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): 576 Minimal number of generators: 97 Number of equivalence classes of cusps: 48 Genus: 25 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/1 -5/1 -9/2 -4/1 -3/1 -11/4 -2/1 -1/1 -11/18 -9/16 -1/2 -5/12 -4/11 -3/10 -1/4 -2/9 -1/8 0/1 1/6 1/4 3/11 2/5 1/2 5/9 13/22 8/13 3/4 1/1 15/13 5/4 4/3 3/2 13/8 7/4 9/5 2/1 5/2 11/4 3/1 7/2 11/3 4/1 9/2 5/1 11/2 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/2 -6/1 -1/1 -11/2 0/1 -5/1 1/0 -9/2 -1/1 -13/3 -3/4 -4/1 -1/1 -15/4 -1/2 0/1 -11/3 1/0 -7/2 0/1 -3/1 -1/2 -11/4 0/1 -19/7 1/0 -8/3 -1/1 -21/8 -1/4 0/1 -13/5 1/0 -18/7 -1/1 -5/2 0/1 -7/3 1/0 -16/7 1/1 -9/4 -1/1 1/0 -2/1 -1/1 -1/1 -1/2 1/0 -2/3 -1/1 -7/11 -1/2 -5/8 -1/1 -1/2 -18/29 -1/1 -13/21 -1/2 -8/13 -1/1 -11/18 -1/2 -14/23 -1/3 -3/5 -1/2 -7/12 -1/2 -1/3 -4/7 -1/3 -9/16 0/1 -14/25 -1/1 -5/9 -1/2 -11/20 -1/3 0/1 -6/11 -1/3 -1/2 0/1 -5/11 1/4 -9/20 0/1 1/2 -4/9 1/1 -7/16 0/1 1/1 -10/23 1/1 -3/7 1/0 -5/12 0/1 -7/17 1/2 -2/5 1/1 -7/18 0/1 -5/13 1/0 -13/34 1/1 -8/21 1/1 -3/8 1/1 1/0 -7/19 1/0 -4/11 1/0 -9/25 1/0 -5/14 -2/1 -6/17 -1/1 -1/3 1/0 -3/10 1/0 -5/17 1/0 -2/7 -1/1 -7/25 1/0 -5/18 -2/1 -3/11 1/0 -7/26 0/1 -4/15 -1/1 -1/4 -1/1 1/0 -3/13 1/0 -2/9 -1/1 -5/23 -1/2 -3/14 0/1 -4/19 -1/1 -1/5 1/0 -2/11 1/1 -1/6 -2/1 -1/7 -3/2 -1/8 -1/1 0/1 -1/1 1/6 -1/1 2/11 -1/1 1/5 -1/2 2/9 -1/1 1/4 -1/1 -1/2 4/15 -3/5 3/11 -1/2 5/18 -4/9 2/7 -1/3 5/17 -1/2 3/10 0/1 4/13 -1/3 1/3 -1/2 5/14 0/1 4/11 -1/3 7/19 -1/4 10/27 -1/5 3/8 -1/4 0/1 2/5 0/1 5/12 0/1 1/2 3/7 1/0 1/2 0/1 6/11 1/1 5/9 1/0 14/25 -1/1 9/16 -1/1 1/0 4/7 -1/1 7/12 -1/1 0/1 17/29 1/0 10/17 -1/1 13/22 -1/1 3/5 -1/2 11/18 0/1 8/13 0/1 13/21 1/6 5/8 0/1 1/2 17/27 1/2 12/19 1/1 7/11 1/0 2/3 -1/1 3/4 0/1 4/5 1/1 9/11 1/0 5/6 0/1 11/13 1/0 6/7 1/1 1/1 1/0 8/7 -1/1 15/13 1/0 7/6 -2/1 13/11 1/0 6/5 -1/1 11/9 -3/2 16/13 -1/1 5/4 -2/1 -1/1 4/3 -1/1 11/8 -1/1 -2/3 18/13 -1/1 25/18 -2/3 7/5 -1/2 3/2 0/1 17/11 1/0 14/9 -3/1 11/7 1/0 8/5 -1/1 13/8 -1/1 18/11 -1/1 23/14 -2/3 5/3 -1/2 22/13 0/1 17/10 0/1 12/7 1/1 19/11 1/0 7/4 0/1 1/0 16/9 1/1 9/5 1/0 11/6 -2/1 2/1 -1/1 5/2 -1/1 8/3 -1/1 27/10 -4/5 19/7 -3/4 30/11 -1/1 41/15 -3/4 11/4 -3/4 -2/3 14/5 -3/5 3/1 -1/2 13/4 0/1 1/0 23/7 1/0 33/10 0/1 43/13 1/0 10/3 -1/1 27/8 -1/1 17/5 -1/2 24/7 -1/1 7/2 0/1 18/5 -1/1 11/3 -1/2 1/0 26/7 -1/1 15/4 -1/1 0/1 4/1 -1/1 13/3 1/0 35/8 0/1 1/0 57/13 1/0 22/5 -1/1 9/2 0/1 23/5 1/0 14/3 -1/1 5/1 1/0 11/2 -2/1 6/1 -1/1 13/2 -2/3 7/1 -1/2 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,14,0,1) (-7/1,1/0) -> (7/1,1/0) Parabolic Matrix(13,82,16,101) (-7/1,-6/1) -> (4/5,9/11) Hyperbolic Matrix(43,240,12,67) (-6/1,-11/2) -> (7/2,18/5) Hyperbolic Matrix(7,36,20,103) (-11/2,-5/1) -> (1/3,5/14) Hyperbolic