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 -7/1 -6/1 -5/1 -13/3 -4/1 -11/3 -7/2 -3/1 -7/3 -2/1 -28/15 -9/5 -7/4 -21/13 -7/5 -7/6 -1/1 -7/9 -7/11 0/1 1/2 7/11 3/4 7/9 1/1 7/6 14/11 7/5 3/2 14/9 21/13 7/4 9/5 2/1 7/3 5/2 14/5 3/1 7/2 11/3 4/1 13/3 9/2 14/3 5/1 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -2/1 0/1 -13/2 1/0 -6/1 -1/2 1/0 -5/1 0/1 1/0 -14/3 1/0 -9/2 1/0 -13/3 -1/1 1/0 -4/1 -1/2 1/0 -15/4 1/0 -26/7 -1/2 1/0 -11/3 0/1 1/0 -7/2 1/0 -3/1 -1/1 1/0 -14/5 -1/1 -11/4 -1/2 -19/7 -1/1 -1/2 -27/10 -1/2 -8/3 -1/2 1/0 -21/8 0/1 -13/5 0/1 1/0 -18/7 1/2 1/0 -5/2 1/0 -7/3 -1/1 -9/4 -1/2 -11/5 -1/1 0/1 -13/6 -1/2 -2/1 -1/2 1/0 -15/8 1/0 -28/15 1/0 -13/7 -1/1 1/0 -11/6 1/0 -9/5 -1/1 1/0 -7/4 -1/1 -5/3 -1/1 -1/2 -13/8 -1/2 -21/13 -1/2 -29/18 -1/2 -8/5 -1/2 -1/4 -19/12 -1/2 -11/7 -1/2 0/1 -14/9 0/1 -3/2 -1/2 -7/5 0/1 -11/8 1/4 -26/19 1/4 1/2 -41/30 1/2 -56/41 1/2 -15/11 0/1 1/2 -4/3 1/2 1/0 -13/10 1/0 -22/17 -3/2 1/0 -9/7 0/1 1/0 -14/11 1/0 -5/4 1/0 -11/9 -1/1 0/1 -6/5 -1/2 1/0 -7/6 -1/1 -1/1 -1/1 0/1 -7/8 -1/1 -6/7 -1/2 1/0 -5/6 -1/2 -14/17 -1/2 -9/11 -1/2 0/1 -13/16 -1/2 -4/5 -1/2 -1/4 -7/9 0/1 -10/13 1/4 1/2 -13/17 0/1 1/2 -3/4 1/0 -14/19 0/1 -11/15 0/1 1/0 -8/11 1/2 1/0 -5/7 -1/1 1/0 -7/10 -1/1 -9/13 -1/1 -1/2 -11/16 -1/2 -2/3 -1/2 1/0 -7/11 -1/1 -12/19 -3/4 -1/2 -17/27 -1/1 -2/3 -5/8 -1/2 -13/21 -1/2 0/1 -21/34 0/1 -8/13 -1/2 1/0 -19/31 -1/1 1/0 -11/18 1/0 -14/23 -1/1 -3/5 -1/1 -1/2 -7/12 -1/2 -11/19 -1/2 0/1 -15/26 -1/2 -4/7 -1/2 1/0 -9/16 -1/2 -14/25 -1/2 -5/9 -1/2 0/1 -1/2 -1/2 0/1 0/1 1/2 1/2 5/9 1/2 1/1 9/16 1/2 4/7 1/2 3/4 3/5 0/1 1/1 11/18 3/2 8/13 1/2 1/0 13/21 1/1 1/0 5/8 1/0 7/11 0/1 9/14 1/2 2/3 1/2 1/0 5/7 0/1 1/2 8/11 1/2 1/0 11/15 0/1 1/1 3/4 1/2 7/9 1/1 11/14 1/0 4/5 1/2 1/0 9/11 1/1 1/0 5/6 1/0 6/7 -1/2 1/0 1/1 0/1 1/1 8/7 -1/2 1/0 7/6 0/1 6/5 1/4 1/2 11/9 0/1 1/2 16/13 1/2 1/0 5/4 1/2 14/11 1/2 23/18 1/2 9/7 1/2 1/1 22/17 1/2 1/0 13/10 1/2 4/3 1/2 1/0 7/5 1/1 10/7 3/2 1/0 13/9 1/1 1/0 16/11 1/2 1/0 3/2 1/0 14/9 0/1 25/16 1/2 11/7 0/1 1/1 19/12 1/0 8/5 1/2 1/0 21/13 0/1 2/1 34/21 1/2 1/0 13/8 1/0 5/3 0/1 1/0 12/7 -1/2 1/0 7/4 0/1 16/9 1/4 1/2 9/5 0/1 1/2 20/11 1/2 3/4 11/6 1/0 13/7 0/1 1/2 2/1 1/2 1/0 7/3 0/1 12/5 1/4 1/2 41/17 1/3 1/2 70/29 1/2 29/12 1/2 17/7 0/1 1/2 5/2 1/2 18/7 1/2 3/4 31/12 1/2 13/5 1/2 1/1 34/13 1/2 3/4 21/8 1/1 8/3 1/2 1/0 27/10 1/2 19/7 1/2 2/3 30/11 1/2 3/4 11/4 3/4 14/5 1/1 17/6 3/2 3/1 0/1 1/1 10/3 1/2 3/4 7/2 1/1 18/5 7/6 5/4 29/8 5/4 11/3 1/1 4/3 26/7 5/4 3/2 41/11 4/3 3/2 56/15 3/2 15/4 3/2 19/5 1/1 3/2 4/1 3/2 1/0 13/3 2/1 1/0 9/2 1/0 14/3 1/0 19/4 1/0 5/1 1/1 1/0 6/1 5/2 1/0 7/1 1/0 8/1 -3/2 1/0 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(13,98,-2,-15) (-7/1,1/0) -> (-7/1,-13/2) Parabolic