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): 1008 Minimal number of generators: 169 Number of equivalence classes of cusps: 48 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 13/11 13/10 13/9 3/2 39/25 13/8 13/7 2/1 13/6 26/11 12/5 5/2 130/51 13/5 52/19 39/14 3/1 13/4 10/3 104/31 7/2 104/29 18/5 11/3 26/7 4/1 13/3 22/5 9/2 78/17 14/3 52/11 24/5 5/1 26/5 16/3 11/2 52/9 6/1 13/2 20/3 7/1 8/1 26/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 3/2 -20/3 3/1 -13/2 1/0 -6/1 0/1 -17/3 1/0 -11/2 1/2 -16/3 1/1 -5/1 3/2 -19/4 11/6 -14/3 2/1 -9/2 1/0 -22/5 4/1 -13/3 1/0 -4/1 1/1 -11/3 5/2 -29/8 1/0 -18/5 2/1 -25/7 1/0 -32/9 3/1 -7/2 3/2 -31/9 5/2 -24/7 3/1 -41/12 5/2 -17/5 1/0 -27/8 1/0 -37/11 1/0 -10/3 2/1 -13/4 5/2 1/0 -16/5 3/1 -3/1 1/0 -17/6 1/0 -14/5 2/1 -39/14 5/2 -64/23 3/1 -25/9 5/2 -11/4 5/2 -30/11 4/1 -19/7 7/2 -27/10 1/0 -35/13 1/0 -8/3 3/1 -13/5 1/0 -18/7 2/1 -23/9 1/0 -51/20 1/0 -28/11 1/1 -5/2 1/0 -27/11 5/2 -22/9 2/1 -17/7 5/2 -46/19 8/3 -29/12 5/2 -41/17 11/4 -53/22 11/4 -12/5 3/1 -7/3 13/4 -30/13 10/3 -53/23 7/2 -23/10 7/2 -16/7 3/1 -41/18 7/2 -25/11 7/2 -34/15 4/1 -9/4 7/2 -29/13 7/2 -20/9 3/1 -51/23 7/2 -31/14 15/4 -42/19 4/1 -11/5 1/0 -24/11 3/1 -13/6 7/2 1/0 -2/1 4/1 -13/7 9/2 1/0 -24/13 5/1 -11/6 1/0 -31/17 17/4 -20/11 5/1 -9/5 9/2 -25/14 9/2 -16/9 5/1 -23/13 9/2 -7/4 19/4 -26/15 5/1 -19/11 51/10 -12/7 5/1 -29/17 11/2 -17/10 11/2 -22/13 6/1 -27/16 11/2 -5/3 1/0 -28/17 7/1 -79/48 1/0 -130/79 1/0 -51/31 1/0 -23/14 1/0 -18/11 6/1 -13/8 1/0 -8/5 5/1 -19/12 9/2 -49/31 1/0 -79/50 1/0 -30/19 4/1 -41/26 19/4 -52/33 5/1 -11/7 11/2 -25/16 11/2 -64/41 5/1 -39/25 11/2 -14/9 6/1 -3/2 1/0 -16/11 5/1 -13/9 11/2 1/0 -10/7 6/1 -57/40 23/4 -104/73 6/1 -47/33 25/4 -37/26 1/0 -27/19 1/0 -17/12 1/0 -24/17 5/1 -7/5 13/2 -32/23 5/1 -57/41 13/2 -25/18 1/0 -43/31 1/0 -104/75 5/1 -61/44 11/2 -18/13 6/1 -29/21 1/0 -40/29 5/1 -51/37 11/2 -11/8 11/2 -26/19 6/1 -15/11 25/4 -4/3 7/1 -13/10 1/0 -22/17 4/1 -9/7 1/0 -32/25 5/1 -55/43 11/2 -78/61 6/1 -23/18 1/0 -14/11 6/1 -33/26 47/8 -52/41 6/1 -19/15 37/6 -24/19 19/3 -5/4 13/2 -26/21 7/1 -21/17 43/6 -16/13 7/1 -27/22 15/2 -11/9 15/2 -28/23 7/1 -17/14 1/0 -23/19 1/0 -52/43 7/1 -29/24 15/2 -6/5 8/1 -13/11 1/0 -20/17 5/1 -7/6 13/2 -8/7 7/1 -17/15 15/2 -26/23 8/1 -9/8 1/0 -1/1 1/0 0/1 1/0 1/1 1/0 7/6 -13/2 20/17 -5/1 13/11 1/0 6/5 -8/1 17/14 1/0 11/9 -15/2 16/13 -7/1 5/4 -13/2 19/15 -37/6 14/11 -6/1 9/7 1/0 22/17 -4/1 13/10 1/0 4/3 -7/1 11/8 -11/2 29/21 1/0 18/13 -6/1 25/18 1/0 32/23 -5/1 7/5 -13/2 31/22 -11/2 24/17 -5/1 41/29 -11/2 17/12 1/0 27/19 1/0 37/26 1/0 10/7 -6/1 13/9 -11/2 1/0 16/11 -5/1 3/2 1/0 17/11 1/0 14/9 -6/1 39/25 -11/2 64/41 -5/1 25/16 -11/2 11/7 -11/2 30/19 -4/1 19/12 -9/2 27/17 1/0 35/22 1/0 8/5 -5/1 13/8 1/0 18/11 -6/1 23/14 1/0 51/31 1/0 28/17 -7/1 5/3 1/0 27/16 -11/2 22/13 -6/1 17/10 -11/2 46/27 -16/3 29/17 -11/2 41/24 -21/4 53/31 -21/4 12/7 -5/1 7/4 -19/4 30/17 -14/3 53/30 -9/2 23/13 -9/2 16/9 -5/1 41/23 -9/2 25/14 -9/2 34/19 -4/1 9/5 -9/2 29/16 -9/2 20/11 -5/1 51/28 -9/2 31/17 -17/4 42/23 -4/1 11/6 1/0 24/13 -5/1 13/7 -9/2 1/0 2/1 -4/1 13/6 -7/2 1/0 24/11 -3/1 11/5 1/0 31/14 -15/4 20/9 -3/1 9/4 -7/2 25/11 -7/2 16/7 -3/1 23/10 -7/2 7/3 -13/4 26/11 -3/1 19/8 -29/10 12/5 -3/1 29/12 -5/2 17/7 -5/2 22/9 -2/1 27/11 -5/2 5/2 1/0 28/11 -1/1 79/31 1/0 130/51 1/0 51/20 1/0 23/9 1/0 18/7 -2/1 13/5 1/0 8/3 -3/1 19/7 -7/2 49/18 1/0 79/29 1/0 30/11 -4/1 41/15 -13/4 52/19 -3/1 11/4 -5/2 25/9 -5/2 64/23 -3/1 39/14 -5/2 14/5 -2/1 3/1 1/0 16/5 -3/1 13/4 -5/2 1/0 10/3 -2/1 57/17 -9/4 104/31 -2/1 47/14 -7/4 37/11 1/0 27/8 1/0 17/5 1/0 24/7 -3/1 7/2 -3/2 32/9 -3/1 57/16 -3/2 25/7 1/0 43/12 1/0 104/29 -3/1 61/17 -5/2 18/5 -2/1 29/8 1/0 40/11 -3/1 51/14 -5/2 11/3 -5/2 26/7 -2/1 15/4 -7/4 4/1 -1/1 13/3 1/0 22/5 -4/1 9/2 1/0 32/7 -3/1 55/12 -5/2 78/17 -2/1 23/5 1/0 14/3 -2/1 33/7 -17/8 52/11 -2/1 19/4 -11/6 24/5 -5/3 5/1 -3/2 26/5 -1/1 21/4 -5/6 16/3 -1/1 27/5 -1/2 11/2 -1/2 28/5 -1/1 17/3 1/0 23/4 1/0 52/9 -1/1 29/5 -1/2 6/1 0/1 13/2 1/0 20/3 -3/1 7/1 -3/2 8/1 -1/1 17/2 -1/2 26/3 0/1 9/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(27,208,-10,-77) (-7/1,1/0) -> (-19/7,-27/10) Hyperbolic