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 -2/1 -1/1 -17/2 -1/1 -8/1 -4/5 -7/1 -1/1 -2/3 -20/3 -4/7 -13/2 -1/2 0/1 -19/3 -1/2 -2/5 -25/4 -1/2 -2/5 -6/1 0/1 -17/3 -1/1 -11/2 -1/1 -2/3 -5/1 -1/2 0/1 -24/5 0/1 -43/9 1/1 2/1 -19/4 1/1 2/1 -33/7 -4/1 1/0 -14/3 0/1 -9/2 -2/1 -3/2 -22/5 -4/3 -35/8 -8/7 -1/1 -13/3 -8/7 -1/1 -17/4 -1/1 -4/1 -4/5 -15/4 -2/3 -7/11 -11/3 -2/3 -1/2 -18/5 -4/5 -7/2 -2/3 -1/2 -17/5 -1/2 -10/3 0/1 -43/13 -2/1 -1/1 -33/10 -1/1 0/1 -56/17 -4/5 -23/7 -2/3 -1/2 -13/4 -1/2 0/1 -3/1 -1/1 0/1 -17/6 -1/1 -14/5 -4/5 -11/4 -1/1 -2/3 -19/7 -2/3 -5/8 -8/3 0/1 -13/5 -1/1 0/1 -18/7 -4/5 -5/2 -1/1 0/1 -17/7 -1/1 -12/5 -4/5 -43/18 -6/7 -5/6 -74/31 -4/5 -31/13 -4/5 -7/9 -19/8 -5/7 -2/3 -7/3 -1/1 -2/3 -16/7 -8/11 -9/4 -2/3 -5/8 -11/5 -2/3 -1/2 -13/6 -4/7 -1/2 -15/7 -6/11 -1/2 -17/8 -1/2 -2/1 0/1 -17/9 -1/1 -15/8 -1/1 -6/7 -13/7 -1/1 -4/5 -11/6 -1/1 -2/3 -9/5 -5/7 -2/3 -34/19 -2/3 -25/14 -2/3 -13/20 -16/9 -8/13 -7/4 -2/3 -1/2 -26/15 0/1 -19/11 -2/3 -5/8 -31/18 -7/12 -4/7 -12/7 -4/7 -17/10 -1/2 -5/3 -1/2 0/1 -18/11 -4/7 -85/52 -1/2 -67/41 -1/2 -8/17 -49/30 -3/7 -2/5 -31/19 -1/1 0/1 -13/8 -1/2 0/1 -34/21 0/1 -21/13 -1/1 0/1 -8/5 0/1 -27/17 -1/1 -2/3 -19/12 -5/7 -2/3 -11/7 -2/3 -1/2 -25/16 -2/3 -5/8 -14/9 -4/7 -17/11 -1/2 -3/2 -1/2 0/1 -19/13 -2/1 -3/2 -16/11 -4/5 -13/9 -1/1 0/1 -23/16 -1/1 -2/3 -33/23 -1/2 0/1 -10/7 0/1 -17/12 -1/1 -7/5 -1/1 -2/3 -18/13 -4/7 -29/21 -1/2 0/1 -11/8 -1/1 -2/3 -15/11 -7/10 -2/3 -34/25 -2/3 -19/14 -2/3 -11/17 -4/3 -4/7 -17/13 -1/2 -13/10 -1/2 -8/17 -48/37 -4/9 -35/27 -1/2 -8/17 -57/44 -7/15 -6/13 -136/105 -6/13 -79/61 -6/13 -11/24 -22/17 -4/9 -31/24 -9/20 -4/9 -102/79 -4/9 -71/55 -4/9 -19/43 -40/31 -4/9 -9/7 -3/7 -2/5 -23/18 -2/5 -1/3 -14/11 0/1 -33/26 -4/11 -1/3 -85/67 -1/3 -52/41 -8/25 -19/15 -2/7 -1/4 -43/34 -2/7 -1/4 -24/19 0/1 -29/23 -1/8 0/1 -34/27 0/1 -5/4 -1/1 0/1 -16/13 -4/5 -11/9 -2/3 -1/2 -17/14 -1/2 -6/5 0/1 -25/21 -2/1 -1/1 -19/16 -2/1 -1/1 -13/11 -1/1 0/1 -33/28 -1/1 0/1 -20/17 -4/5 -27/23 -5/7 -2/3 -34/29 -2/3 -7/6 -2/3 -1/2 -8/7 -4/7 -17/15 -1/2 -9/8 -1/2 -2/5 -10/9 0/1 -1/1 -1/2 0/1 0/1 0/1 1/1 0/1 1/0 9/8 2/1 1/0 17/15 1/0 8/7 -4/1 7/6 -2/1 1/0 20/17 -4/3 13/11 -1/1 0/1 19/16 -1/1 -2/3 25/21 -1/1 -2/3 6/5 0/1 17/14 1/0 11/9 -2/1 1/0 5/4 -1/1 0/1 24/19 0/1 43/34 1/2 2/3 19/15 1/2 2/3 33/26 1/1 4/3 14/11 0/1 9/7 2/1 3/1 22/17 4/1 35/27 8/1 1/0 13/10 8/1 1/0 17/13 1/0 4/3 -4/1 15/11 -2/1 -7/4 11/8 -2/1 -1/1 18/13 -4/1 7/5 -2/1 -1/1 17/12 -1/1 10/7 0/1 43/30 2/1 1/0 33/23 0/1 1/0 56/39 -4/1 23/16 -2/1 -1/1 13/9 -1/1 0/1 3/2 0/1 1/0 17/11 1/0 14/9 -4/1 11/7 -2/1 