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 -6/7 -5/7 -4/7 -1/2 -3/7 -5/12 -11/28 -3/8 -13/42 -3/10 -2/7 -31/112 -15/56 -1/4 -19/84 -5/28 -1/6 -2/13 -1/7 -1/8 0/1 1/7 1/6 2/11 1/5 3/14 2/9 3/13 1/4 3/11 2/7 3/10 1/3 5/14 2/5 5/12 3/7 1/2 5/9 4/7 9/14 2/3 29/42 5/7 11/14 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 1/1 -6/7 0/1 -5/6 0/1 -9/11 1/2 1/1 -4/5 1/1 -11/14 1/1 -7/9 1/1 2/1 -17/22 0/1 -10/13 1/1 -3/4 1/0 -11/15 -3/2 -1/1 -8/11 -1/1 -5/7 0/1 -12/17 1/3 -19/27 0/1 1/1 -7/10 0/1 -9/13 1/3 1/2 -11/16 1/2 -2/3 1/1 -9/14 1/1 -7/11 1/1 3/2 -12/19 5/3 -29/46 2/1 -17/27 1/1 2/1 -5/8 1/0 -13/21 1/1 -8/13 1/1 -11/18 2/1 -3/5 2/1 1/0 -10/17 1/1 -17/29 2/1 3/1 -7/12 1/0 -4/7 1/0 -9/16 1/0 -14/25 -3/1 -19/34 -4/1 -5/9 -3/1 -2/1 -6/11 -1/1 -7/13 -5/4 -1/1 -1/2 0/1 -5/11 1/1 1/0 -4/9 3/1 -3/7 1/0 -8/19 -1/1 -13/31 -2/1 1/0 -5/12 1/0 -17/41 -1/1 1/0 -29/70 1/0 -12/29 -3/1 -7/17 -1/1 1/0 -2/5 -1/1 -11/28 0/1 -9/23 0/1 1/0 -7/18 0/1 -5/13 -1/1 1/0 -13/34 0/1 -8/21 0/1 -11/29 0/1 1/1 -3/8 1/0 -10/27 -1/1 -7/19 0/1 1/1 -4/11 -1/1 -5/14 0/1 -1/3 0/1 1/0 -5/16 1/0 -9/29 -2/1 -1/1 -13/42 -1/1 -4/13 -1/1 -3/10 0/1 -2/7 0/1 -5/18 0/1 -18/65 -1/1 -31/112 0/1 -13/47 0/1 1/5 -8/29 1/3 -3/11 1/2 1/1 -7/26 2/3 -11/41 7/8 1/1 -15/56 1/1 -4/15 1/1 -1/4 1/0 -3/13 1/1 3/2 -5/22 2/1 -12/53 3/1 -19/84 1/0 -7/31 2/1 1/0 -2/9 3/1 -3/14 1/0 -1/5 -2/1 1/0 -2/11 -1/1 -5/28 1/0 -3/17 -3/1 1/0 -1/6 -2/1 -2/13 -1/1 -1/7 -1/1 -1/8 -1/2 0/1 -1/1 1/7 -1/1 1/6 -2/3 2/11 -1/1 1/5 -2/3 -1/2 3/14 -1/2 2/9 -3/7 5/22 -2/5 3/13 -3/8 -1/3 1/4 -1/2 4/15 -1/3 3/11 -1/3 -1/4 2/7 0/1 5/17 -1/1 -1/2 8/27 -1/3 3/10 0/1 4/13 -1/1 5/16 -1/2 1/3 -1/2 0/1 5/14 0/1 4/11 -1/1 7/19 -1/3 0/1 17/46 0/1 10/27 -1/1 3/8 -1/2 8/21 0/1 5/13 -1/1 -1/2 7/18 0/1 2/5 -1/1 7/17 -1/1 -1/2 12/29 -3/5 5/12 -1/2 3/7 -1/2 7/16 -1/2 11/25 -1/2 -2/5 15/34 -2/5 4/9 -3/7 5/11 -1/2 -1/3 6/13 -1/3 1/2 0/1 6/11 -1/1 5/9 -2/3 -3/5 4/7 -1/2 11/19 -4/9 -3/7 18/31 -3/7 7/12 -1/2 24/41 -3/7 41/70 -3/7 17/29 -3/7 -2/5 10/17 -1/3 3/5 -1/2 -2/5 17/28 -2/5 14/23 -1/3 11/18 -2/5 8/13 -1/3 21/34 -2/5 13/21 -1/3 18/29 -1/3 5/8 -1/2 17/27 -2/5 -1/3 12/19 -5/13 7/11 -3/8 -1/3 9/14 -1/3 2/3 -1/3 11/16 -1/4 20/29 -1/3 29/42 -1/4 9/13 -1/4 -1/5 7/10 0/1 5/7 0/1 13/18 0/1 47/65 -1/3 0/1 81/112 0/1 34/47 1/3 21/29 0/1 1/1 8/11 -1/1 19/26 -2/1 30/41 -1/1 41/56 -1/1 11/15 -1/1 -3/4 3/4 -1/2 10/13 -1/3 17/22 0/1 41/53 -1/2 0/1 65/84 -1/2 24/31 -1/3 7/9 -2/5 -1/3 11/14 -1/3 4/5 -1/3 9/11 -1/3 -1/4 23/28 -1/4 14/17 -1/5 5/6 0/1 11/13 -1/5 -1/6 6/7 0/1 7/8 -1/2 1/1 -1/3 0/1 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(85,74,-224,-195) (-1/1,-6/7) -> (-8/21,-11/29) Hyperbolic Matrix(139,118,-364,-309) (-6/7,-5/6) -> (-13/34,-8/21) Hyperbolic Matrix(29,24,-168,-139) (-5/6,-9/11) -> (-3/17,-1/6) Hyperbolic