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 -4/5 -3/4 -3/5 -59/100 -1/2 -2/5 -3/8 -4/15 -1/4 -4/17 -1/5 -1/6 -2/15 -1/8 -1/9 0/1 1/8 1/7 3/20 2/13 1/6 2/11 1/5 4/19 2/9 1/4 4/15 2/7 3/10 1/3 7/20 11/30 3/8 2/5 9/20 1/2 11/20 3/5 19/30 13/20 2/3 7/10 18/25 3/4 4/5 17/20 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/1 -6/7 2/1 1/0 -17/20 1/0 -11/13 1/1 -5/6 1/1 3/1 -4/5 1/0 -11/14 -1/1 1/1 -18/23 -1/1 1/0 -7/9 1/1 -10/13 0/1 1/0 -3/4 1/0 -14/19 -1/1 -2/3 -11/15 0/1 -8/11 -1/1 0/1 -13/18 1/3 1/1 -31/43 1/1 -18/25 1/0 -5/7 1/1 -12/17 1/1 1/0 -7/10 1/0 -2/3 0/1 1/0 -13/20 0/1 -11/17 1/1 -9/14 -1/1 1/1 -7/11 1/1 -26/41 0/1 1/0 -19/30 0/1 -12/19 0/1 1/1 -5/8 1/0 -13/21 -1/1 -21/34 -1/1 -1/3 -8/13 0/1 1/0 -11/18 -3/1 -1/1 -3/5 0/1 -13/22 3/5 1/1 -36/61 8/9 1/1 -59/100 1/1 -23/39 1/1 -10/17 1/1 1/0 -17/29 -1/1 -7/12 0/1 -18/31 1/2 1/1 -11/19 1/1 -4/7 0/1 1/0 -5/9 -1/1 -11/20 0/1 -6/11 0/1 1/3 -1/2 -1/1 1/1 -6/13 2/1 1/0 -5/11 3/1 -9/20 1/0 -4/9 -1/1 1/0 -3/7 1/1 -2/5 1/0 -5/13 -1/1 -13/34 -3/1 -1/1 -8/21 -1/1 0/1 -3/8 1/0 -7/19 -1/1 -18/49 -3/2 -1/1 -11/30 -1/1 -4/11 -1/1 0/1 -5/14 -1/1 1/1 -6/17 1/1 1/0 -7/20 1/0 -1/3 -1/1 -7/22 -5/3 -1/1 -6/19 -1/1 -4/5 -5/16 -1/2 -4/13 -1/2 0/1 -3/10 0/1 -2/7 0/1 1/0 -3/11 1/1 -7/26 -1/1 1/1 -4/15 1/0 -9/34 -3/1 -1/1 -5/19 -1/1 -1/4 0/1 -5/21 1/1 -4/17 1/1 1/0 -3/13 1/1 -2/9 -1/1 1/0 -7/32 0/1 -5/23 -1/1 -3/14 -1/1 1/1 -4/19 -2/1 -1/1 -1/5 0/1 -2/11 0/1 1/1 -1/6 -1/1 1/1 -2/13 -1/2 0/1 -3/20 0/1 -1/7 1/1 -2/15 1/0 -3/23 -1/1 -1/8 0/1 -1/9 -1/1 0/1 0/1 1/0 1/8 0/1 1/7 -1/1 3/20 0/1 2/13 0/1 1/2 1/6 -1/1 1/1 2/11 -1/1 0/1 1/5 0/1 4/19 1/1 2/1 3/14 -1/1 1/1 5/23 1/1 2/9 1/1 1/0 1/4 0/1 5/19 1/1 4/15 1/0 3/11 -1/1 2/7 0/1 1/0 3/10 0/1 4/13 0/1 1/2 1/3 1/1 7/20 1/0 6/17 -1/1 1/0 5/14 -1/1 1/1 4/11 0/1 1/1 11/30 1/1 7/19 1/1 3/8 1/0 2/5 1/0 5/12 1/0 8/19 -2/1 -1/1 11/26 -1/1 1/1 3/7 -1/1 7/16 0/1 4/9 1/1 1/0 9/20 1/0 5/11 -3/1 1/2 -1/1 1/1 6/11 -1/3 0/1 11/20 0/1 5/9 1/1 4/7 0/1 1/0 11/19 -1/1 29/50 -1/1 18/31 -1/1 -1/2 25/43 -1/1 7/12 0/1 24/41 0/1 1/0 17/29 1/1 10/17 -1/1 1/0 3/5 0/1 14/23 1/2 1/1 25/41 1/1 61/100 1/1 36/59 1/1 8/7 11/18 1/1 3/1 8/13 0/1 1/0 21/34 1/3 1/1 13/21 1/1 5/8 1/0 12/19 -1/1 0/1 19/30 0/1 26/41 0/1 1/0 7/11 -1/1 16/25 1/0 25/39 -1/1 9/14 -1/1 1/1 11/17 -1/1 13/20 0/1 2/3 0/1 1/0 7/10 1/0 12/17 -1/1 1/0 29/41 -1/1 17/24 0/1 5/7 -1/1 23/32 0/1 18/25 1/0 49/68 -2/1 31/43 -1/1 13/18 -1/1 -1/3 8/11 0/1 1/1 11/15 0/1 14/19 2/3 1/1 3/4 1/0 16/21 -4/3 -1/1 29/38 -1/1 -5/7 13/17 -1/1 10/13 0/1 1/0 17/22 1/1 3/1 7/9 -1/1 4/5 1/0 9/11 -3/1 14/17 -1/1 1/0 5/6 -3/1 -1/1 11/13 -1/1 17/20 1/0 6/7 -2/1 1/0 1/1 -1/1 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(81,70,140,121) (-1/1,-6/7) -> (4/7,11/19) Hyperbolic Matrix(239,204,280,239) (-6/7,-17/20) -> (17/20,6/7) Hyperbolic