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): 720 Minimal number of generators: 121 Number of equivalence classes of cusps: 50 Genus: 36 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/11 -7/11 -1/2 -5/11 -21/55 -7/22 -10/33 -3/10 -3/11 -5/19 -23/88 -1/4 -1/6 -3/22 -1/8 0/1 1/8 1/7 1/6 3/17 2/11 1/5 2/9 5/22 3/13 1/4 3/11 2/7 3/10 1/3 4/11 2/5 9/22 5/11 7/15 1/2 6/11 5/9 13/22 13/21 7/11 2/3 15/22 23/33 8/11 17/22 9/11 19/22 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/0 -8/9 -1/1 0/1 -7/8 0/1 -6/7 0/1 1/1 -11/13 -1/1 1/0 -5/6 0/1 -9/11 1/0 -13/16 -2/1 -4/5 -1/1 0/1 -11/14 -2/1 -18/23 -1/1 0/1 -25/32 0/1 -7/9 -1/2 0/1 -17/22 0/1 -10/13 0/1 1/3 -13/17 0/1 1/2 -16/21 4/5 1/1 -3/4 0/1 -14/19 1/1 2/1 -11/15 2/1 1/0 -8/11 1/0 -5/7 -1/1 1/0 -7/10 0/1 -9/13 -1/1 -1/2 -11/16 0/1 -2/3 0/1 1/1 -7/11 1/0 -12/19 -4/1 -3/1 -17/27 -2/1 1/0 -22/35 -2/1 -1/1 -5/8 -2/1 -18/29 -1/1 -4/5 -13/21 -1/1 -1/2 -8/13 -2/1 -1/1 -3/5 -1/2 0/1 -13/22 0/1 -10/17 0/1 1/7 -27/46 2/9 -17/29 0/1 1/4 -24/41 0/1 1/3 -7/12 0/1 -25/43 0/1 1/2 -18/31 0/1 1/3 -11/19 0/1 1/4 -4/7 2/3 1/1 -13/23 1/1 1/0 -9/16 2/1 -14/25 1/1 2/1 -19/34 2/1 -5/9 2/1 1/0 -6/11 1/0 -7/13 -3/1 1/0 -1/2 0/1 -5/11 1/0 -9/20 -6/1 -13/29 -4/1 1/0 -4/9 -3/1 -2/1 -11/25 -5/2 -2/1 -29/66 -2/1 -18/41 -2/1 -9/5 -7/16 -2/1 -3/7 -1/1 -1/2 -5/12 0/1 -7/17 -1/4 0/1 -9/22 0/1 -2/5 0/1 1/1 -11/28 2/3 -9/23 3/4 1/1 -16/41 1/1 2/1 -7/18 0/1 -5/13 1/1 3/2 -13/34 2/1 -21/55 1/0 -29/76 0/1 -8/21 0/1 1/1 -19/50 2/1 -11/29 3/2 2/1 -25/66 2/1 -14/37 2/1 3/1 -3/8 2/1 -10/27 3/1 4/1 -17/46 14/3 -7/19 6/1 1/0 -4/11 1/0 -1/3 -1/1 1/0 -7/22 -1/1 -6/19 -1/1 0/1 -5/16 0/1 -9/29 0/1 1/0 -4/13 -2/1 -1/1 -7/23 -1/1 -1/2 -10/33 -1/2 -13/43 -1/2 0/1 -3/10 0/1 -5/17 0/1 1/2 -12/41 2/3 1/1 -19/65 7/8 1/1 -7/24 2/1 -9/31 -1/1 1/0 -2/7 0/1 1/1 -3/11 1/0 -4/15 -6/1 -5/1 -5/19 -4/1 -7/2 -11/42 -16/5 -17/65 -43/14 -3/1 -23/88 -3/1 -6/23 -3/1 -14/5 -1/4 -2/1 -3/13 -5/4 -1/1 -5/22 -1/1 -2/9 -1/1 -2/3 -1/5 0/1 1/0 -2/11 1/0 -3/17 -4/1 1/0 -4/23 -3/1 -8/3 -1/6 -2/1 -1/7 -5/4 -1/1 -3/22 -1/1 -2/15 -1/1 -8/9 -1/8 -2/3 0/1 -1/1 0/1 1/8 -2/1 1/7 -1/1 -5/6 1/6 -2/3 4/23 -8/13 -3/5 3/17 -4/7 -1/2 2/11 -1/2 1/5 -1/2 0/1 2/9 -2/1 -1/1 5/22 -1/1 3/13 -1/1 -5/6 1/4 -2/3 3/11 -1/2 5/18 -4/9 2/7 -1/3 0/1 7/24 -2/5 5/17 -1/4 0/1 3/10 0/1 4/13 -1/1 -2/3 9/29 -1/2 0/1 5/16 0/1 1/3 -1/1 -1/2 4/11 -1/2 7/19 -1/2 -6/13 3/8 -2/5 11/29 -2/5 -3/8 19/50 -2/5 8/21 -1/3 0/1 5/13 -3/8 -1/3 7/18 0/1 9/23 -1/3 -3/10 2/5 -1/3 0/1 9/22 0/1 7/17 0/1 1/2 5/12 0/1 3/7 -1/1 1/0 7/16 -2/3 11/25 -2/3 -5/8 4/9 -2/3 -3/5 5/11 -1/2 6/13 -4/9 -3/7 7/15 -1/2 -2/5 1/2 0/1 7/13 -3/5 -1/2 6/11 -1/2 5/9 -1/2 -2/5 19/34 -2/5 14/25 -2/5 -1/3 37/66 -1/3 23/41 -1/2 -1/3 9/16 -2/5 13/23 -1/2 -1/3 4/7 -1/3 -2/7 15/26 -2/9 26/45 -6/29 -1/5 11/19 -1/6 0/1 18/31 -1/5 0/1 25/43 -1/4 0/1 7/12 0/1 17/29 -1/6 0/1 27/46 -2/13 10/17 -1/9 0/1 13/22 0/1 3/5 0/1 1/0 8/13 -1/1 -2/3 21/34 0/1 55/89 0/1 1/0 34/55 1/0 13/21 -1/1 1/0 18/29 -4/3 -1/1 41/66 -1/1 23/37 -1/1 -9/10 5/8 -2/3 7/11 -1/2 9/14 -2/5 11/17 -1/2 -2/5 13/20 -4/11 2/3 -1/3 0/1 15/22 0/1 13/19 0/1 1/4 11/16 0/1 9/13 -1/1 1/0 16/23 -1/1 -2/3 23/33 -1/2 7/10 0/1 5/7 -1/1 -1/2 8/11 -1/2 11/15 -1/2 -2/5 25/34 -2/5 14/19 -2/5 -1/3 31/42 -6/17 17/23 -1/3 -3/10 3/4 0/1 16/21 -1/3 -4/13 13/17 -1/4 0/1 23/30 0/1 10/13 -1/5 0/1 17/22 0/1 7/9 0/1 1/0 25/32 0/1 43/55 1/0 18/23 -1/1 0/1 11/14 -2/3 15/19 -1/2 -2/5 34/43 -8/23 -1/3 87/110 -1/3 53/67 -1/3 -11/34 19/24 -2/7 4/5 -1/1 0/1 9/11 -1/2 14/17 -2/5 -1/3 19/23 -1/3 -1/4 5/6 0/1 11/13 -1/1 -1/2 17/20 -2/5 6/7 -1/3 0/1 19/22 0/1 13/15 0/1 1/0 7/8 0/1 8/9 -1/1 0/1 1/1 -1/2 