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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -5/6 -4/5 -18/25 -7/10 -2/3 -11/18 -3/5 -14/25 -8/15 -1/2 -9/20 -5/12 -2/5 -8/21 -16/45 -1/3 -14/45 -3/10 -8/27 -4/15 -1/4 -2/9 -3/14 -6/29 -1/5 -4/21 -4/23 -1/6 -2/15 -1/8 -1/9 -1/10 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 2/13 1/6 2/11 1/5 4/19 3/14 2/9 3/13 7/30 4/17 1/4 4/15 2/7 8/27 3/10 1/3 11/30 2/5 5/12 13/30 9/20 7/15 1/2 8/15 14/25 17/30 3/5 11/18 19/30 2/3 31/45 7/10 151/210 18/25 11/15 23/30 4/5 5/6 13/15 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/2 -7/8 1/1 -13/15 1/1 -6/7 0/1 1/1 -5/6 1/2 -14/17 1/2 2/3 -23/28 5/7 -32/39 1/2 2/3 1/1 -9/11 3/4 1/1 -4/5 1/1 -15/19 1/2 1/1 -11/14 1/1 -18/23 1/1 6/5 -25/32 5/3 -32/41 1/1 2/1 -7/9 1/0 -10/13 -1/1 0/1 -23/30 0/1 -13/17 0/1 1/4 -3/4 1/1 -14/19 2/3 1/1 -11/15 1/1 -8/11 1/1 1/0 -21/29 0/1 1/0 -13/18 0/1 -44/61 0/1 1/2 -31/43 0/1 1/0 -18/25 1/3 1/1 -23/32 3/5 -5/7 1/1 1/0 -22/31 3/1 1/0 -17/24 1/0 -12/17 0/1 1/0 -19/27 1/0 -7/10 0/1 -23/33 1/2 -16/23 0/1 1/1 -9/13 0/1 1/2 -2/3 0/1 1/2 1/1 -11/17 0/1 1/2 -9/14 1/1 -16/25 1/1 -39/61 -4/1 1/0 -23/36 0/1 -7/11 1/2 1/1 -19/30 1/1 -12/19 1/1 2/1 -17/27 1/0 -56/89 9/1 1/0 -39/62 -3/1 -22/35 -1/1 1/1 -5/8 1/1 -23/37 1/1 1/0 -18/29 -1/1 1/0 -13/21 1/0 -8/13 0/1 1/1 -19/31 0/1 1/0 -11/18 0/1 -36/59 0/1 1/2 -25/41 1/3 1/2 -14/23 2/3 1/1 -17/28 3/1 -3/5 0/1 -13/22 1/1 -23/39 1/0 -10/17 0/1 1/4 -17/29 2/5 1/2 -7/12 1/2 -4/7 2/3 1/1 -17/30 1/1 -13/23 1/1 7/6 -35/62 9/7 -22/39 1/1 4/3 3/2 -9/16 1/1 -14/25 1/1 -33/59 16/11 3/2 -19/34 5/3 -5/9 1/0 -16/29 1/1 1/0 -11/20 1/0 -17/31 -2/1 1/0 -6/11 -1/1 1/0 -7/13 -1/2 0/1 -8/15 0/1 -9/17 0/1 1/4 -1/2 1/1 -8/17 -1/2 0/1 -7/15 0/1 -6/13 0/1 1/3 -5/11 1/3 1/2 -9/20 1/2 -13/29 1/2 4/7 -4/9 1/2 2/3 1/1 -7/16 1/1 -10/23 10/11 1/1 -13/30 1/1 -3/7 1/1 3/2 -14/33 2/1 3/1 1/0 -25/59 -6/1 1/0 -11/26 1/1 -8/19 1/1 2/1 -29/69 3/2 -21/50 2/1 -13/31 0/1 1/0 -5/12 1/0 -2/5 -1/1 1/1 -7/18 1/0 -12/31 -1/1 1/0 -29/75 1/0 -17/44 -1/1 -5/13 0/1 1/0 -13/34 1/3 -34/89 1/2 5/9 -21/55 1/2 -8/21 0/1 1/2 1/1 -27/71 1/1 1/0 -19/50 0/1 -11/29 2/5 1/2 -14/37 2/3 1/1 -17/45 1/1 -3/8 1/1 -13/35 0/1 -23/62 3/7 -56/151 15/31 1/2 -89/240 1/2 -33/89 1/2 10/19 -10/27 1/2 2/3 1/1 -17/46 1/1 -7/19 3/4 1/1 -11/30 1/1 -4/11 1/1 3/2 -5/14 1/1 -16/45 1/1 -11/31 4/3 3/2 -6/17 2/1 1/0 -1/3 1/0 -5/16 -1/1 -14/45 -1/1 -9/29 -1/2 0/1 -4/13 -1/1 0/1 -7/23 -1/1 1/0 -3/10 0/1 -11/37 1/4 1/3 -8/27 0/1 1/2 1/1 -13/44 1/1 -31/105 1/0 -18/61 0/1 1/0 -5/17 0/1 1/2 -17/58 1/5 -12/41 0/1 1/3 -7/24 1/2 -2/7 0/1 1/1 -5/18 1/0 -8/29 3/1 1/0 -11/40 1/0 -3/11 1/1 1/0 -4/15 1/0 -5/19 -3/1 1/0 -6/23 -1/1 0/1 -7/27 1/0 -8/31 -7/1 1/0 -1/4 -1/1 -5/21 -1/4 -4/17 -1/8 0/1 -7/30 0/1 -3/13 0/1 1/6 -8/35 1/5 1/3 -5/22 1/3 -7/31 2/5 1/2 -2/9 0/1 1/2 1/1 -3/14 1/1 -7/33 1/0 -4/19 1/1 2/1 -5/24 1/0 -6/29 5/1 1/0 -1/5 1/0 -4/21 -2/1 -1/1 1/0 -3/16 -1/1 -2/11 -1/1 -1/2 -3/17 0/1 1/0 -4/23 -1/1 0/1 -5/29 -4/7 -1/2 -1/6 0/1 -3/19 1/1 1/0 -2/13 0/1 1/1 -1/7 1/1 1/0 -2/15 1/0 -3/23 -1/1 1/0 -1/8 -1/1 -1/9 1/0 -1/10 0/1 -1/11 1/1 1/0 0/1 0/1 1/0 1/10 0/1 1/9 1/0 1/8 1/1 2/15 1/0 1/7 -1/1 1/0 2/13 -1/1 0/1 1/6 0/1 3/17 0/1 1/0 2/11 1/2 1/1 1/5 1/0 5/24 1/0 4/19 -2/1 -1/1 3/14 -1/1 2/9 -1/1 -1/2 0/1 5/22 -1/3 8/35 -1/3 -1/5 3/13 -1/6 0/1 7/30 0/1 4/17 0/1 1/8 5/21 1/4 1/4 1/1 4/15 1/0 7/26 -3/1 10/37 -4/1 -3/1 3/11 -1/1 1/0 2/7 -1/1 