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 -1/1 -2/3 -20/3 -3/5 -1/2 -13/2 -1/2 -6/1 -1/3 -17/3 -1/1 0/1 -11/2 -3/7 -2/5 -16/3 -3/8 -1/3 -5/1 -1/3 -2/7 -19/4 -1/5 0/1 -14/3 -1/3 -9/2 -2/7 -3/11 -22/5 -5/19 -13/3 -1/4 -4/1 -1/4 -1/5 -11/3 -1/5 -6/31 -29/8 -4/21 -7/37 -18/5 -5/27 -25/7 -2/11 -3/17 -32/9 -3/17 -1/6 -7/2 -1/5 -2/11 -31/9 -3/17 -4/23 -24/7 -3/17 -1/6 -41/12 -3/19 -2/13 -17/5 -1/5 0/1 -27/8 -2/11 -3/17 -37/11 -1/5 -4/21 -10/3 -3/17 -13/4 -1/6 -16/5 -1/6 -5/31 -3/1 -2/13 -1/7 -17/6 -4/29 -7/51 -14/5 -1/7 -39/14 -3/22 -64/23 -3/22 -5/37 -25/9 -1/7 -2/15 -11/4 -5/37 -2/15 -30/11 -7/53 -19/7 -3/23 -4/31 -27/10 -2/15 -7/53 -35/13 -8/61 -3/23 -8/3 -3/23 -1/8 -13/5 -1/8 -18/7 -7/57 -23/9 -4/33 -3/25 -51/20 -4/33 -3/25 -28/11 -1/8 -3/25 -5/2 -3/25 -2/17 -27/11 -2/17 -5/43 -22/9 -5/43 -17/7 -4/35 -1/9 -46/19 -7/61 -29/12 -4/35 -9/79 -41/17 -2/17 -1/9 -53/22 -4/35 -9/79 -12/5 -5/44 -1/9 -7/3 -1/9 -6/55 -30/13 -7/65 -53/23 -4/37 -7/65 -23/10 -4/37 -7/65 -16/7 -3/28 -5/47 -41/18 -9/85 -2/19 -25/11 -5/47 -2/19 -34/15 -13/123 -9/4 -2/19 -7/67 -29/13 -20/193 -3/29 -20/9 -3/29 -7/68 -51/23 -3/29 -4/39 -31/14 -19/185 -4/39 -42/19 -13/127 -11/5 -5/49 -6/59 -24/11 -11/109 -1/10 -13/6 -1/10 -2/1 -1/11 -13/7 -1/12 -24/13 -1/12 -11/133 -11/6 -6/73 -5/61 -31/17 -4/49 -19/233 -20/11 -7/86 -3/37 -9/5 -7/87 -2/25 -25/14 -2/25 -5/63 -16/9 -5/63 -3/38 -23/13 -7/89 -4/51 -7/4 -6/77 -1/13 -26/15 -1/13 -19/11 -1/13 -16/209 -12/7 -1/13 -5/66 -29/17 -9/119 -4/53 -17/10 -1/13 -4/53 -22/13 -5/67 -27/16 -5/67 -2/27 -5/3 -2/27 -3/41 -28/17 -3/41 -1/14 -79/48 -2/27 -3/41 -130/79 -3/41 -51/31 -3/41 -4/55 -23/14 -3/41 -4/55 -18/11 -7/97 -13/8 -1/14 -8/5 -1/14 -3/43 -19/12 -4/57 -3/43 -49/31 -7/101 -2/29 -79/50 -7/101 -2/29 -30/19 -7/101 -41/26 -19/275 -2/29 -52/33 -2/29 -11/7 -2/29 -5/73 -25/16 -2/29 -1/15 -64/41 -5/73 -3/44 -39/25 -3/44 -14/9 -1/15 -3/2 -1/15 -2/31 -16/11 -5/79 -1/16 -13/9 -1/16 -10/7 -3/49 -57/40 -19/313 -2/33 -104/73 -2/33 -47/33 -2/33 -13/215 -37/26 -4/67 -1/17 -27/19 -3/49 -2/33 -17/12 -1/17 0/1 -24/17 -1/16 -3/49 -7/5 -2/33 -1/17 -32/23 -1/16 -3/49 -57/41 -2/33 -5/83 -25/18 -3/49 -2/33 -43/31 -15/247 -2/33 -104/75 -2/33 -61/44 -2/33 -25/413 -18/13 -5/83 -29/21 -7/117 -4/67 -40/29 -3/50 -1/17 -51/37 -7/117 -4/67 -11/8 -6/101 -1/17 -26/19 -1/17 -15/11 -1/17 -8/137 -4/3 -1/17 -1/18 -13/10 -1/18 -22/17 -5/91 -9/7 -3/55 -2/37 -32/25 -5/94 -1/19 -55/43 -14/265 -1/19 -78/61 -1/19 -23/18 -1/19 -4/77 -14/11 -1/19 -33/26 -1/21 0/1 -52/41 0/1 -19/15 -1/17 0/1 -24/19 -1/18 -1/19 -5/4 -2/37 -1/19 -26/21 -1/19 -21/17 -1/19 -8/153 -16/13 -1/19 -3/58 -27/22 -1/19 -2/39 -11/9 -2/39 -3/59 -28/23 -1/20 -3/61 -17/14 -1/21 0/1 -23/19 -1/23 0/1 -52/43 0/1 -29/24 -1/15 0/1 -6/5 -1/19 -13/11 -1/20 -20/17 -1/20 -3/61 -7/6 -2/41 -1/21 -8/7 -1/20 -1/21 -17/15 -4/83 -1/21 -26/23 -1/21 -9/8 -1/21 -2/43 -1/1 -1/23 0/1 0/1 0/1 1/1 0/1 1/25 7/6 1/23 2/45 20/17 3/67 1/22 13/11 1/22 6/5 1/21 17/14 0/1 1/23 11/9 3/65 2/43 16/13 3/64 1/21 5/4 1/21 2/41 19/15 0/1 1/19 14/11 1/21 9/7 2/41 3/61 22/17 5/101 13/10 1/20 4/3 1/20 1/19 11/8 1/19 6/113 29/21 4/75 7/131 18/13 5/93 25/18 2/37 3/55 32/23 3/55 1/18 7/5 1/19 2/37 31/22 3/55 4/73 24/17 3/55 1/18 41/29 3/53 2/35 17/12 0/1 1/19 27/19 2/37 3/55 37/26 1/19 4/75 10/7 3/55 13/9 1/18 16/11 1/18 5/89 3/2 2/35 1/17 17/11 4/67 7/117 14/9 1/17 39/25 3/50 64/41 3/50 5/83 25/16 1/17 2/33 11/7 