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): 864 Minimal number of generators: 145 Number of equivalence classes of cusps: 48 Genus: 49 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 17/15 17/14 17/13 17/12 3/2 17/11 17/10 17/9 2/1 17/8 34/15 12/5 17/7 5/2 85/33 34/13 17/6 3/1 17/5 7/2 11/3 15/4 34/9 4/1 17/4 13/3 136/31 102/23 9/2 14/3 85/18 34/7 5/1 16/3 11/2 17/3 6/1 19/3 13/2 34/5 7/1 8/1 17/2 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/16 -17/2 1/15 -8/1 1/15 1/14 -7/1 1/12 -20/3 1/19 1/18 -13/2 1/16 2/31 -19/3 3/44 -25/4 1/14 2/27 -6/1 1/15 1/14 -17/3 1/14 -11/2 1/14 2/27 -5/1 1/12 -24/5 1/17 1/16 -43/9 1/16 -19/4 1/16 2/31 -33/7 7/104 -14/3 3/43 1/14 -9/2 0/1 1/14 -22/5 1/14 3/41 -35/8 2/27 3/40 -13/3 3/40 -17/4 1/13 -4/1 1/13 1/12 -15/4 0/1 1/16 -11/3 3/40 -18/5 1/13 1/12 -7/2 2/25 1/12 -17/5 1/12 -10/3 1/12 3/35 -43/13 1/12 -33/10 1/12 2/23 -56/17 5/58 7/81 -23/7 7/80 -13/4 1/12 2/23 -3/1 1/12 -17/6 1/11 -14/5 1/11 5/54 -11/4 2/21 1/10 -19/7 5/52 -8/3 1/10 1/9 -13/5 1/12 -18/7 1/12 1/11 -5/2 2/21 1/10 -17/7 1/10 -12/5 1/10 5/49 -43/18 1/10 2/19 -74/31 1/10 5/49 -31/13 7/68 -19/8 5/48 2/19 -7/3 3/28 -16/7 1/9 1/8 -9/4 0/1 1/10 -11/5 5/48 -13/6 2/19 3/28 -15/7 7/64 -17/8 1/9 -2/1 1/9 1/8 -17/9 1/8 -15/8 1/8 8/63 -13/7 1/8 -11/6 2/15 3/22 -9/5 1/8 -34/19 2/15 -25/14 2/15 3/22 -16/9 1/8 1/7 -7/4 1/8 2/15 -26/15 3/22 13/95 -19/11 5/36 -31/18 3/22 4/29 -12/7 7/50 1/7 -17/10 1/7 -5/3 3/20 -18/11 1/8 1/7 -85/52 1/7 -67/41 15/104 -49/30 7/48 6/41 -31/19 3/20 -13/8 3/20 2/13 -34/21 2/13 -21/13 5/32 -8/5 1/7 1/6 -27/17 5/32 -19/12 3/20 2/13 -11/7 7/44 -25/16 6/37 1/6 -14/9 9/55 1/6 -17/11 1/6 -3/2 1/6 2/11 -19/13 3/16 -16/11 3/16 1/5 -13/9 3/16 -23/16 11/58 4/21 -33/23 23/120 -10/7 7/36 1/5 -17/12 1/5 -7/5 5/24 -18/13 1/5 1/4 -29/21 5/24 -11/8 3/14 2/9 -15/11 7/32 -34/25 2/9 -19/14 2/9 9/40 -4/3 3/13 1/4 -17/13 1/4 -13/10 1/4 10/39 -48/37 23/89 15/58 -35/27 27/104 -57/44 37/142 6/23 -136/105 6/23 -79/61 47/180 -22/17 11/42 5/19 -31/24 9/34 4/15 -102/79 4/15 -71/55 15/56 -40/31 7/26 3/11 -9/7 1/4 -23/18 4/15 7/26 -14/11 3/11 5/18 -33/26 1/4 2/7 -85/67 1/4 -52/41 1/4 3/11 -19/15 1/4 -43/34 18/65 5/18 -24/19 7/25 9/32 -29/23 17/60 -34/27 2/7 -5/4 2/7 3/10 -16/13 5/16 1/3 -11/9 9/28 -17/14 1/3 -6/5 1/3 5/14 -25/21 3/8 -19/16 10/27 3/8 -13/11 3/8 -33/28 3/8 2/5 -20/17 5/13 7/18 -27/23 19/48 -34/29 2/5 -7/6 2/5 5/12 -8/7 7/15 1/2 -17/15 1/2 -9/8 1/2 8/15 -10/9 7/12 3/5 -1/1 1/0 0/1 0/1 1/1 1/32 9/8 8/241 1/30 17/15 1/30 8/7 1/30 7/209 7/6 5/148 2/59 20/17 7/206 5/147 13/11 3/88 19/16 3/88 10/293 25/21 3/88 6/5 5/146 1/29 17/14 1/29 11/9 9/260 5/4 3/86 2/57 24/19 9/256 7/199 43/34 5/142 18/511 19/15 1/28 33/26 2/57 1/28 14/11 5/142 3/85 9/7 1/28 22/17 5/141 11/310 35/27 27/760 13/10 10/281 1/28 17/13 1/28 4/3 1/28 3/83 15/11 7/192 11/8 2/55 3/82 18/13 1/28 1/27 7/5 5/136 17/12 1/27 10/7 1/27 7/188 43/30 26/697 5/134 33/23 23/616 56/39 17/455 21/562 23/16 4/107 11/294 13/9 3/80 3/2 2/53 1/26 17/11 1/26 14/9 1/26 9/233 11/7 7/180 19/12 2/51 3/76 8/5 1/26 1/25 13/8 2/51 3/76 18/11 1/25 1/24 5/3 3/76 17/10 1/25 12/7 1/25 7/174 43/25 5/124 74/43 9/223 13/322 31/18 4/99 3/74 19/11 5/124 7/4 2/49 1/24 16/9 1/25 1/24 9/5 1/24 11/6 3/74 2/49 13/7 1/24 15/8 8/193 1/24 17/9 1/24 2/1 1/24 1/23 17/8 1/23 15/7 7/160 13/6 3/68 2/45 11/5 5/112 9/4 0/1 1/22 34/15 0/1 25/11 1/24 16/7 1/24 1/23 7/3 3/68 26/11 3/67 1/22 19/8 2/45 5/112 31/13 7/156 12/5 5/111 1/22 17/7 1/22 5/2 1/22 2/43 18/7 1/21 1/20 85/33 1/20 67/26 0/1 1/20 49/19 1/20 31/12 0/1 1/22 13/5 1/20 34/13 0/1 21/8 0/1 1/24 8/3 1/23 1/22 27/10 4/87 7/152 19/7 5/108 11/4 1/22 2/43 25/9 3/64 14/5 5/106 1/21 17/6 1/21 3/1 1/20 19/6 2/43 3/64 16/5 1/21 5/104 13/4 2/41 1/20 23/7 7/144 33/10 2/41 1/20 10/3 3/61 1/20 17/5 1/20 7/2 1/20 2/39 18/5 1/20 1/19 29/8 3/58 4/77 11/3 3/56 15/4 0/1 1/16 34/9 0/1 19/5 1/24 4/1 1/20 1/19 17/4 1/19 13/3 3/56 48/11 1/19 1/18 35/8 3/56 2/37 57/13 11/204 136/31 2/37 79/18 2/37 17/314 22/5 3/55 1/18 31/7 3/56 102/23 2/37 71/16 2/37 9/166 40/9 3/55 1/18 9/2 0/1 1/18 23/5 5/92 14/3 1/18 3/53 33/7 7/120 85/18 1/17 52/11 1/17 9/152 19/4 2/33 1/16 43/9 1/16 24/5 1/16 1/15 29/6 0/1 1/10 34/7 0/1 5/1 1/20 16/3 1/19 3/56 11/2 2/37 1/18 17/3 1/18 6/1 1/18 1/17 25/4 2/37 1/18 19/3 3/52 13/2 2/33 1/16 33/5 5/76 20/3 1/14 1/13 27/4 0/1 1/8 34/5 0/1 7/1 1/20 8/1 1/18 1/17 17/2 1/17 9/1 1/16 10/1 1/17 1/16 1/0 0/1 1/16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(33,340,-10,-103) (-9/1,1/0) -> (-43/13,-33/10) Hyperbolic Matrix(35,306,4,35) (-9/1,-17/2) -> (17/2,9/1) Hyperbolic Matrix(33,272,4,33) (-17/2,-8/1) -> (8/1,17/2) Hyperbolic Matrix(33,238,14,101) (-8/1,-7/1) -> (7/3,26/11) Hyperbolic Matrix(101,680,-86,-579) (-7/1,-20/3) -> (-20/17,-27/23) Hyperbolic Matrix(135,884,-104,-681) (-20/3,-13/2) -> (-13/10,-48/37) Hyperbolic Matrix(69,442,32,205) (-13/2,-19/3) -> (15/7,13/6) Hyperbolic Matrix(205,1292,162,1021) (-19/3,-25/4) -> (43/34,19/15) Hyperbolic Matrix(169,1054,38,237) (-25/4,-6/1) -> (40/9,9/2) Hyperbolic Matrix(35,204,6,35) (-6/1,-17/3) -> (17/3,6/1) Hyperbolic