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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -16/3 -5/1 -14/3 -4/1 -15/4 -18/5 -10/3 -8/3 -5/2 -12/5 -16/7 -15/7 -2/1 -12/7 -5/3 -30/19 -10/7 -15/11 -4/3 -5/4 -10/9 0/1 1/1 20/17 5/4 4/3 10/7 3/2 20/13 5/3 100/59 12/7 20/11 15/8 2/1 15/7 20/9 16/7 40/17 160/67 12/5 5/2 100/39 8/3 30/11 25/9 20/7 3/1 10/3 7/2 18/5 40/11 11/3 160/43 15/4 19/5 4/1 80/19 17/4 13/3 40/9 9/2 14/3 19/4 5/1 16/3 11/2 17/3 40/7 6/1 13/2 20/3 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 0/1 1/1 -8/1 1/2 1/0 -7/1 0/1 1/0 -20/3 0/1 -13/2 0/1 1/3 -6/1 1/2 1/0 -17/3 0/1 1/1 -11/2 0/1 1/1 -16/3 1/0 -5/1 0/1 -24/5 1/2 -19/4 1/3 1/2 -14/3 1/2 3/4 -23/5 1/1 2/1 -32/7 1/2 1/0 -9/2 0/1 1/1 -13/3 0/1 1/1 -17/4 1/1 2/1 -4/1 0/1 -23/6 1/3 2/5 -42/11 9/20 1/2 -19/5 1/2 4/7 -15/4 1/1 -11/3 0/1 1/1 -18/5 1/2 1/0 -43/12 0/1 1/1 -25/7 1/1 -7/2 1/1 1/0 -17/5 -1/1 0/1 -10/3 0/1 -23/7 0/1 1/5 -13/4 0/1 1/3 -16/5 1/2 -19/6 1/2 1/1 -3/1 0/1 1/1 -20/7 0/1 -17/6 0/1 1/7 -14/5 1/4 1/2 -11/4 0/1 1/3 -41/15 0/1 1/3 -30/11 1/3 -19/7 2/5 1/2 -8/3 1/2 -21/8 1/3 1/2 -34/13 1/2 3/4 -13/5 0/1 1/1 -31/12 0/1 1/1 -18/7 1/2 1/0 -5/2 0/1 -22/9 1/4 1/2 -61/25 0/1 1/2 -100/41 0/1 -39/16 0/1 1/3 -17/7 0/1 1/3 -29/12 0/1 1/3 -41/17 0/1 1/3 -53/22 0/1 1/3 -12/5 1/3 -55/23 1/3 -43/18 1/3 2/5 -31/13 1/3 2/5 -19/8 1/3 1/2 -26/11 7/16 1/2 -7/3 1/2 2/3 -16/7 1/2 1/0 -41/18 0/1 1/1 -25/11 0/1 -34/15 1/2 1/0 -9/4 0/1 1/1 -20/9 0/1 -11/5 0/1 1/3 -13/6 0/1 1/3 -28/13 1/3 -15/7 1/3 -17/8 2/5 3/7 -2/1 1/2 1/0 -17/9 4/7 3/5 -15/8 2/3 -28/15 2/3 -13/7 2/3 1/1 -11/6 2/3 1/1 -20/11 1/1 -9/5 0/1 1/1 -43/24 0/1 1/1 -34/19 1/2 1/0 -25/14 1/1 -41/23 0/1 1/1 -16/9 1/2 1/0 -39/22 0/1 1/1 -23/13 0/1 1/1 -7/4 1/3 1/2 -40/23 1/2 -33/19 1/2 10/19 -26/15 1/2 9/16 -19/11 1/2 2/3 -50/29 3/5 -31/18 3/5 2/3 -74/43 1/2 5/8 -117/68 3/5 2/3 -160/93 1/2 5/8 -43/25 3/5 2/3 -12/7 2/3 -53/31 2/3 1/1 -41/24 2/3 1/1 -29/17 2/3 1/1 -17/10 2/3 1/1 -5/3 1/1 -23/14 0/1 1/1 -41/25 0/1 1/1 -100/61 1/1 -59/36 1/1 1/0 -18/11 1/2 1/0 -13/8 0/1 1/1 -34/21 1/4 1/2 -55/34 1/3 -21/13 1/2 2/3 -8/5 1/2 -19/12 1/2 3/5 -49/31 3/5 2/3 -30/19 2/3 -71/45 2/3 1/1 -41/26 2/3 1/1 -11/7 2/3 1/1 -25/16 1/1 -39/25 2/3 1/1 -53/34 2/3 1/1 -14/9 1/2 3/4 -17/11 6/7 1/1 -20/13 1/1 -3/2 0/1 1/1 -22/15 1/2 1/0 -19/13 0/1 1/2 -16/11 1/2 -29/20 2/3 1/1 -13/9 2/3 1/1 -10/7 1/1 -27/19 1/1 4/3 -17/12 1/1 2/1 -41/29 1/1 2/1 -24/17 3/2 1/0 -7/5 0/1 1/0 -32/23 1/2 1/0 -57/41 1/1 2/1 -25/18 0/1 -68/49 0/1 -43/31 0/1 1/1 -61/44 1/2 1/1 -18/13 1/2 1/0 -29/21 0/1 1/1 -40/29 1/2 1/0 -11/8 0/1 1/1 -26/19 1/2 1/0 -93/68 0/1 1/1 -160/117 1/2 1/0 -67/49 0/1 1/1 -41/30 0/1 1/1 -15/11 0/1 -34/25 1/4 1/2 -19/14 3/7 1/2 -4/3 1/1 -21/16 5/1 1/0 -80/61 1/0 -59/45 -12/1 1/0 -38/29 -7/2 1/0 -17/13 -1/1 0/1 -13/10 0/1 1/1 -22/17 1/2 1/0 -31/24 0/1 1/1 -40/31 1/2 1/0 -9/7 0/1 1/1 -32/25 1/2 1/0 -23/18 -1/1 0/1 -14/11 1/4 1/2 -19/15 1/2 2/3 -5/4 1/1 -21/17 0/1 1/0 -16/13 1/0 -27/22 0/1 1/1 -11/9 0/1 1/1 -17/14 0/1 1/1 -40/33 1/2 1/0 -23/19 0/1 1/1 -6/5 1/2 1/0 -13/11 2/3 1/1 -20/17 1/1 -7/6 1/1 1/0 -15/13 1/1 -23/20 -1/1 0/1 -8/7 1/2 1/0 -9/8 0/1 1/1 -10/9 1/1 -1/1 0/1 1/1 0/1 1/2 1/0 1/1 0/1 1/1 9/8 0/1 1/1 8/7 1/2 1/0 7/6 1/2 1/1 20/17 1/1 13/11 1/1 2/1 6/5 1/2 1/0 17/14 0/1 1/1 11/9 0/1 1/1 16/13 1/2 5/4 1/1 24/19 1/0 19/15 2/1 1/0 14/11 -1/2 1/0 23/18 0/1 1/3 32/25 1/2 1/0 9/7 0/1 1/1 13/10 0/1 1/1 17/13 0/1 1/3 4/3 1/1 23/17 2/1 3/1 42/31 11/2 1/0 19/14 -3/1 1/0 15/11 0/1 11/8 0/1 1/1 18/13 1/2 1/0 43/31 0/1 1/1 25/18 0/1 7/5 0/1 1/2 17/12 2/3 1/1 10/7 1/1 23/16 1/1 4/3 13/9 1/1 2/1 16/11 1/0 19/13 0/1 1/0 3/2 0/1 1/1 20/13 1/1 17/11 1/1 6/5 14/9 3/2 1/0 11/7 1/1 2/1 41/26 1/1 2/1 30/19 2/1 19/12 3/1 1/0 8/5 1/0 21/13 2/1 1/0 34/21 -1/2 1/0 13/8 0/1 1/1 31/19 0/1 1/1 18/11 1/2 1/0 5/3 1/1 22/13 3/2 1/0 61/36 1/1 1/0 100/59 1/1 39/23 1/1 2/1 17/10 1/1 2/1 29/17 1/1 2/1 41/24 1/1 2/1 53/31 1/1 2/1 12/7 2/1 55/32 2/1 43/25 2/1 3/1 31/18 2/1 3/1 19/11 2/1 1/0 26/15 9/2 1/0 7/4 -1/1 1/0 16/9 1/2 1/0 41/23 0/1 1/1 25/14 1/1 34/19 1/2 1/0 9/5 0/1 1/1 20/11 1/1 11/6 1/1 2/1 13/7 1/1 2/1 28/15 2/1 15/8 2/1 17/9 3/1 4/1 2/1 1/2 1/0 17/8 -3/1 -2/1 15/7 -1/1 28/13 -1/1 13/6 -1/1 0/1 11/5 -1/1 0/1 20/9 0/1 9/4 0/1 1/1 43/19 0/1 1/1 34/15 1/2 1/0 25/11 0/1 41/18 0/1 1/1 16/7 1/2 1/0 39/17 0/1 1/1 23/10 0/1 1/1 7/3 2/1 1/0 40/17 1/0 33/14 -9/1 1/0 26/11 -7/2 1/0 19/8 -1/1 1/0 50/21 -2/1 31/13 -2/1 -1/1 74/31 -3/2 1/0 117/49 -2/1 -1/1 160/67 -3/2 1/0 43/18 -2/1 -1/1 12/5 -1/1 53/22 -1/1 0/1 41/17 -1/1 0/1 29/12 -1/1 0/1 17/7 -1/1 0/1 5/2 0/1 23/9 0/1 1/1 41/16 0/1 1/1 100/39 0/1 59/23 0/1 1/2 18/7 1/2 1/0 13/5 0/1 1/1 34/13 3/2 1/0 55/21 2/1 21/8 -1/1 1/0 8/3 1/0 19/7 -2/1 1/0 49/18 -2/1 -1/1 30/11 -1/1 71/26 -1/1 0/1 41/15 -1/1 0/1 11/4 -1/1 0/1 25/9 0/1 39/14 -1/1 0/1 53/19 -1/1 0/1 14/5 -1/2 1/0 17/6 -1/5 0/1 20/7 0/1 3/1 0/1 1/1 22/7 1/2 1/0 19/6 1/1 1/0 16/5 1/0 29/9 -1/1 0/1 13/4 -1/1 0/1 10/3 0/1 27/8 0/1 1/5 17/5 0/1 1/3 41/12 0/1 1/3 24/7 1/4 1/2 7/2 1/2 1/1 32/9 1/2 1/0 57/16 0/1 1/3 25/7 1/1 68/19 1/1 43/12 0/1 1/1 61/17 0/1 1/0 18/5 1/2 1/0 29/8 0/1 1/1 40/11 1/2 1/0 11/3 0/1 1/1 26/7 1/2 1/0 93/25 0/1 1/1 160/43 1/2 1/0 67/18 0/1 1/1 41/11 0/1 1/1 15/4 1/1 34/9 3/2 1/0 19/5 4/1 1/0 4/1 0/1 21/5 4/9 1/2 80/19 1/2 59/14 1/2 13/25 38/9 1/2 9/16 17/4 2/3 1/1 13/3 0/1 1/1 22/5 1/2 1/0 31/7 0/1 1/1 40/9 1/2 1/0 9/2 0/1 1/1 32/7 1/2 1/0 23/5 2/3 1/1 14/3 3/2 1/0 19/4 -1/1 1/0 5/1 0/1 21/4 1/2 1/1 16/3 1/2 27/5 0/1 1/1 11/2 0/1 1/1 17/3 0/1 1/1 40/7 1/2 1/0 23/4 0/1 1/1 6/1 1/2 1/0 13/2 -1/1 0/1 20/3 0/1 7/1 0/1 1/2 15/2 0/1 23/3 2/3 1/1 8/1 1/2 1/0 9/1 0/1 1/1 10/1 0/1 1/0 0/1 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,440,-26,-279) (-9/1,1/0) -> (-71/45,-41/26) Hyperbolic Matrix(41,360,32,281) (-9/1,-8/1) -> (32/25,9/7) Hyperbolic Matrix(39,280,-28,-201) (-8/1,-7/1) -> (-7/5,-32/23) Hyperbolic Matrix(41,280,6,41) (-7/1,-20/3) -> (20/3,7/1) Hyperbolic Matrix(79,520,12,79) (-20/3,-13/2) -> (13/2,20/3) Hyperbolic Matrix(81,520,50,321) (-13/2,-6/1) -> (34/21,13/8) Hyperbolic Matrix(41,240,-34,-199) (-6/1,-17/3) -> (-23/19,-6/5) Hyperbolic Matrix(121,680,50,281) (-17/3,-11/2) -> (29/12,17/7) Hyperbolic Matrix(119,640,-82,-441) (-11/2,-16/3) -> (-16/11,-29/20) Hyperbolic Matrix(39,200,-8,-41) (-16/3,-5/1) -> (-5/1,-24/5) Parabolic Matrix(159,760,50,239) (-24/5,-19/4) -> (19/6,16/5) Hyperbolic