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 0/1 1/27 -7/8 1/25 1/24 -13/15 1/24 -19/22 1/24 -6/7 0/1 1/24 -17/20 2/47 -11/13 2/47 1/23 -5/6 1/23 -14/17 0/1 1/23 -23/28 1/23 5/114 -9/11 3/68 2/45 -13/16 3/67 1/22 -4/5 1/22 -11/14 1/22 -18/23 2/43 3/64 -25/32 3/64 1/21 -7/9 0/1 2/43 -24/31 2/43 5/107 -17/22 3/64 -10/13 6/127 1/21 -3/4 1/21 1/20 -11/15 1/20 -19/26 1/20 -8/11 1/20 2/39 -21/29 2/39 1/19 -13/18 1/19 -5/7 0/1 1/20 -27/38 1/20 -22/31 2/39 1/19 -17/24 2/39 -12/17 0/1 1/19 -7/10 1/19 -9/13 1/19 2/37 -11/16 1/19 1/18 -13/19 0/1 1/16 -2/3 0/1 2/37 -13/20 0/1 -11/17 0/1 1/19 -9/14 1/18 -16/25 1/18 -23/36 0/1 -7/11 2/37 1/18 -5/8 1/18 1/17 -18/29 2/35 5/87 -31/50 1/17 -13/21 0/1 2/35 -21/34 1/18 -8/13 2/35 1/17 -19/31 2/35 1/17 -11/18 1/17 -3/5 1/17 -16/27 4/67 2/33 -29/49 7/116 2/33 -13/22 1/16 -10/17 1/17 4/67 -17/29 5/83 2/33 -7/12 2/33 -18/31 1/17 2/33 -29/50 3/49 -11/19 4/65 1/16 -15/26 1/16 -34/59 0/1 1/17 -19/33 0/1 2/33 -4/7 4/65 1/16 -9/16 1/16 5/79 -14/25 1/16 -33/59 4/63 3/47 -19/34 1/16 -5/9 4/63 2/31 -16/29 7/109 2/31 -11/20 2/31 -17/31 2/31 5/77 -6/11 2/31 3/46 -7/13 6/91 1/15 -8/15 1/15 -1/2 1/14 -7/15 1/13 -13/28 1/13 11/142 -6/13 1/13 6/77 -11/24 4/51 -5/11 3/38 2/25 -9/20 2/25 -13/29 2/25 7/87 -4/9 2/25 4/49 -11/25 1/12 -7/16 5/61 1/12 -10/23 14/169 1/12 -13/30 1/12 -3/7 1/12 4/47 -14/33 0/1 2/23 -25/59 0/1 1/11 -11/26 1/12 -8/19 1/12 4/47 -29/69 4/47 2/23 -21/50 3/35 -13/31 2/23 1/11 -5/12 2/23 -12/29 2/23 5/57 -31/75 3/34 -19/46 3/34 -7/17 4/45 1/11 -9/22 1/12 -11/27 2/23 4/45 -2/5 1/11 -13/33 0/1 2/21 -24/61 0/1 1/11 -11/28 1/11 1/10 -9/23 2/21 1/10 -7/18 1/11 -12/31 1/11 2/21 -29/75 1/10 -17/44 1/11 1/10 -5/13 1/11 2/21 -23/60 2/21 -18/47 2/21 3/31 -13/34 1/10 -34/89 1/11 2/21 -21/55 1/10 -8/21 0/1 2/21 -27/71 2/21 1/10 -19/50 1/11 -11/29 5/53 2/21 -3/8 1/11 1/10 -7/19 4/41 1/10 -11/30 1/10 -4/11 1/10 2/19 -5/14 1/10 -16/45 1/10 -11/31 3/29 2/19 -6/17 0/1 1/9 -7/20 0/1 -8/23 2/21 1/10 -1/3 0/1 2/19 -5/16 1/10 1/9 -14/45 1/10 -9/29 2/19 1/9 -4/13 2/19 1/9 -3/10 1/9 -5/17 0/1 1/9 -12/41 4/35 3/26 -7/24 2/17 -16/55 1/8 -9/31 1/9 2/17 -2/7 0/1 1/8 -9/32 1/9 1/8 -34/121 0/1 1/9 -59/210 1/9 -25/89 1/9 2/17 -16/57 0/1 2/17 -7/25 1/9 -5/18 1/9 -8/29 1/9 2/17 -11/40 2/17 -3/11 2/17 1/8 -7/26 1/8 -4/15 1/8 -1/4 1/8 1/7 -4/17 8/57 1/7 -7/30 1/7 -3/13 1/7 6/41 -5/22 3/20 -12/53 3/20 8/53 -7/31 5/33 2/13 -2/9 0/1 2/13 -9/41 0/1 1/6 -7/32 1/7 3/20 -5/23 3/20 2/13 -13/60 2/13 -8/37 2/13 5/32 -3/14 1/6 -4/19 0/1 1/6 -5/24 2/13 -6/29 2/13 3/19 -1/5 1/6 -3/16 1/6 3/17 -5/27 4/23 2/11 -7/38 5/28 -9/49 13/72 2/11 -11/60 2/11 -2/11 2/11 3/16 -7/39 2/11 4/21 -5/28 5/26 1/5 -8/45 1/5 -3/17 0/1 1/5 -1/6 1/5 -2/13 1/5 2/9 -3/20 2/9 -4/27 2/9 4/17 -1/7 0/1 1/4 -3/22 1/4 -2/15 1/4 -1/8 1/4 1/3 0/1 0/1 1/1 1/8 -1/1 -1/2 2/15 -1/2 3/22 -1/2 1/7 -1/2 0/1 3/20 -2/5 2/13 -2/5 -1/3 1/6 -1/3 3/17 -1/3 0/1 5/28 -1/3 -5/16 2/11 -3/10 -2/7 3/16 -3/11 -1/4 1/5 -1/4 3/14 -1/4 5/23 -2/9 -3/14 7/32 -3/14 -1/5 2/9 -2/9 0/1 7/31 -2/9 -5/23 5/22 -3/14 3/13 -6/29 -1/5 1/4 -1/5 -1/6 4/15 -1/6 7/26 -1/6 3/11 -1/6 -2/13 8/29 -2/13 -1/7 5/18 -1/7 2/7 -1/6 0/1 11/38 -1/6 9/31 -2/13 -1/7 7/24 -2/13 5/17 -1/7 0/1 3/10 -1/7 4/13 -1/7 -2/15 5/16 -1/7 -1/8 6/19 -1/10 0/1 1/3 -2/15 0/1 7/20 0/1 6/17 -1/7 0/1 5/14 -1/8 9/25 -1/8 13/36 0/1 4/11 -2/15 -1/8 3/8 -1/8 -1/9 11/29 -2/17 -5/43 19/50 -1/9 8/21 -2/17 0/1 13/34 -1/8 5/13 -2/17 -1/9 12/31 -2/17 -1/9 7/18 -1/9 2/5 -1/9 11/27 -4/37 -2/19 20/49 -7/66 -2/19 9/22 -1/10 7/17 -1/9 -4/37 12/29 -5/47 -2/19 5/12 -2/19 13/31 -1/9 -2/19 21/50 -3/29 8/19 -4/39 -1/10 11/26 -1/10 25/59 -1/9 0/1 14/33 -2/19 0/1 3/7 -4/39 -1/10 7/16 -1/10 -5/51 11/25 -1/10 26/59 -4/41 -3/31 15/34 -1/10 4/9 -4/41 -2/21 13/29 -7/73 -2/21 9/20 -2/21 14/31 -2/21 -5/53 5/11 -2/21 -3/32 6/13 -6/65 -1/11 7/15 -1/11 1/2 -1/12 8/15 -1/13 15/28 -1/13 -11/144 7/13 -1/13 -6/79 13/24 -4/53 6/11 -3/40 -2/27 11/20 -2/27 16/29 -2/27 -7/95 5/9 -2/27 -4/55 14/25 -1/14 9/16 -5/69 -1/14 13/23 -14/195 -1/14 17/30 -1/14 4/7 -1/14 -4/57 19/33 -2/29 0/1 34/59 -1/15 0/1 15/26 -1/14 11/19 -1/14 -4/57 40/69 -4/57 -2/29 29/50 -3/43 18/31 -2/29 -1/15 7/12 -2/29 17/29 -2/29 -5/73 44/75 -3/44 27/46 -3/44 10/17 -4/59 -1/15 13/22 -1/14 16/27 -2/29 -4/59 3/5 -1/15 20/33 -2/31 0/1 37/61 -1/15 0/1 17/28 -1/15 -1/16 14/23 -2/31 -1/16 11/18 -1/15 19/31 -1/15 -2/31 46/75 -1/16 27/44 -1/15 -1/16 8/13 -1/15 -2/31 37/60 -2/31 29/47 -2/31 -3/47 21/34 -1/16 55/89 -1/15 -2/31 34/55 -1/16 13/21 -2/31 0/1 44/71 -2/31 -1/16 31/50 -1/15 18/29 -5/77 -2/31 5/8 -1/15 -1/16 12/19 -4/63 -1/16 19/30 -1/16 7/11 -1/16 -2/33 9/14 -1/16 29/45 -1/16 20/31 -3/49 -2/33 11/17 -1/17 0/1 13/20 0/1 15/23 -2/31 -1/16 2/3 -2/33 0/1 11/16 -1/16 -1/17 31/45 -1/16 20/29 -2/33 -1/17 9/13 -2/33 -1/17 7/10 -1/17 12/17 -1/17 0/1 29/41 -4/69 -3/52 17/24 -2/35 39/55 -1/18 22/31 -1/17 -2/35 5/7 -1/18 0/1 23/32 -1/17 -1/18 87/121 -1/17 0/1 151/210 -1/17 64/89 -1/17 -2/35 41/57 -2/35 0/1 18/25 -1/17 13/18 -1/17 21/29 -1/17 -2/35 29/40 -2/35 8/11 -2/35 -1/18 19/26 -1/18 11/15 -1/18 3/4 -1/18 -1/19 13/17 -8/151 -1/19 23/30 -1/19 10/13 -1/19 -6/115 17/22 -3/58 41/53 -3/58 -8/155 24/31 -5/97 -2/39 7/9 -2/39 0/1 32/41 -1/20 0/1 25/32 -1/19 -3/58 18/23 -3/58 -2/39 47/60 -2/39 29/37 -2/39 -5/98 11/14 -1/20 15/19 -1/20 0/1 19/24 -2/39 23/29 -2/39 -3/59 4/5 -1/20 13/16 -1/20 -3/61 22/27 -4/81 -2/41 31/38 -5/102 40/49 -13/266 -2/41 49/60 -2/41 9/11 -2/41 -3/62 32/39 -2/41 -4/83 23/28 -5/104 -1/21 37/45 -1/21 14/17 -1/21 0/1 5/6 -1/21 11/13 -1/21 -2/43 17/20 -2/43 23/27 -2/43 -4/87 6/7 -1/22 0/1 19/22 -1/22 13/15 -1/22 7/8 -1/22 -1/23 1/1 -1/25 0/1 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,-52,1) Matrix(91,80,240,211) -> Matrix(49,-2,-416,17) Matrix(209,182,240,209) -> Matrix(49,-2,-1102,45) Matrix(571,494,660,571) -> Matrix(143,-6,-3122,131) Matrix(121,104,420,361) -> Matrix(1,0,-30,1) Matrix(209,178,-600,-511) -> Matrix(47,-2,494,-21) Matrix(389,330,600,509) -> Matrix(47,-2,-822,35) Matrix(31,26,180,151) -> Matrix(47,-2,-164,7) Matrix(29,24,180,149) -> Matrix(45,-2,-112,5) Matrix(389,320,-840,-691) -> Matrix(139,-6,1784,-77) Matrix(329,270,-1500,-1231) -> Matrix(45,-2,338,-15) Matrix(329,268,-480,-391) -> Matrix(45,-2,788,-35) Matrix(269,218,480,389) -> Matrix(43,-2,-580,27) Matrix(269,212,-420,-331) -> Matrix(43,-2,796,-37) Matrix(181,142,-840,-659) -> Matrix(87,-4,544,-25) Matrix(839,656,1380,1079) -> Matrix(85,-4,-1296,61) Matrix(269,210,-1500,-1171) -> Matrix(41,-2,226,-11) Matrix(299,232,540,419) -> Matrix(87,-4,-1196,55) Matrix(1321,1022,-1860,-1439) -> Matrix(171,-8,3356,-157) Matrix(389,300,660,509) -> Matrix(43,-2,-666,31) Matrix(29,22,-120,-91) -> Matrix(41,-2,308,-15) Matrix(89,66,120,89) -> Matrix(41,-2,-758,37) Matrix(571,418,780,571) -> Matrix(199,-10,-3562,179) Matrix(329,240,780,569) -> Matrix(119,-6,-1170,59) Matrix(361,262,-660,-479) -> Matrix(157,-8,2414,-123) Matrix(661,478,1080,781) -> Matrix(77,-4,-1174,61) Matrix(211,152,-540,-389) -> Matrix(39,-2,410,-21) Matrix(59,42,420,299) -> Matrix(1,0,-22,1) Matrix(299,212,-1440,-1021) -> Matrix(79,-4,494,-25) Matrix(331,234,-720,-509) -> Matrix(115,-6,1476,-77) Matrix(91,64,300,211) -> Matrix(39,-2,-292,15) Matrix(89,62,300,209) -> Matrix(37,-2,-240,13) Matrix(301,208,-780,-539) -> Matrix(1,0,-8,1) Matrix(391,266,-660,-449) -> Matrix(39,-2,644,-33) Matrix(89,58,-600,-391) -> Matrix(35,-2,158,-9) Matrix(509,330,600,389) -> Matrix(39,-2,-838,43) Matrix(421,272,-1020,-659) -> Matrix(75,-4,844,-45) Matrix(751,480,-2580,-1649) -> Matrix(35,-2,298,-17) Matrix(1231,786,1740,1111) -> Matrix(39,-2,-682,35) Matrix(89,56,-240,-151) -> Matrix(35,-2,368,-21) Matrix(29,18,240,149) -> Matrix(35,-2,-52,3) Matrix(1741,1080,3000,1861) -> Matrix(139,-8,-1998,115) Matrix(1891,1172,-4500,-2789) -> Matrix(37,-2,426,-23) Matrix(569,352,-1020,-631) -> Matrix(37,-2,574,-31) Matrix(781,482,-2040,-1259) -> Matrix(71,-4,728,-41) Matrix(241,148,-780,-479) -> Matrix(1,0,-8,1) Matrix(781,478,1080,661) -> Matrix(69,-4,-1190,69) Matrix(151,92,-540,-329) -> Matrix(35,-2,298,-17) Matrix(269,160,-960,-571) -> Matrix(33,-2,314,-19) Matrix(541,320,-2940,-1739) -> Matrix(197,-12,1100,-67) Matrix(509,300,660,389) -> Matrix(35,-2,-682,39) Matrix(361,212,-1020,-599) -> Matrix(67,-4,620,-37) Matrix(301,176,720,421) -> Matrix(133,-8,-1280,77) Matrix(299,174,720,419) -> Matrix(131,-8,-1228,75) Matrix(1861,1080,3000,1741) -> Matrix(131,-8,-2014,123) Matrix(1711,992,-4500,-2609) -> Matrix(33,-2,314,-19) Matrix(211,122,780,451) -> Matrix(97,-6,-598,37) Matrix(1561,900,3540,2041) -> Matrix(65,-4,-666,41) Matrix(1559,898,-3960,-2281) -> Matrix(1,0,-6,1) Matrix(271,156,-780,-449) -> Matrix(33,-2,314,-19) Matrix(209,118,-480,-271) -> Matrix(159,-10,1924,-121) Matrix(389,218,480,269) -> Matrix(31,-2,-604,39) Matrix(811,454,1020,571) -> Matrix(95,-6,-1884,119) Matrix(1499,838,3540,1979) -> Matrix(63,-4,-614,39) Matrix(419,232,540,299) -> Matrix(63,-4,-1244,79) Matrix(541,298,1200,661) -> Matrix(373,-24,-3932,253) Matrix(539,296,1200,659) -> Matrix(371,-24,-3880,251) Matrix(211,114,-720,-389) -> Matrix(91,-6,804,-53) Matrix(149,80,-840,-451) -> Matrix(91,-6,440,-29) Matrix(31,16,60,31) -> Matrix(29,-2,-362,25) Matrix(29,14,60,29) -> Matrix(27,-2,-310,23) Matrix(1381,642,1680,781) -> Matrix(207,-16,-4334,335) Matrix(569,260,720,329) -> Matrix(25,-2,-462,37) Matrix(181,82,-660,-299) -> Matrix(101,-8,846,-67) Matrix(1261,566,1740,781) -> Matrix(199,-16,-3470,279) Matrix(121,54,540,241) -> Matrix(49,-4,-208,17) Matrix(389,172,-1020,-451) -> Matrix(25,-2,238,-19) Matrix(91,40,480,211) -> Matrix(25,-2,-112,9) Matrix(511,222,900,391) -> Matrix(217,-18,-3050,253) Matrix(509,220,900,389) -> Matrix(215,-18,-2998,251) Matrix(61,26,-420,-179) -> Matrix(47,-4,200,-17) Matrix(1769,750,-6300,-2671) -> Matrix(23,-2,196,-17) Matrix(2669,1130,4320,1829) -> Matrix(23,-2,-356,31) Matrix(569,240,780,329) -> Matrix(71,-6,-1266,107) Matrix(2341,984,3000,1261) -> Matrix(47,-4,-928,79) Matrix(1139,478,3000,1259) -> Matrix(93,-8,-802,69) Matrix(421,176,720,301) -> Matrix(93,-8,-1360,117) Matrix(419,174,720,299) -> Matrix(91,-8,-1308,115) Matrix(2399,992,3480,1439) -> Matrix(91,-8,-1490,131) Matrix(2009,830,3120,1289) -> Matrix(23,-2,-402,35) Matrix(151,62,660,271) -> Matrix(21,-2,-94,9) Matrix(299,122,-1620,-661) -> Matrix(91,-8,512,-45) Matrix(119,48,-300,-121) -> Matrix(45,-4,484,-43) Matrix(1501,590,-5340,-2099) -> Matrix(1,0,-2,1) Matrix(301,118,1380,541) -> Matrix(43,-4,-204,19) Matrix(299,116,1080,419) -> Matrix(43,-4,-290,27) Matrix(2399,928,3720,1439) -> Matrix(41,-4,-666,65) Matrix(2189,846,3180,1229) -> Matrix(21,-2,-346,33) Matrix(2221,852,3600,1381) -> Matrix(85,-8,-1328,125) Matrix(2219,850,3600,1379) -> Matrix(83,-8,-1276,123) Matrix(2491,952,4320,1651) -> Matrix(21,-2,-304,29) Matrix(4681,1788,6600,2521) -> Matrix(1,0,-28,1) Matrix(2461,936,3000,1141) -> Matrix(43,-4,-892,83) Matrix(1259,478,3000,1139) -> Matrix(85,-8,-818,77) Matrix(211,80,240,91) -> Matrix(21,-2,-472,45) Matrix(571,210,900,331) -> Matrix(61,-6,-986,97) Matrix(569,208,900,329) -> Matrix(59,-6,-934,95) Matrix(89,32,-420,-151) -> Matrix(19,-2,124,-13) Matrix(1831,652,3120,1111) -> Matrix(17,-2,-246,29) Matrix(2281,810,3720,1321) -> Matrix(39,-4,-614,63) Matrix(91,32,600,211) -> Matrix(17,-2,-42,5) Matrix(89,28,-480,-151) -> Matrix(21,-2,116,-11) Matrix(1951,608,3180,991) -> Matrix(19,-2,-294,31) Matrix(2041,634,3480,1081) -> Matrix(77,-8,-1126,117) Matrix(211,64,300,91) -> Matrix(19,-2,-332,35) Matrix(209,62,300,89) -> Matrix(17,-2,-280,33) Matrix(629,184,1740,509) -> Matrix(17,-2,-110,13) Matrix(4079,1186,6600,1919) -> Matrix(1,0,-24,1) Matrix(421,122,-1860,-539) -> Matrix(67,-8,444,-53) Matrix(751,212,960,271) -> Matrix(19,-2,-370,39) Matrix(31711,8910,44100,12391) -> Matrix(19,-2,-332,35) Matrix(31709,8908,44100,12389) -> Matrix(17,-2,-280,33) Matrix(419,116,1080,299) -> Matrix(35,-4,-306,35) Matrix(959,264,1740,479) -> Matrix(137,-16,-1858,217) Matrix(451,122,780,211) -> Matrix(49,-6,-694,85) Matrix(209,56,780,209) -> Matrix(81,-10,-494,61) Matrix(31,8,120,31) -> Matrix(15,-2,-82,11) Matrix(691,162,900,211) -> Matrix(99,-14,-1888,267) Matrix(689,160,900,209) -> Matrix(97,-14,-1836,265) Matrix(271,62,660,151) -> Matrix(13,-2,-110,17) Matrix(1139,258,1320,299) -> Matrix(53,-8,-1146,173) Matrix(241,54,540,121) -> Matrix(25,-4,-256,41) Matrix(1739,382,3000,659) -> Matrix(25,-4,-356,57) Matrix(689,150,960,209) -> Matrix(13,-2,-214,33) Matrix(2821,612,3600,781) -> Matrix(105,-16,-2054,313) Matrix(2819,610,3600,779) -> Matrix(103,-16,-2002,311) Matrix(391,82,720,151) -> Matrix(15,-2,-202,27) Matrix(449,92,1020,209) -> Matrix(37,-6,-376,61) Matrix(211,40,480,91) -> Matrix(13,-2,-136,21) Matrix(2941,540,3600,661) -> Matrix(177,-32,-3634,657) Matrix(2939,538,3600,659) -> Matrix(175,-32,-3582,655) Matrix(1859,334,3000,539) -> Matrix(21,-4,-320,61) Matrix(899,160,1680,299) -> Matrix(81,-16,-1058,209) Matrix(151,26,180,31) -> Matrix(11,-2,-236,43) Matrix(149,24,180,29) -> Matrix(9,-2,-184,41) Matrix(211,32,600,91) -> Matrix(9,-2,-58,13) Matrix(1021,140,1320,181) -> Matrix(35,-8,-678,155) Matrix(89,12,660,89) -> Matrix(25,-6,-54,13) Matrix(31,4,240,31) -> Matrix(7,-2,-10,3) Matrix(149,18,240,29) -> Matrix(7,-2,-108,31) Matrix(391,-58,600,-89) -> Matrix(5,2,-78,-31) Matrix(451,-80,840,-149) -> Matrix(17,6,-224,-79) Matrix(1171,-210,1500,-269) -> Matrix(7,2,-130,-37) Matrix(151,-28,480,-89) -> Matrix(7,2,-60,-17) Matrix(151,-32,420,-89) -> Matrix(9,2,-68,-15) Matrix(659,-142,840,-181) -> Matrix(17,4,-336,-79) Matrix(1231,-270,1500,-329) -> Matrix(11,2,-226,-41) Matrix(539,-122,1860,-421) -> Matrix(37,8,-236,-51) Matrix(91,-22,120,-29) -> Matrix(11,2,-204,-37) Matrix(299,-82,660,-181) -> Matrix(51,8,-542,-85) Matrix(329,-92,540,-151) -> Matrix(13,2,-202,-31) Matrix(1141,-332,1440,-419) -> Matrix(25,4,-494,-79) Matrix(389,-114,720,-211) -> Matrix(41,6,-540,-79) Matrix(479,-148,780,-241) -> Matrix(1,0,-8,1) Matrix(269,-86,660,-211) -> Matrix(13,2,-124,-19) Matrix(511,-178,600,-209) -> Matrix(17,2,-366,-43) Matrix(599,-212,1020,-361) -> Matrix(29,4,-428,-59) Matrix(1829,-660,2580,-931) -> Matrix(17,2,-298,-35) Matrix(151,-56,240,-89) -> Matrix(17,2,-264,-31) Matrix(2609,-992,4500,-1711) -> Matrix(15,2,-218,-29) Matrix(451,-172,1020,-389) -> Matrix(15,2,-158,-21) Matrix(1259,-482,2040,-781) -> Matrix(33,4,-520,-63) Matrix(539,-208,780,-301) -> Matrix(1,0,-8,1) Matrix(389,-152,540,-211) -> Matrix(17,2,-298,-35) Matrix(691,-280,960,-389) -> Matrix(19,2,-314,-33) Matrix(2399,-980,2940,-1201) -> Matrix(115,12,-2348,-245) Matrix(659,-272,1020,-421) -> Matrix(37,4,-620,-67) Matrix(2789,-1172,4500,-1891) -> Matrix(19,2,-314,-33) Matrix(2401,-1018,3960,-1679) -> Matrix(1,0,-6,1) Matrix(509,-216,780,-331) -> Matrix(19,2,-314,-33) Matrix(271,-118,480,-209) -> Matrix(101,10,-1404,-139) Matrix(509,-234,720,-331) -> Matrix(65,6,-1116,-103) Matrix(691,-320,840,-389) -> Matrix(65,6,-1376,-127) Matrix(479,-262,660,-361) -> Matrix(107,8,-1886,-141) Matrix(631,-352,1020,-569) -> Matrix(27,2,-446,-33) Matrix(359,-206,420,-241) -> Matrix(57,4,-1240,-87) Matrix(4531,-2610,6300,-3629) -> Matrix(29,2,-508,-35) Matrix(1321,-782,1620,-959) -> Matrix(117,8,-2384,-163) Matrix(181,-108,300,-179) -> Matrix(59,4,-900,-61) Matrix(3839,-2330,5340,-3241) -> Matrix(1,0,-2,1) Matrix(331,-212,420,-269) -> Matrix(33,2,-644,-39) Matrix(391,-268,480,-329) -> Matrix(31,2,-636,-41) Matrix(1439,-1022,1860,-1321) -> Matrix(141,8,-2732,-155) 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 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 1/4 4/15 7/26 5/18 7/24 3/10 1/3 7/20 19/50 7/18 2/5 5/12 21/50 4/9 9/20 7/15 1/2 11/20 17/30 7/12 3/5 37/60 19/30 29/45 2/3 7/10 17/24 151/210 23/30 47/60 4/5 49/60 5/6 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/8 -1/1 -1/2 2/15 -1/2 3/22 -1/2 1/7 -1/2 0/1 3/20 -2/5 2/13 -2/5 -1/3 1/6 -1/3 3/17 -1/3 0/1 5/28 -1/3 -5/16 2/11 -3/10 -2/7 3/16 -3/11 -1/4 1/5 -1/4 3/14 -1/4 5/23 -2/9 -3/14 7/32 -3/14 -1/5 2/9 -2/9 0/1 7/31 -2/9 -5/23 5/22 -3/14 3/13 -6/29 -1/5 1/4 -1/5 -1/6 4/15 -1/6 7/26 -1/6 3/11 -1/6 -2/13 8/29 -2/13 -1/7 5/18 -1/7 2/7 -1/6 0/1 11/38 -1/6 9/31 -2/13 -1/7 7/24 -2/13 5/17 -1/7 0/1 3/10 -1/7 4/13 -1/7 -2/15 5/16 -1/7 -1/8 6/19 -1/10 0/1 1/3 -2/15 0/1 7/20 0/1 6/17 -1/7 0/1 5/14 -1/8 9/25 -1/8 13/36 0/1 4/11 -2/15 -1/8 3/8 -1/8 -1/9 11/29 -2/17 -5/43 19/50 -1/9 8/21 -2/17 0/1 13/34 -1/8 5/13 -2/17 -1/9 12/31 -2/17 -1/9 7/18 -1/9 2/5 -1/9 11/27 -4/37 -2/19 20/49 -7/66 -2/19 9/22 -1/10 7/17 -1/9 -4/37 12/29 -5/47 -2/19 5/12 -2/19 13/31 -1/9 -2/19 21/50 -3/29 8/19 -4/39 -1/10 11/26 -1/10 25/59 -1/9 0/1 14/33 -2/19 0/1 3/7 -4/39 -1/10 7/16 -1/10 -5/51 11/25 -1/10 26/59 -4/41 -3/31 15/34 -1/10 4/9 -4/41 -2/21 13/29 -7/73 -2/21 9/20 -2/21 14/31 -2/21 -5/53 5/11 -2/21 -3/32 6/13 -6/65 -1/11 7/15 -1/11 1/2 -1/12 8/15 -1/13 15/28 -1/13 -11/144 7/13 -1/13 -6/79 13/24 -4/53 6/11 -3/40 -2/27 11/20 -2/27 16/29 -2/27 -7/95 5/9 -2/27 -4/55 14/25 -1/14 9/16 -5/69 -1/14 13/23 -14/195 -1/14 17/30 -1/14 4/7 -1/14 -4/57 19/33 -2/29 0/1 34/59 -1/15 0/1 15/26 -1/14 11/19 -1/14 -4/57 40/69 -4/57 -2/29 29/50 -3/43 18/31 -2/29 -1/15 7/12 -2/29 17/29 -2/29 -5/73 44/75 -3/44 27/46 -3/44 10/17 -4/59 -1/15 13/22 -1/14 16/27 -2/29 -4/59 3/5 -1/15 20/33 -2/31 0/1 37/61 -1/15 0/1 17/28 -1/15 -1/16 14/23 -2/31 -1/16 11/18 -1/15 19/31 -1/15 -2/31 46/75 -1/16 27/44 -1/15 -1/16 8/13 -1/15 -2/31 37/60 -2/31 29/47 -2/31 -3/47 21/34 -1/16 55/89 -1/15 -2/31 34/55 -1/16 13/21 -2/31 0/1 44/71 -2/31 -1/16 31/50 -1/15 18/29 -5/77 -2/31 5/8 -1/15 -1/16 12/19 -4/63 -1/16 19/30 -1/16 7/11 -1/16 -2/33 9/14 -1/16 29/45 -1/16 20/31 -3/49 -2/33 11/17 -1/17 0/1 13/20 0/1 15/23 -2/31 -1/16 2/3 -2/33 0/1 11/16 -1/16 -1/17 31/45 -1/16 20/29 -2/33 -1/17 9/13 -2/33 -1/17 7/10 -1/17 12/17 -1/17 0/1 29/41 -4/69 -3/52 17/24 -2/35 39/55 -1/18 22/31 -1/17 -2/35 5/7 -1/18 0/1 23/32 -1/17 -1/18 87/121 -1/17 0/1 151/210 -1/17 64/89 -1/17 -2/35 41/57 -2/35 0/1 18/25 -1/17 13/18 -1/17 21/29 -1/17 -2/35 29/40 -2/35 8/11 -2/35 -1/18 19/26 -1/18 11/15 -1/18 3/4 -1/18 -1/19 13/17 -8/151 -1/19 23/30 -1/19 10/13 -1/19 -6/115 17/22 -3/58 41/53 -3/58 -8/155 24/31 -5/97 -2/39 7/9 -2/39 0/1 32/41 -1/20 0/1 25/32 -1/19 -3/58 18/23 -3/58 -2/39 47/60 -2/39 29/37 -2/39 -5/98 11/14 -1/20 15/19 -1/20 0/1 19/24 -2/39 23/29 -2/39 -3/59 4/5 -1/20 13/16 -1/20 -3/61 22/27 -4/81 -2/41 31/38 -5/102 40/49 -13/266 -2/41 49/60 -2/41 9/11 -2/41 -3/62 32/39 -2/41 -4/83 23/28 -5/104 -1/21 37/45 -1/21 14/17 -1/21 0/1 5/6 -1/21 11/13 -1/21 -2/43 17/20 -2/43 23/27 -2/43 -4/87 6/7 -1/22 0/1 19/22 -1/22 13/15 -1/22 7/8 -1/22 -1/23 1/1 -1/25 0/1 