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 -1/4 -20/3 -4/15 -1/4 -13/2 -1/4 -6/1 -1/4 -17/3 -5/24 -11/2 -1/6 -16/3 -2/9 -1/5 -5/1 -1/6 -19/4 -3/16 -14/3 -1/6 -9/2 -1/4 -22/5 -1/6 -13/3 -1/6 -4/1 -1/6 0/1 -11/3 -1/6 -29/8 -3/20 -18/5 -1/8 -25/7 -3/14 -32/9 -2/11 -1/6 -7/2 -1/6 -31/9 -3/20 -24/7 -2/13 -1/7 -41/12 -3/22 -17/5 -3/20 -27/8 -5/38 -37/11 -1/8 -10/3 -1/6 -13/4 -1/7 -16/5 -1/7 -2/15 -3/1 -1/8 -17/6 -3/26 -14/5 -1/8 -39/14 -1/8 -64/23 -1/8 -10/81 -25/9 -11/90 -11/4 -5/42 -30/11 -7/60 -19/7 -3/26 -27/10 -13/114 -35/13 -9/80 -8/3 -2/17 -1/9 -13/5 -1/9 -18/7 -5/46 -23/9 -1/10 -51/20 -7/62 -28/11 -1/9 -4/37 -5/2 -3/28 -27/11 -17/164 -22/9 -1/10 -17/7 -5/48 -46/19 -7/68 -29/12 -9/88 -41/17 -1/10 -53/22 -17/168 -12/5 -4/39 -1/10 -7/3 -1/10 -30/13 -7/72 -53/23 -25/258 -23/10 -1/10 -16/7 -3/31 -2/21 -41/18 -11/114 -25/11 -19/198 -34/15 -13/136 -9/4 -7/74 -29/13 -3/32 -20/9 -3/32 -4/43 -51/23 -31/332 -31/14 -19/204 -42/19 -13/140 -11/5 -5/54 -24/11 -10/109 -1/11 -13/6 -1/11 -2/1 -1/12 -13/7 -1/13 -24/13 -1/13 -10/131 -11/6 -5/66 -31/17 -19/252 -20/11 -4/53 -3/40 -9/5 -7/94 -25/14 -19/258 -16/9 -2/27 -3/41 -23/13 -1/14 -7/4 -1/14 -26/15 -1/14 -19/11 -1/14 -12/7 -1/14 -4/57 -29/17 -9/128 -17/10 -5/72 -22/13 -1/14 -27/16 -17/244 -5/3 -3/44 -28/17 -4/59 -1/15 -79/48 -15/224 -130/79 -1/15 -51/31 -7/106 -23/14 -1/14 -18/11 -5/74 -13/8 -1/15 -8/5 -1/15 -2/31 -19/12 -3/46 -49/31 -3/46 -79/50 -37/570 -30/19 -7/108 -41/26 -19/294 -52/33 -2/31 -11/7 -5/78 -25/16 -11/174 -64/41 -10/159 -1/16 -39/25 -1/16 -14/9 -1/16 -3/2 -1/16 -16/11 -2/33 -1/17 -13/9 -1/17 -10/7 -1/18 -57/40 -1/26 -104/73 0/1 -47/33 -1/10 -37/26 -1/16 -27/19 -5/82 -17/12 -3/52 -24/17 -1/17 -2/35 -7/5 -1/18 -32/23 -1/18 -2/37 -57/41 -7/130 -25/18 -3/58 -43/31 -1/26 -104/75 0/1 -61/44 -1/6 -18/13 -1/16 -29/21 -3/52 -40/29 -2/35 -1/18 -51/37 -5/92 -11/8 -1/18 -26/19 -1/18 -15/11 -1/18 -4/3 -1/18 0/1 -13/10 -1/18 -22/17 -1/18 -9/7 -1/20 -32/25 -2/35 -1/18 -55/43 -1/18 -78/61 -1/18 -23/18 -1/18 -14/11 -1/18 -33/26 -5/92 -52/41 -2/37 -19/15 -3/56 -24/19 -2/37 -1/19 -5/4 -1/18 -26/21 -1/19 -21/17 -5/96 -16/13 -1/19 -2/39 -27/22 -7/138 -11/9 -1/18 -28/23 -1/19 -4/77 -17/14 -5/96 -23/19 -7/136 -52/43 -2/39 -29/24 -9/176 -6/5 -1/20 -13/11 -1/20 -20/17 -1/20 -4/81 -7/6 -1/20 -8/7 -2/41 -1/21 -17/15 -9/188 -26/23 -1/21 -9/8 -5/106 -1/1 -1/24 0/1 0/1 1/1 1/24 7/6 1/20 20/17 4/81 1/20 13/11 1/20 6/5 1/20 17/14 5/96 11/9 1/18 16/13 2/39 1/19 5/4 1/18 19/15 3/56 14/11 1/18 9/7 1/20 22/17 1/18 13/10 1/18 4/3 0/1 1/18 11/8 1/18 29/21 3/52 18/13 1/16 25/18 3/58 32/23 2/37 1/18 7/5 1/18 31/22 3/52 24/17 2/35 1/17 41/29 3/50 17/12 3/52 27/19 5/82 37/26 1/16 10/7 1/18 13/9 1/17 16/11 1/17 2/33 3/2 1/16 17/11 3/46 14/9 1/16 39/25 1/16 64/41 1/16 10/159 25/16 11/174 11/7 5/78 30/19 7/108 19/12 3/46 27/17 13/198 35/22 9/136 8/5 2/31 1/15 13/8 1/15 18/11 5/74 23/14 1/14 51/31 7/106 28/17 1/15 4/59 5/3 3/44 27/16 17/244 22/13 1/14 17/10 5/72 46/27 7/100 29/17 9/128 41/24 1/14 53/31 17/240 12/7 4/57 1/14 7/4 1/14 30/17 7/96 53/30 25/342 23/13 1/14 16/9 3/41 2/27 41/23 11/150 25/14 19/258 34/19 13/176 9/5 7/94 29/16 3/40 20/11 3/40 4/53 51/28 31/412 31/17 19/252 42/23 13/172 11/6 5/66 24/13 10/131 1/13 13/7 1/13 2/1 1/12 13/6 1/11 24/11 1/11 10/109 11/5 5/54 31/14 19/204 20/9 4/43 3/32 9/4 7/74 25/11 19/198 16/7 2/21 3/31 23/10 1/10 7/3 1/10 26/11 1/10 19/8 1/10 12/5 1/10 4/39 29/12 9/88 17/7 5/48 22/9 1/10 27/11 17/164 5/2 3/28 28/11 4/37 1/9 79/31 15/136 130/51 1/9 51/20 7/62 23/9 1/10 18/7 5/46 13/5 1/9 8/3 1/9 2/17 19/7 3/26 49/18 3/26 79/29 37/318 30/11 7/60 41/15 19/162 52/19 2/17 11/4 5/42 25/9 11/90 64/23 10/81 1/8 39/14 1/8 14/5 1/8 3/1 1/8 16/5 2/15 1/7 13/4 1/7 10/3 1/6 57/17 -1/2 104/31 0/1 47/14 1/14 37/11 1/8 27/8 5/38 17/5 3/20 24/7 1/7 2/13 7/2 1/6 32/9 1/6 2/11 57/16 7/38 25/7 3/14 43/12 -1/2 104/29 