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 0/1 -9/1 0/1 1/1 1/0 -8/1 -1/1 -1/2 0/1 -15/2 0/1 -7/1 0/1 1/0 -13/2 1/1 1/0 -6/1 -1/1 0/1 1/0 -17/3 -1/1 1/0 -11/2 -1/1 1/0 -5/1 -1/2 1/0 -24/5 -1/1 -1/2 0/1 -19/4 -3/5 -1/2 -14/3 -1/3 -1/4 0/1 -9/2 -1/1 -1/2 0/1 -22/5 -1/1 -2/3 -1/2 -35/8 -1/2 -13/3 -1/1 -1/2 -30/7 -1/2 -17/4 -1/2 -1/3 -21/5 -1/1 -1/2 0/1 -4/1 -1/2 -1/3 0/1 -15/4 0/1 -26/7 0/1 1/4 1/3 -37/10 0/1 1/0 -11/3 1/1 1/0 -7/2 -1/2 0/1 -17/5 -1/3 -1/4 -61/18 -1/4 0/1 -44/13 -1/2 -1/3 0/1 -27/8 -1/3 -1/4 0/1 -10/3 0/1 -33/10 0/1 1/1 1/0 -23/7 0/1 1/0 -13/4 -1/1 1/0 -16/5 -1/1 -3/4 -2/3 -3/1 -1/2 -1/3 0/1 -17/6 -1/2 -1/3 -14/5 -1/2 -1/3 0/1 -39/14 -1/2 -2/5 -1/3 -25/9 -1/2 -3/8 -11/4 -3/8 -1/3 -30/11 -1/3 -19/7 -1/3 -7/22 -27/10 -1/3 -4/13 -3/10 -8/3 -1/3 -2/7 -1/4 -37/14 -1/4 0/1 -29/11 -1/4 -2/9 -50/19 0/1 -71/27 -1/1 1/0 -21/8 -1/2 -1/3 0/1 -55/21 -1/2 -1/4 -89/34 -2/3 -1/2 -34/13 -2/5 -3/8 -1/3 -13/5 -1/3 -3/10 -5/2 -1/4 -17/7 -1/5 -1/6 -29/12 -1/4 0/1 -12/5 -1/4 -1/5 0/1 -31/13 -2/11 -1/6 -50/21 0/1 -69/29 -1/2 -1/3 0/1 -19/8 -1/4 -1/5 -26/11 -1/5 -2/11 -1/6 -59/25 -4/23 -1/6 -33/14 -1/6 -1/7 0/1 -7/3 -1/6 0/1 -30/13 0/1 -23/10 0/1 1/4 -16/7 -1/1 0/1 1/0 -9/4 -1/2 -1/3 0/1 -29/13 -2/5 -3/8 -20/9 -1/3 -11/5 -3/11 -1/4 -24/11 -1/4 -1/5 0/1 -13/6 -1/3 -1/4 -15/7 -1/4 -2/1 -1/4 -1/5 0/1 -15/8 -1/5 -28/15 -1/5 -6/31 -5/26 -13/7 -1/5 -1/6 -11/6 -1/5 -1/6 -20/11 -1/5 -9/5 -1/5 -2/11 -1/6 -34/19 -2/11 -3/17 -1/6 -59/33 -1/6 0/1 -25/14 -1/6 -16/9 -1/5 -1/6 0/1 -39/22 -1/5 -2/11 -1/6 -23/13 -2/11 -1/6 -30/17 -1/6 -7/4 -1/6 0/1 -19/11 -1/3 -1/4 -50/29 -1/5 -31/18 -1/6 0/1 -12/7 -1/5 -1/6 0/1 -29/17 -1/4 -2/9 -75/44 -1/5 -46/27 -1/5 -2/11 -1/6 -17/10 -1/5 -1/6 -39/23 -1/6 -1/7 0/1 -22/13 -1/4 -1/5 0/1 -27/16 -1/5 -2/11 -1/6 -5/3 -1/4 -1/6 -33/20 -1/5 -2/11 -1/6 -61/37 -6/35 -1/6 -28/17 -1/6 -2/13 -1/7 -23/14 -1/4 0/1 -41/25 -1/4 -1/5 -100/61 0/1 -59/36 -1/4 0/1 -18/11 -1/4 -1/5 0/1 -31/19 -1/4 0/1 -75/46 -1/5 -44/27 -1/5 -3/16 -2/11 -13/8 -1/4 -1/5 -21/13 -1/5 -2/11 -1/6 -50/31 -1/5 -29/18 -4/21 -3/16 -37/23 -7/38 -2/11 -45/28 -2/11 -8/5 -2/11 -3/17 -1/6 -35/22 -1/6 -27/17 -3/17 -4/23 -1/6 -46/29 -5/29 -11/64 -6/35 -19/12 -9/53 -1/6 -30/19 -1/6 -11/7 -1/6 -5/31 -36/23 -1/6 -2/13 -1/7 -61/39 -2/11 -1/6 -25/16 -1/6 -14/9 -1/6 -3/19 -2/13 -3/2 -1/6 -1/7 0/1 -16/11 -1/6 -3/19 -2/13 -61/42 -5/32 -2/13 -45/31 -2/13 -29/20 -2/13 -3/20 -13/9 -1/6 -1/7 -36/25 -1/6 -1/7 0/1 -59/41 -1/6 -4/25 -23/16 -1/6 -2/13 -10/7 -1/7 -37/26 -3/22 -2/15 -64/45 -2/15 -5/38 -3/23 -91/64 -6/47 -1/8 -27/19 -1/7 -1/8 0/1 -17/12 -1/7 -1/8 -24/17 -1/7 -1/8 0/1 -55/39 -1/6 -1/8 -31/22 -1/8 -2/17 -7/5 -1/6 0/1 -39/28 -1/6 -1/7 0/1 -32/23 -1/5 -1/6 0/1 -121/87 -8/47 -1/6 -210/151 -1/6 -89/64 -1/6 -6/37 -57/41 -1/6 -1/7 0/1 -25/18 -1/6 -43/31 -1/6 -3/19 -61/44 -1/6 -2/13 -18/13 -1/6 -2/13 -1/7 -29/21 -1/6 -2/13 -40/29 -1/7 -11/8 -1/6 -1/7 -15/11 -1/7 -19/14 -1/7 -3/22 -4/3 -1/7 -1/8 0/1 -17/13 -5/34 -1/7 -30/23 -1/7 -13/10 -1/7 -5/36 -9/7 -1/7 -3/22 -2/15 -41/32 -3/23 -1/8 -32/25 -1/7 -4/29 -3/22 -23/18 -7/52 -2/15 -14/11 -2/15 -3/23 -1/8 -5/4 -1/8 -16/13 -1/8 -2/17 -1/9 -27/22 -2/17 -3/26 -1/9 -11/9 -1/9 -1/10 -39/32 -1/7 -1/8 0/1 -28/23 -1/8 -1/9 0/1 -45/37 -1/8 -17/14 -1/8 -1/9 -6/5 -1/8 -1/9 0/1 -19/16 -1/8 -3/25 -32/27 -3/26 -4/35 -1/9 -13/11 -1/9 -1/10 -7/6 -1/8 0/1 -15/13 -1/8 -23/20 -1/8 -2/17 -8/7 -1/8 -1/9 0/1 -9/8 -1/8 -2/17 -1/9 -1/1 -1/10 0/1 0/1 0/1 1/1 0/1 1/10 8/7 0/1 1/9 1/8 15/13 1/8 7/6 0/1 1/8 6/5 0/1 1/9 1/8 17/14 1/9 1/8 28/23 0/1 1/9 1/8 39/32 0/1 1/8 1/7 11/9 1/10 1/9 5/4 1/8 19/15 7/54 3/23 14/11 1/8 3/23 2/15 23/18 2/15 7/52 32/25 3/22 4/29 1/7 41/32 1/8 3/23 9/7 2/15 3/22 1/7 13/10 5/36 1/7 30/23 1/7 17/13 1/7 5/34 4/3 0/1 1/8 1/7 19/14 3/22 1/7 15/11 1/7 11/8 1/7 1/6 29/21 2/13 1/6 18/13 1/7 2/13 1/6 61/44 2/13 1/6 43/31 3/19 1/6 25/18 1/6 32/23 0/1 1/6 1/5 7/5 0/1 1/6 31/22 2/17 1/8 24/17 0/1 1/8 1/7 17/12 1/8 1/7 27/19 0/1 1/8 1/7 10/7 1/7 33/23 1/7 4/27 3/20 23/16 2/13 1/6 13/9 1/7 1/6 3/2 0/1 1/7 1/6 17/11 1/7 1/6 14/9 2/13 3/19 1/6 25/16 1/6 61/39 1/6 2/11 36/23 1/7 2/13 1/6 11/7 5/31 1/6 30/19 1/6 19/12 1/6 9/53 27/17 1/6 4/23 3/17 89/56 2/13 1/6 62/39 1/6 5/29 4/23 35/22 1/6 8/5 1/6 3/17 2/11 37/23 2/11 7/38 29/18 3/16 4/21 21/13 1/6 2/11 1/5 13/8 1/5 1/4 31/19 0/1 1/4 18/11 0/1 1/5 1/4 59/36 0/1 1/4 41/25 1/5 1/4 23/14 0/1 1/4 28/17 1/7 2/13 1/6 5/3 1/6 1/4 22/13 0/1 1/5 1/4 39/23 0/1 1/7 1/6 17/10 1/6 1/5 29/17 2/9 1/4 12/7 0/1 1/6 1/5 7/4 0/1 1/6 30/17 1/6 23/13 1/6 2/11 62/35 1/6 3/17 