Matrix(57,46,140,113) (-9/11,-4/5) -> (2/5,7/17) Hyperbolic Matrix(111,88,140,111) (-4/5,-11/14) -> (11/14,4/5) Hyperbolic Matrix(197,154,252,197) (-11/14,-7/9) -> (7/9,11/14) Hyperbolic Matrix(281,218,-504,-391) (-7/9,-17/22) -> (-19/34,-5/9) Hyperbolic Matrix(449,346,728,561) (-17/22,-10/13) -> (8/13,21/34) Hyperbolic Matrix(29,22,112,85) (-10/13,-3/4) -> (1/4,4/15) Hyperbolic Matrix(27,20,112,83) (-3/4,-11/15) -> (3/13,1/4) Hyperbolic Matrix(167,122,-308,-225) (-11/15,-8/11) -> (-6/11,-7/13) Hyperbolic Matrix(139,100,-196,-141) (-8/11,-5/7) -> (-5/7,-12/17) Parabolic Matrix(559,394,952,671) (-12/17,-19/27) -> (17/29,10/17) Hyperbolic Matrix(953,670,-1512,-1063) (-19/27,-7/10) -> (-29/46,-17/27) Hyperbolic Matrix(141,98,364,253) (-7/10,-9/13) -> (5/13,7/18) Hyperbolic Matrix(337,232,-812,-559) (-9/13,-11/16) -> (-5/12,-17/41) Hyperbolic Matrix(309,212,532,365) (-11/16,-2/3) -> (18/31,7/12) Hyperbolic Matrix(55,36,84,55) (-2/3,-9/14) -> (9/14,2/3) Hyperbolic Matrix(197,126,308,197) (-9/14,-7/11) -> (7/11,9/14) Hyperbolic Matrix(139,88,308,195) (-7/11,-12/19) -> (4/9,5/11) Hyperbolic Matrix(923,582,-3332,-2101) (-12/19,-29/46) -> (-5/18,-18/65) Hyperbolic Matrix(197,124,224,141) (-17/27,-5/8) -> (7/8,1/1) Hyperbolic Matrix(29,18,-224,-139) (-5/8,-13/21) -> (-1/7,-1/8) Hyperbolic Matrix(55,34,-364,-225) (-13/21,-8/13) -> (-2/13,-1/7) Hyperbolic Matrix(111,68,364,223) (-8/13,-11/18) -> (3/10,4/13) Hyperbolic Matrix(197,120,-504,-307) (-11/18,-3/5) -> (-9/23,-7/18) Hyperbolic Matrix(27,16,140,83) (-3/5,-10/17) -> (2/11,1/5) Hyperbolic Matrix(589,346,812,477) (-10/17,-17/29) -> (21/29,8/11) Hyperbolic Matrix(253,148,-812,-475) (-17/29,-7/12) -> (-5/16,-9/29) Hyperbolic Matrix(111,64,-196,-113) (-7/12,-4/7) -> (-4/7,-9/16) Parabolic Matrix(307,172,448,251) (-9/16,-14/25) -> (2/3,11/16) Hyperbolic Matrix(533,298,-2352,-1315) (-14/25,-19/34) -> (-5/22,-12/53) Hyperbolic Matrix(113,62,308,169) (-5/9,-6/11) -> (4/11,7/19) Hyperbolic Matrix(113,60,-420,-223) (-7/13,-1/2) -> (-7/26,-11/41) Hyperbolic Matrix(83,38,-308,-141) (-1/2,-5/11) -> (-3/11,-7/26) Hyperbolic Matrix(195,88,308,139) (-5/11,-4/9) -> (12/19,7/11) Hyperbolic Matrix(83,36,-196,-85) (-4/9,-3/7) -> (-3/7,-8/19) Parabolic Matrix(195,82,-868,-365) (-8/19,-13/31) -> (-7/31,-2/9) Hyperbolic Matrix(167,70,532,223) (-13/31,-5/12) -> (5/16,1/3) Hyperbolic Matrix(1819,754,2632,1091) (-17/41,-29/70) -> (29/42,9/13) Hyperbolic Matrix(2241,928,3248,1345) (-29/70,-12/29) -> (20/29,29/42) Hyperbolic Matrix(281,116,952,393) (-12/29,-7/17) -> (5/17,8/27) Hyperbolic Matrix(113,46,140,57) (-7/17,-2/5) -> (4/5,9/11) Hyperbolic Matrix(477,188,784,309) (-2/5,-11/28) -> (17/28,14/23) Hyperbolic Matrix(475,186,784,307) (-11/28,-9/23) -> (3/5,17/28) Hyperbolic Matrix(253,98,364,141) (-7/18,-5/13) -> (9/13,7/10) Hyperbolic