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 -6/1 -13/3 -21/5 -4/1 -10/3 -13/5 -2/1 -13/7 -39/25 -13/9 -13/11 -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 15/7 13/6 26/11 12/5 5/2 13/5 208/79 8/3 39/14 26/9 3/1 13/4 10/3 7/2 11/3 26/7 4/1 13/3 9/2 23/5 14/3 5/1 26/5 27/5 11/2 17/3 52/9 6/1 19/3 13/2 7/1 8/1 26/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/1 1/0 -13/2 1/0 -19/3 -4/1 1/0 -6/1 -5/2 1/0 -17/3 -2/1 -1/1 -11/2 -3/2 -16/3 -3/2 1/0 -21/4 1/0 -26/5 1/0 -5/1 -2/1 1/0 -9/2 -3/2 -13/3 -1/1 -17/4 1/0 -21/5 -1/1 0/1 -25/6 1/0 -4/1 -3/2 1/0 -15/4 -7/6 -26/7 -1/1 -11/3 -1/1 -2/3 -7/2 -3/2 -24/7 -5/2 1/0 -41/12 -3/2 -17/5 -2/1 -1/1 -27/8 -3/2 -37/11 -4/3 -1/1 -47/14 -3/2 -10/3 -3/2 -5/4 -23/7 -8/7 -1/1 -13/4 -1/1 -3/1 -1/1 1/0 -20/7 -7/8 -5/6 -37/13 -1/1 -4/5 -17/6 -3/4 -14/5 -3/4 -1/2 -53/19 -1/1 -2/3 -39/14 -2/3 -25/9 -2/3 -1/2 -11/4 1/0 -30/11 -5/6 -3/4 -49/18 -7/10 -19/7 -2/3 -1/2 -46/17 -1/2 1/0 -27/10 -1/2 -35/13 -1/3 0/1 -8/3 -1/2 1/0 -13/5 -1/1 -18/7 -7/8 -5/6 -23/9 -4/5 -7/9 -51/20 -3/4 -28/11 -3/4 -13/18 -5/2 -1/2 -27/11 -4/7 -1/2 -49/20 -5/12 -22/9 -1/2 -1/4 -17/7 -1/1 0/1 -12/5 -3/2 1/0 -43/18 1/0 -31/13 -2/1 -1/1 -50/21 -3/2 -11/8 -19/8 -5/4 -26/11 -1/1 -7/3 -1/1 -3/4 -9/4 -1/2 -11/5 -1/1 0/1 -13/6 -1/1 -15/7 -1/1 -2/3 -17/8 -3/4 -2/1 -1/2 1/0 -13/7 0/1 -24/13 1/2 1/0 -11/6 -1/2 -31/17 0/1 1/1 -51/28 1/0 -20/11 -3/2 1/0 -9/5 -2/3 -1/2 -25/14 -1/2 -16/9 -1/2 -3/8 -23/13 -1/3 -2/7 -7/4 -1/4 -26/15 0/1 -19/11 0/1 1/4 -12/7 -1/2 1/0 -29/17 -1/3 0/1 -17/10 1/0 -5/3 -1/2 0/1 -13/8 0/1 -21/13 0/1 1/3 -50/31 5/12 1/2 -129/80 1/2 -208/129 1/2 -79/49 1/2 8/15 -29/18 3/4 -37/23 -1/1 0/1 -8/5 1/2 1/0 -27/17 0/1 1/0 -73/46 1/0 -119/75 -4/1 -3/1 -46/29 -5/2 1/0 -19/12 -3/2 -11/7 -1/1 -2/3 -25/16 -1/2 -39/25 -1/2 -53/34 -1/2 -14/9 -1/2 -3/8 -17/11 -1/3 0/1 -20/13 -1/4 -1/6 -3/2 1/0 -13/9 0/1 -23/16 1/4 -33/23 0/1 1/0 -43/30 1/0 -10/7 1/2 1/0 -37/26 1/2 -27/19 2/1 1/0 -44/31 5/2 1/0 -17/12 1/0 -7/5 -1/1 -1/2 -25/18 -1/2 -43/31 -4/7 -1/2 -104/75 -1/2 -61/44 -1/2 -18/13 -1/2 -3/8 -29/21 -1/5 0/1 -40/29 -1/2 -1/4 -51/37 -1/3 0/1 -11/8 -1/4 -26/19 0/1 -15/11 0/1 1/3 -19/14 1/0 -23/17 1/1 2/1 -27/20 1/0 -4/3 -1/2 1/0 -17/13 -1/3 0/1 -13/10 0/1 -9/7 0/1 1/0 -32/25 -3/2 -5/4 -55/43 -11/10 -1/1 -78/61 -1/1 -23/18 -5/6 -37/29 -2/3 -3/5 -51/40 -1/2 -14/11 -1/2 -1/4 -19/15 0/1 1/2 -43/34 1/2 -24/19 3/2 1/0 -5/4 -1/2 -26/21 0/1 -21/17 0/1 1/3 -37/30 1/0 -16/13 1/2 1/0 -27/22 1/0 -11/9 -1/1 0/1 -17/14 -1/2 -23/19 -1/5 0/1 -52/43 0/1 -29/24 1/4 -6/5 -1/2 1/0 -13/11 0/1 -20/17 1/2 1/0 -7/6 -1/2 -15/13 0/1 1/1 -8/7 -1/2 1/0 -17/15 -1/3 0/1 -26/23 0/1 -9/8 1/0 -10/9 -1/2 1/0 -11/10 -1/2 -1/1 -1/1 0/1 0/1 0/1 1/1 0/1 1/1 10/9 1/2 1/0 9/8 1/0 8/7 1/2 1/0 7/6 1/2 13/11 0/1 19/16 1/4 6/5 1/2 1/0 11/9 0/1 1/1 16/13 -1/2 1/0 21/17 -1/3 0/1 26/21 0/1 5/4 1/2 14/11 1/4 1/2 37/29 3/5 2/3 23/18 5/6 9/7 0/1 1/0 13/10 0/1 17/13 0/1 1/3 4/3 1/2 1/0 19/14 1/0 34/25 -1/2 1/0 15/11 -1/3 0/1 26/19 0/1 11/8 1/4 29/21 0/1 1/5 18/13 3/8 1/2 7/5 1/2 1/1 10/7 -1/2 1/0 13/9 0/1 16/11 1/4 1/2 35/24 1/4 19/13 0/1 1/4 3/2 1/0 14/9 3/8 1/2 39/25 1/2 64/41 1/2 13/24 25/16 1/2 11/7 2/3 1/1 8/5 -1/2 1/0 37/23 0/1 1/1 29/18 -3/4 79/49 -8/15 -1/2 50/31 -1/2 -5/12 21/13 -1/3 0/1 13/8 0/1 5/3 0/1 1/2 12/7 1/2 1/0 31/18 1/0 50/29 -1/2 -3/8 69/40 -1/4 19/11 -1/4 0/1 26/15 0/1 7/4 1/4 30/17 1/6 1/4 53/30 1/4 23/13 2/7 1/3 16/9 3/8 1/2 41/23 2/5 3/7 25/14 1/2 9/5 1/2 2/3 29/16 7/8 20/11 3/2 1/0 31/17 -1/1 0/1 42/23 1/2 1/0 11/6 1/2 13/7 0/1 15/8 1/4 2/1 1/2 1/0 17/8 3/4 15/7 2/3 1/1 13/6 1/1 11/5 0/1 1/1 20/9 1/2 1/0 9/4 1/2 25/11 1/2 4/7 16/7 1/2 5/8 7/3 3/4 1/1 26/11 1/1 19/8 5/4 31/13 1/1 2/1 12/5 3/2 1/0 29/12 -1/2 17/7 0/1 1/1 22/9 1/4 1/2 27/11 1/2 4/7 5/2 1/2 13/5 1/1 21/8 5/4 50/19 17/12 3/2 129/49 40/27 3/2 208/79 3/2 79/30 3/2 29/11 5/3 2/1 8/3 1/2 1/0 27/10 1/2 73/27 3/5 2/3 46/17 1/2 1/0 19/7 1/2 2/3 11/4 1/0 25/9 1/2 2/3 39/14 2/3 53/19 2/3 1/1 14/5 1/2 3/4 31/11 2/3 1/1 17/6 3/4 37/13 4/5 1/1 20/7 5/6 7/8 23/8 15/16 26/9 1/1 3/1 1/1 1/0 13/4 1/1 23/7 1/1 8/7 10/3 5/4 3/2 37/11 1/1 4/3 64/19 23/16 3/2 27/8 3/2 44/13 3/2 7/4 61/18 7/4 78/23 2/1 17/5 1/1 2/1 24/7 5/2 1/0 31/9 0/1 1/1 7/2 3/2 32/9 5/2 1/0 57/16 1/0 25/7 0/1 1/0 43/12 1/0 18/5 -1/2 1/0 11/3 2/3 1/1 26/7 1/1 15/4 7/6 19/5 5/4 4/3 23/6 11/8 27/7 3/2 14/9 4/1 3/2 1/0 13/3 1/1 22/5 5/4 3/2 53/12 3/2 31/7 1/1 2/1 9/2 3/2 32/7 3/2 7/4 23/5 2/1 3/1 37/8 1/0 88/19 3/2 1/0 51/11 1/1 2/1 14/3 3/2 1/0 5/1 2/1 1/0 26/5 1/0 21/4 1/0 58/11 1/2 1/0 37/7 1/1 2/1 16/3 3/2 1/0 27/5 0/1 1/0 11/2 3/2 28/5 5/2 1/0 17/3 1/1 2/1 23/4 7/4 52/9 2/1 29/5 2/1 11/5 6/1 5/2 1/0 19/3 4/1 1/0 13/2 1/0 7/1 1/1 1/0 8/1 7/2 1/0 17/2 1/0 26/3 1/0 9/1 -2/1 