2/11 39/22 1/6 2/11 1/5 16/9 0/1 1/6 1/5 25/14 1/6 59/33 0/1 1/6 34/19 1/6 3/17 2/11 9/5 1/6 2/11 1/5 29/16 3/16 4/21 20/11 1/5 31/17 0/1 1/6 11/6 1/6 1/5 13/7 1/6 1/5 15/8 1/5 17/9 1/5 5/24 2/1 0/1 1/5 1/4 17/8 1/5 1/4 15/7 1/4 13/6 1/4 1/3 11/5 1/4 3/11 20/9 1/3 29/13 3/8 2/5 9/4 0/1 1/3 1/2 16/7 0/1 1/1 1/0 23/10 -1/4 0/1 30/13 0/1 7/3 0/1 1/6 33/14 0/1 1/7 1/6 59/25 1/6 4/23 26/11 1/6 2/11 1/5 19/8 1/5 1/4 69/29 0/1 1/3 1/2 50/21 0/1 31/13 1/6 2/11 12/5 0/1 1/5 1/4 5/2 1/4 18/7 1/4 2/7 1/3 31/12 1/4 2/7 75/29 2/7 44/17 2/7 5/17 3/10 13/5 3/10 1/3 34/13 1/3 3/8 2/5 89/34 1/2 2/3 55/21 1/4 1/2 21/8 0/1 1/3 1/2 71/27 1/1 1/0 50/19 0/1 29/11 2/9 1/4 37/14 0/1 1/4 45/17 1/4 8/3 1/4 2/7 1/3 35/13 1/4 3/10 62/23 5/17 8/27 3/10 151/56 26/87 3/10 240/89 3/10 89/33 3/10 16/53 27/10 3/10 4/13 1/3 46/17 4/13 5/16 1/3 19/7 7/22 1/3 30/11 1/3 11/4 1/3 3/8 14/5 0/1 1/3 1/2 45/16 1/3 31/11 4/11 3/8 17/6 1/3 1/2 3/1 0/1 1/3 1/2 16/5 2/3 3/4 1/1 45/14 1/1 29/9 0/1 1/0 13/4 1/1 1/0 23/7 0/1 1/0 10/3 0/1 37/11 0/1 1/4 27/8 0/1 1/4 1/3 44/13 0/1 1/3 1/2 105/31 0/1 61/18 0/1 1/4 17/5 1/4 1/3 58/17 1/3 4/11 3/8 41/12 3/7 1/2 24/7 0/1 1/3 1/2 7/2 0/1 1/2 18/5 0/1 1/2 1/1 29/8 0/1 1/2 40/11 1/1 11/3 -1/1 1/0 15/4 0/1 19/5 1/6 1/5 23/6 0/1 1/6 27/7 1/5 2/9 1/4 31/8 1/4 4/15 4/1 0/1 1/3 1/2 21/5 0/1 1/2 1/1 17/4 1/3 1/2 30/7 1/2 13/3 1/2 1/1 35/8 1/2 22/5 1/2 2/3 1/1 31/7 2/3 3/4 9/2 0/1 1/2 1/1 14/3 0/1 1/4 1/3 33/7 2/5 3/7 1/2 19/4 1/2 3/5 24/5 0/1 1/2 1/1 29/6 2/5 1/2 5/1 1/2 1/0 21/4 0/1 1/2 1/1 16/3 1/2 2/3 1/1 11/2 1/1 1/0 17/3 1/1 1/0 23/4 2/1 1/0 29/5 4/1 1/0 6/1 0/1 1/1 1/0 19/3 -3/1 1/0 13/2 -1/1 1/0 7/1 0/1 1/0 15/2 0/1 23/3 0/1 1/6 8/1 0/1 1/2 1/1 9/1 -1/1 0/1 1/0 10/1 0/1 11/1 1/1 1/0 1/0 0/1 1/0 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(1,0,-4,1) Matrix(119,1140,50,479) -> Matrix(1,0,2,1) Matrix(61,510,36,301) -> Matrix(1,0,6,1) Matrix(61,480,-38,-299) -> Matrix(5,2,-28,-11) Matrix(119,870,-74,-541) -> Matrix(7,-2,-38,11) Matrix(59,390,18,119) -> Matrix(1,0,0,1) Matrix(61,390,-28,-179) -> Matrix(1,0,-4,1) Matrix(121,690,-84,-479) -> Matrix(1,0,-6,1) Matrix(59,330,32,179) -> Matrix(1,0,6,1) Matrix(61,330,-22,-119) -> Matrix(3,2,-8,-5) Matrix(299,1440,-212,-1021) -> Matrix(1,0,-6,1) Matrix(301,1440,88,421) -> Matrix(1,0,4,1) Matrix(241,1140,-152,-719) -> Matrix(13,6,-76,-35) Matrix(59,270,26,119) -> Matrix(1,0,4,1) Matrix(61,270,-54,-239) -> Matrix(3,2,-26,-17) Matrix(239,1050,150,659) -> Matrix(7,4,40,23) Matrix(419,1830,302,1319) -> Matrix(5,2,32,13) Matrix(181,780,42,181) -> Matrix(3,2,4,3) Matrix(239,1020,56,239) -> Matrix(5,2,12,5) Matrix(241,1020,142,601) -> Matrix(1,0,8,1) Matrix(179,750,100,419) -> Matrix(3,2,16,11) Matrix(119,450,-32,-121) -> Matrix(1,0,6,1) Matrix(899,3330,-632,-2341) -> Matrix(3,-2,-22,15) Matrix(479,1770,292,1079) -> Matrix(1,0,4,1) Matrix(59,210,-34,-121) -> Matrix(1,0,-4,1) Matrix(61,210,-52,-179) -> Matrix(1,0,-6,1) Matrix(1079,3660,778,2639) -> Matrix(9,2,58,13) Matrix(1081,3660,-744,-2519) -> Matrix(3,2,-20,-13) Matrix(719,2430,266,899) -> Matrix(13,4,42,13) Matrix(179,600,-54,-181) -> Matrix(1,0,4,1) Matrix(301,990,128,421) -> Matrix(1,0,6,1) Matrix(119,390,18,59) -> Matrix(1,0,0,1) Matrix(241,780,-148,-479) -> Matrix(1,0,-4,1) Matrix(181,570,-114,-359) -> Matrix(9,4,-52,-23) Matrix(179,510,126,359) -> Matrix(1,0,10,1) Matrix(361,1020,-212,-599) -> Matrix(5,2,-28,-11) Matrix(419,1170,236,659) -> Matrix(1,0,8,1) Matrix(959,2670,366,1019) -> Matrix(5,2,12,5) Matrix(241,660,88,241) -> Matrix(17,6,48,17) Matrix(419,1140,154,419) -> Matrix(43,14,132,43) Matrix(299,810,-244,-661) -> Matrix(19,6,-168,-53) Matrix(301,810,-178,-479) -> Matrix(7,2,-32,-9) Matrix(181,480,-158,-419) -> Matrix(7,2,-60,-17) Matrix(1079,2850,-750,-1981) -> Matrix(7,2,-46,-13) Matrix(1139,3000,478,1259) -> Matrix(1,0,10,1) Matrix(3479,9150,-2122,-5581) -> Matrix(1,0,-4,1) Matrix(1141,3000,936,2461) -> Matrix(1,0,10,1) Matrix(481,1260,92,241) -> Matrix(1,0,4,1) Matrix(779,2040,160,419) -> Matrix(1,0,4,1) Matrix(3359,8790,-2362,-6181) -> Matrix(9,4,-70,-31) Matrix(241,630,184,481) -> Matrix(5,2,32,13) Matrix(59,150,-24,-61) -> Matrix(7,2,-32,-9) Matrix(359,870,-248,-601) -> Matrix(11,2,-72,-13) Matrix(361,870,100,241) -> Matrix(1,0,6,1) Matrix(301,720,176,421) -> Matrix(1,0,10,1) Matrix(1259,3000,478,1139) -> Matrix(1,0,10,1) Matrix(479,1140,50,119) -> Matrix(1,0,2,1) Matrix(1261,3000,984,2341) -> Matrix(7,2,52,15) Matrix(241,570,178,421) -> Matrix(11,2,82,15) Matrix(1499,3540,838,1979) -> Matrix(23,4,132,23) Matrix(1679,3960,-1018,-2401) -> Matrix(13,2,-72,-11) Matrix(599,1410,178,419) -> Matrix(1,0,10,1) Matrix(181,420,78,181) -> Matrix(1,0,12,1) Matrix(599,1380,260,599) -> Matrix(1,0,-8,1) Matrix(301,690,236,541) -> Matrix(1,-2,8,-15) Matrix(119,270,26,59) -> Matrix(1,0,4,1) Matrix(241,540,54,121) -> Matrix(1,0,4,1) Matrix(539,1200,296,659) -> Matrix(5,2,22,9) Matrix(421,930,-244,-539) -> Matrix(7,2,-32,-9) Matrix(301,660,192,421) -> Matrix(9,2,58,13) Matrix(181,390,84,181) -> Matrix(7,2,24,7) Matrix(241,510,-198,-419) -> Matrix(1,0,-4,1) Matrix(239,450,-128,-241) -> Matrix(29,6,-150,-31) Matrix(661,1230,194,361) -> Matrix(11,2,38,7) Matrix(179,330,32,59) -> Matrix(1,0,6,1) Matrix(361,660,-262,-479) -> Matrix(11,2,-72,-13) Matrix(481,870,-298,-539) -> Matrix(1,0,0,1) Matrix(419,750,100,179) -> Matrix(11,2,16,3) Matrix(1979,3540,838,1499) -> Matrix(23,4,132,23) Matrix(1679,3000,1074,1919) -> Matrix(11,2,60,11) Matrix(421,750,270,481) -> Matrix(13,2,84,13) Matrix(541,960,102,181) -> Matrix(11,2,16,3) Matrix(661,1170,-474,-839) -> Matrix(11,2,-72,-13) Matrix(781,1380,442,781) -> Matrix(23,4,132,23) Matrix(239,420,136,239) -> Matrix(1,0,12,1) Matrix(1201,2070,662,1141) -> Matrix(21,4,110,21) Matrix(541,930,210,361) -> Matrix(11,2,38,7) Matrix(421,720,176,301) -> Matrix(1,0,10,1) Matrix(2041,3480,634,1081) -> Matrix(9,2,4,1) Matrix(1919,3270,598,1019) -> Matrix(21,4,26,5) Matrix(601,1020,142,241) -> Matrix(1,0,8,1) Matrix(301,510,36,61) -> Matrix(1,0,6,1) Matrix(179,300,-108,-181) -> Matrix(1,0,0,1) Matrix(3241,5340,-2330,-3839) -> Matrix(13,2,-72,-11) Matrix(839,1380,656,1079) -> Matrix(15,2,112,15) Matrix(841,1380,220,361) -> Matrix(1,0,10,1) Matrix(1319,2160,952,1559) -> Matrix(9,2,58,13) Matrix(661,1080,478,781) -> Matrix(9,2,58,13) Matrix(2281,3720,810,1321) -> Matrix(19,4,52,11) Matrix(1859,3030,662,1079) -> Matrix(11,2,38,7) Matrix(241,390,186,301) -> Matrix(21,4,152,29) Matrix(1619,2610,446,719) -> Matrix(21,4,26,5) Matrix(839,1350,596,959) -> Matrix(11,2,104,19) Matrix(659,1050,150,239) -> Matrix(23,4,40,7) Matrix(1679,2670,-1208,-1921) -> Matrix(23,4,-144,-25) Matrix(721,1140,456,721) -> Matrix(107,18,636,107) Matrix(419,660,266,419) -> Matrix(61,10,372,61) Matrix(479,750,76,119) -> Matrix(13,2,6,1) Matrix(901,1410,154,241) -> Matrix(13,2,6,1) Matrix(1919,3000,1074,1679) -> Matrix(11,2,60,11) Matrix(481,750,270,421) -> Matrix(13,2,84,13) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(6301,9150,1860,2701) -> Matrix(13,2,84,13) Matrix(2461,3570,952,1381) -> Matrix(53,8,192,29) Matrix(3001,4320,1918,2761) -> Matrix(13,2,84,13) Matrix(419,600,-294,-421) -> Matrix(27,4,-196,-29) Matrix(3419,4860,2152,3059) -> Matrix(31,4,178,23) Matrix(359,510,126,179) -> Matrix(1,0,10,1) Matrix(361,510,298,421) -> Matrix(1,0,16,1) Matrix(4681,6600,1788,2521) -> Matrix(1,0,10,1) Matrix(959,1350,596,839) -> Matrix(19,2,104,11) Matrix(1681,2340,1380,1921) -> Matrix(1,0,14,1) Matrix(34319,47730,12726,17699) -> Matrix(237,40,788,133) Matrix(38161,53070,14152,19681) -> Matrix(267,44,892,147) Matrix(2999,4170,776,1079) -> Matrix(13,2,58,9) Matrix(1319,1830,302,419) -> Matrix(13,2,32,5) Matrix(2639,3660,778,1079) -> Matrix(13,2,58,9) Matrix(1559,2160,952,1319) -> Matrix(13,2,58,9) Matrix(781,1080,478,661) -> Matrix(13,2,58,9) Matrix(1261,1740,566,781) -> Matrix(27,4,74,11) Matrix(241,330,176,241) -> Matrix(13,2,84,13) Matrix(419,570,308,419) -> Matrix(43,6,308,43) Matrix(421,570,178,241) -> Matrix(15,2,82,11) Matrix(481,630,184,241) -> Matrix(13,2,32,5) Matrix(781,1020,598,781) -> Matrix(69,10,476,69) Matrix(599,780,460,599) -> Matrix(71,10,504,71) Matrix(301,390,186,241) -> Matrix(29,4,152,21) Matrix(2341,3000,984,1261) -> Matrix(15,2,52,7) Matrix(2881,3690,844,1081) -> Matrix(1,0,10,1) Matrix(1079,1380,656,839) -> Matrix(15,2,112,15) Matrix(541,690,236,301) -> Matrix(15,2,-8,-1) Matrix(119,150,-96,-121) -> Matrix(31,4,-256,-33) Matrix(1319,1620,390,479) -> Matrix(17,2,42,5) Matrix(2461,3000,936,1141) -> Matrix(1,0,10,1) Matrix(2881,3510,1626,1981) -> Matrix(15,2,82,11) Matrix(839,1020,394,479) -> Matrix(17,2,76,9) Matrix(421,510,298,361) -> Matrix(1,0,16,1) Matrix(479,570,100,119) -> Matrix(1,0,10,1) Matrix(1619,1920,1264,1499) -> Matrix(1,0,16,1) Matrix(481,570,254,301) -> Matrix(35,4,166,19) Matrix(181,210,156,181) -> Matrix(1,0,16,1) Matrix(1381,1590,522,601) -> Matrix(17,2,76,9) Matrix(241,270,108,121) -> Matrix(17,2,42,5) Matrix(1,0,2,1) -> Matrix(1,0,20,1) Matrix(239,-270,54,-61) -> Matrix(17,-2,26,-3) Matrix(419,-480,158,-181) -> Matrix(17,-2,60,-7) Matrix(179,-210,52,-61) -> Matrix(1,0,-6,1) Matrix(419,-510,198,-241) -> Matrix(1,0,-4,1) Matrix(121,-150,96,-119) -> Matrix(33,-4,256,-31) Matrix(899,-1140,332,-421) -> Matrix(107,-14,344,-45) Matrix(479,-660,262,-361) -> Matrix(13,-2,72,-11) Matrix(1921,-2670,1208,-1679) -> Matrix(25,-4,144,-23) Matrix(839,-1170,474,-661) -> Matrix(13,-2,72,-11) Matrix(1021,-1440,212,-299) -> Matrix(1,0,-6,1) Matrix(421,-600,294,-419) -> Matrix(29,-4,196,-27) Matrix(961,-1380,250,-359) -> Matrix(13,-2,72,-11) Matrix(479,-690,84,-121) -> Matrix(1,0,-6,1) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(27,-4,88,-13) Matrix(719,-1140,152,-241) -> Matrix(35,-6,76,-13) Matrix(9361,-14880,3472,-5519) -> Matrix(117,-20,392,-67) Matrix(299,-480,38,-61) -> Matrix(11,-2,28,-5) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(479,-780,148,-241) -> Matrix(1,0,-4,1) Matrix(421,-690,36,-59) -> Matrix(1,0,-4,1) Matrix(781,-1290,290,-479) -> Matrix(9,-2,32,-7) Matrix(479,-810,178,-301) -> Matrix(9,-2,32,-7) Matrix(599,-1020,212,-361) -> Matrix(11,-2,28,-5) Matrix(121,-210,34,-59) -> Matrix(1,0,-4,1) Matrix(241,-450,128,-239) -> Matrix(31,-6,150,-29) Matrix(179,-390,28,-61) -> Matrix(1,0,-4,1) Matrix(299,-660,82,-181) -> Matrix(7,-2,4,-1) Matrix(1921,-4530,712,-1679) -> Matrix(27,-4,88,-13) Matrix(61,-150,24,-59) -> Matrix(9,-2,32,-7) Matrix(3061,-7920,904,-2339) -> Matrix(7,-2,4,-1) Matrix(539,-1410,138,-361) -> Matrix(5,-2,18,-7) Matrix(479,-1260,46,-121) -> Matrix(1,0,0,1) Matrix(659,-1740,114,-301) -> Matrix(7,-2,4,-1) Matrix(119,-330,22,-61) -> Matrix(5,-2,8,-3) Matrix(179,-570,38,-121) -> Matrix(3,-2,8,-5) Matrix(181,-600,54,-179) -> Matrix(1,0,4,1) Matrix(121,-450,32,-119) -> Matrix(1,0,6,1) Matrix(61,-450,8,-59) -> Matrix(1,0,6,1) 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 -9/2 -4/1 -15/4 -10/3 -20/9 -2/1 -15/8 -3/2 0/1 1/1 6/5 5/4 15/11 3/2 30/19 18/11 5/3 25/14 9/5 2/1 15/7 20/9 30/13 12/5 5/2 3/1 10/3 7/2 15/4 4/1 30/7 35/8 9/2 19/4 5/1 6/1 13/2 7/1 15/2 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 0/1 1/0 -13/2 1/1 1/0 -6/1 -1/1 0/1 1/0 -5/1 -1/2 1/0 -24/5 -1/1 -1/2 0/1 -19/4 -3/5 -1/2 -14/3 -1/3 -1/4 0/1 -9/2 -1/1 -1/2 0/1 -22/5 -1/1 -2/3 -1/2 -13/3 -1/1 -1/2 -4/1 -1/2 -1/3 0/1 -15/4 0/1 -26/7 0/1 1/4 1/3 -11/3 1/1 1/0 -7/2 -1/2 0/1 -10/3 0/1 -13/4 -1/1 1/0 -16/5 -1/1 -3/4 -2/3 -3/1 -1/2 -1/3 0/1 -5/2 -1/4 -12/5 -1/4 -1/5 0/1 -19/8 -1/4 -1/5 -26/11 -1/5 -2/11 -1/6 -7/3 -1/6 0/1 -16/7 -1/1 0/1 1/0 -9/4 -1/2 -1/3 0/1 -29/13 -2/5 -3/8 -20/9 -1/3 -11/5 -3/11 -1/4 -24/11 -1/4 -1/5 0/1 -13/6 -1/3 -1/4 -15/7 -1/4 -2/1 -1/4 -1/5 0/1 -15/8 -1/5 -13/7 -1/5 -1/6 -11/6 -1/5 -1/6 -20/11 -1/5 -9/5 -1/5 -2/11 -1/6 -25/14 -1/6 -16/9 -1/5 -1/6 0/1 -23/13 -2/11 -1/6 -30/17 -1/6 -7/4 -1/6 0/1 -19/11 -1/3 -1/4 -50/29 -1/5 -31/18 -1/6 0/1 -12/7 -1/5 -1/6 0/1 -5/3 -1/4 -1/6 -18/11 -1/4 -1/5 0/1 -31/19 -1/4 0/1 -44/27 -1/5 -3/16 -2/11 -13/8 -1/4 -1/5 -21/13 -1/5 -2/11 -1/6 -50/31 -1/5 -29/18 -4/21 -3/16 -37/23 -7/38 -2/11 -45/28 -2/11 -8/5 -2/11 -3/17 -1/6 -35/22 -1/6 -27/17 -3/17 -4/23 -1/6 -46/29 -5/29 -11/64 -6/35 -19/12 -9/53 -1/6 -30/19 -1/6 -11/7 -1/6 -5/31 -36/23 -1/6 -2/13 -1/7 -25/16 -1/6 -14/9 -1/6 -3/19 -2/13 -3/2 -1/6 -1/7 0/1 -16/11 -1/6 -3/19 -2/13 -13/9 -1/6 -1/7 -23/16 -1/6 -2/13 -10/7 -1/7 -17/12 -1/7 -1/8 -7/5 -1/6 0/1 -32/23 -1/5 -1/6 0/1 -25/18 -1/6 -18/13 -1/6 -2/13 -1/7 -29/21 -1/6 -2/13 -40/29 -1/7 -11/8 -1/6 -1/7 -15/11 -1/7 -19/14 -1/7 -3/22 -4/3 -1/7 -1/8 0/1 -17/13 -5/34 -1/7 -30/23 -1/7 -13/10 -1/7 -5/36 -9/7 -1/7 -3/22 -2/15 -5/4 -1/8 -6/5 -1/8 -1/9 0/1 -19/16 -1/8 -3/25 -13/11 -1/9 -1/10 -7/6 -1/8 0/1 -15/13 -1/8 -8/7 -1/8 -1/9 0/1 -9/8 -1/8 -2/17 -1/9 -1/1 -1/10 0/1 0/1 0/1 1/1 0/1 1/10 8/7 0/1 1/9 1/8 15/13 1/8 7/6 0/1 1/8 6/5 0/1 1/9 1/8 5/4 1/8 9/7 2/15 3/22 1/7 13/10 5/36 1/7 4/3 0/1 1/8 1/7 19/14 3/22 1/7 15/11 1/7 11/8 1/7 1/6 29/21 2/13 1/6 18/13 1/7 2/13 1/6 25/18 1/6 7/5 0/1 1/6 10/7 1/7 13/9 1/7 1/6 3/2 0/1 1/7 1/6 17/11 1/7 1/6 14/9 2/13 3/19 1/6 25/16 1/6 36/23 1/7 2/13 1/6 11/7 5/31 1/6 30/19 1/6 19/12 1/6 9/53 27/17 1/6 4/23 3/17 35/22 1/6 8/5 1/6 3/17 2/11 37/23 2/11 7/38 29/18 3/16 4/21 21/13 1/6 2/11 1/5 13/8 1/5 1/4 31/19 0/1 1/4 18/11 0/1 1/5 1/4 5/3 1/6 1/4 12/7 0/1 1/6 1/5 7/4 0/1 1/6 16/9 0/1 1/6 1/5 25/14 1/6 9/5 1/6 2/11 1/5 29/16 3/16 4/21 20/11 1/5 31/17 0/1 1/6 11/6 1/6 1/5 2/1 0/1 1/5 1/4 15/7 1/4 13/6 1/4 1/3 11/5 1/4 3/11 20/9 1/3 29/13 3/8 2/5 9/4 0/1 1/3 1/2 16/7 0/1 