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(243,218,418,375) (-1/1,-8/9) -> (18/31,25/43) Hyperbolic Matrix(287,254,374,331) (-8/9,-7/8) -> (23/30,10/13) Hyperbolic Matrix(133,116,-352,-307) (-7/8,-6/7) -> (-14/37,-3/8) Hyperbolic Matrix(89,76,-308,-263) (-6/7,-11/13) -> (-9/31,-2/7) Hyperbolic Matrix(197,166,286,241) (-11/13,-5/6) -> (11/16,9/13) Hyperbolic Matrix(197,162,-242,-199) (-5/6,-9/11) -> (-9/11,-13/16) Parabolic Matrix(87,70,-220,-177) (-13/16,-4/5) -> (-2/5,-11/28) Hyperbolic Matrix(155,122,-418,-329) (-4/5,-11/14) -> (-3/8,-10/27) Hyperbolic Matrix(23,18,198,155) (-11/14,-18/23) -> (0/1,1/8) Hyperbolic Matrix(923,722,-2420,-1893) (-18/23,-25/32) -> (-29/76,-8/21) Hyperbolic Matrix(331,258,594,463) (-25/32,-7/9) -> (5/9,19/34) Hyperbolic Matrix(307,238,396,307) (-7/9,-17/22) -> (17/22,7/9) Hyperbolic Matrix(441,340,572,441) (-17/22,-10/13) -> (10/13,17/22) Hyperbolic Matrix(595,456,-946,-725) (-10/13,-13/17) -> (-17/27,-22/35) Hyperbolic Matrix(131,100,748,571) (-13/17,-16/21) -> (4/23,3/17) Hyperbolic Matrix(419,318,726,551) (-16/21,-3/4) -> (15/26,26/45) Hyperbolic Matrix(197,146,-506,-375) (-3/4,-14/19) -> (-16/41,-7/18) Hyperbolic Matrix(683,502,-1166,-857) (-14/19,-11/15) -> (-17/29,-24/41) Hyperbolic Matrix(241,176,330,241) (-11/15,-8/11) -> (8/11,11/15) Hyperbolic Matrix(111,80,154,111) (-8/11,-5/7) -> (5/7,8/11) Hyperbolic Matrix(65,46,154,109) (-5/7,-7/10) -> (5/12,3/7) Hyperbolic Matrix(219,152,-572,-397) (-7/10,-9/13) -> (-5/13,-13/34) Hyperbolic Matrix(241,166,286,197) (-9/13,-11/16) -> (5/6,11/13) Hyperbolic Matrix(309,212,-704,-483) (-11/16,-2/3) -> (-18/41,-7/16) Hyperbolic Matrix(153,98,-242,-155) (-2/3,-7/11) -> (-7/11,-12/19) Parabolic Matrix(419,264,-1430,-901) (-12/19,-17/27) -> (-5/17,-12/41) Hyperbolic Matrix(309,194,352,221) (-22/35,-5/8) -> (7/8,8/9) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) Hyperbolic Matrix(461,286,814,505) (-18/29,-13/21) -> (13/23,4/7) Hyperbolic Matrix(175,108,-572,-353) (-13/21,-8/13) -> (-4/13,-7/23) Hyperbolic Matrix(23,14,110,67) (-8/13,-3/5) -> (1/5,2/9) Hyperbolic Matrix(131,78,220,131) (-3/5,-13/22) -> (13/22,3/5) Hyperbolic Matrix(441,260,748,441) (-13/22,-10/17) -> (10/17,13/22) Hyperbolic Matrix(507,298,638,375) (-10/17,-27/46) -> (19/24,4/5) Hyperbolic Matrix(351,206,748,439) (-27/46,-17/29) -> (7/15,1/2) Hyperbolic Matrix(947,554,1694,991) (-24/41,-7/12) -> (19/34,14/25) Hyperbolic Matrix(285,166,-946,-551) (-7/12,-25/43) -> (-13/43,-3/10) Hyperbolic Matrix(375,218,418,243) (-25/43,-18/31) -> (8/9,1/1) Hyperbolic Matrix(417,242,946,549) (-18/31,-11/19) -> (11/25,4/9) Hyperbolic Matrix(111,64,-418,-241) (-11/19,-4/7) -> (-4/15,-5/19) Hyperbolic Matrix(505,286,814,461) (-4/7,-13/23) -> (13/21,18/29) Hyperbolic Matrix(397,224,-1012,-571) (-13/23,-9/16) -> (-11/28,-9/23) Hyperbolic Matrix(221,124,-704,-395) (-9/16,-14/25) -> (-6/19,-5/16) Hyperbolic Matrix(1101,616,1496,837) (-14/25,-19/34) -> (25/34,14/19) Hyperbolic Matrix(463,258,594,331) (-19/34,-5/9) -> (7/9,25/32) Hyperbolic Matrix(109,60,198,109) (-5/9,-6/11) -> (6/11,5/9) Hyperbolic Matrix(155,84,286,155) (-6/11,-7/13) -> (7/13,6/11) Hyperbolic Matrix(109,58,-374,-199) (-7/13,-1/2) -> (-7/24,-9/31) Hyperbolic Matrix(109,50,-242,-111) (-1/2,-5/11) -> (-5/11,-9/20) Parabolic Matrix(1123,504,1914,859) (-9/20,-13/29) -> (17/29,27/46) Hyperbolic Matrix(197,88,638,285) (-13/29,-4/9) -> (4/13,9/29) Hyperbolic Matrix(549,242,946,417) (-4/9,-11/25) -> (11/19,18/31) Hyperbolic Matrix(1233,542,1804,793) (-11/25,-29/66) -> (15/22,13/19) Hyperbolic Matrix(747,328,1100,483) (-29/66,-18/41) -> (2/3,15/22) Hyperbolic