Matrix(167,64,728,279) (-5/13,-13/34) -> (5/22,3/13) Hyperbolic Matrix(281,106,448,169) (-11/29,-3/8) -> (5/8,17/27) Hyperbolic Matrix(279,104,448,167) (-3/8,-10/27) -> (18/29,5/8) Hyperbolic Matrix(503,186,-1820,-673) (-10/27,-7/19) -> (-13/47,-8/29) Hyperbolic Matrix(169,62,308,113) (-7/19,-4/11) -> (6/11,5/9) Hyperbolic Matrix(111,40,308,111) (-4/11,-5/14) -> (5/14,4/11) Hyperbolic Matrix(29,10,84,29) (-5/14,-1/3) -> (1/3,5/14) Hyperbolic Matrix(197,62,448,141) (-1/3,-5/16) -> (7/16,11/25) Hyperbolic Matrix(1903,590,3248,1007) (-9/29,-13/42) -> (41/70,17/29) Hyperbolic Matrix(1541,476,2632,813) (-13/42,-4/13) -> (24/41,41/70) Hyperbolic Matrix(223,68,364,111) (-4/13,-3/10) -> (11/18,8/13) Hyperbolic Matrix(55,16,-196,-57) (-3/10,-2/7) -> (-2/7,-5/18) Parabolic Matrix(9073,2512,12544,3473) (-18/65,-31/112) -> (81/112,34/47) Hyperbolic Matrix(9071,2510,12544,3471) (-31/112,-13/47) -> (47/65,81/112) Hyperbolic Matrix(335,92,812,223) (-8/29,-3/11) -> (7/17,12/29) Hyperbolic Matrix(2297,616,3136,841) (-11/41,-15/56) -> (41/56,11/15) Hyperbolic Matrix(2295,614,3136,839) (-15/56,-4/15) -> (30/41,41/56) Hyperbolic Matrix(85,22,112,29) (-4/15,-1/4) -> (3/4,10/13) Hyperbolic Matrix(83,20,112,27) (-1/4,-3/13) -> (11/15,3/4) Hyperbolic Matrix(307,70,364,83) (-3/13,-5/22) -> (5/6,11/13) Hyperbolic Matrix(5461,1236,7056,1597) (-12/53,-19/84) -> (65/84,24/31) Hyperbolic Matrix(5459,1234,7056,1595) (-19/84,-7/31) -> (41/53,65/84) Hyperbolic Matrix(55,12,252,55) (-2/9,-3/14) -> (3/14,2/9) Hyperbolic Matrix(29,6,140,29) (-3/14,-1/5) -> (1/5,3/14) Hyperbolic Matrix(83,16,140,27) (-1/5,-2/11) -> (10/17,3/5) Hyperbolic Matrix(645,116,784,141) (-2/11,-5/28) -> (23/28,14/17) Hyperbolic Matrix(643,114,784,139) (-5/28,-3/17) -> (9/11,23/28) Hyperbolic Matrix(281,44,364,57) (-1/6,-2/13) -> (10/13,17/22) Hyperbolic Matrix(83,10,224,27) (-1/8,0/1) -> (10/27,3/8) Hyperbolic Matrix(139,-18,224,-29) (0/1,1/7) -> (13/21,18/29) Hyperbolic Matrix(225,-34,364,-55) (1/7,1/6) -> (21/34,13/21) Hyperbolic Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(141,-38,308,-83) (4/15,3/11) -> (5/11,6/13) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(2409,-890,3332,-1231) (7/19,17/46) -> (13/18,47/65) Hyperbolic Matrix(195,-74,224,-85) (3/8,8/21) -> (6/7,7/8) Hyperbolic Matrix(309,-118,364,-139) (8/21,5/13) -> (11/13,6/7) Hyperbolic Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(1819,-802,2352,-1037) (11/25,15/34) -> (17/22,41/53) Hyperbolic Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(225,-122,308,-167) (1/2,6/11) -> (8/11,19/26) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(673,-390,868,-503) (11/19,18/31) -> (24/31,7/9) Hyperbolic