Matrix(57,364,44,281) (-13/2,-6/1) -> (22/17,13/10) Hyperbolic Matrix(13,70,18,97) (-6/1,-5/1) -> (5/7,8/11) Hyperbolic Matrix(29,140,-52,-251) (-5/1,-14/3) -> (-14/25,-5/9) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(41,182,66,293) (-9/2,-13/3) -> (13/21,5/8) Hyperbolic Matrix(43,182,30,127) (-13/3,-4/1) -> (10/7,13/9) Hyperbolic Matrix(29,112,-36,-139) (-4/1,-15/4) -> (-13/16,-4/5) Hyperbolic Matrix(113,420,-60,-223) (-15/4,-26/7) -> (-2/1,-15/8) Hyperbolic Matrix(125,462,102,377) (-26/7,-11/3) -> (11/9,16/13) Hyperbolic Matrix(43,154,-74,-265) (-11/3,-7/2) -> (-7/12,-11/19) Hyperbolic Matrix(13,42,-22,-71) (-7/2,-3/1) -> (-3/5,-7/12) Hyperbolic Matrix(29,84,-48,-139) (-3/1,-14/5) -> (-14/23,-3/5) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,-164,-447) (-11/4,-19/7) -> (-9/13,-11/16) Hyperbolic Matrix(295,798,78,211) (-19/7,-27/10) -> (15/4,19/5) Hyperbolic Matrix(379,1022,234,631) (-27/10,-8/3) -> (34/21,13/8) Hyperbolic Matrix(69,182,58,153) (-8/3,-21/8) -> (7/6,6/5) Hyperbolic Matrix(209,546,-338,-883) (-21/8,-13/5) -> (-13/21,-21/34) Hyperbolic Matrix(141,364,-184,-475) (-13/5,-18/7) -> (-10/13,-13/17) Hyperbolic Matrix(71,182,126,323) (-18/7,-5/2) -> (9/16,4/7) Hyperbolic Matrix(41,98,-18,-43) (-5/2,-7/3) -> (-7/3,-9/4) Parabolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(211,462,58,127) (-11/5,-13/6) -> (29/8,11/3) Hyperbolic Matrix(197,420,-144,-307) (-13/6,-2/1) -> (-26/19,-41/30) Hyperbolic Matrix(673,1260,180,337) (-15/8,-28/15) -> (56/15,15/4) Hyperbolic Matrix(1105,2058,458,853) (-28/15,-13/7) -> (41/17,70/29) Hyperbolic Matrix(295,546,114,211) (-13/7,-11/6) -> (31/12,13/5) Hyperbolic Matrix(169,308,-276,-503) (-11/6,-9/5) -> (-19/31,-11/18) Hyperbolic Matrix(71,126,-102,-181) (-9/5,-7/4) -> (-7/10,-9/13) Hyperbolic Matrix(41,70,-58,-99) (-7/4,-5/3) -> (-5/7,-7/10) Hyperbolic Matrix(43,70,78,127) (-5/3,-13/8) -> (1/2,5/9) Hyperbolic Matrix(545,882,-338,-547) (-13/8,-21/13) -> (-21/13,-29/18) Parabolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(97,154,114,181) (-8/5,-19/12) -> (5/6,6/7) Hyperbolic Matrix(239,378,98,155) (-19/12,-11/7) -> (17/7,5/2) Hyperbolic Matrix(197,308,-268,-419) (-11/7,-14/9) -> (-14/19,-11/15) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(69,98,-50,-71) (-3/2,-7/5) -> (-7/5,-11/8) Parabolic Matrix(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) Hyperbolic Matrix(3289,4494,1362,1861) (-41/30,-56/41) -> (70/29,29/12) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(85,112,-148,-195) (-4/3,-13/10) -> (-15/26,-4/7) Hyperbolic Matrix(97,126,10,13) (-13/10,-22/17) -> (8/1,1/0) Hyperbolic Matrix(293,378,162,209) (-22/17,-9/7) -> (9/5,20/11) Hyperbolic