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: 40 Genus: 41 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -9/22 -17/44 -7/22 -10/33 -13/44 -5/22 -19/88 -23/110 -7/44 -3/20 -3/22 -1/8 0/1 1/7 1/6 2/11 3/16 1/5 3/14 2/9 1/4 3/11 5/18 2/7 3/10 1/3 4/11 2/5 5/12 5/11 1/2 6/11 5/9 7/11 2/3 23/33 8/11 9/11 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/21 -6/7 1/19 2/37 -11/13 2/35 1/17 -5/6 1/19 -9/11 1/18 -13/16 1/18 3/53 -4/5 0/1 1/17 -11/14 3/53 -18/23 2/35 1/17 -7/9 4/69 1/17 -3/4 1/17 1/16 -8/11 1/16 -13/18 5/79 -5/7 2/31 1/15 -17/24 1/16 3/47 -12/17 3/47 2/31 -7/10 1/15 -9/13 2/31 5/77 -2/3 1/15 2/29 -9/14 5/71 -7/11 1/14 -5/8 1/14 3/41 -18/29 3/41 8/109 -13/21 2/27 1/13 -8/13 7/95 2/27 -11/18 5/67 -14/23 2/27 1/13 -3/5 4/53 1/13 -7/12 1/13 5/64 -18/31 1/13 6/77 -11/19 4/51 7/89 -4/7 5/63 2/25 -13/23 2/25 7/87 -9/16 5/62 3/37 -14/25 3/37 16/197 -5/9 4/49 5/61 -11/20 9/109 1/12 -6/11 1/12 -1/2 1/11 -5/11 1/10 -9/20 1/10 9/89 -4/9 5/49 4/39 -7/16 3/29 5/48 -10/23 7/67 2/19 -13/30 11/105 -3/7 2/19 5/47 -11/26 7/65 -8/19 7/65 4/37 -21/50 9/83 -13/31 6/55 1/9 -18/43 4/37 1/9 -5/12 5/46 1/9 -7/17 14/127 1/9 -9/22 1/9 -2/5 1/9 4/35 -11/28 3/26 5/43 -9/23 1/9 2/17 -16/41 5/43 2/17 -7/18 5/43 -12/31 17/145 2/17 -17/44 2/17 -5/13 2/17 7/59 -13/34 3/25 -21/55 1/8 -29/76 1/9 1/8 -8/21 1/9 2/17 -3/8 3/25 1/8 -4/11 1/8 -5/14 5/39 -6/17 3/23 2/15 -7/20 1/8 3/23 -1/3 2/15 1/7 -7/22 1/7 -6/19 1/7 12/83 -5/16 1/7 5/34 -4/13 5/33 2/13 -7/23 2/13 3/19 -10/33 1/6 -3/10 1/7 -8/27 5/33 2/13 -13/44 2/13 -5/17 2/13 3/19 -7/24 3/19 1/6 -9/31 2/11 1/5 -2/7 1/7 2/13 -7/25 4/25 5/31 -19/68 3/19 1/6 -12/43 3/19 4/25 -5/18 5/31 -3/11 1/6 -1/4 1/6 1/5 -3/13 6/31 1/5 -5/22 1/5 -2/9 1/5 4/19 -7/32 1/5 3/14 -12/55 3/14 -5/23 1/5 2/9 -8/37 13/59 2/9 -19/88 2/9 -11/51 2/9 19/85 -3/14 3/13 -4/19 0/1 1/3 -9/43 0/1 1/5 -23/110 1/5 -14/67 1/5 2/9 -5/24 1/5 1/4 -1/5 0/1 1/5 -4/21 1/5 2/9 -3/16 3/13 1/4 -2/11 1/4 -1/6 1/3 -4/25 -1/1 0/1 -7/44 0/1 -3/19 0/1 1/7 -2/13 1/5 2/9 -3/20 1/4 3/11 -1/7 2/7 1/3 -3/22 1/3 -2/15 1/3 4/11 -1/8 1/3 1/2 0/1 0/1 1/1 1/7 -1/1 -2/3 2/13 -2/5 -1/3 1/6 -1/1 2/11 -1/2 3/16 -1/2 -3/7 1/5 -1/3 0/1 3/14 -3/7 5/23 -2/5 -1/3 2/9 -4/11 -1/3 1/4 -1/3 -1/4 3/11 -1/4 5/18 -5/21 2/7 -2/9 -1/5 7/24 -1/4 -3/13 5/17 -3/13 -2/9 3/10 -1/5 4/13 -2/9 -5/23 1/3 -1/5 -2/11 5/14 -5/29 4/11 -1/6 3/8 -1/6 -3/19 11/29 -3/19 -8/51 8/21 -2/13 -1/7 5/13 -7/45 -2/13 7/18 -5/33 9/23 -2/13 -1/7 2/5 -4/27 -1/7 5/12 -1/7 -5/36 13/31 -1/7 -6/43 8/19 -4/29 -7/51 3/7 -5/37 -2/15 10/23 -2/15 -7/53 7/16 -5/38 -3/23 11/25 -3/23 -16/123 4/9 -4/31 -5/39 9/20 -9/71 -1/8 5/11 -1/8 1/2 -1/9 6/11 -1/10 11/20 -1/10 -9/91 5/9 -5/51 -4/41 9/16 -3/31 -5/52 13/23 -7/73 -2/21 17/30 -11/115 4/7 -2/21 -5/53 15/26 -7/75 11/19 -7/75 -4/43 29/50 -9/97 18/31 -6/65 -1/11 25/43 -4/43 -1/11 7/12 -5/54 -1/11 10/17 -14/153 -1/11 13/22 -1/11 3/5 -1/11 -4/45 17/28 -3/34 -5/57 14/23 -1/11 -2/23 25/41 -5/57 -2/23 11/18 -5/57 19/31 -17/195 -2/23 27/44 -2/23 8/13 -2/23 -7/81 21/34 -3/35 34/55 -1/12 47/76 -1/11 -1/12 13/21 -1/11 -2/23 5/8 -3/35 -1/12 7/11 -1/12 9/14 -5/61 11/17 -3/37 -2/25 13/20 -1/12 -3/37 2/3 -2/25 -1/13 15/22 -1/13 13/19 -1/13 -12/157 11/16 -1/13 -5/66 9/13 -5/67 -2/27 16/23 -2/27 -3/41 23/33 -1/14 7/10 -1/13 19/27 -5/67 -2/27 31/44 -2/27 12/17 -2/27 -3/41 17/24 -3/41 -1/14 22/31 -2/29 -1/15 5/7 -1/13 -2/27 18/25 -4/55 -5/69 49/68 -3/41 -1/14 31/43 -3/41 -4/55 13/18 -5/69 8/11 -1/14 3/4 -1/14 -1/15 10/13 -6/89 -1/15 17/22 -1/15 7/9 -1/15 -4/61 25/32 -1/15 -3/46 43/55 -3/46 18/23 -1/15 -2/31 29/37 -13/201 -2/31 69/88 -2/31 40/51 -2/31 -19/295 11/14 -3/47 15/19 -1/17 0/1 34/43 -1/15 0/1 87/110 -1/15 53/67 -1/15 -2/31 19/24 -1/15 -1/16 4/5 -1/15 0/1 17/21 -1/15 -2/31 13/16 -3/47 -1/16 9/11 -1/16 5/6 -1/17 21/25 -1/21 0/1 37/44 0/1 16/19 -1/13 0/1 11/13 -1/15 -2/31 17/20 -1/16 -3/49 6/7 -2/33 -1/17 19/22 -1/17 13/15 -1/17 -4/69 7/8 -1/17 -1/18 1/1 -1/19 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(109,96,-176,-155) (-1/1,-6/7) -> (-18/29,-13/21) Hyperbolic Matrix(89,76,-308,-263) (-6/7,-11/13) -> (-9/31,-2/7) Hyperbolic Matrix(351,296,-836,-705) (-11/13,-5/6) -> (-21/50,-13/31) Hyperbolic Matrix(109,90,132,109) (-5/6,-9/11) -> (9/11,5/6) Hyperbolic Matrix(287,234,352,287) (-9/11,-13/16) -> (13/16,9/11) Hyperbolic Matrix(87,70,-220,-177) (-13/16,-4/5) -> (-2/5,-11/28) Hyperbolic