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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/7 -16/21 -3/4 -5/7 -53/84 -7/12 -4/7 -14/25 -1/2 -3/7 -83/196 -5/12 -8/21 -3/8 -2/7 -31/112 -15/56 -1/4 -19/84 -4/21 -1/6 -2/13 -1/7 -1/8 -2/17 -1/10 -1/11 0/1 1/10 1/9 1/8 2/15 1/7 1/6 4/23 5/28 2/11 4/21 1/5 4/19 3/14 2/9 3/13 1/4 2/7 8/27 13/42 1/3 5/14 3/8 8/21 11/28 2/5 5/12 3/7 13/28 1/2 4/7 7/12 17/28 9/14 2/3 29/42 5/7 3/4 16/21 65/84 11/14 23/28 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/0 -7/8 0/1 -6/7 1/0 -17/20 -4/1 -11/13 1/0 -5/6 -3/2 -14/17 -7/6 -1/1 -23/28 -1/1 -9/11 -3/4 -4/5 0/1 1/0 -11/14 1/0 -18/23 -5/1 1/0 -7/9 1/0 -17/22 -3/2 -10/13 -2/1 1/0 -13/17 1/0 -29/38 -3/2 -16/21 -3/2 -19/25 1/0 -3/4 -1/1 -14/19 -1/2 0/1 -25/34 1/2 -11/15 1/0 -8/11 -1/2 0/1 -21/29 1/0 -34/47 -3/2 -1/1 -13/18 -1/2 -18/25 0/1 1/2 -5/7 1/0 -22/31 -2/1 -3/2 -61/86 -3/2 -39/55 1/0 -17/24 -2/1 -12/17 -3/2 -1/1 -19/27 1/0 -7/10 -3/2 -16/23 -1/1 -3/4 -25/36 0/1 -9/13 1/0 -11/16 -1/1 -13/19 -5/4 -2/3 -1/1 -1/2 -9/14 -1/2 -16/25 -1/2 0/1 -7/11 1/0 -19/30 -1/2 -12/19 -1/2 0/1 -53/84 0/1 -41/65 1/4 -29/46 1/2 -17/27 1/0 -5/8 -1/1 -18/29 -1/1 -1/2 -31/50 -1/2 -13/21 -1/2 -8/13 0/1 1/0 -11/18 -3/2 -14/23 -9/8 -1/1 -17/28 -1/1 -3/5 -3/4 -16/27 -1/1 -1/2 -13/22 -1/2 -10/17 -1/1 -5/6 -17/29 -3/4 -41/70 -3/4 -24/41 -3/4 -11/15 -7/12 -2/3 -4/7 -1/2 -9/16 0/1 -14/25 -1/6 0/1 -19/34 1/2 -5/9 1/0 -6/11 -1/2 0/1 -7/13 1/0 -1/2 -1/2 -7/15 -1/4 -13/28 0/1 -6/13 0/1 1/0 -5/11 1/0 -14/31 -1/2 0/1 -23/51 -1/4 -9/20 0/1 -13/29 1/0 -4/9 -1/1 -1/2 -11/25 -7/8 -18/41 -7/9 -3/4 -7/16 -2/3 -24/55 -2/3 -1/2 -17/39 -3/4 -10/23 -5/8 -3/5 -3/7 -1/2 -14/33 -7/16 -3/7 -25/59 -7/16 -36/85 -1/2 -3/7 -83/196 -3/7 -47/111 -5/12 -11/26 -1/2 -8/19 -1/2 -2/5 -21/50 -9/22 -34/81 -25/62 -2/5 -47/112 -2/5 -13/31 -11/28 -5/12 -1/3 -17/41 -1/4 -29/70 -1/2 -12/29 -1/2 -1/3 -7/17 -3/8 -2/5 -1/4 0/1 -11/28 0/1 -9/23 1/8 -16/41 1/5 1/4 -23/59 3/8 -30/77 1/2 -7/18 1/2 -12/31 -1/2 0/1 -17/44 0/1 -22/57 0/1 1/2 -27/70 1/2 -5/13 1/0 -13/34 3/2 -8/21 1/0 -19/50 -5/2 -11/29 1/0 -3/8 -1/1 -10/27 -1/1 -1/2 -7/19 -3/4 -4/11 -2/3 -1/2 -5/14 -1/2 -6/17 -1/2 -3/7 -7/20 -2/5 -8/23 -1/3 -1/4 -1/3 -1/4 -5/16 1/1 -9/29 1/0 -13/42 1/0 -4/13 -2/1 1/0 -3/10 -1/2 -2/7 -1/2 -5/18 -1/2 -18/65 -5/14 -1/3 -31/112 -1/3 -13/47 -1/4 -8/29 -1/2 -1/3 -3/11 -1/4 -7/26 -1/2 -11/41 -3/8 -15/56 -1/3 -4/15 -1/3 -1/4 -9/34 -1/2 -14/53 -1/3 -7/22 -5/19 -1/4 -6/23 -1/4 -1/5 -7/27 -1/4 -1/4 0/1 -4/17 -1/1 -1/2 -11/47 1/0 -7/30 -1/2 -3/13 1/0 -5/22 -3/2 -12/53 -11/10 -1/1 -19/84 -1/1 -7/31 -7/8 -2/9 -1/1 -1/2 -3/14 -1/2 -4/19 -1/2 -2/5 -5/24 -1/3 -11/53 -1/4 -6/29 -1/2 -1/3 -1/5 -1/4 -6/31 -1/2 0/1 -5/26 -1/2 -4/21 -1/2 -11/58 -1/2 -7/37 -3/8 -3/16 -1/3 -5/27 -1/4 -2/11 -1/6 0/1 -5/28 0/1 -3/17 1/4 -4/23 1/1 1/0 -5/29 1/0 -1/6 -1/2 -2/13 0/1 1/0 -1/7 -1/2 -3/22 -1/2 -2/15 -1/3 -1/4 -3/23 1/0 -1/8 0/1 -2/17 -1/2 -1/3 -1/9 -1/4 -1/10 -1/2 -1/11 -1/4 0/1 -1/2 0/1 1/10 -1/2 1/9 1/0 1/8 0/1 2/15 -1/1 1/0 1/7 -1/2 1/6 -1/2 4/23 -1/4 -1/5 3/17 -1/8 5/28 0/1 2/11 0/1 1/2 3/16 -1/1 4/21 -1/2 5/26 -1/2 1/5 1/0 4/19 -2/3 -1/2 3/14 -1/2 2/9 -1/2 -1/3 5/22 -3/10 3/13 -1/4 7/30 -1/2 11/47 -1/4 4/17 -1/2 -1/3 1/4 0/1 5/19 1/0 9/34 -1/2 4/15 -1/1 1/0 7/26 -1/2 3/11 1/0 2/7 -1/2 5/17 -3/8 8/27 -1/2 -1/3 3/10 -1/2 4/13 -2/7 -1/4 13/42 -1/4 9/29 -1/4 5/16 -1/5 1/3 1/0 7/20 -2/3 13/37 -5/8 6/17 -3/5 -1/2 5/14 -1/2 4/11 -1/2 -2/5 7/19 -3/8 17/46 -1/2 10/27 -1/2 -1/3 3/8 -1/3 11/29 -1/4 8/21 -1/4 21/55 -1/4 34/89 -1/4 -3/13 13/34 -3/14 5/13 -1/4 12/31 -1/2 0/1 7/18 -1/6 16/41 -1/8 -1/9 25/64 0/1 9/23 -1/12 11/28 0/1 2/5 0/1 1/0 7/17 -3/4 12/29 -1/1 -1/2 5/12 -1/1 13/31 -11/16 21/50 -9/14 8/19 -2/3 -1/2 11/26 -1/2 3/7 -1/2 13/30 -1/2 36/83 -1/2 -3/7 23/53 -5/12 10/23 -3/7 -5/12 17/39 -3/8 24/55 -1/2 -2/5 7/16 -2/5 18/41 -3/8 -7/19 29/66 -5/14 11/25 -7/20 37/84 -1/3 26/59 -1/3 -11/34 15/34 -3/10 4/9 -1/2 -1/3 9/20 0/1 5/11 -1/4 6/13 -1/4 0/1 13/28 0/1 7/15 1/0 1/2 -1/2 6/11 -1/2 0/1 5/9 -1/4 4/7 -1/2 11/19 -5/12 18/31 -2/5 -7/18 25/43 -3/8 32/55 -1/2 -2/5 7/12 -2/5 24/41 -11/29 -3/8 41/70 -3/8 17/29 -3/8 10/17 -5/14 -1/3 13/22 -1/2 16/27 -1/2 -1/3 3/5 -3/8 17/28 -1/3 14/23 -1/3 -9/28 11/18 -3/10 8/13 -1/4 0/1 21/34 -1/2 13/21 -1/2 44/71 -3/8 -1/3 31/50 -1/2 18/29 -1/2 -1/3 5/8 -1/3 17/27 -1/4 12/19 -1/2 0/1 19/30 -1/2 7/11 -1/4 23/36 0/1 39/61 1/0 55/86 -1/2 16/25 -1/2 0/1 9/14 -1/2 2/3 -1/2 -1/3 15/22 -7/22 13/19 -5/16 37/54 -3/10 24/35 -3/10 11/16 -1/3 20/29 -1/3 -3/10 29/42 -3/10 38/55 -3/10 -2/7 9/13 -1/4 25/36 0/1 41/59 -3/8 16/23 -3/8 -1/3 7/10 -3/10 33/47 -7/24 59/84 -2/7 26/37 -2/7 -5/18 19/27 -1/4 12/17 -1/3 -3/10 17/24 -2/7 5/7 -1/4 23/32 0/1 41/57 -1/4 141/196 -1/5 100/139 -1/5 -1/6 59/82 -1/6 18/25 -1/6 0/1 13/18 -1/2 47/65 -3/8 81/112 -1/3 34/47 -1/3 -3/10 21/29 -1/4 29/40 -1/5 8/11 -1/2 0/1 19/26 -1/2 