Matrix(197,252,-240,-307) (-9/7,-14/11) -> (-14/17,-9/11) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,-180,-223) (-5/4,-11/9) -> (-17/27,-5/8) Hyperbolic Matrix(127,154,174,211) (-11/9,-6/5) -> (8/11,11/15) Hyperbolic Matrix(153,182,58,69) (-6/5,-7/6) -> (21/8,8/3) Hyperbolic Matrix(13,14,-14,-15) (-7/6,-1/1) -> (-1/1,-7/8) Parabolic Matrix(419,364,160,139) (-7/8,-6/7) -> (34/13,21/8) Hyperbolic Matrix(181,154,114,97) (-6/7,-5/6) -> (19/12,8/5) Hyperbolic Matrix(475,392,372,307) (-5/6,-14/17) -> (14/11,23/18) Hyperbolic Matrix(601,490,222,181) (-9/11,-13/16) -> (27/10,19/7) Hyperbolic Matrix(125,98,-162,-127) (-4/5,-7/9) -> (-7/9,-10/13) Parabolic Matrix(239,182,130,99) (-13/17,-3/4) -> (11/6,13/7) Hyperbolic Matrix(531,392,340,251) (-3/4,-14/19) -> (14/9,25/16) Hyperbolic Matrix(211,154,174,127) (-11/15,-8/11) -> (6/5,11/9) Hyperbolic Matrix(97,70,18,13) (-8/11,-5/7) -> (5/1,6/1) Hyperbolic Matrix(265,182,182,125) (-11/16,-2/3) -> (16/11,3/2) Hyperbolic Matrix(153,98,-242,-155) (-2/3,-7/11) -> (-7/11,-12/19) Parabolic Matrix(911,574,246,155) (-12/19,-17/27) -> (11/3,26/7) Hyperbolic Matrix(293,182,66,41) (-5/8,-13/21) -> (13/3,9/2) Hyperbolic Matrix(363,224,316,195) (-21/34,-8/13) -> (8/7,7/6) Hyperbolic Matrix(799,490,618,379) (-8/13,-19/31) -> (9/7,22/17) Hyperbolic Matrix(643,392,228,139) (-11/18,-14/23) -> (14/5,17/6) Hyperbolic Matrix(993,574,410,237) (-11/19,-15/26) -> (29/12,17/7) Hyperbolic Matrix(323,182,126,71) (-4/7,-9/16) -> (5/2,18/7) Hyperbolic Matrix(699,392,148,83) (-9/16,-14/25) -> (14/3,19/4) Hyperbolic Matrix(127,70,78,43) (-5/9,-1/2) -> (13/8,5/3) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(251,-140,52,-29) (5/9,9/16) -> (19/4,5/1) Hyperbolic Matrix(71,-42,22,-13) (4/7,3/5) -> (3/1,10/3) Hyperbolic Matrix(139,-84,48,-29) (3/5,11/18) -> (17/6,3/1) Hyperbolic Matrix(503,-308,276,-169) (11/18,8/13) -> (20/11,11/6) Hyperbolic Matrix(883,-546,338,-209) (8/13,13/21) -> (13/5,34/13) Hyperbolic Matrix(155,-98,242,-153) (5/8,7/11) -> (7/11,9/14) Parabolic Matrix(239,-154,194,-125) (9/14,2/3) -> (16/13,5/4) Hyperbolic Matrix(99,-70,58,-41) (2/3,5/7) -> (5/3,12/7) Hyperbolic Matrix(419,-308,268,-197) (11/15,3/4) -> (25/16,11/7) Hyperbolic Matrix(127,-98,162,-125) (3/4,7/9) -> (7/9,11/14) Parabolic Matrix(407,-322,158,-125) (11/14,4/5) -> (18/7,31/12) Hyperbolic Matrix(139,-112,36,-29) (4/5,9/11) -> (19/5,4/1) Hyperbolic Matrix(307,-252,240,-197) (9/11,5/6) -> (23/18,9/7) Hyperbolic Matrix(15,-14,14,-13) (6/7,1/1) -> (1/1,8/7) Parabolic Matrix(267,-350,74,-97) (13/10,4/3) -> (18/5,29/8) Hyperbolic