5/83 2/33 30/19 7/115 19/12 3/49 4/65 27/17 2/33 7/115 35/22 8/131 3/49 8/5 3/49 1/16 13/8 1/16 18/11 7/111 23/14 4/63 3/47 51/31 4/63 3/47 28/17 1/16 3/47 5/3 3/47 2/31 27/16 2/31 5/77 22/13 5/77 17/10 4/61 1/15 46/27 7/107 29/17 4/61 9/137 41/24 2/31 1/15 53/31 4/61 9/137 12/7 5/76 1/15 7/4 1/15 6/89 30/17 7/103 53/30 4/59 7/103 23/13 4/59 7/103 16/9 3/44 5/73 41/23 9/131 2/29 25/14 5/73 2/29 34/19 13/189 9/5 2/29 7/101 29/16 20/287 3/43 20/11 3/43 7/100 51/28 3/43 4/57 31/17 19/271 4/57 42/23 13/185 11/6 5/71 6/85 24/13 11/155 1/14 13/7 1/14 2/1 1/13 13/6 1/12 24/11 1/12 11/131 11/5 6/71 5/59 31/14 4/47 19/223 20/9 7/82 3/35 9/4 7/81 2/23 25/11 2/23 5/57 16/7 5/57 3/34 23/10 7/79 4/45 7/3 6/67 1/11 26/11 1/11 19/8 1/11 16/175 12/5 1/11 5/54 29/12 9/97 4/43 17/7 1/11 4/43 22/9 5/53 27/11 5/53 2/21 5/2 2/21 3/31 28/11 3/31 1/10 79/31 2/21 3/31 130/51 3/31 51/20 3/31 4/41 23/9 3/31 4/41 18/7 7/71 13/5 1/10 8/3 1/10 3/29 19/7 4/39 3/29 49/18 7/67 2/19 79/29 7/67 2/19 30/11 7/67 41/15 19/181 2/19 52/19 2/19 11/4 2/19 5/47 25/9 2/19 1/9 64/23 5/47 3/28 39/14 3/28 14/5 1/9 3/1 1/9 2/17 16/5 5/41 1/8 13/4 1/8 10/3 3/23 57/17 19/143 2/15 104/31 2/15 47/14 2/15 13/97 37/11 4/29 1/7 27/8 3/23 2/15 17/5 0/1 1/7 24/7 1/8 3/23 7/2 2/15 1/7 32/9 1/8 3/23 57/16 2/15 5/37 25/7 3/23 2/15 43/12 15/113 2/15 104/29 2/15 61/17 2/15 25/187 18/5 5/37 29/8 7/51 4/29 40/11 3/22 1/7 51/14 7/51 4/29 11/3 6/43 1/7 26/7 1/7 15/4 1/7 8/55 4/1 1/7 1/6 13/3 1/6 22/5 5/29 9/2 3/17 2/11 32/7 5/26 1/5 55/12 14/71 1/5 78/17 1/5 23/5 1/5 4/19 14/3 1/5 33/7 0/1 1/3 52/11 0/1 19/4 0/1 1/7 24/5 1/6 1/5 5/1 2/11 1/5 26/5 1/5 21/4 1/5 8/39 16/3 1/5 3/14 27/5 1/5 2/9 11/2 2/9 3/13 28/5 1/4 3/11 17/3 0/1 1/3 23/4 0/1 1/1 52/9 0/1 29/5 0/1 1/9 6/1 1/5 13/2 1/4 20/3 1/4 3/11 7/1 2/7 1/3 8/1 1/4 1/3 17/2 4/13 1/3 26/3 1/3 9/1 1/3 2/5 1/0 0/1 1/1 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(5,2,-38,-15) Matrix(53,364,38,261) -> Matrix(1,0,20,1) Matrix(79,520,12,79) -> Matrix(11,6,42,23) Matrix(25,156,4,25) -> Matrix(5,2,22,9) Matrix(155,884,-64,-365) -> Matrix(5,4,-44,-35) Matrix(157,884,-46,-259) -> Matrix(1,0,-4,1) Matrix(155,832,-68,-365) -> Matrix(31,12,-292,-113) Matrix(79,416,-64,-337) -> Matrix(17,6,-326,-115) Matrix(131,624,-38,-181) -> Matrix(9,2,-50,-11) Matrix(155,728,-122,-573) -> Matrix(1,0,-16,1) Matrix(79,364,-28,-129) -> Matrix(5,2,-38,-15) Matrix(129,572,76,337) -> Matrix(37,10,566,153) Matrix(131,572,30,131) -> Matrix(39,10,230,59) Matrix(25,104,6,25) -> Matrix(9,2,58,13) Matrix(27,104,-20,-77) -> Matrix(9,2,-158,-35) Matrix(415,1508,-172,-625) -> Matrix(41,8,-364,-71) Matrix(259,936,158,571) -> Matrix(85,16,1344,253) Matrix(363,1300,-160,-573) -> Matrix(89,16,-840,-151) Matrix(599,2132,-270,-961) -> Matrix(101,18,-982,-175) Matrix(103,364,88,311) -> Matrix(1,0,28,1) Matrix(287,988,174,599) -> Matrix(35,6,554,95) Matrix(365,1248,198,677) -> Matrix(49,8,692,113) Matrix(415,1404,-154,-521) -> Matrix(43,8,-328,-61) Matrix(911,3068,-378,-1273) -> Matrix(31,6,-274,-53) Matrix(495,1664,-224,-753) -> Matrix(75,14,-734,-137) Matrix(79,260,24,79) -> Matrix(35,6,274,47) Matrix(129,416,40,129) -> Matrix(61,10,494,81) Matrix(131,416,74,235) -> Matrix(63,10,926,147) Matrix(183,520,-82,-233) -> Matrix(101,14,-974,-135) Matrix(391,1092,140,391) -> Matrix(43,6,394,55) Matrix(1793,4992,644,1793) -> Matrix(221,30,2070,281) Matrix(1327,3692,776