Matrix(1317,-830,1820,-1147) (17/27,12/19) -> (34/47,21/29) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(85,74,-224,-195) -> Matrix(1,0,0,1) Matrix(139,118,-364,-309) -> Matrix(1,0,-4,1) Matrix(29,24,-168,-139) -> Matrix(5,-2,-2,1) Matrix(57,46,140,113) -> Matrix(3,-2,-4,3) Matrix(111,88,140,111) -> Matrix(3,-2,-10,7) Matrix(197,154,252,197) -> Matrix(3,-4,-8,11) Matrix(281,218,-504,-391) -> Matrix(1,-4,0,1) Matrix(449,346,728,561) -> Matrix(1,-2,-2,5) Matrix(29,22,112,85) -> Matrix(1,-2,-2,5) Matrix(27,20,112,83) -> Matrix(1,0,-2,1) Matrix(167,122,-308,-225) -> Matrix(3,2,-2,-1) Matrix(139,100,-196,-141) -> Matrix(1,0,4,1) Matrix(559,394,952,671) -> Matrix(5,-2,-12,5) Matrix(953,670,-1512,-1063) -> Matrix(3,-2,2,-1) Matrix(141,98,364,253) -> Matrix(1,0,-4,1) Matrix(337,232,-812,-559) -> Matrix(5,-2,-2,1) Matrix(309,212,532,365) -> Matrix(5,-2,-12,5) Matrix(55,36,84,55) -> Matrix(1,0,-4,1) Matrix(197,126,308,197) -> Matrix(5,-6,-14,17) Matrix(139,88,308,195) -> Matrix(3,-4,-8,11) Matrix(923,582,-3332,-2101) -> Matrix(1,-2,2,-3) Matrix(197,124,224,141) -> Matrix(1,-2,-2,5) Matrix(29,18,-224,-139) -> Matrix(1,0,-2,1) Matrix(55,34,-364,-225) -> Matrix(3,-4,-2,3) Matrix(111,68,364,223) -> Matrix(1,-2,0,1) Matrix(197,120,-504,-307) -> Matrix(1,-2,0,1) Matrix(27,16,140,83) -> Matrix(1,0,-2,1) Matrix(589,346,812,477) -> Matrix(1,-2,0,1) Matrix(253,148,-812,-475) -> Matrix(1,-4,0,1) Matrix(111,64,-196,-113) -> Matrix(1,-6,0,1) Matrix(307,172,448,251) -> Matrix(1,4,-4,-15) Matrix(533,298,-2352,-1315) -> Matrix(1,6,0,1) Matrix(113,62,308,169) -> Matrix(1,2,-2,-3) Matrix(113,60,-420,-223) -> Matrix(3,2,4,3) Matrix(83,38,-308,-141) -> Matrix(1,-2,2,-3) Matrix(195,88,308,139) -> Matrix(3,-4,-8,11) Matrix(83,36,-196,-85) -> Matrix(1,-4,0,1) Matrix(195,82,-868,-365) -> Matrix(1,4,0,1) Matrix(167,70,532,223) -> Matrix(1,2,-2,-3) Matrix(1819,754,2632,1091) -> Matrix(1,0,-4,1) Matrix(2241,928,3248,1345) -> Matrix(1,4,-4,-15) Matrix(281,116,952,393) -> Matrix(1,2,-2,-3) Matrix(113,46,140,57) -> Matrix(1,2,-4,-7) Matrix(477,188,784,309) -> Matrix(3,2,-8,-5) Matrix(475,186,784,307) -> Matrix(1,-2,-2,5) Matrix(253,98,364,141) -> Matrix(1,0,-4,1) Matrix(167,64,728,279) -> Matrix(3,2,-8,-5) Matrix(281,106,448,169) -> Matrix(1,-2,-2,5) Matrix(279,104,448,167) -> Matrix(1,0,-2,1) Matrix(503,186,-1820,-673) -> Matrix(1,0,4,1) Matrix(169,62,308,113) -> Matrix(1,2,-2,-3) Matrix(111,40,308,111) -> Matrix(1,0,0,1) Matrix(29,10,84,29) -> Matrix(1,0,-2,1) Matrix(197,62,448,141) -> Matrix(1,-2,-2,5) Matrix(1903,590,3248,1007) -> Matrix(5,8,-12,-19) Matrix(1541,476,2632,813) -> Matrix(1,-2,-2,5) Matrix(223,68,364,111) -> Matrix(3,2,-8,-5) Matrix(55,16,-196,-57) -> Matrix(1,0,2,1) Matrix(9073,2512,12544,3473) -> Matrix(1,0,4,1) Matrix(9071,2510,12544,3471) -> Matrix(1,0,-8,1) Matrix(335,92,812,223) -> Matrix(3,-2,-4,3) Matrix(2297,616,3136,841) -