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 -9/5 -8/5 -7/5 -6/5 -1/1 -4/5 -3/5 -5/9 -1/2 -2/5 -3/8 -7/20 -1/3 -1/4 -1/5 -1/6 -3/20 -1/7 0/1 1/7 1/6 1/5 2/9 1/4 2/7 3/10 1/3 11/30 3/8 2/5 4/9 9/20 1/2 5/9 4/7 3/5 19/30 2/3 7/10 4/5 1/1 6/5 4/3 7/5 8/5 9/5 2/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -2/1 0/1 2/1 -13/7 -1/1 -11/6 -1/2 -9/5 0/1 -7/4 1/4 1/2 -12/7 0/1 -5/3 1/1 -18/11 0/1 2/3 -13/8 1/2 3/4 -8/5 1/1 -19/12 3/2 1/0 -30/19 4/3 2/1 -11/7 1/1 3/1 -14/9 0/1 2/1 -3/2 1/0 -10/7 -2/1 0/1 -7/5 0/1 -18/13 0/1 2/7 -11/8 1/4 1/2 -26/19 0/1 2/5 -15/11 1/3 1/1 -19/14 1/2 -4/3 0/1 -9/7 1/1 -5/4 1/2 3/4 -11/9 1/1 -6/5 1/1 -13/11 1/1 -7/6 3/2 -1/1 -1/1 1/1 -6/7 0/1 2/3 -5/6 1/2 -4/5 1/1 -11/14 5/4 -7/9 1/1 -3/4 3/2 1/0 -11/15 2/1 -8/11 2/1 -5/7 3/1 -12/17 4/1 -7/10 1/0 -2/3 0/1 2/1 -9/14 1/0 -7/11 1/1 3/1 -26/41 2/1 4/1 -19/30 1/0 -12/19 2/1 -5/8 5/2 1/0 -3/5 1/0 -7/12 -3/2 1/0 -18/31 -2/1 0/1 -11/19 -3/1 -1/1 -15/26 -1/2 -19/33 -1/1 -4/7 0/1 -9/16 1/2 1/0 -5/9 -1/1 1/1 -11/20 1/2 1/0 -6/11 0/1 2/1 -1/2 1/0 -5/11 -1/1 -9/20 -1/2 1/0 -4/9 0/1 -3/7 -1/1 1/1 -2/5 0/1 -5/13 1/3 1/1 -8/21 0/1 -3/8 1/2 1/0 -10/27 0/1 2/3 -7/19 -1/1 1/1 -18/49 0/1 2/1 -11/30 1/0 -4/11 0/1 -9/25 0/1 -5/14 1/2 -6/17 0/1 2/3 -7/20 1/2 1/0 -1/3 1/1 -4/13 2/1 -3/10 1/0 -2/7 -2/1 0/1 -5/18 1/0 -3/11 -1/1 1/1 -1/4 1/2 1/0 -3/13 1/1 -2/9 0/1 2/1 -1/5 1/0 -2/11 -2/1 0/1 -3/17 -1/1 -7/40 -1/2 1/0 -4/23 0/1 -1/6 1/0 -2/13 -2/1 0/1 -3/20 -1/2 1/0 -4/27 0/1 -1/7 -1/1 0/1 0/1 1/7 1/3 1/1 1/6 1/2 1/5 1/1 3/14 1/0 2/9 0/1 2/1 1/4 1/2 1/0 3/11 1/1 2/7 0/1 2/1 3/10 1/0 1/3 -1/1 1/1 5/14 -1/2 4/11 0/1 11/30 1/0 7/19 -1/1 3/8 -1/2 1/0 2/5 0/1 5/12 1/6 1/4 8/19 0/1 3/7 1/3 4/9 0/1 9/20 1/4 1/2 5/11 1/3 1/1 1/2 1/2 6/11 0/1 2/3 11/20 1/2 3/4 5/9 1/1 4/7 2/3 3/5 1/1 8/13 4/3 13/21 1/1 5/8 3/2 1/0 12/19 2/1 19/30 1/0 7/11 1/1 9/14 3/2 11/17 1/1 3/1 13/20 3/2 1/0 2/3 0/1 2/1 7/10 1/0 5/7 -1/1 1/1 8/11 0/1 3/4 1/2 1/0 7/9 -1/1 1/1 4/5 0/1 9/11 1/3 1/1 5/6 1/2 11/13 1/3 1/1 17/20 1/2 1/0 6/7 0/1 2/3 1/1 1/1 8/7 2/1 7/6 1/0 6/5 1/0 17/14 1/0 11/9 -1/1 1/1 5/4 1/2 1/0 14/11 0/1 2/1 9/7 1/1 3/1 13/10 1/0 4/3 0/1 19/14 1/2 15/11 1/1 41/30 1/0 26/19 0/1 2/1 11/8 1/2 1/0 7/5 1/1 17/12 3/2 1/0 27/19 1/1 10/7 0/1 2/1 13/9 1/1 3/2 1/0 14/9 0/1 2/1 11/7 1/1 8/5 1/0 21/13 -3/1 34/21 -2/1 0/1 13/8 -3/2 1/0 31/19 -1/1 49/30 1/0 18/11 -2/1 0/1 23/14 1/0 28/17 0/1 33/20 -1/2 1/0 5/3 -1/1 1/1 17/10 1/0 12/7 -2/1 19/11 -1/1 7/4 -1/2 1/0 16/9 0/1 9/5 0/1 20/11 0/1 11/6 1/2 24/13 0/1 37/20 1/2 1/0 13/7 1/3 1/1 2/1 0/1 2/1 1/0 1/2 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,4,0,1) (-2/1,1/0) -> (2/1,1/0) Parabolic