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 -10/1 -9/1 -8/1 -15/2 -6/1 -5/1 -14/3 -9/2 -35/8 -4/1 -15/4 -27/8 -10/3 -3/1 -5/2 -12/5 -20/9 -2/1 -15/8 -25/14 -5/3 -18/11 -3/2 -10/7 -5/4 -6/5 0/1 1/1 15/13 6/5 5/4 30/23 15/11 10/7 3/2 30/19 18/11 5/3 30/17 25/14 15/8 2/1 15/7 20/9 30/13 12/5 5/2 75/29 21/8 240/89 30/11 45/16 3/1 45/14 10/3 27/8 7/2 15/4 4/1 17/4 30/7 13/3 35/8 9/2 14/3 19/4 29/6 5/1 21/4 11/2 23/4 6/1 13/2 7/1 15/2 8/1 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -2/1 0/1 -9/1 -2/1 -8/1 -2/1 -3/2 -1/1 -15/2 -1/1 -7/1 0/1 -13/2 -2/1 1/0 -6/1 -1/1 -17/3 0/1 -11/2 -2/1 -1/1 -5/1 -2/1 -24/5 -3/2 -19/4 -8/5 -3/2 -14/3 -3/2 -4/3 -1/1 -9/2 -2/1 -4/3 -22/5 -4/3 -9/7 -5/4 -35/8 -4/3 -6/5 -13/3 -6/5 -30/7 -1/1 -17/4 -1/1 0/1 -21/5 -2/1 -4/1 -3/2 -4/3 -1/1 -15/4 -1/1 -26/7 -1/1 -7/8 -6/7 -37/10 -4/5 -3/4 -11/3 -2/3 -7/2 -2/1 -1/1 -17/5 -4/3 -61/18 -2/1 -1/1 -44/13 -2/1 -3/2 -1/1 -27/8 -2/1 -4/3 -10/3 -2/1 -4/3 -33/10 -2/1 -4/3 -23/7 -4/3 -13/4 -2/1 -3/2 -16/5 -3/2 -4/3 -1/1 -3/1 -4/3 -17/6 -4/3 -9/7 -14/5 -5/4 -11/9 -6/5 -39/14 -4/3 -6/5 -25/9 -6/5 -11/4 -6/5 -1/1 -30/11 -1/1 -19/7 -2/1 -27/10 -2/1 -4/3 -8/3 -3/2 -4/3 -1/1 -37/14 -4/3 -13/10 -29/11 -4/3 -50/19 -4/3 -6/5 -71/27 -4/3 -21/8 -4/3 -6/5 -55/21 -4/3 -89/34 -4/3 -5/4 -34/13 -3/2 -4/3 -1/1 -13/5 -4/3 -5/2 -4/3 -6/5 -17/7 -4/3 -29/12 -4/3 -5/4 -12/5 -5/4 -31/13 -6/5 -50/21 -4/3 -6/5 -69/29 -4/3 -19/8 -5/4 -6/5 -26/11 -5/4 -6/5 -1/1 -59/25 -4/3 -33/14 -4/3 -6/5 -7/3 -4/3 -30/13 -5/4 -23/10 -5/4 -26/21 -16/7 -5/4 -11/9 -6/5 -9/4 -16/13 -6/5 -29/13 -28/23 -20/9 -6/5 -11/5 -4/3 -24/11 -11/9 -13/6 -17/14 -6/5 -15/7 -6/5 -2/1 -6/5 -7/6 -1/1 -15/8 -7/6 -28/15 -7/6 -43/37 -36/31 -13/7 -22/19 -11/6 -15/13 -8/7 -20/11 -8/7 -9/5 -8/7 -34/19 -6/5 -7/6 -1/1 -59/33 -8/7 -25/14 -6/5 -8/7 -16/9 -7/6 -8/7 -1/1 -39/22 -22/19 -8/7 -23/13 -8/7 -30/17 -8/7 -7/4 -8/7 -1/1 -19/11 -4/3 -50/29 -6/5 -31/18 -6/5 -7/6 -12/7 -7/6 -29/17 -8/7 -75/44 -7/6 -46/27 -7/6 -43/37 -36/31 -17/10 -22/19 -15/13 -39/23 -8/7 -22/13 -15/13 -23/20 -8/7 -27/16 -38/33 -8/7 -5/3 -8/7 -33/20 -8/7 -58/51 -61/37 -58/51 -28/17 -8/7 -33/29 -25/22 -23/14 -25/22 -42/37 -41/25 -8/7 -100/61 -8/7 -42/37 -59/36 -8/7 -17/15 -18/11 -17/15 -31/19 -44/39 -75/46 -9/8 -44/27 -9/8 -10/9 -1/1 -13/8 -8/7 -9/8 -21/13 -8/7 -50/31 -8/7 -29/18 -8/7 -25/22 -37/23 -42/37 -45/28 -17/15 -8/5 -17/15 -26/23 -9/8 -35/22 -26/23 -44/39 -27/17 -44/39 -46/29 -44/39 -53/47 -9/8 -19/12 -80/71 -9/8 -30/19 -9/8 -11/7 -46/41 -36/23 -19/17 -61/39 -10/9 -25/16 -28/25 -10/9 -14/9 -9/8 -19/17 -10/9 -3/2 -8/7 -10/9 -16/11 -9/8 -19/17 -10/9 -61/42 -19/17 -10/9 -45/31 -10/9 -29/20 -9/8 -10/9 -13/9 -10/9 -36/25 -19/17 -59/41 -10/9 -23/16 -9/8 -10/9 -10/7 -10/9 -37/26 -10/9 -31/28 -64/45 -21/19 -53/48 -32/29 -91/64 -32/29 -11/10 -27/19 -10/9 -17/12 -10/9 -1/1 -24/17 -11/10 -55/39 -12/11 -31/22 -11/10 -12/11 -7/5 -10/9 -39/28 -10/9 -12/11 -32/23 -10/9 -21/19 -11/10 -121/87 -32/29 -210/151 -11/10 -89/64 -11/10 -12/11 -57/41 -10/9 -25/18 -10/9 -12/11 -43/31 -10/9 -61/44 -12/11 -1/1 -18/13 -1/1 -29/21 -28/25 -40/29 -10/9 -11/8 -10/9 -1/1 -15/11 -10/9 -19/14 -10/9 -11/10 -4/3 -10/9 -11/10 -1/1 -17/13 -10/9 -30/23 -10/9 -13/10 -10/9 -11/10 -9/7 -10/9 -41/32 -32/29 -11/10 -32/25 -10/9 -11/10 -1/1 -23/18 -32/29 -11/10 -14/11 -11/10 -12/11 -1/1 -5/4 -10/9 -12/11 -16/13 -11/10 -12/11 -1/1 -27/22 -10/9 -12/11 -11/9 -10/9 -39/32 -8/7 -10/9 -28/23 -9/8 -19/17 -10/9 -45/37 -10/9 -17/14 -10/9 -21/19 -6/5 -11/10 -19/16 -11/10 -34/31 -32/27 -11/10 -12/11 -1/1 -13/11 -34/31 -7/6 -23/21 -12/11 -15/13 -12/11 -23/20 -12/11 -61/56 -8/7 -12/11 -25/23 -13/12 -9/8 -10/9 -12/11 -1/1 -14/13 0/1 -1/1 1/1 -14/15 8/7 -13/14 -25/27 -12/13 15/13 -12/13 7/6 -12/13 -23/25 6/5 -11/12 17/14 -21/23 -10/11 28/23 -10/11 -19/21 -9/10 39/32 -10/11 -8/9 11/9 -10/11 5/4 -12/13 -10/11 19/15 -10/11 14/11 -1/1 -12/13 -11/12 23/18 -11/12 -32/35 32/25 -1/1 -11/12 -10/11 41/32 -11/12 -32/35 9/7 -10/11 13/10 -11/12 -10/11 30/23 -10/11 17/13 -10/11 4/3 -1/1 -11/12 -10/11 19/14 -11/12 -10/11 15/11 -10/11 11/8 -1/1 -10/11 29/21 -28/31 18/13 -1/1 61/44 -1/1 -12/13 43/31 -10/11 25/18 -12/13 -10/11 32/23 -11/12 -21/23 -10/11 7/5 -10/11 31/22 -12/13 -11/12 24/17 -11/12 17/12 -1/1 -10/11 27/19 -10/11 10/7 -10/11 33/23 -10/11 23/16 -10/11 -9/10 13/9 -10/11 3/2 -10/11 -8/9 17/11 -10/11 14/9 -10/11 -19/21 -9/10 25/16 -10/11 -28/31 61/39 -10/11 36/23 -19/21 11/7 -46/51 30/19 -9/10 19/12 -9/10 -80/89 27/17 -44/49 89/56 -9/10 -26/29 62/39 -9/10 -53/59 -44/49 35/22 -44/49 -26/29 8/5 -9/10 -26/29 -17/19 37/23 -42/47 29/18 -25/28 -8/9 21/13 -8/9 13/8 -9/10 -8/9 31/19 -44/49 18/11 -17/19 59/36 -17/19 -8/9 41/25 -8/9 23/14 -42/47 -25/28 28/17 -25/28 -33/37 -8/9 5/3 -8/9 22/13 -8/9 -23/26 -15/17 39/23 -8/9 17/10 -15/17 -22/25 29/17 -8/9 12/7 -7/8 7/4 -1/1 -8/9 30/17 -8/9 23/13 -8/9 62/35 -1/1 -8/9 -7/8 39/22 -8/9 -22/25 16/9 -1/1 -8/9 -7/8 25/14 -8/9 -6/7 59/33 -8/9 34/19 -1/1 -7/8 -6/7 9/5 -8/9 29/16 -9/10 -8/9 20/11 -8/9 31/17 -54/61 11/6 -8/9 -15/17 13/7 -22/25 15/8 -7/8 17/9 -20/23 2/1 -1/1 -7/8 -6/7 17/8 -25/29 -6/7 15/7 -6/7 13/6 -6/7 -17/20 11/5 -4/5 20/9 -6/7 29/13 -28/33 9/4 -6/7 -16/19 16/7 -6/7 -11/13 -5/6 23/10 -26/31 -5/6 30/13 -5/6 7/3 -4/5 33/14 -6/7 -4/5 59/25 -4/5 26/11 -1/1 -6/7 -5/6 19/8 -6/7 -5/6 69/29 -4/5 50/21 -6/7 -4/5 31/13 -6/7 12/5 -5/6 5/2 -6/7 -4/5 18/7 -5/6 31/12 -5/6 -4/5 75/29 -4/5 44/17 -1/1 -5/6 -4/5 13/5 -4/5 34/13 -1/1 -4/5 -3/4 89/34 -5/6 -4/5 55/21 -4/5 21/8 -6/7 -4/5 71/27 -4/5 50/19 -6/7 -4/5 29/11 -4/5 37/14 -13/16 -4/5 45/17 -4/5 8/3 -1/1 -4/5 -3/4 35/13 -4/5 62/23 -1/1 -4/5 -3/4 151/56 -10/13 -3/4 240/89 -3/4 89/33 -2/3 27/10 -4/5 -2/3 46/17 -1/1 -4/5 -3/4 19/7 -2/3 30/11 -1/1 11/4 -1/1 -6/7 14/5 -6/7 -11/13 -5/6 45/16 -5/6 31/11 -14/17 17/6 -9/11 -4/5 3/1 -4/5 16/5 -1/1 -4/5 -3/4 45/14 -3/4 29/9 -14/19 13/4 -3/4 -2/3 23/7 -4/5 10/3 -4/5 -2/3 37/11 -4/5 27/8 -4/5 -2/3 44/13 -1/1 -3/4 -2/3 105/31 -2/3 61/18 -1/1 -2/3 17/5 -4/5 58/17 -3/4 -5/7 -2/3 41/12 -4/5 -3/4 24/7 -3/4 7/2 -1/1 -2/3 18/5 -1/2 29/8 -1/2 0/1 40/11 0/1 11/3 -2/1 15/4 -1/1 19/5 -8/9 23/6 -7/8 -6/7 27/7 -6/7 31/8 -5/6 -4/5 4/1 -1/1 -4/5 -3/4 21/5 -2/3 17/4 -1/1 0/1 30/7 -1/1 13/3 -6/7 35/8 -6/7 -4/5 22/5 -5/6 -9/11 -4/5 31/7 -6/7 9/2 -4/5 -2/3 14/3 -1/1 -4/5 -3/4 33/7 -4/5 19/4 -3/4 -8/11 24/5 -3/4 29/6 -3/4 -2/3 5/1 -2/3 21/4 -2/3 0/1 16/3 -2/3 -3/5 -1/2 11/2 -1/1 -2/3 17/3 0/1 23/4 -1/2 0/1 29/5 0/1 6/1 -1/1 19/3 -8/11 13/2 -2/3 -1/2 7/1 0/1 15/2 -1/1 23/3 -6/7 8/1 -1/1 -3/4 -2/3 9/1 -2/3 10/1 -2/3 0/1 11/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(59,690,-36,-421) (-10/1,1/0) -> (-100/61,-59/36) Hyperbolic Matrix(119,1140,50,479) (-10/1,-9/1) -> (69/29,50/21) Hyperbolic Matrix(61,510,36,301) (-9/1,-8/1) -> (22/13,39/23) Hyperbolic Matrix(61,480,-38,-299) (-8/1,-15/2) -> (-45/28,-8/5) Hyperbolic Matrix(119,870,-74,-541) (-15/2,-7/1) -> (-37/23,-45/28) Hyperbolic Matrix(59,390,18,119) (-7/1,-13/2) -> (13/4,23/7) Hyperbolic Matrix(61,390,-28,-179) (-13/2,-6/1) -> (-24/11,-13/6) Hyperbolic Matrix(121,690,-84,-479) (-6/1,-17/3) -> (-13/9,-36/25) Hyperbolic Matrix(59,330,32,179) (-17/3,-11/2) -> (11/6,13/7) Hyperbolic Matrix(61,330,-22,-119) (-11/2,-5/1) -> (-25/9,-11/4) Hyperbolic Matrix(299,1440,-212,-1021) (-5/1,-24/5) -> (-24/17,-55/39) Hyperbolic Matrix(301,1440,88,421) (-24/5,-19/4) -> (41/12,24/7) Hyperbolic Matrix(241,1140,-152,-719) (-19/4,-14/3) -> (-46/29,-19/12) Hyperbolic Matrix(59,270,26,119) (-14/3,-9/2) -> (9/4,16/7) Hyperbolic Matrix(61,270,-54,-239) (-9/2,-22/5) -> (-8/7,-9/8) Hyperbolic Matrix(239,1050,150,659) (-22/5,-35/8) -> (35/22,8/5) Hyperbolic Matrix(419,1830,302,1319) (-35/8,-13/3) -> (43/31,25/18) Hyperbolic Matrix(181,780,42,181) (-13/3,-30/7) -> (30/7,13/3) Hyperbolic Matrix(239,1020,56,239) (-30/7,-17/4) -> (17/4,30/7) Hyperbolic Matrix(241,1020,142,601) (-17/4,-21/5) -> (39/23,17/10) Hyperbolic Matrix(179,750,100,419) (-21/5,-4/1) -> (34/19,9/5) Hyperbolic Matrix(119,450,-32,-121) (-4/1,-15/4) -> (-15/4,-26/7) Parabolic Matrix(899,3330,-632,-2341) (-26/7,-37/10) -> (-37/26,-64/45) Hyperbolic Matrix(479,1770,292,1079) (-37/10,-11/3) -> (41/25,23/14) Hyperbolic Matrix(59,210,-34,-121) (-11/3,-7/2) -> (-7/4,-19/11) Hyperbolic Matrix(61,210,-52,-179) (-7/2,-17/5) -> (-13/11,-7/6) Hyperbolic Matrix(1079,3660,778,2639) (-17/5,-61/18) -> (61/44,43/31) Hyperbolic Matrix(1081,3660,-744,-2519) (-61/18,-44/13) -> (-16/11,-61/42) Hyperbolic Matrix(719,2430,266,899) (-44/13,-27/8) -> (27/10,46/17) Hyperbolic Matrix(179,600,-54,-181) (-27/8,-10/3) -> (-10/3,-33/10) Parabolic Matrix(301,990,128,421) (-33/10,-23/7) -> (7/3,33/14) Hyperbolic Matrix(119,390,18,59) (-23/7,-13/4) -> (13/2,7/1) Hyperbolic Matrix(241,780,-148,-479) (-13/4,-16/5) -> (-44/27,-13/8) Hyperbolic Matrix(181,570,-114,-359) (-16/5,-3/1) -> (-27/17,-46/29) Hyperbolic Matrix(179,510,126,359) (-3/1,-17/6) -> (17/12,27/19) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(419,1170,236,659) (-14/5,-39/14) -> (39/22,16/9) Hyperbolic Matrix(959,2670,366,1019) (-39/14,-25/9) -> (55/21,21/8) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(299,810,-244,-661) (-19/7,-27/10) -> (-27/22,-11/9) Hyperbolic Matrix(301,810,-178,-479) (-27/10,-8/3) -> (-22/13,-27/16) Hyperbolic Matrix(181,480,-158,-419) (-8/3,-37/14) -> (-23/20,-8/7) Hyperbolic Matrix(1079,2850,-750,-1981) (-37/14,-29/11) -> (-59/41,-23/16) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(3479,9150,-2122,-5581) (-50/19,-71/27) -> (-41/25,-100/61) Hyperbolic Matrix(1141,3000,936,2461) (-71/27,-21/8) -> (39/32,11/9) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(779,2040,160,419) (-55/21,-89/34) -> (29/6,5/1) Hyperbolic Matrix(3359,8790,-2362,-6181) (-89/34,-34/13) -> (-64/45,-91/64) Hyperbolic Matrix(241,630,184,481) (-34/13,-13/5) -> (17/13,4/3) Hyperbolic Matrix(59,150,-24,-61) (-13/5,-5/2) -> (-5/2,-17/7) Parabolic Matrix(359,870,-248,-601) (-17/7,-29/12) -> (-29/20,-13/9) Hyperbolic Matrix(361,870,100,241) (-29/12,-12/5) -> (18/5,29/8) Hyperbolic Matrix(301,720,176,421) (-12/5,-31/13) -> (29/17,12/7) Hyperbolic Matrix(1259,3000,478,1139) (-31/13,-50/21) -> (50/19,29/11) Hyperbolic Matrix(479,1140,50,119) (-50/21,-69/29) -> (9/1,10/1) Hyperbolic Matrix(1261,3000,984,2341) (-69/29,-19/8) -> (41/32,9/7) Hyperbolic Matrix(241,570,178,421) (-19/8,-26/11) -> (4/3,19/14) Hyperbolic Matrix(1499,3540,838,1979) (-26/11,-59/25) -> (59/33,34/19) Hyperbolic Matrix(1679,3960,-1018,-2401) (-59/25,-33/14) -> (-33/20,-61/37) Hyperbolic Matrix(599,1410,178,419) (-33/14,-7/3) -> (37/11,27/8) Hyperbolic Matrix(181,420,78,181) (-7/3,-30/13) -> (30/13,7/3) Hyperbolic Matrix(599,1380,260,599) (-30/13,-23/10) -> (23/10,30/13) Hyperbolic Matrix(301,690,236,541) (-23/10,-16/7) -> (14/11,23/18) Hyperbolic Matrix(119,270,26,59) (-16/7,-9/4) -> (9/2,14/3) Hyperbolic Matrix(241,540,54,121) (-9/4,-29/13) -> (31/7,9/2) Hyperbolic Matrix(539,1200,296,659) (-29/13,-20/9) -> (20/11,31/17) Hyperbolic Matrix(421,930,-244,-539) (-20/9,-11/5) -> (-19/11,-50/29) Hyperbolic Matrix(301,660,192,421) (-11/5,-24/11) -> (36/23,11/7) Hyperbolic Matrix(181,390,84,181) (-13/6,-15/7) -> (15/7,13/6) Hyperbolic Matrix(241,510,-198,-419) (-15/7,-2/1) -> (-28/23,-45/37) Hyperbolic Matrix(239,450,-128,-241) (-2/1,-15/8) -> (-15/8,-28/15) Parabolic Matrix(661,1230,194,361) (-28/15,-13/7) -> (17/5,58/17) Hyperbolic Matrix(179,330,32,59) (-13/7,-11/6) -> (11/2,17/3) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(481,870,-298,-539) (-20/11,-9/5) -> (-21/13,-50/31) Hyperbolic Matrix(419,750,100,179) (-9/5,-34/19) -> (4/1,21/5) Hyperbolic Matrix(1979,3540,838,1499) (-34/19,-59/33) -> (59/25,26/11) Hyperbolic Matrix(1679,3000,1074,1919) (-59/33,-25/14) -> (25/16,61/39) Hyperbolic Matrix(421,750,270,481) (-25/14,-16/9) -> (14/9,25/16) Hyperbolic Matrix(541,960,102,181) (-16/9,-39/22) -> (21/4,16/3) Hyperbolic Matrix(661,1170,-474,-839) (-39/22,-23/13) -> (-7/5,-39/28) Hyperbolic Matrix(781,1380,442,781) (-23/13,-30/17) -> (30/17,23/13) Hyperbolic Matrix(239,420,136,239) (-30/17,-7/4) -> (7/4,30/17) Hyperbolic Matrix(1201,2070,662,1141) (-50/29,-31/18) -> (29/16,20/11) Hyperbolic Matrix(541,930,210,361) (-31/18,-12/7) -> (18/7,31/12) Hyperbolic Matrix(421,720,176,301) (-12/7,-29/17) -> (31/13,12/5) Hyperbolic Matrix(2041,3480,634,1081) (-29/17,-75/44) -> (45/14,29/9) Hyperbolic Matrix(1919,3270,598,1019) (-75/44,-46/27) -> (16/5,45/14) Hyperbolic Matrix(601,1020,142,241) (-17/10,-39/23) -> (21/5,17/4) Hyperbolic Matrix(301,510,36,61) (-39/23,-22/13) -> (8/1,9/1) Hyperbolic Matrix(179,300,-108,-181) (-27/16,-5/3) -> (-5/3,-33/20) Parabolic Matrix(3241,5340,-2330,-3839) (-61/37,-28/17) -> (-32/23,-121/87) Hyperbolic Matrix(839,1380,656,1079) (-28/17,-23/14) -> (23/18,32/25) Hyperbolic Matrix(841,1380,220,361) (-23/14,-41/25) -> (19/5,23/6) Hyperbolic Matrix(1319,2160,952,1559) (-59/36,-18/11) -> (18/13,61/44) Hyperbolic