Matrix(53,364,38,261) (-7/1,-20/3) -> (32/23,7/5) Hyperbolic Matrix(79,520,12,79) (-20/3,-13/2) -> (13/2,20/3) Hyperbolic Matrix(25,156,4,25) (-13/2,-6/1) -> (6/1,13/2) Hyperbolic Matrix(155,884,-64,-365) (-6/1,-17/3) -> (-17/7,-46/19) Hyperbolic Matrix(157,884,-46,-259) (-17/3,-11/2) -> (-41/12,-17/5) Hyperbolic Matrix(155,832,-68,-365) (-11/2,-16/3) -> (-16/7,-41/18) Hyperbolic Matrix(79,416,-64,-337) (-16/3,-5/1) -> (-21/17,-16/13) Hyperbolic Matrix(131,624,-38,-181) (-5/1,-19/4) -> (-7/2,-31/9) Hyperbolic Matrix(155,728,-122,-573) (-19/4,-14/3) -> (-14/11,-33/26) Hyperbolic Matrix(79,364,-28,-129) (-14/3,-9/2) -> (-17/6,-14/5) Hyperbolic Matrix(129,572,76,337) (-9/2,-22/5) -> (22/13,17/10) Hyperbolic Matrix(131,572,30,131) (-22/5,-13/3) -> (13/3,22/5) Hyperbolic Matrix(25,104,6,25) (-13/3,-4/1) -> (4/1,13/3) Hyperbolic Matrix(27,104,-20,-77) (-4/1,-11/3) -> (-15/11,-4/3) Hyperbolic Matrix(415,1508,-172,-625) (-11/3,-29/8) -> (-29/12,-41/17) Hyperbolic Matrix(259,936,158,571) (-29/8,-18/5) -> (18/11,23/14) Hyperbolic Matrix(363,1300,-160,-573) (-18/5,-25/7) -> (-25/11,-34/15) Hyperbolic Matrix(599,2132,-270,-961) (-25/7,-32/9) -> (-20/9,-51/23) Hyperbolic Matrix(103,364,88,311) (-32/9,-7/2) -> (7/6,20/17) Hyperbolic Matrix(287,988,174,599) (-31/9,-24/7) -> (28/17,5/3) Hyperbolic Matrix(365,1248,198,677) (-24/7,-41/12) -> (11/6,24/13) Hyperbolic Matrix(415,1404,-154,-521) (-17/5,-27/8) -> (-27/10,-35/13) Hyperbolic Matrix(911,3068,-378,-1273) (-27/8,-37/11) -> (-41/17,-53/22) Hyperbolic Matrix(495,1664,-224,-753) (-37/11,-10/3) -> (-42/19,-11/5) Hyperbolic Matrix(79,260,24,79) (-10/3,-13/4) -> (13/4,10/3) Hyperbolic Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(131,416,74,235) (-16/5,-3/1) -> (23/13,16/9) Hyperbolic Matrix(183,520,-82,-233) (-3/1,-17/6) -> (-9/4,-29/13) Hyperbolic Matrix(391,1092,140,391) (-14/5,-39/14) -> (39/14,14/5) Hyperbolic Matrix(1793,4992,644,1793) (-39/14,-64/23) -> (64/23,39/14) Hyperbolic Matrix(1327,3692,776,2159) (-64/23,-25/9) -> (53/31,12/7) Hyperbolic Matrix(469,1300,-206,-571) (-25/9,-11/4) -> (-41/18,-25/11) Hyperbolic Matrix(571,1560,-362,-989) (-11/4,-30/11) -> (-30/19,-41/26) Hyperbolic Matrix(287,780,-124,-337) (-30/11,-19/7) -> (-7/3,-30/13) Hyperbolic Matrix(155,416,-136,-365) (-35/13,-8/3) -> (-8/7,-17/15) Hyperbolic Matrix(79,208,30,79) (-8/3,-13/5) -> (13/5,8/3) Hyperbolic Matrix(181,468,70,181) (-13/5,-18/7) -> (18/7,13/5) Hyperbolic Matrix(365,936,264,677) (-18/7,-23/9) -> (29/21,18/13) Hyperbolic Matrix(937,2392,530,1353) (-23/9,-51/20) -> (53/30,23/13) Hyperbolic Matrix(1429,3640,-868,-2211) (-51/20,-28/11) -> (-28/17,-79/48) Hyperbolic Matrix(389,988,276,701) (-28/11,-5/2) -> (31/22,24/17) Hyperbolic Matrix(443,1092,-200,-493) (-5/2,-27/11) -> (-51/23,-31/14) Hyperbolic Matrix(807,1976,-350,-857) (-27/11,-22/9) -> (-30/13,-53/23) Hyperbolic Matrix(235,572,182,443) (-22/9,-17/7) -> (9/7,22/17) Hyperbolic Matrix(623,1508,-516,-1249) (-46/19,-29/12) -> (-29/24,-6/5) Hyperbolic Matrix(1533,3692,982,2365) (-53/22,-12/5) -> (64/41,25/16) Hyperbolic Matrix(131,312,-76,-181) (-12/5,-7/3) -> (-19/11,-12/7) Hyperbolic Matrix(1039,2392,632,1455) (-53/23,-23/10) -> (23/14,51/31) Hyperbolic Matrix(181,416,124,285) (-23/10,-16/7) -> (16/11,3/2) Hyperbolic Matrix(987,2236,-712,-1613) (-34/15,-9/4) -> (-61/44,-18/13) Hyperbolic Matrix(911,2028,-712,-1585) (-29/13,-20/9) -> (-32/25,-55/43) Hyperbolic Matrix(1223,2704,-858,-1897) (-31/14,-42/19) -> (-10/7,-57/40) Hyperbolic Matrix(571,1248,404,883) (-11/5,-24/11) -> (24/17,41/29) Hyperbolic Matrix(287,624,132,287) (-24/11,-13/6) -> (13/6,24/11) Hyperbolic Matrix(25,52,12,25) (-13/6,-2/1) -> (2/1,13/6) Hyperbolic Matrix(27,52,14,27) (-2/1,-13/7) -> (13/7,2/1) Hyperbolic Matrix(337,624,182,337) (-13/7,-24/13) -> (24/13,13/7) Hyperbolic Matrix(311,572,56,103) (-24/13,-11/6) -> (11/2,28/5) Hyperbolic Matrix(911,1664,-640,-1169) (-11/6,-31/17) -> (-47/33,-37/26) Hyperbolic Matrix(1171,2132,-842,-1533) (-31/17,-20/11) -> (-32/23,-57/41) Hyperbolic Matrix(259,468,-202,-365) (-20/11,-9/5) -> (-9/7,-32/25) Hyperbolic