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): 1008 Minimal number of generators: 169 Number of equivalence classes of cusps: 60 Genus: 55 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -11/13 -9/13 -25/39 -7/13 -1/2 -5/12 -5/13 -79/208 -3/8 -9/26 -3/10 -7/25 -1/4 -3/13 -5/23 -9/52 -1/6 -1/8 -3/26 -1/9 0/1 1/7 2/13 3/19 1/6 3/17 2/11 5/26 1/5 2/9 3/13 5/21 1/4 7/26 3/11 2/7 3/10 4/13 1/3 14/39 5/13 2/5 5/12 11/26 6/13 7/15 1/2 7/13 15/26 8/13 25/39 2/3 9/13 19/26 10/13 21/26 11/13 23/26 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 -1/1 1/1 -8/9 -1/1 -7/8 -1/1 1/1 -6/7 -1/1 -11/13 0/1 -16/19 1/1 -5/6 -1/1 1/1 -9/11 0/1 1/0 -13/16 -1/1 -1/3 -17/21 -1/4 0/1 -21/26 0/1 -4/5 1/1 -11/14 -3/1 -1/1 -29/37 -1/2 0/1 -18/23 -1/1 -7/9 -1/1 0/1 -10/13 0/1 -13/17 0/1 1/2 -3/4 -1/1 1/1 -14/19 -1/3 -25/34 -1/1 -1/3 -11/15 -1/4 0/1 -19/26 0/1 -8/11 1/3 -21/29 1/2 1/1 -13/18 1/3 1/1 -5/7 0/1 1/0 -7/10 -1/1 1/1 -9/13 0/1 -11/16 1/3 1/1 -24/35 1/3 -13/19 1/2 1/1 -2/3 1/1 -9/14 1/3 1/1 -25/39 1/1 -41/64 1/1 11/9 -16/25 1/1 -7/11 2/1 1/0 -5/8 1/1 3/1 -23/37 2/1 5/2 -18/29 3/1 -49/79 20/7 3/1 -31/50 3/1 17/5 -13/21 4/1 1/0 -8/13 1/0 -3/5 0/1 1/0 -7/12 -1/1 1/1 -18/31 3/1 -29/50 3/1 11/3 -40/69 3/1 -11/19 5/1 1/0 -15/26 1/0 -4/7 -3/1 -17/30 -5/3 -1/1 -30/53 -1/1 -13/23 -1/1 1/0 -9/16 -3/1 -1/1 -23/41 -2/1 -3/2 -14/25 -1/1 -5/9 -1/1 0/1 -16/29 -1/1 -11/20 -1/1 1/1 -17/31 -1/2 0/1 -23/42 -1/1 1/1 -6/11 1/1 -7/13 1/0 -8/15 -1/1 -1/2 -1/1 1/1 -8/17 -1/1 -7/15 -1/2 0/1 -6/13 0/1 -5/11 0/1 1/0 -9/20 -1/1 1/1 -4/9 -1/1 -11/25 -1/1 -2/3 -7/16 -1/1 -1/3 -3/7 -1/2 0/1 -11/26 0/1 -8/19 1/5 -13/31 0/1 1/2 -5/12 1/3 1/1 -12/29 1/1 -7/17 0/1 1/0 -9/22 1/3 1/1 -11/27 1/1 4/3 -2/5 -1/1 -5/13 0/1 -8/21 1/1 -19/50 5/7 1/1 -49/129 12/13 1/1 -79/208 1/1 -30/79 1/1 -11/29 1/1 1/0 -3/8 -1/1 1/1 -10/27 1/1 -27/73 3/2 2/1 -17/46 1/1 3/1 -7/19 1/1 1/0 -4/11 -1/1 -9/25 -1/1 0/1 -14/39 0/1 -19/53 0/1 1/0 -5/14 -1/1 1/1 -11/31 0/1 1/0 -6/17 -1/1 -13/37 0/1 1/0 -7/20 -1/1 1/1 -8/23 -1/1 -9/26 0/1 -1/3 0/1 1/0 -4/13 1/0 -7/23 -1/1 1/0 -3/10 -1/1 1/1 -11/37 -2/1 1/0 -19/64 -7/5 -1/1 -8/27 -1/1 -13/44 -1/1 -1/3 -18/61 -1/3 -23/78 0/1 -5/17 0/1 1/0 -7/24 -3/1 -1/1 -9/31 -1/2 0/1 -2/7 1/1 -9/32 1/3 1/1 -16/57 3/5 -7/25 1/1 2/1 -12/43 1/1 -5/18 1/1 3/1 -3/11 2/1 1/0 -7/26 1/0 -4/15 -3/1 -5/19 -1/1 1/0 -6/23 -1/1 -7/27 -1/1 -4/5 -1/4 -1/1 1/1 -3/13 1/0 -5/22 -5/1 -3/1 -12/53 -3/1 -7/31 -2/1 1/0 -2/9 -1/1 -7/32 -1/1 1/1 -5/23 -1/1 1/0 -8/37 1/1 -19/88 -1/1 1/1 -11/51 0/1 1/0 -3/14 -1/1 1/1 -1/5 0/1 1/0 -5/26 1/0 -4/21 -9/1 -11/58 -7/1 -5/1 -7/37 -6/1 1/0 -3/16 -5/1 -3/1 -5/27 -3/1 -2/1 -2/11 -3/1 -5/28 -5/1 -3/1 -3/17 -2/1 1/0 -4/23 -1/1 -9/52 1/0 -5/29 -3/1 1/0 -1/6 -3/1 -1/1 -3/19 -1/1 1/0 -2/13 1/0 -1/7 -2/1 1/0 -1/8 -5/3 -1/1 -2/17 -1/1 -3/26 -1/1 -1/9 -1/1 0/1 0/1 -1/1 1/7 -2/3 -1/2 2/13 -1/2 3/19 -1/1 -1/2 1/6 -1/1 -3/5 3/17 -2/3 -1/2 2/11 -3/5 3/16 -3/5 -5/9 4/21 -9/17 5/26 -1/2 1/5 -1/2 0/1 2/9 -1/1 3/13 -1/2 4/17 -3/7 5/21 -1/2 -2/5 6/25 -1/3 1/4 -1/1 -1/3 4/15 -3/5 7/26 -1/2 3/11 -1/2 -2/5 2/7 -1/3 7/24 -1/1 -3/5 12/41 -1/1 5/17 -1/2 0/1 8/27 -1/1 11/37 -2/3 -1/2 14/47 -5/9 3/10 -1/1 -1/3 7/23 -1/1 -1/2 4/13 -1/2 1/3 -1/2 0/1 7/20 -1/1 -1/3 13/37 -1/2 0/1 6/17 -1/1 5/14 -1/1 -1/3 19/53 -1/2 0/1 14/39 0/1 9/25 -1/1 0/1 4/11 -1/1 11/30 -3/7 -1/3 18/49 -1/3 7/19 -1/2 -1/3 17/46 -3/7 -1/3 10/27 -1/3 13/35 -1/4 0/1 3/8 -1/1 -1/3 5/13 0/1 7/18 -1/1 1/1 9/23 -1/1 1/0 20/51 -1/1 11/28 -1/1 -5/7 2/5 -1/1 11/27 -4/11 -1/3 20/49 -1/3 9/22 -1/3 -1/5 7/17 -1/2 0/1 5/12 -1/3 -1/5 18/43 -1/3 13/31 -1/4 0/1 21/50 -1/5 -3/17 8/19 -1/7 11/26 0/1 3/7 0/1 1/0 4/9 -1/1 5/11 -1/2 0/1 6/13 0/1 7/15 0/1 1/0 8/17 -1/1 1/2 -1/1 -1/3 7/13 -1/2 13/24 -3/7 -1/3 6/11 -1/3 17/31 0/1 1/0 28/51 -1/1 11/20 -1/1 -1/3 5/9 -1/1 0/1 14/25 -1/1 9/16 -1/1 -3/5 13/23 -1/1 -1/2 4/7 -3/5 15/26 -1/2 11/19 -1/2 -5/11 7/12 -1/1 -1/3 17/29 -1/1 -1/2 10/17 -1/1 3/5 -1/2 0/1 8/13 -1/2 13/21 -1/2 -4/9 31/50 -17/39 -3/7 80/129 -3/7 129/208 -3/7 49/79 -3/7 -20/47 18/29 -3/7 23/37 -5/12 -2/5 5/8 -3/7 -1/3 17/27 -2/5 -1/3 46/73 -3/11 75/119 -1/4 0/1 29/46 -1/3 -1/5 12/19 -1/3 7/11 -1/2 -2/5 16/25 -1/3 25/39 -1/3 34/53 -1/3 9/14 -1/3 -1/5 11/17 -1/2 0/1 13/20 -1/1 -1/3 2/3 -1/3 9/13 0/1 16/23 -1/1 23/33 -1/1 -1/2 30/43 -1/3 7/10 -1/1 -1/3 26/37 -1/3 19/27 -2/5 -1/3 31/44 -3/7 -1/3 12/17 -1/3 5/7 -1/2 0/1 18/25 -1/3 31/43 -2/5 -1/3 75/104 -1/3 44/61 -1/3 13/18 -1/3 -1/5 21/29 -1/3 -1/4 29/40 -1/3 -1/5 37/51 -1/4 0/1 8/11 -1/5 19/26 0/1 11/15 0/1 1/2 14/19 1/1 17/23 -1/1 1/0 20/27 -1/1 3/4 -1/1 -1/3 13/17 -1/4 0/1 10/13 0/1 7/9 -1/1 0/1 25/32 -1/1 -1/3 43/55 -1/2 0/1 61/78 0/1 18/23 -1/1 29/37 0/1 1/0 40/51 -1/1 11/14 -1/1 -3/5 15/19 -1/2 -3/7 34/43 -1/3 19/24 -5/13 -1/3 4/5 -1/3 21/26 0/1 17/21 0/1 1/2 30/37 -1/1 13/16 -1/1 1/1 22/27 -1/1 9/11 -1/2 0/1 14/17 -1/1 19/23 -1/1 -1/2 43/52 -1/2 24/29 -1/3 5/6 -1/1 -1/3 11/13 0/1 17/20 -1/1 1/1 6/7 -1/1 13/15 0/1 1/0 7/8 -1/1 -1/3 15/17 -1/4 0/1 23/26 0/1 8/9 -1/1 9/10 -1/1 -1/3 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(129,118,-598,-547) (-1/1,-9/10) -> (-19/88,-11/51) Hyperbolic Matrix(363,326,520,467) (-9/10,-8/9) -> (30/43,7/10) Hyperbolic Matrix(261,230,-884,-779) (-8/9,-7/8) -> (-13/44,-18/61) Hyperbolic Matrix(287,248,-390,-337) (-7/8,-6/7) -> (-14/19,-25/34) Hyperbolic Matrix(285,242,-338,-287) (-6/7,-11/13) -> (-11/13,-16/19) Parabolic Matrix(623,524,988,831) (-16/19,-5/6) -> (29/46,12/19) Hyperbolic Matrix(129,106,-286,-235) (-5/6,-9/11) -> (-5/11,-9/20) Hyperbolic Matrix(467,380,-832,-677) (-9/11,-13/16) -> (-9/16,-23/41) Hyperbolic Matrix(755,612,-1378,-1117) (-13/16,-17/21) -> (-17/31,-23/42) Hyperbolic Matrix(883,714,1092,883) (-17/21,-21/26) -> (21/26,17/21) Hyperbolic Matrix(209,168,260,209) (-21/26,-4/5) -> (4/5,21/26) Hyperbolic Matrix(287,226,-494,-389) (-4/5,-11/14) -> (-7/12,-18/31) Hyperbolic Matrix(857,672,-2886,-2263) (-11/14,-29/37) -> (-11/37,-19/64) Hyperbolic Matrix(1195,936,1924,1507) (-29/37,-18/23) -> (18/29,23/37) Hyperbolic Matrix(259,202,-468,-365) (-18/23,-7/9) -> (-5/9,-16/29) Hyperbolic Matrix(181,140,234,181) (-7/9,-10/13) -> (10/13,7/9) Hyperbolic