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 -4/5 -2/3 -3/5 -5/9 -9/20 -13/30 -5/12 -2/5 -23/60 -19/50 -11/30 -1/3 -14/45 -3/10 -7/24 -59/210 -5/18 -7/30 -2/9 -13/60 -5/24 -1/5 -11/60 -1/6 -3/20 0/1 1/8 2/15 3/22 1/7 3/20 2/13 1/6 5/28 2/11 3/16 1/5 3/14 2/9 3/13 1/4 4/15 7/26 3/11 5/18 2/7 3/10 1/3 19/50 2/5 5/12 9/20 7/15 1/2 8/15 5/9 3/5 29/45 2/3 11/15 4/5 13/15 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/2 -7/8 1/3 -13/15 1/2 -19/22 6/11 -6/7 5/8 -17/20 2/3 -11/13 1/2 -5/6 1/1 -14/17 1/0 -23/28 1/1 -9/11 1/2 -13/16 -1/1 -4/5 1/2 -11/14 4/5 -18/23 5/4 -25/32 1/1 -7/9 1/2 -24/31 3/4 -17/22 4/5 -10/13 7/8 -3/4 1/1 -11/15 1/0 -19/26 0/1 -8/11 1/0 -21/29 1/2 -13/18 1/1 -5/7 3/2 -27/38 -2/1 -22/31 1/0 -17/24 0/1 -12/17 1/0 -7/10 1/1 -9/13 3/2 -11/16 -1/1 -13/19 1/2 -2/3 1/0 -13/20 0/1 -11/17 1/2 -9/14 -2/1 -16/25 -1/2 -23/36 0/1 -7/11 -1/2 -5/8 1/1 -18/29 1/0 -31/50 -1/1 -13/21 -1/2 -21/34 0/1 -8/13 1/4 -19/31 1/2 -11/18 1/1 -3/5 1/0 -16/27 1/0 -29/49 -3/2 -13/22 0/1 -10/17 -3/4 -17/29 -1/2 -7/12 0/1 -18/31 1/0 -29/50 -1/1 -11/19 -1/2 -15/26 0/1 -34/59 1/0 -19/33 -1/2 -4/7 -1/4 -9/16 1/5 -14/25 1/2 -33/59 1/2 -19/34 0/1 -5/9 1/2 -16/29 1/0 -11/20 0/1 -17/31 1/2 -6/11 1/0 -7/13 1/2 -8/15 1/0 -1/2 0/1 -7/15 1/2 -13/28 1/1 -6/13 1/0 -11/24 0/1 -5/11 1/2 -9/20 0/1 -13/29 1/2 -4/9 1/0 -11/25 1/0 -7/16 -1/3 -10/23 -1/12 -13/30 0/1 -3/7 1/6 -14/33 1/4 -25/59 1/2 -11/26 0/1 -8/19 1/4 -29/69 1/2 -21/50 1/3 -13/31 1/2 -5/12 0/1 -12/29 1/4 -31/75 1/4 -19/46 4/15 -7/17 3/10 -9/22 0/1 -11/27 1/2 -2/5 1/2 -13/33 1/2 -24/61 3/4 -11/28 1/1 -9/23 3/2 -7/18 1/1 -12/31 1/0 -29/75 1/0 -17/44 -3/1 -5/13 -1/2 -23/60 0/1 -18/47 1/12 -13/34 0/1 -34/89 1/4 -21/55 1/4 -8/21 1/4 -27/71 1/2 -19/50 1/3 -11/29 1/2 -3/8 1/1 -7/19 -1/2 -11/30 0/1 -4/11 1/4 -5/14 2/5 -16/45 1/2 -11/31 1/2 -6/17 1/0 -7/20 0/1 -8/23 1/0 -1/3 1/2 -5/16 1/3 -14/45 1/2 -9/29 1/2 -4/13 3/4 -3/10 1/1 -5/17 1/2 -12/41 1/0 -7/24 0/1 -16/55 1/2 -9/31 1/2 -2/7 3/4 -9/32 1/1 -34/121 1/0 -59/210 1/1 -25/89 3/2 -16/57 1/0 -7/25 1/0 -5/18 1/1 -8/29 1/0 -11/40 0/1 -3/11 1/2 -7/26 0/1 -4/15 1/2 -1/4 1/1 -4/17 7/8 -7/30 1/1 -3/13 7/6 -5/22 4/3 -12/53 13/8 -7/31 3/2 -2/9 1/0 -9/41 1/2 -7/32 1/1 -5/23 5/6 -13/60 1/1 -8/37 13/12 -3/14 4/3 -4/19 1/0 -5/24 2/1 -6/29 1/0 -1/5 1/0 -3/16 1/3 -5/27 1/2 -7/38 2/3 -9/49 5/6 -11/60 1/1 -2/11 1/0 -7/39 1/2 -5/28 1/1 -8/45 1/0 -3/17 1/2 -1/6 1/1 -2/13 1/0 -3/20 2/1 -4/27 1/0 -1/7 5/2 -3/22 6/1 -2/15 1/0 -1/8 -1/1 0/1 1/0 1/8 1/1 2/15 1/0 3/22 -6/1 1/7 -5/2 3/20 -2/1 2/13 1/0 1/6 -1/1 3/17 -1/2 5/28 -1/1 2/11 1/0 3/16 -1/3 1/5 1/0 3/14 -4/3 5/23 -5/6 7/32 -1/1 2/9 1/0 7/31 -3/2 5/22 -4/3 3/13 -7/6 1/4 -1/1 4/15 -1/2 7/26 0/1 3/11 -1/2 8/29 1/0 5/18 -1/1 2/7 -3/4 11/38 -2/5 9/31 -1/2 7/24 0/1 5/17 -1/2 3/10 -1/1 4/13 -3/4 5/16 -1/3 6/19 1/0 1/3 -1/2 7/20 0/1 6/17 1/0 5/14 -2/5 9/25 -1/4 13/36 0/1 4/11 -1/4 3/8 -1/1 11/29 -1/2 19/50 -1/3 8/21 -1/4 13/34 0/1 5/13 1/2 12/31 1/0 7/18 -1/1 2/5 -1/2 11/27 -1/2 20/49 -3/8 9/22 0/1 7/17 -3/10 12/29 -1/4 5/12 0/1 13/31 -1/2 21/50 -1/3 8/19 -1/4 11/26 0/1 25/59 -1/2 14/33 -1/4 3/7 -1/6 7/16 1/3 11/25 1/0 26/59 1/0 15/34 0/1 4/9 1/0 13/29 -1/2 9/20 0/1 14/31 1/0 5/11 -1/2 6/13 1/0 7/15 -1/2 1/2 0/1 8/15 1/0 15/28 -1/1 7/13 -1/2 13/24 0/1 6/11 1/0 11/20 0/1 16/29 1/0 5/9 -1/2 14/25 -1/2 9/16 -1/5 13/23 -1/14 17/30 0/1 4/7 1/4 19/33 1/2 34/59 1/0 15/26 0/1 11/19 1/2 40/69 1/0 29/50 1/1 18/31 1/0 7/12 0/1 17/29 1/2 44/75 1/2 27/46 4/7 10/17 3/4 13/22 0/1 16/27 1/0 3/5 1/0 20/33 1/0 37/61 -3/2 17/28 -1/1 14/23 -3/4 11/18 -1/1 19/31 -1/2 46/75 -1/2 27/44 -3/7 8/13 -1/4 37/60 0/1 29/47 1/10 21/34 0/1 55/89 1/2 34/55 1/2 13/21 1/2 44/71 1/0 31/50 1/1 18/29 1/0 5/8 -1/1 12/19 -1/4 19/30 0/1 7/11 1/2 9/14 2/1 29/45 1/0 20/31 1/0 11/17 -1/2 13/20 0/1 15/23 -1/2 2/3 1/0 11/16 1/1 31/45 1/0 20/29 1/0 9/13 -3/2 7/10 -1/1 12/17 1/0 29/41 -1/2 17/24 0/1 39/55 1/0 22/31 1/0 5/7 -3/2 23/32 -1/1 87/121 -1/2 151/210 -1/1 64/89 -3/4 41/57 -1/2 18/25 -1/2 13/18 -1/1 21/29 -1/2 29/40 0/1 8/11 1/0 19/26 0/1 11/15 1/0 3/4 -1/1 13/17 -7/6 23/30 -1/1 10/13 -7/8 17/22 -4/5 41/53 -13/18 24/31 -3/4 7/9 -1/2 32/41 1/0 25/32 -1/1 18/23 -5/4 47/60 -1/1 29/37 -13/14 11/14 -4/5 15/19 -1/2 19/24 -2/3 23/29 -1/2 4/5 -1/2 13/16 1/1 22/27 1/0 31/38 -2/1 40/49 -5/4 49/60 -1/1 9/11 -1/2 32/39 1/0 23/28 -1/1 37/45 -1/2 14/17 1/0 5/6 -1/1 11/13 -1/2 17/20 -2/3 23/27 -1/2 6/7 -5/8 19/22 -6/11 13/15 -1/2 7/8 -1/3 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(91,80,240,211) (-1/1,-7/8) -> (3/8,11/29) Hyperbolic Matrix(209,182,240,209) (-7/8,-13/15) -> (13/15,7/8) Hyperbolic Matrix(571,494,660,571) (-13/15,-19/22) -> (19/22,13/15) Hyperbolic Matrix(121,104,420,361) (-19/22,-6/7) -> (2/7,11/38) Hyperbolic