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): 432 Minimal number of generators: 73 Number of equivalence classes of cusps: 40 Genus: 17 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -9/2 -4/1 -15/4 -27/8 -3/1 -9/4 -2/1 -3/2 -6/5 0/1 1/1 6/5 9/7 18/13 3/2 18/11 9/5 2/1 9/4 5/2 18/7 3/1 27/8 7/2 18/5 15/4 72/19 4/1 9/2 19/4 5/1 11/2 6/1 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 -1/2 1/0 -7/1 -1/1 1/0 -13/2 -2/1 1/0 -6/1 -1/1 -11/2 -2/1 1/0 -5/1 -2/1 -1/1 -9/2 -1/1 -13/3 -1/1 -4/5 -4/1 -1/2 1/0 -19/5 -1/1 0/1 -15/4 0/1 2/1 -11/3 1/1 1/0 -18/5 1/0 -7/2 -2/1 1/0 -17/5 -1/1 0/1 -27/8 1/0 -10/3 -5/2 1/0 -3/1 -2/1 -11/4 -3/2 -4/3 -30/11 -1/1 -19/7 -2/1 -5/3 -27/10 -3/2 -8/3 -3/2 -5/4 -29/11 -3/2 -1/1 -21/8 -2/1 -4/3 -55/21 -7/5 -4/3 -34/13 -3/2 -5/4 -13/5 -4/3 -1/1 -18/7 -1/1 -5/2 -2/1 -1/1 -12/5 -3/2 -19/8 -2/1 -3/2 -7/3 -3/2 -1/1 -9/4 -3/2 -11/5 -3/2 -7/5 -13/6 -3/2 -4/3 -2/1 -3/2 -5/4 -13/7 -4/3 -1/1 -11/6 -3/2 -4/3 -9/5 -4/3 -7/4 -4/3 -5/4 -12/7 -5/4 -17/10 -5/4 -6/5 -22/13 -7/6 -9/8 -5/3 -4/3 -1/1 -18/11 -4/3 -13/8 -4/3 -5/4 -34/21 -3/2 -5/4 -21/13 -4/3 -8/5 -3/2 -5/4 -3/2 -4/3 -6/5 -10/7 -3/2 -5/4 -37/26 -4/3 -1/1 -27/19 -4/3 -17/12 -4/3 -5/4 -7/5 -9/7 -5/4 -18/13 -5/4 -11/8 -5/4 -26/21 -15/11 -16/13 -34/25 -5/4 -37/30 -53/39 -53/43 -16/13 -72/53 -16/13 -19/14 -16/13 -27/22 -4/3 -5/4 -17/14 -17/13 -11/9 -6/5 -30/23 -23/19 -13/10 -29/24 -6/5 -9/7 -6/5 -5/4 -6/5 -13/11 -6/5 -7/6 -7/6 -6/5 -7/6 -1/1 -8/7 -1/1 0/1 -1/1 1/1 -1/1 -8/9 6/5 -7/8 5/4 -13/15 -6/7 9/7 -6/7 13/10 -6/7 -29/34 17/13 -6/7 -11/13 4/3 -17/20 -5/6 11/8 -26/31 -5/6 18/13 -5/6 7/5 -5/6 -9/11 3/2 -6/7 -4/5 11/7 -5/6 -9/11 19/12 -5/6 -4/5 27/17 -4/5 8/5 -5/6 -3/4 13/8 -5/6 -4/5 18/11 -4/5 5/3 -1/1 -4/5 17/10 -6/7 -5/6 12/7 -5/6 19/11 -1/1 -6/7 7/4 -5/6 -4/5 9/5 -4/5 11/6 -4/5 -3/4 2/1 -5/6 -3/4 9/4 -3/4 16/7 -3/4 -7/10 23/10 -3/4 -2/3 7/3 -1/1 -3/4 19/8 -3/4 -2/3 12/5 -3/4 5/2 -1/1 -2/3 18/7 -1/1 13/5 -1/1 -4/5 34/13 -5/6 -3/4 21/8 -4/5 -2/3 8/3 -5/6 -3/4 27/10 -3/4 19/7 -5/7 -2/3 11/4 -4/5 -3/4 14/5 -3/4 -13/18 17/6 -7/10 -2/3 3/1 -2/3 19/6 -3/4 -2/3 16/5 -5/8 -1/2 13/4 -2/3 -1/2 10/3 -5/8 -1/2 27/8 -1/2 17/5 -1/1 0/1 7/2 -2/3 -1/2 18/5 -1/2 11/3 -1/2 -1/3 26/7 -1/2 -1/4 15/4 -2/5 0/1 34/9 -1/2 -1/4 53/14 -1/6 0/1 72/19 0/1 19/5 -1/1 0/1 4/1 -1/2 1/0 9/2 -1/1 14/3 -7/8 -5/6 19/4 -4/5 -3/4 5/1 -1/1 -2/3 16/3 -3/4 -1/2 11/2 -2/3 -1/2 17/3 -1/3 0/1 6/1 -1/1 19/3 -5/7 -2/3 13/2 -2/3 -1/2 7/1 -1/1 -1/2 8/1 -1/2 1/0 9/1 