Matrix(161,760,68,321) (-19/4,-14/3) -> (26/11,19/8) Hyperbolic Matrix(121,560,78,361) (-14/3,-23/5) -> (17/11,14/9) Hyperbolic Matrix(559,2560,-402,-1841) (-23/5,-32/7) -> (-32/23,-57/41) Hyperbolic Matrix(79,360,70,319) (-32/7,-9/2) -> (9/8,8/7) Hyperbolic Matrix(119,520,-46,-201) (-9/2,-13/3) -> (-13/5,-31/12) Hyperbolic Matrix(121,520,84,361) (-13/3,-17/4) -> (23/16,13/9) Hyperbolic Matrix(39,160,-10,-41) (-17/4,-4/1) -> (-4/1,-23/6) Parabolic Matrix(199,760,94,359) (-23/6,-42/11) -> (2/1,17/8) Hyperbolic Matrix(839,3200,-640,-2441) (-42/11,-19/5) -> (-59/45,-38/29) Hyperbolic Matrix(359,1360,-222,-841) (-19/5,-15/4) -> (-55/34,-21/13) Hyperbolic Matrix(119,440,-76,-281) (-15/4,-11/3) -> (-11/7,-25/16) Hyperbolic Matrix(199,720,-144,-521) (-11/3,-18/5) -> (-18/13,-29/21) Hyperbolic Matrix(279,1000,-190,-681) (-18/5,-43/12) -> (-3/2,-22/15) Hyperbolic Matrix(961,3440,-402,-1439) (-43/12,-25/7) -> (-55/23,-43/18) Hyperbolic Matrix(79,280,-68,-241) (-25/7,-7/2) -> (-7/6,-15/13) Hyperbolic Matrix(81,280,-46,-159) (-7/2,-17/5) -> (-23/13,-7/4) Hyperbolic Matrix(119,400,-36,-121) (-17/5,-10/3) -> (-10/3,-23/7) Parabolic Matrix(159,520,122,399) (-23/7,-13/4) -> (13/10,17/13) Hyperbolic Matrix(199,640,-162,-521) (-13/4,-16/5) -> (-16/13,-27/22) Hyperbolic Matrix(201,640,38,121) (-16/5,-19/6) -> (21/4,16/3) Hyperbolic Matrix(319,1000,-230,-721) (-19/6,-3/1) -> (-43/31,-61/44) Hyperbolic Matrix(41,120,14,41) (-3/1,-20/7) -> (20/7,3/1) Hyperbolic Matrix(239,680,84,239) (-20/7,-17/6) -> (17/6,20/7) Hyperbolic Matrix(199,560,156,439) (-17/6,-14/5) -> (14/11,23/18) Hyperbolic Matrix(159,440,-116,-321) (-14/5,-11/4) -> (-11/8,-26/19) Hyperbolic Matrix(599,1640,248,679) (-11/4,-41/15) -> (41/17,29/12) Hyperbolic Matrix(161,440,-146,-399) (-41/15,-30/11) -> (-10/9,-1/1) Hyperbolic Matrix(559,1520,-324,-881) (-30/11,-19/7) -> (-19/11,-50/29) Hyperbolic Matrix(119,320,74,199) (-19/7,-8/3) -> (8/5,21/13) Hyperbolic Matrix(121,320,76,201) (-8/3,-21/8) -> (19/12,8/5) Hyperbolic Matrix(519,1360,-382,-1001) (-21/8,-34/13) -> (-34/25,-19/14) Hyperbolic Matrix(199,520,168,439) (-34/13,-13/5) -> (13/11,6/5) Hyperbolic Matrix(481,1240,-372,-959) (-31/12,-18/7) -> (-22/17,-31/24) Hyperbolic Matrix(79,200,-32,-81) (-18/7,-5/2) -> (-5/2,-22/9) Parabolic Matrix(999,2440,278,679) (-22/9,-61/25) -> (61/17,18/5) Hyperbolic Matrix(4919,12000,1918,4679) (-61/25,-100/41) -> (100/39,59/23) Hyperbolic Matrix(3281,8000,1280,3121) (-100/41,-39/16) -> (41/16,100/39) Hyperbolic Matrix(559,1360,164,399) (-39/16,-17/7) -> (17/5,41/12) Hyperbolic Matrix(281,680,50,121) (-17/7,-29/12) -> (11/2,17/3) Hyperbolic Matrix(679,1640,248,599) (-29/12,-41/17) -> (41/15,11/4) Hyperbolic Matrix(2041,4920,548,1321) (-41/17,-53/22) -> (67/18,41/11) Hyperbolic Matrix(681,1640,316,761) (-53/22,-12/5) -> (28/13,13/6) Hyperbolic Matrix(719,1720,334,799) (-12/5,-55/23) -> (15/7,28/13) Hyperbolic Matrix(721,1720,-402,-959) (-43/18,-31/13) -> (-9/5,-43/24) Hyperbolic Matrix(639,1520,-404,-961) (-31/13,-19/8) -> (-19/12,-49/31) Hyperbolic Matrix(321,760,68,161) (-19/8,-26/11) -> (14/3,19/4) Hyperbolic Matrix(441,1040,-254,-599) (-26/11,-7/3) -> (-33/19,-26/15) Hyperbolic Matrix(121,280,-86,-199) (-7/3,-16/7) -> (-24/17,-7/5) Hyperbolic Matrix(719,1640,210,479) (-16/7,-41/18) -> (41/12,24/7) Hyperbolic Matrix(879,2000,316,719) (-41/18,-25/11) -> (25/9,39/14) Hyperbolic Matrix(1199,2720,458,1039) (-25/11,-34/15) -> (34/13,55/21) Hyperbolic Matrix(761,1720,-442,-999) (-34/15,-9/4) -> (-31/18,-74/43) Hyperbolic Matrix(161,360,72,161) (-9/4,-20/9) -> (20/9,9/4) Hyperbolic Matrix(199,440,90,199) (-20/9,-11/5) -> (11/5,20/9) Hyperbolic Matrix(201,440,-164,-359) (-11/5,-13/6) -> (-27/22,-11/9) Hyperbolic Matrix(761,1640,316,681) (-13/6,-28/13) -> (12/5,53/22) Hyperbolic Matrix(801,1720,224,481) (-28/13,-15/7) -> (25/7,68/19) Hyperbolic Matrix(599,1280,168,359) (-15/7,-17/8) -> (57/16,25/7) Hyperbolic Matrix(321,680,76,161) (-17/8,-2/1) -> (38/9,17/4) Hyperbolic Matrix(401,760,296,561) (-2/1,-17/9) -> (23/17,42/31) Hyperbolic Matrix(319,600,42,79) (-17/9,-15/8) -> (15/2,23/3) Hyperbolic Matrix(921,1720,536,1001) (-15/8,-28/15) -> (12/7,55/32) Hyperbolic Matrix(879,1640,514,959) (-28/15,-13/7) -> (53/31,12/7) Hyperbolic Matrix(281,520,-194,-359) (-13/7,-11/6) -> (-29/20,-13/9) Hyperbolic Matrix(241,440,132,241) (-11/6,-20/11) -> (20/11,11/6) Hyperbolic Matrix(199,360,110,199) (-20/11,-9/5) -> (9/5,20/11) Hyperbolic Matrix(3999,7160,-2324,-4161) (-43/24,-34/19) -> (-74/43,-117/68) Hyperbolic Matrix(761,1360,202,361) (-34/19,-25/14) -> (15/4,34/9) Hyperbolic Matrix(919,1640,246,439) (-25/14,-41/23) -> (41/11,15/4) Hyperbolic Matrix(719,1280,314,559) (-41/23,-16/9) -> (16/7,39/17) Hyperbolic Matrix(721,1280,316,561) (-16/9,-39/22) -> (41/18,16/7) Hyperbolic Matrix(1039,1840,406,719) (-39/22,-23/13) -> (23/9,41/16) Hyperbolic Matrix(919,1600,390,679) (-7/4,-40/23) -> (40/17,33/14) Hyperbolic Matrix(921,1600,392,681) (-40/23,-33/19) -> (7/3,40/17) Hyperbolic Matrix(439,760,346,599) (-26/15,-19/11) -> (19/15,14/11) Hyperbolic Matrix(441,760,-394,-679) (-50/29,-31/18) -> (-9/8,-10/9) Hyperbolic Matrix(14879,25600,6230,10719) (-117/68,-160/93) -> (160/67,43/18) Hyperbolic Matrix(14881,25600,6232,10721) (-160/93,-43/25) -> (117/49,160/67) Hyperbolic Matrix(2001,3440,-1442,-2479) (-43/25,-12/7) -> (-68/49,-43/31) Hyperbolic Matrix(959,1640,514,879) (-12/7,-53/31) -> (13/7,28/15) Hyperbolic Matrix(2481,4240,890,1521) (-53/31,-41/24) -> (39/14,53/19) Hyperbolic Matrix(961,1640,610,1041) (-41/24,-29/17) -> (11/7,41/26) Hyperbolic Matrix(399,680,328,559) (-29/17,-17/10) -> (17/14,11/9) Hyperbolic Matrix(119,200,-72,-121) (-17/10,-5/3) -> (-5/3,-23/14) Parabolic Matrix(1121,1840,488,801) (-23/14,-41/25) -> (39/17,23/10) Hyperbolic Matrix(4879,8000,2878,4719) (-41/25,-100/61) -> (100/59,39/23) Hyperbolic Matrix(7321,12000,4320,7081) (-100/61,-59/36) -> (61/36,100/59) Hyperbolic Matrix(1001,1640,318,521) (-59/36,-18/11) -> (22/7,19/6) Hyperbolic Matrix(319,520,-246,-401) (-18/11,-13/8) -> (-13/10,-22/17) Hyperbolic Matrix(321,520,50,81) (-13/8,-34/21) -> (6/1,13/2) Hyperbolic Matrix(1681,2720,940,1521) (-34/21,-55/34) -> (25/14,34/19) Hyperbolic Matrix(199,320,74,119) (-21/13,-8/5) -> (8/3,19/7) Hyperbolic Matrix(201,320,76,121) (-8/5,-19/12) -> (21/8,8/3) Hyperbolic