Matrix(35,162,-8,-37) (-5/1,-9/2) -> (-9/2,-13/3) Parabolic Matrix(43,184,68,291) (-13/3,-4/1) -> (12/19,7/11) Hyperbolic Matrix(71,268,40,151) (-4/1,-15/4) -> (7/4,16/9) Hyperbolic Matrix(47,174,-104,-385) (-15/4,-11/3) -> (-5/11,-9/20) Hyperbolic Matrix(5,18,-32,-115) (-11/3,-7/2) -> (-1/6,-1/7) Hyperbolic Matrix(17,58,12,41) (-7/2,-3/1) -> (7/5,3/2) Hyperbolic Matrix(87,242,-32,-89) (-3/1,-11/4) -> (-11/4,-19/7) Parabolic Matrix(67,180,16,43) (-19/7,-8/3) -> (4/1,13/3) Hyperbolic Matrix(145,382,52,137) (-8/3,-21/8) -> (11/4,14/5) Hyperbolic Matrix(129,338,208,545) (-21/8,-13/5) -> (13/21,5/8) Hyperbolic Matrix(107,276,88,227) (-13/5,-18/7) -> (6/5,11/9) Hyperbolic Matrix(19,48,36,91) (-18/7,-5/2) -> (1/2,6/11) Hyperbolic Matrix(9,22,20,49) (-5/2,-7/3) -> (3/7,1/2) Hyperbolic Matrix(55,126,-196,-449) (-7/3,-16/7) -> (-2/7,-7/25) Hyperbolic Matrix(23,52,88,199) (-16/7,-9/4) -> (1/4,4/15) Hyperbolic Matrix(35,78,-92,-205) (-9/4,-2/1) -> (-8/21,-3/8) Hyperbolic Matrix(3,4,-4,-5) (-2/1,-1/1) -> (-1/1,-2/3) Parabolic Matrix(121,78,76,49) (-2/3,-7/11) -> (11/7,8/5) Hyperbolic Matrix(35,22,-148,-93) (-7/11,-5/8) -> (-1/4,-3/13) Hyperbolic Matrix(373,232,664,413) (-5/8,-18/29) -> (14/25,9/16) Hyperbolic Matrix(997,618,292,181) (-18/29,-13/21) -> (17/5,24/7) Hyperbolic Matrix(107,66,368,227) (-13/21,-8/13) -> (2/7,5/17) Hyperbolic Matrix(395,242,-648,-397) (-8/13,-11/18) -> (-11/18,-14/23) Parabolic Matrix(211,128,572,347) (-14/23,-3/5) -> (7/19,10/27) Hyperbolic Matrix(99,58,-268,-157) (-3/5,-7/12) -> (-3/8,-7/19) Hyperbolic Matrix(31,18,136,79) (-7/12,-4/7) -> (2/9,1/4) Hyperbolic Matrix(287,162,-512,-289) (-4/7,-9/16) -> (-9/16,-14/25) Parabolic Matrix(379,212,320,179) (-14/25,-5/9) -> (13/11,6/5) Hyperbolic Matrix(403,222,688,379) (-5/9,-11/20) -> (7/12,17/29) Hyperbolic Matrix(685,376,184,101) (-11/20,-6/11) -> (26/7,15/4) Hyperbolic Matrix(211,114,124,67) (-6/11,-1/2) -> (17/10,12/7) Hyperbolic Matrix(127,58,208,95) (-1/2,-5/11) -> (3/5,11/18) Hyperbolic Matrix(227,102,612,275) (-9/20,-4/9) -> (10/27,3/8) Hyperbolic Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(371,162,300,131) (-7/16,-10/23) -> (16/13,5/4) Hyperbolic Matrix(295,128,348,151) (-10/23,-3/7) -> (11/13,6/7) Hyperbolic Matrix(119,50,-288,-121) (-3/7,-5/12) -> (-5/12,-7/17) Parabolic Matrix(73,30,236,97) (-7/17,-2/5) -> (4/13,1/3) Hyperbolic Matrix(91,36,48,19) (-2/5,-7/18) -> (11/6,2/1) Hyperbolic Matrix(227,88,276,107) (-7/18,-5/13) -> (9/11,5/6) Hyperbolic Matrix(271,104,456,175) (-5/13,-13/34) -> (13/22,3/5) Hyperbolic Matrix(613,234,1040,397) (-13/34,-8/21) -> (10/17,13/22) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(941,338,348,125) (-9/25,-5/14) -> (27/10,19/7) Hyperbolic