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 -10/1 -8/1 -13/2 -6/1 -14/3 -4/1 -13/4 -39/14 -13/6 -2/1 -13/8 -26/17 -13/10 -26/23 0/1 1/1 13/11 26/21 13/10 26/19 13/9 3/2 39/25 13/8 26/15 13/7 2/1 13/6 26/11 5/2 13/5 208/79 39/14 3/1 13/4 27/8 7/2 26/7 4/1 13/3 9/2 14/3 19/4 5/1 26/5 21/4 11/2 23/4 52/9 6/1 13/2 7/1 15/2 8/1 17/2 26/3 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 0/1 -9/1 0/1 1/1 -8/1 0/1 -7/1 0/1 1/3 -13/2 1/2 -19/3 2/3 1/1 -6/1 0/1 -11/2 1/2 1/1 -16/3 0/1 -21/4 -1/2 0/1 -26/5 0/1 -5/1 0/1 1/3 -14/3 0/1 -37/8 0/1 1/2 -23/5 0/1 1/3 -9/2 1/3 1/2 -13/3 1/2 -17/4 1/2 2/3 -4/1 0/1 -19/5 0/1 1/1 -34/9 0/1 -15/4 -1/2 0/1 -26/7 0/1 -11/3 0/1 1/5 -29/8 0/1 1/6 -18/5 2/7 -7/2 0/1 1/2 -10/3 2/5 -13/4 1/2 -16/5 2/3 -35/11 2/3 1/1 -19/6 2/3 3/4 -3/1 0/1 1/1 -14/5 0/1 -39/14 1/4 -64/23 2/7 -25/9 0/1 1/3 -11/4 1/4 1/3 -8/3 2/5 -37/14 2/5 5/12 -29/11 2/5 3/7 -79/30 23/54 3/7 -50/19 10/23 -21/8 4/9 1/2 -13/5 1/2 -5/2 1/2 1/1 -12/5 0/1 -31/13 -1/1 0/1 -50/21 -2/7 -69/29 -1/5 0/1 -19/8 -1/6 0/1 -26/11 0/1 -7/3 0/1 1/5 -30/13 0/1 -53/23 6/31 1/5 -23/10 2/9 1/4 -16/7 2/7 -41/18 3/10 1/3 -25/11 2/7 1/3 -9/4 1/3 3/8 -29/13 1/3 2/5 -20/9 2/5 -31/14 3/8 2/5 -42/19 2/5 -11/5 2/5 3/7 -13/6 1/2 -15/7 4/7 3/5 -2/1 0/1 -17/9 2/5 3/7 -15/8 4/9 1/2 -13/7 1/2 -11/6 1/2 3/5 -20/11 2/3 -9/5 4/5 1/1 -25/14 1/1 3/2 -16/9 2/1 -7/4 0/1 1/0 -26/15 0/1 -19/11 0/1 1/7 -31/18 0/1 1/4 -12/7 0/1 -29/17 0/1 1/1 -17/10 0/1 1/4 -22/13 2/7 -27/16 1/3 3/8 -5/3 1/3 2/5 -13/8 1/2 -21/13 7/13 6/11 -50/31 16/29 -129/80 71/128 5/9 -208/129 5/9 -79/49 5/9 44/79 -29/18 9/16 4/7 -8/5 2/3 -27/17 4/5 1/1 -73/46 0/1 1/0 -46/29 0/1 -19/12 1/2 2/3 -11/7 0/1 1/1 -25/16 1/1 1/0 -39/25 1/0 -53/34 0/1 1/0 -14/9 0/1 -31/20 0/1 1/2 -17/11 0/1 1/1 -37/24 1/2 2/3 -20/13 0/1 -23/15 0/1 1/1 -26/17 0/1 -3/2 0/1 1/2 -13/9 1/2 -23/16 1/2 8/15 -10/7 4/7 -37/26 5/8 2/3 -64/45 2/3 -27/19 4/7 3/5 -44/31 2/3 -61/43 7/11 2/3 -78/55 2/3 -17/12 1/2 2/3 -24/17 4/7 -31/22 5/8 2/3 -7/5 2/3 1/1 -32/23 4/5 -57/41 2/3 1/1 -25/18 1/2 1/1 -43/31 8/9 1/1 -18/13 0/1 -11/8 3/4 1/1 -26/19 1/1 -15/11 1/1 2/1 -19/14 0/1 1/0 -23/17 2/3 1/1 -27/20 1/1 5/4 -4/3 0/1 -13/10 1/2 -22/17 6/11 -53/41 5/9 24/43 -31/24 1/2 4/7 -9/7 4/7 3/5 -32/25 2/3 -23/18 2/3 3/4 -37/29 2/3 1/1 -88/69 2/3 -51/40 1/2 2/3 -14/11 2/3 -5/4 3/4 1/1 -26/21 1/1 -21/17 1/1 8/7 -58/47 6/5 -37/30 5/4 4/3 -16/13 2/1 -27/22 1/1 3/2 -11/9 1/1 2/1 -28/23 -2/1 -17/14 0/1 1/0 -23/19 -1/3 0/1 -52/43 0/1 -29/24 0/1 1/6 -6/5 0/1 -19/16 2/5 1/2 -13/11 1/2 -7/6 1/2 2/3 -8/7 4/5 -17/15 12/13 1/1 -26/23 1/1 -9/8 1/1 5/4 -1/1 0/1 1/1 0/1 0/1 1/1 0/1 1/3 7/6 2/5 1/2 13/11 1/2 19/16 1/2 2/3 6/5 0/1 17/14 0/1 1/4 11/9 2/7 1/3 16/13 2/7 21/17 8/25 1/3 26/21 1/3 5/4 1/3 3/8 9/7 3/7 4/9 13/10 1/2 17/13 3/5 2/3 21/16 1/2 2/3 25/19 6/7 1/1 4/3 0/1 15/11 2/7 1/3 26/19 1/3 11/8 1/3 3/8 7/5 1/3 2/5 24/17 4/9 41/29 0/1 1/3 17/12 2/5 1/2 27/19 3/7 4/9 37/26 2/5 5/12 47/33 14/33 3/7 10/7 4/9 23/16 8/17 1/2 