Matrix(339,260,442,339) (-10/13,-13/17) -> (13/17,10/13) Hyperbolic Matrix(181,138,442,337) (-13/17,-3/4) -> (9/22,7/17) Hyperbolic Matrix(339,250,-598,-441) (-3/4,-14/19) -> (-4/7,-17/30) Hyperbolic Matrix(857,630,1378,1013) (-25/34,-11/15) -> (23/37,5/8) Hyperbolic Matrix(571,418,780,571) (-11/15,-19/26) -> (19/26,11/15) Hyperbolic Matrix(417,304,572,417) (-19/26,-8/11) -> (8/11,19/26) Hyperbolic Matrix(287,208,-1326,-961) (-8/11,-21/29) -> (-5/23,-8/37) Hyperbolic Matrix(365,264,936,677) (-21/29,-13/18) -> (7/18,9/23) Hyperbolic Matrix(25,18,-182,-131) (-13/18,-5/7) -> (-1/7,-1/8) Hyperbolic Matrix(79,56,-182,-129) (-5/7,-7/10) -> (-7/16,-3/7) Hyperbolic Matrix(233,162,-338,-235) (-7/10,-9/13) -> (-9/13,-11/16) Parabolic Matrix(443,304,494,339) (-11/16,-24/35) -> (8/9,9/10) Hyperbolic Matrix(1171,802,1482,1015) (-24/35,-13/19) -> (15/19,34/43) Hyperbolic Matrix(363,248,988,675) (-13/19,-2/3) -> (18/49,7/19) Hyperbolic Matrix(183,118,-442,-285) (-2/3,-9/14) -> (-5/12,-12/29) Hyperbolic Matrix(1949,1250,-3042,-1951) (-9/14,-25/39) -> (-25/39,-41/64) Parabolic Matrix(2835,1816,3614,2315) (-41/64,-16/25) -> (40/51,11/14) Hyperbolic Matrix(729,466,-1300,-831) (-16/25,-7/11) -> (-23/41,-14/25) Hyperbolic Matrix(79,50,-286,-181) (-7/11,-5/8) -> (-5/18,-3/11) Hyperbolic Matrix(363,226,416,259) (-5/8,-23/37) -> (13/15,7/8) Hyperbolic Matrix(1507,936,1924,1195) (-23/37,-18/29) -> (18/23,29/37) Hyperbolic Matrix(1899,1178,4654,2887) (-18/29,-49/79) -> (11/27,20/49) Hyperbolic Matrix(3951,2450,-10400,-6449) (-49/79,-31/50) -> (-19/50,-49/129) Hyperbolic Matrix(1091,676,2600,1611) (-31/50,-13/21) -> (13/31,21/50) Hyperbolic Matrix(337,208,546,337) (-13/21,-8/13) -> (8/13,13/21) Hyperbolic Matrix(79,48,130,79) (-8/13,-3/5) -> (3/5,8/13) Hyperbolic Matrix(27,16,-130,-77) (-3/5,-7/12) -> (-3/14,-1/5) Hyperbolic Matrix(441,256,1118,649) (-18/31,-29/50) -> (11/28,2/5) Hyperbolic Matrix(469,272,988,573) (-29/50,-40/69) -> (8/17,1/2) Hyperbolic Matrix(2157,1250,3094,1793) (-40/69,-11/19) -> (23/33,30/43) Hyperbolic Matrix(571,330,988,571) (-11/19,-15/26) -> (15/26,11/19) Hyperbolic Matrix(209,120,364,209) (-15/26,-4/7) -> (4/7,15/26) Hyperbolic Matrix(233,132,962,545) (-17/30,-30/53) -> (6/25,1/4) Hyperbolic Matrix(937,530,2392,1353) (-30/53,-13/23) -> (9/23,20/51) Hyperbolic Matrix(181,102,598,337) (-13/23,-9/16) -> (3/10,7/23) Hyperbolic Matrix(25,14,-234,-131) (-14/25,-5/9) -> (-1/9,0/1) Hyperbolic Matrix(363,200,-1040,-573) (-16/29,-11/20) -> (-7/20,-8/23) Hyperbolic Matrix(1067,586,-2886,-1585) (-11/20,-17/31) -> (-27/73,-17/46) Hyperbolic Matrix(545,298,-2522,-1379) (-23/42,-6/11) -> (-8/37,-19/88) Hyperbolic Matrix(181,98,-338,-183) (-6/11,-7/13) -> (-7/13,-8/15) Parabolic Matrix(129,68,442,233) (-8/15,-1/2) -> (7/24,12/41) Hyperbolic Matrix(391,186,494,235) (-1/2,-8/17) -> (34/43,19/24) Hyperbolic Matrix(311,146,884,415) (-8/17,-7/15) -> (13/37,6/17) Hyperbolic Matrix(181,84,390,181) (-7/15,-6/13) -> (6/13,7/15) Hyperbolic