Matrix(455,162,132,47) (-5/14,-6/17) -> (24/7,7/2) Hyperbolic Matrix(325,114,516,181) (-6/17,-1/3) -> (17/27,12/19) Hyperbolic Matrix(59,18,-200,-61) (-1/3,-3/10) -> (-3/10,-5/17) Parabolic Matrix(337,98,196,57) (-5/17,-2/7) -> (12/7,19/11) Hyperbolic Matrix(409,114,348,97) (-7/25,-5/18) -> (7/6,13/11) Hyperbolic Matrix(211,58,40,11) (-5/18,-3/11) -> (5/1,11/2) Hyperbolic Matrix(383,104,232,63) (-3/11,-7/26) -> (23/14,5/3) Hyperbolic Matrix(613,164,228,61) (-7/26,-4/15) -> (8/3,27/10) Hyperbolic Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(269,58,320,69) (-5/23,-3/14) -> (5/6,11/13) Hyperbolic Matrix(479,102,108,23) (-3/14,-4/19) -> (22/5,9/2) Hyperbolic Matrix(373,78,636,133) (-4/19,-1/5) -> (17/29,10/17) Hyperbolic Matrix(103,20,36,7) (-1/5,-2/11) -> (14/5,3/1) Hyperbolic Matrix(67,12,240,43) (-2/11,-1/6) -> (5/18,2/7) Hyperbolic Matrix(325,44,96,13) (-1/7,-1/8) -> (27/8,17/5) Hyperbolic Matrix(107,10,32,3) (-1/8,0/1) -> (10/3,27/8) Hyperbolic Matrix(13,-2,72,-11) (0/1,1/6) -> (1/6,2/11) Parabolic Matrix(201,-38,164,-31) (2/11,1/5) -> (11/9,16/13) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(409,-110,264,-71) (4/15,3/11) -> (17/11,14/9) Hyperbolic Matrix(339,-94,220,-61) (3/11,5/18) -> (3/2,17/11) Hyperbolic Matrix(291,-86,44,-13) (5/17,3/10) -> (13/2,7/1) Hyperbolic Matrix(505,-154,364,-111) (3/10,4/13) -> (18/13,25/18) Hyperbolic Matrix(505,-182,308,-111) (5/14,4/11) -> (18/11,23/14) Hyperbolic Matrix(163,-60,144,-53) (4/11,7/19) -> (1/1,8/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(127,-54,40,-17) (5/12,3/7) -> (3/1,13/4) Hyperbolic Matrix(181,-100,324,-179) (6/11,5/9) -> (5/9,14/25) Parabolic Matrix(293,-170,212,-123) (4/7,7/12) -> (11/8,18/13) Hyperbolic Matrix(617,-378,364,-223) (11/18,8/13) -> (22/13,17/10) Hyperbolic Matrix(527,-326,312,-193) (8/13,13/21) -> (5/3,22/13) Hyperbolic Matrix(1049,-660,240,-151) (5/8,17/27) -> (13/3,35/8) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(25,-18,32,-23) (2/3,3/4) -> (3/4,4/5) Parabolic Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(685,-786,156,-179) (8/7,15/13) -> (57/13,22/5) Hyperbolic Matrix(687,-796,208,-241) (15/13,7/6) -> (33/10,43/13) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(579,-806,176,-245) (25/18,7/5) -> (23/7,33/10) Hyperbolic Matrix(209,-338,128,-207) (8/5,13/8) -> (13/8,18/11) Parabolic Matrix(235,-408,72,-125) (19/11,7/4) -> (13/4,23/7) Hyperbolic Matrix(277,-494,60,-107) (16/9,9/5) -> (23/5,14/3) Hyperbolic Matrix(183,-334,40,-73) (9/5,11/6) -> (9/2,23/5) Hyperbolic Matrix(21,-50,8,-19) (2/1,5/2) -> (5/2,8/3) Parabolic Matrix(623,-1700,188,-513) (30/11,41/15) -> (43/13,10/3) Hyperbolic