1/1 1/0 23/10 -1/4 0/1 30/13 0/1 7/3 0/1 1/6 26/11 1/6 2/11 1/5 19/8 1/5 1/4 12/5 0/1 1/5 1/4 5/2 1/4 3/1 0/1 1/3 1/2 16/5 2/3 3/4 1/1 13/4 1/1 1/0 23/7 0/1 1/0 10/3 0/1 17/5 1/4 1/3 41/12 3/7 1/2 24/7 0/1 1/3 1/2 7/2 0/1 1/2 18/5 0/1 1/2 1/1 29/8 0/1 1/2 40/11 1/1 11/3 -1/1 1/0 15/4 0/1 19/5 1/6 1/5 23/6 0/1 1/6 4/1 0/1 1/3 1/2 17/4 1/3 1/2 30/7 1/2 13/3 1/2 1/1 35/8 1/2 22/5 1/2 2/3 1/1 31/7 2/3 3/4 9/2 0/1 1/2 1/1 14/3 0/1 1/4 1/3 33/7 2/5 3/7 1/2 19/4 1/2 3/5 24/5 0/1 1/2 1/1 5/1 1/2 1/0 6/1 0/1 1/1 1/0 19/3 -3/1 1/0 13/2 -1/1 1/0 7/1 0/1 1/0 15/2 0/1 23/3 0/1 1/6 8/1 0/1 1/2 1/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(11,90,-6,-49) (-7/1,1/0) -> (-13/7,-11/6) 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(11,60,2,11) (-6/1,-5/1) -> (5/1,6/1) Hyperbolic Matrix(49,240,10,49) (-5/1,-24/5) -> (24/5,5/1) 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(131,570,-94,-409) (-22/5,-13/3) -> (-7/5,-32/23) Hyperbolic Matrix(71,300,-40,-169) (-13/3,-4/1) -> (-16/9,-23/13) Hyperbolic Matrix(119,450,-32,-121) (-4/1,-15/4) -> (-15/4,-26/7) Parabolic Matrix(349,1290,-214,-791) (-26/7,-11/3) -> (-31/19,-44/27) Hyperbolic Matrix(59,210,-34,-121) (-11/3,-7/2) -> (-7/4,-19/11) Hyperbolic Matrix(71,240,-50,-169) (-7/2,-10/3) -> (-10/7,-17/12) Hyperbolic Matrix(109,360,-76,-251) (-10/3,-13/4) -> (-23/16,-10/7) 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(11,30,4,11) (-3/1,-5/2) -> (5/2,3/1) Hyperbolic Matrix(49,120,20,49) (-5/2,-12/5) -> (12/5,5/2) Hyperbolic Matrix(251,600,-146,-349) (-12/5,-19/8) -> (-31/18,-12/7) Hyperbolic Matrix(241,570,178,421) (-19/8,-26/11) -> (4/3,19/14) Hyperbolic Matrix(229,540,148,349) (-26/11,-7/3) -> (17/11,14/9) Hyperbolic Matrix(131,300,-100,-229) (-7/3,-16/7) -> (-4/3,-17/13) 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(71,150,62,131) (-15/7,-2/1) -> (8/7,15/13) Hyperbolic Matrix(109,210,-68,-131) (-2/1,-15/8) -> (-45/28,-8/5) Hyperbolic Matrix(611,1140,-380,-709) (-15/8,-13/7) -> (-37/23,-45/28) 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(251,450,140,251) (-9/5,-25/14) -> (25/14,9/5) Hyperbolic Matrix(421,750,270,481) (-25/14,-16/9) -> (14/9,25/16) Hyperbolic Matrix(611,1080,142,251) (-23/13,-30/17) -> (30/7,13/3) Hyperbolic Matrix(409,720,96,169) (-30/17,-7/4) -> (17/4,30/7) Hyperbolic Matrix(1201,2070,662,1141) (-50/29,-31/18) -> (29/16,20/11) Hyperbolic Matrix(71,120,42,71) (-12/7,-5/3) -> (5/3,12/7) Hyperbolic Matrix(109,180,66,109) (-5/3,-18/11) -> (18/11,5/3) Hyperbolic Matrix(661,1080,478,781) (-18/11,-31/19) -> (29/21,18/13) 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(1249,2010,366,589) (-29/18,-37/23) -> (17/5,41/12) Hyperbolic Matrix(659,1050,150,239) (-8/5,-35/22) -> (35/8,22/5) Hyperbolic Matrix(1189,1890,748,1189) (-35/22,-27/17) -> (27/17,35/22) 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(1151,1800,736,1151) (-36/23,-25/16) -> (25/16,36/23) 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(311,450,132,191) (-16/11,-13/9) -> (7/3,26/11) Hyperbolic Matrix(229,330,34,49) (-13/9,-23/16) -> (13/2,7/1) Hyperbolic Matrix(191,270,-162,-229) (-17/12,-7/5) -> (-13/11,-7/6) Hyperbolic Matrix(949,1320,596,829) (-32/23,-25/18) -> (35/22,8/5) Hyperbolic Matrix(649,900,468,649) (-25/18,-18/13) -> (18/13,25/18) 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(551,720,238,311) (-17/13,-30/23) -> (30/13,7/3) Hyperbolic Matrix(829,1080,360,469) (-30/23,-13/10) -> (23/10,30/13) Hyperbolic Matrix(301,390,186,241) (-13/10,-9/7) -> (21/13,13/8) Hyperbolic Matrix(71,90,56,71) (-9/7,-5/4) -> (5/4,9/7) Hyperbolic Matrix(49,60,40,49) (-5/4,-6/5) -> (6/5,5/4) Hyperbolic Matrix(479,570,100,119) (-6/5,-19/16) -> (19/4,24/5) Hyperbolic Matrix(911,1080,566,671) (-19/16,-13/11) -> (37/23,29/18) Hyperbolic Matrix(181,210,156,181) (-7/6,-15/13) -> (15/13,7/6) Hyperbolic Matrix(131,150,62,71) (-15/13,-8/7) -> (2/1,15/7) 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(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(229,-300,100,-131) (13/10,4/3) -> (16/7,23/10) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(409,-570,94,-131) (25/18,7/5) -> (13/3,35/8) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) 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(589,-960,154,-251) (13/8,31/19) -> (19/5,23/6) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(49,-90,6,-11) (11/6,2/1) -> (8/1,1/0) Hyperbolic 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(289,-690,80,-191) (19/8,12/5) -> (18/5,29/8) Hyperbolic