Matrix(209,178,-600,-511) (-6/7,-17/20) -> (-7/20,-8/23) Hyperbolic Matrix(389,330,600,509) (-17/20,-11/13) -> (11/17,13/20) Hyperbolic Matrix(31,26,180,151) (-11/13,-5/6) -> (1/6,3/17) Hyperbolic Matrix(29,24,180,149) (-5/6,-14/17) -> (2/13,1/6) Hyperbolic Matrix(389,320,-840,-691) (-14/17,-23/28) -> (-13/28,-6/13) Hyperbolic Matrix(329,270,-1500,-1231) (-23/28,-9/11) -> (-9/41,-7/32) Hyperbolic Matrix(329,268,-480,-391) (-9/11,-13/16) -> (-11/16,-13/19) Hyperbolic Matrix(269,218,480,389) (-13/16,-4/5) -> (14/25,9/16) Hyperbolic Matrix(269,212,-420,-331) (-4/5,-11/14) -> (-9/14,-16/25) Hyperbolic Matrix(181,142,-840,-659) (-11/14,-18/23) -> (-8/37,-3/14) Hyperbolic Matrix(839,656,1380,1079) (-18/23,-25/32) -> (17/28,14/23) Hyperbolic Matrix(269,210,-1500,-1171) (-25/32,-7/9) -> (-7/39,-5/28) Hyperbolic Matrix(299,232,540,419) (-7/9,-24/31) -> (16/29,5/9) Hyperbolic Matrix(1321,1022,-1860,-1439) (-24/31,-17/22) -> (-27/38,-22/31) Hyperbolic Matrix(389,300,660,509) (-17/22,-10/13) -> (10/17,13/22) Hyperbolic Matrix(29,22,-120,-91) (-10/13,-3/4) -> (-1/4,-4/17) Hyperbolic Matrix(89,66,120,89) (-3/4,-11/15) -> (11/15,3/4) Hyperbolic Matrix(571,418,780,571) (-11/15,-19/26) -> (19/26,11/15) Hyperbolic Matrix(329,240,780,569) (-19/26,-8/11) -> (8/19,11/26) Hyperbolic Matrix(361,262,-660,-479) (-8/11,-21/29) -> (-17/31,-6/11) Hyperbolic Matrix(661,478,1080,781) (-21/29,-13/18) -> (11/18,19/31) Hyperbolic Matrix(211,152,-540,-389) (-13/18,-5/7) -> (-9/23,-7/18) Hyperbolic Matrix(59,42,420,299) (-5/7,-27/38) -> (3/22,1/7) Hyperbolic Matrix(299,212,-1440,-1021) (-22/31,-17/24) -> (-5/24,-6/29) Hyperbolic Matrix(331,234,-720,-509) (-17/24,-12/17) -> (-6/13,-11/24) Hyperbolic Matrix(91,64,300,211) (-12/17,-7/10) -> (3/10,4/13) Hyperbolic Matrix(89,62,300,209) (-7/10,-9/13) -> (5/17,3/10) Hyperbolic Matrix(301,208,-780,-539) (-9/13,-11/16) -> (-17/44,-5/13) Hyperbolic Matrix(391,266,-660,-449) (-13/19,-2/3) -> (-16/27,-29/49) Hyperbolic Matrix(89,58,-600,-391) (-2/3,-13/20) -> (-3/20,-4/27) Hyperbolic Matrix(509,330,600,389) (-13/20,-11/17) -> (11/13,17/20) Hyperbolic Matrix(421,272,-1020,-659) (-11/17,-9/14) -> (-19/46,-7/17) Hyperbolic Matrix(751,480,-2580,-1649) (-16/25,-23/36) -> (-7/24,-16/55) Hyperbolic Matrix(1231,786,1740,1111) (-23/36,-7/11) -> (29/41,17/24) Hyperbolic Matrix(89,56,-240,-151) (-7/11,-5/8) -> (-3/8,-7/19) Hyperbolic Matrix(29,18,240,149) (-5/8,-18/29) -> (0/1,1/8) Hyperbolic Matrix(1741,1080,3000,1861) (-18/29,-31/50) -> (29/50,18/31) Hyperbolic Matrix(1891,1172,-4500,-2789) (-31/50,-13/21) -> (-29/69,-21/50) Hyperbolic Matrix(569,352,-1020,-631) (-13/21,-21/34) -> (-19/34,-5/9) Hyperbolic Matrix(781,482,-2040,-1259) (-21/34,-8/13) -> (-18/47,-13/34) Hyperbolic Matrix(241,148,-780,-479) (-8/13,-19/31) -> (-9/29,-4/13) Hyperbolic Matrix(781,478,1080,661) (-19/31,-11/18) -> (13/18,21/29) Hyperbolic Matrix(151,92,-540,-329) (-11/18,-3/5) -> (-7/25,-5/18) Hyperbolic Matrix(269,160,-960,-571) (-3/5,-16/27) -> (-16/57,-7/25) Hyperbolic Matrix(541,320,-2940,-1739) (-29/49,-13/22) -> (-7/38,-9/49) Hyperbolic Matrix(509,300,660,389) (-13/22,-10/17) -> (10/13,17/22) Hyperbolic Matrix(361,212,-1020,-599) (-10/17,-17/29) -> (-11/31,-6/17) Hyperbolic Matrix(301,176,720,421) (-17/29,-7/12) -> (5/12,13/31) Hyperbolic Matrix(299,174,720,419) (-7/12,-18/31) -> (12/29,5/12) Hyperbolic Matrix(1861,1080,3000,1741) (-18/31,-29/50) -> (31/50,18/29) Hyperbolic Matrix(1711,992,-4500,-2609) (-29/50,-11/19) -> (-27/71,-19/50) Hyperbolic Matrix(211,122,780,451) (-11/19,-15/26) -> (7/26,3/11) Hyperbolic Matrix(1561,900,3540,2041) (-15/26,-34/59) -> (26/59,15/34) Hyperbolic Matrix(1559,898,-3960,-2281) (-34/59,-19/33) -> (-13/33,-24/61) Hyperbolic Matrix(271,156,-780,-449) (-19/33,-4/7) -> (-8/23,-1/3) Hyperbolic Matrix(209,118,-480,-271) (-4/7,-9/16) -> (-7/16,-10/23) Hyperbolic Matrix(389,218,480,269) (-9/16,-14/25) -> (4/5,13/16) Hyperbolic Matrix(811,454,1020,571) (-14/25,-33/59) -> (23/29,4/5) Hyperbolic Matrix(1499,838,3540,1979) (-33/59,-19/34) -> (11/26,25/59) Hyperbolic Matrix(419,232,540,299) (-5/9,-16/29) -> (24/31,7/9) Hyperbolic Matrix(541,298,1200,661) (-16/29,-11/20) -> (9/20,14/31) Hyperbolic Matrix(539,296,1200,659) (-11/20,-17/31) -> (13/29,9/20) Hyperbolic Matrix(211,114,-720,-389) (-6/11,-7/13) -> (-5/17,-12/41) Hyperbolic Matrix(149,80,-840,-451) (-7/13,-8/15) -> (-8/45,-3/17) Hyperbolic Matrix(31,16,60,31) (-8/15,-1/2) -> (1/2,8/15) Hyperbolic Matrix(29,14,60,29) (-1/2,-7/15) -> (7/15,1/2) Hyperbolic Matrix(1381,642,1680,781) (-7/15,-13/28) -> (23/28,37/45) Hyperbolic Matrix(569,260,720,329) (-11/24,-5/11) -> (15/19,19/24) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(1261,566,1740,781) (-9/20,-13/29) -> (21/29,29/40) Hyperbolic