Matrix(259,484,160,299) (-2/1,-13/7) -> (21/13,34/21) Hyperbolic Matrix(219,404,-380,-701) (-13/7,-11/6) -> (-15/26,-19/33) Hyperbolic Matrix(79,144,-220,-401) (-11/6,-9/5) -> (-9/25,-5/14) Hyperbolic Matrix(59,104,-80,-141) (-9/5,-7/4) -> (-3/4,-11/15) Hyperbolic Matrix(79,136,-140,-241) (-7/4,-12/7) -> (-4/7,-9/16) Hyperbolic Matrix(19,32,-60,-101) (-12/7,-5/3) -> (-1/3,-4/13) Hyperbolic Matrix(39,64,-220,-361) (-5/3,-18/11) -> (-2/11,-3/17) Hyperbolic Matrix(221,360,-380,-619) (-18/11,-13/8) -> (-7/12,-18/31) Hyperbolic Matrix(159,256,-100,-161) (-13/8,-8/5) -> (-8/5,-19/12) Parabolic Matrix(521,824,380,601) (-19/12,-30/19) -> (26/19,11/8) Hyperbolic Matrix(261,412,140,221) (-30/19,-11/7) -> (13/7,2/1) Hyperbolic Matrix(179,280,140,219) (-11/7,-14/9) -> (14/11,9/7) Hyperbolic Matrix(21,32,40,61) (-14/9,-3/2) -> (1/2,6/11) Hyperbolic Matrix(39,56,-140,-201) (-3/2,-10/7) -> (-2/7,-5/18) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic Matrix(119,164,-320,-441) (-18/13,-11/8) -> (-3/8,-10/27) Hyperbolic Matrix(519,712,320,439) (-11/8,-26/19) -> (34/21,13/8) Hyperbolic Matrix(419,572,-660,-901) (-26/19,-15/11) -> (-7/11,-26/41) Hyperbolic Matrix(341,464,280,381) (-15/11,-19/14) -> (17/14,11/9) Hyperbolic Matrix(59,80,-340,-461) (-19/14,-4/3) -> (-4/23,-1/6) Hyperbolic Matrix(99,128,-140,-181) (-4/3,-9/7) -> (-5/7,-12/17) Hyperbolic Matrix(19,24,-80,-101) (-9/7,-5/4) -> (-1/4,-3/13) Hyperbolic Matrix(139,172,80,99) (-5/4,-11/9) -> (19/11,7/4) Hyperbolic Matrix(119,144,-100,-121) (-11/9,-6/5) -> (-6/5,-13/11) Parabolic Matrix(299,352,220,259) (-13/11,-7/6) -> (19/14,15/11) Hyperbolic Matrix(81,92,-140,-159) (-7/6,-1/1) -> (-11/19,-15/26) Hyperbolic Matrix(59,52,-160,-141) (-1/1,-6/7) -> (-10/27,-7/19) Hyperbolic Matrix(19,16,-120,-101) (-6/7,-5/6) -> (-1/6,-2/13) Hyperbolic Matrix(79,64,-100,-81) (-5/6,-4/5) -> (-4/5,-11/14) Parabolic Matrix(179,140,280,219) (-11/14,-7/9) -> (7/11,9/14) Hyperbolic Matrix(21,16,80,61) (-7/9,-3/4) -> (1/4,3/11) Hyperbolic Matrix(159,116,-440,-321) (-11/15,-8/11) -> (-4/11,-9/25) Hyperbolic Matrix(61,44,140,101) (-8/11,-5/7) -> (3/7,4/9) Hyperbolic Matrix(261,184,200,141) (-12/17,-7/10) -> (13/10,4/3) Hyperbolic Matrix(41,28,60,41) (-7/10,-2/3) -> (2/3,7/10) Hyperbolic Matrix(99,64,-280,-181) (-2/3,-9/14) -> (-5/14,-6/17) Hyperbolic Matrix(181,116,220,141) (-9/14,-7/11) -> (9/11,5/6) Hyperbolic Matrix(2461,1560,1800,1141) (-26/41,-19/30) -> (41/30,26/19) Hyperbolic Matrix(721,456,1140,721) (-19/30,-12/19) -> (12/19,19/30) Hyperbolic