INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/10 -13/15 -5/6 -4/5 -11/15 -7/10 -2/3 -13/21 -3/5 -5/9 -1/2 -7/15 -9/20 -5/12 -2/5 -9/25 -1/3 -14/45 -9/29 -3/10 -59/210 -7/25 -5/18 -1/4 -2/9 -3/14 -1/5 -5/27 -1/6 -3/19 -2/13 -3/23 -1/8 -1/9 0/1 1/8 2/15 1/7 1/6 3/17 2/11 1/5 3/14 2/9 3/13 7/30 1/4 4/15 3/11 5/18 7/25 2/7 3/10 1/3 9/25 11/30 2/5 5/12 13/30 9/20 7/15 1/2 8/15 17/30 3/5 13/21 17/27 19/30 29/45 2/3 31/45 7/10 11/15 23/30 4/5 5/6 13/15 9/10 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/0 -9/10 0/1 -8/9 -1/1 1/1 -7/8 -1/1 1/1 -13/15 0/1 -6/7 1/1 -11/13 0/1 1/0 -5/6 0/1 -14/17 -1/1 -9/11 1/1 1/0 -4/5 0/1 -19/24 1/0 -15/19 0/1 1/0 -11/14 1/1 3/1 -7/9 -1/1 0/1 1/0 -17/22 -1/1 -1/3 -27/35 -1/2 -10/13 -1/3 -23/30 0/1 -13/17 0/1 1/4 -16/21 1/3 1/1 -3/4 -1/1 1/1 -11/15 0/1 -19/26 1/5 1/3 -27/37 1/3 1/2 -8/11 1/1 -5/7 0/1 1/1 -12/17 -1/1 -43/61 0/1 1/0 -31/44 -1/1 1/1 -19/27 -1/1 0/1 1/0 -7/10 0/1 -23/33 0/1 1/4 1/3 -16/23 1/1 -9/13 0/1 1/2 -11/16 1/1 3/1 -2/3 -1/1 1/1 -11/17 0/1 1/0 -9/14 1/1 5/3 -25/39 2/1 3/1 1/0 -16/25 2/1 -7/11 3/1 1/0 -19/30 1/0 -12/19 -3/1 -17/27 -2/1 -1/1 1/0 -5/8 -1/1 1/1 -23/37 1/1 1/0 -18/29 1/1 -31/50 2/1 -44/71 3/1 -13/21 1/1 2/1 1/0 -34/55 2/1 -55/89 14/5 3/1 -21/34 3/1 5/1 -8/13 -1/1 -3/5 1/0 -10/17 -3/1 -17/29 -2/1 -1/1 -7/12 1/0 -18/31 -1/1 -29/50 0/1 -40/69 -1/1 1/1 -11/19 0/1 1/0 -15/26 -3/1 -1/1 -34/59 -1/1 -19/33 -1/1 -1/2 0/1 -4/7 1/1 -17/30 1/0 -13/23 -7/1 1/0 -9/16 -5/1 -3/1 -5/9 -2/1 -1/1 1/0 -16/29 -1/1 -11/20 -1/1 -6/11 -1/1 -13/24 0/1 -7/13 0/1 1/0 -8/15 1/0 -1/2 -1/1 1/1 -7/15 0/1 -13/28 1/3 1/1 -6/13 1/1 -5/11 -1/1 1/0 -9/20 -1/1 -4/9 -1/1 -1/3 -15/34 -1/1 1/1 -26/59 -1/1 -11/25 -1/2 -7/16 -1/1 -1/3 -17/39 -1/4 -1/5 0/1 -10/23 -1/7 -13/30 0/1 -3/7 0/1 1/1 -8/19 1/1 -21/50 1/1 -13/31 1/1 2/1 -5/12 1/0 -12/29 -1/1 -31/75 -1/1 -19/46 -1/1 -5/7 -7/17 -1/2 0/1 -16/39 -1/1 1/1 -9/22 -1/1 1/1 -11/27 -2/1 -1/1 1/0 -2/5 0/1 -13/33 1/2 2/3 1/1 -24/61 1/1 -11/28 1/1 5/3 -9/23 -1/1 1/0 -16/41 1/1 -39/100 0/1 -23/59 0/1 1/0 -7/18 0/1 -12/31 1/1 -29/75 1/1 -17/44 1/1 7/5 -5/13 2/1 1/0 -8/21 -3/1 -1/1 -19/50 -1/1 -11/29 -2/1 -1/1 -14/37 -1/1 -17/45 0/1 -3/8 -1/1 1/1 -13/35 1/0 -10/27 -1/1 -1/3 -17/46 -1/1 -3/5 -7/19 -1/2 0/1 -11/30 0/1 -4/11 1/1 -13/36 0/1 -22/61 1/1 -9/25 1/0 -5/14 -1/1 1/1 -1/3 -1/1 0/1 1/0 -5/16 -1/1 1/1 -19/61 0/1 1/0 -14/45 0/1 -9/29 0/1 1/1 -4/13 -1/1 -11/36 0/1 -18/59 1/1 -7/23 1/1 1/0 -3/10 1/0 -11/37 -1/1 1/0 -19/64 -5/3 -1/1 -27/91 -8/7 -1/1 -8/27 -1/1 1/1 -5/17 0/1 1/0 -7/24 1/0 -16/55 -2/1 -9/31 -1/1 -2/3 -2/7 -1/1 -11/39 0/1 1/2 1/1 -9/32 3/5 1/1 -34/121 1/1 -59/210 1/1 -25/89 1/1 10/9 -16/57 1/1 5/3 -7/25 1/0 -12/43 1/1 -17/61 0/1 1/0 -5/18 0/1 -8/29 1/1 -11/40 1/1 -3/11 1/1 1/0 -4/15 1/0 -5/19 -2/1 1/0 -1/4 -1/1 1/1 -4/17 5/1 -7/30 1/0 -3/13 -4/1 1/0 -2/9 -1/1 1/1 -9/41 0/1 1/0 -7/32 1/3 1/1 -5/23 3/1 1/0 -3/14 -1/1 1/1 -1/5 1/0 -3/16 -3/1 -1/1 -5/27 -2/1 -1/1 1/0 -2/11 -3/1 -7/39 -2/1 -1/1 1/0 -5/28 -1/1 1/1 -8/45 1/0 -3/17 -2/1 1/0 -1/6 1/0 -3/19 -2/1 1/0 -5/32 -3/1 -7/3 -2/13 -3/1 -1/7 -2/1 -1/1 -2/15 -1/1 -3/23 -1/1 1/0 -1/8 -3/1 -1/1 -1/9 -2/1 -3/2 -1/1 0/1 -1/1 1/8 -1/1 -3/5 2/15 -1/1 1/7 -1/1 -2/3 1/6 -1/2 3/17 -2/3 -1/2 5/28 -1/1 -1/3 7/39 -1/1 -2/3 -1/2 2/11 -3/5 1/5 -1/2 4/19 -1/1 3/14 -1/1 -1/3 5/23 -1/2 -3/7 7/32 -1/3 -1/5 9/41 -1/2 0/1 2/9 -1/1 -1/3 3/13 -4/7 -1/2 