Matrix(67,374,12,67) (-17/3,-11/2) -> (11/2,17/3) Hyperbolic Matrix(69,374,-50,-271) (-11/2,-5/1) -> (-29/21,-11/8) Hyperbolic Matrix(169,816,-134,-647) (-5/1,-24/5) -> (-24/19,-29/23) Hyperbolic Matrix(135,646,14,67) (-24/5,-43/9) -> (9/1,10/1) Hyperbolic Matrix(271,1292,228,1087) (-43/9,-19/4) -> (19/16,25/21) Hyperbolic Matrix(611,2890,-374,-1769) (-19/4,-33/7) -> (-67/41,-49/30) Hyperbolic Matrix(441,2074,-340,-1599) (-33/7,-14/3) -> (-48/37,-35/27) Hyperbolic Matrix(103,476,-66,-305) (-14/3,-9/2) -> (-25/16,-14/9) Hyperbolic Matrix(239,1054,-100,-441) (-9/2,-22/5) -> (-12/5,-43/18) Hyperbolic Matrix(613,2686,-186,-815) (-22/5,-35/8) -> (-33/10,-56/17) Hyperbolic Matrix(203,884,-172,-749) (-35/8,-13/3) -> (-13/11,-33/28) Hyperbolic Matrix(103,442,24,103) (-13/3,-17/4) -> (17/4,13/3) Hyperbolic Matrix(33,136,8,33) (-17/4,-4/1) -> (4/1,17/4) Hyperbolic Matrix(35,136,-26,-101) (-4/1,-15/4) -> (-19/14,-4/3) Hyperbolic Matrix(101,374,64,237) (-15/4,-11/3) -> (11/7,19/12) Hyperbolic Matrix(103,374,-84,-305) (-11/3,-18/5) -> (-16/13,-11/9) Hyperbolic Matrix(67,238,38,135) (-18/5,-7/2) -> (7/4,16/9) Hyperbolic Matrix(69,238,20,69) (-7/2,-17/5) -> (17/5,7/2) Hyperbolic Matrix(101,340,30,101) (-17/5,-10/3) -> (10/3,17/5) Hyperbolic Matrix(441,1462,92,305) (-10/3,-43/13) -> (43/9,24/5) Hyperbolic Matrix(1497,4930,-1156,-3807) (-56/17,-23/7) -> (-79/61,-22/17) Hyperbolic Matrix(135,442,62,203) (-23/7,-13/4) -> (13/6,11/5) Hyperbolic Matrix(137,442,-84,-271) (-13/4,-3/1) -> (-31/19,-13/8) Hyperbolic Matrix(35,102,12,35) (-3/1,-17/6) -> (17/6,3/1) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(171,476,-134,-373) (-14/5,-11/4) -> (-23/18,-14/11) Hyperbolic Matrix(137,374,100,273) (-11/4,-19/7) -> (15/11,11/8) Hyperbolic Matrix(239,646,-138,-373) (-19/7,-8/3) -> (-26/15,-19/11) Hyperbolic Matrix(103,272,-64,-169) (-8/3,-13/5) -> (-21/13,-8/5) Hyperbolic Matrix(171,442,-118,-305) (-13/5,-18/7) -> (-16/11,-13/9) Hyperbolic Matrix(67,170,-54,-137) (-18/7,-5/2) -> (-5/4,-16/13) Hyperbolic Matrix(69,170,28,69) (-5/2,-17/7) -> (17/7,5/2) Hyperbolic Matrix(169,408,70,169) (-17/7,-12/5) -> (12/5,17/7) Hyperbolic Matrix(883,2108,142,339) (-43/18,-74/31) -> (6/1,25/4) Hyperbolic Matrix(2721,6494,-2108,-5031) (-74/31,-31/13) -> (-71/55,-40/31) Hyperbolic Matrix(885,2108,-542,-1291) (-31/13,-19/8) -> (-49/30,-31/19) Hyperbolic Matrix(273,646,-172,-407) (-19/8,-7/3) -> (-27/17,-19/12) Hyperbolic Matrix(103,238,74,171) (-7/3,-16/7) -> (18/13,7/5) Hyperbolic Matrix(239,544,-134,-305) (-16/7,-9/4) -> (-25/14,-16/9) Hyperbolic Matrix(169,374,-108,-239) (-9/4,-11/5) -> (-11/7,-25/16) Hyperbolic Matrix(203,442,62,135) (-11/5,-13/6) -> (13/4,23/7) Hyperbolic Matrix(205,442,32,69) (-13/6,-15/7) -> (19/3,13/2) Hyperbolic Matrix(239,510,112,239) (-15/7,-17/8) -> (17/8,15/7) Hyperbolic Matrix(33,68,16,33) (-17/8,-2/1) -> (2/1,17/8) Hyperbolic Matrix(35,68,18,35) (-2/1,-17/9) -> (17/9,2/1) Hyperbolic Matrix(271,510,144,271) (-17/9,-15/8) -> (15/8,17/9) Hyperbolic Matrix(237,442,200,373) (-15/8,-13/7) -> (13/11,19/16) Hyperbolic Matrix(239,442,166,307) (-13/7,-11/6) -> (23/16,13/9) Hyperbolic Matrix(169,306,-132,-239) (-11/6,-9/5) -> (-9/7,-23/18) Hyperbolic Matrix(645,1156,284,509) (-9/5,-34/19) -> (34/15,25/11) Hyperbolic Matrix(647,1156,286,511) (-34/19,-25/14) -> (9/4,34/15) Hyperbolic Matrix(135,238,38,67) (-16/9,-7/4) -> (7/2,18/5) Hyperbolic Matrix(137,238,118,205) (-7/4,-26/15) -> (8/7,7/6) Hyperbolic Matrix(375,646,-256,-441) (-19/11,-31/18) -> (-3/2,-19/13) Hyperbolic Matrix(613,1054,-474,-815) (-31/18,-12/7) -> (-22/17,-31/24) Hyperbolic Matrix(239,408,140,239) (-12/7,-17/10) -> (17/10,12/7) Hyperbolic Matrix(101,170,60,101) (-17/10,-5/3) -> (5/3,17/10) Hyperbolic Matrix(373,612,-270,-443) (-5/3,-18/11) -> (-18/13,-29/21) Hyperbolic Matrix(3639,5950,770,1259) (-18/11,-85/52) -> (85/18,52/11) Hyperbolic Matrix(5201,8500,1102,1801) (-85/52,-67/41) -> (33/7,85/18) Hyperbolic Matrix(713,1156,272,441) (-13/8,-34/21) -> (34/13,21/8) Hyperbolic Matrix(715,1156,274,443) (-34/21,-21/13) -> (13/5,34/13) Hyperbolic Matrix(171,272,22,35) (-8/5,-27/17) -> (7/1,8/1) Hyperbolic Matrix(237,374,64,101) (-19/12,-11/7) -> (11/3,15/4) Hyperbolic Matrix(307,476,198,307) (-14/9,-17/11) -> (17/11,14/9) Hyperbolic Matrix(67,102,44,67) (-17/11,-3/2) -> (3/2,17/11) Hyperbolic Matrix(885,1292,-698,-1019) (-19/13,-16/11) -> (-52/41,-19/15) Hyperbolic Matrix(307,442,166,239) (-13/9,-23/16) -> (11/6,13/7) Hyperbolic Matrix(1871,2686,-1444,-2073) (-23/16,-33/23) -> (-35/27,-57/44) Hyperbolic Matrix(237,340,-214,-307) (-33/23,-10/7) -> (-10/9,-1/1) Hyperbolic Matrix(239,340,168,239) (-10/7,-17/12) -> (17/12,10/7) Hyperbolic Matrix(169,238,120,169) (-17/12,-7/5) -> (7/5,17/12) Hyperbolic Matrix(171,238,74,103) (-7/5,-18/13) -> (16/7,7/3) Hyperbolic Matrix(273,374,100,137) (-11/8,-15/11) -> (19/7,11/4) Hyperbolic Matrix(849,1156,224,305) (-15/11,-34/25) -> (34/9,19/5) Hyperbolic Matrix(851,1156,226,307) (-34/25,-19/14) -> (15/4,34/9) Hyperbolic Matrix(103,136,78,103) (-4/3,-17/13) -> (17/13,4/3) Hyperbolic