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 -1/1 -6/13 -5/12 -4/11 -1/3 -3/10 -2/9 -1/8 0/1 1/6 3/11 1/3 2/5 1/2 5/9 3/4 1/1 4/3 3/2 17/11 5/3 9/5 2/1 11/5 29/13 7/3 5/2 71/27 8/3 3/1 43/13 10/3 17/5 7/2 11/3 4/1 13/3 9/2 23/5 5/1 47/9 11/2 6/1 7/1 8/1 25/3 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/13 -6/13 1/11 -5/11 1/11 -4/9 2/21 1/10 -7/16 3/29 -3/7 1/10 1/9 -8/19 0/1 1/9 -5/12 1/9 -12/29 1/9 2/17 -7/17 1/9 -2/5 0/1 1/9 -7/18 1/9 -5/13 1/9 1/8 -13/34 1/8 -8/21 2/17 1/8 -3/8 1/9 -7/19 1/9 1/8 -4/11 1/8 -9/25 1/8 3/23 -5/14 3/23 -1/3 1/7 -4/13 2/13 3/19 -3/10 1/6 -8/27 4/23 3/17 -5/17 1/6 3/17 -2/7 1/6 2/11 -5/18 1/5 -8/29 1/5 -3/11 1/6 1/5 -4/15 4/21 1/5 -1/4 1/5 -3/13 1/5 -2/9 1/4 -5/23 3/11 -3/14 1/3 -1/5 1/4 1/3 -2/11 2/7 1/3 -1/6 1/3 -1/7 1/3 -1/8 1/2 0/1 0/1 1/1 1/6 1/0 1/5 -1/1 2/9 0/1 1/1 3/13 -1/1 1/0 1/4 -1/1 3/11 -1/1 5/18 -1/1 2/7 -1/1 -2/3 5/17 -1/1 8/27 -1/1 3/10 -1/1 4/13 -1/1 -2/3 1/3 -1/1 -1/2 5/14 -1/3 4/11 -1/2 0/1 3/8 -1/1 2/5 -1/2 5/12 -3/7 8/19 -3/7 -2/5 3/7 -1/3 7/16 -1/1 4/9 -2/3 -1/2 5/11 -1/2 -3/7 6/13 -4/9 -3/7 1/2 -1/3 5/9 -1/3 9/16 -1/3 4/7 -1/3 -4/13 15/26 -1/3 11/19 -1/3 7/12 -5/17 17/29 -3/11 10/17 -1/3 -2/7 13/22 -1/4 3/5 -1/3 -1/4 8/13 -1/3 5/8 -1/3 12/19 -1/3 -2/7 7/11 -1/3 2/3 -2/7 -1/4 9/13 -1/3 7/10 -3/11 19/27 -1/3 12/17 -2/7 -3/11 5/7 -3/11 -1/4 3/4 -1/4 7/9 -1/4 -3/13 11/14 -5/21 15/19 -3/13 4/5 -3/13 -2/9 9/11 -1/4 -1/5 5/6 -1/5 6/7 -1/4 -2/9 1/1 -1/5 6/5 -1/5 0/1 11/9 -1/5 -3/16 5/4 -3/17 4/3 -1/6 11/8 -1/7 18/13 -2/13 -1/7 25/18 -1/7 7/5 -1/6 -1/7 24/17 -4/23 -1/6 41/29 -1/6 17/12 -7/43 27/19 -3/19 10/7 -3/19 -2/13 23/16 -5/33 13/9 -1/7 3/2 -1/7 17/11 0/1 14/9 -1/4 0/1 11/7 -1/5 19/12 -1/5 27/17 -3/17 -1/6 8/5 -1/6 -2/13 29/18 -3/19 21/13 -1/7 13/8 -1/6 18/11 -2/13 -1/7 41/25 -3/19 23/14 -5/33 5/3 -1/6 -1/7 22/13 -1/7 17/10 -3/23 12/7 -1/5 0/1 19/11 -1/7 7/4 -1/7 9/5 -1/7 11/6 -1/7 2/1 -1/7 0/1 15/7 -1/5 13/6 -1/7 11/5 -1/6 -1/7 20/9 -2/13 -1/7 29/13 -1/7 9/4 -1/7 16/7 -1/8 0/1 39/17 0/1 23/10 -1/5 7/3 -1/7 5/2 -1/7 13/5 -1/7 47/18 -9/67 81/31 -2/15 34/13 -2/15 -7/53 21/8 -5/39 71/27 -1/8 50/19 -1/8 -6/49 29/11 -1/8 -1/9 8/3 -1/7 0/1 19/7 -1/7 30/11 -1/8 0/1 41/15 0/1 11/4 -1/7 14/5 -1/7 0/1 3/1 -1/7 -1/8 13/4 -1/7 23/7 -1/7 33/10 -1/7 43/13 -2/15 10/3 -2/15 -1/8 27/8 -1/8 17/5 -1/7 41/12 -5/37 65/19 -2/15 24/7 -2/15 -3/23 7/2 -3/23 11/3 -1/8 15/4 -7/57 4/1 -1/8 -2/17 13/3 -1/8 -3/25 35/8 -3/25 57/13 -3/25 22/5 -3/25 -2/17 9/2 -3/25 23/5 -2/17 37/8 -13/111 14/3 -2/17 -5/43 5/1 -1/9 26/5 -3/25 -2/17 47/9 -2/17 21/4 -5/43 16/3 -4/35 -1/9 11/2 -1/9 6/1 -1/9 7/1 -1/9 -3/28 8/1 -5/47 -2/19 25/3 -2/19 17/2 -11/105 9/1 -3/29 1/0 -1/11 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(265,124,156,73) (-1/2,-6/13) -> (22/13,17/10) Hyperbolic