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 -4/1 -3/1 -8/1 1/0 -7/1 0/1 1/0 -20/3 1/0 -13/2 1/0 -6/1 -1/1 1/0 -17/3 -1/1 0/1 -11/2 -1/2 -16/3 1/2 1/0 -5/1 1/0 -24/5 -7/2 1/0 -19/4 -11/4 -14/3 -2/1 1/0 -23/5 -2/1 -5/3 -32/7 -3/2 -9/2 -3/2 -13/3 -1/1 -1/2 -17/4 -1/2 -4/1 1/0 -23/6 -5/2 -42/11 -9/4 -2/1 -19/5 -2/1 -7/4 -15/4 -3/2 1/0 -11/3 -4/3 -1/1 -18/5 -1/1 -1/2 -43/12 1/0 -25/7 -1/2 1/0 -7/2 -1/2 -17/5 -1/1 0/1 -10/3 1/0 -23/7 -3/1 -2/1 -13/4 1/0 -16/5 -3/2 1/0 -19/6 -7/6 -3/1 -1/1 0/1 -20/7 0/1 -17/6 1/0 -14/5 0/1 1/0 -11/4 -1/2 -41/15 -1/1 -1/2 -30/11 -1/2 1/0 -19/7 -1/2 0/1 -8/3 -1/2 1/0 -21/8 -5/2 -34/13 -3/2 -1/1 -13/5 -1/1 -1/2 -31/12 -3/2 -18/7 -1/1 -1/2 -5/2 -1/2 1/0 -22/9 -1/1 -1/2 -61/25 -2/3 -1/2 -100/41 -1/2 -39/16 -1/2 -17/7 -1/1 0/1 -29/12 1/0 -41/17 -1/1 1/0 -53/22 -1/2 -12/5 -1/2 1/0 -55/23 -1/2 1/0 -43/18 1/0 -31/13 -2/3 -3/5 -19/8 -3/8 -26/11 -1/4 0/1 -7/3 0/1 1/0 -16/7 -1/2 -41/18 -1/2 -25/11 -1/2 -34/15 -1/2 -1/3 -9/4 -1/4 -20/9 0/1 -11/5 0/1 1/3 -13/6 1/0 -28/13 -1/2 1/0 -15/7 -1/2 1/0 -17/8 -1/2 -2/1 0/1 1/0 -17/9 0/1 1/1 -15/8 1/2 1/0 -28/15 1/0 -13/7 -1/1 1/0 -11/6 -1/4 -20/11 0/1 -9/5 0/1 1/5 -43/24 3/10 -34/19 1/3 1/2 -25/14 1/4 1/2 -41/23 3/10 1/3 -16/9 1/2 -39/22 1/2 -23/13 0/1 1/1 -7/4 1/0 -40/23 0/1 -33/19 0/1 1/8 -26/15 0/1 1/4 -19/11 0/1 1/2 -50/29 1/4 1/2 -31/18 1/2 -74/43 1/4 1/3 -117/68 5/16 -160/93 1/3 -43/25 1/3 2/5 -12/7 1/2 -53/31 1/3 1/2 -41/24 1/2 -29/17 3/5 2/3 -17/10 1/2 -5/3 1/2 1/0 -23/14 1/2 -41/25 7/8 1/1 -100/61 1/1 -59/36 9/8 -18/11 1/1 1/0 -13/8 1/0 -34/21 -1/1 1/0 -55/34 -1/2 1/0 -21/13 0/1 1/2 -8/5 1/2 1/0 -19/12 5/2 -49/31 6/1 7/1 -30/19 1/0 -71/45 -8/1 -7/1 -41/26 1/0 -11/7 -2/1 -1/1 -25/16 -1/2 1/0 -39/25 -1/1 -3/4 -53/34 -1/2 -14/9 -1/2 0/1 -17/11 -1/5 0/1 -20/13 0/1 -3/2 1/2 -22/15 1/1 1/0 -19/13 0/1 1/0 -16/11 1/2 1/0 -29/20 -1/2 -13/9 1/2 1/1 -10/7 1/2 1/0 -27/19 1/2 1/1 -17/12 1/2 -41/29 1/1 5/4 -24/17 1/0 -7/5 0/1 1/2 -32/23 1/2 -57/41 2/3 1/1 -25/18 1/2 3/4 -68/49 3/4 -43/31 2/3 1/1 -61/44 9/10 -18/13 1/2 1/1 -29/21 6/7 1/1 -40/29 1/1 -11/8 3/2 -26/19 2/1 1/0 -93/68 1/0 -160/117 1/0 -67/49 1/1 1/0 -41/30 1/0 -15/11 1/0 -34/25 -1/1 1/0 -19/14 -1/4 -4/3 1/2 1/0 -21/16 -1/4 -80/61 0/1 -59/45 0/1 1/12 -38/29 0/1 1/4 -17/13 0/1 1/3 -13/10 1/2 -22/17 1/2 1/1 -31/24 5/6 -40/31 1/1 -9/7 1/1 2/1 -32/25 1/0 -23/18 1/0 -14/11 0/1 1/0 -19/15 0/1 1/2 -5/4 1/2 1/0 -21/17 0/1 1/2 -16/13 1/2 1/0 -27/22 1/0 -11/9 0/1 1/3 -17/14 1/2 -40/33 1/1 -23/19 0/1 1/1 -6/5 1/2 1/1 -13/11 5/6 1/1 -20/17 1/1 -7/6 3/2 -15/13 3/2 1/0 -23/20 1/0 -8/7 1/0 -9/8 1/0 -10/9 1/2 1/0 -1/1 1/1 1/0 0/1 1/0 1/1 -1/1 1/0 9/8 1/0 8/7 1/0 7/6 -3/2 20/17 -1/1 13/11 -1/1 -5/6 6/5 -1/1 -1/2 17/14 -1/2 11/9 -1/3 0/1 16/13 -1/2 1/0 5/4 -1/2 1/0 24/19 -1/2 1/0 19/15 -1/2 0/1 14/11 0/1 1/0 23/18 1/0 32/25 1/0 9/7 -2/1 -1/1 13/10 -1/2 17/13 -1/3 0/1 4/3 -1/2 1/0 23/17 -1/3 0/1 42/31 -1/4 0/1 19/14 1/4 15/11 1/0 11/8 -3/2 18/13 -1/1 -1/2 43/31 -1/1 -2/3 25/18 -3/4 -1/2 7/5 -1/2 0/1 17/12 -1/2 10/7 -1/2 1/0 23/16 -1/2 13/9 -1/1 -1/2 16/11 -1/2 1/0 19/13 0/1 1/0 3/2 -1/2 20/13 0/1 17/11 0/1 1/5 14/9 0/1 1/2 11/7 1/1 2/1 41/26 1/0 30/19 1/0 19/12 -5/2 8/5 -1/2 1/0 21/13 -1/2 0/1 34/21 1/1 1/0 13/8 1/0 31/19 -4/3 -1/1 18/11 -1/1 1/0 5/3 -1/2 1/0 22/13 -1/1 1/0 61/36 -9/8 100/59 -1/1 39/23 -1/1 -7/8 17/10 -1/2 29/17 -2/3 -3/5 41/24 -1/2 53/31 -1/2 -1/3 12/7 -1/2 55/32 -1/2 -3/8 43/25 -2/5 -1/3 31/18 -1/2 19/11 -1/2 0/1 26/15 -1/4 0/1 7/4 1/0 16/9 -1/2 41/23 -1/3 -3/10 25/14 -1/2 -1/4 34/19 -1/2 -1/3 9/5 -1/5 0/1 20/11 0/1 11/6 1/4 13/7 1/1 1/0 28/15 1/0 15/8 -1/2 1/0 17/9 -1/1 0/1 2/1 0/1 1/0 17/8 1/2 15/7 1/2 1/0 28/13 1/2 1/0 13/6 1/0 11/5 -1/3 0/1 20/9 0/1 9/4 1/4 43/19 2/7 1/3 34/15 1/3 1/2 25/11 1/2 41/18 1/2 16/7 1/2 39/17 5/6 1/1 23/10 1/0 7/3 0/1 1/0 40/17 0/1 33/14 1/8 26/11 0/1 1/4 19/8 3/8 50/21 1/2 31/13 3/5 2/3 74/31 3/4 1/1 117/49 6/7 1/1 160/67 1/1 43/18 1/0 12/5 1/2 1/0 53/22 1/2 41/17 1/1 1/0 29/12 1/0 17/7 0/1 1/1 5/2 1/2 1/0 23/9 0/1 1/1 41/16 1/2 100/39 1/2 59/23 1/2 2/3 18/7 1/2 1/1 13/5 1/2 1/1 34/13 1/1 3/2 55/21 3/2 21/8 5/2 8/3 1/2 1/0 19/7 0/1 1/2 49/18 1/2 30/11 1/2 1/0 71/26 1/2 41/15 1/2 1/1 11/4 1/2 25/9 1/0 39/14 1/0 53/19 1/1 1/0 14/5 0/1 1/0 17/6 1/0 20/7 0/1 3/1 0/1 1/1 22/7 1/2 1/1 19/6 7/6 16/5 3/2 1/0 29/9 5/3 2/1 13/4 1/0 10/3 1/0 