Matrix(727,1300,-524,-937) (-9/5,-25/14) -> (-25/18,-43/31) Hyperbolic Matrix(467,832,-380,-677) (-25/14,-16/9) -> (-16/13,-27/22) Hyperbolic Matrix(235,416,74,131) (-16/9,-23/13) -> (3/1,16/5) Hyperbolic Matrix(443,780,-280,-493) (-23/13,-7/4) -> (-19/12,-49/31) Hyperbolic Matrix(389,676,164,285) (-7/4,-26/15) -> (26/11,19/8) Hyperbolic Matrix(391,676,166,287) (-26/15,-19/11) -> (7/3,26/11) Hyperbolic Matrix(883,1508,-640,-1093) (-12/7,-29/17) -> (-29/21,-40/29) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(337,572,76,129) (-17/10,-22/13) -> (22/5,9/2) Hyperbolic Matrix(1507,2548,-954,-1613) (-22/13,-27/16) -> (-79/50,-30/19) Hyperbolic Matrix(987,1664,-710,-1197) (-27/16,-5/3) -> (-57/41,-25/18) Hyperbolic Matrix(157,260,32,53) (-5/3,-28/17) -> (24/5,5/1) Hyperbolic Matrix(10269,16900,4028,6629) (-79/48,-130/79) -> (130/51,51/20) Hyperbolic Matrix(10271,16900,4030,6631) (-130/79,-51/31) -> (79/31,130/51) Hyperbolic Matrix(2625,4316,964,1585) (-51/31,-23/14) -> (49/18,79/29) Hyperbolic Matrix(571,936,158,259) (-23/14,-18/11) -> (18/5,29/8) Hyperbolic Matrix(287,468,176,287) (-18/11,-13/8) -> (13/8,18/11) Hyperbolic Matrix(129,208,80,129) (-13/8,-8/5) -> (8/5,13/8) Hyperbolic Matrix(131,208,-114,-181) (-8/5,-19/12) -> (-7/6,-8/7) Hyperbolic Matrix(2731,4316,1070,1691) (-49/31,-79/50) -> (51/20,23/9) Hyperbolic Matrix(1715,2704,626,987) (-41/26,-52/33) -> (52/19,11/4) Hyperbolic Matrix(1717,2704,628,989) (-52/33,-11/7) -> (41/15,52/19) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(2731,4264,750,1171) (-25/16,-64/41) -> (40/11,51/14) Hyperbolic Matrix(3199,4992,2050,3199) (-64/41,-39/25) -> (39/25,64/41) Hyperbolic Matrix(701,1092,450,701) (-39/25,-14/9) -> (14/9,39/25) Hyperbolic Matrix(235,364,-184,-285) (-14/9,-3/2) -> (-23/18,-14/11) Hyperbolic Matrix(285,416,124,181) (-3/2,-16/11) -> (16/7,23/10) Hyperbolic Matrix(287,416,198,287) (-16/11,-13/9) -> (13/9,16/11) Hyperbolic Matrix(181,260,126,181) (-13/9,-10/7) -> (10/7,13/9) Hyperbolic Matrix(7591,10816,2262,3223) (-57/40,-104/73) -> (104/31,47/14) Hyperbolic Matrix(7593,10816,2264,3225) (-104/73,-47/33) -> (57/17,104/31) Hyperbolic Matrix(1535,2184,-1114,-1585) (-37/26,-27/19) -> (-51/37,-11/8) Hyperbolic Matrix(183,260,-164,-233) (-27/19,-17/12) -> (-9/8,-1/1) Hyperbolic Matrix(625,884,-514,-727) (-17/12,-24/17) -> (-28/23,-17/14) Hyperbolic Matrix(443,624,-350,-493) (-24/17,-7/5) -> (-19/15,-24/19) Hyperbolic Matrix(261,364,38,53) (-7/5,-32/23) -> (20/3,7/1) Hyperbolic Matrix(7799,10816,2174,3015) (-43/31,-104/75) -> (104/29,61/17) Hyperbolic Matrix(7801,10816,2176,3017) (-104/75,-61/44) -> (43/12,104/29) Hyperbolic Matrix(677,936,264,365) (-18/13,-29/21) -> (23/9,18/7) Hyperbolic Matrix(3093,4264,1112,1533) (-40/29,-51/37) -> (25/9,64/23) Hyperbolic Matrix(493,676,132,181) (-11/8,-26/19) -> (26/7,15/4) Hyperbolic Matrix(495,676,134,183) (-26/19,-15/11) -> (11/3,26/7) Hyperbolic Matrix(79,104,60,79) (-4/3,-13/10) -> (13/10,4/3) Hyperbolic Matrix(441,572,340,441) (-13/10,-22/17) -> (22/17,13/10) Hyperbolic Matrix(443,572,182,235) (-22/17,-9/7) -> (17/7,22/9) Hyperbolic Matrix(4757,6084,1036,1325) (-55/43,-78/61) -> (78/17,23/5) Hyperbolic Matrix(4759,6084,1038,1327) (-78/61,-23/18) -> (55/12,78/17) Hyperbolic Matrix(2131,2704,450,571) (-33/26,-52/41) -> (52/11,19/4) Hyperbolic Matrix(2133,2704,452,573) (-52/41,-19/15) -> (33/7,52/11) Hyperbolic Matrix(207,260,82,103) (-24/19,-5/4) -> (5/2,28/11) Hyperbolic Matrix(545,676,104,129) (-5/4,-26/21) -> (26/5,21/4) Hyperbolic Matrix(547,676,106,131) (-26/21,-21/17) -> (5/1,26/5) Hyperbolic Matrix(469,572,214,261) (-11/9,-28/23) -> (24/11,11/5) Hyperbolic Matrix(2235,2704,386,467) (-23/19,-52/43) -> (52/9,29/5) Hyperbolic Matrix(2237,2704,388,469) (-52/43,-29/24) -> (23/4,52/9) Hyperbolic Matrix(131,156,110,131) (-6/5,-13/11) -> (13/11,6/5) Hyperbolic Matrix(441,520,374,441) (-13/11,-20/17) -> (20/17,13/11) Hyperbolic Matrix(311,364,88,103) (-20/17,-7/6) -> (7/2,32/9) Hyperbolic Matrix(597,676,68,77) (-17/15,-26/23) -> (26/3,9/1) Hyperbolic