Matrix(71,-98,50,-69) (4/3,7/5) -> (7/5,10/7) Parabolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(547,-882,338,-545) (8/5,21/13) -> (21/13,34/21) Parabolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(321,-574,118,-211) (16/9,9/5) -> (19/7,30/11) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(15,-98,2,-13) (6/1,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(13,98,-2,-15) -> Matrix(1,0,0,1) Matrix(57,364,44,281) -> Matrix(1,0,2,1) Matrix(13,70,18,97) -> Matrix(1,0,2,1) Matrix(29,140,-52,-251) -> Matrix(1,0,-2,1) Matrix(55,252,12,55) -> Matrix(1,4,0,1) Matrix(41,182,66,293) -> Matrix(1,2,0,1) Matrix(43,182,30,127) -> Matrix(1,2,0,1) Matrix(29,112,-36,-139) -> Matrix(1,0,-2,1) Matrix(113,420,-60,-223) -> Matrix(1,0,0,1) Matrix(125,462,102,377) -> Matrix(1,0,2,1) Matrix(43,154,-74,-265) -> Matrix(1,0,-2,1) Matrix(13,42,-22,-71) -> Matrix(1,2,-2,-3) Matrix(29,84,-48,-139) -> Matrix(1,2,-2,-3) Matrix(111,308,40,111) -> Matrix(5,4,6,5) Matrix(113,308,-164,-447) -> Matrix(1,0,0,1) Matrix(295,798,78,211) -> Matrix(1,2,0,1) Matrix(379,1022,234,631) -> Matrix(1,0,2,1) Matrix(69,182,58,153) -> Matrix(1,0,4,1) Matrix(209,546,-338,-883) -> Matrix(1,0,-2,1) Matrix(141,364,-184,-475) -> Matrix(1,0,2,1) Matrix(71,182,126,323) -> Matrix(1,-2,2,-3) Matrix(41,98,-18,-43) -> Matrix(1,2,-2,-3) Matrix(139,308,88,195) -> Matrix(1,0,2,1) Matrix(211,462,58,127) -> Matrix(3,4,2,3) Matrix(197,420,-144,-307) -> Matrix(1,0,4,1) Matrix(673,1260,180,337) -> Matrix(3,4,2,3) Matrix(1105,2058,458,853) -> Matrix(1,2,2,5) Matrix(295,546,114,211) -> Matrix(1,0,2,1) Matrix(169,308,-276,-503) -> Matrix(1,0,0,1) Matrix(71,126,-102,-181) -> Matrix(1,2,-2,-3) Matrix(41,70,-58,-99) -> Matrix(3,2,-2,-1) Matrix(43,70,78,127) -> Matrix(3,2,4,3) Matrix(545,882,-338,-547) -> Matrix(7,4,-16,-9) Matrix(279,448,104,167) -> Matrix(1,0,4,1) Matrix(97,154,114,181) -> Matrix(1,0,2,1) Matrix(239,378,98,155) -> Matrix(1,0,4,1) Matrix(197,308,-268,-419) -> Matrix(1,0,2,1) Matrix(55,84,36,55) -> Matrix(1,0,2,1) Matrix(69,98,-50,-71) -> Matrix(1,0,6,1) Matrix(449,616,164,225) -> Matrix(5,-2,8,-3) Matrix(3289,4494,1362,1861) -> Matrix(1,0,0,1) Matrix(2297,3136,616,841) -> Matrix(5,-4,4,-3) Matrix(83,112,20,27) -> Matrix(3,-2,2,-1) Matrix(85,112,-148,-195) -> Matrix(1,0,-2,1) Matrix(97,126,10,13) -> Matrix(1,0,0,1) Matrix(293,378,162,209) -> Matrix(1,0,2,1) Matrix(197,252,-240,-307) -> Matrix(1,0,-2,1) Matrix(111,140,88,111) -> Matrix(1,0,2,1) Matrix(113,140,-180,-223) -> Matrix(1,2,-2,-3) Matrix(127,154,174,211) -> Matrix(1,0,2,1) Matrix(153,182,58,69) -> Matrix(1,0,2,1) Matrix(13,14,-14,-15) -> Matrix(1,0,0,1) Matrix(419,364,160,139) -> Matrix(3,2,4,3) Matrix(181,154,114,97) -> Matrix(1,0,2,1) Matrix(475,392,372,307) -> Matrix(3,2,4,3) Matrix(601,490,222,181) -> Matrix(3,2,4,3) Matrix(125,98,-162