1/0 19/12 -2/1 -5/3 8/5 0/1 13/8 0/1 1/0 18/11 -4/1 5/3 0/1 1/0 17/10 1/0 12/7 -4/1 43/25 -6/1 -5/1 74/43 -4/1 31/18 -4/1 -7/2 19/11 -5/2 -2/1 7/4 -2/1 1/0 16/9 -8/3 9/5 -2/1 -5/3 11/6 -2/1 -1/1 13/7 -4/3 -1/1 15/8 -6/5 -1/1 17/9 -1/1 2/1 0/1 17/8 1/0 15/7 -6/1 1/0 13/6 -4/1 1/0 11/5 -2/1 1/0 9/4 -5/2 -2/1 34/15 -2/1 25/11 -2/1 -13/7 16/7 -8/5 7/3 -2/1 -1/1 26/11 0/1 19/8 -2/1 -5/3 31/13 -7/5 -4/3 12/5 -4/3 17/7 -1/1 5/2 -1/1 0/1 18/7 -4/3 85/33 -1/1 67/26 -1/1 -8/9 49/19 -3/4 -2/3 31/12 0/1 1/0 13/5 -1/1 0/1 34/13 0/1 21/8 0/1 1/0 8/3 0/1 27/10 -2/1 1/0 19/7 -5/2 -2/1 11/4 -2/1 -1/1 25/9 -2/1 -5/3 14/5 -4/3 17/6 -1/1 3/1 -1/1 0/1 19/6 2/1 3/1 16/5 -4/1 13/4 0/1 1/0 23/7 -2/1 1/0 33/10 -1/1 0/1 10/3 0/1 17/5 1/0 7/2 -2/1 1/0 18/5 -4/3 29/8 -1/1 0/1 11/3 -2/1 1/0 15/4 -7/3 -2/1 34/9 -2/1 19/5 -2/1 -11/6 4/1 -4/3 17/4 -1/1 13/3 -1/1 -8/9 48/11 -4/5 35/8 -1/1 -8/9 57/13 -7/8 -6/7 136/31 -6/7 79/18 -6/7 -11/13 22/5 -4/5 31/7 -9/11 -4/5 102/23 -4/5 71/16 -4/5 -19/24 40/9 -4/5 9/2 -3/4 -2/3 23/5 -2/3 -1/2 14/3 0/1 33/7 -4/7 -1/2 85/18 -1/2 52/11 -8/17 19/4 -2/5 -1/3 43/9 -2/5 -1/3 24/5 0/1 29/6 -1/7 0/1 34/7 0/1 5/1 0/1 1/0 16/3 -4/1 11/2 -2/1 -1/1 17/3 -1/1 6/1 0/1 25/4 2/1 1/0 19/3 2/1 1/0 13/2 0/1 1/0 33/5 0/1 1/0 20/3 -4/1 27/4 -5/2 -2/1 34/5 -2/1 7/1 -2/1 -1/1 8/1 -4/3 17/2 -1/1 9/1 -1/1 -2/3 10/1 0/1 1/0 -1/1 0/1 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(1,0,0,1) Matrix(35,306,4,35) -> Matrix(3,4,-4,-5) Matrix(33,272,4,33) -> Matrix(9,8,-8,-7) Matrix(33,238,14,101) -> Matrix(5,4,-4,-3) Matrix(101,680,-86,-579) -> Matrix(13,8,-18,-11) Matrix(135,884,-104,-681) -> Matrix(15,8,-32,-17) Matrix(69,442,32,205) -> Matrix(7,4,-2,-1) Matrix(205,1292,162,1021) -> Matrix(1,0,4,1) Matrix(169,1054,38,237) -> Matrix(11,4,-14,-5) Matrix(35,204,6,35) -> Matrix(1,0,0,1) Matrix(67,374,12,67) -> Matrix(5,4,-4,-3) Matrix(69,374,-50,-271) -> Matrix(1,0,0,1) Matrix(169,816,-134,-647) -> Matrix(1,0,-6,1) Matrix(135,646,14,67) -> Matrix(1,0,-2,1) Matrix(271,1292,228,1087) -> Matrix(1,0,-2,1) Matrix(611,2890,-374,-1769) -> Matrix(1,-4,-2,9) Matrix(441,2074,-340,-1599) -> Matrix(1,-4,-2,9) Matrix(103,476,-66,-305) -> Matrix(1,4,-2,-7) Matrix(239,1054,-100,-441) -> Matrix(7,8,-8,-9) Matrix(613,2686,-186,-815) -> Matrix(7,8,-8,-9) Matrix(203,884,-172,-749) -> Matrix(7,8,-8,-9) Matrix(103,442,24,103) -> Matrix(15,16,-16,-17) Matrix(33,136,8,33) -> Matrix(9,8,-8,-7) Matrix(35,136,-26,-101) -> Matrix(11,8,-18,-13) Matrix(101,374,64,237) -> Matrix(7,4,-2,-1) Matrix(103,374,-84,-305) -> Matrix(1,0,0,1) Matrix(67,238,38,135) -> Matrix