Matrix(2279,3600,-1444,-2281) (-49/31,-30/19) -> (-30/19,-71/45) Parabolic Matrix(1041,1640,610,961) (-41/26,-11/7) -> (29/17,41/24) Hyperbolic Matrix(1281,2000,718,1121) (-25/16,-39/25) -> (41/23,25/14) Hyperbolic Matrix(2719,4240,1128,1759) (-39/25,-53/34) -> (53/22,41/17) Hyperbolic Matrix(1721,2680,-1258,-1959) (-53/34,-14/9) -> (-26/19,-93/68) Hyperbolic Matrix(361,560,78,121) (-14/9,-17/11) -> (23/5,14/3) Hyperbolic Matrix(441,680,286,441) (-17/11,-20/13) -> (20/13,17/11) Hyperbolic Matrix(79,120,52,79) (-20/13,-3/2) -> (3/2,20/13) Hyperbolic Matrix(1119,1640,436,639) (-22/15,-19/13) -> (59/23,18/7) Hyperbolic Matrix(521,760,412,601) (-19/13,-16/11) -> (24/19,19/15) Hyperbolic Matrix(279,400,-196,-281) (-13/9,-10/7) -> (-10/7,-27/19) Parabolic Matrix(479,680,112,159) (-27/19,-17/12) -> (17/4,13/3) Hyperbolic Matrix(961,1360,566,801) (-17/12,-41/29) -> (39/23,17/10) Hyperbolic Matrix(1161,1640,652,921) (-41/29,-24/17) -> (16/9,41/23) Hyperbolic Matrix(921,1280,490,681) (-57/41,-25/18) -> (15/8,17/9) Hyperbolic Matrix(1239,1720,662,919) (-25/18,-68/49) -> (28/15,15/8) Hyperbolic Matrix(1761,2440,1040,1441) (-61/44,-18/13) -> (22/13,61/36) Hyperbolic Matrix(1159,1600,318,439) (-29/21,-40/29) -> (40/11,11/3) Hyperbolic Matrix(1161,1600,320,441) (-40/29,-11/8) -> (29/8,40/11) Hyperbolic Matrix(18719,25600,5030,6879) (-93/68,-160/117) -> (160/43,67/18) Hyperbolic Matrix(18721,25600,5032,6881) (-160/117,-67/49) -> (93/25,160/43) Hyperbolic Matrix(3599,4920,2106,2879) (-67/49,-41/30) -> (41/24,53/31) Hyperbolic Matrix(1201,1640,528,721) (-41/30,-15/11) -> (25/11,41/18) Hyperbolic Matrix(999,1360,440,599) (-15/11,-34/25) -> (34/15,25/11) Hyperbolic Matrix(119,160,-90,-121) (-19/14,-4/3) -> (-4/3,-21/16) Parabolic Matrix(4879,6400,1158,1519) (-21/16,-80/61) -> (80/19,59/14) Hyperbolic Matrix(4881,6400,1160,1521) (-80/61,-59/45) -> (21/5,80/19) Hyperbolic Matrix(519,680,274,359) (-38/29,-17/13) -> (17/9,2/1) Hyperbolic Matrix(521,680,154,201) (-17/13,-13/10) -> (27/8,17/5) Hyperbolic Matrix(1239,1600,278,359) (-31/24,-40/31) -> (40/9,9/2) Hyperbolic Matrix(1241,1600,280,361) (-40/31,-9/7) -> (31/7,40/9) Hyperbolic Matrix(281,360,32,41) (-9/7,-32/25) -> (8/1,9/1) Hyperbolic Matrix(719,920,-626,-801) (-32/25,-23/18) -> (-23/20,-8/7) Hyperbolic Matrix(439,560,156,199) (-23/18,-14/11) -> (14/5,17/6) Hyperbolic Matrix(599,760,346,439) (-14/11,-19/15) -> (19/11,26/15) Hyperbolic Matrix(159,200,-128,-161) (-19/15,-5/4) -> (-5/4,-21/17) Parabolic Matrix(519,640,356,439) (-21/17,-16/13) -> (16/11,19/13) Hyperbolic Matrix(559,680,328,399) (-11/9,-17/14) -> (17/10,29/17) Hyperbolic Matrix(1319,1600,230,279) (-17/14,-40/33) -> (40/7,23/4) Hyperbolic Matrix(1321,1600,232,281) (-40/33,-23/19) -> (17/3,40/7) Hyperbolic Matrix(439,520,168,199) (-6/5,-13/11) -> (13/5,34/13) Hyperbolic Matrix(441,520,374,441) (-13/11,-20/17) -> (20/17,13/11) Hyperbolic Matrix(239,280,204,239) (-20/17,-7/6) -> (7/6,20/17) Hyperbolic Matrix(521,600,244,281) (-15/13,-23/20) -> (17/8,15/7) Hyperbolic Matrix(319,360,70,79) (-8/7,-9/8) -> (9/2,32/7) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(399,-440,146,-161) (1/1,9/8) -> (71/26,41/15) Hyperbolic Matrix(241,-280,68,-79) (8/7,7/6) -> (7/2,32/9) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(521,-640,162,-199) (11/9,16/13) -> (16/5,29/9) Hyperbolic Matrix(161,-200,128,-159) (16/13,5/4) -> (5/4,24/19) Parabolic Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(401,-520,246,-319) (9/7,13/10) -> (13/8,31/19) Hyperbolic Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(2361,-3200,560,-759) (42/31,19/14) -> (59/14,38/9) Hyperbolic Matrix(1001,-1360,382,-519) (19/14,15/11) -> (55/21,21/8) Hyperbolic Matrix(321,-440,116,-159) (15/11,11/8) -> (11/4,25/9) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(721,-1000,230,-319) (18/13,43/31) -> (3/1,22/7) Hyperbolic Matrix(2479,-3440,1442,-2001) (43/31,25/18) -> (55/32,43/25) Hyperbolic Matrix(201,-280,28,-39) (25/18,7/5) -> (7/1,15/2) Hyperbolic Matrix(199,-280,86,-121) (7/5,17/12) -> (23/10,7/3) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(441,-640,82,-119) (13/9,16/11) -> (16/3,27/5) Hyperbolic Matrix(681,-1000,190,-279) (19/13,3/2) -> (43/12,61/17) Hyperbolic Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(279,-440,26,-41) (41/26,30/19) -> (10/1,1/0) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(759,-1240,172,-281) (31/19,18/11) -> (22/5,31/7) Hyperbolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(999,-1720,442,-761) (43/25,31/18) -> (9/4,43/19) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(159,-280,46,-81) (7/4,16/9) -> (24/7,7/2) Hyperbolic Matrix(959,-1720,402,-721) (34/19,9/5) -> (31/13,74/31) Hyperbolic Matrix(239,-440,44,-81) (11/6,13/7) -> (27/5,11/2) Hyperbolic Matrix(239,-520,74,-161) (13/6,11/5) -> (29/9,13/4) Hyperbolic Matrix(3161,-7160,1324,-2999) (43/19,34/15) -> (74/31,117/49) Hyperbolic Matrix(319,-760,34,-81) (50/21,31/13) -> (9/1,10/1) Hyperbolic Matrix(1439,-3440,402,-961) (43/18,12/5) -> (68/19,43/12) Hyperbolic Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(201,-520,46,-119) (18/7,13/5) -> (13/3,22/5) Hyperbolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(959,-2680,258,-721) (53/19,14/5) -> (26/7,93/25) Hyperbolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(201,-920,26,-119) (32/7,23/5) -> (23/3,8/1) Hyperbolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,440,-26,-279) -> Matrix(1,-2,2,-3) Matrix(41,360,32,281) -> Matrix(1,0,0,1) Matrix(39,280,-28,-201) -> Matrix(1,0,0,1) Matrix(41,280,6,41) -> Matrix(1,0,2,1) Matrix(79,520,12,79) -> Matrix(1,0,-4,1) Matrix(81,520,50,321) -> Matrix(1,0,-2,1) Matrix(41,240,-34,-199) -> Matrix(1,0,0,1) Matrix(121,680,50,281) -> Matrix(1,0,-2,1) Matrix(119,640,-82,-441) -> Matrix(1,-2,2,-3) Matrix(39,200,-8,-41) -> Matrix(1,0,2,1) Matrix(159,760,50,239) -> Matrix(1,0,-2,1) Matrix(161,760,68,321) -> Matrix(5,-2,-2,1) Matrix(121,560,78,361) -> Matrix(5,-4,4,-3) Matrix(559,2560,-402,-1841) -> Matrix(1,0,0,1) Matrix(79,360,70,319) -> Matrix(1,0,0,1) Matrix(119,520,-46,-201) -> Matrix(1,0,0,1) Matrix(121,520,84,361) -> Matrix(3,-2,2,-1) Matrix(39,160,-10,-41) -> Matrix(1,0,2,1) Matrix(199,760,94,359) -> Matrix(9,-4,-2,1) Matrix(839,3200,-640,-2441) -> Matrix(17,-8,-2,1) Matrix(359,1360,-