13/9 1/2 3/2 0/1 1/2 20/13 0/1 37/24 2/5 1/2 17/11 0/1 1/3 14/9 0/1 53/34 0/1 1/4 39/25 1/4 25/16 1/4 1/3 11/7 0/1 1/3 30/19 2/5 49/31 1/3 4/11 19/12 2/5 1/2 46/29 0/1 27/17 1/3 4/11 35/22 3/8 2/5 8/5 2/5 13/8 1/2 18/11 6/11 23/14 4/7 7/12 51/31 28/47 3/5 28/17 8/13 5/3 2/3 1/1 27/16 3/4 1/1 49/29 1/1 4/3 22/13 2/1 17/10 0/1 1/0 12/7 0/1 43/25 0/1 1/1 31/18 0/1 1/0 50/29 -2/3 19/11 -1/3 0/1 26/15 0/1 7/4 0/1 1/4 9/5 1/3 4/11 11/6 3/7 1/2 13/7 1/2 15/8 1/2 4/7 17/9 3/5 2/3 2/1 0/1 13/6 1/2 24/11 6/11 11/5 3/5 2/3 31/14 2/3 3/4 51/23 1/1 2/1 20/9 2/3 9/4 3/4 1/1 25/11 1/1 2/1 16/7 2/1 23/10 -2/1 1/0 7/3 -1/1 0/1 26/11 0/1 19/8 0/1 1/10 12/5 0/1 29/12 0/1 1/2 17/7 1/5 2/9 5/2 1/3 1/2 13/5 1/2 21/8 1/2 4/7 50/19 10/17 129/49 46/77 3/5 208/79 3/5 79/30 3/5 23/38 29/11 3/5 2/3 37/14 5/8 2/3 8/3 2/3 27/10 1/2 1/1 73/27 0/1 1/1 119/44 4/3 3/2 46/17 2/1 19/7 0/1 1/1 11/4 1/1 1/0 25/9 0/1 1/1 39/14 1/0 53/19 -2/1 -1/1 14/5 0/1 17/6 0/1 1/0 20/7 0/1 3/1 0/1 1/3 13/4 1/2 23/7 4/7 3/5 33/10 5/8 2/3 43/13 3/5 2/3 10/3 2/3 37/11 2/3 1/1 27/8 3/4 1/1 44/13 4/5 17/5 1/1 4/3 7/2 0/1 1/2 25/7 2/3 1/1 43/12 7/8 1/1 104/29 1/1 61/17 1/1 10/9 18/5 2/1 29/8 -1/2 0/1 40/11 0/1 51/14 0/1 1/0 11/3 -1/1 0/1 26/7 0/1 15/4 0/1 1/6 19/5 0/1 1/3 23/6 1/4 2/7 27/7 1/3 6/17 4/1 0/1 17/4 2/5 1/2 13/3 1/2 9/2 1/2 1/1 32/7 0/1 55/12 0/1 1/0 78/17 0/1 23/5 0/1 1/1 37/8 0/1 1/2 51/11 1/1 2/1 14/3 0/1 19/4 0/1 1/6 43/9 0/1 1/5 24/5 2/7 5/1 0/1 1/1 26/5 0/1 21/4 0/1 1/6 37/7 0/1 1/3 16/3 0/1 27/5 0/1 1/3 11/2 1/3 1/2 17/3 1/1 2/1 23/4 -1/2 0/1 52/9 0/1 29/5 0/1 1/7 6/1 0/1 13/2 1/2 20/3 2/3 7/1 0/1 1/1 15/2 0/1 1/4 8/1 0/1 17/2 0/1 1/0 26/3 0/1 9/1 0/1 1/3 10/1 0/1 11/1 0/1 1/1 1/0 0/1 1/2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(51,598,-40,-469) (-10/1,1/0) -> (-88/69,-51/40) Hyperbolic Matrix(53,520,16,157) (-10/1,-9/1) -> (43/13,10/3) Hyperbolic Matrix(105,884,-74,-623) (-9/1,-8/1) -> (-44/31,-61/43) Hyperbolic Matrix(53,390,-14,-103) (-8/1,-7/1) -> (-19/5,-34/9) Hyperbolic Matrix(51,338,-8,-53) (-7/1,-13/2) -> (-13/2,-19/3) Parabolic Matrix(157,988,58,365) (-19/3,-6/1) -> (46/17,19/7) Hyperbolic Matrix(51,286,-28,-157) (-6/1,-11/2) -> (-11/6,-20/11) Hyperbolic Matrix(155,832,-68,-365) (-11/2,-16/3) -> (-16/7,-41/18) Hyperbolic Matrix(261,1378,-118,-623) (-16/3,-21/4) -> (-31/14,-42/19) Hyperbolic Matrix(209,1092,40,209) (-21/4,-26/5) -> (26/5,21/4) Hyperbolic Matrix(51,260,10,51) (-26/5,-5/1) -> (5/1,26/5) Hyperbolic Matrix(105,494,-44,-207) (-5/1,-14/3) -> (-12/5,-31/13) Hyperbolic Matrix(623,2886,-438,-2029) (-14/3,-37/8) -> (-37/26,-64/45) Hyperbolic Matrix(417,1924,158,729) (-37/8,-23/5) -> (29/11,37/14) Hyperbolic Matrix(103,468,-46,-209) (-23/5,-9/2) -> (-9/4,-29/13) Hyperbolic Matrix(53,234,12,53) (-9/2,-13/3) -> (13/3,9/2) Hyperbolic Matrix(103,442,24,103) (-13/3,-17/4) -> (17/4,13/3) Hyperbolic Matrix(105,442,62,261) (-17/4,-4/1) -> (22/13,17/10) Hyperbolic Matrix(157,598,-68,-259) (-4/1,-19/5) -> (-7/3,-30/13) Hyperbolic