Matrix(159,100,380,239) (-12/19,-5/8) -> (5/12,8/19) Hyperbolic Matrix(59,36,-100,-61) (-5/8,-3/5) -> (-3/5,-7/12) Parabolic Matrix(559,324,-1520,-881) (-18/31,-11/19) -> (-7/19,-18/49) Hyperbolic Matrix(139,80,-940,-541) (-19/33,-4/7) -> (-4/27,-1/7) Hyperbolic Matrix(221,124,180,101) (-9/16,-5/9) -> (11/9,5/4) Hyperbolic Matrix(181,100,400,221) (-5/9,-11/20) -> (9/20,5/11) Hyperbolic Matrix(241,132,440,241) (-11/20,-6/11) -> (6/11,11/20) Hyperbolic Matrix(61,32,40,21) (-6/11,-1/2) -> (3/2,14/9) Hyperbolic Matrix(59,28,40,19) (-1/2,-5/11) -> (13/9,3/2) Hyperbolic Matrix(221,100,400,181) (-5/11,-9/20) -> (11/20,5/9) Hyperbolic Matrix(161,72,360,161) (-9/20,-4/9) -> (4/9,9/20) Hyperbolic Matrix(101,44,140,61) (-4/9,-3/7) -> (5/7,8/11) Hyperbolic Matrix(39,16,-100,-41) (-3/7,-2/5) -> (-2/5,-5/13) Parabolic Matrix(21,8,160,61) (-5/13,-8/21) -> (0/1,1/7) Hyperbolic Matrix(201,76,320,121) (-8/21,-3/8) -> (5/8,12/19) Hyperbolic Matrix(2941,1080,1800,661) (-18/49,-11/30) -> (49/30,18/11) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(261,92,400,141) (-6/17,-7/20) -> (13/20,2/3) Hyperbolic Matrix(81,28,-460,-159) (-7/20,-1/3) -> (-3/17,-7/40) Hyperbolic Matrix(341,104,200,61) (-4/13,-3/10) -> (17/10,12/7) Hyperbolic Matrix(41,12,140,41) (-3/10,-2/7) -> (2/7,3/10) Hyperbolic Matrix(101,28,220,61) (-5/18,-3/11) -> (5/11,1/2) Hyperbolic Matrix(61,16,80,21) (-3/11,-1/4) -> (3/4,7/9) Hyperbolic Matrix(281,64,180,41) (-3/13,-2/9) -> (14/9,11/7) Hyperbolic Matrix(19,4,-100,-21) (-2/9,-1/5) -> (-1/5,-2/11) Parabolic Matrix(1879,328,1140,199) (-7/40,-4/23) -> (28/17,33/20) Hyperbolic Matrix(341,52,400,61) (-2/13,-3/20) -> (17/20,6/7) Hyperbolic Matrix(1479,220,800,119) (-3/20,-4/27) -> (24/13,37/20) Hyperbolic Matrix(59,8,140,19) (-1/7,0/1) -> (8/19,3/7) Hyperbolic Matrix(101,-16,120,-19) (1/7,1/6) -> (5/6,11/13) Hyperbolic Matrix(21,-4,100,-19) (1/6,1/5) -> (1/5,3/14) Parabolic Matrix(459,-100,280,-61) (3/14,2/9) -> (18/11,23/14) Hyperbolic Matrix(101,-24,80,-19) (2/9,1/4) -> (5/4,14/11) Hyperbolic Matrix(201,-56,140,-39) (3/11,2/7) -> (10/7,13/9) Hyperbolic Matrix(101,-32,60,-19) (3/10,1/3) -> (5/3,17/10) Hyperbolic Matrix(181,-64,280,-99) (1/3,5/14) -> (9/14,11/17) Hyperbolic Matrix(401,-144,220,-79) (5/14,4/11) -> (20/11,11/6) Hyperbolic Matrix(1861,-684,1140,-419) (11/30,7/19) -> (31/19,49/30) Hyperbolic Matrix(539,-200,380,-141) (7/19,3/8) -> (17/12,27/19) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(241,-136,140,-79) (5/9,4/7) -> (12/7,19/11) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(181,-112,160,-99) (8/13,13/21) -> (1/1,8/7) Hyperbolic