27/8 1/0 17/5 0/1 1/1 41/12 1/0 24/7 1/0 7/2 1/2 32/9 1/0 57/16 1/0 25/7 1/2 1/0 68/19 1/2 1/0 43/12 1/0 61/17 0/1 1/2 18/5 1/2 1/1 29/8 5/6 40/11 1/1 11/3 1/1 4/3 26/7 2/1 1/0 93/25 3/1 1/0 160/43 1/0 67/18 1/0 41/11 1/2 1/1 15/4 3/2 1/0 34/9 1/1 3/2 19/5 7/4 2/1 4/1 1/0 21/5 -1/4 0/1 80/19 0/1 59/14 1/12 38/9 0/1 1/4 17/4 1/2 13/3 1/2 1/1 22/5 1/2 1/1 31/7 4/5 1/1 40/9 1/1 9/2 3/2 32/7 3/2 23/5 5/3 2/1 14/3 2/1 1/0 19/4 11/4 5/1 1/0 21/4 -5/4 16/3 -1/2 1/0 27/5 -1/1 -1/2 11/2 1/2 17/3 0/1 1/1 40/7 1/1 23/4 1/0 6/1 1/1 1/0 13/2 1/0 20/3 1/0 7/1 0/1 1/0 15/2 3/2 1/0 23/3 1/1 2/1 8/1 1/0 9/1 3/1 4/1 10/1 1/0 1/0 1/0 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,-4,0,1) Matrix(41,360,32,281) -> Matrix(1,2,0,1) Matrix(39,280,-28,-201) -> Matrix(1,0,2,1) Matrix(41,280,6,41) -> Matrix(1,0,0,1) Matrix(79,520,12,79) -> Matrix(1,6,0,1) Matrix(81,520,50,321) -> Matrix(1,2,0,1) Matrix(41,240,-34,-199) -> Matrix(1,0,2,1) Matrix(121,680,50,281) -> Matrix(1,0,2,1) Matrix(119,640,-82,-441) -> Matrix(1,0,0,1) Matrix(39,200,-8,-41) -> Matrix(1,-4,0,1) Matrix(159,760,50,239) -> Matrix(3,10,2,7) Matrix(161,760,68,321) -> Matrix(1,2,4,9) Matrix(121,560,78,361) -> Matrix(1,2,2,5) Matrix(559,2560,-402,-1841) -> Matrix(5,8,8,13) Matrix(79,360,70,319) -> Matrix(1,2,-2,-3) Matrix(119,520,-46,-201) -> Matrix(1,0,0,1) Matrix(121,520,84,361) -> Matrix(1,0,0,1) Matrix(39,160,-10,-41) -> Matrix(1,-2,0,1) Matrix(199,760,94,359) -> Matrix(1,2,4,9) Matrix(839,3200,-640,-2441) -> Matrix(1,2,8,17) Matrix(359,1360,-222,-841) -> Matrix(1,2,-2,-3) Matrix(119,440,-76,-281) -> Matrix(1,2,-2,-3) Matrix(199,720,-144,-521) -> Matrix(3,2,4,3) Matrix(279,1000,-190,-681) -> Matrix(1,0,2,1) Matrix(961,3440,-402,-1439) -> Matrix(1,0,0,1) Matrix(79,280,-68,-241) -> Matrix(1,2,0,1) Matrix(81,280,-46,-159) -> Matrix(1,0,2,1) Matrix(119,400,-36,-121) -> Matrix(1,-2,0,1) Matrix(159,520,122,399) -> Matrix(1,2,-2,-3) Matrix(199,640,-162,-521) -> Matrix(1,2,0,1) Matrix(201,640,38,121) -> Matrix(1,2,-2,-3) Matrix(319,1000,-230,-721) -> Matrix(3,2,4,3) Matrix(41,120,14,41) -> Matrix(1,0,2,1) Matrix(239,680,84,239) -> Matrix(1,0,0,1) Matrix(199,560,156,439) -> Matrix(1,0,0,1) Matrix(159,440,-116,-321) -> Matrix(1,2,0,1) Matrix(599,1640,248,679) -> Matrix(1,0,2,1) Matrix(161,440,-146,-399) -> Matrix(1,0,2,1) Matrix(559,1520,-324,-881) -> Matrix(1,0,4,1) Matrix(119,320,74,199) -> Matrix(1,0,0,1) Matrix(121,320,76,201) -> Matrix(1,0,0,1) Matrix(519,1360,-382,-1001) -> Matrix(1,2,-2,-3) Matrix(199,520,168,439) -> Matrix(3,4,-4,-5) Matrix(481,1240,-372,-959) -> Matrix(3,2,4,3) Matrix(79,200,-32,-81) -> Matrix(1,0,0,1) Matrix(999,2440,278,679) -> Matrix(3,2,4,3) Matrix(4919,12000,1918,4679) -> Matrix(7,4,12,7) Matrix(3281,8000,1280,3121) -> Matrix(3,2,4,3) Matrix(559,1360,164,399) -> Matrix(1,0,2,1) Matrix(281,680,50,121) -> Matrix(1,0,2,1) Matrix(679,1640,248,599) -> Matrix(1,0,2,1) Matrix(2041,4920,548,1321) -> Matrix(1,0,2,1) Matrix(681,1640,316,761) -> Matrix(1,0,2,1) Matrix(719,1720,334,799) -> Matrix(1,0,2,1) Matrix(721,1720,-402,-959) -> Matrix(3,2,10,7) Matrix(639,1520,-404,-961) -> Matrix(9,4,2,1) Matrix(321,760,68,161) -> Matrix(9,2,4,1) Matrix(441,1040,-254,-599) -> Matrix(1,0,8,1) Matrix(121,280,-86,-199) -> Matrix(1,0,2,1) 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(11,4,8,3) Matrix(761,1720,-442,-999) -> Matrix(1,0,6,1) Matrix(161,360,72,161) -> Matrix(1,0,8,1) Matrix(199,440,90,199) -> Matrix(1,0,-6,1) Matrix(201,440,-164,-359) -> Matrix(1,0,0,1) Matrix(761,1640,316,681) -> Matrix(1,0,2,1) Matrix(801,1720,224,481) -> Matrix(1,0,2,1) Matrix(599,1280,168,359) -> Matrix(1,0,2,1) Matrix(321,680,76,161) -> Matrix(1,0,4,1) Matrix(401,760,296,561) -> Matrix(1,0,-4,1) Matrix(319,600,42,79) -> Matrix(3,-2,2,-1) Matrix(921,1720,536,1001) -> Matrix(1,-2,-2,5) Matrix(879,1640,514,959) -> Matrix(1,0,-2,1) Matrix(281,520,-194,-359) -> Matrix(1,0,2,1) Matrix(241,440,132,241) -> Matrix(1,0,8,1) Matrix(199,360,110,199) -> Matrix(1,0,-10,1) Matrix(3999,7160,-2324,-4161) -> Matrix(5,-2,18,-7) Matrix(761,1360,202,361) -> Matrix(7,-2,4,-1) Matrix(919,1640,246,439) -> Matrix(7,-2,4,-1) Matrix(719,1280,314,559) -> Matrix(5,-2,8,-3) 