Matrix(131,60,286,131) (-6/13,-5/11) -> (5/11,6/13) Hyperbolic Matrix(103,46,-468,-209) (-9/20,-4/9) -> (-2/9,-7/32) Hyperbolic Matrix(363,160,-1300,-573) (-4/9,-11/25) -> (-7/25,-12/43) Hyperbolic Matrix(155,68,-832,-365) (-11/25,-7/16) -> (-3/16,-5/27) Hyperbolic Matrix(155,66,364,155) (-3/7,-11/26) -> (11/26,3/7) Hyperbolic Matrix(417,176,988,417) (-11/26,-8/19) -> (8/19,11/26) Hyperbolic Matrix(233,98,-806,-339) (-8/19,-13/31) -> (-9/31,-2/7) Hyperbolic Matrix(287,120,-806,-337) (-13/31,-5/12) -> (-5/14,-11/31) Hyperbolic Matrix(155,64,-884,-365) (-12/29,-7/17) -> (-3/17,-4/23) Hyperbolic Matrix(337,138,442,181) (-7/17,-9/22) -> (3/4,13/17) Hyperbolic Matrix(181,74,-702,-287) (-9/22,-11/27) -> (-7/27,-1/4) Hyperbolic Matrix(467,190,-1664,-677) (-11/27,-2/5) -> (-16/57,-7/25) Hyperbolic Matrix(129,50,-338,-131) (-2/5,-5/13) -> (-5/13,-8/21) Parabolic Matrix(599,228,754,287) (-8/21,-19/50) -> (19/24,4/5) Hyperbolic Matrix(26833,10192,43264,16433) (-49/129,-79/208) -> (129/208,49/79) Hyperbolic Matrix(26831,10190,43264,16431) (-79/208,-30/79) -> (80/129,129/208) Hyperbolic Matrix(1923,730,2600,987) (-30/79,-11/29) -> (17/23,20/27) Hyperbolic Matrix(545,206,754,285) (-11/29,-3/8) -> (13/18,21/29) Hyperbolic Matrix(415,154,-1404,-521) (-3/8,-10/27) -> (-8/27,-13/44) Hyperbolic Matrix(573,212,2392,885) (-10/27,-27/73) -> (5/21,6/25) Hyperbolic Matrix(157,58,988,365) (-17/46,-7/19) -> (3/19,1/6) Hyperbolic Matrix(131,48,-494,-181) (-7/19,-4/11) -> (-4/15,-5/19) Hyperbolic Matrix(105,38,-572,-207) (-4/11,-9/25) -> (-5/27,-2/11) Hyperbolic Matrix(701,252,1950,701) (-9/25,-14/39) -> (14/39,9/25) Hyperbolic Matrix(1483,532,4134,1483) (-14/39,-19/53) -> (19/53,14/39) Hyperbolic Matrix(2055,736,2834,1015) (-19/53,-5/14) -> (29/40,37/51) Hyperbolic Matrix(209,74,884,313) (-11/31,-6/17) -> (4/17,5/21) Hyperbolic Matrix(415,146,884,311) (-6/17,-13/37) -> (7/15,8/17) Hyperbolic Matrix(547,192,-2886,-1013) (-13/37,-7/20) -> (-11/58,-7/37) Hyperbolic Matrix(1871,650,2392,831) (-8/23,-9/26) -> (61/78,18/23) Hyperbolic Matrix(1301,448,1664,573) (-9/26,-1/3) -> (43/55,61/78) Hyperbolic Matrix(25,8,78,25) (-1/3,-4/13) -> (4/13,1/3) Hyperbolic Matrix(183,56,598,183) (-4/13,-7/23) -> (7/23,4/13) Hyperbolic Matrix(337,102,598,181) (-7/23,-3/10) -> (9/16,13/23) Hyperbolic Matrix(181,54,-962,-287) (-3/10,-11/37) -> (-7/37,-3/16) Hyperbolic Matrix(2419,718,3770,1119) (-19/64,-8/27) -> (34/53,9/14) Hyperbolic Matrix(2027,598,2288,675) (-18/61,-23/78) -> (23/26,8/9) Hyperbolic Matrix(1561,460,1768,521) (-23/78,-5/17) -> (15/17,23/26) Hyperbolic Matrix(157,46,-884,-259) (-5/17,-7/24) -> (-5/28,-3/17) Hyperbolic Matrix(1273,370,2054,597) (-7/24,-9/31) -> (13/21,31/50) Hyperbolic Matrix(311,88,364,103) (-2/7,-9/32) -> (17/20,6/7) Hyperbolic Matrix(755,212,-3978,-1117) (-9/32,-16/57) -> (-4/21,-11/58) Hyperbolic Matrix(79,22,-650,-181) (-12/43,-5/18) -> (-1/8,-2/17) Hyperbolic Matrix(155,42,572,155) (-3/11,-7/26) -> (7/26,3/11) Hyperbolic Matrix(209,56,780,209) (-7/26,-4/15) -> (4/15,7/26) Hyperbolic