,2159) -> Matrix(163,22,2482,335) Matrix(469,1300,-206,-571) -> Matrix(61,8,-572,-75) Matrix(571,1560,-362,-989) -> Matrix(211,28,-3052,-405) Matrix(287,780,-124,-337) -> Matrix(107,14,-986,-129) Matrix(155,416,-136,-365) -> Matrix(31,4,-628,-81) Matrix(79,208,30,79) -> Matrix(47,6,462,59) Matrix(181,468,70,181) -> Matrix(113,14,1138,141) Matrix(365,936,264,677) -> Matrix(131,16,2448,299) Matrix(937,2392,530,1353) -> Matrix(131,16,1924,235) Matrix(1429,3640,-868,-2211) -> Matrix(49,6,-678,-83) Matrix(389,988,276,701) -> Matrix(49,6,890,109) Matrix(443,1092,-200,-493) -> Matrix(223,26,-2170,-253) Matrix(807,1976,-350,-857) -> Matrix(53,6,-486,-55) Matrix(235,572,182,443) -> Matrix(87,10,1766,203) Matrix(623,1508,-516,-1249) -> Matrix(35,4,-604,-69) Matrix(1533,3692,982,2365) -> Matrix(193,22,3202,365) Matrix(131,312,-76,-181) -> Matrix(89,10,-1166,-131) Matrix(1039,2392,632,1455) -> Matrix(149,16,2356,253) Matrix(181,416,124,285) -> Matrix(93,10,1646,177) Matrix(987,2236,-712,-1613) -> Matrix(341,36,-5636,-595) Matrix(911,2028,-712,-1585) -> Matrix(213,22,-4018,-415) Matrix(1223,2704,-858,-1897) -> Matrix(371,38,-6102,-625) Matrix(571,1248,404,883) -> Matrix(79,8,1412,143) Matrix(287,624,132,287) -> Matrix(219,22,2618,263) Matrix(25,52,12,25) -> Matrix(21,2,262,25) Matrix(27,52,14,27) -> Matrix(23,2,310,27) Matrix(337,624,182,337) -> Matrix(265,22,3722,309) Matrix(311,572,56,103) -> Matrix(97,8,400,33) Matrix(911,1664,-640,-1169) -> Matrix(171,14,-2846,-233) Matrix(1171,2132,-842,-1533) -> Matrix(221,18,-3622,-295) Matrix(259,468,-202,-365) -> Matrix(99,8,-1844,-149) Matrix(727,1300,-524,-937) -> Matrix(201,16,-3304,-263) Matrix(467,832,-380,-677) -> Matrix(151,12,-2932,-233) Matrix(235,416,74,131) -> Matrix(127,10,1054,83) Matrix(443,780,-280,-493) -> Matrix(179,14,-2570,-201) Matrix(389,676,164,285) -> Matrix(285,22,3122,241) Matrix(391,676,166,287) -> Matrix(287,22,3170,243) Matrix(883,1508,-640,-1093) -> Matrix(105,8,-1772,-135) Matrix(519,884,-428,-729) -> Matrix(53,4,-1100,-83) Matrix(337,572,76,129) -> Matrix(133,10,758,57) Matrix(1507,2548,-954,-1613) -> Matrix(55,4,-784,-57) Matrix(987,1664,-710,-1197) -> Matrix(53,4,-888,-67) Matrix(157,260,32,53) -> Matrix(55,4,316,23) Matrix(10269,16900,4028,6629) -> Matrix(245,18,2518,185) Matrix(10271,16900,4030,6631) -> Matrix(247,18,2566,187) Matrix(2625,4316,964,1585) -> Matrix(303,22,2906,211) Matrix(571,936,158,259) -> Matrix(221,16,1616,117) Matrix(287,468,176,287) -> Matrix(195,14,3106,223) Matrix(129,208,80,129) -> Matrix(85,6,1374,97) Matrix(131,208,-114,-181) -> Matrix(29,2,-566,-39) Matrix(2731,4316,1070,1691) -> Matrix(317,22,3242,225) Matrix(1715,2704,626,987) -> Matrix(695,48,6588,455) Matrix(1717,2704,628,989) -> Matrix(697,48,6636,457) Matrix(365,572,-298,-467) -> Matrix(59,4,-1136,-77) Matrix(2731,4264,750,1171) -> Matrix(263,18,1914,131) Matrix(3199,4992,2050,3199) -> Matrix(439,30,7302,499) Matrix(701,1092,450,701) -> Matrix(89,6,1498,101) Matrix(235,364,-184,-285) -> Matrix(29,2,-566,-39) Matrix(285,416,124,181) -> Matrix(157,10,1774,113) Matrix(287,416,198,287) -> Matrix(159,10,2846,179) Matrix(181,260,126,181) -> Matrix(97,6,1762,109) Matrix(7591,10816,2262,3223) -> Matrix(1055,64,7896,479) Matrix(7593,10816,2264,3225) -> Matrix(1057,64,7944,481) Matrix(1535,2184,-1114,-1585) -> Matrix(35,2,-578,-33) Matrix(183,260,-164,-233) -> Matrix