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 1/0 -8/1 1/2 1/0 -15/2 1/0 -7/1 -1/2 -13/2 1/1 1/0 -6/1 0/1 -17/3 3/2 -11/2 -1/2 0/1 -5/1 1/0 -24/5 -1/1 -19/4 -3/2 -1/1 -14/3 -1/2 -1/4 -9/2 -1/1 0/1 -22/5 -1/2 -3/8 -35/8 -1/4 -13/3 -1/6 -30/7 0/1 -17/4 0/1 1/8 -21/5 1/4 -4/1 1/2 1/0 -15/4 1/0 -26/7 -7/2 1/0 -37/10 -5/2 -2/1 -11/3 -3/2 -7/2 -1/1 -1/2 -17/5 -1/6 -61/18 -1/4 0/1 -44/13 -1/4 -1/6 -27/8 -1/5 0/1 -10/3 0/1 -33/10 0/1 1/7 -23/7 1/6 -13/4 1/4 1/3 -16/5 1/2 5/8 -3/1 1/0 -17/6 -3/4 -2/3 -14/5 -1/2 -3/8 -39/14 -1/3 0/1 -25/9 -1/4 -11/4 -1/6 0/1 -30/11 0/1 -19/7 1/10 -27/10 0/1 1/5 -8/3 1/4 1/2 -37/14 1/2 4/7 -29/11 1/2 -50/19 2/3 -71/27 1/2 -21/8 2/3 1/1 -55/21 3/4 -89/34 3/4 1/1 -34/13 3/4 5/6 -13/5 3/2 -5/2 1/0 -17/7 -1/2 -29/12 -1/1 1/0 -12/5 -1/1 -31/13 -1/2 -50/21 0/1 -69/29 1/0 -19/8 -1/1 -1/2 -26/11 -1/2 -1/4 -59/25 -1/2 -33/14 -1/3 0/1 -7/3 -1/2 -30/13 0/1 -23/10 0/1 1/6 -16/7 1/4 1/2 -9/4 0/1 1/1 -29/13 1/2 -20/9 1/1 -11/5 1/2 -24/11 2/1 -13/6 3/1 1/0 -15/7 1/0 -2/1 -1/2 1/0 -15/8 1/0 -28/15 -13/2 1/0 -13/7 -7/2 -11/6 -2/1 -3/2 -20/11 -1/1 -9/5 1/0 -34/19 -7/4 -3/2 -59/33 -3/2 -25/14 -3/2 -16/9 -3/2 1/0 -39/22 -4/3 -1/1 -23/13 -7/6 -30/17 -1/1 -7/4 -1/1 -1/2 -19/11 -3/2 -50/29 -1/1 -31/18 -1/1 1/0 -12/7 -1/1 -29/17 -1/2 -75/44 -1/2 -46/27 -1/2 -7/16 -17/10 -1/4 0/1 -39/23 1/0 -22/13 -1/2 1/0 -27/16 0/1 1/1 -5/3 1/0 -33/20 -2/1 -1/1 -61/37 -3/2 -28/17 -3/2 1/0 -23/14 -2/1 -3/2 -41/25 -5/2 -100/61 -2/1 -59/36 -2/1 1/0 -18/11 -2/1 -31/19 -3/2 -75/46 -3/2 -44/27 -3/2 -23/16 -13/8 -5/4 -1/1 -21/13 1/0 -50/31 -1/1 -29/18 -1/1 1/0 -37/23 -1/2 -45/28 1/0 -8/5 -3/2 1/0 -35/22 -5/4 -27/17 -5/4 -46/29 -7/6 -23/20 -19/12 -11/10 -1/1 -30/19 -1/1 -11/7 -5/6 -36/23 -2/3 -61/39 -1/2 -25/16 -1/2 -14/9 -1/2 1/0 -3/2 -1/1 0/1 -16/11 -1/2 1/0 -61/42 0/1 1/0 -45/31 1/0 -29/20 -1/1 1/0 -13/9 -1/2 -36/25 -2/1 -59/41 -3/2 -23/16 -3/2 -4/3 -10/7 -1/1 -37/26 -9/10 -8/9 -64/45 -7/8 -5/6 -91/64 -1/1 -7/8 -27/19 -7/8 -17/12 -4/5 -3/4 -24/17 -1/1 -55/39 -3/4 -31/22 -1/1 -3/4 -7/5 -1/2 -39/28 -1/1 -4/5 -32/23 -3/4 -1/2 -121/87 -1/2 -210/151 -1/1 -89/64 -1/1 -3/4 -57/41 -3/4 -25/18 -3/4 -43/31 -1/2 -61/44 -3/4 -2/3 -18/13 -2/3 -29/21 -1/2 -40/29 -1/1 -11/8 -2/3 -1/2 -15/11 -1/2 -19/14 -1/2 -1/3 -4/3 -1/2 1/0 -17/13 -7/6 -30/23 -1/1 -13/10 -1/1 -7/8 -9/7 -3/4 -41/32 -1/1 -1/2 -32/25 -3/4 -7/10 -23/18 -7/10 -2/3 -14/11 -3/4 -1/2 -5/4 -1/2 -16/13 -1/2 -1/4 -27/22 -1/3 0/1 -11/9 1/2 -39/32 0/1 1/1 -28/23 3/2 1/0 -45/37 1/0 -17/14 -2/1 1/0 -6/5 -1/1 -19/16 -1/1 -5/6 -32/27 -11/14 -3/4 -13/11 -7/10 -7/6 -3/5 -1/2 -15/13 -1/2 -23/20 -1/2 -6/13 -8/7 -1/2 -3/8 -9/8 -1/1 0/1 -1/1 -1/2 0/1 0/1 1/1 1/2 8/7 3/8 1/2 15/13 1/2 7/6 1/2 3/5 6/5 1/1 17/14 2/1 1/0 28/23 -3/2 1/0 39/32 -1/1 0/1 11/9 -1/2 5/4 1/2 19/15 9/14 14/11 1/2 3/4 23/18 2/3 7/10 32/25 7/10 3/4 41/32 1/2 1/1 9/7 3/4 13/10 7/8 1/1 30/23 1/1 17/13 7/6 4/3 1/2 1/0 19/14 1/3 1/2 15/11 1/2 11/8 1/2 2/3 29/21 1/2 18/13 2/3 61/44 2/3 3/4 43/31 1/2 25/18 3/4 32/23 1/2 3/4 7/5 1/2 31/22 3/4 1/1 24/17 1/1 17/12 3/4 4/5 27/19 7/8 10/7 1/1 33/23 5/4 23/16 4/3 3/2 13/9 1/2 3/2 0/1 1/1 17/11 1/2 14/9 1/2 1/0 25/16 1/2 61/39 1/2 36/23 2/3 11/7 5/6 30/19 1/1 19/12 1/1 11/10 27/17 5/4 89/56 1/1 5/4 62/39 7/6 5/4 35/22 5/4 8/5 3/2 1/0 37/23 1/2 29/18 1/1 1/0 21/13 1/0 13/8 1/1 5/4 31/19 3/2 18/11 2/1 59/36 2/1 1/0 41/25 5/2 23/14 3/2 2/1 28/17 3/2 1/0 5/3 1/0 22/13 1/2 1/0 39/23 1/0 17/10 0/1 1/4 29/17 1/2 12/7 1/1 7/4 1/2 1/1 30/17 1/1 23/13 7/6 62/35 7/6 5/4 39/22 1/1 4/3 16/9 3/2 1/0 25/14 3/2 59/33 3/2 34/19 3/2 7/4 9/5 1/0 29/16 1/1 1/0 20/11 1/1 31/17 3/2 11/6 3/2 2/1 13/7 7/2 15/8 1/0 17/9 -5/2 2/1 1/2 1/0 17/8 4/1 1/0 15/7 1/0 13/6 -3/1 1/0 11/5 -1/2 20/9 -1/1 29/13 -1/2 9/4 -1/1 0/1 16/7 -1/2 -1/4 23/10 -1/6 0/1 30/13 0/1 7/3 1/2 33/14 0/1 1/3 59/25 1/2 26/11 1/4 1/2 19/8 1/2 1/1 69/29 1/0 50/21 0/1 31/13 1/2 12/5 1/1 5/2 1/0 18/7 -1/1 31/12 -1/1 1/0 75/29 1/0 44/17 -3/2 1/0 13/5 -3/2 34/13 -5/6 -3/4 89/34 -1/1 -3/4 55/21 -3/4 21/8 -1/1 -2/3 71/27 -1/2 50/19 -2/3 29/11 -1/2 37/14 -4/7 -1/2 45/17 -1/2 8/3 -1/2 -1/4 35/13 -1/4 62/23 -1/4 -1/6 151/56 -1/4 -1/5 240/89 -1/5 89/33 -1/6 27/10 -1/5 0/1 46/17 -1/4 -1/6 19/7 -1/10 30/11 0/1 11/4 0/1 1/6 14/5 3/8 1/2 45/16 1/2 31/11 1/2 17/6 2/3 3/4 3/1 1/0 16/5 -5/8 -1/2 45/14 -1/2 29/9 -1/2 13/4 -1/3 -1/4 23/7 -1/6 10/3 0/1 37/11 1/6 27/8 0/1 1/5 44/13 1/6 1/4 105/31 1/4 61/18 0/1 1/4 17/5 1/6 58/17 1/4 5/18 41/12 3/10 1/3 24/7 1/3 7/2 1/2 1/1 18/5 1/1 29/8 1/1 1/0 40/11 1/1 11/3 3/2 15/4 1/0 19/5 -5/2 23/6 -2/1 -3/2 27/7 1/0 31/8 -1/1 1/0 4/1 -1/2 1/0 21/5 -1/4 17/4 -1/8 0/1 30/7 0/1 13/3 1/6 35/8 1/4 22/5 3/8 1/2 31/7 1/2 9/2 0/1 1/1 14/3 1/4 1/2 33/7 3/4 19/4 1/1 3/2 24/5 1/1 29/6 1/1 1/0 5/1 1/0 21/4 -1/1 0/1 16/3 -3/4 -1/2 11/2 0/1 1/2 17/3 -3/2 23/4 -2/3 -1/2 29/5 -1/2 6/1 0/1 19/3 3/2 13/2 -1/1 1/0 7/1 1/2 15/2 1/0 23/3 -3/2 8/1 -1/2 1/0 9/1 1/0 10/1 0/1 11/1 1/2 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,-2,0,1) Matrix(119,1140,50,479) -> Matrix(1,0,0,1) Matrix(61,510,36,301) -> Matrix(1,0,0,1) Matrix(61,480,-38,-299) -> Matrix(1,-2,0,1) Matrix(119,870,-74,-541) -> Matrix(1,0,0,1) Matrix(59,390,18,119) -> Matrix(1,0,-4,1) Matrix(61,390,-28,-179) -> Matrix(1,2,0,1) Matrix(121,690,-84,-479) -> Matrix(1,-2,0,1) Matrix(59,330,32,179) -> Matrix(1,2,0,1) Matrix(61,330,-22,-119) -> Matrix(1,0,-4,1) Matrix(299,1440,-212,-1021) -> Matrix(3,4,-4,-5) Matrix(301,1440,88,421) -> Matrix(1,0,4,1) Matrix(241,1140,-152,-719) -> Matrix(9,8,-8,-7) Matrix(59,270,26,119) -> Matrix(1,0,0,1) Matrix(61,270,-54,-239) -> Matrix(1,0,0,1) Matrix(239,1050,150,659) -> Matrix(11,4,8,3) Matrix(419,1830,302,1319) -> Matrix(11,2,16,3) Matrix(181,780,42,181) -> Matrix(1,0,12,1) Matrix(239,1020,56,239) -> Matrix(1,0,-16,1) Matrix(241,1020,142,601) -> Matrix(1,0,-4,1) Matrix(179,750,100,419) -> Matrix(7,-2,4,-1) Matrix(119,450,-32,-121) -> Matrix(1,-4,0,1) Matrix(899,3330,-632,-2341) -> Matrix(7,22,-8,-25) Matrix(479,1770,292,1079) -> Matrix(1,4,0,1) Matrix(59,210,-34,-121) -> Matrix(1,0,0,1) Matrix(61,210,-52,-179) -> Matrix(5,2,-8,-3) Matrix(1079,3660,778,2639) -> Matrix(11,2,16,3) Matrix(1081,3660,-744,-2519) -> Matrix(1,0,4,1) Matrix(719,2430,266,899) -> Matrix(1,0,0,1) Matrix(179,600,-54,-181) -> Matrix(1,0,12,1) Matrix(301,990,128,421) -> Matrix(1,0,-4,1) Matrix(119,390,18,59) -> Matrix(1,0,-4,1) Matrix(241,780,-148,-479) -> Matrix(11,-4,-8,3) Matrix(181,570,-114,-359) -> Matrix(5,-6,-4,5) Matrix(179,510,126,359) -> Matrix(7,6,8,7) Matrix(361,1020,-212,-599) -> Matrix(3,2,-8,-5) Matrix(419,1170,236,659) -> Matrix(11,4,8,3) Matrix(959,2670,366,1019) -> Matrix(5,2,-8,-3) Matrix(241,660,88,241) -> Matrix(1,0,12,1) Matrix(419,1140,154,419) -> Matrix(1,0,-20,1) Matrix(299,810,-244,-661) -> Matrix(1,0,-8,1) Matrix(301,810,-178,-479) -> Matrix(1,0,-4,1) Matrix(181,480,-158,-419) -> Matrix(5,-2,-12,5) Matrix(1079,2850,-750,-1981) -> Matrix(13,-8,-8,5) Matrix(1139,3000,478,1259) -> Matrix(3,-2,8,-5) Matrix(3479,9150,-2122,-5581) -> Matrix(11,-8,-4,3) Matrix(1141,3000,936,2461) -> Matrix(3,-2,-4,3) Matrix(481,1260,92,241) -> Matrix(3,-2,-4,3) Matrix(779,2040,160,419) -> Matrix(5,-4,4,-3) Matrix(3359,8790,-2362,-6181) -> Matrix(11,-10,-12,11) Matrix(241,630,184,481) -> Matrix(5,-4,4,-3) Matrix(59,150,-24,-61) -> Matrix(1,-2,0,1) Matrix(359,870,-248,-601) -> Matrix(1,0,0,1) Matrix(361,870,100,241) -> Matrix(1,2,0,1) Matrix(301,720,176,421) -> Matrix(3,2,4,3) Matrix(1259,3000,478,1139) -> Matrix(5,2,-8,-3) Matrix(479,1140,50,119) -> Matrix(1,0,0,1) Matrix(1261,3000,984,2341) -> Matrix(3,2,4,3) Matrix(241,570,178,421) -> Matrix(1,0,4,1) Matrix(1499,3540,838,1979) -> Matrix(1,2,0,1) Matrix(1679,3960,-1018,-2401) -> Matrix(7,2,-4,-1) Matrix(599,1410,178,419) -> Matrix(1,0,8,1) Matrix(181,420,78,181) -> Matrix(1,0,4,1) Matrix(599,1380,260,599) -> Matrix(1,0,-12,1) Matrix(301,690,236,541) -> Matrix(5,-2,8,-3) Matrix(119,270,26,59) -> Matrix(1,0,0,1) Matrix(241,540,54,121) -> Matrix(1,0,0,1) Matrix(539,1200,296,659) -> Matrix(5,-4,4,-3) Matrix(421,930,-244,-539) -> Matrix(1,-2,0,1) Matrix(301,660,192,421) -> Matrix(3,-4,4,-5) Matrix(181,390,84,181) -> Matrix(1,-6,0,1) Matrix(241,510,-198,-419) -> Matrix(1,2,0,1) Matrix(239,450,-128,-241) -> Matrix(1,-6,0,1) Matrix(661,1230,194,361) -> Matrix(1,4,4,17) Matrix(179,330,32,59) -> Matrix(1,2,0,1) Matrix(361,660,-262,-479) -> Matrix(3,4,-4,-5) Matrix(481,870,-298,-539) -> Matrix(1,0,0,1) Matrix(419,750,100,179) -> Matrix(1,2,-4,-7) Matrix(1979,3540,838,1499) -> Matrix(1,2,0,1) Matrix(1679,3000,1074,1919) -> Matrix(5,8,8,13) Matrix(421,750,270,481) -