7/30 -1/2 4/17 -5/11 1/4 -1/1 -1/3 5/19 -2/3 -1/2 4/15 -1/2 3/11 -1/2 -1/3 8/29 -1/3 5/18 0/1 17/61 -1/2 0/1 12/43 -1/3 7/25 -1/2 9/32 -1/3 -3/11 2/7 -1/1 9/31 -2/1 -1/1 7/24 -1/2 5/17 -1/2 0/1 8/27 -1/1 -1/3 3/10 -1/2 10/33 -3/7 -1/3 7/23 -1/2 -1/3 4/13 -1/1 1/3 -1/1 -1/2 0/1 6/17 -1/1 5/14 -1/1 -1/3 9/25 -1/2 22/61 -1/3 13/36 0/1 4/11 -1/3 11/30 0/1 7/19 0/1 1/0 10/27 -1/1 1/1 33/89 -8/7 -1/1 23/62 -1/1 -7/9 13/35 -1/2 3/8 -1/1 -1/3 14/37 -1/1 11/29 -1/1 -2/3 8/21 -1/1 -3/5 5/13 -1/2 -2/5 12/31 -1/3 7/18 0/1 23/59 -1/2 0/1 16/41 -1/3 9/23 -1/1 -1/2 11/28 -5/13 -1/3 2/5 0/1 9/22 -1/1 -1/3 16/39 -1/1 -1/3 7/17 0/1 1/0 12/29 -1/1 5/12 -1/2 3/7 -1/3 0/1 13/30 0/1 10/23 1/5 27/62 1/3 3/7 17/39 0/1 1/3 1/2 7/16 -1/1 1/1 11/25 1/0 26/59 -1/1 15/34 -1/1 -1/3 4/9 -1/1 1/1 13/29 -1/1 0/1 9/20 -1/1 14/31 -1/1 5/11 -1/1 -1/2 6/13 -1/3 7/15 0/1 8/17 -1/1 1/2 -1/1 -1/3 9/17 -2/3 -1/2 8/15 -1/2 7/13 -1/2 0/1 6/11 -1/1 11/20 -1/1 16/29 -1/1 5/9 -1/1 -2/3 -1/2 9/16 -3/5 -5/9 13/23 -7/13 -1/2 17/30 -1/2 4/7 -1/3 19/33 -1/1 0/1 1/0 34/59 -1/1 15/26 -1/1 -3/5 11/19 -1/2 0/1 40/69 -1/1 -1/3 29/50 0/1 18/31 -1/1 7/12 -1/2 3/5 -1/2 11/18 -1/2 19/31 -1/3 0/1 46/75 0/1 27/44 -1/1 -1/3 8/13 -1/1 21/34 -5/11 -3/7 55/89 -3/7 -14/33 34/55 -2/5 13/21 -1/2 -2/5 -1/3 44/71 -3/7 31/50 -2/5 18/29 -1/3 23/37 -1/2 -1/3 28/45 -1/3 5/8 -1/1 -1/3 22/35 0/1 39/62 -5/3 -1/1 95/151 -14/13 -1/1 151/240 -1/1 56/89 -1/1 17/27 -1/1 -2/3 -1/2 29/46 -1/1 -3/5 12/19 -3/5 19/30 -1/2 7/11 -1/2 -3/7 9/14 -5/13 -1/3 29/45 -1/3 20/31 -1/3 11/17 -1/2 0/1 2/3 -1/1 -1/3 11/16 -3/7 -1/3 31/45 -1/3 20/29 -1/3 9/13 -1/4 0/1 16/23 -1/3 7/10 0/1 26/37 1/1 19/27 -1/1 -1/2 0/1 31/44 -1/1 -1/3 74/105 0/1 43/61 -1/2 0/1 12/17 -1/1 41/58 -1/1 1/1 29/41 -1/2 0/1 17/24 -1/2 5/7 -1/3 0/1 13/18 -1/2 21/29 -2/5 -1/3 29/40 -1/3 8/11 -1/3 11/15 0/1 14/19 1/1 17/23 -1/1 1/0 20/27 -3/1 -1/1 23/31 -1/1 -6/7 3/4 -1/1 -1/3 16/21 -1/3 -1/5 13/17 -1/6 0/1 23/30 0/1 10/13 1/1 27/35 1/0 17/22 -1/1 1/1 24/31 -1/1 7/9 -1/1 -1/2 0/1 11/14 -3/7 -1/3 26/33 -1/1 -1/3 15/19 -1/2 0/1 19/24 -1/2 23/29 -4/11 -1/3 4/5 0/1 17/21 -1/2 -1/3 0/1 13/16 -1/1 1/1 9/11 -1/2 -1/3 14/17 -1/1 19/23 -1/2 -1/3 24/29 -1/3 5/6 0/1 16/19 -1/1 11/13 -1/2 0/1 6/7 -1/3 13/15 0/1 20/23 -1/1 7/8 -1/1 -1/3 8/9 -1/1 -1/3 9/10 0/1 10/11 -1/3 1/1 -1/2 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(269,246,-690,-631) (-1/1,-9/10) -> (-39/100,-23/59) Hyperbolic Matrix(661,592,1140,1021) (-9/10,-8/9) -> (40/69,29/50) Hyperbolic Matrix(209,184,510,449) (-8/9,-7/8) -> (9/22,16/39) Hyperbolic Matrix(181,158,-480,-419) (-7/8,-13/15) -> (-17/45,-3/8) Hyperbolic Matrix(329,284,-870,-751) (-13/15,-6/7) -> (-14/37,-17/45) Hyperbolic Matrix(271,230,390,331) (-6/7,-11/13) -> (9/13,16/23) Hyperbolic Matrix(211,178,-390,-329) (-11/13,-5/6) -> (-13/24,-7/13) Hyperbolic Matrix(211,174,-690,-569) (-5/6,-14/17) -> (-4/13,-11/36) Hyperbolic Matrix(151,124,330,271) (-14/17,-9/11) -> (5/11,6/13) Hyperbolic Matrix(211,172,-330,-269) (-9/11,-4/5) -> (-16/25,-7/11) Hyperbolic Matrix(419,332,-1440,-1141) (-4/5,-19/24) -> (-7/24,-16/55) Hyperbolic Matrix(1019,806,1440,1139) (-19/24,-15/19) -> (29/41,17/24) Hyperbolic Matrix(421,332,-1140,-899) (-15/19,-11/14) -> (-17/46,-7/19) Hyperbolic Matrix(151,118,270,211) (-11/14,-7/9) -> (5/9,9/16) Hyperbolic Matrix(31,24,-270,-209) (-7/9,-17/22) -> (-1/8,-1/9) Hyperbolic