Matrix(441,374,520,441) (-17/20,-11/13) -> (11/13,17/20) Hyperbolic Matrix(161,136,380,321) (-11/13,-5/6) -> (11/26,3/7) Hyperbolic Matrix(79,64,-100,-81) (-5/6,-4/5) -> (-4/5,-11/14) Parabolic Matrix(199,156,560,439) (-11/14,-18/23) -> (6/17,5/14) Hyperbolic Matrix(481,376,820,641) (-18/23,-7/9) -> (17/29,10/17) Hyperbolic Matrix(119,92,-260,-201) (-7/9,-10/13) -> (-6/13,-5/11) Hyperbolic Matrix(81,62,-260,-199) (-10/13,-3/4) -> (-5/16,-4/13) Hyperbolic Matrix(119,88,-380,-281) (-3/4,-14/19) -> (-6/19,-5/16) Hyperbolic Matrix(79,58,380,279) (-14/19,-11/15) -> (1/5,4/19) Hyperbolic Matrix(41,30,220,161) (-11/15,-8/11) -> (2/11,1/5) Hyperbolic Matrix(119,86,220,159) (-8/11,-13/18) -> (1/2,6/11) Hyperbolic Matrix(319,230,-1000,-721) (-13/18,-31/43) -> (-1/3,-7/22) Hyperbolic Matrix(161,116,-1220,-879) (-31/43,-18/25) -> (-2/15,-3/23) Hyperbolic Matrix(39,28,-280,-201) (-18/25,-5/7) -> (-1/7,-2/15) Hyperbolic Matrix(79,56,-340,-241) (-5/7,-12/17) -> (-4/17,-3/13) Hyperbolic Matrix(239,168,340,239) (-12/17,-7/10) -> (7/10,12/17) Hyperbolic Matrix(41,28,60,41) (-7/10,-2/3) -> (2/3,7/10) Hyperbolic Matrix(79,52,120,79) (-2/3,-13/20) -> (13/20,2/3) Hyperbolic Matrix(441,286,680,441) (-13/20,-11/17) -> (11/17,13/20) Hyperbolic Matrix(121,78,560,361) (-11/17,-9/14) -> (3/14,5/23) Hyperbolic Matrix(119,76,-440,-281) (-9/14,-7/11) -> (-3/11,-7/26) Hyperbolic Matrix(961,610,1640,1041) (-7/11,-26/41) -> (24/41,17/29) Hyperbolic Matrix(1559,988,2460,1559) (-26/41,-19/30) -> (19/30,26/41) 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(119,74,320,199) (-5/8,-13/21) -> (7/19,3/8) Hyperbolic Matrix(359,222,-1360,-841) (-13/21,-21/34) -> (-9/34,-5/19) Hyperbolic Matrix(81,50,520,321) (-21/34,-8/13) -> (2/13,1/6) Hyperbolic Matrix(121,74,-260,-159) (-8/13,-11/18) -> (-1/2,-6/13) Hyperbolic Matrix(119,72,-200,-121) (-11/18,-3/5) -> (-3/5,-13/22) Parabolic Matrix(2121,1252,2780,1641) (-13/22,-36/61) -> (16/21,29/38) Hyperbolic Matrix(7321,4320,12000,7081) (-36/61,-59/100) -> (61/100,36/59) Hyperbolic Matrix(4879,2878,8000,4719) (-59/100,-23/39) -> (25/41,61/100) Hyperbolic Matrix(961,566,1360,801) (-23/39,-10/17) -> (12/17,29/41) Hyperbolic Matrix(559,328,680,399) (-10/17,-17/29) -> (9/11,14/17) Hyperbolic Matrix(41,24,-340,-199) (-17/29,-7/12) -> (-1/8,-1/9) Hyperbolic Matrix(241,140,-1100,-639) (-7/12,-18/31) -> (-2/9,-7/32) Hyperbolic Matrix(559,324,-1520,-881) (-18/31,-11/19) -> (-7/19,-18/49) Hyperbolic Matrix(121,70,140,81) (-11/19,-4/7) -> (6/7,1/1) Hyperbolic Matrix(39,22,140,79) (-4/7,-5/9) -> (3/11,2/7) Hyperbolic Matrix(199,110,360,199) (-5/9,-11/20) -> (11/20,5/9) Hyperbolic Matrix(241,132,440,241) (-11/20,-6/11) -> (6/11,11/20) Hyperbolic Matrix(159,86,220,119) (-6/11,-1/2) -> (13/18,8/11) Hyperbolic Matrix(199,90,440,199) (-5/11,-9/20) -> (9/20,5/11) Hyperbolic