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 -1/1 -8/1 0/1 -7/1 -1/1 -20/3 -1/1 -13/2 -1/1 -2/3 -6/1 -1/2 -17/3 1/1 -11/2 -1/1 0/1 -16/3 -2/3 -5/1 -1/2 -24/5 0/1 -19/4 -1/2 -4/9 -14/3 -1/2 -23/5 -1/3 -32/7 -2/5 -9/2 -1/3 0/1 -13/3 -3/7 -17/4 -2/5 -1/3 -4/1 -1/3 -23/6 -1/3 0/1 -42/11 -1/4 -19/5 -1/3 -15/4 -1/3 -11/3 -1/3 -18/5 -1/4 -43/12 -1/3 -2/7 -25/7 -1/4 -7/2 -1/4 0/1 -17/5 -3/11 -10/3 -1/4 -23/7 -3/13 -13/4 -3/13 -2/9 -16/5 0/1 -19/6 -4/15 -1/4 -3/1 -1/5 -20/7 -1/5 -17/6 -1/5 -6/31 -14/5 -3/16 -11/4 -1/5 0/1 -41/15 -7/33 -30/11 -1/5 -19/7 -1/5 -8/3 -2/11 -21/8 -2/11 -1/6 -34/13 -1/6 -13/5 -1/7 -31/12 -1/5 -2/11 -18/7 -1/6 -5/2 -1/6 -22/9 -1/6 -61/25 -3/19 -100/41 -3/19 -39/16 -3/19 -2/13 -17/7 -3/19 -29/12 -2/13 -1/7 -41/17 -3/23 -53/22 -1/3 0/1 -12/5 -1/6 -55/23 -1/6 -43/18 -3/19 -2/13 -31/13 -1/7 -19/8 -1/6 0/1 -26/11 -1/6 -7/3 -1/7 -16/7 -2/13 -41/18 -2/13 -1/7 -25/11 -3/20 -34/15 -3/20 -9/4 -4/27 -1/7 -20/9 -1/7 -11/5 -1/7 -13/6 -5/37 -2/15 -28/13 -1/8 -15/7 -1/8 -17/8 -1/7 -2/15 -2/1 -1/8 -17/9 -1/9 -15/8 -1/8 -28/15 -3/25 -13/7 -5/43 -11/6 -4/35 -1/9 -20/11 -1/9 -9/5 -1/9 -43/24 -5/47 -2/19 -34/19 -1/10 -25/14 -1/9 -41/23 -13/121 -16/9 -2/19 -39/22 -2/19 -3/29 -23/13 -3/29 -7/4 -1/10 0/1 -40/23 0/1 -33/19 -1/7 -26/15 -1/8 -19/11 -1/9 -50/29 -1/9 -31/18 -1/9 -2/19 -74/43 -3/28 -117/68 -9/85 -2/19 -160/93 -2/19 -43/25 -3/29 -12/7 -1/9 -53/31 -9/85 -41/24 -1/9 -2/19 -29/17 -1/9 -17/10 -2/19 -3/29 -5/3 -1/10 -23/14 -1/9 0/1 -41/25 -7/69 -100/61 -1/10 -59/36 -1/10 -10/101 -18/11 -1/10 -13/8 -2/21 -1/11 -34/21 -1/10 -55/34 -1/11 -21/13 -1/11 -8/5 0/1 -19/12 -1/10 0/1 -49/31 -1/11 -30/19 -1/10 -71/45 -3/31 -41/26 -2/21 -1/11 -11/7 -1/11 -25/16 -1/11 -39/25 -3/37 -53/34 -1/17 0/1 -14/9 -1/10 -17/11 -1/11 -20/13 -1/11 -3/2 -1/11 0/1 -22/15 -1/10 -19/13 -1/11 -16/11 0/1 -29/20 -2/21 -1/11 -13/9 -1/9 -10/7 -1/11 -27/19 -3/35 -17/12 -1/11 -2/23 -41/29 -5/61 -24/17 0/1 -7/5 -1/11 -32/23 -2/23 -57/41 -3/35 -25/18 -1/12 -68/49 -1/11 -43/31 -3/35 -61/44 -8/95 -1/12 -18/13 -1/12 -29/21 -1/13 -40/29 0/1 -11/8 -1/11 0/1 -26/19 -3/34 -93/68 -17/195 -2/23 -160/117 -2/23 -67/49 -11/127 -41/30 -2/23 -3/35 -15/11 -1/12 -34/25 -1/12 -19/14 -1/12 0/1 -4/3 -1/12 -21/16 -1/12 -2/25 -80/61 -2/25 -59/45 -1/13 -38/29 -1/12 -17/13 -1/13 -13/10 -2/25 -1/13 -22/17 -1/12 -31/24 -3/37 -2/25 -40/31 -2/25 -9/7 -1/13 -32/25 -2/25 -23/18 -4/51 -1/13 -14/11 -1/12 -19/15 -1/13 -5/4 -1/13 -21/17 -1/13 -16/13 -2/27 -27/22 -1/15 0/1 -11/9 -1/13 -17/14 -5/67 -2/27 -40/33 -2/27 -23/19 -7/95 -6/5 -1/14 -13/11 -7/97 -20/17 -1/14 -7/6 -1/14 -4/57 -15/13 -1/14 -23/20 -4/57 -3/43 -8/7 -2/29 -9/8 -4/59 -1/15 -10/9 -1/15 -1/1 -1/17 0/1 0/1 1/1 1/19 9/8 1/17 4/67 8/7 2/33 7/6 4/65 1/16 20/17 1/16 13/11 7/111 6/5 1/16 17/14 2/31 5/77 11/9 1/15 16/13 2/31 5/4 1/15 24/19 2/29 19/15 1/15 14/11 1/14 23/18 1/15 4/59 32/25 2/29 9/7 1/15 13/10 1/15 2/29 17/13 1/15 4/3 1/14 23/17 1/13 42/31 1/14 19/14 0/1 1/14 15/11 1/14 11/8 0/1 1/13 18/13 1/14 43/31 3/41 25/18 1/14 7/5 1/13 17/12 2/27 1/13 10/7 1/13 23/16 0/1 1/13 13/9 1/11 16/11 0/1 19/13 1/13 3/2 0/1 1/13 20/13 1/13 17/11 1/13 14/9 1/12 11/7 1/13 41/26 1/13 2/25 30/19 1/12 19/12 0/1 1/12 8/5 0/1 21/13 1/13 34/21 1/12 13/8 1/13 2/25 31/19 1/13 18/11 1/12 5/3 1/12 22/13 1/12 61/36 8/97 1/12 100/59 1/12 39/23 9/107 17/10 3/35 2/23 29/17 1/11 41/24 2/23 1/11 53/31 9/103 12/7 1/11 55/32 1/12 43/25 3/35 31/18 2/23 1/11 19/11 1/11 26/15 1/10 7/4 0/1 1/12 16/9 2/23 41/23 13/147 25/14 1/11 34/19 1/12 9/5 1/11 20/11 1/11 11/6 1/11 4/43 13/7 5/53 28/15 3/31 15/8 1/10 17/9 1/11 2/1 1/10 17/8 2/19 