Matrix(391,302,1050,811) (-17/22,-27/35) -> (13/35,3/8) Hyperbolic Matrix(511,394,1830,1411) (-27/35,-10/13) -> (12/43,7/25) Hyperbolic Matrix(599,460,780,599) (-10/13,-23/30) -> (23/30,10/13) Hyperbolic Matrix(781,598,1020,781) (-23/30,-13/17) -> (13/17,23/30) Hyperbolic Matrix(419,320,1020,779) (-13/17,-16/21) -> (16/39,7/17) Hyperbolic Matrix(331,252,750,571) (-16/21,-3/4) -> (15/34,4/9) Hyperbolic Matrix(329,242,-450,-331) (-3/4,-11/15) -> (-11/15,-19/26) Parabolic Matrix(989,722,-3330,-2431) (-19/26,-27/37) -> (-11/37,-19/64) Hyperbolic Matrix(691,504,1770,1291) (-27/37,-8/11) -> (16/41,9/23) Hyperbolic Matrix(89,64,-210,-151) (-8/11,-5/7) -> (-3/7,-8/19) Hyperbolic Matrix(31,22,-210,-149) (-5/7,-12/17) -> (-2/13,-1/7) Hyperbolic Matrix(1021,720,3660,2581) (-12/17,-43/61) -> (17/61,12/43) Hyperbolic Matrix(1141,804,-3660,-2579) (-43/61,-31/44) -> (-5/16,-19/61) Hyperbolic Matrix(1531,1078,2430,1711) (-31/44,-19/27) -> (17/27,29/46) Hyperbolic Matrix(419,294,-600,-421) (-19/27,-7/10) -> (-7/10,-23/33) Parabolic Matrix(569,396,990,689) (-23/33,-16/23) -> (4/7,19/33) Hyperbolic Matrix(331,230,390,271) (-16/23,-9/13) -> (11/13,6/7) Hyperbolic Matrix(301,208,-780,-539) (-9/13,-11/16) -> (-17/44,-5/13) Hyperbolic Matrix(211,144,-570,-389) (-11/16,-2/3) -> (-10/27,-17/46) Hyperbolic Matrix(151,98,510,331) (-2/3,-11/17) -> (5/17,8/27) Hyperbolic Matrix(421,272,-1020,-659) (-11/17,-9/14) -> (-19/46,-7/17) Hyperbolic Matrix(511,328,1170,751) (-9/14,-25/39) -> (17/39,7/16) Hyperbolic Matrix(1651,1058,2670,1711) (-25/39,-16/25) -> (34/55,13/21) Hyperbolic Matrix(419,266,660,419) (-7/11,-19/30) -> (19/30,7/11) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(149,94,-810,-511) (-12/19,-17/27) -> (-5/27,-2/11) Hyperbolic Matrix(331,208,-810,-509) (-17/27,-5/8) -> (-9/22,-11/27) Hyperbolic Matrix(61,38,-480,-299) (-5/8,-23/37) -> (-3/23,-1/8) Hyperbolic Matrix(869,540,-2850,-1771) (-23/37,-18/29) -> (-18/59,-7/23) Hyperbolic Matrix(1741,1080,3000,1861) (-18/29,-31/50) -> (29/50,18/31) Hyperbolic Matrix(3569,2212,-9150,-5671) (-31/50,-44/71) -> (-16/41,-39/100) Hyperbolic Matrix(539,334,3000,1859) (-44/71,-13/21) -> (7/39,2/11) Hyperbolic Matrix(1019,630,1260,779) (-13/21,-34/55) -> (4/5,17/21) Hyperbolic Matrix(1621,1002,2040,1261) (-34/55,-55/89) -> (23/29,4/5) Hyperbolic Matrix(2609,1612,-8790,-5431) (-55/89,-21/34) -> (-19/64,-27/91) Hyperbolic Matrix(149,92,630,389) (-21/34,-8/13) -> (4/17,1/4) Hyperbolic Matrix(89,54,-150,-91) (-8/13,-3/5) -> (-3/5,-10/17) Parabolic Matrix(269,158,-870,-511) (-10/17,-17/29) -> (-9/29,-4/13) Hyperbolic Matrix(629,368,870,509) (-17/29,-7/12) -> (13/18,21/29) 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(1021,592,1140,661) (-29/50,-40/69) -> (8/9,9/10) Hyperbolic Matrix(659,382,3000,1739) (-40/69,-11/19) -> (9/41,2/9) Hyperbolic Matrix(149,86,570,329) (-11/19,-15/26) -> (1/4,5/19) 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(991,570,1410,811) (-19/33,-4/7) -> (26/37,19/27) Hyperbolic Matrix(239,136,420,239) (-4/7,-17/30) -> (17/30,4/7) Hyperbolic Matrix(781,442,1380,781) (-17/30,-13/23) -> (13/23,17/30) Hyperbolic Matrix(149,84,690,389) (-13/23,-9/16) -> (3/14,5/23) Hyperbolic Matrix(211,118,270,151) (-9/16,-5/9) -> (7/9,11/14) 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(391,214,-930,-509) (-11/20,-6/11) -> (-8/19,-21/50) Hyperbolic