0/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(37,306,-26,-215) (-8/1,1/0) -> (-10/7,-37/26) Hyperbolic Matrix(37,270,10,73) (-8/1,-7/1) -> (11/3,26/7) Hyperbolic Matrix(37,252,16,109) (-7/1,-13/2) -> (23/10,7/3) Hyperbolic Matrix(73,468,-56,-359) (-13/2,-6/1) -> (-30/23,-13/10) Hyperbolic Matrix(71,396,-26,-145) (-6/1,-11/2) -> (-11/4,-30/11) Hyperbolic Matrix(37,198,-20,-107) (-11/2,-5/1) -> (-13/7,-11/6) Hyperbolic Matrix(35,162,-8,-37) (-5/1,-9/2) -> (-9/2,-13/3) Parabolic Matrix(71,306,-42,-181) (-13/3,-4/1) -> (-22/13,-5/3) Hyperbolic Matrix(37,144,28,109) (-4/1,-19/5) -> (17/13,4/3) Hyperbolic Matrix(325,1224,-124,-467) (-19/5,-15/4) -> (-21/8,-55/21) Hyperbolic Matrix(179,666,-68,-253) (-15/4,-11/3) -> (-29/11,-21/8) Hyperbolic Matrix(109,396,30,109) (-11/3,-18/5) -> (18/5,11/3) Hyperbolic Matrix(71,252,20,71) (-18/5,-7/2) -> (7/2,18/5) Hyperbolic Matrix(73,252,42,145) (-7/2,-17/5) -> (19/11,7/4) Hyperbolic Matrix(287,972,106,359) (-17/5,-27/8) -> (27/10,19/7) Hyperbolic Matrix(145,486,54,181) (-27/8,-10/3) -> (8/3,27/10) Hyperbolic Matrix(71,234,-44,-145) (-10/3,-3/1) -> (-21/13,-8/5) Hyperbolic Matrix(71,198,-52,-145) (-3/1,-11/4) -> (-11/8,-15/11) Hyperbolic Matrix(397,1080,-304,-827) (-30/11,-19/7) -> (-17/13,-30/23) Hyperbolic Matrix(359,972,106,287) (-19/7,-27/10) -> (27/8,17/5) Hyperbolic Matrix(181,486,54,145) (-27/10,-8/3) -> (10/3,27/8) Hyperbolic Matrix(109,288,14,37) (-8/3,-29/11) -> (7/1,8/1) Hyperbolic Matrix(1403,3672,-1032,-2701) (-55/21,-34/13) -> (-34/25,-53/39) Hyperbolic Matrix(145,378,28,73) (-34/13,-13/5) -> (5/1,16/3) Hyperbolic Matrix(181,468,70,181) (-13/5,-18/7) -> (18/7,13/5) Hyperbolic Matrix(71,180,28,71) (-18/7,-5/2) -> (5/2,18/7) Hyperbolic Matrix(37,90,30,73) (-5/2,-12/5) -> (6/5,5/4) Hyperbolic Matrix(181,432,106,253) (-12/5,-19/8) -> (17/10,12/7) Hyperbolic Matrix(145,342,92,217) (-19/8,-7/3) -> (11/7,19/12) Hyperbolic Matrix(71,162,-32,-73) (-7/3,-9/4) -> (-9/4,-11/5) Parabolic Matrix(107,234,16,35) (-11/5,-13/6) -> (13/2,7/1) Hyperbolic Matrix(109,234,34,73) (-13/6,-2/1) -> (16/5,13/4) Hyperbolic Matrix(251,468,96,179) (-2/1,-13/7) -> (13/5,34/13) Hyperbolic Matrix(109,198,60,109) (-11/6,-9/5) -> (9/5,11/6) Hyperbolic Matrix(71,126,40,71) (-9/5,-7/4) -> (7/4,9/5) Hyperbolic Matrix(73,126,-62,-107) (-7/4,-12/7) -> (-6/5,-7/6) Hyperbolic Matrix(253,432,106,181) (-12/7,-17/10) -> (19/8,12/5) Hyperbolic Matrix(361,612,128,217) (-17/10,-22/13) -> (14/5,17/6) Hyperbolic Matrix(109,180,66,109) (-5/3,-18/11) -> (18/11,5/3) Hyperbolic