Matrix(753,-2062,172,-471) (41/15,11/4) -> (35/8,57/13) Hyperbolic Matrix(133,-484,36,-131) (18/5,11/3) -> (11/3,26/7) Parabolic Matrix(25,-144,4,-23) (11/2,6/1) -> (6/1,13/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,14,0,1) -> Matrix(1,0,0,1) Matrix(13,82,16,101) -> Matrix(1,0,2,1) Matrix(43,240,12,67) -> Matrix(1,0,0,1) Matrix(7,36,20,103) -> Matrix(1,0,-2,1) Matrix(35,162,-8,-37) -> Matrix(3,4,-4,-5) Matrix(43,184,68,291) -> Matrix(3,2,4,3) Matrix(71,268,40,151) -> Matrix(1,0,2,1) Matrix(47,174,-104,-385) -> Matrix(1,0,4,1) Matrix(5,18,-32,-115) -> Matrix(3,2,-2,-1) Matrix(17,58,12,41) -> Matrix(1,0,0,1) Matrix(87,242,-32,-89) -> Matrix(1,0,2,1) Matrix(67,180,16,43) -> Matrix(1,0,0,1) Matrix(145,382,52,137) -> Matrix(5,2,-8,-3) Matrix(129,338,208,545) -> Matrix(1,0,6,1) Matrix(107,276,88,227) -> Matrix(3,2,-2,-1) Matrix(19,48,36,91) -> Matrix(1,0,2,1) Matrix(9,22,20,49) -> Matrix(1,0,0,1) Matrix(55,126,-196,-449) -> Matrix(1,-2,0,1) Matrix(23,52,88,199) -> Matrix(1,2,-2,-3) Matrix(35,78,-92,-205) -> Matrix(1,2,0,1) Matrix(3,4,-4,-5) -> Matrix(1,0,0,1) Matrix(121,78,76,49) -> Matrix(3,2,-2,-1) Matrix(35,22,-148,-93) -> Matrix(3,2,-2,-1) Matrix(373,232,664,413) -> Matrix(3,2,-2,-1) Matrix(997,618,292,181) -> Matrix(1,0,0,1) Matrix(107,66,368,227) -> Matrix(3,2,-8,-5) Matrix(395,242,-648,-397) -> Matrix(3,2,-8,-5) Matrix(211,128,572,347) -> Matrix(1,0,-2,1) Matrix(99,58,-268,-157) -> Matrix(5,2,2,1) Matrix(31,18,136,79) -> Matrix(5,2,-8,-3) Matrix(287,162,-512,-289) -> Matrix(1,0,2,1) Matrix(379,212,320,179) -> Matrix(3,2,-2,-1) Matrix(403,222,688,379) -> Matrix(1,0,2,1) Matrix(685,376,184,101) -> Matrix(1,0,2,1) Matrix(211,114,124,67) -> Matrix(1,0,4,1) Matrix(127,58,208,95) -> Matrix(1,0,-6,1) Matrix(227,102,612,275) -> Matrix(1,0,-6,1) Matrix(199,88,52,23) -> Matrix(1,0,-2,1) Matrix(371,162,300,131) -> Matrix(1,-2,0,1) Matrix(295,128,348,151) -> Matrix(1,0,0,1) Matrix(119,50,-288,-121) -> Matrix(1,0,2,1) Matrix(73,30,236,97) -> Matrix(1,0,-4,1) Matrix(91,36,48,19) -> Matrix(1,-2,0,1) Matrix(227,88,276,107) -> Matrix(1,0,0,1) Matrix(271,104,456,175) -> Matrix(1,0,-2,1) Matrix(613,234,1040,397) -> Matrix(1,-2,0,1) Matrix(175,64,-484,-177) -> Matrix(1,-6,0,1) Matrix(941,338,348,125) -> Matrix(3,10,-4,-13) Matrix(455,162,132,47) -> Matrix(1,2,-2,-3) Matrix(325,114,516,181) -> Matrix(1,0,2,1) Matrix(59,18,-200,-61) -> Matrix(1,-2,0,1) Matrix(337,98,196,57) -> Matrix(1,2,0,1) Matrix(409,114,348,97) -> Matrix(1,0,0,1) Matrix(211,58,40,11) -> Matrix(1,0,0,1) Matrix(383,104,232,63) -> Matrix(1,2,-2,-3) Matrix(613,164,228,61) -> Matrix(3,4,-4,-5) Matrix(151,40,268,71) -> Matrix(1,0,0,1) Matrix(71,16,-324,-73) -> Matrix(1,2,-2,-3) Matrix(269,58,320