30/41 -3/8 -1/3 41/56 -1/3 11/15 -1/4 14/19 -1/2 0/1 17/23 -3/8 20/27 -1/2 -1/3 3/4 -1/3 22/29 -1/3 -3/10 19/25 -1/4 16/21 -3/10 45/59 -13/44 29/38 -3/10 42/55 -3/10 -2/7 13/17 -1/4 10/13 -2/7 -1/4 17/22 -3/10 41/53 -23/80 65/84 -2/7 24/31 -2/7 -13/46 7/9 -1/4 25/32 -4/15 43/55 -1/4 18/23 -5/19 -1/4 11/14 -1/4 4/5 -1/4 0/1 9/11 -3/8 23/28 -1/3 14/17 -1/3 -7/22 5/6 -3/10 16/19 -2/7 -5/18 11/13 -1/4 6/7 -1/4 13/15 -1/4 7/8 0/1 8/9 -1/2 -1/3 1/1 -1/4 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(113,100,-252,-223) (-1/1,-7/8) -> (-9/20,-13/29) Hyperbolic Matrix(167,144,-196,-169) (-7/8,-6/7) -> (-6/7,-17/20) Parabolic Matrix(505,428,728,617) (-17/20,-11/13) -> (9/13,25/36) Hyperbolic Matrix(391,330,-532,-449) (-11/13,-5/6) -> (-25/34,-11/15) Hyperbolic Matrix(281,232,476,393) (-5/6,-14/17) -> (10/17,13/22) Hyperbolic Matrix(783,644,952,783) (-14/17,-23/28) -> (23/28,14/17) Hyperbolic Matrix(505,414,616,505) (-23/28,-9/11) -> (9/11,23/28) 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(505,396,644,505) (-11/14,-18/23) -> (18/23,11/14) Hyperbolic Matrix(169,132,-644,-503) (-18/23,-7/9) -> (-5/19,-6/23) 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(167,128,364,279) (-10/13,-13/17) -> (5/11,6/13) Hyperbolic Matrix(55,42,-588,-449) (-13/17,-29/38) -> (-1/10,-1/11) Hyperbolic Matrix(1287,982,-3304,-2521) (-29/38,-16/21) -> (-30/77,-7/18) Hyperbolic Matrix(1233,938,-3164,-2407) (-16/21,-19/25) -> (-23/59,-30/77) Hyperbolic Matrix(169,128,-812,-615) (-19/25,-3/4) -> (-5/24,-11/53) Hyperbolic Matrix(111,82,-532,-393) (-3/4,-14/19) -> (-4/19,-5/24) Hyperbolic Matrix(671,494,1596,1175) (-14/19,-25/34) -> (21/50,8/19) Hyperbolic Matrix(167,122,-308,-225) (-11/15,-8/11) -> (-6/11,-7/13) Hyperbolic Matrix(113,82,-616,-447) (-8/11,-21/29) -> (-5/27,-2/11) Hyperbolic Matrix(279,202,308,223) (-21/29,-34/47) -> (8/9,1/1) Hyperbolic Matrix(559,404,-2016,-1457) (-34/47,-13/18) -> (-5/18,-18/65) Hyperbolic Matrix(391,282,1008,727) (-13/18,-18/25) -> (12/31,7/18) Hyperbolic Matrix(279,200,-392,-281) (-18/25,-5/7) -> (-5/7,-22/31) Parabolic Matrix(3081,2186,4816,3417) (-22/31,-61/86) -> (55/86,16/25) Hyperbolic Matrix(4647,3296,-10976,-7785) (-61/86,-39/55) -> (-47/111,-11/26) Hyperbolic Matrix(2407,1706,3080,2183) (-39/55,-17/24) -> (25/32,43/55) Hyperbolic Matrix(113,80,476,337) (-17/24,-12/17) -> (4/17,1/4) Hyperbolic 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(393,274,644,449) (-7/10,-16/23) -> (14/23,11/18) Hyperbolic Matrix(449,312,-1288,-895) (-16/23,-25/36) -> (-7/20,-8/23) Hyperbolic Matrix(559,388,644,447) (-25/36,-9/13) -> (13/15,7/8) Hyperbolic Matrix(337,232,-812,-559) (-9/13,-11/16) -> (-5/12,-17/41) Hyperbolic Matrix(169,116,-896,-615) (-11/16,-13/19) -> (-7/37,-3/16) Hyperbolic Matrix(281,192,-1064,-727) (-13/19,-2/3) -> (-14/53,-5/19) Hyperbolic Matrix(55,36,84,55) (-2/3,-9/14) -> (9/14,2/3) Hyperbolic Matrix(449,288,700,449) (-9/14,-16/25) -> (16/25,9/14) Hyperbolic Matrix(279,178,-616,-393) (-16/25,-7/11) -> (-5/11,-14/31) Hyperbolic Matrix(167,106,616,391) (-7/11,-19/30) -> (7/26,3/11) Hyperbolic Matrix(449,284,1064,673) (-19/30,-12/19) -> (8/19,11/26) Hyperbolic Matrix(3305,2086,4704,2969) (-12/19,-53/84) -> (59/84,26/37) Hyperbolic Matrix(6607,4168,9408,5935) (-53/84,-41/65) -> (33/47,59/84) Hyperbolic Matrix(111,70,1064,671) (-41/65,-29/46) -> (1/10,1/9) Hyperbolic Matrix(169,106,448,281) (-17/27,-5/8) -> (3/8,11/29) Hyperbolic Matrix(167,104,448,279) (-5/8,-18/29) -> (10/27,3/8) Hyperbolic Matrix(1177,730,1988,1233) (-18/29,-31/50) -> (13/22,16/27) Hyperbolic Matrix(113,70,-812,-503) (-31/50,-13/21) -> (-1/7,-3/22) 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(449,274,644,393) (-11/18,-14/23) -> (16/23,7/10) Hyperbolic Matrix(783,476,1288,783) (-14/23,-17/28) -> (17/28,14/23) Hyperbolic Matrix(169,102,280,169) (-17/28,-3/5) -> (3/5,17/28) Hyperbolic Matrix(57,34,-280,-167) (-3/5,-16/27) -> (-6/29,-1/5) Hyperbolic Matrix(1233,730,1988,1177) (-16/27,-13/22) -> (31/50,18/29) Hyperbolic Matrix(393,232,476,281) (-13/22,-10/17) -> (14/17,5/6) Hyperbolic Matrix(671,394,952,559) (-10/17,-17/29) -> (19/27,12/17) Hyperbolic Matrix(1007,590,3248,1903) (-17/29,-41/70) -> (13/42,9/29) Hyperbolic Matrix(3361,1968,5740,3361) (-41/70,-24/41) -> (24/41,41/70) Hyperbolic Matrix(503,294,1148,671) (-24/41,-7/12) -> (7/16,18/41) Hyperbolic Matrix(111,64,-196,-113) (-7/12,-4/7) -> (-4/7,-9/16) Parabolic Matrix(617,346,-1596,-895) (-9/16,-14/25) -> (-12/31,-17/44) Hyperbolic Matrix(1681,940,-4004,-2239) (-14/25,-19/34) -> (-21/50,-34/81) 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(111,52,476,223) (-1/2,-7/15) -> (3/13,7/30) Hyperbolic Matrix(391,182,840,391) (-7/15,-13/28) -> (13/28,7/15) Hyperbolic Matrix(337,156,728,337) (-13/28,-6/13) -> (6/13,13/28) Hyperbolic