0/1 5/17 -1/2 0/1 18/61 0/1 1/0 13/44 -1/1 8/27 -1/1 -1/2 0/1 3/10 0/1 10/33 0/1 1/3 1/2 7/23 1/1 1/0 4/13 0/1 1/1 5/16 1/1 1/3 1/0 6/17 -2/1 1/0 5/14 -1/1 14/39 -1/1 0/1 1/0 9/25 1/0 4/11 -3/2 -1/1 11/30 -1/1 7/19 -1/1 -3/4 10/27 -1/1 -2/3 -1/2 3/8 -1/1 14/37 -1/1 -2/3 11/29 -1/2 -2/5 19/50 0/1 27/71 -1/1 1/0 8/21 -1/1 -1/2 0/1 21/55 -1/2 34/89 -5/9 -1/2 13/34 -1/3 5/13 0/1 1/0 2/5 -1/1 1/1 7/17 0/1 1/0 12/29 1/1 1/0 5/12 1/0 13/31 0/1 1/0 21/50 -2/1 29/69 -3/2 8/19 -2/1 -1/1 11/26 -1/1 25/59 6/1 1/0 14/33 -3/1 -2/1 1/0 3/7 -3/2 -1/1 13/30 -1/1 10/23 -1/1 -10/11 7/16 -1/1 4/9 -1/1 -2/3 -1/2 13/29 -4/7 -1/2 9/20 -1/2 5/11 -1/2 -1/3 11/24 0/1 6/13 -1/3 0/1 7/15 0/1 1/2 -1/1 8/15 0/1 15/28 1/5 7/13 0/1 1/2 6/11 1/1 1/0 11/20 1/0 5/9 1/0 19/34 -5/3 33/59 -3/2 -16/11 14/25 -1/1 9/16 -1/1 22/39 -3/2 -4/3 -1/1 13/23 -7/6 -1/1 17/30 -1/1 4/7 -1/1 -2/3 11/19 -1/1 -1/2 29/50 -1/2 18/31 -1/2 -1/3 7/12 -1/2 17/29 -1/2 -2/5 44/75 -1/3 27/46 -1/3 10/17 -1/4 0/1 23/39 1/0 13/22 -1/1 16/27 -1/1 -2/3 -1/2 3/5 0/1 20/33 1/1 2/1 1/0 37/61 10/1 1/0 17/28 -3/1 14/23 -1/1 -2/3 25/41 -1/2 -1/3 61/100 0/1 36/59 -1/2 0/1 11/18 0/1 19/31 0/1 1/0 46/75 -1/1 27/44 -1/1 8/13 -1/1 0/1 13/21 1/0 31/50 1/0 18/29 1/1 1/0 23/37 -1/1 1/0 28/45 1/0 5/8 -1/1 22/35 -1/1 1/1 17/27 1/0 29/46 -1/1 12/19 -2/1 -1/1 19/30 -1/1 7/11 -1/1 -1/2 23/36 0/1 39/61 4/1 1/0 16/25 -1/1 9/14 -1/1 2/3 -1/1 -1/2 0/1 11/16 -1/1 42/61 -2/3 -1/2 31/45 -1/2 20/29 -1/1 -1/2 9/13 -1/2 0/1 25/36 0/1 41/59 -4/1 1/0 16/23 -1/1 0/1 7/10 0/1 26/37 0/1 1/1 45/64 1/1 64/91 7/1 1/0 19/27 1/0 12/17 0/1 1/0 17/24 1/0 39/55 1/0 22/31 -3/1 1/0 5/7 -1/1 1/0 28/39 -1/1 -3/4 -2/3 23/32 -3/5 87/121 -16/31 -1/2 151/210 -1/2 64/89 -1/2 -9/19 41/57 -1/2 18/25 -1/1 -1/3 31/43 0/1 1/0 44/61 -1/2 0/1 13/18 0/1 21/29 0/1 1/0 29/40 1/0 8/11 -1/1 1/0 11/15 -1/1 14/19 -1/1 -2/3 3/4 -1/1 13/17 -1/4 0/1 23/30 0/1 10/13 0/1 1/1 7/9 1/0 32/41 -2/1 -1/1 25/32 -5/3 18/23 -6/5 -1/1 11/14 -1/1 4/5 -1/1 13/16 -1/1 22/27 -1/1 -2/3 -1/2 9/11 -1/1 -3/4 32/39 -1/1 -2/3 -1/2 23/28 -5/7 37/45 -2/3 14/17 -2/3 -1/2 5/6 -1/2 16/19 -1/3 0/1 27/32 -1/5 11/13 -1/2 0/1 6/7 -1/1 0/1 13/15 -1/1 20/23 -1/1 -4/5 7/8 -1/1 8/9 -2/3 -3/5 -1/2 1/1 -1/2 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(61,54,-270,-239) (-1/1,-7/8) -> (-5/22,-7/31) Hyperbolic Matrix(181,158,-480,-419) (-7/8,-13/15) -> (-17/45,-3/8) Hyperbolic Matrix(181,156,210,181) (-13/15,-6/7) -> (6/7,13/15) Hyperbolic Matrix(61,52,-210,-179) (-6/7,-5/6) -> (-7/24,-2/7) Hyperbolic Matrix(361,298,510,421) (-5/6,-14/17) -> (12/17,17/24) Hyperbolic Matrix(241,198,-510,-419) (-14/17,-23/28) -> (-1/2,-8/17) Hyperbolic Matrix(1681,1380,2340,1921) (-23/28,-32/39) -> (28/39,23/32) Hyperbolic Matrix(1141,936,3000,2461) (-32/39,-9/11) -> (27/71,8/21) Hyperbolic Matrix(119,96,-150,-121) (-9/11,-4/5) -> (-4/5,-15/19) Parabolic Matrix(421,332,-1140,-899) (-15/19,-11/14) -> (-17/46,-7/19) Hyperbolic Matrix(301,236,690,541) (-11/14,-18/23) -> (10/23,7/16) Hyperbolic Matrix(839,656,1380,1079) (-18/23,-25/32) -> (17/28,14/23) Hyperbolic Matrix(1619,1264,1920,1499) (-25/32,-32/41) -> (16/19,27/32) Hyperbolic Matrix(1261,984,3000,2341) (-32/41,-7/9) -> (29/69,8/19) Hyperbolic Matrix(241,186,390,301) (-7/9,-10/13) -> (8/13,13/21) Hyperbolic Matrix(599,460,780,599) (-10/13,-23/30) -> (23/30,10/13) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(241,184,630,481) (-13/17,-3/4) -> (13/34,5/13) Hyperbolic