Matrix(153,70,518,237) (-6/13,-5/11) -> (5/17,8/27) Hyperbolic Matrix(103,46,150,67) (-5/11,-4/9) -> (2/3,9/13) Hyperbolic Matrix(199,88,52,23) (-4/9,-7/16) -> (15/4,4/1) Hyperbolic Matrix(51,22,146,63) (-7/16,-3/7) -> (1/3,5/14) Hyperbolic Matrix(47,20,148,63) (-3/7,-8/19) -> (4/13,1/3) Hyperbolic Matrix(239,100,-576,-241) (-8/19,-5/12) -> (-5/12,-12/29) Parabolic Matrix(953,394,670,277) (-12/29,-7/17) -> (27/19,10/7) Hyperbolic Matrix(239,98,378,155) (-7/17,-2/5) -> (12/19,7/11) 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(907,346,270,103) (-13/34,-8/21) -> (10/3,27/8) Hyperbolic Matrix(179,68,408,155) (-8/21,-3/8) -> (7/16,4/9) Hyperbolic Matrix(43,16,180,67) (-3/8,-7/19) -> (3/13,1/4) Hyperbolic Matrix(175,64,-484,-177) (-7/19,-4/11) -> (-4/11,-9/25) Parabolic Matrix(479,172,220,79) (-9/25,-5/14) -> (13/6,11/5) Hyperbolic Matrix(175,62,302,107) (-5/14,-1/3) -> (11/19,7/12) Hyperbolic Matrix(283,88,164,51) (-1/3,-4/13) -> (12/7,19/11) Hyperbolic Matrix(119,36,-400,-121) (-4/13,-3/10) -> (-3/10,-8/27) Parabolic Matrix(237,70,518,153) (-8/27,-5/17) -> (5/11,6/13) Hyperbolic Matrix(159,46,38,11) (-5/17,-2/7) -> (4/1,13/3) Hyperbolic Matrix(351,98,154,43) (-2/7,-5/18) -> (9/4,16/7) Hyperbolic Matrix(231,64,776,215) (-5/18,-8/29) -> (8/27,3/10) Hyperbolic Matrix(387,106,230,63) (-8/29,-3/11) -> (5/3,22/13) Hyperbolic Matrix(231,62,190,51) (-3/11,-4/15) -> (6/5,11/9) Hyperbolic Matrix(151,40,268,71) (-4/15,-1/4) -> (9/16,4/7) Hyperbolic Matrix(291,68,184,43) (-1/4,-3/13) -> (11/7,19/12) Hyperbolic Matrix(71,16,-324,-73) (-3/13,-2/9) -> (-2/9,-5/23) Parabolic Matrix(427,92,608,131) (-5/23,-3/14) -> (7/10,19/27) Hyperbolic Matrix(107,22,34,7) (-3/14,-1/5) -> (3/1,13/4) 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(99,16,68,11) (-1/6,-1/7) -> (13/9,3/2) Hyperbolic Matrix(325,44,96,13) (-1/7,-1/8) -> (27/8,17/5) Hyperbolic Matrix(93,10,158,17) (-1/8,0/1) -> (10/17,13/22) Hyperbolic Matrix(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(365,-82,138,-31) (2/9,3/13) -> (29/11,8/3) Hyperbolic Matrix(67,-18,242,-65) (1/4,3/11) -> (3/11,5/18) Parabolic Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(235,-72,408,-125) (3/10,4/13) -> (4/7,15/26) Hyperbolic Matrix(431,-156,268,-97) (5/14,4/11) -> (8/5,29/18) Hyperbolic Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(435,-182,98,-41) (5/12,8/19) -> (22/5,9/2) Hyperbolic Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(273,-118,118,-51) (3/7,7/16) -> (23/10,7/3) Hyperbolic Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(305,-142,58,-27) (6/13,1/2) -> (21/4,16/3) Hyperbolic Matrix(91,-50,162,-89) (1/2,5/9) -> (5/9,9/16) Parabolic