Matrix(339,442,260,339) (-17/13,-13/10) -> (13/10,17/13) Hyperbolic Matrix(14279,18496,3254,4215) (-57/44,-136/105) -> (136/31,79/18) Hyperbolic Matrix(14281,18496,3256,4217) (-136/105,-79/61) -> (57/13,136/31) Hyperbolic Matrix(8057,10404,1816,2345) (-31/24,-102/79) -> (102/23,71/16) Hyperbolic Matrix(8059,10404,1818,2347) (-102/79,-71/55) -> (31/7,102/23) Hyperbolic Matrix(817,1054,686,885) (-40/31,-9/7) -> (25/21,6/5) Hyperbolic Matrix(883,1122,-750,-953) (-14/11,-33/26) -> (-33/28,-20/17) Hyperbolic Matrix(6699,8500,2600,3299) (-33/26,-85/67) -> (85/33,67/26) Hyperbolic Matrix(4691,5950,1822,2311) (-85/67,-52/41) -> (18/7,85/33) Hyperbolic Matrix(1021,1292,162,205) (-19/15,-43/34) -> (25/4,19/3) Hyperbolic Matrix(1157,1462,808,1021) (-43/34,-24/19) -> (10/7,43/30) Hyperbolic Matrix(917,1156,188,237) (-29/23,-34/27) -> (34/7,5/1) Hyperbolic Matrix(919,1156,190,239) (-34/27,-5/4) -> (29/6,34/7) Hyperbolic Matrix(307,374,252,307) (-11/9,-17/14) -> (17/14,11/9) Hyperbolic Matrix(169,204,140,169) (-17/14,-6/5) -> (6/5,17/14) Hyperbolic Matrix(1769,2108,1028,1225) (-6/5,-25/21) -> (43/25,74/43) Hyperbolic Matrix(1087,1292,228,271) (-25/21,-19/16) -> (19/4,43/9) Hyperbolic Matrix(373,442,200,237) (-19/16,-13/11) -> (13/7,15/8) Hyperbolic Matrix(985,1156,144,169) (-27/23,-34/29) -> (34/5,7/1) Hyperbolic Matrix(987,1156,146,171) (-34/29,-7/6) -> (27/4,34/5) Hyperbolic Matrix(237,272,88,101) (-7/6,-8/7) -> (8/3,27/10) Hyperbolic Matrix(239,272,210,239) (-8/7,-17/15) -> (17/15,8/7) Hyperbolic Matrix(271,306,240,271) (-17/15,-9/8) -> (9/8,17/15) Hyperbolic Matrix(579,646,458,511) (-9/8,-10/9) -> (24/19,43/34) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(307,-340,214,-237) (1/1,9/8) -> (43/30,33/23) Hyperbolic Matrix(579,-680,86,-101) (7/6,20/17) -> (20/3,27/4) Hyperbolic Matrix(749,-884,172,-203) (20/17,13/11) -> (13/3,48/11) Hyperbolic Matrix(305,-374,84,-103) (11/9,5/4) -> (29/8,11/3) Hyperbolic Matrix(647,-816,134,-169) (5/4,24/19) -> (24/5,29/6) Hyperbolic Matrix(2279,-2890,884,-1121) (19/15,33/26) -> (67/26,49/19) Hyperbolic Matrix(1633,-2074,374,-475) (33/26,14/11) -> (48/11,35/8) Hyperbolic Matrix(373,-476,134,-171) (14/11,9/7) -> (25/9,14/5) Hyperbolic Matrix(815,-1054,474,-613) (9/7,22/17) -> (12/7,43/25) Hyperbolic Matrix(2073,-2686,1444,-1871) (22/17,35/27) -> (33/23,56/39) Hyperbolic Matrix(681,-884,104,-135) (35/27,13/10) -> (13/2,33/5) Hyperbolic Matrix(101,-136,26,-35) (4/3,15/11) -> (19/5,4/1) Hyperbolic Matrix(271,-374,50,-69) (11/8,18/13) -> (16/3,11/2) Hyperbolic Matrix(3433,-4930,782,-1123) (56/39,23/16) -> (79/18,22/5) Hyperbolic Matrix(305,-442,118,-171) (13/9,3/2) -> (31/12,13/5) Hyperbolic Matrix(305,-476,66,-103) (14/9,11/7) -> (23/5,14/3) Hyperbolic Matrix(407,-646,172,-273) (19/12,8/5) -> (26/11,19/8) Hyperbolic Matrix(169,-272,64,-103) (8/5,13/8) -> (21/8,8/3) Hyperbolic Matrix(271,-442,84,-137) (13/8,18/11) -> (16/5,13/4) Hyperbolic Matrix(103,-170,20,-33) (18/11,5/3) -> (5/1,16/3) Hyperbolic Matrix(3773,-6494,850,-1463) (74/43,31/18) -> (71/16,40/9) Hyperbolic Matrix(1223,-2108,474,-817) (31/18,19/11) -> (49/19,31/12) Hyperbolic Matrix(373,-646,138,-239) (19/11,7/4) -> (27/10,19/7) Hyperbolic Matrix(305,-544,134,-239) (16/9,9/5) -> (25/11,16/7) Hyperbolic Matrix(205,-374,74,-135) (9/5,11/6) -> (11/4,25/9) Hyperbolic Matrix(137,-306,30,-67) (11/5,9/4) -> (9/2,23/5) Hyperbolic Matrix(271,-646,86,-205) (19/8,31/13) -> (3/1,19/6) Hyperbolic Matrix(441,-1054,100,-239) (31/13,12/5) -> (22/5,31/7) Hyperbolic Matrix(239,-612,66,-169) (5/2,18/7) -> (18/5,29/8) Hyperbolic Matrix(407,-1292,86,-273) (19/6,16/5) -> (52/11,19/4) Hyperbolic Matrix(815,-2686,186,-613) (23/7,33/10) -> (35/8,57/13) Hyperbolic Matrix(103,-340,10,-33) (33/10,10/3) -> (10/1,1/0) Hyperbolic Matrix(239,-1122,36,-169) (14/3,33/7) -> (33/5,20/3) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(33,340,-10,-103) -> Matrix(33,-2,380,-23) Matrix(35,306,4,35) -> Matrix(31,-2,512,-33) Matrix(33,272,4,33) -> Matrix(29,-2,508,-35) Matrix(33,238,14,101) -> Matrix(27,-2,608,-45) Matrix(101,680,-86,-579) -> Matrix(43,-2,108,-5) Matrix(135,884,-104,-681) -> Matrix(129,-8,500,-31) Matrix(69,442,32,205) -> Matrix(61,-4,1388,-91) Matrix(205,1292,162,1021) -> Matrix(117,-8,3320,-227) Matrix(169,1054,38,237) -> Matrix(27,-2,500,-37) Matrix(35,204,6,35) -> Matrix(29,-2,508,-35) Matrix(67,374,12,67) -> Matrix(55,-4,1004,-73) Matrix(69,374,-50,-271) -> Matrix(53,-4,252,-19) Matrix(169,816,-134,-647) -> Matrix(41,-2,144,-7) Matrix(135,646,14,67) -> Matrix(1,0,0,1) Matrix(271,1292,228,1087) -> Matrix(67,-4,1960,-117) Matrix(611,2890,-374,-1769) -> Matrix(121,-8,832,-55) Matrix(441,2074,-340,-1599) -> Matrix(323,-22,1248,-85) Matrix(103,476,-66,-305) -> Matrix(83,-6,512,-37) Matrix(239,1054,-100,-441) -> Matrix(29,-2,276,-19) Matrix(613,2686,-186,-815) -> Matrix(107,-8,1244,-93) Matrix(203,884,-172,-749) -> Matrix(161,-12,416,-31) Matrix(103,442,24,103) -> Matrix(79,-6,1488,-113) Matrix(33,136,8,33) -> Matrix(25,-2,488,-39) Matrix(35,136,-26,-101) -> Matrix(23,-2,104,-9) Matrix(101,374,64,237) -> Matrix(29,-2,740,-51) Matrix(103,374,-84,-305) -> Matrix(77,-6,244,-19) Matrix(67,238,38,135) -> Matrix(1,0,12,1) Matrix(69,238,20,69) -> Matrix(49,-4,968,-79) Matrix(101,340,30,101) -> Matrix(71,-6,1432,-121) Matrix(441,1462,92,305) -> Matrix(23,-2,380,-33) Matrix(1497,4930,-1156,-3807) -> Matrix(601,-52,2300,-199) Matrix(135,442,62,203) -> Matrix(45,-4,1024,-91) Matrix(137,442,-84,-271) -> Matrix(45,-4,304,-27) Matrix(35,102,12,35) -> Matrix(23,-2,472,-41) Matrix(169,476,60,169) -> Matrix(109,-10,2300,-211) Matrix(171,476,-134,-373) -> Matrix(107,-10,396,-37) Matrix(137,374,100,273) -> Matrix(43,-4,1172,-109) Matrix(239,646,-138,-373) -> Matrix(103,-10,752,-73) Matrix(103,272,-64,-169) -> Matrix(19,-2,124,-13) Matrix(171,442,-118,-305) -> Matrix(21,-2,116,-11) Matrix(67,170,-54,-137) -> Matrix(43,-4,140,-13) Matrix(69,170,28,69) -> Matrix(41,-4,892,-87) Matrix(169,408,70,169) -> Matrix(99,-10,2188,-221) Matrix(883,2108,142,339) -> Matrix(39,-4,712,-73) Matrix(2721,6494,-2108,-5031) -> Matrix(313,-32,1164,-119) Matrix(885,2108,-542,-1291) -> Matrix(155,-16,1056,-109) Matrix(273,646,-172,-407) -> Matrix(39,-4,244,-25) Matrix(103,238,74,171) -> Matrix(17,-2,468,-55) Matrix(239,544,-134,-305) -> Matrix(17,-2,128,-15) Matrix(169,374,-108,-239) -> Matrix(59,-6,364,-37) Matrix(203,442,62,135) -> Matrix(37,-4,768,-83) Matrix(205,442,32,69) -> Matrix(37,-4,620,-67) Matrix(239,510,112,239) -> Matrix(127,-14,2912,-321) Matrix(33,68,16,33) -> Matrix(17,-2,400,-47) Matrix(35,68,18,35) -> Matrix(17,-2,400,-47) Matrix(271,510,144,271) -> Matrix(127,-16,3056,-385) Matrix(237,442,200,373) -> Matrix(109,-14,3200,-411) Matrix(239,442,166,307) -> Matrix(77,-10,2056,-267) Matrix(169,306,-132,-239) -> Matrix(17,-2,60,-7) Matrix(645,1156,284,509) -> Matrix(15,-2,368,-49) Matrix(647,1156,286,511) -> Matrix(15,-2,308,-41) Matrix(135,238,38,67) -> Matrix(1,0,12,1) Matrix(137,238,118,205) -> Matrix(59,-8,1748,-237) Matrix(375,646,-256,-441) -> Matrix(15,-2,68,-9) Matrix(613,1054,-474,-815) -> Matrix(173,-24,656,-91) Matrix(239,408,140,239) -> Matrix(99,-14,2468,-349) Matrix(101,170,60,101) -> Matrix(41,-6,1032,-151) Matrix(373,612,-270,-443) -> Matrix(15,-2,68,-9) Matrix(3639,5950,770,1259) -> Matrix(71,-10,1200,-169) Matrix(5201,8500,1102,1801) -> Matrix(153,-22,2608,-375) Matrix(713,1156,272,441) -> Matrix(13,-2,332,-51) Matrix(715,1156,274,443) -> Matrix(13,-2,228,-35) Matrix(171,272,22,35) -> Matrix(13,-2,228,-35) Matrix(237,374,64,101) -> Matrix(13,-2,228,-35) Matrix(307,476,198,307) -> Matrix(109,-18,2828,-467) Matrix(67,102,44,67) -> Matrix(23,-4,604,-105) Matrix(885,1292,-698,-1019) -> Matrix(43,-8,156,-29) Matrix(307,442,166,239) -> Matrix(53,-10,1288,-243) Matrix(1871,2686,-1444,-2073) -> Matrix(429,-82,1648,-315) Matrix(237,340,-214,-307) -> Matrix(73,-14,120,-23) Matrix(239,340,168,239) -> Matrix(71,-14,1912,-377) Matrix(169,238,120,169) -> Matrix(49,-10,1328,-271) Matrix(171,238,74,103) -> Matrix(9,-2,212,-47) Matrix(273,374,100,137) -> Matrix(19,-4,404,-85) Matrix(849,1156,224,305) -> Matrix(9,-2,248,-55) Matrix(851,1156,226,307) -> Matrix(9,-2,104,-23) Matrix(103,136,78,103) -> Matrix(25,-6,696,-167) Matrix(339,442,260,339) -> Matrix(79,-20,2216,-561) Matrix(14279,18496,3254,4215) -> Matrix(675,-176,12476,-3253) Matrix(14281,18496,3256,4217) -> Matrix(613,-160,11352,-2963) Matrix(8057,10404,1816,2345) -> Matrix(203,-54,3748,-997) Matrix(8059,10404,1818,2347) -> Matrix(157,-42,2912,-779) Matrix(817,1054,686,885) -> Matrix(29,-8,852,-235) Matrix(883,1122,-750,-953) -> Matrix(13,-4,36,-11) Matrix(6699,8500,2600,3299) -> Matrix(7,-2,144,-41) Matrix(4691,5950,1822,2311) -> Matrix(15,-4,304,-81) Matrix(1021,1292,162,205) -> Matrix(29,-8,504,-139) Matrix(1157,1462,808,1021) -> Matrix(143,-40,3836,-1073) Matrix(917,1156,188,237) -> Matrix(7,-2,200,-57) Matrix(919,1156,190,239) -> Matrix(7,-2,60,-17) Matrix(307,374,252,307) -> Matrix(55,-18,1592,-521) Matrix(169,204,140,169) -> Matrix(29,-10,844,-291) Matrix(1769,2108,1028,1225) -> Matrix(87,-32,2156,-793) Matrix(1087,1292,228,271) -> Matrix(11,-4,168,-61) Matrix(373,442,200,237) -> Matrix(37,-14,896,-339) Matrix(985,1156,144,169) -> Matrix(5,-2,148,-59) Matrix(987,1156,146,171) -> Matrix(5,-2,28,-11) Matrix(237,272,88,101) -> Matrix(13,-6,284,-131) Matrix(239,272,210,239) -> Matrix(29,-14,868,-419) Matrix(271,306,240,271) -> Matrix(31,-16,932,-481) Matrix(579,646,458,511) -> Matrix(39,-22,1108,-625) Matrix(1,0,2,1) -> Matrix(1,0,32,1) Matrix(307,-340,214,-237) -> Matrix(425,-14,11384,-375) Matrix(579,-680,86,-101) -> Matrix(59,-2,620,-21) Matrix(749,-884,172,-203) -> Matrix(353,-12,6560,-223) Matrix(305,-374,84,-103) -> Matrix(173,-6,3316,-115) Matrix(647,-816,134,-169) -> Matrix(57,-2,656,-23) Matrix(2279,-2890,884,-1121) -> Matrix(57,-2,1112,-39) Matrix(1633,-2074,374,-475) -> Matrix(227,-8,4228,-149) Matrix(373,-476,134,-171) -> Matrix(283,-10,6028,-213) Matrix(815,-1054,474,-613) -> Matrix(677,-24,16784,-595) Matrix(2073,-2686,1444,-1871) -> Matrix(2309,-82,61808,-2195) Matrix(681,-884,104,-135) -> Matrix(225,-8,3572,-127) Matrix(101,-136,26,-35) -> Matrix(55,-2,1128,-41) Matrix(271,-374,50,-69) -> Matrix(109,-4,2044,-75) Matrix(3433,-4930,782,-1123) -> Matrix(1231,-46,22720,-849) Matrix(305,-442,118,-171) -> Matrix(53,-2,1140,-43) Matrix(305,-476,66,-103) -> Matrix(155,-6,2816,-109) Matrix(407,-646,172,-273) -> Matrix(103,-4,2292,-89) Matrix(169,-272,64,-103) -> Matrix(51,-2,1148,-45) Matrix(271,-442,84,-137) -> Matrix(101,-4,2096,-83) Matrix(103,-170,20,-33) -> Matrix(51,-2,944,-37) Matrix(3773,-6494,850,-1463) -> Matrix(743,-30,13696,-553) Matrix(1223,-2108,474,-817) -> Matrix(99,-4,2104,-85) Matrix(373,-646,138,-239) -> Matrix(247,-10,5360,-217) Matrix(305,-544,134,-239) -> Matrix(49,-2,1152,-47) Matrix(205,-374,74,-135) -> Matrix(99,-4,2104,-85) Matrix(137,-306,30,-67) -> Matrix(1,0,-4,1) Matrix(271,-646,86,-205) -> Matrix(89,-4,1936,-87) Matrix(441,-1054,100,-239) -> Matrix(45,-2,788,-35) Matrix(239,-612,66,-169) -> Matrix(41,-2,800,-39) Matrix(407,-1292,86,-273) -> Matrix(85,-4,1424,-67) Matrix(815,-2686,186,-613) -> Matrix(163,-8,3036,-149) Matrix(103,-340,10,-33) -> Matrix(41,-2,636,-31) Matrix(239,-1122,36,-169) -> Matrix(35,-2,508,-29) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 36 Degree of the the map X: 72 Degree of the the map Y: 144 ----------------------------------------------------------------------- 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): 432 Minimal number of generators: 73 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 32 Genus: 21 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/1 17/15 17/14 17/13 17/12 3/2 17/11 17/10 9/5 17/9 2/1 34/15 17/7 5/2 85/33 17/6 3/1 17/5 7/2 11/3 34/9 19/5 4/1 17/4 13/3 9/2 5/1 17/3 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -6/1 1/15 1/14 -5/1 1/12 -4/1 1/13 1/12 -15/4 0/1 1/16 -11/3 3/40 -18/5 1/13 1/12 -7/2 2/25 1/12 -3/1 1/12 -17/6 1/11 -14/5 1/11 5/54 -11/4 2/21 1/10 -19/7 5/52 -8/3 1/10 1/9 -13/5 1/12 -18/7 1/12 1/11 -5/2 2/21 1/10 -7/3 3/28 -16/7 1/9 1/8 -9/4 0/1 1/10 -2/1 1/9 1/8 -13/7 1/8 -11/6 2/15 3/22 -9/5 1/8 -34/19 2/15 -25/14 2/15 3/22 -16/9 1/8 1/7 -7/4 1/8 2/15 -26/15 3/22 13/95 -19/11 5/36 -12/7 7/50 1/7 -17/10 1/7 -5/3 3/20 -8/5 1/7 1/6 -11/7 7/44 -3/2 1/6 2/11 -16/11 3/16 1/5 -13/9 3/16 -10/7 7/36 1/5 -17/12 1/5 -7/5 5/24 -11/8 3/14 2/9 -15/11 7/32 -34/25 2/9 -19/14 2/9 9/40 -4/3 3/13 1/4 -9/7 1/4 -23/18 4/15 7/26 -14/11 3/11 5/18 -5/4 2/7 3/10 -16/13 5/16 1/3 -11/9 9/28 -17/14 1/3 -6/5 1/3 5/14 -7/6 2/5 5/12 -8/7 7/15 1/2 -1/1 1/0 0/1 0/1 1/1 1/32 9/8 8/241 1/30 17/15 1/30 8/7 1/30 7/209 7/6 5/148 2/59 13/11 3/88 6/5 5/146 1/29 17/14 1/29 11/9 9/260 5/4 3/86 2/57 19/15 1/28 33/26 2/57 1/28 14/11 5/142 3/85 9/7 1/28 13/10 10/281 1/28 17/13 1/28 4/3 1/28 3/83 15/11 7/192 11/8 2/55 3/82 18/13 1/28 1/27 7/5 5/136 17/12 1/27 10/7 1/27 7/188 23/16 4/107 11/294 13/9 3/80 3/2 2/53 1/26 17/11 1/26 14/9 1/26 9/233 11/7 7/180 19/12 2/51 3/76 8/5 1/26 1/25 13/8 2/51 3/76 5/3 3/76 17/10 1/25 12/7 1/25 7/174 31/18 4/99 3/74 19/11 5/124 7/4 2/49 1/24 16/9 1/25 1/24 9/5 1/24 11/6 3/74 2/49 13/7 1/24 15/8 8/193 1/24 17/9 1/24 2/1 1/24 1/23 11/5 5/112 9/4 0/1 1/22 34/15 0/1 25/11 1/24 16/7 1/24 1/23 7/3 3/68 12/5 5/111 1/22 17/7 1/22 5/2 1/22 2/43 18/7 1/21 1/20 85/33 1/20 67/26 0/1 1/20 49/19 1/20 31/12 0/1 1/22 13/5 1/20 34/13 0/1 21/8 0/1 1/24 8/3 1/23 1/22 27/10 4/87 7/152 19/7 5/108 11/4 1/22 2/43 25/9 3/64 14/5 5/106 1/21 17/6 1/21 3/1 1/20 10/3 3/61 1/20 17/5 1/20 7/2 1/20 2/39 18/5 1/20 1/19 29/8 3/58 4/77 11/3 3/56 15/4 0/1 1/16 34/9 0/1 19/5 1/24 4/1 1/20 1/19 17/4 1/19 13/3 3/56 9/2 0/1 1/18 5/1 1/20 11/2 2/37 1/18 17/3 1/18 6/1 1/18 1/17 7/1 1/20 1/0 0/1 1/16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(18,119,13,86) (-6/1,1/0) -> (11/8,18/13) Hyperbolic Matrix(16,85,3,16) (-6/1,-5/1) -> (5/1,11/2) Hyperbolic Matrix(18,85,11,52) (-5/1,-4/1) -> (13/8,5/3) Hyperbolic Matrix(35,136,-26,-101) (-4/1,-15/4) -> (-19/14,-4/3) Hyperbolic Matrix(101,374,64,237) (-15/4,-11/3) -> (11/7,19/12) Hyperbolic Matrix(103,374,-84,-305) (-11/3,-18/5) -> (-16/13,-11/9) Hyperbolic Matrix(67,238,38,135) (-18/5,-7/2) -> (7/4,16/9) Hyperbolic Matrix(16,51,5,16) (-7/2,-3/1) -> (3/1,10/3) Hyperbolic Matrix(35,102,12,35) (-3/1,-17/6) -> (17/6,3/1) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(171,476,-134,-373) (-14/5,-11/4) -> (-23/18,-14/11) Hyperbolic Matrix(137,374,100,273) (-11/4,-19/7) -> (15/11,11/8) Hyperbolic Matrix(239,646,-138,-373) (-19/7,-8/3) -> (-26/15,-19/11) Hyperbolic Matrix(84,221,19,50) (-8/3,-13/5) -> (13/3,9/2) Hyperbolic Matrix(171,442,-118,-305) (-13/5,-18/7) -> (-16/11,-13/9) Hyperbolic Matrix(67,170,-54,-137) (-18/7,-5/2) -> (-5/4,-16/13) Hyperbolic Matrix(50,119,21,50) (-5/2,-7/3) -> (7/3,12/5) Hyperbolic Matrix(103,238,74,171) (-7/3,-16/7) -> (18/13,7/5) Hyperbolic Matrix(239,544,-134,-305) (-16/7,-9/4) -> (-25/14,-16/9) Hyperbolic Matrix(84,187,53,118) (-9/4,-2/1) -> (19/12,8/5) Hyperbolic Matrix(118,221,63,118) (-2/1,-13/7) -> (13/7,15/8) Hyperbolic Matrix(239,442,166,307) (-13/7,-11/6) -> (23/16,13/9) Hyperbolic Matrix(169,306,-132,-239) (-11/6,-9/5) -> (-9/7,-23/18) Hyperbolic