Matrix(241,178,570,421) (-3/4,-14/19) -> (8/19,11/26) Hyperbolic Matrix(419,308,570,419) (-14/19,-11/15) -> (11/15,14/19) Hyperbolic Matrix(241,176,330,241) (-11/15,-8/11) -> (8/11,11/15) Hyperbolic Matrix(361,262,-660,-479) (-8/11,-21/29) -> (-17/31,-6/11) Hyperbolic Matrix(661,478,1080,781) (-21/29,-13/18) -> (11/18,19/31) Hyperbolic Matrix(1319,952,2160,1559) (-13/18,-44/61) -> (36/59,11/18) Hyperbolic Matrix(1079,778,3660,2639) (-44/61,-31/43) -> (5/17,18/61) Hyperbolic Matrix(419,302,1830,1319) (-31/43,-18/25) -> (8/35,3/13) Hyperbolic Matrix(1679,1208,-2670,-1921) (-18/25,-23/32) -> (-39/62,-22/35) Hyperbolic Matrix(661,474,-1170,-839) (-23/32,-5/7) -> (-13/23,-35/62) Hyperbolic Matrix(839,596,1350,959) (-5/7,-22/31) -> (18/29,23/37) Hyperbolic Matrix(299,212,-1440,-1021) (-22/31,-17/24) -> (-5/24,-6/29) Hyperbolic Matrix(421,298,510,361) (-17/24,-12/17) -> (14/17,5/6) Hyperbolic Matrix(179,126,510,359) (-12/17,-19/27) -> (1/3,6/17) Hyperbolic Matrix(419,294,-600,-421) (-19/27,-7/10) -> (-7/10,-23/33) Parabolic Matrix(359,250,-1380,-961) (-23/33,-16/23) -> (-6/23,-7/27) Hyperbolic Matrix(121,84,-690,-479) (-16/23,-9/13) -> (-3/17,-4/23) Hyperbolic Matrix(59,40,-90,-61) (-9/13,-2/3) -> (-2/3,-11/17) Parabolic Matrix(359,232,-930,-601) (-11/17,-9/14) -> (-17/44,-5/13) Hyperbolic Matrix(421,270,750,481) (-9/14,-16/25) -> (14/25,9/16) Hyperbolic Matrix(1679,1074,3000,1919) (-16/25,-39/61) -> (33/59,14/25) Hyperbolic Matrix(3001,1918,4320,2761) (-39/61,-23/36) -> (25/36,41/59) Hyperbolic Matrix(301,192,660,421) (-23/36,-7/11) -> (5/11,11/24) Hyperbolic Matrix(419,266,660,419) (-7/11,-19/30) -> (19/30,7/11) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(241,152,-1140,-719) (-12/19,-17/27) -> (-7/33,-4/19) Hyperbolic Matrix(3419,2152,4860,3059) (-17/27,-56/89) -> (64/91,19/27) Hyperbolic Matrix(5519,3472,-14880,-9361) (-56/89,-39/62) -> (-23/62,-56/151) Hyperbolic Matrix(239,150,1050,659) (-22/35,-5/8) -> (5/22,8/35) Hyperbolic Matrix(61,38,-480,-299) (-5/8,-23/37) -> (-3/23,-1/8) Hyperbolic Matrix(959,596,1350,839) (-23/37,-18/29) -> (22/31,5/7) Hyperbolic Matrix(481,298,-870,-539) (-18/29,-13/21) -> (-5/9,-16/29) Hyperbolic Matrix(301,186,390,241) (-13/21,-8/13) -> (10/13,7/9) Hyperbolic Matrix(241,148,-780,-479) (-8/13,-19/31) -> (-9/29,-4/13) Hyperbolic Matrix(781,478,1080,661) (-19/31,-11/18) -> (13/18,21/29) Hyperbolic Matrix(1559,952,2160,1319) (-11/18,-36/59) -> (44/61,13/18) Hyperbolic Matrix(59,36,-690,-421) (-36/59,-25/41) -> (-1/11,0/1) Hyperbolic Matrix(479,292,1770,1079) (-25/41,-14/23) -> (10/37,3/11) Hyperbolic Matrix(1079,656,1380,839) (-14/23,-17/28) -> (25/32,18/23) Hyperbolic Matrix(479,290,-1290,-781) (-17/28,-3/5) -> (-13/35,-23/62) Hyperbolic Matrix(301,178,-810,-479) (-3/5,-13/22) -> (-3/8,-13/35) Hyperbolic Matrix(61,36,510,301) (-13/22,-23/39) -> (1/9,1/8) Hyperbolic Matrix(241,142,1020,601) (-23/39,-10/17) -> (4/17,5/21) Hyperbolic Matrix(361,212,-1020,-599) (-10/17,-17/29) -> (-11/31,-6/17) Hyperbolic Matrix(301,176,720,421) (-17/29,-7/12) -> (5/12,13/31) Hyperbolic Matrix(59,34,-210,-121) (-7/12,-4/7) -> (-2/7,-5/18) Hyperbolic Matrix(239,136,420,239) (-4/7,-17/30) -> (17/30,4/7) Hyperbolic Matrix(781,442,1380,781) (-17/30,-13/23) -> (13/23,17/30) Hyperbolic Matrix(2881,1626,3510,1981) (-35/62,-22/39) -> (32/39,23/28) Hyperbolic