Matrix(1225,-708,372,-215) (15/26,11/19) -> (23/7,33/10) Hyperbolic Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(619,-390,446,-281) (5/8,12/19) -> (18/13,25/18) Hyperbolic Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(429,-298,298,-207) (9/13,7/10) -> (23/16,13/9) Hyperbolic Matrix(1183,-834,722,-509) (19/27,12/17) -> (18/11,41/25) Hyperbolic Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(549,-430,346,-271) (7/9,11/14) -> (19/12,27/17) Hyperbolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) Hyperbolic Matrix(123,-100,16,-13) (4/5,9/11) -> (7/1,8/1) Hyperbolic Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(227,-278,138,-169) (11/9,5/4) -> (23/14,5/3) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(409,-570,94,-131) (25/18,7/5) -> (13/3,35/8) Hyperbolic Matrix(2657,-3754,1010,-1427) (24/17,41/29) -> (71/27,50/19) Hyperbolic Matrix(1461,-2068,556,-787) (41/29,17/12) -> (21/8,71/27) Hyperbolic Matrix(127,-180,12,-17) (17/12,27/19) -> (9/1,1/0) Hyperbolic Matrix(483,-692,104,-149) (10/7,23/16) -> (37/8,14/3) Hyperbolic Matrix(331,-508,144,-221) (3/2,17/11) -> (39/17,23/10) Hyperbolic Matrix(527,-818,230,-357) (17/11,14/9) -> (16/7,39/17) Hyperbolic Matrix(995,-1582,378,-601) (27/17,8/5) -> (50/19,29/11) Hyperbolic Matrix(439,-708,204,-329) (29/18,21/13) -> (15/7,13/6) Hyperbolic Matrix(551,-904,64,-105) (41/25,23/14) -> (17/2,9/1) Hyperbolic Matrix(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(235,-408,72,-125) (19/11,7/4) -> (13/4,23/7) Hyperbolic Matrix(91,-162,50,-89) (7/4,9/5) -> (9/5,11/6) Parabolic Matrix(187,-400,36,-77) (2/1,15/7) -> (5/1,26/5) Hyperbolic Matrix(799,-1778,182,-405) (20/9,29/13) -> (57/13,22/5) Hyperbolic Matrix(683,-1528,156,-349) (29/13,9/4) -> (35/8,57/13) Hyperbolic Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(977,-2552,116,-303) (47/18,81/31) -> (25/3,17/2) Hyperbolic Matrix(573,-1498,70,-183) (81/31,34/13) -> (8/1,25/3) Hyperbolic Matrix(623,-1700,188,-513) (30/11,41/15) -> (43/13,10/3) Hyperbolic Matrix(667,-1826,202,-553) (41/15,11/4) -> (33/10,43/13) Hyperbolic Matrix(119,-330,22,-61) (11/4,14/5) -> (16/3,11/2) Hyperbolic Matrix(963,-3292,184,-629) (41/12,65/19) -> (47/9,21/4) Hyperbolic Matrix(823,-2818,158,-541) (65/19,24/7) -> (26/5,47/9) Hyperbolic Matrix(67,-242,18,-65) (7/2,11/3) -> (11/3,15/4) Parabolic