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: 64 Genus: 65 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -20/3 -6/1 -5/1 -9/2 -18/5 -10/3 -3/1 -50/19 -5/2 -12/5 -20/9 -9/5 -5/3 -45/29 -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 60/23 50/19 30/11 3/1 45/14 10/3 24/7 7/2 210/59 18/5 11/3 26/7 15/4 4/1 30/7 13/3 9/2 60/13 14/3 24/5 5/1 16/3 60/11 11/2 28/5 6/1 13/2 20/3 7/1 22/3 15/2 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 1/0 -15/2 0/1 -22/3 0/1 1/4 -7/1 1/2 1/1 -20/3 0/1 -13/2 1/3 2/5 -6/1 1/1 -17/3 3/1 4/1 -28/5 1/0 -11/2 1/1 1/0 -16/3 1/0 -5/1 0/1 -14/3 2/5 1/2 -23/5 1/2 7/13 -32/7 1/2 -9/2 3/5 1/1 -31/7 2/3 1/1 -22/5 2/3 3/4 -13/3 6/7 1/1 -4/1 1/0 -15/4 0/1 -26/7 0/1 1/6 -11/3 1/4 1/3 -29/8 0/1 1/3 -18/5 1/3 -7/2 1/2 3/5 -38/11 2/3 3/4 -31/9 2/3 1/1 -24/7 2/3 -17/5 7/9 4/5 -10/3 1/1 -13/4 5/3 2/1 -16/5 1/0 -19/6 3/1 1/0 -3/1 -1/1 1/1 -20/7 0/1 -17/6 2/3 1/1 -14/5 0/1 1/2 -25/9 2/3 -36/13 2/3 -11/4 5/6 1/1 -8/3 3/2 -29/11 1/1 2/1 -50/19 1/1 -21/8 1/1 5/3 -34/13 7/4 2/1 -13/5 2/1 7/3 -31/12 2/1 3/1 -18/7 3/1 -5/2 1/0 -27/11 -3/1 -1/1 -49/20 1/1 1/0 -22/9 -2/1 1/0 -17/7 -1/1 -2/3 -29/12 -1/1 0/1 -12/5 0/1 -31/13 0/1 1/1 -50/21 1/1 -19/8 -1/1 1/0 -26/11 0/1 1/2 -59/25 0/1 1/3 -33/14 1/3 1/1 -7/3 1/2 1/1 -16/7 3/2 -25/11 2/1 -59/26 1/1 2/1 -34/15 3/2 2/1 -9/4 1/1 3/1 -29/13 1/1 2/1 -20/9 2/1 -31/14 2/1 3/1 -11/5 5/2 3/1 -13/6 6/1 7/1 -15/7 1/0 -2/1 0/1 1/0 -15/8 1/0 -28/15 1/0 -13/7 -7/1 -6/1 -24/13 -4/1 -11/6 -3/1 -5/2 -20/11 -2/1 -29/16 -2/1 -1/1 -9/5 -3/1 -1/1 -25/14 -2/1 -16/9 -3/2 -23/13 -7/6 -1/1 -30/17 -1/1 -7/4 -1/1 -1/2 -33/19 -1/1 -1/3 -59/34 -1/3 0/1 -26/15 -1/2 0/1 -19/11 1/1 1/0 -69/40 -3/1 -1/1 -50/29 -1/1 -31/18 -1/1 0/1 -12/7 0/1 -29/17 0/1 1/1 -75/44 0/1 -46/27 0/1 1/2 -17/10 2/3 1/1 -22/13 2/1 1/0 -27/16 1/1 3/1 -5/3 1/0 -33/20 -3/1 -1/1 -61/37 -2/1 -1/1 -28/17 1/0 -23/14 -7/1 1/0 -18/11 -3/1 -31/19 -3/1 -2/1 -75/46 -2/1 -44/27 1/0 -13/8 -7/3 -2/1 -60/37 -2/1 -47/29 -2/1 -21/11 -34/21 -2/1 -7/4 -89/55 -2/1 -5/3 -55/34 -2/1 -21/13 -5/3 -1/1 -71/44 -3/2 -7/5 -50/31 -1/1 -29/18 -2/1 -1/1 -8/5 -3/2 -19/12 -11/10 -1/1 -30/19 -1/1 -11/7 -1/1 -5/6 -14/9 -1/2 0/1 -45/29 0/1 -31/20 -1/1 0/1 -17/11 -1/1 -2/3 -20/13 0/1 -23/15 -1/1 1/0 -3/2 -1/1 1/1 -16/11 1/0 -45/31 -2/1 -29/20 -2/1 -1/1 -13/9 -2/1 -5/3 -10/7 -1/1 -17/12 -4/5 -7/9 -41/29 -13/18 -5/7 -24/17 -2/3 -55/39 -2/3 -31/22 -1/1 -2/3 -7/5 -3/5 -1/2 -32/23 -1/2 -121/87 -4/9 -3/7 -210/151 -3/7 -89/64 -3/7 -2/5 -57/41 -3/7 -1/3 -25/18 -1/2 -18/13 -1/3 -29/21 -1/3 0/1 -40/29 0/1 -11/8 -1/3 -1/4 -26/19 -1/6 0/1 -15/11 0/1 -4/3 1/0 -17/13 -8/7 -1/1 -30/23 -1/1 -13/10 -1/1 -6/7 -22/17 -3/4 -2/3 -53/41 -3/5 -1/2 -31/24 -1/1 -2/3 -9/7 -1/1 -3/5 -41/32 -5/9 -1/2 -32/25 -1/2 -23/18 -7/13 -1/2 -60/47 -1/2 -37/29 -1/2 -11/23 -14/11 -1/2 -2/5 -19/15 -1/3 -3/10 -24/19 0/1 -29/23 -1/3 0/1 -5/4 0/1 -16/13 1/0 -27/22 1/1 3/1 -38/31 2/1 1/0 -49/40 5/1 1/0 -60/49 1/0 -11/9 -1/1 1/0 -39/32 1/1 3/1 -28/23 1/0 -45/37 1/0 -17/14 -4/1 -3/1 -6/5 -1/1 -13/11 -2/5 -1/3 -20/17 0/1 -27/23 -1/1 -1/3 -7/6 -1/1 -1/2 -22/19 -1/4 0/1 -15/13 0/1 -8/7 1/0 -1/1 -1/1 0/1 0/1 0/1 1/1 0/1 1/3 8/7 1/2 15/13 0/1 22/19 0/1 1/6 7/6 1/4 1/3 20/17 0/1 13/11 1/5 2/9 6/5 1/3 17/14 3/7 4/9 28/23 1/2 11/9 1/3 1/2 16/13 1/2 5/4 0/1 14/11 2/9 1/4 23/18 1/4 7/27 32/25 1/4 9/7 3/11 1/3 31/24 2/7 1/3 22/17 2/7 3/10 13/10 6/19 1/3 4/3 1/2 15/11 0/1 26/19 0/1 1/8 11/8 1/6 1/5 29/21 0/1 1/5 18/13 1/5 7/5 1/4 3/11 38/27 2/7 3/10 31/22 2/7 1/3 24/17 2/7 17/12 7/23 4/13 10/7 1/3 13/9 5/13 2/5 16/11 1/2 19/13 3/7 1/2 3/2 1/3 1/1 20/13 0/1 17/11 2/7 1/3 14/9 0/1 1/4 25/16 2/7 36/23 2/7 11/7 5/16 1/3 8/5 3/8 29/18 1/3 2/5 50/31 1/3 21/13 1/3 5/13 34/21 7/18 2/5 13/8 2/5 7/17 31/19 2/5 3/7 18/11 3/7 5/3 1/2 27/16 3/5 1/1 49/29 1/3 1/2 22/13 1/2 2/3 17/10 1/1 2/1 29/17 0/1 1/1 12/7 0/1 31/18 0/1 1/3 50/29 1/3 19/11 1/2 1/1 26/15 0/1 1/4 59/34 0/1 1/5 33/19 1/5 1/3 7/4 1/4 1/3 16/9 3/8 25/14 2/5 59/33 1/3 2/5 34/19 3/8 2/5 9/5 1/3 3/7 29/16 1/3 2/5 20/11 2/5 31/17 2/5 3/7 11/6 5/12 3/7 13/7 6/13 7/15 15/8 1/2 2/1 0/1 1/2 15/7 1/2 28/13 1/2 13/6 7/13 6/11 24/11 4/7 11/5 3/5 5/8 20/9 2/3 29/13 2/3 1/1 9/4 3/5 1/1 25/11 2/3 16/7 3/4 23/10 7/8 1/1 30/13 1/1 7/3 1/1 1/0 33/14 -1/1 1/1 59/25 -1/1 0/1 26/11 0/1 1/0 19/8 1/3 1/2 69/29 3/5 1/1 50/21 1/1 31/13 0/1 1/1 12/5 0/1 29/12 0/1 1/3 75/31 0/1 46/19 0/1 1/4 17/7 2/7 1/3 22/9 2/5 1/2 27/11 1/3 3/7 5/2 1/2 33/13 3/5 1/1 61/24 2/3 1/1 28/11 1/2 23/9 1/2 7/13 18/7 3/5 31/12 3/5 2/3 75/29 2/3 44/17 1/2 13/5 7/11 2/3 60/23 2/3 47/18 2/3 21/31 34/13 2/3 7/10 89/34 2/3 5/7 55/21 2/3 21/8 5/7 1/1 71/27 3/4 7/9 50/19 1/1 29/11 2/3 1/1 8/3 3/4 19/7 11/12 1/1 30/11 1/1 11/4 1/1 5/4 14/5 0/1 1/0 45/16 0/1 31/11 0/1 1/1 17/6 1/1 2/1 20/7 0/1 23/8 1/2 1/1 3/1 1/3 1/1 16/5 1/2 45/14 2/3 29/9 2/3 1/1 13/4 2/3 5/7 10/3 1/1 17/5 4/3 7/5 41/12 13/8 5/3 24/7 2/1 55/16 2/1 31/9 1/1 2/1 7/2 3/1 1/0 32/9 1/0 121/34 -4/1 -3/1 210/59 -3/1 89/25 -3/1 -2/1 57/16 -3/1 -1/1 25/7 1/0 18/5 -1/1 29/8 -1/1 0/1 40/11 0/1 11/3 -1/1 -1/2 26/7 -1/4 0/1 15/4 0/1 4/1 1/2 17/4 8/9 1/1 30/7 1/1 13/3 1/1 6/5 22/5 3/2 2/1 53/12 3/1 1/0 31/7 1/1 2/1 9/2 1/1 3/1 41/9 5/1 1/0 32/7 1/0 23/5 7/1 1/0 60/13 1/0 37/8 -11/1 1/0 14/3 -2/1 1/0 19/4 -1/1 -3/4 24/5 0/1 29/6 -1/1 0/1 5/1 0/1 16/3 1/2 27/5 1/3 3/7 38/7 2/5 1/2 49/9 5/11 1/2 60/11 1/2 11/2 1/2 1/1 39/7 1/3 3/7 28/5 1/2 45/8 1/2 17/3 4/7 3/5 6/1 1/1 13/2 -2/1 -1/1 20/3 0/1 27/4 -1/1 1/1 7/1 1/1 1/0 22/3 -1/2 0/1 15/2 0/1 8/1 1/2 1/0 0/1 1/1 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(89,660,12,89) (-15/2,-22/3) -> (22/3,15/2) Hyperbolic Matrix(59,420,42,299) (-22/3,-7/1) -> (7/5,38/27) Hyperbolic Matrix(89,600,-58,-391) (-7/1,-20/3) -> (-20/13,-23/15) Hyperbolic Matrix(91,600,32,211) (-20/3,-13/2) -> (17/6,20/7) Hyperbolic Matrix(29,180,24,149) (-13/2,-6/1) -> (6/5,17/14) Hyperbolic Matrix(31,180,26,151) (-6/1,-17/3) -> (13/11,6/5) Hyperbolic Matrix(149,840,-80,-451) (-17/3,-28/5) -> (-28/15,-13/7) Hyperbolic Matrix(269,1500,-210,-1171) (-28/5,-11/2) -> (-41/32,-32/25) Hyperbolic