> Matrix(11,-10,-12,11) Matrix(2295,614,3136,839) -> Matrix(7,-8,-6,7) Matrix(85,22,112,29) -> Matrix(1,-2,-2,5) Matrix(83,20,112,27) -> Matrix(1,0,-2,1) Matrix(307,70,364,83) -> Matrix(1,-2,-4,9) Matrix(5461,1236,7056,1597) -> Matrix(1,-4,-2,9) Matrix(5459,1234,7056,1595) -> Matrix(1,-2,-2,5) Matrix(55,12,252,55) -> Matrix(1,-6,-2,13) Matrix(29,6,140,29) -> Matrix(1,4,-2,-7) Matrix(83,16,140,27) -> Matrix(1,0,-2,1) Matrix(645,116,784,141) -> Matrix(1,0,-4,1) Matrix(643,114,784,139) -> Matrix(1,4,-4,-15) Matrix(281,44,364,57) -> Matrix(1,2,-4,-7) Matrix(83,10,224,27) -> Matrix(1,0,0,1) Matrix(139,-18,224,-29) -> Matrix(1,0,-2,1) Matrix(225,-34,364,-55) -> Matrix(5,4,-14,-11) Matrix(139,-24,168,-29) -> Matrix(3,2,-14,-9) Matrix(223,-50,504,-113) -> Matrix(1,0,0,1) Matrix(141,-38,308,-83) -> Matrix(7,2,-18,-5) Matrix(57,-16,196,-55) -> Matrix(1,0,2,1) Matrix(559,-166,1512,-449) -> Matrix(1,0,2,1) Matrix(475,-148,812,-253) -> Matrix(7,4,-16,-9) Matrix(2409,-890,3332,-1231) -> Matrix(1,0,0,1) Matrix(195,-74,224,-85) -> Matrix(1,0,0,1) Matrix(309,-118,364,-139) -> Matrix(1,0,-4,1) Matrix(307,-120,504,-197) -> Matrix(3,2,-8,-5) Matrix(559,-232,812,-337) -> Matrix(3,2,-14,-9) Matrix(85,-36,196,-83) -> Matrix(7,4,-16,-9) Matrix(1819,-802,2352,-1037) -> Matrix(5,2,-8,-3) Matrix(307,-144,420,-197) -> Matrix(7,2,-4,-1) Matrix(225,-122,308,-167) -> Matrix(3,2,-2,-1) Matrix(113,-64,196,-111) -> Matrix(11,6,-24,-13) Matrix(673,-390,868,-503) -> Matrix(5,2,-8,-3) Matrix(1317,-830,1820,-1147) -> Matrix(5,2,2,1) Matrix(141,-100,196,-139) -> Matrix(1,0,4,1) 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): 26 Degree of the the map X: 26 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 -1/1 1 14 1/7 -1/1 2 2 1/6 -2/3 1 7 2/11 -1/1 1 14 1/5 (-2/3,-1/2) 0 14 3/14 -1/2 5 1 2/9 -3/7 1 14 5/22 -2/5 1 7 3/13 (-3/8,-1/3) 0 14 1/4 -1/2 1 7 4/15 -1/3 1 14 3/11 (-1/3,-1/4) 0 14 2/7 0/1 1 2 5/17 (-1/1,-1/2) 0 14 8/27 -1/3 1 14 3/10 0/1 1 7 4/13 -1/1 1 14 5/16 -1/2 1 7 1/3 (-1/2,0/1) 0 14 5/14 0/1 1 1 4/11 -1/1 1 14 7/19 (-1/3,0/1) 0 14 17/46 0/1 1 7 10/27 -1/1 1 14 3/8 -1/2 1 7 8/21 0/1 2 2 5/13 (-1/1,-1/2) 0 14 7/18 0/1 1 7 2/5 -1/1 1 14 7/17 (-1/1,-1/2) 0 14 12/29 -3/5 1 14 5/12 -1/2 1 7 3/7 -1/2 2 2 7/16 -1/2 1 7 11/25 (-1/2,-2/5) 0 14 15/34 -2/5 1 7 4/9 -3/7 1 14 5/11 (-1/2,-1/3) 0 14 6/13 -1/3 1 14 1/2 0/1 1 7 6/11 -1/1 1 14 5/9 (-2/3,-3/5) 0 14 4/7 -1/2 3 2 11/19 (-4/9,-3/7) 0 14 18/31 -3/7 1 14 7/12 -1/2 1 7 24/41 -3/7 1 14 41/70 -3/7 1 1 17/29 (-3/7,-2/5) 0 14 10/17 -1/3 1 14 3/5 (-1/2,-2/5) 0 14 17/28 -2/5 1 1 14/23 -1/3 1 14 11/18 -2/5 1 7 8/13 -1/3 1 14 21/34 -2/5 1 7 13/21 -1/3 2 2 18/29 -1/3 1 14 5/8 -1/2 1 7 17/27 (-2/5,-1/3) 0 14 12/19 -5/13 1 14 7/11 (-3/8,-1/3) 0 14 9/14 -1/3 3 1 2/3 -1/3 1 14 11/16 -1/4 1 7 20/29 -1/3 1 14 29/42 -1/4 2 1 9/13 (-1/4,-1/5) 0 14 7/10 0/1 1 7 5/7 0/1 2 2 13/18 0/1 1 7 47/65 (-1/3,0/1) 0 14 81/112 0/1 6 1 34/47 1/3 1 14 21/29 (0/1,1/1) 0 14 8/11 -1/1 1 14 19/26 -2/1 1 7 30/41 -1/1 1 14 41/56 -1/1 9 1 11/15 (-1/1,-3/4) 0 14 3/4 -1/2 1 7 10/13 -1/3 1 14 17/22 0/1 1 7 41/53 (-1/2,0/1) 0 14 65/84 -1/2 1 1 24/31 -1/3 1 14 7/9 (-2/5,-1/3) 0 14 11/14 -1/3 3 1 4/5 -1/3 1 14 9/11 (-1/3,-1/4) 0 14 23/28 -1/4 2 1 14/17 -1/5 1 14 5/6 0/1 1 7 11/13 (-1/5,-1/6) 0 14 6/7 0/1 2 2 7/8 -1/2 1 7 1/1 (-1/3,0/1) 0 14 1/0 0/1 2 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(139,-18,224,-29) (0/1,1/7) -> (13/21,18/29) Hyperbolic Matrix(225,-34,364,-55) (1/7,1/6) -> (21/34,13/21) Hyperbolic Matrix(139,-24,168,-29) (1/6,2/11) -> (14/17,5/6) Hyperbolic Matrix(83,-16,140,-27) (2/11,1/5) -> (10/17,3/5) Glide Reflection Matrix(29,-6,140,-29) (1/5,3/14) -> (1/5,3/14) Reflection Matrix(55,-12,252,-55) (3/14,2/9) -> (3/14,2/9) Reflection Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(307,-70,364,-83) (5/22,3/13) -> (5/6,11/13) Glide Reflection Matrix(83,-20,112,-27) (3/13,1/4) -> (11/15,3/4) Glide Reflection Matrix(85,-22,112,-29) (1/4,4/15) -> (3/4,10/13) Glide Reflection Matrix(141,-38,308,-83) (4/15,3/11) -> (5/11,6/13) Hyperbolic Matrix(57,-16,196,-55) (3/11,2/7) -> (2/7,5/17) Parabolic Matrix(393,-116,952,-281) (5/17,8/27) -> (7/17,12/29) Glide Reflection Matrix(559,-166,1512,-449) (8/27,3/10) -> (17/46,10/27) Hyperbolic Matrix(223,-68,364,-111) (3/10,4/13) -> (11/18,8/13) Glide Reflection Matrix(475,-148,812,-253) (4/13,5/16) -> (7/12,24/41) Hyperbolic Matrix(197,-62,448,-141) (5/16,1/3) -> (7/16,11/25) Glide Reflection Matrix(29,-10,84,-29) (1/3,5/14) -> (1/3,5/14) Reflection Matrix(111,-40,308,-111) (5/14,4/11) -> (5/14,4/11) Reflection Matrix(169,-62,308,-113) (4/11,7/19) -> (6/11,5/9) Glide Reflection Matrix(2409,-890,3332,-1231) (7/19,17/46) -> (13/18,47/65) Hyperbolic Matrix(279,-104,448,-167) (10/27,3/8) -> (18/29,5/8) Glide Reflection Matrix(195,-74,224,-85) (3/8,8/21) -> (6/7,7/8) Hyperbolic Matrix(309,-118,364,-139) (8/21,5/13) -> (11/13,6/7) Hyperbolic Matrix(253,-98,364,-141) (5/13,7/18) -> (9/13,7/10) Glide Reflection Matrix(307,-120,504,-197) (7/18,2/5) -> (14/23,11/18) Hyperbolic Matrix(113,-46,140,-57) (2/5,7/17) -> (4/5,9/11) Glide Reflection Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(85,-36,196,-83) (5/12,3/7) -> (3/7,7/16) Parabolic Matrix(1819,-802,2352,-1037) (11/25,15/34) -> (17/22,41/53) Hyperbolic Matrix(195,-88,308,-139) (4/9,5/11) -> (12/19,7/11) Glide Reflection Matrix(307,-144,420,-197) (6/13,1/2) -> (19/26,30/41) Hyperbolic Matrix(225,-122,308,-167) (1/2,6/11) -> (8/11,19/26) Hyperbolic Matrix(113,-64,196,-111) (5/9,4/7) -> (4/7,11/19) Parabolic Matrix(673,-390,868,-503) (11/19,18/31) -> (24/31,7/9) Hyperbolic