Matrix(231,-1058,50,-229) (9/2,23/5) -> (23/5,37/8) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,24,1) Matrix(265,124,156,73) -> Matrix(23,-2,-172,15) Matrix(153,70,518,237) -> Matrix(21,-2,-10,1) Matrix(103,46,150,67) -> Matrix(1,0,-14,1) Matrix(199,88,52,23) -> Matrix(41,-4,-338,33) Matrix(51,22,146,63) -> Matrix(19,-2,-28,3) Matrix(47,20,148,63) -> Matrix(19,-2,-28,3) Matrix(239,100,-576,-241) -> Matrix(19,-2,162,-17) Matrix(953,394,670,277) -> Matrix(33,-4,-206,25) Matrix(239,98,378,155) -> Matrix(19,-2,-66,7) Matrix(91,36,48,19) -> Matrix(1,0,-16,1) Matrix(227,88,276,107) -> Matrix(17,-2,-76,9) Matrix(271,104,456,175) -> Matrix(1,0,-12,1) Matrix(907,346,270,103) -> Matrix(1,0,-16,1) Matrix(179,68,408,155) -> Matrix(1,0,-10,1) Matrix(43,16,180,67) -> Matrix(17,-2,-8,1) Matrix(175,64,-484,-177) -> Matrix(33,-4,256,-31) Matrix(479,172,220,79) -> Matrix(15,-2,-82,11) Matrix(175,62,302,107) -> Matrix(29,-4,-94,13) Matrix(283,88,164,51) -> Matrix(13,-2,-84,13) Matrix(119,36,-400,-121) -> Matrix(37,-6,216,-35) Matrix(237,70,518,153) -> Matrix(1,0,-8,1) Matrix(159,46,38,11) -> Matrix(1,0,-14,1) Matrix(351,98,154,43) -> Matrix(11,-2,-82,15) Matrix(231,64,776,215) -> Matrix(21,-4,-26,5) Matrix(387,106,230,63) -> Matrix(1,0,-12,1) Matrix(231,62,190,51) -> Matrix(21,-4,-110,21) Matrix(151,40,268,71) -> Matrix(41,-8,-128,25) Matrix(291,68,184,43) -> Matrix(1,0,-10,1) Matrix(71,16,-324,-73) -> Matrix(17,-4,64,-15) Matrix(427,92,608,131) -> Matrix(15,-4,-56,15) Matrix(107,22,34,7) -> Matrix(7,-2,-52,15) Matrix(103,20,36,7) -> Matrix(7,-2,-52,15) Matrix(67,12,240,43) -> Matrix(13,-4,-16,5) Matrix(99,16,68,11) -> Matrix(5,-2,-32,13) Matrix(325,44,96,13) -> Matrix(1,0,-10,1) Matrix(93,10,158,17) -> Matrix(3,-2,-10,7) Matrix(121,-18,74,-11) -> Matrix(1,-2,-6,13) Matrix(191,-34,118,-21) -> Matrix(1,0,-6,1) Matrix(115,-24,24,-5) -> Matrix(3,2,-26,-17) Matrix(365,-82,138,-31) -> Matrix(1,0,-8,1) Matrix(67,-18,242,-65) -> Matrix(5,6,-6,-7) Matrix(173,-50,218,-63) -> Matrix(7,4,-30,-17) Matrix(235,-72,408,-125) -> Matrix(1,2,-4,-7) Matrix(431,-156,268,-97) -> Matrix(3,2,-20,-13) Matrix(103,-38,122,-45) -> Matrix(3,2,-14,-9) Matrix(41,-16,100,-39) -> Matrix(7,4,-16,-9) Matrix(435,-182,98,-41) -> Matrix(1,0,-6,1) Matrix(393,-166,670,-283) -> Matrix(9,4,-34,-15) Matrix(273,-118,118,-51) -> Matrix(1,0,-4,1) Matrix(327,-148,232,-105) -> Matrix(5,2,-28,-11) Matrix(305,-142,58,-27) -> Matrix(19,8,-164,-69) Matrix(91,-50,162,-89) -> Matrix(29,10,-90,-31) Matrix(1225,-708,372,-215) -> Matrix(7,2,-46,-13) Matrix(1519,-890,582,-341) -> Matrix(29,8,-214,-59) Matrix(121,-74,18,-11) -> Matrix(5,2,-48,-19) Matrix(191,-118,34,-21) -> Matrix(19,6,-168,-53) Matrix(619,-390,446,-281) -> Matrix(13,4,-88,-27) Matrix(187,-120,120,-77) -> Matrix(7,2,-32,-9) Matrix(429,-298,298,-207) -> Matrix(13,4,-88,-27) Matrix(1183,-834,722,-509) -> Matrix(15,4,-94,-25) Matrix(327,-232,148,-105) -> Matrix(15,4,-94,-25) Matrix(49,-36,64,-47) -> Matrix(23,6,-96,-25) Matrix(549,-430,346,-271) -> Matrix(25,6,-146,-35) Matrix(1017,-802,298,-235) -> Matrix(43,10,-314,-73) Matrix(123,-100,16,-13) -> Matrix(19,4,-176,-37) Matrix(163,-144,60,-53) -> Matrix(9,2,-68,-15) Matrix(103,-122,38,-45) -> Matrix(1,0,-2,1) Matrix(227,-278,138,-169) -> Matrix(21,4,-142,-27) Matrix(49,-64,36,-47) -> Matrix(23,4,-144,-25) Matrix(283,-390,82,-113) -> Matrix(25,4,-194,-31) Matrix(409,-570,94,-131) -> Matrix(11,2,-94,-17) Matrix(2657,-3754,1010,-1427) -> Matrix(59,10,-478,-81) Matrix(1461,-2068,556,-787) -> Matrix(73,12,-578,-95) Matrix(127,-180,12,-17) -> Matrix(37,6,-364,-59) Matrix(483,-692,104,-149) -> Matrix(103,16,-882,-137) Matrix(331,-508,144,-221) -> Matrix(1,0,2,1) Matrix(527,-818,230,-357) -> Matrix(1,0,-4,1) Matrix(995,-1582,378,-601) -> Matrix(23,4,-190,-33) Matrix(439,-708,204,-329) -> Matrix(13,2,-72,-11) Matrix(551,-904,64,-105) -> Matrix(77,12,-738,-115) Matrix(487,-830,186,-317) -> Matrix(17,2,-128,-15) Matrix(235,-408,72,-125) -> Matrix(13,2,-98,-15) Matrix(91,-162,50,-89) -> Matrix(13,2,-98,-15) Matrix(187,-400,36,-77) -> Matrix(11,2,-94,-17) Matrix(799,-1778,182,-405) -> Matrix(53,8,-444,-67) Matrix(683,-1528,156,-349) -> Matrix(11,2,-94,-17) Matrix(41,-100,16,-39) -> Matrix(13,2,-98,-15) Matrix(977,-2552,116,-303) -> Matrix(299,40,-2848,-381) Matrix(573,-1498,70,-183) -> Matrix(181,24,-1712,-227) Matrix(623,-1700,188,-513) -> Matrix(17,2,-128,-15) Matrix(667,-1826,202,-553) -> Matrix(13,2,-98,-15) Matrix(119,-330,22,-61) -> Matrix(29,4,-254,-35) Matrix(963,-3292,184,-629) -> Matrix(149,20,-1274,-171) Matrix(823,-2818,158,-541) -> Matrix(91,12,-766,-101) Matrix(67,-242,18,-65) -> Matrix(79,10,-640,-81) Matrix(231,-1058,50,-229) -> Matrix(271,32,-2312,-273) 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): 32 Degree of the the map X: 32 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 0/1 12 1 0/1 (0/1,1/1) 0 14 1/6 1/0 1 2 1/5 -1/1 1 7 2/9 (0/1,1/1) 0 14 1/4 -1/1 1 14 3/11 -1/1 3 1 2/7 (-1/1,-2/3) 0 14 5/17 -1/1 1 7 3/10 -1/1 1 14 1/3 0 7 4/11 (-1/2,0/1) 0 14 3/8 -1/1 1 14 2/5 -1/2 2 2 5/12 -3/7 1 14 8/19 (-3/7,-2/5) 0 14 3/7 -1/3 1 7 4/9 (-2/3,-1/2) 0 14 5/11 0 7 1/2 -1/3 1 14 5/9 -1/3 5 1 4/7 (-1/3,-4/13) 0 14 7/12 -5/17 1 14 17/29 -3/11 1 7 10/17 (-1/3,-2/7) 0 14 3/5 0 7 8/13 -1/3 4 2 5/8 -1/3 1 14 7/11 -1/3 1 7 2/3 (-2/7,-1/4) 0 14 7/10 -3/11 1 14 12/17 (-2/7,-3/11) 0 14 5/7 0 7 3/4 -1/4 3 2 7/9 0 7 11/14 -5/21 1 14 15/19 -3/13 1 7 4/5 (-3/13,-2/9) 0 14 5/6 -1/5 1 14 6/7 (-1/4,-2/9) 0 14 1/1 -1/5 1 7 6/5 (-1/5,0/1) 0 14 5/4 -3/17 1 14 4/3 -1/6 2 2 11/8 -1/7 1 14 18/13 (-2/13,-1/7) 0 14 7/5 0 7 24/17 (-4/23,-1/6) 0 14 41/29 -1/6 11 1 17/12 -7/43 1 14 10/7 (-3/19,-2/13) 0 14 3/2 -1/7 1 14 17/11 0/1 3 1 14/9 (-1/4,0/1) 0 14 11/7 -1/5 1 7 8/5 (-1/6,-2/13) 0 14 21/13 -1/7 1 7 13/8 -1/6 1 2 18/11 (-2/13,-1/7) 0 14 5/3 0 7 17/10 -3/23 