Matrix(89,480,-28,-151) (-11/2,-16/3) -> (-16/5,-19/6) Hyperbolic Matrix(91,480,40,211) (-16/3,-5/1) -> (25/11,16/7) Hyperbolic Matrix(89,420,-32,-151) (-5/1,-14/3) -> (-14/5,-25/9) Hyperbolic Matrix(181,840,-142,-659) (-14/3,-23/5) -> (-37/29,-14/11) Hyperbolic Matrix(301,1380,118,541) (-23/5,-32/7) -> (28/11,23/9) Hyperbolic Matrix(329,1500,-270,-1231) (-32/7,-9/2) -> (-39/32,-28/23) Hyperbolic Matrix(121,540,54,241) (-9/2,-31/7) -> (29/13,9/4) Hyperbolic Matrix(421,1860,-122,-539) (-31/7,-22/5) -> (-38/11,-31/9) Hyperbolic Matrix(151,660,62,271) (-22/5,-13/3) -> (17/7,22/9) 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(209,780,56,209) (-15/4,-26/7) -> (26/7,15/4) Hyperbolic Matrix(211,780,122,451) (-26/7,-11/3) -> (19/11,26/15) Hyperbolic Matrix(181,660,-82,-299) (-11/3,-29/8) -> (-31/14,-11/5) Hyperbolic Matrix(299,1080,116,419) (-29/8,-18/5) -> (18/7,31/12) Hyperbolic Matrix(151,540,-92,-329) (-18/5,-7/2) -> (-23/14,-18/11) Hyperbolic Matrix(121,420,104,361) (-7/2,-38/11) -> (22/19,7/6) Hyperbolic Matrix(419,1440,-332,-1141) (-31/9,-24/7) -> (-24/19,-29/23) Hyperbolic Matrix(211,720,-114,-389) (-24/7,-17/5) -> (-13/7,-24/13) 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(241,780,-148,-479) (-13/4,-16/5) -> (-44/27,-13/8) Hyperbolic Matrix(211,660,-86,-269) (-19/6,-3/1) -> (-27/11,-49/20) Hyperbolic Matrix(209,600,-178,-511) (-3/1,-20/7) -> (-20/17,-27/23) Hyperbolic Matrix(211,600,32,91) (-20/7,-17/6) -> (13/2,20/3) Hyperbolic Matrix(361,1020,-212,-599) (-17/6,-14/5) -> (-46/27,-17/10) Hyperbolic Matrix(931,2580,-660,-1829) (-25/9,-36/13) -> (-24/17,-55/39) Hyperbolic Matrix(629,1740,184,509) (-36/13,-11/4) -> (41/12,24/7) 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(1139,3000,478,1259) (-29/11,-50/19) -> (50/21,31/13) Hyperbolic Matrix(1711,4500,-992,-2609) (-50/19,-21/8) -> (-69/40,-50/29) Hyperbolic Matrix(389,1020,-172,-451) (-21/8,-34/13) -> (-34/15,-9/4) Hyperbolic Matrix(781,2040,-482,-1259) (-34/13,-13/5) -> (-47/29,-34/21) Hyperbolic Matrix(301,780,-208,-539) (-13/5,-31/12) -> (-29/20,-13/9) Hyperbolic Matrix(419,1080,116,299) (-31/12,-18/7) -> (18/5,29/8) Hyperbolic Matrix(211,540,-152,-389) (-18/7,-5/2) -> (-25/18,-18/13) Hyperbolic Matrix(389,960,-280,-691) (-5/2,-27/11) -> (-57/41,-25/18) Hyperbolic Matrix(1201,2940,-980,-2399) (-49/20,-22/9) -> (-38/31,-49/40) Hyperbolic Matrix(271,660,62,151) (-22/9,-17/7) -> (13/3,22/5) Hyperbolic Matrix(421,1020,-272,-659) (-17/7,-29/12) -> (-31/20,-17/11) Hyperbolic Matrix(299,720,174,419) (-29/12,-12/5) -> (12/7,31/18) 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(1891,4500,-1172,-2789) (-50/21,-19/8) -> (-71/44,-50/31) Hyperbolic Matrix(329,780,240,569) (-19/8,-26/11) -> (26/19,11/8) 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(331,780,-216,-509) (-33/14,-7/3) -> (-23/15,-3/2) Hyperbolic Matrix(209,480,-118,-271) (-7/3,-16/7) -> (-16/9,-23/13) Hyperbolic Matrix(211,480,40,91) (-16/7,-25/11) -> (5/1,16/3) Hyperbolic Matrix(449,1020,92,209) (-25/11,-59/26) -> (29/6,5/1) Hyperbolic Matrix(1561,3540,900,2041) (-59/26,-34/15) -> (26/15,59/34) 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(541,1200,298,661) (-20/9,-31/14) -> (29/16,20/11) Hyperbolic Matrix(331,720,-234,-509) (-11/5,-13/6) -> (-17/12,-41/29) Hyperbolic Matrix(389,840,-320,-691) (-13/6,-15/7) -> (-45/37,-17/14) 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(899,1680,160,299) (-15/8,-28/15) -> (28/5,45/8) Hyperbolic Matrix(391,720,82,151) (-24/13,-11/6) -> (19/4,24/5) Hyperbolic Matrix(361,660,-262,-479) (-11/6,-20/11) -> (-40/29,-11/8) Hyperbolic Matrix(959,1740,264,479) (-20/11,-29/16) -> (29/8,40/11) Hyperbolic Matrix(299,540,232,419) (-29/16,-9/5) -> (9/7,31/24) Hyperbolic Matrix(569,1020,-352,-631) (-9/5,-25/14) -> (-55/34,-21/13) Hyperbolic Matrix(269,480,218,389) (-25/14,-16/9) -> (16/13,5/4) 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(241,420,-206,-359) (-7/4,-33/19) -> (-27/23,-7/6) Hyperbolic Matrix(3629,6300,-2610,-4531) (-33/19,-59/34) -> (-89/64,-57/41) Hyperbolic Matrix(2491,4320,952,1651) (-59/34,-26/15) -> (34/13,89/34) Hyperbolic Matrix(451,780,122,211) (-26/15,-19/11) -> (11/3,26/7) Hyperbolic Matrix(1739,3000,382,659) (-19/11,-69/40) -> (9/2,41/9) Hyperbolic Matrix(1741,3000,1080,1861) (-50/29,-31/18) -> (29/18,50/31) Hyperbolic Matrix(419,720,174,299) (-31/18,-12/7) -> (12/5,29/12) 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(1831,3120,652,1111) (-75/44,-46/27) -> (14/5,45/16) Hyperbolic Matrix(389,660,300,509) (-17/10,-22/13) -> (22/17,13/10) Hyperbolic Matrix(959,1620,-782,-1321) (-22/13,-27/16) -> (-27/22,-38/31) 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(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(1951,3180,608,991) (-75/46,-44/27) -> (16/5,45/14) Hyperbolic Matrix(2219,3600,850,1379) (-13/8,-60/37) -> (60/23,47/18) Hyperbolic Matrix(2221,3600,852,1381) (-60/37,-47/29) -> (13/5,60/23) Hyperbolic Matrix(2669,4320,1130,1829) (-34/21,-89/55) -> (59/25,26/11) Hyperbolic Matrix(4079,6600,1186,1919) (-89/55,-55/34) -> (55/16,31/9) Hyperbolic Matrix(1859,3000,334,539) (-21/13,-71/44) -> (11/2,39/7) Hyperbolic Matrix(1861,3000,1080,1741) (-50/31,-29/18) -> (31/18,50/29) 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(269,420,-212,-331) (-11/7,-14/9) -> (-14/11,-19/15) Hyperbolic Matrix(2009,3120,830,1289) (-14/9,-45/29) -> (75/31,46/19) Hyperbolic Matrix(2399,3720,928,1439) (-45/29,-31/20) -> (31/12,75/29) Hyperbolic Matrix(389,600,330,509) (-17/11,-20/13) -> (20/17,13/11) Hyperbolic Matrix(329,480,-268,-391) (-3/2,-16/11) -> (-16/13,-27/22) Hyperbolic Matrix(2189,3180,846,1229) (-16/11,-45/31) -> (75/29,44/17) Hyperbolic Matrix(2399,3480,992,1439) (-45/31,-29/20) -> (29/12,75/31) 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(1231,1740,786,1111) (-41/29,-24/17) -> (36/23,11/7) Hyperbolic Matrix(4681,6600,1788,2521) (-55/39,-31/22) -> (89/34,55/21) Hyperbolic Matrix(1321,1860,-1022,-1439) (-31/22,-7/5) -> (-53/41,-31/24) Hyperbolic