0/1 61/17 1/18 18/5 1/8 29/8 3/20 40/11 2/13 1/6 51/14 5/28 11/3 1/6 26/7 1/6 15/4 1/6 4/1 0/1 1/6 13/3 1/6 22/5 1/6 9/2 1/4 32/7 2/13 1/6 55/12 1/6 78/17 1/6 23/5 1/6 14/3 1/6 33/7 5/28 52/11 2/11 19/4 3/16 24/5 2/11 1/5 5/1 1/6 26/5 1/5 21/4 5/24 16/3 1/5 2/9 27/5 7/30 11/2 1/6 28/5 1/5 4/19 17/3 5/24 23/4 7/32 52/9 2/9 29/5 9/40 6/1 1/4 13/2 1/4 20/3 1/4 4/15 7/1 1/4 8/1 2/7 1/3 17/2 9/28 26/3 1/3 9/1 5/14 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(13,4,-114,-35) Matrix(53,364,38,261) -> Matrix(7,2,122,35) Matrix(79,520,12,79) -> Matrix(31,8,120,31) Matrix(25,156,4,25) -> Matrix(9,2,40,9) Matrix(155,884,-64,-365) -> Matrix(47,10,-456,-97) Matrix(157,884,-46,-259) -> Matrix(9,2,-68,-15) Matrix(155,832,-68,-365) -> Matrix(37,8,-384,-83) Matrix(79,416,-64,-337) -> Matrix(19,4,-366,-77) Matrix(131,624,-38,-181) -> Matrix(21,4,-142,-27) Matrix(155,728,-122,-573) -> Matrix(23,4,-420,-73) Matrix(79,364,-28,-129) -> Matrix(11,2,-94,-17) Matrix(129,572,76,337) -> Matrix(13,2,188,29) Matrix(131,572,30,131) -> Matrix(11,2,60,11) Matrix(25,104,6,25) -> Matrix(1,0,12,1) Matrix(27,104,-20,-77) -> Matrix(1,0,-12,1) Matrix(415,1508,-172,-625) -> Matrix(37,6,-364,-59) Matrix(259,936,158,571) -> Matrix(27,4,398,59) Matrix(363,1300,-160,-573) -> Matrix(3,2,-32,-21) Matrix(599,2132,-270,-961) -> Matrix(57,10,-610,-107) Matrix(103,364,88,311) -> Matrix(13,2,266,41) Matrix(287,988,174,599) -> Matrix(41,6,608,89) Matrix(365,1248,198,677) -> Matrix(57,8,748,105) Matrix(415,1404,-154,-521) -> Matrix(43,6,-380,-53) Matrix(911,3068,-378,-1273) -> Matrix(49,6,-482,-59) Matrix(495,1664,-224,-753) -> Matrix(37,4,-398,-43) Matrix(79,260,24,79) -> Matrix(13,2,84,13) Matrix(129,416,40,129) -> Matrix(29,4,210,29) Matrix(131,416,74,235) -> Matrix(31,4,426,55) Matrix(183,520,-82,-233) -> Matrix(67,8,-712,-85) Matrix(391,1092,140,391) -> Matrix(17,2,144,17) Matrix(1793,4992,644,1793) -> Matrix(161,20,1296,161) Matrix(1327,3692,776,2159) -> Matrix(113,14,1590,197) Matrix(469,1300,-206,-571) -> Matrix(149,18,-1548,-187) Matrix(571,1560,-362,-989) -> Matrix(239,28,-3696,-433) Matrix(287,780,-124,-337) -> Matrix(121,14,-1236,-143) Matrix(155,416,-136,-365) -> Matrix(1,0,-12,1) Matrix(79,208,30,79) -> Matrix(35,4,306,35) Matrix(181,468,70,181) -> Matrix(91,10,828,91) Matrix(365,936,264,677) -> Matrix(37,4,638,69) Matrix(937,2392,530,1353) -> Matrix(39,4,536,55) Matrix(1429,3640,-868,-2211) -> Matrix(73,8,-1086,-119) Matrix(389,988,276,701) -> Matrix(55,6,944,103) Matrix(443,1092,-200,-493) -> Matrix(249,26,-2672,-279) Matrix(807,1976,-350,-857) -> Matrix(233,24,-2398,-247) Matrix(235,572,182,443) -> Matrix(19,2,332,35) Matrix(623,1508,-516,-1249) -> Matrix(175,18,-3432,-353) Matrix(1533,3692,982,2365) -> Matrix(139,14,2214,223) Matrix(131,312,-76,-181) -> Matrix(79,8,-1116,-113) Matrix(1039,2392,632,1455) -> Matrix(41,4,584,57) Matrix(181,416,124,285) -> Matrix(41,4,666,65) Matrix(987,2236,-712,-1613) -> Matrix(21,2,-200,-19) Matrix(911,2028,-712,-1585) -> Matrix(107,10,-1894,-177) Matrix(1223,2704,-858,-1897) -> Matrix(43,4,-914,-85) Matrix(571,1248,404,883) -> Matrix(87,8,1468,135) Matrix(287,624,132,287) -> Matrix(219,20,2398,219) Matrix(25,52,12,25) -> Matrix(23,2,264,23) Matrix(27,52,14,27) -> Matrix(25,2,312,25) Matrix(337,624,182,337) -> Matrix(261,20,3406,261) Matrix(311,572,56,103) -> Matrix(79,6,408,31) Matrix(911,1664,-640,-1169) -> Matrix(53,4,-782,-59) Matrix(1171,2132,-842,-1533) -> Matrix(133,10,-2434,-183) Matrix(259,468,-202,-365) -> Matrix(27,2,-446,-33) Matrix(727,1300,-524,-937) -> Matrix(27,2,-608,-45) Matrix(467,832,-380,-677) -> Matrix(109,8,-2112,-155) Matrix(235,416,74,131) -> Matrix(55,4,426,31) Matrix(443,780,-280,-493) -> Matrix(193,14,-2964,-215) Matrix(389,676,164,285) -> Matrix(251,18,2496,179) Matrix(391,676,166,287) -> Matrix(253,18,2544,181) Matrix(883,1508,-640,-1093) -> Matrix(85,6,-1516,-107) Matrix(519,884,-428,-729) -> Matrix(143,10,-2760,-193) Matrix(337,572,76,129) -> Matrix(29,2,188,13) Matrix(1507,2548,-954,-1613) -> Matrix(371,26,-5722,-401) Matrix(987,1664,-710,-1197) -> Matrix(115,8,-2142,-149) Matrix(157,260,32,53) -> Matrix(29,2,130,9) Matrix(10269,16900,4028,6629) -> Matrix(329,22,2946,197) Matrix(10271,16900,4030,6631) -> Matrix(331,22,2994,199) Matrix(2625,4316,964,1585) -> Matrix(25,2,212,17) Matrix(571,936,158,259) -> Matrix(59,4,398,27) Matrix(287,468,176,287) -> Matrix(149,10,2220,149) Matrix(129,208,80,129) -> Matrix(61,4,930,61) Matrix(131,208,-114,-181) -> Matrix(61,4,-1266,-83) Matrix(2731,4316,1070,1691) -> Matrix(31,2,356,23) Matrix(1715,2704,626,987) -> Matrix(743,48,6300,407) Matrix(1717,2704,628,989) -> Matrix(745,48,6348,409) Matrix(365,572,-298,-467) -> Matrix(31,2,-636,-41) Matrix(2731,4264,750,1171) -> Matrix(127,8,746,47) Matrix(3199,4992,2050,3199) -> Matrix(319,20,5088,319) Matrix(701,1092,450,701) -> Matrix(31,2,480,31) Matrix(235,364,-184,-285) -> Matrix(31,2,-574,-37) Matrix(285,416,124,181) -> Matrix(65,4,666,41) Matrix(287,416,198,287) -> Matrix(67,4,1122,67) Matrix(181,260,126,181) -> Matrix(35,2,612,35) Matrix(7591,10816,2262,3223) -> Matrix(1,0,40,1) Matrix(7593,10816,2264,3225) -> Matrix(1,0,8,1) Matrix(1535,2184,-1114,-1585) -> Matrix(1,0,-2,1) Matrix(183,260,-164,-233) -> Matrix(33,2,-710,-43) Matrix(625,884,-514,-727) -> Matrix(33,2,-644,-39) Matrix(443,624,-350,-493) -> Matrix(69,4,-1294,-75) Matrix(261,364,38,53) -> Matrix(35,2,122,7) Matrix(7799,10816,2174,3015) -> Matrix(1,0,44,1) Matrix(7801,10816,2176,3017) -> Matrix(1,0,4,1) Matrix(677,936,264,365) -> Matrix(69,4,638,37) Matrix(3093,4264,1112,1533) -> Matrix(145,8,1178,65) Matrix(493,676,132,181) -> Matrix(35,2,192,11) Matrix(495,676,134,183) -> Matrix(37,2,240,13) Matrix(79,104,60,79) -> Matrix(1,0,36,1) Matrix(441,572,340,441) -> Matrix(37,2,684,37) Matrix(443,572,182,235) -> Matrix(35,2,332,19) Matrix(4757,6084,1036,1325) -> Matrix(179,10,1056,59) Matrix(4759,6084,1038,1327) -> Matrix(181,10,1104,61) Matrix(2131,2704,450,571) -> Matrix(295,16,1604,87) Matrix(2133,2704,452,573) -> Matrix(297,16,1652,89) Matrix(207,260,82,103) -> Matrix(39,2,370,19) Matrix(545,676,104,129) -> Matrix(113,6,546,29) Matrix(547,676,106,131) -> Matrix(115,6,594,31) Matrix(469,572,214,261) -> Matrix(113,6,1224,65) Matrix(2235,2704,386,467) -> Matrix(623,32,2784,143) Matrix(2237,2704,388,469) -> Matrix(625,32,2832,145) Matrix(131,156,110,131) -> Matrix(39,2,760,39) Matrix(441,520,374,441) -> Matrix(161,8,3240,161) Matrix(311,364,88,103) -> Matrix(41,2,266,13) Matrix(597,676,68,77) -> Matrix(293,14,858,41) Matrix(599,676,70,79) -> Matrix(295,14,906,43) Matrix(1,0,2,1) -> Matrix(1,0,48,1) Matrix(181,-208,114,-131) -> Matrix(83,-4,1266,-61) Matrix(729,-884,428,-519) -> Matrix(193,-10,2760,-143) Matrix(727,-884,514,-625) -> Matrix(39,-2,644,-33) Matrix(677,-832,380,-467) -> Matrix(155,-8,2112,-109) Matrix(337,-416,64,-79) -> Matrix(77,-4,366,-19) Matrix(493,-624,350,-443) -> Matrix(75,-4,1294,-69) Matrix(573,-728,122,-155) -> Matrix(73,-4,420,-23) Matrix(285,-364,184,-235) -> Matrix(37,-2,574,-31) Matrix(77,-104,20,-27) -> Matrix(1,0,-12,1) Matrix(1093,-1508,640,-883) -> Matrix(107,-6,1516,-85) Matrix(937,-1300,524,-727) -> Matrix(45,-2,608,-27) Matrix(1533,-2132,842,-1171) -> Matrix(183,-10,2434,-133) Matrix(989,-1404,622,-883) -> Matrix(101,-6,1532,-91) Matrix(2157,-3068,1262,-1795) -> Matrix(95,-6,1346,-85) Matrix(1169,-1664,640,-911) -> Matrix(59,-4,782,-53) Matrix(337,-520,186,-287) -> Matrix(125,-8,1672,-107) Matrix(831,-1300,466,-729) -> Matrix(283,-18,3852,-245) Matrix(989,-1560,362,-571) -> Matrix(433,-28,3696,-239) Matrix(493,-780,280,-443) -> Matrix(215,-14,2964,-193) Matrix(261,-416,32,-51) -> Matrix(1,