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(25,182,-18,-131) (-7/1,1/0) -> (-7/5,-25/18) Hyperbolic Matrix(27,182,4,27) (-7/1,-13/2) -> (13/2,7/1) Hyperbolic Matrix(77,494,12,77) (-13/2,-19/3) -> (19/3,13/2) Hyperbolic Matrix(157,988,58,365) (-19/3,-6/1) -> (46/17,19/7) Hyperbolic Matrix(77,442,-50,-287) (-6/1,-17/3) -> (-17/11,-20/13) Hyperbolic Matrix(157,884,-46,-259) (-17/3,-11/2) -> (-41/12,-17/5) Hyperbolic Matrix(131,702,-92,-493) (-11/2,-16/3) -> (-10/7,-37/26) Hyperbolic Matrix(181,962,-54,-287) (-16/3,-21/4) -> (-47/14,-10/3) 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(27,130,-16,-77) (-5/1,-9/2) -> (-17/10,-5/3) Hyperbolic Matrix(77,338,-18,-79) (-9/2,-13/3) -> (-13/3,-17/4) Parabolic Matrix(209,884,74,313) (-17/4,-21/5) -> (31/11,17/6) Hyperbolic Matrix(573,2392,212,885) (-21/5,-25/6) -> (27/10,73/27) Hyperbolic Matrix(233,962,132,545) (-25/6,-4/1) -> (30/17,53/30) Hyperbolic Matrix(131,494,-48,-181) (-4/1,-15/4) -> (-11/4,-30/11) 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(79,286,-50,-181) (-11/3,-7/2) -> (-19/12,-11/7) Hyperbolic Matrix(233,806,-98,-339) (-7/2,-24/7) -> (-50/21,-19/8) Hyperbolic Matrix(129,442,68,233) (-24/7,-41/12) -> (15/8,2/1) Hyperbolic Matrix(415,1404,-154,-521) (-17/5,-27/8) -> (-27/10,-35/13) Hyperbolic Matrix(857,2886,-672,-2263) (-27/8,-37/11) -> (-37/29,-51/40) Hyperbolic Matrix(2469,8294,-1556,-5227) (-37/11,-47/14) -> (-73/46,-119/75) Hyperbolic Matrix(181,598,102,337) (-10/3,-23/7) -> (23/13,16/9) Hyperbolic Matrix(183,598,56,183) (-23/7,-13/4) -> (13/4,23/7) Hyperbolic Matrix(25,78,8,25) (-13/4,-3/1) -> (3/1,13/4) Hyperbolic Matrix(417,1196,-326,-935) (-3/1,-20/7) -> (-32/25,-55/43) Hyperbolic Matrix(1431,4082,-902,-2573) (-20/7,-37/13) -> (-119/75,-46/29) Hyperbolic Matrix(311,884,146,415) (-37/13,-17/6) -> (17/8,15/7) Hyperbolic Matrix(287,806,-120,-337) (-17/6,-14/5) -> (-12/5,-43/18) Hyperbolic Matrix(521,1456,112,313) (-14/5,-53/19) -> (51/11,14/3) Hyperbolic Matrix(1483,4134,532,1483) (-53/19,-39/14) -> (39/14,53/19) Hyperbolic Matrix(701,1950,252,701) (-39/14,-25/9) -> (25/9,39/14) Hyperbolic Matrix(441,1222,-310,-859) (-25/9,-11/4) -> (-37/26,-27/19) Hyperbolic Matrix(935,2548,-382,-1041) (-30/11,-49/18) -> (-49/20,-22/9) Hyperbolic Matrix(363,988,248,675) (-49/18,-19/7) -> (19/13,3/2) Hyperbolic Matrix(365,988,58,157) (-19/7,-46/17) -> (6/1,19/3) Hyperbolic Matrix(1067,2886,-586,-1585) (-46/17,-27/10) -> (-51/28,-20/11) Hyperbolic Matrix(155,416,-136,-365) (-35/13,-8/3) -> (-8/7,-17/15) Hyperbolic Matrix(129,338,-50,-131) (-8/3,-13/5) -> (-13/5,-18/7) Parabolic Matrix(365,936,264,677) (-18/7,-23/9) -> (29/21,18/13) Hyperbolic Matrix(937,2392,530,1353) (-23/9,-51/20) -> (53/30,23/13) Hyperbolic Matrix(2419,6162,-1500,-3821) (-51/20,-28/11) -> (-50/31,-129/80) Hyperbolic Matrix(441,1118,256,649) (-28/11,-5/2) -> (31/18,50/29) Hyperbolic Matrix(857,2106,-540,-1327) (-5/2,-27/11) -> (-27/17,-73/46) Hyperbolic Matrix(1899,4654,1178,2887) (-27/11,-49/20) -> (29/18,79/49) Hyperbolic Matrix(181,442,138,337) (-22/9,-17/7) -> (17/13,4/3) Hyperbolic Matrix(183,442,-118,-285) (-17/7,-12/5) -> (-14/9,-17/11) Hyperbolic Matrix(675,1612,152,363) (-43/18,-31/13) -> (31/7,9/2) Hyperbolic Matrix(1091,2600,676,1611) (-31/13,-50/21) -> (50/31,21/13) 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(79,182,-56,-129) (-7/3,-9/4) -> (-17/12,-7/5) Hyperbolic Matrix(129,286,-106,-235) (-9/4,-11/5) -> (-11/9,-17/14) Hyperbolic Matrix(131,286,60,131) (-11/5,-13/6) -> (13/6,11/5) Hyperbolic Matrix(181,390,84,181) (-13/6,-15/7) -> (15/7,13/6) Hyperbolic Matrix(415,884,146,311) (-15/7,-17/8) -> (17/6,37/13) Hyperbolic Matrix(469,988,272,573) (-17/8,-2/1) -> (50/29,69/40) Hyperbolic Matrix(181,338,-98,-183) (-2/1,-13/7) -> (-13/7,-24/13) Parabolic Matrix(311,572,56,103) (-24/13,-11/6) -> (11/2,28/5) Hyperbolic Matrix(755,1378,-612,-1117) (-11/6,-31/17) -> (-21/17,-37/30) Hyperbolic Matrix(1769,3224,400,729) (-31/17,-51/28) -> (53/12,31/7) 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(337,598,102,181) (-16/9,-23/13) -> (23/7,10/3) Hyperbolic Matrix(339,598,-250,-441) (-23/13,-7/4) -> (-19/14,-23/17) 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(287,494,-226,-389) (-19/11,-12/7) -> (-14/11,-19/15) Hyperbolic Matrix(883,1508,-640,-1093) (-12/7,-29/17) -> (-29/21,-40/29) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(79,130,48,79) (-5/3,-13/8) -> (13/8,5/3) Hyperbolic Matrix(337,546,208,337) (-13/8,-21/13) -> (21/13,13/8) Hyperbolic Matrix(1273,2054,370,597) (-21/13,-50/31) -> (24/7,31/9) 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(1195,1924,936,1507) (-29/18,-37/23) -> (37/29,23/18) Hyperbolic Matrix(857,1378,630,1013) (-37/23,-8/5) -> (34/25,15/11) Hyperbolic