222,-841) -> Matrix(3,-2,8,-5) Matrix(119,440,-76,-281) -> Matrix(1,-2,2,-3) Matrix(199,720,-144,-521) -> Matrix(1,0,0,1) Matrix(279,1000,-190,-681) -> Matrix(1,0,0,1) Matrix(961,3440,-402,-1439) -> Matrix(3,-2,8,-5) Matrix(79,280,-68,-241) -> Matrix(1,0,0,1) Matrix(81,280,-46,-159) -> Matrix(1,0,2,1) Matrix(119,400,-36,-121) -> Matrix(1,0,6,1) Matrix(159,520,122,399) -> Matrix(1,0,-2,1) Matrix(199,640,-162,-521) -> Matrix(1,0,-2,1) Matrix(201,640,38,121) -> Matrix(1,0,0,1) Matrix(319,1000,-230,-721) -> Matrix(1,0,0,1) Matrix(41,120,14,41) -> Matrix(1,0,0,1) Matrix(239,680,84,239) -> Matrix(1,0,-12,1) Matrix(199,560,156,439) -> Matrix(1,0,-4,1) Matrix(159,440,-116,-321) -> Matrix(1,0,-2,1) Matrix(599,1640,248,679) -> Matrix(1,0,-4,1) Matrix(161,440,-146,-399) -> Matrix(1,0,-2,1) Matrix(559,1520,-324,-881) -> Matrix(9,-4,16,-7) Matrix(119,320,74,199) -> Matrix(1,0,-2,1) Matrix(121,320,76,201) -> Matrix(3,-2,2,-1) Matrix(519,1360,-382,-1001) -> Matrix(3,-2,8,-5) Matrix(199,520,168,439) -> Matrix(3,-2,2,-1) Matrix(481,1240,-372,-959) -> Matrix(1,0,0,1) Matrix(79,200,-32,-81) -> Matrix(1,0,2,1) Matrix(999,2440,278,679) -> Matrix(1,0,-2,1) Matrix(4919,12000,1918,4679) -> Matrix(1,0,0,1) Matrix(3281,8000,1280,3121) -> Matrix(1,0,-2,1) Matrix(559,1360,164,399) -> Matrix(1,0,0,1) Matrix(281,680,50,121) -> Matrix(1,0,-2,1) Matrix(679,1640,248,599) -> Matrix(1,0,-4,1) Matrix(2041,4920,548,1321) -> Matrix(1,0,-2,1) Matrix(681,1640,316,761) -> Matrix(1,0,-4,1) Matrix(719,1720,334,799) -> Matrix(5,-2,-2,1) Matrix(721,1720,-402,-959) -> Matrix(5,-2,8,-3) Matrix(639,1520,-404,-961) -> Matrix(9,-4,16,-7) Matrix(321,760,68,161) -> Matrix(5,-2,-2,1) Matrix(441,1040,-254,-599) -> Matrix(17,-8,32,-15) Matrix(121,280,-86,-199) -> Matrix(3,-2,2,-1) Matrix(719,1640,210,479) -> Matrix(1,0,2,1) Matrix(879,2000,316,719) -> Matrix(1,0,-2,1) Matrix(1199,2720,458,1039) -> Matrix(3,-2,2,-1) Matrix(761,1720,-442,-999) -> Matrix(5,-2,8,-3) Matrix(161,360,72,161) -> Matrix(1,0,0,1) Matrix(199,440,90,199) -> Matrix(1,0,-4,1) Matrix(201,440,-164,-359) -> Matrix(1,0,-2,1) Matrix(761,1640,316,681) -> Matrix(1,0,-4,1) Matrix(801,1720,224,481) -> Matrix(1,0,-2,1) Matrix(599,1280,168,359) -> Matrix(5,-2,8,-3) Matrix(321,680,76,161) -> Matrix(9,-4,16,-7) Matrix(401,760,296,561) -> Matrix(11,-6,2,-1) Matrix(319,600,42,79) -> Matrix(3,-2,8,-5) Matrix(921,1720,536,1001) -> Matrix(7,-4,2,-1) Matrix(879,1640,514,959) -> Matrix(5,-4,4,-3) Matrix(281,520,-194,-359) -> Matrix(1,0,0,1) Matrix(241,440,132,241) -> Matrix(5,-4,4,-3) Matrix(199,360,110,199) -> Matrix(1,0,0,1) Matrix(3999,7160,-2324,-4161) -> Matrix(5,-2,8,-3) Matrix(761,1360,202,361) -> Matrix(3,-2,2,-1) Matrix(919,1640,246,439) -> Matrix(1,0,0,1) Matrix(719,1280,314,559) -> Matrix(1,0,0,1) Matrix(721,1280,316,561) -> Matrix(1,0,0,1) Matrix(1039,1840,406,719) -> Matrix(1,0,0,1) Matrix(919,1600,390,679) -> Matrix(21,-10,-2,1) Matrix(921,1600,392,681) -> Matrix(23,-12,2,-1) Matrix(439,760,346,599) -> Matrix(7,-4,2,-1) Matrix(441,760,-394,-679) -> Matrix(3,-2,8,-5) Matrix(14879,25600,6230,10719) -> Matrix(13,-8,-8,5) Matrix(14881,25600,6232,10721) -> Matrix(13,-8,-8,5) Matrix(2001,3440,-1442,-2479) -> Matrix(3,-2,8,-5) Matrix(959,1640,514,879) -> Matrix(5,-4,4,-3) Matrix(2481,4240,890,1521) -> Matrix(3,-2,-4,3) Matrix(961,1640,610,1041) -> Matrix(5,-4,4,-3) Matrix(399,680,328,559) -> Matrix(3,-2,2,-1) Matrix(119,200,-72,-121) -> Matrix(3,-2,2,-1) Matrix(1121,1840,488,801) -> Matrix(1,0,0,1) Matrix(4879,8000,2878,4719) -> Matrix(3,-2,2,-1) Matrix(7321,12000,4320,7081) -> Matrix(1,0,0,1) Matrix(1001,1640,318,521) -> Matrix(1,0,0,1) Matrix(319,520,-246,-401) -> Matrix(1,0,0,1) Matrix(321,520,50,81) -> Matrix(1,0,-2,1) Matrix(1681,2720,940,1521) -> Matrix(1,0,-2,1) Matrix(199,320,74,119) -> Matrix(1,0,-2,1) Matrix(201,320,76,121) -> Matrix(3,-2,2,-1) Matrix(2279,3600,-1444,-2281) -> Matrix(13,-8,18,-11) Matrix(1041,1640,610,961) -> Matrix(5,-4,4,-3) Matrix(1281,2000,718,1121) -> Matrix(3,-2,2,-1) Matrix(2719,4240,1128,1759) -> Matrix(3,-2,-4,3) Matrix(1721,2680,-1258,-1959) -> Matrix(3,-2,2,-1) Matrix(361,560,78,121) -> Matrix(5,-4,4,-3) Matrix(441,680,286,441) -> Matrix(13,-12,12,-11) Matrix(79,120,52,79) -> Matrix(1,0,0,1) Matrix(1119,1640,436,639) -> Matrix(1,0,0,1) Matrix(521,760,412,601) -> Matrix(3,-2,2,-1) Matrix(279,400,-196,-281) -> Matrix(7,-6,6,-5) Matrix(479,680,112,159) -> Matrix(3,-4,4,-5) Matrix(961,1360,566,801) -> Matrix(1,0,0,1) Matrix(1161,1640,652,921) -> Matrix(1,-2,2,-3) Matrix(921,1280,490,681) -> Matrix(1,2,0,1) Matrix(1239,1720,662,919) -> Matrix(3,-2,2,-1) Matrix(1761,2440,1040,1441) -> Matrix(3,-2,2,-1) Matrix(1159,1600,318,439) -> Matrix(1,0,0,1) Matrix(1161,1600,320,441) -> Matrix(1,0,0,1) Matrix(18719,25600,5030,6879) -> Matrix(1,0,0,1) Matrix(18721,25600,5032,6881) -> Matrix(1,0,0,1) Matrix(3599,4920,2106,2879) -> Matrix(3,-2,2,-1) Matrix(1201,1640,528,721) -> Matrix(1,0,0,1) Matrix(999,1360,440,599) -> Matrix(1,0,-2,1) Matrix(119,160,-90,-121) -> Matrix(3,-2,2,-1) Matrix(4879,6400,1158,1519) -> Matrix(1,-18,2,-35) Matrix(4881,6400,1160,1521) -> Matrix(1,16,2,33) Matrix(519,680,274,359) -> Matrix(1,4,0,1) Matrix(521,680,154,201) -> Matrix(1,0,4,1) Matrix(1239,1600,278,359) -> Matrix(1,0,0,1) Matrix(1241,1600,280,361) -> Matrix(1,0,0,1) Matrix(281,360,32,41) -> Matrix(1,0,0,1) Matrix(719,920,-626,-801) -> Matrix(1,0,0,1) Matrix(439,560,156,199) -> Matrix(1,0,-4,1) Matrix(599,760,346,439) -> Matrix(7,-4,2,-1) Matrix(159,200,-128,-161) -> Matrix(3,-2,2,-1) Matrix(519,640,356,439) -> Matrix(1,0,0,1) Matrix(559,680,328,399) -> Matrix(3,-2,2,-1) Matrix(1319,1600,230,279) -> Matrix(1,0,0,1) Matrix(1321,1600,232,281) -> Matrix(1,0,0,1) Matrix(439,520,168,199) -> Matrix(3,-2,2,-1) Matrix(441,520,374,441) -> Matrix(5,-4,4,-3) Matrix(239,280,204,239) -> Matrix(1,-2,2,-3) Matrix(521,600,244,281) -> Matrix(1,-2,0,1) Matrix(319,360,70,79) -> Matrix(1,0,0,1) Matrix(1,0,2,1) -> Matrix(1,0,0,1) Matrix(399,-440,146,-161) -> Matrix(1,0,-2,1) Matrix(241,-280,68,-79) -> Matrix(1,0,0,1) Matrix(199,-240,34,-41) -> Matrix(1,0,0,1) Matrix(521,-640,162,-199) -> Matrix(1,0,-2,1) Matrix(161,-200,128,-159) -> Matrix(3,-2,2,-1) Matrix(2001,-2560,562,-719) -> Matrix(1,0,0,1) Matrix(401,-520,246,-319) -> Matrix(1,0,0,1) Matrix(121,-160,90,-119) -> Matrix(3,-2,2,-1) Matrix(