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(1,0,8,1) Matrix(921,1600,392,681) -> Matrix(1,0,-8,1) Matrix(439,760,346,599) -> Matrix(1,0,-4,1) Matrix(441,760,-394,-679) -> Matrix(1,0,-2,1) Matrix(14879,25600,6230,10719) -> Matrix(19,-6,16,-5) Matrix(14881,25600,6232,10721) -> Matrix(23,-8,26,-9) Matrix(2001,3440,-1442,-2479) -> Matrix(11,-4,14,-5) Matrix(959,1640,514,879) -> Matrix(1,0,-2,1) Matrix(2481,4240,890,1521) -> Matrix(1,0,-2,1) Matrix(961,1640,610,1041) -> Matrix(7,-4,2,-1) Matrix(399,680,328,559) -> Matrix(3,-2,-4,3) Matrix(119,200,-72,-121) -> Matrix(1,0,0,1) Matrix(1121,1840,488,801) -> Matrix(3,-2,2,-1) Matrix(4879,8000,2878,4719) -> Matrix(15,-14,-16,15) Matrix(7321,12000,4320,7081) -> Matrix(17,-18,-16,17) Matrix(1001,1640,318,521) -> Matrix(1,-2,2,-3) Matrix(319,520,-246,-401) -> Matrix(1,-2,2,-3) Matrix(321,520,50,81) -> Matrix(1,2,0,1) Matrix(1681,2720,940,1521) -> Matrix(1,0,-2,1) Matrix(199,320,74,119) -> Matrix(1,0,0,1) Matrix(201,320,76,121) -> Matrix(1,0,0,1) Matrix(2279,3600,-1444,-2281) -> Matrix(1,-14,0,1) Matrix(1041,1640,610,961) -> Matrix(1,4,-2,-7) Matrix(1281,2000,718,1121) -> Matrix(1,0,-2,1) Matrix(2719,4240,1128,1759) -> Matrix(3,2,4,3) Matrix(1721,2680,-1258,-1959) -> Matrix(5,2,2,1) Matrix(361,560,78,121) -> Matrix(5,2,2,1) Matrix(441,680,286,441) -> Matrix(1,0,10,1) Matrix(79,120,52,79) -> Matrix(1,0,-4,1) Matrix(1119,1640,436,639) -> Matrix(1,-2,2,-3) Matrix(521,760,412,601) -> Matrix(1,0,-2,1) Matrix(279,400,-196,-281) -> Matrix(1,0,0,1) Matrix(479,680,112,159) -> Matrix(1,0,0,1) Matrix(961,1360,566,801) -> Matrix(3,-2,-4,3) Matrix(1161,1640,652,921) -> Matrix(1,-2,-2,5) Matrix(921,1280,490,681) -> Matrix(3,-2,-4,3) Matrix(1239,1720,662,919) -> Matrix(3,-2,-4,3) Matrix(1761,2440,1040,1441) -> Matrix(1,0,-2,1) Matrix(1159,1600,318,439) -> Matrix(11,-10,10,-9) Matrix(1161,1600,320,441) -> Matrix(7,-8,8,-9) Matrix(18719,25600,5030,6879) -> Matrix(1,-4,0,1) Matrix(18721,25600,5032,6881) -> Matrix(1,2,0,1) Matrix(3599,4920,2106,2879) -> Matrix(1,-2,-2,5) Matrix(1201,1640,528,721) -> Matrix(1,-2,2,-3) Matrix(999,1360,440,599) -> Matrix(1,2,2,5) Matrix(119,160,-90,-121) -> Matrix(1,0,0,1) Matrix(4879,6400,1158,1519) -> Matrix(1,0,16,1) Matrix(4881,6400,1160,1521) -> Matrix(1,0,-16,1) Matrix(519,680,274,359) -> Matrix(1,0,-4,1) Matrix(521,680,154,201) -> Matrix(1,0,-2,1) Matrix(1239,1600,278,359) -> Matrix(9,-8,8,-7) Matrix(1241,1600,280,361) -> Matrix(5,-6,6,-7) Matrix(281,360,32,41) -> Matrix(1,2,0,1) Matrix(719,920,-626,-801) -> Matrix(1,2,0,1) Matrix(439,560,156,199) -> Matrix(1,0,0,1) Matrix(599,760,346,439) -> Matrix(1,0,-4,1) Matrix(159,200,-128,-161) -> Matrix(1,0,0,1) Matrix(519,640,356,439) -> Matrix(1,0,-2,1) Matrix(559,680,328,399) -> Matrix(3,-2,-4,3) Matrix(1319,1600,230,279) -> Matrix(3,-2,2,-1) Matrix(1321,1600,232,281) -> Matrix(1,0,0,1) Matrix(439,520,168,199) -> Matrix(5,-4,4,-3) Matrix(441,520,374,441) -> Matrix(11,-10,-12,11) Matrix(239,280,204,239) -> Matrix(5,-6,-4,5) Matrix(521,600,244,281) -> Matrix(1,-2,2,-3) Matrix(319,360,70,79) -> Matrix(3,-2,2,-1) Matrix(1,0,2,1) -> Matrix(1,-2,0,1) Matrix(399,-440,146,-161) -> Matrix(1,0,2,1) Matrix(241,-280,68,-79) -> Matrix(1,2,0,1) Matrix(199,-240,34,-41) -> Matrix(1,0,2,1) Matrix(521,-640,162,-199) -> Matrix(1,2,0,1) Matrix(161,-200,128,-159) -> Matrix(1,0,0,1) Matrix(2001,-2560,562,-719) -> Matrix(1,0,0,1) Matrix(401,-520,246,-319) -> Matrix(3,2,-2,-1) Matrix(121,-160,90,-119) -> Matrix(1,0,0,1) Matrix(2361,-3200,560,-759) -> Matrix(1,0,8,1) Matrix(1001,-1360,382,-519) -> Matrix(3,-2,2,-1) Matrix(321,-440,116,-159) -> Matrix(1,2,0,1) Matrix(521,-720,144,-199) -> Matrix(3,2,4,3) Matrix(721,-1000,230,-319) -> Matrix(3,2,4,3) Matrix(2479,-3440,1442,-2001) -> Matrix(5,4,-14,-11) Matrix(201,-280,28,-39) -> Matrix(1,0,2,1) Matrix(199,-280,86,-121) -> Matrix(1,0,2,1) Matrix(281,-400,196,-279) -> Matrix(1,0,0,1) Matrix(441,-640,82,-119) -> Matrix(1,0,0,1) Matrix(681,-1000,190,-279) -> Matrix(1,0,2,1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-1) Matrix(279,-440,26,-41) -> Matrix(1,-4,0,1) Matrix(961,-1520,404,-639) -> Matrix(1,4,2,9) Matrix(841,-1360,222,-359) -> Matrix(3,-2,2,-1) Matrix(759,-1240,172,-281) -> Matrix(1,0,2,1) Matrix(121,-200,72,-119) -> Matrix(1,0,0,1) Matrix(999,-1720,442,-761) -> Matrix(1,0,6,1) Matrix(881,-1520,324,-559) -> Matrix(1,0,4,1) Matrix(599,-1040,254,