Matrix(287,468,176,287) (-18/11,-13/8) -> (13/8,18/11) Hyperbolic Matrix(611,990,266,431) (-13/8,-34/21) -> (16/7,23/10) Hyperbolic Matrix(757,1224,-556,-899) (-34/21,-21/13) -> (-15/11,-34/25) Hyperbolic Matrix(35,54,-24,-37) (-8/5,-3/2) -> (-3/2,-10/7) Parabolic Matrix(253,360,26,37) (-37/26,-27/19) -> (9/1,1/0) Hyperbolic Matrix(685,972,432,613) (-27/19,-17/12) -> (19/12,27/17) Hyperbolic Matrix(179,252,76,107) (-17/12,-7/5) -> (7/3,19/8) Hyperbolic Matrix(181,252,130,181) (-7/5,-18/13) -> (18/13,7/5) Hyperbolic Matrix(287,396,208,287) (-18/13,-11/8) -> (11/8,18/13) Hyperbolic Matrix(3815,5184,1006,1367) (-53/39,-72/53) -> (72/19,19/5) Hyperbolic Matrix(3817,5184,1008,1369) (-72/53,-19/14) -> (53/14,72/19) Hyperbolic Matrix(253,342,54,73) (-19/14,-4/3) -> (14/3,19/4) Hyperbolic Matrix(109,144,28,37) (-4/3,-17/13) -> (19/5,4/1) Hyperbolic Matrix(181,234,140,181) (-13/10,-9/7) -> (9/7,13/10) Hyperbolic Matrix(71,90,56,71) (-9/7,-5/4) -> (5/4,9/7) Hyperbolic Matrix(73,90,30,37) (-5/4,-6/5) -> (12/5,5/2) Hyperbolic Matrix(109,126,32,37) (-7/6,-1/1) -> (17/5,7/2) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(107,-126,62,-73) (1/1,6/5) -> (12/7,19/11) Hyperbolic Matrix(359,-468,56,-73) (13/10,17/13) -> (19/3,13/2) Hyperbolic Matrix(145,-198,52,-71) (4/3,11/8) -> (11/4,14/5) Hyperbolic Matrix(37,-54,24,-35) (7/5,3/2) -> (3/2,11/7) Parabolic Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(107,-180,22,-37) (5/3,17/10) -> (19/4,5/1) Hyperbolic Matrix(107,-198,20,-37) (11/6,2/1) -> (16/3,11/2) Hyperbolic Matrix(73,-162,32,-71) (2/1,9/4) -> (9/4,16/7) Parabolic Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(253,-666,68,-179) (21/8,8/3) -> (26/7,15/4) Hyperbolic Matrix(145,-396,26,-71) (19/7,11/4) -> (11/2,17/3) Hyperbolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(469,-1494,124,-395) (19/6,16/5) -> (34/9,53/14) Hyperbolic Matrix(37,-162,8,-35) (4/1,9/2) -> (9/2,14/3) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(37,306,-26,-215) -> Matrix(5,4,-4,-3) Matrix(37,270,10,73) -> Matrix(1,0,-2,1) Matrix(37,252,16,109) -> Matrix(3,4,-4,-5) Matrix(73,468,-56,-359) -> Matrix(29,52,-24,-43) Matrix(71,396,-26,-145) -> Matrix(3,2,-2,-1) Matrix(37,198,-20,-107) -> Matrix(3,2,-2,-1) Matrix(35,162,-8,-37) -> Matrix(5,6,-6,-7) Matrix(71,306,-42,-181) -> Matrix(9,8,-8,-7) Matrix(37,144,28,109) -> Matrix(17,6,-20,-7) Matrix(325,1224,-124,-467) -> Matrix(3,-4,-2,3) Matrix(179,666,-68,-253) -> Matrix(3,-4,-2,3) Matrix(109,396,30,109) -> Matrix(1,-2,-2,5) Matrix(71,252,20,71) -> Matrix(1,4,-2,-7) Matrix(73,252,42,145) -> Matrix(5,6,-6,-7) Matrix(287,972,106,359) -> Matrix(3,-2,-4,3) Matrix(145,486,54,181) -> Matrix(3,10,-4,-13) Matrix(71,234,-44,-145) -> Matrix(5,14,-4,-11) Matrix(71,198,-52,-145) -> Matrix(37,58,-30,-47) Matrix(397,1080,-304,-827) -> Matrix(29,52,-24,-43) Matrix(359,972,106,287) -> Matrix(1,2,-4,-7) Matrix(181,486,54,145) -> Matrix(7,10,-12,-17) Matrix(109,288,14,37) -> Matrix(3,4,-4,-5) Matrix(1403,3672,-1032,-2701) -> Matrix(79,100,-64,-81) Matrix(145,378,28,73) -> Matrix(5,6,-6,-7) Matrix(181,468,70,181) -> Matrix(7,8,-8,-9) Matrix(71,180,28,71) -> Matrix(3,4,-4,-5) Matrix(37,90,30,73) -> Matrix(19,32,-22,-37) Matrix(181,432,106,253) -> Matrix(7,8,-8,-9) Matrix(145,342,92,217) -> Matrix(13,22,-16,-27) Matrix(71,162,-32,-73) -> Matrix(11,18,-8,-13) Matrix(107,234,16,35) -> Matrix(7,10,-12,-17) Matrix(109,234,34,73) -> Matrix(7,10,-12,-17) Matrix(251,468,96,179) -> Matrix(7,8,-8,-9) Matrix(109,198,60,109) -> Matrix(17,24,-22,-31) Matrix(71,126,40,71) -> Matrix(31,40,-38,-49) Matrix(73,126,-62,-107) -> Matrix(3,2,-2,-1) Matrix(253,432,106,181) -> Matrix(7,8,-8,-9) Matrix(361,612,128,217) -> Matrix(27,32,-38,-45) Matrix(109,180,66,109) -> Matrix(7,8,-8,-9) Matrix(287,468,176,287) -> Matrix(31,40,-38,-49) Matrix(611,990,266,431) -> Matrix(17,22,-24,-31) Matrix(757,1224,-556,-899) -> Matrix(79,100,-64,-81) Matrix(35,54,-24,-37) -> Matrix(1,0,0,1) Matrix(253,360,26,37) -> Matrix(3,4,-4,-5) Matrix(685,972,432,613) -> Matrix(31,40,-38,-49) Matrix(179,252,76,107) -> Matrix(17,22,-24,-31) Matrix(181,252,130,181) -> Matrix(71,90,-86,-109) Matrix(287,396,208,287) -> Matrix(209,260,-250,-311) Matrix(3815,5184,1006,1367) -> Matrix(13,16,30,37) Matrix(3817,5184,1008,1369) -> Matrix(13,16,-100,-123) Matrix(253,342,54,73) -> Matrix(49,60,-58,-71) Matrix(109,144,28,37) -> Matrix(5,6,4,5) Matrix(181,234,140,181) -> Matrix(289,348,-338,-407) Matrix(71,90,56,71) -> Matrix(131,156,-152,-181) Matrix(73,90,30,37) -> Matrix(27,32,-38,-45) Matrix(109,126,32,37) -> Matrix(7,8,-8,-9) Matrix(1,0,2,1) -> Matrix(15,16,-16,-17) Matrix(107,-126,62,-73) -> Matrix(3,2,-2,-1) Matrix(359,-468,56,-73) -> Matrix(61,52,-88,-75) Matrix(145,-198,52,-71) -> Matrix(69,58,-94,-79) Matrix(37,-54,24,-35) -> Matrix(1,0,0,1) Matrix(181,-288,22,-35) -> Matrix(5,4,-4,-3) Matrix(145,-234,44,-71) -> Matrix(17,14,-28,-23) Matrix(107,-180,22,-37) -> Matrix(3,2,-2,-1) Matrix(107,-