Matrix(521,-324,320,-199) (13/21,5/8) -> (13/8,31/19) Hyperbolic Matrix(901,-572,660,-419) (19/30,7/11) -> (15/11,41/30) Hyperbolic Matrix(661,-428,400,-259) (11/17,13/20) -> (33/20,5/3) Hyperbolic Matrix(181,-128,140,-99) (7/10,5/7) -> (9/7,13/10) Hyperbolic Matrix(141,-104,80,-59) (8/11,3/4) -> (7/4,16/9) Hyperbolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(741,-628,400,-339) (11/13,17/20) -> (37/20,13/7) Hyperbolic Matrix(199,-172,140,-121) (6/7,1/1) -> (27/19,10/7) Hyperbolic Matrix(221,-256,120,-139) (8/7,7/6) -> (11/6,24/13) Hyperbolic Matrix(121,-144,100,-119) (7/6,6/5) -> (6/5,17/14) Parabolic Matrix(461,-624,280,-379) (4/3,19/14) -> (23/14,28/17) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(181,-324,100,-179) (16/9,9/5) -> (9/5,20/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,4,0,1) -> Matrix(1,0,0,1) Matrix(259,484,160,299) -> Matrix(1,-2,0,1) Matrix(219,404,-380,-701) -> Matrix(1,0,0,1) Matrix(79,144,-220,-401) -> Matrix(1,0,4,1) Matrix(59,104,-80,-141) -> Matrix(7,-2,4,-1) Matrix(79,136,-140,-241) -> Matrix(1,0,-2,1) Matrix(19,32,-60,-101) -> Matrix(3,-2,2,-1) Matrix(39,64,-220,-361) -> Matrix(1,0,-2,1) Matrix(221,360,-380,-619) -> Matrix(1,0,-2,1) Matrix(159,256,-100,-161) -> Matrix(5,-4,4,-3) Matrix(521,824,380,601) -> Matrix(1,-2,2,-3) Matrix(261,412,140,221) -> Matrix(1,-2,2,-3) Matrix(179,280,140,219) -> Matrix(1,0,0,1) Matrix(21,32,40,61) -> Matrix(1,-2,2,-3) Matrix(39,56,-140,-201) -> Matrix(1,0,0,1) Matrix(139,196,-100,-141) -> Matrix(1,0,4,1) Matrix(119,164,-320,-441) -> Matrix(1,0,-2,1) Matrix(519,712,320,439) -> Matrix(5,-2,-2,1) Matrix(419,572,-660,-901) -> Matrix(3,-2,2,-1) Matrix(341,464,280,381) -> Matrix(1,0,-2,1) Matrix(59,80,-340,-461) -> Matrix(1,0,-2,1) Matrix(99,128,-140,-181) -> Matrix(7,-4,2,-1) Matrix(19,24,-80,-101) -> Matrix(3,-2,2,-1) Matrix(139,172,80,99) -> Matrix(3,-2,-4,3) Matrix(119,144,-100,-121) -> Matrix(9,-8,8,-7) Matrix(299,352,220,259) -> Matrix(3,-4,4,-5) Matrix(81,92,-140,-159) -> Matrix(1,-2,0,1) Matrix(59,52,-160,-141) -> Matrix(1,0,0,1) Matrix(19,16,-120,-101) -> Matrix(1,0,-2,1) Matrix(79,64,-100,-81) -> Matrix(7,-6,6,-5) Matrix(179,140,280,219) -> Matrix(1,-2,2,-3) Matrix(21,16,80,61) -> Matrix(1,-2,2,-3) Matrix(159,116,-440,-321) -> Matrix(1,-2,0,1) Matrix(61,44,140,101) -> Matrix(1,-2,2,-3) Matrix(261,184,200,141) -> Matrix(1,-4,0,1) Matrix(41,28,60,41) -> Matrix(1,0,0,1) Matrix(99,64,-280,-181) -> Matrix(1,-2,2,-3) Matrix(181,116,220,141) -> Matrix(1,-2,2,-3) Matrix(2461,1560,1800,1141) -> Matrix(1,-2,0,1) Matrix(721,456,1140,721) -> Matrix