-441) -> Matrix(1,0,8,1) Matrix(159,-280,46,-81) -> Matrix(1,0,2,1) Matrix(959,-1720,402,-721) -> Matrix(7,2,10,3) Matrix(239,-440,44,-81) -> Matrix(1,0,-2,1) Matrix(239,-520,74,-161) -> Matrix(1,2,0,1) Matrix(3161,-7160,1324,-2999) -> Matrix(11,-4,14,-5) Matrix(319,-760,34,-81) -> Matrix(11,-6,2,-1) Matrix(1439,-3440,402,-961) -> Matrix(1,0,0,1) Matrix(81,-200,32,-79) -> Matrix(1,0,0,1) Matrix(201,-520,46,-119) -> Matrix(1,0,0,1) Matrix(1321,-3600,484,-1319) -> Matrix(1,0,0,1) Matrix(959,-2680,258,-721) -> Matrix(1,2,0,1) Matrix(121,-400,36,-119) -> Matrix(1,-2,0,1) Matrix(41,-160,10,-39) -> Matrix(1,-2,0,1) Matrix(201,-920,26,-119) -> Matrix(5,-8,2,-3) Matrix(41,-200,8,-39) -> Matrix(1,-4,0,1) 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): 48 Degree of the the map X: 48 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 -8/1 -6/1 -5/1 -4/1 -15/4 -8/3 -5/2 -2/1 -5/3 -25/18 -4/3 -5/4 0/1 1/1 20/17 5/4 4/3 10/7 3/2 20/13 30/19 5/3 100/59 20/11 2/1 20/9 5/2 8/3 30/11 20/7 3/1 10/3 7/2 15/4 4/1 17/4 9/2 19/4 5/1 11/2 6/1 13/2 20/3 7/1 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 1/0 -7/1 0/1 1/0 -20/3 1/0 -13/2 1/0 -6/1 -1/1 1/0 -11/2 -1/2 -5/1 1/0 -19/4 -11/4 -14/3 -2/1 1/0 -23/5 -2/1 -5/3 -9/2 -3/2 -4/1 1/0 -19/5 -2/1 -7/4 -15/4 -3/2 1/0 -11/3 -4/3 -1/1 -7/2 -1/2 -10/3 1/0 -13/4 1/0 -3/1 -1/1 0/1 -20/7 0/1 -17/6 1/0 -14/5 0/1 1/0 -11/4 -1/2 -30/11 -1/2 1/0 -19/7 -1/2 0/1 -8/3 -1/2 1/0 -5/2 -1/2 1/0 -12/5 -1/2 1/0 -19/8 -3/8 -26/11 -1/4 0/1 -7/3 0/1 1/0 -16/7 -1/2 -9/4 -1/4 -20/9 0/1 -11/5 0/1 1/3 -2/1 0/1 1/0 -11/6 -1/4 -20/11 0/1 -9/5 0/1 1/5 -7/4 1/0 -19/11 0/1 1/2 -50/29 1/4 1/2 -31/18 1/2 -43/25 1/3 2/5 -12/7 1/2 -41/24 1/2 -29/17 3/5 2/3 -17/10 1/2 -5/3 1/2 1/0 -23/14 1/2 -41/25 7/8 1/1 -100/61 1/1 -59/36 9/8 -18/11 1/1 1/0 -13/8 1/0 -34/21 -1/1 1/0 -21/13 0/1 1/2 -8/5 1/2 1/0 -19/12 5/2 -30/19 1/0 -41/26 1/0 -11/7 -2/1 -1/1 -25/16 -1/2 1/0 -39/25 -1/1 -3/4 -14/9 -1/2 0/1 -17/11 -1/5 0/1 -20/13 0/1 -3/2 1/2 -10/7 1/2 1/0 -17/12 1/2 -41/29 1/1 5/4 -24/17 1/0 -7/5 0/1 1/2 -32/23 1/2 -25/18 1/2 3/4 -68/49 3/4 -43/31 2/3 1/1 -18/13 1/2 1/1 -11/8 3/2 -15/11 1/0 -19/14 -1/4 -4/3 1/2 1/0 -21/16 -1/4 -38/29 0/1 1/4 -17/13 0/1 1/3 -13/10 1/2 -22/17 1/2 1/1 -9/7 1/1 2/1 -5/4 1/2 1/0 -11/9 0/1 1/3 -17/14 1/2 -6/5 1/2 1/1 -13/11 5/6 1/1 -20/17 1/1 -7/6 3/2 -1/1 1/1 1/0 0/1 1/0 1/1 -1/1 1/0 7/6 -3/2 20/17 -1/1 13/11 -1/1 -5/6 6/5 -1/1 -1/2 5/4 -1/2 1/0 14/11 0/1 1/0 23/18 1/0 9/7 -2/1 -1/1 13/10 -1/2 4/3 -1/2 1/0 19/14 1/4 15/11 1/0 11/8 -3/2 18/13 -1/1 -1/2 43/31 -1/1 -2/3 25/18 -3/4 -1/2 7/5 -1/2 0/1 17/12 -1/2 10/7 -1/2 1/0 3/2 -1/2 20/13 0/1 17/11 0/1 1/5 14/9 0/1 1/2 11/7 1/1 2/1 41/26 1/0 30/19 1/0 19/12 -5/2 8/5 -1/2 1/0 21/13 -1/2 0/1 34/21 1/1 1/0 13/8 1/0 18/11 -1/1 1/0 5/3 -1/2 1/0 22/13 -1/1 1/0 61/36 -9/8 100/59 -1/1 39/23 -1/1 -7/8 17/10 -1/2 29/17 -2/3 -3/5 12/7 -1/2 31/18 -1/2 19/11 -1/2 0/1 7/4 1/0 9/5 -1/5 0/1 20/11 0/1 11/6 1/4 2/1 0/1 1/0 13/6 1/0 11/5 -1/3 0/1 20/9 0/1 9/4 1/4 7/3 0/1 1/0 5/2 1/2 1/0 13/5 1/2 1/1 34/13 1/1 3/2 21/8 5/2 8/3 1/2 1/0 19/7 0/1 1/2 49/18 1/2 30/11 1/2 1/0 11/4 1/2 14/5 0/1 1/0 17/6 1/0 20/7 0/1 3/1 0/1 1/1 22/7 1/2 1/1 19/6 7/6 16/5 3/2 1/0 13/4 1/0 10/3 1/0 7/2 1/2 11/3 1/1 4/3 26/7 2/1 1/0 15/4 3/2 1/0 34/9 1/1 3/2 19/5 7/4 2/1 4/1 1/0 21/5 -1/4 0/1 17/4 1/2 13/3 1/2 1/1 9/2 3/2 32/7 3/2 23/5 5/3 2/1 14/3 2/1 1/0 19/4 11/4 5/1 1/0 11/2 1/2 6/1 1/1 1/0 13/2 1/0 20/3 1/0 7/1 0/1 1/0 15/2 3/2 1/0 23/3 1/1 2/1 8/1 1/0 9/1 3/1 4/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(41,340,-24,-199) (-8/1,1/0) -> (-12/7,-41/24) 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(39,220,14,79) (-6/1,-11/2) -> (11/4,14/5) Hyperbolic Matrix(41,220,30,161) (-11/2,-5/1) -> (15/11,11/8) Hyperbolic Matrix(79,380,58,279) (-5/1,-19/4) -> (19/14,15/11) Hyperbolic Matrix(199,940,76,359) (-19/4,-14/3) -> (34/13,21/8) Hyperbolic Matrix(121,560,78,361) (-14/3,-23/5) -> (17/11,14/9) Hyperbolic Matrix(241,1100,-140,-639) (-23/5,-9/2) -> (-31/18,-43/25) Hyperbolic Matrix(41,180,-18,-79) (-9/2,-4/1) -> (-16/7,-9/4) Hyperbolic Matrix(161,620,-114,-439) (-4/1,-19/5) -> (-41/29,-24/17) Hyperbolic Matrix(281,1060,-180,-679) (-19/5,-15/4) -> (-25/16,-39/25) Hyperbolic Matrix(119,440,-76,-281) (-15/4,-11/3) -> (-11/7,-25/16) Hyperbolic