Matrix(109,86,-308,-243) (-4/5,-11/14) -> (-5/14,-6/17) Hyperbolic Matrix(439,344,-1012,-793) (-11/14,-18/23) -> (-10/23,-13/30) Hyperbolic Matrix(461,360,-1100,-859) (-18/23,-7/9) -> (-13/31,-18/43) Hyperbolic Matrix(21,16,-88,-67) (-7/9,-3/4) -> (-1/4,-3/13) Hyperbolic Matrix(65,48,88,65) (-3/4,-8/11) -> (8/11,3/4) Hyperbolic Matrix(287,208,396,287) (-8/11,-13/18) -> (13/18,8/11) Hyperbolic Matrix(131,94,-308,-221) (-13/18,-5/7) -> (-3/7,-11/26) Hyperbolic Matrix(45,32,-308,-219) (-5/7,-17/24) -> (-3/20,-1/7) Hyperbolic Matrix(263,186,-748,-529) (-17/24,-12/17) -> (-6/17,-7/20) Hyperbolic Matrix(131,92,-440,-309) (-12/17,-7/10) -> (-3/10,-8/27) Hyperbolic Matrix(219,152,-572,-397) (-7/10,-9/13) -> (-5/13,-13/34) Hyperbolic Matrix(197,136,-352,-243) (-9/13,-2/3) -> (-14/25,-5/9) Hyperbolic Matrix(65,42,-308,-199) (-2/3,-9/14) -> (-3/14,-4/19) Hyperbolic Matrix(197,126,308,197) (-9/14,-7/11) -> (7/11,9/14) Hyperbolic Matrix(111,70,176,111) (-7/11,-5/8) -> (5/8,7/11) Hyperbolic Matrix(45,28,-352,-219) (-5/8,-18/29) -> (-2/15,-1/8) Hyperbolic Matrix(175,108,-572,-353) (-13/21,-8/13) -> (-4/13,-7/23) Hyperbolic Matrix(307,188,-792,-485) (-8/13,-11/18) -> (-7/18,-12/31) Hyperbolic Matrix(331,202,-1188,-725) (-11/18,-14/23) -> (-12/43,-5/18) Hyperbolic Matrix(43,26,-220,-133) (-14/23,-3/5) -> (-1/5,-4/21) Hyperbolic Matrix(109,64,-264,-155) (-3/5,-7/12) -> (-5/12,-7/17) Hyperbolic Matrix(241,140,-1100,-639) (-7/12,-18/31) -> (-2/9,-7/32) Hyperbolic Matrix(131,76,-836,-485) (-18/31,-11/19) -> (-3/19,-2/13) Hyperbolic Matrix(87,50,-308,-177) (-11/19,-4/7) -> (-2/7,-7/25) Hyperbolic Matrix(219,124,-1012,-573) (-4/7,-13/23) -> (-5/23,-8/37) 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(243,134,-836,-461) (-5/9,-11/20) -> (-7/24,-9/31) Hyperbolic Matrix(241,132,440,241) (-11/20,-6/11) -> (6/11,11/20) Hyperbolic Matrix(23,12,44,23) (-6/11,-1/2) -> (1/2,6/11) Hyperbolic Matrix(21,10,44,21) (-1/2,-5/11) -> (5/11,1/2) Hyperbolic Matrix(199,90,440,199) (-5/11,-9/20) -> (9/20,5/11) Hyperbolic Matrix(67,30,-440,-197) (-9/20,-4/9) -> (-2/13,-3/20) Hyperbolic Matrix(109,48,-352,-155) (-4/9,-7/16) -> (-5/16,-4/13) Hyperbolic Matrix(133,58,-704,-307) (-7/16,-10/23) -> (-4/21,-3/16) Hyperbolic Matrix(351,152,-1628,-705) (-13/30,-3/7) -> (-11/51,-3/14) Hyperbolic Matrix(549,232,-1408,-595) (-11/26,-8/19) -> (-16/41,-7/18) Hyperbolic Matrix(219,92,-1364,-573) (-8/19,-21/50) -> (-1/6,-4/25) Hyperbolic Matrix(1343,562,-3520,-1473) (-18/43,-5/12) -> (-29/76,-8/21) Hyperbolic Matrix(287,118,484,199) (-7/17,-9/22) -> (13/22,3/5) Hyperbolic Matrix(285,116,484,197) (-9/22,-2/5) -> (10/17,13/22) Hyperbolic Matrix(461,180,-2200,-859) (-9/23,-16/41) -> (-4/19,-9/43) Hyperbolic Matrix(1189,460,1936,749) (-12/31,-17/44) -> (27/44,8/13) Hyperbolic Matrix(1187,458,1936,747) (-17/44,-5/13) -> (19/31,27/44) Hyperbolic Matrix(1167,446,1672,639) (-13/34,-21/55) -> (23/33,7/10) Hyperbolic Matrix(4643,1772,5940,2267) (-21/55,-29/76) -> (25/32,43/55) Hyperbolic Matrix(21,8,-176,-67) (-8/21,-3/8) -> (-1/8,0/1) Hyperbolic Matrix(65,24,176,65) (-3/8,-4/11) -> (4/11,3/8) Hyperbolic Matrix(111,40,308,111) (-4/11,-5/14) -> (5/14,4/11) Hyperbolic Matrix(197,68,-704,-243) (-7/20,-1/3) -> (-7/25,-19/68) Hyperbolic Matrix(331,106,484,155) (-1/3,-7/22) -> (15/22,13/19) Hyperbolic Matrix(329,104,484,153) (-7/22,-6/19) -> (2/3,15/22) Hyperbolic Matrix(441,134,-2024,-615) (-7/23,-10/33) -> (-12/55,-5/23) Hyperbolic Matrix(1033,312,1672,505) (-10/33,-3/10) -> (21/34,34/55) Hyperbolic Matrix(1365,404,1936,573) (-8/27,-13/44) -> (31/44,12/17) Hyperbolic Matrix(1363,402,1936,571) (-13/44,-5/17) -> (19/27,31/44) Hyperbolic Matrix(109,32,-528,-155) (-5/17,-7/24) -> (-5/24,-1/5) Hyperbolic Matrix(1167,326,-5588,-1561) (-19/68,-12/43) -> (-14/67,-5/24) Hyperbolic Matrix(109,30,396,109) (-5/18,-3/11) -> (3/11,5/18) Hyperbolic Matrix(23,6,88,23) (-3/11,-1/4) -> (1/4,3/11) Hyperbolic Matrix(375,86,484,111) (-3/13,-5/22) -> (17/22,7/9) Hyperbolic Matrix(373,84,484,109) (-5/22,-2/9) -> (10/13,17/22) Hyperbolic Matrix(3673,802,5940,1297) (-7/32,-12/55) -> (34/55,47/76) Hyperbolic Matrix(6073,1312,7744,1673) (-8/37,-19/88) -> (69/88,40/51) Hyperbolic Matrix(6071,1310,7744,1671) (-19/88,-11/51) -> (29/37,69/88) Hyperbolic Matrix(9571,2002,12100,2531) (-9/43,-23/110) -> (87/110,53/67) Hyperbolic