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 -10/1 -8/1 -7/1 -6/1 -16/3 -21/4 -4/1 -7/2 -8/3 -21/8 -7/3 -2/1 -7/4 -12/7 -7/5 -4/3 -21/16 -7/6 0/1 1/1 7/6 28/23 14/11 21/16 4/3 7/5 3/2 14/9 84/53 28/17 12/7 7/4 2/1 28/13 7/3 196/83 112/47 5/2 28/11 70/27 21/8 8/3 14/5 3/1 42/13 7/2 112/31 56/15 4/1 13/3 84/19 9/2 14/3 19/4 29/6 5/1 31/6 21/4 16/3 11/2 28/5 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 1/0 -9/1 1/0 -8/1 0/1 -15/2 -1/1 0/1 -7/1 -1/2 1/0 -6/1 -1/2 -23/4 -1/3 0/1 -17/3 -1/4 -28/5 0/1 -11/2 0/1 1/0 -16/3 -1/1 -21/4 -1/1 -1/2 0/1 -26/5 -1/2 -5/1 -1/2 -19/4 -1/3 0/1 -14/3 0/1 -9/2 -1/2 0/1 -22/5 -1/2 -13/3 -3/8 -30/7 -3/10 -47/11 -3/10 -17/4 -2/7 -1/4 -4/1 0/1 -19/5 -1/2 -34/9 -1/2 -15/4 -1/3 0/1 -26/7 1/0 -11/3 -1/2 -7/2 -1/2 -1/3 0/1 -17/5 -1/2 -27/8 -1/1 0/1 -10/3 -1/2 -13/4 -1/2 -1/3 -42/13 -1/3 -29/9 -3/10 -16/5 -1/3 -3/1 -1/4 -20/7 0/1 -37/13 -1/4 -17/6 -1/6 0/1 -14/5 0/1 -11/4 -1/2 0/1 -19/7 -1/2 -46/17 -1/2 -27/10 -2/5 -1/3 -8/3 -1/3 -29/11 -1/4 -21/8 -1/3 -2/7 -1/4 -55/21 -1/4 -89/34 -1/3 -2/7 -34/13 -1/4 -13/5 -3/10 -31/12 -3/11 -1/4 -18/7 -1/4 -41/16 -3/11 -4/15 -64/25 -4/15 -23/9 -1/4 -28/11 -1/4 -5/2 -1/4 -1/5 -17/7 -1/4 -29/12 -3/13 -2/9 -12/5 -1/5 -31/13 -1/4 -50/21 -1/6 -19/8 -1/5 0/1 -26/11 -1/4 -7/3 -1/4 -1/6 -30/13 -1/4 -83/36 -1/5 -2/11 -53/23 -1/6 -23/10 -1/5 0/1 -39/17 -1/4 -55/24 -1/6 0/1 -16/7 0/1 -41/18 -1/3 -2/7 -66/29 -1/4 -25/11 -1/4 -84/37 -1/4 -59/26 -1/4 -5/21 -34/15 -1/4 -9/4 -1/4 0/1 -20/9 -2/9 -11/5 -1/4 -13/6 -5/24 -1/5 -28/13 -1/5 -15/7 -7/36 -2/1 -1/6 -11/6 -1/6 0/1 -9/5 -1/6 -7/4 -1/6 -1/7 0/1 -19/11 -1/6 -31/18 -1/7 -1/8 -43/25 -1/10 -55/32 -1/6 0/1 -12/7 0/1 -41/24 -2/9 -1/5 -70/41 -1/5 -29/17 -1/6 -17/10 -2/11 -1/6 -22/13 -1/6 -27/16 -2/13 -1/7 -5/3 -1/6 -28/17 -1/7 -23/14 -1/7 0/1 -18/11 -1/6 -13/8 -1/6 -1/7 -34/21 -1/8 -21/13 -1/6 -1/8 -71/44 -1/7 0/1 -50/31 -1/6 -29/18 -1/7 0/1 -8/5 -1/7 -27/17 -1/8 -19/12 -1/7 0/1 -30/19 -1/8 -11/7 -1/6 -36/23 -2/13 -61/39 -3/20 -86/55 -3/20 -25/16 -3/20 -1/7 -14/9 -1/7 -3/2 -1/7 -1/8 -22/15 -1/8 -19/13 -1/8 -54/37 -1/8 -35/24 -1/8 -2/17 -1/9 -16/11 -1/9 -29/20 -1/11 0/1 -42/29 0/1 -55/38 -1/4 0/1 -13/9 -1/8 -36/25 0/1 -59/41 -1/6 -23/16 -1/7 0/1 -10/7 -1/8 -47/33 -1/8 -84/59 0/1 -37/26 -1/7 0/1 -27/19 -1/8 -17/12 -1/8 0/1 -24/17 -2/15 -7/5 -1/8 -32/23 -4/33 -57/41 -7/58 -196/141 -3/25 -139/100 -3/25 -8/67 -82/59 -1/8 -25/18 -1/8 -3/25 -18/13 -1/8 -65/47 -1/8 -112/81 -1/8 -47/34 -1/8 -6/49 -29/21 -7/58 -40/29 -3/25 -11/8 -1/8 -2/17 -26/19 -1/8 -41/30 -7/59 -2/17 -56/41 -2/17 -15/11 -3/26 -19/14 -2/17 -1/9 -23/17 -3/26 -27/20 -4/35 -1/9 -4/3 -1/9 -29/22 -1/9 0/1 -25/19 -1/10 -21/16 -1/9 -1/10 0/1 -59/45 -1/10 -38/29 -1/10 -55/42 -1/10 0/1 -17/13 -1/8 -13/10 -1/9 -3/28 -22/17 -1/10 -53/41 -1/8 -84/65 -1/9 -31/24 -1/9 -3/28 -9/7 -1/10 -32/25 0/1 -55/43 -1/10 -23/18 -1/9 0/1 -14/11 -1/9 -5/4 -1/9 -1/10 -11/9 -1/10 -28/23 -1/10 -17/14 -1/10 -4/41 -6/5 -1/10 -19/16 -1/11 0/1 -13/11 -1/10 -7/6 -1/10 -1/11 0/1 -15/13 -1/10 -8/7 0/1 -9/8 -2/19 -1/10 -1/1 -1/12 0/1 0/1 1/1 1/12 8/7 0/1 7/6 0/1 1/11 1/10 20/17 0/1 13/11 1/10 6/5 1/10 17/14 4/41 1/10 28/23 1/10 11/9 1/10 5/4 1/10 1/9 14/11 1/9 23/18 0/1 1/9 9/7 1/10 22/17 1/10 13/10 3/28 1/9 17/13 1/8 38/29 1/10 21/16 0/1 1/10 1/9 25/19 1/10 4/3 1/9 19/14 1/9 2/17 34/25 3/26 15/11 3/26 11/8 2/17 1/8 29/21 7/58 47/34 6/49 1/8 18/13 1/8 25/18 3/25 1/8 7/5 1/8 31/22 1/8 3/23 86/61 1/8 55/39 5/38 24/17 2/15 17/12 0/1 1/8 27/19 1/8 10/7 1/8 23/16 0/1 1/7 36/25 0/1 13/9 1/8 16/11 1/9 19/13 1/8 3/2 1/8 1/7 14/9 1/7 25/16 1/7 3/20 11/7 1/6 30/19 1/8 19/12 0/1 1/7 84/53 0/1 65/41 1/8 46/29 1/8 27/17 1/8 8/5 1/7 29/18 0/1 1/7 50/31 1/6 21/13 1/8 1/6 13/8 1/7 1/6 18/11 1/6 23/14 0/1 1/7 28/17 1/7 5/3 1/6 27/16 1/7 2/13 22/13 1/6 17/10 1/6 2/11 29/17 1/6 70/41 1/5 41/24 1/5 2/9 12/7 0/1 7/4 0/1 1/7 1/6 16/9 0/1 25/14 1/8 1/7 34/19 1/6 9/5 1/6 11/6 0/1 1/6 13/7 1/4 2/1 1/6 15/7 7/36 28/13 1/5 13/6 1/5 5/24 11/5 1/4 31/14 1/5 3/14 51/23 3/14 20/9 2/9 29/13 5/22 9/4 0/1 1/4 25/11 1/4 41/18 2/7 1/3 16/7 0/1 55/24 0/1 1/6 39/17 1/4 23/10 0/1 1/5 7/3 1/6 1/4 33/14 0/1 1/5 59/25 1/6 85/36 2/11 1/5 196/83 1/5 111/47 3/14 26/11 1/4 19/8 0/1 1/5 50/21 1/6 81/34 3/16 1/5 112/47 1/5 31/13 1/4 12/5 1/5 41/17 3/14 70/29 2/9 29/12 2/9 3/13 17/7 1/4 5/2 1/5 1/4 28/11 1/4 23/9 1/4 41/16 4/15 3/11 59/23 1/4 77/30 1/4 3/11 2/7 18/7 1/4 31/12 1/4 3/11 44/17 2/7 57/22 5/18 2/7 70/27 2/7 13/5 3/10 34/13 1/4 21/8 1/4 2/7 1/3 50/19 1/4 29/11 1/4 8/3 1/3 27/10 1/3 2/5 19/7 1/2 11/4 0/1 1/2 14/5 0/1 17/6 0/1 1/6 20/7 0/1 23/8 0/1 1/5 3/1 1/4 16/5 1/3 29/9 3/10 42/13 1/3 13/4 1/3 1/2 10/3 1/2 7/2 0/1 1/3 1/2 18/5 1/2 65/18 4/9 1/2 112/31 1/2 47/13 1/2 29/8 0/1 1/1 11/3 1/2 26/7 1/0 41/11 -1/2 56/15 0/1 15/4 0/1 1/3 34/9 1/2 53/14 1/2 3/5 19/5 1/2 23/6 0/1 1/1 27/7 1/2 4/1 0/1 17/4 1/4 2/7 47/11 3/10 30/7 3/10 13/3 3/8 22/5 1/2 53/12 5/11 1/2 84/19 1/2 31/7 1/2 9/2 0/1 1/2 14/3 0/1 19/4 0/1 1/3 24/5 1/3 53/11 1/2 29/6 1/3 2/5 5/1 1/2 31/6 1/2 1/1 26/5 1/2 21/4 0/1 1/2 1/1 58/11 1/2 37/7 1/2 16/3 1/1 27/5 3/2 11/2 0/1 1/0 28/5 0/1 17/3 1/4 23/4 0/1 1/3 29/5 1/2 6/1 1/2 13/2 1/1 1/0 7/1 1/2 1/0 22/3 1/0 15/2 0/1 1/1 23/3 1/0 8/1 0/1 17/2 0/1 1/2 9/1 1/0 10/1 1/0 11/1 -1/2 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(55,588,-42,-449) (-10/1,1/0) -> (-38/29,-55/42) Hyperbolic