Matrix(883,1404,-622,-989) (-8/5,-27/17) -> (-27/19,-44/31) Hyperbolic Matrix(623,988,524,831) (-46/29,-19/12) -> (19/16,6/5) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(1949,3042,-1250,-1951) (-25/16,-39/25) -> (-39/25,-53/34) Parabolic Matrix(2419,3770,718,1119) (-53/34,-14/9) -> (64/19,27/8) Hyperbolic Matrix(389,598,-322,-495) (-20/13,-3/2) -> (-29/24,-6/5) Hyperbolic Matrix(233,338,-162,-235) (-3/2,-13/9) -> (-13/9,-23/16) Parabolic Matrix(833,1196,218,313) (-23/16,-33/23) -> (19/5,23/6) Hyperbolic Matrix(2157,3094,1250,1793) (-33/23,-43/30) -> (69/40,19/11) Hyperbolic Matrix(363,520,326,467) (-43/30,-10/7) -> (10/9,9/8) Hyperbolic Matrix(2107,2990,-1520,-2157) (-44/31,-17/12) -> (-61/44,-18/13) Hyperbolic Matrix(1481,2054,168,233) (-43/31,-104/75) -> (26/3,9/1) Hyperbolic Matrix(2419,3354,282,391) (-104/75,-61/44) -> (17/2,26/3) Hyperbolic Matrix(545,754,206,285) (-18/13,-29/21) -> (29/11,8/3) Hyperbolic Matrix(2055,2834,736,1015) (-40/29,-51/37) -> (53/19,14/5) Hyperbolic Matrix(415,572,-378,-521) (-51/37,-11/8) -> (-11/10,-1/1) 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(287,390,-248,-337) (-15/11,-19/14) -> (-7/6,-15/13) Hyperbolic Matrix(1923,2600,730,987) (-23/17,-27/20) -> (79/30,29/11) Hyperbolic Matrix(599,806,136,183) (-27/20,-4/3) -> (22/5,53/12) Hyperbolic Matrix(337,442,138,181) (-4/3,-17/13) -> (17/7,22/9) Hyperbolic Matrix(339,442,260,339) (-17/13,-13/10) -> (13/10,17/13) Hyperbolic Matrix(181,234,140,181) (-13/10,-9/7) -> (9/7,13/10) Hyperbolic Matrix(1301,1664,448,573) (-55/43,-78/61) -> (26/9,3/1) Hyperbolic Matrix(1871,2392,650,831) (-78/61,-23/18) -> (23/8,26/9) Hyperbolic Matrix(1507,1924,936,1195) (-23/18,-37/29) -> (37/23,29/18) Hyperbolic Matrix(2835,3614,1816,2315) (-51/40,-14/11) -> (64/41,25/16) Hyperbolic Matrix(1171,1482,802,1015) (-19/15,-43/34) -> (35/24,19/13) Hyperbolic Matrix(391,494,186,235) (-43/34,-24/19) -> (2/1,17/8) Hyperbolic Matrix(599,754,228,287) (-24/19,-5/4) -> (21/8,50/19) 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(443,546,-400,-493) (-37/30,-16/13) -> (-10/9,-11/10) 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(285,338,-242,-287) (-6/5,-13/11) -> (-13/11,-20/17) Parabolic Matrix(311,364,88,103) (-20/17,-7/6) -> (7/2,32/9) Hyperbolic Matrix(363,416,226,259) (-15/13,-8/7) -> (8/5,37/23) Hyperbolic Matrix(1561,1768,460,521) (-17/15,-26/23) -> (78/23,17/5) Hyperbolic Matrix(2027,2288,598,675) (-26/23,-9/8) -> (61/18,78/23) Hyperbolic Matrix(443,494,304,339) (-9/8,-10/9) -> (16/11,35/24) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(547,-598,118,-129) (1/1,10/9) -> (88/19,51/11) Hyperbolic Matrix(779,-884,230,-261) (9/8,8/7) -> (44/13,61/18) Hyperbolic Matrix(337,-390,248,-287) (8/7,7/6) -> (19/14,34/25) Hyperbolic Matrix(287,-338,242,-285) (7/6,13/11) -> (13/11,19/16) Parabolic Matrix(235,-286,106,-129) (6/5,11/9) -> (11/5,20/9) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(1117,-1378,612,-755) (16/13,21/17) -> (31/17,42/23) Hyperbolic Matrix(389,-494,226,-287) (5/4,14/11) -> (12/7,31/18) Hyperbolic Matrix(2263,-2886,672,-857) (14/11,37/29) -> (37/11,64/19) Hyperbolic Matrix(365,-468,202,-259) (23/18,9/7) -> (9/5,29/16) Hyperbolic Matrix(441,-598,250,-339) (4/3,19/14) -> (7/4,30/17) Hyperbolic Matrix(961,-1326,208,-287) (11/8,29/21) -> (23/5,37/8) Hyperbolic Matrix(131,-182,18,-25) (18/13,7/5) -> (7/1,8/1) Hyperbolic Matrix(129,-182,56,-79) (7/5,10/7) -> (16/7,7/3) Hyperbolic Matrix(235,-338,162,-233) (10/7,13/9) -> (13/9,16/11) Parabolic Matrix(285,-442,118,-183) (3/2,14/9) -> (12/5,29/12) Hyperbolic Matrix(1951,-3042,1250,-1949) (14/9,39/25) -> (39/25,64/41) Parabolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(181,-286,50,-79) (11/7,8/5) -> (18/5,11/3) Hyperbolic Matrix(6449,-10400,2450,-3951) (79/49,50/31) -> (50/19,129/49) Hyperbolic Matrix(77,-130,16,-27) (5/3,12/7) -> (14/3,5/1) Hyperbolic Matrix(131,-234,14,-25) (25/14,9/5) -> (9/1,1/0) Hyperbolic Matrix(573,-1040,200,-363) (29/16,20/11) -> (20/7,23/8) Hyperbolic Matrix(1585,-2886,586,-1067) (20/11,31/17) -> (73/27,46/17) Hyperbolic Matrix(1379,-2522,298,-545) (42/23,11/6) -> (37/8,88/19) Hyperbolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic 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(339,-806,98,-233) (19/8,31/13) -> (31/9,7/2) Hyperbolic Matrix(337,-806,120,-287) (31/13,12/5) -> (14/5,31/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(287,-702,74,-181) (22/9,27/11) -> (27/7,4/1) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(131,-338,50,-129) (5/2,13/5) -> (13/5,21/8) Parabolic Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(181,-494,48,-131) (19/7,11/4) -> (15/4,19/5) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1013,-2886,192,-547) (37/13,20/7) -> (58/11,37/7) Hyperbolic