1/9 15/7 1/10 28/13 1/10 13/6 2/19 5/47 11/5 1/9 20/9 1/9 9/4 1/9 4/35 43/19 9/79 34/15 3/26 25/11 3/26 41/18 1/9 2/17 16/7 2/17 39/17 7/57 23/10 0/1 1/9 7/3 1/9 40/17 2/17 33/14 2/17 5/42 26/11 1/8 19/8 0/1 1/8 50/21 1/8 31/13 1/9 74/31 3/26 117/49 9/77 160/67 2/17 43/18 2/17 3/25 12/5 1/8 53/22 0/1 1/5 41/17 3/29 29/12 1/9 2/17 17/7 3/25 5/2 1/8 23/9 1/7 41/16 2/15 1/7 100/39 1/7 59/23 1/7 18/7 1/8 13/5 1/9 34/13 1/8 55/21 1/8 21/8 1/8 2/15 8/3 2/15 19/7 1/7 49/18 6/43 1/7 30/11 1/7 71/26 1/7 8/55 41/15 7/47 11/4 0/1 1/7 25/9 1/8 39/14 3/23 2/15 53/19 11/83 14/5 3/22 17/6 6/43 1/7 20/7 1/7 3/1 1/7 22/7 1/6 19/6 1/6 4/23 16/5 0/1 29/9 1/7 13/4 2/13 3/19 10/3 1/6 27/8 4/23 3/17 17/5 3/17 41/12 3/17 2/11 24/7 2/11 7/2 0/1 1/6 32/9 2/11 57/16 0/1 1/5 25/7 1/6 68/19 1/6 43/12 2/11 1/5 61/17 1/5 18/5 1/6 29/8 3/17 2/11 40/11 2/11 11/3 1/5 26/7 1/6 93/25 15/83 160/43 2/11 67/18 2/11 13/71 41/11 11/59 15/4 1/5 34/9 1/6 19/5 1/5 4/1 1/5 21/5 1/5 80/19 2/9 59/14 2/9 1/4 38/9 1/4 17/4 1/5 2/9 13/3 3/13 22/5 1/4 31/7 1/3 40/9 0/1 9/2 0/1 1/5 32/7 2/9 23/5 1/5 14/3 1/4 19/4 4/17 1/4 5/1 1/4 21/4 2/9 1/4 16/3 2/7 27/5 3/11 11/2 0/1 1/3 17/3 1/1 40/7 0/1 23/4 0/1 1/7 6/1 1/4 13/2 2/7 1/3 20/3 1/3 7/1 1/3 15/2 1/2 23/3 1/1 8/1 0/1 9/1 1/3 10/1 1/2 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,-10,21) Matrix(41,360,32,281) -> Matrix(1,2,14,29) Matrix(39,280,-28,-201) -> Matrix(1,2,-12,-23) Matrix(41,280,6,41) -> Matrix(1,2,2,5) Matrix(79,520,12,79) -> Matrix(5,4,16,13) Matrix(81,520,50,321) -> Matrix(1,0,14,1) Matrix(41,240,-34,-199) -> Matrix(5,2,-68,-27) Matrix(121,680,50,281) -> Matrix(1,2,8,17) Matrix(119,640,-82,-441) -> Matrix(3,2,-32,-21) Matrix(39,200,-8,-41) -> Matrix(3,2,-8,-5) Matrix(159,760,50,239) -> Matrix(1,0,8,1) Matrix(161,760,68,321) -> Matrix(9,4,74,33) Matrix(121,560,78,361) -> Matrix(5,2,62,25) Matrix(559,2560,-402,-1841) -> Matrix(9,4,-106,-47) Matrix(79,360,70,319) -> Matrix(11,4,184,67) Matrix(119,520,-46,-201) -> Matrix(5,2,-28,-11) Matrix(121,520,84,361) -> Matrix(5,2,62,25) Matrix(39,160,-10,-41) -> Matrix(5,2,-18,-7) Matrix(199,760,94,359) -> Matrix(7,2,66,19) Matrix(839,3200,-640,-2441) -> Matrix(7,2,-88,-25) Matrix(359,1360,-222,-841) -> Matrix(7,2,-74,-21) Matrix(119,440,-76,-281) -> Matrix(7,2,-74,-21) Matrix(199,720,-144,-521) -> Matrix(7,2,-88,-25) Matrix(279,1000,-190,-681) -> Matrix(7,2,-74,-21) Matrix(961,3440,-402,-1439) -> Matrix(15,4,-94,-25) Matrix(79,280,-68,-241) -> Matrix(15,4,-214,-57) Matrix(81,280,-46,-159) -> Matrix(1,0,-6,1) Matrix(119,400,-36,-121) -> Matrix(23,6,-96,-25) Matrix(159,520,122,399) -> Matrix(17,4,242,57) Matrix(199,640,-162,-521) -> Matrix(9,2,-122,-27) Matrix(201,640,38,121) -> Matrix(7,2,24,7) Matrix(319,1000,-230,-721) -> Matrix(17,4,-200,-47) Matrix(41,120,14,41) -> Matrix(9,2,58,13) Matrix(239,680,84,239) -> Matrix(61,12,432,85) Matrix(199,560,156,439) -> Matrix(11,2,170,31) Matrix(159,440,-116,-321) -> Matrix(1,0,-6,1) Matrix(599,1640,248,679) -> Matrix(9,2,76,17) Matrix(161,440,-146,-399) -> Matrix(19,4,-290,-61) Matrix(559,1520,-324,-881) -> Matrix(21,4,-184,-35) Matrix(119,320,74,199) -> Matrix(11,2,148,27) Matrix(121,320,76,201) -> Matrix(11,2,126,23) Matrix(519,1360,-382,-1001) -> Matrix(11,2,-138,-25) Matrix(199,520,168,439) -> Matrix(35,6,554,95) Matrix(481,1240,-372,-959) -> Matrix(23,4,-282,-49) Matrix(79,200,-32,-81) -> Matrix(23,4,-144,-25) Matrix(999,2440,278,679) -> Matrix(13,2,84,13) Matrix(4919,12000,1918,4679) -> Matrix(13,2,110,17) Matrix(3281,8000,1280,3121) -> Matrix(51,8,376,59) Matrix(559,1360,164,399) -> Matrix(1