> Matrix(1,2,0,1) Matrix(541,960,102,181) -> Matrix(3,4,-4,-5) Matrix(661,1170,-474,-839) -> Matrix(7,8,-8,-9) Matrix(781,1380,442,781) -> Matrix(13,14,12,13) Matrix(239,420,136,239) -> Matrix(3,2,4,3) Matrix(1201,2070,662,1141) -> Matrix(1,2,0,1) Matrix(541,930,210,361) -> Matrix(1,0,0,1) Matrix(421,720,176,301) -> Matrix(3,2,4,3) Matrix(2041,3480,634,1081) -> Matrix(11,6,-24,-13) Matrix(1919,3270,598,1019) -> Matrix(13,6,-24,-11) Matrix(601,1020,142,241) -> Matrix(1,0,-4,1) Matrix(301,510,36,61) -> Matrix(1,0,0,1) Matrix(179,300,-108,-181) -> Matrix(1,-2,0,1) Matrix(3241,5340,-2330,-3839) -> Matrix(3,4,-4,-5) Matrix(839,1380,656,1079) -> Matrix(3,8,4,11) Matrix(841,1380,220,361) -> Matrix(1,0,0,1) Matrix(1319,2160,952,1559) -> Matrix(3,8,4,11) Matrix(661,1080,478,781) -> Matrix(5,8,8,13) Matrix(2281,3720,810,1321) -> Matrix(13,20,24,37) Matrix(1859,3030,662,1079) -> Matrix(11,16,24,35) Matrix(241,390,186,301) -> Matrix(3,2,4,3) Matrix(1619,2610,446,719) -> Matrix(1,2,0,1) Matrix(839,1350,596,959) -> Matrix(3,2,4,3) Matrix(659,1050,150,239) -> Matrix(3,4,8,11) Matrix(1679,2670,-1208,-1921) -> Matrix(7,8,-8,-9) Matrix(721,1140,456,721) -> Matrix(21,22,20,21) Matrix(419,660,266,419) -> Matrix(11,10,12,11) Matrix(479,750,76,119) -> Matrix(3,2,4,3) Matrix(901,1410,154,241) -> Matrix(3,2,-8,-5) Matrix(1919,3000,1074,1679) -> Matrix(13,8,8,5) Matrix(481,750,270,421) -> Matrix(1,2,0,1) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(6301,9150,1860,2701) -> Matrix(1,0,4,1) Matrix(2461,3570,952,1381) -> Matrix(1,0,0,1) Matrix(3001,4320,1918,2761) -> Matrix(5,8,8,13) Matrix(419,600,-294,-421) -> Matrix(11,12,-12,-13) Matrix(3419,4860,2152,3059) -> Matrix(3,2,4,3) Matrix(359,510,126,179) -> Matrix(7,6,8,7) Matrix(361,510,298,421) -> Matrix(3,2,4,3) Matrix(4681,6600,1788,2521) -> Matrix(1,0,0,1) Matrix(959,1350,596,839) -> Matrix(3,2,4,3) Matrix(1681,2340,1380,1921) -> Matrix(5,4,-4,-3) Matrix(34319,47730,12726,17699) -> Matrix(1,0,-4,1) Matrix(38161,53070,14152,19681) -> Matrix(5,4,-24,-19) Matrix(2999,4170,776,1079) -> Matrix(5,4,-4,-3) Matrix(1319,1830,302,419) -> Matrix(3,2,16,11) Matrix(2639,3660,778,1079) -> Matrix(3,2,16,11) Matrix(1559,2160,952,1319) -> Matrix(11,8,4,3) Matrix(781,1080,478,661) -> Matrix(13,8,8,5) Matrix(1261,1740,566,781) -> Matrix(1,0,0,1) Matrix(241,330,176,241) -> Matrix(7,4,12,7) Matrix(419,570,308,419) -> Matrix(5,2,12,5) Matrix(421,570,178,241) -> Matrix(1,0,4,1) Matrix(481,630,184,241) -> Matrix(3,4,-4,-5) Matrix(781,1020,598,781) -> Matrix(13,14,12,13) Matrix(599,780,460,599) -> Matrix(15,14,16,15) Matrix(301,390,186,241) -> Matrix(3,2,4,3) Matrix(2341,3000,984,1261) -> Matrix(3,2,4,3) Matrix(2881,3690,844,1081) -> Matrix(5,4,16,13) Matrix(1079,1380,656,839) -> Matrix(11,8,4,3) Matrix(541,690,236,301) -> Matrix(3,2,-8,-5) Matrix(119,150,-96,-121) -> Matrix(3,2,-8,-5) Matrix(1319,1620,390,479) -> Matrix(1,0,8,1) Matrix(2461,3000,936,1141) -> Matrix(3,-2,-4,3) Matrix(2881,3510,1626,1981) -> Matrix(5,-4,4,-3) Matrix(839,1020,394,479) -> Matrix(1,6,0,1) Matrix(421,510,298,361) -> Matrix(3,2,4,3) Matrix(479,570,100,119) -> Matrix(3,2,4,3) Matrix(1619,1920,1264,1499) -> Matrix(7,6,8,7) Matrix(481,570,254,301) -> Matrix(5,4,-4,-3) Matrix(181,210,156,181) -> Matrix(11,6,20,11) Matrix(1381,1590,522,601) -> Matrix(21,10,-40,-19) Matrix(241,270,108,121) -> Matrix(1,0,0,1) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(239,-270,54,-61) -> Matrix(1,0,0,1) Matrix(419,-480,158,-181) -> Matrix(5,-2,-12,5) Matrix(179,-210,52,-61) -> Matrix(3,-2,8,-5) Matrix(419,-510,198,-241) -> Matrix(1,2,0,1) Matrix(121,-150,96,-119) -> Matrix(5,-2,8,-3) Matrix(899,-1140,332,-421) -> Matrix(3,-2,-16,11) Matrix(479,-660,262,-361) -> Matrix(5,-4,4,-3) Matrix(1921,-2670,1208,-1679) -> Matrix(9,-8,8,-7) Matrix(839,-1170,474,-661) -> Matrix(9,-8,8,-7) Matrix(1021,-1440,212,-299) -> Matrix(5,-4,4,-3) Matrix(421,-600,294,-419) -> Matrix(13,-12,12,-11) Matrix(961,-1380,250,-359) -> Matrix(5,-6,-4,5) Matrix(479,-690,84,-121) -> Matrix(1,-2,0,1) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(1,-2,0,1) Matrix(719,-1140,152,-241) -> Matrix(7,-8,8,-9) Matrix(9361,-14880,3472,-5519) -> Matrix(5,-6,-24,29) Matrix(299,-480,38,-61) -> Matrix(1,-2,0,1) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