,64,27) -> Matrix(1,0,0,1) Matrix(495,208,188,79) -> Matrix(1,0,0,1) Matrix(183,76,248,103) -> Matrix(1,0,0,1) Matrix(151,62,-548,-225) -> Matrix(3,2,-2,-1) Matrix(87,34,-412,-161) -> Matrix(1,0,0,1) Matrix(1647,638,586,227) -> Matrix(1,1,-4,-3) Matrix(1117,432,468,181) -> Matrix(1,0,2,1) Matrix(407,156,60,23) -> Matrix(1,0,0,1) Matrix(493,188,118,45) -> Matrix(1,1,-2,-1) Matrix(463,176,292,111) -> Matrix(1,0,0,1) Matrix(27,10,116,43) -> Matrix(1,0,-2,1) Matrix(139,50,-392,-141) -> Matrix(1,0,2,1) Matrix(307,108,54,19) -> Matrix(1,-1,0,1) Matrix(79,24,102,31) -> Matrix(1,1,-2,-1) Matrix(255,76,104,31) -> Matrix(1,0,0,1) Matrix(355,104,256,75) -> Matrix(1,0,0,1) Matrix(99,28,152,43) -> Matrix(1,0,0,1) Matrix(773,214,596,165) -> Matrix(1,2,-2,-3) Matrix(23,6,-96,-25) -> Matrix(1,2,-2,-3) Matrix(187,42,138,31) -> Matrix(1,1,-2,-1) Matrix(91,20,232,51) -> Matrix(1,0,0,1) Matrix(339,70,92,19) -> Matrix(1,2,-2,-3) Matrix(23,4,86,15) -> Matrix(1,1,-6,-5) Matrix(63,10,44,7) -> Matrix(3,2,-2,-1) Matrix(45,-8,62,-11) -> Matrix(1,1,-2,-1) Matrix(105,-22,148,-31) -> Matrix(1,0,2,1) Matrix(57,-16,196,-55) -> Matrix(1,0,14,1) Matrix(319,-94,112,-33) -> Matrix(1,0,-8,1) Matrix(303,-92,56,-17) -> Matrix(1,0,-4,1) Matrix(701,-218,164,-51) -> Matrix(3,-2,-4,3) Matrix(93,-34,52,-19) -> Matrix(1,0,0,1) Matrix(131,-50,338,-129) -> Matrix(1,1,-2,-1) Matrix(13,-6,24,-11) -> Matrix(1,0,2,1) Matrix(193,-112,274,-159) -> Matrix(1,-1,0,1) Matrix(499,-292,364,-213) -> Matrix(1,0,0,1) Matrix(159,-94,22,-13) -> Matrix(1,-1,0,1) Matrix(101,-62,44,-27) -> Matrix(1,0,-2,1) Matrix(155,-98,242,-153) -> Matrix(1,-3,0,1) Matrix(85,-58,22,-15) -> Matrix(1,1,-2,-1) Matrix(499,-364,292,-213) -> Matrix(1,2,-2,-3) Matrix(81,-64,100,-79) -> Matrix(1,0,4,1) Matrix(445,-366,276,-227) -> Matrix(1,0,-2,1) Matrix(87,-74,20,-17) -> Matrix(1,0,-2,1) Matrix(41,-50,32,-39) -> Matrix(1,2,-2,-3) Matrix(879,-1136,236,-305) -> Matrix(5,2,-8,-3) Matrix(531,-692,188,-245) -> Matrix(1,0,-2,1) Matrix(259,-354,30,-41) -> Matrix(1,1,-2,-1) Matrix(303,-418,166,-229) -> Matrix(1,1,0,1) Matrix(179,-254,74,-105) -> Matrix(1,1,0,1) Matrix(155,-242,98,-153) -> Matrix(1,1,-2,-1) Matrix(343,-556,124,-201) -> Matrix(1,2,-2,-3) Matrix(185,-302,68,-111) -> Matrix(1,0,0,1) Matrix(341,-578,200,-339) -> Matrix(3,4,-4,-5) Matrix(119,-206,26,-45) -> Matrix(1,1,-2,-1) Matrix(25,-48,12,-23) -> Matrix(1,2,-2,-3) Matrix(345,-754,124,-271) -> Matrix(5,2,-8,-3) Matrix(123,-274,22,-49) -> Matrix(1,1,-2,-1) Matrix(305,-722,128,-303) -> Matrix(1,0,4,1) Matrix(131,-338,50,-129) -> Matrix(1,1,-2,-1) Matrix(97,-262,10,-27) -> Matrix(1,1,-2,-1) Matrix(1839,-5126,428,-1193) -> Matrix(15,8,-32,-17) Matrix(935,-2612,218,-609) -> Matrix(11,5,-20,-9) Matrix(29,-98,8,-27) -> Matrix(1,2,-2,-3) Matrix(525,-1958,122,-455) -> Matrix(5,3,-12,-7) Matrix(31,-150,6,-29) -> Matrix(1,1,-2,-1) 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 -1/1 (-1/1,0/1).(-1/2,1/0) 0 2 0/1 (-1/2,1/0) 0 18 1/5 -1/2 1 6 1/4 (-1/3,0/1) 0 18 2/7 0/1 7 2 3/10 (0/1,1/4) 0 18 4/13 (3/8,1/2) 0 18 1/3 1/0 1 18 3/8 (-1/1,0/1) 0 18 5/13 (-1/1,0/1).(-1/2,1/0) 0 2 2/5 (-1/2,1/0) 0 18 1/2 0/1 2 6 4/7 (1/2,1/0) 0 18 7/12 (0/1,1/0) 0 18 10/17 0/1 1 2 3/5 1/0 1 18 5/8 (1/1,1/0) 0 18 7/11 1/0 3 2 2/3 (-1/2,1/0) 0 18 7/10 (-1/1,1/0) 0 18 5/7 1/0 1 6 8/11 (-1/2,1/0) 0 18 3/4 (-1/1,0/1) 0 18 4/5 0/1 2 2 5/6 (0/1,1/1) 0 18 1/1 1/0 1 18 5/4 -1/1 2 2 9/7 -1/2 1 18 13/10 (-1/2,0/1) 0 18 4/3 (-1/2,1/0) 0 18 11/8 (0/1,1/0) 0 18 7/5 1/0 1 6 3/2 (-1/1,0/1) 0 18 11/7 (-1/1,0/1).(-1/2,1/0) 0 2 8/5 (-1/2,1/0) 0 18 21/13 1/0 1 18 13/8 -1/1 2 6 5/3 1/0 1 18 17/10 -1/1 4 2 12/7 (-3/4,-1/2) 0 18 7/4 (-1/1,0/1) 0 18 9/5 1/0 1 18 11/6 (1/1,1/0) 0 18 2/1 -1/1 1 6 13/6 (-3/5,-1/2) 0 18 11/5 -1/2 1 18 9/4 (-1/1,-1/2) 0 18 7/3 -1/2 1 18 19/8 0/1 4 2 12/5 (-1/2,1/0) 0 18 5/2 (-1/1,0/1) 0 18 13/5 (-1/1,0/1).(-1/2,1/0) 0 2 8/3 (-1/2,1/0) 0 18 19/7 1/0 1 18 11/4 -1/1 2 6 25/9 -1/2 1 18 39/14 (-5/9,-1/2) 0 18 53/19 -1/2 13 2 14/5 (-1/2,-3/8) 0 18 3/1 1/0 1 18 7/2 -1/1 2 2 11/3 -1/2 1 18 15/4 (-1/2,0/1) 0 18 4/1 (-1/2,1/0) 0 18 13/3 -1/2 1 18 9/2 (-1/1,0/1) 0 18 14/3 (1/2,1/0) 0 18 5/1 (-1/1,0/1).(-1/2,1/0) 0 6 16/3 (-3/4,-1/2) 0 18 11/2 (0/1,1/0) 0 18 6/1 (-1/2,1/0) 0 18 7/1 1/0 1 18 8/1 -1/1 1 2 1/0 (-1/1,0/1) 0 18 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(45,-8,62,-11) (0/1,1/5) -> (5/7,8/11) Hyperbolic Matrix(43,-10,30,-7) (1/5,1/4) -> (7/5,3/2) Glide Reflection Matrix(15,-4,56,-15) (1/4,2/7) -> (1/4,2/7) Reflection Matrix(41,-12,140,-41) (2/7,3/10) -> (2/7,3/10) Reflection Matrix(303,-92,56,-17) (3/10,4/13) -> (16/3,11/2) Hyperbolic Matrix(81,-26,28,-9) (4/13,1/3) -> (14/5,3/1) Glide Reflection Matrix(93,-34,52,-19) (1/3,3/8) -> (7/4,9/5) Hyperbolic Matrix(79,-30,208,-79) (3/8,5/13) -> (3/8,5/13) Reflection Matrix(51,-20,130,-51) (5/13,2/5) -> (5/13,2/5) Reflection