0,-12,1) Matrix(2211,-3640,868,-1429) -> Matrix(119,-8,1086,-73) Matrix(649,-1092,356,-599) -> Matrix(375,-26,4976,-345) Matrix(1169,-1976,662,-1119) -> Matrix(343,-24,4702,-329) Matrix(885,-1508,152,-259) -> Matrix(257,-18,1128,-79) Matrix(181,-312,76,-131) -> Matrix(113,-8,1116,-79) Matrix(1249,-2236,348,-623) -> Matrix(27,-2,392,-29) Matrix(1117,-2028,244,-443) -> Matrix(133,-10,838,-63) Matrix(1481,-2704,442,-807) -> Matrix(53,-4,146,-11) Matrix(753,-1664,224,-495) -> Matrix(43,-4,398,-37) Matrix(961,-2132,270,-599) -> Matrix(107,-10,610,-57) Matrix(209,-468,46,-103) -> Matrix(21,-2,158,-15) Matrix(573,-1300,160,-363) -> Matrix(21,-2,32,-3) Matrix(365,-832,68,-155) -> Matrix(83,-8,384,-37) Matrix(337,-780,124,-287) -> Matrix(143,-14,1236,-121) Matrix(625,-1508,172,-415) -> Matrix(59,-6,364,-37) Matrix(365,-884,64,-155) -> Matrix(97,-10,456,-47) Matrix(1041,-2548,382,-935) -> Matrix(253,-26,2170,-223) Matrix(677,-1664,190,-467) -> Matrix(77,-8,414,-43) Matrix(77,-208,10,-27) -> Matrix(35,-4,114,-13) Matrix(207,-572,38,-105) -> Matrix(17,-2,60,-7) Matrix(129,-364,28,-79) -> Matrix(17,-2,94,-11) Matrix(649,-2184,178,-599) -> Matrix(1,0,-2,1) Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(15,-2,68,-9) Matrix(181,-624,38,-131) -> Matrix(27,-4,142,-21) 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): 84 Degree of the the map X: 84 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, 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): 504 Minimal number of generators: 85 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: 36 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 13/6 26/11 12/5 130/51 13/5 52/19 39/14 3/1 13/4 10/3 104/31 104/29 18/5 26/7 4/1 13/3 22/5 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 0/1 0/1 1/1 1/24 7/6 1/20 20/17 4/81 1/20 13/11 1/20 6/5 1/20 17/14 5/96 11/9 1/18 16/13 2/39 1/19 5/4 1/18 19/15 3/56 14/11 1/18 9/7 1/20 22/17 1/18 13/10 1/18 4/3 0/1 1/18 11/8 1/18 29/21 3/52 18/13 1/16 25/18 3/58 32/23 2/37 1/18 7/5 1/18 31/22 3/52 24/17 2/35 1/17 41/29 3/50 17/12 3/52 27/19 5/82 37/26 1/16 10/7 1/18 13/9 1/17 16/11 1/17 2/33 3/2 1/16 17/11 3/46 14/9 1/16 39/25 1/16 64/41 1/16 10/159 25/16 11/174 11/7 5/78 30/19 7/108 19/12 3/46 27/17 13/198 35/22 9/136 8/5 2/31 1/15 13/8 1/15 18/11 5/74 23/14 1/14 51/31 7/106 28/17 1/15 4/59 5/3 3/44 27/16 17/244 22/13 1/14 17/10 5/72 46/27 7/100 29/17 9/128 41/24 1/14 53/31 17/240 12/7 4/57 1/14 7/4 1/14 30/17 7/96 53/30 25/342 23/13 1/14 16/9 3/41 2/27 41/23 11/150 25/14 19/258 34/19 13/176 9/5 7/94 29/16 3/40 20/11 3/40 4/53 51/28 31/412 31/17 19/252 42/23 13/172 11/6 5/66 24/13 10/131 1/13 13/7 1/13 2/1 1/12 13/6 1/11 24/11 1/11 10/109 11/5 5/54 31/14 19/204 20/9 4/43 3/32 9/4 7/74 25/11 19/198 16/7 2/21 3/31 23/10 1/10 7/3 1/10 26/11 1/10 19/8 1/10 12/5 1/10 4/39 29/12 9/88 17/7 5/48 22/9 1/10 27/11 17/164 5/2 3/28 28/11 4/37 1/9 79/31 15/136 130/51 1/9 51/20 7/62 23/9 1/10 18/7 5/46 13/5 1/9 8/3 1/9 2/17 19/7 3/26 49/18 3/26 79/29 37/318 30/11 7/60 41/15 19/162 52/19 2/17 11/4 5/42 25/9 11/90 64/23 10/81 1/8 39/14 1/8 14/5 1/8 3/1 1/8 16/5 2/15 1/7 13/4 1/7 10/3 1/6 57/17 -1/2 104/31 0/1 47/14 1/14 37/11 1/8 27/8 5/38 17/5 3/20 24/7 1/7 2/13 7/2 1/6 32/9 1/6 2/11 57/16 7/38 25/7 3/14 43/12 -1/2 104/29 0/1 61/17 1/18 18/5 1/8 29/8 3/20 40/11 2/13 1/6 51/14 5/28 11/3 1/6 26/7 1/6 15/4 1/6 4/1 0/1 1/6 13/3 1/6 22/5 1/6 9/2 1/4 32/7 2/13 1/6 55/12 1/6 78/17 1/6 23/5 1/6 14/3 1/6 33/7 5/28 52/11 2/11 19/4 3/16 24/5 2/11 1/5 5/1 1/6 26/5 1/5 21/4 5/24 16/3 1/5 2/9 27/5 7/30 11/2 1/6 28/5 1/5 4/19 17/3 5/24 23/4 7/32 52/9 2/9 29/5 9/40 6/1 1/4 13/2 1/4 20/3 1/4 4/15 7/1 1/4 8/1 2/7 1/3 17/2 9/28 26/3 1/3 9/1 5/14 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(181,-208,114,-131) (1/1,7/6) -> (19/12,27/17) Hyperbolic Matrix(311,-364,223,-261) (7/6,20/17) -> (32/23,7/5) Hyperbolic