2361,-3200,560,-759) -> Matrix(1,-10,2,-19) Matrix(1001,-1360,382,-519) -> Matrix(1,2,0,1) Matrix(321,-440,116,-159) -> Matrix(1,0,-2,1) Matrix(521,-720,144,-199) -> Matrix(1,0,0,1) Matrix(721,-1000,230,-319) -> Matrix(1,0,0,1) Matrix(2479,-3440,1442,-2001) -> Matrix(1,2,0,1) Matrix(201,-280,28,-39) -> Matrix(1,0,0,1) Matrix(199,-280,86,-121) -> Matrix(3,-2,2,-1) Matrix(281,-400,196,-279) -> Matrix(7,-6,6,-5) Matrix(441,-640,82,-119) -> Matrix(1,-2,2,-3) Matrix(681,-1000,190,-279) -> Matrix(1,0,0,1) Matrix(281,-440,76,-119) -> Matrix(1,-2,2,-3) Matrix(279,-440,26,-41) -> Matrix(1,-2,2,-3) Matrix(961,-1520,404,-639) -> Matrix(1,-4,0,1) Matrix(841,-1360,222,-359) -> Matrix(1,2,0,1) Matrix(759,-1240,172,-281) -> Matrix(1,0,0,1) Matrix(121,-200,72,-119) -> Matrix(3,-2,2,-1) Matrix(999,-1720,442,-761) -> Matrix(1,-2,0,1) Matrix(881,-1520,324,-559) -> Matrix(1,-4,0,1) Matrix(599,-1040,254,-441) -> Matrix(1,-8,0,1) Matrix(159,-280,46,-81) -> Matrix(1,0,2,1) Matrix(959,-1720,402,-721) -> Matrix(1,-2,0,1) Matrix(239,-440,44,-81) -> Matrix(1,-2,2,-3) Matrix(239,-520,74,-161) -> Matrix(1,0,0,1) Matrix(3161,-7160,1324,-2999) -> Matrix(1,-2,0,1) Matrix(319,-760,34,-81) -> Matrix(1,2,0,1) Matrix(1439,-3440,402,-961) -> Matrix(1,2,0,1) Matrix(81,-200,32,-79) -> Matrix(1,0,2,1) Matrix(201,-520,46,-119) -> Matrix(1,0,0,1) Matrix(1321,-3600,484,-1319) -> Matrix(1,2,-2,-3) Matrix(959,-2680,258,-721) -> Matrix(1,0,2,1) Matrix(121,-400,36,-119) -> Matrix(1,0,6,1) Matrix(41,-160,10,-39) -> Matrix(1,0,2,1) Matrix(201,-920,26,-119) -> Matrix(1,0,0,1) Matrix(41,-200,8,-39) -> Matrix(1,0,2,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 32 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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): 576 Minimal number of generators: 97 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: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 8/7 5/4 4/3 10/7 8/5 5/3 12/7 2/1 20/9 16/7 40/17 160/67 12/5 5/2 100/39 8/3 30/11 25/9 20/7 3/1 16/5 10/3 24/7 25/7 18/5 40/11 160/43 15/4 4/1 80/19 40/9 14/3 19/4 5/1 16/3 11/2 17/3 40/7 6/1 13/2 20/3 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 1/2 1/0 1/1 0/1 1/1 9/8 0/1 1/1 8/7 1/2 1/0 7/6 1/2 1/1 20/17 1/1 13/11 1/1 2/1 6/5 1/2 1/0 17/14 0/1 1/1 11/9 0/1 1/1 16/13 1/2 5/4 1/1 24/19 1/0 19/15 2/1 1/0 14/11 -1/2 1/0 23/18 0/1 1/3 32/25 1/2 1/0 9/7 0/1 1/1 13/10 0/1 1/1 17/13 0/1 1/3 4/3 1/1 23/17 2/1 3/1 42/31 11/2 1/0 19/14 -3/1 1/0 15/11 0/1 11/8 0/1 1/1 18/13 1/2 1/0 43/31 0/1 1/1 25/18 0/1 7/5 0/1 1/2 17/12 2/3 1/1 10/7 1/1 23/16 1/1 4/3 13/9 1/1 2/1 16/11 1/0 19/13 0/1 1/0 3/2 0/1 1/1 20/13 1/1 17/11 1/1 6/5 14/9 3/2 1/0 11/7 1/1 2/1 41/26 1/1 2/1 30/19 2/1 19/12 3/1 1/0 8/5 1/0 21/13 2/1 1/0 34/21 -1/2 1/0 13/8 0/1 1/1 31/19 0/1 1/1 18/11 1/2 1/0 5/3 1/1 22/13 3/2 1/0 61/36 1/1 1/0 100/59 1/1 39/23 1/1 2/1 17/10 1/1 2/1 29/17 1/1 2/1 41/24 1/1 2/1 53/31 1/1 2/1 12/7 2/1 55/32 2/1 43/25 2/1 3/1 31/18 2/1 3/1 19/11 2/1 1/0 26/15 9/2 1/0 7/4 -1/1 1/0 16/9 1/2 1/0 41/23 0/1 1/1 25/14 1/1 34/19 1/2 1/0 9/5 0/1 1/1 20/11 1/1 11/6 1/1 2/1 13/7 1/1 2/1 28/15 2/1 15/8 2/1 17/9 3/1 4/1 2/1 1/2 1/0 17/8 -3/1 -2/1 15/7 -1/1 28/13 -1/1 13/6 -1/1 0/1 11/5 -1/1 0/1 20/9 0/1 9/4 0/1 1/1 43/19 0/1 1/1 34/15 1/2 1/0 25/11 0/1 41/18 0/1 1/1 16/7 1/2 1/0 39/17 0/1 1/1 23/10 0/1 1/1 7/3 2/1 1/0 40/17 1/0 33/14 -9/1 1/0 26/11 -7/2 1/0 19/8 -1/1 1/0 50/21 -2/1 31/13 -2/1 -1/1 74/31 -3/2 1/0 117/49 -2/1 -1/1 160/67 -3/2 1/0 43/18 -2/1 -1/1 12/5 -1/1 53/22 -1/1 0/1 41/17 -1/1 0/1 29/12 -1/1 0/1 17/7 -1/1 0/1 5/2 0/1 23/9 0/1 1/1 41/16 0/1 1/1 100/39 0/1 59/23 0/1 1/2 18/7 1/2 1/0 13/5 0/1 1/1 34/13 3/2 1/0 55/21 2/1 21/8 -1/1 1/0 8/3 1/0 19/7 -2/1 1/0 49/18 -2/1 -1/1 30/11 -1/1 71/26 -1/1 0/1 41/15 -1/1 0/1 11/4 -1/1 0/1 25/9 0/1 39/14 -1/1 0/1 53/19 -1/1 0/1 14/5 -1/2 1/0 17/6 -1/5 0/1 20/7 0/1 3/1 0/1 1/1 22/7 1/2 1/0 19/6 1/1 1/0 16/5 1/0 29/9 -1/1 0/1 13/4 -1/1 0/1 10/3 0/1 27/8 0/1 1/5 17/5 0/1 1/3 41/12 0/1 1/3 24/7 1/4 1/2 7/2 1/2 1/1 32/9 1/2 1/0 57/16 0/1 1/3 25/7 1/1 68/19 1/1 43/12 0/1 1/1 61/17 0/1 1/0 18/5 1/2 1/0 29/8 0/1 1/1 40/11 1/2 1/0 11/3 0/1 1/1 26/7 1/2 1/0 93/25 0/1 1/1 160/43 1/2 1/0 67/18 0/1 1/1 41/11 0/1 1/1 15/4 1/1 34/9 3/2 1/0 19/5 4/1 1/0 4/1 0/1 21/5 4/9 1/2 80/19 1/2 59/14 1/2 13/25 38/9 1/2 9/16 17/4 2/3 1/1 13/3 0/1 1/1 22/5 1/2 1/0 31/7 0/1 1/1 40/9 1/2 1/0 9/2 0/1 1/1 32/7 1/2 1/0 23/5 2/3 1/1 14/3 3/2 1/0 19/4 -1/1 1/0 5/1 0/1 21/4 1/2 1/1 16/3 1/2 27/5 0/1 1/1 11/2 0/1 1/1 17/3 0/1 1/1 40/7 1/2 1/0 23/4 0/1 1/1 6/1 1/2 1/0 13/2 -1/1 0/1 20/3 0/1 7/1 0/1 1/2 15/2 0/1 23/3 2/3 1/1 8/1 1/2 1/0 9/1 0/1 1/1 10/1 0/1 1/0 0/1 1/1 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(399,-440,146,-161) (1/1,9/8) -> (71/26,41/15) Hyperbolic Matrix(319,-360,249,-281) (9/8,8/7) -> (32/25,9/7) Hyperbolic Matrix(241,-280,68,-79) (8/7,7/6) -> (7/2,32/9) Hyperbolic Matrix(239,-280,35,-41) (7/6,20/17) -> (20/3,7/1) Hyperbolic Matrix(441,-520,67,-79) (20/17,13/11) -> (13/2,20/3) Hyperbolic Matrix(439,-520,271,-321) (13/11,6/5) -> (34/21,13/8) Hyperbolic Matrix(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(559,-680,231,-281) (17/14,11/9) -> (29/12,17/7) Hyperbolic Matrix(521,-640,162,-199) (11/9,16/13) -> (16/5,29/9) Hyperbolic Matrix(161,-200,128,-159) (16/13,5/4) -> (5/4,24/19) Parabolic Matrix(601,-760,189,-239) (24/19,19/15) -> (19/6,16/5) Hyperbolic Matrix(599,-760,253,-321) (19/15,14/11) -> (26/11,19/8) Hyperbolic Matrix(439,-560,283,-361) (14/11,23/18) -> (17/11,14/9) Hyperbolic Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(401,-520,246,-319) (9/7,13/10) -> (13/8,31/19) Hyperbolic Matrix(399,-520,277,-361) (13/10,17/13) -> (23/16,13/9) Hyperbolic Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(561,-760,265,-359) (23/17,42/31) -> (2/1,17/8) Hyperbolic Matrix(2361,-3200,560,-759) (42/31,19/14) -> (59/14,38/9) Hyperbolic Matrix(1001,-1360,382,-519) (19/14,15/11) -> (55/21,21/8) Hyperbolic Matrix(321,-440,116,-159) (15/11,11/8) -> (11/4,25/9) Hyperbolic Matrix(521,-720,144,-199) (11/8,18/13) -> (18/5,29/8) Hyperbolic Matrix(721,-1000,230,-319) (18/13,43/31) -> (3/1,22/7) Hyperbolic Matrix(2479,-3440,1442,-2001) (43/31,25/18) -> (55/32,43/25) Hyperbolic Matrix(201,-280,28,-39) (25/18,7/5) -> (7/1,15/2) Hyperbolic Matrix(199,-280,86,-121) (7/5,17/12) -> (23/10,7/3) Hyperbolic