Matrix(365,-212,532,-309) (18/31,7/12) -> (2/3,11/16) Glide Reflection Matrix(3361,-1968,5740,-3361) (24/41,41/70) -> (24/41,41/70) Reflection Matrix(2379,-1394,4060,-2379) (41/70,17/29) -> (41/70,17/29) Reflection Matrix(589,-346,812,-477) (17/29,10/17) -> (21/29,8/11) Glide Reflection Matrix(169,-102,280,-169) (3/5,17/28) -> (3/5,17/28) Reflection Matrix(783,-476,1288,-783) (17/28,14/23) -> (17/28,14/23) Reflection Matrix(561,-346,728,-449) (8/13,21/34) -> (10/13,17/22) Glide Reflection Matrix(197,-124,224,-141) (5/8,17/27) -> (7/8,1/1) Glide Reflection Matrix(1317,-830,1820,-1147) (17/27,12/19) -> (34/47,21/29) Hyperbolic Matrix(197,-126,308,-197) (7/11,9/14) -> (7/11,9/14) Reflection Matrix(55,-36,84,-55) (9/14,2/3) -> (9/14,2/3) Reflection Matrix(1681,-1160,2436,-1681) (20/29,29/42) -> (20/29,29/42) Reflection Matrix(755,-522,1092,-755) (29/42,9/13) -> (29/42,9/13) Reflection Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(10529,-7614,14560,-10529) (47/65,81/112) -> (47/65,81/112) Reflection Matrix(7615,-5508,10528,-7615) (81/112,34/47) -> (81/112,34/47) Reflection Matrix(3361,-2460,4592,-3361) (30/41,41/56) -> (30/41,41/56) Reflection Matrix(1231,-902,1680,-1231) (41/56,11/15) -> (41/56,11/15) Reflection Matrix(6889,-5330,8904,-6889) (41/53,65/84) -> (41/53,65/84) Reflection Matrix(4031,-3120,5208,-4031) (65/84,24/31) -> (65/84,24/31) Reflection Matrix(197,-154,252,-197) (7/9,11/14) -> (7/9,11/14) Reflection Matrix(111,-88,140,-111) (11/14,4/5) -> (11/14,4/5) Reflection Matrix(505,-414,616,-505) (9/11,23/28) -> (9/11,23/28) Reflection Matrix(783,-644,952,-783) (23/28,14/17) -> (23/28,14/17) 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(-1,0,2,1) (0/1,1/0) -> (-1/1,0/1) Matrix(139,-18,224,-29) -> Matrix(1,0,-2,1) 0/1 Matrix(225,-34,364,-55) -> Matrix(5,4,-14,-11) Matrix(139,-24,168,-29) -> Matrix(3,2,-14,-9) Matrix(83,-16,140,-27) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(29,-6,140,-29) -> Matrix(7,4,-12,-7) (1/5,3/14) -> (-2/3,-1/2) Matrix(55,-12,252,-55) -> Matrix(13,6,-28,-13) (3/14,2/9) -> (-1/2,-3/7) Matrix(223,-50,504,-113) -> Matrix(1,0,0,1) Matrix(307,-70,364,-83) -> Matrix(5,2,-22,-9) Matrix(83,-20,112,-27) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(85,-22,112,-29) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(141,-38,308,-83) -> Matrix(7,2,-18,-5) -1/3 Matrix(57,-16,196,-55) -> Matrix(1,0,2,1) 0/1 Matrix(393,-116,952,-281) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(559,-166,1512,-449) -> Matrix(1,0,2,1) 0/1 Matrix(223,-68,364,-111) -> Matrix(1,2,-2,-5) Matrix(475,-148,812,-253) -> Matrix(7,4,-16,-9) -1/2 