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(571,-77,660,-89) (2/15,3/22) -> (19/22,13/15) Hyperbolic Matrix(121,-17,420,-59) (3/22,1/7) -> (2/7,11/38) Hyperbolic Matrix(391,-58,600,-89) (1/7,3/20) -> (13/20,15/23) Hyperbolic Matrix(389,-59,600,-91) (3/20,2/13) -> (11/17,13/20) Hyperbolic Matrix(31,-5,180,-29) (2/13,1/6) -> (1/6,3/17) Parabolic 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(269,-51,480,-91) (3/16,1/5) -> (14/25,9/16) 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(839,-183,1380,-301) (5/23,7/32) -> (17/28,14/23) Hyperbolic Matrix(1231,-270,1500,-329) (7/32,2/9) -> (32/39,23/28) Hyperbolic Matrix(299,-67,540,-121) (2/9,7/31) -> (16/29,5/9) Hyperbolic Matrix(539,-122,1860,-421) (7/31,5/22) -> (11/38,9/31) Hyperbolic Matrix(389,-89,660,-151) (5/22,3/13) -> (10/17,13/22) 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(571,-153,780,-209) (4/15,7/26) -> (19/26,11/15) Hyperbolic Matrix(329,-89,780,-211) (7/26,3/11) -> (8/19,11/26) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(661,-183,1080,-299) (8/29,5/18) -> (11/18,19/31) 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(91,-27,300,-89) (5/17,3/10) -> (3/10,4/13) Parabolic 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(509,-179,600,-211) (7/20,6/17) -> (11/13,17/20) 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(1231,-445,1740,-629) (13/36,4/11) -> (29/41,17/24) Hyperbolic Matrix(151,-56,240,-89) (4/11,3/8) -> (5/8,12/19) Hyperbolic Matrix(1741,-661,3000,-1139) (11/29,19/50) -> (29/50,18/31) 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(781,-303,1080,-419) (12/31,7/18) -> (13/18,21/29) 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(509,-209,660,-271) (9/22,7/17) -> (10/13,17/22) Hyperbolic Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(301,-125,720,-299) (12/29,5/12) -> (5/12,13/31) Parabolic Matrix(1861,-781,3000,-1259) (13/31,21/50) -> (31/50,18/29) Hyperbolic Matrix(2789,-1172,4500,-1891) (21/50,8/19) -> (44/71,31/50) Hyperbolic Matrix(1561,-661,3540,-1499) (11/26,25/59) -> (26/59,15/34) 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(389,-171,480,-211) (7/16,11/25) -> (4/5,13/16) Hyperbolic Matrix(811,-357,1020,-449) (11/25,26/59) -> (23/29,4/5) Hyperbolic Matrix(419,-187,540,-241) (4/9,13/29) -> (24/31,7/9) Hyperbolic Matrix(541,-243,1200,-539) (13/29,9/20) -> (9/20,14/31) Parabolic 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(31,-15,60,-29) (7/15,1/2) -> (1/2,8/15) Parabolic Matrix(1381,-739,1680,-899) (8/15,15/28) -> (23/28,37/45) Hyperbolic Matrix(569,-309,720,-391) (13/24,6/11) -> (15/19,19/24) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(1261,-695,1740,-959) (11/20,16/29) -> (21/29,29/40) Hyperbolic Matrix(631,-352,1020,-569) (5/9,14/25) -> (34/55,13/21) Hyperbolic Matrix(511,-289,900,-509) (13/23,17/30) -> (17/30,4/7) Parabolic 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(2669,-1539,4320,-2491) (34/59,15/26) -> (21/34,55/89) Hyperbolic Matrix(569,-329,780,-451) (15/26,11/19) -> (8/11,19/26) Hyperbolic Matrix(2341,-1357,3000,-1739) (11/19,40/69) -> (7/9,32/41) Hyperbolic Matrix(421,-245,720,-419) (18/31,7/12) -> (7/12,17/29) Parabolic Matrix(2399,-1407,3480,-2041) (17/29,44/75) -> (31/45,20/29) Hyperbolic Matrix(2009,-1179,3120,-1831) (44/75,27/46) -> (9/14,29/45) 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(2399,-1471,3720,-2281) (19/31,46/75) -> (29/45,20/31) Hyperbolic Matrix(2189,-1343,3180,-1951) (46/75,27/44) -> (11/16,31/45) Hyperbolic Matrix(2221,-1369,3600,-2219) (8/13,37/60) -> (37/60,29/47) Parabolic Matrix(4681,-2893,6600,-4079) (55/89,34/55) -> (39/55,22/31) Hyperbolic Matrix(2461,-1525,3000,-1859) (13/21,44/71) -> (9/11,32/39) 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(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(211,-147,300,-209) (9/13,7/10) -> (7/10,12/17) Parabolic Matrix(1439,-1022,1860,-1321) (22/31,5/7) -> (41/53,24/31) Hyperbolic Matrix(751,-539,960,-689) (5/7,23/32) -> (25/32,18/23) Hyperbolic Matrix(31711,-22801,44100,-31709) (87/121,151/210) -> (151/210,64/89) Parabolic Matrix(691,-529,900,-689) (13/17,23/30) -> (23/30,10/13) Parabolic Matrix(1139,-881,1320,-1021) (17/22,41/53) -> (6/7,19/22) Hyperbolic Matrix(2821,-2209,3600,-2819) (18/23,47/60) -> (47/60,29/37) Parabolic Matrix(2941,-2401,3600,-2939) (40/49,49/60) -> (49/60,9/11) 