,69) -> Matrix(1,0,2,1) Matrix(479,102,108,23) -> Matrix(1,0,0,1) Matrix(373,78,636,133) -> Matrix(1,0,0,1) Matrix(103,20,36,7) -> Matrix(1,2,-2,-3) Matrix(67,12,240,43) -> Matrix(1,-2,-2,5) Matrix(325,44,96,13) -> Matrix(3,4,-4,-5) Matrix(107,10,32,3) -> Matrix(1,0,0,1) Matrix(13,-2,72,-11) -> Matrix(1,2,-2,-3) Matrix(201,-38,164,-31) -> Matrix(5,4,-4,-3) Matrix(115,-24,24,-5) -> Matrix(3,2,-2,-1) Matrix(409,-110,264,-71) -> Matrix(11,6,-2,-1) Matrix(339,-94,220,-61) -> Matrix(9,4,2,1) Matrix(291,-86,44,-13) -> Matrix(5,2,-8,-3) Matrix(505,-154,364,-111) -> Matrix(5,2,-8,-3) Matrix(505,-182,308,-111) -> Matrix(5,2,-8,-3) Matrix(163,-60,144,-53) -> Matrix(7,2,-4,-1) Matrix(41,-16,100,-39) -> Matrix(1,0,6,1) Matrix(127,-54,40,-17) -> Matrix(1,0,-2,1) Matrix(181,-100,324,-179) -> Matrix(1,-2,0,1) Matrix(293,-170,212,-123) -> Matrix(1,2,-2,-3) Matrix(617,-378,364,-223) -> Matrix(1,0,8,1) Matrix(527,-326,312,-193) -> Matrix(1,0,-8,1) Matrix(1049,-660,240,-151) -> Matrix(1,0,-2,1) Matrix(187,-120,120,-77) -> Matrix(1,-2,0,1) Matrix(25,-18,32,-23) -> Matrix(1,0,2,1) Matrix(163,-144,60,-53) -> Matrix(3,-2,-4,3) Matrix(685,-786,156,-179) -> Matrix(1,0,0,1) Matrix(687,-796,208,-241) -> Matrix(1,2,0,1) Matrix(49,-64,36,-47) -> Matrix(3,4,-4,-5) Matrix(579,-806,176,-245) -> Matrix(3,2,-2,-1) Matrix(209,-338,128,-207) -> Matrix(3,4,-4,-5) Matrix(235,-408,72,-125) -> Matrix(1,0,0,1) Matrix(277,-494,60,-107) -> Matrix(1,-2,0,1) Matrix(183,-334,40,-73) -> Matrix(1,2,0,1) Matrix(21,-50,8,-19) -> Matrix(3,4,-4,-5) Matrix(623,-1700,188,-513) -> Matrix(5,4,-4,-3) Matrix(753,-2062,172,-471) -> Matrix(3,2,4,3) Matrix(133,-484,36,-131) -> Matrix(1,0,0,1) Matrix(25,-144,4,-23) -> Matrix(3,4,-4,-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): 21 Degree of the the map X: 21 Degree of the the map Y: 96 ----------------------------------------------------------------------- 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 -1/1 (-1/1,0/1) 0 2 -1/2 0/1 2 14 -4/9 1/1 1 14 -7/16 (0/1,1/1) 0 14 -3/7 1/0 1 14 -5/12 0/1 2 2 -7/17 1/2 1 14 -2/5 1/1 1 14 -3/8 (1/1,1/0) 0 14 -4/11 1/0 3 2 -5/14 -2/1 2 14 -1/3 1/0 1 14 -3/10 1/0 2 2 -5/17 1/0 1 14 -2/7 -1/1 1 14 -3/11 1/0 1 14 -4/15 -1/1 1 14 -1/4 (-1/1,1/0) 0 14 -2/9 -1/1 1 2 -3/14 0/1 2 14 -1/5 1/0 1 14 0/1 -1/1 1 14 1/6 -1/1 2 2 2/11 -1/1 1 14 1/5 -1/2 1 14 2/9 -1/1 1 14 1/4 (-1/1,-1/2) 0 14 3/11 -1/2 5 2 5/18 -4/9 2 14 2/7 -1/3 1 14 5/17 -1/2 1 14 3/10 0/1 2 14 4/13 -1/3 1 14 1/3 -1/2 1 14 4/11 -1/3 1 14 7/19 -1/4 1 14 3/8 (-1/4,0/1) 0 14 2/5 0/1 3 2 1/2 0/1 2 14 5/9 1/0 1 2 9/16 (-1/1,1/0) 0 14 4/7 -1/1 1 14 7/12 (-1/1,0/1) 0 14 17/29 1/0 1 14 10/17 -1/1 1 14 3/5 -1/2 1 14 11/18 0/1 2 14 8/13 0/1 8 2 5/8 (0/1,1/2) 