Matrix(599,676,70,79) (-26/23,-9/8) -> (17/2,26/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(181,-208,114,-131) (1/1,7/6) -> (19/12,27/17) Hyperbolic Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(337,-416,64,-79) (16/13,5/4) -> (21/4,16/3) Hyperbolic Matrix(493,-624,350,-443) (5/4,19/15) -> (7/5,31/22) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(285,-364,184,-235) (14/11,9/7) -> (17/11,14/9) Hyperbolic Matrix(77,-104,20,-27) (4/3,11/8) -> (15/4,4/1) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1533,-2132,842,-1171) (25/18,32/23) -> (20/11,51/28) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2157,-3068,1262,-1795) (27/19,37/26) -> (41/24,53/31) Hyperbolic Matrix(1169,-1664,640,-911) (37/26,10/7) -> (42/23,11/6) Hyperbolic Matrix(337,-520,186,-287) (3/2,17/11) -> (9/5,29/16) Hyperbolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(493,-780,280,-443) (30/19,19/12) -> (7/4,30/17) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(2211,-3640,868,-1429) (51/31,28/17) -> (28/11,79/31) Hyperbolic Matrix(649,-1092,356,-599) (5/3,27/16) -> (51/28,31/17) Hyperbolic Matrix(1169,-1976,662,-1119) (27/16,22/13) -> (30/17,53/30) Hyperbolic Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(181,-312,76,-131) (12/7,7/4) -> (19/8,12/5) Hyperbolic Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(1117,-2028,244,-443) (29/16,20/11) -> (32/7,55/12) Hyperbolic Matrix(1481,-2704,442,-807) (31/17,42/23) -> (10/3,57/17) Hyperbolic Matrix(753,-1664,224,-495) (11/5,31/14) -> (47/14,37/11) Hyperbolic Matrix(961,-2132,270,-599) (31/14,20/9) -> (32/9,57/16) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(337,-780,124,-287) (23/10,7/3) -> (19/7,49/18) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(649,-2184,178,-599) (37/11,27/8) -> (51/14,11/3) Hyperbolic Matrix(77,-260,8,-27) (27/8,17/5) -> (9/1,1/0) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(181,-624,38,-131) (24/7,7/2) -> (19/4,24/5) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(27,208,-10,-77) -> Matrix(1,2,0,1) Matrix(53,364,38,261) -> Matrix(1,-8,0,1) Matrix(79,520,12,79) -> Matrix(1,-6,0,1) Matrix(25,156,4,25) -> Matrix(1,0,0,1) Matrix(155,884,-64,-365) -> Matrix(5,-8,2,-3) Matrix(157,884,-46,-259) -> Matrix(1,2,0,1) Matrix(155,832,-68,-365) -> Matrix(13,-10,4,-3) Matrix(79,416,-64,-337) -> Matrix(29,-22,4,-3) Matrix(131,624,-38,-181) -> Matrix(9,-16,4,-7) Matrix(155,728,-122,-573) -> Matrix(11,-28,2,-5) Matrix(79,364,-28,-129) -> Matrix(1,0,0,1) Matrix(129,572,76,337) -> Matrix(11,-38,-2,7) Matrix(131,572,30,131) -> Matrix(1,-8,0,1) Matrix(25,104,6,25) -> Matrix(1,-2,0,1) Matrix(27,104,-20,-77) -> Matrix(13,-20,2,-3) Matrix(415,1508,-172,-625) -> Matrix(5,-18,2,-7) Matrix(259,936,158,571) -> Matrix(1,-8,0,1) Matrix(363,1300,-160,-573) -> Matrix(7,-18,2,-5) Matrix(599,2132,-270,-961) -> Matrix(7,-18,2,-5) Matrix(103,364,88,311) -> Matrix(1,-8,0,1) Matrix(287,988,174,599) -> Matrix(13,-32,-2,5) Matrix(365,1248,198,677) -> Matrix(9,-22,-2,5) Matrix(415,1404,-154,-521) -> Matrix(1,0,0,1) Matrix(911,3068,-378,-1273) -> Matrix(11,-14,4,-5) Matrix(495,1664,-224,-753) -> Matrix(1,2,0,1) Matrix(79,260,24,79) -> Matrix(5,-12,-2,5) Matrix(129,416,40,129) -> Matrix(5,-12,-2,5) Matrix(131,416,74,235) -> Matrix(9,-22,-2,5) Matrix(183,520,-82,-233) -> Matrix(7,-18,2,-5) Matrix(391,1092,140,391) -> Matrix(9,-20,-4,9) Matrix(1793,4992,644,1793) -> Matrix(11,-30,-4,11) Matrix(1327,3692,776,2159) -> Matrix(11,-38,-2,7) Matrix(469,1300,-206,-571) -> Matrix(13,-36,4,-11) Matrix(571,1560,-362,-989) -> Matrix(9,-32,2,-7) Matrix(287,780,-124,-337) -> Matrix(7,-18,2,-5) Matrix(155,416,-136,-365) -> Matrix(15,-38,2,-5) Matrix(79,208,30,79) -> Matrix(1,-6,0,1) Matrix(181,468,70,181) -> Matrix(1,-4,0,1) Matrix(365,936,264,677) -> Matrix(1,-8,0,1) Matrix(937,2392,530,1353) -> Matrix(9,-22,-2,5) Matrix(1429,3640,-868,-2211) -> Matrix(1,6,0,1) Matrix(389,988,276,701) -> Matrix(11,-16,-2,3) Matrix(443,1092,-200,-493) -> Matrix(15,-34,4,-9) Matrix(807,1976,-350,-857) -> Matrix(13,-36,4,-11) Matrix(235,572,182,443) -> Matrix(9,-22,-2,5) Matrix(623,1508,-516,-1249) -> Matrix(29,-80,4,-11) Matrix(1533,3692,982,2365) -> Matrix