(33,2,-710,-43) Matrix(625,884,-514,-727) -> Matrix(1,0,-4,1) Matrix(443,624,-350,-493) -> Matrix(33,2,-578,-35) Matrix(261,364,38,53) -> Matrix(1,0,20,1) Matrix(7799,10816,2174,3015) -> Matrix(1319,80,9876,599) Matrix(7801,10816,2176,3017) -> Matrix(1321,80,9924,601) Matrix(677,936,264,365) -> Matrix(267,16,2720,163) Matrix(3093,4264,1112,1533) -> Matrix(301,18,2826,169) Matrix(493,676,132,181) -> Matrix(237,14,1642,97) Matrix(495,676,134,183) -> Matrix(239,14,1690,99) Matrix(79,104,60,79) -> Matrix(35,2,682,39) Matrix(441,572,340,441) -> Matrix(181,10,3638,201) Matrix(443,572,182,235) -> Matrix(183,10,1958,107) Matrix(4757,6084,1036,1325) -> Matrix(341,18,1686,89) Matrix(4759,6084,1038,1327) -> Matrix(343,18,1734,91) Matrix(2131,2704,450,571) -> Matrix(1,0,28,1) Matrix(2133,2704,452,573) -> Matrix(1,0,20,1) Matrix(207,260,82,103) -> Matrix(73,4,748,41) Matrix(545,676,104,129) -> Matrix(189,10,926,49) Matrix(547,676,106,131) -> Matrix(191,10,974,51) Matrix(469,572,214,261) -> Matrix(159,8,1888,95) Matrix(2235,2704,386,467) -> Matrix(1,0,32,1) Matrix(2237,2704,388,469) -> Matrix(1,0,16,1) Matrix(131,156,110,131) -> Matrix(39,2,838,43) Matrix(441,520,374,441) -> Matrix(121,6,2682,133) Matrix(311,364,88,103) -> Matrix(1,0,28,1) Matrix(597,676,68,77) -> Matrix(125,6,354,17) Matrix(599,676,70,79) -> Matrix(127,6,402,19) Matrix(1,0,2,1) -> Matrix(1,0,48,1) Matrix(181,-208,114,-131) -> Matrix(43,-2,710,-33) Matrix(729,-884,428,-519) -> Matrix(91,-4,1388,-61) Matrix(727,-884,514,-625) -> Matrix(1,0,-4,1) Matrix(677,-832,380,-467) -> Matrix(257,-12,3748,-175) Matrix(337,-416,64,-79) -> Matrix(127,-6,614,-29) Matrix(493,-624,350,-443) -> Matrix(39,-2,722,-37) Matrix(573,-728,122,-155) -> Matrix(1,0,-16,1) Matrix(285,-364,184,-235) -> Matrix(43,-2,710,-33) Matrix(77,-104,20,-27) -> Matrix(39,-2,254,-13) Matrix(1093,-1508,640,-883) -> Matrix(151,-8,2284,-121) Matrix(937,-1300,524,-727) -> Matrix(295,-16,4296,-233) Matrix(1533,-2132,842,-1171) -> Matrix(331,-18,4726,-257) Matrix(989,-1404,622,-883) -> Matrix(149,-8,2440,-131) Matrix(2157,-3068,1262,-1795) -> Matrix(113,-6,1714,-91) Matrix(1169,-1664,640,-911) -> Matrix(261,-14,3710,-199) Matrix(337,-520,186,-287) -> Matrix(235,-14,3374,-201) Matrix(831,-1300,466,-729) -> Matrix(131,-8,1916,-117) Matrix(989,-1560,362,-571) -> Matrix(461,-28,4396,-267) Matrix(493,-780,280,-443) -> Matrix(229,-14,3386,-207) Matrix(261,-416,32,-51) -> Matrix(65,-4,244,-15) Matrix(2211,-3640,868,-1429) -> Matrix(95,-6,966,-61) Matrix(649,-1092,356,-599) -> Matrix(401,-26,5722,-371) Matrix(1169,-1976,662,-1119) -> Matrix(91,-6,1350,-89) Matrix(885,-1508,152,-259) -> Matrix(61,-4,412,-27) Matrix(181,-312,76,-131) -> Matrix(151,-10,1646,-109) Matrix(1249,-2236,348,-623) -> Matrix(523,-36,3908,-269) Matrix(1117,-2028,244,-443) -> Matrix(315,-22,1618,-113) Matrix(1481,-2704,442,-807) -> Matrix(541,-38,4086,-287) Matrix(753,-1664,224,-495) -> Matrix(165,-14,1214,-103) Matrix(961,-2132,270,-599) -> Matrix(211,-18,1606,-137) Matrix(209,-468,46,-103) -> Matrix(93,-8,500,-43) Matrix(573,-1300,160,-363) -> Matrix(183,-16,1384,-121) Matrix(365,-832,68,-155) -> Matrix(137,-12,628,-55) Matrix(337,-780,124,-287) -> Matrix(157,-14,1514,-135) Matrix(625,-1508,172,-415) -> Matrix(87,-8,620,-57) Matrix(365,-884,64,-155) -> Matrix(43,-4,140,-13) Matrix(1041,-2548,382,-935) -> Matrix(41,-4,400,-39) Matrix(677,-1664,190,-467) -> Matrix(43,-4,312,-29) Matrix(77,-208,10,-27) -> Matrix(19,-2,86,-9) Matrix(207,-572,38,-105) -> Matrix(37,-4,176,-19) Matrix(129,-364,28,-79) -> Matrix(19,-2,86,-9) Matrix(649,-2184,178,-599) -> Matrix(13,-2,98,-15) Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(1,0,-4,1) Matrix(181,-624,38,-131) -> Matrix(15,-2,98,-13) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 