Matrix(645,1156,284,509) (-9/5,-34/19) -> (34/15,25/11) Hyperbolic Matrix(647,1156,286,511) (-34/19,-25/14) -> (9/4,34/15) Hyperbolic Matrix(135,238,38,67) (-16/9,-7/4) -> (7/2,18/5) Hyperbolic Matrix(137,238,118,205) (-7/4,-26/15) -> (8/7,7/6) Hyperbolic Matrix(188,323,149,256) (-19/11,-12/7) -> (5/4,19/15) Hyperbolic Matrix(239,408,140,239) (-12/7,-17/10) -> (17/10,12/7) Hyperbolic Matrix(101,170,60,101) (-17/10,-5/3) -> (5/3,17/10) Hyperbolic Matrix(52,85,11,18) (-5/3,-8/5) -> (9/2,5/1) Hyperbolic Matrix(118,187,53,84) (-8/5,-11/7) -> (11/5,9/4) Hyperbolic Matrix(120,187,77,120) (-11/7,-3/2) -> (14/9,11/7) Hyperbolic Matrix(220,323,173,254) (-3/2,-16/11) -> (33/26,14/11) Hyperbolic Matrix(154,221,131,188) (-13/9,-10/7) -> (7/6,13/11) Hyperbolic Matrix(239,340,168,239) (-10/7,-17/12) -> (17/12,10/7) Hyperbolic Matrix(169,238,120,169) (-17/12,-7/5) -> (7/5,17/12) Hyperbolic Matrix(86,119,13,18) (-7/5,-11/8) -> (6/1,7/1) Hyperbolic Matrix(273,374,100,137) (-11/8,-15/11) -> (19/7,11/4) Hyperbolic Matrix(849,1156,224,305) (-15/11,-34/25) -> (34/9,19/5) Hyperbolic Matrix(851,1156,226,307) (-34/25,-19/14) -> (15/4,34/9) Hyperbolic Matrix(118,153,91,118) (-4/3,-9/7) -> (9/7,13/10) Hyperbolic Matrix(256,323,149,188) (-14/11,-5/4) -> (12/7,31/18) Hyperbolic Matrix(307,374,252,307) (-11/9,-17/14) -> (17/14,11/9) Hyperbolic Matrix(169,204,140,169) (-17/14,-6/5) -> (6/5,17/14) Hyperbolic Matrix(188,221,131,154) (-6/5,-7/6) -> (10/7,23/16) Hyperbolic Matrix(237,272,88,101) (-7/6,-8/7) -> (8/3,27/10) Hyperbolic Matrix(16,17,15,16) (-8/7,-1/1) -> (1/1,9/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(256,-289,225,-254) (9/8,17/15) -> (17/15,8/7) Parabolic Matrix(186,-221,101,-120) (13/11,6/5) -> (11/6,13/7) Hyperbolic Matrix(305,-374,84,-103) (11/9,5/4) -> (29/8,11/3) Hyperbolic Matrix(2279,-2890,884,-1121) (19/15,33/26) -> (67/26,49/19) Hyperbolic Matrix(373,-476,134,-171) (14/11,9/7) -> (25/9,14/5) Hyperbolic Matrix(222,-289,169,-220) (13/10,17/13) -> (17/13,4/3) Parabolic Matrix(101,-136,26,-35) (4/3,15/11) -> (19/5,4/1) Hyperbolic Matrix(305,-442,118,-171) (13/9,3/2) -> (31/12,13/5) Hyperbolic Matrix(188,-289,121,-186) (3/2,17/11) -> (17/11,14/9) Parabolic Matrix(169,-272,64,-103) (8/5,13/8) -> (21/8,8/3) Hyperbolic Matrix(1223,-2108,474,-817) (31/18,19/11) -> (49/19,31/12) Hyperbolic Matrix(373,-646,138,-239) (19/11,7/4) -> (27/10,19/7) Hyperbolic Matrix(305,-544,134,-239) (16/9,9/5) -> (25/11,16/7) Hyperbolic Matrix(205,-374,74,-135) (9/5,11/6) -> (11/4,25/9) Hyperbolic Matrix(154,-289,81,-152) (15/8,17/9) -> (17/9,2/1) Parabolic Matrix(86,-187,23,-50) (2/1,11/5) -> (11/3,15/4) Hyperbolic Matrix(52,-119,7,-16) (16/7,7/3) -> (7/1,1/0) Hyperbolic Matrix(120,-289,49,-118) (12/5,17/7) -> (17/7,5/2) Parabolic Matrix(239,-612,66,-169) (5/2,18/7) -> (18/5,29/8) Hyperbolic Matrix(2806,-7225,1089,-2804) (18/7,85/33) -> (85/33,67/26) Parabolic Matrix(254,-663,59,-154) (13/5,34/13) -> (17/4,13/3) Hyperbolic Matrix(188,-493,45,-118) (34/13,21/8) -> (4/1,17/4) Hyperbolic Matrix(86,-289,25,-84) (10/3,17/5) -> (17/5,7/2) Parabolic Matrix(52,-289,9,-50) (11/2,17/3) -> (17/3,6/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(18,119,13,86) -> Matrix(17,-1,460,-27) Matrix(16,85,3,16) -> Matrix(13,-1,248,-19) Matrix(18,85,11,52) -> Matrix(15,-1,376,-25) Matrix(35,136,-26,-101) -> Matrix(23,-2,104,-9) Matrix(101,374,64,237) -> Matrix(29,-2,740,-51) Matrix(103,374,-84,-305) -> Matrix(77,-6,244,-19) Matrix(67,238,38,135) -> Matrix(1,0,12,1) Matrix(16,51,5,16) -> Matrix(11,-1,232,-21) Matrix(35,102,12,35) -> Matrix(23,-2,472,-41) Matrix(169,476,60,169) -> Matrix(109,-10,2300,-211) Matrix(171,476,-134,-373) -> Matrix(107,-10,396,-37) Matrix(137,374,100,273) -> Matrix(43,-4,1172,-109) Matrix(239,646,-138,-373) -> Matrix(103,-10,752,-73) Matrix(84,221,19,50) -> Matrix(9,-1,172,-19) Matrix(171,442,-118,-305) -> Matrix(21,-2,116,-11) Matrix(67,170,-54,-137) -> Matrix(43,-4,140,-13) Matrix(50,119,21,50) -> Matrix(29,-3,648,-67) Matrix(103,238,74,171) -> Matrix(17,-2,468,-55) Matrix(239,544,-134,-305) -> Matrix(17,-2,128,-15) Matrix(84,187,53,118) -> Matrix(11,-1,276,-25) Matrix(118,221,63,118) -> Matrix(55,-7,1328,-169) Matrix(239,442,166,307) -> Matrix(77,-10,2056,-267) Matrix(169,306,-132,-239) -> Matrix(17,-2,60,-7) Matrix(645,1156,284,509) -> Matrix(15,-2,368,-49) Matrix(647,1156,286,511) -> Matrix(15,-2,308,-41) Matrix(135,238,38,67) -> Matrix(1,0,12,1) Matrix(137,238,118,205) -> Matrix(59,-8,1748,-237) Matrix(188,323,149,256) -> Matrix(79,-11,2248,-313) Matrix(239,408,140,239) -> Matrix(99,-14,2468,-349) Matrix(101,170,60,101) -> Matrix(41,-6,1032,-151) Matrix(52,85,11,18) -> Matrix(7,-1,120,-17) Matrix(118,187,53,84) -> Matrix(7,-1,148,-21) Matrix(120,187,77,120) -> Matrix(43,-7,1112,-181) Matrix(220,323,173,254) -> Matrix(37,-7,1052,-199) Matrix(154,221,131,188) -> Matrix(47,-9,1384,-265) Matrix(239,340,168,239) -> Matrix(71,-14,1912,-377) Matrix(169,238,120,169) -> Matrix(49,-10,1328,-271) Matrix(86,119,13,18) -> Matrix(5,-1,76,-15) Matrix(273,374,100,137) -> Matrix(19,-4,404,-85) Matrix(