(9,-22,-2,5) Matrix(131,312,-76,-181) -> Matrix(31,-88,6,-17) Matrix(1039,2392,632,1455) -> Matrix(11,-38,-2,7) Matrix(181,416,124,285) -> Matrix(11,-38,-2,7) Matrix(987,2236,-712,-1613) -> Matrix(1,2,0,1) Matrix(911,2028,-712,-1585) -> Matrix(1,2,0,1) Matrix(1223,2704,-858,-1897) -> Matrix(1,2,0,1) Matrix(571,1248,404,883) -> Matrix(11,-38,-2,7) Matrix(287,624,132,287) -> Matrix(7,-24,-2,7) Matrix(25,52,12,25) -> Matrix(7,-24,-2,7) Matrix(27,52,14,27) -> Matrix(9,-40,-2,9) Matrix(337,624,182,337) -> Matrix(9,-40,-2,9) Matrix(311,572,56,103) -> Matrix(1,-4,-2,9) Matrix(911,1664,-640,-1169) -> Matrix(1,2,0,1) Matrix(1171,2132,-842,-1533) -> Matrix(11,-50,2,-9) Matrix(259,468,-202,-365) -> Matrix(11,-50,2,-9) Matrix(727,1300,-524,-937) -> Matrix(11,-50,2,-9) Matrix(467,832,-380,-677) -> Matrix(29,-138,4,-19) Matrix(235,416,74,131) -> Matrix(5,-22,-2,9) Matrix(443,780,-280,-493) -> Matrix(11,-50,2,-9) Matrix(389,676,164,285) -> Matrix(41,-202,-14,69) Matrix(391,676,166,287) -> Matrix(43,-218,-14,71) Matrix(883,1508,-640,-1093) -> Matrix(9,-50,2,-11) Matrix(519,884,-428,-729) -> Matrix(13,-72,2,-11) Matrix(337,572,76,129) -> Matrix(7,-38,-2,11) Matrix(1507,2548,-954,-1613) -> Matrix(9,-50,2,-11) Matrix(987,1664,-710,-1197) -> Matrix(13,-72,2,-11) Matrix(157,260,32,53) -> Matrix(3,-16,-2,11) Matrix(10269,16900,4028,6629) -> Matrix(1,-16,0,1) Matrix(10271,16900,4030,6631) -> Matrix(1,0,0,1) Matrix(2625,4316,964,1585) -> Matrix(1,-8,0,1) Matrix(571,936,158,259) -> Matrix(1,-8,0,1) Matrix(287,468,176,287) -> Matrix(1,-12,0,1) Matrix(129,208,80,129) -> Matrix(1,-10,0,1) Matrix(131,208,-114,-181) -> Matrix(1,2,0,1) Matrix(2731,4316,1070,1691) -> Matrix(1,-8,0,1) Matrix(1715,2704,626,987) -> Matrix(17,-82,-6,29) Matrix(1717,2704,628,989) -> Matrix(19,-98,-6,31) Matrix(365,572,-298,-467) -> Matrix(1,2,0,1) Matrix(2731,4264,750,1171) -> Matrix(1,-8,0,1) Matrix(3199,4992,2050,3199) -> Matrix(21,-110,-4,21) Matrix(701,1092,450,701) -> Matrix(23,-132,-4,23) Matrix(235,364,-184,-285) -> Matrix(1,0,0,1) Matrix(285,416,124,181) -> Matrix(7,-38,-2,11) Matrix(287,416,198,287) -> Matrix(11,-60,-2,11) Matrix(181,260,126,181) -> Matrix(11,-60,-2,11) Matrix(7591,10816,2262,3223) -> Matrix(15,-88,-8,47) Matrix(7593,10816,2264,3225) -> Matrix(17,-104,-8,49) Matrix(1535,2184,-1114,-1585) -> Matrix(11,-72,2,-13) Matrix(183,260,-164,-233) -> Matrix(1,2,0,1) Matrix(625,884,-514,-727) -> Matrix(1,2,0,1) Matrix(443,624,-350,-493) -> Matrix(25,-144,4,-23) Matrix(261,364,38,53) -> Matrix(1,-8,0,1) Matrix(7799,10816,2174,3015) -> Matrix(5,-22,-2,9) Matrix(7801,10816,2176,3017) -> Matrix(7,-38,-2,11) Matrix(677,936,264,365) -> Matrix(1,-8,0,1) Matrix(3093,4264,1112,1533) -> Matrix(1,-8,0,1) Matrix(493,676,132,181) -> Matrix(11,-64,-6,35) Matrix(495,676,134,183) -> Matrix(13,-80,-6,37) Matrix(79,104,60,79) -> Matrix(1,-14,0,1) Matrix(441,572,340,441) -> Matrix(1,-8,0,1) Matrix(443,572,182,235) -> Matrix(5,-22,-2,9) Matrix(4757,6084,1036,1325) -> Matrix(3,-16,-2,11) Matrix(4759,6084,1038,1327) -> Matrix(5,-32,-2,13) Matrix(2131,2704,450,571) -> Matrix(27,-160,-14,83) Matrix(2133,2704,452,573) -> Matrix(29,-176,-14,85) Matrix(207,260,82,103) -> Matrix(5,-32,-2,13) Matrix(545,676,104,129) -> Matrix(7,-48,-8,55) Matrix(547,676,106,131) -> Matrix(9,-64,-8,57) Matrix(469,572,214,261) -> Matrix(7,-52,-2,15) Matrix(2235,2704,386,467) -> Matrix(1,-6,-2,13) Matrix(2237,2704,388,469) -> Matrix(3,-22,-2,15) Matrix(131,156,110,131) -> Matrix(1,-16,0,1) Matrix(441,520,374,441) -> Matrix(1,-10,0,1) Matrix(311,364,88,103) -> Matrix(1,-8,0,1) Matrix(597,676,68,77) -> Matrix(1,-8,2,-15) Matrix(599,676,70,79) -> Matrix(1,-8,-2,17) Matrix(1,0,2,1) -> Matrix(1,-16,0,1) Matrix(181,-208,114,-131) -> Matrix(1,2,0,1) Matrix(729,-884,428,-519) -> Matrix(11,72,-2,-13) Matrix(727,-884,514,-625) -> Matrix(1,2,0,1) Matrix(677,-832,380,-467) -> Matrix(19,138,-4,-29) Matrix(337,-416,64,-79) -> Matrix(3,22,-4,-29) Matrix(493,-624,350,-443) -> Matrix(23,144,-4,-25) Matrix(573,-728,122,-155) -> Matrix(5,28,-2,-11) Matrix(285,-364,184,-235) -> Matrix(1,0,0,1) Matrix(77,-104,20,-27) -> Matrix(3