Matrix(23,10,154,67) (-7/16,-3/7) -> (1/7,1/6) Hyperbolic Matrix(109,46,154,65) (-3/7,-5/12) -> (7/10,5/7) Hyperbolic Matrix(111,46,374,155) (-5/12,-7/17) -> (5/17,3/10) Hyperbolic Matrix(307,126,748,307) (-7/17,-9/22) -> (9/22,7/17) Hyperbolic Matrix(89,36,220,89) (-9/22,-2/5) -> (2/5,9/22) Hyperbolic Matrix(1055,412,-3608,-1409) (-9/23,-16/41) -> (-12/41,-19/65) Hyperbolic Matrix(67,26,286,111) (-7/18,-5/13) -> (3/13,1/4) Hyperbolic Matrix(2309,882,-6050,-2311) (-13/34,-21/55) -> (-21/55,-29/76) Parabolic Matrix(221,84,1276,485) (-8/21,-19/50) -> (1/6,4/23) Hyperbolic Matrix(595,226,1914,727) (-19/50,-11/29) -> (9/29,5/16) Hyperbolic Matrix(1409,534,1628,617) (-11/29,-25/66) -> (19/22,13/15) Hyperbolic Matrix(1099,416,1276,483) (-25/66,-14/37) -> (6/7,19/22) Hyperbolic Matrix(1189,440,2024,749) (-10/27,-17/46) -> (27/46,10/17) Hyperbolic Matrix(439,162,-1672,-617) (-17/46,-7/19) -> (-5/19,-11/42) Hyperbolic Matrix(153,56,418,153) (-7/19,-4/11) -> (4/11,7/19) Hyperbolic Matrix(23,8,66,23) (-4/11,-1/3) -> (1/3,4/11) Hyperbolic Matrix(617,198,1100,353) (-1/3,-7/22) -> (37/66,23/41) Hyperbolic Matrix(1011,320,1804,571) (-7/22,-6/19) -> (14/25,37/66) Hyperbolic Matrix(727,226,1914,595) (-5/16,-9/29) -> (11/29,19/50) Hyperbolic Matrix(265,82,572,177) (-9/29,-4/13) -> (6/13,7/15) Hyperbolic Matrix(1211,368,1958,595) (-7/23,-10/33) -> (34/55,13/21) Hyperbolic Matrix(3277,992,5302,1605) (-10/33,-13/43) -> (55/89,34/55) Hyperbolic Matrix(155,46,374,111) (-3/10,-5/17) -> (7/17,5/12) Hyperbolic Matrix(1123,328,-4290,-1253) (-19/65,-7/24) -> (-11/42,-17/65) Hyperbolic Matrix(65,18,-242,-67) (-2/7,-3/11) -> (-3/11,-4/15) Parabolic Matrix(10319,2698,13046,3411) (-17/65,-23/88) -> (87/110,53/67) Hyperbolic Matrix(4993,1304,6314,1649) (-23/88,-6/23) -> (34/43,87/110) Hyperbolic Matrix(133,34,176,45) (-6/23,-1/4) -> (3/4,16/21) Hyperbolic Matrix(111,26,286,67) (-1/4,-3/13) -> (5/13,7/18) Hyperbolic Matrix(131,30,572,131) (-3/13,-5/22) -> (5/22,3/13) Hyperbolic Matrix(89,20,396,89) (-5/22,-2/9) -> (2/9,5/22) Hyperbolic Matrix(67,14,110,23) (-2/9,-1/5) -> (3/5,8/13) Hyperbolic Matrix(21,4,110,21) (-1/5,-2/11) -> (2/11,1/5) Hyperbolic Matrix(67,12,374,67) (-2/11,-3/17) -> (3/17,2/11) Hyperbolic Matrix(571,100,748,131) (-3/17,-4/23) -> (16/21,13/17) Hyperbolic Matrix(485,84,1276,221) (-4/23,-1/6) -> (19/50,8/21) Hyperbolic Matrix(67,10,154,23) (-1/6,-1/7) -> (3/7,7/16) Hyperbolic Matrix(793,110,1276,177) (-1/7,-3/22) -> (41/66,23/37) Hyperbolic Matrix(1011,136,1628,219) (-3/22,-2/15) -> (18/29,41/66) Hyperbolic Matrix(155,18,198,23) (-1/8,0/1) -> (18/23,11/14) Hyperbolic Matrix(219,-28,352,-45) (1/8,1/7) -> (23/37,5/8) Hyperbolic Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(177,-50,308,-87) (5/18,2/7) -> (4/7,15/26) Hyperbolic Matrix(263,-76,308,-89) (2/7,7/24) -> (17/20,6/7) Hyperbolic Matrix(485,-142,748,-219) (7/24,5/17) -> (11/17,13/20) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(395,-124,704,-221) (5/16,1/3) -> (23/41,9/16) Hyperbolic Matrix(329,-122,418,-155) (7/19,3/8) -> (11/14,15/19) Hyperbolic Matrix(307,-116,352,-133) (3/8,11/29) -> (13/15,7/8) Hyperbolic Matrix(397,-152,572,-219) (8/21,5/13) -> (9/13,16/23) Hyperbolic Matrix(375,-146,506,-197) (7/18,9/23) -> (17/23,3/4) Hyperbolic Matrix(417,-164,506,-199) (9/23,2/5) -> (14/17,19/23) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(243,-130,286,-153) (1/2,7/13) -> (11/13,17/20) Hyperbolic Matrix(419,-236,506,-285) (9/16,13/23) -> (19/23,5/6) Hyperbolic Matrix(1321,-764,1672,-967) (26/45,11/19) -> (15/19,34/43) Hyperbolic Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(857,-502,1166,-683) (7/12,17/29) -> (11/15,25/34) Hyperbolic Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(573,-370,748,-483) (9/14,11/17) -> (13/17,23/30) Hyperbolic