Matrix(661,1080,478,781) (-18/11,-31/19) -> (29/21,18/13) Hyperbolic Matrix(2281,3720,810,1321) (-31/19,-75/46) -> (45/16,31/11) Hyperbolic Matrix(1859,3030,662,1079) (-75/46,-44/27) -> (14/5,45/16) Hyperbolic Matrix(241,390,186,301) (-13/8,-21/13) -> (9/7,13/10) Hyperbolic Matrix(1619,2610,446,719) (-50/31,-29/18) -> (29/8,40/11) Hyperbolic Matrix(839,1350,596,959) (-29/18,-37/23) -> (7/5,31/22) Hyperbolic Matrix(659,1050,150,239) (-8/5,-35/22) -> (35/8,22/5) Hyperbolic Matrix(1679,2670,-1208,-1921) (-35/22,-27/17) -> (-57/41,-25/18) Hyperbolic Matrix(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(419,660,266,419) (-30/19,-11/7) -> (11/7,30/19) Hyperbolic Matrix(479,750,76,119) (-11/7,-36/23) -> (6/1,19/3) Hyperbolic Matrix(901,1410,154,241) (-36/23,-61/39) -> (29/5,6/1) Hyperbolic Matrix(1919,3000,1074,1679) (-61/39,-25/16) -> (25/14,59/33) Hyperbolic Matrix(481,750,270,421) (-25/16,-14/9) -> (16/9,25/14) Hyperbolic Matrix(59,90,-40,-61) (-14/9,-3/2) -> (-3/2,-16/11) Parabolic Matrix(6301,9150,1860,2701) (-61/42,-45/31) -> (105/31,61/18) Hyperbolic Matrix(2461,3570,952,1381) (-45/31,-29/20) -> (31/12,75/29) Hyperbolic Matrix(3001,4320,1918,2761) (-36/25,-59/41) -> (61/39,36/23) Hyperbolic Matrix(419,600,-294,-421) (-23/16,-10/7) -> (-10/7,-37/26) Parabolic Matrix(3419,4860,2152,3059) (-91/64,-27/19) -> (27/17,89/56) Hyperbolic Matrix(359,510,126,179) (-27/19,-17/12) -> (17/6,3/1) Hyperbolic Matrix(361,510,298,421) (-17/12,-24/17) -> (6/5,17/14) Hyperbolic Matrix(4681,6600,1788,2521) (-55/39,-31/22) -> (89/34,55/21) Hyperbolic Matrix(959,1350,596,839) (-31/22,-7/5) -> (37/23,29/18) Hyperbolic Matrix(1681,2340,1380,1921) (-39/28,-32/23) -> (28/23,39/32) Hyperbolic Matrix(34319,47730,12726,17699) (-121/87,-210/151) -> (240/89,89/33) Hyperbolic Matrix(38161,53070,14152,19681) (-210/151,-89/64) -> (151/56,240/89) Hyperbolic Matrix(2999,4170,776,1079) (-89/64,-57/41) -> (27/7,31/8) Hyperbolic Matrix(1319,1830,302,419) (-25/18,-43/31) -> (13/3,35/8) Hyperbolic Matrix(2639,3660,778,1079) (-43/31,-61/44) -> (61/18,17/5) Hyperbolic Matrix(1559,2160,952,1319) (-61/44,-18/13) -> (18/11,59/36) Hyperbolic Matrix(781,1080,478,661) (-18/13,-29/21) -> (31/19,18/11) Hyperbolic Matrix(1261,1740,566,781) (-29/21,-40/29) -> (20/9,29/13) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(419,570,308,419) (-15/11,-19/14) -> (19/14,15/11) Hyperbolic Matrix(421,570,178,241) (-19/14,-4/3) -> (26/11,19/8) Hyperbolic Matrix(481,630,184,241) (-4/3,-17/13) -> (13/5,34/13) Hyperbolic Matrix(781,1020,598,781) (-17/13,-30/23) -> (30/23,17/13) Hyperbolic Matrix(599,780,460,599) (-30/23,-13/10) -> (13/10,30/23) Hyperbolic Matrix(301,390,186,241) (-13/10,-9/7) -> (21/13,13/8) Hyperbolic Matrix(2341,3000,984,1261) (-9/7,-41/32) -> (19/8,69/29) Hyperbolic Matrix(2881,3690,844,1081) (-41/32,-32/25) -> (58/17,41/12) Hyperbolic Matrix(1079,1380,656,839) (-32/25,-23/18) -> (23/14,28/17) Hyperbolic Matrix(541,690,236,301) (-23/18,-14/11) -> (16/7,23/10) Hyperbolic Matrix(119,150,-96,-121) (-14/11,-5/4) -> (-5/4,-16/13) Parabolic Matrix(1319,1620,390,479) (-16/13,-27/22) -> (27/8,44/13) Hyperbolic Matrix(2461,3000,936,1141) (-11/9,-39/32) -> (21/8,71/27) Hyperbolic Matrix(2881,3510,1626,1981) (-39/32,-28/23) -> (62/35,39/22) Hyperbolic Matrix(839,1020,394,479) (-45/37,-17/14) -> (17/8,15/7) Hyperbolic Matrix(421,510,298,361) (-17/14,-6/5) -> (24/17,17/12) Hyperbolic Matrix(479,570,100,119) (-6/5,-19/16) -> (19/4,24/5) Hyperbolic Matrix(1619,1920,1264,1499) (-19/16,-32/27) -> (32/25,41/32) Hyperbolic Matrix(481,570,254,301) (-32/27,-13/11) -> (17/9,2/1) Hyperbolic Matrix(181,210,156,181) (-7/6,-15/13) -> (15/13,7/6) Hyperbolic Matrix(1381,1590,522,601) (-15/13,-23/20) -> (37/14,45/17) Hyperbolic Matrix(241,270,108,121) (-9/8,-1/1) -> (29/13,9/4) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(239,-270,54,-61) (1/1,8/7) -> (22/5,31/7) Hyperbolic Matrix(419,-480,158,-181) (8/7,15/13) -> (45/17,8/3) Hyperbolic Matrix(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(419,-510,198,-241) (17/14,28/23) -> (2/1,17/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(1921,-2670,1208,-1679) (25/18,32/23) -> (62/39,35/22) Hyperbolic Matrix(839,-1170,474,-661) (32/23,7/5) -> (23/13,62/35) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(421,-600,294,-419) (27/19,10/7) -> (10/7,33/23) Parabolic Matrix(961,-1380,250,-359) (33/23,23/16) -> (23/6,27/7) Hyperbolic Matrix(479,-690,84,-121) (23/16,13/9) -> (17/3,23/4) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(601,-930,232,-359) (17/11,14/9) -> (44/17,13/5) Hyperbolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(9361,-14880,3472,-5519) (89/56,62/39) -> (62/23,151/56) Hyperbolic Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(421,-690,36,-59) (59/36,41/25) -> (11/1,1/0) Hyperbolic Matrix(781,-1290,290,-479) (28/17,5/3) -> (35/13,62/23) Hyperbolic Matrix(479,-810,178,-301) (5/3,22/13) -> (8/3,35/13) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(241,-450,128,-239) (13/7,15/8) -> (15/8,17/9) Parabolic Matrix(179,-390,28,-61) (13/6,11/5) -> (19/3,13/2) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(1921,-4530,712,-1679) (33/14,59/25) -> (89/33,27/10) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(3061,-7920,904,-2339) (75/29,44/17) -> (44/13,105/31) Hyperbolic Matrix(539,-1410,138,-361) (34/13,89/34) -> (31/8,4/1) Hyperbolic Matrix(479,-1260,46,-121) (71/27,50/19) -> (10/1,11/1) Hyperbolic Matrix(659,-1740,114,-301) (29/11,37/14) -> (23/4,29/5) Hyperbolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(179,-570,38,-121) (3/1,16/5) -> (14/3,33/7) Hyperbolic