Matrix(9569,2000,12100,2529) (-23/110,-14/67) -> (34/43,87/110) Hyperbolic Matrix(65,12,352,65) (-3/16,-2/11) -> (2/11,3/16) Hyperbolic Matrix(23,4,132,23) (-2/11,-1/6) -> (1/6,2/11) Hyperbolic Matrix(1629,260,1936,309) (-4/25,-7/44) -> (37/44,16/19) Hyperbolic Matrix(1627,258,1936,307) (-7/44,-3/19) -> (21/25,37/44) Hyperbolic Matrix(419,58,484,67) (-1/7,-3/22) -> (19/22,13/15) Hyperbolic Matrix(417,56,484,65) (-3/22,-2/15) -> (6/7,19/22) Hyperbolic Matrix(67,-8,176,-21) (0/1,1/7) -> (11/29,8/21) Hyperbolic Matrix(219,-32,308,-45) (1/7,2/13) -> (22/31,5/7) Hyperbolic Matrix(485,-76,836,-131) (2/13,1/6) -> (29/50,18/31) Hyperbolic Matrix(133,-26,220,-43) (3/16,1/5) -> (3/5,17/28) Hyperbolic Matrix(199,-42,308,-65) (1/5,3/14) -> (9/14,11/17) Hyperbolic Matrix(573,-124,1012,-219) (3/14,5/23) -> (13/23,17/30) Hyperbolic Matrix(639,-140,1100,-241) (5/23,2/9) -> (18/31,25/43) Hyperbolic Matrix(67,-16,88,-21) (2/9,1/4) -> (3/4,10/13) Hyperbolic 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(309,-92,440,-131) (5/17,3/10) -> (7/10,19/27) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(155,-48,352,-109) (4/13,1/3) -> (11/25,4/9) Hyperbolic Matrix(243,-86,308,-109) (1/3,5/14) -> (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(485,-188,792,-307) (5/13,7/18) -> (11/18,19/31) Hyperbolic Matrix(857,-334,1188,-463) (7/18,9/23) -> (31/43,13/18) Hyperbolic Matrix(177,-70,220,-87) (9/23,2/5) -> (4/5,17/21) Hyperbolic Matrix(155,-64,264,-109) (2/5,5/12) -> (7/12,10/17) Hyperbolic Matrix(859,-360,1100,-461) (5/12,13/31) -> (7/9,25/32) Hyperbolic Matrix(705,-296,836,-351) (13/31,8/19) -> (16/19,11/13) Hyperbolic Matrix(221,-94,308,-131) (8/19,3/7) -> (5/7,18/25) Hyperbolic Matrix(793,-344,1012,-439) (3/7,10/23) -> (18/23,29/37) Hyperbolic Matrix(615,-268,1012,-441) (10/23,7/16) -> (17/28,14/23) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(593,-266,836,-375) (4/9,9/20) -> (17/24,22/31) Hyperbolic Matrix(373,-206,440,-243) (11/20,5/9) -> (11/13,17/20) Hyperbolic Matrix(243,-136,352,-197) (5/9,9/16) -> (11/16,9/13) Hyperbolic Matrix(571,-322,704,-397) (9/16,13/23) -> (17/21,13/16) Hyperbolic Matrix(1277,-724,1628,-923) (17/30,4/7) -> (40/51,11/14) Hyperbolic Matrix(859,-496,1408,-813) (15/26,11/19) -> (25/41,11/18) Hyperbolic Matrix(1145,-664,1364,-791) (11/19,29/50) -> (5/6,21/25) Hyperbolic Matrix(2177,-1266,3520,-2047) (25/43,7/12) -> (47/76,13/21) Hyperbolic Matrix(1739,-1060,2200,-1341) (14/23,25/41) -> (15/19,34/43) Hyperbolic Matrix(155,-96,176,-109) (13/21,5/8) -> (7/8,1/1) Hyperbolic Matrix(507,-332,704,-461) (13/20,2/3) -> (18/25,49/68) Hyperbolic Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(419,-296,528,-373) (12/17,17/24) -> (19/24,4/5) Hyperbolic Matrix(4421,-3186,5588,-4027) (49/68,31/43) -> (53/67,19/24) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-40,1) Matrix(109,96,-176,-155) -> Matrix(41,-2,554,-27) Matrix(89,76,-308,-263) -> Matrix(1,0,-12,1) Matrix(351,296,-836,-705) -> Matrix(67,-4,620,-37) Matrix(109,90,132,109) -> Matrix(37,-2,-610,33) Matrix(287,234,352,287) -> Matrix(107,-6,-1694,95) Matrix(87,70,-220,-177) -> Matrix(69,-4,604,-35) Matrix(109,86,-308,-243) -> Matrix(37,-2,278,-15) Matrix(439,344,-1012,-793) -> Matrix(279,-16,2668,-153) Matrix(461,360,-1100,-859) -> Matrix(33,-2,314,-19) Matrix(21,16,-88,-67) -> Matrix(33,-2,182,-11) Matrix(65,48,88,65) -> Matrix(33,-2,-478,29) Matrix(287,208,396,287) -> Matrix(159,-10,-2210,139) Matrix(131,94,-308,-221) -> Matrix(125,-8,1172,-75) Matrix(45,32,-308,-219) -> Matrix(1,0,-12,1) Matrix(263,186,-748,-529) -> Matrix(1,0,-8,1) Matrix(131,92,-440,-309) -> Matrix(61,-4,412,-27) Matrix(219,152,-572,-397) -> Matrix(63,-4,520,-33) Matrix(197,136,-352,-243) -> Matrix(153,-10,1882,-123) Matrix(65,42,-308,-199) -> Matrix(29,-2,102,-7) Matrix(197,126,308,197) -> Matrix(141,-10,-1706,121) Matrix(111,70,176,111) -> Matrix(83,-6,-982,71) Matrix(45,28,-352,-219) -> Matrix(55,-4,124,-9) Matrix(175,108,-572,-353) -> Matrix(55,-4,344,-25) Matrix(307,188,-792,-485) -> Matrix(269,-20,2300,-171) Matrix(331,202,-1188,-725) -> Matrix(133,-10,838,-63) Matrix(43,26,-220,-133) -> Matrix(53,-4,252,-19) Matrix(109,64,-264,-155) -> Matrix(129,-10,1174,-91) Matrix(241,140,-1100,-639) -> Matrix(25,-2,138,-11) Matrix(131,76,-836,-485) -> Matrix(51,-4,268,-21) Matrix(87,50,-308,-177) -> Matrix(101,-8,644,-51) Matrix(219,124,-1012,