Matrix(161,72,360,161) (-9/20,-4/9) -> (4/9,9/20) Hyperbolic Matrix(41,18,-180,-79) (-4/9,-3/7) -> (-3/13,-2/9) Hyperbolic Matrix(39,16,-100,-41) (-3/7,-2/5) -> (-2/5,-5/13) Parabolic Matrix(439,168,520,199) (-5/13,-13/34) -> (5/6,11/13) Hyperbolic Matrix(199,76,940,359) (-13/34,-8/21) -> (4/19,3/14) Hyperbolic Matrix(201,76,320,121) (-8/21,-3/8) -> (5/8,12/19) Hyperbolic Matrix(199,74,320,119) (-3/8,-7/19) -> (13/21,5/8) Hyperbolic Matrix(1961,720,3380,1241) (-18/49,-11/30) -> (29/50,18/31) Hyperbolic Matrix(241,88,660,241) (-11/30,-4/11) -> (4/11,11/30) Hyperbolic Matrix(39,14,220,79) (-4/11,-5/14) -> (1/6,2/11) Hyperbolic Matrix(281,100,340,121) (-5/14,-6/17) -> (14/17,5/6) Hyperbolic Matrix(239,84,680,239) (-6/17,-7/20) -> (7/20,6/17) Hyperbolic Matrix(41,14,120,41) (-7/20,-1/3) -> (1/3,7/20) Hyperbolic Matrix(1001,318,1640,521) (-7/22,-6/19) -> (36/59,11/18) Hyperbolic Matrix(79,24,260,79) (-4/13,-3/10) -> (3/10,4/13) Hyperbolic Matrix(41,12,140,41) (-3/10,-2/7) -> (2/7,3/10) Hyperbolic Matrix(79,22,140,39) (-2/7,-3/11) -> (5/9,4/7) Hyperbolic Matrix(239,64,-900,-241) (-7/26,-4/15) -> (-4/15,-9/34) Parabolic Matrix(39,10,-160,-41) (-5/19,-1/4) -> (-1/4,-5/21) Parabolic Matrix(719,170,1180,279) (-5/21,-4/17) -> (14/23,25/41) Hyperbolic Matrix(119,26,-920,-201) (-7/32,-5/23) -> (-3/23,-1/8) Hyperbolic Matrix(361,78,560,121) (-5/23,-3/14) -> (9/14,11/17) Hyperbolic Matrix(321,68,760,161) (-3/14,-4/19) -> (8/19,11/26) Hyperbolic Matrix(279,58,380,79) (-4/19,-1/5) -> (11/15,14/19) Hyperbolic Matrix(161,30,220,41) (-1/5,-2/11) -> (8/11,11/15) Hyperbolic Matrix(79,14,220,39) (-2/11,-1/6) -> (5/14,4/11) Hyperbolic Matrix(321,50,520,81) (-1/6,-2/13) -> (8/13,21/34) Hyperbolic Matrix(79,12,520,79) (-2/13,-3/20) -> (3/20,2/13) Hyperbolic Matrix(41,6,280,41) (-3/20,-1/7) -> (1/7,3/20) Hyperbolic Matrix(241,26,380,41) (-1/9,0/1) -> (26/41,7/11) Hyperbolic Matrix(199,-24,340,-41) (0/1,1/8) -> (7/12,24/41) Hyperbolic Matrix(201,-28,280,-39) (1/8,1/7) -> (5/7,23/32) Hyperbolic Matrix(639,-140,1100,-241) (5/23,2/9) -> (18/31,25/43) Hyperbolic Matrix(79,-18,180,-41) (2/9,1/4) -> (7/16,4/9) Hyperbolic Matrix(439,-114,620,-161) (1/4,5/19) -> (29/41,17/24) Hyperbolic Matrix(679,-180,1060,-281) (5/19,4/15) -> (16/25,25/39) Hyperbolic Matrix(281,-76,440,-119) (4/15,3/11) -> (7/11,16/25) Hyperbolic Matrix(199,-62,260,-81) (4/13,1/3) -> (13/17,10/13) Hyperbolic Matrix(881,-324,1520,-559) (11/30,7/19) -> (11/19,29/50) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(199,-86,280,-121) (3/7,7/16) -> (17/24,5/7) Hyperbolic Matrix(201,-92,260,-119) (5/11,1/2) -> (17/22,7/9) Hyperbolic Matrix(2479,-1442,3440,-2001) (25/43,7/12) -> (49/68,31/43) Hyperbolic Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(401,-246,520,-319) (11/18,8/13) -> (10/13,17/22) Hyperbolic