Matrix(689,960,150,209) (-7/5,-32/23) -> (32/7,23/5) Hyperbolic Matrix(31709,44100,8908,12389) (-121/87,-210/151) -> (210/59,89/25) Hyperbolic Matrix(31711,44100,8910,12391) (-210/151,-89/64) -> (121/34,210/59) 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(569,780,240,329) (-11/8,-26/19) -> (26/11,19/8) Hyperbolic Matrix(571,780,418,571) (-26/19,-15/11) -> (15/11,26/19) 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(509,660,300,389) (-13/10,-22/17) -> (22/13,17/10) Hyperbolic Matrix(1021,1320,140,181) (-22/17,-53/41) -> (7/1,22/3) Hyperbolic Matrix(419,540,232,299) (-31/24,-9/7) -> (9/5,29/16) Hyperbolic Matrix(2341,3000,984,1261) (-9/7,-41/32) -> (19/8,69/29) Hyperbolic Matrix(751,960,212,271) (-32/25,-23/18) -> (7/2,32/9) Hyperbolic Matrix(2819,3600,610,779) (-23/18,-60/47) -> (60/13,37/8) Hyperbolic Matrix(2821,3600,612,781) (-60/47,-37/29) -> (23/5,60/13) Hyperbolic Matrix(569,720,260,329) (-19/15,-24/19) -> (24/11,11/5) Hyperbolic Matrix(811,1020,454,571) (-29/23,-5/4) -> (25/14,59/33) Hyperbolic Matrix(389,480,218,269) (-5/4,-16/13) -> (16/9,25/14) Hyperbolic Matrix(2939,3600,538,659) (-49/40,-60/49) -> (60/11,11/2) Hyperbolic Matrix(2941,3600,540,661) (-60/49,-11/9) -> (49/9,60/11) Hyperbolic Matrix(2461,3000,936,1141) (-11/9,-39/32) -> (21/8,71/27) Hyperbolic Matrix(1381,1680,642,781) (-28/23,-45/37) -> (15/7,28/13) 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(509,600,330,389) (-13/11,-20/17) -> (20/13,17/11) Hyperbolic Matrix(1139,1320,258,299) (-7/6,-22/19) -> (22/5,53/12) Hyperbolic Matrix(571,660,494,571) (-22/19,-15/13) -> (15/13,22/19) 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(511,-600,178,-209) (7/6,20/17) -> (20/7,23/8) Hyperbolic Matrix(691,-840,320,-389) (17/14,28/23) -> (28/13,13/6) Hyperbolic Matrix(1231,-1500,270,-329) (28/23,11/9) -> (41/9,32/7) Hyperbolic Matrix(391,-480,268,-329) (11/9,16/13) -> (16/11,19/13) Hyperbolic Matrix(331,-420,212,-269) (5/4,14/11) -> (14/9,25/16) Hyperbolic Matrix(659,-840,142,-181) (14/11,23/18) -> (37/8,14/3) Hyperbolic Matrix(1171,-1500,210,-269) (32/25,9/7) -> (39/7,28/5) Hyperbolic Matrix(1439,-1860,1022,-1321) (31/24,22/17) -> (38/27,31/22) Hyperbolic Matrix(91,-120,22,-29) (13/10,4/3) -> (4/1,17/4) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(389,-540,152,-211) (18/13,7/5) -> (23/9,18/7) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(509,-720,234,-331) (24/17,17/12) -> (13/6,24/11) Hyperbolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(449,-660,266,-391) (19/13,3/2) -> (27/16,49/29) Hyperbolic Matrix(391,-600,58,-89) (3/2,20/13) -> (20/3,27/4) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(1649,-2580,480,-751) (25/16,36/23) -> (24/7,55/16) Hyperbolic Matrix(151,-240,56,-89) (11/7,8/5) -> (8/3,19/7) Hyperbolic Matrix(2789,-4500,1172,-1891) (50/31,21/13) -> (69/29,50/21) Hyperbolic Matrix(631,-1020,352,-569) (21/13,34/21) -> (34/19,9/5) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(329,-540,92,-151) (18/11,5/3) -> (25/7,18/5) Hyperbolic Matrix(571,-960,160,-269) (5/3,27/16) -> (57/16,25/7) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(2609,-4500,992,-1711) (50/29,19/11) -> (71/27,50/19) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(449,-780,156,-271) (33/19,7/4) -> (23/8,3/1) Hyperbolic Matrix(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(389,-720,114,-211) (11/6,13/7) -> (17/5,41/12) Hyperbolic Matrix(451,-840,80,-149) (13/7,15/8) -> (45/8,17/3) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(451,-1020,172,-389) (9/4,25/11) -> (55/21,21/8) Hyperbolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(2671,-6300,750,-1769) (33/14,59/25) -> (89/25,57/16) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(151,-420,32,-89) (11/4,14/5) -> (14/3,19/4) Hyperbolic Matrix(151,-480,28,-89) (3/1,16/5) -> (16/3,27/5) Hyperbolic Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,240,18,149) -> Matrix(3,-2,8,-5) Matrix(31,240,4,31) -> Matrix(1,0,2,1) Matrix(89,660,12,89) -> Matrix(1,0,-6,1) Matrix(59,420,42,299) -> Matrix(5,-2,18,-7) Matrix(89,600,-58,-391) -> Matrix(1,0,-2,1) Matrix(91,600,32,211) -> Matrix(1,0,-2,1) Matrix(29,180,24,149) -> Matrix(3,-2,8,-5) Matrix(31,180,26,151) -> Matrix(1,-2,4,-7) Matrix(149,840,-80,-451) -> Matrix(1,-10,0,1) Matrix(269,1500,-210,-1171) -> Matrix(1,4,-2,-7) Matrix(89,480,-28,-151) -> Matrix(1,2,0,1) Matrix(91,480,40,211) -> Matrix(3,2,4,3) Matrix(89,420,-32,-151) -> Matrix(5,-2,8,-3) Matrix(181,840,-142,-659) -> Matrix(9,-4,-20,9) Matrix(301,1380,118,541) -> Matrix(1,0,0,1) Matrix(329,1500,-270,-1231) -> Matrix(7,-4,2,-1) Matrix(121,540,54,241) -> Matrix(1,0,0,1) Matrix(421,1860,-122,-539) -> Matrix(1,0,0,1) Matrix(151,660,62,271) -> Matrix(5,-4,14,-11) Matrix(29,120,-22,-91) -> Matrix(1,-2,0,1) Matrix(31,120,8,31) -> Matrix(1,0,2,1) Matrix(209,780,56,209) -> Matrix(1,0,-10,1) Matrix(211,780,122,451) -> Matrix(1,0,-2,1) Matrix(181,660,-82,-299) -> Matrix(3,-2,2,-1) Matrix(299,1080,116,419) -> Matrix(9,-2,14,-3) Matrix(151,540,-92,-329) -> Matrix(9,-4,-2,1) Matrix(121,420,104,361) -> Matrix(3,-2,14,-9) Matrix(419,1440,-332,-1141) -> Matrix(3,-2,-10,7) Matrix(211,720,-114,-389) -> Matrix(19,-14,-4,3) Matrix(89,300,62,209) -> Matrix(7,-6,20,-17) Matrix(91,300,64,211) -> Matrix(5,-6,16,-19) Matrix(241,780,-148,-479) -> Matrix(1,-4,0,1) Matrix(211,660,-86,-269) -> Matrix(1,-2,0,1) Matrix(209,600,-178,-511) -> Matrix(1,0,-2,1) Matrix(211,600,32,91) -> Matrix(1,0,-2,1) Matrix(361,1020,-212,-599) -> Matrix(1,0,0,1) Matrix(931,2580,-660,-1829) -> Matrix(5,-4,-6,5) Matrix(629,1740,184,509) -> Matrix(17,-12,10,-7) Matrix(89,240,-56,-151) -> Matrix(5,-6,-4,5) Matrix(91,240,80,211) -> Matrix(1,-2,4,-7) Matrix(1139,3000,478,1259) -> Matrix(1,-2,2,-3) Matrix(1711,4500,-992,-2609) -> Matrix(3,-4,-2,3) Matrix(389,1020,-172,-451) -> Matrix(5,-8,2,-3) Matrix(781,2040,-482,-1259) -> Matrix(15,-28,-8,15) Matrix(301,780,-208,-539) -> Matrix(1,-4,0,1) Matrix(419,1080,116,299) -> Matrix(1,-2,-2,5) Matrix(211,540,-152,-389) -> Matrix(1,-4,-2,9) Matrix(389,960,-280,-691) -> Matrix(1,0,-2,1) Matrix(1201,2940,-980,-2399) -> Matrix(1,4,0,1) Matrix(271,660,62,151) -> Matrix(3,4,2,3) Matrix(421,1020,-272,-659) -> Matrix(1,0,0,1) Matrix(299,720,174,419) -> Matrix(1,0,4,1) Matrix(301,720,176,421) -> Matrix(1,0,0,1) Matrix(1259,3000,478,1139) -> Matrix(1,-2,2,-3) Matrix(1891,4500,-1172,-2789) -> Matrix(3,-4,-2,3) Matrix(329,780,240,569) -> Matrix(1,0,6,1) Matrix(1499,3540,838,1979) -> Matrix(7,-2,18,-5) Matrix(1679,3960,-1018,-2401) -> Matrix(5,-2,-2,1) Matrix(331,780,-216,-509) -> Matrix(1,0,-2,1) Matrix(209,480,-118,-271) -> Matrix(5,-6,-4,5) Matrix(211,480,40,91) -> Matrix(1,-2,4,-7) Matrix(449,1020,92,209) -> Matrix(1,-2,0,1) Matrix(1561,3540,900,2041) -> Matrix(1,-2,6,-11) Matrix(241,540,54,121) -> Matrix(1,0,0,1) Matrix(539,1200,296,659) -> Matrix(5,-8,12,-19) Matrix(541,1200,298,661) -> Matrix(3,-8,8,-21) Matrix(331,720,-234,-509) -> Matrix(3,-14,-4,19) Matrix(389,840,-320,-691) -> Matrix(1,-10,0,1) Matrix(29,60,14,29) -> Matrix(1,0,2,1) Matrix(31,60,16,31) -> Matrix(1,0,2,1) Matrix(899,1680,160,299) -> Matrix(1,14,2,29) Matrix(391,720,82,151) -> Matrix(1,4,-2,-7) Matrix(361,660,-262,-479) -> Matrix(1,2,-2,-3) Matrix(959,1740,264,479) -> Matrix(1,2,-2,-3) Matrix(299,540,232,419) -> Matrix(1,0,4,1) Matrix(569,1020,-352,-631) -> Matrix(3,8,-2,-5) Matrix(269,480,218,389) -> Matrix(1,2,0,1) Matrix(509,900,220,389) -> Matrix(7,8,6,7) Matrix(511,900,222,391) -> Matrix(9,8,10,9) Matrix(241,420,-206,-359) -> Matrix(1,0,0,1) Matrix(3629,6300,-2610,-4531) -> Matrix(3,2,-8,-5) Matrix(2491,4320,952,1651) -> Matrix(11,2,16,3) Matrix(451,780,122,211) -> Matrix(1,0,-2,1) Matrix(1739,3000,382,659) -> Matrix(1,4,0,1) Matrix(1741,3000,1080,1861) -> Matrix(1,2,2,5) Matrix(419,720,174,299) -> Matrix(1,0,4,1) Matrix(421,720,176,301) -> Matrix(1,0,0,1) Matrix(2041,3480,634,1081) -> Matrix(1,-2,2,-3) Matrix(1831,3120,652,1111) -> Matrix(1,0,-2,1) Matrix(389,660,300,509) -> Matrix(3,-4,10,-13) Matrix(959,1620,-782,-1321) -> Matrix(1,0,0,1) Matrix(179,300,-108,-181) -> Matrix(1,-4,0,1) Matrix(3241,5340,-2330,-3839) -> Matrix(1,-2,-2,5) Matrix(839,1380,656,1079) -> Matrix(1,0,4,1) Matrix(661,1080,478,781) -> Matrix(1,2,6,13) Matrix(2281,3720,810,1321) -> Matrix(1,2,2,5) Matrix(1951,3180,608,991) -> Matrix(1,0,2,1) Matrix(2219,3600,850,1379) -> Matrix(27,56,40,83) Matrix(2221,3600,852,1381) -> Matrix(29,56,44,85) Matrix(2669,4320,1130,1829) -> Matrix(1,2,-4,-7) Matrix(4079,6600,1186,1919) -> Matrix(7,12,4,7) Matrix(1859,3000,334,539) -> Matrix(3,4,8,11) Matrix(1861,3000,1080,1741) -> Matrix(1,2,2,5) Matrix(149,240,18,29) -> Matrix(1,2,0,1) Matrix(569,900,208,329) -> Matrix(15,16,14,15) Matrix(571,900,210,331) -> Matrix(17,16,18,17) Matrix(269,420,-212,-331) -> Matrix(3,2,-8,-5) Matrix(2009,3120,830,1289) -> Matrix(1,0,6,1) Matrix(2399,3720,928,1439) -> Matrix(1,-2,2,-3) Matrix(389,600,330,509) -> Matrix(1,0,6,1) Matrix(329,480,-268,-391) -> Matrix(1,2,0,1) Matrix(2189,3180,846,1229) -> Matrix(1,0,2,1) Matrix(2399,3480,992,1439) -> Matrix(1,2,2,5) Matrix(209,300,62,89) -> Matrix(5,6,4,5) Matrix(211,300,64,91) -> Matrix(7,6,8,7) Matrix(1231,1740,786,1111) -> Matrix(17,12,58,41) Matrix(4681,6600,1788,2521) -> Matrix(17,12,24,17) Matrix(1321,1860,-1022,-1439) -> Matrix(1,0,0,1) Matrix(689,960,150,209) -> Matrix(9,4,2,1) Matrix(31709,44100,8908,12389) -> Matrix(41,18,-16,-7) Matrix(31711,44100,8910,12391) -> Matrix(43,18,-12,-5) Matrix(781,1080,478,661) -> Matrix(9,2,22,5) Matrix(1261,1740,566,781) -> Matrix(7,2,10,3) Matrix(569,780,240,329) -> Matrix(1,0,6,1) Matrix(571,780,418,571) -> Matrix(1,0,14,1) Matrix(89,120,66,89) -> Matrix(1,0,2,1) Matrix(689,900,160,209) -> Matrix(13,14,12,13) Matrix(691,900,162,211) -> Matrix(15,14,16,15) Matrix(509,660,300,389) -> Matrix(5,4,6,5) Matrix(1021,1320,140,181) -> Matrix(3,2,-2,-1) Matrix(419,540,232,299) -> Matrix(1,0,4,1) Matrix(2341,3000,984,1261) -> Matrix(7,4,12,7) Matrix(751,960,212,271) -> Matrix(7,4,-2,-1) Matrix(2819,3600,610,779) -> Matrix(35,18,-2,-1) Matrix(2821,3600,612,781) -> Matrix(37,18,2,1) Matrix(569,720,260,329) -> Matrix(15,4,26,7) Matrix(811,1020,454,571) -> Matrix(5,2,12,5) Matrix(389,480,218,269) -> Matrix(3,-2,8,-5) Matrix(2939,3600,538,659) -> Matrix(1,-6,2,-11) Matrix(2941,3600,540,661) -> Matrix(1,6,2,13) Matrix(2461,3000,936,1141) -> Matrix(3,-4,4,-5) Matrix(1381,1680,642,781) -> Matrix(1,-14,2,-27) Matrix(149,180,24,29) -> Matrix(1,2,0,1) Matrix(151,180,26,31) -> Matrix(3,2,4,3) Matrix(509,600,330,389) -> Matrix(1,0,6,1) Matrix(1139,1320,258,299) -> Matrix(5,2,2,1) Matrix(571,660,494,571) -> Matrix(1,0,10,1) Matrix(209,240,182,209) -> Matrix(1,0,2,1) Matrix(211,240,80,91) -> Matrix(3,2,4,3) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(511,-600,178,-209) -> Matrix(1,0,-2,1) Matrix(691,-840,320,-389) -> Matrix(21,-10,40,-19) Matrix(1231,-1500,270,-329) -> Matrix(7,-4,2,-1) Matrix(391,-480,268,-329) -> Matrix(3,-2,8,-5) Matrix(331,-420,212,-269) -> Matrix(9,-2,32,-7) Matrix(659,-840,142,-181) -> Matrix(17,-4,-4,1) Matrix(1171,-1500,210,-269) -> Matrix(15,-4,34,-9) Matrix(1439,-1860,1022,-1321) -> Matrix(1,0,0,1) Matrix(91,-120,22,-29) -> Matrix(5,-2,8,-3) Matrix(479,-660,262,-361) -> Matrix(7,-2,18,-5) Matrix(389,-540,152,-211) -> Matrix(17,-4,30,-7) Matrix(1021,-1440,212,-299) -> Matrix(7,-2,-10,3) Matrix(509,-720,234,-331) -> Matrix(47,-14,84,-25) Matrix(539,-780,208,-301) -> Matrix(9,-4,16,-7) Matrix(449,-660,266,-391) -> Matrix(5,-2,8,-3) Matrix(391,-600,58,-89) -> Matrix(1,0,-2,1) Matrix(659,-1020,272,-421) -> Matrix(1,0,0,1) Matrix(1649,-2580,480,-751) -> Matrix(13,-4,10,-3) Matrix(151,-240,56,-89) -> Matrix(17,-6,20,-7) Matrix(2789,-4500,1172,-1891) -> Matrix(11,-4,14,-5) Matrix(631,-1020,352,-569) -> Matrix(21,-8,50,-19) Matrix(1259,-2040,482,-781) -> Matrix(71,-28,104,-41) Matrix(479,-780,148,-241) -> Matrix(9,-4,16,-7) Matrix(329,-540,92,-151) -> Matrix(9,-4,-2,1) Matrix(571,-960,160,-269) -> Matrix(1,0,-2,1) Matrix(1739,-2940,320,-541) -> Matrix(7,-4,16,-9) Matrix(599,-1020,212,-361) -> Matrix(1,0,0,1) Matrix(2609,-4500,992,-1711) -> Matrix(11,-4,14,-5) Matrix(2281,-3960,898,-1559) -> Matrix(9,-2,14,-3) Matrix(449,-780,156,-271) -> Matrix(1,0,-2,1) Matrix(271,-480,118,-209) -> Matrix(17,-6,20,-7) Matrix(389,-720,114,-211) -> Matrix(31,-14,20,-9) Matrix(451,-840,80,-149) -> Matrix(21,-10,40,-19) Matrix(299,-660,82,-181) -> Matrix(3,-2,2,-1) Matrix(451,-1020,172,-389) -> Matrix(13,-8,18,-11) Matrix(179,-420,26,-61) -> Matrix(1,0,0,1) Matrix(2671,-6300,750,-1769) -> Matrix(1,-2,0,1) Matrix(661,-1620,122,-299) -> Matrix(1,0,0,1) Matrix(121,-300,48,-119) -> Matrix(9,-4,16,-7) Matrix(2099,-5340,590,-1501) -> Matrix(5,-2,-2,1) Matrix(151,-420,32,-89) -> Matrix(1,-2,0,1) Matrix(151,-480,28,-89) -> Matrix(3,-2,8,-5) Matrix(539,-1860,122,-421) -> Matrix(1,0,0,1) 