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,-26,1) Matrix(91,-11,240,-29) -> Matrix(3,2,-26,-17) Matrix(209,-27,240,-31) -> Matrix(3,2,-68,-45) Matrix(571,-77,660,-89) -> Matrix(13,6,-284,-131) Matrix(121,-17,420,-59) -> Matrix(1,0,-4,1) Matrix(391,-58,600,-89) -> Matrix(5,2,-78,-31) Matrix(389,-59,600,-91) -> Matrix(5,2,-88,-35) Matrix(31,-5,180,-29) -> Matrix(5,2,-18,-7) Matrix(451,-80,840,-149) -> Matrix(17,6,-224,-79) Matrix(1171,-210,1500,-269) -> Matrix(7,2,-130,-37) Matrix(151,-28,480,-89) -> Matrix(7,2,-60,-17) Matrix(269,-51,480,-91) -> Matrix(9,2,-122,-27) Matrix(151,-32,420,-89) -> Matrix(9,2,-68,-15) Matrix(659,-142,840,-181) -> Matrix(17,4,-336,-79) Matrix(839,-183,1380,-301) -> Matrix(19,4,-290,-61) Matrix(1231,-270,1500,-329) -> Matrix(11,2,-226,-41) Matrix(299,-67,540,-121) -> Matrix(17,4,-234,-55) Matrix(539,-122,1860,-421) -> Matrix(37,8,-236,-51) Matrix(389,-89,660,-151) -> Matrix(9,2,-140,-31) Matrix(91,-22,120,-29) -> Matrix(11,2,-204,-37) Matrix(89,-23,120,-31) -> Matrix(11,2,-204,-37) Matrix(571,-153,780,-209) -> Matrix(61,10,-1092,-179) Matrix(329,-89,780,-211) -> Matrix(37,6,-364,-59) Matrix(299,-82,660,-181) -> Matrix(51,8,-542,-85) Matrix(661,-183,1080,-299) -> Matrix(27,4,-412,-61) Matrix(329,-92,540,-151) -> Matrix(13,2,-202,-31) Matrix(1141,-332,1440,-419) -> Matrix(25,4,-494,-79) Matrix(389,-114,720,-211) -> Matrix(41,6,-540,-79) Matrix(91,-27,300,-89) -> Matrix(13,2,-98,-15) Matrix(479,-148,780,-241) -> Matrix(1,0,-8,1) Matrix(269,-86,660,-211) -> Matrix(13,2,-124,-19) Matrix(511,-178,600,-209) -> Matrix(17,2,-366,-43) Matrix(509,-179,600,-211) -> Matrix(13,2,-280,-43) Matrix(599,-212,1020,-361) -> Matrix(29,4,-428,-59) Matrix(1829,-660,2580,-931) -> Matrix(17,2,-298,-35) Matrix(1231,-445,1740,-629) -> Matrix(13,2,-228,-35) Matrix(151,-56,240,-89) -> Matrix(17,2,-264,-31) Matrix(1741,-661,3000,-1139) -> Matrix(69,8,-992,-115) Matrix(2609,-992,4500,-1711) -> Matrix(15,2,-218,-29) Matrix(451,-172,1020,-389) -> Matrix(15,2,-158,-21) Matrix(1259,-482,2040,-781) -> Matrix(33,4,-520,-63) Matrix(539,-208,780,-301) -> Matrix(1,0,-8,1) Matrix(781,-303,1080,-419) -> Matrix(35,4,-604,-69) Matrix(389,-152,540,-211) -> Matrix(17,2,-298,-35) Matrix(691,-280,960,-389) -> Matrix(19,2,-314,-33) Matrix(2399,-980,2940,-1201) -> Matrix(115,12,-2348,-245) Matrix(509,-209,660,-271) -> Matrix(17,2,-332,-39) Matrix(659,-272,1020,-421) -> Matrix(37,4,-620,-67) Matrix(301,-125,720,-299) -> Matrix(75,8,-722,-77) Matrix(1861,-781,3000,-1259) -> Matrix(77,8,-1184,-123) Matrix(2789,-1172,4500,-1891) -> Matrix(19,2,-314,-33) Matrix(1561,-661,3540,-1499) -> Matrix(39,4,-400,-41) Matrix(2401,-1018,3960,-1679) -> Matrix(1,0,-6,1) Matrix(509,-216,780,-331) -> Matrix(19,2,-314,-33) Matrix(271,-118,480,-209) -> Matrix(101,10,-1404,-139) Matrix(389,-171,480,-211) -> Matrix(21,2,-410,-39) Matrix(811,-357,1020,-449) -> Matrix(61,6,-1210,-119) Matrix(419,-187,540,-241) -> Matrix(41,4,-810,-79) Matrix(541,-243,1200,-539) -> Matrix(251,24,-2646,-253) Matrix(509,-234,720,-331) -> Matrix(65,6,-1116,-103) Matrix(691,-320,840,-389) -> Matrix(65,6,-1376,-127) Matrix(31,-15,60,-29) -> Matrix(23,2,-288,-25) Matrix(1381,-739,1680,-899) -> Matrix(209,16,-4376,-335) Matrix(569,-309,720,-391) -> Matrix(27,2,-500,-37) Matrix(479,-262,660,-361) -> Matrix(107,8,-1886,-141) Matrix(1261,-695,1740,-959) -> Matrix(217,16,-3784,-279) Matrix(631,-352,1020,-569) -> Matrix(27,2,-446,-33) Matrix(511,-289,900,-509) -> Matrix(251,18,-3528,-253) Matrix(359,-206,420,-241) -> Matrix(57,4,-1240,-87) Matrix(4531,-2610,6300,-3629) -> Matrix(29,2,-508,-35) Matrix(2669,-1539,4320,-2491) -> Matrix(29,2,-450,-31) Matrix(569,-329,780,-451) -> Matrix(85,6,-1516,-107) Matrix(2341,-1357,3000,-1739) -> Matrix(57,4,-1126,-79) Matrix(421,-245,720,-419) -> Matrix(115,8,-1682,-117) Matrix(2399,-1407,3480,-2041) -> Matrix(117,8,-1916,-131) Matrix(2009,-1179,3120,-1831) -> Matrix(29,2,-508,-35) Matrix(1321,-782,1620,-959) -> Matrix(117,8,-2384,-163) Matrix(181,-108,300,-179) -> Matrix(59,4,-900,-61) Matrix(3839,-2330,5340,-3241) -> Matrix(1,0,-2,1) Matrix(2399,-1471,3720,-2281) -> Matrix(63,4,-1024,-65) Matrix(2189,-1343,3180,-1951) -> Matrix(31,2,-512,-33) Matrix(2221,-1369,3600,-2219) -> Matrix(123,8,-1922,-125) Matrix(4681,-2893,6600,-4079) -> Matrix(1,0,-2,1) Matrix(2461,-1525,3000,-1859) -> Matrix(61,4,-1266,-83) Matrix(211,-131,240,-149) -> Matrix(31,2,-698,-45) Matrix(571,-361,900,-569) -> Matrix(95,6,-1536,-97) Matrix(331,-212,420,-269) -> Matrix(33,2,-644,-39) Matrix(391,-268,480,-329) -> Matrix(31,2,-636,-41) Matrix(211,-147,300,-209) -> Matrix(33,2,-578,-35) Matrix(1439,-1022,1860,-1321) -> Matrix(141,8,-2732,-155) Matrix(751,-539,960,-689) -> Matrix(33,2,-644,-39) Matrix(31711,-22801,44100,-31709) -> Matrix(33,2,-578,-35) Matrix(691,-529,900,-689) -> Matrix(265,14,-5054,-267) Matrix(1139,-881,1320,-1021) -> Matrix(155,8,-3352,-173) Matrix(2821,-2209,3600,-2819) -> Matrix(311,16,-6084,-313) Matrix(2941,-2401,3600,-2939) -> Matrix(655,32,-13448,-657) Matrix(151,-125,180,-149) -> Matrix(41,2,-882,-43) 