Matrix(121,54,540,241) (-13/29,-4/9) -> (2/9,7/31) Hyperbolic Matrix(389,172,-1020,-451) (-4/9,-11/25) -> (-21/55,-8/21) Hyperbolic Matrix(91,40,480,211) (-11/25,-7/16) -> (3/16,1/5) Hyperbolic Matrix(511,222,900,391) (-10/23,-13/30) -> (17/30,4/7) Hyperbolic Matrix(509,220,900,389) (-13/30,-3/7) -> (13/23,17/30) Hyperbolic Matrix(61,26,-420,-179) (-3/7,-14/33) -> (-4/27,-1/7) Hyperbolic Matrix(1769,750,-6300,-2671) (-14/33,-25/59) -> (-25/89,-16/57) Hyperbolic Matrix(2669,1130,4320,1829) (-25/59,-11/26) -> (21/34,55/89) Hyperbolic Matrix(569,240,780,329) (-11/26,-8/19) -> (8/11,19/26) Hyperbolic Matrix(2341,984,3000,1261) (-8/19,-29/69) -> (7/9,32/41) Hyperbolic Matrix(1139,478,3000,1259) (-21/50,-13/31) -> (11/29,19/50) Hyperbolic Matrix(421,176,720,301) (-13/31,-5/12) -> (7/12,17/29) Hyperbolic Matrix(419,174,720,299) (-5/12,-12/29) -> (18/31,7/12) Hyperbolic Matrix(2399,992,3480,1439) (-12/29,-31/75) -> (31/45,20/29) Hyperbolic Matrix(2009,830,3120,1289) (-31/75,-19/46) -> (9/14,29/45) Hyperbolic Matrix(151,62,660,271) (-7/17,-9/22) -> (5/22,3/13) Hyperbolic Matrix(299,122,-1620,-661) (-9/22,-11/27) -> (-5/27,-7/38) Hyperbolic Matrix(119,48,-300,-121) (-11/27,-2/5) -> (-2/5,-13/33) Parabolic Matrix(1501,590,-5340,-2099) (-24/61,-11/28) -> (-9/32,-34/121) Hyperbolic Matrix(301,118,1380,541) (-11/28,-9/23) -> (5/23,7/32) Hyperbolic Matrix(299,116,1080,419) (-7/18,-12/31) -> (8/29,5/18) Hyperbolic Matrix(2399,928,3720,1439) (-12/31,-29/75) -> (29/45,20/31) Hyperbolic Matrix(2189,846,3180,1229) (-29/75,-17/44) -> (11/16,31/45) Hyperbolic Matrix(2221,852,3600,1381) (-5/13,-23/60) -> (37/60,29/47) Hyperbolic Matrix(2219,850,3600,1379) (-23/60,-18/47) -> (8/13,37/60) Hyperbolic Matrix(2491,952,4320,1651) (-13/34,-34/89) -> (34/59,15/26) Hyperbolic Matrix(4681,1788,6600,2521) (-34/89,-21/55) -> (39/55,22/31) Hyperbolic Matrix(2461,936,3000,1141) (-8/21,-27/71) -> (9/11,32/39) Hyperbolic Matrix(1259,478,3000,1139) (-19/50,-11/29) -> (13/31,21/50) Hyperbolic Matrix(211,80,240,91) (-11/29,-3/8) -> (7/8,1/1) Hyperbolic Matrix(571,210,900,331) (-7/19,-11/30) -> (19/30,7/11) Hyperbolic Matrix(569,208,900,329) (-11/30,-4/11) -> (12/19,19/30) Hyperbolic Matrix(89,32,-420,-151) (-4/11,-5/14) -> (-3/14,-4/19) Hyperbolic Matrix(1831,652,3120,1111) (-5/14,-16/45) -> (44/75,27/46) Hyperbolic Matrix(2281,810,3720,1321) (-16/45,-11/31) -> (19/31,46/75) Hyperbolic Matrix(91,32,600,211) (-6/17,-7/20) -> (3/20,2/13) Hyperbolic Matrix(89,28,-480,-151) (-1/3,-5/16) -> (-3/16,-5/27) Hyperbolic Matrix(1951,608,3180,991) (-5/16,-14/45) -> (46/75,27/44) Hyperbolic Matrix(2041,634,3480,1081) (-14/45,-9/29) -> (17/29,44/75) Hyperbolic Matrix(211,64,300,91) (-4/13,-3/10) -> (7/10,12/17) Hyperbolic Matrix(209,62,300,89) (-3/10,-5/17) -> (9/13,7/10) Hyperbolic Matrix(629,184,1740,509) (-12/41,-7/24) -> (13/36,4/11) Hyperbolic Matrix(4079,1186,6600,1919) (-16/55,-9/31) -> (55/89,34/55) Hyperbolic Matrix(421,122,-1860,-539) (-9/31,-2/7) -> (-12/53,-7/31) Hyperbolic Matrix(751,212,960,271) (-2/7,-9/32) -> (25/32,18/23) Hyperbolic Matrix(31711,8910,44100,12391) (-34/121,-59/210) -> (151/210,64/89) Hyperbolic Matrix(31709,8908,44100,12389) (-59/210,-25/89) -> (87/121,151/210) Hyperbolic Matrix(419,116,1080,299) (-5/18,-8/29) -> (12/31,7/18) Hyperbolic Matrix(959,264,1740,479) (-8/29,-11/40) -> (11/20,16/29) Hyperbolic Matrix(451,122,780,211) (-3/11,-7/26) -> (15/26,11/19) Hyperbolic Matrix(209,56,780,209) (-7/26,-4/15) -> (4/15,7/26) Hyperbolic Matrix(31,8,120,31) (-4/15,-1/4) -> (1/4,4/15) Hyperbolic Matrix(691,162,900,211) (-4/17,-7/30) -> (23/30,10/13) Hyperbolic Matrix(689,160,900,209) (-7/30,-3/13) -> (13/17,23/30) Hyperbolic Matrix(271,62,660,151) (-3/13,-5/22) -> (9/22,7/17) Hyperbolic Matrix(1139,258,1320,299) (-5/22,-12/53) -> (6/7,19/22) Hyperbolic Matrix(241,54,540,121) (-7/31,-2/9) -> (4/9,13/29) Hyperbolic Matrix(1739,382,3000,659) (-2/9,-9/41) -> (11/19,40/69) Hyperbolic Matrix(689,150,960,209) (-7/32,-5/23) -> (5/7,23/32) Hyperbolic Matrix(2821,612,3600,781) (-5/23,-13/60) -> (47/60,29/37) Hyperbolic Matrix(2819,610,3600,779) (-13/60,-8/37) -> (18/23,47/60) Hyperbolic Matrix(391,82,720,151) (-4/19,-5/24) -> (13/24,6/11) Hyperbolic Matrix(449,92,1020,209) (-6/29,-1/5) -> (11/25,26/59) Hyperbolic Matrix(211,40,480,91) (-1/5,-3/16) -> (7/16,11/25) Hyperbolic Matrix(2941,540,3600,661) (-9/49,-11/60) -> (49/60,9/11) Hyperbolic Matrix(2939,538,3600,659) (-11/60,-2/11) -> (40/49,49/60) Hyperbolic Matrix(1859,334,3000,539) (-2/11,-7/39) -> (13/21,44/71) Hyperbolic Matrix(899,160,1680,299) (-5/28,-8/45) -> (8/15,15/28) Hyperbolic Matrix(151,26,180,31) (-3/17,-1/6) -> (5/6,11/13) Hyperbolic