Matrix(1039,-642,1620,-1001) (21/34,13/21) -> (25/39,9/14) Hyperbolic Matrix(1801,-1296,2500,-1799) (23/32,18/25) -> (18/25,49/68) Parabolic Matrix(1481,-1068,1940,-1399) (31/43,13/18) -> (29/38,13/17) Hyperbolic Matrix(121,-90,160,-119) (14/19,3/4) -> (3/4,16/21) Parabolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(81,70,140,121) -> Matrix(1,-2,0,1) Matrix(239,204,280,239) -> Matrix(1,-4,0,1) Matrix(441,374,520,441) -> Matrix(1,-2,0,1) Matrix(161,136,380,321) -> Matrix(1,-2,0,1) Matrix(79,64,-100,-81) -> Matrix(1,-2,0,1) Matrix(199,156,560,439) -> Matrix(1,0,0,1) Matrix(481,376,820,641) -> Matrix(1,0,0,1) Matrix(119,92,-260,-201) -> Matrix(1,2,0,1) Matrix(81,62,-260,-199) -> Matrix(1,0,-2,1) Matrix(119,88,-380,-281) -> Matrix(1,2,-2,-3) Matrix(79,58,380,279) -> Matrix(1,0,2,1) Matrix(41,30,220,161) -> Matrix(1,0,0,1) Matrix(119,86,220,159) -> Matrix(1,0,-2,1) Matrix(319,230,-1000,-721) -> Matrix(1,-2,0,1) Matrix(161,116,-1220,-879) -> Matrix(1,-2,0,1) Matrix(39,28,-280,-201) -> Matrix(1,0,0,1) Matrix(79,56,-340,-241) -> Matrix(1,0,0,1) Matrix(239,168,340,239) -> Matrix(1,-2,0,1) Matrix(41,28,60,41) -> Matrix(1,0,0,1) Matrix(79,52,120,79) -> Matrix(1,0,0,1) Matrix(441,286,680,441) -> Matrix(1,0,-2,1) Matrix(121,78,560,361) -> Matrix(1,0,0,1) Matrix(119,76,-440,-281) -> Matrix(1,0,0,1) Matrix(961,610,1640,1041) -> Matrix(1,0,0,1) Matrix(1559,988,2460,1559) -> Matrix(1,0,0,1) Matrix(721,456,1140,721) -> Matrix(1,0,-2,1) Matrix(159,100,380,239) -> Matrix(1,-2,0,1) Matrix(119,74,320,199) -> Matrix(1,2,0,1) Matrix(359,222,-1360,-841) -> Matrix(3,2,-2,-1) Matrix(81,50,520,321) -> Matrix(1,0,2,1) Matrix(121,74,-260,-159) -> Matrix(1,2,0,1) Matrix(119,72,-200,-121) -> Matrix(1,0,2,1) Matrix(2121,1252,2780,1641) -> Matrix(5,-4,-6,5) Matrix(7321,4320,12000,7081) -> Matrix(17,-16,16,-15) Matrix(4879,2878,8000,4719) -> Matrix(9,-10,10,-11) Matrix(961,566,1360,801) -> Matrix(1,-2,0,1) Matrix(559,328,680,399) -> Matrix(1,-2,0,1) Matrix(41,24,-340,-199) -> Matrix(1,0,0,1) Matrix(241,140,-1100,-639) -> Matrix(1,0,-2,1) Matrix(559,324,-1520,-881) -> Matrix(1,-2,0,1) Matrix(121,70,140,81) -> Matrix(1,-2,0,1) Matrix(39,22,140,79) -> Matrix(1,0,0,1) Matrix(199,110,360,199) -> Matrix(1,0,2,1) Matrix(241,132,440,241) -> Matrix(1,0,-6,1) Matrix(159,86,220,119) -> Matrix(1,0,-2,1) Matrix(199,90,440,199) -> Matrix(1,-6,0,1) Matrix(161,72,360,161) -> Matrix(1,2,0,1) Matrix(41,18,-180,-79) -> Matrix(1,0,0,1) Matrix(39,16,-100,-41) -> Matrix(1,-2,0,1) Matrix(439,168,520,199) -> Matrix(1,0,0,1) Matrix(199,76,940,359) -> Matrix(1,2,0,1) Matrix(201,76,320,121) -> Matrix(1,0,0,1) Matrix(199,74,320,119) -> Matrix(1,2,0,1) Matrix(1961,720,3380,1241) -> Matrix(3,4,-4,-5) Matrix(241,88,660,241) -> Matrix(1,0,2,1) Matrix(39,14,220,79) -> Matrix(1,0,0,1) Matrix(281,100,340,121) -> Matrix(1,-2,0,1) Matrix(239,84,680,239) -> Matrix(1,-2,0,1) Matrix(41,14,120,41) -> Matrix(1,2,0,1) Matrix(1001,318,1640,521) -> Matrix(3,4,2,3) Matrix(79,24,260,79) -> Matrix(1,0,4,1) Matrix(41,12,140,41) -> Matrix(1,0,0,1) Matrix(79,22,140,39) -> Matrix(1,0,0,1) Matrix(239,64,-900,-241) -> Matrix(1,-2,0,1) Matrix(39,10,-160,-41) -> Matrix(1,0,2,1) Matrix(719,170,1180,279) -> Matrix(1,-2,2,-3) Matrix(119,26,-920,-201) -> Matrix(1,0,0,1) Matrix(361,78,560,121) -> Matrix(1,0,0,1) Matrix(321,68,760,161) -> Matrix(1,0,0,1) Matrix(279,58,380,79) -> Matrix(1,0,2,1) Matrix(161,30,220,41) -> Matrix(1,0,0,1) Matrix(79,14,220,39) -> Matrix(1,0,0,1) Matrix(321,50,520,81) -> Matrix(1,0,2,1) Matrix(79,12,520,79) -> Matrix(1,0,4,1) Matrix(41,6,280,41) -> Matrix(1,0,-2,1) Matrix(241,26,380,41) -> Matrix(1,0,0,1) Matrix(199,-24,340,-41) -> Matrix(1,0,0,1) Matrix(201,-28,280,-39) -> Matrix(1,0,0,1) Matrix(639,-140,1100,-241) -> Matrix(1,0,-2,1) Matrix(79,-18,180,-41) -> Matrix(1,0,0,1) Matrix(439,-114,620,-161) -> Matrix(1,0,-2,1) Matrix(679,-180,1060,-281) -> Matrix(1,-2,0,1) Matrix(281,-76,440,-119) -> Matrix(1,0,0,1) Matrix(199,-62,260,-81) -> Matrix(1,0,-2,1) Matrix(881,-324,1520,-559) -> Matrix(1,-2,0,1) Matrix(41,-16,100,-39) -> Matrix(1,-2,0,1) Matrix(199,-86,280,-121) -> Matrix(1,0,0,1) Matrix(201,-92,260,-119) -> Matrix(1,2,0,1) Matrix(2479,-1442,3440,-2001) -> Matrix(3,2,-2,-1) Matrix(121,-72,200,-119) -> Matrix(1,0,2,1) Matrix(401,-246,520,-319) -> Matrix(1,0,0,1) Matrix(1039,-642,1620,-1001) -> Matrix(1,0,-2,1) Matrix(1801,-1296,2500,-1799) -> Matrix(1,-2,0,1) Matrix(1481,-1068,1940,-1399) -> Matrix(1,2,-2,-3) Matrix(121,-90,160,-119) -> Matrix(1,-2,0,1) Matrix(81,-64,100,-79) -> Matrix(1,-2,0,1) 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): 20 Degree of the the map X: 20 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 0/1 (0/1,1/0) 0 20 1/8 0/1 1 5 1/7 -1/1 1 20 3/20 0/1 3 1 2/13 (0/1,1/2) 0 20 1/6 0 10 2/11 (-1/1,0/1) 0 20 1/5 0/1 1 4 4/19 (1/1,2/1) 0 20 3/14 0 10 5/23 1/1 1 20 2/9 (1/1,1/0) 0 20 1/4 0/1 1 5 5/19 1/1 1 20 4/15 1/0 2 4 3/11 -1/1 1 20 2/7 (0/1,1/0) 0 20 3/10 0/1 2 2 4/13 (0/1,1/2) 0 20 1/3 1/1 1 20 7/20 1/0 2 1 6/17 (-1/1,1/0) 0 20 5/14 0 10 4/11 (0/1,1/1) 0 20 11/30 1/1 3 2 7/19 1/1 1 20 3/8 1/0 1 5 2/5 1/0 2 4 5/12 1/0 1 5 8/19 (-2/1,-1/1) 0 20 11/26 0 10 3/7 -1/1 1 20 7/16 0/1 1 5 4/9 (1/1,1/0) 0 20 9/20 1/0 4 1 5/11 -3/1 1 20 1/2 0 10 6/11 (-1/3,0/1) 0 20 11/20 0/1 4 1 5/9 1/1 1 20 4/7 (0/1,1/0) 0 20 11/19 -1/1 1 20 29/50 -1/1 3 2 18/31 (-1/1,-1/2) 0 20 25/43 -1/1 1 20 7/12 0/1 1 5 24/41 (0/1,1/0) 0 20 17/29 1/1 1 20 10/17 (-1/1,1/0) 0 20 3/5 0/1 1 4 14/23 (1/2,1/1) 0 20 25/41 1/1 1 20 61/100 1/1 13 1 36/59 (1/1,8/7) 0 20 11/18 0 10 8/13 (0/1,1/0) 0 20 21/34 0 10 13/21 1/1 1 20 5/8 1/0 1 5 12/19 (-1/1,0/1) 0 20 19/30 