Matrix(181,-600,54,-179) (23/7,10/3) -> (10/3,37/11) Parabolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(61,-450,8,-59) (7/1,15/2) -> (15/2,23/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(59,690,-36,-421) -> Matrix(25,8,-22,-7) Matrix(119,1140,50,479) -> Matrix(5,6,-6,-7) Matrix(61,510,36,301) -> Matrix(7,22,-8,-25) Matrix(61,480,-38,-299) -> Matrix(43,60,-38,-53) Matrix(119,870,-74,-541) -> Matrix(59,42,-52,-37) Matrix(59,390,18,119) -> Matrix(3,4,-4,-5) Matrix(61,390,-28,-179) -> Matrix(17,28,-14,-23) Matrix(121,690,-84,-479) -> Matrix(9,-10,-8,9) Matrix(59,330,32,179) -> Matrix(7,22,-8,-25) Matrix(61,330,-22,-119) -> Matrix(5,4,-4,-3) Matrix(299,1440,-212,-1021) -> Matrix(35,58,-32,-53) Matrix(301,1440,88,421) -> Matrix(7,12,-10,-17) Matrix(241,1140,-152,-719) -> Matrix(115,168,-102,-149) Matrix(59,270,26,119) -> Matrix(27,38,-32,-45) Matrix(61,270,-54,-239) -> Matrix(9,8,-8,-7) Matrix(239,1050,150,659) -> Matrix(131,166,-146,-185) Matrix(419,1830,302,1319) -> Matrix(15,16,-16,-17) Matrix(181,780,42,181) -> Matrix(11,12,-12,-13) Matrix(239,1020,56,239) -> Matrix(1,0,0,1) Matrix(241,1020,142,601) -> Matrix(7,22,-8,-25) Matrix(179,750,100,419) -> Matrix(9,10,-10,-11) Matrix(119,450,-32,-121) -> Matrix(9,10,-10,-11) Matrix(899,3330,-632,-2341) -> Matrix(115,94,-104,-85) Matrix(479,1770,292,1079) -> Matrix(43,26,-48,-29) Matrix(59,210,-34,-121) -> Matrix(7,6,-6,-5) Matrix(61,210,-52,-179) -> Matrix(35,58,-32,-53) Matrix(1079,3660,778,2639) -> Matrix(13,14,-14,-15) Matrix(1081,3660,-744,-2519) -> Matrix(29,48,-26,-43) Matrix(719,2430,266,899) -> Matrix(5,6,-6,-7) Matrix(179,600,-54,-181) -> Matrix(1,0,0,1) Matrix(301,990,128,421) -> Matrix(7,8,-8,-9) Matrix(119,390,18,59) -> Matrix(3,4,-4,-5) Matrix(241,780,-148,-479) -> Matrix(7,6,-6,-5) Matrix(181,570,-114,-359) -> Matrix(115,168,-102,-149) Matrix(179,510,126,359) -> Matrix(73,94,-80,-103) Matrix(361,1020,-212,-599) -> Matrix(109,138,-94,-119) Matrix(419,1170,236,659) -> Matrix(67,82,-76,-93) Matrix(959,2670,366,1019) -> Matrix(9,10,-10,-11) Matrix(241,660,88,241) -> Matrix(11,12,-12,-13) Matrix(419,1140,154,419) -> Matrix(3,4,-4,-5) Matrix(299,810,-244,-661) -> Matrix(9,8,-8,-7) Matrix(301,810,-178,-479) -> Matrix(53,68,-46,-59) Matrix(181,480,-158,-419) -> Matrix(63,88,-58,-81) Matrix(1079,2850,-750,-1981) -> Matrix(127,166,-114,-149) Matrix(1139,3000,478,1259) -> Matrix(9,10,-10,-11) Matrix(3479,9150,-2122,-5581) -> Matrix(43,60,-38,-53) Matrix(1141,3000,936,2461) -> Matrix(13,14,-14,-15) Matrix(481,1260,92,241) -> Matrix(5,6,-6,-7) Matrix(779,2040,160,419) -> Matrix(17,22,-24,-31) Matrix(3359,8790,-2362,-6181) -> Matrix(95,116,-86,-105) Matrix(241,630,184,481) -> Matrix(13,14,-14,-15) Matrix(59,150,-24,-61) -> Matrix(1,0,0,1) Matrix(359,870,-248,-601) -> Matrix(67,86,-60,-77) Matrix(361,870,100,241) -> Matrix(3,4,-10,-13) Matrix(301,720,176,421) -> Matrix(67,82,-76,-93) Matrix(1259,3000,478,1139) -> Matrix(9,10,-10,-11) Matrix(479,1140,50,119) -> Matrix(5,6,-6,-7) Matrix(1261,3000,984,2341) -> Matrix(73,94,-80,-103) Matrix(241,570,178,421) -> Matrix(15,16,-16,-17) Matrix(1499,3540,838,1979) -> Matrix(11,12,-12,-13) Matrix(1679,3960,-1018,-2401) -> Matrix(157,190,-138,-167) Matrix(599,1410,178,419) -> Matrix(7,8,-8,-9) Matrix(181,420,78,181) -> Matrix(31,40,-38,-49) Matrix(599,1380,260,599) -> Matrix(209,260,-250,-311) Matrix(301,690,236,541) -> Matrix(103,126,-112,-137) Matrix(119,270,26,59) -> Matrix(31,38,-40,-49) Matrix(241,540,54,121) -> Matrix(31,38,-40,-49) Matrix(539,1200,296,659) -> Matrix(227,274,-256,-309) Matrix(421,930,-244,-539) -> Matrix(1,0,0,1) Matrix(301,660,192,421) -> Matrix(157,194,-174,-215) Matrix(181,390,84,181) -> Matrix(169,204,-198,-239) Matrix(241,510,-198,-419) -> Matrix(105,124,-94,-111) Matrix(239,450,-128,-241) -> Matrix(251,294,-216,-253) Matrix(661,1230,194,361) -> Matrix(81,94,-106,-123) Matrix(179,330,32,59) -> Matrix(19,22,-32,-37) Matrix(361,660,-262,-479) -> Matrix(137,158,-124,-143) Matrix(481,870,-298,-539) -> Matrix(111,128,-98,-113) Matrix(419,750,100,179) -> Matrix(9,10,-10,-11) Matrix(1979,3540,838,1499) -> Matrix(11,12,-12,-13) Matrix(1679,3000,1074,1919) -> Matrix(123,142,-136,-157) Matrix(421,750,270,481) -> Matrix(123,142,-136,-157) Matrix(541,960,102,181) -> Matrix(19,22,-32,-37) Matrix(661,1170,-474,-839) -> Matrix(137,158,-124,-143) Matrix(781,1380,442,781) -> Matrix(209,240,-236,-271) Matrix(239,420,136,239) -> Matrix(15,16,-16,-17) Matrix(1201,2070,662,1141) -> Matrix(93,110,-104,-123) Matrix(541,930,210,361) -> Matrix(49,58,-60,-71) Matrix(421,720,176,301) -> Matrix(71,82,-84,-97) Matrix(2041,3480,634,1081) -> Matrix(63,74,-86,-101) Matrix(1919,3270,598,1019) -> Matrix(117,136,-154,-179) Matrix(601,1020,142,241) -> Matrix(19,22,-32,-37) Matrix(301,510,36,61) -> Matrix(19,22,-32,-37) Matrix(179,300,-108,-181) -> Matrix(335,384,-294,-337) Matrix(3241,5340,-2330,-3839) -> Matrix(143,162,-128,-145) Matrix(839,1380,656,1079) -> Matrix(297,338,-326,-371) Matrix(841,1380,220,361) -> Matrix(127,144,-142,-161) Matrix(1319,2160,952,1559) -> Matrix(187,212,-202,-229) Matrix(661,1080,478,781) -> Matrix(127,144,-142,-161) Matrix(2281,3720,810,1321) -> Matrix(307,346,-370,-417) Matrix(1859,3030,662,1079) -> Matrix(93,104,-110,-123) Matrix(241,390,186,301) -> Matrix(157,178,-172,-195) Matrix(1619,2610,446,719) -> Matrix(7,8,-36,-41) Matrix(839,1350,596,959) -> Matrix(187,212,-202,-229) Matrix(659,1050,150,239) -> Matrix(147,166,-178,-201) Matrix(1679,2670,-1208,-1921) -> Matrix(349,394,-318,-359) Matrix(721,1140,456,721) -> Matrix(1279,1440,-1422,-1601) Matrix(419,660,266,419) -> Matrix(737,828,-818,-919) Matrix(479,750,76,119) -> Matrix(59,66,-76,-85) Matrix(901,1410,154,241) -> Matrix(9,10,8,9) Matrix(1919,3000,1074,1679) -> Matrix(127,142,-144,-161) Matrix(481,750,270,421) -> Matrix(127,142,-144,-161) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(6301,9150,1860,2701) -> Matrix(25,28,-42,-47) Matrix(2461,3570,952,1381) -> Matrix(13,14,-14,-15) Matrix(3001,4320,1918,2761) -> Matrix(341,380,-376,-419) Matrix(419,600,-294,-421) -> Matrix(359,400,-324,-361) Matrix(3419,4860,2152,3059) -> Matrix(521,574,-580,-639) Matrix(359,510,126,179) -> Matrix(85,94,-104,-115) Matrix(361,510,298,421) -> Matrix(199,220,-218,-241) Matrix(4681,6600,1788,2521) -> Matrix(15,16,-16,-17) Matrix(959,1350,596,839) -> Matrix(195,212,-218,-237) Matrix(1681,2340,1380,1921) -> Matrix(19,20,-20,-21) Matrix(34319,47730,12726,17699) -> Matrix(107,118,-146,-161) Matrix(38161,53070,14152,19681) -> Matrix(133,146,-174,-191) Matrix(2999,4170,776,1079) -> Matrix(15,16,-16,-17) Matrix(1319,1830,302,419) -> Matrix(15,16,-16,-17) Matrix(2639,3660,778,1079) -> Matrix(13,14,-14,-15) Matrix(1559,2160,952,1319) -> Matrix(195,212,-218,-237) Matrix(781,1080,478,661) -> Matrix(127,144,-142,-161) Matrix(1261,1740,566,781) -> Matrix(201,224,-236,-263) Matrix(241,330,176,241) -> Matrix(19,20,-20,-21) Matrix(419,570,308,419) -> Matrix(199,220,-218,-241) Matrix(421,570,178,241) -> Matrix(15,16,-16,-17) Matrix(481,630,184,241) -> Matrix(13,14,-14,-15) Matrix(781,1020,598,781) -> Matrix(161,180,-178,-199) Matrix(599,780,460,599) -> Matrix(199,220,-218,-241) Matrix(301,390,186,241) -> Matrix(161,178,-180,-199) Matrix(2341,3000,984,1261) -> Matrix(85,94,-104,-115) Matrix(2881,3690,844,1081) -> Matrix(47,52,-66,-73) Matrix(1079,1380,656,839) -> Matrix(305,338,-342,-379) Matrix(541,690,236,301) -> Matrix(115,126,-136,-149) Matrix(119,150,-96,-121) -> Matrix(1,0,0,1) Matrix(1319,1620,390,479) -> Matrix(13,14,-14,-15) Matrix(2461,3000,936,1141) -> Matrix(13,14,-14,-15) Matrix(2881,3510,1626,1981) -> Matrix(127,142,-144,-161) Matrix(839,1020,394,479) -> Matrix(339,376,-394,-437) Matrix(421,510,298,361) -> Matrix(199,220,-218,-241) Matrix(479,570,100,119) -> Matrix(13,14,-14,-15) Matrix(1619,1920,1264,1499) -> Matrix(21,22,-22,-23) Matrix(481,570,254,301) -> Matrix(17,18,-18,-19) Matrix(181,210,156,181) -> Matrix(505,552,-548,-599) Matrix(1381,1590,522,601) -> Matrix(367,400,-456,-497) Matrix(241,270,108,121) -> Matrix(115,126,-136,-149) Matrix(1,0,2,1) -> Matrix(27,28,-28,-29) Matrix(239,-270,54,-61) -> Matrix(9,8,-8,-7) Matrix(419,-480,158,-181) -> Matrix(95,88,-122,-113) Matrix(179,-210,52,-61) -> Matrix(63,58,-88,-81) Matrix(419,-510,198,-241) -> Matrix(137,124,-158,-143) Matrix(121,-150,96,-119) -> Matrix(1,0,0,1) Matrix(899,-1140,332,-421) -> Matrix(9,8,-8,-7) Matrix(479,-660,262,-361) -> Matrix(173,158,-196,-179) Matrix(1921,-2670,1208,-1679) -> Matrix(429,394,-478,-439) Matrix(839,-1170,474,-661) -> Matrix(173,158,-196,-179) Matrix(1021,-1440,212,-299) -> Matrix(63,58,-88,-81) Matrix(421,-600,294,-419) -> Matrix(439,400,-484,-441) Matrix(961,-1380,250,-359) -> Matrix(137,124,-158,-143) Matrix(479,-690,84,-121) -> Matrix(11,10,-32,-29) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(95,86,-116,-105) Matrix(719,-1140,152,-241) -> Matrix(187,168,-246,-221) Matrix(9361,-14880,3472,-5519) -> Matrix(187,168,-246,-221) Matrix(299,-480,38,-61) -> Matrix(67,60,-86,-77) Matrix(539,-870,298,-481) -> Matrix(143,128,-162,-145) Matrix(479,-780,148,-241) -> Matrix(7,6,-6,-5) Matrix(421,-690,36,-59) -> Matrix(9,8,10,9) Matrix(781,-1290,290,-479) -> Matrix(139,124,-176,-157) Matrix(479,-810,178,-301) -> Matrix(77,68,-94,-83) Matrix(599,-1020,212,-361) -> Matrix(157,138,-190,-167) Matrix(121,-210,34,-59) -> Matrix(7,6,-6,-5) Matrix(241,-450,128,-239) -> Matrix(335,294,-384,-337) Matrix(179,-390,28,-61) -> Matrix(33,28,-46,-39) Matrix(299,-660,82,-181) -> Matrix(7,6,-6,-5) Matrix(1921,-4530,712,-1679) -> Matrix(3,2,-2,-1) Matrix(61,-150,24,-59) -> Matrix(1,0,0,1) Matrix(3061,-7920,904,-2339) -> Matrix(3,2,-2,-1) Matrix(539,-1410,138,-361) -> Matrix(1,0,0,1) Matrix(479,-1260,46,-121) -> Matrix(5,4,-4,-3) Matrix(659,-1740,114,-301) -> Matrix(5,4,6,5) Matrix(119,-330,22,-61) -> Matrix(5,4,-4,-3) Matrix(179,-570,38,-121) -> Matrix(1,0,0,1) Matrix(181,-600,54,-179) -> Matrix(1,0,0,1) Matrix(121,-450,32,-119) -> Matrix(9,10,-10,-11) Matrix(61,-450,8,-59) -> Matrix(5,6,-6,-7) 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): 48 Degree of the the map X: 48 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. ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 40 Genus: 29 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -15/2 -6/1 -4/1 -15/4 -5/2 -12/5 -2/1 -5/4 0/1 1/1 5/4 15/11 10/7 3/2 5/3 30/17 2/1 15/7 20/9 12/5 5/2 30/11 3/1 10/3 27/8 7/2 15/4 4/1 17/4 30/7 9/2 5/1 21/4 11/2 6/1 7/1 15/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 -2/1 -8/1 -2/1 -3/2 -1/1 -15/2 -1/1 -7/1 0/1 -6/1 -1/1 -17/3 0/1 -11/2 -2/1 -1/1 -5/1 -2/1 -9/2 -2/1 -4/3 -4/1 -3/2 -4/3 -1/1 -15/4 -1/1 -26/7 -1/1 -7/8 -6/7 -11/3 -2/3 -7/2 -2/1 -1/1 -17/5 -4/3 -27/8 -2/1 -4/3 -10/3 -2/1 -4/3 -3/1 -4/3 -17/6 -4/3 -9/7 -14/5 -5/4 -11/9 -6/5 -25/9 -6/5 -11/4 -6/5 -1/1 -30/11 -1/1 -19/7 -2/1 -27/10 -2/1 -4/3 -8/3 -3/2 -4/3 -1/1 -29/11 -4/3 -50/19 -4/3 -6/5 -21/8 -4/3 -6/5 -55/21 -4/3 -34/13 -3/2 -4/3 -1/1 -13/5 -4/3 -5/2 -4/3 -6/5 -17/7 -4/3 -12/5 -5/4 -31/13 -6/5 -50/21 -4/3 -6/5 -69/29 -4/3 -19/8 -5/4 -6/5 -26/11 -5/4 -6/5 -1/1 -33/14 -4/3 -6/5 -7/3 -4/3 -30/13 -5/4 -23/10 -5/4 -26/21 -16/7 -5/4 -11/9 -6/5 -9/4 -16/13 -6/5 -20/9 -6/5 -11/5 -4/3 -2/1 -6/5 -7/6 -1/1 -15/8 -7/6 -13/7 -22/19 -11/6 -15/13 -8/7 -20/11 -8/7 -9/5 -8/7 -7/4 -8/7 -1/1 -19/11 -4/3 -12/7 -7/6 -29/17 -8/7 -46/27 -7/6 -43/37 -36/31 -17/10 -22/19 -15/13 -22/13 -15/13 -23/20 -8/7 -27/16 -38/33 -8/7 -5/3 -8/7 -3/2 -8/7 -10/9 -10/7 -10/9 -27/19 -10/9 -17/12 -10/9 -1/1 -24/17 -11/10 -7/5 -10/9 -18/13 -1/1 -29/21 -28/25 -40/29 -10/9 -11/8 -10/9 -1/1 -15/11 -10/9 -19/14 -10/9 -11/10 -4/3 -10/9 -11/10 -1/1 -17/13 -10/9 -30/23 -10/9 -13/10 -10/9 -11/10 -9/7 -10/9 -32/25 -10/9 -11/10 -1/1 -23/18 -32/29 -11/10 -14/11 -11/10 -12/11 -1/1 -5/4 -10/9 -12/11 -16/13 -11/10 -12/11 -1/1 -27/22 -10/9 -12/11 -11/9 -10/9 -28/23 -9/8 -19/17 -10/9 -17/14 -10/9 -21/19 -6/5 -11/10 -13/11 -34/31 -7/6 -23/21 -12/11 -15/13 -12/11 -23/20 -12/11 -61/56 -8/7 -12/11 -25/23 -13/12 -1/1 -14/13 0/1 -1/1 1/1 -14/15 7/6 -12/13 -23/25 6/5 -11/12 17/14 -21/23 -10/11 11/9 -10/11 5/4 -12/13 -10/11 19/15 -10/11 14/11 -1/1 -12/13 -11/12 23/18 -11/12 -32/35 9/7 -10/11 4/3 -1/1 -11/12 -10/11 19/14 -11/12 -10/11 15/11 -10/11 11/8 -1/1 -10/11 18/13 -1/1 7/5 -10/11 24/17 -11/12 17/12 -1/1 -10/11 27/19 -10/11 10/7 -10/11 3/2 -10/11 -8/9 5/3 -8/9 22/13 -8/9 -23/26 -15/17 39/23 -8/9 17/10 -15/17 -22/25 29/17 -8/9 12/7 -7/8 7/4 -1/1 -8/9 30/17 -8/9 23/13 -8/9 16/9 -1/1 -8/9 -7/8 9/5 -8/9 20/11 -8/9 11/6 -8/9 -15/17 13/7 -22/25 15/8 -7/8 2/1 -1/1 -7/8 -6/7 15/7 -6/7 13/6 -6/7 -17/20 11/5 -4/5 20/9 -6/7 9/4 -6/7 -16/19 7/3 -4/5 26/11 -1/1 -6/7 -5/6 19/8 -6/7 -5/6 50/21 -6/7 -4/5 31/13 -6/7 12/5 -5/6 5/2 -6/7 -4/5 18/7 -5/6 13/5 -4/5 34/13 -1/1 -4/5 -3/4 21/8 -6/7 -4/5 50/19 -6/7 -4/5 29/11 -4/5 37/14 -13/16 -4/5 45/17 -4/5 8/3 -1/1 -4/5 -3/4 35/13 -4/5 27/10 -4/5 -2/3 46/17 -1/1 -4/5 -3/4 19/7 -2/3 30/11 -1/1 11/4 -1/1 -6/7 14/5 -6/7 -11/13 -5/6 17/6 -9/11 -4/5 3/1 -4/5 10/3 -4/5 -2/3 27/8 -4/5 -2/3 44/13 -1/1 -3/4 -2/3 17/5 -4/5 7/2 -1/1 -2/3 18/5 -1/2 29/8 -1/2 0/1 40/11 0/1 11/3 -2/1 15/4 -1/1 19/5 -8/9 23/6 -7/8 -6/7 4/1 -1/1 -4/5 -3/4 17/4 -1/1 0/1 30/7 -1/1 13/3 -6/7 9/2 -4/5 -2/3 5/1 -2/3 21/4 -2/3 0/1 16/3 -2/3 -3/5 -1/2 11/2 -1/1 -2/3 17/3 0/1 6/1 -1/1 13/2 -2/3 -1/2 7/1 0/1 15/2 -1/1 8/1 -1/1 -3/4 -2/3 9/1 -2/3 10/1 -2/3 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(19,240,-8,-101) (-9/1,1/0) -> (-69/29,-19/8) Hyperbolic Matrix(61,510,36,301) (-9/1,-8/1) -> (22/13,39/23) Hyperbolic Matrix(19,150,10,79) (-8/1,-15/2) -> (15/8,2/1) Hyperbolic