,0,12,1) Matrix(281,680,50,121) -> Matrix(13,2,32,5) Matrix(679,1640,248,599) -> Matrix(13,2,84,13) Matrix(2041,4920,548,1321) -> Matrix(19,2,104,11) Matrix(681,1640,316,761) -> Matrix(11,2,104,19) Matrix(719,1720,334,799) -> Matrix(1,0,16,1) Matrix(721,1720,-402,-959) -> Matrix(27,4,-250,-37) Matrix(639,1520,-404,-961) -> Matrix(1,0,-4,1) Matrix(321,760,68,161) -> Matrix(25,4,106,17) Matrix(441,1040,-254,-599) -> Matrix(13,2,-98,-15) Matrix(121,280,-86,-199) -> Matrix(13,2,-150,-23) Matrix(719,1640,210,479) -> Matrix(53,8,298,45) Matrix(879,2000,316,719) -> Matrix(53,8,404,61) Matrix(1199,2720,458,1039) -> Matrix(53,8,404,61) Matrix(761,1720,-442,-999) -> Matrix(41,6,-376,-55) Matrix(161,360,72,161) -> Matrix(55,8,488,71) Matrix(199,440,90,199) -> Matrix(71,10,646,91) Matrix(201,440,-164,-359) -> Matrix(15,2,-188,-25) Matrix(761,1640,316,681) -> Matrix(15,2,112,15) Matrix(801,1720,224,481) -> Matrix(31,4,178,23) Matrix(599,1280,168,359) -> Matrix(15,2,82,11) Matrix(321,680,76,161) -> Matrix(1,0,12,1) Matrix(401,760,296,561) -> Matrix(1,0,22,1) Matrix(319,600,42,79) -> Matrix(1,0,10,1) Matrix(921,1720,536,1001) -> Matrix(17,2,212,25) Matrix(879,1640,514,959) -> Matrix(67,8,762,91) Matrix(281,520,-194,-359) -> Matrix(17,2,-196,-23) Matrix(241,440,132,241) -> Matrix(71,8,772,87) Matrix(199,360,110,199) -> Matrix(55,6,614,67) Matrix(3999,7160,-2324,-4161) -> Matrix(77,8,-722,-75) Matrix(761,1360,202,361) -> Matrix(19,2,104,11) Matrix(919,1640,246,439) -> Matrix(55,6,284,31) Matrix(719,1280,314,559) -> Matrix(75,8,628,67) Matrix(721,1280,316,561) -> Matrix(77,8,664,69) Matrix(1039,1840,406,719) -> Matrix(39,4,302,31) Matrix(919,1600,390,679) -> Matrix(25,2,212,17) Matrix(921,1600,392,681) -> Matrix(13,2,110,17) Matrix(439,760,346,599) -> Matrix(17,2,246,29) Matrix(441,760,-394,-679) -> Matrix(55,6,-816,-89) Matrix(14879,25600,6230,10719) -> Matrix(227,24,1920,203) Matrix(14881,25600,6232,10721) -> Matrix(229,24,1956,205) Matrix(2001,3440,-1442,-2479) -> Matrix(1,0,-2,1) Matrix(959,1640,514,879) -> Matrix(75,8,778,83) Matrix(2481,4240,890,1521) -> Matrix(39,4,302,31) Matrix(961,1640,610,1041) -> Matrix(1,0,22,1) Matrix(399,680,328,559) -> Matrix(37,4,564,61) Matrix(119,200,-72,-121) -> Matrix(19,2,-200,-21) Matrix(1121,1840,488,801) -> Matrix(1,0,18,1) Matrix(4879,8000,2878,4719) -> Matrix(159,16,1898,191) Matrix(7321,12000,4320,7081) -> Matrix(181,18,2182,217) Matrix(1001,1640,318,521) -> Matrix(61,6,376,37) Matrix(319,520,-246,-401) -> Matrix(1,0,-2,1) Matrix(321,520,50,81) -> Matrix(1,0,14,1) Matrix(1681,2720,940,1521) -> Matrix(1,0,22,1) Matrix(199,320,74,119) -> Matrix(23,2,172,15) Matrix(201,320,76,121) -> Matrix(19,2,142,15) Matrix(2279,3600,-1444,-2281) -> Matrix(19,2,-200,-21) Matrix(1041,1640,610,961) -> Matrix(1,0,22,1) Matrix(1281,2000,718,1121) -> Matrix(45,4,506,45) Matrix(2719,4240,1128,1759) -> Matrix(1,0,22,1) Matrix(1721,2680,-1258,-1959) -> Matrix(17,2,-196,-23) Matrix(361,560,78,121) -> Matrix(21,2,94,9) Matrix(441,680,286,441) -> Matrix(21,2,262,25) Matrix(79,120,52,79) -> Matrix(1,0,24,1) Matrix(1119,1640,436,639) -> Matrix(1,0,18,1) Matrix(521,760,412,601) -> Matrix(21,2,304,29) Matrix(279,400,-196,-281) -> Matrix(21,2,-242,-23) Matrix(479,680,112,159) -> Matrix(1,0,16,1) Matrix(961,1360,566,801) -> Matrix(47,4,552,47) Matrix(1161,1640,652,921) -> Matrix(27,2,310,23) Matrix(921,1280,490,681) -> Matrix(23,2,218,19) Matrix(1239,1720,662,919) -> Matrix(25,2,262,21) Matrix(1761,2440,1040,1441) -> Matrix(1,0,24,1) Matrix(1159,1600,318,439) -> Matrix(27,2,148,11) Matrix(1161,1600,320