Matrix(419,236,1170,659) (-22/39,-9/16) -> (5/14,14/39) Hyperbolic Matrix(481,270,750,421) (-9/16,-14/25) -> (16/25,9/14) Hyperbolic Matrix(1919,1074,3000,1679) (-14/25,-33/59) -> (39/61,16/25) Hyperbolic Matrix(1499,838,3540,1979) (-33/59,-19/34) -> (11/26,25/59) Hyperbolic Matrix(179,100,750,419) (-19/34,-5/9) -> (5/21,1/4) Hyperbolic Matrix(1201,662,2070,1141) (-16/29,-11/20) -> (29/50,18/31) Hyperbolic Matrix(539,296,1200,659) (-11/20,-17/31) -> (13/29,9/20) Hyperbolic Matrix(59,32,330,179) (-6/11,-7/13) -> (3/17,2/11) Hyperbolic Matrix(239,128,-450,-241) (-7/13,-8/15) -> (-8/15,-9/17) Parabolic Matrix(481,254,570,301) (-9/17,-1/2) -> (27/32,11/13) Hyperbolic Matrix(839,394,1020,479) (-8/17,-7/15) -> (37/45,14/17) Hyperbolic Matrix(181,84,390,181) (-7/15,-6/13) -> (6/13,7/15) Hyperbolic Matrix(61,28,-390,-179) (-6/13,-5/11) -> (-3/19,-2/13) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(1261,566,1740,781) (-9/20,-13/29) -> (21/29,29/40) Hyperbolic Matrix(241,108,270,121) (-13/29,-4/9) -> (8/9,1/1) Hyperbolic Matrix(59,26,270,119) (-4/9,-7/16) -> (3/14,2/9) Hyperbolic Matrix(541,236,690,301) (-7/16,-10/23) -> (18/23,11/14) Hyperbolic Matrix(599,260,1380,599) (-10/23,-13/30) -> (13/30,10/23) Hyperbolic Matrix(181,78,420,181) (-13/30,-3/7) -> (3/7,13/30) Hyperbolic Matrix(301,128,990,421) (-3/7,-14/33) -> (10/33,7/23) Hyperbolic Matrix(1679,712,-4530,-1921) (-14/33,-25/59) -> (-33/89,-10/27) Hyperbolic Matrix(1979,838,3540,1499) (-25/59,-11/26) -> (19/34,33/59) Hyperbolic Matrix(421,178,570,241) (-11/26,-8/19) -> (14/19,3/4) Hyperbolic Matrix(2341,984,3000,1261) (-8/19,-29/69) -> (7/9,32/41) Hyperbolic Matrix(119,50,1140,479) (-29/69,-21/50) -> (1/10,1/9) Hyperbolic Matrix(1139,478,3000,1259) (-21/50,-13/31) -> (11/29,19/50) Hyperbolic Matrix(421,176,720,301) (-13/31,-5/12) -> (7/12,17/29) Hyperbolic Matrix(59,24,-150,-61) (-5/12,-2/5) -> (-2/5,-7/18) Parabolic Matrix(541,210,930,361) (-7/18,-12/31) -> (18/31,7/12) Hyperbolic Matrix(2461,952,3570,1381) (-12/31,-29/75) -> (31/45,20/29) Hyperbolic Matrix(2339,904,-7920,-3061) (-29/75,-17/44) -> (-13/44,-31/105) Hyperbolic Matrix(481,184,630,241) (-5/13,-13/34) -> (3/4,13/17) Hyperbolic Matrix(361,138,-1410,-539) (-13/34,-34/89) -> (-8/31,-1/4) Hyperbolic Matrix(4681,1788,6600,2521) (-34/89,-21/55) -> (39/55,22/31) Hyperbolic Matrix(959,366,2670,1019) (-21/55,-8/21) -> (14/39,9/25) Hyperbolic Matrix(2461,936,3000,1141) (-8/21,-27/71) -> (9/11,32/39) Hyperbolic Matrix(121,46,-1260,-479) (-27/71,-19/50) -> (-1/10,-1/11) Hyperbolic Matrix(1259,478,3000,1139) (-19/50,-11/29) -> (13/31,21/50) Hyperbolic Matrix(301,114,-1740,-659) (-11/29,-14/37) -> (-4/23,-5/29) Hyperbolic Matrix(1381,522,1590,601) (-14/37,-17/45) -> (13/15,20/23) Hyperbolic Matrix(38161,14152,53070,19681) (-56/151,-89/240) -> (151/210,64/89) Hyperbolic Matrix(34319,12726,47730,17699) (-89/240,-33/89) -> (87/121,151/210) Hyperbolic Matrix(719,266,2430,899) (-10/27,-17/46) -> (13/44,8/27) Hyperbolic Matrix(419,154,1140,419) (-7/19,-11/30) -> (11/30,7/19) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(61,22,-330,-119) (-4/11,-5/14) -> (-3/16,-2/11) Hyperbolic Matrix(1859,662,3030,1079) (-5/14,-16/45) -> (46/75,27/44) Hyperbolic Matrix(2281,810,3720,1321) (-16/45,-11/31) -> (19/31,46/75) Hyperbolic Matrix(359,126,510,179) (-6/17,-1/3) -> (19/27,12/17) Hyperbolic Matrix(121,38,-570,-179) (-1/3,-5/16) -> (-3/14,-7/33) Hyperbolic