-573) -> Matrix(199,-16,908,-73) Matrix(397,224,-1012,-571) -> Matrix(199,-16,1704,-137) Matrix(221,124,-704,-395) -> Matrix(247,-20,1692,-137) Matrix(243,134,-836,-461) -> Matrix(73,-6,426,-35) Matrix(241,132,440,241) -> Matrix(217,-18,-2182,181) Matrix(23,12,44,23) -> Matrix(23,-2,-218,19) Matrix(21,10,44,21) -> Matrix(21,-2,-178,17) Matrix(199,90,440,199) -> Matrix(179,-18,-1422,143) Matrix(67,30,-440,-197) -> Matrix(59,-6,246,-25) Matrix(109,48,-352,-155) -> Matrix(97,-10,650,-67) Matrix(133,58,-704,-307) -> Matrix(115,-12,508,-53) Matrix(351,152,-1628,-705) -> Matrix(267,-28,1192,-125) Matrix(549,232,-1408,-595) -> Matrix(55,-6,486,-53) Matrix(219,92,-1364,-573) -> Matrix(37,-4,28,-3) Matrix(1343,562,-3520,-1473) -> Matrix(55,-6,486,-53) Matrix(287,118,484,199) -> Matrix(163,-18,-1802,199) Matrix(285,116,484,197) -> Matrix(161,-18,-1762,197) Matrix(461,180,-2200,-859) -> Matrix(17,-2,94,-11) Matrix(1189,460,1936,749) -> Matrix(409,-48,-4712,553) Matrix(1187,458,1936,747) -> Matrix(407,-48,-4672,551) Matrix(1167,446,1672,639) -> Matrix(17,-2,-246,29) Matrix(4643,1772,5940,2267) -> Matrix(19,-2,-294,31) Matrix(21,8,-176,-67) -> Matrix(17,-2,26,-3) Matrix(65,24,176,65) -> Matrix(49,-6,-302,37) Matrix(111,40,308,111) -> Matrix(79,-10,-466,59) Matrix(197,68,-704,-243) -> Matrix(47,-6,290,-37) Matrix(331,106,484,155) -> Matrix(99,-14,-1294,183) Matrix(329,104,484,153) -> Matrix(97,-14,-1254,181) Matrix(441,134,-2024,-615) -> Matrix(51,-8,236,-37) Matrix(1033,312,1672,505) -> Matrix(11,-2,-126,23) Matrix(1365,404,1936,573) -> Matrix(105,-16,-1424,217) Matrix(1363,402,1936,571) -> Matrix(103,-16,-1384,215) Matrix(109,32,-528,-155) -> Matrix(13,-2,46,-7) Matrix(1167,326,-5588,-1561) -> Matrix(13,-2,46,-7) Matrix(109,30,396,109) -> Matrix(61,-10,-250,41) Matrix(23,6,88,23) -> Matrix(11,-2,-38,7) Matrix(375,86,484,111) -> Matrix(51,-10,-770,151) Matrix(373,84,484,109) -> Matrix(49,-10,-730,149) Matrix(3673,802,5940,1297) -> Matrix(9,-2,-94,21) Matrix(6073,1312,7744,1673) -> Matrix(289,-64,-4484,993) Matrix(6071,1310,7744,1671) -> Matrix(287,-64,-4444,991) Matrix(9571,2002,12100,2531) -> Matrix(11,-2,-170,31) Matrix(9569,2000,12100,2529) -> Matrix(9,-2,-130,29) Matrix(65,12,352,65) -> Matrix(25,-6,-54,13) Matrix(23,4,132,23) -> Matrix(7,-2,-10,3) Matrix(1629,260,1936,309) -> Matrix(1,0,-12,1) Matrix(1627,258,1936,307) -> Matrix(1,0,-28,1) Matrix(419,58,484,67) -> Matrix(19,-6,-326,103) Matrix(417,56,484,65) -> Matrix(17,-6,-286,101) Matrix(67,-8,176,-21) -> Matrix(1,-2,-6,13) Matrix(219,-32,308,-45) -> Matrix(1,0,-12,1) Matrix(485,-76,836,-131) -> Matrix(13,4,-140,-43) Matrix(133,-26,220,-43) -> Matrix(11,4,-124,-45) Matrix(199,-42,308,-65) -> Matrix(3,2,-38,-25) Matrix(573,-124,1012,-219) -> Matrix(41,16,-428,-167) Matrix(639,-140,1100,-241) -> Matrix(7,2,-74,-21) Matrix(67,-16,88,-21) -> Matrix(7,2,-102,-29) Matrix(177,-50,308,-87) -> Matrix(35,8,-372,-85) Matrix(263,-76,308,-89) -> Matrix(1,0,-12,1) Matrix(485,-142,748,-219) -> Matrix(1,0,-8,1) Matrix(309,-92,440,-131) -> Matrix(19,4,-252,-53) Matrix(353,-108,572,-175) -> Matrix(17,4,-200,-47) Matrix(155,-48,352,-109) -> Matrix(47,10,-362,-77) Matrix(243,-86,308,-109) -> Matrix(11,2,-182,-33) Matrix(307,-116,352,-133) -> Matrix(25,4,-444,-71) Matrix(397,-152,572,-219) -> Matrix(25,4,-344,-55) Matrix(485,-188,792,-307) -> Matrix(131,20,-1500,-229) Matrix(857,-334,1188,-463) -> Matrix(67,10,-918,-137) Matrix(177,-70,220,-87) -> Matrix(27,4,-412,-61) Matrix(155,-64,264,-109) -> Matrix(71,10,-774,-109) Matrix(859,-360,1100,-461) -> Matrix(15,2,-218,-29) Matrix(705,-296,836,-351) -> Matrix(29,4,-428,-59) Matrix(221,-94,308,-131) -> Matrix(59,8,-804,-109) Matrix(793,-344,1012,-439) -> Matrix(121,16,-1868,-247) Matrix(615,-268,1012,-441) -> Matrix(121,16,-1384,-183) Matrix(483,-212,704,-309) -> Matrix(153,20,-2012,-263) Matrix(593,-266,836,-375) -> Matrix(47,6,-666,-85) Matrix(373,-206,440,-243) -> Matrix(61,6,-966,-95) Matrix(243,-136,352,-197) -> Matrix(103,10,-1370,-133) Matrix(571,-322,704,-397) -> Matrix(125,12,-1948,-187) Matrix(1277,-724,1628,-923) -> Matrix(293,28,-4552,-435) Matrix(859,-496,1408,-813) -> Matrix(65,6,-726,-67) Matrix(1145,-664,1364,-791) -> Matrix(43,4,-828,-77) Matrix(2177,-1266,3520,-2047) -> Matrix(65,6,-726,-67) Matrix(1739,-1060,2200,-1341) -> Matrix(23,2,-334,-29) Matrix(155,-96,176,-109) -> Matrix(23,2,-426,-37) Matrix(507,-332,704,-461) -> Matrix(73,6,-1010,-83) Matrix(1583,-1102,2024,-1409) -> Matrix(109,8,-1676,-123) Matrix(419,-296,528,-373) -> Matrix(27,2,-446,-33) Matrix(4421,-3186,5588,-4027) -> Matrix(27,2,-446,-33) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 