,441) -> Matrix(19,2,104,11) Matrix(18719,25600,5030,6879) -> Matrix(689,60,3778,329) Matrix(18721,25600,5032,6881) -> Matrix(599,52,3306,287) Matrix(3599,4920,2106,2879) -> Matrix(47,4,552,47) Matrix(1201,1640,528,721) -> Matrix(93,8,802,69) Matrix(999,1360,440,599) -> Matrix(21,2,178,17) Matrix(119,160,-90,-121) -> Matrix(23,2,-288,-25) Matrix(4879,6400,1158,1519) -> Matrix(49,4,208,17) Matrix(4881,6400,1160,1521) -> Matrix(51,4,242,19) Matrix(519,680,274,359) -> Matrix(25,2,262,21) Matrix(521,680,154,201) -> Matrix(23,2,126,11) Matrix(1239,1600,278,359) -> Matrix(25,2,162,13) Matrix(1241,1600,280,361) -> Matrix(25,2,62,5) Matrix(281,360,32,41) -> Matrix(25,2,62,5) Matrix(719,920,-626,-801) -> Matrix(101,8,-1452,-115) Matrix(439,560,156,199) -> Matrix(27,2,202,15) Matrix(599,760,346,439) -> Matrix(25,2,262,21) Matrix(159,200,-128,-161) -> Matrix(51,4,-676,-53) Matrix(519,640,356,439) -> Matrix(27,2,364,27) Matrix(559,680,328,399) -> Matrix(53,4,596,45) Matrix(1319,1600,230,279) -> Matrix(27,2,256,19) Matrix(1321,1600,232,281) -> Matrix(27,2,-68,-5) Matrix(439,520,168,199) -> Matrix(83,6,650,47) Matrix(441,520,374,441) -> Matrix(195,14,3106,223) Matrix(239,280,204,239) -> Matrix(113,8,1822,129) Matrix(521,600,244,281) -> Matrix(29,2,304,21) Matrix(319,360,70,79) -> Matrix(59,4,280,19) Matrix(1,0,2,1) -> Matrix(1,0,36,1) Matrix(399,-440,146,-161) -> Matrix(69,-4,466,-27) Matrix(241,-280,68,-79) -> Matrix(65,-4,374,-23) Matrix(199,-240,34,-41) -> Matrix(31,-2,140,-9) Matrix(521,-640,162,-199) -> Matrix(31,-2,202,-13) Matrix(161,-200,128,-159) -> Matrix(61,-4,900,-59) Matrix(2001,-2560,562,-719) -> Matrix(59,-4,310,-21) Matrix(401,-520,246,-319) -> Matrix(1,0,-2,1) Matrix(121,-160,90,-119) -> Matrix(29,-2,392,-27) Matrix(2361,-3200,560,-759) -> Matrix(27,-2,122,-9) Matrix(1001,-1360,382,-519) -> Matrix(29,-2,218,-15) Matrix(321,-440,116,-159) -> Matrix(1,0,-6,1) Matrix(521,-720,144,-199) -> Matrix(29,-2,160,-11) Matrix(721,-1000,230,-319) -> Matrix(55,-4,344,-25) Matrix(2479,-3440,1442,-2001) -> Matrix(1,0,-2,1) Matrix(201,-280,28,-39) -> Matrix(27,-2,68,-5) Matrix(199,-280,86,-121) -> Matrix(27,-2,230,-17) Matrix(281,-400,196,-279) -> Matrix(27,-2,338,-25) Matrix(441,-640,82,-119) -> Matrix(25,-2,88,-7) Matrix(681,-1000,190,-279) -> Matrix(25,-2,138,-11) Matrix(281,-440,76,-119) -> Matrix(25,-2,138,-11) Matrix(279,-440,26,-41) -> Matrix(25,-2,38,-3) Matrix(961,-1520,404,-639) -> Matrix(1,0,-4,1) Matrix(841,-1360,222,-359) -> Matrix(25,-2,138,-11) Matrix(759,-1240,172,-281) -> Matrix(25,-2,88,-7) Matrix(121,-200,72,-119) -> Matrix(25,-2,288,-23) Matrix(999,-1720,442,-761) -> Matrix(67,-6,592,-53) Matrix(881,-1520,324,-559) -> Matrix(43,-4,312,-29) Matrix(599,-1040,254,-441) -> Matrix(19,-2,162,-17) Matrix(159,-280,46,-81) -> Matrix(1,0,-6,1) Matrix(959,-1720,402,-721) -> Matrix(45,-4,394,-35) Matrix(239,-440,44,-81) -> Matrix(43,-4,140,-13) Matrix(239,-520,74,-161) -> Matrix(37,-4,250,-27) Matrix(3161,-7160,1324,-2999) -> Matrix(157,-18,1352,-155) Matrix(319,-760,34,-81) -> Matrix(1,0,-6,1) Matrix(1439,-3440,402,-961) -> Matrix(33,-4,190,-23) Matrix(81,-200,32,-79) -> Matrix(33,-4,256,-31) Matrix(201,-520,46,-119) -> Matrix(15,-2,68,-9) Matrix(1321,-3600,484,-1319) -> Matrix(99,-14,686,-97) Matrix(959,-2680,258,-721) -> Matrix(59,-8,332,-45) Matrix(121,-400,36,-119) -> Matrix(37,-6,216,-35) Matrix(41,-160,10,-39) -> Matrix(11,-2,50,-9) Matrix(201,-920,26,-119) -> Matrix(9,-2,14,-3) Matrix(41,-200,8,-39) -> Matrix(9,-2,32,-7) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 64 Degree of the the map X: 64 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. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 18 1 1/1 1/19 1 20 9/8 (1/17,4/67) 0 20 8/7 2/33 2 5 7/6 (4/65,1/16) 0 20 20/17 1/16 11 1 13/11 7/111 1 20 6/5 1/16 1 10 17/14 (2/31,5/77) 0 20 11/9 1/15 1 20 16/13 2/31 1 5 5/4 1/15 2 4 24/19 2/29 1 5 19/15 1/15 1 20 14/11 1/14 1 10 23/18 (1/15,4/59) 0 20 32/25 2/29 2 5 9/7 1/15 1 20 13/10 (1/15,2/29) 0 20 17/13 1/15 1 20 4/3 1/14 1 5 23/17 1/13 1 20 42/31 1/14 1 10 19/14 (0/1,1/14) 0 20 15/11 1/14 1 4 11/8 (0/1,1/13) 0 20 18/13 1/14 1 10 43/31 3/41 1 20 25/18 1/14 2 4 7/5 1/13 1 20 17/12 (2/27,1/13) 0 20 10/7 1/13 1 2 23/16 (0/1,1/13) 0 20 13/9 1/11 1 20 16/11 0/1 1 5 19/13 1/13 1 20 3/2 (0/1,1/13) 0 20 20/13 1/13 1 1 17/11 1/13 1 20 14/9 1/12 1 10 11/7 1/13 1 20 41/26 (1/13,2/25) 0 20 30/19 1/12 1 2 19/12 (0/1,1/12) 0 20 8/5 0/1 1 5 21/13 1/13 1 20 34/21 1/12 1 10 13/8 (1/13,2/25) 0 20 31/19 1/13 1 20 18/11 1/12 1 10 5/3 1/12 1 4 22/13 1/12 1 10 61/36 (8/97,1/12) 0 20 100/59 1/12 17 1 39/23 9/107 1 20 17/10 (3/35,2/23) 0 20 29/17 1/11 1 20 41/24 (2/23,1/11) 0 20 53/31 9/103 1 20 12/7 1/11 1 5 55/32 1/12 2 4 43/25 3/35 1 20 31/18 (2/23,1/11) 0 20 19/11 1/11 1 20 26/15 1/10 1 10 7/4 (0/1,1/12) 0 20 16/9 2/23 2 5 41/23 13/147 1 20 25/14 1/11 2 4 34/19 1/12 1 10 9/5 1/11 1 20 20/11 1/11 7 1 11/6 (1/11,4/43) 0 20 13/7 5/53 1 20 28/15 3/31 1 5 15/8 1/10 2 4 17/9 1/11 1 20 2/1 1/10 1 10 17/8 (2/19,1/9) 0 20 15/7 1/10 1 4 28/13 1/10 1 5 13/6 (2/19,5/47) 0 20 11/5 1/9 1 20 20/9 1/9 9 1 9/4 (1/9,4/35) 0 20 43/19 9/79 1 20 34/15 3/26 1 10 25/11 3/26 1 4 41/18 (1/9,2/17) 0 20 16/7 2/17 2 5 39/17 7/57 1 20 23/10 (0/1,1/9) 0 20 7/3 1/9 1 20 40/17 2/17 3 1 33/14 (2/17,5/42) 0 20 26/11 1/8 1 10 19/8 (0/1,1/8) 0 20 50/21 1/8 1 2 31/13 1/9 1 20 74/31 3/26 1 10 117/49 9/77 1 20 160/67 2/17 6 1 43/18 (2/17,3/25) 0 20 12/5 1/8 1 5 53/22 (0/1,1/5) 0 20 41/17 3/29 1 20 29/12 (1/9,2/17) 0 20 17/7 3/25 1 20 5/2 1/8 2 4 23/9 1/7 1 20 41/16 (2/15,1/7) 0 20 100/39 1/7 1 1 59/23 1/7 1 20 18/7 1/8 1 10 13/5 1/9 1 20 34/13 1/8 1 10 55/21 1/8 1 4 21/8 (1/8,2/15) 0 20 8/3 2/15 1 5 19/7 1/7 1 20 49/18 (6/43,1/7) 0 20 30/11 1/7 7 2 71/26 (1/7,8/55) 0 20 41/15 7/47 1 20 11/4 (0/1,1/7) 0 20 25/9 1/8 1 4 39/14 (3/23,2/15) 0 20 53/19 11/83 1 20 14/5 3/22 1 10 17/6 (6/43,1/7) 0 20 20/7 1/7 7 1 3/1 1/7 1 20 22/7 1/6 1 10 19/6 (1/6,4/23) 0 20 16/5 0/1 1 5 29/9 1/7 1 20 13/4 (2/13,3/19) 0 20 10/3 1/6 3 2 27/8 (4/23,3/17) 0 20 17/5 3/17 1 20 41/12 (3/17,2/11) 0 20 24/7 2/11 2 5 7/2 (0/1,1/6) 0 20 32/9 2/11 2 5 57/16 (0/1,1/5) 0 20 25/7 1/6 1 4 68/19 1/6 1 5 43/12 (2/11,1/5) 0 20 61/17 1/5 1 20 18/5 1/6 1 10 29/8 (3/17,2/11) 0 20 40/11 2/11 2 1 11/3 1/5 1 20 26/7 1/6 1 10 93/25 15/83 1 20 160/43 2/11 14 1 67/18 (2/11,13/71) 0 20 41/11 11/59 1 20 15/4 1/5 2 4 34/9 1/6 1 10 19/5 1/5 1 20 4/1 1/5 1 5 21/5 1/5 1 20 80/19 2/9 1 1 59/14 (2/9,1/4) 0 20 38/9 1/4 1 10 17/4 (1/5,2/9) 0 20 13/3 3/13 1 20 22/5 1/4 1 10 31/7 1/3 1 20 40/9 0/1 2 1 9/2 (0/1,1/5) 0 20 32/7 2/9 2 5 23/5 1/5 1 20 14/3 1/4 1 10 19/4 (4/17,1/4) 0 20 5/1 1/4 1 4 21/4 (2/9,1/4) 0 20 16/3 2/7 1 5 27/5 3/11 1 20 11/2 (0/1,1/3) 0 20 17/3 1/1 1 20 40/7 0/1 6 1 23/4 (0/1,1/7) 0 20 6/1 1/4 1 10 13/2 (2/7,1/3) 0 20 20/3 1/3 3 1 7/1 1/3 1 20 15/2 1/2 2 4 23/3 1/1 1 20 8/1 0/1 2 5 9/1 1/3 1 20 10/1 1/2 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(399,-440,146,-161) (1/1,9/8) -> (71/26,41/15) Hyperbolic Matrix(319,-360,70,-79) (9/8,8/7) -> (9/2,32/7) Glide Reflection Matrix(241,-280,68,-79) (8/7,7/6) -> (7/2,32/9) Hyperbolic 