Matrix(287,-962,54,-181) (10/3,37/11) -> (37/7,16/3) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(1117,-3978,212,-755) (32/9,57/16) -> (21/4,58/11) Hyperbolic Matrix(181,-650,22,-79) (43/12,18/5) -> (8/1,17/2) Hyperbolic Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(233,-1066,40,-183) (32/7,23/5) -> (29/5,6/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(25,182,-18,-131) -> Matrix(1,2,-2,-3) Matrix(27,182,4,27) -> Matrix(1,2,0,1) Matrix(77,494,12,77) -> Matrix(1,8,0,1) Matrix(157,988,58,365) -> Matrix(1,2,2,5) Matrix(77,442,-50,-287) -> Matrix(1,2,-4,-7) Matrix(157,884,-46,-259) -> Matrix(1,0,0,1) Matrix(131,702,-92,-493) -> Matrix(1,2,0,1) Matrix(181,962,-54,-287) -> Matrix(3,2,-2,-1) Matrix(209,1092,40,209) -> Matrix(1,2,0,1) Matrix(51,260,10,51) -> Matrix(1,4,0,1) Matrix(27,130,-16,-77) -> Matrix(1,2,-2,-3) Matrix(77,338,-18,-79) -> Matrix(1,2,-2,-3) Matrix(209,884,74,313) -> Matrix(3,2,4,3) Matrix(573,2392,212,885) -> Matrix(1,-2,2,-3) Matrix(233,962,132,545) -> Matrix(1,2,4,9) Matrix(131,494,-48,-181) -> Matrix(5,6,-6,-7) Matrix(209,780,56,209) -> Matrix(13,14,12,13) Matrix(155,572,42,155) -> Matrix(5,4,6,5) Matrix(79,286,-50,-181) -> Matrix(1,0,0,1) Matrix(233,806,-98,-339) -> Matrix(3,2,-2,-1) Matrix(129,442,68,233) -> Matrix(1,2,2,5) Matrix(415,1404,-154,-521) -> Matrix(1,2,-4,-7) Matrix(857,2886,-672,-2263) -> Matrix(7,10,-12,-17) Matrix(2469,8294,-1556,-5227) -> Matrix(5,8,-2,-3) Matrix(181,598,102,337) -> Matrix(5,6,14,17) Matrix(183,598,56,183) -> Matrix(15,16,14,15) Matrix(25,78,8,25) -> Matrix(1,2,0,1) Matrix(417,1196,-326,-935) -> Matrix(11,10,-10,-9) Matrix(1431,4082,-902,-2573) -> Matrix(19,16,-6,-5) Matrix(311,884,146,415) -> Matrix(7,6,8,7) Matrix(287,806,-120,-337) -> Matrix(5,4,-4,-3) Matrix(521,1456,112,313) -> Matrix(1,0,2,1) Matrix(1483,4134,532,1483) -> Matrix(5,4,6,5) Matrix(701,1950,252,701) -> Matrix(7,4,12,7) Matrix(441,1222,-310,-859) -> Matrix(1,0,2,1) Matrix(935,2548,-382,-1041) -> Matrix(5,4,-14,-11) Matrix(363,988,248,675) -> Matrix(3,2,10,7) Matrix(365,988,58,157) -> Matrix(5,2,2,1) Matrix(1067,2886,-586,-1585) -> Matrix(3,2,-2,-1) Matrix(155,416,-136,-365) -> Matrix(1,0,0,1) Matrix(129,338,-50,-131) -> Matrix(5,6,-6,-7) Matrix(365,936,264,677) -> Matrix(5,4,16,13) Matrix(937,2392,530,1353) -> Matrix(13,10,48,37) Matrix(2419,6162,-1500,-3821) -> Matrix(19,14,42,31) Matrix(441,1118,256,649) -> Matrix(3,2,-2,-1) Matrix(857,2106,-540,-1327) -> Matrix(7,4,-2,-1) Matrix(1899,4654,1178,2887) -> Matrix(9,4,-16,-7) Matrix(181,442,138,337) -> Matrix(1,0,4,1) Matrix(183,442,-118,-285) -> Matrix(1,0,-2,1) Matrix(675,1612,152,363) -> Matrix(3,4,2,3) Matrix(1091,2600,676,1611) -> Matrix(1,2,-4,-7) Matrix(417,988,176,417) -> Matrix(9,10,8,9) Matrix(155,364,66,155) -> Matrix(7,6,8,7) Matrix(79,182,-56,-129) -> Matrix(3,2,-2,-1) Matrix(129,286,-106,-235) -> Matrix(1,0,0,1) Matrix(131,286,60,131) -> Matrix(1,0,2,1) Matrix(181,390,84,181) -> Matrix(5,4,6,5) Matrix(415,884,146,311) -> Matrix(7,6,8,7) Matrix(469,988,272,573) -> Matrix(3,2,-8,-5) Matrix(181,338,-98,-183) -> Matrix(1,0,2,1) Matrix(311,572,56,103) -> Matrix(1,2,0,1) Matrix(755,1378,-612,-1117) -> Matrix(1,0,2,1) Matrix(1769,3224,400,729) -> Matrix(3,-2,2,-1) Matrix(259,468,-202,-365) -> Matrix(3,2,-2,-1) Matrix(727,1300,-524,-937) -> Matrix(5,2,-8,-3) Matrix(467,832,-380,-677) -> Matrix(5,2,2,1) Matrix(337,598,102,181) -> Matrix(17,6,14,5) Matrix(339,598,-250,-441) -> Matrix(1,0,4,1) Matrix(209,364,120,209) -> Matrix(1,0,8,1) Matrix(571,988,330,571) -> Matrix(1,0,-8,1) Matrix(287,494,-226,-389) -> Matrix(1,0,-2,1) Matrix(883,1508,-640,-1093) -> Matrix(1,0,-2,1) Matrix(519,884,-428,-729) -> Matrix(1,0,-2,1) Matrix(79,130,48,79) -> Matrix(1,0,4,1) Matrix(337,546,208,337) -> Matrix(1,0,-6,1) Matrix(1273,2054,370,597) -> Matrix(1,0,-2,1) Matrix(26831,43264,10190,16431) -> Matrix(127,-62,84,-41) Matrix(26833,43264,10192,16433) -> Matrix(125,-64,84,-43) Matrix(1613,2600,420,677) -> Matrix(17,-10,12,-7) Matrix(1195,1924,936,1507) -> Matrix(1,-2,2,-3) Matrix(857,1378,630,1013) -> Matrix(1,0,-2,1) Matrix(883,1404,-622,-989) -> Matrix(1,2,0,1) Matrix(623,988,524,831) -> Matrix(1,2,2,5) Matrix(365,572,-298,-467) -> Matrix(3,2,-2,-1) Matrix(1949,3042,-1250,-1951) -> Matrix(15,8,-32,-17) Matrix(2419,3770,718,1119) -> Matrix(35,16,24,11) Matrix(389,598,-322,-495) -> Matrix(1,0,4,1) Matrix(233,338,-162,-235) -> Matrix(1,0,4,1) Matrix(833,1196,218,313) -> Matrix(5,-4,4,-3) Matrix(2157,3094,1250,1793) -> Matrix(1,0,-4,1) Matrix(363,520,326,467) -> Matrix(1,0,0,1) Matrix(2107,2990,-1520,-2157) -> Matrix(1,-4,-2,9) Matrix(1481,2054,168,233) -> Matrix(11,6,-2,-1) Matrix(2419,3354,282,391) -> Matrix(33,16,2,1) Matrix(545,754,206,285) -> Matrix(5,2,2,1) Matrix(2055,2834,736,1015) -> Matrix(7,2,10,3) Matrix(415,572,-378,-521) -> Matrix(1,0,2,1) Matrix(417,572,304,417) -> Matrix(1,0,8,1) Matrix(571,780,418,571) -> Matrix(1,0,-6,1) Matrix(287,390,-248,-337) -> Matrix(1,0,-2,1) Matrix(1923,2600,730,987) -> Matrix(3,-8,2,-5) Matrix(599,806,136,183) -> Matrix(3,4,2,3) Matrix(337,442,138,181) -> Matrix(1,0,4,1) Matrix(339,442,260,339) -> Matrix(1,0,6,1) Matrix(181,234,140,181) -> Matrix(1,0,0,1) Matrix(1301,1664,448,573) -> Matrix(11,12,10,11) Matrix(1871,2392,650,831) -> Matrix(21,20,22,21) Matrix(1507,1924,936,1195) -> Matrix(3,2,-2,-1) Matrix(2835,3614,1816,2315) -> Matrix(11,6,20,11) Matrix(1171,1482,802,1015) -> Matrix(1,0,2,1) Matrix(391,494,186,235) -> Matrix(1,-2,2,-3) Matrix(599,754,228,287) -> Matrix(3,4,2,3) Matrix(209,260,168,209) -> Matrix(1,0,4,1) Matrix(883,1092,714,883) -> Matrix(1,0,-6,1) Matrix(443,546,-400,-493) -> Matrix(1,0,-2,1) Matrix(2235,2704,386,467) -> Matrix(21,2,10,1) Matrix(2237,2704,388,469) -> Matrix(15,-2,8,-1) Matrix(285,338,-242,-287) -> Matrix(1,0,2,1) Matrix(311,364,88,103) -> Matrix(1,2,0,1) Matrix(363,416,226,259) -> Matrix(1,0,0,1) Matrix(1561,1768,460,521) -> Matrix(5,2,2,1) Matrix(2027,2288,598,675) -> Matrix(7,-2,4,-1) Matrix(443,494,304,339) -> Matrix(1,0,4,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(547,-598,118,-129) -> Matrix(3,-2,2,-1) Matrix(779,-884,230,-261) -> Matrix(7,-2,4,-1) Matrix(337,-390,248,-287) -> Matrix(1,0,-2,1) Matrix(287,-338,242,-285) -> Matrix(1,0,2,1) Matrix(235,-286,106,-129) -> Matrix(1,0,0,1) Matrix(677,-832,380,-467) -> Matrix(1,2,2,5) Matrix(1117,-1378,612,-755) -> Matrix(1,0,2,1) Matrix(389,-494,226,-287) -> Matrix(1,0,-2,1) Matrix(2263,-2886,672,-857) -> Matrix(17,-10,12,-7) Matrix(365,-468,202,-259) -> Matrix(1,-2,2,-3) Matrix(441,-598,250,-339) -> Matrix(1,0,4,1) Matrix(961,-1326,208,-287) -> Matrix(7,-2,4,-1) Matrix(131,-182,18,-25) -> Matrix(3,-2,2,-1) Matrix(129,-182,56,-79) -> Matrix(1,-2,2,-3) Matrix(235,-338,162,-233) -> Matrix(1,0,4,1) Matrix(285,-442,118,-183) -> Matrix(1,0,-2,1) Matrix(1951,-3042,1250,-1949) -> Matrix(17,-8,32,-15) Matrix(831,-1300,466,-729) -> Matrix(7,-4,16,-9) Matrix(181,-286,50,-79) -> Matrix(1,0,0,1) Matrix(6449,-10400,2450,-3951) -> Matrix(35,16,24,11) Matrix(77,-130,16,-27) -> Matrix(3,-2,2,-1) Matrix(131,-234,14,-25) -> Matrix(1,0,-2,1) Matrix(573,-1040,200,-363) -> Matrix(7,-8,8,-9) Matrix(1585,-2886,586,-1067) -> Matrix(1,-2,2,-3) Matrix(1379,-2522,298,-545) -> Matrix(3,-2,2,-1) Matrix(183,-338,98,-181) -> Matrix(1,0,2,1) Matrix(209,-468,46,-103) -> Matrix(7,-2,4,-1) Matrix(573,-1300,160,-363) -> Matrix(7,-4,2,-1) Matrix(365,-832,68,-155) -> Matrix(7,-4,2,-1) Matrix(339,-806,98,-233) -> Matrix(1,-2,2,-3) Matrix(337,-806,120,-287) -> Matrix(3,-4,4,-5) Matrix(365,-884,64,-155) -> Matrix(3,-2,2,-1) Matrix(287,-702,74,-181) -> Matrix(7,-2,4,-1) Matrix(677,-1664,190,-467) -> Matrix(7,-4,2,-1) Matrix(131,-338,50,-129) -> Matrix(7,-6,6,-5) Matrix(521,-1404,154,-415) -> Matrix(7,-2,4,-1) Matrix(181,-494,48,-131) -> Matrix(7,-6,6,-5) Matrix(207,-572,38,-105) -> Matrix(3,-2,2,-1) Matrix(1013,-2886,192,-547) -> Matrix(7,-6,6,-5) Matrix(287,-962,54,-181) -> Matrix(1,-2,2,-3) Matrix(259,-884,46,-157) -> Matrix(1,0,0,1) Matrix(1117,-3978,212,-755) -> Matrix(1,-2,0,1) Matrix(181,-650,22,-79) -> Matrix(1,4,0,1) Matrix(79,-338,18,-77) -> Matrix(3,-2,2,-1) Matrix(233,-1066,40,-183) -> Matrix(9,-16,4,-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 cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 50 Degree of the the map X: 50 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. ----------------------------------------------------------------------- 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 1/1 (0/1,1/1) 0 26 10/9 0 13 9/8 1/0 1 26 8/7 0 13 7/6 1/2 1 26 13/11 0/1 2 2 19/16 1/4 1 26 6/5 0 13 11/9 (0/1,1/1) 0 26 16/13 0 13 21/17 (-1/3,0/1) 0 26 26/21 0/1 5 1 5/4 1/2 1 26 14/11 0 13 37/29 (3/5,2/3) 0 26 23/18 5/6 1 26 9/7 (0/1,1/0) 0 26 13/10 0/1 3 2 17/13 (0/1,1/3) 0 26 4/3 0 13 19/14 1/0 1 26 34/25 0 13 15/11 (-1/3,0/1) 0 26 26/19 0/1 7 1 11/8 1/4 1 26 29/21 (0/1,1/5) 0 26 18/13 0 13 7/5 (1/2,1/1) 0 26 10/7 0 13 13/9 0/1 4 2 16/11 0 13 35/24 1/4 1 26 19/13 (0/1,1/4) 0 26 3/2 1/0 1 26 14/9 0 13 39/25 1/2 8 2 64/41 0 13 25/16 1/2 1 26 11/7 (2/3,1/1) 0 26 8/5 0 13 37/23 (0/1,1/1) 0 26 29/18 -3/4 1 26 79/49 (-8/15,-1/2) 0 26 50/31 0 13 21/13 (-1/3,0/1) 0 26 13/8 0/1 5 2 5/3 (0/1,1/2) 0 26 12/7 0 13 31/18 1/0 1 26 50/29 0 13 69/40 -1/4 1 26 19/11 (-1/4,0/1) 0 26 26/15 0/1 8 1 7/4 1/4 1 26 30/17 0 13 53/30 1/4 1 26 23/13 (2/7,1/3) 0 26 16/9 0 13 41/23 (2/5,3/7) 0 26 25/14 1/2 1 26 9/5 (1/2,2/3) 0 26 29/16 7/8 1 26 20/11 0 13 31/17 (-1/1,0/1) 0 26 42/23 0 13 11/6 1/2 1 26 13/7 0/1 2 2 15/8 1/4 1 26 2/1 0 13 17/8 3/4 1 26 15/7 (2/3,1/1) 0 26 13/6 1/1 2 2 11/5 (0/1,1/1) 0 26 20/9 0 13 9/4 1/2 1 26 25/11 (1/2,4/7) 0 26 16/7 0 13 7/3 (3/4,1/1) 0 26 26/11 1/1 8 1 19/8 5/4 1 26 31/13 (1/1,2/1) 0 26 12/5 0 13 29/12 -1/2 1 26 17/7 (0/1,1/1) 0 26 22/9 0 13 27/11 (1/2,4/7) 0 26 5/2 1/2 1 26 13/5 1/1 6 2 21/8 5/4 1 26 50/19 0 13 129/49 (40/27,3/2) 0 26 208/79 3/2 21 1 79/30 3/2 1 26 29/11 (5/3,2/1) 0 26 8/3 0 13 27/10 1/2 1 26 73/27 (3/5,2/3) 0 26 46/17 0 13 19/7 (1/2,2/3) 0 26 11/4 1/0 1 26 25/9 (1/2,2/3) 0 26 39/14 2/3 1 2 53/19 (2/3,1/1) 0 26 14/5 0 13 31/11 (2/3,1/1) 0 26 17/6 3/4 1 26 37/13 (4/5,1/1) 0 26 20/7 0 13 23/8 15/16 1 26 26/9 1/1 16 1 3/1 (1/1,1/0) 0 26 13/4 1/1 7 2 23/7 (1/1,8/7) 0 26 10/3 0 13 37/11 (1/1,4/3) 0 26 64/19 0 13 27/8 3/2 1 26 44/13 0 13 61/18 7/4 1 26 78/23 2/1 3 1 17/5 (1/1,2/1) 0 26 24/7 0 13 31/9 (0/1,1/1) 0 26 7/2 3/2 1 26 32/9 0 13 57/16 1/0 1 26 25/7 (0/1,1/0) 0 26 43/12 1/0 1 26 18/5 0 13 11/3 (2/3,1/1) 0 26 26/7 1/1 9 1 15/4 7/6 1 26 19/5 (5/4,4/3) 0 26 23/6 11/8 1 26 27/7 (3/2,14/9) 0 26 4/1 0 13 13/3 1/1 2 2 22/5 0 13 53/12 3/2 1 26 31/7 (1/1,2/1) 0 26 9/2 3/2 1 26 32/7 0 13 23/5 (2/1,3/1) 0 26 37/8 1/0 1 26 88/19 0 13 51/11 (1/1,2/1) 0 26 14/3 0 13 5/1 (2/1,1/0) 0 26 26/5 1/0 1 1 21/4 1/0 1 26 58/11 0 13 37/7 (1/1,2/1) 0 26 16/3 0 13 27/5 (0/1,1/0) 0 26 11/2 3/2 1 26 28/5 0 13 17/3 (1/1,2/1) 0 26 23/4 7/4 1 26 52/9 2/1 9 1 29/5 (2/1,11/5) 0 26 6/1 0 13 19/3 (4/1,1/0) 0 26 13/2 1/0 3 2 7/1 (1/1,1/0) 0 26 8/1 0 13 17/2 1/0 1 26 26/3 1/0 11 1 9/1 (-2/1,1/0) 0 26 1/0 1/0 1 26 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(547,-598,118,-129) (1/1,10/9) -> (88/19,51/11) Hyperbolic Matrix(443,-494,304,-339) (10/9,9/8) -> (16/11,35/24) Glide Reflection Matrix(779,-884,230,-261) (9/8,8/7) -> (44/13,61/18) Hyperbolic Matrix(337,-390,248,-287) (8/7,7/6) -> (19/14,34/25) Hyperbolic Matrix(287,-338,242,-285) (7/6,13/11) -> (13/11,19/16) Parabolic Matrix(547,-650,154,-183) (19/16,6/5) -> (7/2,32/9) Glide Reflection Matrix(235,-286,106,-129) (6/5,11/9) -> (11/5,20/9) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(1117,-1378,612,-755) (16/13,21/17) -> (31/17,42/23) Hyperbolic Matrix(883,-1092,714,-883) (21/17,26/21) -> (21/17,26/21) Reflection Matrix(209,-260,168,-209) (26/21,5/4) -> (26/21,5/4) Reflection Matrix(389,-494,226,-287) (5/4,14/11) -> (12/7,31/18) Hyperbolic Matrix(2263,-2886,672,-857) (14/11,37/29) -> (37/11,64/19) Hyperbolic Matrix(1507,-1924,936,-1195) (37/29,23/18) -> (37/23,29/18) Glide Reflection Matrix(365,-468,202,-259) (23/18,9/7) -> (9/5,29/16) Hyperbolic Matrix(181,-234,140,-181) (9/7,13/10) -> (9/7,13/10) Reflection Matrix(339,-442,260,-339) (13/10,17/13) -> (13/10,17/13) Reflection Matrix(337,-442,138,-181) (17/13,4/3) -> (17/7,22/9) Glide Reflection Matrix(441,-598,250,-339) (4/3,19/14) -> (7/4,30/17) Hyperbolic Matrix(1013,-1378,630,-857) (34/25,15/11) -> (8/5,37/23) Glide Reflection Matrix(571,-780,418,-571) (15/11,26/19) -> (15/11,26/19) Reflection Matrix(417,-572,304,-417) (26/19,11/8) -> (26/19,11/8) Reflection Matrix(961,-1326,208,-287) (11/8,29/21) -> (23/5,37/8) Hyperbolic Matrix(545,-754,206,-285) (29/21,18/13) -> (29/11,8/3) Glide Reflection Matrix(131,-182,18,-25) (18/13,7/5) -> (7/1,8/1) Hyperbolic Matrix(129,-182,56,-79) (7/5,10/7) -> (16/7,7/3) Hyperbolic Matrix(235,-338,162,-233) (10/7,13/9) -> (13/9,16/11) Parabolic Matrix(1353,-1976,784,-1145) (35/24,19/13) -> (69/40,19/11) Glide Reflection Matrix(337,-494,88,-129) (19/13,3/2) -> (19/5,23/6) Glide Reflection Matrix(285,-442,118,-183) (3/2,14/9) -> (12/5,29/12) Hyperbolic Matrix(1951,-3042,1250,-1949) (14/9,39/25) -> (39/25,64/41) Parabolic Matrix(2131,-3328,632,-987) (64/41,25/16) -> (64/19,27/8) Glide Reflection Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(181,-286,50,-79) (11/7,8/5) -> (18/5,11/3) Hyperbolic Matrix(1613,-2600,420,-677) (29/18,79/49) -> (23/6,27/7) Glide Reflection Matrix(6449,-10400,2450,-3951) (79/49,50/31) -> (50/19,129/49) Hyperbolic Matrix(1273,-2054,370,-597) (50/31,21/13) -> (24/7,31/9) Glide Reflection Matrix(337,-546,208,-337) (21/13,13/8) -> (21/13,13/8) Reflection Matrix(79,-130,48,-79) (13/8,5/3) -> (13/8,5/3) Reflection Matrix(77,-130,16,-27) (5/3,12/7) -> (14/3,5/1) Hyperbolic Matrix(1509,-2600,574,-989) (31/18,50/29) -> (21/8,50/19) Glide Reflection Matrix(573,-988,272,-469) (50/29,69/40) -> (2/1,17/8) Glide Reflection Matrix(571,-988,330,-571) (19/11,26/15) -> (19/11,26/15) Reflection Matrix(209,-364,120,-209) (26/15,7/4) -> (26/15,7/4) Reflection Matrix(1561,-2756,354,-625) (30/17,53/30) -> (22/5,53/12) Glide Reflection