Matrix(111,1064,70,671) (-10/1,-9/1) -> (65/41,46/29) Hyperbolic Matrix(57,476,-20,-167) (-9/1,-8/1) -> (-20/7,-37/13) Hyperbolic Matrix(169,1288,-66,-503) (-8/1,-15/2) -> (-41/16,-64/25) Hyperbolic Matrix(113,812,-70,-503) (-15/2,-7/1) -> (-21/13,-71/44) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(225,1316,-86,-503) (-6/1,-23/4) -> (-89/34,-34/13) Hyperbolic Matrix(225,1288,98,561) (-23/4,-17/3) -> (39/17,23/10) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(169,896,-116,-615) (-16/3,-21/4) -> (-35/24,-16/11) Hyperbolic Matrix(391,2044,-268,-1401) (-21/4,-26/5) -> (-54/37,-35/24) Hyperbolic Matrix(391,2016,-250,-1289) (-26/5,-5/1) -> (-61/39,-86/55) Hyperbolic Matrix(111,532,-82,-393) (-5/1,-19/4) -> (-19/14,-23/17) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(111,476,52,223) (-13/3,-30/7) -> (2/1,15/7) Hyperbolic Matrix(727,3108,-498,-2129) (-30/7,-47/11) -> (-19/13,-54/37) Hyperbolic Matrix(223,952,26,111) (-47/11,-17/4) -> (17/2,9/1) Hyperbolic Matrix(113,476,80,337) (-17/4,-4/1) -> (24/17,17/12) Hyperbolic Matrix(169,644,-132,-503) (-4/1,-19/5) -> (-9/7,-32/25) Hyperbolic Matrix(281,1064,-192,-727) (-19/5,-34/9) -> (-22/15,-19/13) Hyperbolic Matrix(839,3164,-520,-1961) (-34/9,-15/4) -> (-71/44,-50/31) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(337,1092,104,337) (-13/4,-42/13) -> (42/13,13/4) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(449,1288,-312,-895) (-3/1,-20/7) -> (-36/25,-59/41) Hyperbolic Matrix(503,1428,118,335) (-37/13,-17/6) -> (17/4,47/11) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(671,1764,-256,-673) (-29/11,-21/8) -> (-21/8,-55/21) Parabolic Matrix(1401,3668,364,953) (-55/21,-89/34) -> (23/6,27/7) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(1343,3444,-590,-1513) (-18/7,-41/16) -> (-41/18,-66/29) Hyperbolic Matrix(1455,3724,656,1679) (-64/25,-23/9) -> (51/23,20/9) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(223,532,70,167) (-12/5,-31/13) -> (3/1,16/5) Hyperbolic Matrix(1399,3332,-1082,-2577) (-31/13,-50/21) -> (-22/17,-53/41) Hyperbolic Matrix(671,1596,494,1175) (-50/21,-19/8) -> (19/14,34/25) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(2575,5936,534,1231) (-83/36,-53/23) -> (53/11,29/6) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(561,1288,98,225) (-23/10,-39/17) -> (17/3,23/4) Hyperbolic Matrix(1343,3080,-1026,-2353) (-39/17,-55/24) -> (-55/42,-17/13) Hyperbolic Matrix(1455,3332,562,1287) (-55/24,-16/7) -> (44/17,57/22) Hyperbolic Matrix(503,1148,294,671) (-16/7,-41/18) -> (41/24,12/7) Hyperbolic Matrix(2129,4844,-1624,-3695) (-66/29,-25/11) -> (-59/45,-38/29) Hyperbolic Matrix(2071,4704,468,1063) (-25/11,-84/37) -> (84/19,31/7) Hyperbolic Matrix(4145,9408,938,2129) (-84/37,-59/26) -> (53/12,84/19) Hyperbolic Matrix(1679,3808,444,1007) (-59/26,-34/15) -> (34/9,53/14) Hyperbolic Matrix(113,252,-100,-223) (-9/4,-20/9) -> (-8/7,-9/8) Hyperbolic Matrix(279,616,-178,-393) (-20/9,-11/5) -> (-11/7,-36/23) Hyperbolic Matrix(167,364,128,279) (-11/5,-13/6) -> (13/10,17/13) Hyperbolic Matrix(337,728,156,337) (-13/6,-28/13) -> (28/13,13/6) Hyperbolic Matrix(391,840,182,391) (-28/13,-15/7) -> (15/7,28/13) Hyperbolic Matrix(223,476,52,111) (-15/7,-2/1) -> (30/7,13/3) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(1791,3080,-1238,-2129) (-43/25,-55/32) -> (-55/38,-13/9) Hyperbolic Matrix(897,1540,392,673) (-55/32,-12/7) -> (16/7,55/24) Hyperbolic Matrix(671,1148,294,503) (-12/7,-41/24) -> (41/18,16/7) Hyperbolic Matrix(3361,5740,1968,3361) (-41/24,-70/41) -> (70/41,41/24) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(281,476,232,393) (-17/10,-22/13) -> (6/5,17/14) Hyperbolic Matrix(1177,1988,730,1233) (-22/13,-27/16) -> (29/18,50/31) Hyperbolic Matrix(449,756,-332,-559) (-27/16,-5/3) -> (-23/17,-27/20) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(393,644,274,449) (-23/14,-18/11) -> (10/7,23/16) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1233,1988,730,1177) (-50/31,-29/18) -> (27/16,22/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(841,1316,108,169) (-36/23,-61/39) -> (23/3,8/1) Hyperbolic Matrix(3081,4816,2186,3417) (-86/55,-25/16) -> (31/22,86/61) Hyperbolic Matrix(449,700,288,449) (-25/16,-14/9) -> (14/9,25/16) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(839,1232,190,279) (-3/2,-22/15) -> (22/5,53/12) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(4313,6244,1664,2409) (-42/29,-55/38) -> (57/22,70/27) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(449,644,274,393) (-23/16,-10/7) -> (18/11,23/14) Hyperbolic Matrix(393,560,40,57) (-10/7,-47/33) -> (9/1,10/1) Hyperbolic Matrix(6607,9408,4168,5935) (-47/33,-84/59) -> (84/53,65/41) Hyperbolic Matrix(3305,4704,2086,2969) (-84/59,-37/26) -> (19/12,84/53) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(337,476,80,113) (-17/12,-24/17) -> (4/1,17/4) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(785,1092,202,281) (-32/23,-57/41) -> (27/7,4/1) Hyperbolic Matrix(23687,32928,10030,13943) (-57/41,-196/141) -> (196/83,111/47) Hyperbolic Matrix(31585,43904,13376,18593) (-196/141,-139/100) -> (85/36,196/83) Hyperbolic Matrix(2297,3192,444,617) (-82/59,-25/18) -> (31/6,26/5) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(391,532,-330,-449) (-15/11,-19/14) -> (-19/16,-13/11) Hyperbolic