Matrix(13,-6,24,-11) (2/5,1/2) -> (1/2,4/7) Parabolic Matrix(125,-72,92,-53) (4/7,7/12) -> (4/3,11/8) Glide Reflection Matrix(239,-140,408,-239) (7/12,10/17) -> (7/12,10/17) Reflection Matrix(159,-94,22,-13) (10/17,3/5) -> (7/1,8/1) Hyperbolic Matrix(101,-62,44,-27) (3/5,5/8) -> (9/4,7/3) Hyperbolic Matrix(111,-70,176,-111) (5/8,7/11) -> (5/8,7/11) Reflection Matrix(43,-28,66,-43) (7/11,2/3) -> (7/11,2/3) Reflection Matrix(85,-58,22,-15) (2/3,7/10) -> (15/4,4/1) Hyperbolic Matrix(147,-104,106,-75) (7/10,5/7) -> (11/8,7/5) Glide Reflection Matrix(103,-76,42,-31) (8/11,3/4) -> (12/5,5/2) Glide Reflection Matrix(31,-24,40,-31) (3/4,4/5) -> (3/4,4/5) Reflection Matrix(49,-40,60,-49) (4/5,5/6) -> (4/5,5/6) Reflection Matrix(87,-74,20,-17) (5/6,1/1) -> (13/3,9/2) Hyperbolic Matrix(41,-50,32,-39) (1/1,5/4) -> (5/4,9/7) Parabolic Matrix(173,-224,78,-101) (9/7,13/10) -> (11/5,9/4) Glide Reflection Matrix(93,-122,16,-21) (13/10,4/3) -> (11/2,6/1) Glide Reflection 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(117,-188,28,-45) (8/5,21/13) -> (4/1,13/3) Glide Reflection Matrix(343,-556,124,-201) (21/13,13/8) -> (11/4,25/9) Hyperbolic Matrix(185,-302,68,-111) (13/8,5/3) -> (19/7,11/4) Hyperbolic Matrix(127,-214,54,-91) (5/3,17/10) -> (7/3,19/8) Glide Reflection Matrix(253,-432,106,-181) (17/10,12/7) -> (19/8,12/5) Glide Reflection Matrix(119,-206,26,-45) (12/7,7/4) -> (9/2,14/3) Hyperbolic Matrix(141,-256,38,-69) (9/5,11/6) -> (11/3,15/4) Glide Reflection Matrix(25,-48,12,-23) (11/6,2/1) -> (2/1,13/6) Parabolic Matrix(345,-754,124,-271) (13/6,11/5) -> (25/9,39/14) Hyperbolic Matrix(51,-130,20,-51) (5/2,13/5) -> (5/2,13/5) Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(63,-170,10,-27) (8/3,19/7) -> (6/1,7/1) Glide Reflection Matrix(1483,-4134,532,-1483) (39/14,53/19) -> (39/14,53/19) Reflection Matrix(531,-1484,190,-531) (53/19,14/5) -> (53/19,14/5) Reflection Matrix(29,-98,8,-27) (3/1,7/2) -> (7/2,11/3) Parabolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic Matrix(-1,16,0,1) (8/1,1/0) -> (8/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,1,0,-1) (-1/1,0/1) -> (-1/2,1/0) Matrix(45,-8,62,-11) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(43,-10,30,-7) -> Matrix(3,1,-2,-1) Matrix(15,-4,56,-15) -> Matrix(-1,0,6,1) (1/4,2/7) -> (-1/3,0/1) Matrix(41,-12,140,-41) -> Matrix(1,0,8,-1) (2/7,3/10) -> (0/1,1/4) Matrix(303,-92,56,-17) -> Matrix(1,0,-4,1) 0/1 