(1,0,0,1) Matrix(159,100,380,239) -> Matrix(1,-2,4,-7) Matrix(59,36,-100,-61) -> Matrix(1,-4,0,1) Matrix(559,324,-1520,-881) -> Matrix(1,2,0,1) Matrix(139,80,-940,-541) -> Matrix(1,0,0,1) Matrix(221,124,180,101) -> Matrix(1,0,0,1) Matrix(181,100,400,221) -> Matrix(1,0,2,1) Matrix(241,132,440,241) -> Matrix(1,-2,2,-3) Matrix(61,32,40,21) -> Matrix(1,0,0,1) Matrix(59,28,40,19) -> Matrix(1,2,0,1) Matrix(221,100,400,181) -> Matrix(3,2,4,3) Matrix(161,72,360,161) -> Matrix(1,0,4,1) Matrix(101,44,140,61) -> Matrix(1,0,0,1) Matrix(39,16,-100,-41) -> Matrix(1,0,2,1) Matrix(21,8,160,61) -> Matrix(1,0,0,1) Matrix(201,76,320,121) -> Matrix(3,-2,2,-1) Matrix(2941,1080,1800,661) -> Matrix(1,-2,0,1) Matrix(241,88,660,241) -> Matrix(1,0,0,1) Matrix(261,92,400,141) -> Matrix(3,-2,2,-1) Matrix(81,28,-460,-159) -> Matrix(1,0,-2,1) Matrix(341,104,200,61) -> Matrix(1,-4,0,1) Matrix(41,12,140,41) -> Matrix(1,2,0,1) Matrix(101,28,220,61) -> Matrix(1,0,2,1) Matrix(61,16,80,21) -> Matrix(1,0,0,1) Matrix(281,64,180,41) -> Matrix(1,0,0,1) Matrix(19,4,-100,-21) -> Matrix(1,-2,0,1) Matrix(1879,328,1140,199) -> Matrix(1,0,0,1) Matrix(341,52,400,61) -> Matrix(1,0,2,1) Matrix(1479,220,800,119) -> Matrix(1,0,2,1) Matrix(59,8,140,19) -> Matrix(1,0,4,1) Matrix(101,-16,120,-19) -> Matrix(1,0,0,1) Matrix(21,-4,100,-19) -> Matrix(3,-2,2,-1) Matrix(459,-100,280,-61) -> Matrix(1,-2,0,1) Matrix(101,-24,80,-19) -> Matrix(1,0,0,1) Matrix(201,-56,140,-39) -> Matrix(1,0,0,1) Matrix(101,-32,60,-19) -> Matrix(1,0,0,1) Matrix(181,-64,280,-99) -> Matrix(1,2,0,1) Matrix(401,-144,220,-79) -> Matrix(1,0,4,1) Matrix(1861,-684,1140,-419) -> Matrix(1,0,0,1) Matrix(539,-200,380,-141) -> Matrix(1,2,0,1) Matrix(41,-16,100,-39) -> Matrix(1,0,6,1) Matrix(241,-136,140,-79) -> Matrix(1,0,-2,1) Matrix(61,-36,100,-59) -> Matrix(7,-6,6,-5) Matrix(181,-112,160,-99) -> Matrix(1,-2,2,-3) Matrix(521,-324,320,-199) -> Matrix(3,-4,-2,3) Matrix(901,-572,660,-419) -> Matrix(1,0,0,1) Matrix(661,-428,400,-259) -> Matrix(1,-2,0,1) Matrix(181,-128,140,-99) -> Matrix(1,2,0,1) Matrix(141,-104,80,-59) -> Matrix(1,0,-2,1) Matrix(81,-64,100,-79) -> Matrix(1,0,2,1) Matrix(741,-628,400,-339) -> Matrix(1,0,0,1) Matrix(199,-172,140,-121) -> Matrix(3,-2,2,-1) Matrix(221,-256,120,-139) -> Matrix(1,-2,2,-3) Matrix(121,-144,100,-119) -> Matrix(1,-2,0,1) Matrix(461,-624,280,-379) -> Matrix(1,0,-2,1) Matrix(141,-196,100,-139) -> Matrix(3,-2,2,-1) Matrix(161,-256,100,-159) -> Matrix(1,-4,0,1) Matrix(181,-324,100,-179) -> Matrix(1,0,6,1) 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): 18 Degree of the the map X: 