Matrix(167,224,-126,-169) (-27/20,-4/3) -> (-4/3,-29/22) Parabolic Matrix(2913,3836,1234,1625) (-29/22,-25/19) -> (59/25,85/36) Hyperbolic Matrix(1343,1764,-1024,-1345) (-25/19,-21/16) -> (-21/16,-59/45) Parabolic Matrix(279,364,128,167) (-17/13,-13/10) -> (13/6,11/5) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(6607,8540,2772,3583) (-53/41,-84/65) -> (112/47,31/13) Hyperbolic Matrix(7953,10276,3338,4313) (-84/65,-31/24) -> (81/34,112/47) Hyperbolic Matrix(2407,3080,1706,2183) (-32/25,-55/43) -> (55/39,24/17) Hyperbolic Matrix(1511,1932,262,335) (-55/43,-23/18) -> (23/4,29/5) Hyperbolic Matrix(505,644,396,505) (-23/18,-14/11) -> (14/11,23/18) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(393,476,232,281) (-17/14,-6/5) -> (22/13,17/10) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(167,196,-144,-169) (-13/11,-7/6) -> (-7/6,-15/13) Parabolic Matrix(559,644,388,447) (-15/13,-8/7) -> (36/25,13/9) Hyperbolic Matrix(279,308,202,223) (-9/8,-1/1) -> (29/21,47/34) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(223,-252,100,-113) (1/1,8/7) -> (20/9,29/13) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(503,-644,132,-169) (23/18,9/7) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(449,-588,42,-55) (17/13,38/29) -> (10/1,11/1) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2407,-3164,938,-1233) (21/16,25/19) -> (59/23,77/30) Hyperbolic Matrix(615,-812,128,-169) (25/19,4/3) -> (24/5,53/11) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(503,-812,70,-113) (50/31,21/13) -> (7/1,22/3) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(895,-1596,346,-617) (16/9,25/14) -> (31/12,44/17) Hyperbolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1513,-3444,590,-1343) (25/11,41/18) -> (41/16,59/23) Hyperbolic Matrix(281,-644,24,-55) (55/24,39/17) -> (11/1,1/0) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(673,-1764,256,-671) (34/13,21/8) -> (21/8,50/19) Parabolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(167,-476,20,-57) (17/6,20/7) -> (8/1,17/2) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(897,-3836,170,-727) (47/11,30/7) -> (58/11,37/7) Hyperbolic Matrix(337,-1764,64,-335) (26/5,21/4) -> (21/4,58/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(55,588,-42,-449) -> Matrix(1,0,-10,1) Matrix(111,1064,70,671) -> Matrix(1,0,8,1) Matrix(57,476,-20,-167) -> Matrix(1,0,-4,1) Matrix(169,1288,-66,-503) -> Matrix(1,4,-4,-15) Matrix(113,812,-70,-503) -> Matrix(1,0,-6,1) Matrix(55,364,-34,-225) -> Matrix(1,0,-6,1) Matrix(225,1316,-86,-503) -> Matrix(5,2,-18,-7) Matrix(225,1288,98,561) -> Matrix(1,0,8,1) Matrix(169,952,30,169) -> Matrix(1,0,8,1) Matrix(111,616,20,111) -> Matrix(1,0,0,1) Matrix(113,616,-82,-447) -> Matrix(1,-2,-8,17) Matrix(169,896,-116,-615) -> Matrix(3,2,-26,-17) Matrix(391,2044,-268,-1401) -> Matrix(3,2,-26,-17) Matrix(391,2016,-250,-1289) -> Matrix(5,4,-34,-27) Matrix(111,532,-82,-393) -> Matrix(7,2,-60,-17) Matrix(113,532,24,113) -> Matrix(1,0,6,1) Matrix(55,252,12,55) -> Matrix(1,0,4,1) Matrix(113,504,-50,-223) -> Matrix(1,0,-2,1) Matrix(167,728,64,279) -> Matrix(1,0,6,1) Matrix(111,476,52,223) -> Matrix(13,4,68,21) Matrix(727,3108,-498,-2129) -> Matrix(13,4,-114,-35) Matrix(223,952,26,111) -> Matrix(7,2,10,3) Matrix(113,476,80,337) -> Matrix(7,2,52,15) Matrix(169,644,-132,-503) -> Matrix(1,0,-8,1) Matrix(281,1064,-192,-727) -> Matrix(3,2,-26,-17) Matrix(839,3164,-520,-1961) -> Matrix(1,0,-4,1) Matrix(391,1456,-286,-1065) -> Matrix(1,-2,-8,17) Matrix(167,616,106,391) -> Matrix(1,0,8,1) Matrix(55,196,-16,-57) -> Matrix(1,0,0,1) Matrix(281,952,116,393) -> Matrix(5,2,22,9) Matrix(449,1512,-166,-559) -> Matrix(3,2,-8,-5) Matrix(111,364,68,223) -> Matrix(5,2,32,13) Matrix(337,1092,104,337) -> Matrix(5,2,12,5) Matrix(1007,3248,590,1903) -> Matrix(13,4,68,21) Matrix(279,896,52,167) -> Matrix(1,0,4,1) Matrix(167,532,70,223) -> Matrix(1,0,8,1) Matrix(449,1288,-312,-895) -> Matrix(1,0,-2,1) Matrix(503,1428,118,335) -> Matrix(11,2,38,7) Matrix(169,476,60,169) -> Matrix(1,0,12,1) Matrix(111,308,40,111) -> Matrix(1,0,4,1) Matrix(113,308,62,169) -> Matrix(1,0,8,1) Matrix(1231,3332,-890,-2409) -> Matrix(1,0,-6,1) Matrix(167,448,104,279) -> Matrix(5,2,32,13) Matrix(169,448,106,281) -> Matrix(7,2,52,15) Matrix(671,1764,-256,-673) -> Matrix(1,0,0,1) Matrix(1401,3668,364,953) -> Matrix(7,2,10,3) Matrix(279,728,64,167) -> Matrix(1,0,6,1) Matrix(671,1736,-390,-1009) -> Matrix(7,2,-60,-17) Matrix(391,1008,282,727) -> Matrix(1,0,12,1) Matrix(1343,3444,-590,-1513) -> Matrix(7,2,-32,-9) Matrix(1455,3724,656,1679) -> Matrix(53,14,246,65) Matrix(505,1288,198,505) -> Matrix(47,12,184,47) Matrix(111,280,44,111) -> Matrix(9,2,40,9) Matrix(57,140,46,113) -> Matrix(1,0,14,1) Matrix(335,812,92,223) -> Matrix(9,2,22,5) Matrix(337,812,-232,-559) -> Matrix(9,2,-86,-19) Matrix(223,532,70,167) -> Matrix(1,0,8,1) Matrix(1399,3332,-1082,-2577) -> Matrix(1,0,-4,1) Matrix(671,1596,494,1175) -> Matrix(9,2,76,17) Matrix(449,1064,284,673) -> Matrix(1,0,12,1) Matrix(167,392,-72,-169) -> Matrix(1,0,0,1) Matrix(4759,10976,-3424,-7897) -> Matrix(7,2,-60,-17) Matrix(2575,5936,534,1231) -> Matrix(1,0,8,1) Matrix(559,1288,194,447) -> Matrix(1,0,10,1) Matrix(561,1288,98,225