Matrix(39,140,22,79) (-11/3,-7/2) -> (7/4,9/5) Hyperbolic Matrix(41,140,12,41) (-7/2,-10/3) -> (10/3,7/2) Hyperbolic Matrix(79,260,24,79) (-10/3,-13/4) -> (13/4,10/3) Hyperbolic Matrix(81,260,-62,-199) (-13/4,-3/1) -> (-17/13,-13/10) 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(79,220,14,39) (-14/5,-11/4) -> (11/2,6/1) Hyperbolic Matrix(241,660,88,241) (-11/4,-30/11) -> (30/11,11/4) 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(39,100,-16,-41) (-8/3,-5/2) -> (-5/2,-12/5) Parabolic Matrix(159,380,100,239) (-12/5,-19/8) -> (19/12,8/5) Hyperbolic Matrix(321,760,68,161) (-19/8,-26/11) -> (14/3,19/4) Hyperbolic Matrix(161,380,136,321) (-26/11,-7/3) -> (13/11,6/5) Hyperbolic Matrix(121,280,-86,-199) (-7/3,-16/7) -> (-24/17,-7/5) 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(119,260,-92,-201) (-11/5,-2/1) -> (-22/17,-9/7) Hyperbolic Matrix(119,220,86,159) (-2/1,-11/6) -> (11/8,18/13) 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(79,140,22,39) (-9/5,-7/4) -> (7/2,11/3) Hyperbolic Matrix(81,140,70,121) (-7/4,-19/11) -> (1/1,7/6) Hyperbolic Matrix(1961,3380,720,1241) (-50/29,-31/18) -> (49/18,30/11) Hyperbolic Matrix(2001,3440,-1442,-2479) (-43/25,-12/7) -> (-68/49,-43/31) Hyperbolic Matrix(961,1640,610,1041) (-41/24,-29/17) -> (11/7,41/26) Hyperbolic Matrix(481,820,376,641) (-29/17,-17/10) -> (23/18,9/7) Hyperbolic Matrix(119,200,-72,-121) (-17/10,-5/3) -> (-5/3,-23/14) Parabolic Matrix(719,1180,170,279) (-23/14,-41/25) -> (21/5,17/4) 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(1001,1620,-642,-1039) (-34/21,-21/13) -> (-39/25,-14/9) 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(721,1140,456,721) (-19/12,-30/19) -> (30/19,19/12) Hyperbolic Matrix(1559,2460,988,1559) (-30/19,-41/26) -> (41/26,30/19) Hyperbolic Matrix(241,380,26,41) (-41/26,-11/7) -> (9/1,1/0) 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(41,60,28,41) (-3/2,-10/7) -> (10/7,3/2) Hyperbolic Matrix(239,340,168,239) (-10/7,-17/12) -> (17/12,10/7) Hyperbolic Matrix(961,1360,566,801) (-17/12,-41/29) -> (39/23,17/10) Hyperbolic Matrix(1799,2500,-1296,-1801) (-32/23,-25/18) -> (-25/18,-68/49) Parabolic Matrix(1399,1940,-1068,-1481) (-43/31,-18/13) -> (-38/29,-17/13) Hyperbolic Matrix(159,220,86,119) (-18/13,-11/8) -> (11/6,2/1) Hyperbolic Matrix(161,220,30,41) (-11/8,-15/11) -> (5/1,11/2) Hyperbolic Matrix(279,380,58,79) (-15/11,-19/14) -> (19/4,5/1) Hyperbolic Matrix(119,160,-90,-121) (-19/14,-4/3) -> (-4/3,-21/16) Parabolic Matrix(2121,2780,1252,1641) (-21/16,-38/29) -> (22/13,61/36) Hyperbolic Matrix(79,100,-64,-81) (-9/7,-5/4) -> (-5/4,-11/9) Parabolic Matrix(559,680,328,399) (-11/9,-17/14) -> (17/10,29/17) Hyperbolic Matrix(281,340,100,121) (-17/14,-6/5) -> (14/5,17/6) 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(121,140,70,81) (-7/6,-1/1) -> (19/11,7/4) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(201,-260,92,-119) (9/7,13/10) -> (13/6,11/5) Hyperbolic Matrix(199,-260,62,-81) (13/10,4/3) -> (16/5,13/4) Hyperbolic Matrix(281,-380,88,-119) (4/3,19/14) -> (19/6,16/5) Hyperbolic Matrix(721,-1000,230,-319) (18/13,43/31) -> (3/1,22/7) Hyperbolic Matrix(879,-1220,116,-161) (43/31,25/18) -> (15/2,23/3) Hyperbolic Matrix(201,-280,28,-39) (25/18,7/5) -> (7/1,15/2) Hyperbolic Matrix(241,-340,56,-79) (7/5,17/12) -> (17/4,13/3) Hyperbolic Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(159,-260,74,-121) (13/8,18/11) -> (2/1,13/6) Hyperbolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(199,-340,24,-41) (29/17,12/7) -> (8/1,9/1) Hyperbolic Matrix(639,-1100,140,-241) (12/7,31/18) -> (9/2,32/7) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) 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 IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(41,340,-24,-199) -> Matrix(1,1,2,3) Matrix(39,280,-28,-201) -> Matrix(1,0,2,1) Matrix(41,280,6,41) -> Matrix(1,0,0,1) Matrix(79,520,12,79) -> Matrix(1,6,0,1) Matrix(81,520,50,321) -> Matrix(1,2,0,1) Matrix(39,220,14,79) -> Matrix(1,1,0,1) Matrix(41,220,30,161) -> Matrix(1,-1,0,1) Matrix(79,380,58,279) -> Matrix(1,3,0,1) Matrix(199,940,76,359) -> Matrix(3,7,2,5) Matrix(121,560,78,361) -> Matrix(1,2,2,5) Matrix(241,1100,-140,-639) -> Matrix(1,1,4,5) Matrix(41,180,-18,-79) -> Matrix(1,1,-2,-1) Matrix(161,620,-114,-439) -> Matrix(1,3,0,1) Matrix(281,1060,-180,-679) -> Matrix(1,1,0,1) Matrix(119,440,-76,-281) -> Matrix(1,2,-2,-3) Matrix(39,140,22,79) -> Matrix(1,1,-2,-1) Matrix(41,140,12,41) -> Matrix(1,1,0,1) Matrix(79,260,24,79) -> Matrix(1,3,0,1) Matrix(81,260,-62,-199) -> Matrix(1,1,2,3) Matrix(41,120,14,41) -> Matrix(1,0,2,1) Matrix(239,680,84,239) -> Matrix(1,0,0,1) Matrix(199,560,156,439) -> Matrix(1,0,0,1) Matrix(79,220,14,39) -> Matrix(1,1,0,1) Matrix(241,660,88,241) -> Matrix(1,1,0,1) Matrix(559,1520,-324,-881) -> Matrix(1,0,4,1) Matrix(119,320,74,199) -> Matrix(1,0,0,1) Matrix(39,100,-16,-41) -> Matrix(1,1,-2,-1) Matrix(159,380,100,239) -> Matrix(1,1,-2,-1) Matrix(321,760,68,161) -> Matrix(9,2,4,1) Matrix(161,380,136,321) -> Matrix(5,1,-6,-1) Matrix(121,280,-86,-199) -> Matrix(1,0,2,1) Matrix(161,360,72,161) -> Matrix(1,0,8,1) Matrix(199,440,90,199) -> Matrix(1,0,-6,1) Matrix(119,260,-92,-201) -> Matrix(1,-1,2,-1) Matrix(119,220,86,159) -> Matrix(1,1,-2,-1) Matrix(241,440,132,241) -> Matrix(1,0,8,1) Matrix(199,360,110,199) -> Matrix(1,0,-10,1) Matrix(79,140,22,39) -> Matrix(1,-1,2,-1) Matrix(81,140,70,121) -> Matrix(3,-1,-2,1) Matrix(1961,3380,720,1241) -> Matrix(3,-1,4,-1) Matrix(2001,3440,-1442,-2479) -> Matrix(11,-4,14,-5) Matrix(961,1640,610,1041) -> Matrix(7,-4,2,-1) Matrix(481,820,376,641) -> Matrix(1,-1,2,-1) Matrix(119,200,-72,-121) -> Matrix(1,0,0,1) Matrix(719,1180,170,279) -> Matrix(1,-1,4,-3) Matrix(4879,8000,2878,4719) -> Matrix(15,-14,-16,15) Matrix(7321,12000,4320,7081) -> Matrix(17,-18,-16,17) Matrix(1001,1640,318,521) -> Matrix(1,-2,2,-3) Matrix(319,520,-246,-401) -> Matrix(1,-2,2,-3) Matrix(321,520,50,81) -> Matrix(1,2,0,1) Matrix(1001,1620,-642,-1039) -> Matrix(1,1,-2,-1) Matrix(199,320,74,119) -> Matrix(1,0,0,1) Matrix(201,320,76,121) -> Matrix(1,0,0,1) Matrix(721,1140,456,721) -> Matrix(1,-5,0,1) Matrix(1559,2460,988,1559) -> Matrix(1,9,0,1) Matrix(241,380,26,41) -> Matrix(1,5,0,1) Matrix(361,560,78,121) -> Matrix(5,2,2,1) Matrix(441,680,286,441) -> Matrix(1,0,10,1) Matrix(79,120,52,79) -> Matrix(1,0,-4,1) Matrix(41,60,28,41) -> Matrix(1,-1,0,1) Matrix(239,340,168,239) -> Matrix(1,-1,0,1) Matrix(961,1360,566,801) -> Matrix(3,-2,-4,3) Matrix(1799,2500,-1296,-1801) -> Matrix(7,-5,10,-7) Matrix(1399,1940,-1068,-1481) -> Matrix(1,-1,6,-5) Matrix(159,220,86,119) -> Matrix(1,-1,2,-1) Matrix(161,220,30,41) -> Matrix(1,-1,0,1) Matrix(279,380,58,79) -> Matrix(1,3,0,1) Matrix(119,160,-90,-121) -> Matrix(1,0,0,1) Matrix(2121,2780,1252,1641) -> Matrix(5,-1,-4,1) Matrix(79,100,-64,-81) -> Matrix(1,-1,2,-1) Matrix(559,680,328,399) -> Matrix(3,-2,-4,3) Matrix(281,340,100,121) -> Matrix(1,-1,2,-1) Matrix(439,520,168,199) -> Matrix(5,-4,4,-3) Matrix(441,520,374,441) -> Matrix(11,-10,-12,11) Matrix(239,280,204,239) -> Matrix(5,-6,-4,5) Matrix(121,140,70,81) -> Matrix(1,-1,-2,3) Matrix(1,0,2,1) -> Matrix(1,-2,0,1) Matrix(81,-100,64,-79) -> Matrix(1,1,-2,-1) Matrix(201,-260,92,-119) -> Matrix(1,1,-2,-1) Matrix(199,-260,62,-81) -> Matrix(3,1,2,1) Matrix(281,-380,88,-119) -> Matrix(3,1,2,1) Matrix(721,-1000,230,-319) -> Matrix(3,2,4,3) Matrix(879,-1220,116,-161) -> Matrix(7,5,4,3) Matrix(201,-280,28,-39) -> Matrix(1,0,2,1) Matrix(241,-340,56,-79) -> Matrix(1,1,0,1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-1) Matrix(841,-1360,222,-359) -> Matrix(3,-2,2,-1) Matrix(159,-260,74,-121) -> Matrix(1,1,0,1) Matrix(121,-200,72,-119) -> Matrix(1,0,0,1) Matrix(199,-340,24,-41) -> Matrix(3,1,2,1) Matrix(639,-1100,140,-241) -> Matrix(5,1,4,1) Matrix(881,-1520,324,-559) -> Matrix(1,0,4,1) Matrix(79,-180,18,-41) -> Matrix(1,-1,2,-1) Matrix(41,-100,16,-39) -> Matrix(1,-1,2,-1) Matrix(241,-900,64,-239) -> Matrix(3,-5,2,-3) Matrix(41,-160,10,-39) -> Matrix(1,-2,0,1) Matrix(201,-920,26,-119) -> Matrix(5,-8,2,-3) 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): 48 ----------------------------------------------------------------------- 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 1/0 1 1 1/1 (-1/1,1/0) 0 20 7/6 -3/2 1 20 20/17 -1/1 8 1 13/11 (-1/1,-5/6) 0 20 6/5 0 10 5/4 (-1/1,0/1).(-1/2,1/0) 0 4 14/11 0 10 23/18 1/0 1 20 9/7 (-2/1,-1/1) 0 20 13/10 -1/2 1 20 4/3 0 5 19/14 1/4 1 20 15/11 1/0 2 4 11/8 -3/2 1 20 18/13 0 10 43/31 (-1/1,-2/3) 0 20 25/18 (-1/1,-2/3).