Matrix(1919,598,3270,1019) (-5/16,-14/45) -> (44/75,27/46) Hyperbolic Matrix(2041,634,3480,1081) (-14/45,-9/29) -> (17/29,44/75) Hyperbolic Matrix(59,18,390,119) (-4/13,-7/23) -> (1/7,2/13) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(599,178,1410,419) (-11/37,-8/27) -> (14/33,3/7) Hyperbolic Matrix(1319,390,1620,479) (-8/27,-13/44) -> (13/16,22/27) Hyperbolic Matrix(6301,1860,9150,2701) (-31/105,-18/61) -> (42/61,31/45) Hyperbolic Matrix(2639,778,3660,1079) (-18/61,-5/17) -> (31/43,44/61) Hyperbolic Matrix(661,194,1230,361) (-5/17,-17/58) -> (15/28,7/13) Hyperbolic Matrix(2881,844,3690,1081) (-17/58,-12/41) -> (32/41,25/32) Hyperbolic Matrix(301,88,1440,421) (-12/41,-7/24) -> (5/24,4/19) Hyperbolic Matrix(361,100,870,241) (-5/18,-8/29) -> (12/29,5/12) Hyperbolic Matrix(1619,446,2610,719) (-8/29,-11/40) -> (31/50,18/29) Hyperbolic Matrix(119,32,-450,-121) (-3/11,-4/15) -> (-4/15,-5/19) Parabolic Matrix(841,220,1380,361) (-5/19,-6/23) -> (14/23,25/41) Hyperbolic Matrix(2999,776,4170,1079) (-7/27,-8/31) -> (64/89,41/57) Hyperbolic Matrix(419,100,750,179) (-1/4,-5/21) -> (5/9,19/34) Hyperbolic Matrix(601,142,1020,241) (-5/21,-4/17) -> (10/17,23/39) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(181,42,780,181) (-7/30,-3/13) -> (3/13,7/30) Hyperbolic Matrix(1319,302,1830,419) (-3/13,-8/35) -> (18/25,31/43) Hyperbolic Matrix(659,150,1050,239) (-8/35,-5/22) -> (5/8,22/35) Hyperbolic Matrix(241,54,540,121) (-7/31,-2/9) -> (4/9,13/29) Hyperbolic Matrix(119,26,270,59) (-2/9,-3/14) -> (7/16,4/9) Hyperbolic Matrix(479,100,570,119) (-4/19,-5/24) -> (5/6,16/19) Hyperbolic Matrix(779,160,2040,419) (-6/29,-1/5) -> (21/55,34/89) Hyperbolic Matrix(481,92,1260,241) (-1/5,-4/21) -> (8/21,21/55) Hyperbolic Matrix(541,102,960,181) (-4/21,-3/16) -> (9/16,22/39) Hyperbolic Matrix(179,32,330,59) (-2/11,-3/17) -> (7/13,6/11) Hyperbolic Matrix(901,154,1410,241) (-5/29,-1/6) -> (23/36,39/61) Hyperbolic Matrix(479,76,750,119) (-1/6,-3/19) -> (7/11,23/36) Hyperbolic Matrix(119,18,390,59) (-2/13,-1/7) -> (7/23,4/13) Hyperbolic Matrix(59,8,-450,-61) (-1/7,-2/15) -> (-2/15,-3/23) Parabolic Matrix(301,36,510,61) (-1/8,-1/9) -> (23/39,13/22) Hyperbolic Matrix(479,50,1140,119) (-1/9,-1/10) -> (21/50,29/69) Hyperbolic Matrix(421,-36,690,-59) (0/1,1/10) -> (61/100,36/59) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(541,-74,870,-119) (2/15,1/7) -> (23/37,28/45) Hyperbolic Matrix(179,-28,390,-61) (2/13,1/6) -> (11/24,6/13) Hyperbolic Matrix(479,-84,690,-121) (1/6,3/17) -> (9/13,25/36) Hyperbolic Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(1021,-212,1440,-299) (1/5,5/24) -> (17/24,39/55) Hyperbolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(239,-54,270,-61) (2/9,5/22) -> (7/8,8/9) Hyperbolic Matrix(121,-32,450,-119) (1/4,4/15) -> (4/15,7/26) Parabolic Matrix(2341,-632,3330,-899) (7/26,10/37) -> (26/37,45/64) Hyperbolic Matrix(121,-34,210,-59) (3/11,2/7) -> (4/7,11/19) Hyperbolic Matrix(179,-52,210,-61) (2/7,5/17) -> (11/13,6/7) Hyperbolic Matrix(2519,-744,3660,-1081) (18/61,13/44) -> (11/16,42/61) Hyperbolic Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(479,-148,780,-241) (4/13,5/16) -> (27/44,8/13) Hyperbolic Matrix(359,-114,570,-181) (5/16,1/3) -> (17/27,29/46) Hyperbolic Matrix(599,-212,1020,-361) (6/17,5/14) -> (27/46,10/17) Hyperbolic Matrix(661,-244,810,-299) (7/19,10/27) -> (22/27,9/11) Hyperbolic