Matrix(41,300,22,161) (-15/2,-7/1) -> (13/7,15/8) Hyperbolic Matrix(19,120,-16,-101) (-7/1,-6/1) -> (-6/5,-13/11) Hyperbolic Matrix(79,450,56,319) (-6/1,-17/3) -> (7/5,24/17) Hyperbolic Matrix(59,330,32,179) (-17/3,-11/2) -> (11/6,13/7) Hyperbolic Matrix(61,330,-22,-119) (-11/2,-5/1) -> (-25/9,-11/4) Hyperbolic Matrix(19,90,4,19) (-5/1,-9/2) -> (9/2,5/1) Hyperbolic Matrix(41,180,-18,-79) (-9/2,-4/1) -> (-16/7,-9/4) Hyperbolic Matrix(119,450,-32,-121) (-4/1,-15/4) -> (-15/4,-26/7) Parabolic Matrix(341,1260,-200,-739) (-26/7,-11/3) -> (-29/17,-46/27) Hyperbolic Matrix(59,210,-34,-121) (-11/3,-7/2) -> (-7/4,-19/11) Hyperbolic Matrix(61,210,-52,-179) (-7/2,-17/5) -> (-13/11,-7/6) Hyperbolic Matrix(221,750,-94,-319) (-17/5,-27/8) -> (-33/14,-7/3) Hyperbolic Matrix(161,540,48,161) (-27/8,-10/3) -> (10/3,27/8) Hyperbolic Matrix(19,60,6,19) (-10/3,-3/1) -> (3/1,10/3) Hyperbolic Matrix(179,510,126,359) (-3/1,-17/6) -> (17/12,27/19) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(581,1620,-222,-619) (-14/5,-25/9) -> (-55/21,-34/13) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) Hyperbolic Matrix(419,1140,154,419) (-30/11,-19/7) -> (19/7,30/11) Hyperbolic Matrix(299,810,-244,-661) (-19/7,-27/10) -> (-27/22,-11/9) Hyperbolic Matrix(301,810,-178,-479) (-27/10,-8/3) -> (-22/13,-27/16) Hyperbolic Matrix(341,900,-280,-739) (-8/3,-29/11) -> (-11/9,-28/23) Hyperbolic Matrix(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(799,2100,304,799) (-50/19,-21/8) -> (21/8,50/19) Hyperbolic Matrix(481,1260,92,241) (-21/8,-55/21) -> (5/1,21/4) Hyperbolic Matrix(379,990,214,559) (-34/13,-13/5) -> (23/13,16/9) Hyperbolic Matrix(59,150,-24,-61) (-13/5,-5/2) -> (-5/2,-17/7) Parabolic Matrix(161,390,116,281) (-17/7,-12/5) -> (18/13,7/5) Hyperbolic Matrix(301,720,176,421) (-12/5,-31/13) -> (29/17,12/7) Hyperbolic Matrix(1259,3000,478,1139) (-31/13,-50/21) -> (50/19,29/11) Hyperbolic Matrix(479,1140,50,119) (-50/21,-69/29) -> (9/1,10/1) Hyperbolic Matrix(241,570,178,421) (-19/8,-26/11) -> (4/3,19/14) Hyperbolic Matrix(941,2220,348,821) (-26/11,-33/14) -> (27/10,46/17) Hyperbolic Matrix(259,600,60,139) (-7/3,-30/13) -> (30/7,13/3) Hyperbolic Matrix(521,1200,122,281) (-30/13,-23/10) -> (17/4,30/7) Hyperbolic Matrix(301,690,236,541) (-23/10,-16/7) -> (14/11,23/18) Hyperbolic Matrix(161,360,72,161) (-9/4,-20/9) -> (20/9,9/4) Hyperbolic Matrix(461,1020,-334,-739) (-20/9,-11/5) -> (-29/21,-40/29) Hyperbolic Matrix(41,90,-36,-79) (-11/5,-2/1) -> (-8/7,-1/1) Hyperbolic Matrix(79,150,10,19) (-2/1,-15/8) -> (15/2,8/1) Hyperbolic Matrix(161,300,22,41) (-15/8,-13/7) -> (7/1,15/2) Hyperbolic Matrix(179,330,32,59) (-13/7,-11/6) -> (11/2,17/3) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(101,180,-78,-139) (-9/5,-7/4) -> (-13/10,-9/7) Hyperbolic Matrix(401,690,-290,-499) (-19/11,-12/7) -> (-18/13,-29/21) Hyperbolic Matrix(421,720,176,301) (-12/7,-29/17) -> (31/13,12/5) Hyperbolic Matrix(619,1050,-484,-821) (-17/10,-22/13) -> (-32/25,-23/18) Hyperbolic Matrix(641,1080,238,401) (-27/16,-5/3) -> (35/13,27/10) Hyperbolic Matrix(19,30,12,19) (-5/3,-3/2) -> (3/2,5/3) Hyperbolic Matrix(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(379,540,266,379) (-10/7,-27/19) -> (27/19,10/7) Hyperbolic Matrix(359,510,126,179) (-27/19,-17/12) -> (17/6,3/1) Hyperbolic Matrix(361,510,298,421) (-17/12,-24/17) -> (6/5,17/14) Hyperbolic Matrix(319,450,56,79) (-24/17,-7/5) -> (17/3,6/1) Hyperbolic Matrix(259,360,100,139) (-7/5,-18/13) -> (18/7,13/5) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(419,570,308,419) (-15/11,-19/14) -> (19/14,15/11) Hyperbolic Matrix(421,570,178,241) (-19/14,-4/3) -> (26/11,19/8) Hyperbolic Matrix(481,630,184,241) (-4/3,-17/13) -> (13/5,34/13) Hyperbolic Matrix(919,1200,520,679) (-17/13,-30/23) -> (30/17,23/13) Hyperbolic Matrix(461,600,262,341) (-30/23,-13/10) -> (7/4,30/17) Hyperbolic Matrix(281,360,32,41) (-9/7,-32/25) -> (8/1,9/1) Hyperbolic Matrix(259,330,62,79) (-23/18,-14/11) -> (4/1,17/4) Hyperbolic Matrix(119,150,-96,-121) (-14/11,-5/4) -> (-5/4,-16/13) Parabolic Matrix(1319,1620,390,479) (-16/13,-27/22) -> (27/8,44/13) Hyperbolic Matrix(641,780,-558,-679) (-28/23,-17/14) -> (-23/20,-8/7) Hyperbolic Matrix(421,510,298,361) (-17/14,-6/5) -> (24/17,17/12) Hyperbolic Matrix(259,300,120,139) (-7/6,-15/13) -> (15/7,13/6) Hyperbolic Matrix(1381,1590,522,601) (-15/13,-23/20) -> (37/14,45/17) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(79,-90,36,-41) (1/1,7/6) -> (13/6,11/5) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(739,-900,280,-341) (17/14,11/9) -> (29/11,37/14) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(821,-1050,484,-619) (23/18,9/7) -> (39/23,17/10) Hyperbolic Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(479,-810,178,-301) (5/3,22/13) -> (8/3,35/13) Hyperbolic Matrix(581,-990,152,-259) (17/10,29/17) -> (19/5,23/6) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(101,-210,38,-79) (2/1,15/7) -> (45/17,8/3) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(319,-750,94,-221) (7/3,26/11) -> (44/13,17/5) Hyperbolic Matrix(101,-240,8,-19) (19/8,50/21) -> (10/1,1/0) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(401,-1050,76,-199) (34/13,21/8) -> (21/4,16/3) Hyperbolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(139,-390,36,-101) (14/5,17/6) -> (23/6,4/1) Hyperbolic Matrix(79,-270,12,-41) (17/5,7/2) -> (13/2,7/1) Hyperbolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(19,240,-8,-101) -> Matrix(1,6,-1,-5) Matrix(61,510,36,301) -> Matrix(7,22,-8,-25) Matrix(19,150,10,79) -> Matrix(13,20,-15,-23) Matrix(41,300,22,161) -> Matrix(29,22,-33,-25) Matrix(19,120,-16,-101) -> Matrix(23,34,-21,-31) Matrix(79,450,56,319) -> Matrix(1,-10,-1,11) Matrix(59,330,32,179) -> Matrix(7,22,-8,-25) Matrix(61,330,-22,-119) -> Matrix(5,4,-4,-3) Matrix(19,90,4,19) -> Matrix(5,8,-7,-11) Matrix(41,180,-18,-79) -> Matrix(21,26,-17,-21) Matrix(119,450,-32,-121) -> Matrix(9,10,-10,-11) Matrix(341,1260,-200,-739) -> Matrix(13,6,-11,-5) Matrix(59,210,-34,-121) -> Matrix(7,6,-6,-5) Matrix(61,210,-52,-179) -> Matrix(35,58,-32,-53) Matrix(221,750,-94,-319) -> Matrix(11,16,-9,-13) Matrix(161,540,48,161) -> Matrix(5,8,-7,-11) Matrix(19,60,6,19) -> Matrix(5,8,-7,-11) Matrix(179,510,126,359) -> Matrix(73,94,-80,-103) Matrix(361,1020,-212,-599) -> Matrix(109,138,-94,-119) Matrix(581,1620,-222,-619) -> Matrix(21,26,-17,-21) Matrix(241,660,88,241) -> Matrix(11,12,-12,-13) Matrix(419,1140,154,419) -> Matrix(3,4,-4,-5) Matrix(299,810,-244,-661) -> Matrix(9,8,-8,-7) Matrix(301,810,-178,-479) -> Matrix(53,68,-46,-59) Matrix(341,900,-280,-739) -> Matrix(37,46,-33,-41) Matrix(1139,3000,478,1259) -> Matrix(9,10,-10,-11) Matrix(799,2100,304,799) -> Matrix(19,24,-23,-29) Matrix(481,1260,92,241) -> Matrix(5,6,-6,-7) Matrix(379,990,214,559) -> Matrix(13,20,-15,-23) Matrix(59,150,-24,-61) -> Matrix(1,0,0,1) Matrix(161,390,116,281) -> Matrix(43,54,-47,-59) Matrix(301,720,176,421) -> Matrix(67,82,-76,-93) Matrix(1259,3000,478,1139) -> Matrix(9,10,-10,-11) Matrix(479,1140,50,119) -> Matrix(5,6,-6,-7) Matrix(241,570,178,421) -> Matrix(15,16,-16,-17) Matrix(941,2220,348,821) -> Matrix(11,14,-15,-19) Matrix(259,600,60,139) -> Matrix(27,34,-31,-39) Matrix(521,1200,122,281) -> Matrix(21,26,-17,-21) Matrix(301,690,236,541) -> Matrix(103,126,-112,-137) Matrix(161,360,72,161) -> Matrix(79,96,-93,-113) Matrix(461,1020,-334,-739) -> Matrix(55,64,-49,-57) Matrix(41,90,-36,-79) -> Matrix(53,66,-49,-61) Matrix(79,150,10,19) -> Matrix(17,20,-23,-27) Matrix(161,300,22,41) -> Matrix(19,22,-13,-15) Matrix(179,330,32,59) -> Matrix(19,22,-32,-37) Matrix(361,660,-262,-479) -> Matrix(137,158,-124,-143) Matrix(199,360,110,199) -> Matrix(41,48,-47,-55) Matrix(101,180,-78,-139) -> Matrix(67,78,-61,-71) Matrix(401,690,-290,-499) -> Matrix(55,64,-49,-57) Matrix(421,720,176,301) -> Matrix(71,82,-84,-97) Matrix(619,1050,-484,-821) -> Matrix(207,238,-187,-215) Matrix(641,1080,238,401) -> Matrix(73,84,-93,-107) Matrix(19,30,12,19) -> Matrix(71,80,-79,-89) Matrix(41,60,28,41) -> Matrix(71,80,-79,-89) Matrix(379,540,266,379) -> Matrix(289,320,-317,-351) Matrix(359,510,126,179) -> Matrix(85,94,-104,-115) Matrix(361,510,298,421) -> Matrix(199,220,-218,-241) Matrix(319,450,56,79) -> Matrix(9,10,-19,-21) Matrix(259,360,100,139) -> Matrix(49,54,-59,-65) Matrix(241,330,176,241) -> Matrix(19,20,-20,-21) Matrix(419,570,308,419) -> Matrix(199,220,-218,-241) Matrix(421,570,178,241) -> Matrix(15,16,-16,-17) Matrix(481,630,184,241) -> Matrix(13,14,-14,-15) Matrix(919,1200,520,679) -> Matrix(199,222,-225,-251) Matrix(461,600,262,341) -> Matrix(89,98,-99,-109) Matrix(281,360,32,41) -> Matrix(29,32,-39,-43) Matrix(259,330,62,79) -> Matrix(29,32,-39,-43) Matrix(119,150,-96,-121) -> Matrix(1,0,0,1) Matrix(1319,1620,390,479) -> Matrix(13,14,-14,-15) Matrix(641,780,-558,-679) -> Matrix(321,358,-295,-329) Matrix(421,510,298,361) -> Matrix(199,220,-218,-241) Matrix(259,300,120,139) -> Matrix(313,342,-367,-401) Matrix(1381,1590,522,601) -> Matrix(367,400,-456,-497) Matrix(1,0,2,1) -> Matrix(27,28,-28,-29) Matrix(79,-90,36,-41) -> Matrix(71,66,-85,-79) Matrix(101,-120,16,-19) -> Matrix(37,34,-49,-45) Matrix(739,-900,280,-341) -> Matrix(51,46,-61,-55) Matrix(121,-150,96,-119) -> Matrix(1,0,0,1) Matrix(899,-1140,332,-421) -> Matrix(9,8,-8,-7) Matrix(821,-1050,484,-619) -> Matrix(261,238,-295,-269) Matrix(139,-180,78,-101) -> Matrix(85,78,-97,-89) Matrix(521,-720,144,-199) -> Matrix(11,10,-21,-19) Matrix(479,-810,178,-301) -> Matrix(77,68,-94,-83) Matrix(581,-990,152,-259) -> Matrix(73,64,-81,-71) Matrix(121,-210,34,-59) -> Matrix(7,6,-6,-5) Matrix(559,-1020,154,-281) -> Matrix(9,8,-35,-31) Matrix(101,-210,38,-79) -> Matrix(25,22,-33,-29) Matrix(299,-660,82,-181) -> Matrix(7,6,-6,-5) Matrix(79,-180,18,-41) -> Matrix(31,26,-37,-31) Matrix(319,-750,94,-221) -> Matrix(19,16,-25,-21) Matrix(101,-240,8,-19) -> Matrix(7,6,-13,-11) Matrix(61,-150,24,-59) -> Matrix(1,0,0,1) Matrix(401,-1050,76,-199) -> Matrix(7,6,-13,-11) Matrix(119,-330,22,-61) -> Matrix(5,4,-4,-3) Matrix(139,-390,36,-101) -> Matrix(31,26,-37,-31) Matrix(79,-270,12,-41) -> Matrix(5,4,-9,-7) Matrix(121,-450,32,-119) -> Matrix(9,10,-10,-11) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 48 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 14 1 1/1 -14/15 1 30 7/6 (-12/13,-23/25) 0 30 6/5 -11/12 2 5 17/14 (-21/23,-10/11) 0 30 11/9 -10/11 1 30 5/4 0 6 19/15 -10/11 1 30 14/11 0 15 23/18 (-11/12,-32/35) 0 30 9/7 -10/11 1 10 4/3 0 15 19/14 (-11/12,-10/11) 0 30 15/11 -10/11 1 2 11/8 (-1/1,-10/11) 0 30 18/13 -1/1 2 5 7/5 -10/11 1 30 24/17 -11/12 2 5 17/12 (-1/1,-10/11) 0 30 27/19 -10/11 1 10 10/7 -10/11 2 3 3/2 (-10/11,-8/9) 0 10 5/3 -8/9 3 6 22/13 0 15 39/23 -8/9 1 10 17/10 (-15/17,-22/25) 0 30 29/17 -8/9 1 30 12/7 -7/8 2 5 7/4 (-1/1,-8/9) 0 30 30/17 -8/9 2 1 23/13 -8/9 1 30 16/9 0 15 9/5 -8/9 1 10 20/11 -8/9 4 3 11/6 (-8/9,-15/17) 0 30 13/7 -22/25 1 30 15/8 -7/8 6 2 2/1 0 15 15/7 -6/7 7 2 13/6 (-6/7,-17/20) 0 30 11/5 -4/5 1 30 20/9 -6/7 4 3 9/4 (-6/7,-16/19) 0 10 7/3 -4/5 1 30 26/11 0 15 19/8 (-6/7,-5/6) 0 30 50/21 (-6/7,-4/5) 0 3 31/13 -6/7 1 30 12/5 -5/6 2 5 5/2 0 6 18/7 -5/6 2 5 13/5 -4/5 1 30 34/13 0 15 21/8 (-6/7,-4/5) 0 10 50/19 (-6/7,-4/5) 0 3 29/11 -4/5 1 30 37/14 (-13/16,-4/5) 0 30 45/17 -4/5 7 2 8/3 0 15 35/13 -4/5 3 6 27/10 (-4/5,-2/3) 0 10 46/17 0 15 19/7 -2/3 1 30 30/11 -1/1 4 1 11/4 (-1/1,-6/7) 0 30 14/5 0 15 17/6 (-9/11,-4/5) 0 30 3/1 -4/5 1 10 10/3 (-4/5,-2/3) 0 3 27/8 (-4/5,-2/3) 0 10 44/13 0 15 17/5 -4/5 1 30 7/2 (-1/1,-2/3) 0 30 18/5 -1/2 2 5 29/8 (-1/2,0/1) 0 30 40/11 0/1 4 3 11/3 -2/1 1 30 15/4 -1/1 10 2 19/5 -8/9 1 30 23/6 (-7/8,-6/7) 0 30 4/1 0 15 17/4 (-1/1,0/1) 0 30 30/7 -1/1 6 1 13/3 -6/7 1 30 9/2 (-4/5,-2/3) 0 10 5/1 -2/3 1 6 21/4 (-2/3,0/1) 0 10 16/3 0 15 11/2 (-1/1,-2/3) 0 30 17/3 0/1 1 30 6/1 -1/1 2 5 13/2 (-2/3,-1/2) 0 30 7/1 0/1 1 30 15/2 -1/1 6 2 8/1 0 15 9/1 -2/3 1 10 10/1 (-2/3,0/1) 0 3 1/0 (-1/1,0/1) 0 30 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(79,-90,36,-41) (1/1,7/6) -> (13/6,11/5) Hyperbolic Matrix(101,-120,16,-19) (7/6,6/5) -> (6/1,13/2) Hyperbolic Matrix(421,-510,298,-361) (6/5,17/14) -> (24/17,17/12) Glide Reflection Matrix(739,-900,280,-341) (17/14,11/9) -> (29/11,37/14) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(899,-1140,332,-421) (19/15,14/11) -> (46/17,19/7) Hyperbolic Matrix(259,-330,62,-79) (14/11,23/18) -> (4/1,17/4) Glide Reflection Matrix(821,-1050,484,-619) (23/18,9/7) -> (39/23,17/10) Hyperbolic Matrix(139,-180,78,-101) (9/7,4/3) -> (16/9,9/5) Hyperbolic Matrix(421,-570,178,-241) (4/3,19/14) -> (26/11,19/8) Glide Reflection Matrix(419,-570,308,-419) (19/14,15/11) -> (19/14,15/11) Reflection Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(259,-360,100,-139) (18/13,7/5) -> (18/7,13/5) Glide Reflection Matrix(319,-450,56,-79) (7/5,24/17) -> (17/3,6/1) Glide