) -> Matrix(1,0,8,1) Matrix(1343,3080,-1026,-2353) -> Matrix(1,0,-4,1) Matrix(1455,3332,562,1287) -> Matrix(7,2,24,7) Matrix(503,1148,294,671) -> Matrix(1,0,8,1) Matrix(2129,4844,-1624,-3695) -> Matrix(1,0,-6,1) Matrix(2071,4704,468,1063) -> Matrix(15,4,26,7) Matrix(4145,9408,938,2129) -> Matrix(41,10,86,21) Matrix(1679,3808,444,1007) -> Matrix(9,2,22,5) Matrix(113,252,-100,-223) -> Matrix(9,2,-86,-19) Matrix(279,616,-178,-393) -> Matrix(1,0,-2,1) Matrix(167,364,128,279) -> Matrix(9,2,76,17) Matrix(337,728,156,337) -> Matrix(49,10,240,49) Matrix(391,840,182,391) -> Matrix(71,14,360,71) Matrix(223,476,52,111) -> Matrix(21,4,68,13) Matrix(167,308,-122,-225) -> Matrix(11,2,-94,-17) Matrix(169,308,62,113) -> Matrix(1,0,8,1) Matrix(111,196,-64,-113) -> Matrix(1,0,0,1) Matrix(503,868,-390,-673) -> Matrix(13,2,-124,-19) Matrix(1791,3080,-1238,-2129) -> Matrix(1,0,2,1) Matrix(897,1540,392,673) -> Matrix(1,0,12,1) Matrix(671,1148,294,503) -> Matrix(1,0,8,1) Matrix(3361,5740,1968,3361) -> Matrix(19,4,90,19) Matrix(1903,3248,590,1007) -> Matrix(21,4,68,13) Matrix(559,952,394,671) -> Matrix(11,2,82,15) Matrix(281,476,232,393) -> Matrix(13,2,136,21) Matrix(1177,1988,730,1233) -> Matrix(13,2,84,13) Matrix(449,756,-332,-559) -> Matrix(15,2,-128,-17) Matrix(169,280,102,169) -> Matrix(13,2,84,13) Matrix(783,1288,476,783) -> Matrix(1,0,14,1) Matrix(393,644,274,449) -> Matrix(1,0,14,1) Matrix(223,364,68,111) -> Matrix(13,2,32,5) Matrix(449,728,346,561) -> Matrix(15,2,142,19) Matrix(1233,1988,730,1177) -> Matrix(13,2,84,13) Matrix(279,448,104,167) -> Matrix(13,2,32,5) Matrix(281,448,106,169) -> Matrix(15,2,52,7) Matrix(953,1512,-670,-1063) -> Matrix(1,0,0,1) Matrix(673,1064,284,449) -> Matrix(1,0,12,1) Matrix(391,616,106,167) -> Matrix(1,0,8,1) Matrix(841,1316,108,169) -> Matrix(13,2,-20,-3) Matrix(3081,4816,2186,3417) -> Matrix(53,8,404,61) Matrix(449,700,288,449) -> Matrix(41,6,280,41) Matrix(55,84,36,55) -> Matrix(15,2,112,15) Matrix(839,1232,190,279) -> Matrix(33,4,74,9) Matrix(2241,3248,928,1345) -> Matrix(25,2,112,9) Matrix(4313,6244,1664,2409) -> Matrix(3,2,10,7) Matrix(505,728,428,617) -> Matrix(1,0,18,1) Matrix(2297,3304,974,1401) -> Matrix(1,0,12,1) Matrix(449,644,274,393) -> Matrix(1,0,14,1) Matrix(393,560,40,57) -> Matrix(1,0,8,1) Matrix(6607,9408,4168,5935) -> Matrix(1,0,16,1) Matrix(3305,4704,2086,2969) -> Matrix(1,0,14,1) Matrix(671,952,394,559) -> Matrix(15,2,82,11) Matrix(337,476,80,113) -> Matrix(15,2,52,7) Matrix(279,392,-200,-281) -> Matrix(47,6,-384,-49) Matrix(785,1092,202,281) -> Matrix(33,4,8,1) Matrix(23687,32928,10030,13943) -> Matrix(133,16,640,77) Matrix(31585,43904,13376,18593) -> Matrix(117,14,610,73) Matrix(2297,3192,444,617) -> Matrix(17,2,42,5) Matrix(727,1008,282,391) -> Matrix(1,0,12,1) Matrix(9071,12544,2510,3471) -> Matrix(31,4,54,7) Matrix(9073,12544,2512,3473) -> Matrix(81,10,170,21) Matrix(1175,1624,526,727) -> Matrix(49,6,204,25) Matrix(1177,1624,366,505) -> Matrix(17,2,76,9) Matrix(2295,3136,614,839) -> Matrix(17,2,110,13) Matrix(2297,3136,616,841) -> Matrix(17,2,-60,-7) Matrix(391,532,-330,-449) -> Matrix(17,2,-196,-23) Matrix(167,224,-126,-169) -> Matrix(35,4,-324,-37) Matrix(2913,3836,1234,1625) -> Matrix(19,2,104,11) Matrix(1343,1764,-1024,-1345) -> Matrix(1,0,0,1) Matrix(279,364,128,167) -> Matrix(17,2,76,9) Matrix(281,364,44,57) -> Matrix(19,2,28,3) Matrix(6607,8540,2772,3583) -> Matrix(17,2,76,9) Matrix(7953,10276,3338,4313) -> Matrix(55,6,284,31) Matrix(2407,3080,1706,2183) -> Matrix(15,2,112,15) Matrix(1511,1932,262,335) -> Matrix(1,0,12,1) Matrix(505,644,396,505) -> Matrix(1,0,18,1) Matrix(111,140,88,111) -> Matrix(19,2,180,19) Matrix(113,140,46,57) -> Matrix(1,0,14,1) Matrix(505,616,414,505) -> Matrix(59,6,580,59) Matrix(783,952,644,783) -> Matrix(81,8,820,81) Matrix(393,476,232,281) -> Matrix(21,2,136,13) Matrix(895,1064,376,447) -> Matrix(1,0,16,1) Matrix(167,196,-144,-169) -> Matrix(1,0,0,1) Matrix(559,644,388,447) -> Matrix(1,0,18,1) Matrix(279,308,202,223) -> Matrix(41,4,338,33) Matrix(1,0,2,1) -> Matrix(1,0,24,1) Matrix(223,-252,100,-113) -> Matrix(19,-2,86,-9) Matrix(169,-196,144,-167) -> Matrix(1,0,0,1) Matrix(449,-532,330,-391) -> Matrix(23,-2,196,-17) Matrix(503,-644,132,-169) -> Matrix(1,0,-8,1) Matrix(391,-504,218,-281) -> Matrix(19,-2,124,-13) Matrix(449,-588,42,-55) -> Matrix(1,0,-10,1) Matrix(2521,-3304,982,-1287) -> Matrix(21,-2,74,-7) Matrix(2407,-3164,938,-1233) -> Matrix(21,-2,74,-7) Matrix(615,-812,128,-169) -> Matrix(19,-2,48,-5) Matrix(393,-532,82,-111) -> Matrix(17,-2,60,-7) Matrix(225,-308,122,-167) -> Matrix(17,-2,94,-11) Matrix(447,-616,82,-113) -> Matrix(17,-2,-8,1) Matrix(1457,-2016,404,-559) -> Matrix(17,-2,26,-3) Matrix(281,-392,200,-279) -> Matrix(49,-6,384,-47) Matrix(7785,-10976,3296,-4647) -> Matrix(31,-4,132,-17) Matrix(1063,-1512,670,-953) -> Matrix(1,0,0,1) Matrix(895,-1288,312,-449) -> Matrix(1,0,-2,1) Matrix(559,-812,232,-337) -> Matrix(19,-2,86,-9) Matrix(615,-896,116,-169) -> Matrix(17,-2,26,-3) Matrix(727,-1064,192,-281) -> Matrix(17,-2,26,-3) Matrix(393,-616,178,-279) -> Matrix(1,0,-2,1) Matrix(503,-812,70,-113) -> Matrix(1,0,-6,1) Matrix(225,-364,34,-55) -> Matrix(1,0,-6,1) Matrix(167,-280,34,-57) -> Matrix(1,0,-4,1) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(895,