(-3/4,-1/2) 0 4 7/5 (-1/2,0/1) 0 20 17/12 -1/2 1 20 10/7 (-1/2,1/0) 0 2 3/2 -1/2 1 20 20/13 0/1 7 1 17/11 (0/1,1/5) 0 20 14/9 0 10 11/7 (1/1,2/1) 0 20 41/26 1/0 1 20 30/19 1/0 7 2 19/12 -5/2 1 20 8/5 0 5 21/13 (-1/2,0/1) 0 20 34/21 0 10 13/8 1/0 1 20 18/11 0 10 5/3 0 4 22/13 0 10 61/36 -9/8 1 20 100/59 -1/1 16 1 39/23 (-1/1,-7/8) 0 20 17/10 -1/2 1 20 29/17 (-2/3,-3/5) 0 20 12/7 -1/2 1 5 31/18 -1/2 1 20 19/11 (-1/2,0/1) 0 20 7/4 1/0 1 20 9/5 (-1/5,0/1) 0 20 20/11 0/1 9 1 11/6 1/4 1 20 2/1 0 10 13/6 1/0 1 20 11/5 (-1/3,0/1) 0 20 20/9 0/1 7 1 9/4 1/4 1 20 7/3 (0/1,1/0) 0 20 5/2 (0/1,1/1).(1/2,1/0) 0 4 13/5 (1/2,1/1) 0 20 34/13 0 10 21/8 5/2 1 20 8/3 0 5 19/7 (0/1,1/2) 0 20 49/18 1/2 1 20 30/11 (1/2,1/0) 0 2 11/4 1/2 1 20 14/5 0 10 17/6 1/0 1 20 20/7 0/1 1 1 3/1 (0/1,1/1) 0 20 22/7 0 10 19/6 7/6 1 20 16/5 0 5 13/4 1/0 1 20 10/3 1/0 1 2 7/2 1/2 1 20 11/3 (1/1,4/3) 0 20 26/7 0 10 15/4 (1/1,2/1).(3/2,1/0) 0 4 34/9 0 10 19/5 (7/4,2/1) 0 20 4/1 1/0 1 5 21/5 (-1/4,0/1) 0 20 17/4 1/2 1 20 13/3 (1/2,1/1) 0 20 9/2 3/2 1 20 32/7 3/2 1 5 23/5 (5/3,2/1) 0 20 14/3 0 10 19/4 11/4 1 20 5/1 1/0 2 4 11/2 1/2 1 20 6/1 0 10 13/2 1/0 1 20 20/3 1/0 3 1 7/1 (0/1,1/0) 0 20 15/2 (1/1,2/1).(3/2,1/0) 0 4 23/3 (1/1,2/1) 0 20 8/1 1/0 1 5 9/1 (3/1,4/1) 0 20 1/0 1/0 1 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(121,-140,70,-81) (1/1,7/6) -> (19/11,7/4) Glide Reflection Matrix(239,-280,204,-239) (7/6,20/17) -> (7/6,20/17) Reflection Matrix(441,-520,374,-441) (20/17,13/11) -> (20/17,13/11) Reflection Matrix(439,-520,168,-199) (13/11,6/5) -> (13/5,34/13) Glide Reflection Matrix(81,-100,64,-79) (6/5,5/4) -> (5/4,14/11) Parabolic Matrix(439,-560,156,-199) (14/11,23/18) -> (14/5,17/6) Glide Reflection Matrix(641,-820,376,-481) (23/18,9/7) -> (17/10,29/17) Glide Reflection Matrix(201,-260,92,-119) (9/7,13/10) -> (13/6,11/5) Hyperbolic Matrix(199,-260,62,-81) (13/10,4/3) -> (16/5,13/4) Hyperbolic Matrix(281,-380,88,-119) (4/3,19/14) -> (19/6,16/5) Hyperbolic Matrix(279,-380,58,-79) (19/14,15/11) -> (19/4,5/1) Glide Reflection Matrix(161,-220,30,-41) (15/11,11/8) -> (5/1,11/2) Glide Reflection Matrix(159,-220,86,-119) (11/8,18/13) -> (11/6,2/1) Glide Reflection Matrix(721,-1000,230,-319) (18/13,43/31) -> (3/1,22/7) Hyperbolic Matrix(879,-1220,116,-161) (43/31,25/18) -> (15/2,23/3) Hyperbolic Matrix(201,-280,28,-39) (25/18,7/5) -> (7/1,15/2) Hyperbolic Matrix(241,-340,56,-79) (7/5,17/12) -> (17/4,13/3) Hyperbolic Matrix(239,-340,168,-239) (17/12,10/7) -> (17/12,10/7) Reflection Matrix(41,-60,28,-41) (10/7,3/2) -> (10/7,3/2) Reflection Matrix(79,-120,52,-79) (3/2,20/13) -> (3/2,20/13) Reflection Matrix(441,-680,286,-441) (20/13,17/11) -> (20/13,17/11) Reflection Matrix(361,-560,78,-121) (17/11,14/9) -> (23/5,14/3) Glide Reflection Matrix(281,-440,76,-119) (14/9,11/7) -> (11/3,26/7) Hyperbolic Matrix(241,-380,26,-41) (11/7,41/26) -> (9/1,1/0) Glide Reflection Matrix(1559,-2460,988,-1559) (41/26,30/19) -> (41/26,30/19) Reflection Matrix(721,-1140,456,-721) (30/19,19/12) -> (30/19,19/12) Reflection Matrix(201,-320,76,-121) (19/12,8/5) -> (21/8,8/3) Glide Reflection Matrix(199,-320,74,-119) (8/5,21/13) -> (8/3,19/7) Glide Reflection Matrix(841,-1360,222,-359) (21/13,34/21) -> (34/9,19/5) Hyperbolic Matrix(321,-520,50,-81) (34/21,13/8) -> (6/1,13/2) Glide Reflection Matrix(159,-260,74,-121) (13/8,18/11) -> (2/1,13/6) Hyperbolic Matrix(121,-200,72,-119) (18/11,5/3) -> (5/3,22/13) Parabolic Matrix(1039,-1760,330,-559) (22/13,61/36) -> (22/7,19/6) Glide Reflection Matrix(7199,-12200,4248,-7199) (61/36,100/59) -> (61/36,100/59) Reflection Matrix(4601,-7800,2714,-4601) (100/59,39/23) -> (100/59,39/23) Reflection Matrix(601,-1020,142,-241) (39/23,17/10) -> (21/5,17/4) Glide Reflection Matrix(199,-340,24,-41) (29/17,12/7) -> (8/1,9/1) Hyperbolic Matrix(639,-1100,140,-241) (12/7,31/18) -> (9/2,32/7) Hyperbolic Matrix(881,-1520,324,-559) (31/18,19/11) -> (19/7,49/18) Hyperbolic Matrix(79,-140,22,-39) (7/4,9/5) -> (7/2,11/3) Glide Reflection Matrix(199,-360,110,-199) (9/5,20/11) -> (9/5,20/11) Reflection Matrix(241,-440,132,-241) (20/11,11/6) -> (20/11,11/6) 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(79,-180,18,-41) (9/4,7/3) -> (13/3,9/2) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(359,-940,76,-199) (34/13,21/8) -> (14/3,19/4) Glide Reflection