1 14 12/7 (-1/5,0/1) 0 14 7/4 -1/7 1 14 9/5 -1/7 1 1 2/1 (-1/7,0/1) 0 14 11/5 0 7 20/9 (-2/13,-1/7) 0 14 29/13 -1/7 1 1 9/4 -1/7 1 14 7/3 -1/7 1 7 5/2 -1/7 1 2 13/5 -1/7 1 7 47/18 -9/67 1 14 81/31 -2/15 8 1 34/13 (-2/15,-7/53) 0 14 21/8 -5/39 1 14 8/3 (-1/7,0/1) 0 14 19/7 -1/7 1 7 30/11 (-1/8,0/1) 0 14 41/15 0/1 1 1 11/4 -1/7 1 14 3/1 0 7 10/3 (-2/15,-1/8) 0 14 17/5 -1/7 1 7 41/12 -5/37 1 14 65/19 -2/15 4 1 24/7 (-2/15,-3/23) 0 14 7/2 -3/23 1 14 11/3 -1/8 5 1 4/1 (-1/8,-2/17) 0 14 9/2 -3/25 1 14 23/5 -2/17 4 1 14/3 (-2/17,-5/43) 0 14 5/1 -1/9 1 7 11/2 -1/9 1 14 6/1 -1/9 4 2 7/1 0 7 1/0 -1/11 1 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(121,-18,74,-11) (0/1,1/6) -> (13/8,18/11) Hyperbolic Matrix(191,-34,118,-21) (1/6,1/5) -> (21/13,13/8) Hyperbolic Matrix(115,-24,24,-5) (1/5,2/9) -> (14/3,5/1) Hyperbolic Matrix(67,-16,46,-11) (2/9,1/4) -> (10/7,3/2) Glide Reflection Matrix(23,-6,88,-23) (1/4,3/11) -> (1/4,3/11) Reflection Matrix(43,-12,154,-43) (3/11,2/7) -> (3/11,2/7) Reflection Matrix(173,-50,218,-63) (2/7,5/17) -> (15/19,4/5) Hyperbolic Matrix(237,-70,44,-13) (5/17,3/10) -> (5/1,11/2) Glide Reflection Matrix(63,-20,22,-7) (3/10,1/3) -> (11/4,3/1) Glide Reflection Matrix(63,-22,20,-7) (1/3,4/11) -> (3/1,10/3) Glide Reflection Matrix(103,-38,122,-45) (4/11,3/8) -> (5/6,6/7) Hyperbolic Matrix(41,-16,100,-39) (3/8,2/5) -> (2/5,5/12) Parabolic Matrix(277,-116,394,-165) (5/12,8/19) -> (7/10,12/17) Glide Reflection Matrix(393,-166,670,-283) (8/19,3/7) -> (17/29,10/17) Hyperbolic Matrix(155,-68,98,-43) (3/7,4/9) -> (11/7,8/5) Glide Reflection Matrix(327,-148,232,-105) (4/9,5/11) -> (7/5,24/17) Hyperbolic Matrix(135,-62,172,-79) (5/11,1/2) -> (7/9,11/14) Glide Reflection Matrix(19,-10,36,-19) (1/2,5/9) -> (1/2,5/9) Reflection Matrix(71,-40,126,-71) (5/9,4/7) -> (5/9,4/7) Reflection Matrix(107,-62,88,-51) (4/7,7/12) -> (6/5,5/4) Glide Reflection Matrix(1519,-890,582,-341) (7/12,17/29) -> (13/5,47/18) Hyperbolic Matrix(175,-104,106,-63) (10/17,3/5) -> (18/11,5/3) Glide Reflection Matrix(121,-74,18,-11) (3/5,8/13) -> (6/1,7/1) Hyperbolic Matrix(191,-118,34,-21) (8/13,5/8) -> (11/2,6/1) Hyperbolic Matrix(155,-98,68,-43) (5/8,7/11) -> (9/4,7/3) Glide Reflection Matrix(187,-120,120,-77) (7/11,2/3) -> (14/9,11/7) Hyperbolic Matrix(67,-46,16,-11) (2/3,7/10) -> (4/1,9/2) Glide Reflection Matrix(327,-232,148,-105) (12/17,5/7) -> (11/5,20/9) Hyperbolic Matrix(49,-36,64,-47) (5/7,3/4) -> (3/4,7/9) Parabolic Matrix(1017,-802,298,-235) (11/14,15/19) -> (17/5,41/12) Hyperbolic Matrix(107,-88,62,-51) (4/5,5/6) -> (12/7,7/4) Glide Reflection Matrix(163,-144,60,-53) (6/7,1/1) -> (19/7,30/11) Hyperbolic Matrix(103,-122,38,-45) (1/1,6/5) -> (8/3,19/7) Hyperbolic