Matrix(281,-400,196,-279) (17/12,10/7) -> (10/7,23/16) Parabolic Matrix(441,-640,82,-119) (13/9,16/11) -> (16/3,27/5) Hyperbolic Matrix(439,-640,83,-121) (16/11,19/13) -> (21/4,16/3) Hyperbolic Matrix(681,-1000,190,-279) (19/13,3/2) -> (43/12,61/17) Hyperbolic Matrix(79,-120,27,-41) (3/2,20/13) -> (20/7,3/1) Hyperbolic Matrix(441,-680,155,-239) (20/13,17/11) -> (17/6,20/7) Hyperbolic Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(1041,-1640,431,-679) (11/7,41/26) -> (41/17,29/12) Hyperbolic Matrix(279,-440,26,-41) (41/26,30/19) -> (10/1,1/0) Hyperbolic Matrix(961,-1520,404,-639) (30/19,19/12) -> (19/8,50/21) Hyperbolic Matrix(201,-320,125,-199) (19/12,8/5) -> (8/5,21/13) Parabolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(759,-1240,172,-281) (31/19,18/11) -> (22/5,31/7) Hyperbolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(1441,-2440,401,-679) (22/13,61/36) -> (61/17,18/5) Hyperbolic Matrix(7081,-12000,2761,-4679) (61/36,100/59) -> (100/39,59/23) Hyperbolic Matrix(4719,-8000,1841,-3121) (100/59,39/23) -> (41/16,100/39) Hyperbolic Matrix(801,-1360,235,-399) (39/23,17/10) -> (17/5,41/12) Hyperbolic Matrix(399,-680,71,-121) (17/10,29/17) -> (11/2,17/3) Hyperbolic Matrix(961,-1640,351,-599) (29/17,41/24) -> (41/15,11/4) Hyperbolic Matrix(2879,-4920,773,-1321) (41/24,53/31) -> (67/18,41/11) Hyperbolic Matrix(959,-1640,445,-761) (53/31,12/7) -> (28/13,13/6) Hyperbolic Matrix(1001,-1720,465,-799) (12/7,55/32) -> (15/7,28/13) Hyperbolic Matrix(999,-1720,442,-761) (43/25,31/18) -> (9/4,43/19) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(439,-760,93,-161) (19/11,26/15) -> (14/3,19/4) Hyperbolic Matrix(599,-1040,254,-441) (26/15,7/4) -> (33/14,26/11) Hyperbolic Matrix(159,-280,46,-81) (7/4,16/9) -> (24/7,7/2) Hyperbolic Matrix(921,-1640,269,-479) (16/9,41/23) -> (41/12,24/7) Hyperbolic Matrix(1121,-2000,403,-719) (41/23,25/14) -> (25/9,39/14) Hyperbolic Matrix(1521,-2720,581,-1039) (25/14,34/19) -> (34/13,55/21) Hyperbolic Matrix(959,-1720,402,-721) (34/19,9/5) -> (31/13,74/31) Hyperbolic Matrix(199,-360,89,-161) (9/5,20/11) -> (20/9,9/4) Hyperbolic Matrix(241,-440,109,-199) (20/11,11/6) -> (11/5,20/9) Hyperbolic Matrix(239,-440,44,-81) (11/6,13/7) -> (27/5,11/2) Hyperbolic Matrix(879,-1640,365,-681) (13/7,28/15) -> (12/5,53/22) Hyperbolic Matrix(919,-1720,257,-481) (28/15,15/8) -> (25/7,68/19) Hyperbolic Matrix(681,-1280,191,-359) (15/8,17/9) -> (57/16,25/7) Hyperbolic Matrix(359,-680,85,-161) (17/9,2/1) -> (38/9,17/4) Hyperbolic Matrix(281,-600,37,-79) (17/8,15/7) -> (15/2,23/3) Hyperbolic Matrix(239,-520,74,-161) (13/6,11/5) -> (29/9,13/4) Hyperbolic Matrix(3161,-7160,1324,-2999) (43/19,34/15) -> (74/31,117/49) Hyperbolic Matrix(599,-1360,159,-361) (34/15,25/11) -> (15/4,34/9) Hyperbolic Matrix(721,-1640,193,-439) (25/11,41/18) -> (41/11,15/4) Hyperbolic Matrix(561,-1280,245,-559) (41/18,16/7) -> (16/7,39/17) Parabolic Matrix(801,-1840,313,-719) (39/17,23/10) -> (23/9,41/16) Hyperbolic Matrix(681,-1600,289,-679) (7/3,40/17) -> (40/17,33/14) Parabolic Matrix(319,-760,34,-81) (50/21,31/13) -> (9/1,10/1) Hyperbolic Matrix(10721,-25600,4489,-10719) (117/49,160/67) -> (160/67,43/18) Parabolic Matrix(1439,-3440,402,-961) (43/18,12/5) -> (68/19,43/12) Hyperbolic Matrix(1759,-4240,631,-1521) (53/22,41/17) -> (39/14,53/19) Hyperbolic Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(639,-1640,203,-521) (59/23,18/7) -> (22/7,19/6) Hyperbolic Matrix(201,-520,46,-119) (18/7,13/5) -> (13/3,22/5) Hyperbolic Matrix(199,-520,31,-81) (13/5,34/13) -> (6/1,13/2) Hyperbolic Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(1321,-3600,484,-1319) (49/18,30/11) -> (30/11,71/26) Parabolic Matrix(959,-2680,258,-721) (53/19,14/5) -> (26/7,93/25) Hyperbolic Matrix(199,-560,43,-121) (14/5,17/6) -> (23/5,14/3) Hyperbolic Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(201,-680,47,-159) (27/8,17/5) -> (17/4,13/3) Hyperbolic Matrix(441,-1600,121,-439) (29/8,40/11) -> (40/11,11/3) Parabolic Matrix(6881,-25600,1849,-6879) (93/25,160/43) -> (160/43,67/18) Parabolic Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(1521,-6400,361,-1519) (21/5,80/19) -> (80/19,59/14) Parabolic Matrix(361,-1600,81,-359) (31/7,40/9) -> (40/9,9/2) Parabolic Matrix(79,-360,9,-41) (9/2,32/7) -> (8/1,9/1) Hyperbolic Matrix(201,-920,26,-119) (32/7,23/5) -> (23/3,8/1) Hyperbolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic Matrix(281,-1600,49,-279) (17/3,40/7) -> (40/7,23/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,-1,2,-1) Matrix(399,-440,146,-161) -> Matrix(1,0,-2,1) Matrix(319,-360,249,-281) -> Matrix(1,-1,2,-1) Matrix(241,-280,68,-79) -> Matrix(1,0,0,1) Matrix(239,-280,35,-41) -> Matrix(1,-1,4,-3) Matrix(441,-520,67,-79) -> Matrix(1,-1,-2,3) Matrix(439,-520,271,-321) -> Matrix(1,-1,0,1) Matrix(199,-240,34,-41) -> Matrix(1,0,0,1) Matrix(559,-680,231,-281) -> Matrix(1,-1,0,1) Matrix(521,-640,162,-199) -> Matrix(1,0,-2,1) Matrix(161,-200,128,-159) -> Matrix(3,-2,2,-1) Matrix(601,-760,189,-239) -> Matrix(1,-1,0,1) Matrix(599,-760,253,-321) -> Matrix(1,-3,0,1) Matrix(439,-560,283,-361) -> Matrix(3,1,2,1) Matrix(2001,-2560,562,-719) -> Matrix(1,0,0,1) Matrix(401,-520,246,-319) -> Matrix(1,0,0,1) Matrix(399,-520,277,-361) -> Matrix(1,1,0,1) Matrix(121,-160,90,-119) -> Matrix(3,-2,2,-1) Matrix(561,-760,265,-359) -> Matrix(1,-5,0,1) Matrix(2361,-3200,560,-759) -> Matrix(1,-10,2,-19) Matrix(1001,-1360,382,-519) -> Matrix(1,2,0,1) Matrix(321,-440,116,-159) -> Matrix(1,0,-2,1) Matrix(521,-720,144,-199) -> Matrix(1,0,0,1) Matrix(721,-1000,230,-319) -> Matrix(1,0,0,1) Matrix(2479,-3440,1442,-2001) -> Matrix(1,2,0,1) Matrix(201,-280,28,-39) -> Matrix(1,0,0,1) Matrix(199,-280,86,-121) -> Matrix(3,-2,2,-1) Matrix(281,-400,196,-279) -> Matrix(7,-6,6,-5) Matrix(441,-640,82,-119) -> Matrix(1,-2,2,-3) Matrix(439,-640,83,-121) -> Matrix(1,-1,2,-1) Matrix(681,-1000,190,-279) -> Matrix(1,0,0,1) Matrix(79,-120,27,-41) -> Matrix(1,-1,2,-1) Matrix(441,-680,155,-239) -> Matrix(1,-1,-10,11) Matrix(281,-440,76,-119) -> Matrix(1,-2,2,-3) Matrix(1041,-1640,431,-679) -> Matrix(1,-1,-2,3) Matrix(279,-440,26,-41) -> Matrix(1,-2,2,-3) Matrix(961,-1520,404,-639) -> Matrix(1,-4,0,1) Matrix(201,-320,125,-199) -> Matrix(1,-1,0,1) Matrix(841,-1360,222,-359) -> Matrix(1,2,0,1) Matrix(759,-1240,172,-281) -> Matrix(1,0,0,1) Matrix(121,-200,72,-119) -> Matrix(3,-2,2,-1) Matrix(1441,-2440,401,-679) -> Matrix(1,-1,0,1) Matrix(7081,-12000,2761,-4679) -> Matrix(1,-1,2,-1) Matrix(4719,-8000,1841,-3121) -> Matrix(1,-1,0,1) Matrix(801,-1360,235,-399) -> Matrix(1,-1,2,-1) Matrix(399,-680,71,-121) -> Matrix(1,-1,0,1) Matrix(961,-1640,351,-599) -> Matrix(1,-1,-2,3) Matrix(2879,-4920,773,-1321) -> Matrix(1,-1,0,1) Matrix(959,-1640,445,-761) -> Matrix(1,-1,-2,3) Matrix(1001,-1720,465,-799) -> Matrix(1,-3,0,1) Matrix(999,-1720,442,-761) -> Matrix(1,-2,0,1) Matrix(881,-1520,324,-559) -> Matrix(1,-4,0,1) Matrix(439,-760,93,-161) -> Matrix(1,-3,0,1) Matrix(599,-1040,254,-441) -> Matrix(1,-8,0,1) Matrix(159,-280,46,-81) -> Matrix(1,0,2,1) Matrix(921,-1640,269,-479) -> Matrix(1,-1,4,-3) Matrix(1121,-2000,403,-719) -> Matrix(1,-1,0,1) Matrix(1521,-2720,581,-1039) -> Matrix(1,1,0,1) Matrix(959,-1720,402,-721) -> Matrix(1,-2,0,1) Matrix(199,-360,89,-161) -> Matrix(1,-1,2,-1) Matrix(241,-440,109,-199) -> Matrix(1,-1,-2,3) Matrix(239,-440,44,-81) -> Matrix(1,-2,2,-3) Matrix(879,-1640,365,-681) -> Matrix(1,-1,-2,3) Matrix(919,-1720,257,-481) -> Matrix(1,-1,0,1) Matrix(681,-1280,191,-359) -> Matrix(1,-3,2,-5) Matrix(359,-680,85,-161) -> Matrix(1,-5,2,-9) Matrix(281,-600,37,-79) -> Matrix(1,1,2,3) Matrix(239,-520,74,-161) -> Matrix(1,0,0,1) Matrix(3161,-7160,1324,-2999) -> Matrix(1,-2,0,1) Matrix(599,-1360,159,-361) -> Matrix(1,1,0,1) Matrix(721,-1640,193,-439) -> Matrix(1,-1,2,-1) Matrix(561,-1280,245,-559) -> Matrix(1,-1,2,-1) Matrix(801,-1840,313,-719) -> Matrix(1,-1,2,-1) Matrix(681,-1600,289,-679) -> Matrix(1,-11,0,1) Matrix(319,-760,34,-81) -> Matrix(1,2,0,1) Matrix(10721,-25600,4489,-10719) -> Matrix(3,5,-2,-3) Matrix(1439,-3440,402,-961) -> Matrix(1,2,0,1) Matrix(1759,-4240,631,-1521) -> Matrix(1,1,-2,-1) Matrix(81,-200,32,-79) -> Matrix(1,0,2,1) Matrix(639,-1640,203,-521) -> Matrix(1,-1,2,-1) Matrix(201,-520,46,-119) -> Matrix(1,0,0,1) Matrix(199,-520,31,-81) -> Matrix(1,-1,0,1) Matrix(121,-320,45,-119) -> Matrix(1,-1,0,1) Matrix(1321,-3600,484,-1319) -> Matrix(1,2,-2,-3) Matrix(959,-2680,258,-721) -> Matrix(1,0,2,1) Matrix(199,-560,43,-121) -> Matrix(3,1,2,1) Matrix(121,-400,36,-119) -> Matrix(1,0,6,1) Matrix(201,-680,47,-159) -> Matrix(5,-1,6,-1) Matrix(441,-1600,121,-439) -> Matrix(1,-1,2,-1) Matrix(6881,-25600,1849,-6879) -> Matrix(1,-1,2,-1) Matrix(41,-160,10,-39) -> Matrix(1,0,2,1) Matrix(1521,-6400,361,-1519) -> Matrix(35,-17,68,-33) Matrix(361,-1600,81,-359) -> Matrix(1,-1,2,-1) Matrix(79,-360,9,-41) -> Matrix(1,-1,2,-1) Matrix(201,-920,26,-119) -> Matrix(1,0,0,1) Matrix(41,-200,8,-39) -> Matrix(1,0,2,1) Matrix(281,-1600,49,-279) -> Matrix(1,-1,2,-1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- 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).(1/2,1/0) 0 1 2/1 (1/2,1/0) 0 10 17/8 (-3/1,-2/1) 0 20 15/7 -1/1 1 4 28/13 -1/1 1 5 13/6 (-1/1,0/1) 0 20 11/5 (-1/1,0/1) 0 20 20/9 0/1 2 1 9/4 (0/1,1/1) 0 20 34/15 (1/2,1/0) 0 10 25/11 0/1 1 4 41/18 (0/1,1/1) 0 20 16/7 (0/1,1/1).(1/2,1/0) 0 5 7/3 (2/1,1/0) 0 20 40/17 1/0 11 1 26/11 (-7/2,1/0) 0 10 19/8 (-1/1,1/0) 0 20 31/13 (-2/1,-1/1) 0 20 74/31 (-3/2,1/0) 0 10 160/67 (-2/1,-1/1).(-3/2,1/0) 0 1 43/18 (-2/1,-1/1) 0 20 12/5 -1/1 1 5 53/22 (-1/1,0/1) 0 20 41/17 (-1/1,0/1) 0 20 29/12 (-1/1,0/1) 0 20 17/7 (-1/1,0/1) 0 20 5/2 0/1 1 4 23/9 (0/1,1/1) 0 20 41/16 (0/1,1/1) 0 20 100/39 0/1 1 1 59/23 (0/1,1/2) 0 20 18/7 (1/2,1/0) 0 10 13/5 (0/1,1/1) 0 20 34/13 (3/2,1/0) 0 10 21/8 (-1/1,1/0) 0 20 8/3 1/0 1 5 19/7 (-2/1,1/0) 0 20 49/18 (-2/1,-1/1) 0 20 30/11 -1/1 1 2 41/15 (-1/1,0/1) 0 20 11/4 (-1/1,0/1) 0 20 14/5 (-1/2,1/0) 0 10 17/6 (-1/5,0/1) 0 20 20/7 0/1 6 1 3/1 (0/1,1/1) 0 20 19/6 (1/1,1/0) 0 20 16/5 1/0 1 5 13/4 (-1/1,0/1) 0 20 10/3 0/1 3 2 27/8 (0/1,1/5) 0 20 17/5 (0/1,1/3) 0 20 41/12 (0/1,1/3) 0 20 24/7 (0/1,1/3).(1/4,1/2) 0 5 7/2 (1/2,1/1) 0 20 25/7 1/1 1 4 68/19 1/1 1 5 43/12 (0/1,1/1) 0 20 61/17 (0/1,1/0) 0 20 18/5 (1/2,1/0) 0 10 40/11 (0/1,1/1).(1/2,1/0) 0 1 11/3 (0/1,1/1) 0 20 26/7 (1/2,1/0) 0 10 160/43 (0/1,1/1).(1/2,1/0) 0 1 67/18 (0/1,1/1) 0 20 41/11 (0/1,1/1) 0 20 15/4 1/1 1 4 34/9 (3/2,1/0) 0 10 19/5 (4/1,1/0) 0 20 4/1 0/1 1 5 21/5 (4/9,1/2) 0 20 80/19 1/2 17 1 38/9 (1/2,9/16) 0 10 17/4 (2/3,1/1) 0 20 13/3 (0/1,1/1) 0 20 22/5 (1/2,1/0) 0 10 40/9 (0/1,1/1).(1/2,1/0) 0 1 9/2 (0/1,1/1) 0 20 32/7 (0/1,1/1).(1/2,1/0) 0 5 23/5 (2/3,1/1) 0 20 14/3 (3/2,1/0) 0 10 19/4 (-1/1,1/0) 0 20 5/1 0/1 1 4 21/4 (1/2,1/1) 0 20 16/3 1/2 1 5 27/5 (0/1,1/1) 0 20 11/2 (0/1,1/1) 0 20 17/3 (0/1,1/1) 0 20 40/7 (0/1,1/1).(1/2,1/0) 0 1 6/1 (1/2,1/0) 0 10 13/2 (-1/1,0/1) 0 20 20/3 0/1 3 1 7/1 (0/1,1/2) 0 20 15/2 0/1 1 4 23/3 (2/3,1/1) 0 20 8/1 (0/1,1/1).(1/2,1/0) 0 5 9/1 (0/1,1/1) 0 20 10/1 0/1 1 2 1/0 (0/1,1/1) 0 20 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(321,-680,76,-161) (2/1,17/8) -> (38/9,17/4) Glide Reflection Matrix(281,-600,37,-79) (17/8,15/7) -> (15/2,23/3) Hyperbolic Matrix(801,-1720,224,-481) (15/7,28/13) -> (25/7,68/19) Glide Reflection Matrix(761,-1640,316,-681) (28/13,13/6) -> (12/5,53/22) Glide Reflection Matrix(201,-440,37,-81) (13/6,11/5) -> (27/5,11/2) Glide Reflection Matrix(199,-440,90,-199) (11/5,20/9) -> (11/5,20/9) Reflection Matrix(161,-360,72,-161) (20/9,9/4) -> (20/9,9/4) Reflection Matrix(761,-1720,319,-721) (9/4,34/15) -> (31/13,74/31) Glide Reflection Matrix(599,-1360,159,-361) (34/15,25/11) -> (15/4,34/9) Hyperbolic Matrix(721,-1640,193,-439) (25/11,41/18) -> (41/11,15/4) Hyperbolic Matrix(719,-1640,210,-479) (41/18,16/7) -> (41/12,24/7) Glide Reflection Matrix(121,-280,35,-81) (16/7,7/3) -> (24/7,7/2) Glide Reflection Matrix(239,-560,102,-239) (7/3,40/17) -> (7/3,40/17) Reflection Matrix(441,-1040,187,-441) (40/17,26/11) -> (40/17,26/11) Reflection Matrix(321,-760,68,-161) (26/11,19/8) -> (14/3,19/4) Glide Reflection Matrix(639,-1520,235,-559) (19/8,31/13) -> (19/7,49/18) Glide Reflection Matrix(4959,-11840,2077,-4959) (74/31,160/67) -> (74/31,160/67) Reflection Matrix(5761,-13760,2412,-5761) (160/67,43/18) -> (160/67,43/18) Reflection Matrix(1439,-3440,402,-961) (43/18,12/5) -> (68/19,43/12) Hyperbolic Matrix(2041,-4920,548,-1321) (53/22,41/17) -> (67/18,41/11) Glide Reflection Matrix(679,-1640,248,-599) (41/17,29/12) -> (41/15,11/4) Glide Reflection Matrix(281,-680,50,-121) (29/12,17/7) -> (11/2,17/3) Glide Reflection