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 (0/1,1/1) 0 30 1/8 (-1/1,-1/2) 0 15 2/15 -1/2 4 2 3/22 -1/2 2 15 1/7 (-1/2,0/1) 0 30 3/20 -2/5 2 3 2/13 (-2/5,-1/3) 0 30 1/6 -1/3 2 5 3/17 (-1/3,0/1) 0 30 5/28 (-1/3,-5/16) 0 15 2/11 (-3/10,-2/7) 0 30 3/16 (-3/11,-1/4) 0 15 1/5 -1/4 2 6 3/14 -1/4 2 15 13/60 -2/9 4 1 5/23 (-2/9,-3/14) 0 30 7/32 (-3/14,-1/5) 0 15 9/41 (-1/4,0/1) 0 30 2/9 0 10 7/31 (-2/9,-5/23) 0 30 5/22 -3/14 2 15 3/13 (-6/29,-1/5) 0 30 7/30 -1/5 14 1 1/4 (-1/5,-1/6) 0 15 4/15 -1/6 6 2 7/26 -1/6 2 15 3/11 (-1/6,-2/13) 0 30 8/29 (-2/13,-1/7) 0 30 5/18 -1/7 2 5 2/7 (-1/6,0/1) 0 30 11/38 -1/6 2 15 9/31 (-2/13,-1/7) 0 30 7/24 -2/13 2 5 5/17 (-1/7,0/1) 0 30 3/10 -1/7 2 3 4/13 (-1/7,-2/15) 0 30 5/16 (-1/7,-1/8) 0 15 6/19 (-1/10,0/1) 0 30 1/3 0 10 7/20 0/1 2 3 6/17 (-1/7,0/1) 0 30 5/14 -1/8 2 15 9/25 -1/8 2 6 22/61 (-1/9,0/1) 0 30 13/36 0/1 2 5 4/11 (-2/15,-1/8) 0 30 11/30 -1/8 6 1 3/8 (-1/8,-1/9) 0 15 11/29 (-2/17,-5/43) 0 30 19/50 -1/9 2 3 8/21 0 10 13/34 -1/8 2 15 23/60 -2/17 2 1 5/13 (-2/17,-1/9) 0 30 17/44 (-1/8,-1/9) 0 15 29/75 -1/8 2 2 12/31 (-2/17,-1/9) 0 30 7/18 -1/9 2 5 9/23 (-1/8,-2/17) 0 30 11/28 (-1/8,-1/9) 0 15 2/5 -1/9 2 6 13/32 (-1/9,-3/28) 0 15 11/27 0 10 20/49 (-7/66,-2/19) 0 30 49/120 -2/19 8 1 9/22 -1/10 2 15 7/17 (-1/9,-4/37) 0 30 19/46 -3/28 2 15 31/75 -3/28 2 2 12/29 (-5/47,-2/19) 0 30 5/12 -2/19 2 5 13/31 (-1/9,-2/19) 0 30 21/50 -3/29 2 3 29/69 0 10 8/19 (-4/39,-1/10) 0 30 11/26 -1/10 2 15 25/59 (-1/9,0/1) 0 30 89/210 -1/9 2 1 39/92 (-1/9,-1/10) 0 15 14/33 0 10 17/40 -2/19 2 3 3/7 (-4/39,-1/10) 0 30 13/30 -1/10 18 1 7/16 (-1/10,-5/51) 0 15 11/25 -1/10 2 6 26/59 (-4/41,-3/31) 0 30 15/34 -1/10 2 15 4/9 0 10 13/29 (-7/73,-2/21) 0 30 9/20 -2/21 6 3 14/31 (-2/21,-5/53) 0 30 5/11 (-2/21,-3/32) 0 30 11/24 -4/43 2 5 6/13 (-6/65,-1/11) 0 30 13/28 (-11/120,-1/11) 0 15 7/15 -1/11 12 2 1/2 -1/12 2 15 1/0 0/1 26 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(89,-12,660,-89) (2/15,3/22) -> (2/15,3/22) Reflection Matrix(121,-17,420,-59) (3/22,1/7) -> (2/7,11/38) Hyperbolic Matrix(179,-26,420,-61) (1/7,3/20) -> (17/40,3/7) Hyperbolic Matrix(211,-32,600,-91) (3/20,2/13) -> (7/20,6/17) Glide Reflection Matrix(31,-5,180,-29) (2/13,1/6) -> (1/6,3/17) Parabolic Matrix(389,-69,840,-149) (3/17,5/28) -> (6/13,13/28) Glide Reflection Matrix(329,-59,1500,-269) (5/28,2/11) -> (7/32,9/41) Glide Reflection Matrix(151,-28,480,-89) (2/11,3/16) -> (5/16,6/19) Hyperbolic Matrix(211,-40,480,-91) (3/16,1/5) -> (7/16,11/25) Glide Reflection Matrix(151,-32,420,-89) (1/5,3/14) -> (5/14,9/25) Hyperbolic Matrix(181,-39,840,-181) (3/14,13/60) -> (3/14,13/60) Reflection Matrix(599,-130,2760,-599) (13/60,5/23) -> (13/60,5/23) Reflection Matrix(541,-118,1380,-301) (5/23,7/32) -> (9/23,11/28) Glide Reflection Matrix(1261,-277,3000,-659) (9/41,2/9) -> (29/69,8/19) Hyperbolic Matrix(241,-54,540,-121) (2/9,7/31) -> (4/9,13/29) Glide Reflection Matrix(539,-122,1860,-421) (7/31,5/22) -> (11/38,9/31) Hyperbolic Matrix(271,-62,660,-151) (5/22,3/13) -> (9/22,7/17) 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(209,-56,780,-209) (4/15,7/26) -> (4/15,7/26) Reflection Matrix(329,-89,780,-211) (7/26,3/11) -> (8/19,11/26) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(419,-116,1080,-299) (8/29,5/18) -> (12/31,7/18) Glide Reflection Matrix(211,-59,540,-151) (5/18,2/7) -> (7/18,9/23) Glide Reflection Matrix(931,-271,2580,-751) (9/31,7/24) -> (22/61,13/36) Glide Reflection Matrix(331,-97,720,-211) (7/24,5/17) -> (11/24,6/13) Glide Reflection Matrix(91,-27,300,-89) (5/17,3/10) -> (3/10,4/13) Parabolic Matrix(301,-93,780,-241) (4/13,5/16) -> (5/13,17/44) Glide Reflection Matrix(269,-86,660,-211) (6/19,1/3) -> (11/27,20/49) Hyperbolic Matrix(331,-115,780,-271) (1/3,7/20) -> (14/33,17/40) Glide Reflection Matrix(421,-149,1020,-361) (6/17,5/14) -> (7/17,19/46) Glide Reflection Matrix(1321,-476,3000,-1081) (9/25,22/61) -> (11/25,26/59) Glide Reflection Matrix(301,-109,660,-239) (13/36,4/11) -> (5/11,11/24) Hyperbolic 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(1259,-478,3000,-1139) (11/29,19/50) -> (13/31,21/50) Glide Reflection Matrix(1891,-719,4500,-1711) (19/50,8/21) -> (21/50,29/69) Glide Reflection Matrix(451,-172,1020,-389) (8/21,13/34) -> (15/34,4/9) Hyperbolic Matrix(781,-299,2040,-781) (13/34,23/60) -> (13/34,23/60) Reflection Matrix(599,-230,1560,-599) (23/60,5/13) -> (23/60,5/13) Reflection Matrix(2551,-986,6600,-2551) (17/44,29/75) -> (17/44,29/75) Reflection Matrix(1861,-720,4500,-1741) (29/75,12/31) -> (31/75,12/29) Glide Reflection