,-127) -> Matrix(1,0,6,1) Matrix(239,182,130,99) -> Matrix(1,0,0,1) Matrix(531,392,340,251) -> Matrix(1,0,2,1) Matrix(211,154,174,127) -> Matrix(1,0,2,1) Matrix(97,70,18,13) -> Matrix(1,2,0,1) Matrix(265,182,182,125) -> Matrix(1,0,2,1) Matrix(153,98,-242,-155) -> Matrix(1,2,-2,-3) Matrix(911,574,246,155) -> Matrix(1,2,0,1) Matrix(293,182,66,41) -> Matrix(5,2,2,1) Matrix(363,224,316,195) -> Matrix(1,0,0,1) Matrix(799,490,618,379) -> Matrix(1,0,2,1) Matrix(643,392,228,139) -> Matrix(3,4,2,3) Matrix(993,574,410,237) -> Matrix(1,0,4,1) Matrix(323,182,126,71) -> Matrix(3,2,4,3) Matrix(699,392,148,83) -> Matrix(3,2,-2,-1) Matrix(127,70,78,43) -> Matrix(1,0,2,1) Matrix(1,0,4,1) -> Matrix(1,0,4,1) Matrix(251,-140,52,-29) -> Matrix(3,-2,2,-1) Matrix(71,-42,22,-13) -> Matrix(1,0,0,1) Matrix(139,-84,48,-29) -> Matrix(1,0,0,1) Matrix(503,-308,276,-169) -> Matrix(1,-2,2,-3) Matrix(883,-546,338,-209) -> Matrix(1,-2,2,-3) Matrix(155,-98,242,-153) -> Matrix(1,0,2,1) Matrix(239,-154,194,-125) -> Matrix(1,0,0,1) Matrix(99,-70,58,-41) -> Matrix(1,0,-2,1) Matrix(419,-308,268,-197) -> Matrix(1,0,0,1) Matrix(127,-98,162,-125) -> Matrix(3,-2,2,-1) Matrix(407,-322,158,-125) -> Matrix(1,-2,2,-3) Matrix(139,-112,36,-29) -> Matrix(3,-2,2,-1) Matrix(307,-252,240,-197) -> Matrix(1,-2,2,-3) Matrix(15,-14,14,-13) -> Matrix(1,0,0,1) Matrix(267,-350,74,-97) -> Matrix(7,-6,6,-5) Matrix(71,-98,50,-69) -> Matrix(3,-2,2,-1) Matrix(559,-812,232,-337) -> Matrix(1,0,2,1) Matrix(547,-882,338,-545) -> Matrix(1,0,0,1) Matrix(113,-196,64,-111) -> Matrix(1,0,4,1) Matrix(321,-574,118,-211) -> Matrix(5,-2,8,-3) Matrix(223,-420,60,-113) -> Matrix(5,-4,4,-3) Matrix(43,-98,18,-41) -> Matrix(1,0,2,1) Matrix(57,-196,16,-55) -> Matrix(9,-8,8,-7) Matrix(15,-98,2,-13) -> Matrix(1,-4,0,1) 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): 16 Degree of the the map X: 16 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 -5/1 (0/1,1/0) 0 14 -14/3 1/0 3 2 -9/2 1/0 1 14 -4/1 0 14 -15/4 1/0 1 14 -11/3 (0/1,1/0) 0 14 -7/2 1/0 1 2 -3/1 (-1/1,1/0) 0 14 -14/5 -1/1 5 2 -11/4 -1/2 1 14 -19/7 (-1/1,-1/2) 0 14 -8/3 0 14 -21/8 0/1 3 2 -13/5 (0/1,1/0) 0 14 -5/2 1/0 1 14 -7/3 -1/1 2 2 -9/4 -1/2 1 14 -11/5 (-1/1,0/1) 0 14 -2/1 0 14 -11/6 1/0 1 14 -9/5 (-1/1,1/0) 0 14 -7/4 -1/1 2 2 -5/3 (-1/1,-1/2) 0 14 -8/5 0 14 -11/7 (-1/2,0/1) 0 14 -14/9 0/1 1 2 -3/2 -1/2 1 14 -7/5 0/1 6 2 -11/8 1/4 1 14 -15/11 (0/1,1/2) 0 14 -4/3 0 14 -13/10 1/0 1 14 -9/7 (0/1,1/0) 0 14 -14/11 1/0 1 2 -5/4 1/0 1 14 -6/5 0 14 -7/6 -1/1 1 2 -1/1 (-1/1,0/1) 0 14 0/1 0/1 2 2 1/1 (0/1,1/1) 0 14 7/6 0/1 3 2 6/5 0 14 11/9 (0/1,1/2) 0 14 5/4 1/2 1 14 14/11 1/2 1 2 9/7 (1/2,1/1) 0 14 22/17 0 14 13/10 1/2 1 14 4/3 0 14 7/5 1/1 2 2 10/7 0 14 13/9 (1/1,1/0) 0 14 16/11 0 14 3/2 1/0 1 14 14/9 0/1 1 2 11/7 (0/1,1/1) 0 14 19/12 1/0 1 14 8/5 0 14 21/13 0 2 34/21 0 14 13/8 1/0 1 14 5/3 (0/1,1/0) 0 14 7/4 0/1 2 2 9/5 (0/1,1/2) 0 14 11/6 1/0 1 14 13/7 (0/1,1/2) 0 14 2/1 0 14 7/3 0/1 2 2 12/5 0 14 41/17 (1/3,1/2) 0 14 70/29 1/2 1 2 29/12 1/2 1 14 17/7 (0/1,1/2) 0 14 5/2 1/2 1 14 18/7 0 14 13/5 (1/2,1/1) 0 14 21/8 1/1 1 2 8/3 0 14 27/10 1/2 1 14 19/7 (1/2,2/3) 0 14 11/4 3/4 1 14 14/5 1/1 5 2 3/1 (0/1,1/1) 0 14 7/2 1/1 4 2 11/3 (1/1,4/3) 0 14 26/7 0 14 41/11 (4/3,3/2) 0 14 56/15 3/2 1 2 15/4 3/2 1 14 4/1 0 14 13/3 (2/1,1/0) 0 14 9/2 1/0 1 14 14/3 1/0 3 2 5/1 (1/1,1/0) 0 14 6/1 0 14 7/1 1/0 4 2 8/1 0 14 1/0 1/0 1 14 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(13,70,8,43) (-5/1,1/0) -> (13/8,5/3) Glide Reflection Matrix(29,140,-6,-29) (-5/1,-14/3) -> (-5/1,-14/3) Reflection Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(41,182,16,71) (-9/2,-4/1) -> (5/2,18/7) Glide Reflection Matrix(29,112,-22,-85) (-4/1,-15/4) -> (-4/3,-13/10) Glide Reflection Matrix(155,574,64,237) (-15/4,-11/3) -> (29/12,17/7) Glide Reflection Matrix(43,154,-12,-43) (-11/3,-7/2) -> (-11/3,-7/2) Reflection Matrix(13,42,-4,-13) (-7/2,-3/1) -> (-7/2,-3/1) Reflection Matrix(29,84,-10,-29) (-3/1,-14/5) -> (-3/1,-14/5) Reflection Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,-62,-169) (-11/4,-19/7) -> (-11/6,-9/5) Glide Reflection Matrix(181,490,140,379) (-19/7,-8/3) -> (9/7,22/17) Glide Reflection Matrix(69,182,58,153) (-8/3,-21/8) -> (7/6,6/5) Hyperbolic Matrix(209,546,-80,-209) (-21/8,-13/5) -> (-21/8,-13/5) Reflection Matrix(71,182,16,41) (-13/5,-5/2) -> (13/3,9/2) Glide Reflection Matrix(41,98,-18,-43) (-5/2,-7/3) -> (-7/3,-9/4) Parabolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(141,308,38,83) (-11/5,-2/1) -> (11/3,26/7) Glide Reflection Matrix(99,182,68,125) (-2/1,-11/6) -> (16/11,3/2) Glide Reflection Matrix(71,126,-40,-71) (-9/5,-7/4) -> (-9/5,-7/4) Reflection Matrix(41,70,-24,-41) (-7/4,-5/3) -> (-7/4,-5/3) Reflection Matrix(43,70,8,13) (-5/3,-8/5) -> (5/1,6/1) Glide Reflection Matrix(97,154,80,127) (-8/5,-11/7) -> (6/5,11/9) Glide Reflection Matrix(197,308,-126,-197) (-11/7,-14/9) -> (-11/7,-14/9) Reflection Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(69,98,-50,-71) (-3/2,-7/5) -> (-7/5,-11/8) Parabolic Matrix(225,308,122,167) (-11/8,-15/11) -> (11/6,13/7) Glide Reflection Matrix(83,112,20,27) (-15/11,-4/3) -> (4/1,13/3) Hyperbolic Matrix(379,490,140,181) (-13/10,-9/7) -> (27/10,19/7) Glide Reflection Matrix(197,252,-154,-197) (-9/7,-14/11) -> (-9/7,-14/11) Reflection Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(127,154,80,97) (-5/4,-6/5) -> (19/12,8/5) Glide Reflection