Matrix(373,-244,506,-331) (13/20,2/3) -> (14/19,31/42) Hyperbolic Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(1255,-876,1606,-1121) (23/33,7/10) -> (25/32,43/55) Hyperbolic Matrix(2663,-1966,3366,-2485) (31/42,17/23) -> (53/67,19/24) Hyperbolic Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(243,218,418,375) -> Matrix(1,0,-4,1) Matrix(287,254,374,331) -> Matrix(1,0,-4,1) Matrix(133,116,-352,-307) -> Matrix(1,2,0,1) Matrix(89,76,-308,-263) -> Matrix(1,0,0,1) Matrix(197,166,286,241) -> Matrix(1,0,0,1) Matrix(197,162,-242,-199) -> Matrix(1,-2,0,1) Matrix(87,70,-220,-177) -> Matrix(1,0,2,1) Matrix(155,122,-418,-329) -> Matrix(1,4,0,1) Matrix(23,18,198,155) -> Matrix(1,0,0,1) Matrix(923,722,-2420,-1893) -> Matrix(1,0,2,1) Matrix(331,258,594,463) -> Matrix(3,2,-8,-5) Matrix(307,238,396,307) -> Matrix(1,0,2,1) Matrix(441,340,572,441) -> Matrix(1,0,-8,1) Matrix(595,456,-946,-725) -> Matrix(5,-2,-2,1) Matrix(131,100,748,571) -> Matrix(7,-4,-12,7) Matrix(419,318,726,551) -> Matrix(1,-2,-4,9) Matrix(197,146,-506,-375) -> Matrix(1,0,0,1) Matrix(683,502,-1166,-857) -> Matrix(1,-2,4,-7) Matrix(241,176,330,241) -> Matrix(1,-4,-2,9) Matrix(111,80,154,111) -> Matrix(1,2,-2,-3) Matrix(65,46,154,109) -> Matrix(1,0,0,1) Matrix(219,152,-572,-397) -> Matrix(1,2,0,1) Matrix(241,166,286,197) -> Matrix(1,0,0,1) Matrix(309,212,-704,-483) -> Matrix(7,2,-4,-1) Matrix(153,98,-242,-155) -> Matrix(1,-4,0,1) Matrix(419,264,-1430,-901) -> Matrix(1,2,2,5) Matrix(309,194,352,221) -> Matrix(1,2,-2,-3) Matrix(45,28,-352,-219) -> Matrix(3,4,-4,-5) Matrix(461,286,814,505) -> Matrix(3,2,-8,-5) Matrix(175,108,-572,-353) -> Matrix(1,0,0,1) Matrix(23,14,110,67) -> Matrix(1,0,0,1) Matrix(131,78,220,131) -> Matrix(1,0,2,1) Matrix(441,260,748,441) -> Matrix(1,0,-16,1) Matrix(507,298,638,375) -> Matrix(1,0,-8,1) Matrix(351,206,748,439) -> Matrix(9,-2,-22,5) Matrix(947,554,1694,991) -> Matrix(5,-2,-12,5) Matrix(285,166,-946,-551) -> Matrix(1,0,-4,1) Matrix(375,218,418,243) -> Matrix(1,0,-4,1) Matrix(417,242,946,549) -> Matrix(3,-2,-4,3) Matrix(111,64,-418,-241) -> Matrix(9,-4,-2,1) Matrix(505,286,814,461) -> Matrix(1,-2,0,1) Matrix(397,224,-1012,-571) -> Matrix(3,-4,4,-5) Matrix(221,124,-704,-395) -> Matrix(1,-2,0,1) Matrix(1101,616,1496,837) -> Matrix(3,-4,-8,11) Matrix(463,258,594,331) -> Matrix(1,-2,0,1) Matrix(109,60,198,109) -> Matrix(1,-4,-2,9) Matrix(155,84,286,155) -> Matrix(1,6,-2,-11) Matrix(109,58,-374,-199) -> Matrix(1,2,0,1) Matrix(109,50,-242,-111) -> Matrix(1,-6,0,1) Matrix(1123,504,1914,859) -> Matrix(1,4,-6,-23) Matrix(197,88,638,285) -> Matrix(1,4,-2,-7) Matrix(549,242,946,417) -> Matrix(1,2,-4,-7) Matrix(1233,542,1804,793) -> Matrix(1,2,6,13) Matrix(747,328,1100,483) -> Matrix(1,2,-8,-15) Matrix(23,10,154,67) -> Matrix(3,4,-4,-5) Matrix(109,46,154,65) -> Matrix(1,0,0,1) Matrix(111,46,374,155) -> Matrix(1,0,0,1) Matrix(307,126,748,307) -> Matrix(1,0,6,1) Matrix(89,36,220,89) -> Matrix(1,0,-4,1) Matrix(1055,412,-3608,-1409) -> Matrix(3,-4,4,-5) Matrix(67,26,286,111) -> Matrix(3,-2,-4,3) Matrix(2309,882,-6050,-2311) -> Matrix(1,-2,0,1) Matrix(221,84,1276,485) -> Matrix(5,-8,-8,13) Matrix(595,226,1914,727) -> Matrix(1,-2,0,1) Matrix(1409,534,1628,617) -> Matrix(1,-2,2,-3) Matrix(1099,416,1276,483) -> Matrix(1,-2,-4,9) Matrix(1189,440,2024,749) -> Matrix(1,-4,-8,33) Matrix(439,162,-1672,-617) -> Matrix(7,-38,-2,11) Matrix(153,56,418,153) -> Matrix(1,-12,-2,25) Matrix(23,8,66,23) -> Matrix(1,2,-2,-3) Matrix(617,198,1100,353) -> Matrix(1