Matrix(149,24,180,29) (-1/6,-2/13) -> (14/17,5/6) Hyperbolic Matrix(211,32,600,91) (-2/13,-3/20) -> (7/20,6/17) Hyperbolic Matrix(1021,140,1320,181) (-1/7,-3/22) -> (17/22,41/53) Hyperbolic Matrix(89,12,660,89) (-3/22,-2/15) -> (2/15,3/22) Hyperbolic Matrix(31,4,240,31) (-2/15,-1/8) -> (1/8,2/15) Hyperbolic Matrix(149,18,240,29) (-1/8,0/1) -> (18/29,5/8) Hyperbolic Matrix(391,-58,600,-89) (1/7,3/20) -> (13/20,15/23) Hyperbolic Matrix(451,-80,840,-149) (3/17,5/28) -> (15/28,7/13) Hyperbolic Matrix(1171,-210,1500,-269) (5/28,2/11) -> (32/41,25/32) Hyperbolic Matrix(151,-28,480,-89) (2/11,3/16) -> (5/16,6/19) Hyperbolic Matrix(151,-32,420,-89) (1/5,3/14) -> (5/14,9/25) Hyperbolic Matrix(659,-142,840,-181) (3/14,5/23) -> (29/37,11/14) Hyperbolic Matrix(1231,-270,1500,-329) (7/32,2/9) -> (32/39,23/28) Hyperbolic Matrix(539,-122,1860,-421) (7/31,5/22) -> (11/38,9/31) Hyperbolic Matrix(91,-22,120,-29) (3/13,1/4) -> (3/4,13/17) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(329,-92,540,-151) (5/18,2/7) -> (14/23,11/18) Hyperbolic Matrix(1141,-332,1440,-419) (9/31,7/24) -> (19/24,23/29) Hyperbolic Matrix(389,-114,720,-211) (7/24,5/17) -> (7/13,13/24) Hyperbolic Matrix(479,-148,780,-241) (4/13,5/16) -> (27/44,8/13) Hyperbolic Matrix(269,-86,660,-211) (6/19,1/3) -> (11/27,20/49) Hyperbolic Matrix(511,-178,600,-209) (1/3,7/20) -> (17/20,23/27) Hyperbolic Matrix(599,-212,1020,-361) (6/17,5/14) -> (27/46,10/17) Hyperbolic Matrix(1829,-660,2580,-931) (9/25,13/36) -> (17/24,39/55) Hyperbolic Matrix(151,-56,240,-89) (4/11,3/8) -> (5/8,12/19) Hyperbolic Matrix(2609,-992,4500,-1711) (19/50,8/21) -> (40/69,29/50) Hyperbolic Matrix(451,-172,1020,-389) (8/21,13/34) -> (15/34,4/9) Hyperbolic Matrix(1259,-482,2040,-781) (13/34,5/13) -> (29/47,21/34) Hyperbolic Matrix(539,-208,780,-301) (5/13,12/31) -> (20/29,9/13) Hyperbolic Matrix(389,-152,540,-211) (7/18,2/5) -> (18/25,13/18) Hyperbolic Matrix(691,-280,960,-389) (2/5,11/27) -> (41/57,18/25) Hyperbolic Matrix(2399,-980,2940,-1201) (20/49,9/22) -> (31/38,40/49) Hyperbolic Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(2789,-1172,4500,-1891) (21/50,8/19) -> (44/71,31/50) Hyperbolic Matrix(2401,-1018,3960,-1679) (25/59,14/33) -> (20/33,37/61) Hyperbolic Matrix(509,-216,780,-331) (14/33,3/7) -> (15/23,2/3) Hyperbolic Matrix(271,-118,480,-209) (3/7,7/16) -> (9/16,13/23) Hyperbolic Matrix(509,-234,720,-331) (5/11,6/13) -> (12/17,29/41) Hyperbolic Matrix(691,-320,840,-389) (6/13,7/15) -> (37/45,14/17) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(631,-352,1020,-569) (5/9,14/25) -> (34/55,13/21) Hyperbolic Matrix(359,-206,420,-241) (4/7,19/33) -> (23/27,6/7) Hyperbolic Matrix(4531,-2610,6300,-3629) (19/33,34/59) -> (64/89,41/57) Hyperbolic Matrix(1321,-782,1620,-959) (13/22,16/27) -> (22/27,31/38) Hyperbolic Matrix(181,-108,300,-179) (16/27,3/5) -> (3/5,20/33) Parabolic Matrix(3839,-2330,5340,-3241) (37/61,17/28) -> (23/32,87/121) Hyperbolic Matrix(331,-212,420,-269) (7/11,9/14) -> (11/14,15/19) Hyperbolic Matrix(391,-268,480,-329) (2/3,11/16) -> (13/16,22/27) Hyperbolic Matrix(1439,-1022,1860,-1321) (22/31,5/7) -> (41/53,24/31) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(91,80,240,211) -> Matrix(1,0,-4,1) Matrix(209,182,240,209) -> Matrix(5,-2,-12,5) Matrix(571,494,660,571) -> Matrix(23,-12,-44,23) Matrix(121,104,420,361) -> Matrix(7,-4,-12,7) Matrix(209,178,-600,-511) -> Matrix(3,-2,8,-5) Matrix(389,330,600,509) -> Matrix(3,-2,-4,3) Matrix(31,26,180,151) -> Matrix(3,-2,-4,3) Matrix(29,24,180,149) -> Matrix(1,-2,0,1) Matrix(389,320,-840,-691) -> Matrix(1,0,0,1) Matrix(329,270,-1500,-1231) -> Matrix(1,0,0,1) Matrix(329,268,-480,-391) -> Matrix(1,0,0,1) Matrix(269,218,480,389) -> Matrix(1,0,-4,1) Matrix(269,212,-420,-331) -> Matrix(3,-2,-4,3) Matrix(181,142,-840,-659) -> Matrix(9,-8,8,-7) Matrix(839,656,1380,1079) -> Matrix(1,-2,0,1) Matrix(269,210,-1500,-1171) -> Matrix(1,0,0,1) Matrix(299,232,540,419) -> Matrix(3,-2,-4,3) Matrix(1321,1022,-1860,-1439) -> Matrix(3,-2,-4,3) Matrix(389,300,660,509) -> Matrix(5,-4,4,-3) Matrix(29,22,-120,-91) -> Matrix(1,0,0,1) Matrix(89,66,120,89) -> Matrix(1,-2,0,1) Matrix(571,418,780,571) -> Matrix(1,0,0,1) Matrix(329,240,780,569) -> Matrix(1,0,-4,1) Matrix(361,262,-660,-479) -> Matrix(1,0,0,1) Matrix(661,478,1080,781) -> Matrix(3,-2,-4,3) Matrix(211,152,-540,-389) -> Matrix(1,0,0,1) Matrix(59,42,420,299) -> Matrix(1,-4,0,1) Matrix(299,212,-1440,-1021) -> Matrix(1,2,0,1) Matrix(331,234,-720,-509) -> Matrix(1,0,0,1) Matrix(91,64,300,211) -> Matrix(3,-2,-4,3) Matrix(89,62,300,209) -> Matrix(1,-2,0,1) Matrix(301,208,-780,-539) -> Matrix(1,-2,0,1) Matrix(391,266,-660,-449) -> Matrix