Matrix(441,-520,67,-79) (20/17,13/11) -> (13/2,20/3) Hyperbolic Matrix(131,-156,21,-25) (13/11,6/5) -> (6/1,13/2) 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(443,-572,261,-337) (9/7,22/17) -> (22/13,17/10) Hyperbolic Matrix(441,-572,101,-131) (22/17,13/10) -> (13/3,22/5) 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(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(677,-936,413,-571) (29/21,18/13) -> (18/11,23/14) 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(701,-988,425,-599) (31/22,24/17) -> (28/17,5/3) Hyperbolic Matrix(883,-1248,479,-677) (24/17,41/29) -> (11/6,24/13) 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(181,-260,55,-79) (10/7,13/9) -> (13/4,10/3) Hyperbolic Matrix(287,-416,89,-129) (13/9,16/11) -> (16/5,13/4) Hyperbolic Matrix(285,-416,161,-235) (16/11,3/2) -> (23/13,16/9) Hyperbolic Matrix(337,-520,186,-287) (3/2,17/11) -> (9/5,29/16) Hyperbolic Matrix(701,-1092,251,-391) (14/9,39/25) -> (39/14,14/5) Hyperbolic Matrix(3199,-4992,1149,-1793) (39/25,64/41) -> (64/23,39/14) Hyperbolic Matrix(2365,-3692,1383,-2159) (64/41,25/16) -> (53/31,12/7) 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(129,-208,49,-79) (8/5,13/8) -> (13/5,8/3) Hyperbolic Matrix(287,-468,111,-181) (13/8,18/11) -> (18/7,13/5) Hyperbolic Matrix(1455,-2392,823,-1353) (23/14,51/31) -> (53/30,23/13) 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(337,-624,155,-287) (24/13,13/7) -> (13/6,24/11) Hyperbolic Matrix(27,-52,13,-25) (13/7,2/1) -> (2/1,13/6) Parabolic Matrix(261,-572,47,-103) (24/11,11/5) -> (11/2,28/5) 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(181,-416,57,-131) (16/7,23/10) -> (3/1,16/5) Hyperbolic Matrix(337,-780,124,-287) (23/10,7/3) -> (19/7,49/18) Hyperbolic Matrix(287,-676,121,-285) (7/3,26/11) -> (26/11,19/8) Parabolic 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(235,-572,53,-129) (17/7,22/9) -> (22/5,9/2) 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(103,-260,21,-53) (5/2,28/11) -> (24/5,5/1) Hyperbolic Matrix(6631,-16900,2601,-6629) (79/31,130/51) -> (130/51,51/20) Parabolic Matrix(1691,-4316,621,-1585) (51/20,23/9) -> (49/18,79/29) Hyperbolic Matrix(365,-936,101,-259) (23/9,18/7) -> (18/5,29/8) Hyperbolic Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(989,-2704,361,-987) (41/15,52/19) -> (52/19,11/4) Parabolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1533,-4264,421,-1171) (25/9,64/23) -> (40/11,51/14) Hyperbolic Matrix(129,-364,28,-79) (14/5,3/1) -> (23/5,14/3) Hyperbolic Matrix(3225,-10816,961,-3223) (57/17,104/31) -> (104/31,47/14) Parabolic 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 Matrix(103,-364,15,-53) (7/2,32/9) -> (20/3,7/1) Hyperbolic Matrix(3017,-10816,841,-3015) (43/12,104/29) -> (104/29,61/17) Parabolic Matrix(183,-676,49,-181) (11/3,26/7) -> (26/7,15/4) Parabolic Matrix(1327,-6084,289,-1325) (55/12,78/17) -> (78/17,23/5) Parabolic Matrix(573,-2704,121,-571) (33/7,52/11) -> (52/11,19/4) Parabolic 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(1,0,24,1) Matrix(181,-208,114,-131) -> Matrix(83,-4,1266,-61) Matrix(311,-364,223,-261) -> Matrix(41,-2,718,-35) Matrix(441,-520,67,-79) -> Matrix(161,-8,624,-31) Matrix(131,-156,21,-25) -> Matrix(39,-2,176,-9) Matrix(729,-884,428,-519) -> Matrix(193,-10,2760,-143) Matrix(727,-884,514,-625) -> Matrix(39,-2,644,-33) Matrix(677,-832,380,-467) -> Matrix(155,-8,2112,-109) Matrix(337,-416,64,-79) -> Matrix(77,-4,366,-19) Matrix(493,-624,350,-443) -> Matrix(75,-4,1294,-69) Matrix(573,-728,122,-155) -> Matrix(73,-4,420,-23) Matrix(285,-364,184,-235) -> Matrix(37,-2,574,-31) Matrix(443,-572,261,-337) -> Matrix(35,-2,508,-29) Matrix(441,-572,101,-131) -> Matrix(37,-2,204,-11) Matrix(79,-104,19,-25) -> Matrix(1,0,-12,1) Matrix(77,-104,20,-27) -> Matrix(1,0,-12,1) Matrix(1093,-1508,