849,1156,224,305) -> Matrix(9,-2,248,-55) Matrix(851,1156,226,307) -> Matrix(9,-2,104,-23) Matrix(118,153,91,118) -> Matrix(27,-7,760,-197) Matrix(256,323,149,188) -> Matrix(39,-11,968,-273) Matrix(307,374,252,307) -> Matrix(55,-18,1592,-521) Matrix(169,204,140,169) -> Matrix(29,-10,844,-291) Matrix(188,221,131,154) -> Matrix(23,-9,616,-241) Matrix(237,272,88,101) -> Matrix(13,-6,284,-131) Matrix(16,17,15,16) -> Matrix(1,-1,32,-31) Matrix(1,0,2,1) -> Matrix(1,0,32,1) Matrix(256,-289,225,-254) -> Matrix(451,-15,13500,-449) Matrix(186,-221,101,-120) -> Matrix(205,-7,5008,-171) Matrix(305,-374,84,-103) -> Matrix(173,-6,3316,-115) Matrix(2279,-2890,884,-1121) -> Matrix(57,-2,1112,-39) Matrix(373,-476,134,-171) -> Matrix(283,-10,6028,-213) Matrix(222,-289,169,-220) -> Matrix(365,-13,10192,-363) Matrix(101,-136,26,-35) -> Matrix(55,-2,1128,-41) Matrix(305,-442,118,-171) -> Matrix(53,-2,1140,-43) Matrix(188,-289,121,-186) -> Matrix(287,-11,7436,-285) Matrix(169,-272,64,-103) -> Matrix(51,-2,1148,-45) Matrix(1223,-2108,474,-817) -> Matrix(99,-4,2104,-85) Matrix(373,-646,138,-239) -> Matrix(247,-10,5360,-217) Matrix(305,-544,134,-239) -> Matrix(49,-2,1152,-47) Matrix(205,-374,74,-135) -> Matrix(99,-4,2104,-85) Matrix(154,-289,81,-152) -> Matrix(217,-9,5184,-215) Matrix(86,-187,23,-50) -> Matrix(23,-1,392,-17) Matrix(52,-119,7,-16) -> Matrix(23,-1,392,-17) Matrix(120,-289,49,-118) -> Matrix(155,-7,3388,-153) Matrix(239,-612,66,-169) -> Matrix(41,-2,800,-39) Matrix(2806,-7225,1089,-2804) -> Matrix(21,-1,400,-19) Matrix(254,-663,59,-154) -> Matrix(17,-1,324,-19) Matrix(188,-493,45,-118) -> Matrix(25,-1,476,-19) Matrix(86,-289,25,-84) -> Matrix(101,-5,2000,-99) Matrix(52,-289,9,-50) -> Matrix(55,-3,972,-53) 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): 36 ----------------------------------------------------------------------- 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 16 1 1/1 1/32 1 17 17/15 1/30 15 1 8/7 (1/30,7/209) 0 17 7/6 (5/148,2/59) 0 17 6/5 (5/146,1/29) 0 17 17/14 1/29 14 1 11/9 9/260 1 17 5/4 (3/86,2/57) 0 17 14/11 (5/142,3/85) 0 17 9/7 1/28 1 17 17/13 1/28 13 1 4/3 (1/28,3/83) 0 17 15/11 7/192 1 17 11/8 (2/55,3/82) 0 17 7/5 5/136 1 17 17/12 1/27 12 1 10/7 (1/27,7/188) 0 17 23/16 (4/107,11/294) 0 17 13/9 3/80 1 17 3/2 (2/53,1/26) 0 17 17/11 1/26 11 1 11/7 7/180 1 17 8/5 (1/26,1/25) 0 17 5/3 3/76 1 17 17/10 1/25 10 1 12/7 (1/25,7/174) 0 17 31/18 (4/99,3/74) 0 17 19/11 5/124 1 17 7/4 (2/49,1/24) 0 17 16/9 (1/25,1/24) 0 17 9/5 1/24 1 17 11/6 (3/74,2/49) 0 17 13/7 1/24 1 17 17/9 1/24 9 1 2/1 (1/24,1/23) 0 17 11/5 5/112 1 17 9/4 (0/1,1/22) 0 17 34/15 0/1 2 1 25/11 1/24 1 17 16/7 (1/24,1/23) 0 17 7/3 3/68 1 17 17/7 1/22 7 1 5/2 (1/22,2/43) 0 17 18/7 (1/21,1/20) 0 17 85/33 1/20 1 1 49/19 1/20 1 17 31/12 (0/1,1/22) 0 17 13/5 1/20 1 17 8/3 (1/23,1/22) 0 17 27/10 (4/87,7/152) 0 17 19/7 5/108 1 17 11/4 (1/22,2/43) 0 17 25/9 3/64 1 17 14/5 (5/106,1/21) 0 17 17/6 1/21 6 1 3/1 1/20 1 17 17/5 1/20 5 1 7/2 (1/20,2/39) 0 17 18/5 (1/20,1/19) 0 17 29/8 (3/58,4/77) 0 17 11/3 3/56 1 17 15/4 (0/1,1/16) 0 17 34/9 0/1 8 1 19/5 1/24 1 17 4/1 (1/20,1/19) 0 17 17/4 1/19 4 1 13/3 3/56 1 17 9/2 (0/1,1/18) 0 17 5/1 1/20 1 17 17/3 1/18 3 1 6/1 (1/18,1/17) 0 17 7/1 1/20 1 17 1/0 (0/1,1/16) 0 17 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(16,-17,15,-16) (1/1,17/15) -> (1/1,17/15) Reflection Matrix(239,-272,210,-239) (17/15,8/7) -> (17/15,8/7) Reflection Matrix(237,-272,88,-101) (8/7,7/6) -> (8/3,27/10) Glide Reflection Matrix(188,-221,131,-154) (7/6,6/5) -> (10/7,23/16) Glide Reflection Matrix(169,-204,140,-169) (6/5,17/14) -> (6/5,17/14) Reflection Matrix(307,-374,252,-307) (17/14,11/9) -> (17/14,11/9) Reflection Matrix(305,-374,84,-103) (11/9,5/4) -> (29/8,11/3) Hyperbolic Matrix(256,-323,149,-188) (5/4,14/11) -> (12/7,31/18) Glide Reflection Matrix(373,-476,134,-171) (14/11,9/7) -> (25/9,14/5) Hyperbolic Matrix(118,-153,91,-118) (9/7,17/13) -> (9/7,17/13) Reflection Matrix(103,-136,78,-103) (17/13,4/3) -> (17/13,4/3) Reflection Matrix(101,-136,26,-35) (4/3,15/11) -> (19/5,4/1) Hyperbolic Matrix(273,-374,100,-137) (15/11,11/8) -> (19/7,11/4) Glide Reflection Matrix(86,-119,13,-18) (11/8,7/5) -> (6/1,7/1) Glide Reflection Matrix(169,-238,120,-169) (7/5,17/12) -> (7/5,17/12) Reflection Matrix(239,-340,168,-239) (17/12,10/7) -> (17/12,10/7) Reflection Matrix(307,-442,166,-239) (23/16,13/9) -> (11/6,13/7) Glide Reflection Matrix(305,-442,118,-171) (13/9,3/2) -> (31/12,13/5) Hyperbolic Matrix(67,-102,44,-67) (3/2,17/11) -> (3/2,17/11) Reflection Matrix(120,-187,77,-120) (17/11,11/7) -> (17/11,11/7) Reflection Matrix(118,-187,53,-84) (11/7,8/5) -> (11/5,9/4) Glide Reflection Matrix(52,-85,11,-18) (8/5,5/3) -> (9/2,5/1) Glide Reflection Matrix(101,-170,60,-101) (5/3,17/10) -> (5/3,17/10) Reflection Matrix(239,-408,140,-239) (17/10,12/7) -> (17/10,12/7) Reflection Matrix(1223,-2108,474,-817) (31/18,19/11) -> (49/19,31/12) Hyperbolic Matrix(373,-646,138,-239) (19/11,7/4) -> (27/10,19/7) Hyperbolic Matrix(135,-238,38,-67) (7/4,16/9) -> (7/2,18/5) Glide Reflection