,20,-2,-13) Matrix(1093,-1508,640,-883) -> Matrix(11,50,-2,-9) Matrix(937,-1300,524,-727) -> Matrix(9,50,-2,-11) Matrix(1533,-2132,842,-1171) -> Matrix(9,50,-2,-11) Matrix(989,-1404,622,-883) -> Matrix(1,0,0,1) Matrix(2157,-3068,1262,-1795) -> Matrix(21,142,-4,-27) Matrix(1169,-1664,640,-911) -> Matrix(1,2,0,1) Matrix(337,-520,186,-287) -> Matrix(9,50,-2,-11) Matrix(831,-1300,466,-729) -> Matrix(19,100,-4,-21) Matrix(989,-1560,362,-571) -> Matrix(7,32,-2,-9) Matrix(493,-780,280,-443) -> Matrix(9,50,-2,-11) Matrix(261,-416,32,-51) -> Matrix(1,6,-2,-11) Matrix(2211,-3640,868,-1429) -> Matrix(1,6,0,1) Matrix(649,-1092,356,-599) -> Matrix(17,98,-4,-23) Matrix(1169,-1976,662,-1119) -> Matrix(19,100,-4,-21) Matrix(885,-1508,152,-259) -> Matrix(3,16,-4,-21) Matrix(181,-312,76,-131) -> Matrix(17,88,-6,-31) Matrix(1249,-2236,348,-623) -> Matrix(1,2,0,1) Matrix(1117,-2028,244,-443) -> Matrix(1,2,0,1) Matrix(1481,-2704,442,-807) -> Matrix(1,2,0,1) Matrix(753,-1664,224,-495) -> Matrix(1,2,0,1) Matrix(961,-2132,270,-599) -> Matrix(5,18,-2,-7) Matrix(209,-468,46,-103) -> Matrix(5,18,-2,-7) Matrix(573,-1300,160,-363) -> Matrix(5,18,-2,-7) Matrix(365,-832,68,-155) -> Matrix(3,10,-4,-13) Matrix(337,-780,124,-287) -> Matrix(5,18,-2,-7) Matrix(625,-1508,172,-415) -> Matrix(7,18,-2,-5) Matrix(365,-884,64,-155) -> Matrix(3,8,-2,-5) Matrix(1041,-2548,382,-935) -> Matrix(7,18,-2,-5) Matrix(677,-1664,190,-467) -> Matrix(3,8,-2,-5) Matrix(77,-208,10,-27) -> Matrix(1,2,0,1) Matrix(207,-572,38,-105) -> Matrix(1,2,0,1) Matrix(129,-364,28,-79) -> Matrix(1,0,0,1) Matrix(649,-2184,178,-599) -> Matrix(5,8,-2,-3) Matrix(77,-260,8,-27) -> Matrix(1,2,0,1) Matrix(259,-884,46,-157) -> Matrix(1,2,0,1) Matrix(181,-624,38,-131) -> Matrix(7,16,-4,-9) 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): 44 Degree of the the map X: 44 Degree of the the map Y: 168 ----------------------------------------------------------------------- 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): 252 Minimal number of generators: 43 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: 24 Genus: 10 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 13/6 26/11 13/5 39/14 3/1 13/4 10/3 26/7 4/1 13/3 14/3 5/1 26/5 11/2 52/9 6/1 13/2 7/1 8/1 26/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/1 1/0 7/6 -13/2 13/11 1/0 6/5 -8/1 11/9 -15/2 16/13 -7/1 5/4 -13/2 9/7 1/0 13/10 1/0 4/3 -7/1 11/8 -11/2 7/5 -13/2 10/7 -6/1 13/9 -11/2 1/0 3/2 1/0 14/9 -6/1 39/25 -11/2 25/16 -11/2 11/7 -11/2 8/5 -5/1 13/8 1/0 5/3 1/0 12/7 -5/1 7/4 -19/4 9/5 -9/2 11/6 1/0 13/7 -9/2 1/0 2/1 -4/1 13/6 -7/2 1/0 11/5 1/0 20/9 -3/1 9/4 -7/2 25/11 -7/2 16/7 -3/1 7/3 -13/4 26/11 -3/1 19/8 -29/10 12/5 -3/1 29/12 -5/2 17/7 -5/2 5/2 1/0 13/5 1/0 8/3 -3/1 19/7 -7/2 11/4 -5/2 25/9 -5/2 39/14 -5/2 14/5 -2/1 3/1 1/0 13/4 -5/2 1/0 10/3 -2/1 37/11 1/0 27/8 1/0 17/5 1/0 7/2 -3/2 25/7 1/0 43/12 1/0 18/5 -2/1 11/3 -5/2 26/7 -2/1 15/4 -7/4 4/1 -1/1 13/3 1/0 9/2 1/0 32/7 -3/1 23/5 1/0 14/3 -2/1 5/1 -3/2 26/5 -1/1 21/4 -5/6 16/3 -1/1 27/5 -1/2 11/2 -1/2 17/3 1/0 23/4 1/0 52/9 -1/1 29/5 -1/2 6/1 0/1 13/2 1/0 7/1 -3/2 8/1 -1/1 17/2 -1/2 26/3 0/1 9/1 1/0 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(157,-182,44,-51) (1/1,7/6) -> (7/2,25/7) Hyperbolic Matrix(155,-182,23,-27) (7/6,13/11) -> (13/2,7/1) Hyperbolic Matrix(131,-156,21,-25) (13/11,6/5) -> (6/1,13/2) Hyperbolic Matrix(235,-286,106,-129) (6/5,11/9) -> (11/5,20/9) Hyperbolic Matrix(571,-702,170,-209) (11/9,16/13) -> (10/3,37/11) Hyperbolic Matrix(337,-416,64,-79) (16/13,5/4) -> (21/4,16/3) Hyperbolic Matrix(103,-130,42,-53) (5/4,9/7) -> (17/7,5/2) Hyperbolic Matrix(181,-234,41,-53) (9/7,13/10) -> (13/3,9/2) Hyperbolic Matrix(79,-104,19,-25) (13/10,4/3) -> (4/1,13/3) Hyperbolic Matrix(77,-104,20,-27) (4/3,11/8) -> (15/4,4/1) Hyperbolic Matrix(207,-286,76,-105) (11/8,7/5) -> (19/7,11/4) Hyperbolic Matrix(129,-182,56,-79) (7/5,10/7) -> (16/7,7/3) Hyperbolic Matrix(181,-260,55,-79) (10/7,13/9) -> (13/4,10/3) Hyperbolic Matrix(53,-78,17,-25) (13/9,3/2) -> (3/1,13/4) Hyperbolic Matrix(285,-442,118,-183) (3/2,14/9) -> (12/5,29/12) Hyperbolic