(1,-2,0,1) Matrix(89,58,-600,-391) -> Matrix(1,2,0,1) Matrix(509,330,600,389) -> Matrix(3,-2,-4,3) Matrix(421,272,-1020,-659) -> Matrix(1,-2,4,-7) Matrix(751,480,-2580,-1649) -> Matrix(1,0,4,1) Matrix(1231,786,1740,1111) -> Matrix(1,0,0,1) Matrix(89,56,-240,-151) -> Matrix(1,0,0,1) Matrix(29,18,240,149) -> Matrix(1,0,0,1) Matrix(1741,1080,3000,1861) -> Matrix(1,2,0,1) Matrix(1891,1172,-4500,-2789) -> Matrix(1,0,4,1) Matrix(569,352,-1020,-631) -> Matrix(1,0,4,1) Matrix(781,482,-2040,-1259) -> Matrix(1,0,8,1) Matrix(241,148,-780,-479) -> Matrix(5,-2,8,-3) Matrix(781,478,1080,661) -> Matrix(3,-2,-4,3) Matrix(151,92,-540,-329) -> Matrix(1,0,0,1) Matrix(269,160,-960,-571) -> Matrix(1,2,0,1) Matrix(541,320,-2940,-1739) -> Matrix(3,2,4,3) Matrix(509,300,660,389) -> Matrix(3,4,-4,-5) Matrix(361,212,-1020,-599) -> Matrix(3,2,4,3) Matrix(301,176,720,421) -> Matrix(1,0,0,1) Matrix(299,174,720,419) -> Matrix(1,0,-4,1) Matrix(1861,1080,3000,1741) -> Matrix(1,2,0,1) Matrix(1711,992,-4500,-2609) -> Matrix(1,0,4,1) Matrix(211,122,780,451) -> Matrix(1,0,0,1) Matrix(1561,900,3540,2041) -> Matrix(1,0,0,1) Matrix(1559,898,-3960,-2281) -> Matrix(3,2,4,3) Matrix(271,156,-780,-449) -> Matrix(1,0,4,1) Matrix(209,118,-480,-271) -> Matrix(1,0,-8,1) Matrix(389,218,480,269) -> Matrix(1,0,-4,1) Matrix(811,454,1020,571) -> Matrix(3,-2,-4,3) Matrix(1499,838,3540,1979) -> Matrix(1,0,-4,1) Matrix(419,232,540,299) -> Matrix(3,-2,-4,3) Matrix(541,298,1200,661) -> Matrix(1,0,0,1) Matrix(539,296,1200,659) -> Matrix(1,0,-4,1) Matrix(211,114,-720,-389) -> Matrix(1,0,0,1) Matrix(149,80,-840,-451) -> Matrix(1,0,0,1) Matrix(31,16,60,31) -> Matrix(1,0,0,1) Matrix(29,14,60,29) -> Matrix(1,0,-4,1) Matrix(1381,642,1680,781) -> Matrix(3,-2,-4,3) Matrix(569,260,720,329) -> Matrix(3,-2,-4,3) Matrix(181,82,-660,-299) -> Matrix(1,0,0,1) Matrix(1261,566,1740,781) -> Matrix(1,0,-4,1) Matrix(121,54,540,241) -> Matrix(1,-2,0,1) Matrix(389,172,-1020,-451) -> Matrix(1,0,4,1) Matrix(91,40,480,211) -> Matrix(1,0,0,1) Matrix(511,222,900,391) -> Matrix(1,0,16,1) Matrix(509,220,900,389) -> Matrix(1,0,-20,1) Matrix(61,26,-420,-179) -> Matrix(7,-2,4,-1) Matrix(1769,750,-6300,-2671) -> Matrix(7,-2,4,-1) Matrix(2669,1130,4320,1829) -> Matrix(1,0,0,1) Matrix(569,240,780,329) -> Matrix(1,0,-4,1) Matrix(2341,984,3000,1261) -> Matrix(1,0,-4,1) Matrix(1139,478,3000,1259) -> Matrix(5,-2,-12,5) Matrix(421,176,720,301) -> Matrix(1,0,0,1) Matrix(419,174,720,299) -> Matrix(1,0,-4,1) Matrix(2399,992,3480,1439) -> Matrix(25,-6,-4,1) Matrix(2009,830,3120,1289) -> Matrix(23,-6,4,-1) Matrix(151,62,660,271) -> Matrix(11,-4,-8,3) Matrix(299,122,-1620,-661) -> Matrix(5,-2,8,-3) Matrix(119,48,-300,-121) -> Matrix(5,-2,8,-3) Matrix(1501,590,-5340,-2099) -> Matrix(5,-4,4,-3) Matrix(301,118,1380,541) -> Matrix(3,-2,-4,3) Matrix(299,116,1080,419) -> Matrix(1,-2,0,1) Matrix(2399,928,3720,1439) -> Matrix(1,-6,0,1) Matrix(2189,846,3180,1229) -> Matrix(1,4,0,1) Matrix(2221,852,3600,1381) -> Matrix(1,0,12,1) Matrix(2219,850,3600,1379) -> Matrix(1,0,-16,1) Matrix(2491,952,4320,1651) -> Matrix(1,0,-4,1) Matrix(4681,1788,6600,2521) -> Matrix(1,0,-4,1) Matrix(2461,936,3000,1141) -> Matrix(1,0,-4,1) Matrix(1259,478,3000,1139) -> Matrix(5,-2,-12,5) Matrix(211,80,240,91) -> Matrix(1,0,-4,1) Matrix(571,210,900,331) -> Matrix(1,0,4,1) Matrix(569,208,900,329) -> Matrix(1,0,-8,1) Matrix(89,32,-420,-151) -> Matrix(7,-2,4,-1) Matrix(1831,652,3120,1111) -> Matrix(13,-6,24,-11) Matrix(2281,810,3720,1321) -> Matrix(11,-6,-20,11) Matrix(91,32,600,211) -> Matrix(1,-2,0,1) Matrix(89,28,-480,-151) -> Matrix(1,0,0,1) Matrix(1951,608,3180,991) -> Matrix(9,-4,-20,9) Matrix(2041,634,3480,1081) -> Matrix(11,-6,24,-13) Matrix(211,64,300,91) -> Matrix(3,-2,-4,3) Matrix(209,62,300,89) -> Matrix(1,-2,0,1) Matrix(629,184,1740,509) -> Matrix(1,0,-4,1) Matrix(4079,1186,6600,1919) -> Matrix(1,0,0,1) Matrix(421,122,-1860,-539) -> Matrix(7,-2,4,-1) Matrix(751,212,960,271) -> Matrix(1,-2,0,1) Matrix(31711,8910,44100,12391) -> Matrix(3,-2,-4,3) Matrix(31709,8908,44100,12389) -> Matrix(1,-2,0,1) Matrix(419,116,1080,299) -> Matrix(1,-2,0,1) Matrix(959,264,1740,479) -> Matrix(1,0,0,1) Matrix(451,122,780,211) -> Matrix(1,0,0,1) Matrix(209,56,780,209) -> Matrix(1,0,-4,1) Matrix(31,8,120,31) -> Matrix(3,-2,-4,3) Matrix(691,162,900,211) -> Matrix(15,-14,-16,15) Matrix(689,160,900,209) -> Matrix(13,-14,-12,13) Matrix(271,62,660,151) -> Matrix(3,-4,-8,11) Matrix(1139,258,1320,299) -> Matrix(9,-14,-16,25) Matrix(241,54,540,121) -> Matrix(1,-2,0,1) Matrix(1739,382,3000,659) -> Matrix(1,0,0,1) Matrix(689,150,960,209) -> Matrix(3,-2,-4,3) Matrix(2821,612,3600,781) -> Matrix(19,-18,-20,19) Matrix(2819,610,3600,779) -> Matrix(17,