Matrix(833,218,1196,313) (-5/19,-6/23) -> (16/23,23/33) Hyperbolic Matrix(1613,420,2600,677) (-6/23,-7/27) -> (49/79,18/29) Hyperbolic Matrix(77,18,-338,-79) (-1/4,-3/13) -> (-3/13,-5/22) Parabolic Matrix(599,136,806,183) (-5/22,-12/53) -> (20/27,3/4) Hyperbolic Matrix(1769,400,3224,729) (-12/53,-7/31) -> (17/31,28/51) Hyperbolic Matrix(675,152,1612,363) (-7/31,-2/9) -> (18/43,13/31) Hyperbolic Matrix(183,40,-1066,-233) (-7/32,-5/23) -> (-5/29,-1/6) Hyperbolic Matrix(521,112,1456,313) (-11/51,-3/14) -> (5/14,19/53) Hyperbolic Matrix(51,10,260,51) (-1/5,-5/26) -> (5/26,1/5) Hyperbolic Matrix(209,40,1092,209) (-5/26,-4/21) -> (4/21,5/26) Hyperbolic Matrix(311,56,572,103) (-2/11,-5/28) -> (13/24,6/11) Hyperbolic Matrix(2237,388,2704,469) (-4/23,-9/52) -> (43/52,24/29) Hyperbolic Matrix(2235,386,2704,467) (-9/52,-5/29) -> (19/23,43/52) Hyperbolic Matrix(365,58,988,157) (-1/6,-3/19) -> (7/19,17/46) Hyperbolic Matrix(77,12,494,77) (-3/19,-2/13) -> (2/13,3/19) Hyperbolic Matrix(27,4,182,27) (-2/13,-1/7) -> (1/7,2/13) Hyperbolic Matrix(2419,282,3354,391) (-2/17,-3/26) -> (75/104,44/61) Hyperbolic Matrix(1481,168,2054,233) (-3/26,-1/9) -> (31/43,75/104) Hyperbolic Matrix(131,-18,182,-25) (0/1,1/7) -> (5/7,18/25) Hyperbolic Matrix(287,-50,442,-77) (1/6,3/17) -> (11/17,13/20) Hyperbolic Matrix(259,-46,884,-157) (3/17,2/11) -> (12/41,5/17) Hyperbolic Matrix(493,-92,702,-131) (2/11,3/16) -> (7/10,26/37) Hyperbolic Matrix(287,-54,962,-181) (3/16,4/21) -> (14/47,3/10) Hyperbolic Matrix(77,-16,130,-27) (1/5,2/9) -> (10/17,3/5) Hyperbolic Matrix(79,-18,338,-77) (2/9,3/13) -> (3/13,4/17) Parabolic Matrix(181,-48,494,-131) (1/4,4/15) -> (4/11,11/30) Hyperbolic Matrix(181,-50,286,-79) (3/11,2/7) -> (12/19,7/11) Hyperbolic Matrix(339,-98,806,-233) (2/7,7/24) -> (21/50,8/19) Hyperbolic Matrix(521,-154,1404,-415) (5/17,8/27) -> (10/27,13/35) Hyperbolic Matrix(2263,-672,2886,-857) (8/27,11/37) -> (29/37,40/51) Hyperbolic Matrix(5227,-1556,8294,-2469) (11/37,14/47) -> (46/73,75/119) Hyperbolic Matrix(935,-326,1196,-417) (1/3,7/20) -> (25/32,43/55) Hyperbolic Matrix(2573,-902,4082,-1431) (7/20,13/37) -> (75/119,29/46) Hyperbolic Matrix(337,-120,806,-287) (6/17,5/14) -> (5/12,18/43) Hyperbolic Matrix(859,-310,1222,-441) (9/25,4/11) -> (26/37,19/27) Hyperbolic Matrix(1041,-382,2548,-935) (11/30,18/49) -> (20/49,9/22) Hyperbolic Matrix(1585,-586,2886,-1067) (17/46,10/27) -> (28/51,11/20) Hyperbolic Matrix(365,-136,416,-155) (13/35,3/8) -> (7/8,15/17) Hyperbolic Matrix(131,-50,338,-129) (3/8,5/13) -> (5/13,7/18) Parabolic Matrix(3821,-1500,6162,-2419) (20/51,11/28) -> (31/50,80/129) Hyperbolic Matrix(1327,-540,2106,-857) (2/5,11/27) -> (17/27,46/73) Hyperbolic Matrix(285,-118,442,-183) (7/17,5/12) -> (9/14,11/17) Hyperbolic Matrix(129,-56,182,-79) (3/7,4/9) -> (12/17,5/7) Hyperbolic Matrix(235,-106,286,-129) (4/9,5/11) -> (9/11,14/17) Hyperbolic Matrix(183,-98,338,-181) (1/2,7/13) -> (7/13,13/24) Parabolic Matrix(1117,-612,1378,-755) (6/11,17/31) -> (17/21,30/37) Hyperbolic Matrix(365,-202,468,-259) (11/20,5/9) -> (7/9,25/32) Hyperbolic