Matrix(365,1378,138,521) (-34/9,-15/4) -> (37/14,8/3) Hyperbolic Matrix(209,780,56,209) (-15/4,-26/7) -> (26/7,15/4) Hyperbolic Matrix(155,572,42,155) (-26/7,-11/3) -> (11/3,26/7) Hyperbolic Matrix(365,1326,-286,-1039) (-11/3,-29/8) -> (-23/18,-37/29) Hyperbolic Matrix(259,936,158,571) (-29/8,-18/5) -> (18/11,23/14) Hyperbolic Matrix(51,182,-44,-157) (-18/5,-7/2) -> (-7/6,-8/7) Hyperbolic Matrix(53,182,-30,-103) (-7/2,-10/3) -> (-16/9,-7/4) Hyperbolic Matrix(103,338,-32,-105) (-10/3,-13/4) -> (-13/4,-16/5) Parabolic Matrix(155,494,16,51) (-16/5,-35/11) -> (9/1,10/1) Hyperbolic Matrix(467,1482,98,311) (-35/11,-19/6) -> (19/4,43/9) Hyperbolic Matrix(313,988,198,625) (-19/6,-3/1) -> (49/31,19/12) Hyperbolic Matrix(157,442,-92,-259) (-3/1,-14/5) -> (-12/7,-29/17) Hyperbolic Matrix(1091,3042,-392,-1093) (-14/5,-39/14) -> (-39/14,-64/23) Parabolic Matrix(1299,3614,280,779) (-64/23,-25/9) -> (51/11,14/3) Hyperbolic Matrix(469,1300,-206,-571) (-25/9,-11/4) -> (-41/18,-25/11) Hyperbolic Matrix(105,286,-76,-207) (-11/4,-8/3) -> (-18/13,-11/8) Hyperbolic Matrix(157,416,20,53) (-8/3,-37/14) -> (15/2,8/1) Hyperbolic Matrix(729,1924,158,417) (-37/14,-29/11) -> (23/5,37/8) Hyperbolic Matrix(1767,4654,1046,2755) (-29/11,-79/30) -> (27/16,49/29) Hyperbolic Matrix(3951,10400,-2450,-6449) (-79/30,-50/19) -> (-50/31,-129/80) Hyperbolic Matrix(989,2600,574,1509) (-50/19,-21/8) -> (31/18,50/29) Hyperbolic Matrix(209,546,80,209) (-21/8,-13/5) -> (13/5,21/8) Hyperbolic Matrix(51,130,20,51) (-13/5,-5/2) -> (5/2,13/5) Hyperbolic Matrix(53,130,-42,-103) (-5/2,-12/5) -> (-14/11,-5/4) Hyperbolic Matrix(469,1118,284,677) (-31/13,-50/21) -> (28/17,5/3) Hyperbolic Matrix(415,988,218,519) (-50/21,-69/29) -> (17/9,2/1) Hyperbolic Matrix(1301,3094,394,937) (-69/29,-19/8) -> (33/10,43/13) Hyperbolic Matrix(417,988,176,417) (-19/8,-26/11) -> (26/11,19/8) Hyperbolic Matrix(155,364,66,155) (-26/11,-7/3) -> (7/3,26/11) Hyperbolic Matrix(417,962,316,729) (-30/13,-53/23) -> (25/19,4/3) Hyperbolic Matrix(1039,2392,632,1455) (-53/23,-23/10) -> (23/14,51/31) Hyperbolic Matrix(261,598,182,417) (-23/10,-16/7) -> (10/7,23/16) Hyperbolic Matrix(103,234,-92,-209) (-25/11,-9/4) -> (-9/8,-1/1) Hyperbolic Matrix(467,1040,-304,-677) (-29/13,-20/9) -> (-20/13,-23/15) Hyperbolic Matrix(1301,2886,-820,-1819) (-20/9,-31/14) -> (-73/46,-46/29) Hyperbolic Matrix(1143,2522,-896,-1977) (-42/19,-11/5) -> (-37/29,-88/69) Hyperbolic Matrix(155,338,-72,-157) (-11/5,-13/6) -> (-13/6,-15/7) Parabolic Matrix(209,442,148,313) (-15/7,-2/1) -> (24/17,41/29) Hyperbolic Matrix(259,494,54,103) (-2/1,-17/9) -> (43/9,24/5) Hyperbolic Matrix(469,884,304,573) (-17/9,-15/8) -> (37/24,17/11) Hyperbolic Matrix(209,390,112,209) (-15/8,-13/7) -> (13/7,15/8) Hyperbolic Matrix(155,286,84,155) (-13/7,-11/6) -> (11/6,13/7) Hyperbolic Matrix(259,468,-202,-365) (-20/11,-9/5) -> (-9/7,-32/25) Hyperbolic Matrix(727,1300,-524,-937) (-9/5,-25/14) -> (-25/18,-43/31) Hyperbolic