Matrix(701,-1092,251,-391) (14/9,39/25) -> (39/14,14/5) Hyperbolic Matrix(1249,-1950,449,-701) (39/25,25/16) -> (25/9,39/14) Hyperbolic Matrix(781,-1222,232,-363) (25/16,11/7) -> (37/11,27/8) Hyperbolic Matrix(181,-286,50,-79) (11/7,8/5) -> (18/5,11/3) Hyperbolic Matrix(129,-208,49,-79) (8/5,13/8) -> (13/5,8/3) Hyperbolic Matrix(79,-130,31,-51) (13/8,5/3) -> (5/2,13/5) Hyperbolic Matrix(77,-130,16,-27) (5/3,12/7) -> (14/3,5/1) Hyperbolic Matrix(181,-312,76,-131) (12/7,7/4) -> (19/8,12/5) Hyperbolic Matrix(103,-182,30,-53) (7/4,9/5) -> (17/5,7/2) Hyperbolic Matrix(157,-286,28,-51) (9/5,11/6) -> (11/2,17/3) Hyperbolic Matrix(155,-286,71,-131) (11/6,13/7) -> (13/6,11/5) Hyperbolic Matrix(27,-52,13,-25) (13/7,2/1) -> (2/1,13/6) Parabolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(287,-676,121,-285) (7/3,26/11) -> (26/11,19/8) Parabolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(77,-260,8,-27) (27/8,17/5) -> (9/1,1/0) Hyperbolic Matrix(181,-650,22,-79) (43/12,18/5) -> (8/1,17/2) Hyperbolic Matrix(183,-676,49,-181) (11/3,26/7) -> (26/7,15/4) Parabolic Matrix(233,-1066,40,-183) (32/7,23/5) -> (29/5,6/1) Hyperbolic Matrix(131,-676,25,-129) (5/1,26/5) -> (26/5,21/4) Parabolic Matrix(469,-2704,81,-467) (23/4,52/9) -> (52/9,29/5) Parabolic Matrix(79,-676,9,-77) (17/2,26/3) -> (26/3,9/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,-8,0,1) Matrix(157,-182,44,-51) -> Matrix(1,5,0,1) Matrix(155,-182,23,-27) -> Matrix(1,5,0,1) Matrix(131,-156,21,-25) -> Matrix(1,8,0,1) Matrix(235,-286,106,-129) -> Matrix(7,53,-2,-15) Matrix(571,-702,170,-209) -> Matrix(3,23,-2,-15) Matrix(337,-416,64,-79) -> Matrix(3,22,-4,-29) Matrix(103,-130,42,-53) -> Matrix(5,33,-2,-13) Matrix(181,-234,41,-53) -> Matrix(1,3,0,1) Matrix(79,-104,19,-25) -> Matrix(1,6,0,1) Matrix(77,-104,20,-27) -> Matrix(3,20,-2,-13) Matrix(207,-286,76,-105) -> Matrix(1,3,0,1) Matrix(129,-182,56,-79) -> Matrix(7,39,-2,-11) Matrix(181,-260,55,-79) -> Matrix(5,28,-2,-11) Matrix(53,-78,17,-25) -> Matrix(1,3,0,1) Matrix(285,-442,118,-183) -> Matrix(5,33,-2,-13) Matrix(701,-1092,251,-391) -> Matrix(9,52,-4,-23) Matrix(1249,-1950,449,-701) -> Matrix(1,3,0,1) Matrix(781,-1222,232,-363) -> Matrix(3,17,-2,-11) Matrix(181,-286,50,-79) -> Matrix(1,3,0,1) Matrix(129,-208,49,-79) -> Matrix(1,2,0,1) Matrix(79,-130,31,-51) -> Matrix(1,3,0,1) Matrix(77,-130,16,-27) -> Matrix(3,17,-2,-11) Matrix(181,-312,76,-131) -> Matrix(17,88,-6,-31) Matrix(103,-182,30,-53) -> Matrix(5,23,-2,-9) Matrix(157,-286,28,-51) -> Matrix(1,5,-2,-9) Matrix(155,-286,71,-131) -> Matrix(1,1,0,1) Matrix(27,-52,13,-25) -> Matrix(7,32,-2,-9) Matrix(209,-468,46,-103) -> Matrix(5,18,-2,-7) Matrix(573,-1300,160,-363) -> Matrix(5,18,-2,-7) Matrix(365,-832,68,-155) -> Matrix(3,10,-4,-13) Matrix(287,-676,121,-285) -> Matrix(41,126,-14,-43) Matrix(365,-884,64,-155) -> Matrix(3,8,-2,-5) Matrix(77,-208,10,-27) -> Matrix(1,2,0,1) Matrix(207,-572,38,-105) -> Matrix(1,2,0,1) Matrix(129,-364,28,-79) -> Matrix(1,0,0,1) Matrix(77,-260,8,-27) -> Matrix(1,2,0,1) Matrix(181,-650,22,-79) -> Matrix(1,3,-2,-5) Matrix(183,-676,49,-181) -> Matrix(11,24,-6,-13) Matrix(233,-1066,40,-183) -> Matrix(1,3,-2,-5) Matrix(131,-676,25,-129) -> Matrix(7,8,-8,-9) Matrix(469,-2704,81,-467) -> Matrix(1,2,-2,-3) Matrix(79,-676,9,-77) -> Matrix(1,0,2,1) 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): 22 ----------------------------------------------------------------------- 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 1/0 8 1 2/1 -4/1 2 13 13/6 (-4/1,-3/1).(-7/2,1/0) 0 2 11/5 1/0 1 26 9/4 -7/2 1 26 7/3 -13/4 1 26 26/11 -3/1 14 1 12/5 -3/1 2 13 5/2 1/0 1 26 13/5 1/0 1 2 8/3 -3/1 2 13 11/4 -5/2 1 26 25/9 -5/2 1 26 39/14 -5/2 1 2 14/5 -2/1 2 13 3/1 1/0 1 26 13/4 (-3/1,-2/1).