-18,-16,17) Matrix(391,82,720,151) -> Matrix(1,-2,0,1) Matrix(449,92,1020,209) -> Matrix(1,-2,0,1) Matrix(211,40,480,91) -> Matrix(1,0,0,1) Matrix(2941,540,3600,661) -> Matrix(7,-6,-8,7) Matrix(2939,538,3600,659) -> Matrix(5,-6,-4,5) Matrix(1859,334,3000,539) -> Matrix(1,0,0,1) Matrix(899,160,1680,299) -> Matrix(1,-2,0,1) Matrix(151,26,180,31) -> Matrix(3,-2,-4,3) Matrix(149,24,180,29) -> Matrix(1,-2,0,1) Matrix(211,32,600,91) -> Matrix(1,-2,0,1) Matrix(1021,140,1320,181) -> Matrix(3,-14,-4,19) Matrix(89,12,660,89) -> Matrix(1,-12,0,1) Matrix(31,4,240,31) -> Matrix(1,2,0,1) Matrix(149,18,240,29) -> Matrix(1,0,0,1) Matrix(391,-58,600,-89) -> Matrix(1,2,0,1) Matrix(451,-80,840,-149) -> Matrix(1,0,0,1) Matrix(1171,-210,1500,-269) -> Matrix(1,0,0,1) Matrix(151,-28,480,-89) -> Matrix(1,0,0,1) Matrix(151,-32,420,-89) -> Matrix(1,2,-4,-7) Matrix(659,-142,840,-181) -> Matrix(7,8,-8,-9) Matrix(1231,-270,1500,-329) -> Matrix(1,0,0,1) Matrix(539,-122,1860,-421) -> Matrix(1,2,-4,-7) Matrix(91,-22,120,-29) -> Matrix(1,0,0,1) Matrix(299,-82,660,-181) -> Matrix(1,0,0,1) Matrix(329,-92,540,-151) -> Matrix(1,0,0,1) Matrix(1141,-332,1440,-419) -> Matrix(5,2,-8,-3) Matrix(389,-114,720,-211) -> Matrix(1,0,0,1) Matrix(479,-148,780,-241) -> Matrix(3,2,-8,-5) Matrix(269,-86,660,-211) -> Matrix(3,2,-8,-5) Matrix(511,-178,600,-209) -> Matrix(5,2,-8,-3) Matrix(599,-212,1020,-361) -> Matrix(3,2,4,3) Matrix(1829,-660,2580,-931) -> Matrix(1,0,4,1) Matrix(151,-56,240,-89) -> Matrix(1,0,0,1) Matrix(2609,-992,4500,-1711) -> Matrix(1,0,4,1) Matrix(451,-172,1020,-389) -> Matrix(1,0,4,1) Matrix(1259,-482,2040,-781) -> Matrix(1,0,8,1) Matrix(539,-208,780,-301) -> Matrix(1,-2,0,1) Matrix(389,-152,540,-211) -> Matrix(1,0,0,1) Matrix(691,-280,960,-389) -> Matrix(5,2,-8,-3) Matrix(2399,-980,2940,-1201) -> Matrix(7,2,-4,-1) Matrix(659,-272,1020,-421) -> Matrix(7,2,-4,-1) Matrix(2789,-1172,4500,-1891) -> Matrix(1,0,4,1) Matrix(2401,-1018,3960,-1679) -> Matrix(7,2,-4,-1) Matrix(509,-216,780,-331) -> Matrix(1,0,4,1) Matrix(271,-118,480,-209) -> Matrix(1,0,-8,1) Matrix(509,-234,720,-331) -> Matrix(1,0,0,1) Matrix(691,-320,840,-389) -> Matrix(1,0,0,1) Matrix(479,-262,660,-361) -> Matrix(1,0,0,1) Matrix(631,-352,1020,-569) -> Matrix(1,0,4,1) Matrix(359,-206,420,-241) -> Matrix(3,-2,-4,3) Matrix(4531,-2610,6300,-3629) -> Matrix(3,-2,-4,3) Matrix(1321,-782,1620,-959) -> Matrix(1,-2,0,1) Matrix(181,-108,300,-179) -> Matrix(1,-2,0,1) Matrix(3839,-2330,5340,-3241) -> Matrix(3,4,-4,-5) Matrix(331,-212,420,-269) -> Matrix(3,-2,-4,3) Matrix(391,-268,480,-329) -> Matrix(1,0,0,1) Matrix(1439,-1022,1860,-1321) -> Matrix(3,-2,-4,3) 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): 288 Minimal number of generators: 49 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: 32 Genus: 9 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/8 2/15 1/7 1/6 2/11 1/5 3/14 2/9 3/13 1/4 4/15 3/10 1/3 2/5 5/12 4/9 9/20 7/15 1/2 11/20 17/30 7/12 3/5 19/30 2/3 31/45 7/10 23/30 4/5 5/6 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/0 1/8 1/1 2/15 1/0 1/7 -5/2 1/6 -1/1 3/17 -1/2 2/11 1/0 1/5 1/0 3/14 -4/3 2/9 1/0 3/13 -7/6 1/4 -1/1 4/15 -1/2 3/11 -1/2 2/7 -3/4 5/17 -1/2 3/10 -1/1 4/13 -3/4 1/3 -1/2 6/17 1/0 5/14 -2/5 9/25 -1/4 4/11 -1/4 3/8 -1/1 11/29 -1/2 8/21 -1/4 5/13 1/2 2/5 -1/2 7/17 -3/10 12/29 -1/4 5/12 0/1 3/7 -1/6 7/16 1/3 4/9 1/0 13/29 -1/2 9/20 0/1 5/11 -1/2 6/13 1/0 7/15 -1/2 1/2 0/1 8/15 1/0 7/13 -1/2 6/11 1/0 11/20 0/1 5/9 -1/2 9/16 -1/5 13/23 -1/14 17/30 0/1 4/7 1/4 11/19 1/2 29/50 1/1 18/31 1/0 7/12 0/1 3/5 1/0 11/18 -1/1 19/31 -1/2 46/75 -1/2 27/44 -3/7 8/13 -1/4 13/21 1/2 31/50 1/1 18/29 1/0 5/8 -1/1 12/19 -1/4 19/30 0/1 7/11 1/2 9/14 2/1 2/3 1/0 11/16 1/1 31/45 1/0 20/29 1/0 9/13 -3/2 7/10 -1/1 12/17 1/0 17/24 0/1 5/7 -3/2 13/18 -1/1 21/29 -1/2 29/40 0/1 8/11 1/0 11/15 1/0 3/4 -1/1 13/17 -7/6 23/30 -1/1 10/13 -7/8 7/9 -1/2 11/14 -4/5 4/5 -1/2 13/16 1/1 9/11 -1/2 14/17 1/0 5/6 -1/1 11/13 -1/2 6/7 -5/8 13/15 -1/2 7/8 -1/3 1/1 -1/2 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(91,-11,240,-29) (0/1,1/8) -> (3/8,11/29) Hyperbolic Matrix(209,-27,240,-31) (1/8,2/15) -> (13/15,7/8) Hyperbolic Matrix(181,-25,210,-29) (2/15,1/7) -> (6/7,13/15) Hyperbolic Matrix(149,-22,210,-31) (1/7,1/6) -> (17/24,5/7) Hyperbolic Matrix(361,-63,510,-89) (1/6,3/17) -> (12/17,17/24) Hyperbolic Matrix(151,-27,330,-59) (3/17,2/11) -> (5/11,6/13) Hyperbolic Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(151,-32,420,-89) (1/5,3/14) -> (5/14,9/25) Hyperbolic Matrix(151,-33,270,-59) (3/14,2/9) -> (5/9,9/16) Hyperbolic Matrix(241,-55,390,-89) (2/9,3/13) -> (8/13,13/21) Hyperbolic Matrix(91,-22,120,-29) (3/13,1/4) -> (3/4,13/17) Hyperbolic