Matrix(1897,-3354,720,-1273) (53/30,23/13) -> (79/30,29/11) Glide Reflection Matrix(337,-598,102,-181) (23/13,16/9) -> (23/7,10/3) Glide Reflection Matrix(131,-234,14,-25) (25/14,9/5) -> (9/1,1/0) Hyperbolic Matrix(573,-1040,200,-363) (29/16,20/11) -> (20/7,23/8) Hyperbolic Matrix(1585,-2886,586,-1067) (20/11,31/17) -> (73/27,46/17) Hyperbolic Matrix(1379,-2522,298,-545) (42/23,11/6) -> (37/8,88/19) Hyperbolic Matrix(183,-338,98,-181) (11/6,13/7) -> (13/7,15/8) Parabolic Matrix(235,-442,42,-79) (15/8,2/1) -> (11/2,28/5) Glide Reflection Matrix(415,-884,146,-311) (17/8,15/7) -> (17/6,37/13) Glide Reflection Matrix(181,-390,84,-181) (15/7,13/6) -> (15/7,13/6) Reflection Matrix(131,-286,60,-131) (13/6,11/5) -> (13/6,11/5) Reflection 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(155,-364,66,-155) (7/3,26/11) -> (7/3,26/11) Reflection Matrix(417,-988,176,-417) (26/11,19/8) -> (26/11,19/8) Reflection Matrix(339,-806,98,-233) (19/8,31/13) -> (31/9,7/2) Hyperbolic Matrix(337,-806,120,-287) (31/13,12/5) -> (14/5,31/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(287,-702,74,-181) (22/9,27/11) -> (27/7,4/1) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(131,-338,50,-129) (5/2,13/5) -> (13/5,21/8) Parabolic Matrix(20383,-53664,7742,-20383) (129/49,208/79) -> (129/49,208/79) Reflection Matrix(12481,-32864,4740,-12481) (208/79,79/30) -> (208/79,79/30) Reflection Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(1741,-4706,394,-1065) (27/10,73/27) -> (53/12,31/7) Glide Reflection Matrix(365,-988,58,-157) (46/17,19/7) -> (6/1,19/3) Glide Reflection Matrix(181,-494,48,-131) (19/7,11/4) -> (15/4,19/5) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(701,-1950,252,-701) (25/9,39/14) -> (25/9,39/14) Reflection Matrix(1483,-4134,532,-1483) (39/14,53/19) -> (39/14,53/19) Reflection Matrix(521,-1456,112,-313) (53/19,14/5) -> (51/11,14/3) Glide Reflection Matrix(285,-806,64,-181) (31/11,17/6) -> (31/7,9/2) Glide Reflection Matrix(1013,-2886,192,-547) (37/13,20/7) -> (58/11,37/7) Hyperbolic Matrix(415,-1196,144,-415) (23/8,26/9) -> (23/8,26/9) Reflection Matrix(53,-156,18,-53) (26/9,3/1) -> (26/9,3/1) Reflection Matrix(25,-78,8,-25) (3/1,13/4) -> (3/1,13/4) Reflection Matrix(183,-598,56,-183) (13/4,23/7) -> (13/4,23/7) Reflection Matrix(287,-962,54,-181) (10/3,37/11) -> (37/7,16/3) Hyperbolic Matrix(2807,-9516,828,-2807) (61/18,78/23) -> (61/18,78/23) Reflection Matrix(781,-2652,230,-781) (78/23,17/5) -> (78/23,17/5) Reflection Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(1117,-3978,212,-755) (32/9,57/16) -> (21/4,58/11) Hyperbolic Matrix(181,-650,22,-79) (43/12,18/5) -> (8/1,17/2) Hyperbolic Matrix(155,-572,42,-155) (11/3,26/7) -> (11/3,26/7) Reflection Matrix(209,-780,56,-209) (26/7,15/4) -> (26/7,15/4) Reflection Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(233,-1066,40,-183) (32/7,23/5) -> (29/5,6/1) Hyperbolic Matrix(51,-260,10,-51) (5/1,26/5) -> (5/1,26/5) Reflection Matrix(209,-1092,40,-209) (26/5,21/4) -> (26/5,21/4) Reflection Matrix(415,-2392,72,-415) (23/4,52/9) -> (23/4,52/9) Reflection Matrix(521,-3016,90,-521) (52/9,29/5) -> (52/9,29/5) Reflection Matrix(77,-494,12,-77) (19/3,13/2) -> (19/3,13/2) Reflection Matrix(27,-182,4,-27) (13/2,7/1) -> (13/2,7/1) Reflection Matrix(103,-884,12,-103) (17/2,26/3) -> (17/2,26/3) Reflection Matrix(53,-468,6,-53) (26/3,9/1) -> (26/3,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Matrix(547,-598,118,-129) -> Matrix(3,-2,2,-1) 1/1 Matrix(443,-494,304,-339) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(779,-884,230,-261) -> Matrix(7,-2,4,-1) Matrix(337,-390,248,-287) -> Matrix(1,0,-2,1) 0/1 Matrix(287,-338,242,-285) -> Matrix(1,0,2,1) 0/1 Matrix(547,-650,154,-183) -> Matrix(5,-2,2,-1) Matrix(235,-286,106,-129) -> Matrix(1,0,0,1) Matrix(677,-832,380,-467) -> Matrix(1,2,2,5) Matrix(1117,-1378,612,-755) -> Matrix(1,0,2,1) 0/1 Matrix(883,-1092,714,-883) -> Matrix(-1,0,6,1) (21/17,26/21) -> (-1/3,0/1) Matrix(209,-260,168,-209) -> Matrix(1,0,4,-1) (26/21,5/4) -> (0/1,1/2) Matrix(389,-494,226,-287) -> Matrix(1,0,-2,1) 0/1 Matrix(2263,-2886,672,-857) -> Matrix(17,-10,12,-7) Matrix(1507,-1924,936,-1195) -> Matrix(3,-2,-2,1) Matrix(365,-468,202,-259) -> Matrix(1,-2,2,-3) 1/1 Matrix(181,-234,140,-181) -> Matrix(1,0,0,-1) (9/7,13/10) -> (0/1,1/0) Matrix(339,-442,260,-339) -> Matrix(1,0,6,-1) (13/10,17/13) -> (0/1,1/3) Matrix(337,-442,138,-181) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(441,-598,250,-339) -> Matrix(1,0,4,1) 0/1 Matrix(1013,-1378,630,-857) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(571,-780,418,-571) -> Matrix(-1,0,6,1) (15/11,26/19) -> (-1/3,0/1) Matrix(417,-572,304,-417) -> Matrix(1,0,8,-1) (26/19,11/8) -> (0/1,1/4) Matrix(961,-1326,208,-287) -> Matrix(7,-2,4,-1) Matrix(545,-754,206,-285) -> Matrix(5,-2,2,-1) Matrix(131,-182,18,-25) -> Matrix(3,-2,2,-1) 