0/1 1 2 26/41 (0/1,1/0) 0 20 7/11 -1/1 1 20 16/25 1/0 2 4 25/39 -1/1 1 20 9/14 0 10 11/17 -1/1 1 20 13/20 0/1 1 1 2/3 (0/1,1/0) 0 20 7/10 1/0 1 2 12/17 (-1/1,1/0) 0 20 29/41 -1/1 1 20 17/24 0/1 1 5 5/7 -1/1 1 20 23/32 0/1 1 5 18/25 1/0 2 4 49/68 -2/1 1 5 31/43 -1/1 1 20 13/18 0 10 8/11 (0/1,1/1) 0 20 11/15 0/1 1 4 14/19 (2/3,1/1) 0 20 3/4 1/0 1 5 16/21 (-4/3,-1/1) 0 20 29/38 0 10 13/17 -1/1 1 20 10/13 (0/1,1/0) 0 20 17/22 0 10 7/9 -1/1 1 20 4/5 1/0 2 4 9/11 -3/1 1 20 14/17 (-1/1,1/0) 0 20 5/6 0 10 11/13 -1/1 1 20 17/20 1/0 1 1 6/7 (-2/1,1/0) 0 20 1/1 -1/1 1 20 1/0 0/1 1 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(199,-24,340,-41) (0/1,1/8) -> (7/12,24/41) Hyperbolic Matrix(201,-28,280,-39) (1/8,1/7) -> (5/7,23/32) Hyperbolic Matrix(41,-6,280,-41) (1/7,3/20) -> (1/7,3/20) Reflection Matrix(79,-12,520,-79) (3/20,2/13) -> (3/20,2/13) Reflection Matrix(321,-50,520,-81) (2/13,1/6) -> (8/13,21/34) Glide Reflection Matrix(79,-14,220,-39) (1/6,2/11) -> (5/14,4/11) Glide Reflection Matrix(161,-30,220,-41) (2/11,1/5) -> (8/11,11/15) Glide Reflection Matrix(279,-58,380,-79) (1/5,4/19) -> (11/15,14/19) Glide Reflection Matrix(321,-68,760,-161) (4/19,3/14) -> (8/19,11/26) Glide Reflection Matrix(361,-78,560,-121) (3/14,5/23) -> (9/14,11/17) Glide Reflection Matrix(639,-140,1100,-241) (5/23,2/9) -> (18/31,25/43) Hyperbolic Matrix(79,-18,180,-41) (2/9,1/4) -> (7/16,4/9) Hyperbolic Matrix(439,-114,620,-161) (1/4,5/19) -> (29/41,17/24) Hyperbolic Matrix(679,-180,1060,-281) (5/19,4/15) -> (16/25,25/39) Hyperbolic Matrix(281,-76,440,-119) (4/15,3/11) -> (7/11,16/25) Hyperbolic Matrix(79,-22,140,-39) (3/11,2/7) -> (5/9,4/7) Glide Reflection Matrix(41,-12,140,-41) (2/7,3/10) -> (2/7,3/10) Reflection Matrix(79,-24,260,-79) (3/10,4/13) -> (3/10,4/13) Reflection Matrix(199,-62,260,-81) (4/13,1/3) -> (13/17,10/13) Hyperbolic Matrix(41,-14,120,-41) (1/3,7/20) -> (1/3,7/20) Reflection Matrix(239,-84,680,-239) (7/20,6/17) -> (7/20,6/17) Reflection Matrix(281,-100,340,-121) (6/17,5/14) -> (14/17,5/6) Glide Reflection Matrix(241,-88,660,-241) (4/11,11/30) -> (4/11,11/30) Reflection Matrix(881,-324,1520,-559) (11/30,7/19) -> (11/19,29/50) Hyperbolic Matrix(199,-74,320,-119) (7/19,3/8) -> (13/21,5/8) Glide Reflection Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(239,-100,380,-159) (5/12,8/19) -> (5/8,12/19) Glide Reflection Matrix(321,-136,380,-161) (11/26,3/7) -> (5/6,11/13) Glide Reflection Matrix(199,-86,280,-121) (3/7,7/16) -> (17/24,5/7) Hyperbolic Matrix(161,-72,360,-161) (4/9,9/20) -> (4/9,9/20) Reflection Matrix(199,-90,440,-199) (9/20,5/11) -> (9/20,5/11) Reflection Matrix(201,-92,260,-119) (5/11,1/2) -> (17/22,7/9) Hyperbolic Matrix(159,-86,220,-119) (1/2,6/11) -> (13/18,8/11) Glide Reflection Matrix(241,-132,440,-241) (6/11,11/20) -> (6/11,11/20) Reflection