Matrix(89,-23,120,-31) (1/4,4/15) -> (11/15,3/4) Hyperbolic Matrix(241,-65,330,-89) (4/15,3/11) -> (8/11,11/15) Hyperbolic Matrix(121,-34,210,-59) (3/11,2/7) -> (4/7,11/19) Hyperbolic Matrix(179,-52,210,-61) (2/7,5/17) -> (11/13,6/7) Hyperbolic Matrix(91,-27,300,-89) (5/17,3/10) -> (3/10,4/13) Parabolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(571,-202,930,-329) (6/17,5/14) -> (27/44,8/13) Hyperbolic Matrix(151,-56,240,-89) (4/11,3/8) -> (5/8,12/19) Hyperbolic Matrix(389,-148,870,-331) (11/29,8/21) -> (4/9,13/29) Hyperbolic Matrix(301,-115,390,-149) (8/21,5/13) -> (10/13,7/9) Hyperbolic Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(601,-248,870,-359) (7/17,12/29) -> (20/29,9/13) Hyperbolic Matrix(629,-261,870,-361) (12/29,5/12) -> (13/18,21/29) Hyperbolic Matrix(151,-64,210,-89) (5/12,3/7) -> (5/7,13/18) Hyperbolic Matrix(271,-118,480,-209) (3/7,7/16) -> (9/16,13/23) Hyperbolic Matrix(211,-93,270,-119) (7/16,4/9) -> (7/9,11/14) Hyperbolic Matrix(1201,-539,2070,-929) (13/29,9/20) -> (29/50,18/31) Hyperbolic Matrix(539,-244,930,-421) (9/20,5/11) -> (11/19,29/50) Hyperbolic Matrix(209,-97,390,-181) (6/13,7/15) -> (8/15,7/13) Hyperbolic Matrix(31,-15,60,-29) (7/15,1/2) -> (1/2,8/15) Parabolic Matrix(271,-147,330,-179) (7/13,6/11) -> (9/11,14/17) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(539,-298,870,-481) (11/20,5/9) -> (13/21,31/50) Hyperbolic Matrix(511,-289,900,-509) (13/23,17/30) -> (17/30,4/7) Parabolic Matrix(569,-331,930,-541) (18/31,7/12) -> (11/18,19/31) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(2461,-1509,3570,-2189) (19/31,46/75) -> (31/45,20/29) Hyperbolic Matrix(2189,-1343,3180,-1951) (46/75,27/44) -> (11/16,31/45) Hyperbolic Matrix(1891,-1173,2610,-1619) (31/50,18/29) -> (21/29,29/40) Hyperbolic Matrix(211,-131,240,-149) (18/29,5/8) -> (7/8,1/1) Hyperbolic Matrix(571,-361,900,-569) (12/19,19/30) -> (19/30,7/11) Parabolic Matrix(269,-172,330,-211) (7/11,9/14) -> (13/16,9/11) Hyperbolic Matrix(61,-40,90,-59) (9/14,2/3) -> (2/3,11/16) Parabolic Matrix(211,-147,300,-209) (9/13,7/10) -> (7/10,12/17) Parabolic Matrix(691,-529,900,-689) (13/17,23/30) -> (23/30,10/13) Parabolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(151,-125,180,-149) (14/17,5/6) -> (5/6,11/13) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-2,1) Matrix(91,-11,240,-29) -> Matrix(1,0,-2,1) Matrix(209,-27,240,-31) -> Matrix(1,-2,-2,5) Matrix(181,-25,210,-29) -> Matrix(1,5,-2,-9) Matrix(149,-22,210,-31) -> Matrix(1,1,0,1) Matrix(361,-63,510,-89) -> Matrix(1,1,-2,-1) Matrix(151,-27,330,-59) -> Matrix(1,1,-2,-1) Matrix(119,-22,330,-61) -> Matrix(1,1,-4,-3) Matrix(151,-32,420,-89) -> Matrix(1,2,-4,-7) Matrix(151,-33,270,-59) -> Matrix(1,1,-2,-1) Matrix(241,-55,390,-89) -> Matrix(1,1,2,3) Matrix(91,-22,120,-29) -> Matrix(1,0,0,1) Matrix(89,-23,120,-31) -> Matrix(3,2,-2,-1) Matrix(241,-65,330,-89) -> Matrix(1,1,-2,-1) Matrix(121,-34,210,-59) -> Matrix(1,1,0,1) Matrix(179,-52,210,-61) -> Matrix(3,1,-4,-1) Matrix(91,-27,300,-89) -> Matrix(1,2,-2,-3) Matrix(31,-10,90,-29) -> Matrix(1,1,-4,-3) Matrix(571,-202,930,-329) -> Matrix(1,1,-4,-3) Matrix(151,-56,240,-89) -> Matrix(1,0,0,1) Matrix(389,-148,870,-331) -> Matrix(3,1,-4,-1) Matrix(301,-115,390,-149) -> Matrix(5,1,-6,-1) Matrix(61,-24,150,-59) -> Matrix(1,1,-4,-3) Matrix(601,-248,870,-359) -> Matrix(11,3,-4,-1) Matrix(629,-261,870,-361) -> Matrix(5,1,-6,-1) Matrix(151,-64,210,-89) -> Matrix(3,1,-4,-1) Matrix(271,-118,480,-209) -> Matrix(1,0,-8,1) Matrix(211,-93,270,-119) -> Matrix(1,1,-2,-1) Matrix(1201,-539,2070,-929) -> Matrix(3,1,2,1) Matrix(539,-244,930,-421) -> Matrix(1,1,0,1) Matrix(209,-97,390,-181) -> Matrix(1,1,-2,-1) Matrix(31,-15,60,-29) -> Matrix(1,0,2,1) Matrix(271,-147,330,-179) -> Matrix(1,1,-2,-1) Matrix(479,-262,660,-361) -> Matrix(1,0,0,1) Matrix(539,-298,870,-481) -> Matrix(1,1,0,1) Matrix(511,-289,900,-509) -> Matrix(1,0,18,1) Matrix(569,-331,930,-541) -> Matrix(1,1,-2,-1) Matrix(91,-54,150,-89) -> Matrix(1,-1,0,1) Matrix(2461,-1509,3570,-2189) -> Matrix(13,7,-2,-1) Matrix(2189,-1343,3180,-1951) -> Matrix(9,4,2,1) Matrix(1891,-1173,2610,-1619) -> Matrix(1,-1,-2,3) Matrix(211,-131,240,-149) -> Matrix(1,0,-2,1) Matrix(571,-361,900,-569) -> Matrix(1,0,6,1) Matrix(269,-172,330,-211) -> Matrix(1,-1,0,1) Matrix(61,-40,90,-59) -> Matrix(1,-1,0,1) Matrix(211,-147,300,-209) -> Matrix(1,2,-2,-3) Matrix(691,-529,900,-689) -> Matrix(13,14,-14,-15) Matrix(121,-96,150,-119) -> Matrix(1,1,-4,-3) Matrix(151,-125,180,-149) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 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 1/0 1 30 1/8 1/1 2 15 2/15 1/0 7 2 1/7 -5/2 1 30 1/6 -1/1 2 5 3/17 -1/2 1 30 2/11 1/0 1 30 1/5 1/0 1 6 