Matrix(279,128,364,167) (-6/13,-5/11) -> (13/17,10/13) Hyperbolic Matrix(337,152,-1736,-783) (-14/31,-23/51) -> (-1/5,-6/31) Hyperbolic Matrix(1455,656,3724,1679) (-23/51,-9/20) -> (25/64,9/23) Hyperbolic Matrix(1175,526,1624,727) (-13/29,-4/9) -> (34/47,21/29) Hyperbolic Matrix(113,50,-504,-223) (-4/9,-11/25) -> (-7/31,-2/9) Hyperbolic Matrix(1343,590,-3444,-1513) (-11/25,-18/41) -> (-16/41,-23/59) Hyperbolic Matrix(671,294,1148,503) (-18/41,-7/16) -> (7/12,24/41) Hyperbolic Matrix(897,392,1540,673) (-7/16,-24/55) -> (32/55,7/12) Hyperbolic Matrix(55,24,-644,-281) (-24/55,-17/39) -> (-1/11,0/1) Hyperbolic Matrix(225,98,1288,561) (-17/39,-10/23) -> (4/23,3/17) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(2297,974,3304,1401) (-14/33,-25/59) -> (41/59,16/23) Hyperbolic Matrix(2913,1234,3836,1625) (-25/59,-36/85) -> (22/29,19/25) Hyperbolic Matrix(31585,13376,43904,18593) (-36/85,-83/196) -> (141/196,100/139) Hyperbolic Matrix(23687,10030,32928,13943) (-83/196,-47/111) -> (41/57,141/196) Hyperbolic Matrix(673,284,1064,449) (-11/26,-8/19) -> (12/19,19/30) Hyperbolic Matrix(895,376,1064,447) (-8/19,-21/50) -> (5/6,16/19) Hyperbolic Matrix(7953,3338,10276,4313) (-34/81,-47/112) -> (65/84,24/31) Hyperbolic Matrix(6607,2772,8540,3583) (-47/112,-13/31) -> (41/53,65/84) Hyperbolic Matrix(167,70,532,223) (-13/31,-5/12) -> (5/16,1/3) Hyperbolic Matrix(1457,604,-3780,-1567) (-17/41,-29/70) -> (-27/70,-5/13) 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(111,44,280,111) (-2/5,-11/28) -> (11/28,2/5) Hyperbolic Matrix(505,198,1288,505) (-11/28,-9/23) -> (9/23,11/28) Hyperbolic Matrix(169,66,-1288,-503) (-9/23,-16/41) -> (-2/15,-3/23) Hyperbolic Matrix(727,282,1008,391) (-7/18,-12/31) -> (18/25,13/18) Hyperbolic Matrix(1455,562,3332,1287) (-17/44,-22/57) -> (24/55,7/16) Hyperbolic Matrix(4313,1664,6244,2409) (-22/57,-27/70) -> (29/42,38/55) Hyperbolic Matrix(167,64,728,279) (-5/13,-13/34) -> (5/22,3/13) Hyperbolic Matrix(671,256,-1764,-673) (-13/34,-8/21) -> (-8/21,-19/50) Parabolic Matrix(279,106,-1624,-617) (-19/50,-11/29) -> (-5/29,-1/6) 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(169,60,476,169) (-5/14,-6/17) -> (6/17,5/14) Hyperbolic Matrix(57,20,-476,-167) (-6/17,-7/20) -> (-1/8,-2/17) Hyperbolic Matrix(559,194,1288,447) (-8/23,-1/3) -> (23/53,10/23) Hyperbolic Matrix(223,70,532,167) (-1/3,-5/16) -> (5/12,13/31) Hyperbolic Matrix(1177,366,1624,505) (-5/16,-9/29) -> (21/29,29/40) Hyperbolic Matrix(1903,590,3248,1007) (-9/29,-13/42) -> (41/70,17/29) Hyperbolic Matrix(337,104,1092,337) (-13/42,-4/13) -> (4/13,13/42) 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(391,106,616,167) (-3/11,-7/26) -> (19/30,7/11) 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(113,30,-840,-223) (-4/15,-9/34) -> (-3/22,-2/15) Hyperbolic Matrix(1679,444,3808,1007) (-9/34,-14/53) -> (26/59,15/34) Hyperbolic Matrix(1401,364,3668,953) (-6/23,-7/27) -> (21/55,34/89) Hyperbolic Matrix(785,202,1092,281) (-7/27,-1/4) -> (23/32,41/57) Hyperbolic Matrix(337,80,476,113) (-1/4,-4/17) -> (12/17,17/24) Hyperbolic Matrix(503,118,1428,335) (-4/17,-11/47) -> (13/37,6/17) Hyperbolic Matrix(727,170,-3836,-897) (-11/47,-7/30) -> (-11/58,-7/37) Hyperbolic Matrix(223,52,476,111) (-7/30,-3/13) -> (7/15,1/2) Hyperbolic Matrix(279,64,728,167) (-3/13,-5/22) -> (13/34,5/13) Hyperbolic Matrix(839,190,1232,279) (-5/22,-12/53) -> (2/3,15/22) Hyperbolic Matrix(4145,938,9408,2129) (-12/53,-19/84) -> (37/84,26/59) Hyperbolic Matrix(2071,468,4704,1063) (-19/84,-7/31) -> (11/25,37/84) Hyperbolic Matrix(55,12,252,55) (-2/9,-3/14) -> (3/14,2/9) Hyperbolic Matrix(113,24,532,113) (-3/14,-4/19) -> (4/19,3/14) Hyperbolic Matrix(2575,534,5936,1231) (-11/53,-6/29) -> (36/83,23/53) Hyperbolic Matrix(2297,444,3192,617) (-6/31,-5/26) -> (59/82,18/25) Hyperbolic Matrix(335,64,-1764,-337) (-5/26,-4/21) -> (-4/21,-11/58) Parabolic Matrix(279,52,896,167) (-3/16,-5/27) -> (9/29,5/16) Hyperbolic Matrix(111,20,616,111) (-2/11,-5/28) -> (5/28,2/11) Hyperbolic Matrix(169,30,952,169) (-5/28,-3/17) -> (3/17,5/28) Hyperbolic Matrix(561,98,1288,225) (-3/17,-4/23) -> (10/23,17/39) Hyperbolic Matrix(1511,262,1932,335) (-4/23,-5/29) -> (43/55,18/23) Hyperbolic Matrix(281,44,364,57) (-1/6,-2/13) -> (10/13,17/22) Hyperbolic Matrix(841,108,1316,169) (-3/23,-1/8) -> (23/36,39/61) Hyperbolic Matrix(223,26,952,111) (-2/17,-1/9) -> (11/47,4/17) Hyperbolic Matrix(393,40,560,57) (-1/9,-1/10) -> (7/10,33/47) Hyperbolic Matrix(449,-42,588,-55) (0/1,1/10) -> (29/38,42/55) Hyperbolic Matrix(167,-20,476,-57) (1/9,1/8) -> (7/20,13/37) Hyperbolic Matrix(503,-66,1288,-169) (1/8,2/15) -> (16/41,25/64) Hyperbolic Matrix(503,-70,812,-113) (2/15,1/7) -> (13/21,44/71) Hyperbolic Matrix(225,-34,364,-55) (1/7,1/6) -> (21/34,13/21) Hyperbolic Matrix(503,-86,1316,-225) (1/6,4/23) -> (34/89,13/34) Hyperbolic