18 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 -3/2 1/0 1 10 -10/7 0 10 -7/5 0/1 2 2 -18/13 0 10 -11/8 0 10 -15/11 0 10 -4/3 0/1 1 10 -9/7 1/1 1 10 -5/4 0 10 -6/5 1/1 4 2 -7/6 3/2 1 10 -1/1 0 10 -6/7 0 10 -5/6 1/2 1 10 -4/5 1/1 3 2 -11/14 5/4 1 10 -7/9 1/1 1 10 -3/4 0 10 -11/15 2/1 4 2 -8/11 2/1 1 10 -5/7 3/1 1 10 -7/10 1/0 3 2 -2/3 0 10 -9/14 1/0 1 10 -7/11 0 10 -19/30 1/0 1 2 -12/19 2/1 1 10 -5/8 0 10 -3/5 1/0 2 2 -7/12 0 10 -18/31 0 10 -11/19 0 10 -15/26 -1/2 1 10 -4/7 0/1 1 10 -5/9 0 10 -11/20 (1/2,1/0) 0 2 -1/2 1/0 1 10 -9/20 (-1/2,1/0) 0 2 -4/9 0/1 1 10 -3/7 0 10 -2/5 0/1 1 2 -5/13 0 10 -8/21 0/1 1 10 -3/8 0 10 -10/27 0 10 -7/19 0 10 -18/49 0 10 -11/30 1/0 1 2 -4/11 0/1 1 10 -9/25 0/1 4 2 -5/14 1/2 1 10 -6/17 0 10 -7/20 (1/2,1/0) 0 2 -1/3 1/1 1 10 -4/13 2/1 1 10 -3/10 1/0 3 2 -2/7 0 10 -5/18 1/0 1 10 -3/11 0 10 -1/4 0 10 -3/13 1/1 1 10 -2/9 0 10 -1/5 1/0 1 2 -2/11 0 10 -3/17 -1/1 1 10 -7/40 (-1/2,1/0) 0 2 -1/6 1/0 1 10 -2/13 0 10 -3/20 (-1/2,1/0) 0 2 -1/7 -1/1 1 10 0/1 0/1 1 10 1/7 0 10 3/20 (1/2,1/0) 0 2 1/6 1/2 1 10 1/5 1/1 1 2 3/14 1/0 1 10 2/9 0 10 1/4 0 10 3/11 1/1 1 10 2/7 0 10 3/10 1/0 3 2 1/3 0 10 7/20 (-1/2,1/0) 0 2 5/14 -1/2 1 10 4/11 0/1 1 10 11/30 1/0 1 2 7/19 -1/1 1 10 3/8 0 10 2/5 0/1 3 2 5/12 0 10 8/19 0/1 1 10 3/7 1/3 1 10 4/9 0/1 1 10 9/20 (1/4,1/2) 0 2 5/11 0 10 1/2 1/2 1 10 1/0 (1/2,1/0) 0 2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,3,0,-1) (-3/2,1/0) -> (-3/2,1/0) Reflection Matrix(39,56,-140,-201) (-3/2,-10/7) -> (-2/7,-5/18) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic Matrix(119,164,-320,-441) (-18/13,-11/8) -> (-3/8,-10/27) Hyperbolic Matrix(221,303,-380,-521) (-11/8,-15/11) -> (-7/12,-18/31) Glide Reflection Matrix(39,53,-220,-299) (-15/11,-4/3) -> (-2/11,-3/17) Glide Reflection Matrix(19,25,-60,-79) (-4/3,-9/7) -> (-1/3,-4/13) Glide Reflection Matrix(19,24,-80,-101) (-9/7,-5/4) -> (-1/4,-3/13) Hyperbolic Matrix(59,73,-80,-99) (-5/4,-6/5) -> (-3/4,-11/15) Glide Reflection Matrix(79,93,-220,-259) (-6/5,-7/6) -> (-9/25,-5/14) Glide Reflection Matrix(81,92,-140,-159) (-7/6,-1/1) -> (-11/19,-15/26) Hyperbolic Matrix(59,52,-160,-141) (-1/1,-6/7) -> (-10/27,-7/19) Hyperbolic Matrix(19,16,-120,-101) (-6/7,-5/6) -> (-1/6,-2/13) Hyperbolic Matrix(79,64,-100,-81) (-5/6,-4/5) -> (-4/5,-11/14) Parabolic Matrix(101,79,280,219) (-11/14,-7/9) -> (5/14,4/11) Glide Reflection Matrix(21,16,80,61) (-7/9,-3/4) -> (1/4,3/11) Hyperbolic Matrix(159,116,-440,-321) (-11/15,-8/11) -> (-4/11,-9/25) Hyperbolic Matrix(61,44,140,101) (-8/11,-5/7) -> (3/7,4/9) Hyperbolic