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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 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 0/1 6/5 5/4 10/7 3/2 5/3 12/7 20/11 2/1 15/7 20/9 9/4 30/13 50/21 12/5 5/2 18/7 60/23 50/19 30/11 20/7 3/1 45/14 10/3 24/7 210/59 18/5 26/7 15/4 4/1 30/7 9/2 60/13 14/3 24/5 5/1 16/3 60/11 11/2 28/5 6/1 13/2 20/3 7/1 22/3 15/2 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 0/1 1/3 8/7 1/2 15/13 0/1 22/19 0/1 1/6 7/6 1/4 1/3 20/17 0/1 13/11 1/5 2/9 6/5 1/3 17/14 3/7 4/9 28/23 1/2 11/9 1/3 1/2 16/13 1/2 5/4 0/1 14/11 2/9 1/4 23/18 1/4 7/27 32/25 1/4 9/7 3/11 1/3 31/24 2/7 1/3 22/17 2/7 3/10 13/10 6/19 1/3 4/3 1/2 15/11 0/1 26/19 0/1 1/8 11/8 1/6 1/5 29/21 0/1 1/5 18/13 1/5 7/5 1/4 3/11 38/27 2/7 3/10 31/22 2/7 1/3 24/17 2/7 17/12 7/23 4/13 10/7 1/3 13/9 5/13 2/5 16/11 1/2 19/13 3/7 1/2 3/2 1/3 1/1 20/13 0/1 17/11 2/7 1/3 14/9 0/1 1/4 25/16 2/7 36/23 2/7 11/7 5/16 1/3 8/5 3/8 29/18 1/3 2/5 50/31 1/3 21/13 1/3 5/13 34/21 7/18 2/5 13/8 2/5 7/17 31/19 2/5 3/7 18/11 3/7 5/3 1/2 27/16 3/5 1/1 49/29 1/3 1/2 22/13 1/2 2/3 17/10 1/1 2/1 29/17 0/1 1/1 12/7 0/1 31/18 0/1 1/3 50/29 1/3 19/11 1/2 1/1 26/15 0/1 1/4 59/34 0/1 1/5 33/19 1/5 1/3 7/4 1/4 1/3 16/9 3/8 25/14 2/5 59/33 1/3 2/5 34/19 3/8 2/5 9/5 1/3 3/7 29/16 1/3 2/5 20/11 2/5 31/17 2/5 3/7 11/6 5/12 3/7 13/7 6/13 7/15 15/8 1/2 2/1 0/1 1/2 15/7 1/2 28/13 1/2 13/6 7/13 6/11 24/11 4/7 11/5 3/5 5/8 20/9 2/3 29/13 2/3 1/1 9/4 3/5 1/1 25/11 2/3 16/7 3/4 23/10 7/8 1/1 30/13 1/1 7/3 1/1 1/0 33/14 -1/1 1/1 59/25 -1/1 0/1 26/11 0/1 1/0 19/8 1/3 1/2 69/29 3/5 1/1 50/21 1/1 31/13 0/1 1/1 12/5 0/1 29/12 0/1 1/3 75/31 0/1 46/19 0/1 1/4 17/7 2/7 1/3 22/9 2/5 1/2 27/11 1/3 3/7 5/2 1/2 33/13 3/5 1/1 61/24 2/3 1/1 28/11 1/2 23/9 1/2 7/13 18/7 3/5 31/12 3/5 2/3 75/29 2/3 44/17 1/2 13/5 7/11 2/3 60/23 2/3 47/18 2/3 21/31 34/13 2/3 7/10 89/34 2/3 5/7 55/21 2/3 21/8 5/7 1/1 71/27 3/4 7/9 50/19 1/1 29/11 2/3 1/1 8/3 3/4 19/7 11/12 1/1 30/11 1/1 11/4 1/1 5/4 14/5 0/1 1/0 45/16 0/1 31/11 0/1 1/1 17/6 1/1 2/1 20/7 0/1 23/8 1/2 1/1 3/1 1/3 1/1 16/5 1/2 45/14 2/3 29/9 2/3 1/1 13/4 2/3 5/7 10/3 1/1 17/5 4/3 7/5 41/12 13/8 5/3 24/7 2/1 55/16 2/1 31/9 1/1 2/1 7/2 3/1 1/0 32/9 1/0 121/34 -4/1 -3/1 210/59 -3/1 89/25 -3/1 -2/1 57/16 -3/1 -1/1 25/7 1/0 18/5 -1/1 29/8 -1/1 0/1 40/11 0/1 11/3 -1/1 -1/2 26/7 -1/4 0/1 15/4 0/1 4/1 1/2 17/4 8/9 1/1 30/7 1/1 13/3 1/1 6/5 22/5 3/2 2/1 53/12 3/1 1/0 31/7 1/1 2/1 9/2 1/1 3/1 41/9 5/1 1/0 32/7 1/0 23/5 7/1 1/0 60/13 1/0 37/8 -11/1 1/0 14/3 -2/1 1/0 19/4 -1/1 -3/4 24/5 0/1 29/6 -1/1 0/1 5/1 0/1 16/3 1/2 27/5 1/3 3/7 38/7 2/5 1/2 49/9 5/11 1/2 60/11 1/2 11/2 1/2 1/1 39/7 1/3 3/7 28/5 1/2 45/8 1/2 17/3 4/7 3/5 6/1 1/1 13/2 -2/1 -1/1 20/3 0/1 27/4 -1/1 1/1 7/1 1/1 1/0 22/3 -1/2 0/1 15/2 0/1 8/1 1/2 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(211,-240,131,-149) (1/1,8/7) -> (8/5,29/18) Hyperbolic Matrix(209,-240,27,-31) (8/7,15/13) -> (15/2,8/1) Hyperbolic Matrix(571,-660,77,-89) (15/13,22/19) -> (22/3,15/2) Hyperbolic Matrix(361,-420,257,-299) (22/19,7/6) -> (7/5,38/27) Hyperbolic Matrix(511,-600,178,-209) (7/6,20/17) -> (20/7,23/8) Hyperbolic Matrix(509,-600,179,-211) (20/17,13/11) -> (17/6,20/7) Hyperbolic Matrix(151,-180,125,-149) (13/11,6/5) -> (6/5,17/14) Parabolic Matrix(691,-840,320,-389) (17/14,28/23) -> (28/13,13/6) Hyperbolic Matrix(1231,-1500,270,-329) (28/23,11/9) -> (41/9,32/7) Hyperbolic Matrix(391,-480,268,-329) (11/9,16/13) -> (16/11,19/13) Hyperbolic Matrix(389,-480,171,-211) (16/13,5/4) -> (25/11,16/7) Hyperbolic Matrix(331,-420,212,-269) (5/4,14/11) -> (14/9,25/16) Hyperbolic Matrix(659,-840,142,-181) (14/11,23/18) -> (37/8,14/3) Hyperbolic Matrix(1079,-1380,423,-541) (23/18,32/25) -> (28/11,23/9) Hyperbolic Matrix(1171,-1500,210,-269) (32/25,9/7) -> (39/7,28/5) Hyperbolic Matrix(419,-540,187,-241) (9/7,31/24) -> (29/13,9/4) Hyperbolic Matrix(1439,-1860,1022,-1321) (31/24,22/17) -> (38/27,31/22) Hyperbolic Matrix(509,-660,209,-271) (22/17,13/10) -> (17/7,22/9) Hyperbolic Matrix(91,-120,22,-29) (13/10,4/3) -> (4/1,17/4) Hyperbolic Matrix(89,-120,23,-31) (4/3,15/11) -> (15/4,4/1) Hyperbolic Matrix(571,-780,153,-209) (15/11,26/19) -> (26/7,15/4) Hyperbolic Matrix(569,-780,329,-451) (26/19,11/8) -> (19/11,26/15) Hyperbolic Matrix(479,-660,262,-361) (11/8,29/21) -> (31/17,11/6) Hyperbolic Matrix(781,-1080,303,-419) (29/21,18/13) -> (18/7,31/12) Hyperbolic Matrix(389,-540,152,-211) (18/13,7/5) -> (23/9,18/7) Hyperbolic Matrix(1021,-1440,212,-299) (31/22,24/17) -> (24/5,29/6) Hyperbolic Matrix(509,-720,234,-331) (24/17,17/12) -> (13/6,24/11) Hyperbolic Matrix(211,-300,147,-209) (17/12,10/7) -> (10/7,13/9) Parabolic Matrix(539,-780,208,-301) (13/9,16/11) -> (44/17,13/5) Hyperbolic Matrix(449,-660,266,-391) (19/13,3/2) -> (27/16,49/29) Hyperbolic Matrix(391,-600,58,-89) (3/2,20/13) -> (20/3,27/4) Hyperbolic Matrix(389,-600,59,-91) (20/13,17/11) -> (13/2,20/3) Hyperbolic Matrix(659,-1020,272,-421) (17/11,14/9) -> (46/19,17/7) Hyperbolic Matrix(1649,-2580,480,-751) (25/16,36/23) -> (24/7,55/16) Hyperbolic Matrix(1111,-1740,325,-509) (36/23,11/7) -> (41/12,24/7) Hyperbolic