Matrix(121,-48,300,-119) (11/28,2/5) -> (2/5,13/32) Parabolic Matrix(1501,-611,3540,-1441) (13/32,11/27) -> (39/92,14/33) Glide Reflection Matrix(4801,-1960,11760,-4801) (20/49,49/120) -> (20/49,49/120) Reflection Matrix(1079,-441,2640,-1079) (49/120,9/22) -> (49/120,9/22) Reflection Matrix(2851,-1178,6900,-2851) (19/46,31/75) -> (19/46,31/75) Reflection Matrix(301,-125,720,-299) (12/29,5/12) -> (5/12,13/31) Parabolic Matrix(1561,-661,3540,-1499) (11/26,25/59) -> (26/59,15/34) Hyperbolic Matrix(10501,-4450,24780,-10501) (25/59,89/210) -> (25/59,89/210) Reflection Matrix(8189,-3471,19320,-8189) (89/210,39/92) -> (89/210,39/92) 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(391,-182,840,-391) (13/28,7/15) -> (13/28,7/15) 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(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(91,-11,240,-29) -> Matrix(3,2,-26,-17) Matrix(31,-4,240,-31) -> Matrix(3,2,-4,-3) (1/8,2/15) -> (-1/1,-1/2) Matrix(89,-12,660,-89) -> Matrix(13,6,-28,-13) (2/15,3/22) -> (-1/2,-3/7) Matrix(121,-17,420,-59) -> Matrix(1,0,-4,1) 0/1 Matrix(179,-26,420,-61) -> Matrix(9,4,-88,-39) Matrix(211,-32,600,-91) -> Matrix(5,2,-32,-13) Matrix(31,-5,180,-29) -> Matrix(5,2,-18,-7) -1/3 Matrix(389,-69,840,-149) -> Matrix(17,6,-184,-65) Matrix(329,-59,1500,-269) -> Matrix(7,2,-38,-11) Matrix(151,-28,480,-89) -> Matrix(7,2,-60,-17) Matrix(211,-40,480,-91) -> Matrix(9,2,-94,-21) Matrix(151,-32,420,-89) -> Matrix(9,2,-68,-15) Matrix(181,-39,840,-181) -> Matrix(17,4,-72,-17) (3/14,13/60) -> (-1/4,-2/9) Matrix(599,-130,2760,-599) -> Matrix(55,12,-252,-55) (13/60,5/23) -> (-2/9,-3/14) Matrix(541,-118,1380,-301) -> Matrix(19,4,-166,-35) Matrix(1261,-277,3000,-659) -> Matrix(17,4,-166,-39) Matrix(241,-54,540,-121) -> Matrix(17,4,-174,-41) Matrix(539,-122,1860,-421) -> Matrix(37,8,-236,-51) Matrix(271,-62,660,-151) -> Matrix(9,2,-76,-17) Matrix(181,-42,780,-181) -> Matrix(59,12,-290,-59) (3/13,7/30) -> (-6/29,-1/5) Matrix(29,-7,120,-29) -> Matrix(11,2,-60,-11) (7/30,1/4) -> (-1/5,-1/6) Matrix(31,-8,120,-31) -> Matrix(11,2,-60,-11) (1/4,4/15) -> (-1/5,-1/6) Matrix(209,-56,780,-209) -> Matrix(61,10,-372,-61) (4/15,7/26) -> (-1/6,-5/31) Matrix(329,-89,780,-211) -> Matrix(37,6,-364,-59) Matrix(299,-82,660,-181) -> Matrix(51,8,-542,-85) Matrix(419,-116,1080,-299) -> Matrix(27,4,-236,-35) Matrix(211,-59,540,-151) -> Matrix(13,2,-110,-17) Matrix(931,-271,2580,-751) -> Matrix(13,2,-110,-17) Matrix(331,-97,720,-211) -> Matrix(41,6,-444,-65) Matrix(91,-27,300,-89) -> Matrix(13,2,-98,-15) -1/7 Matrix(301,-93,780,-241) -> Matrix(-1,0,16,1) *** -> (-1/8,0/1) Matrix(269,-86,660,-211) -> Matrix(13,2,-124,-19) Matrix(331,-115,780,-271) -> Matrix(15,2,-142,-19) Matrix(421,-149,1020,-361) -> Matrix(29,4,-268,-37) Matrix(1321,-476,3000,-1081) -> Matrix(33,4,-338,-41) Matrix(301,-109,660,-239) -> Matrix(29,4,-312,-43) Matrix(241,-88,660,-241) -> Matrix(31,4,-240,-31) (4/11,11/30) -> (-2/15,-1/8) Matrix(89,-33,240,-89) -> Matrix(17,2,-144,-17) (11/30,3/8) -> (-1/8,-1/9) Matrix(1259,-478,3000,-1139) -> Matrix(69,8,-664,-77) Matrix(1891,-719,4500,-1711) -> Matrix(15,2,-142,-19) Matrix(451,-172,1020,-389) -> Matrix(15,2,-158,-21) Matrix(781,-299,2040,-781) -> Matrix(33,4,-272,-33) (13/34,23/60) -> (-1/8,-2/17) Matrix(599,-230,1560,-599) -> Matrix(35,4,-306,-35) (23/60,5/13) -> (-2/17,-1/9) Matrix(2551,-986,6600,-2551) -> Matrix(17,2,-144,-17) (17/44,29/75) -> (-1/8,-1/9) Matrix(1861,-720,4500,-1741) -> Matrix(67,8,-628,-75) Matrix(121,-48,300,-119) -> Matrix(35,4,-324,-37) -1/9 Matrix(1501,-611,3540,-1441) -> Matrix(37,4,-342,-37) *** -> (-1/9,-2/19) Matrix(4801,-1960,11760,-4801) -> Matrix(265,28,-2508,-265) (20/49,49/120) -> (-7/66,-2/19) Matrix(1079,-441,2640,-1079) -> Matrix(39,4,-380,-39) (49/120,9/22) -> (-2/19,-1/10) Matrix(2851,-1178,6900,-2851) -> Matrix(55,6,-504,-55) (19/46,31/75) -> (-1/9,-3/28) Matrix(301,-125,720,-299) -> Matrix(75,8,-722,-77) -2/19 Matrix(1561,-661,3540,-1499) -> Matrix(39,4,-400,-41) -1/10 Matrix(10501,-4450,24780,-10501) -> Matrix(-1,0,18,1) (25/59,89/210) -> (-1/9,0/1) Matrix(8189,-3471,19320,-8189) -> Matrix(19,2,-180,-19) (89/210,39/92) -> (-1/9,-1/10) Matrix(181,-78,420,-181) -> Matrix(79,8,-780,-79) (3/7,13/30) -> (-4/39,-1/10) Matrix(209,-91,480,-209) -> Matrix(101,10,-1020,-101) (13/30,7/16) -> (-1/10,-5/51) Matrix(541,-243,1200,-539) -> Matrix(251,24,-2646,-253) -2/21 Matrix(391,-182,840,-391) -> Matrix(241,22,-2640,-241) (13/28,7/15) -> (-11/120,-1/11) Matrix(29,-14,60,-29) -> Matrix(23,2,-264,-23) (7/15,1/2) -> (-1/11,-1/12) Matrix(-1,1,0,1) -> Matrix(-1,0,24,1) (1/2,1/0) -> (-1/12,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.