198,20,-37) -> Matrix(3,2,-2,-1) Matrix(73,-162,32,-71) -> Matrix(23,18,-32,-25) Matrix(467,-1224,124,-325) -> Matrix(5,4,-14,-11) Matrix(253,-666,68,-179) -> Matrix(5,4,-14,-11) Matrix(145,-396,26,-71) -> Matrix(3,2,-2,-1) Matrix(37,-108,12,-35) -> Matrix(11,8,-18,-13) Matrix(469,-1494,124,-395) -> Matrix(3,2,-14,-9) Matrix(37,-162,8,-35) -> Matrix(5,6,-6,-7) Matrix(37,-216,6,-35) -> Matrix(1,2,-2,-3) 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): 18 Degree of the the map X: 18 Degree of the the map Y: 72 ----------------------------------------------------------------------- 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 8 1 1/1 (-1/1,-8/9) 0 18 6/5 -7/8 1 3 5/4 (-13/15,-6/7) 0 18 9/7 -6/7 7 2 13/10 (-6/7,-29/34) 0 18 17/13 (-6/7,-11/13) 0 18 4/3 0 9 11/8 (-26/31,-5/6) 0 18 18/13 -5/6 7 1 7/5 (-5/6,-9/11) 0 18 3/2 0 6 11/7 (-5/6,-9/11) 0 18 19/12 (-5/6,-4/5) 0 18 27/17 -4/5 1 2 8/5 0 9 13/8 (-5/6,-4/5) 0 18 18/11 -4/5 1 1 5/3 (-1/1,-4/5) 0 18 17/10 (-6/7,-5/6) 0 18 12/7 -5/6 1 3 19/11 (-1/1,-6/7) 0 18 7/4 (-5/6,-4/5) 0 18 9/5 -4/5 2 2 11/6 (-4/5,-3/4) 0 18 2/1 0 9 9/4 -3/4 2 2 16/7 0 9 23/10 (-3/4,-2/3) 0 18 7/3 (-1/1,-3/4) 0 18 19/8 (-3/4,-2/3) 0 18 12/5 -3/4 1 3 5/2 (-1/1,-2/3) 0 18 18/7 -1/1 2 1 13/5 (-1/1,-4/5) 0 18 34/13 0 9 21/8 0 6 8/3 0 9 27/10 -3/4 4 2 19/7 (-5/7,-2/3) 0 18 11/4 (-4/5,-3/4) 0 18 14/5 0 9 17/6 (-7/10,-2/3) 0 18 3/1 -2/3 1 6 19/6 (-3/4,-2/3) 0 18 16/5 0 9 13/4 (-2/3,-1/2) 0 18 10/3 0 9 27/8 -1/2 4 2 17/5 (-1/1,0/1) 0 18 7/2 (-2/3,-1/2) 0 18 18/5 -1/2 3 1 11/3 (-1/2,-1/3) 0 18 26/7 0 9 15/4 0 6 34/9 0 9 53/14 (-1/6,0/1) 0 18 72/19 0/1 5 1 19/5 (-1/1,0/1) 0 18 4/1 0 9 9/2 -1/1 6 2 14/3 0 9 19/4 (-4/5,-3/4) 0 18 5/1 (-1/1,-2/3) 0 18 16/3 0 9 11/2 (-2/3,-1/2) 0 18 17/3 (-1/3,0/1) 0 18 6/1 -1/1 1 3 19/3 (-5/7,-2/3) 0 18 13/2 (-2/3,-1/2) 0 18 7/1 (-1/1,-1/2) 0 18 8/1 0 9 9/1 0/1 1 2 1/0 (-1/1,0/1) 0 18 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(107,-126,62,-73) (1/1,6/5) -> (12/7,19/11) Hyperbolic Matrix(73,-90,30,-37) (6/5,5/4) -> (12/5,5/2) Glide Reflection Matrix(71,-90,56,-71) (5/4,9/7) -> (5/4,9/7) Reflection Matrix(181,-234,140,-181) (9/7,13/10) -> (9/7,13/10) Reflection Matrix(359,-468,56,-73) (13/10,17/13) -> (19/3,13/2) Hyperbolic Matrix(109,-144,28,-37) (17/13,4/3) -> (19/5,4/1) Glide Reflection Matrix(145,-198,52,-71) (4/3,11/8) -> (11/4,14/5) Hyperbolic Matrix(287,-396,208,-287) (11/8,18/13) -> (11/8,18/13) Reflection Matrix(181,-252,130,-181) (18/13,7/5) -> (18/13,7/5) Reflection