(479,-780,148,-241) -> Matrix(3,-4,-8,11) Matrix(421,-690,36,-59) -> Matrix(1,-2,0,1) Matrix(781,-1290,290,-479) -> Matrix(1,-2,-4,9) Matrix(479,-810,178,-301) -> Matrix(1,0,-4,1) Matrix(599,-1020,212,-361) -> Matrix(5,-2,8,-3) Matrix(121,-210,34,-59) -> Matrix(1,0,0,1) Matrix(241,-450,128,-239) -> Matrix(1,-6,0,1) Matrix(179,-390,28,-61) -> Matrix(1,2,0,1) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) Matrix(1921,-4530,712,-1679) -> Matrix(1,0,-8,1) Matrix(61,-150,24,-59) -> Matrix(1,-2,0,1) Matrix(3061,-7920,904,-2339) -> Matrix(1,2,4,9) Matrix(539,-1410,138,-361) -> Matrix(5,4,-4,-3) Matrix(479,-1260,46,-121) -> Matrix(3,2,4,3) Matrix(659,-1740,114,-301) -> Matrix(3,2,-8,-5) Matrix(119,-330,22,-61) -> Matrix(1,0,-4,1) Matrix(179,-570,38,-121) -> Matrix(3,2,4,3) Matrix(181,-600,54,-179) -> Matrix(1,0,12,1) Matrix(121,-450,32,-119) -> Matrix(1,-4,0,1) Matrix(61,-450,8,-59) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 64 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -5/1 -9/2 -10/3 -3/1 -5/2 -12/5 -20/9 -9/5 -5/3 -3/2 -5/4 0/1 1/1 15/13 5/4 15/11 3/2 5/3 9/5 15/8 2/1 15/7 20/9 30/13 12/5 5/2 75/29 30/11 3/1 45/14 10/3 7/2 11/3 15/4 4/1 30/7 13/3 9/2 14/3 5/1 11/2 6/1 13/2 7/1 15/2 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 1/2 1/0 -15/2 1/0 -7/1 -1/2 -6/1 0/1 -17/3 3/2 -11/2 -1/2 0/1 -5/1 1/0 -14/3 -1/2 -1/4 -9/2 -1/1 0/1 -13/3 -1/6 -4/1 1/2 1/0 -15/4 1/0 -11/3 -3/2 -7/2 -1/1 -1/2 -17/5 -1/6 -10/3 0/1 -13/4 1/4 1/3 -3/1 1/0 -17/6 -3/4 -2/3 -14/5 -1/2 -3/8 -25/9 -1/4 -11/4 -1/6 0/1 -8/3 1/4 1/2 -29/11 1/2 -21/8 2/3 1/1 -13/5 3/2 -5/2 1/0 -17/7 -1/2 -29/12 -1/1 1/0 -12/5 -1/1 -7/3 -1/2 -16/7 1/4 1/2 -9/4 0/1 1/1 -29/13 1/2 -20/9 1/1 -11/5 1/2 -13/6 3/1 1/0 -15/7 1/0 -2/1 -1/2 1/0 -15/8 1/0 -13/7 -7/2 -11/6 -2/1 -3/2 -20/11 -1/1 -9/5 1/0 -16/9 -3/2 1/0 -23/13 -7/6 -30/17 -1/1 -7/4 -1/1 -1/2 -19/11 -3/2 -50/29 -1/1 -31/18 -1/1 1/0 -12/7 -1/1 -5/3 1/0 -18/11 -2/1 -31/19 -3/2 -75/46 -3/2 -44/27 -3/2 -23/16 -13/8 -5/4 -1/1 -21/13 1/0 -50/31 -1/1 -29/18 -1/1 1/0 -8/5 -3/2 1/0 -19/12 -11/10 -1/1 -30/19 -1/1 -11/7 -5/6 -14/9 -1/2 1/0 -3/2 -1/1 0/1 -16/11 -1/2 1/0 -45/31 1/0 -29/20 -1/1 1/0 -13/9 -1/2 -10/7 -1/1 -17/12 -4/5 -3/4 -24/17 -1/1 -7/5 -1/2 -18/13 -2/3 -29/21 -1/2 -40/29 -1/1 -11/8 -2/3 -1/2 -15/11 -1/2 -4/3 -1/2 1/0 -17/13 -7/6 -30/23 -1/1 -13/10 -1/1 -7/8 -9/7 -3/4 -14/11 -3/4 -1/2 -5/4 -1/2 -16/13 -1/2 -1/4 -11/9 1/2 -17/14 -2/1 1/0 -6/5 -1/1 -13/11 -7/10 -7/6 -3/5 -1/2 -15/13 -1/2 -8/7 -1/2 -3/8 -1/1 -1/2 0/1 0/1 1/1 1/2 8/7 3/8 1/2 15/13 1/2 7/6 1/2 3/5 6/5 1/1 17/14 2/1 1/0 11/9 -1/2 5/4 1/2 14/11 1/2 3/4 9/7 3/4 13/10 7/8 1/1 4/3 1/2 1/0 15/11 1/2 11/8 1/2 2/3 7/5 1/2 17/12 3/4 4/5 10/7 1/1 13/9 1/2 3/2 0/1 1/1 17/11 1/2 14/9 1/2 1/0 25/16 1/2 11/7 5/6 8/5 3/2 1/0 29/18 1/1 1/0 21/13 1/0 13/8 1/1 5/4 5/3 1/0 17/10 0/1 1/4 29/17 1/2 12/7 1/1 7/4 1/2 1/1 16/9 3/2 1/0 9/5 1/0 29/16 1/1 1/0 20/11 1/1 11/6 3/2 2/1 13/7 7/2 15/8 1/0 2/1 1/2 1/0 15/7 1/0 13/6 -3/1 1/0 11/5 -1/2 20/9 -1/1 9/4 -1/1 0/1 16/7 -1/2 -1/4 23/10 -1/6 0/1 30/13 0/1 7/3 1/2 19/8 1/2 1/1 50/21 0/1 31/13 1/2 12/5 1/1 5/2 1/0 18/7 -1/1 31/12 -1/1 1/0 75/29 1/0 44/17 -3/2 1/0 13/5 -3/2 21/8 -1/1 -2/3 50/19 -2/3 29/11 -1/2 8/3 -1/2 -1/4 19/7 -1/10 30/11 0/1 11/4 0/1 1/6 14/5 3/8 1/2 3/1 1/0 16/5 -5/8 -1/2 45/14 -1/2 29/9 -1/2 13/4 -1/3 -1/4 10/3 0/1 17/5 1/6 24/7 1/3 7/2 1/2 1/1 18/5 1/1 29/8 1/1 1/0 40/11 1/1 11/3 3/2 15/4 1/0 4/1 -1/2 1/0 17/4 -1/8 0/1 30/7 0/1 13/3 1/6 9/2 0/1 1/1 14/3 1/4 1/2 5/1 1/0 16/3 -3/4 -1/2 11/2 0/1 1/2 17/3 -3/2 6/1 0/1 13/2 -1/1 1/0 7/1 1/2 15/2 1/0 8/1 -1/2 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,240,18,149) (-8/1,1/0) -> (8/5,29/18) Hyperbolic Matrix(31,240,4,31) (-8/1,-15/2) -> (15/2,8/1) Hyperbolic Matrix(29,210,4,29) (-15/2,-7/1) -> (7/1,15/2) Hyperbolic Matrix(31,210,-22,-149) (-7/1,-6/1) -> (-24/17,-7/5) Hyperbolic Matrix(89,510,26,149) (-6/1,-17/3) -> (17/5,24/7) 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(89,420,-32,-151) (-5/1,-14/3) -> (-14/5,-25/9) Hyperbolic Matrix(59,270,26,119) (-14/3,-9/2) -> (9/4,16/7) Hyperbolic Matrix(89,390,34,149) (-9/2,-13/3) -> (13/5,21/8) Hyperbolic Matrix(29,120,-22,-91) (-13/3,-4/1) -> (-4/3,-17/13) Hyperbolic Matrix(31,120,8,31) (-4/1,-15/4) -> (15/4,4/1) Hyperbolic