3/14 -4/3 2 15 2/9 1/0 1 10 3/13 -7/6 1 30 7/30 -1/1 14 1 1/4 -1/1 2 15 4/15 -1/2 1 2 3/11 -1/2 1 30 2/7 -3/4 1 30 7/24 0/1 2 5 5/17 -1/2 1 30 3/10 -1/1 2 3 4/13 -3/4 1 30 1/3 -1/2 1 10 6/17 1/0 1 30 5/14 -2/5 2 15 9/25 -1/4 1 6 4/11 -1/4 1 30 11/30 0/1 6 1 3/8 -1/1 2 15 11/29 -1/2 1 30 8/21 -1/4 1 10 5/13 1/2 1 30 2/5 -1/2 1 6 7/17 -3/10 1 30 19/46 -4/15 2 15 31/75 -1/4 11 2 12/29 -1/4 1 30 5/12 0/1 2 5 13/31 -1/2 1 30 8/19 -1/4 1 30 3/7 -1/6 1 30 13/30 0/1 18 1 7/16 1/3 2 15 4/9 1/0 1 10 13/29 -1/2 1 30 9/20 0/1 2 3 14/31 1/0 1 30 5/11 -1/2 1 30 6/13 1/0 1 30 7/15 -1/2 1 2 1/2 0/1 2 15 1/0 0/1 2 1 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(91,-11,240,-29) (0/1,1/8) -> (3/8,11/29) Hyperbolic Matrix(31,-4,240,-31) (1/8,2/15) -> (1/8,2/15) Reflection Matrix(29,-4,210,-29) (2/15,1/7) -> (2/15,1/7) Reflection Matrix(61,-9,210,-31) (1/7,1/6) -> (2/7,7/24) Glide Reflection Matrix(149,-26,510,-89) (1/6,3/17) -> (7/24,5/17) Glide Reflection Matrix(151,-27,330,-59) (3/17,2/11) -> (5/11,6/13) Hyperbolic Matrix(119,-22,330,-61) (2/11,1/5) -> (9/25,4/11) Hyperbolic Matrix(151,-32,420,-89) (1/5,3/14) -> (5/14,9/25) Hyperbolic Matrix(119,-26,270,-59) (3/14,2/9) -> (7/16,4/9) Glide Reflection Matrix(149,-34,390,-89) (2/9,3/13) -> (8/21,5/13) Glide Reflection Matrix(181,-42,780,-181) (3/13,7/30) -> (3/13,7/30) Reflection Matrix(29,-7,120,-29) (7/30,1/4) -> (7/30,1/4) Reflection Matrix(31,-8,120,-31) (1/4,4/15) -> (1/4,4/15) Reflection Matrix(89,-24,330,-89) (4/15,3/11) -> (4/15,3/11) Reflection Matrix(89,-25,210,-59) (3/11,2/7) -> (8/19,3/7) Glide Reflection Matrix(91,-27,300,-89) (5/17,3/10) -> (3/10,4/13) Parabolic Matrix(31,-10,90,-29) (4/13,1/3) -> (1/3,6/17) Parabolic Matrix(421,-149,1020,-361) (6/17,5/14) -> (7/17,19/46) Glide Reflection Matrix(241,-88,660,-241) (4/11,11/30) -> (4/11,11/30) Reflection Matrix(89,-33,240,-89) (11/30,3/8) -> (11/30,3/8) Reflection Matrix(389,-148,870,-331) (11/29,8/21) -> (4/9,13/29) Hyperbolic Matrix(61,-24,150,-59) (5/13,2/5) -> (2/5,7/17) Parabolic Matrix(2851,-1178,6900,-2851) (19/46,31/75) -> (19/46,31/75) Reflection Matrix(1799,-744,4350,-1799) (31/75,12/29) -> (31/75,12/29) Reflection Matrix(301,-125,720,-299) (12/29,5/12) -> (5/12,13/31) Parabolic Matrix(421,-177,930,-391) (13/31,8/19) -> (14/31,5/11) Glide Reflection Matrix(181,-78,420,-181) (3/7,13/30) -> (3/7,13/30) Reflection Matrix(209,-91,480,-209) (13/30,7/16) -> (13/30,7/16) Reflection Matrix(541,-243,1200,-539) (13/29,9/20) -> (9/20,14/31) Parabolic Matrix(181,-84,390,-181) (6/13,7/15) -> (6/13,7/15) Reflection Matrix(29,-14,60,-29) (7/15,1/2) -> (7/15,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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(91,-11,240,-29) -> Matrix(1,0,-2,1) 0/1 Matrix(31,-4,240,-31) -> Matrix(-1,2,0,1) (1/8,2/15) -> (1/1,1/0) Matrix(29,-4,210,-29) -> Matrix(1,5,0,-1) (2/15,1/7) -> (-5/2,1/0) Matrix(61,-9,210,-31) -> Matrix(1,1,-2,-3) Matrix(149,-26,510,-89) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(151,-27,330,-59) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(119,-22,330,-61) -> Matrix(1,1,-4,-3) -1/2 Matrix(151,-32,420,-89) -> Matrix(1,2,-4,-7) Matrix(119,-26,270,-59) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(149,-34,390,-89) -> Matrix(1,1,-4,-5) Matrix(181,-42,780,-181) -> Matrix(13,14,-12,-13) (3/13,7/30) -> (-7/6,-1/1) Matrix(29,-7,120,-29) -> Matrix(-1,0,2,1) (7/30,1/4) -> (-1/1,0/1) Matrix(31,-8,120,-31) -> Matrix(3,2,-4,-3) (1/4,4/15) -> (-1/1,-1/2) Matrix(89,-24,330,-89) -> Matrix(1,1,0,-1) (4/15,3/11) -> (-1/2,1/0) Matrix(89,-25,210,-59) -> Matrix(1,1,-2,-3) Matrix(91,-27,300,-89) -> Matrix(1,2,-2,-3) -1/1 Matrix(31,-10,90,-29) -> Matrix(1,1,-4,-3) -1/2 Matrix(421,-149,1020,-361) -> Matrix(3,2,-10,-7) Matrix(241,-88,660,-241) -> Matrix(-1,0,8,1) (4/11,11/30) -> (-1/4,0/1) Matrix(89,-33,240,-89) -> Matrix(-1,0,2,1) (11/30,3/8) -> (-1/1,0/1) Matrix(389,-148,870,-331) -> Matrix(3,1,-4,-1) -1/2 Matrix(61,-24,150,-59) -> Matrix(1,1,-4,-3) -1/2 Matrix(2851,-1178,6900,-2851) -> Matrix(31,8,-120,-31) (19/46,31/75) -> (-4/15,-1/4) Matrix(1799,-744,4350,-1799) -> Matrix(13,3,-56,-13) (31/75,12/29) -> (-1/4,-3/14) Matrix(301,-125,720,-299) -> Matrix(1,0,2,1) 0/1 Matrix(421,-177,930,-391) -> Matrix(3,1,-2,-1) Matrix(181,-78,420,-181) -> Matrix(-1,0,12,1) (3/7,13/30) -> (-1/6,0/1) Matrix(209,-91,480,-209) -> Matrix(1,0,6,-1) (13/30,7/16) -> (0/1,1/3) Matrix(541,-243,1200,-539) -> Matrix(1,0,2,1) 0/1 Matrix(181,-84,390,-181) -> Matrix(1,1,0,-1) (6/13,7/15) -> (-1/2,1/0) Matrix(29,-14,60,-29) -> Matrix(-1,0,4,1) (7/15,1/2) -> (-1/2,0/1) Matrix(-1,1,0,1) -> Matrix(-1,0,2,1) (1/2,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.