,0,-2,1) Matrix(1011,320,1804,571) -> Matrix(3,2,-8,-5) Matrix(727,226,1914,595) -> Matrix(3,2,-8,-5) Matrix(265,82,572,177) -> Matrix(1,-2,-2,5) Matrix(1211,368,1958,595) -> Matrix(3,2,-2,-1) Matrix(3277,992,5302,1605) -> Matrix(1,0,2,1) Matrix(155,46,374,111) -> Matrix(1,0,0,1) Matrix(1123,328,-4290,-1253) -> Matrix(19,-22,-6,7) Matrix(65,18,-242,-67) -> Matrix(1,-6,0,1) Matrix(10319,2698,13046,3411) -> Matrix(25,76,-76,-231) Matrix(4993,1304,6314,1649) -> Matrix(13,38,-38,-111) Matrix(133,34,176,45) -> Matrix(1,2,-2,-3) Matrix(111,26,286,67) -> Matrix(1,2,-4,-7) Matrix(131,30,572,131) -> Matrix(9,10,-10,-11) Matrix(89,20,396,89) -> Matrix(5,4,-4,-3) Matrix(67,14,110,23) -> Matrix(1,0,0,1) Matrix(21,4,110,21) -> Matrix(1,0,-2,1) Matrix(67,12,374,67) -> Matrix(1,8,-2,-15) Matrix(571,100,748,131) -> Matrix(1,4,-4,-15) Matrix(485,84,1276,221) -> Matrix(3,8,-8,-21) Matrix(67,10,154,23) -> Matrix(3,4,-4,-5) Matrix(793,110,1276,177) -> Matrix(13,14,-14,-15) Matrix(1011,136,1628,219) -> Matrix(13,12,-12,-11) Matrix(155,18,198,23) -> Matrix(1,0,0,1) Matrix(219,-28,352,-45) -> Matrix(3,4,-4,-5) Matrix(67,-18,242,-65) -> Matrix(11,6,-24,-13) Matrix(177,-50,308,-87) -> Matrix(5,2,-18,-7) Matrix(263,-76,308,-89) -> Matrix(1,0,0,1) Matrix(485,-142,748,-219) -> Matrix(7,2,-18,-5) Matrix(353,-108,572,-175) -> Matrix(1,0,0,1) Matrix(395,-124,704,-221) -> Matrix(3,2,-8,-5) Matrix(329,-122,418,-155) -> Matrix(9,4,-16,-7) Matrix(307,-116,352,-133) -> Matrix(5,2,-8,-3) Matrix(397,-152,572,-219) -> Matrix(5,2,-8,-3) Matrix(375,-146,506,-197) -> Matrix(1,0,0,1) Matrix(417,-164,506,-199) -> Matrix(7,2,-18,-5) Matrix(483,-212,704,-309) -> Matrix(3,2,4,3) Matrix(111,-50,242,-109) -> Matrix(11,6,-24,-13) Matrix(243,-130,286,-153) -> Matrix(3,2,-8,-5) Matrix(419,-236,506,-285) -> Matrix(5,2,-18,-7) Matrix(1321,-764,1672,-967) -> Matrix(11,2,-28,-5) Matrix(1563,-910,2530,-1473) -> Matrix(1,0,4,1) Matrix(857,-502,1166,-683) -> Matrix(11,2,-28,-5) Matrix(155,-98,242,-153) -> Matrix(7,4,-16,-9) Matrix(573,-370,748,-483) -> Matrix(5,2,-18,-7) Matrix(373,-244,506,-331) -> Matrix(7,2,-18,-5) Matrix(1583,-1102,2024,-1409) -> Matrix(3,2,-2,-1) Matrix(1255,-876,1606,-1121) -> Matrix(1,0,2,1) Matrix(2663,-1966,3366,-2485) -> Matrix(23,8,-72,-25) Matrix(199,-162,242,-197) -> Matrix(3,2,-8,-5) 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): 40 Degree of the the map X: 40 Degree of the the map Y: 120 ----------------------------------------------------------------------- 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 (-1/1,0/1) 0 22 1/8 -2/1 1 11 1/7 (-1/1,-5/6) 0 22 1/6 -2/3 1 11 4/23 (-8/13,-3/5) 0 22 3/17 (-4/7,-1/2) 0 22 2/11 -1/2 4 2 1/5 (-1/2,0/1) 0 22 2/9 (-2/1,-1/1) 0 22 5/22 -1/1 7 1 3/13 (-1/1,-5/6) 0 22 1/4 -2/3 1 11 3/11 -1/2 6 2 5/18 -4/9 1 11 2/7 (-1/3,0/1) 0 22 7/24 -2/5 1 11 5/17 (-1/4,0/1) 0 22 3/10 0/1 1 11 4/13 (-1/1,-2/3) 0 22 9/29 (-1/2,0/1) 0 22 5/16 0/1 1 11 1/3 (-1/1,-1/2) 0 22 4/11 -1/2 7 2 7/19 (-1/2,-6/13) 0 22 3/8 -2/5 1 11 11/29 (-2/5,-3/8) 0 22 19/50 -2/5 1 11 8/21 (-1/3,0/1) 0 22 5/13 (-3/8,-1/3) 0 22 7/18 0/1 1 11 9/23 (-1/3,-3/10) 0 22 2/5 (-1/3,0/1) 0 22 9/22 0/1 5 1 7/17 (0/1,1/2) 0 22 5/12 0/1 1 11 3/7 (-1/1,1/0) 0 22 7/16 -2/3 1 11 11/25 (-2/3,-5/8) 0 22 4/9 (-2/3,-3/5) 0 22 5/11 -1/2 6 2 6/13 (-4/9,-3/7) 0 22 7/15 (-1/2,-2/5) 0 22 1/2 0/1 1 11 7/13 (-3/5,-1/2) 0 22 6/11 -1/2 5 2 5/9 (-1/2,-2/5) 0 22 19/34 -2/5 1 11 14/25 (-2/5,-1/3) 0 22 37/66 -1/3 1 1 23/41 (-1/2,-1/3) 0 22 9/16 -2/5 1 11 13/23 (-1/2,-1/3) 0 22 4/7 (-1/3,-2/7) 0 22 15/26 -2/9 1 11 26/45 (-6/29,-1/5) 0 22 11/19 (-1/6,0/1) 0 22 18/31 (-1/5,0/1) 0 22 25/43 (-1/4,0/1) 0 22 