Matrix(199,-110,360,-199) (11/20,5/9) -> (11/20,5/9) Reflection Matrix(121,-70,140,-81) (4/7,11/19) -> (6/7,1/1) Glide Reflection Matrix(1799,-1044,3100,-1799) (29/50,18/31) -> (29/50,18/31) Reflection Matrix(2479,-1442,3440,-2001) (25/43,7/12) -> (49/68,31/43) Hyperbolic Matrix(1041,-610,1640,-961) (24/41,17/29) -> (26/41,7/11) Glide Reflection Matrix(559,-328,680,-399) (17/29,10/17) -> (9/11,14/17) Glide Reflection Matrix(121,-72,200,-119) (10/17,3/5) -> (3/5,14/23) Parabolic Matrix(1159,-706,1640,-999) (14/23,25/41) -> (12/17,29/41) Glide Reflection Matrix(5001,-3050,8200,-5001) (25/41,61/100) -> (25/41,61/100) Reflection Matrix(7199,-4392,11800,-7199) (61/100,36/59) -> (61/100,36/59) Reflection Matrix(1999,-1220,2620,-1599) (36/59,11/18) -> (16/21,29/38) Glide Reflection Matrix(401,-246,520,-319) (11/18,8/13) -> (10/13,17/22) Hyperbolic Matrix(1039,-642,1620,-1001) (21/34,13/21) -> (25/39,9/14) Hyperbolic Matrix(721,-456,1140,-721) (12/19,19/30) -> (12/19,19/30) Reflection Matrix(1559,-988,2460,-1559) (19/30,26/41) -> (19/30,26/41) Reflection Matrix(441,-286,680,-441) (11/17,13/20) -> (11/17,13/20) Reflection Matrix(79,-52,120,-79) (13/20,2/3) -> (13/20,2/3) Reflection Matrix(41,-28,60,-41) (2/3,7/10) -> (2/3,7/10) Reflection Matrix(239,-168,340,-239) (7/10,12/17) -> (7/10,12/17) Reflection Matrix(1801,-1296,2500,-1799) (23/32,18/25) -> (18/25,49/68) Parabolic Matrix(1481,-1068,1940,-1399) (31/43,13/18) -> (29/38,13/17) Hyperbolic Matrix(121,-90,160,-119) (14/19,3/4) -> (3/4,16/21) Parabolic Matrix(81,-64,100,-79) (7/9,4/5) -> (4/5,9/11) Parabolic Matrix(441,-374,520,-441) (11/13,17/20) -> (11/13,17/20) Reflection Matrix(239,-204,280,-239) (17/20,6/7) -> (17/20,6/7) Reflection Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(199,-24,340,-41) -> Matrix(1,0,0,1) Matrix(201,-28,280,-39) -> Matrix(1,0,0,1) Matrix(41,-6,280,-41) -> Matrix(-1,0,2,1) (1/7,3/20) -> (-1/1,0/1) Matrix(79,-12,520,-79) -> Matrix(1,0,4,-1) (3/20,2/13) -> (0/1,1/2) Matrix(321,-50,520,-81) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(79,-14,220,-39) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(161,-30,220,-41) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(279,-58,380,-79) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(321,-68,760,-161) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(361,-78,560,-121) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(639,-140,1100,-241) -> Matrix(1,0,-2,1) 0/1 Matrix(79,-18,180,-41) -> Matrix(1,0,0,1) Matrix(439,-114,620,-161) -> Matrix(1,0,-2,1) 0/1 Matrix(679,-180,1060,-281) -> Matrix(1,-2,0,1) 1/0 Matrix(281,-76,440,-119) -> Matrix(1,0,0,1) Matrix(79,-22,140,-39) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(41,-12,140,-41) -> Matrix(1,0,0,-1) (2/7,3/10) -> (0/1,1/0) Matrix(79,-24,260,-79) -> Matrix(1,0,4,-1) (3/10,4/13) -> (0/1,1/2) Matrix(199,-62,260,-81) -> Matrix(1,0,-2,1) 