-1596,346,-617) -> Matrix(17,-2,60,-7) Matrix(2239,-4004,940,-1681) -> Matrix(13,-2,72,-11) Matrix(223,-420,60,-113) -> Matrix(1,0,-6,1) Matrix(783,-1736,152,-337) -> Matrix(19,-4,24,-5) Matrix(223,-504,50,-113) -> Matrix(1,0,-2,1) Matrix(1513,-3444,590,-1343) -> Matrix(9,-2,32,-7) Matrix(281,-644,24,-55) -> Matrix(1,0,-6,1) Matrix(169,-392,72,-167) -> Matrix(1,0,0,1) Matrix(1567,-3780,604,-1457) -> Matrix(55,-12,188,-41) Matrix(503,-1288,66,-169) -> Matrix(15,-4,4,-1) Matrix(673,-1764,256,-671) -> Matrix(1,0,0,1) Matrix(617,-1624,106,-279) -> Matrix(7,-2,18,-5) Matrix(673,-1820,186,-503) -> Matrix(5,-2,8,-3) Matrix(167,-476,20,-57) -> Matrix(1,0,-4,1) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(223,-840,30,-113) -> Matrix(1,0,-2,1) Matrix(897,-3836,170,-727) -> Matrix(7,-2,4,-1) Matrix(337,-1764,64,-335) -> Matrix(1,0,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 46 Degree of the the map X: 46 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: 36 Genus: 31 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -4/1 -7/2 -8/3 -12/5 -7/4 -7/6 0/1 1/1 7/6 28/23 7/5 3/2 28/17 7/4 2/1 7/3 5/2 28/11 8/3 14/5 3/1 42/13 10/3 7/2 56/15 15/4 4/1 14/3 19/4 5/1 16/3 11/2 28/5 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -7/1 -1/2 1/0 -6/1 -1/2 -17/3 -1/4 -28/5 0/1 -11/2 0/1 1/0 -5/1 -1/2 -4/1 0/1 -19/5 -1/2 -15/4 -1/3 0/1 -26/7 1/0 -11/3 -1/2 -7/2 -1/2 -1/3 0/1 -17/5 -1/2 -27/8 -1/1 0/1 -10/3 -1/2 -13/4 -1/2 -1/3 -42/13 -1/3 -29/9 -3/10 -16/5 -1/3 -3/1 -1/4 -14/5 0/1 -11/4 -1/2 0/1 -19/7 -1/2 -27/10 -2/5 -1/3 -8/3 -1/3 -29/11 -1/4 -21/8 -1/3 -2/7 -1/4 -13/5 -3/10 -18/7 -1/4 -41/16 -3/11 -4/15 -23/9 -1/4 -28/11 -1/4 -5/2 -1/4 -1/5 -17/7 -1/4 -29/12 -3/13 -2/9 -12/5 -1/5 -31/13 -1/4 -50/21 -1/6 -19/8 -1/5 0/1 -26/11 -1/4 -7/3 -1/4 -1/6 -2/1 -1/6 -11/6 -1/6 0/1 -9/5 -1/6 -7/4 -1/6 -1/7 0/1 -19/11 -1/6 -31/18 -1/7 -1/8 -12/7 0/1 -17/10 -2/11 -1/6 -22/13 -1/6 -27/16 -2/13 -1/7 -5/3 -1/6 -28/17 -1/7 -23/14 -1/7 0/1 -18/11 -1/6 -13/8 -1/6 -1/7 -21/13 -1/6 -1/8 -50/31 -1/6 -29/18 -1/7 0/1 -8/5 -1/7 -27/17 -1/8 -19/12 -1/7 0/1 -30/19 -1/8 -11/7 -1/6 -14/9 -1/7 -3/2 -1/7 -1/8 -16/11 -1/9 -29/20 -1/11 0/1 -42/29 0/1 -13/9 -1/8 -23/16 -1/7 0/1 -10/7 -1/8 -7/5 -1/8 -18/13 -1/8 -29/21 -7/58 -40/29 -3/25 -11/8 -1/8 -2/17 -26/19 -1/8 -41/30 -7/59 -2/17 -56/41 -2/17 -15/11 -3/26 -19/14 -2/17 -1/9 -4/3 -1/9 -9/7 -1/10 -32/25 0/1 -23/18 -1/9 0/1 -14/11 -1/9 -5/4 -1/9 -1/10 -11/9 -1/10 -28/23 -1/10 -17/14 -1/10 -4/41 -6/5 -1/10 -19/16 -1/11 0/1 -13/11 -1/10 -7/6 -1/10 -1/11 0/1 -1/1 -1/12 0/1 0/1 1/1 1/12 7/6 0/1 1/11 1/10 13/11 1/10 6/5 1/10 17/14 4/41 1/10 28/23 1/10 11/9 1/10 5/4 1/10 1/9 4/3 1/9 19/14 1/9 2/17 34/25 3/26 15/11 3/26 11/8 2/17 1/8 18/13 1/8 7/5 1/8 10/7 1/8 23/16 0/1 1/7 13/9 1/8 3/2 1/8 1/7 14/9 1/7 11/7 1/6 30/19 1/8 19/12 0/1 1/7 27/17 1/8 8/5 1/7 29/18 0/1 1/7 50/31 1/6 21/13 1/8 1/6 13/8 1/7 1/6 18/11 1/6 23/14 0/1 1/7 28/17 1/7 5/3 1/6 22/13 1/6 17/10 1/6 2/11 29/17 1/6 12/7 0/1 7/4 0/1 1/7 1/6 16/9 0/1 9/5 1/6 11/6 0/1 1/6 13/7 1/4 2/1 1/6 7/3 1/6 1/4 26/11 1/4 19/8 0/1 1/5 31/13 1/4 12/5 1/5 41/17 3/14 70/29 2/9 29/12 2/9 3/13 17/7 1/4 5/2 1/5 1/4 28/11 1/4 23/9 1/4 18/7 1/4 31/12 1/4 3/11 13/5 3/10 21/8 1/4 2/7 1/3 29/11 1/4 8/3 1/3 27/10 1/3 2/5 19/7 1/2 11/4 0/1 1/2 14/5 0/1 3/1 1/4 16/5 1/3 29/9 3/10 42/13 1/3 13/4 1/3 1/2 10/3 1/2 7/2 0/1 1/3 1/2 18/5 1/2 47/13 1/2 29/8 0/1 1/1 11/3 1/2 26/7 1/0 41/11 -1/2 56/15 0/1 15/4 0/1 1/3 34/9 1/2 19/5 1/2 4/1 0/1 9/2 0/1 1/2 14/3 0/1 19/4 0/1 1/3 24/5 1/3 5/1 1/2 16/3 1/1 27/5 3/2 11/2 0/1 1/0 28/5 0/1 17/3 1/4 23/4 0/1 1/3 6/1 1/2 7/1 1/2 1/0 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(13,112,8,69) (-7/1,1/0) -> (21/13,13/8) Hyperbolic Matrix(13,84,2,13) (-7/1,-6/1) -> (6/1,7/1) Hyperbolic Matrix(181,1036,-76,-435) (-6/1,-17/3) -> (-31/13,-50/21) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(69,364,-40,-211) (-11/2,-5/1) -> (-19/11,-31/18) Hyperbolic Matrix(13,56,-10,-43) (-5/1,-4/1) -> (-4/3,-9/7) Hyperbolic Matrix(169,644,-132,-503) (-4/1,-19/5) -> (-9/7,-32/25) Hyperbolic Matrix(155,588,-92,-349) (-19/5,-15/4) -> (-27/16,-5/3) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(267,896,-104,-349) (-27/8,-10/3) -> (-18/7,-41/16) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(337,1092,104,337) (-13/4,-42/13) -> (42/13,13/4) Hyperbolic Matrix(1163,3752,482,1555) (-42/13,-29/9) -> (41/17,70/29) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(69,196,44,125) (-3/1,-14/5) -> (14/9,11/7) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(517,1400,-202,-547) (-19/7,-27/10) -> (-41/16,-23/9) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(181,476,154,405) (-29/11,-21/8) -> (7/6,13/11) Hyperbolic Matrix(43,112,38,99) (-21/8,-13/5) -> (1/1,7/6) Hyperbolic Matrix(293,756,-212,-547) (-13/5,-18/7) -> (-18/13,-29/21) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(223,532,70,167) (-12/5,-31/13) -> (3/1,16/5) Hyperbolic Matrix(671,1596,494,1175) (-50/21,-19/8) -> (19/14,34/25) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(155,364,66,155) (-26/11,-7/3) -> (7/3,26/11) Hyperbolic Matrix(13,28,6,13) (-7/3,-2/1) -> (2/1,7/3) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(797,1372,-578,-995) (-31/18,-12/7) -> (-40/29,-11/8) Hyperbolic Matrix(181,308,-124,-211) (-12/7,-17/10) -> (-3/2,-16/11) Hyperbolic Matrix(281,476,232,393) (-17/10,-22/13) -> (6/5,17/14) Hyperbolic Matrix(1177,1988,730,1233) (-22/13,-27/16) -> (29/18,50/31) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(393,644,274,449) (-23/14,-18/11) -> (10/7,23/16) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(69,112,8,13) (-13/8,-21/13) -> (7/1,1/0) Hyperbolic Matrix(1301,2100,806,1301) (-21/13,-50/31) -> (50/31,21/13) Hyperbolic Matrix(1077,1736,286,461) (-50/31,-29/18) -> (15/4,34/9) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(547,868,380,603) (-27/17,-19/12) -> (23/16,13/9) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(125,196,44,69) (-11/7,-14/9) -> (14/5,3/1) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(1219,1764,378,547) (-42/29,-13/9) -> (29/9,42/13) Hyperbolic Matrix(603,868,380,547) (-13/9,-23/16) -> (19/12,27/17) Hyperbolic Matrix(449,644,274,393) (-23/16,-10/7) -> (18/11,23/14) Hyperbolic Matrix(99,140,70,99) (-10/7,-7/5) -> (7/5,10/7) Hyperbolic Matrix(181,252,130,181) (-7/5,-18/13) -> (18/13,7/5) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(391,532,-330,-449) (-15/11,-19/14) -> (-19/16,-13/11) Hyperbolic Matrix(517,700,-404,-547) (-19/14,-4/3) -> (-32/25,-23/18) Hyperbolic Matrix(461,588,98,125) (-23/18,-14/11) -> (14/3,19/4) Hyperbolic Matrix(155,196,34,43) (-14/11,-5/4) -> (9/2,14/3) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(393,476,232,281) (-17/14,-6/5) -> (22/13,17/10) Hyperbolic Matrix(211,252,36,43) (-6/5,-19/16) -> (23/4,6/1) Hyperbolic Matrix(405,476,154,181) (-13/11,-7/6) -> (21/8,29/11) Hyperbolic Matrix(99,112,38,43) (-7/6,-1/1) -> (13/5,21/8) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(43,-56,10,-13) (5/4,4/3) -> (4/1,9/2) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(547,-756,212,-293) (11/8,18/13) -> (18/7,31/12) Hyperbolic Matrix(211,-308,124,-181) (13/9,3/2) -> (17/10,29/17) Hyperbolic Matrix(349,-588,92,-155) (5/3,22/13) -> (34/9,19/5) Hyperbolic Matrix(491,-840,204,-349) (29/17,12/7) -> (12/5,41/17) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(125,-224,24,-43) (16/9,9/5) -> (5/1,16/3) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(491,-1260,136,-349) (23/9,18/7) -> (18/5,47/13) Hyperbolic Matrix(379,-980,70,-181) (31/12,13/5) -> (27/5,11/2) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(125,-476,26,-99) (19/5,4/1) -> (24/5,5/1) Hyperbolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(13,112,8,69) -> Matrix(1,1,6,7) Matrix(13,84,2,13) -> Matrix(1,1,0,1) Matrix(181,1036,-76,-435) -> Matrix(3,1,-16,-5) Matrix(169,952,30,169) -> Matrix(1,0,8,1) Matrix(111,616,20,111) -> Matrix(1,0,0,1) Matrix(69,364,-40,-211) -> Matrix(1,1,-8,-7) Matrix(13,56,-10,-43) -> Matrix(3,1,-28,-9) Matrix(169,644,-132,-503) -> Matrix(1,0,-8,1) Matrix(155,588,-92,-349) -> Matrix(1,1,-8,-7) Matrix(391,1456,-286,-1065) -> Matrix(1,-2,-8,17) Matrix(167,616,106,391) -> Matrix(1,0,8,1) Matrix(55,196,-16,-57) -> Matrix(1,0,0,1) Matrix(281,952,116,393) -> Matrix(5,2,22,9) Matrix(267,896,-104,-349) -> Matrix(7,3,-26,-11) Matrix(111,364,68,223) -> Matrix(5,2,32,13) Matrix(337,1092,104,337) -> Matrix(5,2,12,5) Matrix(1163,3752,482,1555) -> Matrix(29,9,132,41) Matrix(279,896,52,167) -> Matrix(1,0,4,1) Matrix(167,532,70,223) -> Matrix(1,0,8,1) Matrix(69,196,44,125) -> Matrix(5,1,34,7) Matrix(111,308,40,111) -> Matrix(1,0,4,1) Matrix(113,308,62,169) -> Matrix(1,0,8,1) Matrix(517,1400,-202,-547) -> Matrix(11,5,-42,-19) Matrix(167,448,104,279) -> Matrix(5,2,32,13) Matrix(169,448,106,281) -> Matrix(7,2,52,15) Matrix(181,476,154,405) -> Matrix(3,1,26,9) Matrix(43,112,38,99) -> Matrix(3,1,26,9) Matrix(293,756,-212,-547) -> Matrix(19,5,-156,-41) Matrix(505,1288,198,505) -> Matrix(47,12,184,47) Matrix(111,280,44,111) -> Matrix(9,2,40,9) Matrix(57,140,46,113) -> Matrix(1,0,14,1) Matrix(335,812,92,223) -> Matrix(9,2,22,5) Matrix(337,812,-232,-559) -> Matrix(9,2,-86,-19) Matrix(223,532,70,167) -> Matrix(1,0,8,1) Matrix(671,1596,494,1175) -> Matrix(9,2,76,17) Matrix(449,1064,284,673) -> Matrix(1,0,12,1) Matrix(155,364,66,155) -> Matrix(5,1,24,5) Matrix(13,28,6,13) -> Matrix(5,1,24,5) Matrix(167,308,-122,-225) -> Matrix(11,2,-94,-17) Matrix(169,308,62,113) -> Matrix(1,0,8,1) Matrix(111,196,-64,-113) -> Matrix(1,0,0,1) Matrix(797,1372,-578,-995) -> Matrix(23,3,-192,-25) Matrix(181,308,-124,-211) -> Matrix(5,1,-46,-9) Matrix(281,476,232,393) -> Matrix(13,2,136,21) Matrix(1177,1988,730,1233) -> Matrix(13,2,84,13) Matrix(169,280,102,169) -> Matrix(13,2,84,13) Matrix(783,1288,476,783) -> Matrix(1,0,14,1) Matrix(393,644,274,449) -> Matrix(1,0,14,1) Matrix(223,364,68,111) -> Matrix(13,2,32,5) Matrix(69,112,8,13) -> Matrix(7,1,6,1) Matrix(1301,2100,806,1301) -> Matrix(7,1,48,7) Matrix(1077,1736,286,461) -> Matrix(7,1,20,3) Matrix(279,448,104,167) -> Matrix(13,2,32,5) Matrix(281,448,106,169) -> Matrix(15,2,52,7) Matrix(547,868,380,603) -> Matrix(7,1,48,7) Matrix(673,1064,284,449) -> Matrix(1,0,12,1) Matrix(391,616,106,167) -> Matrix(1,0,8,1) Matrix(125,196,44,69) -> Matrix(7,1,34,5) Matrix(55,84,36,55) -> Matrix(15,2,112,15) Matrix(2241,3248,928,1345) -> Matrix(25,2,112,9) Matrix(1219,1764,378,547) -> Matrix(5,1,14,3) Matrix(603,868,380,547) -> Matrix(7,1,48,7) Matrix(449,644