Matrix(37,-54,24,-35) (7/5,3/2) -> (3/2,11/7) Parabolic Matrix(217,-342,92,-145) (11/7,19/12) -> (7/3,19/8) Glide Reflection Matrix(647,-1026,408,-647) (19/12,27/17) -> (19/12,27/17) Reflection Matrix(181,-288,22,-35) (27/17,8/5) -> (8/1,9/1) Hyperbolic Matrix(145,-234,44,-71) (8/5,13/8) -> (13/4,10/3) Hyperbolic Matrix(287,-468,176,-287) (13/8,18/11) -> (13/8,18/11) Reflection Matrix(109,-180,66,-109) (18/11,5/3) -> (18/11,5/3) Reflection Matrix(107,-180,22,-37) (5/3,17/10) -> (19/4,5/1) Hyperbolic Matrix(253,-432,106,-181) (17/10,12/7) -> (19/8,12/5) Glide Reflection Matrix(145,-252,42,-73) (19/11,7/4) -> (17/5,7/2) 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(107,-198,20,-37) (11/6,2/1) -> (16/3,11/2) Hyperbolic Matrix(73,-162,32,-71) (2/1,9/4) -> (9/4,16/7) Parabolic Matrix(251,-576,78,-179) (16/7,23/10) -> (16/5,13/4) Glide Reflection Matrix(109,-252,16,-37) (23/10,7/3) -> (13/2,7/1) Glide Reflection Matrix(71,-180,28,-71) (5/2,18/7) -> (5/2,18/7) Reflection Matrix(181,-468,70,-181) (18/7,13/5) -> (18/7,13/5) Reflection Matrix(145,-378,28,-73) (13/5,34/13) -> (5/1,16/3) Glide Reflection Matrix(467,-1224,124,-325) (34/13,21/8) -> (15/4,34/9) Hyperbolic Matrix(253,-666,68,-179) (21/8,8/3) -> (26/7,15/4) Hyperbolic Matrix(181,-486,54,-145) (8/3,27/10) -> (10/3,27/8) Glide Reflection Matrix(359,-972,106,-287) (27/10,19/7) -> (27/8,17/5) Glide Reflection Matrix(145,-396,26,-71) (19/7,11/4) -> (11/2,17/3) Hyperbolic Matrix(179,-504,38,-107) (14/5,17/6) -> (14/3,19/4) Glide Reflection Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(469,-1494,124,-395) (19/6,16/5) -> (34/9,53/14) Hyperbolic Matrix(71,-252,20,-71) (7/2,18/5) -> (7/2,18/5) Reflection Matrix(109,-396,30,-109) (18/5,11/3) -> (18/5,11/3) Reflection Matrix(73,-270,10,-37) (11/3,26/7) -> (7/1,8/1) Glide Reflection Matrix(2015,-7632,532,-2015) (53/14,72/19) -> (53/14,72/19) Reflection Matrix(721,-2736,190,-721) (72/19,19/5) -> (72/19,19/5) Reflection Matrix(37,-162,8,-35) (4/1,9/2) -> (9/2,14/3) Parabolic Matrix(37,-216,6,-35) (17/3,6/1) -> (6/1,19/3) Parabolic Matrix(-1,18,0,1) (9/1,1/0) -> (9/1,1/0) 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(1,0,2,-1) -> Matrix(17,16,-18,-17) (0/1,1/1) -> (-1/1,-8/9) Matrix(107,-126,62,-73) -> Matrix(3,2,-2,-1) -1/1 