(7,4,-2,-1) Matrix(69,238,20,69) -> Matrix(7,4,-2,-1) Matrix(101,340,30,101) -> Matrix(1,0,2,1) Matrix(441,1462,92,305) -> Matrix(1,0,-2,1) Matrix(1497,4930,-1156,-3807) -> Matrix(21,16,-46,-35) Matrix(135,442,62,203) -> Matrix(7,4,-2,-1) Matrix(137,442,-84,-271) -> Matrix(1,0,0,1) Matrix(35,102,12,35) -> Matrix(1,0,0,1) Matrix(169,476,60,169) -> Matrix(9,8,-8,-7) Matrix(171,476,-134,-373) -> Matrix(5,4,-14,-11) Matrix(137,374,100,273) -> Matrix(5,4,-4,-3) Matrix(239,646,-138,-373) -> Matrix(1,0,0,1) Matrix(103,272,-64,-169) -> Matrix(1,0,0,1) Matrix(171,442,-118,-305) -> Matrix(1,0,0,1) Matrix(67,170,-54,-137) -> Matrix(1,0,0,1) Matrix(69,170,28,69) -> Matrix(1,0,0,1) Matrix(169,408,70,169) -> Matrix(9,8,-8,-7) Matrix(883,2108,142,339) -> Matrix(5,4,6,5) Matrix(2721,6494,-2108,-5031) -> Matrix(59,48,-134,-109) Matrix(885,2108,-542,-1291) -> Matrix(5,4,-14,-11) Matrix(273,646,-172,-407) -> Matrix(1,0,0,1) Matrix(103,238,74,171) -> Matrix(5,4,-4,-3) Matrix(239,544,-134,-305) -> Matrix(23,16,-36,-25) Matrix(169,374,-108,-239) -> Matrix(1,0,0,1) Matrix(203,442,62,135) -> Matrix(7,4,-2,-1) Matrix(205,442,32,69) -> Matrix(7,4,-2,-1) Matrix(239,510,112,239) -> Matrix(23,12,-2,-1) Matrix(33,68,16,33) -> Matrix(1,0,2,1) Matrix(35,68,18,35) -> Matrix(1,0,0,1) Matrix(271,510,144,271) -> Matrix(13,12,-12,-11) Matrix(237,442,200,373) -> Matrix(5,4,-4,-3) Matrix(239,442,166,307) -> Matrix(5,4,-4,-3) Matrix(169,306,-132,-239) -> Matrix(5,4,-14,-11) Matrix(645,1156,284,509) -> Matrix(53,36,-28,-19) Matrix(647,1156,286,511) -> Matrix(55,36,-26,-17) Matrix(135,238,38,67) -> Matrix(7,4,-2,-1) Matrix(137,238,118,205) -> Matrix(7,4,-2,-1) Matrix(375,646,-256,-441) -> Matrix(7,4,-2,-1) Matrix(613,1054,-474,-815) -> Matrix(15,8,-32,-17) Matrix(239,408,140,239) -> Matrix(15,8,-2,-1) Matrix(101,170,60,101) -> Matrix(1,0,2,1) Matrix(373,612,-270,-443) -> Matrix(1,0,0,1) Matrix(3639,5950,770,1259) -> Matrix(23,12,-48,-25) Matrix(5201,8500,1102,1801) -> Matrix(25,12,-48,-23) Matrix(713,1156,272,441) -> Matrix(1,0,2,1) Matrix(715,1156,274,443) -> Matrix(1,0,0,1) Matrix(171,272,22,35) -> Matrix(5,4,-4,-3) Matrix(237,374,64,101) -> Matrix(7,4,-2,-1) Matrix(307,476,198,307) -> Matrix(15,8,-2,-1) Matrix(67,102,44,67) -> Matrix(1,0,2,1) Matrix(885,1292,-698,-1019) -> Matrix(3,4,-10,-13) Matrix(307,442,166,239) -> Matrix(5,4,-4,-3) Matrix(1871,2686,-1444,-2073) -> Matrix(15,8,-32,-17) Matrix(237,340,-214,-307) -> Matrix(1,0,0,1) Matrix(239,340,168,239) -> Matrix(1,0,0,1) Matrix(169,238,120,169) -> Matrix(5,4,-4,-3) Matrix(171,238,74,103) -> Matrix(5,4,-4,-3) Matrix(273,374,100,137) -> Matrix(5,4,-4,-3) Matrix(849,1156,224,305) -> Matrix(53,36,-28,-19) Matrix(851,1156,226,307) -> Matrix(55,36,-26,-17) Matrix(103,136,78,103) -> Matrix(15,8,-2,-1) Matrix(339,442,260,339) -> Matrix(33,16,2,1) Matrix(14279,18496,3254,4215) -> Matrix(233,108,-274,-127) Matrix(14281,18496,3256,4217) -> Matrix(235,108,-272,-125) Matrix(8057,10404,1816,2345) -> Matrix(251,112,-316,-141) Matrix(8059,10404,1818,2347) -> Matrix(253,112,-314,-139) Matrix(817,1054,686,885) -> Matrix(9,4,-16,-7) Matrix(883,1122,-750,-953) -> Matrix(11,4,-14,-5) Matrix(6699,8500,2600,3299) -> Matrix(35,12,-38,-13) Matrix(4691,5950,1822,2311) -> Matrix(37,12,-34,-11) Matrix(1021,1292,162,205) -> Matrix(1,0,4,1) Matrix(1157,1462,808,1021) -> Matrix(1,0,4,1) Matrix(917,1156,188,237) -> Matrix(1,0,8,1) Matrix(919,1156,190,239) -> Matrix(1,0,-6,1) Matrix(307,374,252,307) -> Matrix(7,4,-2,-1) Matrix(169,204,140,169) -> Matrix(1,0,2,1) Matrix(1769,2108,1028,1225) -> Matrix(1,-4,0,1) Matrix(1087,1292,228,271) -> Matrix(1,0,-2,1) Matrix(373,442,200,237) -> Matrix(5,4,-4,-3) Matrix(985,1156,144,169) -> Matrix(17,12,-10,-7) Matrix(987,1156,146,171) -> Matrix(19,12,-8,-5) Matrix(237,272,88,101) -> Matrix(7,4,-2,-1) Matrix(239,272,210,239) -> Matrix(15,8,-2,-1) Matrix(271,306,240,271) -> Matrix(9,4,2,1) Matrix(579,646,458,511) -> Matrix(1,0,4,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(307,-340,214,-237) -> Matrix(1,0,0,1) Matrix(579,-680,86,-101) -> Matrix(5,8,-2,-3) Matrix(749,-884,172,-203) -> Matrix(7,8,-8,-9) Matrix(305,-374,84,-103) -> Matrix(1,0,0,1) Matrix(647,-816,134,-169) -> Matrix(1,0,-6,1) Matrix(2279,-2890,884,-1121) -> Matrix(5,-4,-6,5) Matrix(1633,-2074,374,-475) -> Matrix(5,-4,-6,5) Matrix(373,-476,134,-171) -> Matrix(3,-4,-2,3) Matrix(815,-1054,474,-613) -> Matrix(1,-8,0,1) Matrix(2073,-2686,1444,-1871) -> Matrix(1,-8,0,1) Matrix(681,-884,104,-135) -> Matrix(1,-8,0,1) Matrix(101,-136,26,-35) -> Matrix(3,8,-2,-5) Matrix(271,-374,50,-69) -> Matrix(1,0,0,1) Matrix(3433,-4930,782,-1123) -> Matrix(5,16,-6,-19) Matrix(305,-442,118,-171) -> Matrix(1,0,0,1) Matrix(305,-476,66,-103) -> Matrix(1,4,-2,-7) Matrix(407,-646,172,-273) -> Matrix(1,0,0,1) Matrix(169,-272,64,-103) -> Matrix(1,0,0,1) Matrix(271,-442,84,-137) -> Matrix(1,0,0,1) Matrix(103,-170,20,-33) -> Matrix(1,0,0,1) Matrix(3773,-6494,850,-1463) -> Matrix(11,48,-14,-61) Matrix(1223,-2108,474,-817) -> Matrix(1,4,-2,-7) Matrix(373,-646,138,-239) -> Matrix(1,0,0,1) Matrix(305,-544,134,-239) -> Matrix(7,16,-4,-9) Matrix(205,-374,74,-135) -> Matrix(1,0,0,1) Matrix(137,-306,30,-67) -> Matrix(1,4,-2,-7) Matrix(271,-646,86,-205) -> Matrix(3,4,2,3) Matrix(441,-1054,100,-239) -> Matrix(7,8,-8,-9) Matrix(239,-612,66,-169) -> Matrix(1,0,0,1) Matrix(407,-1292,86,-273) -> Matrix(1,-4,-2,9) Matrix(815,-2686,186,-613) -> Matrix(7,8,-8,-9) Matrix(103,-340,10,-33) -> Matrix(1,0,0,1) Matrix(239,-1122,36,-169) -> Matrix(7,4,-2,-1) 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): 24 Degree of the the map X: 48 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): 216 Minimal number of generators: 41 Number of equivalence classes of elliptic points of order 2: 8 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 16 Genus: 9 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 2/1 17/7 3/1 17/5 34/9 4/1 17/4 14/3 34/7 6/1 34/5 7/1 17/2 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 0/1 1/0 7/6 -2/1 1/0 20/17 -4/3 13/11 -1/1 0/1 19/16 -1/1 -2/3 6/5 0/1 5/4 -1/1 0/1 24/19 0/1 43/34 1/2 2/3 19/15 1/2 2/3 14/11 0/1 9/7 2/1 3/1 22/17 4/1 35/27 8/1 1/0 13/10 8/1 1/0 17/13 1/0 4/3 -4/1 11/8 -2/1 -1/1 7/5 -2/1 -1/1 17/12 -1/1 10/7 0/1 3/2 0/1 1/0 5/3 0/1 1/0 17/10 1/0 12/7 -4/1 19/11 -5/2 -2/1 7/4 -2/1 1/0 16/9 -8/3 9/5 -2/1 -5/3 11/6 -2/1 -1/1 13/7 -4/3 -1/1 15/8 -6/5 -1/1 17/9 -1/1 2/1 0/1 11/5 -2/1 1/0 9/4 -5/2 -2/1 7/3 -2/1 -1/1 19/8 -2/1 -5/3 12/5 -4/3 17/7 -1/1 5/2 -1/1 0/1 3/1 -1/1 0/1 10/3 0/1 17/5 1/0 7/2 -2/1 1/0 11/3 -2/1 1/0 15/4 -7/3 -2/1 34/9 -2/1 19/5 -2/1 -11/6 4/1 -4/3 17/4 -1/1 13/3 -1/1 -8/9 35/8 -1/1 -8/9 22/5 -4/5 9/2 -3/4 -2/3 14/3 0/1 19/4 -2/5 -1/3 24/5 0/1 29/6 -1/7 0/1 34/7 0/1 5/1 0/1 1/0 6/1 0/1 25/4 2/1 1/0 19/3 2/1 1/0 13/2 0/1 1/0 20/3 -4/1 27/4 -5/2 -2/1 34/5 -2/1 7/1 -2/1 -1/1 8/1 -4/3 17/2 -1/1 9/1 -1/1 -2/3 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(89,-102,48,-55) (1/1,7/6) -> (11/6,13/7) Hyperbolic Matrix(579,-680,86,-101) (7/6,20/17) -> (20/3,27/4) Hyperbolic Matrix(837,-986,191,-225) (20/17,13/11) -> (35/8,22/5) Hyperbolic Matrix(115,-136,11,-13) (13/11,19/16) -> (9/1,1/0) Hyperbolic Matrix(599,-714,474,-565) (19/16,6/5) -> (24/19,43/34) Hyperbolic Matrix(55,-68,17,-21) (6/5,5/4) -> (3/1,10/3) Hyperbolic Matrix(647,-816,134,-169) (5/4,24/19) -> (24/5,29/6) Hyperbolic Matrix(1747,-2210,1381,-1747) (43/34,19/15) -> (43/34,19/15) Elliptic Matrix(429,-544,97,-123) (19/15,14/11) -> (22/5,9/2) Hyperbolic Matrix(293,-374,123,-157) (14/11,9/7) -> (19/8,12/5) Hyperbolic Matrix(421,-544,89,-115) (9/7,22/17) -> (14/3,19/4) Hyperbolic Matrix(761,-986,115,-149) (22/17,35/27) -> (13/2,20/3) Hyperbolic