Matrix(61,43,-200,-141) (-5/7,-7/10) -> (-4/13,-3/10) Glide Reflection Matrix(19,13,60,41) (-7/10,-2/3) -> (3/10,1/3) Glide Reflection Matrix(99,64,-280,-181) (-2/3,-9/14) -> (-5/14,-6/17) Hyperbolic Matrix(61,39,280,179) (-9/14,-7/11) -> (3/14,2/9) Glide Reflection Matrix(661,419,-1800,-1141) (-7/11,-19/30) -> (-18/49,-11/30) Glide Reflection Matrix(419,265,1140,721) (-19/30,-12/19) -> (11/30,7/19) Glide Reflection Matrix(159,100,380,239) (-12/19,-5/8) -> (5/12,8/19) Hyperbolic Matrix(59,36,-100,-61) (-5/8,-3/5) -> (-3/5,-7/12) Parabolic Matrix(559,324,-1520,-881) (-18/31,-11/19) -> (-7/19,-18/49) Hyperbolic Matrix(599,345,-1040,-599) (-15/26,-23/40) -> (-15/26,-23/40) Reflection Matrix(61,35,-420,-241) (-19/33,-4/7) -> (-4/27,-1/7) Glide Reflection Matrix(41,23,-180,-101) (-4/7,-5/9) -> (-3/13,-2/9) Glide Reflection Matrix(181,100,400,221) (-5/9,-11/20) -> (9/20,5/11) Hyperbolic Matrix(21,11,-40,-21) (-11/20,-1/2) -> (-11/20,-1/2) Reflection Matrix(19,9,-40,-19) (-1/2,-9/20) -> (-1/2,-9/20) Reflection Matrix(161,72,360,161) (-9/20,-4/9) -> (4/9,9/20) Hyperbolic Matrix(39,17,140,61) (-4/9,-3/7) -> (3/11,2/7) Glide Reflection Matrix(39,16,-100,-41) (-3/7,-2/5) -> (-2/5,-5/13) Parabolic Matrix(21,8,160,61) (-5/13,-8/21) -> (0/1,1/7) Hyperbolic Matrix(119,45,320,121) (-8/21,-3/8) -> (7/19,3/8) Glide Reflection Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(139,49,400,141) (-6/17,-7/20) -> (1/3,7/20) Glide Reflection Matrix(81,28,-460,-159) (-7/20,-1/3) -> (-3/17,-7/40) Hyperbolic Matrix(41,12,140,41) (-3/10,-2/7) -> (2/7,3/10) Hyperbolic Matrix(101,28,220,61) (-5/18,-3/11) -> (5/11,1/2) Hyperbolic Matrix(19,5,80,21) (-3/11,-1/4) -> (2/9,1/4) Glide Reflection Matrix(19,4,-100,-21) (-2/9,-1/5) -> (-1/5,-2/11) Parabolic Matrix(41,7,-240,-41) (-7/40,-1/6) -> (-7/40,-1/6) Reflection Matrix(59,9,400,61) (-2/13,-3/20) -> (1/7,3/20) Glide Reflection Matrix(101,15,-680,-101) (-3/20,-5/34) -> (-3/20,-5/34) Reflection Matrix(59,8,140,19) (-1/7,0/1) -> (8/19,3/7) Hyperbolic Matrix(19,-3,120,-19) (3/20,1/6) -> (3/20,1/6) Reflection Matrix(21,-4,100,-19) (1/6,1/5) -> (1/5,3/14) Parabolic Matrix(99,-35,280,-99) (7/20,5/14) -> (7/20,5/14) Reflection Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic 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(1,3,0,-1) -> Matrix(-1,1,0,1) (-3/2,1/0) -> (1/2,1/0) Matrix(39,56,-140,-201) -> Matrix(1,0,0,1) Matrix(139,196,-100,-141) -> Matrix(1,0,4,1) 0/1 Matrix(119,164,-320,-441) -> Matrix(1,0,-2,1) 0/1 Matrix(221,303,-380,-521) -> Matrix(1,-1,-2,1) Matrix(39,53,-220,-299) -> Matrix(1,-1,-2,1) Matrix(19,25,-60,-79) -> Matrix(3,-1,2,-1) Matrix(19,24,-80,-101) -> Matrix(3,-2,2,-1) 