Matrix(239,130,660,359) (-6/11,-13/24) -> (13/36,4/11) Hyperbolic Matrix(209,112,390,209) (-7/13,-8/15) -> (8/15,7/13) Hyperbolic Matrix(91,48,-510,-269) (-8/15,-1/2) -> (-5/28,-8/45) Hyperbolic Matrix(209,98,-450,-211) (-1/2,-7/15) -> (-7/15,-13/28) Parabolic Matrix(869,402,1230,569) (-13/28,-6/13) -> (12/17,41/58) Hyperbolic Matrix(271,124,330,151) (-6/13,-5/11) -> (9/11,14/17) Hyperbolic Matrix(181,82,-660,-299) (-5/11,-9/20) -> (-11/40,-3/11) Hyperbolic Matrix(331,148,-870,-389) (-9/20,-4/9) -> (-8/21,-19/50) Hyperbolic Matrix(571,252,750,331) (-4/9,-15/34) -> (3/4,16/21) Hyperbolic Matrix(2041,900,3540,1561) (-15/34,-26/59) -> (34/59,15/26) Hyperbolic Matrix(1081,476,3000,1321) (-26/59,-11/25) -> (9/25,22/61) Hyperbolic Matrix(269,118,750,329) (-11/25,-7/16) -> (5/14,9/25) Hyperbolic Matrix(779,340,960,419) (-7/16,-17/39) -> (17/21,13/16) Hyperbolic Matrix(331,144,-1170,-509) (-17/39,-10/23) -> (-2/7,-11/39) Hyperbolic Matrix(599,260,1380,599) (-10/23,-13/30) -> (13/30,10/23) Hyperbolic Matrix(181,78,420,181) (-13/30,-3/7) -> (3/7,13/30) Hyperbolic Matrix(929,390,2070,869) (-21/50,-13/31) -> (13/29,9/20) Hyperbolic Matrix(569,238,930,389) (-13/31,-5/12) -> (11/18,19/31) 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(2251,930,3270,1351) (-31/75,-19/46) -> (11/16,31/45) Hyperbolic Matrix(779,320,1020,419) (-7/17,-16/39) -> (16/21,13/17) Hyperbolic Matrix(449,184,510,209) (-16/39,-9/22) -> (7/8,8/9) 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(1019,398,1380,539) (-9/23,-16/41) -> (14/19,17/23) Hyperbolic Matrix(601,234,2160,841) (-23/59,-7/18) -> (5/18,17/61) 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(1951,754,3030,1171) (-29/75,-17/44) -> (9/14,29/45) Hyperbolic Matrix(89,34,390,149) (-5/13,-8/21) -> (2/9,3/13) Hyperbolic Matrix(1891,718,2610,991) (-19/50,-11/29) -> (21/29,29/40) Hyperbolic Matrix(391,148,1350,511) (-11/29,-14/37) -> (2/7,9/31) Hyperbolic Matrix(811,302,1050,391) (-3/8,-13/35) -> (27/35,17/22) Hyperbolic Matrix(749,278,-2670,-991) (-13/35,-10/27) -> (-16/57,-7/25) Hyperbolic Matrix(419,154,1140,419) (-7/19,-11/30) -> (11/30,7/19) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(631,228,750,271) (-4/11,-13/36) -> (5/6,16/19) Hyperbolic Matrix(1169,422,1410,509) (-13/36,-22/61) -> (24/29,5/6) Hyperbolic Matrix(1321,476,3000,1081) (-22/61,-9/25) -> (11/25,26/59) Hyperbolic Matrix(329,118,750,269) (-9/25,-5/14) -> (7/16,11/25) Hyperbolic Matrix(29,10,-90,-31) (-5/14,-1/3) -> (-1/3,-5/16) Parabolic Matrix(6449,2008,9150,2849) (-19/61,-14/45) -> (74/105,43/61) Hyperbolic Matrix(2189,680,3570,1109) (-14/45,-9/29) -> (19/31,46/75) Hyperbolic Matrix(1559,476,4320,1319) (-11/36,-18/59) -> (22/61,13/36) Hyperbolic Matrix(179,54,-600,-181) (-7/23,-3/10) -> (-3/10,-11/37) Parabolic Matrix(1801,534,4860,1441) (-27/91,-8/27) -> (10/27,33/89) Hyperbolic Matrix(331,98,510,151) (-8/27,-5/17) -> (11/17,2/3) Hyperbolic Matrix(89,26,510,149) (-5/17,-7/24) -> (1/6,3/17) Hyperbolic Matrix(4079,1186,6600,1919) (-16/55,-9/31) -> (55/89,34/55) Hyperbolic Matrix(511,148,1350,391) (-9/31,-2/7) -> (14/37,11/29) Hyperbolic Matrix(419,118,2340,659) (-11/39,-9/32) -> (5/28,7/39) Hyperbolic Matrix(30031,8438,47730,13411) (-34/121,-59/210) -> (151/240,56/89) Hyperbolic