Matrix(49,-64,36,-47) (5/4,4/3) -> (4/3,11/8) Parabolic Matrix(283,-390,82,-113) (11/8,18/13) -> (24/7,7/2) Hyperbolic Matrix(153,-212,70,-97) (18/13,7/5) -> (2/1,11/5) Glide Reflection Matrix(1393,-1968,986,-1393) (24/17,41/29) -> (24/17,41/29) Reflection Matrix(985,-1394,696,-985) (41/29,17/12) -> (41/29,17/12) Reflection Matrix(243,-346,92,-131) (17/12,10/7) -> (21/8,8/3) Glide Reflection Matrix(67,-102,44,-67) (3/2,17/11) -> (3/2,17/11) Reflection Matrix(307,-476,198,-307) (17/11,14/9) -> (17/11,14/9) Reflection Matrix(215,-346,64,-103) (8/5,21/13) -> (10/3,17/5) Glide Reflection Matrix(73,-124,10,-17) (5/3,17/10) -> (7/1,1/0) Glide Reflection Matrix(487,-830,186,-317) (17/10,12/7) -> (34/13,21/8) Hyperbolic Matrix(71,-126,40,-71) (7/4,9/5) -> (7/4,9/5) Reflection Matrix(19,-36,10,-19) (9/5,2/1) -> (9/5,2/1) Reflection Matrix(521,-1160,234,-521) (20/9,29/13) -> (20/9,29/13) Reflection Matrix(233,-522,104,-233) (29/13,9/4) -> (29/13,9/4) Reflection Matrix(41,-100,16,-39) (7/3,5/2) -> (5/2,13/5) Parabolic Matrix(2915,-7614,1116,-2915) (47/18,81/31) -> (47/18,81/31) Reflection Matrix(2107,-5508,806,-2107) (81/31,34/13) -> (81/31,34/13) Reflection Matrix(901,-2460,330,-901) (30/11,41/15) -> (30/11,41/15) Reflection Matrix(329,-902,120,-329) (41/15,11/4) -> (41/15,11/4) Reflection Matrix(1559,-5330,456,-1559) (41/12,65/19) -> (41/12,65/19) Reflection Matrix(911,-3120,266,-911) (65/19,24/7) -> (65/19,24/7) Reflection Matrix(43,-154,12,-43) (7/2,11/3) -> (7/2,11/3) Reflection Matrix(23,-88,6,-23) (11/3,4/1) -> (11/3,4/1) Reflection Matrix(91,-414,20,-91) (9/2,23/5) -> (9/2,23/5) Reflection Matrix(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,22,1) (-1/1,1/0) -> (-1/11,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,2,-1) (-1/1,0/1) -> (0/1,1/1) Matrix(121,-18,74,-11) -> Matrix(1,-2,-6,13) Matrix(191,-34,118,-21) -> Matrix(1,0,-6,1) 0/1 Matrix(115,-24,24,-5) -> Matrix(3,2,-26,-17) Matrix(67,-16,46,-11) -> Matrix(1,2,-6,-13) Matrix(23,-6,88,-23) -> Matrix(1,2,0,-1) (1/4,3/11) -> (-1/1,1/0) Matrix(43,-12,154,-43) -> Matrix(5,4,-6,-5) (3/11,2/7) -> (-1/1,-2/3) Matrix(173,-50,218,-63) -> Matrix(7,4,-30,-17) Matrix(237,-70,44,-13) -> Matrix(1,2,-8,-17) Matrix(63,-20,22,-7) -> Matrix(3,2,-22,-15) Matrix(63,-22,20,-7) -> Matrix(3,2,-22,-15) Matrix(103,-38,122,-45) -> Matrix(3,2,-14,-9) Matrix(41,-16,100,-39) -> Matrix(7,4,-16,-9) -1/2 