Matrix(179,-570,38,-121) (3/1,16/5) -> (14/3,33/7) Hyperbolic Matrix(131,-420,34,-109) (16/5,13/4) -> (23/6,4/1) Hyperbolic 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(11,90,-6,-49) -> Matrix(1,1,-6,-5) Matrix(59,390,18,119) -> Matrix(1,0,0,1) Matrix(61,390,-28,-179) -> Matrix(1,0,-4,1) Matrix(11,60,2,11) -> Matrix(1,1,0,1) Matrix(49,240,10,49) -> Matrix(1,1,0,1) Matrix(301,1440,88,421) -> Matrix(1,0,4,1) Matrix(241,1140,-152,-719) -> Matrix(13,6,-76,-35) Matrix(59,270,26,119) -> Matrix(1,0,4,1) Matrix(61,270,-54,-239) -> Matrix(3,2,-26,-17) Matrix(131,570,-94,-409) -> Matrix(1,1,-8,-7) Matrix(71,300,-40,-169) -> Matrix(3,1,-16,-5) Matrix(119,450,-32,-121) -> Matrix(1,0,6,1) Matrix(349,1290,-214,-791) -> Matrix(1,-1,-4,5) Matrix(59,210,-34,-121) -> Matrix(1,0,-4,1) Matrix(71,240,-50,-169) -> Matrix(3,1,-22,-7) Matrix(109,360,-76,-251) -> Matrix(1,-1,-6,7) Matrix(241,780,-148,-479) -> Matrix(1,0,-4,1) Matrix(181,570,-114,-359) -> Matrix(9,4,-52,-23) Matrix(11,30,4,11) -> Matrix(3,1,8,3) Matrix(49,120,20,49) -> Matrix(5,1,24,5) Matrix(251,600,-146,-349) -> Matrix(5,1,-26,-5) Matrix(241,570,178,421) -> Matrix(11,2,82,15) Matrix(229,540,148,349) -> Matrix(7,1,48,7) Matrix(131,300,-100,-229) -> Matrix(1,1,-8,-7) Matrix(119,270,26,59) -> Matrix(1,0,4,1) Matrix(241,540,54,121) -> Matrix(1,0,4,1) Matrix(539,1200,296,659) -> Matrix(5,2,22,9) Matrix(421,930,-244,-539) -> Matrix(7,2,-32,-9) Matrix(301,660,192,421) -> Matrix(9,2,58,13) Matrix(181,390,84,181) -> Matrix(7,2,24,7) Matrix(71,150,62,131) -> Matrix(5,1,44,9) Matrix(109,210,-68,-131) -> Matrix(13,3,-74,-17) Matrix(611,1140,-380,-709) -> Matrix(47,9,-256,-49) Matrix(361,660,-262,-479) -> Matrix(11,2,-72,-13) Matrix(481,870,-298,-539) -> Matrix(1,0,0,1) Matrix(251,450,140,251) -> Matrix(17,3,96,17) Matrix(421,750,270,481) -> Matrix(13,2,84,13) Matrix(611,1080,142,251) -> Matrix(17,3,28,5) Matrix(409,720,96,169) -> Matrix(7,1,20,3) Matrix(1201,2070,662,1141) -> Matrix(21,4,110,21) Matrix(71,120,42,71) -> Matrix(5,1,24,5) Matrix(109,180,66,109) -> Matrix(5,1,24,5) Matrix(661,1080,478,781) -> Matrix(9,2,58,13) Matrix(241,390,186,301) -> Matrix(21,4,152,29) Matrix(1619,2610,446,719) -> Matrix(21,4,26,5) Matrix(1249,2010,366,589) -> Matrix(27,5,70,13) Matrix(659,1050,150,239) -> Matrix(23,4,40,7) Matrix(1189,1890,748,1189) -> Matrix(41,7,240,41) Matrix(721,1140,456,721) -> Matrix(107,18,636,107) Matrix(419,660,266,419) -> Matrix(61,10,372,61) Matrix(479,750,76,119) -> Matrix(13,2,6,1) Matrix(1151,1800,736,1151) -> Matrix(19,3,120,19) Matrix(481,750,270,421) -> Matrix(13,2,84,13) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(311,450,132,191) -> Matrix(7,1,48,7) Matrix(229,330,34,49) -> Matrix(7,1,6,1) Matrix(191,270,-162,-229) -> Matrix(7,1,-64,-9) Matrix(949,1320,596,829) -> Matrix(17,3,96,17) Matrix(649,900,468,649) -> Matrix(19,3,120,19) Matrix(781,1080,478,661) -> Matrix(13,2,58,9) Matrix(1261,1740,566,781) -> Matrix(27,4,74,11) Matrix(241,330,176,241) -> Matrix(13,2,84,13) Matrix(419,570,308,419) -> Matrix(43,6,308,43) Matrix(421,570,178,241) -> Matrix(15,2,82,11) Matrix(551,720,238,311) -> Matrix(7,1,76,11) Matrix(829,1080,360,469) -> Matrix(7,1,-64,-9) Matrix(301,390,186,241) -> Matrix(29,4,152,21) Matrix(71,90,56,71) -> Matrix(23,3,176,23) Matrix(49,60,40,49) -> Matrix(9,1,80,9) Matrix(479,570,100,119) -> Matrix(1,0,10,1) Matrix(911,1080,566,671) -> Matrix(43,5,232,27) Matrix(181,210,156,181) -> Matrix(1,0,16,1) Matrix(131,150,62,71) -> Matrix(9,1,44,5) Matrix(241,270,108,121) -> Matrix(17,2,42,5) Matrix(1,0,2,1) -> Matrix(1,0,20,1) Matrix(239,-270,54,-61) -> Matrix(17,-2,26,-3) Matrix(179,-210,52,-61) -> Matrix(1,0,-6,1) Matrix(229,-300,100,-131) -> Matrix(7,-1,8,-1) Matrix(479,-660,262,-361) -> Matrix(13,-2,72,-11) Matrix(409,-570,94,-131) -> Matrix(7,-1,8,-1) Matrix(169,-240,50,-71) -> Matrix(7,-1,22,-3) Matrix(251,-360,76,-109) -> Matrix(7,-1,-6,1) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(719,-1140,152,-241) -> Matrix(35,-6,76,-13) Matrix(299,-480,38,-61) -> Matrix(11,-2,28,-5) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(589,-960,154,-251) -> Matrix(5,-1,26,-5) Matrix(121,-210,34,-59) -> Matrix(1,0,-4,1) Matrix(169,-300,40,-71) -> Matrix(5,-1,16,-3) Matrix(49,-90,6,-11) -> Matrix(5,-1,6,-1) Matrix(179,-390,28,-61) -> Matrix(1,0,-4,1) Matrix(299,-660,82,-181) -> Matrix(7,-2,4,-1) Matrix(289,-690,80,-191) -> Matrix(5,-1,6,-1) Matrix(179,-570,38,-121) -> Matrix(3,-2,8,-5) Matrix(131,-420,34,-109) -> Matrix(1,-1,6,-5) Matrix(121,-450,32,-119) -> Matrix(1,0,6,1) Matrix(61,-450,8,-59) -> Matrix(1,0,6,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 