30 Degree of the the map X: 60 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. ----------------------------------------------------------------------- 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): 360 Minimal number of generators: 61 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: 30 Genus: 16 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 1/7 1/6 2/11 3/16 1/5 3/14 2/9 1/4 3/11 5/18 3/10 1/3 4/11 3/8 5/12 9/20 5/11 1/2 13/22 27/44 15/22 23/33 31/44 17/22 69/88 87/110 37/44 19/22 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/7 -1/1 -2/3 2/13 -2/5 -1/3 1/6 -1/1 2/11 -1/2 3/16 -1/2 -3/7 1/5 -1/3 0/1 3/14 -3/7 5/23 -2/5 -1/3 2/9 -4/11 -1/3 1/4 -1/3 -1/4 3/11 -1/4 5/18 -5/21 2/7 -2/9 -1/5 7/24 -1/4 -3/13 5/17 -3/13 -2/9 3/10 -1/5 4/13 -2/9 -5/23 1/3 -1/5 -2/11 5/14 -5/29 4/11 -1/6 3/8 -1/6 -3/19 11/29 -3/19 -8/51 8/21 -2/13 -1/7 5/13 -7/45 -2/13 7/18 -5/33 9/23 -2/13 -1/7 2/5 -4/27 -1/7 5/12 -1/7 -5/36 13/31 -1/7 -6/43 8/19 -4/29 -7/51 3/7 -5/37 -2/15 10/23 -2/15 -7/53 7/16 -5/38 -3/23 11/25 -3/23 -16/123 4/9 -4/31 -5/39 9/20 -9/71 -1/8 5/11 -1/8 1/2 -1/9 6/11 -1/10 11/20 -1/10 -9/91 5/9 -5/51 -4/41 9/16 -3/31 -5/52 13/23 -7/73 -2/21 17/30 -11/115 4/7 -2/21 -5/53 15/26 -7/75 11/19 -7/75 -4/43 29/50 -9/97 18/31 -6/65 -1/11 25/43 -4/43 -1/11 7/12 -5/54 -1/11 10/17 -14/153 -1/11 13/22 -1/11 3/5 -1/11 -4/45 17/28 -3/34 -5/57 14/23 -1/11 -2/23 25/41 -5/57 -2/23 11/18 -5/57 19/31 -17/195 -2/23 27/44 -2/23 8/13 -2/23 -7/81 21/34 -3/35 34/55 -1/12 47/76 -1/11 -1/12 13/21 -1/11 -2/23 5/8 -3/35 -1/12 7/11 -1/12 9/14 -5/61 11/17 -3/37 -2/25 13/20 -1/12 -3/37 2/3 -2/25 -1/13 15/22 -1/13 13/19 -1/13 -12/157 11/16 -1/13 -5/66 9/13 -5/67 -2/27 16/23 -2/27 -3/41 23/33 -1/14 7/10 -1/13 19/27 -5/67 -2/27 31/44 -2/27 12/17 -2/27 -3/41 17/24 -3/41 -1/14 22/31 -2/29 -1/15 5/7 -1/13 -2/27 18/25 -4/55 -5/69 49/68 -3/41 -1/14 31/43 -3/41 -4/55 13/18 -5/69 8/11 -1/14 3/4 -1/14 -1/15 10/13 -6/89 -1/15 17/22 -1/15 7/9 -1/15 -4/61 25/32 -1/15 -3/46 43/55 -3/46 18/23 -1/15 -2/31 29/37 -13/201 -2/31 69/88 -2/31 40/51 -2/31 -19/295 11/14 -3/47 15/19 -1/17 0/1 34/43 -1/15 0/1 87/110 -1/15 53/67 -1/15 -2/31 19/24 -1/15 -1/16 4/5 -1/15 0/1 17/21 -1/15 -2/31 13/16 -3/47 -1/16 9/11 -1/16 5/6 -1/17 21/25 -1/21 0/1 37/44 0/1 16/19 -1/13 0/1 11/13 -1/15 -2/31 17/20 -1/16 -3/49 6/7 -2/33 -1/17 19/22 -1/17 13/15 -1/17 -4/69 7/8 -1/17 -1/18 1/1 -1/19 0/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,1,0,1) (0/1,1/0) -> (1/1,1/0) Parabolic Matrix(67,-8,176,-21) (0/1,1/7) -> (11/29,8/21) Hyperbolic Matrix(219,-32,308,-45) (1/7,2/13) -> (22/31,5/7) Hyperbolic Matrix(485,-76,836,-131) (2/13,1/6) -> (29/50,18/31) Hyperbolic Matrix(109,-19,132,-23) (1/6,2/11) -> (9/11,5/6) Hyperbolic Matrix(287,-53,352,-65) (2/11,3/16) -> (13/16,9/11) Hyperbolic Matrix(133,-26,220,-43) (3/16,1/5) -> (3/5,17/28) Hyperbolic Matrix(199,-42,308,-65) (1/5,3/14) -> (9/14,11/17) Hyperbolic Matrix(573,-124,1012,-219) (3/14,5/23) -> (13/23,17/30) Hyperbolic Matrix(639,-140,1100,-241) (5/23,2/9) -> (18/31,25/43) Hyperbolic Matrix(67,-16,88,-21) (2/9,1/4) -> (3/4,10/13) Hyperbolic Matrix(65,-17,88,-23) (1/4,3/11) -> (8/11,3/4) Hyperbolic Matrix(287,-79,396,-109) (3/11,5/18) -> (13/18,8/11) Hyperbolic 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(309,-92,440,-131) (5/17,3/10) -> (7/10,19/27) Hyperbolic Matrix(353,-108,572,-175) (3/10,4/13) -> (8/13,21/34) Hyperbolic Matrix(155,-48,352,-109) (4/13,1/3) -> (11/25,4/9) Hyperbolic Matrix(243,-86,308,-109) (1/3,5/14) -> (11/14,15/19) Hyperbolic Matrix(197,-71,308,-111) (5/14,4/11) -> (7/11,9/14) Hyperbolic Matrix(111,-41,176,-65) (4/11,3/8) -> (5/8,7/11) 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(485,-188,792,-307) (5/13,7/18) -> (11/18,19/31) Hyperbolic Matrix(857,-334,1188,-463) (7/18,9/23) -> (31/43,13/18) Hyperbolic Matrix(177,-70,220,-87) (9/23,2/5) -> (4/5,17/21) Hyperbolic Matrix(155,-64,264,-109) (2/5,5/12) -> (7/12,10/17) Hyperbolic Matrix(859,-360,1100,-461) (5/12,13/31) -> (7/9,25/32) Hyperbolic