640,-883) -> Matrix(107,-6,1516,-85) Matrix(677,-936,413,-571) -> Matrix(69,-4,1018,-59) Matrix(937,-1300,524,-727) -> Matrix(45,-2,608,-27) Matrix(1533,-2132,842,-1171) -> Matrix(183,-10,2434,-133) Matrix(701,-988,425,-599) -> Matrix(103,-6,1528,-89) Matrix(883,-1248,479,-677) -> Matrix(135,-8,1772,-105) Matrix(989,-1404,622,-883) -> Matrix(101,-6,1532,-91) Matrix(2157,-3068,1262,-1795) -> Matrix(95,-6,1346,-85) Matrix(1169,-1664,640,-911) -> Matrix(59,-4,782,-53) Matrix(181,-260,55,-79) -> Matrix(35,-2,228,-13) Matrix(287,-416,89,-129) -> Matrix(67,-4,486,-29) Matrix(285,-416,161,-235) -> Matrix(65,-4,894,-55) Matrix(337,-520,186,-287) -> Matrix(125,-8,1672,-107) Matrix(701,-1092,251,-391) -> Matrix(31,-2,264,-17) Matrix(3199,-4992,1149,-1793) -> Matrix(319,-20,2568,-161) Matrix(2365,-3692,1383,-2159) -> Matrix(223,-14,3138,-197) Matrix(831,-1300,466,-729) -> Matrix(283,-18,3852,-245) Matrix(989,-1560,362,-571) -> Matrix(433,-28,3696,-239) Matrix(493,-780,280,-443) -> Matrix(215,-14,2964,-193) Matrix(261,-416,32,-51) -> Matrix(1,0,-12,1) Matrix(129,-208,49,-79) -> Matrix(61,-4,534,-35) Matrix(287,-468,111,-181) -> Matrix(149,-10,1356,-91) Matrix(1455,-2392,823,-1353) -> Matrix(57,-4,784,-55) Matrix(2211,-3640,868,-1429) -> Matrix(119,-8,1086,-73) Matrix(649,-1092,356,-599) -> Matrix(375,-26,4976,-345) Matrix(1169,-1976,662,-1119) -> Matrix(343,-24,4702,-329) Matrix(885,-1508,152,-259) -> Matrix(257,-18,1128,-79) Matrix(181,-312,76,-131) -> Matrix(113,-8,1116,-79) Matrix(1249,-2236,348,-623) -> Matrix(27,-2,392,-29) Matrix(1117,-2028,244,-443) -> Matrix(133,-10,838,-63) Matrix(1481,-2704,442,-807) -> Matrix(53,-4,146,-11) Matrix(337,-624,155,-287) -> Matrix(261,-20,2858,-219) Matrix(27,-52,13,-25) -> Matrix(25,-2,288,-23) Matrix(261,-572,47,-103) -> Matrix(65,-6,336,-31) Matrix(753,-1664,224,-495) -> Matrix(43,-4,398,-37) Matrix(961,-2132,270,-599) -> Matrix(107,-10,610,-57) Matrix(209,-468,46,-103) -> Matrix(21,-2,158,-15) Matrix(573,-1300,160,-363) -> Matrix(21,-2,32,-3) Matrix(365,-832,68,-155) -> Matrix(83,-8,384,-37) Matrix(181,-416,57,-131) -> Matrix(41,-4,318,-31) Matrix(337,-780,124,-287) -> Matrix(143,-14,1236,-121) Matrix(287,-676,121,-285) -> Matrix(181,-18,1800,-179) Matrix(625,-1508,172,-415) -> Matrix(59,-6,364,-37) Matrix(365,-884,64,-155) -> Matrix(97,-10,456,-47) Matrix(235,-572,53,-129) -> Matrix(19,-2,124,-13) Matrix(1041,-2548,382,-935) -> Matrix(253,-26,2170,-223) Matrix(677,-1664,190,-467) -> Matrix(77,-8,414,-43) Matrix(103,-260,21,-53) -> Matrix(19,-2,86,-9) Matrix(6631,-16900,2601,-6629) -> Matrix(199,-22,1782,-197) Matrix(1691,-4316,621,-1585) -> Matrix(23,-2,196,-17) Matrix(365,-936,101,-259) -> Matrix(37,-4,250,-27) Matrix(77,-208,10,-27) -> Matrix(35,-4,114,-13) Matrix(989,-2704,361,-987) -> Matrix(409,-48,3468,-407) Matrix(207,-572,38,-105) -> Matrix(17,-2,60,-7) Matrix(1533,-4264,421,-1171) -> Matrix(65,-8,382,-47) Matrix(129,-364,28,-79) -> Matrix(17,-2,94,-11) Matrix(3225,-10816,961,-3223) -> Matrix(1,0,16,1) Matrix(649,-2184,178,-599) -> Matrix(1,0,-2,1) Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(15,-2,68,-9) Matrix(181,-624,38,-131) -> Matrix(27,-4,142,-21) Matrix(103,-364,15,-53) -> Matrix(13,-2,46,-7) Matrix(3017,-10816,841,-3015) -> Matrix(1,0,20,1) Matrix(183,-676,49,-181) -> Matrix(13,-2,72,-11) Matrix(1327,-6084,289,-1325) -> Matrix(61,-10,360,-59) Matrix(573,-2704,121,-571) -> Matrix(89,-16,484,-87) Matrix(131,-676,25,-129) -> Matrix(31,-6,150,-29) Matrix(469,-2704,81,-467) -> Matrix(145,-32,648,-143) Matrix(79,-676,9,-77) -> Matrix(43,-14,126,-41) 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): 42 ----------------------------------------------------------------------- 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 24 1 2/1 1/12 2 13 13/6 1/11 11 2 24/11 (1/11,10/109) 0 13 11/5 5/54 1 