7/12 0/1 1 11 17/29 (-1/6,0/1) 0 22 27/46 -2/13 1 11 10/17 (-1/9,0/1) 0 22 13/22 0/1 9 1 3/5 (0/1,1/0) 0 22 8/13 (-1/1,-2/3) 0 22 21/34 0/1 1 11 55/89 (0/1,1/0) 0 22 34/55 1/0 1 2 13/21 (-1/1,1/0) 0 22 18/29 (-4/3,-1/1) 0 22 41/66 -1/1 13 1 23/37 (-1/1,-9/10) 0 22 5/8 -2/3 1 11 7/11 -1/2 4 2 9/14 -2/5 1 11 11/17 (-1/2,-2/5) 0 22 13/20 -4/11 1 11 2/3 (-1/3,0/1) 0 22 15/22 0/1 7 1 13/19 (0/1,1/4) 0 22 11/16 0/1 1 11 9/13 (-1/1,1/0) 0 22 16/23 (-1/1,-2/3) 0 22 23/33 -1/2 2 2 7/10 0/1 1 11 5/7 (-1/1,-1/2) 0 22 8/11 -1/2 3 2 11/15 (-1/2,-2/5) 0 22 25/34 -2/5 1 11 14/19 (-2/5,-1/3) 0 22 31/42 -6/17 1 11 17/23 (-1/3,-3/10) 0 22 3/4 0/1 1 11 16/21 (-1/3,-4/13) 0 22 13/17 (-1/4,0/1) 0 22 23/30 0/1 1 11 10/13 (-1/5,0/1) 0 22 17/22 0/1 5 1 7/9 (0/1,1/0) 0 22 25/32 0/1 1 11 43/55 1/0 2 2 18/23 (-1/1,0/1) 0 22 11/14 -2/3 1 11 15/19 (-1/2,-2/5) 0 22 34/43 (-8/23,-1/3) 0 22 87/110 -1/3 19 1 53/67 (-1/3,-11/34) 0 22 19/24 -2/7 1 11 4/5 (-1/1,0/1) 0 22 9/11 -1/2 2 2 14/17 (-2/5,-1/3) 0 22 19/23 (-1/3,-1/4) 0 22 5/6 0/1 1 11 11/13 (-1/1,-1/2) 0 22 17/20 -2/5 1 11 6/7 (-1/3,0/1) 0 22 19/22 0/1 3 1 13/15 (0/1,1/0) 0 22 7/8 0/1 1 11 8/9 (-1/1,0/1) 0 22 1/1 (-1/2,0/1) 0 22 1/0 0/1 1 1 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(155,-18,198,-23) (0/1,1/8) -> (18/23,11/14) Glide Reflection Matrix(219,-28,352,-45) (1/8,1/7) -> (23/37,5/8) Hyperbolic Matrix(67,-10,154,-23) (1/7,1/6) -> (3/7,7/16) Glide Reflection Matrix(485,-84,1276,-221) (1/6,4/23) -> (19/50,8/21) Glide Reflection Matrix(571,-100,748,-131) (4/23,3/17) -> (16/21,13/17) Glide Reflection Matrix(67,-12,374,-67) (3/17,2/11) -> (3/17,2/11) Reflection Matrix(21,-4,110,-21) (2/11,1/5) -> (2/11,1/5) Reflection Matrix(67,-14,110,-23) (1/5,2/9) -> (3/5,8/13) Glide Reflection Matrix(89,-20,396,-89) (2/9,5/22) -> (2/9,5/22) Reflection Matrix(131,-30,572,-131) (5/22,3/13) -> (5/22,3/13) Reflection Matrix(111,-26,286,-67) (3/13,1/4) -> (5/13,7/18) Glide Reflection Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(177,-50,308,-87) (5/18,2/7) -> (4/7,15/26) Hyperbolic Matrix(263,-76,308,-89) (2/7,7/24) -> (17/20,6/7) Hyperbolic Matrix(485,-142,748,-219) (7/24,5/17) -> (11/17,13/20) Hyperbolic Matrix(155,-46,374,-111) (5/17,3/10) -> (7/17,5/12) Glide Reflection Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(265,-82,572,-177) (4/13,9/29) -> (6/13,7/15) Glide Reflection Matrix(727,-226,1914,-595) (9/29,5/16) -> (11/29,19/50) Glide Reflection Matrix(395,-124,704,-221) (5/16,1/3) -> (23/41,9/16) Hyperbolic Matrix(23,-8,66,-23) (1/3,4/11) -> (1/3,4/11) Reflection Matrix(153,-56,418,-153) (4/11,7/19) -> (4/11,7/19) Reflection Matrix(329,-122,418,-155) (7/19,3/8) -> (11/14,15/19) Hyperbolic Matrix(307,-116,352,-133) (3/8,11/29) -> (13/15,7/8) Hyperbolic Matrix(397,-152,572,-219) (8/21,5/13) -> (9/13,16/23) Hyperbolic Matrix(375,-146,506,-197) (7/18,9/23) -> (17/23,3/4) Hyperbolic Matrix(417,-164,506,-199) (9/23,2/5) -> (14/17,19/23) Hyperbolic Matrix(89,-36,220,-89) (2/5,9/22) -> (2/5,9/22) Reflection Matrix(307,-126,748,-307) (9/22,7/17) -> (9/22,7/17) Reflection Matrix(109,-46,154,-65) (5/12,3/7) -> (7/10,5/7) Glide Reflection Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(549,-242,946,-417) (11/25,4/9) -> (11/19,18/31) Glide Reflection Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(439,-206,748,-351) (7/15,1/2) -> (17/29,27/46) Glide Reflection Matrix(243,-130,286,-153) (1/2,7/13) -> (11/13,17/20) Hyperbolic Matrix(155,-84,286,-155) (7/13,6/11) -> (7/13,6/11) Reflection Matrix(109,-60,198,-109) (6/11,5/9) -> (6/11,5/9) Reflection Matrix(463,-258,594,-331) (5/9,19/34) -> (7/9,25/32) Glide Reflection