Matrix(151,-240,56,-89) (11/7,8/5) -> (8/3,19/7) Hyperbolic Matrix(1861,-3000,781,-1259) (29/18,50/31) -> (50/21,31/13) Hyperbolic Matrix(2789,-4500,1172,-1891) (50/31,21/13) -> (69/29,50/21) Hyperbolic Matrix(631,-1020,352,-569) (21/13,34/21) -> (34/19,9/5) Hyperbolic Matrix(1259,-2040,482,-781) (34/21,13/8) -> (47/18,34/13) Hyperbolic Matrix(479,-780,148,-241) (13/8,31/19) -> (29/9,13/4) Hyperbolic Matrix(661,-1080,183,-299) (31/19,18/11) -> (18/5,29/8) Hyperbolic Matrix(329,-540,92,-151) (18/11,5/3) -> (25/7,18/5) Hyperbolic Matrix(571,-960,160,-269) (5/3,27/16) -> (57/16,25/7) Hyperbolic Matrix(1739,-2940,320,-541) (49/29,22/13) -> (38/7,49/9) Hyperbolic Matrix(389,-660,89,-151) (22/13,17/10) -> (13/3,22/5) Hyperbolic Matrix(599,-1020,212,-361) (17/10,29/17) -> (31/11,17/6) Hyperbolic Matrix(421,-720,245,-419) (29/17,12/7) -> (12/7,31/18) Parabolic Matrix(1741,-3000,661,-1139) (31/18,50/29) -> (50/19,29/11) Hyperbolic Matrix(2609,-4500,992,-1711) (50/29,19/11) -> (71/27,50/19) Hyperbolic Matrix(2041,-3540,1141,-1979) (26/15,59/34) -> (59/33,34/19) Hyperbolic Matrix(2281,-3960,898,-1559) (59/34,33/19) -> (33/13,61/24) Hyperbolic Matrix(449,-780,156,-271) (33/19,7/4) -> (23/8,3/1) Hyperbolic Matrix(271,-480,118,-209) (7/4,16/9) -> (16/7,23/10) Hyperbolic Matrix(269,-480,51,-91) (16/9,25/14) -> (5/1,16/3) Hyperbolic Matrix(571,-1020,117,-209) (25/14,59/33) -> (29/6,5/1) Hyperbolic Matrix(299,-540,67,-121) (9/5,29/16) -> (31/7,9/2) Hyperbolic Matrix(661,-1200,363,-659) (29/16,20/11) -> (20/11,31/17) Parabolic Matrix(389,-720,114,-211) (11/6,13/7) -> (17/5,41/12) Hyperbolic Matrix(451,-840,80,-149) (13/7,15/8) -> (45/8,17/3) Hyperbolic Matrix(31,-60,15,-29) (15/8,2/1) -> (2/1,15/7) Parabolic Matrix(781,-1680,139,-299) (15/7,28/13) -> (28/5,45/8) Hyperbolic Matrix(329,-720,69,-151) (24/11,11/5) -> (19/4,24/5) Hyperbolic Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(781,-1740,215,-479) (20/9,29/13) -> (29/8,40/11) Hyperbolic Matrix(451,-1020,172,-389) (9/4,25/11) -> (55/21,21/8) Hyperbolic Matrix(391,-900,169,-389) (23/10,30/13) -> (30/13,7/3) Parabolic Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(2671,-6300,750,-1769) (33/14,59/25) -> (89/25,57/16) Hyperbolic Matrix(1829,-4320,699,-1651) (59/25,26/11) -> (34/13,89/34) Hyperbolic Matrix(329,-780,89,-211) (26/11,19/8) -> (11/3,26/7) Hyperbolic Matrix(1261,-3000,277,-659) (19/8,69/29) -> (9/2,41/9) Hyperbolic Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(1439,-3480,447,-1081) (29/12,75/31) -> (45/14,29/9) Hyperbolic Matrix(1289,-3120,459,-1111) (75/31,46/19) -> (14/5,45/16) Hyperbolic Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(121,-300,48,-119) (27/11,5/2) -> (5/2,33/13) Parabolic Matrix(2099,-5340,590,-1501) (61/24,28/11) -> (32/9,121/34) Hyperbolic Matrix(1439,-3720,511,-1321) (31/12,75/29) -> (45/16,31/11) Hyperbolic Matrix(1229,-3180,383,-991) (75/29,44/17) -> (16/5,45/14) Hyperbolic Matrix(1381,-3600,529,-1379) (13/5,60/23) -> (60/23,47/18) Parabolic Matrix(2521,-6600,733,-1919) (89/34,55/21) -> (55/16,31/9) Hyperbolic Matrix(1141,-3000,205,-539) (21/8,71/27) -> (11/2,39/7) Hyperbolic Matrix(91,-240,11,-29) (29/11,8/3) -> (8/1,1/0) Hyperbolic Matrix(331,-900,121,-329) (19/7,30/11) -> (30/11,11/4) Parabolic Matrix(151,-420,32,-89) (11/4,14/5) -> (14/3,19/4) Hyperbolic Matrix(151,-480,28,-89) (3/1,16/5) -> (16/3,27/5) Hyperbolic Matrix(91,-300,27,-89) (13/4,10/3) -> (10/3,17/5) Parabolic Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(271,-960,59,-209) (7/2,32/9) -> (32/7,23/5) Hyperbolic Matrix(12391,-44100,3481,-12389) (121/34,210/59) -> (210/59,89/25) Parabolic Matrix(211,-900,49,-209) (17/4,30/7) -> (30/7,13/3) Parabolic Matrix(299,-1320,41,-181) (22/5,53/12) -> (7/1,22/3) Hyperbolic Matrix(781,-3600,169,-779) (23/5,60/13) -> (60/13,37/8) Parabolic Matrix(661,-3600,121,-659) (49/9,60/11) -> (60/11,11/2) Parabolic Matrix(31,-180,5,-29) (17/3,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,2,1) Matrix(211,-240,131,-149) -> Matrix(7,-2,18,-5) Matrix(209,-240,27,-31) -> Matrix(1,0,0,1) Matrix(571,-660,77,-89) -> Matrix(1,0,-8,1) Matrix(361,-420,257,-299) -> Matrix(9,-2,32,-7) Matrix(511,-600,178,-209) -> Matrix(1,0,-2,1) Matrix(509,-600,179,-211) -> Matrix(1,0,-4,1) Matrix(151,-180,125,-149) -> Matrix(7,-2,18,-5) Matrix(691,-840,320,-389) -> Matrix(21,-10,40,-19) Matrix(1231,-1500,270,-329) -> Matrix(7,-4,2,-1) Matrix(391,-480,268,-329) -> Matrix(3,-2,8,-5) Matrix(389,-480,171,-211) -> Matrix(1,-2,2,-3) Matrix(331,-420,212,-269) -> Matrix(9,-2,32,-7) Matrix(659,-840,142,-181) -> Matrix(17,-4,-4,1) Matrix(1079,-1380,423,-541) -> Matrix(1,0,-2,1) Matrix(1171,-1500,210,-269) -> Matrix(15,-4,34,-9) Matrix(419,-540,187,-241) -> Matrix(1,0,-2,1) Matrix(1439,-1860,1022,-1321) -> Matrix(1,0,0,1) Matrix(509,-660,209,-271) -> Matrix(13,-4,36,-11) Matrix(91,-120,22,-29) -> Matrix(5,-2,8,-3) Matrix(89,-120,23,-31) -> Matrix(1,0,0,1) Matrix(571,-780,153,-209) -> Matrix(1,0,-12,1) Matrix(569,-780,329,-451) -> Matrix(1,0,-4,1) Matrix(479,-660,262,-361) -> Matrix(7,-2,18,-5) Matrix(781,-1080,303,-419) -> Matrix(13,-2,20,-3) Matrix(389,-540,152,-211) -> Matrix(17,-4,30,-7) Matrix(1021,-1440,212,-299) -> Matrix(7,-2,-10,3) Matrix(509,-720,234,-331) -> Matrix(47,-14,84,-25) Matrix(211,-300,147,-209) -> Matrix(19,-6,54,-17) Matrix(539,-780,208,-301) -> Matrix(9,-4,16,-7) Matrix(449,-660,266,-391) -> Matrix(5,-2,8,-3) Matrix(391,-600,58,-89) -> Matrix(1,0,-2,1) Matrix(389,-600,59,-91) -> Matrix(1,0,-4,1) Matrix(659,-1020,272,-421) -> Matrix(1,0,0,1) Matrix(1649,-2580,480,-751) -> Matrix(13,-4,10,-3) Matrix(1111,-1740,325,-509) -> Matrix(41,-12,24,-7) Matrix(151,-240,56,-89) -> Matrix(17,-6,20,-7) Matrix(1861,-3000,781,-1259) -> Matrix(5,-2,8,-3) Matrix(2789,-4500,1172,-1891) -> Matrix(11,-4,14,-5) Matrix(631,-1020,352,-569) -> Matrix(21,-8,50,-19) Matrix(1259,-2040,482,-781) -> Matrix(71,-28,104,-41) Matrix(479,-780,148,-241) -> Matrix(9,-4,16,-7) Matrix(661,-1080,183,-299) -> Matrix(5,-2,-12,5) Matrix(329,-540,92,-151) -> Matrix(9,-4,-2,1) Matrix(571,-960,160,-269) -> Matrix(1,0,-2,1) Matrix(1739,-2940,320,-541) -> Matrix(7,-4,16,-9) Matrix(389,-660,89,-151) -> Matrix(5,-4,4,-3) Matrix(599,-1020,212,-361) -> Matrix(1,0,0,1) Matrix(421,-720,245,-419) -> Matrix(1,0,2,1) Matrix(1741,-3000,661,-1139) -> Matrix(5,-2,8,-3) Matrix(2609,-4500,992,-1711) -> Matrix(11,-4,14,-5) Matrix(2041,-3540,1141,-1979) -> Matrix(11,-2,28,-5) Matrix(2281,-3960,898,-1559) -> Matrix(9,-2,14,-3) Matrix(449,-780,156,-271) -> Matrix(1,0,-2,1) Matrix(271,-480,118,-209) -> Matrix(17,-6,20,-7) Matrix(269,-480,51,-91) -> Matrix(5,-2,18,-7) Matrix(571,-1020,117,-209) -> Matrix(5,-2,-2,1) Matrix(299,-540,67,-121) -> Matrix(1,0,-2,1) Matrix(661,-1200,363,-659) -> Matrix(21,-8,50,-19) Matrix(389,-720,114,-211) -> Matrix(31,-14,20,-9) Matrix(451,-840,80,-149) -> Matrix(21,-10,40,-19) Matrix(31,-60,15,-29) -> Matrix(1,0,0,1) Matrix(781,-1680,139,-299) -> Matrix(27,-14,56,-29) Matrix(329,-720,69,-151) -> Matrix(7,-4,-12,7) Matrix(299,-660,82,-181) -> Matrix(3,-2,2,-1) Matrix(781,-1740,215,-479) -> Matrix(3,-2,-4,3) Matrix(451,-1020,172,-389) -> Matrix(13,-8,18,-11) Matrix(391,-900,169,-389) -> Matrix(9,-8,8,-7) Matrix(179,-420,26,-61) -> Matrix(1,0,0,1) Matrix(2671,-6300,750,-1769) -> Matrix(1,-2,0,1) Matrix(1829,-4320,699,-1651) -> Matrix(7,2,10,3) Matrix(329,-780,89,-211) -> Matrix(1,0,-4,1) Matrix(1261,-3000,277,-659) -> Matrix(7,-4,2,-1) Matrix(301,-720,125,-299) -> Matrix(1,0,2,1) Matrix(1439,-3480,447,-1081) -> Matrix(5,-2,8,-3) Matrix(1289,-3120,459,-1111) -> Matrix(1,0,-4,1) Matrix(661,-1620,122,-299) -> Matrix(1,0,0,1) Matrix(121,-300,48,-119) -> Matrix(9,-4,16,-7) Matrix(2099,-5340,590,-1501) -> Matrix(5,-2,-2,1) Matrix(1439,-3720,511,-1321) -> Matrix(3,-2,8,-5) Matrix(1229,-3180,383,-991) -> Matrix(1,0,0,1) Matrix(1381,-3600,529,-1379) -> Matrix(85,-56,126,-83) Matrix(2521,-6600,733,-1919) -> Matrix(17,-12,10,-7) Matrix(1141,-3000,205,-539) -> Matrix(5,-4,14,-11) Matrix(91,-240,11,-29) -> Matrix(3,-2,2,-1) Matrix(331,-900,121,-329) -> Matrix(17,-16,16,-15) Matrix(151,-420,32,-89) -> Matrix(1,-2,0,1) Matrix(151,-480,28,-89) -> Matrix(3,-2,8,-5) Matrix(91,-300,27,-89) -> Matrix(7,-6,6,-5) Matrix(539,-1860,122,-421) -> Matrix(1,0,0,1) Matrix(271,-960,59,-209) -> Matrix(1,4,0,1) Matrix(12391,-44100,3481,-12389) -> Matrix(5,18,-2,-7) Matrix(211,-900,49,-209) -> Matrix(15,-14,14,-13) Matrix(299,-1320,41,-181) -> Matrix(1,-2,0,1) Matrix(781,-3600,169,-779) -> Matrix(1,-18,0,1) Matrix(661,-3600,121,-659) -> Matrix(13,-6,24,-11) Matrix(31,-180,5,-29) -> Matrix(3,-2,2,-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 2/1 (0/1,1/2) 0 15 15/7 1/2 12 2 13/6 (7/13,6/11) 0 30 11/5 (3/5,5/8) 0 30 20/9 2/3 2 3 29/13 (2/3,1/1) 0 30 9/4 0 10 25/11 2/3 2 6 16/7 3/4 2 15 30/13 1/1 8 1 7/3 (1/1,1/0) 0 30 33/14 0 10 59/25 (-1/1,0/1) 0 30 26/11 (0/1,1/0) 0 15 19/8 (1/3,1/2) 0 30 50/21 1/1 2 3 31/13 (0/1,1/1) 0 30 12/5 0/1 2 5 29/12 (0/1,1/3) 0 30 17/7 (2/7,1/3) 0 30 22/9 (2/5,1/2) 0 15 27/11 0 10 5/2 1/2 2 6 18/7 3/5 2 5 31/12 (3/5,2/3) 0 30 13/5 (7/11,2/3) 0 30 60/23 2/3 14 1 34/13 (2/3,7/10) 0 15 89/34 (2/3,5/7) 0 30 55/21 2/3 2 6 21/8 0 10 71/27 (3/4,7/9) 0 30 50/19 1/1 2 3 29/11 (2/3,1/1) 0 30 8/3 3/4 2 15 30/11 1/1 16 1 11/4 (1/1,5/4) 0 30 14/5 (0/1,1/0) 0 15 45/16 0/1 2 2 31/11 (0/1,1/1) 0 30 17/6 (1/1,2/1) 0 30 20/7 0/1 2 3 3/1 0 10 16/5 1/2 2 15 45/14 2/3 2 2 29/9 (2/3,1/1) 0 30 13/4 (2/3,5/7) 0 30 10/3 1/1 6 3 17/5 (4/3,7/5) 0 30 41/12 (13/8,5/3) 0 30 24/7 2/1 2 5 31/9 (1/1,2/1) 0 30 7/2 (3/1,1/0) 0 30 32/9 1/0 2 15 210/59 -3/1 2 1 89/25 (-3/1,-2/1) 0 30 57/16 0 10 25/7 1/0 2 6 18/5 -1/1 2 5 29/8 (-1/1,0/1) 0 30 40/11 0/1 2 3 11/3 (-1/1,-1/2) 0 30 26/7 (-1/4,0/1) 0 15 15/4 0/1 6 2 4/1 1/2 2 15 30/7 1/1 14 1 13/3 (1/1,6/5) 0 30 22/5 (3/2,2/1) 0 15 53/12 (3/1,1/0) 0 30 31/7 (1/1,2/1) 0 30 9/2 0 10 32/7 1/0 2 15 23/5 (7/1,1/0) 0 30 60/13 1/0 18 1 14/3 (-2/1,1/0) 0 15 19/4 (-1/1,-3/4) 0 30 24/5 0/1 2 5 29/6 (-1/1,0/1) 0 30 5/1 0/1 2 6 16/3 1/2 2 15 27/5 0 10 38/7 (2/5,1/2) 0 15 60/11 1/2 6 1 11/2 (1/2,1/1) 0 30 39/7 0 10 28/5 1/2 2 15 45/8 1/2 12 2 17/3 (4/7,3/5) 0 30 6/1 1/1 2 5 13/2 (-2/1,-1/1) 0 30 20/3 0/1 2 3 27/4 0 10 7/1 (1/1,1/0) 0 30 22/3 (-1/2,0/1) 0 15 15/2 0/1 4 2 8/1 1/2 2 15 1/0 (0/1,1/1) 0 30 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(29,-60,14,-29) (2/1,15/7) -> (2/1,15/7) Reflection Matrix(389,-840,69,-149) (15/7,13/6) -> (45/8,17/3) Glide Reflection Matrix(331,-720,97,-211) (13/6,11/5) -> (17/5,41/12) Glide Reflection Matrix(299,-660,82,-181) (11/5,20/9) -> (40/11,11/3) Hyperbolic Matrix(781,-1740,215,-479) (20/9,29/13) -> (29/8,40/11) Hyperbolic Matrix(241,-540,54,-121) (29/13,9/4) -> (31/7,9/2) Glide Reflection Matrix(451,-1020,172,-389) (9/4,25/11) -> (55/21,21/8) Hyperbolic Matrix(211,-480,40,-91) (25/11,16/7) -> (5/1,16/3) Glide Reflection Matrix(209,-480,91,-209) (16/7,30/13) -> (16/7,30/13) Reflection Matrix(181,-420,78,-181) (30/13,7/3) -> (30/13,7/3) Reflection Matrix(179,-420,26,-61) (7/3,33/14) -> (27/4,7/1) Hyperbolic Matrix(2671,-6300,750,-1769) (33/14,59/25) -> (89/25,57/16) Hyperbolic Matrix(1829,-4320,699,-1651) (59/25,26/11) -> (34/13,89/34) Hyperbolic Matrix(329,-780,89,-211) (26/11,19/8) -> (11/3,26/7) Hyperbolic Matrix(1891,-4500,719,-1711) (19/8,50/21) -> (71/27,50/19) Glide Reflection Matrix(1259,-3000,478,-1139) (50/21,31/13) -> (50/19,29/11) Glide Reflection Matrix(301,-720,125,-299) (31/13,12/5) -> (12/5,29/12) Parabolic Matrix(421,-1020,149,-361) (29/12,17/7) -> (31/11,17/6) Glide Reflection Matrix(271,-660,62,-151) (17/7,22/9) -> (13/3,22/5) Glide Reflection Matrix(661,-1620,122,-299) (22/9,27/11) -> (27/5,38/7) Hyperbolic Matrix(389,-960,109,-269) (27/11,5/2) -> (57/16,25/7) Glide Reflection Matrix(211,-540,59,-151) (5/2,18/7) -> (25/7,18/5) Glide Reflection Matrix(419,-1080,116,-299) (18/7,31/12) -> (18/5,29/8) Glide Reflection Matrix(301,-780,93,-241) (31/12,13/5) -> (29/9,13/4) Glide Reflection Matrix(599,-1560,230,-599) (13/5,60/23) -> (13/5,60/23) Reflection