Matrix(447,-82,616,-113) (2/11,3/16) -> (29/40,8/11) Hyperbolic Matrix(615,-116,896,-169) (3/16,4/21) -> (24/35,11/16) Hyperbolic Matrix(1401,-268,2044,-391) (4/21,5/26) -> (37/54,24/35) Hyperbolic Matrix(1289,-250,2016,-391) (5/26,1/5) -> (39/61,55/86) Hyperbolic Matrix(393,-82,532,-111) (1/5,4/19) -> (14/19,17/23) Hyperbolic Matrix(223,-50,504,-113) (2/9,5/22) -> (15/34,4/9) Hyperbolic Matrix(2129,-498,3108,-727) (7/30,11/47) -> (13/19,37/54) Hyperbolic Matrix(503,-132,644,-169) (1/4,5/19) -> (7/9,25/32) Hyperbolic Matrix(727,-192,1064,-281) (5/19,9/34) -> (15/22,13/19) Hyperbolic Matrix(1961,-520,3164,-839) (9/34,4/15) -> (44/71,31/50) Hyperbolic Matrix(1065,-286,1456,-391) (4/15,7/26) -> (19/26,30/41) 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(895,-312,1288,-449) (1/3,7/20) -> (25/36,41/59) Hyperbolic Matrix(2409,-890,3332,-1231) (7/19,17/46) -> (13/18,47/65) Hyperbolic Matrix(673,-256,1764,-671) (11/29,8/21) -> (8/21,21/55) Parabolic Matrix(1009,-390,1736,-671) (5/13,12/31) -> (18/31,25/43) Hyperbolic Matrix(1513,-590,3444,-1343) (7/18,16/41) -> (18/41,29/66) Hyperbolic Matrix(559,-232,812,-337) (12/29,5/12) -> (11/16,20/29) Hyperbolic Matrix(2577,-1082,3332,-1399) (13/31,21/50) -> (17/22,41/53) Hyperbolic Matrix(169,-72,392,-167) (11/26,3/7) -> (3/7,13/30) Parabolic Matrix(7897,-3424,10976,-4759) (13/30,36/83) -> (100/139,59/82) Hyperbolic Matrix(2353,-1026,3080,-1343) (17/39,24/55) -> (42/55,13/17) Hyperbolic Matrix(3695,-1624,4844,-2129) (29/66,11/25) -> (45/59,29/38) Hyperbolic Matrix(223,-100,252,-113) (4/9,9/20) -> (7/8,8/9) Hyperbolic Matrix(393,-178,616,-279) (9/20,5/11) -> (7/11,23/36) 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(2129,-1238,3080,-1791) (25/43,32/55) -> (38/55,9/13) Hyperbolic Matrix(559,-332,756,-449) (16/27,3/5) -> (17/23,20/27) Hyperbolic Matrix(1063,-670,1512,-953) (17/27,12/19) -> (26/37,19/27) Hyperbolic Matrix(281,-200,392,-279) (17/24,5/7) -> (5/7,23/32) Parabolic Matrix(449,-330,532,-391) (11/15,14/19) -> (16/19,11/13) Hyperbolic Matrix(169,-126,224,-167) (20/27,3/4) -> (3/4,22/29) Parabolic Matrix(1345,-1024,1764,-1343) (19/25,16/21) -> (16/21,45/59) Parabolic Matrix(169,-144,196,-167) (11/13,6/7) -> (6/7,13/15) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-4,1) Matrix(113,100,-252,-223) -> Matrix(1,0,0,1) Matrix(167,144,-196,-169) -> Matrix(1,-4,0,1) Matrix(505,428,728,617) -> Matrix(1,4,-4,-15) Matrix(391,330,-532,-449) -> Matrix(1,2,0,1) Matrix(281,232,476,393) -> Matrix(1,2,-4,-7) Matrix(783,644,952,783) -> Matrix(13,14,-40,-43) Matrix(505,414,616,505) -> Matrix(7,6,-20,-17) Matrix(57,46,140,113) -> Matrix(1,0,0,1) Matrix(111,88,140,111) -> Matrix(1,0,-4,1) Matrix(505,396,644,505) -> Matrix(1,10,-4,-39) Matrix(169,132,-644,-503) -> Matrix(1,4,-4,-15) Matrix(281,218,-504,-391) -> Matrix(1,2,0,1) Matrix(449,346,728,561) -> Matrix(1,2,-4,-7) Matrix(167,128,364,279) -> Matrix(1,2,-4,-7) Matrix(55,42,-588,-449) -> Matrix(1,2,-4,-7) Matrix(1287,982,-3304,-2521) -> Matrix(1,2,0,1) Matrix(1233,938,-3164,-2407) -> Matrix(3,4,8,11) Matrix(169,128,-812,-615) -> Matrix(1,2,-4,-7) Matrix(111,82,-532,-393) -> Matrix(3,2,-8,-5) Matrix(671,494,1596,1175) -> Matrix(5,2,-8,-3) Matrix(167,122,-308,-225) -> Matrix(1,0,0,1) Matrix(113,82,-616,-447) -> Matrix(1,0,-4,1) Matrix(279,202,308,223) -> Matrix(1,2,-4,-7) Matrix(559,404,-2016,-1457) -> Matrix(3,2,-8,-5) Matrix(391,282,1008,727) -> Matrix(1,0,-4,1) Matrix(279,200,-392,-281) -> Matrix(1,-2,0,1) Matrix(3081,2186,4816,3417) -> Matrix(1,2,-4,-7) Matrix(4647,3296,-10976,-7785) -> Matrix(5,8,-12,-19) Matrix(2407,1706,3080,2183) -> Matrix(1,6,-4,-23) Matrix(113,80,476,337) -> Matrix(1,2,-4,-7) Matrix(559,394,952,671) -> Matrix(3,2,-8,-5) Matrix(953,670,-1512,-1063) -> Matrix(1,2,0,1) Matrix(393,274,644,449) -> Matrix(5,6,-16,-19) Matrix(449,312,-1288,-895) -> Matrix(3,2,-8,-5) Matrix(559,388,644,447) -> Matrix(1,0,-4,1) Matrix(337,232,-812,-559) -> Matrix(1,2,-4,-7) Matrix(169,116,-896,-615) -> Matrix(1,2,-4,-7) Matrix(281,192,-1064,-727) -> Matrix(5,6,-16,-19) Matrix(55,36,84,55) -> Matrix(3,2,-8,-5) Matrix(449,288,700,449) -> Matrix(1,0,0,1) Matrix(279,178,-616,-393) -> Matrix(1,0,0,1) Matrix(167,106,616,391) -> Matrix(1,0,0,1) Matrix(449,284,1064,673) -> Matrix(5,2,-8,-3) Matrix(3305,2086,4704,2969) -> Matrix(9,2,-32,-7) Matrix(6607,4168,9408,5935) -> Matrix(15,-2,-52,7) Matrix(111,70,1064,671) -> Matrix(1,0,-4,1) Matrix(169,106,448,281) -> Matrix(1,2,-4,-7) Matrix(167,104,448,279) -> Matrix(3,2,-8,-5) Matrix(1177,730,1988,1233) -> Matrix(3,2,-8,-5) Matrix(113,70,-812,-503) -> Matrix(3,2,-8,-5) Matrix(55,34,-364,-225) -> Matrix(1,0,0,1) Matrix(111,68,364,223) -> Matrix(1,2,-4,-7) Matrix(449,274,644,393) -> Matrix(5,6,-16,-19) Matrix(783,476,1288,783) -> Matrix(17,18,-52,-55) Matrix(169,102,280,169) -> Matrix(7