Matrix(305,-544,134,-239) (16/9,9/5) -> (25/11,16/7) Hyperbolic Matrix(205,-374,74,-135) (9/5,11/6) -> (11/4,25/9) Hyperbolic Matrix(118,-221,63,-118) (13/7,17/9) -> (13/7,17/9) Reflection Matrix(35,-68,18,-35) (17/9,2/1) -> (17/9,2/1) Reflection Matrix(86,-187,23,-50) (2/1,11/5) -> (11/3,15/4) Hyperbolic Matrix(271,-612,120,-271) (9/4,34/15) -> (9/4,34/15) Reflection Matrix(749,-1700,330,-749) (34/15,25/11) -> (34/15,25/11) Reflection Matrix(52,-119,7,-16) (16/7,7/3) -> (7/1,1/0) Hyperbolic Matrix(50,-119,21,-50) (7/3,17/7) -> (7/3,17/7) Reflection Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(239,-612,66,-169) (5/2,18/7) -> (18/5,29/8) Hyperbolic Matrix(1189,-3060,462,-1189) (18/7,85/33) -> (18/7,85/33) Reflection Matrix(1616,-4165,627,-1616) (85/33,49/19) -> (85/33,49/19) Reflection Matrix(84,-221,19,-50) (13/5,8/3) -> (13/3,9/2) Glide Reflection Matrix(169,-476,60,-169) (14/5,17/6) -> (14/5,17/6) Reflection Matrix(35,-102,12,-35) (17/6,3/1) -> (17/6,3/1) Reflection Matrix(16,-51,5,-16) (3/1,17/5) -> (3/1,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(271,-1020,72,-271) (15/4,34/9) -> (15/4,34/9) Reflection Matrix(341,-1292,90,-341) (34/9,19/5) -> (34/9,19/5) Reflection Matrix(33,-136,8,-33) (4/1,17/4) -> (4/1,17/4) Reflection Matrix(103,-442,24,-103) (17/4,13/3) -> (17/4,13/3) Reflection Matrix(16,-85,3,-16) (5/1,17/3) -> (5/1,17/3) Reflection Matrix(35,-204,6,-35) (17/3,6/1) -> (17/3,6/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,32,-1) (0/1,1/0) -> (0/1,1/16) Matrix(1,0,2,-1) -> Matrix(1,0,64,-1) (0/1,1/1) -> (0/1,1/32) Matrix(16,-17,15,-16) -> Matrix(31,-1,960,-31) (1/1,17/15) -> (1/32,1/30) Matrix(239,-272,210,-239) -> Matrix(419,-14,12540,-419) (17/15,8/7) -> (1/30,7/209) Matrix(237,-272,88,-101) -> Matrix(179,-6,3908,-131) Matrix(188,-221,131,-154) -> Matrix(265,-9,7096,-241) Matrix(169,-204,140,-169) -> Matrix(291,-10,8468,-291) (6/5,17/14) -> (5/146,1/29) Matrix(307,-374,252,-307) -> Matrix(521,-18,15080,-521) (17/14,11/9) -> (1/29,9/260) Matrix(305,-374,84,-103) -> Matrix(173,-6,3316,-115) Matrix(256,-323,149,-188) -> Matrix(313,-11,7768,-273) Matrix(373,-476,134,-171) -> Matrix(283,-10,6028,-213) Matrix(118,-153,91,-118) -> Matrix(197,-7,5544,-197) (9/7,17/13) -> (7/198,1/28) Matrix(103,-136,78,-103) -> Matrix(167,-6,4648,-167) (17/13,4/3) -> (1/28,3/83) Matrix(101,-136,26,-35) -> Matrix(55,-2,1128,-41) Matrix(273,-374,100,-137) -> Matrix(109,-4,2316,-85) Matrix(86,-119,13,-18) -> Matrix(27,-1,404,-15) Matrix(169,-238,120,-169) -> Matrix(271,-10,7344,-271) (7/5,17/12) -> (5/136,1/27) Matrix(239,-340,168,-239) -> Matrix(377,-14,10152,-377) (17/12,10/7) -> (1/27,7/188) Matrix(307,-442,166,-239) -> Matrix(267,-10,6488,-243) Matrix(305,-442,118,-171) -> Matrix(53,-2,1140,-43) Matrix(67,-102,44,-67) -> Matrix(105,-4,2756,-105) (3/2,17/11) -> (2/53,1/26) Matrix(120,-187,77,-120) -> Matrix(181,-7,4680,-181) (17/11,11/7) -> (1/26,7/180) Matrix(118,-187,53,-84) -> Matrix(25,-1,524,-21) Matrix(52,-85,11,-18) -> Matrix(25,-1,424,-17) Matrix(101,-170,60,-101) -> Matrix(151,-6,3800,-151) (5/3,17/10) -> (3/76,1/25) Matrix(239,-408,140,-239) -> Matrix(349,-14,8700,-349) (17/10,12/7) -> (1/25,7/174) Matrix(1223,-2108,474,-817) -> Matrix(99,-4,2104,-85) Matrix(373,-646,138,-239) -> Matrix(247,-10,5360,-217) Matrix(135,-238,38,-67) -> Matrix(1,0,44,-1) *** -> (0/1,1/22) Matrix(305,-544,134,-239) -> Matrix(49,-2,1152,-47) 1/24 Matrix(205,-374,74,-135) -> Matrix(99,-4,2104,-85) Matrix(118,-221,63,-118) -> Matrix(169,-7,4080,-169) (13/7,17/9) -> (7/170,1/24) Matrix(35,-68,18,-35) -> Matrix(47,-2,1104,-47) (17/9,2/1) -> (1/24,1/23) Matrix(86,-187,23,-50) -> Matrix(23,-1,392,-17) Matrix(271,-612,120,-271) -> Matrix(1,0,44,-1) (9/4,34/15) -> (0/1,1/22) Matrix(749,-1700,330,-749) -> Matrix(1,0,48,-1) (34/15,25/11) -> (0/1,1/24) Matrix(52,-119,7,-16) -> Matrix(23,-1,392,-17) Matrix(50,-119,21,-50) -> Matrix(67,-3,1496,-67) (7/3,17/7) -> (3/68,1/22) Matrix(69,-170,28,-69) -> Matrix(87,-4,1892,-87) (17/7,5/2) -> (1/22,2/43) Matrix(239,-612,66,-169) -> Matrix(41,-2,800,-39) 1/20 Matrix(1189,-3060,462,-1189) -> Matrix(41,-2,840,-41) (18/7,85/33) -> (1/21,1/20) Matrix(1616,-4165,627,-1616) -> Matrix(21,-1,440,-21) (85/33,49/19) -> (1/22,1/20) Matrix(84,-221,19,-50) -> Matrix(23,-1,436,-19) Matrix(169,-476,60,-169) -> Matrix(211,-10,4452,-211) (14/5,17/6) -> (5/106,1/21) Matrix(35,-102,12,-35) -> Matrix(41,-2,840,-41) (17/6,3/1) -> (1/21,1/20) Matrix(16,-51,5,-16) -> Matrix(21,-1,440,-21) (3/1,17/5) -> (1/22,1/20) Matrix(69,-238,20,-69) -> Matrix(79,-4,1560,-79) (17/5,7/2) -> (1/20,2/39) Matrix(271,-1020,72,-271) -> Matrix(1,0,32,-1) (15/4,34/9) -> (0/1,1/16) Matrix(341,-1292,90,-341) -> Matrix(1,0,48,-1) (34/9,19/5) -> (0/1,1/24) Matrix(33,-136,8,-33) -> Matrix(39,-2,760,-39) (4/1,17/4) -> (1/20,1/19) Matrix(103,-442,24,-103) -> Matrix(113,-6,2128,-113) (17/4,13/3) -> (1/19,3/56) Matrix(16,-85,3,-16) -> Matrix(19,-1,360,-19) (5/1,17/3) -> (1/20,1/18) Matrix(35,-204,6,-35) -> Matrix(35,-2,612,-35) (17/3,6/1) -> (1/18,1/17) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.