0/1 Matrix(41,-14,120,-41) -> Matrix(-1,2,0,1) (1/3,7/20) -> (1/1,1/0) Matrix(239,-84,680,-239) -> Matrix(1,2,0,-1) (7/20,6/17) -> (-1/1,1/0) Matrix(281,-100,340,-121) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(241,-88,660,-241) -> Matrix(1,0,2,-1) (4/11,11/30) -> (0/1,1/1) Matrix(881,-324,1520,-559) -> Matrix(1,-2,0,1) 1/0 Matrix(199,-74,320,-119) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(41,-16,100,-39) -> Matrix(1,-2,0,1) 1/0 Matrix(239,-100,380,-159) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(321,-136,380,-161) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(199,-86,280,-121) -> Matrix(1,0,0,1) Matrix(161,-72,360,-161) -> Matrix(-1,2,0,1) (4/9,9/20) -> (1/1,1/0) Matrix(199,-90,440,-199) -> Matrix(1,6,0,-1) (9/20,5/11) -> (-3/1,1/0) Matrix(201,-92,260,-119) -> Matrix(1,2,0,1) 1/0 Matrix(159,-86,220,-119) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(241,-132,440,-241) -> Matrix(-1,0,6,1) (6/11,11/20) -> (-1/3,0/1) Matrix(199,-110,360,-199) -> Matrix(1,0,2,-1) (11/20,5/9) -> (0/1,1/1) Matrix(121,-70,140,-81) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(1799,-1044,3100,-1799) -> Matrix(3,2,-4,-3) (29/50,18/31) -> (-1/1,-1/2) Matrix(2479,-1442,3440,-2001) -> Matrix(3,2,-2,-1) -1/1 Matrix(1041,-610,1640,-961) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(559,-328,680,-399) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(121,-72,200,-119) -> Matrix(1,0,2,1) 0/1 Matrix(1159,-706,1640,-999) -> Matrix(3,-2,-2,1) Matrix(5001,-3050,8200,-5001) -> Matrix(11,-10,12,-11) (25/41,61/100) -> (5/6,1/1) Matrix(7199,-4392,11800,-7199) -> Matrix(15,-16,14,-15) (61/100,36/59) -> (1/1,8/7) Matrix(1999,-1220,2620,-1599) -> Matrix(3,-4,-4,5) Matrix(401,-246,520,-319) -> Matrix(1,0,0,1) Matrix(1039,-642,1620,-1001) -> Matrix(1,0,-2,1) 0/1 Matrix(721,-456,1140,-721) -> Matrix(-1,0,2,1) (12/19,19/30) -> (-1/1,0/1) Matrix(1559,-988,2460,-1559) -> Matrix(1,0,0,-1) (19/30,26/41) -> (0/1,1/0) Matrix(441,-286,680,-441) -> Matrix(-1,0,2,1) (11/17,13/20) -> (-1/1,0/1) Matrix(79,-52,120,-79) -> Matrix(1,0,0,-1) (13/20,2/3) -> (0/1,1/0) Matrix(41,-28,60,-41) -> Matrix(1,0,0,-1) (2/3,7/10) -> (0/1,1/0) Matrix(239,-168,340,-239) -> Matrix(1,2,0,-1) (7/10,12/17) -> (-1/1,1/0) Matrix(1801,-1296,2500,-1799) -> Matrix(1,-2,0,1) 1/0 Matrix(1481,-1068,1940,-1399) -> Matrix(1,2,-2,-3) -1/1 Matrix(121,-90,160,-119) -> Matrix(1,-2,0,1) 1/0 Matrix(81,-64,100,-79) -> Matrix(1,-2,0,1) 1/0 Matrix(441,-374,520,-441) -> Matrix(1,2,0,-1) (11/13,17/20) -> (-1/1,1/0) Matrix(239,-204,280,-239) -> Matrix(1,4,0,-1) (17/20,6/7) -> (-2/1,1/0) Matrix(-1,2,0,1) -> Matrix(-1,0,2,1) (1/1,1/0) -> (-1/1,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.