,274,393) -> Matrix(1,0,14,1) Matrix(99,140,70,99) -> Matrix(7,1,48,7) Matrix(181,252,130,181) -> Matrix(41,5,336,41) Matrix(1177,1624,366,505) -> Matrix(17,2,76,9) Matrix(2295,3136,614,839) -> Matrix(17,2,110,13) Matrix(2297,3136,616,841) -> Matrix(17,2,-60,-7) Matrix(391,532,-330,-449) -> Matrix(17,2,-196,-23) Matrix(517,700,-404,-547) -> Matrix(9,1,-64,-7) Matrix(461,588,98,125) -> Matrix(9,1,26,3) Matrix(155,196,34,43) -> Matrix(9,1,8,1) Matrix(113,140,46,57) -> Matrix(1,0,14,1) Matrix(505,616,414,505) -> Matrix(59,6,580,59) Matrix(783,952,644,783) -> Matrix(81,8,820,81) Matrix(393,476,232,281) -> Matrix(21,2,136,13) Matrix(211,252,36,43) -> Matrix(11,1,32,3) Matrix(405,476,154,181) -> Matrix(9,1,26,3) Matrix(99,112,38,43) -> Matrix(9,1,26,3) Matrix(1,0,2,1) -> Matrix(1,0,24,1) Matrix(449,-532,330,-391) -> Matrix(23,-2,196,-17) Matrix(43,-56,10,-13) -> Matrix(9,-1,28,-3) Matrix(393,-532,82,-111) -> Matrix(17,-2,60,-7) Matrix(225,-308,122,-167) -> Matrix(17,-2,94,-11) Matrix(547,-756,212,-293) -> Matrix(41,-5,156,-19) Matrix(211,-308,124,-181) -> Matrix(9,-1,46,-5) Matrix(349,-588,92,-155) -> Matrix(7,-1,8,-1) Matrix(491,-840,204,-349) -> Matrix(3,-1,16,-5) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(125,-224,24,-43) -> Matrix(7,-1,8,-1) Matrix(223,-420,60,-113) -> Matrix(1,0,-6,1) Matrix(435,-1036,76,-181) -> Matrix(5,-1,16,-3) Matrix(491,-1260,136,-349) -> Matrix(11,-3,26,-7) Matrix(379,-980,70,-181) -> Matrix(11,-3,4,-1) Matrix(673,-1820,186,-503) -> Matrix(5,-2,8,-3) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(125,-476,26,-99) -> Matrix(1,-1,4,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 46 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 12 1 1/1 1/12 1 28 7/6 0 4 13/11 1/10 1 28 6/5 1/10 1 14 17/14 (4/41,1/10) 0 28 28/23 1/10 7 1 11/9 1/10 1 28 5/4 (1/10,1/9) 0 28 4/3 1/9 2 7 19/14 (1/9,2/17) 0 28 34/25 3/26 1 14 15/11 3/26 1 28 11/8 (2/17,1/8) 0 28 18/13 1/8 1 14 7/5 1/8 3 4 10/7 1/8 1 14 23/16 (0/1,1/7) 0 28 13/9 1/8 1 28 3/2 (1/8,1/7) 0 28 14/9 1/7 4 2 11/7 1/6 1 28 30/19 1/8 1 14 19/12 (0/1,1/7) 0 28 27/17 1/8 1 28 8/5 1/7 2 7 29/18 (0/1,1/7) 0 28 50/31 1/6 1 14 21/13 (1/8,1/6) 0 4 13/8 (1/7,1/6) 0 28 18/11 1/6 1 14 23/14 (0/1,1/7) 0 28 28/17 1/7 1 1 5/3 1/6 1 28 22/13 1/6 1 14 17/10 (1/6,2/11) 0 28 29/17 1/6 1 28 12/7 0/1 2 7 7/4 0 4 16/9 0/1 2 7 9/5 1/6 1 28 11/6 (0/1,1/6) 0 28 13/7 1/4 1 28 2/1 1/6 1 14 7/3 (1/6,1/4) 0 4 26/11 1/4 1 14 19/8 (0/1,1/5) 0 28 31/13 1/4 1 28 12/5 1/5 2 7 41/17 3/14 1 28 70/29 2/9 7 2 29/12 (2/9,3/13) 0 28 17/7 1/4 1 28 5/2 (1/5,1/4) 0 28 28/11 1/4 7 1 23/9 1/4 1 28 18/7 1/4 1 14 31/12 (1/4,3/11) 0 28 13/5 3/10 1 28 21/8 0 4 29/11 1/4 1 28 8/3 1/3 2 7 27/10 (1/3,2/5) 0 28 19/7 1/2 1 28 11/4 (0/1,1/2) 0 28 14/5 0/1 4 2 3/1 1/4 1 28 16/5 1/3 2 7 29/9 3/10 1 28 42/13 1/3 7 2 13/4 (1/3,1/2) 0 28 10/3 1/2 1 14 7/2 0 4 18/5 1/2 1 14 47/13 1/2 1 28 29/8 (0/1,1/1) 0 28 11/3 1/2 1 28 26/7 1/0 1 14 41/11 -1/2 1 28 56/15 0/1 5 1 15/4 (0/1,1/3) 0 28 34/9 1/2 1 14 19/5 1/2 1 28 4/1 0/1 2 7 9/2 (0/1,1/2) 0 28 14/3 0/1 1 2 19/4 (0/1,1/3) 0 28 24/5 1/3 2 7 5/1 1/2 1 28 16/3 1/1 2 7 27/5 3/2 1 28 11/2 (0/1,1/0) 0 28 28/5 0/1 4 1 17/3 1/4 1 28 23/4 (0/1,1/3) 0 28 6/1 1/2 1 14 7/1 (1/2,1/0) 0 4 1/0 (0/1,1/0) 0 28 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(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(99,-112,38,-43) (1/1,7/6) -> (13/5,21/8) Glide Reflection Matrix(405,-476,154,-181) (7/6,13/11) -> (21/8,29/11) Glide Reflection Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(393,-476,232,-281) (6/5,17/14) -> (22/13,17/10) Glide Reflection Matrix(783,-952,644,-783) (17/14,28/23) -> (17/14,28/23) Reflection Matrix(505,-616,414,-505) (28/23,11/9) -> (28/23,11/9) Reflection Matrix(113,-140,46,-57) (11/9,5/4) -> (17/7,5/2) Glide Reflection Matrix(43,-56,10,-13) (5/4,4/3) -> (4/1,9/2) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(659,-896,114,-155) (19/14,34/25) -> (23/4,6/1) Glide Reflection Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(547,-756,212,-293) (11/8,18/13) -> (18/7,31/12) Hyperbolic Matrix(181,-252,130,-181) (18/13,7/5) -> (18/13,7/5) Reflection Matrix(99,-140,70,-99) (7/5,10/7) -> (7/5,10/7) Reflection Matrix(449,-644,274,-393) (10/7,23/16) -> (18/11,23/14) Glide Reflection Matrix(603,-868,380,-547) (23/16,13/9) -> (19/12,27/17) Glide Reflection Matrix(211,-308,124,-181) (13/9,3/2) -> (17/10,29/17) Hyperbolic Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(125,-196,44,-69) (14/9,11/7) -> (14/5,3/1) Glide Reflection Matrix(391,-616,106,-167) (11/7,30/19) -> (11/3,26/7) Glide Reflection Matrix(673,-1064,284,-449) (30/19,19/12) -> (26/11,19/8) Glide Reflection Matrix(281,-448,106,-169) (27/17,8/5) -> (29/11,8/3) Glide Reflection Matrix(279,-448,104,-167) (8/5,29/18) -> (8/3,27/10) Glide Reflection Matrix(1077,-1736,286,-461) (29/18,50/31) -> (15/4,34/9) Glide Reflection Matrix(1301,-2100,806,-1301) (50/31,21/13) -> (50/31,21/13) Reflection Matrix(69,-112,8,-13) (21/13,13/8) -> (7/1,1/0) Glide Reflection Matrix(223,-364,68,-111) (13/8,18/11) -> (13/4,10/3) Glide Reflection Matrix(783,-1288,476,-783) (23/14,28/17) -> (23/14,28/17) Reflection Matrix(169,-280,102,-169) (28/17,5/3) -> (28/17,5/3) Reflection Matrix(349,-588,92,-155) (5/3,22/13) -> (34/9,19/5) Hyperbolic