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(199,-240,34,-41) (6/5,17/14) -> (23/4,6/1) Hyperbolic Matrix(559,-680,328,-399) (17/14,11/9) -> (17/10,29/17) Glide Reflection 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,-760,412,-521) (24/19,19/15) -> (16/11,19/13) Glide Reflection Matrix(599,-760,346,-439) (19/15,14/11) -> (19/11,26/15) Glide Reflection Matrix(439,-560,156,-199) (14/11,23/18) -> (14/5,17/6) Glide Reflection Matrix(2001,-2560,562,-719) (23/18,32/25) -> (32/9,57/16) Hyperbolic Matrix(281,-360,32,-41) (32/25,9/7) -> (8/1,9/1) Glide Reflection Matrix(401,-520,246,-319) (9/7,13/10) -> (13/8,31/19) Hyperbolic Matrix(521,-680,154,-201) (13/10,17/13) -> (27/8,17/5) Glide Reflection Matrix(121,-160,90,-119) (17/13,4/3) -> (4/3,23/17) Parabolic Matrix(561,-760,296,-401) (23/17,42/31) -> (17/9,2/1) Glide Reflection 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(361,-520,84,-121) (23/16,13/9) -> (17/4,13/3) Glide Reflection 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(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(1041,-1640,610,-961) (11/7,41/26) -> (29/17,41/24) Glide Reflection 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,-320,76,-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(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(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(919,-1560,400,-679) (39/23,17/10) -> (39/17,23/10) Glide Reflection Matrix(2481,-4240,890,-1521) (41/24,53/31) -> (39/14,53/19) Glide Reflection Matrix(959,-1640,514,-879) (53/31,12/7) -> (13/7,28/15) Glide Reflection Matrix(1001,-1720,536,-921) (12/7,55/32) -> (28/15,15/8) Glide Reflection 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(719,-1280,314,-559) (16/9,41/23) -> (16/7,39/17) Glide Reflection Matrix(919,-1640,246,-439) (41/23,25/14) -> (41/11,15/4) Glide Reflection Matrix(761,-1360,202,-361) (25/14,34/19) -> (15/4,34/9) Glide Reflection Matrix(959,-1720,402,-721) (34/19,9/5) -> (31/13,74/31) Hyperbolic 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(239,-440,44,-81) (11/6,13/7) -> (27/5,11/2) Hyperbolic Matrix(319,-600,42,-79) (15/8,17/9) -> (15/2,23/3) Glide Reflection Matrix(321,-680,76,-161) (2/1,17/8) -> (38/9,17/4) Glide Reflection Matrix(599,-1280,168,-359) (17/8,15/7) -> (57/16,25/7) Glide Reflection 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(239,-520,74,-161) (13/6,11/5) -> (29/9,13/4) Hyperbolic 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(3161,-7160,1324,-2999) (43/19,34/15) -> (74/31,117/49) Hyperbolic Matrix(1199,-2720,458,-1039) (34/15,25/11) -> (34/13,55/21) Glide Reflection Matrix(879,-2000,316,-719) (25/11,41/18) -> (25/9,39/14) Glide Reflection Matrix(719,-1640,210,-479) (41/18,16/7) -> (41/12,24/7) Glide Reflection Matrix(239,-560,102,-239) (7/3,40/17) -> (7/3,40/17) Reflection Matrix(1121,-2640,476,-1121) (40/17,33/14) -> (40/17,33/14) Reflection Matrix(321,-760,68,-161) (26/11,19/8) -> (14/3,19/4) Glide Reflection Matrix(319,-760,34,-81) (50/21,31/13) -> (9/1,10/1) Hyperbolic Matrix(15679,-37440,6566,-15679) (117/49,160/67) -> (117/49,160/67) 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(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(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(201,-640,38,-121) (19/6,16/5) -> (21/4,16/3) Glide Reflection Matrix(121,-400,36,-119) (13/4,10/3) -> (10/3,27/8) Parabolic Matrix(639,-2320,176,-639) (29/8,40/11) -> (29/8,40/11) Reflection Matrix(241,-880,66,-241) (40/11,11/3) -> (40/11,11/3) Reflection Matrix(7999,-29760,2150,-7999) (93/25,160/43) -> (93/25,160/43) 