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 0/1 10 1 1/1 (0/1,1/10) 0 30 8/7 0 15 15/13 1/8 2 2 7/6 (0/1,1/8) 0 30 6/5 (1/10,1/8) 0 5 5/4 1/8 4 6 9/7 (1/8,3/22) 0 10 13/10 (5/36,1/7) 0 30 4/3 0 15 19/14 (3/22,1/7) 0 30 15/11 1/7 4 2 11/8 (1/7,1/6) 0 30 29/21 (2/13,1/6) 0 30 18/13 (3/20,1/6) 0 5 25/18 1/6 2 6 7/5 (0/1,1/6) 0 30 10/7 1/7 2 3 13/9 (1/7,1/6) 0 30 3/2 0 10 17/11 (1/7,1/6) 0 30 14/9 0 15 25/16 1/6 4 6 36/23 (3/20,1/6) 0 5 11/7 (5/31,1/6) 0 30 30/19 1/6 14 1 19/12 (1/6,9/53) 0 30 27/17 (1/6,7/40) 0 10 35/22 1/6 2 6 8/5 0 15 37/23 (2/11,7/38) 0 30 29/18 (3/16,4/21) 0 30 21/13 (1/6,3/16) 0 10 13/8 (1/5,1/4) 0 30 31/19 (0/1,1/4) 0 30 18/11 (1/6,1/4) 0 5 5/3 (1/6,1/4) 0 6 12/7 (1/6,1/4) 0 5 7/4 (0/1,1/6) 0 30 16/9 0 15 25/14 1/6 4 6 9/5 (1/6,3/16) 0 10 29/16 (3/16,4/21) 0 30 20/11 1/5 4 3 31/17 (0/1,1/6) 0 30 11/6 (1/6,1/5) 0 30 2/1 0 15 15/7 1/4 2 2 13/6 (1/4,1/3) 0 30 11/5 (1/4,3/11) 0 30 20/9 1/3 4 3 29/13 (3/8,2/5) 0 30 9/4 0 10 16/7 0 15 23/10 (-1/4,0/1) 0 30 30/13 0/1 10 1 7/3 (0/1,1/6) 0 30 26/11 0 15 19/8 (1/5,1/4) 0 30 12/5 (1/6,1/4) 0 5 5/2 1/4 2 6 3/1 (1/4,1/2) 0 10 16/5 0 15 13/4 (1/1,1/0) 0 30 23/7 (0/1,1/0) 0 30 10/3 0/1 2 3 17/5 (1/4,1/3) 0 30 41/12 (3/7,1/2) 0 30 24/7 (1/4,1/2) 0 5 7/2 (0/1,1/2) 0 30 18/5 (1/2,1/0) 0 5 29/8 (0/1,1/2) 0 30 40/11 1/1 4 3 11/3 (-1/1,1/0) 0 30 15/4 0/1 6 2 19/5 (1/6,1/5) 0 30 23/6 (0/1,1/6) 0 30 4/1 0 15 17/4 (1/3,1/2) 0 30 30/7 1/2 2 1 13/3 (1/2,1/1) 0 30 35/8 1/2 2 6 22/5 0 15 31/7 (2/3,3/4) 0 30 9/2 0 10 14/3 0 15 33/7 (5/12,1/2) 0 10 19/4 (1/2,3/5) 0 30 24/5 (1/2,1/0) 0 5 5/1 (1/2,1/0) 0 6 6/1 (1/2,1/0) 0 5 19/3 (-3/1,1/0) 0 30 13/2 (-1/1,1/0) 0 30 7/1 (0/1,1/0) 0 30 15/2 0/1 6 2 23/3 (0/1,1/6) 0 30 8/1 0 15 1/0 (0/1,1/0) 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(239,-270,54,-61) (1/1,8/7) -> (22/5,31/7) Hyperbolic Matrix(131,-150,62,-71) (8/7,15/13) -> (2/1,15/7) Glide Reflection Matrix(181,-210,156,-181) (15/13,7/6) -> (15/13,7/6) Reflection Matrix(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(49,-60,40,-49) (6/5,5/4) -> (6/5,5/4) Reflection Matrix(71,-90,56,-71) (5/4,9/7) -> (5/4,9/7) Reflection Matrix(301,-390,186,-241) (9/7,13/10) -> (21/13,13/8) Glide Reflection Matrix(229,-300,100,-131) (13/10,4/3) -> (16/7,23/10) 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(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(781,-1080,478,-661) (29/21,18/13) -> (31/19,18/11) Glide Reflection Matrix(649,-900,468,-649) (18/13,25/18) -> (18/13,25/18) Reflection Matrix(409,-570,94,-131) (25/18,7/5) -> (13/3,35/8) Hyperbolic Matrix(169,-240,50,-71) (7/5,10/7) -> (10/3,17/5) Hyperbolic Matrix(251,-360,76,-109) (10/7,13/9) -> (23/7,10/3) Hyperbolic Matrix(61,-90,40,-59) (13/9,3/2) -> (3/2,17/11) Parabolic Matrix(349,-540,148,-229) (17/11,14/9) -> (7/3,26/11) Glide Reflection Matrix(481,-750,270,-421) (14/9,25/16) -> (16/9,25/14) Glide Reflection Matrix(1151,-1800,736,-1151) (25/16,36/23) -> (25/16,36/23) Reflection Matrix(479,-750,76,-119) (36/23,11/7) -> (6/1,19/3) Glide Reflection Matrix(419,-660,266,-419) (11/7,30/19) -> (11/7,30/19) Reflection Matrix(721,-1140,456,-721) (30/19,19/12) -> (30/19,19/12) Reflection Matrix(719,-1140,152,-241) (19/12,27/17) -> (33/7,19/4) Hyperbolic Matrix(1189,-1890,748,-1189) (27/17,35/22) -> (27/17,35/22) Reflection Matrix(659,-1050,150,-239) (35/22,8/5) -> (35/8,22/5) Glide Reflection Matrix(299,-480,38,-61) (8/5,37/23) -> (23/3,8/1) Hyperbolic Matrix(1249,-2010,366,-589) (37/23,29/18) -> (17/5,41/12) Glide Reflection Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(589,-960,154,-251) (13/8,31/19) -> (19/5,23/6) Hyperbolic Matrix(109,-180,66,-109) (18/11,5/3) -> (18/11,5/3) Reflection Matrix(71,-120,42,-71) (5/3,12/7) -> (5/3,12/7) Reflection Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(169,-300,40,-71) (7/4,16/9) -> (4/1,17/4) Hyperbolic Matrix(251,-450,140,-251) (25/14,9/5) -> (25/14,9/5) Reflection Matrix(959,-1740,264,-479) (29/16,20/11) -> (29/8,40/11) Glide Reflection Matrix(659,-1200,296,-539) (20/11,31/17) -> (20/9,29/13) Glide Reflection Matrix(49,-90,6,-11) (11/6,2/1) -> (8/1,1/0) Hyperbolic Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection 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(241,-540,54,-121) (29/13,9/4) -> (31/7,9/2) Glide Reflection Matrix(119,-270,26,-59) (9/4,16/7) -> (9/2,14/3) Glide