Matrix(1075,-1394,829,-1075) (35/27,13/10) -> (35/27,13/10) Elliptic Matrix(339,-442,79,-103) (13/10,17/13) -> (17/4,13/3) Hyperbolic Matrix(103,-136,25,-33) (17/13,4/3) -> (4/1,17/4) Hyperbolic Matrix(149,-204,84,-115) (4/3,11/8) -> (7/4,16/9) Hyperbolic Matrix(123,-170,89,-123) (11/8,7/5) -> (11/8,7/5) Elliptic Matrix(169,-238,49,-69) (7/5,17/12) -> (17/5,7/2) Hyperbolic Matrix(239,-340,71,-101) (17/12,10/7) -> (10/3,17/5) Hyperbolic Matrix(47,-68,9,-13) (10/7,3/2) -> (5/1,6/1) Hyperbolic Matrix(21,-34,13,-21) (3/2,5/3) -> (3/2,5/3) Elliptic Matrix(101,-170,41,-69) (5/3,17/10) -> (17/7,5/2) Hyperbolic Matrix(239,-408,99,-169) (17/10,12/7) -> (12/5,17/7) Hyperbolic Matrix(217,-374,47,-81) (12/7,19/11) -> (9/2,14/3) Hyperbolic Matrix(157,-272,71,-123) (19/11,7/4) -> (11/5,9/4) Hyperbolic Matrix(191,-340,50,-89) (16/9,9/5) -> (19/5,4/1) Hyperbolic Matrix(149,-272,63,-115) (9/5,11/6) -> (7/3,19/8) Hyperbolic Matrix(237,-442,37,-69) (13/7,15/8) -> (19/3,13/2) Hyperbolic Matrix(217,-408,25,-47) (15/8,17/9) -> (17/2,9/1) Hyperbolic Matrix(89,-170,11,-21) (17/9,2/1) -> (8/1,17/2) Hyperbolic Matrix(47,-102,6,-13) (2/1,11/5) -> (7/1,8/1) Hyperbolic Matrix(89,-204,24,-55) (9/4,7/3) -> (11/3,15/4) Hyperbolic Matrix(13,-34,5,-13) (5/2,3/1) -> (5/2,3/1) Elliptic Matrix(47,-170,13,-47) (7/2,11/3) -> (7/2,11/3) Elliptic Matrix(307,-1156,81,-305) (15/4,34/9) -> (34/9,19/5) Parabolic Matrix(319,-1394,73,-319) (13/3,35/8) -> (13/3,35/8) Elliptic Matrix(149,-714,24,-115) (19/4,24/5) -> (6/1,25/4) Hyperbolic Matrix(239,-1156,49,-237) (29/6,34/7) -> (34/7,5/1) Parabolic Matrix(157,-986,25,-157) (25/4,19/3) -> (25/4,19/3) Elliptic Matrix(171,-1156,25,-169) (27/4,34/5) -> (34/5,7/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(89,-102,48,-55) -> Matrix(1,4,-1,-3) Matrix(579,-680,86,-101) -> Matrix(5,8,-2,-3) Matrix(837,-986,191,-225) -> Matrix(7,8,-8,-9) Matrix(115,-136,11,-13) -> Matrix(1,0,0,1) Matrix(599,-714,474,-565) -> Matrix(1,0,3,1) Matrix(55,-68,17,-21) -> Matrix(1,0,0,1) Matrix(647,-816,134,-169) -> Matrix(1,0,-6,1) Matrix(1747,-2210,1381,-1747) -> Matrix(1,0,0,1) Matrix(429,-544,97,-123) -> Matrix(5,-4,-6,5) Matrix(293,-374,123,-157) -> Matrix(3,-4,-2,3) Matrix(421,-544,89,-115) -> Matrix(1,-4,-2,9) Matrix(761,-986,115,-149) -> Matrix(1,-8,0,1) Matrix(1075,-1394,829,-1075) -> Matrix(1,0,0,1) Matrix(339,-442,79,-103) -> Matrix(1,-16,-1,17) Matrix(103,-136,25,-33) -> Matrix(1,8,-1,-7) Matrix(149,-204,84,-115) -> Matrix(3,4,-1,-1) Matrix(123,-170,89,-123) -> Matrix(1,0,0,1) Matrix(169,-238,49,-69) -> Matrix(3,4,-1,-1) Matrix(239,-340