Matrix(153,182,58,69) (-6/5,-7/6) -> (21/8,8/3) Hyperbolic Matrix(13,14,-12,-13) (-7/6,-1/1) -> (-7/6,-1/1) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(13,-14,12,-13) (1/1,7/6) -> (1/1,7/6) Reflection Matrix(113,-140,46,-57) (11/9,5/4) -> (17/7,5/2) Glide Reflection Matrix(197,-252,154,-197) (14/11,9/7) -> (14/11,9/7) Reflection Matrix(561,-728,346,-449) (22/17,13/10) -> (34/21,13/8) Glide Reflection Matrix(85,-112,22,-29) (13/10,4/3) -> (15/4,4/1) Glide Reflection Matrix(71,-98,50,-69) (4/3,7/5) -> (7/5,10/7) Parabolic Matrix(253,-364,98,-141) (10/7,13/9) -> (18/7,13/5) Glide Reflection Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(197,-308,126,-197) (14/9,11/7) -> (14/9,11/7) Reflection Matrix(547,-882,338,-545) (8/5,21/13) -> (21/13,34/21) Parabolic Matrix(41,-70,24,-41) (5/3,7/4) -> (5/3,7/4) Reflection Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(169,-308,62,-113) (9/5,11/6) -> (19/7,11/4) Glide Reflection Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(43,-98,18,-41) (2/1,7/3) -> (7/3,12/5) Parabolic Matrix(2379,-5740,986,-2379) (41/17,70/29) -> (41/17,70/29) Reflection Matrix(1107,-2674,296,-715) (70/29,29/12) -> (56/15,15/4) Glide Reflection Matrix(209,-546,80,-209) (13/5,21/8) -> (13/5,21/8) Reflection Matrix(83,-224,10,-27) (8/3,27/10) -> (8/1,1/0) Glide Reflection Matrix(29,-84,10,-29) (14/5,3/1) -> (14/5,3/1) Reflection Matrix(13,-42,4,-13) (3/1,7/2) -> (3/1,7/2) Reflection Matrix(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(1231,-4592,330,-1231) (41/11,56/15) -> (41/11,56/15) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection Matrix(15,-98,2,-13) (6/1,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(13,70,8,43) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(29,140,-6,-29) -> Matrix(1,0,0,-1) (-5/1,-14/3) -> (0/1,1/0) Matrix(55,252,12,55) -> Matrix(1,4,0,1) 1/0 Matrix(41,182,16,71) -> Matrix(1,2,2,3) Matrix(29,112,-22,-85) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(155,574,64,237) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(43,154,-12,-43) -> Matrix(1,0,0,-1) (-11/3,-7/2) -> (0/1,1/0) Matrix(13,42,-4,-13) -> Matrix(1,2,0,-1) (-7/2,-3/1) -> (-1/1,1/0) Matrix(29,84,-10,-29) -> Matrix(1,2,0,-1) (-3/1,-14/5) -> (-1/1,1/0) Matrix(111,308,40,111) -> Matrix(5,4,6,5) Matrix(113,308,-62,-169) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(181,490,140,379) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(69,182,58,153) -> Matrix(1,0,4,1) 0/1 Matrix(209,546,-80,-209) -> Matrix(1,0,0,-1) (-21/8,-13/5) -> (0/1,1/0) Matrix(71,182,16,41) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(41,98,-18,-43) -> Matrix(1,2,-2,-3) -1/1 Matrix(139,308,88,195) -> Matrix(1,0,2,1) 