Matrix(467,832,-380,-677) (-25/14,-16/9) -> (-16/13,-27/22) Hyperbolic Matrix(209,364,120,209) (-7/4,-26/15) -> (26/15,7/4) Hyperbolic Matrix(571,988,330,571) (-26/15,-19/11) -> (19/11,26/15) Hyperbolic Matrix(467,806,-332,-573) (-19/11,-31/18) -> (-31/22,-7/5) Hyperbolic Matrix(469,806,-302,-519) (-31/18,-12/7) -> (-14/9,-31/20) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(261,442,62,105) (-17/10,-22/13) -> (4/1,17/4) Hyperbolic Matrix(415,702,-308,-521) (-22/13,-27/16) -> (-27/20,-4/3) Hyperbolic Matrix(987,1664,-710,-1197) (-27/16,-5/3) -> (-57/41,-25/18) Hyperbolic Matrix(207,338,-128,-209) (-5/3,-13/8) -> (-13/8,-21/13) Parabolic Matrix(467,754,96,155) (-21/13,-50/31) -> (24/5,5/1) Hyperbolic Matrix(26831,43264,10190,16431) (-129/80,-208/129) -> (208/79,79/30) Hyperbolic Matrix(26833,43264,10192,16433) (-208/129,-79/49) -> (129/49,208/79) Hyperbolic Matrix(1613,2600,420,677) (-79/49,-29/18) -> (23/6,27/7) Hyperbolic Matrix(469,754,130,209) (-29/18,-8/5) -> (18/5,29/8) Hyperbolic Matrix(883,1404,-622,-989) (-8/5,-27/17) -> (-27/19,-44/31) Hyperbolic Matrix(1507,2392,1146,1819) (-27/17,-73/46) -> (21/16,25/19) Hyperbolic Matrix(623,988,524,831) (-46/29,-19/12) -> (19/16,6/5) Hyperbolic Matrix(313,494,-230,-363) (-19/12,-11/7) -> (-15/11,-19/14) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(1249,1950,800,1249) (-25/16,-39/25) -> (39/25,25/16) Hyperbolic Matrix(2651,4134,1700,2651) (-39/25,-53/34) -> (53/34,39/25) Hyperbolic Matrix(1819,2834,500,779) (-53/34,-14/9) -> (40/11,51/14) Hyperbolic Matrix(571,884,436,675) (-31/20,-17/11) -> (17/13,21/16) Hyperbolic Matrix(573,884,304,469) (-17/11,-37/24) -> (15/8,17/9) Hyperbolic Matrix(1873,2886,-1518,-2339) (-37/24,-20/13) -> (-58/47,-37/30) Hyperbolic Matrix(1561,2392,340,521) (-23/15,-26/17) -> (78/17,23/5) Hyperbolic Matrix(1091,1664,238,363) (-26/17,-3/2) -> (55/12,78/17) Hyperbolic Matrix(53,78,36,53) (-3/2,-13/9) -> (13/9,3/2) Hyperbolic Matrix(415,598,288,415) (-13/9,-23/16) -> (23/16,13/9) Hyperbolic Matrix(417,598,182,261) (-23/16,-10/7) -> (16/7,23/10) Hyperbolic Matrix(675,962,-548,-781) (-10/7,-37/26) -> (-37/30,-16/13) Hyperbolic Matrix(2651,3770,950,1351) (-64/45,-27/19) -> (53/19,14/5) Hyperbolic Matrix(1613,2288,184,261) (-61/43,-78/55) -> (26/3,9/1) Hyperbolic Matrix(1247,1768,146,207) (-78/55,-17/12) -> (17/2,26/3) Hyperbolic Matrix(625,884,-514,-727) (-17/12,-24/17) -> (-28/23,-17/14) Hyperbolic Matrix(1457,2054,554,781) (-24/17,-31/22) -> (21/8,50/19) Hyperbolic Matrix(261,364,38,53) (-7/5,-32/23) -> (20/3,7/1) Hyperbolic Matrix(2861,3978,-2318,-3223) (-32/23,-57/41) -> (-21/17,-58/47) Hyperbolic Matrix(469,650,-412,-571) (-43/31,-18/13) -> (-8/7,-17/15) Hyperbolic Matrix(417,572,304,417) (-11/8,-26/19) -> (26/19,11/8) Hyperbolic Matrix(571,780,418,571) (-26/19,-15/11) -> (15/11,26/19) Hyperbolic Matrix(883,1196,268,363) (-19/14,-23/17) -> (23/7,33/10) Hyperbolic