Matrix(277,-116,394,-165) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(393,-166,670,-283) -> Matrix(9,4,-34,-15) Matrix(155,-68,98,-43) -> Matrix(-1,0,8,1) *** -> (-1/4,0/1) Matrix(327,-148,232,-105) -> Matrix(5,2,-28,-11) Matrix(135,-62,172,-79) -> Matrix(13,6,-54,-25) Matrix(19,-10,36,-19) -> Matrix(5,2,-12,-5) (1/2,5/9) -> (-1/2,-1/3) Matrix(71,-40,126,-71) -> Matrix(25,8,-78,-25) (5/9,4/7) -> (-1/3,-4/13) Matrix(107,-62,88,-51) -> Matrix(13,4,-68,-21) Matrix(1519,-890,582,-341) -> Matrix(29,8,-214,-59) Matrix(175,-104,106,-63) -> Matrix(-1,0,10,1) *** -> (-1/5,0/1) Matrix(121,-74,18,-11) -> Matrix(5,2,-48,-19) Matrix(191,-118,34,-21) -> Matrix(19,6,-168,-53) Matrix(155,-98,68,-43) -> Matrix(7,2,-52,-15) Matrix(187,-120,120,-77) -> Matrix(7,2,-32,-9) -1/4 Matrix(67,-46,16,-11) -> Matrix(-1,0,12,1) *** -> (-1/6,0/1) Matrix(327,-232,148,-105) -> Matrix(15,4,-94,-25) Matrix(49,-36,64,-47) -> Matrix(23,6,-96,-25) -1/4 Matrix(1017,-802,298,-235) -> Matrix(43,10,-314,-73) Matrix(107,-88,62,-51) -> Matrix(9,2,-58,-13) Matrix(163,-144,60,-53) -> Matrix(9,2,-68,-15) Matrix(103,-122,38,-45) -> Matrix(1,0,-2,1) 0/1 Matrix(49,-64,36,-47) -> Matrix(23,4,-144,-25) -1/6 Matrix(283,-390,82,-113) -> Matrix(25,4,-194,-31) Matrix(153,-212,70,-97) -> Matrix(13,2,-84,-13) *** -> (-1/6,-1/7) Matrix(1393,-1968,986,-1393) -> Matrix(47,8,-276,-47) (24/17,41/29) -> (-4/23,-1/6) Matrix(985,-1394,696,-985) -> Matrix(85,14,-516,-85) (41/29,17/12) -> (-1/6,-7/43) Matrix(243,-346,92,-131) -> Matrix(13,2,-110,-17) Matrix(67,-102,44,-67) -> Matrix(-1,0,14,1) (3/2,17/11) -> (-1/7,0/1) Matrix(307,-476,198,-307) -> Matrix(-1,0,8,1) (17/11,14/9) -> (-1/4,0/1) Matrix(215,-346,64,-103) -> Matrix(-1,0,14,1) *** -> (-1/7,0/1) Matrix(73,-124,10,-17) -> Matrix(15,2,-142,-19) Matrix(487,-830,186,-317) -> Matrix(17,2,-128,-15) -1/8 Matrix(71,-126,40,-71) -> Matrix(13,2,-84,-13) (7/4,9/5) -> (-1/6,-1/7) Matrix(19,-36,10,-19) -> Matrix(-1,0,14,1) (9/5,2/1) -> (-1/7,0/1) Matrix(521,-1160,234,-521) -> Matrix(27,4,-182,-27) (20/9,29/13) -> (-2/13,-1/7) Matrix(233,-522,104,-233) -> Matrix(13,2,-84,-13) (29/13,9/4) -> (-1/6,-1/7) Matrix(41,-100,16,-39) -> Matrix(13,2,-98,-15) -1/7 Matrix(2915,-7614,1116,-2915) -> Matrix(269,36,-2010,-269) (47/18,81/31) -> (-9/67,-2/15) Matrix(2107,-5508,806,-2107) -> Matrix(211,28,-1590,-211) (81/31,34/13) -> (-2/15,-7/53) Matrix(901,-2460,330,-901) -> Matrix(-1,0,16,1) (30/11,41/15) -> (-1/8,0/1) Matrix(329,-902,120,-329) -> Matrix(-1,0,14,1) (41/15,11/4) -> (-1/7,0/1) Matrix(1559,-5330,456,-1559) -> Matrix(149,20,-1110,-149) (41/12,65/19) -> (-5/37,-2/15) Matrix(911,-3120,266,-911) -> Matrix(91,12,-690,-91) (65/19,24/7) -> (-2/15,-3/23) Matrix(43,-154,12,-43) -> Matrix(47,6,-368,-47) (7/2,11/3) -> (-3/23,-1/8) Matrix(23,-88,6,-23) -> Matrix(33,4,-272,-33) (11/3,4/1) -> (-1/8,-2/17) Matrix(91,-414,20,-91) -> Matrix(101,12,-850,-101) (9/2,23/5) -> (-3/25,-2/17) Matrix(139,-644,30,-139) -> Matrix(171,20,-1462,-171) (23/5,14/3) -> (-2/17,-5/43) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.