Matrix(705,-296,836,-351) (13/31,8/19) -> (16/19,11/13) Hyperbolic Matrix(221,-94,308,-131) (8/19,3/7) -> (5/7,18/25) Hyperbolic Matrix(793,-344,1012,-439) (3/7,10/23) -> (18/23,29/37) Hyperbolic Matrix(615,-268,1012,-441) (10/23,7/16) -> (17/28,14/23) Hyperbolic Matrix(483,-212,704,-309) (7/16,11/25) -> (13/19,11/16) Hyperbolic Matrix(593,-266,836,-375) (4/9,9/20) -> (17/24,22/31) Hyperbolic Matrix(241,-109,440,-199) (9/20,5/11) -> (6/11,11/20) Hyperbolic Matrix(23,-11,44,-21) (5/11,1/2) -> (1/2,6/11) Parabolic Matrix(373,-206,440,-243) (11/20,5/9) -> (11/13,17/20) Hyperbolic Matrix(243,-136,352,-197) (5/9,9/16) -> (11/16,9/13) Hyperbolic Matrix(571,-322,704,-397) (9/16,13/23) -> (17/21,13/16) Hyperbolic Matrix(1277,-724,1628,-923) (17/30,4/7) -> (40/51,11/14) Hyperbolic Matrix(859,-496,1408,-813) (15/26,11/19) -> (25/41,11/18) Hyperbolic Matrix(1145,-664,1364,-791) (11/19,29/50) -> (5/6,21/25) Hyperbolic Matrix(2177,-1266,3520,-2047) (25/43,7/12) -> (47/76,13/21) Hyperbolic Matrix(287,-169,484,-285) (10/17,13/22) -> (13/22,3/5) Parabolic Matrix(1739,-1060,2200,-1341) (14/23,25/41) -> (15/19,34/43) Hyperbolic Matrix(1189,-729,1936,-1187) (19/31,27/44) -> (27/44,8/13) Parabolic Matrix(1167,-721,1672,-1033) (21/34,34/55) -> (23/33,7/10) Hyperbolic Matrix(4643,-2871,5940,-3673) (34/55,47/76) -> (25/32,43/55) Hyperbolic Matrix(155,-96,176,-109) (13/21,5/8) -> (7/8,1/1) Hyperbolic Matrix(507,-332,704,-461) (13/20,2/3) -> (18/25,49/68) Hyperbolic Matrix(331,-225,484,-329) (2/3,15/22) -> (15/22,13/19) Parabolic Matrix(1583,-1102,2024,-1409) (16/23,23/33) -> (43/55,18/23) Hyperbolic Matrix(1365,-961,1936,-1363) (19/27,31/44) -> (31/44,12/17) Parabolic Matrix(419,-296,528,-373) (12/17,17/24) -> (19/24,4/5) Hyperbolic Matrix(4421,-3186,5588,-4027) (49/68,31/43) -> (53/67,19/24) Hyperbolic Matrix(375,-289,484,-373) (10/13,17/22) -> (17/22,7/9) Parabolic Matrix(6073,-4761,7744,-6071) (29/37,69/88) -> (69/88,40/51) Parabolic Matrix(9571,-7569,12100,-9569) (34/43,87/110) -> (87/110,53/67) Parabolic Matrix(1629,-1369,1936,-1627) (21/25,37/44) -> (37/44,16/19) Parabolic Matrix(419,-361,484,-417) (6/7,19/22) -> (19/22,13/15) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,1,0,1) -> Matrix(1,0,-20,1) Matrix(67,-8,176,-21) -> Matrix(1,-2,-6,13) Matrix(219,-32,308,-45) -> Matrix(1,0,-12,1) Matrix(485,-76,836,-131) -> Matrix(13,4,-140,-43) Matrix(109,-19,132,-23) -> Matrix(3,2,-50,-33) Matrix(287,-53,352,-65) -> Matrix(13,6,-206,-95) Matrix(133,-26,220,-43) -> Matrix(11,4,-124,-45) Matrix(199,-42,308,-65) -> Matrix(3,2,-38,-25) Matrix(573,-124,1012,-219) -> Matrix(41,16,-428,-167) Matrix(639,-140,1100,-241) -> Matrix(7,2,-74,-21) Matrix(67,-16,88,-21) -> Matrix(7,2,-102,-29) Matrix(65,-17,88,-23) -> Matrix(7,2,-102,-29) Matrix(287,-79,396,-109) -> Matrix(41,10,-570,-139) Matrix(177,-50,308,-87) -> Matrix(35,8,-372,-85) Matrix(263,-76,308,-89) -> Matrix(1,0,-12,1) Matrix(485,-142,748,-219) -> Matrix(1,0,-8,1) Matrix(309,-92,440,-131) -> Matrix(19,4,-252,-53) Matrix(353,-108,572,-175) -> Matrix(17,4,-200,-47) Matrix(155,-48,352,-109) -> Matrix(47,10,-362,-77) Matrix(243,-86,308,-109) -> Matrix(11,2,-182,-33) Matrix(197,-71,308,-111) -> Matrix(59,10,-714,-121) Matrix(111,-41,176,-65) -> Matrix(37,6,-438,-71) Matrix(307,-116,352,-133) -> Matrix(25,4,-444,-71) Matrix(397,-152,572,-219) -> Matrix(25,4,-344,-55) Matrix(485,-188,792,-307) -> Matrix(131,20,-1500,-229) Matrix(857,-334,1188,-463) -> Matrix(67,10,-918,-137) Matrix(177,-70,220,-87) -> Matrix(27,4,-412,-61) Matrix(155,-64,264,-109) -> Matrix(71,10,-774,-109) Matrix(859,-360,1100,-461) -> Matrix(15,2,-218,-29) Matrix(705,-296,836,-351) -> Matrix(29,4,-428,-59) Matrix(221,-94,308,-131) -> Matrix(59,8,-804,-109) Matrix(793,-344,1012,-439) -> Matrix(121,16,-1868,-247) Matrix(615,-268,1012,-441) -> Matrix(121,16,-1384,-183) Matrix(483,-212,704,-309) -> Matrix(153,20,-2012,-263) Matrix(593,-266,836,-375) -> Matrix(47,6,-666,-85) Matrix(241,-109,440,-199) -> Matrix(143,18,-1438,-181) Matrix(23,-11,44,-21) -> Matrix(17,2,-162,-19) Matrix(373,-206,440,-243) -> Matrix(61,6,-966,-95) Matrix(243,-136,352,-197) -> Matrix(103,10,-1370,-133) Matrix(571,-322,704,-397) -> Matrix(125,12,-1948,-187) Matrix(1277,-724,1628,-923) -> Matrix(293,28,-4552,-435) Matrix(859,-496,1408,-813) -> Matrix(65,6,-726,-67) Matrix(1145,-664,1364,-791) -> Matrix(43,4,-828,-77) Matrix(2177,-1266,3520,-2047) -> Matrix(65,6,-726,-67) Matrix(287,-169,484,-285) -> Matrix(197,18,-2178,-199) Matrix(1739,-1060,2200,-1341) -> Matrix(23,2,-334,-29) Matrix(1189,-729,1936,-1187) -> Matrix(551,48,-6348,-553) Matrix(1167,-721,1672,-1033) -> Matrix(23,2,-334,-29) Matrix(4643,-2871,5940,-3673) -> Matrix(21,2,-326,-31) Matrix(155,-96,176,-109) -> Matrix(23,2,-426,-37) Matrix(507,-332,704,-461) -> Matrix(73,6,-1010,-83) Matrix(331,-225,484,-329) -> Matrix(181,14,-2366,-183) Matrix(1583,-1102,2024,-1409) -> Matrix(109,8,-1676,-123) Matrix(1365,-961,1936,-1363) -> Matrix(215,16,-2916,-217) Matrix(419,-296,528,-373) -> Matrix(27,2,-446,-33) Matrix(4421,-3186,5588,-4027) -> Matrix(27,2,-446,-33) Matrix(375,-289,484,-373) -> Matrix(149,10,-2250,-151) Matrix(6073,-4761,7744,-6071) -> Matrix(991,64,-15376,-993) Matrix(9571,-7569,12100,-9569) -> Matrix(29,2,-450,-31) Matrix(1629,-1369,1936,-1627) -> Matrix(1,0,8,1) Matrix(419,-361,484,-417) -> Matrix(101,6,-1734,-103) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 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: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 15 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 (0/1,1/1) 0 22 1/7 (-1/1,-2/3) 0 22 2/13 (-2/5,-1/3) 0 22 1/6 -1/1 2 11 2/11 -1/2 4 2 3/16 (-1/2,-3/7) 0 11 1/5 (-1/3,0/1) 0 22 3/14 -3/7 2 11 5/23 (-2/5,-1/3) 0 22 2/9 (-4/11,-1/3) 0 22 5/22 -1/3 10 1 1/4 (-1/3,-1/4) 0 11 3/11 -1/4 6 2 5/18 -5/21 2 11 2/7 (-2/9,-1/5) 0 22 7/24 (-1/4,-3/13) 0 11 5/17 (-3/13,-2/9) 0 22 13/44 -2/9 4 1 3/10 -1/5 2 11 4/13 (-2/9,-5/23) 0 22 1/3 (-1/5,-2/11) 0 22 7/20 (-3/17,-1/6) 0 11 6/17 (-2/11,-3/17) 0 22 5/14 -5/29 2 11 4/11 -1/6 8 2 3/8 (-1/6,-3/19) 0 11 25/66 -3/19 6 1 11/29 (-3/19,-8/51) 0 22 8/21 (-2/13,-1/7) 0 22 21/55 -1/6 2 2 13/34 -3/19 2 11 5/13 (-7/45,-2/13) 0 22 17/44 -2/13 12 1 7/18 -5/33 2 11 9/23 (-2/13,-1/7) 0 22 2/5 (-4/27,-1/7) 0 22 9/22 -1/7 18 1 5/12 (-1/7,-5/36) 0 11 23/55 -5/36 2 2 18/43 (-1/7,-4/29) 0 22 13/31 (-1/7,-6/43) 0 22 21/50 -9/65 2 11 37/88 -4/29 8 1 8/19 (-4/29,-7/51) 0 22 27/64 (-1/7,-3/22) 0 11 65/154 -1/7 2 1 19/45 (-1/7,-4/29) 0 22 11/26 -7/51 2 11 3/7 (-5/37,-2/15) 0 22 19/44 -2/15 16 1 13/30 -11/83 2 11 10/23 (-2/15,-7/53) 0 22 17/39 (-7/53,-12/91) 0 22 7/16 (-5/38,-3/23) 0 11 29/66 -3/23 14 1 11/25 (-3/23,-16/123) 0 22 4/9 (-4/31,-5/39) 0 22 13/29 (-7/55,-8/63) 0 22 9/20 (-9/71,-1/8) 0 11 5/11 -1/8 10 2 1/2 -1/9 2 11 1/0 0/1 20 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(67,-8,176,-21) (0/1,1/7) -> (11/29,8/21) Hyperbolic Matrix(197,-30,440,-67) (1/7,2/13) -> (4/9,13/29) Hyperbolic Matrix(351,-55,836,-131) (2/13,1/6) -> (13/31,21/50) Glide Reflection Matrix(23,-4,132,-23) (1/6,2/11) -> (1/6,2/11) Reflection Matrix(65,-12,352,-65) (2/11,3/16) -> (2/11,3/16) Reflection Matrix(307,-58,704,-133) (3/16,1/5) -> (17/39,7/16) Hyperbolic Matrix(109,-23,308,-65) (1/5,3/14) -> (6/17,5/14) Glide Reflection Matrix(439,-95,1012,-219) (3/14,5/23) -> (13/30,10/23) Glide Reflection Matrix(461,-101,1100,-241) (5/23,2/9) -> (18/43,13/31) Glide Reflection Matrix(89,-20,396,-89) (2/9,5/22) -> (2/9,5/22) Reflection Matrix(21,-5,88,-21) (5/22,1/4) -> (5/22,1/4) Reflection Matrix(23,-6,88,-23) (1/4,3/11) -> (1/4,3/11) Reflection Matrix(109,-30,396,-109) (3/11,5/18) -> (3/11,5/18) Reflection Matrix(131,-37,308,-87) (5/18,2/7) -> (11/26,3/7) Glide Reflection Matrix(375,-109,836,-243) (2/7,7/24) -> (13/29,9/20) Glide Reflection Matrix(263,-77,748,-219) (7/24,5/17) -> (7/20,6/17) Glide Reflection Matrix(441,-130,1496,-441) (5/17,13/44) -> (5/17,13/44) Reflection Matrix(131,-39,440,-131) (13/44,3/10) -> (13/44,3/10) Reflection Matrix(219,-67,572,-175) (3/10,4/13) -> (13/34,5/13) Glide Reflection Matrix(155,-48,352,-109) (4/13,1/3) -> (11/25,4/9) Hyperbolic Matrix(241,-83,572,-197) (1/3,7/20) -> (8/19,27/64) Glide Reflection Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(65,-24,176,-65) (4/11,3/8) -> (4/11,3/8) Reflection Matrix(199,-75,528,-199) (3/8,25/66) -> (3/8,25/66) Reflection Matrix(1451,-550,3828,-1451) (25/66,11/29) -> (25/66,11/29) Reflection Matrix(1473,-562,3520,-1343) (8/21,21/55) -> (23/55,18/43) Hyperbolic Matrix(1429,-546,3740,-1429) (21/55,13/34) -> (21/55,13/34) Reflection Matrix(441,-170,1144,-441) (5/13,17/44) -> (5/13,17/44) Reflection Matrix(307,-119,792,-307) (17/44,7/18) -> (17/44,7/18) Reflection