Matrix(81,-200,32,-79) (17/7,5/2) -> (5/2,23/9) Parabolic Matrix(641,-1640,188,-481) (23/9,41/16) -> (17/5,41/12) Glide Reflection Matrix(3199,-8200,1248,-3199) (41/16,100/39) -> (41/16,100/39) Reflection Matrix(4601,-11800,1794,-4601) (100/39,59/23) -> (100/39,59/23) Reflection Matrix(841,-2160,234,-601) (59/23,18/7) -> (61/17,18/5) Glide Reflection Matrix(201,-520,46,-119) (18/7,13/5) -> (13/3,22/5) Hyperbolic Matrix(199,-520,31,-81) (13/5,34/13) -> (6/1,13/2) Hyperbolic Matrix(519,-1360,137,-359) (34/13,21/8) -> (34/9,19/5) Glide Reflection Matrix(121,-320,45,-119) (21/8,8/3) -> (8/3,19/7) Parabolic Matrix(279,-760,29,-79) (49/18,30/11) -> (9/1,10/1) Glide Reflection Matrix(161,-440,15,-41) (30/11,41/15) -> (10/1,1/0) Glide Reflection Matrix(159,-440,43,-119) (11/4,14/5) -> (11/3,26/7) Glide Reflection Matrix(199,-560,43,-121) (14/5,17/6) -> (23/5,14/3) Hyperbolic Matrix(239,-680,84,-239) (17/6,20/7) -> (17/6,20/7) Reflection Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(319,-1000,89,-279) (3/1,19/6) -> (43/12,61/17) Glide Reflection Matrix(201,-640,38,-121) (19/6,16/5) -> (21/4,16/3) Glide Reflection Matrix(199,-640,37,-119) (16/5,13/4) -> (16/3,27/5) Glide Reflection Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(201,-680,47,-159) (27/8,17/5) -> (17/4,13/3) Hyperbolic Matrix(79,-280,11,-39) (7/2,25/7) -> (7/1,15/2) Glide Reflection Matrix(199,-720,55,-199) (18/5,40/11) -> (18/5,40/11) Reflection Matrix(241,-880,66,-241) (40/11,11/3) -> (40/11,11/3) Reflection Matrix(1119,-4160,301,-1119) (26/7,160/43) -> (26/7,160/43) Reflection Matrix(5761,-21440,1548,-5761) (160/43,67/18) -> (160/43,67/18) Reflection Matrix(41,-160,10,-39) (19/5,4/1) -> (4/1,21/5) Parabolic Matrix(799,-3360,190,-799) (21/5,80/19) -> (21/5,80/19) Reflection Matrix(721,-3040,171,-721) (80/19,38/9) -> (80/19,38/9) Reflection Matrix(199,-880,45,-199) (22/5,40/9) -> (22/5,40/9) Reflection Matrix(161,-720,36,-161) (40/9,9/2) -> (40/9,9/2) Reflection Matrix(79,-360,9,-41) (9/2,32/7) -> (8/1,9/1) Hyperbolic Matrix(201,-920,26,-119) (32/7,23/5) -> (23/3,8/1) Hyperbolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic Matrix(239,-1360,42,-239) (17/3,40/7) -> (17/3,40/7) Reflection Matrix(41,-240,7,-41) (40/7,6/1) -> (40/7,6/1) Reflection Matrix(79,-520,12,-79) (13/2,20/3) -> (13/2,20/3) Reflection Matrix(41,-280,6,-41) (20/3,7/1) -> (20/3,7/1) 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) -> (0/1,1/1) Matrix(1,0,1,-1) -> Matrix(-1,1,0,1) (0/1,2/1) -> (1/2,1/0) Matrix(321,-680,76,-161) -> Matrix(1,4,2,7) Matrix(281,-600,37,-79) -> Matrix(1,1,2,3) Matrix(801,-1720,224,-481) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(761,-1640,316,-681) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(201,-440,37,-81) -> Matrix(1,1,2,1) Matrix(199,-440,90,-199) -> Matrix(-1,0,2,1) (11/5,20/9) -> (-1/1,0/1) Matrix(161,-360,72,-161) -> Matrix(1,0,2,-1) (20/9,9/4) -> (0/1,1/1) Matrix(761,-1720,319,-721) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(599,-1360,159,-361) -> Matrix(1,1,0,1) 1/0 Matrix(721,-1640,193,-439) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(719,-1640,210,-479) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(121,-280,35,-81) -> Matrix(1,-1,2,-3) Matrix(239,-560,102,-239) -> Matrix(-1,4,0,1) (7/3,40/17) -> (2/1,1/0) Matrix(441,-1040,187,-441) -> Matrix(1,7,0,-1) (40/17,26/11) -> (-7/2,1/0) Matrix(321,-760,68,-161) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(639,-1520,235,-559) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(4959,-11840,2077,-4959) -> Matrix(1,3,0,-1) (74/31,160/67) -> (-3/2,1/0) Matrix(5761,-13760,2412,-5761) -> Matrix(3,4,-2,-3) (160/67,43/18) -> (-2/1,-1/1) Matrix(1439,-3440,402,-961) -> Matrix(1,2,0,1) 1/0 Matrix(2041,-4920,548,-1321) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(679,-1640,248,-599) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(281,-680,50,-121) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(81,-200,32,-79) -> Matrix(1,0,2,1) 0/1 Matrix(641,-1640,188,-481) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(3199,-8200,1248,-3199) -> Matrix(1,0,2,-1) (41/16,100/39) -> (0/1,1/1) Matrix(4601,-11800,1794,-4601) -> Matrix(1,0,4,-1) (100/39,59/23) -> (0/1,1/2) Matrix(841,-2160,234,-601) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(201,-520,46,-119) -> Matrix(1,0,0,1) Matrix(199,-520,31,-81) -> Matrix(1,-1,0,1) 1/0 Matrix(519,-1360,137,-359) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(121,-320,45,-119) -> Matrix(1,-1,0,1) 1/0 Matrix(279,-760,29,-79) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(161,-440,15,-41) -> Matrix(1,1,2,1) Matrix(159,-440,43,-119) -> Matrix(1,1,2,1) Matrix(199,-560,43,-121) -> Matrix(3,1,2,1) Matrix(239,-680,84,-239) -> Matrix(-1,0,10,1) (17/6,20/7) -> (-1/5,0/1) Matrix(41,-120,14,-41) -> Matrix(1,0,2,-1) (20/7,3/1) -> (0/1,1/1) Matrix(319,-1000,89,-279) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(201,-640,38,-121) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(199,-640,37,-119) -> Matrix(1,1,2,1) Matrix(121,-400,36,-119) -> Matrix(1,0,6,1) 0/1 Matrix(201,-680,47,-159) -> Matrix(5,-1,6,-1) Matrix(79,-280,11,-39) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(199,-720,55,-199) -> Matrix(-1,1,0,1) (18/5,40/11) -> (1/2,1/0) Matrix(241,-880,66,-241) -> Matrix(1,0,2,-1) (40/11,11/3) -> (0/1,1/1) Matrix(1119,-4160,301,-1119) -> Matrix(-1,1,0,1) (26/7,160/43) -> (1/2,1/0) Matrix(5761,-21440,1548,-5761) -> Matrix(1,0,2,-1) (160/43,67/18) -> (0/1,1/1) Matrix(41,-160,10,-39) -> Matrix(1,0,2,1) 0/1 Matrix(799,-3360,190,-799) -> Matrix(17,-8,36,-17) (21/5,80/19) -> (4/9,1/2) Matrix(721,-3040,171,-721) -> Matrix(17,-9,32,-17) (80/19,38/9) -> (1/2,9/16) Matrix(199,-880,45,-199) -> Matrix(-1,1,0,1) (22/5,40/9) -> (1/2,1/0) Matrix(161,-720,36,-161) -> Matrix(1,0,2,-1) (40/9,9/2) -> (0/1,1/1) Matrix(79,-360,9,-41) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(201,-920,26,-119) -> Matrix(1,0,0,1) Matrix(41,-200,8,-39) -> Matrix(1,0,2,1) 0/1 Matrix(239,-1360,42,-239) -> Matrix(1,0,2,-1) (17/3,40/7) -> (0/1,1/1) Matrix(41,-240,7,-41) -> Matrix(-1,1,0,1) (40/7,6/1) -> (1/2,1/0) Matrix(79,-520,12,-79) -> Matrix(-1,0,2,1) (13/2,20/3) -> (-1/1,0/1) Matrix(41,-280,6,-41) -> Matrix(1,0,4,-1) (20/3,7/1) -> (0/1,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.