Matrix(33389,9380,53070,14909) (-59/210,-25/89) -> (95/151,151/240) Hyperbolic Matrix(3091,868,4170,1171) (-25/89,-16/57) -> (20/27,23/31) Hyperbolic Matrix(1411,394,1830,511) (-7/25,-12/43) -> (10/13,27/35) Hyperbolic Matrix(2581,720,3660,1021) (-12/43,-17/61) -> (43/61,12/17) Hyperbolic Matrix(841,234,2160,601) (-17/61,-5/18) -> (7/18,23/59) 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(89,24,330,89) (-3/11,-4/15) -> (4/15,3/11) Hyperbolic Matrix(151,40,570,151) (-4/15,-5/19) -> (5/19,4/15) Hyperbolic Matrix(329,86,570,149) (-5/19,-1/4) -> (15/26,11/19) Hyperbolic Matrix(389,92,630,149) (-1/4,-4/17) -> (8/13,21/34) Hyperbolic Matrix(239,56,1020,239) (-4/17,-7/30) -> (7/30,4/17) Hyperbolic Matrix(181,42,780,181) (-7/30,-3/13) -> (3/13,7/30) Hyperbolic Matrix(149,34,390,89) (-3/13,-2/9) -> (8/21,5/13) Hyperbolic Matrix(1739,382,3000,659) (-2/9,-9/41) -> (11/19,40/69) Hyperbolic Matrix(2609,572,3690,809) (-9/41,-7/32) -> (41/58,29/41) Hyperbolic Matrix(541,118,1380,301) (-7/32,-5/23) -> (9/23,11/28) Hyperbolic Matrix(389,84,690,149) (-5/23,-3/14) -> (9/16,13/23) Hyperbolic Matrix(29,6,-150,-31) (-3/14,-1/5) -> (-1/5,-3/16) Parabolic Matrix(1141,212,1620,301) (-3/16,-5/27) -> (19/27,31/44) Hyperbolic Matrix(1859,334,3000,539) (-2/11,-7/39) -> (13/21,44/71) Hyperbolic Matrix(1529,274,3510,629) (-7/39,-5/28) -> (27/62,17/39) Hyperbolic Matrix(541,96,1020,181) (-8/45,-3/17) -> (9/17,8/15) Hyperbolic Matrix(149,26,510,89) (-3/17,-1/6) -> (7/24,5/17) Hyperbolic Matrix(451,72,570,91) (-1/6,-3/19) -> (15/19,19/24) Hyperbolic Matrix(421,66,1920,301) (-3/19,-5/32) -> (7/32,9/41) Hyperbolic Matrix(269,42,570,89) (-5/32,-2/13) -> (8/17,1/2) Hyperbolic Matrix(29,4,210,29) (-1/7,-2/15) -> (2/15,1/7) Hyperbolic Matrix(989,130,1590,209) (-2/15,-3/23) -> (23/37,28/45) Hyperbolic Matrix(149,16,270,29) (-1/9,0/1) -> (16/29,5/9) Hyperbolic Matrix(209,-24,270,-31) (0/1,1/8) -> (17/22,24/31) Hyperbolic Matrix(299,-38,480,-61) (1/8,2/15) -> (28/45,5/8) Hyperbolic Matrix(149,-22,210,-31) (1/7,1/6) -> (17/24,5/7) Hyperbolic Matrix(269,-48,510,-91) (3/17,5/28) -> (1/2,9/17) Hyperbolic Matrix(31,-6,150,-29) (2/11,1/5) -> (1/5,4/19) Parabolic Matrix(719,-152,1140,-241) (4/19,3/14) -> (29/46,12/19) Hyperbolic Matrix(299,-82,660,-181) (3/11,8/29) -> (14/31,5/11) Hyperbolic Matrix(991,-278,2670,-749) (7/25,9/32) -> (23/62,13/35) Hyperbolic Matrix(509,-144,1170,-331) (9/32,2/7) -> (10/23,27/62) Hyperbolic Matrix(1141,-332,1440,-419) (9/31,7/24) -> (19/24,23/29) Hyperbolic Matrix(181,-54,600,-179) (8/27,3/10) -> (3/10,10/33) Parabolic Matrix(1021,-310,1380,-419) (10/33,7/23) -> (17/23,20/27) Hyperbolic Matrix(569,-174,690,-211) (7/23,4/13) -> (14/17,19/23) Hyperbolic 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(899,-332,1140,-421) (7/19,10/27) -> (26/33,15/19) Hyperbolic Matrix(9361,-3472,14880,-5519) (33/89,23/62) -> (39/62,95/151) Hyperbolic Matrix(419,-158,480,-181) (3/8,14/37) -> (20/23,7/8) Hyperbolic Matrix(389,-148,870,-331) (11/29,8/21) -> (4/9,13/29) Hyperbolic Matrix(539,-208,780,-301) (5/13,12/31) -> (20/29,9/13) Hyperbolic Matrix(631,-246,690,-269) (23/59,16/41) -> (10/11,1/1) Hyperbolic Matrix(811,-320,1290,-509) (11/28,2/5) -> (22/35,39/62) Hyperbolic Matrix(509,-208,810,-331) (2/5,9/22) -> (5/8,22/35) Hyperbolic Matrix(659,-272,1020,-421) (7/17,12/29) -> (20/31,11/17) Hyperbolic