0/1 Matrix(141,308,38,83) -> Matrix(5,4,4,3) Matrix(99,182,68,125) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(71,126,-40,-71) -> Matrix(1,2,0,-1) (-9/5,-7/4) -> (-1/1,1/0) Matrix(41,70,-24,-41) -> Matrix(3,2,-4,-3) (-7/4,-5/3) -> (-1/1,-1/2) Matrix(43,70,8,13) -> Matrix(3,2,2,1) Matrix(97,154,80,127) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(197,308,-126,-197) -> Matrix(-1,0,4,1) (-11/7,-14/9) -> (-1/2,0/1) Matrix(55,84,36,55) -> Matrix(1,0,2,1) 0/1 Matrix(69,98,-50,-71) -> Matrix(1,0,6,1) 0/1 Matrix(225,308,122,167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(83,112,20,27) -> Matrix(3,-2,2,-1) 1/1 Matrix(379,490,140,181) -> Matrix(1,2,2,3) Matrix(197,252,-154,-197) -> Matrix(1,0,0,-1) (-9/7,-14/11) -> (0/1,1/0) Matrix(111,140,88,111) -> Matrix(1,0,2,1) 0/1 Matrix(127,154,80,97) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(153,182,58,69) -> Matrix(1,0,2,1) 0/1 Matrix(13,14,-12,-13) -> Matrix(-1,0,2,1) (-7/6,-1/1) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Matrix(1,0,2,-1) -> Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Matrix(13,-14,12,-13) -> Matrix(1,0,2,-1) (1/1,7/6) -> (0/1,1/1) Matrix(113,-140,46,-57) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(197,-252,154,-197) -> Matrix(3,-2,4,-3) (14/11,9/7) -> (1/2,1/1) Matrix(561,-728,346,-449) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(85,-112,22,-29) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(71,-98,50,-69) -> Matrix(3,-2,2,-1) 1/1 Matrix(253,-364,98,-141) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(559,-812,232,-337) -> Matrix(1,0,2,1) 0/1 Matrix(197,-308,126,-197) -> Matrix(1,0,2,-1) (14/9,11/7) -> (0/1,1/1) Matrix(547,-882,338,-545) -> Matrix(1,0,0,1) Matrix(41,-70,24,-41) -> Matrix(1,0,0,-1) (5/3,7/4) -> (0/1,1/0) Matrix(71,-126,40,-71) -> Matrix(1,0,4,-1) (7/4,9/5) -> (0/1,1/2) Matrix(169,-308,62,-113) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(223,-420,60,-113) -> Matrix(5,-4,4,-3) 1/1 Matrix(43,-98,18,-41) -> Matrix(1,0,2,1) 0/1 Matrix(2379,-5740,986,-2379) -> Matrix(5,-2,12,-5) (41/17,70/29) -> (1/3,1/2) Matrix(1107,-2674,296,-715) -> Matrix(11,-4,8,-3) Matrix(209,-546,80,-209) -> Matrix(3,-2,4,-3) (13/5,21/8) -> (1/2,1/1) Matrix(83,-224,10,-27) -> Matrix(3,-2,-2,1) Matrix(29,-84,10,-29) -> Matrix(1,0,2,-1) (14/5,3/1) -> (0/1,1/1) Matrix(13,-42,4,-13) -> Matrix(1,0,2,-1) (3/1,7/2) -> (0/1,1/1) Matrix(43,-154,12,-43) -> Matrix(7,-8,6,-7) (7/2,11/3) -> (1/1,4/3) Matrix(1231,-4592,330,-1231) -> Matrix(17,-24,12,-17) (41/11,56/15) -> (4/3,3/2) Matrix(29,-140,6,-29) -> Matrix(-1,2,0,1) (14/3,5/1) -> (1/1,1/0) Matrix(15,-98,2,-13) -> Matrix(1,-4,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.