Matrix(89,330,24,89) (-15/4,-11/3) -> (11/3,15/4) 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(89,300,62,209) (-17/5,-10/3) -> (10/7,13/9) Hyperbolic Matrix(91,300,64,211) (-10/3,-13/4) -> (17/12,10/7) Hyperbolic Matrix(29,90,-10,-31) (-13/4,-3/1) -> (-3/1,-17/6) Parabolic Matrix(329,930,-202,-571) (-17/6,-14/5) -> (-44/27,-13/8) Hyperbolic Matrix(89,240,-56,-151) (-11/4,-8/3) -> (-8/5,-19/12) Hyperbolic Matrix(91,240,80,211) (-8/3,-29/11) -> (1/1,8/7) Hyperbolic Matrix(331,870,-148,-389) (-29/11,-21/8) -> (-9/4,-29/13) Hyperbolic Matrix(149,390,34,89) (-21/8,-13/5) -> (13/3,9/2) 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(89,210,-64,-151) (-12/5,-7/3) -> (-7/5,-18/13) Hyperbolic Matrix(209,480,-118,-271) (-7/3,-16/7) -> (-16/9,-23/13) Hyperbolic Matrix(119,270,26,59) (-16/7,-9/4) -> (9/2,14/3) Hyperbolic Matrix(929,2070,390,869) (-29/13,-20/9) -> (50/21,31/13) Hyperbolic Matrix(421,930,-244,-539) (-20/9,-11/5) -> (-19/11,-50/29) Hyperbolic Matrix(151,330,124,271) (-11/5,-13/6) -> (17/14,11/9) Hyperbolic Matrix(181,390,84,181) (-13/6,-15/7) -> (15/7,13/6) Hyperbolic Matrix(29,60,14,29) (-15/7,-2/1) -> (2/1,15/7) Hyperbolic Matrix(31,60,16,31) (-2/1,-15/8) -> (15/8,2/1) Hyperbolic Matrix(209,390,112,209) (-15/8,-13/7) -> (13/7,15/8) 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(151,270,118,211) (-9/5,-16/9) -> (14/11,9/7) Hyperbolic Matrix(509,900,220,389) (-23/13,-30/17) -> (30/13,7/3) Hyperbolic Matrix(511,900,222,391) (-30/17,-7/4) -> (23/10,30/13) 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(89,150,-54,-91) (-12/7,-5/3) -> (-5/3,-18/11) Parabolic Matrix(569,930,238,389) (-18/11,-31/19) -> (31/13,12/5) Hyperbolic Matrix(2189,3570,680,1109) (-31/19,-75/46) -> (45/14,29/9) Hyperbolic Matrix(1951,3180,608,991) (-75/46,-44/27) -> (16/5,45/14) 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(149,240,18,29) (-29/18,-8/5) -> (8/1,1/0) Hyperbolic Matrix(569,900,208,329) (-19/12,-30/19) -> (30/11,11/4) Hyperbolic Matrix(571,900,210,331) (-30/19,-11/7) -> (19/7,30/11) Hyperbolic Matrix(211,330,-172,-269) (-11/7,-14/9) -> (-16/13,-11/9) Hyperbolic Matrix(59,90,-40,-61) (-14/9,-3/2) -> (-3/2,-16/11) Parabolic Matrix(2189,3180,846,1229) (-16/11,-45/31) -> (75/29,44/17) Hyperbolic Matrix(2461,3570,952,1381) (-45/31,-29/20) -> (31/12,75/29) Hyperbolic Matrix(209,300,62,89) (-13/9,-10/7) -> (10/3,17/5) Hyperbolic Matrix(211,300,64,91) (-10/7,-17/12) -> (13/4,10/3) Hyperbolic Matrix(361,510,298,421) (-17/12,-24/17) -> (6/5,17/14) Hyperbolic Matrix(629,870,368,509) (-18/13,-29/21) -> (29/17,12/7) Hyperbolic Matrix(1891,2610,718,991) (-29/21,-40/29) -> (50/19,29/11) Hyperbolic Matrix(241,330,176,241) (-11/8,-15/11) -> (15/11,11/8) Hyperbolic Matrix(89,120,66,89) (-15/11,-4/3) -> (4/3,15/11) Hyperbolic Matrix(689,900,160,209) (-17/13,-30/23) -> (30/7,13/3) Hyperbolic Matrix(691,900,162,211) (-30/23,-13/10) -> (17/4,30/7) Hyperbolic Matrix(301,390,186,241) (-13/10,-9/7) -> (21/13,13/8) Hyperbolic Matrix(211,270,118,151) (-9/7,-14/11) -> (16/9,9/5) Hyperbolic Matrix(119,150,-96,-121) (-14/11,-5/4) -> (-5/4,-16/13) Parabolic Matrix(271,330,124,151) (-11/9,-17/14) -> (13/6,11/5) Hyperbolic Matrix(149,180,24,29) (-17/14,-6/5) -> (6/1,13/2) Hyperbolic Matrix(151,180,26,31) (-6/5,-13/11) -> (17/3,6/1) Hyperbolic Matrix(181,210,156,181) (-7/6,-15/13) -> (15/13,7/6) Hyperbolic Matrix(209,240,182,209) (-15/13,-8/7) -> (8/7,15/13) Hyperbolic Matrix(211,240,80,91) (-8/7,-1/1) -> (29/11,8/3) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(179,-210,52,-61) (7/6,6/5) -> (24/7,7/2) Hyperbolic Matrix(269,-330,172,-211) (11/9,5/4) -> (25/16,11/7) Hyperbolic Matrix(331,-420,212,-269) (5/4,14/11) -> (14/9,25/16) Hyperbolic Matrix(91,-120,22,-29) (13/10,4/3) -> (4/1,17/4) Hyperbolic Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(149,-210,22,-31) (7/5,17/12) -> (13/2,7/1) 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(151,-240,56,-89) (11/7,8/5) -> (8/3,19/7) Hyperbolic Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(511,-870,158,-269) (17/10,29/17) -> (29/9,13/4) Hyperbolic Matrix(121,-210,34,-59) (12/7,7/4) -> (7/2,18/5) Hyperbolic