Matrix(1923,2600,730,987) (-23/17,-27/20) -> (79/30,29/11) Hyperbolic Matrix(259,338,-200,-261) (-4/3,-13/10) -> (-13/10,-22/17) Parabolic Matrix(623,806,160,207) (-22/17,-53/41) -> (27/7,4/1) Hyperbolic Matrix(2495,3224,1126,1455) (-53/41,-31/24) -> (31/14,51/23) Hyperbolic Matrix(1249,1612,726,937) (-31/24,-9/7) -> (43/25,31/18) Hyperbolic Matrix(833,1066,-690,-883) (-32/25,-23/18) -> (-29/24,-6/5) Hyperbolic Matrix(1143,1456,734,935) (-51/40,-14/11) -> (14/9,53/34) Hyperbolic Matrix(209,260,168,209) (-5/4,-26/21) -> (26/21,5/4) Hyperbolic Matrix(883,1092,714,883) (-26/21,-21/17) -> (21/17,26/21) Hyperbolic Matrix(469,572,214,261) (-11/9,-28/23) -> (24/11,11/5) Hyperbolic Matrix(2235,2704,386,467) (-23/19,-52/43) -> (52/9,29/5) Hyperbolic Matrix(2237,2704,388,469) (-52/43,-29/24) -> (23/4,52/9) Hyperbolic Matrix(831,988,524,623) (-6/5,-19/16) -> (19/12,46/29) Hyperbolic Matrix(417,494,352,417) (-19/16,-13/11) -> (13/11,19/16) Hyperbolic Matrix(155,182,132,155) (-13/11,-7/6) -> (7/6,13/11) Hyperbolic Matrix(2963,3354,826,935) (-17/15,-26/23) -> (104/29,61/17) Hyperbolic Matrix(1821,2054,508,573) (-26/23,-9/8) -> (43/12,104/29) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(157,-182,44,-51) (1/1,7/6) -> (7/2,25/7) Hyperbolic Matrix(365,-442,128,-155) (6/5,17/14) -> (17/6,20/7) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(571,-702,170,-209) (11/9,16/13) -> (10/3,37/11) Hyperbolic Matrix(781,-962,548,-675) (16/13,21/17) -> (47/33,10/7) Hyperbolic Matrix(103,-130,42,-53) (5/4,9/7) -> (17/7,5/2) Hyperbolic Matrix(261,-338,200,-259) (9/7,13/10) -> (13/10,17/13) Parabolic Matrix(363,-494,230,-313) (4/3,15/11) -> (11/7,30/19) Hyperbolic Matrix(207,-286,76,-105) (11/8,7/5) -> (19/7,11/4) Hyperbolic Matrix(573,-806,332,-467) (7/5,24/17) -> (50/29,19/11) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2029,-2886,438,-623) (27/19,37/26) -> (37/8,51/11) Hyperbolic Matrix(5825,-8294,2154,-3067) (37/26,47/33) -> (73/27,119/44) Hyperbolic Matrix(779,-1196,170,-261) (3/2,20/13) -> (32/7,55/12) Hyperbolic Matrix(2651,-4082,980,-1509) (20/13,37/24) -> (119/44,46/17) Hyperbolic Matrix(519,-806,302,-469) (17/11,14/9) -> (12/7,43/25) Hyperbolic Matrix(781,-1222,232,-363) (25/16,11/7) -> (37/11,27/8) Hyperbolic Matrix(1613,-2548,954,-1507) (30/19,49/31) -> (49/29,22/13) Hyperbolic Matrix(1819,-2886,820,-1301) (46/29,27/17) -> (51/23,20/9) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(209,-338,128,-207) (8/5,13/8) -> (13/8,18/11) Parabolic Matrix(3743,-6162,1422,-2341) (51/31,28/17) -> (50/19,129/49) Hyperbolic Matrix(1249,-2106,462,-779) (5/3,27/16) -> (27/10,73/27) Hyperbolic Matrix(259,-442,92,-157) (17/10,12/7) -> (14/5,17/6) Hyperbolic Matrix(103,-182,30,-53) (7/4,9/5) -> (17/5,7/2) Hyperbolic Matrix(157,-286,28,-51) (9/5,11/6) -> (11/2,17/3) Hyperbolic Matrix(157,-338,72,-155) (2/1,13/6) -> (13/6,24/11) Parabolic