1/1 Matrix(59,73,-80,-99) -> Matrix(7,-5,4,-3) Matrix(79,93,-220,-259) -> Matrix(1,-1,4,-5) Matrix(81,92,-140,-159) -> Matrix(1,-2,0,1) 1/0 Matrix(59,52,-160,-141) -> Matrix(1,0,0,1) Matrix(19,16,-120,-101) -> Matrix(1,0,-2,1) 0/1 Matrix(79,64,-100,-81) -> Matrix(7,-6,6,-5) 1/1 Matrix(101,79,280,219) -> Matrix(1,-1,2,-3) Matrix(21,16,80,61) -> Matrix(1,-2,2,-3) 1/1 Matrix(159,116,-440,-321) -> Matrix(1,-2,0,1) 1/0 Matrix(61,44,140,101) -> Matrix(1,-2,2,-3) 1/1 Matrix(61,43,-200,-141) -> Matrix(-1,5,0,1) *** -> (5/2,1/0) Matrix(19,13,60,41) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(99,64,-280,-181) -> Matrix(1,-2,2,-3) 1/1 Matrix(61,39,280,179) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(661,419,-1800,-1141) -> Matrix(-1,3,0,1) *** -> (3/2,1/0) Matrix(419,265,1140,721) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(159,100,380,239) -> Matrix(1,-2,4,-7) Matrix(59,36,-100,-61) -> Matrix(1,-4,0,1) 1/0 Matrix(559,324,-1520,-881) -> Matrix(1,2,0,1) 1/0 Matrix(599,345,-1040,-599) -> Matrix(1,1,0,-1) (-15/26,-23/40) -> (-1/2,1/0) Matrix(61,35,-420,-241) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(41,23,-180,-101) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(181,100,400,221) -> Matrix(1,0,2,1) 0/1 Matrix(21,11,-40,-21) -> Matrix(-1,1,0,1) (-11/20,-1/2) -> (1/2,1/0) Matrix(19,9,-40,-19) -> Matrix(1,1,0,-1) (-1/2,-9/20) -> (-1/2,1/0) Matrix(161,72,360,161) -> Matrix(1,0,4,1) 0/1 Matrix(39,17,140,61) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(39,16,-100,-41) -> Matrix(1,0,2,1) 0/1 Matrix(21,8,160,61) -> Matrix(1,0,0,1) Matrix(119,45,320,121) -> Matrix(1,-1,-2,1) Matrix(241,88,660,241) -> Matrix(1,0,0,1) Matrix(139,49,400,141) -> Matrix(1,-1,-2,1) Matrix(81,28,-460,-159) -> Matrix(1,0,-2,1) 0/1 Matrix(41,12,140,41) -> Matrix(1,2,0,1) 1/0 Matrix(101,28,220,61) -> Matrix(1,0,2,1) 0/1 Matrix(19,5,80,21) -> Matrix(-1,1,0,1) *** -> (1/2,1/0) Matrix(19,4,-100,-21) -> Matrix(1,-2,0,1) 1/0 Matrix(41,7,-240,-41) -> Matrix(1,1,0,-1) (-7/40,-1/6) -> (-1/2,1/0) Matrix(59,9,400,61) -> Matrix(1,1,2,1) Matrix(101,15,-680,-101) -> Matrix(1,1,0,-1) (-3/20,-5/34) -> (-1/2,1/0) Matrix(59,8,140,19) -> Matrix(1,0,4,1) 0/1 Matrix(19,-3,120,-19) -> Matrix(-1,1,0,1) (3/20,1/6) -> (1/2,1/0) Matrix(21,-4,100,-19) -> Matrix(3,-2,2,-1) 1/1 Matrix(99,-35,280,-99) -> Matrix(1,1,0,-1) (7/20,5/14) -> (-1/2,1/0) Matrix(41,-16,100,-39) -> Matrix(1,0,6,1) 0/1 Matrix(-1,1,0,1) -> Matrix(-1,1,0,1) (1/2,1/0) -> (1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.