Matrix(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(509,-930,214,-391) (20/11,11/6) -> (19/8,50/21) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(389,-870,148,-331) (20/9,9/4) -> (21/8,50/19) Hyperbolic Matrix(61,-150,24,-59) (12/5,5/2) -> (5/2,18/7) Parabolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,240,18,149) -> Matrix(1,1,0,1) Matrix(31,240,4,31) -> Matrix(1,-1,0,1) Matrix(29,210,4,29) -> Matrix(1,1,0,1) Matrix(31,210,-22,-149) -> Matrix(3,1,-4,-1) Matrix(89,510,26,149) -> Matrix(1,-1,4,-3) Matrix(59,330,32,179) -> Matrix(1,2,0,1) Matrix(61,330,-22,-119) -> Matrix(1,0,-4,1) Matrix(89,420,-32,-151) -> Matrix(1,1,-4,-3) Matrix(59,270,26,119) -> Matrix(1,0,0,1) Matrix(89,390,34,149) -> Matrix(3,1,-4,-1) Matrix(29,120,-22,-91) -> Matrix(1,-1,0,1) Matrix(31,120,8,31) -> Matrix(1,-1,0,1) Matrix(89,330,24,89) -> Matrix(1,3,0,1) Matrix(59,210,-34,-121) -> Matrix(1,0,0,1) Matrix(61,210,-52,-179) -> Matrix(5,2,-8,-3) Matrix(89,300,62,209) -> Matrix(5,1,4,1) Matrix(91,300,64,211) -> Matrix(7,-1,8,-1) Matrix(29,90,-10,-31) -> Matrix(1,-1,0,1) Matrix(329,930,-202,-571) -> Matrix(11,7,-8,-5) Matrix(89,240,-56,-151) -> Matrix(5,-1,-4,1) Matrix(91,240,80,211) -> Matrix(1,-1,4,-3) Matrix(331,870,-148,-389) -> Matrix(1,-1,4,-3) Matrix(149,390,34,89) -> Matrix(1,-1,4,-3) Matrix(59,150,-24,-61) -> Matrix(1,-2,0,1) Matrix(359,870,-248,-601) -> Matrix(1,0,0,1) Matrix(361,870,100,241) -> Matrix(1,2,0,1) Matrix(89,210,-64,-151) -> Matrix(3,1,-4,-1) Matrix(209,480,-118,-271) -> Matrix(5,-1,-4,1) Matrix(119,270,26,59) -> Matrix(1,0,0,1) Matrix(929,2070,390,869) -> Matrix(1,-1,4,-3) Matrix(421,930,-244,-539) -> Matrix(1,-2,0,1) Matrix(151,330,124,271) -> Matrix(1,-1,0,1) Matrix(181,390,84,181) -> Matrix(1,-6,0,1) Matrix(29,60,14,29) -> Matrix(1,1,0,1) Matrix(31,60,16,31) -> Matrix(1,1,0,1) Matrix(209,390,112,209) -> Matrix(1,7,0,1) Matrix(179,330,32,59) -> Matrix(1,2,0,1) Matrix(361,660,-262,-479) -> Matrix(3,4,-4,-5) Matrix(481,870,-298,-539) -> Matrix(1,0,0,1) Matrix(151,270,118,211) -> Matrix(3,5,4,7) Matrix(509,900,220,389) -> Matrix(1,1,8,9) Matrix(511,900,222,391) -> Matrix(1,1,-8,-7) Matrix(1201,2070,662,1141) -> Matrix(1,2,0,1) Matrix(541,930,210,361) -> Matrix(1,0,0,1) Matrix(89,150,-54,-91) -> Matrix(1,-1,0,1) Matrix(569,930,238,389) -> Matrix(3,5,4,7) Matrix(2189,3570,680,1109) -> Matrix(11,17,-24,-37) Matrix(1951,3180,608,991) -> Matrix(13,19,-24,-35) Matrix(241,390,186,301) -> Matrix(3,2,4,3) Matrix(1619,2610,446,719) -> Matrix(1,2,0,1) Matrix(149,240,18,29) -> Matrix(1,1,0,1) Matrix(569,900,208,329) -> Matrix(1,1,16,17) Matrix(571,900,210,331) -> Matrix(1,1,-16,-15) Matrix(211,330,-172,-269) -> Matrix(1,1,-4,-3) Matrix(59,90,-40,-61) -> Matrix(1,0,0,1) Matrix(2189,3180,846,1229) -> Matrix(1,-1,0,1) Matrix(2461,3570,952,1381) -> Matrix(1,0,0,1) Matrix(209,300,62,89) -> Matrix(1,1,4,5) Matrix(211,300,64,91) -> Matrix(1,1,-8,-7) Matrix(361,510,298,421) -> Matrix(3,2,4,3) Matrix(629,870,368,509) -> Matrix(5,3,8,5) Matrix(1891,2610,718,991) -> Matrix(3,1,-4,-1) Matrix(241,330,176,241) -> Matrix(7,4,12,7) Matrix(89,120,66,89) -> Matrix(1,1,0,1) Matrix(689,900,160,209) -> Matrix(1,1,12,13) Matrix(691,900,162,211) -> Matrix(1,1,-16,-15) Matrix(301,390,186,241) -> Matrix(3,2,4,3) Matrix(211,270,118,151) -> Matrix(7,5,4,3) Matrix(119,150,-96,-121) -> Matrix(3,2,-8,-5) Matrix(271,330,124,151) -> Matrix(1,-1,0,1) Matrix(149,180,24,29) -> Matrix(1,1,0,1) Matrix(151,180,26,31) -> Matrix(1,1,-4,-3) Matrix(181,210,156,181) -> Matrix(11,6,20,11) Matrix(209,240,182,209) -> Matrix(7,3,16,7) Matrix(211,240,80,91) -> Matrix(3,1,-4,-1) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(179,-210,52,-61) -> Matrix(3,-2,8,-5) Matrix(269,-330,172,-211) -> Matrix(3,-1,4,-1) Matrix(331,-420,212,-269) -> Matrix(1,-1,4,-3) Matrix(91,-120,22,-29) -> Matrix(1,-1,0,1) Matrix(151,-210,64,-89) -> Matrix(1,-1,4,-3) Matrix(149,-210,22,-31) -> Matrix(1,-1,4,-3) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(1,-2,0,1) Matrix(151,-240,56,-89) -> Matrix(1,-1,-4,5) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(91,-150,54,-89) -> Matrix(1,-1,0,1) Matrix(511,-870,158,-269) -> Matrix(3,-1,-8,3) Matrix(121,-210,34,-59) -> Matrix(1,0,0,1) Matrix(271,-480,118,-209) -> Matrix(1,-1,-4,5) Matrix(509,-930,214,-391) -> Matrix(1,-1,0,1) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) Matrix(389,-870,148,-331) -> Matrix(3,1,-4,-1) Matrix(61,-150,24,-59) -> Matrix(1,-2,0,1) Matrix(119,-330,22,-61) -> Matrix(1,0,-4,1) Matrix(31,-90,10,-29) -> Matrix(1,-1,0,1) Matrix(31,-150,6,-29) -> Matrix(1,-1,0,1) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- 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 2 1 1/1 1/2 1 30 8/7 (3/8,1/2) 0 15 15/13 1/2 9 2 7/6 (1/2,3/5) 0 30 6/5 1/1 2 5 17/14 (2/1,1/0) 0 30 11/9 -1/2 1 30 5/4 1/2 2 6 14/11 (1/2,3/4) 0 15 9/7 3/4 1 10 13/10 (7/8,1/1) 0 30 4/3 (1/2,1/0) 0 15 15/11 1/2 3 2 11/8 (1/2,2/3) 0 30 7/5 1/2 1 30 17/12 (3/4,4/5) 0 30 10/7 1/1 6 3 13/9 1/2 1 30 3/2 0 10 17/11 1/2 1 30 14/9 (1/2,1/0) 0 15 25/16 1/2 2 6 11/7 5/6 1 30 8/5 (3/2,1/0) 0 15 29/18 (1/1,1/0) 0 30 21/13 1/0 1 10 13/8 (1/1,5/4) 0 30 5/3 1/0 1 6 17/10 (0/1,1/4) 0 30 29/17 1/2 1 30 12/7 1/1 2 5 7/4 (1/2,1/1) 0 30 16/9 (3/2,1/0) 0 15 9/5 1/0 1 10 29/16 (1/1,1/0) 0 30 20/11 1/1 2 3 11/6 (3/2,2/1) 0 30 13/7 7/2 1 30 15/8 1/0 6 2 2/1 (1/2,1/0) 0 15 15/7 1/0 7 2 13/6 (-3/1,1/0) 0 30 11/5 -1/2 1 30 20/9 -1/1 2 3 9/4 0 10 16/7 (-1/2,-1/4) 0 15 23/10 (-1/6,0/1) 0 30 30/13 0/1 8 1 7/3 1/2 1 30 19/8 (1/2,1/1) 0 30 50/21 0/1 2 3 31/13 1/2 1 30 12/5 1/1 2 5 5/2 1/0 2 6 18/7 -1/1 2 5 31/12 (-1/1,1/0) 0 30 75/29 1/0 1 2 44/17 (-3/2,1/0) 0 15 13/5 -3/2 1 30 21/8 0 10 50/19 -2/3 2 3 29/11 -1/2 1 30 8/3 (-1/2,-1/4) 0 15 19/7 -1/10 1 30 30/11 0/1 16 1 11/4 (0/1,1/6) 0 30 14/5 (3/8,1/2) 0 15 3/1 1/0 1 10 16/5 (-5/8,-1/2) 0 15 45/14 -1/2 12 2 29/9 -1/2 1 30 13/4 (-1/3,-1/4) 0 30 10/3 0/1 6 3 17/5 1/6 1 30 24/7 1/3 2 5 7/2 (1/2,1/1) 0 30 18/5 1/1 2 5 29/8 (1/1,1/0) 0 30 40/11 1/1 2 3 11/3 3/2 1 30 15/4 1/0 4 2 4/1 (-1/2,1/0) 0 15 17/4 (-1/8,0/1) 0 30 30/7 0/1 14 1 13/3 1/6 1 30 9/2 0 10 14/3 (1/4,1/2) 0 15 5/1 1/0 1 6 16/3 (-3/4,-1/2) 0 15 11/2 (0/1,1/2) 0 30 17/3 -3/2 1 30 6/1 0/1 2 5 13/2 (-1/1,1/0) 0 30 7/1 1/2 1 30 15/2 1/0 2 2 8/1 (-1/2,1/0) 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(211,-240,80,-91) (1/1,8/7) -> (29/11,8/3) Glide Reflection Matrix(209,-240,182,-209) (8/7,15/13) -> (8/7,15/13) 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(149,-180,24,-29) (6/5,17/14) -> (6/1,13/2) Glide Reflection Matrix(271,-330,124,-151) (17/14,11/9) -> (13/6,11/5) Glide Reflection Matrix(269,-330,172,-211) (11/9,5/4) -> (25/16,11/7) Hyperbolic Matrix(331,-420,212,-269) (5/4,14/11) -> (14/9,25/16) Hyperbolic Matrix(211,-270,118,-151) (14/11,9/7) -> (16/9,9/5) Glide Reflection Matrix(301,-390,186,-241) (9/7,13/10) -> (21/13,13/8) Glide Reflection Matrix(91,-120,22,-29) (13/10,4/3) -> (4/1,17/4) Hyperbolic Matrix(89,-120,66,-89) (4/3,15/11) -> (4/3,15/11) Reflection Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(151,-210,64,-89) (11/8,7/5) -> (7/3,19/8) Hyperbolic Matrix(149,-210,22,-31) (7/5,17/12) -> (13/2,7/1) Hyperbolic Matrix(211,-300,64,-91) (17/12,10/7) -> (13/4,10/3) Glide Reflection Matrix(209,-300,62,-89) (10/7,13/9) -> (10/3,17/5) Glide Reflection 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(151,-240,56,-89) (11/7,8/5) -> (8/3,19/7) Hyperbolic Matrix(149,-240,18,-29) (8/5,29/18) -> (8/1,1/0) Glide Reflection Matrix(539,-870,298,-481) (29/18,21/13) -> (9/5,29/16) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(511,-870,158,-269) (17/10,29/17) -> (29/9,13/4) 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(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(959,-1740,264,-479) (29/16,20/11) -> (29/8,40/11) Glide Reflection Matrix(509,-930,214,-391) (20/11,11/6) -> (19/8,50/21) Hyperbolic Matrix(179,-330,32,-59) (11/6,13/7) -> (11/2,17/3) Glide Reflection Matrix(209,-390,112,-209) (13/7,15/8) -> (13/7,15/8) Reflection Matrix(31,-60,16,-31) (15/8,2/1) -> (15/8,2/1) Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection 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(389,-870,148,-331) (20/9,9/4) -> (21/8,50/19) Hyperbolic 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(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(419,-1080,116,-299) (18/7,31/12) -> (18/5,29/8) Glide Reflection Matrix(1799,-4650,696,-1799) (31/12,75/29) -> (31/12,75/29) Reflection Matrix(2551,-6600,986,-2551) (75/29,44/17) -> (75/29,44/17) Reflection Matrix(149,-390,34,-89) (13/5,21/8) -> (13/3,9/2) 