,6,-20,-17) Matrix(57,34,-280,-167) -> Matrix(3,2,-8,-5) Matrix(1233,730,1988,1177) -> Matrix(3,2,-8,-5) Matrix(393,232,476,281) -> Matrix(1,2,-4,-7) Matrix(671,394,952,559) -> Matrix(3,2,-8,-5) Matrix(1007,590,3248,1903) -> Matrix(21,16,-88,-67) Matrix(3361,1968,5740,3361) -> Matrix(89,66,-236,-175) Matrix(503,294,1148,671) -> Matrix(17,12,-44,-31) Matrix(111,64,-196,-113) -> Matrix(3,2,-8,-5) Matrix(617,346,-1596,-895) -> Matrix(1,0,4,1) Matrix(1681,940,-4004,-2239) -> Matrix(13,-2,-32,5) Matrix(113,62,308,169) -> Matrix(3,2,-8,-5) Matrix(113,60,-420,-223) -> Matrix(3,2,-8,-5) Matrix(111,52,476,223) -> Matrix(1,0,0,1) Matrix(391,182,840,391) -> Matrix(1,0,4,1) Matrix(337,156,728,337) -> Matrix(1,0,-4,1) Matrix(279,128,364,167) -> Matrix(1,2,-4,-7) Matrix(337,152,-1736,-783) -> Matrix(1,0,0,1) Matrix(1455,656,3724,1679) -> Matrix(1,0,-8,1) Matrix(1175,526,1624,727) -> Matrix(1,2,-4,-7) Matrix(113,50,-504,-223) -> Matrix(1,0,0,1) Matrix(1343,590,-3444,-1513) -> Matrix(5,4,16,13) Matrix(671,294,1148,503) -> Matrix(17,12,-44,-31) Matrix(897,392,1540,673) -> Matrix(7,4,-16,-9) Matrix(55,24,-644,-281) -> Matrix(3,2,-8,-5) Matrix(225,98,1288,561) -> Matrix(3,2,-20,-13) Matrix(167,72,-392,-169) -> Matrix(11,6,-24,-13) Matrix(2297,974,3304,1401) -> Matrix(5,2,-8,-3) Matrix(2913,1234,3836,1625) -> Matrix(23,10,-76,-33) Matrix(31585,13376,43904,18593) -> Matrix(9,4,-52,-23) Matrix(23687,10030,32928,13943) -> Matrix(19,8,-88,-37) Matrix(673,284,1064,449) -> Matrix(5,2,-8,-3) Matrix(895,376,1064,447) -> Matrix(29,12,-104,-43) Matrix(7953,3338,10276,4313) -> Matrix(189,76,-664,-267) Matrix(6607,2772,8540,3583) -> Matrix(171,68,-596,-237) Matrix(167,70,532,223) -> Matrix(5,2,-28,-11) Matrix(1457,604,-3780,-1567) -> Matrix(1,0,4,1) Matrix(2241,928,3248,1345) -> Matrix(11,4,-36,-13) Matrix(281,116,952,393) -> Matrix(1,0,0,1) Matrix(113,46,140,57) -> Matrix(1,0,0,1) Matrix(111,44,280,111) -> Matrix(1,0,4,1) Matrix(505,198,1288,505) -> Matrix(1,0,-20,1) Matrix(169,66,-1288,-503) -> Matrix(1,0,-8,1) Matrix(727,282,1008,391) -> Matrix(1,0,-4,1) Matrix(1455,562,3332,1287) -> Matrix(5,-2,-12,5) Matrix(4313,1664,6244,2409) -> Matrix(7,-2,-24,7) Matrix(167,64,728,279) -> Matrix(1,0,-4,1) Matrix(671,256,-1764,-673) -> Matrix(1,-4,0,1) Matrix(279,106,-1624,-617) -> Matrix(1,2,0,1) Matrix(281,106,448,169) -> Matrix(1,2,-4,-7) Matrix(279,104,448,167) -> Matrix(3,2,-8,-5) Matrix(503,186,-1820,-673) -> Matrix(3,2,-8,-5) Matrix(169,62,308,113) -> Matrix(3,2,-8,-5) Matrix(111,40,308,111) -> Matrix(7,4,-16,-9) Matrix(169,60,476,169) -> Matrix(13,6,-24,-11) Matrix(57,20,-476,-167) -> Matrix(5,2,-8,-3) Matrix(559,194,1288,447) -> Matrix(3,2,-8,-5) Matrix(223,70,532,167) -> Matrix(3,-2,-4,3) Matrix(1177,366,1624,505) -> Matrix(1,-2,-4,9) Matrix(1903,590,3248,1007) -> Matrix(3,-16,-8,43) Matrix(337,104,1092,337) -> Matrix(1,4,-4,-15) Matrix(223,68,364,111) -> Matrix(1,2,-4,-7) Matrix(55,16,-196,-57) -> Matrix(3,2,-8,-5) Matrix(9073,2512,12544,3473) -> Matrix(23,8,-72,-25) Matrix(9071,2510,12544,3471) -> Matrix(13,4,-36,-11) Matrix(335,92,812,223) -> Matrix(5,2,-8,-3) Matrix(391,106,616,167) -> Matrix(1,0,0,1) Matrix(2297,616,3136,841) -> Matrix(11,4,-36,-13) Matrix(2295,614,3136,839) -> Matrix(13,4,-36,-11) Matrix(113,30,-840,-223) -> Matrix(1,0,0,1) Matrix(1679,444,3808,1007) -> Matrix(11,4,-36,-13) Matrix(1401,364,3668,953) -> Matrix(7,2,-32,-9) Matrix(785,202,1092,281) -> Matrix(1,0,0,1) Matrix(337,80,476,113) -> Matrix(1,2,-4,-7) Matrix(503,118,1428,335) -> Matrix(5,2,-8,-3) Matrix(727,170,-3836,-897) -> Matrix(3,2,-8,-5) Matrix(223,52,476,111) -> Matrix(1,0,0,1) Matrix(279,64,728,167) -> Matrix(1,0,-4,1) Matrix(839,190,1232,279) -> Matrix(9,10,-28,-31) Matrix(4145,938,9408,2129) -> Matrix(21,22,-64,-67) Matrix(2071,468,4704,1063) -> Matrix(15,14,-44,-41) Matrix(55,12,252,55) -> Matrix(3,2,-8,-5) Matrix(113,24,532,113) -> Matrix(9,4,-16,-7) Matrix(2575,534,5936,1231) -> Matrix(3,2,-8,-5) Matrix(2297,444,3192,617) -> Matrix(1,0,-4,1) Matrix(335,64,-1764,-337) -> Matrix(3,2,-8,-5) Matrix(279,52,896,167) -> Matrix(7,2,-32,-9) Matrix(111,20,616,111) -> Matrix(1,0,8,1) Matrix(169,30,952,169) -> Matrix(1,0,-12,1) Matrix(561,98,1288,225) -> Matrix(5,-2,-12,5) Matrix(1511,262,1932,335) -> Matrix(1,4,-4,-15) Matrix(281,44,364,57) -> Matrix(1,2,-4,-7) Matrix(841,108,1316,169) -> Matrix(1,0,0,1) Matrix(223,26,952,111) -> Matrix(1,0,0,1) Matrix(393,40,560,57) -> Matrix(1,2,-4,-7) Matrix(449,-42,588,-55) -> Matrix(1,2,-4,-7) Matrix(167,-20,476,-57) -> Matrix(5,2,-8,-3) Matrix(503,-66,1288,-169) -> Matrix(1,0,-8,1) Matrix(503,-70,812,-113) -> Matrix(3,2,-8,-5) Matrix(225,-34,364,-55) -> Matrix(1,0,0,1) Matrix(503,-86,1316,-225) -> Matrix(7,2,-32,-9) Matrix(447,-82,616,-113) -> Matrix(1,0,-4,1) Matrix(615,-116,896,-169) -> Matrix(1,2,-4,-7) Matrix(1401,-268