Matrix(1101,-616,1496,-837) (19/34,14/25) -> (25/34,14/19) Glide Reflection Matrix(1849,-1036,3300,-1849) (14/25,37/66) -> (14/25,37/66) Reflection Matrix(3035,-1702,5412,-3035) (37/66,23/41) -> (37/66,23/41) Reflection Matrix(419,-236,506,-285) (9/16,13/23) -> (19/23,5/6) Hyperbolic Matrix(505,-286,814,-461) (13/23,4/7) -> (13/21,18/29) Glide Reflection Matrix(551,-318,726,-419) (15/26,26/45) -> (3/4,16/21) Glide Reflection Matrix(1321,-764,1672,-967) (26/45,11/19) -> (15/19,34/43) Hyperbolic Matrix(375,-218,418,-243) (18/31,25/43) -> (8/9,1/1) Glide Reflection Matrix(1563,-910,2530,-1473) (25/43,7/12) -> (21/34,55/89) Hyperbolic Matrix(857,-502,1166,-683) (7/12,17/29) -> (11/15,25/34) Hyperbolic Matrix(507,-298,638,-375) (27/46,10/17) -> (19/24,4/5) Glide Reflection Matrix(441,-260,748,-441) (10/17,13/22) -> (10/17,13/22) Reflection Matrix(131,-78,220,-131) (13/22,3/5) -> (13/22,3/5) Reflection Matrix(6051,-3740,9790,-6051) (55/89,34/55) -> (55/89,34/55) Reflection Matrix(1429,-884,2310,-1429) (34/55,13/21) -> (34/55,13/21) Reflection Matrix(2377,-1476,3828,-2377) (18/29,41/66) -> (18/29,41/66) Reflection Matrix(3035,-1886,4884,-3035) (41/66,23/37) -> (41/66,23/37) Reflection Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(573,-370,748,-483) (9/14,11/17) -> (13/17,23/30) Hyperbolic Matrix(373,-244,506,-331) (13/20,2/3) -> (14/19,31/42) Hyperbolic Matrix(89,-60,132,-89) (2/3,15/22) -> (2/3,15/22) Reflection Matrix(571,-390,836,-571) (15/22,13/19) -> (15/22,13/19) Reflection Matrix(241,-166,286,-197) (11/16,9/13) -> (5/6,11/13) Glide Reflection Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(1255,-876,1606,-1121) (23/33,7/10) -> (25/32,43/55) Hyperbolic Matrix(111,-80,154,-111) (5/7,8/11) -> (5/7,8/11) Reflection Matrix(241,-176,330,-241) (8/11,11/15) -> (8/11,11/15) Reflection Matrix(2663,-1966,3366,-2485) (31/42,17/23) -> (53/67,19/24) Hyperbolic Matrix(331,-254,374,-287) (23/30,10/13) -> (7/8,8/9) Glide Reflection Matrix(441,-340,572,-441) (10/13,17/22) -> (10/13,17/22) Reflection Matrix(307,-238,396,-307) (17/22,7/9) -> (17/22,7/9) Reflection Matrix(7481,-5916,9460,-7481) (34/43,87/110) -> (34/43,87/110) Reflection Matrix(11659,-9222,14740,-11659) (87/110,53/67) -> (87/110,53/67) Reflection Matrix(199,-162,242,-197) (4/5,9/11) -> (9/11,14/17) Parabolic Matrix(265,-228,308,-265) (6/7,19/22) -> (6/7,19/22) Reflection Matrix(571,-494,660,-571) (19/22,13/15) -> (19/22,13/15) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(155,-18,198,-23) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(219,-28,352,-45) -> Matrix(3,4,-4,-5) -1/1 Matrix(67,-10,154,-23) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(485,-84,1276,-221) -> Matrix(13,8,-34,-21) Matrix(571,-100,748,-131) -> Matrix(7,4,-26,-15) Matrix(67,-12,374,-67) -> Matrix(15,8,-28,-15) (3/17,2/11) -> (-4/7,-1/2) Matrix(21,-4,110,-21) -> Matrix(-1,0,4,1) (2/11,1/5) -> (-1/2,0/1) Matrix(67,-14,110,-23) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(89,-20,396,-89) -> Matrix(3,4,-2,-3) (2/9,5/22) -> (-2/1,-1/1) Matrix(131,-30,572,-131) -> Matrix(11,10,-12,-11) (5/22,3/13) -> (-1/1,-5/6) Matrix(111,-26,286,-67) -> Matrix(3,2,-10,-7) Matrix(67,-18,242,-65) -> Matrix(11,6,-24,-13) -1/2 Matrix(177,-50,308,-87) -> Matrix(5,2,-18,-7) -1/3 Matrix(263,-76,308,-89) -> Matrix(1,0,0,1) Matrix(485,-142,748,-219) -> Matrix(7,2,-18,-5) -1/3 Matrix(155,-46,374,-111) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(353,-108,572,-175) -> Matrix(1,0,0,1) Matrix(265,-82,572,-177) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(727,-226,1914,-595) -> Matrix(1,2,-2,-5) Matrix(395,-124,704,-221) -> Matrix(3,2,-8,-5) -1/2 