Matrix(197,-62,448,-141) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(29,-10,84,-29) -> Matrix(-1,0,4,1) (1/3,5/14) -> (-1/2,0/1) Matrix(111,-40,308,-111) -> Matrix(-1,0,2,1) (5/14,4/11) -> (-1/1,0/1) Matrix(169,-62,308,-113) -> Matrix(3,2,-4,-3) *** -> (-1/1,-1/2) Matrix(2409,-890,3332,-1231) -> Matrix(1,0,0,1) Matrix(279,-104,448,-167) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(195,-74,224,-85) -> Matrix(1,0,0,1) Matrix(309,-118,364,-139) -> Matrix(1,0,-4,1) 0/1 Matrix(253,-98,364,-141) -> Matrix(-1,0,6,1) *** -> (-1/3,0/1) Matrix(307,-120,504,-197) -> Matrix(3,2,-8,-5) -1/2 Matrix(113,-46,140,-57) -> Matrix(3,2,-10,-7) Matrix(559,-232,812,-337) -> Matrix(3,2,-14,-9) Matrix(85,-36,196,-83) -> Matrix(7,4,-16,-9) -1/2 Matrix(1819,-802,2352,-1037) -> Matrix(5,2,-8,-3) -1/2 Matrix(195,-88,308,-139) -> Matrix(11,4,-30,-11) *** -> (-2/5,-1/3) Matrix(307,-144,420,-197) -> Matrix(7,2,-4,-1) Matrix(225,-122,308,-167) -> Matrix(3,2,-2,-1) -1/1 Matrix(113,-64,196,-111) -> Matrix(11,6,-24,-13) -1/2 Matrix(673,-390,868,-503) -> Matrix(5,2,-8,-3) -1/2 Matrix(365,-212,532,-309) -> Matrix(5,2,-22,-9) Matrix(3361,-1968,5740,-3361) -> Matrix(13,6,-28,-13) (24/41,41/70) -> (-1/2,-3/7) Matrix(2379,-1394,4060,-2379) -> Matrix(29,12,-70,-29) (41/70,17/29) -> (-3/7,-2/5) Matrix(589,-346,812,-477) -> Matrix(5,2,-2,-1) Matrix(169,-102,280,-169) -> Matrix(9,4,-20,-9) (3/5,17/28) -> (-1/2,-2/5) Matrix(783,-476,1288,-783) -> Matrix(11,4,-30,-11) (17/28,14/23) -> (-2/5,-1/3) Matrix(561,-346,728,-449) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(197,-124,224,-141) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(1317,-830,1820,-1147) -> Matrix(5,2,2,1) Matrix(197,-126,308,-197) -> Matrix(17,6,-48,-17) (7/11,9/14) -> (-3/8,-1/3) Matrix(55,-36,84,-55) -> Matrix(-1,0,6,1) (9/14,2/3) -> (-1/3,0/1) Matrix(1681,-1160,2436,-1681) -> Matrix(7,2,-24,-7) (20/29,29/42) -> (-1/3,-1/4) Matrix(755,-522,1092,-755) -> Matrix(9,2,-40,-9) (29/42,9/13) -> (-1/4,-1/5) Matrix(141,-100,196,-139) -> Matrix(1,0,4,1) 0/1 Matrix(10529,-7614,14560,-10529) -> Matrix(-1,0,6,1) (47/65,81/112) -> (-1/3,0/1) Matrix(7615,-5508,10528,-7615) -> Matrix(1,0,6,-1) (81/112,34/47) -> (0/1,1/3) Matrix(3361,-2460,4592,-3361) -> Matrix(11,12,-10,-11) (30/41,41/56) -> (-6/5,-1/1) Matrix(1231,-902,1680,-1231) -> Matrix(7,6,-8,-7) (41/56,11/15) -> (-1/1,-3/4) Matrix(6889,-5330,8904,-6889) -> Matrix(-1,0,4,1) (41/53,65/84) -> (-1/2,0/1) Matrix(4031,-3120,5208,-4031) -> Matrix(5,2,-12,-5) (65/84,24/31) -> (-1/2,-1/3) Matrix(197,-154,252,-197) -> Matrix(11,4,-30,-11) (7/9,11/14) -> (-2/5,-1/3) Matrix(111,-88,140,-111) -> Matrix(7,2,-24,-7) (11/14,4/5) -> (-1/3,-1/4) Matrix(505,-414,616,-505) -> Matrix(7,2,-24,-7) (9/11,23/28) -> (-1/3,-1/4) Matrix(783,-644,952,-783) -> Matrix(9,2,-40,-9) (23/28,14/17) -> (-1/4,-1/5) Matrix(-1,2,0,1) -> Matrix(-1,0,6,1) (1/1,1/0) -> (-1/3,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.