,2044,-391) -> Matrix(11,4,-36,-13) Matrix(1289,-250,2016,-391) -> Matrix(1,0,0,1) Matrix(393,-82,532,-111) -> Matrix(3,2,-8,-5) Matrix(223,-50,504,-113) -> Matrix(1,0,0,1) Matrix(2129,-498,3108,-727) -> Matrix(11,4,-36,-13) Matrix(503,-132,644,-169) -> Matrix(1,4,-4,-15) Matrix(727,-192,1064,-281) -> Matrix(5,6,-16,-19) Matrix(1961,-520,3164,-839) -> Matrix(3,2,-8,-5) Matrix(1065,-286,1456,-391) -> Matrix(3,2,-8,-5) Matrix(57,-16,196,-55) -> Matrix(3,2,-8,-5) Matrix(559,-166,1512,-449) -> Matrix(1,0,0,1) Matrix(895,-312,1288,-449) -> Matrix(3,2,-8,-5) Matrix(2409,-890,3332,-1231) -> Matrix(1,0,0,1) Matrix(673,-256,1764,-671) -> Matrix(15,4,-64,-17) Matrix(1009,-390,1736,-671) -> Matrix(11,2,-28,-5) Matrix(1513,-590,3444,-1343) -> Matrix(29,4,-80,-11) Matrix(559,-232,812,-337) -> Matrix(1,2,-4,-7) Matrix(2577,-1082,3332,-1399) -> Matrix(37,24,-128,-83) Matrix(169,-72,392,-167) -> Matrix(11,6,-24,-13) Matrix(7897,-3424,10976,-4759) -> Matrix(9,4,-52,-23) Matrix(2353,-1026,3080,-1343) -> Matrix(11,4,-36,-13) Matrix(3695,-1624,4844,-2129) -> Matrix(61,22,-208,-75) Matrix(223,-100,252,-113) -> Matrix(1,0,0,1) Matrix(393,-178,616,-279) -> Matrix(1,0,0,1) Matrix(225,-122,308,-167) -> Matrix(1,0,0,1) Matrix(113,-64,196,-111) -> Matrix(3,2,-8,-5) Matrix(673,-390,868,-503) -> Matrix(29,12,-104,-43) Matrix(2129,-1238,3080,-1791) -> Matrix(11,4,-36,-13) Matrix(559,-332,756,-449) -> Matrix(1,0,0,1) Matrix(1063,-670,1512,-953) -> Matrix(9,2,-32,-7) Matrix(281,-200,392,-279) -> Matrix(7,2,-32,-9) Matrix(449,-330,532,-391) -> Matrix(9,2,-32,-7) Matrix(169,-126,224,-167) -> Matrix(11,4,-36,-13) Matrix(1345,-1024,1764,-1343) -> Matrix(59,18,-200,-61) Matrix(169,-144,196,-167) -> Matrix(15,4,-64,-17) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 64 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 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 1/0 -6/7 1/0 -5/6 -3/2 -9/11 -3/4 -4/5 0/1 1/0 -11/14 1/0 -7/9 1/0 -17/22 -3/2 -10/13 -2/1 1/0 -3/4 -1/1 -11/15 1/0 -8/11 -1/2 0/1 -5/7 1/0 -12/17 -3/2 -1/1 -19/27 1/0 -7/10 -3/2 -9/13 1/0 -11/16 -1/1 -2/3 -1/1 -1/2 -9/14 -1/2 -7/11 1/0 -12/19 -1/2 0/1 -29/46 1/2 -17/27 1/0 -5/8 -1/1 -13/21 -1/2 -8/13 0/1 1/0 -11/18 -3/2 -3/5 -3/4 -10/17 -1/1 -5/6 -17/29 -3/4 -7/12 -2/3 -4/7 -1/2 -9/16 0/1 -14/25 -1/6 0/1 -19/34 1/2 -5/9 1/0 -6/11 -1/2 0/1 -7/13 1/0 -1/2 -1/2 -5/11 1/0 -4/9 -1/1 -1/2 -3/7 -1/2 -8/19 -1/2 -2/5 -13/31 -11/28 -5/12 -1/3 -17/41 -1/4 -29/70 -1/2 -12/29 -1/2 -1/3 -7/17 -3/8 -2/5 -1/4 0/1 -11/28 0/1 -9/23 1/8 -7/18 1/2 -5/13 1/0 -13/34 3/2 -8/21 1/0 -11/29 1/0 -3/8 -1/1 -10/27 -1/1 -1/2 -7/19 -3/4 -4/11 -2/3 -1/2 -5/14 -1/2 -1/3 -1/4 -5/16 1/1 -9/29 1/0 -13/42 1/0 -4/13 -2/1 1/0 -3/10 -1/2 -2/7 -1/2 -5/18 -1/2 -18/65 -5/14 -1/3 -31/112 -1/3 -13/47 -1/4 -8/29 -1/2 -1/3 -3/11 -1/4 -7/26 -1/2 -11/41 -3/8 -15/56 -1/3 -4/15 -1/3 -1/4 -1/4 0/1 -3/13 1/0 -5/22 -3/2 -12/53 -11/10 -1/1 -19/84 -1/1 -7/31 -7/8 -2/9 -1/1 -1/2 -3/14 -1/2 -1/5 -1/4 -2/11 -1/6 0/1 -5/28 0/1 -3/17 1/4 -1/6 -1/2 -2/13 0/1 1/0 -1/7 -1/2 -1/8 0/1 0/1 -1/2 0/1 1/7 -1/2 1/6 -1/2 2/11 0/1 1/2 1/5 1/0 3/14 -1/2 2/9 -1/2 -1/3 5/22 -3/10 3/13 -1/4 1/4 0/1 4/15 -1/1 1/0 3/11 1/0 2/7 -1/2 5/17 -3/8 8/27 -1/2 -1/3 3/10 -1/2 4/13 -2/7 -1/4 5/16 -1/5 1/3 1/0 5/14 -1/2 4/11 -1/2 -2/5 7/19 -3/8 17/46 -1/2 10/27 -1/2 -1/3 3/8 -1/3 8/21 -1/4 5/13 -1/4 7/18 -1/6 2/5 0/1 1/0 7/17 -3/4 12/29 -1/1 -1/2 5/12 -1/1 3/7 -1/2 7/16 -2/5 11/25 -7/20 15/34 -3/10 4/9 -1/2 -1/3 5/11 -1/4 6/13 -1/4 0/1 1/2 -1/2 6/11 -1/2 0/1 5/9 -1/4 4/7 -1/2 11/19 -5/12 18/31 -2/5 -7/18 7/12 -2/5 24/41 -11/29 -3/8 41/70 -3/8 17/29 -3/8 10/17 -5/14 -1/3 3/5 -3/8 17/28 -1/3 14/23 -1/3 -9/28 11/18 -3/10 8/13 -1/4 0/1 21/34 -1/2 13/21 -1/2 18/29 -1/2 -1/3 5/8 -1/3 17/27 -1/4 12/19 -1/2 0/1 7/11 -1/4 9/14 -1/2 2/3 -1/2 -1/3 11/16 -1/3 20/29 -1/3 -3/10 29/42 -3/10 9/13 -1/4 7/10 -3/10 5/7 -1/4 13/18 -1/2 47/65 -3/8 81/112 -1/3 34/47 -1/3 -3/10 21/29 -1/4 8/11 -1/2 0/1 19/26 -1/2 30/41 -3/8 -1/3 41/56 -1/3 11/15 -1/4 3/4 -1/3 10/13 -2/7 -1/4 17/22 -3/10 41/53 -23/80 65/84 -2/7 24/31 -2/7 -13/46 7/9 -1/4 11/14 -1/4 4/5 -1/4 0/1 9/11 -3/8 23/28 -1/3 14/17 -1/3 -7/22 5/6 -3/10 11/13 -1/4 6/7 -1/4 7/8 0/1 1/1 -1/4 