Matrix(479,-178,810,-301) (10/27,3/8) -> (13/22,16/27) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(1981,-750,2850,-1079) (14/37,11/29) -> (41/59,16/23) Hyperbolic Matrix(5581,-2122,9150,-3479) (19/50,27/71) -> (25/41,61/100) Hyperbolic Matrix(6181,-2362,8790,-3359) (34/89,13/34) -> (45/64,64/91) Hyperbolic Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(601,-248,870,-359) (7/17,12/29) -> (20/29,9/13) Hyperbolic Matrix(2401,-1018,3960,-1679) (25/59,14/33) -> (20/33,37/61) Hyperbolic Matrix(539,-244,930,-421) (9/20,5/11) -> (11/19,29/50) Hyperbolic Matrix(419,-198,510,-241) (7/15,1/2) -> (23/28,37/45) Hyperbolic Matrix(241,-128,450,-239) (1/2,8/15) -> (8/15,15/28) Parabolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(539,-298,870,-481) (11/20,5/9) -> (13/21,31/50) Hyperbolic Matrix(839,-474,1170,-661) (22/39,13/23) -> (5/7,28/39) Hyperbolic Matrix(181,-108,300,-179) (16/27,3/5) -> (3/5,20/33) Parabolic Matrix(3839,-2330,5340,-3241) (37/61,17/28) -> (23/32,87/121) Hyperbolic Matrix(1921,-1208,2670,-1679) (22/35,17/27) -> (41/57,18/25) Hyperbolic Matrix(61,-40,90,-59) (9/14,2/3) -> (2/3,11/16) Parabolic Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(61,54,-270,-239) -> Matrix(3,-2,8,-5) Matrix(181,158,-480,-419) -> Matrix(3,-2,2,-1) Matrix(181,156,210,181) -> Matrix(1,0,-2,1) Matrix(61,52,-210,-179) -> Matrix(1,0,0,1) Matrix(361,298,510,421) -> Matrix(3,-2,2,-1) Matrix(241,198,-510,-419) -> Matrix(3,-2,-4,3) Matrix(1681,1380,2340,1921) -> Matrix(5,-4,-6,5) Matrix(1141,936,3000,2461) -> Matrix(3,-2,-4,3) Matrix(119,96,-150,-121) -> Matrix(3,-2,2,-1) Matrix(421,332,-1140,-899) -> Matrix(1,-2,2,-3) Matrix(301,236,690,541) -> Matrix(5,-4,-6,5) Matrix(839,656,1380,1079) -> Matrix(3,-4,-2,3) Matrix(1619,1264,1920,1499) -> Matrix(1,-2,-2,5) Matrix(1261,984,3000,2341) -> Matrix(3,-4,-2,3) Matrix(241,186,390,301) -> Matrix(1,0,0,1) Matrix(599,460,780,599) -> Matrix(1,0,2,1) Matrix(781,598,1020,781) -> Matrix(1,0,-8,1) Matrix(241,184,630,481) -> Matrix(1,0,-4,1) Matrix(241,178,570,421) -> Matrix(1,0,-2,1) Matrix(419,308,570,419) -> Matrix(5,-4,-6,5) Matrix(241,176,330,241) -> Matrix(1,-2,0,1) Matrix(361,262,-660,-479) -> Matrix(1,-2,0,1) Matrix(661,478,1080,781) -> Matrix(1,0,0,1) Matrix(1319,952,2160,1559) -> Matrix(1,0,-4,1) Matrix(1079,778,3660,2639) -> Matrix(1,0,-2,1) Matrix(419,302,1830,1319) -> Matrix(1,0,-6,1) Matrix(1679,1208,-2670,-1921) -> Matrix(1,0,-2,1) Matrix(661,474,-1170,-839) -> Matrix(7,-6,6,-5) Matrix(839,596,1350,959) -> Matrix(1,-2,0,1) Matrix(299,212,-1440,-1021) -> Matrix(1,2,0,1) Matrix(421,298,510,361) -> Matrix(1,2,-2,-3) Matrix(179,126,510,359) -> Matrix(1,-2,0,1) Matrix(419,294,-600,-421) -> Matrix(1,0,2,1) Matrix(359,250,-1380,-961) -> Matrix(1,0,-2,1) Matrix(121,84,-690,-479) -> Matrix(1,0,-2,1) Matrix(59,40,-90,-61) -> Matrix(1,0,0,1) Matrix(359,232,-930,-601) -> Matrix(1,0,-2,1) Matrix(421,270,750,481) -> Matrix(1,-2,0,1) Matrix(1679,1074,3000,1919) -> Matrix(3,-4,-2,3) Matrix(3001,1918,4320,2761) -> Matrix(1,0,0,1) Matrix(301,192,660,421) -> Matrix(1,0,-4,1) Matrix(419,266,660,419) -> Matrix(3,-2,-4,3) Matrix(721,456,1140,721) -> Matrix(3,-4,-2,3) Matrix(241,152,-1140,-719) -> Matrix(1,0,0,1) Matrix(3419,2152,4860,3059) -> Matrix(1,-2,0,1) Matrix(5519,3472,-14880,-9361) -> Matrix(1,6,2,13) Matrix(239,150,1050,659) -> Matrix(1,0,-4,1) Matrix(61,38,-480,-299) -> Matrix(1,-2,0,1) Matrix(959,596,1350,839) -> Matrix(1,-2,0,1) Matrix(481,298,-870,-539) -> Matrix(1,2,0,1) Matrix(301,186,390,241) -> Matrix(1,0,0,1) Matrix(241,148,-780,-479) -> Matrix(1,0,-2,1) Matrix(781,478,1080,661) -> Matrix(1,0,0,1) Matrix(1559,952,2160,1319) -> Matrix(1,0,-4,1) Matrix(59,36,-690,-421) -> Matrix(1,0,-2,1) Matrix(479,292,1770,1079) -> Matrix(5,-2,-2,1) Matrix(1079,656,1380,839) -> Matrix(3,-4,-2,3) Matrix(479,290,-1290,-781) -> Matrix(1,0,2,1) Matrix(301,178,-810,-479) -> Matrix(1,0,0,1) Matrix(61,36,510,301) -> Matrix(1,0,0,1) Matrix(241,142,1020,601) -> Matrix(1,0,4,1) Matrix(361,212,-1020,-599) -> Matrix(7,-2,4,-1) Matrix(301,176,720,421) -> Matrix(5,-2,-2,1) Matrix(59,34,-210,-121) -> Matrix(3,-2,2,-1) Matrix(239,136,420,239) -> Matrix(5,-4,-6,5) Matrix(781,442,1380,781) -> Matrix(13,-14,-12,13) Matrix(2881,1626,3510,1981) -> Matrix(1,-2,0,1) Matrix(419,236,1170,659) -> Matrix(3,-4,-2,3) Matrix(481,270,750,421) -> Matrix(1,-2,0,1) Matrix(1919,1074,3000,1679) -> Matrix(3,-4,-2,3) Matrix(1499,838,3540,1979) -> Matrix(1,-2,2,-3) Matrix(179,100,750,419) -> Matrix(1,-2,4,-7) Matrix(1201,662,2070,1141) -> Matrix(1,-2,-2,5) Matrix(539,296,1200,659) -> Matrix(1,6,-2,-11) Matrix(59,32,330,179) -> Matrix(1,0,2,1) Matrix(239,128,-450,-241) -> Matrix(1,0,6,1) Matrix(481,254,570,301) -> Matrix(1,0,-6,1) Matrix(839,394,1020,479) -> Matrix(5,2,-8,-3) Matrix(181,84,390,181) -> Matrix(1,0,-6,1) Matrix(61,28,-390,-179) -> Matrix(1,0,-2,1) Matrix(181,82,-660,-299) -> Matrix(1,0,-2,1) Matrix(1261,566,1740,781) -> Matrix(7,-4,2,-1) Matrix(241,108,270,121) -> Matrix(7,-4,-12,7) Matrix(59,26,270,119) -> Matrix(3,-2,-4,3) Matrix(541,236,690,301) -> Matrix(5,-4,-6,5) Matrix(599,260,1380,599) -> Matrix(21,-20,-22,21) Matrix(181,78,420,181) -> Matrix(5,-6,-4,5) Matrix(301,128,990,421) -> Matrix(1,-2,2,-3) Matrix(1679,712,-4530,-1921) -> Matrix(1,-4,2,-7) Matrix(1979,838,3540,1499) -> Matrix(3,2,-2,-1) Matrix(421,178,570,241) -> Matrix(1,0,-2,1) Matrix(2341,984,3000,1261) -> Matrix(3,-4,-2,3) Matrix(119,50,1140,479) -> Matrix(1,-2,2,-3) Matrix(1139,478,3000,1259) -> Matrix(1,-2,-2,5) Matrix(421,176,720,301) -> Matrix(1,-2,-2,5) Matrix(59,24,-150,-61) -> Matrix(1,0,0,1) Matrix(541,210,930,361) -> Matrix(1,0,-2,1) Matrix(2461,952,3570,1381) -> Matrix(1,2,-2,-3) Matrix(2339,904,-7920,-3061) -> Matrix(1,2,0,1) Matrix(481,184,630,241) -> Matrix(1,0,-4,1) Matrix(361,138,-1410,-539) -> Matrix(5,-2,-2,1) Matrix(4681,1788,6600,2521) -> Matrix(3,-2,2,-1) Matrix(959,366,2670,1019) -> Matrix(1,0,-2,1) Matrix(2461,936,3000,1141) -> Matrix(3,-2,-4,3) Matrix(121,46,-1260,-479) -> Matrix(1,0,0,1) Matrix(1259,478,3000,1139) -> Matrix(5,-2,-2,1) Matrix(301,114,-1740,-659) -> Matrix(3,-2,-4,3) Matrix(1381,522,1590,601) -> Matrix(7,-6,-8,7) Matrix(38161,14152,53070,19681) -> Matrix(49,-24,-100,49) Matrix(34319,12726,47730,17699) -> Matrix(51,-26,-100,51) Matrix(719,266,2430,899) -> Matrix(3,-2,-4,3) Matrix(419,154,1140,419) -> Matrix(7,-6,-8,7) Matrix(241,88,660,241) -> Matrix(5,-6,-4,5) Matrix(61,22,-330,-119) -> Matrix(1,-2,0,1) Matrix(1859,662,3030,1079) -> Matrix(1,-2,0,1) Matrix(2281,810,3720,1321) -> Matrix(3,-4,-2,3) Matrix(359,126,510,179) -> Matrix(1,-2,0,1) Matrix(121,38,-570,-179) -> Matrix(1,2,0,1) Matrix(1919,598,3270,1019) -> Matrix(1,0,-2,1) Matrix(2041,634,3480,1081) -> Matrix(3,2,-8,-5) Matrix(59,18,390,119) -> Matrix(1,0