Matrix(491,-840,204,-349) (29/17,12/7) -> (12/5,41/17) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(125,-224,24,-43) (16/9,9/5) -> (5/1,16/3) Hyperbolic Matrix(169,-308,62,-113) (9/5,11/6) -> (19/7,11/4) Glide Reflection Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(13,-28,6,-13) (2/1,7/3) -> (2/1,7/3) Reflection Matrix(155,-364,66,-155) (7/3,26/11) -> (7/3,26/11) Reflection Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(223,-532,70,-167) (31/13,12/5) -> (3/1,16/5) Glide Reflection Matrix(1555,-3752,482,-1163) (41/17,70/29) -> (29/9,42/13) Glide Reflection Matrix(1681,-4060,696,-1681) (70/29,29/12) -> (70/29,29/12) Reflection Matrix(335,-812,92,-223) (29/12,17/7) -> (29/8,11/3) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(505,-1288,198,-505) (28/11,23/9) -> (28/11,23/9) Reflection Matrix(491,-1260,136,-349) (23/9,18/7) -> (18/5,47/13) Hyperbolic Matrix(379,-980,70,-181) (31/12,13/5) -> (27/5,11/2) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(279,-896,52,-167) (16/5,29/9) -> (16/3,27/5) Glide Reflection Matrix(337,-1092,104,-337) (42/13,13/4) -> (42/13,13/4) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(1231,-4592,330,-1231) (41/11,56/15) -> (41/11,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(125,-476,26,-99) (19/5,4/1) -> (24/5,5/1) Hyperbolic Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(113,-532,24,-113) (14/3,19/4) -> (14/3,19/4) Reflection Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection Matrix(13,-84,2,-13) (6/1,7/1) -> (6/1,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,24,-1) (0/1,1/1) -> (0/1,1/12) Matrix(99,-112,38,-43) -> Matrix(9,-1,26,-3) Matrix(405,-476,154,-181) -> Matrix(9,-1,26,-3) Matrix(449,-532,330,-391) -> Matrix(23,-2,196,-17) Matrix(393,-476,232,-281) -> Matrix(21,-2,136,-13) Matrix(783,-952,644,-783) -> Matrix(81,-8,820,-81) (17/14,28/23) -> (4/41,1/10) Matrix(505,-616,414,-505) -> Matrix(59,-6,580,-59) (28/23,11/9) -> (1/10,3/29) Matrix(113,-140,46,-57) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(43,-56,10,-13) -> Matrix(9,-1,28,-3) Matrix(393,-532,82,-111) -> Matrix(17,-2,60,-7) Matrix(659,-896,114,-155) -> Matrix(9,-1,44,-5) Matrix(225,-308,122,-167) -> Matrix(17,-2,94,-11) Matrix(547,-756,212,-293) -> Matrix(41,-5,156,-19) Matrix(181,-252,130,-181) -> Matrix(41,-5,336,-41) (18/13,7/5) -> (5/42,1/8) Matrix(99,-140,70,-99) -> Matrix(7,-1,48,-7) (7/5,10/7) -> (1/8,1/6) Matrix(449,-644,274,-393) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(603,-868,380,-547) -> Matrix(7,-1,48,-7) *** -> (1/8,1/6) Matrix(211,-308,124,-181) -> Matrix(9,-1,46,-5) Matrix(55,-84,36,-55) -> Matrix(15,-2,112,-15) (3/2,14/9) -> (1/8,1/7) Matrix(125,-196,44,-69) -> Matrix(7,-1,34,-5) Matrix(391,-616,106,-167) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(673,-1064,284,-449) -> Matrix(1,0,12,-1) *** -> (0/1,1/6) Matrix(281,-448,106,-169) -> Matrix(15,-2,52,-7) Matrix(279,-448,104,-167) -> Matrix(13,-2,32,-5) Matrix(1077,-1736,286,-461) -> Matrix(7,-1,20,-3) Matrix(1301,-2100,806,-1301) -> Matrix(7,-1,48,-7) (50/31,21/13) -> (1/8,1/6) Matrix(69,-112,8,-13) -> Matrix(7,-1,6,-1) Matrix(223,-364,68,-111) -> Matrix(13,-2,32,-5) Matrix(783,-1288,476,-783) -> Matrix(1,0,14,-1) (23/14,28/17) -> (0/1,1/7) Matrix(169,-280,102,-169) -> Matrix(13,-2,84,-13) (28/17,5/3) -> (1/7,1/6) Matrix(349,-588,92,-155) -> Matrix(7,-1,8,-1) Matrix(491,-840,204,-349) -> Matrix(3,-1,16,-5) 1/4 Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(125,-224,24,-43) -> Matrix(7,-1,8,-1) Matrix(169,-308,62,-113) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(223,-420,60,-113) -> Matrix(1,0,-6,1) 0/1 Matrix(13,-28,6,-13) -> Matrix(5,-1,24,-5) (2/1,7/3) -> (1/6,1/4) Matrix(155,-364,66,-155) -> Matrix(5,-1,24,-5) (7/3,26/11) -> (1/6,1/4) Matrix(435,-1036,76,-181) -> Matrix(5,-1,16,-3) 1/4 Matrix(223,-532,70,-167) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(1555,-3752,482,-1163) -> Matrix(41,-9,132,-29) Matrix(1681,-4060,696,-1681) -> Matrix(53,-12,234,-53) (70/29,29/12) -> (2/9,3/13) Matrix(335,-812,92,-223) -> Matrix(9,-2,22,-5) Matrix(111,-280,44,-111) -> Matrix(9,-2,40,-9) (5/2,28/11) -> (1/5,1/4) Matrix(505,-1288,198,-505) -> Matrix(47,-12,184,-47) (28/11,23/9) -> (1/4,6/23) Matrix(491,-1260,136,-349) -> Matrix(11,-3,26,-7) Matrix(379,-980,70,-181) -> Matrix(11,-3,4,-1) Matrix(673,-1820,186,-503) -> Matrix(5,-2,8,-3) 1/2 Matrix(111,-308,40,-111) -> Matrix(1,0,4,-1) (11/4,14/5) -> (0/1,1/2) Matrix(279,-896,52,-167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(337,-1092,104,-337) -> Matrix(5,-2,12,-5) (42/13,13/4) -> (1/3,1/2) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(1231,-4592,330,-1231) -> Matrix(-1,0,4,1) (41/11,56/15) -> (-1/2,0/1) Matrix(449,-1680,120,-449) -> Matrix(1,0,6,-1) (56/15,15/4) -> (0/1,1/3) Matrix(125,-476,26,-99) -> Matrix(1,-1,4,-3) 1/2 Matrix(55,-252,12,-55) -> Matrix(1,0,4,-1) (9/2,14/3) -> (0/1,1/2) Matrix(113,-532,24,-113) -> Matrix(1,0,6,-1) (14/3,19/4) -> (0/1,1/3) Matrix(111,-616,20,-111) -> Matrix(1,0,0,-1) (11/2,28/5) -> (0/1,1/0) Matrix(169,-952,30,-169) -> Matrix(1,0,8,-1) (28/5,17/3) -> (0/1,1/4) Matrix(13,-84,2,-13) -> Matrix(-1,1,0,1) (6/1,7/1) -> (1/2,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.