Matrix(1079,-2940,396,-1079) (49/18,30/11) -> (49/18,30/11) Reflection Matrix(241,-660,88,-241) (30/11,11/4) -> (30/11,11/4) Reflection Matrix(79,-220,14,-39) (11/4,14/5) -> (11/2,6/1) Glide Reflection 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(79,-260,24,-79) (13/4,10/3) -> (13/4,10/3) Reflection Matrix(41,-140,12,-41) (10/3,7/2) -> (10/3,7/2) Reflection Matrix(241,-900,64,-239) (26/7,15/4) -> (15/4,34/9) 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(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(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,2,0,-1) (0/1,1/1) -> (-1/1,1/0) Matrix(121,-140,70,-81) -> Matrix(1,1,-2,-3) Matrix(239,-280,204,-239) -> Matrix(5,6,-4,-5) (7/6,20/17) -> (-3/2,-1/1) Matrix(441,-520,374,-441) -> Matrix(11,10,-12,-11) (20/17,13/11) -> (-1/1,-5/6) Matrix(439,-520,168,-199) -> Matrix(5,4,4,3) Matrix(81,-100,64,-79) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(439,-560,156,-199) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(641,-820,376,-481) -> Matrix(1,-1,-2,1) Matrix(201,-260,92,-119) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(199,-260,62,-81) -> Matrix(3,1,2,1) Matrix(281,-380,88,-119) -> Matrix(3,1,2,1) Matrix(279,-380,58,-79) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(161,-220,30,-41) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(159,-220,86,-119) -> Matrix(1,1,2,1) Matrix(721,-1000,230,-319) -> Matrix(3,2,4,3) Matrix(879,-1220,116,-161) -> Matrix(7,5,4,3) Matrix(201,-280,28,-39) -> Matrix(1,0,2,1) 0/1 Matrix(241,-340,56,-79) -> Matrix(1,1,0,1) 1/0 Matrix(239,-340,168,-239) -> Matrix(1,1,0,-1) (17/12,10/7) -> (-1/2,1/0) Matrix(41,-60,28,-41) -> Matrix(1,1,0,-1) (10/7,3/2) -> (-1/2,1/0) Matrix(79,-120,52,-79) -> Matrix(-1,0,4,1) (3/2,20/13) -> (-1/2,0/1) Matrix(441,-680,286,-441) -> Matrix(1,0,10,-1) (20/13,17/11) -> (0/1,1/5) Matrix(361,-560,78,-121) -> Matrix(5,-2,2,-1) Matrix(281,-440,76,-119) -> Matrix(3,-2,2,-1) 1/1 Matrix(241,-380,26,-41) -> Matrix(-1,5,0,1) *** -> (5/2,1/0) Matrix(1559,-2460,988,-1559) -> Matrix(-1,9,0,1) (41/26,30/19) -> (9/2,1/0) Matrix(721,-1140,456,-721) -> Matrix(1,5,0,-1) (30/19,19/12) -> (-5/2,1/0) Matrix(201,-320,76,-121) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(199,-320,74,-119) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(841,-1360,222,-359) -> Matrix(3,-2,2,-1) 1/1 Matrix(321,-520,50,-81) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(159,-260,74,-121) -> Matrix(1,1,0,1) 1/0 Matrix(121,-200,72,-119) -> Matrix(1,0,0,1) Matrix(1039,-1760,330,-559) -> Matrix(1,2,2,3) Matrix(7199,-12200,4248,-7199) -> Matrix(17,18,-16,-17) (61/36,100/59) -> (-9/8,-1/1) Matrix(4601,-7800,2714,-4601) -> Matrix(15,14,-16,-15) (100/59,39/23) -> (-1/1,-7/8) Matrix(601,-1020,142,-241) -> Matrix(1,1,4,3) Matrix(199,-340,24,-41) -> Matrix(3,1,2,1) Matrix(639,-1100,140,-241) -> Matrix(5,1,4,1) Matrix(881,-1520,324,-559) -> Matrix(1,0,4,1) 0/1 Matrix(79,-140,22,-39) -> Matrix(1,1,2,1) Matrix(199,-360,110,-199) -> Matrix(-1,0,10,1) (9/5,20/11) -> (-1/5,0/1) Matrix(241,-440,132,-241) -> Matrix(1,0,8,-1) (20/11,11/6) -> (0/1,1/4) Matrix(199,-440,90,-199) -> Matrix(-1,0,6,1) (11/5,20/9) -> (-1/3,0/1) Matrix(161,-360,72,-161) -> Matrix(1,0,8,-1) (20/9,9/4) -> (0/1,1/4) Matrix(79,-180,18,-41) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(41,-100,16,-39) -> Matrix(1,-1,2,-1) (0/1,1/1).(1/2,1/0) Matrix(359,-940,76,-199) -> Matrix(5,-7,2,-3) Matrix(1079,-2940,396,-1079) -> Matrix(-1,1,0,1) (49/18,30/11) -> (1/2,1/0) Matrix(241,-660,88,-241) -> Matrix(-1,1,0,1) (30/11,11/4) -> (1/2,1/0) Matrix(79,-220,14,-39) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(239,-680,84,-239) -> Matrix(1,0,0,-1) (17/6,20/7) -> (0/1,1/0) Matrix(41,-120,14,-41) -> Matrix(1,0,2,-1) (20/7,3/1) -> (0/1,1/1) Matrix(79,-260,24,-79) -> Matrix(-1,3,0,1) (13/4,10/3) -> (3/2,1/0) Matrix(41,-140,12,-41) -> Matrix(-1,1,0,1) (10/3,7/2) -> (1/2,1/0) Matrix(241,-900,64,-239) -> Matrix(3,-5,2,-3) (1/1,2/1).(3/2,1/0) Matrix(41,-160,10,-39) -> Matrix(1,-2,0,1) 1/0 Matrix(201,-920,26,-119) -> Matrix(5,-8,2,-3) 2/1 Matrix(79,-520,12,-79) -> Matrix(-1,6,0,1) (13/2,20/3) -> (3/1,1/0) Matrix(41,-280,6,-41) -> Matrix(1,0,0,-1) (20/3,7/1) -> (0/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.