,71,-101) -> Matrix(1,0,1,1) Matrix(47,-68,9,-13) -> Matrix(1,0,0,1) Matrix(21,-34,13,-21) -> Matrix(1,0,0,1) Matrix(101,-170,41,-69) -> Matrix(1,0,-1,1) Matrix(239,-408,99,-169) -> Matrix(1,8,-1,-7) Matrix(217,-374,47,-81) -> Matrix(1,4,-2,-7) Matrix(157,-272,71,-123) -> Matrix(1,0,0,1) Matrix(191,-340,50,-89) -> Matrix(5,12,-3,-7) Matrix(149,-272,63,-115) -> Matrix(1,0,0,1) Matrix(237,-442,37,-69) -> Matrix(3,4,-1,-1) Matrix(217,-408,25,-47) -> Matrix(7,8,-8,-9) Matrix(89,-170,11,-21) -> Matrix(5,4,-4,-3) Matrix(47,-102,6,-13) -> Matrix(1,4,-1,-3) Matrix(89,-204,24,-55) -> Matrix(3,4,-1,-1) Matrix(13,-34,5,-13) -> Matrix(1,0,0,1) Matrix(47,-170,13,-47) -> Matrix(1,0,0,1) Matrix(307,-1156,81,-305) -> Matrix(17,36,-9,-19) Matrix(319,-1394,73,-319) -> Matrix(1,0,0,1) Matrix(149,-714,24,-115) -> Matrix(1,0,3,1) Matrix(239,-1156,49,-237) -> Matrix(1,0,7,1) Matrix(157,-986,25,-157) -> Matrix(1,0,0,1) Matrix(171,-1156,25,-169) -> Matrix(5,12,-3,-7) 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): 12 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 1 1 2/1 0/1 1 17 11/5 (-2/1,1/0) 0 17 9/4 (-5/2,-2/1) 0 17 7/3 (-2/1,-1/1) 0 17 19/8 (-2/1,-5/3) 0 17 12/5 -4/3 1 17 17/7 -1/1 4 1 5/2 (-1/1,0/1) 0 17 3/1 (-1/1,0/1) 0 17 10/3 0/1 1 17 17/5 1/0 2 1 7/2 (-2/1,1/0) 0 17 11/3 (-2/1,1/0) 0 17 15/4 (-7/3,-2/1) 0 17 34/9 -2/1 9 1 4/1 -4/3 1 17 17/4 -1/1 12 1 13/3 (-1/1,-8/9) 0 17 35/8 (-1/1,-8/9) 0 17 22/5 -4/5 1 17 9/2 (-3/4,-2/3) 0 17 14/3 0/1 1 17 19/4 (-2/5,-1/3) 0 17 24/5 0/1 1 17 34/7 0/1 7 1 5/1 (0/1,1/0) 0 17 6/1 0/1 1 17 25/4 (2/1,1/0) 0 17 19/3 (2/1,1/0) 0 17 13/2 (0/1,1/0) 0 17 20/3 -4/1 1 17 34/5 -2/1 3 1 7/1 (-2/1,-1/1) 0 17 8/1 -4/3 1 17 17/2 -1/1 6 1 9/1 (-1/1,-2/3) 0 17 1/0 (-1/1,0/1) 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(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(47,-102,6,-13) (2/1,11/5) -> (7/1,8/1) Hyperbolic Matrix(123,-272,52,-115) (11/5,9/4) -> (7/3,19/8) Glide Reflection Matrix(89,-204,24,-55) (9/4,7/3) -> (11/3,15/4) Hyperbolic Matrix(157,-374,34,-81) (19/8,12/5) -> (9/2,14/3) Glide Reflection Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(13,-34,5,-13) (5/2,3/1) -> (5/2,3/1) Elliptic Matrix(21,-68,4,-13) (3/1,10/3) -> (5/1,6/1) Glide Reflection Matrix(101,-340,30,-101) (10/3,17/5) -> (10/3,17/5) Reflection Matrix(69,-238,20,-69) (17/5,7/2) -> (17/5,7/2) Reflection Matrix(47,-170,13,-47) (7/2,11/3) -> (7/2,11/3) Elliptic Matrix(271,-1020,72,-271) (15/4,34/9) -> (15/4,34/9) Reflection Matrix(35,-136,9,-35) (34/9,4/1) -> (34/9,4/1) 