Matrix(623,-1378,118,-261) (11/5,31/14) -> (21/4,37/7) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(259,-598,68,-157) (23/10,7/3) -> (19/5,23/6) Hyperbolic Matrix(207,-494,44,-105) (19/8,12/5) -> (14/3,19/4) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1093,-3042,392,-1091) (25/9,39/14) -> (39/14,53/19) Parabolic Matrix(209,-598,36,-103) (20/7,3/1) -> (29/5,6/1) Hyperbolic Matrix(105,-338,32,-103) (3/1,13/4) -> (13/4,23/7) Parabolic Matrix(883,-2990,246,-833) (44/13,17/5) -> (61/17,18/5) Hyperbolic Matrix(157,-572,14,-51) (51/14,11/3) -> (11/1,1/0) Hyperbolic Matrix(103,-390,14,-53) (15/4,19/5) -> (7/1,15/2) Hyperbolic Matrix(103,-546,10,-53) (37/7,16/3) -> (10/1,11/1) Hyperbolic Matrix(53,-338,8,-51) (6/1,13/2) -> (13/2,20/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(51,598,-40,-469) -> Matrix(5,-2,8,-3) Matrix(53,520,16,157) -> Matrix(5,-2,8,-3) Matrix(105,884,-74,-623) -> Matrix(9,-2,14,-3) Matrix(53,390,-14,-103) -> Matrix(1,0,-2,1) Matrix(51,338,-8,-53) -> Matrix(5,-2,8,-3) Matrix(157,988,58,365) -> Matrix(3,-2,2,-1) Matrix(51,286,-28,-157) -> Matrix(5,-2,8,-3) Matrix(155,832,-68,-365) -> Matrix(1,-2,4,-7) Matrix(261,1378,-118,-623) -> Matrix(1,2,2,5) Matrix(209,1092,40,209) -> Matrix(1,0,8,1) Matrix(51,260,10,51) -> Matrix(1,0,-2,1) Matrix(105,494,-44,-207) -> Matrix(1,0,-4,1) Matrix(623,2886,-438,-2029) -> Matrix(9,-2,14,-3) Matrix(417,1924,158,729) -> Matrix(9,-2,14,-3) Matrix(103,468,-46,-209) -> Matrix(7,-2,18,-5) Matrix(53,234,12,53) -> Matrix(5,-2,8,-3) Matrix(103,442,24,103) -> Matrix(7,-4,16,-9) Matrix(105,442,62,261) -> Matrix(3,-2,2,-1) Matrix(157,598,-68,-259) -> Matrix(1,0,4,1) Matrix(365,1378,138,521) -> Matrix(1,-2,2,-3) Matrix(209,780,56,209) -> Matrix(1,0,8,1) Matrix(155,572,42,155) -> Matrix(1,0,-6,1) Matrix(365,1326,-286,-1039) -> Matrix(9,-2,14,-3) Matrix(259,936,158,571) -> Matrix(17,-4,30,-7) Matrix(51,182,-44,-157) -> Matrix(5,-2,8,-3) Matrix(53,182,-30,-103) -> Matrix(1,0,-2,1) Matrix(103,338,-32,-105) -> Matrix(9,-4,16,-7) Matrix(155,494,16,51) -> Matrix(3,-2,8,-5) Matrix(467,1482,98,311) -> Matrix(3,-2,14,-9) Matrix(313,988,198,625) -> Matrix(5,-4,14,-11) Matrix(157,442,-92,-259) -> Matrix(1,0,0,1) Matrix(1091,3042,-392,-1093) -> Matrix(9,-2,32,-7) Matrix(1299,3614,280,779) -> Matrix(7,-2,4,-1) Matrix(469,1300,-206,-571) -> Matrix(5,-2,18,-7) Matrix(105,286,-76,-207) -> Matrix(5,-2,8,-3) Matrix(157,416,20,53) -> Matrix(5,-2,8,-3) Matrix(729,1924,158,417) -> Matrix(5,-2,-2,1) Matrix(1767,4654,1046,2755) -> Matrix(33,-14,26,-11) Matrix(3951,10400,-2450,-6449) -> Matrix(227,-98,410,-177) Matrix(989,2600,574,1509) -> Matrix(9,-4,-2,1) Matrix(209,546,80,209) -> Matrix(17,-8,32,-15) Matrix(51,130,20,51) -> Matrix(3,-2,8,-5) Matrix(53,130,-42,-103) -> Matrix(1,-2,2,-3) Matrix(469,1118,284,677) -> Matrix(3,2,4,3) Matrix(415,988,218,519) -> Matrix(7,2,10,3) Matrix(1301,3094,394,937) -> Matrix(7,2,10,3) Matrix(417,988,176,417) -> Matrix(1,0,16,1) Matrix(155,364,66,155) -> Matrix(1,0,-6,1) Matrix(417,962,316,729) -