Matrix(151,-64,210,-89) (5/12,3/7) -> (5/7,13/18) Hyperbolic Matrix(211,-98,450,-209) (6/13,7/15) -> (7/15,8/17) Parabolic Matrix(329,-178,390,-211) (7/13,6/11) -> (16/19,11/13) Hyperbolic Matrix(479,-262,660,-361) (6/11,11/20) -> (29/40,8/11) Hyperbolic Matrix(2851,-1642,4530,-2609) (19/33,34/59) -> (56/89,17/27) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(5581,-3424,7920,-4859) (46/75,27/44) -> (31/44,74/105) Hyperbolic Matrix(1049,-648,1410,-871) (21/34,55/89) -> (23/31,3/4) Hyperbolic Matrix(1139,-706,1260,-781) (44/71,31/50) -> (9/10,10/11) Hyperbolic Matrix(1439,-894,1740,-1081) (18/29,23/37) -> (19/23,24/29) Hyperbolic Matrix(269,-172,330,-211) (7/11,9/14) -> (13/16,9/11) Hyperbolic Matrix(449,-308,570,-391) (2/3,11/16) -> (11/14,26/33) Hyperbolic Matrix(421,-294,600,-419) (16/23,7/10) -> (7/10,26/37) Parabolic Matrix(331,-242,450,-329) (8/11,11/15) -> (11/15,14/19) Parabolic Matrix(391,-338,450,-389) (6/7,13/15) -> (13/15,20/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(269,246,-690,-631) -> Matrix(1,0,0,1) Matrix(661,592,1140,1021) -> Matrix(1,0,-2,1) Matrix(209,184,510,449) -> Matrix(1,0,-2,1) Matrix(181,158,-480,-419) -> Matrix(1,0,0,1) Matrix(329,284,-870,-751) -> Matrix(1,0,-2,1) Matrix(271,230,390,331) -> Matrix(1,0,-4,1) Matrix(211,178,-390,-329) -> Matrix(1,0,0,1) Matrix(211,174,-690,-569) -> Matrix(1,0,0,1) Matrix(151,124,330,271) -> Matrix(1,0,-2,1) Matrix(211,172,-330,-269) -> Matrix(1,2,0,1) Matrix(419,332,-1440,-1141) -> Matrix(1,-2,0,1) Matrix(1019,806,1440,1139) -> Matrix(1,0,-2,1) Matrix(421,332,-1140,-899) -> Matrix(1,0,-2,1) Matrix(151,118,270,211) -> Matrix(1,2,-2,-3) Matrix(31,24,-270,-209) -> Matrix(3,2,-2,-1) Matrix(391,302,1050,811) -> Matrix(1,0,0,1) Matrix(511,394,1830,1411) -> Matrix(1,0,0,1) Matrix(599,460,780,599) -> Matrix(1,0,4,1) Matrix(781,598,1020,781) -> Matrix(1,0,-10,1) Matrix(419,320,1020,779) -> Matrix(1,0,-4,1) Matrix(331,252,750,571) -> Matrix(1,0,-2,1) Matrix(329,242,-450,-331) -> Matrix(1,0,4,1) Matrix(989,722,-3330,-2431) -> Matrix(5,-2,-2,1) Matrix(691,504,1770,1291) -> Matrix(1,0,-4,1) Matrix(89,64,-210,-151) -> Matrix(1,0,0,1) Matrix(31,22,-210,-149) -> Matrix(1,-2,0,1) Matrix(1021,720,3660,2581) -> Matrix(1,0,-2,1) Matrix(1141,804,-3660,-2579) -> Matrix(1,0,0,1) Matrix(1531,1078,2430,1711) -> Matrix(1,2,-2,-3) Matrix(419,294,-600,-421) -> Matrix(1,0,4,1) Matrix(569,396,990,689) -> Matrix(1,0,-4,1) Matrix(331,230,390,271) -> Matrix(1,0,-4,1) Matrix(301,208,-780,-539) -> Matrix(3,-2,2,-1) Matrix(211,144,-570,-389) -> Matrix(1,0,-2,1) Matrix(151,98,510,331) -> Matrix(1,0,-2,1) Matrix(421,272,-1020,-659) -> Matrix(1,0,-2,1) Matrix(511,328,1170,751) -> Matrix(1,-2,2,-3) Matrix(1651,1058,2670,1711) -> Matrix(1,-4,-2,9) Matrix(419,266,660,419) -> Matrix(1,-6,-2,13) Matrix(721,456,1140,721) -> Matrix(1,6,-2,-11) Matrix(149,94,-810,-511) -> Matrix(1,0,0,1) Matrix(331,208,-810,-509) -> Matrix(1,0,0,1) Matrix(61,38,-480,-299) -> Matrix(1,-2,0,1) Matrix(869,540,-2850,-1771) -> Matrix(1,0,0,1) Matrix(1741,1080,3000,1861) -> Matrix(1,-2,0,1) Matrix(3569,2212,-9150,-5671) -> Matrix(1,-2,0,1) Matrix(539,334,3000,1859) -> Matrix(1,0,-2,1) Matrix(1019,630,1260,779) -> Matrix(1,-2,-2,5) Matrix(1621,1002,2040,1261) -> Matrix(1,-2,-4,9) Matrix(2609,1612,-8790,-5431) -> Matrix(3,-10,-2,7) Matrix(149,92,630,389) -> Matrix(1,-4,-2