0 14 7/11 1/0 1 14 2/3 -1/1 1 14 3/4 0/1 2 2 4/5 1/1 1 14 5/6 0/1 2 14 11/13 1/0 1 14 6/7 1/1 1 14 1/1 1/0 1 14 8/7 -1/1 1 14 15/13 1/0 2 2 7/6 -2/1 2 14 6/5 -1/1 1 14 5/4 (-2/1,-1/1) 0 14 4/3 -1/1 2 2 3/2 0/1 2 14 14/9 -3/1 1 14 11/7 1/0 1 14 8/5 -1/1 1 14 13/8 -1/1 4 2 18/11 -1/1 1 14 5/3 -1/2 1 14 17/10 0/1 2 14 12/7 1/1 1 14 19/11 1/0 1 14 7/4 (0/1,1/0) 0 14 9/5 1/0 2 2 11/6 -2/1 2 14 2/1 -1/1 1 14 5/2 -1/1 4 2 8/3 -1/1 1 14 27/10 -4/5 2 14 19/7 -3/4 1 14 30/11 -1/1 1 14 41/15 -3/4 2 2 11/4 (-3/4,-2/3) 0 14 3/1 -1/2 1 14 10/3 -1/1 1 14 17/5 -1/2 1 14 24/7 -1/1 1 14 7/2 0/1 2 14 11/3 (-1/1,0/1) 0 2 15/4 (-1/1,0/1) 0 14 4/1 -1/1 1 14 9/2 0/1 2 14 14/3 -1/1 1 14 5/1 1/0 1 14 11/2 -2/1 2 14 6/1 -1/1 2 2 1/0 (-1/1,0/1) 0 14 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(3,2,-4,-3) (-1/1,-1/2) -> (-1/1,-1/2) Reflection Matrix(177,80,104,47) (-1/2,-4/9) -> (17/10,12/7) Glide Reflection Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(321,140,548,239) (-7/16,-3/7) -> (7/12,17/29) Glide Reflection Matrix(119,50,-288,-121) (-3/7,-5/12) -> (-5/12,-7/17) Parabolic Matrix(73,30,236,97) (-7/17,-2/5) -> (4/13,1/3) Hyperbolic Matrix(21,8,92,35) (-2/5,-3/8) -> (2/9,1/4) Glide Reflection Matrix(65,24,-176,-65) (-3/8,-4/11) -> (-3/8,-4/11) Reflection Matrix(111,40,-308,-111) (-4/11,-5/14) -> (-4/11,-5/14) Reflection Matrix(347,122,128,45) (-5/14,-1/3) -> (27/10,19/7) Glide Reflection Matrix(59,18,-200,-61) (-1/3,-3/10) -> (-3/10,-5/17) Parabolic Matrix(337,98,196,57) (-5/17,-2/7) -> (12/7,19/11) Hyperbolic Matrix(57,16,196,55) (-2/7,-3/11) -> (2/7,5/17) Glide Reflection Matrix(519,140,152,41) (-3/11,-4/15) -> (17/5,24/7) Glide Reflection Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(17,4,-72,-17) (-1/4,-2/9) -> (-1/4,-2/9) Reflection Matrix(55,12,-252,-55) (-2/9,-3/14) -> (-2/9,-3/14) Reflection Matrix(179,38,212,45) (-3/14,-1/5) -> (5/6,11/13) Glide Reflection Matrix(51,8,32,5) (-1/5,0/1) -> (11/7,8/5) Glide Reflection Matrix(13,-2,72,-11) (0/1,1/6) -> (1/6,2/11) Parabolic Matrix(83,-16,140,-27) (2/11,1/5) -> (10/17,3/5) Glide Reflection Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic 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(273,-76,176,-49) (5/18,2/7) -> (3/2,14/9) Glide Reflection Matrix(237,-70,44,-13) (5/17,3/10) -> (5/1,11/2) Glide Reflection Matrix(151,-46,128,-39) (3/10,4/13) -> (7/6,6/5) Glide Reflection Matrix(63,-22,20,-7) (1/3,4/11) -> (3/1,10/3) Glide Reflection Matrix(163,-60,144,-53) (4/11,7/19) -> (1/1,8/7) Hyperbolic Matrix(285,-106,164,-61) (7/19,3/8) -> (19/11,7/4) Glide Reflection Matrix(31,-12,80,-31) (3/8,2/5) -> (3/8,2/5) Reflection Matrix(9,-4,20,-9) (2/5,1/2) -> (2/5,1/2) Reflection