42 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 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): 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 0/1 1/25 7/6 1/23 2/45 20/17 3/67 1/22 13/11 1/22 6/5 1/21 17/14 0/1 1/23 11/9 3/65 2/43 16/13 3/64 1/21 5/4 1/21 2/41 19/15 0/1 1/19 14/11 1/21 9/7 2/41 3/61 22/17 5/101 13/10 1/20 4/3 1/20 1/19 11/8 1/19 6/113 29/21 4/75 7/131 18/13 5/93 25/18 2/37 3/55 32/23 3/55 1/18 7/5 1/19 2/37 31/22 3/55 4/73 24/17 3/55 1/18 41/29 3/53 2/35 17/12 0/1 1/19 27/19 2/37 3/55 37/26 1/19 4/75 10/7 3/55 13/9 1/18 16/11 1/18 5/89 3/2 2/35 1/17 17/11 4/67 7/117 14/9 1/17 39/25 3/50 64/41 3/50 5/83 25/16 1/17 2/33 11/7 5/83 2/33 30/19 7/115 19/12 3/49 4/65 27/17 2/33 7/115 35/22 8/131 3/49 8/5 3/49 1/16 13/8 1/16 18/11 7/111 23/14 4/63 3/47 51/31 4/63 3/47 28/17 1/16 3/47 5/3 3/47 2/31 27/16 2/31 5/77 22/13 5/77 17/10 4/61 1/15 46/27 7/107 29/17 4/61 9/137 41/24 2/31 1/15 53/31 4/61 9/137 12/7 5/76 1/15 7/4 1/15 6/89 30/17 7/103 53/30 4/59 7/103 23/13 4/59 7/103 16/9 3/44 5/73 41/23 9/131 2/29 25/14 5/73 2/29 34/19 13/189 9/5 2/29 7/101 29/16 20/287 3/43 20/11 3/43 7/100 51/28 3/43 4/57 31/17 19/271 4/57 42/23 13/185 11/6 5/71 6/85 24/13 11/155 1/14 13/7 1/14 2/1 1/13 13/6 1/12 24/11 1/12 11/131 11/5 6/71 5/59 31/14 4/47 19/223 20/9 7/82 3/35 9/4 7/81 2/23 25/11 2/23 5/57 16/7 5/57 3/34 23/10 7/79 4/45 7/3 6/67 1/11 26/11 1/11 19/8 1/11 16/175 12/5 1/11 5/54 29/12 9/97 4/43 17/7 1/11 4/43 22/9 5/53 27/11 5/53 2/21 5/2 2/21 3/31 28/11 3/31 1/10 79/31 2/21 3/31 130/51 3/31 51/20 3/31 4/41 23/9 3/31 4/41 18/7 7/71 13/5 1/10 8/3 1/10 3/29 19/7 4/39 3/29 49/18 7/67 2/19 79/29 7/67 2/19 30/11 7/67 41/15 19/181 2/19 52/19 2/19 11/4 2/19 5/47 25/9 2/19 1/9 64/23 5/47 3/28 39/14 3/28 14/5 1/9 3/1 1/9 2/17 16/5 5/41 1/8 13/4 1/8 10/3 3/23 57/17 19/143 2/15 104/31 2/15 47/14 2/15 13/97 37/11 4/29 1/7 27/8 3/23 2/15 17/5 0/1 1/7 24/7 1/8 3/23 7/2 2/15 1/7 32/9 1/8 3/23 57/16 2/15 5/37 25/7 3/23 2/15 43/12 15/113 2/15 104/29 2/15 61/17 2/15 25/187 18/5 5/37 29/8 7/51 4/29 40/11 3/22 1/7 51/14 7/51 4/29 11/3 6/43 1/7 26/7 1/7 15/4 1/7 8/55 4/1 1/7 1/6 13/3 1/6 22/5 5/29 9/2 3/17 2/11 32/7 5/26 1/5 55/12 14/71 1/5 78/17 1/5 23/5 1/5 4/19 14/3 1/5 33/7 0/1 1/3 52/11 0/1 19/4 0/1 1/7 24/5 1/6 1/5 5/1 2/11 1/5 26/5 1/5 21/4 1/5 8/39 16/3 1/5 3/14 27/5 1/5 2/9 11/2 2/9 3/13 28/5 1/4 3/11 17/3 0/1 1/3 23/4 0/1 1/1 52/9 0/1 29/5 0/1 1/9 6/1 1/5 13/2 1/4 20/3 1/4 3/11 7/1 2/7 1/3 8/1 1/4 1/3 17/2 4/13 1/3 26/3 1/3 9/1 1/3 2/5 