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,-1,0,1) Matrix(139,118,-364,-309) -> Matrix(1,3,0,1) Matrix(29,24,-168,-139) -> Matrix(1,1,0,1) Matrix(57,46,140,113) -> Matrix(1,0,0,1) Matrix(111,88,140,111) -> Matrix(1,0,-4,1) Matrix(197,154,252,197) -> Matrix(1,5,-4,-19) Matrix(281,218,-504,-391) -> Matrix(1,2,0,1) Matrix(449,346,728,561) -> Matrix(1,2,-4,-7) Matrix(29,22,112,85) -> Matrix(1,1,0,1) Matrix(27,20,112,83) -> Matrix(1,1,-4,-3) Matrix(167,122,-308,-225) -> Matrix(1,0,0,1) Matrix(139,100,-196,-141) -> Matrix(1,-1,0,1) Matrix(559,394,952,671) -> Matrix(3,2,-8,-5) Matrix(953,670,-1512,-1063) -> Matrix(1,2,0,1) Matrix(141,98,364,253) -> Matrix(1,1,-4,-3) Matrix(337,232,-812,-559) -> Matrix(1,2,-4,-7) Matrix(309,212,532,365) -> Matrix(3,5,-8,-13) Matrix(55,36,84,55) -> Matrix(3,2,-8,-5) Matrix(197,126,308,197) -> Matrix(1,1,-4,-3) Matrix(139,88,308,195) -> Matrix(1,1,-4,-3) Matrix(923,582,-3332,-2101) -> Matrix(3,-1,-8,3) Matrix(197,124,224,141) -> Matrix(1,1,-4,-3) Matrix(29,18,-224,-139) -> Matrix(1,1,-4,-3) Matrix(55,34,-364,-225) -> Matrix(1,0,0,1) Matrix(111,68,364,223) -> Matrix(1,2,-4,-7) Matrix(197,120,-504,-307) -> Matrix(1,1,4,5) Matrix(27,16,140,83) -> Matrix(1,1,-4,-3) Matrix(589,346,812,477) -> Matrix(1,1,-8,-7) Matrix(253,148,-812,-475) -> Matrix(7,5,4,3) Matrix(111,64,-196,-113) -> Matrix(3,2,-8,-5) Matrix(307,172,448,251) -> Matrix(5,1,-16,-3) Matrix(533,298,-2352,-1315) -> Matrix(5,-1,-4,1) Matrix(113,62,308,169) -> Matrix(3,2,-8,-5) Matrix(113,60,-420,-223) -> Matrix(3,2,-8,-5) Matrix(83,38,-308,-141) -> Matrix(1,1,-4,-3) Matrix(195,88,308,139) -> Matrix(1,1,-4,-3) Matrix(83,36,-196,-85) -> Matrix(5,3,-12,-7) Matrix(195,82,-868,-365) -> Matrix(7,3,-12,-5) Matrix(167,70,532,223) -> Matrix(5,2,-28,-11) Matrix(1819,754,2632,1091) -> Matrix(5,1,-16,-3) Matrix(2241,928,3248,1345) -> Matrix(11,4,-36,-13) Matrix(281,116,952,393) -> Matrix(1,0,0,1) Matrix(113,46,140,57) -> Matrix(1,0,0,1) Matrix(477,188,784,309) -> Matrix(13,1,-40,-3) Matrix(475,186,784,307) -> Matrix(11,-1,-32,3) Matrix(253,98,364,141) -> Matrix(1,1,-4,-3) Matrix(167,64,728,279) -> Matrix(1,0,-4,1) Matrix(281,106,448,169) -> Matrix(1,2,-4,-7) Matrix(279,104,448,167) -> Matrix(3,2,-8,-5) Matrix(503,186,-1820,-673) -> Matrix(3,2,-8,-5) Matrix(169,62,308,113) -> Matrix(3,2,-8,-5) Matrix(111,40,308,111) -> Matrix(7,4,-16,-9) Matrix(29,10,84,29) -> Matrix(3,1,-4,-1) Matrix(197,62,448,141) -> Matrix(3,-1,-8,3) Matrix(1903,590,3248,1007) -> Matrix(3,-16,-8,43) Matrix(1541,476,2632,813) -> Matrix(3,17,-8,-45) Matrix(223,68,364,111) -> Matrix(1,2,-4,-7) Matrix(55,16,-196,-57) -> Matrix(3,2,-8,-5) Matrix(9073,2512,12544,3473) -> Matrix(23,8,-72,-25) Matrix(9071,2510,12544,3471) -> Matrix(13,4,-36,-11) Matrix(335,92,812,223) -> Matrix(5,2,-8,-3) Matrix(2297,616,3136,841) -> Matrix(11,4,-36,-13) Matrix(2295,614,3136,839) -> Matrix(13,4,-36,-11) Matrix(85,22,112,29) -> Matrix(5,1,-16,-3) Matrix(83,20,112,27) -> Matrix(1,1,-4,-3) Matrix(307,70,364,83) -> Matrix(1,3,-4,-11) Matrix(5461,1236,7056,1597) -> Matrix(33,35,-116,-123) Matrix(5459,1234,7056,1595) -> Matrix(39,37,-136,-129) Matrix(55,12,252,55) -> Matrix(3,2,-8,-5) Matrix(29,6,140,29) -> Matrix(3,1,-4,-1) Matrix(83,16,140,27) -> Matrix(1,1,-4,-3) Matrix(645,116,784,141) -> Matrix(13,1,-40,-3) Matrix(643,114,784,139) -> Matrix(7,-1,-20,3) Matrix(281,44,364,57) -> Matrix(1,2,-4,-7) Matrix(83,10,224,27) -> Matrix(1,1,-4,-3) Matrix(139,-18,224,-29) -> Matrix(1,1,-4,-3) Matrix(225,-34,364,-55) -> Matrix(1,0,0,1) Matrix(139,-24,168,-29) -> Matrix(5,1,-16,-3) Matrix(223,-50,504,-113) -> Matrix(1,0,0,1) Matrix(141,-38,308,-83) -> Matrix(1,1,-4,-3) Matrix(57,-16,196,-55) -> Matrix(3,2,-8,-5) Matrix(559,-166,1512,-449) -> Matrix(1,0,0,1) Matrix(475,-148,812,-253) -> Matrix(23,5,-60,-13) Matrix(2409,-890,3332,-1231) -> Matrix(1,0,0,1) Matrix(195,-74,224,-85) -> Matrix(3,1,-16,-5) Matrix(309,-118,364,-139) -> Matrix(13,3,-48,-11) Matrix(307,-120,504,-197) -> Matrix(9,1,-28,-3) Matrix(559,-232,812,-337) -> Matrix(1,2,-4,-7) Matrix(85,-36,196,-83) -> Matrix(5,3,-12,-7) Matrix(1819,-802,2352,-1037) -> Matrix(29,9,-100,-31) Matrix(307,-144,420,-197) -> Matrix(1,1,-4,-3) Matrix(225,-122,308,-167) -> Matrix(1,0,0,1) Matrix(113,-64,196,-111) -> Matrix(3,2,-8,-5) Matrix(673,-390,868,-503) -> Matrix(29,12,-104,-43) Matrix(1317,-830,1820,-1147) -> Matrix(5,1,-16,-3) Matrix(141,-100,196,-139) -> Matrix(3,1,-16,-5) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 ----------------------------------------------------------------------- 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 (-1/2,0/1) 0 28 1/7 -1/2 1 4 1/6 -1/2 1 14 2/11 (0/1,1/2) 0 28 1/5 1/0 1 28 3/14 -1/2 3 2 2/9 (-1/2,-1/3) 0 28 5/22 -3/10 1 14 3/13 -1/4 1 28 1/4 0/1 2 7 4/15 (-1/1,1/0) 0 28 3/11 1/0 1 28 2/7 -1/2 2 4 5/17 -3/8 1 28 8/27 (-1/2,-1/3) 0 28 3/10 -1/2 1 14 4/13 (-2/7,-1/4) 0 28 5/16 -1/5 2 7 1/3 1/0 1 28 5/14 -1/2 5 2 4/11 (-1/2,-2/5) 0 28 7/19 -3/8 1 28 17/46 -1/2 1 14 10/27 (-1/2,-1/3) 0 28 3/8 -1/3 2 7 8/21 -1/4 4 4 5/13 -1/4 1 28 7/18 -1/6 1 14 2/5 (0/1,1/0) 0 28 7/17 -3/4 1 28 12/29 (-1/1,-1/2) 0 28 5/12 -1/1 2 7 3/7 -1/2 3 4 7/16 -2/5 2 7 11/25 -7/20 1 28 15/34 -3/10 1 14 4/9 (-1/2,-1/3) 0 28 5/11 -1/4 1 28 6/13 (-1/4,0/1) 0 28 1/2 -1/2 1 14 6/11 (-1/2,0/1) 0 28 5/9 -1/4 1 28 4/7 -1/2 2 4 11/19 -5/12 1 28 18/31 (-2/5,-7/18) 0 28 7/12 -2/5 2 7 24/41 (-11/29,-3/8) 0 28 41/70 -3/8 11 2 17/29 -3/8 1 28 10/17 (-5/14,-1/3) 0 28 3/5 -3/8 1 28 17/28 -1/3 12 1 14/23 (-1/3,-9/28) 0 28 11/18 -3/10 1 14 8/13 (-1/4,0/1) 0 28 21/34 -1/2 1 14 13/21 -1/2 1 4 18/29 (-1/2,-1/3) 0 28 5/8 -1/3 2 7 17/27 -1/4 1 28 12/19 (-1/2,0/1) 0 28 7/11 -1/4 1 28 9/14 -1/2 1 2 2/3 (-1/2,-1/3) 0 28 11/16 -1/3 2 7 20/29 (-1/3,-3/10) 0 28 29/42 -3/10 1 2 9/13 -1/4 1 28 7/10 -3/10 1 14 5/7 -1/4 1 4 13/18 -1/2 1 14 47/65 -3/8 1 28 81/112 -1/3 6 1 34/47 (-1/3,-3/10) 0 28 21/29 -1/4 1 28 8/11 (-1/2,0/1) 0 28 19/26 -1/2 1 14 30/41 (-3/8,-1/3) 0 28 41/56 -1/3 4 1 11/15 -1/4 1 28 3/4 -1/3 2 7 10/13 (-2/7,-1/4) 0 28 17/22 -3/10 1 14 41/53 -23/80 1 28 65/84 -2/7 18 1 24/31 (-2/7,-13/46) 0 28 7/9 -1/4 1 28 11/14 -1/4 5 2 4/5 (-1/4,0/1) 0 28 9/11 -3/8 1 28 23/28 -1/3 10 1 14/17 (-1/3,-7/22) 0 28 5/6 -3/10 1 14 11/13 -1/4 1 28 6/7 -1/4 4 4 7/8 0/1 2 7 1/1 -1/4 1 28 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(-1,0,4,1) (0/1,1/0) -> (-1/2,0/1) Matrix(139,-18,224,-29) -> Matrix(1,1,-4,-3) -1/2 Matrix(225,-34,364,-55) -> Matrix(1,0,0,1) Matrix(139,-24,168,-29) -> Matrix(5,1,-16,-3) -1/4 Matrix(83,-16,140,-27) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(29,-6,140,-29) -> Matrix(1,1,0,-1) (1/5,3/14) -> (-1/2,1/0) Matrix(55,-12,252,-55) -> Matrix(5,2,-12,-5) (3/14,2/9) -> (-1/2,-1/3) Matrix(223,-50,504,-113) -> Matrix(1,0,0,1) Matrix(307,-70,364,-83) -> Matrix(11,3,-40,-11) *** -> (-3/10,-1/4) Matrix(83,-20,112,-27) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(85,-22,112,-29) -> Matrix(1,-1,-4,3) Matrix(141,-38,308,-83) -> Matrix(1,1,-4,-3) -1/2 Matrix(57,-16,196,-55) -> Matrix(3,2,-8,-5) -1/2 Matrix(393,-116,952,-281) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(559,-166,1512,-449) -> Matrix(1,0,0,1) Matrix(223,-68,364,-111) -> Matrix(7,2,-24,-7) *** -> (-1/3,-1/4) Matrix(475,-148,812,-253) -> Matrix(23,5,-60,-13) Matrix(197,-62,448,-141) -> Matrix(7,1,-20,-3) Matrix(29,-10,84,-29) -> Matrix(1,1,0,-1) (1/3,5/14) -> (-1/2,1/0) Matrix(111,-40,308,-111) -> Matrix(9,4,-20,-9) (5/14,4/11) -> (-1/2,-2/5) Matrix(169,-62,308,-113) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(2409,-890,3332,-1231) -> Matrix(1,0,0,1) Matrix(279,-104,448,-167) -> Matrix(5,2,-12,-5) *** -> (-1/2,-1/3) Matrix(195,-74,224,-85) -> Matrix(3,1,-16,-5) -1/4 Matrix(309,-118,364,-139) -> Matrix(13,3,-48,-11) -1/4 Matrix(253,-98,364,-141) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(307,-120,504,-197) -> Matrix(9,1,-28,-3) Matrix(113,-46,140,-57) -> Matrix(-1,0,4,1) *** -> (-1/2,0/1) Matrix(559,-232,812,-337) -> Matrix(1,2,-4,-7) Matrix(85,-36,196,-83) -> Matrix(5,3,-12,-7) -1/2 Matrix(1819,-802,2352,-1037) -> Matrix(29,9,-100,-31) -3/10 Matrix(195,-88,308,-139) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(307,-144,420,-197) -> Matrix(1,1,-4,-3) -1/2 Matrix(225,-122,308,-167) -> Matrix(1,0,0,1) Matrix(113,-64,196,-111) -> Matrix(3,2,-8,-5) -1/2 Matrix(673,-390,868,-503) -> Matrix(29,12,-104,-43) Matrix(365,-212,532,-309) -> Matrix(13,5,-44,-17) Matrix(3361,-1968,5740,-3361) -> Matrix(175,66,-464,-175) (24/41,41/70) -> (-11/29,-3/8) Matrix(2379,-1394,4060,-2379) -> Matrix(89,33,-240,-89) (41/70,17/29) -> (-3/8,-11/30) Matrix(589,-346,812,-477) -> Matrix(3,1,-20,-7) Matrix(169,-102,280,-169) -> Matrix(17,6,-48,-17) (3/5,17/28) -> (-3/8,-1/3) Matrix(783,-476,1288,-783) -> Matrix(55,18,-168,-55) (17/28,14/23) -> (-1/3,-9/28) Matrix(561,-346,728,-449) -> Matrix(7,2,-24,-7) *** -> (-1/3,-1/4) Matrix(197,-124,224,-141) -> Matrix(3,1,-8,-3) *** -> (-1/2,-1/4) Matrix(1317,-830,1820,-1147) -> Matrix(5,1,-16,-3) -1/4 Matrix(197,-126,308,-197) -> Matrix(3,1,-8,-3) (7/11,9/14) -> (-1/2,-1/4) Matrix(55,-36,84,-55) -> Matrix(5,2,-12,-5) (9/14,2/3) -> (-1/2,-1/3) Matrix(1681,-1160,2436,-1681) -> Matrix(19,6,-60,-19) (20/29,29/42) -> (-1/3,-3/10) Matrix(755,-522,1092,-755) -> Matrix(11,3,-40,-11) (29/42,9/13) -> (-3/10,-1/4) Matrix(141,-100,196,-139) -> Matrix(3,1,-16,-5) -1/4 Matrix(10529,-7614,14560,-10529) -> Matrix(17,6,-48,-17) (47/65,81/112) -> (-3/8,-1/3) Matrix(7615,-5508,10528,-7615) -> Matrix(19,6,-60,-19) (81/112,34/47) -> (-1/3,-3/10) Matrix(3361,-2460,4592,-3361) -> Matrix(17,6,-48,-17) (30/41,41/56) -> (-3/8,-1/3) Matrix(1231,-902,1680,-1231) -> Matrix(7,2,-24,-7) (41/56,11/15) -> (-1/3,-1/4) Matrix(6889,-5330,8904,-6889) -> Matrix(321,92,-1120,-321) (41/53,65/84) -> (-23/80,-2/7) Matrix(4031,-3120,5208,-4031) -> Matrix(183,52,-644,-183) (65/84,24/31) -> (-2/7,-13/46) Matrix(197,-154,252,-197) -> Matrix(19,5,-72,-19) (7/9,11/14) -> (-5/18,-1/4) Matrix(111,-88,140,-111) -> Matrix(-1,0,8,1) (11/14,4/5) -> (-1/4,0/1) Matrix(505,-414,616,-505) -> Matrix(17,6,-48,-17) (9/11,23/28) -> (-3/8,-1/3) Matrix(783,-644,952,-783) -> Matrix(43,14,-132,-43) (23/28,14/17) -> (-1/3,-7/22) Matrix(-1,2,0,1) -> Matrix(-1,0,8,1) (1/1,1/0) -> (-1/4,0/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.