Matrix(19,-10,36,-19) (1/2,5/9) -> (1/2,5/9) Reflection Matrix(161,-90,288,-161) (5/9,9/16) -> (5/9,9/16) Reflection Matrix(107,-62,88,-51) (4/7,7/12) -> (6/5,5/4) Glide Reflection Matrix(361,-212,424,-249) (17/29,10/17) -> (11/13,6/7) Glide Reflection Matrix(175,-106,104,-63) (3/5,11/18) -> (5/3,17/10) Glide Reflection Matrix(287,-176,468,-287) (11/18,8/13) -> (11/18,8/13) Reflection Matrix(129,-80,208,-129) (8/13,5/8) -> (8/13,5/8) Reflection Matrix(145,-92,52,-33) (5/8,7/11) -> (11/4,3/1) Glide Reflection Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(25,-18,32,-23) (2/3,3/4) -> (3/4,4/5) Parabolic Matrix(69,-56,16,-13) (4/5,5/6) -> (4/1,9/2) Glide Reflection Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(677,-778,248,-285) (8/7,15/13) -> (30/11,41/15) Glide Reflection Matrix(181,-210,156,-181) (15/13,7/6) -> (15/13,7/6) Reflection Matrix(31,-40,24,-31) (5/4,4/3) -> (5/4,4/3) Reflection Matrix(17,-24,12,-17) (4/3,3/2) -> (4/3,3/2) Reflection Matrix(209,-338,128,-207) (8/5,13/8) -> (13/8,18/11) Parabolic Matrix(217,-356,64,-105) (18/11,5/3) -> (10/3,17/5) Glide Reflection Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(109,-198,60,-109) (9/5,11/6) -> (9/5,11/6) Reflection Matrix(93,-172,20,-37) (11/6,2/1) -> (9/2,14/3) Glide Reflection Matrix(21,-50,8,-19) (2/1,5/2) -> (5/2,8/3) Parabolic Matrix(261,-704,76,-205) (8/3,27/10) -> (24/7,7/2) Glide Reflection Matrix(329,-902,120,-329) (41/15,11/4) -> (41/15,11/4) Reflection Matrix(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(89,-330,24,-89) (11/3,15/4) -> (11/3,15/4) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(-1,12,0,1) (6/1,1/0) -> (6/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(3,2,-4,-3) -> Matrix(-1,0,2,1) (-1/1,-1/2) -> (-1/1,0/1) Matrix(177,80,104,47) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(199,88,52,23) -> Matrix(1,0,-2,1) 0/1 Matrix(321,140,548,239) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(119,50,-288,-121) -> Matrix(1,0,2,1) 0/1 Matrix(73,30,236,97) -> Matrix(1,0,-4,1) 0/1 Matrix(21,8,92,35) -> Matrix(1,-2,-2,3) Matrix(65,24,-176,-65) -> Matrix(-1,2,0,1) (-3/8,-4/11) -> (1/1,1/0) Matrix(111,40,-308,-111) -> Matrix(1,4,0,-1) (-4/11,-5/14) -> (-2/1,1/0) Matrix(347,122,128,45) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(59,18,-200,-61) -> Matrix(1,-2,0,1) 1/0 Matrix(337,98,196,57) -> Matrix(1,2,0,1) 1/0 Matrix(57,16,196,55) -> Matrix(1,2,-2,-5) Matrix(519,140,152,41) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(151,40,268,71) -> Matrix(1,0,0,1) Matrix(17,4,-72,-17) -> Matrix(1,2,0,-1) (-1/4,-2/9) -> (-1/1,1/0) Matrix(55,12,-252,-55) -> Matrix(-1,0,2,1) (-2/9,-3/14) -> (-1/1,0/1) Matrix(179,38,212,45) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(51,8,32,5) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(13,-2,72,-11) -> Matrix(1,2,-2,-3) -1/1 