Matrix(73,-90,30,-37) -> Matrix(37,32,-52,-45) Matrix(71,-90,56,-71) -> Matrix(181,156,-210,-181) (5/4,9/7) -> (-13/15,-6/7) Matrix(181,-234,140,-181) -> Matrix(407,348,-476,-407) (9/7,13/10) -> (-6/7,-29/34) Matrix(359,-468,56,-73) -> Matrix(61,52,-88,-75) Matrix(109,-144,28,-37) -> Matrix(7,6,6,5) Matrix(145,-198,52,-71) -> Matrix(69,58,-94,-79) Matrix(287,-396,208,-287) -> Matrix(311,260,-372,-311) (11/8,18/13) -> (-26/31,-5/6) Matrix(181,-252,130,-181) -> Matrix(109,90,-132,-109) (18/13,7/5) -> (-5/6,-9/11) Matrix(37,-54,24,-35) -> Matrix(1,0,0,1) Matrix(217,-342,92,-145) -> Matrix(27,22,-38,-31) Matrix(647,-1026,408,-647) -> Matrix(49,40,-60,-49) (19/12,27/17) -> (-5/6,-4/5) Matrix(181,-288,22,-35) -> Matrix(5,4,-4,-3) -1/1 Matrix(145,-234,44,-71) -> Matrix(17,14,-28,-23) Matrix(287,-468,176,-287) -> Matrix(49,40,-60,-49) (13/8,18/11) -> (-5/6,-4/5) Matrix(109,-180,66,-109) -> Matrix(9,8,-10,-9) (18/11,5/3) -> (-1/1,-4/5) Matrix(107,-180,22,-37) -> Matrix(3,2,-2,-1) -1/1 Matrix(253,-432,106,-181) -> Matrix(9,8,-10,-9) *** -> (-1/1,-4/5) Matrix(145,-252,42,-73) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(71,-126,40,-71) -> Matrix(49,40,-60,-49) (7/4,9/5) -> (-5/6,-4/5) Matrix(109,-198,60,-109) -> Matrix(31,24,-40,-31) (9/5,11/6) -> (-4/5,-3/4) Matrix(107,-198,20,-37) -> Matrix(3,2,-2,-1) -1/1 Matrix(73,-162,32,-71) -> Matrix(23,18,-32,-25) -3/4 Matrix(251,-576,78,-179) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(109,-252,16,-37) -> Matrix(5,4,-6,-5) *** -> (-1/1,-2/3) Matrix(71,-180,28,-71) -> Matrix(5,4,-6,-5) (5/2,18/7) -> (-1/1,-2/3) Matrix(181,-468,70,-181) -> Matrix(9,8,-10,-9) (18/7,13/5) -> (-1/1,-4/5) Matrix(145,-378,28,-73) -> Matrix(7,6,-8,-7) *** -> (-1/1,-3/4) Matrix(467,-1224,124,-325) -> Matrix(5,4,-14,-11) Matrix(253,-666,68,-179) -> Matrix(5,4,-14,-11) Matrix(181,-486,54,-145) -> Matrix(13,10,-22,-17) Matrix(359,-972,106,-287) -> Matrix(3,2,-10,-7) Matrix(145,-396,26,-71) -> Matrix(3,2,-2,-1) -1/1 Matrix(179,-504,38,-107) -> Matrix(31,22,-38,-27) Matrix(37,-108,12,-35) -> Matrix(11,8,-18,-13) -2/3 Matrix(469,-1494,124,-395) -> Matrix(3,2,-14,-9) Matrix(71,-252,20,-71) -> Matrix(7,4,-12,-7) (7/2,18/5) -> (-2/3,-1/2) Matrix(109,-396,30,-109) -> Matrix(5,2,-12,-5) (18/5,11/3) -> (-1/2,-1/3) Matrix(73,-270,10,-37) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(2015,-7632,532,-2015) -> Matrix(-1,0,12,1) (53/14,72/19) -> (-1/6,0/1) Matrix(721,-2736,190,-721) -> Matrix(-1,0,2,1) (72/19,19/5) -> (-1/1,0/1) Matrix(37,-162,8,-35) -> Matrix(5,6,-6,-7) -1/1 Matrix(37,-216,6,-35) -> Matrix(1,2,-2,-3) -1/1 Matrix(-1,18,0,1) -> Matrix(-1,0,2,1) (9/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.