Matrix(23,-8,66,-23) -> Matrix(3,2,-4,-3) (1/3,4/11) -> (-1/1,-1/2) Matrix(153,-56,418,-153) -> Matrix(25,12,-52,-25) (4/11,7/19) -> (-1/2,-6/13) Matrix(329,-122,418,-155) -> Matrix(9,4,-16,-7) -1/2 Matrix(307,-116,352,-133) -> Matrix(5,2,-8,-3) -1/2 Matrix(397,-152,572,-219) -> Matrix(5,2,-8,-3) -1/2 Matrix(375,-146,506,-197) -> Matrix(1,0,0,1) Matrix(417,-164,506,-199) -> Matrix(7,2,-18,-5) -1/3 Matrix(89,-36,220,-89) -> Matrix(-1,0,6,1) (2/5,9/22) -> (-1/3,0/1) Matrix(307,-126,748,-307) -> Matrix(1,0,4,-1) (9/22,7/17) -> (0/1,1/2) Matrix(109,-46,154,-65) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(483,-212,704,-309) -> Matrix(3,2,4,3) Matrix(549,-242,946,-417) -> Matrix(3,2,-10,-7) Matrix(111,-50,242,-109) -> Matrix(11,6,-24,-13) -1/2 Matrix(439,-206,748,-351) -> Matrix(5,2,-32,-13) Matrix(243,-130,286,-153) -> Matrix(3,2,-8,-5) -1/2 Matrix(155,-84,286,-155) -> Matrix(11,6,-20,-11) (7/13,6/11) -> (-3/5,-1/2) Matrix(109,-60,198,-109) -> Matrix(9,4,-20,-9) (6/11,5/9) -> (-1/2,-2/5) Matrix(463,-258,594,-331) -> Matrix(5,2,-2,-1) Matrix(1101,-616,1496,-837) -> Matrix(11,4,-30,-11) *** -> (-2/5,-1/3) Matrix(1849,-1036,3300,-1849) -> Matrix(11,4,-30,-11) (14/25,37/66) -> (-2/5,-1/3) Matrix(3035,-1702,5412,-3035) -> Matrix(5,2,-12,-5) (37/66,23/41) -> (-1/2,-1/3) Matrix(419,-236,506,-285) -> Matrix(5,2,-18,-7) -1/3 Matrix(505,-286,814,-461) -> Matrix(5,2,-2,-1) Matrix(551,-318,726,-419) -> Matrix(9,2,-22,-5) Matrix(1321,-764,1672,-967) -> Matrix(11,2,-28,-5) Matrix(375,-218,418,-243) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(1563,-910,2530,-1473) -> Matrix(1,0,4,1) 0/1 Matrix(857,-502,1166,-683) -> Matrix(11,2,-28,-5) Matrix(507,-298,638,-375) -> Matrix(-1,0,10,1) *** -> (-1/5,0/1) Matrix(441,-260,748,-441) -> Matrix(-1,0,18,1) (10/17,13/22) -> (-1/9,0/1) Matrix(131,-78,220,-131) -> Matrix(1,0,0,-1) (13/22,3/5) -> (0/1,1/0) Matrix(6051,-3740,9790,-6051) -> Matrix(1,0,0,-1) (55/89,34/55) -> (0/1,1/0) Matrix(1429,-884,2310,-1429) -> Matrix(1,2,0,-1) (34/55,13/21) -> (-1/1,1/0) Matrix(2377,-1476,3828,-2377) -> Matrix(7,8,-6,-7) (18/29,41/66) -> (-4/3,-1/1) Matrix(3035,-1886,4884,-3035) -> Matrix(19,18,-20,-19) (41/66,23/37) -> (-1/1,-9/10) Matrix(155,-98,242,-153) -> Matrix(7,4,-16,-9) -1/2 Matrix(573,-370,748,-483) -> Matrix(5,2,-18,-7) -1/3 Matrix(373,-244,506,-331) -> Matrix(7,2,-18,-5) -1/3 Matrix(89,-60,132,-89) -> Matrix(-1,0,6,1) (2/3,15/22) -> (-1/3,0/1) Matrix(571,-390,836,-571) -> Matrix(1,0,8,-1) (15/22,13/19) -> (0/1,1/4) Matrix(241,-166,286,-197) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(1583,-1102,2024,-1409) -> Matrix(3,2,-2,-1) -1/1 Matrix(1255,-876,1606,-1121) -> Matrix(1,0,2,1) 0/1 Matrix(111,-80,154,-111) -> Matrix(3,2,-4,-3) (5/7,8/11) -> (-1/1,-1/2) Matrix(241,-176,330,-241) -> Matrix(9,4,-20,-9) (8/11,11/15) -> (-1/2,-2/5) Matrix(2663,-1966,3366,-2485) -> Matrix(23,8,-72,-25) -1/3 Matrix(331,-254,374,-287) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(441,-340,572,-441) -> Matrix(-1,0,10,1) (10/13,17/22) -> (-1/5,0/1) Matrix(307,-238,396,-307) -> Matrix(1,0,0,-1) (17/22,7/9) -> (0/1,1/0) Matrix(7481,-5916,9460,-7481) -> Matrix(47,16,-138,-47) (34/43,87/110) -> (-8/23,-1/3) Matrix(11659,-9222,14740,-11659) -> Matrix(67,22,-204,-67) (87/110,53/67) -> (-1/3,-11/34) Matrix(199,-162,242,-197) -> Matrix(3,2,-8,-5) -1/2 Matrix(265,-228,308,-265) -> Matrix(-1,0,6,1) (6/7,19/22) -> (-1/3,0/1) Matrix(571,-494,660,-571) -> Matrix(1,0,0,-1) (19/22,13/15) -> (0/1,1/0) Matrix(-1,2,0,1) -> Matrix(-1,0,4,1) (1/1,1/0) -> (-1/2,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.