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(2241,-9440,532,-2241) (80/19,59/14) -> (80/19,59/14) Reflection Matrix(559,-2480,126,-559) (31/7,40/9) -> (31/7,40/9) Reflection Matrix(161,-720,36,-161) (40/9,9/2) -> (40/9,9/2) Reflection 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(321,-1840,56,-321) (40/7,23/4) -> (40/7,23/4) 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(1,0,2,-1) -> Matrix(1,0,38,-1) (0/1,1/1) -> (0/1,1/19) Matrix(399,-440,146,-161) -> Matrix(69,-4,466,-27) Matrix(319,-360,70,-79) -> Matrix(67,-4,318,-19) Matrix(241,-280,68,-79) -> Matrix(65,-4,374,-23) Matrix(239,-280,204,-239) -> Matrix(129,-8,2080,-129) (7/6,20/17) -> (4/65,1/16) Matrix(441,-520,374,-441) -> Matrix(223,-14,3552,-223) (20/17,13/11) -> (1/16,7/111) Matrix(439,-520,168,-199) -> Matrix(95,-6,744,-47) Matrix(199,-240,34,-41) -> Matrix(31,-2,140,-9) Matrix(559,-680,328,-399) -> Matrix(61,-4,686,-45) Matrix(521,-640,162,-199) -> Matrix(31,-2,202,-13) Matrix(161,-200,128,-159) -> Matrix(61,-4,900,-59) 1/15 Matrix(601,-760,412,-521) -> Matrix(29,-2,362,-25) Matrix(599,-760,346,-439) -> Matrix(29,-2,304,-21) Matrix(439,-560,156,-199) -> Matrix(31,-2,232,-15) Matrix(2001,-2560,562,-719) -> Matrix(59,-4,310,-21) Matrix(281,-360,32,-41) -> Matrix(29,-2,72,-5) Matrix(401,-520,246,-319) -> Matrix(1,0,-2,1) 0/1 Matrix(521,-680,154,-201) -> Matrix(27,-2,148,-11) Matrix(121,-160,90,-119) -> Matrix(29,-2,392,-27) 1/14 Matrix(561,-760,296,-401) -> Matrix(1,0,24,-1) *** -> (0/1,1/12) Matrix(2361,-3200,560,-759) -> Matrix(27,-2,122,-9) Matrix(1001,-1360,382,-519) -> Matrix(29,-2,218,-15) Matrix(321,-440,116,-159) -> Matrix(1,0,-6,1) 0/1 Matrix(521,-720,144,-199) -> Matrix(29,-2,160,-11) Matrix(721,-1000,230,-319) -> Matrix(55,-4,344,-25) Matrix(2479,-3440,1442,-2001) -> Matrix(1,0,-2,1) 0/1 Matrix(201,-280,28,-39) -> Matrix(27,-2,68,-5) Matrix(199,-280,86,-121) -> Matrix(27,-2,230,-17) Matrix(281,-400,196,-279) -> Matrix(27,-2,338,-25) 1/13 Matrix(361,-520,84,-121) -> Matrix(25,-2,112,-9) Matrix(441,-640,82,-119) -> Matrix(25,-2,88,-7) Matrix(681,-1000,190,-279) -> Matrix(25,-2,138,-11) Matrix(79,-120,52,-79) -> Matrix(1,0,26,-1) (3/2,20/13) -> (0/1,1/13) Matrix(441,-680,286,-441) -> Matrix(25,-2,312,-25) (20/13,17/11) -> (1/13,1/12) Matrix(361,-560,78,-121) -> Matrix(25,-2,112,-9) Matrix(281,-440,76,-119) -> Matrix(25,-2,138,-11) Matrix(1041,-1640,610,-961) -> Matrix(1,0,24,-1) *** -> (0/1,1/12) Matrix(279,-440,26,-41) -> Matrix(25,-2,38,-3) Matrix(961,-1520,404,-639) -> Matrix(1,0,-4,1) 0/1 Matrix(201,-320,76,-121) -> Matrix(23,-2,172,-15) Matrix(199,-320,74,-119) -> Matrix(27,-2,202,-15) Matrix(841,-1360,222,-359) -> Matrix(25,-2,138,-11) Matrix(321,-520,50,-81) -> Matrix(1,0,16,-1) *** -> (0/1,1/8) Matrix(759,-1240,172,-281) -> Matrix(25,-2,88,-7) Matrix(121,-200,72,-119) -> Matrix(25,-2,288,-23) 1/12 Matrix(1039,-1760,330,-559) -> Matrix(49,-4,306,-25) Matrix(7199,-12200,4248,-7199) -> Matrix(193,-16,2328,-193) (61/36,100/59) -> (8/97,1/12) Matrix(4601,-7800,2714,-4601) -> Matrix(215,-18,2568,-215) (100/59,39/23) -> (1/12,9/107) Matrix(919,-1560,400,-679) -> Matrix(23,-2,172,-15) Matrix(2481,-4240,890,-1521) -> Matrix(47,-4,364,-31) Matrix(959,-1640,514,-879) -> Matrix(91,-8,944,-83) Matrix(1001,-1720,536,-921) -> Matrix(25,-2,262,-21) Matrix(999,-1720,442,-761) -> Matrix(67,-6,592,-53) Matrix(881,-1520,324,-559) -> Matrix(43,-4,312,-29) Matrix(599,-1040,254,-441) -> Matrix(19,-2,162,-17) 1/9 Matrix(159,-280,46,-81) -> Matrix(1,0,-6,1) 0/1 