Matrix(81,-26,28,-9) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(93,-34,52,-19) -> Matrix(1,0,0,1) Matrix(79,-30,208,-79) -> Matrix(-1,0,2,1) (3/8,5/13) -> (-1/1,0/1) Matrix(51,-20,130,-51) -> Matrix(1,1,0,-1) (5/13,2/5) -> (-1/2,1/0) Matrix(13,-6,24,-11) -> Matrix(1,0,2,1) 0/1 Matrix(125,-72,92,-53) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(239,-140,408,-239) -> Matrix(1,0,0,-1) (7/12,10/17) -> (0/1,1/0) Matrix(159,-94,22,-13) -> Matrix(1,-1,0,1) 1/0 Matrix(101,-62,44,-27) -> Matrix(1,0,-2,1) 0/1 Matrix(111,-70,176,-111) -> Matrix(-1,2,0,1) (5/8,7/11) -> (1/1,1/0) Matrix(43,-28,66,-43) -> Matrix(1,1,0,-1) (7/11,2/3) -> (-1/2,1/0) Matrix(85,-58,22,-15) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(147,-104,106,-75) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(103,-76,42,-31) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(31,-24,40,-31) -> Matrix(-1,0,2,1) (3/4,4/5) -> (-1/1,0/1) Matrix(49,-40,60,-49) -> Matrix(1,0,2,-1) (4/5,5/6) -> (0/1,1/1) Matrix(87,-74,20,-17) -> Matrix(1,0,-2,1) 0/1 Matrix(41,-50,32,-39) -> Matrix(1,2,-2,-3) -1/1 Matrix(173,-224,78,-101) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(93,-122,16,-21) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(43,-66,28,-43) -> Matrix(-1,0,2,1) (3/2,11/7) -> (-1/1,0/1) Matrix(111,-176,70,-111) -> Matrix(1,1,0,-1) (11/7,8/5) -> (-1/2,1/0) Matrix(117,-188,28,-45) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(343,-556,124,-201) -> Matrix(1,2,-2,-3) -1/1 Matrix(185,-302,68,-111) -> Matrix(1,0,0,1) Matrix(127,-214,54,-91) -> Matrix(1,1,-2,-3) Matrix(253,-432,106,-181) -> Matrix(1,1,2,1) Matrix(119,-206,26,-45) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(141,-256,38,-69) -> Matrix(1,-1,-2,1) Matrix(25,-48,12,-23) -> Matrix(1,2,-2,-3) -1/1 Matrix(345,-754,124,-271) -> Matrix(5,2,-8,-3) -1/2 Matrix(51,-130,20,-51) -> Matrix(-1,0,2,1) (5/2,13/5) -> (-1/1,0/1) Matrix(79,-208,30,-79) -> Matrix(1,1,0,-1) (13/5,8/3) -> (-1/2,1/0) Matrix(63,-170,10,-27) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(1483,-4134,532,-1483) -> Matrix(19,10,-36,-19) (39/14,53/19) -> (-5/9,-1/2) Matrix(531,-1484,190,-531) -> Matrix(7,3,-16,-7) (53/19,14/5) -> (-1/2,-3/8) Matrix(29,-98,8,-27) -> Matrix(1,2,-2,-3) -1/1 Matrix(31,-150,6,-29) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(-1,16,0,1) -> Matrix(-1,0,2,1) (8/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.