26 31/14 19/204 1 26 20/9 (4/43,3/32) 0 13 9/4 7/74 1 26 25/11 19/198 1 26 16/7 (2/21,3/31) 0 13 23/10 1/10 1 26 7/3 1/10 1 26 26/11 1/10 18 1 12/5 (1/10,4/39) 0 13 29/12 9/88 1 26 17/7 5/48 1 26 22/9 1/10 2 13 27/11 17/164 1 26 5/2 3/28 1 26 28/11 (4/37,1/9) 0 13 130/51 1/9 22 1 51/20 7/62 1 26 23/9 1/10 1 26 18/7 5/46 2 13 13/5 1/9 7 2 8/3 (1/9,2/17) 0 13 19/7 3/26 1 26 49/18 3/26 1 26 79/29 37/318 1 26 30/11 7/60 2 13 52/19 2/17 12 1 11/4 5/42 1 26 25/9 11/90 1 26 64/23 (10/81,1/8) 0 13 39/14 1/8 9 2 14/5 1/8 2 13 3/1 1/8 1 26 16/5 (2/15,1/7) 0 13 13/4 1/7 3 2 10/3 1/6 2 13 104/31 0/1 16 1 47/14 1/14 1 26 37/11 1/8 1 26 27/8 5/38 1 26 17/5 3/20 1 26 24/7 (1/7,2/13) 0 13 7/2 1/6 1 26 32/9 (1/6,2/11) 0 13 57/16 7/38 1 26 25/7 3/14 1 26 43/12 -1/2 1 26 104/29 0/1 20 1 18/5 1/8 2 13 29/8 3/20 1 26 40/11 (2/13,1/6) 0 13 51/14 5/28 1 26 11/3 1/6 1 26 26/7 1/6 2 1 4/1 (0/1,1/6) 0 13 13/3 1/6 1 2 22/5 1/6 2 13 9/2 1/4 1 26 32/7 (2/13,1/6) 0 13 78/17 1/6 10 1 23/5 1/6 1 26 14/3 1/6 2 13 52/11 2/11 4 1 19/4 3/16 1 26 24/5 (2/11,1/5) 0 13 5/1 1/6 1 26 26/5 1/5 6 1 16/3 (1/5,2/9) 0 13 27/5 7/30 1 26 11/2 1/6 1 26 28/5 (1/5,4/19) 0 13 17/3 5/24 1 26 23/4 7/32 1 26 52/9 2/9 8 1 6/1 1/4 2 13 13/2 1/4 5 2 20/3 (1/4,4/15) 0 13 7/1 1/4 1 26 8/1 (2/7,1/3) 0 13 26/3 1/3 14 1 9/1 5/14 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(287,-624,132,-287) (13/6,24/11) -> (13/6,24/11) Reflection Matrix(261,-572,47,-103) (24/11,11/5) -> (11/2,28/5) 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(181,-416,57,-131) (16/7,23/10) -> (3/1,16/5) Hyperbolic Matrix(337,-780,124,-287) (23/10,7/3) -> (19/7,49/18) Hyperbolic 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(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(235,-572,53,-129) (17/7,22/9) -> (22/5,9/2) 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(103,-260,21,-53) (5/2,28/11) -> (24/5,5/1) Hyperbolic Matrix(1429,-3640,561,-1429) (28/11,130/51) -> (28/11,130/51) Reflection Matrix(5201,-13260,2040,-5201) (130/51,51/20) -> (130/51,51/20) Reflection Matrix(1691,-4316,621,-1585) (51/20,23/9) -> (49/18,79/29) Hyperbolic Matrix(365,-936,101,-259) (23/9,18/7) -> (18/5,29/8) Hyperbolic Matrix(181,-468,70,-181) (18/7,13/5) -> (18/7,13/5) Reflection Matrix(79,-208,30,-79) (13/5,8/3) -> (13/5,8/3) Reflection Matrix(77,-208,10,-27) (8/3,19/7) -> (7/1,8/1) Hyperbolic Matrix(571,-1560,209,-571) (30/11,52/19) -> (30/11,52/19) Reflection Matrix(417,-1144,152,-417) (52/19,11/4) -> (52/19,11/4) Reflection Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1533,-4264,421,-1171) (25/9,64/23) -> (40/11,51/14) Hyperbolic Matrix(1793,-4992,644,-1793) (64/23,39/14) -> (64/23,39/14) 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(129,-416,40,-129) (16/5,13/4) -> (16/5,13/4) Reflection Matrix(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(311,-1040,93,-311) (10/3,104/31) -> (10/3,104/31) Reflection Matrix(2913,-9776,868,-2913) (104/31,47/14) -> (104/31,47/14) Reflection 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 Matrix(103,-364,15,-53) (7/2,32/9) -> (20/3,7/1) Hyperbolic Matrix(2495,-8944,696,-2495) (43/12,104/29) -> (43/12,104/29) Reflection Matrix(521,-1872,145,-521) (104/29,18/5) -> (104/29,18/5) 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(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(545,-2496,119,-545) (32/7,78/17) -> (32/7,78/17) Reflection Matrix(781,-3588,170,-781) (78/17,23/5) -> (78/17,23/5) Reflection Matrix(155,-728,33,-155) (14/3,52/11) -> (14/3,52/11) Reflection Matrix(417,-1976,88,-417) (52/11,19/4) -> (52/11,19/4) 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(79,-520,12,-79) (13/2,20/3) -> (13/2,20/3) 