Matrix(83,-16,140,-27) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(115,-24,24,-5) -> Matrix(3,2,-2,-1) -1/1 Matrix(23,-6,88,-23) -> Matrix(3,2,-4,-3) (1/4,3/11) -> (-1/1,-1/2) Matrix(109,-30,396,-109) -> Matrix(17,8,-36,-17) (3/11,5/18) -> (-1/2,-4/9) Matrix(273,-76,176,-49) -> Matrix(9,4,-2,-1) Matrix(237,-70,44,-13) -> Matrix(5,2,-2,-1) Matrix(151,-46,128,-39) -> Matrix(5,2,-2,-1) Matrix(63,-22,20,-7) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(163,-60,144,-53) -> Matrix(7,2,-4,-1) Matrix(285,-106,164,-61) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(31,-12,80,-31) -> Matrix(-1,0,8,1) (3/8,2/5) -> (-1/4,0/1) Matrix(9,-4,20,-9) -> Matrix(-1,0,2,1) (2/5,1/2) -> (-1/1,0/1) Matrix(19,-10,36,-19) -> Matrix(1,0,0,-1) (1/2,5/9) -> (0/1,1/0) Matrix(161,-90,288,-161) -> Matrix(1,2,0,-1) (5/9,9/16) -> (-1/1,1/0) Matrix(107,-62,88,-51) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(361,-212,424,-249) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(175,-106,104,-63) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(287,-176,468,-287) -> Matrix(-1,0,12,1) (11/18,8/13) -> (-1/6,0/1) Matrix(129,-80,208,-129) -> Matrix(1,0,4,-1) (8/13,5/8) -> (0/1,1/2) Matrix(145,-92,52,-33) -> Matrix(1,-2,-2,3) Matrix(187,-120,120,-77) -> Matrix(1,-2,0,1) 1/0 Matrix(25,-18,32,-23) -> Matrix(1,0,2,1) 0/1 Matrix(69,-56,16,-13) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(163,-144,60,-53) -> Matrix(3,-2,-4,3) Matrix(677,-778,248,-285) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(181,-210,156,-181) -> Matrix(1,4,0,-1) (15/13,7/6) -> (-2/1,1/0) Matrix(31,-40,24,-31) -> Matrix(3,4,-2,-3) (5/4,4/3) -> (-2/1,-1/1) Matrix(17,-24,12,-17) -> Matrix(-1,0,2,1) (4/3,3/2) -> (-1/1,0/1) Matrix(209,-338,128,-207) -> Matrix(3,4,-4,-5) -1/1 Matrix(217,-356,64,-105) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(71,-126,40,-71) -> Matrix(1,0,0,-1) (7/4,9/5) -> (0/1,1/0) Matrix(109,-198,60,-109) -> Matrix(1,4,0,-1) (9/5,11/6) -> (-2/1,1/0) Matrix(93,-172,20,-37) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(21,-50,8,-19) -> Matrix(3,4,-4,-5) -1/1 Matrix(261,-704,76,-205) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(329,-902,120,-329) -> Matrix(17,12,-24,-17) (41/15,11/4) -> (-3/4,-2/3) Matrix(43,-154,12,-43) -> Matrix(-1,0,2,1) (7/2,11/3) -> (-1/1,0/1) Matrix(89,-330,24,-89) -> Matrix(-1,0,2,1) (11/3,15/4) -> (-1/1,0/1) Matrix(23,-132,4,-23) -> Matrix(3,4,-2,-3) (11/2,6/1) -> (-2/1,-1/1) Matrix(-1,12,0,1) -> Matrix(-1,0,2,1) (6/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.