Reflection Matrix(359,-510,126,-179) (17/12,27/19) -> (17/6,3/1) Glide Reflection Matrix(379,-540,266,-379) (27/19,10/7) -> (27/19,10/7) Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(19,-30,12,-19) (3/2,5/3) -> (3/2,5/3) Reflection Matrix(479,-810,178,-301) (5/3,22/13) -> (8/3,35/13) Hyperbolic Matrix(301,-510,36,-61) (22/13,39/23) -> (8/1,9/1) Glide Reflection Matrix(581,-990,152,-259) (17/10,29/17) -> (19/5,23/6) Hyperbolic Matrix(421,-720,176,-301) (29/17,12/7) -> (31/13,12/5) Glide Reflection Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(239,-420,136,-239) (7/4,30/17) -> (7/4,30/17) Reflection Matrix(781,-1380,442,-781) (30/17,23/13) -> (30/17,23/13) Reflection Matrix(559,-990,214,-379) (23/13,16/9) -> (13/5,34/13) Glide Reflection Matrix(199,-360,110,-199) (9/5,20/11) -> (9/5,20/11) Reflection Matrix(559,-1020,154,-281) (20/11,11/6) -> (29/8,40/11) Hyperbolic Matrix(179,-330,32,-59) (11/6,13/7) -> (11/2,17/3) Glide Reflection Matrix(161,-300,22,-41) (13/7,15/8) -> (7/1,15/2) Glide Reflection Matrix(79,-150,10,-19) (15/8,2/1) -> (15/2,8/1) Glide Reflection Matrix(101,-210,38,-79) (2/1,15/7) -> (45/17,8/3) Hyperbolic Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(161,-360,72,-161) (20/9,9/4) -> (20/9,9/4) Reflection Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(319,-750,94,-221) (7/3,26/11) -> (44/13,17/5) Hyperbolic Matrix(101,-240,8,-19) (19/8,50/21) -> (10/1,1/0) Hyperbolic Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(401,-1050,76,-199) (34/13,21/8) -> (21/4,16/3) Hyperbolic Matrix(799,-2100,304,-799) (21/8,50/19) -> (21/8,50/19) Reflection Matrix(1259,-3330,476,-1259) (37/14,45/17) -> (37/14,45/17) Reflection Matrix(701,-1890,260,-701) (35/13,27/10) -> (35/13,27/10) Reflection Matrix(899,-2430,266,-719) (27/10,46/17) -> (27/8,44/13) Glide Reflection Matrix(419,-1140,154,-419) (19/7,30/11) -> (19/7,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(139,-390,36,-101) (14/5,17/6) -> (23/6,4/1) Hyperbolic Matrix(19,-60,6,-19) (3/1,10/3) -> (3/1,10/3) Reflection Matrix(161,-540,48,-161) (10/3,27/8) -> (10/3,27/8) Reflection Matrix(79,-270,12,-41) (17/5,7/2) -> (13/2,7/1) Hyperbolic Matrix(121,-450,32,-119) (11/3,15/4) -> (15/4,19/5) Parabolic Matrix(239,-1020,56,-239) (17/4,30/7) -> (17/4,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(19,-90,4,-19) (9/2,5/1) -> (9/2,5/1) Reflection Matrix(41,-210,8,-41) (5/1,21/4) -> (5/1,21/4) Reflection Matrix(19,-180,2,-19) (9/1,10/1) -> (9/1,10/1) 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) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(29,28,-30,-29) (0/1,1/1) -> (-1/1,-14/15) Matrix(79,-90,36,-41) -> Matrix(71,66,-85,-79) Matrix(101,-120,16,-19) -> Matrix(37,34,-49,-45) Matrix(421,-510,298,-361) -> Matrix(241,220,-264,-241) *** -> (-11/12,-10/11) Matrix(739,-900,280,-341) -> Matrix(51,46,-61,-55) Matrix(121,-150,96,-119) -> Matrix(1,0,0,1) Matrix(899,-1140,332,-421) -> Matrix(9,8,-8,-7) -1/1 Matrix(259,-330,62,-79) -> Matrix(35,32,-47,-43) Matrix(821,-1050,484,-619) -> Matrix(261,238,-295,-269) Matrix(139,-180,78,-101) -> Matrix(85,78,-97,-89) Matrix(421,-570,178,-241) -> Matrix(17,16,-18,-17) *** -> (-1/1,-8/9) Matrix(419,-570,308,-419) -> Matrix(241,220,-264,-241) (19/14,15/11) -> (-11/12,-10/11) Matrix(241,-330,176,-241) -> Matrix(21,20,-22,-21) (15/11,11/8) -> (-1/1,-10/11) Matrix(521,-720,144,-199) -> Matrix(11,10,-21,-19) Matrix(259,-360,100,-139) -> Matrix(59,54,-71,-65) Matrix(319,-450,56,-79) -> Matrix(11,10,-23,-21) Matrix(359,-510,126,-179) -> Matrix(103,94,-126,-115) Matrix(379,-540,266,-379) -> Matrix(351,320,-385,-351) (27/19,10/7) -> (-32/35,-10/11) Matrix(41,-60,28,-41) -> Matrix(89,80,-99,-89) (10/7,3/2) -> (-10/11,-8/9) Matrix(19,-30,12,-19) -> Matrix(89,80,-99,-89) (3/2,5/3) -> (-10/11,-8/9) Matrix(479,-810,178,-301) -> Matrix(77,68,-94,-83) Matrix(301,-510,36,-61) -> Matrix(25,22,-42,-37) Matrix(581,-990,152,-259) -> Matrix(73,64,-81,-71) -8/9 Matrix(421,-720,176,-301) -> Matrix(93,82,-110,-97) Matrix(121,-210,34,-59) -> Matrix(7,6,-6,-5) -1/1 Matrix(239,-420,136,-239) -> Matrix(17,16,-18,-17) (7/4,30/17) -> (-1/1,-8/9) Matrix(781,-1380,442,-781) -> Matrix(271,240,-306,-271) (30/17,23/13) -> (-8/9,-15/17) Matrix(559,-990,214,-379) -> Matrix(23,20,-31,-27) Matrix(199,-360,110,-199) -> Matrix(55,48,-63,-55) (9/5,20/11) -> (-8/9,-6/7) Matrix(559,-1020,154,-281) -> Matrix(9,8,-35,-31) Matrix(179,-330,32,-59) -> Matrix(25,22,-42,-37) Matrix(161,-300,22,-41) -> Matrix(25,22,-17,-15) Matrix(79,-150,10,-19) -> Matrix(23,20,-31,-27) Matrix(101,-210,38,-79) -> Matrix(25,22,-33,-29) Matrix(181,-390,84,-181) -> Matrix(239,204,-280,-239) (15/7,13/6) -> (-6/7,-17/20) Matrix(299,-660,82,-181) -> Matrix(7,6,-6,-5) -1/1 Matrix(161,-360,72,-161) -> Matrix(113,96,-133,-113) (20/9,9/4) -> (-6/7,-16/19) Matrix(79,-180,18,-41) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(319,-750,94,-221) -> Matrix(19,16,-25,-21) -4/5 Matrix(101,-240,8,-19) -> Matrix(7,6,-13,-11) Matrix(1259,-3000,478,-1139) -> Matrix(11,10,-12,-11) *** -> (-1/1,-5/6) Matrix(61,-150,24,-59) -> Matrix(1,0,0,1) Matrix(401,-1050,76,-199) -> Matrix(7,6,-13,-11) Matrix(799,-2100,304,-799) -> Matrix(29,24,-35,-29) (21/8,50/19) -> (-6/7,-4/5) Matrix(1259,-3330,476,-1259) -> Matrix(129,104,-160,-129) (37/14,45/17) -> (-13/16,-4/5) Matrix(701,-1890,260,-701) -> Matrix(11,8,-15,-11) (35/13,27/10) -> (-4/5,-2/3) Matrix(899,-2430,266,-719) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(419,-1140,154,-419) -> Matrix(5,4,-6,-5) (19/7,30/11) -> (-1/1,-2/3) Matrix(241,-660,88,-241) -> Matrix(13,12,-14,-13) (30/11,11/4) -> (-1/1,-6/7) Matrix(119,-330,22,-61) -> Matrix(5,4,-4,-3) -1/1 Matrix(139,-390,36,-101) -> Matrix(31,26,-37,-31) (-1/1,-5/6).(-6/7,-4/5) Matrix(19,-60,6,-19) -> Matrix(11,8,-15,-11) (3/1,10/3) -> (-4/5,-2/3) Matrix(161,-540,48,-161) -> Matrix(11,8,-15,-11) (10/3,27/8) -> (-4/5,-2/3) Matrix(79,-270,12,-41) -> Matrix(5,4,-9,-7) -2/3 Matrix(121,-450,32,-119) -> Matrix(9,10,-10,-11) -1/1 Matrix(239,-1020,56,-239) -> Matrix(-1,0,2,1) (17/4,30/7) -> (-1/1,0/1) Matrix(181,-780,42,-181) -> Matrix(13,12,-14,-13) (30/7,13/3) -> (-1/1,-6/7) Matrix(19,-90,4,-19) -> Matrix(11,8,-15,-11) (9/2,5/1) -> (-4/5,-2/3) Matrix(41,-210,8,-41) -> Matrix(-1,0,3,1) (5/1,21/4) -> (-2/3,0/1) Matrix(19,-180,2,-19) -> Matrix(-1,0,3,1) (9/1,10/1) -> (-2/3,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.