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(1,0,24,-1) (0/1,2/1) -> (0/1,1/12) Matrix(25,-52,12,-25) -> Matrix(23,-2,264,-23) (2/1,13/6) -> (1/12,1/11) Matrix(287,-624,132,-287) -> Matrix(219,-20,2398,-219) (13/6,24/11) -> (1/11,10/109) Matrix(261,-572,47,-103) -> Matrix(65,-6,336,-31) Matrix(753,-1664,224,-495) -> Matrix(43,-4,398,-37) Matrix(961,-2132,270,-599) -> Matrix(107,-10,610,-57) Matrix(209,-468,46,-103) -> Matrix(21,-2,158,-15) Matrix(573,-1300,160,-363) -> Matrix(21,-2,32,-3) Matrix(365,-832,68,-155) -> Matrix(83,-8,384,-37) Matrix(181,-416,57,-131) -> Matrix(41,-4,318,-31) Matrix(337,-780,124,-287) -> Matrix(143,-14,1236,-121) Matrix(155,-364,66,-155) -> Matrix(101,-10,1020,-101) (7/3,26/11) -> (5/51,1/10) Matrix(131,-312,55,-131) -> Matrix(79,-8,780,-79) (26/11,12/5) -> (1/10,4/39) Matrix(625,-1508,172,-415) -> Matrix(59,-6,364,-37) Matrix(365,-884,64,-155) -> Matrix(97,-10,456,-47) Matrix(235,-572,53,-129) -> Matrix(19,-2,124,-13) Matrix(1041,-2548,382,-935) -> Matrix(253,-26,2170,-223) Matrix(677,-1664,190,-467) -> Matrix(77,-8,414,-43) Matrix(103,-260,21,-53) -> Matrix(19,-2,86,-9) Matrix(1429,-3640,561,-1429) -> Matrix(73,-8,666,-73) (28/11,130/51) -> (4/37,1/9) Matrix(5201,-13260,2040,-5201) -> Matrix(125,-14,1116,-125) (130/51,51/20) -> (1/9,7/62) Matrix(1691,-4316,621,-1585) -> Matrix(23,-2,196,-17) Matrix(365,-936,101,-259) -> Matrix(37,-4,250,-27) Matrix(181,-468,70,-181) -> Matrix(91,-10,828,-91) (18/7,13/5) -> (5/46,1/9) Matrix(79,-208,30,-79) -> Matrix(35,-4,306,-35) (13/5,8/3) -> (1/9,2/17) Matrix(77,-208,10,-27) -> Matrix(35,-4,114,-13) Matrix(571,-1560,209,-571) -> Matrix(239,-28,2040,-239) (30/11,52/19) -> (7/60,2/17) Matrix(417,-1144,152,-417) -> Matrix(169,-20,1428,-169) (52/19,11/4) -> (2/17,5/42) Matrix(207,-572,38,-105) -> Matrix(17,-2,60,-7) Matrix(1533,-4264,421,-1171) -> Matrix(65,-8,382,-47) Matrix(1793,-4992,644,-1793) -> Matrix(161,-20,1296,-161) (64/23,39/14) -> (10/81,1/8) Matrix(391,-1092,140,-391) -> Matrix(17,-2,144,-17) (39/14,14/5) -> (1/9,1/8) Matrix(129,-364,28,-79) -> Matrix(17,-2,94,-11) Matrix(129,-416,40,-129) -> Matrix(29,-4,210,-29) (16/5,13/4) -> (2/15,1/7) Matrix(79,-260,24,-79) -> Matrix(13,-2,84,-13) (13/4,10/3) -> (1/7,1/6) Matrix(311,-1040,93,-311) -> Matrix(1,0,12,-1) (10/3,104/31) -> (0/1,1/6) Matrix(2913,-9776,868,-2913) -> Matrix(1,0,28,-1) (104/31,47/14) -> (0/1,1/14) Matrix(649,-2184,178,-599) -> Matrix(1,0,-2,1) 0/1 Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(15,-2,68,-9) Matrix(181,-624,38,-131) -> Matrix(27,-4,142,-21) Matrix(103,-364,15,-53) -> Matrix(13,-2,46,-7) Matrix(2495,-8944,696,-2495) -> Matrix(-1,0,4,1) (43/12,104/29) -> (-1/2,0/1) Matrix(521,-1872,145,-521) -> Matrix(1,0,16,-1) (104/29,18/5) -> (0/1,1/8) Matrix(155,-572,42,-155) -> Matrix(13,-2,84,-13) (11/3,26/7) -> (1/7,1/6) Matrix(27,-104,7,-27) -> Matrix(1,0,12,-1) (26/7,4/1) -> (0/1,1/6) Matrix(25,-104,6,-25) -> Matrix(1,0,12,-1) (4/1,13/3) -> (0/1,1/6) Matrix(131,-572,30,-131) -> Matrix(11,-2,60,-11) (13/3,22/5) -> (1/6,1/5) Matrix(545,-2496,119,-545) -> Matrix(25,-4,156,-25) (32/7,78/17) -> (2/13,1/6) Matrix(781,-3588,170,-781) -> Matrix(35,-6,204,-35) (78/17,23/5) -> (1/6,3/17) Matrix(155,-728,33,-155) -> Matrix(23,-4,132,-23) (14/3,52/11) -> (1/6,2/11) Matrix(417,-1976,88,-417) -> Matrix(65,-12,352,-65) (52/11,19/4) -> (2/11,3/16) Matrix(51,-260,10,-51) -> Matrix(11,-2,60,-11) (5/1,26/5) -> (1/6,1/5) Matrix(79,-416,15,-79) -> Matrix(19,-4,90,-19) (26/5,16/3) -> (1/5,2/9) Matrix(415,-2392,72,-415) -> Matrix(127,-28,576,-127) (23/4,52/9) -> (7/32,2/9) Matrix(53,-312,9,-53) -> Matrix(17,-4,72,-17) (52/9,6/1) -> (2/9,1/4) Matrix(25,-156,4,-25) -> Matrix(9,-2,40,-9) (6/1,13/2) -> (1/5,1/4) Matrix(79,-520,12,-79) -> Matrix(31,-8,120,-31) (13/2,20/3) -> (1/4,4/15) Matrix(25,-208,3,-25) -> Matrix(13,-4,42,-13) (8/1,26/3) -> (2/7,1/3) Matrix(53,-468,6,-53) -> Matrix(29,-10,84,-29) (26/3,9/1) -> (1/3,5/14) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.