Reflection Matrix(599,-1380,260,-599) (23/10,30/13) -> (23/10,30/13) Reflection Matrix(181,-420,78,-181) (30/13,7/3) -> (30/13,7/3) Reflection Matrix(289,-690,80,-191) (19/8,12/5) -> (18/5,29/8) Hyperbolic Matrix(49,-120,20,-49) (12/5,5/2) -> (12/5,5/2) Reflection Matrix(11,-30,4,-11) (5/2,3/1) -> (5/2,3/1) Reflection Matrix(179,-570,38,-121) (3/1,16/5) -> (14/3,33/7) Hyperbolic Matrix(131,-420,34,-109) (16/5,13/4) -> (23/6,4/1) Hyperbolic Matrix(119,-390,18,-59) (13/4,23/7) -> (13/2,7/1) Glide Reflection Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection 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(49,-240,10,-49) (24/5,5/1) -> (24/5,5/1) Reflection Matrix(11,-60,2,-11) (5/1,6/1) -> (5/1,6/1) Reflection Matrix(61,-450,8,-59) (7/1,15/2) -> (15/2,23/3) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,20,-1) (0/1,1/1) -> (0/1,1/10) Matrix(239,-270,54,-61) -> Matrix(17,-2,26,-3) Matrix(131,-150,62,-71) -> Matrix(9,-1,44,-5) Matrix(181,-210,156,-181) -> Matrix(1,0,16,-1) (15/13,7/6) -> (0/1,1/8) Matrix(179,-210,52,-61) -> Matrix(1,0,-6,1) 0/1 Matrix(49,-60,40,-49) -> Matrix(9,-1,80,-9) (6/5,5/4) -> (1/10,1/8) Matrix(71,-90,56,-71) -> Matrix(23,-3,176,-23) (5/4,9/7) -> (1/8,3/22) Matrix(301,-390,186,-241) -> Matrix(29,-4,152,-21) Matrix(229,-300,100,-131) -> Matrix(7,-1,8,-1) Matrix(421,-570,178,-241) -> Matrix(15,-2,82,-11) Matrix(419,-570,308,-419) -> Matrix(43,-6,308,-43) (19/14,15/11) -> (3/22,1/7) Matrix(241,-330,176,-241) -> Matrix(13,-2,84,-13) (15/11,11/8) -> (1/7,1/6) Matrix(479,-660,262,-361) -> Matrix(13,-2,72,-11) 1/6 Matrix(781,-1080,478,-661) -> Matrix(13,-2,58,-9) Matrix(649,-900,468,-649) -> Matrix(19,-3,120,-19) (18/13,25/18) -> (3/20,1/6) Matrix(409,-570,94,-131) -> Matrix(7,-1,8,-1) Matrix(169,-240,50,-71) -> Matrix(7,-1,22,-3) Matrix(251,-360,76,-109) -> Matrix(7,-1,-6,1) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(349,-540,148,-229) -> Matrix(7,-1,48,-7) *** -> (1/8,1/6) Matrix(481,-750,270,-421) -> Matrix(13,-2,84,-13) *** -> (1/7,1/6) Matrix(1151,-1800,736,-1151) -> Matrix(19,-3,120,-19) (25/16,36/23) -> (3/20,1/6) Matrix(479,-750,76,-119) -> Matrix(13,-2,6,-1) Matrix(419,-660,266,-419) -> Matrix(61,-10,372,-61) (11/7,30/19) -> (5/31,1/6) Matrix(721,-1140,456,-721) -> Matrix(107,-18,636,-107) (30/19,19/12) -> (1/6,9/53) Matrix(719,-1140,152,-241) -> Matrix(35,-6,76,-13) Matrix(1189,-1890,748,-1189) -> Matrix(41,-7,240,-41) (27/17,35/22) -> (1/6,7/40) Matrix(659,-1050,150,-239) -> Matrix(23,-4,40,-7) Matrix(299,-480,38,-61) -> Matrix(11,-2,28,-5) Matrix(1249,-2010,366,-589) -> Matrix(27,-5,70,-13) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(589,-960,154,-251) -> Matrix(5,-1,26,-5) (0/1,1/5).(1/6,1/4) Matrix(109,-180,66,-109) -> Matrix(5,-1,24,-5) (18/11,5/3) -> (1/6,1/4) Matrix(71,-120,42,-71) -> Matrix(5,-1,24,-5) (5/3,12/7) -> (1/6,1/4) Matrix(121,-210,34,-59) -> Matrix(1,0,-4,1) 0/1 Matrix(169,-300,40,-71) -> Matrix(5,-1,16,-3) 1/4 Matrix(251,-450,140,-251) -> Matrix(17,-3,96,-17) (25/14,9/5) -> (1/6,3/16) Matrix(959,-1740,264,-479) -> Matrix(21,-4,26,-5) Matrix(659,-1200,296,-539) -> Matrix(9,-2,22,-5) Matrix(49,-90,6,-11) -> Matrix(5,-1,6,-1) Matrix(181,-390,84,-181) -> Matrix(7,-2,24,-7) (15/7,13/6) -> (1/4,1/3) Matrix(179,-390,28,-61) -> Matrix(1,0,-4,1) 0/1 Matrix(299,-660,82,-181) -> Matrix(7,-2,4,-1) Matrix(241,-540,54,-121) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(119,-270,26,-59) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(599,-1380,260,-599) -> Matrix(-1,0,8,1) (23/10,30/13) -> (-1/4,0/1) Matrix(181,-420,78,-181) -> Matrix(1,0,12,-1) (30/13,7/3) -> (0/1,1/6) Matrix(289,-690,80,-191) -> Matrix(5,-1,6,-1) Matrix(49,-120,20,-49) -> Matrix(5,-1,24,-5) (12/5,5/2) -> (1/6,1/4) Matrix(11,-30,4,-11) -> Matrix(3,-1,8,-3) (5/2,3/1) -> (1/4,1/2) Matrix(179,-570,38,-121) -> Matrix(3,-2,8,-5) 1/2 Matrix(131,-420,34,-109) -> Matrix(1,-1,6,-5) Matrix(119,-390,18,-59) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(421,-1440,88,-301) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(121,-450,32,-119) -> Matrix(1,0,6,1) 0/1 Matrix(239,-1020,56,-239) -> Matrix(5,-2,12,-5) (17/4,30/7) -> (1/3,1/2) Matrix(181,-780,42,-181) -> Matrix(3,-2,4,-3) (30/7,13/3) -> (1/2,1/1) Matrix(49,-240,10,-49) -> Matrix(-1,1,0,1) (24/5,5/1) -> (1/2,1/0) Matrix(11,-60,2,-11) -> Matrix(-1,1,0,1) (5/1,6/1) -> (1/2,1/0) Matrix(61,-450,8,-59) -> Matrix(1,0,6,1) 0/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.