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(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(43,-2,710,-33) Matrix(311,-364,223,-261) -> Matrix(1,0,-4,1) Matrix(441,-520,67,-79) -> Matrix(133,-6,510,-23) Matrix(131,-156,21,-25) -> Matrix(43,-2,194,-9) Matrix(729,-884,428,-519) -> Matrix(91,-4,1388,-61) Matrix(727,-884,514,-625) -> Matrix(1,0,-4,1) Matrix(677,-832,380,-467) -> Matrix(257,-12,3748,-175) Matrix(337,-416,64,-79) -> Matrix(127,-6,614,-29) Matrix(493,-624,350,-443) -> Matrix(39,-2,722,-37) Matrix(573,-728,122,-155) -> Matrix(1,0,-16,1) Matrix(285,-364,184,-235) -> Matrix(43,-2,710,-33) Matrix(443,-572,261,-337) -> Matrix(203,-10,3106,-153) Matrix(441,-572,101,-131) -> Matrix(201,-10,1186,-59) Matrix(79,-104,19,-25) -> Matrix(39,-2,254,-13) Matrix(77,-104,20,-27) -> Matrix(39,-2,254,-13) Matrix(1093,-1508,640,-883) -> Matrix(151,-8,2284,-121) Matrix(677,-936,413,-571) -> Matrix(299,-16,4728,-253) Matrix(937,-1300,524,-727) -> Matrix(295,-16,4296,-233) Matrix(1533,-2132,842,-1171) -> Matrix(331,-18,4726,-257) Matrix(701,-988,425,-599) -> Matrix(109,-6,1726,-95) Matrix(883,-1248,479,-677) -> Matrix(143,-8,2020,-113) Matrix(989,-1404,622,-883) -> Matrix(149,-8,2440,-131) Matrix(2157,-3068,1262,-1795) -> Matrix(113,-6,1714,-91) Matrix(1169,-1664,640,-911) -> Matrix(261,-14,3710,-199) Matrix(181,-260,55,-79) -> Matrix(109,-6,854,-47) Matrix(287,-416,89,-129) -> Matrix(179,-10,1450,-81) Matrix(285,-416,161,-235) -> Matrix(177,-10,2602,-147) Matrix(337,-520,186,-287) -> Matrix(235,-14,3374,-201) Matrix(701,-1092,251,-391) -> Matrix(101,-6,926,-55) Matrix(3199,-4992,1149,-1793) -> Matrix(499,-30,4674,-281) Matrix(2365,-3692,1383,-2159) -> Matrix(365,-22,5558,-335) Matrix(831,-1300,466,-729) -> Matrix(131,-8,1916,-117) Matrix(989,-1560,362,-571) -> Matrix(461,-28,4396,-267) Matrix(493,-780,280,-443) -> Matrix(229,-14,3386,-207) Matrix(261,-416,32,-51) -> Matrix(65,-4,244,-15) Matrix(129,-208,49,-79) -> Matrix(97,-6,954,-59) Matrix(287,-468,111,-181) -> Matrix(223,-14,2246,-141) Matrix(1455,-2392,823,-1353) -> Matrix(253,-16,3716,-235) Matrix(2211,-3640,868,-1429) -> Matrix(95,-6,966,-61) Matrix(649,-1092,356,-599) -> Matrix(401,-26,5722,-371) Matrix(1169,-1976,662,-1119) -> Matrix(91,-6,1350,-89) Matrix(885,-1508,152,-259) -> Matrix(61,-4,412,-27) Matrix(181,-312,76,-131) -> Matrix(151,-10,1646,-109) Matrix(1249,-2236,348,-623) -> Matrix(523,-36,3908,-269) Matrix(1117,-2028,244,-443) -> Matrix(315,-22,1618,-113) Matrix(1481,-2704,442,-807) -> Matrix(541,-38,4086,-287) Matrix(337,-624,155,-287) -> Matrix(309,-22,3694,-263) Matrix(27,-52,13,-25) -> Matrix(27,-2,338,-25) Matrix(261,-572,47,-103) -> Matrix(95,-8,392,-33) Matrix(753,-1664,224,-495) -> Matrix(165,-14,1214,-103) Matrix(961,-2132,270,-599) -> Matrix(211,-18,1606,-137) Matrix(209,-468,46,-103) -> Matrix(93,-8,500,-43) Matrix(573,-1300,160,-363) -> Matrix(183,-16,1384,-121) Matrix(365,-832,68,-155) -> Matrix(137,-12,628,-55) Matrix(181,-416,57,-131) -> Matrix(113,-10,938,-83) Matrix(337,-780,124,-287) -> Matrix(157,-14,1514,-135) Matrix(287,-676,121,-285) -> Matrix(243,-22,2662,-241) Matrix(625,-1508,172,-415) -> Matrix(87,-8,620,-57) Matrix(365,-884,64,-155) -> Matrix(43,-4,140,-13) Matrix(235,-572,53,-129) -> Matrix(107,-10,610,-57) Matrix(1041,-2548,382,-935) -> Matrix(41,-4,400,-39) Matrix(677,-1664,190,-467) -> Matrix(43,-4,312,-29) Matrix(103,-260,21,-53) -> Matrix(41,-4,236,-23) Matrix(6631,-16900,2601,-6629) -> Matrix(187,-18,1922,-185) Matrix(1691,-4316,621,-1585) -> Matrix(225,-22,2158,-211) Matrix(365,-936,101,-259) -> Matrix(163,-16,1192,-117) Matrix(77,-208,10,-27) -> Matrix(19,-2,86,-9) Matrix(989,-2704,361,-987) -> Matrix(457,-48,4332,-455) Matrix(207,-572,38,-105) -> Matrix(37,-4,176,-19) Matrix(1533,-4264,421,-1171) -> Matrix(169,-18,1230,-131) Matrix(129,-364,28,-79) -> Matrix(19,-2,86,-9) Matrix(3225,-10816,961,-3223) -> Matrix(481,-64,3600,-479) Matrix(649,-2184,178,-599) -> Matrix(13,-2,98,-15) Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(1,0,-4,1) Matrix(181,-624,38,-131) -> Matrix(15,-2,98,-13) Matrix(103,-364,15,-53) -> Matrix(1,0,-4,1) Matrix(3017,-10816,841,-3015) -> Matrix(601,-80,4500,-599) Matrix(183,-676,49,-181) -> Matrix(99,-14,686,-97) Matrix(1327,-6084,289,-1325) -> Matrix(91,-18,450,-89) Matrix(573,-2704,121,-571) -> Matrix(1,0,4,1) Matrix(131,-676,25,-129) -> Matrix(51,-10,250,-49) Matrix(469,-2704,81,-467) -> Matrix(1,0,8,1) Matrix(79,-676,9,-77) -> Matrix(19,-6,54,-17) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 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: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 21 ----------------------------------------------------------------------- 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 1/13 2 13 13/6 1/12 12 2 24/11 (1/12,11/131) 0 13 11/5 (6/71,5/59) 0 26 31/14 (4/47,19/223) 0 26 20/9 (7/82,3/35) 0 13 9/4 (7/81,2/23) 0 26 25/11 (2/23,5/57) 0 26 16/7 (5/57,3/34) 0 13 23/10 (7/79,4/45) 0 26 7/3 (6/67,1/11) 0 26 26/11 1/11 22 1 12/5 (1/11,5/54) 0 13 29/12 (9/97,4/43) 0 26 17/7 (1/11,4/43) 0 26 22/9 5/53 2 13 27/11 (5/53,2/21) 0 26 5/2 (2/21,3/31) 0 26 28/11 (3/31,1/10) 0 13 130/51 3/31 2 1 51/20 (3/31,4/41) 0 26 23/9 (3/31,4/41) 0 26 18/7 7/71 2 13 13/5 1/10 10 2 8/3 (1/10,3/29) 0 13 19/7 (4/39,3/29) 0 26 49/18 (7/67,2/19) 0 26 79/29 (7/67,2/19) 0 26 30/11 7/67 2 13 52/19 2/19 12 1 11/4 (2/19,5/47) 0 26 25/9 (2/19,1/9) 0 26 64/23 (5/47,3/28) 0 13 39/14 3/28 2 2 14/5 1/9 2 13 3/1 (1/9,2/17) 0 26 16/5 (5/41,1/8) 0 13 13/4 1/8 8 2 10/3 3/23 2 13 104/31 2/15 16 1 47/14 (2/15,13/97) 0 26 37/11 (4/29,1/7) 0 26 27/8 (3/23,2/15) 0 26 17/5 (0/1,1/7) 0 26 24/7 (1/8,3/23) 0 13 7/2 (2/15,1/7) 0 26 32/9 (1/8,3/23) 0 13 57/16 (2/15,5/37) 0 26 25/7 (3/23,2/15) 0 26 43/12 (15/113,2/15) 0 26 104/29 2/15 20 1 18/5 5/37 2 13 29/8 (7/51,4/29) 0 26 40/11 (3/22,1/7) 0 13 51/14 (7/51,4/29) 0 26 11/3 (6/43,1/7) 0 26 26/7 1/7 14 1 4/1 (1/7,1/6) 0 13 13/3 1/6 6 2 22/5 5/29 2 13 9/2 (3/17,2/11) 0 26 32/7 (5/26,1/5) 0 13 78/17 1/5 18 1 23/5 (1/5,4/19) 0 26 14/3 1/5 2 13 52/11 0/1 4 1 19/4 (0/1,1/7) 0 26 24/5 (1/6,1/5) 0 13 5/1 (2/11,1/5) 0 26 26/5 1/5 10 1 16/3 (1/5,3/14) 0 13 27/5 (1/5,2/9) 0 26 11/2 (2/9,3/13) 0 26 28/5 (1/4,3/11) 0 13 17/3 (0/1,1/3) 0 26 23/4 (0/1,1/1) 0 26 52/9 0/1 8 1 6/1 1/5 2 13 13/2 1/4 4 2 20/3 (1/4,3/11) 0 13 7/1 (2/7,1/3) 0 26 8/1 (1/4,1/3) 0 13 26/3 1/3 6 1 9/1 (1/3,2/5) 0 26 1/0 (0/1,1/1) 0 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(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(1,0,1,-1) -> Matrix(1,0,26,-1) (0/1,2/1) -> (0/1,1/13) Matrix(25,-52,12,-25) -> Matrix(25,-2,312,-25) (2/1,13/6) -> (1/13,1/12) Matrix(287,-624,132,-287) -> Matrix(263,-22,3144,-263) (13/6,24/11) -> (1/12,11/131) Matrix(261,-572,47,-103) -> Matrix(95,-8,392,-33) Matrix(753,-1664,224,-495) -> Matrix(165,-14,1214,-103) Matrix(961,-2132,270,-599) -> Matrix(211,-18,1606,-137) Matrix(209,-468,46,-103) -> Matrix(93,-8,500,-43) Matrix(573,-1300,160,-363) -> Matrix(183,-16,1384,-121) Matrix(365,-832,68,-155) -> Matrix(137,-12,628,-55) Matrix(181,-416,57,-131) -> Matrix(113,-10,938,-83) Matrix(337,-780,124,-287) -> Matrix(157,-14,1514,-135) Matrix(155,-364,66,-155) -> Matrix(133,-12,1474,-133) (7/3,26/11) -> (6/67,1/11) Matrix(131,-312,55,-131) -> Matrix(109,-10,1188,-109) (26/11,12/5) -> (1/11,5/54) Matrix(625,-1508,172,-415) -> Matrix(87,-8,620,-57) Matrix(365,-884,64,-155) -> Matrix(43,-4,140,-13) Matrix(235,-572,53,-129) -> Matrix(107,-10,610,-57) Matrix(1041,-2548,382,-935) -> Matrix(41,-4,400,-39) 