(-5/2,1/0) 0 2 10/3 -2/1 2 13 27/8 1/0 1 26 17/5 1/0 1 26 7/2 -3/2 1 26 18/5 -2/1 2 13 11/3 -5/2 1 26 26/7 -2/1 6 1 4/1 -1/1 2 13 13/3 1/0 3 2 9/2 1/0 1 26 23/5 1/0 1 26 14/3 -2/1 2 13 5/1 -3/2 1 26 26/5 -1/1 8 1 16/3 -1/1 2 13 27/5 -1/2 1 26 11/2 -1/2 1 26 17/3 1/0 1 26 23/4 1/0 1 26 52/9 -1/1 2 1 6/1 0/1 2 13 13/2 1/0 3 2 7/1 -3/2 1 26 8/1 -1/1 2 13 26/3 0/1 2 1 9/1 1/0 1 26 1/0 1/0 1 26 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(25,-52,12,-25) (2/1,13/6) -> (2/1,13/6) Reflection Matrix(131,-286,60,-131) (13/6,11/5) -> (13/6,11/5) Reflection Matrix(129,-286,23,-51) (11/5,9/4) -> (11/2,17/3) Glide Reflection Matrix(79,-182,23,-53) (9/4,7/3) -> (17/5,7/2) Glide Reflection Matrix(155,-364,66,-155) (7/3,26/11) -> (7/3,26/11) Reflection Matrix(131,-312,55,-131) (26/11,12/5) -> (26/11,12/5) Reflection Matrix(53,-130,11,-27) (12/5,5/2) -> (14/3,5/1) Glide Reflection 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(105,-286,29,-79) (8/3,11/4) -> (18/5,11/3) Glide Reflection Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(701,-1950,252,-701) (25/9,39/14) -> (25/9,39/14) Reflection Matrix(391,-1092,140,-391) (39/14,14/5) -> (39/14,14/5) Reflection Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(25,-78,8,-25) (3/1,13/4) -> (3/1,13/4) Reflection Matrix(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(209,-702,39,-131) (10/3,27/8) -> (16/3,27/5) Glide Reflection Matrix(77,-260,8,-27) (27/8,17/5) -> (9/1,1/0) Hyperbolic Matrix(51,-182,7,-25) (7/2,18/5) -> (7/1,8/1) Glide Reflection Matrix(155,-572,42,-155) (11/3,26/7) -> (11/3,26/7) Reflection Matrix(27,-104,7,-27) (26/7,4/1) -> (26/7,4/1) Reflection Matrix(25,-104,6,-25) (4/1,13/3) -> (4/1,13/3) Reflection Matrix(53,-234,12,-53) (13/3,9/2) -> (13/3,9/2) Reflection Matrix(131,-598,23,-105) (9/2,23/5) -> (17/3,23/4) Glide Reflection Matrix(51,-260,10,-51) (5/1,26/5) -> (5/1,26/5) Reflection Matrix(79,-416,15,-79) (26/5,16/3) -> (26/5,16/3) Reflection Matrix(415,-2392,72,-415) (23/4,52/9) -> (23/4,52/9) Reflection Matrix(53,-312,9,-53) (52/9,6/1) -> (52/9,6/1) Reflection Matrix(25,-156,4,-25) (6/1,13/2) -> (6/1,13/2) Reflection Matrix(27,-182,4,-27) (13/2,7/1) -> (13/2,7/1) Reflection Matrix(25,-208,3,-25) (8/1,26/3) -> (8/1,26/3) Reflection Matrix(53,-468,6,-53) (26/3,9/1) -> (26/3,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,8,0,-1) (0/1,2/1) -> (-4/1,1/0) Matrix(25,-52,12,-25) -> Matrix(7,24,-2,-7) (2/1,13/6) -> (-4/1,-3/1) Matrix(131,-286,60,-131) -> Matrix(1,7,0,-1) (13/6,11/5) -> (-7/2,1/0) Matrix(129,-286,23,-51) -> Matrix(1,3,-2,-7) Matrix(79,-182,23,-53) -> Matrix(5,17,-2,-7) Matrix(155,-364,66,-155) -> Matrix(25,78,-8,-25) (7/3,26/11) -> (-13/4,-3/1) Matrix(131,-312,55,-131) -> Matrix(17,48,-6,-17) (26/11,12/5) -> (-3/1,-8/3) Matrix(53,-130,11,-27) -> Matrix(3,7,-2,-5) Matrix(51,-130,20,-51) -> Matrix(1,5,0,-1) (5/2,13/5) -> (-5/2,1/0) Matrix(79,-208,30,-79) -> Matrix(1,6,0,-1) (13/5,8/3) -> (-3/1,1/0) Matrix(105,-286,29,-79) -> Matrix(1,5,0,-1) *** -> (-5/2,1/0) Matrix(207,-572,38,-105) -> Matrix(1,2,0,1) 1/0 Matrix(701,-1950,252,-701) -> Matrix(1,5,0,-1) (25/9,39/14) -> (-5/2,1/0) Matrix(391,-1092,140,-391) -> Matrix(9,20,-4,-9) (39/14,14/5) -> (-5/2,-2/1) Matrix(129,-364,28,-79) -> Matrix(1,0,0,1) Matrix(25,-78,8,-25) -> Matrix(1,5,0,-1) (3/1,13/4) -> (-5/2,1/0) Matrix(79,-260,24,-79) -> Matrix(5,12,-2,-5) (13/4,10/3) -> (-3/1,-2/1) Matrix(209,-702,39,-131) -> Matrix(1,1,-2,-3) Matrix(77,-260,8,-27) -> Matrix(1,2,0,1) 1/0 Matrix(51,-182,7,-25) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(155,-572,42,-155) -> Matrix(9,20,-4,-9) (11/3,26/7) -> (-5/2,-2/1) Matrix(27,-104,7,-27) -> Matrix(3,4,-2,-3) (26/7,4/1) -> (-2/1,-1/1) Matrix(25,-104,6,-25) -> Matrix(1,2,0,-1) (4/1,13/3) -> (-1/1,1/0) Matrix(53,-234,12,-53) -> Matrix(1,5,0,-1) (13/3,9/2) -> (-5/2,1/0) Matrix(131,-598,23,-105) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(51,-260,10,-51) -> Matrix(5,6,-4,-5) (5/1,26/5) -> (-3/2,-1/1) Matrix(79,-416,15,-79) -> Matrix(3,2,-4,-3) (26/5,16/3) -> (-1/1,-1/2) Matrix(415,-2392,72,-415) -> Matrix(1,2,0,-1) (23/4,52/9) -> (-1/1,1/0) Matrix(53,-312,9,-53) -> Matrix(-1,0,2,1) (52/9,6/1) -> (-1/1,0/1) Matrix(25,-156,4,-25) -> Matrix(1,0,0,-1) (6/1,13/2) -> (0/1,1/0) Matrix(27,-182,4,-27) -> Matrix(1,3,0,-1) (13/2,7/1) -> (-3/2,1/0) Matrix(25,-208,3,-25) -> Matrix(-1,0,2,1) (8/1,26/3) -> (-1/1,0/1) Matrix(53,-468,6,-53) -> Matrix(1,0,0,-1) (26/3,9/1) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.