Matrix(781,-2040,299,-781) (60/23,34/13) -> (60/23,34/13) Reflection Matrix(779,-2040,160,-419) (89/34,55/21) -> (29/6,5/1) Glide Reflection Matrix(1141,-3000,205,-539) (21/8,71/27) -> (11/2,39/7) Hyperbolic Matrix(91,-240,11,-29) (29/11,8/3) -> (8/1,1/0) Hyperbolic Matrix(89,-240,33,-89) (8/3,30/11) -> (8/3,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(151,-420,32,-89) (11/4,14/5) -> (14/3,19/4) Hyperbolic Matrix(449,-1260,160,-449) (14/5,45/16) -> (14/5,45/16) Reflection Matrix(959,-2700,298,-839) (45/16,31/11) -> (45/14,29/9) Glide Reflection Matrix(211,-600,32,-91) (17/6,20/7) -> (13/2,20/3) Glide Reflection Matrix(209,-600,31,-89) (20/7,3/1) -> (20/3,27/4) Glide Reflection Matrix(151,-480,28,-89) (3/1,16/5) -> (16/3,27/5) Hyperbolic Matrix(449,-1440,140,-449) (16/5,45/14) -> (16/5,45/14) Reflection Matrix(91,-300,27,-89) (13/4,10/3) -> (10/3,17/5) Parabolic Matrix(421,-1440,88,-301) (41/12,24/7) -> (19/4,24/5) Glide Reflection Matrix(419,-1440,87,-299) (24/7,31/9) -> (24/5,29/6) Glide Reflection Matrix(539,-1860,122,-421) (31/9,7/2) -> (53/12,31/7) Hyperbolic Matrix(271,-960,59,-209) (7/2,32/9) -> (32/7,23/5) Hyperbolic Matrix(1889,-6720,531,-1889) (32/9,210/59) -> (32/9,210/59) Reflection Matrix(10501,-37380,2950,-10501) (210/59,89/25) -> (210/59,89/25) Reflection Matrix(209,-780,56,-209) (26/7,15/4) -> (26/7,15/4) Reflection Matrix(31,-120,8,-31) (15/4,4/1) -> (15/4,4/1) Reflection Matrix(29,-120,7,-29) (4/1,30/7) -> (4/1,30/7) Reflection Matrix(181,-780,42,-181) (30/7,13/3) -> (30/7,13/3) Reflection Matrix(299,-1320,41,-181) (22/5,53/12) -> (7/1,22/3) Hyperbolic Matrix(329,-1500,59,-269) (9/2,32/7) -> (39/7,28/5) Glide Reflection Matrix(599,-2760,130,-599) (23/5,60/13) -> (23/5,60/13) Reflection Matrix(181,-840,39,-181) (60/13,14/3) -> (60/13,14/3) Reflection Matrix(419,-2280,77,-419) (38/7,60/11) -> (38/7,60/11) Reflection Matrix(241,-1320,44,-241) (60/11,11/2) -> (60/11,11/2) Reflection Matrix(449,-2520,80,-449) (28/5,45/8) -> (28/5,45/8) Reflection Matrix(31,-180,5,-29) (17/3,6/1) -> (6/1,13/2) Parabolic Matrix(89,-660,12,-89) (22/3,15/2) -> (22/3,15/2) 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(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(1,0,1,-1) -> Matrix(1,0,4,-1) (0/1,2/1) -> (0/1,1/2) Matrix(29,-60,14,-29) -> Matrix(1,0,4,-1) (2/1,15/7) -> (0/1,1/2) Matrix(389,-840,69,-149) -> Matrix(19,-10,36,-19) *** -> (1/2,5/9) Matrix(331,-720,97,-211) -> Matrix(25,-14,16,-9) Matrix(299,-660,82,-181) -> Matrix(3,-2,2,-1) 1/1 Matrix(781,-1740,215,-479) -> Matrix(3,-2,-4,3) Matrix(241,-540,54,-121) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(451,-1020,172,-389) -> Matrix(13,-8,18,-11) 2/3 Matrix(211,-480,40,-91) -> Matrix(3,-2,10,-7) Matrix(209,-480,91,-209) -> Matrix(7,-6,8,-7) (16/7,30/13) -> (3/4,1/1) Matrix(181,-420,78,-181) -> Matrix(-1,2,0,1) (30/13,7/3) -> (1/1,1/0) Matrix(179,-420,26,-61) -> Matrix(1,0,0,1) Matrix(2671,-6300,750,-1769) -> Matrix(1,-2,0,1) 1/0 Matrix(1829,-4320,699,-1651) -> Matrix(7,2,10,3) Matrix(329,-780,89,-211) -> Matrix(1,0,-4,1) 0/1 Matrix(1891,-4500,719,-1711) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(1259,-3000,478,-1139) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(301,-720,125,-299) -> Matrix(1,0,2,1) 0/1 Matrix(421,-1020,149,-361) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(271,-660,62,-151) -> Matrix(11,-4,8,-3) Matrix(661,-1620,122,-299) -> Matrix(1,0,0,1) Matrix(389,-960,109,-269) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(211,-540,59,-151) -> Matrix(7,-4,-2,1) Matrix(419,-1080,116,-299) -> Matrix(3,-2,-8,5) Matrix(301,-780,93,-241) -> Matrix(7,-4,12,-7) *** -> (1/2,2/3) Matrix(599,-1560,230,-599) -> Matrix(43,-28,66,-43) (13/5,60/23) -> (7/11,2/3) Matrix(781,-2040,299,-781) -> Matrix(41,-28,60,-41) (60/23,34/13) -> (2/3,7/10) Matrix(779,-2040,160,-419) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(1141,-3000,205,-539) -> Matrix(5,-4,14,-11) Matrix(91,-240,11,-29) -> Matrix(3,-2,2,-1) 1/1 Matrix(89,-240,33,-89) -> Matrix(7,-6,8,-7) (8/3,30/11) -> (3/4,1/1) Matrix(241,-660,88,-241) -> Matrix(9,-10,8,-9) (30/11,11/4) -> (1/1,5/4) Matrix(151,-420,32,-89) -> Matrix(1,-2,0,1) 1/0 Matrix(449,-1260,160,-449) -> Matrix(1,0,0,-1) (14/5,45/16) -> (0/1,1/0) Matrix(959,-2700,298,-839) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(211,-600,32,-91) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(209,-600,31,-89) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(151,-480,28,-89) -> Matrix(3,-2,8,-5) 1/2 Matrix(449,-1440,140,-449) -> Matrix(7,-4,12,-7) (16/5,45/14) -> (1/2,2/3) Matrix(91,-300,27,-89) -> Matrix(7,-6,6,-5) 1/1 Matrix(421,-1440,88,-301) -> Matrix(1,-2,-4,7) Matrix(419,-1440,87,-299) -> Matrix(1,-2,-2,3) Matrix(539,-1860,122,-421) -> Matrix(1,0,0,1) Matrix(271,-960,59,-209) -> Matrix(1,4,0,1) 1/0 Matrix(1889,-6720,531,-1889) -> Matrix(1,6,0,-1) (32/9,210/59) -> (-3/1,1/0) Matrix(10501,-37380,2950,-10501) -> Matrix(5,12,-2,-5) (210/59,89/25) -> (-3/1,-2/1) Matrix(209,-780,56,-209) -> Matrix(-1,0,8,1) (26/7,15/4) -> (-1/4,0/1) Matrix(31,-120,8,-31) -> Matrix(1,0,4,-1) (15/4,4/1) -> (0/1,1/2) Matrix(29,-120,7,-29) -> Matrix(3,-2,4,-3) (4/1,30/7) -> (1/2,1/1) Matrix(181,-780,42,-181) -> Matrix(11,-12,10,-11) (30/7,13/3) -> (1/1,6/5) Matrix(299,-1320,41,-181) -> Matrix(1,-2,0,1) 1/0 Matrix(329,-1500,59,-269) -> Matrix(1,-4,2,-9) Matrix(599,-2760,130,-599) -> Matrix(-1,14,0,1) (23/5,60/13) -> (7/1,1/0) Matrix(181,-840,39,-181) -> Matrix(1,4,0,-1) (60/13,14/3) -> (-2/1,1/0) Matrix(419,-2280,77,-419) -> Matrix(9,-4,20,-9) (38/7,60/11) -> (2/5,1/2) Matrix(241,-1320,44,-241) -> Matrix(3,-2,4,-3) (60/11,11/2) -> (1/2,1/1) Matrix(449,-2520,80,-449) -> Matrix(9,-4,20,-9) (28/5,45/8) -> (2/5,1/2) Matrix(31,-180,5,-29) -> Matrix(3,-2,2,-1) 1/1 Matrix(89,-660,12,-89) -> Matrix(-1,0,4,1) (22/3,15/2) -> (-1/2,0/1) Matrix(31,-240,4,-31) -> Matrix(1,0,4,-1) (15/2,8/1) -> (0/1,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.