Matrix(937,-524,1300,-727) (5/9,14/25) -> (18/25,31/43) Hyperbolic Matrix(677,-380,832,-467) (14/25,9/16) -> (13/16,22/27) Hyperbolic Matrix(441,-250,598,-339) (13/23,4/7) -> (14/19,17/23) Hyperbolic Matrix(389,-226,494,-287) (11/19,7/12) -> (11/14,15/19) Hyperbolic Matrix(1093,-640,1508,-883) (7/12,17/29) -> (21/29,29/40) Hyperbolic Matrix(729,-428,884,-519) (17/29,10/17) -> (14/17,19/23) Hyperbolic Matrix(989,-622,1404,-883) (5/8,17/27) -> (19/27,31/44) Hyperbolic Matrix(467,-298,572,-365) (7/11,16/25) -> (22/27,9/11) Hyperbolic Matrix(1951,-1250,3042,-1949) (16/25,25/39) -> (25/39,34/53) Parabolic Matrix(495,-322,598,-389) (13/20,2/3) -> (24/29,5/6) Hyperbolic Matrix(235,-162,338,-233) (2/3,9/13) -> (9/13,16/23) Parabolic Matrix(2157,-1520,2990,-2107) (31/44,12/17) -> (44/61,13/18) Hyperbolic Matrix(521,-378,572,-415) (37/51,8/11) -> (10/11,1/1) Hyperbolic Matrix(337,-248,390,-287) (11/15,14/19) -> (6/7,13/15) Hyperbolic Matrix(493,-400,546,-443) (30/37,13/16) -> (9/10,10/11) Hyperbolic Matrix(287,-242,338,-285) (5/6,11/13) -> (11/13,17/20) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(129,118,-598,-547) -> Matrix(1,0,0,1) Matrix(363,326,520,467) -> Matrix(1,0,-2,1) Matrix(261,230,-884,-779) -> Matrix(1,0,-2,1) Matrix(287,248,-390,-337) -> Matrix(1,0,-2,1) Matrix(285,242,-338,-287) -> Matrix(1,0,2,1) Matrix(623,524,988,831) -> Matrix(1,0,-4,1) Matrix(129,106,-286,-235) -> Matrix(1,0,0,1) Matrix(467,380,-832,-677) -> Matrix(3,2,-2,-1) Matrix(755,612,-1378,-1117) -> Matrix(1,0,2,1) Matrix(883,714,1092,883) -> Matrix(1,0,6,1) Matrix(209,168,260,209) -> Matrix(1,0,-4,1) Matrix(287,226,-494,-389) -> Matrix(1,2,0,1) Matrix(857,672,-2886,-2263) -> Matrix(3,2,-2,-1) Matrix(1195,936,1924,1507) -> Matrix(1,-2,-2,5) Matrix(259,202,-468,-365) -> Matrix(1,0,0,1) Matrix(181,140,234,181) -> Matrix(1,0,0,1) Matrix(339,260,442,339) -> Matrix(1,0,-6,1) Matrix(181,138,442,337) -> Matrix(1,0,-4,1) Matrix(339,250,-598,-441) -> Matrix(3,2,-2,-1) Matrix(857,630,1378,1013) -> Matrix(3,2,-8,-5) Matrix(571,418,780,571) -> Matrix(1,0,6,1) Matrix(417,304,572,417) -> Matrix(1,0,-8,1) Matrix(287,208,-1326,-961) -> Matrix(1,0,-2,1) Matrix(365,264,936,677) -> Matrix(1,0,-2,1) Matrix(25,18,-182,-131) -> Matrix(1,-2,0,1) Matrix(79,56,-182,-129) -> Matrix(1,0,-2,1) Matrix(233,162,-338,-235) -> Matrix(1,0,2,1) Matrix(443,304,494,339) -> Matrix(1,0,-4,1) Matrix(1171,802,1482,1015) -> Matrix(5,-2,-12,5) Matrix(363,248,988,675) -> Matrix(1,0,-4,1) Matrix(183,118,-442,-285) -> Matrix(1,0,0,1) Matrix(1949,1250,-3042,-1951) -> Matrix(7,-6,6,-5) Matrix(2835,1816,3614,2315) -> Matrix(3,-4,-2,3) Matrix(729,466,-1300,-831) -> Matrix(3,-4,-2,3) Matrix(79,50,-286,-181) -> Matrix(1,0,0,1) Matrix(363,226,416,259) -> Matrix(1,-2,-2,5) Matrix(1507,936,1924,1195) -> Matrix(1,-2,-2,5) Matrix(1899,1178,4654,2887) -> Matrix(3,-8,-10,27) Matrix(3951,2450,-10400,-6449) -> Matrix(5,-16,6,-19) Matrix(1091,676,2600,1611) -> Matrix(1,-4,-4,17) Matrix(337,208,546,337) -> Matrix(1,-8,-2,17) Matrix(79,48,