1/10 Matrix(677,-1664,190,-467) -> Matrix(43,-4,312,-29) Matrix(103,-260,21,-53) -> Matrix(41,-4,236,-23) Matrix(1429,-3640,561,-1429) -> Matrix(61,-6,620,-61) (28/11,130/51) -> (3/31,1/10) Matrix(5201,-13260,2040,-5201) -> Matrix(247,-24,2542,-247) (130/51,51/20) -> (3/31,4/41) Matrix(1691,-4316,621,-1585) -> Matrix(225,-22,2158,-211) Matrix(365,-936,101,-259) -> Matrix(163,-16,1192,-117) Matrix(181,-468,70,-181) -> Matrix(141,-14,1420,-141) (18/7,13/5) -> (7/71,1/10) Matrix(79,-208,30,-79) -> Matrix(59,-6,580,-59) (13/5,8/3) -> (1/10,3/29) Matrix(77,-208,10,-27) -> Matrix(19,-2,86,-9) Matrix(571,-1560,209,-571) -> Matrix(267,-28,2546,-267) (30/11,52/19) -> (7/67,2/19) Matrix(417,-1144,152,-417) -> Matrix(189,-20,1786,-189) (52/19,11/4) -> (2/19,5/47) Matrix(207,-572,38,-105) -> Matrix(37,-4,176,-19) Matrix(1533,-4264,421,-1171) -> Matrix(169,-18,1230,-131) Matrix(1793,-4992,644,-1793) -> Matrix(281,-30,2632,-281) (64/23,39/14) -> (5/47,3/28) Matrix(391,-1092,140,-391) -> Matrix(55,-6,504,-55) (39/14,14/5) -> (3/28,1/9) Matrix(129,-364,28,-79) -> Matrix(19,-2,86,-9) Matrix(129,-416,40,-129) -> Matrix(81,-10,656,-81) (16/5,13/4) -> (5/41,1/8) Matrix(79,-260,24,-79) -> Matrix(47,-6,368,-47) (13/4,10/3) -> (1/8,3/23) Matrix(311,-1040,93,-311) -> Matrix(91,-12,690,-91) (10/3,104/31) -> (3/23,2/15) Matrix(2913,-9776,868,-2913) -> Matrix(389,-52,2910,-389) (104/31,47/14) -> (2/15,13/97) Matrix(649,-2184,178,-599) -> Matrix(13,-2,98,-15) 1/7 Matrix(77,-260,8,-27) -> Matrix(15,-2,38,-5) Matrix(259,-884,46,-157) -> Matrix(1,0,-4,1) 0/1 Matrix(181,-624,38,-131) -> Matrix(15,-2,98,-13) 1/7 Matrix(103,-364,15,-53) -> Matrix(1,0,-4,1) 0/1 Matrix(2495,-8944,696,-2495) -> Matrix(451,-60,3390,-451) (43/12,104/29) -> (15/113,2/15) Matrix(521,-1872,145,-521) -> Matrix(149,-20,1110,-149) (104/29,18/5) -> (2/15,5/37) Matrix(155,-572,42,-155) -> Matrix(85,-12,602,-85) (11/3,26/7) -> (6/43,1/7) Matrix(27,-104,7,-27) -> Matrix(13,-2,84,-13) (26/7,4/1) -> (1/7,1/6) Matrix(25,-104,6,-25) -> Matrix(13,-2,84,-13) (4/1,13/3) -> (1/7,1/6) Matrix(131,-572,30,-131) -> Matrix(59,-10,348,-59) (13/3,22/5) -> (1/6,5/29) Matrix(545,-2496,119,-545) -> Matrix(51,-10,260,-51) (32/7,78/17) -> (5/26,1/5) Matrix(781,-3588,170,-781) -> Matrix(39,-8,190,-39) (78/17,23/5) -> (1/5,4/19) Matrix(155,-728,33,-155) -> Matrix(1,0,10,-1) (14/3,52/11) -> (0/1,1/5) Matrix(417,-1976,88,-417) -> Matrix(1,0,14,-1) (52/11,19/4) -> (0/1,1/7) Matrix(51,-260,10,-51) -> Matrix(21,-4,110,-21) (5/1,26/5) -> (2/11,1/5) Matrix(79,-416,15,-79) -> Matrix(29,-6,140,-29) (26/5,16/3) -> (1/5,3/14) Matrix(415,-2392,72,-415) -> Matrix(1,0,2,-1) (23/4,52/9) -> (0/1,1/1) Matrix(53,-312,9,-53) -> Matrix(1,0,10,-1) (52/9,6/1) -> (0/1,1/5) Matrix(25,-156,4,-25) -> Matrix(9,-2,40,-9) (6/1,13/2) -> (1/5,1/4) Matrix(79,-520,12,-79) -> Matrix(23,-6,88,-23) (13/2,20/3) -> (1/4,3/11) Matrix(25,-208,3,-25) -> Matrix(7,-2,24,-7) (8/1,26/3) -> (1/4,1/3) Matrix(53,-468,6,-53) -> Matrix(11,-4,30,-11) (26/3,9/1) -> (1/3,2/5) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.