1/1 Matrix(129,-182,56,-79) -> Matrix(1,-2,2,-3) 1/1 Matrix(235,-338,162,-233) -> Matrix(1,0,4,1) 0/1 Matrix(1353,-1976,784,-1145) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(337,-494,88,-129) -> Matrix(11,-4,8,-3) Matrix(285,-442,118,-183) -> Matrix(1,0,-2,1) 0/1 Matrix(1951,-3042,1250,-1949) -> Matrix(17,-8,32,-15) 1/2 Matrix(2131,-3328,632,-987) -> Matrix(13,-8,8,-5) Matrix(831,-1300,466,-729) -> Matrix(7,-4,16,-9) 1/2 Matrix(181,-286,50,-79) -> Matrix(1,0,0,1) Matrix(1613,-2600,420,-677) -> Matrix(17,10,12,7) Matrix(6449,-10400,2450,-3951) -> Matrix(35,16,24,11) Matrix(1273,-2054,370,-597) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(337,-546,208,-337) -> Matrix(-1,0,6,1) (21/13,13/8) -> (-1/3,0/1) Matrix(79,-130,48,-79) -> Matrix(1,0,4,-1) (13/8,5/3) -> (0/1,1/2) Matrix(77,-130,16,-27) -> Matrix(3,-2,2,-1) 1/1 Matrix(1509,-2600,574,-989) -> Matrix(5,4,4,3) Matrix(573,-988,272,-469) -> Matrix(5,2,8,3) Matrix(571,-988,330,-571) -> Matrix(-1,0,8,1) (19/11,26/15) -> (-1/4,0/1) Matrix(209,-364,120,-209) -> Matrix(1,0,8,-1) (26/15,7/4) -> (0/1,1/4) Matrix(1561,-2756,354,-625) -> Matrix(19,-4,14,-3) Matrix(1897,-3354,720,-1273) -> Matrix(29,-8,18,-5) Matrix(337,-598,102,-181) -> Matrix(17,-6,14,-5) Matrix(131,-234,14,-25) -> Matrix(1,0,-2,1) 0/1 Matrix(573,-1040,200,-363) -> Matrix(7,-8,8,-9) 1/1 Matrix(1585,-2886,586,-1067) -> Matrix(1,-2,2,-3) 1/1 Matrix(1379,-2522,298,-545) -> Matrix(3,-2,2,-1) 1/1 Matrix(183,-338,98,-181) -> Matrix(1,0,2,1) 0/1 Matrix(235,-442,42,-79) -> Matrix(5,-2,2,-1) Matrix(415,-884,146,-311) -> Matrix(7,-6,8,-7) *** -> (3/4,1/1) Matrix(181,-390,84,-181) -> Matrix(5,-4,6,-5) (15/7,13/6) -> (2/3,1/1) Matrix(131,-286,60,-131) -> Matrix(1,0,2,-1) (13/6,11/5) -> (0/1,1/1) Matrix(209,-468,46,-103) -> Matrix(7,-2,4,-1) Matrix(573,-1300,160,-363) -> Matrix(7,-4,2,-1) Matrix(365,-832,68,-155) -> Matrix(7,-4,2,-1) Matrix(155,-364,66,-155) -> Matrix(7,-6,8,-7) (7/3,26/11) -> (3/4,1/1) Matrix(417,-988,176,-417) -> Matrix(9,-10,8,-9) (26/11,19/8) -> (1/1,5/4) Matrix(339,-806,98,-233) -> Matrix(1,-2,2,-3) 1/1 Matrix(337,-806,120,-287) -> Matrix(3,-4,4,-5) 1/1 Matrix(365,-884,64,-155) -> Matrix(3,-2,2,-1) 1/1 Matrix(287,-702,74,-181) -> Matrix(7,-2,4,-1) Matrix(677,-1664,190,-467) -> Matrix(7,-4,2,-1) Matrix(131,-338,50,-129) -> Matrix(7,-6,6,-5) 1/1 Matrix(20383,-53664,7742,-20383) -> Matrix(161,-240,108,-161) (129/49,208/79) -> (40/27,3/2) Matrix(12481,-32864,4740,-12481) -> Matrix(91,-138,60,-91) (208/79,79/30) -> (3/2,23/15) Matrix(521,-1404,154,-415) -> Matrix(7,-2,4,-1) Matrix(1741,-4706,394,-1065) -> Matrix(13,-8,8,-5) Matrix(365,-988,58,-157) -> Matrix(5,-2,2,-1) Matrix(181,-494,48,-131) -> Matrix(7,-6,6,-5) 1/1 Matrix(207,-572,38,-105) -> Matrix(3,-2,2,-1) 1/1 Matrix(701,-1950,252,-701) -> Matrix(7,-4,12,-7) (25/9,39/14) -> (1/2,2/3) Matrix(1483,-4134,532,-1483) -> Matrix(5,-4,6,-5) (39/14,53/19) -> (2/3,1/1) Matrix(521,-1456,112,-313) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(285,-806,64,-181) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1013,-2886,192,-547) -> Matrix(7,-6,6,-5) 1/1 Matrix(415,-1196,144,-415) -> Matrix(31,-30,32,-31) (23/8,26/9) -> (15/16,1/1) Matrix(53,-156,18,-53) -> Matrix(-1,2,0,1) (26/9,3/1) -> (1/1,1/0) Matrix(25,-78,8,-25) -> Matrix(-1,2,0,1) (3/1,13/4) -> (1/1,1/0) Matrix(183,-598,56,-183) -> Matrix(15,-16,14,-15) (13/4,23/7) -> (1/1,8/7) Matrix(287,-962,54,-181) -> Matrix(1,-2,2,-3) 1/1 Matrix(2807,-9516,828,-2807) -> Matrix(15,-28,8,-15) (61/18,78/23) -> (7/4,2/1) Matrix(781,-2652,230,-781) -> Matrix(3,-4,2,-3) (78/23,17/5) -> (1/1,2/1) Matrix(259,-884,46,-157) -> Matrix(1,0,0,1) Matrix(1117,-3978,212,-755) -> Matrix(1,-2,0,1) 1/0 Matrix(181,-650,22,-79) -> Matrix(1,4,0,1) 1/0 Matrix(155,-572,42,-155) -> Matrix(5,-4,6,-5) (11/3,26/7) -> (2/3,1/1) Matrix(209,-780,56,-209) -> Matrix(13,-14,12,-13) (26/7,15/4) -> (1/1,7/6) Matrix(79,-338,18,-77) -> Matrix(3,-2,2,-1) 1/1 Matrix(233,-1066,40,-183) -> Matrix(9,-16,4,-7) 2/1 Matrix(51,-260,10,-51) -> Matrix(-1,4,0,1) (5/1,26/5) -> (2/1,1/0) Matrix(209,-1092,40,-209) -> Matrix(-1,2,0,1) (26/5,21/4) -> (1/1,1/0) Matrix(415,-2392,72,-415) -> Matrix(15,-28,8,-15) (23/4,52/9) -> (7/4,2/1) Matrix(521,-3016,90,-521) -> Matrix(21,-44,10,-21) (52/9,29/5) -> (2/1,11/5) Matrix(77,-494,12,-77) -> Matrix(-1,8,0,1) (19/3,13/2) -> (4/1,1/0) Matrix(27,-182,4,-27) -> Matrix(-1,2,0,1) (13/2,7/1) -> (1/1,1/0) Matrix(103,-884,12,-103) -> Matrix(-1,18,0,1) (17/2,26/3) -> (9/1,1/0) Matrix(53,-468,6,-53) -> Matrix(1,4,0,-1) (26/3,9/1) -> (-2/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.