130,79) -> Matrix(1,0,-2,1) Matrix(27,16,-130,-77) -> Matrix(1,0,0,1) Matrix(441,256,1118,649) -> Matrix(1,-2,-2,5) Matrix(469,272,988,573) -> Matrix(1,-4,0,1) Matrix(2157,1250,3094,1793) -> Matrix(1,-4,-2,9) Matrix(571,330,988,571) -> Matrix(1,-10,-2,21) Matrix(209,120,364,209) -> Matrix(1,6,-2,-11) Matrix(233,132,962,545) -> Matrix(1,2,-4,-7) Matrix(937,530,2392,1353) -> Matrix(1,0,0,1) Matrix(181,102,598,337) -> Matrix(1,2,-2,-3) Matrix(25,14,-234,-131) -> Matrix(1,0,0,1) Matrix(363,200,-1040,-573) -> Matrix(1,0,0,1) Matrix(1067,586,-2886,-1585) -> Matrix(1,2,0,1) Matrix(545,298,-2522,-1379) -> Matrix(1,0,0,1) Matrix(181,98,-338,-183) -> Matrix(1,-2,0,1) Matrix(129,68,442,233) -> Matrix(1,2,-2,-3) Matrix(391,186,494,235) -> Matrix(3,2,-8,-5) Matrix(311,146,884,415) -> Matrix(1,0,0,1) Matrix(181,84,390,181) -> Matrix(1,0,2,1) Matrix(131,60,286,131) -> Matrix(1,0,-2,1) Matrix(103,46,-468,-209) -> Matrix(1,0,0,1) Matrix(363,160,-1300,-573) -> Matrix(1,0,2,1) Matrix(155,68,-832,-365) -> Matrix(7,4,-2,-1) Matrix(155,66,364,155) -> Matrix(1,0,2,1) Matrix(417,176,988,417) -> Matrix(1,0,-12,1) Matrix(233,98,-806,-339) -> Matrix(1,0,-4,1) Matrix(287,120,-806,-337) -> Matrix(1,0,-2,1) Matrix(155,64,-884,-365) -> Matrix(1,-2,0,1) Matrix(337,138,442,181) -> Matrix(1,0,-4,1) Matrix(181,74,-702,-287) -> Matrix(1,0,-2,1) Matrix(467,190,-1664,-677) -> Matrix(1,-2,2,-3) Matrix(129,50,-338,-131) -> Matrix(1,0,2,1) Matrix(599,228,754,287) -> Matrix(1,0,-4,1) Matrix(26833,10192,43264,16433) -> Matrix(59,-56,-138,131) Matrix(26831,10190,43264,16431) -> Matrix(55,-58,-128,135) Matrix(1923,730,2600,987) -> Matrix(1,-2,0,1) Matrix(545,206,754,285) -> Matrix(1,0,-4,1) Matrix(415,154,-1404,-521) -> Matrix(1,0,-2,1) Matrix(573,212,2392,885) -> Matrix(3,-4,-8,11) Matrix(157,58,988,365) -> Matrix(1,0,-2,1) Matrix(131,48,-494,-181) -> Matrix(1,-2,0,1) Matrix(105,38,-572,-207) -> Matrix(1,-2,0,1) Matrix(701,252,1950,701) -> Matrix(1,0,0,1) Matrix(1483,532,4134,1483) -> Matrix(1,0,-2,1) Matrix(2055,736,2834,1015) -> Matrix(1,0,-4,1) Matrix(209,74,884,313) -> Matrix(1,-2,-2,5) Matrix(415,146,884,311) -> Matrix(1,0,0,1) Matrix(547,192,-2886,-1013) -> Matrix(1,-6,0,1) Matrix(1871,650,2392,831) -> Matrix(1,0,0,1) Matrix(1301,448,1664,573) -> Matrix(1,0,-2,1) Matrix(25,8,78,25) -> Matrix(1,0,-2,1) Matrix(183,56,598,183) -> Matrix(1,2,-2,-3) Matrix(337,102,598,181) -> Matrix(1,2,-2,-3) Matrix(181,54,-962,-287) -> Matrix(1,-4,0,1) Matrix(2419,718,3770,1119) -> Matrix(3,4,-10,-13) Matrix(2027,598,2288,675) -> Matrix(1,0,2,1) Matrix(1561,460,1768,521) -> Matrix(1,0,-4,1) Matrix(157,46,-884,-259) -> Matrix(1,-2,0,1) Matrix(1273,370,2054,597) -> Matrix(7,4,-16,-9) Matrix(311,88,364,103) -> Matrix(1,0,-2,1) Matrix(755,212,-3978,-1117) -> Matrix(13,-6,-2,1) Matrix(79,22,-650,-181) -> Matrix(3,-4,-2,3) Matrix(155,42,572,155) -> Matrix(1,-4,-2,9) Matrix(209,56,780,209) -> Matrix(1,6,-2,-11) Matrix(833,218,1196,313) -> Matrix(1,2,-2,-3) Matrix(1613,420,2600,677) -> Matrix(5,8,-12,-19) Matrix(77,18,-338,-79) -> Matrix(1,-4,0,1) Matrix(599,136,806,183) -> Matrix(1,4,-2,-7) Matrix(1769,400,3224,729) -> Matrix(1,2,0,1) Matrix(675,152,1612,363) -> Matrix(1,2,-4,-7) Matrix(183,40,-1066,-233) -> Matrix(1,-2,0,1) Matrix(521,112,1456,313) -> Matrix(1,0,-2,1) Matrix(51,10,260,51) -> Matrix(1,0,-2,1) Matrix(209,40,1092,209) -> Matrix(1,18,-2,-35) Matrix(311,56,572,103) -> Matrix(1,2,-2,-3) Matrix(2237,388,2704,469) -> Matrix(1,0,-2,1) Matrix(2235,386,2704,467) -> Matrix(1,4,-2,-7) Matrix(365,58,988,157) -> Matrix(1,0,-2,1) Matrix(77,12,494,77) -> Matrix(1,2,-2,-3) Matrix(27,4,182,27) -> Matrix(1,4,-2,-7) Matrix(2419,282,3354,391) -> Matrix(7,8,-22,-25) Matrix(1481,168,2054,233) -> Matrix(3,2,-8,-5) Matrix(131,-18,182,-25) -> Matrix(3,2,-8,-5) Matrix(287,-50,442,-77) -> Matrix(3,2,-8,-5) Matrix(259,-46,884,-157) -> Matrix(3,2,-8,-5) Matrix(493,-92,702,-131) -> Matrix(7,4,-16,-9) Matrix(287,-54,962,-181) -> Matrix(7,4,-16,-9) Matrix(77,-16,130,-27) -> Matrix(1,0,0,1) Matrix(79,-18,338,-77) -> Matrix(7,4,-16,-9) Matrix(181,-48,494,-131) -> Matrix(3,2,-8,-5) Matrix(181,-50,286,-79) -> Matrix(1,0,0,1) Matrix(339,-98,806,-233) -> Matrix(1,0,-4,1) Matrix(521,-154,1404,-415) -> Matrix(1,0,-2,1) Matrix(2263,-672,2886,-857) -> Matrix(3,2,-2,-1) Matrix(5227,-1556,8294,-2469) -> Matrix(3,2,-14,-9) Matrix(935,-326,1196,-417) -> Matrix(1,0,0,1) Matrix(2573,-902,4082,-1431) -> Matrix(1,0,-2,1) Matrix(337,-120,806,-287) -> Matrix(1,0,-2,1) Matrix(859,-310,1222,-441) -> Matrix(3,2,-8,-5) Matrix(1041,-382,2548,-935) -> Matrix(5,2,-18,-7) Matrix(1585,-586,2886,-1067) -> Matrix(5,2,-8,-3) Matrix(365,-136,416,-155) -> Matrix(1,0,0,1) Matrix(131,-50,338,-129) -> Matrix(1,0,2,1) Matrix(3821,-1500,6162,-2419) -> Matrix(19,16,-44,-37) Matrix(1327,-540,2106,-857) -> Matrix(5,2,-18,-7) Matrix(285,-118,442,-183) -> Matrix(1,0,0,1) Matrix(129,-56,182,-79) -> Matrix(1,0,-2,1) Matrix(235,-106,286,-129) -> Matrix(1,0,0,1) Matrix(183,-98,338,-181) -> Matrix(3,2,-8,-5) Matrix(1117,-612,1378,-755) -> Matrix(1,0,2,1) Matrix(365,-202,468,-259) -> Matrix(1,0,0,1) Matrix(937,-524,1300,-727) -> Matrix(3,2,-8,-5) Matrix(677,-380,832,-467) -> Matrix(3,2,-2,-1) Matrix(441,-250,598,-339) -> Matrix(3,2,-2,-1) Matrix(389,-226,494,-287) -> Matrix(5,2,-8,-3) Matrix(1093,-640,1508,-883) -> Matrix(1,0,-2,1) Matrix(729,-428,884,-519) -> Matrix(1,0,0,1) Matrix(989,-622,1404,-883) -> Matrix(1,0,0,1) Matrix(467,-298,572,-365) -> Matrix(5,2,-8,-3) Matrix(1951,-1250,3042,-1949) -> Matrix(17,6,-54,-19) Matrix(495,-322,598,-389) -> Matrix(1,0,0,1) Matrix(235,-162,338,-233) -> Matrix(1,0,2,1) Matrix(2157,-1520,2990,-2107) -> Matrix(5,2,-18,-7) Matrix(521,-378,572,-415) -> Matrix(1,0,2,1) Matrix(337,-248,390,-287) -> Matrix(1,0,-2,1) Matrix(493,-400,546,-443) -> Matrix(1,0,-2,1) Matrix(287,-242,338,-285) -> 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): 36 Degree of the the map X: 36 Degree of the the map Y: 168 ----------------------------------------------------------------------- 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.