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(31,-90,10,-29) (14/5,3/1) -> (3/1,16/5) Parabolic Matrix(449,-1440,140,-449) (16/5,45/14) -> (16/5,45/14) Reflection Matrix(811,-2610,252,-811) (45/14,29/9) -> (45/14,29/9) Reflection Matrix(149,-510,26,-89) (17/5,24/7) -> (17/3,6/1) Glide Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection 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(31,-150,6,-29) (14/3,5/1) -> (5/1,16/3) Parabolic Matrix(29,-210,4,-29) (7/1,15/2) -> (7/1,15/2) Reflection Matrix(31,-240,4,-31) (15/2,8/1) -> (15/2,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,4,-1) (0/1,1/1) -> (0/1,1/2) Matrix(211,-240,80,-91) -> Matrix(3,-1,-4,1) Matrix(209,-240,182,-209) -> Matrix(7,-3,16,-7) (8/7,15/13) -> (3/8,1/2) Matrix(181,-210,156,-181) -> Matrix(11,-6,20,-11) (15/13,7/6) -> (1/2,3/5) Matrix(179,-210,52,-61) -> Matrix(3,-2,8,-5) 1/2 Matrix(149,-180,24,-29) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(271,-330,124,-151) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(269,-330,172,-211) -> Matrix(3,-1,4,-1) 1/2 Matrix(331,-420,212,-269) -> Matrix(1,-1,4,-3) 1/2 Matrix(211,-270,118,-151) -> Matrix(7,-5,4,-3) Matrix(301,-390,186,-241) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(91,-120,22,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(89,-120,66,-89) -> Matrix(-1,1,0,1) (4/3,15/11) -> (1/2,1/0) Matrix(241,-330,176,-241) -> Matrix(7,-4,12,-7) (15/11,11/8) -> (1/2,2/3) Matrix(151,-210,64,-89) -> Matrix(1,-1,4,-3) 1/2 Matrix(149,-210,22,-31) -> Matrix(1,-1,4,-3) 1/2 Matrix(211,-300,64,-91) -> Matrix(1,-1,-8,7) Matrix(209,-300,62,-89) -> Matrix(1,-1,4,-5) Matrix(61,-90,40,-59) -> Matrix(1,0,0,1) Matrix(601,-930,232,-359) -> Matrix(1,-2,0,1) 1/0 Matrix(151,-240,56,-89) -> Matrix(1,-1,-4,5) Matrix(149,-240,18,-29) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(539,-870,298,-481) -> Matrix(1,0,0,1) Matrix(91,-150,54,-89) -> Matrix(1,-1,0,1) 1/0 Matrix(511,-870,158,-269) -> Matrix(3,-1,-8,3) Matrix(421,-720,176,-301) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(121,-210,34,-59) -> Matrix(1,0,0,1) Matrix(271,-480,118,-209) -> Matrix(1,-1,-4,5) Matrix(959,-1740,264,-479) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(509,-930,214,-391) -> Matrix(1,-1,0,1) 1/0 Matrix(179,-330,32,-59) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(209,-390,112,-209) -> Matrix(-1,7,0,1) (13/7,15/8) -> (7/2,1/0) Matrix(31,-60,16,-31) -> Matrix(-1,1,0,1) (15/8,2/1) -> (1/2,1/0) Matrix(29,-60,14,-29) -> Matrix(-1,1,0,1) (2/1,15/7) -> (1/2,1/0) Matrix(181,-390,84,-181) -> Matrix(1,6,0,-1) (15/7,13/6) -> (-3/1,1/0) Matrix(299,-660,82,-181) -> Matrix(1,2,0,1) 1/0 Matrix(389,-870,148,-331) -> Matrix(3,1,-4,-1) -1/2 Matrix(119,-270,26,-59) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(599,-1380,260,-599) -> Matrix(-1,0,12,1) (23/10,30/13) -> (-1/6,0/1) Matrix(181,-420,78,-181) -> Matrix(1,0,4,-1) (30/13,7/3) -> (0/1,1/2) Matrix(1259,-3000,478,-1139) -> Matrix(5,-2,-8,3) Matrix(61,-150,24,-59) -> Matrix(1,-2,0,1) 1/0 Matrix(419,-1080,116,-299) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1799,-4650,696,-1799) -> Matrix(1,2,0,-1) (31/12,75/29) -> (-1/1,1/0) Matrix(2551,-6600,986,-2551) -> Matrix(1,3,0,-1) (75/29,44/17) -> (-3/2,1/0) Matrix(149,-390,34,-89) -> Matrix(1,1,4,3) Matrix(419,-1140,154,-419) -> Matrix(-1,0,20,1) (19/7,30/11) -> (-1/10,0/1) Matrix(241,-660,88,-241) -> Matrix(1,0,12,-1) (30/11,11/4) -> (0/1,1/6) Matrix(119,-330,22,-61) -> Matrix(1,0,-4,1) 0/1 Matrix(31,-90,10,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(449,-1440,140,-449) -> Matrix(9,5,-16,-9) (16/5,45/14) -> (-5/8,-1/2) Matrix(811,-2610,252,-811) -> Matrix(15,7,-32,-15) (45/14,29/9) -> (-1/2,-7/16) Matrix(149,-510,26,-89) -> Matrix(3,-1,-4,1) Matrix(89,-330,24,-89) -> Matrix(-1,3,0,1) (11/3,15/4) -> (3/2,1/0) Matrix(31,-120,8,-31) -> Matrix(1,1,0,-1) (15/4,4/1) -> (-1/2,1/0) Matrix(239,-1020,56,-239) -> Matrix(-1,0,16,1) (17/4,30/7) -> (-1/8,0/1) Matrix(181,-780,42,-181) -> Matrix(1,0,12,-1) (30/7,13/3) -> (0/1,1/6) Matrix(31,-150,6,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(29,-210,4,-29) -> Matrix(-1,1,0,1) (7/1,15/2) -> (1/2,1/0) Matrix(31,-240,4,-31) -> Matrix(1,1,0,-1) (15/2,8/1) -> (-1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.