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(319,-1394,73,-319) (13/3,35/8) -> (13/3,35/8) Elliptic Matrix(225,-986,34,-149) (35/8,22/5) -> (13/2,20/3) Glide Reflection Matrix(123,-544,26,-115) (22/5,9/2) -> (14/3,19/4) Glide Reflection Matrix(149,-714,24,-115) (19/4,24/5) -> (6/1,25/4) Hyperbolic Matrix(169,-816,35,-169) (24/5,34/7) -> (24/5,34/7) Reflection Matrix(69,-340,14,-69) (34/7,5/1) -> (34/7,5/1) Reflection Matrix(157,-986,25,-157) (25/4,19/3) -> (25/4,19/3) Elliptic Matrix(21,-136,2,-13) (19/3,13/2) -> (9/1,1/0) Glide Reflection Matrix(101,-680,15,-101) (20/3,34/5) -> (20/3,34/5) Reflection Matrix(69,-476,10,-69) (34/5,7/1) -> (34/5,7/1) Reflection Matrix(33,-272,4,-33) (8/1,17/2) -> (8/1,17/2) Reflection Matrix(35,-306,4,-35) (17/2,9/1) -> (17/2,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(1,0,1,-1) -> Matrix(-1,0,1,1) (0/1,2/1) -> (-2/1,0/1) Matrix(47,-102,6,-13) -> Matrix(1,4,-1,-3) -2/1 Matrix(123,-272,52,-115) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(89,-204,24,-55) -> Matrix(3,4,-1,-1) -2/1 Matrix(157,-374,34,-81) -> Matrix(3,4,-5,-7) Matrix(169,-408,70,-169) -> Matrix(7,8,-6,-7) (12/5,17/7) -> (-4/3,-1/1) Matrix(69,-170,28,-69) -> Matrix(-1,0,2,1) (17/7,5/2) -> (-1/1,0/1) Matrix(13,-34,5,-13) -> Matrix(1,0,0,1) Matrix(21,-68,4,-13) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(101,-340,30,-101) -> Matrix(1,0,0,-1) (10/3,17/5) -> (0/1,1/0) Matrix(69,-238,20,-69) -> Matrix(1,4,0,-1) (17/5,7/2) -> (-2/1,1/0) Matrix(47,-170,13,-47) -> Matrix(1,0,0,1) Matrix(271,-1020,72,-271) -> Matrix(13,28,-6,-13) (15/4,34/9) -> (-7/3,-2/1) Matrix(35,-136,9,-35) -> Matrix(5,8,-3,-5) (34/9,4/1) -> (-2/1,-4/3) Matrix(33,-136,8,-33) -> Matrix(7,8,-6,-7) (4/1,17/4) -> (-4/3,-1/1) Matrix(103,-442,24,-103) -> Matrix(17,16,-18,-17) (17/4,13/3) -> (-1/1,-8/9) Matrix(319,-1394,73,-319) -> Matrix(1,0,0,1) Matrix(225,-986,34,-149) -> Matrix(9,8,-1,-1) Matrix(123,-544,26,-115) -> Matrix(5,4,-11,-9) Matrix(149,-714,24,-115) -> Matrix(1,0,3,1) 0/1 Matrix(169,-816,35,-169) -> Matrix(-1,0,7,1) (24/5,34/7) -> (-2/7,0/1) Matrix(69,-340,14,-69) -> Matrix(1,0,0,-1) (34/7,5/1) -> (0/1,1/0) Matrix(157,-986,25,-157) -> Matrix(1,0,0,1) Matrix(21,-136,2,-13) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(101,-680,15,-101) -> Matrix(3,8,-1,-3) (20/3,34/5) -> (-4/1,-2/1) Matrix(69,-476,10,-69) -> Matrix(3,4,-2,-3) (34/5,7/1) -> (-2/1,-1/1) Matrix(33,-272,4,-33) -> Matrix(7,8,-6,-7) (8/1,17/2) -> (-4/3,-1/1) Matrix(35,-306,4,-35) -> Matrix(5,4,-6,-5) (17/2,9/1) -> (-1/1,-2/3) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.