> Matrix(1,0,-4,1) Matrix(1039,2392,632,1455) -> Matrix(47,-10,80,-17) Matrix(261,598,182,417) -> Matrix(23,-6,50,-13) Matrix(103,234,-92,-209) -> Matrix(7,-2,4,-1) Matrix(467,1040,-304,-677) -> Matrix(5,-2,8,-3) Matrix(1301,2886,-820,-1819) -> Matrix(5,-2,8,-3) Matrix(1143,2522,-896,-1977) -> Matrix(9,-4,16,-7) Matrix(155,338,-72,-157) -> Matrix(13,-6,24,-11) Matrix(209,442,148,313) -> Matrix(7,-4,16,-9) Matrix(259,494,54,103) -> Matrix(5,-2,18,-7) Matrix(469,884,304,573) -> Matrix(5,-2,8,-3) Matrix(209,390,112,209) -> Matrix(17,-8,32,-15) Matrix(155,286,84,155) -> Matrix(11,-6,24,-13) Matrix(259,468,-202,-365) -> Matrix(11,-8,18,-13) Matrix(727,1300,-524,-937) -> Matrix(3,-4,4,-5) Matrix(467,832,-380,-677) -> Matrix(1,0,0,1) Matrix(209,364,120,209) -> Matrix(1,0,4,1) Matrix(571,988,330,571) -> Matrix(1,0,-10,1) Matrix(467,806,-332,-573) -> Matrix(13,-2,20,-3) Matrix(469,806,-302,-519) -> Matrix(1,0,-2,1) Matrix(519,884,-428,-729) -> Matrix(1,0,-4,1) Matrix(261,442,62,105) -> Matrix(7,-2,18,-5) Matrix(415,702,-308,-521) -> Matrix(7,-2,4,-1) Matrix(987,1664,-710,-1197) -> Matrix(11,-4,14,-5) Matrix(207,338,-128,-209) -> Matrix(17,-8,32,-15) Matrix(467,754,96,155) -> Matrix(11,-6,24,-13) Matrix(26831,43264,10190,16431) -> Matrix(591,-328,982,-545) Matrix(26833,43264,10192,16433) -> Matrix(651,-362,1088,-605) Matrix(1613,2600,420,677) -> Matrix(25,-14,84,-47) Matrix(469,754,130,209) -> Matrix(7,-4,2,-1) Matrix(883,1404,-622,-989) -> Matrix(11,-8,18,-13) Matrix(1507,2392,1146,1819) -> Matrix(1,-2,2,-3) Matrix(623,988,524,831) -> Matrix(1,0,0,1) Matrix(313,494,-230,-363) -> Matrix(3,-2,2,-1) Matrix(365,572,-298,-467) -> Matrix(3,-2,2,-1) Matrix(1249,1950,800,1249) -> Matrix(1,-2,4,-7) Matrix(2651,4134,1700,2651) -> Matrix(1,0,4,1) Matrix(1819,2834,500,779) -> Matrix(1,0,0,1) Matrix(571,884,436,675) -> Matrix(5,-2,8,-3) Matrix(573,884,304,469) -> Matrix(5,-2,8,-3) Matrix(1873,2886,-1518,-2339) -> Matrix(7,-6,6,-5) Matrix(1561,2392,340,521) -> Matrix(1,0,0,1) Matrix(1091,1664,238,363) -> Matrix(1,0,-2,1) Matrix(53,78,36,53) -> Matrix(1,0,0,1) Matrix(415,598,288,415) -> Matrix(31,-16,64,-33) Matrix(417,598,182,261) -> Matrix(11,-6,2,-1) Matrix(675,962,-548,-781) -> Matrix(17,-10,12,-7) Matrix(2651,3770,950,1351) -> Matrix(3,-2,2,-1) Matrix(1613,2288,184,261) -> Matrix(3,-2,20,-13) Matrix(1247,1768,146,207) -> Matrix(3,-2,2,-1) Matrix(625,884,-514,-727) -> Matrix(3,-2,2,-1) Matrix(1457,2054,554,781) -> Matrix(29,-18,50,-31) Matrix(261,364,38,53) -> Matrix(3,-2,2,-1) Matrix(2861,3978,-2318,-3223) -> Matrix(11,-10,10,-9) Matrix(469,650,-412,-571) -> Matrix(3,-4,4,-5) Matrix(417,572,304,417) -> Matrix(7,-6,20,-17) Matrix(571,780,418,571) -> Matrix(3,-4,10,-13) Matrix(883,1196,268,363) -> Matrix(5,-2,8,-3) Matrix(1923,2600,730,987) -> Matrix(11,-8,18,-13) Matrix(259,338,-200,-261) -> Matrix(13,-6,24,-11) Matrix(623,806,160,207) -> Matrix(11,-6,24,-13) Matrix(2495,3224,1126,1455) -> Matrix(25,-14