Matrix(595,-232,1408,-549) (7/18,9/23) -> (19/45,11/26) Hyperbolic Matrix(441,-173,1012,-397) (9/23,2/5) -> (10/23,17/39) Glide Reflection Matrix(89,-36,220,-89) (2/5,9/22) -> (2/5,9/22) Reflection Matrix(109,-45,264,-109) (9/22,5/12) -> (9/22,5/12) Reflection Matrix(551,-230,1320,-551) (5/12,23/55) -> (5/12,23/55) Reflection Matrix(1849,-777,4400,-1849) (21/50,37/88) -> (21/50,37/88) Reflection Matrix(1407,-592,3344,-1407) (37/88,8/19) -> (37/88,8/19) Reflection Matrix(4159,-1755,9856,-4159) (27/64,65/154) -> (27/64,65/154) Reflection Matrix(5851,-2470,13860,-5851) (65/154,19/45) -> (65/154,19/45) Reflection Matrix(265,-114,616,-265) (3/7,19/44) -> (3/7,19/44) Reflection Matrix(571,-247,1320,-571) (19/44,13/30) -> (19/44,13/30) Reflection Matrix(463,-203,1056,-463) (7/16,29/66) -> (7/16,29/66) Reflection Matrix(1451,-638,3300,-1451) (29/66,11/25) -> (29/66,11/25) Reflection Matrix(199,-90,440,-199) (9/20,5/11) -> (9/20,5/11) Reflection Matrix(21,-10,44,-21) (5/11,1/2) -> (5/11,1/2) Reflection Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) 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) -> (0/1,1/1) Matrix(67,-8,176,-21) -> Matrix(1,-2,-6,13) Matrix(197,-30,440,-67) -> Matrix(13,6,-102,-47) Matrix(351,-55,836,-131) -> Matrix(13,4,-94,-29) Matrix(23,-4,132,-23) -> Matrix(3,2,-4,-3) (1/6,2/11) -> (-1/1,-1/2) Matrix(65,-12,352,-65) -> Matrix(13,6,-28,-13) (2/11,3/16) -> (-1/2,-3/7) Matrix(307,-58,704,-133) -> Matrix(29,12,-220,-91) Matrix(109,-23,308,-65) -> Matrix(3,2,-16,-11) Matrix(439,-95,1012,-219) -> Matrix(41,16,-310,-121) Matrix(461,-101,1100,-241) -> Matrix(7,2,-52,-15) Matrix(89,-20,396,-89) -> Matrix(23,8,-66,-23) (2/9,5/22) -> (-4/11,-1/3) Matrix(21,-5,88,-21) -> Matrix(7,2,-24,-7) (5/22,1/4) -> (-1/3,-1/4) Matrix(23,-6,88,-23) -> Matrix(7,2,-24,-7) (1/4,3/11) -> (-1/3,-1/4) Matrix(109,-30,396,-109) -> Matrix(41,10,-168,-41) (3/11,5/18) -> (-1/4,-5/21) Matrix(131,-37,308,-87) -> Matrix(35,8,-258,-59) Matrix(375,-109,836,-243) -> Matrix(23,6,-180,-47) Matrix(263,-77,748,-219) -> Matrix(-1,0,10,1) *** -> (-1/5,0/1) Matrix(441,-130,1496,-441) -> Matrix(53,12,-234,-53) (5/17,13/44) -> (-3/13,-2/9) Matrix(131,-39,440,-131) -> Matrix(19,4,-90,-19) (13/44,3/10) -> (-2/9,-1/5) Matrix(219,-67,572,-175) -> Matrix(17,4,-106,-25) Matrix(155,-48,352,-109) -> Matrix(47,10,-362,-77) Matrix(241,-83,572,-197) -> Matrix(57,10,-416,-73) Matrix(111,-40,308,-111) -> Matrix(59,10,-348,-59) (5/14,4/11) -> (-5/29,-1/6) Matrix(65,-24,176,-65) -> Matrix(37,6,-228,-37) (4/11,3/8) -> (-1/6,-3/19) Matrix(199,-75,528,-199) -> Matrix(37,6,-228,-37) (3/8,25/66) -> (-1/6,-3/19) Matrix(1451,-550,3828,-1451) -> Matrix(305,48,-1938,-305) (25/66,11/29) -> (-3/19,-8/51) Matrix(1473,-562,3520,-1343) -> Matrix(41,6,-294,-43) -1/7 Matrix(1429,-546,3740,-1429) -> Matrix(37,6,-228,-37) (21/55,13/34) -> (-1/6,-3/19) Matrix(441,-170,1144,-441) -> Matrix(181,28,-1170,-181) (5/13,17/44) -> (-7/45,-2/13) Matrix(307,-119,792,-307) -> Matrix(131,20,-858,-131) (17/44,7/18) -> (-2/13,-5/33) Matrix(595,-232,1408,-549) -> Matrix(41,6,-294,-43) -1/7 Matrix(441,-173,1012,-397) -> Matrix(105,16,-794,-121) Matrix(89,-36,220,-89) -> Matrix(55,8,-378,-55) (2/5,9/22) -> (-4/27,-1/7) Matrix(109,-45,264,-109) -> Matrix(71,10,-504,-71) (9/22,5/12) -> (-1/7,-5/36) Matrix(551,-230,1320,-551) -> Matrix(71,10,-504,-71) (5/12,23/55) -> (-1/7,-5/36) Matrix(1849,-777,4400,-1849) -> Matrix(521,72,-3770,-521) (21/50,37/88) -> (-9/65,-4/29) Matrix(1407,-592,3344,-1407) -> Matrix(407,56,-2958,-407) (37/88,8/19) -> (-4/29,-7/51) Matrix(4159,-1755,9856,-4159) -> Matrix(43,6,-308,-43) (27/64,65/154) -> (-1/7,-3/22) Matrix(5851,-2470,13860,-5851) -> Matrix(57,8,-406,-57) (65/154,19/45) -> (-1/7,-4/29) Matrix(265,-114,616,-265) -> Matrix(149,20,-1110,-149) (3/7,19/44) -> (-5/37,-2/15) Matrix(571,-247,1320,-571) -> Matrix(331,44,-2490,-331) (19/44,13/30) -> (-2/15,-11/83) Matrix(463,-203,1056,-463) -> Matrix(229,30,-1748,-229) (7/16,29/66) -> (-5/38,-3/23) Matrix(1451,-638,3300,-1451) -> Matrix(737,96,-5658,-737) (29/66,11/25) -> (-3/23,-16/123) Matrix(199,-90,440,-199) -> Matrix(143,18,-1136,-143) (9/20,5/11) -> (-9/71,-1/8) Matrix(21,-10,44,-21) -> Matrix(17,2,-144,-17) (5/11,1/2) -> (-1/8,-1/9) Matrix(-1,1,0,1) -> Matrix(-1,0,18,1) (1/2,1/0) -> (-1/9,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.