,9) Matrix(89,54,-150,-91) -> Matrix(1,-2,0,1) Matrix(269,158,-870,-511) -> Matrix(1,2,0,1) Matrix(629,368,870,509) -> Matrix(1,0,-2,1) Matrix(299,174,720,419) -> Matrix(1,2,-2,-3) Matrix(1861,1080,3000,1741) -> Matrix(3,2,-8,-5) Matrix(1021,592,1140,661) -> Matrix(1,0,-2,1) Matrix(659,382,3000,1739) -> Matrix(1,0,-2,1) Matrix(149,86,570,329) -> Matrix(1,2,-2,-3) Matrix(1561,900,3540,2041) -> Matrix(1,2,-2,-3) Matrix(1559,898,-3960,-2281) -> Matrix(3,2,4,3) Matrix(991,570,1410,811) -> Matrix(1,0,0,1) Matrix(239,136,420,239) -> Matrix(1,-2,-2,5) Matrix(781,442,1380,781) -> Matrix(1,14,-2,-27) Matrix(149,84,690,389) -> Matrix(1,4,-2,-7) Matrix(211,118,270,151) -> Matrix(1,2,-2,-3) Matrix(419,232,540,299) -> Matrix(1,2,-2,-3) Matrix(541,298,1200,661) -> Matrix(3,4,-4,-5) Matrix(391,214,-930,-509) -> Matrix(1,0,2,1) Matrix(239,130,660,359) -> Matrix(1,0,-2,1) Matrix(209,112,390,209) -> Matrix(1,0,-2,1) Matrix(91,48,-510,-269) -> Matrix(1,0,0,1) Matrix(209,98,-450,-211) -> Matrix(1,0,2,1) Matrix(869,402,1230,569) -> Matrix(1,0,-2,1) Matrix(271,124,330,151) -> Matrix(1,0,-2,1) Matrix(181,82,-660,-299) -> Matrix(1,2,0,1) Matrix(331,148,-870,-389) -> Matrix(3,2,-2,-1) Matrix(571,252,750,331) -> Matrix(1,0,-2,1) Matrix(2041,900,3540,1561) -> Matrix(1,2,-2,-3) Matrix(1081,476,3000,1321) -> Matrix(3,2,-8,-5) Matrix(269,118,750,329) -> Matrix(1,0,0,1) Matrix(779,340,960,419) -> Matrix(1,0,2,1) Matrix(331,144,-1170,-509) -> Matrix(1,0,6,1) Matrix(599,260,1380,599) -> Matrix(1,0,12,1) Matrix(181,78,420,181) -> Matrix(1,0,-4,1) Matrix(929,390,2070,869) -> Matrix(1,-2,0,1) Matrix(569,238,930,389) -> Matrix(1,-2,-2,5) Matrix(419,174,720,299) -> Matrix(1,2,-2,-3) Matrix(2399,992,3480,1439) -> Matrix(3,4,-10,-13) Matrix(2251,930,3270,1351) -> Matrix(5,4,-14,-11) Matrix(779,320,1020,419) -> Matrix(1,0,-4,1) Matrix(449,184,510,209) -> Matrix(1,0,-2,1) Matrix(119,48,-300,-121) -> Matrix(1,0,2,1) Matrix(1501,590,-5340,-2099) -> Matrix(3,-4,4,-5) Matrix(301,118,1380,541) -> Matrix(1,-2,-2,5) Matrix(1019,398,1380,539) -> Matrix(1,0,0,1) Matrix(601,234,2160,841) -> Matrix(1,0,-2,1) Matrix(299,116,1080,419) -> Matrix(1,0,-4,1) Matrix(2399,928,3720,1439) -> Matrix(3,-2,-10,7) Matrix(1951,754,3030,1171) -> Matrix(5,-6,-14,17) Matrix(89,34,390,149) -> Matrix(1,2,-2,-3) Matrix(1891,718,2610,991) -> Matrix(1,0,-2,1) Matrix(391,148,1350,511) -> Matrix(1,0,0,1) Matrix(811,302,1050,391) -> Matrix(1,0,0,1) Matrix(749,278,-2670,-991) -> Matrix(1,2,0,1) Matrix(419,154,1140,419) -> Matrix(1,0,2,1) Matrix(241,88,660,241) -> Matrix(1,0,-4,1) Matrix(631,228,750,271) -> Matrix(1,0,-2,1) Matrix(1169,422,1410,509) -> Matrix(1,0,-4,1) Matrix(1321,476,3000,1081) -> Matrix(1,-2,0,1) Matrix(329,118,750,269) -> Matrix(1,0,0,1) Matrix(29,10,-90,-31) -> Matrix(1,0,0,1) Matrix(6449,2008,9150,2849) -> Matrix(1,0,-2,1) Matrix(2189,680,3570,1109) -> Matrix(1,0,-4,1) Matrix(1559,476,4320,1319) -> Matrix(1,0,-4,1) Matrix(179,54,-600,-181) -> Matrix(1,-2,0,1) Matrix(1801,534,4860,1441) -> Matrix(1,0,0,1) Matrix(331,98,510,151) -> Matrix(1,0,-2,1) Matrix(89,26,510,149) -> Matrix(1,2,-2,-3) Matrix(4079,1186,6600,1919) -> Matrix(5,8,-12,-19) Matrix(511,148,1350,391) -> Matrix(1,0,0,1) Matrix(419,118,2340,659) -> Matrix(3,-2,-4,3) Matrix(30031,8438,47730,13411) -> Matrix(23,-22,-24,23) Matrix(33389,9380,53070,14909) -> Matrix(23,-24,-22,23) Matrix(3091,868,4170,1171) -> Matrix(3,-4,-2,3) Matrix(1411,394,1830,511) -> Matrix(1,0,0,1) Matrix(2581,720,3660,1021) -> Matrix(1,0,-2,1) Matrix(841,234,2160,601) -> Matrix(1,0,-2,1) Matrix(419,116,1080,299) -> Matrix(1,0,-4,1) Matrix(959,264,1740,479) -> Matrix(3,-2,-4,3) Matrix(89,24,330,89) -> Matrix(1,-2,-2,5) Matrix(151,40,570,151) -> Matrix(1,4,-2,-7) Matrix(329,86,570,149) -> Matrix(1,2,-2,-3) Matrix(389,92,630,149) -> Matrix(1,-4,-2,9) Matrix(239,56,1020,239) -> Matrix(1,-10,-2,21) Matrix(181,42,780,181) -> Matrix(1,8,-2,-15) Matrix(149,34,390,89) -> Matrix(1,2,-2,-3) Matrix(1739,382,3000,659) -> Matrix(1,0,-2,1) Matrix(2609,572,3690,809) -> Matrix(1,0,-2,1) Matrix(541,118,1380,301) -> Matrix(1,-2,-2,5) Matrix(389,84,690,149) -> Matrix(1,4,-2,-7) Matrix(29,6,-150,-31) -> Matrix(1,-2,0,1) Matrix(1141,212,1620,301) -> Matrix(1,2,-2,-3) Matrix(1859,334,3000,539) -> Matrix(1,0,-2,1) Matrix(1529,274,3510,629) -> Matrix(1,2,2,5) Matrix(541,96,1020,181) -> Matrix(1,4,-2,-7) Matrix(149,26,510,89) -> Matrix(1,2,-2,-3) Matrix(451,72,570,91) -> Matrix(1,2,-2,-3) Matrix(421,66,1920,301) -> Matrix(1,2,-2,-3) Matrix(269,42,570,89) -> Matrix(1,2,0,1) Matrix(29,4,210,29) -> Matrix(3,4,-4,-5) Matrix(989,130,1590,209) -> Matrix(1,0,-2,1) Matrix(149,16,270,29) -> Matrix(3,4,-4,-5) Matrix(209,-24,270,-31) -> Matrix(3,2,-2,-1) Matrix(299,-38,480,-61) -> Matrix(3,2,-8,-5) Matrix(149,-22,210,-31) -> Matrix(3,2,-8,-5) Matrix(269,-48,510,-91) -> Matrix(1,0,0,1) Matrix(31,-6,150,-29) -> Matrix(3,2,-8,-5) Matrix(719,-152,1140,-241) -> Matrix(5,2,-8,-3) Matrix(299,-82,660,-181) -> Matrix(5,2,-8,-3) Matrix(991,-278,2670,-749) -> Matrix(5,2,-8,-3) Matrix(509,-144,1170,-331) -> Matrix(1,0,6,1) Matrix(1141,-332,1440,-419) -> Matrix(3,2,-8,-5) Matrix(181,-54,600,-179) -> Matrix(3,2,-8,-5) Matrix(1021,-310,1380,-419) -> Matrix(1,0,2,1) Matrix(569,-174,690,-211) -> Matrix(1,0,0,1) Matrix(31,-10,90,-29) -> Matrix(1,0,0,1) Matrix(571,-202,930,-329) -> Matrix(1,0,0,1) Matrix(899,-332,1140,-421) -> Matrix(1,0,-2,1) Matrix(9361,-3472,14880,-5519) -> Matrix(7,6,-6,-5) Matrix(419,-158,480,-181) -> Matrix(1,0,0,1) Matrix(389,-148,870,-331) -> Matrix(3,2,-2,-1) Matrix(539,-208,780,-301) -> Matrix(5,2,-18,-7) Matrix(631,-246,690,-269) -> Matrix(1,0,0,1) Matrix(811,-320,1290,-509) -> Matrix(1,0,2,1) Matrix(509,-208,810,-331) -> Matrix(1,0,0,1) Matrix(659,-272,1020,-421) -> Matrix(1,0,-2,1) Matrix(151,-64,210,-89) -> Matrix(1,0,0,1) Matrix(211,-98,450,-209) -> Matrix(1,0,2,1) Matrix(329,-178,390,-211) -> Matrix(1,0,0,1) Matrix(479,-262,660,-361) -> Matrix(1,0,-2,1) Matrix(2851,-1642,4530,-2609) -> Matrix(1,2,-2,-3) Matrix(91,-54,150,-89) -> Matrix(3,2,-8,-5) Matrix(5581,-3424,7920,-4859) -> Matrix(1,0,0,1) Matrix(1049,-648,1410,-871) -> Matrix(9,4,-16,-7) Matrix(1139,-706,1260,-781) -> Matrix(5,2,-8,-3) Matrix(1439,-894,1740,-1081) -> Matrix(1,0,0,1) Matrix(269,-172,330,-211) -> Matrix(5,2,-8,-3) Matrix(449,-308,570,-391) -> Matrix(1,0,0,1) Matrix(421,-294,600,-419) -> Matrix(1,0,4,1) Matrix(331,-242,450,-329) -> Matrix(1,0,4,1) Matrix(391,-338,450,-389) -> Matrix(1,0,2,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 42 Degree of the the map X: 42 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. Imminent integer overflow caused the modular group computation to abort.