,34,-19) Matrix(1249,1612,726,937) -> Matrix(7,-4,2,-1) Matrix(833,1066,-690,-883) -> Matrix(3,-2,14,-9) Matrix(1143,1456,734,935) -> Matrix(3,-2,14,-9) Matrix(209,260,168,209) -> Matrix(7,-6,20,-17) Matrix(883,1092,714,883) -> Matrix(15,-16,46,-49) Matrix(469,572,214,261) -> Matrix(1,-4,2,-7) Matrix(2235,2704,386,467) -> Matrix(1,0,10,1) Matrix(2237,2704,388,469) -> Matrix(1,0,-8,1) Matrix(831,988,524,623) -> Matrix(1,0,0,1) Matrix(417,494,352,417) -> Matrix(9,-4,16,-7) Matrix(155,182,132,155) -> Matrix(7,-4,16,-9) Matrix(2963,3354,826,935) -> Matrix(23,-22,22,-21) Matrix(1821,2054,508,573) -> Matrix(11,-12,12,-13) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(157,-182,44,-51) -> Matrix(5,-2,8,-3) Matrix(365,-442,128,-155) -> Matrix(1,0,-4,1) Matrix(727,-884,514,-625) -> Matrix(7,-2,18,-5) Matrix(571,-702,170,-209) -> Matrix(1,0,-2,1) Matrix(781,-962,548,-675) -> Matrix(33,-10,76,-23) Matrix(103,-130,42,-53) -> Matrix(5,-2,18,-7) Matrix(261,-338,200,-259) -> Matrix(13,-6,24,-11) Matrix(363,-494,230,-313) -> Matrix(7,-2,18,-5) Matrix(207,-286,76,-105) -> Matrix(5,-2,8,-3) Matrix(573,-806,332,-467) -> Matrix(5,-2,-12,5) Matrix(989,-1404,622,-883) -> Matrix(19,-8,50,-21) Matrix(2029,-2886,438,-623) -> Matrix(5,-2,-2,1) Matrix(5825,-8294,2154,-3067) -> Matrix(33,-14,26,-11) Matrix(779,-1196,170,-261) -> Matrix(1,0,-2,1) Matrix(2651,-4082,980,-1509) -> Matrix(7,-2,4,-1) Matrix(519,-806,302,-469) -> Matrix(1,0,-2,1) Matrix(781,-1222,232,-363) -> Matrix(5,-2,8,-3) Matrix(1613,-2548,954,-1507) -> Matrix(1,0,-2,1) Matrix(1819,-2886,820,-1301) -> Matrix(5,-2,8,-3) Matrix(261,-416,32,-51) -> Matrix(5,-2,8,-3) Matrix(209,-338,128,-207) -> Matrix(17,-8,32,-15) Matrix(3743,-6162,1422,-2341) -> Matrix(89,-54,150,-91) Matrix(1249,-2106,462,-779) -> Matrix(3,-2,2,-1) Matrix(259,-442,92,-157) -> Matrix(1,0,0,1) Matrix(103,-182,30,-53) -> Matrix(1,0,-2,1) Matrix(157,-286,28,-51) -> Matrix(5,-2,8,-3) Matrix(157,-338,72,-155) -> Matrix(13,-6,24,-11) Matrix(623,-1378,118,-261) -> Matrix(3,-2,14,-9) Matrix(209,-468,46,-103) -> Matrix(3,-2,2,-1) Matrix(573,-1300,160,-363) -> Matrix(3,-4,4,-5) Matrix(365,-832,68,-155) -> Matrix(1,-2,4,-7) Matrix(259,-598,68,-157) -> Matrix(1,0,4,1) Matrix(207,-494,44,-105) -> Matrix(1,0,-4,1) Matrix(625,-1508,172,-415) -> Matrix(1,0,-4,1) Matrix(365,-884,64,-155) -> Matrix(1,0,-4,1) Matrix(521,-1404,154,-415) -> Matrix(1,-2,2,-3) Matrix(207,-572,38,-105) -> Matrix(1,0,2,1) Matrix(1093,-3042,392,-1091) -> Matrix(1,-2,0,1) Matrix(209,-598,36,-103) -> Matrix(1,0,4,1) Matrix(105,-338,32,-103) -> Matrix(9,-4,16,-7) Matrix(883,-2990,246,-833) -> Matrix(7,-6,6,-5) Matrix(157,-572,14,-51) -> Matrix(1,0,2,1) Matrix(103,-390,14,-53) -> Matrix(1,0,-2,1) Matrix(103,-546,10,-53) -> Matrix(1,0,-2,1) Matrix(53,-338,8,-51) -> Matrix(5,-2,8,-3) 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): 56 Degree of the the map X: 56 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.