Matrix(719,-1280,314,-559) -> Matrix(91,-8,762,-67) Matrix(919,-1640,246,-439) -> Matrix(67,-6,346,-31) Matrix(761,-1360,202,-361) -> Matrix(23,-2,126,-11) Matrix(959,-1720,402,-721) -> Matrix(45,-4,394,-35) Matrix(199,-360,110,-199) -> Matrix(67,-6,748,-67) (9/5,20/11) -> (3/34,1/11) Matrix(241,-440,132,-241) -> Matrix(87,-8,946,-87) (20/11,11/6) -> (1/11,4/43) Matrix(239,-440,44,-81) -> Matrix(43,-4,140,-13) Matrix(319,-600,42,-79) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(321,-680,76,-161) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(599,-1280,168,-359) -> Matrix(19,-2,104,-11) Matrix(801,-1720,224,-481) -> Matrix(39,-4,224,-23) Matrix(761,-1640,316,-681) -> Matrix(19,-2,142,-15) Matrix(239,-520,74,-161) -> Matrix(37,-4,250,-27) Matrix(199,-440,90,-199) -> Matrix(91,-10,828,-91) (11/5,20/9) -> (5/46,1/9) Matrix(161,-360,72,-161) -> Matrix(71,-8,630,-71) (20/9,9/4) -> (1/9,4/35) Matrix(3161,-7160,1324,-2999) -> Matrix(157,-18,1352,-155) 3/26 Matrix(1199,-2720,458,-1039) -> Matrix(69,-8,526,-61) Matrix(879,-2000,316,-719) -> Matrix(69,-8,526,-61) Matrix(719,-1640,210,-479) -> Matrix(69,-8,388,-45) Matrix(239,-560,102,-239) -> Matrix(35,-4,306,-35) (7/3,40/17) -> (1/9,2/17) Matrix(1121,-2640,476,-1121) -> Matrix(169,-20,1428,-169) (40/17,33/14) -> (2/17,5/42) Matrix(321,-760,68,-161) -> Matrix(33,-4,140,-17) Matrix(319,-760,34,-81) -> Matrix(1,0,-6,1) 0/1 Matrix(15679,-37440,6566,-15679) -> Matrix(307,-36,2618,-307) (117/49,160/67) -> (9/77,2/17) Matrix(5761,-13760,2412,-5761) -> Matrix(101,-12,850,-101) (160/67,43/18) -> (2/17,3/25) Matrix(1439,-3440,402,-961) -> Matrix(33,-4,190,-23) Matrix(2041,-4920,548,-1321) -> Matrix(23,-2,126,-11) Matrix(679,-1640,248,-599) -> Matrix(17,-2,110,-13) Matrix(281,-680,50,-121) -> Matrix(17,-2,42,-5) Matrix(81,-200,32,-79) -> Matrix(33,-4,256,-31) 1/8 Matrix(641,-1640,188,-481) -> Matrix(31,-4,178,-23) Matrix(3199,-8200,1248,-3199) -> Matrix(29,-4,210,-29) (41/16,100/39) -> (2/15,1/7) Matrix(4601,-11800,1794,-4601) -> Matrix(15,-2,112,-15) (100/39,59/23) -> (1/8,1/7) Matrix(841,-2160,234,-601) -> Matrix(15,-2,82,-11) Matrix(201,-520,46,-119) -> Matrix(15,-2,68,-9) Matrix(1321,-3600,484,-1319) -> Matrix(99,-14,686,-97) 1/7 Matrix(959,-2680,258,-721) -> Matrix(59,-8,332,-45) Matrix(239,-680,84,-239) -> Matrix(85,-12,602,-85) (17/6,20/7) -> (6/43,1/7) Matrix(41,-120,14,-41) -> Matrix(13,-2,84,-13) (20/7,3/1) -> (1/7,1/6) Matrix(201,-640,38,-121) -> Matrix(11,-2,38,-7) Matrix(121,-400,36,-119) -> Matrix(37,-6,216,-35) 1/6 Matrix(639,-2320,176,-639) -> Matrix(67,-12,374,-67) (29/8,40/11) -> (3/17,2/11) Matrix(241,-880,66,-241) -> Matrix(21,-4,110,-21) (40/11,11/3) -> (2/11,1/5) Matrix(7999,-29760,2150,-7999) -> Matrix(331,-60,1826,-331) (93/25,160/43) -> (15/83,2/11) Matrix(5761,-21440,1548,-5761) -> Matrix(285,-52,1562,-285) (160/43,67/18) -> (2/11,13/71) Matrix(41,-160,10,-39) -> Matrix(11,-2,50,-9) 1/5 Matrix(799,-3360,190,-799) -> Matrix(19,-4,90,-19) (21/5,80/19) -> (1/5,2/9) Matrix(2241,-9440,532,-2241) -> Matrix(17,-4,72,-17) (80/19,59/14) -> (2/9,1/4) Matrix(559,-2480,126,-559) -> Matrix(1,0,6,-1) (31/7,40/9) -> (0/1,1/3) Matrix(161,-720,36,-161) -> Matrix(1,0,10,-1) (40/9,9/2) -> (0/1,1/5) Matrix(201,-920,26,-119) -> Matrix(9,-2,14,-3) Matrix(41,-200,8,-39) -> Matrix(9,-2,32,-7) 1/4 Matrix(239,-1360,42,-239) -> Matrix(1,0,2,-1) (17/3,40/7) -> (0/1,1/1) Matrix(321,-1840,56,-321) -> Matrix(1,0,14,-1) (40/7,23/4) -> (0/1,1/7) Matrix(79,-520,12,-79) -> Matrix(13,-4,42,-13) (13/2,20/3) -> (2/7,1/3) Matrix(41,-280,6,-41) -> Matrix(5,-2,12,-5) (20/3,7/1) -> (1/3,1/2) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.