,0,1) Matrix(179,54,-600,-181) -> Matrix(1,0,4,1) Matrix(599,178,1410,419) -> Matrix(5,-2,-2,1) Matrix(1319,390,1620,479) -> Matrix(3,-2,-4,3) Matrix(6301,1860,9150,2701) -> Matrix(1,2,-2,-3) Matrix(2639,778,3660,1079) -> Matrix(1,0,-2,1) Matrix(661,194,1230,361) -> Matrix(1,0,0,1) Matrix(2881,844,3690,1081) -> Matrix(5,-2,-2,1) Matrix(301,88,1440,421) -> Matrix(5,-2,-2,1) Matrix(361,100,870,241) -> Matrix(1,-2,0,1) Matrix(1619,446,2610,719) -> Matrix(1,-2,0,1) Matrix(119,32,-450,-121) -> Matrix(1,-4,0,1) Matrix(841,220,1380,361) -> Matrix(1,2,-2,-3) Matrix(2999,776,4170,1079) -> Matrix(1,-2,-2,5) Matrix(419,100,750,179) -> Matrix(7,2,-4,-1) Matrix(601,142,1020,241) -> Matrix(1,0,4,1) Matrix(239,56,1020,239) -> Matrix(1,0,16,1) Matrix(181,42,780,181) -> Matrix(1,0,-12,1) Matrix(1319,302,1830,419) -> Matrix(1,0,-6,1) Matrix(659,150,1050,239) -> Matrix(1,0,-4,1) Matrix(241,54,540,121) -> Matrix(3,-2,-4,3) Matrix(119,26,270,59) -> Matrix(3,-2,-4,3) Matrix(479,100,570,119) -> Matrix(1,-2,-2,5) Matrix(779,160,2040,419) -> Matrix(1,0,-2,1) Matrix(481,92,1260,241) -> Matrix(1,2,-2,-3) Matrix(541,102,960,181) -> Matrix(3,2,-2,-1) Matrix(179,32,330,59) -> Matrix(1,0,2,1) Matrix(901,154,1410,241) -> Matrix(1,0,2,1) Matrix(479,76,750,119) -> Matrix(1,0,-2,1) Matrix(119,18,390,59) -> Matrix(1,0,0,1) Matrix(59,8,-450,-61) -> Matrix(1,-2,0,1) Matrix(301,36,510,61) -> Matrix(1,0,0,1) Matrix(479,50,1140,119) -> Matrix(3,2,-2,-1) Matrix(421,-36,690,-59) -> Matrix(1,0,-2,1) Matrix(299,-38,480,-61) -> Matrix(1,-2,0,1) Matrix(541,-74,870,-119) -> Matrix(1,0,0,1) Matrix(179,-28,390,-61) -> Matrix(1,0,-2,1) Matrix(479,-84,690,-121) -> Matrix(1,0,-2,1) Matrix(119,-22,330,-61) -> Matrix(1,-2,0,1) Matrix(1021,-212,1440,-299) -> Matrix(1,2,0,1) Matrix(719,-152,1140,-241) -> Matrix(1,0,0,1) Matrix(239,-54,270,-61) -> Matrix(5,2,-8,-3) Matrix(121,-32,450,-119) -> Matrix(1,-4,0,1) Matrix(2341,-632,3330,-899) -> Matrix(1,4,0,1) Matrix(121,-34,210,-59) -> Matrix(1,2,-2,-3) Matrix(179,-52,210,-61) -> Matrix(1,0,0,1) Matrix(2519,-744,3660,-1081) -> Matrix(1,2,-2,-3) Matrix(181,-54,600,-179) -> Matrix(1,0,4,1) Matrix(479,-148,780,-241) -> Matrix(1,0,-2,1) Matrix(359,-114,570,-181) -> Matrix(1,-2,0,1) Matrix(599,-212,1020,-361) -> Matrix(1,2,-4,-7) Matrix(661,-244,810,-299) -> Matrix(1,0,0,1) Matrix(479,-178,810,-301) -> Matrix(1,0,0,1) Matrix(419,-158,480,-181) -> Matrix(1,2,-2,-3) Matrix(1981,-750,2850,-1079) -> Matrix(3,2,-2,-1) Matrix(5581,-2122,9150,-3479) -> Matrix(1,0,-2,1) Matrix(6181,-2362,8790,-3359) -> Matrix(5,2,2,1) Matrix(61,-24,150,-59) -> Matrix(1,0,0,1) Matrix(601,-248,870,-359) -> Matrix(1,0,-2,1) Matrix(2401,-1018,3960,-1679) -> Matrix(1,4,0,1) Matrix(539,-244,930,-421) -> Matrix(5,2,-8,-3) Matrix(419,-198,510,-241) -> Matrix(3,-2,-4,3) Matrix(241,-128,450,-239) -> Matrix(1,0,6,1) Matrix(479,-262,660,-361) -> Matrix(1,-2,0,1) Matrix(539,-298,870,-481) -> Matrix(1,2,0,1) Matrix(839,-474,1170,-661) -> Matrix(5,6,-6,-7) Matrix(181,-108,300,-179) -> Matrix(1,0,2,1) Matrix(3839,-2330,5340,-3241) -> Matrix(1,6,-2,-11) Matrix(1921,-1208,2670,-1679) -> Matrix(1,0,-2,1) Matrix(61,-40,90,-59) -> Matrix(1,0,0,1) Matrix(421,-294,600,-419) -> Matrix(1,0,2,1) Matrix(121,-96,150,-119) -> Matrix(1,2,-2,-3) 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): 52 Degree of the the map X: 52 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.